LMFDB - Embedded newform 177.12.a.b.1.12

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:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-18.7578 q^{2} +243.000 q^{3} -1696.14 q^{4} -6326.10 q^{5} -4558.15 q^{6} -59668.2 q^{7} +70231.9 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-18.7578 q^{2} +243.000 q^{3} -1696.14 q^{4} -6326.10 q^{5} -4558.15 q^{6} -59668.2 q^{7} +70231.9 q^{8} +59049.0 q^{9} +118664. q^{10} -623024. q^{11} -412163. q^{12} +528715. q^{13} +1.11924e6 q^{14} -1.53724e6 q^{15} +2.15631e6 q^{16} +8.97468e6 q^{17} -1.10763e6 q^{18} -1.60580e7 q^{19} +1.07300e7 q^{20} -1.44994e7 q^{21} +1.16866e7 q^{22} +2.78241e7 q^{23} +1.70664e7 q^{24} -8.80856e6 q^{25} -9.91753e6 q^{26} +1.43489e7 q^{27} +1.01206e8 q^{28} +1.64181e8 q^{29} +2.88353e7 q^{30} -1.62798e7 q^{31} -1.84283e8 q^{32} -1.51395e8 q^{33} -1.68345e8 q^{34} +3.77467e8 q^{35} -1.00156e8 q^{36} +2.65231e8 q^{37} +3.01212e8 q^{38} +1.28478e8 q^{39} -4.44294e8 q^{40} +8.26019e8 q^{41} +2.71976e8 q^{42} +1.62764e9 q^{43} +1.05674e9 q^{44} -3.73550e8 q^{45} -5.21918e8 q^{46} -7.37241e8 q^{47} +5.23983e8 q^{48} +1.58297e9 q^{49} +1.65229e8 q^{50} +2.18085e9 q^{51} -8.96777e8 q^{52} -5.01219e9 q^{53} -2.69154e8 q^{54} +3.94131e9 q^{55} -4.19061e9 q^{56} -3.90208e9 q^{57} -3.07968e9 q^{58} -7.14924e8 q^{59} +2.60739e9 q^{60} +1.38051e9 q^{61} +3.05374e8 q^{62} -3.52335e9 q^{63} -9.59383e8 q^{64} -3.34470e9 q^{65} +2.83983e9 q^{66} -1.90823e10 q^{67} -1.52224e10 q^{68} +6.76125e9 q^{69} -7.08045e9 q^{70} +1.84853e10 q^{71} +4.14712e9 q^{72} -7.34829e9 q^{73} -4.97515e9 q^{74} -2.14048e9 q^{75} +2.72366e10 q^{76} +3.71747e10 q^{77} -2.40996e9 q^{78} -8.78770e9 q^{79} -1.36410e10 q^{80} +3.48678e9 q^{81} -1.54943e10 q^{82} +4.09401e10 q^{83} +2.45930e10 q^{84} -5.67747e10 q^{85} -3.05310e10 q^{86} +3.98961e10 q^{87} -4.37562e10 q^{88} +3.82223e10 q^{89} +7.00698e9 q^{90} -3.15475e10 q^{91} -4.71937e10 q^{92} -3.95600e9 q^{93} +1.38290e10 q^{94} +1.01584e11 q^{95} -4.47807e10 q^{96} -9.18220e10 q^{97} -2.96930e10 q^{98} -3.67889e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * 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 $

$2$	−18.7578	−0.414493	−0.207246	−	0.978289i	$-0.566450\pi$
$2$	−18.7578	−0.414493	−0.207246	+	0.978289i	$0.566450\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1696.14	−0.828196
$5$	−6326.10	−0.905318	−0.452659	−	0.891684i	$-0.649525\pi$
$5$	−6326.10	−0.905318	−0.452659	+	0.891684i	$0.649525\pi$
$6$	−4558.15	−0.239308
$7$	−59668.2	−1.34185	−0.670925	−	0.741525i	$-0.734103\pi$
$7$	−59668.2	−1.34185	−0.670925	+	0.741525i	$0.734103\pi$
$8$	70231.9	0.757774
$9$	59049.0	0.333333
$10$	118664.	0.375248
$11$	−623024.	−1.16639	−0.583197	−	0.812331i	$-0.698198\pi$
$11$	−623024.	−1.16639	−0.583197	+	0.812331i	$0.698198\pi$
$12$	−412163.	−0.478159
$13$	528715.	0.394942	0.197471	−	0.980309i	$-0.436727\pi$
$13$	528715.	0.394942	0.197471	+	0.980309i	$0.436727\pi$
$14$	1.11924e6	0.556187
$15$	−1.53724e6	−0.522686
$16$	2.15631e6	0.514104
$17$	8.97468e6	1.53303	0.766513	−	0.642228i	$-0.221990\pi$
$17$	8.97468e6	1.53303	0.766513	+	0.642228i	$0.221990\pi$
$18$	−1.10763e6	−0.138164
$19$	−1.60580e7	−1.48780	−0.743902	−	0.668289i	$-0.767027\pi$
$19$	−1.60580e7	−1.48780	−0.743902	+	0.668289i	$0.767027\pi$
$20$	1.07300e7	0.749780
$21$	−1.44994e7	−0.774717
$22$	1.16866e7	0.483462
$23$	2.78241e7	0.901400	0.450700	−	0.892675i	$-0.351174\pi$
$23$	2.78241e7	0.901400	0.450700	+	0.892675i	$0.351174\pi$
$24$	1.70664e7	0.437501
$25$	−8.80856e6	−0.180399
$26$	−9.91753e6	−0.163700
$27$	1.43489e7	0.192450
$28$	1.01206e8	1.11131
$29$	1.64181e8	1.48640	0.743199	−	0.669071i	$-0.233308\pi$
$29$	1.64181e8	1.48640	0.743199	+	0.669071i	$0.233308\pi$
$30$	2.88353e7	0.216649
$31$	−1.62798e7	−0.102132	−0.0510658	−	0.998695i	$-0.516262\pi$
$31$	−1.62798e7	−0.102132	−0.0510658	+	0.998695i	$0.516262\pi$
$32$	−1.84283e8	−0.970866
$33$	−1.51395e8	−0.673418
$34$	−1.68345e8	−0.635429
$35$	3.77467e8	1.21480
$36$	−1.00156e8	−0.276065
$37$	2.65231e8	0.628803	0.314402	−	0.949290i	$-0.398196\pi$
$37$	2.65231e8	0.628803	0.314402	+	0.949290i	$0.398196\pi$
$38$	3.01212e8	0.616684
$39$	1.28478e8	0.228020
$40$	−4.44294e8	−0.686026
$41$	8.26019e8	1.11347	0.556735	−	0.830690i	$-0.312054\pi$
$41$	8.26019e8	1.11347	0.556735	+	0.830690i	$0.312054\pi$
$42$	2.71976e8	0.321115
$43$	1.62764e9	1.68843	0.844214	−	0.536007i	$-0.180068\pi$
$43$	1.62764e9	1.68843	0.844214	+	0.536007i	$0.180068\pi$
$44$	1.05674e9	0.966002
$45$	−3.73550e8	−0.301773
$46$	−5.21918e8	−0.373624
$47$	−7.37241e8	−0.468891	−0.234445	−	0.972129i	$-0.575327\pi$
$47$	−7.37241e8	−0.468891	−0.234445	+	0.972129i	$0.575327\pi$
$48$	5.23983e8	0.296818
$49$	1.58297e9	0.800560
$50$	1.65229e8	0.0747742
$51$	2.18085e9	0.885094
$52$	−8.96777e8	−0.327089
$53$	−5.01219e9	−1.64630	−0.823152	−	0.567821i	$-0.807787\pi$
$53$	−5.01219e9	−1.64630	−0.823152	+	0.567821i	$0.807787\pi$
$54$	−2.69154e8	−0.0797692
$55$	3.94131e9	1.05596
$56$	−4.19061e9	−1.01682
$57$	−3.90208e9	−0.858983
$58$	−3.07968e9	−0.616101
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	2.60739e9	0.432886
$61$	1.38051e9	0.209280	0.104640	−	0.994510i	$-0.466631\pi$
$61$	1.38051e9	0.209280	0.104640	+	0.994510i	$0.466631\pi$
$62$	3.05374e8	0.0423328
$63$	−3.52335e9	−0.447283
$64$	−9.59383e8	−0.111687
$65$	−3.34470e9	−0.357548
$66$	2.83983e9	0.279127
$67$	−1.90823e10	−1.72671	−0.863356	−	0.504596i	$-0.831641\pi$
$67$	−1.90823e10	−1.72671	−0.863356	+	0.504596i	$0.831641\pi$
$68$	−1.52224e10	−1.26965
$69$	6.76125e9	0.520424
$70$	−7.08045e9	−0.503526
$71$	1.84853e10	1.21592	0.607961	−	0.793967i	$-0.291988\pi$
$71$	1.84853e10	1.21592	0.607961	+	0.793967i	$0.291988\pi$
$72$	4.14712e9	0.252591
$73$	−7.34829e9	−0.414869	−0.207434	−	0.978249i	$-0.566511\pi$
$73$	−7.34829e9	−0.414869	−0.207434	+	0.978249i	$0.566511\pi$
$74$	−4.97515e9	−0.260634
$75$	−2.14048e9	−0.104154
$76$	2.72366e10	1.23219
$77$	3.71747e10	1.56512
$78$	−2.40996e9	−0.0945125
$79$	−8.78770e9	−0.321312	−0.160656	−	0.987010i	$-0.551361\pi$
$79$	−8.78770e9	−0.321312	−0.160656	+	0.987010i	$0.551361\pi$
$80$	−1.36410e10	−0.465428
$81$	3.48678e9	0.111111
$82$	−1.54943e10	−0.461525
$83$	4.09401e10	1.14083	0.570413	−	0.821358i	$-0.306783\pi$
$83$	4.09401e10	1.14083	0.570413	+	0.821358i	$0.306783\pi$
$84$	2.45930e10	0.641617
$85$	−5.67747e10	−1.38788
$86$	−3.05310e10	−0.699841
$87$	3.98961e10	0.858172
$88$	−4.37562e10	−0.883862
$89$	3.82223e10	0.725557	0.362779	−	0.931875i	$-0.381828\pi$
$89$	3.82223e10	0.725557	0.362779	+	0.931875i	$0.381828\pi$
$90$	7.00698e9	0.125083
$91$	−3.15475e10	−0.529952
$92$	−4.71937e10	−0.746536
$93$	−3.95600e9	−0.0589657
$94$	1.38290e10	0.194352
$95$	1.01584e11	1.34693
$96$	−4.47807e10	−0.560530
$97$	−9.18220e10	−1.08568	−0.542840	−	0.839836i	$-0.682651\pi$
$97$	−9.18220e10	−1.08568	−0.542840	+	0.839836i	$0.682651\pi$
$98$	−2.96930e10	−0.331826
$99$	−3.67889e10	−0.388798
$100$	1.49406e10	0.149406
$101$	6.50888e10	0.616224	0.308112	−	0.951350i	$-0.400303\pi$
$101$	6.50888e10	0.616224	0.308112	+	0.951350i	$0.400303\pi$
$102$	−4.09079e10	−0.366865
$103$	4.83624e10	0.411058	0.205529	−	0.978651i	$-0.434109\pi$
$103$	4.83624e10	0.411058	0.205529	+	0.978651i	$0.434109\pi$
$104$	3.71327e10	0.299277
$105$	9.17245e10	0.701365
$106$	9.40177e10	0.682381
$107$	−4.20598e10	−0.289905	−0.144953	−	0.989439i	$-0.546303\pi$
$107$	−4.20598e10	−0.289905	−0.144953	+	0.989439i	$0.546303\pi$
$108$	−2.43378e10	−0.159386
$109$	2.20437e10	0.137227	0.0686135	−	0.997643i	$-0.478142\pi$
$109$	2.20437e10	0.137227	0.0686135	+	0.997643i	$0.478142\pi$
$110$	−7.39304e10	−0.437686
$111$	6.44511e10	0.363040
$112$	−1.28663e11	−0.689850
$113$	1.79343e11	0.915699	0.457850	−	0.889030i	$-0.348620\pi$
$113$	1.79343e11	0.915699	0.457850	+	0.889030i	$0.348620\pi$
$114$	7.31945e10	0.356042
$115$	−1.76018e11	−0.816054
$116$	−2.78475e11	−1.23103
$117$	3.12201e10	0.131647
$118$	1.34104e10	0.0539624
$119$	−5.35503e11	−2.05709
$120$	−1.07964e11	−0.396077
$121$	1.02847e11	0.360474
$122$	−2.58954e10	−0.0867448
$123$	2.00723e11	0.642862
$124$	2.76129e10	0.0845850
$125$	3.64616e11	1.06864
$126$	6.60903e10	0.185396
$127$	1.43876e11	0.386427	0.193214	−	0.981157i	$-0.438109\pi$
$127$	1.43876e11	0.386427	0.193214	+	0.981157i	$0.438109\pi$
$128$	3.95407e11	1.01716
$129$	3.95517e11	0.974814
$130$	6.27393e10	0.148201
$131$	−3.73006e10	−0.0844741	−0.0422371	−	0.999108i	$-0.513448\pi$
$131$	−3.73006e10	−0.0844741	−0.0422371	+	0.999108i	$0.513448\pi$
$132$	2.56788e11	0.557722
$133$	9.58149e11	1.99641
$134$	3.57942e11	0.715709
$135$	−9.07726e10	−0.174229
$136$	6.30309e11	1.16169
$137$	−5.11099e11	−0.904777	−0.452389	−	0.891821i	$-0.649428\pi$
$137$	−5.11099e11	−0.904777	−0.452389	+	0.891821i	$0.649428\pi$
$138$	−1.26826e11	−0.215712
$139$	−6.28312e9	−0.0102706	−0.00513528	−	0.999987i	$-0.501635\pi$
$139$	−6.28312e9	−0.0102706	−0.00513528	+	0.999987i	$0.501635\pi$
$140$	−6.40239e11	−1.00609
$141$	−1.79150e11	−0.270714
$142$	−3.46744e11	−0.503991
$143$	−3.29402e11	−0.460657
$144$	1.27328e11	0.171368
$145$	−1.03863e12	−1.34566
$146$	1.37838e11	0.171960
$147$	3.84661e11	0.462203
$148$	−4.49870e11	−0.520772
$149$	−1.58987e12	−1.77353	−0.886764	−	0.462222i	$-0.847052\pi$
$149$	−1.58987e12	−1.77353	−0.886764	+	0.462222i	$0.847052\pi$
$150$	4.01507e10	0.0431709
$151$	−1.39363e12	−1.44469	−0.722346	−	0.691531i	$-0.756936\pi$
$151$	−1.39363e12	−1.44469	−0.722346	+	0.691531i	$0.756936\pi$
$152$	−1.12778e12	−1.12742
$153$	5.29946e11	0.511009
$154$	−6.97316e11	−0.648733
$155$	1.02988e11	0.0924616
$156$	−2.17917e11	−0.188845
$157$	8.72531e11	0.730017	0.365008	−	0.931004i	$-0.381066\pi$
$157$	8.72531e11	0.730017	0.365008	+	0.931004i	$0.381066\pi$
$158$	1.64838e11	0.133181
$159$	−1.21796e12	−0.950495
$160$	1.16579e12	0.878943
$161$	−1.66021e12	−1.20954
$162$	−6.54044e10	−0.0460548
$163$	−9.01074e11	−0.613379	−0.306689	−	0.951810i	$-0.599221\pi$
$163$	−9.01074e11	−0.613379	−0.306689	+	0.951810i	$0.599221\pi$
$164$	−1.40105e12	−0.922171
$165$	9.57739e11	0.609657
$166$	−7.67946e11	−0.472864
$167$	1.09087e12	0.649879	0.324939	−	0.945735i	$-0.394656\pi$
$167$	1.09087e12	0.649879	0.324939	+	0.945735i	$0.394656\pi$
$168$	−1.01832e12	−0.587060
$169$	−1.51262e12	−0.844021
$170$	1.06497e12	0.575265
$171$	−9.48206e11	−0.495934
$172$	−2.76072e12	−1.39835
$173$	−1.06231e12	−0.521194	−0.260597	−	0.965448i	$-0.583919\pi$
$173$	−1.06231e12	−0.521194	−0.260597	+	0.965448i	$0.583919\pi$
$174$	−7.48363e11	−0.355706
$175$	5.25591e11	0.242069
$176$	−1.34343e12	−0.599647
$177$	−1.73727e11	−0.0751646
$178$	−7.16966e11	−0.300738
$179$	−1.26946e12	−0.516329	−0.258164	−	0.966101i	$-0.583118\pi$
$179$	−1.26946e12	−0.516329	−0.258164	+	0.966101i	$0.583118\pi$
$180$	6.33595e11	0.249927
$181$	2.39028e12	0.914570	0.457285	−	0.889320i	$-0.348822\pi$
$181$	2.39028e12	0.914570	0.457285	+	0.889320i	$0.348822\pi$
$182$	5.91761e11	0.219661
$183$	3.35465e11	0.120828
$184$	1.95414e12	0.683058
$185$	−1.67788e12	−0.569267
$186$	7.42058e10	0.0244409
$187$	−5.59144e12	−1.78811
$188$	1.25047e12	0.388333
$189$	−8.56174e11	−0.258239
$190$	−1.90550e12	−0.558295
$191$	−2.56355e12	−0.729725	−0.364862	−	0.931061i	$-0.618884\pi$
$191$	−2.56355e12	−0.729725	−0.364862	+	0.931061i	$0.618884\pi$
$192$	−2.33130e11	−0.0644825
$193$	2.55408e12	0.686546	0.343273	−	0.939236i	$-0.388464\pi$
$193$	2.55408e12	0.686546	0.343273	+	0.939236i	$0.388464\pi$
$194$	1.72238e12	0.450007
$195$	−8.12763e11	−0.206430
$196$	−2.68494e12	−0.663020
$197$	5.14227e12	1.23478	0.617392	−	0.786656i	$-0.288189\pi$
$197$	5.14227e12	1.23478	0.617392	+	0.786656i	$0.288189\pi$
$198$	6.90080e11	0.161154
$199$	−5.85424e12	−1.32978	−0.664888	−	0.746943i	$-0.731521\pi$
$199$	−5.85424e12	−1.32978	−0.664888	+	0.746943i	$0.731521\pi$
$200$	−6.18642e11	−0.136702
$201$	−4.63700e12	−0.996917
$202$	−1.22092e12	−0.255420
$203$	−9.79641e12	−1.99452
$204$	−3.69903e12	−0.733031
$205$	−5.22548e12	−1.00804
$206$	−9.07172e11	−0.170381
$207$	1.64298e12	0.300467
$208$	1.14007e12	0.203041
$209$	1.00045e13	1.73536
$210$	−1.72055e12	−0.290711
$211$	1.23214e12	0.202819	0.101409	−	0.994845i	$-0.467665\pi$
$211$	1.23214e12	0.202819	0.101409	+	0.994845i	$0.467665\pi$
$212$	8.50140e12	1.36346
$213$	4.49193e12	0.702013
$214$	7.88949e11	0.120164
$215$	−1.02966e13	−1.52856
$216$	1.00775e12	0.145834
$217$	9.71388e11	0.137045
$218$	−4.13492e11	−0.0568796
$219$	−1.78564e12	−0.239525
$220$	−6.68504e12	−0.874539
$221$	4.74505e12	0.605456
$222$	−1.20896e12	−0.150477
$223$	−7.29706e12	−0.886076	−0.443038	−	0.896503i	$-0.646099\pi$
$223$	−7.29706e12	−0.886076	−0.443038	+	0.896503i	$0.646099\pi$
$224$	1.09958e13	1.30276
$225$	−5.20137e11	−0.0601331
$226$	−3.36408e12	−0.379551
$227$	−7.25121e12	−0.798488	−0.399244	−	0.916845i	$-0.630727\pi$
$227$	−7.25121e12	−0.798488	−0.399244	+	0.916845i	$0.630727\pi$
$228$	6.61850e12	0.711406
$229$	−1.60900e13	−1.68834	−0.844170	−	0.536076i	$-0.819906\pi$
$229$	−1.60900e13	−1.68834	−0.844170	+	0.536076i	$0.819906\pi$
$230$	3.30171e12	0.338248
$231$	9.03346e12	0.903625
$232$	1.15308e13	1.12635
$233$	2.77609e12	0.264835	0.132418	−	0.991194i	$-0.457726\pi$
$233$	2.77609e12	0.264835	0.132418	+	0.991194i	$0.457726\pi$
$234$	−5.85620e11	−0.0545668
$235$	4.66386e12	0.424495
$236$	1.21262e12	0.107822
$237$	−2.13541e12	−0.185509
$238$	1.00449e13	0.852649
$239$	−1.58836e13	−1.31753	−0.658767	−	0.752347i	$-0.728922\pi$
$239$	−1.58836e13	−1.31753	−0.658767	+	0.752347i	$0.728922\pi$
$240$	−3.31477e12	−0.268715
$241$	1.69760e13	1.34506	0.672530	−	0.740070i	$-0.265208\pi$
$241$	1.69760e13	1.34506	0.672530	+	0.740070i	$0.265208\pi$
$242$	−1.92919e12	−0.149414
$243$	8.47289e11	0.0641500
$244$	−2.34155e12	−0.173324
$245$	−1.00140e13	−0.724761
$246$	−3.76511e12	−0.266462
$247$	−8.49008e12	−0.587596
$248$	−1.14336e12	−0.0773927
$249$	9.94844e12	0.658656
$250$	−6.83939e12	−0.442942
$251$	−1.71441e13	−1.08620	−0.543099	−	0.839669i	$-0.682749\pi$
$251$	−1.71441e13	−1.08620	−0.543099	+	0.839669i	$0.682749\pi$
$252$	5.97611e12	0.370438
$253$	−1.73351e13	−1.05139
$254$	−2.69880e12	−0.160171
$255$	−1.37963e13	−0.801291
$256$	−5.45214e12	−0.309918
$257$	−1.41542e13	−0.787507	−0.393754	−	0.919216i	$-0.628824\pi$
$257$	−1.41542e13	−0.787507	−0.393754	+	0.919216i	$0.628824\pi$
$258$	−7.41903e12	−0.404053
$259$	−1.58259e13	−0.843759
$260$	5.67310e12	0.296120
$261$	9.69475e12	0.495466
$262$	6.99677e11	0.0350139
$263$	1.53226e13	0.750887	0.375444	−	0.926845i	$-0.377490\pi$
$263$	1.53226e13	0.750887	0.375444	+	0.926845i	$0.377490\pi$
$264$	−1.06328e13	−0.510298
$265$	3.17076e13	1.49043
$266$	−1.79728e13	−0.827496
$267$	9.28802e12	0.418901
$268$	3.23664e13	1.43005
$269$	−2.27171e13	−0.983365	−0.491683	−	0.870775i	$-0.663618\pi$
$269$	−2.27171e13	−0.983365	−0.491683	+	0.870775i	$0.663618\pi$
$270$	1.70270e12	0.0722165
$271$	1.49874e13	0.622869	0.311434	−	0.950268i	$-0.399191\pi$
$271$	1.49874e13	0.622869	0.311434	+	0.950268i	$0.399191\pi$
$272$	1.93522e13	0.788135
$273$	−7.66603e12	−0.305968
$274$	9.58709e12	0.375024
$275$	5.48795e12	0.210417
$276$	−1.14681e13	−0.431013
$277$	3.51795e13	1.29614	0.648068	−	0.761583i	$-0.275577\pi$
$277$	3.51795e13	1.29614	0.648068	+	0.761583i	$0.275577\pi$
$278$	1.17858e11	0.00425707
$279$	−9.61307e11	−0.0340439
$280$	2.65102e13	0.920544
$281$	8.76473e12	0.298438	0.149219	−	0.988804i	$-0.452324\pi$
$281$	8.76473e12	0.298438	0.149219	+	0.988804i	$0.452324\pi$
$282$	3.36045e12	0.112209
$283$	2.93454e13	0.960981	0.480491	−	0.877000i	$-0.340459\pi$
$283$	2.93454e13	0.960981	0.480491	+	0.877000i	$0.340459\pi$
$284$	−3.13538e13	−1.00702
$285$	2.46850e13	0.777653
$286$	6.17886e12	0.190939
$287$	−4.92870e13	−1.49411
$288$	−1.08817e13	−0.323622
$289$	4.62729e13	1.35017
$290$	1.94824e13	0.557767
$291$	−2.23127e13	−0.626818
$292$	1.24638e13	0.343593
$293$	−1.32769e13	−0.359191	−0.179596	−	0.983741i	$-0.557479\pi$
$293$	−1.32769e13	−0.359191	−0.179596	+	0.983741i	$0.557479\pi$
$294$	−7.21540e12	−0.191580
$295$	4.52268e12	0.117862
$296$	1.86277e13	0.476491
$297$	−8.93971e12	−0.224473
$298$	2.98225e13	0.735115
$299$	1.47110e13	0.356001
$300$	3.63057e12	0.0862596
$301$	−9.71185e13	−2.26562
$302$	2.61415e13	0.598815
$303$	1.58166e13	0.355777
$304$	−3.46259e13	−0.764885
$305$	−8.73327e12	−0.189465
$306$	−9.94062e12	−0.211810
$307$	8.01846e13	1.67815	0.839074	−	0.544018i	$-0.183098\pi$
$307$	8.01846e13	1.67815	0.839074	+	0.544018i	$0.183098\pi$
$308$	−6.30537e13	−1.29623
$309$	1.17521e13	0.237324
$310$	−1.93182e12	−0.0383247
$311$	−5.11605e13	−0.997132	−0.498566	−	0.866852i	$-0.666140\pi$
$311$	−5.11605e13	−0.997132	−0.498566	+	0.866852i	$0.666140\pi$
$312$	9.02324e12	0.172787
$313$	1.16380e13	0.218970	0.109485	−	0.993988i	$-0.465080\pi$
$313$	1.16380e13	0.218970	0.109485	+	0.993988i	$0.465080\pi$
$314$	−1.63668e13	−0.302587
$315$	2.22891e13	0.404933
$316$	1.49052e13	0.266109
$317$	3.66542e13	0.643129	0.321565	−	0.946888i	$-0.395791\pi$
$317$	3.66542e13	0.643129	0.321565	+	0.946888i	$0.395791\pi$
$318$	2.28463e13	0.393973
$319$	−1.02289e14	−1.73372
$320$	6.06916e12	0.101112
$321$	−1.02205e13	−0.167377
$322$	3.11419e13	0.501347
$323$	−1.44115e14	−2.28084
$324$	−5.91409e12	−0.0920218
$325$	−4.65722e12	−0.0712472
$326$	1.69022e13	0.254241
$327$	5.35663e12	0.0792280
$328$	5.80129e13	0.843759
$329$	4.39899e13	0.629181
$330$	−1.79651e13	−0.252698
$331$	−5.91325e13	−0.818035	−0.409018	−	0.912526i	$-0.634129\pi$
$331$	−5.91325e13	−0.818035	−0.409018	+	0.912526i	$0.634129\pi$
$332$	−6.94403e13	−0.944827
$333$	1.56616e13	0.209601
$334$	−2.04623e13	−0.269370
$335$	1.20717e14	1.56322
$336$	−3.12651e13	−0.398285
$337$	6.68543e12	0.0837847	0.0418924	−	0.999122i	$-0.486661\pi$
$337$	6.68543e12	0.0837847	0.0418924	+	0.999122i	$0.486661\pi$
$338$	2.83734e13	0.349841
$339$	4.35803e13	0.528679
$340$	9.62982e13	1.14943
$341$	1.01427e13	0.119126
$342$	1.77863e13	0.205561
$343$	2.35307e13	0.267619
$344$	1.14312e14	1.27945
$345$	−4.27724e13	−0.471149
$346$	1.99267e13	0.216031
$347$	−4.83060e13	−0.515453	−0.257727	−	0.966218i	$-0.582973\pi$
$347$	−4.83060e13	−0.515453	−0.257727	+	0.966218i	$0.582973\pi$
$348$	−6.76695e13	−0.710734
$349$	4.03826e13	0.417498	0.208749	−	0.977969i	$-0.433061\pi$
$349$	4.03826e13	0.417498	0.208749	+	0.977969i	$0.433061\pi$
$350$	−9.85893e12	−0.100336
$351$	7.58648e12	0.0760066
$352$	1.14812e14	1.13241
$353$	−4.44917e13	−0.432034	−0.216017	−	0.976390i	$-0.569307\pi$
$353$	−4.44917e13	−0.432034	−0.216017	+	0.976390i	$0.569307\pi$
$354$	3.25873e12	0.0311552
$355$	−1.16940e14	−1.10080
$356$	−6.48306e13	−0.600904
$357$	−1.30127e14	−1.18766
$358$	2.38122e13	0.214015
$359$	2.44086e13	0.216035	0.108017	−	0.994149i	$-0.465550\pi$
$359$	2.44086e13	0.216035	0.108017	+	0.994149i	$0.465550\pi$
$360$	−2.62351e13	−0.228675
$361$	1.41368e14	1.21356
$362$	−4.48364e13	−0.379083
$363$	2.49919e13	0.208119
$364$	5.35091e13	0.438904
$365$	4.64861e13	0.375588
$366$	−6.29258e12	−0.0500822
$367$	−1.78838e14	−1.40215	−0.701077	−	0.713086i	$-0.747297\pi$
$367$	−1.78838e14	−1.40215	−0.701077	+	0.713086i	$0.747297\pi$
$368$	5.99973e13	0.463413
$369$	4.87756e13	0.371157
$370$	3.14733e13	0.235957
$371$	2.99068e14	2.20909
$372$	6.70994e12	0.0488352
$373$	1.62695e14	1.16674	0.583371	−	0.812206i	$-0.301733\pi$
$373$	1.62695e14	1.16674	0.583371	+	0.812206i	$0.301733\pi$
$374$	1.04883e14	0.741160
$375$	8.86016e13	0.616978
$376$	−5.17779e13	−0.355313
$377$	8.68051e13	0.587040
$378$	1.60599e13	0.107038
$379$	2.00828e14	1.31919	0.659596	−	0.751620i	$-0.270727\pi$
$379$	2.00828e14	1.31919	0.659596	+	0.751620i	$0.270727\pi$
$380$	−1.72302e14	−1.11553
$381$	3.49618e13	0.223104
$382$	4.80867e13	0.302466
$383$	3.29956e13	0.204580	0.102290	−	0.994755i	$-0.467383\pi$
$383$	3.29956e13	0.204580	0.102290	+	0.994755i	$0.467383\pi$
$384$	9.60838e13	0.587257
$385$	−2.35171e14	−1.41694
$386$	−4.79090e13	−0.284568
$387$	9.61106e13	0.562809
$388$	1.55743e14	0.899156
$389$	−2.55943e14	−1.45687	−0.728435	−	0.685114i	$-0.759752\pi$
$389$	−2.55943e14	−1.45687	−0.728435	+	0.685114i	$0.759752\pi$
$390$	1.52456e13	0.0855639
$391$	2.49712e14	1.38187
$392$	1.11175e14	0.606643
$393$	−9.06405e12	−0.0487712
$394$	−9.64577e13	−0.511809
$395$	5.55919e13	0.290889
$396$	6.23994e13	0.322001
$397$	2.41106e14	1.22704	0.613522	−	0.789678i	$-0.289752\pi$
$397$	2.41106e14	1.22704	0.613522	+	0.789678i	$0.289752\pi$
$398$	1.09813e14	0.551182
$399$	2.32830e14	1.15263
$400$	−1.89940e13	−0.0927440
$401$	2.65952e14	1.28088	0.640441	−	0.768007i	$-0.278751\pi$
$401$	2.65952e14	1.28088	0.640441	+	0.768007i	$0.278751\pi$
$402$	8.69800e13	0.413215
$403$	−8.60738e12	−0.0403360
$404$	−1.10400e14	−0.510354
$405$	−2.20578e13	−0.100591
$406$	1.83759e14	0.826715
$407$	−1.65245e14	−0.733432
$408$	1.53165e14	0.670701
$409$	−1.75601e14	−0.758665	−0.379332	−	0.925260i	$-0.623846\pi$
$409$	−1.75601e14	−0.758665	−0.379332	+	0.925260i	$0.623846\pi$
$410$	9.80185e13	0.417827
$411$	−1.24197e14	−0.522373
$412$	−8.20296e13	−0.340436
$413$	4.26583e13	0.174694
$414$	−3.08188e13	−0.124541
$415$	−2.58991e14	−1.03281
$416$	−9.74329e13	−0.383436
$417$	−1.52680e12	−0.00592971
$418$	−1.87662e14	−0.719296
$419$	−2.79295e14	−1.05654	−0.528270	−	0.849076i	$-0.677159\pi$
$419$	−2.79295e14	−1.05654	−0.528270	+	0.849076i	$0.677159\pi$
$420$	−1.55578e14	−0.580868
$421$	−3.58421e14	−1.32082	−0.660408	−	0.750907i	$-0.729617\pi$
$421$	−3.58421e14	−1.32082	−0.660408	+	0.750907i	$0.729617\pi$
$422$	−2.31123e13	−0.0840668
$423$	−4.35334e13	−0.156297
$424$	−3.52016e14	−1.24753
$425$	−7.90540e13	−0.276557
$426$	−8.42588e13	−0.290979
$427$	−8.23728e13	−0.280822
$428$	7.13395e13	0.240098
$429$	−8.00447e13	−0.265961
$430$	1.93142e14	0.633579
$431$	5.72779e14	1.85508	0.927539	−	0.373725i	$-0.121920\pi$
$431$	5.72779e14	1.85508	0.927539	+	0.373725i	$0.121920\pi$
$432$	3.09407e13	0.0989394
$433$	3.58056e14	1.13049	0.565246	−	0.824922i	$-0.308781\pi$
$433$	3.58056e14	1.13049	0.565246	+	0.824922i	$0.308781\pi$
$434$	−1.82211e13	−0.0568043
$435$	−2.52387e14	−0.776919
$436$	−3.73894e13	−0.113651
$437$	−4.46798e14	−1.34111
$438$	3.34946e13	0.0992812
$439$	7.80496e13	0.228463	0.114231	−	0.993454i	$-0.463559\pi$
$439$	7.80496e13	0.228463	0.114231	+	0.993454i	$0.463559\pi$
$440$	2.76806e14	0.800177
$441$	9.34727e13	0.266853
$442$	−8.90066e13	−0.250957
$443$	−1.83273e14	−0.510362	−0.255181	−	0.966893i	$-0.582135\pi$
$443$	−1.83273e14	−0.510362	−0.255181	+	0.966893i	$0.582135\pi$
$444$	−1.09318e14	−0.300668
$445$	−2.41798e14	−0.656860
$446$	1.36877e14	0.367272
$447$	−3.86339e14	−1.02395
$448$	5.72447e13	0.149867
$449$	6.91658e13	0.178870	0.0894349	−	0.995993i	$-0.471494\pi$
$449$	6.91658e13	0.178870	0.0894349	+	0.995993i	$0.471494\pi$
$450$	9.75662e12	0.0249247
$451$	−5.14629e14	−1.29874
$452$	−3.04192e14	−0.758378
$453$	−3.38653e14	−0.834094
$454$	1.36017e14	0.330967
$455$	1.99572e14	0.479775
$456$	−2.74051e14	−0.650915
$457$	−9.59403e12	−0.0225145	−0.0112572	−	0.999937i	$-0.503583\pi$
$457$	−9.59403e12	−0.0225145	−0.0112572	+	0.999937i	$0.503583\pi$
$458$	3.01812e14	0.699805
$459$	1.28777e14	0.295031
$460$	2.98552e14	0.675852
$461$	3.95833e14	0.885436	0.442718	−	0.896661i	$-0.354014\pi$
$461$	3.95833e14	0.885436	0.442718	+	0.896661i	$0.354014\pi$
$462$	−1.69448e14	−0.374546
$463$	6.66262e14	1.45529	0.727645	−	0.685954i	$-0.240615\pi$
$463$	6.66262e14	1.45529	0.727645	+	0.685954i	$0.240615\pi$
$464$	3.54026e14	0.764163
$465$	2.50260e13	0.0533827
$466$	−5.20733e13	−0.109772
$467$	−5.46946e14	−1.13947	−0.569733	−	0.821830i	$-0.692953\pi$
$467$	−5.46946e14	−1.13947	−0.569733	+	0.821830i	$0.692953\pi$
$468$	−5.29538e13	−0.109030
$469$	1.13861e15	2.31699
$470$	−8.74838e13	−0.175950
$471$	2.12025e14	0.421475
$472$	−5.02105e13	−0.0986538
$473$	−1.01406e15	−1.96937
$474$	4.00556e13	0.0768923
$475$	1.41448e14	0.268399
$476$	9.08291e14	1.70367
$477$	−2.95965e14	−0.548768
$478$	2.97942e14	0.546108
$479$	−6.19015e14	−1.12165	−0.560823	−	0.827936i	$-0.689515\pi$
$479$	−6.19015e14	−1.12165	−0.560823	+	0.827936i	$0.689515\pi$
$480$	2.83287e14	0.507458
$481$	1.40232e14	0.248341
$482$	−3.18433e14	−0.557518
$483$	−4.03432e14	−0.698330
$484$	−1.74444e14	−0.298543
$485$	5.80875e14	0.982886
$486$	−1.58933e13	−0.0265897
$487$	−7.04223e14	−1.16493	−0.582467	−	0.812855i	$-0.697912\pi$
$487$	−7.04223e14	−1.16493	−0.582467	+	0.812855i	$0.697912\pi$
$488$	9.69562e13	0.158587
$489$	−2.18961e14	−0.354135
$490$	1.87841e14	0.300408
$491$	−7.66078e14	−1.21150	−0.605752	−	0.795653i	$-0.707128\pi$
$491$	−7.66078e14	−1.21150	−0.605752	+	0.795653i	$0.707128\pi$
$492$	−3.40454e14	−0.532416
$493$	1.47348e15	2.27869
$494$	1.59255e14	0.243554
$495$	2.32731e14	0.351986
$496$	−3.51043e13	−0.0525063
$497$	−1.10299e15	−1.63159
$498$	−1.86611e14	−0.273008
$499$	−6.43649e13	−0.0931314	−0.0465657	−	0.998915i	$-0.514828\pi$
$499$	−6.43649e13	−0.0931314	−0.0465657	+	0.998915i	$0.514828\pi$
$500$	−6.18441e14	−0.885040
$501$	2.65081e14	0.375208
$502$	3.21585e14	0.450221
$503$	−1.10390e14	−0.152864	−0.0764322	−	0.997075i	$-0.524353\pi$
$503$	−1.10390e14	−0.152864	−0.0764322	+	0.997075i	$0.524353\pi$
$504$	−2.47452e14	−0.338939
$505$	−4.11758e14	−0.557879
$506$	3.25168e14	0.435792
$507$	−3.67567e14	−0.487296
$508$	−2.44034e14	−0.320037
$509$	1.83785e14	0.238430	0.119215	−	0.992868i	$-0.461962\pi$
$509$	1.83785e14	0.238430	0.119215	+	0.992868i	$0.461962\pi$
$510$	2.58787e14	0.332129
$511$	4.38459e14	0.556691
$512$	−7.07523e14	−0.888701
$513$	−2.30414e14	−0.286328
$514$	2.65503e14	0.326416
$515$	−3.05945e14	−0.372138
$516$	−6.70854e14	−0.807337
$517$	4.59319e14	0.546911
$518$	2.96858e14	0.349732
$519$	−2.58142e14	−0.300912
$520$	−2.34905e14	−0.270940
$521$	1.42304e15	1.62409	0.812043	−	0.583597i	$-0.198355\pi$
$521$	1.42304e15	1.62409	0.812043	+	0.583597i	$0.198355\pi$
$522$	−1.81852e14	−0.205367
$523$	1.72810e15	1.93112	0.965558	−	0.260188i	$-0.0837844\pi$
$523$	1.72810e15	1.93112	0.965558	+	0.260188i	$0.0837844\pi$
$524$	6.32672e13	0.0699611
$525$	1.27719e14	0.139758
$526$	−2.87417e14	−0.311237
$527$	−1.46106e14	−0.156571
$528$	−3.26454e14	−0.346207
$529$	−1.78631e14	−0.187478
$530$	−5.94765e14	−0.617772
$531$	−4.22156e13	−0.0433963
$532$	−1.62516e15	−1.65342
$533$	4.36728e14	0.439756
$534$	−1.74223e14	−0.173631
$535$	2.66075e14	0.262457
$536$	−1.34019e15	−1.30846
$537$	−3.08478e14	−0.298103
$538$	4.26122e14	0.407598
$539$	−9.86227e14	−0.933768
$540$	1.53964e14	0.144295
$541$	1.38184e15	1.28195	0.640977	−	0.767560i	$-0.278529\pi$
$541$	1.38184e15	1.28195	0.640977	+	0.767560i	$0.278529\pi$
$542$	−2.81132e14	−0.258175
$543$	5.80839e14	0.528027
$544$	−1.65388e15	−1.48836
$545$	−1.39451e14	−0.124234
$546$	1.43798e14	0.126822
$547$	−1.56163e15	−1.36348	−0.681738	−	0.731596i	$-0.738776\pi$
$547$	−1.56163e15	−1.36348	−0.681738	+	0.731596i	$0.738776\pi$
$548$	8.66898e14	0.749333
$549$	8.15180e13	0.0697598
$550$	−1.02942e14	−0.0872162
$551$	−2.63642e15	−2.21147
$552$	4.74856e14	0.394363
$553$	5.24347e14	0.431152
$554$	−6.59889e14	−0.537239
$555$	−4.07724e14	−0.328666
$556$	1.06571e13	0.00850604
$557$	8.19309e13	0.0647507	0.0323753	−	0.999476i	$-0.489693\pi$
$557$	8.19309e13	0.0647507	0.0323753	+	0.999476i	$0.489693\pi$
$558$	1.80320e13	0.0141109
$559$	8.60558e14	0.666830
$560$	8.13936e14	0.624534
$561$	−1.35872e15	−1.03237
$562$	−1.64407e14	−0.123700
$563$	1.44215e15	1.07452	0.537260	−	0.843417i	$-0.319459\pi$
$563$	1.44215e15	1.07452	0.537260	+	0.843417i	$0.319459\pi$
$564$	3.03864e14	0.224204
$565$	−1.13454e15	−0.828999
$566$	−5.50456e14	−0.398320
$567$	−2.08050e14	−0.149094
$568$	1.29826e15	0.921395
$569$	−1.65138e15	−1.16073	−0.580364	−	0.814357i	$-0.697090\pi$
$569$	−1.65138e15	−1.16073	−0.580364	+	0.814357i	$0.697090\pi$
$570$	−4.63036e14	−0.322332
$571$	−3.40796e14	−0.234961	−0.117481	−	0.993075i	$-0.537482\pi$
$571$	−3.40796e14	−0.234961	−0.117481	+	0.993075i	$0.537482\pi$
$572$	5.58714e14	0.381515
$573$	−6.22944e14	−0.421307
$574$	9.24517e14	0.619297
$575$	−2.45090e14	−0.162612
$576$	−5.66506e13	−0.0372290
$577$	−1.73380e15	−1.12858	−0.564290	−	0.825577i	$-0.690850\pi$
$577$	−1.73380e15	−1.12858	−0.564290	+	0.825577i	$0.690850\pi$
$578$	−8.67979e14	−0.559636
$579$	6.20642e14	0.396378
$580$	1.76166e15	1.11447
$581$	−2.44282e15	−1.53082
$582$	4.18538e14	0.259812
$583$	3.12271e15	1.92024
$584$	−5.16085e14	−0.314377
$585$	−1.97501e14	−0.119183
$586$	2.49046e14	0.148882
$587$	1.20999e14	0.0716590	0.0358295	−	0.999358i	$-0.488593\pi$
$587$	1.20999e14	0.0716590	0.0358295	+	0.999358i	$0.488593\pi$
$588$	−6.52441e14	−0.382795
$589$	2.61421e14	0.151952
$590$	−8.48356e13	−0.0488531
$591$	1.24957e15	0.712903
$592$	5.71920e14	0.323270
$593$	−1.87568e15	−1.05041	−0.525205	−	0.850976i	$-0.676011\pi$
$593$	−1.87568e15	−1.05041	−0.525205	+	0.850976i	$0.676011\pi$
$594$	1.67689e14	0.0930422
$595$	3.38765e15	1.86232
$596$	2.69666e15	1.46883
$597$	−1.42258e15	−0.767746
$598$	−2.75946e14	−0.147560
$599$	−2.77141e15	−1.46843	−0.734215	−	0.678917i	$-0.762449\pi$
$599$	−2.77141e15	−1.46843	−0.734215	+	0.678917i	$0.762449\pi$
$600$	−1.50330e14	−0.0789249
$601$	−2.64870e15	−1.37792	−0.688958	−	0.724801i	$-0.741932\pi$
$601$	−2.64870e15	−1.37792	−0.688958	+	0.724801i	$0.741932\pi$
$602$	1.82173e15	0.939081
$603$	−1.12679e15	−0.575570
$604$	2.36381e15	1.19649
$605$	−6.50623e14	−0.326343
$606$	−2.96684e14	−0.147467
$607$	−3.55601e15	−1.75156	−0.875780	−	0.482710i	$-0.839652\pi$
$607$	−3.55601e15	−1.75156	−0.875780	+	0.482710i	$0.839652\pi$
$608$	2.95920e15	1.44446
$609$	−2.38053e15	−1.15154
$610$	1.63817e14	0.0785317
$611$	−3.89790e14	−0.185184
$612$	−8.98865e14	−0.423215
$613$	1.55534e14	0.0725761	0.0362881	−	0.999341i	$-0.488447\pi$
$613$	1.55534e14	0.0725761	0.0362881	+	0.999341i	$0.488447\pi$
$614$	−1.50409e15	−0.695580
$615$	−1.26979e15	−0.581995
$616$	2.61085e15	1.18601
$617$	6.40049e14	0.288167	0.144084	−	0.989566i	$-0.453977\pi$
$617$	6.40049e14	0.288167	0.144084	+	0.989566i	$0.453977\pi$
$618$	−2.20443e14	−0.0983692
$619$	−9.15332e14	−0.404837	−0.202418	−	0.979299i	$-0.564880\pi$
$619$	−9.15332e14	−0.404837	−0.202418	+	0.979299i	$0.564880\pi$
$620$	−1.74682e14	−0.0765763
$621$	3.99245e14	0.173475
$622$	9.59659e14	0.413304
$623$	−2.28066e15	−0.973589
$624$	2.77038e14	0.117226
$625$	−1.87649e15	−0.787057
$626$	−2.18303e14	−0.0907615
$627$	2.43109e15	1.00191
$628$	−1.47994e15	−0.604597
$629$	2.38036e15	0.963972
$630$	−4.18094e14	−0.167842
$631$	−4.83096e15	−1.92252	−0.961262	−	0.275637i	$-0.911111\pi$
$631$	−4.83096e15	−1.92252	−0.961262	+	0.275637i	$0.911111\pi$
$632$	−6.17177e14	−0.243482
$633$	2.99411e14	0.117097
$634$	−6.87553e14	−0.266572
$635$	−9.10174e14	−0.349839
$636$	2.06584e15	0.787196
$637$	8.36939e14	0.316174
$638$	1.91872e15	0.718616
$639$	1.09154e15	0.405308
$640$	−2.50138e15	−0.920853
$641$	−4.80211e15	−1.75272	−0.876361	−	0.481656i	$-0.840036\pi$
$641$	−4.80211e15	−1.75272	−0.876361	+	0.481656i	$0.840036\pi$
$642$	1.91715e14	0.0693765
$643$	2.91474e15	1.04578	0.522889	−	0.852401i	$-0.324854\pi$
$643$	2.91474e15	1.04578	0.522889	+	0.852401i	$0.324854\pi$
$644$	2.81596e15	1.00174
$645$	−2.50208e15	−0.882517
$646$	2.70328e15	0.945393
$647$	4.69134e15	1.62676	0.813380	−	0.581732i	$-0.197625\pi$
$647$	4.69134e15	1.62676	0.813380	+	0.581732i	$0.197625\pi$
$648$	2.44884e14	0.0841971
$649$	4.45415e14	0.151851
$650$	8.73592e13	0.0295315
$651$	2.36047e14	0.0791231
$652$	1.52835e15	0.507998
$653$	1.45232e15	0.478675	0.239338	−	0.970936i	$-0.423070\pi$
$653$	1.45232e15	0.478675	0.239338	+	0.970936i	$0.423070\pi$
$654$	−1.00479e14	−0.0328394
$655$	2.35967e14	0.0764759
$656$	1.78115e15	0.572439
$657$	−4.33909e14	−0.138290
$658$	−8.25153e14	−0.260791
$659$	5.40645e15	1.69450	0.847252	−	0.531191i	$-0.178255\pi$
$659$	5.40645e15	1.69450	0.847252	+	0.531191i	$0.178255\pi$
$660$	−1.62446e15	−0.504915
$661$	−5.16445e15	−1.59190	−0.795950	−	0.605363i	$-0.793028\pi$
$661$	−5.16445e15	−1.59190	−0.795950	+	0.605363i	$0.793028\pi$
$662$	1.10920e15	0.339070
$663$	1.15305e15	0.349560
$664$	2.87530e15	0.864488
$665$	−6.06135e15	−1.80738
$666$	−2.93778e14	−0.0868781
$667$	4.56820e15	1.33984
$668$	−1.85027e15	−0.538227
$669$	−1.77319e15	−0.511576
$670$	−2.26438e15	−0.647944
$671$	−8.60093e14	−0.244102
$672$	2.67198e15	0.752147
$673$	1.36310e15	0.380580	0.190290	−	0.981728i	$-0.439057\pi$
$673$	1.36310e15	0.380580	0.190290	+	0.981728i	$0.439057\pi$
$674$	−1.25404e14	−0.0347282
$675$	−1.26393e14	−0.0347179
$676$	2.56562e15	0.699015
$677$	3.81268e15	1.03037	0.515184	−	0.857080i	$-0.327724\pi$
$677$	3.81268e15	1.03037	0.515184	+	0.857080i	$0.327724\pi$
$678$	−8.17471e14	−0.219134
$679$	5.47885e15	1.45682
$680$	−3.98740e15	−1.05170
$681$	−1.76204e15	−0.461007
$682$	−1.90255e14	−0.0493767
$683$	5.05328e14	0.130095	0.0650474	−	0.997882i	$-0.479280\pi$
$683$	5.05328e14	0.130095	0.0650474	+	0.997882i	$0.479280\pi$
$684$	1.60830e15	0.410731
$685$	3.23326e15	0.819111
$686$	−4.41383e14	−0.110926
$687$	−3.90986e15	−0.974764
$688$	3.50970e15	0.868027
$689$	−2.65002e15	−0.650194
$690$	8.02315e14	0.195288
$691$	4.43928e15	1.07197	0.535986	−	0.844227i	$-0.319940\pi$
$691$	4.43928e15	1.07197	0.535986	+	0.844227i	$0.319940\pi$
$692$	1.80184e15	0.431651
$693$	2.19513e15	0.521708
$694$	9.06115e14	0.213652
$695$	3.97477e13	0.00929813
$696$	2.80198e15	0.650300
$697$	7.41325e15	1.70698
$698$	−7.57489e14	−0.173050
$699$	6.74590e14	0.152903
$700$	−8.91479e14	−0.200480
$701$	−1.42493e15	−0.317940	−0.158970	−	0.987283i	$-0.550817\pi$
$701$	−1.42493e15	−0.317940	−0.158970	+	0.987283i	$0.550817\pi$
$702$	−1.42306e14	−0.0315042
$703$	−4.25907e15	−0.935535
$704$	5.97719e14	0.130271
$705$	1.13332e15	0.245082
$706$	8.34566e14	0.179075
$707$	−3.88373e15	−0.826880
$708$	2.94665e14	0.0622510
$709$	−4.12853e14	−0.0865449	−0.0432725	−	0.999063i	$-0.513778\pi$
$709$	−4.12853e14	−0.0865449	−0.0432725	+	0.999063i	$0.513778\pi$
$710$	2.19354e15	0.456272
$711$	−5.18905e14	−0.107104
$712$	2.68443e15	0.549808
$713$	−4.52971e14	−0.0920615
$714$	2.44090e15	0.492277
$715$	2.08383e15	0.417041
$716$	2.15318e15	0.427621
$717$	−3.85973e15	−0.760678
$718$	−4.57852e14	−0.0895448
$719$	7.07599e15	1.37334	0.686670	−	0.726969i	$-0.259072\pi$
$719$	7.07599e15	1.37334	0.686670	+	0.726969i	$0.259072\pi$
$720$	−8.05489e14	−0.155143
$721$	−2.88570e15	−0.551578
$722$	−2.65175e15	−0.503011
$723$	4.12517e15	0.776571
$724$	−4.05427e15	−0.757443
$725$	−1.44620e15	−0.268145
$726$	−4.68793e14	−0.0862640
$727$	−9.41983e15	−1.72030	−0.860149	−	0.510042i	$-0.829630\pi$
$727$	−9.41983e15	−1.72030	−0.860149	+	0.510042i	$0.829630\pi$
$728$	−2.21564e15	−0.401584
$729$	2.05891e14	0.0370370
$730$	−8.71976e14	−0.155679
$731$	1.46076e16	2.58840
$732$	−5.68997e14	−0.100069
$733$	1.10606e15	0.193066	0.0965329	−	0.995330i	$-0.469225\pi$
$733$	1.10606e15	0.193066	0.0965329	+	0.995330i	$0.469225\pi$
$734$	3.35460e15	0.581183
$735$	−2.43341e15	−0.418441
$736$	−5.12749e15	−0.875139
$737$	1.18887e16	2.01402
$738$	−9.14922e14	−0.153842
$739$	1.02129e16	1.70454	0.852269	−	0.523104i	$-0.175226\pi$
$739$	1.02129e16	1.70454	0.852269	+	0.523104i	$0.175226\pi$
$740$	2.84592e15	0.471464
$741$	−2.06309e15	−0.339248
$742$	−5.60987e15	−0.915653
$743$	−9.97555e15	−1.61621	−0.808106	−	0.589037i	$-0.799507\pi$
$743$	−9.97555e15	−1.61621	−0.808106	+	0.589037i	$0.799507\pi$
$744$	−2.77837e14	−0.0446827
$745$	1.00577e16	1.60561
$746$	−3.05180e15	−0.483606
$747$	2.41747e15	0.380275
$748$	9.48389e15	1.48091
$749$	2.50963e15	0.389009
$750$	−1.66197e15	−0.255733
$751$	1.28086e16	1.95650	0.978252	−	0.207418i	$-0.0665061\pi$
$751$	1.28086e16	1.95650	0.978252	+	0.207418i	$0.0665061\pi$
$752$	−1.58972e15	−0.241059
$753$	−4.16601e15	−0.627116
$754$	−1.62827e15	−0.243324
$755$	8.81627e15	1.30791
$756$	1.45219e15	0.213872
$757$	−2.95980e15	−0.432748	−0.216374	−	0.976311i	$-0.569423\pi$
$757$	−2.95980e15	−0.432748	−0.216374	+	0.976311i	$0.569423\pi$
$758$	−3.76709e15	−0.546796
$759$	−4.21242e15	−0.607019
$760$	7.13446e15	1.02067
$761$	−3.46860e15	−0.492650	−0.246325	−	0.969187i	$-0.579223\pi$
$761$	−3.46860e15	−0.492650	−0.246325	+	0.969187i	$0.579223\pi$
$762$	−6.55807e14	−0.0924749
$763$	−1.31531e15	−0.184138
$764$	4.34816e15	0.604355
$765$	−3.35249e15	−0.462626
$766$	−6.18925e14	−0.0847969
$767$	−3.77991e14	−0.0514170
$768$	−1.32487e15	−0.178931
$769$	1.31193e15	0.175920	0.0879599	−	0.996124i	$-0.471965\pi$
$769$	1.31193e15	0.175920	0.0879599	+	0.996124i	$0.471965\pi$
$770$	4.41129e15	0.587309
$771$	−3.43948e15	−0.454668
$772$	−4.33210e15	−0.568595
$773$	5.62151e15	0.732598	0.366299	−	0.930497i	$-0.380625\pi$
$773$	5.62151e15	0.732598	0.366299	+	0.930497i	$0.380625\pi$
$774$	−1.80282e15	−0.233280
$775$	1.43402e14	0.0184245
$776$	−6.44884e15	−0.822701
$777$	−3.84568e15	−0.487145
$778$	4.80093e15	0.603862
$779$	−1.32642e16	−1.65662
$780$	1.37856e15	0.170965
$781$	−1.15168e16	−1.41824
$782$	−4.68405e15	−0.572775
$783$	2.35582e15	0.286057
$784$	3.41337e15	0.411571
$785$	−5.51972e15	−0.660897
$786$	1.70022e14	0.0202153
$787$	1.18717e16	1.40169	0.700847	−	0.713312i	$-0.252806\pi$
$787$	1.18717e16	1.40169	0.700847	+	0.713312i	$0.252806\pi$
$788$	−8.72204e15	−1.02264
$789$	3.72338e15	0.433525
$790$	−1.04278e15	−0.120571
$791$	−1.07011e16	−1.22873
$792$	−2.58376e15	−0.294621
$793$	7.29898e14	0.0826532
$794$	−4.52262e15	−0.508601
$795$	7.70495e15	0.860500
$796$	9.92963e15	1.10131
$797$	−2.99495e15	−0.329890	−0.164945	−	0.986303i	$-0.552745\pi$
$797$	−2.99495e15	−0.329890	−0.164945	+	0.986303i	$0.552745\pi$
$798$	−4.36738e15	−0.477755
$799$	−6.61650e15	−0.718822
$800$	1.62326e15	0.175144
$801$	2.25699e15	0.241852
$802$	−4.98868e15	−0.530917
$803$	4.57816e15	0.483900
$804$	7.86503e15	0.825643
$805$	1.05027e16	1.09502
$806$	1.61456e14	0.0167190
$807$	−5.52025e15	−0.567746
$808$	4.57131e15	0.466959
$809$	−6.24312e15	−0.633410	−0.316705	−	0.948524i	$-0.602577\pi$
$809$	−6.24312e15	−0.633410	−0.316705	+	0.948524i	$0.602577\pi$
$810$	4.13755e14	0.0416942
$811$	−1.60844e16	−1.60987	−0.804934	−	0.593364i	$-0.797799\pi$
$811$	−1.60844e16	−1.60987	−0.804934	+	0.593364i	$0.797799\pi$
$812$	1.66161e16	1.65185
$813$	3.64195e15	0.359613
$814$	3.09964e15	0.304002
$815$	5.70029e15	0.555303
$816$	4.70258e15	0.455030
$817$	−2.61366e16	−2.51205
$818$	3.29390e15	0.314461
$819$	−1.86285e15	−0.176651
$820$	8.86317e15	0.834858
$821$	−1.49902e16	−1.40255	−0.701275	−	0.712890i	$-0.747386\pi$
$821$	−1.49902e16	−1.40255	−0.701275	+	0.712890i	$0.747386\pi$
$822$	2.32966e15	0.216520
$823$	−9.82787e13	−0.00907320	−0.00453660	−	0.999990i	$-0.501444\pi$
$823$	−9.82787e13	−0.00907320	−0.00453660	+	0.999990i	$0.501444\pi$
$824$	3.39658e15	0.311489
$825$	1.33357e15	0.121484
$826$	−8.00175e14	−0.0724094
$827$	−1.33337e16	−1.19859	−0.599297	−	0.800527i	$-0.704553\pi$
$827$	−1.33337e16	−1.19859	−0.599297	+	0.800527i	$0.704553\pi$
$828$	−2.78674e15	−0.248845
$829$	6.17427e15	0.547691	0.273845	−	0.961774i	$-0.411704\pi$
$829$	6.17427e15	0.547691	0.273845	+	0.961774i	$0.411704\pi$
$830$	4.85810e15	0.428092
$831$	8.54861e15	0.748324
$832$	−5.07240e14	−0.0441098
$833$	1.42066e16	1.22728
$834$	2.86394e13	0.00245782
$835$	−6.90095e15	−0.588347
$836$	−1.69691e16	−1.43722
$837$	−2.33598e14	−0.0196552
$838$	5.23896e15	0.437928
$839$	−5.50384e15	−0.457062	−0.228531	−	0.973537i	$-0.573392\pi$
$839$	−5.50384e15	−0.457062	−0.228531	+	0.973537i	$0.573392\pi$
$840$	6.44199e15	0.531476
$841$	1.47550e16	1.20938
$842$	6.72320e15	0.547469
$843$	2.12983e15	0.172303
$844$	−2.08989e15	−0.167973
$845$	9.56899e15	0.764107
$846$	8.16590e14	0.0647839
$847$	−6.13671e15	−0.483701
$848$	−1.08078e16	−0.846372
$849$	7.13094e15	0.554823
$850$	1.48288e15	0.114631
$851$	7.37981e15	0.566803
$852$	−7.61897e15	−0.581405
$853$	−4.69851e15	−0.356238	−0.178119	−	0.984009i	$-0.557001\pi$
$853$	−4.69851e15	−0.356238	−0.178119	+	0.984009i	$0.557001\pi$
$854$	1.54513e15	0.116399
$855$	5.99845e15	0.448978
$856$	−2.95394e15	−0.219683
$857$	3.62402e15	0.267791	0.133896	−	0.990995i	$-0.457251\pi$
$857$	3.62402e15	0.267791	0.133896	+	0.990995i	$0.457251\pi$
$858$	1.50146e15	0.110239
$859$	4.53693e15	0.330978	0.165489	−	0.986212i	$-0.447080\pi$
$859$	4.53693e15	0.330978	0.165489	+	0.986212i	$0.447080\pi$
$860$	1.74646e16	1.26595
$861$	−1.19768e16	−0.862624
$862$	−1.07441e16	−0.768917
$863$	−2.51827e16	−1.79078	−0.895392	−	0.445278i	$-0.853105\pi$
$863$	−2.51827e16	−1.79078	−0.895392	+	0.445278i	$0.853105\pi$
$864$	−2.64425e15	−0.186843
$865$	6.72031e15	0.471846
$866$	−6.71635e15	−0.468581
$867$	1.12443e16	0.779522
$868$	−1.64761e15	−0.113500
$869$	5.47495e15	0.374776
$870$	4.73422e15	0.322027
$871$	−1.00891e16	−0.681950
$872$	1.54817e15	0.103987
$873$	−5.42200e15	−0.361894
$874$	8.38094e15	0.555879
$875$	−2.17560e16	−1.43395
$876$	3.02870e15	0.198373
$877$	1.39459e16	0.907713	0.453857	−	0.891075i	$-0.350048\pi$
$877$	1.39459e16	0.907713	0.453857	+	0.891075i	$0.350048\pi$
$878$	−1.46404e15	−0.0946962
$879$	−3.22629e15	−0.207379
$880$	8.49869e15	0.542872
$881$	−1.04395e16	−0.662690	−0.331345	−	0.943510i	$-0.607502\pi$
$881$	−1.04395e16	−0.662690	−0.331345	+	0.943510i	$0.607502\pi$
$882$	−1.75334e15	−0.110609
$883$	−8.98179e15	−0.563092	−0.281546	−	0.959548i	$-0.590847\pi$
$883$	−8.98179e15	−0.563092	−0.281546	+	0.959548i	$0.590847\pi$
$884$	−8.04828e15	−0.501436
$885$	1.09901e15	0.0680479
$886$	3.43780e15	0.211541
$887$	−3.94709e15	−0.241378	−0.120689	−	0.992690i	$-0.538510\pi$
$887$	−3.94709e15	−0.241378	−0.120689	+	0.992690i	$0.538510\pi$
$888$	4.52653e15	0.275102
$889$	−8.58482e15	−0.518527
$890$	4.53560e15	0.272264
$891$	−2.17235e15	−0.129599
$892$	1.23769e16	0.733845
$893$	1.18386e16	0.697617
$894$	7.24687e15	0.424419
$895$	8.03072e15	0.467442
$896$	−2.35932e16	−1.36488
$897$	3.57477e15	0.205537
$898$	−1.29740e15	−0.0741402
$899$	−2.67284e15	−0.151808
$900$	8.82227e14	0.0498020
$901$	−4.49828e16	−2.52383
$902$	9.65332e15	0.538320
$903$	−2.35998e16	−1.30805
$904$	1.25956e16	0.693893
$905$	−1.51212e16	−0.827977
$906$	6.35239e15	0.345726
$907$	1.05811e16	0.572389	0.286194	−	0.958172i	$-0.407610\pi$
$907$	1.05811e16	0.572389	0.286194	+	0.958172i	$0.407610\pi$
$908$	1.22991e16	0.661304
$909$	3.84343e15	0.205408
$910$	−3.74354e15	−0.198863
$911$	1.66134e16	0.877218	0.438609	−	0.898678i	$-0.355471\pi$
$911$	1.66134e16	0.877218	0.438609	+	0.898678i	$0.355471\pi$
$912$	−8.41409e15	−0.441607
$913$	−2.55067e16	−1.33065
$914$	1.79963e14	0.00933209
$915$	−2.12219e15	−0.109387
$916$	2.72909e16	1.39828
$917$	2.22566e15	0.113352
$918$	−2.41557e15	−0.122288
$919$	−2.03950e16	−1.02633	−0.513167	−	0.858289i	$-0.671528\pi$
$919$	−2.03950e16	−1.02633	−0.513167	+	0.858289i	$0.671528\pi$
$920$	−1.23621e16	−0.618384
$921$	1.94849e16	0.968879
$922$	−7.42496e15	−0.367007
$923$	9.77346e15	0.480219
$924$	−1.53221e16	−0.748378
$925$	−2.33630e15	−0.113436
$926$	−1.24976e16	−0.603207
$927$	2.85575e15	0.137019
$928$	−3.02558e16	−1.44309
$929$	−3.59026e16	−1.70231	−0.851156	−	0.524912i	$-0.824098\pi$
$929$	−3.59026e16	−1.70231	−0.851156	+	0.524912i	$0.824098\pi$
$930$	−4.69433e14	−0.0221268
$931$	−2.54192e16	−1.19108
$932$	−4.70865e15	−0.219335
$933$	−1.24320e16	−0.575695
$934$	1.02595e16	0.472301
$935$	3.53720e16	1.61881
$936$	2.19265e15	0.0997588
$937$	−3.02293e16	−1.36729	−0.683645	−	0.729815i	$-0.739606\pi$
$937$	−3.02293e16	−1.36729	−0.683645	+	0.729815i	$0.739606\pi$
$938$	−2.13578e16	−0.960374
$939$	2.82804e15	0.126422
$940$	−7.91059e15	−0.351565
$941$	−2.08747e16	−0.922313	−0.461157	−	0.887319i	$-0.652565\pi$
$941$	−2.08747e16	−0.922313	−0.461157	+	0.887319i	$0.652565\pi$
$942$	−3.97712e15	−0.174699
$943$	2.29832e16	1.00368
$944$	−1.54160e15	−0.0669306
$945$	5.41624e15	0.233788
$946$	1.90215e16	0.816290
$947$	−1.68268e16	−0.717920	−0.358960	−	0.933353i	$-0.616869\pi$
$947$	−1.68268e16	−0.717920	−0.358960	+	0.933353i	$0.616869\pi$
$948$	3.62197e15	0.153638
$949$	−3.88515e15	−0.163849
$950$	−2.65324e15	−0.111249
$951$	8.90698e15	0.371311
$952$	−3.76094e16	−1.55881
$953$	−1.46538e16	−0.603866	−0.301933	−	0.953329i	$-0.597632\pi$
$953$	−1.46538e16	−0.603866	−0.301933	+	0.953329i	$0.597632\pi$
$954$	5.55165e15	0.227460
$955$	1.62173e16	0.660633
$956$	2.69410e16	1.09118
$957$	−2.48562e16	−1.00097
$958$	1.16114e16	0.464914
$959$	3.04963e16	1.21407
$960$	1.47480e15	0.0583771
$961$	−2.51434e16	−0.989569
$962$	−2.63044e15	−0.102935
$963$	−2.48359e15	−0.0966351
$964$	−2.87938e16	−1.11397
$965$	−1.61574e16	−0.621543
$966$	7.56749e15	0.289453
$967$	−4.43380e16	−1.68628	−0.843141	−	0.537693i	$-0.819296\pi$
$967$	−4.43380e16	−1.68628	−0.843141	+	0.537693i	$0.819296\pi$
$968$	7.22316e15	0.273157
$969$	−3.50199e16	−1.31684
$970$	−1.08959e16	−0.407399
$971$	−2.70153e16	−1.00439	−0.502196	−	0.864754i	$-0.667475\pi$
$971$	−2.70153e16	−1.00439	−0.502196	+	0.864754i	$0.667475\pi$
$972$	−1.43712e15	−0.0531288
$973$	3.74903e14	0.0137815
$974$	1.32097e16	0.482856
$975$	−1.13170e15	−0.0411346
$976$	2.97681e15	0.107591
$977$	−1.90954e16	−0.686292	−0.343146	−	0.939282i	$-0.611493\pi$
$977$	−1.90954e16	−0.686292	−0.343146	+	0.939282i	$0.611493\pi$
$978$	4.10723e15	0.146786
$979$	−2.38134e16	−0.846285
$980$	1.69852e16	0.600244
$981$	1.30166e15	0.0457423
$982$	1.43699e16	0.502160
$983$	−2.94931e16	−1.02489	−0.512443	−	0.858721i	$-0.671259\pi$
$983$	−2.94931e16	−1.02489	−0.512443	+	0.858721i	$0.671259\pi$
$984$	1.40971e16	0.487144
$985$	−3.25305e16	−1.11787
$986$	−2.76392e16	−0.944500
$987$	1.06895e16	0.363258
$988$	1.44004e16	0.486644
$989$	4.52876e16	1.52195
$990$	−4.36551e15	−0.145895
$991$	5.85273e16	1.94515	0.972575	−	0.232587i	$-0.0747192\pi$
$991$	5.85273e16	1.94515	0.972575	+	0.232587i	$0.0747192\pi$
$992$	3.00009e15	0.0991562
$993$	−1.43692e16	−0.472293
$994$	2.06896e16	0.676280
$995$	3.70345e16	1.20387
$996$	−1.68740e16	−0.545496
$997$	−3.07013e16	−0.987038	−0.493519	−	0.869735i	$-0.664290\pi$
$997$	−3.07013e16	−0.987038	−0.493519	+	0.869735i	$0.664290\pi$
$998$	1.20734e15	0.0386023
$999$	3.80577e15	0.121013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.12	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.12	✓	27	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)

\(f(q)\)	\(=\)	\(q-18.7578 q^{2} +243.000 q^{3} -1696.14 q^{4} -6326.10 q^{5} -4558.15 q^{6} -59668.2 q^{7} +70231.9 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-18.7578 q^{2} +243.000 q^{3} -1696.14 q^{4} -6326.10 q^{5} -4558.15 q^{6} -59668.2 q^{7} +70231.9 q^{8} +59049.0 q^{9} +118664. q^{10} -623024. q^{11} -412163. q^{12} +528715. q^{13} +1.11924e6 q^{14} -1.53724e6 q^{15} +2.15631e6 q^{16} +8.97468e6 q^{17} -1.10763e6 q^{18} -1.60580e7 q^{19} +1.07300e7 q^{20} -1.44994e7 q^{21} +1.16866e7 q^{22} +2.78241e7 q^{23} +1.70664e7 q^{24} -8.80856e6 q^{25} -9.91753e6 q^{26} +1.43489e7 q^{27} +1.01206e8 q^{28} +1.64181e8 q^{29} +2.88353e7 q^{30} -1.62798e7 q^{31} -1.84283e8 q^{32} -1.51395e8 q^{33} -1.68345e8 q^{34} +3.77467e8 q^{35} -1.00156e8 q^{36} +2.65231e8 q^{37} +3.01212e8 q^{38} +1.28478e8 q^{39} -4.44294e8 q^{40} +8.26019e8 q^{41} +2.71976e8 q^{42} +1.62764e9 q^{43} +1.05674e9 q^{44} -3.73550e8 q^{45} -5.21918e8 q^{46} -7.37241e8 q^{47} +5.23983e8 q^{48} +1.58297e9 q^{49} +1.65229e8 q^{50} +2.18085e9 q^{51} -8.96777e8 q^{52} -5.01219e9 q^{53} -2.69154e8 q^{54} +3.94131e9 q^{55} -4.19061e9 q^{56} -3.90208e9 q^{57} -3.07968e9 q^{58} -7.14924e8 q^{59} +2.60739e9 q^{60} +1.38051e9 q^{61} +3.05374e8 q^{62} -3.52335e9 q^{63} -9.59383e8 q^{64} -3.34470e9 q^{65} +2.83983e9 q^{66} -1.90823e10 q^{67} -1.52224e10 q^{68} +6.76125e9 q^{69} -7.08045e9 q^{70} +1.84853e10 q^{71} +4.14712e9 q^{72} -7.34829e9 q^{73} -4.97515e9 q^{74} -2.14048e9 q^{75} +2.72366e10 q^{76} +3.71747e10 q^{77} -2.40996e9 q^{78} -8.78770e9 q^{79} -1.36410e10 q^{80} +3.48678e9 q^{81} -1.54943e10 q^{82} +4.09401e10 q^{83} +2.45930e10 q^{84} -5.67747e10 q^{85} -3.05310e10 q^{86} +3.98961e10 q^{87} -4.37562e10 q^{88} +3.82223e10 q^{89} +7.00698e9 q^{90} -3.15475e10 q^{91} -4.71937e10 q^{92} -3.95600e9 q^{93} +1.38290e10 q^{94} +1.01584e11 q^{95} -4.47807e10 q^{96} -9.18220e10 q^{97} -2.96930e10 q^{98} -3.67889e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more