LMFDB - Embedded newform 12.12.b.a.11.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,12,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, 12, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 12 $
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:	$9.22011816672$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 247 x^{18} - 23916 x^{16} + 14713536 x^{14} - 45723119616 x^{12} + 40864324780032 x^{10} + \cdots + 12\!\cdots\!24 $ x^20 - 247x^18 - 23916x^16 + 14713536x^14 - 45723119616x^12 + 40864324780032x^10 - 11986041468616704x^8 + 1011106494856298496x^6 - 430832354752771129344x^4 - 1166424521268802367782912*x^2 + 1237940039285380274899124224
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{104}\cdot 3^{42}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.18
Root			$20.8511 + 8.78821i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.12.b.a.11.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(41.7022 + 17.5764i) q^{2} +(-364.303 - 210.784i) q^{3} +(1430.14 + 1465.95i) q^{4} +505.366i q^{5} +(-11487.4 - 15193.3i) q^{6} +77554.9i q^{7} +(33873.8 + 86269.9i) q^{8} +(88286.9 + 153579. i) q^{9} +O(q^{10})$	\(q+(41.7022 + 17.5764i) q^{2} +(-364.303 - 210.784i) q^{3} +(1430.14 + 1465.95i) q^{4} +505.366i q^{5} +(-11487.4 - 15193.3i) q^{6} +77554.9i q^{7} +(33873.8 + 86269.9i) q^{8} +(88286.9 + 153579. i) q^{9} +(-8882.52 + 21074.9i) q^{10} -731355. q^{11} +(-212006. - 835501. i) q^{12} +1.14210e6 q^{13} +(-1.36314e6 + 3.23421e6i) q^{14} +(106523. - 184107. i) q^{15} +(-103706. + 4.19302e6i) q^{16} +3.04203e6i q^{17} +(982390. + 7.95634e6i) q^{18} -4.99643e6i q^{19} +(-740841. + 722744. i) q^{20} +(1.63474e7 - 2.82535e7i) q^{21} +(-3.04991e7 - 1.28546e7i) q^{22} -5.14282e6 q^{23} +(5.84402e6 - 3.85685e7i) q^{24} +4.85727e7 q^{25} +(4.76280e7 + 2.00740e7i) q^{26} +(208788. - 7.45588e7i) q^{27} +(-1.13692e8 + 1.10914e8i) q^{28} -1.44501e8i q^{29} +(7.67818e6 - 5.80535e6i) q^{30} +2.51898e7i q^{31} +(-7.80231e7 + 1.73035e8i) q^{32} +(2.66435e8 + 1.54158e8i) q^{33} +(-5.34679e7 + 1.26859e8i) q^{34} -3.91936e7 q^{35} +(-9.88761e7 + 3.49063e8i) q^{36} -1.69193e8 q^{37} +(8.78194e7 - 2.08362e8i) q^{38} +(-4.16071e8 - 2.40737e8i) q^{39} +(-4.35979e7 + 1.71187e7i) q^{40} +3.25800e8i q^{41} +(1.17832e9 - 8.90905e8i) q^{42} +1.17931e9i q^{43} +(-1.04594e9 - 1.07213e9i) q^{44} +(-7.76136e7 + 4.46172e7i) q^{45} +(-2.14467e8 - 9.03923e7i) q^{46} +1.82705e9 q^{47} +(9.21604e8 - 1.50567e9i) q^{48} -4.03744e9 q^{49} +(2.02559e9 + 8.53734e8i) q^{50} +(6.41211e8 - 1.10822e9i) q^{51} +(1.63336e9 + 1.67426e9i) q^{52} -5.85339e7i q^{53} +(1.31918e9 - 3.10559e9i) q^{54} -3.69602e8i q^{55} +(-6.69066e9 + 2.62708e9i) q^{56} +(-1.05317e9 + 1.82022e9i) q^{57} +(2.53981e9 - 6.02601e9i) q^{58} +5.59090e8 q^{59} +(4.22234e8 - 1.07141e8i) q^{60} +8.08270e9 q^{61} +(-4.42746e8 + 1.05047e9i) q^{62} +(-1.19108e10 + 6.84709e9i) q^{63} +(-6.29507e9 + 5.84458e9i) q^{64} +5.77179e8i q^{65} +(8.40137e9 + 1.11117e10i) q^{66} -2.71710e9i q^{67} +(-4.45945e9 + 4.35052e9i) q^{68} +(1.87355e9 + 1.08403e9i) q^{69} +(-1.63446e9 - 6.88883e8i) q^{70} +1.89778e10 q^{71} +(-1.02586e10 + 1.28188e10i) q^{72} +1.88173e10 q^{73} +(-7.05570e9 - 2.97380e9i) q^{74} +(-1.76952e10 - 1.02384e10i) q^{75} +(7.32451e9 - 7.14560e9i) q^{76} -5.67202e10i q^{77} +(-1.31198e10 - 1.73523e10i) q^{78} -4.26966e10i q^{79} +(-2.11901e9 - 5.24098e7i) q^{80} +(-1.57919e10 + 2.71180e10i) q^{81} +(-5.72640e9 + 1.35866e10i) q^{82} +3.76005e10 q^{83} +(6.47972e10 - 1.64421e10i) q^{84} -1.53734e9 q^{85} +(-2.07281e10 + 4.91798e10i) q^{86} +(-3.04586e10 + 5.26422e10i) q^{87} +(-2.47738e10 - 6.30940e10i) q^{88} +5.79261e10i q^{89} +(-4.02086e9 + 4.96467e8i) q^{90} +8.85755e10i q^{91} +(-7.35495e9 - 7.53911e9i) q^{92} +(5.30961e9 - 9.17673e9i) q^{93} +(7.61920e10 + 3.21130e10i) q^{94} +2.52503e9 q^{95} +(6.48972e10 - 4.65913e10i) q^{96} -9.56525e10 q^{97} +(-1.68370e11 - 7.09637e10i) q^{98} +(-6.45691e10 - 1.12321e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9}+O(q^{10}) $ 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9	$ 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9} + 202000 q^{10} + 1064760 q^{12} + 1543864 q^{13} + 3482912 q^{16} + 2557392 q^{18} - 12211752 q^{21} - 5920464 q^{22} + 12133152 q^{24} - 141128700 q^{25} - 3604848 q^{28} + 73456080 q^{30} + 229769760 q^{33} + 222167104 q^{34} + 298087896 q^{36} - 44517800 q^{37} - 439643840 q^{40} + 281776944 q^{42} + 1020227520 q^{45} - 2392795680 q^{46} + 689090592 q^{48} - 1018138084 q^{49} - 3959246384 q^{52} - 4249352520 q^{54} + 1438636392 q^{57} + 9671853040 q^{58} + 5688375360 q^{60} + 6873199864 q^{61} - 1452752512 q^{64} - 10961242896 q^{66} - 13308470976 q^{69} + 35188514400 q^{70} + 30438127680 q^{72} - 12426469112 q^{73} - 60088673808 q^{76} - 81037845456 q^{78} - 42462874764 q^{81} + 88180337440 q^{82} + 125502443664 q^{84} + 17135502080 q^{85} - 166086469440 q^{88} - 257976145200 q^{90} + 114387515256 q^{93} + 391966360512 q^{94} + 446868262272 q^{96} + 75764383528 q^{97}+O(q^{100}) $ 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9 + 202000 * q^10 + 1064760 * q^12 + 1543864 * q^13 + 3482912 * q^16 + 2557392 * q^18 - 12211752 * q^21 - 5920464 * q^22 + 12133152 * q^24 - 141128700 * q^25 - 3604848 * q^28 + 73456080 * q^30 + 229769760 * q^33 + 222167104 * q^34 + 298087896 * q^36 - 44517800 * q^37 - 439643840 * q^40 + 281776944 * q^42 + 1020227520 * q^45 - 2392795680 * q^46 + 689090592 * q^48 - 1018138084 * q^49 - 3959246384 * q^52 - 4249352520 * q^54 + 1438636392 * q^57 + 9671853040 * q^58 + 5688375360 * q^60 + 6873199864 * q^61 - 1452752512 * q^64 - 10961242896 * q^66 - 13308470976 * q^69 + 35188514400 * q^70 + 30438127680 * q^72 - 12426469112 * q^73 - 60088673808 * q^76 - 81037845456 * q^78 - 42462874764 * q^81 + 88180337440 * q^82 + 125502443664 * q^84 + 17135502080 * q^85 - 166086469440 * q^88 - 257976145200 * q^90 + 114387515256 * q^93 + 391966360512 * q^94 + 446868262272 * q^96 + 75764383528 * 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 $

$2$	41.7022	+	17.5764i	0.921496	+	0.388388i
$2$	41.7022	+	17.5764i	0.921496	+	0.388388i
$3$	−364.303	−	210.784i	−0.865558	−	0.500808i
$3$	−364.303	−	210.784i	−0.865558	−	0.500808i
$4$	1430.14	+	1465.95i	0.698310	+	0.715795i
$5$			505.366i			0.0723221i	0.999346	+	0.0361611i	$0.0115129\pi$
$5$			505.366i			0.0723221i	−0.999346	+	0.0361611i	$0.988487\pi$
$6$	−11487.4	−	15193.3i	−0.603101	−	0.797665i
$7$			77554.9i			1.74409i	0.489422	+	0.872047i	$0.337208\pi$
$7$			77554.9i			1.74409i	−0.489422	+	0.872047i	$0.662792\pi$
$8$	33873.8	+	86269.9i	0.365484	+	0.930818i
$9$	88286.9	+	153579.i	0.498382	+	0.866957i
$10$	−8882.52	+	21074.9i	−0.0280890	+	0.0666446i
$11$	−731355.			−1.36921			−0.684603	−	0.728916i	$-0.740024\pi$
$11$	−731355.			−1.36921			−0.684603	+	0.728916i	$0.740024\pi$
$12$	−212006.	−	835501.i	−0.245952	−	0.969282i
$13$	1.14210e6			0.853131			0.426566	−	0.904457i	$-0.359723\pi$
$13$	1.14210e6			0.853131			0.426566	+	0.904457i	$0.359723\pi$
$14$	−1.36314e6	+	3.23421e6i	−0.677385	+	1.60718i
$15$	106523.	−	184107.i	0.0362195	−	0.0625990i
$16$	−103706.	+	4.19302e6i	−0.0247256	+	0.999694i
$17$			3.04203e6i			0.519630i	0.965658	+	0.259815i	$0.0836615\pi$
$17$			3.04203e6i			0.519630i	−0.965658	+	0.259815i	$0.916338\pi$
$18$	982390.	+	7.95634e6i	0.122542	+	0.992463i
$19$		−	4.99643e6i		−	0.462930i	−0.972843	−	0.231465i	$-0.925648\pi$
$19$		−	4.99643e6i		−	0.462930i	0.972843	−	0.231465i	$-0.0743519\pi$
$20$	−740841.	+	722744.i	−0.0517678	+	0.0505033i
$21$	1.63474e7	−	2.82535e7i	0.873457	−	1.50962i
$22$	−3.04991e7	−	1.28546e7i	−1.26172	−	0.531782i
$23$	−5.14282e6			−0.166609			−0.0833044	−	0.996524i	$-0.526547\pi$
$23$	−5.14282e6			−0.166609			−0.0833044	+	0.996524i	$0.526547\pi$
$24$	5.84402e6	−	3.85685e7i	0.149813	−	0.988714i
$25$	4.85727e7			0.994770
$26$	4.76280e7	+	2.00740e7i	0.786157	+	0.331346i
$27$	208788.	−	7.45588e7i	0.00280031	−	0.999996i
$28$	−1.13692e8	+	1.10914e8i	−1.24841	+	1.21792i
$29$		−	1.44501e8i		−	1.30822i	−0.756398	−	0.654112i	$-0.773043\pi$
$29$		−	1.44501e8i		−	1.30822i	0.756398	−	0.654112i	$-0.226957\pi$
$30$	7.67818e6	−	5.80535e6i	0.0576888	−	0.0436175i
$31$			2.51898e7i			0.158028i	0.996873	+	0.0790142i	$0.0251773\pi$
$31$			2.51898e7i			0.158028i	−0.996873	+	0.0790142i	$0.974823\pi$
$32$	−7.80231e7	+	1.73035e8i	−0.411053	+	0.911611i
$33$	2.66435e8	+	1.54158e8i	1.18513	+	0.685709i
$34$	−5.34679e7	+	1.26859e8i	−0.201818	+	0.478837i
$35$	−3.91936e7			−0.126137
$36$	−9.88761e7	+	3.49063e8i	−0.272538	+	0.962145i
$37$	−1.69193e8			−0.401118			−0.200559	−	0.979682i	$-0.564276\pi$
$37$	−1.69193e8			−0.401118			−0.200559	+	0.979682i	$0.564276\pi$
$38$	8.78194e7	−	2.08362e8i	0.179796	−	0.426588i
$39$	−4.16071e8	−	2.40737e8i	−0.738435	−	0.427255i
$40$	−4.35979e7	+	1.71187e7i	−0.0673187	+	0.0264326i
$41$			3.25800e8i			0.439177i	0.975593	+	0.219589i	$0.0704715\pi$
$41$			3.25800e8i			0.439177i	−0.975593	+	0.219589i	$0.929528\pi$
$42$	1.17832e9	−	8.90905e8i	1.39120	−	1.05187i
$43$			1.17931e9i			1.22335i	0.791108	+	0.611677i	$0.209505\pi$
$43$			1.17931e9i			1.22335i	−0.791108	+	0.611677i	$0.790495\pi$
$44$	−1.04594e9	−	1.07213e9i	−0.956130	−	0.980071i
$45$	−7.76136e7	+	4.46172e7i	−0.0627002	+	0.0360441i
$46$	−2.14467e8	−	9.03923e7i	−0.153529	−	0.0647088i
$47$	1.82705e9			1.16202			0.581009	−	0.813897i	$-0.302658\pi$
$47$	1.82705e9			1.16202			0.581009	+	0.813897i	$0.302658\pi$
$48$	9.21604e8	−	1.50567e9i	0.522056	−	0.852911i
$49$	−4.03744e9			−2.04187
$50$	2.02559e9	+	8.53734e8i	0.916676	+	0.386356i
$51$	6.41211e8	−	1.10822e9i	0.260235	−	0.449770i
$52$	1.63336e9	+	1.67426e9i	0.595750	+	0.610667i
$53$		−	5.85339e7i		−	0.0192260i	−0.999954	−	0.00961302i	$-0.996940\pi$
$53$		−	5.85339e7i		−	0.0192260i	0.999954	−	0.00961302i	$-0.00305997\pi$
$54$	1.31918e9	−	3.10559e9i	0.390966	−	0.920405i
$55$		−	3.69602e8i		−	0.0990238i
$56$	−6.69066e9	+	2.62708e9i	−1.62343	+	0.637439i
$57$	−1.05317e9	+	1.82022e9i	−0.231839	+	0.400693i
$58$	2.53981e9	−	6.02601e9i	0.508098	−	1.20552i
$59$	5.59090e8			0.101811			0.0509056	−	0.998703i	$-0.483789\pi$
$59$	5.59090e8			0.101811			0.0509056	+	0.998703i	$0.483789\pi$
$60$	4.22234e8	−	1.07141e8i	0.0701005	−	0.0177878i
$61$	8.08270e9			1.22530			0.612650	−	0.790354i	$-0.290103\pi$
$61$	8.08270e9			1.22530			0.612650	+	0.790354i	$0.290103\pi$
$62$	−4.42746e8	+	1.05047e9i	−0.0613763	+	0.145623i
$63$	−1.19108e10	+	6.84709e9i	−1.51206	+	0.869226i
$64$	−6.29507e9	+	5.84458e9i	−0.732842	+	0.680398i
$65$			5.77179e8i			0.0617003i
$66$	8.40137e9	+	1.11117e10i	0.825769	+	1.09217i
$67$		−	2.71710e9i		−	0.245864i	−0.992415	−	0.122932i	$-0.960770\pi$
$67$		−	2.71710e9i		−	0.245864i	0.992415	−	0.122932i	$-0.0392297\pi$
$68$	−4.45945e9	+	4.35052e9i	−0.371948	+	0.362863i
$69$	1.87355e9	+	1.08403e9i	0.144210	+	0.0834391i
$70$	−1.63446e9	−	6.88883e8i	−0.116234	−	0.0489899i
$71$	1.89778e10			1.24832			0.624160	−	0.781296i	$-0.285441\pi$
$71$	1.89778e10			1.24832			0.624160	+	0.781296i	$0.285441\pi$
$72$	−1.02586e10	+	1.28188e10i	−0.624828	+	0.780762i
$73$	1.88173e10			1.06238			0.531192	−	0.847252i	$-0.321744\pi$
$73$	1.88173e10			1.06238			0.531192	+	0.847252i	$0.321744\pi$
$74$	−7.05570e9	−	2.97380e9i	−0.369628	−	0.155789i
$75$	−1.76952e10	−	1.02384e10i	−0.861031	−	0.498189i
$76$	7.32451e9	−	7.14560e9i	0.331363	−	0.323269i
$77$		−	5.67202e10i		−	2.38802i
$78$	−1.31198e10	−	1.73523e10i	−0.514524	−	0.680513i
$79$		−	4.26966e10i		−	1.56115i	−0.625064	−	0.780574i	$-0.714927\pi$
$79$		−	4.26966e10i		−	1.56115i	0.625064	−	0.780574i	$-0.285073\pi$
$80$	−2.11901e9	−	5.24098e7i	−0.0723000	−	0.00178820i
$81$	−1.57919e10	+	2.71180e10i	−0.503230	+	0.864152i
$82$	−5.72640e9	+	1.35866e10i	−0.170571	+	0.404700i
$83$	3.76005e10			1.04777			0.523883	−	0.851790i	$-0.324483\pi$
$83$	3.76005e10			1.04777			0.523883	+	0.851790i	$0.324483\pi$
$84$	6.47972e10	−	1.64421e10i	1.69052	−	0.428964i
$85$	−1.53734e9			−0.0375807
$86$	−2.07281e10	+	4.91798e10i	−0.475135	+	1.12732i
$87$	−3.04586e10	+	5.26422e10i	−0.655169	+	1.13234i
$88$	−2.47738e10	−	6.30940e10i	−0.500423	−	1.27448i
$89$			5.79261e10i			1.09959i	0.835301	+	0.549794i	$0.185294\pi$
$89$			5.79261e10i			1.09959i	−0.835301	+	0.549794i	$0.814706\pi$
$90$	−4.02086e9	+	4.96467e8i	−0.0717771	+	0.00886250i
$91$			8.85755e10i			1.48794i
$92$	−7.35495e9	−	7.53911e9i	−0.116345	−	0.119258i
$93$	5.30961e9	−	9.17673e9i	0.0791419	−	0.136783i
$94$	7.61920e10	+	3.21130e10i	1.07079	+	0.451313i
$95$	2.52503e9			0.0334801
$96$	6.48972e10	−	4.65913e10i	0.812333	−	0.583194i
$97$	−9.56525e10			−1.13097			−0.565486	−	0.824758i	$-0.691311\pi$
$97$	−9.56525e10			−1.13097			−0.565486	+	0.824758i	$0.691311\pi$
$98$	−1.68370e11	−	7.09637e10i	−1.88157	−	0.793035i
$99$	−6.45691e10	−	1.12321e11i	−0.682388	−	1.18704i
$100$	6.94658e10	+	7.12051e10i	0.694658	+	0.712051i
$101$			1.13327e11i			1.07292i	0.843927	+	0.536458i	$0.180238\pi$
$101$			1.13327e11i			1.07292i	−0.843927	+	0.536458i	$0.819762\pi$
$102$	4.62184e10	−	3.49450e10i	0.414490	−	0.313389i
$103$			2.45239e10i			0.208442i	0.994554	+	0.104221i	$0.0332349\pi$
$103$			2.45239e10i			0.208442i	−0.994554	+	0.104221i	$0.966765\pi$
$104$	3.86873e10	+	9.85289e10i	0.311806	+	0.794109i
$105$	1.42784e10	+	8.26140e9i	0.109179	+	0.0631702i
$106$	1.02882e9	−	2.44099e9i	0.00746716	−	0.0177167i
$107$	1.56226e11			1.07682			0.538409	−	0.842684i	$-0.319026\pi$
$107$	1.56226e11			1.07682			0.538409	+	0.842684i	$0.319026\pi$
$108$	1.09598e11	−	1.06323e11i	0.717748	−	0.696303i
$109$	−1.15285e11			−0.717677			−0.358838	−	0.933400i	$-0.616827\pi$
$109$	−1.15285e11			−0.717677			−0.358838	+	0.933400i	$0.616827\pi$
$110$	6.49628e9	−	1.54132e10i	0.0384596	−	0.0912501i
$111$	6.16374e10	+	3.56631e10i	0.347191	+	0.200883i
$112$	−3.25189e11	−	8.04295e9i	−1.74356	−	0.0431237i
$113$		−	3.80801e11i		−	1.94432i	−0.234326	−	0.972158i	$-0.575288\pi$
$113$		−	3.80801e11i		−	1.94432i	0.234326	−	0.972158i	$-0.424712\pi$
$114$	−7.59123e10	+	5.73960e10i	−0.369263	+	0.279193i
$115$		−	2.59901e9i		−	0.0120495i
$116$	2.11831e11	−	2.06657e11i	0.936420	−	0.913546i
$117$	1.00833e11	+	1.75403e11i	0.425186	+	0.739628i
$118$	2.33153e10	+	9.82680e9i	0.0938187	+	0.0395422i
$119$	−2.35924e11			−0.906283
$120$	1.94912e10	+	2.95337e9i	0.0715059	+	0.0108348i
$121$	2.49569e11			0.874724
$122$	3.37066e11	+	1.42065e11i	1.12911	+	0.475891i
$123$	6.86735e10	−	1.18690e11i	0.219944	−	0.380134i
$124$	−3.69269e10	+	3.60249e10i	−0.113116	+	0.110353i
$125$			4.92231e10i			0.144266i
$126$	−6.17053e11	+	7.61891e10i	−1.73095	+	0.213725i
$127$		−	4.62478e10i		−	0.124214i	−0.998069	−	0.0621070i	$-0.980218\pi$
$127$		−	4.62478e10i		−	0.124214i	0.998069	−	0.0621070i	$-0.0197820\pi$
$128$	−3.65245e11	+	1.33087e11i	−0.939570	+	0.342358i
$129$	2.48580e11	−	4.29627e11i	0.612666	−	1.05888i
$130$	−1.01447e10	+	2.40696e10i	−0.0239636	+	0.0568565i
$131$	−2.16097e11			−0.489392			−0.244696	−	0.969600i	$-0.578688\pi$
$131$	−2.16097e11			−0.489392			−0.244696	+	0.969600i	$0.578688\pi$
$132$	1.55051e11	+	6.11048e11i	0.336759	+	1.32715i
$133$	3.87498e11			0.807394
$134$	4.77569e10	−	1.13309e11i	0.0954905	−	0.226563i
$135$	3.76795e10	+	1.05515e8i	0.0723218	+	0.000202524i
$136$	−2.62435e11	+	1.03045e11i	−0.483680	+	0.189916i
$137$			7.22337e11i			1.27872i	0.768906	+	0.639362i	$0.220801\pi$
$137$			7.22337e11i			1.27872i	−0.768906	+	0.639362i	$0.779199\pi$
$138$	5.90776e10	+	7.81364e10i	0.100482	+	0.132898i
$139$		−	4.62835e11i		−	0.756562i	−0.925691	−	0.378281i	$-0.876515\pi$
$139$		−	4.62835e11i		−	0.756562i	0.925691	−	0.378281i	$-0.123485\pi$
$140$	−5.60523e10	−	5.74558e10i	−0.0880825	−	0.0902880i
$141$	−6.65601e11	−	3.85114e11i	−1.00579	−	0.581948i
$142$	7.91417e11	+	3.33562e11i	1.15032	+	0.484832i
$143$	−8.35281e11			−1.16811
$144$	−6.53116e11	+	3.54262e11i	−0.879015	+	0.476794i
$145$	7.30259e10			0.0946135
$146$	7.84721e11	+	3.30740e11i	0.978982	+	0.412616i
$147$	1.47085e12	+	8.51028e11i	1.76735	+	1.02258i
$148$	−2.41969e11	−	2.48028e11i	−0.280105	−	0.287118i
$149$			2.22822e11i			0.248562i	0.992247	+	0.124281i	$0.0396624\pi$
$149$			2.22822e11i			0.248562i	−0.992247	+	0.124281i	$0.960338\pi$
$150$	−5.57975e11	−	7.37980e11i	−0.599946	−	0.793493i
$151$			6.54960e11i			0.678956i	0.940614	+	0.339478i	$0.110250\pi$
$151$			6.54960e11i			0.678956i	−0.940614	+	0.339478i	$0.889750\pi$
$152$	4.31042e11	−	1.69248e11i	0.430903	−	0.169194i
$153$	−4.67191e11	+	2.68571e11i	−0.450497	+	0.258974i
$154$	9.96938e11	−	2.36535e12i	0.927479	−	2.20055i
$155$	−1.27301e10			−0.0114290
$156$	−2.42132e11	−	9.54226e11i	−0.209829	−	0.826925i
$157$	−1.23576e12			−1.03392			−0.516959	−	0.856010i	$-0.672936\pi$
$157$	−1.23576e12			−1.03392			−0.516959	+	0.856010i	$0.672936\pi$
$158$	7.50452e11	−	1.78054e12i	0.606330	−	1.43859i
$159$	−1.23380e10	+	2.13241e10i	−0.00962856	+	0.0166413i
$160$	−8.74462e10	−	3.94302e10i	−0.0659297	−	0.0297282i
$161$		−	3.98851e11i		−	0.290582i
$162$	−1.13519e12	+	8.53315e11i	−0.799351	+	0.600865i
$163$		−	1.71507e12i		−	1.16748i	−0.811939	−	0.583742i	$-0.801588\pi$
$163$		−	1.71507e12i		−	1.16748i	0.811939	−	0.583742i	$-0.198412\pi$
$164$	−4.77606e11	+	4.65939e11i	−0.314361	+	0.306682i
$165$	−7.79064e10	+	1.34647e11i	−0.0495920	+	0.0857109i
$166$	1.56802e12	+	6.60883e11i	0.965513	+	0.406940i
$167$	−3.29971e11			−0.196578			−0.0982890	−	0.995158i	$-0.531337\pi$
$167$	−3.29971e11			−0.196578			−0.0982890	+	0.995158i	$0.531337\pi$
$168$	2.99118e12	+	4.53232e11i	1.72441	+	0.261288i
$169$	−4.87767e11			−0.272167
$170$	−6.41103e10	−	2.70209e10i	−0.0346305	−	0.0145959i
$171$	7.67347e11	−	4.41120e11i	0.401340	−	0.230716i
$172$	−1.72881e12	+	1.68658e12i	−0.875671	+	0.854281i
$173$			1.18941e12i			0.583551i	0.956487	+	0.291775i	$0.0942460\pi$
$173$			1.18941e12i			0.583551i	−0.956487	+	0.291775i	$0.905754\pi$
$174$	−2.19545e12	+	1.65994e12i	−1.04352	+	0.788991i
$175$			3.76705e12i			1.73497i
$176$	7.58463e10	−	3.06659e12i	0.0338544	−	1.36879i
$177$	−2.03679e11	−	1.17847e11i	−0.0881236	−	0.0509879i
$178$	−1.01813e12	+	2.41565e12i	−0.427066	+	1.01327i
$179$	1.49151e12			0.606644			0.303322	−	0.952888i	$-0.401904\pi$
$179$	1.49151e12			0.606644			0.303322	+	0.952888i	$0.401904\pi$
$180$	−1.76405e11	−	4.99686e10i	−0.0695844	−	0.0197106i
$181$	2.14728e12			0.821592			0.410796	−	0.911727i	$-0.365251\pi$
$181$	2.14728e12			0.821592			0.410796	+	0.911727i	$0.365251\pi$
$182$	−1.55684e12	+	3.69379e12i	−0.577898	+	1.37113i
$183$	−2.94456e12	−	1.70371e12i	−1.06057	−	0.613640i
$184$	−1.74207e11	−	4.43671e11i	−0.0608929	−	0.155082i
$185$		−	8.55042e10i		−	0.0290097i
$186$	3.82716e11	−	2.89365e11i	0.126054	−	0.0953071i
$187$		−	2.22480e12i		−	0.711480i
$188$	2.61294e12	+	2.67836e12i	0.811449	+	0.831767i
$189$	5.78240e12	+	1.61926e10i	1.74409	+	0.00488400i
$190$	1.05299e11	+	4.43809e10i	0.0308518	+	0.0130032i
$191$	−5.22439e12			−1.48714			−0.743571	−	0.668657i	$-0.766869\pi$
$191$	−5.22439e12			−1.48714			−0.743571	+	0.668657i	$0.766869\pi$
$192$	3.52526e12	−	8.02298e11i	0.975067	−	0.221911i
$193$	−2.77245e11			−0.0745243			−0.0372622	−	0.999306i	$-0.511864\pi$
$193$	−2.77245e11			−0.0745243			−0.0372622	+	0.999306i	$0.511864\pi$
$194$	−3.98892e12	−	1.68123e12i	−1.04219	−	0.439255i
$195$	1.21660e11	−	2.10268e11i	0.0309000	−	0.0534052i
$196$	−5.77410e12	−	5.91867e12i	−1.42586	−	1.46156i
$197$		−	7.26515e12i		−	1.74454i	−0.489026	−	0.872269i	$-0.662648\pi$
$197$		−	7.26515e12i		−	1.74454i	0.489026	−	0.872269i	$-0.337352\pi$
$198$	−7.18476e11	−	5.81891e12i	−0.167785	−	1.35889i
$199$			5.35168e11i			0.121562i	0.998151	+	0.0607811i	$0.0193592\pi$
$199$			5.35168e11i			0.121562i	−0.998151	+	0.0607811i	$0.980641\pi$
$200$	1.64534e12	+	4.19037e12i	0.363573	+	0.925949i
$201$	−5.72723e11	+	9.89850e11i	−0.123131	+	0.212810i
$202$	−1.99188e12	+	4.72598e12i	−0.416707	+	0.988688i
$203$	1.12068e13			2.28167
$204$	2.54162e12	−	6.44927e11i	0.503668	−	0.127804i
$205$	−1.64648e11			−0.0317622
$206$	−4.31042e11	+	1.02270e12i	−0.0809561	+	0.192078i
$207$	−4.54044e11	−	7.89828e11i	−0.0830349	−	0.144443i
$208$	−1.18443e11	+	4.78885e12i	−0.0210941	+	0.852870i
$209$			3.65417e12i			0.633846i
$210$	4.50233e11	+	5.95481e11i	0.0760731	+	0.100615i
$211$		−	1.06659e12i		−	0.175568i	−0.996140	−	0.0877841i	$-0.972021\pi$
$211$		−	1.06659e12i		−	0.175568i	0.996140	−	0.0877841i	$-0.0279786\pi$
$212$	8.58076e10	−	8.37116e10i	0.0137619	−	0.0134257i
$213$	−6.91369e12	−	4.00023e12i	−1.08049	−	0.625169i
$214$	6.51495e12	+	2.74589e12i	0.992283	+	0.418222i
$215$	−5.95984e11			−0.0884756
$216$	6.43926e12	−	2.50758e12i	0.931837	−	0.362876i
$217$	−1.95359e12			−0.275617
$218$	−4.80765e12	−	2.02631e12i	−0.661336	−	0.278737i
$219$	−6.85520e12	−	3.96639e12i	−0.919554	−	0.532050i
$220$	5.41818e11	−	5.28583e11i	0.0708808	−	0.0691494i
$221$			3.47430e12i			0.443312i
$222$	1.94358e12	+	2.57060e12i	0.241915	+	0.319958i
$223$			1.96117e12i			0.238144i	0.992886	+	0.119072i	$0.0379919\pi$
$223$			1.96117e12i			0.238144i	−0.992886	+	0.119072i	$0.962008\pi$
$224$	−1.34197e13	−	6.05107e12i	−1.58994	−	0.716916i
$225$	4.28834e12	+	7.45975e12i	0.495776	+	0.862423i
$226$	6.69312e12	−	1.58802e13i	0.755148	−	1.79168i
$227$	9.93085e12			1.09356			0.546782	−	0.837275i	$-0.315853\pi$
$227$	9.93085e12			1.09356			0.546782	+	0.837275i	$0.315853\pi$
$228$	−4.17452e12	+	1.05927e12i	−0.448710	+	0.113859i
$229$	−3.89609e12			−0.408822			−0.204411	−	0.978885i	$-0.565528\pi$
$229$	−3.89609e12			−0.408822			−0.204411	+	0.978885i	$0.565528\pi$
$230$	4.56812e10	−	1.08384e11i	0.00467988	−	0.0111036i
$231$	−1.19557e13	+	2.06634e13i	−1.19594	+	2.06697i
$232$	1.24661e13	−	4.89480e12i	1.21772	−	0.478135i
$233$		−	1.13944e12i		−	0.108701i	−0.998522	−	0.0543503i	$-0.982691\pi$
$233$		−	1.13944e12i		−	0.108701i	0.998522	−	0.0543503i	$-0.0173088\pi$
$234$	1.12199e12	+	9.08694e12i	0.104544	+	0.846701i
$235$			9.23330e11i			0.0840396i
$236$	7.99577e11	+	8.19598e11i	0.0710959	+	0.0728760i
$237$	−8.99976e12	+	1.55545e13i	−0.781835	+	1.35126i
$238$	−9.83854e12	−	4.14670e12i	−0.835136	−	0.351989i
$239$	−9.12985e12			−0.757313			−0.378656	−	0.925537i	$-0.623614\pi$
$239$	−9.12985e12			−0.757313			−0.378656	+	0.925537i	$0.623614\pi$
$240$	7.60916e11	+	4.65747e11i	0.0616843	+	0.0377562i
$241$	6.57145e12			0.520676			0.260338	−	0.965518i	$-0.416166\pi$
$241$	6.57145e12			0.520676			0.260338	+	0.965518i	$0.416166\pi$
$242$	1.04076e13	+	4.38653e12i	0.806055	+	0.339732i
$243$	1.14691e13	−	6.55050e12i	0.868350	−	0.495953i
$244$	1.15594e13	+	1.18488e13i	0.855640	+	0.877064i
$245$		−	2.04038e12i		−	0.147672i
$246$	4.94998e12	−	3.74260e12i	0.350316	−	0.264868i
$247$		−	5.70643e12i		−	0.394940i
$248$	−2.17312e12	+	8.53273e11i	−0.147096	+	0.0577569i
$249$	−1.36980e13	−	7.92561e12i	−0.906903	−	0.524730i
$250$	−8.65165e11	+	2.05271e12i	−0.0560311	+	0.132941i
$251$	1.36590e13			0.865390			0.432695	−	0.901540i	$-0.357563\pi$
$251$	1.36590e13			0.865390			0.432695	+	0.901540i	$0.357563\pi$
$252$	−2.70716e13	−	7.66833e12i	−1.67807	−	0.475333i
$253$	3.76123e12			0.228122
$254$	8.12870e11	−	1.92863e12i	0.0482431	−	0.114463i
$255$	5.60057e11	+	3.24047e11i	0.0325283	+	0.0188207i
$256$	−1.75707e13	−	8.69687e11i	−0.998777	−	0.0494360i
$257$		−	2.66227e13i		−	1.48122i	−0.671934	−	0.740611i	$-0.734536\pi$
$257$		−	2.66227e13i		−	1.48122i	0.671934	−	0.740611i	$-0.265464\pi$
$258$	1.79176e13	−	1.35472e13i	0.975826	−	0.737806i
$259$		−	1.31217e13i		−	0.699587i
$260$	−8.46115e11	+	8.25446e11i	−0.0441647	+	0.0430859i
$261$	2.21923e13	−	1.27576e13i	1.13417	−	0.651996i
$262$	−9.01172e12	−	3.79821e12i	−0.450973	−	0.190074i
$263$	−6.65684e12			−0.326221			−0.163110	−	0.986608i	$-0.552153\pi$
$263$	−6.65684e12			−0.326221			−0.163110	+	0.986608i	$0.552153\pi$
$264$	−4.27405e12	+	2.82073e13i	−0.205125	+	1.35375i
$265$	2.95810e10			0.00139047
$266$	1.61595e13	+	6.81082e12i	0.744010	+	0.313582i
$267$	1.22099e13	−	2.11027e13i	0.550682	−	0.951757i
$268$	3.98313e12	−	3.88584e12i	0.175988	−	0.171689i
$269$			3.68058e13i			1.59323i	0.604486	+	0.796615i	$0.293378\pi$
$269$			3.68058e13i			1.59323i	−0.604486	+	0.796615i	$0.706622\pi$
$270$	1.56946e12	+	6.66671e11i	0.0665656	+	0.0282755i
$271$			6.28990e11i			0.0261404i	0.999915	+	0.0130702i	$0.00416050\pi$
$271$			6.28990e11i			0.0261404i	−0.999915	+	0.0130702i	$0.995840\pi$
$272$	−1.27553e13	−	3.15478e11i	−0.519471	−	0.0128481i
$273$	1.86703e13	−	3.22684e13i	0.745173	−	1.28790i
$274$	−1.26961e13	+	3.01230e13i	−0.496640	+	1.17834i
$275$	−3.55239e13			−1.36204
$276$	1.09031e12	+	4.29683e12i	0.0409778	+	0.161491i
$277$	9.90495e12			0.364933			0.182467	−	0.983212i	$-0.441592\pi$
$277$	9.90495e12			0.364933			0.182467	+	0.983212i	$0.441592\pi$
$278$	8.13497e12	−	1.93012e13i	0.293839	−	0.697169i
$279$	−3.86862e12	+	2.22393e12i	−0.137004	+	0.0787586i
$280$	−1.32764e12	−	3.38123e12i	−0.0461010	−	0.117410i
$281$			1.54091e13i			0.524677i	0.964976	+	0.262338i	$0.0844937\pi$
$281$			1.54091e13i			0.524677i	−0.964976	+	0.262338i	$0.915506\pi$
$282$	−2.09881e13	−	2.77590e13i	−0.700814	−	0.926900i
$283$			4.11728e13i			1.34829i	0.738597	+	0.674147i	$0.235489\pi$
$283$			4.11728e13i			1.34829i	−0.738597	+	0.674147i	$0.764511\pi$
$284$	2.71410e13	+	2.78205e13i	0.871715	+	0.893542i
$285$	−9.19876e11	−	5.32236e11i	−0.0289790	−	0.0167671i
$286$	−3.48330e13	−	1.46812e13i	−1.07641	−	0.453680i
$287$	−2.52674e13			−0.765967
$288$	−3.34630e13	+	3.29406e12i	−0.995190	+	0.0979653i
$289$	2.50180e13			0.729985
$290$	3.04534e12	+	1.28353e12i	0.0871860	+	0.0367467i
$291$	3.48465e13	+	2.01620e13i	0.978922	+	0.566400i
$292$	2.69113e13	+	2.75852e13i	0.741873	+	0.760449i
$293$		−	1.37583e13i		−	0.372213i	−0.982530	−	0.186107i	$-0.940413\pi$
$293$		−	1.37583e13i		−	0.372213i	0.982530	−	0.186107i	$-0.0595870\pi$
$294$	4.63797e13	+	6.13420e13i	1.23145	+	1.62872i
$295$			2.82545e11i			0.00736321i
$296$	−5.73119e12	−	1.45962e13i	−0.146602	−	0.373367i
$297$	−1.52698e11	+	5.45290e13i	−0.00383420	+	1.36920i
$298$	−3.91642e12	+	9.29217e12i	−0.0965382	+	0.229049i
$299$	−5.87362e12			−0.142139
$300$	−1.02977e13	−	4.05826e13i	−0.244666	−	0.964212i
$301$	−9.14614e13			−2.13365
$302$	−1.15119e13	+	2.73133e13i	−0.263698	+	0.625655i
$303$	2.38876e13	−	4.12854e13i	0.537325	−	0.928672i
$304$	2.09502e13	+	5.18163e11i	0.462788	+	0.0114462i
$305$			4.08472e12i			0.0886163i
$306$	−2.42034e13	+	2.98846e12i	−0.515713	+	0.0636765i
$307$		−	5.30312e13i		−	1.10987i	−0.831895	−	0.554933i	$-0.812744\pi$
$307$		−	5.30312e13i		−	1.10987i	0.831895	−	0.554933i	$-0.187256\pi$
$308$	8.31489e13	−	8.11178e13i	1.70934	−	1.66758i
$309$	5.16925e12	−	8.93413e12i	0.104389	−	0.180418i
$310$	−5.30871e11	−	2.23749e11i	−0.0105317	−	0.00443886i
$311$	1.40535e13			0.273907			0.136954	−	0.990577i	$-0.456269\pi$
$311$	1.40535e13			0.273907			0.136954	+	0.990577i	$0.456269\pi$
$312$	6.67445e12	−	4.40491e13i	0.127810	−	0.843503i
$313$	−3.38361e13			−0.636630			−0.318315	−	0.947985i	$-0.603117\pi$
$313$	−3.38361e13			−0.636630			−0.318315	+	0.947985i	$0.603117\pi$
$314$	−5.15339e13	−	2.17202e13i	−0.952752	−	0.401561i
$315$	−3.46029e12	−	6.01931e12i	−0.0628643	−	0.109355i
$316$	6.25910e13	−	6.10620e13i	1.11746	−	1.09017i
$317$		−	4.49687e13i		−	0.789013i	−0.918893	−	0.394507i	$-0.870916\pi$
$317$		−	4.49687e13i		−	0.789013i	0.918893	−	0.394507i	$-0.129084\pi$
$318$	−8.89323e11	+	6.72402e11i	−0.0153359	+	0.0115952i
$319$			1.05682e14i			1.79123i
$320$	−2.95365e12	−	3.18131e12i	−0.0492078	−	0.0530007i
$321$	−5.69136e13	−	3.29300e13i	−0.932048	−	0.539279i
$322$	7.01037e12	−	1.66329e13i	0.112858	−	0.267770i
$323$	1.51993e13			0.240552
$324$	−6.23382e13	+	1.56324e13i	−0.969967	+	0.243237i
$325$	5.54749e13			0.848669
$326$	3.01448e13	−	7.15222e13i	0.453436	−	1.07583i
$327$	4.19989e13	+	2.43004e13i	0.621191	+	0.359418i
$328$	−2.81067e13	+	1.10361e13i	−0.408794	+	0.160512i
$329$			1.41697e14i			2.02667i
$330$	−5.61548e12	+	4.24577e12i	−0.0789878	+	0.0597214i
$331$		−	2.48156e13i		−	0.343298i	−0.985158	−	0.171649i	$-0.945090\pi$
$331$		−	2.48156e13i		−	0.343298i	0.985158	−	0.171649i	$-0.0549095\pi$
$332$	5.37740e13	+	5.51205e13i	0.731666	+	0.749987i
$333$	−1.49375e13	−	2.59844e13i	−0.199910	−	0.347752i
$334$	−1.37605e13	−	5.79970e12i	−0.181146	−	0.0763484i
$335$	1.37313e12			0.0177814
$336$	1.16772e14	+	7.14749e13i	1.48756	+	0.910516i
$337$	−8.33363e12			−0.104441			−0.0522204	−	0.998636i	$-0.516630\pi$
$337$	−8.33363e12			−0.104441			−0.0522204	+	0.998636i	$0.516630\pi$
$338$	−2.03409e13	−	8.57320e12i	−0.250801	−	0.105706i
$339$	−8.02669e13	+	1.38727e14i	−0.973729	+	1.68292i
$340$	−2.19861e12	−	2.25366e12i	−0.0262430	−	0.0269001i
$341$		−	1.84227e13i		−	0.216373i
$342$	3.97533e13	−	4.90844e12i	0.459441	−	0.0567284i
$343$		−	1.59772e14i		−	1.81711i
$344$	−1.01739e14	+	3.99477e13i	−1.13872	+	0.447117i
$345$	−5.47830e11	+	9.46827e11i	−0.00603449	+	0.0104296i
$346$	−2.09056e13	+	4.96010e13i	−0.226644	+	0.537740i
$347$	−6.31737e13			−0.674100			−0.337050	−	0.941487i	$-0.609429\pi$
$347$	−6.31737e13			−0.674100			−0.337050	+	0.941487i	$0.609429\pi$
$348$	−1.20731e14	+	3.06350e13i	−1.26804	+	0.321760i
$349$	1.44146e14			1.49027			0.745134	−	0.666915i	$-0.232386\pi$
$349$	1.44146e14			1.49027			0.745134	+	0.666915i	$0.232386\pi$
$350$	−6.62113e13	+	1.57094e14i	−0.673842	+	1.59877i
$351$	2.38457e11	−	8.51537e13i	0.00238903	−	0.853128i
$352$	5.70626e13	−	1.26550e14i	0.562816	−	1.24818i
$353$		−	1.33570e14i		−	1.29702i	−0.761205	−	0.648511i	$-0.775392\pi$
$353$		−	1.33570e14i		−	1.29702i	0.761205	−	0.648511i	$-0.224608\pi$
$354$	−6.42250e12	−	8.49443e12i	−0.0614025	−	0.0812113i
$355$			9.59076e12i			0.0902812i
$356$	−8.49168e13	+	8.28425e13i	−0.787079	+	0.767853i
$357$	8.59479e13	+	4.97291e13i	0.784441	+	0.453874i
$358$	6.21991e13	+	2.62154e13i	0.559020	+	0.235613i
$359$	7.04733e13			0.623742			0.311871	−	0.950124i	$-0.399044\pi$
$359$	7.04733e13			0.623742			0.311871	+	0.950124i	$0.399044\pi$
$360$	−6.47819e12	−	5.18436e12i	−0.0564664	−	0.0451889i
$361$	9.15259e13			0.785696
$362$	8.95461e13	+	3.77414e13i	0.757094	+	0.319096i
$363$	−9.09188e13	−	5.26052e13i	−0.757124	−	0.438069i
$364$	−1.29847e14	+	1.26675e14i	−1.06506	+	1.03904i
$365$			9.50962e12i			0.0768338i
$366$	−9.28493e13	−	1.22803e14i	−0.738980	−	0.977379i
$367$			6.12669e12i			0.0480356i	0.999712	+	0.0240178i	$0.00764583\pi$
$367$			6.12669e12i			0.0480356i	−0.999712	+	0.0240178i	$0.992354\pi$
$368$	5.33344e11	−	2.15640e13i	0.00411950	−	0.166558i
$369$	−5.00360e13	+	2.87639e13i	−0.380748	+	0.218878i
$370$	1.50286e12	−	3.56571e12i	0.0112670	−	0.0267323i
$371$	4.53959e12			0.0335320
$372$	2.10461e13	−	5.34038e12i	0.153174	−	0.0388674i
$373$	−1.06348e14			−0.762660			−0.381330	−	0.924439i	$-0.624534\pi$
$373$	−1.06348e14			−0.762660			−0.381330	+	0.924439i	$0.624534\pi$
$374$	3.91040e13	−	9.27790e13i	0.276330	−	0.655626i
$375$	1.03755e13	−	1.79321e13i	0.0722496	−	0.124871i
$376$	6.18891e13	+	1.57620e14i	0.424699	+	1.08163i
$377$		−	1.65035e14i		−	1.11609i
$378$	2.40854e14	+	1.02309e14i	1.60527	+	0.681883i
$379$			1.05026e14i			0.689889i	0.938623	+	0.344944i	$0.112102\pi$
$379$			1.05026e14i			0.689889i	−0.938623	+	0.344944i	$0.887898\pi$
$380$	3.61114e12	+	3.70156e12i	0.0233795	+	0.0239649i
$381$	−9.74830e12	+	1.68482e13i	−0.0622074	+	0.107514i
$382$	−2.17868e14	−	9.18261e13i	−1.37040	−	0.577587i
$383$	3.04841e14			1.89008			0.945041	−	0.326951i	$-0.106021\pi$
$383$	3.04841e14			1.89008			0.945041	+	0.326951i	$0.106021\pi$
$384$	1.61112e14	+	2.85039e13i	0.984708	+	0.174214i
$385$	2.86645e13			0.172707
$386$	−1.15617e13	−	4.87297e12i	−0.0686739	−	0.0289443i
$387$	−1.81117e14	+	1.04118e14i	−1.06060	+	0.609698i
$388$	−1.36796e14	−	1.40222e14i	−0.789769	−	0.809544i
$389$		−	6.90022e12i		−	0.0392771i	−0.999807	−	0.0196386i	$-0.993748\pi$
$389$		−	6.90022e12i		−	0.0392771i	0.999807	−	0.0196386i	$-0.00625155\pi$
$390$	8.76926e12	−	6.63029e12i	0.0492161	−	0.0372115i
$391$		−	1.56446e13i		−	0.0865749i
$392$	−1.36763e14	−	3.48309e14i	−0.746270	−	1.90060i
$393$	7.87250e13	+	4.55499e13i	0.423597	+	0.245092i
$394$	1.27695e14	−	3.02973e14i	0.677557	−	1.60759i
$395$	2.15774e13			0.112905
$396$	7.23136e13	−	2.55289e14i	0.373161	−	1.31737i
$397$	−2.38561e14			−1.21409			−0.607045	−	0.794667i	$-0.707645\pi$
$397$	−2.38561e14			−1.21409			−0.607045	+	0.794667i	$0.707645\pi$
$398$	−9.40634e12	+	2.23177e13i	−0.0472132	+	0.112019i
$399$	−1.41167e14	−	8.16785e13i	−0.698846	−	0.404349i
$400$	−5.03731e12	+	2.03667e14i	−0.0245962	+	0.994465i
$401$			1.43134e14i			0.689366i	0.938719	+	0.344683i	$0.112014\pi$
$401$			1.43134e14i			0.689366i	−0.938719	+	0.344683i	$0.887986\pi$
$402$	−4.12818e13	+	3.12125e13i	−0.196117	+	0.148281i
$403$			2.87693e13i			0.134819i
$404$	−1.66132e14	+	1.62073e14i	−0.767989	+	0.749229i
$405$	−1.37045e13	−	7.98069e12i	−0.0624973	−	0.0363947i
$406$	4.67346e14	+	1.96975e14i	2.10255	+	0.886171i
$407$	1.23740e14			0.549213
$408$	1.17326e14	+	1.77777e13i	0.513765	+	0.0778473i
$409$	−1.53844e14			−0.664664			−0.332332	−	0.943163i	$-0.607835\pi$
$409$	−1.53844e14			−0.664664			−0.332332	+	0.943163i	$0.607835\pi$
$410$	−6.86619e12	−	2.89393e12i	−0.0292688	−	0.0123361i
$411$	1.52257e14	−	2.63150e14i	0.640395	−	1.10681i
$412$	−3.59507e13	+	3.50726e13i	−0.149201	+	0.145557i
$413$			4.33602e13i			0.177569i
$414$	−5.05225e12	−	4.09180e13i	−0.0204166	−	0.165353i
$415$			1.90020e13i			0.0757767i
$416$	−8.91102e13	+	1.97624e14i	−0.350682	+	0.777724i
$417$	−9.75583e13	+	1.68612e14i	−0.378892	+	0.654848i
$418$	−6.42272e13	+	1.52387e14i	−0.246178	+	0.584087i
$419$	−3.85506e14			−1.45833			−0.729163	−	0.684340i	$-0.760090\pi$
$419$	−3.85506e14			−1.45833			−0.729163	+	0.684340i	$0.760090\pi$
$420$	8.30927e12	+	3.27463e13i	0.0310236	+	0.122262i
$421$	−3.12752e14			−1.15252			−0.576261	−	0.817266i	$-0.695489\pi$
$421$	−3.12752e14			−1.15252			−0.576261	+	0.817266i	$0.695489\pi$
$422$	1.87469e13	−	4.44793e13i	0.0681885	−	0.161785i
$423$	1.61305e14	+	2.80597e14i	0.579129	+	1.00742i
$424$	5.04971e12	−	1.98276e12i	0.0178959	−	0.00702682i
$425$			1.47760e14i			0.516912i
$426$	−2.18006e14	−	2.88336e14i	−0.752863	−	0.995741i
$427$			6.26853e14i			2.13704i
$428$	2.23425e14	+	2.29019e14i	0.751953	+	0.770781i
$429$	3.04296e14	+	1.76064e14i	1.01107	+	0.585000i
$430$	−2.48538e13	−	1.04753e13i	−0.0815299	−	0.0343628i
$431$	1.80047e14			0.583123			0.291562	−	0.956552i	$-0.405825\pi$
$431$	1.80047e14			0.583123			0.291562	+	0.956552i	$0.405825\pi$
$432$	3.12605e14	+	8.60769e12i	0.999621	+	0.0275249i
$433$	5.38712e14			1.70088			0.850438	−	0.526075i	$-0.176337\pi$
$433$	5.38712e14			1.70088			0.850438	+	0.526075i	$0.176337\pi$
$434$	−8.14690e13	−	3.43371e13i	−0.253980	−	0.107046i
$435$	−2.66036e13	−	1.53927e13i	−0.0818935	−	0.0473832i
$436$	−1.64874e14	−	1.69003e14i	−0.501161	−	0.513710i
$437$			2.56958e13i			0.0771282i
$438$	−2.16162e14	−	2.85897e14i	−0.640724	−	0.847426i
$439$		−	5.40243e14i		−	1.58137i	−0.612222	−	0.790686i	$-0.709724\pi$
$439$		−	5.40243e14i		−	1.58137i	0.612222	−	0.790686i	$-0.290276\pi$
$440$	3.18856e13	−	1.25198e13i	0.0921731	−	0.0361917i
$441$	−3.56453e14	−	6.20065e14i	−1.01763	−	1.77021i
$442$	−6.10657e13	+	1.44886e14i	−0.172177	+	0.408510i
$443$	−4.31343e14			−1.20116			−0.600582	−	0.799564i	$-0.705064\pi$
$443$	−4.31343e14			−1.20116			−0.600582	+	0.799564i	$0.705064\pi$
$444$	3.58698e13	+	1.41361e14i	0.0986558	+	0.388796i
$445$	−2.92739e13			−0.0795245
$446$	−3.44704e13	+	8.17852e13i	−0.0924921	+	0.219449i
$447$	4.69674e13	−	8.11749e13i	0.124482	−	0.215145i
$448$	−4.53276e14	−	4.88213e14i	−1.18668	−	1.27815i
$449$		−	2.09001e14i		−	0.540496i	−0.962791	−	0.270248i	$-0.912894\pi$
$449$		−	2.09001e14i		−	0.540496i	0.962791	−	0.270248i	$-0.0871057\pi$
$450$	4.77174e13	+	3.86461e14i	0.121901	+	0.987272i
$451$		−	2.38276e14i		−	0.601324i
$452$	5.58235e14	−	5.44599e14i	1.39173	−	1.35774i
$453$	1.38055e14	−	2.38604e14i	0.340027	−	0.587676i
$454$	4.14138e14	+	1.74549e14i	1.00772	+	0.424727i
$455$	−4.47631e13			−0.107611
$456$	−1.92705e14	−	2.91992e13i	−0.457705	−	0.0693529i
$457$	4.30977e14			1.01138			0.505691	−	0.862715i	$-0.331237\pi$
$457$	4.30977e14			1.01138			0.505691	+	0.862715i	$0.331237\pi$
$458$	−1.62475e14	−	6.84793e13i	−0.376728	−	0.158781i
$459$	2.26810e14	+	6.35140e11i	0.519628	+	0.00145512i
$460$	3.81001e12	−	3.71694e12i	0.00862498	−	0.00841430i
$461$			3.84344e14i			0.859736i	0.902892	+	0.429868i	$0.141440\pi$
$461$			3.84344e14i			0.859736i	−0.902892	+	0.429868i	$0.858560\pi$
$462$	−8.61767e14	+	6.51568e14i	−1.90484	+	1.44022i
$463$		−	3.84713e14i		−	0.840313i	−0.907452	−	0.420157i	$-0.861975\pi$
$463$		−	3.84713e14i		−	0.840313i	0.907452	−	0.420157i	$-0.138025\pi$
$464$	6.05896e14	+	1.49857e13i	1.30782	+	0.0323466i
$465$	4.63761e12	+	2.68330e12i	0.00989242	+	0.00572371i
$466$	2.00272e13	−	4.75169e13i	0.0422180	−	0.100167i
$467$	4.41899e14			0.920619			0.460310	−	0.887758i	$-0.347738\pi$
$467$	4.41899e14			0.920619			0.460310	+	0.887758i	$0.347738\pi$
$468$	−1.12926e14	+	3.98665e14i	−0.232511	+	0.820836i
$469$	2.10725e14			0.428810
$470$	−1.62288e13	+	3.85049e13i	−0.0326399	+	0.0774421i
$471$	4.50192e14	+	2.60479e14i	0.894917	+	0.517795i
$472$	1.89385e13	+	4.82327e13i	0.0372104	+	0.0947677i
$473$		−	8.62496e14i		−	1.67502i
$474$	−6.48702e14	+	4.90473e14i	−1.24527	+	0.941529i
$475$		−	2.42690e14i		−	0.460509i
$476$	−3.37404e14	−	3.45853e14i	−0.632867	−	0.648713i
$477$	8.98957e12	−	5.16778e12i	0.0166682	−	0.00958192i
$478$	−3.80735e14	−	1.60470e14i	−0.697861	−	0.294131i
$479$	−9.63435e14			−1.74573			−0.872865	−	0.487962i	$-0.837741\pi$
$479$	−9.63435e14			−1.74573			−0.872865	+	0.487962i	$0.837741\pi$
$480$	2.35457e13	+	3.27968e13i	0.0421778	+	0.0587496i
$481$	−1.93235e14			−0.342206
$482$	2.74044e14	+	1.15503e14i	0.479801	+	0.202224i
$483$	−8.40715e13	+	1.45303e14i	−0.145526	+	0.251515i
$484$	3.56918e14	+	3.65855e14i	0.610829	+	0.626123i
$485$		−	4.83395e13i		−	0.0817943i
$486$	5.93420e14	−	7.15846e13i	0.992803	−	0.119762i
$487$			2.68363e14i			0.443928i	0.975055	+	0.221964i	$0.0712468\pi$
$487$			2.68363e14i			0.443928i	−0.975055	+	0.221964i	$0.928753\pi$
$488$	2.73792e14	+	6.97294e14i	0.447828	+	1.14053i
$489$	−3.61510e14	+	6.24807e14i	−0.584685	+	1.01053i
$490$	3.58626e13	−	8.50884e13i	0.0573540	−	0.136079i
$491$	−3.19688e14			−0.505566			−0.252783	−	0.967523i	$-0.581346\pi$
$491$	−3.19688e14			−0.505566			−0.252783	+	0.967523i	$0.581346\pi$
$492$	2.72206e14	−	6.90715e13i	0.425687	−	0.108017i
$493$	4.39576e14			0.679792
$494$	1.00299e14	−	2.37970e14i	0.153390	−	0.363936i
$495$	5.67631e13	−	3.26311e13i	0.0858494	−	0.0493517i
$496$	−1.05621e14	−	2.61234e12i	−0.157980	−	0.00390734i
$497$			1.47183e15i			2.17719i
$498$	−4.31933e14	−	5.71277e14i	−0.631909	−	0.835767i
$499$			2.17704e14i			0.315002i	0.987519	+	0.157501i	$0.0503438\pi$
$499$			2.17704e14i			0.315002i	−0.987519	+	0.157501i	$0.949656\pi$
$500$	−7.21585e13	+	7.03959e13i	−0.103265	+	0.100742i
$501$	1.20209e14	+	6.95527e13i	0.170150	+	0.0984479i
$502$	5.69608e14	+	2.40075e14i	0.797454	+	0.336107i
$503$	−1.94437e13			−0.0269250			−0.0134625	−	0.999909i	$-0.504285\pi$
$503$	−1.94437e13			−0.0269250			−0.0134625	+	0.999909i	$0.504285\pi$
$504$	−9.94161e14	−	7.95607e14i	−1.36172	−	1.08976i
$505$	−5.72716e13			−0.0775956
$506$	1.56851e14	+	6.61089e13i	0.210213	+	0.0885997i
$507$	1.77695e14	+	1.02814e14i	0.235577	+	0.136304i
$508$	6.77969e13	−	6.61408e13i	0.0889117	−	0.0867399i
$509$		−	7.49490e14i		−	0.972340i	−0.873864	−	0.486170i	$-0.838394\pi$
$509$		−	7.49490e14i		−	0.972340i	0.873864	−	0.486170i	$-0.161606\pi$
$510$	1.76600e13	+	2.33572e13i	0.0226650	+	0.0299768i
$511$			1.45937e15i			1.85290i
$512$	−7.17449e14	−	3.45097e14i	−0.901169	−	0.433468i
$513$	−3.72528e14	−	1.04320e12i	−0.462928	−	0.00129635i
$514$	4.67932e14	−	1.11022e15i	0.575288	−	1.36494i
$515$	−1.23935e13			−0.0150749
$516$	9.85316e14	−	2.50021e14i	1.18577	−	0.300887i
$517$	−1.33622e15			−1.59104
$518$	2.30633e14	−	5.47204e14i	0.271711	−	0.644667i
$519$	2.50709e14	−	4.33307e14i	0.292247	−	0.505097i
$520$	−4.97932e13	+	1.95512e13i	−0.0574317	+	0.0225505i
$521$			9.08358e14i			1.03669i	0.855171	+	0.518346i	$0.173452\pi$
$521$			9.08358e14i			1.03669i	−0.855171	+	0.518346i	$0.826548\pi$
$522$	1.14970e15	−	1.41956e14i	1.29836	−	0.160312i
$523$		−	1.33745e15i		−	1.49458i	−0.664497	−	0.747291i	$-0.731354\pi$
$523$		−	1.33745e15i		−	1.49458i	0.664497	−	0.747291i	$-0.268646\pi$
$524$	−3.09049e14	−	3.16787e14i	−0.341748	−	0.350305i
$525$	7.94036e14	−	1.37235e15i	0.868888	−	1.50172i
$526$	−2.77605e14	−	1.17003e14i	−0.300611	−	0.126700i
$527$	−7.66280e13			−0.0821163
$528$	−6.74020e14	+	1.10118e15i	−0.714803	+	1.16781i
$529$	−9.26361e14			−0.972241
$530$	1.23359e12	+	5.19928e11i	0.00128131	+	0.000540040i
$531$	4.93604e13	+	8.58645e13i	0.0507410	+	0.0882660i
$532$	5.54176e14	+	5.68052e14i	0.563811	+	0.577928i
$533$			3.72096e14i			0.374676i
$534$	8.80090e14	−	6.65421e14i	0.877102	−	0.663162i
$535$			7.89512e13i			0.0778777i
$536$	2.34404e14	−	9.20386e13i	0.228854	−	0.0898594i
$537$	−5.43361e14	−	3.14386e14i	−0.525086	−	0.303812i
$538$	−6.46914e14	+	1.53488e15i	−0.618791	+	1.46816i
$539$	2.95280e15			2.79573
$540$	5.37323e13	+	5.53871e13i	0.0503581	+	0.0519090i
$541$	−1.55267e15			−1.44043			−0.720217	−	0.693749i	$-0.755958\pi$
$541$	−1.55267e15			−1.44043			−0.720217	+	0.693749i	$0.755958\pi$
$542$	−1.10554e13	+	2.62302e13i	−0.0101526	+	0.0240883i
$543$	−7.82261e14	−	4.52613e14i	−0.711136	−	0.411460i
$544$	−5.26378e14	−	2.37348e14i	−0.473700	−	0.213595i
$545$		−	5.82614e13i		−	0.0519039i
$546$	1.34575e15	−	1.01750e15i	1.18688	−	0.897379i
$547$			2.34140e14i			0.204431i	0.994762	+	0.102215i	$0.0325931\pi$
$547$			2.34140e14i			0.204431i	−0.994762	+	0.102215i	$0.967407\pi$
$548$	−1.05891e15	+	1.03304e15i	−0.915304	+	0.892946i
$549$	7.13597e14	+	1.24133e15i	0.610668	+	1.06228i
$550$	−1.48142e15	−	6.24383e14i	−1.25512	−	0.529001i
$551$	−7.21990e14			−0.605616
$552$	−3.00547e13	+	1.98351e14i	−0.0249602	+	0.164729i
$553$	3.31133e15			2.72279
$554$	4.13058e14	+	1.74094e14i	0.336285	+	0.141736i
$555$	−1.80229e13	+	3.11495e13i	−0.0145283	+	0.0251096i
$556$	6.78492e14	−	6.61918e14i	0.541543	−	0.528315i
$557$		−	2.18048e15i		−	1.72325i	−0.507544	−	0.861626i	$-0.669447\pi$
$557$		−	2.18048e15i		−	1.72325i	0.507544	−	0.861626i	$-0.330553\pi$
$558$	−2.00419e14	+	2.47462e13i	−0.156837	+	0.0193651i
$559$			1.34689e15i			1.04368i
$560$	4.06463e12	−	1.64340e14i	0.00311880	−	0.126098i
$561$	−4.68953e14	+	8.10503e14i	−0.356315	+	0.615827i
$562$	−2.70836e14	+	6.42592e14i	−0.203778	+	0.483488i
$563$	−1.37826e15			−1.02691			−0.513457	−	0.858116i	$-0.671635\pi$
$563$	−1.37826e15			−1.02691			−0.513457	+	0.858116i	$0.671635\pi$
$564$	−3.87345e14	−	1.52650e15i	−0.285801	−	1.12632i
$565$	1.92444e14			0.140617
$566$	−7.23670e14	+	1.71699e15i	−0.523661	+	1.24245i
$567$	−2.10314e15	−	1.22474e15i	−1.50716	−	0.877681i
$568$	6.42851e14	+	1.63722e15i	0.456241	+	1.16196i
$569$		−	2.17790e15i		−	1.53081i	−0.643551	−	0.765404i	$-0.722539\pi$
$569$		−	2.17790e15i		−	1.53081i	0.643551	−	0.765404i	$-0.277461\pi$
$570$	−2.90060e13	−	3.83635e13i	−0.0201919	−	0.0267059i
$571$		−	1.03214e15i		−	0.711608i	−0.934561	−	0.355804i	$-0.884207\pi$
$571$		−	1.03214e15i		−	0.711608i	0.934561	−	0.355804i	$-0.115793\pi$
$572$	−1.19457e15	−	1.22448e15i	−0.815705	−	0.836129i
$573$	1.90326e15	+	1.10122e15i	1.28721	+	0.744773i
$574$	−1.05370e15	−	4.44110e14i	−0.705835	−	0.297492i
$575$	−2.49801e14			−0.165737
$576$	−1.45338e15	−	4.50790e14i	−0.955112	−	0.296245i
$577$	6.71388e14			0.437025			0.218513	−	0.975834i	$-0.429880\pi$
$577$	6.71388e14			0.437025			0.218513	+	0.975834i	$0.429880\pi$
$578$	1.04330e15	+	4.39726e14i	0.672678	+	0.283517i
$579$	1.01001e14	+	5.84388e13i	0.0645052	+	0.0373224i
$580$	1.04437e14	+	1.07052e14i	0.0660696	+	0.0677239i
$581$			2.91611e15i			1.82740i
$582$	1.09880e15	+	1.45328e15i	0.682090	+	0.902137i
$583$			4.28091e13i			0.0263244i
$584$	6.37412e14	+	1.62337e15i	0.388284	+	0.988885i
$585$	−8.86425e13	+	5.09574e13i	−0.0534915	+	0.0307503i
$586$	2.41821e14	−	5.73750e14i	0.144563	−	0.342993i
$587$	1.59850e15			0.946680			0.473340	−	0.880880i	$-0.343048\pi$
$587$	1.59850e15			0.946680			0.473340	+	0.880880i	$0.343048\pi$
$588$	8.55960e14	+	3.37328e15i	0.502201	+	1.97914i
$589$	1.25859e14			0.0731561
$590$	−4.96613e12	+	1.17827e13i	−0.00285978	+	0.00678517i
$591$	−1.53138e15	+	2.64672e15i	−0.873679	+	1.51000i
$592$	1.75464e13	−	7.09428e14i	0.00991786	−	0.400995i
$593$		−	2.53418e15i		−	1.41918i	−0.704617	−	0.709588i	$-0.748881\pi$
$593$		−	2.53418e15i		−	1.41918i	0.704617	−	0.709588i	$-0.251119\pi$
$594$	−9.64792e14	+	2.27129e15i	−0.535313	+	1.26022i
$595$		−	1.19228e14i		−	0.0655443i
$596$	−3.26646e14	+	3.18667e14i	−0.177919	+	0.173573i
$597$	1.12805e14	−	1.94964e14i	0.0608794	−	0.105219i
$598$	−2.44942e14	−	1.03237e14i	−0.130981	−	0.0552051i
$599$	2.55437e15			1.35343			0.676717	−	0.736244i	$-0.263402\pi$
$599$	2.55437e15			1.35343			0.676717	+	0.736244i	$0.263402\pi$
$600$	2.83860e14	−	1.87338e15i	0.149029	−	0.983543i
$601$	1.88826e14			0.0982320			0.0491160	−	0.998793i	$-0.484360\pi$
$601$	1.88826e14			0.0982320			0.0491160	+	0.998793i	$0.484360\pi$
$602$	−3.81414e15	−	1.60756e15i	−1.96615	−	0.828681i
$603$	4.17290e14	−	2.39885e14i	0.213154	−	0.122534i
$604$	−9.60138e14	+	9.36684e14i	−0.485994	+	0.474122i
$605$			1.26124e14i			0.0632619i
$606$	1.72181e15	−	1.30183e15i	0.855828	−	0.647077i
$607$		−	2.94257e15i		−	1.44940i	−0.689064	−	0.724701i	$-0.741978\pi$
$607$		−	2.94257e15i		−	1.44940i	0.689064	−	0.724701i	$-0.258022\pi$
$608$	8.64559e14	+	3.89837e14i	0.422012	+	0.190289i
$609$	−4.08266e15	−	2.36221e15i	−1.97491	−	1.14268i
$610$	−7.17948e13	+	1.70342e14i	−0.0344175	+	0.0816596i
$611$	2.08668e15			0.991353
$612$	−1.06186e15	−	3.00784e14i	−0.499959	−	0.141619i
$613$	−9.74927e14			−0.454925			−0.227462	−	0.973787i	$-0.573043\pi$
$613$	−9.74927e14			−0.454925			−0.227462	+	0.973787i	$0.573043\pi$
$614$	9.32099e14	−	2.21152e15i	0.431058	−	1.02274i
$615$	5.99819e13	+	3.47053e13i	0.0274921	+	0.0159068i
$616$	4.89325e15	−	1.92133e15i	2.22281	−	0.872785i
$617$			2.46447e15i			1.10957i	0.831993	+	0.554786i	$0.187200\pi$
$617$			2.46447e15i			1.10957i	−0.831993	+	0.554786i	$0.812800\pi$
$618$	3.72599e14	−	2.81716e14i	0.166266	−	0.125711i
$619$		−	2.24621e15i		−	0.993465i	−0.867904	−	0.496732i	$-0.834533\pi$
$619$		−	2.24621e15i		−	0.993465i	0.867904	−	0.496732i	$-0.165467\pi$
$620$	−1.82058e13	−	1.86616e13i	−0.00798095	−	0.00818079i
$621$	−1.07376e12	+	3.83443e14i	−0.000466556	+	0.166608i
$622$	5.86063e14	+	2.47011e14i	0.252405	+	0.106382i
$623$	−4.49246e15			−1.91778
$624$	1.05256e15	−	1.71963e15i	0.445383	−	0.727645i
$625$	2.34684e15			0.984336
$626$	−1.41104e15	−	5.94718e14i	−0.586652	−	0.247259i
$627$	7.70241e14	−	1.33123e15i	0.317435	−	0.548631i
$628$	−1.76731e15	−	1.81156e15i	−0.721996	−	0.740074i
$629$		−	5.14688e14i		−	0.208433i
$630$	−3.85034e13	−	3.11838e14i	−0.0154570	−	0.125186i
$631$			4.03426e15i			1.60547i	0.596335	+	0.802735i	$0.296623\pi$
$631$			4.03426e15i			1.60547i	−0.596335	+	0.802735i	$0.703377\pi$
$632$	3.68343e15	−	1.44629e15i	1.45314	−	0.570575i
$633$	−2.24821e14	+	3.88564e14i	−0.0879260	+	0.151965i
$634$	7.90388e14	−	1.87529e15i	0.306443	−	0.727073i
$635$	2.33721e13			0.00898342
$636$	−4.89051e13	+	1.24095e13i	−0.0186355	+	0.00472869i
$637$	−4.61116e15			−1.74198
$638$	−1.85750e15	+	4.40715e15i	−0.695690	+	1.65061i
$639$	1.67550e15	+	2.91460e15i	0.622141	+	1.08224i
$640$	−6.72575e13	−	1.84582e14i	−0.0247600	−	0.0679517i
$641$			1.25335e15i			0.457461i	0.973490	+	0.228731i	$0.0734575\pi$
$641$			1.25335e15i			0.457461i	−0.973490	+	0.228731i	$0.926543\pi$
$642$	−1.79463e15	−	2.37359e15i	−0.649430	−	0.858939i
$643$			3.13336e15i			1.12422i	0.827064	+	0.562108i	$0.190009\pi$
$643$			3.13336e15i			1.12422i	−0.827064	+	0.562108i	$0.809991\pi$
$644$	5.84695e14	−	5.70412e14i	0.207997	−	0.202916i
$645$	2.17119e14	+	1.25624e14i	0.0765807	+	0.0443093i
$646$	6.33843e14	+	2.67149e14i	0.221668	+	0.0934274i
$647$	2.26843e15			0.786598			0.393299	−	0.919411i	$-0.371334\pi$
$647$	2.26843e15			0.786598			0.393299	+	0.919411i	$0.371334\pi$
$648$	−2.87440e15	−	4.43776e14i	−0.988291	−	0.152581i
$649$	−4.08894e14			−0.139401
$650$	2.31342e15	+	9.75050e14i	0.782045	+	0.329612i
$651$	7.11700e14	+	4.11787e14i	0.238562	+	0.138031i
$652$	2.51421e15	−	2.45279e15i	0.835679	−	0.815266i
$653$			2.05557e15i			0.677500i	0.940876	+	0.338750i	$0.110004\pi$
$653$			2.05557e15i			0.677500i	−0.940876	+	0.338750i	$0.889996\pi$
$654$	1.32433e15	+	1.75157e15i	0.432832	+	0.572466i
$655$		−	1.09208e14i		−	0.0353939i
$656$	−1.36609e15	−	3.37876e13i	−0.439043	−	0.0108589i
$657$	1.66132e15	+	2.88994e15i	0.529473	+	0.921041i
$658$	−2.49052e15	+	5.90906e15i	−0.787133	+	1.86757i
$659$	−4.06559e15			−1.27425			−0.637123	−	0.770762i	$-0.719876\pi$
$659$	−4.06559e15			−1.27425			−0.637123	+	0.770762i	$0.719876\pi$
$660$	−3.08803e14	+	7.83578e13i	−0.0959820	+	0.0243551i
$661$	−1.73015e15			−0.533306			−0.266653	−	0.963793i	$-0.585918\pi$
$661$	−1.73015e15			−0.533306			−0.266653	+	0.963793i	$0.585918\pi$
$662$	4.36170e14	−	1.03487e15i	0.133333	−	0.316348i
$663$	7.32328e14	−	1.26570e15i	0.222014	−	0.383713i
$664$	1.27367e15	+	3.24380e15i	0.382942	+	0.975280i
$665$			1.95828e14i			0.0583924i
$666$	−1.66213e14	−	1.34615e15i	−0.0491538	−	0.398095i
$667$			7.43143e14i			0.217962i
$668$	−4.71904e14	−	4.83720e14i	−0.137272	−	0.140710i
$669$	4.13385e14	−	7.14463e14i	0.119264	−	0.206127i
$670$	5.72626e13	+	2.41347e13i	0.0163855	+	0.00690607i
$671$	−5.91133e15			−1.67769
$672$	3.61338e15	+	5.03310e15i	1.01715	+	1.41679i
$673$	5.48741e15			1.53209			0.766045	−	0.642787i	$-0.222222\pi$
$673$	5.48741e15			1.53209			0.766045	+	0.642787i	$0.222222\pi$
$674$	−3.47530e14	−	1.46475e14i	−0.0962417	−	0.0405635i
$675$	1.01414e13	−	3.62153e15i	0.00278566	−	0.994766i
$676$	−6.97575e14	−	7.15042e14i	−0.190057	−	0.194816i
$677$		−	2.81283e15i		−	0.760161i	−0.924953	−	0.380080i	$-0.875896\pi$
$677$		−	2.81283e15i		−	0.760161i	0.924953	−	0.380080i	$-0.124104\pi$
$678$	−5.78563e15	+	4.37442e15i	−1.55091	+	1.17262i
$679$		−	7.41832e15i		−	1.97252i
$680$	−5.20754e13	−	1.32626e14i	−0.0137352	−	0.0349808i
$681$	−3.61784e15	−	2.09327e15i	−0.946544	−	0.547666i
$682$	3.23805e14	−	7.68266e14i	0.0840367	−	0.199387i
$683$	5.83869e15			1.50315			0.751574	−	0.659649i	$-0.229295\pi$
$683$	5.83869e15			1.50315			0.751574	+	0.659649i	$0.229295\pi$
$684$	1.74407e15	+	4.94028e14i	0.445406	+	0.126166i
$685$	−3.65045e14			−0.0924800
$686$	2.80821e15	−	6.66282e15i	0.705744	−	1.67446i
$687$	1.41936e15	+	8.21235e14i	0.353859	+	0.204741i
$688$	−4.94488e15	−	1.22302e14i	−1.22298	−	0.0302481i
$689$		−	6.68515e13i		−	0.0164023i
$690$	−3.94875e13	+	2.98558e13i	−0.00961147	+	0.00726707i
$691$			4.36803e15i			1.05477i	0.849627	+	0.527383i	$0.176827\pi$
$691$			4.36803e15i			1.05477i	−0.849627	+	0.527383i	$0.823173\pi$
$692$	−1.74362e15	+	1.70102e15i	−0.417703	+	0.407499i
$693$	8.71102e15	−	5.00765e15i	2.07031	−	1.19015i
$694$	−2.63448e15	−	1.11037e15i	−0.621181	−	0.261812i
$695$	2.33901e14			0.0547162
$696$	−5.57319e15	−	8.44467e14i	−1.29346	−	0.195989i
$697$	−9.91092e14			−0.228210
$698$	6.01122e15	+	2.53358e15i	1.37328	+	0.578801i
$699$	−2.40175e14	+	4.15100e14i	−0.0544382	+	0.0940868i
$700$	−5.52231e15	+	5.38741e15i	−1.24188	+	1.21155i
$701$			8.98486e14i			0.200476i	0.994963	+	0.100238i	$0.0319604\pi$
$701$			8.98486e14i			0.200476i	−0.994963	+	0.100238i	$0.968040\pi$
$702$	1.50664e15	−	3.54690e15i	0.333546	−	0.785226i
$703$			8.45359e14i			0.185689i
$704$	4.60393e15	−	4.27446e15i	1.00341	−	0.931605i
$705$	1.94624e14	−	3.36372e14i	0.0420877	−	0.0727411i
$706$	2.34768e15	−	5.57015e15i	0.503747	−	1.19520i
$707$	−8.78907e15			−1.87127
$708$	−1.18530e14	−	4.67121e14i	−0.0250407	−	0.0986838i
$709$	−8.60538e14			−0.180391			−0.0901957	−	0.995924i	$-0.528749\pi$
$709$	−8.60538e14			−0.180391			−0.0901957	+	0.995924i	$0.528749\pi$
$710$	−1.68571e14	+	3.99955e14i	−0.0350641	+	0.0831938i
$711$	6.55729e15	−	3.76955e15i	1.35345	−	0.778048i
$712$	−4.99729e15	+	1.96218e15i	−1.02351	+	0.401882i
$713$		−	1.29547e14i		−	0.0263289i
$714$	2.71015e15	+	3.58447e15i	0.546580	+	0.722910i
$715$		−	4.22123e14i		−	0.0844803i
$716$	2.13306e15	+	2.18647e15i	0.423626	+	0.434233i
$717$	3.32604e15	+	1.92443e15i	0.655499	+	0.379269i
$718$	2.93889e15	+	1.23867e15i	0.574776	+	0.242254i
$719$	4.00739e15			0.777773			0.388887	−	0.921286i	$-0.372860\pi$
$719$	4.00739e15			0.777773			0.388887	+	0.921286i	$0.372860\pi$
$720$	−1.79032e14	−	3.30063e14i	−0.0344828	−	0.0635722i
$721$	−1.90195e15			−0.363542
$722$	3.81683e15	+	1.60870e15i	0.724016	+	0.305154i
$723$	−2.39400e15	−	1.38516e15i	−0.450676	−	0.260759i
$724$	3.07091e15	+	3.14780e15i	0.573726	+	0.588092i
$725$		−	7.01881e15i		−	1.30138i
$726$	−2.86690e15	−	3.79178e15i	−0.527547	−	0.697736i
$727$			4.93911e15i			0.902006i	0.892522	+	0.451003i	$0.148934\pi$
$727$			4.93911e15i			0.902006i	−0.892522	+	0.451003i	$0.851066\pi$
$728$	−7.64140e15	+	3.00039e15i	−1.38500	+	0.543819i
$729$	−5.55897e15	−	3.11340e13i	−0.999984	−	0.00560059i
$730$	−1.67145e14	+	3.96572e14i	−0.0298413	+	0.0708020i
$731$	−3.58750e15			−0.635691
$732$	−1.71358e15	−	6.75311e15i	−0.301365	−	1.18766i
$733$	7.04019e15			1.22889			0.614444	−	0.788960i	$-0.289380\pi$
$733$	7.04019e15			1.22889			0.614444	+	0.788960i	$0.289380\pi$
$734$	−1.07685e14	+	2.55496e14i	−0.0186564	+	0.0442646i
$735$	−4.30081e14	+	7.43319e14i	−0.0739554	+	0.127819i
$736$	4.01259e14	−	8.89889e14i	0.0684851	−	0.151883i
$737$			1.98717e15i			0.336638i
$738$	−2.59218e15	+	3.20063e14i	−0.435867	+	0.0538177i
$739$		−	8.57116e14i		−	0.143052i	−0.997439	−	0.0715262i	$-0.977213\pi$
$739$		−	8.57116e14i		−	0.143052i	0.997439	−	0.0715262i	$-0.0227870\pi$
$740$	1.25345e14	−	1.22283e14i	0.0207650	−	0.0202578i
$741$	−1.20283e15	+	2.07887e15i	−0.197789	+	0.341844i
$742$	1.89311e14	+	7.97897e13i	0.0308996	+	0.0130234i
$743$	1.31097e15			0.212401			0.106200	−	0.994345i	$-0.466132\pi$
$743$	1.31097e15			0.212401			0.106200	+	0.994345i	$0.466132\pi$
$744$	9.71532e14	+	1.47210e14i	0.156245	+	0.0236747i
$745$	−1.12607e14			−0.0179765
$746$	−4.43494e15	−	1.86922e15i	−0.702788	−	0.296208i
$747$	3.31964e15	+	5.77465e15i	0.522189	+	0.908369i
$748$	3.26145e15	−	3.18178e15i	0.509274	−	0.496834i
$749$			1.21161e16i			1.87807i
$750$	7.47862e14	−	5.65446e14i	0.115076	−	0.0870069i
$751$		−	4.90022e15i		−	0.748507i	−0.927326	−	0.374254i	$-0.877899\pi$
$751$		−	4.90022e15i		−	0.748507i	0.927326	−	0.374254i	$-0.122101\pi$
$752$	−1.89477e14	+	7.66087e15i	−0.0287315	+	1.16166i
$753$	−4.97601e15	−	2.87909e15i	−0.749046	−	0.433395i
$754$	2.90072e15	−	6.88230e15i	0.433474	−	1.02847i
$755$	−3.30995e14			−0.0491035
$756$	8.24590e15	+	8.49986e15i	1.21442	+	1.25182i
$757$	−9.55984e15			−1.39773			−0.698865	−	0.715254i	$-0.746311\pi$
$757$	−9.55984e15			−1.39773			−0.698865	+	0.715254i	$0.746311\pi$
$758$	−1.84597e15	+	4.37979e15i	−0.267944	+	0.635730i
$759$	−1.37023e15	−	7.92808e14i	−0.197453	−	0.114245i
$760$	8.55322e13	+	2.17834e14i	0.0122364	+	0.0311638i
$761$			5.54500e15i			0.787565i	0.919204	+	0.393782i	$0.128834\pi$
$761$			5.54500e15i			0.787565i	−0.919204	+	0.393782i	$0.871166\pi$
$762$	−7.02657e14	+	5.31267e14i	−0.0990811	+	0.0749136i
$763$		−	8.94096e15i		−	1.25170i
$764$	−7.47161e15	−	7.65869e15i	−1.03849	−	1.06449i
$765$	−1.35727e14	−	2.36103e14i	−0.0187296	−	0.0325809i
$766$	1.27125e16	+	5.35802e15i	1.74170	+	0.734084i
$767$	6.38537e14			0.0868584
$768$	6.21774e15	+	4.02045e15i	0.839742	+	0.542986i
$769$	8.41846e15			1.12885			0.564427	−	0.825483i	$-0.309097\pi$
$769$	8.41846e15			1.12885			0.564427	+	0.825483i	$0.309097\pi$
$770$	1.19537e15	+	5.03818e14i	0.159149	+	0.0670772i
$771$	−5.61165e15	+	9.69874e15i	−0.741808	+	1.28208i
$772$	−3.96499e14	−	4.06426e14i	−0.0520411	−	0.0533442i
$773$		−	4.73191e15i		−	0.616665i	−0.951279	−	0.308332i	$-0.900229\pi$
$773$		−	4.73191e15i		−	0.616665i	0.951279	−	0.308332i	$-0.0997709\pi$
$774$	−9.38300e15	+	1.15854e15i	−1.21413	+	0.149912i
$775$			1.22354e15i			0.157202i
$776$	−3.24011e15	−	8.25194e15i	−0.413352	−	1.05273i
$777$	−2.76585e15	+	4.78029e15i	−0.350359	+	0.605534i
$778$	1.21281e14	−	2.87754e14i	0.0152548	−	0.0361937i
$779$	1.62784e15			0.203308
$780$	4.82234e14	−	1.22365e14i	0.0598049	−	0.0151753i
$781$	−1.38795e16			−1.70921
$782$	2.74976e14	−	6.52413e14i	0.0336246	−	0.0797784i
$783$	−1.07738e16	−	3.01701e13i	−1.30822	−	0.00366343i
$784$	4.18708e14	−	1.69291e16i	0.0504863	−	2.04124i
$785$		−	6.24512e14i		−	0.0747752i
$786$	2.48240e15	+	3.28323e15i	0.295153	+	0.390371i
$787$			1.61054e16i			1.90156i	0.309860	+	0.950782i	$0.399718\pi$
$787$			1.61054e16i			1.90156i	−0.309860	+	0.950782i	$0.600282\pi$
$788$	1.06503e16	−	1.03902e16i	1.24873	−	1.21823i
$789$	2.42511e15	+	1.40316e15i	0.282363	+	0.163374i
$790$	8.99824e14	+	3.79253e14i	0.104042	+	0.0438511i
$791$	2.95330e16			3.39107
$792$	7.50270e15	−	9.37510e15i	0.855518	−	1.06902i
$793$	9.23126e15			1.04534
$794$	−9.94849e15	−	4.19304e15i	−1.11878	−	0.471538i
$795$	−1.07765e13	−	6.23522e12i	−0.00120353	−	0.000696358i
$796$	−7.84529e14	+	7.65366e14i	−0.0870137	+	0.0848881i
$797$		−	6.80430e15i		−	0.749485i	−0.927129	−	0.374742i	$-0.877731\pi$
$797$		−	6.80430e15i		−	0.749485i	0.927129	−	0.374742i	$-0.122269\pi$
$798$	−4.45135e15	−	5.88737e15i	−0.486940	−	0.644029i
$799$			5.55794e15i			0.603819i
$800$	−3.78979e15	+	8.40479e15i	−0.408903	+	0.906843i
$801$	−8.89623e15	+	5.11412e15i	−0.953295	+	0.548015i
$802$	−2.51579e15	+	5.96901e15i	−0.267741	+	0.635248i
$803$	−1.37621e16			−1.45462
$804$	−2.27014e15	+	5.76041e14i	−0.238311	+	0.0604708i
$805$	2.01566e14			0.0210155
$806$	−5.05661e14	+	1.19974e15i	−0.0523620	+	0.124235i
$807$	7.75809e15	−	1.34085e16i	0.797903	−	1.37903i
$808$	−9.77672e15	+	3.83881e15i	−0.998690	+	0.392134i
$809$		−	1.45048e16i		−	1.47162i	−0.677190	−	0.735808i	$-0.736802\pi$
$809$		−	1.45048e16i		−	1.47162i	0.677190	−	0.735808i	$-0.263198\pi$
$810$	−4.31237e14	−	5.73688e14i	−0.0434558	−	0.0578107i
$811$		−	1.48621e16i		−	1.48753i	−0.668443	−	0.743763i	$-0.733039\pi$
$811$		−	1.48621e16i		−	1.48753i	0.668443	−	0.743763i	$-0.266961\pi$
$812$	1.60272e16	+	1.64285e16i	1.59331	+	1.63321i
$813$	1.32581e14	−	2.29143e14i	0.0130913	−	0.0226261i
$814$	5.16022e15	+	2.17490e15i	0.506097	+	0.213307i
$815$	8.66740e14			0.0844349
$816$	4.58029e15	+	2.80354e15i	0.443198	+	0.271276i
$817$	5.89235e15			0.566327
$818$	−6.41562e15	−	2.70402e15i	−0.612485	−	0.258147i
$819$	−1.36033e16	+	7.82006e15i	−1.28998	+	0.741564i
$820$	−2.35470e14	−	2.41366e14i	−0.0221799	−	0.0227353i
$821$		−	4.24824e14i		−	0.0397486i	−0.999802	−	0.0198743i	$-0.993673\pi$
$821$		−	4.24824e14i		−	0.0397486i	0.999802	−	0.0198743i	$-0.00632660\pi$
$822$	1.09747e16	−	8.29777e15i	1.01999	−	0.771199i
$823$		−	2.02219e16i		−	1.86691i	−0.358691	−	0.933456i	$-0.616777\pi$
$823$		−	2.02219e16i		−	1.86691i	0.358691	−	0.933456i	$-0.383223\pi$
$824$	−2.11567e15	+	8.30716e14i	−0.194021	+	0.0761821i
$825$	1.29415e16	+	7.48789e15i	1.17893	+	0.682123i
$826$	−7.62117e14	+	1.80821e15i	−0.0689654	+	0.163629i
$827$	7.68912e15			0.691188			0.345594	−	0.938384i	$-0.387677\pi$
$827$	7.68912e15			0.691188			0.345594	+	0.938384i	$0.387677\pi$
$828$	5.08502e14	−	1.79517e15i	0.0454073	−	0.160302i
$829$	4.70297e15			0.417178			0.208589	−	0.978003i	$-0.433113\pi$
$829$	4.70297e15			0.417178			0.208589	+	0.978003i	$0.433113\pi$
$830$	−3.33988e14	+	7.92426e14i	−0.0294307	+	0.0698280i
$831$	−3.60841e15	−	2.08781e15i	−0.315871	−	0.182762i
$832$	−7.18960e15	+	6.67509e15i	−0.625211	+	0.580469i
$833$		−	1.22820e16i		−	1.06101i
$834$	−7.03199e15	+	5.31677e15i	−0.603483	+	0.456283i
$835$		−	1.66756e14i		−	0.0142169i
$836$	−5.35682e15	+	5.22597e15i	−0.453704	+	0.442621i
$837$	1.87812e15	+	5.25934e12i	0.158028	+	0.000442528i
$838$	−1.60764e16	−	6.77582e15i	−1.34384	−	0.566395i
$839$	−6.91869e15			−0.574557			−0.287279	−	0.957847i	$-0.592751\pi$
$839$	−6.91869e15			−0.574557			−0.287279	+	0.957847i	$0.592751\pi$
$840$	−2.29048e14	+	1.51164e15i	−0.0188969	+	0.124713i
$841$	−8.68004e15			−0.711449
$842$	−1.30424e16	−	5.49706e15i	−1.06204	−	0.447625i
$843$	3.24799e15	−	5.61358e15i	0.262762	−	0.454138i
$844$	1.56357e15	−	1.52538e15i	0.125671	−	0.122601i
$845$		−	2.46501e14i		−	0.0196837i
$846$	1.79488e15	+	1.45366e16i	0.142396	+	1.15326i
$847$			1.93553e16i			1.52560i
$848$	2.45434e14	+	6.07034e12i	0.0192202	+	0.000475375i
$849$	8.67858e15	−	1.49994e16i	0.675237	−	1.16703i
$850$	−2.59708e15	+	6.16189e15i	−0.200762	+	0.476332i
$851$	8.70127e14			0.0668298
$852$	−4.02341e15	−	1.58560e16i	−0.307027	−	1.20997i
$853$	1.49731e16			1.13525			0.567626	−	0.823287i	$-0.307862\pi$
$853$	1.49731e16			1.13525			0.567626	+	0.823287i	$0.307862\pi$
$854$	−1.10178e16	+	2.61411e16i	−0.830000	+	1.96927i
$855$	2.22927e14	+	3.87791e14i	0.0166859	+	0.0290258i
$856$	5.29196e15	+	1.34776e16i	0.393560	+	1.00232i
$857$			2.16185e16i			1.59747i	0.601686	+	0.798733i	$0.294496\pi$
$857$			2.16185e16i			1.59747i	−0.601686	+	0.798733i	$0.705504\pi$
$858$	9.59521e15	+	1.26907e16i	0.704490	+	0.931762i
$859$			1.97593e16i			1.44148i	0.693204	+	0.720741i	$0.256198\pi$
$859$			1.97593e16i			1.44148i	−0.693204	+	0.720741i	$0.743802\pi$
$860$	−8.52341e14	−	8.73682e14i	−0.0617834	−	0.0633304i
$861$	9.20500e15	+	5.32597e15i	0.662989	+	0.383602i
$862$	7.50834e15	+	3.16458e15i	0.537346	+	0.226478i
$863$	−2.79214e15			−0.198554			−0.0992770	−	0.995060i	$-0.531653\pi$
$863$	−2.79214e15			−0.198554			−0.0992770	+	0.995060i	$0.531653\pi$
$864$	1.28850e16	+	5.85344e15i	0.910457	+	0.413604i
$865$	−6.01088e14			−0.0422036
$866$	2.24654e16	+	9.46862e15i	1.56735	+	0.660599i
$867$	−9.11413e15	−	5.27340e15i	−0.631845	−	0.365583i
$868$	−2.79391e15	−	2.86387e15i	−0.192466	−	0.197285i
$869$			3.12264e16i			2.13753i
$870$	−8.38879e14	−	1.10951e15i	−0.0570615	−	0.0754699i
$871$		−	3.10320e15i		−	0.209754i
$872$	−3.90515e15	−	9.94567e15i	−0.262300	−	0.668026i
$873$	−8.44487e15	−	1.46902e16i	−0.563656	−	0.980504i
$874$	−4.51639e14	+	1.07157e15i	−0.0299556	+	0.0710734i
$875$	−3.81749e15			−0.251613
$876$	−3.98937e15	−	1.57219e16i	−0.261295	−	1.02975i
$877$	−2.32303e16			−1.51202			−0.756010	−	0.654560i	$-0.772854\pi$
$877$	−2.32303e16			−1.51202			−0.756010	+	0.654560i	$0.772854\pi$
$878$	9.49553e15	−	2.25293e16i	0.614185	−	1.45723i
$879$	−2.90003e15	+	5.01219e15i	−0.186408	+	0.322172i
$880$	1.54975e15	+	3.83302e13i	0.0989936	+	0.00244842i
$881$		−	1.98246e16i		−	1.25845i	−0.777223	−	0.629225i	$-0.783372\pi$
$881$		−	1.98246e16i		−	1.25845i	0.777223	−	0.629225i	$-0.216628\pi$
$882$	−3.96634e15	−	3.21232e16i	−0.250214	−	2.02648i
$883$		−	3.94151e15i		−	0.247103i	−0.992338	−	0.123552i	$-0.960572\pi$
$883$		−	3.94151e15i		−	0.247103i	0.992338	−	0.123552i	$-0.0394285\pi$
$884$	−5.09314e15	+	4.96873e15i	−0.317321	+	0.309569i
$885$	5.95561e13	−	1.02932e14i	0.00368755	−	0.00637329i
$886$	−1.79879e16	−	7.58146e15i	−1.10687	−	0.466517i
$887$	−1.79857e15			−0.109989			−0.0549943	−	0.998487i	$-0.517514\pi$
$887$	−1.79857e15			−0.109989			−0.0549943	+	0.998487i	$0.517514\pi$
$888$	−9.88764e14	+	6.52550e15i	−0.0600927	+	0.396591i
$889$	3.58674e15			0.216641
$890$	−1.22079e15	−	5.14530e14i	−0.0732815	−	0.0308863i
$891$	1.15495e16	−	1.98329e16i	0.689025	−	1.18320i
$892$	−2.87498e15	+	2.80475e15i	−0.170462	+	0.166298i
$893$		−	9.12874e15i		−	0.537933i
$894$	3.38541e15	−	2.55965e15i	0.198269	−	0.149908i
$895$			7.53758e14i			0.0438738i
$896$	−1.03215e16	−	2.83265e16i	−0.597104	−	1.63870i
$897$	2.13978e15	+	1.23807e15i	0.123030	+	0.0711845i
$898$	3.67348e15	−	8.71577e15i	0.209922	−	0.498065i
$899$	3.63995e15			0.206737
$900$	−4.80268e15	+	1.69550e16i	−0.271113	+	0.957112i
$901$	1.78062e14			0.00999042
$902$	4.18803e15	−	9.93660e15i	0.233547	−	0.554118i
$903$	3.33197e16	+	1.92786e16i	1.84679	+	1.06855i
$904$	3.28517e16	−	1.28992e16i	1.80980	−	0.710617i
$905$			1.08516e15i			0.0594193i
$906$	9.95101e15	−	7.52379e15i	0.541579	−	0.409479i
$907$		−	1.26952e15i		−	0.0686750i	−0.999410	−	0.0343375i	$-0.989068\pi$
$907$		−	1.26952e15i		−	0.0686750i	0.999410	−	0.0343375i	$-0.0109321\pi$
$908$	1.42025e16	+	1.45581e16i	0.763647	+	0.782768i
$909$	−1.74046e16	+	1.00053e16i	−0.930173	+	0.534723i
$910$	−1.86672e15	−	7.86774e14i	−0.0991632	−	0.0417948i
$911$	−1.64917e16			−0.870791			−0.435396	−	0.900239i	$-0.643392\pi$
$911$	−1.64917e16			−0.870791			−0.435396	+	0.900239i	$0.643392\pi$
$912$	−7.52299e15	−	4.60473e15i	−0.394838	−	0.241676i
$913$	−2.74994e16			−1.43461
$914$	1.79727e16	+	7.57504e15i	0.931985	+	0.392808i
$915$	8.60996e14	−	1.48808e15i	0.0443798	−	0.0767026i
$916$	−5.57195e15	−	5.71147e15i	−0.285484	−	0.292633i
$917$		−	1.67594e16i		−	0.853546i
$918$	9.44730e15	+	4.01299e15i	0.478270	+	0.203158i
$919$		−	2.18676e16i		−	1.10044i	−0.835020	−	0.550220i	$-0.814544\pi$
$919$		−	2.18676e16i		−	1.10044i	0.835020	−	0.550220i	$-0.185456\pi$
$920$	2.24216e14	−	8.80382e13i	0.0112159	−	0.00440391i
$921$	−1.11782e16	+	1.93195e16i	−0.555830	+	0.960654i
$922$	−6.75539e15	+	1.60280e16i	−0.333911	+	0.792244i
$923$	2.16746e16			1.06498
$924$	−4.73898e16	+	1.20250e16i	−2.31467	+	0.587340i
$925$	−8.21815e15			−0.399020
$926$	6.76187e15	−	1.60433e16i	0.326367	−	0.774345i
$927$	−3.76635e15	+	2.16514e15i	−0.180710	+	0.103884i
$928$	2.50038e16	+	1.12744e16i	1.19259	+	0.537750i
$929$			2.26978e16i			1.07621i	0.842878	+	0.538105i	$0.180860\pi$
$929$			2.26978e16i			1.07621i	−0.842878	+	0.538105i	$0.819140\pi$
$930$	1.46235e14	+	1.93412e14i	0.00689281	+	0.00911647i
$931$			2.01728e16i			0.945241i
$932$	1.67035e15	−	1.62955e15i	0.0778074	−	0.0759068i
$933$	−5.11976e15	−	2.96227e15i	−0.237083	−	0.137175i
$934$	1.84281e16	+	7.76700e15i	0.848347	+	0.357557i
$935$	1.12434e15			0.0514557
$936$	−1.17164e16	+	1.46404e16i	−0.533060	+	0.666093i
$937$	1.07803e16			0.487598			0.243799	−	0.969826i	$-0.421606\pi$
$937$	1.07803e16			0.487598			0.243799	+	0.969826i	$0.421606\pi$
$938$	8.78767e15	+	3.70378e15i	0.395147	+	0.166544i
$939$	1.23266e16	+	7.13213e15i	0.551040	+	0.318829i
$940$	−1.35355e15	+	1.32049e15i	−0.0601551	+	0.0586857i
$941$		−	8.03746e15i		−	0.355121i	−0.984110	−	0.177560i	$-0.943179\pi$
$941$		−	8.03746e15i		−	0.355121i	0.984110	−	0.177560i	$-0.0568205\pi$
$942$	1.41957e16	+	1.87753e16i	0.623557	+	0.824720i
$943$		−	1.67553e15i		−	0.0731708i
$944$	−5.79813e13	+	2.34428e15i	−0.00251734	+	0.101780i
$945$	−8.18317e12	+	2.92223e15i	−0.000353221	+	0.126136i
$946$	1.51596e16	−	3.59679e16i	0.650558	−	1.54353i
$947$	−2.79197e16			−1.19120			−0.595602	−	0.803280i	$-0.703086\pi$
$947$	−2.79197e16			−1.19120			−0.595602	+	0.803280i	$0.703086\pi$
$948$	−3.56730e16	+	9.05191e15i	−1.51319	+	0.383968i
$949$	2.14912e16			0.906352
$950$	4.26563e15	−	1.01207e16i	0.178856	−	0.424357i
$951$	−9.47869e15	+	1.63822e16i	−0.395144	+	0.682937i
$952$	−7.99164e15	−	2.03532e16i	−0.331232	−	0.843584i
$953$			2.77345e16i			1.14290i	0.820636	+	0.571451i	$0.193619\pi$
$953$			2.77345e16i			1.14290i	−0.820636	+	0.571451i	$0.806381\pi$
$954$	4.65715e14	−	5.75031e13i	0.0190811	−	0.00235600i
$955$		−	2.64023e15i		−	0.107553i
$956$	−1.30570e16	−	1.33839e16i	−0.528839	−	0.542081i
$957$	2.22760e16	−	3.85002e16i	0.897061	−	1.55041i
$958$	−4.01773e16	−	1.69337e16i	−1.60868	−	0.678020i
$959$	−5.60208e16			−2.23021
$960$	4.05454e14	+	1.78155e15i	0.0160491	+	0.0705189i
$961$	2.47740e16			0.975027
$962$	−8.05831e15	−	3.39638e15i	−0.315342	−	0.132909i
$963$	1.37927e16	+	2.39930e16i	0.536667	+	0.933555i
$964$	9.39810e15	+	9.63341e15i	0.363594	+	0.372698i
$965$		−	1.40110e14i		−	0.00538976i
$966$	−6.05986e15	+	4.58176e15i	−0.231787	+	0.175250i
$967$		−	3.61833e15i		−	0.137614i	−0.997630	−	0.0688069i	$-0.978081\pi$
$967$		−	3.61833e15i		−	0.137614i	0.997630	−	0.0688069i	$-0.0219192\pi$
$968$	8.45384e15	+	2.15303e16i	0.319698	+	0.814208i
$969$	−5.53715e15	−	3.20377e15i	−0.208212	−	0.120470i
$970$	8.49636e14	−	2.01586e15i	0.0317679	−	0.0753731i
$971$	7.15439e15			0.265991			0.132995	−	0.991117i	$-0.457540\pi$
$971$	7.15439e15			0.265991			0.132995	+	0.991117i	$0.457540\pi$
$972$	2.60051e16	+	7.44497e15i	0.961378	+	0.275232i
$973$	3.58951e16			1.31952
$974$	−4.71685e15	+	1.11913e16i	−0.172416	+	0.409078i
$975$	−2.02097e16	−	1.16932e16i	−0.734572	−	0.425020i
$976$	−8.38229e14	+	3.38910e16i	−0.0302962	+	1.22493i
$977$			3.00252e16i			1.07911i	0.841951	+	0.539554i	$0.181407\pi$
$977$			3.00252e16i			1.07911i	−0.841951	+	0.539554i	$0.818593\pi$
$978$	−2.60576e16	+	1.97017e16i	−0.931260	+	0.704110i
$979$		−	4.23646e16i		−	1.50556i
$980$	2.99110e15	−	2.91803e15i	0.105703	−	0.103121i
$981$	−1.01782e16	−	1.77054e16i	−0.357677	−	0.622195i
$982$	−1.33317e16	−	5.61896e15i	−0.465877	−	0.196355i
$983$	1.80182e16			0.626135			0.313067	−	0.949731i	$-0.398643\pi$
$983$	1.80182e16			0.626135			0.313067	+	0.949731i	$0.398643\pi$
$984$	1.25656e16	+	1.90398e15i	0.434221	+	0.0657945i
$985$	3.67156e15			0.126169
$986$	1.83313e16	+	7.72617e15i	0.626425	+	0.264023i
$987$	2.98675e16	−	5.16206e16i	1.01497	−	1.75420i
$988$	8.36533e15	−	8.16099e15i	0.282696	−	0.275791i
$989$		−	6.06499e15i		−	0.203822i
$990$	2.94068e15	−	3.63093e14i	0.0982775	−	0.0121346i
$991$			2.41463e16i			0.802500i	0.915969	+	0.401250i	$0.131424\pi$
$991$			2.41463e16i			0.802500i	−0.915969	+	0.401250i	$0.868576\pi$
$992$	−4.35872e15	−	1.96538e15i	−0.144061	−	0.0649581i
$993$	−5.23075e15	+	9.04042e15i	−0.171926	+	0.297144i
$994$	−2.58694e16	+	6.13783e16i	−0.845593	+	2.00627i
$995$	−2.70456e14			−0.00879164
$996$	−7.97153e15	−	3.14153e16i	−0.257701	−	1.01558i
$997$	−1.62174e16			−0.521385			−0.260692	−	0.965422i	$-0.583951\pi$
$997$	−1.62174e16			−0.521385			−0.260692	+	0.965422i	$0.583951\pi$
$998$	−3.82646e15	+	9.07874e15i	−0.122343	+	0.290274i
$999$	−3.53254e13	+	1.26148e16i	−0.00112325	+	0.401116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.12.b.a.11.18	yes	20
3.2	odd	2	inner	12.12.b.a.11.3	✓	20
4.3	odd	2	inner	12.12.b.a.11.4	yes	20
8.3	odd	2		192.12.c.d.191.3		20
8.5	even	2		192.12.c.d.191.18		20
12.11	even	2	inner	12.12.b.a.11.17	yes	20
24.5	odd	2		192.12.c.d.191.4		20
24.11	even	2		192.12.c.d.191.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.12.b.a.11.3	✓	20	3.2	odd	2	inner
12.12.b.a.11.4	yes	20	4.3	odd	2	inner
12.12.b.a.11.17	yes	20	12.11	even	2	inner
12.12.b.a.11.18	yes	20	1.1	even	1	trivial
192.12.c.d.191.3		20	8.3	odd	2
192.12.c.d.191.4		20	24.5	odd	2
192.12.c.d.191.17		20	24.11	even	2
192.12.c.d.191.18		20	8.5	even	2

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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(41.7022 + 17.5764i) q^{2} +(-364.303 - 210.784i) q^{3} +(1430.14 + 1465.95i) q^{4} +505.366i q^{5} +(-11487.4 - 15193.3i) q^{6} +77554.9i q^{7} +(33873.8 + 86269.9i) q^{8} +(88286.9 + 153579. i) q^{9} +O(q^{10})\)	\(q+(41.7022 + 17.5764i) q^{2} +(-364.303 - 210.784i) q^{3} +(1430.14 + 1465.95i) q^{4} +505.366i q^{5} +(-11487.4 - 15193.3i) q^{6} +77554.9i q^{7} +(33873.8 + 86269.9i) q^{8} +(88286.9 + 153579. i) q^{9} +(-8882.52 + 21074.9i) q^{10} -731355. q^{11} +(-212006. - 835501. i) q^{12} +1.14210e6 q^{13} +(-1.36314e6 + 3.23421e6i) q^{14} +(106523. - 184107. i) q^{15} +(-103706. + 4.19302e6i) q^{16} +3.04203e6i q^{17} +(982390. + 7.95634e6i) q^{18} -4.99643e6i q^{19} +(-740841. + 722744. i) q^{20} +(1.63474e7 - 2.82535e7i) q^{21} +(-3.04991e7 - 1.28546e7i) q^{22} -5.14282e6 q^{23} +(5.84402e6 - 3.85685e7i) q^{24} +4.85727e7 q^{25} +(4.76280e7 + 2.00740e7i) q^{26} +(208788. - 7.45588e7i) q^{27} +(-1.13692e8 + 1.10914e8i) q^{28} -1.44501e8i q^{29} +(7.67818e6 - 5.80535e6i) q^{30} +2.51898e7i q^{31} +(-7.80231e7 + 1.73035e8i) q^{32} +(2.66435e8 + 1.54158e8i) q^{33} +(-5.34679e7 + 1.26859e8i) q^{34} -3.91936e7 q^{35} +(-9.88761e7 + 3.49063e8i) q^{36} -1.69193e8 q^{37} +(8.78194e7 - 2.08362e8i) q^{38} +(-4.16071e8 - 2.40737e8i) q^{39} +(-4.35979e7 + 1.71187e7i) q^{40} +3.25800e8i q^{41} +(1.17832e9 - 8.90905e8i) q^{42} +1.17931e9i q^{43} +(-1.04594e9 - 1.07213e9i) q^{44} +(-7.76136e7 + 4.46172e7i) q^{45} +(-2.14467e8 - 9.03923e7i) q^{46} +1.82705e9 q^{47} +(9.21604e8 - 1.50567e9i) q^{48} -4.03744e9 q^{49} +(2.02559e9 + 8.53734e8i) q^{50} +(6.41211e8 - 1.10822e9i) q^{51} +(1.63336e9 + 1.67426e9i) q^{52} -5.85339e7i q^{53} +(1.31918e9 - 3.10559e9i) q^{54} -3.69602e8i q^{55} +(-6.69066e9 + 2.62708e9i) q^{56} +(-1.05317e9 + 1.82022e9i) q^{57} +(2.53981e9 - 6.02601e9i) q^{58} +5.59090e8 q^{59} +(4.22234e8 - 1.07141e8i) q^{60} +8.08270e9 q^{61} +(-4.42746e8 + 1.05047e9i) q^{62} +(-1.19108e10 + 6.84709e9i) q^{63} +(-6.29507e9 + 5.84458e9i) q^{64} +5.77179e8i q^{65} +(8.40137e9 + 1.11117e10i) q^{66} -2.71710e9i q^{67} +(-4.45945e9 + 4.35052e9i) q^{68} +(1.87355e9 + 1.08403e9i) q^{69} +(-1.63446e9 - 6.88883e8i) q^{70} +1.89778e10 q^{71} +(-1.02586e10 + 1.28188e10i) q^{72} +1.88173e10 q^{73} +(-7.05570e9 - 2.97380e9i) q^{74} +(-1.76952e10 - 1.02384e10i) q^{75} +(7.32451e9 - 7.14560e9i) q^{76} -5.67202e10i q^{77} +(-1.31198e10 - 1.73523e10i) q^{78} -4.26966e10i q^{79} +(-2.11901e9 - 5.24098e7i) q^{80} +(-1.57919e10 + 2.71180e10i) q^{81} +(-5.72640e9 + 1.35866e10i) q^{82} +3.76005e10 q^{83} +(6.47972e10 - 1.64421e10i) q^{84} -1.53734e9 q^{85} +(-2.07281e10 + 4.91798e10i) q^{86} +(-3.04586e10 + 5.26422e10i) q^{87} +(-2.47738e10 - 6.30940e10i) q^{88} +5.79261e10i q^{89} +(-4.02086e9 + 4.96467e8i) q^{90} +8.85755e10i q^{91} +(-7.35495e9 - 7.53911e9i) q^{92} +(5.30961e9 - 9.17673e9i) q^{93} +(7.61920e10 + 3.21130e10i) q^{94} +2.52503e9 q^{95} +(6.48972e10 - 4.65913e10i) q^{96} -9.56525e10 q^{97} +(-1.68370e11 - 7.09637e10i) q^{98} +(-6.45691e10 - 1.12321e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9}+O(q^{10}) \) 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9	\( 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9} + 202000 q^{10} + 1064760 q^{12} + 1543864 q^{13} + 3482912 q^{16} + 2557392 q^{18} - 12211752 q^{21} - 5920464 q^{22} + 12133152 q^{24} - 141128700 q^{25} - 3604848 q^{28} + 73456080 q^{30} + 229769760 q^{33} + 222167104 q^{34} + 298087896 q^{36} - 44517800 q^{37} - 439643840 q^{40} + 281776944 q^{42} + 1020227520 q^{45} - 2392795680 q^{46} + 689090592 q^{48} - 1018138084 q^{49} - 3959246384 q^{52} - 4249352520 q^{54} + 1438636392 q^{57} + 9671853040 q^{58} + 5688375360 q^{60} + 6873199864 q^{61} - 1452752512 q^{64} - 10961242896 q^{66} - 13308470976 q^{69} + 35188514400 q^{70} + 30438127680 q^{72} - 12426469112 q^{73} - 60088673808 q^{76} - 81037845456 q^{78} - 42462874764 q^{81} + 88180337440 q^{82} + 125502443664 q^{84} + 17135502080 q^{85} - 166086469440 q^{88} - 257976145200 q^{90} + 114387515256 q^{93} + 391966360512 q^{94} + 446868262272 q^{96} + 75764383528 q^{97}+O(q^{100}) \) 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9 + 202000 * q^10 + 1064760 * q^12 + 1543864 * q^13 + 3482912 * q^16 + 2557392 * q^18 - 12211752 * q^21 - 5920464 * q^22 + 12133152 * q^24 - 141128700 * q^25 - 3604848 * q^28 + 73456080 * q^30 + 229769760 * q^33 + 222167104 * q^34 + 298087896 * q^36 - 44517800 * q^37 - 439643840 * q^40 + 281776944 * q^42 + 1020227520 * q^45 - 2392795680 * q^46 + 689090592 * q^48 - 1018138084 * q^49 - 3959246384 * q^52 - 4249352520 * q^54 + 1438636392 * q^57 + 9671853040 * q^58 + 5688375360 * q^60 + 6873199864 * q^61 - 1452752512 * q^64 - 10961242896 * q^66 - 13308470976 * q^69 + 35188514400 * q^70 + 30438127680 * q^72 - 12426469112 * q^73 - 60088673808 * q^76 - 81037845456 * q^78 - 42462874764 * q^81 + 88180337440 * q^82 + 125502443664 * q^84 + 17135502080 * q^85 - 166086469440 * q^88 - 257976145200 * q^90 + 114387515256 * q^93 + 391966360512 * q^94 + 446868262272 * q^96 + 75764383528 * q^97

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