LMFDB - Embedded newform 177.12.a.a.1.6

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			1.6
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)

$f(q)$	$=$	$q-60.8905 q^{2} -243.000 q^{3} +1659.66 q^{4} -4960.99 q^{5} +14796.4 q^{6} -87058.0 q^{7} +23646.5 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-60.8905 q^{2} -243.000 q^{3} +1659.66 q^{4} -4960.99 q^{5} +14796.4 q^{6} -87058.0 q^{7} +23646.5 q^{8} +59049.0 q^{9} +302077. q^{10} -683008. q^{11} -403296. q^{12} -974154. q^{13} +5.30101e6 q^{14} +1.20552e6 q^{15} -4.83882e6 q^{16} -6.81665e6 q^{17} -3.59552e6 q^{18} +1.81310e7 q^{19} -8.23354e6 q^{20} +2.11551e7 q^{21} +4.15887e7 q^{22} -3.49174e7 q^{23} -5.74610e6 q^{24} -2.42167e7 q^{25} +5.93168e7 q^{26} -1.43489e7 q^{27} -1.44486e8 q^{28} +9.30111e7 q^{29} -7.34048e7 q^{30} -1.05378e8 q^{31} +2.46210e8 q^{32} +1.65971e8 q^{33} +4.15070e8 q^{34} +4.31894e8 q^{35} +9.80010e7 q^{36} -2.32051e8 q^{37} -1.10401e9 q^{38} +2.36720e8 q^{39} -1.17310e8 q^{40} +1.02676e9 q^{41} -1.28815e9 q^{42} -1.24232e9 q^{43} -1.13356e9 q^{44} -2.92942e8 q^{45} +2.12614e9 q^{46} -2.18627e9 q^{47} +1.17583e9 q^{48} +5.60177e9 q^{49} +1.47457e9 q^{50} +1.65645e9 q^{51} -1.61676e9 q^{52} -4.40486e9 q^{53} +8.73712e8 q^{54} +3.38840e9 q^{55} -2.05862e9 q^{56} -4.40584e9 q^{57} -5.66350e9 q^{58} +7.14924e8 q^{59} +2.00075e9 q^{60} +8.44479e9 q^{61} +6.41652e9 q^{62} -5.14069e9 q^{63} -5.08197e9 q^{64} +4.83277e9 q^{65} -1.01061e10 q^{66} +2.45494e9 q^{67} -1.13133e10 q^{68} +8.48493e9 q^{69} -2.62983e10 q^{70} +1.56746e10 q^{71} +1.39630e9 q^{72} +1.89412e10 q^{73} +1.41297e10 q^{74} +5.88465e9 q^{75} +3.00913e10 q^{76} +5.94613e10 q^{77} -1.44140e10 q^{78} +1.99876e10 q^{79} +2.40054e10 q^{80} +3.48678e9 q^{81} -6.25200e10 q^{82} +6.31770e10 q^{83} +3.51102e10 q^{84} +3.38174e10 q^{85} +7.56453e10 q^{86} -2.26017e10 q^{87} -1.61508e10 q^{88} +1.84273e10 q^{89} +1.78374e10 q^{90} +8.48080e10 q^{91} -5.79509e10 q^{92} +2.56068e10 q^{93} +1.33123e11 q^{94} -8.99479e10 q^{95} -5.98291e10 q^{96} +4.38615e10 q^{97} -3.41095e11 q^{98} -4.03310e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−60.8905	−1.34550	−0.672752	−	0.739868i	$-0.734888\pi$
$2$	−60.8905	−1.34550	−0.672752	+	0.739868i	$0.734888\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	1659.66	0.810379
$5$	−4960.99	−0.709959	−0.354980	−	0.934874i	$-0.615512\pi$
$5$	−4960.99	−0.709959	−0.354980	+	0.934874i	$0.615512\pi$
$6$	14796.4	0.776827
$7$	−87058.0	−1.95781	−0.978903	−	0.204326i	$-0.934500\pi$
$7$	−87058.0	−1.95781	−0.978903	+	0.204326i	$0.934500\pi$
$8$	23646.5	0.255136
$9$	59049.0	0.333333
$10$	302077.	0.955253
$11$	−683008.	−1.27869	−0.639346	−	0.768919i	$-0.720795\pi$
$11$	−683008.	−1.27869	−0.639346	+	0.768919i	$0.720795\pi$
$12$	−403296.	−0.467872
$13$	−974154.	−0.727678	−0.363839	−	0.931462i	$-0.618534\pi$
$13$	−974154.	−0.727678	−0.363839	+	0.931462i	$0.618534\pi$
$14$	5.30101e6	2.63423
$15$	1.20552e6	0.409895
$16$	−4.83882e6	−1.15367
$17$	−6.81665e6	−1.16440	−0.582200	−	0.813046i	$-0.697808\pi$
$17$	−6.81665e6	−1.16440	−0.582200	+	0.813046i	$0.697808\pi$
$18$	−3.59552e6	−0.448501
$19$	1.81310e7	1.67988	0.839939	−	0.542681i	$-0.182591\pi$
$19$	1.81310e7	1.67988	0.839939	+	0.542681i	$0.182591\pi$
$20$	−8.23354e6	−0.575336
$21$	2.11551e7	1.13034
$22$	4.15887e7	1.72048
$23$	−3.49174e7	−1.13120	−0.565599	−	0.824680i	$-0.691355\pi$
$23$	−3.49174e7	−1.13120	−0.565599	+	0.824680i	$0.691355\pi$
$24$	−5.74610e6	−0.147303
$25$	−2.42167e7	−0.495958
$26$	5.93168e7	0.979093
$27$	−1.43489e7	−0.192450
$28$	−1.44486e8	−1.58656
$29$	9.30111e7	0.842066	0.421033	−	0.907045i	$-0.361668\pi$
$29$	9.30111e7	0.842066	0.421033	+	0.907045i	$0.361668\pi$
$30$	−7.34048e7	−0.551515
$31$	−1.05378e8	−0.661090	−0.330545	−	0.943790i	$-0.607233\pi$
$31$	−1.05378e8	−0.661090	−0.330545	+	0.943790i	$0.607233\pi$
$32$	2.46210e8	1.29712
$33$	1.65971e8	0.738253
$34$	4.15070e8	1.56670
$35$	4.31894e8	1.38996
$36$	9.80010e7	0.270126
$37$	−2.32051e8	−0.550141	−0.275071	−	0.961424i	$-0.588701\pi$
$37$	−2.32051e8	−0.550141	−0.275071	+	0.961424i	$0.588701\pi$
$38$	−1.10401e9	−2.26028
$39$	2.36720e8	0.420125
$40$	−1.17310e8	−0.181136
$41$	1.02676e9	1.38407	0.692035	−	0.721864i	$-0.256714\pi$
$41$	1.02676e9	1.38407	0.692035	+	0.721864i	$0.256714\pi$
$42$	−1.28815e9	−1.52088
$43$	−1.24232e9	−1.28871	−0.644355	−	0.764726i	$-0.722874\pi$
$43$	−1.24232e9	−1.28871	−0.644355	+	0.764726i	$0.722874\pi$
$44$	−1.13356e9	−1.03623
$45$	−2.92942e8	−0.236653
$46$	2.12614e9	1.52203
$47$	−2.18627e9	−1.39048	−0.695242	−	0.718776i	$-0.744703\pi$
$47$	−2.18627e9	−1.39048	−0.695242	+	0.718776i	$0.744703\pi$
$48$	1.17583e9	0.666069
$49$	5.60177e9	2.83300
$50$	1.47457e9	0.667313
$51$	1.65645e9	0.672267
$52$	−1.61676e9	−0.589695
$53$	−4.40486e9	−1.44682	−0.723411	−	0.690418i	$-0.757427\pi$
$53$	−4.40486e9	−1.44682	−0.723411	+	0.690418i	$0.757427\pi$
$54$	8.73712e8	0.258942
$55$	3.38840e9	0.907820
$56$	−2.05862e9	−0.499507
$57$	−4.40584e9	−0.969878
$58$	−5.66350e9	−1.13300
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	2.00075e9	0.332170
$61$	8.44479e9	1.28019	0.640096	−	0.768295i	$-0.278895\pi$
$61$	8.44479e9	1.28019	0.640096	+	0.768295i	$0.278895\pi$
$62$	6.41652e9	0.889498
$63$	−5.14069e9	−0.652602
$64$	−5.08197e9	−0.591619
$65$	4.83277e9	0.516622
$66$	−1.01061e10	−0.993322
$67$	2.45494e9	0.222141	0.111071	−	0.993813i	$-0.464572\pi$
$67$	2.45494e9	0.222141	0.111071	+	0.993813i	$0.464572\pi$
$68$	−1.13133e10	−0.943605
$69$	8.48493e9	0.653098
$70$	−2.62983e10	−1.87020
$71$	1.56746e10	1.03104	0.515521	−	0.856877i	$-0.327598\pi$
$71$	1.56746e10	1.03104	0.515521	+	0.856877i	$0.327598\pi$
$72$	1.39630e9	0.0850454
$73$	1.89412e10	1.06938	0.534689	−	0.845049i	$-0.320429\pi$
$73$	1.89412e10	1.06938	0.534689	+	0.845049i	$0.320429\pi$
$74$	1.41297e10	0.740217
$75$	5.88465e9	0.286341
$76$	3.00913e10	1.36134
$77$	5.94613e10	2.50343
$78$	−1.44140e10	−0.565280
$79$	1.99876e10	0.730821	0.365410	−	0.930846i	$-0.380929\pi$
$79$	1.99876e10	0.730821	0.365410	+	0.930846i	$0.380929\pi$
$80$	2.40054e10	0.819055
$81$	3.48678e9	0.111111
$82$	−6.25200e10	−1.86227
$83$	6.31770e10	1.76047	0.880237	−	0.474535i	$-0.157384\pi$
$83$	6.31770e10	1.76047	0.880237	+	0.474535i	$0.157384\pi$
$84$	3.51102e10	0.916003
$85$	3.38174e10	0.826677
$86$	7.56453e10	1.73396
$87$	−2.26017e10	−0.486167
$88$	−1.61508e10	−0.326241
$89$	1.84273e10	0.349798	0.174899	−	0.984586i	$-0.444040\pi$
$89$	1.84273e10	0.349798	0.174899	+	0.984586i	$0.444040\pi$
$90$	1.78374e10	0.318418
$91$	8.48080e10	1.42465
$92$	−5.79509e10	−0.916699
$93$	2.56068e10	0.381680
$94$	1.33123e11	1.87090
$95$	−8.99479e10	−1.19265
$96$	−5.98291e10	−0.748895
$97$	4.38615e10	0.518607	0.259304	−	0.965796i	$-0.416507\pi$
$97$	4.38615e10	0.518607	0.259304	+	0.965796i	$0.416507\pi$
$98$	−3.41095e11	−3.81181
$99$	−4.03310e10	−0.426231
$100$	−4.01913e10	−0.401913
$101$	4.59353e9	0.0434889	0.0217445	−	0.999764i	$-0.493078\pi$
$101$	4.59353e9	0.0434889	0.0217445	+	0.999764i	$0.493078\pi$
$102$	−1.00862e11	−0.904537
$103$	−8.20219e10	−0.697148	−0.348574	−	0.937281i	$-0.613334\pi$
$103$	−8.20219e10	−0.697148	−0.348574	+	0.937281i	$0.613334\pi$
$104$	−2.30353e10	−0.185657
$105$	−1.04950e11	−0.802495
$106$	2.68214e11	1.94670
$107$	−4.02988e9	−0.0277767	−0.0138884	−	0.999904i	$-0.504421\pi$
$107$	−4.02988e9	−0.0277767	−0.0138884	+	0.999904i	$0.504421\pi$
$108$	−2.38142e10	−0.155957
$109$	−1.10801e11	−0.689761	−0.344881	−	0.938647i	$-0.612081\pi$
$109$	−1.10801e11	−0.689761	−0.344881	+	0.938647i	$0.612081\pi$
$110$	−2.06321e11	−1.22147
$111$	5.63884e10	0.317624
$112$	4.21258e11	2.25865
$113$	3.21195e11	1.63998	0.819988	−	0.572380i	$-0.193980\pi$
$113$	3.21195e11	1.63998	0.819988	+	0.572380i	$0.193980\pi$
$114$	2.68274e11	1.30497
$115$	1.73225e11	0.803105
$116$	1.54366e11	0.682392
$117$	−5.75228e10	−0.242559
$118$	−4.35321e10	−0.175170
$119$	5.93444e11	2.27967
$120$	2.85064e10	0.104579
$121$	1.81189e11	0.635055
$122$	−5.14208e11	−1.72250
$123$	−2.49503e11	−0.799094
$124$	−1.74891e11	−0.535733
$125$	3.62375e11	1.06207
$126$	3.13019e11	0.878078
$127$	−5.54356e11	−1.48891	−0.744454	−	0.667674i	$-0.767290\pi$
$127$	−5.54356e11	−1.48891	−0.744454	+	0.667674i	$0.767290\pi$
$128$	−1.94795e11	−0.501099
$129$	3.01883e11	0.744038
$130$	−2.94270e11	−0.695116
$131$	5.36802e11	1.21569	0.607843	−	0.794057i	$-0.292035\pi$
$131$	5.36802e11	1.21569	0.607843	+	0.794057i	$0.292035\pi$
$132$	2.75455e11	0.598265
$133$	−1.57845e12	−3.28887
$134$	−1.49482e11	−0.298892
$135$	7.11848e10	0.136632
$136$	−1.61190e11	−0.297081
$137$	6.22947e9	0.0110278	0.00551389	−	0.999985i	$-0.498245\pi$
$137$	6.22947e9	0.0110278	0.00551389	+	0.999985i	$0.498245\pi$
$138$	−5.16652e11	−0.878745
$139$	1.94678e11	0.318226	0.159113	−	0.987260i	$-0.449137\pi$
$139$	1.94678e11	0.318226	0.159113	+	0.987260i	$0.449137\pi$
$140$	7.16796e11	1.12640
$141$	5.31264e11	0.802796
$142$	−9.54436e11	−1.38727
$143$	6.65355e11	0.930477
$144$	−2.85728e11	−0.384555
$145$	−4.61427e11	−0.597832
$146$	−1.15334e12	−1.43885
$147$	−1.36123e12	−1.63564
$148$	−3.85125e11	−0.445823
$149$	−7.82207e11	−0.872564	−0.436282	−	0.899810i	$-0.643705\pi$
$149$	−7.82207e11	−0.872564	−0.436282	+	0.899810i	$0.643705\pi$
$150$	−3.58320e11	−0.385273
$151$	−7.19235e11	−0.745586	−0.372793	−	0.927915i	$-0.621600\pi$
$151$	−7.19235e11	−0.745586	−0.372793	+	0.927915i	$0.621600\pi$
$152$	4.28736e11	0.428598
$153$	−4.02517e11	−0.388133
$154$	−3.62063e12	−3.36837
$155$	5.22779e11	0.469347
$156$	3.92873e11	0.340460
$157$	7.68037e11	0.642590	0.321295	−	0.946979i	$-0.395882\pi$
$157$	7.68037e11	0.642590	0.321295	+	0.946979i	$0.395882\pi$
$158$	−1.21705e12	−0.983322
$159$	1.07038e12	0.835323
$160$	−1.22145e12	−0.920905
$161$	3.03984e12	2.21467
$162$	−2.12312e11	−0.149500
$163$	2.10422e11	0.143238	0.0716192	−	0.997432i	$-0.477183\pi$
$163$	2.10422e11	0.143238	0.0716192	+	0.997432i	$0.477183\pi$
$164$	1.70407e12	1.12162
$165$	−8.23381e11	−0.524130
$166$	−3.84688e12	−2.36872
$167$	1.90238e12	1.13333	0.566664	−	0.823949i	$-0.308234\pi$
$167$	1.90238e12	1.13333	0.566664	+	0.823949i	$0.308234\pi$
$168$	5.00244e11	0.288391
$169$	−8.43184e11	−0.470484
$170$	−2.05916e12	−1.11230
$171$	1.07062e12	0.559959
$172$	−2.06182e12	−1.04434
$173$	−7.99218e11	−0.392113	−0.196057	−	0.980593i	$-0.562814\pi$
$173$	−7.99218e11	−0.392113	−0.196057	+	0.980593i	$0.562814\pi$
$174$	1.37623e12	0.654139
$175$	2.10826e12	0.970989
$176$	3.30496e12	1.47518
$177$	−1.73727e11	−0.0751646
$178$	−1.12205e12	−0.470655
$179$	−4.49912e12	−1.82994	−0.914968	−	0.403526i	$-0.867784\pi$
$179$	−4.49912e12	−1.82994	−0.914968	+	0.403526i	$0.867784\pi$
$180$	−4.86182e11	−0.191779
$181$	−3.39167e12	−1.29772	−0.648860	−	0.760908i	$-0.724754\pi$
$181$	−3.39167e12	−1.29772	−0.648860	+	0.760908i	$0.724754\pi$
$182$	−5.16400e12	−1.91687
$183$	−2.05209e12	−0.739119
$184$	−8.25675e11	−0.288610
$185$	1.15120e12	0.390578
$186$	−1.55921e12	−0.513552
$187$	4.65583e12	1.48891
$188$	−3.62846e12	−1.12682
$189$	1.24919e12	0.376780
$190$	5.47698e12	1.60471
$191$	−5.32518e11	−0.151583	−0.0757916	−	0.997124i	$-0.524148\pi$
$191$	−5.32518e11	−0.151583	−0.0757916	+	0.997124i	$0.524148\pi$
$192$	1.23492e12	0.341571
$193$	−5.16210e12	−1.38759	−0.693795	−	0.720172i	$-0.744063\pi$
$193$	−5.16210e12	−1.38759	−0.693795	+	0.720172i	$0.744063\pi$
$194$	−2.67075e12	−0.697787
$195$	−1.17436e12	−0.298272
$196$	9.29701e12	2.29581
$197$	4.31197e12	1.03541	0.517704	−	0.855560i	$-0.326787\pi$
$197$	4.31197e12	1.03541	0.517704	+	0.855560i	$0.326787\pi$
$198$	2.45577e12	0.573495
$199$	−8.47690e12	−1.92551	−0.962754	−	0.270380i	$-0.912851\pi$
$199$	−8.47690e12	−1.92551	−0.962754	+	0.270380i	$0.912851\pi$
$200$	−5.72640e11	−0.126537
$201$	−5.96550e11	−0.128253
$202$	−2.79702e11	−0.0585145
$203$	−8.09736e12	−1.64860
$204$	2.74913e12	0.544790
$205$	−5.09375e12	−0.982634
$206$	4.99436e12	0.938015
$207$	−2.06184e12	−0.377066
$208$	4.71376e12	0.839497
$209$	−1.23836e13	−2.14805
$210$	6.39048e12	1.07976
$211$	2.82447e12	0.464925	0.232463	−	0.972605i	$-0.425322\pi$
$211$	2.82447e12	0.464925	0.232463	+	0.972605i	$0.425322\pi$
$212$	−7.31055e12	−1.17247
$213$	−3.80893e12	−0.595272
$214$	2.45381e11	0.0373737
$215$	6.16312e12	0.914932
$216$	−3.39301e11	−0.0491010
$217$	9.17400e12	1.29429
$218$	6.74674e12	0.928076
$219$	−4.60271e12	−0.617406
$220$	5.62357e12	0.735678
$221$	6.64047e12	0.847308
$222$	−3.43352e12	−0.427364
$223$	8.45247e11	0.102638	0.0513188	−	0.998682i	$-0.483658\pi$
$223$	8.45247e11	0.102638	0.0513188	+	0.998682i	$0.483658\pi$
$224$	−2.14346e13	−2.53952
$225$	−1.42997e12	−0.165319
$226$	−1.95577e13	−2.20659
$227$	7.13636e12	0.785841	0.392921	−	0.919572i	$-0.371465\pi$
$227$	7.13636e12	0.785841	0.392921	+	0.919572i	$0.371465\pi$
$228$	−7.31218e12	−0.785968
$229$	−8.15017e12	−0.855208	−0.427604	−	0.903966i	$-0.640642\pi$
$229$	−8.15017e12	−0.855208	−0.427604	+	0.903966i	$0.640642\pi$
$230$	−1.05478e13	−1.08058
$231$	−1.44491e13	−1.44536
$232$	2.19939e12	0.214841
$233$	−1.14160e12	−0.108907	−0.0544536	−	0.998516i	$-0.517342\pi$
$233$	−1.14160e12	−0.108907	−0.0544536	+	0.998516i	$0.517342\pi$
$234$	3.50260e12	0.326364
$235$	1.08461e13	0.987187
$236$	1.18653e12	0.105502
$237$	−4.85698e12	−0.421940
$238$	−3.61351e13	−3.06730
$239$	1.86809e12	0.154956	0.0774782	−	0.996994i	$-0.475313\pi$
$239$	1.86809e12	0.154956	0.0774782	+	0.996994i	$0.475313\pi$
$240$	−5.83330e12	−0.472882
$241$	−4.14653e12	−0.328542	−0.164271	−	0.986415i	$-0.552527\pi$
$241$	−4.14653e12	−0.328542	−0.164271	+	0.986415i	$0.552527\pi$
$242$	−1.10327e13	−0.854468
$243$	−8.47289e11	−0.0641500
$244$	1.40154e13	1.03744
$245$	−2.77904e13	−2.01132
$246$	1.51924e13	1.07518
$247$	−1.76624e13	−1.22241
$248$	−2.49182e12	−0.168668
$249$	−1.53520e13	−1.01641
$250$	−2.20652e13	−1.42902
$251$	2.14857e13	1.36127	0.680636	−	0.732622i	$-0.261704\pi$
$251$	2.14857e13	1.36127	0.680636	+	0.732622i	$0.261704\pi$
$252$	−8.53177e12	−0.528855
$253$	2.38489e13	1.44646
$254$	3.37550e13	2.00333
$255$	−8.21762e12	−0.477282
$256$	2.22690e13	1.26585
$257$	1.30208e12	0.0724445	0.0362222	−	0.999344i	$-0.488468\pi$
$257$	1.30208e12	0.0724445	0.0362222	+	0.999344i	$0.488468\pi$
$258$	−1.83818e13	−1.00110
$259$	2.02019e13	1.07707
$260$	8.02074e12	0.418659
$261$	5.49221e12	0.280689
$262$	−3.26861e13	−1.63571
$263$	1.67130e13	0.819026	0.409513	−	0.912304i	$-0.365699\pi$
$263$	1.67130e13	0.819026	0.409513	+	0.912304i	$0.365699\pi$
$264$	3.92463e12	0.188355
$265$	2.18525e13	1.02718
$266$	9.61128e13	4.42519
$267$	−4.47784e12	−0.201956
$268$	4.07435e12	0.180018
$269$	4.83228e12	0.209177	0.104589	−	0.994516i	$-0.466647\pi$
$269$	4.83228e12	0.209177	0.104589	+	0.994516i	$0.466647\pi$
$270$	−4.33448e12	−0.183838
$271$	−1.47869e13	−0.614535	−0.307268	−	0.951623i	$-0.599415\pi$
$271$	−1.47869e13	−0.614535	−0.307268	+	0.951623i	$0.599415\pi$
$272$	3.29846e13	1.34333
$273$	−2.06083e13	−0.822523
$274$	−3.79316e11	−0.0148379
$275$	1.65402e13	0.634177
$276$	1.40821e13	0.529256
$277$	−4.09753e13	−1.50968	−0.754838	−	0.655911i	$-0.772284\pi$
$277$	−4.09753e13	−1.50968	−0.754838	+	0.655911i	$0.772284\pi$
$278$	−1.18540e13	−0.428174
$279$	−6.22246e12	−0.220363
$280$	1.02128e13	0.354630
$281$	3.23692e13	1.10217	0.551083	−	0.834450i	$-0.314215\pi$
$281$	3.23692e13	1.10217	0.551083	+	0.834450i	$0.314215\pi$
$282$	−3.23489e13	−1.08016
$283$	4.42602e13	1.44940	0.724700	−	0.689064i	$-0.241978\pi$
$283$	4.42602e13	1.44940	0.724700	+	0.689064i	$0.241978\pi$
$284$	2.60145e13	0.835534
$285$	2.18573e13	0.688574
$286$	−4.05138e13	−1.25196
$287$	−8.93878e13	−2.70974
$288$	1.45385e13	0.432375
$289$	1.21949e13	0.355827
$290$	2.80966e13	0.804385
$291$	−1.06583e13	−0.299418
$292$	3.14358e13	0.866601
$293$	3.46245e13	0.936724	0.468362	−	0.883537i	$-0.344844\pi$
$293$	3.46245e13	0.936724	0.468362	+	0.883537i	$0.344844\pi$
$294$	8.28861e13	2.20075
$295$	−3.54673e12	−0.0924288
$296$	−5.48720e12	−0.140361
$297$	9.80042e12	0.246084
$298$	4.76290e13	1.17404
$299$	3.40149e13	0.823148
$300$	9.76650e12	0.232045
$301$	1.08154e14	2.52305
$302$	4.37946e13	1.00319
$303$	−1.11623e12	−0.0251083
$304$	−8.77328e13	−1.93802
$305$	−4.18946e13	−0.908884
$306$	2.45094e13	0.522235
$307$	−1.40721e13	−0.294509	−0.147255	−	0.989099i	$-0.547044\pi$
$307$	−1.40721e13	−0.294509	−0.147255	+	0.989099i	$0.547044\pi$
$308$	9.86853e13	2.02873
$309$	1.99313e13	0.402499
$310$	−3.18323e13	−0.631508
$311$	−2.59276e12	−0.0505336	−0.0252668	−	0.999681i	$-0.508044\pi$
$311$	−2.59276e12	−0.0505336	−0.0252668	+	0.999681i	$0.508044\pi$
$312$	5.59759e12	0.107189
$313$	6.91494e13	1.30105	0.650526	−	0.759484i	$-0.274549\pi$
$313$	6.91494e13	1.30105	0.650526	+	0.759484i	$0.274549\pi$
$314$	−4.67662e13	−0.864607
$315$	2.55029e13	0.463321
$316$	3.31725e13	0.592242
$317$	−5.31356e13	−0.932308	−0.466154	−	0.884704i	$-0.654361\pi$
$317$	−5.31356e13	−0.932308	−0.466154	+	0.884704i	$0.654361\pi$
$318$	−6.51761e13	−1.12393
$319$	−6.35274e13	−1.07674
$320$	2.52116e13	0.420026
$321$	9.79260e11	0.0160369
$322$	−1.85097e14	−2.97984
$323$	−1.23593e14	−1.95605
$324$	5.78686e12	0.0900421
$325$	2.35908e13	0.360898
$326$	−1.28127e13	−0.192728
$327$	2.69247e13	0.398234
$328$	2.42793e13	0.353126
$329$	1.90333e14	2.72230
$330$	5.01361e13	0.705219
$331$	−1.19507e14	−1.65325	−0.826626	−	0.562751i	$-0.809743\pi$
$331$	−1.19507e14	−1.65325	−0.826626	+	0.562751i	$0.809743\pi$
$332$	1.04852e14	1.42665
$333$	−1.37024e13	−0.183380
$334$	−1.15837e14	−1.52490
$335$	−1.21789e13	−0.157711
$336$	−1.02366e14	−1.30403
$337$	1.13746e14	1.42551	0.712755	−	0.701413i	$-0.247447\pi$
$337$	1.13746e14	1.42551	0.712755	+	0.701413i	$0.247447\pi$
$338$	5.13419e13	0.633038
$339$	−7.80505e13	−0.946841
$340$	5.61252e13	0.669921
$341$	7.19740e13	0.845331
$342$	−6.51906e13	−0.753427
$343$	−3.15537e14	−3.58866
$344$	−2.93764e13	−0.328797
$345$	−4.20937e13	−0.463673
$346$	4.86648e13	0.527589
$347$	−5.34150e12	−0.0569969	−0.0284985	−	0.999594i	$-0.509073\pi$
$347$	−5.34150e12	−0.0569969	−0.0284985	+	0.999594i	$0.509073\pi$
$348$	−3.75110e13	−0.393979
$349$	−1.19303e14	−1.23342	−0.616712	−	0.787189i	$-0.711536\pi$
$349$	−1.19303e14	−1.23342	−0.616712	+	0.787189i	$0.711536\pi$
$350$	−1.28373e14	−1.30647
$351$	1.39781e13	0.140042
$352$	−1.68164e14	−1.65862
$353$	1.07357e14	1.04248	0.521240	−	0.853410i	$-0.325470\pi$
$353$	1.07357e14	1.04248	0.521240	+	0.853410i	$0.325470\pi$
$354$	1.05783e13	0.101134
$355$	−7.77617e13	−0.731998
$356$	3.05830e13	0.283469
$357$	−1.44207e14	−1.31617
$358$	2.73954e14	2.46218
$359$	−1.16906e14	−1.03471	−0.517355	−	0.855771i	$-0.673083\pi$
$359$	−1.16906e14	−1.03471	−0.517355	+	0.855771i	$0.673083\pi$
$360$	−6.92705e12	−0.0603788
$361$	2.12244e14	1.82199
$362$	2.06520e14	1.74609
$363$	−4.40288e13	−0.366649
$364$	1.40752e14	1.15451
$365$	−9.39670e13	−0.759215
$366$	1.24953e14	0.994487
$367$	−7.67484e13	−0.601736	−0.300868	−	0.953666i	$-0.597276\pi$
$367$	−7.67484e13	−0.601736	−0.300868	+	0.953666i	$0.597276\pi$
$368$	1.68959e14	1.30502
$369$	6.06292e13	0.461357
$370$	−7.00974e13	−0.525524
$371$	3.83478e14	2.83260
$372$	4.24985e13	0.309306
$373$	1.46951e14	1.05384	0.526920	−	0.849915i	$-0.323347\pi$
$373$	1.46951e14	1.05384	0.526920	+	0.849915i	$0.323347\pi$
$374$	−2.83496e14	−2.00333
$375$	−8.80571e13	−0.613186
$376$	−5.16977e13	−0.354763
$377$	−9.06072e13	−0.612753
$378$	−7.60637e13	−0.506959
$379$	−1.11895e14	−0.735010	−0.367505	−	0.930021i	$-0.619788\pi$
$379$	−1.11895e14	−0.735010	−0.367505	+	0.930021i	$0.619788\pi$
$380$	−1.49283e14	−0.966494
$381$	1.34708e14	0.859622
$382$	3.24253e13	0.203956
$383$	−1.07972e14	−0.669448	−0.334724	−	0.942316i	$-0.608643\pi$
$383$	−1.07972e14	−0.669448	−0.334724	+	0.942316i	$0.608643\pi$
$384$	4.73352e13	0.289309
$385$	−2.94987e14	−1.77733
$386$	3.14323e14	1.86701
$387$	−7.33575e13	−0.429570
$388$	7.27949e13	0.420268
$389$	1.40085e14	0.797389	0.398694	−	0.917084i	$-0.369463\pi$
$389$	1.40085e14	0.797389	0.398694	+	0.917084i	$0.369463\pi$
$390$	7.15076e13	0.401326
$391$	2.38020e14	1.31717
$392$	1.32462e14	0.722802
$393$	−1.30443e14	−0.701877
$394$	−2.62558e14	−1.39315
$395$	−9.91582e13	−0.518853
$396$	−6.69355e13	−0.345408
$397$	−2.93432e14	−1.49334	−0.746671	−	0.665194i	$-0.768349\pi$
$397$	−2.93432e14	−1.49334	−0.746671	+	0.665194i	$0.768349\pi$
$398$	5.16163e14	2.59078
$399$	3.83564e14	1.89883
$400$	1.17180e14	0.572169
$401$	−1.66166e14	−0.800293	−0.400146	−	0.916451i	$-0.631041\pi$
$401$	−1.66166e14	−0.800293	−0.400146	+	0.916451i	$0.631041\pi$
$402$	3.63242e13	0.172565
$403$	1.02654e14	0.481061
$404$	7.62367e12	0.0352425
$405$	−1.72979e13	−0.0788844
$406$	4.93053e14	2.21820
$407$	1.58493e14	0.703462
$408$	3.91692e13	0.171520
$409$	4.04981e14	1.74967	0.874836	−	0.484420i	$-0.160969\pi$
$409$	4.04981e14	1.74967	0.874836	+	0.484420i	$0.160969\pi$
$410$	3.10161e14	1.32214
$411$	−1.51376e12	−0.00636689
$412$	−1.36128e14	−0.564954
$413$	−6.22399e13	−0.254885
$414$	1.25546e14	0.507344
$415$	−3.13421e14	−1.24986
$416$	−2.39847e14	−0.943889
$417$	−4.73067e13	−0.183728
$418$	7.54047e14	2.89020
$419$	−4.37489e14	−1.65497	−0.827485	−	0.561488i	$-0.810229\pi$
$419$	−4.37489e14	−1.65497	−0.827485	+	0.561488i	$0.810229\pi$
$420$	−1.74181e14	−0.650325
$421$	−2.90114e14	−1.06910	−0.534548	−	0.845138i	$-0.679518\pi$
$421$	−2.90114e14	−1.06910	−0.534548	+	0.845138i	$0.679518\pi$
$422$	−1.71983e14	−0.625558
$423$	−1.29097e14	−0.463495
$424$	−1.04160e14	−0.369136
$425$	1.65077e14	0.577493
$426$	2.31928e14	0.800941
$427$	−7.35187e14	−2.50637
$428$	−6.68821e12	−0.0225097
$429$	−1.61681e14	−0.537211
$430$	−3.75276e14	−1.23104
$431$	3.55443e14	1.15119	0.575593	−	0.817736i	$-0.304771\pi$
$431$	3.55443e14	1.15119	0.575593	+	0.817736i	$0.304771\pi$
$432$	6.94318e13	0.222023
$433$	1.26989e14	0.400942	0.200471	−	0.979700i	$-0.435753\pi$
$433$	1.26989e14	0.400942	0.200471	+	0.979700i	$0.435753\pi$
$434$	−5.58610e14	−1.74147
$435$	1.12127e14	0.345159
$436$	−1.83892e14	−0.558968
$437$	−6.33089e14	−1.90028
$438$	2.80261e14	0.830721
$439$	4.00751e14	1.17306	0.586530	−	0.809928i	$-0.300494\pi$
$439$	4.00751e14	1.17306	0.586530	+	0.809928i	$0.300494\pi$
$440$	8.01238e13	0.231618
$441$	3.30779e14	0.944334
$442$	−4.04342e14	−1.14006
$443$	−3.89507e14	−1.08466	−0.542331	−	0.840165i	$-0.682458\pi$
$443$	−3.89507e14	−1.08466	−0.542331	+	0.840165i	$0.682458\pi$
$444$	9.35854e13	0.257396
$445$	−9.14179e13	−0.248343
$446$	−5.14675e13	−0.138099
$447$	1.90076e14	0.503775
$448$	4.42426e14	1.15828
$449$	−4.11391e14	−1.06390	−0.531949	−	0.846776i	$-0.678540\pi$
$449$	−4.11391e14	−1.06390	−0.531949	+	0.846776i	$0.678540\pi$
$450$	8.70717e13	0.222438
$451$	−7.01286e14	−1.76980
$452$	5.33073e14	1.32900
$453$	1.74774e14	0.430464
$454$	−4.34537e14	−1.05735
$455$	−4.20732e14	−1.01145
$456$	−1.04183e14	−0.247451
$457$	3.04151e14	0.713758	0.356879	−	0.934151i	$-0.383841\pi$
$457$	3.04151e14	0.713758	0.356879	+	0.934151i	$0.383841\pi$
$458$	4.96268e14	1.15068
$459$	9.78115e13	0.224089
$460$	2.87494e14	0.650819
$461$	8.14598e14	1.82217	0.911084	−	0.412221i	$-0.135247\pi$
$461$	8.14598e14	1.82217	0.911084	+	0.412221i	$0.135247\pi$
$462$	8.79814e14	1.94473
$463$	5.28967e14	1.15540	0.577701	−	0.816248i	$-0.303950\pi$
$463$	5.28967e14	1.15540	0.577701	+	0.816248i	$0.303950\pi$
$464$	−4.50064e14	−0.971462
$465$	−1.27035e14	−0.270978
$466$	6.95126e13	0.146535
$467$	4.17896e14	0.870613	0.435307	−	0.900282i	$-0.356640\pi$
$467$	4.17896e14	0.870613	0.435307	+	0.900282i	$0.356640\pi$
$468$	−9.54681e13	−0.196565
$469$	−2.13722e14	−0.434909
$470$	−6.60423e14	−1.32826
$471$	−1.86633e14	−0.371000
$472$	1.69055e13	0.0332159
$473$	8.48512e14	1.64787
$474$	2.95744e14	0.567721
$475$	−4.39073e14	−0.833148
$476$	9.84913e14	1.84739
$477$	−2.60103e14	−0.482274
$478$	−1.13749e14	−0.208494
$479$	7.53061e14	1.36453	0.682267	−	0.731103i	$-0.260994\pi$
$479$	7.53061e14	1.36453	0.682267	+	0.731103i	$0.260994\pi$
$480$	2.96812e14	0.531685
$481$	2.26054e14	0.400326
$482$	2.52484e14	0.442054
$483$	−7.38681e14	−1.27864
$484$	3.00710e14	0.514635
$485$	−2.17596e14	−0.368190
$486$	5.15918e13	0.0863141
$487$	3.30902e14	0.547382	0.273691	−	0.961818i	$-0.411755\pi$
$487$	3.30902e14	0.547382	0.273691	+	0.961818i	$0.411755\pi$
$488$	1.99690e14	0.326623
$489$	−5.11326e13	−0.0826987
$490$	1.69217e15	2.70623
$491$	−1.25595e14	−0.198620	−0.0993101	−	0.995057i	$-0.531664\pi$
$491$	−1.25595e14	−0.198620	−0.0993101	+	0.995057i	$0.531664\pi$
$492$	−4.14089e14	−0.647568
$493$	−6.34025e14	−0.980501
$494$	1.07547e15	1.64476
$495$	2.00082e14	0.302607
$496$	5.09905e14	0.762676
$497$	−1.36460e15	−2.01858
$498$	9.34792e14	1.36758
$499$	7.30727e13	0.105731	0.0528655	−	0.998602i	$-0.483165\pi$
$499$	7.30727e13	0.105731	0.0528655	+	0.998602i	$0.483165\pi$
$500$	6.01417e14	0.860678
$501$	−4.62277e14	−0.654327
$502$	−1.30828e15	−1.83160
$503$	−1.16655e15	−1.61540	−0.807701	−	0.589592i	$-0.799289\pi$
$503$	−1.16655e15	−1.61540	−0.807701	+	0.589592i	$0.799289\pi$
$504$	−1.21559e14	−0.166502
$505$	−2.27885e13	−0.0308754
$506$	−1.45217e15	−1.94621
$507$	2.04894e14	0.271634
$508$	−9.20039e14	−1.20658
$509$	5.44791e14	0.706776	0.353388	−	0.935477i	$-0.385030\pi$
$509$	5.44791e14	0.706776	0.353388	+	0.935477i	$0.385030\pi$
$510$	5.00375e14	0.642184
$511$	−1.64898e15	−2.09363
$512$	−9.57033e14	−1.20210
$513$	−2.60161e14	−0.323293
$514$	−7.92843e13	−0.0974743
$515$	4.06910e14	0.494947
$516$	5.01021e14	0.602952
$517$	1.49324e15	1.77800
$518$	−1.23011e15	−1.44920
$519$	1.94210e14	0.226387
$520$	1.14278e14	0.131809
$521$	−5.49458e14	−0.627085	−0.313543	−	0.949574i	$-0.601516\pi$
$521$	−5.49458e14	−0.627085	−0.313543	+	0.949574i	$0.601516\pi$
$522$	−3.34424e14	−0.377667
$523$	−6.96940e14	−0.778818	−0.389409	−	0.921065i	$-0.627321\pi$
$523$	−6.96940e14	−0.778818	−0.389409	+	0.921065i	$0.627321\pi$
$524$	8.90906e14	0.985167
$525$	−5.12306e14	−0.560601
$526$	−1.01766e15	−1.10200
$527$	7.18325e14	0.769773
$528$	−8.03104e14	−0.851697
$529$	2.66415e14	0.279610
$530$	−1.33061e15	−1.38208
$531$	4.22156e13	0.0433963
$532$	−2.61969e15	−2.66523
$533$	−1.00022e15	−1.00716
$534$	2.72658e14	0.271733
$535$	1.99922e13	0.0197204
$536$	5.80507e13	0.0566762
$537$	1.09329e15	1.05651
$538$	−2.94240e14	−0.281448
$539$	−3.82606e15	−3.62254
$540$	1.18142e14	0.110723
$541$	8.39054e14	0.778404	0.389202	−	0.921153i	$-0.372751\pi$
$541$	8.39054e14	0.778404	0.389202	+	0.921153i	$0.372751\pi$
$542$	9.00383e14	0.826859
$543$	8.24175e14	0.749239
$544$	−1.67833e15	−1.51037
$545$	5.49684e14	0.489702
$546$	1.25485e15	1.10671
$547$	7.76092e13	0.0677615	0.0338807	−	0.999426i	$-0.489213\pi$
$547$	7.76092e13	0.0677615	0.0338807	+	0.999426i	$0.489213\pi$
$548$	1.03388e13	0.00893667
$549$	4.98657e14	0.426731
$550$	−1.00714e15	−0.853288
$551$	1.68639e15	1.41457
$552$	2.00639e14	0.166629
$553$	−1.74008e15	−1.43081
$554$	2.49501e15	2.03127
$555$	−2.79743e14	−0.225500
$556$	3.23098e14	0.257883
$557$	3.82777e14	0.302511	0.151256	−	0.988495i	$-0.451668\pi$
$557$	3.82777e14	0.302511	0.151256	+	0.988495i	$0.451668\pi$
$558$	3.78889e14	0.296499
$559$	1.21021e15	0.937767
$560$	−2.08986e15	−1.60355
$561$	−1.13137e15	−0.859622
$562$	−1.97098e15	−1.48297
$563$	1.66881e15	1.24340	0.621699	−	0.783256i	$-0.286443\pi$
$563$	1.66881e15	1.24340	0.621699	+	0.783256i	$0.286443\pi$
$564$	8.81715e14	0.650569
$565$	−1.59345e15	−1.16432
$566$	−2.69503e15	−1.95017
$567$	−3.03553e14	−0.217534
$568$	3.70650e14	0.263056
$569$	2.65262e14	0.186448	0.0932239	−	0.995645i	$-0.470283\pi$
$569$	2.65262e14	0.186448	0.0932239	+	0.995645i	$0.470283\pi$
$570$	−1.33090e15	−0.926478
$571$	−1.76526e15	−1.21706	−0.608528	−	0.793532i	$-0.708240\pi$
$571$	−1.76526e15	−1.21706	−0.608528	+	0.793532i	$0.708240\pi$
$572$	1.10426e15	0.754038
$573$	1.29402e14	0.0875166
$574$	5.44287e15	3.64597
$575$	8.45584e14	0.561027
$576$	−3.00085e14	−0.197206
$577$	1.87176e14	0.121838	0.0609191	−	0.998143i	$-0.480597\pi$
$577$	1.87176e14	0.121838	0.0609191	+	0.998143i	$0.480597\pi$
$578$	−7.42552e14	−0.478767
$579$	1.25439e15	0.801126
$580$	−7.65811e14	−0.484471
$581$	−5.50007e15	−3.44667
$582$	6.48991e14	0.402868
$583$	3.00856e15	1.85004
$584$	4.47893e14	0.272837
$585$	2.85370e14	0.172207
$586$	−2.10830e15	−1.26036
$587$	−5.72887e13	−0.0339281	−0.0169641	−	0.999856i	$-0.505400\pi$
$587$	−5.72887e13	−0.0339281	−0.0169641	+	0.999856i	$0.505400\pi$
$588$	−2.25917e15	−1.32548
$589$	−1.91061e15	−1.11055
$590$	2.15962e14	0.124363
$591$	−1.04781e15	−0.597793
$592$	1.12285e15	0.634679
$593$	−1.39022e15	−0.778544	−0.389272	−	0.921123i	$-0.627273\pi$
$593$	−1.39022e15	−0.778544	−0.389272	+	0.921123i	$0.627273\pi$
$594$	−5.96753e14	−0.331107
$595$	−2.94407e15	−1.61847
$596$	−1.29819e15	−0.707107
$597$	2.05989e15	1.11169
$598$	−2.07119e15	−1.10755
$599$	−1.83862e15	−0.974192	−0.487096	−	0.873348i	$-0.661944\pi$
$599$	−1.83862e15	−0.974192	−0.487096	+	0.873348i	$0.661944\pi$
$600$	1.39151e14	0.0730560
$601$	−4.19499e14	−0.218233	−0.109117	−	0.994029i	$-0.534802\pi$
$601$	−4.19499e14	−0.218233	−0.109117	+	0.994029i	$0.534802\pi$
$602$	−6.58553e15	−3.39477
$603$	1.44962e14	0.0740471
$604$	−1.19368e15	−0.604207
$605$	−8.98875e14	−0.450863
$606$	6.79676e13	0.0337834
$607$	1.29935e15	0.640011	0.320005	−	0.947416i	$-0.396315\pi$
$607$	1.29935e15	0.640011	0.320005	+	0.947416i	$0.396315\pi$
$608$	4.46405e15	2.17901
$609$	1.96766e15	0.951820
$610$	2.55098e15	1.22291
$611$	2.12977e15	1.01182
$612$	−6.68039e14	−0.314535
$613$	−7.25013e14	−0.338309	−0.169154	−	0.985590i	$-0.554104\pi$
$613$	−7.25013e14	−0.338309	−0.169154	+	0.985590i	$0.554104\pi$
$614$	8.56860e14	0.396263
$615$	1.23778e15	0.567324
$616$	1.40605e15	0.638716
$617$	6.49787e14	0.292552	0.146276	−	0.989244i	$-0.453271\pi$
$617$	6.49787e14	0.292552	0.146276	+	0.989244i	$0.453271\pi$
$618$	−1.21363e15	−0.541563
$619$	1.59102e14	0.0703684	0.0351842	−	0.999381i	$-0.488798\pi$
$619$	1.59102e14	0.0703684	0.0351842	+	0.999381i	$0.488798\pi$
$620$	8.67633e14	0.380349
$621$	5.01027e14	0.217699
$622$	1.57875e14	0.0679931
$623$	−1.60425e15	−0.684837
$624$	−1.14544e15	−0.484684
$625$	−6.15283e14	−0.258068
$626$	−4.21054e15	−1.75057
$627$	3.00923e15	1.24018
$628$	1.27468e15	0.520741
$629$	1.58181e15	0.640585
$630$	−1.55289e15	−0.623400
$631$	4.44997e15	1.77091	0.885453	−	0.464728i	$-0.153848\pi$
$631$	4.44997e15	1.77091	0.885453	+	0.464728i	$0.153848\pi$
$632$	4.72636e14	0.186459
$633$	−6.86346e14	−0.268425
$634$	3.23545e15	1.25442
$635$	2.75015e15	1.05706
$636$	1.77646e15	0.676928
$637$	−5.45699e15	−2.06151
$638$	3.86821e15	1.44876
$639$	9.25571e14	0.343681
$640$	9.66377e14	0.355760
$641$	−5.79024e14	−0.211338	−0.105669	−	0.994401i	$-0.533698\pi$
$641$	−5.79024e14	−0.211338	−0.105669	+	0.994401i	$0.533698\pi$
$642$	−5.96277e13	−0.0215777
$643$	−4.91174e15	−1.76228	−0.881141	−	0.472854i	$-0.843224\pi$
$643$	−4.91174e15	−1.76228	−0.881141	+	0.472854i	$0.843224\pi$
$644$	5.04509e15	1.79472
$645$	−1.49764e15	−0.528237
$646$	7.52564e15	2.63187
$647$	2.42235e15	0.839970	0.419985	−	0.907531i	$-0.362035\pi$
$647$	2.42235e15	0.839970	0.419985	+	0.907531i	$0.362035\pi$
$648$	8.24503e13	0.0283485
$649$	−4.88299e14	−0.166472
$650$	−1.43646e15	−0.485589
$651$	−2.22928e15	−0.747256
$652$	3.49228e14	0.116077
$653$	−1.71942e15	−0.566707	−0.283353	−	0.959016i	$-0.591447\pi$
$653$	−1.71942e15	−0.566707	−0.283353	+	0.959016i	$0.591447\pi$
$654$	−1.63946e15	−0.535825
$655$	−2.66307e15	−0.863088
$656$	−4.96832e15	−1.59675
$657$	1.11846e15	0.356459
$658$	−1.15894e16	−3.66286
$659$	−1.26828e14	−0.0397509	−0.0198754	−	0.999802i	$-0.506327\pi$
$659$	−1.26828e14	−0.0397509	−0.0198754	+	0.999802i	$0.506327\pi$
$660$	−1.36653e15	−0.424744
$661$	4.61309e15	1.42195	0.710974	−	0.703218i	$-0.248254\pi$
$661$	4.61309e15	1.42195	0.710974	+	0.703218i	$0.248254\pi$
$662$	7.27684e15	2.22446
$663$	−1.61363e15	−0.489194
$664$	1.49392e15	0.449161
$665$	7.83069e15	2.33497
$666$	8.34346e14	0.246739
$667$	−3.24771e15	−0.952543
$668$	3.15729e15	0.918425
$669$	−2.05395e14	−0.0592579
$670$	7.41581e14	0.212201
$671$	−5.76786e15	−1.63697
$672$	5.20860e15	1.46619
$673$	5.73851e15	1.60220	0.801099	−	0.598531i	$-0.204249\pi$
$673$	5.73851e15	1.60220	0.801099	+	0.598531i	$0.204249\pi$
$674$	−6.92603e15	−1.91803
$675$	3.47483e14	0.0954471
$676$	−1.39939e15	−0.381271
$677$	−1.95747e15	−0.529003	−0.264501	−	0.964385i	$-0.585207\pi$
$677$	−1.95747e15	−0.529003	−0.264501	+	0.964385i	$0.585207\pi$
$678$	4.75253e15	1.27398
$679$	−3.81849e15	−1.01533
$680$	7.99663e14	0.210915
$681$	−1.73414e15	−0.453706
$682$	−4.38254e15	−1.13740
$683$	−3.45210e15	−0.888730	−0.444365	−	0.895846i	$-0.646571\pi$
$683$	−3.45210e15	−0.888730	−0.444365	+	0.895846i	$0.646571\pi$
$684$	1.77686e15	0.453779
$685$	−3.09043e13	−0.00782927
$686$	1.92132e16	4.82856
$687$	1.98049e15	0.493754
$688$	6.01135e15	1.48674
$689$	4.29101e15	1.05282
$690$	2.56311e15	0.623873
$691$	−1.20060e15	−0.289914	−0.144957	−	0.989438i	$-0.546304\pi$
$691$	−1.20060e15	−0.289914	−0.144957	+	0.989438i	$0.546304\pi$
$692$	−1.32643e15	−0.317760
$693$	3.51113e15	0.834477
$694$	3.25247e14	0.0766895
$695$	−9.65796e14	−0.225927
$696$	−5.34451e14	−0.124039
$697$	−6.99908e15	−1.61161
$698$	7.26444e15	1.65958
$699$	2.77409e14	0.0628776
$700$	3.49898e15	0.786868
$701$	−6.69273e14	−0.149333	−0.0746663	−	0.997209i	$-0.523789\pi$
$701$	−6.69273e14	−0.149333	−0.0746663	+	0.997209i	$0.523789\pi$
$702$	−8.51131e14	−0.188427
$703$	−4.20733e15	−0.924170
$704$	3.47103e15	0.756499
$705$	−2.63560e15	−0.569953
$706$	−6.53699e15	−1.40266
$707$	−3.99903e14	−0.0851429
$708$	−2.88326e14	−0.0609118
$709$	−2.58351e15	−0.541572	−0.270786	−	0.962640i	$-0.587284\pi$
$709$	−2.58351e15	−0.541572	−0.270786	+	0.962640i	$0.587284\pi$
$710$	4.73495e15	0.984905
$711$	1.18025e15	0.243607
$712$	4.35742e14	0.0892462
$713$	3.67952e15	0.747824
$714$	8.78084e15	1.77091
$715$	−3.30082e15	−0.660601
$716$	−7.46699e15	−1.48294
$717$	−4.53946e14	−0.0894641
$718$	7.11849e15	1.39221
$719$	2.22712e15	0.432249	0.216125	−	0.976366i	$-0.430658\pi$
$719$	2.22712e15	0.432249	0.216125	+	0.976366i	$0.430658\pi$
$720$	1.41749e15	0.273018
$721$	7.14066e15	1.36488
$722$	−1.29237e16	−2.45149
$723$	1.00761e15	0.189684
$724$	−5.62900e15	−1.05164
$725$	−2.25242e15	−0.417629
$726$	2.68094e15	0.493327
$727$	8.31113e13	0.0151782	0.00758911	−	0.999971i	$-0.497584\pi$
$727$	8.31113e13	0.0151782	0.00758911	+	0.999971i	$0.497584\pi$
$728$	2.00541e15	0.363480
$729$	2.05891e14	0.0370370
$730$	5.72170e15	1.02153
$731$	8.46844e15	1.50058
$732$	−3.40575e15	−0.598966
$733$	8.81391e15	1.53850	0.769249	−	0.638950i	$-0.220631\pi$
$733$	8.81391e15	1.53850	0.769249	+	0.638950i	$0.220631\pi$
$734$	4.67325e15	0.809638
$735$	6.75306e15	1.16123
$736$	−8.59703e15	−1.46730
$737$	−1.67674e15	−0.284050
$738$	−3.69175e15	−0.620757
$739$	2.56306e15	0.427774	0.213887	−	0.976858i	$-0.431388\pi$
$739$	2.56306e15	0.427774	0.213887	+	0.976858i	$0.431388\pi$
$740$	1.91060e15	0.316516
$741$	4.29197e15	0.705759
$742$	−2.33502e16	−3.81127
$743$	9.06237e15	1.46826	0.734130	−	0.679009i	$-0.237590\pi$
$743$	9.06237e15	1.46826	0.734130	+	0.679009i	$0.237590\pi$
$744$	6.05512e14	0.0973805
$745$	3.88052e15	0.619485
$746$	−8.94794e15	−1.41794
$747$	3.73054e15	0.586825
$748$	7.72707e15	1.20658
$749$	3.50833e14	0.0543814
$750$	5.36184e15	0.825044
$751$	2.67908e15	0.409229	0.204614	−	0.978843i	$-0.434406\pi$
$751$	2.67908e15	0.409229	0.204614	+	0.978843i	$0.434406\pi$
$752$	1.05790e16	1.60415
$753$	−5.22104e15	−0.785931
$754$	5.51712e15	0.824461
$755$	3.56812e15	0.529336
$756$	2.07322e15	0.305334
$757$	1.54640e15	0.226097	0.113049	−	0.993589i	$-0.463938\pi$
$757$	1.54640e15	0.226097	0.113049	+	0.993589i	$0.463938\pi$
$758$	6.81332e15	0.988959
$759$	−5.79528e15	−0.835111
$760$	−2.12695e15	−0.304287
$761$	6.80674e15	0.966771	0.483385	−	0.875408i	$-0.339407\pi$
$761$	6.80674e15	0.966771	0.483385	+	0.875408i	$0.339407\pi$
$762$	−8.20247e15	−1.15662
$763$	9.64613e15	1.35042
$764$	−8.83797e14	−0.122840
$765$	1.99688e15	0.275559
$766$	6.57445e15	0.900744
$767$	−6.96447e14	−0.0947356
$768$	−5.41138e15	−0.730838
$769$	7.08886e15	0.950564	0.475282	−	0.879834i	$-0.342346\pi$
$769$	7.08886e15	0.950564	0.475282	+	0.879834i	$0.342346\pi$
$770$	1.79619e16	2.39141
$771$	−3.16405e14	−0.0418258
$772$	−8.56731e15	−1.12447
$773$	1.17195e16	1.52729	0.763643	−	0.645639i	$-0.223409\pi$
$773$	1.17195e16	1.52729	0.763643	+	0.645639i	$0.223409\pi$
$774$	4.46678e15	0.577988
$775$	2.55190e15	0.327873
$776$	1.03717e15	0.132315
$777$	−4.90907e15	−0.621847
$778$	−8.52988e15	−1.07289
$779$	1.86162e16	2.32507
$780$	−1.94904e15	−0.241713
$781$	−1.07059e16	−1.31839
$782$	−1.44932e16	−1.77225
$783$	−1.33461e15	−0.162056
$784$	−2.71060e16	−3.26834
$785$	−3.81022e15	−0.456213
$786$	7.94273e15	0.944378
$787$	1.65457e16	1.95354	0.976772	−	0.214279i	$-0.0687402\pi$
$787$	1.65457e16	1.95354	0.976772	+	0.214279i	$0.0687402\pi$
$788$	7.15639e15	0.839073
$789$	−4.06126e15	−0.472865
$790$	6.03779e15	0.698119
$791$	−2.79626e16	−3.21076
$792$	−9.53686e14	−0.108747
$793$	−8.22653e15	−0.931568
$794$	1.78672e16	2.00930
$795$	−5.31015e15	−0.593045
$796$	−1.40687e16	−1.56039
$797$	1.06176e16	1.16952	0.584758	−	0.811208i	$-0.301189\pi$
$797$	1.06176e16	1.16952	0.584758	+	0.811208i	$0.301189\pi$
$798$	−2.33554e16	−2.55489
$799$	1.49031e16	1.61908
$800$	−5.96240e15	−0.643318
$801$	1.08812e15	0.116599
$802$	1.01180e16	1.07680
$803$	−1.29370e16	−1.36741
$804$	−9.90067e14	−0.103934
$805$	−1.50806e16	−1.57232
$806$	−6.25068e15	−0.647269
$807$	−1.17424e15	−0.120768
$808$	1.08621e14	0.0110956
$809$	1.07657e15	0.109226	0.0546130	−	0.998508i	$-0.482607\pi$
$809$	1.07657e15	0.109226	0.0546130	+	0.998508i	$0.482607\pi$
$810$	1.05328e15	0.106139
$811$	3.90930e15	0.391277	0.195639	−	0.980676i	$-0.437322\pi$
$811$	3.90930e15	0.391277	0.195639	+	0.980676i	$0.437322\pi$
$812$	−1.34388e16	−1.33599
$813$	3.59322e15	0.354802
$814$	−9.65071e15	−0.946510
$815$	−1.04390e15	−0.101693
$816$	−8.01525e15	−0.775571
$817$	−2.25245e16	−2.16488
$818$	−2.46595e16	−2.35419
$819$	5.00782e15	0.474884
$820$	−8.45388e15	−0.796306
$821$	1.05915e16	0.990989	0.495495	−	0.868611i	$-0.334987\pi$
$821$	1.05915e16	0.990989	0.495495	+	0.868611i	$0.334987\pi$
$822$	9.21737e13	0.00856667
$823$	1.08752e16	1.00401	0.502006	−	0.864864i	$-0.332596\pi$
$823$	1.08752e16	1.00401	0.502006	+	0.864864i	$0.332596\pi$
$824$	−1.93953e15	−0.177868
$825$	−4.01927e15	−0.366142
$826$	3.78982e15	0.342948
$827$	2.27647e15	0.204636	0.102318	−	0.994752i	$-0.467374\pi$
$827$	2.27647e15	0.204636	0.102318	+	0.994752i	$0.467374\pi$
$828$	−3.42194e15	−0.305566
$829$	8.11215e15	0.719592	0.359796	−	0.933031i	$-0.382846\pi$
$829$	8.11215e15	0.719592	0.359796	+	0.933031i	$0.382846\pi$
$830$	1.90843e16	1.68170
$831$	9.95700e15	0.871612
$832$	4.95062e15	0.430508
$833$	−3.81853e16	−3.29875
$834$	2.88053e15	0.247206
$835$	−9.43767e15	−0.804617
$836$	−2.05526e16	−1.74073
$837$	1.51206e15	0.127227
$838$	2.66389e16	2.22677
$839$	−4.64454e15	−0.385702	−0.192851	−	0.981228i	$-0.561773\pi$
$839$	−4.64454e15	−0.385702	−0.192851	+	0.981228i	$0.561773\pi$
$840$	−2.48171e15	−0.204746
$841$	−3.54944e15	−0.290926
$842$	1.76652e16	1.43847
$843$	−7.86572e15	−0.636336
$844$	4.68764e15	0.376766
$845$	4.18303e15	0.334025
$846$	7.86079e15	0.623633
$847$	−1.57739e16	−1.24331
$848$	2.13143e16	1.66915
$849$	−1.07552e16	−0.836812
$850$	−1.00516e16	−0.777019
$851$	8.10262e15	0.622319
$852$	−6.32152e15	−0.482396
$853$	−2.47562e16	−1.87700	−0.938500	−	0.345279i	$-0.887784\pi$
$853$	−2.47562e16	−1.87700	−0.938500	+	0.345279i	$0.887784\pi$
$854$	4.47659e16	3.37232
$855$	−5.31133e15	−0.397548
$856$	−9.52925e13	−0.00708685
$857$	−2.43666e16	−1.80053	−0.900264	−	0.435344i	$-0.856627\pi$
$857$	−2.43666e16	−1.80053	−0.900264	+	0.435344i	$0.856627\pi$
$858$	9.84486e15	0.722819
$859$	−1.82706e16	−1.33288	−0.666440	−	0.745559i	$-0.732183\pi$
$859$	−1.82706e16	−1.33288	−0.666440	+	0.745559i	$0.732183\pi$
$860$	1.02287e16	0.741442
$861$	2.17212e16	1.56447
$862$	−2.16431e16	−1.54892
$863$	2.15127e16	1.52980	0.764901	−	0.644148i	$-0.222788\pi$
$863$	2.15127e16	1.52980	0.764901	+	0.644148i	$0.222788\pi$
$864$	−3.53285e15	−0.249632
$865$	3.96491e15	0.278384
$866$	−7.73241e15	−0.539469
$867$	−2.96335e15	−0.205437
$868$	1.52257e16	1.04886
$869$	−1.36517e16	−0.934495
$870$	−6.82746e15	−0.464412
$871$	−2.39149e15	−0.161647
$872$	−2.62006e15	−0.175983
$873$	2.58997e15	0.172869
$874$	3.85491e16	2.55683
$875$	−3.15476e16	−2.07933
$876$	−7.63891e15	−0.500332
$877$	−1.62970e16	−1.06074	−0.530372	−	0.847765i	$-0.677948\pi$
$877$	−1.62970e16	−1.06074	−0.530372	+	0.847765i	$0.677948\pi$
$878$	−2.44019e16	−1.57835
$879$	−8.41375e15	−0.540818
$880$	−1.63959e16	−1.04732
$881$	−2.42995e15	−0.154252	−0.0771259	−	0.997021i	$-0.524574\pi$
$881$	−2.42995e15	−0.154252	−0.0771259	+	0.997021i	$0.524574\pi$
$882$	−2.01413e16	−1.27060
$883$	−1.73372e16	−1.08691	−0.543456	−	0.839438i	$-0.682884\pi$
$883$	−1.73372e16	−1.08691	−0.543456	+	0.839438i	$0.682884\pi$
$884$	1.10209e16	0.686641
$885$	8.61856e14	0.0533638
$886$	2.37173e16	1.45942
$887$	1.04560e16	0.639418	0.319709	−	0.947516i	$-0.396415\pi$
$887$	1.04560e16	0.639418	0.319709	+	0.947516i	$0.396415\pi$
$888$	1.33339e15	0.0810374
$889$	4.82611e16	2.91499
$890$	5.56648e15	0.334146
$891$	−2.38150e15	−0.142077
$892$	1.40282e15	0.0831754
$893$	−3.96394e16	−2.33584
$894$	−1.15738e16	−0.677831
$895$	2.23201e16	1.29918
$896$	1.69585e16	0.981054
$897$	−8.26563e15	−0.475245
$898$	2.50498e16	1.43148
$899$	−9.80132e15	−0.556681
$900$	−2.37326e15	−0.133971
$901$	3.00264e16	1.68468
$902$	4.27017e16	2.38127
$903$	−2.62813e16	−1.45668
$904$	7.59515e15	0.418417
$905$	1.68260e16	0.921329
$906$	−1.06421e16	−0.579191
$907$	−1.16136e16	−0.628243	−0.314121	−	0.949383i	$-0.601710\pi$
$907$	−1.16136e16	−0.628243	−0.314121	+	0.949383i	$0.601710\pi$
$908$	1.18439e16	0.636829
$909$	2.71243e14	0.0144963
$910$	2.56186e16	1.36090
$911$	−2.10621e16	−1.11212	−0.556058	−	0.831144i	$-0.687687\pi$
$911$	−2.10621e16	−1.11212	−0.556058	+	0.831144i	$0.687687\pi$
$912$	2.13191e16	1.11891
$913$	−4.31504e16	−2.25110
$914$	−1.85199e16	−0.960363
$915$	1.01804e16	0.524745
$916$	−1.35265e16	−0.693042
$917$	−4.67329e16	−2.38008
$918$	−5.95580e15	−0.301512
$919$	−1.96640e15	−0.0989545	−0.0494772	−	0.998775i	$-0.515756\pi$
$919$	−1.96640e15	−0.0989545	−0.0494772	+	0.998775i	$0.515756\pi$
$920$	4.09616e15	0.204901
$921$	3.41953e15	0.170035
$922$	−4.96013e16	−2.45173
$923$	−1.52695e16	−0.750266
$924$	−2.39805e16	−1.17129
$925$	5.61951e15	0.272847
$926$	−3.22091e16	−1.55460
$927$	−4.84331e15	−0.232383
$928$	2.29003e16	1.09226
$929$	−1.42554e16	−0.675917	−0.337958	−	0.941161i	$-0.609736\pi$
$929$	−1.42554e16	−0.675917	−0.337958	+	0.941161i	$0.609736\pi$
$930$	7.73525e15	0.364601
$931$	1.01566e17	4.75910
$932$	−1.89466e15	−0.0882561
$933$	6.30041e14	0.0291756
$934$	−2.54459e16	−1.17141
$935$	−2.30975e16	−1.05707
$936$	−1.36021e15	−0.0618857
$937$	2.82587e16	1.27816	0.639079	−	0.769141i	$-0.279316\pi$
$937$	2.82587e16	1.27816	0.639079	+	0.769141i	$0.279316\pi$
$938$	1.30136e16	0.585172
$939$	−1.68033e16	−0.751162
$940$	1.80008e16	0.799995
$941$	3.12522e15	0.138082	0.0690412	−	0.997614i	$-0.478006\pi$
$941$	3.12522e15	0.138082	0.0690412	+	0.997614i	$0.478006\pi$
$942$	1.13642e16	0.499181
$943$	−3.58518e16	−1.56566
$944$	−3.45939e15	−0.150194
$945$	−6.19721e15	−0.267498
$946$	−5.16663e16	−2.21721
$947$	−8.86812e14	−0.0378361	−0.0189181	−	0.999821i	$-0.506022\pi$
$947$	−8.86812e14	−0.0378361	−0.0189181	+	0.999821i	$0.506022\pi$
$948$	−8.06091e15	−0.341931
$949$	−1.84516e16	−0.778163
$950$	2.67354e16	1.12100
$951$	1.29119e16	0.538268
$952$	1.40329e16	0.581626
$953$	3.73597e16	1.53954	0.769772	−	0.638319i	$-0.220370\pi$
$953$	3.73597e16	1.53954	0.769772	+	0.638319i	$0.220370\pi$
$954$	1.58378e16	0.648901
$955$	2.64182e15	0.107618
$956$	3.10039e15	0.125573
$957$	1.54371e16	0.621658
$958$	−4.58542e16	−1.83599
$959$	−5.42325e14	−0.0215902
$960$	−6.12642e15	−0.242502
$961$	−1.43040e16	−0.562960
$962$	−1.37645e16	−0.538640
$963$	−2.37960e14	−0.00925891
$964$	−6.88180e15	−0.266243
$965$	2.56091e16	0.985133
$966$	4.49787e16	1.72041
$967$	6.73354e15	0.256093	0.128047	−	0.991768i	$-0.459129\pi$
$967$	6.73354e15	0.256093	0.128047	+	0.991768i	$0.459129\pi$
$968$	4.28447e15	0.162025
$969$	3.00331e16	1.12933
$970$	1.32496e16	0.495401
$971$	4.27408e16	1.58905	0.794524	−	0.607233i	$-0.207720\pi$
$971$	4.27408e16	1.58905	0.794524	+	0.607233i	$0.207720\pi$
$972$	−1.40621e15	−0.0519858
$973$	−1.69483e16	−0.623024
$974$	−2.01488e16	−0.736504
$975$	−5.73256e15	−0.208364
$976$	−4.08629e16	−1.47691
$977$	−4.16013e16	−1.49516	−0.747579	−	0.664173i	$-0.768784\pi$
$977$	−4.16013e16	−1.49516	−0.747579	+	0.664173i	$0.768784\pi$
$978$	3.11349e15	0.111271
$979$	−1.25860e16	−0.447284
$980$	−4.61224e16	−1.62993
$981$	−6.54270e15	−0.229920
$982$	7.64753e15	0.267244
$983$	2.02106e16	0.702320	0.351160	−	0.936315i	$-0.385787\pi$
$983$	2.02106e16	0.702320	0.351160	+	0.936315i	$0.385787\pi$
$984$	−5.89987e15	−0.203878
$985$	−2.13917e16	−0.735098
$986$	3.86061e16	1.31927
$987$	−4.62508e16	−1.57172
$988$	−2.93135e16	−0.990615
$989$	4.33784e16	1.45779
$990$	−1.21831e16	−0.407158
$991$	2.16397e15	0.0719194	0.0359597	−	0.999353i	$-0.488551\pi$
$991$	2.16397e15	0.0719194	0.0359597	+	0.999353i	$0.488551\pi$
$992$	−2.59451e16	−0.857515
$993$	2.90402e16	0.954506
$994$	8.30913e16	2.71600
$995$	4.20538e16	1.36703
$996$	−2.54791e16	−0.823677
$997$	3.16920e15	0.101889	0.0509444	−	0.998701i	$-0.483777\pi$
$997$	3.16920e15	0.101889	0.0509444	+	0.998701i	$0.483777\pi$
$998$	−4.44944e15	−0.142261
$999$	3.32968e15	0.105875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.6	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-60.8905 q^{2} -243.000 q^{3} +1659.66 q^{4} -4960.99 q^{5} +14796.4 q^{6} -87058.0 q^{7} +23646.5 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-60.8905 q^{2} -243.000 q^{3} +1659.66 q^{4} -4960.99 q^{5} +14796.4 q^{6} -87058.0 q^{7} +23646.5 q^{8} +59049.0 q^{9} +302077. q^{10} -683008. q^{11} -403296. q^{12} -974154. q^{13} +5.30101e6 q^{14} +1.20552e6 q^{15} -4.83882e6 q^{16} -6.81665e6 q^{17} -3.59552e6 q^{18} +1.81310e7 q^{19} -8.23354e6 q^{20} +2.11551e7 q^{21} +4.15887e7 q^{22} -3.49174e7 q^{23} -5.74610e6 q^{24} -2.42167e7 q^{25} +5.93168e7 q^{26} -1.43489e7 q^{27} -1.44486e8 q^{28} +9.30111e7 q^{29} -7.34048e7 q^{30} -1.05378e8 q^{31} +2.46210e8 q^{32} +1.65971e8 q^{33} +4.15070e8 q^{34} +4.31894e8 q^{35} +9.80010e7 q^{36} -2.32051e8 q^{37} -1.10401e9 q^{38} +2.36720e8 q^{39} -1.17310e8 q^{40} +1.02676e9 q^{41} -1.28815e9 q^{42} -1.24232e9 q^{43} -1.13356e9 q^{44} -2.92942e8 q^{45} +2.12614e9 q^{46} -2.18627e9 q^{47} +1.17583e9 q^{48} +5.60177e9 q^{49} +1.47457e9 q^{50} +1.65645e9 q^{51} -1.61676e9 q^{52} -4.40486e9 q^{53} +8.73712e8 q^{54} +3.38840e9 q^{55} -2.05862e9 q^{56} -4.40584e9 q^{57} -5.66350e9 q^{58} +7.14924e8 q^{59} +2.00075e9 q^{60} +8.44479e9 q^{61} +6.41652e9 q^{62} -5.14069e9 q^{63} -5.08197e9 q^{64} +4.83277e9 q^{65} -1.01061e10 q^{66} +2.45494e9 q^{67} -1.13133e10 q^{68} +8.48493e9 q^{69} -2.62983e10 q^{70} +1.56746e10 q^{71} +1.39630e9 q^{72} +1.89412e10 q^{73} +1.41297e10 q^{74} +5.88465e9 q^{75} +3.00913e10 q^{76} +5.94613e10 q^{77} -1.44140e10 q^{78} +1.99876e10 q^{79} +2.40054e10 q^{80} +3.48678e9 q^{81} -6.25200e10 q^{82} +6.31770e10 q^{83} +3.51102e10 q^{84} +3.38174e10 q^{85} +7.56453e10 q^{86} -2.26017e10 q^{87} -1.61508e10 q^{88} +1.84273e10 q^{89} +1.78374e10 q^{90} +8.48080e10 q^{91} -5.79509e10 q^{92} +2.56068e10 q^{93} +1.33123e11 q^{94} -8.99479e10 q^{95} -5.98291e10 q^{96} +4.38615e10 q^{97} -3.41095e11 q^{98} -4.03310e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 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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