LMFDB - Embedded newform 177.12.a.a.1.22

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			1.22
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)

$f(q)$	$=$	$q+60.2204 q^{2} -243.000 q^{3} +1578.50 q^{4} -10580.7 q^{5} -14633.6 q^{6} +72271.5 q^{7} -28273.6 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+60.2204 q^{2} -243.000 q^{3} +1578.50 q^{4} -10580.7 q^{5} -14633.6 q^{6} +72271.5 q^{7} -28273.6 q^{8} +59049.0 q^{9} -637177. q^{10} +271871. q^{11} -383575. q^{12} -546888. q^{13} +4.35222e6 q^{14} +2.57112e6 q^{15} -4.93541e6 q^{16} +17551.1 q^{17} +3.55596e6 q^{18} -1.54579e6 q^{19} -1.67017e7 q^{20} -1.75620e7 q^{21} +1.63722e7 q^{22} +2.86475e7 q^{23} +6.87048e6 q^{24} +6.31240e7 q^{25} -3.29338e7 q^{26} -1.43489e7 q^{27} +1.14080e8 q^{28} +1.81331e8 q^{29} +1.54834e8 q^{30} -2.76482e8 q^{31} -2.39308e8 q^{32} -6.60647e7 q^{33} +1.05694e6 q^{34} -7.64686e8 q^{35} +9.32087e7 q^{36} +4.29304e8 q^{37} -9.30883e7 q^{38} +1.32894e8 q^{39} +2.99156e8 q^{40} +7.55351e7 q^{41} -1.05759e9 q^{42} +1.28422e9 q^{43} +4.29148e8 q^{44} -6.24782e8 q^{45} +1.72516e9 q^{46} -4.08831e8 q^{47} +1.19931e9 q^{48} +3.24585e9 q^{49} +3.80135e9 q^{50} -4.26492e6 q^{51} -8.63261e8 q^{52} -5.10167e9 q^{53} -8.64097e8 q^{54} -2.87660e9 q^{55} -2.04338e9 q^{56} +3.75628e8 q^{57} +1.09199e10 q^{58} +7.14924e8 q^{59} +4.05851e9 q^{60} -5.06312e9 q^{61} -1.66499e10 q^{62} +4.26756e9 q^{63} -4.30352e9 q^{64} +5.78648e9 q^{65} -3.97844e9 q^{66} -2.02454e10 q^{67} +2.77044e7 q^{68} -6.96134e9 q^{69} -4.60497e10 q^{70} -5.57130e9 q^{71} -1.66953e9 q^{72} -1.58821e10 q^{73} +2.58529e10 q^{74} -1.53391e10 q^{75} -2.44003e9 q^{76} +1.96486e10 q^{77} +8.00291e9 q^{78} -1.93324e10 q^{79} +5.22203e10 q^{80} +3.48678e9 q^{81} +4.54875e9 q^{82} -6.53551e10 q^{83} -2.77216e10 q^{84} -1.85704e8 q^{85} +7.73365e10 q^{86} -4.40635e10 q^{87} -7.68678e9 q^{88} -4.74435e10 q^{89} -3.76246e10 q^{90} -3.95244e10 q^{91} +4.52200e10 q^{92} +6.71852e10 q^{93} -2.46200e10 q^{94} +1.63556e10 q^{95} +5.81519e10 q^{96} -1.44690e11 q^{97} +1.95466e11 q^{98} +1.60537e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	60.2204	1.33070	0.665348	−	0.746533i	$-0.268283\pi$
$2$	60.2204	1.33070	0.665348	+	0.746533i	$0.268283\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	1578.50	0.770751
$5$	−10580.7	−1.51419	−0.757096	−	0.653303i	$-0.773383\pi$
$5$	−10580.7	−1.51419	−0.757096	+	0.653303i	$0.773383\pi$
$6$	−14633.6	−0.768278
$7$	72271.5	1.62528	0.812640	−	0.582766i	$-0.198030\pi$
$7$	72271.5	1.62528	0.812640	+	0.582766i	$0.198030\pi$
$8$	−28273.6	−0.305061
$9$	59049.0	0.333333
$10$	−637177.	−2.01493
$11$	271871.	0.508983	0.254492	−	0.967075i	$-0.418092\pi$
$11$	271871.	0.508983	0.254492	+	0.967075i	$0.418092\pi$
$12$	−383575.	−0.444993
$13$	−546888.	−0.408517	−0.204258	−	0.978917i	$-0.565478\pi$
$13$	−546888.	−0.408517	−0.204258	+	0.978917i	$0.565478\pi$
$14$	4.35222e6	2.16275
$15$	2.57112e6	0.874219
$16$	−4.93541e6	−1.17669
$17$	17551.1	0.00299803	0.00149901	−	0.999999i	$-0.499523\pi$
$17$	17551.1	0.00299803	0.00149901	+	0.999999i	$0.499523\pi$
$18$	3.55596e6	0.443565
$19$	−1.54579e6	−0.143221	−0.0716105	−	0.997433i	$-0.522814\pi$
$19$	−1.54579e6	−0.143221	−0.0716105	+	0.997433i	$0.522814\pi$
$20$	−1.67017e7	−1.16707
$21$	−1.75620e7	−0.938356
$22$	1.63722e7	0.677302
$23$	2.86475e7	0.928076	0.464038	−	0.885815i	$-0.346400\pi$
$23$	2.86475e7	0.928076	0.464038	+	0.885815i	$0.346400\pi$
$24$	6.87048e6	0.176127
$25$	6.31240e7	1.29278
$26$	−3.29338e7	−0.543611
$27$	−1.43489e7	−0.192450
$28$	1.14080e8	1.25269
$29$	1.81331e8	1.64166	0.820832	−	0.571170i	$-0.193510\pi$
$29$	1.81331e8	1.64166	0.820832	+	0.571170i	$0.193510\pi$
$30$	1.54834e8	1.16332
$31$	−2.76482e8	−1.73452	−0.867258	−	0.497859i	$-0.834120\pi$
$31$	−2.76482e8	−1.73452	−0.867258	+	0.497859i	$0.834120\pi$
$32$	−2.39308e8	−1.26076
$33$	−6.60647e7	−0.293862
$34$	1.05694e6	0.00398946
$35$	−7.64686e8	−2.46099
$36$	9.32087e7	0.256917
$37$	4.29304e8	1.01778	0.508892	−	0.860831i	$-0.330055\pi$
$37$	4.29304e8	1.01778	0.508892	+	0.860831i	$0.330055\pi$
$38$	−9.30883e7	−0.190584
$39$	1.32894e8	0.235857
$40$	2.99156e8	0.461920
$41$	7.55351e7	0.101821	0.0509105	−	0.998703i	$-0.483788\pi$
$41$	7.55351e7	0.101821	0.0509105	+	0.998703i	$0.483788\pi$
$42$	−1.05759e9	−1.24867
$43$	1.28422e9	1.33218	0.666092	−	0.745870i	$-0.267966\pi$
$43$	1.28422e9	1.33218	0.666092	+	0.745870i	$0.267966\pi$
$44$	4.29148e8	0.392299
$45$	−6.24782e8	−0.504731
$46$	1.72516e9	1.23499
$47$	−4.08831e8	−0.260020	−0.130010	−	0.991513i	$-0.541501\pi$
$47$	−4.08831e8	−0.260020	−0.130010	+	0.991513i	$0.541501\pi$
$48$	1.19931e9	0.679365
$49$	3.24585e9	1.64153
$50$	3.80135e9	1.72030
$51$	−4.26492e6	−0.00173091
$52$	−8.63261e8	−0.314865
$53$	−5.10167e9	−1.67569	−0.837847	−	0.545905i	$-0.816186\pi$
$53$	−5.10167e9	−1.67569	−0.837847	+	0.545905i	$0.816186\pi$
$54$	−8.64097e8	−0.256093
$55$	−2.87660e9	−0.770699
$56$	−2.04338e9	−0.495809
$57$	3.75628e8	0.0826887
$58$	1.09199e10	2.18455
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	4.05851e9	0.673806
$61$	−5.06312e9	−0.767546	−0.383773	−	0.923427i	$-0.625375\pi$
$61$	−5.06312e9	−0.767546	−0.383773	+	0.923427i	$0.625375\pi$
$62$	−1.66499e10	−2.30811
$63$	4.26756e9	0.541760
$64$	−4.30352e9	−0.500995
$65$	5.78648e9	0.618573
$66$	−3.97844e9	−0.391040
$67$	−2.02454e10	−1.83195	−0.915976	−	0.401233i	$-0.868582\pi$
$67$	−2.02454e10	−1.83195	−0.915976	+	0.401233i	$0.868582\pi$
$68$	2.77044e7	0.00231073
$69$	−6.96134e9	−0.535825
$70$	−4.60497e10	−3.27482
$71$	−5.57130e9	−0.366468	−0.183234	−	0.983069i	$-0.558657\pi$
$71$	−5.57130e9	−0.366468	−0.183234	+	0.983069i	$0.558657\pi$
$72$	−1.66953e9	−0.101687
$73$	−1.58821e10	−0.896672	−0.448336	−	0.893865i	$-0.647983\pi$
$73$	−1.58821e10	−0.896672	−0.448336	+	0.893865i	$0.647983\pi$
$74$	2.58529e10	1.35436
$75$	−1.53391e10	−0.746386
$76$	−2.44003e9	−0.110388
$77$	1.96486e10	0.827240
$78$	8.00291e9	0.313854
$79$	−1.93324e10	−0.706865	−0.353432	−	0.935460i	$-0.614986\pi$
$79$	−1.93324e10	−0.706865	−0.353432	+	0.935460i	$0.614986\pi$
$80$	5.22203e10	1.78174
$81$	3.48678e9	0.111111
$82$	4.54875e9	0.135493
$83$	−6.53551e10	−1.82117	−0.910584	−	0.413324i	$-0.864368\pi$
$83$	−6.53551e10	−1.82117	−0.910584	+	0.413324i	$0.864368\pi$
$84$	−2.77216e10	−0.723239
$85$	−1.85704e8	−0.00453959
$86$	7.73365e10	1.77273
$87$	−4.40635e10	−0.947815
$88$	−7.68678e9	−0.155271
$89$	−4.74435e10	−0.900600	−0.450300	−	0.892877i	$-0.648683\pi$
$89$	−4.74435e10	−0.900600	−0.450300	+	0.892877i	$0.648683\pi$
$90$	−3.76246e10	−0.671643
$91$	−3.95244e10	−0.663954
$92$	4.52200e10	0.715316
$93$	6.71852e10	1.00142
$94$	−2.46200e10	−0.346007
$95$	1.63556e10	0.216864
$96$	5.81519e10	0.727901
$97$	−1.44690e11	−1.71078	−0.855392	−	0.517981i	$-0.826684\pi$
$97$	−1.44690e11	−1.71078	−0.855392	+	0.517981i	$0.826684\pi$
$98$	1.95466e11	2.18438
$99$	1.60537e10	0.169661
$100$	9.96411e10	0.996411
$101$	−1.14979e10	−0.108856	−0.0544279	−	0.998518i	$-0.517334\pi$
$101$	−1.14979e10	−0.108856	−0.0544279	+	0.998518i	$0.517334\pi$
$102$	−2.56835e8	−0.00230332
$103$	−2.72025e10	−0.231209	−0.115604	−	0.993295i	$-0.536881\pi$
$103$	−2.72025e10	−0.231209	−0.115604	+	0.993295i	$0.536881\pi$
$104$	1.54625e10	0.124622
$105$	1.85819e11	1.42085
$106$	−3.07224e11	−2.22984
$107$	−2.12775e11	−1.46659	−0.733296	−	0.679909i	$-0.762019\pi$
$107$	−2.12775e11	−1.46659	−0.733296	+	0.679909i	$0.762019\pi$
$108$	−2.26497e10	−0.148331
$109$	2.20305e11	1.37145	0.685723	−	0.727863i	$-0.259486\pi$
$109$	2.20305e11	1.37145	0.685723	+	0.727863i	$0.259486\pi$
$110$	−1.73230e11	−1.02557
$111$	−1.04321e11	−0.587617
$112$	−3.56690e11	−1.91246
$113$	3.47152e10	0.177251	0.0886254	−	0.996065i	$-0.471753\pi$
$113$	3.47152e10	0.177251	0.0886254	+	0.996065i	$0.471753\pi$
$114$	2.26205e10	0.110033
$115$	−3.03112e11	−1.40529
$116$	2.86231e11	1.26531
$117$	−3.22932e10	−0.136172
$118$	4.30530e10	0.173242
$119$	1.26845e9	0.00487263
$120$	−7.26948e10	−0.266690
$121$	−2.11398e11	−0.740936
$122$	−3.04903e11	−1.02137
$123$	−1.83550e10	−0.0587864
$124$	−4.36427e11	−1.33688
$125$	−1.51261e11	−0.443324
$126$	2.56994e11	0.720918
$127$	−5.88133e11	−1.57963	−0.789815	−	0.613346i	$-0.789823\pi$
$127$	−5.88133e11	−1.57963	−0.789815	+	0.613346i	$0.789823\pi$
$128$	2.30944e11	0.594089
$129$	−3.12066e11	−0.769137
$130$	3.48464e11	0.823132
$131$	2.67992e11	0.606919	0.303459	−	0.952844i	$-0.401858\pi$
$131$	2.67992e11	0.606919	0.303459	+	0.952844i	$0.401858\pi$
$132$	−1.04283e11	−0.226494
$133$	−1.11717e11	−0.232774
$134$	−1.21918e12	−2.43777
$135$	1.51822e11	0.291406
$136$	−4.96233e8	−0.000914580 0
$137$	8.69217e11	1.53874	0.769370	−	0.638804i	$-0.220570\pi$
$137$	8.69217e11	1.53874	0.769370	+	0.638804i	$0.220570\pi$
$138$	−4.19215e11	−0.713020
$139$	−2.13982e11	−0.349781	−0.174891	−	0.984588i	$-0.555957\pi$
$139$	−2.13982e11	−0.349781	−0.174891	+	0.984588i	$0.555957\pi$
$140$	−1.20706e12	−1.89681
$141$	9.93460e10	0.150122
$142$	−3.35506e11	−0.487657
$143$	−1.48683e11	−0.207928
$144$	−2.91431e11	−0.392231
$145$	−1.91862e12	−2.48579
$146$	−9.56430e11	−1.19320
$147$	−7.88741e11	−0.947740
$148$	6.77655e11	0.784457
$149$	−1.02330e12	−1.14150	−0.570751	−	0.821123i	$-0.693348\pi$
$149$	−1.02330e12	−1.14150	−0.570751	+	0.821123i	$0.693348\pi$
$150$	−9.23728e11	−0.993213
$151$	8.02192e11	0.831582	0.415791	−	0.909460i	$-0.363505\pi$
$151$	8.02192e11	0.831582	0.415791	+	0.909460i	$0.363505\pi$
$152$	4.37051e10	0.0436911
$153$	1.03638e9	0.000999343 0
$154$	1.18324e12	1.10080
$155$	2.92539e12	2.62639
$156$	2.09772e11	0.181787
$157$	4.16854e11	0.348767	0.174384	−	0.984678i	$-0.444207\pi$
$157$	4.16854e11	0.348767	0.174384	+	0.984678i	$0.444207\pi$
$158$	−1.16420e12	−0.940622
$159$	1.23970e12	0.967462
$160$	2.53206e12	1.90903
$161$	2.07040e12	1.50838
$162$	2.09976e11	0.147855
$163$	2.08094e12	1.41654	0.708269	−	0.705942i	$-0.249476\pi$
$163$	2.08094e12	1.41654	0.708269	+	0.705942i	$0.249476\pi$
$164$	1.19232e11	0.0784786
$165$	6.99014e11	0.444963
$166$	−3.93571e12	−2.42342
$167$	1.59680e12	0.951286	0.475643	−	0.879638i	$-0.342215\pi$
$167$	1.59680e12	0.951286	0.475643	+	0.879638i	$0.342215\pi$
$168$	4.96540e11	0.286255
$169$	−1.49307e12	−0.833114
$170$	−1.11832e10	−0.00604081
$171$	−9.12776e10	−0.0477403
$172$	2.02714e12	1.02678
$173$	1.26910e12	0.622650	0.311325	−	0.950304i	$-0.399227\pi$
$173$	1.26910e12	0.622650	0.311325	+	0.950304i	$0.399227\pi$
$174$	−2.65352e12	−1.26125
$175$	4.56207e12	2.10113
$176$	−1.34180e12	−0.598917
$177$	−1.73727e11	−0.0751646
$178$	−2.85707e12	−1.19842
$179$	2.19909e12	0.894439	0.447220	−	0.894424i	$-0.352414\pi$
$179$	2.19909e12	0.894439	0.447220	+	0.894424i	$0.352414\pi$
$180$	−9.86218e11	−0.389022
$181$	2.31193e12	0.884590	0.442295	−	0.896870i	$-0.354164\pi$
$181$	2.31193e12	0.884590	0.442295	+	0.896870i	$0.354164\pi$
$182$	−2.38018e12	−0.883520
$183$	1.23034e12	0.443143
$184$	−8.09968e11	−0.283119
$185$	−4.54235e12	−1.54112
$186$	4.04592e12	1.33259
$187$	4.77164e9	0.00152595
$188$	−6.45340e11	−0.200410
$189$	−1.03702e12	−0.312785
$190$	9.84944e11	0.288580
$191$	−2.82113e12	−0.803044	−0.401522	−	0.915849i	$-0.631519\pi$
$191$	−2.82113e12	−0.803044	−0.401522	+	0.915849i	$0.631519\pi$
$192$	1.04575e12	0.289250
$193$	−8.99959e10	−0.0241912	−0.0120956	−	0.999927i	$-0.503850\pi$
$193$	−8.99959e10	−0.0241912	−0.0120956	+	0.999927i	$0.503850\pi$
$194$	−8.71332e12	−2.27653
$195$	−1.40611e12	−0.357133
$196$	5.12357e12	1.26521
$197$	−1.49426e12	−0.358807	−0.179403	−	0.983776i	$-0.557417\pi$
$197$	−1.49426e12	−0.358807	−0.179403	+	0.983776i	$0.557417\pi$
$198$	9.66762e11	0.225767
$199$	3.35067e12	0.761096	0.380548	−	0.924761i	$-0.375735\pi$
$199$	3.35067e12	0.761096	0.380548	+	0.924761i	$0.375735\pi$
$200$	−1.78474e12	−0.394376
$201$	4.91962e12	1.05768
$202$	−6.92410e11	−0.144854
$203$	1.31051e13	2.66816
$204$	−6.73217e9	−0.00133410
$205$	−7.99217e11	−0.154177
$206$	−1.63815e12	−0.307669
$207$	1.69161e12	0.309359
$208$	2.69912e12	0.480699
$209$	−4.20257e11	−0.0728971
$210$	1.11901e13	1.89072
$211$	−2.00542e12	−0.330105	−0.165052	−	0.986285i	$-0.552779\pi$
$211$	−2.00542e12	−0.330105	−0.165052	+	0.986285i	$0.552779\pi$
$212$	−8.05297e12	−1.29154
$213$	1.35383e12	0.211580
$214$	−1.28134e13	−1.95159
$215$	−1.35880e13	−2.01718
$216$	4.05695e11	0.0587089
$217$	−1.99818e13	−2.81907
$218$	1.32669e13	1.82498
$219$	3.85936e12	0.517694
$220$	−4.54071e12	−0.594017
$221$	−9.59849e9	−0.00122474
$222$	−6.28224e12	−0.781940
$223$	−5.22181e12	−0.634080	−0.317040	−	0.948412i	$-0.602689\pi$
$223$	−5.22181e12	−0.634080	−0.317040	+	0.948412i	$0.602689\pi$
$224$	−1.72952e13	−2.04909
$225$	3.72741e12	0.430926
$226$	2.09056e12	0.235867
$227$	2.44041e12	0.268733	0.134366	−	0.990932i	$-0.457100\pi$
$227$	2.44041e12	0.268733	0.134366	+	0.990932i	$0.457100\pi$
$228$	5.92928e11	0.0637324
$229$	−1.37439e13	−1.44216	−0.721081	−	0.692850i	$-0.756355\pi$
$229$	−1.37439e13	−1.44216	−0.721081	+	0.692850i	$0.756355\pi$
$230$	−1.82535e13	−1.87001
$231$	−4.77460e12	−0.477607
$232$	−5.12689e12	−0.500807
$233$	1.11387e13	1.06262	0.531308	−	0.847179i	$-0.321701\pi$
$233$	1.11387e13	1.06262	0.531308	+	0.847179i	$0.321701\pi$
$234$	−1.94471e12	−0.181204
$235$	4.32574e12	0.393720
$236$	1.12851e12	0.100343
$237$	4.69777e12	0.408108
$238$	7.63863e10	0.00648399
$239$	−1.36418e12	−0.113157	−0.0565787	−	0.998398i	$-0.518019\pi$
$239$	−1.36418e12	−0.113157	−0.0565787	+	0.998398i	$0.518019\pi$
$240$	−1.26895e13	−1.02869
$241$	−1.82710e13	−1.44766	−0.723831	−	0.689977i	$-0.757621\pi$
$241$	−1.82710e13	−1.44766	−0.723831	+	0.689977i	$0.757621\pi$
$242$	−1.27305e13	−0.985961
$243$	−8.47289e11	−0.0641500
$244$	−7.99213e12	−0.591587
$245$	−3.43435e13	−2.48560
$246$	−1.10535e12	−0.0782268
$247$	8.45375e11	0.0585081
$248$	7.81715e12	0.529132
$249$	1.58813e13	1.05145
$250$	−9.10898e12	−0.589929
$251$	−4.99770e12	−0.316639	−0.158320	−	0.987388i	$-0.550608\pi$
$251$	−4.99770e12	−0.316639	−0.158320	+	0.987388i	$0.550608\pi$
$252$	6.73634e12	0.417562
$253$	7.78843e12	0.472375
$254$	−3.54176e13	−2.10201
$255$	4.51260e10	0.00262093
$256$	2.27211e13	1.29155
$257$	−2.11473e12	−0.117658	−0.0588291	−	0.998268i	$-0.518737\pi$
$257$	−2.11473e12	−0.117658	−0.0588291	+	0.998268i	$0.518737\pi$
$258$	−1.87928e13	−1.02349
$259$	3.10264e13	1.65418
$260$	9.13394e12	0.476766
$261$	1.07074e13	0.547221
$262$	1.61386e13	0.807624
$263$	−2.27554e13	−1.11514	−0.557568	−	0.830131i	$-0.688266\pi$
$263$	−2.27554e13	−1.11514	−0.557568	+	0.830131i	$0.688266\pi$
$264$	1.86789e12	0.0896456
$265$	5.39794e13	2.53732
$266$	−6.72764e12	−0.309752
$267$	1.15288e13	0.519961
$268$	−3.19573e13	−1.41198
$269$	−7.23012e12	−0.312974	−0.156487	−	0.987680i	$-0.550017\pi$
$269$	−7.23012e12	−0.312974	−0.156487	+	0.987680i	$0.550017\pi$
$270$	9.14279e12	0.387773
$271$	−2.87461e13	−1.19467	−0.597334	−	0.801992i	$-0.703773\pi$
$271$	−2.87461e13	−1.19467	−0.597334	+	0.801992i	$0.703773\pi$
$272$	−8.66220e10	−0.00352776
$273$	9.60443e12	0.383334
$274$	5.23446e13	2.04759
$275$	1.71616e13	0.658003
$276$	−1.09885e13	−0.412988
$277$	2.37373e13	0.874566	0.437283	−	0.899324i	$-0.355941\pi$
$277$	2.37373e13	0.874566	0.437283	+	0.899324i	$0.355941\pi$
$278$	−1.28861e13	−0.465453
$279$	−1.63260e13	−0.578172
$280$	2.16204e13	0.750750
$281$	−1.69968e13	−0.578737	−0.289369	−	0.957218i	$-0.593445\pi$
$281$	−1.69968e13	−0.578737	−0.289369	+	0.957218i	$0.593445\pi$
$282$	5.98266e12	0.199767
$283$	−1.11630e13	−0.365556	−0.182778	−	0.983154i	$-0.558509\pi$
$283$	−1.11630e13	−0.365556	−0.182778	+	0.983154i	$0.558509\pi$
$284$	−8.79429e12	−0.282456
$285$	−3.97442e12	−0.125207
$286$	−8.95375e12	−0.276689
$287$	5.45904e12	0.165488
$288$	−1.41309e13	−0.420254
$289$	−3.42716e13	−0.999991
$290$	−1.15540e14	−3.30784
$291$	3.51598e13	0.987722
$292$	−2.50699e13	−0.691111
$293$	−9.31969e11	−0.0252133	−0.0126066	−	0.999921i	$-0.504013\pi$
$293$	−9.31969e11	−0.0252133	−0.0126066	+	0.999921i	$0.504013\pi$
$294$	−4.74983e13	−1.26115
$295$	−7.56443e12	−0.197131
$296$	−1.21380e13	−0.310485
$297$	−3.90105e12	−0.0979539
$298$	−6.16233e13	−1.51899
$299$	−1.56670e13	−0.379134
$300$	−2.42128e13	−0.575278
$301$	9.28128e13	2.16517
$302$	4.83083e13	1.10658
$303$	2.79399e12	0.0628480
$304$	7.62913e12	0.168527
$305$	5.35716e13	1.16221
$306$	6.24110e10	0.00132982
$307$	−4.57224e13	−0.956902	−0.478451	−	0.878114i	$-0.658802\pi$
$307$	−4.57224e13	−0.956902	−0.478451	+	0.878114i	$0.658802\pi$
$308$	3.10152e13	0.637596
$309$	6.61022e12	0.133489
$310$	1.76168e14	3.49493
$311$	3.92854e13	0.765682	0.382841	−	0.923814i	$-0.374946\pi$
$311$	3.92854e13	0.765682	0.382841	+	0.923814i	$0.374946\pi$
$312$	−3.75738e12	−0.0719507
$313$	−3.49347e13	−0.657299	−0.328650	−	0.944452i	$-0.606594\pi$
$313$	−3.49347e13	−0.657299	−0.328650	+	0.944452i	$0.606594\pi$
$314$	2.51031e13	0.464103
$315$	−4.51540e13	−0.820329
$316$	−3.05161e13	−0.544817
$317$	−9.26365e13	−1.62538	−0.812692	−	0.582693i	$-0.801999\pi$
$317$	−9.26365e13	−1.62538	−0.812692	+	0.582693i	$0.801999\pi$
$318$	7.46555e13	1.28740
$319$	4.92988e13	0.835579
$320$	4.55344e13	0.758603
$321$	5.17043e13	0.846738
$322$	1.24680e14	2.00720
$323$	−2.71304e10	−0.000429381 0
$324$	5.50388e12	0.0856390
$325$	−3.45217e13	−0.528122
$326$	1.25315e14	1.88498
$327$	−5.35341e13	−0.791804
$328$	−2.13565e12	−0.0310616
$329$	−2.95469e13	−0.422605
$330$	4.20949e13	0.592110
$331$	5.60914e13	0.775966	0.387983	−	0.921667i	$-0.373172\pi$
$331$	5.60914e13	0.775966	0.387983	+	0.921667i	$0.373172\pi$
$332$	−1.03163e14	−1.40367
$333$	2.53500e13	0.339261
$334$	9.61602e13	1.26587
$335$	2.14211e14	2.77393
$336$	8.66756e13	1.10416
$337$	−9.34576e13	−1.17125	−0.585626	−	0.810582i	$-0.699151\pi$
$337$	−9.34576e13	−1.17125	−0.585626	+	0.810582i	$0.699151\pi$
$338$	−8.99136e13	−1.10862
$339$	−8.43579e12	−0.102336
$340$	−2.93133e11	−0.00349889
$341$	−7.51676e13	−0.882839
$342$	−5.49677e12	−0.0635279
$343$	9.16780e13	1.04267
$344$	−3.63096e13	−0.406397
$345$	7.36562e13	0.811342
$346$	7.64260e13	0.828557
$347$	1.10432e14	1.17838	0.589188	−	0.807996i	$-0.299448\pi$
$347$	1.10432e14	1.17838	0.589188	+	0.807996i	$0.299448\pi$
$348$	−6.95542e13	−0.730529
$349$	−1.84292e14	−1.90532	−0.952659	−	0.304040i	$-0.901664\pi$
$349$	−1.84292e14	−1.90532	−0.952659	+	0.304040i	$0.901664\pi$
$350$	2.74730e14	2.79596
$351$	7.84724e12	0.0786190
$352$	−6.50610e13	−0.641706
$353$	−9.33906e12	−0.0906864	−0.0453432	−	0.998971i	$-0.514438\pi$
$353$	−9.33906e12	−0.0906864	−0.0453432	+	0.998971i	$0.514438\pi$
$354$	−1.04619e13	−0.100021
$355$	5.89485e13	0.554903
$356$	−7.48895e13	−0.694138
$357$	−3.08232e11	−0.00281322
$358$	1.32430e14	1.19023
$359$	7.66828e13	0.678701	0.339350	−	0.940660i	$-0.389793\pi$
$359$	7.66828e13	0.678701	0.339350	+	0.940660i	$0.389793\pi$
$360$	1.76648e13	0.153973
$361$	−1.14101e14	−0.979488
$362$	1.39225e14	1.17712
$363$	5.13696e13	0.427780
$364$	−6.23892e13	−0.511743
$365$	1.68045e14	1.35773
$366$	7.40915e13	0.589688
$367$	−1.15789e14	−0.907829	−0.453914	−	0.891045i	$-0.649973\pi$
$367$	−1.15789e14	−0.907829	−0.453914	+	0.891045i	$0.649973\pi$
$368$	−1.41387e14	−1.09206
$369$	4.46027e12	0.0339403
$370$	−2.73542e14	−2.05076
$371$	−3.68705e14	−2.72347
$372$	1.06052e14	0.771848
$373$	4.15227e13	0.297774	0.148887	−	0.988854i	$-0.452431\pi$
$373$	4.15227e13	0.297774	0.148887	+	0.988854i	$0.452431\pi$
$374$	2.87350e11	0.00203057
$375$	3.67563e13	0.255953
$376$	1.15591e13	0.0793217
$377$	−9.91679e13	−0.670647
$378$	−6.24496e13	−0.416222
$379$	1.74723e14	1.14772	0.573858	−	0.818955i	$-0.305446\pi$
$379$	1.74723e14	1.14772	0.573858	+	0.818955i	$0.305446\pi$
$380$	2.58174e13	0.167148
$381$	1.42916e14	0.911999
$382$	−1.69890e14	−1.06861
$383$	1.90325e14	1.18005	0.590027	−	0.807384i	$-0.299117\pi$
$383$	1.90325e14	1.18005	0.590027	+	0.807384i	$0.299117\pi$
$384$	−5.61193e13	−0.342997
$385$	−2.07896e14	−1.25260
$386$	−5.41959e12	−0.0321911
$387$	7.58321e13	0.444061
$388$	−2.28394e14	−1.31859
$389$	8.37280e13	0.476593	0.238297	−	0.971192i	$-0.423411\pi$
$389$	8.37280e13	0.476593	0.238297	+	0.971192i	$0.423411\pi$
$390$	−8.46768e13	−0.475235
$391$	5.02795e11	0.00278240
$392$	−9.17718e13	−0.500767
$393$	−6.51222e13	−0.350405
$394$	−8.99847e13	−0.477463
$395$	2.04551e14	1.07033
$396$	2.53408e13	0.130766
$397$	9.06523e13	0.461351	0.230675	−	0.973031i	$-0.425906\pi$
$397$	9.06523e13	0.461351	0.230675	+	0.973031i	$0.425906\pi$
$398$	2.01779e14	1.01279
$399$	2.71472e13	0.134392
$400$	−3.11543e14	−1.52121
$401$	1.91294e14	0.921312	0.460656	−	0.887579i	$-0.347614\pi$
$401$	1.91294e14	0.921312	0.460656	+	0.887579i	$0.347614\pi$
$402$	2.96262e14	1.40745
$403$	1.51205e14	0.708578
$404$	−1.81494e13	−0.0839008
$405$	−3.68928e13	−0.168244
$406$	7.89195e14	3.55051
$407$	1.16715e14	0.518034
$408$	1.20585e11	0.000528033 0
$409$	3.07393e14	1.32805	0.664026	−	0.747709i	$-0.268846\pi$
$409$	3.07393e14	1.32805	0.664026	+	0.747709i	$0.268846\pi$
$410$	−4.81292e13	−0.205162
$411$	−2.11220e14	−0.888392
$412$	−4.29391e13	−0.178205
$413$	5.16687e13	0.211593
$414$	1.01869e14	0.411662
$415$	6.91506e14	2.75760
$416$	1.30875e14	0.515042
$417$	5.19977e13	0.201946
$418$	−2.53080e13	−0.0970038
$419$	8.82048e13	0.333669	0.166834	−	0.985985i	$-0.446646\pi$
$419$	8.82048e13	0.333669	0.166834	+	0.985985i	$0.446646\pi$
$420$	2.93315e14	1.09512
$421$	−7.66855e13	−0.282593	−0.141297	−	0.989967i	$-0.545127\pi$
$421$	−7.66855e13	−0.282593	−0.141297	+	0.989967i	$0.545127\pi$
$422$	−1.20767e14	−0.439269
$423$	−2.41411e13	−0.0866732
$424$	1.44242e14	0.511188
$425$	1.10790e12	0.00387579
$426$	8.15280e13	0.281549
$427$	−3.65920e14	−1.24748
$428$	−3.35865e14	−1.13038
$429$	3.61300e13	0.120047
$430$	−8.18277e14	−2.68426
$431$	4.40817e14	1.42769	0.713845	−	0.700304i	$-0.246952\pi$
$431$	4.40817e14	1.42769	0.713845	+	0.700304i	$0.246952\pi$
$432$	7.08178e13	0.226455
$433$	−2.03364e14	−0.642082	−0.321041	−	0.947065i	$-0.604033\pi$
$433$	−2.03364e14	−0.642082	−0.321041	+	0.947065i	$0.604033\pi$
$434$	−1.20331e15	−3.75133
$435$	4.66225e14	1.43517
$436$	3.47751e14	1.05704
$437$	−4.42831e13	−0.132920
$438$	2.32412e14	0.688893
$439$	2.71140e14	0.793668	0.396834	−	0.917890i	$-0.370109\pi$
$439$	2.71140e14	0.793668	0.396834	+	0.917890i	$0.370109\pi$
$440$	8.13318e13	0.235110
$441$	1.91664e14	0.547178
$442$	−5.78025e11	−0.00162976
$443$	−3.26496e14	−0.909195	−0.454597	−	0.890697i	$-0.650217\pi$
$443$	−3.26496e14	−0.909195	−0.454597	+	0.890697i	$0.650217\pi$
$444$	−1.64670e14	−0.452907
$445$	5.01987e14	1.36368
$446$	−3.14459e14	−0.843768
$447$	2.48661e14	0.659046
$448$	−3.11022e14	−0.814257
$449$	5.36119e14	1.38646	0.693228	−	0.720719i	$-0.256188\pi$
$449$	5.36119e14	1.38646	0.693228	+	0.720719i	$0.256188\pi$
$450$	2.24466e14	0.573432
$451$	2.05358e13	0.0518252
$452$	5.47979e13	0.136616
$453$	−1.94933e14	−0.480114
$454$	1.46962e14	0.357601
$455$	4.18198e14	1.00535
$456$	−1.06203e13	−0.0252251
$457$	−7.62845e14	−1.79018	−0.895091	−	0.445883i	$-0.852890\pi$
$457$	−7.62845e14	−1.79018	−0.895091	+	0.445883i	$0.852890\pi$
$458$	−8.27662e14	−1.91908
$459$	−2.51839e11	−0.000576971 0
$460$	−4.78461e14	−1.08313
$461$	2.64452e14	0.591551	0.295775	−	0.955257i	$-0.404422\pi$
$461$	2.64452e14	0.591551	0.295775	+	0.955257i	$0.404422\pi$
$462$	−2.87528e14	−0.635550
$463$	−6.38847e14	−1.39541	−0.697704	−	0.716386i	$-0.745795\pi$
$463$	−6.38847e14	−1.39541	−0.697704	+	0.716386i	$0.745795\pi$
$464$	−8.94945e14	−1.93174
$465$	−7.10870e14	−1.51635
$466$	6.70776e14	1.41402
$467$	2.37097e14	0.493950	0.246975	−	0.969022i	$-0.420564\pi$
$467$	2.37097e14	0.493950	0.246975	+	0.969022i	$0.420564\pi$
$468$	−5.09747e13	−0.104955
$469$	−1.46316e15	−2.97743
$470$	2.60498e14	0.523921
$471$	−1.01295e14	−0.201361
$472$	−2.02135e13	−0.0397155
$473$	3.49143e14	0.678059
$474$	2.82901e14	0.543068
$475$	−9.75766e13	−0.185153
$476$	2.00224e12	0.00375559
$477$	−3.01248e14	−0.558565
$478$	−8.21514e13	−0.150578
$479$	−2.41888e14	−0.438297	−0.219149	−	0.975691i	$-0.570328\pi$
$479$	−2.41888e14	−0.438297	−0.219149	+	0.975691i	$0.570328\pi$
$480$	−6.15290e14	−1.10218
$481$	−2.34781e14	−0.415781
$482$	−1.10028e15	−1.92640
$483$	−5.03107e14	−0.870865
$484$	−3.33691e14	−0.571077
$485$	1.53093e15	2.59046
$486$	−5.10241e13	−0.0853642
$487$	−2.22716e14	−0.368418	−0.184209	−	0.982887i	$-0.558972\pi$
$487$	−2.22716e14	−0.368418	−0.184209	+	0.982887i	$0.558972\pi$
$488$	1.43153e14	0.234148
$489$	−5.05669e14	−0.817839
$490$	−2.06818e15	−3.30757
$491$	−5.53939e14	−0.876019	−0.438010	−	0.898970i	$-0.644316\pi$
$491$	−5.53939e14	−0.876019	−0.438010	+	0.898970i	$0.644316\pi$
$492$	−2.89734e13	−0.0453097
$493$	3.18257e12	0.00492175
$494$	5.09089e13	0.0778565
$495$	−1.69860e14	−0.256900
$496$	1.36455e15	2.04099
$497$	−4.02647e14	−0.595613
$498$	9.56378e14	1.39916
$499$	−3.19570e13	−0.0462395	−0.0231197	−	0.999733i	$-0.507360\pi$
$499$	−3.19570e13	−0.0462395	−0.0231197	+	0.999733i	$0.507360\pi$
$500$	−2.38765e14	−0.341692
$501$	−3.88023e14	−0.549225
$502$	−3.00963e14	−0.421350
$503$	−6.92782e14	−0.959340	−0.479670	−	0.877449i	$-0.659244\pi$
$503$	−6.92782e14	−0.959340	−0.479670	+	0.877449i	$0.659244\pi$
$504$	−1.20659e14	−0.165270
$505$	1.21657e14	0.164829
$506$	4.69022e14	0.628588
$507$	3.62817e14	0.480999
$508$	−9.28367e14	−1.21750
$509$	1.40246e15	1.81946	0.909729	−	0.415203i	$-0.136289\pi$
$509$	1.40246e15	1.81946	0.909729	+	0.415203i	$0.136289\pi$
$510$	2.71751e12	0.00348767
$511$	−1.14783e15	−1.45734
$512$	8.95303e14	1.12457
$513$	2.21804e13	0.0275629
$514$	−1.27350e14	−0.156567
$515$	2.87823e14	0.350095
$516$	−4.92596e14	−0.592813
$517$	−1.11149e14	−0.132346
$518$	1.86843e15	2.20121
$519$	−3.08392e14	−0.359487
$520$	−1.63604e14	−0.188702
$521$	−1.57947e15	−1.80262	−0.901312	−	0.433170i	$-0.857395\pi$
$521$	−1.57947e15	−1.80262	−0.901312	+	0.433170i	$0.857395\pi$
$522$	6.44807e14	0.728185
$523$	4.67432e14	0.522347	0.261173	−	0.965292i	$-0.415891\pi$
$523$	4.67432e14	0.522347	0.261173	+	0.965292i	$0.415891\pi$
$524$	4.23026e14	0.467783
$525$	−1.10858e15	−1.21309
$526$	−1.37034e15	−1.48391
$527$	−4.85257e12	−0.00520013
$528$	3.26057e14	0.345785
$529$	−1.32131e14	−0.138675
$530$	3.25066e15	3.37641
$531$	4.22156e13	0.0433963
$532$	−1.76345e14	−0.179411
$533$	−4.13092e13	−0.0415956
$534$	6.94267e14	0.691910
$535$	2.25132e15	2.22070
$536$	5.72409e14	0.558856
$537$	−5.34378e14	−0.516405
$538$	−4.35401e14	−0.416473
$539$	8.82453e14	0.835513
$540$	2.39651e14	0.224602
$541$	−2.81135e14	−0.260813	−0.130406	−	0.991461i	$-0.541628\pi$
$541$	−2.81135e14	−0.260813	−0.130406	+	0.991461i	$0.541628\pi$
$542$	−1.73110e15	−1.58974
$543$	−5.61798e14	−0.510718
$544$	−4.20013e12	−0.00377980
$545$	−2.33099e15	−2.07663
$546$	5.78383e14	0.510101
$547$	1.18965e15	1.03870	0.519349	−	0.854562i	$-0.326174\pi$
$547$	1.18965e15	1.03870	0.519349	+	0.854562i	$0.326174\pi$
$548$	1.37206e15	1.18599
$549$	−2.98972e14	−0.255849
$550$	1.03348e15	0.875601
$551$	−2.80301e14	−0.235121
$552$	1.96822e14	0.163459
$553$	−1.39718e15	−1.14885
$554$	1.42947e15	1.16378
$555$	1.10379e15	0.889766
$556$	−3.37771e14	−0.269594
$557$	3.74465e14	0.295943	0.147971	−	0.988992i	$-0.452726\pi$
$557$	3.74465e14	0.295943	0.147971	+	0.988992i	$0.452726\pi$
$558$	−9.83159e14	−0.769371
$559$	−7.02326e14	−0.544219
$560$	3.77404e15	2.89583
$561$	−1.15951e12	−0.000881005 0
$562$	−1.02355e15	−0.770123
$563$	−3.61189e13	−0.0269115	−0.0134558	−	0.999909i	$-0.504283\pi$
$563$	−3.61189e13	−0.0269115	−0.0134558	+	0.999909i	$0.504283\pi$
$564$	1.56818e14	0.115707
$565$	−3.67312e14	−0.268392
$566$	−6.72238e14	−0.486444
$567$	2.51995e14	0.180587
$568$	1.57521e14	0.111795
$569$	−1.41723e15	−0.996144	−0.498072	−	0.867136i	$-0.665959\pi$
$569$	−1.41723e15	−0.996144	−0.498072	+	0.867136i	$0.665959\pi$
$570$	−2.39341e14	−0.166612
$571$	−5.84698e14	−0.403119	−0.201559	−	0.979476i	$-0.564601\pi$
$571$	−5.84698e14	−0.403119	−0.201559	+	0.979476i	$0.564601\pi$
$572$	−2.34696e14	−0.160261
$573$	6.85534e14	0.463638
$574$	3.28745e14	0.220214
$575$	1.80834e15	1.19980
$576$	−2.54118e14	−0.166998
$577$	−1.82207e15	−1.18604	−0.593020	−	0.805188i	$-0.702064\pi$
$577$	−1.82207e15	−1.18604	−0.593020	+	0.805188i	$0.702064\pi$
$578$	−2.06385e15	−1.33068
$579$	2.18690e13	0.0139668
$580$	−3.02854e15	−1.91593
$581$	−4.72331e15	−2.95991
$582$	2.11734e15	1.31436
$583$	−1.38700e15	−0.852900
$584$	4.49045e14	0.273539
$585$	3.41686e14	0.206191
$586$	−5.61235e13	−0.0335512
$587$	2.12988e15	1.26138	0.630690	−	0.776035i	$-0.282772\pi$
$587$	2.12988e15	1.26138	0.630690	+	0.776035i	$0.282772\pi$
$588$	−1.24503e15	−0.730472
$589$	4.27385e14	0.248419
$590$	−4.55533e14	−0.262321
$591$	3.63104e14	0.207157
$592$	−2.11879e15	−1.19762
$593$	3.36610e15	1.88507	0.942533	−	0.334113i	$-0.108437\pi$
$593$	3.36610e15	1.88507	0.942533	+	0.334113i	$0.108437\pi$
$594$	−2.34923e14	−0.130347
$595$	−1.34211e13	−0.00737810
$596$	−1.61527e15	−0.879814
$597$	−8.14212e14	−0.439419
$598$	−9.43471e14	−0.504512
$599$	−1.26182e15	−0.668575	−0.334287	−	0.942471i	$-0.608496\pi$
$599$	−1.26182e15	−0.668575	−0.334287	+	0.942471i	$0.608496\pi$
$600$	4.33692e14	0.227693
$601$	3.33140e15	1.73307	0.866537	−	0.499114i	$-0.166341\pi$
$601$	3.33140e15	1.73307	0.866537	+	0.499114i	$0.166341\pi$
$602$	5.58923e15	2.88118
$603$	−1.19547e15	−0.610651
$604$	1.26626e15	0.640943
$605$	2.23674e15	1.12192
$606$	1.68256e14	0.0836315
$607$	9.30726e14	0.458442	0.229221	−	0.973374i	$-0.426382\pi$
$607$	9.30726e14	0.458442	0.229221	+	0.973374i	$0.426382\pi$
$608$	3.69921e14	0.180567
$609$	−3.18454e15	−1.54046
$610$	3.22610e15	1.54655
$611$	2.23585e14	0.106222
$612$	1.63592e12	0.000770244 0
$613$	−2.95946e15	−1.38096	−0.690478	−	0.723353i	$-0.742600\pi$
$613$	−2.95946e15	−1.38096	−0.690478	+	0.723353i	$0.742600\pi$
$614$	−2.75342e15	−1.27335
$615$	1.94210e14	0.0890139
$616$	−5.55535e14	−0.252358
$617$	3.82949e15	1.72414	0.862070	−	0.506789i	$-0.169168\pi$
$617$	3.82949e15	1.72414	0.862070	+	0.506789i	$0.169168\pi$
$618$	3.98070e14	0.177633
$619$	−2.08118e15	−0.920474	−0.460237	−	0.887796i	$-0.652236\pi$
$619$	−2.08118e15	−0.920474	−0.460237	+	0.887796i	$0.652236\pi$
$620$	4.61772e15	2.02429
$621$	−4.11060e14	−0.178608
$622$	2.36578e15	1.01889
$623$	−3.42882e15	−1.46373
$624$	−6.55885e14	−0.277532
$625$	−1.48178e15	−0.621502
$626$	−2.10378e15	−0.874665
$627$	1.02122e14	0.0420872
$628$	6.58003e14	0.268813
$629$	7.53476e12	0.00305134
$630$	−2.71919e15	−1.09161
$631$	−4.91710e15	−1.95681	−0.978403	−	0.206708i	$-0.933725\pi$
$631$	−4.91710e15	−1.95681	−0.978403	+	0.206708i	$0.933725\pi$
$632$	5.46596e14	0.215636
$633$	4.87317e14	0.190586
$634$	−5.57861e15	−2.16289
$635$	6.22289e15	2.39186
$636$	1.95687e15	0.745673
$637$	−1.77511e15	−0.670594
$638$	2.96879e15	1.11190
$639$	−3.28980e14	−0.122156
$640$	−2.44356e15	−0.899565
$641$	−4.55696e15	−1.66324	−0.831621	−	0.555343i	$-0.812587\pi$
$641$	−4.55696e15	−1.66324	−0.831621	+	0.555343i	$0.812587\pi$
$642$	3.11365e15	1.12675
$643$	6.14757e14	0.220568	0.110284	−	0.993900i	$-0.464824\pi$
$643$	6.14757e14	0.220568	0.110284	+	0.993900i	$0.464824\pi$
$644$	3.26812e15	1.16259
$645$	3.30189e15	1.16462
$646$	−1.63380e12	−0.000571375 0
$647$	2.37438e15	0.823337	0.411668	−	0.911334i	$-0.364946\pi$
$647$	2.37438e15	0.823337	0.411668	+	0.911334i	$0.364946\pi$
$648$	−9.85839e13	−0.0338956
$649$	1.94367e14	0.0662640
$650$	−2.07891e15	−0.702769
$651$	4.85558e15	1.62759
$652$	3.28477e15	1.09180
$653$	−3.85797e15	−1.27156	−0.635779	−	0.771871i	$-0.719321\pi$
$653$	−3.85797e15	−1.27156	−0.635779	+	0.771871i	$0.719321\pi$
$654$	−3.22385e15	−1.05365
$655$	−2.83556e15	−0.918992
$656$	−3.72797e14	−0.119812
$657$	−9.37825e14	−0.298891
$658$	−1.77933e15	−0.562358
$659$	−3.32746e15	−1.04290	−0.521450	−	0.853282i	$-0.674609\pi$
$659$	−3.32746e15	−1.04290	−0.521450	+	0.853282i	$0.674609\pi$
$660$	1.10339e15	0.342956
$661$	4.49012e15	1.38404	0.692022	−	0.721876i	$-0.256720\pi$
$661$	4.49012e15	1.38404	0.692022	+	0.721876i	$0.256720\pi$
$662$	3.37785e15	1.03257
$663$	2.33243e12	0.000707106 0
$664$	1.84782e15	0.555567
$665$	1.18205e15	0.352465
$666$	1.52659e15	0.451453
$667$	5.19469e15	1.52359
$668$	2.52055e15	0.733205
$669$	1.26890e15	0.366086
$670$	1.28999e16	3.69125
$671$	−1.37652e15	−0.390668
$672$	4.20273e15	1.18304
$673$	−2.57597e15	−0.719213	−0.359606	−	0.933104i	$-0.617089\pi$
$673$	−2.57597e15	−0.719213	−0.359606	+	0.933104i	$0.617089\pi$
$674$	−5.62806e15	−1.55858
$675$	−9.05760e14	−0.248795
$676$	−2.35682e15	−0.642124
$677$	−3.48738e15	−0.942457	−0.471229	−	0.882011i	$-0.656189\pi$
$677$	−3.48738e15	−0.942457	−0.471229	+	0.882011i	$0.656189\pi$
$678$	−5.08007e14	−0.136178
$679$	−1.04570e16	−2.78050
$680$	5.25051e12	0.00138485
$681$	−5.93020e14	−0.155153
$682$	−4.52662e15	−1.17479
$683$	7.56829e15	1.94843	0.974213	−	0.225629i	$-0.0724439\pi$
$683$	7.56829e15	1.94843	0.974213	+	0.225629i	$0.0724439\pi$
$684$	−1.44081e14	−0.0367959
$685$	−9.19696e15	−2.32995
$686$	5.52089e15	1.38748
$687$	3.33976e15	0.832633
$688$	−6.33817e15	−1.56757
$689$	2.79004e15	0.684549
$690$	4.43560e15	1.07965
$691$	−2.98790e15	−0.721502	−0.360751	−	0.932662i	$-0.617480\pi$
$691$	−2.98790e15	−0.721502	−0.360751	+	0.932662i	$0.617480\pi$
$692$	2.00328e15	0.479908
$693$	1.16023e15	0.275747
$694$	6.65027e15	1.56806
$695$	2.26409e15	0.529637
$696$	1.24583e15	0.289141
$697$	1.32572e12	0.000305262 0
$698$	−1.10982e16	−2.53540
$699$	−2.70670e15	−0.613501
$700$	7.20121e15	1.61945
$701$	−5.12968e15	−1.14457	−0.572283	−	0.820056i	$-0.693942\pi$
$701$	−5.12968e15	−1.14457	−0.572283	+	0.820056i	$0.693942\pi$
$702$	4.72564e14	0.104618
$703$	−6.63615e14	−0.145768
$704$	−1.17000e15	−0.254998
$705$	−1.05115e15	−0.227314
$706$	−5.62402e14	−0.120676
$707$	−8.30972e14	−0.176921
$708$	−2.74227e14	−0.0579332
$709$	2.21160e15	0.463609	0.231805	−	0.972762i	$-0.425537\pi$
$709$	2.21160e15	0.463609	0.231805	+	0.972762i	$0.425537\pi$
$710$	3.54991e15	0.738407
$711$	−1.14156e15	−0.235622
$712$	1.34140e15	0.274737
$713$	−7.92053e15	−1.60976
$714$	−1.85619e13	−0.00374353
$715$	1.57318e15	0.314843
$716$	3.47126e15	0.689390
$717$	3.31495e14	0.0653314
$718$	4.61787e15	0.903144
$719$	4.96793e15	0.964198	0.482099	−	0.876117i	$-0.339874\pi$
$719$	4.96793e15	0.964198	0.482099	+	0.876117i	$0.339874\pi$
$720$	3.08356e15	0.593914
$721$	−1.96597e15	−0.375779
$722$	−6.87120e15	−1.30340
$723$	4.43984e15	0.835809
$724$	3.64937e15	0.681799
$725$	1.14464e16	2.12231
$726$	3.09350e15	0.569245
$727$	5.58242e15	1.01949	0.509745	−	0.860325i	$-0.329740\pi$
$727$	5.58242e15	1.01949	0.509745	+	0.860325i	$0.329740\pi$
$728$	1.11750e15	0.202546
$729$	2.05891e14	0.0370370
$730$	1.01197e16	1.80673
$731$	2.25396e13	0.00399392
$732$	1.94209e15	0.341553
$733$	−3.22472e15	−0.562886	−0.281443	−	0.959578i	$-0.590813\pi$
$733$	−3.22472e15	−0.562886	−0.281443	+	0.959578i	$0.590813\pi$
$734$	−6.97286e15	−1.20804
$735$	8.34547e15	1.43506
$736$	−6.85558e15	−1.17008
$737$	−5.50413e15	−0.932433
$738$	2.68599e14	0.0451643
$739$	−4.12810e15	−0.688979	−0.344489	−	0.938790i	$-0.611948\pi$
$739$	−4.12810e15	−0.688979	−0.344489	+	0.938790i	$0.611948\pi$
$740$	−7.17010e15	−1.18782
$741$	−2.05426e14	−0.0337797
$742$	−2.22036e16	−3.62411
$743$	−2.39676e15	−0.388317	−0.194158	−	0.980970i	$-0.562198\pi$
$743$	−2.39676e15	−0.388317	−0.194158	+	0.980970i	$0.562198\pi$
$744$	−1.89957e15	−0.305495
$745$	1.08272e16	1.72845
$746$	2.50052e15	0.396247
$747$	−3.85915e15	−0.607056
$748$	7.53203e12	0.00117612
$749$	−1.53776e16	−2.38362
$750$	2.21348e15	0.340596
$751$	−4.56496e15	−0.697296	−0.348648	−	0.937254i	$-0.613359\pi$
$751$	−4.56496e15	−0.697296	−0.348648	+	0.937254i	$0.613359\pi$
$752$	2.01775e15	0.305963
$753$	1.21444e15	0.182812
$754$	−5.97193e15	−0.892427
$755$	−8.48778e15	−1.25917
$756$	−1.63693e15	−0.241080
$757$	1.25124e16	1.82941	0.914706	−	0.404119i	$-0.132422\pi$
$757$	1.25124e16	1.82941	0.914706	+	0.404119i	$0.132422\pi$
$758$	1.05219e16	1.52726
$759$	−1.89259e15	−0.272726
$760$	−4.62433e14	−0.0661567
$761$	3.98552e15	0.566070	0.283035	−	0.959110i	$-0.408659\pi$
$761$	3.98552e15	0.566070	0.283035	+	0.959110i	$0.408659\pi$
$762$	8.60648e15	1.21359
$763$	1.59218e16	2.22898
$764$	−4.45315e15	−0.618947
$765$	−1.09656e13	−0.00151320
$766$	1.14614e16	1.57029
$767$	−3.90983e14	−0.0531843
$768$	−5.52123e15	−0.745675
$769$	−6.39979e15	−0.858165	−0.429082	−	0.903265i	$-0.641163\pi$
$769$	−6.39979e15	−0.858165	−0.429082	+	0.903265i	$0.641163\pi$
$770$	−1.25196e16	−1.66683
$771$	5.13879e14	0.0679300
$772$	−1.42058e14	−0.0186454
$773$	−3.99226e14	−0.0520274	−0.0260137	−	0.999662i	$-0.508281\pi$
$773$	−3.99226e14	−0.0520274	−0.0260137	+	0.999662i	$0.508281\pi$
$774$	4.56664e15	0.590910
$775$	−1.74527e16	−2.24235
$776$	4.09092e15	0.521893
$777$	−7.53943e15	−0.955042
$778$	5.04213e15	0.634200
$779$	−1.16762e14	−0.0145829
$780$	−2.21955e15	−0.275261
$781$	−1.51468e15	−0.186526
$782$	3.02785e13	0.00370252
$783$	−2.60191e15	−0.315938
$784$	−1.60196e16	−1.93158
$785$	−4.41062e15	−0.528101
$786$	−3.92168e15	−0.466282
$787$	9.03929e15	1.06727	0.533634	−	0.845716i	$-0.320826\pi$
$787$	9.03929e15	1.06727	0.533634	+	0.845716i	$0.320826\pi$
$788$	−2.35868e15	−0.276551
$789$	5.52957e15	0.643825
$790$	1.23181e16	1.42428
$791$	2.50892e15	0.288082
$792$	−4.53896e14	−0.0517569
$793$	2.76896e15	0.313555
$794$	5.45912e15	0.613917
$795$	−1.31170e16	−1.46492
$796$	5.28902e15	0.586616
$797$	−1.25066e15	−0.137759	−0.0688793	−	0.997625i	$-0.521942\pi$
$797$	−1.25066e15	−0.137759	−0.0688793	+	0.997625i	$0.521942\pi$
$798$	1.63482e15	0.178835
$799$	−7.17545e12	−0.000779546 0
$800$	−1.51061e16	−1.62989
$801$	−2.80149e15	−0.300200
$802$	1.15198e16	1.22599
$803$	−4.31790e15	−0.456391
$804$	7.76562e15	0.815207
$805$	−2.19064e16	−2.28398
$806$	9.10562e15	0.942902
$807$	1.75692e15	0.180696
$808$	3.25088e14	0.0332076
$809$	1.61191e16	1.63540	0.817699	−	0.575645i	$-0.195249\pi$
$809$	1.61191e16	1.63540	0.817699	+	0.575645i	$0.195249\pi$
$810$	−2.22170e15	−0.223881
$811$	1.28888e16	1.29003	0.645013	−	0.764171i	$-0.276852\pi$
$811$	1.28888e16	1.29003	0.645013	+	0.764171i	$0.276852\pi$
$812$	2.06864e16	2.05649
$813$	6.98530e15	0.689742
$814$	7.02865e15	0.689346
$815$	−2.20179e16	−2.14491
$816$	2.10491e13	0.00203675
$817$	−1.98514e15	−0.190797
$818$	1.85113e16	1.76723
$819$	−2.33388e15	−0.221318
$820$	−1.26156e15	−0.118832
$821$	−4.50064e14	−0.0421101	−0.0210551	−	0.999778i	$-0.506703\pi$
$821$	−4.50064e14	−0.0421101	−0.0210551	+	0.999778i	$0.506703\pi$
$822$	−1.27197e16	−1.18218
$823$	4.42512e15	0.408532	0.204266	−	0.978915i	$-0.434519\pi$
$823$	4.42512e15	0.408532	0.204266	+	0.978915i	$0.434519\pi$
$824$	7.69113e14	0.0705327
$825$	−4.17027e15	−0.379898
$826$	3.11151e15	0.281566
$827$	−1.31229e16	−1.17964	−0.589821	−	0.807534i	$-0.700802\pi$
$827$	−1.31229e16	−1.17964	−0.589821	+	0.807534i	$0.700802\pi$
$828$	2.67020e15	0.238439
$829$	1.94702e16	1.72711	0.863556	−	0.504253i	$-0.168232\pi$
$829$	1.94702e16	1.72711	0.863556	+	0.504253i	$0.168232\pi$
$830$	4.16428e16	3.66953
$831$	−5.76816e15	−0.504931
$832$	2.35354e15	0.204665
$833$	5.69683e13	0.00492136
$834$	3.13133e15	0.268729
$835$	−1.68954e16	−1.44043
$836$	−6.63375e14	−0.0561855
$837$	3.96722e15	0.333808
$838$	5.31173e15	0.444011
$839$	−5.38401e15	−0.447111	−0.223555	−	0.974691i	$-0.571766\pi$
$839$	−5.38401e15	−0.447111	−0.223555	+	0.974691i	$0.571766\pi$
$840$	−5.25377e15	−0.433446
$841$	2.06806e16	1.69506
$842$	−4.61803e15	−0.376046
$843$	4.13021e15	0.334134
$844$	−3.16555e15	−0.254429
$845$	1.57978e16	1.26150
$846$	−1.45379e15	−0.115336
$847$	−1.52780e16	−1.20423
$848$	2.51788e16	1.97178
$849$	2.71260e15	0.211054
$850$	6.67180e13	0.00515749
$851$	1.22985e16	0.944580
$852$	2.13701e15	0.163076
$853$	2.47846e16	1.87916	0.939578	−	0.342335i	$-0.111218\pi$
$853$	2.47846e16	1.87916	0.939578	+	0.342335i	$0.111218\pi$
$854$	−2.20358e16	−1.66001
$855$	9.65784e14	0.0722881
$856$	6.01591e15	0.447400
$857$	−4.78471e14	−0.0353558	−0.0176779	−	0.999844i	$-0.505627\pi$
$857$	−4.78471e14	−0.0353558	−0.0176779	+	0.999844i	$0.505627\pi$
$858$	2.17576e15	0.159746
$859$	−1.55690e16	−1.13579	−0.567897	−	0.823100i	$-0.692243\pi$
$859$	−1.55690e16	−1.13579	−0.567897	+	0.823100i	$0.692243\pi$
$860$	−2.14487e16	−1.55475
$861$	−1.32655e15	−0.0955443
$862$	2.65462e16	1.89982
$863$	9.85390e15	0.700727	0.350364	−	0.936614i	$-0.386058\pi$
$863$	9.85390e15	0.700727	0.350364	+	0.936614i	$0.386058\pi$
$864$	3.43381e15	0.242634
$865$	−1.34281e16	−0.942811
$866$	−1.22467e16	−0.854416
$867$	8.32800e15	0.577345
$868$	−3.15413e16	−2.17280
$869$	−5.25592e15	−0.359782
$870$	2.80763e16	1.90978
$871$	1.10719e16	0.748383
$872$	−6.22881e15	−0.418374
$873$	−8.54382e15	−0.570261
$874$	−2.66675e15	−0.176876
$875$	−1.09318e16	−0.720525
$876$	6.09200e15	0.399013
$877$	−5.55455e15	−0.361536	−0.180768	−	0.983526i	$-0.557858\pi$
$877$	−5.55455e15	−0.361536	−0.180768	+	0.983526i	$0.557858\pi$
$878$	1.63282e16	1.05613
$879$	2.26468e14	0.0145569
$880$	1.41972e16	0.906876
$881$	6.25867e15	0.397297	0.198648	−	0.980071i	$-0.436345\pi$
$881$	6.25867e15	0.397297	0.198648	+	0.980071i	$0.436345\pi$
$882$	1.15421e16	0.728127
$883$	−7.69702e15	−0.482546	−0.241273	−	0.970457i	$-0.577565\pi$
$883$	−7.69702e15	−0.482546	−0.241273	+	0.970457i	$0.577565\pi$
$884$	−1.51512e13	−0.000943973 0
$885$	1.83816e15	0.113814
$886$	−1.96617e16	−1.20986
$887$	−1.58445e16	−0.968941	−0.484471	−	0.874807i	$-0.660988\pi$
$887$	−1.58445e16	−0.968941	−0.484471	+	0.874807i	$0.660988\pi$
$888$	2.94952e15	0.179259
$889$	−4.25053e16	−2.56734
$890$	3.02299e16	1.81464
$891$	9.47956e14	0.0565537
$892$	−8.24261e15	−0.488718
$893$	6.31969e14	0.0372403
$894$	1.49745e16	0.876990
$895$	−2.32680e16	−1.35435
$896$	1.66907e16	0.965560
$897$	3.80707e15	0.218893
$898$	3.22853e16	1.84495
$899$	−5.01350e16	−2.84749
$900$	5.88371e15	0.332137
$901$	−8.95399e13	−0.00502378
$902$	1.23667e15	0.0689635
$903$	−2.25535e16	−1.25006
$904$	−9.81523e14	−0.0540722
$905$	−2.44619e16	−1.33944
$906$	−1.17389e16	−0.638886
$907$	−2.40161e16	−1.29916	−0.649580	−	0.760293i	$-0.725055\pi$
$907$	−2.40161e16	−1.29916	−0.649580	+	0.760293i	$0.725055\pi$
$908$	3.85218e15	0.207126
$909$	−6.78941e14	−0.0362853
$910$	2.51840e16	1.33782
$911$	1.15571e16	0.610235	0.305118	−	0.952315i	$-0.401304\pi$
$911$	1.15571e16	0.610235	0.305118	+	0.952315i	$0.401304\pi$
$912$	−1.85388e15	−0.0972993
$913$	−1.77682e16	−0.926944
$914$	−4.59389e16	−2.38219
$915$	−1.30179e16	−0.671004
$916$	−2.16947e16	−1.11155
$917$	1.93682e16	0.986413
$918$	−1.51659e13	−0.000767772 0
$919$	−1.41751e16	−0.713331	−0.356665	−	0.934232i	$-0.616086\pi$
$919$	−1.41751e16	−0.713331	−0.356665	+	0.934232i	$0.616086\pi$
$920$	8.57006e15	0.428697
$921$	1.11105e16	0.552468
$922$	1.59254e16	0.787174
$923$	3.04688e15	0.149708
$924$	−7.53669e15	−0.368116
$925$	2.70994e16	1.31577
$926$	−3.84716e16	−1.85686
$927$	−1.60628e15	−0.0770696
$928$	−4.33941e16	−2.06975
$929$	−1.41176e16	−0.669381	−0.334690	−	0.942328i	$-0.608632\pi$
$929$	−1.41176e16	−0.669381	−0.334690	+	0.942328i	$0.608632\pi$
$930$	−4.28089e16	−2.01780
$931$	−5.01741e15	−0.235102
$932$	1.75824e16	0.819012
$933$	−9.54634e15	−0.442067
$934$	1.42781e16	0.657297
$935$	−5.04875e13	−0.00231058
$936$	9.13044e14	0.0415408
$937$	2.30681e16	1.04338	0.521691	−	0.853135i	$-0.325301\pi$
$937$	2.30681e16	1.04338	0.521691	+	0.853135i	$0.325301\pi$
$938$	−8.81123e16	−3.96206
$939$	8.48913e15	0.379492
$940$	6.82817e15	0.303460
$941$	2.13136e16	0.941704	0.470852	−	0.882212i	$-0.343947\pi$
$941$	2.13136e16	0.941704	0.470852	+	0.882212i	$0.343947\pi$
$942$	−6.10005e15	−0.267950
$943$	2.16389e15	0.0944976
$944$	−3.52845e15	−0.153192
$945$	1.09724e16	0.473617
$946$	2.10256e16	0.902290
$947$	6.27878e15	0.267886	0.133943	−	0.990989i	$-0.457236\pi$
$947$	6.27878e15	0.267886	0.133943	+	0.990989i	$0.457236\pi$
$948$	7.41542e15	0.314550
$949$	8.68575e15	0.366305
$950$	−5.87611e15	−0.246382
$951$	2.25107e16	0.938416
$952$	−3.58635e13	−0.00148645
$953$	−4.84286e15	−0.199568	−0.0997839	−	0.995009i	$-0.531815\pi$
$953$	−4.84286e15	−0.199568	−0.0997839	+	0.995009i	$0.531815\pi$
$954$	−1.81413e16	−0.743280
$955$	2.98496e16	1.21596
$956$	−2.15335e15	−0.0872162
$957$	−1.19796e16	−0.482422
$958$	−1.45666e16	−0.583241
$959$	6.28197e16	2.50088
$960$	−1.10649e16	−0.437980
$961$	5.10340e16	2.00854
$962$	−1.41386e16	−0.553278
$963$	−1.25641e16	−0.488864
$964$	−2.88407e16	−1.11579
$965$	9.52224e14	0.0366301
$966$	−3.02973e16	−1.15886
$967$	5.51501e15	0.209749	0.104875	−	0.994485i	$-0.466556\pi$
$967$	5.51501e15	0.209749	0.104875	+	0.994485i	$0.466556\pi$
$968$	5.97697e15	0.226030
$969$	6.59269e12	0.000247903 0
$970$	9.21934e16	3.44711
$971$	−2.93418e16	−1.09089	−0.545444	−	0.838147i	$-0.683639\pi$
$971$	−2.93418e16	−1.09089	−0.545444	+	0.838147i	$0.683639\pi$
$972$	−1.33744e15	−0.0494437
$973$	−1.54648e16	−0.568493
$974$	−1.34120e16	−0.490253
$975$	8.38878e15	0.304911
$976$	2.49886e16	0.903166
$977$	−3.77338e16	−1.35616	−0.678080	−	0.734988i	$-0.737188\pi$
$977$	−3.77338e16	−1.35616	−0.678080	+	0.734988i	$0.737188\pi$
$978$	−3.04516e16	−1.08829
$979$	−1.28985e16	−0.458390
$980$	−5.42111e16	−1.91578
$981$	1.30088e16	0.457148
$982$	−3.33584e16	−1.16571
$983$	−1.48891e16	−0.517399	−0.258699	−	0.965958i	$-0.583294\pi$
$983$	−1.48891e16	−0.517399	−0.258699	+	0.965958i	$0.583294\pi$
$984$	5.18962e14	0.0179334
$985$	1.58103e16	0.543303
$986$	1.91656e14	0.00654936
$987$	7.17989e15	0.243991
$988$	1.33442e15	0.0450952
$989$	3.67898e16	1.23637
$990$	−1.02291e16	−0.341855
$991$	5.16898e16	1.71791	0.858954	−	0.512053i	$-0.171115\pi$
$991$	5.16898e16	1.71791	0.858954	+	0.512053i	$0.171115\pi$
$992$	6.61645e16	2.18681
$993$	−1.36302e16	−0.448004
$994$	−2.42476e16	−0.792579
$995$	−3.54525e16	−1.15245
$996$	2.50686e16	0.810408
$997$	−3.77168e16	−1.21258	−0.606291	−	0.795243i	$-0.707344\pi$
$997$	−3.77168e16	−1.21258	−0.606291	+	0.795243i	$0.707344\pi$
$998$	−1.92446e15	−0.0615307
$999$	−6.16004e15	−0.195872

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.22	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.22	✓	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)

\(f(q)\)	\(=\)	\(q+60.2204 q^{2} -243.000 q^{3} +1578.50 q^{4} -10580.7 q^{5} -14633.6 q^{6} +72271.5 q^{7} -28273.6 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+60.2204 q^{2} -243.000 q^{3} +1578.50 q^{4} -10580.7 q^{5} -14633.6 q^{6} +72271.5 q^{7} -28273.6 q^{8} +59049.0 q^{9} -637177. q^{10} +271871. q^{11} -383575. q^{12} -546888. q^{13} +4.35222e6 q^{14} +2.57112e6 q^{15} -4.93541e6 q^{16} +17551.1 q^{17} +3.55596e6 q^{18} -1.54579e6 q^{19} -1.67017e7 q^{20} -1.75620e7 q^{21} +1.63722e7 q^{22} +2.86475e7 q^{23} +6.87048e6 q^{24} +6.31240e7 q^{25} -3.29338e7 q^{26} -1.43489e7 q^{27} +1.14080e8 q^{28} +1.81331e8 q^{29} +1.54834e8 q^{30} -2.76482e8 q^{31} -2.39308e8 q^{32} -6.60647e7 q^{33} +1.05694e6 q^{34} -7.64686e8 q^{35} +9.32087e7 q^{36} +4.29304e8 q^{37} -9.30883e7 q^{38} +1.32894e8 q^{39} +2.99156e8 q^{40} +7.55351e7 q^{41} -1.05759e9 q^{42} +1.28422e9 q^{43} +4.29148e8 q^{44} -6.24782e8 q^{45} +1.72516e9 q^{46} -4.08831e8 q^{47} +1.19931e9 q^{48} +3.24585e9 q^{49} +3.80135e9 q^{50} -4.26492e6 q^{51} -8.63261e8 q^{52} -5.10167e9 q^{53} -8.64097e8 q^{54} -2.87660e9 q^{55} -2.04338e9 q^{56} +3.75628e8 q^{57} +1.09199e10 q^{58} +7.14924e8 q^{59} +4.05851e9 q^{60} -5.06312e9 q^{61} -1.66499e10 q^{62} +4.26756e9 q^{63} -4.30352e9 q^{64} +5.78648e9 q^{65} -3.97844e9 q^{66} -2.02454e10 q^{67} +2.77044e7 q^{68} -6.96134e9 q^{69} -4.60497e10 q^{70} -5.57130e9 q^{71} -1.66953e9 q^{72} -1.58821e10 q^{73} +2.58529e10 q^{74} -1.53391e10 q^{75} -2.44003e9 q^{76} +1.96486e10 q^{77} +8.00291e9 q^{78} -1.93324e10 q^{79} +5.22203e10 q^{80} +3.48678e9 q^{81} +4.54875e9 q^{82} -6.53551e10 q^{83} -2.77216e10 q^{84} -1.85704e8 q^{85} +7.73365e10 q^{86} -4.40635e10 q^{87} -7.68678e9 q^{88} -4.74435e10 q^{89} -3.76246e10 q^{90} -3.95244e10 q^{91} +4.52200e10 q^{92} +6.71852e10 q^{93} -2.46200e10 q^{94} +1.63556e10 q^{95} +5.81519e10 q^{96} -1.44690e11 q^{97} +1.95466e11 q^{98} +1.60537e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 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

Modular forms

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Database

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