LMFDB - Embedded newform 177.9.c.a.58.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,9,Mod(58,177)]

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, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	177.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$72.1060139808$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.4
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.77

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-29.4383i q^{2} -46.7654 q^{3} -610.615 q^{4} -616.312 q^{5} +1376.69i q^{6} -3233.41 q^{7} +10439.3i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q-29.4383i q^{2} -46.7654 q^{3} -610.615 q^{4} -616.312 q^{5} +1376.69i q^{6} -3233.41 q^{7} +10439.3i q^{8} +2187.00 q^{9} +18143.2i q^{10} -16327.4i q^{11} +28555.6 q^{12} +22558.2i q^{13} +95186.3i q^{14} +28822.1 q^{15} +150997. q^{16} -11817.3 q^{17} -64381.6i q^{18} +184894. q^{19} +376330. q^{20} +151212. q^{21} -480653. q^{22} +365066. i q^{23} -488197. i q^{24} -10784.2 q^{25} +664076. q^{26} -102276. q^{27} +1.97437e6 q^{28} +333403. q^{29} -848474. i q^{30} -730489. i q^{31} -1.77266e6i q^{32} +763559. i q^{33} +347881. i q^{34} +1.99279e6 q^{35} -1.33542e6 q^{36} +2.68652e6i q^{37} -5.44297e6i q^{38} -1.05494e6i q^{39} -6.43385e6i q^{40} -5.13105e6 q^{41} -4.45142e6i q^{42} +1.15417e6i q^{43} +9.96978e6i q^{44} -1.34787e6 q^{45} +1.07469e7 q^{46} +6.97887e6i q^{47} -7.06145e6 q^{48} +4.69017e6 q^{49} +317469. i q^{50} +552639. q^{51} -1.37744e7i q^{52} -1.05640e7 q^{53} +3.01083e6i q^{54} +1.00628e7i q^{55} -3.37545e7i q^{56} -8.64663e6 q^{57} -9.81481e6i q^{58} +(-1.21170e7 - 90073.3i) q^{59} -1.75992e7 q^{60} -1.31445e7i q^{61} -2.15044e7 q^{62} -7.07148e6 q^{63} -1.35287e7 q^{64} -1.39029e7i q^{65} +2.24779e7 q^{66} -9.27099e6i q^{67} +7.21581e6 q^{68} -1.70725e7i q^{69} -5.86645e7i q^{70} -6.40244e6 q^{71} +2.28307e7i q^{72} -1.74523e7i q^{73} +7.90865e7 q^{74} +504327. q^{75} -1.12899e8 q^{76} +5.27934e7i q^{77} -3.10558e7 q^{78} +5.50300e7 q^{79} -9.30615e7 q^{80} +4.78297e6 q^{81} +1.51050e8i q^{82} +6.16543e6i q^{83} -9.23322e7 q^{84} +7.28313e6 q^{85} +3.39770e7 q^{86} -1.55917e7 q^{87} +1.70447e8 q^{88} -7.65784e7i q^{89} +3.96792e7i q^{90} -7.29401e7i q^{91} -2.22915e8i q^{92} +3.41616e7i q^{93} +2.05446e8 q^{94} -1.13952e8 q^{95} +8.28989e7i q^{96} +6.58511e7i q^{97} -1.38071e8i q^{98} -3.57081e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	29.4383i		−	1.83990i	−0.392041	−	0.919948i	$-0.628231\pi$
$2$		−	29.4383i		−	1.83990i	0.392041	−	0.919948i	$-0.371769\pi$
$3$	−46.7654			−0.577350
$3$	−46.7654			−0.577350
$4$	−610.615			−2.38522
$5$	−616.312			−0.986100			−0.493050	−	0.870001i	$-0.664118\pi$
$5$	−616.312			−0.986100			−0.493050	+	0.870001i	$0.664118\pi$
$6$			1376.69i			1.06226i
$7$	−3233.41			−1.34670			−0.673348	−	0.739326i	$-0.735144\pi$
$7$	−3233.41			−1.34670			−0.673348	+	0.739326i	$0.735144\pi$
$8$			10439.3i			2.54865i
$9$	2187.00			0.333333
$10$			18143.2i			1.81432i
$11$		−	16327.4i		−	1.11519i	−0.830114	−	0.557593i	$-0.811725\pi$
$11$		−	16327.4i		−	1.11519i	0.830114	−	0.557593i	$-0.188275\pi$
$12$	28555.6			1.37710
$13$			22558.2i			0.789826i	0.918719	+	0.394913i	$0.129225\pi$
$13$			22558.2i			0.789826i	−0.918719	+	0.394913i	$0.870775\pi$
$14$			95186.3i			2.47778i
$15$	28822.1			0.569325
$16$	150997.			2.30404
$17$	−11817.3			−0.141489			−0.0707444	−	0.997494i	$-0.522537\pi$
$17$	−11817.3			−0.141489			−0.0707444	+	0.997494i	$0.522537\pi$
$18$		−	64381.6i		−	0.613299i
$19$	184894.			1.41876			0.709379	−	0.704828i	$-0.248976\pi$
$19$	184894.			1.41876			0.709379	+	0.704828i	$0.248976\pi$
$20$	376330.			2.35206
$21$	151212.			0.777515
$22$	−480653.			−2.05183
$23$			365066.i			1.30455i	0.757983	+	0.652274i	$0.226185\pi$
$23$			365066.i			1.30455i	−0.757983	+	0.652274i	$0.773815\pi$
$24$		−	488197.i		−	1.47146i
$25$	−10784.2			−0.0276075
$26$	664076.			1.45320
$27$	−102276.			−0.192450
$28$	1.97437e6			3.21216
$29$	333403.			0.471386			0.235693	−	0.971828i	$-0.424264\pi$
$29$	333403.			0.471386			0.235693	+	0.971828i	$0.424264\pi$
$30$		−	848474.i		−	1.04750i
$31$		−	730489.i		−	0.790982i	−0.918470	−	0.395491i	$-0.870574\pi$
$31$		−	730489.i		−	0.790982i	0.918470	−	0.395491i	$-0.129426\pi$
$32$		−	1.77266e6i		−	1.69054i
$33$			763559.i			0.643853i
$34$			347881.i			0.260324i
$35$	1.99279e6			1.32798
$36$	−1.33542e6			−0.795072
$37$			2.68652e6i			1.43345i	0.697356	+	0.716725i	$0.254360\pi$
$37$			2.68652e6i			1.43345i	−0.697356	+	0.716725i	$0.745640\pi$
$38$		−	5.44297e6i		−	2.61037i
$39$		−	1.05494e6i		−	0.456006i
$40$		−	6.43385e6i		−	2.51322i
$41$	−5.13105e6			−1.81581			−0.907906	−	0.419173i	$-0.862320\pi$
$41$	−5.13105e6			−1.81581			−0.907906	+	0.419173i	$0.862320\pi$
$42$		−	4.45142e6i		−	1.43055i
$43$			1.15417e6i			0.337596i	0.985651	+	0.168798i	$0.0539886\pi$
$43$			1.15417e6i			0.337596i	−0.985651	+	0.168798i	$0.946011\pi$
$44$			9.96978e6i			2.65996i
$45$	−1.34787e6			−0.328700
$46$	1.07469e7			2.40023
$47$			6.97887e6i			1.43019i	0.699027	+	0.715095i	$0.253617\pi$
$47$			6.97887e6i			1.43019i	−0.699027	+	0.715095i	$0.746383\pi$
$48$	−7.06145e6			−1.33024
$49$	4.69017e6			0.813588
$50$			317469.i			0.0507950i
$51$	552639.			0.0816886
$52$		−	1.37744e7i		−	1.88390i
$53$	−1.05640e7			−1.33883			−0.669413	−	0.742890i	$-0.733454\pi$
$53$	−1.05640e7			−1.33883			−0.669413	+	0.742890i	$0.733454\pi$
$54$			3.01083e6i			0.354088i
$55$			1.00628e7i			1.09968i
$56$		−	3.37545e7i		−	3.43226i
$57$	−8.64663e6			−0.819120
$58$		−	9.81481e6i		−	0.867301i
$59$	−1.21170e7	−	90073.3i	−0.999972	−	0.00743341i
$59$	−1.21170e7	−	90073.3i	−0.999972	−	0.00743341i
$60$	−1.75992e7			−1.35796
$61$		−	1.31445e7i		−	0.949345i	−0.880162	−	0.474673i	$-0.842567\pi$
$61$		−	1.31445e7i		−	0.949345i	0.880162	−	0.474673i	$-0.157433\pi$
$62$	−2.15044e7			−1.45533
$63$	−7.07148e6			−0.448898
$64$	−1.35287e7			−0.806373
$65$		−	1.39029e7i		−	0.778847i
$66$	2.24779e7			1.18462
$67$		−	9.27099e6i		−	0.460073i	−0.973182	−	0.230037i	$-0.926115\pi$
$67$		−	9.27099e6i		−	0.460073i	0.973182	−	0.230037i	$-0.0738846\pi$
$68$	7.21581e6			0.337481
$69$		−	1.70725e7i		−	0.753181i
$70$		−	5.86645e7i		−	2.44334i
$71$	−6.40244e6			−0.251949			−0.125974	−	0.992034i	$-0.540206\pi$
$71$	−6.40244e6			−0.251949			−0.125974	+	0.992034i	$0.540206\pi$
$72$			2.28307e7i			0.849551i
$73$		−	1.74523e7i		−	0.614554i	−0.951620	−	0.307277i	$-0.900582\pi$
$73$		−	1.74523e7i		−	0.614554i	0.951620	−	0.307277i	$-0.0994178\pi$
$74$	7.90865e7			2.63740
$75$	504327.			0.0159392
$76$	−1.12899e8			−3.38404
$77$			5.27934e7i			1.50182i
$78$	−3.10558e7			−0.839004
$79$	5.50300e7			1.41284			0.706418	−	0.707795i	$-0.250310\pi$
$79$	5.50300e7			1.41284			0.706418	+	0.707795i	$0.250310\pi$
$80$	−9.30615e7			−2.27201
$81$	4.78297e6			0.111111
$82$			1.51050e8i			3.34091i
$83$			6.16543e6i			0.129912i	0.997888	+	0.0649562i	$0.0206908\pi$
$83$			6.16543e6i			0.129912i	−0.997888	+	0.0649562i	$0.979309\pi$
$84$	−9.23322e7			−1.85454
$85$	7.28313e6			0.139522
$86$	3.39770e7			0.621142
$87$	−1.55917e7			−0.272155
$88$	1.70447e8			2.84222
$89$		−	7.65784e7i		−	1.22052i	−0.792200	−	0.610262i	$-0.791064\pi$
$89$		−	7.65784e7i		−	1.22052i	0.792200	−	0.610262i	$-0.208936\pi$
$90$			3.96792e7i			0.604773i
$91$		−	7.29401e7i		−	1.06365i
$92$		−	2.22915e8i		−	3.11163i
$93$			3.41616e7i			0.456674i
$94$	2.05446e8			2.63140
$95$	−1.13952e8			−1.39904
$96$			8.28989e7i			0.976032i
$97$			6.58511e7i			0.743834i	0.928266	+	0.371917i	$0.121299\pi$
$97$			6.58511e7i			0.743834i	−0.928266	+	0.371917i	$0.878701\pi$
$98$		−	1.38071e8i		−	1.49692i
$99$		−	3.57081e7i		−	0.371729i
$100$	6.58499e6			0.0658499
$101$			1.13495e8i			1.09067i	0.838219	+	0.545334i	$0.183597\pi$
$101$			1.13495e8i			1.09067i	−0.838219	+	0.545334i	$0.816403\pi$
$102$		−	1.62688e7i		−	0.150298i
$103$			1.77831e8i			1.58000i	0.613105	+	0.790002i	$0.289920\pi$
$103$			1.77831e8i			1.58000i	−0.613105	+	0.790002i	$0.710080\pi$
$104$	−2.35491e8			−2.01299
$105$	−9.31937e7			−0.766707
$106$			3.10986e8i			2.46330i
$107$	−6.98484e7			−0.532870			−0.266435	−	0.963853i	$-0.585846\pi$
$107$	−6.98484e7			−0.532870			−0.266435	+	0.963853i	$0.585846\pi$
$108$	6.24512e7			0.459035
$109$		−	8.41201e6i		−	0.0595928i	−0.999556	−	0.0297964i	$-0.990514\pi$
$109$		−	8.41201e6i		−	0.0595928i	0.999556	−	0.0297964i	$-0.00948589\pi$
$110$	2.96232e8			2.02330
$111$		−	1.25636e8i		−	0.827603i
$112$	−4.88237e8			−3.10284
$113$		−	1.36911e8i		−	0.839699i	−0.907594	−	0.419850i	$-0.862083\pi$
$113$		−	1.36911e8i		−	0.839699i	0.907594	−	0.419850i	$-0.137917\pi$
$114$			2.54542e8i			1.50710i
$115$		−	2.24995e8i		−	1.28641i
$116$	−2.03581e8			−1.12436
$117$			4.93348e7i			0.263275i
$118$	−2.65161e6	+	3.56705e8i	−0.0136767	+	1.83984i
$119$	3.82102e7			0.190542
$120$			3.00882e8i			1.45101i
$121$	−5.22265e7			−0.243640
$122$	−3.86952e8			−1.74670
$123$	2.39956e8			1.04836
$124$			4.46048e8i			1.88666i
$125$	2.47393e8			1.01332
$126$			2.08172e8i			0.825926i
$127$	−9.99127e7			−0.384066			−0.192033	−	0.981388i	$-0.561508\pi$
$127$	−9.99127e7			−0.384066			−0.192033	+	0.981388i	$0.561508\pi$
$128$		−	5.55379e7i		−	0.206895i
$129$		−	5.39754e7i		−	0.194911i
$130$	−4.09278e8			−1.43300
$131$			5.59034e8i			1.89825i	0.314902	+	0.949124i	$0.398028\pi$
$131$			5.59034e8i			1.89825i	−0.314902	+	0.949124i	$0.601972\pi$
$132$		−	4.66241e8i		−	1.53573i
$133$	−5.97839e8			−1.91063
$134$	−2.72923e8			−0.846487
$135$	6.30339e7			0.189775
$136$		−	1.23364e8i		−	0.360605i
$137$	2.76211e8			0.784078			0.392039	−	0.919949i	$-0.371770\pi$
$137$	2.76211e8			0.784078			0.392039	+	0.919949i	$0.371770\pi$
$138$	−5.02584e8			−1.38577
$139$	2.88032e8			0.771582			0.385791	−	0.922586i	$-0.373929\pi$
$139$	2.88032e8			0.771582			0.385791	+	0.922586i	$0.373929\pi$
$140$	−1.21683e9			−3.16751
$141$		−	3.26370e8i		−	0.825721i
$142$			1.88477e8i			0.463559i
$143$	3.68318e8			0.880803
$144$	3.30231e8			0.768012
$145$	−2.05480e8			−0.464834
$146$	−5.13765e8			−1.13072
$147$	−2.19338e8			−0.469725
$148$		−	1.64043e9i		−	3.41909i
$149$		−	3.52277e8i		−	0.714725i	−0.933966	−	0.357363i	$-0.883676\pi$
$149$		−	3.52277e8i		−	0.714725i	0.933966	−	0.357363i	$-0.116324\pi$
$150$		−	1.48465e7i		−	0.0293265i
$151$			8.12741e7i			0.156331i	0.996940	+	0.0781653i	$0.0249062\pi$
$151$			8.12741e7i			0.156331i	−0.996940	+	0.0781653i	$0.975094\pi$
$152$			1.93016e9i			3.61592i
$153$	−2.58444e7			−0.0471629
$154$	1.55415e9			2.76318
$155$			4.50209e8i			0.779987i
$156$			6.44164e8i			1.08767i
$157$		−	2.90473e8i		−	0.478088i	−0.971009	−	0.239044i	$-0.923166\pi$
$157$		−	2.90473e8i		−	0.478088i	0.971009	−	0.239044i	$-0.0768340\pi$
$158$		−	1.61999e9i		−	2.59947i
$159$	4.94029e8			0.772972
$160$			1.09251e9i			1.66704i
$161$		−	1.18041e9i		−	1.75683i
$162$		−	1.40803e8i		−	0.204433i
$163$	−5.34854e8			−0.757679			−0.378839	−	0.925462i	$-0.623677\pi$
$163$	−5.34854e8			−0.757679			−0.378839	+	0.925462i	$0.623677\pi$
$164$	3.13310e9			4.33110
$165$		−	4.70591e8i		−	0.634903i
$166$	1.81500e8			0.239025
$167$	−7.99654e8			−1.02810			−0.514051	−	0.857760i	$-0.671856\pi$
$167$	−7.99654e8			−1.02810			−0.514051	+	0.857760i	$0.671856\pi$
$168$			1.57854e9i			1.98161i
$169$	3.06858e8			0.376175
$170$		−	2.14403e8i		−	0.256706i
$171$	4.04363e8			0.472919
$172$		−	7.04756e8i		−	0.805240i
$173$		−	1.00169e9i		−	1.11828i	−0.829074	−	0.559138i	$-0.811132\pi$
$173$		−	1.00169e9i		−	1.11828i	0.829074	−	0.559138i	$-0.188868\pi$
$174$			4.58993e8i			0.500737i
$175$	3.48698e7			0.0371789
$176$		−	2.46540e9i		−	2.56943i
$177$	5.66657e8	+	4.21231e6i	0.577334	+	0.00429168i
$178$	−2.25434e9			−2.24564
$179$		−	5.88886e8i		−	0.573613i	−0.957989	−	0.286806i	$-0.907406\pi$
$179$		−	5.88886e8i		−	0.573613i	0.957989	−	0.286806i	$-0.0925937\pi$
$180$	8.23033e8			0.784020
$181$	1.08898e9			1.01462			0.507310	−	0.861763i	$-0.330640\pi$
$181$	1.08898e9			1.01462			0.507310	+	0.861763i	$0.330640\pi$
$182$	−2.14723e9			−1.95701
$183$			6.14707e8i			0.548105i
$184$	−3.81103e9			−3.32484
$185$		−	1.65573e9i		−	1.41352i
$186$	1.00566e9			0.840232
$187$			1.92946e8i			0.157786i
$188$		−	4.26141e9i		−	3.41131i
$189$	3.30700e8			0.259172
$190$			3.35457e9i			2.57408i
$191$		−	1.49793e9i		−	1.12554i	−0.826615	−	0.562768i	$-0.809737\pi$
$191$		−	1.49793e9i		−	1.12554i	0.826615	−	0.562768i	$-0.190263\pi$
$192$	6.32674e8			0.465560
$193$	−2.05695e9			−1.48250			−0.741251	−	0.671228i	$-0.765767\pi$
$193$	−2.05695e9			−1.48250			−0.741251	+	0.671228i	$0.765767\pi$
$194$	1.93855e9			1.36858
$195$			6.50175e8i			0.449668i
$196$	−2.86389e9			−1.94058
$197$	1.32713e9			0.881146			0.440573	−	0.897717i	$-0.354775\pi$
$197$	1.32713e9			0.881146			0.440573	+	0.897717i	$0.354775\pi$
$198$	−1.05119e9			−0.683942
$199$	−1.43410e9			−0.914464			−0.457232	−	0.889347i	$-0.651159\pi$
$199$	−1.43410e9			−0.914464			−0.457232	+	0.889347i	$0.651159\pi$
$200$		−	1.12579e8i		−	0.0703620i
$201$			4.33561e8i			0.265623i
$202$	3.34111e9			2.00672
$203$	−1.07803e9			−0.634814
$204$	−3.37450e8			−0.194845
$205$	3.16233e9			1.79057
$206$	5.23504e9			2.90704
$207$			7.98400e8i			0.434849i
$208$			3.40623e9i			1.81979i
$209$		−	3.01884e9i		−	1.58218i
$210$			2.74347e9i			1.41066i
$211$		−	9.39980e8i		−	0.474230i	−0.971482	−	0.237115i	$-0.923798\pi$
$211$		−	9.39980e8i		−	0.474230i	0.971482	−	0.237115i	$-0.0762018\pi$
$212$	6.45053e9			3.19339
$213$	2.99412e8			0.145463
$214$			2.05622e9i			0.980426i
$215$		−	7.11332e8i		−	0.332903i
$216$		−	1.06769e9i		−	0.490488i
$217$			2.36197e9i			1.06521i
$218$	−2.47636e8			−0.109645
$219$			8.16161e8i			0.354813i
$220$		−	6.14450e9i		−	2.62298i
$221$		−	2.66577e8i		−	0.111751i
$222$	−3.69851e9			−1.52270
$223$	−3.59919e9			−1.45541			−0.727705	−	0.685891i	$-0.759413\pi$
$223$	−3.59919e9			−1.45541			−0.727705	+	0.685891i	$0.759413\pi$
$224$			5.73173e9i			2.27664i
$225$	−2.35850e7			−0.00920251
$226$	−4.03042e9			−1.54496
$227$		−	2.67506e9i		−	1.00747i	−0.863859	−	0.503733i	$-0.831960\pi$
$227$		−	2.67506e9i		−	1.00747i	0.863859	−	0.503733i	$-0.168040\pi$
$228$	5.27976e9			1.95378
$229$		−	8.27102e8i		−	0.300758i	−0.988628	−	0.150379i	$-0.951951\pi$
$229$		−	8.27102e8i		−	0.300758i	0.988628	−	0.150379i	$-0.0480494\pi$
$230$	−6.62347e9			−2.36687
$231$		−	2.46890e9i		−	0.867074i
$232$			3.48048e9i			1.20140i
$233$		−	4.11175e7i		−	0.0139509i	−0.999976	−	0.00697546i	$-0.997780\pi$
$233$		−	4.11175e7i		−	0.0139509i	0.999976	−	0.00697546i	$-0.00222038\pi$
$234$	1.45233e9			0.484399
$235$		−	4.30116e9i		−	1.41031i
$236$	7.39884e9	+	5.50001e7i	2.38515	+	0.0177303i
$237$	−2.57350e9			−0.815701
$238$		−	1.12484e9i		−	0.350578i
$239$	−5.22238e9			−1.60058			−0.800289	−	0.599614i	$-0.795321\pi$
$239$	−5.22238e9			−1.60058			−0.800289	+	0.599614i	$0.795321\pi$
$240$	4.35206e9			1.31175
$241$	2.85572e9			0.846539			0.423270	−	0.906004i	$-0.360882\pi$
$241$	2.85572e9			0.846539			0.423270	+	0.906004i	$0.360882\pi$
$242$			1.53746e9i			0.448273i
$243$	−2.23677e8			−0.0641500
$244$			8.02622e9i			2.26439i
$245$	−2.89061e9			−0.802278
$246$		−	7.06389e9i		−	1.92887i
$247$			4.17088e9i			1.12057i
$248$	7.62578e9			2.01594
$249$		−	2.88328e8i		−	0.0750050i
$250$		−	7.28285e9i		−	1.86441i
$251$	6.65166e9			1.67585			0.837926	−	0.545784i	$-0.183768\pi$
$251$	6.65166e9			1.67585			0.837926	+	0.545784i	$0.183768\pi$
$252$	4.31795e9			1.07072
$253$	5.96059e9			1.45481
$254$			2.94126e9i			0.706641i
$255$	−3.40598e8			−0.0805531
$256$	−5.09829e9			−1.18704
$257$	−4.78161e9			−1.09608			−0.548039	−	0.836453i	$-0.684626\pi$
$257$	−4.78161e9			−1.09608			−0.548039	+	0.836453i	$0.684626\pi$
$258$	−1.58894e9			−0.358616
$259$		−	8.68662e9i		−	1.93042i
$260$			8.48932e9i			1.85772i
$261$	7.29151e8			0.157129
$262$	1.64570e10			3.49258
$263$	−3.74519e9			−0.782800			−0.391400	−	0.920221i	$-0.628009\pi$
$263$	−3.74519e9			−0.782800			−0.391400	+	0.920221i	$0.628009\pi$
$264$	−7.97100e9			−1.64096
$265$	6.51071e9			1.32022
$266$			1.75994e10i			3.51537i
$267$			3.58122e9i			0.704670i
$268$			5.66101e9i			1.09737i
$269$			9.90529e9i			1.89173i	0.324567	+	0.945863i	$0.394781\pi$
$269$			9.90529e9i			1.89173i	−0.324567	+	0.945863i	$0.605219\pi$
$270$		−	1.85561e9i		−	0.349166i
$271$	−7.68454e9			−1.42476			−0.712379	−	0.701795i	$-0.752382\pi$
$271$	−7.68454e9			−1.42476			−0.712379	+	0.701795i	$0.752382\pi$
$272$	−1.78438e9			−0.325995
$273$			3.41107e9i			0.614101i
$274$		−	8.13120e9i		−	1.44262i
$275$			1.76078e8i			0.0307875i
$276$			1.04247e10i			1.79650i
$277$	1.39902e9			0.237633			0.118816	−	0.992916i	$-0.462090\pi$
$277$	1.39902e9			0.237633			0.118816	+	0.992916i	$0.462090\pi$
$278$		−	8.47919e9i		−	1.41963i
$279$		−	1.59758e9i		−	0.263661i
$280$			2.08033e10i			3.38455i
$281$	−2.81269e8			−0.0451124			−0.0225562	−	0.999746i	$-0.507180\pi$
$281$	−2.81269e8			−0.0451124			−0.0225562	+	0.999746i	$0.507180\pi$
$282$	−9.60777e9			−1.51924
$283$			3.94330e9i			0.614772i	0.951585	+	0.307386i	$0.0994542\pi$
$283$			3.94330e9i			0.614772i	−0.951585	+	0.307386i	$0.900546\pi$
$284$	3.90943e9			0.600952
$285$	5.32903e9			0.807734
$286$		−	1.08427e10i		−	1.62059i
$287$	1.65908e10			2.44535
$288$		−	3.87680e9i		−	0.563512i
$289$	−6.83611e9			−0.979981
$290$			6.04899e9i			0.855246i
$291$		−	3.07955e9i		−	0.429453i
$292$			1.06566e10i			1.46584i
$293$	1.41198e10			1.91584			0.957918	−	0.287042i	$-0.0926718\pi$
$293$	1.41198e10			1.91584			0.957918	+	0.287042i	$0.0926718\pi$
$294$			6.45693e9i			0.864245i
$295$	7.46787e9	+	5.55133e7i	0.986072	+	0.00733008i
$296$	−2.80453e10			−3.65336
$297$			1.66990e9i			0.214618i
$298$	−1.03704e10			−1.31502
$299$	−8.23524e9			−1.03037
$300$	−3.07950e8			−0.0380185
$301$		−	3.73192e9i		−	0.454639i
$302$	2.39257e9			0.287632
$303$		−	5.30765e9i		−	0.629697i
$304$	2.79185e10			3.26887
$305$			8.10110e9i			0.936149i
$306$			7.60816e8i			0.0867748i
$307$	8.30008e9			0.934391			0.467195	−	0.884154i	$-0.345264\pi$
$307$	8.30008e9			0.934391			0.467195	+	0.884154i	$0.345264\pi$
$308$		−	3.22364e10i		−	3.58215i
$309$		−	8.31632e9i		−	0.912215i
$310$	1.32534e10			1.43510
$311$	6.15653e9			0.658103			0.329052	−	0.944312i	$-0.393271\pi$
$311$	6.15653e9			0.658103			0.329052	+	0.944312i	$0.393271\pi$
$312$	1.10128e10			1.16220
$313$		−	1.44649e10i		−	1.50708i	−0.657399	−	0.753542i	$-0.728343\pi$
$313$		−	1.44649e10i		−	1.50708i	0.657399	−	0.753542i	$-0.271657\pi$
$314$	−8.55105e9			−0.879631
$315$	4.35824e9			0.442658
$316$	−3.36022e10			−3.36992
$317$	−1.63270e10			−1.61685			−0.808424	−	0.588601i	$-0.799679\pi$
$317$	−1.63270e10			−1.61685			−0.808424	+	0.588601i	$0.799679\pi$
$318$		−	1.45434e10i		−	1.42219i
$319$		−	5.44361e9i		−	0.525683i
$320$	8.33790e9			0.795164
$321$	3.26649e9			0.307653
$322$	−3.47493e10			−3.23238
$323$	−2.18494e9			−0.200738
$324$	−2.92055e9			−0.265024
$325$		−	2.43272e8i		−	0.0218051i
$326$			1.57452e10i			1.39405i
$327$			3.93391e8i			0.0344059i
$328$		−	5.35645e10i		−	4.62787i
$329$		−	2.25656e10i		−	1.92603i
$330$	−1.38534e10			−1.16816
$331$	8.97447e9			0.747648			0.373824	−	0.927500i	$-0.378046\pi$
$331$	8.97447e9			0.747648			0.373824	+	0.927500i	$0.378046\pi$
$332$		−	3.76470e9i		−	0.309869i
$333$			5.87541e9i			0.477817i
$334$			2.35405e10i			1.89160i
$335$			5.71383e9i			0.453678i
$336$	2.28326e10			1.79142
$337$			1.97815e10i			1.53369i	0.641830	+	0.766847i	$0.278176\pi$
$337$			1.97815e10i			1.53369i	−0.641830	+	0.766847i	$0.721824\pi$
$338$		−	9.03338e9i		−	0.692123i
$339$			6.40268e9i			0.484800i
$340$	−4.44719e9			−0.332790
$341$	−1.19270e10			−0.882093
$342$		−	1.19038e10i		−	0.870122i
$343$	3.47473e9			0.251041
$344$	−1.20487e10			−0.860415
$345$			1.05220e10i			0.742712i
$346$	−2.94881e10			−2.05751
$347$		−	1.90497e10i		−	1.31392i	−0.753925	−	0.656961i	$-0.771842\pi$
$347$		−	1.90497e10i		−	1.31392i	0.753925	−	0.656961i	$-0.228158\pi$
$348$	9.52052e9			0.649148
$349$		−	2.41925e10i		−	1.63072i	−0.578953	−	0.815361i	$-0.696539\pi$
$349$		−	2.41925e10i		−	1.63072i	0.578953	−	0.815361i	$-0.303461\pi$
$350$		−	1.02651e9i		−	0.0684053i
$351$		−	2.30716e9i		−	0.152002i
$352$	−2.89429e10			−1.88526
$353$		−	1.42526e9i		−	0.0917900i	−0.998946	−	0.0458950i	$-0.985386\pi$
$353$		−	1.42526e9i		−	0.0917900i	0.998946	−	0.0458950i	$-0.0146140\pi$
$354$	1.24003e8	−	1.66814e10i	0.00789625	−	1.06223i
$355$	3.94590e9			0.248446
$356$			4.67599e10i			2.91121i
$357$	−1.78691e9			−0.110010
$358$	−1.73358e10			−1.05539
$359$	−2.34055e10			−1.40910			−0.704548	−	0.709656i	$-0.748850\pi$
$359$	−2.34055e10			−1.40910			−0.704548	+	0.709656i	$0.748850\pi$
$360$		−	1.40708e10i		−	0.837742i
$361$	1.72022e10			1.01287
$362$		−	3.20576e10i		−	1.86680i
$363$	2.44239e9			0.140666
$364$			4.45383e10i			2.53705i
$365$			1.07560e10i			0.606011i
$366$	1.80959e10			1.00846
$367$		−	1.28919e10i		−	0.710646i	−0.934744	−	0.355323i	$-0.884371\pi$
$367$		−	1.28919e10i		−	0.710646i	0.934744	−	0.355323i	$-0.115629\pi$
$368$			5.51240e10i			3.00573i
$369$	−1.12216e10			−0.605271
$370$	−4.87420e10			−2.60074
$371$	3.41577e10			1.80299
$372$		−	2.08596e10i		−	1.08927i
$373$	5.00658e9			0.258646			0.129323	−	0.991603i	$-0.458720\pi$
$373$	5.00658e9			0.258646			0.129323	+	0.991603i	$0.458720\pi$
$374$	5.68001e9			0.290310
$375$	−1.15694e10			−0.585043
$376$	−7.28544e10			−3.64506
$377$			7.52097e9i			0.372313i
$378$		−	9.73526e9i		−	0.476849i
$379$	2.65952e9			0.128898			0.0644490	−	0.997921i	$-0.479471\pi$
$379$	2.65952e9			0.128898			0.0644490	+	0.997921i	$0.479471\pi$
$380$	6.95810e10			3.33700
$381$	4.67245e9			0.221741
$382$	−4.40967e10			−2.07087
$383$	−9.02518e9			−0.419431			−0.209716	−	0.977762i	$-0.567254\pi$
$383$	−9.02518e9			−0.419431			−0.209716	+	0.977762i	$0.567254\pi$
$384$			2.59725e9i			0.119451i
$385$		−	3.25372e10i		−	1.48094i
$386$			6.05533e10i			2.72765i
$387$			2.52418e9i			0.112532i
$388$		−	4.02097e10i		−	1.77420i
$389$	3.33795e10			1.45775			0.728873	−	0.684649i	$-0.240045\pi$
$389$	3.33795e10			1.45775			0.728873	+	0.684649i	$0.240045\pi$
$390$	1.91401e10			0.827341
$391$		−	4.31409e9i		−	0.184579i
$392$			4.89620e10i			2.07355i
$393$		−	2.61434e10i		−	1.09595i
$394$		−	3.90684e10i		−	1.62122i
$395$	−3.39157e10			−1.39320
$396$			2.18039e10i			0.886653i
$397$			4.12240e10i			1.65954i	0.558103	+	0.829771i	$0.311529\pi$
$397$			4.12240e10i			1.65954i	−0.558103	+	0.829771i	$0.688471\pi$
$398$			4.22175e10i			1.68252i
$399$	2.79581e10			1.10310
$400$	−1.62839e9			−0.0636088
$401$		−	9.37756e9i		−	0.362671i	−0.983421	−	0.181335i	$-0.941958\pi$
$401$		−	9.37756e9i		−	0.362671i	0.983421	−	0.181335i	$-0.0580419\pi$
$402$	1.27633e10			0.488719
$403$	1.64785e10			0.624738
$404$		−	6.93020e10i		−	2.60148i
$405$	−2.94780e9			−0.109567
$406$			3.17354e10i			1.16799i
$407$	4.38639e10			1.59856
$408$			5.76916e9i			0.208196i
$409$			1.15949e10i			0.414355i	0.978303	+	0.207178i	$0.0664278\pi$
$409$			1.15949e10i			0.414355i	−0.978303	+	0.207178i	$0.933572\pi$
$410$		−	9.30937e10i		−	3.29447i
$411$	−1.29171e10			−0.452688
$412$		−	1.08586e11i		−	3.76865i
$413$	3.91794e10	+	2.91244e8i	1.34666	+	0.0100105i
$414$	2.35035e10			0.800077
$415$		−	3.79983e9i		−	0.128107i
$416$	3.99880e10			1.33523
$417$	−1.34699e10			−0.445473
$418$	−8.88697e10			−2.91104
$419$		−	1.45775e10i		−	0.472963i	−0.971636	−	0.236482i	$-0.924006\pi$
$419$		−	1.45775e10i		−	0.472963i	0.971636	−	0.236482i	$-0.0759943\pi$
$420$	5.69055e10			1.82876
$421$			5.70750e10i			1.81684i	0.418054	+	0.908422i	$0.362712\pi$
$421$			5.70750e10i			1.81684i	−0.418054	+	0.908422i	$0.637288\pi$
$422$	−2.76714e10			−0.872533
$423$			1.52628e10i			0.476730i
$424$		−	1.10280e11i		−	3.41220i
$425$	1.27440e8			0.00390616
$426$		−	8.81420e9i		−	0.267636i
$427$			4.25016e10i			1.27848i
$428$	4.26505e10			1.27101
$429$	−1.72245e10			−0.508532
$430$	−2.09404e10			−0.612508
$431$			1.05104e10i			0.304588i	0.988335	+	0.152294i	$0.0486660\pi$
$431$			1.05104e10i			0.304588i	−0.988335	+	0.152294i	$0.951334\pi$
$432$	−1.54434e10			−0.443412
$433$	−5.48474e9			−0.156029			−0.0780144	−	0.996952i	$-0.524858\pi$
$433$	−5.48474e9			−0.156029			−0.0780144	+	0.996952i	$0.524858\pi$
$434$	6.95326e10			1.95988
$435$	9.60935e9			0.268372
$436$			5.13650e9i			0.142142i
$437$			6.74985e10i			1.85084i
$438$	2.40264e10			0.652819
$439$	5.74417e10			1.54657			0.773285	−	0.634059i	$-0.218612\pi$
$439$	5.74417e10			1.54657			0.773285	+	0.634059i	$0.218612\pi$
$440$	−1.05048e11			−2.80271
$441$	1.02574e10			0.271196
$442$	−7.84757e9			−0.205611
$443$			8.28816e8i			0.0215200i	0.999942	+	0.0107600i	$0.00342509\pi$
$443$			8.28816e8i			0.0215200i	−0.999942	+	0.0107600i	$0.996575\pi$
$444$			7.67152e10i			1.97401i
$445$			4.71962e10i			1.20356i
$446$			1.05954e11i			2.67780i
$447$			1.64744e10i			0.412647i
$448$	4.37439e10			1.08594
$449$	7.91407e9			0.194722			0.0973609	−	0.995249i	$-0.468960\pi$
$449$	7.91407e9			0.194722			0.0973609	+	0.995249i	$0.468960\pi$
$450$			6.94304e8i			0.0169317i
$451$			8.37770e10i			2.02497i
$452$			8.35998e10i			2.00286i
$453$		−	3.80081e9i		−	0.0902576i
$454$	−7.87493e10			−1.85363
$455$			4.49539e10i			1.04887i
$456$		−	9.02646e10i		−	2.08765i
$457$			1.24447e9i			0.0285312i	0.999898	+	0.0142656i	$0.00454103\pi$
$457$			1.24447e9i			0.0285312i	−0.999898	+	0.0142656i	$0.995459\pi$
$458$	−2.43485e10			−0.553363
$459$	1.20862e9			0.0272295
$460$			1.37385e11i			3.06838i
$461$	−6.86301e10			−1.51954			−0.759768	−	0.650195i	$-0.774687\pi$
$461$	−6.86301e10			−1.51954			−0.759768	+	0.650195i	$0.774687\pi$
$462$	−7.26804e10			−1.59533
$463$			1.84478e10i			0.401441i	0.979649	+	0.200720i	$0.0643283\pi$
$463$			1.84478e10i			0.401441i	−0.979649	+	0.200720i	$0.935672\pi$
$464$	5.03429e10			1.08609
$465$		−	2.10542e10i		−	0.450326i
$466$	−1.21043e9			−0.0256682
$467$		−	1.62022e10i		−	0.340647i	−0.985388	−	0.170324i	$-0.945519\pi$
$467$		−	1.62022e10i		−	0.340647i	0.985388	−	0.170324i	$-0.0544813\pi$
$468$		−	3.01246e10i		−	0.627968i
$469$			2.99770e10i			0.619578i
$470$	−1.26619e11			−2.59482
$471$			1.35841e10i			0.276024i
$472$	9.40300e8	−	1.26493e11i	0.0189452	−	2.54858i
$473$	1.88447e10			0.376483
$474$			7.57596e10i			1.50080i
$475$	−1.99393e9			−0.0391684
$476$	−2.33317e10			−0.454484
$477$	−2.31034e10			−0.446276
$478$			1.53738e11i			2.94490i
$479$	−5.69459e10			−1.08173			−0.540867	−	0.841108i	$-0.681904\pi$
$479$	−5.69459e10			−1.08173			−0.540867	+	0.841108i	$0.681904\pi$
$480$		−	5.10916e10i		−	0.962464i
$481$	−6.06030e10			−1.13218
$482$		−	8.40675e10i		−	1.55754i
$483$			5.52023e10i			1.01431i
$484$	3.18903e10			0.581134
$485$		−	4.05848e10i		−	0.733494i
$486$			6.58469e9i			0.118029i
$487$	7.90104e10			1.40465			0.702325	−	0.711856i	$-0.252145\pi$
$487$	7.90104e10			1.40465			0.702325	+	0.711856i	$0.252145\pi$
$488$	1.37219e11			2.41955
$489$	2.50127e10			0.437446
$490$			8.50947e10i			1.47611i
$491$	6.68721e9			0.115059			0.0575293	−	0.998344i	$-0.481678\pi$
$491$	6.68721e9			0.115059			0.0575293	+	0.998344i	$0.481678\pi$
$492$	−1.46521e11			−2.50056
$493$	−3.93991e9			−0.0666958
$494$	1.22784e11			2.06173
$495$			2.20073e10i			0.366562i
$496$		−	1.10302e11i		−	1.82245i
$497$	2.07017e10			0.339298
$498$	−8.48791e9			−0.138001
$499$	4.76231e10			0.768095			0.384048	−	0.923313i	$-0.374530\pi$
$499$	4.76231e10			0.768095			0.384048	+	0.923313i	$0.374530\pi$
$500$	−1.51062e11			−2.41699
$501$	3.73961e10			0.593575
$502$		−	1.95814e11i		−	3.08339i
$503$		−	7.43371e10i		−	1.16127i	−0.814164	−	0.580636i	$-0.802804\pi$
$503$		−	7.43371e10i		−	1.16127i	0.814164	−	0.580636i	$-0.197196\pi$
$504$		−	7.38211e10i		−	1.14409i
$505$		−	6.99486e10i		−	1.07551i
$506$		−	1.75470e11i		−	2.67671i
$507$	−1.43503e10			−0.217185
$508$	6.10082e10			0.916080
$509$		−	3.07711e10i		−	0.458428i	−0.973376	−	0.229214i	$-0.926384\pi$
$509$		−	3.07711e10i		−	0.458428i	0.973376	−	0.229214i	$-0.0736156\pi$
$510$			1.00267e10i			0.148209i
$511$			5.64304e10i			0.827617i
$512$			1.35867e11i			1.97713i
$513$	−1.89102e10			−0.273040
$514$			1.40763e11i			2.01667i
$515$		−	1.09599e11i		−	1.55804i
$516$			3.29582e10i			0.464905i
$517$	1.13947e11			1.59493
$518$	−2.55720e11			−3.55177
$519$			4.68444e10i			0.645637i
$520$	1.45136e11			1.98501
$521$	1.13520e11			1.54071			0.770354	−	0.637617i	$-0.220080\pi$
$521$	1.13520e11			1.54071			0.770354	+	0.637617i	$0.220080\pi$
$522$		−	2.14650e10i		−	0.289100i
$523$	4.57237e10			0.611131			0.305566	−	0.952171i	$-0.401154\pi$
$523$	4.57237e10			0.611131			0.305566	+	0.952171i	$0.401154\pi$
$524$		−	3.41355e11i		−	4.52773i
$525$	−1.63070e9			−0.0214653
$526$			1.10252e11i			1.44027i
$527$			8.63239e9i			0.111915i
$528$			1.15295e11i			1.48346i
$529$	−5.49623e10			−0.701846
$530$		−	1.91665e11i		−	2.42906i
$531$	−2.64999e10	−	1.96990e8i	−0.333324	−	0.00247780i
$532$	3.65049e11			4.55727
$533$		−	1.15747e11i		−	1.43418i
$534$	1.05425e11			1.29652
$535$	4.30485e10			0.525463
$536$	9.67825e10			1.17257
$537$			2.75395e10i			0.331176i
$538$	2.91595e11			3.48058
$539$		−	7.65785e10i		−	0.907302i
$540$	−3.84894e10			−0.452654
$541$			9.23499e10i			1.07807i	0.842283	+	0.539036i	$0.181211\pi$
$541$			9.23499e10i			1.07807i	−0.842283	+	0.539036i	$0.818789\pi$
$542$			2.26220e11i			2.62141i
$543$	−5.09263e10			−0.585792
$544$			2.09480e10i			0.239192i
$545$			5.18443e9i			0.0587644i
$546$	1.00416e11			1.12988
$547$	−1.17140e11			−1.30845			−0.654225	−	0.756300i	$-0.727005\pi$
$547$	−1.17140e11			−1.30845			−0.654225	+	0.756300i	$0.727005\pi$
$548$	−1.68659e11			−1.87019
$549$		−	2.87470e10i		−	0.316448i
$550$	5.18345e9			0.0566459
$551$	6.16441e10			0.668783
$552$	1.78224e11			1.91960
$553$	−1.77935e11			−1.90266
$554$		−	4.11850e10i		−	0.437220i
$555$			7.74309e10i			0.816099i
$556$	−1.75877e11			−1.84039
$557$	2.93443e10			0.304861			0.152431	−	0.988314i	$-0.451290\pi$
$557$	2.93443e10			0.304861			0.152431	+	0.988314i	$0.451290\pi$
$558$	−4.70301e10			−0.485108
$559$	−2.60361e10			−0.266642
$560$	3.00907e11			3.05971
$561$		−	9.02319e9i		−	0.0910979i
$562$			8.28008e9i			0.0830021i
$563$		−	5.32789e10i		−	0.530300i	−0.964207	−	0.265150i	$-0.914579\pi$
$563$		−	5.32789e10i		−	0.530300i	0.964207	−	0.265150i	$-0.0854215\pi$
$564$			1.99286e11i			1.96952i
$565$			8.43797e10i			0.828027i
$566$	1.16084e11			1.13112
$567$	−1.54653e10			−0.149633
$568$		−	6.68368e10i		−	0.642129i
$569$			8.35642e10i			0.797207i	0.917123	+	0.398604i	$0.130505\pi$
$569$			8.35642e10i			0.797207i	−0.917123	+	0.398604i	$0.869495\pi$
$570$		−	1.56878e11i		−	1.48615i
$571$		−	1.30068e11i		−	1.22357i	−0.791025	−	0.611783i	$-0.790452\pi$
$571$		−	1.30068e11i		−	1.22357i	0.791025	−	0.611783i	$-0.209548\pi$
$572$	−2.24901e11			−2.10090
$573$			7.00514e10i			0.649828i
$574$		−	4.88406e11i		−	4.49918i
$575$		−	3.93694e9i		−	0.0360154i
$576$	−2.95872e10			−0.268791
$577$	9.70636e10			0.875695			0.437848	−	0.899049i	$-0.355741\pi$
$577$	9.70636e10			0.875695			0.437848	+	0.899049i	$0.355741\pi$
$578$			2.01244e11i			1.80306i
$579$	9.61942e10			0.855923
$580$	1.25469e11			1.10873
$581$		−	1.99354e10i		−	0.174952i
$582$	−9.06568e10			−0.790148
$583$			1.72483e11i			1.49304i
$584$	1.82189e11			1.56628
$585$		−	3.04057e10i		−	0.259616i
$586$		−	4.15664e11i		−	3.52494i
$587$		−	3.18566e10i		−	0.268317i	−0.990960	−	0.134158i	$-0.957167\pi$
$587$		−	3.18566e10i		−	0.268317i	0.990960	−	0.134158i	$-0.0428331\pi$
$588$	1.33931e11			1.12040
$589$		−	1.35063e11i		−	1.12221i
$590$	1.63422e9	−	2.19842e11i	0.0134866	−	1.81427i
$591$	−6.20636e10			−0.508730
$592$			4.05657e11i			3.30272i
$593$	3.25607e10			0.263314			0.131657	−	0.991295i	$-0.457970\pi$
$593$	3.25607e10			0.263314			0.131657	+	0.991295i	$0.457970\pi$
$594$	4.91592e10			0.394874
$595$	−2.35494e10			−0.187894
$596$			2.15106e11i			1.70477i
$597$	6.70661e10			0.527966
$598$			2.42432e11i			1.89577i
$599$	1.11453e11			0.865733			0.432867	−	0.901458i	$-0.357502\pi$
$599$	1.11453e11			0.865733			0.432867	+	0.901458i	$0.357502\pi$
$600$			5.26481e9i			0.0406235i
$601$		−	1.13029e11i		−	0.866350i	−0.901310	−	0.433175i	$-0.857393\pi$
$601$		−	1.13029e11i		−	0.866350i	0.901310	−	0.433175i	$-0.142607\pi$
$602$	−1.09862e11			−0.836488
$603$		−	2.02757e10i		−	0.153358i
$604$		−	4.96272e10i		−	0.372882i
$605$	3.21878e10			0.240254
$606$	−1.56248e11			−1.15858
$607$	8.24145e10			0.607084			0.303542	−	0.952818i	$-0.401831\pi$
$607$	8.24145e10			0.607084			0.303542	+	0.952818i	$0.401831\pi$
$608$		−	3.27753e11i		−	2.39846i
$609$	5.04144e10			0.366510
$610$	2.38483e11			1.72242
$611$	−1.57431e11			−1.12960
$612$	1.57810e10			0.112494
$613$		−	1.46159e11i		−	1.03510i	−0.855652	−	0.517551i	$-0.826844\pi$
$613$		−	1.46159e11i		−	1.03510i	0.855652	−	0.517551i	$-0.173156\pi$
$614$		−	2.44340e11i		−	1.71918i
$615$	−1.47888e11			−1.03379
$616$	−5.51125e11			−3.82761
$617$	3.77837e10			0.260714			0.130357	−	0.991467i	$-0.458388\pi$
$617$	3.77837e10			0.260714			0.130357	+	0.991467i	$0.458388\pi$
$618$	−2.44819e11			−1.67838
$619$	−8.71499e10			−0.593614			−0.296807	−	0.954937i	$-0.595922\pi$
$619$	−8.71499e10			−0.593614			−0.296807	+	0.954937i	$0.595922\pi$
$620$		−	2.74905e11i		−	1.86044i
$621$		−	3.73375e10i		−	0.251060i
$622$		−	1.81238e11i		−	1.21084i
$623$			2.47610e11i			1.64367i
$624$		−	1.59294e11i		−	1.05066i
$625$	−1.48259e11			−0.971630
$626$	−4.25822e11			−2.77288
$627$			1.41177e11i			0.913471i
$628$			1.77367e11i			1.14034i
$629$		−	3.17473e10i		−	0.202817i
$630$		−	1.28299e11i		−	0.814445i
$631$	1.73868e10			0.109673			0.0548367	−	0.998495i	$-0.482536\pi$
$631$	1.73868e10			0.109673			0.0548367	+	0.998495i	$0.482536\pi$
$632$			5.74474e11i			3.60082i
$633$			4.39585e10i			0.273797i
$634$			4.80639e11i			2.97483i
$635$	6.15774e10			0.378727
$636$	−3.01661e11			−1.84370
$637$			1.05802e11i			0.642592i
$638$	−1.60251e11			−0.967203
$639$	−1.40021e10			−0.0839829
$640$			3.42287e10i			0.204019i
$641$	−1.81064e11			−1.07251			−0.536254	−	0.844057i	$-0.680161\pi$
$641$	−1.81064e11			−1.07251			−0.536254	+	0.844057i	$0.680161\pi$
$642$		−	9.61600e10i		−	0.566049i
$643$	2.43062e11			1.42191			0.710957	−	0.703236i	$-0.248262\pi$
$643$	2.43062e11			1.42191			0.710957	+	0.703236i	$0.248262\pi$
$644$			7.20776e11i			4.19041i
$645$			3.32657e10i			0.192202i
$646$			6.43211e10i			0.369337i
$647$	−5.58877e9			−0.0318933			−0.0159467	−	0.999873i	$-0.505076\pi$
$647$	−5.58877e9			−0.0318933			−0.0159467	+	0.999873i	$0.505076\pi$
$648$			4.99307e10i			0.283184i
$649$	−1.47067e9	+	1.97840e11i	−0.00828964	+	1.11516i
$650$	−7.16153e9			−0.0401192
$651$		−	1.10459e11i		−	0.615001i
$652$	3.26590e11			1.80723
$653$	−1.06895e11			−0.587903			−0.293951	−	0.955820i	$-0.594970\pi$
$653$	−1.06895e11			−0.587903			−0.293951	+	0.955820i	$0.594970\pi$
$654$	1.15808e10			0.0633033
$655$		−	3.44539e11i		−	1.87186i
$656$	−7.74776e11			−4.18370
$657$		−	3.81681e10i		−	0.204851i
$658$	−6.64293e11			−3.54369
$659$		−	4.28516e10i		−	0.227209i	−0.993526	−	0.113604i	$-0.963760\pi$
$659$		−	4.28516e10i		−	0.227209i	0.993526	−	0.113604i	$-0.0362397\pi$
$660$			2.87350e11i			1.51438i
$661$	−1.87993e11			−0.984772			−0.492386	−	0.870377i	$-0.663875\pi$
$661$	−1.87993e11			−0.984772			−0.492386	+	0.870377i	$0.663875\pi$
$662$		−	2.64193e11i		−	1.37559i
$663$			1.24666e10i			0.0645197i
$664$	−6.43626e10			−0.331102
$665$	3.68455e11			1.88408
$666$	1.72962e11			0.879132
$667$			1.21714e11i			0.614946i
$668$	4.88281e11			2.45225
$669$	1.68317e11			0.840281
$670$	1.68206e11			0.834720
$671$	−2.14616e11			−1.05870
$672$		−	2.68047e11i		−	1.31442i
$673$			4.47608e10i			0.218191i	0.994031	+	0.109096i	$0.0347955\pi$
$673$			4.47608e10i			0.218191i	−0.994031	+	0.109096i	$0.965204\pi$
$674$	5.82333e11			2.82184
$675$	1.10296e9			0.00531307
$676$	−1.87372e11			−0.897259
$677$	3.80002e11			1.80897			0.904484	−	0.426508i	$-0.140256\pi$
$677$	3.80002e11			1.80897			0.904484	+	0.426508i	$0.140256\pi$
$678$	1.88484e11			0.891982
$679$		−	2.12924e11i		−	1.00172i
$680$			7.60307e10i			0.355593i
$681$			1.25100e11i			0.581661i
$682$			3.51111e11i			1.62296i
$683$		−	2.97625e11i		−	1.36769i	−0.729629	−	0.683843i	$-0.760307\pi$
$683$		−	2.97625e11i		−	1.36769i	0.729629	−	0.683843i	$-0.239693\pi$
$684$	−2.46910e11			−1.12801
$685$	−1.70232e11			−0.773179
$686$		−	1.02290e11i		−	0.461889i
$687$			3.86797e10i			0.173643i
$688$			1.74277e11i			0.777834i
$689$		−	2.38305e11i		−	1.05744i
$690$	3.09749e11			1.36651
$691$			1.55039e11i			0.680033i	0.940420	+	0.340016i	$0.110433\pi$
$691$			1.55039e11i			0.680033i	−0.940420	+	0.340016i	$0.889567\pi$
$692$			6.11648e11i			2.66733i
$693$			1.15459e11i			0.500605i
$694$	−5.60790e11			−2.41748
$695$	−1.77518e11			−0.760857
$696$		−	1.62766e11i		−	0.693628i
$697$	6.06351e10			0.256917
$698$	−7.12188e11			−3.00036
$699$			1.92288e9i			0.00805457i
$700$	−2.12920e10			−0.0886798
$701$		−	1.01201e11i		−	0.419096i	−0.977798	−	0.209548i	$-0.932801\pi$
$701$		−	1.01201e11i		−	0.419096i	0.977798	−	0.209548i	$-0.0671993\pi$
$702$	−6.79190e10			−0.279668
$703$			4.96720e11i			2.03372i
$704$			2.20889e11i			0.899256i
$705$			2.01146e11i			0.814243i
$706$	−4.19573e10			−0.168884
$707$		−	3.66978e11i		−	1.46880i
$708$	−3.46010e11	−	2.57210e9i	−1.37707	−	0.0102366i
$709$	−3.76546e10			−0.149016			−0.0745081	−	0.997220i	$-0.523739\pi$
$709$	−3.76546e10			−0.149016			−0.0745081	+	0.997220i	$0.523739\pi$
$710$		−	1.16161e11i		−	0.457115i
$711$	1.20351e11			0.470945
$712$	7.99423e11			3.11069
$713$	2.66677e11			1.03187
$714$			5.26037e10i			0.202406i
$715$	−2.26999e11			−0.868559
$716$			3.59583e11i			1.36819i
$717$	2.44227e11			0.924094
$718$			6.89020e11i			2.59259i
$719$		−	4.00517e11i		−	1.49867i	−0.662191	−	0.749335i	$-0.730373\pi$
$719$		−	4.00517e11i		−	1.49867i	0.662191	−	0.749335i	$-0.269627\pi$
$720$	−2.03526e11			−0.757337
$721$		−	5.75001e11i		−	2.12778i
$722$		−	5.06404e11i		−	1.86358i
$723$	−1.33549e11			−0.488750
$724$	−6.64945e11			−2.42009
$725$	−3.59548e9			−0.0130138
$726$		−	7.18999e10i		−	0.258810i
$727$	1.06855e11			0.382524			0.191262	−	0.981539i	$-0.438742\pi$
$727$	1.06855e11			0.382524			0.191262	+	0.981539i	$0.438742\pi$
$728$	7.61442e11			2.71089
$729$	1.04604e10			0.0370370
$730$	3.16640e11			1.11500
$731$		−	1.36392e10i		−	0.0477661i
$732$		−	3.75349e11i		−	1.30735i
$733$	4.55913e11			1.57931			0.789653	−	0.613554i	$-0.210261\pi$
$733$	4.55913e11			1.57931			0.789653	+	0.613554i	$0.210261\pi$
$734$	−3.79517e11			−1.30751
$735$	1.35180e11			0.463196
$736$	6.47137e11			2.20539
$737$	−1.51372e11			−0.513067
$738$			3.30346e11i			1.11364i
$739$			2.16091e10i			0.0724534i	0.999344	+	0.0362267i	$0.0115338\pi$
$739$			2.16091e10i			0.0724534i	−0.999344	+	0.0362267i	$0.988466\pi$
$740$			1.01102e12i			3.37156i
$741$		−	1.95053e11i		−	0.646962i
$742$		−	1.00555e12i		−	3.31732i
$743$	1.25286e11			0.411100			0.205550	−	0.978647i	$-0.434102\pi$
$743$	1.25286e11			0.411100			0.205550	+	0.978647i	$0.434102\pi$
$744$	−3.56622e11			−1.16390
$745$			2.17113e11i			0.704790i
$746$		−	1.47385e11i		−	0.475882i
$747$			1.34838e10i			0.0433042i
$748$		−	1.17816e11i		−	0.376354i
$749$	2.25849e11			0.717614
$750$			3.40585e11i			1.07642i
$751$		−	4.84579e11i		−	1.52337i	−0.647949	−	0.761683i	$-0.724373\pi$
$751$		−	4.84579e11i		−	1.52337i	0.647949	−	0.761683i	$-0.275627\pi$
$752$			1.05379e12i			3.29521i
$753$	−3.11068e11			−0.967553
$754$	2.21405e11			0.685017
$755$		−	5.00902e10i		−	0.154158i
$756$	−2.01931e11			−0.618180
$757$	3.11094e11			0.947346			0.473673	−	0.880701i	$-0.342928\pi$
$757$	3.11094e11			0.947346			0.473673	+	0.880701i	$0.342928\pi$
$758$		−	7.82918e10i		−	0.237159i
$759$	−2.78749e11			−0.839937
$760$		−	1.18958e12i		−	3.56566i
$761$	5.50313e11			1.64086			0.820429	−	0.571749i	$-0.193735\pi$
$761$	5.50313e11			1.64086			0.820429	+	0.571749i	$0.193735\pi$
$762$		−	1.37549e11i		−	0.407979i
$763$			2.71995e10i			0.0802533i
$764$			9.14661e11i			2.68464i
$765$	1.59282e10			0.0465073
$766$			2.65686e11i			0.771709i
$767$	2.03189e9	−	2.73338e11i	0.00587110	−	0.789804i
$768$	2.38423e11			0.685336
$769$		−	3.14849e11i		−	0.900321i	−0.892948	−	0.450161i	$-0.851367\pi$
$769$		−	3.14849e11i		−	0.900321i	0.892948	−	0.450161i	$-0.148633\pi$
$770$	−9.57841e11			−2.72477
$771$	2.23614e11			0.632821
$772$	1.25601e12			3.53609
$773$		−	3.75244e11i		−	1.05098i	−0.850799	−	0.525492i	$-0.823881\pi$
$773$		−	3.75244e11i		−	1.05098i	0.850799	−	0.525492i	$-0.176119\pi$
$774$	7.43076e10			0.207047
$775$			7.87773e9i			0.0218371i
$776$	−6.87438e11			−1.89577
$777$			4.06233e11i			1.11453i
$778$		−	9.82637e11i		−	2.68210i
$779$	−9.48700e11			−2.57620
$780$		−	3.97006e11i		−	1.07255i
$781$			1.04535e11i			0.280970i
$782$	−1.27000e11			−0.339606
$783$	−3.40990e10			−0.0907183
$784$	7.08203e11			1.87454
$785$			1.79022e11i			0.471442i
$786$	−7.69619e11			−2.01644
$787$	−2.83186e11			−0.738199			−0.369099	−	0.929390i	$-0.620334\pi$
$787$	−2.83186e11			−0.738199			−0.369099	+	0.929390i	$0.620334\pi$
$788$	−8.10364e11			−2.10172
$789$	1.75145e11			0.451950
$790$			9.98421e11i			2.56334i
$791$			4.42689e11i			1.13082i
$792$	3.72767e11			0.947407
$793$	2.96516e11			0.749817
$794$	1.21357e12			3.05339
$795$	−3.04476e11			−0.762227
$796$	8.75682e11			2.18119
$797$			1.74361e11i			0.432131i	0.976379	+	0.216066i	$0.0693226\pi$
$797$			1.74361e11i			0.432131i	−0.976379	+	0.216066i	$0.930677\pi$
$798$		−	8.23041e11i		−	2.02960i
$799$		−	8.24713e10i		−	0.202356i
$800$			1.91167e10i			0.0466715i
$801$		−	1.67477e11i		−	0.406841i
$802$	−2.76060e11			−0.667276
$803$	−2.84951e11			−0.685342
$804$		−	2.64739e11i		−	0.633569i
$805$			7.27501e11i			1.73241i
$806$		−	4.85100e11i		−	1.14945i
$807$		−	4.63225e11i		−	1.09219i
$808$	−1.18481e12			−2.77973
$809$		−	4.99746e11i		−	1.16669i	−0.812224	−	0.583345i	$-0.801744\pi$
$809$		−	4.99746e11i		−	1.16669i	0.812224	−	0.583345i	$-0.198256\pi$
$810$			8.67784e10i			0.201591i
$811$			1.47017e11i			0.339847i	0.985457	+	0.169923i	$0.0543520\pi$
$811$			1.47017e11i			0.339847i	−0.985457	+	0.169923i	$0.945648\pi$
$812$	6.58261e11			1.51417
$813$	3.59371e11			0.822584
$814$		−	1.29128e12i		−	2.94119i
$815$	3.29637e11			0.747147
$816$	8.34471e10			0.188213
$817$			2.13400e11i			0.478967i
$818$	3.41334e11			0.762371
$819$		−	1.59520e11i		−	0.354552i
$820$	−1.93097e12			−4.27090
$821$			7.80909e10i			0.171881i	0.996300	+	0.0859405i	$0.0273895\pi$
$821$			7.80909e10i			0.171881i	−0.996300	+	0.0859405i	$0.972611\pi$
$822$			3.80259e11i			0.832898i
$823$		−	2.51188e11i		−	0.547518i	−0.961798	−	0.273759i	$-0.911733\pi$
$823$		−	2.51188e11i		−	0.547518i	0.961798	−	0.273759i	$-0.0882671\pi$
$824$	−1.85643e12			−4.02688
$825$		−	8.23437e9i		−	0.0177752i
$826$	8.57375e9	−	1.15338e12i	0.0184183	−	2.47771i
$827$	−7.49319e11			−1.60194			−0.800968	−	0.598708i	$-0.795681\pi$
$827$	−7.49319e11			−1.60194			−0.800968	+	0.598708i	$0.795681\pi$
$828$		−	4.87515e11i		−	1.03721i
$829$	−2.28211e11			−0.483191			−0.241595	−	0.970377i	$-0.577671\pi$
$829$	−2.28211e11			−0.483191			−0.241595	+	0.970377i	$0.577671\pi$
$830$	−1.11861e11			−0.235703
$831$	−6.54259e10			−0.137197
$832$		−	3.05183e11i		−	0.636894i
$833$	−5.54251e10			−0.115113
$834$			3.96533e11i			0.819624i
$835$	4.92837e11			1.01381
$836$			1.84335e12i			3.77384i
$837$			7.47114e10i			0.152225i
$838$	−4.29138e11			−0.870203
$839$		−	7.11244e11i		−	1.43539i	−0.696356	−	0.717696i	$-0.745197\pi$
$839$		−	7.11244e11i		−	1.43539i	0.696356	−	0.717696i	$-0.254803\pi$
$840$		−	9.72875e11i		−	1.95407i
$841$	−3.89089e11			−0.777795
$842$	1.68019e12			3.34280
$843$	1.31536e10			0.0260457
$844$			5.73966e11i			1.13114i
$845$	−1.89120e11			−0.370946
$846$	4.49311e11			0.877134
$847$	1.68870e11			0.328109
$848$	−1.59513e12			−3.08471
$849$		−	1.84410e11i		−	0.354939i
$850$		−	3.75162e9i		−	0.00718692i
$851$	−9.80756e11			−1.87000
$852$	−1.82826e11			−0.346960
$853$	5.49233e11			1.03743			0.518717	−	0.854946i	$-0.326410\pi$
$853$	5.49233e11			1.03743			0.518717	+	0.854946i	$0.326410\pi$
$854$	1.25117e12			2.35227
$855$	−2.49214e11			−0.466345
$856$		−	7.29167e11i		−	1.35810i
$857$			7.84321e10i			0.145402i	0.997354	+	0.0727010i	$0.0231619\pi$
$857$			7.84321e10i			0.145402i	−0.997354	+	0.0727010i	$0.976838\pi$
$858$			5.07061e11i			0.935645i
$859$			3.79996e11i			0.697921i	0.937138	+	0.348960i	$0.113465\pi$
$859$			3.79996e11i			0.697921i	−0.937138	+	0.348960i	$0.886535\pi$
$860$			4.34350e11i			0.794046i
$861$	−7.75876e11			−1.41182
$862$	3.09410e11			0.560409
$863$			9.84581e11i			1.77504i	0.460769	+	0.887520i	$0.347574\pi$
$863$			9.84581e11i			1.77504i	−0.460769	+	0.887520i	$0.652426\pi$
$864$			1.81300e11i			0.325344i
$865$			6.17354e11i			1.10273i
$866$			1.61462e11i			0.287077i
$867$	3.19693e11			0.565792
$868$		−	1.44226e12i		−	2.54076i
$869$		−	8.98500e11i		−	1.57557i
$870$		−	2.82883e11i		−	0.493776i
$871$	2.09137e11			0.363378
$872$	8.78153e10			0.151881
$873$			1.44016e11i			0.247945i
$874$	1.98704e12			3.40535
$875$	−7.99926e11			−1.36464
$876$		−	4.98360e11i		−	0.846305i
$877$	−2.99863e11			−0.506903			−0.253451	−	0.967348i	$-0.581566\pi$
$877$	−2.99863e11			−0.506903			−0.253451	+	0.967348i	$0.581566\pi$
$878$		−	1.69099e12i		−	2.84553i
$879$	−6.60318e11			−1.10611
$880$			1.51946e12i			2.53371i
$881$		−	1.15461e12i		−	1.91661i	−0.285753	−	0.958303i	$-0.592244\pi$
$881$		−	1.15461e12i		−	1.91661i	0.285753	−	0.958303i	$-0.407756\pi$
$882$		−	3.01961e11i		−	0.498972i
$883$	−2.92132e11			−0.480548			−0.240274	−	0.970705i	$-0.577237\pi$
$883$	−2.92132e11			−0.480548			−0.240274	+	0.970705i	$0.577237\pi$
$884$			1.62776e11i			0.266551i
$885$	−3.49238e11	−	2.59610e9i	−0.569309	−	0.00423203i
$886$	2.43989e10			0.0395946
$887$			3.35308e11i			0.541689i	0.962623	+	0.270844i	$0.0873029\pi$
$887$			3.35308e11i			0.541689i	−0.962623	+	0.270844i	$0.912697\pi$
$888$	1.31155e12			2.10927
$889$	3.23059e11			0.517220
$890$	1.38938e12			2.21442
$891$		−	7.80936e10i		−	0.123910i
$892$	2.19772e12			3.47146
$893$			1.29035e12i			2.02909i
$894$	4.84978e11			0.759227
$895$			3.62938e11i			0.565639i
$896$			1.79577e11i			0.278624i
$897$	3.85124e11			0.594882
$898$		−	2.32977e11i		−	0.358268i
$899$		−	2.43547e11i		−	0.372858i
$900$	1.44014e10			0.0219500
$901$	1.24838e11			0.189429
$902$	2.46625e12			3.72573
$903$			1.74525e11i			0.262486i
$904$	1.42925e12			2.14010
$905$	−6.71149e11			−1.00052
$906$	−1.11890e11			−0.166064
$907$	−8.27955e11			−1.22343			−0.611713	−	0.791080i	$-0.709519\pi$
$907$	−8.27955e11			−1.22343			−0.611713	+	0.791080i	$0.709519\pi$
$908$			1.63343e12i			2.40302i
$909$			2.48214e11i			0.363556i
$910$	1.32337e12			1.92981
$911$	−5.93160e11			−0.861189			−0.430594	−	0.902546i	$-0.641696\pi$
$911$	−5.93160e11			−0.861189			−0.430594	+	0.902546i	$0.641696\pi$
$912$	−1.30562e12			−1.88728
$913$	1.00666e11			0.144877
$914$	3.66351e10			0.0524943
$915$		−	3.78851e11i		−	0.540486i
$916$			5.05041e11i			0.717372i
$917$		−	1.80759e12i		−	2.55636i
$918$		−	3.55798e10i		−	0.0500995i
$919$			1.20289e12i			1.68641i	0.537594	+	0.843204i	$0.319333\pi$
$919$			1.20289e12i			1.68641i	−0.537594	+	0.843204i	$0.680667\pi$
$920$	2.34878e12			3.27862
$921$	−3.88156e11			−0.539471
$922$			2.02035e12i			2.79579i
$923$		−	1.44428e11i		−	0.198996i
$924$			1.50755e12i			2.06816i
$925$		−	2.89719e10i		−	0.0395740i
$926$	5.43073e11			0.738609
$927$			3.88916e11i			0.526668i
$928$		−	5.91008e11i		−	0.796896i
$929$		−	1.13793e12i		−	1.52776i	−0.645360	−	0.763879i	$-0.723293\pi$
$929$		−	1.13793e12i		−	1.52776i	0.645360	−	0.763879i	$-0.276707\pi$
$930$	−6.19801e11			−0.828553
$931$	8.67184e11			1.15428
$932$			2.51070e10i			0.0332760i
$933$	−2.87912e11			−0.379956
$934$	−4.76964e11			−0.626756
$935$		−	1.18915e11i		−	0.155593i
$936$	−5.15020e11			−0.670997
$937$		−	1.50247e12i		−	1.94916i	−0.224048	−	0.974578i	$-0.571927\pi$
$937$		−	1.50247e12i		−	1.94916i	0.224048	−	0.974578i	$-0.428073\pi$
$938$	8.82472e11			1.13996
$939$			6.76456e11i			0.870116i
$940$			2.62636e12i			3.36389i
$941$			1.23345e12i			1.57313i	0.617508	+	0.786564i	$0.288142\pi$
$941$			1.23345e12i			1.57313i	−0.617508	+	0.786564i	$0.711858\pi$
$942$	3.99893e11			0.507855
$943$		−	1.87317e12i		−	2.36882i
$944$	−1.82964e12	−	1.36008e10i	−2.30397	−	0.0171269i
$945$	−2.03815e11			−0.255569
$946$		−	5.54757e11i		−	0.692689i
$947$	−3.01042e11			−0.374307			−0.187153	−	0.982331i	$-0.559926\pi$
$947$	−3.01042e11			−0.374307			−0.187153	+	0.982331i	$0.559926\pi$
$948$	1.57142e12			1.94562
$949$	3.93692e11			0.485391
$950$			5.86980e10i			0.0720658i
$951$	7.63538e11			0.933487
$952$			3.98887e11i			0.485626i
$953$	1.11906e12			1.35669			0.678345	−	0.734743i	$-0.262697\pi$
$953$	1.11906e12			1.35669			0.678345	+	0.734743i	$0.262697\pi$
$954$			6.80127e11i			0.821100i
$955$			9.23195e11i			1.10989i
$956$	3.18886e12			3.81772
$957$			2.54572e11i			0.303503i
$958$			1.67639e12i			1.99028i
$959$	−8.93106e11			−1.05591
$960$	−3.89925e11			−0.459088
$961$	3.19277e11			0.374347
$962$			1.78405e12i			2.08308i
$963$	−1.52759e11			−0.177623
$964$	−1.74374e12			−2.01918
$965$	1.26773e12			1.46189
$966$	1.62506e12			1.86622
$967$			1.58833e12i			1.81649i	0.418435	+	0.908247i	$0.362579\pi$
$967$			1.58833e12i			1.81649i	−0.418435	+	0.908247i	$0.637421\pi$
$968$		−	5.45206e11i		−	0.620954i
$969$	1.02180e11			0.115896
$970$	−1.19475e12			−1.34955
$971$	−1.34837e12			−1.51682			−0.758409	−	0.651779i	$-0.774023\pi$
$971$	−1.34837e12			−1.51682			−0.758409	+	0.651779i	$0.774023\pi$
$972$	1.36581e11			0.153012
$973$	−9.31328e11			−1.03909
$974$		−	2.32593e12i		−	2.58441i
$975$			1.13767e10i			0.0125892i
$976$		−	1.98478e12i		−	2.18733i
$977$			1.70214e12i			1.86817i	0.357046	+	0.934087i	$0.383784\pi$
$977$			1.70214e12i			1.86817i	−0.357046	+	0.934087i	$0.616216\pi$
$978$		−	7.36331e11i		−	0.804855i
$979$	−1.25033e12			−1.36111
$980$	1.76505e12			1.91361
$981$		−	1.83971e10i		−	0.0198643i
$982$		−	1.96860e11i		−	0.211696i
$983$		−	7.46758e10i		−	0.0799771i	−0.999200	−	0.0399886i	$-0.987268\pi$
$983$		−	7.46758e10i		−	0.0799771i	0.999200	−	0.0399886i	$-0.0127322\pi$
$984$			2.50496e12i			2.67190i
$985$	−8.17925e11			−0.868898
$986$			1.15984e11i			0.122713i
$987$			1.05529e12i			1.11199i
$988$		−	2.54680e12i		−	2.67280i
$989$	−4.21350e11			−0.440410
$990$	6.47860e11			0.674435
$991$		−	1.53942e12i		−	1.59611i	−0.602586	−	0.798054i	$-0.705863\pi$
$991$		−	1.53942e12i		−	1.59611i	0.602586	−	0.798054i	$-0.294137\pi$
$992$	−1.29491e12			−1.33718
$993$	−4.19695e11			−0.431655
$994$		−	6.09424e11i		−	0.624273i
$995$	8.83852e11			0.901753
$996$			1.76058e11i			0.178903i
$997$	−3.22501e11			−0.326400			−0.163200	−	0.986593i	$-0.552182\pi$
$997$	−3.22501e11			−0.326400			−0.163200	+	0.986593i	$0.552182\pi$
$998$		−	1.40194e12i		−	1.41322i
$999$		−	2.74766e11i		−	0.275868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.4	✓	80
59.58	odd	2	inner	177.9.c.a.58.77	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.4	✓	80	1.1	even	1	trivial
177.9.c.a.58.77	yes	80	59.58	odd	2	inner

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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-29.4383i q^{2} -46.7654 q^{3} -610.615 q^{4} -616.312 q^{5} +1376.69i q^{6} -3233.41 q^{7} +10439.3i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q-29.4383i q^{2} -46.7654 q^{3} -610.615 q^{4} -616.312 q^{5} +1376.69i q^{6} -3233.41 q^{7} +10439.3i q^{8} +2187.00 q^{9} +18143.2i q^{10} -16327.4i q^{11} +28555.6 q^{12} +22558.2i q^{13} +95186.3i q^{14} +28822.1 q^{15} +150997. q^{16} -11817.3 q^{17} -64381.6i q^{18} +184894. q^{19} +376330. q^{20} +151212. q^{21} -480653. q^{22} +365066. i q^{23} -488197. i q^{24} -10784.2 q^{25} +664076. q^{26} -102276. q^{27} +1.97437e6 q^{28} +333403. q^{29} -848474. i q^{30} -730489. i q^{31} -1.77266e6i q^{32} +763559. i q^{33} +347881. i q^{34} +1.99279e6 q^{35} -1.33542e6 q^{36} +2.68652e6i q^{37} -5.44297e6i q^{38} -1.05494e6i q^{39} -6.43385e6i q^{40} -5.13105e6 q^{41} -4.45142e6i q^{42} +1.15417e6i q^{43} +9.96978e6i q^{44} -1.34787e6 q^{45} +1.07469e7 q^{46} +6.97887e6i q^{47} -7.06145e6 q^{48} +4.69017e6 q^{49} +317469. i q^{50} +552639. q^{51} -1.37744e7i q^{52} -1.05640e7 q^{53} +3.01083e6i q^{54} +1.00628e7i q^{55} -3.37545e7i q^{56} -8.64663e6 q^{57} -9.81481e6i q^{58} +(-1.21170e7 - 90073.3i) q^{59} -1.75992e7 q^{60} -1.31445e7i q^{61} -2.15044e7 q^{62} -7.07148e6 q^{63} -1.35287e7 q^{64} -1.39029e7i q^{65} +2.24779e7 q^{66} -9.27099e6i q^{67} +7.21581e6 q^{68} -1.70725e7i q^{69} -5.86645e7i q^{70} -6.40244e6 q^{71} +2.28307e7i q^{72} -1.74523e7i q^{73} +7.90865e7 q^{74} +504327. q^{75} -1.12899e8 q^{76} +5.27934e7i q^{77} -3.10558e7 q^{78} +5.50300e7 q^{79} -9.30615e7 q^{80} +4.78297e6 q^{81} +1.51050e8i q^{82} +6.16543e6i q^{83} -9.23322e7 q^{84} +7.28313e6 q^{85} +3.39770e7 q^{86} -1.55917e7 q^{87} +1.70447e8 q^{88} -7.65784e7i q^{89} +3.96792e7i q^{90} -7.29401e7i q^{91} -2.22915e8i q^{92} +3.41616e7i q^{93} +2.05446e8 q^{94} -1.13952e8 q^{95} +8.28989e7i q^{96} +6.58511e7i q^{97} -1.38071e8i q^{98} -3.57081e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more