LMFDB - Embedded newform 177.14.a.d.1.28

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			1.28
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)

$f(q)$	$=$	$q+134.873 q^{2} -729.000 q^{3} +9998.64 q^{4} -13365.0 q^{5} -98322.2 q^{6} -353556. q^{7} +243667. q^{8} +531441. q^{9} +O(q^{10})$	\(q+134.873 q^{2} -729.000 q^{3} +9998.64 q^{4} -13365.0 q^{5} -98322.2 q^{6} -353556. q^{7} +243667. q^{8} +531441. q^{9} -1.80258e6 q^{10} -9.42765e6 q^{11} -7.28901e6 q^{12} -1.09585e7 q^{13} -4.76850e7 q^{14} +9.74312e6 q^{15} -4.90449e7 q^{16} -1.60632e8 q^{17} +7.16769e7 q^{18} +9.95959e7 q^{19} -1.33632e8 q^{20} +2.57742e8 q^{21} -1.27153e9 q^{22} -2.99818e8 q^{23} -1.77633e8 q^{24} -1.04208e9 q^{25} -1.47800e9 q^{26} -3.87420e8 q^{27} -3.53508e9 q^{28} +5.79956e9 q^{29} +1.31408e9 q^{30} +5.74669e9 q^{31} -8.61093e9 q^{32} +6.87275e9 q^{33} -2.16648e10 q^{34} +4.72529e9 q^{35} +5.31369e9 q^{36} +2.31057e10 q^{37} +1.34328e10 q^{38} +7.98872e9 q^{39} -3.25662e9 q^{40} -4.49802e10 q^{41} +3.47624e10 q^{42} +2.69208e8 q^{43} -9.42637e10 q^{44} -7.10274e9 q^{45} -4.04372e10 q^{46} -2.90282e10 q^{47} +3.57537e10 q^{48} +2.81127e10 q^{49} -1.40548e11 q^{50} +1.17101e11 q^{51} -1.09570e11 q^{52} -6.80349e10 q^{53} -5.22524e10 q^{54} +1.26001e11 q^{55} -8.61498e10 q^{56} -7.26054e10 q^{57} +7.82202e11 q^{58} +4.21805e10 q^{59} +9.74180e10 q^{60} -3.36989e11 q^{61} +7.75071e11 q^{62} -1.87894e11 q^{63} -7.59604e11 q^{64} +1.46460e11 q^{65} +9.26947e11 q^{66} +3.18870e11 q^{67} -1.60610e12 q^{68} +2.18567e11 q^{69} +6.37313e11 q^{70} -1.62243e12 q^{71} +1.29495e11 q^{72} +1.10954e12 q^{73} +3.11633e12 q^{74} +7.59675e11 q^{75} +9.95824e11 q^{76} +3.33320e12 q^{77} +1.07746e12 q^{78} +1.22044e12 q^{79} +6.55487e11 q^{80} +2.82430e11 q^{81} -6.06661e12 q^{82} +2.99798e12 q^{83} +2.57707e12 q^{84} +2.14685e12 q^{85} +3.63088e10 q^{86} -4.22788e12 q^{87} -2.29721e12 q^{88} -9.36783e10 q^{89} -9.57965e11 q^{90} +3.87443e12 q^{91} -2.99777e12 q^{92} -4.18934e12 q^{93} -3.91511e12 q^{94} -1.33110e12 q^{95} +6.27737e12 q^{96} +3.56244e12 q^{97} +3.79163e12 q^{98} -5.01024e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	134.873	1.49015	0.745073	−	0.666982i	$-0.232414\pi$
$2$	134.873	1.49015	0.745073	+	0.666982i	$0.232414\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	9998.64	1.22054
$5$	−13365.0	−0.382530	−0.191265	−	0.981538i	$-0.561259\pi$
$5$	−13365.0	−0.382530	−0.191265	+	0.981538i	$0.561259\pi$
$6$	−98322.2	−0.860337
$7$	−353556.	−1.13585	−0.567925	−	0.823081i	$-0.692253\pi$
$7$	−353556.	−1.13585	−0.567925	+	0.823081i	$0.692253\pi$
$8$	243667.	0.328633
$9$	531441.	0.333333
$10$	−1.80258e6	−0.570026
$11$	−9.42765e6	−1.60454	−0.802271	−	0.596961i	$-0.796375\pi$
$11$	−9.42765e6	−1.60454	−0.802271	+	0.596961i	$0.796375\pi$
$12$	−7.28901e6	−0.704678
$13$	−1.09585e7	−0.629677	−0.314838	−	0.949145i	$-0.601950\pi$
$13$	−1.09585e7	−0.629677	−0.314838	+	0.949145i	$0.601950\pi$
$14$	−4.76850e7	−1.69258
$15$	9.74312e6	0.220854
$16$	−4.90449e7	−0.730826
$17$	−1.60632e8	−1.61404	−0.807018	−	0.590527i	$-0.798920\pi$
$17$	−1.60632e8	−1.61404	−0.807018	+	0.590527i	$0.798920\pi$
$18$	7.16769e7	0.496716
$19$	9.95959e7	0.485672	0.242836	−	0.970067i	$-0.421922\pi$
$19$	9.95959e7	0.485672	0.242836	+	0.970067i	$0.421922\pi$
$20$	−1.33632e8	−0.466892
$21$	2.57742e8	0.655783
$22$	−1.27153e9	−2.39100
$23$	−2.99818e8	−0.422305	−0.211153	−	0.977453i	$-0.567722\pi$
$23$	−2.99818e8	−0.422305	−0.211153	+	0.977453i	$0.567722\pi$
$24$	−1.77633e8	−0.189737
$25$	−1.04208e9	−0.853671
$26$	−1.47800e9	−0.938311
$27$	−3.87420e8	−0.192450
$28$	−3.53508e9	−1.38635
$29$	5.79956e9	1.81054	0.905270	−	0.424838i	$-0.139669\pi$
$29$	5.79956e9	1.81054	0.905270	+	0.424838i	$0.139669\pi$
$30$	1.31408e9	0.329105
$31$	5.74669e9	1.16296	0.581482	−	0.813559i	$-0.302473\pi$
$31$	5.74669e9	1.16296	0.581482	+	0.813559i	$0.302473\pi$
$32$	−8.61093e9	−1.41767
$33$	6.87275e9	0.926382
$34$	−2.16648e10	−2.40515
$35$	4.72529e9	0.434496
$36$	5.31369e9	0.406846
$37$	2.31057e10	1.48050	0.740249	−	0.672333i	$-0.234708\pi$
$37$	2.31057e10	1.48050	0.740249	+	0.672333i	$0.234708\pi$
$38$	1.34328e10	0.723723
$39$	7.98872e9	0.363544
$40$	−3.25662e9	−0.125712
$41$	−4.49802e10	−1.47886	−0.739429	−	0.673234i	$-0.764905\pi$
$41$	−4.49802e10	−1.47886	−0.739429	+	0.673234i	$0.764905\pi$
$42$	3.47624e10	0.977213
$43$	2.69208e8	0.00649445	0.00324723	−	0.999995i	$-0.498966\pi$
$43$	2.69208e8	0.00649445	0.00324723	+	0.999995i	$0.498966\pi$
$44$	−9.42637e10	−1.95840
$45$	−7.10274e9	−0.127510
$46$	−4.04372e10	−0.629297
$47$	−2.90282e10	−0.392811	−0.196406	−	0.980523i	$-0.562927\pi$
$47$	−2.90282e10	−0.392811	−0.196406	+	0.980523i	$0.562927\pi$
$48$	3.57537e10	0.421942
$49$	2.81127e10	0.290153
$50$	−1.40548e11	−1.27209
$51$	1.17101e11	0.931864
$52$	−1.09570e11	−0.768544
$53$	−6.80349e10	−0.421637	−0.210818	−	0.977525i	$-0.567613\pi$
$53$	−6.80349e10	−0.421637	−0.210818	+	0.977525i	$0.567613\pi$
$54$	−5.22524e10	−0.286779
$55$	1.26001e11	0.613785
$56$	−8.61498e10	−0.373278
$57$	−7.26054e10	−0.280403
$58$	7.82202e11	2.69797
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	9.74180e10	0.269560
$61$	−3.36989e11	−0.837475	−0.418737	−	0.908107i	$-0.637527\pi$
$61$	−3.36989e11	−0.837475	−0.418737	+	0.908107i	$0.637527\pi$
$62$	7.75071e11	1.73299
$63$	−1.87894e11	−0.378616
$64$	−7.59604e11	−1.38171
$65$	1.46460e11	0.240870
$66$	9.26947e11	1.38045
$67$	3.18870e11	0.430654	0.215327	−	0.976542i	$-0.430918\pi$
$67$	3.18870e11	0.430654	0.215327	+	0.976542i	$0.430918\pi$
$68$	−1.60610e12	−1.96999
$69$	2.18567e11	0.243818
$70$	6.37313e11	0.647463
$71$	−1.62243e12	−1.50309	−0.751547	−	0.659680i	$-0.770692\pi$
$71$	−1.62243e12	−1.50309	−0.751547	+	0.659680i	$0.770692\pi$
$72$	1.29495e11	0.109544
$73$	1.10954e12	0.858113	0.429057	−	0.903278i	$-0.358846\pi$
$73$	1.10954e12	0.858113	0.429057	+	0.903278i	$0.358846\pi$
$74$	3.11633e12	2.20616
$75$	7.59675e11	0.492867
$76$	9.95824e11	0.592781
$77$	3.33320e12	1.82252
$78$	1.07746e12	0.541734
$79$	1.22044e12	0.564860	0.282430	−	0.959288i	$-0.408859\pi$
$79$	1.22044e12	0.564860	0.282430	+	0.959288i	$0.408859\pi$
$80$	6.55487e11	0.279563
$81$	2.82430e11	0.111111
$82$	−6.06661e12	−2.20372
$83$	2.99798e12	1.00652	0.503258	−	0.864136i	$-0.332135\pi$
$83$	2.99798e12	1.00652	0.503258	+	0.864136i	$0.332135\pi$
$84$	2.57707e12	0.800408
$85$	2.14685e12	0.617417
$86$	3.63088e10	0.00967769
$87$	−4.22788e12	−1.04532
$88$	−2.29721e12	−0.527306
$89$	−9.36783e10	−0.0199804	−0.00999020	−	0.999950i	$-0.503180\pi$
$89$	−9.36783e10	−0.0199804	−0.00999020	+	0.999950i	$0.503180\pi$
$90$	−9.57965e11	−0.190009
$91$	3.87443e12	0.715218
$92$	−2.99777e12	−0.515439
$93$	−4.18934e12	−0.671438
$94$	−3.91511e12	−0.585346
$95$	−1.33110e12	−0.185784
$96$	6.27737e12	0.818493
$97$	3.56244e12	0.434241	0.217121	−	0.976145i	$-0.430334\pi$
$97$	3.56244e12	0.434241	0.217121	+	0.976145i	$0.430334\pi$
$98$	3.79163e12	0.432371
$99$	−5.01024e12	−0.534847
$100$	−1.04194e13	−1.04194
$101$	1.88394e12	0.176595	0.0882974	−	0.996094i	$-0.471857\pi$
$101$	1.88394e12	0.176595	0.0882974	+	0.996094i	$0.471857\pi$
$102$	1.57937e13	1.38861
$103$	−1.09156e13	−0.900752	−0.450376	−	0.892839i	$-0.648710\pi$
$103$	−1.09156e13	−0.900752	−0.450376	+	0.892839i	$0.648710\pi$
$104$	−2.67021e12	−0.206933
$105$	−3.44474e12	−0.250857
$106$	−9.17605e12	−0.628301
$107$	−1.15538e13	−0.744273	−0.372136	−	0.928178i	$-0.621375\pi$
$107$	−1.15538e13	−0.744273	−0.372136	+	0.928178i	$0.621375\pi$
$108$	−3.87368e12	−0.234893
$109$	−9.47523e12	−0.541150	−0.270575	−	0.962699i	$-0.587214\pi$
$109$	−9.47523e12	−0.541150	−0.270575	+	0.962699i	$0.587214\pi$
$110$	1.69941e13	0.914630
$111$	−1.68440e13	−0.854765
$112$	1.73401e13	0.830108
$113$	−3.63046e13	−1.64041	−0.820203	−	0.572072i	$-0.806140\pi$
$113$	−3.63046e13	−1.64041	−0.820203	+	0.572072i	$0.806140\pi$
$114$	−9.79249e12	−0.417842
$115$	4.00708e12	0.161544
$116$	5.79877e13	2.20983
$117$	−5.82378e12	−0.209892
$118$	5.68900e12	0.194001
$119$	5.67923e13	1.83330
$120$	2.37408e12	0.0725799
$121$	5.43578e13	1.57455
$122$	−4.54506e13	−1.24796
$123$	3.27906e13	0.853819
$124$	5.74591e13	1.41944
$125$	3.02422e13	0.709085
$126$	−2.53418e13	−0.564194
$127$	1.85606e13	0.392526	0.196263	−	0.980551i	$-0.437119\pi$
$127$	1.85606e13	0.392526	0.196263	+	0.980551i	$0.437119\pi$
$128$	−3.19091e13	−0.641283
$129$	−1.96252e11	−0.00374957
$130$	1.97535e13	0.358932
$131$	−2.70313e12	−0.0467308	−0.0233654	−	0.999727i	$-0.507438\pi$
$131$	−2.70313e12	−0.0467308	−0.0233654	+	0.999727i	$0.507438\pi$
$132$	6.87182e13	1.13068
$133$	−3.52127e13	−0.551650
$134$	4.30069e13	0.641737
$135$	5.17789e12	0.0736179
$136$	−3.91406e13	−0.530426
$137$	6.79986e13	0.878651	0.439326	−	0.898328i	$-0.355217\pi$
$137$	6.79986e13	0.878651	0.439326	+	0.898328i	$0.355217\pi$
$138$	2.94787e13	0.363325
$139$	6.20107e13	0.729240	0.364620	−	0.931156i	$-0.381199\pi$
$139$	6.20107e13	0.729240	0.364620	+	0.931156i	$0.381199\pi$
$140$	4.72465e13	0.530319
$141$	2.11616e13	0.226790
$142$	−2.18821e14	−2.23983
$143$	1.03313e14	1.01034
$144$	−2.60645e13	−0.243609
$145$	−7.75114e13	−0.692586
$146$	1.49647e14	1.27871
$147$	−2.04941e13	−0.167520
$148$	2.31025e14	1.80700
$149$	−1.07837e14	−0.807339	−0.403670	−	0.914905i	$-0.632265\pi$
$149$	−1.07837e14	−0.807339	−0.403670	+	0.914905i	$0.632265\pi$
$150$	1.02459e14	0.734444
$151$	2.83406e14	1.94562	0.972812	−	0.231595i	$-0.0743943\pi$
$151$	2.83406e14	1.94562	0.972812	+	0.231595i	$0.0743943\pi$
$152$	2.42682e13	0.159608
$153$	−8.53663e13	−0.538012
$154$	4.49558e14	2.71582
$155$	−7.68048e13	−0.444869
$156$	7.98764e13	0.443719
$157$	2.00887e14	1.07054	0.535271	−	0.844680i	$-0.320209\pi$
$157$	2.00887e14	1.07054	0.535271	+	0.844680i	$0.320209\pi$
$158$	1.64604e14	0.841725
$159$	4.95974e13	0.243432
$160$	1.15086e14	0.542302
$161$	1.06002e14	0.479675
$162$	3.80920e13	0.165572
$163$	−3.11533e14	−1.30102	−0.650511	−	0.759497i	$-0.725445\pi$
$163$	−3.11533e14	−1.30102	−0.650511	+	0.759497i	$0.725445\pi$
$164$	−4.49741e14	−1.80500
$165$	−9.18547e13	−0.354369
$166$	4.04345e14	1.49986
$167$	−4.84594e14	−1.72870	−0.864352	−	0.502887i	$-0.832271\pi$
$167$	−4.84594e14	−1.72870	−0.864352	+	0.502887i	$0.832271\pi$
$168$	6.28032e13	0.215512
$169$	−1.82787e14	−0.603507
$170$	2.89552e14	0.920043
$171$	5.29294e13	0.161891
$172$	2.69171e12	0.00792672
$173$	6.88902e13	0.195370	0.0976850	−	0.995217i	$-0.468856\pi$
$173$	6.88902e13	0.195370	0.0976850	+	0.995217i	$0.468856\pi$
$174$	−5.70225e14	−1.55767
$175$	3.68433e14	0.969641
$176$	4.62378e14	1.17264
$177$	−3.07496e13	−0.0751646
$178$	−1.26346e13	−0.0297737
$179$	3.89607e14	0.885283	0.442642	−	0.896699i	$-0.354041\pi$
$179$	3.89607e14	0.885283	0.442642	+	0.896699i	$0.354041\pi$
$180$	−7.10177e13	−0.155631
$181$	7.18852e14	1.51960	0.759799	−	0.650158i	$-0.225297\pi$
$181$	7.18852e14	1.51960	0.759799	+	0.650158i	$0.225297\pi$
$182$	5.22554e14	1.06578
$183$	2.45665e14	0.483516
$184$	−7.30557e13	−0.138784
$185$	−3.08809e14	−0.566335
$186$	−5.65027e14	−1.00054
$187$	1.51438e15	2.58979
$188$	−2.90243e14	−0.479441
$189$	1.36975e14	0.218594
$190$	−1.79530e14	−0.276846
$191$	−1.19898e15	−1.78688	−0.893442	−	0.449179i	$-0.851717\pi$
$191$	−1.19898e15	−1.78688	−0.893442	+	0.449179i	$0.851717\pi$
$192$	5.53752e14	0.797732
$193$	7.48580e14	1.04260	0.521298	−	0.853375i	$-0.325448\pi$
$193$	7.48580e14	1.04260	0.521298	+	0.853375i	$0.325448\pi$
$194$	4.80475e14	0.647083
$195$	−1.06770e14	−0.139067
$196$	2.81089e14	0.354143
$197$	7.53566e14	0.918525	0.459263	−	0.888301i	$-0.348114\pi$
$197$	7.53566e14	0.918525	0.459263	+	0.888301i	$0.348114\pi$
$198$	−6.75744e14	−0.797001
$199$	−9.62550e14	−1.09870	−0.549349	−	0.835593i	$-0.685124\pi$
$199$	−9.62550e14	−1.09870	−0.549349	+	0.835593i	$0.685124\pi$
$200$	−2.53920e14	−0.280545
$201$	−2.32457e14	−0.248638
$202$	2.54092e14	0.263152
$203$	−2.05047e15	−2.05650
$204$	1.17085e15	1.13738
$205$	6.01163e14	0.565708
$206$	−1.47221e15	−1.34225
$207$	−1.59335e14	−0.140768
$208$	5.37456e14	0.460184
$209$	−9.38955e14	−0.779281
$210$	−4.64601e14	−0.373813
$211$	−6.09445e14	−0.475443	−0.237722	−	0.971333i	$-0.576401\pi$
$211$	−6.09445e14	−0.475443	−0.237722	+	0.971333i	$0.576401\pi$
$212$	−6.80257e14	−0.514624
$213$	1.18275e15	0.867812
$214$	−1.55830e15	−1.10908
$215$	−3.59797e12	−0.00248432
$216$	−9.44016e13	−0.0632455
$217$	−2.03177e15	−1.32095
$218$	−1.27795e15	−0.806392
$219$	−8.08855e14	−0.495432
$220$	1.25984e15	0.749148
$221$	1.76028e15	1.01632
$222$	−2.27180e15	−1.27373
$223$	3.88147e14	0.211356	0.105678	−	0.994400i	$-0.466299\pi$
$223$	3.88147e14	0.211356	0.105678	+	0.994400i	$0.466299\pi$
$224$	3.04445e15	1.61026
$225$	−5.53803e14	−0.284557
$226$	−4.89649e15	−2.44445
$227$	1.55355e15	0.753630	0.376815	−	0.926288i	$-0.377019\pi$
$227$	1.55355e15	0.753630	0.376815	+	0.926288i	$0.377019\pi$
$228$	−7.25956e14	−0.342242
$229$	−7.19730e14	−0.329791	−0.164896	−	0.986311i	$-0.552729\pi$
$229$	−7.19730e14	−0.329791	−0.164896	+	0.986311i	$0.552729\pi$
$230$	5.40446e14	0.240725
$231$	−2.42990e15	−1.05223
$232$	1.41316e15	0.595004
$233$	−3.44097e15	−1.40886	−0.704430	−	0.709774i	$-0.748797\pi$
$233$	−3.44097e15	−1.40886	−0.704430	+	0.709774i	$0.748797\pi$
$234$	−7.85468e14	−0.312770
$235$	3.87963e14	0.150262
$236$	4.21748e14	0.158900
$237$	−8.89702e14	−0.326122
$238$	7.65973e15	2.73189
$239$	−1.07855e15	−0.374331	−0.187165	−	0.982328i	$-0.559930\pi$
$239$	−1.07855e15	−0.374331	−0.187165	+	0.982328i	$0.559930\pi$
$240$	−4.77850e14	−0.161406
$241$	−1.88321e15	−0.619138	−0.309569	−	0.950877i	$-0.600185\pi$
$241$	−1.88321e15	−0.619138	−0.309569	+	0.950877i	$0.600185\pi$
$242$	7.33138e15	2.34631
$243$	−2.05891e14	−0.0641500
$244$	−3.36943e15	−1.02217
$245$	−3.75727e14	−0.110992
$246$	4.42256e15	1.27232
$247$	−1.09142e15	−0.305817
$248$	1.40028e15	0.382189
$249$	−2.18553e15	−0.581112
$250$	4.07885e15	1.05664
$251$	−2.35512e15	−0.594475	−0.297238	−	0.954803i	$-0.596065\pi$
$251$	−2.35512e15	−0.594475	−0.297238	+	0.954803i	$0.596065\pi$
$252$	−1.87869e15	−0.462116
$253$	2.82658e15	0.677606
$254$	2.50332e15	0.584921
$255$	−1.56505e15	−0.356466
$256$	1.91901e15	0.426106
$257$	5.69908e15	1.23378	0.616892	−	0.787048i	$-0.288391\pi$
$257$	5.69908e15	1.23378	0.616892	+	0.787048i	$0.288391\pi$
$258$	−2.64691e13	−0.00558741
$259$	−8.16915e15	−1.68162
$260$	1.46441e15	0.293991
$261$	3.08212e15	0.603513
$262$	−3.64578e14	−0.0696358
$263$	1.19642e15	0.222932	0.111466	−	0.993768i	$-0.464445\pi$
$263$	1.19642e15	0.222932	0.111466	+	0.993768i	$0.464445\pi$
$264$	1.67466e15	0.304440
$265$	9.09290e14	0.161289
$266$	−4.74923e15	−0.822040
$267$	6.82915e13	0.0115357
$268$	3.18827e15	0.525629
$269$	−2.53966e15	−0.408683	−0.204341	−	0.978900i	$-0.565505\pi$
$269$	−2.53966e15	−0.408683	−0.204341	+	0.978900i	$0.565505\pi$
$270$	6.98357e14	0.109702
$271$	−3.13351e15	−0.480541	−0.240270	−	0.970706i	$-0.577236\pi$
$271$	−3.13351e15	−0.480541	−0.240270	+	0.970706i	$0.577236\pi$
$272$	7.87816e15	1.17958
$273$	−2.82446e15	−0.412931
$274$	9.17116e15	1.30932
$275$	9.82435e15	1.36975
$276$	2.18538e15	0.297589
$277$	−5.57015e15	−0.740880	−0.370440	−	0.928856i	$-0.620793\pi$
$277$	−5.57015e15	−0.740880	−0.370440	+	0.928856i	$0.620793\pi$
$278$	8.36355e15	1.08668
$279$	3.05403e15	0.387655
$280$	1.15140e15	0.142790
$281$	5.84308e15	0.708029	0.354015	−	0.935240i	$-0.384816\pi$
$281$	5.84308e15	0.708029	0.354015	+	0.935240i	$0.384816\pi$
$282$	2.85412e15	0.337950
$283$	1.70979e15	0.197847	0.0989237	−	0.995095i	$-0.468460\pi$
$283$	1.70979e15	0.197847	0.0989237	+	0.995095i	$0.468460\pi$
$284$	−1.62221e16	−1.83458
$285$	9.70375e14	0.107263
$286$	1.39340e16	1.50556
$287$	1.59030e16	1.67976
$288$	−4.57620e15	−0.472557
$289$	1.58980e16	1.60511
$290$	−1.04542e16	−1.03205
$291$	−2.59702e15	−0.250709
$292$	1.10939e16	1.04736
$293$	1.05078e15	0.0970220	0.0485110	−	0.998823i	$-0.484552\pi$
$293$	1.05078e15	0.0970220	0.0485110	+	0.998823i	$0.484552\pi$
$294$	−2.76410e15	−0.249630
$295$	−5.63745e14	−0.0498012
$296$	5.63009e15	0.486541
$297$	3.65246e15	0.308794
$298$	−1.45442e16	−1.20305
$299$	3.28554e15	0.265916
$300$	7.59572e15	0.601563
$301$	−9.51799e13	−0.00737672
$302$	3.82237e16	2.89927
$303$	−1.37339e15	−0.101957
$304$	−4.88467e15	−0.354942
$305$	4.50387e15	0.320359
$306$	−1.15136e16	−0.801717
$307$	5.35873e15	0.365311	0.182655	−	0.983177i	$-0.441531\pi$
$307$	5.35873e15	0.365311	0.182655	+	0.983177i	$0.441531\pi$
$308$	3.33275e16	2.22445
$309$	7.95746e15	0.520049
$310$	−1.03589e16	−0.662920
$311$	1.92965e16	1.20930	0.604652	−	0.796490i	$-0.293312\pi$
$311$	1.92965e16	1.20930	0.604652	+	0.796490i	$0.293312\pi$
$312$	1.94659e15	0.119473
$313$	−1.29491e16	−0.778395	−0.389197	−	0.921154i	$-0.627248\pi$
$313$	−1.29491e16	−0.778395	−0.389197	+	0.921154i	$0.627248\pi$
$314$	2.70942e16	1.59527
$315$	2.51121e15	0.144832
$316$	1.22028e16	0.689433
$317$	2.23239e16	1.23562	0.617809	−	0.786329i	$-0.288021\pi$
$317$	2.23239e16	1.23562	0.617809	+	0.786329i	$0.288021\pi$
$318$	6.68934e15	0.362750
$319$	−5.46762e16	−2.90508
$320$	1.01521e16	0.528546
$321$	8.42275e15	0.429706
$322$	1.42968e16	0.714786
$323$	−1.59983e16	−0.783893
$324$	2.82391e15	0.135615
$325$	1.14196e16	0.537537
$326$	−4.20173e16	−1.93871
$327$	6.90744e15	0.312433
$328$	−1.09602e16	−0.486002
$329$	1.02631e16	0.446174
$330$	−1.23887e16	−0.528062
$331$	8.35829e15	0.349329	0.174665	−	0.984628i	$-0.444116\pi$
$331$	8.35829e15	0.349329	0.174665	+	0.984628i	$0.444116\pi$
$332$	2.99757e16	1.22849
$333$	1.22793e16	0.493499
$334$	−6.53585e16	−2.57602
$335$	−4.26172e15	−0.164738
$336$	−1.26409e16	−0.479263
$337$	−7.92605e15	−0.294756	−0.147378	−	0.989080i	$-0.547083\pi$
$337$	−7.92605e15	−0.294756	−0.147378	+	0.989080i	$0.547083\pi$
$338$	−2.46530e16	−0.899314
$339$	2.64660e16	0.947089
$340$	2.14656e16	0.753581
$341$	−5.41777e16	−1.86603
$342$	7.13873e15	0.241241
$343$	2.43163e16	0.806279
$344$	6.55970e13	0.00213429
$345$	−2.92116e15	−0.0932677
$346$	9.29141e15	0.291130
$347$	2.58718e16	0.795581	0.397791	−	0.917476i	$-0.369777\pi$
$347$	2.58718e16	0.795581	0.397791	+	0.917476i	$0.369777\pi$
$348$	−4.22730e16	−1.27585
$349$	−5.08818e16	−1.50729	−0.753646	−	0.657281i	$-0.771707\pi$
$349$	−5.08818e16	−1.50729	−0.753646	+	0.657281i	$0.771707\pi$
$350$	4.96915e16	1.44491
$351$	4.24553e15	0.121181
$352$	8.11808e16	2.27471
$353$	−4.64269e16	−1.27713	−0.638563	−	0.769569i	$-0.720471\pi$
$353$	−4.64269e16	−1.27713	−0.638563	+	0.769569i	$0.720471\pi$
$354$	−4.14728e15	−0.112006
$355$	2.16838e16	0.574979
$356$	−9.36656e14	−0.0243868
$357$	−4.14016e16	−1.05846
$358$	5.25474e16	1.31920
$359$	−4.19247e16	−1.03361	−0.516805	−	0.856103i	$-0.672879\pi$
$359$	−4.19247e16	−1.03361	−0.516805	+	0.856103i	$0.672879\pi$
$360$	−1.73070e15	−0.0419040
$361$	−3.21336e16	−0.764123
$362$	9.69535e16	2.26442
$363$	−3.96268e16	−0.909068
$364$	3.87390e16	0.872951
$365$	−1.48291e16	−0.328254
$366$	3.31335e16	0.720510
$367$	3.96632e16	0.847340	0.423670	−	0.905817i	$-0.360742\pi$
$367$	3.96632e16	0.847340	0.423670	+	0.905817i	$0.360742\pi$
$368$	1.47045e16	0.308631
$369$	−2.39043e16	−0.492953
$370$	−4.16498e16	−0.843922
$371$	2.40541e16	0.478916
$372$	−4.18877e16	−0.819515
$373$	−2.43484e16	−0.468127	−0.234063	−	0.972221i	$-0.575202\pi$
$373$	−2.43484e16	−0.468127	−0.234063	+	0.972221i	$0.575202\pi$
$374$	2.04248e17	3.85916
$375$	−2.20466e16	−0.409390
$376$	−7.07321e15	−0.129091
$377$	−6.35542e16	−1.14005
$378$	1.84742e16	0.325738
$379$	−2.87789e16	−0.498793	−0.249396	−	0.968402i	$-0.580232\pi$
$379$	−2.87789e16	−0.498793	−0.249396	+	0.968402i	$0.580232\pi$
$380$	−1.33092e16	−0.226757
$381$	−1.35307e16	−0.226625
$382$	−1.61710e17	−2.66272
$383$	1.90404e16	0.308237	0.154118	−	0.988052i	$-0.450746\pi$
$383$	1.90404e16	0.308237	0.154118	+	0.988052i	$0.450746\pi$
$384$	2.32617e16	0.370245
$385$	−4.45484e16	−0.697167
$386$	1.00963e17	1.55362
$387$	1.43068e14	0.00216482
$388$	3.56195e16	0.530008
$389$	−1.61772e16	−0.236718	−0.118359	−	0.992971i	$-0.537763\pi$
$389$	−1.61772e16	−0.236718	−0.118359	+	0.992971i	$0.537763\pi$
$390$	−1.44003e16	−0.207230
$391$	4.81602e16	0.681616
$392$	6.85013e15	0.0953541
$393$	1.97058e15	0.0269801
$394$	1.01636e17	1.36874
$395$	−1.63113e16	−0.216076
$396$	−5.00956e16	−0.652801
$397$	−8.32889e16	−1.06770	−0.533849	−	0.845580i	$-0.679255\pi$
$397$	−8.32889e16	−1.06770	−0.533849	+	0.845580i	$0.679255\pi$
$398$	−1.29822e17	−1.63722
$399$	2.56701e16	0.318495
$400$	5.11086e16	0.623884
$401$	8.60887e16	1.03397	0.516985	−	0.855995i	$-0.327054\pi$
$401$	8.60887e16	1.03397	0.516985	+	0.855995i	$0.327054\pi$
$402$	−3.13520e16	−0.370507
$403$	−6.29749e16	−0.732292
$404$	1.88368e16	0.215540
$405$	−3.77468e15	−0.0425033
$406$	−2.76552e17	−3.06449
$407$	−2.17832e17	−2.37552
$408$	2.85335e16	0.306242
$409$	−5.96685e16	−0.630294	−0.315147	−	0.949043i	$-0.602054\pi$
$409$	−5.96685e16	−0.630294	−0.315147	+	0.949043i	$0.602054\pi$
$410$	8.10805e16	0.842988
$411$	−4.95710e16	−0.507290
$412$	−1.09141e17	−1.09940
$413$	−1.49132e16	−0.147875
$414$	−2.14900e16	−0.209766
$415$	−4.00681e16	−0.385023
$416$	9.43626e16	0.892675
$417$	−4.52058e16	−0.421027
$418$	−1.26639e17	−1.16124
$419$	1.85874e17	1.67813	0.839067	−	0.544027i	$-0.183101\pi$
$419$	1.85874e17	1.67813	0.839067	+	0.544027i	$0.183101\pi$
$420$	−3.44427e16	−0.306180
$421$	1.26858e17	1.11041	0.555206	−	0.831713i	$-0.312639\pi$
$421$	1.26858e17	1.11041	0.555206	+	0.831713i	$0.312639\pi$
$422$	−8.21975e16	−0.708480
$423$	−1.54268e16	−0.130937
$424$	−1.65779e16	−0.138564
$425$	1.67391e17	1.37786
$426$	1.59521e17	1.29317
$427$	1.19144e17	0.951245
$428$	−1.15523e17	−0.908413
$429$	−7.53148e16	−0.583322
$430$	−4.85268e14	−0.00370201
$431$	5.47767e16	0.411618	0.205809	−	0.978592i	$-0.434018\pi$
$431$	5.47767e16	0.411618	0.205809	+	0.978592i	$0.434018\pi$
$432$	1.90010e16	0.140647
$433$	−1.49315e17	−1.08876	−0.544379	−	0.838840i	$-0.683235\pi$
$433$	−1.49315e17	−1.08876	−0.544379	+	0.838840i	$0.683235\pi$
$434$	−2.74031e17	−1.96841
$435$	5.65058e16	0.399865
$436$	−9.47394e16	−0.660493
$437$	−2.98606e16	−0.205102
$438$	−1.09092e17	−0.738266
$439$	−1.17806e17	−0.785501	−0.392751	−	0.919645i	$-0.628476\pi$
$439$	−1.17806e17	−0.785501	−0.392751	+	0.919645i	$0.628476\pi$
$440$	3.07023e16	0.201710
$441$	1.49402e16	0.0967178
$442$	2.37413e17	1.51447
$443$	7.22267e16	0.454019	0.227009	−	0.973893i	$-0.427105\pi$
$443$	7.22267e16	0.454019	0.227009	+	0.973893i	$0.427105\pi$
$444$	−1.68418e17	−1.04327
$445$	1.25202e15	0.00764310
$446$	5.23504e16	0.314952
$447$	7.86130e16	0.466118
$448$	2.68562e17	1.56942
$449$	−9.25530e16	−0.533076	−0.266538	−	0.963824i	$-0.585880\pi$
$449$	−9.25530e16	−0.533076	−0.266538	+	0.963824i	$0.585880\pi$
$450$	−7.46929e16	−0.424032
$451$	4.24058e17	2.37289
$452$	−3.62996e17	−2.00218
$453$	−2.06603e17	−1.12331
$454$	2.09532e17	1.12302
$455$	−5.17819e16	−0.273592
$456$	−1.76915e16	−0.0921498
$457$	−3.20856e17	−1.64761	−0.823806	−	0.566872i	$-0.808153\pi$
$457$	−3.20856e17	−1.64761	−0.823806	+	0.566872i	$0.808153\pi$
$458$	−9.70720e16	−0.491437
$459$	6.22320e16	0.310621
$460$	4.00654e16	0.197171
$461$	−1.49409e17	−0.724972	−0.362486	−	0.931989i	$-0.618072\pi$
$461$	−1.49409e17	−0.724972	−0.362486	+	0.931989i	$0.618072\pi$
$462$	−3.27727e17	−1.56798
$463$	−1.00024e17	−0.471876	−0.235938	−	0.971768i	$-0.575816\pi$
$463$	−1.00024e17	−0.471876	−0.235938	+	0.971768i	$0.575816\pi$
$464$	−2.84439e17	−1.32319
$465$	5.59907e16	0.256845
$466$	−4.64093e17	−2.09941
$467$	1.17638e17	0.524793	0.262396	−	0.964960i	$-0.415487\pi$
$467$	1.17638e17	0.524793	0.262396	+	0.964960i	$0.415487\pi$
$468$	−5.82299e16	−0.256181
$469$	−1.12738e17	−0.489158
$470$	5.23256e16	0.223913
$471$	−1.46447e17	−0.618078
$472$	1.02780e16	0.0427844
$473$	−2.53799e15	−0.0104206
$474$	−1.19997e17	−0.485970
$475$	−1.03787e17	−0.414604
$476$	5.67846e17	2.23761
$477$	−3.61565e16	−0.140546
$478$	−1.45467e17	−0.557808
$479$	−4.54898e17	−1.72081	−0.860406	−	0.509610i	$-0.829790\pi$
$479$	−4.54898e17	−1.72081	−0.860406	+	0.509610i	$0.829790\pi$
$480$	−8.38974e16	−0.313098
$481$	−2.53203e17	−0.932235
$482$	−2.53993e17	−0.922606
$483$	−7.72757e16	−0.276941
$484$	5.43504e17	1.92180
$485$	−4.76121e16	−0.166110
$486$	−2.77691e16	−0.0955930
$487$	3.44834e17	1.17131	0.585655	−	0.810560i	$-0.300837\pi$
$487$	3.44834e17	1.17131	0.585655	+	0.810560i	$0.300837\pi$
$488$	−8.21131e16	−0.275222
$489$	2.27108e17	0.751146
$490$	−5.06754e16	−0.165395
$491$	2.77257e17	0.893002	0.446501	−	0.894783i	$-0.352670\pi$
$491$	2.77257e17	0.893002	0.446501	+	0.894783i	$0.352670\pi$
$492$	3.27861e17	1.04212
$493$	−9.31593e17	−2.92228
$494$	−1.47203e17	−0.455712
$495$	6.69621e16	0.204595
$496$	−2.81846e17	−0.849925
$497$	5.73619e17	1.70729
$498$	−2.94768e17	−0.865943
$499$	−3.32049e17	−0.962829	−0.481414	−	0.876493i	$-0.659877\pi$
$499$	−3.32049e17	−0.962829	−0.481414	+	0.876493i	$0.659877\pi$
$500$	3.02381e17	0.865465
$501$	3.53269e17	0.998068
$502$	−3.17641e17	−0.885856
$503$	4.23206e17	1.16509	0.582546	−	0.812798i	$-0.302056\pi$
$503$	4.23206e17	1.16509	0.582546	+	0.812798i	$0.302056\pi$
$504$	−4.57836e16	−0.124426
$505$	−2.51789e16	−0.0675528
$506$	3.81228e17	1.00973
$507$	1.33252e17	0.348435
$508$	1.85581e17	0.479093
$509$	−4.47151e17	−1.13970	−0.569848	−	0.821750i	$-0.692998\pi$
$509$	−4.47151e17	−1.13970	−0.569848	+	0.821750i	$0.692998\pi$
$510$	−2.11083e17	−0.531187
$511$	−3.92284e17	−0.974687
$512$	5.20222e17	1.27624
$513$	−3.85855e16	−0.0934677
$514$	7.68650e17	1.83852
$515$	1.45887e17	0.344565
$516$	−1.96226e15	−0.00457650
$517$	2.73668e17	0.630282
$518$	−1.10179e18	−2.50586
$519$	−5.02210e16	−0.112797
$520$	3.56876e16	0.0791580
$521$	−4.31177e17	−0.944518	−0.472259	−	0.881460i	$-0.656561\pi$
$521$	−4.31177e17	−0.944518	−0.472259	+	0.881460i	$0.656561\pi$
$522$	4.15694e17	0.899323
$523$	8.27295e17	1.76766	0.883831	−	0.467806i	$-0.154956\pi$
$523$	8.27295e17	1.76766	0.883831	+	0.467806i	$0.154956\pi$
$524$	−2.70276e16	−0.0570367
$525$	−2.68588e17	−0.559823
$526$	1.61365e17	0.332201
$527$	−9.23100e17	−1.87707
$528$	−3.37073e17	−0.677024
$529$	−4.14146e17	−0.821658
$530$	1.22638e17	0.240344
$531$	2.24165e16	0.0433963
$532$	−3.52079e17	−0.673310
$533$	4.92914e17	0.931203
$534$	9.21066e15	0.0171899
$535$	1.54418e17	0.284707
$536$	7.76982e16	0.141527
$537$	−2.84024e17	−0.511119
$538$	−3.42531e17	−0.608997
$539$	−2.65036e17	−0.465563
$540$	5.17719e16	0.0898535
$541$	−2.74537e17	−0.470781	−0.235390	−	0.971901i	$-0.575637\pi$
$541$	−2.74537e17	−0.470781	−0.235390	+	0.971901i	$0.575637\pi$
$542$	−4.22624e17	−0.716076
$543$	−5.24043e17	−0.877340
$544$	1.38319e18	2.28817
$545$	1.26637e17	0.207006
$546$	−3.80942e17	−0.615328
$547$	8.76432e17	1.39895	0.699473	−	0.714659i	$-0.253418\pi$
$547$	8.76432e17	1.39895	0.699473	+	0.714659i	$0.253418\pi$
$548$	6.79894e17	1.07243
$549$	−1.79090e17	−0.279158
$550$	1.32504e18	2.04113
$551$	5.77612e17	0.879329
$552$	5.32576e16	0.0801267
$553$	−4.31494e17	−0.641596
$554$	−7.51260e17	−1.10402
$555$	2.25121e17	0.326973
$556$	6.20023e17	0.890065
$557$	3.70670e17	0.525931	0.262965	−	0.964805i	$-0.415299\pi$
$557$	3.70670e17	0.525931	0.262965	+	0.964805i	$0.415299\pi$
$558$	4.11905e17	0.577663
$559$	−2.95010e15	−0.00408941
$560$	−2.31751e17	−0.317541
$561$	−1.10398e18	−1.49521
$562$	7.88073e17	1.05507
$563$	5.19288e17	0.687232	0.343616	−	0.939110i	$-0.388348\pi$
$563$	5.19288e17	0.687232	0.343616	+	0.939110i	$0.388348\pi$
$564$	2.11587e17	0.276805
$565$	4.85212e17	0.627505
$566$	2.30604e17	0.294822
$567$	−9.98546e16	−0.126205
$568$	−3.95332e17	−0.493967
$569$	1.31973e18	1.63025	0.815125	−	0.579285i	$-0.196668\pi$
$569$	1.31973e18	1.63025	0.815125	+	0.579285i	$0.196668\pi$
$570$	1.30877e17	0.159837
$571$	8.34383e17	1.00747	0.503734	−	0.863859i	$-0.331959\pi$
$571$	8.34383e17	1.00747	0.503734	+	0.863859i	$0.331959\pi$
$572$	1.03298e18	1.23316
$573$	8.74059e17	1.03166
$574$	2.14488e18	2.50309
$575$	3.12434e17	0.360510
$576$	−4.03685e17	−0.460571
$577$	−1.47811e18	−1.66750	−0.833749	−	0.552144i	$-0.813810\pi$
$577$	−1.47811e18	−1.66750	−0.833749	+	0.552144i	$0.813810\pi$
$578$	2.14420e18	2.39185
$579$	−5.45715e17	−0.601943
$580$	−7.75009e17	−0.845327
$581$	−1.05995e18	−1.14325
$582$	−3.50267e17	−0.373594
$583$	6.41409e17	0.676534
$584$	2.70358e17	0.282005
$585$	7.78351e16	0.0802901
$586$	1.41721e17	0.144577
$587$	−3.85324e17	−0.388757	−0.194379	−	0.980927i	$-0.562269\pi$
$587$	−3.85324e17	−0.388757	−0.194379	+	0.980927i	$0.562269\pi$
$588$	−2.04914e17	−0.204465
$589$	5.72347e17	0.564820
$590$	−7.60338e16	−0.0742111
$591$	−5.49350e17	−0.530311
$592$	−1.13322e18	−1.08199
$593$	2.28206e17	0.215512	0.107756	−	0.994177i	$-0.465633\pi$
$593$	2.28206e17	0.215512	0.107756	+	0.994177i	$0.465633\pi$
$594$	4.92618e17	0.460149
$595$	−7.59032e17	−0.701293
$596$	−1.07822e18	−0.985388
$597$	7.01699e17	0.634333
$598$	4.43130e17	0.396254
$599$	−1.99623e18	−1.76578	−0.882888	−	0.469583i	$-0.844404\pi$
$599$	−1.99623e18	−1.76578	−0.882888	+	0.469583i	$0.844404\pi$
$600$	1.85108e17	0.161973
$601$	−7.04930e17	−0.610186	−0.305093	−	0.952323i	$-0.598687\pi$
$601$	−7.04930e17	−0.610186	−0.305093	+	0.952323i	$0.598687\pi$
$602$	−1.28372e16	−0.0109924
$603$	1.69461e17	0.143551
$604$	2.83368e18	2.37471
$605$	−7.26495e17	−0.602313
$606$	−1.85233e17	−0.151931
$607$	−1.22628e18	−0.995093	−0.497546	−	0.867437i	$-0.665766\pi$
$607$	−1.22628e18	−0.995093	−0.497546	+	0.867437i	$0.665766\pi$
$608$	−8.57614e17	−0.688523
$609$	1.49479e18	1.18732
$610$	6.07450e17	0.477382
$611$	3.18104e17	0.247344
$612$	−8.53547e17	−0.656664
$613$	1.22158e18	0.929885	0.464942	−	0.885341i	$-0.346075\pi$
$613$	1.22158e18	0.929885	0.464942	+	0.885341i	$0.346075\pi$
$614$	7.22746e17	0.544367
$615$	−4.38248e17	−0.326612
$616$	8.12190e17	0.598940
$617$	2.06587e18	1.50747	0.753736	−	0.657178i	$-0.228250\pi$
$617$	2.06587e18	1.50747	0.753736	+	0.657178i	$0.228250\pi$
$618$	1.07324e18	0.774950
$619$	−3.43252e17	−0.245258	−0.122629	−	0.992453i	$-0.539133\pi$
$619$	−3.43252e17	−0.245258	−0.122629	+	0.992453i	$0.539133\pi$
$620$	−7.67944e17	−0.542979
$621$	1.16156e17	0.0812727
$622$	2.60257e18	1.80204
$623$	3.31205e16	0.0226947
$624$	−3.91806e17	−0.265687
$625$	8.67880e17	0.582425
$626$	−1.74647e18	−1.15992
$627$	6.84498e17	0.449918
$628$	2.00860e18	1.30664
$629$	−3.71151e18	−2.38958
$630$	3.38694e17	0.215821
$631$	−1.41568e18	−0.892841	−0.446421	−	0.894823i	$-0.647301\pi$
$631$	−1.41568e18	−0.892841	−0.446421	+	0.894823i	$0.647301\pi$
$632$	2.97381e17	0.185632
$633$	4.44285e17	0.274497
$634$	3.01088e18	1.84125
$635$	−2.48064e17	−0.150153
$636$	4.95907e17	0.297118
$637$	−3.08072e17	−0.182703
$638$	−7.37432e18	−4.32900
$639$	−8.62225e17	−0.501031
$640$	4.26467e17	0.245310
$641$	−1.97048e18	−1.12200	−0.561001	−	0.827815i	$-0.689584\pi$
$641$	−1.97048e18	−1.12200	−0.561001	+	0.827815i	$0.689584\pi$
$642$	1.13600e18	0.640325
$643$	1.68474e18	0.940075	0.470038	−	0.882646i	$-0.344240\pi$
$643$	1.68474e18	0.940075	0.470038	+	0.882646i	$0.344240\pi$
$644$	1.05988e18	0.585461
$645$	2.62292e15	0.00143432
$646$	−2.15773e18	−1.16812
$647$	−2.33694e18	−1.25247	−0.626237	−	0.779632i	$-0.715406\pi$
$647$	−2.33694e18	−1.25247	−0.626237	+	0.779632i	$0.715406\pi$
$648$	6.88187e16	0.0365148
$649$	−3.97663e17	−0.208893
$650$	1.54019e18	0.801009
$651$	1.48116e18	0.762652
$652$	−3.11491e18	−1.58795
$653$	−1.68273e18	−0.849334	−0.424667	−	0.905350i	$-0.639609\pi$
$653$	−1.68273e18	−0.849334	−0.424667	+	0.905350i	$0.639609\pi$
$654$	9.31625e17	0.465571
$655$	3.61275e16	0.0178759
$656$	2.20605e18	1.08079
$657$	5.89655e17	0.286038
$658$	1.38421e18	0.664865
$659$	−5.93277e17	−0.282164	−0.141082	−	0.989998i	$-0.545058\pi$
$659$	−5.93277e17	−0.282164	−0.141082	+	0.989998i	$0.545058\pi$
$660$	−9.18422e17	−0.432521
$661$	1.31036e17	0.0611057	0.0305529	−	0.999533i	$-0.490273\pi$
$661$	1.31036e17	0.0611057	0.0305529	+	0.999533i	$0.490273\pi$
$662$	1.12730e18	0.520552
$663$	−1.28324e18	−0.586774
$664$	7.30508e17	0.330775
$665$	4.70620e17	0.211023
$666$	1.65614e18	0.735386
$667$	−1.73881e18	−0.764600
$668$	−4.84528e18	−2.10995
$669$	−2.82959e17	−0.122026
$670$	−5.74790e17	−0.245484
$671$	3.17701e18	1.34376
$672$	−2.21940e18	−0.929684
$673$	1.17397e18	0.487034	0.243517	−	0.969897i	$-0.421699\pi$
$673$	1.17397e18	0.487034	0.243517	+	0.969897i	$0.421699\pi$
$674$	−1.06901e18	−0.439229
$675$	4.03723e17	0.164289
$676$	−1.82762e18	−0.736603
$677$	4.52500e18	1.80631	0.903155	−	0.429314i	$-0.141245\pi$
$677$	4.52500e18	1.80631	0.903155	+	0.429314i	$0.141245\pi$
$678$	3.56954e18	1.41130
$679$	−1.25952e18	−0.493232
$680$	5.23117e17	0.202904
$681$	−1.13254e18	−0.435109
$682$	−7.30710e18	−2.78065
$683$	−2.60120e18	−0.980481	−0.490240	−	0.871587i	$-0.663091\pi$
$683$	−2.60120e18	−0.980481	−0.490240	+	0.871587i	$0.663091\pi$
$684$	5.29222e17	0.197594
$685$	−9.08805e17	−0.336110
$686$	3.27960e18	1.20147
$687$	5.24683e17	0.190405
$688$	−1.32033e16	−0.00474631
$689$	7.45558e17	0.265495
$690$	−3.93985e17	−0.138983
$691$	−1.92826e18	−0.673842	−0.336921	−	0.941533i	$-0.609385\pi$
$691$	−1.92826e18	−0.673842	−0.336921	+	0.941533i	$0.609385\pi$
$692$	6.88809e17	0.238456
$693$	1.77140e18	0.607506
$694$	3.48940e18	1.18553
$695$	−8.28776e17	−0.278956
$696$	−1.03019e18	−0.343526
$697$	7.22525e18	2.38693
$698$	−6.86257e18	−2.24609
$699$	2.50847e18	0.813405
$700$	3.68383e18	1.18348
$701$	−7.68422e17	−0.244587	−0.122293	−	0.992494i	$-0.539025\pi$
$701$	−7.68422e17	−0.244587	−0.122293	+	0.992494i	$0.539025\pi$
$702$	5.72606e17	0.180578
$703$	2.30123e18	0.719036
$704$	7.16128e18	2.21701
$705$	−2.82825e17	−0.0867539
$706$	−6.26172e18	−1.90311
$707$	−6.66077e17	−0.200585
$708$	−3.07454e17	−0.0917412
$709$	4.17120e18	1.23328	0.616639	−	0.787246i	$-0.288494\pi$
$709$	4.17120e18	1.23328	0.616639	+	0.787246i	$0.288494\pi$
$710$	2.92456e18	0.856802
$711$	6.48593e17	0.188287
$712$	−2.28263e16	−0.00656622
$713$	−1.72296e18	−0.491126
$714$	−5.58394e18	−1.57726
$715$	−1.38078e18	−0.386486
$716$	3.89554e18	1.08052
$717$	7.86266e17	0.216120
$718$	−5.65450e18	−1.54023
$719$	4.38509e18	1.18370	0.591849	−	0.806049i	$-0.298398\pi$
$719$	4.38509e18	1.18370	0.591849	+	0.806049i	$0.298398\pi$
$720$	3.48353e17	0.0931876
$721$	3.85927e18	1.02312
$722$	−4.33395e18	−1.13865
$723$	1.37286e18	0.357459
$724$	7.18755e18	1.85473
$725$	−6.04360e18	−1.54560
$726$	−5.34458e18	−1.35464
$727$	1.53855e18	0.386491	0.193245	−	0.981150i	$-0.438099\pi$
$727$	1.53855e18	0.386491	0.193245	+	0.981150i	$0.438099\pi$
$728$	9.44070e17	0.235045
$729$	1.50095e17	0.0370370
$730$	−2.00004e18	−0.489147
$731$	−4.32433e16	−0.0104823
$732$	2.45632e18	0.590150
$733$	−7.85998e18	−1.87174	−0.935870	−	0.352346i	$-0.885384\pi$
$733$	−7.85998e18	−1.87174	−0.935870	+	0.352346i	$0.885384\pi$
$734$	5.34948e18	1.26266
$735$	2.73905e17	0.0640815
$736$	2.58171e18	0.598690
$737$	−3.00620e18	−0.691001
$738$	−3.22404e18	−0.734572
$739$	8.34433e18	1.88453	0.942264	−	0.334872i	$-0.108693\pi$
$739$	8.34433e18	1.88453	0.942264	+	0.334872i	$0.108693\pi$
$740$	−3.08767e18	−0.691233
$741$	7.95644e17	0.176563
$742$	3.24425e18	0.713655
$743$	−1.70635e18	−0.372084	−0.186042	−	0.982542i	$-0.559566\pi$
$743$	−1.70635e18	−0.372084	−0.186042	+	0.982542i	$0.559566\pi$
$744$	−1.02080e18	−0.220657
$745$	1.44124e18	0.308832
$746$	−3.28394e18	−0.697578
$747$	1.59325e18	0.335505
$748$	1.51417e19	3.16093
$749$	4.08493e18	0.845381
$750$	−2.97348e18	−0.610052
$751$	−7.13654e17	−0.145154	−0.0725769	−	0.997363i	$-0.523122\pi$
$751$	−7.13654e17	−0.145154	−0.0725769	+	0.997363i	$0.523122\pi$
$752$	1.42368e18	0.287077
$753$	1.71688e18	0.343221
$754$	−8.57173e18	−1.69885
$755$	−3.78774e18	−0.744260
$756$	1.36956e18	0.266803
$757$	5.61909e18	1.08528	0.542641	−	0.839964i	$-0.317424\pi$
$757$	5.61909e18	1.08528	0.542641	+	0.839964i	$0.317424\pi$
$758$	−3.88149e18	−0.743274
$759$	−2.06057e18	−0.391216
$760$	−3.24346e17	−0.0610549
$761$	−6.17927e18	−1.15329	−0.576643	−	0.816996i	$-0.695638\pi$
$761$	−6.17927e18	−1.15329	−0.576643	+	0.816996i	$0.695638\pi$
$762$	−1.82492e18	−0.337705
$763$	3.35002e18	0.614664
$764$	−1.19882e19	−2.18096
$765$	1.14092e18	0.205806
$766$	2.56803e18	0.459318
$767$	−4.62234e17	−0.0819770
$768$	−1.39896e18	−0.246013
$769$	−4.33858e18	−0.756530	−0.378265	−	0.925697i	$-0.623479\pi$
$769$	−4.33858e18	−0.756530	−0.378265	+	0.925697i	$0.623479\pi$
$770$	−6.00836e18	−1.03888
$771$	−4.15463e18	−0.712326
$772$	7.48479e18	1.27253
$773$	−4.48737e18	−0.756528	−0.378264	−	0.925698i	$-0.623479\pi$
$773$	−4.48737e18	−0.756528	−0.378264	+	0.925698i	$0.623479\pi$
$774$	1.92960e16	0.00322590
$775$	−5.98850e18	−0.992789
$776$	8.68048e17	0.142706
$777$	5.95531e18	0.970885
$778$	−2.18187e18	−0.352745
$779$	−4.47985e18	−0.718241
$780$	−1.06755e18	−0.169736
$781$	1.52957e19	2.41178
$782$	6.49550e18	1.01571
$783$	−2.24687e18	−0.348438
$784$	−1.37878e18	−0.212052
$785$	−2.68486e18	−0.409515
$786$	2.65778e17	0.0402042
$787$	1.09647e19	1.64498	0.822490	−	0.568780i	$-0.192584\pi$
$787$	1.09647e19	1.64498	0.822490	+	0.568780i	$0.192584\pi$
$788$	7.53464e18	1.12109
$789$	−8.72192e17	−0.128710
$790$	−2.19994e18	−0.321985
$791$	1.28357e19	1.86325
$792$	−1.22083e18	−0.175769
$793$	3.69288e18	0.527339
$794$	−1.12334e19	−1.59103
$795$	−6.62872e17	−0.0931201
$796$	−9.62419e18	−1.34100
$797$	1.28001e19	1.76902	0.884511	−	0.466519i	$-0.154492\pi$
$797$	1.28001e19	1.76902	0.884511	+	0.466519i	$0.154492\pi$
$798$	3.46219e18	0.474605
$799$	4.66285e18	0.634012
$800$	8.97327e18	1.21022
$801$	−4.97845e16	−0.00666013
$802$	1.16110e19	1.54077
$803$	−1.04604e19	−1.37688
$804$	−2.32425e18	−0.303472
$805$	−1.41673e18	−0.183490
$806$	−8.49359e18	−1.09122
$807$	1.85141e18	0.235953
$808$	4.59053e17	0.0580349
$809$	−1.31724e19	−1.65196	−0.825980	−	0.563699i	$-0.809378\pi$
$809$	−1.31724e19	−1.65196	−0.825980	+	0.563699i	$0.809378\pi$
$810$	−5.09102e17	−0.0633362
$811$	1.30307e19	1.60817	0.804084	−	0.594516i	$-0.202656\pi$
$811$	1.30307e19	1.60817	0.804084	+	0.594516i	$0.202656\pi$
$812$	−2.05019e19	−2.51003
$813$	2.28433e18	0.277440
$814$	−2.93796e19	−3.53987
$815$	4.16366e18	0.497680
$816$	−5.74318e18	−0.681030
$817$	2.68120e16	0.00315417
$818$	−8.04765e18	−0.939231
$819$	2.05903e18	0.238406
$820$	6.01082e18	0.690468
$821$	−7.13270e18	−0.812874	−0.406437	−	0.913679i	$-0.633229\pi$
$821$	−7.13270e18	−0.812874	−0.406437	+	0.913679i	$0.633229\pi$
$822$	−6.68578e18	−0.755936
$823$	8.28500e17	0.0929381	0.0464690	−	0.998920i	$-0.485203\pi$
$823$	8.28500e17	0.0929381	0.0464690	+	0.998920i	$0.485203\pi$
$824$	−2.65977e18	−0.296017
$825$	−7.16195e18	−0.790825
$826$	−2.01138e18	−0.220355
$827$	9.87805e18	1.07371	0.536853	−	0.843676i	$-0.319613\pi$
$827$	9.87805e18	1.07371	0.536853	+	0.843676i	$0.319613\pi$
$828$	−1.59314e18	−0.171813
$829$	8.12329e18	0.869216	0.434608	−	0.900620i	$-0.356887\pi$
$829$	8.12329e18	0.869216	0.434608	+	0.900620i	$0.356887\pi$
$830$	−5.40409e18	−0.573740
$831$	4.06064e18	0.427747
$832$	8.32409e18	0.870032
$833$	−4.51579e18	−0.468318
$834$	−6.09703e18	−0.627392
$835$	6.47662e18	0.661281
$836$	−9.38828e18	−0.951142
$837$	−2.22638e18	−0.223813
$838$	2.50693e19	2.50067
$839$	−1.04529e19	−1.03462	−0.517312	−	0.855797i	$-0.673067\pi$
$839$	−1.04529e19	−1.03462	−0.517312	+	0.855797i	$0.673067\pi$
$840$	−8.39368e17	−0.0824399
$841$	2.33742e19	2.27805
$842$	1.71097e19	1.65468
$843$	−4.25961e18	−0.408781
$844$	−6.09362e18	−0.580296
$845$	2.44296e18	0.230860
$846$	−2.08065e18	−0.195115
$847$	−1.92185e19	−1.78845
$848$	3.33676e18	0.308143
$849$	−1.24644e18	−0.114227
$850$	2.25765e19	2.05321
$851$	−6.92749e18	−0.625222
$852$	1.18259e19	1.05920
$853$	1.41550e18	0.125818	0.0629089	−	0.998019i	$-0.479962\pi$
$853$	1.41550e18	0.125818	0.0629089	+	0.998019i	$0.479962\pi$
$854$	1.60693e19	1.41749
$855$	−7.07404e17	−0.0619281
$856$	−2.81529e18	−0.244593
$857$	−2.56090e18	−0.220809	−0.110405	−	0.993887i	$-0.535215\pi$
$857$	−2.56090e18	−0.220809	−0.110405	+	0.993887i	$0.535215\pi$
$858$	−1.01579e19	−0.869235
$859$	1.82650e19	1.55119	0.775594	−	0.631232i	$-0.217450\pi$
$859$	1.82650e19	1.55119	0.775594	+	0.631232i	$0.217450\pi$
$860$	−3.59749e16	−0.00303221
$861$	−1.15933e19	−0.969810
$862$	7.38788e18	0.613371
$863$	2.10135e19	1.73153	0.865763	−	0.500454i	$-0.166834\pi$
$863$	2.10135e19	1.73153	0.865763	+	0.500454i	$0.166834\pi$
$864$	3.33605e18	0.272831
$865$	−9.20721e17	−0.0747349
$866$	−2.01385e19	−1.62241
$867$	−1.15896e19	−0.926713
$868$	−2.03150e19	−1.61227
$869$	−1.15059e19	−0.906341
$870$	7.62109e18	0.595857
$871$	−3.49433e18	−0.271173
$872$	−2.30880e18	−0.177840
$873$	1.89323e18	0.144747
$874$	−4.02738e18	−0.305632
$875$	−1.06923e19	−0.805413
$876$	−8.08745e18	−0.604693
$877$	9.25588e18	0.686942	0.343471	−	0.939163i	$-0.388397\pi$
$877$	9.25588e18	0.686942	0.343471	+	0.939163i	$0.388397\pi$
$878$	−1.58888e19	−1.17051
$879$	−7.66015e17	−0.0560157
$880$	−6.17970e18	−0.448570
$881$	2.04727e19	1.47514	0.737568	−	0.675272i	$-0.235974\pi$
$881$	2.04727e19	1.47514	0.737568	+	0.675272i	$0.235974\pi$
$882$	2.01503e18	0.144124
$883$	1.55094e19	1.10116	0.550581	−	0.834781i	$-0.314406\pi$
$883$	1.55094e19	1.10116	0.550581	+	0.834781i	$0.314406\pi$
$884$	1.76004e19	1.24046
$885$	4.10970e17	0.0287527
$886$	9.74141e18	0.676555
$887$	1.17929e19	0.813053	0.406527	−	0.913639i	$-0.366740\pi$
$887$	1.17929e19	0.813053	0.406527	+	0.913639i	$0.366740\pi$
$888$	−4.10434e18	−0.280904
$889$	−6.56222e18	−0.445850
$890$	1.68863e17	0.0113893
$891$	−2.66265e18	−0.178282
$892$	3.88094e18	0.257968
$893$	−2.89109e18	−0.190777
$894$	1.06027e19	0.694584
$895$	−5.20712e18	−0.338648
$896$	1.12816e19	0.728401
$897$	−2.39516e18	−0.153527
$898$	−1.24829e19	−0.794362
$899$	3.33283e19	2.10559
$900$	−5.53728e18	−0.347312
$901$	1.09286e19	0.680537
$902$	5.71938e19	3.53595
$903$	6.93862e16	0.00425895
$904$	−8.84622e18	−0.539092
$905$	−9.60749e18	−0.581292
$906$	−2.78651e19	−1.67389
$907$	−2.96915e19	−1.77086	−0.885430	−	0.464772i	$-0.846136\pi$
$907$	−2.96915e19	−1.77086	−0.885430	+	0.464772i	$0.846136\pi$
$908$	1.55334e19	0.919834
$909$	1.00120e18	0.0588649
$910$	−6.98397e18	−0.407693
$911$	−7.50588e18	−0.435043	−0.217521	−	0.976056i	$-0.569797\pi$
$911$	−7.50588e18	−0.435043	−0.217521	+	0.976056i	$0.569797\pi$
$912$	3.56092e18	0.204926
$913$	−2.82639e19	−1.61500
$914$	−4.32747e19	−2.45518
$915$	−3.28332e18	−0.184959
$916$	−7.19633e18	−0.402523
$917$	9.55707e17	0.0530792
$918$	8.39340e18	0.462872
$919$	−2.60241e19	−1.42503	−0.712517	−	0.701655i	$-0.752445\pi$
$919$	−2.60241e19	−1.42503	−0.712517	+	0.701655i	$0.752445\pi$
$920$	9.76393e17	0.0530889
$921$	−3.90651e18	−0.210912
$922$	−2.01512e19	−1.08031
$923$	1.77793e19	0.946464
$924$	−2.42957e19	−1.28429
$925$	−2.40779e19	−1.26386
$926$	−1.34905e19	−0.703165
$927$	−5.80099e18	−0.300251
$928$	−4.99396e19	−2.56675
$929$	3.50576e19	1.78929	0.894643	−	0.446782i	$-0.147430\pi$
$929$	3.50576e19	1.78929	0.894643	+	0.446782i	$0.147430\pi$
$930$	7.55161e18	0.382737
$931$	2.79991e18	0.140919
$932$	−3.44050e19	−1.71957
$933$	−1.40671e19	−0.698192
$934$	1.58662e19	0.782018
$935$	−2.02398e19	−0.990672
$936$	−1.41906e18	−0.0689776
$937$	2.45513e19	1.18513	0.592567	−	0.805521i	$-0.298114\pi$
$937$	2.45513e19	1.18513	0.592567	+	0.805521i	$0.298114\pi$
$938$	−1.52053e19	−0.728917
$939$	9.43986e18	0.449407
$940$	3.87911e18	0.183401
$941$	2.50855e19	1.17785	0.588925	−	0.808188i	$-0.299551\pi$
$941$	2.50855e19	1.17785	0.588925	+	0.808188i	$0.299551\pi$
$942$	−1.97516e19	−0.921027
$943$	1.34859e19	0.624530
$944$	−2.06874e18	−0.0951454
$945$	−1.83067e18	−0.0836189
$946$	−3.42306e17	−0.0155282
$947$	2.91836e19	1.31481	0.657407	−	0.753535i	$-0.271653\pi$
$947$	2.91836e19	1.31481	0.657407	+	0.753535i	$0.271653\pi$
$948$	−8.89581e18	−0.398044
$949$	−1.21589e19	−0.540334
$950$	−1.39980e19	−0.617821
$951$	−1.62741e19	−0.713384
$952$	1.38384e19	0.602484
$953$	−2.68165e19	−1.15957	−0.579786	−	0.814769i	$-0.696864\pi$
$953$	−2.68165e19	−1.15957	−0.579786	+	0.814769i	$0.696864\pi$
$954$	−4.87653e18	−0.209434
$955$	1.60245e19	0.683537
$956$	−1.07841e19	−0.456885
$957$	3.98589e19	1.67725
$958$	−6.13533e19	−2.56426
$959$	−2.40413e19	−0.998015
$960$	−7.40092e18	−0.305156
$961$	8.60688e18	0.352487
$962$	−3.41501e19	−1.38917
$963$	−6.14019e18	−0.248091
$964$	−1.88295e19	−0.755681
$965$	−1.00048e19	−0.398824
$966$	−1.04224e19	−0.412682
$967$	−1.19721e19	−0.470869	−0.235434	−	0.971890i	$-0.575651\pi$
$967$	−1.19721e19	−0.470869	−0.235434	+	0.971890i	$0.575651\pi$
$968$	1.32452e19	0.517450
$969$	1.16627e19	0.452581
$970$	−6.42158e18	−0.247529
$971$	1.06370e19	0.407280	0.203640	−	0.979046i	$-0.434723\pi$
$971$	1.06370e19	0.407280	0.203640	+	0.979046i	$0.434723\pi$
$972$	−2.05863e18	−0.0782975
$973$	−2.19243e19	−0.828307
$974$	4.65087e19	1.74542
$975$	−8.32487e18	−0.310347
$976$	1.65276e19	0.612048
$977$	4.17938e19	1.53744	0.768718	−	0.639588i	$-0.220895\pi$
$977$	4.17938e19	1.53744	0.768718	+	0.639588i	$0.220895\pi$
$978$	3.06306e19	1.11932
$979$	8.83166e17	0.0320594
$980$	−3.75676e18	−0.135470
$981$	−5.03552e18	−0.180383
$982$	3.73944e19	1.33070
$983$	4.45066e19	1.57336	0.786678	−	0.617364i	$-0.211799\pi$
$983$	4.45066e19	1.57336	0.786678	+	0.617364i	$0.211799\pi$
$984$	7.98998e18	0.280594
$985$	−1.00715e19	−0.351363
$986$	−1.25646e20	−4.35462
$987$	−7.48179e18	−0.257599
$988$	−1.09127e19	−0.373261
$989$	−8.07132e16	−0.00274264
$990$	9.03136e18	0.304877
$991$	3.42352e19	1.14814	0.574069	−	0.818807i	$-0.305364\pi$
$991$	3.42352e19	1.14814	0.574069	+	0.818807i	$0.305364\pi$
$992$	−4.94844e19	−1.64870
$993$	−6.09319e18	−0.201685
$994$	7.73655e19	2.54411
$995$	1.28645e19	0.420285
$996$	−2.18523e19	−0.709270
$997$	2.62716e19	0.847164	0.423582	−	0.905858i	$-0.360773\pi$
$997$	2.62716e19	0.847164	0.423582	+	0.905858i	$0.360773\pi$
$998$	−4.47844e19	−1.43476
$999$	−8.95161e18	−0.284922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.d.1.28	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.d.1.28	✓	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)

\(f(q)\)	\(=\)	\(q+134.873 q^{2} -729.000 q^{3} +9998.64 q^{4} -13365.0 q^{5} -98322.2 q^{6} -353556. q^{7} +243667. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+134.873 q^{2} -729.000 q^{3} +9998.64 q^{4} -13365.0 q^{5} -98322.2 q^{6} -353556. q^{7} +243667. q^{8} +531441. q^{9} -1.80258e6 q^{10} -9.42765e6 q^{11} -7.28901e6 q^{12} -1.09585e7 q^{13} -4.76850e7 q^{14} +9.74312e6 q^{15} -4.90449e7 q^{16} -1.60632e8 q^{17} +7.16769e7 q^{18} +9.95959e7 q^{19} -1.33632e8 q^{20} +2.57742e8 q^{21} -1.27153e9 q^{22} -2.99818e8 q^{23} -1.77633e8 q^{24} -1.04208e9 q^{25} -1.47800e9 q^{26} -3.87420e8 q^{27} -3.53508e9 q^{28} +5.79956e9 q^{29} +1.31408e9 q^{30} +5.74669e9 q^{31} -8.61093e9 q^{32} +6.87275e9 q^{33} -2.16648e10 q^{34} +4.72529e9 q^{35} +5.31369e9 q^{36} +2.31057e10 q^{37} +1.34328e10 q^{38} +7.98872e9 q^{39} -3.25662e9 q^{40} -4.49802e10 q^{41} +3.47624e10 q^{42} +2.69208e8 q^{43} -9.42637e10 q^{44} -7.10274e9 q^{45} -4.04372e10 q^{46} -2.90282e10 q^{47} +3.57537e10 q^{48} +2.81127e10 q^{49} -1.40548e11 q^{50} +1.17101e11 q^{51} -1.09570e11 q^{52} -6.80349e10 q^{53} -5.22524e10 q^{54} +1.26001e11 q^{55} -8.61498e10 q^{56} -7.26054e10 q^{57} +7.82202e11 q^{58} +4.21805e10 q^{59} +9.74180e10 q^{60} -3.36989e11 q^{61} +7.75071e11 q^{62} -1.87894e11 q^{63} -7.59604e11 q^{64} +1.46460e11 q^{65} +9.26947e11 q^{66} +3.18870e11 q^{67} -1.60610e12 q^{68} +2.18567e11 q^{69} +6.37313e11 q^{70} -1.62243e12 q^{71} +1.29495e11 q^{72} +1.10954e12 q^{73} +3.11633e12 q^{74} +7.59675e11 q^{75} +9.95824e11 q^{76} +3.33320e12 q^{77} +1.07746e12 q^{78} +1.22044e12 q^{79} +6.55487e11 q^{80} +2.82430e11 q^{81} -6.06661e12 q^{82} +2.99798e12 q^{83} +2.57707e12 q^{84} +2.14685e12 q^{85} +3.63088e10 q^{86} -4.22788e12 q^{87} -2.29721e12 q^{88} -9.36783e10 q^{89} -9.57965e11 q^{90} +3.87443e12 q^{91} -2.99777e12 q^{92} -4.18934e12 q^{93} -3.91511e12 q^{94} -1.33110e12 q^{95} +6.27737e12 q^{96} +3.56244e12 q^{97} +3.79163e12 q^{98} -5.01024e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) \) 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

L-functions

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