LMFDB - Embedded newform 177.11.c.a.58.81

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			58.81
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+44.5197i q^{2} +140.296 q^{3} -958.005 q^{4} -404.139 q^{5} +6245.94i q^{6} -20369.6 q^{7} +2938.10i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q+44.5197i q^{2} +140.296 q^{3} -958.005 q^{4} -404.139 q^{5} +6245.94i q^{6} -20369.6 q^{7} +2938.10i q^{8} +19683.0 q^{9} -17992.1i q^{10} -217841. i q^{11} -134404. q^{12} -504544. i q^{13} -906847. i q^{14} -56699.1 q^{15} -1.11180e6 q^{16} +782310. q^{17} +876281. i q^{18} +1.77007e6 q^{19} +387167. q^{20} -2.85777e6 q^{21} +9.69824e6 q^{22} +1.01853e7i q^{23} +412204. i q^{24} -9.60230e6 q^{25} +2.24622e7 q^{26} +2.76145e6 q^{27} +1.95141e7 q^{28} +3.48342e6 q^{29} -2.52423e6i q^{30} +3.18716e7i q^{31} -4.64884e7i q^{32} -3.05623e7i q^{33} +3.48282e7i q^{34} +8.23213e6 q^{35} -1.88564e7 q^{36} -6.84669e7i q^{37} +7.88030e7i q^{38} -7.07856e7i q^{39} -1.18740e6i q^{40} +1.22130e8 q^{41} -1.27227e8i q^{42} -3.24896e7i q^{43} +2.08693e8i q^{44} -7.95466e6 q^{45} -4.53445e8 q^{46} +4.40737e8i q^{47} -1.55981e8 q^{48} +1.32444e8 q^{49} -4.27491e8i q^{50} +1.09755e8 q^{51} +4.83355e8i q^{52} +7.76026e8 q^{53} +1.22939e8i q^{54} +8.80382e7i q^{55} -5.98478e7i q^{56} +2.48334e8 q^{57} +1.55081e8i q^{58} +(-5.68858e8 - 4.33033e8i) q^{59} +5.43180e7 q^{60} +1.05370e9i q^{61} -1.41891e9 q^{62} -4.00934e8 q^{63} +9.31167e8 q^{64} +2.03906e8i q^{65} +1.36063e9 q^{66} -7.80318e8i q^{67} -7.49456e8 q^{68} +1.42895e9i q^{69} +3.66492e8i q^{70} +9.51934e8 q^{71} +5.78306e7i q^{72} +1.89948e9i q^{73} +3.04812e9 q^{74} -1.34716e9 q^{75} -1.69573e9 q^{76} +4.43734e9i q^{77} +3.15135e9 q^{78} -1.34494e9 q^{79} +4.49321e8 q^{80} +3.87420e8 q^{81} +5.43720e9i q^{82} +8.04031e8i q^{83} +2.73776e9 q^{84} -3.16162e8 q^{85} +1.44643e9 q^{86} +4.88711e8 q^{87} +6.40040e8 q^{88} +8.55267e9i q^{89} -3.54139e8i q^{90} +1.02773e10i q^{91} -9.75752e9i q^{92} +4.47146e9i q^{93} -1.96215e10 q^{94} -7.15354e8 q^{95} -6.52214e9i q^{96} +1.17842e10i q^{97} +5.89638e9i q^{98} -4.28777e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			44.5197i			1.39124i	0.718409	+	0.695620i	$0.244870\pi$
$2$			44.5197i			1.39124i	−0.718409	+	0.695620i	$0.755130\pi$
$3$	140.296			0.577350
$3$	140.296			0.577350
$4$	−958.005			−0.935551
$5$	−404.139			−0.129324			−0.0646622	−	0.997907i	$-0.520597\pi$
$5$	−404.139			−0.129324			−0.0646622	+	0.997907i	$0.520597\pi$
$6$			6245.94i			0.803233i
$7$	−20369.6			−1.21197			−0.605985	−	0.795476i	$-0.707221\pi$
$7$	−20369.6			−1.21197			−0.605985	+	0.795476i	$0.707221\pi$
$8$			2938.10i			0.0896637i
$9$	19683.0			0.333333
$10$		−	17992.1i		−	0.179921i
$11$		−	217841.i		−	1.35262i	−0.736615	−	0.676312i	$-0.763577\pi$
$11$		−	217841.i		−	1.35262i	0.736615	−	0.676312i	$-0.236423\pi$
$12$	−134404.			−0.540141
$13$		−	504544.i		−	1.35888i	−0.733729	−	0.679442i	$-0.762222\pi$
$13$		−	504544.i		−	1.35888i	0.733729	−	0.679442i	$-0.237778\pi$
$14$		−	906847.i		−	1.68614i
$15$	−56699.1			−0.0746655
$16$	−1.11180e6			−1.06030
$17$	782310.			0.550978			0.275489	−	0.961304i	$-0.411160\pi$
$17$	782310.			0.550978			0.275489	+	0.961304i	$0.411160\pi$
$18$			876281.i			0.463747i
$19$	1.77007e6			0.714862			0.357431	−	0.933940i	$-0.383653\pi$
$19$	1.77007e6			0.714862			0.357431	+	0.933940i	$0.383653\pi$
$20$	387167.			0.120990
$21$	−2.85777e6			−0.699731
$22$	9.69824e6			1.88183
$23$			1.01853e7i			1.58246i	0.611518	+	0.791230i	$0.290559\pi$
$23$			1.01853e7i			1.58246i	−0.611518	+	0.791230i	$0.709441\pi$
$24$			412204.i			0.0517674i
$25$	−9.60230e6			−0.983275
$26$	2.24622e7			1.89053
$27$	2.76145e6			0.192450
$28$	1.95141e7			1.13386
$29$	3.48342e6			0.169831			0.0849154	−	0.996388i	$-0.472938\pi$
$29$	3.48342e6			0.169831			0.0849154	+	0.996388i	$0.472938\pi$
$30$		−	2.52423e6i		−	0.103878i
$31$			3.18716e7i			1.11326i	0.830762	+	0.556628i	$0.187905\pi$
$31$			3.18716e7i			1.11326i	−0.830762	+	0.556628i	$0.812095\pi$
$32$		−	4.64884e7i		−	1.38546i
$33$		−	3.05623e7i		−	0.780938i
$34$			3.48282e7i			0.766543i
$35$	8.23213e6			0.156737
$36$	−1.88564e7			−0.311850
$37$		−	6.84669e7i		−	0.987351i	−0.869646	−	0.493676i	$-0.835653\pi$
$37$		−	6.84669e7i		−	0.987351i	0.869646	−	0.493676i	$-0.164347\pi$
$38$			7.88030e7i			0.994545i
$39$		−	7.07856e7i		−	0.784552i
$40$		−	1.18740e6i		−	0.0115957i
$41$	1.22130e8			1.05415			0.527077	−	0.849818i	$-0.323288\pi$
$41$	1.22130e8			1.05415			0.527077	+	0.849818i	$0.323288\pi$
$42$		−	1.27227e8i		−	0.973494i
$43$		−	3.24896e7i		−	0.221005i	−0.993876	−	0.110502i	$-0.964754\pi$
$43$		−	3.24896e7i		−	0.221005i	0.993876	−	0.110502i	$-0.0352460\pi$
$44$			2.08693e8i			1.26545i
$45$	−7.95466e6			−0.0431081
$46$	−4.53445e8			−2.20158
$47$			4.40737e8i			1.92172i	0.277034	+	0.960860i	$0.410649\pi$
$47$			4.40737e8i			1.92172i	−0.277034	+	0.960860i	$0.589351\pi$
$48$	−1.55981e8			−0.612162
$49$	1.32444e8			0.468870
$50$		−	4.27491e8i		−	1.36797i
$51$	1.09755e8			0.318107
$52$			4.83355e8i			1.27131i
$53$	7.76026e8			1.85565			0.927827	−	0.373011i	$-0.121675\pi$
$53$	7.76026e8			1.85565			0.927827	+	0.373011i	$0.121675\pi$
$54$			1.22939e8i			0.267744i
$55$			8.80382e7i			0.174927i
$56$		−	5.98478e7i		−	0.108670i
$57$	2.48334e8			0.412726
$58$			1.55081e8i			0.236276i
$59$	−5.68858e8	−	4.33033e8i	−0.795689	−	0.605705i
$59$	−5.68858e8	−	4.33033e8i	−0.795689	−	0.605705i
$60$	5.43180e7			0.0698534
$61$			1.05370e9i			1.24758i	0.781593	+	0.623788i	$0.214407\pi$
$61$			1.05370e9i			1.24758i	−0.781593	+	0.623788i	$0.785593\pi$
$62$	−1.41891e9			−1.54881
$63$	−4.00934e8			−0.403990
$64$	9.31167e8			0.867217
$65$			2.03906e8i			0.175737i
$66$	1.36063e9			1.08647
$67$		−	7.80318e8i		−	0.577960i	−0.957335	−	0.288980i	$-0.906684\pi$
$67$		−	7.80318e8i		−	0.577960i	0.957335	−	0.288980i	$-0.0933161\pi$
$68$	−7.49456e8			−0.515468
$69$			1.42895e9i			0.913634i
$70$			3.66492e8i			0.218059i
$71$	9.51934e8			0.527612			0.263806	−	0.964576i	$-0.415022\pi$
$71$	9.51934e8			0.527612			0.263806	+	0.964576i	$0.415022\pi$
$72$			5.78306e7i			0.0298879i
$73$			1.89948e9i			0.916266i	0.888884	+	0.458133i	$0.151482\pi$
$73$			1.89948e9i			0.916266i	−0.888884	+	0.458133i	$0.848518\pi$
$74$	3.04812e9			1.37364
$75$	−1.34716e9			−0.567694
$76$	−1.69573e9			−0.668790
$77$			4.43734e9i			1.63934i
$78$	3.15135e9			1.09150
$79$	−1.34494e9			−0.437085			−0.218542	−	0.975827i	$-0.570130\pi$
$79$	−1.34494e9			−0.437085			−0.218542	+	0.975827i	$0.570130\pi$
$80$	4.49321e8			0.137122
$81$	3.87420e8			0.111111
$82$			5.43720e9i			1.46658i
$83$			8.04031e8i			0.204119i	0.994778	+	0.102059i	$0.0325431\pi$
$83$			8.04031e8i			0.204119i	−0.994778	+	0.102059i	$0.967457\pi$
$84$	2.73776e9			0.654634
$85$	−3.16162e8			−0.0712549
$86$	1.44643e9			0.307471
$87$	4.88711e8			0.0980519
$88$	6.40040e8			0.121281
$89$			8.55267e9i			1.53162i	0.643065	+	0.765811i	$0.277662\pi$
$89$			8.55267e9i			1.53162i	−0.643065	+	0.765811i	$0.722338\pi$
$90$		−	3.54139e8i		−	0.0599738i
$91$			1.02773e10i			1.64693i
$92$		−	9.75752e9i		−	1.48047i
$93$			4.47146e9i			0.642739i
$94$	−1.96215e10			−2.67358
$95$	−7.15354e8			−0.0924491
$96$		−	6.52214e9i		−	0.799897i
$97$			1.17842e10i			1.37227i	0.727474	+	0.686135i	$0.240694\pi$
$97$			1.17842e10i			1.37227i	−0.727474	+	0.686135i	$0.759306\pi$
$98$			5.89638e9i			0.652311i
$99$		−	4.28777e9i		−	0.450875i
$100$	9.19904e9			0.919904
$101$		−	1.28240e10i		−	1.22016i	−0.792339	−	0.610082i	$-0.791137\pi$
$101$		−	1.28240e10i		−	1.22016i	0.792339	−	0.610082i	$-0.208863\pi$
$102$			4.88626e9i			0.442564i
$103$		−	1.49310e10i		−	1.28796i	−0.765040	−	0.643982i	$-0.777281\pi$
$103$		−	1.49310e10i		−	1.28796i	0.765040	−	0.643982i	$-0.222719\pi$
$104$	1.48240e9			0.121843
$105$	1.15494e9			0.0904923
$106$			3.45485e10i			2.58166i
$107$	2.44078e10			1.74025			0.870123	−	0.492835i	$-0.164039\pi$
$107$	2.44078e10			1.74025			0.870123	+	0.492835i	$0.164039\pi$
$108$	−2.64548e9			−0.180047
$109$		−	5.84380e9i		−	0.379807i	−0.981803	−	0.189904i	$-0.939182\pi$
$109$		−	5.84380e9i		−	0.379807i	0.981803	−	0.189904i	$-0.0608175\pi$
$110$	−3.91943e9			−0.243366
$111$		−	9.60563e9i		−	0.570048i
$112$	2.26469e10			1.28505
$113$			1.61853e10i			0.878474i	0.898371	+	0.439237i	$0.144751\pi$
$113$			1.61853e10i			0.878474i	−0.898371	+	0.439237i	$0.855249\pi$
$114$			1.10557e10i			0.574201i
$115$		−	4.11626e9i		−	0.204651i
$116$	−3.33714e9			−0.158885
$117$		−	9.93094e9i		−	0.452961i
$118$	1.92785e10	−	2.53254e10i	0.842682	−	1.10700i
$119$	−1.59353e10			−0.667768
$120$		−	1.66588e8i		−	0.00669478i
$121$	−2.15175e10			−0.829592
$122$	−4.69104e10			−1.73568
$123$	1.71344e10			0.608616
$124$		−	3.05331e10i		−	1.04151i
$125$	7.82733e9			0.256486
$126$		−	1.78495e10i		−	0.562047i
$127$	3.67473e10			1.11226			0.556130	−	0.831095i	$-0.312286\pi$
$127$	3.67473e10			1.11226			0.556130	+	0.831095i	$0.312286\pi$
$128$		−	6.14885e9i		−	0.178955i
$129$		−	4.55816e9i		−	0.127597i
$130$	−9.07783e9			−0.244492
$131$			8.52392e9i			0.220944i	0.993879	+	0.110472i	$0.0352363\pi$
$131$			8.52392e9i			0.220944i	−0.993879	+	0.110472i	$0.964764\pi$
$132$			2.92788e10i			0.730607i
$133$	−3.60555e10			−0.866391
$134$	3.47395e10			0.804082
$135$	−1.11601e9			−0.0248885
$136$			2.29850e9i			0.0494027i
$137$	2.32685e10			0.482132			0.241066	−	0.970509i	$-0.422503\pi$
$137$	2.32685e10			0.482132			0.241066	+	0.970509i	$0.422503\pi$
$138$	−6.36165e10			−1.27108
$139$	−7.85021e10			−1.51289			−0.756445	−	0.654057i	$-0.773066\pi$
$139$	−7.85021e10			−1.51289			−0.756445	+	0.654057i	$0.773066\pi$
$140$	−7.88642e9			−0.146636
$141$			6.18337e10i			1.10951i
$142$			4.23798e10i			0.734036i
$143$	−1.09911e11			−1.83806
$144$	−2.18836e10			−0.353432
$145$	−1.40779e9			−0.0219633
$146$	−8.45645e10			−1.27475
$147$	1.85814e10			0.270702
$148$			6.55916e10i			0.923718i
$149$			4.42223e10i			0.602157i	0.953599	+	0.301079i	$0.0973467\pi$
$149$			4.42223e10i			0.602157i	−0.953599	+	0.301079i	$0.902653\pi$
$150$		−	5.99754e10i		−	0.789799i
$151$			4.09572e10i			0.521729i	0.965375	+	0.260865i	$0.0840077\pi$
$151$			4.09572e10i			0.521729i	−0.965375	+	0.260865i	$0.915992\pi$
$152$			5.20064e9i			0.0640972i
$153$	1.53982e10			0.183659
$154$	−1.97549e11			−2.28072
$155$		−	1.28805e10i		−	0.143971i
$156$			6.78129e10i			0.733988i
$157$			7.64414e10i			0.801365i	0.916217	+	0.400682i	$0.131227\pi$
$157$			7.64414e10i			0.801365i	−0.916217	+	0.400682i	$0.868773\pi$
$158$		−	5.98761e10i		−	0.608090i
$159$	1.08873e11			1.07136
$160$			1.87878e10i			0.179174i
$161$		−	2.07469e11i		−	1.91789i
$162$			1.72478e10i			0.154582i
$163$	−1.37094e11			−1.19146			−0.595731	−	0.803184i	$-0.703137\pi$
$163$	−1.37094e11			−1.19146			−0.595731	+	0.803184i	$0.703137\pi$
$164$	−1.17001e11			−0.986215
$165$			1.23514e10i			0.100994i
$166$	−3.57952e10			−0.283978
$167$	−1.91516e11			−1.47443			−0.737213	−	0.675660i	$-0.763859\pi$
$167$	−1.91516e11			−1.47443			−0.737213	+	0.675660i	$0.763859\pi$
$168$		−	8.39642e9i		−	0.0627405i
$169$	−1.16706e11			−0.846565
$170$		−	1.40754e10i		−	0.0991327i
$171$	3.48403e10			0.238287
$172$			3.11252e10i			0.206761i
$173$			4.21931e10i			0.272277i	0.990690	+	0.136139i	$0.0434692\pi$
$173$			4.21931e10i			0.272277i	−0.990690	+	0.136139i	$0.956531\pi$
$174$			2.17573e10i			0.136414i
$175$	1.95595e11			1.19170
$176$			2.42196e11i			1.43418i
$177$	−7.98085e10	−	6.07529e10i	−0.459391	−	0.349704i
$178$	−3.80763e11			−2.13086
$179$		−	2.23288e11i		−	1.21507i	−0.794294	−	0.607534i	$-0.792159\pi$
$179$		−	2.23288e11i		−	1.21507i	0.794294	−	0.607534i	$-0.207841\pi$
$180$	7.62060e9			0.0403299
$181$	1.43418e11			0.738265			0.369132	−	0.929377i	$-0.379655\pi$
$181$	1.43418e11			0.738265			0.369132	+	0.929377i	$0.379655\pi$
$182$	−4.57544e11			−2.29127
$183$			1.47830e11i			0.720289i
$184$	−2.99253e10			−0.141889
$185$			2.76701e10i			0.127689i
$186$	−1.99068e11			−0.894205
$187$		−	1.70420e11i		−	0.745266i
$188$		−	4.22228e11i		−	1.79787i
$189$	−5.62495e10			−0.233244
$190$		−	3.18473e10i		−	0.128619i
$191$			2.93853e11i			1.15602i	0.816031	+	0.578008i	$0.196170\pi$
$191$			2.93853e11i			1.15602i	−0.816031	+	0.578008i	$0.803830\pi$
$192$	1.30639e11			0.500688
$193$	1.32219e11			0.493751			0.246876	−	0.969047i	$-0.420596\pi$
$193$	1.32219e11			0.493751			0.246876	+	0.969047i	$0.420596\pi$
$194$	−5.24627e11			−1.90916
$195$			2.86072e10i			0.101462i
$196$	−1.26882e11			−0.438652
$197$	4.33826e11			1.46213			0.731063	−	0.682310i	$-0.239024\pi$
$197$	4.33826e11			1.46213			0.731063	+	0.682310i	$0.239024\pi$
$198$	1.90890e11			0.627275
$199$	5.60523e11			1.79609			0.898045	−	0.439904i	$-0.144988\pi$
$199$	5.60523e11			1.79609			0.898045	+	0.439904i	$0.144988\pi$
$200$		−	2.82125e10i		−	0.0881641i
$201$		−	1.09476e11i		−	0.333685i
$202$	5.70922e11			1.69754
$203$	−7.09559e10			−0.205830
$204$	−1.05146e11			−0.297606
$205$	−4.93576e10			−0.136328
$206$	6.64725e11			1.79187
$207$			2.00476e11i			0.527487i
$208$			5.60952e11i			1.44082i
$209$		−	3.85594e11i		−	0.966939i
$210$			5.14174e10i			0.125897i
$211$			4.46975e11i			1.06874i	0.845252	+	0.534368i	$0.179450\pi$
$211$			4.46975e11i			1.06874i	−0.845252	+	0.534368i	$0.820550\pi$
$212$	−7.43436e11			−1.73606
$213$	1.33553e11			0.304617
$214$			1.08663e12i			2.42110i
$215$			1.31303e10i			0.0285813i
$216$			8.11341e9i			0.0172558i
$217$		−	6.49211e11i		−	1.34923i
$218$	2.60164e11			0.528403
$219$			2.66490e11i			0.529006i
$220$		−	8.43410e10i		−	0.163653i
$221$		−	3.94710e11i		−	0.748715i
$222$	4.27640e11			0.793074
$223$	−1.83058e11			−0.331944			−0.165972	−	0.986130i	$-0.553076\pi$
$223$	−1.83058e11			−0.331944			−0.165972	+	0.986130i	$0.553076\pi$
$224$			9.46949e11i			1.67914i
$225$	−1.89002e11			−0.327758
$226$	−7.20566e11			−1.22217
$227$		−	5.28624e11i		−	0.877037i	−0.898722	−	0.438518i	$-0.855503\pi$
$227$		−	5.28624e11i		−	0.877037i	0.898722	−	0.438518i	$-0.144497\pi$
$228$	−2.37905e11			−0.386126
$229$			1.02826e12i			1.63277i	0.577509	+	0.816384i	$0.304025\pi$
$229$			1.02826e12i			1.63277i	−0.577509	+	0.816384i	$0.695975\pi$
$230$	1.83255e11			0.284718
$231$			6.22541e11i			0.946473i
$232$			1.02347e10i			0.0152277i
$233$		−	5.29944e10i		−	0.0771703i	−0.999255	−	0.0385852i	$-0.987715\pi$
$233$		−	5.29944e10i		−	0.0771703i	0.999255	−	0.0385852i	$-0.0122851\pi$
$234$	4.42123e11			0.630178
$235$		−	1.78119e11i		−	0.248525i
$236$	5.44968e11	+	4.14848e11i	0.744408	+	0.566668i
$237$	−1.88689e11			−0.252351
$238$		−	7.09436e11i		−	0.929027i
$239$	−7.56160e11			−0.969670			−0.484835	−	0.874606i	$-0.661120\pi$
$239$	−7.56160e11			−0.969670			−0.484835	+	0.874606i	$0.661120\pi$
$240$	6.30381e10			0.0791674
$241$	1.24623e12			1.53290			0.766451	−	0.642302i	$-0.222021\pi$
$241$	1.24623e12			1.53290			0.766451	+	0.642302i	$0.222021\pi$
$242$		−	9.57952e11i		−	1.15416i
$243$	5.43536e10			0.0641500
$244$		−	1.00945e12i		−	1.16717i
$245$	−5.35258e10			−0.0606363
$246$			7.62819e11i			0.846732i
$247$		−	8.93078e11i		−	0.971414i
$248$	−9.36419e10			−0.0998187
$249$			1.12802e11i			0.117848i
$250$			3.48470e11i			0.356834i
$251$	−6.99905e11			−0.702539			−0.351270	−	0.936274i	$-0.614250\pi$
$251$	−6.99905e11			−0.702539			−0.351270	+	0.936274i	$0.614250\pi$
$252$	3.84097e11			0.377953
$253$	2.21877e12			2.14047
$254$			1.63598e12i			1.54742i
$255$	−4.43563e10			−0.0411390
$256$	1.22726e12			1.11619
$257$	−1.71467e12			−1.52938			−0.764688	−	0.644401i	$-0.777107\pi$
$257$	−1.71467e12			−1.52938			−0.764688	+	0.644401i	$0.777107\pi$
$258$	2.02928e11			0.177519
$259$			1.39464e12i			1.19664i
$260$		−	1.95343e11i		−	0.164411i
$261$	6.85643e10			0.0566103
$262$	−3.79483e11			−0.307387
$263$	1.23966e11			0.0985200			0.0492600	−	0.998786i	$-0.484314\pi$
$263$	1.23966e11			0.0985200			0.0492600	+	0.998786i	$0.484314\pi$
$264$	8.97951e10			0.0700218
$265$	−3.13622e11			−0.239981
$266$		−	1.60518e12i		−	1.20536i
$267$			1.19991e12i			0.884283i
$268$			7.47549e11i			0.540711i
$269$			2.34489e10i			0.0166479i	0.999965	+	0.00832397i	$0.00264963\pi$
$269$			2.34489e10i			0.0166479i	−0.999965	+	0.00832397i	$0.997350\pi$
$270$		−	4.96844e10i		−	0.0346259i
$271$	1.77300e12			1.21300			0.606501	−	0.795083i	$-0.292573\pi$
$271$	1.77300e12			1.21300			0.606501	+	0.795083i	$0.292573\pi$
$272$	−8.69772e11			−0.584199
$273$			1.44187e12i			0.950853i
$274$			1.03591e12i			0.670761i
$275$			2.09178e12i			1.33000i
$276$		−	1.36894e12i		−	0.854751i
$277$	2.94048e12			1.80310			0.901549	−	0.432677i	$-0.142431\pi$
$277$	2.94048e12			1.80310			0.901549	+	0.432677i	$0.142431\pi$
$278$		−	3.49489e12i		−	2.10480i
$279$			6.27329e11i			0.371086i
$280$			2.41868e10i			0.0140536i
$281$	7.51601e11			0.428999			0.214499	−	0.976724i	$-0.431188\pi$
$281$	7.51601e11			0.428999			0.214499	+	0.976724i	$0.431188\pi$
$282$	−2.75282e12			−1.54359
$283$		−	8.77176e11i		−	0.483231i	−0.970372	−	0.241615i	$-0.922323\pi$
$283$		−	8.77176e11i		−	0.483231i	0.970372	−	0.241615i	$-0.0776772\pi$
$284$	−9.11957e11			−0.493608
$285$	−1.00361e11			−0.0533755
$286$		−	4.89319e12i		−	2.55718i
$287$	−2.48774e12			−1.27760
$288$		−	9.15031e11i		−	0.461821i
$289$	−1.40399e12			−0.696423
$290$		−	6.26743e10i		−	0.0305562i
$291$			1.65327e12i			0.792281i
$292$		−	1.81971e12i		−	0.857214i
$293$	4.81109e11			0.222795			0.111398	−	0.993776i	$-0.464467\pi$
$293$	4.81109e11			0.222795			0.111398	+	0.993776i	$0.464467\pi$
$294$			8.27239e11i			0.376612i
$295$	2.29897e11	+	1.75006e11i	0.102902	+	0.0783325i
$296$	2.01162e11			0.0885296
$297$		−	6.01558e11i		−	0.260313i
$298$	−1.96876e12			−0.837746
$299$	5.13891e12			2.15038
$300$	1.29059e12			0.531107
$301$			6.61799e11i			0.267851i
$302$	−1.82340e12			−0.725851
$303$		−	1.79916e12i		−	0.704461i
$304$	−1.96796e12			−0.757965
$305$		−	4.25841e11i		−	0.161342i
$306$			6.85524e11i			0.255514i
$307$	2.86946e12			1.05222			0.526112	−	0.850415i	$-0.323649\pi$
$307$	2.86946e12			1.05222			0.526112	+	0.850415i	$0.323649\pi$
$308$		−	4.25099e12i		−	1.53369i
$309$		−	2.09477e12i		−	0.743607i
$310$	5.73438e11			0.200299
$311$	−3.23107e12			−1.11057			−0.555284	−	0.831661i	$-0.687390\pi$
$311$	−3.23107e12			−1.11057			−0.555284	+	0.831661i	$0.687390\pi$
$312$	2.07975e11			0.0703458
$313$			4.31323e12i			1.43576i	0.696168	+	0.717879i	$0.254887\pi$
$313$			4.31323e12i			1.43576i	−0.696168	+	0.717879i	$0.745113\pi$
$314$	−3.40315e12			−1.11489
$315$	1.62033e11			0.0522457
$316$	1.28845e12			0.408915
$317$	−3.32947e12			−1.04011			−0.520054	−	0.854133i	$-0.674088\pi$
$317$	−3.32947e12			−1.04011			−0.520054	+	0.854133i	$0.674088\pi$
$318$			4.84701e12i			1.49052i
$319$		−	7.58834e11i		−	0.229717i
$320$	−3.76321e11			−0.112152
$321$	3.42433e12			1.00473
$322$	9.23647e12			2.66825
$323$	1.38474e12			0.393873
$324$	−3.71151e11			−0.103950
$325$			4.84478e12i			1.33616i
$326$		−	6.10338e12i		−	1.65761i
$327$		−	8.19863e11i		−	0.219282i
$328$			3.58831e11i			0.0945193i
$329$		−	8.97762e12i		−	2.32907i
$330$	−5.49881e11			−0.140507
$331$	6.08638e11			0.153186			0.0765929	−	0.997062i	$-0.475596\pi$
$331$	6.08638e11			0.153186			0.0765929	+	0.997062i	$0.475596\pi$
$332$		−	7.70266e11i		−	0.190963i
$333$		−	1.34763e12i		−	0.329117i
$334$		−	8.52625e12i		−	2.05128i
$335$			3.15357e11i			0.0747443i
$336$	3.17727e12			0.741921
$337$		−	3.59578e12i		−	0.827264i	−0.910444	−	0.413632i	$-0.864260\pi$
$337$		−	3.59578e12i		−	0.827264i	0.910444	−	0.413632i	$-0.135740\pi$
$338$		−	5.19572e12i		−	1.17778i
$339$			2.27074e12i			0.507187i
$340$	3.02884e11			0.0666626
$341$	6.94295e12			1.50582
$342$			1.55108e12i			0.331515i
$343$	3.05607e12			0.643713
$344$	9.54577e10			0.0198161
$345$		−	5.77495e11i		−	0.118155i
$346$	−1.87843e12			−0.378803
$347$			9.14707e11i			0.181817i	0.995859	+	0.0909085i	$0.0289771\pi$
$347$			9.14707e11i			0.181817i	−0.995859	+	0.0909085i	$0.971023\pi$
$348$	−4.68187e11			−0.0917325
$349$		−	9.57475e12i		−	1.84927i	−0.380854	−	0.924635i	$-0.624370\pi$
$349$		−	9.57475e12i		−	1.84927i	0.380854	−	0.924635i	$-0.375630\pi$
$350$			8.70782e12i			1.65794i
$351$		−	1.39327e12i		−	0.261517i
$352$	−1.01271e13			−1.87401
$353$			6.77934e12i			1.23684i	0.785847	+	0.618420i	$0.212227\pi$
$353$			6.77934e12i			1.23684i	−0.785847	+	0.618420i	$0.787773\pi$
$354$	2.70470e12	−	3.55305e12i	0.486523	−	0.639124i
$355$	−3.84713e11			−0.0682331
$356$		−	8.19350e12i		−	1.43291i
$357$	−2.23566e12			−0.385536
$358$	9.94072e12			1.69045
$359$	1.09240e13			1.83193			0.915963	−	0.401263i	$-0.131429\pi$
$359$	1.09240e13			1.83193			0.915963	+	0.401263i	$0.131429\pi$
$360$		−	2.33716e10i		−	0.00386523i
$361$	−2.99792e12			−0.488972
$362$			6.38495e12i			1.02710i
$363$	−3.01882e12			−0.478965
$364$		−	9.84574e12i		−	1.54078i
$365$		−	7.67655e11i		−	0.118496i
$366$	−6.58134e12			−1.00210
$367$			5.47292e12i			0.822032i	0.911628	+	0.411016i	$0.134826\pi$
$367$			5.47292e12i			0.822032i	−0.911628	+	0.411016i	$0.865174\pi$
$368$		−	1.13240e13i		−	1.67787i
$369$	2.40389e12			0.351385
$370$	−1.23187e12			−0.177646
$371$	−1.58073e13			−2.24900
$372$		−	4.28368e12i		−	0.601315i
$373$	−4.26707e12			−0.590997			−0.295499	−	0.955343i	$-0.595486\pi$
$373$	−4.26707e12			−0.590997			−0.295499	+	0.955343i	$0.595486\pi$
$374$	7.58703e12			1.03684
$375$	1.09814e12			0.148082
$376$	−1.29493e12			−0.172309
$377$		−	1.75754e12i		−	0.230780i
$378$		−	2.50421e12i		−	0.324498i
$379$	−7.08379e12			−0.905877			−0.452939	−	0.891542i	$-0.649624\pi$
$379$	−7.08379e12			−0.905877			−0.452939	+	0.891542i	$0.649624\pi$
$380$	6.85312e11			0.0864909
$381$	5.15550e12			0.642164
$382$	−1.30823e13			−1.60830
$383$	1.13036e13			1.37158			0.685791	−	0.727799i	$-0.259456\pi$
$383$	1.13036e13			1.37158			0.685791	+	0.727799i	$0.259456\pi$
$384$		−	8.62659e11i		−	0.103320i
$385$		−	1.79330e12i		−	0.212007i
$386$			5.88636e12i			0.686927i
$387$		−	6.39493e11i		−	0.0736683i
$388$		−	1.12893e13i		−	1.28383i
$389$	1.56295e13			1.75467			0.877337	−	0.479874i	$-0.159318\pi$
$389$	1.56295e13			1.75467			0.877337	+	0.479874i	$0.159318\pi$
$390$	−1.27358e12			−0.141158
$391$			7.96803e12i			0.871901i
$392$			3.89134e11i			0.0420406i
$393$			1.19587e12i			0.127562i
$394$			1.93138e13i			2.03417i
$395$	5.43540e11			0.0565258
$396$			4.10771e12i			0.421816i
$397$			3.48262e12i			0.353145i	0.984288	+	0.176573i	$0.0565011\pi$
$397$			3.48262e12i			0.353145i	−0.984288	+	0.176573i	$0.943499\pi$
$398$			2.49543e13i			2.49879i
$399$	−5.05845e12			−0.500211
$400$	1.06758e13			1.04256
$401$			6.73309e12i			0.649370i	0.945822	+	0.324685i	$0.105258\pi$
$401$			6.73309e12i			0.649370i	−0.945822	+	0.324685i	$0.894742\pi$
$402$	4.87382e12			0.464237
$403$	1.60806e13			1.51279
$404$			1.22855e13i			1.14153i
$405$	−1.56572e11			−0.0143694
$406$		−	3.15893e12i		−	0.286359i
$407$	−1.49149e13			−1.33552
$408$			3.22471e11i			0.0285227i
$409$		−	5.82257e12i		−	0.508742i	−0.967107	−	0.254371i	$-0.918131\pi$
$409$		−	5.82257e12i		−	0.508742i	0.967107	−	0.254371i	$-0.0818685\pi$
$410$		−	2.19739e12i		−	0.189665i
$411$	3.26448e12			0.278359
$412$			1.43040e13i			1.20496i
$413$	1.15874e13	+	8.82070e12i	0.964351	+	0.734096i
$414$	−8.92515e12			−0.733861
$415$		−	3.24940e11i		−	0.0263975i
$416$	−2.34554e13			−1.88268
$417$	−1.10135e13			−0.873468
$418$	1.71666e13			1.34525
$419$			1.84198e13i			1.42632i	0.701004	+	0.713158i	$0.252736\pi$
$419$			1.84198e13i			1.42632i	−0.701004	+	0.713158i	$0.747264\pi$
$420$	−1.10643e12			−0.0846602
$421$			1.05826e13i			0.800170i	0.916478	+	0.400085i	$0.131019\pi$
$421$			1.05826e13i			0.800170i	−0.916478	+	0.400085i	$0.868981\pi$
$422$	−1.98992e13			−1.48687
$423$			8.67503e12i			0.640573i
$424$			2.28004e12i			0.166385i
$425$	−7.51197e12			−0.541763
$426$			5.94572e12i			0.423796i
$427$		−	2.14634e13i		−	1.51203i
$428$	−2.33828e13			−1.62809
$429$	−1.54200e13			−1.06120
$430$	−5.84557e11			−0.0397635
$431$		−	4.63964e12i		−	0.311959i	−0.987760	−	0.155980i	$-0.950147\pi$
$431$		−	4.63964e12i		−	0.311959i	0.987760	−	0.155980i	$-0.0498535\pi$
$432$	−3.07018e12			−0.204054
$433$	2.71254e13			1.78212			0.891058	−	0.453889i	$-0.149964\pi$
$433$	2.71254e13			1.78212			0.891058	+	0.453889i	$0.149964\pi$
$434$	2.89027e13			1.87711
$435$	−1.97507e11			−0.0126805
$436$			5.59839e12i			0.355329i
$437$			1.80286e13i			1.13124i
$438$	−1.18641e13			−0.735975
$439$	9.17569e11			0.0562751			0.0281375	−	0.999604i	$-0.491042\pi$
$439$	9.17569e11			0.0562751			0.0281375	+	0.999604i	$0.491042\pi$
$440$	−2.58665e11			−0.0156846
$441$	2.60690e12			0.156290
$442$	1.75724e13			1.04164
$443$			1.91563e13i			1.12278i	0.827552	+	0.561389i	$0.189733\pi$
$443$			1.91563e13i			1.12278i	−0.827552	+	0.561389i	$0.810267\pi$
$444$			9.20224e12i			0.533309i
$445$		−	3.45647e12i		−	0.198076i
$446$		−	8.14969e12i		−	0.461814i
$447$			6.20422e12i			0.347656i
$448$	−1.89675e13			−1.05104
$449$	2.20311e13			1.20727			0.603634	−	0.797262i	$-0.293719\pi$
$449$	2.20311e13			1.20727			0.603634	+	0.797262i	$0.293719\pi$
$450$		−	8.41431e12i		−	0.455991i
$451$		−	2.66050e13i		−	1.42587i
$452$		−	1.55056e13i		−	0.821858i
$453$			5.74613e12i			0.301221i
$454$	2.35342e13			1.22017
$455$		−	4.15347e12i		−	0.212988i
$456$			7.29630e11i			0.0370065i
$457$		−	2.51973e13i		−	1.26408i	−0.774938	−	0.632038i	$-0.782219\pi$
$457$		−	2.51973e13i		−	1.26408i	0.774938	−	0.632038i	$-0.217781\pi$
$458$	−4.57777e13			−2.27157
$459$	2.16031e12			0.106036
$460$			3.94339e12i			0.191461i
$461$	2.32158e13			1.11501			0.557504	−	0.830174i	$-0.311759\pi$
$461$	2.32158e13			1.11501			0.557504	+	0.830174i	$0.311759\pi$
$462$	−2.77154e13			−1.31677
$463$			1.16250e13i			0.546371i	0.961961	+	0.273186i	$0.0880773\pi$
$463$			1.16250e13i			0.546371i	−0.961961	+	0.273186i	$0.911923\pi$
$464$	−3.87287e12			−0.180071
$465$		−	1.80709e12i		−	0.0831218i
$466$	2.35929e12			0.107362
$467$			3.39054e13i			1.52645i	0.646130	+	0.763227i	$0.276386\pi$
$467$			3.39054e13i			1.52645i	−0.646130	+	0.763227i	$0.723614\pi$
$468$			9.51388e12i			0.423768i
$469$			1.58948e13i			0.700470i
$470$	7.92980e12			0.345759
$471$			1.07244e13i			0.462668i
$472$	1.27230e12	−	1.67136e12i	0.0543098	−	0.0713444i
$473$	−7.07758e12			−0.298937
$474$		−	8.40039e12i		−	0.351081i
$475$	−1.69967e13			−0.702906
$476$	1.52661e13			0.624732
$477$	1.52745e13			0.618551
$478$		−	3.36640e13i		−	1.34905i
$479$	−1.20587e13			−0.478213			−0.239106	−	0.970993i	$-0.576854\pi$
$479$	−1.20587e13			−0.478213			−0.239106	+	0.970993i	$0.576854\pi$
$480$			2.63585e12i			0.103446i
$481$	−3.45445e13			−1.34170
$482$			5.54820e13i			2.13264i
$483$		−	2.91071e13i		−	1.10730i
$484$	2.06138e13			0.776126
$485$		−	4.76243e12i		−	0.177468i
$486$			2.41981e12i			0.0892481i
$487$	−2.37666e13			−0.867606			−0.433803	−	0.901008i	$-0.642829\pi$
$487$	−2.37666e13			−0.867606			−0.433803	+	0.901008i	$0.642829\pi$
$488$	−3.09587e12			−0.111862
$489$	−1.92337e13			−0.687891
$490$		−	2.38295e12i		−	0.0843598i
$491$	−6.53918e12			−0.229148			−0.114574	−	0.993415i	$-0.536550\pi$
$491$	−6.53918e12			−0.229148			−0.114574	+	0.993415i	$0.536550\pi$
$492$	−1.64148e13			−0.569392
$493$	2.72512e12			0.0935730
$494$	3.97596e13			1.35147
$495$			1.73286e12i			0.0583091i
$496$		−	3.54348e13i		−	1.18038i
$497$	−1.93905e13			−0.639450
$498$	−5.02193e12			−0.163955
$499$	4.86138e13			1.57129			0.785646	−	0.618676i	$-0.212331\pi$
$499$	4.86138e13			1.57129			0.785646	+	0.618676i	$0.212331\pi$
$500$	−7.49862e12			−0.239956
$501$	−2.68690e13			−0.851261
$502$		−	3.11596e13i		−	0.977401i
$503$		−	1.05896e13i		−	0.328883i	−0.986387	−	0.164441i	$-0.947418\pi$
$503$		−	1.05896e13i		−	0.328883i	0.986387	−	0.164441i	$-0.0525821\pi$
$504$		−	1.17799e12i		−	0.0362232i
$505$			5.18269e12i			0.157797i
$506$			9.87790e13i			2.97791i
$507$	−1.63734e13			−0.488764
$508$	−3.52040e13			−1.04058
$509$		−	2.81554e13i		−	0.824087i	−0.911164	−	0.412044i	$-0.864815\pi$
$509$		−	2.81554e13i		−	0.824087i	0.911164	−	0.412044i	$-0.135185\pi$
$510$		−	1.97473e12i		−	0.0572343i
$511$		−	3.86917e13i		−	1.11049i
$512$			4.83408e13i			1.37393i
$513$	4.88795e12			0.137575
$514$		−	7.63365e13i		−	2.12773i
$515$			6.03421e12i			0.166565i
$516$			4.36674e12i			0.119374i
$517$	9.60108e13			2.59936
$518$	−6.20890e13			−1.66481
$519$			5.91953e12i			0.157199i
$520$	−5.99096e11			−0.0157572
$521$	−3.10161e13			−0.807975			−0.403987	−	0.914765i	$-0.632376\pi$
$521$	−3.10161e13			−0.807975			−0.403987	+	0.914765i	$0.632376\pi$
$522$			3.05246e12i			0.0787585i
$523$	−2.84566e13			−0.727235			−0.363617	−	0.931548i	$-0.618458\pi$
$523$	−2.84566e13			−0.727235			−0.363617	+	0.931548i	$0.618458\pi$
$524$		−	8.16596e12i		−	0.206705i
$525$	2.74412e13			0.688028
$526$			5.51894e12i			0.137065i
$527$			2.49335e13i			0.613380i
$528$			3.39792e13i			0.828025i
$529$	−6.23130e13			−1.50418
$530$		−	1.39624e13i		−	0.333872i
$531$	−1.11968e13	−	8.52339e12i	−0.265230	−	0.201902i
$532$	3.45414e13			0.810553
$533$		−	6.16201e13i		−	1.43247i
$534$	−5.34195e13			−1.23025
$535$	−9.86416e12			−0.225056
$536$	2.29265e12			0.0518220
$537$		−	3.13264e13i		−	0.701519i
$538$	−1.04394e12			−0.0231613
$539$		−	2.88518e13i		−	0.634205i
$540$	1.06914e12			0.0232845
$541$		−	4.88003e12i		−	0.105302i	−0.998613	−	0.0526509i	$-0.983233\pi$
$541$		−	4.88003e12i		−	0.105302i	0.998613	−	0.0526509i	$-0.0167671\pi$
$542$			7.89333e13i			1.68758i
$543$	2.01211e13			0.426237
$544$		−	3.63683e13i		−	0.763359i
$545$			2.36171e12i			0.0491183i
$546$	−6.41917e13			−1.32287
$547$	7.70756e12			0.157391			0.0786955	−	0.996899i	$-0.474925\pi$
$547$	7.70756e12			0.157391			0.0786955	+	0.996899i	$0.474925\pi$
$548$	−2.22913e13			−0.451059
$549$			2.07400e13i			0.415859i
$550$	−9.31254e13			−1.85035
$551$	6.16590e12			0.121406
$552$	−4.19840e12			−0.0819198
$553$	2.73958e13			0.529734
$554$			1.30909e14i			2.50854i
$555$			3.88201e12i			0.0737211i
$556$	7.52054e13			1.41539
$557$	−8.10191e13			−1.51116			−0.755582	−	0.655054i	$-0.772646\pi$
$557$	−8.10191e13			−1.51116			−0.755582	+	0.655054i	$0.772646\pi$
$558$	−2.79285e13			−0.516269
$559$	−1.63924e13			−0.300320
$560$	−9.15249e12			−0.166188
$561$		−	2.39092e13i		−	0.430279i
$562$			3.34611e13i			0.596840i
$563$		−	1.43723e13i		−	0.254089i	−0.991897	−	0.127044i	$-0.959451\pi$
$563$		−	1.43723e13i		−	0.254089i	0.991897	−	0.127044i	$-0.0405491\pi$
$564$		−	5.92369e13i		−	1.03800i
$565$		−	6.54111e12i		−	0.113608i
$566$	3.90516e13			0.672290
$567$	−7.89159e12			−0.134663
$568$			2.79688e12i			0.0473077i
$569$		−	3.15550e13i		−	0.529063i	−0.964377	−	0.264532i	$-0.914783\pi$
$569$		−	3.15550e13i		−	0.529063i	0.964377	−	0.264532i	$-0.0852173\pi$
$570$		−	4.46806e12i		−	0.0742582i
$571$			6.11208e13i			1.00695i	0.864010	+	0.503475i	$0.167946\pi$
$571$			6.11208e13i			1.00695i	−0.864010	+	0.503475i	$0.832054\pi$
$572$	1.05295e14			1.71960
$573$			4.12265e13i			0.667426i
$574$		−	1.10754e14i		−	1.77745i
$575$		−	9.78019e13i		−	1.55599i
$576$	1.83282e13			0.289072
$577$	7.26221e13			1.13551			0.567754	−	0.823199i	$-0.307813\pi$
$577$	7.26221e13			1.13551			0.567754	+	0.823199i	$0.307813\pi$
$578$		−	6.25050e13i		−	0.968893i
$579$	1.85499e13			0.285067
$580$	1.34867e12			0.0205478
$581$		−	1.63778e13i		−	0.247385i
$582$	−7.36032e13			−1.10225
$583$		−	1.69051e14i		−	2.51000i
$584$	−5.58088e12			−0.0821558
$585$			4.01348e12i			0.0585789i
$586$			2.14189e13i			0.309962i
$587$		−	1.17608e14i		−	1.68750i	−0.536733	−	0.843752i	$-0.680342\pi$
$587$		−	1.17608e14i		−	1.68750i	0.536733	−	0.843752i	$-0.319658\pi$
$588$	−1.78011e13			−0.253256
$589$			5.64149e13i			0.795825i
$590$	−7.79120e12	+	1.02350e13i	−0.108979	+	0.143162i
$591$	6.08642e13			0.844159
$592$			7.61214e13i			1.04688i
$593$	5.71849e13			0.779845			0.389922	−	0.920848i	$-0.372502\pi$
$593$	5.71849e13			0.779845			0.389922	+	0.920848i	$0.372502\pi$
$594$	2.67812e13			0.362158
$595$	6.44008e12			0.0863588
$596$		−	4.23652e13i		−	0.563349i
$597$	7.86392e13			1.03697
$598$			2.28783e14i			2.99170i
$599$	−1.04476e13			−0.135482			−0.0677412	−	0.997703i	$-0.521579\pi$
$599$	−1.04476e13			−0.135482			−0.0677412	+	0.997703i	$0.521579\pi$
$600$		−	3.95811e12i		−	0.0509016i
$601$			3.38326e13i			0.431483i	0.976451	+	0.215741i	$0.0692168\pi$
$601$			3.38326e13i			0.431483i	−0.976451	+	0.215741i	$0.930783\pi$
$602$	−2.94631e13			−0.372646
$603$		−	1.53590e13i		−	0.192653i
$604$		−	3.92372e13i		−	0.488105i
$605$	8.69604e12			0.107286
$606$	8.00982e13			0.980076
$607$	8.28195e12			0.100505			0.0502526	−	0.998737i	$-0.483997\pi$
$607$	8.28195e12			0.100505			0.0502526	+	0.998737i	$0.483997\pi$
$608$		−	8.22877e13i		−	0.990414i
$609$	−9.95483e12			−0.118836
$610$	1.89583e13			0.224466
$611$	2.22371e14			2.61139
$612$	−1.47515e13			−0.171823
$613$			1.35326e14i			1.56343i	0.623636	+	0.781715i	$0.285655\pi$
$613$			1.35326e14i			1.56343i	−0.623636	+	0.781715i	$0.714345\pi$
$614$			1.27748e14i			1.46390i
$615$	−6.92468e12			−0.0787089
$616$	−1.30373e13			−0.146989
$617$	−1.17189e14			−1.31058			−0.655289	−	0.755379i	$-0.727453\pi$
$617$	−1.17189e14			−1.31058			−0.655289	+	0.755379i	$0.727453\pi$
$618$	9.32584e13			1.03454
$619$	−3.39180e13			−0.373231			−0.186615	−	0.982433i	$-0.559752\pi$
$619$	−3.39180e13			−0.373231			−0.186615	+	0.982433i	$0.559752\pi$
$620$			1.23396e13i			0.134692i
$621$			2.81261e13i			0.304545i
$622$		−	1.43847e14i		−	1.54507i
$623$		−	1.74214e14i		−	1.85628i
$624$			7.86994e13i			0.831856i
$625$	9.06091e13			0.950105
$626$	−1.92024e14			−1.99749
$627$		−	5.40974e13i		−	0.558263i
$628$		−	7.32312e13i		−	0.749718i
$629$		−	5.35623e13i		−	0.544009i
$630$			7.21367e12i			0.0726864i
$631$	−1.41485e13			−0.141437			−0.0707186	−	0.997496i	$-0.522529\pi$
$631$	−1.41485e13			−0.141437			−0.0707186	+	0.997496i	$0.522529\pi$
$632$		−	3.95155e12i		−	0.0391907i
$633$			6.27088e13i			0.617035i
$634$		−	1.48227e14i		−	1.44704i
$635$	−1.48510e13			−0.143842
$636$	−1.04301e14			−1.00231
$637$		−	6.68239e13i		−	0.637140i
$638$	3.37831e13			0.319592
$639$	1.87369e13			0.175871
$640$			2.48499e12i			0.0231432i
$641$	−7.49349e13			−0.692459			−0.346229	−	0.938150i	$-0.612538\pi$
$641$	−7.49349e13			−0.692459			−0.346229	+	0.938150i	$0.612538\pi$
$642$			1.52450e14i			1.39782i
$643$	7.12517e13			0.648247			0.324123	−	0.946015i	$-0.394931\pi$
$643$	7.12517e13			0.648247			0.324123	+	0.946015i	$0.394931\pi$
$644$			1.98757e14i			1.79429i
$645$			1.84213e12i			0.0165014i
$646$			6.16483e13i			0.547972i
$647$	1.07039e14			0.944105			0.472052	−	0.881571i	$-0.343513\pi$
$647$	1.07039e14			0.944105			0.472052	+	0.881571i	$0.343513\pi$
$648$			1.13828e12i			0.00996263i
$649$	−9.43326e13	+	1.23921e14i	−0.819291	+	1.07627i
$650$	−2.15688e14			−1.85892
$651$		−	9.10817e13i		−	0.778980i
$652$	1.31337e14			1.11467
$653$	4.66881e12			0.0393224			0.0196612	−	0.999807i	$-0.493741\pi$
$653$	4.66881e12			0.0393224			0.0196612	+	0.999807i	$0.493741\pi$
$654$	3.65001e13			0.305074
$655$		−	3.44485e12i		−	0.0285735i
$656$	−1.35784e14			−1.11771
$657$			3.73876e13i			0.305422i
$658$	3.99681e14			3.24029
$659$			1.26192e14i			1.01533i	0.861556	+	0.507663i	$0.169491\pi$
$659$			1.26192e14i			1.01533i	−0.861556	+	0.507663i	$0.830509\pi$
$660$		−	1.18327e13i		−	0.0944854i
$661$	2.02053e14			1.60125			0.800624	−	0.599167i	$-0.204501\pi$
$661$	2.02053e14			1.60125			0.800624	+	0.599167i	$0.204501\pi$
$662$			2.70964e13i			0.213118i
$663$		−	5.53762e13i		−	0.432271i
$664$	−2.36232e12			−0.0183020
$665$	1.45714e13			0.112045
$666$	5.99962e13			0.457881
$667$			3.54796e13i			0.268751i
$668$	1.83473e14			1.37940
$669$	−2.56823e13			−0.191648
$670$	−1.40396e13			−0.103987
$671$	2.29539e14			1.68750
$672$			1.32853e14i			0.969451i
$673$		−	1.94663e14i		−	1.40997i	−0.709223	−	0.704984i	$-0.750954\pi$
$673$		−	1.94663e14i		−	1.40997i	0.709223	−	0.704984i	$-0.249046\pi$
$674$	1.60083e14			1.15092
$675$	−2.65162e13			−0.189231
$676$	1.11805e14			0.792005
$677$	4.09581e13			0.288003			0.144001	−	0.989577i	$-0.454003\pi$
$677$	4.09581e13			0.288003			0.144001	+	0.989577i	$0.454003\pi$
$678$	−1.01093e14			−0.705620
$679$		−	2.40038e14i		−	1.66315i
$680$		−	9.28915e11i		−	0.00638898i
$681$		−	7.41639e13i		−	0.506357i
$682$			3.09098e14i			2.09496i
$683$			2.42465e14i			1.63135i	0.578513	+	0.815673i	$0.303633\pi$
$683$			2.42465e14i			1.63135i	−0.578513	+	0.815673i	$0.696367\pi$
$684$	−3.33771e13			−0.222930
$685$	−9.40371e12			−0.0623514
$686$			1.36055e14i			0.895560i
$687$			1.44261e14i			0.942680i
$688$			3.61219e13i			0.234330i
$689$		−	3.91539e14i		−	2.52162i
$690$	2.57099e13			0.164382
$691$		−	1.97068e14i		−	1.25091i	−0.780259	−	0.625456i	$-0.784913\pi$
$691$		−	1.97068e14i		−	1.25091i	0.780259	−	0.625456i	$-0.215087\pi$
$692$		−	4.04212e13i		−	0.254729i
$693$			8.73401e13i			0.546446i
$694$	−4.07225e13			−0.252951
$695$	3.17258e13			0.195654
$696$			1.43588e12i			0.00879169i
$697$	9.55437e13			0.580816
$698$	4.26265e14			2.57278
$699$		−	7.43491e12i		−	0.0445543i
$700$	−1.87381e14			−1.11490
$701$		−	2.17248e14i		−	1.28341i	−0.766952	−	0.641705i	$-0.778227\pi$
$701$		−	2.17248e14i		−	1.28341i	0.766952	−	0.641705i	$-0.221773\pi$
$702$	6.20281e13			0.363834
$703$		−	1.21191e14i		−	0.705820i
$704$		−	2.02847e14i		−	1.17302i
$705$		−	2.49894e13i		−	0.143486i
$706$	−3.01814e14			−1.72074
$707$			2.61220e14i			1.47880i
$708$	7.64569e13	+	5.82015e13i	0.429784	+	0.327166i
$709$	6.87942e13			0.383991			0.191995	−	0.981396i	$-0.438504\pi$
$709$	6.87942e13			0.383991			0.191995	+	0.981396i	$0.438504\pi$
$710$		−	1.71273e13i		−	0.0949287i
$711$	−2.64724e13			−0.145695
$712$	−2.51286e13			−0.137331
$713$	−3.24620e14			−1.76168
$714$		−	9.95311e13i		−	0.536374i
$715$	4.44191e13			0.237706
$716$			2.13911e14i			1.13676i
$717$	−1.06086e14			−0.559839
$718$			4.86332e14i			2.54865i
$719$		−	1.36484e14i		−	0.710291i	−0.934811	−	0.355145i	$-0.884431\pi$
$719$		−	1.36484e14i		−	0.710291i	0.934811	−	0.355145i	$-0.115569\pi$
$720$	8.84399e12			0.0457073
$721$			3.04139e14i			1.56097i
$722$		−	1.33467e14i		−	0.680278i
$723$	1.74842e14			0.885022
$724$	−1.37396e14			−0.690685
$725$	−3.34489e13			−0.166990
$726$		−	1.34397e14i		−	0.666356i
$727$	1.12919e14			0.556028			0.278014	−	0.960577i	$-0.410324\pi$
$727$	1.12919e14			0.556028			0.278014	+	0.960577i	$0.410324\pi$
$728$	−3.01959e13			−0.147669
$729$	7.62560e12			0.0370370
$730$	3.41758e13			0.164856
$731$		−	2.54169e13i		−	0.121769i
$732$		−	1.41622e14i		−	0.673867i
$733$	−1.55631e14			−0.735488			−0.367744	−	0.929927i	$-0.619870\pi$
$733$	−1.55631e14			−0.735488			−0.367744	+	0.929927i	$0.619870\pi$
$734$	−2.43653e14			−1.14365
$735$	−7.50947e12			−0.0350084
$736$	4.73496e14			2.19244
$737$	−1.69986e14			−0.781763
$738$			1.07020e14i			0.488861i
$739$		−	3.63072e13i		−	0.164729i	−0.996602	−	0.0823646i	$-0.973753\pi$
$739$		−	3.63072e13i		−	0.164729i	0.996602	−	0.0823646i	$-0.0262472\pi$
$740$		−	2.65081e13i		−	0.119459i
$741$		−	1.25295e14i		−	0.560846i
$742$		−	7.03737e14i		−	3.12889i
$743$	6.28873e13			0.277728			0.138864	−	0.990311i	$-0.455655\pi$
$743$	6.28873e13			0.277728			0.138864	+	0.990311i	$0.455655\pi$
$744$	−1.31376e13			−0.0576304
$745$		−	1.78719e13i		−	0.0778736i
$746$		−	1.89969e14i		−	0.822220i
$747$			1.58257e13i			0.0680395i
$748$			1.63263e14i			0.697235i
$749$	−4.97177e14			−2.10912
$750$			4.88890e13i			0.206018i
$751$			1.72446e13i			0.0721863i	0.999348	+	0.0360931i	$0.0114913\pi$
$751$			1.72446e13i			0.0721863i	−0.999348	+	0.0360931i	$0.988509\pi$
$752$		−	4.90011e14i		−	2.03759i
$753$	−9.81940e13			−0.405611
$754$	7.82452e13			0.321071
$755$		−	1.65524e13i		−	0.0674723i
$756$	5.38873e13			0.218211
$757$	−1.41562e13			−0.0569466			−0.0284733	−	0.999595i	$-0.509065\pi$
$757$	−1.41562e13			−0.0569466			−0.0284733	+	0.999595i	$0.509065\pi$
$758$		−	3.15368e14i		−	1.26029i
$759$	3.11285e14			1.23580
$760$		−	2.10178e12i		−	0.00828933i
$761$	−3.21252e14			−1.25870			−0.629350	−	0.777122i	$-0.716679\pi$
$761$	−3.21252e14			−1.25870			−0.629350	+	0.777122i	$0.716679\pi$
$762$			2.29521e14i			0.893404i
$763$			1.19036e14i			0.460315i
$764$		−	2.81513e14i		−	1.08151i
$765$	−6.22301e12			−0.0237516
$766$			5.03232e14i			1.90820i
$767$	−2.18484e14	+	2.87014e14i	−0.823083	+	1.08125i
$768$	1.72180e14			0.644430
$769$		−	1.72173e14i		−	0.640225i	−0.947380	−	0.320113i	$-0.896279\pi$
$769$		−	1.72173e14i		−	0.640225i	0.947380	−	0.320113i	$-0.103721\pi$
$770$	7.98372e13			0.294952
$771$	−2.40561e14			−0.882985
$772$	−1.26667e14			−0.461930
$773$		−	3.04500e14i		−	1.10329i	−0.834079	−	0.551644i	$-0.814001\pi$
$773$		−	3.04500e14i		−	1.10329i	0.834079	−	0.551644i	$-0.185999\pi$
$774$	2.84700e13			0.102490
$775$		−	3.06040e14i		−	1.09464i
$776$	−3.46230e13			−0.123043
$777$			1.95663e14i			0.690880i
$778$			6.95820e14i			2.44118i
$779$	2.16179e14			0.753575
$780$		−	2.74058e13i		−	0.0949226i
$781$		−	2.07371e14i		−	0.713661i
$782$	−3.54734e14			−1.21302
$783$	9.61930e12			0.0326840
$784$	−1.47251e14			−0.497141
$785$		−	3.08929e13i		−	0.103636i
$786$	−5.32399e13			−0.177470
$787$	−3.29923e14			−1.09280			−0.546398	−	0.837526i	$-0.684001\pi$
$787$	−3.29923e14			−1.09280			−0.546398	+	0.837526i	$0.684001\pi$
$788$	−4.15608e14			−1.36789
$789$	1.73920e13			0.0568805
$790$			2.41983e13i			0.0786409i
$791$		−	3.29688e14i		−	1.06468i
$792$	1.25979e13			0.0404271
$793$	5.31637e14			1.69531
$794$	−1.55045e14			−0.491310
$795$	−4.40000e13			−0.138553
$796$	−5.36983e14			−1.68033
$797$		−	5.70321e14i		−	1.77348i	−0.462264	−	0.886742i	$-0.652963\pi$
$797$		−	5.70321e14i		−	1.77348i	0.462264	−	0.886742i	$-0.347037\pi$
$798$		−	2.25201e14i		−	0.695914i
$799$			3.44793e14i			1.05883i
$800$			4.46395e14i			1.36229i
$801$			1.68342e14i			0.510541i
$802$	−2.99755e14			−0.903431
$803$	4.13786e14			1.23936
$804$			1.04878e14i			0.312180i
$805$			8.38464e13i			0.248030i
$806$			7.15905e14i			2.10465i
$807$			3.28979e12i			0.00961169i
$808$	3.76783e13			0.109404
$809$		−	3.63195e14i		−	1.04809i	−0.851692	−	0.524043i	$-0.824423\pi$
$809$		−	3.63195e14i		−	1.04809i	0.851692	−	0.524043i	$-0.175577\pi$
$810$		−	6.97052e12i		−	0.0199913i
$811$			3.10010e14i			0.883632i	0.897106	+	0.441816i	$0.145666\pi$
$811$			3.10010e14i			0.883632i	−0.897106	+	0.441816i	$0.854334\pi$
$812$	6.79760e13			0.192564
$813$	2.48745e14			0.700327
$814$		−	6.64008e14i		−	1.85802i
$815$	5.54049e13			0.154085
$816$	−1.22026e14			−0.337288
$817$		−	5.75088e13i		−	0.157988i
$818$	2.59219e14			0.707783
$819$			2.02289e14i			0.548975i
$820$	4.72848e13			0.127542
$821$			6.49538e14i			1.74136i	0.491849	+	0.870680i	$0.336321\pi$
$821$			6.49538e14i			1.74136i	−0.491849	+	0.870680i	$0.663679\pi$
$822$			1.45334e14i			0.387264i
$823$		−	4.49316e14i		−	1.19002i	−0.803720	−	0.595008i	$-0.797149\pi$
$823$		−	4.49316e14i		−	1.19002i	0.803720	−	0.595008i	$-0.202851\pi$
$824$	4.38689e13			0.115484
$825$			2.93468e14i			0.767877i
$826$	−3.92695e14	+	5.15867e14i	−1.02130	+	1.34164i
$827$	−1.91387e14			−0.494750			−0.247375	−	0.968920i	$-0.579568\pi$
$827$	−1.91387e14			−0.494750			−0.247375	+	0.968920i	$0.579568\pi$
$828$		−	1.92057e14i		−	0.493491i
$829$	4.26497e14			1.08929			0.544645	−	0.838667i	$-0.316665\pi$
$829$	4.26497e14			1.08929			0.544645	+	0.838667i	$0.316665\pi$
$830$	1.44662e13			0.0367253
$831$	4.12538e14			1.04102
$832$		−	4.69815e14i		−	1.17845i
$833$	1.03612e14			0.258337
$834$		−	4.90320e14i		−	1.21520i
$835$	7.73991e13			0.190679
$836$			3.69401e14i			0.904621i
$837$			8.80118e13i			0.214246i
$838$	−8.20045e14			−1.98435
$839$		−	3.72513e14i		−	0.896049i	−0.894021	−	0.448025i	$-0.852128\pi$
$839$		−	3.72513e14i		−	0.896049i	0.894021	−	0.448025i	$-0.147872\pi$
$840$			3.39332e12i			0.00811387i
$841$	−4.08573e14			−0.971157
$842$	−4.71135e14			−1.11323
$843$	1.05447e14			0.247682
$844$		−	4.28204e14i		−	0.999857i
$845$	4.71655e13			0.109481
$846$	−3.86210e14			−0.891192
$847$	4.38302e14			1.00544
$848$	−8.62786e14			−1.96754
$849$		−	1.23064e14i		−	0.278993i
$850$		−	3.34431e14i		−	0.753723i
$851$	6.97353e14			1.56244
$852$	−1.27944e14			−0.284985
$853$	−3.51963e14			−0.779386			−0.389693	−	0.920945i	$-0.627419\pi$
$853$	−3.51963e14			−0.779386			−0.389693	+	0.920945i	$0.627419\pi$
$854$	9.55544e14			2.10359
$855$	−1.40803e13			−0.0308164
$856$			7.17127e13i			0.156037i
$857$		−	6.73226e13i		−	0.145632i	−0.997345	−	0.0728159i	$-0.976801\pi$
$857$		−	6.73226e13i		−	0.145632i	0.997345	−	0.0728159i	$-0.0231986\pi$
$858$		−	6.86495e14i		−	1.47639i
$859$			7.93071e14i			1.69569i	0.530245	+	0.847844i	$0.322100\pi$
$859$			7.93071e14i			1.69569i	−0.530245	+	0.847844i	$0.677900\pi$
$860$		−	1.25789e13i		−	0.0267393i
$861$	−3.49020e14			−0.737624
$862$	2.06556e14			0.434011
$863$		−	5.56905e14i		−	1.16340i	−0.813405	−	0.581698i	$-0.802389\pi$
$863$		−	5.56905e14i		−	1.16340i	0.813405	−	0.581698i	$-0.197611\pi$
$864$		−	1.28375e14i		−	0.266632i
$865$		−	1.70519e13i		−	0.0352121i
$866$			1.20761e15i			2.47935i
$867$	−1.96974e14			−0.402080
$868$			6.21947e14i			1.26228i
$869$			2.92983e14i			0.591212i
$870$		−	8.79296e12i		−	0.0176416i
$871$	−3.93705e14			−0.785381
$872$	1.71697e13			0.0340549
$873$			2.31948e14i			0.457424i
$874$	−8.02628e14			−1.57383
$875$	−1.59439e14			−0.310853
$876$		−	2.55299e14i		−	0.494912i
$877$	2.79098e14			0.537972			0.268986	−	0.963144i	$-0.413312\pi$
$877$	2.79098e14			0.537972			0.268986	+	0.963144i	$0.413312\pi$
$878$			4.08499e13i			0.0782922i
$879$	6.74978e13			0.128631
$880$		−	9.78808e13i		−	0.185475i
$881$			5.32991e14i			1.00425i	0.864796	+	0.502124i	$0.167448\pi$
$881$			5.32991e14i			1.00425i	−0.864796	+	0.502124i	$0.832552\pi$
$882$			1.16058e14i			0.217437i
$883$	−3.41246e14			−0.635716			−0.317858	−	0.948138i	$-0.602964\pi$
$883$	−3.41246e14			−0.635716			−0.317858	+	0.948138i	$0.602964\pi$
$884$			3.78134e14i			0.700461i
$885$	3.22537e13	+	2.45526e13i	0.0594105	+	0.0452253i
$886$	−8.52835e14			−1.56206
$887$		−	4.19099e14i		−	0.763306i	−0.924306	−	0.381653i	$-0.875355\pi$
$887$		−	4.19099e14i		−	0.763306i	0.924306	−	0.381653i	$-0.124645\pi$
$888$	2.82223e13			0.0511126
$889$	−7.48526e14			−1.34803
$890$	1.53881e14			0.275572
$891$		−	8.43962e13i		−	0.150292i
$892$	1.75370e14			0.310550
$893$			7.80135e14i			1.37376i
$894$	−2.76210e14			−0.483673
$895$			9.02393e13i			0.157138i
$896$			1.25249e14i			0.216888i
$897$	7.20969e14			1.24152
$898$			9.80816e14i			1.67960i
$899$			1.11022e14i			0.189065i
$900$	1.81065e14			0.306635
$901$	6.07093e14			1.02242
$902$	1.18445e15			1.98373
$903$			9.28478e13i			0.154644i
$904$	−4.75541e13			−0.0787672
$905$	−5.79610e13			−0.0954756
$906$	−2.55816e14			−0.419070
$907$	−5.97479e13			−0.0973389			−0.0486695	−	0.998815i	$-0.515498\pi$
$907$	−5.97479e13			−0.0973389			−0.0486695	+	0.998815i	$0.515498\pi$
$908$			5.06424e14i			0.820513i
$909$		−	2.52415e14i		−	0.406721i
$910$	1.84911e14			0.296317
$911$	−9.05683e14			−1.44339			−0.721696	−	0.692210i	$-0.756637\pi$
$911$	−9.05683e14			−1.44339			−0.721696	+	0.692210i	$0.756637\pi$
$912$	−2.76098e14			−0.437611
$913$	1.75151e14			0.276096
$914$	1.12178e15			1.75863
$915$		−	5.97438e13i		−	0.0931509i
$916$		−	9.85076e14i		−	1.52754i
$917$		−	1.73629e14i		−	0.267778i
$918$			9.61763e13i			0.147521i
$919$			2.27163e14i			0.346545i	0.984874	+	0.173273i	$0.0554342\pi$
$919$			2.27163e14i			0.346545i	−0.984874	+	0.173273i	$0.944566\pi$
$920$	1.20940e13			0.0183497
$921$	4.02574e14			0.607502
$922$			1.03356e15i			1.55125i
$923$		−	4.80292e14i		−	0.716964i
$924$		−	5.96397e14i		−	0.885474i
$925$			6.57439e14i			0.970838i
$926$	−5.17541e14			−0.760134
$927$		−	2.93888e14i		−	0.429321i
$928$		−	1.61939e14i		−	0.235294i
$929$			1.02054e15i			1.47486i	0.675423	+	0.737430i	$0.263961\pi$
$929$			1.02054e15i			1.47486i	−0.675423	+	0.737430i	$0.736039\pi$
$930$	8.04511e13			0.115643
$931$	2.34435e14			0.335177
$932$			5.07689e13i			0.0721968i
$933$	−4.53307e14			−0.641187
$934$	−1.50946e15			−2.12367
$935$			6.88731e13i			0.0963811i
$936$	2.91781e13			0.0406142
$937$			7.80593e14i			1.08075i	0.841423	+	0.540377i	$0.181718\pi$
$937$			7.80593e14i			1.08075i	−0.841423	+	0.540377i	$0.818282\pi$
$938$	−7.07630e14			−0.974523
$939$			6.05130e14i			0.828935i
$940$			1.70639e14i			0.232508i
$941$			6.53257e14i			0.885393i	0.896672	+	0.442697i	$0.145978\pi$
$941$			6.53257e14i			0.885393i	−0.896672	+	0.442697i	$0.854022\pi$
$942$	−4.77448e14			−0.643683
$943$			1.24393e15i			1.66816i
$944$	6.32456e14	+	4.81446e14i	0.843665	+	0.642226i
$945$	2.27326e13			0.0301641
$946$		−	3.15092e14i		−	0.415893i
$947$	3.59587e13			0.0472122			0.0236061	−	0.999721i	$-0.492485\pi$
$947$	3.59587e13			0.0472122			0.0236061	+	0.999721i	$0.492485\pi$
$948$	1.80765e14			0.236087
$949$	9.58373e14			1.24510
$950$		−	7.56689e14i		−	0.977912i
$951$	−4.67111e14			−0.600507
$952$		−	4.68196e13i		−	0.0598746i
$953$	9.16640e14			1.16610			0.583048	−	0.812438i	$-0.301860\pi$
$953$	9.16640e14			1.16610			0.583048	+	0.812438i	$0.301860\pi$
$954$			6.80017e14i			0.860554i
$955$		−	1.18758e14i		−	0.149501i
$956$	7.24405e14			0.907176
$957$		−	1.06462e14i		−	0.132627i
$958$		−	5.36848e14i		−	0.665309i
$959$	−4.73970e14			−0.584329
$960$	−5.27963e13			−0.0647511
$961$	−1.96170e14			−0.239340
$962$		−	1.53791e15i		−	1.86662i
$963$	4.80420e14			0.580082
$964$	−1.19390e15			−1.43411
$965$	−5.34349e13			−0.0638541
$966$	1.29584e15			1.54052
$967$			4.87672e14i			0.576760i	0.957516	+	0.288380i	$0.0931167\pi$
$967$			4.87672e14i			0.576760i	−0.957516	+	0.288380i	$0.906883\pi$
$968$		−	6.32205e13i		−	0.0743843i
$969$	1.94274e14			0.227403
$970$	2.12022e14			0.246901
$971$	−5.91035e14			−0.684726			−0.342363	−	0.939568i	$-0.611227\pi$
$971$	−5.91035e14			−0.684726			−0.342363	+	0.939568i	$0.611227\pi$
$972$	−5.20710e13			−0.0600156
$973$	1.59906e15			1.83358
$974$		−	1.05808e15i		−	1.20705i
$975$			6.79704e14i			0.771430i
$976$		−	1.17150e15i		−	1.32280i
$977$		−	1.46245e15i		−	1.64289i	−0.570287	−	0.821446i	$-0.693168\pi$
$977$		−	1.46245e15i		−	1.64289i	0.570287	−	0.821446i	$-0.306832\pi$
$978$		−	8.56280e14i		−	0.957021i
$979$	1.86313e15			2.07171
$980$	5.12780e13			0.0567284
$981$		−	1.15024e14i		−	0.126602i
$982$		−	2.91122e14i		−	0.318800i
$983$		−	3.84447e14i		−	0.418860i	−0.977824	−	0.209430i	$-0.932839\pi$
$983$		−	3.84447e14i		−	0.418860i	0.977824	−	0.209430i	$-0.0671608\pi$
$984$			5.03426e13i			0.0545708i
$985$	−1.75326e14			−0.189089
$986$			1.21321e14i			0.130183i
$987$		−	1.25953e15i		−	1.34469i
$988$			8.55572e14i			0.908808i
$989$	3.30915e14			0.349732
$990$	−7.71462e13			−0.0811220
$991$			4.95750e14i			0.518674i	0.965787	+	0.259337i	$0.0835041\pi$
$991$			4.95750e14i			0.518674i	−0.965787	+	0.259337i	$0.916496\pi$
$992$	1.48166e15			1.54238
$993$	8.53895e13			0.0884419
$994$		−	8.63258e14i		−	0.889629i
$995$	−2.26529e14			−0.232278
$996$		−	1.08065e14i		−	0.110253i
$997$	−1.43966e15			−1.46145			−0.730724	−	0.682673i	$-0.760818\pi$
$997$	−1.43966e15			−1.46145			−0.730724	+	0.682673i	$0.760818\pi$
$998$			2.16427e15i			2.18605i
$999$		−	1.89068e14i		−	0.190016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.81	yes	100
59.58	odd	2	inner	177.11.c.a.58.20	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.20	✓	100	59.58	odd	2	inner
177.11.c.a.58.81	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)

\(f(q)\)	\(=\)	\(q+44.5197i q^{2} +140.296 q^{3} -958.005 q^{4} -404.139 q^{5} +6245.94i q^{6} -20369.6 q^{7} +2938.10i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q+44.5197i q^{2} +140.296 q^{3} -958.005 q^{4} -404.139 q^{5} +6245.94i q^{6} -20369.6 q^{7} +2938.10i q^{8} +19683.0 q^{9} -17992.1i q^{10} -217841. i q^{11} -134404. q^{12} -504544. i q^{13} -906847. i q^{14} -56699.1 q^{15} -1.11180e6 q^{16} +782310. q^{17} +876281. i q^{18} +1.77007e6 q^{19} +387167. q^{20} -2.85777e6 q^{21} +9.69824e6 q^{22} +1.01853e7i q^{23} +412204. i q^{24} -9.60230e6 q^{25} +2.24622e7 q^{26} +2.76145e6 q^{27} +1.95141e7 q^{28} +3.48342e6 q^{29} -2.52423e6i q^{30} +3.18716e7i q^{31} -4.64884e7i q^{32} -3.05623e7i q^{33} +3.48282e7i q^{34} +8.23213e6 q^{35} -1.88564e7 q^{36} -6.84669e7i q^{37} +7.88030e7i q^{38} -7.07856e7i q^{39} -1.18740e6i q^{40} +1.22130e8 q^{41} -1.27227e8i q^{42} -3.24896e7i q^{43} +2.08693e8i q^{44} -7.95466e6 q^{45} -4.53445e8 q^{46} +4.40737e8i q^{47} -1.55981e8 q^{48} +1.32444e8 q^{49} -4.27491e8i q^{50} +1.09755e8 q^{51} +4.83355e8i q^{52} +7.76026e8 q^{53} +1.22939e8i q^{54} +8.80382e7i q^{55} -5.98478e7i q^{56} +2.48334e8 q^{57} +1.55081e8i q^{58} +(-5.68858e8 - 4.33033e8i) q^{59} +5.43180e7 q^{60} +1.05370e9i q^{61} -1.41891e9 q^{62} -4.00934e8 q^{63} +9.31167e8 q^{64} +2.03906e8i q^{65} +1.36063e9 q^{66} -7.80318e8i q^{67} -7.49456e8 q^{68} +1.42895e9i q^{69} +3.66492e8i q^{70} +9.51934e8 q^{71} +5.78306e7i q^{72} +1.89948e9i q^{73} +3.04812e9 q^{74} -1.34716e9 q^{75} -1.69573e9 q^{76} +4.43734e9i q^{77} +3.15135e9 q^{78} -1.34494e9 q^{79} +4.49321e8 q^{80} +3.87420e8 q^{81} +5.43720e9i q^{82} +8.04031e8i q^{83} +2.73776e9 q^{84} -3.16162e8 q^{85} +1.44643e9 q^{86} +4.88711e8 q^{87} +6.40040e8 q^{88} +8.55267e9i q^{89} -3.54139e8i q^{90} +1.02773e10i q^{91} -9.75752e9i q^{92} +4.47146e9i q^{93} -1.96215e10 q^{94} -7.15354e8 q^{95} -6.52214e9i q^{96} +1.17842e10i q^{97} +5.89638e9i q^{98} -4.28777e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 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

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