LMFDB - Embedded newform 177.12.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-26.3367 q^{2} -243.000 q^{3} -1354.38 q^{4} +12487.3 q^{5} +6399.81 q^{6} -48376.8 q^{7} +89607.3 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-26.3367 q^{2} -243.000 q^{3} -1354.38 q^{4} +12487.3 q^{5} +6399.81 q^{6} -48376.8 q^{7} +89607.3 q^{8} +59049.0 q^{9} -328874. q^{10} +524591. q^{11} +329114. q^{12} -36137.3 q^{13} +1.27408e6 q^{14} -3.03441e6 q^{15} +413811. q^{16} +2.33652e6 q^{17} -1.55515e6 q^{18} -1.72596e7 q^{19} -1.69125e7 q^{20} +1.17556e7 q^{21} -1.38160e7 q^{22} -3.09864e7 q^{23} -2.17746e7 q^{24} +1.07104e8 q^{25} +951736. q^{26} -1.43489e7 q^{27} +6.55206e7 q^{28} +2.08422e8 q^{29} +7.99163e7 q^{30} -2.18649e8 q^{31} -1.94414e8 q^{32} -1.27476e8 q^{33} -6.15361e7 q^{34} -6.04096e8 q^{35} -7.99748e7 q^{36} -4.80083e8 q^{37} +4.54559e8 q^{38} +8.78136e6 q^{39} +1.11895e9 q^{40} -2.86197e8 q^{41} -3.09603e8 q^{42} +1.35383e9 q^{43} -7.10496e8 q^{44} +7.37362e8 q^{45} +8.16079e8 q^{46} -2.88733e9 q^{47} -1.00556e8 q^{48} +3.62993e8 q^{49} -2.82077e9 q^{50} -5.67774e8 q^{51} +4.89436e7 q^{52} +2.98644e9 q^{53} +3.77902e8 q^{54} +6.55072e9 q^{55} -4.33492e9 q^{56} +4.19407e9 q^{57} -5.48913e9 q^{58} +7.14924e8 q^{59} +4.10974e9 q^{60} +1.17517e10 q^{61} +5.75848e9 q^{62} -2.85660e9 q^{63} +4.27274e9 q^{64} -4.51257e8 q^{65} +3.35729e9 q^{66} -1.30914e10 q^{67} -3.16453e9 q^{68} +7.52970e9 q^{69} +1.59099e10 q^{70} +4.46502e9 q^{71} +5.29122e9 q^{72} +2.16645e10 q^{73} +1.26438e10 q^{74} -2.60263e10 q^{75} +2.33760e10 q^{76} -2.53781e10 q^{77} -2.31272e8 q^{78} +3.67905e10 q^{79} +5.16738e9 q^{80} +3.48678e9 q^{81} +7.53747e9 q^{82} +1.84426e10 q^{83} -1.59215e10 q^{84} +2.91768e10 q^{85} -3.56554e10 q^{86} -5.06465e10 q^{87} +4.70073e10 q^{88} -2.23424e10 q^{89} -1.94197e10 q^{90} +1.74821e9 q^{91} +4.19674e10 q^{92} +5.31317e10 q^{93} +7.60425e10 q^{94} -2.15525e11 q^{95} +4.72427e10 q^{96} +2.89892e10 q^{97} -9.56002e9 q^{98} +3.09766e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) $ 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * 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 $

$2$	−26.3367	−0.581964	−0.290982	−	0.956729i	$-0.593982\pi$
$2$	−26.3367	−0.581964	−0.290982	+	0.956729i	$0.593982\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1354.38	−0.661318
$5$	12487.3	1.78703	0.893517	−	0.449028i	$-0.148230\pi$
$5$	12487.3	1.78703	0.893517	+	0.449028i	$0.148230\pi$
$6$	6399.81	0.335997
$7$	−48376.8	−1.08792	−0.543962	−	0.839110i	$-0.683076\pi$
$7$	−48376.8	−1.08792	−0.543962	+	0.839110i	$0.683076\pi$
$8$	89607.3	0.966827
$9$	59049.0	0.333333
$10$	−328874.	−1.03999
$11$	524591.	0.982113	0.491056	−	0.871128i	$-0.336611\pi$
$11$	524591.	0.982113	0.491056	+	0.871128i	$0.336611\pi$
$12$	329114.	0.381812
$13$	−36137.3	−0.0269940	−0.0134970	−	0.999909i	$-0.504296\pi$
$13$	−36137.3	−0.0269940	−0.0134970	+	0.999909i	$0.504296\pi$
$14$	1.27408e6	0.633132
$15$	−3.03441e6	−1.03175
$16$	413811.	0.0986603
$17$	2.33652e6	0.399117	0.199558	−	0.979886i	$-0.436049\pi$
$17$	2.33652e6	0.399117	0.199558	+	0.979886i	$0.436049\pi$
$18$	−1.55515e6	−0.193988
$19$	−1.72596e7	−1.59913	−0.799567	−	0.600577i	$-0.794938\pi$
$19$	−1.72596e7	−1.59913	−0.799567	+	0.600577i	$0.794938\pi$
$20$	−1.69125e7	−1.18180
$21$	1.17556e7	0.628113
$22$	−1.38160e7	−0.571554
$23$	−3.09864e7	−1.00385	−0.501924	−	0.864912i	$-0.667374\pi$
$23$	−3.09864e7	−1.00385	−0.501924	+	0.864912i	$0.667374\pi$
$24$	−2.17746e7	−0.558198
$25$	1.07104e8	2.19349
$26$	951736.	0.0157095
$27$	−1.43489e7	−0.192450
$28$	6.55206e7	0.719464
$29$	2.08422e8	1.88692	0.943461	−	0.331485i	$-0.107550\pi$
$29$	2.08422e8	1.88692	0.943461	+	0.331485i	$0.107550\pi$
$30$	7.99163e7	0.600438
$31$	−2.18649e8	−1.37170	−0.685848	−	0.727745i	$-0.740568\pi$
$31$	−2.18649e8	−1.37170	−0.685848	+	0.727745i	$0.740568\pi$
$32$	−1.94414e8	−1.02424
$33$	−1.27476e8	−0.567023
$34$	−6.15361e7	−0.232271
$35$	−6.04096e8	−1.94416
$36$	−7.99748e7	−0.220439
$37$	−4.80083e8	−1.13817	−0.569085	−	0.822279i	$-0.692702\pi$
$37$	−4.80083e8	−1.13817	−0.569085	+	0.822279i	$0.692702\pi$
$38$	4.54559e8	0.930638
$39$	8.78136e6	0.0155850
$40$	1.11895e9	1.72775
$41$	−2.86197e8	−0.385792	−0.192896	−	0.981219i	$-0.561788\pi$
$41$	−2.86197e8	−0.385792	−0.192896	+	0.981219i	$0.561788\pi$
$42$	−3.09603e8	−0.365539
$43$	1.35383e9	1.40439	0.702195	−	0.711985i	$-0.252204\pi$
$43$	1.35383e9	1.40439	0.702195	+	0.711985i	$0.252204\pi$
$44$	−7.10496e8	−0.649489
$45$	7.37362e8	0.595678
$46$	8.16079e8	0.584203
$47$	−2.88733e9	−1.83636	−0.918179	−	0.396165i	$-0.870341\pi$
$47$	−2.88733e9	−1.83636	−0.918179	+	0.396165i	$0.870341\pi$
$48$	−1.00556e8	−0.0569615
$49$	3.62993e8	0.183578
$50$	−2.82077e9	−1.27653
$51$	−5.67774e8	−0.230430
$52$	4.89436e7	0.0178516
$53$	2.98644e9	0.980927	0.490464	−	0.871462i	$-0.336827\pi$
$53$	2.98644e9	0.980927	0.490464	+	0.871462i	$0.336827\pi$
$54$	3.77902e8	0.111999
$55$	6.55072e9	1.75507
$56$	−4.33492e9	−1.05183
$57$	4.19407e9	0.923260
$58$	−5.48913e9	−1.09812
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	4.10974e9	0.682312
$61$	1.17517e10	1.78150	0.890749	−	0.454495i	$-0.150180\pi$
$61$	1.17517e10	1.78150	0.890749	+	0.454495i	$0.150180\pi$
$62$	5.75848e9	0.798277
$63$	−2.85660e9	−0.362641
$64$	4.27274e9	0.497412
$65$	−4.51257e8	−0.0482392
$66$	3.35729e9	0.329987
$67$	−1.30914e10	−1.18461	−0.592303	−	0.805715i	$-0.701781\pi$
$67$	−1.30914e10	−1.18461	−0.592303	+	0.805715i	$0.701781\pi$
$68$	−3.16453e9	−0.263943
$69$	7.52970e9	0.579572
$70$	1.59099e10	1.13143
$71$	4.46502e9	0.293699	0.146850	−	0.989159i	$-0.453087\pi$
$71$	4.46502e9	0.293699	0.146850	+	0.989159i	$0.453087\pi$
$72$	5.29122e9	0.322276
$73$	2.16645e10	1.22313	0.611565	−	0.791194i	$-0.290540\pi$
$73$	2.16645e10	1.22313	0.611565	+	0.791194i	$0.290540\pi$
$74$	1.26438e10	0.662373
$75$	−2.60263e10	−1.26641
$76$	2.33760e10	1.05754
$77$	−2.53781e10	−1.06846
$78$	−2.31272e8	−0.00906990
$79$	3.67905e10	1.34520	0.672600	−	0.740006i	$-0.265177\pi$
$79$	3.67905e10	1.34520	0.672600	+	0.740006i	$0.265177\pi$
$80$	5.16738e9	0.176309
$81$	3.48678e9	0.111111
$82$	7.53747e9	0.224517
$83$	1.84426e10	0.513917	0.256958	−	0.966422i	$-0.417280\pi$
$83$	1.84426e10	0.513917	0.256958	+	0.966422i	$0.417280\pi$
$84$	−1.59215e10	−0.415383
$85$	2.91768e10	0.713235
$86$	−3.56554e10	−0.817304
$87$	−5.06465e10	−1.08941
$88$	4.70073e10	0.949533
$89$	−2.23424e10	−0.424117	−0.212058	−	0.977257i	$-0.568017\pi$
$89$	−2.23424e10	−0.424117	−0.212058	+	0.977257i	$0.568017\pi$
$90$	−1.94197e10	−0.346663
$91$	1.74821e9	0.0293674
$92$	4.19674e10	0.663863
$93$	5.31317e10	0.791949
$94$	7.60425e10	1.06869
$95$	−2.15525e11	−2.85771
$96$	4.72427e10	0.591347
$97$	2.89892e10	0.342761	0.171381	−	0.985205i	$-0.445177\pi$
$97$	2.89892e10	0.342761	0.171381	+	0.985205i	$0.445177\pi$
$98$	−9.56002e9	−0.106835
$99$	3.09766e10	0.327371
$100$	−1.45060e11	−1.45060
$101$	−9.13004e9	−0.0864380	−0.0432190	−	0.999066i	$-0.513761\pi$
$101$	−9.13004e9	−0.0864380	−0.0432190	+	0.999066i	$0.513761\pi$
$102$	1.49533e10	0.134102
$103$	−5.62201e10	−0.477845	−0.238923	−	0.971039i	$-0.576794\pi$
$103$	−5.62201e10	−0.477845	−0.238923	+	0.971039i	$0.576794\pi$
$104$	−3.23817e9	−0.0260985
$105$	1.46795e11	1.12246
$106$	−7.86529e10	−0.570864
$107$	−1.76188e11	−1.21441	−0.607204	−	0.794546i	$-0.707709\pi$
$107$	−1.76188e11	−1.21441	−0.607204	+	0.794546i	$0.707709\pi$
$108$	1.94339e10	0.127271
$109$	−4.75790e9	−0.0296189	−0.0148095	−	0.999890i	$-0.504714\pi$
$109$	−4.75790e9	−0.0296189	−0.0148095	+	0.999890i	$0.504714\pi$
$110$	−1.72524e11	−1.02139
$111$	1.16660e11	0.657122
$112$	−2.00189e10	−0.107335
$113$	8.06303e10	0.411687	0.205843	−	0.978585i	$-0.434006\pi$
$113$	8.06303e10	0.411687	0.205843	+	0.978585i	$0.434006\pi$
$114$	−1.10458e11	−0.537304
$115$	−3.86936e11	−1.79391
$116$	−2.82282e11	−1.24786
$117$	−2.13387e9	−0.00899800
$118$	−1.88287e10	−0.0757652
$119$	−1.13033e11	−0.434208
$120$	−2.71905e11	−0.997519
$121$	−1.01155e10	−0.0354541
$122$	−3.09500e11	−1.03677
$123$	6.95458e10	0.222737
$124$	2.96134e11	0.907127
$125$	7.27710e11	2.13282
$126$	7.52334e10	0.211044
$127$	7.84337e10	0.210660	0.105330	−	0.994437i	$-0.466410\pi$
$127$	7.84337e10	0.210660	0.105330	+	0.994437i	$0.466410\pi$
$128$	2.85631e11	0.734768
$129$	−3.28981e11	−0.810825
$130$	1.18846e10	0.0280735
$131$	−3.75789e11	−0.851043	−0.425521	−	0.904948i	$-0.639909\pi$
$131$	−3.75789e11	−0.851043	−0.425521	+	0.904948i	$0.639909\pi$
$132$	1.72651e11	0.374983
$133$	8.34963e11	1.73974
$134$	3.44783e11	0.689397
$135$	−1.79179e11	−0.343915
$136$	2.09369e11	0.385877
$137$	−5.28340e11	−0.935299	−0.467649	−	0.883914i	$-0.654899\pi$
$137$	−5.28340e11	−0.935299	−0.467649	+	0.883914i	$0.654899\pi$
$138$	−1.98307e11	−0.337290
$139$	−6.91093e11	−1.12968	−0.564840	−	0.825201i	$-0.691062\pi$
$139$	−6.91093e11	−1.12968	−0.564840	+	0.825201i	$0.691062\pi$
$140$	8.18175e11	1.28571
$141$	7.01620e11	1.06022
$142$	−1.17594e11	−0.170922
$143$	−1.89573e10	−0.0265112
$144$	2.44351e10	0.0328868
$145$	2.60262e12	3.37199
$146$	−5.70570e11	−0.711817
$147$	−8.82072e10	−0.105989
$148$	6.50215e11	0.752692
$149$	3.32192e11	0.370565	0.185283	−	0.982685i	$-0.440680\pi$
$149$	3.32192e11	0.370565	0.185283	+	0.982685i	$0.440680\pi$
$150$	6.85447e11	0.737007
$151$	−6.81029e11	−0.705980	−0.352990	−	0.935627i	$-0.614835\pi$
$151$	−6.81029e11	−0.705980	−0.352990	+	0.935627i	$0.614835\pi$
$152$	−1.54658e12	−1.54609
$153$	1.37969e11	0.133039
$154$	6.68374e11	0.621807
$155$	−2.73033e12	−2.45127
$156$	−1.18933e10	−0.0103066
$157$	−1.09900e12	−0.919497	−0.459749	−	0.888049i	$-0.652061\pi$
$157$	−1.09900e12	−0.919497	−0.459749	+	0.888049i	$0.652061\pi$
$158$	−9.68940e11	−0.782858
$159$	−7.25705e11	−0.566339
$160$	−2.42771e12	−1.83036
$161$	1.49902e12	1.09211
$162$	−9.18303e10	−0.0646626
$163$	5.96889e11	0.406314	0.203157	−	0.979146i	$-0.434880\pi$
$163$	5.96889e11	0.406314	0.203157	+	0.979146i	$0.434880\pi$
$164$	3.87619e11	0.255132
$165$	−1.59183e12	−1.01329
$166$	−4.85717e11	−0.299081
$167$	1.69444e11	0.100945	0.0504725	−	0.998725i	$-0.483927\pi$
$167$	1.69444e11	0.100945	0.0504725	+	0.998725i	$0.483927\pi$
$168$	1.05339e12	0.607276
$169$	−1.79085e12	−0.999271
$170$	−7.68419e11	−0.415077
$171$	−1.01916e12	−0.533045
$172$	−1.83360e12	−0.928749
$173$	−2.02888e12	−0.995412	−0.497706	−	0.867346i	$-0.665824\pi$
$173$	−2.02888e12	−0.995412	−0.497706	+	0.867346i	$0.665824\pi$
$174$	1.33386e12	0.634000
$175$	−5.18136e12	−2.38635
$176$	2.17082e11	0.0968955
$177$	−1.73727e11	−0.0751646
$178$	5.88425e11	0.246820
$179$	1.76691e12	0.718660	0.359330	−	0.933211i	$-0.383005\pi$
$179$	1.76691e12	0.718660	0.359330	+	0.933211i	$0.383005\pi$
$180$	−9.98668e11	−0.393933
$181$	−1.48789e12	−0.569295	−0.284647	−	0.958632i	$-0.591877\pi$
$181$	−1.48789e12	−0.569295	−0.284647	+	0.958632i	$0.591877\pi$
$182$	−4.60420e10	−0.0170908
$183$	−2.85566e12	−1.02855
$184$	−2.77661e12	−0.970547
$185$	−5.99493e12	−2.03395
$186$	−1.39931e12	−0.460885
$187$	1.22572e12	0.391978
$188$	3.91054e12	1.21442
$189$	6.94155e11	0.209371
$190$	5.67621e12	1.66308
$191$	2.18296e10	0.00621386	0.00310693	−	0.999995i	$-0.499011\pi$
$191$	2.18296e10	0.00621386	0.00310693	+	0.999995i	$0.499011\pi$
$192$	−1.03828e12	−0.287181
$193$	−6.17050e12	−1.65865	−0.829325	−	0.558766i	$-0.811275\pi$
$193$	−6.17050e12	−1.65865	−0.829325	+	0.558766i	$0.811275\pi$
$194$	−7.63479e11	−0.199475
$195$	1.09655e11	0.0278509
$196$	−4.91630e11	−0.121403
$197$	−3.05266e12	−0.733018	−0.366509	−	0.930414i	$-0.619447\pi$
$197$	−3.05266e12	−0.733018	−0.366509	+	0.930414i	$0.619447\pi$
$198$	−8.15820e11	−0.190518
$199$	−2.46535e12	−0.559998	−0.279999	−	0.960000i	$-0.590334\pi$
$199$	−2.46535e12	−0.559998	−0.279999	+	0.960000i	$0.590334\pi$
$200$	9.59732e12	2.12073
$201$	3.18120e12	0.683932
$202$	2.40455e11	0.0503038
$203$	−1.00828e13	−2.05283
$204$	7.68981e11	0.152388
$205$	−3.57382e12	−0.689424
$206$	1.48065e12	0.278088
$207$	−1.82972e12	−0.334616
$208$	−1.49540e10	−0.00266324
$209$	−9.05421e12	−1.57053
$210$	−3.86610e12	−0.653231
$211$	4.65591e12	0.766392	0.383196	−	0.923667i	$-0.374823\pi$
$211$	4.65591e12	0.766392	0.383196	+	0.923667i	$0.374823\pi$
$212$	−4.04478e12	−0.648705
$213$	−1.08500e12	−0.169567
$214$	4.64019e12	0.706741
$215$	1.69057e13	2.50969
$216$	−1.28577e12	−0.186066
$217$	1.05775e13	1.49230
$218$	1.25307e11	0.0172371
$219$	−5.26447e12	−0.706174
$220$	−8.87217e12	−1.16066
$221$	−8.44354e10	−0.0107738
$222$	−3.07244e12	−0.382421
$223$	−1.14935e13	−1.39565	−0.697823	−	0.716271i	$-0.745848\pi$
$223$	−1.14935e13	−1.39565	−0.697823	+	0.716271i	$0.745848\pi$
$224$	9.40515e12	1.11430
$225$	6.32440e12	0.731165
$226$	−2.12353e12	−0.239587
$227$	1.45997e13	1.60769	0.803844	−	0.594840i	$-0.202785\pi$
$227$	1.45997e13	1.60769	0.803844	+	0.594840i	$0.202785\pi$
$228$	−5.68037e12	−0.610569
$229$	6.11729e12	0.641895	0.320947	−	0.947097i	$-0.395999\pi$
$229$	6.11729e12	0.641895	0.320947	+	0.947097i	$0.395999\pi$
$230$	1.01906e13	1.04399
$231$	6.16687e12	0.616878
$232$	1.86761e13	1.82433
$233$	−1.11247e13	−1.06128	−0.530641	−	0.847597i	$-0.678049\pi$
$233$	−1.11247e13	−1.06128	−0.530641	+	0.847597i	$0.678049\pi$
$234$	5.61991e10	0.00523651
$235$	−3.60549e13	−3.28164
$236$	−9.68279e11	−0.0860963
$237$	−8.94010e12	−0.776652
$238$	2.97692e12	0.252694
$239$	2.31592e12	0.192104	0.0960518	−	0.995376i	$-0.469379\pi$
$239$	2.31592e12	0.192104	0.0960518	+	0.995376i	$0.469379\pi$
$240$	−1.25567e12	−0.101792
$241$	−1.59364e13	−1.26269	−0.631343	−	0.775504i	$-0.717496\pi$
$241$	−1.59364e13	−1.26269	−0.631343	+	0.775504i	$0.717496\pi$
$242$	2.66408e11	0.0206330
$243$	−8.47289e11	−0.0641500
$244$	−1.59162e13	−1.17814
$245$	4.53279e12	0.328059
$246$	−1.83161e12	−0.129625
$247$	6.23714e11	0.0431670
$248$	−1.95925e13	−1.32619
$249$	−4.48155e12	−0.296710
$250$	−1.91655e13	−1.24122
$251$	−3.67863e12	−0.233067	−0.116533	−	0.993187i	$-0.537178\pi$
$251$	−3.67863e12	−0.233067	−0.116533	+	0.993187i	$0.537178\pi$
$252$	3.86893e12	0.239821
$253$	−1.62552e13	−0.985892
$254$	−2.06568e12	−0.122596
$255$	−7.08995e12	−0.411787
$256$	−1.62731e13	−0.925020
$257$	−1.35585e13	−0.754364	−0.377182	−	0.926139i	$-0.623107\pi$
$257$	−1.35585e13	−0.754364	−0.377182	+	0.926139i	$0.623107\pi$
$258$	8.66425e12	0.471871
$259$	2.32249e13	1.23824
$260$	6.11173e11	0.0319015
$261$	1.23071e13	0.628974
$262$	9.89702e12	0.495276
$263$	3.83441e13	1.87907	0.939533	−	0.342459i	$-0.111260\pi$
$263$	3.83441e13	1.87907	0.939533	+	0.342459i	$0.111260\pi$
$264$	−1.14228e13	−0.548213
$265$	3.72926e13	1.75295
$266$	−2.19901e13	−1.01246
$267$	5.42921e12	0.244864
$268$	1.77307e13	0.783401
$269$	2.94324e13	1.27405	0.637027	−	0.770841i	$-0.280164\pi$
$269$	2.94324e13	1.27405	0.637027	+	0.770841i	$0.280164\pi$
$270$	4.71898e12	0.200146
$271$	1.59914e13	0.664591	0.332295	−	0.943175i	$-0.392177\pi$
$271$	1.59914e13	0.664591	0.332295	+	0.943175i	$0.392177\pi$
$272$	9.66877e11	0.0393770
$273$	−4.24815e11	−0.0169553
$274$	1.39147e13	0.544310
$275$	5.61859e13	2.15426
$276$	−1.01981e13	−0.383282
$277$	4.56572e13	1.68217	0.841087	−	0.540900i	$-0.181916\pi$
$277$	4.56572e13	1.68217	0.841087	+	0.540900i	$0.181916\pi$
$278$	1.82011e13	0.657432
$279$	−1.29110e13	−0.457232
$280$	−5.41314e13	−1.87966
$281$	−2.99031e13	−1.01820	−0.509098	−	0.860708i	$-0.670021\pi$
$281$	−2.99031e13	−1.01820	−0.509098	+	0.860708i	$0.670021\pi$
$282$	−1.84783e13	−0.617011
$283$	−3.77834e13	−1.23730	−0.618651	−	0.785666i	$-0.712321\pi$
$283$	−3.77834e13	−1.23730	−0.618651	+	0.785666i	$0.712321\pi$
$284$	−6.04734e12	−0.194229
$285$	5.23726e13	1.64990
$286$	4.99273e11	0.0154285
$287$	1.38453e13	0.419713
$288$	−1.14800e13	−0.341415
$289$	−2.88126e13	−0.840706
$290$	−6.85443e13	−1.96238
$291$	−7.04438e12	−0.197893
$292$	−2.93419e13	−0.808878
$293$	−2.20547e13	−0.596664	−0.298332	−	0.954462i	$-0.596430\pi$
$293$	−2.20547e13	−0.596664	−0.298332	+	0.954462i	$0.596430\pi$
$294$	2.32308e12	0.0616815
$295$	8.92746e12	0.232652
$296$	−4.30190e13	−1.10041
$297$	−7.52731e12	−0.189008
$298$	−8.74883e12	−0.215655
$299$	1.11976e12	0.0270979
$300$	3.52495e13	0.837503
$301$	−6.54940e13	−1.52787
$302$	1.79360e13	0.410855
$303$	2.21860e12	0.0499050
$304$	−7.14220e12	−0.157771
$305$	1.46746e14	3.18360
$306$	−3.63364e12	−0.0774238
$307$	−4.50168e13	−0.942136	−0.471068	−	0.882097i	$-0.656131\pi$
$307$	−4.50168e13	−0.942136	−0.471068	+	0.882097i	$0.656131\pi$
$308$	3.43716e13	0.706595
$309$	1.36615e13	0.275884
$310$	7.19078e13	1.42655
$311$	2.82077e12	0.0549776	0.0274888	−	0.999622i	$-0.491249\pi$
$311$	2.82077e12	0.0549776	0.0274888	+	0.999622i	$0.491249\pi$
$312$	7.86875e11	0.0150680
$313$	−1.18762e12	−0.0223451	−0.0111726	−	0.999938i	$-0.503556\pi$
$313$	−1.18762e12	−0.0223451	−0.0111726	+	0.999938i	$0.503556\pi$
$314$	2.89441e13	0.535114
$315$	−3.56712e13	−0.648052
$316$	−4.98284e13	−0.889606
$317$	−5.05554e13	−0.887037	−0.443518	−	0.896265i	$-0.646270\pi$
$317$	−5.05554e13	−0.887037	−0.443518	+	0.896265i	$0.646270\pi$
$318$	1.91127e13	0.329588
$319$	1.09336e14	1.85317
$320$	5.33549e13	0.888893
$321$	4.28136e13	0.701138
$322$	−3.94793e13	−0.635568
$323$	−4.03272e13	−0.638241
$324$	−4.72243e12	−0.0734798
$325$	−3.87046e12	−0.0592112
$326$	−1.57201e13	−0.236460
$327$	1.15617e12	0.0171005
$328$	−2.56453e13	−0.372994
$329$	1.39680e14	1.99782
$330$	4.19234e13	0.589698
$331$	8.19340e13	1.13347	0.566735	−	0.823900i	$-0.308206\pi$
$331$	8.19340e13	1.13347	0.566735	+	0.823900i	$0.308206\pi$
$332$	−2.49783e13	−0.339862
$333$	−2.83484e13	−0.379390
$334$	−4.46258e12	−0.0587463
$335$	−1.63476e14	−2.11693
$336$	4.86459e12	0.0619698
$337$	1.18757e14	1.48832	0.744158	−	0.668003i	$-0.232851\pi$
$337$	1.18757e14	1.48832	0.744158	+	0.668003i	$0.232851\pi$
$338$	4.71651e13	0.581540
$339$	−1.95932e13	−0.237687
$340$	−3.95164e13	−0.471676
$341$	−1.14701e14	−1.34716
$342$	2.68413e13	0.310213
$343$	7.80964e13	0.888205
$344$	1.21313e14	1.35780
$345$	9.40255e13	1.03572
$346$	5.34339e13	0.579293
$347$	3.64520e13	0.388964	0.194482	−	0.980906i	$-0.437697\pi$
$347$	3.64520e13	0.388964	0.194482	+	0.980906i	$0.437697\pi$
$348$	6.85945e13	0.720450
$349$	−1.03842e14	−1.07358	−0.536789	−	0.843717i	$-0.680363\pi$
$349$	−1.03842e14	−1.07358	−0.536789	+	0.843717i	$0.680363\pi$
$350$	1.36460e14	1.38877
$351$	5.18531e11	0.00519500
$352$	−1.01988e14	−1.00592
$353$	−1.35379e14	−1.31459	−0.657297	−	0.753632i	$-0.728300\pi$
$353$	−1.35379e14	−1.31459	−0.657297	+	0.753632i	$0.728300\pi$
$354$	4.57538e12	0.0437431
$355$	5.57560e13	0.524851
$356$	3.02601e13	0.280476
$357$	2.74671e13	0.250690
$358$	−4.65346e13	−0.418234
$359$	−1.06092e14	−0.938998	−0.469499	−	0.882933i	$-0.655565\pi$
$359$	−1.06092e14	−0.938998	−0.469499	+	0.882933i	$0.655565\pi$
$360$	6.60730e13	0.575918
$361$	1.81402e14	1.55723
$362$	3.91859e13	0.331309
$363$	2.45806e12	0.0204694
$364$	−2.36774e12	−0.0194212
$365$	2.70531e14	2.18578
$366$	7.52085e13	0.598578
$367$	1.60911e14	1.26160	0.630801	−	0.775945i	$-0.282727\pi$
$367$	1.60911e14	1.26160	0.630801	+	0.775945i	$0.282727\pi$
$368$	−1.28225e13	−0.0990399
$369$	−1.68996e13	−0.128597
$370$	1.57887e14	1.18368
$371$	−1.44475e14	−1.06717
$372$	−7.19604e13	−0.523730
$373$	−4.09228e13	−0.293472	−0.146736	−	0.989176i	$-0.546877\pi$
$373$	−4.09228e13	−0.293472	−0.146736	+	0.989176i	$0.546877\pi$
$374$	−3.22813e13	−0.228117
$375$	−1.76834e14	−1.23138
$376$	−2.58726e14	−1.77544
$377$	−7.53179e12	−0.0509356
$378$	−1.82817e13	−0.121846
$379$	1.53430e13	0.100785	0.0503924	−	0.998729i	$-0.483953\pi$
$379$	1.53430e13	0.100785	0.0503924	+	0.998729i	$0.483953\pi$
$380$	2.91903e14	1.88985
$381$	−1.90594e13	−0.121625
$382$	−5.74918e11	−0.00361624
$383$	−1.76593e14	−1.09492	−0.547458	−	0.836833i	$-0.684404\pi$
$383$	−1.76593e14	−1.09492	−0.547458	+	0.836833i	$0.684404\pi$
$384$	−6.94083e13	−0.424218
$385$	−3.16903e14	−1.90938
$386$	1.62510e14	0.965274
$387$	7.99423e13	0.468130
$388$	−3.92624e13	−0.226674
$389$	−3.21024e14	−1.82732	−0.913660	−	0.406480i	$-0.866756\pi$
$389$	−3.21024e14	−1.82732	−0.913660	+	0.406480i	$0.866756\pi$
$390$	−2.88796e12	−0.0162082
$391$	−7.24003e13	−0.400653
$392$	3.25268e13	0.177488
$393$	9.13166e13	0.491350
$394$	8.03970e13	0.426590
$395$	4.59414e14	2.40392
$396$	−4.19541e13	−0.216496
$397$	−3.26179e14	−1.66000	−0.830001	−	0.557762i	$-0.811660\pi$
$397$	−3.26179e14	−1.66000	−0.830001	+	0.557762i	$0.811660\pi$
$398$	6.49290e13	0.325898
$399$	−2.02896e14	−1.00444
$400$	4.43209e13	0.216411
$401$	−1.49182e14	−0.718494	−0.359247	−	0.933243i	$-0.616966\pi$
$401$	−1.49182e14	−0.718494	−0.359247	+	0.933243i	$0.616966\pi$
$402$	−8.37823e13	−0.398024
$403$	7.90138e12	0.0370276
$404$	1.23655e13	0.0571631
$405$	4.35405e13	0.198559
$406$	2.65547e14	1.19467
$407$	−2.51847e14	−1.11781
$408$	−5.08767e13	−0.222786
$409$	−1.06632e14	−0.460689	−0.230344	−	0.973109i	$-0.573985\pi$
$409$	−1.06632e14	−0.460689	−0.230344	+	0.973109i	$0.573985\pi$
$410$	9.41226e13	0.401220
$411$	1.28387e14	0.539995
$412$	7.61434e13	0.316008
$413$	−3.45858e13	−0.141636
$414$	4.81886e13	0.194734
$415$	2.30298e14	0.918387
$416$	7.02561e12	0.0276484
$417$	1.67936e14	0.652221
$418$	2.38458e14	0.913991
$419$	−2.41998e14	−0.915451	−0.457726	−	0.889093i	$-0.651336\pi$
$419$	−2.41998e14	−0.915451	−0.457726	+	0.889093i	$0.651336\pi$
$420$	−1.98817e14	−0.742303
$421$	3.95612e14	1.45787	0.728934	−	0.684584i	$-0.240016\pi$
$421$	3.95612e14	1.45787	0.728934	+	0.684584i	$0.240016\pi$
$422$	−1.22621e14	−0.446012
$423$	−1.70494e14	−0.612119
$424$	2.67607e14	0.948387
$425$	2.50251e14	0.875460
$426$	2.85753e13	0.0986820
$427$	−5.68509e14	−1.93813
$428$	2.38625e14	0.803110
$429$	4.60663e12	0.0153062
$430$	−4.45239e14	−1.46055
$431$	−4.83344e14	−1.56542	−0.782711	−	0.622385i	$-0.786164\pi$
$431$	−4.83344e14	−1.56542	−0.782711	+	0.622385i	$0.786164\pi$
$432$	−5.93774e12	−0.0189872
$433$	−3.08341e14	−0.973526	−0.486763	−	0.873534i	$-0.661822\pi$
$433$	−3.08341e14	−0.973526	−0.486763	+	0.873534i	$0.661822\pi$
$434$	−2.78577e14	−0.868464
$435$	−6.32437e14	−1.94682
$436$	6.44400e12	0.0195875
$437$	5.34811e14	1.60529
$438$	1.38649e14	0.410968
$439$	5.22632e14	1.52982	0.764912	−	0.644135i	$-0.222782\pi$
$439$	5.22632e14	1.52982	0.764912	+	0.644135i	$0.222782\pi$
$440$	5.86993e14	1.69685
$441$	2.14344e13	0.0611925
$442$	2.22375e12	0.00626993
$443$	5.54397e14	1.54383	0.771916	−	0.635724i	$-0.219298\pi$
$443$	5.54397e14	1.54383	0.771916	+	0.635724i	$0.219298\pi$
$444$	−1.58002e14	−0.434567
$445$	−2.78996e14	−0.757911
$446$	3.02700e14	0.812215
$447$	−8.07226e13	−0.213946
$448$	−2.06702e14	−0.541146
$449$	−2.36672e14	−0.612057	−0.306028	−	0.952022i	$-0.599000\pi$
$449$	−2.36672e14	−0.612057	−0.306028	+	0.952022i	$0.599000\pi$
$450$	−1.66564e14	−0.425511
$451$	−1.50136e14	−0.378892
$452$	−1.09204e14	−0.272256
$453$	1.65490e14	0.407598
$454$	−3.84507e14	−0.935616
$455$	2.18304e13	0.0524806
$456$	3.75820e14	0.892633
$457$	−2.39897e14	−0.562970	−0.281485	−	0.959566i	$-0.590827\pi$
$457$	−2.39897e14	−0.562970	−0.281485	+	0.959566i	$0.590827\pi$
$458$	−1.61109e14	−0.373559
$459$	−3.35265e13	−0.0768100
$460$	5.24058e14	1.18635
$461$	6.67770e14	1.49373	0.746864	−	0.664977i	$-0.231559\pi$
$461$	6.67770e14	1.49373	0.746864	+	0.664977i	$0.231559\pi$
$462$	−1.62415e14	−0.359000
$463$	−1.98612e14	−0.433821	−0.216910	−	0.976192i	$-0.569598\pi$
$463$	−1.98612e14	−0.433821	−0.216910	+	0.976192i	$0.569598\pi$
$464$	8.62472e13	0.186164
$465$	6.63470e14	1.41524
$466$	2.92988e14	0.617628
$467$	−8.55770e14	−1.78285	−0.891424	−	0.453170i	$-0.850293\pi$
$467$	−8.55770e14	−1.78285	−0.891424	+	0.453170i	$0.850293\pi$
$468$	2.89007e12	0.00595054
$469$	6.33319e14	1.28876
$470$	9.49565e14	1.90979
$471$	2.67058e14	0.530872
$472$	6.40625e13	0.125870
$473$	7.10208e14	1.37927
$474$	2.35452e14	0.451983
$475$	−1.84857e15	−3.50769
$476$	1.53090e14	0.287150
$477$	1.76346e14	0.326976
$478$	−6.09937e13	−0.111797
$479$	−1.35120e14	−0.244835	−0.122417	−	0.992479i	$-0.539065\pi$
$479$	−1.35120e14	−0.244835	−0.122417	+	0.992479i	$0.539065\pi$
$480$	5.89933e14	1.05676
$481$	1.73489e13	0.0307237
$482$	4.19711e14	0.734837
$483$	−3.64263e14	−0.630530
$484$	1.37002e13	0.0234464
$485$	3.61997e14	0.612527
$486$	2.23148e13	0.0373330
$487$	−7.97829e14	−1.31978	−0.659889	−	0.751363i	$-0.729397\pi$
$487$	−7.97829e14	−1.31978	−0.659889	+	0.751363i	$0.729397\pi$
$488$	1.05304e15	1.72240
$489$	−1.45044e14	−0.234585
$490$	−1.19379e14	−0.190919
$491$	−1.65399e14	−0.261568	−0.130784	−	0.991411i	$-0.541750\pi$
$491$	−1.65399e14	−0.261568	−0.130784	+	0.991411i	$0.541750\pi$
$492$	−9.41915e13	−0.147300
$493$	4.86981e14	0.753102
$494$	−1.64265e13	−0.0251216
$495$	3.86814e14	0.585023
$496$	−9.04793e13	−0.135332
$497$	−2.16004e14	−0.319522
$498$	1.18029e14	0.172674
$499$	1.35908e15	1.96649	0.983246	−	0.182285i	$-0.0583492\pi$
$499$	1.35908e15	1.96649	0.983246	+	0.182285i	$0.0583492\pi$
$500$	−9.85596e14	−1.41047
$501$	−4.11748e13	−0.0582806
$502$	9.68827e13	0.135636
$503$	−1.17264e14	−0.162383	−0.0811913	−	0.996699i	$-0.525872\pi$
$503$	−1.17264e14	−0.162383	−0.0811913	+	0.996699i	$0.525872\pi$
$504$	−2.55973e14	−0.350611
$505$	−1.14009e14	−0.154468
$506$	4.28108e14	0.573754
$507$	4.35178e14	0.576930
$508$	−1.06229e14	−0.139313
$509$	−6.28883e12	−0.00815872	−0.00407936	−	0.999992i	$-0.501299\pi$
$509$	−6.28883e12	−0.00815872	−0.00407936	+	0.999992i	$0.501299\pi$
$510$	1.86726e14	0.239645
$511$	−1.04806e15	−1.33067
$512$	−1.56392e14	−0.196440
$513$	2.47656e14	0.307753
$514$	3.57087e14	0.439012
$515$	−7.02037e14	−0.853926
$516$	4.45565e14	0.536213
$517$	−1.51467e15	−1.80351
$518$	−6.11667e14	−0.720611
$519$	4.93018e14	0.574701
$520$	−4.04359e13	−0.0466390
$521$	−5.25502e14	−0.599746	−0.299873	−	0.953979i	$-0.596944\pi$
$521$	−5.25502e14	−0.599746	−0.299873	+	0.953979i	$0.596944\pi$
$522$	−3.24128e14	−0.366040
$523$	−1.36794e15	−1.52865	−0.764326	−	0.644830i	$-0.776928\pi$
$523$	−1.36794e15	−1.52865	−0.764326	+	0.644830i	$0.776928\pi$
$524$	5.08960e14	0.562810
$525$	1.25907e15	1.37776
$526$	−1.00986e15	−1.09355
$527$	−5.10877e14	−0.547467
$528$	−5.27509e13	−0.0559427
$529$	7.34736e12	0.00771126
$530$	−9.82162e14	−1.02015
$531$	4.22156e13	0.0433963
$532$	−1.13086e15	−1.15052
$533$	1.03424e13	0.0104141
$534$	−1.42987e14	−0.142502
$535$	−2.20010e15	−2.17019
$536$	−1.17308e15	−1.14531
$537$	−4.29360e14	−0.414918
$538$	−7.75151e14	−0.741453
$539$	1.90423e14	0.180294
$540$	2.42676e14	0.227437
$541$	5.35959e14	0.497217	0.248609	−	0.968604i	$-0.420027\pi$
$541$	5.35959e14	0.497217	0.248609	+	0.968604i	$0.420027\pi$
$542$	−4.21159e14	−0.386768
$543$	3.61556e14	0.328683
$544$	−4.54252e14	−0.408793
$545$	−5.94132e13	−0.0529301
$546$	1.11882e13	0.00986736
$547$	1.04435e15	0.911836	0.455918	−	0.890022i	$-0.349311\pi$
$547$	1.04435e15	0.911836	0.455918	+	0.890022i	$0.349311\pi$
$548$	7.15573e14	0.618530
$549$	6.93924e14	0.593833
$550$	−1.47975e15	−1.25370
$551$	−3.59726e15	−3.01744
$552$	6.74716e14	0.560346
$553$	−1.77981e15	−1.46348
$554$	−1.20246e15	−0.978964
$555$	1.45677e15	1.17430
$556$	9.36003e14	0.747078
$557$	−1.96163e15	−1.55029	−0.775145	−	0.631783i	$-0.782323\pi$
$557$	−1.96163e15	−1.55029	−0.775145	+	0.631783i	$0.782323\pi$
$558$	3.40033e14	0.266092
$559$	−4.89238e13	−0.0379101
$560$	−2.49981e14	−0.191811
$561$	−2.97849e14	−0.226308
$562$	7.87548e14	0.592553
$563$	−1.43165e15	−1.06670	−0.533348	−	0.845896i	$-0.679066\pi$
$563$	−1.43165e15	−1.06670	−0.533348	+	0.845896i	$0.679066\pi$
$564$	−9.50260e14	−0.701144
$565$	1.00685e15	0.735699
$566$	9.95089e14	0.720065
$567$	−1.68680e14	−0.120880
$568$	4.00099e14	0.283956
$569$	−1.48396e15	−1.04305	−0.521524	−	0.853237i	$-0.674636\pi$
$569$	−1.48396e15	−1.04305	−0.521524	+	0.853237i	$0.674636\pi$
$570$	−1.37932e15	−0.960181
$571$	−5.40035e12	−0.00372326	−0.00186163	−	0.999998i	$-0.500593\pi$
$571$	−5.40035e12	−0.00372326	−0.00186163	+	0.999998i	$0.500593\pi$
$572$	2.56754e13	0.0175323
$573$	−5.30458e12	−0.00358757
$574$	−3.64639e14	−0.244257
$575$	−3.31877e15	−2.20194
$576$	2.52301e14	0.165804
$577$	2.11173e15	1.37458	0.687291	−	0.726382i	$-0.258800\pi$
$577$	2.11173e15	1.37458	0.687291	+	0.726382i	$0.258800\pi$
$578$	7.58827e14	0.489260
$579$	1.49943e15	0.957622
$580$	−3.52494e15	−2.22996
$581$	−8.92195e14	−0.559102
$582$	1.85525e14	0.115167
$583$	1.56666e15	0.963381
$584$	1.94130e15	1.18255
$585$	−2.66463e13	−0.0160797
$586$	5.80848e14	0.347237
$587$	−2.44871e15	−1.45020	−0.725099	−	0.688644i	$-0.758206\pi$
$587$	−2.44871e15	−1.45020	−0.725099	+	0.688644i	$0.758206\pi$
$588$	1.19466e14	0.0700922
$589$	3.77378e15	2.19352
$590$	−2.35120e14	−0.135395
$591$	7.41797e14	0.423208
$592$	−1.98664e14	−0.112292
$593$	2.23333e15	1.25070	0.625350	−	0.780345i	$-0.284956\pi$
$593$	2.23333e15	1.25070	0.625350	+	0.780345i	$0.284956\pi$
$594$	1.98244e14	0.109996
$595$	−1.41148e15	−0.775946
$596$	−4.49914e14	−0.245061
$597$	5.99079e14	0.323315
$598$	−2.94909e13	−0.0157700
$599$	8.49048e14	0.449868	0.224934	−	0.974374i	$-0.427783\pi$
$599$	8.49048e14	0.449868	0.224934	+	0.974374i	$0.427783\pi$
$600$	−2.33215e15	−1.22440
$601$	−1.56134e15	−0.812246	−0.406123	−	0.913818i	$-0.633120\pi$
$601$	−1.56134e15	−0.812246	−0.406123	+	0.913818i	$0.633120\pi$
$602$	1.72489e15	0.889164
$603$	−7.73033e14	−0.394869
$604$	9.22372e14	0.466878
$605$	−1.26315e14	−0.0633577
$606$	−5.84305e13	−0.0290429
$607$	1.26588e15	0.623526	0.311763	−	0.950160i	$-0.399080\pi$
$607$	1.26588e15	0.623526	0.311763	+	0.950160i	$0.399080\pi$
$608$	3.35550e15	1.63790
$609$	2.45012e15	1.18520
$610$	−3.86481e15	−1.85274
$611$	1.04340e14	0.0495707
$612$	−1.86862e14	−0.0879811
$613$	−3.11063e15	−1.45149	−0.725747	−	0.687961i	$-0.758506\pi$
$613$	−3.11063e15	−1.45149	−0.725747	+	0.687961i	$0.758506\pi$
$614$	1.18559e15	0.548289
$615$	8.68439e14	0.398039
$616$	−2.27406e15	−1.03302
$617$	1.28911e15	0.580394	0.290197	−	0.956967i	$-0.406279\pi$
$617$	1.28911e15	0.580394	0.290197	+	0.956967i	$0.406279\pi$
$618$	−3.59798e14	−0.160554
$619$	−4.72039e14	−0.208775	−0.104388	−	0.994537i	$-0.533288\pi$
$619$	−4.72039e14	−0.208775	−0.104388	+	0.994537i	$0.533288\pi$
$620$	3.69790e15	1.62107
$621$	4.44621e14	0.193191
$622$	−7.42897e13	−0.0319950
$623$	1.08086e15	0.461406
$624$	3.63383e12	0.00153762
$625$	3.85743e15	1.61792
$626$	3.12779e13	0.0130040
$627$	2.20017e15	0.906746
$628$	1.48847e15	0.608080
$629$	−1.12172e15	−0.454262
$630$	9.39462e14	0.377143
$631$	−2.79261e15	−1.11134	−0.555672	−	0.831401i	$-0.687539\pi$
$631$	−2.79261e15	−1.11134	−0.555672	+	0.831401i	$0.687539\pi$
$632$	3.29670e15	1.30058
$633$	−1.13139e15	−0.442476
$634$	1.33146e15	0.516223
$635$	9.79424e14	0.376457
$636$	9.82881e14	0.374530
$637$	−1.31176e13	−0.00495549
$638$	−2.87955e15	−1.07848
$639$	2.63655e14	0.0978998
$640$	3.56675e15	1.31306
$641$	−5.70990e13	−0.0208406	−0.0104203	−	0.999946i	$-0.503317\pi$
$641$	−5.70990e13	−0.0208406	−0.0104203	+	0.999946i	$0.503317\pi$
$642$	−1.12757e15	−0.408037
$643$	−3.74924e14	−0.134519	−0.0672593	−	0.997736i	$-0.521425\pi$
$643$	−3.74924e14	−0.134519	−0.0672593	+	0.997736i	$0.521425\pi$
$644$	−2.03025e15	−0.722232
$645$	−4.10808e15	−1.44897
$646$	1.06209e15	0.371433
$647$	−6.23178e14	−0.216092	−0.108046	−	0.994146i	$-0.534459\pi$
$647$	−6.23178e14	−0.216092	−0.108046	+	0.994146i	$0.534459\pi$
$648$	3.12442e14	0.107425
$649$	3.75043e14	0.127860
$650$	1.01935e14	0.0344588
$651$	−2.57034e15	−0.861580
$652$	−8.08414e14	−0.268703
$653$	5.00096e15	1.64828	0.824140	−	0.566387i	$-0.191659\pi$
$653$	5.00096e15	1.64828	0.824140	+	0.566387i	$0.191659\pi$
$654$	−3.04496e13	−0.00995187
$655$	−4.69258e15	−1.52084
$656$	−1.18431e14	−0.0380624
$657$	1.27927e15	0.407710
$658$	−3.67870e15	−1.16266
$659$	1.57034e15	0.492181	0.246091	−	0.969247i	$-0.420854\pi$
$659$	1.57034e15	0.492181	0.246091	+	0.969247i	$0.420854\pi$
$660$	2.15594e15	0.670107
$661$	−1.30021e15	−0.400780	−0.200390	−	0.979716i	$-0.564221\pi$
$661$	−1.30021e15	−0.400780	−0.200390	+	0.979716i	$0.564221\pi$
$662$	−2.15787e15	−0.659639
$663$	2.05178e13	0.00622023
$664$	1.65259e15	0.496868
$665$	1.04264e16	3.10897
$666$	7.46603e14	0.220791
$667$	−6.45824e15	−1.89418
$668$	−2.29491e14	−0.0667568
$669$	2.79292e15	0.805776
$670$	4.30541e15	1.23198
$671$	6.16483e15	1.74963
$672$	−2.28545e15	−0.643341
$673$	−1.61815e15	−0.451790	−0.225895	−	0.974152i	$-0.572531\pi$
$673$	−1.61815e15	−0.451790	−0.225895	+	0.974152i	$0.572531\pi$
$674$	−3.12767e15	−0.866146
$675$	−1.53683e15	−0.422138
$676$	2.42550e15	0.660836
$677$	−2.27778e15	−0.615564	−0.307782	−	0.951457i	$-0.599587\pi$
$677$	−2.27778e15	−0.615564	−0.307782	+	0.951457i	$0.599587\pi$
$678$	5.16019e14	0.138325
$679$	−1.40241e15	−0.372898
$680$	2.61445e15	0.689575
$681$	−3.54773e15	−0.928199
$682$	3.02085e15	0.783998
$683$	−3.00858e14	−0.0774548	−0.0387274	−	0.999250i	$-0.512330\pi$
$683$	−3.00858e14	−0.0774548	−0.0387274	+	0.999250i	$0.512330\pi$
$684$	1.38033e15	0.352512
$685$	−6.59753e15	−1.67141
$686$	−2.05680e15	−0.516903
$687$	−1.48650e15	−0.370598
$688$	5.60230e14	0.138557
$689$	−1.07922e14	−0.0264791
$690$	−2.47632e15	−0.602749
$691$	−4.82000e15	−1.16391	−0.581953	−	0.813223i	$-0.697711\pi$
$691$	−4.82000e15	−1.16391	−0.581953	+	0.813223i	$0.697711\pi$
$692$	2.74787e15	0.658284
$693$	−1.49855e15	−0.356155
$694$	−9.60024e14	−0.226363
$695$	−8.62988e15	−2.01878
$696$	−4.53829e15	−1.05328
$697$	−6.68704e14	−0.153976
$698$	2.73485e15	0.624783
$699$	2.70330e15	0.612732
$700$	7.01754e15	1.57814
$701$	4.76905e14	0.106410	0.0532051	−	0.998584i	$-0.483056\pi$
$701$	4.76905e14	0.106410	0.0532051	+	0.998584i	$0.483056\pi$
$702$	−1.36564e13	−0.00302330
$703$	8.28602e15	1.82008
$704$	2.24144e15	0.488515
$705$	8.76133e15	1.89465
$706$	3.56544e15	0.765045
$707$	4.41682e14	0.0940380
$708$	2.35292e14	0.0497077
$709$	−9.36719e15	−1.96361	−0.981804	−	0.189897i	$-0.939185\pi$
$709$	−9.36719e15	−1.96361	−0.981804	+	0.189897i	$0.939185\pi$
$710$	−1.46843e15	−0.305444
$711$	2.17244e15	0.448400
$712$	−2.00205e15	−0.410047
$713$	6.77514e15	1.37697
$714$	−7.23392e14	−0.145893
$715$	−2.36725e14	−0.0473764
$716$	−2.39307e15	−0.475263
$717$	−5.62769e14	−0.110911
$718$	2.79412e15	0.546462
$719$	7.76886e15	1.50782	0.753908	−	0.656980i	$-0.228166\pi$
$719$	7.76886e15	1.50782	0.753908	+	0.656980i	$0.228166\pi$
$720$	3.05129e14	0.0587698
$721$	2.71975e15	0.519859
$722$	−4.77752e15	−0.906250
$723$	3.87254e15	0.729012
$724$	2.01516e15	0.376485
$725$	2.23228e16	4.13895
$726$	−6.47371e13	−0.0119125
$727$	6.75552e15	1.23373	0.616864	−	0.787070i	$-0.288403\pi$
$727$	6.75552e15	1.23373	0.616864	+	0.787070i	$0.288403\pi$
$728$	1.56652e14	0.0283932
$729$	2.05891e14	0.0370370
$730$	−7.12488e15	−1.27204
$731$	3.16325e15	0.560515
$732$	3.86764e15	0.680198
$733$	−5.62650e15	−0.982124	−0.491062	−	0.871125i	$-0.663391\pi$
$733$	−5.62650e15	−0.982124	−0.491062	+	0.871125i	$0.663391\pi$
$734$	−4.23786e15	−0.734206
$735$	−1.10147e15	−0.189405
$736$	6.02420e15	1.02819
$737$	−6.86762e15	−1.16342
$738$	4.45080e14	0.0748390
$739$	3.13907e15	0.523909	0.261955	−	0.965080i	$-0.415633\pi$
$739$	3.13907e15	0.523909	0.261955	+	0.965080i	$0.415633\pi$
$740$	8.11942e15	1.34509
$741$	−1.51562e14	−0.0249225
$742$	3.80498e15	0.621056
$743$	6.84927e15	1.10970	0.554850	−	0.831950i	$-0.312776\pi$
$743$	6.84927e15	1.10970	0.554850	+	0.831950i	$0.312776\pi$
$744$	4.76099e15	0.765677
$745$	4.14817e15	0.662213
$746$	1.07777e15	0.170790
$747$	1.08902e15	0.171306
$748$	−1.66009e15	−0.259222
$749$	8.52340e15	1.32118
$750$	4.65721e15	0.716619
$751$	−7.39272e15	−1.12924	−0.564618	−	0.825352i	$-0.690977\pi$
$751$	−7.39272e15	−1.12924	−0.564618	+	0.825352i	$0.690977\pi$
$752$	−1.19481e15	−0.181176
$753$	8.93906e14	0.134561
$754$	1.98362e14	0.0296426
$755$	−8.50421e15	−1.26161
$756$	−9.40149e14	−0.138461
$757$	−8.61752e15	−1.25995	−0.629977	−	0.776614i	$-0.716936\pi$
$757$	−8.61752e15	−1.25995	−0.629977	+	0.776614i	$0.716936\pi$
$758$	−4.04084e14	−0.0586531
$759$	3.95001e15	0.569205
$760$	−1.93126e16	−2.76291
$761$	−1.03952e16	−1.47645	−0.738225	−	0.674554i	$-0.764336\pi$
$761$	−1.03952e16	−1.47645	−0.738225	+	0.674554i	$0.764336\pi$
$762$	5.01961e14	0.0707811
$763$	2.30172e14	0.0322231
$764$	−2.95655e13	−0.00410934
$765$	1.72286e15	0.237745
$766$	4.65088e15	0.637201
$767$	−2.58354e13	−0.00351432
$768$	3.95437e15	0.534061
$769$	1.31344e16	1.76122	0.880611	−	0.473839i	$-0.157132\pi$
$769$	1.31344e16	1.76122	0.880611	+	0.473839i	$0.157132\pi$
$770$	8.34618e15	1.11119
$771$	3.29473e15	0.435532
$772$	8.35720e15	1.09690
$773$	−6.94848e15	−0.905530	−0.452765	−	0.891630i	$-0.649562\pi$
$773$	−6.94848e15	−0.905530	−0.452765	+	0.891630i	$0.649562\pi$
$774$	−2.10541e15	−0.272435
$775$	−2.34182e16	−3.00881
$776$	2.59765e15	0.331391
$777$	−5.64365e15	−0.714899
$778$	8.45470e15	1.06343
$779$	4.93963e15	0.616933
$780$	−1.48515e14	−0.0184183
$781$	2.34231e15	0.288446
$782$	1.90678e15	0.233165
$783$	−2.99062e15	−0.363138
$784$	1.50210e14	0.0181118
$785$	−1.37236e16	−1.64317
$786$	−2.40498e15	−0.285948
$787$	8.13204e15	0.960149	0.480075	−	0.877228i	$-0.340610\pi$
$787$	8.13204e15	0.960149	0.480075	+	0.877228i	$0.340610\pi$
$788$	4.13447e15	0.484758
$789$	−9.31762e15	−1.08488
$790$	−1.20994e16	−1.39899
$791$	−3.90064e15	−0.447884
$792$	2.77573e15	0.316511
$793$	−4.24674e14	−0.0480898
$794$	8.59047e15	0.966061
$795$	−9.06209e15	−1.01207
$796$	3.33902e15	0.370337
$797$	−1.08942e16	−1.19999	−0.599993	−	0.800005i	$-0.704830\pi$
$797$	−1.08942e16	−1.19999	−0.599993	+	0.800005i	$0.704830\pi$
$798$	5.34360e15	0.584546
$799$	−6.74628e15	−0.732921
$800$	−2.08226e16	−2.24667
$801$	−1.31930e15	−0.141372
$802$	3.92896e15	0.418137
$803$	1.13650e16	1.20125
$804$	−4.30856e15	−0.452297
$805$	1.87187e16	1.95164
$806$	−2.08096e14	−0.0215487
$807$	−7.15207e15	−0.735575
$808$	−8.18118e14	−0.0835706
$809$	−6.93189e15	−0.703290	−0.351645	−	0.936133i	$-0.614378\pi$
$809$	−6.93189e15	−0.703290	−0.351645	+	0.936133i	$0.614378\pi$
$810$	−1.14671e15	−0.115554
$811$	−2.04337e15	−0.204518	−0.102259	−	0.994758i	$-0.532607\pi$
$811$	−2.04337e15	−0.204518	−0.102259	+	0.994758i	$0.532607\pi$
$812$	1.36559e16	1.35757
$813$	−3.88590e15	−0.383702
$814$	6.63282e15	0.650525
$815$	7.45352e15	0.726097
$816$	−2.34951e14	−0.0227343
$817$	−2.33665e16	−2.24581
$818$	2.80832e15	0.268104
$819$	1.03230e14	0.00978914
$820$	4.84031e15	0.455929
$821$	1.84447e15	0.172578	0.0862889	−	0.996270i	$-0.472499\pi$
$821$	1.84447e15	0.172578	0.0862889	+	0.996270i	$0.472499\pi$
$822$	−3.38128e15	−0.314257
$823$	−1.78380e15	−0.164682	−0.0823411	−	0.996604i	$-0.526240\pi$
$823$	−1.78380e15	−0.164682	−0.0823411	+	0.996604i	$0.526240\pi$
$824$	−5.03774e15	−0.461993
$825$	−1.36532e16	−1.24376
$826$	9.10874e14	0.0824268
$827$	1.54315e16	1.38717	0.693584	−	0.720376i	$-0.256031\pi$
$827$	1.54315e16	1.38717	0.693584	+	0.720376i	$0.256031\pi$
$828$	2.47813e15	0.221288
$829$	2.03589e15	0.180594	0.0902971	−	0.995915i	$-0.471218\pi$
$829$	2.03589e15	0.180594	0.0902971	+	0.995915i	$0.471218\pi$
$830$	−6.06528e15	−0.534468
$831$	−1.10947e16	−0.971203
$832$	−1.54405e14	−0.0134271
$833$	8.48139e14	0.0732689
$834$	−4.42287e15	−0.379569
$835$	2.11589e15	0.180392
$836$	1.22628e16	1.03862
$837$	3.13737e15	0.263983
$838$	6.37343e15	0.532759
$839$	−1.88602e16	−1.56623	−0.783116	−	0.621876i	$-0.786371\pi$
$839$	−1.88602e16	−1.56623	−0.783116	+	0.621876i	$0.786371\pi$
$840$	1.31539e16	1.08522
$841$	3.12391e16	2.56047
$842$	−1.04191e16	−0.848426
$843$	7.26646e15	0.587856
$844$	−6.30587e15	−0.506829
$845$	−2.23629e16	−1.78573
$846$	4.49023e15	0.356231
$847$	4.89354e14	0.0385713
$848$	1.23582e15	0.0967785
$849$	9.18137e15	0.714357
$850$	−6.59077e15	−0.509486
$851$	1.48760e16	1.14255
$852$	1.46950e15	0.112138
$853$	−8.85786e15	−0.671598	−0.335799	−	0.941934i	$-0.609006\pi$
$853$	−8.85786e15	−0.671598	−0.335799	+	0.941934i	$0.609006\pi$
$854$	1.49726e16	1.12792
$855$	−1.27265e16	−0.952569
$856$	−1.57877e16	−1.17412
$857$	9.83544e15	0.726774	0.363387	−	0.931638i	$-0.381620\pi$
$857$	9.83544e15	0.726774	0.363387	+	0.931638i	$0.381620\pi$
$858$	−1.21323e14	−0.00890767
$859$	4.25863e15	0.310676	0.155338	−	0.987861i	$-0.450353\pi$
$859$	4.25863e15	0.310676	0.155338	+	0.987861i	$0.450353\pi$
$860$	−2.28967e16	−1.65971
$861$	−3.36441e15	−0.242321
$862$	1.27297e16	0.911019
$863$	−8.53353e15	−0.606833	−0.303417	−	0.952858i	$-0.598127\pi$
$863$	−8.53353e15	−0.606833	−0.303417	+	0.952858i	$0.598127\pi$
$864$	2.78963e15	0.197116
$865$	−2.53352e16	−1.77884
$866$	8.12067e15	0.566557
$867$	7.00146e15	0.485382
$868$	−1.43260e16	−0.986885
$869$	1.93000e16	1.32114
$870$	1.66563e16	1.13298
$871$	4.73087e14	0.0319772
$872$	−4.26343e14	−0.0286364
$873$	1.71178e15	0.114254
$874$	−1.40852e16	−0.934219
$875$	−3.52043e16	−2.32034
$876$	7.13009e15	0.467006
$877$	−5.44470e15	−0.354386	−0.177193	−	0.984176i	$-0.556702\pi$
$877$	−5.44470e15	−0.354386	−0.177193	+	0.984176i	$0.556702\pi$
$878$	−1.37644e16	−0.890302
$879$	5.35930e15	0.344484
$880$	2.71076e15	0.173156
$881$	−2.95851e15	−0.187805	−0.0939023	−	0.995581i	$-0.529934\pi$
$881$	−2.95851e15	−0.187805	−0.0939023	+	0.995581i	$0.529934\pi$
$882$	−5.64510e14	−0.0356118
$883$	8.77592e15	0.550185	0.275092	−	0.961418i	$-0.411292\pi$
$883$	8.77592e15	0.550185	0.275092	+	0.961418i	$0.411292\pi$
$884$	1.14358e14	0.00712488
$885$	−2.16937e15	−0.134322
$886$	−1.46010e16	−0.898454
$887$	−2.94302e16	−1.79976	−0.899878	−	0.436142i	$-0.856344\pi$
$887$	−2.94302e16	−1.79976	−0.899878	+	0.436142i	$0.856344\pi$
$888$	1.04536e16	0.635324
$889$	−3.79437e15	−0.229182
$890$	7.34783e15	0.441077
$891$	1.82914e15	0.109124
$892$	1.55665e16	0.922966
$893$	4.98339e16	2.93658
$894$	2.12596e15	0.124509
$895$	2.20639e16	1.28427
$896$	−1.38179e16	−0.799371
$897$	−2.72103e14	−0.0156450
$898$	6.23315e15	0.356195
$899$	−4.55711e16	−2.58828
$900$	−8.56564e15	−0.483533
$901$	6.97787e15	0.391504
$902$	3.95409e15	0.220501
$903$	1.59150e16	0.882115
$904$	7.22507e15	0.398030
$905$	−1.85797e16	−1.01735
$906$	−4.35846e15	−0.237207
$907$	7.61735e14	0.0412063	0.0206032	−	0.999788i	$-0.493441\pi$
$907$	7.61735e14	0.0412063	0.0206032	+	0.999788i	$0.493441\pi$
$908$	−1.97735e16	−1.06319
$909$	−5.39119e14	−0.0288127
$910$	−5.74940e14	−0.0305418
$911$	1.78047e16	0.940122	0.470061	−	0.882634i	$-0.344232\pi$
$911$	1.78047e16	0.940122	0.470061	+	0.882634i	$0.344232\pi$
$912$	1.73555e15	0.0910891
$913$	9.67483e15	0.504724
$914$	6.31808e15	0.327628
$915$	−3.56594e16	−1.83805
$916$	−8.28513e15	−0.424497
$917$	1.81795e16	0.925870
$918$	8.82975e14	0.0447006
$919$	−2.59175e16	−1.30424	−0.652121	−	0.758115i	$-0.726121\pi$
$919$	−2.59175e16	−1.30424	−0.652121	+	0.758115i	$0.726121\pi$
$920$	−3.46723e16	−1.73440
$921$	1.09391e16	0.543942
$922$	−1.75868e16	−0.869296
$923$	−1.61354e14	−0.00792812
$924$	−8.35229e15	−0.407953
$925$	−5.14189e16	−2.49657
$926$	5.23078e15	0.252468
$927$	−3.31974e15	−0.159282
$928$	−4.05201e16	−1.93267
$929$	1.93663e16	0.918247	0.459124	−	0.888372i	$-0.348164\pi$
$929$	1.93663e16	0.918247	0.459124	+	0.888372i	$0.348164\pi$
$930$	−1.74736e16	−0.823618
$931$	−6.26509e15	−0.293565
$932$	1.50671e16	0.701845
$933$	−6.85448e14	−0.0317413
$934$	2.25381e16	1.03755
$935$	1.53059e16	0.700478
$936$	−1.91211e14	−0.00869951
$937$	1.94280e16	0.878738	0.439369	−	0.898307i	$-0.355202\pi$
$937$	1.94280e16	0.878738	0.439369	+	0.898307i	$0.355202\pi$
$938$	−1.66795e16	−0.750012
$939$	2.88591e14	0.0129010
$940$	4.88320e16	2.17021
$941$	−6.94877e15	−0.307019	−0.153510	−	0.988147i	$-0.549058\pi$
$941$	−6.94877e15	−0.307019	−0.153510	+	0.988147i	$0.549058\pi$
$942$	−7.03341e15	−0.308948
$943$	8.86821e15	0.387277
$944$	2.95844e14	0.0128445
$945$	8.66811e15	0.374153
$946$	−1.87045e16	−0.802685
$947$	2.18006e16	0.930131	0.465066	−	0.885276i	$-0.346031\pi$
$947$	2.18006e16	0.930131	0.465066	+	0.885276i	$0.346031\pi$
$948$	1.21083e16	0.513614
$949$	−7.82896e14	−0.0330172
$950$	4.86852e16	2.04135
$951$	1.22850e16	0.512131
$952$	−1.01286e16	−0.419804
$953$	2.38204e16	0.981608	0.490804	−	0.871270i	$-0.336703\pi$
$953$	2.38204e16	0.981608	0.490804	+	0.871270i	$0.336703\pi$
$954$	−4.64438e15	−0.190288
$955$	2.72592e14	0.0111044
$956$	−3.13664e15	−0.127042
$957$	−2.65687e16	−1.06993
$958$	3.55860e15	0.142485
$959$	2.55594e16	1.01753
$960$	−1.29652e16	−0.513203
$961$	2.23988e16	0.881549
$962$	−4.56912e14	−0.0178801
$963$	−1.04037e16	−0.404802
$964$	2.15839e16	0.835037
$965$	−7.70528e16	−2.96407
$966$	9.59347e15	0.366946
$967$	4.40469e16	1.67521	0.837606	−	0.546275i	$-0.183954\pi$
$967$	4.40469e16	1.67521	0.837606	+	0.546275i	$0.183954\pi$
$968$	−9.06420e14	−0.0342780
$969$	9.79952e15	0.368489
$970$	−9.53378e15	−0.356468
$971$	−3.21209e16	−1.19421	−0.597106	−	0.802162i	$-0.703683\pi$
$971$	−3.21209e16	−1.19421	−0.597106	+	0.802162i	$0.703683\pi$
$972$	1.14755e15	0.0424236
$973$	3.34329e16	1.22900
$974$	2.10122e16	0.768062
$975$	9.40521e14	0.0341856
$976$	4.86297e15	0.175763
$977$	−8.06446e15	−0.289838	−0.144919	−	0.989444i	$-0.546292\pi$
$977$	−8.06446e15	−0.289838	−0.144919	+	0.989444i	$0.546292\pi$
$978$	3.81998e15	0.136520
$979$	−1.17206e16	−0.416530
$980$	−6.13913e15	−0.216952
$981$	−2.80949e14	−0.00987298
$982$	4.35607e15	0.152223
$983$	2.83361e15	0.0984681	0.0492340	−	0.998787i	$-0.484322\pi$
$983$	2.83361e15	0.0984681	0.0492340	+	0.998787i	$0.484322\pi$
$984$	6.23182e15	0.215348
$985$	−3.81195e16	−1.30993
$986$	−1.28254e16	−0.438278
$987$	−3.39422e16	−1.15344
$988$	−8.44745e14	−0.0285471
$989$	−4.19503e16	−1.40979
$990$	−1.01874e16	−0.340462
$991$	4.17181e15	0.138650	0.0693250	−	0.997594i	$-0.477915\pi$
$991$	4.17181e15	0.138650	0.0693250	+	0.997594i	$0.477915\pi$
$992$	4.25084e16	1.40495
$993$	−1.99100e16	−0.654409
$994$	5.68882e15	0.185950
$995$	−3.07855e16	−1.00074
$996$	6.06972e15	0.196220
$997$	−5.18055e16	−1.66553	−0.832765	−	0.553627i	$-0.813243\pi$
$997$	−5.18055e16	−1.66553	−0.832765	+	0.553627i	$0.813243\pi$
$998$	−3.57936e16	−1.14443
$999$	6.88867e15	0.219041

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.11	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.11	✓	26	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-26.3367 q^{2} -243.000 q^{3} -1354.38 q^{4} +12487.3 q^{5} +6399.81 q^{6} -48376.8 q^{7} +89607.3 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-26.3367 q^{2} -243.000 q^{3} -1354.38 q^{4} +12487.3 q^{5} +6399.81 q^{6} -48376.8 q^{7} +89607.3 q^{8} +59049.0 q^{9} -328874. q^{10} +524591. q^{11} +329114. q^{12} -36137.3 q^{13} +1.27408e6 q^{14} -3.03441e6 q^{15} +413811. q^{16} +2.33652e6 q^{17} -1.55515e6 q^{18} -1.72596e7 q^{19} -1.69125e7 q^{20} +1.17556e7 q^{21} -1.38160e7 q^{22} -3.09864e7 q^{23} -2.17746e7 q^{24} +1.07104e8 q^{25} +951736. q^{26} -1.43489e7 q^{27} +6.55206e7 q^{28} +2.08422e8 q^{29} +7.99163e7 q^{30} -2.18649e8 q^{31} -1.94414e8 q^{32} -1.27476e8 q^{33} -6.15361e7 q^{34} -6.04096e8 q^{35} -7.99748e7 q^{36} -4.80083e8 q^{37} +4.54559e8 q^{38} +8.78136e6 q^{39} +1.11895e9 q^{40} -2.86197e8 q^{41} -3.09603e8 q^{42} +1.35383e9 q^{43} -7.10496e8 q^{44} +7.37362e8 q^{45} +8.16079e8 q^{46} -2.88733e9 q^{47} -1.00556e8 q^{48} +3.62993e8 q^{49} -2.82077e9 q^{50} -5.67774e8 q^{51} +4.89436e7 q^{52} +2.98644e9 q^{53} +3.77902e8 q^{54} +6.55072e9 q^{55} -4.33492e9 q^{56} +4.19407e9 q^{57} -5.48913e9 q^{58} +7.14924e8 q^{59} +4.10974e9 q^{60} +1.17517e10 q^{61} +5.75848e9 q^{62} -2.85660e9 q^{63} +4.27274e9 q^{64} -4.51257e8 q^{65} +3.35729e9 q^{66} -1.30914e10 q^{67} -3.16453e9 q^{68} +7.52970e9 q^{69} +1.59099e10 q^{70} +4.46502e9 q^{71} +5.29122e9 q^{72} +2.16645e10 q^{73} +1.26438e10 q^{74} -2.60263e10 q^{75} +2.33760e10 q^{76} -2.53781e10 q^{77} -2.31272e8 q^{78} +3.67905e10 q^{79} +5.16738e9 q^{80} +3.48678e9 q^{81} +7.53747e9 q^{82} +1.84426e10 q^{83} -1.59215e10 q^{84} +2.91768e10 q^{85} -3.56554e10 q^{86} -5.06465e10 q^{87} +4.70073e10 q^{88} -2.23424e10 q^{89} -1.94197e10 q^{90} +1.74821e9 q^{91} +4.19674e10 q^{92} +5.31317e10 q^{93} +7.60425e10 q^{94} -2.15525e11 q^{95} +4.72427e10 q^{96} +2.89892e10 q^{97} -9.56002e9 q^{98} +3.09766e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * q^99

Introduction

L-functions

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