LMFDB - Embedded newform 12.14.b.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,14,Mod(11,12)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	12.b (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:	$12.8677114742$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	12.11
Dual form			12.14.b.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-63.1407 + 64.8479i) q^{2} +(-1256.10 + 128.555i) q^{3} +(-218.513 - 8189.09i) q^{4} -1788.84i q^{5} +(70974.7 - 89572.8i) q^{6} -316886. i q^{7} +(544842. + 502894. i) q^{8} +(1.56127e6 - 322956. i) q^{9} +O(q^{10})$	\(q+(-63.1407 + 64.8479i) q^{2} +(-1256.10 + 128.555i) q^{3} +(-218.513 - 8189.09i) q^{4} -1788.84i q^{5} +(70974.7 - 89572.8i) q^{6} -316886. i q^{7} +(544842. + 502894. i) q^{8} +(1.56127e6 - 322956. i) q^{9} +(116003. + 112949. i) q^{10} -5.24655e6 q^{11} +(1.32722e6 + 1.02583e7i) q^{12} -7.16394e6 q^{13} +(2.05494e7 + 2.00084e7i) q^{14} +(229964. + 2.24697e6i) q^{15} +(-6.70134e7 + 3.57884e6i) q^{16} +1.30275e8i q^{17} +(-7.76366e7 + 1.21637e8i) q^{18} +1.09425e8i q^{19} +(-1.46490e7 + 390884. i) q^{20} +(4.07372e7 + 3.98042e8i) q^{21} +(3.31270e8 - 3.40228e8i) q^{22} +5.41194e8 q^{23} +(-7.49028e8 - 5.61645e8i) q^{24} +1.21750e9 q^{25} +(4.52336e8 - 4.64567e8i) q^{26} +(-1.91960e9 + 6.06375e8i) q^{27} +(-2.59501e9 + 6.92437e7i) q^{28} -4.73901e9i q^{29} +(-1.60231e8 - 1.26962e8i) q^{30} +8.25158e9i q^{31} +(3.99919e9 - 4.57165e9i) q^{32} +(6.59021e9 - 6.74468e8i) q^{33} +(-8.44807e9 - 8.22566e9i) q^{34} -5.66859e8 q^{35} +(-2.98587e9 - 1.27148e10i) q^{36} +1.92180e10 q^{37} +(-7.09599e9 - 6.90917e9i) q^{38} +(8.99865e9 - 9.20957e8i) q^{39} +(8.99598e8 - 9.74636e8i) q^{40} +4.37343e10i q^{41} +(-2.83844e10 - 2.24909e10i) q^{42} +6.99550e10i q^{43} +(1.14644e9 + 4.29644e10i) q^{44} +(-5.77717e8 - 2.79286e9i) q^{45} +(-3.41714e10 + 3.50953e10i) q^{46} -3.55446e10 q^{47} +(8.37157e10 - 1.31103e10i) q^{48} -3.52800e9 q^{49} +(-7.68740e10 + 7.89526e10i) q^{50} +(-1.67475e10 - 1.63639e11i) q^{51} +(1.56541e9 + 5.86661e10i) q^{52} -7.53075e10i q^{53} +(8.18827e10 - 1.62769e11i) q^{54} +9.38523e9i q^{55} +(1.59360e11 - 1.72653e11i) q^{56} +(-1.40671e10 - 1.37449e11i) q^{57} +(3.07315e11 + 2.99224e11i) q^{58} +2.47157e11 q^{59} +(1.83504e10 - 2.37418e9i) q^{60} -5.16877e11 q^{61} +(-5.35098e11 - 5.21011e11i) q^{62} +(-1.02340e11 - 4.94745e11i) q^{63} +(4.39507e10 + 5.47996e11i) q^{64} +1.28151e10i q^{65} +(-3.72372e11 + 4.69948e11i) q^{66} -1.50785e11i q^{67} +(1.06683e12 - 2.84667e10i) q^{68} +(-6.79796e11 + 6.95730e10i) q^{69} +(3.57919e10 - 3.67597e10i) q^{70} +3.92382e11 q^{71} +(1.01306e12 + 6.09194e11i) q^{72} +5.99093e11 q^{73} +(-1.21344e12 + 1.24625e12i) q^{74} +(-1.52931e12 + 1.56516e11i) q^{75} +(8.96091e11 - 2.39107e10i) q^{76} +1.66256e12i q^{77} +(-5.08459e11 + 6.41694e11i) q^{78} -1.31879e11i q^{79} +(6.40197e9 + 1.19876e11i) q^{80} +(2.33326e12 - 1.00844e12i) q^{81} +(-2.83608e12 - 2.76141e12i) q^{82} +1.71178e12 q^{83} +(3.25070e12 - 4.20578e11i) q^{84} +2.33041e11 q^{85} +(-4.53644e12 - 4.41701e12i) q^{86} +(6.09222e11 + 5.95269e12i) q^{87} +(-2.85854e12 - 2.63846e12i) q^{88} +3.37721e12i q^{89} +(2.17589e11 + 1.38880e11i) q^{90} +2.27015e12i q^{91} +(-1.18258e11 - 4.43188e12i) q^{92} +(-1.06078e12 - 1.03648e13i) q^{93} +(2.24431e12 - 2.30500e12i) q^{94} +1.95744e11 q^{95} +(-4.43569e12 + 6.25658e12i) q^{96} +1.18771e13 q^{97} +(2.22760e11 - 2.28784e11i) q^{98} +(-8.19128e12 + 1.69440e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9}+O(q^{10}) $ 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9	$ 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9} + 4403568 q^{10} - 139896 q^{12} - 17520048 q^{13} + 41046816 q^{16} - 102153744 q^{18} + 340864272 q^{21} + 401914896 q^{22} + 14766624 q^{24} - 3043252488 q^{25} + 3306349488 q^{28} + 3523891248 q^{30} - 10577805696 q^{33} + 5461322688 q^{34} + 16126437096 q^{36} - 29352930672 q^{37} - 5243368896 q^{40} + 35399300688 q^{42} + 36221734656 q^{45} + 1675946784 q^{46} + 27878547744 q^{48} - 165718477944 q^{49} - 6459860112 q^{52} - 10955701656 q^{54} + 590611321584 q^{57} - 440462601456 q^{58} - 208761511104 q^{60} + 555426186192 q^{61} - 741528997248 q^{64} + 263546293968 q^{66} - 122266973952 q^{69} - 885399371232 q^{70} + 625428177984 q^{72} + 365028975600 q^{73} + 1427271642000 q^{76} + 1481181276240 q^{78} - 2327652239400 q^{81} + 874644720480 q^{82} - 6757787638224 q^{84} - 3308476422144 q^{85} + 11607512359104 q^{88} + 4426488729648 q^{90} - 3971016902448 q^{93} - 3078833939904 q^{94} - 6470779487616 q^{96} - 4159752429648 q^{97}+O(q^{100}) $ 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9 + 4403568 * q^10 - 139896 * q^12 - 17520048 * q^13 + 41046816 * q^16 - 102153744 * q^18 + 340864272 * q^21 + 401914896 * q^22 + 14766624 * q^24 - 3043252488 * q^25 + 3306349488 * q^28 + 3523891248 * q^30 - 10577805696 * q^33 + 5461322688 * q^34 + 16126437096 * q^36 - 29352930672 * q^37 - 5243368896 * q^40 + 35399300688 * q^42 + 36221734656 * q^45 + 1675946784 * q^46 + 27878547744 * q^48 - 165718477944 * q^49 - 6459860112 * q^52 - 10955701656 * q^54 + 590611321584 * q^57 - 440462601456 * q^58 - 208761511104 * q^60 + 555426186192 * q^61 - 741528997248 * q^64 + 263546293968 * q^66 - 122266973952 * q^69 - 885399371232 * q^70 + 625428177984 * q^72 + 365028975600 * q^73 + 1427271642000 * q^76 + 1481181276240 * q^78 - 2327652239400 * q^81 + 874644720480 * q^82 - 6757787638224 * q^84 - 3308476422144 * q^85 + 11607512359104 * q^88 + 4426488729648 * q^90 - 3971016902448 * q^93 - 3078833939904 * q^94 - 6470779487616 * q^96 - 4159752429648 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−63.1407	+	64.8479i	−0.697612	+	0.716475i
$2$	−63.1407	+	64.8479i	−0.697612	+	0.716475i
$3$	−1256.10	+	128.555i	−0.994804	+	0.101812i
$3$	−1256.10	+	128.555i	−0.994804	+	0.101812i
$4$	−218.513	−	8189.09i	−0.0266739	−	0.999644i
$5$		−	1788.84i		−	0.0511996i	−0.999672	−	0.0255998i	$-0.991850\pi$
$5$		−	1788.84i		−	0.0511996i	0.999672	−	0.0255998i	$-0.00814956\pi$
$6$	70974.7	−	89572.8i	0.621041	−	0.783778i
$7$		−	316886.i		−	1.01804i	−0.860754	−	0.509022i	$-0.830007\pi$
$7$		−	316886.i		−	1.01804i	0.860754	−	0.509022i	$-0.169993\pi$
$8$	544842.	+	502894.i	0.734828	+	0.678253i
$9$	1.56127e6	−	322956.i	0.979269	−	0.202566i
$10$	116003.	+	112949.i	0.0366833	+	0.0357175i
$11$	−5.24655e6			−0.892937			−0.446469	−	0.894799i	$-0.647319\pi$
$11$	−5.24655e6			−0.892937			−0.446469	+	0.894799i	$0.647319\pi$
$12$	1.32722e6	+	1.02583e7i	0.128311	+	0.991734i
$13$	−7.16394e6			−0.411642			−0.205821	−	0.978590i	$-0.565987\pi$
$13$	−7.16394e6			−0.411642			−0.205821	+	0.978590i	$0.565987\pi$
$14$	2.05494e7	+	2.00084e7i	0.729403	+	0.710200i
$15$	229964.	+	2.24697e6i	0.00521274	+	0.0509336i
$16$	−6.70134e7	+	3.57884e6i	−0.998577	+	0.0533288i
$17$			1.30275e8i			1.30901i	0.756057	+	0.654506i	$0.227123\pi$
$17$			1.30275e8i			1.30901i	−0.756057	+	0.654506i	$0.772877\pi$
$18$	−7.76366e7	+	1.21637e8i	−0.538016	+	0.842934i
$19$			1.09425e8i			0.533603i	0.963752	+	0.266801i	$0.0859668\pi$
$19$			1.09425e8i			0.533603i	−0.963752	+	0.266801i	$0.914033\pi$
$20$	−1.46490e7	+	390884.i	−0.0511814	+	0.00136569i
$21$	4.07372e7	+	3.98042e8i	0.103649	+	1.01275i
$22$	3.31270e8	−	3.40228e8i	0.622924	−	0.639768i
$23$	5.41194e8			0.762293			0.381147	−	0.924515i	$-0.375529\pi$
$23$	5.41194e8			0.762293			0.381147	+	0.924515i	$0.375529\pi$
$24$	−7.49028e8	−	5.61645e8i	−0.800064	−	0.599914i
$25$	1.21750e9			0.997379
$26$	4.52336e8	−	4.64567e8i	0.287167	−	0.294932i
$27$	−1.91960e9	+	6.06375e8i	−0.953556	+	0.301215i
$28$	−2.59501e9	+	6.92437e7i	−1.01768	+	0.0271552i
$29$		−	4.73901e9i		−	1.47945i	−0.672908	−	0.739726i	$-0.734955\pi$
$29$		−	4.73901e9i		−	1.47945i	0.672908	−	0.739726i	$-0.265045\pi$
$30$	−1.60231e8	−	1.26962e8i	−0.0401291	−	0.0317971i
$31$			8.25158e9i			1.66988i	0.550338	+	0.834942i	$0.314499\pi$
$31$			8.25158e9i			1.66988i	−0.550338	+	0.834942i	$0.685501\pi$
$32$	3.99919e9	−	4.57165e9i	0.658411	−	0.752659i
$33$	6.59021e9	−	6.74468e8i	0.888297	−	0.0909118i
$34$	−8.44807e9	−	8.22566e9i	−0.937874	−	0.913183i
$35$	−5.66859e8			−0.0521234
$36$	−2.98587e9	−	1.27148e10i	−0.228615	−	0.973517i
$37$	1.92180e10			1.23140			0.615698	−	0.787982i	$-0.288874\pi$
$37$	1.92180e10			1.23140			0.615698	+	0.787982i	$0.288874\pi$
$38$	−7.09599e9	−	6.90917e9i	−0.382313	−	0.372248i
$39$	8.99865e9	−	9.20957e8i	0.409503	−	0.0419102i
$40$	8.99598e8	−	9.74636e8i	0.0347263	−	0.0376229i
$41$			4.37343e10i			1.43789i	0.695065	+	0.718947i	$0.255376\pi$
$41$			4.37343e10i			1.43789i	−0.695065	+	0.718947i	$0.744624\pi$
$42$	−2.83844e10	−	2.24909e10i	−0.797920	−	0.632247i
$43$			6.99550e10i			1.68762i	0.536645	+	0.843808i	$0.319692\pi$
$43$			6.99550e10i			1.68762i	−0.536645	+	0.843808i	$0.680308\pi$
$44$	1.14644e9	+	4.29644e10i	0.0238181	+	0.892620i
$45$	−5.77717e8	−	2.79286e9i	−0.0103713	−	0.0501382i
$46$	−3.41714e10	+	3.50953e10i	−0.531785	+	0.546164i
$47$	−3.55446e10			−0.480992			−0.240496	−	0.970650i	$-0.577310\pi$
$47$	−3.55446e10			−0.480992			−0.240496	+	0.970650i	$0.577310\pi$
$48$	8.37157e10	−	1.31103e10i	0.987959	−	0.154719i
$49$	−3.52800e9			−0.0364128
$50$	−7.68740e10	+	7.89526e10i	−0.695784	+	0.714597i
$51$	−1.67475e10	−	1.63639e11i	−0.133273	−	1.30221i
$52$	1.56541e9	+	5.86661e10i	0.0109801	+	0.411496i
$53$		−	7.53075e10i		−	0.466708i	−0.972392	−	0.233354i	$-0.925030\pi$
$53$		−	7.53075e10i		−	0.466708i	0.972392	−	0.233354i	$-0.0749701\pi$
$54$	8.18827e10	−	1.62769e11i	0.449400	−	0.893331i
$55$			9.38523e9i			0.0457180i
$56$	1.59360e11	−	1.72653e11i	0.690491	−	0.748087i
$57$	−1.40671e10	−	1.37449e11i	−0.0543272	−	0.530830i
$58$	3.07315e11	+	2.99224e11i	1.05999	+	1.03208i
$59$	2.47157e11			0.762842			0.381421	−	0.924401i	$-0.375435\pi$
$59$	2.47157e11			0.762842			0.381421	+	0.924401i	$0.375435\pi$
$60$	1.83504e10	−	2.37418e9i	0.0507764	−	0.00656948i
$61$	−5.16877e11			−1.28453			−0.642264	−	0.766484i	$-0.722005\pi$
$61$	−5.16877e11			−1.28453			−0.642264	+	0.766484i	$0.722005\pi$
$62$	−5.35098e11	−	5.21011e11i	−1.19643	−	1.16493i
$63$	−1.02340e11	−	4.94745e11i	−0.206221	−	0.996938i
$64$	4.39507e10	+	5.47996e11i	0.0799458	+	0.996799i
$65$			1.28151e10i			0.0210759i
$66$	−3.72372e11	+	4.69948e11i	−0.554551	+	0.699864i
$67$		−	1.50785e11i		−	0.203644i	−0.994803	−	0.101822i	$-0.967533\pi$
$67$		−	1.50785e11i		−	0.203644i	0.994803	−	0.101822i	$-0.0324673\pi$
$68$	1.06683e12	−	2.84667e10i	1.30855	−	0.0349164i
$69$	−6.79796e11	+	6.95730e10i	−0.758332	+	0.0776107i
$70$	3.57919e10	−	3.67597e10i	0.0363620	−	0.0373452i
$71$	3.92382e11			0.363522			0.181761	−	0.983343i	$-0.441820\pi$
$71$	3.92382e11			0.363522			0.181761	+	0.983343i	$0.441820\pi$
$72$	1.01306e12	+	6.09194e11i	0.856986	+	0.515340i
$73$	5.99093e11			0.463336			0.231668	−	0.972795i	$-0.425582\pi$
$73$	5.99093e11			0.463336			0.231668	+	0.972795i	$0.425582\pi$
$74$	−1.21344e12	+	1.24625e12i	−0.859038	+	0.882266i
$75$	−1.52931e12	+	1.56516e11i	−0.992196	+	0.101545i
$76$	8.96091e11	−	2.39107e10i	0.533413	−	0.0142333i
$77$			1.66256e12i			0.909049i
$78$	−5.08459e11	+	6.41694e11i	−0.255647	+	0.322636i
$79$		−	1.31879e11i		−	0.0610381i	−0.999534	−	0.0305190i	$-0.990284\pi$
$79$		−	1.31879e11i		−	0.0610381i	0.999534	−	0.0305190i	$-0.00971602\pi$
$80$	6.40197e9	+	1.19876e11i	0.00273041	+	0.0511268i
$81$	2.33326e12	−	1.00844e12i	0.917934	−	0.396733i
$82$	−2.83608e12	−	2.76141e12i	−1.03022	−	1.00309i
$83$	1.71178e12			0.574698			0.287349	−	0.957826i	$-0.407226\pi$
$83$	1.71178e12			0.574698			0.287349	+	0.957826i	$0.407226\pi$
$84$	3.25070e12	−	4.20578e11i	1.00963	−	0.130626i
$85$	2.33041e11			0.0670209
$86$	−4.53644e12	−	4.41701e12i	−1.20914	−	1.17730i
$87$	6.09222e11	+	5.95269e12i	0.150626	+	1.47176i
$88$	−2.85854e12	−	2.63846e12i	−0.656156	−	0.605637i
$89$			3.37721e12i			0.720317i	0.932891	+	0.360158i	$0.117277\pi$
$89$			3.37721e12i			0.720317i	−0.932891	+	0.360158i	$0.882723\pi$
$90$	2.17589e11	+	1.38880e11i	0.0431579	+	0.0275462i
$91$			2.27015e12i			0.419070i
$92$	−1.18258e11	−	4.43188e12i	−0.0203333	−	0.762022i
$93$	−1.06078e12	−	1.03648e13i	−0.170014	−	1.66121i
$94$	2.24431e12	−	2.30500e12i	0.335546	−	0.344619i
$95$	1.95744e11			0.0273203
$96$	−4.43569e12	+	6.25658e12i	−0.578360	+	0.815782i
$97$	1.18771e13			1.44776			0.723879	−	0.689927i	$-0.242357\pi$
$97$	1.18771e13			1.44776			0.723879	+	0.689927i	$0.242357\pi$
$98$	2.22760e11	−	2.28784e11i	0.0254020	−	0.0260889i
$99$	−8.19128e12	+	1.69440e12i	−0.874425	+	0.180879i
$100$	−2.66040e11	−	9.97024e12i	−0.0266040	−	0.997024i
$101$			3.92540e12i			0.367955i	0.982930	+	0.183978i	$0.0588974\pi$
$101$			3.92540e12i			0.367955i	−0.982930	+	0.183978i	$0.941103\pi$
$102$	1.16691e13	+	9.24624e12i	1.02597	+	0.812950i
$103$		−	1.33502e13i		−	1.10166i	−0.834618	−	0.550829i	$-0.814312\pi$
$103$		−	1.33502e13i		−	1.10166i	0.834618	−	0.550829i	$-0.185688\pi$
$104$	−3.90322e12	−	3.60270e12i	−0.302487	−	0.279198i
$105$	7.12034e11	−	7.28724e10i	0.0518526	−	0.00530680i
$106$	4.88354e12	+	4.75497e12i	0.334385	+	0.325581i
$107$	1.88456e13			1.21399			0.606995	−	0.794706i	$-0.292375\pi$
$107$	1.88456e13			1.21399			0.606995	+	0.794706i	$0.292375\pi$
$108$	5.38511e12	+	1.55873e13i	0.326543	+	0.945182i
$109$	−2.97310e13			−1.69800			−0.848998	−	0.528396i	$-0.822794\pi$
$109$	−2.97310e13			−1.69800			−0.848998	+	0.528396i	$0.822794\pi$
$110$	−6.08613e11	−	5.92590e11i	−0.0327559	−	0.0318935i
$111$	−2.41399e13	+	2.47057e12i	−1.22500	+	0.125371i
$112$	1.13408e12	+	2.12356e13i	0.0542911	+	1.01659i
$113$			2.52666e13i			1.14166i	0.821068	+	0.570831i	$0.193379\pi$
$113$			2.52666e13i			1.14166i	−0.821068	+	0.570831i	$0.806621\pi$
$114$	9.80150e12	+	7.76641e12i	0.418226	+	0.331389i
$115$		−	9.68110e11i		−	0.0390291i
$116$	−3.88082e13	+	1.03553e12i	−1.47893	+	0.0394627i
$117$	−1.11848e13	+	2.31364e12i	−0.403108	+	0.0833848i
$118$	−1.56057e13	+	1.60276e13i	−0.532168	+	0.546558i
$119$	4.12824e13			1.33263
$120$	−1.00469e12	+	1.33989e12i	−0.0307154	+	0.0409630i
$121$	−6.99647e12			−0.202663
$122$	3.26360e13	−	3.35184e13i	0.896102	−	0.920332i
$123$	−5.62224e12	−	5.49348e13i	−0.146395	−	1.43042i
$124$	6.75729e13	−	1.80308e12i	1.66929	−	0.0445423i
$125$		−	4.36156e12i		−	0.102265i
$126$	3.85451e13	+	2.46020e13i	0.858144	+	0.547724i
$127$		−	5.63834e12i		−	0.119241i	−0.998221	−	0.0596207i	$-0.981011\pi$
$127$		−	5.63834e12i		−	0.119241i	0.998221	−	0.0596207i	$-0.0189891\pi$
$128$	−3.83115e13	−	3.17507e13i	−0.769953	−	0.638100i
$129$	−8.99304e12	−	8.78707e13i	−0.171820	−	1.67885i
$130$	−8.31036e11	−	8.09157e11i	−0.0151004	−	0.0147028i
$131$	−5.50956e13			−0.952474			−0.476237	−	0.879317i	$-0.658000\pi$
$131$	−5.50956e13			−0.952474			−0.476237	+	0.879317i	$0.658000\pi$
$132$	−6.96331e12	−	5.38204e13i	−0.114574	−	0.885556i
$133$	3.46753e13			0.543231
$134$	9.77811e12	+	9.52067e12i	0.145906	+	0.142065i
$135$	1.08471e12	+	3.43386e12i	0.0154221	+	0.0488217i
$136$	−6.55146e13	+	7.09794e13i	−0.887841	+	0.961899i
$137$			1.91320e12i			0.0247216i	0.999924	+	0.0123608i	$0.00393466\pi$
$137$			1.91320e12i			0.0247216i	−0.999924	+	0.0123608i	$0.996065\pi$
$138$	3.84111e13	−	4.84763e13i	0.473416	−	0.597468i
$139$			1.24160e14i			1.46011i	0.683388	+	0.730056i	$0.260506\pi$
$139$			1.24160e14i			1.46011i	−0.683388	+	0.730056i	$0.739494\pi$
$140$	1.23866e11	+	4.64206e12i	0.00139034	+	0.0521049i
$141$	4.46478e13	−	4.56943e12i	0.478493	−	0.0489708i
$142$	−2.47753e13	+	2.54452e13i	−0.253597	+	0.260454i
$143$	3.75859e13			0.367571
$144$	−1.03470e14	+	2.72299e13i	−0.967072	+	0.254501i
$145$	−8.47734e12			−0.0757473
$146$	−3.78272e13	+	3.88500e13i	−0.323229	+	0.331969i
$147$	4.43153e12	−	4.53541e11i	0.0362236	−	0.00370726i
$148$	−4.19939e12	−	1.57378e14i	−0.0328462	−	1.23096i
$149$			1.44479e14i			1.08167i	0.841130	+	0.540833i	$0.181891\pi$
$149$			1.44479e14i			1.08167i	−0.841130	+	0.540833i	$0.818109\pi$
$150$	8.64120e13	−	1.09055e14i	0.619413	−	0.781723i
$151$			7.48494e13i			0.513852i	0.966431	+	0.256926i	$0.0827097\pi$
$151$			7.48494e13i			0.513852i	−0.966431	+	0.256926i	$0.917290\pi$
$152$	−5.50292e13	+	5.96194e13i	−0.361918	+	0.392107i
$153$	4.20731e13	+	2.03395e14i	0.265161	+	1.28187i
$154$	−1.07814e14	−	1.04975e14i	−0.651311	−	0.634164i
$155$	1.47608e13			0.0854974
$156$	−9.50811e12	−	7.34895e13i	−0.0528183	−	0.408240i
$157$	2.08506e14			1.11114			0.555572	−	0.831468i	$-0.312499\pi$
$157$	2.08506e14			1.11114			0.555572	+	0.831468i	$0.312499\pi$
$158$	8.55211e12	+	8.32695e12i	0.0437323	+	0.0425809i
$159$	9.68113e12	+	9.45941e13i	0.0475165	+	0.464283i
$160$	−8.17795e12	−	7.15391e12i	−0.0385358	−	0.0337104i
$161$		−	1.71497e14i		−	0.776048i
$162$	−8.19285e13	+	2.14981e14i	−0.356112	+	0.934443i
$163$		−	1.33816e14i		−	0.558841i	−0.960169	−	0.279420i	$-0.909858\pi$
$163$		−	1.33816e14i		−	0.558841i	0.960169	−	0.279420i	$-0.0901423\pi$
$164$	3.58144e14	−	9.55649e12i	1.43738	−	0.0383542i
$165$	−1.20652e12	−	1.17888e13i	−0.00465465	−	0.0454805i
$166$	−1.08083e14	+	1.11005e14i	−0.400917	+	0.411757i
$167$	−1.42615e14			−0.508754			−0.254377	−	0.967105i	$-0.581870\pi$
$167$	−1.42615e14			−0.508754			−0.254377	+	0.967105i	$0.581870\pi$
$168$	−1.77978e14	+	2.37357e14i	−0.610739	+	0.814500i
$169$	−2.51553e14			−0.830551
$170$	−1.47144e13	+	1.51123e13i	−0.0467546	+	0.0480188i
$171$	3.53394e13	+	1.70842e14i	0.108090	+	0.522540i
$172$	5.72867e14	−	1.52860e13i	1.68702	−	0.0450153i
$173$		−	5.82603e14i		−	1.65224i	−0.563495	−	0.826119i	$-0.690544\pi$
$173$		−	5.82603e14i		−	1.65224i	0.563495	−	0.826119i	$-0.309456\pi$
$174$	−4.24486e14	−	3.36350e14i	−1.15956	−	0.918801i
$175$		−	3.85810e14i		−	1.01537i
$176$	3.51589e14	−	1.87765e13i	0.891667	−	0.0476193i
$177$	−3.10455e14	+	3.17732e13i	−0.758878	+	0.0776666i
$178$	−2.19005e14	−	2.13240e14i	−0.516089	−	0.502502i
$179$	−3.68459e14			−0.837230			−0.418615	−	0.908164i	$-0.637484\pi$
$179$	−3.68459e14			−0.837230			−0.418615	+	0.908164i	$0.637484\pi$
$180$	−2.27448e13	+	5.34125e12i	−0.0498437	+	0.0117050i
$181$	−1.07619e14			−0.227499			−0.113749	−	0.993509i	$-0.536286\pi$
$181$	−1.07619e14			−0.227499			−0.113749	+	0.993509i	$0.536286\pi$
$182$	−1.47215e14	−	1.43339e14i	−0.300253	−	0.292348i
$183$	6.49251e14	−	6.64469e13i	1.27785	−	0.130780i
$184$	2.94865e14	+	2.72163e14i	0.560155	+	0.517028i
$185$		−	3.43780e13i		−	0.0630470i
$186$	7.39117e14	+	5.85654e14i	1.30882	+	1.03707i
$187$		−	6.83494e14i		−	1.16887i
$188$	7.76695e12	+	2.91078e14i	0.0128299	+	0.480821i
$189$	1.92152e14	+	6.08295e14i	0.306650	+	0.970762i
$190$	−1.23594e13	+	1.26936e13i	−0.0190589	+	0.0195743i
$191$	3.12597e14			0.465874			0.232937	−	0.972492i	$-0.425166\pi$
$191$	3.12597e14			0.465874			0.232937	+	0.972492i	$0.425166\pi$
$192$	−1.25654e14	−	6.82690e14i	−0.181017	−	0.983480i
$193$	−5.06705e14			−0.705720			−0.352860	−	0.935676i	$-0.614791\pi$
$193$	−5.06705e14			−0.705720			−0.352860	+	0.935676i	$0.614791\pi$
$194$	−7.49931e14	+	7.70209e14i	−1.00997	+	1.03728i
$195$	−1.64745e12	−	1.60972e13i	−0.00214578	−	0.0209664i
$196$	7.70912e11	+	2.88911e13i	0.000971271	+	0.0363998i
$197$			4.60855e14i			0.561738i	0.959746	+	0.280869i	$0.0906227\pi$
$197$			4.60855e14i			0.561738i	−0.959746	+	0.280869i	$0.909377\pi$
$198$	4.07324e14	−	6.38173e14i	0.480415	−	0.752688i
$199$			4.45986e14i			0.509068i	0.967064	+	0.254534i	$0.0819221\pi$
$199$			4.45986e14i			0.509068i	−0.967064	+	0.254534i	$0.918078\pi$
$200$	6.63347e14	+	6.12275e14i	0.732902	+	0.676475i
$201$	1.93841e13	+	1.89402e14i	0.0207335	+	0.202586i
$202$	−2.54554e14	−	2.47853e14i	−0.263631	−	0.256690i
$203$	−1.50173e15			−1.50615
$204$	−1.33639e15	+	1.72904e14i	−1.29819	+	0.167961i
$205$	7.82336e13			0.0736196
$206$	8.65735e14	+	8.42942e14i	0.789311	+	0.768530i
$207$	8.44950e14	−	1.74782e14i	0.746490	−	0.154415i
$208$	4.80080e14	−	2.56386e13i	0.411057	−	0.0219524i
$209$		−	5.74103e14i		−	0.476474i
$210$	−4.02327e13	+	5.07752e13i	−0.0323708	+	0.0408532i
$211$			8.55634e14i			0.667502i	0.942661	+	0.333751i	$0.108314\pi$
$211$			8.55634e14i			0.667502i	−0.942661	+	0.333751i	$0.891686\pi$
$212$	−6.16700e14	+	1.64556e13i	−0.466542	+	0.0124489i
$213$	−4.92873e14	+	5.04425e13i	−0.361633	+	0.0370109i
$214$	−1.18992e15	+	1.22210e15i	−0.846895	+	0.869794i
$215$	1.25138e14			0.0864053
$216$	−1.35082e15	−	6.34977e14i	−0.905000	−	0.425411i
$217$	2.61482e15			1.70001
$218$	1.87723e15	−	1.92799e15i	1.18454	−	1.21657i
$219$	−7.52524e14	+	7.70162e13i	−0.460928	+	0.0471732i
$220$	7.68565e13	−	2.05079e12i	0.0457018	−	0.00121948i
$221$		−	9.33283e14i		−	0.538844i
$222$	1.36400e15	−	1.72141e15i	0.764749	−	0.965141i
$223$			2.84800e15i			1.55081i	0.631464	+	0.775405i	$0.282454\pi$
$223$			2.84800e15i			1.55081i	−0.631464	+	0.775405i	$0.717546\pi$
$224$	−1.44869e15	−	1.26729e15i	−0.766239	−	0.670291i
$225$	1.90085e15	−	3.93200e14i	0.976702	−	0.202035i
$226$	−1.63849e15	−	1.59535e15i	−0.817973	−	0.796438i
$227$	7.52617e14			0.365095			0.182548	−	0.983197i	$-0.441566\pi$
$227$	7.52617e14			0.365095			0.182548	+	0.983197i	$0.441566\pi$
$228$	−1.12251e15	+	1.45231e14i	−0.529192	+	0.0684672i
$229$	−1.06088e15			−0.486110			−0.243055	−	0.970012i	$-0.578150\pi$
$229$	−1.06088e15			−0.486110			−0.243055	+	0.970012i	$0.578150\pi$
$230$	6.27799e13	+	6.11271e13i	0.0279634	+	0.0272272i
$231$	−2.13730e14	−	2.08835e15i	−0.0925522	−	0.904325i
$232$	2.38322e15	−	2.58201e15i	1.00344	−	1.08714i
$233$			5.68775e14i			0.232877i	0.993198	+	0.116439i	$0.0371478\pi$
$233$			5.68775e14i			0.232877i	−0.993198	+	0.116439i	$0.962852\pi$
$234$	5.56184e14	−	8.71399e14i	0.221470	−	0.346988i
$235$			6.35837e13i			0.0246266i
$236$	−5.40069e13	−	2.02399e15i	−0.0203480	−	0.762571i
$237$	1.69537e13	+	1.65654e14i	0.00621441	+	0.0607209i
$238$	−2.60660e15	+	2.67708e15i	−0.929660	+	0.954797i
$239$	4.42367e15			1.53531			0.767655	−	0.640864i	$-0.221424\pi$
$239$	4.42367e15			1.53531			0.767655	+	0.640864i	$0.221424\pi$
$240$	−2.34522e13	−	1.49754e14i	−0.00792155	−	0.0505831i
$241$	−3.03878e14			−0.0999054			−0.0499527	−	0.998752i	$-0.515907\pi$
$241$	−3.03878e14			−0.0999054			−0.0499527	+	0.998752i	$0.515907\pi$
$242$	4.41762e14	−	4.53707e14i	0.141380	−	0.145203i
$243$	−2.80118e15	+	1.56666e15i	−0.872772	+	0.488129i
$244$	1.12944e14	+	4.23275e15i	0.0342634	+	1.28407i
$245$			6.31103e12i			0.00186432i
$246$	3.91740e15	+	3.10403e15i	1.12699	+	0.892992i
$247$		−	7.83914e14i		−	0.219654i
$248$	−4.14967e15	+	4.49581e15i	−1.13260	+	1.22708i
$249$	−2.15017e15	+	2.20057e14i	−0.571712	+	0.0585113i
$250$	2.82838e14	+	2.75392e14i	0.0732704	+	0.0713413i
$251$	−6.10800e15			−1.54177			−0.770886	−	0.636973i	$-0.780186\pi$
$251$	−6.10800e15			−1.54177			−0.770886	+	0.636973i	$0.780186\pi$
$252$	−4.02915e15	+	9.46182e14i	−0.991083	+	0.232740i
$253$	−2.83940e15			−0.680680
$254$	3.65634e14	+	3.56008e14i	0.0854335	+	0.0831842i
$255$	−2.92724e14	+	2.99585e13i	−0.0666726	+	0.00682354i
$256$	4.47798e15	−	4.79660e14i	0.994312	−	0.106506i
$257$			6.36142e15i			1.37717i	0.725154	+	0.688587i	$0.241769\pi$
$257$			6.36142e15i			1.37717i	−0.725154	+	0.688587i	$0.758231\pi$
$258$	6.26606e15	+	4.96504e15i	1.32272	+	1.04808i
$259$		−	6.08994e15i		−	1.25362i
$260$	1.04944e14	−	2.80027e12i	0.0210684	−	0.000562177i
$261$	−1.53049e15	−	7.39888e15i	−0.299687	−	1.44878i
$262$	3.47877e15	−	3.57283e15i	0.664458	−	0.682424i
$263$	9.36245e15			1.74453			0.872263	−	0.489038i	$-0.162652\pi$
$263$	9.36245e15			1.74453			0.872263	+	0.489038i	$0.162652\pi$
$264$	3.92981e15	+	2.94670e15i	0.714407	+	0.535686i
$265$	−1.34713e14			−0.0238953
$266$	−2.18942e15	+	2.24862e15i	−0.378965	+	0.389212i
$267$	−4.34156e14	−	4.24213e15i	−0.0733370	−	0.716574i
$268$	−1.23479e15	+	3.29485e13i	−0.203572	+	0.00543199i
$269$			7.10340e15i			1.14308i	0.820574	+	0.571540i	$0.193654\pi$
$269$			7.10340e15i			1.14308i	−0.820574	+	0.571540i	$0.806346\pi$
$270$	−2.91168e14	−	1.46475e14i	−0.0457382	−	0.0230091i
$271$		−	7.38648e15i		−	1.13276i	−0.824145	−	0.566379i	$-0.808344\pi$
$271$		−	7.38648e15i		−	1.13276i	0.824145	−	0.566379i	$-0.191656\pi$
$272$	−4.66233e14	−	8.73017e15i	−0.0698080	−	1.30715i
$273$	−2.91839e14	−	2.85155e15i	−0.0426664	−	0.416892i
$274$	−1.24067e14	−	1.20801e14i	−0.0177124	−	0.0172461i
$275$	−6.38769e15			−0.890597
$276$	7.18283e14	+	5.55170e15i	0.0978107	+	0.755992i
$277$	−1.88430e14			−0.0250629			−0.0125315	−	0.999921i	$-0.503989\pi$
$277$	−1.88430e14			−0.0250629			−0.0125315	+	0.999921i	$0.503989\pi$
$278$	−8.05153e15	−	7.83955e15i	−1.04613	−	1.01859i
$279$	2.66490e15	+	1.28830e16i	0.338262	+	1.63527i
$280$	−3.08849e14	−	2.85070e14i	−0.0383018	−	0.0353529i
$281$		−	7.74830e15i		−	0.938892i	−0.882961	−	0.469446i	$-0.844454\pi$
$281$		−	7.74830e15i		−	0.938892i	0.882961	−	0.469446i	$-0.155546\pi$
$282$	−2.52277e15	+	3.18383e15i	−0.298716	+	0.376991i
$283$			5.33701e15i			0.617570i	0.951132	+	0.308785i	$0.0999223\pi$
$283$			5.33701e15i			0.617570i	−0.951132	+	0.308785i	$0.900078\pi$
$284$	−8.57405e13	−	3.21325e15i	−0.00969654	−	0.363392i
$285$	−2.45875e14	+	2.51638e13i	−0.0271783	+	0.00278153i
$286$	−2.37320e15	+	2.43737e15i	−0.256422	+	0.263355i
$287$	1.38588e16			1.46384
$288$	4.76737e15	−	8.42914e15i	0.492298	−	0.870427i
$289$	−7.06702e15			−0.713511
$290$	5.35265e14	−	5.49738e14i	0.0528423	−	0.0542711i
$291$	−1.49189e16	+	1.52686e15i	−1.44023	+	0.147399i
$292$	−1.30909e14	−	4.90603e15i	−0.0123590	−	0.463171i
$293$		−	3.38792e15i		−	0.312819i	−0.987692	−	0.156410i	$-0.950008\pi$
$293$		−	3.38792e15i		−	0.312819i	0.987692	−	0.156410i	$-0.0499920\pi$
$294$	−2.50399e14	+	3.16013e14i	−0.0226139	+	0.0285395i
$295$		−	4.42125e14i		−	0.0390572i
$296$	1.04708e16	+	9.66464e15i	0.904866	+	0.835199i
$297$	1.00713e16	−	3.18137e15i	0.851466	−	0.268966i
$298$	−9.36915e15	−	9.12249e15i	−0.774987	−	0.754584i
$299$	−3.87708e15			−0.313792
$300$	1.61589e15	+	1.24895e16i	0.127975	+	0.989134i
$301$	2.21678e16			1.71807
$302$	−4.85383e15	−	4.72604e15i	−0.368162	−	0.358470i
$303$	−5.04629e14	−	4.93071e15i	−0.0374623	−	0.366043i
$304$	−3.91614e14	−	7.33294e15i	−0.0284564	−	0.532843i
$305$			9.24611e14i			0.0657673i
$306$	−1.58462e16	−	1.01141e16i	−1.10341	−	0.704269i
$307$			7.78500e15i			0.530712i	0.964150	+	0.265356i	$0.0854895\pi$
$307$			7.78500e15i			0.530712i	−0.964150	+	0.265356i	$0.914510\pi$
$308$	1.36148e16	−	3.63290e14i	0.908726	−	0.0242479i
$309$	1.71623e15	+	1.67693e16i	0.112162	+	1.09593i
$310$	−9.32005e14	+	9.57206e14i	−0.0596441	+	0.0612568i
$311$	1.15198e14			0.00721945			0.00360972	−	0.999993i	$-0.498851\pi$
$311$	1.15198e14			0.00721945			0.00360972	+	0.999993i	$0.498851\pi$
$312$	5.36599e15	+	4.02359e15i	0.329340	+	0.246950i
$313$	8.05900e15			0.484444			0.242222	−	0.970221i	$-0.422124\pi$
$313$	8.05900e15			0.484444			0.242222	+	0.970221i	$0.422124\pi$
$314$	−1.31652e16	+	1.35212e16i	−0.775148	+	0.796108i
$315$	−8.85021e14	+	1.83071e14i	−0.0510428	+	0.0105584i
$316$	−1.07997e15	+	2.88173e13i	−0.0610163	+	0.00162812i
$317$			1.06234e16i			0.588002i	0.955805	+	0.294001i	$0.0949870\pi$
$317$			1.06234e16i			0.588002i	−0.955805	+	0.294001i	$0.905013\pi$
$318$	−6.74550e15	−	5.34493e15i	−0.365795	−	0.289845i
$319$			2.48634e16i			1.32106i
$320$	9.80278e14	−	7.86207e13i	0.0510357	−	0.00409319i
$321$	−2.36720e16	+	2.42269e15i	−1.20768	+	0.123599i
$322$	1.11212e16	+	1.08284e16i	0.556019	+	0.541381i
$323$	−1.42554e16			−0.698492
$324$	−8.76807e15	−	1.88869e16i	−0.421077	−	0.907025i
$325$	−8.72212e15			−0.410563
$326$	8.67768e15	+	8.44922e15i	0.400396	+	0.389854i
$327$	3.73452e16	−	3.82205e15i	1.68917	−	0.172877i
$328$	−2.19937e16	+	2.38283e16i	−0.975256	+	1.05661i
$329$			1.12636e16i			0.489671i
$330$	8.40661e14	+	6.66114e14i	0.0358328	+	0.0283928i
$331$			7.41293e14i			0.0309819i	0.999880	+	0.0154910i	$0.00493112\pi$
$331$			7.41293e14i			0.0309819i	−0.999880	+	0.0154910i	$0.995069\pi$
$332$	−3.74045e14	−	1.40179e16i	−0.0153295	−	0.574494i
$333$	3.00046e16	−	6.20658e15i	1.20587	−	0.249439i
$334$	9.00480e15	−	9.24829e15i	0.354913	−	0.364510i
$335$	−2.69731e14			−0.0104265
$336$	−4.15447e15	−	2.65284e16i	−0.157511	−	1.00578i
$337$	−3.51015e16			−1.30536			−0.652681	−	0.757632i	$-0.726356\pi$
$337$	−3.51015e16			−1.30536			−0.652681	+	0.757632i	$0.726356\pi$
$338$	1.58832e16	−	1.63127e16i	0.579402	−	0.595069i
$339$	−3.24814e15	−	3.17375e16i	−0.116235	−	1.13573i
$340$	−5.09225e13	−	1.90840e15i	−0.00178771	−	0.0669970i
$341$		−	4.32923e16i		−	1.49110i
$342$	−1.33101e16	−	8.49539e15i	−0.449792	−	0.287087i
$343$		−	2.95848e16i		−	0.980974i
$344$	−3.51800e16	+	3.81144e16i	−1.14463	+	1.24011i
$345$	1.24455e14	+	1.21605e15i	0.00397364	+	0.0388263i
$346$	3.77806e16	+	3.67859e16i	1.18379	+	1.15262i
$347$	−4.19373e16			−1.28961			−0.644806	−	0.764347i	$-0.723062\pi$
$347$	−4.19373e16			−1.28961			−0.644806	+	0.764347i	$0.723062\pi$
$348$	4.86140e16	−	6.28971e15i	1.46722	−	0.189830i
$349$	−1.77946e12			−5.27136e−5			−2.63568e−5	−	1.00000i	$-0.500008\pi$
$349$	−1.77946e12			−5.27136e−5			−2.63568e−5		1.00000i	$0.500008\pi$
$350$	2.50190e16	+	2.43603e16i	0.727491	+	0.708338i
$351$	1.37519e16	−	4.34403e15i	0.392524	−	0.123993i
$352$	−2.09819e16	+	2.39854e16i	−0.587920	+	0.672077i
$353$		−	4.75732e16i		−	1.30866i	−0.756209	−	0.654330i	$-0.772951\pi$
$353$		−	4.75732e16i		−	1.30866i	0.756209	−	0.654330i	$-0.227049\pi$
$354$	1.75419e16	−	2.21385e16i	0.473757	−	0.597899i
$355$		−	7.01909e14i		−	0.0186122i
$356$	2.76563e16	−	7.37964e14i	0.720061	−	0.0192137i
$357$	−5.18550e16	+	5.30704e15i	−1.32571	+	0.135678i
$358$	2.32648e16	−	2.38938e16i	0.584062	−	0.599855i
$359$	1.62038e16			0.399488			0.199744	−	0.979848i	$-0.435989\pi$
$359$	1.62038e16			0.399488			0.199744	+	0.979848i	$0.435989\pi$
$360$	1.08975e15	−	1.81220e15i	0.0263852	−	0.0438773i
$361$	3.00792e16			0.715268
$362$	6.79514e15	−	6.97888e15i	0.158706	−	0.162997i
$363$	8.78830e15	−	8.99429e14i	0.201610	−	0.0206335i
$364$	1.85905e16	−	4.96057e14i	0.418921	−	0.0111782i
$365$		−	1.07168e15i		−	0.0237226i
$366$	−3.66852e16	+	4.62981e16i	−0.797745	+	1.00678i
$367$		−	8.88940e15i		−	0.189908i	−0.995482	−	0.0949540i	$-0.969730\pi$
$367$		−	8.88940e15i		−	0.189908i	0.995482	−	0.0949540i	$-0.0302704\pi$
$368$	−3.62672e16	+	1.93684e15i	−0.761209	+	0.0406522i
$369$	1.41242e16	+	6.82810e16i	0.291269	+	1.40808i
$370$	2.22934e15	+	2.17065e15i	0.0451717	+	0.0439824i
$371$	−2.38639e16			−0.475129
$372$	−8.46468e16	+	1.09517e16i	−1.65608	+	0.214265i
$373$	−4.65222e16			−0.894443			−0.447222	−	0.894423i	$-0.647587\pi$
$373$	−4.65222e16			−0.894443			−0.447222	+	0.894423i	$0.647587\pi$
$374$	4.43232e16	+	4.31563e16i	0.837463	+	0.815415i
$375$	5.60699e14	+	5.47858e15i	0.0104118	+	0.101734i
$376$	−1.93662e16	−	1.78752e16i	−0.353447	−	0.326234i
$377$			3.39500e16i			0.609005i
$378$	−5.15793e16	−	2.59475e16i	−0.909450	−	0.457508i
$379$		−	3.84672e16i		−	0.666708i	−0.942802	−	0.333354i	$-0.891820\pi$
$379$		−	3.84672e16i		−	0.666708i	0.942802	−	0.333354i	$-0.108180\pi$
$380$	−4.27725e13	−	1.60296e15i	−0.000728738	−	0.0273105i
$381$	7.24834e14	+	7.08233e15i	0.0121402	+	0.118622i
$382$	−1.97376e16	+	2.02713e16i	−0.324999	+	0.333787i
$383$	3.86061e16			0.624976			0.312488	−	0.949922i	$-0.398838\pi$
$383$	3.86061e16			0.624976			0.312488	+	0.949922i	$0.398838\pi$
$384$	5.22049e16	+	3.49571e16i	0.830919	+	0.556394i
$385$	2.97405e15			0.0465430
$386$	3.19937e16	−	3.28588e16i	0.492319	−	0.505631i
$387$	2.25924e16	+	1.09219e17i	0.341854	+	1.65263i
$388$	−2.59531e15	−	9.72630e16i	−0.0386173	−	1.44724i
$389$			6.33262e16i			0.926640i	0.886191	+	0.463320i	$0.153342\pi$
$389$			6.33262e16i			0.926640i	−0.886191	+	0.463320i	$0.846658\pi$
$390$	1.14789e15	+	9.09551e14i	0.0165188	+	0.0130890i
$391$			7.05041e16i			0.997851i
$392$	−1.92220e15	−	1.77421e15i	−0.0267572	−	0.0246971i
$393$	6.92058e16	−	7.08279e15i	0.947525	−	0.0969734i
$394$	−2.98855e16	−	2.90987e16i	−0.402472	−	0.391876i
$395$	−2.35911e14			−0.00312513
$396$	1.56655e16	+	6.67088e16i	0.204139	+	0.869290i
$397$	7.37354e16			0.945231			0.472615	−	0.881269i	$-0.343310\pi$
$397$	7.37354e16			0.945231			0.472615	+	0.881269i	$0.343310\pi$
$398$	−2.89213e16	−	2.81598e16i	−0.364735	−	0.355132i
$399$	−4.35558e16	+	4.45767e15i	−0.540408	+	0.0553075i
$400$	−8.15890e16	+	4.35724e15i	−0.995959	+	0.0531890i
$401$		−	9.15807e16i		−	1.09993i	−0.835187	−	0.549966i	$-0.814641\pi$
$401$		−	9.15807e16i		−	1.09993i	0.835187	−	0.549966i	$-0.185359\pi$
$402$	−1.35062e16	−	1.07019e16i	−0.159612	−	0.126472i
$403$		−	5.91138e16i		−	0.687395i
$404$	3.21455e16	−	8.57750e14i	0.367825	−	0.00981481i
$405$	−1.80394e15	−	4.17384e15i	−0.0203126	−	0.0469979i
$406$	9.48201e16	−	9.73840e16i	1.05071	−	1.07912i
$407$	−1.00828e17			−1.09956
$408$	7.31684e16	−	9.75797e16i	0.785294	−	1.04729i
$409$	1.03722e17			1.09564			0.547822	−	0.836595i	$-0.315457\pi$
$409$	1.03722e17			1.09564			0.547822	+	0.836595i	$0.315457\pi$
$410$	−4.93972e15	+	5.07329e15i	−0.0513579	+	0.0527466i
$411$	−2.45950e14	−	2.40317e15i	−0.00251696	−	0.0245931i
$412$	−1.09326e17	+	2.91719e15i	−1.10127	+	0.0293855i
$413$		−	7.83207e16i		−	0.776607i
$414$	−4.20165e16	+	6.58291e16i	−0.410126	+	0.642563i
$415$		−	3.06210e15i		−	0.0294243i
$416$	−2.86499e16	+	3.27510e16i	−0.271030	+	0.309826i
$417$	−1.59614e16	−	1.55958e17i	−0.148657	−	1.45252i
$418$	3.72294e16	+	3.62493e16i	0.341382	+	0.332394i
$419$	1.23965e17			1.11920			0.559601	−	0.828762i	$-0.310954\pi$
$419$	1.23965e17			1.11920			0.559601	+	0.828762i	$0.310954\pi$
$420$	−7.52347e14	−	5.81499e15i	−0.00668802	−	0.0516926i
$421$	−7.28664e16			−0.637813			−0.318907	−	0.947786i	$-0.603316\pi$
$421$	−7.28664e16			−0.637813			−0.318907	+	0.947786i	$0.603316\pi$
$422$	−5.54861e16	−	5.40253e16i	−0.478248	−	0.465657i
$423$	−5.54948e16	+	1.14793e16i	−0.471020	+	0.0974327i
$424$	3.78717e16	−	4.10307e16i	0.316546	−	0.342950i
$425$			1.58610e17i			1.30558i
$426$	2.78492e16	−	3.51468e16i	0.225762	−	0.284920i
$427$			1.63791e17i			1.30771i
$428$	−4.11800e15	−	1.54328e17i	−0.0323819	−	1.21356i
$429$	−4.72118e16	+	4.83184e15i	−0.365661	+	0.0374232i
$430$	−7.90132e15	+	8.11497e15i	−0.0602774	+	0.0619073i
$431$	3.76579e16			0.282979			0.141490	−	0.989940i	$-0.454811\pi$
$431$	3.76579e16			0.282979			0.141490	+	0.989940i	$0.454811\pi$
$432$	1.26469e17	−	4.75051e16i	0.936136	−	0.351638i
$433$	−8.76052e16			−0.638791			−0.319395	−	0.947622i	$-0.603480\pi$
$433$	−8.76052e16			−0.638791			−0.319395	+	0.947622i	$0.603480\pi$
$434$	−1.65101e17	+	1.69565e17i	−1.18595	+	1.21802i
$435$	1.06484e16	−	1.08980e15i	0.0753537	−	0.00771200i
$436$	6.49659e15	+	2.43469e17i	0.0452922	+	1.69739i
$437$			5.92202e16i			0.406762i
$438$	4.25205e16	−	5.36625e16i	0.287751	−	0.363152i
$439$		−	1.18917e17i		−	0.792913i	−0.918053	−	0.396457i	$-0.870240\pi$
$439$		−	1.18917e17i		−	0.792913i	0.918053	−	0.396457i	$-0.129760\pi$
$440$	−4.71978e15	+	5.11347e15i	−0.0310084	+	0.0335949i
$441$	−5.50816e15	+	1.13939e15i	−0.0356579	+	0.00737600i
$442$	6.05215e16	+	5.89281e16i	0.386069	+	0.375905i
$443$	6.21038e16			0.390386			0.195193	−	0.980765i	$-0.437467\pi$
$443$	6.21038e16			0.390386			0.195193	+	0.980765i	$0.437467\pi$
$444$	2.55066e16	+	1.97144e17i	0.158002	+	1.22122i
$445$	6.04130e15			0.0368799
$446$	−1.84687e17	−	1.79825e17i	−1.11112	−	1.08186i
$447$	−1.85734e16	−	1.81480e17i	−0.110127	−	1.07605i
$448$	1.73653e17	−	1.39274e16i	1.01479	−	0.0813883i
$449$			2.73790e17i			1.57695i	0.615069	+	0.788473i	$0.289128\pi$
$449$			2.73790e17i			1.57695i	−0.615069	+	0.788473i	$0.710872\pi$
$450$	−9.45228e16	+	1.48093e17i	−0.536606	+	0.840725i
$451$		−	2.29454e17i		−	1.28395i
$452$	2.06911e17	−	5.52108e15i	1.14126	−	0.0304526i
$453$	−9.62223e15	−	9.40186e16i	−0.0523164	−	0.511182i
$454$	−4.75208e16	+	4.88057e16i	−0.254695	+	0.261582i
$455$	4.06095e15			0.0214562
$456$	6.14580e16	−	8.19624e16i	0.320116	−	0.426917i
$457$	−1.45847e17			−0.748932			−0.374466	−	0.927241i	$-0.622174\pi$
$457$	−1.45847e17			−0.748932			−0.374466	+	0.927241i	$0.622174\pi$
$458$	6.69846e16	−	6.87958e16i	0.339117	−	0.348286i
$459$	−7.89955e16	−	2.50076e17i	−0.394294	−	1.24822i
$460$	−7.92794e15	+	2.11544e14i	−0.0390152	+	0.00104106i
$461$			4.44849e16i			0.215852i	0.994159	+	0.107926i	$0.0344210\pi$
$461$			4.44849e16i			0.215852i	−0.994159	+	0.107926i	$0.965579\pi$
$462$	1.48920e17	+	1.18000e17i	0.712492	+	0.564557i
$463$			3.11730e17i			1.47063i	0.677727	+	0.735313i	$0.262965\pi$
$463$			3.11730e17i			1.47063i	−0.677727	+	0.735313i	$0.737035\pi$
$464$	1.69601e16	+	3.17577e17i	0.0788974	+	1.47735i
$465$	−1.85411e16	+	1.89756e15i	−0.0850531	+	0.00870467i
$466$	−3.68839e16	−	3.59128e16i	−0.166851	−	0.162458i
$467$	2.31156e17			1.03120			0.515602	−	0.856828i	$-0.327568\pi$
$467$	2.31156e17			1.03120			0.515602	+	0.856828i	$0.327568\pi$
$468$	2.13906e16	+	9.10881e16i	0.0941076	+	0.400741i
$469$	−4.77818e16			−0.207319
$470$	−4.12327e15	−	4.01472e15i	−0.0176444	−	0.0171798i
$471$	−2.61905e17	+	2.68044e16i	−1.10537	+	0.113128i
$472$	1.34662e17	+	1.24294e17i	0.560558	+	0.517400i
$473$		−	3.67022e17i		−	1.50694i
$474$	−1.18128e16	−	9.36010e15i	−0.0478403	−	0.0379072i
$475$			1.33225e17i			0.532204i
$476$	−9.02073e15	−	3.38065e17i	−0.0355465	−	1.33216i
$477$	−2.43210e16	−	1.17575e17i	−0.0945392	−	0.457032i
$478$	−2.79313e17	+	2.86866e17i	−1.07105	+	1.10001i
$479$	−2.59872e17			−0.983056			−0.491528	−	0.870862i	$-0.663561\pi$
$479$	−2.59872e17			−0.983056			−0.491528	+	0.870862i	$0.663561\pi$
$480$	1.11920e16	+	7.93474e15i	0.0417677	+	0.0296118i
$481$	−1.37677e17			−0.506895
$482$	1.91871e16	−	1.97059e16i	0.0696953	−	0.0715798i
$483$	2.20467e16	+	2.15418e17i	0.0790111	+	0.772015i
$484$	1.52882e15	+	5.72947e16i	0.00540581	+	0.202591i
$485$		−	2.12463e16i		−	0.0741246i
$486$	7.52738e16	−	2.80571e17i	0.259124	−	0.965844i
$487$		−	3.49867e17i		−	1.18841i	−0.804315	−	0.594203i	$-0.797467\pi$
$487$		−	3.49867e17i		−	1.18841i	0.804315	−	0.594203i	$-0.202533\pi$
$488$	−2.81617e17	−	2.59935e17i	−0.943908	−	0.871235i
$489$	1.72026e16	+	1.68087e17i	0.0568968	+	0.555937i
$490$	−4.09257e14	−	3.98483e14i	−0.00133574	−	0.00130057i
$491$	5.00685e17			1.61263			0.806315	−	0.591486i	$-0.201459\pi$
$491$	5.00685e17			1.61263			0.806315	+	0.591486i	$0.201459\pi$
$492$	−4.48637e17	+	5.80450e16i	−1.42601	+	0.184498i
$493$	6.17375e17			1.93662
$494$	5.08352e16	+	4.94968e16i	0.157376	+	0.153233i
$495$	3.03102e15	+	1.46529e16i	0.00926093	+	0.0447702i
$496$	−2.95311e16	−	5.52966e17i	−0.0890529	−	1.66751i
$497$		−	1.24341e17i		−	0.370081i
$498$	1.21493e17	−	1.53329e17i	0.356912	−	0.450436i
$499$			4.75665e17i			1.37927i	0.724159	+	0.689633i	$0.242228\pi$
$499$			4.75665e17i			1.37927i	−0.724159	+	0.689633i	$0.757772\pi$
$500$	−3.57172e16	+	9.53056e14i	−0.102229	+	0.00272781i
$501$	1.79139e17	−	1.83338e16i	0.506110	−	0.0517973i
$502$	3.85663e17	−	3.96092e17i	1.07556	−	1.10464i
$503$	−3.16406e17			−0.871069			−0.435535	−	0.900172i	$-0.643441\pi$
$503$	−3.16406e17			−0.871069			−0.435535	+	0.900172i	$0.643441\pi$
$504$	1.93045e17	−	3.21025e17i	0.524639	−	0.872449i
$505$	7.02192e15			0.0188392
$506$	1.79282e17	−	1.84129e17i	0.474851	−	0.487691i
$507$	3.15977e17	−	3.23383e16i	0.826235	−	0.0845601i
$508$	−4.61728e16	+	1.23205e15i	−0.119199	+	0.00318063i
$509$			4.09801e17i			1.04450i	0.852793	+	0.522249i	$0.174907\pi$
$509$			4.09801e17i			1.04450i	−0.852793	+	0.522249i	$0.825093\pi$
$510$	1.65401e16	−	2.08742e16i	0.0416227	−	0.0525295i
$511$		−	1.89845e17i		−	0.471696i
$512$	−2.51638e17	+	3.20674e17i	−0.617336	+	0.786700i
$513$	−6.63525e16	−	2.10052e17i	−0.160729	−	0.508820i
$514$	−4.12525e17	−	4.01664e17i	−0.986711	−	0.960734i
$515$	−2.38814e16			−0.0564045
$516$	−7.17616e17	+	9.28456e16i	−1.67367	+	0.216540i
$517$	1.86487e17			0.429496
$518$	3.94920e17	+	3.84523e17i	0.898185	+	0.874538i
$519$	7.48962e16	+	7.31809e17i	0.168218	+	1.64365i
$520$	−6.44466e15	+	6.98223e15i	−0.0142948	+	0.0154872i
$521$			1.05152e17i			0.230341i	0.993346	+	0.115170i	$0.0367414\pi$
$521$			1.05152e17i			0.230341i	−0.993346	+	0.115170i	$0.963259\pi$
$522$	5.76438e17	+	3.67921e17i	1.24708	+	0.795969i
$523$			9.10911e15i			0.0194632i	0.999953	+	0.00973162i	$0.00309772\pi$
$523$			9.10911e15i			0.0194632i	−0.999953	+	0.00973162i	$0.996902\pi$
$524$	1.20391e16	+	4.51182e17i	0.0254062	+	0.952135i
$525$	4.95977e16	+	4.84618e17i	0.103377	+	1.01010i
$526$	−5.91152e17	+	6.07136e17i	−1.21700	+	1.24991i
$527$	−1.07498e18			−2.18590
$528$	−4.39218e17	+	6.87836e16i	−0.882185	+	0.138154i
$529$	−2.11145e17			−0.418909
$530$	8.50588e15	−	8.73587e15i	0.0166696	−	0.0171204i
$531$	3.85879e17	−	7.98208e16i	0.747028	−	0.154526i
$532$	−7.57699e15	−	2.83959e17i	−0.0144901	−	0.543038i
$533$		−	3.13310e17i		−	0.591898i
$534$	3.02507e17	+	2.39697e17i	0.564568	+	0.447347i
$535$		−	3.37118e16i		−	0.0621558i
$536$	7.58290e16	−	8.21541e16i	0.138122	−	0.149644i
$537$	4.62823e17	−	4.73671e16i	0.832879	−	0.0852402i
$538$	−4.60641e17	−	4.48513e17i	−0.818988	−	0.797427i
$539$	1.85098e16			0.0325143
$540$	2.78831e16	−	9.63310e15i	0.0483930	−	0.0167189i
$541$	−3.93369e17			−0.674555			−0.337278	−	0.941405i	$-0.609506\pi$
$541$	−3.93369e17			−0.674555			−0.337278	+	0.941405i	$0.609506\pi$
$542$	4.78998e17	+	4.66387e17i	0.811593	+	0.790226i
$543$	1.35181e17	−	1.38349e16i	0.226316	−	0.0231621i
$544$	5.95572e17	+	5.20995e17i	0.985239	+	0.861867i
$545$			5.31840e16i			0.0869367i
$546$	2.03344e17	+	1.61124e17i	0.328458	+	0.260260i
$547$		−	7.32254e17i		−	1.16881i	−0.811462	−	0.584405i	$-0.801328\pi$
$547$		−	7.32254e17i		−	1.16881i	0.811462	−	0.584405i	$-0.198672\pi$
$548$	1.56673e16	−	4.18058e14i	0.0247128	−	0.000659421i
$549$	−8.06985e17	+	1.66929e17i	−1.25790	+	0.260202i
$550$	4.03323e17	−	4.14228e17i	0.621291	−	0.638091i
$551$	5.18566e17			0.789440
$552$	−4.05369e17	−	3.03959e17i	−0.609884	−	0.457310i
$553$	−4.17908e16			−0.0621394
$554$	1.18976e16	−	1.22193e16i	0.0174842	−	0.0179570i
$555$	4.41945e15	+	4.31824e16i	0.00641895	+	0.0627194i
$556$	1.01676e18	−	2.71306e16i	1.45959	−	0.0389469i
$557$		−	7.49330e17i		−	1.06320i	−0.846996	−	0.531599i	$-0.821591\pi$
$557$		−	7.49330e17i		−	1.06320i	0.846996	−	0.531599i	$-0.178409\pi$
$558$	−1.00370e18	−	6.40625e17i	−1.40760	−	0.898425i
$559$		−	5.01153e17i		−	0.694694i
$560$	3.79872e16	−	2.02870e15i	0.0520493	−	0.00277968i
$561$	8.78663e16	+	8.58540e17i	0.119005	+	1.16279i
$562$	5.02462e17	+	4.89233e17i	0.672693	+	0.654982i
$563$	−1.98594e17			−0.262822			−0.131411	−	0.991328i	$-0.541951\pi$
$563$	−1.98594e17			−0.262822			−0.131411	+	0.991328i	$0.541951\pi$
$564$	−4.71755e16	−	3.64626e17i	−0.0617167	−	0.477016i
$565$	4.51980e16			0.0584527
$566$	−3.46094e17	−	3.36982e17i	−0.442474	−	0.430824i
$567$	−3.19562e17	−	7.39380e17i	−0.403892	−	0.934497i
$568$	2.13787e17	+	1.97327e17i	0.267126	+	0.246560i
$569$		−	1.02440e18i		−	1.26543i	−0.774384	−	0.632716i	$-0.781940\pi$
$569$		−	1.02440e18i		−	1.26543i	0.774384	−	0.632716i	$-0.218060\pi$
$570$	1.38929e16	−	1.75333e16i	0.0169670	−	0.0214130i
$571$			3.30960e17i			0.399614i	0.979835	+	0.199807i	$0.0640315\pi$
$571$			3.30960e17i			0.399614i	−0.979835	+	0.199807i	$0.935968\pi$
$572$	−8.21300e15	−	3.07794e17i	−0.00980455	−	0.367440i
$573$	−3.92655e17	+	4.01858e16i	−0.463453	+	0.0474316i
$574$	−8.75054e17	+	8.98715e17i	−1.02119	+	1.04880i
$575$	6.58905e17			0.760295
$576$	2.45597e17	+	8.41376e17i	0.280206	+	0.959940i
$577$	1.05738e17			0.119286			0.0596430	−	0.998220i	$-0.481004\pi$
$577$	1.05738e17			0.119286			0.0596430	+	0.998220i	$0.481004\pi$
$578$	4.46217e17	−	4.58282e17i	0.497754	−	0.511213i
$579$	6.36474e17	−	6.51392e16i	0.702053	−	0.0718509i
$580$	1.85240e15	+	6.94216e16i	0.00202048	+	0.0757204i
$581$		−	5.42439e17i		−	0.585068i
$582$	8.42977e17	−	1.06387e18i	0.899117	−	1.13472i
$583$			3.95104e17i			0.416741i
$584$	3.26412e17	+	3.01281e17i	0.340472	+	0.314259i
$585$	4.13873e15	+	2.00079e16i	0.00426927	+	0.0206390i
$586$	2.19700e17	+	2.13916e17i	0.224127	+	0.218227i
$587$	−3.63668e17			−0.366909			−0.183454	−	0.983028i	$-0.558728\pi$
$587$	−3.63668e17			−0.366909			−0.183454	+	0.983028i	$0.558728\pi$
$588$	−4.68243e15	−	3.61911e16i	−0.00467217	−	0.0361118i
$589$	−9.02930e17			−0.891055
$590$	2.86709e16	+	2.79160e16i	0.0279835	+	0.0272468i
$591$	−5.92451e16	−	5.78882e17i	−0.0571918	−	0.558819i
$592$	−1.28787e18	+	6.87783e16i	−1.22964	+	0.0656689i
$593$			9.27896e17i			0.876282i	0.898906	+	0.438141i	$0.144363\pi$
$593$			9.27896e17i			0.876282i	−0.898906	+	0.438141i	$0.855637\pi$
$594$	−4.29601e17	+	8.53975e17i	−0.401286	+	0.797688i
$595$		−	7.38477e16i		−	0.0682302i
$596$	1.18315e18	−	3.15704e16i	1.08128	−	0.0288523i
$597$	−5.73335e16	−	5.60204e17i	−0.0518293	−	0.506423i
$598$	2.44801e17	−	2.51421e17i	0.218905	−	0.224824i
$599$	−1.60075e18			−1.41596			−0.707979	−	0.706234i	$-0.750393\pi$
$599$	−1.60075e18			−1.41596			−0.707979	+	0.706234i	$0.750393\pi$
$600$	−9.11944e17	−	6.83805e17i	−0.797967	−	0.598341i
$601$	−9.72916e17			−0.842154			−0.421077	−	0.907025i	$-0.638348\pi$
$601$	−9.72916e17			−0.842154			−0.421077	+	0.907025i	$0.638348\pi$
$602$	−1.39969e18	+	1.43754e18i	−1.19855	+	1.23095i
$603$	−4.86969e16	−	2.35416e17i	−0.0412514	−	0.199422i
$604$	6.12948e17	−	1.63555e16i	0.513669	−	0.0137064i
$605$			1.25156e16i			0.0103763i
$606$	3.51609e17	+	2.78604e17i	0.288395	+	0.228516i
$607$			1.66818e18i			1.35368i	0.736131	+	0.676839i	$0.236651\pi$
$607$			1.66818e18i			1.35368i	−0.736131	+	0.676839i	$0.763349\pi$
$608$	5.00253e17	+	4.37611e17i	0.401621	+	0.351330i
$609$	1.88633e18	−	1.93054e17i	1.49832	−	0.153344i
$610$	−5.99591e16	−	5.83806e16i	−0.0471207	−	0.0458801i
$611$	2.54640e17			0.197997
$612$	1.65642e18	−	3.88985e17i	1.27434	−	0.299260i
$613$	2.26145e18			1.72145			0.860723	−	0.509074i	$-0.170012\pi$
$613$	2.26145e18			1.72145			0.860723	+	0.509074i	$0.170012\pi$
$614$	−5.04841e17	−	4.91550e17i	−0.380242	−	0.370232i
$615$	−9.82696e16	+	1.00573e16i	−0.0732370	+	0.00749537i
$616$	−8.36091e17	+	9.05833e17i	−0.616565	+	0.667995i
$617$			1.79353e18i			1.30875i	0.756171	+	0.654374i	$0.227068\pi$
$617$			1.79353e18i			1.30875i	−0.756171	+	0.654374i	$0.772932\pi$
$618$	−1.19582e18	−	9.47529e17i	−0.863455	−	0.684175i
$619$			2.48548e17i			0.177591i	0.996050	+	0.0887956i	$0.0283018\pi$
$619$			2.48548e17i			0.177591i	−0.996050	+	0.0887956i	$0.971698\pi$
$620$	−3.22541e15	−	1.20877e17i	−0.00228055	−	0.0854670i
$621$	−1.03888e18	+	3.28166e17i	−0.726890	+	0.229614i
$622$	−7.27371e15	+	7.47038e15i	−0.00503638	+	0.00517256i
$623$	1.07019e18			0.733314
$624$	−5.99734e17	+	9.39211e16i	−0.406686	+	0.0636889i
$625$	1.47841e18			0.992143
$626$	−5.08851e17	+	5.22610e17i	−0.337954	+	0.347092i
$627$	7.38036e16	+	7.21133e17i	0.0485108	+	0.473998i
$628$	−4.55612e16	−	1.70747e18i	−0.0296386	−	1.11075i
$629$			2.50363e18i			1.61191i
$630$	4.40091e16	−	6.89510e16i	0.0280433	−	0.0439366i
$631$			1.92320e17i			0.121293i	0.998159	+	0.0606463i	$0.0193162\pi$
$631$			1.92320e17i			0.121293i	−0.998159	+	0.0606463i	$0.980684\pi$
$632$	6.63214e16	−	7.18535e16i	0.0413992	−	0.0448525i
$633$	−1.09996e17	−	1.07477e18i	−0.0679597	−	0.664033i
$634$	−6.88907e17	−	6.70770e17i	−0.421289	−	0.410198i
$635$	−1.00861e16			−0.00610511
$636$	7.72523e17	−	9.99496e16i	0.462850	−	0.0598838i
$637$	2.52744e16			0.0149890
$638$	−1.61234e18	−	1.56989e18i	−0.946505	−	0.921586i
$639$	6.12615e17	−	1.26722e17i	0.355985	−	0.0736371i
$640$	−5.67970e16	+	6.85332e16i	−0.0326705	+	0.0394213i
$641$		−	2.47396e18i		−	1.40869i	−0.709857	−	0.704346i	$-0.751241\pi$
$641$		−	2.47396e18i		−	1.40869i	0.709857	−	0.704346i	$-0.248759\pi$
$642$	1.33756e18	−	1.68805e18i	0.753938	−	0.951499i
$643$			1.18379e18i			0.660547i	0.943885	+	0.330273i	$0.107141\pi$
$643$			1.18379e18i			0.660547i	−0.943885	+	0.330273i	$0.892859\pi$
$644$	−1.40440e18	+	3.74743e16i	−0.775772	+	0.0207002i
$645$	−1.57187e17	+	1.60871e16i	−0.0859563	+	0.00879711i
$646$	9.00092e17	−	9.24430e17i	0.487277	−	0.500452i
$647$	1.71926e18			0.921432			0.460716	−	0.887548i	$-0.347593\pi$
$647$	1.71926e18			0.921432			0.460716	+	0.887548i	$0.347593\pi$
$648$	1.77840e18	+	6.23943e17i	0.943610	+	0.331061i
$649$	−1.29672e18			−0.681171
$650$	5.50720e17	−	5.65611e17i	0.286414	−	0.294158i
$651$	−3.28448e18	+	3.36147e17i	−1.69118	+	0.173082i
$652$	−1.09583e18	+	2.92404e16i	−0.558642	+	0.0149065i
$653$		−	4.21980e17i		−	0.212989i	−0.994313	−	0.106494i	$-0.966037\pi$
$653$		−	4.21980e17i		−	0.212989i	0.994313	−	0.106494i	$-0.0339626\pi$
$654$	−2.11015e18	+	2.66308e18i	−1.05453	+	1.33085i
$655$			9.85572e16i			0.0487663i
$656$	−1.56518e17	−	2.93078e18i	−0.0766812	−	1.43585i
$657$	9.35347e17	−	1.93481e17i	0.453730	−	0.0938562i
$658$	−7.30422e17	−	7.11192e17i	−0.350837	−	0.341601i
$659$	−3.13225e17			−0.148971			−0.0744853	−	0.997222i	$-0.523731\pi$
$659$	−3.13225e17			−0.148971			−0.0744853	+	0.997222i	$0.523731\pi$
$660$	−9.62761e16	+	1.24563e16i	−0.0453401	+	0.00586614i
$661$	6.69745e17			0.312320			0.156160	−	0.987732i	$-0.450088\pi$
$661$	6.69745e17			0.312320			0.156160	+	0.987732i	$0.450088\pi$
$662$	−4.80713e16	−	4.68058e16i	−0.0221978	−	0.0216134i
$663$	1.19978e17	+	1.17230e18i	0.0548609	+	0.536044i
$664$	9.32650e17	+	8.60844e17i	0.422305	+	0.389791i
$665$		−	6.20286e16i		−	0.0278132i
$666$	−1.49202e18	+	2.33762e18i	−0.662512	+	1.03799i
$667$		−	2.56472e18i		−	1.12778i
$668$	3.11632e16	+	1.16789e18i	0.0135705	+	0.508573i
$669$	−3.66124e17	−	3.57739e18i	−0.157891	−	1.54275i
$670$	1.70310e16	−	1.74915e16i	0.00727366	−	0.00747034i
$671$	2.71182e18			1.14700
$672$	1.98263e18	+	1.40561e18i	0.830501	+	0.588796i
$673$	−9.97615e17			−0.413871			−0.206936	−	0.978355i	$-0.566349\pi$
$673$	−9.97615e17			−0.413871			−0.206936	+	0.978355i	$0.566349\pi$
$674$	2.21633e18	−	2.27626e18i	0.910637	−	0.935260i
$675$	−2.33712e18	+	7.38263e17i	−0.951057	+	0.300425i
$676$	5.49675e16	+	2.05999e18i	0.0221540	+	0.830255i
$677$			3.37660e17i			0.134788i	0.997726	+	0.0673942i	$0.0214685\pi$
$677$			3.37660e17i			0.134788i	−0.997726	+	0.0673942i	$0.978531\pi$
$678$	2.26320e18	+	1.79329e18i	0.894809	+	0.709019i
$679$		−	3.76371e18i		−	1.47388i
$680$	1.26971e17	+	1.17195e17i	0.0492488	+	0.0454571i
$681$	−9.45366e17	+	9.67524e16i	−0.363198	+	0.0371711i
$682$	2.80742e18	+	2.73351e18i	1.06834	+	1.04021i
$683$	−1.58747e18			−0.598373			−0.299187	−	0.954195i	$-0.596715\pi$
$683$	−1.58747e18			−0.598373			−0.299187	+	0.954195i	$0.596715\pi$
$684$	1.39132e18	−	3.26729e17i	0.519471	−	0.121990i
$685$	3.42241e15			0.00126574
$686$	1.91852e18	+	1.86801e18i	0.702844	+	0.684339i
$687$	1.33257e18	−	1.36381e17i	0.483584	−	0.0494919i
$688$	−2.50357e17	−	4.68792e18i	−0.0899986	−	1.68522i
$689$			5.39498e17i			0.192117i
$690$	−8.67163e16	−	6.87113e16i	−0.0305902	−	0.0242387i
$691$		−	3.36744e18i		−	1.17677i	−0.808580	−	0.588386i	$-0.799763\pi$
$691$		−	3.36744e18i		−	1.17677i	0.808580	−	0.588386i	$-0.200237\pi$
$692$	−4.77098e18	+	1.27306e17i	−1.65165	+	0.0440716i
$693$	5.36933e17	+	2.59570e18i	0.184143	+	0.890203i
$694$	2.64795e18	−	2.71955e18i	0.899649	−	0.923975i
$695$	2.22103e17			0.0747571
$696$	−2.66164e18	+	3.54965e18i	−0.887544	+	1.18366i
$697$	−5.69749e18			−1.88222
$698$	1.12356e14	−	1.15394e14i	3.67737e−5	−	3.77680e-5i
$699$	−7.31186e16	−	7.14440e17i	−0.0237097	−	0.231667i
$700$	−3.15943e18	+	8.43044e16i	−1.01501	+	0.0270840i
$701$			3.26825e18i			1.04027i	0.854083	+	0.520137i	$0.174119\pi$
$701$			3.26825e18i			1.04027i	−0.854083	+	0.520137i	$0.825881\pi$
$702$	−5.86603e17	+	1.16607e18i	−0.184992	+	0.367733i
$703$			2.10293e18i			0.657077i
$704$	−2.30589e17	−	2.87509e18i	−0.0713866	−	0.890079i
$705$	−8.17398e15	−	7.98677e16i	−0.00250729	−	0.0244986i
$706$	3.08502e18	+	3.00380e18i	0.937622	+	0.912937i
$707$	1.24391e18			0.374595
$708$	3.28032e17	+	2.53540e18i	0.0978812	+	0.756537i
$709$	4.71445e18			1.39390			0.696948	−	0.717122i	$-0.254541\pi$
$709$	4.71445e18			1.39390			0.696948	+	0.717122i	$0.254541\pi$
$710$	4.55174e16	+	4.43190e16i	0.0133352	+	0.0129841i
$711$	−4.25912e16	−	2.05899e17i	−0.0123642	−	0.0597727i
$712$	−1.69838e18	+	1.84005e18i	−0.488557	+	0.529309i
$713$			4.46571e18i			1.27294i
$714$	2.93001e18	−	3.69778e18i	0.827619	−	1.04449i
$715$		−	6.72352e16i		−	0.0188195i
$716$	8.05130e16	+	3.01734e18i	0.0223322	+	0.836932i
$717$	−5.55658e18	+	5.68683e17i	−1.52733	+	0.156313i
$718$	−1.02312e18	+	1.05079e18i	−0.278688	+	0.286223i
$719$	5.84388e18			1.57748			0.788739	−	0.614728i	$-0.210734\pi$
$719$	5.84388e18			1.57748			0.788739	+	0.614728i	$0.210734\pi$
$720$	4.87099e16	+	1.85092e17i	0.0130304	+	0.0495137i
$721$	−4.23051e18			−1.12154
$722$	−1.89922e18	+	1.95057e18i	−0.498980	+	0.512472i
$723$	3.81703e17	−	3.90650e16i	0.0993863	−	0.0101716i
$724$	2.35161e16	+	8.81302e17i	0.00606827	+	0.227418i
$725$		−	5.76976e18i		−	1.47557i
$726$	−4.96573e17	+	6.26694e17i	−0.125862	+	0.158843i
$727$			2.76249e18i			0.693948i	0.937875	+	0.346974i	$0.112791\pi$
$727$			2.76249e18i			0.693948i	−0.937875	+	0.346974i	$0.887209\pi$
$728$	−1.14165e18	+	1.23688e18i	−0.284235	+	0.307944i
$729$	3.31717e18	−	2.32799e18i	0.818539	−	0.574451i
$730$	6.94964e16	+	6.76668e16i	0.0169967	+	0.0165492i
$731$	−9.11339e18			−2.20911
$732$	−6.86009e17	−	5.30226e18i	−0.164819	−	1.27391i
$733$	6.30081e18			1.50045			0.750224	−	0.661184i	$-0.229946\pi$
$733$	6.30081e18			1.50045			0.750224	+	0.661184i	$0.229946\pi$
$734$	5.76459e17	+	5.61283e17i	0.136064	+	0.132482i
$735$	−8.11312e14	−	7.92731e15i	−0.000189810	−	0.00185463i
$736$	2.16434e18	−	2.47415e18i	0.501902	−	0.573747i
$737$			7.91101e17i			0.181842i
$738$	−5.31970e18	−	3.39538e18i	−1.21205	−	0.773610i
$739$			4.64548e18i			1.04916i	0.851361	+	0.524580i	$0.175777\pi$
$739$			4.64548e18i			1.04916i	−0.851361	+	0.524580i	$0.824223\pi$
$740$	−2.81525e17	+	7.51203e15i	−0.0630246	+	0.00168171i
$741$	1.00776e17	+	9.84677e17i	0.0223634	+	0.218512i
$742$	1.50678e18	−	1.54753e18i	0.331456	−	0.340418i
$743$	−2.73266e18			−0.595879			−0.297939	−	0.954585i	$-0.596299\pi$
$743$	−2.73266e18			−0.595879			−0.297939	+	0.954585i	$0.596299\pi$
$744$	4.63446e18	−	6.18067e18i	1.00179	−	1.33601i
$745$	2.58450e17			0.0553809
$746$	2.93744e18	−	3.01687e18i	0.623975	−	0.640847i
$747$	2.67255e18	−	5.52829e17i	0.562784	−	0.116414i
$748$	−5.59719e18	+	1.49352e17i	−1.16845	+	0.0311782i
$749$		−	5.97191e18i		−	1.23590i
$750$	−3.90677e17	−	3.09561e17i	−0.0801530	−	0.0635108i
$751$		−	6.35433e18i		−	1.29244i	−0.763151	−	0.646220i	$-0.776349\pi$
$751$		−	6.35433e18i		−	1.29244i	0.763151	−	0.646220i	$-0.223651\pi$
$752$	2.38197e18	−	1.27208e17i	0.480308	−	0.0256507i
$753$	7.67229e18	−	7.85212e17i	1.53376	−	0.156971i
$754$	−2.20159e18	−	2.14362e18i	−0.436337	−	0.424849i
$755$	1.33894e17			0.0263090
$756$	4.93939e18	−	1.70647e18i	0.962237	−	0.332435i
$757$	1.08734e18			0.210011			0.105005	−	0.994472i	$-0.466514\pi$
$757$	1.08734e18			0.210011			0.105005	+	0.994472i	$0.466514\pi$
$758$	2.49452e18	+	2.42884e18i	0.477680	+	0.465104i
$759$	3.56658e18	−	3.65018e17i	0.677143	−	0.0693015i
$760$	1.06650e17	+	9.84385e16i	0.0200757	+	0.0185300i
$761$		−	7.92289e18i		−	1.47871i	−0.673315	−	0.739355i	$-0.735130\pi$
$761$		−	7.92289e18i		−	1.47871i	0.673315	−	0.739355i	$-0.264870\pi$
$762$	−5.05041e17	−	4.00179e17i	−0.0934587	−	0.0740538i
$763$			9.42134e18i			1.72863i
$764$	−6.83064e16	−	2.55989e18i	−0.0124267	−	0.465708i
$765$	3.63841e17	−	7.52621e16i	0.0656314	−	0.0135762i
$766$	−2.43761e18	+	2.50352e18i	−0.435991	+	0.447780i
$767$	−1.77062e18			−0.314018
$768$	−5.56315e18	+	1.17817e18i	−0.978302	+	0.207185i
$769$	1.39981e18			0.244089			0.122044	−	0.992525i	$-0.461055\pi$
$769$	1.39981e18			0.244089			0.122044	+	0.992525i	$0.461055\pi$
$770$	−1.87784e17	+	1.92861e17i	−0.0324689	+	0.0333469i
$771$	−8.17790e17	−	7.99061e18i	−0.140213	−	1.37002i
$772$	1.10721e17	+	4.14945e18i	0.0188243	+	0.705469i
$773$			8.94905e18i			1.50873i	0.656458	+	0.754363i	$0.272054\pi$
$773$			8.94905e18i			1.50873i	−0.656458	+	0.754363i	$0.727946\pi$
$774$	−8.50910e18	−	5.43107e18i	−1.42255	−	0.907965i
$775$			1.00463e19i			1.66551i
$776$	6.47117e18	+	5.97295e18i	1.06385	+	0.981946i
$777$	7.82890e17	+	7.64959e18i	0.127633	+	1.24710i
$778$	−4.10657e18	−	3.99846e18i	−0.663915	−	0.646435i
$779$	−4.78562e18			−0.767264
$780$	−1.31461e17	+	1.70085e16i	−0.0209017	+	0.00270428i
$781$	−2.05865e18			−0.324602
$782$	−4.57205e18	−	4.45168e18i	−0.714935	−	0.696113i
$783$	2.87362e18	+	9.09701e18i	0.445633	+	1.41074i
$784$	2.36423e17	−	1.26261e16i	0.0363610	−	0.00194185i
$785$		−	3.72984e17i		−	0.0568902i
$786$	−3.91039e18	+	4.93506e18i	−0.591526	+	0.746528i
$787$		−	5.02137e17i		−	0.0753332i	−0.999290	−	0.0376666i	$-0.988008\pi$
$787$		−	5.02137e17i		−	0.0753332i	0.999290	−	0.0376666i	$-0.0119925\pi$
$788$	3.77398e18	−	1.00703e17i	0.561539	−	0.0149838i
$789$	−1.17602e19	+	1.20359e18i	−1.73546	+	0.177614i
$790$	1.48956e16	−	1.52984e16i	0.00218013	−	0.00223908i
$791$	8.00665e18			1.16226
$792$	−5.31506e18	−	3.19616e18i	−0.765234	−	0.460167i
$793$	3.70288e18			0.528766
$794$	−4.65570e18	+	4.78159e18i	−0.659405	+	0.677234i
$795$	1.69214e17	−	1.73180e16i	0.0237711	−	0.00243283i
$796$	3.65221e18	−	9.74535e16i	0.508887	−	0.0135788i
$797$			2.10171e18i			0.290464i	0.989398	+	0.145232i	$0.0463929\pi$
$797$			2.10171e18i			0.290464i	−0.989398	+	0.145232i	$0.953607\pi$
$798$	2.46107e18	−	3.10596e18i	0.337369	−	0.425772i
$799$		−	4.63058e18i		−	0.629624i
$800$	4.86902e18	−	5.56600e18i	0.656685	−	0.750686i
$801$	1.09069e18	+	5.27275e18i	0.145912	+	0.705384i
$802$	5.93882e18	+	5.78247e18i	0.788074	+	0.767326i
$803$	−3.14317e18			−0.413730
$804$	1.54679e18	−	2.00125e17i	0.201961	−	0.0261298i
$805$	−3.06781e17			−0.0397333
$806$	3.83341e18	+	3.73249e18i	0.492502	+	0.479535i
$807$	−9.13175e17	−	8.92261e18i	−0.116379	−	1.13714i
$808$	−1.97406e18	+	2.13873e18i	−0.249567	+	0.270384i
$809$		−	6.05125e18i		−	0.758891i	−0.925214	−	0.379446i	$-0.876115\pi$
$809$		−	6.05125e18i		−	0.758891i	0.925214	−	0.379446i	$-0.123885\pi$
$810$	3.84567e17	+	1.46557e17i	0.0478431	+	0.0182328i
$811$		−	1.16185e19i		−	1.43388i	−0.697134	−	0.716941i	$-0.745542\pi$
$811$		−	1.16185e19i		−	1.43388i	0.697134	−	0.716941i	$-0.254458\pi$
$812$	3.28147e17	+	1.22978e19i	0.0401748	+	1.50561i
$813$	9.49566e17	+	9.27819e18i	0.115329	+	1.12687i
$814$	6.36637e18	−	6.53851e18i	0.767067	−	0.787808i
$815$	−2.39375e17			−0.0286124
$816$	1.70794e18	+	1.09061e19i	0.202529	+	1.29325i
$817$	−7.65482e18			−0.900517
$818$	−6.54908e18	+	6.72616e18i	−0.764335	+	0.785002i
$819$	7.33160e17	+	3.54433e18i	0.0848894	+	0.410382i
$820$	−1.70950e16	−	6.40662e17i	−0.00196372	−	0.0735934i
$821$		−	9.79468e18i		−	1.11625i	−0.829758	−	0.558123i	$-0.811522\pi$
$821$		−	9.79468e18i		−	1.11625i	0.829758	−	0.558123i	$-0.188478\pi$
$822$	1.71370e17	+	1.35789e17i	0.0193762	+	0.0153531i
$823$		−	9.32929e18i		−	1.04653i	−0.852171	−	0.523263i	$-0.824715\pi$
$823$		−	9.32929e18i		−	1.04653i	0.852171	−	0.523263i	$-0.175285\pi$
$824$	6.71375e18	−	7.27377e18i	0.747203	−	0.809530i
$825$	8.02360e18	−	8.21166e17i	0.885969	−	0.0906735i
$826$	5.07894e18	+	4.94522e18i	0.556420	+	0.541771i
$827$	2.50267e18			0.272031			0.136015	−	0.990707i	$-0.456570\pi$
$827$	2.50267e18			0.272031			0.136015	+	0.990707i	$0.456570\pi$
$828$	−1.61594e18	−	6.88118e18i	−0.174272	−	0.742105i
$829$	−1.42390e18			−0.152362			−0.0761808	−	0.997094i	$-0.524273\pi$
$829$	−1.42390e18			−0.152362			−0.0761808	+	0.997094i	$0.524273\pi$
$830$	1.98571e17	+	1.93343e17i	0.0210818	+	0.0205268i
$831$	2.36688e17	−	2.42235e16i	0.0249327	−	0.00255171i
$832$	−3.14860e17	−	3.92581e18i	−0.0329091	−	0.410325i
$833$		−	4.59610e17i		−	0.0476648i
$834$	1.11214e19	+	8.81223e18i	1.14440	+	0.906790i
$835$			2.55115e17i			0.0260480i
$836$	−4.70138e18	+	1.25449e17i	−0.476304	+	0.0127094i
$837$	−5.00355e18	−	1.58397e19i	−0.502994	−	1.59233i
$838$	−7.82724e18	+	8.03889e18i	−0.780769	+	0.801881i
$839$	−1.99310e19			−1.97277			−0.986386	−	0.164447i	$-0.947416\pi$
$839$	−1.99310e19			−1.97277			−0.986386	+	0.164447i	$0.947416\pi$
$840$	4.24594e17	+	3.18374e17i	0.0417021	+	0.0312696i
$841$	−1.21976e19			−1.18878
$842$	4.60083e18	−	4.72523e18i	0.444946	−	0.456977i
$843$	9.96080e17	+	9.73267e18i	0.0955905	+	0.934013i
$844$	7.00686e18	−	1.86967e17i	0.667264	−	0.0178049i
$845$			4.49988e17i			0.0425239i
$846$	2.75957e18	−	4.32354e18i	0.258782	−	0.405445i
$847$			2.21709e18i			0.206320i
$848$	2.69513e17	+	5.04661e18i	0.0248890	+	0.466044i
$849$	−6.86097e17	−	6.70384e18i	−0.0628761	−	0.614361i
$850$	−1.02856e19	−	1.00148e19i	−0.935416	−	0.910789i
$851$	1.04007e19			0.938686
$852$	5.20777e17	+	4.02516e18i	0.0466439	+	0.360517i
$853$	4.79427e18			0.426142			0.213071	−	0.977037i	$-0.431654\pi$
$853$	4.79427e18			0.426142			0.213071	+	0.977037i	$0.431654\pi$
$854$	−1.06215e19	−	1.03419e19i	−0.936939	−	0.912271i
$855$	3.05609e17	−	6.32166e16i	0.0267539	−	0.00553416i
$856$	1.02679e19	+	9.47734e18i	0.892075	+	0.823393i
$857$			5.72863e18i			0.493941i	0.969023	+	0.246970i	$0.0794351\pi$
$857$			5.72863e18i			0.493941i	−0.969023	+	0.246970i	$0.920565\pi$
$858$	2.66765e18	−	3.36668e18i	0.228277	−	0.288094i
$859$		−	1.48983e19i		−	1.26527i	−0.774452	−	0.632633i	$-0.781974\pi$
$859$		−	1.48983e19i		−	1.26527i	0.774452	−	0.632633i	$-0.218026\pi$
$860$	−2.73443e16	−	1.02477e18i	−0.00230477	−	0.0863746i
$861$	−1.74081e19	+	1.78161e18i	−1.45623	+	0.149037i
$862$	−2.37775e18	+	2.44204e18i	−0.197410	+	0.202748i
$863$	1.36371e19			1.12370			0.561852	−	0.827238i	$-0.310089\pi$
$863$	1.36371e19			1.12370			0.561852	+	0.827238i	$0.310089\pi$
$864$	−4.90471e18	+	1.12007e19i	−0.401120	+	0.916026i
$865$	−1.04218e18			−0.0845940
$866$	5.53145e18	−	5.68102e18i	0.445628	−	0.457678i
$867$	8.87691e18	−	9.08498e17i	0.709803	−	0.0726440i
$868$	−5.71370e17	−	2.14129e19i	−0.0453460	−	1.69941i
$869$			6.91911e17i			0.0545032i
$870$	−6.01677e17	+	7.59339e17i	−0.0470422	+	0.0593691i
$871$			1.08022e18i			0.0838286i
$872$	−1.61987e19	−	1.49515e19i	−1.24774	−	1.15167i
$873$	1.85434e19	−	3.83579e18i	1.41774	−	0.293267i
$874$	−3.84031e18	−	3.73920e18i	−0.291435	−	0.283762i
$875$	−1.38212e18			−0.104110
$876$	7.95128e17	+	6.14565e18i	0.0594512	+	0.459506i
$877$	1.84679e19			1.37063			0.685314	−	0.728248i	$-0.259665\pi$
$877$	1.84679e19			1.37063			0.685314	+	0.728248i	$0.259665\pi$
$878$	7.71154e18	+	7.50852e18i	0.568103	+	0.553146i
$879$	4.35533e17	+	4.25558e18i	0.0318488	+	0.311194i
$880$	−3.35882e16	−	6.28936e17i	−0.00243809	−	0.0456530i
$881$			2.60544e19i			1.87732i	0.344849	+	0.938658i	$0.387930\pi$
$881$			2.60544e19i			1.87732i	−0.344849	+	0.938658i	$0.612070\pi$
$882$	2.73902e17	−	4.29135e17i	0.0195907	−	0.0306936i
$883$			1.78355e19i			1.26631i	0.774024	+	0.633156i	$0.218241\pi$
$883$			1.78355e19i			1.26631i	−0.774024	+	0.633156i	$0.781759\pi$
$884$	−7.64273e18	+	2.03934e17i	−0.538653	+	0.0143731i
$885$	5.68371e16	+	5.55354e17i	0.00397650	+	0.0388543i
$886$	−3.92128e18	+	4.02731e18i	−0.272338	+	0.279702i
$887$	−2.53453e19			−1.74741			−0.873703	−	0.486459i	$-0.838288\pi$
$887$	−2.53453e19			−1.74741			−0.873703	+	0.486459i	$0.838288\pi$
$888$	−1.43949e19	−	1.07937e19i	−0.985197	−	0.738732i
$889$	−1.78671e18			−0.121393
$890$	−3.81452e17	+	3.91766e17i	−0.0257279	+	0.0264236i
$891$	−1.22416e19	+	5.29084e18i	−0.819657	+	0.354258i
$892$	2.33225e19	−	6.22324e17i	1.55026	−	0.0413662i
$893$		−	3.88947e18i		−	0.256659i
$894$	1.29414e19	+	1.02543e19i	0.847786	+	0.671760i
$895$			6.59115e17i			0.0428658i
$896$	−1.00614e19	+	1.21404e19i	−0.649614	+	0.783846i
$897$	4.87002e18	−	4.98417e17i	0.312162	−	0.0319478i
$898$	−1.77547e19	−	1.72873e19i	−1.12984	−	1.10010i
$899$	3.91044e19			2.47051
$900$	−3.63531e18	−	1.54803e19i	−0.228016	−	0.970965i
$901$	9.81069e18			0.610926
$902$	1.48796e19	+	1.44879e19i	0.919918	+	0.895699i
$903$	−2.78450e19	+	2.84977e18i	−1.70914	+	0.174920i
$904$	−1.27064e19	+	1.37663e19i	−0.774336	+	0.838926i
$905$			1.92513e17i			0.0116478i
$906$	6.70447e18	+	5.31241e18i	0.402746	+	0.319123i
$907$			2.35608e18i			0.140522i	0.997529	+	0.0702608i	$0.0223832\pi$
$907$			2.35608e18i			0.140522i	−0.997529	+	0.0702608i	$0.977617\pi$
$908$	−1.64456e17	−	6.16325e18i	−0.00973851	−	0.364965i
$909$	1.26773e18	+	6.12861e18i	0.0745353	+	0.360327i
$910$	−2.56411e17	+	2.63344e17i	−0.0149681	+	0.0153728i
$911$	6.64483e18			0.385136			0.192568	−	0.981284i	$-0.438318\pi$
$911$	6.64483e18			0.385136			0.192568	+	0.981284i	$0.438318\pi$
$912$	1.43459e18	+	9.16059e18i	0.0825585	+	0.527177i
$913$	−8.98093e18			−0.513170
$914$	9.20888e18	−	9.45788e18i	0.522464	−	0.536591i
$915$	−1.18863e17	−	1.16141e18i	−0.00669591	−	0.0654256i
$916$	2.31815e17	+	8.68762e18i	0.0129665	+	0.485937i
$917$			1.74590e19i			0.969660i
$918$	2.12048e19	+	1.06673e19i	1.16938	+	0.588269i
$919$			1.92947e19i			1.05654i	0.849075	+	0.528272i	$0.177160\pi$
$919$			1.92947e19i			1.05654i	−0.849075	+	0.528272i	$0.822840\pi$
$920$	4.86857e17	−	5.27467e17i	0.0264716	−	0.0286797i
$921$	−1.00080e18	−	9.77877e18i	−0.0540329	−	0.527955i
$922$	−2.88476e18	−	2.80881e18i	−0.154653	−	0.150581i
$923$	−2.81100e18			−0.149641
$924$	−1.70549e19	+	2.20658e18i	−0.901535	+	0.116641i
$925$	2.33980e19			1.22817
$926$	−2.02151e19	−	1.96828e19i	−1.05367	−	1.02593i
$927$	−4.31154e18	−	2.08433e19i	−0.223159	−	1.07882i
$928$	−2.16651e19	−	1.89522e19i	−1.11352	−	0.974087i
$929$		−	3.25782e19i		−	1.66274i	−0.555718	−	0.831371i	$-0.687557\pi$
$929$		−	3.25782e19i		−	1.66274i	0.555718	−	0.831371i	$-0.312443\pi$
$930$	1.04764e18	−	1.32216e18i	0.0530974	−	0.0670110i
$931$		−	3.86051e17i		−	0.0194300i
$932$	4.65775e18	−	1.24284e17i	0.232794	−	0.00621174i
$933$	−1.44701e17	+	1.48093e16i	−0.00718193	+	0.000735027i
$934$	−1.45953e19	+	1.49900e19i	−0.719381	+	0.738832i
$935$	−1.22266e18			−0.0598454
$936$	−7.25749e18	−	4.36423e18i	−0.352772	−	0.212136i
$937$	−1.70547e19			−0.823259			−0.411629	−	0.911351i	$-0.635040\pi$
$937$	−1.70547e19			−0.823259			−0.411629	+	0.911351i	$0.635040\pi$
$938$	3.01697e18	−	3.09855e18i	0.144628	−	0.148539i
$939$	−1.01229e19	+	1.03602e18i	−0.481926	+	0.0493222i
$940$	5.20692e17	−	1.38938e16i	0.0246178	−	0.000656888i
$941$			8.10167e18i			0.380402i	0.981745	+	0.190201i	$0.0609139\pi$
$941$			8.10167e18i			0.380402i	−0.981745	+	0.190201i	$0.939086\pi$
$942$	1.47987e19	−	1.86765e19i	0.690067	−	0.870891i
$943$			2.36687e19i			1.09610i
$944$	−1.65628e19	+	8.84535e17i	−0.761757	+	0.0406815i
$945$	1.08814e18	−	3.43729e17i	0.0497026	−	0.0157004i
$946$	2.38006e19	+	2.31740e19i	1.07968	+	1.05126i
$947$	1.95651e19			0.881469			0.440735	−	0.897637i	$-0.354718\pi$
$947$	1.95651e19			0.881469			0.440735	+	0.897637i	$0.354718\pi$
$948$	1.35285e18	−	1.75033e17i	0.0605335	−	0.00783187i
$949$	−4.29187e18			−0.190729
$950$	−8.63939e18	−	8.41193e18i	−0.381311	−	0.371272i
$951$	−1.36569e18	−	1.33441e19i	−0.0598658	−	0.584947i
$952$	2.24924e19	+	2.07607e19i	0.979255	+	0.903861i
$953$			1.96532e19i			0.849823i	0.905235	+	0.424912i	$0.139695\pi$
$953$			1.96532e19i			0.849823i	−0.905235	+	0.424912i	$0.860305\pi$
$954$	9.16017e18	+	5.84662e18i	0.393404	+	0.251096i
$955$		−	5.59187e17i		−	0.0238526i
$956$	−9.66627e17	−	3.62258e19i	−0.0409527	−	1.53476i
$957$	−3.19631e18	−	3.12311e19i	−0.134500	−	1.31419i
$958$	1.64085e19	−	1.68522e19i	0.685792	−	0.704336i
$959$	6.06266e17			0.0251676
$960$	−1.22122e18	+	2.24775e17i	−0.0503538	+	0.00926798i
$961$	−4.36711e19			−1.78851
$962$	8.69301e18	−	8.92806e18i	0.353616	−	0.363178i
$963$	2.94231e19	−	6.08629e18i	1.18882	−	0.245913i
$964$	6.64013e16	+	2.48849e18i	0.00266487	+	0.0998699i
$965$			9.06414e17i			0.0361326i
$966$	−1.53615e19	−	1.21720e19i	−0.608249	−	0.481958i
$967$		−	3.32463e19i		−	1.30759i	−0.756672	−	0.653795i	$-0.773176\pi$
$967$		−	3.32463e19i		−	1.30759i	0.756672	−	0.653795i	$-0.226824\pi$
$968$	−3.81198e18	−	3.51849e18i	−0.148923	−	0.137457i
$969$	1.79062e19	−	1.83259e18i	0.694863	−	0.0711150i
$970$	1.37778e18	+	1.34151e18i	0.0531085	+	0.0517103i
$971$	9.19049e17			0.0351896			0.0175948	−	0.999845i	$-0.494399\pi$
$971$	9.19049e17			0.0351896			0.0175948	+	0.999845i	$0.494399\pi$
$972$	1.34416e19	+	2.25968e19i	0.511235	+	0.859441i
$973$	3.93447e19			1.48646
$974$	2.26882e19	+	2.20908e19i	0.851464	+	0.829047i
$975$	1.09559e19	−	1.12127e18i	0.408430	−	0.0418003i
$976$	3.46377e19	−	1.84982e18i	1.28270	−	0.0685023i
$977$		−	2.35075e19i		−	0.864753i	−0.901693	−	0.432377i	$-0.857675\pi$
$977$		−	2.35075e19i		−	0.864753i	0.901693	−	0.432377i	$-0.142325\pi$
$978$	−1.19863e19	−	9.49754e18i	−0.438007	−	0.347063i
$979$		−	1.77187e19i		−	0.643198i
$980$	5.16816e16	−	1.37904e15i	0.00186366	−	4.97287e-5i
$981$	−4.64181e19	+	9.60179e18i	−1.66279	+	0.343956i
$982$	−3.16136e19	+	3.24684e19i	−1.12499	+	1.15541i
$983$	−4.06782e19			−1.43802			−0.719009	−	0.695001i	$-0.755404\pi$
$983$	−4.06782e19			−1.43802			−0.719009	+	0.695001i	$0.755404\pi$
$984$	2.45631e19	−	3.27582e19i	0.862613	−	1.15041i
$985$	8.24397e17			0.0287608
$986$	−3.89815e19	+	4.00355e19i	−1.35101	+	1.38754i
$987$	−1.44799e18	−	1.41483e19i	−0.0498544	−	0.487126i
$988$	−6.41954e18	+	1.71295e17i	−0.219575	+	0.00585902i
$989$			3.78592e19i			1.28646i
$990$	−1.14159e18	−	7.28638e17i	−0.0385373	−	0.0245971i
$991$		−	2.87604e19i		−	0.964532i	−0.876025	−	0.482266i	$-0.839814\pi$
$991$		−	2.87604e19i		−	0.964532i	0.876025	−	0.482266i	$-0.160186\pi$
$992$	3.77234e19	+	3.29996e19i	1.25685	+	1.09947i
$993$	−9.52967e16	−	9.31141e17i	−0.00315433	−	0.0308209i
$994$	8.06323e18	+	7.85095e18i	0.265154	+	0.258173i
$995$	7.97797e17			0.0260641
$996$	2.27191e18	+	1.75599e19i	0.0737402	+	0.569948i
$997$	−1.53349e19			−0.494496			−0.247248	−	0.968952i	$-0.579526\pi$
$997$	−1.53349e19			−0.494496			−0.247248	+	0.968952i	$0.579526\pi$
$998$	−3.08459e19	−	3.00338e19i	−0.988210	−	0.962193i
$999$	−3.68910e19	+	1.16533e19i	−1.17421	+	0.370915i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.14.b.a.11.6	yes	24
3.2	odd	2	inner	12.14.b.a.11.19	yes	24
4.3	odd	2	inner	12.14.b.a.11.20	yes	24
12.11	even	2	inner	12.14.b.a.11.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.14.b.a.11.5	✓	24	12.11	even	2	inner
12.14.b.a.11.6	yes	24	1.1	even	1	trivial
12.14.b.a.11.19	yes	24	3.2	odd	2	inner
12.14.b.a.11.20	yes	24	4.3	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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-63.1407 + 64.8479i) q^{2} +(-1256.10 + 128.555i) q^{3} +(-218.513 - 8189.09i) q^{4} -1788.84i q^{5} +(70974.7 - 89572.8i) q^{6} -316886. i q^{7} +(544842. + 502894. i) q^{8} +(1.56127e6 - 322956. i) q^{9} +O(q^{10})\)	\(q+(-63.1407 + 64.8479i) q^{2} +(-1256.10 + 128.555i) q^{3} +(-218.513 - 8189.09i) q^{4} -1788.84i q^{5} +(70974.7 - 89572.8i) q^{6} -316886. i q^{7} +(544842. + 502894. i) q^{8} +(1.56127e6 - 322956. i) q^{9} +(116003. + 112949. i) q^{10} -5.24655e6 q^{11} +(1.32722e6 + 1.02583e7i) q^{12} -7.16394e6 q^{13} +(2.05494e7 + 2.00084e7i) q^{14} +(229964. + 2.24697e6i) q^{15} +(-6.70134e7 + 3.57884e6i) q^{16} +1.30275e8i q^{17} +(-7.76366e7 + 1.21637e8i) q^{18} +1.09425e8i q^{19} +(-1.46490e7 + 390884. i) q^{20} +(4.07372e7 + 3.98042e8i) q^{21} +(3.31270e8 - 3.40228e8i) q^{22} +5.41194e8 q^{23} +(-7.49028e8 - 5.61645e8i) q^{24} +1.21750e9 q^{25} +(4.52336e8 - 4.64567e8i) q^{26} +(-1.91960e9 + 6.06375e8i) q^{27} +(-2.59501e9 + 6.92437e7i) q^{28} -4.73901e9i q^{29} +(-1.60231e8 - 1.26962e8i) q^{30} +8.25158e9i q^{31} +(3.99919e9 - 4.57165e9i) q^{32} +(6.59021e9 - 6.74468e8i) q^{33} +(-8.44807e9 - 8.22566e9i) q^{34} -5.66859e8 q^{35} +(-2.98587e9 - 1.27148e10i) q^{36} +1.92180e10 q^{37} +(-7.09599e9 - 6.90917e9i) q^{38} +(8.99865e9 - 9.20957e8i) q^{39} +(8.99598e8 - 9.74636e8i) q^{40} +4.37343e10i q^{41} +(-2.83844e10 - 2.24909e10i) q^{42} +6.99550e10i q^{43} +(1.14644e9 + 4.29644e10i) q^{44} +(-5.77717e8 - 2.79286e9i) q^{45} +(-3.41714e10 + 3.50953e10i) q^{46} -3.55446e10 q^{47} +(8.37157e10 - 1.31103e10i) q^{48} -3.52800e9 q^{49} +(-7.68740e10 + 7.89526e10i) q^{50} +(-1.67475e10 - 1.63639e11i) q^{51} +(1.56541e9 + 5.86661e10i) q^{52} -7.53075e10i q^{53} +(8.18827e10 - 1.62769e11i) q^{54} +9.38523e9i q^{55} +(1.59360e11 - 1.72653e11i) q^{56} +(-1.40671e10 - 1.37449e11i) q^{57} +(3.07315e11 + 2.99224e11i) q^{58} +2.47157e11 q^{59} +(1.83504e10 - 2.37418e9i) q^{60} -5.16877e11 q^{61} +(-5.35098e11 - 5.21011e11i) q^{62} +(-1.02340e11 - 4.94745e11i) q^{63} +(4.39507e10 + 5.47996e11i) q^{64} +1.28151e10i q^{65} +(-3.72372e11 + 4.69948e11i) q^{66} -1.50785e11i q^{67} +(1.06683e12 - 2.84667e10i) q^{68} +(-6.79796e11 + 6.95730e10i) q^{69} +(3.57919e10 - 3.67597e10i) q^{70} +3.92382e11 q^{71} +(1.01306e12 + 6.09194e11i) q^{72} +5.99093e11 q^{73} +(-1.21344e12 + 1.24625e12i) q^{74} +(-1.52931e12 + 1.56516e11i) q^{75} +(8.96091e11 - 2.39107e10i) q^{76} +1.66256e12i q^{77} +(-5.08459e11 + 6.41694e11i) q^{78} -1.31879e11i q^{79} +(6.40197e9 + 1.19876e11i) q^{80} +(2.33326e12 - 1.00844e12i) q^{81} +(-2.83608e12 - 2.76141e12i) q^{82} +1.71178e12 q^{83} +(3.25070e12 - 4.20578e11i) q^{84} +2.33041e11 q^{85} +(-4.53644e12 - 4.41701e12i) q^{86} +(6.09222e11 + 5.95269e12i) q^{87} +(-2.85854e12 - 2.63846e12i) q^{88} +3.37721e12i q^{89} +(2.17589e11 + 1.38880e11i) q^{90} +2.27015e12i q^{91} +(-1.18258e11 - 4.43188e12i) q^{92} +(-1.06078e12 - 1.03648e13i) q^{93} +(2.24431e12 - 2.30500e12i) q^{94} +1.95744e11 q^{95} +(-4.43569e12 + 6.25658e12i) q^{96} +1.18771e13 q^{97} +(2.22760e11 - 2.28784e11i) q^{98} +(-8.19128e12 + 1.69440e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9}+O(q^{10}) \) 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9	\( 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9} + 4403568 q^{10} - 139896 q^{12} - 17520048 q^{13} + 41046816 q^{16} - 102153744 q^{18} + 340864272 q^{21} + 401914896 q^{22} + 14766624 q^{24} - 3043252488 q^{25} + 3306349488 q^{28} + 3523891248 q^{30} - 10577805696 q^{33} + 5461322688 q^{34} + 16126437096 q^{36} - 29352930672 q^{37} - 5243368896 q^{40} + 35399300688 q^{42} + 36221734656 q^{45} + 1675946784 q^{46} + 27878547744 q^{48} - 165718477944 q^{49} - 6459860112 q^{52} - 10955701656 q^{54} + 590611321584 q^{57} - 440462601456 q^{58} - 208761511104 q^{60} + 555426186192 q^{61} - 741528997248 q^{64} + 263546293968 q^{66} - 122266973952 q^{69} - 885399371232 q^{70} + 625428177984 q^{72} + 365028975600 q^{73} + 1427271642000 q^{76} + 1481181276240 q^{78} - 2327652239400 q^{81} + 874644720480 q^{82} - 6757787638224 q^{84} - 3308476422144 q^{85} + 11607512359104 q^{88} + 4426488729648 q^{90} - 3971016902448 q^{93} - 3078833939904 q^{94} - 6470779487616 q^{96} - 4159752429648 q^{97}+O(q^{100}) \) 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9 + 4403568 * q^10 - 139896 * q^12 - 17520048 * q^13 + 41046816 * q^16 - 102153744 * q^18 + 340864272 * q^21 + 401914896 * q^22 + 14766624 * q^24 - 3043252488 * q^25 + 3306349488 * q^28 + 3523891248 * q^30 - 10577805696 * q^33 + 5461322688 * q^34 + 16126437096 * q^36 - 29352930672 * q^37 - 5243368896 * q^40 + 35399300688 * q^42 + 36221734656 * q^45 + 1675946784 * q^46 + 27878547744 * q^48 - 165718477944 * q^49 - 6459860112 * q^52 - 10955701656 * q^54 + 590611321584 * q^57 - 440462601456 * q^58 - 208761511104 * q^60 + 555426186192 * q^61 - 741528997248 * q^64 + 263546293968 * q^66 - 122266973952 * q^69 - 885399371232 * q^70 + 625428177984 * q^72 + 365028975600 * q^73 + 1427271642000 * q^76 + 1481181276240 * q^78 - 2327652239400 * q^81 + 874644720480 * q^82 - 6757787638224 * q^84 - 3308476422144 * q^85 + 11607512359104 * q^88 + 4426488729648 * q^90 - 3971016902448 * q^93 - 3078833939904 * q^94 - 6470779487616 * q^96 - 4159752429648 * q^97

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