LMFDB - Embedded newform 177.11.c.a.58.16

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			58.16
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.85

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-47.5424i q^{2} +140.296 q^{3} -1236.28 q^{4} -4974.64 q^{5} -6670.02i q^{6} +12474.7 q^{7} +10092.4i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q-47.5424i q^{2} +140.296 q^{3} -1236.28 q^{4} -4974.64 q^{5} -6670.02i q^{6} +12474.7 q^{7} +10092.4i q^{8} +19683.0 q^{9} +236507. i q^{10} +91525.3i q^{11} -173446. q^{12} -581654. i q^{13} -593078. i q^{14} -697923. q^{15} -786135. q^{16} +253586. q^{17} -935778. i q^{18} -3.54734e6 q^{19} +6.15006e6 q^{20} +1.75015e6 q^{21} +4.35134e6 q^{22} -7.87195e6i q^{23} +1.41593e6i q^{24} +1.49815e7 q^{25} -2.76532e7 q^{26} +2.76145e6 q^{27} -1.54223e7 q^{28} -3.50297e7 q^{29} +3.31810e7i q^{30} +4.69488e7i q^{31} +4.77094e7i q^{32} +1.28406e7i q^{33} -1.20561e7i q^{34} -6.20573e7 q^{35} -2.43337e7 q^{36} +7.93633e7i q^{37} +1.68649e8i q^{38} -8.16037e7i q^{39} -5.02061e7i q^{40} +9.67573e6 q^{41} -8.32066e7i q^{42} -7.78354e7i q^{43} -1.13151e8i q^{44} -9.79159e7 q^{45} -3.74251e8 q^{46} -4.77102e7i q^{47} -1.10292e8 q^{48} -1.26857e8 q^{49} -7.12255e8i q^{50} +3.55772e7 q^{51} +7.19088e8i q^{52} +6.70282e8 q^{53} -1.31286e8i q^{54} -4.55306e8i q^{55} +1.25900e8i q^{56} -4.97678e8 q^{57} +1.66540e9i q^{58} +(7.02192e8 + 1.34322e8i) q^{59} +8.62830e8 q^{60} -1.29266e9i q^{61} +2.23206e9 q^{62} +2.45540e8 q^{63} +1.46322e9 q^{64} +2.89352e9i q^{65} +6.10475e8 q^{66} +1.73077e9i q^{67} -3.13504e8 q^{68} -1.10440e9i q^{69} +2.95035e9i q^{70} -3.39938e9 q^{71} +1.98649e8i q^{72} +1.89958e7i q^{73} +3.77312e9 q^{74} +2.10184e9 q^{75} +4.38551e9 q^{76} +1.14175e9i q^{77} -3.87964e9 q^{78} +2.81385e9 q^{79} +3.91074e9 q^{80} +3.87420e8 q^{81} -4.60008e8i q^{82} -3.49802e9i q^{83} -2.16368e9 q^{84} -1.26150e9 q^{85} -3.70048e9 q^{86} -4.91453e9 q^{87} -9.23711e8 q^{88} +2.25318e9i q^{89} +4.65516e9i q^{90} -7.25596e9i q^{91} +9.73195e9i q^{92} +6.58674e9i q^{93} -2.26826e9 q^{94} +1.76468e10 q^{95} +6.69344e9i q^{96} +1.06360e10i q^{97} +6.03108e9i q^{98} +1.80149e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	47.5424i		−	1.48570i	−0.669457	−	0.742850i	$-0.733473\pi$
$2$		−	47.5424i		−	1.48570i	0.669457	−	0.742850i	$-0.266527\pi$
$3$	140.296			0.577350
$3$	140.296			0.577350
$4$	−1236.28			−1.20731
$5$	−4974.64			−1.59189			−0.795943	−	0.605371i	$-0.793025\pi$
$5$	−4974.64			−1.59189			−0.795943	+	0.605371i	$0.793025\pi$
$6$		−	6670.02i		−	0.857770i
$7$	12474.7			0.742233			0.371117	−	0.928586i	$-0.378975\pi$
$7$	12474.7			0.742233			0.371117	+	0.928586i	$0.378975\pi$
$8$			10092.4i			0.307996i
$9$	19683.0			0.333333
$10$			236507.i			2.36507i
$11$			91525.3i			0.568300i	0.958780	+	0.284150i	$0.0917114\pi$
$11$			91525.3i			0.568300i	−0.958780	+	0.284150i	$0.908289\pi$
$12$	−173446.			−0.697039
$13$		−	581654.i		−	1.56656i	−0.621668	−	0.783281i	$-0.713545\pi$
$13$		−	581654.i		−	1.56656i	0.621668	−	0.783281i	$-0.286455\pi$
$14$		−	593078.i		−	1.10274i
$15$	−697923.			−0.919076
$16$	−786135.			−0.749717
$17$	253586.			0.178600			0.0892999	−	0.996005i	$-0.471537\pi$
$17$	253586.			0.178600			0.0892999	+	0.996005i	$0.471537\pi$
$18$		−	935778.i		−	0.495234i
$19$	−3.54734e6			−1.43263			−0.716316	−	0.697776i	$-0.754173\pi$
$19$	−3.54734e6			−1.43263			−0.716316	+	0.697776i	$0.754173\pi$
$20$	6.15006e6			1.92189
$21$	1.75015e6			0.428529
$22$	4.35134e6			0.844324
$23$		−	7.87195e6i		−	1.22305i	−0.791226	−	0.611523i	$-0.790557\pi$
$23$		−	7.87195e6i		−	1.22305i	0.791226	−	0.611523i	$-0.209443\pi$
$24$			1.41593e6i			0.177821i
$25$	1.49815e7			1.53410
$26$	−2.76532e7			−2.32744
$27$	2.76145e6			0.192450
$28$	−1.54223e7			−0.896103
$29$	−3.50297e7			−1.70784			−0.853919	−	0.520406i	$-0.825781\pi$
$29$	−3.50297e7			−1.70784			−0.853919	+	0.520406i	$0.825781\pi$
$30$			3.31810e7i			1.36547i
$31$			4.69488e7i			1.63990i	0.572438	+	0.819948i	$0.305998\pi$
$31$			4.69488e7i			1.63990i	−0.572438	+	0.819948i	$0.694002\pi$
$32$			4.77094e7i			1.42185i
$33$			1.28406e7i			0.328108i
$34$		−	1.20561e7i		−	0.265346i
$35$	−6.20573e7			−1.18155
$36$	−2.43337e7			−0.402436
$37$			7.93633e7i			1.14449i	0.820084	+	0.572244i	$0.193927\pi$
$37$			7.93633e7i			1.14449i	−0.820084	+	0.572244i	$0.806073\pi$
$38$			1.68649e8i			2.12846i
$39$		−	8.16037e7i		−	0.904455i
$40$		−	5.02061e7i		−	0.490294i
$41$	9.67573e6			0.0835150			0.0417575	−	0.999128i	$-0.486704\pi$
$41$	9.67573e6			0.0835150			0.0417575	+	0.999128i	$0.486704\pi$
$42$		−	8.32066e7i		−	0.636665i
$43$		−	7.78354e7i		−	0.529462i	−0.964322	−	0.264731i	$-0.914717\pi$
$43$		−	7.78354e7i		−	0.529462i	0.964322	−	0.264731i	$-0.0852832\pi$
$44$		−	1.13151e8i		−	0.686113i
$45$	−9.79159e7			−0.530629
$46$	−3.74251e8			−1.81708
$47$		−	4.77102e7i		−	0.208028i	−0.994576	−	0.104014i	$-0.966831\pi$
$47$		−	4.77102e7i		−	0.208028i	0.994576	−	0.104014i	$-0.0331687\pi$
$48$	−1.10292e8			−0.432849
$49$	−1.26857e8			−0.449090
$50$		−	7.12255e8i		−	2.27922i
$51$	3.55772e7			0.103115
$52$			7.19088e8i			1.89132i
$53$	6.70282e8			1.60280			0.801398	−	0.598131i	$-0.204090\pi$
$53$	6.70282e8			1.60280			0.801398	+	0.598131i	$0.204090\pi$
$54$		−	1.31286e8i		−	0.285923i
$55$		−	4.55306e8i		−	0.904669i
$56$			1.25900e8i			0.228605i
$57$	−4.97678e8			−0.827131
$58$			1.66540e9i			2.53734i
$59$	7.02192e8	+	1.34322e8i	0.982191	+	0.187883i
$59$	7.02192e8	+	1.34322e8i	0.982191	+	0.187883i
$60$	8.62830e8			1.10961
$61$		−	1.29266e9i		−	1.53051i	−0.643727	−	0.765255i	$-0.722613\pi$
$61$		−	1.29266e9i		−	1.53051i	0.643727	−	0.765255i	$-0.277387\pi$
$62$	2.23206e9			2.43639
$63$	2.45540e8			0.247411
$64$	1.46322e9			1.36273
$65$			2.89352e9i			2.49379i
$66$	6.10475e8			0.487471
$67$			1.73077e9i			1.28193i	0.767569	+	0.640966i	$0.221466\pi$
$67$			1.73077e9i			1.28193i	−0.767569	+	0.640966i	$0.778534\pi$
$68$	−3.13504e8			−0.215625
$69$		−	1.10440e9i		−	0.706126i
$70$			2.95035e9i			1.75543i
$71$	−3.39938e9			−1.88412			−0.942058	−	0.335451i	$-0.891111\pi$
$71$	−3.39938e9			−1.88412			−0.942058	+	0.335451i	$0.891111\pi$
$72$			1.98649e8i			0.102665i
$73$			1.89958e7i			0.00916311i	0.999990	+	0.00458155i	$0.00145836\pi$
$73$			1.89958e7i			0.00916311i	−0.999990	+	0.00458155i	$0.998542\pi$
$74$	3.77312e9			1.70037
$75$	2.10184e9			0.885714
$76$	4.38551e9			1.72963
$77$			1.14175e9i			0.421811i
$78$	−3.87964e9			−1.34375
$79$	2.81385e9			0.914460			0.457230	−	0.889348i	$-0.348842\pi$
$79$	2.81385e9			0.914460			0.457230	+	0.889348i	$0.348842\pi$
$80$	3.91074e9			1.19346
$81$	3.87420e8			0.111111
$82$		−	4.60008e8i		−	0.124078i
$83$		−	3.49802e9i		−	0.888038i	−0.896017	−	0.444019i	$-0.853552\pi$
$83$		−	3.49802e9i		−	0.888038i	0.896017	−	0.444019i	$-0.146448\pi$
$84$	−2.16368e9			−0.517365
$85$	−1.26150e9			−0.284311
$86$	−3.70048e9			−0.786622
$87$	−4.91453e9			−0.986021
$88$	−9.23711e8			−0.175034
$89$			2.25318e9i			0.403503i	0.979437	+	0.201751i	$0.0646633\pi$
$89$			2.25318e9i			0.403503i	−0.979437	+	0.201751i	$0.935337\pi$
$90$			4.65516e9i			0.788356i
$91$		−	7.25596e9i		−	1.16275i
$92$			9.73195e9i			1.47659i
$93$			6.58674e9i			0.946794i
$94$	−2.26826e9			−0.309067
$95$	1.76468e10			2.28059
$96$			6.69344e9i			0.820906i
$97$			1.06360e10i			1.23857i	0.785167	+	0.619284i	$0.212577\pi$
$97$			1.06360e10i			1.23857i	−0.785167	+	0.619284i	$0.787423\pi$
$98$			6.03108e9i			0.667213i
$99$			1.80149e9i			0.189433i
$100$	−1.85213e10			−1.85213
$101$		−	1.46879e9i		−	0.139750i	−0.997556	−	0.0698752i	$-0.977740\pi$
$101$		−	1.46879e9i		−	0.139750i	0.997556	−	0.0698752i	$-0.0222601\pi$
$102$		−	1.69142e9i		−	0.153198i
$103$			1.96079e10i			1.69139i	0.533666	+	0.845695i	$0.320814\pi$
$103$			1.96079e10i			1.69139i	−0.533666	+	0.845695i	$0.679186\pi$
$104$	5.87028e9			0.482495
$105$	−8.70639e9			−0.682169
$106$		−	3.18668e10i		−	2.38128i
$107$	1.03987e10			0.741416			0.370708	−	0.928749i	$-0.379115\pi$
$107$	1.03987e10			0.741416			0.370708	+	0.928749i	$0.379115\pi$
$108$	−3.41393e9			−0.232346
$109$			6.75429e9i			0.438983i	0.975614	+	0.219491i	$0.0704397\pi$
$109$			6.75429e9i			0.438983i	−0.975614	+	0.219491i	$0.929560\pi$
$110$	−2.16463e10			−1.34407
$111$			1.11344e10i			0.660770i
$112$	−9.80682e9			−0.556465
$113$		−	1.66808e10i		−	0.905367i	−0.891671	−	0.452683i	$-0.850467\pi$
$113$		−	1.66808e10i		−	0.905367i	0.891671	−	0.452683i	$-0.149533\pi$
$114$			2.36608e10i			1.22887i
$115$			3.91601e10i			1.94695i
$116$	4.33066e10			2.06188
$117$		−	1.14487e10i		−	0.522187i
$118$	6.38601e9	−	3.33839e10i	0.279138	−	1.45924i
$119$	3.16342e9			0.132563
$120$		−	7.04372e9i		−	0.283072i
$121$	1.75605e10			0.677035
$122$	−6.14563e10			−2.27388
$123$	1.35747e9			0.0482174
$124$		−	5.80420e10i		−	1.97986i
$125$	−2.59469e10			−0.850229
$126$		−	1.16736e10i		−	0.367579i
$127$	4.88844e10			1.47962			0.739812	−	0.672814i	$-0.234915\pi$
$127$	4.88844e10			1.47962			0.739812	+	0.672814i	$0.234915\pi$
$128$		−	2.07105e10i		−	0.602755i
$129$		−	1.09200e10i		−	0.305685i
$130$	1.37565e11			3.70502
$131$		−	3.48703e10i		−	0.903857i	−0.892054	−	0.451928i	$-0.850736\pi$
$131$		−	3.48703e10i		−	0.903857i	0.892054	−	0.451928i	$-0.149264\pi$
$132$		−	1.58747e10i		−	0.396127i
$133$	−4.42520e10			−1.06335
$134$	8.22849e10			1.90457
$135$	−1.37372e10			−0.306359
$136$			2.55929e9i			0.0550080i
$137$	−6.88870e10			−1.42736			−0.713681	−	0.700471i	$-0.752974\pi$
$137$	−6.88870e10			−1.42736			−0.713681	+	0.700471i	$0.752974\pi$
$138$	−5.25060e10			−1.04909
$139$	1.14551e10			0.220763			0.110381	−	0.993889i	$-0.464793\pi$
$139$	1.14551e10			0.220763			0.110381	+	0.993889i	$0.464793\pi$
$140$	7.67203e10			1.42649
$141$		−	6.69355e9i		−	0.120105i
$142$			1.61615e11i			2.79923i
$143$	5.32360e10			0.890278
$144$	−1.54735e10			−0.249906
$145$	1.74260e11			2.71868
$146$	9.03105e8			0.0136136
$147$	−1.77975e10			−0.259282
$148$		−	9.81154e10i		−	1.38175i
$149$			1.15357e11i			1.57076i	0.619011	+	0.785382i	$0.287534\pi$
$149$			1.15357e11i			1.57076i	−0.619011	+	0.785382i	$0.712466\pi$
$150$		−	9.99266e10i		−	1.31591i
$151$			1.05286e11i			1.34118i	0.741830	+	0.670588i	$0.233958\pi$
$151$			1.05286e11i			1.34118i	−0.741830	+	0.670588i	$0.766042\pi$
$152$		−	3.58012e10i		−	0.441245i
$153$	4.99134e9			0.0595333
$154$	5.42817e10			0.626685
$155$		−	2.33554e11i		−	2.61053i
$156$			1.00885e11i			1.09195i
$157$			1.54569e10i			0.162041i	0.996712	+	0.0810204i	$0.0258179\pi$
$157$			1.54569e10i			0.162041i	−0.996712	+	0.0810204i	$0.974182\pi$
$158$		−	1.33777e11i		−	1.35861i
$159$	9.40380e10			0.925375
$160$		−	2.37337e11i		−	2.26343i
$161$		−	9.82003e10i		−	0.907786i
$162$		−	1.84189e10i		−	0.165078i
$163$	1.75392e11			1.52431			0.762153	−	0.647397i	$-0.224142\pi$
$163$	1.75392e11			1.52431			0.762153	+	0.647397i	$0.224142\pi$
$164$	−1.19619e10			−0.100828
$165$		−	6.38776e10i		−	0.522311i
$166$	−1.66304e11			−1.31936
$167$	5.47488e10			0.421494			0.210747	−	0.977541i	$-0.432410\pi$
$167$	5.47488e10			0.421494			0.210747	+	0.977541i	$0.432410\pi$
$168$			1.76633e10i			0.131985i
$169$	−2.00462e11			−1.45412
$170$			5.99748e10i			0.422400i
$171$	−6.98223e10			−0.477544
$172$			9.62265e10i			0.639223i
$173$		−	1.16508e11i		−	0.751841i	−0.926652	−	0.375920i	$-0.877327\pi$
$173$		−	1.16508e11i		−	0.751841i	0.926652	−	0.375920i	$-0.122673\pi$
$174$			2.33649e11i			1.46493i
$175$	1.86889e11			1.13866
$176$		−	7.19513e10i		−	0.426064i
$177$	9.85149e10	+	1.88449e10i	0.567068	+	0.108474i
$178$	1.07122e11			0.599485
$179$		−	2.34414e11i		−	1.27561i	−0.770198	−	0.637805i	$-0.779843\pi$
$179$		−	2.34414e11i		−	1.27561i	0.770198	−	0.637805i	$-0.220157\pi$
$180$	1.21052e11			0.640632
$181$	1.22529e11			0.630736			0.315368	−	0.948969i	$-0.397872\pi$
$181$	1.22529e11			0.630736			0.315368	+	0.948969i	$0.397872\pi$
$182$	−3.44966e11			−1.72751
$183$		−	1.81356e11i		−	0.883640i
$184$	7.94469e10			0.376693
$185$		−	3.94804e11i		−	1.82189i
$186$	3.13149e11			1.40665
$187$			2.32096e10i			0.101498i
$188$			5.89833e10i			0.251154i
$189$	3.44483e10			0.142843
$190$		−	8.38969e11i		−	3.38827i
$191$			4.02313e11i			1.58269i	0.611368	+	0.791347i	$0.290620\pi$
$191$			4.02313e11i			1.58269i	−0.611368	+	0.791347i	$0.709380\pi$
$192$	2.05284e11			0.786771
$193$	−1.97970e11			−0.739288			−0.369644	−	0.929173i	$-0.620520\pi$
$193$	−1.97970e11			−0.739288			−0.369644	+	0.929173i	$0.620520\pi$
$194$	5.05662e11			1.84014
$195$			4.05950e11i			1.43979i
$196$	1.56831e11			0.542189
$197$	−3.75407e11			−1.26523			−0.632617	−	0.774465i	$-0.718019\pi$
$197$	−3.75407e11			−1.26523			−0.632617	+	0.774465i	$0.718019\pi$
$198$	8.56473e10			0.281441
$199$	2.97679e11			0.953856			0.476928	−	0.878942i	$-0.341750\pi$
$199$	2.97679e11			0.953856			0.476928	+	0.878942i	$0.341750\pi$
$200$			1.51199e11i			0.472497i
$201$			2.42820e11i			0.740124i
$202$	−6.98299e10			−0.207627
$203$	−4.36986e11			−1.26761
$204$	−4.39834e10			−0.124491
$205$	−4.81333e10			−0.132946
$206$	9.32205e11			2.51290
$207$		−	1.54944e11i		−	0.407682i
$208$			4.57259e11i			1.17448i
$209$		−	3.24671e11i		−	0.814165i
$210$			4.13923e11i			1.01350i
$211$			3.79905e11i			0.908370i	0.890907	+	0.454185i	$0.150069\pi$
$211$			3.79905e11i			0.908370i	−0.890907	+	0.454185i	$0.849931\pi$
$212$	−8.28658e11			−1.93507
$213$	−4.76919e11			−1.08779
$214$		−	4.94382e11i		−	1.10152i
$215$			3.87203e11i			0.842843i
$216$			2.78697e10i			0.0592738i
$217$			5.85673e11i			1.21719i
$218$	3.21115e11			0.652197
$219$			2.66503e9i			0.00529032i
$220$			5.62886e11i			1.09221i
$221$		−	1.47499e11i		−	0.279788i
$222$	5.29354e11			0.981707
$223$	−9.15378e11			−1.65988			−0.829939	−	0.557854i	$-0.811625\pi$
$223$	−9.15378e11			−1.65988			−0.829939	+	0.557854i	$0.811625\pi$
$224$			5.95161e11i			1.05535i
$225$	2.94880e11			0.511367
$226$	−7.93045e11			−1.34510
$227$			3.00794e11i			0.499045i	0.968369	+	0.249523i	$0.0802737\pi$
$227$			3.00794e11i			0.499045i	−0.968369	+	0.249523i	$0.919726\pi$
$228$	6.15270e11			0.998600
$229$			5.50473e11i			0.874094i	0.899439	+	0.437047i	$0.143976\pi$
$229$			5.50473e11i			0.874094i	−0.899439	+	0.437047i	$0.856024\pi$
$230$	1.86177e12			2.89259
$231$			1.60183e11i			0.243533i
$232$		−	3.53534e11i		−	0.526007i
$233$		−	8.38036e11i		−	1.22035i	−0.792268	−	0.610173i	$-0.791100\pi$
$233$		−	8.38036e11i		−	1.22035i	0.792268	−	0.610173i	$-0.208900\pi$
$234$	−5.44298e11			−0.775814
$235$			2.37341e11i			0.331157i
$236$	−8.68108e11	−	1.66060e11i	−1.18581	−	0.226833i
$237$	3.94772e11			0.527964
$238$		−	1.50396e11i		−	0.196949i
$239$	−9.21230e11			−1.18135			−0.590675	−	0.806909i	$-0.701138\pi$
$239$	−9.21230e11			−1.18135			−0.590675	+	0.806909i	$0.701138\pi$
$240$	5.48662e11			0.689047
$241$	2.06797e11			0.254366			0.127183	−	0.991879i	$-0.459406\pi$
$241$	2.06797e11			0.254366			0.127183	+	0.991879i	$0.459406\pi$
$242$		−	8.34871e11i		−	1.00587i
$243$	5.43536e10			0.0641500
$244$			1.59810e12i			1.84779i
$245$	6.31067e11			0.714900
$246$		−	6.45373e10i		−	0.0716366i
$247$			2.06332e12i			2.24431i
$248$	−4.73827e11			−0.505081
$249$		−	4.90758e11i		−	0.512709i
$250$			1.23358e12i			1.26319i
$251$	7.95542e11			0.798536			0.399268	−	0.916834i	$-0.369264\pi$
$251$	7.95542e11			0.798536			0.399268	+	0.916834i	$0.369264\pi$
$252$	−3.03556e11			−0.298701
$253$	7.20482e11			0.695058
$254$		−	2.32408e12i		−	2.19828i
$255$	−1.76984e11			−0.164147
$256$	5.13708e11			0.467214
$257$	1.25101e12			1.11583			0.557913	−	0.829900i	$-0.311602\pi$
$257$	1.25101e12			1.11583			0.557913	+	0.829900i	$0.311602\pi$
$258$	−5.19163e11			−0.454157
$259$			9.90034e11i			0.849477i
$260$		−	3.57721e12i		−	3.01077i
$261$	−6.89490e11			−0.569279
$262$	−1.65782e12			−1.34286
$263$	−2.17127e12			−1.72558			−0.862790	−	0.505562i	$-0.831285\pi$
$263$	−2.17127e12			−1.72558			−0.862790	+	0.505562i	$0.831285\pi$
$264$	−1.29593e11			−0.101056
$265$	−3.33442e12			−2.55147
$266$			2.10385e12i			1.57982i
$267$			3.16113e11i			0.232963i
$268$		−	2.13972e12i		−	1.54768i
$269$			6.00038e10i			0.0426007i	0.999773	+	0.0213004i	$0.00678063\pi$
$269$			6.00038e10i			0.0426007i	−0.999773	+	0.0213004i	$0.993219\pi$
$270$			6.53101e11i			0.455157i
$271$	1.84863e12			1.26475			0.632374	−	0.774663i	$-0.282081\pi$
$271$	1.84863e12			1.26475			0.632374	+	0.774663i	$0.282081\pi$
$272$	−1.99353e11			−0.133899
$273$		−	1.01798e12i		−	0.671317i
$274$			3.27505e12i			2.12063i
$275$			1.37118e12i			0.871830i
$276$			1.36535e12i			0.852511i
$277$	1.48046e12			0.907815			0.453908	−	0.891049i	$-0.350030\pi$
$277$	1.48046e12			0.907815			0.453908	+	0.891049i	$0.350030\pi$
$278$		−	5.44605e11i		−	0.327988i
$279$			9.24094e11i			0.546632i
$280$		−	6.26307e11i		−	0.363913i
$281$	−1.16588e11			−0.0665463			−0.0332731	−	0.999446i	$-0.510593\pi$
$281$	−1.16588e11			−0.0665463			−0.0332731	+	0.999446i	$0.510593\pi$
$282$	−3.18228e11			−0.178440
$283$			2.02531e12i			1.11573i	0.829932	+	0.557865i	$0.188379\pi$
$283$			2.02531e12i			1.11573i	−0.829932	+	0.557865i	$0.811621\pi$
$284$	4.20259e12			2.27471
$285$	2.47577e12			1.31670
$286$		−	2.53097e12i		−	1.32269i
$287$	1.20702e11			0.0619876
$288$			9.39064e11i			0.473950i
$289$	−1.95169e12			−0.968102
$290$		−	8.28476e12i		−	4.03915i
$291$			1.49219e12i			0.715088i
$292$		−	2.34841e10i		−	0.0110627i
$293$	4.07698e11			0.188799			0.0943997	−	0.995534i	$-0.469907\pi$
$293$	4.07698e11			0.188799			0.0943997	+	0.995534i	$0.469907\pi$
$294$			8.46137e11i			0.385216i
$295$	−3.49316e12	−	6.68206e11i	−1.56354	−	0.299089i
$296$	−8.00966e11			−0.352497
$297$			2.52742e11i			0.109369i
$298$	5.48433e12			2.33369
$299$	−4.57875e12			−1.91598
$300$	−2.59847e12			−1.06933
$301$		−	9.70974e11i		−	0.392984i
$302$	5.00555e12			1.99259
$303$		−	2.06066e11i		−	0.0806849i
$304$	2.78869e12			1.07407
$305$			6.43054e12i			2.43640i
$306$		−	2.37300e11i		−	0.0884486i
$307$	3.87561e11			0.142118			0.0710589	−	0.997472i	$-0.477362\pi$
$307$	3.87561e11			0.142118			0.0710589	+	0.997472i	$0.477362\pi$
$308$		−	1.41153e12i		−	0.509256i
$309$			2.75091e12i			0.976525i
$310$	−1.11037e13			−3.87846
$311$	−2.53610e12			−0.871696			−0.435848	−	0.900020i	$-0.643551\pi$
$311$	−2.53610e12			−0.871696			−0.435848	+	0.900020i	$0.643551\pi$
$312$	8.23578e11			0.278568
$313$			1.19694e12i			0.398427i	0.979956	+	0.199214i	$0.0638388\pi$
$313$			1.19694e12i			0.398427i	−0.979956	+	0.199214i	$0.936161\pi$
$314$	7.34859e11			0.240744
$315$	−1.22147e12			−0.393850
$316$	−3.47871e12			−1.10403
$317$	3.26824e12			1.02098			0.510490	−	0.859884i	$-0.329464\pi$
$317$	3.26824e12			1.02098			0.510490	+	0.859884i	$0.329464\pi$
$318$		−	4.47079e12i		−	1.37483i
$319$		−	3.20611e12i		−	0.970564i
$320$	−7.27899e12			−2.16931
$321$	1.45890e12			0.428057
$322$	−4.66868e12			−1.34870
$323$	−8.99556e11			−0.255868
$324$	−4.78961e11			−0.134145
$325$		−	8.71402e12i		−	2.40327i
$326$		−	8.33857e12i		−	2.26466i
$327$			9.47601e11i			0.253447i
$328$			9.76514e10i			0.0257223i
$329$		−	5.95171e11i		−	0.154405i
$330$	−3.03690e12			−0.775998
$331$	3.09341e12			0.778571			0.389285	−	0.921117i	$-0.372722\pi$
$331$	3.09341e12			0.778571			0.389285	+	0.921117i	$0.372722\pi$
$332$			4.32454e12i			1.07213i
$333$			1.56211e12i			0.381496i
$334$		−	2.60289e12i		−	0.626215i
$335$		−	8.60996e12i		−	2.04069i
$336$	−1.37586e12			−0.321275
$337$			7.64173e11i			0.175809i	0.996129	+	0.0879047i	$0.0280171\pi$
$337$			7.64173e11i			0.175809i	−0.996129	+	0.0879047i	$0.971983\pi$
$338$			9.53047e12i			2.16038i
$339$		−	2.34025e12i		−	0.522714i
$340$	1.55957e12			0.343250
$341$	−4.29701e12			−0.931953
$342$			3.31952e12i			0.709488i
$343$	−5.10630e12			−1.07556
$344$	7.85546e11			0.163072
$345$			5.49402e12i			1.12407i
$346$	−5.53908e12			−1.11701
$347$		−	3.69950e11i		−	0.0735353i	−0.999324	−	0.0367677i	$-0.988294\pi$
$347$		−	3.69950e11i		−	0.0735353i	0.999324	−	0.0367677i	$-0.0117061\pi$
$348$	6.07575e12			1.19043
$349$			8.71421e11i			0.168306i	0.996453	+	0.0841532i	$0.0268185\pi$
$349$			8.71421e11i			0.168306i	−0.996453	+	0.0841532i	$0.973181\pi$
$350$		−	8.88518e12i		−	1.69171i
$351$		−	1.60621e12i		−	0.301485i
$352$	−4.36662e12			−0.808038
$353$			5.40604e12i			0.986292i	0.869947	+	0.493146i	$0.164153\pi$
$353$			5.40604e12i			0.986292i	−0.869947	+	0.493146i	$0.835847\pi$
$354$	8.95932e11	−	4.68364e12i	0.161161	−	0.842494i
$355$	1.69107e13			2.99930
$356$		−	2.78557e12i		−	0.487152i
$357$	4.43815e11			0.0765351
$358$	−1.11446e13			−1.89517
$359$	−1.06964e13			−1.79377			−0.896885	−	0.442264i	$-0.854176\pi$
$359$	−1.06964e13			−1.79377			−0.896885	+	0.442264i	$0.854176\pi$
$360$		−	9.88207e11i		−	0.163431i
$361$	6.45255e12			1.05243
$362$		−	5.82535e12i		−	0.937085i
$363$	2.46368e12			0.390886
$364$			8.97042e12i			1.40380i
$365$		−	9.44972e10i		−	0.0145866i
$366$	−8.62209e12			−1.31283
$367$			8.00075e12i			1.20171i	0.799358	+	0.600856i	$0.205173\pi$
$367$			8.00075e12i			1.20171i	−0.799358	+	0.600856i	$0.794827\pi$
$368$			6.18842e12i			0.916939i
$369$	1.90447e11			0.0278383
$370$	−1.87699e13			−2.70679
$371$	8.36158e12			1.18965
$372$		−	8.14307e12i		−	1.14307i
$373$	−1.08064e12			−0.149670			−0.0748351	−	0.997196i	$-0.523843\pi$
$373$	−1.08064e12			−0.149670			−0.0748351	+	0.997196i	$0.523843\pi$
$374$	1.10344e12			0.150796
$375$	−3.64025e12			−0.490880
$376$	4.81511e11			0.0640718
$377$			2.03752e13i			2.67543i
$378$		−	1.63775e12i		−	0.212222i
$379$	−4.13823e12			−0.529198			−0.264599	−	0.964359i	$-0.585240\pi$
$379$	−4.13823e12			−0.529198			−0.264599	+	0.964359i	$0.585240\pi$
$380$	−2.18164e13			−2.75337
$381$	6.85828e12			0.854261
$382$	1.91269e13			2.35141
$383$	−2.76676e12			−0.335720			−0.167860	−	0.985811i	$-0.553686\pi$
$383$	−2.76676e12			−0.335720			−0.167860	+	0.985811i	$0.553686\pi$
$384$		−	2.90560e12i		−	0.348001i
$385$		−	5.67981e12i		−	0.671476i
$386$			9.41200e12i			1.09836i
$387$		−	1.53203e12i		−	0.176487i
$388$		−	1.31491e13i		−	1.49533i
$389$	1.31884e13			1.48062			0.740311	−	0.672265i	$-0.234678\pi$
$389$	1.31884e13			1.48062			0.740311	+	0.672265i	$0.234678\pi$
$390$	1.92998e13			2.13910
$391$		−	1.99622e12i		−	0.218436i
$392$		−	1.28029e12i		−	0.138318i
$393$		−	4.89217e12i		−	0.521842i
$394$			1.78477e13i			1.87976i
$395$	−1.39979e13			−1.45572
$396$		−	2.22715e12i		−	0.228704i
$397$			6.53060e12i			0.662218i	0.943593	+	0.331109i	$0.107423\pi$
$397$			6.53060e12i			0.662218i	−0.943593	+	0.331109i	$0.892577\pi$
$398$		−	1.41524e13i		−	1.41714i
$399$	−6.20839e12			−0.613924
$400$	−1.17775e13			−1.15014
$401$		−	1.79410e13i		−	1.73032i	−0.501500	−	0.865158i	$-0.667218\pi$
$401$		−	1.79410e13i		−	1.73032i	0.501500	−	0.865158i	$-0.332782\pi$
$402$	1.15443e13			1.09960
$403$	2.73080e13			2.56900
$404$			1.81584e12i			0.168722i
$405$	−1.92728e12			−0.176876
$406$			2.07754e13i			1.88330i
$407$	−7.26375e12			−0.650412
$408$			3.59059e11i			0.0317589i
$409$			1.13865e13i			0.994889i	0.867496	+	0.497445i	$0.165728\pi$
$409$			1.13865e13i			0.994889i	−0.867496	+	0.497445i	$0.834272\pi$
$410$			2.28837e12i			0.197519i
$411$	−9.66458e12			−0.824088
$412$		−	2.42408e13i		−	2.04203i
$413$	8.75965e12	+	1.67563e12i	0.729015	+	0.139453i
$414$	−7.36639e12			−0.605694
$415$			1.74014e13i			1.41366i
$416$	2.77504e13			2.22742
$417$	1.60711e12			0.127458
$418$	−1.54357e13			−1.20961
$419$			1.39833e12i			0.108278i	0.998533	+	0.0541390i	$0.0172414\pi$
$419$			1.39833e12i			0.108278i	−0.998533	+	0.0541390i	$0.982759\pi$
$420$	1.07636e13			0.823587
$421$			7.96565e12i			0.602297i	0.953577	+	0.301149i	$0.0973700\pi$
$421$			7.96565e12i			0.602297i	−0.953577	+	0.301149i	$0.902630\pi$
$422$	1.80616e13			1.34957
$423$		−	9.39080e11i		−	0.0693427i
$424$			6.76476e12i			0.493654i
$425$	3.79909e12			0.273990
$426$			2.26739e13i			1.61614i
$427$		−	1.61256e13i		−	1.13600i
$428$	−1.28558e13			−0.895117
$429$	7.46881e12			0.514002
$430$	1.84086e13			1.25221
$431$			5.37574e12i			0.361453i	0.983533	+	0.180726i	$0.0578448\pi$
$431$			5.37574e12i			0.361453i	−0.983533	+	0.180726i	$0.942155\pi$
$432$	−2.17087e12			−0.144283
$433$	−1.42980e13			−0.939369			−0.469685	−	0.882834i	$-0.655632\pi$
$433$	−1.42980e13			−0.939369			−0.469685	+	0.882834i	$0.655632\pi$
$434$	2.78443e13			1.80837
$435$	2.44481e13			1.56963
$436$		−	8.35021e12i		−	0.529987i
$437$			2.79245e13i			1.75218i
$438$	1.26702e11			0.00785983
$439$	−9.94179e12			−0.609736			−0.304868	−	0.952395i	$-0.598612\pi$
$439$	−9.94179e12			−0.609736			−0.304868	+	0.952395i	$0.598612\pi$
$440$	4.59513e12			0.278634
$441$	−2.49692e12			−0.149697
$442$	−7.01248e12			−0.415681
$443$		−	1.00600e13i		−	0.589630i	−0.955554	−	0.294815i	$-0.904742\pi$
$443$		−	1.00600e13i		−	0.589630i	0.955554	−	0.294815i	$-0.0952581\pi$
$444$		−	1.37652e13i		−	0.797752i
$445$		−	1.12088e13i		−	0.642331i
$446$			4.35193e13i			2.46608i
$447$			1.61841e13i			0.906881i
$448$	1.82532e13			1.01146
$449$	3.03874e13			1.66518			0.832592	−	0.553886i	$-0.186856\pi$
$449$	3.03874e13			1.66518			0.832592	+	0.553886i	$0.186856\pi$
$450$		−	1.40193e13i		−	0.759739i
$451$			8.85574e11i			0.0474616i
$452$			2.06222e13i			1.09306i
$453$			1.47712e13i			0.774329i
$454$	1.43005e13			0.741432
$455$			3.60958e13i			1.85097i
$456$		−	5.02277e12i		−	0.254753i
$457$		−	2.85028e13i		−	1.42990i	−0.699173	−	0.714952i	$-0.746448\pi$
$457$		−	2.85028e13i		−	1.42990i	0.699173	−	0.714952i	$-0.253552\pi$
$458$	2.61708e13			1.29864
$459$	7.00265e11			0.0343715
$460$		−	4.84130e13i		−	2.35057i
$461$	−7.52318e12			−0.361324			−0.180662	−	0.983545i	$-0.557824\pi$
$461$	−7.52318e12			−0.361324			−0.180662	+	0.983545i	$0.557824\pi$
$462$	7.61551e12			0.361817
$463$		−	3.38232e12i		−	0.158968i	−0.996836	−	0.0794841i	$-0.974673\pi$
$463$		−	3.38232e12i		−	0.158968i	0.996836	−	0.0794841i	$-0.0253273\pi$
$464$	2.75381e13			1.28040
$465$		−	3.27667e13i		−	1.50719i
$466$	−3.98423e13			−1.81307
$467$			3.58012e13i			1.61181i	0.592046	+	0.805904i	$0.298320\pi$
$467$			3.58012e13i			1.61181i	−0.592046	+	0.805904i	$0.701680\pi$
$468$			1.41538e13i			0.630440i
$469$			2.15908e13i			0.951492i
$470$	1.12838e13			0.492000
$471$			2.16854e12i			0.0935543i
$472$	−1.35564e12	+	7.08681e12i	−0.0578672	+	0.302511i
$473$	7.12391e12			0.300893
$474$		−	1.87684e13i		−	0.784396i
$475$	−5.31443e13			−2.19780
$476$	−3.91087e12			−0.160044
$477$	1.31932e13			0.534265
$478$			4.37975e13i			1.75513i
$479$	−3.00548e13			−1.19189			−0.595945	−	0.803025i	$-0.703223\pi$
$479$	−3.00548e13			−1.19189			−0.595945	+	0.803025i	$0.703223\pi$
$480$		−	3.32975e13i		−	1.30679i
$481$	4.61619e13			1.79291
$482$		−	9.83163e12i		−	0.377912i
$483$		−	1.37771e13i		−	0.524110i
$484$	−2.17098e13			−0.817389
$485$		−	5.29104e13i		−	1.97166i
$486$		−	2.58410e12i		−	0.0953077i
$487$	−4.04542e13			−1.47679			−0.738396	−	0.674368i	$-0.764416\pi$
$487$	−4.04542e13			−1.47679			−0.738396	+	0.674368i	$0.764416\pi$
$488$	1.30461e13			0.471391
$489$	2.46068e13			0.880059
$490$		−	3.00025e13i		−	1.06213i
$491$	−4.42270e13			−1.54982			−0.774908	−	0.632074i	$-0.782204\pi$
$491$	−4.42270e13			−1.54982			−0.774908	+	0.632074i	$0.782204\pi$
$492$	−1.67821e12			−0.0582132
$493$	−8.88305e12			−0.305019
$494$	9.80954e13			3.33437
$495$		−	8.96179e12i		−	0.301556i
$496$		−	3.69081e13i		−	1.22946i
$497$	−4.24062e13			−1.39845
$498$	−2.33318e13			−0.761732
$499$	−5.35177e13			−1.72980			−0.864898	−	0.501947i	$-0.832617\pi$
$499$	−5.35177e13			−1.72980			−0.864898	+	0.501947i	$0.832617\pi$
$500$	3.20777e13			1.02649
$501$	7.68104e12			0.243350
$502$		−	3.78220e13i		−	1.18638i
$503$			4.96500e13i			1.54198i	0.636846	+	0.770991i	$0.280239\pi$
$503$			4.96500e13i			1.54198i	−0.636846	+	0.770991i	$0.719761\pi$
$504$			2.47809e12i			0.0762016i
$505$			7.30671e12i			0.222467i
$506$		−	3.42535e13i		−	1.03265i
$507$	−2.81241e13			−0.839535
$508$	−6.04348e13			−1.78636
$509$			2.10201e13i			0.615240i	0.951509	+	0.307620i	$0.0995326\pi$
$509$			2.10201e13i			0.615240i	−0.951509	+	0.307620i	$0.900467\pi$
$510$			8.41423e12i			0.243873i
$511$			2.36967e11i			0.00680116i
$512$		−	4.56305e13i		−	1.29690i
$513$	−9.79579e12			−0.275710
$514$		−	5.94762e13i		−	1.65778i
$515$		−	9.75421e13i		−	2.69250i
$516$			1.35002e13i			0.369056i
$517$	4.36669e12			0.118222
$518$	4.70686e13			1.26207
$519$		−	1.63456e13i		−	0.434075i
$520$	−2.92026e13			−0.768077
$521$	9.13680e12			0.238016			0.119008	−	0.992893i	$-0.462029\pi$
$521$	9.13680e12			0.238016			0.119008	+	0.992893i	$0.462029\pi$
$522$			3.27800e13i			0.845779i
$523$	3.04103e12			0.0777164			0.0388582	−	0.999245i	$-0.487628\pi$
$523$	3.04103e12			0.0777164			0.0388582	+	0.999245i	$0.487628\pi$
$524$			4.31096e13i			1.09123i
$525$	2.62199e13			0.657406
$526$			1.03227e14i			2.56370i
$527$			1.19056e13i			0.292885i
$528$		−	1.00945e13i		−	0.245988i
$529$	−2.05410e13			−0.495843
$530$			1.58526e14i			3.79072i
$531$	1.38213e13	+	2.64387e12i	0.327397	+	0.0626277i
$532$	5.47080e13			1.28379
$533$		−	5.62792e12i		−	0.130831i
$534$	1.50288e13			0.346113
$535$	−5.17301e13			−1.18025
$536$	−1.74676e13			−0.394830
$537$		−	3.28873e13i		−	0.736473i
$538$	2.85272e12			0.0632919
$539$		−	1.16106e13i		−	0.255218i
$540$	1.69831e13			0.369869
$541$		−	1.97545e12i		−	0.0426266i	−0.999773	−	0.0213133i	$-0.993215\pi$
$541$		−	1.97545e12i		−	0.0426266i	0.999773	−	0.0213133i	$-0.00678474\pi$
$542$		−	8.78884e13i		−	1.87904i
$543$	1.71904e13			0.364155
$544$			1.20984e13i			0.253942i
$545$		−	3.36002e13i		−	0.698810i
$546$	−4.83974e13			−0.997376
$547$	−1.58960e13			−0.324601			−0.162301	−	0.986741i	$-0.551891\pi$
$547$	−1.58960e13			−0.324601			−0.162301	+	0.986741i	$0.551891\pi$
$548$	8.51637e13			1.72326
$549$		−	2.54435e13i		−	0.510170i
$550$	6.51894e13			1.29528
$551$	1.24262e14			2.44670
$552$	1.11461e13			0.217484
$553$	3.51019e13			0.678743
$554$		−	7.03846e13i		−	1.34874i
$555$		−	5.53895e13i		−	1.05187i
$556$	−1.41618e13			−0.266529
$557$	−8.16098e12			−0.152218			−0.0761091	−	0.997099i	$-0.524250\pi$
$557$	−8.16098e12			−0.152218			−0.0761091	+	0.997099i	$0.524250\pi$
$558$	4.39337e13			0.812132
$559$	−4.52732e13			−0.829435
$560$	4.87854e13			0.885829
$561$			3.25621e12i			0.0586001i
$562$			5.54289e12i			0.0988678i
$563$			2.87343e12i			0.0507995i	0.999677	+	0.0253997i	$0.00808585\pi$
$563$			2.87343e12i			0.0507995i	−0.999677	+	0.0253997i	$0.991914\pi$
$564$			8.27512e12i			0.145004i
$565$			8.29810e13i			1.44124i
$566$	9.62881e13			1.65764
$567$	4.83296e12			0.0824704
$568$		−	3.43079e13i		−	0.580300i
$569$			8.08683e12i			0.135587i	0.997699	+	0.0677933i	$0.0215958\pi$
$569$			8.08683e12i			0.135587i	−0.997699	+	0.0677933i	$0.978404\pi$
$570$		−	1.17704e14i		−	1.95622i
$571$			2.30233e13i			0.379304i	0.981851	+	0.189652i	$0.0607360\pi$
$571$			2.30233e13i			0.379304i	−0.981851	+	0.189652i	$0.939264\pi$
$572$	−6.58148e13			−1.07484
$573$			5.64429e13i			0.913768i
$574$		−	5.73846e12i		−	0.0920950i
$575$		−	1.17933e14i		−	1.87628i
$576$	2.88005e13			0.454243
$577$	−7.83551e13			−1.22515			−0.612573	−	0.790414i	$-0.709866\pi$
$577$	−7.83551e13			−1.22515			−0.612573	+	0.790414i	$0.709866\pi$
$578$			9.27880e13i			1.43831i
$579$	−2.77745e13			−0.426828
$580$	−2.15435e14			−3.28228
$581$		−	4.36368e13i		−	0.659132i
$582$	7.09424e13			1.06241
$583$			6.13478e13i			0.910869i
$584$	−1.91713e11			−0.00282220
$585$			5.69532e13i			0.831263i
$586$		−	1.93830e13i		−	0.280499i
$587$		−	1.36868e13i		−	0.196386i	−0.995167	−	0.0981929i	$-0.968694\pi$
$587$		−	1.36868e13i		−	0.196386i	0.995167	−	0.0981929i	$-0.0313062\pi$
$588$	2.20027e13			0.313033
$589$		−	1.66543e14i		−	2.34937i
$590$	−3.17681e13	+	1.66073e14i	−0.444356	+	2.32295i
$591$	−5.26681e13			−0.730483
$592$		−	6.23903e13i		−	0.858042i
$593$	−1.74570e13			−0.238066			−0.119033	−	0.992890i	$-0.537979\pi$
$593$	−1.74570e13			−0.238066			−0.119033	+	0.992890i	$0.537979\pi$
$594$	1.20160e13			0.162490
$595$	−1.57369e13			−0.211025
$596$		−	1.42613e14i		−	1.89639i
$597$	4.17632e13			0.550709
$598$			2.17685e14i			2.84657i
$599$	−7.08734e13			−0.919071			−0.459536	−	0.888159i	$-0.651984\pi$
$599$	−7.08734e13			−0.919071			−0.459536	+	0.888159i	$0.651984\pi$
$600$			2.12126e13i			0.272796i
$601$		−	1.17177e14i		−	1.49442i	−0.664590	−	0.747208i	$-0.731394\pi$
$601$		−	1.17177e14i		−	1.49442i	0.664590	−	0.747208i	$-0.268606\pi$
$602$	−4.61625e13			−0.583857
$603$			3.40667e13i			0.427311i
$604$		−	1.30163e14i		−	1.61921i
$605$	−8.73575e13			−1.07776
$606$	−9.79686e12			−0.119874
$607$	−1.78667e11			−0.00216821			−0.00108411	−	0.999999i	$-0.500345\pi$
$607$	−1.78667e11			−0.00216821			−0.00108411	+	0.999999i	$0.500345\pi$
$608$		−	1.69241e14i		−	2.03699i
$609$	−6.13074e13			−0.731857
$610$	3.05723e14			3.61976
$611$	−2.77508e13			−0.325889
$612$	−6.17070e12			−0.0718749
$613$			3.48149e13i			0.402219i	0.979569	+	0.201109i	$0.0644547\pi$
$613$			3.48149e13i			0.402219i	−0.979569	+	0.201109i	$0.935545\pi$
$614$		−	1.84256e13i		−	0.211144i
$615$	−6.75292e12			−0.0767566
$616$	−1.15230e13			−0.129916
$617$	−8.79881e13			−0.984006			−0.492003	−	0.870593i	$-0.663735\pi$
$617$	−8.79881e13			−0.984006			−0.492003	+	0.870593i	$0.663735\pi$
$618$	1.30785e14			1.45082
$619$	−8.43433e12			−0.0928105			−0.0464053	−	0.998923i	$-0.514777\pi$
$619$	−8.43433e12			−0.0928105			−0.0464053	+	0.998923i	$0.514777\pi$
$620$			2.88738e14i			3.15171i
$621$		−	2.17380e13i		−	0.235375i
$622$			1.20572e14i			1.29508i
$623$			2.81078e13i			0.299493i
$624$			6.41516e13i			0.678086i
$625$	−1.72266e13			−0.180634
$626$	5.69052e13			0.591944
$627$		−	4.55501e13i		−	0.470058i
$628$		−	1.91091e13i		−	0.195633i
$629$			2.01254e13i			0.204405i
$630$			5.80718e13i			0.585144i
$631$	3.67916e13			0.367791			0.183896	−	0.982946i	$-0.441129\pi$
$631$	3.67916e13			0.367791			0.183896	+	0.982946i	$0.441129\pi$
$632$			2.83985e13i			0.281650i
$633$			5.32992e13i			0.524448i
$634$		−	1.55380e14i		−	1.51687i
$635$	−2.43182e14			−2.35539
$636$	−1.16257e14			−1.11721
$637$			7.37867e13i			0.703527i
$638$	−1.52426e14			−1.44197
$639$	−6.69099e13			−0.628038
$640$			1.03027e14i			0.959518i
$641$	−1.03346e13			−0.0955000			−0.0477500	−	0.998859i	$-0.515205\pi$
$641$	−1.03346e13			−0.0955000			−0.0477500	+	0.998859i	$0.515205\pi$
$642$		−	6.93598e13i		−	0.635965i
$643$	−5.05738e13			−0.460120			−0.230060	−	0.973176i	$-0.573892\pi$
$643$	−5.05738e13			−0.460120			−0.230060	+	0.973176i	$0.573892\pi$
$644$			1.21403e14i			1.09598i
$645$			5.43231e13i			0.486616i
$646$			4.27671e13i			0.380143i
$647$	−1.17517e14			−1.03652			−0.518261	−	0.855222i	$-0.673421\pi$
$647$	−1.17517e14			−1.03652			−0.518261	+	0.855222i	$0.673421\pi$
$648$			3.91000e12i			0.0342218i
$649$	−1.22939e13	+	6.42684e13i	−0.106774	+	0.558180i
$650$	−4.14286e14			−3.57053
$651$			8.21677e13i			0.702742i
$652$	−2.16834e14			−1.84031
$653$	4.49008e13			0.378171			0.189086	−	0.981961i	$-0.439448\pi$
$653$	4.49008e13			0.378171			0.189086	+	0.981961i	$0.439448\pi$
$654$	4.50512e13			0.376546
$655$			1.73468e14i			1.43884i
$656$	−7.60643e12			−0.0626126
$657$			3.73894e11i			0.00305437i
$658$	−2.82959e13			−0.229400
$659$			1.77691e14i			1.42968i	0.699287	+	0.714841i	$0.253501\pi$
$659$			1.77691e14i			1.42968i	−0.699287	+	0.714841i	$0.746499\pi$
$660$			7.89708e13i			0.630590i
$661$	1.37183e14			1.08716			0.543580	−	0.839358i	$-0.317069\pi$
$661$	1.37183e14			1.08716			0.543580	+	0.839358i	$0.317069\pi$
$662$		−	1.47068e14i		−	1.15672i
$663$		−	2.06936e13i		−	0.161536i
$664$	3.53034e13			0.273512
$665$	2.20138e14			1.69273
$666$	7.42664e13			0.566789
$667$			2.75752e14i			2.08877i
$668$	−6.76849e13			−0.508873
$669$	−1.28424e14			−0.958331
$670$	−4.09338e14			−3.03185
$671$	1.18311e14			0.869789
$672$			8.34988e13i			0.609304i
$673$		−	2.51484e14i		−	1.82153i	−0.412929	−	0.910763i	$-0.635494\pi$
$673$		−	2.51484e14i		−	1.82153i	0.412929	−	0.910763i	$-0.364506\pi$
$674$	3.63306e13			0.261200
$675$	4.13705e13			0.295238
$676$	2.47828e14			1.75557
$677$	1.43537e14			1.00930			0.504650	−	0.863324i	$-0.331621\pi$
$677$	1.43537e14			1.00930			0.504650	+	0.863324i	$0.331621\pi$
$678$	−1.11261e14			−0.776596
$679$			1.32681e14i			0.919307i
$680$		−	1.27316e13i		−	0.0875665i
$681$			4.22002e13i			0.288124i
$682$			2.04290e14i			1.38460i
$683$			7.42403e13i			0.499501i	0.968310	+	0.249750i	$0.0803486\pi$
$683$			7.42403e13i			0.499501i	−0.968310	+	0.249750i	$0.919651\pi$
$684$	8.63200e13			0.576542
$685$	3.42688e14			2.27220
$686$			2.42766e14i			1.59796i
$687$			7.72292e13i			0.504659i
$688$			6.11892e13i			0.396947i
$689$		−	3.89872e14i		−	2.51088i
$690$	2.61199e14			1.67004
$691$		−	1.72147e14i		−	1.09272i	−0.837549	−	0.546362i	$-0.816012\pi$
$691$		−	1.72147e14i		−	1.09272i	0.837549	−	0.546362i	$-0.183988\pi$
$692$			1.44037e14i			0.907702i
$693$			2.24731e13i			0.140604i
$694$	−1.75883e13			−0.109251
$695$	−5.69852e13			−0.351429
$696$		−	4.95995e13i		−	0.303690i
$697$	2.45363e12			0.0149158
$698$	4.14295e13			0.250053
$699$		−	1.17573e14i		−	0.704568i
$700$	−2.31048e14			−1.37471
$701$		−	2.95827e14i		−	1.74762i	−0.486265	−	0.873811i	$-0.661641\pi$
$701$		−	2.95827e14i		−	1.74762i	0.486265	−	0.873811i	$-0.338359\pi$
$702$	−7.63630e13			−0.447917
$703$		−	2.81528e14i		−	1.63963i
$704$			1.33921e14i			0.774439i
$705$			3.32981e13i			0.191194i
$706$	2.57016e14			1.46533
$707$		−	1.83227e13i		−	0.103727i
$708$	−1.21792e14	−	2.32976e13i	−0.684626	−	0.130962i
$709$	−1.50979e13			−0.0842723			−0.0421361	−	0.999112i	$-0.513416\pi$
$709$	−1.50979e13			−0.0842723			−0.0421361	+	0.999112i	$0.513416\pi$
$710$		−	8.03975e14i		−	4.45606i
$711$	5.53849e13			0.304820
$712$	−2.27401e13			−0.124277
$713$	3.69579e14			2.00567
$714$		−	2.11000e13i		−	0.113708i
$715$	−2.64830e14			−1.41722
$716$			2.89801e14i			1.54005i
$717$	−1.29245e14			−0.682053
$718$			5.08534e14i			2.66501i
$719$		−	8.37386e13i		−	0.435794i	−0.975972	−	0.217897i	$-0.930080\pi$
$719$		−	8.37386e13i		−	0.435794i	0.975972	−	0.217897i	$-0.0699197\pi$
$720$	7.69752e13			0.397821
$721$			2.44602e14i			1.25541i
$722$		−	3.06770e14i		−	1.56360i
$723$	2.90128e13			0.146858
$724$	−1.51481e14			−0.761492
$725$	−5.24796e14			−2.62000
$726$		−	1.17129e14i		−	0.580740i
$727$	−2.86584e14			−1.41117			−0.705586	−	0.708624i	$-0.749316\pi$
$727$	−2.86584e14			−1.41117			−0.705586	+	0.708624i	$0.749316\pi$
$728$	7.32301e13			0.358124
$729$	7.62560e12			0.0370370
$730$	−4.49263e12			−0.0216714
$731$		−	1.97380e13i		−	0.0945618i
$732$			2.24207e14i			1.06682i
$733$	−6.41426e13			−0.303128			−0.151564	−	0.988447i	$-0.548431\pi$
$733$	−6.41426e13			−0.303128			−0.151564	+	0.988447i	$0.548431\pi$
$734$	3.80375e14			1.78538
$735$	8.85363e13			0.412748
$736$	3.75566e14			1.73899
$737$	−1.58409e14			−0.728522
$738$		−	9.05433e12i		−	0.0413594i
$739$		−	4.93707e13i		−	0.223999i	−0.993708	−	0.112000i	$-0.964274\pi$
$739$		−	4.93707e13i		−	0.223999i	0.993708	−	0.112000i	$-0.0357256\pi$
$740$			4.88089e14i			2.19958i
$741$			2.89476e14i			1.29575i
$742$		−	3.97530e14i		−	1.76746i
$743$	3.80616e13			0.168090			0.0840451	−	0.996462i	$-0.473216\pi$
$743$	3.80616e13			0.168090			0.0840451	+	0.996462i	$0.473216\pi$
$744$	−6.64760e13			−0.291609
$745$		−	5.73858e14i		−	2.50048i
$746$			5.13761e13i			0.222365i
$747$		−	6.88515e13i		−	0.296013i
$748$		−	2.86936e13i		−	0.122540i
$749$	1.29721e14			0.550304
$750$			1.73066e14i			0.729301i
$751$		−	5.78775e13i		−	0.242276i	−0.992636	−	0.121138i	$-0.961346\pi$
$751$		−	5.78775e13i		−	0.242276i	0.992636	−	0.121138i	$-0.0386543\pi$
$752$			3.75067e13i			0.155962i
$753$	1.11611e14			0.461035
$754$	9.68685e14			3.97490
$755$		−	5.23760e14i		−	2.13500i
$756$	−4.25878e13			−0.172455
$757$	−1.62750e14			−0.654700			−0.327350	−	0.944903i	$-0.606156\pi$
$757$	−1.62750e14			−0.654700			−0.327350	+	0.944903i	$0.606156\pi$
$758$			1.96741e14i			0.786230i
$759$	1.01081e14			0.401292
$760$			1.78098e14i			0.702411i
$761$	−3.92113e14			−1.53634			−0.768171	−	0.640245i	$-0.778833\pi$
$761$	−3.92113e14			−1.53634			−0.768171	+	0.640245i	$0.778833\pi$
$762$		−	3.26059e14i		−	1.26918i
$763$			8.42578e13i			0.325827i
$764$		−	4.97372e14i		−	1.91080i
$765$	−2.48301e13			−0.0947702
$766$			1.31538e14i			0.498780i
$767$	7.81291e13	−	4.08433e14i	0.294331	−	1.53866i
$768$	7.20712e13			0.269746
$769$			1.65204e14i			0.614313i	0.951659	+	0.307157i	$0.0993775\pi$
$769$			1.65204e14i			0.614313i	−0.951659	+	0.307157i	$0.900622\pi$
$770$	−2.70032e14			−0.997612
$771$	1.75512e14			0.644222
$772$	2.44747e14			0.892548
$773$			4.04252e14i			1.46472i	0.680918	+	0.732360i	$0.261581\pi$
$773$			4.04252e14i			1.46472i	−0.680918	+	0.732360i	$0.738419\pi$
$774$	−7.28366e13			−0.262207
$775$			7.03362e14i			2.51577i
$776$	−1.07343e14			−0.381474
$777$			1.38898e14i			0.490446i
$778$		−	6.27009e14i		−	2.19976i
$779$	−3.43231e13			−0.119646
$780$		−	5.01868e14i		−	1.73827i
$781$		−	3.11129e14i		−	1.07074i
$782$	−9.49050e13			−0.324530
$783$	−9.67328e13			−0.328674
$784$	9.97266e13			0.336690
$785$		−	7.68926e13i		−	0.257950i
$786$	−2.32586e14			−0.775301
$787$	−2.01809e14			−0.668447			−0.334224	−	0.942494i	$-0.608474\pi$
$787$	−2.01809e14			−0.668447			−0.334224	+	0.942494i	$0.608474\pi$
$788$	4.64108e14			1.52753
$789$	−3.04621e14			−0.996265
$790$			6.65493e14i			2.16276i
$791$		−	2.08088e14i		−	0.671993i
$792$	−1.81814e13			−0.0583447
$793$	−7.51882e14			−2.39764
$794$	3.10481e14			0.983857
$795$	−4.67806e14			−1.47309
$796$	−3.68015e14			−1.15160
$797$		−	6.11946e14i		−	1.90292i	−0.307766	−	0.951462i	$-0.599582\pi$
$797$		−	6.11946e14i		−	1.90292i	0.307766	−	0.951462i	$-0.400418\pi$
$798$			2.95162e14i			0.912107i
$799$		−	1.20986e13i		−	0.0371538i
$800$			7.14757e14i			2.18126i
$801$			4.43494e13i			0.134501i
$802$	−8.52960e14			−2.57073
$803$	−1.73859e12			−0.00520739
$804$		−	3.00194e14i		−	0.893556i
$805$			4.88512e14i			1.44509i
$806$		−	1.29829e15i		−	3.81676i
$807$			8.41829e12i			0.0245955i
$808$	1.48236e13			0.0430425
$809$		−	3.26582e14i		−	0.942431i	−0.882018	−	0.471216i	$-0.843815\pi$
$809$		−	3.26582e14i		−	0.942431i	0.882018	−	0.471216i	$-0.156185\pi$
$810$			9.16275e13i			0.262785i
$811$		−	5.83491e14i		−	1.66314i	−0.555417	−	0.831572i	$-0.687441\pi$
$811$		−	5.83491e14i		−	1.66314i	0.555417	−	0.831572i	$-0.312559\pi$
$812$	5.40238e14			1.53040
$813$	2.59356e14			0.730202
$814$			3.45336e14i			0.966318i
$815$	−8.72514e14			−2.42652
$816$	−2.79685e13			−0.0773068
$817$			2.76109e14i			0.758524i
$818$	5.41343e14			1.47811
$819$		−	1.42819e14i		−	0.387585i
$820$	5.95064e13			0.160507
$821$			1.57813e14i			0.423085i	0.977369	+	0.211542i	$0.0678486\pi$
$821$			1.57813e14i			0.423085i	−0.977369	+	0.211542i	$0.932151\pi$
$822$			4.59477e14i			1.22435i
$823$		−	5.55993e13i		−	0.147255i	−0.997286	−	0.0736275i	$-0.976542\pi$
$823$		−	5.55993e13i		−	0.147255i	0.997286	−	0.0736275i	$-0.0234576\pi$
$824$	−1.97890e14			−0.520941
$825$			1.92372e14i			0.503351i
$826$	7.96636e13	−	4.16455e14i	0.207186	−	1.08310i
$827$	6.21209e14			1.60587			0.802935	−	0.596067i	$-0.203271\pi$
$827$	6.21209e14			1.60587			0.802935	+	0.596067i	$0.203271\pi$
$828$			1.91554e14i			0.492197i
$829$	−4.72134e14			−1.20585			−0.602924	−	0.797799i	$-0.705998\pi$
$829$	−4.72134e14			−1.20585			−0.602924	+	0.797799i	$0.705998\pi$
$830$	8.27305e14			2.10027
$831$	2.07703e14			0.524128
$832$		−	8.51086e14i		−	2.13480i
$833$	−3.21691e13			−0.0802073
$834$		−	7.64059e13i		−	0.189364i
$835$	−2.72356e14			−0.670971
$836$			4.01385e14i			0.982947i
$837$			1.29647e14i			0.315598i
$838$	6.64801e13			0.160869
$839$			4.84153e13i			0.116459i	0.998303	+	0.0582295i	$0.0185455\pi$
$839$			4.84153e13i			0.116459i	−0.998303	+	0.0582295i	$0.981454\pi$
$840$		−	8.78685e13i		−	0.210105i
$841$	8.06374e14			1.91671
$842$	3.78707e14			0.894834
$843$	−1.63569e13			−0.0384205
$844$		−	4.69670e14i		−	1.09668i
$845$	9.97230e14			2.31479
$846$	−4.46461e13			−0.103022
$847$	2.19063e14			0.502518
$848$	−5.26933e14			−1.20164
$849$			2.84143e14i			0.644167i
$850$		−	1.80618e14i		−	0.407068i
$851$	6.24744e14			1.39976
$852$	5.89607e14			1.31330
$853$	−3.39041e14			−0.750770			−0.375385	−	0.926869i	$-0.622489\pi$
$853$	−3.39041e14			−0.750770			−0.375385	+	0.926869i	$0.622489\pi$
$854$	−7.66650e14			−1.68775
$855$	3.47341e14			0.760196
$856$			1.04948e14i			0.228353i
$857$			3.69786e14i			0.799919i	0.916533	+	0.399960i	$0.130976\pi$
$857$			3.69786e14i			0.799919i	−0.916533	+	0.399960i	$0.869024\pi$
$858$		−	3.55085e14i		−	0.763653i
$859$		−	2.05420e14i		−	0.439214i	−0.975588	−	0.219607i	$-0.929523\pi$
$859$		−	2.05420e14i		−	0.439214i	0.975588	−	0.219607i	$-0.0704775\pi$
$860$		−	4.78693e14i		−	1.01757i
$861$	1.69340e13			0.0357886
$862$	2.55576e14			0.537011
$863$			3.55387e14i			0.742416i	0.928550	+	0.371208i	$0.121056\pi$
$863$			3.55387e14i			0.742416i	−0.928550	+	0.371208i	$0.878944\pi$
$864$			1.31747e14i			0.273635i
$865$			5.79587e14i			1.19684i
$866$			6.79762e14i			1.39562i
$867$	−2.73814e14			−0.558934
$868$		−	7.24057e14i		−	1.46952i
$869$			2.57538e14i			0.519688i
$870$		−	1.16232e15i		−	2.33200i
$871$	1.00671e15			2.00823
$872$	−6.81670e13			−0.135205
$873$			2.09349e14i			0.412856i
$874$	1.32760e15			2.60321
$875$	−3.23681e14			−0.631068
$876$		−	3.29473e12i		−	0.00638704i
$877$	1.27466e14			0.245694			0.122847	−	0.992426i	$-0.460797\pi$
$877$	1.27466e14			0.245694			0.122847	+	0.992426i	$0.460797\pi$
$878$			4.72657e14i			0.905886i
$879$	5.71985e13			0.109003
$880$			3.57932e14i			0.678246i
$881$			6.92437e14i			1.30467i	0.757931	+	0.652335i	$0.226211\pi$
$881$			6.92437e14i			1.30467i	−0.757931	+	0.652335i	$0.773789\pi$
$882$			1.18710e14i			0.222404i
$883$	−1.09840e14			−0.204625			−0.102312	−	0.994752i	$-0.532624\pi$
$883$	−1.09840e14			−0.204625			−0.102312	+	0.994752i	$0.532624\pi$
$884$			1.82351e14i			0.337790i
$885$	−4.90076e14	−	9.37467e13i	−0.902708	−	0.172679i
$886$	−4.78277e14			−0.876014
$887$			9.34334e14i			1.70170i	0.525406	+	0.850852i	$0.323914\pi$
$887$			9.34334e14i			1.70170i	−0.525406	+	0.850852i	$0.676086\pi$
$888$	−1.12372e14			−0.203514
$889$	6.09818e14			1.09823
$890$	−5.32893e14			−0.954311
$891$			3.54588e13i			0.0631445i
$892$	1.13167e15			2.00398
$893$			1.69244e14i			0.298028i
$894$	7.69430e14			1.34735
$895$			1.16612e15i			2.03062i
$896$		−	2.58358e14i		−	0.447385i
$897$	−6.42380e14			−1.10619
$898$		−	1.44469e15i		−	2.47397i
$899$		−	1.64460e15i		−	2.80068i
$900$	−3.64555e14			−0.617377
$901$	1.69974e14			0.286259
$902$	4.21023e13			0.0705137
$903$		−	1.36224e14i		−	0.226890i
$904$	1.68349e14			0.278849
$905$	−6.09540e14			−1.00406
$906$	7.02260e14			1.15042
$907$	4.62853e14			0.754062			0.377031	−	0.926201i	$-0.376945\pi$
$907$	4.62853e14			0.754062			0.377031	+	0.926201i	$0.376945\pi$
$908$		−	3.71866e14i		−	0.602500i
$909$		−	2.89102e13i		−	0.0465835i
$910$	1.71608e15			2.74999
$911$	4.23336e14			0.674673			0.337337	−	0.941384i	$-0.390474\pi$
$911$	4.23336e14			0.674673			0.337337	+	0.941384i	$0.390474\pi$
$912$	3.91242e14			0.620114
$913$	3.20157e14			0.504672
$914$	−1.35509e15			−2.12441
$915$			9.02180e14i			1.40665i
$916$		−	6.80540e14i		−	1.05530i
$917$		−	4.34998e14i		−	0.670873i
$918$		−	3.32923e13i		−	0.0510658i
$919$			4.78489e14i			0.729952i	0.931017	+	0.364976i	$0.118923\pi$
$919$			4.78489e14i			0.729952i	−0.931017	+	0.364976i	$0.881077\pi$
$920$	−3.95220e14			−0.599653
$921$	5.43733e13			0.0820517
$922$			3.57670e14i			0.536820i
$923$			1.97726e15i			2.95158i
$924$		−	1.98032e14i		−	0.294019i
$925$			1.18898e15i			1.75576i
$926$	−1.60804e14			−0.236179
$927$			3.85941e14i			0.563797i
$928$		−	1.67125e15i		−	2.42829i
$929$		−	3.29545e14i		−	0.476252i	−0.971234	−	0.238126i	$-0.923467\pi$
$929$		−	3.29545e14i		−	0.476252i	0.971234	−	0.238126i	$-0.0765330\pi$
$930$	−1.55781e15			−2.23923
$931$	4.50004e14			0.643380
$932$			1.03605e15i			1.47333i
$933$	−3.55805e14			−0.503274
$934$	1.70208e15			2.39466
$935$		−	1.15459e14i		−	0.161574i
$936$	1.15545e14			0.160832
$937$		−	5.89156e14i		−	0.815704i	−0.913048	−	0.407852i	$-0.866278\pi$
$937$		−	5.89156e14i		−	0.815704i	0.913048	−	0.407852i	$-0.133722\pi$
$938$	1.02648e15			1.41363
$939$			1.67925e14i			0.230032i
$940$		−	2.93421e14i		−	0.399808i
$941$			8.32873e14i			1.12883i	0.825489	+	0.564417i	$0.190899\pi$
$941$			8.32873e14i			1.12883i	−0.825489	+	0.564417i	$0.809101\pi$
$942$	1.03098e14			0.138994
$943$		−	7.61668e13i		−	0.102143i
$944$	−5.52018e14	−	1.05596e14i	−0.736366	−	0.140859i
$945$	−1.71368e14			−0.227390
$946$		−	3.38688e14i		−	0.447038i
$947$	2.84071e14			0.372972			0.186486	−	0.982458i	$-0.440290\pi$
$947$	2.84071e14			0.372972			0.186486	+	0.982458i	$0.440290\pi$
$948$	−4.88049e14			−0.637414
$949$	1.10490e13			0.0143546
$950$			2.52661e15i			3.26528i
$951$	4.58521e14			0.589463
$952$			3.19265e13i			0.0408288i
$953$	−9.15181e14			−1.16424			−0.582120	−	0.813103i	$-0.697777\pi$
$953$	−9.15181e14			−1.16424			−0.582120	+	0.813103i	$0.697777\pi$
$954$		−	6.27235e14i		−	0.793758i
$955$		−	2.00136e15i		−	2.51947i
$956$	1.13890e15			1.42625
$957$		−	4.49804e14i		−	0.560356i
$958$			1.42888e15i			1.77079i
$959$	−8.59345e14			−1.05944
$960$	−1.02121e15			−1.25245
$961$	−1.38456e15			−1.68926
$962$		−	2.19465e15i		−	2.66373i
$963$	2.04679e14			0.247139
$964$	−2.55659e14			−0.307098
$965$	9.84833e14			1.17686
$966$	−6.54998e14			−0.778671
$967$			1.12141e15i			1.32627i	0.748501	+	0.663133i	$0.230774\pi$
$967$			1.12141e15i			1.32627i	−0.748501	+	0.663133i	$0.769226\pi$
$968$			1.77228e14i			0.208524i
$969$	−1.26204e14			−0.147725
$970$	−2.51549e15			−2.92930
$971$	3.73519e14			0.432729			0.216365	−	0.976313i	$-0.430580\pi$
$971$	3.73519e14			0.432729			0.216365	+	0.976313i	$0.430580\pi$
$972$	−6.71964e13			−0.0774488
$973$	1.42899e14			0.163858
$974$			1.92329e15i			2.19407i
$975$		−	1.22254e15i		−	1.38753i
$976$			1.01621e15i			1.14745i
$977$			1.25728e15i			1.41241i	0.708009	+	0.706203i	$0.249594\pi$
$977$			1.25728e15i			1.41241i	−0.708009	+	0.706203i	$0.750406\pi$
$978$		−	1.16987e15i		−	1.30750i
$979$	−2.06223e14			−0.229311
$980$	−7.80177e14			−0.863103
$981$			1.32945e14i			0.146328i
$982$			2.10266e15i			2.30256i
$983$		−	9.08229e14i		−	0.989527i	−0.869028	−	0.494763i	$-0.835255\pi$
$983$		−	9.08229e14i		−	0.989527i	0.869028	−	0.494763i	$-0.164745\pi$
$984$			1.37001e13i			0.0148508i
$985$	1.86751e15			2.01411
$986$			4.22322e14i			0.453168i
$987$		−	8.35002e13i		−	0.0891460i
$988$		−	2.55085e15i		−	2.70957i
$989$	−6.12716e14			−0.647557
$990$	−4.26065e14			−0.448023
$991$			1.06447e15i			1.11369i	0.830617	+	0.556844i	$0.187988\pi$
$991$			1.06447e15i			1.11369i	−0.830617	+	0.556844i	$0.812012\pi$
$992$	−2.23990e15			−2.33169
$993$	4.33994e14			0.449508
$994$			2.01610e15i			2.07768i
$995$	−1.48085e15			−1.51843
$996$			6.06716e14i			0.618997i
$997$	3.36798e14			0.341895			0.170948	−	0.985280i	$-0.445317\pi$
$997$	3.36798e14			0.341895			0.170948	+	0.985280i	$0.445317\pi$
$998$			2.54436e15i			2.56996i
$999$			2.19158e14i			0.220257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.16	✓	100
59.58	odd	2	inner	177.11.c.a.58.85	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.16	✓	100	1.1	even	1	trivial
177.11.c.a.58.85	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)

\(f(q)\)	\(=\)	\(q-47.5424i q^{2} +140.296 q^{3} -1236.28 q^{4} -4974.64 q^{5} -6670.02i q^{6} +12474.7 q^{7} +10092.4i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q-47.5424i q^{2} +140.296 q^{3} -1236.28 q^{4} -4974.64 q^{5} -6670.02i q^{6} +12474.7 q^{7} +10092.4i q^{8} +19683.0 q^{9} +236507. i q^{10} +91525.3i q^{11} -173446. q^{12} -581654. i q^{13} -593078. i q^{14} -697923. q^{15} -786135. q^{16} +253586. q^{17} -935778. i q^{18} -3.54734e6 q^{19} +6.15006e6 q^{20} +1.75015e6 q^{21} +4.35134e6 q^{22} -7.87195e6i q^{23} +1.41593e6i q^{24} +1.49815e7 q^{25} -2.76532e7 q^{26} +2.76145e6 q^{27} -1.54223e7 q^{28} -3.50297e7 q^{29} +3.31810e7i q^{30} +4.69488e7i q^{31} +4.77094e7i q^{32} +1.28406e7i q^{33} -1.20561e7i q^{34} -6.20573e7 q^{35} -2.43337e7 q^{36} +7.93633e7i q^{37} +1.68649e8i q^{38} -8.16037e7i q^{39} -5.02061e7i q^{40} +9.67573e6 q^{41} -8.32066e7i q^{42} -7.78354e7i q^{43} -1.13151e8i q^{44} -9.79159e7 q^{45} -3.74251e8 q^{46} -4.77102e7i q^{47} -1.10292e8 q^{48} -1.26857e8 q^{49} -7.12255e8i q^{50} +3.55772e7 q^{51} +7.19088e8i q^{52} +6.70282e8 q^{53} -1.31286e8i q^{54} -4.55306e8i q^{55} +1.25900e8i q^{56} -4.97678e8 q^{57} +1.66540e9i q^{58} +(7.02192e8 + 1.34322e8i) q^{59} +8.62830e8 q^{60} -1.29266e9i q^{61} +2.23206e9 q^{62} +2.45540e8 q^{63} +1.46322e9 q^{64} +2.89352e9i q^{65} +6.10475e8 q^{66} +1.73077e9i q^{67} -3.13504e8 q^{68} -1.10440e9i q^{69} +2.95035e9i q^{70} -3.39938e9 q^{71} +1.98649e8i q^{72} +1.89958e7i q^{73} +3.77312e9 q^{74} +2.10184e9 q^{75} +4.38551e9 q^{76} +1.14175e9i q^{77} -3.87964e9 q^{78} +2.81385e9 q^{79} +3.91074e9 q^{80} +3.87420e8 q^{81} -4.60008e8i q^{82} -3.49802e9i q^{83} -2.16368e9 q^{84} -1.26150e9 q^{85} -3.70048e9 q^{86} -4.91453e9 q^{87} -9.23711e8 q^{88} +2.25318e9i q^{89} +4.65516e9i q^{90} -7.25596e9i q^{91} +9.73195e9i q^{92} +6.58674e9i q^{93} -2.26826e9 q^{94} +1.76468e10 q^{95} +6.69344e9i q^{96} +1.06360e10i q^{97} +6.03108e9i q^{98} +1.80149e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 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

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Database

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