LMFDB - Embedded newform 177.14.a.c.1.16

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			1.16
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)

$f(q)$	$=$	$q+15.7636 q^{2} +729.000 q^{3} -7943.51 q^{4} -18232.0 q^{5} +11491.7 q^{6} -139545. q^{7} -254354. q^{8} +531441. q^{9} +O(q^{10})$	\(q+15.7636 q^{2} +729.000 q^{3} -7943.51 q^{4} -18232.0 q^{5} +11491.7 q^{6} -139545. q^{7} -254354. q^{8} +531441. q^{9} -287402. q^{10} +3.23072e6 q^{11} -5.79082e6 q^{12} -2.38685e7 q^{13} -2.19974e6 q^{14} -1.32911e7 q^{15} +6.10637e7 q^{16} -1.01242e8 q^{17} +8.37742e6 q^{18} -2.58492e8 q^{19} +1.44826e8 q^{20} -1.01729e8 q^{21} +5.09278e7 q^{22} +4.75562e8 q^{23} -1.85424e8 q^{24} -8.88297e8 q^{25} -3.76253e8 q^{26} +3.87420e8 q^{27} +1.10848e9 q^{28} -4.16682e9 q^{29} -2.09516e8 q^{30} +3.82269e9 q^{31} +3.04625e9 q^{32} +2.35519e9 q^{33} -1.59594e9 q^{34} +2.54420e9 q^{35} -4.22151e9 q^{36} -2.63978e9 q^{37} -4.07477e9 q^{38} -1.74001e10 q^{39} +4.63738e9 q^{40} -1.28469e10 q^{41} -1.60361e9 q^{42} -9.65991e9 q^{43} -2.56633e10 q^{44} -9.68924e9 q^{45} +7.49657e9 q^{46} -8.50024e9 q^{47} +4.45154e10 q^{48} -7.74161e10 q^{49} -1.40027e10 q^{50} -7.38057e10 q^{51} +1.89599e11 q^{52} -2.27914e11 q^{53} +6.10714e9 q^{54} -5.89025e10 q^{55} +3.54939e10 q^{56} -1.88441e11 q^{57} -6.56840e10 q^{58} -4.21805e10 q^{59} +1.05578e11 q^{60} -2.60650e11 q^{61} +6.02594e10 q^{62} -7.41602e10 q^{63} -4.52214e11 q^{64} +4.35170e11 q^{65} +3.71263e10 q^{66} +5.68861e11 q^{67} +8.04220e11 q^{68} +3.46685e11 q^{69} +4.01057e10 q^{70} -7.25827e11 q^{71} -1.35174e11 q^{72} +8.77552e11 q^{73} -4.16124e10 q^{74} -6.47568e11 q^{75} +2.05334e12 q^{76} -4.50832e11 q^{77} -2.74288e11 q^{78} -1.57064e12 q^{79} -1.11331e12 q^{80} +2.82430e11 q^{81} -2.02513e11 q^{82} -2.61026e12 q^{83} +8.08083e11 q^{84} +1.84585e12 q^{85} -1.52275e11 q^{86} -3.03761e12 q^{87} -8.21745e11 q^{88} -8.27525e11 q^{89} -1.52737e11 q^{90} +3.33074e12 q^{91} -3.77763e12 q^{92} +2.78674e12 q^{93} -1.33994e11 q^{94} +4.71284e12 q^{95} +2.22071e12 q^{96} +1.71471e12 q^{97} -1.22036e12 q^{98} +1.71694e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	15.7636	0.174165	0.0870824	−	0.996201i	$-0.472246\pi$
$2$	15.7636	0.174165	0.0870824	+	0.996201i	$0.472246\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−7943.51	−0.969667
$5$	−18232.0	−0.521831	−0.260915	−	0.965362i	$-0.584024\pi$
$5$	−18232.0	−0.521831	−0.260915	+	0.965362i	$0.584024\pi$
$6$	11491.7	0.100554
$7$	−139545.	−0.448310	−0.224155	−	0.974553i	$-0.571962\pi$
$7$	−139545.	−0.448310	−0.224155	+	0.974553i	$0.571962\pi$
$8$	−254354.	−0.343046
$9$	531441.	0.333333
$10$	−287402.	−0.0908845
$11$	3.23072e6	0.549853	0.274927	−	0.961465i	$-0.411346\pi$
$11$	3.23072e6	0.549853	0.274927	+	0.961465i	$0.411346\pi$
$12$	−5.79082e6	−0.559837
$13$	−2.38685e7	−1.37149	−0.685745	−	0.727842i	$-0.740524\pi$
$13$	−2.38685e7	−1.37149	−0.685745	+	0.727842i	$0.740524\pi$
$14$	−2.19974e6	−0.0780798
$15$	−1.32911e7	−0.301279
$16$	6.10637e7	0.909920
$17$	−1.01242e8	−1.01729	−0.508644	−	0.860977i	$-0.669853\pi$
$17$	−1.01242e8	−1.01729	−0.508644	+	0.860977i	$0.669853\pi$
$18$	8.37742e6	0.0580549
$19$	−2.58492e8	−1.26052	−0.630260	−	0.776384i	$-0.717052\pi$
$19$	−2.58492e8	−1.26052	−0.630260	+	0.776384i	$0.717052\pi$
$20$	1.44826e8	0.506002
$21$	−1.01729e8	−0.258832
$22$	5.09278e7	0.0957651
$23$	4.75562e8	0.669848	0.334924	−	0.942245i	$-0.391289\pi$
$23$	4.75562e8	0.669848	0.334924	+	0.942245i	$0.391289\pi$
$24$	−1.85424e8	−0.198058
$25$	−8.88297e8	−0.727693
$26$	−3.76253e8	−0.238865
$27$	3.87420e8	0.192450
$28$	1.10848e9	0.434711
$29$	−4.16682e9	−1.30082	−0.650411	−	0.759583i	$-0.725403\pi$
$29$	−4.16682e9	−1.30082	−0.650411	+	0.759583i	$0.725403\pi$
$30$	−2.09516e8	−0.0524722
$31$	3.82269e9	0.773603	0.386802	−	0.922163i	$-0.373580\pi$
$31$	3.82269e9	0.773603	0.386802	+	0.922163i	$0.373580\pi$
$32$	3.04625e9	0.501522
$33$	2.35519e9	0.317458
$34$	−1.59594e9	−0.177176
$35$	2.54420e9	0.233942
$36$	−4.22151e9	−0.323222
$37$	−2.63978e9	−0.169144	−0.0845720	−	0.996417i	$-0.526952\pi$
$37$	−2.63978e9	−0.169144	−0.0845720	+	0.996417i	$0.526952\pi$
$38$	−4.07477e9	−0.219538
$39$	−1.74001e10	−0.791830
$40$	4.63738e9	0.179012
$41$	−1.28469e10	−0.422380	−0.211190	−	0.977445i	$-0.567734\pi$
$41$	−1.28469e10	−0.422380	−0.211190	+	0.977445i	$0.567734\pi$
$42$	−1.60361e9	−0.0450794
$43$	−9.65991e9	−0.233039	−0.116519	−	0.993188i	$-0.537174\pi$
$43$	−9.65991e9	−0.233039	−0.116519	+	0.993188i	$0.537174\pi$
$44$	−2.56633e10	−0.533174
$45$	−9.68924e9	−0.173944
$46$	7.49657e9	0.116664
$47$	−8.50024e9	−0.115026	−0.0575129	−	0.998345i	$-0.518317\pi$
$47$	−8.50024e9	−0.115026	−0.0575129	+	0.998345i	$0.518317\pi$
$48$	4.45154e10	0.525343
$49$	−7.74161e10	−0.799018
$50$	−1.40027e10	−0.126738
$51$	−7.38057e10	−0.587332
$52$	1.89599e11	1.32989
$53$	−2.27914e11	−1.41246	−0.706232	−	0.707980i	$-0.749606\pi$
$53$	−2.27914e11	−1.41246	−0.706232	+	0.707980i	$0.749606\pi$
$54$	6.10714e9	0.0335180
$55$	−5.89025e10	−0.286930
$56$	3.54939e10	0.153791
$57$	−1.88441e11	−0.727761
$58$	−6.56840e10	−0.226557
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	1.05578e11	0.292140
$61$	−2.60650e11	−0.647759	−0.323879	−	0.946098i	$-0.604987\pi$
$61$	−2.60650e11	−0.647759	−0.323879	+	0.946098i	$0.604987\pi$
$62$	6.02594e10	0.134734
$63$	−7.41602e10	−0.149437
$64$	−4.52214e11	−0.822573
$65$	4.35170e11	0.715686
$66$	3.71263e10	0.0552900
$67$	5.68861e11	0.768281	0.384141	−	0.923275i	$-0.374498\pi$
$67$	5.68861e11	0.768281	0.384141	+	0.923275i	$0.374498\pi$
$68$	8.04220e11	0.986431
$69$	3.46685e11	0.386737
$70$	4.01057e10	0.0407445
$71$	−7.25827e11	−0.672440	−0.336220	−	0.941783i	$-0.609149\pi$
$71$	−7.25827e11	−0.672440	−0.336220	+	0.941783i	$0.609149\pi$
$72$	−1.35174e11	−0.114349
$73$	8.77552e11	0.678694	0.339347	−	0.940661i	$-0.389794\pi$
$73$	8.77552e11	0.678694	0.339347	+	0.940661i	$0.389794\pi$
$74$	−4.16124e10	−0.0294589
$75$	−6.47568e11	−0.420134
$76$	2.05334e12	1.22228
$77$	−4.50832e11	−0.246505
$78$	−2.74288e11	−0.137909
$79$	−1.57064e12	−0.726944	−0.363472	−	0.931605i	$-0.618409\pi$
$79$	−1.57064e12	−0.726944	−0.363472	+	0.931605i	$0.618409\pi$
$80$	−1.11331e12	−0.474824
$81$	2.82430e11	0.111111
$82$	−2.02513e11	−0.0735636
$83$	−2.61026e12	−0.876346	−0.438173	−	0.898891i	$-0.644374\pi$
$83$	−2.61026e12	−0.876346	−0.438173	+	0.898891i	$0.644374\pi$
$84$	8.08083e11	0.250981
$85$	1.84585e12	0.530853
$86$	−1.52275e11	−0.0405871
$87$	−3.03761e12	−0.751030
$88$	−8.21745e11	−0.188625
$89$	−8.27525e11	−0.176501	−0.0882503	−	0.996098i	$-0.528128\pi$
$89$	−8.27525e11	−0.176501	−0.0882503	+	0.996098i	$0.528128\pi$
$90$	−1.52737e11	−0.0302948
$91$	3.33074e12	0.614853
$92$	−3.77763e12	−0.649529
$93$	2.78674e12	0.446640
$94$	−1.33994e11	−0.0200334
$95$	4.71284e12	0.657778
$96$	2.22071e12	0.289554
$97$	1.71471e12	0.209014	0.104507	−	0.994524i	$-0.466674\pi$
$97$	1.71471e12	0.209014	0.104507	+	0.994524i	$0.466674\pi$
$98$	−1.22036e12	−0.139161
$99$	1.71694e12	0.183284
$100$	7.05619e12	0.705619
$101$	1.17495e13	1.10136	0.550681	−	0.834716i	$-0.314368\pi$
$101$	1.17495e13	1.10136	0.550681	+	0.834716i	$0.314368\pi$
$102$	−1.16344e12	−0.102293
$103$	6.37459e12	0.526030	0.263015	−	0.964792i	$-0.415283\pi$
$103$	6.37459e12	0.526030	0.263015	+	0.964792i	$0.415283\pi$
$104$	6.07103e12	0.470485
$105$	1.85472e12	0.135066
$106$	−3.59274e12	−0.246001
$107$	1.04542e13	0.673434	0.336717	−	0.941606i	$-0.390683\pi$
$107$	1.04542e13	0.673434	0.336717	+	0.941606i	$0.390683\pi$
$108$	−3.07748e12	−0.186612
$109$	2.75248e13	1.57200	0.785999	−	0.618228i	$-0.212149\pi$
$109$	2.75248e13	1.57200	0.785999	+	0.618228i	$0.212149\pi$
$110$	−9.28516e11	−0.0499732
$111$	−1.92440e12	−0.0976553
$112$	−8.52116e12	−0.407926
$113$	2.37831e13	1.07463	0.537316	−	0.843381i	$-0.319438\pi$
$113$	2.37831e13	1.07463	0.537316	+	0.843381i	$0.319438\pi$
$114$	−2.97051e12	−0.126750
$115$	−8.67046e12	−0.349547
$116$	3.30992e13	1.26136
$117$	−1.26847e13	−0.457163
$118$	−6.64917e11	−0.0226743
$119$	1.41279e13	0.456061
$120$	3.38065e12	0.103353
$121$	−2.40852e13	−0.697661
$122$	−4.10878e12	−0.112817
$123$	−9.36538e12	−0.243861
$124$	−3.03656e13	−0.750137
$125$	3.84513e13	0.901563
$126$	−1.16903e12	−0.0260266
$127$	−4.11078e13	−0.869360	−0.434680	−	0.900585i	$-0.643139\pi$
$127$	−4.11078e13	−0.869360	−0.434680	+	0.900585i	$0.643139\pi$
$128$	−3.20834e13	−0.644786
$129$	−7.04207e12	−0.134545
$130$	6.85985e12	0.124647
$131$	1.23740e13	0.213918	0.106959	−	0.994263i	$-0.465889\pi$
$131$	1.23740e13	0.213918	0.106959	+	0.994263i	$0.465889\pi$
$132$	−1.87085e13	−0.307828
$133$	3.60715e13	0.565104
$134$	8.96730e12	0.133808
$135$	−7.06346e12	−0.100426
$136$	2.57514e13	0.348977
$137$	−3.40714e13	−0.440257	−0.220129	−	0.975471i	$-0.570648\pi$
$137$	−3.40714e13	−0.440257	−0.220129	+	0.975471i	$0.570648\pi$
$138$	5.46500e12	0.0673560
$139$	1.13870e14	1.33910	0.669548	−	0.742768i	$-0.266488\pi$
$139$	1.13870e14	1.33910	0.669548	+	0.742768i	$0.266488\pi$
$140$	−2.02098e13	−0.226846
$141$	−6.19668e12	−0.0664102
$142$	−1.14416e13	−0.117115
$143$	−7.71123e13	−0.754119
$144$	3.24518e13	0.303307
$145$	7.59695e13	0.678809
$146$	1.38334e13	0.118205
$147$	−5.64363e13	−0.461313
$148$	2.09691e13	0.164013
$149$	−1.47280e14	−1.10264	−0.551319	−	0.834295i	$-0.685875\pi$
$149$	−1.47280e14	−1.10264	−0.551319	+	0.834295i	$0.685875\pi$
$150$	−1.02080e13	−0.0731724
$151$	4.88280e13	0.335211	0.167606	−	0.985854i	$-0.446396\pi$
$151$	4.88280e13	0.335211	0.167606	+	0.985854i	$0.446396\pi$
$152$	6.57485e13	0.432417
$153$	−5.38043e13	−0.339096
$154$	−7.10674e12	−0.0429324
$155$	−6.96954e13	−0.403690
$156$	1.38218e14	0.767812
$157$	−3.25508e12	−0.0173466	−0.00867329	−	0.999962i	$-0.502761\pi$
$157$	−3.25508e12	−0.0173466	−0.00867329	+	0.999962i	$0.502761\pi$
$158$	−2.47589e13	−0.126608
$159$	−1.66149e14	−0.815487
$160$	−5.55393e13	−0.261710
$161$	−6.63626e13	−0.300300
$162$	4.45210e12	0.0193516
$163$	−6.74761e13	−0.281793	−0.140897	−	0.990024i	$-0.544999\pi$
$163$	−6.74761e13	−0.281793	−0.140897	+	0.990024i	$0.544999\pi$
$164$	1.02049e14	0.409567
$165$	−4.29400e13	−0.165659
$166$	−4.11470e13	−0.152629
$167$	−3.07390e14	−1.09656	−0.548280	−	0.836295i	$-0.684717\pi$
$167$	−3.07390e14	−1.09656	−0.548280	+	0.836295i	$0.684717\pi$
$168$	2.58751e13	0.0887914
$169$	2.66829e14	0.880986
$170$	2.90973e13	0.0924558
$171$	−1.37373e14	−0.420173
$172$	7.67335e13	0.225970
$173$	3.08654e14	0.875331	0.437666	−	0.899138i	$-0.355805\pi$
$173$	3.08654e14	0.875331	0.437666	+	0.899138i	$0.355805\pi$
$174$	−4.78837e13	−0.130803
$175$	1.23958e14	0.326232
$176$	1.97280e14	0.500323
$177$	−3.07496e13	−0.0751646
$178$	−1.30448e13	−0.0307402
$179$	−3.28530e14	−0.746501	−0.373251	−	0.927731i	$-0.621757\pi$
$179$	−3.28530e14	−0.746501	−0.373251	+	0.927731i	$0.621757\pi$
$180$	7.69666e13	0.168667
$181$	5.32127e14	1.12488	0.562438	−	0.826840i	$-0.309864\pi$
$181$	5.32127e14	1.12488	0.562438	+	0.826840i	$0.309864\pi$
$182$	5.25044e13	0.107086
$183$	−1.90014e14	−0.373984
$184$	−1.20961e14	−0.229789
$185$	4.81285e13	0.0882645
$186$	4.39291e13	0.0777890
$187$	−3.27086e14	−0.559360
$188$	6.75218e13	0.111537
$189$	−5.40628e13	−0.0862773
$190$	7.42913e13	0.114562
$191$	2.94971e14	0.439605	0.219802	−	0.975544i	$-0.429459\pi$
$191$	2.94971e14	0.439605	0.219802	+	0.975544i	$0.429459\pi$
$192$	−3.29664e14	−0.474912
$193$	1.06851e15	1.48818	0.744089	−	0.668081i	$-0.232884\pi$
$193$	1.06851e15	1.48818	0.744089	+	0.668081i	$0.232884\pi$
$194$	2.70300e13	0.0364028
$195$	3.17239e14	0.413202
$196$	6.14955e14	0.774781
$197$	7.01474e14	0.855030	0.427515	−	0.904008i	$-0.359389\pi$
$197$	7.01474e14	0.855030	0.427515	+	0.904008i	$0.359389\pi$
$198$	2.70651e13	0.0319217
$199$	−2.11109e14	−0.240969	−0.120485	−	0.992715i	$-0.538445\pi$
$199$	−2.11109e14	−0.240969	−0.120485	+	0.992715i	$0.538445\pi$
$200$	2.25941e14	0.249632
$201$	4.14700e14	0.443567
$202$	1.85214e14	0.191818
$203$	5.81461e14	0.583171
$204$	5.86276e14	0.569516
$205$	2.34225e14	0.220411
$206$	1.00487e14	0.0916159
$207$	2.52733e14	0.223283
$208$	−1.45750e15	−1.24795
$209$	−8.35117e14	−0.693101
$210$	2.92370e13	0.0235238
$211$	1.62145e15	1.26493	0.632466	−	0.774588i	$-0.282043\pi$
$211$	1.62145e15	1.26493	0.632466	+	0.774588i	$0.282043\pi$
$212$	1.81044e15	1.36962
$213$	−5.29128e14	−0.388234
$214$	1.64795e14	0.117288
$215$	1.76120e14	0.121607
$216$	−9.85418e13	−0.0660193
$217$	−5.33439e14	−0.346814
$218$	4.33890e14	0.273787
$219$	6.39735e14	0.391844
$220$	4.67893e14	0.278227
$221$	2.41650e15	1.39520
$222$	−3.03354e13	−0.0170081
$223$	−1.10451e15	−0.601434	−0.300717	−	0.953713i	$-0.597226\pi$
$223$	−1.10451e15	−0.601434	−0.300717	+	0.953713i	$0.597226\pi$
$224$	−4.25090e14	−0.224838
$225$	−4.72077e14	−0.242564
$226$	3.74908e14	0.187163
$227$	−2.06780e15	−1.00309	−0.501546	−	0.865131i	$-0.667235\pi$
$227$	−2.06780e15	−1.00309	−0.501546	+	0.865131i	$0.667235\pi$
$228$	1.49688e15	0.705686
$229$	−4.51272e14	−0.206779	−0.103390	−	0.994641i	$-0.532969\pi$
$229$	−4.51272e14	−0.206779	−0.103390	+	0.994641i	$0.532969\pi$
$230$	−1.36678e14	−0.0608788
$231$	−3.28657e14	−0.142320
$232$	1.05985e15	0.446242
$233$	−1.49728e15	−0.613043	−0.306521	−	0.951864i	$-0.599165\pi$
$233$	−1.49728e15	−0.613043	−0.306521	+	0.951864i	$0.599165\pi$
$234$	−1.99956e14	−0.0796218
$235$	1.54977e14	0.0600240
$236$	3.35061e14	0.126240
$237$	−1.14500e15	−0.419701
$238$	2.22707e14	0.0794297
$239$	3.83611e15	1.33139	0.665694	−	0.746224i	$-0.268135\pi$
$239$	3.83611e15	1.33139	0.665694	+	0.746224i	$0.268135\pi$
$240$	−8.11606e14	−0.274140
$241$	4.70369e15	1.54642	0.773211	−	0.634149i	$-0.218649\pi$
$241$	4.70369e15	1.54642	0.773211	+	0.634149i	$0.218649\pi$
$242$	−3.79669e14	−0.121508
$243$	2.05891e14	0.0641500
$244$	2.07047e15	0.628110
$245$	1.41145e15	0.416952
$246$	−1.47632e14	−0.0424720
$247$	6.16982e15	1.72879
$248$	−9.72316e14	−0.265382
$249$	−1.90288e15	−0.505959
$250$	6.06131e14	0.157021
$251$	4.10602e14	0.103643	0.0518217	−	0.998656i	$-0.483497\pi$
$251$	4.10602e14	0.103643	0.0518217	+	0.998656i	$0.483497\pi$
$252$	5.89092e14	0.144904
$253$	1.53641e15	0.368318
$254$	−6.48006e14	−0.151412
$255$	1.34563e15	0.306488
$256$	3.19879e15	0.710274
$257$	−4.75664e14	−0.102976	−0.0514879	−	0.998674i	$-0.516396\pi$
$257$	−4.75664e14	−0.102976	−0.0514879	+	0.998674i	$0.516396\pi$
$258$	−1.11008e14	−0.0234330
$259$	3.68369e14	0.0758289
$260$	−3.45678e15	−0.693977
$261$	−2.21442e15	−0.433607
$262$	1.95059e14	0.0372570
$263$	1.53185e15	0.285434	0.142717	−	0.989764i	$-0.454416\pi$
$263$	1.53185e15	0.285434	0.142717	+	0.989764i	$0.454416\pi$
$264$	−5.99052e14	−0.108903
$265$	4.15533e15	0.737067
$266$	5.68616e14	0.0984211
$267$	−6.03266e14	−0.101903
$268$	−4.51876e15	−0.744977
$269$	1.68579e15	0.271278	0.135639	−	0.990758i	$-0.456691\pi$
$269$	1.68579e15	0.271278	0.135639	+	0.990758i	$0.456691\pi$
$270$	−1.11345e14	−0.0174907
$271$	6.76700e15	1.03776	0.518879	−	0.854848i	$-0.326350\pi$
$271$	6.76700e15	1.03776	0.518879	+	0.854848i	$0.326350\pi$
$272$	−6.18223e15	−0.925652
$273$	2.42811e15	0.354986
$274$	−5.37088e14	−0.0766773
$275$	−2.86984e15	−0.400124
$276$	−2.75389e15	−0.375006
$277$	3.37402e15	0.448776	0.224388	−	0.974500i	$-0.427962\pi$
$277$	3.37402e15	0.448776	0.224388	+	0.974500i	$0.427962\pi$
$278$	1.79500e15	0.233223
$279$	2.03154e15	0.257868
$280$	−6.47125e14	−0.0802530
$281$	3.77808e15	0.457804	0.228902	−	0.973449i	$-0.426486\pi$
$281$	3.77808e15	0.457804	0.228902	+	0.973449i	$0.426486\pi$
$282$	−9.76819e13	−0.0115663
$283$	5.13345e15	0.594015	0.297008	−	0.954875i	$-0.404011\pi$
$283$	5.13345e15	0.594015	0.297008	+	0.954875i	$0.404011\pi$
$284$	5.76561e15	0.652043
$285$	3.43566e15	0.379768
$286$	−1.21557e15	−0.131341
$287$	1.79273e15	0.189357
$288$	1.61890e15	0.167174
$289$	3.45440e14	0.0348768
$290$	1.19755e15	0.118225
$291$	1.25003e15	0.120674
$292$	−6.97084e15	−0.658107
$293$	2.49166e15	0.230065	0.115032	−	0.993362i	$-0.463303\pi$
$293$	2.49166e15	0.230065	0.115032	+	0.993362i	$0.463303\pi$
$294$	−8.89639e14	−0.0803445
$295$	7.69036e14	0.0679366
$296$	6.71437e14	0.0580242
$297$	1.25165e15	0.105819
$298$	−2.32166e15	−0.192041
$299$	−1.13509e16	−0.918690
$300$	5.14396e15	0.407389
$301$	1.34800e15	0.104474
$302$	7.69704e14	0.0583820
$303$	8.56537e15	0.635871
$304$	−1.57845e16	−1.14697
$305$	4.75217e15	0.338021
$306$	−8.48150e14	−0.0590586
$307$	−1.26502e16	−0.862377	−0.431188	−	0.902262i	$-0.641906\pi$
$307$	−1.26502e16	−0.862377	−0.431188	+	0.902262i	$0.641906\pi$
$308$	3.58119e15	0.239027
$309$	4.64708e15	0.303704
$310$	−1.09865e15	−0.0703086
$311$	−9.93149e15	−0.622403	−0.311202	−	0.950344i	$-0.600731\pi$
$311$	−9.93149e15	−0.622403	−0.311202	+	0.950344i	$0.600731\pi$
$312$	4.42578e15	0.271635
$313$	−2.22102e16	−1.33510	−0.667550	−	0.744565i	$-0.732657\pi$
$313$	−2.22102e16	−1.33510	−0.667550	+	0.744565i	$0.732657\pi$
$314$	−5.13118e13	−0.00302116
$315$	1.35209e15	0.0779807
$316$	1.24764e16	0.704893
$317$	1.61054e16	0.891429	0.445715	−	0.895175i	$-0.352950\pi$
$317$	1.61054e16	0.891429	0.445715	+	0.895175i	$0.352950\pi$
$318$	−2.61911e15	−0.142029
$319$	−1.34618e16	−0.715261
$320$	8.24477e15	0.429244
$321$	7.62109e15	0.388807
$322$	−1.04611e15	−0.0523016
$323$	2.61704e16	1.28231
$324$	−2.24348e15	−0.107741
$325$	2.12023e16	0.998023
$326$	−1.06367e15	−0.0490784
$327$	2.00656e16	0.907593
$328$	3.26765e15	0.144896
$329$	1.18617e15	0.0515672
$330$	−6.76888e14	−0.0288520
$331$	1.38595e16	0.579251	0.289625	−	0.957140i	$-0.406469\pi$
$331$	1.38595e16	0.579251	0.289625	+	0.957140i	$0.406469\pi$
$332$	2.07346e16	0.849764
$333$	−1.40289e15	−0.0563813
$334$	−4.84557e15	−0.190982
$335$	−1.03715e16	−0.400913
$336$	−6.21193e15	−0.235516
$337$	3.12002e16	1.16028	0.580141	−	0.814516i	$-0.302997\pi$
$337$	3.12002e16	1.16028	0.580141	+	0.814516i	$0.302997\pi$
$338$	4.20618e15	0.153437
$339$	1.73379e16	0.620439
$340$	−1.46625e16	−0.514750
$341$	1.23500e16	0.425368
$342$	−2.16550e15	−0.0731793
$343$	2.43235e16	0.806518
$344$	2.45703e15	0.0799431
$345$	−6.32076e15	−0.201811
$346$	4.86550e15	0.152452
$347$	−6.10608e16	−1.87768	−0.938838	−	0.344359i	$-0.888096\pi$
$347$	−6.10608e16	−1.87768	−0.938838	+	0.344359i	$0.888096\pi$
$348$	2.41293e16	0.728248
$349$	1.98135e16	0.586943	0.293471	−	0.955968i	$-0.405189\pi$
$349$	1.98135e16	0.586943	0.293471	+	0.955968i	$0.405189\pi$
$350$	1.95402e15	0.0568181
$351$	−9.24713e15	−0.263943
$352$	9.84157e15	0.275764
$353$	8.83504e15	0.243037	0.121519	−	0.992589i	$-0.461224\pi$
$353$	8.83504e15	0.243037	0.121519	+	0.992589i	$0.461224\pi$
$354$	−4.84724e14	−0.0130910
$355$	1.32333e16	0.350900
$356$	6.57345e15	0.171147
$357$	1.02993e16	0.263307
$358$	−5.17882e15	−0.130014
$359$	−1.66153e16	−0.409632	−0.204816	−	0.978801i	$-0.565660\pi$
$359$	−1.66153e16	−0.409632	−0.204816	+	0.978801i	$0.565660\pi$
$360$	2.46449e15	0.0596707
$361$	2.47654e16	0.588909
$362$	8.38823e15	0.195914
$363$	−1.75581e16	−0.402795
$364$	−2.64577e16	−0.596202
$365$	−1.59995e16	−0.354164
$366$	−2.99530e15	−0.0651348
$367$	−5.49392e16	−1.17369	−0.586844	−	0.809700i	$-0.699630\pi$
$367$	−5.49392e16	−1.17369	−0.586844	+	0.809700i	$0.699630\pi$
$368$	2.90396e16	0.609508
$369$	−6.82736e15	−0.140793
$370$	7.58678e14	0.0153726
$371$	3.18043e16	0.633222
$372$	−2.21365e16	−0.433092
$373$	−8.97584e15	−0.172571	−0.0862855	−	0.996270i	$-0.527500\pi$
$373$	−8.97584e15	−0.172571	−0.0862855	+	0.996270i	$0.527500\pi$
$374$	−5.15605e15	−0.0974207
$375$	2.80310e16	0.520518
$376$	2.16207e15	0.0394592
$377$	9.94556e16	1.78406
$378$	−8.52224e14	−0.0150265
$379$	−1.06818e16	−0.185135	−0.0925677	−	0.995706i	$-0.529507\pi$
$379$	−1.06818e16	−0.185135	−0.0925677	+	0.995706i	$0.529507\pi$
$380$	−3.74365e16	−0.637825
$381$	−2.99676e16	−0.501925
$382$	4.64980e15	0.0765637
$383$	−1.62056e16	−0.262345	−0.131172	−	0.991360i	$-0.541874\pi$
$383$	−1.62056e16	−0.262345	−0.131172	+	0.991360i	$0.541874\pi$
$384$	−2.33888e16	−0.372267
$385$	8.21958e15	0.128634
$386$	1.68435e16	0.259188
$387$	−5.13367e15	−0.0776795
$388$	−1.36208e16	−0.202674
$389$	2.24733e16	0.328848	0.164424	−	0.986390i	$-0.447423\pi$
$389$	2.24733e16	0.328848	0.164424	+	0.986390i	$0.447423\pi$
$390$	5.00083e15	0.0719651
$391$	−4.81470e16	−0.681429
$392$	1.96911e16	0.274100
$393$	9.02066e15	0.123506
$394$	1.10578e16	0.148916
$395$	2.86359e16	0.379342
$396$	−1.36385e16	−0.177725
$397$	−7.11388e15	−0.0911944	−0.0455972	−	0.998960i	$-0.514519\pi$
$397$	−7.11388e15	−0.0911944	−0.0455972	+	0.998960i	$0.514519\pi$
$398$	−3.32784e15	−0.0419684
$399$	2.62961e16	0.326263
$400$	−5.42427e16	−0.662142
$401$	4.23862e16	0.509080	0.254540	−	0.967062i	$-0.418076\pi$
$401$	4.23862e16	0.509080	0.254540	+	0.967062i	$0.418076\pi$
$402$	6.53716e15	0.0772538
$403$	−9.12418e16	−1.06099
$404$	−9.33321e16	−1.06795
$405$	−5.14926e15	−0.0579812
$406$	9.16591e15	0.101568
$407$	−8.52839e15	−0.0930044
$408$	1.87727e16	0.201482
$409$	−1.56061e17	−1.64851	−0.824256	−	0.566218i	$-0.808406\pi$
$409$	−1.56061e17	−1.64851	−0.824256	+	0.566218i	$0.808406\pi$
$410$	3.69222e15	0.0383878
$411$	−2.48381e16	−0.254183
$412$	−5.06366e16	−0.510074
$413$	5.88610e15	0.0583650
$414$	3.98398e15	0.0388880
$415$	4.75903e16	0.457304
$416$	−7.27093e16	−0.687833
$417$	8.30110e16	0.773128
$418$	−1.31644e16	−0.120714
$419$	−1.09388e17	−0.987590	−0.493795	−	0.869578i	$-0.664391\pi$
$419$	−1.09388e17	−0.987590	−0.493795	+	0.869578i	$0.664391\pi$
$420$	−1.47330e16	−0.130969
$421$	−9.24208e16	−0.808977	−0.404488	−	0.914543i	$-0.632550\pi$
$421$	−9.24208e16	−0.808977	−0.404488	+	0.914543i	$0.632550\pi$
$422$	2.55598e16	0.220306
$423$	−4.51738e15	−0.0383419
$424$	5.79707e16	0.484541
$425$	8.99333e16	0.740274
$426$	−8.34096e15	−0.0676166
$427$	3.63725e16	0.290397
$428$	−8.30428e16	−0.653006
$429$	−5.62149e16	−0.435391
$430$	2.77628e15	0.0211796
$431$	2.57918e16	0.193811	0.0969055	−	0.995294i	$-0.469106\pi$
$431$	2.57918e16	0.193811	0.0969055	+	0.995294i	$0.469106\pi$
$432$	2.36573e16	0.175114
$433$	2.50867e16	0.182924	0.0914622	−	0.995809i	$-0.470846\pi$
$433$	2.50867e16	0.182924	0.0914622	+	0.995809i	$0.470846\pi$
$434$	−8.40892e15	−0.0604028
$435$	5.53818e16	0.391910
$436$	−2.18644e17	−1.52431
$437$	−1.22929e17	−0.844357
$438$	1.00845e16	0.0682455
$439$	−2.02033e17	−1.34711	−0.673554	−	0.739138i	$-0.735233\pi$
$439$	−2.02033e17	−1.34711	−0.673554	+	0.739138i	$0.735233\pi$
$440$	1.49821e16	0.0984305
$441$	−4.11421e16	−0.266339
$442$	3.80927e16	0.242995
$443$	−3.97660e16	−0.249970	−0.124985	−	0.992159i	$-0.539888\pi$
$443$	−3.97660e16	−0.249970	−0.124985	+	0.992159i	$0.539888\pi$
$444$	1.52865e16	0.0946931
$445$	1.50875e16	0.0921034
$446$	−1.74110e16	−0.104749
$447$	−1.07367e17	−0.636608
$448$	6.31044e16	0.368768
$449$	−1.30832e17	−0.753553	−0.376776	−	0.926304i	$-0.622967\pi$
$449$	−1.30832e17	−0.753553	−0.376776	+	0.926304i	$0.622967\pi$
$450$	−7.44163e15	−0.0422461
$451$	−4.15047e16	−0.232247
$452$	−1.88922e17	−1.04203
$453$	3.55956e16	0.193534
$454$	−3.25960e16	−0.174703
$455$	−6.07261e16	−0.320849
$456$	4.79306e16	0.249656
$457$	−2.28383e17	−1.17276	−0.586380	−	0.810036i	$-0.699448\pi$
$457$	−2.28383e17	−1.17276	−0.586380	+	0.810036i	$0.699448\pi$
$458$	−7.11366e15	−0.0360137
$459$	−3.92234e16	−0.195777
$460$	6.88739e16	0.338944
$461$	−2.20757e17	−1.07117	−0.535585	−	0.844482i	$-0.679909\pi$
$461$	−2.20757e17	−1.07117	−0.535585	+	0.844482i	$0.679909\pi$
$462$	−5.18081e15	−0.0247871
$463$	7.89781e16	0.372589	0.186295	−	0.982494i	$-0.440352\pi$
$463$	7.89781e16	0.372589	0.186295	+	0.982494i	$0.440352\pi$
$464$	−2.54441e17	−1.18364
$465$	−5.08079e16	−0.233071
$466$	−2.36026e16	−0.106770
$467$	2.06630e17	0.921792	0.460896	−	0.887454i	$-0.347528\pi$
$467$	2.06630e17	0.921792	0.460896	+	0.887454i	$0.347528\pi$
$468$	1.00761e17	0.443296
$469$	−7.93820e16	−0.344428
$470$	2.44299e15	0.0104541
$471$	−2.37295e15	−0.0100151
$472$	1.07288e16	0.0446608
$473$	−3.12084e16	−0.128137
$474$	−1.80493e16	−0.0730971
$475$	2.29618e17	0.917271
$476$	−1.12225e17	−0.442227
$477$	−1.21123e17	−0.470821
$478$	6.04709e16	0.231881
$479$	−2.57008e17	−0.972224	−0.486112	−	0.873897i	$-0.661585\pi$
$479$	−2.57008e17	−0.972224	−0.486112	+	0.873897i	$0.661585\pi$
$480$	−4.04881e16	−0.151098
$481$	6.30075e16	0.231979
$482$	7.41471e16	0.269332
$483$	−4.83783e16	−0.173378
$484$	1.91321e17	0.676499
$485$	−3.12627e16	−0.109070
$486$	3.24558e15	0.0111727
$487$	1.92173e17	0.652761	0.326380	−	0.945239i	$-0.394171\pi$
$487$	1.92173e17	0.652761	0.326380	+	0.945239i	$0.394171\pi$
$488$	6.62972e16	0.222211
$489$	−4.91901e16	−0.162693
$490$	2.22495e16	0.0726184
$491$	−2.06038e17	−0.663618	−0.331809	−	0.943347i	$-0.607659\pi$
$491$	−2.06038e17	−0.663618	−0.331809	+	0.943347i	$0.607659\pi$
$492$	7.43940e16	0.236464
$493$	4.21859e17	1.32331
$494$	9.72585e16	0.301094
$495$	−3.13032e16	−0.0956435
$496$	2.33428e17	0.703917
$497$	1.01286e17	0.301462
$498$	−2.99962e16	−0.0881202
$499$	−4.93431e17	−1.43078	−0.715390	−	0.698725i	$-0.753751\pi$
$499$	−4.93431e17	−1.43078	−0.715390	+	0.698725i	$0.753751\pi$
$500$	−3.05438e17	−0.874216
$501$	−2.24087e17	−0.633099
$502$	6.47256e15	0.0180510
$503$	6.15141e17	1.69349	0.846745	−	0.531998i	$-0.178559\pi$
$503$	6.15141e17	1.69349	0.846745	+	0.531998i	$0.178559\pi$
$504$	1.88629e16	0.0512637
$505$	−2.14217e17	−0.574724
$506$	2.42193e16	0.0641481
$507$	1.94518e17	0.508638
$508$	3.26540e17	0.842990
$509$	1.78379e17	0.454651	0.227325	−	0.973819i	$-0.427002\pi$
$509$	1.78379e17	0.454651	0.227325	+	0.973819i	$0.427002\pi$
$510$	2.12119e16	0.0533794
$511$	−1.22458e17	−0.304266
$512$	3.13251e17	0.768490
$513$	−1.00145e17	−0.242587
$514$	−7.49817e15	−0.0179347
$515$	−1.16222e17	−0.274499
$516$	5.59388e16	0.130464
$517$	−2.74619e16	−0.0632473
$518$	5.80682e15	0.0132067
$519$	2.25009e17	0.505373
$520$	−1.10687e17	−0.245514
$521$	−2.18660e17	−0.478987	−0.239493	−	0.970898i	$-0.576981\pi$
$521$	−2.18660e17	−0.478987	−0.239493	+	0.970898i	$0.576981\pi$
$522$	−3.49072e16	−0.0755191
$523$	1.56982e17	0.335420	0.167710	−	0.985836i	$-0.446363\pi$
$523$	1.56982e17	0.335420	0.167710	+	0.985836i	$0.446363\pi$
$524$	−9.82932e16	−0.207429
$525$	9.03652e16	0.188350
$526$	2.41475e16	0.0497125
$527$	−3.87018e17	−0.786978
$528$	1.43817e17	0.288861
$529$	−2.77877e17	−0.551303
$530$	6.55029e16	0.128371
$531$	−2.24165e16	−0.0433963
$532$	−2.86534e17	−0.547962
$533$	3.06636e17	0.579290
$534$	−9.50964e15	−0.0177478
$535$	−1.90601e17	−0.351418
$536$	−1.44692e17	−0.263556
$537$	−2.39498e17	−0.430993
$538$	2.65741e16	0.0472470
$539$	−2.50110e17	−0.439343
$540$	5.61086e16	0.0973801
$541$	−6.46967e17	−1.10943	−0.554715	−	0.832040i	$-0.687173\pi$
$541$	−6.46967e17	−1.10943	−0.554715	+	0.832040i	$0.687173\pi$
$542$	1.06672e17	0.180741
$543$	3.87920e17	0.649447
$544$	−3.08409e17	−0.510193
$545$	−5.01833e17	−0.820317
$546$	3.82757e16	0.0618260
$547$	8.98334e17	1.43390	0.716952	−	0.697122i	$-0.245537\pi$
$547$	8.98334e17	1.43390	0.716952	+	0.697122i	$0.245537\pi$
$548$	2.70646e17	0.426903
$549$	−1.38520e17	−0.215920
$550$	−4.52390e16	−0.0696875
$551$	1.07709e18	1.63971
$552$	−8.81805e16	−0.132669
$553$	2.19176e17	0.325896
$554$	5.31867e16	0.0781609
$555$	3.50857e16	0.0509595
$556$	−9.04525e17	−1.29848
$557$	−7.42893e17	−1.05406	−0.527032	−	0.849845i	$-0.676695\pi$
$557$	−7.42893e17	−1.05406	−0.527032	+	0.849845i	$0.676695\pi$
$558$	3.20243e16	0.0449115
$559$	2.30567e17	0.319610
$560$	1.55358e17	0.212869
$561$	−2.38446e17	−0.322946
$562$	5.95561e16	0.0797334
$563$	−8.33322e17	−1.10283	−0.551415	−	0.834231i	$-0.685912\pi$
$563$	−8.33322e17	−1.10283	−0.551415	+	0.834231i	$0.685912\pi$
$564$	4.92234e16	0.0643957
$565$	−4.33615e17	−0.560776
$566$	8.09217e16	0.103457
$567$	−3.94118e16	−0.0498122
$568$	1.84617e17	0.230678
$569$	6.40960e17	0.791774	0.395887	−	0.918299i	$-0.370437\pi$
$569$	6.40960e17	0.791774	0.395887	+	0.918299i	$0.370437\pi$
$570$	5.41583e16	0.0661422
$571$	5.18121e17	0.625600	0.312800	−	0.949819i	$-0.398733\pi$
$571$	5.18121e17	0.625600	0.312800	+	0.949819i	$0.398733\pi$
$572$	6.12543e17	0.731244
$573$	2.15034e17	0.253806
$574$	2.82598e16	0.0329793
$575$	−4.22440e17	−0.487444
$576$	−2.40325e17	−0.274191
$577$	5.83813e17	0.658614	0.329307	−	0.944223i	$-0.393185\pi$
$577$	5.83813e17	0.658614	0.329307	+	0.944223i	$0.393185\pi$
$578$	5.44538e15	0.00607431
$579$	7.78941e17	0.859200
$580$	−6.03465e17	−0.658218
$581$	3.64250e17	0.392875
$582$	1.97049e16	0.0210172
$583$	−7.36326e17	−0.776648
$584$	−2.23209e17	−0.232824
$585$	2.31267e17	0.238562
$586$	3.92775e16	0.0400691
$587$	−4.95142e17	−0.499554	−0.249777	−	0.968303i	$-0.580357\pi$
$587$	−4.95142e17	−0.499554	−0.249777	+	0.968303i	$0.580357\pi$
$588$	4.48302e17	0.447320
$589$	−9.88137e17	−0.975142
$590$	1.21228e16	0.0118322
$591$	5.11375e17	0.493652
$592$	−1.61195e17	−0.153907
$593$	1.75043e18	1.65307	0.826533	−	0.562889i	$-0.190310\pi$
$593$	1.75043e18	1.65307	0.826533	+	0.562889i	$0.190310\pi$
$594$	1.97305e16	0.0184300
$595$	−2.57580e17	−0.237987
$596$	1.16992e18	1.06919
$597$	−1.53899e17	−0.139124
$598$	−1.78932e17	−0.160003
$599$	6.76756e17	0.598629	0.299315	−	0.954154i	$-0.403242\pi$
$599$	6.76756e17	0.598629	0.299315	+	0.954154i	$0.403242\pi$
$600$	1.64711e17	0.144125
$601$	−1.42278e18	−1.23155	−0.615777	−	0.787921i	$-0.711158\pi$
$601$	−1.42278e18	−1.23155	−0.615777	+	0.787921i	$0.711158\pi$
$602$	2.12493e16	0.0181956
$603$	3.02316e17	0.256094
$604$	−3.87865e17	−0.325043
$605$	4.39121e17	0.364061
$606$	1.35021e17	0.110746
$607$	4.69979e17	0.381375	0.190688	−	0.981651i	$-0.438928\pi$
$607$	4.69979e17	0.381375	0.190688	+	0.981651i	$0.438928\pi$
$608$	−7.87432e17	−0.632179
$609$	4.23885e17	0.336694
$610$	7.49113e16	0.0588713
$611$	2.02888e17	0.157757
$612$	4.27395e17	0.328810
$613$	−1.20625e18	−0.918215	−0.459108	−	0.888381i	$-0.651831\pi$
$613$	−1.20625e18	−0.918215	−0.459108	+	0.888381i	$0.651831\pi$
$614$	−1.99412e17	−0.150196
$615$	1.70750e17	0.127254
$616$	1.14671e17	0.0845626
$617$	−1.16341e18	−0.848944	−0.424472	−	0.905441i	$-0.639540\pi$
$617$	−1.16341e18	−0.848944	−0.424472	+	0.905441i	$0.639540\pi$
$618$	7.32547e16	0.0528945
$619$	−3.75951e17	−0.268622	−0.134311	−	0.990939i	$-0.542882\pi$
$619$	−3.75951e17	−0.268622	−0.134311	+	0.990939i	$0.542882\pi$
$620$	5.53626e17	0.391445
$621$	1.84243e17	0.128912
$622$	−1.56556e17	−0.108401
$623$	1.15477e17	0.0791270
$624$	−1.06252e18	−0.720502
$625$	3.83301e17	0.257229
$626$	−3.50112e17	−0.232527
$627$	−6.08800e17	−0.400162
$628$	2.58568e16	0.0168204
$629$	2.67258e17	0.172068
$630$	2.13138e16	0.0135815
$631$	2.70281e16	0.0170461	0.00852305	−	0.999964i	$-0.497287\pi$
$631$	2.70281e16	0.0170461	0.00852305	+	0.999964i	$0.497287\pi$
$632$	3.99498e17	0.249375
$633$	1.18204e18	0.730309
$634$	2.53879e17	0.155256
$635$	7.49478e17	0.453659
$636$	1.31981e18	0.790750
$637$	1.84780e18	1.09585
$638$	−2.12207e17	−0.124573
$639$	−3.85734e17	−0.224147
$640$	5.84945e17	0.336469
$641$	2.48481e18	1.41487	0.707434	−	0.706779i	$-0.249852\pi$
$641$	2.48481e18	1.41487	0.707434	+	0.706779i	$0.249852\pi$
$642$	1.20136e17	0.0677165
$643$	−1.45568e17	−0.0812259	−0.0406129	−	0.999175i	$-0.512931\pi$
$643$	−1.45568e17	−0.0812259	−0.0406129	+	0.999175i	$0.512931\pi$
$644$	5.27152e17	0.291191
$645$	1.28391e17	0.0702097
$646$	4.12539e17	0.223334
$647$	2.92156e18	1.56580	0.782901	−	0.622147i	$-0.213739\pi$
$647$	2.92156e18	1.56580	0.782901	+	0.622147i	$0.213739\pi$
$648$	−7.18370e16	−0.0381163
$649$	−1.36273e17	−0.0715848
$650$	3.34224e17	0.173821
$651$	−3.88877e17	−0.200233
$652$	5.35997e17	0.273246
$653$	2.21261e18	1.11678	0.558392	−	0.829578i	$-0.311419\pi$
$653$	2.21261e18	1.11678	0.558392	+	0.829578i	$0.311419\pi$
$654$	3.16306e17	0.158071
$655$	−2.25603e17	−0.111629
$656$	−7.84479e17	−0.384332
$657$	4.66367e17	0.226231
$658$	1.86983e16	0.00898120
$659$	3.78224e18	1.79884	0.899422	−	0.437081i	$-0.143988\pi$
$659$	3.78224e18	1.79884	0.899422	+	0.437081i	$0.143988\pi$
$660$	3.41094e17	0.160634
$661$	−3.18733e18	−1.48634	−0.743170	−	0.669103i	$-0.766679\pi$
$661$	−3.18733e18	−1.48634	−0.743170	+	0.669103i	$0.766679\pi$
$662$	2.18476e17	0.100885
$663$	1.76163e18	0.805520
$664$	6.63928e17	0.300628
$665$	−6.57655e17	−0.294888
$666$	−2.21145e16	−0.00981964
$667$	−1.98158e18	−0.871353
$668$	2.44175e18	1.06330
$669$	−8.05187e17	−0.347238
$670$	−1.63492e17	−0.0698249
$671$	−8.42086e17	−0.356172
$672$	−3.09891e17	−0.129810
$673$	−2.91932e18	−1.21111	−0.605555	−	0.795803i	$-0.707049\pi$
$673$	−2.91932e18	−1.21111	−0.605555	+	0.795803i	$0.707049\pi$
$674$	4.91828e17	0.202080
$675$	−3.44144e17	−0.140045
$676$	−2.11956e18	−0.854263
$677$	3.61300e18	1.44225	0.721126	−	0.692804i	$-0.243625\pi$
$677$	3.61300e18	1.44225	0.721126	+	0.692804i	$0.243625\pi$
$678$	2.73308e17	0.108059
$679$	−2.39280e17	−0.0937030
$680$	−4.69499e17	−0.182107
$681$	−1.50743e18	−0.579136
$682$	1.94681e17	0.0740842
$683$	−2.60194e18	−0.980759	−0.490379	−	0.871509i	$-0.663142\pi$
$683$	−2.60194e18	−0.980759	−0.490379	+	0.871509i	$0.663142\pi$
$684$	1.09123e18	0.407428
$685$	6.21190e17	0.229740
$686$	3.83426e17	0.140467
$687$	−3.28977e17	−0.119384
$688$	−5.89870e17	−0.212047
$689$	5.43995e18	1.93718
$690$	−9.96380e16	−0.0351484
$691$	3.85234e17	0.134622	0.0673112	−	0.997732i	$-0.478558\pi$
$691$	3.85234e17	0.134622	0.0673112	+	0.997732i	$0.478558\pi$
$692$	−2.45180e18	−0.848780
$693$	−2.39591e17	−0.0821683
$694$	−9.62537e17	−0.327025
$695$	−2.07607e18	−0.698782
$696$	7.72627e17	0.257638
$697$	1.30065e18	0.429682
$698$	3.12332e17	0.102225
$699$	−1.09152e18	−0.353941
$700$	−9.84660e17	−0.316336
$701$	−6.06621e18	−1.93086	−0.965429	−	0.260667i	$-0.916057\pi$
$701$	−6.06621e18	−1.93086	−0.965429	+	0.260667i	$0.916057\pi$
$702$	−1.45768e17	−0.0459696
$703$	6.82363e17	0.213209
$704$	−1.46098e18	−0.452294
$705$	1.12978e17	0.0346549
$706$	1.39272e17	0.0423285
$707$	−1.63959e18	−0.493751
$708$	2.44260e17	0.0728846
$709$	−2.16340e18	−0.639642	−0.319821	−	0.947478i	$-0.603623\pi$
$709$	−2.16340e18	−0.639642	−0.319821	+	0.947478i	$0.603623\pi$
$710$	2.08604e17	0.0611144
$711$	−8.34703e17	−0.242315
$712$	2.10484e17	0.0605479
$713$	1.81793e18	0.518197
$714$	1.62353e17	0.0458588
$715$	1.40591e18	0.393522
$716$	2.60968e18	0.723857
$717$	2.79653e18	0.768678
$718$	−2.61916e17	−0.0713434
$719$	5.11957e18	1.38196	0.690980	−	0.722874i	$-0.257179\pi$
$719$	5.11957e18	1.38196	0.690980	+	0.722874i	$0.257179\pi$
$720$	−5.91661e17	−0.158275
$721$	−8.89546e17	−0.235825
$722$	3.90391e17	0.102567
$723$	3.42899e18	0.892827
$724$	−4.22695e18	−1.09075
$725$	3.70137e18	0.946598
$726$	−2.76778e17	−0.0701527
$727$	4.51835e18	1.13503	0.567513	−	0.823364i	$-0.307906\pi$
$727$	4.51835e18	1.13503	0.567513	+	0.823364i	$0.307906\pi$
$728$	−8.47185e17	−0.210923
$729$	1.50095e17	0.0370370
$730$	−2.52210e17	−0.0616828
$731$	9.77992e17	0.237068
$732$	1.50938e18	0.362640
$733$	4.95103e17	0.117902	0.0589508	−	0.998261i	$-0.481224\pi$
$733$	4.95103e17	0.117902	0.0589508	+	0.998261i	$0.481224\pi$
$734$	−8.66039e17	−0.204415
$735$	1.02895e18	0.240727
$736$	1.44868e18	0.335944
$737$	1.83783e18	0.422442
$738$	−1.07624e17	−0.0245212
$739$	2.42268e18	0.547150	0.273575	−	0.961851i	$-0.411794\pi$
$739$	2.42268e18	0.547150	0.273575	+	0.961851i	$0.411794\pi$
$740$	−3.82309e17	−0.0855872
$741$	4.49780e18	0.998117
$742$	5.01351e17	0.110285
$743$	−3.28077e18	−0.715398	−0.357699	−	0.933837i	$-0.616439\pi$
$743$	−3.28077e18	−0.715398	−0.357699	+	0.933837i	$0.616439\pi$
$744$	−7.08818e17	−0.153218
$745$	2.68521e18	0.575390
$746$	−1.41492e17	−0.0300558
$747$	−1.38720e18	−0.292115
$748$	2.59821e18	0.542392
$749$	−1.45883e18	−0.301907
$750$	4.41870e17	0.0906558
$751$	−7.28331e18	−1.48139	−0.740695	−	0.671841i	$-0.765504\pi$
$751$	−7.28331e18	−1.48139	−0.740695	+	0.671841i	$0.765504\pi$
$752$	−5.19056e17	−0.104664
$753$	2.99329e17	0.0598386
$754$	1.56778e18	0.310721
$755$	−8.90232e17	−0.174924
$756$	4.29448e17	0.0836602
$757$	−5.35060e18	−1.03343	−0.516713	−	0.856159i	$-0.672844\pi$
$757$	−5.35060e18	−1.03343	−0.516713	+	0.856159i	$0.672844\pi$
$758$	−1.68384e17	−0.0322441
$759$	1.12004e18	0.212649
$760$	−1.19873e18	−0.225648
$761$	6.63517e18	1.23837	0.619187	−	0.785244i	$-0.287462\pi$
$761$	6.63517e18	1.23837	0.619187	+	0.785244i	$0.287462\pi$
$762$	−4.72397e17	−0.0874177
$763$	−3.84096e18	−0.704743
$764$	−2.34310e18	−0.426270
$765$	9.80962e17	0.176951
$766$	−2.55458e17	−0.0456912
$767$	1.00678e18	0.178553
$768$	2.33192e18	0.410077
$769$	−1.29357e18	−0.225564	−0.112782	−	0.993620i	$-0.535976\pi$
$769$	−1.29357e18	−0.225564	−0.112782	+	0.993620i	$0.535976\pi$
$770$	1.29570e17	0.0224035
$771$	−3.46759e17	−0.0594531
$772$	−8.48769e18	−1.44304
$773$	−4.23657e18	−0.714245	−0.357123	−	0.934058i	$-0.616242\pi$
$773$	−4.23657e18	−0.714245	−0.357123	+	0.934058i	$0.616242\pi$
$774$	−8.09251e16	−0.0135290
$775$	−3.39568e18	−0.562945
$776$	−4.36143e17	−0.0717015
$777$	2.68541e17	0.0437799
$778$	3.54261e17	0.0572737
$779$	3.32082e18	0.532418
$780$	−2.51999e18	−0.400668
$781$	−2.34494e18	−0.369744
$782$	−7.58970e17	−0.118681
$783$	−1.61431e18	−0.250343
$784$	−4.72731e18	−0.727043
$785$	5.93467e16	0.00905198
$786$	1.42198e17	0.0215103
$787$	−1.20264e19	−1.80426	−0.902129	−	0.431467i	$-0.857996\pi$
$787$	−1.20264e19	−1.80426	−0.902129	+	0.431467i	$0.857996\pi$
$788$	−5.57217e18	−0.829094
$789$	1.11672e18	0.164795
$790$	4.51405e17	0.0660679
$791$	−3.31883e18	−0.481768
$792$	−4.36709e17	−0.0628751
$793$	6.22131e18	0.888395
$794$	−1.12140e17	−0.0158829
$795$	3.02923e18	0.425546
$796$	1.67695e18	0.233660
$797$	8.20407e18	1.13384	0.566918	−	0.823774i	$-0.308136\pi$
$797$	8.20407e18	1.13384	0.566918	+	0.823774i	$0.308136\pi$
$798$	4.14521e17	0.0568235
$799$	8.60585e17	0.117015
$800$	−2.70597e18	−0.364954
$801$	−4.39781e17	−0.0588335
$802$	6.68158e17	0.0886637
$803$	2.83512e18	0.373182
$804$	−3.29417e18	−0.430113
$805$	1.20992e18	0.156706
$806$	−1.43830e18	−0.184787
$807$	1.22894e18	0.156622
$808$	−2.98852e18	−0.377818
$809$	7.02387e18	0.880868	0.440434	−	0.897785i	$-0.354825\pi$
$809$	7.02387e18	0.880868	0.440434	+	0.897785i	$0.354825\pi$
$810$	−8.11708e16	−0.0100983
$811$	6.61867e18	0.816836	0.408418	−	0.912795i	$-0.366081\pi$
$811$	6.61867e18	0.816836	0.408418	+	0.912795i	$0.366081\pi$
$812$	−4.61884e18	−0.565482
$813$	4.93314e18	0.599150
$814$	−1.34438e17	−0.0161981
$815$	1.23023e18	0.147048
$816$	−4.50685e18	−0.534425
$817$	2.49701e18	0.293750
$818$	−2.46008e18	−0.287113
$819$	1.77009e18	0.204951
$820$	−1.86057e18	−0.213725
$821$	−5.90029e18	−0.672424	−0.336212	−	0.941786i	$-0.609146\pi$
$821$	−5.90029e18	−0.672424	−0.336212	+	0.941786i	$0.609146\pi$
$822$	−3.91537e17	−0.0442696
$823$	−1.71526e19	−1.92412	−0.962059	−	0.272842i	$-0.912037\pi$
$823$	−1.71526e19	−1.92412	−0.962059	+	0.272842i	$0.912037\pi$
$824$	−1.62140e18	−0.180453
$825$	−2.09211e18	−0.231012
$826$	9.27861e16	0.0101651
$827$	1.00880e19	1.09653	0.548263	−	0.836306i	$-0.315289\pi$
$827$	1.00880e19	1.09653	0.548263	+	0.836306i	$0.315289\pi$
$828$	−2.00759e18	−0.216510
$829$	4.06157e18	0.434599	0.217300	−	0.976105i	$-0.430275\pi$
$829$	4.06157e18	0.434599	0.217300	+	0.976105i	$0.430275\pi$
$830$	7.50194e17	0.0796463
$831$	2.45966e18	0.259101
$832$	1.07937e19	1.12815
$833$	7.83779e18	0.812832
$834$	1.30855e18	0.134652
$835$	5.60433e18	0.572219
$836$	6.63376e18	0.672077
$837$	1.48099e18	0.148880
$838$	−1.72434e18	−0.172003
$839$	1.07822e19	1.06722	0.533609	−	0.845731i	$-0.320835\pi$
$839$	1.07822e19	1.06722	0.533609	+	0.845731i	$0.320835\pi$
$840$	−4.71754e17	−0.0463341
$841$	7.10175e18	0.692136
$842$	−1.45688e18	−0.140895
$843$	2.75422e18	0.264314
$844$	−1.28800e19	−1.22656
$845$	−4.86483e18	−0.459726
$846$	−7.12101e16	−0.00667781
$847$	3.36098e18	0.312769
$848$	−1.39173e19	−1.28523
$849$	3.74229e18	0.342955
$850$	1.41767e18	0.128930
$851$	−1.25538e18	−0.113301
$852$	4.20313e18	0.376457
$853$	−1.01275e19	−0.900185	−0.450093	−	0.892982i	$-0.648609\pi$
$853$	−1.01275e19	−0.900185	−0.450093	+	0.892982i	$0.648609\pi$
$854$	5.73361e17	0.0505769
$855$	2.50460e18	0.219259
$856$	−2.65906e18	−0.231019
$857$	7.67025e17	0.0661354	0.0330677	−	0.999453i	$-0.489472\pi$
$857$	7.67025e17	0.0661354	0.0330677	+	0.999453i	$0.489472\pi$
$858$	−8.86149e17	−0.0758297
$859$	−6.06115e18	−0.514754	−0.257377	−	0.966311i	$-0.582858\pi$
$859$	−6.06115e18	−0.514754	−0.257377	+	0.966311i	$0.582858\pi$
$860$	−1.39901e18	−0.117918
$861$	1.30690e18	0.109325
$862$	4.06571e17	0.0337551
$863$	−1.02067e19	−0.841041	−0.420520	−	0.907283i	$-0.638152\pi$
$863$	−1.02067e19	−0.841041	−0.420520	+	0.907283i	$0.638152\pi$
$864$	1.18018e18	0.0965180
$865$	−5.62739e18	−0.456775
$866$	3.95456e17	0.0318590
$867$	2.51826e17	0.0201361
$868$	4.23738e18	0.336294
$869$	−5.07430e18	−0.399712
$870$	8.73016e17	0.0682570
$871$	−1.35779e19	−1.05369
$872$	−7.00103e18	−0.539268
$873$	9.11268e17	0.0696713
$874$	−1.93781e18	−0.147057
$875$	−5.36571e18	−0.404180
$876$	−5.08174e18	−0.379958
$877$	−1.88380e19	−1.39809	−0.699047	−	0.715075i	$-0.746392\pi$
$877$	−1.88380e19	−1.39809	−0.699047	+	0.715075i	$0.746392\pi$
$878$	−3.18476e18	−0.234619
$879$	1.81642e18	0.132828
$880$	−3.59681e18	−0.261084
$881$	1.43776e19	1.03596	0.517982	−	0.855392i	$-0.326684\pi$
$881$	1.43776e19	1.03596	0.517982	+	0.855392i	$0.326684\pi$
$882$	−6.48547e17	−0.0463869
$883$	−8.90008e18	−0.631902	−0.315951	−	0.948776i	$-0.602323\pi$
$883$	−8.90008e18	−0.631902	−0.315951	+	0.948776i	$0.602323\pi$
$884$	−1.91955e19	−1.35288
$885$	5.60627e17	0.0392232
$886$	−6.26854e17	−0.0435359
$887$	−1.38680e19	−0.956115	−0.478057	−	0.878329i	$-0.658659\pi$
$887$	−1.38680e19	−0.956115	−0.478057	+	0.878329i	$0.658659\pi$
$888$	4.89478e17	0.0335003
$889$	5.73640e18	0.389743
$890$	2.37832e17	0.0160412
$891$	9.12451e17	0.0610948
$892$	8.77368e18	0.583190
$893$	2.19725e18	0.144992
$894$	−1.69249e18	−0.110875
$895$	5.98977e18	0.389547
$896$	4.47709e18	0.289064
$897$	−8.27484e18	−0.530406
$898$	−2.06239e18	−0.131242
$899$	−1.59285e19	−1.00632
$900$	3.74995e18	0.235206
$901$	2.30745e19	1.43688
$902$	−6.54263e17	−0.0404492
$903$	9.82689e17	0.0603178
$904$	−6.04933e18	−0.368648
$905$	−9.70174e18	−0.586995
$906$	5.61114e17	0.0337068
$907$	−2.39637e19	−1.42924	−0.714621	−	0.699512i	$-0.753401\pi$
$907$	−2.39637e19	−1.42924	−0.714621	+	0.699512i	$0.753401\pi$
$908$	1.64256e19	0.972666
$909$	6.24416e18	0.367120
$910$	−9.57261e17	−0.0558806
$911$	−1.36444e19	−0.790834	−0.395417	−	0.918502i	$-0.629400\pi$
$911$	−1.36444e19	−0.790834	−0.395417	+	0.918502i	$0.629400\pi$
$912$	−1.15069e19	−0.662204
$913$	−8.43301e18	−0.481862
$914$	−3.60014e18	−0.204253
$915$	3.46433e18	0.195156
$916$	3.58468e18	0.200507
$917$	−1.72674e18	−0.0959016
$918$	−6.18301e17	−0.0340975
$919$	−2.82254e19	−1.54557	−0.772785	−	0.634667i	$-0.781137\pi$
$919$	−2.82254e19	−1.54557	−0.772785	+	0.634667i	$0.781137\pi$
$920$	2.20536e18	0.119911
$921$	−9.22197e18	−0.497893
$922$	−3.47992e18	−0.186560
$923$	1.73244e19	0.922246
$924$	2.61069e18	0.138003
$925$	2.34491e18	0.123085
$926$	1.24498e18	0.0648919
$927$	3.38772e18	0.175343
$928$	−1.26932e19	−0.652391
$929$	−4.94985e18	−0.252633	−0.126316	−	0.991990i	$-0.540315\pi$
$929$	−4.94985e18	−0.252633	−0.126316	+	0.991990i	$0.540315\pi$
$930$	−8.00916e17	−0.0405927
$931$	2.00115e19	1.00718
$932$	1.18937e19	0.594447
$933$	−7.24006e18	−0.359345
$934$	3.25723e18	0.160544
$935$	5.96343e18	0.291891
$936$	3.22640e18	0.156828
$937$	−7.56255e18	−0.365057	−0.182529	−	0.983201i	$-0.558428\pi$
$937$	−7.56255e18	−0.365057	−0.182529	+	0.983201i	$0.558428\pi$
$938$	−1.25135e18	−0.0599873
$939$	−1.61912e19	−0.770821
$940$	−1.23106e18	−0.0582033
$941$	3.25933e19	1.53037	0.765184	−	0.643812i	$-0.222648\pi$
$941$	3.25933e19	1.53037	0.765184	+	0.643812i	$0.222648\pi$
$942$	−3.74063e16	−0.00174427
$943$	−6.10949e18	−0.282930
$944$	−2.57570e18	−0.118461
$945$	9.85674e17	0.0450222
$946$	−4.91957e17	−0.0223170
$947$	1.86275e19	0.839227	0.419614	−	0.907703i	$-0.362166\pi$
$947$	1.86275e19	0.839227	0.419614	+	0.907703i	$0.362166\pi$
$948$	9.09529e18	0.406970
$949$	−2.09458e19	−0.930823
$950$	3.61960e18	0.159756
$951$	1.17409e19	0.514667
$952$	−3.59349e18	−0.156450
$953$	2.69966e19	1.16736	0.583681	−	0.811983i	$-0.301612\pi$
$953$	2.69966e19	1.16736	0.583681	+	0.811983i	$0.301612\pi$
$954$	−1.90933e18	−0.0820005
$955$	−5.37792e18	−0.229399
$956$	−3.04722e19	−1.29100
$957$	−9.81367e18	−0.412956
$958$	−4.05137e18	−0.169327
$959$	4.75451e18	0.197372
$960$	6.01044e18	0.247824
$961$	−9.80457e18	−0.401538
$962$	9.93225e17	0.0404026
$963$	5.55577e18	0.224478
$964$	−3.73638e19	−1.49951
$965$	−1.94810e19	−0.776577
$966$	−7.62616e17	−0.0301964
$967$	−5.49531e18	−0.216132	−0.108066	−	0.994144i	$-0.534466\pi$
$967$	−5.49531e18	−0.216132	−0.108066	+	0.994144i	$0.534466\pi$
$968$	6.12615e18	0.239330
$969$	1.90782e19	0.740343
$970$	−4.92812e17	−0.0189961
$971$	−4.70150e19	−1.80016	−0.900082	−	0.435721i	$-0.856493\pi$
$971$	−4.70150e19	−1.80016	−0.900082	+	0.435721i	$0.856493\pi$
$972$	−1.63550e18	−0.0622041
$973$	−1.58900e19	−0.600331
$974$	3.02934e18	0.113688
$975$	1.54565e19	0.576209
$976$	−1.59162e19	−0.589409
$977$	1.66428e19	0.612227	0.306114	−	0.951995i	$-0.400971\pi$
$977$	1.66428e19	0.612227	0.306114	+	0.951995i	$0.400971\pi$
$978$	−7.75412e17	−0.0283355
$979$	−2.67350e18	−0.0970494
$980$	−1.12119e19	−0.404305
$981$	1.46278e19	0.523999
$982$	−3.24790e18	−0.115579
$983$	−1.54727e19	−0.546975	−0.273488	−	0.961875i	$-0.588177\pi$
$983$	−1.54727e19	−0.546975	−0.273488	+	0.961875i	$0.588177\pi$
$984$	2.38212e18	0.0836556
$985$	−1.27893e19	−0.446181
$986$	6.65001e18	0.230474
$987$	8.64719e17	0.0297724
$988$	−4.90100e19	−1.67635
$989$	−4.59389e18	−0.156100
$990$	−4.93451e17	−0.0166577
$991$	4.34221e19	1.45624	0.728118	−	0.685452i	$-0.240395\pi$
$991$	4.34221e19	1.45624	0.728118	+	0.685452i	$0.240395\pi$
$992$	1.16449e19	0.387979
$993$	1.01036e19	0.334430
$994$	1.59663e18	0.0525040
$995$	3.84894e18	0.125745
$996$	1.51155e19	0.490611
$997$	4.09575e19	1.32073	0.660367	−	0.750943i	$-0.270401\pi$
$997$	4.09575e19	1.32073	0.660367	+	0.750943i	$0.270401\pi$
$998$	−7.77825e18	−0.249192
$999$	−1.02270e18	−0.0325518

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.16	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+15.7636 q^{2} +729.000 q^{3} -7943.51 q^{4} -18232.0 q^{5} +11491.7 q^{6} -139545. q^{7} -254354. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+15.7636 q^{2} +729.000 q^{3} -7943.51 q^{4} -18232.0 q^{5} +11491.7 q^{6} -139545. q^{7} -254354. q^{8} +531441. q^{9} -287402. q^{10} +3.23072e6 q^{11} -5.79082e6 q^{12} -2.38685e7 q^{13} -2.19974e6 q^{14} -1.32911e7 q^{15} +6.10637e7 q^{16} -1.01242e8 q^{17} +8.37742e6 q^{18} -2.58492e8 q^{19} +1.44826e8 q^{20} -1.01729e8 q^{21} +5.09278e7 q^{22} +4.75562e8 q^{23} -1.85424e8 q^{24} -8.88297e8 q^{25} -3.76253e8 q^{26} +3.87420e8 q^{27} +1.10848e9 q^{28} -4.16682e9 q^{29} -2.09516e8 q^{30} +3.82269e9 q^{31} +3.04625e9 q^{32} +2.35519e9 q^{33} -1.59594e9 q^{34} +2.54420e9 q^{35} -4.22151e9 q^{36} -2.63978e9 q^{37} -4.07477e9 q^{38} -1.74001e10 q^{39} +4.63738e9 q^{40} -1.28469e10 q^{41} -1.60361e9 q^{42} -9.65991e9 q^{43} -2.56633e10 q^{44} -9.68924e9 q^{45} +7.49657e9 q^{46} -8.50024e9 q^{47} +4.45154e10 q^{48} -7.74161e10 q^{49} -1.40027e10 q^{50} -7.38057e10 q^{51} +1.89599e11 q^{52} -2.27914e11 q^{53} +6.10714e9 q^{54} -5.89025e10 q^{55} +3.54939e10 q^{56} -1.88441e11 q^{57} -6.56840e10 q^{58} -4.21805e10 q^{59} +1.05578e11 q^{60} -2.60650e11 q^{61} +6.02594e10 q^{62} -7.41602e10 q^{63} -4.52214e11 q^{64} +4.35170e11 q^{65} +3.71263e10 q^{66} +5.68861e11 q^{67} +8.04220e11 q^{68} +3.46685e11 q^{69} +4.01057e10 q^{70} -7.25827e11 q^{71} -1.35174e11 q^{72} +8.77552e11 q^{73} -4.16124e10 q^{74} -6.47568e11 q^{75} +2.05334e12 q^{76} -4.50832e11 q^{77} -2.74288e11 q^{78} -1.57064e12 q^{79} -1.11331e12 q^{80} +2.82430e11 q^{81} -2.02513e11 q^{82} -2.61026e12 q^{83} +8.08083e11 q^{84} +1.84585e12 q^{85} -1.52275e11 q^{86} -3.03761e12 q^{87} -8.21745e11 q^{88} -8.27525e11 q^{89} -1.52737e11 q^{90} +3.33074e12 q^{91} -3.77763e12 q^{92} +2.78674e12 q^{93} -1.33994e11 q^{94} +4.71284e12 q^{95} +2.22071e12 q^{96} +1.71471e12 q^{97} -1.22036e12 q^{98} +1.71694e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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

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