LMFDB - Embedded newform 177.11.c.a.58.92

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,11,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, 11, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 11 $
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:	$112.458233723$
Analytic rank:	$0$
Dimension:	$100$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.92
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+55.6543i q^{2} +140.296 q^{3} -2073.41 q^{4} -1651.80 q^{5} +7808.09i q^{6} -6427.48 q^{7} -58404.0i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q+55.6543i q^{2} +140.296 q^{3} -2073.41 q^{4} -1651.80 q^{5} +7808.09i q^{6} -6427.48 q^{7} -58404.0i q^{8} +19683.0 q^{9} -91929.7i q^{10} +42364.0i q^{11} -290891. q^{12} +179652. i q^{13} -357717. i q^{14} -231741. q^{15} +1.12727e6 q^{16} -2.44515e6 q^{17} +1.09544e6i q^{18} -2.94996e6 q^{19} +3.42485e6 q^{20} -901750. q^{21} -2.35774e6 q^{22} -4.47755e6i q^{23} -8.19385e6i q^{24} -7.03719e6 q^{25} -9.99843e6 q^{26} +2.76145e6 q^{27} +1.33268e7 q^{28} +3.67308e7 q^{29} -1.28974e7i q^{30} -595402. i q^{31} +2.93168e6i q^{32} +5.94350e6i q^{33} -1.36083e8i q^{34} +1.06169e7 q^{35} -4.08108e7 q^{36} +1.07486e7i q^{37} -1.64178e8i q^{38} +2.52045e7i q^{39} +9.64716e7i q^{40} +1.47249e8 q^{41} -5.01863e7i q^{42} -2.36868e8i q^{43} -8.78377e7i q^{44} -3.25123e7 q^{45} +2.49195e8 q^{46} +3.78784e8i q^{47} +1.58151e8 q^{48} -2.41163e8 q^{49} -3.91650e8i q^{50} -3.43046e8 q^{51} -3.72492e8i q^{52} -2.09357e8 q^{53} +1.53687e8i q^{54} -6.99767e7i q^{55} +3.75390e8i q^{56} -4.13868e8 q^{57} +2.04423e9i q^{58} +(2.07411e8 - 6.84177e8i) q^{59} +4.80493e8 q^{60} +3.23023e8i q^{61} +3.31367e7 q^{62} -1.26512e8 q^{63} +9.91162e8 q^{64} -2.96749e8i q^{65} -3.30782e8 q^{66} +1.67595e9i q^{67} +5.06980e9 q^{68} -6.28183e8i q^{69} +5.90876e8i q^{70} +1.42921e9 q^{71} -1.14957e9i q^{72} -2.75324e9i q^{73} -5.98206e8 q^{74} -9.87291e8 q^{75} +6.11647e9 q^{76} -2.72293e8i q^{77} -1.40274e9 q^{78} +4.89865e9 q^{79} -1.86202e9 q^{80} +3.87420e8 q^{81} +8.19506e9i q^{82} +4.90223e8i q^{83} +1.86969e9 q^{84} +4.03890e9 q^{85} +1.31827e10 q^{86} +5.15318e9 q^{87} +2.47422e9 q^{88} +6.61963e9i q^{89} -1.80945e9i q^{90} -1.15471e9i q^{91} +9.28378e9i q^{92} -8.35325e7i q^{93} -2.10810e10 q^{94} +4.87274e9 q^{95} +4.11304e8i q^{96} +1.12096e9i q^{97} -1.34218e10i q^{98} +8.33850e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) $ 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9	$ 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9} + 620136 q^{12} + 662904 q^{15} + 27925160 q^{16} - 2053136 q^{17} - 5169828 q^{19} - 1076324 q^{20} - 1829224 q^{22} + 215378180 q^{25} - 22082700 q^{26} - 102921320 q^{28} - 112503588 q^{29} - 76491392 q^{35} - 1007769600 q^{36} + 473464516 q^{41} + 1215405588 q^{46} - 1676272320 q^{48} + 1975297276 q^{49} + 733970808 q^{51} + 3267506728 q^{53} + 591502824 q^{57} + 508142200 q^{59} + 1264196808 q^{60} - 6538206968 q^{62} + 362009736 q^{63} - 10324137972 q^{64} - 2764346616 q^{66} + 9997685952 q^{68} + 14908523204 q^{71} + 4863508712 q^{74} + 1890481680 q^{75} + 2044437240 q^{76} - 758396196 q^{78} - 3599839500 q^{79} - 23217941144 q^{80} + 38742048900 q^{81} - 13094894808 q^{84} + 23360564412 q^{85} + 12186923752 q^{86} + 7965322272 q^{87} + 32415437996 q^{88} - 22098322280 q^{94} + 7834510028 q^{95}+O(q^{100}) $ 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9 + 620136 * q^12 + 662904 * q^15 + 27925160 * q^16 - 2053136 * q^17 - 5169828 * q^19 - 1076324 * q^20 - 1829224 * q^22 + 215378180 * q^25 - 22082700 * q^26 - 102921320 * q^28 - 112503588 * q^29 - 76491392 * q^35 - 1007769600 * q^36 + 473464516 * q^41 + 1215405588 * q^46 - 1676272320 * q^48 + 1975297276 * q^49 + 733970808 * q^51 + 3267506728 * q^53 + 591502824 * q^57 + 508142200 * q^59 + 1264196808 * q^60 - 6538206968 * q^62 + 362009736 * q^63 - 10324137972 * q^64 - 2764346616 * q^66 + 9997685952 * q^68 + 14908523204 * q^71 + 4863508712 * q^74 + 1890481680 * q^75 + 2044437240 * q^76 - 758396196 * q^78 - 3599839500 * q^79 - 23217941144 * q^80 + 38742048900 * q^81 - 13094894808 * q^84 + 23360564412 * q^85 + 12186923752 * q^86 + 7965322272 * q^87 + 32415437996 * q^88 - 22098322280 * q^94 + 7834510028 * 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 $

$2$			55.6543i			1.73920i	0.493758	+	0.869599i	$0.335623\pi$
$2$			55.6543i			1.73920i	−0.493758	+	0.869599i	$0.664377\pi$
$3$	140.296			0.577350
$3$	140.296			0.577350
$4$	−2073.41			−2.02481
$5$	−1651.80			−0.528575			−0.264288	−	0.964444i	$-0.585137\pi$
$5$	−1651.80			−0.528575			−0.264288	+	0.964444i	$0.585137\pi$
$6$			7808.09i			1.00413i
$7$	−6427.48			−0.382429			−0.191214	−	0.981548i	$-0.561243\pi$
$7$	−6427.48			−0.382429			−0.191214	+	0.981548i	$0.561243\pi$
$8$		−	58404.0i		−	1.78235i
$9$	19683.0			0.333333
$10$		−	91929.7i		−	0.919297i
$11$			42364.0i			0.263047i	0.991313	+	0.131523i	$0.0419869\pi$
$11$			42364.0i			0.263047i	−0.991313	+	0.131523i	$0.958013\pi$
$12$	−290891.			−1.16902
$13$			179652.i			0.483856i	0.970294	+	0.241928i	$0.0777798\pi$
$13$			179652.i			0.483856i	−0.970294	+	0.241928i	$0.922220\pi$
$14$		−	357717.i		−	0.665119i
$15$	−231741.			−0.305173
$16$	1.12727e6			1.07505
$17$	−2.44515e6			−1.72211			−0.861056	−	0.508509i	$-0.830197\pi$
$17$	−2.44515e6			−1.72211			−0.861056	+	0.508509i	$0.830197\pi$
$18$			1.09544e6i			0.579733i
$19$	−2.94996e6			−1.19137			−0.595687	−	0.803216i	$-0.703120\pi$
$19$	−2.94996e6			−1.19137			−0.595687	+	0.803216i	$0.703120\pi$
$20$	3.42485e6			1.07026
$21$	−901750.			−0.220795
$22$	−2.35774e6			−0.457491
$23$		−	4.47755e6i		−	0.695667i	−0.937556	−	0.347834i	$-0.886917\pi$
$23$		−	4.47755e6i		−	0.695667i	0.937556	−	0.347834i	$-0.113083\pi$
$24$		−	8.19385e6i		−	1.02904i
$25$	−7.03719e6			−0.720608
$26$	−9.99843e6			−0.841521
$27$	2.76145e6			0.192450
$28$	1.33268e7			0.774345
$29$	3.67308e7			1.79077			0.895385	−	0.445292i	$-0.146900\pi$
$29$	3.67308e7			1.79077			0.895385	+	0.445292i	$0.146900\pi$
$30$		−	1.28974e7i		−	0.530756i
$31$		−	595402.i		−	0.0207970i	−0.999946	−	0.0103985i	$-0.996690\pi$
$31$		−	595402.i		−	0.0207970i	0.999946	−	0.0103985i	$-0.00331001\pi$
$32$			2.93168e6i			0.0873710i
$33$			5.94350e6i			0.151870i
$34$		−	1.36083e8i		−	2.99510i
$35$	1.06169e7			0.202142
$36$	−4.08108e7			−0.674937
$37$			1.07486e7i			0.155004i	0.996992	+	0.0775021i	$0.0246944\pi$
$37$			1.07486e7i			0.155004i	−0.996992	+	0.0775021i	$0.975306\pi$
$38$		−	1.64178e8i		−	2.07204i
$39$			2.52045e7i			0.279354i
$40$			9.64716e7i			0.942105i
$41$	1.47249e8			1.27097			0.635483	−	0.772115i	$-0.280801\pi$
$41$	1.47249e8			1.27097			0.635483	+	0.772115i	$0.280801\pi$
$42$		−	5.01863e7i		−	0.384007i
$43$		−	2.36868e8i		−	1.61126i	−0.592422	−	0.805628i	$-0.701828\pi$
$43$		−	2.36868e8i		−	1.61126i	0.592422	−	0.805628i	$-0.298172\pi$
$44$		−	8.78377e7i		−	0.532620i
$45$	−3.25123e7			−0.176192
$46$	2.49195e8			1.20990
$47$			3.78784e8i			1.65159i	0.563969	+	0.825796i	$0.309274\pi$
$47$			3.78784e8i			1.65159i	−0.563969	+	0.825796i	$0.690726\pi$
$48$	1.58151e8			0.620679
$49$	−2.41163e8			−0.853748
$50$		−	3.91650e8i		−	1.25328i
$51$	−3.43046e8			−0.994262
$52$		−	3.72492e8i		−	0.979717i
$53$	−2.09357e8			−0.500620			−0.250310	−	0.968166i	$-0.580532\pi$
$53$	−2.09357e8			−0.500620			−0.250310	+	0.968166i	$0.580532\pi$
$54$			1.53687e8i			0.334709i
$55$		−	6.99767e7i		−	0.139040i
$56$			3.75390e8i			0.681621i
$57$	−4.13868e8			−0.687840
$58$			2.04423e9i			3.11451i
$59$	2.07411e8	−	6.84177e8i	0.290116	−	0.956992i
$59$	2.07411e8	−	6.84177e8i	0.290116	−	0.956992i
$60$	4.80493e8			0.617917
$61$			3.23023e8i			0.382458i	0.981545	+	0.191229i	$0.0612473\pi$
$61$			3.23023e8i			0.382458i	−0.981545	+	0.191229i	$0.938753\pi$
$62$	3.31367e7			0.0361702
$63$	−1.26512e8			−0.127476
$64$	9.91162e8			0.923091
$65$		−	2.96749e8i		−	0.255754i
$66$	−3.30782e8			−0.264132
$67$			1.67595e9i			1.24133i	0.784075	+	0.620666i	$0.213138\pi$
$67$			1.67595e9i			1.24133i	−0.784075	+	0.620666i	$0.786862\pi$
$68$	5.06980e9			3.48695
$69$		−	6.28183e8i		−	0.401644i
$70$			5.90876e8i			0.351565i
$71$	1.42921e9			0.792143			0.396071	−	0.918220i	$-0.370373\pi$
$71$	1.42921e9			0.792143			0.396071	+	0.918220i	$0.370373\pi$
$72$		−	1.14957e9i		−	0.594116i
$73$		−	2.75324e9i		−	1.32810i	−0.747689	−	0.664049i	$-0.768836\pi$
$73$		−	2.75324e9i		−	1.32810i	0.747689	−	0.664049i	$-0.231164\pi$
$74$	−5.98206e8			−0.269583
$75$	−9.87291e8			−0.416043
$76$	6.11647e9			2.41231
$77$		−	2.72293e8i		−	0.100597i
$78$	−1.40274e9			−0.485853
$79$	4.89865e9			1.59199			0.795996	−	0.605301i	$-0.206947\pi$
$79$	4.89865e9			1.59199			0.795996	+	0.605301i	$0.206947\pi$
$80$	−1.86202e9			−0.568243
$81$	3.87420e8			0.111111
$82$			8.19506e9i			2.21046i
$83$			4.90223e8i			0.124452i	0.998062	+	0.0622261i	$0.0198200\pi$
$83$			4.90223e8i			0.124452i	−0.998062	+	0.0622261i	$0.980180\pi$
$84$	1.86969e9			0.447068
$85$	4.03890e9			0.910266
$86$	1.31827e10			2.80229
$87$	5.15318e9			1.03390
$88$	2.47422e9			0.468841
$89$			6.61963e9i			1.18545i	0.805405	+	0.592725i	$0.201948\pi$
$89$			6.61963e9i			1.18545i	−0.805405	+	0.592725i	$0.798052\pi$
$90$		−	1.80945e9i		−	0.306432i
$91$		−	1.15471e9i		−	0.185040i
$92$			9.28378e9i			1.40859i
$93$		−	8.35325e7i		−	0.0120072i
$94$	−2.10810e10			−2.87245
$95$	4.87274e9			0.629731
$96$			4.11304e8i			0.0504437i
$97$			1.12096e9i			0.130537i	0.997868	+	0.0652683i	$0.0207903\pi$
$97$			1.12096e9i			0.130537i	−0.997868	+	0.0652683i	$0.979210\pi$
$98$		−	1.34218e10i		−	1.48484i
$99$			8.33850e8i			0.0876823i
$100$	1.45910e10			1.45910
$101$		−	4.89302e9i		−	0.465554i	−0.972530	−	0.232777i	$-0.925219\pi$
$101$		−	4.89302e9i		−	0.465554i	0.972530	−	0.232777i	$-0.0747813\pi$
$102$		−	1.90920e10i		−	1.72922i
$103$		−	6.05488e8i		−	0.0522300i	−0.999659	−	0.0261150i	$-0.991686\pi$
$103$		−	6.05488e8i		−	0.0522300i	0.999659	−	0.0261150i	$-0.00831360\pi$
$104$	1.04924e10			0.862400
$105$	1.48951e9			0.116707
$106$		−	1.16516e10i		−	0.870677i
$107$	−1.34731e10			−0.960612			−0.480306	−	0.877101i	$-0.659474\pi$
$107$	−1.34731e10			−0.960612			−0.480306	+	0.877101i	$0.659474\pi$
$108$	−5.72560e9			−0.389675
$109$			2.45190e10i			1.59357i	0.604265	+	0.796783i	$0.293467\pi$
$109$			2.45190e10i			1.59357i	−0.604265	+	0.796783i	$0.706533\pi$
$110$	3.89451e9			0.241818
$111$			1.50799e9i			0.0894917i
$112$	−7.24549e9			−0.411129
$113$		−	3.11336e10i		−	1.68981i	−0.534917	−	0.844904i	$-0.679657\pi$
$113$		−	3.11336e10i		−	1.68981i	0.534917	−	0.844904i	$-0.320343\pi$
$114$		−	2.30336e10i		−	1.19629i
$115$			7.39601e9i			0.367712i
$116$	−7.61578e10			−3.62597
$117$			3.53610e9i			0.161285i
$118$	3.80774e10	+	1.15433e10i	1.66440	+	0.504569i
$119$	1.57162e10			0.658585
$120$			1.35346e10i			0.543925i
$121$	2.41427e10			0.930806
$122$	−1.79776e10			−0.665171
$123$	2.06585e10			0.733792
$124$			1.23451e9i			0.0421101i
$125$	2.77548e10			0.909471
$126$		−	7.04094e9i		−	0.221706i
$127$	−2.06395e10			−0.624713			−0.312356	−	0.949965i	$-0.601118\pi$
$127$	−2.06395e10			−0.624713			−0.312356	+	0.949965i	$0.601118\pi$
$128$			5.81645e10i			1.69281i
$129$		−	3.32317e10i		−	0.930259i
$130$	1.65154e10			0.444807
$131$		−	5.93554e10i		−	1.53852i	−0.638934	−	0.769261i	$-0.720624\pi$
$131$		−	5.93554e10i		−	1.53852i	0.638934	−	0.769261i	$-0.279376\pi$
$132$		−	1.23233e10i		−	0.307508i
$133$	1.89608e10			0.455616
$134$	−9.32741e10			−2.15892
$135$	−4.56135e9			−0.101724
$136$			1.42807e11i			3.06941i
$137$	−6.49128e10			−1.34502			−0.672508	−	0.740090i	$-0.734783\pi$
$137$	−6.49128e10			−1.34502			−0.672508	+	0.740090i	$0.734783\pi$
$138$	3.49611e10			0.698538
$139$	8.69158e10			1.67504			0.837519	−	0.546408i	$-0.184005\pi$
$139$	8.69158e10			1.67504			0.837519	+	0.546408i	$0.184005\pi$
$140$	−2.20131e10			−0.409300
$141$			5.31420e10i			0.953547i
$142$			7.95416e10i			1.37769i
$143$	−7.61078e9			−0.127277
$144$	2.21880e10			0.358349
$145$	−6.06718e10			−0.946557
$146$	1.53230e11			2.30983
$147$	−3.38342e10			−0.492912
$148$		−	2.22862e10i		−	0.313854i
$149$			7.01159e10i			0.954741i	0.878702	+	0.477370i	$0.158410\pi$
$149$			7.01159e10i			0.954741i	−0.878702	+	0.477370i	$0.841590\pi$
$150$		−	5.49470e10i		−	0.723582i
$151$		−	3.25291e10i		−	0.414369i	−0.978302	−	0.207184i	$-0.933570\pi$
$151$		−	3.25291e10i		−	0.414369i	0.978302	−	0.207184i	$-0.0664300\pi$
$152$			1.72290e11i			2.12344i
$153$	−4.81280e10			−0.574038
$154$	1.51543e10			0.174958
$155$			9.83483e8i			0.0109928i
$156$		−	5.22592e10i		−	0.565640i
$157$			1.35643e11i			1.42200i	0.703194	+	0.710998i	$0.251756\pi$
$157$			1.35643e11i			1.42200i	−0.703194	+	0.710998i	$0.748244\pi$
$158$			2.72631e11i			2.76879i
$159$	−2.93720e10			−0.289033
$160$		−	4.84255e9i		−	0.0461821i
$161$			2.87794e10i			0.266043i
$162$			2.15616e10i			0.193244i
$163$	−2.53362e10			−0.220193			−0.110097	−	0.993921i	$-0.535116\pi$
$163$	−2.53362e10			−0.220193			−0.110097	+	0.993921i	$0.535116\pi$
$164$	−3.05307e11			−2.57346
$165$		−	9.81746e9i		−	0.0802748i
$166$	−2.72830e10			−0.216447
$167$	−8.34235e10			−0.642253			−0.321126	−	0.947036i	$-0.604061\pi$
$167$	−8.34235e10			−0.642253			−0.321126	+	0.947036i	$0.604061\pi$
$168$			5.26658e10i			0.393534i
$169$	1.05584e11			0.765883
$170$			2.24782e11i			1.58313i
$171$	−5.80641e10			−0.397125
$172$			4.91124e11i			3.26249i
$173$		−	2.37750e11i		−	1.53423i	−0.641509	−	0.767115i	$-0.721691\pi$
$173$		−	2.37750e11i		−	1.53423i	0.641509	−	0.767115i	$-0.278309\pi$
$174$			2.86797e11i			1.79816i
$175$	4.52314e10			0.275581
$176$			4.77556e10i			0.282788i
$177$	2.90989e10	−	9.59873e10i	0.167498	−	0.552519i
$178$	−3.68411e11			−2.06173
$179$			2.07663e11i			1.13004i	0.825077	+	0.565020i	$0.191132\pi$
$179$			2.07663e11i			1.13004i	−0.825077	+	0.565020i	$0.808868\pi$
$180$	6.74112e10			0.356755
$181$	8.92034e10			0.459186			0.229593	−	0.973287i	$-0.426260\pi$
$181$	8.92034e10			0.459186			0.229593	+	0.973287i	$0.426260\pi$
$182$	6.42647e10			0.321822
$183$			4.53188e10i			0.220812i
$184$	−2.61507e11			−1.23992
$185$		−	1.77545e10i		−	0.0819313i
$186$	4.64895e9			0.0208829
$187$		−	1.03586e11i		−	0.452996i
$188$		−	7.85374e11i		−	3.34416i
$189$	−1.77491e10			−0.0735984
$190$			2.71189e11i			1.09523i
$191$		−	8.84099e10i		−	0.347804i	−0.984763	−	0.173902i	$-0.944362\pi$
$191$		−	8.84099e10i		−	0.347804i	0.984763	−	0.173902i	$-0.0556375\pi$
$192$	1.39056e11			0.532947
$193$	−2.58894e11			−0.966796			−0.483398	−	0.875401i	$-0.660598\pi$
$193$	−2.58894e11			−0.966796			−0.483398	+	0.875401i	$0.660598\pi$
$194$	−6.23864e10			−0.227029
$195$		−	4.16328e10i		−	0.147660i
$196$	5.00028e11			1.72868
$197$	2.60482e11			0.877904			0.438952	−	0.898510i	$-0.355350\pi$
$197$	2.60482e11			0.877904			0.438952	+	0.898510i	$0.355350\pi$
$198$	−4.64074e10			−0.152497
$199$	1.43116e11			0.458589			0.229294	−	0.973357i	$-0.426358\pi$
$199$	1.43116e11			0.458589			0.229294	+	0.973357i	$0.426358\pi$
$200$			4.11000e11i			1.28438i
$201$			2.35130e11i			0.716683i
$202$	2.72318e11			0.809692
$203$	−2.36086e11			−0.684842
$204$	7.11273e11			2.01319
$205$	−2.43226e11			−0.671801
$206$	3.36981e10			0.0908383
$207$		−	8.81317e10i		−	0.231889i
$208$			2.02516e11i			0.520168i
$209$		−	1.24972e11i		−	0.313387i
$210$			8.28976e10i			0.202976i
$211$		−	5.72585e11i		−	1.36908i	−0.728977	−	0.684538i	$-0.760004\pi$
$211$		−	5.72585e11i		−	1.36908i	0.728977	−	0.684538i	$-0.239996\pi$
$212$	4.34082e11			1.01366
$213$	2.00512e11			0.457344
$214$		−	7.49835e11i		−	1.67069i
$215$			3.91258e11i			0.851670i
$216$		−	1.61280e11i		−	0.343013i
$217$			3.82693e9i			0.00795338i
$218$	−1.36459e12			−2.77153
$219$		−	3.86269e11i		−	0.766778i
$220$			1.45090e11i			0.281530i
$221$		−	4.39278e11i		−	0.833255i
$222$	−8.39260e10			−0.155644
$223$	1.04640e12			1.89746			0.948731	−	0.316085i	$-0.102368\pi$
$223$	1.04640e12			1.89746			0.948731	+	0.316085i	$0.102368\pi$
$224$		−	1.88433e10i		−	0.0334132i
$225$	−1.38513e11			−0.240203
$226$	1.73272e12			2.93891
$227$			7.11857e11i			1.18104i	0.807024	+	0.590519i	$0.201077\pi$
$227$			7.11857e11i			1.18104i	−0.807024	+	0.590519i	$0.798923\pi$
$228$	8.58117e11			1.39275
$229$		−	1.23805e12i		−	1.96589i	−0.183900	−	0.982945i	$-0.558872\pi$
$229$		−	1.23805e12i		−	1.96589i	0.183900	−	0.982945i	$-0.441128\pi$
$230$	−4.11620e11			−0.639525
$231$		−	3.82017e10i		−	0.0580795i
$232$		−	2.14522e12i		−	3.19178i
$233$			4.46825e11i			0.650666i	0.945599	+	0.325333i	$0.105476\pi$
$233$			4.46825e11i			0.650666i	−0.945599	+	0.325333i	$0.894524\pi$
$234$	−1.96799e11			−0.280507
$235$		−	6.25675e11i		−	0.872991i
$236$	−4.30047e11	+	1.41858e12i	−0.587429	+	1.93773i
$237$	6.87262e11			0.919138
$238$			8.74673e11i			1.14541i
$239$	−8.29032e11			−1.06312			−0.531559	−	0.847021i	$-0.678394\pi$
$239$	−8.29032e11			−1.06312			−0.531559	+	0.847021i	$0.678394\pi$
$240$	−2.61234e11			−0.328075
$241$	−4.35002e11			−0.535065			−0.267532	−	0.963549i	$-0.586208\pi$
$241$	−4.35002e11			−0.535065			−0.267532	+	0.963549i	$0.586208\pi$
$242$			1.34365e12i			1.61886i
$243$	5.43536e10			0.0641500
$244$		−	6.69757e11i		−	0.774405i
$245$	3.98352e11			0.451270
$246$			1.14973e12i			1.27621i
$247$		−	5.29967e11i		−	0.576454i
$248$	−3.47738e10			−0.0370676
$249$			6.87763e10i			0.0718526i
$250$			1.54468e12i			1.58175i
$251$	6.03262e11			0.605532			0.302766	−	0.953065i	$-0.402090\pi$
$251$	6.03262e11			0.605532			0.302766	+	0.953065i	$0.402090\pi$
$252$	2.62311e11			0.258115
$253$	1.89687e11			0.182993
$254$		−	1.14868e12i		−	1.08650i
$255$	5.66642e11			0.525542
$256$	−2.22216e12			−2.02104
$257$	−1.71456e12			−1.52928			−0.764640	−	0.644458i	$-0.777083\pi$
$257$	−1.71456e12			−1.52928			−0.764640	+	0.644458i	$0.777083\pi$
$258$	1.84949e12			1.61790
$259$		−	6.90864e10i		−	0.0592780i
$260$			6.15282e11i			0.517854i
$261$	7.22972e11			0.596924
$262$	3.30339e12			2.67580
$263$	1.07745e12			0.856288			0.428144	−	0.903710i	$-0.359168\pi$
$263$	1.07745e12			0.856288			0.428144	+	0.903710i	$0.359168\pi$
$264$	3.47124e11			0.270686
$265$	3.45815e11			0.264615
$266$			1.05525e12i			0.792406i
$267$			9.28708e11i			0.684420i
$268$		−	3.47493e12i		−	2.51346i
$269$		−	1.28198e12i		−	0.910165i	−0.890449	−	0.455083i	$-0.849610\pi$
$269$		−	1.28198e12i		−	0.910165i	0.890449	−	0.455083i	$-0.150390\pi$
$270$		−	2.53859e11i		−	0.176919i
$271$	4.50951e11			0.308520			0.154260	−	0.988030i	$-0.450701\pi$
$271$	4.50951e11			0.308520			0.154260	+	0.988030i	$0.450701\pi$
$272$	−2.75634e12			−1.85135
$273$		−	1.62001e11i		−	0.106833i
$274$		−	3.61268e12i		−	2.33925i
$275$		−	2.98123e11i		−	0.189554i
$276$			1.30248e12i			0.813252i
$277$	1.91181e12			1.17232			0.586160	−	0.810195i	$-0.300639\pi$
$277$	1.91181e12			1.17232			0.586160	+	0.810195i	$0.300639\pi$
$278$			4.83724e12i			2.91322i
$279$		−	1.17193e10i		−	0.00693235i
$280$		−	6.20069e11i		−	0.360288i
$281$	−4.01203e11			−0.228998			−0.114499	−	0.993423i	$-0.536526\pi$
$281$	−4.01203e11			−0.228998			−0.114499	+	0.993423i	$0.536526\pi$
$282$	−2.95758e12			−1.65841
$283$			3.77846e11i			0.208153i	0.994569	+	0.104077i	$0.0331887\pi$
$283$			3.77846e11i			0.208153i	−0.994569	+	0.104077i	$0.966811\pi$
$284$	−2.96333e12			−1.60394
$285$	6.83626e11			0.363575
$286$		−	4.23573e11i		−	0.221360i
$287$	−9.46441e11			−0.486053
$288$			5.77043e10i			0.0291237i
$289$	3.96278e12			1.96567
$290$		−	3.37665e12i		−	1.64625i
$291$			1.57267e11i			0.0753653i
$292$			5.70859e12i			2.68915i
$293$	1.67521e12			0.775767			0.387883	−	0.921708i	$-0.373206\pi$
$293$	1.67521e12			0.775767			0.387883	+	0.921708i	$0.373206\pi$
$294$		−	1.88302e12i		−	0.857271i
$295$	−3.42601e11	+	1.13012e12i	−0.153348	+	0.505842i
$296$	6.27761e11			0.276271
$297$			1.16986e11i			0.0506234i
$298$	−3.90226e12			−1.66048
$299$	8.04403e11			0.336603
$300$	2.04705e12			0.842409
$301$			1.52246e12i			0.616190i
$302$	1.81038e12			0.720669
$303$		−	6.86472e11i		−	0.268788i
$304$	−3.32540e12			−1.28078
$305$		−	5.33568e11i		−	0.202158i
$306$		−	2.67853e12i		−	0.998365i
$307$	−1.64568e12			−0.603466			−0.301733	−	0.953392i	$-0.597565\pi$
$307$	−1.64568e12			−0.603466			−0.301733	+	0.953392i	$0.597565\pi$
$308$			5.64575e11i			0.203689i
$309$		−	8.49477e10i		−	0.0301550i
$310$	−5.47351e10			−0.0191187
$311$	4.42075e11			0.151948			0.0759739	−	0.997110i	$-0.475793\pi$
$311$	4.42075e11			0.151948			0.0759739	+	0.997110i	$0.475793\pi$
$312$	1.47204e12			0.497907
$313$		−	4.05890e12i		−	1.35110i	−0.737316	−	0.675548i	$-0.763907\pi$
$313$		−	4.05890e12i		−	1.35110i	0.737316	−	0.675548i	$-0.236093\pi$
$314$	−7.54911e12			−2.47313
$315$	2.08972e11			0.0673807
$316$	−1.01569e13			−3.22348
$317$	−4.01843e12			−1.25534			−0.627669	−	0.778481i	$-0.715991\pi$
$317$	−4.01843e12			−1.25534			−0.627669	+	0.778481i	$0.715991\pi$
$318$		−	1.63468e12i		−	0.502686i
$319$			1.55606e12i			0.471057i
$320$	−1.63720e12			−0.487923
$321$	−1.89022e12			−0.554610
$322$	−1.60170e12			−0.462702
$323$	7.21311e12			2.05168
$324$	−8.03280e11			−0.224979
$325$		−	1.26425e12i		−	0.348671i
$326$		−	1.41007e12i		−	0.382960i
$327$			3.43992e12i			0.920046i
$328$		−	8.59994e12i		−	2.26530i
$329$		−	2.43463e12i		−	0.631616i
$330$	5.46384e11			0.139614
$331$	4.62890e11			0.116503			0.0582516	−	0.998302i	$-0.481447\pi$
$331$	4.62890e11			0.116503			0.0582516	+	0.998302i	$0.481447\pi$
$332$		−	1.01643e12i		−	0.251992i
$333$			2.11565e11i			0.0516680i
$334$		−	4.64288e12i		−	1.11700i
$335$		−	2.76833e12i		−	0.656137i
$336$	−1.01651e12			−0.237365
$337$		−	2.91225e11i		−	0.0670007i	−0.999439	−	0.0335003i	$-0.989335\pi$
$337$		−	2.91225e11i		−	0.0670007i	0.999439	−	0.0335003i	$-0.0106655\pi$
$338$			5.87618e12i			1.33202i
$339$		−	4.36793e12i		−	0.975612i
$340$	−8.37428e12			−1.84312
$341$	2.52236e10			0.00547060
$342$		−	3.23152e12i		−	0.690679i
$343$	3.36567e12			0.708926
$344$	−1.38340e13			−2.87182
$345$			1.03763e12i			0.212299i
$346$	1.32318e13			2.66833
$347$		−	9.42217e12i		−	1.87285i	−0.350864	−	0.936427i	$-0.614112\pi$
$347$		−	9.42217e12i		−	1.87285i	0.350864	−	0.936427i	$-0.385888\pi$
$348$	−1.06846e13			−2.09346
$349$		−	2.22714e12i		−	0.430150i	−0.976598	−	0.215075i	$-0.931000\pi$
$349$		−	2.22714e12i		−	0.430150i	0.976598	−	0.215075i	$-0.0689996\pi$
$350$			2.51732e12i			0.479290i
$351$			4.96101e11i			0.0931181i
$352$	−1.24198e11			−0.0229827
$353$			1.90174e11i			0.0346959i	0.999850	+	0.0173479i	$0.00552230\pi$
$353$			1.90174e11i			0.0346959i	−0.999850	+	0.0173479i	$0.994478\pi$
$354$	5.34211e12	+	1.61948e12i	0.960941	+	0.291313i
$355$	−2.36076e12			−0.418707
$356$		−	1.37252e13i		−	2.40031i
$357$	2.20492e12			0.380234
$358$	−1.15573e13			−1.96536
$359$	−5.83565e12			−0.978627			−0.489314	−	0.872108i	$-0.662753\pi$
$359$	−5.83565e12			−0.978627			−0.489314	+	0.872108i	$0.662753\pi$
$360$			1.89885e12i			0.314035i
$361$	2.57121e12			0.419373
$362$			4.96456e12i			0.798616i
$363$	3.38713e12			0.537401
$364$			2.39418e12i			0.374672i
$365$			4.54780e12i			0.702000i
$366$	−2.52219e12			−0.384036
$367$			4.45054e12i			0.668471i	0.942490	+	0.334236i	$0.108478\pi$
$367$			4.45054e12i			0.668471i	−0.942490	+	0.334236i	$0.891522\pi$
$368$		−	5.04740e12i		−	0.747875i
$369$	2.89831e12			0.423655
$370$	9.88115e11			0.142495
$371$	1.34564e12			0.191451
$372$			1.73197e11i			0.0243123i
$373$	−6.13757e12			−0.850066			−0.425033	−	0.905178i	$-0.639737\pi$
$373$	−6.13757e12			−0.850066			−0.425033	+	0.905178i	$0.639737\pi$
$374$	5.76503e12			0.787851
$375$	3.89390e12			0.525083
$376$	2.21225e13			2.94371
$377$			6.59877e12i			0.866475i
$378$		−	9.87817e11i		−	0.128002i
$379$	2.88638e12			0.369111			0.184555	−	0.982822i	$-0.440915\pi$
$379$	2.88638e12			0.369111			0.184555	+	0.982822i	$0.440915\pi$
$380$	−1.01032e13			−1.27509
$381$	−2.89564e12			−0.360678
$382$	4.92039e12			0.604899
$383$	9.06675e12			1.10017			0.550083	−	0.835110i	$-0.314596\pi$
$383$	9.06675e12			1.10017			0.550083	+	0.835110i	$0.314596\pi$
$384$			8.16025e12i			0.977344i
$385$			4.49774e11i			0.0531729i
$386$		−	1.44086e13i		−	1.68145i
$387$		−	4.66228e12i		−	0.537085i
$388$		−	2.32421e12i		−	0.264312i
$389$	1.21502e13			1.36406			0.682030	−	0.731324i	$-0.261097\pi$
$389$	1.21502e13			1.36406			0.682030	+	0.731324i	$0.261097\pi$
$390$	2.31704e12			0.256810
$391$			1.09483e13i			1.19802i
$392$			1.40849e13i			1.52168i
$393$		−	8.32733e12i		−	0.888266i
$394$			1.44970e13i			1.52685i
$395$	−8.09158e12			−0.841488
$396$		−	1.72891e12i		−	0.177540i
$397$			3.53287e12i			0.358241i	0.983827	+	0.179121i	$0.0573252\pi$
$397$			3.53287e12i			0.358241i	−0.983827	+	0.179121i	$0.942675\pi$
$398$			7.96504e12i			0.797577i
$399$	2.66013e12			0.263050
$400$	−7.93280e12			−0.774688
$401$		−	8.52789e12i		−	0.822469i	−0.911530	−	0.411234i	$-0.865098\pi$
$401$		−	8.52789e12i		−	0.822469i	0.911530	−	0.411234i	$-0.134902\pi$
$402$	−1.30860e13			−1.24645
$403$	1.06965e11			0.0100628
$404$			1.01452e13i			0.942660i
$405$	−6.39940e11			−0.0587306
$406$		−	1.31392e13i		−	1.19108i
$407$	−4.55353e11			−0.0407734
$408$			2.00352e13i			1.77212i
$409$			6.06947e12i			0.530316i	0.964205	+	0.265158i	$0.0854241\pi$
$409$			6.06947e12i			0.530316i	−0.964205	+	0.265158i	$0.914576\pi$
$410$		−	1.35366e13i		−	1.16839i
$411$	−9.10701e12			−0.776545
$412$			1.25542e12i			0.105756i
$413$	−1.33313e12	+	4.39753e12i	−0.110949	+	0.365981i
$414$	4.90491e12			0.403301
$415$		−	8.09748e11i		−	0.0657824i
$416$	−5.26684e11			−0.0422750
$417$	1.21939e13			0.967084
$418$	6.95524e12			0.545043
$419$		−	8.83996e12i		−	0.684511i	−0.939607	−	0.342255i	$-0.888809\pi$
$419$		−	8.83996e12i		−	0.684511i	0.939607	−	0.342255i	$-0.111191\pi$
$420$	−3.08836e12			−0.236309
$421$		−	1.43920e12i		−	0.108820i	−0.998519	−	0.0544102i	$-0.982672\pi$
$421$		−	1.43920e12i		−	0.108820i	0.998519	−	0.0544102i	$-0.0173279\pi$
$422$	3.18668e13			2.38109
$423$			7.45561e12i			0.550531i
$424$			1.22273e13i			0.892279i
$425$	1.72070e13			1.24097
$426$			1.11594e13i			0.795412i
$427$		−	2.07622e12i		−	0.146263i
$428$	2.79352e13			1.94506
$429$	−1.06776e12			−0.0734833
$430$	−2.17752e13			−1.48122
$431$			4.30204e12i			0.289260i	0.989486	+	0.144630i	$0.0461991\pi$
$431$			4.30204e12i			0.289260i	−0.989486	+	0.144630i	$0.953801\pi$
$432$	3.11289e12			0.206893
$433$	2.66770e13			1.75266			0.876330	−	0.481712i	$-0.159985\pi$
$433$	2.66770e13			1.75266			0.876330	+	0.481712i	$0.159985\pi$
$434$	−2.12985e11			−0.0138325
$435$	−8.51201e12			−0.546495
$436$		−	5.08378e13i		−	3.22667i
$437$			1.32086e13i			0.828800i
$438$	2.14976e13			1.33358
$439$	1.51588e13			0.929701			0.464850	−	0.885389i	$-0.346108\pi$
$439$	1.51588e13			0.929701			0.464850	+	0.885389i	$0.346108\pi$
$440$	−4.08692e12			−0.247818
$441$	−4.74681e12			−0.284583
$442$	2.44477e13			1.44919
$443$		−	1.75776e13i		−	1.03024i	−0.857117	−	0.515122i	$-0.827747\pi$
$443$		−	1.75776e13i		−	1.03024i	0.857117	−	0.515122i	$-0.172253\pi$
$444$		−	3.12667e12i		−	0.181204i
$445$		−	1.09343e13i		−	0.626600i
$446$			5.82367e13i			3.30006i
$447$			9.83699e12i			0.551220i
$448$	−6.37067e12			−0.353016
$449$	3.46668e11			0.0189968			0.00949842	−	0.999955i	$-0.496977\pi$
$449$	3.46668e11			0.0189968			0.00949842	+	0.999955i	$0.496977\pi$
$450$		−	7.70885e12i		−	0.417760i
$451$			6.23806e12i			0.334323i
$452$			6.45527e13i			3.42154i
$453$		−	4.56370e12i		−	0.239236i
$454$	−3.96179e13			−2.05406
$455$			1.90735e12i			0.0978077i
$456$			2.41716e13i			1.22597i
$457$		−	2.42767e13i		−	1.21789i	−0.793212	−	0.608945i	$-0.791593\pi$
$457$		−	2.42767e13i		−	1.21789i	0.793212	−	0.608945i	$-0.208407\pi$
$458$	6.89026e13			3.41907
$459$	−6.75217e12			−0.331421
$460$		−	1.53349e13i		−	0.744548i
$461$	−3.10274e12			−0.149019			−0.0745093	−	0.997220i	$-0.523739\pi$
$461$	−3.10274e12			−0.149019			−0.0745093	+	0.997220i	$0.523739\pi$
$462$	2.12609e12			0.101012
$463$		−	2.46401e13i		−	1.15808i	−0.815300	−	0.579038i	$-0.803428\pi$
$463$		−	2.46401e13i		−	1.15808i	0.815300	−	0.579038i	$-0.196572\pi$
$464$	4.14054e13			1.92516
$465$			1.37979e11i			0.00634670i
$466$	−2.48678e13			−1.13164
$467$		−	3.96954e13i		−	1.78713i	−0.448937	−	0.893564i	$-0.648197\pi$
$467$		−	3.96954e13i		−	1.78713i	0.448937	−	0.893564i	$-0.351803\pi$
$468$		−	7.33176e12i		−	0.326572i
$469$		−	1.07722e13i		−	0.474721i
$470$	3.48215e13			1.51830
$471$			1.90301e13i			0.820989i
$472$	−3.99586e13	−	1.21136e13i	−1.70569	−	0.517087i
$473$	1.00347e13			0.423836
$474$			3.82491e13i			1.59856i
$475$	2.07594e13			0.858514
$476$	−3.25860e13			−1.33351
$477$	−4.12077e12			−0.166873
$478$		−	4.61392e13i		−	1.84897i
$479$	2.53641e13			1.00587			0.502934	−	0.864325i	$-0.332254\pi$
$479$	2.53641e13			1.00587			0.502934	+	0.864325i	$0.332254\pi$
$480$		−	6.79391e11i		−	0.0266633i
$481$	−1.93101e12			−0.0749997
$482$		−	2.42098e13i		−	0.930584i
$483$			4.03763e12i			0.153600i
$484$	−5.00577e13			−1.88471
$485$		−	1.85160e12i		−	0.0689984i
$486$			3.02501e12i			0.111570i
$487$	−1.22072e13			−0.445628			−0.222814	−	0.974861i	$-0.571524\pi$
$487$	−1.22072e13			−0.445628			−0.222814	+	0.974861i	$0.571524\pi$
$488$	1.88658e13			0.681674
$489$	−3.55457e12			−0.127129
$490$			2.21700e13i			0.784848i
$491$	−4.37652e13			−1.53363			−0.766817	−	0.641866i	$-0.778160\pi$
$491$	−4.37652e13			−1.53363			−0.766817	+	0.641866i	$0.778160\pi$
$492$	−4.28334e13			−1.48579
$493$	−8.98124e13			−3.08391
$494$	2.94950e13			1.00257
$495$		−	1.37735e12i		−	0.0463467i
$496$		−	6.71177e11i		−	0.0223578i
$497$	−9.18620e12			−0.302938
$498$	−3.82770e12			−0.124966
$499$	−3.80257e13			−1.22906			−0.614531	−	0.788893i	$-0.710655\pi$
$499$	−3.80257e13			−1.22906			−0.614531	+	0.788893i	$0.710655\pi$
$500$	−5.75471e13			−1.84151
$501$	−1.17040e13			−0.370805
$502$			3.35741e13i			1.05314i
$503$		−	7.64477e12i		−	0.237424i	−0.992929	−	0.118712i	$-0.962124\pi$
$503$		−	7.64477e12i		−	0.237424i	0.992929	−	0.118712i	$-0.0378765\pi$
$504$			7.38881e12i			0.227207i
$505$			8.08228e12i			0.246081i
$506$			1.05569e13i			0.318261i
$507$	1.48130e13			0.442183
$508$	4.27940e13			1.26493
$509$			6.27268e13i			1.83596i	0.396621	+	0.917982i	$0.370183\pi$
$509$			6.27268e13i			1.83596i	−0.396621	+	0.917982i	$0.629817\pi$
$510$			3.15361e13i			0.914022i
$511$			1.76964e13i			0.507903i
$512$		−	6.41123e13i		−	1.82218i
$513$	−8.14617e12			−0.229280
$514$		−	9.54227e13i		−	2.65972i
$515$			1.00014e12i			0.0276075i
$516$			6.89028e13i			1.88360i
$517$	−1.60468e13			−0.434446
$518$	3.84496e12			0.103096
$519$		−	3.33555e13i		−	0.885788i
$520$	−1.73313e13			−0.455843
$521$	6.93620e12			0.180690			0.0903448	−	0.995911i	$-0.471203\pi$
$521$	6.93620e12			0.180690			0.0903448	+	0.995911i	$0.471203\pi$
$522$			4.02365e13i			1.03817i
$523$	3.19441e13			0.816360			0.408180	−	0.912901i	$-0.366164\pi$
$523$	3.19441e13			0.816360			0.408180	+	0.912901i	$0.366164\pi$
$524$			1.23068e14i			3.11522i
$525$	6.34579e12			0.159107
$526$			5.99650e13i			1.48926i
$527$			1.45585e12i			0.0358149i
$528$			6.69992e12i			0.163268i
$529$	2.13780e13			0.516047
$530$			1.92461e13i			0.460218i
$531$	4.08247e12	−	1.34666e13i	0.0967052	−	0.318997i
$532$	−3.93135e13			−0.922535
$533$			2.64537e13i			0.614964i
$534$	−5.16866e13			−1.19034
$535$	2.22548e13			0.507756
$536$	9.78824e13			2.21249
$537$			2.91343e13i			0.652429i
$538$	7.13478e13			1.58296
$539$		−	1.02166e13i		−	0.224576i
$540$	9.45754e12			0.205972
$541$		−	2.47793e13i		−	0.534691i	−0.963601	−	0.267345i	$-0.913854\pi$
$541$		−	2.47793e13i		−	0.534691i	0.963601	−	0.267345i	$-0.0861464\pi$
$542$			2.50974e13i			0.536577i
$543$	1.25149e13			0.265111
$544$		−	7.16842e12i		−	0.150463i
$545$		−	4.05004e13i		−	0.842319i
$546$	9.01609e12			0.185804
$547$	−3.88238e13			−0.792797			−0.396398	−	0.918079i	$-0.629740\pi$
$547$	−3.88238e13			−0.792797			−0.396398	+	0.918079i	$0.629740\pi$
$548$	1.34591e14			2.72340
$549$			6.35806e12i			0.127486i
$550$	1.65919e13			0.329672
$551$	−1.08354e14			−2.13348
$552$	−3.66884e13			−0.715869
$553$	−3.14860e13			−0.608824
$554$			1.06401e14i			2.03890i
$555$		−	2.49089e12i		−	0.0473031i
$556$	−1.80212e14			−3.39163
$557$	7.83101e13			1.46064			0.730318	−	0.683107i	$-0.239372\pi$
$557$	7.83101e13			1.46064			0.730318	+	0.683107i	$0.239372\pi$
$558$	6.52229e11			0.0120567
$559$	4.25539e13			0.779616
$560$	1.19681e13			0.217312
$561$		−	1.45328e13i		−	0.261538i
$562$		−	2.23287e13i		−	0.398274i
$563$		−	6.47119e13i		−	1.14404i	−0.820239	−	0.572021i	$-0.806160\pi$
$563$		−	6.47119e13i		−	1.14404i	0.820239	−	0.572021i	$-0.193840\pi$
$564$		−	1.10185e14i		−	1.93075i
$565$			5.14264e13i			0.893191i
$566$	−2.10288e13			−0.362020
$567$	−2.49014e12			−0.0424921
$568$		−	8.34714e13i		−	1.41187i
$569$			3.52782e13i			0.591487i	0.955267	+	0.295743i	$0.0955673\pi$
$569$			3.52782e13i			0.591487i	−0.955267	+	0.295743i	$0.904433\pi$
$570$			3.80468e13i			0.632330i
$571$		−	9.85801e13i		−	1.62409i	−0.583598	−	0.812043i	$-0.698356\pi$
$571$		−	9.85801e13i		−	1.62409i	0.583598	−	0.812043i	$-0.301644\pi$
$572$	1.57802e13			0.257711
$573$		−	1.24036e13i		−	0.200804i
$574$		−	5.26735e13i		−	0.845343i
$575$			3.15094e13i			0.501304i
$576$	1.95090e13			0.307697
$577$	−2.85789e13			−0.446855			−0.223427	−	0.974721i	$-0.571725\pi$
$577$	−2.85789e13			−0.446855			−0.223427	+	0.974721i	$0.571725\pi$
$578$			2.20546e14i			3.41869i
$579$	−3.63218e13			−0.558180
$580$	1.25797e14			1.91660
$581$		−	3.15089e12i		−	0.0475941i
$582$	−8.75257e12			−0.131075
$583$		−	8.86919e12i		−	0.131686i
$584$	−1.60800e14			−2.36713
$585$		−	5.84091e12i		−	0.0852514i
$586$			9.32327e13i			1.34921i
$587$		−	1.17700e14i		−	1.68883i	−0.535692	−	0.844413i	$-0.679949\pi$
$587$		−	1.17700e14i		−	1.68883i	0.535692	−	0.844413i	$-0.320051\pi$
$588$	7.01520e13			0.998053
$589$			1.75641e12i			0.0247771i
$590$	−6.28961e13	−	1.90672e13i	−0.879759	−	0.266702i
$591$	3.65447e13			0.506858
$592$			1.21166e13i			0.166637i
$593$	−5.84651e13			−0.797302			−0.398651	−	0.917103i	$-0.630522\pi$
$593$	−5.84651e13			−0.797302			−0.398651	+	0.917103i	$0.630522\pi$
$594$	−6.51077e12			−0.0880441
$595$	−2.59599e13			−0.348112
$596$		−	1.45379e14i		−	1.93317i
$597$	2.00786e13			0.264766
$598$			4.47685e13i			0.585419i
$599$	−1.34740e14			−1.74728			−0.873639	−	0.486575i	$-0.838246\pi$
$599$	−1.34740e14			−1.74728			−0.873639	+	0.486575i	$0.838246\pi$
$600$			5.76617e13i			0.741534i
$601$		−	1.67071e13i		−	0.213073i	−0.994309	−	0.106536i	$-0.966024\pi$
$601$		−	1.67071e13i		−	0.213073i	0.994309	−	0.106536i	$-0.0339761\pi$
$602$	−8.47318e13			−1.07168
$603$			3.29878e13i			0.413777i
$604$			6.74459e13i			0.839018i
$605$	−3.98789e13			−0.492001
$606$	3.82052e13			0.467476
$607$	2.65267e13			0.321914			0.160957	−	0.986961i	$-0.448542\pi$
$607$	2.65267e13			0.321914			0.160957	+	0.986961i	$0.448542\pi$
$608$		−	8.64836e12i		−	0.104092i
$609$	−3.31220e13			−0.395394
$610$	2.96954e13			0.351593
$611$	−6.80495e13			−0.799133
$612$	9.97888e13			1.16232
$613$		−	2.40505e13i		−	0.277857i	−0.990302	−	0.138928i	$-0.955634\pi$
$613$		−	2.40505e13i		−	0.277857i	0.990302	−	0.138928i	$-0.0443658\pi$
$614$		−	9.15892e13i		−	1.04955i
$615$	−3.41236e13			−0.387864
$616$	−1.59030e13			−0.179298
$617$	−5.25545e13			−0.587738			−0.293869	−	0.955846i	$-0.594943\pi$
$617$	−5.25545e13			−0.587738			−0.293869	+	0.955846i	$0.594943\pi$
$618$	4.72771e12			0.0524455
$619$	3.62492e13			0.398882			0.199441	−	0.979910i	$-0.436087\pi$
$619$	3.62492e13			0.398882			0.199441	+	0.979910i	$0.436087\pi$
$620$		−	2.03916e12i		−	0.0222583i
$621$		−	1.23645e13i		−	0.133881i
$622$			2.46034e13i			0.264267i
$623$		−	4.25475e13i		−	0.453350i
$624$			2.84123e13i			0.300319i
$625$	2.28772e13			0.239885
$626$	2.25895e14			2.34982
$627$		−	1.75331e13i		−	0.180934i
$628$		−	2.81242e14i		−	2.87927i
$629$		−	2.62820e13i		−	0.266935i
$630$			1.16302e13i			0.117188i
$631$	−2.24031e13			−0.223956			−0.111978	−	0.993711i	$-0.535719\pi$
$631$	−2.24031e13			−0.223956			−0.111978	+	0.993711i	$0.535719\pi$
$632$		−	2.86101e14i		−	2.83749i
$633$		−	8.03314e13i		−	0.790436i
$634$		−	2.23643e14i		−	2.18328i
$635$	3.40923e13			0.330208
$636$	6.09000e13			0.585237
$637$		−	4.33255e13i		−	0.413091i
$638$	−8.66015e13			−0.819261
$639$	2.81311e13			0.264048
$640$		−	9.60760e13i		−	0.894777i
$641$	−2.86399e13			−0.264656			−0.132328	−	0.991206i	$-0.542245\pi$
$641$	−2.86399e13			−0.264656			−0.132328	+	0.991206i	$0.542245\pi$
$642$		−	1.05199e14i		−	0.964576i
$643$	−1.20323e13			−0.109470			−0.0547350	−	0.998501i	$-0.517431\pi$
$643$	−1.20323e13			−0.109470			−0.0547350	+	0.998501i	$0.517431\pi$
$644$		−	5.96713e13i		−	0.538687i
$645$			5.48920e13i			0.491712i
$646$			4.01441e14i			3.56828i
$647$	3.55855e13			0.313871			0.156936	−	0.987609i	$-0.449838\pi$
$647$	3.55855e13			0.313871			0.156936	+	0.987609i	$0.449838\pi$
$648$		−	2.26269e13i		−	0.198039i
$649$	2.89844e13	+	8.78674e12i	0.251734	+	0.0763140i
$650$	7.03609e13			0.606407
$651$			5.36903e11i			0.00459189i
$652$	5.25323e13			0.445849
$653$	−6.82597e13			−0.574908			−0.287454	−	0.957794i	$-0.592809\pi$
$653$	−6.82597e13			−0.574908			−0.287454	+	0.957794i	$0.592809\pi$
$654$	−1.91446e14			−1.60014
$655$			9.80431e13i			0.813225i
$656$	1.65989e14			1.36635
$657$		−	5.41921e13i		−	0.442700i
$658$	1.35498e14			1.09851
$659$		−	1.49491e14i		−	1.20278i	−0.798954	−	0.601392i	$-0.794613\pi$
$659$		−	1.49491e14i		−	1.20278i	0.798954	−	0.601392i	$-0.205387\pi$
$660$			2.03556e13i			0.162541i
$661$	1.75015e14			1.38697			0.693487	−	0.720469i	$-0.256073\pi$
$661$	1.75015e14			1.38697			0.693487	+	0.720469i	$0.256073\pi$
$662$			2.57618e13i			0.202622i
$663$		−	6.16289e13i		−	0.481080i
$664$	2.86310e13			0.221817
$665$	−3.13194e13			−0.240827
$666$	−1.17745e13			−0.0898610
$667$		−	1.64464e14i		−	1.24578i
$668$	1.72971e14			1.30044
$669$	1.46806e14			1.09550
$670$	1.54070e14			1.14115
$671$	−1.36845e13			−0.100604
$672$		−	2.64365e12i		−	0.0192911i
$673$			2.32901e13i			0.168693i	0.996437	+	0.0843463i	$0.0268802\pi$
$673$			2.32901e13i			0.168693i	−0.996437	+	0.0843463i	$0.973120\pi$
$674$	1.62079e13			0.116527
$675$	−1.94328e13			−0.138681
$676$	−2.18918e14			−1.55077
$677$	−9.46918e13			−0.665838			−0.332919	−	0.942955i	$-0.608034\pi$
$677$	−9.46918e13			−0.665838			−0.332919	+	0.942955i	$0.608034\pi$
$678$	2.43094e14			1.69678
$679$		−	7.20496e12i		−	0.0499209i
$680$		−	2.35888e14i		−	1.62241i
$681$			9.98708e13i			0.681872i
$682$			1.40380e12i			0.00951445i
$683$		−	2.43084e13i		−	0.163551i	−0.996651	−	0.0817754i	$-0.973941\pi$
$683$		−	2.43084e13i		−	0.163551i	0.996651	−	0.0817754i	$-0.0260590\pi$
$684$	1.20390e14			0.804103
$685$	1.07223e14			0.710942
$686$			1.87314e14i			1.23296i
$687$		−	1.73693e14i		−	1.13501i
$688$		−	2.67014e14i		−	1.73218i
$689$		−	3.76115e13i		−	0.242228i
$690$	−5.77487e13			−0.369230
$691$			2.82671e14i			1.79428i	0.441745	+	0.897141i	$0.354360\pi$
$691$			2.82671e14i			1.79428i	−0.441745	+	0.897141i	$0.645640\pi$
$692$			4.92953e14i			3.10653i
$693$		−	5.35955e12i		−	0.0335322i
$694$	5.24385e14			3.25726
$695$	−1.43567e14			−0.885384
$696$		−	3.00966e14i		−	1.84277i
$697$	−3.60047e14			−2.18875
$698$	1.23950e14			0.748116
$699$			6.26879e13i			0.375662i
$700$	−9.37830e13			−0.558000
$701$			1.30823e14i			0.772850i	0.922321	+	0.386425i	$0.126290\pi$
$701$			1.30823e14i			0.772850i	−0.922321	+	0.386425i	$0.873710\pi$
$702$	−2.76102e13			−0.161951
$703$		−	3.17080e13i		−	0.184668i
$704$			4.19895e13i			0.242816i
$705$		−	8.77798e13i		−	0.504021i
$706$	−1.05840e13			−0.0603430
$707$			3.14498e13i			0.178041i
$708$	−6.03339e13	+	1.99021e14i	−0.339152	+	1.11875i
$709$	−2.90493e14			−1.62145			−0.810726	−	0.585425i	$-0.800928\pi$
$709$	−2.90493e14			−1.62145			−0.810726	+	0.585425i	$0.800928\pi$
$710$		−	1.31387e14i		−	0.728214i
$711$	9.64202e13			0.530664
$712$	3.86613e14			2.11289
$713$	−2.66594e12			−0.0144678
$714$			1.22713e14i			0.661303i
$715$	1.25715e13			0.0672754
$716$		−	4.30569e14i		−	2.28812i
$717$	−1.16310e14			−0.613792
$718$		−	3.24779e14i		−	1.70203i
$719$		−	2.13909e14i		−	1.11323i	−0.830770	−	0.556616i	$-0.812100\pi$
$719$		−	2.13909e14i		−	1.11323i	0.830770	−	0.556616i	$-0.187900\pi$
$720$	−3.66501e13			−0.189414
$721$			3.89176e12i			0.0199742i
$722$			1.43099e14i			0.729374i
$723$	−6.10291e13			−0.308920
$724$	−1.84955e14			−0.929765
$725$	−2.58481e14			−1.29044
$726$			1.88508e14i			0.934647i
$727$	−2.68389e13			−0.132158			−0.0660789	−	0.997814i	$-0.521049\pi$
$727$	−2.68389e13			−0.132158			−0.0660789	+	0.997814i	$0.521049\pi$
$728$	−6.74397e13			−0.329806
$729$	7.62560e12			0.0370370
$730$	−2.53105e14			−1.22092
$731$			5.79179e14i			2.77476i
$732$		−	9.39644e13i		−	0.447103i
$733$	3.37680e14			1.59582			0.797912	−	0.602774i	$-0.205938\pi$
$733$	3.37680e14			1.59582			0.797912	+	0.602774i	$0.205938\pi$
$734$	−2.47692e14			−1.16260
$735$	5.58872e13			0.260541
$736$	1.31268e13			0.0607811
$737$	−7.10000e13			−0.326528
$738$			1.61303e14i			0.736820i
$739$			1.09944e14i			0.498828i	0.968397	+	0.249414i	$0.0802380\pi$
$739$			1.09944e14i			0.498828i	−0.968397	+	0.249414i	$0.919762\pi$
$740$			3.68123e13i			0.165895i
$741$		−	7.43524e13i		−	0.332816i
$742$			7.48905e13i			0.332972i
$743$	−3.17357e14			−1.40154			−0.700769	−	0.713389i	$-0.747159\pi$
$743$	−3.17357e14			−1.40154			−0.700769	+	0.713389i	$0.747159\pi$
$744$	−4.87863e12			−0.0214010
$745$		−	1.15817e14i		−	0.504652i
$746$		−	3.41583e14i		−	1.47843i
$747$			9.64905e12i			0.0414841i
$748$			2.14777e14i			0.917232i
$749$	8.65979e13			0.367365
$750$			2.16712e14i			0.913224i
$751$		−	7.95007e13i		−	0.332791i	−0.986059	−	0.166395i	$-0.946787\pi$
$751$		−	7.95007e13i		−	0.332791i	0.986059	−	0.166395i	$-0.0532128\pi$
$752$			4.26992e14i			1.77554i
$753$	8.46353e13			0.349604
$754$	−3.67250e14			−1.50697
$755$			5.37314e13i			0.219025i
$756$	3.68012e13			0.149023
$757$	−2.85972e13			−0.115039			−0.0575193	−	0.998344i	$-0.518319\pi$
$757$	−2.85972e13			−0.115039			−0.0575193	+	0.998344i	$0.518319\pi$
$758$			1.60639e14i			0.641957i
$759$	2.66123e13			0.105651
$760$		−	2.84587e14i		−	1.12240i
$761$	−6.02955e12			−0.0236245			−0.0118122	−	0.999930i	$-0.503760\pi$
$761$	−6.02955e12			−0.0236245			−0.0118122	+	0.999930i	$0.503760\pi$
$762$		−	1.61155e14i		−	0.627291i
$763$		−	1.57595e14i		−	0.609425i
$764$			1.83310e14i			0.704236i
$765$	7.94976e13			0.303422
$766$			5.04604e14i			1.91341i
$767$	1.22914e14	+	3.72618e13i	0.463046	+	0.140374i
$768$	−3.11760e14			−1.16685
$769$		−	2.20971e14i		−	0.821681i	−0.911707	−	0.410841i	$-0.865235\pi$
$769$		−	2.20971e14i		−	0.821681i	0.911707	−	0.410841i	$-0.134765\pi$
$770$	−2.50318e13			−0.0924782
$771$	−2.40546e14			−0.882930
$772$	5.36792e14			1.95758
$773$			4.20413e14i			1.52328i	0.648003	+	0.761638i	$0.275605\pi$
$773$			4.20413e14i			1.52328i	−0.648003	+	0.761638i	$0.724395\pi$
$774$	2.59476e14			0.934098
$775$			4.18995e12i			0.0149865i
$776$	6.54687e13			0.232662
$777$		−	9.69255e12i		−	0.0342242i
$778$			6.76209e14i			2.37237i
$779$	−4.34379e14			−1.51420
$780$			8.63216e13i			0.298983i
$781$			6.05469e13i			0.208371i
$782$	−6.09321e14			−2.08359
$783$	1.01430e14			0.344634
$784$	−2.71855e14			−0.917819
$785$		−	2.24054e14i		−	0.751631i
$786$	4.63452e14			1.54487
$787$	−4.78749e14			−1.58575			−0.792875	−	0.609385i	$-0.791416\pi$
$787$	−4.78749e14			−1.58575			−0.792875	+	0.609385i	$0.791416\pi$
$788$	−5.40086e14			−1.77759
$789$	1.51163e14			0.494378
$790$		−	4.50332e14i		−	1.46351i
$791$			2.00111e14i			0.646231i
$792$	4.87002e13			0.156280
$793$	−5.80318e13			−0.185055
$794$	−1.96620e14			−0.623053
$795$	4.85165e13			0.152776
$796$	−2.96738e14			−0.928555
$797$		−	4.93856e14i		−	1.53571i	−0.640625	−	0.767854i	$-0.721325\pi$
$797$		−	4.93856e14i		−	1.53571i	0.640625	−	0.767854i	$-0.278675\pi$
$798$			1.48048e14i			0.457496i
$799$		−	9.26186e14i		−	2.84423i
$800$		−	2.06308e13i		−	0.0629603i
$801$			1.30294e14i			0.395150i
$802$	4.74614e14			1.43044
$803$	1.16638e14			0.349352
$804$		−	4.87519e14i		−	1.45115i
$805$		−	4.75377e13i		−	0.140624i
$806$			5.95308e12i			0.0175012i
$807$		−	1.79857e14i		−	0.525484i
$808$	−2.85772e14			−0.829780
$809$			9.25380e13i			0.267041i	0.991046	+	0.133520i	$0.0426281\pi$
$809$			9.25380e13i			0.267041i	−0.991046	+	0.133520i	$0.957372\pi$
$810$		−	3.56154e13i		−	0.102144i
$811$		−	6.34401e14i		−	1.80825i	−0.427263	−	0.904127i	$-0.640522\pi$
$811$		−	6.34401e14i		−	1.80825i	0.427263	−	0.904127i	$-0.359478\pi$
$812$	4.89502e14			1.38667
$813$	6.32667e13			0.178124
$814$		−	2.53424e13i		−	0.0709129i
$815$	4.18503e13			0.116389
$816$	−3.86704e14			−1.06888
$817$			6.98752e14i			1.91961i
$818$	−3.37793e14			−0.922324
$819$		−	2.27282e13i		−	0.0616801i
$820$	5.04306e14			1.36027
$821$		−	1.09119e14i		−	0.292541i	−0.989245	−	0.146270i	$-0.953273\pi$
$821$		−	1.09119e14i		−	0.292541i	0.989245	−	0.146270i	$-0.0467269\pi$
$822$		−	5.06845e14i		−	1.35057i
$823$		−	2.44551e14i		−	0.647694i	−0.946109	−	0.323847i	$-0.895024\pi$
$823$		−	2.44551e14i		−	0.647694i	0.946109	−	0.323847i	$-0.104976\pi$
$824$	−3.53629e13			−0.0930920
$825$		−	4.18255e13i		−	0.109439i
$826$	−2.44742e14	−	7.41944e13i	−0.636513	−	0.192961i
$827$	−4.06102e14			−1.04980			−0.524901	−	0.851163i	$-0.675898\pi$
$827$	−4.06102e14			−1.04980			−0.524901	+	0.851163i	$0.675898\pi$
$828$			1.82733e14i			0.469531i
$829$	−1.59092e14			−0.406326			−0.203163	−	0.979145i	$-0.565122\pi$
$829$	−1.59092e14			−0.406326			−0.203163	+	0.979145i	$0.565122\pi$
$830$	4.50660e13			0.114409
$831$	2.68220e14			0.676840
$832$			1.78065e14i			0.446643i
$833$	5.89680e14			1.47025
$834$			6.78646e14i			1.68195i
$835$	1.37799e14			0.339479
$836$			2.59118e14i			0.634550i
$837$		−	1.64417e12i		−	0.00400239i
$838$	4.91982e14			1.19050
$839$			4.92866e14i			1.18555i	0.805369	+	0.592774i	$0.201967\pi$
$839$			4.92866e14i			1.18555i	−0.805369	+	0.592774i	$0.798033\pi$
$840$		−	8.69932e13i		−	0.208012i
$841$	9.28442e14			2.20686
$842$	8.00977e13			0.189260
$843$	−5.62872e13			−0.132212
$844$			1.18720e15i			2.77212i
$845$	−1.74403e14			−0.404827
$846$	−4.14937e14			−0.957482
$847$	−1.55177e14			−0.355967
$848$	−2.36001e14			−0.538190
$849$			5.30104e13i			0.120177i
$850$			9.57645e14i			2.15829i
$851$	4.81274e13			0.107831
$852$	−4.15743e14			−0.926034
$853$	1.59774e14			0.353803			0.176901	−	0.984229i	$-0.443393\pi$
$853$	1.59774e14			0.353803			0.176901	+	0.984229i	$0.443393\pi$
$854$	1.15551e14			0.254380
$855$	9.59101e13			0.209910
$856$			7.86882e14i			1.71215i
$857$			1.09954e14i			0.237852i	0.992903	+	0.118926i	$0.0379451\pi$
$857$			1.09954e14i			0.237852i	−0.992903	+	0.118926i	$0.962055\pi$
$858$		−	5.94257e13i		−	0.127802i
$859$		−	7.81085e14i		−	1.67006i	−0.550204	−	0.835031i	$-0.685450\pi$
$859$		−	7.81085e14i		−	1.67006i	0.550204	−	0.835031i	$-0.314550\pi$
$860$		−	8.11237e14i		−	1.72447i
$861$	−1.32782e14			−0.280623
$862$	−2.39427e14			−0.503080
$863$		−	3.33766e14i		−	0.697248i	−0.937263	−	0.348624i	$-0.886649\pi$
$863$		−	3.33766e14i		−	0.697248i	0.937263	−	0.348624i	$-0.113351\pi$
$864$			8.09569e12i			0.0168146i
$865$			3.92715e14i			0.810956i
$866$			1.48469e15i			3.04822i
$867$	5.55963e14			1.13488
$868$		−	7.93478e12i		−	0.0161041i
$869$			2.07526e14i			0.418769i
$870$		−	4.73731e14i		−	0.950463i
$871$	−3.01089e14			−0.600626
$872$	1.43201e15			2.84029
$873$			2.20639e13i			0.0435122i
$874$	−7.35116e14			−1.44145
$875$	−1.78394e14			−0.347808
$876$			8.00893e14i			1.55258i
$877$	−3.31106e14			−0.638218			−0.319109	−	0.947718i	$-0.603384\pi$
$877$	−3.31106e14			−0.638218			−0.319109	+	0.947718i	$0.603384\pi$
$878$			8.43655e14i			1.61693i
$879$	2.35026e14			0.447889
$880$		−	7.88825e13i		−	0.149475i
$881$			4.85114e14i			0.914038i	0.889457	+	0.457019i	$0.151083\pi$
$881$			4.85114e14i			0.914038i	−0.889457	+	0.457019i	$0.848917\pi$
$882$		−	2.64180e14i		−	0.494946i
$883$	6.48208e14			1.20757			0.603783	−	0.797149i	$-0.293659\pi$
$883$	6.48208e14			1.20757			0.603783	+	0.797149i	$0.293659\pi$
$884$			9.10801e14i			1.68718i
$885$	−4.80655e13	+	1.58552e14i	−0.0885355	+	0.292048i
$886$	9.78267e14			1.79180
$887$		−	6.85382e14i		−	1.24829i	−0.781310	−	0.624144i	$-0.785448\pi$
$887$		−	6.85382e14i		−	1.24829i	0.781310	−	0.624144i	$-0.214552\pi$
$888$	8.80725e13			0.159505
$889$	1.32660e14			0.238908
$890$	6.08540e14			1.08978
$891$			1.64127e13i			0.0292274i
$892$	−2.16961e15			−3.84200
$893$		−	1.11740e15i		−	1.96766i
$894$	−5.47471e14			−0.958680
$895$		−	3.43017e14i		−	0.597311i
$896$		−	3.73851e14i		−	0.647379i
$897$	1.12855e14			0.194338
$898$			1.92936e13i			0.0330393i
$899$		−	2.18696e13i		−	0.0372427i
$900$	2.87194e14			0.486365
$901$	5.11910e14			0.862124
$902$	−3.47175e14			−0.581455
$903$			2.13596e14i			0.355758i
$904$	−1.81833e15			−3.01183
$905$	−1.47346e14			−0.242714
$906$	2.53990e14			0.416078
$907$	1.19500e15			1.94685			0.973424	−	0.229009i	$-0.0735485\pi$
$907$	1.19500e15			1.94685			0.973424	+	0.229009i	$0.0735485\pi$
$908$		−	1.47597e15i		−	2.39138i
$909$		−	9.63094e13i		−	0.155185i
$910$	−1.06152e14			−0.170107
$911$	3.08835e14			0.492192			0.246096	−	0.969245i	$-0.420852\pi$
$911$	3.08835e14			0.492192			0.246096	+	0.969245i	$0.420852\pi$
$912$	−4.66540e14			−0.739461
$913$	−2.07678e13			−0.0327368
$914$	1.35110e15			2.11815
$915$		−	7.48575e13i		−	0.116716i
$916$			2.56697e15i			3.98055i
$917$			3.81506e14i			0.588375i
$918$		−	3.75787e14i		−	0.576406i
$919$			1.14883e15i			1.75258i	0.481783	+	0.876290i	$0.339989\pi$
$919$			1.14883e15i			1.75258i	−0.481783	+	0.876290i	$0.660011\pi$
$920$	4.31957e14			0.655392
$921$	−2.30882e14			−0.348412
$922$		−	1.72681e14i		−	0.259173i
$923$			2.56760e14i			0.383283i
$924$			7.92076e13i			0.117600i
$925$		−	7.56399e13i		−	0.111697i
$926$	1.37133e15			2.01412
$927$		−	1.19178e13i		−	0.0174100i
$928$			1.07683e14i			0.156461i
$929$			1.54664e14i			0.223518i	0.993735	+	0.111759i	$0.0356484\pi$
$929$			1.54664e14i			0.223518i	−0.993735	+	0.111759i	$0.964352\pi$
$930$	−7.67912e12			−0.0110382
$931$	7.11421e14			1.01713
$932$		−	9.26450e14i		−	1.31748i
$933$	6.20214e13			0.0877271
$934$	2.20922e15			3.10817
$935$			1.71104e14i			0.239443i
$936$	2.06522e14			0.287467
$937$			2.56353e14i			0.354928i	0.984127	+	0.177464i	$0.0567893\pi$
$937$			2.56353e14i			0.354928i	−0.984127	+	0.177464i	$0.943211\pi$
$938$	5.99517e14			0.825633
$939$		−	5.69447e14i		−	0.780056i
$940$			1.29728e15i			1.76764i
$941$		−	7.73582e14i		−	1.04848i	−0.851572	−	0.524238i	$-0.824350\pi$
$941$		−	7.73582e14i		−	1.04848i	0.851572	−	0.524238i	$-0.175650\pi$
$942$	−1.05911e15			−1.42786
$943$		−	6.59316e14i		−	0.884169i
$944$	2.33808e14	−	7.71250e14i	0.311888	−	1.02881i
$945$	2.93180e13			0.0389023
$946$			5.58473e14i			0.737134i
$947$	2.14831e14			0.282064			0.141032	−	0.990005i	$-0.454958\pi$
$947$	2.14831e14			0.282064			0.141032	+	0.990005i	$0.454958\pi$
$948$	−1.42497e15			−1.86108
$949$	4.94627e14			0.642609
$950$			1.15535e15i			1.49313i
$951$	−5.63770e14			−0.724769
$952$		−	9.17887e14i		−	1.17383i
$953$	−6.29224e14			−0.800462			−0.400231	−	0.916414i	$-0.631070\pi$
$953$	−6.29224e14			−0.800462			−0.400231	+	0.916414i	$0.631070\pi$
$954$		−	2.29339e14i		−	0.290226i
$955$			1.46035e14i			0.183840i
$956$	1.71892e15			2.15261
$957$			2.18309e14i			0.271965i
$958$			1.41162e15i			1.74941i
$959$	4.17225e14			0.514372
$960$	−2.29693e14			−0.281703
$961$	8.19274e14			0.999567
$962$		−	1.07469e14i		−	0.130439i
$963$	−2.65191e14			−0.320204
$964$	9.01936e14			1.08340
$965$	4.27640e14			0.511024
$966$	−2.24712e14			−0.267141
$967$			7.83997e14i			0.927219i	0.886040	+	0.463609i	$0.153446\pi$
$967$			7.83997e14i			0.927219i	−0.886040	+	0.463609i	$0.846554\pi$
$968$		−	1.41003e15i		−	1.65902i
$969$	1.01197e15			1.18454
$970$	1.03050e14			0.120002
$971$	8.31366e14			0.963154			0.481577	−	0.876404i	$-0.340064\pi$
$971$	8.31366e14			0.963154			0.481577	+	0.876404i	$0.340064\pi$
$972$	−1.12697e14			−0.129892
$973$	−5.58649e14			−0.640582
$974$		−	6.79386e14i		−	0.775035i
$975$		−	1.77369e14i		−	0.201305i
$976$			3.64133e14i			0.411160i
$977$		−	4.72935e14i		−	0.531286i	−0.964071	−	0.265643i	$-0.914416\pi$
$977$		−	4.72935e14i		−	0.531286i	0.964071	−	0.265643i	$-0.0855842\pi$
$978$		−	1.97827e14i		−	0.221102i
$979$	−2.80434e14			−0.311829
$980$	−8.25945e14			−0.913737
$981$			4.82607e14i			0.531189i
$982$		−	2.43572e15i		−	2.66729i
$983$			4.74234e14i			0.516684i	0.966054	+	0.258342i	$0.0831761\pi$
$983$			4.74234e14i			0.516684i	−0.966054	+	0.258342i	$0.916824\pi$
$984$		−	1.20654e15i		−	1.30787i
$985$	−4.30264e14			−0.464038
$986$		−	4.99845e15i		−	5.36353i
$987$		−	3.41569e14i		−	0.364664i
$988$			1.09884e15i			1.16721i
$989$	−1.06059e15			−1.12090
$990$	7.66556e13			0.0806061
$991$			9.12271e14i			0.954456i	0.878780	+	0.477228i	$0.158358\pi$
$991$			9.12271e14i			0.954456i	−0.878780	+	0.477228i	$0.841642\pi$
$992$	1.74553e12			0.00181706
$993$	6.49416e13			0.0672631
$994$		−	5.11252e14i		−	0.526869i
$995$	−2.36399e14			−0.242399
$996$		−	1.42601e14i		−	0.145488i
$997$	−4.89180e14			−0.496584			−0.248292	−	0.968685i	$-0.579869\pi$
$997$	−4.89180e14			−0.496584			−0.248292	+	0.968685i	$0.579869\pi$
$998$		−	2.11629e15i		−	2.13758i
$999$			2.96817e13i			0.0298306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.92	yes	100
59.58	odd	2	inner	177.11.c.a.58.9	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.9	✓	100	59.58	odd	2	inner
177.11.c.a.58.92	yes	100	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+55.6543i q^{2} +140.296 q^{3} -2073.41 q^{4} -1651.80 q^{5} +7808.09i q^{6} -6427.48 q^{7} -58404.0i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q+55.6543i q^{2} +140.296 q^{3} -2073.41 q^{4} -1651.80 q^{5} +7808.09i q^{6} -6427.48 q^{7} -58404.0i q^{8} +19683.0 q^{9} -91929.7i q^{10} +42364.0i q^{11} -290891. q^{12} +179652. i q^{13} -357717. i q^{14} -231741. q^{15} +1.12727e6 q^{16} -2.44515e6 q^{17} +1.09544e6i q^{18} -2.94996e6 q^{19} +3.42485e6 q^{20} -901750. q^{21} -2.35774e6 q^{22} -4.47755e6i q^{23} -8.19385e6i q^{24} -7.03719e6 q^{25} -9.99843e6 q^{26} +2.76145e6 q^{27} +1.33268e7 q^{28} +3.67308e7 q^{29} -1.28974e7i q^{30} -595402. i q^{31} +2.93168e6i q^{32} +5.94350e6i q^{33} -1.36083e8i q^{34} +1.06169e7 q^{35} -4.08108e7 q^{36} +1.07486e7i q^{37} -1.64178e8i q^{38} +2.52045e7i q^{39} +9.64716e7i q^{40} +1.47249e8 q^{41} -5.01863e7i q^{42} -2.36868e8i q^{43} -8.78377e7i q^{44} -3.25123e7 q^{45} +2.49195e8 q^{46} +3.78784e8i q^{47} +1.58151e8 q^{48} -2.41163e8 q^{49} -3.91650e8i q^{50} -3.43046e8 q^{51} -3.72492e8i q^{52} -2.09357e8 q^{53} +1.53687e8i q^{54} -6.99767e7i q^{55} +3.75390e8i q^{56} -4.13868e8 q^{57} +2.04423e9i q^{58} +(2.07411e8 - 6.84177e8i) q^{59} +4.80493e8 q^{60} +3.23023e8i q^{61} +3.31367e7 q^{62} -1.26512e8 q^{63} +9.91162e8 q^{64} -2.96749e8i q^{65} -3.30782e8 q^{66} +1.67595e9i q^{67} +5.06980e9 q^{68} -6.28183e8i q^{69} +5.90876e8i q^{70} +1.42921e9 q^{71} -1.14957e9i q^{72} -2.75324e9i q^{73} -5.98206e8 q^{74} -9.87291e8 q^{75} +6.11647e9 q^{76} -2.72293e8i q^{77} -1.40274e9 q^{78} +4.89865e9 q^{79} -1.86202e9 q^{80} +3.87420e8 q^{81} +8.19506e9i q^{82} +4.90223e8i q^{83} +1.86969e9 q^{84} +4.03890e9 q^{85} +1.31827e10 q^{86} +5.15318e9 q^{87} +2.47422e9 q^{88} +6.61963e9i q^{89} -1.80945e9i q^{90} -1.15471e9i q^{91} +9.28378e9i q^{92} -8.35325e7i q^{93} -2.10810e10 q^{94} +4.87274e9 q^{95} +4.11304e8i q^{96} +1.12096e9i q^{97} -1.34218e10i q^{98} +8.33850e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9} + 620136 q^{12} + 662904 q^{15} + 27925160 q^{16} - 2053136 q^{17} - 5169828 q^{19} - 1076324 q^{20} - 1829224 q^{22} + 215378180 q^{25} - 22082700 q^{26} - 102921320 q^{28} - 112503588 q^{29} - 76491392 q^{35} - 1007769600 q^{36} + 473464516 q^{41} + 1215405588 q^{46} - 1676272320 q^{48} + 1975297276 q^{49} + 733970808 q^{51} + 3267506728 q^{53} + 591502824 q^{57} + 508142200 q^{59} + 1264196808 q^{60} - 6538206968 q^{62} + 362009736 q^{63} - 10324137972 q^{64} - 2764346616 q^{66} + 9997685952 q^{68} + 14908523204 q^{71} + 4863508712 q^{74} + 1890481680 q^{75} + 2044437240 q^{76} - 758396196 q^{78} - 3599839500 q^{79} - 23217941144 q^{80} + 38742048900 q^{81} - 13094894808 q^{84} + 23360564412 q^{85} + 12186923752 q^{86} + 7965322272 q^{87} + 32415437996 q^{88} - 22098322280 q^{94} + 7834510028 q^{95}+O(q^{100}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9 + 620136 * q^12 + 662904 * q^15 + 27925160 * q^16 - 2053136 * q^17 - 5169828 * q^19 - 1076324 * q^20 - 1829224 * q^22 + 215378180 * q^25 - 22082700 * q^26 - 102921320 * q^28 - 112503588 * q^29 - 76491392 * q^35 - 1007769600 * q^36 + 473464516 * q^41 + 1215405588 * q^46 - 1676272320 * q^48 + 1975297276 * q^49 + 733970808 * q^51 + 3267506728 * q^53 + 591502824 * q^57 + 508142200 * q^59 + 1264196808 * q^60 - 6538206968 * q^62 + 362009736 * q^63 - 10324137972 * q^64 - 2764346616 * q^66 + 9997685952 * q^68 + 14908523204 * q^71 + 4863508712 * q^74 + 1890481680 * q^75 + 2044437240 * q^76 - 758396196 * q^78 - 3599839500 * q^79 - 23217941144 * q^80 + 38742048900 * q^81 - 13094894808 * q^84 + 23360564412 * q^85 + 12186923752 * q^86 + 7965322272 * q^87 + 32415437996 * q^88 - 22098322280 * q^94 + 7834510028 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more