LMFDB - Embedded newform 12.14.b.a.11.11

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			11.11
Character	$\chi$	$=$	12.11
Dual form			12.14.b.a.11.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.20327 - 90.0405i) q^{2} +(-618.744 + 1100.67i) q^{3} +(-8022.60 + 1657.33i) q^{4} +49220.1i q^{5} +(104800. + 45582.3i) q^{6} -527913. i q^{7} +(223061. + 707106. i) q^{8} +(-828634. - 1.36207e6i) q^{9} +O(q^{10})$	\(q+(-9.20327 - 90.0405i) q^{2} +(-618.744 + 1100.67i) q^{3} +(-8022.60 + 1657.33i) q^{4} +49220.1i q^{5} +(104800. + 45582.3i) q^{6} -527913. i q^{7} +(223061. + 707106. i) q^{8} +(-828634. - 1.36207e6i) q^{9} +(4.43181e6 - 452986. i) q^{10} +4.09935e6 q^{11} +(3.13976e6 - 9.85572e6i) q^{12} -8.75980e6 q^{13} +(-4.75336e7 + 4.85853e6i) q^{14} +(-5.41752e7 - 3.04547e7i) q^{15} +(6.16153e7 - 2.65923e7i) q^{16} -5.78391e7i q^{17} +(-1.15015e8 + 8.71461e7i) q^{18} -2.75386e8i q^{19} +(-8.15743e7 - 3.94873e8i) q^{20} +(5.81059e8 + 3.26643e8i) q^{21} +(-3.77274e7 - 3.69108e8i) q^{22} +4.87892e8 q^{23} +(-9.16310e8 - 1.92001e8i) q^{24} -1.20192e9 q^{25} +(8.06188e7 + 7.88737e8i) q^{26} +(2.01190e9 - 6.92818e7i) q^{27} +(8.74929e8 + 4.23523e9i) q^{28} -2.09177e9i q^{29} +(-2.24357e9 + 5.15825e9i) q^{30} -7.35378e8i q^{31} +(-2.96144e9 - 5.30314e9i) q^{32} +(-2.53645e9 + 4.51204e9i) q^{33} +(-5.20786e9 + 5.32309e8i) q^{34} +2.59840e10 q^{35} +(8.90520e9 + 9.55401e9i) q^{36} +8.45510e9 q^{37} +(-2.47959e10 + 2.53445e9i) q^{38} +(5.42007e9 - 9.64166e9i) q^{39} +(-3.48039e10 + 1.09791e10i) q^{40} +2.02458e10i q^{41} +(2.40635e10 - 5.53251e10i) q^{42} -6.24875e10i q^{43} +(-3.28874e10 + 6.79400e9i) q^{44} +(6.70412e10 - 4.07855e10i) q^{45} +(-4.49020e9 - 4.39301e10i) q^{46} -5.46971e10 q^{47} +(-8.85478e9 + 8.42721e10i) q^{48} -1.81803e11 q^{49} +(1.10616e10 + 1.08221e11i) q^{50} +(6.36619e10 + 3.57876e10i) q^{51} +(7.02763e10 - 1.45179e10i) q^{52} -4.50715e10i q^{53} +(-2.47543e10 - 1.80515e11i) q^{54} +2.01771e11i q^{55} +(3.73291e11 - 1.17757e11i) q^{56} +(3.03109e11 + 1.70393e11i) q^{57} +(-1.88344e11 + 1.92511e10i) q^{58} -1.17530e11 q^{59} +(4.85100e11 + 1.54539e11i) q^{60} -1.79980e11 q^{61} +(-6.62138e10 + 6.76788e9i) q^{62} +(-7.19054e11 + 4.37447e11i) q^{63} +(-4.50243e11 + 3.15456e11i) q^{64} -4.31158e11i q^{65} +(4.29610e11 + 1.86858e11i) q^{66} +2.45720e11i q^{67} +(9.58588e10 + 4.64020e11i) q^{68} +(-3.01880e11 + 5.37009e11i) q^{69} +(-2.39137e11 - 2.33961e12i) q^{70} -5.79753e11 q^{71} +(7.78291e11 - 8.89757e11i) q^{72} +2.56979e11 q^{73} +(-7.78146e10 - 7.61302e11i) q^{74} +(7.43681e11 - 1.32292e12i) q^{75} +(4.56406e11 + 2.20931e12i) q^{76} -2.16410e12i q^{77} +(-9.18023e11 - 3.99292e11i) q^{78} -2.18325e12i q^{79} +(1.30888e12 + 3.03272e12i) q^{80} +(-1.16860e12 + 2.25731e12i) q^{81} +(1.82294e12 - 1.86328e11i) q^{82} +1.53790e12 q^{83} +(-5.20296e12 - 1.65752e12i) q^{84} +2.84685e12 q^{85} +(-5.62641e12 + 5.75089e11i) q^{86} +(2.30235e12 + 1.29427e12i) q^{87} +(9.14407e11 + 2.89868e12i) q^{88} +2.56448e12i q^{89} +(-4.28935e12 - 5.66107e12i) q^{90} +4.62441e12i q^{91} +(-3.91416e12 + 8.08600e11i) q^{92} +(8.09410e11 + 4.55011e11i) q^{93} +(5.03392e11 + 4.92495e12i) q^{94} +1.35545e13 q^{95} +(7.66940e12 + 2.17108e10i) q^{96} -3.42281e12 q^{97} +(1.67318e12 + 1.63697e13i) q^{98} +(-3.39686e12 - 5.58360e12i) 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 $

$2$	−9.20327	−	90.0405i	−0.101683	−	0.994817i
$2$	−9.20327	−	90.0405i	−0.101683	−	0.994817i
$3$	−618.744	+	1100.67i	−0.490030	+	0.871705i
$3$	−618.744	+	1100.67i	−0.490030	+	0.871705i
$4$	−8022.60	+	1657.33i	−0.979321	+	0.202311i
$5$			49220.1i			1.40876i	0.709822	+	0.704381i	$0.248775\pi$
$5$			49220.1i			1.40876i	−0.709822	+	0.704381i	$0.751225\pi$
$6$	104800.	+	45582.3i	0.917015	+	0.398853i
$7$		−	527913.i		−	1.69600i	−0.529999	−	0.847999i	$-0.677808\pi$
$7$		−	527913.i		−	1.69600i	0.529999	−	0.847999i	$-0.322192\pi$
$8$	223061.	+	707106.i	0.300843	+	0.953674i
$9$	−828634.	−	1.36207e6i	−0.519740	−	0.854324i
$10$	4.43181e6	−	452986.i	1.40146	−	0.143247i
$11$	4.09935e6			0.697690			0.348845	−	0.937180i	$-0.386574\pi$
$11$	4.09935e6			0.697690			0.348845	+	0.937180i	$0.386574\pi$
$12$	3.13976e6	−	9.85572e6i	0.303541	−	0.952818i
$13$	−8.75980e6			−0.503341			−0.251670	−	0.967813i	$-0.580980\pi$
$13$	−8.75980e6			−0.503341			−0.251670	+	0.967813i	$0.580980\pi$
$14$	−4.75336e7	+	4.85853e6i	−1.68721	+	0.172454i
$15$	−5.41752e7	−	3.04547e7i	−1.22803	−	0.690337i
$16$	6.16153e7	−	2.65923e7i	0.918140	−	0.396256i
$17$		−	5.78391e7i		−	0.581170i	−0.956849	−	0.290585i	$-0.906150\pi$
$17$		−	5.78391e7i		−	0.581170i	0.956849	−	0.290585i	$-0.0938500\pi$
$18$	−1.15015e8	+	8.71461e7i	−0.797048	+	0.603917i
$19$		−	2.75386e8i		−	1.34290i	−0.741051	−	0.671449i	$-0.765672\pi$
$19$		−	2.75386e8i		−	1.34290i	0.741051	−	0.671449i	$-0.234328\pi$
$20$	−8.15743e7	−	3.94873e8i	−0.285009	−	1.37963i
$21$	5.81059e8	+	3.26643e8i	1.47841	+	0.831090i
$22$	−3.77274e7	−	3.69108e8i	−0.0709430	−	0.694074i
$23$	4.87892e8			0.687215			0.343608	−	0.939113i	$-0.388351\pi$
$23$	4.87892e8			0.687215			0.343608	+	0.939113i	$0.388351\pi$
$24$	−9.16310e8	−	1.92001e8i	−0.978745	−	0.205083i
$25$	−1.20192e9			−0.984612
$26$	8.06188e7	+	7.88737e8i	0.0511811	+	0.500732i
$27$	2.01190e9	−	6.92818e7i	0.999408	−	0.0344156i
$28$	8.74929e8	+	4.23523e9i	0.343119	+	1.66093i
$29$		−	2.09177e9i		−	0.653020i	−0.945194	−	0.326510i	$-0.894127\pi$
$29$		−	2.09177e9i		−	0.653020i	0.945194	−	0.326510i	$-0.105873\pi$
$30$	−2.24357e9	+	5.15825e9i	−0.561889	+	1.29186i
$31$		−	7.35378e8i		−	0.148819i	−0.997228	−	0.0744097i	$-0.976293\pi$
$31$		−	7.35378e8i		−	0.148819i	0.997228	−	0.0744097i	$-0.0237073\pi$
$32$	−2.96144e9	−	5.30314e9i	−0.487561	−	0.873089i
$33$	−2.53645e9	+	4.51204e9i	−0.341889	+	0.608180i
$34$	−5.20786e9	+	5.32309e8i	−0.578158	+	0.0590950i
$35$	2.59840e10			2.38926
$36$	8.90520e9	+	9.55401e9i	0.681832	+	0.731509i
$37$	8.45510e9			0.541761			0.270880	−	0.962613i	$-0.412685\pi$
$37$	8.45510e9			0.541761			0.270880	+	0.962613i	$0.412685\pi$
$38$	−2.47959e10	+	2.53445e9i	−1.33594	+	0.136549i
$39$	5.42007e9	−	9.64166e9i	0.246652	−	0.438765i
$40$	−3.48039e10	+	1.09791e10i	−1.34350	+	0.423816i
$41$			2.02458e10i			0.665641i	0.942990	+	0.332821i	$0.108000\pi$
$41$			2.02458e10i			0.665641i	−0.942990	+	0.332821i	$0.892000\pi$
$42$	2.40635e10	−	5.53251e10i	0.676454	−	1.55525i
$43$		−	6.24875e10i		−	1.50747i	−0.657179	−	0.753734i	$-0.728251\pi$
$43$		−	6.24875e10i		−	1.50747i	0.657179	−	0.753734i	$-0.271749\pi$
$44$	−3.28874e10	+	6.79400e9i	−0.683263	+	0.141151i
$45$	6.70412e10	−	4.07855e10i	1.20354	−	0.732191i
$46$	−4.49020e9	−	4.39301e10i	−0.0698779	−	0.683653i
$47$	−5.46971e10			−0.740164			−0.370082	−	0.928999i	$-0.620670\pi$
$47$	−5.46971e10			−0.740164			−0.370082	+	0.928999i	$0.620670\pi$
$48$	−8.85478e9	+	8.42721e10i	−0.104498	+	0.994525i
$49$	−1.81803e11			−1.87641
$50$	1.10616e10	+	1.08221e11i	0.100118	+	0.979509i
$51$	6.36619e10	+	3.57876e10i	0.506609	+	0.284791i
$52$	7.02763e10	−	1.45179e10i	0.492933	−	0.101832i
$53$		−	4.50715e10i		−	0.279324i	−0.990199	−	0.139662i	$-0.955398\pi$
$53$		−	4.50715e10i		−	0.279324i	0.990199	−	0.139662i	$-0.0446016\pi$
$54$	−2.47543e10	−	1.80515e11i	−0.135860	−	0.990728i
$55$			2.01771e11i			0.982880i
$56$	3.73291e11	−	1.17757e11i	1.61743	−	0.510229i
$57$	3.03109e11	+	1.70393e11i	1.17061	+	0.658060i
$58$	−1.88344e11	+	1.92511e10i	−0.649636	+	0.0664009i
$59$	−1.17530e11			−0.362751			−0.181376	−	0.983414i	$-0.558055\pi$
$59$	−1.17530e11			−0.362751			−0.181376	+	0.983414i	$0.558055\pi$
$60$	4.85100e11	+	1.54539e11i	1.34229	+	0.427618i
$61$	−1.79980e11			−0.447280			−0.223640	−	0.974672i	$-0.571794\pi$
$61$	−1.79980e11			−0.447280			−0.223640	+	0.974672i	$0.571794\pi$
$62$	−6.62138e10	+	6.76788e9i	−0.148048	+	0.0151324i
$63$	−7.19054e11	+	4.37447e11i	−1.44893	+	0.881478i
$64$	−4.50243e11	+	3.15456e11i	−0.818987	+	0.573812i
$65$		−	4.31158e11i		−	0.709088i
$66$	4.29610e11	+	1.86858e11i	0.639792	+	0.278276i
$67$			2.45720e11i			0.331860i	0.986138	+	0.165930i	$0.0530625\pi$
$67$			2.45720e11i			0.331860i	−0.986138	+	0.165930i	$0.946937\pi$
$68$	9.58588e10	+	4.64020e11i	0.117577	+	0.569153i
$69$	−3.01880e11	+	5.37009e11i	−0.336756	+	0.599049i
$70$	−2.39137e11	−	2.33961e12i	−0.242946	−	2.37687i
$71$	−5.79753e11			−0.537110			−0.268555	−	0.963264i	$-0.586546\pi$
$71$	−5.79753e11			−0.537110			−0.268555	+	0.963264i	$0.586546\pi$
$72$	7.78291e11	−	8.89757e11i	0.658386	−	0.752680i
$73$	2.56979e11			0.198746			0.0993731	−	0.995050i	$-0.468316\pi$
$73$	2.56979e11			0.198746			0.0993731	+	0.995050i	$0.468316\pi$
$74$	−7.78146e10	−	7.61302e11i	−0.0550877	−	0.538953i
$75$	7.43681e11	−	1.32292e12i	0.482490	−	0.858292i
$76$	4.56406e11	+	2.20931e12i	0.271683	+	1.31513i
$77$		−	2.16410e12i		−	1.18328i
$78$	−9.18023e11	−	3.99292e11i	−0.461571	−	0.200759i
$79$		−	2.18325e12i		−	1.01048i	−0.862979	−	0.505239i	$-0.831404\pi$
$79$		−	2.18325e12i		−	1.01048i	0.862979	−	0.505239i	$-0.168596\pi$
$80$	1.30888e12	+	3.03272e12i	0.558230	+	1.29344i
$81$	−1.16860e12	+	2.25731e12i	−0.459740	+	0.888054i
$82$	1.82294e12	−	1.86328e11i	0.662191	−	0.0676842i
$83$	1.53790e12			0.516320			0.258160	−	0.966102i	$-0.416884\pi$
$83$	1.53790e12			0.516320			0.258160	+	0.966102i	$0.416884\pi$
$84$	−5.20296e12	−	1.65752e12i	−1.61598	−	0.514805i
$85$	2.84685e12			0.818731
$86$	−5.62641e12	+	5.75089e11i	−1.49966	+	0.153284i
$87$	2.30235e12	+	1.29427e12i	0.569241	+	0.320000i
$88$	9.14407e11	+	2.89868e12i	0.209895	+	0.665369i
$89$			2.56448e12i			0.546972i	0.961876	+	0.273486i	$0.0881766\pi$
$89$			2.56448e12i			0.546972i	−0.961876	+	0.273486i	$0.911823\pi$
$90$	−4.28935e12	−	5.66107e12i	−0.850775	−	1.12285i
$91$			4.62441e12i			0.853665i
$92$	−3.91416e12	+	8.08600e11i	−0.673004	+	0.139031i
$93$	8.09410e11	+	4.55011e11i	0.129727	+	0.0729260i
$94$	5.03392e11	+	4.92495e12i	0.0752619	+	0.736328i
$95$	1.35545e13			1.89182
$96$	7.66940e12	+	2.17108e10i	0.999996	+	0.00283083i
$97$	−3.42281e12			−0.417221			−0.208610	−	0.977999i	$-0.566894\pi$
$97$	−3.42281e12			−0.417221			−0.208610	+	0.977999i	$0.566894\pi$
$98$	1.67318e12	+	1.63697e13i	0.190798	+	1.86668i
$99$	−3.39686e12	−	5.58360e12i	−0.362618	−	0.596054i
$100$	9.64252e12	−	1.99198e12i	0.964252	−	0.199198i
$101$		−	2.05330e13i		−	1.92470i	−0.271805	−	0.962352i	$-0.587621\pi$
$101$		−	2.05330e13i		−	1.92470i	0.271805	−	0.962352i	$-0.412379\pi$
$102$	2.63644e12	−	6.06151e12i	0.231802	−	0.532942i
$103$		−	1.07013e13i		−	0.883073i	−0.897243	−	0.441536i	$-0.854434\pi$
$103$		−	1.07013e13i		−	0.883073i	0.897243	−	0.441536i	$-0.145566\pi$
$104$	−1.95397e12	−	6.19411e12i	−0.151427	−	0.480023i
$105$	−1.60774e13	+	2.85998e13i	−1.17081	+	2.08273i
$106$	−4.05826e12	+	4.14805e11i	−0.277876	+	0.0284024i
$107$	−2.38330e13			−1.53527			−0.767635	−	0.640887i	$-0.778567\pi$
$107$	−2.38330e13			−1.53527			−0.767635	+	0.640887i	$0.778567\pi$
$108$	−1.60259e13	+	3.89022e12i	−0.971778	+	0.235895i
$109$	2.39968e13			1.37051			0.685253	−	0.728305i	$-0.259691\pi$
$109$	2.39968e13			1.37051			0.685253	+	0.728305i	$0.259691\pi$
$110$	1.81675e13	−	1.85695e12i	0.977786	−	0.0999419i
$111$	−5.23154e12	+	9.30629e12i	−0.265479	+	0.472256i
$112$	−1.40384e13	−	3.25275e13i	−0.672048	−	1.55716i
$113$		−	2.92288e13i		−	1.32069i	−0.750962	−	0.660345i	$-0.770410\pi$
$113$		−	2.92288e13i		−	1.32069i	0.750962	−	0.660345i	$-0.229590\pi$
$114$	1.25527e13	−	2.88603e13i	0.535619	−	1.23146i
$115$			2.40141e13i			0.968123i
$116$	3.46676e12	+	1.67814e13i	0.132113	+	0.639517i
$117$	7.25867e12	+	1.19314e13i	0.261607	+	0.430016i
$118$	1.08166e12	+	1.05824e13i	0.0368855	+	0.360871i
$119$	−3.05340e13			−0.985663
$120$	9.45029e12	−	4.51009e13i	0.288913	−	1.37882i
$121$	−1.77180e13			−0.513228
$122$	1.65640e12	+	1.62055e13i	0.0454807	+	0.444962i
$123$	−2.22840e13	−	1.25270e13i	−0.580243	−	0.326184i
$124$	1.21877e12	+	5.89964e12i	0.0301079	+	0.145742i
$125$			9.24543e11i			0.0216776i
$126$	4.60056e13	+	6.07181e13i	1.02424	+	1.35179i
$127$		−	3.83455e9i		−	8.10943e-5i	−1.00000		4.05471e-5i	$-0.999987\pi$
$127$		−	3.83455e9i		−	8.10943e-5i	1.00000		4.05471e-5i	$-1.29066e-5\pi$
$128$	3.25476e13	+	3.76369e13i	0.654115	+	0.756396i
$129$	6.87782e13	+	3.86638e13i	1.31407	+	0.738706i
$130$	−3.88217e13	+	3.96807e12i	−0.705413	+	0.0721020i
$131$	8.64267e13			1.49412			0.747058	−	0.664759i	$-0.231466\pi$
$131$	8.64267e13			1.49412			0.747058	+	0.664759i	$0.231466\pi$
$132$	1.28710e13	−	4.04020e13i	0.211778	−	0.664772i
$133$	−1.45380e14			−2.27755
$134$	2.21248e13	−	2.26143e12i	0.330140	−	0.0337444i
$135$	3.41006e12	+	9.90262e13i	0.0484833	+	1.40793i
$136$	4.08984e13	−	1.29017e13i	0.554247	−	0.174841i
$137$		−	7.14563e13i		−	0.923330i	−0.887054	−	0.461665i	$-0.847252\pi$
$137$		−	7.14563e13i		−	0.923330i	0.887054	−	0.461665i	$-0.152748\pi$
$138$	5.11309e13	+	2.22392e13i	0.630186	+	0.274098i
$139$		−	1.00772e13i		−	0.118507i	−0.998243	−	0.0592533i	$-0.981128\pi$
$139$		−	1.00772e13i		−	0.118507i	0.998243	−	0.0592533i	$-0.0188720\pi$
$140$	−2.08459e14	+	4.30641e13i	−2.33985	+	0.483374i
$141$	3.38435e13	−	6.02035e13i	0.362703	−	0.645205i
$142$	5.33562e12	+	5.22012e13i	0.0546148	+	0.534326i
$143$	−3.59095e13			−0.351176
$144$	−8.72771e13	−	6.18891e13i	−0.815725	−	0.578439i
$145$	1.02957e14			0.919950
$146$	−2.36505e12	−	2.31385e13i	−0.0202091	−	0.197716i
$147$	1.12490e14	−	2.00106e14i	0.919496	−	1.63567i
$148$	−6.78319e13	+	1.40129e13i	−0.530558	+	0.109604i
$149$			2.28589e14i			1.71137i	0.517496	+	0.855686i	$0.326864\pi$
$149$			2.28589e14i			1.71137i	−0.517496	+	0.855686i	$0.673136\pi$
$150$	−1.25961e14	−	5.47862e13i	−0.902904	−	0.392716i
$151$		−	1.61803e14i		−	1.11080i	−0.831583	−	0.555400i	$-0.812565\pi$
$151$		−	1.61803e14i		−	1.11080i	0.831583	−	0.555400i	$-0.187435\pi$
$152$	1.94727e14	−	6.14279e13i	1.28069	−	0.404001i
$153$	−7.87808e13	+	4.79274e13i	−0.496508	+	0.302058i
$154$	−1.94857e14	+	1.99168e13i	−1.17715	+	0.120319i
$155$	3.61954e13			0.209651
$156$	−2.75036e13	+	8.63341e13i	−0.152785	+	0.479592i
$157$	2.30285e14			1.22721			0.613605	−	0.789613i	$-0.289719\pi$
$157$	2.30285e14			1.22721			0.613605	+	0.789613i	$0.289719\pi$
$158$	−1.96581e14	+	2.00930e13i	−1.00524	+	0.102748i
$159$	4.96089e13	+	2.78877e13i	0.243488	+	0.136877i
$160$	2.61021e14	−	1.45763e14i	1.22998	−	0.686857i
$161$		−	2.57564e14i		−	1.16551i
$162$	2.14005e14	+	8.44465e13i	0.930198	+	0.367057i
$163$		−	9.20685e12i		−	0.0384496i	−0.999815	−	0.0192248i	$-0.993880\pi$
$163$		−	9.20685e12i		−	0.0384496i	0.999815	−	0.0192248i	$-0.00611982\pi$
$164$	−3.35541e13	−	1.62424e14i	−0.134667	−	0.651877i
$165$	−2.22083e14	−	1.24844e14i	−0.856782	−	0.481641i
$166$	−1.41537e13	−	1.38473e14i	−0.0525008	−	0.513644i
$167$	2.66617e14			0.951110			0.475555	−	0.879686i	$-0.342247\pi$
$167$	2.66617e14			0.951110			0.475555	+	0.879686i	$0.342247\pi$
$168$	−1.01360e14	+	4.83732e14i	−0.347820	+	1.65995i
$169$	−2.26141e14			−0.746648
$170$	−2.62003e13	−	2.56332e14i	−0.0832508	−	0.814488i
$171$	−3.75094e14	+	2.28194e14i	−1.14727	+	0.697958i
$172$	1.03563e14	+	5.01312e14i	0.304978	+	1.47630i
$173$			3.55555e14i			1.00834i	0.863604	+	0.504171i	$0.168202\pi$
$173$			3.55555e14i			1.00834i	−0.863604	+	0.504171i	$0.831798\pi$
$174$	9.53476e13	−	2.19216e14i	0.260459	−	0.598829i
$175$			6.34509e14i			1.66990i
$176$	2.52583e14	−	1.09011e14i	0.640577	−	0.276464i
$177$	7.27207e13	−	1.29361e14i	0.177759	−	0.316212i
$178$	2.30907e14	−	2.36016e13i	0.544137	−	0.0556176i
$179$	−6.27826e14			−1.42657			−0.713287	−	0.700872i	$-0.752795\pi$
$179$	−6.27826e14			−1.42657			−0.713287	+	0.700872i	$0.752795\pi$
$180$	−4.70250e14	+	4.38315e14i	−1.03052	+	0.960540i
$181$	7.51181e13			0.158794			0.0793970	−	0.996843i	$-0.474701\pi$
$181$	7.51181e13			0.158794			0.0793970	+	0.996843i	$0.474701\pi$
$182$	4.16384e14	−	4.25597e13i	0.849240	−	0.0868030i
$183$	1.11361e14	−	1.98099e14i	0.219181	−	0.389897i
$184$	1.08830e14	+	3.44991e14i	0.206744	+	0.655379i
$185$			4.16161e14i			0.763212i
$186$	3.35202e13	−	7.70673e13i	0.0593571	−	0.136470i
$187$		−	2.37103e14i		−	0.405477i
$188$	4.38813e14	−	9.06513e13i	0.724858	−	0.149744i
$189$	−3.65748e13	−	1.06211e15i	−0.0583687	−	1.69499i
$190$	−1.24746e14	−	1.22046e15i	−0.192366	−	1.88202i
$191$	−3.32118e14			−0.494966			−0.247483	−	0.968892i	$-0.579603\pi$
$191$	−3.32118e14			−0.494966			−0.247483	+	0.968892i	$0.579603\pi$
$192$	−6.86287e13	−	6.90757e14i	−0.0988662	−	0.995101i
$193$	7.84204e14			1.09221			0.546106	−	0.837716i	$-0.316110\pi$
$193$	7.84204e14			1.09221			0.546106	+	0.837716i	$0.316110\pi$
$194$	3.15010e13	+	3.08191e14i	0.0424242	+	0.415058i
$195$	4.74564e14	+	2.66777e14i	0.618116	+	0.347475i
$196$	1.45853e15	−	3.01309e14i	1.83760	−	0.379618i
$197$			1.30881e15i			1.59532i	0.603108	+	0.797660i	$0.293929\pi$
$197$			1.30881e15i			1.59532i	−0.603108	+	0.797660i	$0.706071\pi$
$198$	−4.71488e14	+	3.57243e14i	−0.556092	+	0.421347i
$199$			3.24256e14i			0.370120i	0.982727	+	0.185060i	$0.0592480\pi$
$199$			3.24256e14i			0.370120i	−0.982727	+	0.185060i	$0.940752\pi$
$200$	−2.68102e14	−	8.49885e14i	−0.296214	−	0.938999i
$201$	−2.70457e14	−	1.52038e14i	−0.289284	−	0.162621i
$202$	−1.84881e15	+	1.88971e14i	−1.91473	+	0.195709i
$203$	−1.10427e15			−1.10752
$204$	−5.70046e14	−	1.81601e14i	−0.553750	−	0.176409i
$205$	−9.96502e14			−0.937731
$206$	−9.63555e14	+	9.84874e13i	−0.878496	+	0.0897933i
$207$	−4.04284e14	−	6.64542e14i	−0.357173	−	0.587105i
$208$	−5.39738e14	+	2.32943e14i	−0.462138	+	0.199452i
$209$		−	1.12890e15i		−	0.936926i
$210$	2.72311e15	+	1.18441e15i	2.19098	+	0.952963i
$211$		−	2.32319e15i		−	1.81238i	−0.422871	−	0.906190i	$-0.638978\pi$
$211$		−	2.32319e15i		−	1.81238i	0.422871	−	0.906190i	$-0.361022\pi$
$212$	7.46985e13	+	3.61590e14i	0.0565105	+	0.273548i
$213$	3.58719e14	−	6.38117e14i	0.263200	−	0.468202i
$214$	2.19342e14	+	2.14594e15i	0.156111	+	1.52731i
$215$	3.07564e15			2.12367
$216$	4.97768e14	+	1.40718e15i	0.333486	+	0.942755i
$217$	−3.88216e14			−0.252397
$218$	−2.20849e14	−	2.16069e15i	−0.139357	−	1.36340i
$219$	−1.59004e14	+	2.82849e14i	−0.0973917	+	0.173248i
$220$	−3.34401e14	−	1.61872e15i	−0.198848	−	0.962555i
$221$			5.06659e14i			0.292527i
$222$	8.86091e14	+	3.85403e14i	0.496803	+	0.216083i
$223$			2.70943e15i			1.47535i	0.675155	+	0.737676i	$0.264077\pi$
$223$			2.70943e15i			1.47535i	−0.675155	+	0.737676i	$0.735923\pi$
$224$	−2.79960e15	+	1.56339e15i	−1.48076	+	0.826902i
$225$	9.95951e14	+	1.63710e15i	0.511743	+	0.841178i
$226$	−2.63178e15	+	2.69000e14i	−1.31384	+	0.134291i
$227$	3.14155e15			1.52397			0.761983	−	0.647597i	$-0.224226\pi$
$227$	3.14155e15			1.52397			0.761983	+	0.647597i	$0.224226\pi$
$228$	−2.71412e15	−	8.64643e14i	−1.27954	−	0.407625i
$229$	4.47910e14			0.205239			0.102620	−	0.994721i	$-0.467278\pi$
$229$	4.47910e14			0.205239			0.102620	+	0.994721i	$0.467278\pi$
$230$	2.16224e15	−	2.21008e14i	0.963105	−	0.0984414i
$231$	2.38196e15	+	1.33902e15i	1.03147	+	0.579843i
$232$	1.47910e15	−	4.66593e14i	0.622768	−	0.196456i
$233$			1.56301e15i			0.639953i	0.947425	+	0.319977i	$0.103675\pi$
$233$			1.56301e15i			0.639953i	−0.947425	+	0.319977i	$0.896325\pi$
$234$	1.00751e15	−	7.63383e14i	0.401187	−	0.303976i
$235$		−	2.69220e15i		−	1.04272i
$236$	9.42893e14	−	1.94786e14i	0.355250	−	0.0733887i
$237$	2.40304e15	+	1.35087e15i	0.880840	+	0.495165i
$238$	2.81013e14	+	2.74930e15i	0.100225	+	0.980555i
$239$	−4.33256e15			−1.50369			−0.751845	−	0.659340i	$-0.770836\pi$
$239$	−4.33256e15			−1.50369			−0.751845	+	0.659340i	$0.770836\pi$
$240$	−4.14788e15	−	4.35834e14i	−1.40105	−	0.147214i
$241$	−3.97669e15			−1.30741			−0.653704	−	0.756750i	$-0.726786\pi$
$241$	−3.97669e15			−1.30741			−0.653704	+	0.756750i	$0.726786\pi$
$242$	1.63064e14	+	1.59534e15i	0.0521865	+	0.510568i
$243$	−1.76150e15	−	2.68294e15i	−0.548835	−	0.835931i
$244$	1.44391e15	−	2.98287e14i	0.438031	−	0.0904899i
$245$		−	8.94838e15i		−	2.64341i
$246$	−9.22851e14	+	2.12175e15i	−0.265493	+	0.610403i
$247$			2.41232e15i			0.675935i
$248$	5.19990e14	−	1.64034e14i	0.141925	−	0.0447712i
$249$	−9.51564e14	+	1.69272e15i	−0.253013	+	0.450079i
$250$	8.32463e13	−	8.50882e12i	0.0215653	−	0.00220424i
$251$	−4.43051e15			−1.11834			−0.559171	−	0.829052i	$-0.688881\pi$
$251$	−4.43051e15			−1.11834			−0.559171	+	0.829052i	$0.688881\pi$
$252$	5.04369e15	−	4.70117e15i	1.24064	−	1.15639i
$253$	2.00004e15			0.479463
$254$	−3.45265e11	+	3.52904e10i	−8.06740e−5	+	8.24589e-6i
$255$	−1.76147e15	+	3.13345e15i	−0.401203	+	0.713692i
$256$	3.08930e15	−	3.27698e15i	0.685963	−	0.727637i
$257$			2.89981e15i			0.627775i	0.949460	+	0.313888i	$0.101632\pi$
$257$			2.89981e15i			0.627775i	−0.949460	+	0.313888i	$0.898368\pi$
$258$	2.84832e15	−	6.54866e15i	0.601259	−	1.38237i
$259$		−	4.46356e15i		−	0.918824i
$260$	7.14574e14	+	3.45901e15i	0.143457	+	0.694425i
$261$	−2.84913e15	+	1.73331e15i	−0.557891	+	0.339401i
$262$	−7.95408e14	−	7.78191e15i	−0.151926	−	1.48637i
$263$	2.93990e15			0.547798			0.273899	−	0.961758i	$-0.411687\pi$
$263$	2.93990e15			0.547798			0.273899	+	0.961758i	$0.411687\pi$
$264$	−3.75628e15	−	7.87077e14i	−0.682861	−	0.143084i
$265$	2.21842e15			0.393502
$266$	1.33797e15	+	1.30901e16i	0.231587	+	2.26574i
$267$	−2.82265e15	−	1.58676e15i	−0.476798	−	0.268033i
$268$	−4.07241e14	−	1.97131e15i	−0.0671390	−	0.324997i
$269$		−	2.74060e14i		−	0.0441018i	−0.999757	−	0.0220509i	$-0.992980\pi$
$269$		−	2.74060e14i		−	0.0441018i	0.999757	−	0.0220509i	$-0.00701959\pi$
$270$	8.88499e15	−	1.21841e15i	1.39570	−	0.191394i
$271$			9.97560e15i			1.52981i	0.644141	+	0.764907i	$0.277215\pi$
$271$			9.97560e15i			1.52981i	−0.644141	+	0.764907i	$0.722785\pi$
$272$	−1.53807e15	−	3.56378e15i	−0.230292	−	0.533596i
$273$	−5.08996e15	−	2.86133e15i	−0.744144	−	0.418322i
$274$	−6.43397e15	+	6.57632e14i	−0.918544	+	0.0938867i
$275$	−4.92709e15			−0.686954
$276$	1.53186e15	−	4.80852e15i	0.208598	−	0.654791i
$277$	1.12569e16			1.49728			0.748638	−	0.662979i	$-0.230708\pi$
$277$	1.12569e16			1.49728			0.748638	+	0.662979i	$0.230708\pi$
$278$	−9.07354e14	+	9.27429e13i	−0.117892	+	0.0120501i
$279$	−1.00164e15	+	6.09359e14i	−0.127140	+	0.0773474i
$280$	5.79602e15	+	1.83734e16i	0.718791	+	2.27857i
$281$		−	5.26374e15i		−	0.637827i	−0.947784	−	0.318914i	$-0.896682\pi$
$281$		−	5.26374e15i		−	0.637827i	0.947784	−	0.318914i	$-0.103318\pi$
$282$	−5.73223e15	−	2.49322e15i	−0.678741	−	0.295217i
$283$			3.51084e15i			0.406255i	0.979152	+	0.203128i	$0.0651106\pi$
$283$			3.51084e15i			0.406255i	−0.979152	+	0.203128i	$0.934889\pi$
$284$	4.65112e15	−	9.60844e14i	0.526004	−	0.108664i
$285$	−8.38678e15	+	1.49191e16i	−0.927051	+	1.64911i
$286$	3.30485e14	+	3.23331e15i	0.0357085	+	0.349356i
$287$	1.06880e16			1.12893
$288$	−4.76929e15	+	8.42806e15i	−0.492496	+	0.870315i
$289$	6.55922e15			0.662241
$290$	−9.47542e14	−	9.27032e15i	−0.0935431	−	0.915182i
$291$	2.11784e15	−	3.76739e15i	0.204451	−	0.363694i
$292$	−2.06164e15	+	4.25900e14i	−0.194636	+	0.0402086i
$293$		−	7.62439e15i		−	0.703989i	−0.936002	−	0.351994i	$-0.885504\pi$
$293$		−	7.62439e15i		−	0.703989i	0.936002	−	0.351994i	$-0.114496\pi$
$294$	−1.90529e16	−	8.28700e15i	−1.72069	−	0.748410i
$295$		−	5.78482e15i		−	0.511031i
$296$	1.88601e15	+	5.97865e15i	0.162985	+	0.516663i
$297$	8.24750e15	−	2.84010e14i	0.697277	−	0.0240114i
$298$	2.05823e16	−	2.10376e15i	1.70250	−	0.174017i
$299$	−4.27383e15			−0.345904
$300$	−3.77373e15	+	1.18458e16i	−0.298870	+	0.938157i
$301$	−3.29880e16			−2.55666
$302$	−1.45688e16	+	1.48912e15i	−1.10504	+	0.112949i
$303$	2.26001e16	+	1.27047e16i	1.67778	+	0.943164i
$304$	−7.32313e15	−	1.69680e16i	−0.532131	−	1.23297i
$305$		−	8.85863e15i		−	0.630112i
$306$	5.04045e15	+	6.65238e15i	0.350978	+	0.463221i
$307$		−	1.85695e16i		−	1.26590i	−0.774191	−	0.632952i	$-0.781843\pi$
$307$		−	1.85695e16i		−	1.26590i	0.774191	−	0.632952i	$-0.218157\pi$
$308$	3.58664e15	+	1.73617e16i	0.239391	+	1.15881i
$309$	1.17787e16	+	6.62140e15i	0.769779	+	0.432733i
$310$	−3.33116e14	−	3.25905e15i	−0.0213179	−	0.208565i
$311$	2.49686e16			1.56478			0.782388	−	0.622791i	$-0.214001\pi$
$311$	2.49686e16			1.56478			0.782388	+	0.622791i	$0.214001\pi$
$312$	8.02669e15	+	1.68189e15i	0.492642	+	0.103227i
$313$	9.41838e15			0.566158			0.283079	−	0.959097i	$-0.408644\pi$
$313$	9.41838e15			0.566158			0.283079	+	0.959097i	$0.408644\pi$
$314$	−2.11938e15	−	2.07350e16i	−0.124786	−	1.22085i
$315$	−2.15312e16	−	3.53919e16i	−1.24179	−	2.04120i
$316$	3.61837e15	+	1.75153e16i	0.204431	+	0.989583i
$317$			1.93840e16i			1.07290i	0.843933	+	0.536449i	$0.180234\pi$
$317$			1.93840e16i			1.07290i	−0.843933	+	0.536449i	$0.819766\pi$
$318$	2.05446e15	−	4.72347e15i	0.111409	−	0.256144i
$319$		−	8.57489e15i		−	0.455606i
$320$	−1.55268e16	−	2.21610e16i	−0.808365	−	1.15376i
$321$	1.47466e16	−	2.62324e16i	0.752329	−	1.33830i
$322$	−2.31912e16	+	2.37044e15i	−1.15947	+	0.118513i
$323$	−1.59281e16			−0.780452
$324$	5.63406e15	−	2.00463e16i	0.270570	−	0.962700i
$325$	1.05286e16			0.495596
$326$	−8.28990e14	+	8.47331e13i	−0.0382503	+	0.00390966i
$327$	−1.48479e16	+	2.64126e16i	−0.671590	+	1.19468i
$328$	−1.43159e16	+	4.51606e15i	−0.634805	+	0.200253i
$329$			2.88753e16i			1.25532i
$330$	−9.19717e15	+	2.11455e16i	−0.392025	+	0.901315i
$331$			1.26206e16i			0.527470i	0.964595	+	0.263735i	$0.0849544\pi$
$331$			1.26206e16i			0.527470i	−0.964595	+	0.263735i	$0.915046\pi$
$332$	−1.23379e16	+	2.54881e15i	−0.505643	+	0.104457i
$333$	−7.00618e15	−	1.15164e16i	−0.281575	−	0.462839i
$334$	−2.45375e15	−	2.40063e16i	−0.0967115	−	0.946181i
$335$	−1.20944e16			−0.467512
$336$	4.44883e16	+	4.67456e15i	1.68671	+	0.177229i
$337$	−2.56450e16			−0.953693			−0.476847	−	0.878987i	$-0.658220\pi$
$337$	−2.56450e16			−0.953693			−0.476847	+	0.878987i	$0.658220\pi$
$338$	2.08124e15	+	2.03619e16i	0.0759212	+	0.742778i
$339$	3.21713e16	+	1.80851e16i	1.15125	+	0.647178i
$340$	−2.28391e16	+	4.71818e15i	−0.801801	+	0.165639i
$341$		−	3.01457e15i		−	0.103830i
$342$	2.39988e16	+	3.16735e16i	0.810998	+	1.07035i
$343$			4.48273e16i			1.48638i
$344$	4.41853e16	−	1.39386e16i	1.43763	−	0.453511i
$345$	−2.64317e16	−	1.48586e16i	−0.843918	−	0.474410i
$346$	3.20144e16	−	3.27227e15i	1.00311	−	0.102531i
$347$	3.04483e15			0.0936312			0.0468156	−	0.998904i	$-0.485093\pi$
$347$	3.04483e15			0.0936312			0.0468156	+	0.998904i	$0.485093\pi$
$348$	−2.06159e16	−	6.56764e15i	−0.622210	−	0.198219i
$349$	2.44852e16			0.725336			0.362668	−	0.931918i	$-0.381866\pi$
$349$	2.44852e16			0.725336			0.362668	+	0.931918i	$0.381866\pi$
$350$	5.71315e16	−	5.83956e15i	1.66124	−	0.169800i
$351$	−1.76239e16	+	6.06895e14i	−0.503043	+	0.0173228i
$352$	−1.21400e16	−	2.17394e16i	−0.340166	−	0.609146i
$353$			2.63621e16i			0.725177i	0.931949	+	0.362588i	$0.118107\pi$
$353$			2.63621e16i			0.725177i	−0.931949	+	0.362588i	$0.881893\pi$
$354$	−1.23170e16	−	5.35727e15i	−0.332648	−	0.144685i
$355$		−	2.85355e16i		−	0.756661i
$356$	−4.25021e15	−	2.05738e16i	−0.110659	−	0.535661i
$357$	1.88927e16	−	3.36079e16i	0.483005	−	0.859208i
$358$	5.77805e15	+	5.65298e16i	0.145058	+	1.41918i
$359$	−6.24103e16			−1.53866			−0.769329	−	0.638853i	$-0.779409\pi$
$359$	−6.24103e16			−1.53866			−0.769329	+	0.638853i	$0.779409\pi$
$360$	4.37940e16	+	3.83076e16i	1.06035	+	0.927510i
$361$	−3.37842e16			−0.803373
$362$	−6.91332e14	−	6.76367e15i	−0.0161466	−	0.157971i
$363$	1.09629e16	−	1.95017e16i	0.251498	−	0.447384i
$364$	−7.66420e15	−	3.70998e16i	−0.172706	−	0.836012i
$365$			1.26485e16i			0.279986i
$366$	−1.88618e16	−	8.20389e15i	−0.410163	−	0.178399i
$367$			4.34629e16i			0.928516i	0.885700	+	0.464258i	$0.153679\pi$
$367$			4.34629e16i			0.928516i	−0.885700	+	0.464258i	$0.846321\pi$
$368$	3.00616e16	−	1.29742e16i	0.630960	−	0.272313i
$369$	2.75762e16	−	1.67764e16i	0.568673	−	0.345961i
$370$	3.74714e16	−	3.83004e15i	0.759256	−	0.0776055i
$371$	−2.37938e16			−0.473733
$372$	−7.24768e15	−	2.30891e15i	−0.141798	−	0.0451728i
$373$	−3.43156e16			−0.659758			−0.329879	−	0.944023i	$-0.607008\pi$
$373$	−3.43156e16			−0.659758			−0.329879	+	0.944023i	$0.607008\pi$
$374$	−2.13489e16	+	2.18212e15i	−0.403375	+	0.0412300i
$375$	−1.01762e15	−	5.72056e14i	−0.0188965	−	0.0106227i
$376$	−1.22008e16	−	3.86766e16i	−0.222673	−	0.705875i
$377$			1.83235e16i			0.328692i
$378$	−9.52964e16	+	1.30681e16i	−1.68027	+	0.230418i
$379$		−	7.25568e16i		−	1.25754i	−0.777590	−	0.628772i	$-0.783558\pi$
$379$		−	7.25568e16i		−	1.25754i	0.777590	−	0.628772i	$-0.216442\pi$
$380$	−1.08742e17	+	2.24644e16i	−1.85270	+	0.382737i
$381$	4.22058e12	+	2.37261e12i	7.06903e−5	+	3.97387e-5i
$382$	3.05657e15	+	2.99041e16i	0.0503295	+	0.492400i
$383$	7.87317e16			1.27455			0.637276	−	0.770636i	$-0.280061\pi$
$383$	7.87317e16			1.27455			0.637276	+	0.770636i	$0.280061\pi$
$384$	−6.15645e16	+	1.25366e16i	−0.979890	+	0.199538i
$385$	1.06517e17			1.66696
$386$	−7.21724e15	−	7.06102e16i	−0.111059	−	1.08655i
$387$	−8.51123e16	+	5.17793e16i	−1.28787	+	0.783492i
$388$	2.74598e16	−	5.67274e15i	0.408593	−	0.0844085i
$389$		−	6.41150e15i		−	0.0938183i	−0.998899	−	0.0469091i	$-0.985063\pi$
$389$		−	6.41150e15i		−	0.0938183i	0.998899	−	0.0469091i	$-0.0149371\pi$
$390$	1.96532e16	−	4.51852e16i	0.282822	−	0.650244i
$391$		−	2.82192e16i		−	0.399389i
$392$	−4.05533e16	−	1.28554e17i	−0.564503	−	1.78948i
$393$	−5.34760e16	+	9.51274e16i	−0.732163	+	1.30243i
$394$	1.17846e17	−	1.20454e16i	1.58705	−	0.162216i
$395$	1.07460e17			1.42352
$396$	3.65055e16	+	3.91652e16i	0.475708	+	0.510366i
$397$	8.11799e16			1.04066			0.520332	−	0.853964i	$-0.325808\pi$
$397$	8.11799e16			1.04066			0.520332	+	0.853964i	$0.325808\pi$
$398$	2.91962e16	−	2.98421e15i	0.368202	−	0.0376348i
$399$	8.99528e16	−	1.60015e17i	1.11607	−	1.98535i
$400$	−7.40567e16	+	3.19618e16i	−0.904012	+	0.390158i
$401$		−	9.47629e16i		−	1.13815i	−0.822285	−	0.569076i	$-0.807301\pi$
$401$		−	9.47629e16i		−	1.13815i	0.822285	−	0.569076i	$-0.192699\pi$
$402$	−1.12005e16	+	2.57514e16i	−0.132363	+	0.304320i
$403$			6.44176e15i			0.0749069i
$404$	3.40301e16	+	1.64728e17i	0.389390	+	1.88490i
$405$	−1.11105e17	−	5.75185e16i	−1.25106	−	0.647664i
$406$	1.01629e16	+	9.94292e16i	0.112616	+	1.10178i
$407$	3.46604e16			0.377981
$408$	−1.11051e16	+	5.29986e16i	−0.119188	+	0.568817i
$409$	−1.09007e17			−1.15147			−0.575736	−	0.817635i	$-0.695285\pi$
$409$	−1.09007e17			−1.15147			−0.575736	+	0.817635i	$0.695285\pi$
$410$	9.17108e15	+	8.97256e16i	0.0953510	+	0.932870i
$411$	7.86500e16	+	4.42132e16i	0.804872	+	0.452460i
$412$	1.77357e16	+	8.58526e16i	0.178656	+	0.864812i
$413$			6.20454e16i			0.615225i
$414$	−5.61150e16	+	4.25179e16i	−0.547743	+	0.415021i
$415$			7.56954e16i			0.727373i
$416$	2.59417e16	+	4.64545e16i	0.245409	+	0.439461i
$417$	1.10917e16	+	6.23519e15i	0.103303	+	0.0580718i
$418$	−1.01647e17	+	1.03896e16i	−0.932070	+	0.0952692i
$419$	−1.23240e17			−1.11265			−0.556325	−	0.830965i	$-0.687789\pi$
$419$	−1.23240e17			−1.11265			−0.556325	+	0.830965i	$0.687789\pi$
$420$	8.15833e16	−	2.56090e17i	0.725238	−	2.27653i
$421$	4.87165e16			0.426425			0.213212	−	0.977006i	$-0.431607\pi$
$421$	4.87165e16			0.426425			0.213212	+	0.977006i	$0.431607\pi$
$422$	−2.09181e17	+	2.13810e16i	−1.80299	+	0.184288i
$423$	4.53238e16	+	7.45012e16i	0.384693	+	0.632340i
$424$	3.18703e16	−	1.00537e16i	0.266384	−	0.0840327i
$425$			6.95179e16i			0.572228i
$426$	−6.07578e16	−	2.64265e16i	−0.492538	−	0.214228i
$427$			9.50137e16i			0.758586i
$428$	1.91203e17	−	3.94993e16i	1.50352	−	0.310603i
$429$	2.22188e16	−	3.95246e16i	0.172087	−	0.306122i
$430$	−2.83060e16	−	2.76933e17i	−0.215940	−	2.11266i
$431$	−1.45511e16			−0.109344			−0.0546718	−	0.998504i	$-0.517411\pi$
$431$	−1.45511e16			−0.109344			−0.0546718	+	0.998504i	$0.517411\pi$
$432$	1.22122e17	−	5.77699e16i	0.903959	−	0.427619i
$433$	7.62883e16			0.556272			0.278136	−	0.960542i	$-0.410283\pi$
$433$	7.62883e16			0.556272			0.278136	+	0.960542i	$0.410283\pi$
$434$	3.57285e15	+	3.49551e16i	0.0256644	+	0.251089i
$435$	−6.37041e16	+	1.13322e17i	−0.450804	+	0.801926i
$436$	−1.92517e17	+	3.97707e16i	−1.34217	+	0.277269i
$437$		−	1.34358e17i		−	0.922859i
$438$	2.69313e16	+	1.17137e16i	0.182253	+	0.0792706i
$439$		−	2.42015e17i		−	1.61370i	−0.590757	−	0.806849i	$-0.701171\pi$
$439$		−	2.42015e17i		−	1.61370i	0.590757	−	0.806849i	$-0.298829\pi$
$440$	−1.42673e17	+	4.50073e16i	−0.937347	+	0.295692i
$441$	1.50648e17	+	2.47628e17i	0.975244	+	1.60306i
$442$	4.56198e16	−	4.66292e15i	0.291011	−	0.0297449i
$443$	8.73756e15			0.0549245			0.0274622	−	0.999623i	$-0.491257\pi$
$443$	8.73756e15			0.0549245			0.0274622	+	0.999623i	$0.491257\pi$
$444$	2.65469e16	−	8.33311e16i	0.164447	−	0.516199i
$445$	−1.26224e17			−0.770553
$446$	2.43958e17	−	2.49356e16i	1.46770	−	0.150018i
$447$	−2.51601e17	−	1.41438e17i	−1.49181	−	0.838624i
$448$	1.66534e17	+	2.37689e17i	0.973183	+	1.38900i
$449$		−	3.10255e17i		−	1.78697i	−0.449089	−	0.893487i	$-0.648251\pi$
$449$		−	3.10255e17i		−	1.78697i	0.449089	−	0.893487i	$-0.351749\pi$
$450$	1.38239e17	−	1.04743e17i	0.784783	−	0.594624i
$451$			8.29947e16i			0.464411i
$452$	4.84419e16	+	2.34491e17i	0.267191	+	1.29338i
$453$	1.78092e17	+	1.00115e17i	0.968291	+	0.544326i
$454$	−2.89125e16	−	2.82866e17i	−0.154961	−	1.51607i
$455$	−2.27614e17			−1.20261
$456$	−5.28742e16	+	2.52339e17i	−0.275405	+	1.31435i
$457$	−3.43727e17			−1.76506			−0.882528	−	0.470259i	$-0.844160\pi$
$457$	−3.43727e17			−1.76506			−0.882528	+	0.470259i	$0.844160\pi$
$458$	−4.12223e15	−	4.03300e16i	−0.0208693	−	0.204175i
$459$	−4.00720e15	−	1.16367e17i	−0.0200013	−	0.580826i
$460$	−3.97994e16	−	1.92656e17i	−0.195862	−	0.948103i
$461$			1.21112e17i			0.587667i	0.955857	+	0.293834i	$0.0949311\pi$
$461$			1.21112e17i			0.587667i	−0.955857	+	0.293834i	$0.905069\pi$
$462$	9.86447e16	−	2.26797e17i	0.471955	−	1.08509i
$463$		−	1.19669e16i		−	0.0564554i	−0.999602	−	0.0282277i	$-0.991014\pi$
$463$		−	1.19669e16i		−	0.0564554i	0.999602	−	0.0282277i	$-0.00898635\pi$
$464$	−5.56249e16	−	1.28885e17i	−0.258763	−	0.599564i
$465$	−2.23957e16	+	3.98393e16i	−0.102735	+	0.182754i
$466$	1.40734e17	−	1.43848e16i	0.636636	−	0.0650722i
$467$	2.06001e17			0.918988			0.459494	−	0.888181i	$-0.348031\pi$
$467$	2.06001e17			0.918988			0.459494	+	0.888181i	$0.348031\pi$
$468$	−7.80078e16	−	8.36912e16i	−0.343194	−	0.368198i
$469$	1.29719e17			0.562833
$470$	−2.42407e17	+	2.47770e16i	−1.03731	+	0.106026i
$471$	−1.42488e17	+	2.53469e17i	−0.601370	+	1.06976i
$472$	−2.62163e16	−	8.31059e16i	−0.109131	−	0.345946i
$473$		−	2.56158e17i		−	1.05175i
$474$	9.95175e16	−	2.28804e17i	0.403033	−	0.926624i
$475$			3.30991e17i			1.32223i
$476$	2.44962e17	−	5.06051e16i	0.965281	−	0.199411i
$477$	−6.13904e16	+	3.73478e16i	−0.238633	+	0.145176i
$478$	3.98737e16	+	3.90106e17i	0.152899	+	1.49590i
$479$	−1.72158e17			−0.651247			−0.325624	−	0.945499i	$-0.605574\pi$
$479$	−1.72158e17			−0.651247			−0.325624	+	0.945499i	$0.605574\pi$
$480$	−1.06861e15	+	3.77489e17i	−0.00398796	+	1.40876i
$481$	−7.40650e16			−0.272690
$482$	3.65986e16	+	3.58063e17i	0.132941	+	1.30063i
$483$	2.83494e17	+	1.59367e17i	1.01599	+	0.571138i
$484$	1.42145e17	−	2.93647e16i	0.502615	−	0.103832i
$485$		−	1.68471e17i		−	0.587765i
$486$	−2.25362e17	+	1.83298e17i	−0.775791	+	0.630990i
$487$		−	2.74668e17i		−	0.932976i	−0.884528	−	0.466488i	$-0.845519\pi$
$487$		−	2.74668e17i		−	0.932976i	0.884528	−	0.466488i	$-0.154481\pi$
$488$	−4.01466e16	−	1.27265e17i	−0.134561	−	0.426559i
$489$	1.01337e16	+	5.69669e15i	0.0335167	+	0.0188415i
$490$	−8.05717e17	+	8.23543e16i	−2.62971	+	0.268789i
$491$	1.32648e17			0.427238			0.213619	−	0.976917i	$-0.431475\pi$
$491$	1.32648e17			0.427238			0.213619	+	0.976917i	$0.431475\pi$
$492$	1.99537e17	+	6.35669e16i	0.634235	+	0.202050i
$493$	−1.20986e17			−0.379516
$494$	2.17207e17	−	2.22012e16i	0.672432	−	0.0687309i
$495$	2.74825e17	−	1.67194e17i	0.839698	−	0.510842i
$496$	−1.95554e16	−	4.53106e16i	−0.0589705	−	0.136637i
$497$			3.06059e17i			0.910938i
$498$	1.61171e17	+	7.01008e16i	0.473473	+	0.205936i
$499$		−	9.78217e16i		−	0.283649i	−0.989892	−	0.141825i	$-0.954703\pi$
$499$		−	9.78217e16i		−	0.283649i	0.989892	−	0.141825i	$-0.0452969\pi$
$500$	−1.53228e15	−	7.41724e15i	−0.00438563	−	0.0212294i
$501$	−1.64968e17	+	2.93458e17i	−0.466073	+	0.829088i
$502$	4.07752e16	+	3.98926e17i	0.113716	+	1.11255i
$503$	2.26003e17			0.622190			0.311095	−	0.950379i	$-0.399304\pi$
$503$	2.26003e17			0.622190			0.311095	+	0.950379i	$0.399304\pi$
$504$	−4.69715e17	−	4.10870e17i	−1.27654	−	1.11662i
$505$	1.01064e18			2.71145
$506$	−1.84069e16	−	1.80085e17i	−0.0487531	−	0.476978i
$507$	1.39923e17	−	2.48907e17i	0.365880	−	0.650857i
$508$	6.35513e12	+	3.07631e13i	1.64063e−5	+	7.94173e-5i
$509$			5.67729e17i			1.44702i	0.690313	+	0.723511i	$0.257473\pi$
$509$			5.67729e17i			1.44702i	−0.690313	+	0.723511i	$0.742527\pi$
$510$	2.98349e17	+	1.29766e17i	0.750789	+	0.326554i
$511$		−	1.35663e17i		−	0.337073i
$512$	−3.23493e17	−	2.48003e17i	−0.793616	−	0.608419i
$513$	−1.90792e16	−	5.54049e17i	−0.0462165	−	1.34210i
$514$	2.61100e17	−	2.66877e16i	0.624521	−	0.0638339i
$515$	5.26722e17			1.24404
$516$	−6.15859e17	−	1.96196e17i	−1.43634	−	0.457579i
$517$	−2.24222e17			−0.516405
$518$	−4.01901e17	+	4.10793e16i	−0.914062	+	0.0934286i
$519$	−3.91350e17	−	2.19998e17i	−0.878976	−	0.494118i
$520$	3.04875e17	−	9.61748e16i	0.676239	−	0.213324i
$521$		−	1.00733e17i		−	0.220662i	−0.993895	−	0.110331i	$-0.964809\pi$
$521$		−	1.00733e17i		−	0.220662i	0.993895	−	0.110331i	$-0.0351911\pi$
$522$	1.82290e17	+	2.40585e17i	0.394370	+	0.520488i
$523$			5.74099e17i			1.22666i	0.789825	+	0.613332i	$0.210171\pi$
$523$			5.74099e17i			1.22666i	−0.789825	+	0.613332i	$0.789829\pi$
$524$	−6.93367e17	+	1.43238e17i	−1.46322	+	0.302277i
$525$	−6.98386e17	−	3.92599e17i	−1.45566	−	0.818302i
$526$	−2.70567e16	−	2.64710e17i	−0.0557016	−	0.544959i
$527$	−4.25336e16			−0.0864894
$528$	−3.62989e16	+	3.45461e17i	−0.0729076	+	0.693870i
$529$	−2.65998e17			−0.527735
$530$	−2.04168e16	−	1.99748e17i	−0.0400123	−	0.391462i
$531$	9.73890e16	+	1.60083e17i	0.188537	+	0.309907i
$532$	1.16632e18	−	2.40943e17i	2.23045	−	0.460774i
$533$		−	1.77349e17i		−	0.335044i
$534$	−1.16895e17	+	2.68757e17i	−0.218161	+	0.501581i
$535$		−	1.17307e18i		−	2.16283i
$536$	−1.73750e17	+	5.48107e16i	−0.316486	+	0.0998376i
$537$	3.88464e17	−	6.91030e17i	0.699065	−	1.24355i
$538$	−2.46765e16	+	2.52225e15i	−0.0438732	+	0.00448439i
$539$	−7.45275e17			−1.30915
$540$	−1.91477e17	−	7.88796e17i	−0.332321	−	1.36901i
$541$	4.53483e17			0.777641			0.388821	−	0.921314i	$-0.372883\pi$
$541$	4.53483e17			0.777641			0.388821	+	0.921314i	$0.372883\pi$
$542$	8.98209e17	−	9.18081e16i	1.52189	−	0.155556i
$543$	−4.64789e16	+	8.26804e16i	−0.0778139	+	0.138422i
$544$	−3.06729e17	+	1.71287e17i	−0.507414	+	0.283356i
$545$			1.18113e18i			1.93072i
$546$	−2.10791e17	+	4.84636e17i	−0.340487	+	0.782823i
$547$			3.69128e17i			0.589196i	0.955621	+	0.294598i	$0.0951858\pi$
$547$			3.69128e17i			0.589196i	−0.955621	+	0.294598i	$0.904814\pi$
$548$	1.18427e17	+	5.73266e17i	0.186800	+	0.904237i
$549$	1.49137e17	+	2.45145e17i	0.232470	+	0.382122i
$550$	4.53453e16	+	4.43638e17i	0.0698514	+	0.683394i
$551$	−5.76043e17			−0.876939
$552$	−4.47060e17	−	9.36755e16i	−0.672608	−	0.140936i
$553$	−1.15257e18			−1.71377
$554$	−1.03601e17	−	1.01358e18i	−0.152247	−	1.48952i
$555$	−4.58057e17	−	2.57497e17i	−0.665296	−	0.373997i
$556$	1.67012e16	+	8.08451e16i	0.0239752	+	0.116056i
$557$		−	7.29365e16i		−	0.103487i	−0.998660	−	0.0517435i	$-0.983522\pi$
$557$		−	7.29365e16i		−	0.103487i	0.998660	−	0.0517435i	$-0.0164778\pi$
$558$	6.40853e16	+	8.45797e16i	0.0898745	+	0.118616i
$559$			5.47378e17i			0.758771i
$560$	1.60101e18	−	6.90972e17i	2.19367	−	0.946757i
$561$	2.60972e17	+	1.46706e17i	0.353456	+	0.198696i
$562$	−4.73950e17	+	4.84436e16i	−0.634521	+	0.0648560i
$563$	5.03770e17			0.666695			0.333348	−	0.942804i	$-0.391822\pi$
$563$	5.03770e17			0.666695			0.333348	+	0.942804i	$0.391822\pi$
$564$	−1.71735e17	+	5.39079e17i	−0.224670	+	0.705242i
$565$	1.43864e18			1.86054
$566$	3.16118e17	−	3.23112e16i	0.404149	−	0.0413091i
$567$	1.19166e18	+	6.16918e17i	1.50614	+	0.779718i
$568$	−1.29320e17	−	4.09947e17i	−0.161586	−	0.512228i
$569$		−	2.25742e17i		−	0.278857i	−0.990232	−	0.139429i	$-0.955473\pi$
$569$		−	2.25742e17i		−	0.278857i	0.990232	−	0.139429i	$-0.0445266\pi$
$570$	1.42051e18	+	6.17846e17i	1.73483	+	0.754560i
$571$			1.43242e18i			1.72956i	0.502150	+	0.864780i	$0.332542\pi$
$571$			1.43242e18i			1.72956i	−0.502150	+	0.864780i	$0.667458\pi$
$572$	2.88087e17	−	5.95140e16i	0.343914	−	0.0710469i
$573$	2.05496e17	−	3.65553e17i	0.242548	−	0.431464i
$574$	−9.83648e16	−	9.62356e17i	−0.114792	−	1.12307i
$575$	−5.86407e17			−0.676640
$576$	8.02760e17	+	3.51864e17i	0.915882	+	0.401447i
$577$	−9.45292e17			−1.06641			−0.533204	−	0.845987i	$-0.679012\pi$
$577$	−9.45292e17			−1.06641			−0.533204	+	0.845987i	$0.679012\pi$
$578$	−6.03662e16	−	5.90595e17i	−0.0673385	−	0.658808i
$579$	−4.85222e17	+	8.63152e17i	−0.535217	+	0.952087i
$580$	−8.25984e17	+	1.70634e17i	−0.900927	+	0.186116i
$581$		−	8.11875e17i		−	0.875678i
$582$	−3.58709e17	−	1.56019e17i	−0.382598	−	0.166410i
$583$		−	1.84764e17i		−	0.194882i
$584$	5.73221e16	+	1.81711e17i	0.0597914	+	0.189539i
$585$	−5.87268e17	+	3.57273e17i	−0.605791	+	0.368542i
$586$	−6.86505e17	+	7.01694e16i	−0.700340	+	0.0715835i
$587$	−6.78124e17			−0.684166			−0.342083	−	0.939670i	$-0.611132\pi$
$587$	−6.78124e17			−0.684166			−0.342083	+	0.939670i	$0.611132\pi$
$588$	−5.70817e17	+	1.79180e18i	−0.569567	+	1.78787i
$589$	−2.02512e17			−0.199849
$590$	−5.20868e17	+	5.32393e16i	−0.508382	+	0.0519630i
$591$	−1.44058e18	−	8.09822e17i	−1.39065	−	0.781755i
$592$	5.20964e17	−	2.24840e17i	0.497412	−	0.214676i
$593$			1.62966e18i			1.53901i	0.638638	+	0.769507i	$0.279498\pi$
$593$			1.62966e18i			1.53901i	−0.638638	+	0.769507i	$0.720502\pi$
$594$	−1.01476e17	−	7.39995e17i	−0.0947880	−	0.691221i
$595$		−	1.50289e18i		−	1.38857i
$596$	−3.78848e17	−	1.83388e18i	−0.346230	−	1.67598i
$597$	−3.56899e17	−	2.00631e17i	−0.322636	−	0.181370i
$598$	3.93333e16	+	3.84818e17i	0.0351724	+	0.344111i
$599$	9.82836e17			0.869374			0.434687	−	0.900582i	$-0.356859\pi$
$599$	9.82836e17			0.869374			0.434687	+	0.900582i	$0.356859\pi$
$600$	1.10133e18	+	2.30769e17i	0.963684	+	0.201927i
$601$	5.42866e17			0.469904			0.234952	−	0.972007i	$-0.424507\pi$
$601$	5.42866e17			0.469904			0.234952	+	0.972007i	$0.424507\pi$
$602$	3.03597e17	+	2.97025e18i	0.259968	+	2.54341i
$603$	3.34688e17	−	2.03612e17i	0.283516	−	0.172481i
$604$	2.68162e17	+	1.29808e18i	0.224728	+	1.08783i
$605$		−	8.72084e17i		−	0.723017i
$606$	9.35943e17	−	2.15185e18i	0.767675	−	1.76498i
$607$			3.36121e17i			0.272753i	0.990657	+	0.136376i	$0.0435457\pi$
$607$			3.36121e17i			0.272753i	−0.990657	+	0.136376i	$0.956454\pi$
$608$	−1.46041e18	+	8.15539e17i	−1.17247	+	0.654744i
$609$	6.83262e17	−	1.21544e18i	0.542719	−	0.965431i
$610$	−7.97636e17	+	8.15284e16i	−0.626846	+	0.0640715i
$611$	4.79135e17			0.372555
$612$	5.52595e17	−	5.15069e17i	0.425131	−	0.396261i
$613$	−9.08484e17			−0.691551			−0.345776	−	0.938317i	$-0.612384\pi$
$613$	−9.08484e17			−0.691551			−0.345776	+	0.938317i	$0.612384\pi$
$614$	−1.67201e18	+	1.70900e17i	−1.25934	+	0.128721i
$615$	6.16580e17	−	1.09682e18i	0.459516	−	0.817425i
$616$	1.53025e18	−	4.82727e17i	1.12846	−	0.355981i
$617$			6.14000e17i			0.448038i	0.974585	+	0.224019i	$0.0719177\pi$
$617$			6.14000e17i			0.448038i	−0.974585	+	0.224019i	$0.928082\pi$
$618$	4.87792e17	−	1.12150e18i	0.352216	−	0.809791i
$619$		−	2.15042e18i		−	1.53650i	−0.640148	−	0.768251i	$-0.721127\pi$
$619$		−	2.15042e18i		−	1.53650i	0.640148	−	0.768251i	$-0.278873\pi$
$620$	−2.90381e17	+	5.99879e16i	−0.205316	+	0.0424148i
$621$	9.81591e17	−	3.38020e16i	0.686808	−	0.0236509i
$622$	−2.29793e17	−	2.24819e18i	−0.159111	−	1.55667i
$623$	1.35382e18			0.927662
$624$	7.75661e16	−	7.38206e17i	0.0525984	−	0.500585i
$625$	−1.51269e18			−1.01515
$626$	−8.66799e16	−	8.48036e17i	−0.0575685	−	0.563224i
$627$	1.24255e18	+	6.98502e17i	0.816724	+	0.459122i
$628$	−1.84749e18	+	3.81660e17i	−1.20183	+	0.248278i
$629$		−	4.89035e17i		−	0.314855i
$630$	−2.98855e18	+	2.26440e18i	−1.90435	+	1.44291i
$631$			9.19804e17i			0.580102i	0.957011	+	0.290051i	$0.0936723\pi$
$631$			9.19804e17i			0.580102i	−0.957011	+	0.290051i	$0.906328\pi$
$632$	1.54379e18	−	4.86999e17i	0.963667	−	0.303995i
$633$	2.55707e18	+	1.43746e18i	1.57986	+	0.888121i
$634$	1.74535e18	−	1.78396e17i	1.06734	−	0.109095i
$635$	1.88737e14			0.000114243
$636$	−4.44212e17	−	1.41513e17i	−0.266145	−	0.0847864i
$637$	1.59256e18			0.944472
$638$	−7.72088e17	+	7.89170e16i	−0.453244	+	0.0463272i
$639$	4.80403e17	+	7.89663e17i	0.279158	+	0.458866i
$640$	−1.85249e18	+	1.60200e18i	−1.06558	+	0.921492i
$641$		−	6.52230e17i		−	0.371384i	−0.982608	−	0.185692i	$-0.940547\pi$
$641$		−	6.52230e17i		−	0.371384i	0.982608	−	0.185692i	$-0.0594527\pi$
$642$	−2.49769e18	−	1.08636e18i	−1.40787	−	0.612348i
$643$		−	1.93024e18i		−	1.07706i	−0.842607	−	0.538530i	$-0.818980\pi$
$643$		−	1.93024e18i		−	1.07706i	0.842607	−	0.538530i	$-0.181020\pi$
$644$	4.26871e17	+	2.06634e18i	0.235797	+	1.14141i
$645$	−1.90304e18	+	3.38528e18i	−1.04066	+	1.85121i
$646$	1.46590e17	+	1.43417e18i	0.0793585	+	0.776407i
$647$	−1.02710e18			−0.550472			−0.275236	−	0.961377i	$-0.588756\pi$
$647$	−1.02710e18			−0.550472			−0.275236	+	0.961377i	$0.588756\pi$
$648$	−1.85683e18	−	3.22803e17i	−0.985223	−	0.171277i
$649$	−4.81795e17			−0.253088
$650$	−9.68973e16	−	9.47998e17i	−0.0503935	−	0.493027i
$651$	2.40206e17	−	4.27298e17i	0.123682	−	0.220016i
$652$	1.52588e16	+	7.38629e16i	0.00777879	+	0.0376545i
$653$			6.54158e17i			0.330177i	0.986279	+	0.165088i	$0.0527910\pi$
$653$			6.54158e17i			0.330177i	−0.986279	+	0.165088i	$0.947209\pi$
$654$	2.51485e18	+	1.09383e18i	1.25678	+	0.546631i
$655$			4.25393e18i			2.10486i
$656$	5.38382e17	+	1.24745e18i	0.263764	+	0.611152i
$657$	−2.12941e17	−	3.50023e17i	−0.103296	−	0.169794i
$658$	2.59995e18	−	2.65747e17i	1.24881	−	0.127644i
$659$	7.27186e17			0.345852			0.172926	−	0.984935i	$-0.444678\pi$
$659$	7.27186e17			0.345852			0.172926	+	0.984935i	$0.444678\pi$
$660$	1.98859e18	+	6.33511e17i	0.936506	+	0.298345i
$661$	−6.28035e17			−0.292870			−0.146435	−	0.989220i	$-0.546780\pi$
$661$	−6.28035e17			−0.292870			−0.146435	+	0.989220i	$0.546780\pi$
$662$	1.13636e18	−	1.16151e17i	0.524736	−	0.0536345i
$663$	−5.57665e17	−	3.13492e17i	−0.254997	−	0.143347i
$664$	3.43045e17	+	1.08746e18i	0.155331	+	0.492401i
$665$		−	7.15561e18i		−	3.20853i
$666$	−9.72466e17	+	7.36829e17i	−0.431809	+	0.327178i
$667$		−	1.02056e18i		−	0.448765i
$668$	−2.13896e18	+	4.41874e17i	−0.931443	+	0.192420i
$669$	−2.98219e18	−	1.67644e18i	−1.28607	−	0.722967i
$670$	1.11308e17	+	1.08898e18i	0.0475379	+	0.465088i
$671$	−7.37800e17			−0.312063
$672$	1.14614e16	−	4.04877e18i	0.00480108	−	1.69599i
$673$	2.06850e18			0.858139			0.429069	−	0.903272i	$-0.358842\pi$
$673$	2.06850e18			0.858139			0.429069	+	0.903272i	$0.358842\pi$
$674$	2.36018e17	+	2.30909e18i	0.0969741	+	0.948750i
$675$	−2.41815e18	+	8.32711e16i	−0.984029	+	0.0338860i
$676$	1.81424e18	−	3.74791e17i	0.731208	−	0.151055i
$677$			2.65046e18i			1.05802i	0.848615	+	0.529011i	$0.177437\pi$
$677$			2.65046e18i			1.05802i	−0.848615	+	0.529011i	$0.822563\pi$
$678$	1.33232e18	−	3.06316e18i	0.526761	−	1.21109i
$679$			1.80694e18i			0.707605i
$680$	6.35022e17	+	2.01302e18i	0.246309	+	0.780803i
$681$	−1.94381e18	+	3.45781e18i	−0.746790	+	1.32845i
$682$	−2.71434e17	+	2.77439e16i	−0.103292	+	0.0105577i
$683$	2.00098e18			0.754238			0.377119	−	0.926165i	$-0.376915\pi$
$683$	2.00098e18			0.754238			0.377119	+	0.926165i	$0.376915\pi$
$684$	2.63104e18	−	2.45236e18i	0.982341	−	0.915631i
$685$	3.51709e18			1.30075
$686$	4.03627e18	−	4.12557e17i	1.47868	−	0.151139i
$687$	−2.77142e17	+	4.93002e17i	−0.100573	+	0.178908i
$688$	−1.66168e18	−	3.85019e18i	−0.597343	−	1.38407i
$689$			3.94817e17i			0.140595i
$690$	−1.09462e18	+	2.51667e18i	−0.386139	+	0.887783i
$691$			8.69527e17i			0.303862i	0.988391	+	0.151931i	$0.0485491\pi$
$691$			8.69527e17i			0.303862i	−0.988391	+	0.151931i	$0.951451\pi$
$692$	−5.89274e17	−	2.85248e18i	−0.203999	−	0.987490i
$693$	−2.94765e18	+	1.79325e18i	−1.01091	+	0.614999i
$694$	−2.80223e16	−	2.74158e17i	−0.00952068	−	0.0931459i
$695$	4.96000e17			0.166948
$696$	−4.01621e17	+	1.91671e18i	−0.133923	+	0.639140i
$697$	1.17100e18			0.386851
$698$	−2.25344e17	−	2.20466e18i	−0.0737541	−	0.721576i
$699$	−1.72036e18	−	9.67104e17i	−0.557851	−	0.313597i
$700$	−1.05159e18	−	5.09041e18i	−0.337840	−	1.63537i
$701$		−	3.30170e18i		−	1.05092i	−0.850818	−	0.525461i	$-0.823893\pi$
$701$		−	3.30170e18i		−	1.05092i	0.850818	−	0.525461i	$-0.176107\pi$
$702$	2.16842e17	+	1.58128e18i	0.0683837	+	0.498674i
$703$		−	2.32841e18i		−	0.727529i
$704$	−1.84570e18	+	1.29317e18i	−0.571399	+	0.400343i
$705$	2.96323e18	+	1.66578e18i	0.908941	+	0.510962i
$706$	2.37366e18	−	2.42617e17i	0.721418	−	0.0737380i
$707$	−1.08397e19			−3.26429
$708$	−3.69014e17	+	1.15834e18i	−0.110110	+	0.345636i
$709$	3.57119e17			0.105588			0.0527938	−	0.998605i	$-0.483187\pi$
$709$	3.57119e17			0.105588			0.0527938	+	0.998605i	$0.483187\pi$
$710$	−2.56935e18	+	2.62620e17i	−0.752739	+	0.0769394i
$711$	−2.97374e18	+	1.80911e18i	−0.863277	+	0.525187i
$712$	−1.81336e18	+	5.72037e17i	−0.521632	+	0.164552i
$713$		−	3.58785e17i		−	0.102271i
$714$	−3.19995e18	−	1.39181e18i	−0.903868	−	0.393135i
$715$		−	1.76747e18i		−	0.494724i
$716$	5.03680e18	−	1.04052e18i	1.39707	−	0.288612i
$717$	2.68075e18	−	4.76873e18i	0.736854	−	1.31077i
$718$	5.74379e17	+	5.61946e18i	0.156455	+	1.53068i
$719$	4.48341e18			1.21024			0.605119	−	0.796135i	$-0.293125\pi$
$719$	4.48341e18			1.21024			0.605119	+	0.796135i	$0.293125\pi$
$720$	3.04619e18	−	4.29579e18i	0.814884	−	1.14916i
$721$	−5.64938e18			−1.49769
$722$	3.10925e17	+	3.04195e18i	0.0816891	+	0.799209i
$723$	2.46055e18	−	4.37703e18i	0.640670	−	1.13967i
$724$	−6.02642e17	+	1.24496e17i	−0.155510	+	0.0321258i
$725$			2.51414e18i			0.642972i
$726$	−1.85684e18	−	8.07629e17i	−0.470638	−	0.204703i
$727$		−	5.55901e17i		−	0.139644i	−0.997559	−	0.0698222i	$-0.977757\pi$
$727$		−	5.55901e17i		−	0.139644i	0.997559	−	0.0698222i	$-0.0222432\pi$
$728$	−3.26995e18	+	1.03153e18i	−0.814118	+	0.256819i
$729$	4.04296e18	−	2.78777e17i	0.997631	−	0.0687903i
$730$	1.13888e18	−	1.16408e17i	0.278535	−	0.0284698i
$731$	−3.61422e18			−0.876096
$732$	−5.65093e17	+	1.77383e18i	−0.135768	+	0.426177i
$733$	3.09019e18			0.735885			0.367943	−	0.929849i	$-0.380062\pi$
$733$	3.09019e18			0.735885			0.367943	+	0.929849i	$0.380062\pi$
$734$	3.91342e18	−	4.00001e17i	0.923703	−	0.0944140i
$735$	9.84922e18	+	5.53676e18i	2.30428	+	1.29535i
$736$	−1.44487e18	−	2.58736e18i	−0.335059	−	0.600000i
$737$			1.00729e18i			0.231535i
$738$	−1.76434e18	−	2.32858e18i	−0.401992	−	0.530548i
$739$			7.03938e18i			1.58981i	0.606734	+	0.794905i	$0.292479\pi$
$739$			7.03938e18i			1.58981i	−0.606734	+	0.794905i	$0.707521\pi$
$740$	−6.89718e17	−	3.33869e18i	−0.154407	−	0.747430i
$741$	−2.65517e18	−	1.49261e18i	−0.589216	−	0.331229i
$742$	2.18981e17	+	2.14241e18i	0.0481705	+	0.471278i
$743$	6.48514e18			1.41414			0.707069	−	0.707145i	$-0.250017\pi$
$743$	6.48514e18			1.41414			0.707069	+	0.707145i	$0.250017\pi$
$744$	−1.41193e17	+	6.73834e17i	−0.0305203	+	0.145656i
$745$	−1.12512e19			−2.41092
$746$	3.15816e17	+	3.08980e18i	0.0670859	+	0.656338i
$747$	−1.27435e18	−	2.09472e18i	−0.268352	−	0.441105i
$748$	3.92959e17	+	1.90218e18i	0.0820326	+	0.397092i
$749$			1.25818e19i			2.60381i
$750$	−4.21428e16	+	9.68917e16i	−0.00864619	+	0.0198787i
$751$		−	8.32640e17i		−	0.169355i	−0.996408	−	0.0846774i	$-0.973014\pi$
$751$		−	8.32640e17i		−	0.169355i	0.996408	−	0.0846774i	$-0.0269860\pi$
$752$	−3.37018e18	+	1.45452e18i	−0.679574	+	0.293294i
$753$	2.74135e18	−	4.87654e18i	0.548022	−	0.974865i
$754$	1.64986e18	−	1.68636e17i	0.326988	−	0.0334223i
$755$	7.96396e18			1.56485
$756$	2.05370e18	+	8.46027e18i	0.400078	+	1.64813i
$757$	9.06444e17			0.175072			0.0875362	−	0.996161i	$-0.472101\pi$
$757$	9.06444e17			0.175072			0.0875362	+	0.996161i	$0.472101\pi$
$758$	−6.53305e18	+	6.67760e17i	−1.25103	+	0.127871i
$759$	−1.23751e18	+	2.20139e18i	−0.234952	+	0.417951i
$760$	3.02349e18	+	9.58448e18i	0.569141	+	1.80418i
$761$		−	3.65698e18i		−	0.682531i	−0.939967	−	0.341265i	$-0.889144\pi$
$761$		−	3.65698e18i		−	0.682531i	0.939967	−	0.341265i	$-0.110856\pi$
$762$	1.74788e14	−	4.01859e14i	3.23447e−5	−	7.43647e-5i
$763$		−	1.26682e19i		−	2.32438i
$764$	2.66445e18	−	5.50430e17i	0.484730	−	0.100137i
$765$	−2.35900e18	−	3.87760e18i	−0.425528	−	0.699462i
$766$	−7.24589e17	−	7.08904e18i	−0.129600	−	1.26795i
$767$	1.02954e18			0.182588
$768$	1.69540e18	+	5.42792e18i	0.298142	+	0.954522i
$769$	5.95767e18			1.03886			0.519428	−	0.854514i	$-0.326145\pi$
$769$	5.95767e18			1.03886			0.519428	+	0.854514i	$0.326145\pi$
$770$	−9.80308e17	−	9.59088e18i	−0.169501	−	1.65832i
$771$	−3.19174e18	−	1.79424e18i	−0.547235	−	0.307629i
$772$	−6.29136e18	+	1.29969e18i	−1.06963	+	0.220967i
$773$		−	8.00181e18i		−	1.34903i	−0.738261	−	0.674515i	$-0.764353\pi$
$773$		−	8.00181e18i		−	1.34903i	0.738261	−	0.674515i	$-0.235647\pi$
$774$	5.44555e18	+	7.18702e18i	0.910385	+	1.20152i
$775$			8.83865e17i			0.146529i
$776$	−7.63496e17	−	2.42029e18i	−0.125518	−	0.397893i
$777$	4.91291e18	+	2.76180e18i	0.800944	+	0.450252i
$778$	−5.77295e17	+	5.90068e16i	−0.0933320	+	0.00953970i
$779$	5.57541e18			0.893888
$780$	−4.24938e18	−	1.35373e18i	−0.675632	−	0.215237i
$781$	−2.37661e18			−0.374737
$782$	−2.54088e18	+	2.59709e17i	−0.397319	+	0.0406110i
$783$	−1.44922e17	−	4.20844e18i	−0.0224741	−	0.652633i
$784$	−1.12019e19	+	4.83456e18i	−1.72280	+	0.743536i
$785$			1.13347e19i			1.72885i
$786$	9.05748e18	+	3.93953e18i	1.37013	+	0.595933i
$787$			7.05514e18i			1.05845i	0.848482	+	0.529225i	$0.177517\pi$
$787$			7.05514e18i			1.05845i	−0.848482	+	0.529225i	$0.822483\pi$
$788$	−2.16914e18	−	1.05001e19i	−0.322751	−	1.56233i
$789$	−1.81905e18	+	3.23587e18i	−0.268438	+	0.477519i
$790$	−9.88982e17	−	9.67574e18i	−0.144748	−	1.41615i
$791$	−1.54303e19			−2.23989
$792$	3.19049e18	−	3.64743e18i	0.459350	−	0.525137i
$793$	1.57659e18			0.225134
$794$	−7.47120e17	−	7.30948e18i	−0.105817	−	1.03527i
$795$	−1.37264e18	+	2.44176e18i	−0.192828	+	0.343017i
$796$	−5.37400e17	−	2.60137e18i	−0.0748795	−	0.362466i
$797$			1.54726e18i			0.213837i	0.994268	+	0.106919i	$0.0340984\pi$
$797$			1.54726e18i			0.213837i	−0.994268	+	0.106919i	$0.965902\pi$
$798$	−1.52357e19	−	6.62674e18i	−2.08855	−	0.908408i
$799$			3.16363e18i			0.430161i
$800$	3.55942e18	+	6.37395e18i	0.480058	+	0.859654i
$801$	3.49300e18	−	2.12502e18i	0.467291	−	0.284283i
$802$	−8.53251e18	+	8.72129e17i	−1.13225	+	0.115730i
$803$	1.05345e18			0.138663
$804$	2.42175e18	+	7.71501e17i	0.316202	+	0.100733i
$805$	1.26774e19			1.64193
$806$	5.80020e17	−	5.92853e16i	0.0745186	−	0.00761674i
$807$	3.01650e17	+	1.69573e17i	0.0384438	+	0.0216112i
$808$	1.45190e19	−	4.58013e18i	1.83554	−	0.579034i
$809$		−	2.59627e18i		−	0.325600i	−0.986659	−	0.162800i	$-0.947947\pi$
$809$		−	2.59627e18i		−	0.325600i	0.986659	−	0.162800i	$-0.0520525\pi$
$810$	−4.15647e18	+	1.05333e19i	−0.517097	+	1.31043i
$811$		−	1.12759e19i		−	1.39161i	−0.718233	−	0.695803i	$-0.755049\pi$
$811$		−	1.12759e19i		−	1.39161i	0.718233	−	0.695803i	$-0.244951\pi$
$812$	8.85913e18	−	1.83015e18i	1.08462	−	0.224064i
$813$	−1.09799e19	−	6.17235e18i	−1.33355	−	0.749656i
$814$	−3.18989e17	−	3.12084e18i	−0.0384341	−	0.376022i
$815$	4.53162e17			0.0541663
$816$	4.87422e18	+	5.12153e17i	0.577989	+	0.0607314i
$817$	−1.72082e19			−2.02438
$818$	1.00322e18	+	9.81507e18i	0.117085	+	1.14550i
$819$	6.29877e18	−	3.83194e18i	0.729307	−	0.443684i
$820$	7.99454e18	−	1.65154e18i	0.918339	−	0.189714i
$821$		−	1.91918e18i		−	0.218719i	−0.994002	−	0.109359i	$-0.965120\pi$
$821$		−	1.91918e18i		−	0.218719i	0.994002	−	0.109359i	$-0.0348799\pi$
$822$	3.25714e18	−	7.48859e18i	0.368273	−	0.846707i
$823$		−	1.70141e18i		−	0.190858i	−0.995436	−	0.0954290i	$-0.969578\pi$
$823$		−	1.70141e18i		−	0.190858i	0.995436	−	0.0954290i	$-0.0304223\pi$
$824$	7.56699e18	−	2.38706e18i	0.842163	−	0.265666i
$825$	3.04861e18	−	5.42311e18i	0.336629	−	0.598822i
$826$	5.58660e18	−	5.71020e17i	0.612036	−	0.0625578i
$827$	−1.08462e19			−1.17894			−0.589470	−	0.807790i	$-0.700663\pi$
$827$	−1.08462e19			−1.17894			−0.589470	+	0.807790i	$0.700663\pi$
$828$	4.34478e18	+	4.66132e18i	0.468565	+	0.502704i
$829$	−3.51366e16			−0.00375971			−0.00187986	−	0.999998i	$-0.500598\pi$
$829$	−3.51366e16			−0.00375971			−0.00187986	+	0.999998i	$0.500598\pi$
$830$	6.81566e18	−	6.96645e17i	0.723603	−	0.0739612i
$831$	−6.96517e18	+	1.23902e19i	−0.733711	+	1.30518i
$832$	3.94404e18	−	2.76333e18i	0.412230	−	0.288823i
$833$			1.05153e19i			1.09051i
$834$	4.59341e17	−	1.05608e18i	0.0472667	−	0.108672i
$835$			1.31229e19i			1.33989i
$836$	1.87097e18	+	9.05673e18i	0.189551	+	0.917552i
$837$	−5.09483e16	−	1.47951e18i	−0.00512170	−	0.148731i
$838$	1.13421e18	+	1.10966e19i	0.113137	+	1.10688i
$839$	−1.06507e19			−1.05421			−0.527104	−	0.849801i	$-0.676722\pi$
$839$	−1.06507e19			−1.05421			−0.527104	+	0.849801i	$0.676722\pi$
$840$	−2.38094e19	−	4.98893e18i	−2.33847	−	0.489996i
$841$	5.88513e18			0.573565
$842$	−4.48351e17	−	4.38646e18i	−0.0433600	−	0.424214i
$843$	5.79365e18	+	3.25691e18i	0.555997	+	0.312555i
$844$	3.85031e18	+	1.86380e19i	0.366665	+	1.77490i
$845$		−	1.11307e19i		−	1.05185i
$846$	6.29100e18	−	4.76664e18i	0.589946	−	0.446997i
$847$			9.35358e18i			0.870434i
$848$	−1.19855e18	−	2.77709e18i	−0.110684	−	0.256459i
$849$	−3.86428e18	−	2.17231e18i	−0.354135	−	0.199077i
$850$	6.25943e18	−	6.39792e17i	0.569262	−	0.0581857i
$851$	4.12517e18			0.372306
$852$	−1.82028e18	+	5.71388e18i	−0.163035	+	0.511769i
$853$	1.23277e19			1.09575			0.547876	−	0.836559i	$-0.315436\pi$
$853$	1.23277e19			1.09575			0.547876	+	0.836559i	$0.315436\pi$
$854$	8.55508e18	−	8.74436e17i	0.754654	−	0.0771351i
$855$	−1.12317e19	−	1.84622e19i	−0.983257	−	1.61623i
$856$	−5.31623e18	−	1.68525e19i	−0.461875	−	1.46415i
$857$			1.52269e19i			1.31291i	0.754363	+	0.656457i	$0.227946\pi$
$857$			1.52269e19i			1.31291i	−0.754363	+	0.656457i	$0.772054\pi$
$858$	−3.76330e18	−	1.63684e18i	−0.322034	−	0.140068i
$859$			1.30108e19i			1.10496i	0.833525	+	0.552482i	$0.186319\pi$
$859$			1.30108e19i			1.10496i	−0.833525	+	0.552482i	$0.813681\pi$
$860$	−2.46747e19	+	5.09737e18i	−2.07975	+	0.429642i
$861$	−6.61316e18	+	1.17640e19i	−0.553208	+	0.984090i
$862$	1.33918e17	+	1.31019e18i	0.0111184	+	0.108777i
$863$	1.81153e19			1.49271			0.746357	−	0.665546i	$-0.231801\pi$
$863$	1.81153e19			1.49271			0.746357	+	0.665546i	$0.231801\pi$
$864$	−6.32555e18	−	1.04642e19i	−0.517320	−	0.855792i
$865$	−1.75005e19			−1.42051
$866$	−7.02102e17	−	6.86904e18i	−0.0565632	−	0.553388i
$867$	−4.05848e18	+	7.21954e18i	−0.324518	+	0.577279i
$868$	3.11450e18	−	6.43403e17i	0.247178	−	0.0510628i
$869$		−	8.94990e18i		−	0.705001i
$870$	1.07899e19	+	4.69302e18i	0.843608	+	0.366925i
$871$		−	2.15246e18i		−	0.167039i
$872$	5.35276e18	+	1.69683e19i	0.412307	+	1.30702i
$873$	2.83625e18	+	4.66210e18i	0.216847	+	0.356442i
$874$	−1.20977e19	+	1.23654e18i	−0.918076	+	0.0938388i
$875$	4.88078e17			0.0367652
$876$	8.06851e17	−	2.53271e18i	0.0603277	−	0.189369i
$877$	2.11895e19			1.57262			0.786311	−	0.617831i	$-0.211989\pi$
$877$	2.11895e19			1.57262			0.786311	+	0.617831i	$0.211989\pi$
$878$	−2.17911e19	+	2.22733e18i	−1.60533	+	0.164085i
$879$	8.39196e18	+	4.71755e18i	0.613671	+	0.344976i
$880$	5.36554e18	+	1.24322e19i	0.389472	+	0.902422i
$881$		−	2.01295e19i		−	1.45040i	−0.688537	−	0.725202i	$-0.741747\pi$
$881$		−	2.01295e19i		−	1.45040i	0.688537	−	0.725202i	$-0.258253\pi$
$882$	2.09101e19	−	1.58434e19i	1.49558	−	1.13319i
$883$		−	1.64419e19i		−	1.16737i	−0.811980	−	0.583685i	$-0.801610\pi$
$883$		−	1.64419e19i		−	1.16737i	0.811980	−	0.583685i	$-0.198390\pi$
$884$	−8.39703e17	−	4.06472e18i	−0.0591815	−	0.286478i
$885$	6.36719e18	+	3.57933e18i	0.445468	+	0.250421i
$886$	−8.04141e16	−	7.86734e17i	−0.00558487	−	0.0546398i
$887$	1.36464e19			0.940837			0.470418	−	0.882444i	$-0.344103\pi$
$887$	1.36464e19			0.940837			0.470418	+	0.882444i	$0.344103\pi$
$888$	−7.74749e18	−	1.62338e18i	−0.530245	−	0.111106i
$889$	−2.02431e15			−0.000137536
$890$	1.16168e18	+	1.13653e19i	0.0783519	+	0.766559i
$891$	−4.79049e18	+	9.25352e18i	−0.320756	+	0.619586i
$892$	−4.49043e18	−	2.17366e19i	−0.298480	−	1.44484i
$893$			1.50628e19i			0.993964i
$894$	−1.04196e19	+	2.39560e19i	−0.682586	+	1.56935i
$895$		−	3.09017e19i		−	2.00971i
$896$	1.98690e19	−	1.71823e19i	1.28284	−	1.10938i
$897$	2.64441e18	−	4.70409e18i	0.169503	−	0.301526i
$898$	−2.79356e19	+	2.85536e18i	−1.77771	+	0.181704i
$899$	−1.53824e18			−0.0971821
$900$	−1.07033e19	−	1.14831e19i	−0.671340	−	0.720252i
$901$	−2.60689e18			−0.162335
$902$	7.47289e18	−	7.63823e17i	0.462004	−	0.0472226i
$903$	2.04111e19	−	3.63089e19i	1.25284	−	2.22866i
$904$	2.06679e19	−	6.51982e18i	1.25951	−	0.397320i
$905$			3.69732e18i			0.223703i
$906$	7.37535e18	−	1.69569e19i	0.443046	−	1.01862i
$907$		−	1.15982e19i		−	0.691742i	−0.938282	−	0.345871i	$-0.887583\pi$
$907$		−	1.15982e19i		−	0.691742i	0.938282	−	0.345871i	$-0.112417\pi$
$908$	−2.52034e19	+	5.20659e18i	−1.49245	+	0.308316i
$909$	−2.79674e19	+	1.70144e19i	−1.64432	+	1.00035i
$910$	2.09479e18	+	2.04945e19i	0.122285	+	1.19638i
$911$	−1.71163e19			−0.992065			−0.496033	−	0.868304i	$-0.665210\pi$
$911$	−1.71163e19			−0.992065			−0.496033	+	0.868304i	$0.665210\pi$
$912$	2.32073e19	+	2.43848e18i	1.33554	+	0.140331i
$913$	6.30437e18			0.360232
$914$	3.16341e18	+	3.09494e19i	0.179476	+	1.75591i
$915$	9.75044e18	+	5.48123e18i	0.549272	+	0.308774i
$916$	−3.59340e18	+	7.42337e17i	−0.200995	+	0.0415222i
$917$		−	4.56258e19i		−	2.53402i
$918$	−1.04408e19	+	1.43176e18i	−0.575782	+	0.0789576i
$919$		−	3.23618e17i		−	0.0177207i	−0.999961	−	0.00886036i	$-0.997180\pi$
$919$		−	3.23618e17i		−	0.0177207i	0.999961	−	0.00886036i	$-0.00282038\pi$
$920$	−1.69805e19	+	5.35662e18i	−0.923274	+	0.291253i
$921$	2.04389e19	+	1.14898e19i	1.10350	+	0.620332i
$922$	1.09050e19	−	1.11463e18i	0.584621	−	0.0597556i
$923$	5.07852e18			0.270350
$924$	−2.13288e19	−	6.79475e18i	−1.12745	−	0.359175i
$925$	−1.01623e19			−0.533424
$926$	−1.07751e18	+	1.10135e17i	−0.0561628	+	0.00574054i
$927$	−1.45760e19	+	8.86750e18i	−0.754431	+	0.458969i
$928$	−1.10929e19	+	6.19466e18i	−0.570145	+	0.318387i
$929$		−	2.67688e19i		−	1.36624i	−0.730307	−	0.683120i	$-0.760623\pi$
$929$		−	2.67688e19i		−	1.36624i	0.730307	−	0.683120i	$-0.239377\pi$
$930$	3.79326e18	+	1.64987e18i	0.192253	+	0.0836201i
$931$			5.00660e19i			2.51982i
$932$	−2.59043e18	−	1.25394e19i	−0.129470	−	0.626720i
$933$	−1.54492e19	+	2.74823e19i	−0.766788	+	1.36402i
$934$	−1.89588e18	−	1.85485e19i	−0.0934452	−	0.914225i
$935$	1.16702e19			0.571221
$936$	−6.81767e18	+	7.79410e18i	−0.331393	+	0.378855i
$937$	−3.43661e19			−1.65891			−0.829455	−	0.558573i	$-0.811349\pi$
$937$	−3.43661e19			−1.65891			−0.829455	+	0.558573i	$0.811349\pi$
$938$	−1.19384e18	−	1.16800e19i	−0.0572304	−	0.559916i
$939$	−5.82757e18	+	1.03665e19i	−0.277435	+	0.493523i
$940$	4.46187e18	+	2.15984e19i	0.210953	+	1.02115i
$941$			2.33762e19i			1.09759i	0.835956	+	0.548797i	$0.184914\pi$
$941$			2.33762e19i			1.09759i	−0.835956	+	0.548797i	$0.815086\pi$
$942$	2.41338e19	+	1.04969e19i	1.12537	+	0.489476i
$943$			9.87777e18i			0.457439i
$944$	−7.24162e18	+	3.12538e18i	−0.333057	+	0.143742i
$945$	5.22772e19	−	1.80022e18i	2.38784	−	0.0822276i
$946$	−2.30646e19	+	2.35749e18i	−1.04629	+	0.106944i
$947$	4.03339e19			1.81717			0.908583	−	0.417703i	$-0.137165\pi$
$947$	4.03339e19			1.81717			0.908583	+	0.417703i	$0.137165\pi$
$948$	−2.15175e19	−	6.85487e18i	−0.962803	−	0.306722i
$949$	−2.25108e18			−0.100037
$950$	2.98026e19	−	3.04620e18i	1.31538	−	0.134448i
$951$	−2.13354e19	−	1.19937e19i	−0.935250	−	0.525752i
$952$	−6.81096e18	−	2.15908e19i	−0.296530	−	0.940001i
$953$		−	1.76491e19i		−	0.763164i	−0.924335	−	0.381582i	$-0.875379\pi$
$953$		−	1.76491e19i		−	0.763164i	0.924335	−	0.381582i	$-0.124621\pi$
$954$	3.92781e18	+	5.18391e18i	0.168689	+	0.222635i
$955$		−	1.63469e19i		−	0.697289i
$956$	3.47584e19	−	7.18050e18i	1.47260	−	0.304214i
$957$	9.43814e18	+	5.30567e18i	0.397154	+	0.223261i
$958$	1.58441e18	+	1.55012e19i	0.0662206	+	0.647872i
$959$	−3.77227e19			−1.56597
$960$	3.39991e19	−	3.37791e18i	1.40186	−	0.139279i
$961$	2.38768e19			0.977853
$962$	6.81640e17	+	6.66885e18i	0.0277279	+	0.271277i
$963$	1.97489e19	+	3.24622e19i	0.797942	+	1.31162i
$964$	3.19034e19	−	6.59071e18i	1.28037	−	0.264503i
$965$			3.85986e19i			1.53867i
$966$	1.17404e19	−	2.69926e19i	0.464869	−	1.06879i
$967$		−	3.33843e19i		−	1.31302i	−0.754319	−	0.656508i	$-0.772033\pi$
$967$		−	3.33843e19i		−	1.31302i	0.754319	−	0.656508i	$-0.227967\pi$
$968$	−3.95221e18	−	1.25285e19i	−0.154401	−	0.489452i
$969$	9.85539e18	−	1.75316e19i	0.382445	−	0.680324i
$970$	−1.51692e19	+	1.55048e18i	−0.584719	+	0.0597656i
$971$	−1.46430e19			−0.560667			−0.280333	−	0.959903i	$-0.590445\pi$
$971$	−1.46430e19			−0.560667			−0.280333	+	0.959903i	$0.590445\pi$
$972$	1.85783e19	+	1.86048e19i	0.706604	+	0.707610i
$973$	−5.31987e18			−0.200987
$974$	−2.47313e19	+	2.52785e18i	−0.928140	+	0.0948675i
$975$	−6.51449e18	+	1.15885e19i	−0.242857	+	0.432013i
$976$	−1.10895e19	+	4.78607e18i	−0.410666	+	0.177237i
$977$			1.86239e19i			0.685102i	0.939499	+	0.342551i	$0.111291\pi$
$977$			1.86239e19i			0.685102i	−0.939499	+	0.342551i	$0.888709\pi$
$978$	4.19669e17	−	9.64874e17i	0.0153357	−	0.0352588i
$979$			1.05127e19i			0.381617i
$980$	1.48305e19	+	7.17892e19i	0.534792	+	2.58875i
$981$	−1.98846e19	−	3.26853e19i	−0.712308	−	1.17086i
$982$	−1.22079e18	−	1.19437e19i	−0.0434428	−	0.425024i
$983$	−1.56001e19			−0.551479			−0.275740	−	0.961232i	$-0.588923\pi$
$983$	−1.56001e19			−0.551479			−0.275740	+	0.961232i	$0.588923\pi$
$984$	3.88721e18	−	1.85514e19i	0.136512	−	0.651493i
$985$	−6.44200e19			−2.24743
$986$	1.11347e18	+	1.08936e19i	0.0385902	+	0.377549i
$987$	−3.17822e19	−	1.78664e19i	−1.09427	−	0.615143i
$988$	−3.99802e18	−	1.93531e19i	−0.136749	−	0.661958i
$989$		−	3.04872e19i		−	1.03596i
$990$	−1.75835e19	−	2.32067e19i	−0.593577	−	0.783402i
$991$			5.39018e19i			1.80769i	0.427858	+	0.903846i	$0.359268\pi$
$991$			5.39018e19i			1.80769i	−0.427858	+	0.903846i	$0.640732\pi$
$992$	−3.89981e18	+	2.17778e18i	−0.129933	+	0.0725585i
$993$	−1.38911e19	−	7.80891e18i	−0.459798	−	0.258476i
$994$	2.75577e19	−	2.81674e18i	0.906216	−	0.0926266i
$995$	−1.59599e19			−0.521411
$996$	4.82862e18	−	1.51571e19i	0.156725	−	0.491959i
$997$	2.11185e19			0.680995			0.340497	−	0.940245i	$-0.389405\pi$
$997$	2.11185e19			0.680995			0.340497	+	0.940245i	$0.389405\pi$
$998$	−8.80792e18	+	9.00280e17i	−0.282179	+	0.0288422i
$999$	1.70108e19	−	5.85785e17i	0.541440	−	0.0186450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.14.b.a.11.11	✓	24
3.2	odd	2	inner	12.14.b.a.11.14	yes	24
4.3	odd	2	inner	12.14.b.a.11.13	yes	24
12.11	even	2	inner	12.14.b.a.11.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.14.b.a.11.11	✓	24	1.1	even	1	trivial
12.14.b.a.11.12	yes	24	12.11	even	2	inner
12.14.b.a.11.13	yes	24	4.3	odd	2	inner
12.14.b.a.11.14	yes	24	3.2	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)

\(f(q)\)	\(=\)	\(q+(-9.20327 - 90.0405i) q^{2} +(-618.744 + 1100.67i) q^{3} +(-8022.60 + 1657.33i) q^{4} +49220.1i q^{5} +(104800. + 45582.3i) q^{6} -527913. i q^{7} +(223061. + 707106. i) q^{8} +(-828634. - 1.36207e6i) q^{9} +O(q^{10})\)	\(q+(-9.20327 - 90.0405i) q^{2} +(-618.744 + 1100.67i) q^{3} +(-8022.60 + 1657.33i) q^{4} +49220.1i q^{5} +(104800. + 45582.3i) q^{6} -527913. i q^{7} +(223061. + 707106. i) q^{8} +(-828634. - 1.36207e6i) q^{9} +(4.43181e6 - 452986. i) q^{10} +4.09935e6 q^{11} +(3.13976e6 - 9.85572e6i) q^{12} -8.75980e6 q^{13} +(-4.75336e7 + 4.85853e6i) q^{14} +(-5.41752e7 - 3.04547e7i) q^{15} +(6.16153e7 - 2.65923e7i) q^{16} -5.78391e7i q^{17} +(-1.15015e8 + 8.71461e7i) q^{18} -2.75386e8i q^{19} +(-8.15743e7 - 3.94873e8i) q^{20} +(5.81059e8 + 3.26643e8i) q^{21} +(-3.77274e7 - 3.69108e8i) q^{22} +4.87892e8 q^{23} +(-9.16310e8 - 1.92001e8i) q^{24} -1.20192e9 q^{25} +(8.06188e7 + 7.88737e8i) q^{26} +(2.01190e9 - 6.92818e7i) q^{27} +(8.74929e8 + 4.23523e9i) q^{28} -2.09177e9i q^{29} +(-2.24357e9 + 5.15825e9i) q^{30} -7.35378e8i q^{31} +(-2.96144e9 - 5.30314e9i) q^{32} +(-2.53645e9 + 4.51204e9i) q^{33} +(-5.20786e9 + 5.32309e8i) q^{34} +2.59840e10 q^{35} +(8.90520e9 + 9.55401e9i) q^{36} +8.45510e9 q^{37} +(-2.47959e10 + 2.53445e9i) q^{38} +(5.42007e9 - 9.64166e9i) q^{39} +(-3.48039e10 + 1.09791e10i) q^{40} +2.02458e10i q^{41} +(2.40635e10 - 5.53251e10i) q^{42} -6.24875e10i q^{43} +(-3.28874e10 + 6.79400e9i) q^{44} +(6.70412e10 - 4.07855e10i) q^{45} +(-4.49020e9 - 4.39301e10i) q^{46} -5.46971e10 q^{47} +(-8.85478e9 + 8.42721e10i) q^{48} -1.81803e11 q^{49} +(1.10616e10 + 1.08221e11i) q^{50} +(6.36619e10 + 3.57876e10i) q^{51} +(7.02763e10 - 1.45179e10i) q^{52} -4.50715e10i q^{53} +(-2.47543e10 - 1.80515e11i) q^{54} +2.01771e11i q^{55} +(3.73291e11 - 1.17757e11i) q^{56} +(3.03109e11 + 1.70393e11i) q^{57} +(-1.88344e11 + 1.92511e10i) q^{58} -1.17530e11 q^{59} +(4.85100e11 + 1.54539e11i) q^{60} -1.79980e11 q^{61} +(-6.62138e10 + 6.76788e9i) q^{62} +(-7.19054e11 + 4.37447e11i) q^{63} +(-4.50243e11 + 3.15456e11i) q^{64} -4.31158e11i q^{65} +(4.29610e11 + 1.86858e11i) q^{66} +2.45720e11i q^{67} +(9.58588e10 + 4.64020e11i) q^{68} +(-3.01880e11 + 5.37009e11i) q^{69} +(-2.39137e11 - 2.33961e12i) q^{70} -5.79753e11 q^{71} +(7.78291e11 - 8.89757e11i) q^{72} +2.56979e11 q^{73} +(-7.78146e10 - 7.61302e11i) q^{74} +(7.43681e11 - 1.32292e12i) q^{75} +(4.56406e11 + 2.20931e12i) q^{76} -2.16410e12i q^{77} +(-9.18023e11 - 3.99292e11i) q^{78} -2.18325e12i q^{79} +(1.30888e12 + 3.03272e12i) q^{80} +(-1.16860e12 + 2.25731e12i) q^{81} +(1.82294e12 - 1.86328e11i) q^{82} +1.53790e12 q^{83} +(-5.20296e12 - 1.65752e12i) q^{84} +2.84685e12 q^{85} +(-5.62641e12 + 5.75089e11i) q^{86} +(2.30235e12 + 1.29427e12i) q^{87} +(9.14407e11 + 2.89868e12i) q^{88} +2.56448e12i q^{89} +(-4.28935e12 - 5.66107e12i) q^{90} +4.62441e12i q^{91} +(-3.91416e12 + 8.08600e11i) q^{92} +(8.09410e11 + 4.55011e11i) q^{93} +(5.03392e11 + 4.92495e12i) q^{94} +1.35545e13 q^{95} +(7.66940e12 + 2.17108e10i) q^{96} -3.42281e12 q^{97} +(1.67318e12 + 1.63697e13i) q^{98} +(-3.39686e12 - 5.58360e12i) 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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