LMFDB - Embedded newform 177.14.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,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, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
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:	$189.798744245$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-61.5481 q^{2} -729.000 q^{3} -4403.84 q^{4} -24160.8 q^{5} +44868.5 q^{6} -453377. q^{7} +775249. q^{8} +531441. q^{9} +O(q^{10})$	\(q-61.5481 q^{2} -729.000 q^{3} -4403.84 q^{4} -24160.8 q^{5} +44868.5 q^{6} -453377. q^{7} +775249. q^{8} +531441. q^{9} +1.48705e6 q^{10} -3.42724e6 q^{11} +3.21040e6 q^{12} +2.82171e7 q^{13} +2.79045e7 q^{14} +1.76132e7 q^{15} -1.16389e7 q^{16} -1.40646e6 q^{17} -3.27092e7 q^{18} +1.58679e8 q^{19} +1.06400e8 q^{20} +3.30512e8 q^{21} +2.10940e8 q^{22} +7.54520e8 q^{23} -5.65157e8 q^{24} -6.36957e8 q^{25} -1.73671e9 q^{26} -3.87420e8 q^{27} +1.99660e9 q^{28} +1.51354e9 q^{29} -1.08406e9 q^{30} +3.17450e8 q^{31} -5.63449e9 q^{32} +2.49846e9 q^{33} +8.65651e7 q^{34} +1.09540e10 q^{35} -2.34038e9 q^{36} -2.81383e9 q^{37} -9.76636e9 q^{38} -2.05702e10 q^{39} -1.87307e10 q^{40} -4.48557e10 q^{41} -2.03424e10 q^{42} +9.92897e9 q^{43} +1.50930e10 q^{44} -1.28401e10 q^{45} -4.64393e10 q^{46} +7.22011e10 q^{47} +8.48473e9 q^{48} +1.08662e11 q^{49} +3.92035e10 q^{50} +1.02531e9 q^{51} -1.24263e11 q^{52} -1.02601e11 q^{53} +2.38450e10 q^{54} +8.28051e10 q^{55} -3.51480e11 q^{56} -1.15677e11 q^{57} -9.31557e10 q^{58} +4.21805e10 q^{59} -7.75659e10 q^{60} -1.81929e10 q^{61} -1.95384e10 q^{62} -2.40943e11 q^{63} +4.42138e11 q^{64} -6.81748e11 q^{65} -1.53775e11 q^{66} -1.08524e12 q^{67} +6.19384e9 q^{68} -5.50045e11 q^{69} -6.74195e11 q^{70} -1.30313e11 q^{71} +4.11999e11 q^{72} +1.33249e12 q^{73} +1.73186e11 q^{74} +4.64342e11 q^{75} -6.98795e11 q^{76} +1.55383e12 q^{77} +1.26606e12 q^{78} +7.14250e11 q^{79} +2.81205e11 q^{80} +2.82430e11 q^{81} +2.76078e12 q^{82} -1.75835e12 q^{83} -1.45552e12 q^{84} +3.39813e10 q^{85} -6.11109e11 q^{86} -1.10337e12 q^{87} -2.65697e12 q^{88} +4.04760e12 q^{89} +7.90281e11 q^{90} -1.27930e13 q^{91} -3.32278e12 q^{92} -2.31421e11 q^{93} -4.44384e12 q^{94} -3.83381e12 q^{95} +4.10755e12 q^{96} -5.18632e12 q^{97} -6.68791e12 q^{98} -1.82138e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) $ 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9} + 6145337 q^{10} + 400846 q^{11} - 101457846 q^{12} + 9411686 q^{13} - 36368387 q^{14} - 1630044 q^{15} + 734877786 q^{16} + 228113833 q^{17} + 6377292 q^{18} + 524233755 q^{19} - 420745331 q^{20} - 544450005 q^{21} - 1844479318 q^{22} - 399937087 q^{23} + 534588093 q^{24} + 8617402914 q^{25} - 499433574 q^{26} - 12397455648 q^{27} + 12648993070 q^{28} - 225284149 q^{29} - 4479950673 q^{30} + 9454638761 q^{31} + 11648295118 q^{32} - 292216734 q^{33} + 39279537096 q^{34} + 17608963479 q^{35} + 73962769734 q^{36} + 37463929597 q^{37} + 65554547351 q^{38} - 6861119094 q^{39} + 144414252742 q^{40} + 22650227173 q^{41} + 26512554123 q^{42} + 96253617602 q^{43} - 132186868002 q^{44} + 1188302076 q^{45} + 327853892309 q^{46} + 239981844027 q^{47} - 535725905994 q^{48} + 286262776863 q^{49} - 671840368399 q^{50} - 166294984257 q^{51} - 952971648498 q^{52} - 47446514136 q^{53} - 4649045868 q^{54} - 474454082548 q^{55} - 1167728875984 q^{56} - 382166407395 q^{57} + 547596592762 q^{58} + 1349777076512 q^{59} + 306723346299 q^{60} + 661498471821 q^{61} + 555821093242 q^{62} + 396904053645 q^{63} + 3522679273173 q^{64} + 1269187682756 q^{65} + 1344625422822 q^{66} + 2838711491386 q^{67} + 1395029358261 q^{68} + 291554136423 q^{69} + 5677102514386 q^{70} + 1912914480734 q^{71} - 389714719797 q^{72} + 2403595726697 q^{73} - 742136417562 q^{74} - 6282086724306 q^{75} - 4020161987188 q^{76} - 4878303804101 q^{77} + 364087075446 q^{78} - 1705546365970 q^{79} - 4347383766449 q^{80} + 9037745167392 q^{81} - 6943720239935 q^{82} - 2549647313691 q^{83} - 9221115948030 q^{84} - 8455706309615 q^{85} - 33993832711012 q^{86} + 164232144621 q^{87} - 42970239360587 q^{88} - 17356719361241 q^{89} + 3265884040617 q^{90} - 30776775043291 q^{91} - 13184590997480 q^{92} - 6892431656769 q^{93} - 35604563339520 q^{94} + 219501126195 q^{95} - 8491607141022 q^{96} - 4427131429152 q^{97} - 32707332037060 q^{98} + 213025999086 q^{99}+O(q^{100}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9 + 6145337 * q^10 + 400846 * q^11 - 101457846 * q^12 + 9411686 * q^13 - 36368387 * q^14 - 1630044 * q^15 + 734877786 * q^16 + 228113833 * q^17 + 6377292 * q^18 + 524233755 * q^19 - 420745331 * q^20 - 544450005 * q^21 - 1844479318 * q^22 - 399937087 * q^23 + 534588093 * q^24 + 8617402914 * q^25 - 499433574 * q^26 - 12397455648 * q^27 + 12648993070 * q^28 - 225284149 * q^29 - 4479950673 * q^30 + 9454638761 * q^31 + 11648295118 * q^32 - 292216734 * q^33 + 39279537096 * q^34 + 17608963479 * q^35 + 73962769734 * q^36 + 37463929597 * q^37 + 65554547351 * q^38 - 6861119094 * q^39 + 144414252742 * q^40 + 22650227173 * q^41 + 26512554123 * q^42 + 96253617602 * q^43 - 132186868002 * q^44 + 1188302076 * q^45 + 327853892309 * q^46 + 239981844027 * q^47 - 535725905994 * q^48 + 286262776863 * q^49 - 671840368399 * q^50 - 166294984257 * q^51 - 952971648498 * q^52 - 47446514136 * q^53 - 4649045868 * q^54 - 474454082548 * q^55 - 1167728875984 * q^56 - 382166407395 * q^57 + 547596592762 * q^58 + 1349777076512 * q^59 + 306723346299 * q^60 + 661498471821 * q^61 + 555821093242 * q^62 + 396904053645 * q^63 + 3522679273173 * q^64 + 1269187682756 * q^65 + 1344625422822 * q^66 + 2838711491386 * q^67 + 1395029358261 * q^68 + 291554136423 * q^69 + 5677102514386 * q^70 + 1912914480734 * q^71 - 389714719797 * q^72 + 2403595726697 * q^73 - 742136417562 * q^74 - 6282086724306 * q^75 - 4020161987188 * q^76 - 4878303804101 * q^77 + 364087075446 * q^78 - 1705546365970 * q^79 - 4347383766449 * q^80 + 9037745167392 * q^81 - 6943720239935 * q^82 - 2549647313691 * q^83 - 9221115948030 * q^84 - 8455706309615 * q^85 - 33993832711012 * q^86 + 164232144621 * q^87 - 42970239360587 * q^88 - 17356719361241 * q^89 + 3265884040617 * q^90 - 30776775043291 * q^91 - 13184590997480 * q^92 - 6892431656769 * q^93 - 35604563339520 * q^94 + 219501126195 * q^95 - 8491607141022 * q^96 - 4427131429152 * q^97 - 32707332037060 * q^98 + 213025999086 * 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 $

$2$	−61.5481	−0.680016	−0.340008	−	0.940422i	$-0.610430\pi$
$2$	−61.5481	−0.680016	−0.340008	+	0.940422i	$0.610430\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−4403.84	−0.537578
$5$	−24160.8	−0.691523	−0.345762	−	0.938322i	$-0.612379\pi$
$5$	−24160.8	−0.691523	−0.345762	+	0.938322i	$0.612379\pi$
$6$	44868.5	0.392608
$7$	−453377.	−1.45654	−0.728269	−	0.685291i	$-0.759675\pi$
$7$	−453377.	−1.45654	−0.728269	+	0.685291i	$0.759675\pi$
$8$	775249.	1.04558
$9$	531441.	0.333333
$10$	1.48705e6	0.470247
$11$	−3.42724e6	−0.583301	−0.291650	−	0.956525i	$-0.594204\pi$
$11$	−3.42724e6	−0.583301	−0.291650	+	0.956525i	$0.594204\pi$
$12$	3.21040e6	0.310371
$13$	2.82171e7	1.62136	0.810681	−	0.585488i	$-0.199097\pi$
$13$	2.82171e7	1.62136	0.810681	+	0.585488i	$0.199097\pi$
$14$	2.79045e7	0.990470
$15$	1.76132e7	0.399251
$16$	−1.16389e7	−0.173433
$17$	−1.40646e6	−0.0141322	−0.00706611	−	0.999975i	$-0.502249\pi$
$17$	−1.40646e6	−0.0141322	−0.00706611	+	0.999975i	$0.502249\pi$
$18$	−3.27092e7	−0.226672
$19$	1.58679e8	0.773785	0.386892	−	0.922125i	$-0.373548\pi$
$19$	1.58679e8	0.773785	0.386892	+	0.922125i	$0.373548\pi$
$20$	1.06400e8	0.371748
$21$	3.30512e8	0.840933
$22$	2.10940e8	0.396654
$23$	7.54520e8	1.06277	0.531386	−	0.847130i	$-0.321671\pi$
$23$	7.54520e8	1.06277	0.531386	+	0.847130i	$0.321671\pi$
$24$	−5.65157e8	−0.603665
$25$	−6.36957e8	−0.521795
$26$	−1.73671e9	−1.10255
$27$	−3.87420e8	−0.192450
$28$	1.99660e9	0.783003
$29$	1.51354e9	0.472507	0.236253	−	0.971691i	$-0.424080\pi$
$29$	1.51354e9	0.472507	0.236253	+	0.971691i	$0.424080\pi$
$30$	−1.08406e9	−0.271497
$31$	3.17450e8	0.0642428	0.0321214	−	0.999484i	$-0.489774\pi$
$31$	3.17450e8	0.0642428	0.0321214	+	0.999484i	$0.489774\pi$
$32$	−5.63449e9	−0.927641
$33$	2.49846e9	0.336769
$34$	8.65651e7	0.00961015
$35$	1.09540e10	1.00723
$36$	−2.34038e9	−0.179193
$37$	−2.81383e9	−0.180297	−0.0901483	−	0.995928i	$-0.528734\pi$
$37$	−2.81383e9	−0.180297	−0.0901483	+	0.995928i	$0.528734\pi$
$38$	−9.76636e9	−0.526186
$39$	−2.05702e10	−0.936094
$40$	−1.87307e10	−0.723042
$41$	−4.48557e10	−1.47476	−0.737382	−	0.675476i	$-0.763938\pi$
$41$	−4.48557e10	−1.47476	−0.737382	+	0.675476i	$0.763938\pi$
$42$	−2.03424e10	−0.571848
$43$	9.92897e9	0.239530	0.119765	−	0.992802i	$-0.461786\pi$
$43$	9.92897e9	0.239530	0.119765	+	0.992802i	$0.461786\pi$
$44$	1.50930e10	0.313570
$45$	−1.28401e10	−0.230508
$46$	−4.64393e10	−0.722702
$47$	7.22011e10	0.977030	0.488515	−	0.872555i	$-0.337539\pi$
$47$	7.22011e10	0.977030	0.488515	+	0.872555i	$0.337539\pi$
$48$	8.48473e9	0.100131
$49$	1.08662e11	1.12151
$50$	3.92035e10	0.354829
$51$	1.02531e9	0.00815925
$52$	−1.24263e11	−0.871608
$53$	−1.02601e11	−0.635853	−0.317927	−	0.948115i	$-0.602987\pi$
$53$	−1.02601e11	−0.635853	−0.317927	+	0.948115i	$0.602987\pi$
$54$	2.38450e10	0.130869
$55$	8.28051e10	0.403366
$56$	−3.51480e11	−1.52293
$57$	−1.15677e11	−0.446745
$58$	−9.31557e10	−0.321312
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−7.75659e10	−0.214629
$61$	−1.81929e10	−0.0452123	−0.0226062	−	0.999744i	$-0.507196\pi$
$61$	−1.81929e10	−0.0452123	−0.0226062	+	0.999744i	$0.507196\pi$
$62$	−1.95384e10	−0.0436862
$63$	−2.40943e11	−0.485513
$64$	4.42138e11	0.804244
$65$	−6.81748e11	−1.12121
$66$	−1.53775e11	−0.229008
$67$	−1.08524e12	−1.46568	−0.732839	−	0.680402i	$-0.761805\pi$
$67$	−1.08524e12	−1.46568	−0.732839	+	0.680402i	$0.761805\pi$
$68$	6.19384e9	0.00759717
$69$	−5.50045e11	−0.613591
$70$	−6.74195e11	−0.684933
$71$	−1.30313e11	−0.120728	−0.0603641	−	0.998176i	$-0.519226\pi$
$71$	−1.30313e11	−0.120728	−0.0603641	+	0.998176i	$0.519226\pi$
$72$	4.11999e11	0.348526
$73$	1.33249e12	1.03054	0.515270	−	0.857028i	$-0.327692\pi$
$73$	1.33249e12	1.03054	0.515270	+	0.857028i	$0.327692\pi$
$74$	1.73186e11	0.122605
$75$	4.64342e11	0.301259
$76$	−6.98795e11	−0.415969
$77$	1.55383e12	0.849600
$78$	1.26606e12	0.636559
$79$	7.14250e11	0.330578	0.165289	−	0.986245i	$-0.447144\pi$
$79$	7.14250e11	0.330578	0.165289	+	0.986245i	$0.447144\pi$
$80$	2.81205e11	0.119933
$81$	2.82430e11	0.111111
$82$	2.76078e12	1.00286
$83$	−1.75835e12	−0.590334	−0.295167	−	0.955446i	$-0.595375\pi$
$83$	−1.75835e12	−0.590334	−0.295167	+	0.955446i	$0.595375\pi$
$84$	−1.45552e12	−0.452067
$85$	3.39813e10	0.00977277
$86$	−6.11109e11	−0.162884
$87$	−1.10337e12	−0.272802
$88$	−2.65697e12	−0.609887
$89$	4.04760e12	0.863302	0.431651	−	0.902041i	$-0.357931\pi$
$89$	4.04760e12	0.863302	0.431651	+	0.902041i	$0.357931\pi$
$90$	7.90281e11	0.156749
$91$	−1.27930e13	−2.36158
$92$	−3.32278e12	−0.571322
$93$	−2.31421e11	−0.0370906
$94$	−4.44384e12	−0.664396
$95$	−3.83381e12	−0.535090
$96$	4.10755e12	0.535574
$97$	−5.18632e12	−0.632183	−0.316091	−	0.948729i	$-0.602371\pi$
$97$	−5.18632e12	−0.632183	−0.316091	+	0.948729i	$0.602371\pi$
$98$	−6.68791e12	−0.762642
$99$	−1.82138e12	−0.194434
$100$	2.80506e12	0.280506
$101$	−2.45689e12	−0.230302	−0.115151	−	0.993348i	$-0.536735\pi$
$101$	−2.45689e12	−0.230302	−0.115151	+	0.993348i	$0.536735\pi$
$102$	−6.31060e10	−0.00554842
$103$	−2.34924e13	−1.93859	−0.969294	−	0.245906i	$-0.920915\pi$
$103$	−2.34924e13	−1.93859	−0.969294	+	0.245906i	$0.920915\pi$
$104$	2.18753e13	1.69526
$105$	−7.98544e12	−0.581525
$106$	6.31487e12	0.432391
$107$	1.99286e13	1.28376	0.641878	−	0.766807i	$-0.278155\pi$
$107$	1.99286e13	1.28376	0.641878	+	0.766807i	$0.278155\pi$
$108$	1.70614e12	0.103457
$109$	−2.58737e12	−0.147770	−0.0738850	−	0.997267i	$-0.523540\pi$
$109$	−2.58737e12	−0.147770	−0.0738850	+	0.997267i	$0.523540\pi$
$110$	−5.09649e12	−0.274296
$111$	2.05129e12	0.104094
$112$	5.27679e12	0.252611
$113$	−2.33004e13	−1.05282	−0.526409	−	0.850232i	$-0.676462\pi$
$113$	−2.33004e13	−1.05282	−0.526409	+	0.850232i	$0.676462\pi$
$114$	7.11968e12	0.303794
$115$	−1.82298e13	−0.734931
$116$	−6.66540e12	−0.254009
$117$	1.49957e13	0.540454
$118$	−2.59613e12	−0.0885306
$119$	6.37658e11	0.0205841
$120$	1.36547e13	0.417448
$121$	−2.27767e13	−0.659760
$122$	1.11974e12	0.0307451
$123$	3.26998e13	0.851455
$124$	−1.39800e12	−0.0345355
$125$	4.48826e13	1.05236
$126$	1.48296e13	0.330157
$127$	−3.78409e12	−0.0800270	−0.0400135	−	0.999199i	$-0.512740\pi$
$127$	−3.78409e12	−0.0800270	−0.0400135	+	0.999199i	$0.512740\pi$
$128$	1.89450e13	0.380742
$129$	−7.23822e12	−0.138292
$130$	4.19603e13	0.762441
$131$	3.75557e13	0.649250	0.324625	−	0.945843i	$-0.394762\pi$
$131$	3.75557e13	0.649250	0.324625	+	0.945843i	$0.394762\pi$
$132$	−1.10028e13	−0.181039
$133$	−7.19412e13	−1.12705
$134$	6.67943e13	0.996685
$135$	9.36040e12	0.133084
$136$	−1.09036e12	−0.0147763
$137$	8.65162e12	0.111793	0.0558964	−	0.998437i	$-0.482198\pi$
$137$	8.65162e12	0.111793	0.0558964	+	0.998437i	$0.482198\pi$
$138$	3.38542e13	0.417252
$139$	−8.80117e13	−1.03501	−0.517504	−	0.855681i	$-0.673139\pi$
$139$	−8.80117e13	−1.03501	−0.517504	+	0.855681i	$0.673139\pi$
$140$	−4.82395e13	−0.541465
$141$	−5.26346e13	−0.564089
$142$	8.02051e12	0.0820971
$143$	−9.67068e13	−0.945742
$144$	−6.18537e12	−0.0578109
$145$	−3.65685e13	−0.326750
$146$	−8.20120e13	−0.700784
$147$	−7.92143e13	−0.647502
$148$	1.23917e13	0.0969234
$149$	−4.70594e13	−0.352319	−0.176159	−	0.984362i	$-0.556367\pi$
$149$	−4.70594e13	−0.352319	−0.176159	+	0.984362i	$0.556367\pi$
$150$	−2.85793e13	−0.204861
$151$	−2.25042e14	−1.54495	−0.772474	−	0.635047i	$-0.780981\pi$
$151$	−2.25042e14	−1.54495	−0.772474	+	0.635047i	$0.780981\pi$
$152$	1.23016e14	0.809052
$153$	−7.47453e11	−0.00471074
$154$	−9.56354e13	−0.577742
$155$	−7.66986e12	−0.0444254
$156$	9.05880e13	0.503223
$157$	2.19795e14	1.17130	0.585652	−	0.810562i	$-0.300838\pi$
$157$	2.19795e14	1.17130	0.585652	+	0.810562i	$0.300838\pi$
$158$	−4.39607e13	−0.224798
$159$	7.47959e13	0.367110
$160$	1.36134e14	0.641486
$161$	−3.42082e14	−1.54797
$162$	−1.73830e13	−0.0755574
$163$	1.95426e14	0.816136	0.408068	−	0.912952i	$-0.366203\pi$
$163$	1.95426e14	0.816136	0.408068	+	0.912952i	$0.366203\pi$
$164$	1.97537e14	0.792800
$165$	−6.03649e13	−0.232884
$166$	1.08223e14	0.401437
$167$	−3.21431e14	−1.14665	−0.573325	−	0.819328i	$-0.694347\pi$
$167$	−3.21431e14	−1.14665	−0.573325	+	0.819328i	$0.694347\pi$
$168$	2.56229e14	0.879261
$169$	4.93328e14	1.62882
$170$	−2.09149e12	−0.00664564
$171$	8.43284e13	0.257928
$172$	−4.37256e13	−0.128766
$173$	−6.64735e14	−1.88516	−0.942581	−	0.333978i	$-0.891609\pi$
$173$	−6.64735e14	−1.88516	−0.942581	+	0.333978i	$0.891609\pi$
$174$	6.79105e13	0.185510
$175$	2.88782e14	0.760015
$176$	3.98892e13	0.101163
$177$	−3.07496e13	−0.0751646
$178$	−2.49122e14	−0.587059
$179$	−3.70064e14	−0.840877	−0.420439	−	0.907321i	$-0.638124\pi$
$179$	−3.70064e14	−0.840877	−0.420439	+	0.907321i	$0.638124\pi$
$180$	5.65455e13	0.123916
$181$	2.34613e14	0.495954	0.247977	−	0.968766i	$-0.420234\pi$
$181$	2.34613e14	0.495954	0.247977	+	0.968766i	$0.420234\pi$
$182$	7.87382e14	1.60591
$183$	1.32626e13	0.0261034
$184$	5.84941e14	1.11121
$185$	6.79846e13	0.124679
$186$	1.42435e13	0.0252222
$187$	4.82030e12	0.00824334
$188$	−3.17962e14	−0.525230
$189$	1.75647e14	0.280311
$190$	2.35964e14	0.363870
$191$	9.76734e14	1.45566	0.727829	−	0.685758i	$-0.240529\pi$
$191$	9.76734e14	1.45566	0.727829	+	0.685758i	$0.240529\pi$
$192$	−3.22318e14	−0.464330
$193$	3.37766e14	0.470428	0.235214	−	0.971944i	$-0.424421\pi$
$193$	3.37766e14	0.470428	0.235214	+	0.971944i	$0.424421\pi$
$194$	3.19208e14	0.429895
$195$	4.96994e14	0.647331
$196$	−4.78528e14	−0.602896
$197$	−2.19689e14	−0.267780	−0.133890	−	0.990996i	$-0.542747\pi$
$197$	−2.19689e14	−0.267780	−0.133890	+	0.990996i	$0.542747\pi$
$198$	1.12102e14	0.132218
$199$	1.26246e14	0.144103	0.0720516	−	0.997401i	$-0.477045\pi$
$199$	1.26246e14	0.144103	0.0720516	+	0.997401i	$0.477045\pi$
$200$	−4.93801e14	−0.545578
$201$	7.91138e14	0.846210
$202$	1.51217e14	0.156609
$203$	−6.86206e14	−0.688225
$204$	−4.51531e12	−0.00438623
$205$	1.08375e15	1.01983
$206$	1.44591e15	1.31827
$207$	4.00983e14	0.354257
$208$	−3.28415e14	−0.281197
$209$	−5.43831e14	−0.451349
$210$	4.91488e14	0.395447
$211$	1.70060e15	1.32668	0.663338	−	0.748320i	$-0.269139\pi$
$211$	1.70060e15	1.32668	0.663338	+	0.748320i	$0.269139\pi$
$212$	4.51836e14	0.341821
$213$	9.49982e13	0.0697024
$214$	−1.22657e15	−0.872976
$215$	−2.39892e14	−0.165640
$216$	−3.00347e14	−0.201222
$217$	−1.43925e14	−0.0935721
$218$	1.59248e14	0.100486
$219$	−9.71384e14	−0.594982
$220$	−3.64660e14	−0.216841
$221$	−3.96863e13	−0.0229135
$222$	−1.26253e14	−0.0707858
$223$	−1.78711e15	−0.973127	−0.486563	−	0.873645i	$-0.661750\pi$
$223$	−1.78711e15	−0.973127	−0.486563	+	0.873645i	$0.661750\pi$
$224$	2.55455e15	1.35115
$225$	−3.38505e14	−0.173932
$226$	1.43409e15	0.715933
$227$	1.46785e15	0.712056	0.356028	−	0.934475i	$-0.384131\pi$
$227$	1.46785e15	0.712056	0.356028	+	0.934475i	$0.384131\pi$
$228$	5.09422e14	0.240160
$229$	−6.19206e14	−0.283729	−0.141865	−	0.989886i	$-0.545310\pi$
$229$	−6.19206e14	−0.283729	−0.141865	+	0.989886i	$0.545310\pi$
$230$	1.12201e15	0.499765
$231$	−1.13274e15	−0.490517
$232$	1.17337e15	0.494043
$233$	1.05482e15	0.431883	0.215942	−	0.976406i	$-0.430718\pi$
$233$	1.05482e15	0.431883	0.215942	+	0.976406i	$0.430718\pi$
$234$	−9.22957e14	−0.367518
$235$	−1.74444e15	−0.675639
$236$	−1.85756e14	−0.0699867
$237$	−5.20688e14	−0.190859
$238$	−3.92466e13	−0.0139976
$239$	2.71795e15	0.943311	0.471655	−	0.881783i	$-0.343657\pi$
$239$	2.71795e15	0.943311	0.471655	+	0.881783i	$0.343657\pi$
$240$	−2.04998e14	−0.0692432
$241$	4.77435e15	1.56965	0.784826	−	0.619716i	$-0.212752\pi$
$241$	4.77435e15	1.56965	0.784826	+	0.619716i	$0.212752\pi$
$242$	1.40186e15	0.448648
$243$	−2.05891e14	−0.0641500
$244$	8.01184e13	0.0243051
$245$	−2.62535e15	−0.775547
$246$	−2.01261e15	−0.579003
$247$	4.47745e15	1.25459
$248$	2.46103e14	0.0671709
$249$	1.28184e15	0.340830
$250$	−2.76244e15	−0.715620
$251$	2.92218e15	0.737613	0.368806	−	0.929506i	$-0.379767\pi$
$251$	2.92218e15	0.737613	0.368806	+	0.929506i	$0.379767\pi$
$252$	1.06107e15	0.261001
$253$	−2.58593e15	−0.619916
$254$	2.32903e14	0.0544197
$255$	−2.47724e13	−0.00564231
$256$	−4.78802e15	−1.06315
$257$	3.10651e15	0.672523	0.336261	−	0.941769i	$-0.390837\pi$
$257$	3.10651e15	0.672523	0.336261	+	0.941769i	$0.390837\pi$
$258$	4.45498e14	0.0940412
$259$	1.27573e15	0.262609
$260$	3.00231e15	0.602738
$261$	8.04359e14	0.157502
$262$	−2.31148e15	−0.441501
$263$	3.15750e14	0.0588344	0.0294172	−	0.999567i	$-0.490635\pi$
$263$	3.15750e14	0.0588344	0.0294172	+	0.999567i	$0.490635\pi$
$264$	1.93693e15	0.352118
$265$	2.47892e15	0.439707
$266$	4.42784e15	0.766411
$267$	−2.95070e15	−0.498428
$268$	4.77921e15	0.787916
$269$	4.34274e14	0.0698834	0.0349417	−	0.999389i	$-0.488875\pi$
$269$	4.34274e14	0.0698834	0.0349417	+	0.999389i	$0.488875\pi$
$270$	−5.76115e14	−0.0904991
$271$	1.07663e16	1.65107	0.825533	−	0.564354i	$-0.190875\pi$
$271$	1.07663e16	1.65107	0.825533	+	0.564354i	$0.190875\pi$
$272$	1.63696e13	0.00245099
$273$	9.32607e15	1.36346
$274$	−5.32490e14	−0.0760209
$275$	2.18301e15	0.304364
$276$	2.42231e15	0.329853
$277$	1.01148e16	1.34536	0.672682	−	0.739931i	$-0.265142\pi$
$277$	1.01148e16	1.34536	0.672682	+	0.739931i	$0.265142\pi$
$278$	5.41695e15	0.703823
$279$	1.68706e14	0.0214143
$280$	8.49205e15	1.05314
$281$	−1.14258e16	−1.38451	−0.692256	−	0.721652i	$-0.743383\pi$
$281$	−1.14258e16	−1.38451	−0.692256	+	0.721652i	$0.743383\pi$
$282$	3.23956e15	0.383589
$283$	−5.42748e15	−0.628039	−0.314019	−	0.949417i	$-0.601676\pi$
$283$	−5.42748e15	−0.628039	−0.314019	+	0.949417i	$0.601676\pi$
$284$	5.73877e14	0.0649008
$285$	2.79485e15	0.308935
$286$	5.95212e15	0.643120
$287$	2.03365e16	2.14805
$288$	−2.99440e15	−0.309214
$289$	−9.90260e15	−0.999800
$290$	2.25072e15	0.222195
$291$	3.78082e15	0.364991
$292$	−5.86806e15	−0.553995
$293$	−5.06244e15	−0.467434	−0.233717	−	0.972305i	$-0.575089\pi$
$293$	−5.06244e15	−0.467434	−0.233717	+	0.972305i	$0.575089\pi$
$294$	4.87549e15	0.440312
$295$	−1.01912e15	−0.0900287
$296$	−2.18142e15	−0.188514
$297$	1.32778e15	0.112256
$298$	2.89642e15	0.239583
$299$	2.12904e16	1.72314
$300$	−2.04489e15	−0.161950
$301$	−4.50156e15	−0.348884
$302$	1.38509e16	1.05059
$303$	1.79107e15	0.132965
$304$	−1.84684e15	−0.134199
$305$	4.39555e14	0.0312654
$306$	4.60043e13	0.00320338
$307$	−6.45213e15	−0.439849	−0.219925	−	0.975517i	$-0.570581\pi$
$307$	−6.45213e15	−0.439849	−0.219925	+	0.975517i	$0.570581\pi$
$308$	−6.84283e15	−0.456726
$309$	1.71260e16	1.11924
$310$	4.72065e14	0.0302100
$311$	−2.20422e16	−1.38138	−0.690689	−	0.723152i	$-0.742693\pi$
$311$	−2.20422e16	−1.38138	−0.690689	+	0.723152i	$0.742693\pi$
$312$	−1.59471e16	−0.978760
$313$	1.43435e16	0.862217	0.431109	−	0.902300i	$-0.358123\pi$
$313$	1.43435e16	0.862217	0.431109	+	0.902300i	$0.358123\pi$
$314$	−1.35279e16	−0.796506
$315$	5.82138e15	0.335744
$316$	−3.14544e15	−0.177711
$317$	−1.96881e16	−1.08973	−0.544865	−	0.838524i	$-0.683419\pi$
$317$	−1.96881e16	−1.08973	−0.544865	+	0.838524i	$0.683419\pi$
$318$	−4.60354e15	−0.249641
$319$	−5.18729e15	−0.275614
$320$	−1.06824e16	−0.556153
$321$	−1.45280e16	−0.741177
$322$	2.10545e16	1.05264
$323$	−2.23176e14	−0.0109353
$324$	−1.24377e15	−0.0597309
$325$	−1.79731e16	−0.846020
$326$	−1.20281e16	−0.554986
$327$	1.88619e15	0.0853150
$328$	−3.47743e16	−1.54198
$329$	−3.27343e16	−1.42308
$330$	3.71534e15	0.158365
$331$	3.12897e16	1.30774	0.653868	−	0.756609i	$-0.273145\pi$
$331$	3.12897e16	1.30774	0.653868	+	0.756609i	$0.273145\pi$
$332$	7.74349e15	0.317351
$333$	−1.49539e15	−0.0600988
$334$	1.97835e16	0.779741
$335$	2.62202e16	1.01355
$336$	−3.84678e15	−0.145845
$337$	−1.91992e16	−0.713985	−0.356993	−	0.934107i	$-0.616198\pi$
$337$	−1.91992e16	−0.713985	−0.356993	+	0.934107i	$0.616198\pi$
$338$	−3.03634e16	−1.10762
$339$	1.69860e16	0.607845
$340$	−1.49648e14	−0.00525362
$341$	−1.08798e15	−0.0374729
$342$	−5.19025e15	−0.175395
$343$	−5.33740e15	−0.176977
$344$	7.69743e15	0.250447
$345$	1.32896e16	0.424313
$346$	4.09131e16	1.28194
$347$	−3.69054e16	−1.13487	−0.567437	−	0.823416i	$-0.692065\pi$
$347$	−3.69054e16	−1.13487	−0.567437	+	0.823416i	$0.692065\pi$
$348$	4.85908e15	0.146652
$349$	2.09105e16	0.619438	0.309719	−	0.950828i	$-0.399765\pi$
$349$	2.09105e16	0.619438	0.309719	+	0.950828i	$0.399765\pi$
$350$	−1.77740e16	−0.516823
$351$	−1.09319e16	−0.312031
$352$	1.93108e16	0.541094
$353$	−1.31127e16	−0.360710	−0.180355	−	0.983602i	$-0.557725\pi$
$353$	−1.31127e16	−0.360710	−0.180355	+	0.983602i	$0.557725\pi$
$354$	1.89258e15	0.0511132
$355$	3.14847e15	0.0834863
$356$	−1.78250e16	−0.464092
$357$	−4.64853e14	−0.0118843
$358$	2.27767e16	0.571810
$359$	8.62291e15	0.212589	0.106294	−	0.994335i	$-0.466101\pi$
$359$	8.62291e15	0.212589	0.106294	+	0.994335i	$0.466101\pi$
$360$	−9.95425e15	−0.241014
$361$	−1.68741e16	−0.401257
$362$	−1.44400e16	−0.337257
$363$	1.66042e16	0.380913
$364$	5.63381e16	1.26953
$365$	−3.21940e16	−0.712642
$366$	−8.16287e14	−0.0177507
$367$	3.50773e16	0.749370	0.374685	−	0.927152i	$-0.377751\pi$
$367$	3.50773e16	0.749370	0.374685	+	0.927152i	$0.377751\pi$
$368$	−8.78176e15	−0.184319
$369$	−2.38381e16	−0.491588
$370$	−4.18432e15	−0.0847840
$371$	4.65168e16	0.926145
$372$	1.01914e15	0.0199391
$373$	4.45891e16	0.857277	0.428638	−	0.903476i	$-0.358993\pi$
$373$	4.45891e16	0.857277	0.428638	+	0.903476i	$0.358993\pi$
$374$	−2.96680e14	−0.00560561
$375$	−3.27194e16	−0.607579
$376$	5.59739e16	1.02156
$377$	4.27078e16	0.766105
$378$	−1.08108e16	−0.190616
$379$	1.01350e17	1.75658	0.878292	−	0.478125i	$-0.158683\pi$
$379$	1.01350e17	1.75658	0.878292	+	0.478125i	$0.158683\pi$
$380$	1.68835e16	0.287653
$381$	2.75860e15	0.0462036
$382$	−6.01161e16	−0.989872
$383$	−1.36942e16	−0.221690	−0.110845	−	0.993838i	$-0.535356\pi$
$383$	−1.36942e16	−0.221690	−0.110845	+	0.993838i	$0.535356\pi$
$384$	−1.38109e16	−0.219822
$385$	−3.75419e16	−0.587519
$386$	−2.07888e16	−0.319899
$387$	5.27666e15	0.0798432
$388$	2.28397e16	0.339847
$389$	−4.88391e16	−0.714653	−0.357326	−	0.933980i	$-0.616312\pi$
$389$	−4.88391e16	−0.714653	−0.357326	+	0.933980i	$0.616312\pi$
$390$	−3.05890e16	−0.440196
$391$	−1.06121e15	−0.0150193
$392$	8.42398e16	1.17262
$393$	−2.73781e16	−0.374845
$394$	1.35214e16	0.182095
$395$	−1.72569e16	−0.228602
$396$	8.02105e15	0.104523
$397$	−1.33805e17	−1.71527	−0.857636	−	0.514257i	$-0.828068\pi$
$397$	−1.33805e17	−1.71527	−0.857636	+	0.514257i	$0.828068\pi$
$398$	−7.77022e15	−0.0979926
$399$	5.24452e16	0.650701
$400$	7.41346e15	0.0904963
$401$	−1.06625e17	−1.28062	−0.640312	−	0.768115i	$-0.721195\pi$
$401$	−1.06625e17	−1.28062	−0.640312	+	0.768115i	$0.721195\pi$
$402$	−4.86930e16	−0.575436
$403$	8.95751e15	0.104161
$404$	1.08198e16	0.123805
$405$	−6.82373e15	−0.0768359
$406$	4.22346e16	0.468004
$407$	9.64370e15	0.105167
$408$	7.94873e14	0.00853113
$409$	−1.02031e17	−1.07778	−0.538892	−	0.842375i	$-0.681157\pi$
$409$	−1.02031e17	−1.07778	−0.538892	+	0.842375i	$0.681157\pi$
$410$	−6.67027e16	−0.693503
$411$	−6.30703e15	−0.0645436
$412$	1.03457e17	1.04214
$413$	−1.91237e16	−0.189625
$414$	−2.46797e16	−0.240901
$415$	4.24832e16	0.408230
$416$	−1.58989e17	−1.50404
$417$	6.41605e16	0.597563
$418$	3.34717e16	0.306925
$419$	−1.53747e17	−1.38809	−0.694043	−	0.719933i	$-0.744172\pi$
$419$	−1.53747e17	−1.38809	−0.694043	+	0.719933i	$0.744172\pi$
$420$	3.51666e16	0.312615
$421$	−3.35041e16	−0.293268	−0.146634	−	0.989191i	$-0.546844\pi$
$421$	−3.35041e16	−0.293268	−0.146634	+	0.989191i	$0.546844\pi$
$422$	−1.04668e17	−0.902162
$423$	3.83706e16	0.325677
$424$	−7.95411e16	−0.664834
$425$	8.95857e14	0.00737413
$426$	−5.84695e15	−0.0473988
$427$	8.24822e15	0.0658535
$428$	−8.77624e16	−0.690119
$429$	7.04993e16	0.546025
$430$	1.47649e16	0.112638
$431$	−1.09478e17	−0.822666	−0.411333	−	0.911485i	$-0.634937\pi$
$431$	−1.09478e17	−0.822666	−0.411333	+	0.911485i	$0.634937\pi$
$432$	4.50913e15	0.0333771
$433$	−1.20437e17	−0.878187	−0.439093	−	0.898441i	$-0.644700\pi$
$433$	−1.20437e17	−0.878187	−0.439093	+	0.898441i	$0.644700\pi$
$434$	8.85828e15	0.0636306
$435$	2.66584e16	0.188649
$436$	1.13943e16	0.0794378
$437$	1.19726e17	0.822357
$438$	5.97868e16	0.404598
$439$	−2.28838e17	−1.52584	−0.762920	−	0.646493i	$-0.776235\pi$
$439$	−2.28838e17	−1.52584	−0.762920	+	0.646493i	$0.776235\pi$
$440$	6.41946e16	0.421751
$441$	5.77472e16	0.373835
$442$	2.44261e15	0.0155815
$443$	−2.19371e17	−1.37897	−0.689484	−	0.724301i	$-0.742163\pi$
$443$	−2.19371e17	−1.37897	−0.689484	+	0.724301i	$0.742163\pi$
$444$	−9.03353e15	−0.0559588
$445$	−9.77934e16	−0.596993
$446$	1.09993e17	0.661742
$447$	3.43063e16	0.203411
$448$	−2.00455e17	−1.17141
$449$	−8.11931e16	−0.467647	−0.233823	−	0.972279i	$-0.575124\pi$
$449$	−8.11931e16	−0.467647	−0.233823	+	0.972279i	$0.575124\pi$
$450$	2.08343e16	0.118276
$451$	1.53731e17	0.860231
$452$	1.02611e17	0.565971
$453$	1.64056e17	0.891976
$454$	−9.03435e16	−0.484210
$455$	3.09089e17	1.63309
$456$	−8.96783e16	−0.467107
$457$	2.39301e15	0.0122882	0.00614411	−	0.999981i	$-0.498044\pi$
$457$	2.39301e15	0.0122882	0.00614411	+	0.999981i	$0.498044\pi$
$458$	3.81109e16	0.192941
$459$	5.44893e14	0.00271975
$460$	8.02812e16	0.395083
$461$	−1.75704e17	−0.852560	−0.426280	−	0.904591i	$-0.640176\pi$
$461$	−1.75704e17	−0.852560	−0.426280	+	0.904591i	$0.640176\pi$
$462$	6.97182e16	0.333560
$463$	−1.51481e17	−0.714633	−0.357316	−	0.933983i	$-0.616308\pi$
$463$	−1.51481e17	−0.714633	−0.357316	+	0.933983i	$0.616308\pi$
$464$	−1.76159e16	−0.0819481
$465$	5.59133e15	0.0256490
$466$	−6.49223e16	−0.293688
$467$	2.28018e17	1.01721	0.508604	−	0.861000i	$-0.330162\pi$
$467$	2.28018e17	1.01721	0.508604	+	0.861000i	$0.330162\pi$
$468$	−6.60387e16	−0.290536
$469$	4.92022e17	2.13482
$470$	1.07367e17	0.459446
$471$	−1.60230e17	−0.676253
$472$	3.27004e16	0.136123
$473$	−3.40290e16	−0.139718
$474$	3.20473e16	0.129787
$475$	−1.01072e17	−0.403757
$476$	−2.80814e15	−0.0110656
$477$	−5.45262e16	−0.211951
$478$	−1.67284e17	−0.641467
$479$	4.62842e17	1.75086	0.875430	−	0.483345i	$-0.160578\pi$
$479$	4.62842e17	1.75086	0.875430	+	0.483345i	$0.160578\pi$
$480$	−9.92417e16	−0.370362
$481$	−7.93982e16	−0.292326
$482$	−2.93852e17	−1.06739
$483$	2.49378e17	0.893720
$484$	1.00305e17	0.354672
$485$	1.25306e17	0.437169
$486$	1.26722e16	0.0436231
$487$	3.15364e17	1.07121	0.535605	−	0.844469i	$-0.320084\pi$
$487$	3.15364e17	1.07121	0.535605	+	0.844469i	$0.320084\pi$
$488$	−1.41040e16	−0.0472730
$489$	−1.42465e17	−0.471196
$490$	1.61585e17	0.527385
$491$	−7.61610e16	−0.245303	−0.122652	−	0.992450i	$-0.539140\pi$
$491$	−7.61610e16	−0.245303	−0.122652	+	0.992450i	$0.539140\pi$
$492$	−1.44005e17	−0.457723
$493$	−2.12875e15	−0.00667757
$494$	−2.75578e17	−0.853139
$495$	4.40060e16	0.134455
$496$	−3.69476e15	−0.0111418
$497$	5.90809e16	0.175845
$498$	−7.88946e16	−0.231770
$499$	2.07843e17	0.602674	0.301337	−	0.953518i	$-0.402567\pi$
$499$	2.07843e17	0.602674	0.301337	+	0.953518i	$0.402567\pi$
$500$	−1.97656e17	−0.565724
$501$	2.34323e17	0.662019
$502$	−1.79855e17	−0.501589
$503$	−4.92414e17	−1.35562	−0.677810	−	0.735237i	$-0.737071\pi$
$503$	−4.92414e17	−1.35562	−0.677810	+	0.735237i	$0.737071\pi$
$504$	−1.86791e17	−0.507642
$505$	5.93606e16	0.159259
$506$	1.59159e17	0.421553
$507$	−3.59636e17	−0.940398
$508$	1.66645e16	0.0430208
$509$	−4.49265e17	−1.14508	−0.572541	−	0.819876i	$-0.694042\pi$
$509$	−4.49265e17	−1.14508	−0.572541	+	0.819876i	$0.694042\pi$
$510$	1.52469e15	0.00383686
$511$	−6.04119e17	−1.50102
$512$	1.39496e17	0.342220
$513$	−6.14754e16	−0.148915
$514$	−1.91199e17	−0.457327
$515$	5.67596e17	1.34058
$516$	3.18759e16	0.0743430
$517$	−2.47451e17	−0.569903
$518$	−7.85186e16	−0.178578
$519$	4.84592e17	1.08840
$520$	−5.28525e17	−1.17231
$521$	2.59780e17	0.569064	0.284532	−	0.958667i	$-0.408162\pi$
$521$	2.59780e17	0.569064	0.284532	+	0.958667i	$0.408162\pi$
$522$	−4.95068e16	−0.107104
$523$	7.92805e17	1.69397	0.846985	−	0.531617i	$-0.178415\pi$
$523$	7.92805e17	1.69397	0.846985	+	0.531617i	$0.178415\pi$
$524$	−1.65389e17	−0.349022
$525$	−2.10522e17	−0.438795
$526$	−1.94338e16	−0.0400084
$527$	−4.46482e14	−0.000907894 0
$528$	−2.90792e16	−0.0584067
$529$	6.52644e16	0.129484
$530$	−1.52573e17	−0.299008
$531$	2.24165e16	0.0433963
$532$	3.16817e17	0.605876
$533$	−1.26570e18	−2.39113
$534$	1.81610e17	0.338939
$535$	−4.81492e17	−0.887748
$536$	−8.41330e17	−1.53248
$537$	2.69777e17	0.485481
$538$	−2.67287e16	−0.0475218
$539$	−3.72410e17	−0.654175
$540$	−4.12217e16	−0.0715428
$541$	−3.73567e17	−0.640600	−0.320300	−	0.947316i	$-0.603784\pi$
$541$	−3.73567e17	−0.640600	−0.320300	+	0.947316i	$0.603784\pi$
$542$	−6.62642e17	−1.12275
$543$	−1.71033e17	−0.286339
$544$	7.92471e15	0.0131096
$545$	6.25130e16	0.102186
$546$	−5.74002e17	−0.927174
$547$	7.83212e17	1.25015	0.625074	−	0.780565i	$-0.285069\pi$
$547$	7.83212e17	1.25015	0.625074	+	0.780565i	$0.285069\pi$
$548$	−3.81003e16	−0.0600973
$549$	−9.66843e15	−0.0150708
$550$	−1.34360e17	−0.206972
$551$	2.40167e17	0.365619
$552$	−4.26422e17	−0.641558
$553$	−3.23824e17	−0.481500
$554$	−6.22548e17	−0.914870
$555$	−4.95608e16	−0.0719836
$556$	3.87589e17	0.556398
$557$	1.05144e18	1.49185	0.745926	−	0.666028i	$-0.232007\pi$
$557$	1.05144e18	1.49185	0.745926	+	0.666028i	$0.232007\pi$
$558$	−1.03835e16	−0.0145621
$559$	2.80166e17	0.388364
$560$	−1.27492e17	−0.174687
$561$	−3.51400e15	−0.00475930
$562$	7.03238e17	0.941491
$563$	−1.28402e18	−1.69929	−0.849646	−	0.527353i	$-0.823184\pi$
$563$	−1.28402e18	−1.69929	−0.849646	+	0.527353i	$0.823184\pi$
$564$	2.31794e17	0.303241
$565$	5.62957e17	0.728048
$566$	3.34051e17	0.427077
$567$	−1.28047e17	−0.161838
$568$	−1.01025e17	−0.126231
$569$	2.74431e17	0.339003	0.169502	−	0.985530i	$-0.445784\pi$
$569$	2.74431e17	0.339003	0.169502	+	0.985530i	$0.445784\pi$
$570$	−1.72017e17	−0.210081
$571$	−9.64668e17	−1.16478	−0.582389	−	0.812910i	$-0.697882\pi$
$571$	−9.64668e17	−1.16478	−0.582389	+	0.812910i	$0.697882\pi$
$572$	4.25881e17	0.508410
$573$	−7.12039e17	−0.840425
$574$	−1.25167e18	−1.46071
$575$	−4.80597e17	−0.554549
$576$	2.34970e17	0.268081
$577$	−5.69948e16	−0.0642972	−0.0321486	−	0.999483i	$-0.510235\pi$
$577$	−5.69948e16	−0.0642972	−0.0321486	+	0.999483i	$0.510235\pi$
$578$	6.09486e17	0.679881
$579$	−2.46231e17	−0.271602
$580$	1.61042e17	0.175653
$581$	7.97196e17	0.859845
$582$	−2.32702e17	−0.248200
$583$	3.51638e17	0.370894
$584$	1.03301e18	1.07751
$585$	−3.62309e17	−0.373737
$586$	3.11583e17	0.317863
$587$	8.15914e17	0.823184	0.411592	−	0.911368i	$-0.364973\pi$
$587$	8.15914e17	0.823184	0.411592	+	0.911368i	$0.364973\pi$
$588$	3.48847e17	0.348082
$589$	5.03726e16	0.0497101
$590$	6.27247e16	0.0612210
$591$	1.60153e17	0.154603
$592$	3.27498e16	0.0312693
$593$	−4.40139e17	−0.415656	−0.207828	−	0.978165i	$-0.566639\pi$
$593$	−4.40139e17	−0.415656	−0.207828	+	0.978165i	$0.566639\pi$
$594$	−8.17226e16	−0.0763361
$595$	−1.54064e16	−0.0142344
$596$	2.07242e17	0.189399
$597$	−9.20336e16	−0.0831980
$598$	−1.31038e18	−1.17176
$599$	3.73998e17	0.330822	0.165411	−	0.986225i	$-0.447105\pi$
$599$	3.73998e17	0.330822	0.165411	+	0.986225i	$0.447105\pi$
$600$	3.59981e17	0.314989
$601$	1.37432e18	1.18961	0.594803	−	0.803872i	$-0.297230\pi$
$601$	1.37432e18	1.18961	0.594803	+	0.803872i	$0.297230\pi$
$602$	2.77063e17	0.237247
$603$	−5.76740e17	−0.488559
$604$	9.91049e17	0.830529
$605$	5.50304e17	0.456239
$606$	−1.10237e17	−0.0904182
$607$	1.65528e18	1.34321	0.671607	−	0.740907i	$-0.265604\pi$
$607$	1.65528e18	1.34321	0.671607	+	0.740907i	$0.265604\pi$
$608$	−8.94074e17	−0.717795
$609$	5.00244e17	0.397347
$610$	−2.70537e16	−0.0212610
$611$	2.03730e18	1.58412
$612$	3.29166e15	0.00253239
$613$	−3.90949e17	−0.297596	−0.148798	−	0.988868i	$-0.547540\pi$
$613$	−3.90949e17	−0.297596	−0.148798	+	0.988868i	$0.547540\pi$
$614$	3.97116e17	0.299105
$615$	−7.90054e17	−0.588801
$616$	1.20461e18	0.888324
$617$	−1.14596e18	−0.836213	−0.418106	−	0.908398i	$-0.637306\pi$
$617$	−1.14596e18	−0.836213	−0.418106	+	0.908398i	$0.637306\pi$
$618$	−1.05407e18	−0.761104
$619$	2.72924e18	1.95008	0.975041	−	0.222023i	$-0.0712661\pi$
$619$	2.72924e18	1.95008	0.975041	+	0.222023i	$0.0712661\pi$
$620$	3.37768e16	0.0238821
$621$	−2.92317e17	−0.204530
$622$	1.35666e18	0.939360
$623$	−1.83509e18	−1.25743
$624$	2.39414e17	0.162349
$625$	−3.06866e17	−0.205934
$626$	−8.82814e17	−0.586322
$627$	3.96453e17	0.260587
$628$	−9.67941e17	−0.629667
$629$	3.95756e15	0.00254799
$630$	−3.58295e17	−0.228311
$631$	1.52089e17	0.0959197	0.0479598	−	0.998849i	$-0.484728\pi$
$631$	1.52089e17	0.0959197	0.0479598	+	0.998849i	$0.484728\pi$
$632$	5.53721e17	0.345645
$633$	−1.23973e18	−0.765957
$634$	1.21177e18	0.741035
$635$	9.14267e16	0.0553406
$636$	−3.29389e17	−0.197350
$637$	3.06611e18	1.81837
$638$	3.19267e17	0.187422
$639$	−6.92537e16	−0.0402427
$640$	−4.57728e17	−0.263292
$641$	1.83478e18	1.04474	0.522368	−	0.852720i	$-0.325049\pi$
$641$	1.83478e18	1.04474	0.522368	+	0.852720i	$0.325049\pi$
$642$	8.94168e17	0.504013
$643$	1.97470e18	1.10187	0.550934	−	0.834548i	$-0.314271\pi$
$643$	1.97470e18	1.10187	0.550934	+	0.834548i	$0.314271\pi$
$644$	1.50647e18	0.832153
$645$	1.74881e17	0.0956325
$646$	1.37360e16	0.00743619
$647$	−2.21517e18	−1.18722	−0.593609	−	0.804754i	$-0.702297\pi$
$647$	−2.21517e18	−1.18722	−0.593609	+	0.804754i	$0.702297\pi$
$648$	2.18953e17	0.116175
$649$	−1.44563e17	−0.0759393
$650$	1.10621e18	0.575307
$651$	1.04921e17	0.0540239
$652$	−8.60623e17	−0.438737
$653$	4.42522e17	0.223357	0.111678	−	0.993744i	$-0.464377\pi$
$653$	4.42522e17	0.223357	0.111678	+	0.993744i	$0.464377\pi$
$654$	−1.16091e17	−0.0580156
$655$	−9.07376e17	−0.448972
$656$	5.22069e17	0.255772
$657$	7.08139e17	0.343513
$658$	2.01473e18	0.967719
$659$	4.58167e17	0.217906	0.108953	−	0.994047i	$-0.465250\pi$
$659$	4.58167e17	0.217906	0.108953	+	0.994047i	$0.465250\pi$
$660$	2.65837e17	0.125193
$661$	3.46439e18	1.61554	0.807769	−	0.589499i	$-0.200675\pi$
$661$	3.46439e18	1.61554	0.807769	+	0.589499i	$0.200675\pi$
$662$	−1.92582e18	−0.889282
$663$	2.89313e16	0.0132291
$664$	−1.36316e18	−0.617241
$665$	1.73816e18	0.779380
$666$	9.20382e16	0.0408682
$667$	1.14200e18	0.502167
$668$	1.41553e18	0.616414
$669$	1.30280e18	0.561835
$670$	−1.61380e18	−0.689231
$671$	6.23514e16	0.0263724
$672$	−1.86227e18	−0.780084
$673$	1.39394e18	0.578292	0.289146	−	0.957285i	$-0.406629\pi$
$673$	1.39394e18	0.578292	0.289146	+	0.957285i	$0.406629\pi$
$674$	1.18167e18	0.485522
$675$	2.46770e17	0.100420
$676$	−2.17254e18	−0.875616
$677$	−4.89466e17	−0.195387	−0.0976935	−	0.995217i	$-0.531146\pi$
$677$	−4.89466e17	−0.195387	−0.0976935	+	0.995217i	$0.531146\pi$
$678$	−1.04545e18	−0.413344
$679$	2.35136e18	0.920799
$680$	2.63440e16	0.0102182
$681$	−1.07006e18	−0.411106
$682$	6.69630e16	0.0254822
$683$	3.07382e18	1.15863	0.579314	−	0.815104i	$-0.303320\pi$
$683$	3.07382e18	1.15863	0.579314	+	0.815104i	$0.303320\pi$
$684$	−3.71368e17	−0.138656
$685$	−2.09030e17	−0.0773073
$686$	3.28507e17	0.120348
$687$	4.51401e17	0.163811
$688$	−1.15562e17	−0.0415422
$689$	−2.89509e18	−1.03095
$690$	−8.17946e17	−0.288540
$691$	4.23095e18	1.47853	0.739266	−	0.673414i	$-0.235173\pi$
$691$	4.23095e18	1.47853	0.739266	+	0.673414i	$0.235173\pi$
$692$	2.92738e18	1.01342
$693$	8.25771e17	0.283200
$694$	2.27145e18	0.771734
$695$	2.12643e18	0.715733
$696$	−8.55390e17	−0.285236
$697$	6.30879e16	0.0208417
$698$	−1.28700e18	−0.421228
$699$	−7.68966e17	−0.249348
$700$	−1.27175e18	−0.408567
$701$	7.49692e15	0.00238625	0.00119312	−	0.999999i	$-0.499620\pi$
$701$	7.49692e15	0.00238625	0.00119312	+	0.999999i	$0.499620\pi$
$702$	6.72836e17	0.212186
$703$	−4.46496e17	−0.139511
$704$	−1.51531e18	−0.469116
$705$	1.27170e18	0.390080
$706$	8.07063e17	0.245288
$707$	1.11390e18	0.335443
$708$	1.35416e17	0.0404068
$709$	2.07940e18	0.614806	0.307403	−	0.951579i	$-0.400540\pi$
$709$	2.07940e18	0.614806	0.307403	+	0.951579i	$0.400540\pi$
$710$	−1.93782e17	−0.0567721
$711$	3.79581e17	0.110193
$712$	3.13790e18	0.902649
$713$	2.39523e17	0.0682754
$714$	2.86108e16	0.00808149
$715$	2.33652e18	0.654003
$716$	1.62970e18	0.452037
$717$	−1.98138e18	−0.544621
$718$	−5.30724e17	−0.144564
$719$	2.71840e16	0.00733797	0.00366899	−	0.999993i	$-0.498832\pi$
$719$	2.71840e16	0.00733797	0.00366899	+	0.999993i	$0.498832\pi$
$720$	1.49444e17	0.0399776
$721$	1.06509e19	2.82363
$722$	1.03857e18	0.272861
$723$	−3.48050e18	−0.906239
$724$	−1.03320e18	−0.266614
$725$	−9.64063e17	−0.246552
$726$	−1.02196e18	−0.259027
$727$	−4.38172e18	−1.10070	−0.550352	−	0.834933i	$-0.685506\pi$
$727$	−4.38172e18	−1.10070	−0.550352	+	0.834933i	$0.685506\pi$
$728$	−9.91774e18	−2.46921
$729$	1.50095e17	0.0370370
$730$	1.98148e18	0.484608
$731$	−1.39647e16	−0.00338509
$732$	−5.84063e16	−0.0140326
$733$	−1.83097e17	−0.0436019	−0.0218009	−	0.999762i	$-0.506940\pi$
$733$	−1.83097e17	−0.0436019	−0.0218009	+	0.999762i	$0.506940\pi$
$734$	−2.15894e18	−0.509584
$735$	1.91388e18	0.447762
$736$	−4.25134e18	−0.985871
$737$	3.71937e18	0.854931
$738$	1.46719e18	0.334288
$739$	3.34444e17	0.0755326	0.0377663	−	0.999287i	$-0.487976\pi$
$739$	3.34444e17	0.0755326	0.0377663	+	0.999287i	$0.487976\pi$
$740$	−2.99393e17	−0.0670248
$741$	−3.26406e18	−0.724335
$742$	−2.86302e18	−0.629794
$743$	3.63712e18	0.793104	0.396552	−	0.918012i	$-0.370207\pi$
$743$	3.63712e18	0.793104	0.396552	+	0.918012i	$0.370207\pi$
$744$	−1.79409e17	−0.0387811
$745$	1.13699e18	0.243637
$746$	−2.74437e18	−0.582962
$747$	−9.34460e17	−0.196778
$748$	−2.12278e16	−0.00443144
$749$	−9.03518e18	−1.86984
$750$	2.01382e18	0.413163
$751$	−2.81334e18	−0.572220	−0.286110	−	0.958197i	$-0.592362\pi$
$751$	−2.81334e18	−0.572220	−0.286110	+	0.958197i	$0.592362\pi$
$752$	−8.40339e17	−0.169449
$753$	−2.13027e18	−0.425861
$754$	−2.62858e18	−0.520964
$755$	5.43721e18	1.06837
$756$	−7.73523e17	−0.150689
$757$	7.31262e17	0.141237	0.0706187	−	0.997503i	$-0.477503\pi$
$757$	7.31262e17	0.141237	0.0706187	+	0.997503i	$0.477503\pi$
$758$	−6.23790e18	−1.19451
$759$	1.88514e18	0.357908
$760$	−2.97216e18	−0.559479
$761$	7.59414e18	1.41735	0.708677	−	0.705533i	$-0.249292\pi$
$761$	7.59414e18	1.41735	0.708677	+	0.705533i	$0.249292\pi$
$762$	−1.69786e17	−0.0314192
$763$	1.17305e18	0.215233
$764$	−4.30138e18	−0.782530
$765$	1.80591e16	0.00325759
$766$	8.42852e17	0.150753
$767$	1.19021e18	0.211083
$768$	3.49047e18	0.613813
$769$	−4.33887e18	−0.756580	−0.378290	−	0.925687i	$-0.623488\pi$
$769$	−4.33887e18	−0.756580	−0.378290	+	0.925687i	$0.623488\pi$
$770$	2.31063e18	0.399522
$771$	−2.26464e18	−0.388281
$772$	−1.48746e18	−0.252891
$773$	−9.96113e17	−0.167935	−0.0839677	−	0.996468i	$-0.526759\pi$
$773$	−9.96113e17	−0.167935	−0.0839677	+	0.996468i	$0.526759\pi$
$774$	−3.24768e17	−0.0542947
$775$	−2.02202e17	−0.0335216
$776$	−4.02069e18	−0.660996
$777$	−9.30005e17	−0.151617
$778$	3.00595e18	0.485976
$779$	−7.11764e18	−1.14115
$780$	−2.18868e18	−0.347991
$781$	4.46615e17	0.0704208
$782$	6.53151e16	0.0102134
$783$	−5.86378e17	−0.0909340
$784$	−1.26470e18	−0.194506
$785$	−5.31043e18	−0.809985
$786$	1.68507e18	0.254900
$787$	−1.20616e19	−1.80954	−0.904772	−	0.425897i	$-0.859959\pi$
$787$	−1.20616e19	−1.80954	−0.904772	+	0.425897i	$0.859959\pi$
$788$	9.67474e17	0.143952
$789$	−2.30182e17	−0.0339681
$790$	1.06213e18	0.155453
$791$	1.05639e19	1.53347
$792$	−1.41202e18	−0.203296
$793$	−5.13349e17	−0.0733056
$794$	8.23542e18	1.16641
$795$	−1.80713e18	−0.253865
$796$	−5.55968e17	−0.0774667
$797$	−3.77242e18	−0.521364	−0.260682	−	0.965425i	$-0.583947\pi$
$797$	−3.77242e18	−0.521364	−0.260682	+	0.965425i	$0.583947\pi$
$798$	−3.22790e18	−0.442488
$799$	−1.01548e17	−0.0138076
$800$	3.58893e18	0.484039
$801$	2.15106e18	0.287767
$802$	6.56258e18	0.870845
$803$	−4.56676e18	−0.601115
$804$	−3.48404e18	−0.454903
$805$	8.26499e18	1.07046
$806$	−5.51318e17	−0.0708311
$807$	−3.16586e17	−0.0403472
$808$	−1.90470e18	−0.240798
$809$	1.39972e17	0.0175540	0.00877702	−	0.999961i	$-0.497206\pi$
$809$	1.39972e17	0.0175540	0.00877702	+	0.999961i	$0.497206\pi$
$810$	4.19988e17	0.0522497
$811$	−3.99853e18	−0.493474	−0.246737	−	0.969082i	$-0.579358\pi$
$811$	−3.99853e18	−0.493474	−0.246737	+	0.969082i	$0.579358\pi$
$812$	3.02194e18	0.369974
$813$	−7.84860e18	−0.953243
$814$	−5.93551e17	−0.0715154
$815$	−4.72165e18	−0.564377
$816$	−1.19335e16	−0.00141508
$817$	1.57552e18	0.185344
$818$	6.27983e18	0.732911
$819$	−6.79871e18	−0.787193
$820$	−4.77266e18	−0.548240
$821$	−6.44249e18	−0.734215	−0.367107	−	0.930179i	$-0.619652\pi$
$821$	−6.44249e18	−0.734215	−0.367107	+	0.930179i	$0.619652\pi$
$822$	3.88185e17	0.0438907
$823$	7.66591e17	0.0859933	0.0429967	−	0.999075i	$-0.486310\pi$
$823$	7.66591e17	0.0859933	0.0429967	+	0.999075i	$0.486310\pi$
$824$	−1.82125e19	−2.02694
$825$	−1.59141e18	−0.175724
$826$	1.17703e18	0.128948
$827$	9.48487e18	1.03097	0.515484	−	0.856899i	$-0.327612\pi$
$827$	9.48487e18	1.03097	0.515484	+	0.856899i	$0.327612\pi$
$828$	−1.76586e18	−0.190441
$829$	−7.29321e18	−0.780395	−0.390198	−	0.920731i	$-0.627593\pi$
$829$	−7.29321e18	−0.780395	−0.390198	+	0.920731i	$0.627593\pi$
$830$	−2.61476e18	−0.277603
$831$	−7.37371e18	−0.776747
$832$	1.24758e19	1.30397
$833$	−1.52829e17	−0.0158494
$834$	−3.94895e18	−0.406352
$835$	7.76605e18	0.792936
$836$	2.39494e18	0.242635
$837$	−1.22987e17	−0.0123635
$838$	9.46285e18	0.943922
$839$	−1.58114e19	−1.56501	−0.782506	−	0.622643i	$-0.786059\pi$
$839$	−1.58114e19	−1.56501	−0.782506	+	0.622643i	$0.786059\pi$
$840$	−6.19071e18	−0.608030
$841$	−7.96981e18	−0.776737
$842$	2.06211e18	0.199427
$843$	8.32943e18	0.799348
$844$	−7.48914e18	−0.713192
$845$	−1.19192e19	−1.12637
$846$	−2.36164e18	−0.221465
$847$	1.03264e19	0.960966
$848$	1.19415e18	0.110278
$849$	3.95663e18	0.362598
$850$	−5.51383e16	−0.00501453
$851$	−2.12310e18	−0.191614
$852$	−4.18356e17	−0.0374705
$853$	−1.20836e19	−1.07406	−0.537029	−	0.843564i	$-0.680453\pi$
$853$	−1.20836e19	−1.07406	−0.537029	+	0.843564i	$0.680453\pi$
$854$	−5.07662e17	−0.0447815
$855$	−2.03744e18	−0.178363
$856$	1.54496e19	1.34227
$857$	2.01047e19	1.73349	0.866746	−	0.498750i	$-0.166208\pi$
$857$	2.01047e19	1.73349	0.866746	+	0.498750i	$0.166208\pi$
$858$	−4.33909e18	−0.371306
$859$	1.50342e19	1.27680	0.638401	−	0.769704i	$-0.279596\pi$
$859$	1.50342e19	1.27680	0.638401	+	0.769704i	$0.279596\pi$
$860$	1.05645e18	0.0890445
$861$	−1.48253e19	−1.24018
$862$	6.73814e18	0.559426
$863$	6.00385e18	0.494720	0.247360	−	0.968924i	$-0.420437\pi$
$863$	6.00385e18	0.494720	0.247360	+	0.968924i	$0.420437\pi$
$864$	2.18292e18	0.178525
$865$	1.60605e19	1.30363
$866$	7.41263e18	0.597181
$867$	7.21900e18	0.577235
$868$	6.33820e17	0.0503023
$869$	−2.44791e18	−0.192826
$870$	−1.64077e18	−0.128284
$871$	−3.06222e19	−2.37640
$872$	−2.00586e18	−0.154505
$873$	−2.75622e18	−0.210728
$874$	−7.36892e18	−0.559216
$875$	−2.03487e19	−1.53280
$876$	4.27781e18	0.319849
$877$	1.58455e19	1.17600	0.588002	−	0.808859i	$-0.299915\pi$
$877$	1.58455e19	1.17600	0.588002	+	0.808859i	$0.299915\pi$
$878$	1.40845e19	1.03760
$879$	3.69052e18	0.269873
$880$	−9.63757e17	−0.0699568
$881$	−1.32724e19	−0.956327	−0.478163	−	0.878271i	$-0.658697\pi$
$881$	−1.32724e19	−0.956327	−0.478163	+	0.878271i	$0.658697\pi$
$882$	−3.55423e18	−0.254214
$883$	2.09002e19	1.48390	0.741952	−	0.670453i	$-0.233900\pi$
$883$	2.09002e19	1.48390	0.741952	+	0.670453i	$0.233900\pi$
$884$	1.74772e17	0.0123178
$885$	7.42936e17	0.0519781
$886$	1.35018e19	0.937721
$887$	−1.62170e19	−1.11807	−0.559033	−	0.829145i	$-0.688828\pi$
$887$	−1.62170e19	−1.11807	−0.559033	+	0.829145i	$0.688828\pi$
$888$	1.59026e18	0.108839
$889$	1.71562e18	0.116562
$890$	6.01899e18	0.405965
$891$	−9.67955e17	−0.0648112
$892$	7.87014e18	0.523131
$893$	1.14568e19	0.756011
$894$	−2.11149e18	−0.138323
$895$	8.94106e18	0.581486
$896$	−8.58925e18	−0.554566
$897$	−1.55207e19	−0.994854
$898$	4.99728e18	0.318008
$899$	4.80475e17	0.0303552
$900$	1.49072e18	0.0935018
$901$	1.44304e17	0.00898602
$902$	−9.46187e18	−0.584971
$903$	3.28164e18	0.201428
$904$	−1.80636e19	−1.10080
$905$	−5.66844e18	−0.342964
$906$	−1.00973e19	−0.606558
$907$	−8.20749e18	−0.489512	−0.244756	−	0.969585i	$-0.578708\pi$
$907$	−8.20749e18	−0.489512	−0.244756	+	0.969585i	$0.578708\pi$
$908$	−6.46418e18	−0.382785
$909$	−1.30569e18	−0.0767673
$910$	−1.90238e19	−1.11053
$911$	−5.42210e18	−0.314266	−0.157133	−	0.987577i	$-0.550225\pi$
$911$	−5.42210e18	−0.314266	−0.157133	+	0.987577i	$0.550225\pi$
$912$	1.34635e18	0.0774801
$913$	6.02630e18	0.344343
$914$	−1.47285e17	−0.00835619
$915$	−3.20435e17	−0.0180511
$916$	2.72688e18	0.152527
$917$	−1.70269e19	−0.945658
$918$	−3.35371e16	−0.00184947
$919$	1.51477e18	0.0829463	0.0414732	−	0.999140i	$-0.486795\pi$
$919$	1.51477e18	0.0829463	0.0414732	+	0.999140i	$0.486795\pi$
$920$	−1.41327e19	−0.768428
$921$	4.70360e18	0.253947
$922$	1.08142e19	0.579755
$923$	−3.67705e18	−0.195744
$924$	4.98842e18	0.263691
$925$	1.79229e18	0.0940779
$926$	9.32338e18	0.485962
$927$	−1.24848e19	−0.646196
$928$	−8.52805e18	−0.438317
$929$	−3.28197e19	−1.67507	−0.837535	−	0.546384i	$-0.816004\pi$
$929$	−3.28197e19	−1.67507	−0.837535	+	0.546384i	$0.816004\pi$
$930$	−3.44135e17	−0.0174418
$931$	1.72423e19	0.867804
$932$	−4.64527e18	−0.232171
$933$	1.60688e19	0.797539
$934$	−1.40341e19	−0.691719
$935$	−1.16462e17	−0.00570046
$936$	1.16254e19	0.565087
$937$	−1.28498e19	−0.620283	−0.310141	−	0.950690i	$-0.600376\pi$
$937$	−1.28498e19	−0.620283	−0.310141	+	0.950690i	$0.600376\pi$
$938$	−3.02830e19	−1.45171
$939$	−1.04564e19	−0.497801
$940$	7.68223e18	0.363209
$941$	−2.54541e19	−1.19516	−0.597579	−	0.801810i	$-0.703871\pi$
$941$	−2.54541e19	−1.19516	−0.597579	+	0.801810i	$0.703871\pi$
$942$	9.86187e18	0.459863
$943$	−3.38445e19	−1.56734
$944$	−4.90933e17	−0.0225790
$945$	−4.24379e18	−0.193842
$946$	2.09442e18	0.0950104
$947$	2.44252e19	1.10043	0.550216	−	0.835022i	$-0.314545\pi$
$947$	2.44252e19	1.10043	0.550216	+	0.835022i	$0.314545\pi$
$948$	2.29302e18	0.102602
$949$	3.75989e19	1.67088
$950$	6.22076e18	0.274562
$951$	1.43526e19	0.629156
$952$	4.94344e17	0.0215223
$953$	1.94706e19	0.841928	0.420964	−	0.907077i	$-0.361692\pi$
$953$	1.94706e19	0.841928	0.420964	+	0.907077i	$0.361692\pi$
$954$	3.35598e18	0.144130
$955$	−2.35987e19	−1.00662
$956$	−1.19694e19	−0.507103
$957$	3.78153e18	0.159126
$958$	−2.84870e19	−1.19061
$959$	−3.92244e18	−0.162830
$960$	7.78748e18	0.321095
$961$	−2.43168e19	−0.995873
$962$	4.88680e18	0.198787
$963$	1.05909e19	0.427919
$964$	−2.10255e19	−0.843810
$965$	−8.16070e18	−0.325312
$966$	−1.53487e19	−0.607744
$967$	4.18845e19	1.64733	0.823666	−	0.567076i	$-0.191925\pi$
$967$	4.18845e19	1.64733	0.823666	+	0.567076i	$0.191925\pi$
$968$	−1.76576e19	−0.689831
$969$	1.62695e17	0.00631350
$970$	−7.71232e18	−0.297282
$971$	3.16904e18	0.121340	0.0606699	−	0.998158i	$-0.480676\pi$
$971$	3.16904e18	0.121340	0.0606699	+	0.998158i	$0.480676\pi$
$972$	9.06711e17	0.0344856
$973$	3.99024e19	1.50753
$974$	−1.94101e19	−0.728440
$975$	1.31024e19	0.488450
$976$	2.11744e17	0.00784129
$977$	3.87547e19	1.42564	0.712819	−	0.701348i	$-0.247418\pi$
$977$	3.87547e19	1.42564	0.712819	+	0.701348i	$0.247418\pi$
$978$	8.76847e18	0.320421
$979$	−1.38721e19	−0.503565
$980$	1.15616e19	0.416917
$981$	−1.37503e18	−0.0492567
$982$	4.68756e18	0.166810
$983$	−3.73311e19	−1.31969	−0.659847	−	0.751400i	$-0.729379\pi$
$983$	−3.73311e19	−1.31969	−0.659847	+	0.751400i	$0.729379\pi$
$984$	2.53505e19	0.890263
$985$	5.30787e18	0.185176
$986$	1.31020e17	0.00454086
$987$	2.38633e19	0.821617
$988$	−1.97179e19	−0.674437
$989$	7.49161e18	0.254565
$990$	−2.70849e18	−0.0914319
$991$	−2.54439e18	−0.0853307	−0.0426653	−	0.999089i	$-0.513585\pi$
$991$	−2.54439e18	−0.0853307	−0.0426653	+	0.999089i	$0.513585\pi$
$992$	−1.78867e18	−0.0595943
$993$	−2.28102e19	−0.755022
$994$	−3.63632e18	−0.119578
$995$	−3.05022e18	−0.0996508
$996$	−5.64501e18	−0.183222
$997$	1.81254e19	0.584478	0.292239	−	0.956345i	$-0.405600\pi$
$997$	1.81254e19	0.584478	0.292239	+	0.956345i	$0.405600\pi$
$998$	−1.27923e19	−0.409828
$999$	1.09014e18	0.0346981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.d.1.11	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.d.1.11	✓	32	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-61.5481 q^{2} -729.000 q^{3} -4403.84 q^{4} -24160.8 q^{5} +44868.5 q^{6} -453377. q^{7} +775249. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-61.5481 q^{2} -729.000 q^{3} -4403.84 q^{4} -24160.8 q^{5} +44868.5 q^{6} -453377. q^{7} +775249. q^{8} +531441. q^{9} +1.48705e6 q^{10} -3.42724e6 q^{11} +3.21040e6 q^{12} +2.82171e7 q^{13} +2.79045e7 q^{14} +1.76132e7 q^{15} -1.16389e7 q^{16} -1.40646e6 q^{17} -3.27092e7 q^{18} +1.58679e8 q^{19} +1.06400e8 q^{20} +3.30512e8 q^{21} +2.10940e8 q^{22} +7.54520e8 q^{23} -5.65157e8 q^{24} -6.36957e8 q^{25} -1.73671e9 q^{26} -3.87420e8 q^{27} +1.99660e9 q^{28} +1.51354e9 q^{29} -1.08406e9 q^{30} +3.17450e8 q^{31} -5.63449e9 q^{32} +2.49846e9 q^{33} +8.65651e7 q^{34} +1.09540e10 q^{35} -2.34038e9 q^{36} -2.81383e9 q^{37} -9.76636e9 q^{38} -2.05702e10 q^{39} -1.87307e10 q^{40} -4.48557e10 q^{41} -2.03424e10 q^{42} +9.92897e9 q^{43} +1.50930e10 q^{44} -1.28401e10 q^{45} -4.64393e10 q^{46} +7.22011e10 q^{47} +8.48473e9 q^{48} +1.08662e11 q^{49} +3.92035e10 q^{50} +1.02531e9 q^{51} -1.24263e11 q^{52} -1.02601e11 q^{53} +2.38450e10 q^{54} +8.28051e10 q^{55} -3.51480e11 q^{56} -1.15677e11 q^{57} -9.31557e10 q^{58} +4.21805e10 q^{59} -7.75659e10 q^{60} -1.81929e10 q^{61} -1.95384e10 q^{62} -2.40943e11 q^{63} +4.42138e11 q^{64} -6.81748e11 q^{65} -1.53775e11 q^{66} -1.08524e12 q^{67} +6.19384e9 q^{68} -5.50045e11 q^{69} -6.74195e11 q^{70} -1.30313e11 q^{71} +4.11999e11 q^{72} +1.33249e12 q^{73} +1.73186e11 q^{74} +4.64342e11 q^{75} -6.98795e11 q^{76} +1.55383e12 q^{77} +1.26606e12 q^{78} +7.14250e11 q^{79} +2.81205e11 q^{80} +2.82430e11 q^{81} +2.76078e12 q^{82} -1.75835e12 q^{83} -1.45552e12 q^{84} +3.39813e10 q^{85} -6.11109e11 q^{86} -1.10337e12 q^{87} -2.65697e12 q^{88} +4.04760e12 q^{89} +7.90281e11 q^{90} -1.27930e13 q^{91} -3.32278e12 q^{92} -2.31421e11 q^{93} -4.44384e12 q^{94} -3.83381e12 q^{95} +4.10755e12 q^{96} -5.18632e12 q^{97} -6.68791e12 q^{98} -1.82138e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9} + 6145337 q^{10} + 400846 q^{11} - 101457846 q^{12} + 9411686 q^{13} - 36368387 q^{14} - 1630044 q^{15} + 734877786 q^{16} + 228113833 q^{17} + 6377292 q^{18} + 524233755 q^{19} - 420745331 q^{20} - 544450005 q^{21} - 1844479318 q^{22} - 399937087 q^{23} + 534588093 q^{24} + 8617402914 q^{25} - 499433574 q^{26} - 12397455648 q^{27} + 12648993070 q^{28} - 225284149 q^{29} - 4479950673 q^{30} + 9454638761 q^{31} + 11648295118 q^{32} - 292216734 q^{33} + 39279537096 q^{34} + 17608963479 q^{35} + 73962769734 q^{36} + 37463929597 q^{37} + 65554547351 q^{38} - 6861119094 q^{39} + 144414252742 q^{40} + 22650227173 q^{41} + 26512554123 q^{42} + 96253617602 q^{43} - 132186868002 q^{44} + 1188302076 q^{45} + 327853892309 q^{46} + 239981844027 q^{47} - 535725905994 q^{48} + 286262776863 q^{49} - 671840368399 q^{50} - 166294984257 q^{51} - 952971648498 q^{52} - 47446514136 q^{53} - 4649045868 q^{54} - 474454082548 q^{55} - 1167728875984 q^{56} - 382166407395 q^{57} + 547596592762 q^{58} + 1349777076512 q^{59} + 306723346299 q^{60} + 661498471821 q^{61} + 555821093242 q^{62} + 396904053645 q^{63} + 3522679273173 q^{64} + 1269187682756 q^{65} + 1344625422822 q^{66} + 2838711491386 q^{67} + 1395029358261 q^{68} + 291554136423 q^{69} + 5677102514386 q^{70} + 1912914480734 q^{71} - 389714719797 q^{72} + 2403595726697 q^{73} - 742136417562 q^{74} - 6282086724306 q^{75} - 4020161987188 q^{76} - 4878303804101 q^{77} + 364087075446 q^{78} - 1705546365970 q^{79} - 4347383766449 q^{80} + 9037745167392 q^{81} - 6943720239935 q^{82} - 2549647313691 q^{83} - 9221115948030 q^{84} - 8455706309615 q^{85} - 33993832711012 q^{86} + 164232144621 q^{87} - 42970239360587 q^{88} - 17356719361241 q^{89} + 3265884040617 q^{90} - 30776775043291 q^{91} - 13184590997480 q^{92} - 6892431656769 q^{93} - 35604563339520 q^{94} + 219501126195 q^{95} - 8491607141022 q^{96} - 4427131429152 q^{97} - 32707332037060 q^{98} + 213025999086 q^{99}+O(q^{100}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9 + 6145337 * q^10 + 400846 * q^11 - 101457846 * q^12 + 9411686 * q^13 - 36368387 * q^14 - 1630044 * q^15 + 734877786 * q^16 + 228113833 * q^17 + 6377292 * q^18 + 524233755 * q^19 - 420745331 * q^20 - 544450005 * q^21 - 1844479318 * q^22 - 399937087 * q^23 + 534588093 * q^24 + 8617402914 * q^25 - 499433574 * q^26 - 12397455648 * q^27 + 12648993070 * q^28 - 225284149 * q^29 - 4479950673 * q^30 + 9454638761 * q^31 + 11648295118 * q^32 - 292216734 * q^33 + 39279537096 * q^34 + 17608963479 * q^35 + 73962769734 * q^36 + 37463929597 * q^37 + 65554547351 * q^38 - 6861119094 * q^39 + 144414252742 * q^40 + 22650227173 * q^41 + 26512554123 * q^42 + 96253617602 * q^43 - 132186868002 * q^44 + 1188302076 * q^45 + 327853892309 * q^46 + 239981844027 * q^47 - 535725905994 * q^48 + 286262776863 * q^49 - 671840368399 * q^50 - 166294984257 * q^51 - 952971648498 * q^52 - 47446514136 * q^53 - 4649045868 * q^54 - 474454082548 * q^55 - 1167728875984 * q^56 - 382166407395 * q^57 + 547596592762 * q^58 + 1349777076512 * q^59 + 306723346299 * q^60 + 661498471821 * q^61 + 555821093242 * q^62 + 396904053645 * q^63 + 3522679273173 * q^64 + 1269187682756 * q^65 + 1344625422822 * q^66 + 2838711491386 * q^67 + 1395029358261 * q^68 + 291554136423 * q^69 + 5677102514386 * q^70 + 1912914480734 * q^71 - 389714719797 * q^72 + 2403595726697 * q^73 - 742136417562 * q^74 - 6282086724306 * q^75 - 4020161987188 * q^76 - 4878303804101 * q^77 + 364087075446 * q^78 - 1705546365970 * q^79 - 4347383766449 * q^80 + 9037745167392 * q^81 - 6943720239935 * q^82 - 2549647313691 * q^83 - 9221115948030 * q^84 - 8455706309615 * q^85 - 33993832711012 * q^86 + 164232144621 * q^87 - 42970239360587 * q^88 - 17356719361241 * q^89 + 3265884040617 * q^90 - 30776775043291 * q^91 - 13184590997480 * q^92 - 6892431656769 * q^93 - 35604563339520 * q^94 + 219501126195 * q^95 - 8491607141022 * q^96 - 4427131429152 * q^97 - 32707332037060 * q^98 + 213025999086 * q^99

Introduction

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