LMFDB - Embedded newform 12.14.b.a.11.14

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			11.14
Character	$\chi$	$=$	12.11
Dual form			12.14.b.a.11.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.20327 + 90.0405i) q^{2} +(618.744 + 1100.67i) q^{3} +(-8022.60 + 1657.33i) q^{4} -49220.1i q^{5} +(-93410.6 + 65841.9i) q^{6} -527913. i q^{7} +(-223061. - 707106. i) q^{8} +(-828634. + 1.36207e6i) q^{9} +O(q^{10})$	\(q+(9.20327 + 90.0405i) q^{2} +(618.744 + 1100.67i) q^{3} +(-8022.60 + 1657.33i) q^{4} -49220.1i q^{5} +(-93410.6 + 65841.9i) 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} +(-6.78812e6 - 7.80478e6i) 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} +(-1.30268e8 - 6.20752e7i) 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} +(6.40274e8 - 6.83036e8i) 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} +(3.24075e9 + 4.59768e9i) 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} +(4.39039e9 - 1.23007e10i) 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} +(3.47588e10 + 4.93127e10i) 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} +(6.73935e10 + 5.13645e10i) 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} +(-1.22779e10 - 1.81790e11i) 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} +(-3.84153e11 + 3.34112e11i) 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} +(3.82923e11 - 2.69909e11i) 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} +(1.14796e12 + 2.82107e11i) 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} +(8.18258e11 - 5.76761e11i) 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} +(-4.12025e12 + 3.58354e12i) 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} +(-3.05535e12 + 6.41179e12i) 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} +(-4.00464e12 + 6.54087e12i) 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	$-0.751225\pi$
$5$		−	49220.1i		−	1.40876i	0.709822	−	0.704381i	$-0.248775\pi$
$6$	−93410.6	+	65841.9i	−0.817360	+	0.576128i
$7$		−	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	$-0.613426\pi$
$11$	−4.09935e6			−0.697690			−0.348845	+	0.937180i	$0.613426\pi$
$12$	−6.78812e6	−	7.80478e6i	−0.656253	−	0.754541i
$13$	−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	$0.0938500\pi$
$17$			5.78391e7i			0.581170i	−0.956849	+	0.290585i	$0.906150\pi$
$18$	−1.30268e8	−	6.20752e7i	−0.902745	−	0.430176i
$19$		−	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	$-0.611649\pi$
$23$	−4.87892e8			−0.687215			−0.343608	+	0.939113i	$0.611649\pi$
$24$	6.40274e8	−	6.83036e8i	0.683900	−	0.729575i
$25$	−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	$0.105873\pi$
$29$			2.09177e9i			0.653020i	−0.945194	+	0.326510i	$0.894127\pi$
$30$	3.24075e9	+	4.59768e9i	0.811628	+	1.15147i
$31$		−	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
$36$	4.39039e9	−	1.23007e10i	0.336153	−	0.941807i
$37$	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	$-0.892000\pi$
$41$		−	2.02458e10i		−	0.665641i	0.942990	−	0.332821i	$-0.108000\pi$
$42$	3.47588e10	+	4.93127e10i	0.977111	+	1.38624i
$43$		−	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	$-0.379330\pi$
$47$	5.46971e10			0.740164			0.370082	+	0.928999i	$0.379330\pi$
$48$	6.73935e10	+	5.13645e10i	0.795335	+	0.606170i
$49$	−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	$0.0446016\pi$
$53$			4.50715e10i			0.279324i	−0.990199	+	0.139662i	$0.955398\pi$
$54$	−1.22779e10	−	1.81790e11i	−0.0673853	−	0.997727i
$55$			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	$-0.441945\pi$
$59$	1.17530e11			0.362751			0.181376	+	0.983414i	$0.441945\pi$
$60$	−3.84153e11	+	3.34112e11i	−1.06297	+	0.924505i
$61$	−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
$66$	3.82923e11	−	2.69909e11i	0.570264	−	0.401959i
$67$			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	$-0.413454\pi$
$71$	5.79753e11			0.537110			0.268555	+	0.963264i	$0.413454\pi$
$72$	1.14796e12	+	2.82107e11i	0.971107	+	0.238645i
$73$	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
$78$	8.18258e11	−	5.76761e11i	0.411411	−	0.289989i
$79$		−	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	$-0.583116\pi$
$83$	−1.53790e12			−0.516320			−0.258160	+	0.966102i	$0.583116\pi$
$84$	−4.12025e12	+	3.58354e12i	−1.27970	+	1.11300i
$85$	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	$-0.911823\pi$
$89$		−	2.56448e12i		−	0.546972i	0.961876	−	0.273486i	$-0.0881766\pi$
$90$	−3.05535e12	+	6.41179e12i	−0.606017	+	1.27175i
$91$			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
$96$	−4.00464e12	+	6.54087e12i	−0.522157	+	0.852850i
$97$	−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	$0.412379\pi$
$101$			2.05330e13i			1.92470i	−0.271805	+	0.962352i	$0.587621\pi$
$102$	−3.80823e12	−	5.40279e12i	−0.334829	−	0.475025i
$103$		−	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	$-0.221433\pi$
$107$	2.38330e13			1.53527			0.767635	+	0.640887i	$0.221433\pi$
$108$	1.62555e13	−	2.77858e12i	0.985704	−	0.168488i
$109$	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	$0.229590\pi$
$113$			2.92288e13i			1.32069i	−0.750962	+	0.660345i	$0.770410\pi$
$114$	1.81319e13	+	2.57239e13i	0.773681	+	1.09763i
$115$			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
$120$	−3.36191e13	−	3.15144e13i	−1.02780	−	0.963453i
$121$	−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
$126$	−3.27703e13	+	6.87699e13i	−0.729578	+	1.53105i
$127$		−	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	$-0.768534\pi$
$131$	−8.64267e13			−1.49412			−0.747058	+	0.664759i	$0.768534\pi$
$132$	2.78269e13	+	3.19945e13i	0.457861	+	0.526436i
$133$	−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	$0.152748\pi$
$137$			7.14563e13i			0.923330i	−0.887054	+	0.461665i	$0.847252\pi$
$138$	4.55743e13	−	3.21237e13i	0.561702	−	0.395924i
$139$		−	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
$144$	−1.48361e13	+	1.05960e14i	−0.138664	+	0.990340i
$145$	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	$-0.673136\pi$
$149$		−	2.28589e14i		−	1.71137i	0.517496	−	0.855686i	$-0.326864\pi$
$150$	1.12272e14	−	7.91366e13i	0.804782	−	0.567263i
$151$		−	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
$156$	5.94626e13	+	6.83683e13i	0.330319	+	0.379791i
$157$	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
$162$	1.92495e14	−	1.25996e14i	0.836703	−	0.547657i
$163$		−	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	$-0.657753\pi$
$167$	−2.66617e14			−0.951110			−0.475555	+	0.879686i	$0.657753\pi$
$168$	−3.60583e14	−	3.38009e14i	−1.23736	−	1.15989i
$169$	−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	$-0.831798\pi$
$173$		−	3.55555e14i		−	1.00834i	0.863604	−	0.504171i	$-0.168202\pi$
$174$	−1.37726e14	−	1.95393e14i	−0.376223	−	0.533752i
$175$			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	$-0.247205\pi$
$179$	6.27826e14			1.42657			0.713287	+	0.700872i	$0.247205\pi$
$180$	−6.05440e14	−	2.16096e14i	−1.32678	−	0.473560i
$181$	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
$186$	4.84186e13	+	6.86921e13i	0.0857390	+	0.121639i
$187$		−	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	$-0.420397\pi$
$191$	3.32118e14			0.494966			0.247483	+	0.968892i	$0.420397\pi$
$192$	−6.25799e14	−	3.00383e14i	−0.901523	−	0.432730i
$193$	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	$-0.706071\pi$
$197$		−	1.30881e15i		−	1.59532i	0.603108	−	0.797660i	$-0.293929\pi$
$198$	5.34012e14	+	2.54468e14i	0.629836	+	0.300130i
$199$			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
$204$	4.51422e14	−	3.92619e14i	0.438517	−	0.381395i
$205$	−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
$210$	2.42718e15	−	1.71083e15i	1.95288	−	1.37652i
$211$		−	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
$216$	3.99789e14	+	1.43808e15i	0.267843	+	0.963462i
$217$	−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
$222$	−7.89796e14	+	5.56699e14i	−0.442813	+	0.312123i
$223$			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	$-0.775774\pi$
$227$	−3.14155e15			−1.52397			−0.761983	+	0.647597i	$0.775774\pi$
$228$	−2.14932e15	+	1.86935e15i	−1.01327	+	0.881280i
$229$	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	$-0.896325\pi$
$233$		−	1.56301e15i		−	0.639953i	0.947425	−	0.319977i	$-0.103675\pi$
$234$	1.14112e15	+	5.43766e14i	0.454388	+	0.216525i
$235$		−	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	$-0.229164\pi$
$239$	4.33256e15			1.50369			0.751845	+	0.659340i	$0.229164\pi$
$240$	2.52817e15	−	3.31712e15i	0.853950	−	1.12044i
$241$	−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
$246$	1.33302e15	+	1.89117e15i	0.383494	+	0.544068i
$247$			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	$-0.311119\pi$
$251$	4.43051e15			1.11834			0.559171	+	0.829052i	$0.311119\pi$
$252$	−6.49368e15	−	2.31775e15i	−1.59730	−	0.570115i
$253$	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	$-0.898368\pi$
$257$		−	2.89981e15i		−	0.627775i	0.949460	−	0.313888i	$-0.101632\pi$
$258$	4.11429e15	+	5.83700e15i	0.868495	+	1.23214i
$259$		−	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	$-0.588313\pi$
$263$	−2.93990e15			−0.547798			−0.273899	+	0.961758i	$0.588313\pi$
$264$	−2.62471e15	+	2.80000e15i	−0.477151	+	0.509018i
$265$	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	$0.00701959\pi$
$269$			2.74060e14i			0.0441018i	−0.999757	+	0.0220509i	$0.992980\pi$
$270$	−8.94775e15	+	6.04321e14i	−1.40556	+	0.0949299i
$271$			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
$276$	3.31187e15	+	3.80789e15i	0.450987	+	0.518532i
$277$	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	$0.103318\pi$
$281$			5.26374e15i			0.637827i	−0.947784	+	0.318914i	$0.896682\pi$
$282$	−5.10929e15	+	3.60136e15i	−0.604980	+	0.426429i
$283$			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
$288$	−9.67720e15	−	3.60673e14i	−0.999306	−	0.0372446i
$289$	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	$0.114496\pi$
$293$			7.62439e15i			0.703989i	−0.936002	+	0.351994i	$0.885504\pi$
$294$	1.69823e16	−	1.19703e16i	1.53370	−	1.08105i
$295$		−	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
$300$	8.15877e15	+	9.38072e15i	0.646155	+	0.742930i
$301$	−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
$306$	3.59037e15	−	7.53456e15i	0.250006	−	0.524649i
$307$		−	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	$-0.785999\pi$
$311$	−2.49686e16			−1.56478			−0.782388	+	0.622791i	$0.785999\pi$
$312$	−5.60867e15	+	5.98325e15i	−0.344235	+	0.367225i
$313$	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	$-0.819766\pi$
$317$		−	1.93840e16i		−	1.07290i	0.843933	−	0.536449i	$-0.180234\pi$
$318$	−2.96759e15	−	4.21015e15i	−0.160926	−	0.228308i
$319$		−	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
$324$	1.31163e16	+	1.61728e16i	0.629896	+	0.776679i
$325$	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
$330$	−1.32850e16	−	1.88475e16i	−0.566265	−	0.803366i
$331$			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
$336$	2.71160e16	−	3.55779e16i	1.02806	−	1.34889i
$337$	−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
$342$	−1.70946e16	+	3.58738e16i	−0.577683	+	1.21229i
$343$			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	$-0.514907\pi$
$347$	−3.04483e15			−0.0936312			−0.0468156	+	0.998904i	$0.514907\pi$
$348$	1.63258e16	−	1.41992e16i	0.492730	−	0.428547i
$349$	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	$-0.881893\pi$
$353$		−	2.63621e16i		−	0.725177i	0.931949	−	0.362588i	$-0.118107\pi$
$354$	−1.09785e16	+	7.73836e15i	−0.296498	+	0.208991i
$355$		−	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	$-0.220591\pi$
$359$	6.24103e16			1.53866			0.769329	+	0.638853i	$0.220591\pi$
$360$	1.38854e16	−	5.65029e16i	0.336195	−	1.36806i
$361$	−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
$366$	1.68120e16	−	1.18502e16i	0.365589	−	0.257691i
$367$			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
$372$	−5.73946e15	+	4.99183e15i	−0.112290	+	0.0976632i
$373$	−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
$378$	−9.59696e16	+	6.48167e15i	−1.69214	+	0.114285i
$379$		−	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	$-0.719939\pi$
$383$	−7.87317e16			−1.27455			−0.637276	+	0.770636i	$0.719939\pi$
$384$	2.12872e16	−	5.91118e16i	0.338818	−	0.940852i
$385$	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	$0.0149371\pi$
$389$			6.41150e15i			0.0938183i	−0.998899	+	0.0469091i	$0.985063\pi$
$390$	−2.83883e16	−	4.02748e16i	−0.408525	−	0.579580i
$391$		−	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
$396$	−1.79978e16	+	5.04247e16i	−0.234531	+	0.657090i
$397$	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	$0.192699\pi$
$401$			9.47629e16i			1.13815i	−0.822285	+	0.569076i	$0.807301\pi$
$402$	−1.61787e16	−	2.29529e16i	−0.191194	−	0.271249i
$403$			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
$408$	3.95062e16	+	3.70329e16i	0.424008	+	0.397463i
$409$	−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
$414$	6.35565e16	+	3.02860e16i	0.620380	+	0.295624i
$415$			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	$-0.312211\pi$
$419$	1.23240e17			1.11265			0.556325	+	0.830965i	$0.312211\pi$
$420$	1.76382e17	+	2.02799e17i	1.56796	+	1.80279i
$421$	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
$426$	−5.41551e16	+	3.81720e16i	−0.439012	+	0.309444i
$427$			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	$-0.482589\pi$
$431$	1.45511e16			0.109344			0.0546718	+	0.998504i	$0.482589\pi$
$432$	−1.25806e17	+	4.92322e16i	−0.931234	+	0.364423i
$433$	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
$438$	−2.40046e16	+	1.69200e16i	−0.162447	+	0.114503i
$439$		−	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	$-0.508743\pi$
$443$	−8.73756e15			−0.0549245			−0.0274622	+	0.999623i	$0.508743\pi$
$444$	−5.73942e16	−	6.59902e16i	−0.355532	−	0.408781i
$445$	−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	$0.351749\pi$
$449$			3.10255e17i			1.78697i	−0.449089	+	0.893487i	$0.648251\pi$
$450$	1.56571e17	+	7.46093e16i	0.888854	+	0.423557i
$451$			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
$456$	−1.88098e17	−	1.76322e17i	−0.979745	−	0.918408i
$457$	−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	$-0.905069\pi$
$461$		−	1.21112e17i		−	0.587667i	0.955857	−	0.293834i	$-0.0949311\pi$
$462$	−1.42488e17	−	2.02150e17i	−0.681721	−	0.967166i
$463$		−	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	$-0.651969\pi$
$467$	−2.06001e17			−0.918988			−0.459494	+	0.888181i	$0.651969\pi$
$468$	−3.84590e16	+	1.07751e17i	−0.169200	+	0.474050i
$469$	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
$474$	1.43749e17	+	2.03939e17i	0.582165	+	0.825924i
$475$			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	$-0.394426\pi$
$479$	1.72158e17			0.651247			0.325624	+	0.945499i	$0.394426\pi$
$480$	3.21942e17	+	1.97109e17i	1.20146	+	0.735595i
$481$	−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
$486$	2.57785e17	+	1.33914e17i	0.887405	+	0.460990i
$487$		−	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	$-0.568525\pi$
$491$	−1.32648e17			−0.427238			−0.213619	+	0.976917i	$0.568525\pi$
$492$	−1.58014e17	+	1.37431e17i	−0.502253	+	0.436829i
$493$	−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
$498$	1.43656e17	−	1.01258e17i	0.422019	−	0.297466i
$499$		−	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	$-0.600696\pi$
$503$	−2.26003e17			−0.622190			−0.311095	+	0.950379i	$0.600696\pi$
$504$	1.48928e17	−	6.06025e17i	0.404742	−	1.64699i
$505$	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	$-0.742527\pi$
$509$		−	5.67729e17i		−	1.44702i	0.690313	−	0.723511i	$-0.257473\pi$
$510$	−2.65926e17	+	1.87442e17i	−0.669198	+	0.471694i
$511$		−	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
$516$	−4.87702e17	+	4.24173e17i	−1.13745	+	0.989281i
$517$	−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	$0.0351911\pi$
$521$			1.00733e17i			0.220662i	−0.993895	+	0.110331i	$0.964809\pi$
$522$	1.29847e17	−	2.72490e17i	0.280914	−	0.589511i
$523$			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
$528$	−2.76270e17	−	2.10561e17i	−0.554897	−	0.422919i
$529$	−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
$534$	1.68850e17	+	2.39550e17i	0.315126	+	0.447072i
$535$		−	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
$540$	−1.36762e17	−	8.00099e17i	−0.237359	−	1.38862i
$541$	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
$546$	−3.04480e17	−	4.31969e17i	−0.491820	−	0.697751i
$547$			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
$552$	−3.12385e17	+	3.33248e17i	−0.469987	+	0.501375i
$553$	−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	$0.0164778\pi$
$557$			7.29365e16i			0.103487i	−0.998660	+	0.0517435i	$0.983522\pi$
$558$	−4.56487e16	+	9.57959e16i	−0.0640186	+	0.134346i
$559$			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	$-0.608178\pi$
$563$	−5.03770e17			−0.666695			−0.333348	+	0.942804i	$0.608178\pi$
$564$	−3.71290e17	−	4.26899e17i	−0.485735	−	0.558484i
$565$	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	$0.0445266\pi$
$569$			2.25742e17i			0.278857i	−0.990232	+	0.139429i	$0.955473\pi$
$570$	1.26614e18	−	8.92454e17i	1.54630	−	1.08993i
$571$			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
$576$	−5.65867e16	−	8.74660e17i	−0.0645607	−	0.997914i
$577$	−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
$582$	3.19726e17	−	2.25364e17i	0.341019	−	0.240373i
$583$		−	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	$-0.388868\pi$
$587$	6.78124e17			0.684166			0.342083	+	0.939670i	$0.388868\pi$
$588$	1.23410e18	+	1.41893e18i	1.23140	+	1.41582i
$589$	−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	$-0.720502\pi$
$593$		−	1.62966e18i		−	1.53901i	0.638638	−	0.769507i	$-0.279498\pi$
$594$	5.03315e16	+	7.45223e17i	0.0470141	+	0.696104i
$595$		−	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	$-0.643141\pi$
$599$	−9.82836e17			−0.869374			−0.434687	+	0.900582i	$0.643141\pi$
$600$	−7.69558e17	+	8.20954e17i	−0.673377	+	0.718349i
$601$	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
$606$	−1.35193e18	−	1.91800e18i	−1.10888	−	1.57318i
$607$			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
$612$	7.11459e17	+	2.53936e17i	0.547351	+	0.195362i
$613$	−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	$-0.928082\pi$
$617$		−	6.14000e17i		−	0.448038i	0.974585	−	0.224019i	$-0.0719177\pi$
$618$	7.04597e17	+	9.99620e17i	0.508763	+	0.721788i
$619$		−	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
$624$	−5.90353e17	−	4.49942e17i	−0.400325	−	0.305110i
$625$	−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
$630$	3.38487e18	+	1.61296e18i	2.15689	+	1.02780i
$631$			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
$636$	3.51773e17	−	3.05951e17i	0.210762	−	0.183307i
$637$	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	$0.0594527\pi$
$641$			6.52230e17i			0.371384i	−0.982608	+	0.185692i	$0.940547\pi$
$642$	−2.22626e18	+	1.56921e18i	−1.25487	+	0.884512i
$643$		−	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	$-0.411244\pi$
$647$	1.02710e18			0.550472			0.275236	+	0.961377i	$0.411244\pi$
$648$	−1.33549e18	+	1.32984e18i	−0.708604	+	0.705606i
$649$	−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	$-0.947209\pi$
$653$		−	6.54158e17i		−	0.330177i	0.986279	−	0.165088i	$-0.0527910\pi$
$654$	−2.24156e18	+	1.57999e18i	−1.12020	+	0.789587i
$655$			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	$-0.555322\pi$
$659$	−7.27186e17			−0.345852			−0.172926	+	0.984935i	$0.555322\pi$
$660$	1.57478e18	−	1.36964e18i	0.741623	−	0.645018i
$661$	−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
$666$	−1.10143e18	−	5.24852e17i	−0.489072	−	0.233053i
$667$		−	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
$672$	3.45301e18	+	2.11410e18i	1.44643	+	0.885576i
$673$	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	$-0.822563\pi$
$677$		−	2.65046e18i		−	1.05802i	0.848615	−	0.529011i	$-0.177437\pi$
$678$	−1.92448e18	−	2.73028e18i	−0.760886	−	1.07948i
$679$			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	$-0.623085\pi$
$683$	−2.00098e18			−0.754238			−0.377119	+	0.926165i	$0.623085\pi$
$684$	−3.38742e18	−	1.20905e18i	−1.26475	−	0.451419i
$685$	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
$690$	−1.58113e18	−	2.24317e18i	−0.557763	−	0.791305i
$691$			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
$696$	1.42875e18	+	1.33931e18i	0.476428	+	0.446601i
$697$	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	$0.176107\pi$
$701$			3.30170e18i			1.05092i	−0.850818	+	0.525461i	$0.823893\pi$
$702$	1.07552e17	+	1.59245e18i	0.0339178	+	0.502197i
$703$		−	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
$708$	−7.97805e17	−	9.17293e17i	−0.238057	−	0.273711i
$709$	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
$714$	−2.85220e18	+	2.01042e18i	−0.805641	+	0.567868i
$715$		−	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	$-0.706875\pi$
$719$	−4.48341e18			−1.21024			−0.605119	+	0.796135i	$0.706875\pi$
$720$	5.21535e18	+	7.30234e17i	1.39515	+	0.195344i
$721$	−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
$726$	1.65505e18	−	1.16659e18i	0.419492	−	0.295685i
$727$		−	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
$732$	1.22172e18	+	1.40470e18i	0.293529	+	0.337491i
$733$	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
$738$	−1.25676e18	+	2.63737e18i	−0.286343	+	0.600904i
$739$			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	$-0.749983\pi$
$743$	−6.48514e18			−1.41414			−0.707069	+	0.707145i	$0.749983\pi$
$744$	−5.02289e17	−	4.70843e17i	−0.108575	−	0.101778i
$745$	−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
$750$	6.08736e16	+	8.63621e16i	0.0124891	+	0.0177184i
$751$		−	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
$756$	−1.46685e18	−	8.58150e18i	−0.285755	−	1.67175i
$757$	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	$0.110856\pi$
$761$			3.65698e18i			0.682531i	−0.939967	+	0.341265i	$0.889144\pi$
$762$	2.52474e14	+	3.58188e14i	4.67207e−5	+	6.62832e-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
$768$	5.51837e18	+	1.37269e18i	0.970427	+	0.241393i
$769$	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	$0.235647\pi$
$773$			8.00181e18i			1.34903i	−0.738261	+	0.674515i	$0.764353\pi$
$774$	−3.87892e18	+	8.14010e18i	−0.648478	+	1.36086i
$775$			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
$780$	3.36510e18	−	2.92676e18i	0.535036	−	0.465341i
$781$	−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
$786$	8.07317e18	−	5.69049e18i	1.22123	−	0.860802i
$787$			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
$792$	−4.70591e18	−	1.15646e18i	−0.677532	−	0.166501i
$793$	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	$-0.965902\pi$
$797$		−	1.54726e18i		−	0.213837i	0.994268	−	0.106919i	$-0.0340984\pi$
$798$	1.35800e19	−	9.57206e18i	1.86158	−	1.31216i
$799$			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
$804$	1.91779e18	−	1.66798e18i	0.250402	−	0.217784i
$805$	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	$0.0520525\pi$
$809$			2.59627e18i			0.325600i	−0.986659	+	0.162800i	$0.947947\pi$
$810$	−6.20153e18	−	9.47462e18i	−0.771518	−	1.17872i
$811$		−	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
$816$	−2.97087e18	+	3.89798e18i	−0.352288	+	0.462225i
$817$	−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	$0.0348799\pi$
$821$			1.91918e18i			0.218719i	−0.994002	+	0.109359i	$0.965120\pi$
$822$	−4.70482e18	−	6.67478e18i	−0.531956	−	0.754693i
$823$		−	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	$-0.299337\pi$
$827$	1.08462e19			1.17894			0.589470	+	0.807790i	$0.299337\pi$
$828$	−2.14204e18	+	6.00139e18i	−0.231010	+	0.647224i
$829$	−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
$834$	6.63500e17	+	9.41315e17i	0.0682750	+	0.0968625i
$835$			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	$-0.323278\pi$
$839$	1.06507e19			1.05421			0.527104	+	0.849801i	$0.323278\pi$
$840$	−1.66369e19	+	1.77480e19i	−1.63401	+	1.74314i
$841$	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
$846$	−7.12525e18	−	3.39533e18i	−0.668179	−	0.318401i
$847$			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
$852$	−3.93543e18	−	4.52484e18i	−0.352480	−	0.405272i
$853$	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	$-0.772054\pi$
$857$		−	1.52269e19i		−	1.31291i	0.754363	−	0.656457i	$-0.227946\pi$
$858$	−3.35433e18	+	2.36435e18i	−0.287037	+	0.202322i
$859$			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	$-0.768199\pi$
$863$	−1.81153e19			−1.49271			−0.746357	+	0.665546i	$0.768199\pi$
$864$	−5.59073e18	−	1.08746e19i	−0.457224	−	0.889351i
$865$	−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
$870$	−9.61729e18	+	6.77889e18i	−0.751930	+	0.530009i
$871$		−	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
$876$	−1.74440e18	−	2.00566e18i	−0.130428	−	0.149962i
$877$	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	$0.258253\pi$
$881$			2.01295e19i			1.45040i	−0.688537	+	0.725202i	$0.741747\pi$
$882$	2.36830e19	+	1.12855e19i	1.69392	+	0.807186i
$883$		−	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	$-0.655897\pi$
$887$	−1.36464e19			−0.940837			−0.470418	+	0.882444i	$0.655897\pi$
$888$	5.41358e18	−	5.77513e18i	0.370510	−	0.395255i
$889$	−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
$894$	1.50507e19	+	2.13526e19i	0.985969	+	1.39881i
$895$		−	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
$900$	−5.27690e18	+	1.47844e19i	−0.330981	+	0.927315i
$901$	−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
$906$	1.06534e19	+	1.51141e19i	0.639963	+	0.907923i
$907$		−	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	$-0.334790\pi$
$911$	1.71163e19			0.992065			0.496033	+	0.868304i	$0.334790\pi$
$912$	1.41450e19	−	1.85592e19i	0.814024	−	1.06805i
$913$	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
$918$	1.05146e19	−	7.10144e17i	0.579849	−	0.0391624i
$919$		−	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
$924$	1.68903e19	−	1.46902e19i	0.892833	−	0.776532i
$925$	−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	$0.239377\pi$
$929$			2.67688e19i			1.36624i	−0.730307	+	0.683120i	$0.760623\pi$
$930$	3.38104e18	−	2.38317e18i	0.171360	−	0.120786i
$931$			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
$936$	−1.00559e19	−	2.47120e18i	−0.488798	−	0.120120i
$937$	−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	$-0.815086\pi$
$941$		−	2.33762e19i		−	1.09759i	0.835956	−	0.548797i	$-0.184914\pi$
$942$	−2.15111e19	+	1.51624e19i	−1.00307	+	0.707030i
$943$			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	$-0.862835\pi$
$947$	−4.03339e19			−1.81717			−0.908583	+	0.417703i	$0.862835\pi$
$948$	−1.70398e19	+	1.48202e19i	−0.762447	+	0.663130i
$949$	−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	$0.124621\pi$
$953$			1.76491e19i			0.763164i	−0.924335	+	0.381582i	$0.875379\pi$
$954$	2.79782e18	−	5.87135e18i	0.120159	−	0.252158i
$955$		−	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
$960$	−1.47849e19	+	3.08019e19i	−0.609614	+	1.27003i
$961$	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
$966$	−1.69585e19	−	2.40593e19i	−0.671486	−	0.952645i
$967$		−	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	$-0.409555\pi$
$971$	1.46430e19			0.560667			0.280333	+	0.959903i	$0.409555\pi$
$972$	−9.68526e18	+	2.44436e19i	−0.368367	+	0.929680i
$973$	−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	$-0.888709\pi$
$977$		−	1.86239e19i		−	0.685102i	0.939499	−	0.342551i	$-0.111291\pi$
$978$	6.06196e17	+	8.60017e17i	0.0221519	+	0.0314271i
$979$			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	$-0.411077\pi$
$983$	1.56001e19			0.551479			0.275740	+	0.961232i	$0.411077\pi$
$984$	−1.38286e19	−	1.29629e19i	−0.485635	−	0.455232i
$985$	−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
$990$	1.25249e19	−	2.62842e19i	0.422812	−	0.887290i
$991$			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
$996$	1.04394e19	+	1.20029e19i	0.338837	+	0.389585i
$997$	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.11.14	yes	24
3.2	odd	2	inner	12.14.b.a.11.11	✓	24
4.3	odd	2	inner	12.14.b.a.11.12	yes	24
12.11	even	2	inner	12.14.b.a.11.13	yes	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(9.20327 + 90.0405i) q^{2} +(618.744 + 1100.67i) q^{3} +(-8022.60 + 1657.33i) q^{4} -49220.1i q^{5} +(-93410.6 + 65841.9i) q^{6} -527913. i q^{7} +(-223061. - 707106. i) q^{8} +(-828634. + 1.36207e6i) q^{9} +O(q^{10})\)	\(q+(9.20327 + 90.0405i) q^{2} +(618.744 + 1100.67i) q^{3} +(-8022.60 + 1657.33i) q^{4} -49220.1i q^{5} +(-93410.6 + 65841.9i) 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} +(-6.78812e6 - 7.80478e6i) 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} +(-1.30268e8 - 6.20752e7i) 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} +(6.40274e8 - 6.83036e8i) 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} +(3.24075e9 + 4.59768e9i) 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} +(4.39039e9 - 1.23007e10i) 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} +(3.47588e10 + 4.93127e10i) 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} +(6.73935e10 + 5.13645e10i) 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} +(-1.22779e10 - 1.81790e11i) 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} +(-3.84153e11 + 3.34112e11i) 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} +(3.82923e11 - 2.69909e11i) 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} +(1.14796e12 + 2.82107e11i) 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} +(8.18258e11 - 5.76761e11i) 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} +(-4.12025e12 + 3.58354e12i) 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} +(-3.05535e12 + 6.41179e12i) 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} +(-4.00464e12 + 6.54087e12i) 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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