LMFDB - Embedded newform 177.14.a.d.1.1

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			1.1
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)

$f(q)$	$=$	$q-173.834 q^{2} -729.000 q^{3} +22026.2 q^{4} +30477.2 q^{5} +126725. q^{6} +24653.9 q^{7} -2.40484e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q-173.834 q^{2} -729.000 q^{3} +22026.2 q^{4} +30477.2 q^{5} +126725. q^{6} +24653.9 q^{7} -2.40484e6 q^{8} +531441. q^{9} -5.29796e6 q^{10} +1.05253e7 q^{11} -1.60571e7 q^{12} +946211. q^{13} -4.28568e6 q^{14} -2.22179e7 q^{15} +2.37605e8 q^{16} +5.94481e6 q^{17} -9.23824e7 q^{18} -3.42762e8 q^{19} +6.71295e8 q^{20} -1.79727e7 q^{21} -1.82965e9 q^{22} -9.47657e8 q^{23} +1.75313e9 q^{24} -2.91844e8 q^{25} -1.64483e8 q^{26} -3.87420e8 q^{27} +5.43031e8 q^{28} -5.66692e9 q^{29} +3.86222e9 q^{30} -1.24604e9 q^{31} -2.16032e10 q^{32} -7.67294e9 q^{33} -1.03341e9 q^{34} +7.51382e8 q^{35} +1.17056e10 q^{36} +2.29670e10 q^{37} +5.95836e10 q^{38} -6.89788e8 q^{39} -7.32929e10 q^{40} +3.02035e8 q^{41} +3.12426e9 q^{42} -9.98790e9 q^{43} +2.31832e11 q^{44} +1.61968e10 q^{45} +1.64735e11 q^{46} +6.43741e10 q^{47} -1.73214e11 q^{48} -9.62812e10 q^{49} +5.07323e10 q^{50} -4.33376e9 q^{51} +2.08414e10 q^{52} -2.60770e9 q^{53} +6.73467e10 q^{54} +3.20782e11 q^{55} -5.92888e10 q^{56} +2.49874e11 q^{57} +9.85101e11 q^{58} +4.21805e10 q^{59} -4.89374e11 q^{60} +1.85782e11 q^{61} +2.16603e11 q^{62} +1.31021e10 q^{63} +1.80891e12 q^{64} +2.88379e10 q^{65} +1.33382e12 q^{66} +1.49401e11 q^{67} +1.30941e11 q^{68} +6.90842e11 q^{69} -1.30616e11 q^{70} -9.18525e11 q^{71} -1.27803e12 q^{72} +7.21425e11 q^{73} -3.99244e12 q^{74} +2.12754e11 q^{75} -7.54973e12 q^{76} +2.59490e11 q^{77} +1.19908e11 q^{78} +5.05508e11 q^{79} +7.24152e12 q^{80} +2.82430e11 q^{81} -5.25038e10 q^{82} +5.73285e10 q^{83} -3.95870e11 q^{84} +1.81181e11 q^{85} +1.73623e12 q^{86} +4.13118e12 q^{87} -2.53117e13 q^{88} -2.89609e12 q^{89} -2.81556e12 q^{90} +2.33278e10 q^{91} -2.08733e13 q^{92} +9.08360e11 q^{93} -1.11904e13 q^{94} -1.04464e13 q^{95} +1.57487e13 q^{96} +1.07213e13 q^{97} +1.67369e13 q^{98} +5.59358e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−173.834	−1.92061	−0.960305	−	0.278953i	$-0.910013\pi$
$2$	−173.834	−1.92061	−0.960305	+	0.278953i	$0.910013\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	22026.2	2.68874
$5$	30477.2	0.872308	0.436154	−	0.899872i	$-0.356340\pi$
$5$	30477.2	0.872308	0.436154	+	0.899872i	$0.356340\pi$
$6$	126725.	1.10886
$7$	24653.9	0.0792043	0.0396022	−	0.999216i	$-0.487391\pi$
$7$	24653.9	0.0792043	0.0396022	+	0.999216i	$0.487391\pi$
$8$	−2.40484e6	−3.24341
$9$	531441.	0.333333
$10$	−5.29796e6	−1.67536
$11$	1.05253e7	1.79136	0.895678	−	0.444703i	$-0.146691\pi$
$11$	1.05253e7	1.79136	0.895678	+	0.444703i	$0.146691\pi$
$12$	−1.60571e7	−1.55234
$13$	946211.	0.0543696	0.0271848	−	0.999630i	$-0.491346\pi$
$13$	946211.	0.0543696	0.0271848	+	0.999630i	$0.491346\pi$
$14$	−4.28568e6	−0.152121
$15$	−2.22179e7	−0.503627
$16$	2.37605e8	3.54058
$17$	5.94481e6	0.0597337	0.0298669	−	0.999554i	$-0.490492\pi$
$17$	5.94481e6	0.0597337	0.0298669	+	0.999554i	$0.490492\pi$
$18$	−9.23824e7	−0.640203
$19$	−3.42762e8	−1.67145	−0.835727	−	0.549146i	$-0.814953\pi$
$19$	−3.42762e8	−1.67145	−0.835727	+	0.549146i	$0.814953\pi$
$20$	6.71295e8	2.34541
$21$	−1.79727e7	−0.0457286
$22$	−1.82965e9	−3.44050
$23$	−9.47657e8	−1.33481	−0.667406	−	0.744694i	$-0.732596\pi$
$23$	−9.47657e8	−1.33481	−0.667406	+	0.744694i	$0.732596\pi$
$24$	1.75313e9	1.87258
$25$	−2.91844e8	−0.239078
$26$	−1.64483e8	−0.104423
$27$	−3.87420e8	−0.192450
$28$	5.43031e8	0.212960
$29$	−5.66692e9	−1.76913	−0.884565	−	0.466416i	$-0.845545\pi$
$29$	−5.66692e9	−1.76913	−0.884565	+	0.466416i	$0.845545\pi$
$30$	3.86222e9	0.967271
$31$	−1.24604e9	−0.252162	−0.126081	−	0.992020i	$-0.540240\pi$
$31$	−1.24604e9	−0.252162	−0.126081	+	0.992020i	$0.540240\pi$
$32$	−2.16032e10	−3.55667
$33$	−7.67294e9	−1.03424
$34$	−1.03341e9	−0.114725
$35$	7.51382e8	0.0690906
$36$	1.17056e10	0.896247
$37$	2.29670e10	1.47161	0.735805	−	0.677193i	$-0.236804\pi$
$37$	2.29670e10	1.47161	0.735805	+	0.677193i	$0.236804\pi$
$38$	5.95836e10	3.21021
$39$	−6.89788e8	−0.0313903
$40$	−7.32929e10	−2.82925
$41$	3.02035e8	0.00993028	0.00496514	−	0.999988i	$-0.498420\pi$
$41$	3.02035e8	0.00993028	0.00496514	+	0.999988i	$0.498420\pi$
$42$	3.12426e9	0.0878268
$43$	−9.98790e9	−0.240951	−0.120476	−	0.992716i	$-0.538442\pi$
$43$	−9.98790e9	−0.240951	−0.120476	+	0.992716i	$0.538442\pi$
$44$	2.31832e11	4.81649
$45$	1.61968e10	0.290769
$46$	1.64735e11	2.56365
$47$	6.43741e10	0.871114	0.435557	−	0.900161i	$-0.356551\pi$
$47$	6.43741e10	0.871114	0.435557	+	0.900161i	$0.356551\pi$
$48$	−1.73214e11	−2.04416
$49$	−9.62812e10	−0.993727
$50$	5.07323e10	0.459176
$51$	−4.33376e9	−0.0344873
$52$	2.08414e10	0.146186
$53$	−2.60770e9	−0.0161609	−0.00808043	−	0.999967i	$-0.502572\pi$
$53$	−2.60770e9	−0.0161609	−0.00808043	+	0.999967i	$0.502572\pi$
$54$	6.73467e10	0.369621
$55$	3.20782e11	1.56261
$56$	−5.92888e10	−0.256892
$57$	2.49874e11	0.965014
$58$	9.85101e11	3.39781
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−4.89374e11	−1.35412
$61$	1.85782e11	0.461699	0.230850	−	0.972989i	$-0.425849\pi$
$61$	1.85782e11	0.461699	0.230850	+	0.972989i	$0.425849\pi$
$62$	2.16603e11	0.484305
$63$	1.31021e10	0.0264014
$64$	1.80891e12	3.29038
$65$	2.88379e10	0.0474271
$66$	1.33382e12	1.98637
$67$	1.49401e11	0.201775	0.100887	−	0.994898i	$-0.467832\pi$
$67$	1.49401e11	0.201775	0.100887	+	0.994898i	$0.467832\pi$
$68$	1.30941e11	0.160608
$69$	6.90842e11	0.770655
$70$	−1.30616e11	−0.132696
$71$	−9.18525e11	−0.850965	−0.425482	−	0.904967i	$-0.639896\pi$
$71$	−9.18525e11	−0.850965	−0.425482	+	0.904967i	$0.639896\pi$
$72$	−1.27803e12	−1.08114
$73$	7.21425e11	0.557946	0.278973	−	0.960299i	$-0.410006\pi$
$73$	7.21425e11	0.557946	0.278973	+	0.960299i	$0.410006\pi$
$74$	−3.99244e12	−2.82639
$75$	2.12754e11	0.138032
$76$	−7.54973e12	−4.49410
$77$	2.59490e11	0.141883
$78$	1.19908e11	0.0602885
$79$	5.05508e11	0.233966	0.116983	−	0.993134i	$-0.462678\pi$
$79$	5.05508e11	0.233966	0.116983	+	0.993134i	$0.462678\pi$
$80$	7.24152e12	3.08848
$81$	2.82430e11	0.111111
$82$	−5.25038e10	−0.0190722
$83$	5.73285e10	0.0192470	0.00962350	−	0.999954i	$-0.496937\pi$
$83$	5.73285e10	0.0192470	0.00962350	+	0.999954i	$0.496937\pi$
$84$	−3.95870e11	−0.122952
$85$	1.81181e11	0.0521062
$86$	1.73623e12	0.462773
$87$	4.13118e12	1.02141
$88$	−2.53117e13	−5.81010
$89$	−2.89609e12	−0.617700	−0.308850	−	0.951111i	$-0.599944\pi$
$89$	−2.89609e12	−0.617700	−0.308850	+	0.951111i	$0.599944\pi$
$90$	−2.81556e12	−0.558454
$91$	2.33278e10	0.00430631
$92$	−2.08733e13	−3.58897
$93$	9.08360e11	0.145586
$94$	−1.11904e13	−1.67307
$95$	−1.04464e13	−1.45802
$96$	1.57487e13	2.05344
$97$	1.07213e13	1.30687	0.653435	−	0.756983i	$-0.273327\pi$
$97$	1.07213e13	1.30687	0.653435	+	0.756983i	$0.273327\pi$
$98$	1.67369e13	1.90856
$99$	5.59358e12	0.597119
$100$	−6.42820e12	−0.642820
$101$	−1.26570e13	−1.18643	−0.593213	−	0.805046i	$-0.702141\pi$
$101$	−1.26570e13	−1.18643	−0.593213	+	0.805046i	$0.702141\pi$
$102$	7.53354e11	0.0662366
$103$	1.29943e13	1.07229	0.536143	−	0.844127i	$-0.319881\pi$
$103$	1.29943e13	1.07229	0.536143	+	0.844127i	$0.319881\pi$
$104$	−2.27549e12	−0.176343
$105$	−5.47758e11	−0.0398895
$106$	4.53306e11	0.0310387
$107$	2.35144e13	1.51474	0.757372	−	0.652984i	$-0.226483\pi$
$107$	2.35144e13	1.51474	0.757372	+	0.652984i	$0.226483\pi$
$108$	−8.53339e12	−0.517448
$109$	3.22747e13	1.84327	0.921636	−	0.388056i	$-0.126853\pi$
$109$	3.22747e13	1.84327	0.921636	+	0.388056i	$0.126853\pi$
$110$	−5.57627e13	−3.00117
$111$	−1.67429e13	−0.849635
$112$	5.85788e12	0.280429
$113$	6.26172e12	0.282933	0.141467	−	0.989943i	$-0.454818\pi$
$113$	6.26172e12	0.282933	0.141467	+	0.989943i	$0.454818\pi$
$114$	−4.34364e13	−1.85342
$115$	−2.88819e13	−1.16437
$116$	−1.24820e14	−4.75673
$117$	5.02855e11	0.0181232
$118$	−7.33240e12	−0.250042
$119$	1.46563e11	0.00473117
$120$	5.34305e13	1.63347
$121$	7.62592e13	2.20896
$122$	−3.22951e13	−0.886744
$123$	−2.20183e11	−0.00573325
$124$	−2.74454e13	−0.677998
$125$	−4.60982e13	−1.08086
$126$	−2.27759e12	−0.0507068
$127$	4.33508e13	0.916796	0.458398	−	0.888747i	$-0.348423\pi$
$127$	4.33508e13	0.916796	0.458398	+	0.888747i	$0.348423\pi$
$128$	−1.37476e14	−2.76288
$129$	7.28118e12	0.139113
$130$	−5.01299e12	−0.0910889
$131$	−2.06963e13	−0.357791	−0.178895	−	0.983868i	$-0.557252\pi$
$131$	−2.06963e13	−0.357791	−0.178895	+	0.983868i	$0.557252\pi$
$132$	−1.69005e14	−2.78080
$133$	−8.45043e12	−0.132386
$134$	−2.59709e13	−0.387530
$135$	−1.18075e13	−0.167876
$136$	−1.42963e13	−0.193741
$137$	−8.66036e13	−1.11906	−0.559528	−	0.828811i	$-0.689018\pi$
$137$	−8.66036e13	−1.11906	−0.559528	+	0.828811i	$0.689018\pi$
$138$	−1.20092e14	−1.48013
$139$	−6.02807e13	−0.708896	−0.354448	−	0.935076i	$-0.615331\pi$
$139$	−6.02807e13	−0.708896	−0.354448	+	0.935076i	$0.615331\pi$
$140$	1.65501e13	0.185767
$141$	−4.69287e13	−0.502938
$142$	1.59671e14	1.63437
$143$	9.95916e12	0.0973954
$144$	1.26273e14	1.18019
$145$	−1.72712e14	−1.54323
$146$	−1.25408e14	−1.07160
$147$	7.01890e13	0.573728
$148$	5.05875e14	3.95678
$149$	−1.16071e14	−0.868983	−0.434492	−	0.900676i	$-0.643072\pi$
$149$	−1.16071e14	−0.868983	−0.434492	+	0.900676i	$0.643072\pi$
$150$	−3.69838e13	−0.265106
$151$	7.55362e13	0.518567	0.259283	−	0.965801i	$-0.416514\pi$
$151$	7.55362e13	0.518567	0.259283	+	0.965801i	$0.416514\pi$
$152$	8.24289e14	5.42121
$153$	3.15931e12	0.0199112
$154$	−4.51081e13	−0.272502
$155$	−3.79757e13	−0.219963
$156$	−1.51934e13	−0.0844004
$157$	−2.46146e13	−0.131173	−0.0655865	−	0.997847i	$-0.520892\pi$
$157$	−2.46146e13	−0.131173	−0.0655865	+	0.997847i	$0.520892\pi$
$158$	−8.78744e13	−0.449357
$159$	1.90101e12	0.00933048
$160$	−6.58405e14	−3.10251
$161$	−2.33635e13	−0.105723
$162$	−4.90958e13	−0.213401
$163$	−5.41784e13	−0.226259	−0.113130	−	0.993580i	$-0.536088\pi$
$163$	−5.41784e13	−0.226259	−0.113130	+	0.993580i	$0.536088\pi$
$164$	6.65266e12	0.0266999
$165$	−2.33850e14	−0.902176
$166$	−9.96563e12	−0.0369660
$167$	2.89734e14	1.03358	0.516789	−	0.856113i	$-0.327127\pi$
$167$	2.89734e14	1.03358	0.516789	+	0.856113i	$0.327127\pi$
$168$	4.32215e13	0.148317
$169$	−3.01980e14	−0.997044
$170$	−3.14954e13	−0.100076
$171$	−1.82158e14	−0.557151
$172$	−2.19995e14	−0.647855
$173$	6.27616e14	1.77990	0.889948	−	0.456062i	$-0.150740\pi$
$173$	6.27616e14	1.77990	0.889948	+	0.456062i	$0.150740\pi$
$174$	−7.18139e14	−1.96173
$175$	−7.19510e12	−0.0189360
$176$	2.50086e15	6.34245
$177$	−3.07496e13	−0.0751646
$178$	5.03439e14	1.18636
$179$	−5.62501e14	−1.27814	−0.639070	−	0.769149i	$-0.720681\pi$
$179$	−5.62501e14	−1.27814	−0.639070	+	0.769149i	$0.720681\pi$
$180$	3.56754e14	0.781803
$181$	−6.01109e13	−0.127070	−0.0635349	−	0.997980i	$-0.520237\pi$
$181$	−6.01109e13	−0.127070	−0.0635349	+	0.997980i	$0.520237\pi$
$182$	−4.05516e12	−0.00827073
$183$	−1.35435e14	−0.266562
$184$	2.27897e15	4.32935
$185$	6.99969e14	1.28370
$186$	−1.57904e14	−0.279613
$187$	6.25709e13	0.107004
$188$	1.41791e15	2.34220
$189$	−9.55144e12	−0.0152429
$190$	1.81594e15	2.80029
$191$	−8.14509e14	−1.21389	−0.606945	−	0.794744i	$-0.707605\pi$
$191$	−8.14509e14	−1.21389	−0.606945	+	0.794744i	$0.707605\pi$
$192$	−1.31869e15	−1.89970
$193$	−5.24297e14	−0.730221	−0.365111	−	0.930964i	$-0.618969\pi$
$193$	−5.24297e14	−0.730221	−0.365111	+	0.930964i	$0.618969\pi$
$194$	−1.86373e15	−2.50999
$195$	−2.10228e13	−0.0273820
$196$	−2.12070e15	−2.67187
$197$	1.04281e14	0.127108	0.0635541	−	0.997978i	$-0.479756\pi$
$197$	1.04281e14	0.127108	0.0635541	+	0.997978i	$0.479756\pi$
$198$	−9.72352e14	−1.14683
$199$	1.69271e15	1.93214	0.966069	−	0.258285i	$-0.0831572\pi$
$199$	1.69271e15	1.93214	0.966069	+	0.258285i	$0.0831572\pi$
$200$	7.01839e14	0.775429
$201$	−1.08913e14	−0.116495
$202$	2.20021e15	2.27866
$203$	−1.39712e14	−0.140123
$204$	−9.54562e13	−0.0927274
$205$	9.20516e12	0.00866226
$206$	−2.25885e15	−2.05944
$207$	−5.03624e14	−0.444938
$208$	2.24824e14	0.192500
$209$	−3.60767e15	−2.99417
$210$	9.52188e13	0.0766121
$211$	1.85697e15	1.44867	0.724334	−	0.689449i	$-0.242147\pi$
$211$	1.85697e15	1.44867	0.724334	+	0.689449i	$0.242147\pi$
$212$	−5.74376e13	−0.0434524
$213$	6.69605e14	0.491305
$214$	−4.08760e15	−2.90923
$215$	−3.04403e14	−0.210184
$216$	9.31685e14	0.624195
$217$	−3.07197e13	−0.0199723
$218$	−5.61042e15	−3.54020
$219$	−5.25919e14	−0.322130
$220$	7.06559e15	4.20147
$221$	5.62504e12	0.00324770
$222$	2.91049e15	1.63182
$223$	−3.58230e15	−1.95066	−0.975328	−	0.220761i	$-0.929146\pi$
$223$	−3.58230e15	−1.95066	−0.975328	+	0.220761i	$0.929146\pi$
$224$	−5.32604e14	−0.281703
$225$	−1.55098e14	−0.0796928
$226$	−1.08850e15	−0.543404
$227$	2.84899e15	1.38205	0.691024	−	0.722831i	$-0.257160\pi$
$227$	2.84899e15	1.38205	0.691024	+	0.722831i	$0.257160\pi$
$228$	5.50375e15	2.59467
$229$	−2.46004e14	−0.112723	−0.0563614	−	0.998410i	$-0.517950\pi$
$229$	−2.46004e14	−0.112723	−0.0563614	+	0.998410i	$0.517950\pi$
$230$	5.02065e15	2.23630
$231$	−1.89168e14	−0.0819163
$232$	1.36280e16	5.73802
$233$	1.17127e15	0.479560	0.239780	−	0.970827i	$-0.422925\pi$
$233$	1.17127e15	0.479560	0.239780	+	0.970827i	$0.422925\pi$
$234$	−8.74132e13	−0.0348076
$235$	1.96194e15	0.759880
$236$	9.29075e14	0.350044
$237$	−3.68516e14	−0.135080
$238$	−2.54776e13	−0.00908673
$239$	2.24252e15	0.778305	0.389153	−	0.921173i	$-0.372768\pi$
$239$	2.24252e15	0.778305	0.389153	+	0.921173i	$0.372768\pi$
$240$	−5.27907e15	−1.78313
$241$	4.51372e15	1.48397	0.741983	−	0.670418i	$-0.233885\pi$
$241$	4.51372e15	1.48397	0.741983	+	0.670418i	$0.233885\pi$
$242$	−1.32564e16	−4.24254
$243$	−2.05891e14	−0.0641500
$244$	4.09206e15	1.24139
$245$	−2.93438e15	−0.866836
$246$	3.82753e13	0.0110113
$247$	−3.24325e14	−0.0908763
$248$	2.99652e15	0.817864
$249$	−4.17925e13	−0.0111123
$250$	8.01342e15	2.07591
$251$	6.87745e15	1.73599	0.867996	−	0.496570i	$-0.165408\pi$
$251$	6.87745e15	1.73599	0.867996	+	0.496570i	$0.165408\pi$
$252$	2.88589e14	0.0709866
$253$	−9.97438e15	−2.39113
$254$	−7.53582e15	−1.76081
$255$	−1.32081e14	−0.0300835
$256$	9.07935e15	2.01602
$257$	5.80381e15	1.25646	0.628228	−	0.778029i	$-0.283780\pi$
$257$	5.80381e15	1.25646	0.628228	+	0.778029i	$0.283780\pi$
$258$	−1.26571e15	−0.267182
$259$	5.66226e14	0.116558
$260$	6.35187e14	0.127519
$261$	−3.01163e15	−0.589710
$262$	3.59771e15	0.687176
$263$	5.63678e15	1.05031	0.525157	−	0.851005i	$-0.324007\pi$
$263$	5.63678e15	1.05031	0.525157	+	0.851005i	$0.324007\pi$
$264$	1.84522e16	3.35446
$265$	−7.94754e13	−0.0140973
$266$	1.46897e15	0.254262
$267$	2.11125e15	0.356629
$268$	3.29072e15	0.542519
$269$	−9.31921e15	−1.49965	−0.749824	−	0.661637i	$-0.769862\pi$
$269$	−9.31921e15	−1.49965	−0.749824	+	0.661637i	$0.769862\pi$
$270$	2.05254e15	0.322424
$271$	6.88183e15	1.05537	0.527684	−	0.849441i	$-0.323061\pi$
$271$	6.88183e15	1.05537	0.527684	+	0.849441i	$0.323061\pi$
$272$	1.41251e15	0.211492
$273$	−1.70060e13	−0.00248625
$274$	1.50546e16	2.14927
$275$	−3.07174e15	−0.428275
$276$	1.52166e16	2.07209
$277$	1.48317e16	1.97276	0.986378	−	0.164494i	$-0.0525992\pi$
$277$	1.48317e16	1.97276	0.986378	+	0.164494i	$0.0525992\pi$
$278$	1.04788e16	1.36151
$279$	−6.62194e14	−0.0840540
$280$	−1.80696e15	−0.224089
$281$	2.06282e15	0.249960	0.124980	−	0.992159i	$-0.460113\pi$
$281$	2.06282e15	0.249960	0.124980	+	0.992159i	$0.460113\pi$
$282$	8.15779e15	0.965947
$283$	3.37566e15	0.390613	0.195307	−	0.980742i	$-0.437430\pi$
$283$	3.37566e15	0.390613	0.195307	+	0.980742i	$0.437430\pi$
$284$	−2.02316e16	−2.28802
$285$	7.61544e15	0.841790
$286$	−1.73124e15	−0.187058
$287$	7.44634e12	0.000786521 0
$288$	−1.14808e16	−1.18556
$289$	−9.86924e15	−0.996432
$290$	3.00231e16	2.96394
$291$	−7.81585e15	−0.754522
$292$	1.58902e16	1.50017
$293$	5.84157e15	0.539374	0.269687	−	0.962948i	$-0.413080\pi$
$293$	5.84157e15	0.539374	0.269687	+	0.962948i	$0.413080\pi$
$294$	−1.22012e16	−1.10191
$295$	1.28554e15	0.113565
$296$	−5.52320e16	−4.77304
$297$	−4.07772e15	−0.344747
$298$	2.01770e16	1.66898
$299$	−8.96684e14	−0.0725733
$300$	4.68616e15	0.371132
$301$	−2.46241e14	−0.0190844
$302$	−1.31307e16	−0.995964
$303$	9.22692e15	0.684983
$304$	−8.14418e16	−5.91792
$305$	5.66211e15	0.402744
$306$	−5.49195e14	−0.0382417
$307$	−9.63570e15	−0.656877	−0.328438	−	0.944525i	$-0.606522\pi$
$307$	−9.63570e15	−0.656877	−0.328438	+	0.944525i	$0.606522\pi$
$308$	5.71557e15	0.381487
$309$	−9.47285e15	−0.619085
$310$	6.60145e15	0.422463
$311$	8.51498e14	0.0533631	0.0266815	−	0.999644i	$-0.491506\pi$
$311$	8.51498e14	0.0533631	0.0266815	+	0.999644i	$0.491506\pi$
$312$	1.65883e15	0.101812
$313$	1.25371e16	0.753630	0.376815	−	0.926289i	$-0.377019\pi$
$313$	1.25371e16	0.753630	0.376815	+	0.926289i	$0.377019\pi$
$314$	4.27884e15	0.251932
$315$	3.99315e14	0.0230302
$316$	1.11344e16	0.629073
$317$	−9.81211e15	−0.543097	−0.271548	−	0.962425i	$-0.587536\pi$
$317$	−9.81211e15	−0.543097	−0.271548	+	0.962425i	$0.587536\pi$
$318$	−3.30460e14	−0.0179202
$319$	−5.96460e16	−3.16914
$320$	5.51304e16	2.87023
$321$	−1.71420e16	−0.874538
$322$	4.06136e15	0.203052
$323$	−2.03765e15	−0.0998422
$324$	6.22084e15	0.298749
$325$	−2.76146e14	−0.0129986
$326$	9.41803e15	0.434556
$327$	−2.35282e16	−1.06421
$328$	−7.26346e14	−0.0322080
$329$	1.58707e15	0.0689960
$330$	4.06510e16	1.73273
$331$	1.65589e16	0.692069	0.346035	−	0.938222i	$-0.387528\pi$
$331$	1.65589e16	0.692069	0.346035	+	0.938222i	$0.387528\pi$
$332$	1.26273e15	0.0517502
$333$	1.22056e16	0.490537
$334$	−5.03656e16	−1.98510
$335$	4.55331e15	0.176010
$336$	−4.27040e15	−0.161906
$337$	3.95407e16	1.47045	0.735225	−	0.677824i	$-0.237077\pi$
$337$	3.95407e16	1.47045	0.735225	+	0.677824i	$0.237077\pi$
$338$	5.24943e16	1.91493
$339$	−4.56479e15	−0.163351
$340$	3.99072e15	0.140100
$341$	−1.31149e16	−0.451712
$342$	3.16652e16	1.07007
$343$	−4.76240e15	−0.157912
$344$	2.40193e16	0.781504
$345$	2.10549e16	0.672248
$346$	−1.09101e17	−3.41848
$347$	−1.77460e16	−0.545707	−0.272854	−	0.962056i	$-0.587967\pi$
$347$	−1.77460e16	−0.545707	−0.272854	+	0.962056i	$0.587967\pi$
$348$	9.09941e16	2.74630
$349$	2.08941e16	0.618954	0.309477	−	0.950907i	$-0.399846\pi$
$349$	2.08941e16	0.618954	0.309477	+	0.950907i	$0.399846\pi$
$350$	1.25075e15	0.0363687
$351$	−3.66582e14	−0.0104634
$352$	−2.27380e17	−6.37126
$353$	−8.53609e15	−0.234814	−0.117407	−	0.993084i	$-0.537458\pi$
$353$	−8.53609e15	−0.234814	−0.117407	+	0.993084i	$0.537458\pi$
$354$	5.34532e15	0.144362
$355$	−2.79941e16	−0.742304
$356$	−6.37898e16	−1.66084
$357$	−1.06844e14	−0.00273154
$358$	9.77816e16	2.45481
$359$	−7.68395e16	−1.89440	−0.947198	−	0.320649i	$-0.896099\pi$
$359$	−7.68395e16	−1.89440	−0.947198	+	0.320649i	$0.896099\pi$
$360$	−3.89508e16	−0.943084
$361$	7.54328e16	1.79376
$362$	1.04493e16	0.244052
$363$	−5.55930e16	−1.27534
$364$	5.13822e14	0.0115785
$365$	2.19870e16	0.486701
$366$	2.35432e16	0.511962
$367$	−7.01466e16	−1.49857	−0.749285	−	0.662248i	$-0.769603\pi$
$367$	−7.01466e16	−1.49857	−0.749285	+	0.662248i	$0.769603\pi$
$368$	−2.25168e17	−4.72602
$369$	1.60514e14	0.00331009
$370$	−1.21678e17	−2.46548
$371$	−6.42901e13	−0.00128001
$372$	2.00077e16	0.391442
$373$	1.35042e16	0.259634	0.129817	−	0.991538i	$-0.458561\pi$
$373$	1.35042e16	0.259634	0.129817	+	0.991538i	$0.458561\pi$
$374$	−1.08769e16	−0.205514
$375$	3.36056e16	0.624034
$376$	−1.54810e17	−2.82538
$377$	−5.36210e15	−0.0961870
$378$	1.66036e15	0.0292756
$379$	7.91477e16	1.37178	0.685888	−	0.727707i	$-0.259414\pi$
$379$	7.91477e16	1.37178	0.685888	+	0.727707i	$0.259414\pi$
$380$	−2.30095e17	−3.92024
$381$	−3.16027e16	−0.529312
$382$	1.41589e17	2.33141
$383$	−3.22851e16	−0.522649	−0.261325	−	0.965251i	$-0.584159\pi$
$383$	−3.22851e16	−0.522649	−0.261325	+	0.965251i	$0.584159\pi$
$384$	1.00220e17	1.59515
$385$	7.90852e15	0.123766
$386$	9.11404e16	1.40247
$387$	−5.30798e15	−0.0803171
$388$	2.36150e17	3.51383
$389$	3.38046e15	0.0494656	0.0247328	−	0.999694i	$-0.492126\pi$
$389$	3.38046e15	0.0494656	0.0247328	+	0.999694i	$0.492126\pi$
$390$	3.65447e15	0.0525902
$391$	−5.63364e15	−0.0797334
$392$	2.31541e17	3.22306
$393$	1.50876e16	0.206571
$394$	−1.81275e16	−0.244125
$395$	1.54065e16	0.204090
$396$	1.23205e17	1.60550
$397$	−4.34041e16	−0.556406	−0.278203	−	0.960522i	$-0.589739\pi$
$397$	−4.34041e16	−0.556406	−0.278203	+	0.960522i	$0.589739\pi$
$398$	−2.94250e17	−3.71088
$399$	6.16036e15	0.0764333
$400$	−6.93434e16	−0.846477
$401$	8.64452e16	1.03825	0.519126	−	0.854698i	$-0.326258\pi$
$401$	8.64452e16	1.03825	0.519126	+	0.854698i	$0.326258\pi$
$402$	1.89328e16	0.223741
$403$	−1.17901e15	−0.0137099
$404$	−2.78784e17	−3.18999
$405$	8.60766e15	0.0969231
$406$	2.42866e16	0.269121
$407$	2.41734e17	2.63618
$408$	1.04220e16	0.111856
$409$	5.10814e15	0.0539587	0.0269794	−	0.999636i	$-0.491411\pi$
$409$	5.10814e15	0.0539587	0.0269794	+	0.999636i	$0.491411\pi$
$410$	−1.60017e15	−0.0166368
$411$	6.31340e16	0.646088
$412$	2.86215e17	2.88310
$413$	1.03992e15	0.0103115
$414$	8.75468e16	0.854551
$415$	1.74721e15	0.0167893
$416$	−2.04412e16	−0.193375
$417$	4.39447e16	0.409281
$418$	6.27135e17	5.75063
$419$	−1.48508e17	−1.34078	−0.670391	−	0.742008i	$-0.733874\pi$
$419$	−1.48508e17	−1.34078	−0.670391	+	0.742008i	$0.733874\pi$
$420$	−1.20650e16	−0.107252
$421$	2.03771e17	1.78365	0.891823	−	0.452384i	$-0.149427\pi$
$421$	2.03771e17	1.78365	0.891823	+	0.452384i	$0.149427\pi$
$422$	−3.22804e17	−2.78233
$423$	3.42110e16	0.290371
$424$	6.27111e15	0.0524163
$425$	−1.73495e15	−0.0142810
$426$	−1.16400e17	−0.943605
$427$	4.58025e15	0.0365686
$428$	5.17932e17	4.07275
$429$	−7.26022e15	−0.0562312
$430$	5.29155e16	0.403681
$431$	−2.48357e15	−0.0186627	−0.00933134	−	0.999956i	$-0.502970\pi$
$431$	−2.48357e15	−0.0186627	−0.00933134	+	0.999956i	$0.502970\pi$
$432$	−9.20529e16	−0.681386
$433$	1.94498e17	1.41822	0.709112	−	0.705096i	$-0.249096\pi$
$433$	1.94498e17	1.41822	0.709112	+	0.705096i	$0.249096\pi$
$434$	5.34011e15	0.0383590
$435$	1.25907e17	0.890983
$436$	7.10887e17	4.95608
$437$	3.24821e17	2.23108
$438$	9.14224e16	0.618687
$439$	−3.21188e16	−0.214161	−0.107080	−	0.994250i	$-0.534150\pi$
$439$	−3.21188e16	−0.214161	−0.107080	+	0.994250i	$0.534150\pi$
$440$	−7.71429e17	−5.06820
$441$	−5.11678e16	−0.331242
$442$	−9.77822e14	−0.00623756
$443$	1.27869e17	0.803790	0.401895	−	0.915686i	$-0.368352\pi$
$443$	1.27869e17	0.803790	0.401895	+	0.915686i	$0.368352\pi$
$444$	−3.68783e17	−2.28445
$445$	−8.82648e16	−0.538825
$446$	6.22725e17	3.74645
$447$	8.46154e16	0.501708
$448$	4.45967e16	0.260613
$449$	−2.31342e17	−1.33246	−0.666228	−	0.745748i	$-0.732092\pi$
$449$	−2.31342e17	−1.33246	−0.666228	+	0.745748i	$0.732092\pi$
$450$	2.69612e16	0.153059
$451$	3.17900e15	0.0177887
$452$	1.37922e17	0.760733
$453$	−5.50659e16	−0.299395
$454$	−4.95251e17	−2.65438
$455$	7.10966e14	0.00375643
$456$	−6.00907e17	−3.12994
$457$	−6.45908e16	−0.331677	−0.165839	−	0.986153i	$-0.553033\pi$
$457$	−6.45908e16	−0.331677	−0.165839	+	0.986153i	$0.553033\pi$
$458$	4.27638e16	0.216496
$459$	−2.30314e15	−0.0114958
$460$	−6.36158e17	−3.13068
$461$	−2.44100e17	−1.18444	−0.592218	−	0.805778i	$-0.701748\pi$
$461$	−2.44100e17	−1.18444	−0.592218	+	0.805778i	$0.701748\pi$
$462$	3.28838e16	0.157329
$463$	−4.15528e17	−1.96031	−0.980153	−	0.198240i	$-0.936477\pi$
$463$	−4.15528e17	−1.96031	−0.980153	+	0.198240i	$0.936477\pi$
$464$	−1.34649e18	−6.26375
$465$	2.76843e16	0.126996
$466$	−2.03606e17	−0.921047
$467$	−1.19295e17	−0.532183	−0.266092	−	0.963948i	$-0.585732\pi$
$467$	−1.19295e17	−0.532183	−0.266092	+	0.963948i	$0.585732\pi$
$468$	1.10760e16	0.0487286
$469$	3.68331e15	0.0159814
$470$	−3.41052e17	−1.45943
$471$	1.79440e16	0.0757328
$472$	−1.01438e17	−0.422256
$473$	−1.05126e17	−0.431630
$474$	6.40604e16	0.259436
$475$	1.00033e17	0.399609
$476$	3.22822e15	0.0127209
$477$	−1.38584e15	−0.00538696
$478$	−3.89826e17	−1.49482
$479$	2.58750e17	0.978811	0.489406	−	0.872056i	$-0.337214\pi$
$479$	2.58750e17	0.978811	0.489406	+	0.872056i	$0.337214\pi$
$480$	4.79977e17	1.79123
$481$	2.17316e16	0.0800109
$482$	−7.84637e17	−2.85012
$483$	1.70320e16	0.0610392
$484$	1.67970e18	5.93931
$485$	3.26756e17	1.13999
$486$	3.57908e16	0.123207
$487$	−3.02414e17	−1.02722	−0.513610	−	0.858024i	$-0.671692\pi$
$487$	−3.02414e17	−1.02722	−0.513610	+	0.858024i	$0.671692\pi$
$488$	−4.46776e17	−1.49748
$489$	3.94960e16	0.130631
$490$	5.10094e17	1.66485
$491$	5.24893e17	1.69060	0.845301	−	0.534291i	$-0.179421\pi$
$491$	5.24893e17	1.69060	0.845301	+	0.534291i	$0.179421\pi$
$492$	−4.84979e15	−0.0154152
$493$	−3.36887e16	−0.105677
$494$	5.63787e16	0.174538
$495$	1.70476e17	0.520872
$496$	−2.96064e17	−0.892800
$497$	−2.26452e16	−0.0674001
$498$	7.26494e15	0.0213423
$499$	4.90043e17	1.42096	0.710478	−	0.703720i	$-0.248479\pi$
$499$	4.90043e17	1.42096	0.710478	+	0.703720i	$0.248479\pi$
$500$	−1.01537e18	−2.90615
$501$	−2.11216e17	−0.596736
$502$	−1.19553e18	−3.33416
$503$	−2.13455e16	−0.0587645	−0.0293822	−	0.999568i	$-0.509354\pi$
$503$	−2.13455e16	−0.0587645	−0.0293822	+	0.999568i	$0.509354\pi$
$504$	−3.15085e16	−0.0856307
$505$	−3.85749e17	−1.03493
$506$	1.73388e18	4.59242
$507$	2.20143e17	0.575644
$508$	9.54851e17	2.46503
$509$	−2.42564e17	−0.618246	−0.309123	−	0.951022i	$-0.600035\pi$
$509$	−2.42564e17	−0.618246	−0.309123	+	0.951022i	$0.600035\pi$
$510$	2.29601e16	0.0577787
$511$	1.77859e16	0.0441918
$512$	−4.52096e17	−1.10911
$513$	1.32793e17	0.321671
$514$	−1.00890e18	−2.41316
$515$	3.96030e17	0.935365
$516$	1.60376e17	0.374040
$517$	6.77557e17	1.56048
$518$	−9.84292e16	−0.223862
$519$	−4.57532e17	−1.02762
$520$	−6.93505e16	−0.153825
$521$	−1.83719e17	−0.402447	−0.201224	−	0.979545i	$-0.564492\pi$
$521$	−1.83719e17	−0.402447	−0.201224	+	0.979545i	$0.564492\pi$
$522$	5.23523e17	1.13260
$523$	5.03808e17	1.07648	0.538238	−	0.842793i	$-0.319090\pi$
$523$	5.03808e17	1.07648	0.538238	+	0.842793i	$0.319090\pi$
$524$	−4.55860e17	−0.962006
$525$	5.24522e15	0.0109327
$526$	−9.79863e17	−2.01724
$527$	−7.40744e15	−0.0150626
$528$	−1.82313e18	−3.66181
$529$	3.94018e17	0.781726
$530$	1.38155e16	0.0270753
$531$	2.24165e16	0.0433963
$532$	−1.86130e17	−0.355952
$533$	2.85788e14	0.000539906 0
$534$	−3.67007e17	−0.684946
$535$	7.16653e17	1.32132
$536$	−3.59285e17	−0.654438
$537$	4.10063e17	0.737934
$538$	1.61999e18	2.88024
$539$	−1.01339e18	−1.78012
$540$	−2.60074e17	−0.451374
$541$	6.53607e16	0.112082	0.0560408	−	0.998428i	$-0.482152\pi$
$541$	6.53607e16	0.112082	0.0560408	+	0.998428i	$0.482152\pi$
$542$	−1.19629e18	−2.02695
$543$	4.38209e16	0.0733638
$544$	−1.28427e17	−0.212453
$545$	9.83641e17	1.60790
$546$	2.95621e15	0.00477511
$547$	6.25361e17	0.998189	0.499095	−	0.866548i	$-0.333666\pi$
$547$	6.25361e17	0.998189	0.499095	+	0.866548i	$0.333666\pi$
$548$	−1.90754e18	−3.00885
$549$	9.87321e16	0.153900
$550$	5.33973e17	0.822548
$551$	1.94240e18	2.95702
$552$	−1.66137e18	−2.49955
$553$	1.24628e16	0.0185311
$554$	−2.57826e18	−3.78889
$555$	−5.10278e17	−0.741143
$556$	−1.32775e18	−1.90604
$557$	4.06837e17	0.577248	0.288624	−	0.957443i	$-0.406802\pi$
$557$	4.06837e17	0.577248	0.288624	+	0.957443i	$0.406802\pi$
$558$	1.15112e17	0.161435
$559$	−9.45066e15	−0.0131004
$560$	1.78532e17	0.244621
$561$	−4.56142e16	−0.0617790
$562$	−3.58588e17	−0.480076
$563$	−5.42658e17	−0.718161	−0.359081	−	0.933307i	$-0.616910\pi$
$563$	−5.42658e17	−0.718161	−0.359081	+	0.933307i	$0.616910\pi$
$564$	−1.03366e18	−1.35227
$565$	1.90840e17	0.246805
$566$	−5.86804e17	−0.750215
$567$	6.96300e15	0.00880048
$568$	2.20891e18	2.76003
$569$	9.00601e17	1.11251	0.556253	−	0.831013i	$-0.312238\pi$
$569$	9.00601e17	1.11251	0.556253	+	0.831013i	$0.312238\pi$
$570$	−1.32382e18	−1.61675
$571$	2.53848e17	0.306507	0.153253	−	0.988187i	$-0.451025\pi$
$571$	2.53848e17	0.306507	0.153253	+	0.988187i	$0.451025\pi$
$572$	2.19362e17	0.261871
$573$	5.93777e17	0.700839
$574$	−1.29442e15	−0.00151060
$575$	2.76568e17	0.319125
$576$	9.61328e17	1.09679
$577$	−2.05569e17	−0.231908	−0.115954	−	0.993255i	$-0.536992\pi$
$577$	−2.05569e17	−0.231908	−0.115954	+	0.993255i	$0.536992\pi$
$578$	1.71561e18	1.91376
$579$	3.82212e17	0.421593
$580$	−3.80418e18	−4.14934
$581$	1.41337e15	0.00152445
$582$	1.35866e18	1.44914
$583$	−2.74468e16	−0.0289499
$584$	−1.73491e18	−1.80965
$585$	1.53256e16	0.0158090
$586$	−1.01546e18	−1.03593
$587$	−4.84625e17	−0.488943	−0.244471	−	0.969657i	$-0.578614\pi$
$587$	−4.84625e17	−0.488943	−0.244471	+	0.969657i	$0.578614\pi$
$588$	1.54599e18	1.54261
$589$	4.27094e17	0.421477
$590$	−2.23471e17	−0.218114
$591$	−7.60207e16	−0.0733860
$592$	5.45706e18	5.21036
$593$	−6.57663e17	−0.621080	−0.310540	−	0.950560i	$-0.600510\pi$
$593$	−6.57663e17	−0.621080	−0.310540	+	0.950560i	$0.600510\pi$
$594$	7.08845e17	0.662124
$595$	4.46682e15	0.00412704
$596$	−2.55659e18	−2.33647
$597$	−1.23399e18	−1.11552
$598$	1.55874e17	0.139385
$599$	7.34111e16	0.0649363	0.0324681	−	0.999473i	$-0.489663\pi$
$599$	7.34111e16	0.0649363	0.0324681	+	0.999473i	$0.489663\pi$
$600$	−5.11640e17	−0.447694
$601$	−1.71404e18	−1.48367	−0.741834	−	0.670584i	$-0.766044\pi$
$601$	−1.71404e18	−1.48367	−0.741834	+	0.670584i	$0.766044\pi$
$602$	4.28050e16	0.0366536
$603$	7.93977e16	0.0672582
$604$	1.66377e18	1.39429
$605$	2.32417e18	1.92689
$606$	−1.60395e18	−1.31558
$607$	1.51454e18	1.22901	0.614504	−	0.788914i	$-0.289356\pi$
$607$	1.51454e18	1.22901	0.614504	+	0.788914i	$0.289356\pi$
$608$	7.40476e18	5.94480
$609$	1.01850e17	0.0808999
$610$	−9.84265e17	−0.773514
$611$	6.09115e16	0.0473621
$612$	6.95875e16	0.0535362
$613$	−9.30792e16	−0.0708532	−0.0354266	−	0.999372i	$-0.511279\pi$
$613$	−9.30792e16	−0.0708532	−0.0354266	+	0.999372i	$0.511279\pi$
$614$	1.67501e18	1.26160
$615$	−6.71056e15	−0.00500116
$616$	−6.24033e17	−0.460185
$617$	5.23051e17	0.381672	0.190836	−	0.981622i	$-0.438880\pi$
$617$	5.23051e17	0.381672	0.190836	+	0.981622i	$0.438880\pi$
$618$	1.64670e18	1.18902
$619$	−2.48437e18	−1.77512	−0.887560	−	0.460692i	$-0.847601\pi$
$619$	−2.48437e18	−1.77512	−0.887560	+	0.460692i	$0.847601\pi$
$620$	−8.36458e17	−0.591423
$621$	3.67142e17	0.256885
$622$	−1.48019e17	−0.102490
$623$	−7.14001e16	−0.0489245
$624$	−1.63897e17	−0.111140
$625$	−1.04869e18	−0.703763
$626$	−2.17937e18	−1.44743
$627$	2.62999e18	1.72868
$628$	−5.42165e17	−0.352690
$629$	1.36534e17	0.0879048
$630$	−6.94145e16	−0.0442320
$631$	1.60732e18	1.01371	0.506854	−	0.862032i	$-0.330808\pi$
$631$	1.60732e18	1.01371	0.506854	+	0.862032i	$0.330808\pi$
$632$	−1.21567e18	−0.758847
$633$	−1.35373e18	−0.836389
$634$	1.70568e18	1.04308
$635$	1.32121e18	0.799728
$636$	4.18720e16	0.0250872
$637$	−9.11023e16	−0.0540285
$638$	1.03685e19	6.08669
$639$	−4.88142e17	−0.283655
$640$	−4.18988e18	−2.41008
$641$	−7.23726e17	−0.412095	−0.206047	−	0.978542i	$-0.566060\pi$
$641$	−7.23726e17	−0.412095	−0.206047	+	0.978542i	$0.566060\pi$
$642$	2.97986e18	1.67965
$643$	−1.05151e18	−0.586734	−0.293367	−	0.956000i	$-0.594776\pi$
$643$	−1.05151e18	−0.586734	−0.293367	+	0.956000i	$0.594776\pi$
$644$	−5.14608e17	−0.284261
$645$	2.21910e17	0.121350
$646$	3.54213e17	0.191758
$647$	2.99435e18	1.60482	0.802408	−	0.596776i	$-0.203552\pi$
$647$	2.99435e18	1.60482	0.802408	+	0.596776i	$0.203552\pi$
$648$	−6.79199e17	−0.360379
$649$	4.43963e17	0.233215
$650$	4.80035e16	0.0249652
$651$	2.23946e16	0.0115310
$652$	−1.19334e18	−0.608353
$653$	−1.06505e18	−0.537568	−0.268784	−	0.963201i	$-0.586622\pi$
$653$	−1.06505e18	−0.537568	−0.268784	+	0.963201i	$0.586622\pi$
$654$	4.09000e18	2.04394
$655$	−6.30765e17	−0.312104
$656$	7.17648e16	0.0351590
$657$	3.83395e17	0.185982
$658$	−2.75887e17	−0.132514
$659$	2.72342e18	1.29527	0.647633	−	0.761952i	$-0.275759\pi$
$659$	2.72342e18	1.29527	0.647633	+	0.761952i	$0.275759\pi$
$660$	−5.15081e18	−2.42572
$661$	1.81863e17	0.0848075	0.0424038	−	0.999101i	$-0.486498\pi$
$661$	1.81863e17	0.0848075	0.0424038	+	0.999101i	$0.486498\pi$
$662$	−2.87850e18	−1.32919
$663$	−4.10066e15	−0.00187506
$664$	−1.37866e17	−0.0624259
$665$	−2.57545e17	−0.115482
$666$	−2.12174e18	−0.942130
$667$	5.37030e18	2.36146
$668$	6.38173e18	2.77902
$669$	2.61150e18	1.12621
$670$	−7.91520e17	−0.338046
$671$	1.95541e18	0.827068
$672$	3.88268e17	0.162641
$673$	−4.69279e17	−0.194686	−0.0973428	−	0.995251i	$-0.531034\pi$
$673$	−4.69279e17	−0.194686	−0.0973428	+	0.995251i	$0.531034\pi$
$674$	−6.87351e18	−2.82416
$675$	1.13066e17	0.0460107
$676$	−6.65145e18	−2.68079
$677$	−4.67360e18	−1.86563	−0.932814	−	0.360359i	$-0.882654\pi$
$677$	−4.67360e18	−1.86563	−0.932814	+	0.360359i	$0.882654\pi$
$678$	7.93515e17	0.313734
$679$	2.64323e17	0.103510
$680$	−4.35712e17	−0.169002
$681$	−2.07692e18	−0.797926
$682$	2.27981e18	0.867562
$683$	−8.89969e16	−0.0335460	−0.0167730	−	0.999859i	$-0.505339\pi$
$683$	−8.89969e16	−0.0335460	−0.0167730	+	0.999859i	$0.505339\pi$
$684$	−4.01224e18	−1.49803
$685$	−2.63943e18	−0.976162
$686$	8.27866e17	0.303287
$687$	1.79337e17	0.0650805
$688$	−2.37317e18	−0.853108
$689$	−2.46744e15	−0.000878660 0
$690$	−3.66006e18	−1.29113
$691$	−3.65107e17	−0.127589	−0.0637945	−	0.997963i	$-0.520320\pi$
$691$	−3.65107e17	−0.127589	−0.0637945	+	0.997963i	$0.520320\pi$
$692$	1.38240e19	4.78568
$693$	1.37904e17	0.0472944
$694$	3.08486e18	1.04809
$695$	−1.83719e18	−0.618376
$696$	−9.93485e18	−3.31284
$697$	1.79554e15	0.000593173 0
$698$	−3.63210e18	−1.18877
$699$	−8.53854e17	−0.276874
$700$	−1.58480e17	−0.0509141
$701$	5.47833e18	1.74374	0.871869	−	0.489739i	$-0.162908\pi$
$701$	5.47833e18	1.74374	0.871869	+	0.489739i	$0.162908\pi$
$702$	6.37242e16	0.0200962
$703$	−7.87221e18	−2.45973
$704$	1.90393e19	5.89425
$705$	−1.43026e18	−0.438717
$706$	1.48386e18	0.450985
$707$	−3.12044e17	−0.0939700
$708$	−6.77296e17	−0.202098
$709$	4.88049e18	1.44299	0.721495	−	0.692420i	$-0.243455\pi$
$709$	4.88049e18	1.44299	0.721495	+	0.692420i	$0.243455\pi$
$710$	4.86631e18	1.42568
$711$	2.68648e17	0.0779886
$712$	6.96465e18	2.00345
$713$	1.18081e18	0.336589
$714$	1.85731e16	0.00524622
$715$	3.03527e17	0.0849588
$716$	−1.23897e19	−3.43659
$717$	−1.63480e18	−0.449355
$718$	1.33573e19	3.63840
$719$	5.29070e18	1.42815	0.714077	−	0.700067i	$-0.246847\pi$
$719$	5.29070e18	1.42815	0.714077	+	0.700067i	$0.246847\pi$
$720$	3.84844e18	1.02949
$721$	3.20361e17	0.0849297
$722$	−1.31128e19	−3.44511
$723$	−3.29050e18	−0.856769
$724$	−1.32401e18	−0.341658
$725$	1.65385e18	0.422961
$726$	9.66393e18	2.44943
$727$	3.88991e18	0.977162	0.488581	−	0.872519i	$-0.337515\pi$
$727$	3.88991e18	0.977162	0.488581	+	0.872519i	$0.337515\pi$
$728$	−5.60997e16	−0.0139671
$729$	1.50095e17	0.0370370
$730$	−3.82208e18	−0.934763
$731$	−5.93761e16	−0.0143929
$732$	−2.98311e18	−0.716716
$733$	−4.61436e18	−1.09884	−0.549421	−	0.835545i	$-0.685152\pi$
$733$	−4.61436e18	−1.09884	−0.549421	+	0.835545i	$0.685152\pi$
$734$	1.21938e19	2.87817
$735$	2.13916e18	0.500468
$736$	2.04724e19	4.74748
$737$	1.57249e18	0.361450
$738$	−2.79027e16	−0.00635740
$739$	−8.08736e18	−1.82649	−0.913246	−	0.407408i	$-0.866433\pi$
$739$	−8.08736e18	−1.82649	−0.913246	+	0.407408i	$0.866433\pi$
$740$	1.54176e19	3.45153
$741$	2.36433e17	0.0524674
$742$	1.11758e16	0.00245840
$743$	4.01520e18	0.875549	0.437774	−	0.899085i	$-0.355767\pi$
$743$	4.01520e18	0.875549	0.437774	+	0.899085i	$0.355767\pi$
$744$	−2.18446e18	−0.472194
$745$	−3.53751e18	−0.758021
$746$	−2.34748e18	−0.498655
$747$	3.04667e16	0.00641567
$748$	1.37820e18	0.287707
$749$	5.79722e17	0.119974
$750$	−5.84178e18	−1.19853
$751$	1.03427e18	0.210365	0.105182	−	0.994453i	$-0.466457\pi$
$751$	1.03427e18	0.210365	0.105182	+	0.994453i	$0.466457\pi$
$752$	1.52956e19	3.08425
$753$	−5.01366e18	−1.00228
$754$	9.32114e17	0.184738
$755$	2.30213e18	0.452350
$756$	−2.10381e17	−0.0409841
$757$	−8.07535e18	−1.55969	−0.779845	−	0.625973i	$-0.784702\pi$
$757$	−8.07535e18	−1.55969	−0.779845	+	0.625973i	$0.784702\pi$
$758$	−1.37585e19	−2.63465
$759$	7.27132e18	1.38052
$760$	2.51220e19	4.72896
$761$	−1.86755e18	−0.348556	−0.174278	−	0.984696i	$-0.555759\pi$
$761$	−1.86755e18	−0.348556	−0.174278	+	0.984696i	$0.555759\pi$
$762$	5.49362e18	1.01660
$763$	7.95697e17	0.145995
$764$	−1.79405e19	−3.26383
$765$	9.62870e16	0.0173687
$766$	5.61224e18	1.00381
$767$	3.99117e16	0.00707832
$768$	−6.61885e18	−1.16395
$769$	5.83433e18	1.01735	0.508674	−	0.860959i	$-0.330136\pi$
$769$	5.83433e18	1.01735	0.508674	+	0.860959i	$0.330136\pi$
$770$	−1.37477e18	−0.237706
$771$	−4.23097e18	−0.725416
$772$	−1.15482e19	−1.96338
$773$	1.05089e18	0.177170	0.0885849	−	0.996069i	$-0.471766\pi$
$773$	1.05089e18	0.177170	0.0885849	+	0.996069i	$0.471766\pi$
$774$	9.22706e17	0.154258
$775$	3.63648e17	0.0602865
$776$	−2.57831e19	−4.23872
$777$	−4.12779e17	−0.0672947
$778$	−5.87638e17	−0.0950041
$779$	−1.03526e17	−0.0165980
$780$	−4.63052e17	−0.0736232
$781$	−9.66775e18	−1.52438
$782$	9.79316e17	0.153137
$783$	2.19548e18	0.340469
$784$	−2.28768e19	−3.51837
$785$	−7.50183e17	−0.114423
$786$	−2.62273e18	−0.396741
$787$	−1.09632e19	−1.64476	−0.822378	−	0.568941i	$-0.807353\pi$
$787$	−1.09632e19	−1.64476	−0.822378	+	0.568941i	$0.807353\pi$
$788$	2.29690e18	0.341761
$789$	−4.10922e18	−0.606399
$790$	−2.67816e18	−0.391977
$791$	1.54376e17	0.0224095
$792$	−1.34517e19	−1.93670
$793$	1.75789e17	0.0251024
$794$	7.54509e18	1.06864
$795$	5.79376e16	0.00813905
$796$	3.72839e19	5.19502
$797$	−5.75761e18	−0.795725	−0.397862	−	0.917445i	$-0.630248\pi$
$797$	−5.75761e18	−0.795725	−0.397862	+	0.917445i	$0.630248\pi$
$798$	−1.07088e18	−0.146798
$799$	3.82692e17	0.0520349
$800$	6.30476e18	0.850322
$801$	−1.53910e18	−0.205900
$802$	−1.50271e19	−1.99408
$803$	7.59321e18	0.999481
$804$	−2.39894e18	−0.313224
$805$	−7.12053e17	−0.0922230
$806$	2.04952e17	0.0263315
$807$	6.79371e18	0.865822
$808$	3.04380e19	3.84806
$809$	−1.07406e19	−1.34699	−0.673494	−	0.739192i	$-0.735207\pi$
$809$	−1.07406e19	−1.34699	−0.673494	+	0.739192i	$0.735207\pi$
$810$	−1.49630e18	−0.186151
$811$	−7.66453e18	−0.945910	−0.472955	−	0.881087i	$-0.656813\pi$
$811$	−7.66453e18	−0.945910	−0.472955	+	0.881087i	$0.656813\pi$
$812$	−3.07731e18	−0.376754
$813$	−5.01686e18	−0.609317
$814$	−4.20216e19	−5.06307
$815$	−1.65120e18	−0.197368
$816$	−1.02972e18	−0.122105
$817$	3.42347e18	0.402739
$818$	−8.87968e17	−0.103634
$819$	1.23974e16	0.00143544
$820$	2.02754e17	0.0232906
$821$	3.92109e18	0.446865	0.223433	−	0.974719i	$-0.428274\pi$
$821$	3.92109e18	0.446865	0.223433	+	0.974719i	$0.428274\pi$
$822$	−1.09748e19	−1.24088
$823$	4.12915e18	0.463192	0.231596	−	0.972812i	$-0.425605\pi$
$823$	4.12915e18	0.463192	0.231596	+	0.972812i	$0.425605\pi$
$824$	−3.12493e19	−3.47787
$825$	2.23930e18	0.247265
$826$	−1.80772e17	−0.0198044
$827$	1.51395e19	1.64560	0.822802	−	0.568328i	$-0.192410\pi$
$827$	1.51395e19	1.64560	0.822802	+	0.568328i	$0.192410\pi$
$828$	−1.10929e19	−1.19632
$829$	−1.14367e17	−0.0122376	−0.00611880	−	0.999981i	$-0.501948\pi$
$829$	−1.14367e17	−0.0122376	−0.00611880	+	0.999981i	$0.501948\pi$
$830$	−3.03724e17	−0.0322457
$831$	−1.08123e19	−1.13897
$832$	1.71161e18	0.178897
$833$	−5.72373e17	−0.0593590
$834$	−7.63906e18	−0.786069
$835$	8.83029e18	0.901598
$836$	−7.94632e19	−8.05054
$837$	4.82740e17	0.0485286
$838$	2.58157e19	2.57512
$839$	−1.79933e19	−1.78097	−0.890486	−	0.455011i	$-0.849635\pi$
$839$	−1.79933e19	−1.78097	−0.890486	+	0.455011i	$0.849635\pi$
$840$	1.31727e18	0.129378
$841$	2.18533e19	2.12982
$842$	−3.54223e19	−3.42569
$843$	−1.50380e18	−0.144315
$844$	4.09019e19	3.89509
$845$	−9.20350e18	−0.869730
$846$	−5.94703e18	−0.557690
$847$	1.88009e18	0.174959
$848$	−6.19602e17	−0.0572189
$849$	−2.46086e18	−0.225521
$850$	3.01594e17	0.0274283
$851$	−2.17648e19	−1.96432
$852$	1.47488e19	1.32099
$853$	1.46116e19	1.29876	0.649381	−	0.760463i	$-0.275028\pi$
$853$	1.46116e19	1.29876	0.649381	+	0.760463i	$0.275028\pi$
$854$	−7.96202e17	−0.0702339
$855$	−5.55166e18	−0.486008
$856$	−5.65484e19	−4.91294
$857$	7.36674e18	0.635185	0.317592	−	0.948227i	$-0.397126\pi$
$857$	7.36674e18	0.635185	0.317592	+	0.948227i	$0.397126\pi$
$858$	1.26207e18	0.107998
$859$	1.88070e19	1.59722	0.798610	−	0.601849i	$-0.205569\pi$
$859$	1.88070e19	1.59722	0.798610	+	0.601849i	$0.205569\pi$
$860$	−6.70483e18	−0.565130
$861$	−5.42838e15	−0.000454098 0
$862$	4.31728e17	0.0358437
$863$	2.05627e19	1.69438	0.847188	−	0.531293i	$-0.178294\pi$
$863$	2.05627e19	1.69438	0.847188	+	0.531293i	$0.178294\pi$
$864$	8.36952e18	0.684481
$865$	1.91280e19	1.55262
$866$	−3.38104e19	−2.72385
$867$	7.19467e18	0.575290
$868$	−6.76636e17	−0.0537003
$869$	5.32063e18	0.419116
$870$	−2.18869e19	−1.71123
$871$	1.41365e17	0.0109704
$872$	−7.76155e19	−5.97849
$873$	5.69776e18	0.435623
$874$	−5.64648e19	−4.28503
$875$	−1.13650e18	−0.0856086
$876$	−1.15840e19	−0.866125
$877$	1.67318e19	1.24178	0.620892	−	0.783896i	$-0.286771\pi$
$877$	1.67318e19	1.24178	0.620892	+	0.783896i	$0.286771\pi$
$878$	5.58333e18	0.411319
$879$	−4.25850e18	−0.311408
$880$	7.62191e19	5.53257
$881$	1.12486e18	0.0810505	0.0405252	−	0.999179i	$-0.487097\pi$
$881$	1.12486e18	0.0810505	0.0405252	+	0.999179i	$0.487097\pi$
$882$	8.89468e18	0.636187
$883$	−1.06718e19	−0.757695	−0.378848	−	0.925459i	$-0.623680\pi$
$883$	−1.06718e19	−0.757695	−0.378848	+	0.925459i	$0.623680\pi$
$884$	1.23898e17	0.00873222
$885$	−9.37162e17	−0.0655667
$886$	−2.22280e19	−1.54377
$887$	1.60301e19	1.10518	0.552590	−	0.833453i	$-0.313639\pi$
$887$	1.60301e19	1.10518	0.552590	+	0.833453i	$0.313639\pi$
$888$	4.02641e19	2.75571
$889$	1.06877e18	0.0726142
$890$	1.53434e19	1.03487
$891$	2.97266e18	0.199040
$892$	−7.89044e19	−5.24481
$893$	−2.20650e19	−1.45603
$894$	−1.47090e19	−0.963584
$895$	−1.71434e19	−1.11493
$896$	−3.38932e18	−0.218832
$897$	6.53683e17	0.0419002
$898$	4.02150e19	2.55913
$899$	7.06118e18	0.446107
$900$	−3.41621e18	−0.214273
$901$	−1.55023e16	−0.000965349 0
$902$	−5.52618e17	−0.0341651
$903$	1.79510e17	0.0110184
$904$	−1.50585e19	−0.917668
$905$	−1.83201e18	−0.110844
$906$	9.57230e18	0.575020
$907$	−5.16869e18	−0.308271	−0.154136	−	0.988050i	$-0.549259\pi$
$907$	−5.16869e18	−0.308271	−0.154136	+	0.988050i	$0.549259\pi$
$908$	6.27524e19	3.71597
$909$	−6.72643e18	−0.395475
$910$	−1.23590e17	−0.00721463
$911$	−1.10356e19	−0.639624	−0.319812	−	0.947481i	$-0.603620\pi$
$911$	−1.10356e19	−0.639624	−0.319812	+	0.947481i	$0.603620\pi$
$912$	5.93711e19	3.41671
$913$	6.03400e17	0.0344782
$914$	1.12281e19	0.637022
$915$	−4.12768e18	−0.232524
$916$	−5.41852e18	−0.303082
$917$	−5.10245e17	−0.0283386
$918$	4.00363e17	0.0220789
$919$	1.30760e19	0.716016	0.358008	−	0.933718i	$-0.383456\pi$
$919$	1.30760e19	0.716016	0.358008	+	0.933718i	$0.383456\pi$
$920$	6.94565e19	3.77652
$921$	7.02442e18	0.379248
$922$	4.24328e19	2.27484
$923$	−8.69118e17	−0.0462666
$924$	−4.16665e18	−0.220252
$925$	−6.70277e18	−0.351830
$926$	7.22328e19	3.76498
$927$	6.90570e18	0.357429
$928$	1.22424e20	6.29221
$929$	−1.08276e19	−0.552625	−0.276312	−	0.961068i	$-0.589112\pi$
$929$	−1.08276e19	−0.552625	−0.276312	+	0.961068i	$0.589112\pi$
$930$	−4.81246e18	−0.243909
$931$	3.30015e19	1.66097
$932$	2.57985e19	1.28941
$933$	−6.20742e17	−0.0308092
$934$	2.07374e19	1.02212
$935$	1.90698e18	0.0933408
$936$	−1.20929e18	−0.0587810
$937$	−2.98007e19	−1.43853	−0.719265	−	0.694736i	$-0.755521\pi$
$937$	−2.98007e19	−1.43853	−0.719265	+	0.694736i	$0.755521\pi$
$938$	−6.40284e17	−0.0306941
$939$	−9.13953e18	−0.435109
$940$	4.32140e19	2.04312
$941$	−1.02355e19	−0.480591	−0.240295	−	0.970700i	$-0.577244\pi$
$941$	−1.02355e19	−0.480591	−0.240295	+	0.970700i	$0.577244\pi$
$942$	−3.11928e18	−0.145453
$943$	−2.86225e17	−0.0132551
$944$	1.00223e19	0.460945
$945$	−2.91101e17	−0.0132965
$946$	1.82744e19	0.828992
$947$	−1.48155e19	−0.667486	−0.333743	−	0.942664i	$-0.608312\pi$
$947$	−1.48155e19	−0.667486	−0.333743	+	0.942664i	$0.608312\pi$
$948$	−8.11698e18	−0.363195
$949$	6.82620e17	0.0303353
$950$	−1.73891e19	−0.767492
$951$	7.15303e18	0.313557
$952$	−3.52460e17	−0.0153451
$953$	−7.01791e18	−0.303462	−0.151731	−	0.988422i	$-0.548485\pi$
$953$	−7.01791e18	−0.303462	−0.151731	+	0.988422i	$0.548485\pi$
$954$	2.40906e17	0.0103462
$955$	−2.48240e19	−1.05889
$956$	4.93941e19	2.09266
$957$	4.34819e19	1.82971
$958$	−4.49794e19	−1.87991
$959$	−2.13512e18	−0.0886341
$960$	−4.01901e19	−1.65713
$961$	−2.28649e19	−0.936414
$962$	−3.77769e18	−0.153670
$963$	1.24965e19	0.504915
$964$	9.94200e19	3.99000
$965$	−1.59791e19	−0.636978
$966$	−2.96073e18	−0.117232
$967$	−2.50340e19	−0.984596	−0.492298	−	0.870427i	$-0.663843\pi$
$967$	−2.50340e19	−0.984596	−0.492298	+	0.870427i	$0.663843\pi$
$968$	−1.83391e20	−7.16456
$969$	1.48545e18	0.0576439
$970$	−5.68012e19	−2.18948
$971$	3.90249e19	1.49423	0.747113	−	0.664696i	$-0.231439\pi$
$971$	3.90249e19	1.49423	0.747113	+	0.664696i	$0.231439\pi$
$972$	−4.53499e18	−0.172483
$973$	−1.48616e18	−0.0561476
$974$	5.25698e19	1.97289
$975$	2.01310e17	0.00750475
$976$	4.41426e19	1.63468
$977$	−2.43154e19	−0.894473	−0.447237	−	0.894416i	$-0.647592\pi$
$977$	−2.43154e19	−0.894473	−0.447237	+	0.894416i	$0.647592\pi$
$978$	−6.86574e18	−0.250891
$979$	−3.04823e19	−1.10652
$980$	−6.46331e19	−2.33070
$981$	1.71521e19	0.614424
$982$	−9.12441e19	−3.24699
$983$	7.00559e18	0.247655	0.123827	−	0.992304i	$-0.460483\pi$
$983$	7.00559e18	0.247655	0.123827	+	0.992304i	$0.460483\pi$
$984$	5.29506e17	0.0185953
$985$	3.17818e18	0.110878
$986$	5.85624e18	0.202964
$987$	−1.15698e18	−0.0398349
$988$	−7.14364e18	−0.244343
$989$	9.46511e18	0.321625
$990$	−2.96346e19	−1.00039
$991$	−1.96898e19	−0.660331	−0.330166	−	0.943923i	$-0.607105\pi$
$991$	−1.96898e19	−0.660331	−0.330166	+	0.943923i	$0.607105\pi$
$992$	2.69184e19	0.896856
$993$	−1.20714e19	−0.399566
$994$	3.93651e18	0.129449
$995$	5.15891e19	1.68542
$996$	−9.20528e17	−0.0298780
$997$	−7.17073e18	−0.231231	−0.115615	−	0.993294i	$-0.536884\pi$
$997$	−7.17073e18	−0.231231	−0.115615	+	0.993294i	$0.536884\pi$
$998$	−8.51860e19	−2.72910
$999$	−8.89788e18	−0.283212

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.d.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-173.834 q^{2} -729.000 q^{3} +22026.2 q^{4} +30477.2 q^{5} +126725. q^{6} +24653.9 q^{7} -2.40484e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q-173.834 q^{2} -729.000 q^{3} +22026.2 q^{4} +30477.2 q^{5} +126725. q^{6} +24653.9 q^{7} -2.40484e6 q^{8} +531441. q^{9} -5.29796e6 q^{10} +1.05253e7 q^{11} -1.60571e7 q^{12} +946211. q^{13} -4.28568e6 q^{14} -2.22179e7 q^{15} +2.37605e8 q^{16} +5.94481e6 q^{17} -9.23824e7 q^{18} -3.42762e8 q^{19} +6.71295e8 q^{20} -1.79727e7 q^{21} -1.82965e9 q^{22} -9.47657e8 q^{23} +1.75313e9 q^{24} -2.91844e8 q^{25} -1.64483e8 q^{26} -3.87420e8 q^{27} +5.43031e8 q^{28} -5.66692e9 q^{29} +3.86222e9 q^{30} -1.24604e9 q^{31} -2.16032e10 q^{32} -7.67294e9 q^{33} -1.03341e9 q^{34} +7.51382e8 q^{35} +1.17056e10 q^{36} +2.29670e10 q^{37} +5.95836e10 q^{38} -6.89788e8 q^{39} -7.32929e10 q^{40} +3.02035e8 q^{41} +3.12426e9 q^{42} -9.98790e9 q^{43} +2.31832e11 q^{44} +1.61968e10 q^{45} +1.64735e11 q^{46} +6.43741e10 q^{47} -1.73214e11 q^{48} -9.62812e10 q^{49} +5.07323e10 q^{50} -4.33376e9 q^{51} +2.08414e10 q^{52} -2.60770e9 q^{53} +6.73467e10 q^{54} +3.20782e11 q^{55} -5.92888e10 q^{56} +2.49874e11 q^{57} +9.85101e11 q^{58} +4.21805e10 q^{59} -4.89374e11 q^{60} +1.85782e11 q^{61} +2.16603e11 q^{62} +1.31021e10 q^{63} +1.80891e12 q^{64} +2.88379e10 q^{65} +1.33382e12 q^{66} +1.49401e11 q^{67} +1.30941e11 q^{68} +6.90842e11 q^{69} -1.30616e11 q^{70} -9.18525e11 q^{71} -1.27803e12 q^{72} +7.21425e11 q^{73} -3.99244e12 q^{74} +2.12754e11 q^{75} -7.54973e12 q^{76} +2.59490e11 q^{77} +1.19908e11 q^{78} +5.05508e11 q^{79} +7.24152e12 q^{80} +2.82430e11 q^{81} -5.25038e10 q^{82} +5.73285e10 q^{83} -3.95870e11 q^{84} +1.81181e11 q^{85} +1.73623e12 q^{86} +4.13118e12 q^{87} -2.53117e13 q^{88} -2.89609e12 q^{89} -2.81556e12 q^{90} +2.33278e10 q^{91} -2.08733e13 q^{92} +9.08360e11 q^{93} -1.11904e13 q^{94} -1.04464e13 q^{95} +1.57487e13 q^{96} +1.07213e13 q^{97} +1.67369e13 q^{98} +5.59358e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) \) 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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