LMFDB - Embedded newform 177.11.c.a.58.3

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			58.3
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.98

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-59.8859i q^{2} +140.296 q^{3} -2562.32 q^{4} +3689.76 q^{5} -8401.76i q^{6} +4188.49 q^{7} +92123.7i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q-59.8859i q^{2} +140.296 q^{3} -2562.32 q^{4} +3689.76 q^{5} -8401.76i q^{6} +4188.49 q^{7} +92123.7i q^{8} +19683.0 q^{9} -220965. i q^{10} -108701. i q^{11} -359484. q^{12} +582935. i q^{13} -250832. i q^{14} +517660. q^{15} +2.89309e6 q^{16} +733229. q^{17} -1.17873e6i q^{18} -2.47781e6 q^{19} -9.45436e6 q^{20} +587629. q^{21} -6.50964e6 q^{22} +273388. i q^{23} +1.29246e7i q^{24} +3.84873e6 q^{25} +3.49096e7 q^{26} +2.76145e6 q^{27} -1.07323e7 q^{28} -7.13464e6 q^{29} -3.10005e7i q^{30} +8.58497e6i q^{31} -7.89208e7i q^{32} -1.52503e7i q^{33} -4.39101e7i q^{34} +1.54546e7 q^{35} -5.04341e7 q^{36} +1.12871e8i q^{37} +1.48386e8i q^{38} +8.17835e7i q^{39} +3.39915e8i q^{40} +5.07042e7 q^{41} -3.51907e7i q^{42} +6.60375e7i q^{43} +2.78526e8i q^{44} +7.26256e7 q^{45} +1.63721e7 q^{46} +4.56783e8i q^{47} +4.05890e8 q^{48} -2.64932e8 q^{49} -2.30485e8i q^{50} +1.02869e8 q^{51} -1.49367e9i q^{52} +5.34760e8 q^{53} -1.65372e8i q^{54} -4.01080e8i q^{55} +3.85859e8i q^{56} -3.47628e8 q^{57} +4.27264e8i q^{58} +(3.64006e8 + 6.15318e8i) q^{59} -1.32641e9 q^{60} -5.64631e8i q^{61} +5.14118e8 q^{62} +8.24421e7 q^{63} -1.76372e9 q^{64} +2.15089e9i q^{65} -9.13277e8 q^{66} -3.92311e8i q^{67} -1.87877e9 q^{68} +3.83553e7i q^{69} -9.25510e8i q^{70} +2.57751e9 q^{71} +1.81327e9i q^{72} -1.12186e9i q^{73} +6.75937e9 q^{74} +5.39962e8 q^{75} +6.34895e9 q^{76} -4.55292e8i q^{77} +4.89768e9 q^{78} +2.65793e9 q^{79} +1.06748e10 q^{80} +3.87420e8 q^{81} -3.03647e9i q^{82} -1.54998e8i q^{83} -1.50569e9 q^{84} +2.70544e9 q^{85} +3.95471e9 q^{86} -1.00096e9 q^{87} +1.00139e10 q^{88} +7.28833e9i q^{89} -4.34925e9i q^{90} +2.44162e9i q^{91} -7.00509e8i q^{92} +1.20444e9i q^{93} +2.73549e10 q^{94} -9.14255e9 q^{95} -1.10723e10i q^{96} +3.03929e9i q^{97} +1.58657e10i q^{98} -2.13956e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	59.8859i		−	1.87143i	−0.352751	−	0.935717i	$-0.614754\pi$
$2$		−	59.8859i		−	1.87143i	0.352751	−	0.935717i	$-0.385246\pi$
$3$	140.296			0.577350
$3$	140.296			0.577350
$4$	−2562.32			−2.50227
$5$	3689.76			1.18072			0.590362	−	0.807138i	$-0.298985\pi$
$5$	3689.76			1.18072			0.590362	+	0.807138i	$0.298985\pi$
$6$		−	8401.76i		−	1.08047i
$7$	4188.49			0.249211			0.124606	−	0.992206i	$-0.460233\pi$
$7$	4188.49			0.249211			0.124606	+	0.992206i	$0.460233\pi$
$8$			92123.7i			2.81139i
$9$	19683.0			0.333333
$10$		−	220965.i		−	2.20965i
$11$		−	108701.i		−	0.674946i	−0.941335	−	0.337473i	$-0.890428\pi$
$11$		−	108701.i		−	0.674946i	0.941335	−	0.337473i	$-0.109572\pi$
$12$	−359484.			−1.44468
$13$			582935.i			1.57001i	0.619487	+	0.785007i	$0.287341\pi$
$13$			582935.i			1.57001i	−0.619487	+	0.785007i	$0.712659\pi$
$14$		−	250832.i		−	0.466382i
$15$	517660.			0.681692
$16$	2.89309e6			2.75907
$17$	733229.			0.516410			0.258205	−	0.966090i	$-0.416869\pi$
$17$	733229.			0.516410			0.258205	+	0.966090i	$0.416869\pi$
$18$		−	1.17873e6i		−	0.623811i
$19$	−2.47781e6			−1.00069			−0.500346	−	0.865825i	$-0.666794\pi$
$19$	−2.47781e6			−1.00069			−0.500346	+	0.865825i	$0.666794\pi$
$20$	−9.45436e6			−2.95449
$21$	587629.			0.143882
$22$	−6.50964e6			−1.26312
$23$			273388.i			0.0424757i	0.999774	+	0.0212379i	$0.00676073\pi$
$23$			273388.i			0.0424757i	−0.999774	+	0.0212379i	$0.993239\pi$
$24$			1.29246e7i			1.62316i
$25$	3.84873e6			0.394110
$26$	3.49096e7			2.93818
$27$	2.76145e6			0.192450
$28$	−1.07323e7			−0.623593
$29$	−7.13464e6			−0.347842			−0.173921	−	0.984760i	$-0.555644\pi$
$29$	−7.13464e6			−0.347842			−0.173921	+	0.984760i	$0.555644\pi$
$30$		−	3.10005e7i		−	1.27574i
$31$			8.58497e6i			0.299868i	0.988696	+	0.149934i	$0.0479061\pi$
$31$			8.58497e6i			0.299868i	−0.988696	+	0.149934i	$0.952094\pi$
$32$		−	7.89208e7i		−	2.35202i
$33$		−	1.52503e7i		−	0.389680i
$34$		−	4.39101e7i		−	0.966428i
$35$	1.54546e7			0.294250
$36$	−5.04341e7			−0.834089
$37$			1.12871e8i			1.62770i	0.581078	+	0.813848i	$0.302631\pi$
$37$			1.12871e8i			1.62770i	−0.581078	+	0.813848i	$0.697369\pi$
$38$			1.48386e8i			1.87273i
$39$			8.17835e7i			0.906448i
$40$			3.39915e8i			3.31948i
$41$	5.07042e7			0.437648			0.218824	−	0.975764i	$-0.429778\pi$
$41$	5.07042e7			0.437648			0.218824	+	0.975764i	$0.429778\pi$
$42$		−	3.51907e7i		−	0.269266i
$43$			6.60375e7i			0.449209i	0.974450	+	0.224604i	$0.0721090\pi$
$43$			6.60375e7i			0.449209i	−0.974450	+	0.224604i	$0.927891\pi$
$44$			2.78526e8i			1.68889i
$45$	7.26256e7			0.393575
$46$	1.63721e7			0.0794906
$47$			4.56783e8i			1.99169i	0.0910858	+	0.995843i	$0.470966\pi$
$47$			4.56783e8i			1.99169i	−0.0910858	+	0.995843i	$0.529034\pi$
$48$	4.05890e8			1.59295
$49$	−2.64932e8			−0.937894
$50$		−	2.30485e8i		−	0.737551i
$51$	1.02869e8			0.298150
$52$		−	1.49367e9i		−	3.92859i
$53$	5.34760e8			1.27873			0.639366	−	0.768902i	$-0.279197\pi$
$53$	5.34760e8			1.27873			0.639366	+	0.768902i	$0.279197\pi$
$54$		−	1.65372e8i		−	0.360158i
$55$		−	4.01080e8i		−	0.796925i
$56$			3.85859e8i			0.700630i
$57$	−3.47628e8			−0.577750
$58$			4.27264e8i			0.650963i
$59$	3.64006e8	+	6.15318e8i	0.509153	+	0.860676i
$59$	3.64006e8	+	6.15318e8i	0.509153	+	0.860676i
$60$	−1.32641e9			−1.70577
$61$		−	5.64631e8i		−	0.668522i	−0.942481	−	0.334261i	$-0.891513\pi$
$61$		−	5.64631e8i		−	0.668522i	0.942481	−	0.334261i	$-0.108487\pi$
$62$	5.14118e8			0.561183
$63$	8.24421e7			0.0830704
$64$	−1.76372e9			−1.64259
$65$			2.15089e9i			1.85375i
$66$	−9.13277e8			−0.729261
$67$		−	3.92311e8i		−	0.290574i	−0.989390	−	0.145287i	$-0.953589\pi$
$67$		−	3.92311e8i		−	0.290574i	0.989390	−	0.145287i	$-0.0464106\pi$
$68$	−1.87877e9			−1.29220
$69$			3.83553e7i			0.0245234i
$70$		−	9.25510e8i		−	0.550669i
$71$	2.57751e9			1.42860			0.714298	−	0.699842i	$-0.246746\pi$
$71$	2.57751e9			1.42860			0.714298	+	0.699842i	$0.246746\pi$
$72$			1.81327e9i			0.937131i
$73$		−	1.12186e9i		−	0.541159i	−0.962698	−	0.270579i	$-0.912785\pi$
$73$		−	1.12186e9i		−	0.541159i	0.962698	−	0.270579i	$-0.0872152\pi$
$74$	6.75937e9			3.04613
$75$	5.39962e8			0.227540
$76$	6.34895e9			2.50400
$77$		−	4.55292e8i		−	0.168204i
$78$	4.89768e9			1.69636
$79$	2.65793e9			0.863791			0.431895	−	0.901924i	$-0.357845\pi$
$79$	2.65793e9			0.863791			0.431895	+	0.901924i	$0.357845\pi$
$80$	1.06748e10			3.25770
$81$	3.87420e8			0.111111
$82$		−	3.03647e9i		−	0.819029i
$83$		−	1.54998e8i		−	0.0393492i	−0.999806	−	0.0196746i	$-0.993737\pi$
$83$		−	1.54998e8i		−	0.0393492i	0.999806	−	0.0196746i	$-0.00626302\pi$
$84$	−1.50569e9			−0.360031
$85$	2.70544e9			0.609738
$86$	3.95471e9			0.840665
$87$	−1.00096e9			−0.200827
$88$	1.00139e10			1.89754
$89$			7.28833e9i			1.30520i	0.757701	+	0.652602i	$0.226322\pi$
$89$			7.28833e9i			1.30520i	−0.757701	+	0.652602i	$0.773678\pi$
$90$		−	4.34925e9i		−	0.736549i
$91$			2.44162e9i			0.391265i
$92$		−	7.00509e8i		−	0.106286i
$93$			1.20444e9i			0.173129i
$94$	2.73549e10			3.72731
$95$	−9.14255e9			−1.18154
$96$		−	1.10723e10i		−	1.35794i
$97$			3.03929e9i			0.353927i	0.984217	+	0.176963i	$0.0566274\pi$
$97$			3.03929e9i			0.353927i	−0.984217	+	0.176963i	$0.943373\pi$
$98$			1.58657e10i			1.75521i
$99$		−	2.13956e9i		−	0.224982i
$100$	−9.86168e9			−0.986168
$101$		−	2.69242e9i		−	0.256174i	−0.991763	−	0.128087i	$-0.959116\pi$
$101$		−	2.69242e9i		−	0.256174i	0.991763	−	0.128087i	$-0.0408837\pi$
$102$		−	6.16041e9i		−	0.557968i
$103$			4.44428e7i			0.00383368i	0.999998	+	0.00191684i	$0.000610149\pi$
$103$			4.44428e7i			0.00383368i	−0.999998	+	0.00191684i	$0.999390\pi$
$104$	−5.37021e10			−4.41392
$105$	2.16821e9			0.169885
$106$		−	3.20246e10i		−	2.39306i
$107$	−9.08377e9			−0.647660			−0.323830	−	0.946115i	$-0.604971\pi$
$107$	−9.08377e9			−0.647660			−0.323830	+	0.946115i	$0.604971\pi$
$108$	−7.07572e9			−0.481561
$109$			5.38541e9i			0.350015i	0.984567	+	0.175007i	$0.0559949\pi$
$109$			5.38541e9i			0.350015i	−0.984567	+	0.175007i	$0.944005\pi$
$110$	−2.40190e10			−1.49139
$111$			1.58353e10i			0.939751i
$112$	1.21177e10			0.687591
$113$			3.54688e9i			0.192510i	0.995357	+	0.0962552i	$0.0306865\pi$
$113$			3.54688e9i			0.192510i	−0.995357	+	0.0962552i	$0.969313\pi$
$114$			2.08180e10i			1.08122i
$115$			1.00874e9i			0.0501521i
$116$	1.82812e10			0.870393
$117$			1.14739e10i			0.523338i
$118$	3.68489e10	−	2.17988e10i	1.61070	−	0.952847i
$119$	3.07112e9			0.128695
$120$			4.76887e10i			1.91650i
$121$	1.41216e10			0.544448
$122$	−3.38134e10			−1.25109
$123$	7.11360e9			0.252676
$124$		−	2.19974e10i		−	0.750350i
$125$	−2.18319e10			−0.715389
$126$		−	4.93712e9i		−	0.155461i
$127$	−1.69243e10			−0.512262			−0.256131	−	0.966642i	$-0.582448\pi$
$127$	−1.69243e10			−0.512262			−0.256131	+	0.966642i	$0.582448\pi$
$128$			2.48068e10i			0.721973i
$129$			9.26480e9i			0.259351i
$130$	1.28808e11			3.46918
$131$		−	5.73326e9i		−	0.148609i	−0.997236	−	0.0743045i	$-0.976326\pi$
$131$		−	5.73326e9i		−	0.148609i	0.997236	−	0.0743045i	$-0.0236737\pi$
$132$			3.90761e10i			0.975083i
$133$	−1.03783e10			−0.249384
$134$	−2.34939e10			−0.543790
$135$	1.01891e10			0.227231
$136$			6.75478e10i			1.45183i
$137$	3.13369e10			0.649313			0.324656	−	0.945832i	$-0.394751\pi$
$137$	3.13369e10			0.649313			0.324656	+	0.945832i	$0.394751\pi$
$138$	2.29694e9			0.0458939
$139$	−4.94543e10			−0.953082			−0.476541	−	0.879152i	$-0.658110\pi$
$139$	−4.94543e10			−0.953082			−0.476541	+	0.879152i	$0.658110\pi$
$140$	−3.95995e10			−0.736291
$141$			6.40849e10i			1.14990i
$142$		−	1.54357e11i		−	2.67352i
$143$	6.33654e10			1.05967
$144$	5.69448e10			0.919690
$145$	−2.63251e10			−0.410706
$146$	−6.71836e10			−1.01274
$147$	−3.71689e10			−0.541493
$148$		−	2.89211e11i		−	4.07293i
$149$			1.08170e11i			1.47290i	0.676490	+	0.736452i	$0.263500\pi$
$149$			1.08170e11i			1.47290i	−0.676490	+	0.736452i	$0.736500\pi$
$150$		−	3.23361e10i		−	0.425825i
$151$		−	8.13371e10i		−	1.03611i	−0.855349	−	0.518053i	$-0.826657\pi$
$151$		−	8.13371e10i		−	1.03611i	0.855349	−	0.518053i	$-0.173343\pi$
$152$		−	2.28265e11i		−	2.81334i
$153$	1.44321e10			0.172137
$154$	−2.72656e10			−0.314783
$155$			3.16765e10i			0.354062i
$156$		−	2.09556e11i		−	2.26817i
$157$			7.35807e10i			0.771375i	0.922630	+	0.385687i	$0.126036\pi$
$157$			7.35807e10i			0.771375i	−0.922630	+	0.385687i	$0.873964\pi$
$158$		−	1.59173e11i		−	1.61653i
$159$	7.50248e10			0.738276
$160$		−	2.91199e11i		−	2.77709i
$161$			1.14509e9i			0.0105854i
$162$		−	2.32010e10i		−	0.207937i
$163$	−1.86149e11			−1.61779			−0.808894	−	0.587954i	$-0.799934\pi$
$163$	−1.86149e11			−1.61779			−0.808894	+	0.587954i	$0.799934\pi$
$164$	−1.29920e11			−1.09511
$165$		−	5.62699e10i		−	0.460105i
$166$	−9.28219e9			−0.0736394
$167$	1.29426e11			0.996413			0.498206	−	0.867059i	$-0.333992\pi$
$167$	1.29426e11			0.996413			0.498206	+	0.867059i	$0.333992\pi$
$168$			5.41346e10i			0.404509i
$169$	−2.01955e11			−1.46494
$170$		−	1.62018e11i		−	1.14109i
$171$	−4.87708e10			−0.333564
$172$		−	1.69209e11i		−	1.12404i
$173$		−	2.96176e11i		−	1.91126i	−0.294574	−	0.955629i	$-0.595178\pi$
$173$		−	2.96176e11i		−	1.91126i	0.294574	−	0.955629i	$-0.404822\pi$
$174$			5.99435e10i			0.375834i
$175$	1.61204e10			0.0982167
$176$		−	3.14481e11i		−	1.86222i
$177$	5.10686e10	+	8.63267e10i	0.293960	+	0.496911i
$178$	4.36468e11			2.44260
$179$			1.75062e11i			0.952635i	0.879273	+	0.476318i	$0.158029\pi$
$179$			1.75062e11i			0.952635i	−0.879273	+	0.476318i	$0.841971\pi$
$180$	−1.86090e11			−0.984829
$181$	1.31742e11			0.678158			0.339079	−	0.940758i	$-0.389885\pi$
$181$	1.31742e11			0.678158			0.339079	+	0.940758i	$0.389885\pi$
$182$	1.46219e11			0.732227
$183$		−	7.92156e10i		−	0.385971i
$184$	−2.51856e10			−0.119416
$185$			4.16467e11i			1.92186i
$186$	7.21288e10			0.323999
$187$		−	7.97025e10i		−	0.348549i
$188$		−	1.17042e12i		−	4.98373i
$189$	1.15663e10			0.0479607
$190$			5.47510e11i			2.21118i
$191$		−	1.80546e11i		−	0.710266i	−0.934816	−	0.355133i	$-0.884436\pi$
$191$		−	1.80546e11i		−	0.710266i	0.934816	−	0.355133i	$-0.115564\pi$
$192$	−2.47443e11			−0.948349
$193$	3.40553e11			1.27174			0.635870	−	0.771796i	$-0.280641\pi$
$193$	3.40553e11			1.27174			0.635870	+	0.771796i	$0.280641\pi$
$194$	1.82011e11			0.662351
$195$			3.01762e11i			1.07026i
$196$	6.78840e11			2.34686
$197$	2.99654e10			0.100993			0.0504963	−	0.998724i	$-0.483920\pi$
$197$	2.99654e10			0.100993			0.0504963	+	0.998724i	$0.483920\pi$
$198$	−1.28129e11			−0.421039
$199$	−3.92538e11			−1.25781			−0.628906	−	0.777481i	$-0.716497\pi$
$199$	−3.92538e11			−1.25781			−0.628906	+	0.777481i	$0.716497\pi$
$200$			3.54559e11i			1.10800i
$201$		−	5.50398e10i		−	0.167763i
$202$	−1.61238e11			−0.479414
$203$	−2.98834e10			−0.0866861
$204$	−2.63584e11			−0.746050
$205$	1.87086e11			0.516741
$206$	2.66150e9			0.00717447
$207$			5.38110e9i			0.0141586i
$208$			1.68649e12i			4.33177i
$209$			2.69340e11i			0.675413i
$210$		−	1.29845e11i		−	0.317929i
$211$		−	6.00627e11i		−	1.43613i	−0.695978	−	0.718063i	$-0.745029\pi$
$211$		−	6.00627e11i		−	1.43613i	0.695978	−	0.718063i	$-0.254971\pi$
$212$	−1.37023e12			−3.19973
$213$	3.61615e11			0.824800
$214$			5.43989e11i			1.21205i
$215$			2.43663e11i			0.530392i
$216$			2.54395e11i			0.541053i
$217$			3.59581e10i			0.0747305i
$218$	3.22510e11			0.655029
$219$		−	1.57393e11i		−	0.312438i
$220$			1.02770e12i			1.99412i
$221$			4.27425e11i			0.810771i
$222$	9.48314e11			1.75868
$223$	−5.76487e11			−1.04536			−0.522679	−	0.852529i	$-0.675067\pi$
$223$	−5.76487e11			−1.04536			−0.522679	+	0.852529i	$0.675067\pi$
$224$		−	3.30559e11i		−	0.586151i
$225$	7.57546e10			0.131370
$226$	2.12408e11			0.360271
$227$		−	4.22740e9i		−	0.00701366i	−0.999994	−	0.00350683i	$-0.998884\pi$
$227$		−	4.22740e9i		−	0.00701366i	0.999994	−	0.00350683i	$-0.00111626\pi$
$228$	8.90734e11			1.44568
$229$			8.05126e11i			1.27846i	0.769016	+	0.639229i	$0.220746\pi$
$229$			8.05126e11i			1.27846i	−0.769016	+	0.639229i	$0.779254\pi$
$230$	6.04092e10			0.0938564
$231$		−	6.38757e10i		−	0.0971127i
$232$		−	6.57269e11i		−	0.977920i
$233$		−	3.62083e11i		−	0.527264i	−0.964623	−	0.263632i	$-0.915080\pi$
$233$		−	3.62083e11i		−	0.527264i	0.964623	−	0.263632i	$-0.0849205\pi$
$234$	6.87125e11			0.979392
$235$			1.68542e12i			2.35163i
$236$	−9.32700e11	−	1.57664e12i	−1.27404	−	2.15364i
$237$	3.72898e11			0.498710
$238$		−	1.83917e11i		−	0.240845i
$239$	−1.53434e12			−1.96758			−0.983791	−	0.179319i	$-0.942611\pi$
$239$	−1.53434e12			−1.96758			−0.983791	+	0.179319i	$0.942611\pi$
$240$	1.49764e12			1.88083
$241$	6.63824e11			0.816522			0.408261	−	0.912865i	$-0.366135\pi$
$241$	6.63824e11			0.816522			0.408261	+	0.912865i	$0.366135\pi$
$242$		−	8.45684e11i		−	1.01890i
$243$	5.43536e10			0.0641500
$244$			1.44677e12i			1.67282i
$245$	−9.77536e11			−1.10739
$246$		−	4.26004e11i		−	0.472866i
$247$		−	1.44440e12i		−	1.57110i
$248$	−7.90879e11			−0.843047
$249$		−	2.17456e10i		−	0.0227182i
$250$			1.30743e12i			1.33880i
$251$	1.52621e12			1.53195			0.765977	−	0.642868i	$-0.222256\pi$
$251$	1.52621e12			1.53195			0.765977	+	0.642868i	$0.222256\pi$
$252$	−2.11243e11			−0.207864
$253$	2.97175e10			0.0286688
$254$			1.01353e12i			0.958664i
$255$	3.79563e11			0.352033
$256$	−3.20468e11			−0.291464
$257$	1.83131e12			1.63342			0.816709	−	0.577050i	$-0.195796\pi$
$257$	1.83131e12			1.63342			0.816709	+	0.577050i	$0.195796\pi$
$258$	5.54831e11			0.485358
$259$			4.72759e11i			0.405640i
$260$		−	5.51128e12i		−	4.63858i
$261$	−1.40431e11			−0.115947
$262$	−3.43341e11			−0.278112
$263$	5.40085e11			0.429223			0.214612	−	0.976699i	$-0.431151\pi$
$263$	5.40085e11			0.429223			0.214612	+	0.976699i	$0.431151\pi$
$264$	1.40491e12			1.09554
$265$	1.97314e12			1.50983
$266$			6.21514e11i			0.466706i
$267$			1.02252e12i			0.753559i
$268$			1.00523e12i			0.727094i
$269$		−	1.39002e12i		−	0.986868i	−0.869783	−	0.493434i	$-0.835741\pi$
$269$		−	1.39002e12i		−	0.986868i	0.869783	−	0.493434i	$-0.164259\pi$
$270$		−	6.10183e11i		−	0.425247i
$271$	5.54735e11			0.379524			0.189762	−	0.981830i	$-0.439228\pi$
$271$	5.54735e11			0.379524			0.189762	+	0.981830i	$0.439228\pi$
$272$	2.12130e12			1.42481
$273$			3.42550e11i			0.225897i
$274$		−	1.87664e12i		−	1.21515i
$275$		−	4.18360e11i		−	0.266003i
$276$		−	9.82787e10i		−	0.0613640i
$277$	−1.21573e12			−0.745484			−0.372742	−	0.927935i	$-0.621582\pi$
$277$	−1.21573e12			−0.745484			−0.372742	+	0.927935i	$0.621582\pi$
$278$			2.96162e12i			1.78363i
$279$			1.68978e11i			0.0999560i
$280$			1.42373e12i			0.827251i
$281$	2.31227e12			1.31979			0.659897	−	0.751356i	$-0.270600\pi$
$281$	2.31227e12			1.31979			0.659897	+	0.751356i	$0.270600\pi$
$282$	3.83778e12			2.15196
$283$		−	2.17126e12i		−	1.19613i	−0.801447	−	0.598065i	$-0.795936\pi$
$283$		−	2.17126e12i		−	1.19613i	0.801447	−	0.598065i	$-0.204064\pi$
$284$	−6.60441e12			−3.57472
$285$	−1.28266e12			−0.682164
$286$		−	3.79470e12i		−	1.98311i
$287$	2.12374e11			0.109067
$288$		−	1.55340e12i		−	0.784008i
$289$	−1.47837e12			−0.733320
$290$			1.57650e12i			0.768608i
$291$			4.26401e11i			0.204340i
$292$			2.87457e12i			1.35412i
$293$	1.50545e12			0.697155			0.348578	−	0.937280i	$-0.386665\pi$
$293$	1.50545e12			0.697155			0.348578	+	0.937280i	$0.386665\pi$
$294$			2.22589e12i			1.01337i
$295$	1.34310e12	+	2.27038e12i	0.601170	+	1.01622i
$296$	−1.03981e13			−4.57609
$297$		−	3.00171e11i		−	0.129893i
$298$	6.47784e12			2.75644
$299$	−1.59368e11			−0.0666875
$300$	−1.38356e12			−0.569365
$301$			2.76598e11i			0.111948i
$302$	−4.87095e12			−1.93900
$303$		−	3.77736e11i		−	0.147902i
$304$	−7.16855e12			−2.76098
$305$		−	2.08336e12i		−	0.789340i
$306$		−	8.64282e11i		−	0.322143i
$307$	3.98881e12			1.46269			0.731344	−	0.682009i	$-0.238894\pi$
$307$	3.98881e12			1.46269			0.731344	+	0.682009i	$0.238894\pi$
$308$			1.16660e12i			0.420891i
$309$			6.23515e9i			0.00221337i
$310$	1.89698e12			0.662603
$311$	−8.53242e11			−0.293272			−0.146636	−	0.989191i	$-0.546845\pi$
$311$	−8.53242e11			−0.293272			−0.146636	+	0.989191i	$0.546845\pi$
$312$	−7.53420e12			−2.54838
$313$			2.21559e12i			0.737510i	0.929527	+	0.368755i	$0.120216\pi$
$313$			2.21559e12i			0.737510i	−0.929527	+	0.368755i	$0.879784\pi$
$314$	4.40644e12			1.44358
$315$	3.04192e11			0.0980833
$316$	−6.81048e12			−2.16143
$317$	8.88746e11			0.277639			0.138820	−	0.990318i	$-0.455669\pi$
$317$	8.88746e11			0.277639			0.138820	+	0.990318i	$0.455669\pi$
$318$		−	4.49292e12i		−	1.38164i
$319$			7.75540e11i			0.234774i
$320$	−6.50770e12			−1.93944
$321$	−1.27442e12			−0.373927
$322$	6.85745e10			0.0198099
$323$	−1.81681e12			−0.516768
$324$	−9.92695e11			−0.278030
$325$			2.24356e12i			0.618758i
$326$			1.11477e13i			3.02758i
$327$			7.55552e11i			0.202081i
$328$			4.67106e12i			1.23040i
$329$			1.91323e12i			0.496351i
$330$	−3.36978e12			−0.861056
$331$	2.15439e12			0.542232			0.271116	−	0.962547i	$-0.412607\pi$
$331$	2.15439e12			0.542232			0.271116	+	0.962547i	$0.412607\pi$
$332$			3.97154e11i			0.0984621i
$333$			2.22164e12i			0.542565i
$334$		−	7.75079e12i		−	1.86472i
$335$		−	1.44754e12i		−	0.343088i
$336$	1.70007e12			0.396981
$337$			6.35856e12i			1.46288i	0.681905	+	0.731441i	$0.261152\pi$
$337$			6.35856e12i			1.46288i	−0.681905	+	0.731441i	$0.738848\pi$
$338$			1.20942e13i			2.74154i
$339$			4.97614e11i			0.111146i
$340$	−6.93221e12			−1.52573
$341$	9.33192e11			0.202395
$342$			2.92068e12i			0.624244i
$343$	−2.29281e12			−0.482945
$344$	−6.08362e12			−1.26290
$345$			1.41522e11i			0.0289554i
$346$	−1.77368e13			−3.57679
$347$			2.39510e12i			0.476076i	0.971256	+	0.238038i	$0.0765043\pi$
$347$			2.39510e12i			0.476076i	−0.971256	+	0.238038i	$0.923496\pi$
$348$	2.56479e12			0.502522
$349$			5.67456e12i			1.09599i	0.836483	+	0.547993i	$0.184608\pi$
$349$			5.67456e12i			1.09599i	−0.836483	+	0.547993i	$0.815392\pi$
$350$		−	9.65384e11i		−	0.183806i
$351$			1.60974e12i			0.302149i
$352$	−8.57875e12			−1.58749
$353$			6.15338e12i			1.12264i	0.827599	+	0.561320i	$0.189706\pi$
$353$			6.15338e12i			1.12264i	−0.827599	+	0.561320i	$0.810294\pi$
$354$	5.16975e12	−	3.05829e12i	0.929937	−	0.550126i
$355$	9.51041e12			1.68678
$356$		−	1.86750e13i		−	3.26597i
$357$	4.30867e11			0.0743023
$358$	1.04837e13			1.78279
$359$	−1.09396e11			−0.0183454			−0.00917271	−	0.999958i	$-0.502920\pi$
$359$	−1.09396e11			−0.0183454			−0.00917271	+	0.999958i	$0.502920\pi$
$360$			6.69054e12i			1.10649i
$361$	8.49956e9			0.00138631
$362$		−	7.88948e12i		−	1.26913i
$363$	1.98120e12			0.314337
$364$		−	6.25621e12i		−	0.979049i
$365$		−	4.13940e12i		−	0.638959i
$366$	−4.74389e12			−0.722320
$367$		−	3.95385e12i		−	0.593868i	−0.954898	−	0.296934i	$-0.904036\pi$
$367$		−	3.95385e12i		−	0.593868i	0.954898	−	0.296934i	$-0.0959641\pi$
$368$			7.90938e11i			0.117193i
$369$	9.98011e11			0.145883
$370$	2.49405e13			3.59664
$371$	2.23984e12			0.318674
$372$		−	3.08616e12i		−	0.433215i
$373$	9.57607e12			1.32630			0.663152	−	0.748485i	$-0.269218\pi$
$373$	9.57607e12			1.32630			0.663152	+	0.748485i	$0.269218\pi$
$374$	−4.77306e12			−0.652287
$375$	−3.06294e12			−0.413030
$376$	−4.20806e13			−5.59941
$377$		−	4.15903e12i		−	0.546117i
$378$		−	6.92659e11i		−	0.0897553i
$379$	1.54106e13			1.97071			0.985356	−	0.170509i	$-0.0545412\pi$
$379$	1.54106e13			1.97071			0.985356	+	0.170509i	$0.0545412\pi$
$380$	2.34261e13			2.95653
$381$	−2.37441e12			−0.295754
$382$	−1.08122e13			−1.32922
$383$	−3.03341e12			−0.368076			−0.184038	−	0.982919i	$-0.558917\pi$
$383$	−3.03341e12			−0.368076			−0.184038	+	0.982919i	$0.558917\pi$
$384$			3.48030e12i			0.416831i
$385$		−	1.67992e12i		−	0.198603i
$386$		−	2.03943e13i		−	2.37998i
$387$			1.29982e12i			0.149736i
$388$		−	7.78764e12i		−	0.885619i
$389$	−1.30546e13			−1.46560			−0.732799	−	0.680446i	$-0.761786\pi$
$389$	−1.30546e13			−1.46560			−0.732799	+	0.680446i	$0.761786\pi$
$390$	1.80713e13			2.00293
$391$			2.00456e11i			0.0219349i
$392$		−	2.44065e13i		−	2.63679i
$393$		−	8.04354e11i		−	0.0857994i
$394$		−	1.79451e12i		−	0.189001i
$395$	9.80715e12			1.01990
$396$			5.48223e12i			0.562965i
$397$		−	1.07348e13i		−	1.08853i	−0.838914	−	0.544264i	$-0.816809\pi$
$397$		−	1.07348e13i		−	1.08853i	0.838914	−	0.544264i	$-0.183191\pi$
$398$			2.35075e13i			2.35391i
$399$	−1.45604e12			−0.143982
$400$	1.11347e13			1.08738
$401$			1.62822e13i			1.57033i	0.619286	+	0.785166i	$0.287422\pi$
$401$			1.62822e13i			1.57033i	−0.619286	+	0.785166i	$0.712578\pi$
$402$	−3.29611e12			−0.313957
$403$	−5.00448e12			−0.470797
$404$			6.89884e12i			0.641016i
$405$	1.42949e12			0.131192
$406$			1.78959e12i			0.162227i
$407$	1.22691e13			1.09861
$408$			9.47669e12i			0.838216i
$409$			6.46721e12i			0.565068i	0.959257	+	0.282534i	$0.0911750\pi$
$409$			6.46721e12i			0.565068i	−0.959257	+	0.282534i	$0.908825\pi$
$410$		−	1.12038e13i		−	0.967047i
$411$	4.39645e12			0.374881
$412$		−	1.13877e11i		−	0.00959288i
$413$	1.52464e12	+	2.57726e12i	0.126887	+	0.214490i
$414$	3.22252e11			0.0264969
$415$		−	5.71906e11i		−	0.0464605i
$416$	4.60057e13			3.69271
$417$	−6.93825e12			−0.550262
$418$	1.61297e13			1.26399
$419$		−	6.56873e12i		−	0.508641i	−0.967120	−	0.254320i	$-0.918148\pi$
$419$		−	6.56873e12i		−	0.508641i	0.967120	−	0.254320i	$-0.0818518\pi$
$420$	−5.55566e12			−0.425098
$421$		−	5.80550e12i		−	0.438964i	−0.975617	−	0.219482i	$-0.929563\pi$
$421$		−	5.80550e12i		−	0.438964i	0.975617	−	0.219482i	$-0.0704367\pi$
$422$	−3.59691e13			−2.68762
$423$			8.99086e12i			0.663895i
$424$			4.92641e13i			3.59502i
$425$	2.82200e12			0.203523
$426$		−	2.16556e13i		−	1.54356i
$427$		−	2.36495e12i		−	0.166603i
$428$	2.32755e13			1.62062
$429$	8.88992e12			0.611803
$430$	1.45920e13			0.992593
$431$			1.22660e13i			0.824737i	0.911017	+	0.412369i	$0.135298\pi$
$431$			1.22660e13i			0.824737i	−0.911017	+	0.412369i	$0.864702\pi$
$432$	7.98913e12			0.530983
$433$	−4.42984e12			−0.291037			−0.145518	−	0.989356i	$-0.546485\pi$
$433$	−4.42984e12			−0.291037			−0.145518	+	0.989356i	$0.546485\pi$
$434$	2.15338e12			0.139853
$435$	−3.69331e12			−0.237121
$436$		−	1.37991e13i		−	0.875830i
$437$		−	6.77406e11i		−	0.0425052i
$438$	−9.42560e12			−0.584707
$439$	−9.48510e12			−0.581727			−0.290864	−	0.956765i	$-0.593943\pi$
$439$	−9.48510e12			−0.581727			−0.290864	+	0.956765i	$0.593943\pi$
$440$	3.69490e13			2.24047
$441$	−5.21465e12			−0.312631
$442$	2.55967e13			1.51731
$443$		−	1.92750e13i		−	1.12973i	−0.825182	−	0.564867i	$-0.808928\pi$
$443$		−	1.92750e13i		−	1.12973i	0.825182	−	0.564867i	$-0.191072\pi$
$444$		−	4.05752e13i		−	2.35151i
$445$			2.68922e13i			1.54109i
$446$			3.45234e13i			1.95632i
$447$			1.51758e13i			0.850382i
$448$	−7.38731e12			−0.409352
$449$	−1.18642e13			−0.650139			−0.325069	−	0.945690i	$-0.605388\pi$
$449$	−1.18642e13			−0.650139			−0.325069	+	0.945690i	$0.605388\pi$
$450$		−	4.53663e12i		−	0.245850i
$451$		−	5.51158e12i		−	0.295388i
$452$		−	9.08824e12i		−	0.481712i
$453$		−	1.14113e13i		−	0.598196i
$454$	−2.53162e11			−0.0131256
$455$			9.00900e12i			0.461976i
$456$		−	3.20248e13i		−	1.62428i
$457$		−	1.68398e12i		−	0.0844804i	−0.999107	−	0.0422402i	$-0.986551\pi$
$457$		−	1.68398e12i		−	0.0844804i	0.999107	−	0.0422402i	$-0.0134495\pi$
$458$	4.82157e13			2.39255
$459$	2.02477e12			0.0993832
$460$		−	2.58471e12i		−	0.125494i
$461$	−3.27427e13			−1.57257			−0.786286	−	0.617863i	$-0.787999\pi$
$461$	−3.27427e13			−1.57257			−0.786286	+	0.617863i	$0.787999\pi$
$462$	−3.82525e12			−0.181740
$463$			2.15339e13i			1.01208i	0.862509	+	0.506042i	$0.168892\pi$
$463$			2.15339e13i			1.01208i	−0.862509	+	0.506042i	$0.831108\pi$
$464$	−2.06412e13			−0.959720
$465$			4.44409e12i			0.204418i
$466$	−2.16837e13			−0.986740
$467$		−	6.68552e11i		−	0.0300989i	−0.999887	−	0.0150495i	$-0.995209\pi$
$467$		−	6.68552e11i		−	0.0300989i	0.999887	−	0.0150495i	$-0.00479057\pi$
$468$		−	2.93998e13i		−	1.30953i
$469$		−	1.64319e12i		−	0.0724143i
$470$	1.00933e14			4.40093
$471$			1.03231e13i			0.445353i
$472$	−5.66854e13	+	3.35336e13i	−2.41970	+	1.43143i
$473$	7.17832e12			0.303192
$474$		−	2.23313e13i		−	0.933303i
$475$	−9.53645e12			−0.394383
$476$	−7.86921e12			−0.322030
$477$	1.05257e13			0.426244
$478$			9.18855e13i			3.68220i
$479$	1.30537e13			0.517673			0.258836	−	0.965921i	$-0.416661\pi$
$479$	1.30537e13			0.517673			0.258836	+	0.965921i	$0.416661\pi$
$480$		−	4.08541e13i		−	1.60335i
$481$	−6.57964e13			−2.55550
$482$		−	3.97537e13i		−	1.52807i
$483$			1.60651e11i			0.00611150i
$484$	−3.61840e13			−1.36235
$485$			1.12143e13i			0.417890i
$486$		−	3.25501e12i		−	0.120053i
$487$	2.60567e13			0.951206			0.475603	−	0.879660i	$-0.342230\pi$
$487$	2.60567e13			0.951206			0.475603	+	0.879660i	$0.342230\pi$
$488$	5.20159e13			1.87948
$489$	−2.61159e13			−0.934031
$490$			5.85406e13i			2.07242i
$491$	3.68761e13			1.29222			0.646112	−	0.763243i	$-0.276394\pi$
$491$	3.68761e13			1.29222			0.646112	+	0.763243i	$0.276394\pi$
$492$	−1.82273e13			−0.632262
$493$	−5.23132e12			−0.179629
$494$	−8.64995e13			−2.94021
$495$		−	7.89445e12i		−	0.265642i
$496$			2.48371e13i			0.827357i
$497$	1.07959e13			0.356022
$498$	−1.30226e12			−0.0425157
$499$	−6.15494e13			−1.98939			−0.994697	−	0.102849i	$-0.967204\pi$
$499$	−6.15494e13			−1.98939			−0.994697	+	0.102849i	$0.967204\pi$
$500$	5.59404e13			1.79009
$501$	1.81580e13			0.575279
$502$		−	9.13984e13i		−	2.86695i
$503$		−	2.81370e13i		−	0.873852i	−0.899497	−	0.436926i	$-0.856067\pi$
$503$		−	2.81370e13i		−	0.873852i	0.899497	−	0.436926i	$-0.143933\pi$
$504$			7.59487e12i			0.233543i
$505$		−	9.93439e12i		−	0.302471i
$506$		−	1.77966e12i		−	0.0536518i
$507$	−2.83335e13			−0.845785
$508$	4.33654e13			1.28181
$509$		−	6.37637e13i		−	1.86631i	−0.359469	−	0.933157i	$-0.617042\pi$
$509$		−	6.37637e13i		−	1.86631i	0.359469	−	0.933157i	$-0.382958\pi$
$510$		−	2.27305e13i		−	0.658806i
$511$		−	4.69891e12i		−	0.134863i
$512$			4.45937e13i			1.26743i
$513$	−6.84236e12			−0.192583
$514$		−	1.09670e14i		−	3.05683i
$515$			1.63983e11i			0.00452651i
$516$		−	2.37394e13i		−	0.648965i
$517$	4.96527e13			1.34428
$518$	2.83116e13			0.759129
$519$		−	4.15523e13i		−	1.10346i
$520$	−1.98148e14			−5.21163
$521$	7.61660e12			0.198414			0.0992070	−	0.995067i	$-0.468369\pi$
$521$	7.61660e12			0.198414			0.0992070	+	0.995067i	$0.468369\pi$
$522$			8.40984e12i			0.216988i
$523$	3.85918e13			0.986248			0.493124	−	0.869959i	$-0.335855\pi$
$523$	3.85918e13			0.986248			0.493124	+	0.869959i	$0.335855\pi$
$524$			1.46904e13i			0.371859i
$525$	2.26163e12			0.0567054
$526$		−	3.23434e13i		−	0.803263i
$527$			6.29475e12i			0.154855i
$528$		−	4.41205e13i		−	1.07515i
$529$	4.13518e13			0.998196
$530$		−	1.18163e14i		−	2.82555i
$531$	7.16473e12	+	1.21113e13i	0.169718	+	0.286892i
$532$	2.65926e13			0.624025
$533$			2.95572e13i			0.687113i
$534$	6.12348e13			1.41024
$535$	−3.35169e13			−0.764708
$536$	3.61412e13			0.816918
$537$			2.45605e13i			0.550004i
$538$	−8.32425e13			−1.84686
$539$			2.87983e13i			0.633027i
$540$	−2.61077e13			−0.568591
$541$			4.17389e13i			0.900646i	0.892866	+	0.450323i	$0.148691\pi$
$541$			4.17389e13i			0.900646i	−0.892866	+	0.450323i	$0.851309\pi$
$542$		−	3.32208e13i		−	0.710254i
$543$	1.84829e13			0.391535
$544$		−	5.78670e13i		−	1.21461i
$545$			1.98709e13i			0.413271i
$546$	2.05139e13			0.422751
$547$	−5.05567e13			−1.03239			−0.516193	−	0.856472i	$-0.672651\pi$
$547$	−5.05567e13			−1.03239			−0.516193	+	0.856472i	$0.672651\pi$
$548$	−8.02953e13			−1.62475
$549$		−	1.11136e13i		−	0.222841i
$550$	−2.50539e13			−0.497807
$551$	1.76783e13			0.348083
$552$	−3.53343e12			−0.0689448
$553$	1.11327e13			0.215266
$554$			7.28051e13i			1.39512i
$555$			5.84287e13i			1.10959i
$556$	1.26718e14			2.38486
$557$	−1.34896e12			−0.0251607			−0.0125803	−	0.999921i	$-0.504005\pi$
$557$	−1.34896e12			−0.0251607			−0.0125803	+	0.999921i	$0.504005\pi$
$558$	1.01194e13			0.187061
$559$	−3.84956e13			−0.705264
$560$	4.47115e13			0.811855
$561$		−	1.11820e13i		−	0.201235i
$562$		−	1.38472e14i		−	2.46991i
$563$		−	8.53764e11i		−	0.0150937i	−0.999972	−	0.00754685i	$-0.997598\pi$
$563$		−	8.53764e11i		−	0.0150937i	0.999972	−	0.00754685i	$-0.00240226\pi$
$564$		−	1.64206e14i		−	2.87736i
$565$			1.30872e13i			0.227302i
$566$	−1.30028e14			−2.23848
$567$	1.62271e12			0.0276901
$568$			2.37450e14i			4.01634i
$569$			3.89773e13i			0.653507i	0.945110	+	0.326754i	$0.105955\pi$
$569$			3.89773e13i			0.653507i	−0.945110	+	0.326754i	$0.894045\pi$
$570$			7.68135e13i			1.27662i
$571$		−	2.89747e13i		−	0.477351i	−0.971099	−	0.238676i	$-0.923287\pi$
$571$		−	2.89747e13i		−	0.477351i	0.971099	−	0.238676i	$-0.0767133\pi$
$572$	−1.62363e14			−2.65159
$573$		−	2.53299e13i		−	0.410072i
$574$		−	1.27182e13i		−	0.204111i
$575$			1.05220e12i			0.0167401i
$576$	−3.47152e13			−0.547530
$577$	3.30742e13			0.517142			0.258571	−	0.965992i	$-0.416748\pi$
$577$	3.30742e13			0.517142			0.258571	+	0.965992i	$0.416748\pi$
$578$			8.85335e13i			1.37236i
$579$	4.77783e13			0.734240
$580$	6.74534e13			1.02769
$581$		−	6.49208e11i		−	0.00980625i
$582$	2.55354e13			0.382408
$583$		−	5.81288e13i		−	0.863075i
$584$	1.03350e14			1.52141
$585$			4.23360e13i			0.617918i
$586$		−	9.01555e13i		−	1.30468i
$587$		−	3.07500e13i		−	0.441219i	−0.975362	−	0.220609i	$-0.929195\pi$
$587$		−	3.07500e13i		−	0.441219i	0.975362	−	0.220609i	$-0.0708046\pi$
$588$	9.52386e13			1.35496
$589$		−	2.12720e13i		−	0.300076i
$590$	1.35964e14	−	8.04325e13i	1.90179	−	1.12505i
$591$	4.20403e12			0.0583081
$592$			3.26546e14i			4.49092i
$593$	6.88754e13			0.939271			0.469635	−	0.882860i	$-0.344385\pi$
$593$	6.88754e13			0.939271			0.469635	+	0.882860i	$0.344385\pi$
$594$	−1.79760e13			−0.243087
$595$	1.13317e13			0.151954
$596$		−	2.77166e14i		−	3.68560i
$597$	−5.50715e13			−0.726198
$598$			9.54388e12i			0.124801i
$599$	−9.66992e13			−1.25398			−0.626988	−	0.779029i	$-0.715712\pi$
$599$	−9.66992e13			−1.25398			−0.626988	+	0.779029i	$0.715712\pi$
$600$			4.97433e13i			0.639703i
$601$			9.80497e13i			1.25047i	0.780436	+	0.625236i	$0.214997\pi$
$601$			9.80497e13i			1.25047i	−0.780436	+	0.625236i	$0.785003\pi$
$602$	1.65643e13			0.209503
$603$		−	7.72187e12i		−	0.0968580i
$604$			2.08412e14i			2.59261i
$605$	5.21053e13			0.642843
$606$	−2.26211e13			−0.276790
$607$	−1.27930e14			−1.55248			−0.776242	−	0.630435i	$-0.782877\pi$
$607$	−1.27930e14			−1.55248			−0.776242	+	0.630435i	$0.782877\pi$
$608$			1.95551e14i			2.35365i
$609$	−4.19252e12			−0.0500483
$610$	−1.24764e14			−1.47720
$611$	−2.66275e14			−3.12697
$612$	−3.69798e13			−0.430732
$613$			1.02278e14i			1.18162i	0.806810	+	0.590811i	$0.201192\pi$
$613$			1.02278e14i			1.18162i	−0.806810	+	0.590811i	$0.798808\pi$
$614$		−	2.38873e14i		−	2.73732i
$615$	2.62475e13			0.298341
$616$	4.19432e13			0.472888
$617$	−1.44309e14			−1.61387			−0.806936	−	0.590639i	$-0.798876\pi$
$617$	−1.44309e14			−1.61387			−0.806936	+	0.590639i	$0.798876\pi$
$618$	3.73398e11			0.00414218
$619$	−6.82218e13			−0.750706			−0.375353	−	0.926882i	$-0.622479\pi$
$619$	−6.82218e13			−0.750706			−0.375353	+	0.926882i	$0.622479\pi$
$620$		−	8.11653e13i		−	0.885956i
$621$			7.54948e11i			0.00817446i
$622$			5.10971e13i			0.548839i
$623$			3.05271e13i			0.325271i
$624$			2.36607e14i			2.50095i
$625$	−1.18140e14			−1.23879
$626$	1.32683e14			1.38020
$627$			3.77874e13i			0.389950i
$628$		−	1.88537e14i		−	1.93019i
$629$			8.27602e13i			0.840559i
$630$		−	1.82168e13i		−	0.183556i
$631$	−5.13267e13			−0.513093			−0.256547	−	0.966532i	$-0.582585\pi$
$631$	−5.13267e13			−0.513093			−0.256547	+	0.966532i	$0.582585\pi$
$632$			2.44859e14i			2.42845i
$633$		−	8.42656e13i		−	0.829148i
$634$		−	5.32233e13i		−	0.519584i
$635$	−6.24466e13			−0.604840
$636$	−1.92237e14			−1.84736
$637$		−	1.54438e14i		−	1.47251i
$638$	4.64439e13			0.439365
$639$	5.07332e13			0.476198
$640$			9.15312e13i			0.852451i
$641$	−1.34940e14			−1.24696			−0.623478	−	0.781841i	$-0.714281\pi$
$641$	−1.34940e14			−1.24696			−0.623478	+	0.781841i	$0.714281\pi$
$642$			7.63196e13i			0.699779i
$643$	1.94621e14			1.77066			0.885328	−	0.464966i	$-0.153934\pi$
$643$	1.94621e14			1.77066			0.885328	+	0.464966i	$0.153934\pi$
$644$		−	2.93408e12i		−	0.0264876i
$645$			3.41849e13i			0.306222i
$646$			1.08801e14i			0.967098i
$647$	4.61702e13			0.407230			0.203615	−	0.979051i	$-0.434731\pi$
$647$	4.61702e13			0.407230			0.203615	+	0.979051i	$0.434731\pi$
$648$			3.56906e13i			0.312377i
$649$	6.68855e13	−	3.95677e13i	0.580910	−	0.343651i
$650$	1.34358e14			1.15797
$651$			5.04478e12i			0.0431457i
$652$	4.76972e14			4.04814
$653$	−1.65374e14			−1.39284			−0.696420	−	0.717635i	$-0.745225\pi$
$653$	−1.65374e14			−1.39284			−0.696420	+	0.717635i	$0.745225\pi$
$654$	4.52469e13			0.378181
$655$		−	2.11544e13i		−	0.175466i
$656$	1.46692e14			1.20750
$657$		−	2.20816e13i		−	0.180386i
$658$	1.14576e14			0.928887
$659$		−	1.51824e14i		−	1.22156i	−0.791801	−	0.610779i	$-0.790856\pi$
$659$		−	1.51824e14i		−	1.22156i	0.791801	−	0.610779i	$-0.209144\pi$
$660$			1.44182e14i			1.15130i
$661$	−1.09780e13			−0.0869994			−0.0434997	−	0.999053i	$-0.513851\pi$
$661$	−1.09780e13			−0.0869994			−0.0434997	+	0.999053i	$0.513851\pi$
$662$		−	1.29018e14i		−	1.01475i
$663$			5.99660e13i			0.468099i
$664$	1.42790e13			0.110626
$665$	−3.82935e13			−0.294454
$666$	1.33045e14			1.01538
$667$		−	1.95053e12i		−	0.0147748i
$668$	−3.31631e14			−2.49329
$669$	−8.08789e13			−0.603538
$670$	−8.66870e13			−0.642067
$671$	−6.13758e13			−0.451216
$672$		−	4.63762e13i		−	0.338414i
$673$		−	1.83915e13i		−	0.133211i	−0.997779	−	0.0666057i	$-0.978783\pi$
$673$		−	1.83915e13i		−	0.133211i	0.997779	−	0.0666057i	$-0.0212170\pi$
$674$	3.80788e14			2.73769
$675$	1.06281e13			0.0758465
$676$	5.17473e14			3.66567
$677$	−8.09994e13			−0.569559			−0.284779	−	0.958593i	$-0.591920\pi$
$677$	−8.09994e13			−0.569559			−0.284779	+	0.958593i	$0.591920\pi$
$678$	2.98000e13			0.208002
$679$			1.27301e13i			0.0882026i
$680$			2.49235e14i			1.71421i
$681$		−	5.93088e11i		−	0.00404934i
$682$		−	5.58850e13i		−	0.378768i
$683$			2.28666e14i			1.53850i	0.638947	+	0.769251i	$0.279370\pi$
$683$			2.28666e14i			1.53850i	−0.638947	+	0.769251i	$0.720630\pi$
$684$	1.24966e14			0.834667
$685$	1.15626e14			0.766659
$686$			1.37307e14i			0.903800i
$687$			1.12956e14i			0.738118i
$688$			1.91053e14i			1.23940i
$689$			3.11730e14i			2.00763i
$690$	8.47518e12			0.0541880
$691$			1.24377e14i			0.789497i	0.918789	+	0.394749i	$0.129168\pi$
$691$			1.24377e14i			0.789497i	−0.918789	+	0.394749i	$0.870832\pi$
$692$			7.58897e14i			4.78247i
$693$		−	8.96151e12i		−	0.0560680i
$694$	1.43433e14			0.890946
$695$	−1.82475e14			−1.12533
$696$		−	9.22123e13i		−	0.564602i
$697$	3.71778e13			0.226006
$698$	3.39826e14			2.05107
$699$		−	5.07988e13i		−	0.304416i
$700$	−4.13056e13			−0.245764
$701$		−	2.12939e14i		−	1.25796i	−0.777423	−	0.628978i	$-0.783473\pi$
$701$		−	2.12939e14i		−	1.25796i	0.777423	−	0.628978i	$-0.216527\pi$
$702$	9.64010e13			0.565452
$703$		−	2.79673e14i		−	1.62882i
$704$			1.91717e14i			1.10866i
$705$			2.36458e14i			1.35772i
$706$	3.68501e14			2.10095
$707$		−	1.12772e13i		−	0.0638415i
$708$	−1.30854e14	−	2.21197e14i	−0.735565	−	1.24340i
$709$	−1.03181e14			−0.575930			−0.287965	−	0.957641i	$-0.592979\pi$
$709$	−1.03181e14			−0.575930			−0.287965	+	0.957641i	$0.592979\pi$
$710$		−	5.69540e14i		−	3.15669i
$711$	5.23161e13			0.287930
$712$	−6.71428e14			−3.66944
$713$	−2.34703e12			−0.0127371
$714$		−	2.58028e13i		−	0.139052i
$715$	2.33803e14			1.25118
$716$		−	4.48565e14i		−	2.38375i
$717$	−2.15262e14			−1.13598
$718$			6.55126e12i			0.0343323i
$719$		−	2.82697e14i		−	1.47122i	−0.677408	−	0.735608i	$-0.736897\pi$
$719$		−	2.82697e14i		−	1.47122i	0.677408	−	0.735608i	$-0.263103\pi$
$720$	2.10113e14			1.08590
$721$			1.86148e11i			0.000955395i
$722$		−	5.09004e11i		−	0.00259439i
$723$	9.31319e13			0.471419
$724$	−3.37565e14			−1.69693
$725$	−2.74593e13			−0.137088
$726$		−	1.18646e14i		−	0.588262i
$727$	−3.94443e14			−1.94228			−0.971140	−	0.238510i	$-0.923341\pi$
$727$	−3.94443e14			−1.94228			−0.971140	+	0.238510i	$0.923341\pi$
$728$	−2.24931e14			−1.10000
$729$	7.62560e12			0.0370370
$730$	−2.47892e14			−1.19577
$731$			4.84206e13i			0.231976i
$732$			2.02976e14i			0.965803i
$733$	−1.37662e14			−0.650572			−0.325286	−	0.945616i	$-0.605461\pi$
$733$	−1.37662e14			−0.650572			−0.325286	+	0.945616i	$0.605461\pi$
$734$	−2.36780e14			−1.11138
$735$	−1.37144e14			−0.639354
$736$	2.15760e13			0.0999039
$737$	−4.26445e13			−0.196122
$738$		−	5.97668e13i		−	0.273010i
$739$			1.66109e14i			0.753654i	0.926284	+	0.376827i	$0.122985\pi$
$739$			1.66109e14i			0.753654i	−0.926284	+	0.376827i	$0.877015\pi$
$740$		−	1.06712e15i		−	4.80901i
$741$		−	2.02644e14i		−	0.907076i
$742$		−	1.34135e14i		−	0.596378i
$743$	2.91675e14			1.28812			0.644058	−	0.764976i	$-0.277249\pi$
$743$	2.91675e14			1.28812			0.644058	+	0.764976i	$0.277249\pi$
$744$	−1.10957e14			−0.486733
$745$			3.99121e14i			1.73909i
$746$		−	5.73471e14i		−	2.48209i
$747$		−	3.05082e12i		−	0.0131164i
$748$			2.04223e14i			0.872162i
$749$	−3.80473e13			−0.161404
$750$			1.83427e14i			0.772958i
$751$		−	2.42985e13i		−	0.101714i	−0.998706	−	0.0508569i	$-0.983805\pi$
$751$		−	2.42985e13i		−	0.101714i	0.998706	−	0.0508569i	$-0.0161952\pi$
$752$			1.32152e15i			5.49520i
$753$	2.14121e14			0.884474
$754$	−2.49067e14			−1.02202
$755$		−	3.00115e14i		−	1.22336i
$756$	−2.96366e13			−0.120010
$757$	3.15140e14			1.26772			0.633861	−	0.773447i	$-0.281469\pi$
$757$	3.15140e14			1.26772			0.633861	+	0.773447i	$0.281469\pi$
$758$		−	9.22877e14i		−	3.68806i
$759$	4.16925e12			0.0165520
$760$		−	8.42245e14i		−	3.32178i
$761$	−2.69468e14			−1.05581			−0.527903	−	0.849305i	$-0.677022\pi$
$761$	−2.69468e14			−1.05581			−0.527903	+	0.849305i	$0.677022\pi$
$762$			1.42194e14i			0.553485i
$763$			2.25568e13i			0.0872276i
$764$			4.62617e14i			1.77727i
$765$	5.32512e13			0.203246
$766$			1.81658e14i			0.688829i
$767$	−3.58690e14	+	2.12192e14i	−1.35127	+	0.799377i
$768$	−4.49604e13			−0.168277
$769$			4.26168e14i			1.58471i	0.610063	+	0.792353i	$0.291144\pi$
$769$			4.26168e14i			1.58471i	−0.610063	+	0.792353i	$0.708856\pi$
$770$	−1.00604e14			−0.371672
$771$	2.56926e14			0.943054
$772$	−8.72607e14			−3.18223
$773$		−	4.02297e14i		−	1.45764i	−0.684707	−	0.728818i	$-0.740070\pi$
$773$		−	4.02297e14i		−	1.45764i	0.684707	−	0.728818i	$-0.259930\pi$
$774$	7.78406e13			0.280222
$775$			3.30412e13i			0.118181i
$776$	−2.79991e14			−0.995027
$777$			6.63262e13i			0.234196i
$778$			7.81785e14i			2.74277i
$779$	−1.25636e14			−0.437951
$780$		−	7.73210e14i		−	2.67809i
$781$		−	2.80177e14i		−	0.964224i
$782$	1.20045e13			0.0410498
$783$	−1.97019e13			−0.0669422
$784$	−7.66472e14			−2.58771
$785$			2.71495e14i			0.910781i
$786$	−4.81695e13			−0.160568
$787$	−4.45257e13			−0.147481			−0.0737407	−	0.997277i	$-0.523494\pi$
$787$	−4.45257e13			−0.147481			−0.0737407	+	0.997277i	$0.523494\pi$
$788$	−7.67810e13			−0.252710
$789$	7.57718e13			0.247812
$790$		−	5.87310e14i		−	1.90867i
$791$			1.48561e13i			0.0479758i
$792$	1.97104e14			0.632512
$793$	3.29143e14			1.04959
$794$	−6.42861e14			−2.03711
$795$	2.76824e14			0.871701
$796$	1.00581e15			3.14738
$797$			3.77346e14i			1.17341i	0.809802	+	0.586703i	$0.199575\pi$
$797$			3.77346e14i			1.17341i	−0.809802	+	0.586703i	$0.800425\pi$
$798$			8.71961e13i			0.269453i
$799$			3.34927e14i			1.02853i
$800$		−	3.03745e14i		−	0.926956i
$801$			1.43456e14i			0.435068i
$802$	9.75074e14			2.93877
$803$	−1.21947e14			−0.365253
$804$			1.41030e14i			0.419788i
$805$			4.22510e12i			0.0124985i
$806$			2.99698e14i			0.881065i
$807$		−	1.95014e14i		−	0.569768i
$808$	2.48036e14			0.720207
$809$		−	1.55441e14i		−	0.448564i	−0.974524	−	0.224282i	$-0.927996\pi$
$809$		−	1.55441e14i		−	0.448564i	0.974524	−	0.224282i	$-0.0720036\pi$
$810$		−	8.56063e13i		−	0.245516i
$811$			3.61757e14i			1.03113i	0.856851	+	0.515563i	$0.172417\pi$
$811$			3.61757e14i			1.03113i	−0.856851	+	0.515563i	$0.827583\pi$
$812$	7.65708e13			0.216912
$813$	7.78271e13			0.219118
$814$		−	7.34749e14i		−	2.05597i
$815$	−6.86844e14			−1.91016
$816$	2.97610e14			0.822616
$817$		−	1.63629e14i		−	0.449520i
$818$	3.87295e14			1.05749
$819$			4.80584e13i			0.130422i
$820$	−4.79376e14			−1.29302
$821$			4.29545e14i			1.15158i	0.817599	+	0.575788i	$0.195305\pi$
$821$			4.29545e14i			1.15158i	−0.817599	+	0.575788i	$0.804695\pi$
$822$		−	2.63285e14i		−	0.701565i
$823$			1.59700e14i			0.422967i	0.977382	+	0.211484i	$0.0678295\pi$
$823$			1.59700e14i			0.422967i	−0.977382	+	0.211484i	$0.932171\pi$
$824$	−4.09424e12			−0.0107780
$825$		−	5.86943e13i		−	0.153577i
$826$	1.54341e14	−	9.13042e13i	0.401404	−	0.237460i
$827$	6.59003e14			1.70357			0.851784	−	0.523893i	$-0.175521\pi$
$827$	6.59003e14			1.70357			0.851784	+	0.523893i	$0.175521\pi$
$828$		−	1.37881e13i		−	0.0354285i
$829$	1.37351e14			0.350800			0.175400	−	0.984497i	$-0.443878\pi$
$829$	1.37351e14			0.350800			0.175400	+	0.984497i	$0.443878\pi$
$830$	−3.42491e13			−0.0869478
$831$	−1.70562e14			−0.430405
$832$		−	1.02813e15i		−	2.57889i
$833$	−1.94256e14			−0.484338
$834$			4.15503e14i			1.02978i
$835$	4.77551e14			1.17649
$836$		−	6.90136e14i		−	1.69006i
$837$			2.37069e13i			0.0577096i
$838$	−3.93374e14			−0.951888
$839$			3.04420e14i			0.732257i	0.930564	+	0.366128i	$0.119317\pi$
$839$			3.04420e14i			0.732257i	−0.930564	+	0.366128i	$0.880683\pi$
$840$			1.99744e14i			0.477614i
$841$	−3.69804e14			−0.879006
$842$	−3.47667e14			−0.821492
$843$	3.24402e14			0.761983
$844$			1.53900e15i			3.59357i
$845$	−7.45165e14			−1.72969
$846$	5.38426e14			1.24244
$847$	5.91482e13			0.135683
$848$	1.54711e15			3.52811
$849$		−	3.04619e14i		−	0.690587i
$850$		−	1.68998e14i		−	0.380879i
$851$	−3.08576e13			−0.0691376
$852$	−9.26574e14			−2.06387
$853$	3.25749e14			0.721338			0.360669	−	0.932694i	$-0.382548\pi$
$853$	3.25749e14			0.721338			0.360669	+	0.932694i	$0.382548\pi$
$854$	−1.41627e14			−0.311787
$855$	−1.79953e14			−0.393848
$856$		−	8.36830e14i		−	1.82083i
$857$		−	6.18698e14i		−	1.33837i	−0.743098	−	0.669183i	$-0.766644\pi$
$857$		−	6.18698e14i		−	1.33837i	0.743098	−	0.669183i	$-0.233356\pi$
$858$		−	5.32381e14i		−	1.14495i
$859$			4.26341e14i			0.911573i	0.890089	+	0.455786i	$0.150642\pi$
$859$			4.26341e14i			0.911573i	−0.890089	+	0.455786i	$0.849358\pi$
$860$		−	6.24342e14i		−	1.32718i
$861$	2.97953e13			0.0629697
$862$	7.34559e14			1.54344
$863$			1.07136e14i			0.223810i	0.993719	+	0.111905i	$0.0356952\pi$
$863$			1.07136e14i			0.223810i	−0.993719	+	0.111905i	$0.964305\pi$
$864$		−	2.17936e14i		−	0.452647i
$865$		−	1.09282e15i		−	2.25667i
$866$			2.65285e14i			0.544656i
$867$	−2.07409e14			−0.423383
$868$		−	9.21361e13i		−	0.186996i
$869$		−	2.88919e14i		−	0.583012i
$870$			2.21177e14i			0.443756i
$871$	2.28692e14			0.456205
$872$	−4.96124e14			−0.984028
$873$			5.98224e13i			0.117976i
$874$	−4.05671e13			−0.0795456
$875$	−9.14429e13			−0.178283
$876$			4.03290e14i			0.781803i
$877$	−1.66758e14			−0.321432			−0.160716	−	0.987001i	$-0.551380\pi$
$877$	−1.66758e14			−0.321432			−0.160716	+	0.987001i	$0.551380\pi$
$878$			5.68024e14i			1.08866i
$879$	2.11209e14			0.402503
$880$		−	1.16036e15i		−	2.19877i
$881$		−	1.46706e14i		−	0.276419i	−0.990403	−	0.138209i	$-0.955865\pi$
$881$		−	1.46706e14i		−	0.276419i	0.990403	−	0.138209i	$-0.0441347\pi$
$882$			3.12284e14i			0.585069i
$883$	−9.41163e14			−1.75332			−0.876661	−	0.481109i	$-0.840234\pi$
$883$	−9.41163e14			−1.75332			−0.876661	+	0.481109i	$0.840234\pi$
$884$		−	1.09520e15i		−	2.02877i
$885$	1.88431e14	+	3.18525e14i	0.347085	+	0.586716i
$886$	−1.15430e15			−2.11422
$887$		−	3.31171e14i		−	0.603163i	−0.953440	−	0.301581i	$-0.902486\pi$
$887$		−	3.31171e14i		−	0.603163i	0.953440	−	0.301581i	$-0.0975145\pi$
$888$	−1.45881e15			−2.64201
$889$	−7.08873e13			−0.127661
$890$	1.61046e15			2.88404
$891$		−	4.21129e13i		−	0.0749940i
$892$	1.47714e15			2.61577
$893$		−	1.13182e15i		−	1.99307i
$894$	9.08816e14			1.59143
$895$			6.45937e14i			1.12480i
$896$			1.03903e14i			0.179924i
$897$	−2.23587e13			−0.0385020
$898$			7.10497e14i			1.21669i
$899$		−	6.12507e13i		−	0.104307i
$900$	−1.94108e14			−0.328723
$901$	3.92102e14			0.660351
$902$	−3.30066e14			−0.552800
$903$			3.88056e13i			0.0646331i
$904$	−3.26752e14			−0.541222
$905$	4.86096e14			0.800718
$906$	−6.83375e14			−1.11948
$907$	7.74383e14			1.26159			0.630797	−	0.775948i	$-0.282728\pi$
$907$	7.74383e14			1.26159			0.630797	+	0.775948i	$0.282728\pi$
$908$			1.08320e13i			0.0175500i
$909$		−	5.29949e13i		−	0.0853915i
$910$	5.39512e14			0.864558
$911$	9.32031e14			1.48538			0.742692	−	0.669634i	$-0.233549\pi$
$911$	9.32031e14			1.48538			0.742692	+	0.669634i	$0.233549\pi$
$912$	−1.00572e15			−1.59405
$913$	−1.68484e13			−0.0265585
$914$	−1.00847e14			−0.158100
$915$		−	2.92287e14i		−	0.455726i
$916$		−	2.06299e15i		−	3.19904i
$917$		−	2.40137e13i		−	0.0370350i
$918$		−	1.21255e14i		−	0.185989i
$919$			4.86822e14i			0.742664i	0.928500	+	0.371332i	$0.121099\pi$
$919$			4.86822e14i			0.742664i	−0.928500	+	0.371332i	$0.878901\pi$
$920$	−9.29287e13			−0.140997
$921$	5.59614e14			0.844483
$922$			1.96083e15i			2.94296i
$923$			1.50252e15i			2.24291i
$924$			1.63670e14i			0.243002i
$925$			4.34410e14i			0.641492i
$926$	1.28957e15			1.89405
$927$			8.74768e11i			0.00127789i
$928$			5.63072e14i			0.818133i
$929$			9.38539e14i			1.35636i	0.734898	+	0.678178i	$0.237230\pi$
$929$			9.38539e14i			1.35636i	−0.734898	+	0.678178i	$0.762770\pi$
$930$	2.66138e14			0.382554
$931$	6.56452e14			0.938544
$932$			9.27772e14i			1.31936i
$933$	−1.19706e14			−0.169320
$934$	−4.00368e13			−0.0563281
$935$		−	2.94083e14i		−	0.411540i
$936$	−1.05702e15			−1.47131
$937$		−	7.79446e14i		−	1.07916i	−0.841933	−	0.539582i	$-0.818582\pi$
$937$		−	7.79446e14i		−	1.07916i	0.841933	−	0.539582i	$-0.181418\pi$
$938$	−9.84041e13			−0.135519
$939$			3.10839e14i			0.425802i
$940$		−	4.31859e15i		−	5.88441i
$941$			5.05583e14i			0.685242i	0.939474	+	0.342621i	$0.111315\pi$
$941$			5.05583e14i			0.685242i	−0.939474	+	0.342621i	$0.888685\pi$
$942$	6.18207e14			0.833450
$943$			1.38619e13i			0.0185894i
$944$	1.05310e15	+	1.78017e15i	1.40479	+	2.37466i
$945$	4.26769e13			0.0566284
$946$		−	4.29880e14i		−	0.567403i
$947$	−6.47854e14			−0.850604			−0.425302	−	0.905051i	$-0.639832\pi$
$947$	−6.47854e14			−0.850604			−0.425302	+	0.905051i	$0.639832\pi$
$948$	−9.55483e14			−1.24790
$949$	6.53972e14			0.849626
$950$			5.71099e14i			0.738062i
$951$	1.24688e14			0.160295
$952$			2.82923e14i			0.361813i
$953$	9.29642e14			1.18264			0.591318	−	0.806438i	$-0.298608\pi$
$953$	9.29642e14			1.18264			0.591318	+	0.806438i	$0.298608\pi$
$954$		−	6.30340e14i		−	0.797688i
$955$		−	6.66172e14i		−	0.838629i
$956$	3.93148e15			4.92341
$957$			1.08805e14i			0.135547i
$958$		−	7.81731e14i		−	0.968790i
$959$	1.31255e14			0.161816
$960$	−9.13004e14			−1.11974
$961$	7.45927e14			0.910079
$962$			3.94028e15i			4.78246i
$963$	−1.78796e14			−0.215887
$964$	−1.70093e15			−2.04315
$965$	1.25656e15			1.50158
$966$	9.62073e12			0.0114373
$967$			3.68363e14i			0.435656i	0.975987	+	0.217828i	$0.0698971\pi$
$967$			3.68363e14i			0.435656i	−0.975987	+	0.217828i	$0.930103\pi$
$968$			1.30093e15i			1.53066i
$969$	−2.54891e14			−0.298356
$970$	6.71576e14			0.782054
$971$	3.97937e14			0.461018			0.230509	−	0.973070i	$-0.425961\pi$
$971$	3.97937e14			0.461018			0.230509	+	0.973070i	$0.425961\pi$
$972$	−1.39271e14			−0.160520
$973$	−2.07139e14			−0.237519
$974$		−	1.56043e15i		−	1.78012i
$975$			3.14763e14i			0.357240i
$976$		−	1.63353e15i		−	1.84450i
$977$			9.78481e13i			0.109921i	0.998489	+	0.0549603i	$0.0175032\pi$
$977$			9.78481e13i			0.109921i	−0.998489	+	0.0549603i	$0.982497\pi$
$978$			1.56398e15i			1.74798i
$979$	7.92247e14			0.880941
$980$	2.50476e15			2.77099
$981$			1.06001e14i			0.116672i
$982$		−	2.20836e15i		−	2.41831i
$983$		−	5.70380e13i		−	0.0621436i	−0.999517	−	0.0310718i	$-0.990108\pi$
$983$		−	5.70380e13i		−	0.0621436i	0.999517	−	0.0310718i	$-0.00989206\pi$
$984$			6.55331e14i			0.710371i
$985$	1.10565e14			0.119244
$986$			3.13283e14i			0.336164i
$987$			2.68419e14i			0.286568i
$988$			3.70103e15i			3.93131i
$989$	−1.80539e13			−0.0190805
$990$	−4.72766e14			−0.497131
$991$		−	5.44837e14i		−	0.570031i	−0.958523	−	0.285016i	$-0.908001\pi$
$991$		−	5.44837e14i		−	0.570031i	0.958523	−	0.285016i	$-0.0919988\pi$
$992$	6.77533e14			0.705297
$993$	3.02253e14			0.313058
$994$		−	6.46522e14i		−	0.666272i
$995$	−1.44837e15			−1.48513
$996$			5.57192e13i			0.0568471i
$997$	−4.59934e14			−0.466896			−0.233448	−	0.972369i	$-0.575001\pi$
$997$	−4.59934e14			−0.466896			−0.233448	+	0.972369i	$0.575001\pi$
$998$			3.68594e15i			3.72302i
$999$			3.11687e14i			0.313250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.3	✓	100
59.58	odd	2	inner	177.11.c.a.58.98	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.3	✓	100	1.1	even	1	trivial
177.11.c.a.58.98	yes	100	59.58	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-59.8859i q^{2} +140.296 q^{3} -2562.32 q^{4} +3689.76 q^{5} -8401.76i q^{6} +4188.49 q^{7} +92123.7i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q-59.8859i q^{2} +140.296 q^{3} -2562.32 q^{4} +3689.76 q^{5} -8401.76i q^{6} +4188.49 q^{7} +92123.7i q^{8} +19683.0 q^{9} -220965. i q^{10} -108701. i q^{11} -359484. q^{12} +582935. i q^{13} -250832. i q^{14} +517660. q^{15} +2.89309e6 q^{16} +733229. q^{17} -1.17873e6i q^{18} -2.47781e6 q^{19} -9.45436e6 q^{20} +587629. q^{21} -6.50964e6 q^{22} +273388. i q^{23} +1.29246e7i q^{24} +3.84873e6 q^{25} +3.49096e7 q^{26} +2.76145e6 q^{27} -1.07323e7 q^{28} -7.13464e6 q^{29} -3.10005e7i q^{30} +8.58497e6i q^{31} -7.89208e7i q^{32} -1.52503e7i q^{33} -4.39101e7i q^{34} +1.54546e7 q^{35} -5.04341e7 q^{36} +1.12871e8i q^{37} +1.48386e8i q^{38} +8.17835e7i q^{39} +3.39915e8i q^{40} +5.07042e7 q^{41} -3.51907e7i q^{42} +6.60375e7i q^{43} +2.78526e8i q^{44} +7.26256e7 q^{45} +1.63721e7 q^{46} +4.56783e8i q^{47} +4.05890e8 q^{48} -2.64932e8 q^{49} -2.30485e8i q^{50} +1.02869e8 q^{51} -1.49367e9i q^{52} +5.34760e8 q^{53} -1.65372e8i q^{54} -4.01080e8i q^{55} +3.85859e8i q^{56} -3.47628e8 q^{57} +4.27264e8i q^{58} +(3.64006e8 + 6.15318e8i) q^{59} -1.32641e9 q^{60} -5.64631e8i q^{61} +5.14118e8 q^{62} +8.24421e7 q^{63} -1.76372e9 q^{64} +2.15089e9i q^{65} -9.13277e8 q^{66} -3.92311e8i q^{67} -1.87877e9 q^{68} +3.83553e7i q^{69} -9.25510e8i q^{70} +2.57751e9 q^{71} +1.81327e9i q^{72} -1.12186e9i q^{73} +6.75937e9 q^{74} +5.39962e8 q^{75} +6.34895e9 q^{76} -4.55292e8i q^{77} +4.89768e9 q^{78} +2.65793e9 q^{79} +1.06748e10 q^{80} +3.87420e8 q^{81} -3.03647e9i q^{82} -1.54998e8i q^{83} -1.50569e9 q^{84} +2.70544e9 q^{85} +3.95471e9 q^{86} -1.00096e9 q^{87} +1.00139e10 q^{88} +7.28833e9i q^{89} -4.34925e9i q^{90} +2.44162e9i q^{91} -7.00509e8i q^{92} +1.20444e9i q^{93} +2.73549e10 q^{94} -9.14255e9 q^{95} -1.10723e10i q^{96} +3.03929e9i q^{97} +1.58657e10i q^{98} -2.13956e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 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

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Database

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