LMFDB - Embedded newform 177.12.a.d.1.25

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:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
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)

$f(q)$	$=$	$q+77.3966 q^{2} +243.000 q^{3} +3942.23 q^{4} +12412.6 q^{5} +18807.4 q^{6} +77263.0 q^{7} +146607. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+77.3966 q^{2} +243.000 q^{3} +3942.23 q^{4} +12412.6 q^{5} +18807.4 q^{6} +77263.0 q^{7} +146607. q^{8} +59049.0 q^{9} +960690. q^{10} -726732. q^{11} +957963. q^{12} +502858. q^{13} +5.97989e6 q^{14} +3.01625e6 q^{15} +3.27321e6 q^{16} +5.93238e6 q^{17} +4.57019e6 q^{18} -285255. q^{19} +4.89332e7 q^{20} +1.87749e7 q^{21} -5.62466e7 q^{22} -3.99141e7 q^{23} +3.56256e7 q^{24} +1.05244e8 q^{25} +3.89195e7 q^{26} +1.43489e7 q^{27} +3.04589e8 q^{28} -1.60191e8 q^{29} +2.33448e8 q^{30} +1.72822e8 q^{31} -4.69162e7 q^{32} -1.76596e8 q^{33} +4.59146e8 q^{34} +9.59032e8 q^{35} +2.32785e8 q^{36} -4.59961e8 q^{37} -2.20777e7 q^{38} +1.22195e8 q^{39} +1.81977e9 q^{40} -5.35805e7 q^{41} +1.45311e9 q^{42} -7.31230e8 q^{43} -2.86495e9 q^{44} +7.32949e8 q^{45} -3.08922e9 q^{46} -7.00419e8 q^{47} +7.95391e8 q^{48} +3.99224e9 q^{49} +8.14549e9 q^{50} +1.44157e9 q^{51} +1.98239e9 q^{52} -5.47327e8 q^{53} +1.11056e9 q^{54} -9.02061e9 q^{55} +1.13273e10 q^{56} -6.93169e7 q^{57} -1.23982e10 q^{58} +7.14924e8 q^{59} +1.18908e10 q^{60} -6.37855e9 q^{61} +1.33758e10 q^{62} +4.56230e9 q^{63} -1.03347e10 q^{64} +6.24176e9 q^{65} -1.36679e10 q^{66} -8.96714e9 q^{67} +2.33868e10 q^{68} -9.69913e9 q^{69} +7.42258e10 q^{70} +6.32421e9 q^{71} +8.65702e9 q^{72} -1.17466e10 q^{73} -3.55994e10 q^{74} +2.55742e10 q^{75} -1.12454e9 q^{76} -5.61495e10 q^{77} +9.45745e9 q^{78} -2.87455e10 q^{79} +4.06290e10 q^{80} +3.48678e9 q^{81} -4.14695e9 q^{82} -5.71170e10 q^{83} +7.40151e10 q^{84} +7.36360e10 q^{85} -5.65947e10 q^{86} -3.89264e10 q^{87} -1.06544e11 q^{88} +7.05259e10 q^{89} +5.67278e10 q^{90} +3.88524e10 q^{91} -1.57351e11 q^{92} +4.19957e10 q^{93} -5.42101e10 q^{94} -3.54074e9 q^{95} -1.14006e10 q^{96} -1.00638e11 q^{97} +3.08986e11 q^{98} -4.29128e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) $ 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * 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 $

$2$	77.3966	1.71024	0.855120	−	0.518430i	$-0.173484\pi$
$2$	77.3966	1.71024	0.855120	+	0.518430i	$0.173484\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	3942.23	1.92492
$5$	12412.6	1.77634	0.888171	−	0.459514i	$-0.151976\pi$
$5$	12412.6	1.77634	0.888171	+	0.459514i	$0.151976\pi$
$6$	18807.4	0.987407
$7$	77263.0	1.73753	0.868765	−	0.495225i	$-0.164914\pi$
$7$	77263.0	1.73753	0.868765	+	0.495225i	$0.164914\pi$
$8$	146607.	1.58183
$9$	59049.0	0.333333
$10$	960690.	3.03797
$11$	−726732.	−1.36055	−0.680275	−	0.732957i	$-0.738140\pi$
$11$	−726732.	−1.36055	−0.680275	+	0.732957i	$0.738140\pi$
$12$	957963.	1.11135
$13$	502858.	0.375627	0.187814	−	0.982205i	$-0.439860\pi$
$13$	502858.	0.375627	0.187814	+	0.982205i	$0.439860\pi$
$14$	5.97989e6	2.97159
$15$	3.01625e6	1.02557
$16$	3.27321e6	0.780395
$17$	5.93238e6	1.01335	0.506675	−	0.862137i	$-0.330874\pi$
$17$	5.93238e6	1.01335	0.506675	+	0.862137i	$0.330874\pi$
$18$	4.57019e6	0.570080
$19$	−285255.	−0.0264294	−0.0132147	−	0.999913i	$-0.504206\pi$
$19$	−285255.	−0.0264294	−0.0132147	+	0.999913i	$0.504206\pi$
$20$	4.89332e7	3.41931
$21$	1.87749e7	1.00316
$22$	−5.62466e7	−2.32687
$23$	−3.99141e7	−1.29307	−0.646537	−	0.762883i	$-0.723783\pi$
$23$	−3.99141e7	−1.29307	−0.646537	+	0.762883i	$0.723783\pi$
$24$	3.56256e7	0.913272
$25$	1.05244e8	2.15539
$26$	3.89195e7	0.642413
$27$	1.43489e7	0.192450
$28$	3.04589e8	3.34460
$29$	−1.60191e8	−1.45027	−0.725135	−	0.688607i	$-0.758222\pi$
$29$	−1.60191e8	−1.45027	−0.725135	+	0.688607i	$0.758222\pi$
$30$	2.33448e8	1.75397
$31$	1.72822e8	1.08420	0.542100	−	0.840314i	$-0.317629\pi$
$31$	1.72822e8	1.08420	0.542100	+	0.840314i	$0.317629\pi$
$32$	−4.69162e7	−0.247171
$33$	−1.76596e8	−0.785514
$34$	4.59146e8	1.73307
$35$	9.59032e8	3.08645
$36$	2.32785e8	0.641640
$37$	−4.59961e8	−1.09046	−0.545232	−	0.838285i	$-0.683558\pi$
$37$	−4.59961e8	−1.09046	−0.545232	+	0.838285i	$0.683558\pi$
$38$	−2.20777e7	−0.0452007
$39$	1.22195e8	0.216869
$40$	1.81977e9	2.80988
$41$	−5.35805e7	−0.0722263	−0.0361132	−	0.999348i	$-0.511498\pi$
$41$	−5.35805e7	−0.0722263	−0.0361132	+	0.999348i	$0.511498\pi$
$42$	1.45311e9	1.71565
$43$	−7.31230e8	−0.758538	−0.379269	−	0.925286i	$-0.623825\pi$
$43$	−7.31230e8	−0.758538	−0.379269	+	0.925286i	$0.623825\pi$
$44$	−2.86495e9	−2.61895
$45$	7.32949e8	0.592114
$46$	−3.08922e9	−2.21147
$47$	−7.00419e8	−0.445471	−0.222736	−	0.974879i	$-0.571499\pi$
$47$	−7.00419e8	−0.445471	−0.222736	+	0.974879i	$0.571499\pi$
$48$	7.95391e8	0.450561
$49$	3.99224e9	2.01901
$50$	8.14549e9	3.68623
$51$	1.44157e9	0.585058
$52$	1.98239e9	0.723053
$53$	−5.47327e8	−0.179775	−0.0898876	−	0.995952i	$-0.528651\pi$
$53$	−5.47327e8	−0.179775	−0.0898876	+	0.995952i	$0.528651\pi$
$54$	1.11056e9	0.329136
$55$	−9.02061e9	−2.41680
$56$	1.13273e10	2.74848
$57$	−6.93169e7	−0.0152590
$58$	−1.23982e10	−2.48031
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	1.18908e10	1.97414
$61$	−6.37855e9	−0.966958	−0.483479	−	0.875356i	$-0.660627\pi$
$61$	−6.37855e9	−0.966958	−0.483479	+	0.875356i	$0.660627\pi$
$62$	1.33758e10	1.85424
$63$	4.56230e9	0.579177
$64$	−1.03347e10	−1.20312
$65$	6.24176e9	0.667242
$66$	−1.36679e10	−1.34342
$67$	−8.96714e9	−0.811414	−0.405707	−	0.914003i	$-0.632975\pi$
$67$	−8.96714e9	−0.811414	−0.405707	+	0.914003i	$0.632975\pi$
$68$	2.33868e10	1.95062
$69$	−9.69913e9	−0.746557
$70$	7.42258e10	5.27856
$71$	6.32421e9	0.415992	0.207996	−	0.978130i	$-0.433306\pi$
$71$	6.32421e9	0.415992	0.207996	+	0.978130i	$0.433306\pi$
$72$	8.65702e9	0.527278
$73$	−1.17466e10	−0.663187	−0.331594	−	0.943422i	$-0.607586\pi$
$73$	−1.17466e10	−0.663187	−0.331594	+	0.943422i	$0.607586\pi$
$74$	−3.55994e10	−1.86495
$75$	2.55742e10	1.24441
$76$	−1.12454e9	−0.0508745
$77$	−5.61495e10	−2.36400
$78$	9.45745e9	0.370897
$79$	−2.87455e10	−1.05105	−0.525523	−	0.850780i	$-0.676130\pi$
$79$	−2.87455e10	−1.05105	−0.525523	+	0.850780i	$0.676130\pi$
$80$	4.06290e10	1.38625
$81$	3.48678e9	0.111111
$82$	−4.14695e9	−0.123524
$83$	−5.71170e10	−1.59161	−0.795803	−	0.605556i	$-0.792951\pi$
$83$	−5.71170e10	−1.59161	−0.795803	+	0.605556i	$0.792951\pi$
$84$	7.40151e10	1.93101
$85$	7.36360e10	1.80006
$86$	−5.65947e10	−1.29728
$87$	−3.89264e10	−0.837313
$88$	−1.06544e11	−2.15216
$89$	7.05259e10	1.33876	0.669381	−	0.742919i	$-0.266559\pi$
$89$	7.05259e10	1.33876	0.669381	+	0.742919i	$0.266559\pi$
$90$	5.67278e10	1.01266
$91$	3.88524e10	0.652664
$92$	−1.57351e11	−2.48906
$93$	4.19957e10	0.625963
$94$	−5.42101e10	−0.761863
$95$	−3.54074e9	−0.0469477
$96$	−1.14006e10	−0.142704
$97$	−1.00638e11	−1.18992	−0.594961	−	0.803755i	$-0.702832\pi$
$97$	−1.00638e11	−1.18992	−0.594961	+	0.803755i	$0.702832\pi$
$98$	3.08986e11	3.45299
$99$	−4.29128e10	−0.453517
$100$	4.14895e11	4.14895
$101$	1.58782e11	1.50325	0.751627	−	0.659588i	$-0.229269\pi$
$101$	1.58782e11	1.50325	0.751627	+	0.659588i	$0.229269\pi$
$102$	1.11572e11	1.00059
$103$	1.39007e11	1.18150	0.590748	−	0.806856i	$-0.298833\pi$
$103$	1.39007e11	1.18150	0.590748	+	0.806856i	$0.298833\pi$
$104$	7.37227e10	0.594180
$105$	2.33045e11	1.78196
$106$	−4.23613e10	−0.307459
$107$	2.19957e11	1.51610	0.758048	−	0.652199i	$-0.226153\pi$
$107$	2.19957e11	1.51610	0.758048	+	0.652199i	$0.226153\pi$
$108$	5.65668e10	0.370451
$109$	−2.46139e11	−1.53227	−0.766135	−	0.642680i	$-0.777823\pi$
$109$	−2.46139e11	−1.53227	−0.766135	+	0.642680i	$0.777823\pi$
$110$	−6.98165e11	−4.13331
$111$	−1.11770e11	−0.629580
$112$	2.52898e11	1.35596
$113$	1.62734e11	0.830899	0.415449	−	0.909616i	$-0.363624\pi$
$113$	1.62734e11	0.830899	0.415449	+	0.909616i	$0.363624\pi$
$114$	−5.36489e9	−0.0260966
$115$	−4.95436e11	−2.29694
$116$	−6.31510e11	−2.79165
$117$	2.96933e10	0.125209
$118$	5.53327e10	0.222654
$119$	4.58353e11	1.76073
$120$	4.42205e11	1.62228
$121$	2.42828e11	0.851098
$122$	−4.93678e11	−1.65373
$123$	−1.30201e10	−0.0416999
$124$	6.81304e11	2.08700
$125$	7.00260e11	2.05236
$126$	3.53107e11	0.990531
$127$	5.47637e11	1.47086	0.735431	−	0.677599i	$-0.236980\pi$
$127$	5.47637e11	1.47086	0.735431	+	0.677599i	$0.236980\pi$
$128$	−7.03786e11	−1.81045
$129$	−1.77689e11	−0.437942
$130$	4.83091e11	1.14114
$131$	2.72269e11	0.616604	0.308302	−	0.951289i	$-0.400239\pi$
$131$	2.72269e11	0.616604	0.308302	+	0.951289i	$0.400239\pi$
$132$	−6.96183e11	−1.51205
$133$	−2.20396e10	−0.0459220
$134$	−6.94026e11	−1.38771
$135$	1.78107e11	0.341857
$136$	8.69730e11	1.60295
$137$	9.29114e11	1.64477	0.822386	−	0.568930i	$-0.192642\pi$
$137$	9.29114e11	1.64477	0.822386	+	0.568930i	$0.192642\pi$
$138$	−7.50680e11	−1.27679
$139$	−4.04240e11	−0.660782	−0.330391	−	0.943844i	$-0.607181\pi$
$139$	−4.04240e11	−0.660782	−0.330391	+	0.943844i	$0.607181\pi$
$140$	3.78073e12	5.94116
$141$	−1.70202e11	−0.257193
$142$	4.89472e11	0.711447
$143$	−3.65444e11	−0.511060
$144$	1.93280e11	0.260132
$145$	−1.98838e12	−2.57617
$146$	−9.09146e11	−1.13421
$147$	9.70115e11	1.16568
$148$	−1.81327e12	−2.09906
$149$	1.57810e11	0.176040	0.0880198	−	0.996119i	$-0.471946\pi$
$149$	1.57810e11	0.176040	0.0880198	+	0.996119i	$0.471946\pi$
$150$	1.97935e12	2.12825
$151$	1.80274e12	1.86878	0.934392	−	0.356248i	$-0.115944\pi$
$151$	1.80274e12	1.86878	0.934392	+	0.356248i	$0.115944\pi$
$152$	−4.18204e10	−0.0418070
$153$	3.50301e11	0.337783
$154$	−4.34578e12	−4.04300
$155$	2.14516e12	1.92591
$156$	4.81720e11	0.417455
$157$	−3.65569e11	−0.305859	−0.152930	−	0.988237i	$-0.548871\pi$
$157$	−3.65569e11	−0.305859	−0.152930	+	0.988237i	$0.548871\pi$
$158$	−2.22481e12	−1.79754
$159$	−1.33001e11	−0.103793
$160$	−5.82350e11	−0.439060
$161$	−3.08388e12	−2.24675
$162$	2.69865e11	0.190027
$163$	1.97642e12	1.34539	0.672693	−	0.739921i	$-0.265137\pi$
$163$	1.97642e12	1.34539	0.672693	+	0.739921i	$0.265137\pi$
$164$	−2.11227e11	−0.139030
$165$	−2.19201e12	−1.39534
$166$	−4.42066e12	−2.72203
$167$	1.11585e12	0.664761	0.332380	−	0.943145i	$-0.392148\pi$
$167$	1.11585e12	0.664761	0.332380	+	0.943145i	$0.392148\pi$
$168$	2.75254e12	1.58684
$169$	−1.53929e12	−0.858904
$170$	5.69917e12	3.07853
$171$	−1.68440e10	−0.00880982
$172$	−2.88268e12	−1.46013
$173$	−3.81662e10	−0.0187252	−0.00936258	−	0.999956i	$-0.502980\pi$
$173$	−3.81662e10	−0.0187252	−0.00936258	+	0.999956i	$0.502980\pi$
$174$	−3.01277e12	−1.43201
$175$	8.13143e12	3.74505
$176$	−2.37875e12	−1.06177
$177$	1.73727e11	0.0751646
$178$	5.45846e12	2.28960
$179$	−1.31044e12	−0.532996	−0.266498	−	0.963835i	$-0.585867\pi$
$179$	−1.31044e12	−0.532996	−0.266498	+	0.963835i	$0.585867\pi$
$180$	2.88946e12	1.13977
$181$	−4.02496e12	−1.54003	−0.770015	−	0.638025i	$-0.779751\pi$
$181$	−4.02496e12	−1.54003	−0.770015	+	0.638025i	$0.779751\pi$
$182$	3.00704e12	1.11621
$183$	−1.54999e12	−0.558274
$184$	−5.85170e12	−2.04543
$185$	−5.70929e12	−1.93704
$186$	3.25032e12	1.07055
$187$	−4.31125e12	−1.37871
$188$	−2.76122e12	−0.857496
$189$	1.10864e12	0.334388
$190$	−2.74041e11	−0.0802918
$191$	−6.87127e11	−0.195593	−0.0977966	−	0.995206i	$-0.531179\pi$
$191$	−6.87127e11	−0.195593	−0.0977966	+	0.995206i	$0.531179\pi$
$192$	−2.51133e12	−0.694620
$193$	−5.63247e12	−1.51403	−0.757014	−	0.653399i	$-0.773342\pi$
$193$	−5.63247e12	−1.51403	−0.757014	+	0.653399i	$0.773342\pi$
$194$	−7.78905e12	−2.03505
$195$	1.51675e12	0.385233
$196$	1.57384e13	3.88643
$197$	2.15772e12	0.518121	0.259061	−	0.965861i	$-0.416587\pi$
$197$	2.15772e12	0.518121	0.259061	+	0.965861i	$0.416587\pi$
$198$	−3.32131e12	−0.775623
$199$	4.84982e12	1.10163	0.550813	−	0.834629i	$-0.314318\pi$
$199$	4.84982e12	1.10163	0.550813	+	0.834629i	$0.314318\pi$
$200$	1.54295e13	3.40946
$201$	−2.17901e12	−0.468470
$202$	1.22892e13	2.57092
$203$	−1.23768e13	−2.51989
$204$	5.68300e12	1.12619
$205$	−6.65071e11	−0.128299
$206$	1.07587e13	2.02064
$207$	−2.35689e12	−0.431025
$208$	1.64596e12	0.293138
$209$	2.07304e11	0.0359586
$210$	1.80369e13	3.04758
$211$	−4.36669e12	−0.718784	−0.359392	−	0.933187i	$-0.617016\pi$
$211$	−4.36669e12	−0.718784	−0.359392	+	0.933187i	$0.617016\pi$
$212$	−2.15769e12	−0.346053
$213$	1.53678e12	0.240173
$214$	1.70239e13	2.59289
$215$	−9.07644e12	−1.34742
$216$	2.10366e12	0.304424
$217$	1.33527e13	1.88383
$218$	−1.90503e13	−2.62055
$219$	−2.85442e12	−0.382891
$220$	−3.55614e13	−4.65215
$221$	2.98315e12	0.380642
$222$	−8.65066e12	−1.07673
$223$	1.00236e13	1.21716	0.608581	−	0.793492i	$-0.291739\pi$
$223$	1.00236e13	1.21716	0.608581	+	0.793492i	$0.291739\pi$
$224$	−3.62488e12	−0.429467
$225$	6.21452e12	0.718462
$226$	1.25951e13	1.42104
$227$	1.72365e13	1.89804	0.949022	−	0.315209i	$-0.102075\pi$
$227$	1.72365e13	1.89804	0.949022	+	0.315209i	$0.102075\pi$
$228$	−2.73263e11	−0.0293724
$229$	1.05046e13	1.10226	0.551131	−	0.834419i	$-0.314197\pi$
$229$	1.05046e13	1.10226	0.551131	+	0.834419i	$0.314197\pi$
$230$	−3.83451e13	−3.92832
$231$	−1.36443e13	−1.36485
$232$	−2.34851e13	−2.29408
$233$	1.05480e13	1.00627	0.503134	−	0.864208i	$-0.332180\pi$
$233$	1.05480e13	1.00627	0.503134	+	0.864208i	$0.332180\pi$
$234$	2.29816e12	0.214138
$235$	−8.69399e12	−0.791309
$236$	2.81840e12	0.250603
$237$	−6.98517e12	−0.606821
$238$	3.54750e13	3.01126
$239$	−1.44562e13	−1.19913	−0.599564	−	0.800326i	$-0.704660\pi$
$239$	−1.44562e13	−1.19913	−0.599564	+	0.800326i	$0.704660\pi$
$240$	9.87284e12	0.800350
$241$	−1.88955e13	−1.49715	−0.748573	−	0.663053i	$-0.769260\pi$
$241$	−1.88955e13	−1.49715	−0.748573	+	0.663053i	$0.769260\pi$
$242$	1.87941e13	1.45558
$243$	8.47289e11	0.0641500
$244$	−2.51457e13	−1.86132
$245$	4.95540e13	3.58645
$246$	−1.00771e12	−0.0713168
$247$	−1.43443e11	−0.00992763
$248$	2.53369e13	1.71502
$249$	−1.38794e13	−0.918914
$250$	5.41977e13	3.51003
$251$	1.76113e12	0.111580	0.0557899	−	0.998443i	$-0.482232\pi$
$251$	1.76113e12	0.111580	0.0557899	+	0.998443i	$0.482232\pi$
$252$	1.79857e13	1.11487
$253$	2.90069e13	1.75929
$254$	4.23852e13	2.51553
$255$	1.78935e13	1.03926
$256$	−3.33052e13	−1.89318
$257$	−8.25501e12	−0.459288	−0.229644	−	0.973275i	$-0.573756\pi$
$257$	−8.25501e12	−0.459288	−0.229644	+	0.973275i	$0.573756\pi$
$258$	−1.37525e13	−0.748986
$259$	−3.55380e13	−1.89471
$260$	2.46065e13	1.28439
$261$	−9.45911e12	−0.483423
$262$	2.10727e13	1.05454
$263$	2.71837e13	1.33215	0.666074	−	0.745886i	$-0.267974\pi$
$263$	2.71837e13	1.33215	0.666074	+	0.745886i	$0.267974\pi$
$264$	−2.58903e13	−1.24255
$265$	−6.79373e12	−0.319342
$266$	−1.70579e12	−0.0785375
$267$	1.71378e13	0.772935
$268$	−3.53506e13	−1.56191
$269$	−2.25407e13	−0.975730	−0.487865	−	0.872919i	$-0.662224\pi$
$269$	−2.25407e13	−0.975730	−0.487865	+	0.872919i	$0.662224\pi$
$270$	1.37849e13	0.584657
$271$	7.62432e12	0.316862	0.158431	−	0.987370i	$-0.449356\pi$
$271$	7.62432e12	0.316862	0.158431	+	0.987370i	$0.449356\pi$
$272$	1.94179e13	0.790814
$273$	9.44112e12	0.376816
$274$	7.19102e13	2.81295
$275$	−7.64839e13	−2.93251
$276$	−3.82362e13	−1.43706
$277$	2.33976e13	0.862052	0.431026	−	0.902340i	$-0.358152\pi$
$277$	2.33976e13	0.862052	0.431026	+	0.902340i	$0.358152\pi$
$278$	−3.12868e13	−1.13010
$279$	1.02050e13	0.361400
$280$	1.40601e14	4.88224
$281$	3.21932e13	1.09617	0.548087	−	0.836421i	$-0.315356\pi$
$281$	3.21932e13	1.09617	0.548087	+	0.836421i	$0.315356\pi$
$282$	−1.31730e13	−0.439862
$283$	1.83398e13	0.600577	0.300288	−	0.953848i	$-0.402917\pi$
$283$	1.83398e13	0.600577	0.300288	+	0.953848i	$0.402917\pi$
$284$	2.49315e13	0.800752
$285$	−8.60400e11	−0.0271053
$286$	−2.82841e13	−0.874035
$287$	−4.13979e12	−0.125495
$288$	−2.77035e12	−0.0823904
$289$	9.21192e11	0.0268789
$290$	−1.53894e14	−4.40587
$291$	−2.44551e13	−0.687001
$292$	−4.63078e13	−1.27658
$293$	−2.33266e13	−0.631074	−0.315537	−	0.948913i	$-0.602185\pi$
$293$	−2.33266e13	−0.631074	−0.315537	+	0.948913i	$0.602185\pi$
$294$	7.50836e13	1.99359
$295$	8.87404e12	0.231260
$296$	−6.74336e13	−1.72493
$297$	−1.04278e13	−0.261838
$298$	1.22140e13	0.301070
$299$	−2.00711e13	−0.485714
$300$	1.00819e14	2.39540
$301$	−5.64970e13	−1.31798
$302$	1.39526e14	3.19607
$303$	3.85839e13	0.867904
$304$	−9.33700e11	−0.0206254
$305$	−7.91741e13	−1.71765
$306$	2.71121e13	0.577691
$307$	6.11194e12	0.127914	0.0639570	−	0.997953i	$-0.479628\pi$
$307$	6.11194e12	0.127914	0.0639570	+	0.997953i	$0.479628\pi$
$308$	−2.21355e14	−4.55050
$309$	3.37787e13	0.682137
$310$	1.66028e14	3.29376
$311$	−6.37514e13	−1.24253	−0.621266	−	0.783600i	$-0.713381\pi$
$311$	−6.37514e13	−1.24253	−0.621266	+	0.783600i	$0.713381\pi$
$312$	1.79146e13	0.343050
$313$	7.36202e13	1.38517	0.692585	−	0.721337i	$-0.256472\pi$
$313$	7.36202e13	1.38517	0.692585	+	0.721337i	$0.256472\pi$
$314$	−2.82938e13	−0.523092
$315$	5.66299e13	1.02882
$316$	−1.13322e14	−2.02318
$317$	−6.52364e13	−1.14463	−0.572313	−	0.820035i	$-0.693954\pi$
$317$	−6.52364e13	−1.14463	−0.572313	+	0.820035i	$0.693954\pi$
$318$	−1.02938e13	−0.177511
$319$	1.16416e14	1.97316
$320$	−1.28280e14	−2.13715
$321$	5.34495e13	0.875318
$322$	−2.38682e14	−3.84249
$323$	−1.69224e12	−0.0267823
$324$	1.37457e13	0.213880
$325$	5.29226e13	0.809623
$326$	1.52968e14	2.30093
$327$	−5.98119e13	−0.884656
$328$	−7.85530e12	−0.114250
$329$	−5.41165e13	−0.774020
$330$	−1.69654e14	−2.38637
$331$	−7.58226e13	−1.04893	−0.524463	−	0.851433i	$-0.675734\pi$
$331$	−7.58226e13	−1.04893	−0.524463	+	0.851433i	$0.675734\pi$
$332$	−2.25168e14	−3.06371
$333$	−2.71602e13	−0.363488
$334$	8.63630e13	1.13690
$335$	−1.11305e14	−1.44135
$336$	6.14543e13	0.782864
$337$	−6.01192e13	−0.753440	−0.376720	−	0.926327i	$-0.622948\pi$
$337$	−6.01192e13	−0.753440	−0.376720	+	0.926327i	$0.622948\pi$
$338$	−1.19136e14	−1.46893
$339$	3.95445e13	0.479719
$340$	2.90290e14	3.46496
$341$	−1.25595e14	−1.47511
$342$	−1.30367e12	−0.0150669
$343$	1.55678e14	1.77056
$344$	−1.07204e14	−1.19988
$345$	−1.20391e14	−1.32614
$346$	−2.95393e12	−0.0320245
$347$	7.44183e13	0.794086	0.397043	−	0.917800i	$-0.370036\pi$
$347$	7.44183e13	0.794086	0.397043	+	0.917800i	$0.370036\pi$
$348$	−1.53457e14	−1.61176
$349$	−9.23279e13	−0.954538	−0.477269	−	0.878757i	$-0.658373\pi$
$349$	−9.23279e13	−0.954538	−0.477269	+	0.878757i	$0.658373\pi$
$350$	6.29345e14	6.40493
$351$	7.21547e12	0.0722895
$352$	3.40955e13	0.336289
$353$	−4.78410e13	−0.464558	−0.232279	−	0.972649i	$-0.574618\pi$
$353$	−4.78410e13	−0.464558	−0.232279	+	0.972649i	$0.574618\pi$
$354$	1.34458e13	0.128549
$355$	7.84997e13	0.738944
$356$	2.78029e14	2.57701
$357$	1.11380e14	1.01656
$358$	−1.01423e14	−0.911551
$359$	1.12348e14	0.994365	0.497182	−	0.867646i	$-0.334368\pi$
$359$	1.12348e14	0.994365	0.497182	+	0.867646i	$0.334368\pi$
$360$	1.07456e14	0.936625
$361$	−1.16409e14	−0.999301
$362$	−3.11518e14	−2.63382
$363$	5.90073e13	0.491382
$364$	1.53165e14	1.25633
$365$	−1.45805e14	−1.17805
$366$	−1.19964e14	−0.954782
$367$	−1.16586e14	−0.914078	−0.457039	−	0.889447i	$-0.651090\pi$
$367$	−1.16586e14	−0.914078	−0.457039	+	0.889447i	$0.651090\pi$
$368$	−1.30647e14	−1.00911
$369$	−3.16388e12	−0.0240754
$370$	−4.41880e14	−3.31280
$371$	−4.22882e13	−0.312365
$372$	1.65557e14	1.20493
$373$	−1.28184e13	−0.0919253	−0.0459626	−	0.998943i	$-0.514636\pi$
$373$	−1.28184e13	−0.0919253	−0.0459626	+	0.998943i	$0.514636\pi$
$374$	−3.33676e14	−2.35793
$375$	1.70163e14	1.18493
$376$	−1.02687e14	−0.704661
$377$	−8.05533e13	−0.544761
$378$	8.58049e13	0.571883
$379$	−2.48760e13	−0.163405	−0.0817024	−	0.996657i	$-0.526036\pi$
$379$	−2.48760e13	−0.163405	−0.0817024	+	0.996657i	$0.526036\pi$
$380$	−1.39584e13	−0.0903705
$381$	1.33076e14	0.849203
$382$	−5.31813e13	−0.334511
$383$	−2.29051e14	−1.42017	−0.710083	−	0.704118i	$-0.751343\pi$
$383$	−2.29051e14	−1.42017	−0.710083	+	0.704118i	$0.751343\pi$
$384$	−1.71020e14	−1.04526
$385$	−6.96959e14	−4.19927
$386$	−4.35934e14	−2.58935
$387$	−4.31784e13	−0.252846
$388$	−3.96739e14	−2.29050
$389$	1.22918e14	0.699669	0.349835	−	0.936811i	$-0.386238\pi$
$389$	1.22918e14	0.699669	0.349835	+	0.936811i	$0.386238\pi$
$390$	1.17391e14	0.658840
$391$	−2.36786e14	−1.31034
$392$	5.85292e14	3.19374
$393$	6.61614e13	0.355997
$394$	1.67000e14	0.886111
$395$	−3.56806e14	−1.86702
$396$	−1.69172e14	−0.872983
$397$	−9.44813e13	−0.480837	−0.240419	−	0.970669i	$-0.577285\pi$
$397$	−9.44813e13	−0.480837	−0.240419	+	0.970669i	$0.577285\pi$
$398$	3.75360e14	1.88404
$399$	−5.35563e12	−0.0265131
$400$	3.44485e14	1.68205
$401$	−2.27859e14	−1.09742	−0.548709	−	0.836013i	$-0.684881\pi$
$401$	−2.27859e14	−1.09742	−0.548709	+	0.836013i	$0.684881\pi$
$402$	−1.68648e14	−0.801196
$403$	8.69049e13	0.407255
$404$	6.25954e14	2.89364
$405$	4.32799e13	0.197371
$406$	−9.57924e14	−4.30961
$407$	3.34268e14	1.48363
$408$	2.11344e14	0.925465
$409$	1.21428e13	0.0524615	0.0262308	−	0.999656i	$-0.491650\pi$
$409$	1.21428e13	0.0524615	0.0262308	+	0.999656i	$0.491650\pi$
$410$	−5.14743e13	−0.219421
$411$	2.25775e14	0.949610
$412$	5.47999e14	2.27428
$413$	5.52372e13	0.226207
$414$	−1.82415e14	−0.737155
$415$	−7.08968e14	−2.82723
$416$	−2.35922e13	−0.0928443
$417$	−9.82304e13	−0.381503
$418$	1.60446e13	0.0614978
$419$	−9.80337e12	−0.0370850	−0.0185425	−	0.999828i	$-0.505903\pi$
$419$	−9.80337e12	−0.0370850	−0.0185425	+	0.999828i	$0.505903\pi$
$420$	9.18717e14	3.43013
$421$	2.64312e14	0.974016	0.487008	−	0.873397i	$-0.338088\pi$
$421$	2.64312e14	0.974016	0.487008	+	0.873397i	$0.338088\pi$
$422$	−3.37967e14	−1.22929
$423$	−4.13590e13	−0.148490
$424$	−8.02422e13	−0.284375
$425$	6.24344e14	2.18416
$426$	1.18942e14	0.410754
$427$	−4.92826e14	−1.68012
$428$	8.67121e14	2.91836
$429$	−8.88028e13	−0.295061
$430$	−7.02486e14	−2.30442
$431$	2.63861e14	0.854574	0.427287	−	0.904116i	$-0.359469\pi$
$431$	2.63861e14	0.854574	0.427287	+	0.904116i	$0.359469\pi$
$432$	4.69670e13	0.150187
$433$	2.11153e14	0.666673	0.333337	−	0.942808i	$-0.391825\pi$
$433$	2.11153e14	0.666673	0.333337	+	0.942808i	$0.391825\pi$
$434$	1.03346e15	3.22180
$435$	−4.83176e14	−1.48735
$436$	−9.70339e14	−2.94950
$437$	1.13857e13	0.0341752
$438$	−2.20923e14	−0.654836
$439$	4.28039e14	1.25293	0.626467	−	0.779448i	$-0.284500\pi$
$439$	4.28039e14	1.25293	0.626467	+	0.779448i	$0.284500\pi$
$440$	−1.32249e15	−3.82298
$441$	2.35738e14	0.673003
$442$	2.30885e14	0.650989
$443$	−5.30553e14	−1.47744	−0.738718	−	0.674015i	$-0.764568\pi$
$443$	−5.30553e14	−1.47744	−0.738718	+	0.674015i	$0.764568\pi$
$444$	−4.40626e14	−1.21189
$445$	8.75406e14	2.37810
$446$	7.75795e14	2.08164
$447$	3.83479e13	0.101637
$448$	−7.98489e14	−2.09045
$449$	−2.14183e13	−0.0553898	−0.0276949	−	0.999616i	$-0.508817\pi$
$449$	−2.14183e13	−0.0553898	−0.0276949	+	0.999616i	$0.508817\pi$
$450$	4.80983e14	1.22874
$451$	3.89387e13	0.0982676
$452$	6.41537e14	1.59941
$453$	4.38065e14	1.07894
$454$	1.33405e15	3.24611
$455$	4.82257e14	1.15935
$456$	−1.01624e13	−0.0241373
$457$	−9.49930e13	−0.222922	−0.111461	−	0.993769i	$-0.535553\pi$
$457$	−9.49930e13	−0.222922	−0.111461	+	0.993769i	$0.535553\pi$
$458$	8.13021e14	1.88513
$459$	8.51231e13	0.195019
$460$	−1.95313e15	−4.42142
$461$	−2.40804e14	−0.538652	−0.269326	−	0.963049i	$-0.586801\pi$
$461$	−2.40804e14	−0.538652	−0.269326	+	0.963049i	$0.586801\pi$
$462$	−1.05603e15	−2.33423
$463$	−7.26702e14	−1.58731	−0.793653	−	0.608371i	$-0.791823\pi$
$463$	−7.26702e14	−1.58731	−0.793653	+	0.608371i	$0.791823\pi$
$464$	−5.24339e14	−1.13178
$465$	5.21274e14	1.11192
$466$	8.16381e14	1.72096
$467$	3.98067e14	0.829303	0.414651	−	0.909980i	$-0.363904\pi$
$467$	3.98067e14	0.829303	0.414651	+	0.909980i	$0.363904\pi$
$468$	1.17058e14	0.241018
$469$	−6.92828e14	−1.40986
$470$	−6.72886e14	−1.35333
$471$	−8.88333e13	−0.176588
$472$	1.04813e14	0.205937
$473$	5.31409e14	1.03203
$474$	−5.40628e14	−1.03781
$475$	−3.00212e13	−0.0569657
$476$	1.80694e15	3.38926
$477$	−3.23191e13	−0.0599251
$478$	−1.11886e15	−2.05080
$479$	7.59907e14	1.37694	0.688470	−	0.725265i	$-0.258283\pi$
$479$	7.59907e14	1.37694	0.688470	+	0.725265i	$0.258283\pi$
$480$	−1.41511e14	−0.253492
$481$	−2.31295e14	−0.409608
$482$	−1.46245e15	−2.56048
$483$	−7.49384e14	−1.29716
$484$	9.57286e14	1.63830
$485$	−1.24918e15	−2.11371
$486$	6.55773e13	0.109712
$487$	9.16434e14	1.51597	0.757987	−	0.652269i	$-0.226183\pi$
$487$	9.16434e14	1.51597	0.757987	+	0.652269i	$0.226183\pi$
$488$	−9.35142e14	−1.52957
$489$	4.80270e14	0.776759
$490$	3.83531e15	6.13369
$491$	5.98902e14	0.947125	0.473562	−	0.880760i	$-0.342968\pi$
$491$	5.98902e14	0.947125	0.473562	+	0.880760i	$0.342968\pi$
$492$	−5.13281e13	−0.0802689
$493$	−9.50312e14	−1.46963
$494$	−1.11020e13	−0.0169786
$495$	−5.32658e14	−0.805601
$496$	5.65683e14	0.846104
$497$	4.88627e14	0.722799
$498$	−1.07422e15	−1.57156
$499$	4.89635e14	0.708467	0.354234	−	0.935157i	$-0.384742\pi$
$499$	4.89635e14	0.708467	0.354234	+	0.935157i	$0.384742\pi$
$500$	2.76059e15	3.95063
$501$	2.71152e14	0.383800
$502$	1.36305e14	0.190828
$503$	1.36627e13	0.0189196	0.00945978	−	0.999955i	$-0.496989\pi$
$503$	1.36627e13	0.0189196	0.00945978	+	0.999955i	$0.496989\pi$
$504$	6.68867e14	0.916161
$505$	1.97089e15	2.67029
$506$	2.24503e15	3.00881
$507$	−3.74048e14	−0.495888
$508$	2.15891e15	2.83129
$509$	4.31218e14	0.559434	0.279717	−	0.960082i	$-0.409759\pi$
$509$	4.31218e14	0.559434	0.279717	+	0.960082i	$0.409759\pi$
$510$	1.38490e15	1.77739
$511$	−9.07577e14	−1.15231
$512$	−1.13636e15	−1.42735
$513$	−4.09309e12	−0.00508635
$514$	−6.38910e14	−0.785493
$515$	1.72543e15	2.09874
$516$	−7.00491e14	−0.843004
$517$	5.09017e14	0.606086
$518$	−2.75052e15	−3.24042
$519$	−9.27439e12	−0.0108110
$520$	9.15088e14	1.05547
$521$	4.85049e14	0.553577	0.276788	−	0.960931i	$-0.410730\pi$
$521$	4.85049e14	0.553577	0.276788	+	0.960931i	$0.410730\pi$
$522$	−7.32103e14	−0.826769
$523$	−1.32274e15	−1.47814	−0.739068	−	0.673631i	$-0.764734\pi$
$523$	−1.32274e15	−1.47814	−0.739068	+	0.673631i	$0.764734\pi$
$524$	1.07335e15	1.18691
$525$	1.97594e15	2.16221
$526$	2.10393e15	2.27829
$527$	1.02524e15	1.09867
$528$	−5.78036e14	−0.613011
$529$	6.40326e14	0.672040
$530$	−5.25812e14	−0.546152
$531$	4.22156e13	0.0433963
$532$	−8.68854e13	−0.0883961
$533$	−2.69434e13	−0.0271302
$534$	1.32641e15	1.32190
$535$	2.73023e15	2.69310
$536$	−1.31465e15	−1.28352
$537$	−3.18436e14	−0.307725
$538$	−1.74457e15	−1.66873
$539$	−2.90129e15	−2.74697
$540$	7.02138e14	0.658047
$541$	−8.34284e14	−0.773978	−0.386989	−	0.922084i	$-0.626485\pi$
$541$	−8.34284e14	−0.773978	−0.386989	+	0.922084i	$0.626485\pi$
$542$	5.90097e14	0.541910
$543$	−9.78065e14	−0.889137
$544$	−2.78324e14	−0.250471
$545$	−3.05522e15	−2.72183
$546$	7.30711e14	0.644445
$547$	−4.72916e14	−0.412909	−0.206454	−	0.978456i	$-0.566193\pi$
$547$	−4.72916e14	−0.412909	−0.206454	+	0.978456i	$0.566193\pi$
$548$	3.66278e15	3.16605
$549$	−3.76647e14	−0.322319
$550$	−5.91959e15	−5.01530
$551$	4.56952e13	0.0383298
$552$	−1.42196e15	−1.18093
$553$	−2.22097e15	−1.82622
$554$	1.81090e15	1.47432
$555$	−1.38736e15	−1.11835
$556$	−1.59361e15	−1.27195
$557$	2.75884e14	0.218034	0.109017	−	0.994040i	$-0.465230\pi$
$557$	2.75884e14	0.218034	0.109017	+	0.994040i	$0.465230\pi$
$558$	7.89829e14	0.618080
$559$	−3.67705e14	−0.284928
$560$	3.13912e15	2.40865
$561$	−1.04763e15	−0.796001
$562$	2.49165e15	1.87472
$563$	−9.55873e14	−0.712203	−0.356102	−	0.934447i	$-0.615894\pi$
$563$	−9.55873e14	−0.712203	−0.356102	+	0.934447i	$0.615894\pi$
$564$	−6.70975e14	−0.495076
$565$	2.01995e15	1.47596
$566$	1.41944e15	1.02713
$567$	2.69399e14	0.193059
$568$	9.27176e14	0.658031
$569$	5.00706e14	0.351938	0.175969	−	0.984396i	$-0.443694\pi$
$569$	5.00706e14	0.351938	0.175969	+	0.984396i	$0.443694\pi$
$570$	−6.65921e13	−0.0463565
$571$	−1.99843e15	−1.37782	−0.688908	−	0.724849i	$-0.741910\pi$
$571$	−1.99843e15	−1.37782	−0.688908	+	0.724849i	$0.741910\pi$
$572$	−1.44066e15	−0.983750
$573$	−1.66972e14	−0.112926
$574$	−3.20406e14	−0.214627
$575$	−4.20070e15	−2.78708
$576$	−6.10253e14	−0.401039
$577$	−1.44221e15	−0.938774	−0.469387	−	0.882993i	$-0.655525\pi$
$577$	−1.44221e15	−0.938774	−0.469387	+	0.882993i	$0.655525\pi$
$578$	7.12972e13	0.0459694
$579$	−1.36869e15	−0.874124
$580$	−7.83865e15	−4.95892
$581$	−4.41303e15	−2.76546
$582$	−1.89274e15	−1.17494
$583$	3.97761e14	0.244593
$584$	−1.72214e15	−1.04905
$585$	3.68570e14	0.222414
$586$	−1.80540e15	−1.07929
$587$	−2.85121e15	−1.68857	−0.844285	−	0.535894i	$-0.819975\pi$
$587$	−2.85121e15	−1.68857	−0.844285	+	0.535894i	$0.819975\pi$
$588$	3.82442e15	2.24383
$589$	−4.92982e13	−0.0286548
$590$	6.86821e14	0.395510
$591$	5.24326e14	0.299137
$592$	−1.50555e15	−0.850993
$593$	−9.54533e14	−0.534552	−0.267276	−	0.963620i	$-0.586124\pi$
$593$	−9.54533e14	−0.534552	−0.267276	+	0.963620i	$0.586124\pi$
$594$	−8.07078e14	−0.447806
$595$	5.68934e15	3.12765
$596$	6.22125e14	0.338862
$597$	1.17851e15	0.636024
$598$	−1.55344e15	−0.830687
$599$	2.16118e15	1.14510	0.572549	−	0.819870i	$-0.305955\pi$
$599$	2.16118e15	1.14510	0.572549	+	0.819870i	$0.305955\pi$
$600$	3.74936e15	1.96845
$601$	1.76622e15	0.918830	0.459415	−	0.888222i	$-0.348059\pi$
$601$	1.76622e15	0.918830	0.459415	+	0.888222i	$0.348059\pi$
$602$	−4.37268e15	−2.25407
$603$	−5.29500e14	−0.270471
$604$	7.10681e15	3.59726
$605$	3.01412e15	1.51184
$606$	2.98626e15	1.48432
$607$	−8.36311e14	−0.411936	−0.205968	−	0.978559i	$-0.566034\pi$
$607$	−8.36311e14	−0.411936	−0.205968	+	0.978559i	$0.566034\pi$
$608$	1.33831e13	0.00653260
$609$	−3.00757e15	−1.45486
$610$	−6.12781e15	−2.93759
$611$	−3.52212e14	−0.167331
$612$	1.38097e15	0.650206
$613$	−2.43270e15	−1.13515	−0.567577	−	0.823320i	$-0.692119\pi$
$613$	−2.43270e15	−1.13515	−0.567577	+	0.823320i	$0.692119\pi$
$614$	4.73044e14	0.218764
$615$	−1.61612e14	−0.0740732
$616$	−8.23193e15	−3.73945
$617$	2.08936e15	0.940687	0.470343	−	0.882483i	$-0.344130\pi$
$617$	2.08936e15	0.940687	0.470343	+	0.882483i	$0.344130\pi$
$618$	2.61436e15	1.16662
$619$	4.22000e15	1.86644	0.933220	−	0.359304i	$-0.116986\pi$
$619$	4.22000e15	1.86644	0.933220	+	0.359304i	$0.116986\pi$
$620$	8.45673e15	3.70722
$621$	−5.72724e14	−0.248852
$622$	−4.93414e15	−2.12503
$623$	5.44904e15	2.32614
$624$	3.99969e14	0.169243
$625$	3.55317e15	1.49031
$626$	5.69795e15	2.36897
$627$	5.03748e13	0.0207607
$628$	−1.44116e15	−0.588754
$629$	−2.72866e15	−1.10502
$630$	4.38296e15	1.75952
$631$	−2.03571e15	−0.810130	−0.405065	−	0.914288i	$-0.632751\pi$
$631$	−2.03571e15	−0.810130	−0.405065	+	0.914288i	$0.632751\pi$
$632$	−4.21431e15	−1.66258
$633$	−1.06110e15	−0.414990
$634$	−5.04907e15	−1.95759
$635$	6.79757e15	2.61275
$636$	−5.24319e14	−0.199794
$637$	2.00753e15	0.758396
$638$	9.01019e15	3.37458
$639$	3.73438e14	0.138664
$640$	−8.73579e15	−3.21597
$641$	−6.82488e14	−0.249101	−0.124551	−	0.992213i	$-0.539749\pi$
$641$	−6.82488e14	−0.249101	−0.124551	+	0.992213i	$0.539749\pi$
$642$	4.13681e15	1.49700
$643$	−5.48591e15	−1.96829	−0.984144	−	0.177373i	$-0.943240\pi$
$643$	−5.48591e15	−1.96829	−0.984144	+	0.177373i	$0.943240\pi$
$644$	−1.21574e16	−4.32482
$645$	−2.20557e15	−0.777935
$646$	−1.30974e14	−0.0458041
$647$	4.07894e15	1.41440	0.707202	−	0.707012i	$-0.249957\pi$
$647$	4.07894e15	1.41440	0.707202	+	0.707012i	$0.249957\pi$
$648$	5.11188e14	0.175759
$649$	−5.19559e14	−0.177129
$650$	4.09603e15	1.38465
$651$	3.24471e15	1.08763
$652$	7.79151e15	2.58976
$653$	4.18064e14	0.137791	0.0688953	−	0.997624i	$-0.478053\pi$
$653$	4.18064e14	0.137791	0.0688953	+	0.997624i	$0.478053\pi$
$654$	−4.62923e15	−1.51297
$655$	3.37956e15	1.09530
$656$	−1.75380e14	−0.0563651
$657$	−6.93624e14	−0.221062
$658$	−4.18843e15	−1.32376
$659$	−2.33867e15	−0.732992	−0.366496	−	0.930420i	$-0.619443\pi$
$659$	−2.33867e15	−0.732992	−0.366496	+	0.930420i	$0.619443\pi$
$660$	−8.64141e15	−2.68592
$661$	1.60254e15	0.493972	0.246986	−	0.969019i	$-0.420560\pi$
$661$	1.60254e15	0.493972	0.246986	+	0.969019i	$0.420560\pi$
$662$	−5.86841e15	−1.79391
$663$	7.24904e14	0.219764
$664$	−8.37377e15	−2.51766
$665$	−2.73568e14	−0.0815730
$666$	−2.10211e15	−0.621652
$667$	6.39387e15	1.87531
$668$	4.39894e15	1.27961
$669$	2.43574e15	0.702729
$670$	−8.61464e15	−2.46505
$671$	4.63550e15	1.31560
$672$	−8.80847e14	−0.247953
$673$	5.77319e15	1.61188	0.805941	−	0.591996i	$-0.201660\pi$
$673$	5.77319e15	1.61188	0.805941	+	0.591996i	$0.201660\pi$
$674$	−4.65302e15	−1.28856
$675$	1.51013e15	0.414804
$676$	−6.06826e15	−1.65332
$677$	2.93250e15	0.792503	0.396251	−	0.918142i	$-0.370311\pi$
$677$	2.93250e15	0.792503	0.396251	+	0.918142i	$0.370311\pi$
$678$	3.06061e15	0.820435
$679$	−7.77561e15	−2.06752
$680$	1.07956e16	2.84739
$681$	4.18847e15	1.09584
$682$	−9.72064e15	−2.52279
$683$	5.69673e15	1.46660	0.733300	−	0.679905i	$-0.237979\pi$
$683$	5.69673e15	1.46660	0.733300	+	0.679905i	$0.237979\pi$
$684$	−6.64030e13	−0.0169582
$685$	1.15327e16	2.92168
$686$	1.20490e16	3.02808
$687$	2.55262e15	0.636391
$688$	−2.39347e15	−0.591960
$689$	−2.75228e14	−0.0675285
$690$	−9.31786e15	−2.26802
$691$	5.88029e15	1.41994	0.709970	−	0.704232i	$-0.248709\pi$
$691$	5.88029e15	1.41994	0.709970	+	0.704232i	$0.248709\pi$
$692$	−1.50460e14	−0.0360444
$693$	−3.31557e15	−0.787999
$694$	5.75972e15	1.35808
$695$	−5.01766e15	−1.17377
$696$	−5.70689e15	−1.32449
$697$	−3.17860e14	−0.0731906
$698$	−7.14587e15	−1.63249
$699$	2.56317e15	0.580969
$700$	3.20560e16	7.20892
$701$	−6.21098e15	−1.38583	−0.692917	−	0.721017i	$-0.743675\pi$
$701$	−6.21098e15	−1.38583	−0.692917	+	0.721017i	$0.743675\pi$
$702$	5.58453e14	0.123632
$703$	1.31206e14	0.0288204
$704$	7.51056e15	1.63690
$705$	−2.11264e15	−0.456862
$706$	−3.70273e15	−0.794505
$707$	1.22679e16	2.61195
$708$	6.84871e14	0.144686
$709$	5.50469e15	1.15393	0.576964	−	0.816770i	$-0.304237\pi$
$709$	5.50469e15	1.15393	0.576964	+	0.816770i	$0.304237\pi$
$710$	6.07561e15	1.26377
$711$	−1.69740e15	−0.350349
$712$	1.03396e16	2.11770
$713$	−6.89803e15	−1.40195
$714$	8.62042e15	1.73855
$715$	−4.53609e15	−0.907817
$716$	−5.16605e15	−1.02597
$717$	−3.51286e15	−0.692317
$718$	8.69535e15	1.70060
$719$	−8.85581e14	−0.171878	−0.0859388	−	0.996300i	$-0.527389\pi$
$719$	−8.85581e14	−0.171878	−0.0859388	+	0.996300i	$0.527389\pi$
$720$	2.39910e15	0.462083
$721$	1.07401e16	2.05288
$722$	−9.00965e15	−1.70904
$723$	−4.59160e15	−0.864377
$724$	−1.58673e16	−2.96443
$725$	−1.68590e16	−3.12589
$726$	4.56696e15	0.840381
$727$	1.76107e15	0.321617	0.160808	−	0.986986i	$-0.448590\pi$
$727$	1.76107e15	0.321617	0.160808	+	0.986986i	$0.448590\pi$
$728$	5.69604e15	1.03241
$729$	2.05891e14	0.0370370
$730$	−1.12848e16	−2.01474
$731$	−4.33793e15	−0.768665
$732$	−6.11041e15	−1.07463
$733$	−9.65469e15	−1.68526	−0.842629	−	0.538494i	$-0.818994\pi$
$733$	−9.65469e15	−1.68526	−0.842629	+	0.538494i	$0.818994\pi$
$734$	−9.02336e15	−1.56329
$735$	1.20416e16	2.07064
$736$	1.87262e15	0.319611
$737$	6.51671e15	1.10397
$738$	−2.44873e14	−0.0411748
$739$	1.63652e13	0.00273134	0.00136567	−	0.999999i	$-0.499565\pi$
$739$	1.63652e13	0.00273134	0.00136567	+	0.999999i	$0.499565\pi$
$740$	−2.25074e16	−3.72864
$741$	−3.48566e13	−0.00573172
$742$	−3.27296e15	−0.534219
$743$	−7.37900e15	−1.19553	−0.597763	−	0.801673i	$-0.703943\pi$
$743$	−7.37900e15	−1.19553	−0.597763	+	0.801673i	$0.703943\pi$
$744$	6.15688e15	0.990169
$745$	1.95883e15	0.312706
$746$	−9.92100e14	−0.157214
$747$	−3.37270e15	−0.530535
$748$	−1.69960e16	−2.65391
$749$	1.69945e16	2.63426
$750$	1.31700e16	2.02652
$751$	8.82429e15	1.34791	0.673954	−	0.738774i	$-0.264595\pi$
$751$	8.82429e15	1.34791	0.673954	+	0.738774i	$0.264595\pi$
$752$	−2.29262e15	−0.347644
$753$	4.27954e14	0.0644206
$754$	−6.23455e15	−0.931672
$755$	2.23766e16	3.31960
$756$	4.37052e15	0.643670
$757$	−1.00032e16	−1.46255	−0.731275	−	0.682083i	$-0.761074\pi$
$757$	−1.00032e16	−1.46255	−0.731275	+	0.682083i	$0.761074\pi$
$758$	−1.92532e15	−0.279461
$759$	7.04867e15	1.01573
$760$	−5.19099e14	−0.0742635
$761$	2.54390e15	0.361314	0.180657	−	0.983546i	$-0.442178\pi$
$761$	2.54390e15	0.361314	0.180657	+	0.983546i	$0.442178\pi$
$762$	1.02996e16	1.45234
$763$	−1.90175e16	−2.66236
$764$	−2.70882e15	−0.376501
$765$	4.34813e15	0.600019
$766$	−1.77278e16	−2.42883
$767$	3.59506e14	0.0489025
$768$	−8.09316e15	−1.09303
$769$	5.48267e15	0.735186	0.367593	−	0.929987i	$-0.380182\pi$
$769$	5.48267e15	0.735186	0.367593	+	0.929987i	$0.380182\pi$
$770$	−5.39423e16	−7.18175
$771$	−2.00597e15	−0.265170
$772$	−2.22045e16	−2.91438
$773$	2.10509e15	0.274336	0.137168	−	0.990548i	$-0.456200\pi$
$773$	2.10509e15	0.274336	0.137168	+	0.990548i	$0.456200\pi$
$774$	−3.34186e15	−0.432427
$775$	1.81884e16	2.33687
$776$	−1.47543e16	−1.88226
$777$	−8.63572e15	−1.09391
$778$	9.51344e15	1.19660
$779$	1.52841e13	0.00190890
$780$	5.97938e15	0.741542
$781$	−4.59601e15	−0.565979
$782$	−1.83264e16	−2.24099
$783$	−2.29856e15	−0.279104
$784$	1.30675e16	1.57563
$785$	−4.53765e15	−0.543310
$786$	5.12067e15	0.608839
$787$	6.90166e15	0.814877	0.407439	−	0.913233i	$-0.366422\pi$
$787$	6.90166e15	0.814877	0.407439	+	0.913233i	$0.366422\pi$
$788$	8.50625e15	0.997341
$789$	6.60564e15	0.769116
$790$	−2.76156e16	−3.19304
$791$	1.25733e16	1.44371
$792$	−6.29133e15	−0.717388
$793$	−3.20751e15	−0.363216
$794$	−7.31253e15	−0.822347
$795$	−1.65088e15	−0.184372
$796$	1.91191e16	2.12054
$797$	3.07983e15	0.339239	0.169619	−	0.985510i	$-0.445746\pi$
$797$	3.07983e15	0.339239	0.169619	+	0.985510i	$0.445746\pi$
$798$	−4.14508e14	−0.0453437
$799$	−4.15515e15	−0.451418
$800$	−4.93762e15	−0.532750
$801$	4.16448e15	0.446254
$802$	−1.76355e16	−1.87685
$803$	8.53663e15	0.902300
$804$	−8.59018e15	−0.901767
$805$	−3.82789e16	−3.99100
$806$	6.72615e15	0.696504
$807$	−5.47739e15	−0.563338
$808$	2.32785e16	2.37790
$809$	8.15540e15	0.827424	0.413712	−	0.910408i	$-0.364232\pi$
$809$	8.15540e15	0.827424	0.413712	+	0.910408i	$0.364232\pi$
$810$	3.34972e15	0.337552
$811$	−5.66860e15	−0.567364	−0.283682	−	0.958918i	$-0.591556\pi$
$811$	−5.66860e15	−0.567364	−0.283682	+	0.958918i	$0.591556\pi$
$812$	−4.87923e16	−4.85058
$813$	1.85271e15	0.182940
$814$	2.58712e16	2.53737
$815$	2.45324e16	2.38987
$816$	4.71856e15	0.456576
$817$	2.08587e14	0.0200478
$818$	9.39812e14	0.0897218
$819$	2.29419e15	0.217555
$820$	−2.62187e15	−0.246964
$821$	1.69177e16	1.58290	0.791449	−	0.611235i	$-0.209327\pi$
$821$	1.69177e16	1.58290	0.791449	+	0.611235i	$0.209327\pi$
$822$	1.74742e16	1.62406
$823$	5.46082e15	0.504148	0.252074	−	0.967708i	$-0.418887\pi$
$823$	5.46082e15	0.504148	0.252074	+	0.967708i	$0.418887\pi$
$824$	2.03795e16	1.86893
$825$	−1.85856e16	−1.69309
$826$	4.27517e15	0.386868
$827$	1.01650e16	0.913750	0.456875	−	0.889531i	$-0.348969\pi$
$827$	1.01650e16	0.913750	0.456875	+	0.889531i	$0.348969\pi$
$828$	−9.29141e15	−0.829688
$829$	−1.39742e16	−1.23959	−0.619794	−	0.784765i	$-0.712784\pi$
$829$	−1.39742e16	−1.23959	−0.619794	+	0.784765i	$0.712784\pi$
$830$	−5.48717e16	−4.83525
$831$	5.68563e15	0.497706
$832$	−5.19689e15	−0.451924
$833$	2.36835e16	2.04596
$834$	−7.60270e15	−0.652461
$835$	1.38506e16	1.18084
$836$	8.17240e14	0.0692174
$837$	2.47980e15	0.208654
$838$	−7.58748e14	−0.0634243
$839$	−1.09041e16	−0.905524	−0.452762	−	0.891631i	$-0.649561\pi$
$839$	−1.09041e16	−0.905524	−0.452762	+	0.891631i	$0.649561\pi$
$840$	3.41661e16	2.81876
$841$	1.34606e16	1.10328
$842$	2.04569e16	1.66580
$843$	7.82295e15	0.632877
$844$	−1.72145e16	−1.38360
$845$	−1.91066e16	−1.52571
$846$	−3.20105e15	−0.253954
$847$	1.87616e16	1.47881
$848$	−1.79152e15	−0.140296
$849$	4.45657e15	0.346743
$850$	4.83221e16	3.73544
$851$	1.83589e16	1.41005
$852$	6.05836e15	0.462314
$853$	−6.60017e15	−0.500421	−0.250210	−	0.968192i	$-0.580500\pi$
$853$	−6.60017e15	−0.500421	−0.250210	+	0.968192i	$0.580500\pi$
$854$	−3.81430e16	−2.87341
$855$	−2.09077e14	−0.0156492
$856$	3.22473e16	2.39821
$857$	1.43770e16	1.06237	0.531183	−	0.847257i	$-0.321748\pi$
$857$	1.43770e16	1.06237	0.531183	+	0.847257i	$0.321748\pi$
$858$	−6.87303e15	−0.504625
$859$	−2.26977e15	−0.165584	−0.0827922	−	0.996567i	$-0.526384\pi$
$859$	−2.26977e15	−0.165584	−0.0827922	+	0.996567i	$0.526384\pi$
$860$	−3.57815e16	−2.59368
$861$	−1.00597e15	−0.0724548
$862$	2.04219e16	1.46153
$863$	−2.60695e16	−1.85384	−0.926922	−	0.375254i	$-0.877556\pi$
$863$	−2.60695e16	−1.85384	−0.926922	+	0.375254i	$0.877556\pi$
$864$	−6.73196e14	−0.0475681
$865$	−4.73740e14	−0.0332623
$866$	1.63425e16	1.14017
$867$	2.23850e14	0.0155186
$868$	5.26396e16	3.62622
$869$	2.08903e16	1.43000
$870$	−3.73962e16	−2.54373
$871$	−4.50920e15	−0.304789
$872$	−3.60858e16	−2.42380
$873$	−5.94258e15	−0.396640
$874$	8.81214e14	0.0584478
$875$	5.41041e16	3.56604
$876$	−1.12528e16	−0.737035
$877$	−8.67986e15	−0.564956	−0.282478	−	0.959274i	$-0.591156\pi$
$877$	−8.67986e15	−0.564956	−0.282478	+	0.959274i	$0.591156\pi$
$878$	3.31287e16	2.14282
$879$	−5.66837e15	−0.364351
$880$	−2.95264e16	−1.88606
$881$	2.62973e15	0.166933	0.0834667	−	0.996511i	$-0.473401\pi$
$881$	2.62973e15	0.166933	0.0834667	+	0.996511i	$0.473401\pi$
$882$	1.82453e16	1.15100
$883$	−2.47037e16	−1.54874	−0.774370	−	0.632733i	$-0.781933\pi$
$883$	−2.47037e16	−1.54874	−0.774370	+	0.632733i	$0.781933\pi$
$884$	1.17603e16	0.732706
$885$	2.15639e15	0.133518
$886$	−4.10630e16	−2.52677
$887$	−2.26506e16	−1.38516	−0.692580	−	0.721341i	$-0.743526\pi$
$887$	−2.26506e16	−1.38516	−0.692580	+	0.721341i	$0.743526\pi$
$888$	−1.63864e16	−0.995890
$889$	4.23120e16	2.55567
$890$	6.77535e16	4.06712
$891$	−2.53396e15	−0.151172
$892$	3.95155e16	2.34294
$893$	1.99798e14	0.0117736
$894$	2.96799e15	0.173823
$895$	−1.62659e16	−0.946783
$896$	−5.43766e16	−3.14571
$897$	−4.87729e15	−0.280427
$898$	−1.65770e15	−0.0947298
$899$	−2.76845e16	−1.57238
$900$	2.44991e16	1.38298
$901$	−3.24695e15	−0.182175
$902$	3.01372e15	0.168061
$903$	−1.37288e16	−0.760938
$904$	2.38581e16	1.31434
$905$	−4.99601e16	−2.73562
$906$	3.39047e16	1.84525
$907$	8.06706e15	0.436390	0.218195	−	0.975905i	$-0.429983\pi$
$907$	8.06706e15	0.436390	0.218195	+	0.975905i	$0.429983\pi$
$908$	6.79503e16	3.65358
$909$	9.37589e15	0.501085
$910$	3.73251e16	1.98277
$911$	−9.61065e15	−0.507460	−0.253730	−	0.967275i	$-0.581657\pi$
$911$	−9.61065e15	−0.507460	−0.253730	+	0.967275i	$0.581657\pi$
$912$	−2.26889e14	−0.0119081
$913$	4.15087e16	2.16546
$914$	−7.35214e15	−0.381250
$915$	−1.92393e16	−0.991684
$916$	4.14116e16	2.12176
$917$	2.10363e16	1.07137
$918$	6.58824e15	0.333530
$919$	−2.52885e15	−0.127259	−0.0636294	−	0.997974i	$-0.520268\pi$
$919$	−2.52885e15	−0.127259	−0.0636294	+	0.997974i	$0.520268\pi$
$920$	−7.26346e16	−3.63338
$921$	1.48520e15	0.0738512
$922$	−1.86374e16	−0.921224
$923$	3.18018e15	0.156258
$924$	−5.37892e16	−2.62724
$925$	−4.84079e16	−2.35037
$926$	−5.62442e16	−2.71467
$927$	8.20823e15	0.393832
$928$	7.51554e15	0.358465
$929$	−3.25688e16	−1.54424	−0.772122	−	0.635475i	$-0.780804\pi$
$929$	−3.25688e16	−1.54424	−0.772122	+	0.635475i	$0.780804\pi$
$930$	4.03449e16	1.90166
$931$	−1.13881e15	−0.0533613
$932$	4.15828e16	1.93698
$933$	−1.54916e16	−0.717376
$934$	3.08090e16	1.41831
$935$	−5.35137e16	−2.44907
$936$	4.35325e15	0.198060
$937$	−1.68435e16	−0.761841	−0.380921	−	0.924608i	$-0.624393\pi$
$937$	−1.68435e16	−0.761841	−0.380921	+	0.924608i	$0.624393\pi$
$938$	−5.36225e16	−2.41119
$939$	1.78897e16	0.799728
$940$	−3.42738e16	−1.52321
$941$	5.16036e15	0.228001	0.114000	−	0.993481i	$-0.463633\pi$
$941$	5.16036e15	0.228001	0.114000	+	0.993481i	$0.463633\pi$
$942$	−6.87540e15	−0.302008
$943$	2.13862e15	0.0933940
$944$	2.34010e15	0.101599
$945$	1.37611e16	0.593987
$946$	4.11292e16	1.76502
$947$	4.56753e15	0.194875	0.0974376	−	0.995242i	$-0.468935\pi$
$947$	4.56753e15	0.194875	0.0974376	+	0.995242i	$0.468935\pi$
$948$	−2.75372e16	−1.16808
$949$	−5.90687e15	−0.249111
$950$	−2.32354e15	−0.0974250
$951$	−1.58524e16	−0.660850
$952$	6.71979e16	2.78518
$953$	2.40100e16	0.989420	0.494710	−	0.869058i	$-0.335274\pi$
$953$	2.40100e16	0.989420	0.494710	+	0.869058i	$0.335274\pi$
$954$	−2.50139e15	−0.102486
$955$	−8.52901e15	−0.347440
$956$	−5.69898e16	−2.30823
$957$	2.82891e16	1.13921
$958$	5.88142e16	2.35490
$959$	7.17861e16	2.85784
$960$	−3.11720e16	−1.23388
$961$	4.45890e15	0.175489
$962$	−1.79015e16	−0.700528
$963$	1.29882e16	0.505365
$964$	−7.44904e16	−2.88188
$965$	−6.99134e16	−2.68943
$966$	−5.79998e16	−2.21846
$967$	4.65846e16	1.77173	0.885863	−	0.463947i	$-0.153567\pi$
$967$	4.65846e16	1.77173	0.885863	+	0.463947i	$0.153567\pi$
$968$	3.56004e16	1.34630
$969$	−4.11214e14	−0.0154628
$970$	−9.66821e16	−3.61494
$971$	−3.10673e16	−1.15504	−0.577521	−	0.816376i	$-0.695980\pi$
$971$	−3.10673e16	−1.15504	−0.577521	+	0.816376i	$0.695980\pi$
$972$	3.34021e15	0.123484
$973$	−3.12328e16	−1.14813
$974$	7.09289e16	2.59268
$975$	1.28602e16	0.467436
$976$	−2.08783e16	−0.754609
$977$	2.36700e16	0.850704	0.425352	−	0.905028i	$-0.360150\pi$
$977$	2.36700e16	0.850704	0.425352	+	0.905028i	$0.360150\pi$
$978$	3.71713e16	1.32844
$979$	−5.12534e16	−1.82145
$980$	1.95353e17	6.90363
$981$	−1.45343e16	−0.510757
$982$	4.63530e16	1.61981
$983$	3.54121e16	1.23057	0.615286	−	0.788304i	$-0.289040\pi$
$983$	3.54121e16	1.23057	0.615286	+	0.788304i	$0.289040\pi$
$984$	−1.90884e15	−0.0659623
$985$	2.67829e16	0.920360
$986$	−7.35509e16	−2.51342
$987$	−1.31503e16	−0.446880
$988$	−5.65485e14	−0.0191099
$989$	2.91864e16	0.980846
$990$	−4.12259e16	−1.37777
$991$	−4.69570e16	−1.56061	−0.780306	−	0.625398i	$-0.784937\pi$
$991$	−4.69570e16	−1.56061	−0.780306	+	0.625398i	$0.784937\pi$
$992$	−8.10814e15	−0.267983
$993$	−1.84249e16	−0.605598
$994$	3.78181e16	1.23616
$995$	6.01987e16	1.95686
$996$	−5.47159e16	−1.76884
$997$	−1.95671e16	−0.629077	−0.314538	−	0.949245i	$-0.601850\pi$
$997$	−1.95671e16	−0.629077	−0.314538	+	0.949245i	$0.601850\pi$
$998$	3.78961e16	1.21165
$999$	−6.59994e15	−0.209860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.25	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.25	✓	28	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)

\(f(q)\)	\(=\)	\(q+77.3966 q^{2} +243.000 q^{3} +3942.23 q^{4} +12412.6 q^{5} +18807.4 q^{6} +77263.0 q^{7} +146607. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+77.3966 q^{2} +243.000 q^{3} +3942.23 q^{4} +12412.6 q^{5} +18807.4 q^{6} +77263.0 q^{7} +146607. q^{8} +59049.0 q^{9} +960690. q^{10} -726732. q^{11} +957963. q^{12} +502858. q^{13} +5.97989e6 q^{14} +3.01625e6 q^{15} +3.27321e6 q^{16} +5.93238e6 q^{17} +4.57019e6 q^{18} -285255. q^{19} +4.89332e7 q^{20} +1.87749e7 q^{21} -5.62466e7 q^{22} -3.99141e7 q^{23} +3.56256e7 q^{24} +1.05244e8 q^{25} +3.89195e7 q^{26} +1.43489e7 q^{27} +3.04589e8 q^{28} -1.60191e8 q^{29} +2.33448e8 q^{30} +1.72822e8 q^{31} -4.69162e7 q^{32} -1.76596e8 q^{33} +4.59146e8 q^{34} +9.59032e8 q^{35} +2.32785e8 q^{36} -4.59961e8 q^{37} -2.20777e7 q^{38} +1.22195e8 q^{39} +1.81977e9 q^{40} -5.35805e7 q^{41} +1.45311e9 q^{42} -7.31230e8 q^{43} -2.86495e9 q^{44} +7.32949e8 q^{45} -3.08922e9 q^{46} -7.00419e8 q^{47} +7.95391e8 q^{48} +3.99224e9 q^{49} +8.14549e9 q^{50} +1.44157e9 q^{51} +1.98239e9 q^{52} -5.47327e8 q^{53} +1.11056e9 q^{54} -9.02061e9 q^{55} +1.13273e10 q^{56} -6.93169e7 q^{57} -1.23982e10 q^{58} +7.14924e8 q^{59} +1.18908e10 q^{60} -6.37855e9 q^{61} +1.33758e10 q^{62} +4.56230e9 q^{63} -1.03347e10 q^{64} +6.24176e9 q^{65} -1.36679e10 q^{66} -8.96714e9 q^{67} +2.33868e10 q^{68} -9.69913e9 q^{69} +7.42258e10 q^{70} +6.32421e9 q^{71} +8.65702e9 q^{72} -1.17466e10 q^{73} -3.55994e10 q^{74} +2.55742e10 q^{75} -1.12454e9 q^{76} -5.61495e10 q^{77} +9.45745e9 q^{78} -2.87455e10 q^{79} +4.06290e10 q^{80} +3.48678e9 q^{81} -4.14695e9 q^{82} -5.71170e10 q^{83} +7.40151e10 q^{84} +7.36360e10 q^{85} -5.65947e10 q^{86} -3.89264e10 q^{87} -1.06544e11 q^{88} +7.05259e10 q^{89} +5.67278e10 q^{90} +3.88524e10 q^{91} -1.57351e11 q^{92} +4.19957e10 q^{93} -5.42101e10 q^{94} -3.54074e9 q^{95} -1.14006e10 q^{96} -1.00638e11 q^{97} +3.08986e11 q^{98} -4.29128e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more