LMFDB - Embedded newform 12.20.b.a.11.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,20,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, 20, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 20 $
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:	$27.4580035868$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.36
Character	$\chi$	$=$	12.11
Dual form			12.20.b.a.11.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(723.867 + 17.4378i) q^{2} +(-2865.95 - 33971.3i) q^{3} +(523680. + 25245.3i) q^{4} +5.49376e6i q^{5} +(-1.48218e6 - 2.46407e7i) q^{6} +1.05257e8i q^{7} +(3.78635e8 + 2.74060e7i) q^{8} +(-1.14583e9 + 1.94720e8i) q^{9} +O(q^{10})$	\(q+(723.867 + 17.4378i) q^{2} +(-2865.95 - 33971.3i) q^{3} +(523680. + 25245.3i) q^{4} +5.49376e6i q^{5} +(-1.48218e6 - 2.46407e7i) q^{6} +1.05257e8i q^{7} +(3.78635e8 + 2.74060e7i) q^{8} +(-1.14583e9 + 1.94720e8i) q^{9} +(-9.57989e7 + 3.97675e9i) q^{10} -7.09412e9 q^{11} +(-6.43225e8 - 1.78624e10i) q^{12} -6.63179e10 q^{13} +(-1.83545e9 + 7.61923e10i) q^{14} +(1.86630e11 - 1.57448e10i) q^{15} +(2.73603e11 + 2.64409e10i) q^{16} +6.50375e11i q^{17} +(-8.32827e11 + 1.20971e11i) q^{18} +8.23681e11i q^{19} +(-1.38691e11 + 2.87697e12i) q^{20} +(3.57572e12 - 3.01662e11i) q^{21} +(-5.13520e12 - 1.23706e11i) q^{22} +1.08842e13 q^{23} +(-1.54129e11 - 1.29412e13i) q^{24} -1.11079e13 q^{25} +(-4.80054e13 - 1.15644e12i) q^{26} +(9.89878e12 + 3.83674e13i) q^{27} +(-2.65725e12 + 5.51211e13i) q^{28} -9.35164e13i q^{29} +(1.35370e14 - 8.14275e12i) q^{30} +1.40022e14i q^{31} +(1.97591e14 + 2.39107e13i) q^{32} +(2.03314e13 + 2.40996e14i) q^{33} +(-1.13411e13 + 4.70785e14i) q^{34} -5.78258e14 q^{35} +(-6.04966e14 + 7.30440e13i) q^{36} +2.24836e14 q^{37} +(-1.43632e13 + 5.96236e14i) q^{38} +(1.90064e14 + 2.25290e15i) q^{39} +(-1.50562e14 + 2.08013e15i) q^{40} +3.53533e14i q^{41} +(2.59361e15 - 1.56010e14i) q^{42} -1.91080e15i q^{43} +(-3.71505e15 - 1.79093e14i) q^{44} +(-1.06974e15 - 6.29494e15i) q^{45} +(7.87870e15 + 1.89796e14i) q^{46} -1.54874e15 q^{47} +(1.14098e14 - 9.37043e15i) q^{48} +3.19812e14 q^{49} +(-8.04064e15 - 1.93697e14i) q^{50} +(2.20941e16 - 1.86394e15i) q^{51} +(-3.47294e16 - 1.67421e15i) q^{52} -2.30947e16i q^{53} +(6.49636e15 + 2.79455e16i) q^{54} -3.89734e16i q^{55} +(-2.88468e15 + 3.98540e16i) q^{56} +(2.79815e16 - 2.36063e15i) q^{57} +(1.63072e15 - 6.76934e16i) q^{58} -7.28318e16 q^{59} +(9.81318e16 - 3.53372e15i) q^{60} -3.87008e16 q^{61} +(-2.44167e15 + 1.01357e17i) q^{62} +(-2.04957e16 - 1.20607e17i) q^{63} +(1.42613e17 + 2.07537e16i) q^{64} -3.64335e17i q^{65} +(1.05148e16 + 1.74804e17i) q^{66} +3.26594e17i q^{67} +(-1.64189e16 + 3.40588e17i) q^{68} +(-3.11935e16 - 3.69749e17i) q^{69} +(-4.18582e17 - 1.00835e16i) q^{70} +1.37293e17 q^{71} +(-4.39189e17 + 4.23249e16i) q^{72} +2.84381e17 q^{73} +(1.62751e17 + 3.92063e15i) q^{74} +(3.18346e16 + 3.77349e17i) q^{75} +(-2.07941e16 + 4.31345e17i) q^{76} -7.46708e17i q^{77} +(9.82953e16 + 1.63412e18i) q^{78} +3.04622e17i q^{79} +(-1.45260e17 + 1.50311e18i) q^{80} +(1.27502e18 - 4.46233e17i) q^{81} +(-6.16484e15 + 2.55911e17i) q^{82} +1.54227e18 q^{83} +(1.88015e18 - 6.77041e16i) q^{84} -3.57300e18 q^{85} +(3.33201e16 - 1.38317e18i) q^{86} +(-3.17687e18 + 2.68013e17i) q^{87} +(-2.68608e18 - 1.94422e17i) q^{88} -1.94738e18i q^{89} +(-6.64583e17 - 4.57535e18i) q^{90} -6.98044e18i q^{91} +(5.69982e18 + 2.74774e17i) q^{92} +(4.75672e18 - 4.01295e17i) q^{93} +(-1.12108e18 - 2.70066e16i) q^{94} -4.52511e18 q^{95} +(2.45991e17 - 6.78096e18i) q^{96} +3.32711e17 q^{97} +(2.31502e17 + 5.57681e15i) q^{98} +(8.12869e18 - 1.38137e18i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9}+O(q^{10}) $ 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9	$ 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9} - 4162950000 q^{10} - 2268767880 q^{12} - 25913431656 q^{13} + 791689296672 q^{16} + 2852271258192 q^{18} - 1650825908424 q^{21} + 7247870602416 q^{22} + 23719435803936 q^{24} - 118879690462380 q^{25} - 7629081673968 q^{28} + 37456727138640 q^{30} + 529254701828640 q^{33} - 248241675948480 q^{34} - 11\!\cdots\!16 q^{36}+ \cdots + 12\!\cdots\!88 q^{97}+O(q^{100}) $ 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9 - 4162950000 * q^10 - 2268767880 * q^12 - 25913431656 * q^13 + 791689296672 * q^16 + 2852271258192 * q^18 - 1650825908424 * q^21 + 7247870602416 * q^22 + 23719435803936 * q^24 - 118879690462380 * q^25 - 7629081673968 * q^28 + 37456727138640 * q^30 + 529254701828640 * q^33 - 248241675948480 * q^34 - 1177548745309416 * q^36 + 1847838600168120 * q^37 - 40433256181440 * q^40 - 2709671988768336 * q^42 - 4365410114088000 * q^45 + 17206125364795104 * q^46 + 1561106052682272 * q^48 - 49399737041580084 * q^49 + 16558671470242896 * q^52 + 40087412948587896 * q^54 + 44803667812766472 * q^57 - 34645536255764880 * q^58 + 50260381053157440 * q^60 + 174742350239997144 * q^61 - 139766490424918656 * q^64 - 87772097712685968 * q^66 - 957190369821780672 * q^69 + 244663962371376480 * q^70 + 54134736422921280 * q^72 - 1445122541399481432 * q^73 + 2744130151937256048 * q^76 + 1125465917961999024 * q^78 + 1033298241353042436 * q^81 + 1064985418859680800 * q^82 + 1920709484261873424 * q^84 - 1802899595088057600 * q^85 - 9209792381828477760 * q^88 - 5194944179528261040 * q^90 + 6719944190337314136 * q^93 - 3835186345170303552 * q^94 - 11947184361208227456 * q^96 + 12765226159947004488 * 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 $

$2$	723.867	+	17.4378i	0.999710	+	0.0240828i
$2$	723.867	+	17.4378i	0.999710	+	0.0240828i
$3$	−2865.95	−	33971.3i	−0.0840652	−	0.996460i
$3$	−2865.95	−	33971.3i	−0.0840652	−	0.996460i
$4$	523680.	+	25245.3i	0.998840	+	0.0481515i
$5$			5.49376e6i			1.25792i	0.777436	+	0.628962i	$0.216520\pi$
$5$			5.49376e6i			1.25792i	−0.777436	+	0.628962i	$0.783480\pi$
$6$	−1.48218e6	−	2.46407e7i	−0.0600434	−	0.998196i
$7$			1.05257e8i			0.985872i	0.870066	+	0.492936i	$0.164076\pi$
$7$			1.05257e8i			0.985872i	−0.870066	+	0.492936i	$0.835924\pi$
$8$	3.78635e8	+	2.74060e7i	0.997391	+	0.0721924i
$9$	−1.14583e9	+	1.94720e8i	−0.985866	+	0.167535i
$10$	−9.57989e7	+	3.97675e9i	−0.0302943	+	1.25756i
$11$	−7.09412e9			−0.907127			−0.453564	−	0.891224i	$-0.649848\pi$
$11$	−7.09412e9			−0.907127			−0.453564	+	0.891224i	$0.649848\pi$
$12$	−6.43225e8	−	1.78624e10i	−0.0359866	−	0.999352i
$13$	−6.63179e10			−1.73448			−0.867240	−	0.497891i	$-0.834108\pi$
$13$	−6.63179e10			−1.73448			−0.867240	+	0.497891i	$0.834108\pi$
$14$	−1.83545e9	+	7.61923e10i	−0.0237425	+	0.985586i
$15$	1.86630e11	−	1.57448e10i	1.25347	−	0.105748i
$16$	2.73603e11	+	2.64409e10i	0.995363	+	0.0961914i
$17$			6.50375e11i			1.33015i	0.746779	+	0.665073i	$0.231599\pi$
$17$			6.50375e11i			1.33015i	−0.746779	+	0.665073i	$0.768401\pi$
$18$	−8.32827e11	+	1.20971e11i	−0.989615	+	0.143744i
$19$			8.23681e11i			0.585598i	0.956174	+	0.292799i	$0.0945868\pi$
$19$			8.23681e11i			0.585598i	−0.956174	+	0.292799i	$0.905413\pi$
$20$	−1.38691e11	+	2.87697e12i	−0.0605710	+	1.25647i
$21$	3.57572e12	−	3.01662e11i	0.982382	−	0.0828776i
$22$	−5.13520e12	−	1.23706e11i	−0.906864	−	0.0218461i
$23$	1.08842e13			1.26003			0.630015	−	0.776583i	$-0.283049\pi$
$23$	1.08842e13			1.26003			0.630015	+	0.776583i	$0.283049\pi$
$24$	−1.54129e11	−	1.29412e13i	−0.0119090	−	0.999929i
$25$	−1.11079e13			−0.582373
$26$	−4.80054e13	−	1.15644e12i	−1.73398	−	0.0417710i
$27$	9.89878e12	+	3.83674e13i	0.249819	+	0.968292i
$28$	−2.65725e12	+	5.51211e13i	−0.0474713	+	0.984728i
$29$		−	9.35164e13i		−	1.19703i	−0.801110	−	0.598517i	$-0.795757\pi$
$29$		−	9.35164e13i		−	1.19703i	0.801110	−	0.598517i	$-0.204243\pi$
$30$	1.35370e14	−	8.14275e12i	1.25565	−	0.0755300i
$31$			1.40022e14i			0.951173i	0.879669	+	0.475587i	$0.157764\pi$
$31$			1.40022e14i			0.951173i	−0.879669	+	0.475587i	$0.842236\pi$
$32$	1.97591e14	+	2.39107e13i	0.992758	+	0.120135i
$33$	2.03314e13	+	2.40996e14i	0.0762579	+	0.903916i
$34$	−1.13411e13	+	4.70785e14i	−0.0320336	+	1.32976i
$35$	−5.78258e14			−1.24015
$36$	−6.04966e14	+	7.30440e13i	−0.992790	+	0.119870i
$37$	2.24836e14			0.284413			0.142206	−	0.989837i	$-0.454580\pi$
$37$	2.24836e14			0.284413			0.142206	+	0.989837i	$0.454580\pi$
$38$	−1.43632e13	+	5.96236e14i	−0.0141028	+	0.585429i
$39$	1.90064e14	+	2.25290e15i	0.145809	+	1.72834i
$40$	−1.50562e14	+	2.08013e15i	−0.0908126	+	1.25464i
$41$			3.53533e14i			0.168649i	0.996438	+	0.0843245i	$0.0268732\pi$
$41$			3.53533e14i			0.168649i	−0.996438	+	0.0843245i	$0.973127\pi$
$42$	2.59361e15	−	1.56010e14i	0.984093	−	0.0591951i
$43$		−	1.91080e15i		−	0.579783i	−0.957060	−	0.289891i	$-0.906381\pi$
$43$		−	1.91080e15i		−	0.579783i	0.957060	−	0.289891i	$-0.0936192\pi$
$44$	−3.71505e15	−	1.79093e14i	−0.906075	−	0.0436796i
$45$	−1.06974e15	−	6.29494e15i	−0.210747	−	1.24014i
$46$	7.87870e15	+	1.89796e14i	1.25966	+	0.0303450i
$47$	−1.54874e15			−0.201860			−0.100930	−	0.994894i	$-0.532182\pi$
$47$	−1.54874e15			−0.201860			−0.100930	+	0.994894i	$0.532182\pi$
$48$	1.14098e14	−	9.37043e15i	0.0121755	−	0.999926i
$49$	3.19812e14			0.0280564
$50$	−8.04064e15	−	1.93697e14i	−0.582205	−	0.0140252i
$51$	2.20941e16	−	1.86394e15i	1.32544	−	0.111819i
$52$	−3.47294e16	−	1.67421e15i	−1.73247	−	0.0835179i
$53$		−	2.30947e16i		−	0.961374i	−0.876892	−	0.480687i	$-0.840387\pi$
$53$		−	2.30947e16i		−	0.961374i	0.876892	−	0.480687i	$-0.159613\pi$
$54$	6.49636e15	+	2.79455e16i	0.226428	+	0.974028i
$55$		−	3.89734e16i		−	1.14110i
$56$	−2.88468e15	+	3.98540e16i	−0.0711725	+	0.983300i
$57$	2.79815e16	−	2.36063e15i	0.583526	−	0.0492285i
$58$	1.63072e15	−	6.76934e16i	0.0288279	−	1.19669i
$59$	−7.28318e16			−1.09453			−0.547264	−	0.836960i	$-0.684331\pi$
$59$	−7.28318e16			−1.09453			−0.547264	+	0.836960i	$0.684331\pi$
$60$	9.81318e16	−	3.53372e15i	1.25711	−	0.0452685i
$61$	−3.87008e16			−0.423727			−0.211864	−	0.977299i	$-0.567953\pi$
$61$	−3.87008e16			−0.423727			−0.211864	+	0.977299i	$0.567953\pi$
$62$	−2.44167e15	+	1.01357e17i	−0.0229069	+	0.950898i
$63$	−2.04957e16	−	1.20607e17i	−0.165168	−	0.971938i
$64$	1.42613e17	+	2.07537e16i	0.989577	+	0.144008i
$65$		−	3.64335e17i		−	2.18184i
$66$	1.05148e16	+	1.74804e17i	0.0544670	+	0.905491i
$67$			3.26594e17i			1.46655i	0.679931	+	0.733276i	$0.262010\pi$
$67$			3.26594e17i			1.46655i	−0.679931	+	0.733276i	$0.737990\pi$
$68$	−1.64189e16	+	3.40588e17i	−0.0640486	+	1.32860i
$69$	−3.11935e16	−	3.69749e17i	−0.105925	−	1.25557i
$70$	−4.18582e17	−	1.00835e16i	−1.23979	−	0.0298663i
$71$	1.37293e17			0.355381			0.177691	−	0.984086i	$-0.443137\pi$
$71$	1.37293e17			0.355381			0.177691	+	0.984086i	$0.443137\pi$
$72$	−4.39189e17	+	4.23249e16i	−0.995388	+	0.0959262i
$73$	2.84381e17			0.565371			0.282685	−	0.959213i	$-0.408775\pi$
$73$	2.84381e17			0.565371			0.282685	+	0.959213i	$0.408775\pi$
$74$	1.62751e17	+	3.92063e15i	0.284330	+	0.00684944i
$75$	3.18346e16	+	3.77349e17i	0.0489574	+	0.580312i
$76$	−2.07941e16	+	4.31345e17i	−0.0281975	+	0.584919i
$77$		−	7.46708e17i		−	0.894311i
$78$	9.82953e16	+	1.63412e18i	0.104144	+	1.73135i
$79$			3.04622e17i			0.285959i	0.989726	+	0.142980i	$0.0456683\pi$
$79$			3.04622e17i			0.285959i	−0.989726	+	0.142980i	$0.954332\pi$
$80$	−1.45260e17	+	1.50311e18i	−0.121001	+	1.25209i
$81$	1.27502e18	−	4.46233e17i	0.943864	−	0.330335i
$82$	−6.16484e15	+	2.55911e17i	−0.00406153	+	0.168600i
$83$	1.54227e18			0.905561			0.452781	−	0.891622i	$-0.350432\pi$
$83$	1.54227e18			0.905561			0.452781	+	0.891622i	$0.350432\pi$
$84$	1.88015e18	−	6.77041e16i	0.985233	−	0.0354782i
$85$	−3.57300e18			−1.67322
$86$	3.33201e16	−	1.38317e18i	0.0139628	−	0.579615i
$87$	−3.17687e18	+	2.68013e17i	−1.19280	+	0.100629i
$88$	−2.68608e18	−	1.94422e17i	−0.904760	−	0.0654877i
$89$		−	1.94738e18i		−	0.589175i	−0.955624	−	0.294588i	$-0.904818\pi$
$89$		−	1.94738e18i		−	0.589175i	0.955624	−	0.294588i	$-0.0951823\pi$
$90$	−6.64583e17	−	4.57535e18i	−0.180820	−	1.24486i
$91$		−	6.98044e18i		−	1.70997i
$92$	5.69982e18	+	2.74774e17i	1.25857	+	0.0606724i
$93$	4.75672e18	−	4.01295e17i	0.947807	−	0.0799606i
$94$	−1.12108e18	−	2.70066e16i	−0.201801	−	0.00486133i
$95$	−4.52511e18			−0.736638
$96$	2.45991e17	−	6.78096e18i	0.0362529	−	0.999343i
$97$	3.32711e17			0.0444360			0.0222180	−	0.999753i	$-0.492927\pi$
$97$	3.32711e17			0.0444360			0.0222180	+	0.999753i	$0.492927\pi$
$98$	2.31502e17	+	5.57681e15i	0.0280483	+	0.000675676i
$99$	8.12869e18	−	1.38137e18i	0.894306	−	0.151976i
$100$	−5.81698e18	−	2.80422e17i	−0.581698	−	0.0280422i
$101$			1.42998e19i			1.30100i	0.759506	+	0.650500i	$0.225441\pi$
$101$			1.42998e19i			1.30100i	−0.759506	+	0.650500i	$0.774559\pi$
$102$	1.60257e19	−	9.63975e17i	1.32775	−	0.0798664i
$103$			8.86762e18i			0.669659i	0.942279	+	0.334829i	$0.108679\pi$
$103$			8.86762e18i			0.669659i	−0.942279	+	0.334829i	$0.891321\pi$
$104$	−2.51103e19	−	1.81751e18i	−1.72995	−	0.125216i
$105$	1.65726e18	+	1.96442e19i	0.104254	+	1.23576i
$106$	4.02721e17	−	1.67175e19i	0.0231525	−	0.961095i
$107$	1.45474e19			0.764964			0.382482	−	0.923963i	$-0.375069\pi$
$107$	1.45474e19			0.764964			0.382482	+	0.923963i	$0.375069\pi$
$108$	4.21520e18	+	2.03421e19i	0.202905	+	0.979198i
$109$	−3.71134e19			−1.63674			−0.818370	−	0.574692i	$-0.805122\pi$
$109$	−3.71134e19			−1.63674			−0.818370	+	0.574692i	$0.805122\pi$
$110$	6.79609e17	−	2.82116e19i	0.0274808	−	1.14077i
$111$	−6.44367e17	−	7.63795e18i	−0.0239092	−	0.283406i
$112$	−2.78309e18	+	2.87987e19i	−0.0948324	+	0.981300i
$113$			3.44993e19i			1.08035i	0.841552	+	0.540176i	$0.181642\pi$
$113$			3.44993e19i			1.08035i	−0.841552	+	0.540176i	$0.818358\pi$
$114$	2.02961e19	−	1.22085e18i	0.584542	−	0.0351613i
$115$			5.97950e19i			1.58502i
$116$	2.36085e18	−	4.89726e19i	0.0576391	−	1.19565i
$117$	7.59893e19	−	1.29134e19i	1.70996	−	0.290587i
$118$	−5.27205e19	−	1.27002e18i	−1.09421	−	0.0263592i
$119$	−6.84567e19			−1.31135
$120$	7.10961e19	−	8.46746e17i	1.25784	−	0.0149807i
$121$	−1.08325e19			−0.177120
$122$	−2.80142e19	−	6.74856e17i	−0.423604	−	0.0102045i
$123$	1.20100e19	−	1.01321e18i	0.168052	−	0.0141775i
$124$	−3.53489e18	+	7.33266e19i	−0.0458005	+	0.950070i
$125$			4.37611e19i			0.525343i
$126$	−1.27330e19	−	8.76611e19i	−0.141714	−	0.975634i
$127$		−	1.13482e20i		−	1.17163i	−0.810445	−	0.585815i	$-0.800774\pi$
$127$		−	1.13482e20i		−	1.17163i	0.810445	−	0.585815i	$-0.199226\pi$
$128$	1.02871e20	+	1.75098e19i	0.985821	+	0.167798i
$129$	−6.49124e19	+	5.47626e18i	−0.577730	+	0.0487396i
$130$	6.35319e18	−	2.63730e20i	0.0525448	−	2.18121i
$131$	1.43356e20			1.10240			0.551199	−	0.834374i	$-0.314170\pi$
$131$	1.43356e20			1.10240			0.551199	+	0.834374i	$0.314170\pi$
$132$	4.56312e18	+	1.26718e20i	0.0326445	+	0.906540i
$133$	−8.66984e19			−0.577325
$134$	−5.69507e18	+	2.36411e20i	−0.0353186	+	1.46613i
$135$	−2.10781e20	+	5.43815e19i	−1.21804	+	0.314254i
$136$	−1.78242e19	+	2.46254e20i	−0.0960264	+	1.32667i
$137$		−	2.56625e20i		−	1.28960i	−0.764353	−	0.644799i	$-0.776941\pi$
$137$		−	2.56625e20i		−	1.28960i	0.764353	−	0.644799i	$-0.223059\pi$
$138$	−1.61323e19	−	2.68193e20i	−0.0756564	−	1.25776i
$139$		−	2.13819e20i		−	0.936278i	−0.883655	−	0.468139i	$-0.844925\pi$
$139$		−	2.13819e20i		−	0.936278i	0.883655	−	0.468139i	$-0.155075\pi$
$140$	−3.02822e20	−	1.45983e19i	−1.23871	−	0.0597152i
$141$	4.43861e18	+	5.26127e19i	0.0169694	+	0.201145i
$142$	9.93820e19	+	2.39409e18i	0.355278	+	0.00855856i
$143$	4.70468e20			1.57339
$144$	−3.18653e20	+	2.29791e19i	−0.997410	+	0.0719266i
$145$	5.13756e20			1.50578
$146$	2.05854e20	+	4.95897e18i	0.565207	+	0.0136157i
$147$	−9.16565e17	−	1.08644e19i	−0.00235857	−	0.0279571i
$148$	1.17742e20	+	5.67604e18i	0.284083	+	0.0136949i
$149$		−	7.51323e20i		−	1.70042i	−0.526440	−	0.850212i	$-0.676474\pi$
$149$		−	7.51323e20i		−	1.70042i	0.526440	−	0.850212i	$-0.323526\pi$
$150$	1.64639e19	+	2.73706e20i	0.0349677	+	0.581323i
$151$			3.32254e20i			0.662504i	0.943542	+	0.331252i	$0.107471\pi$
$151$			3.32254e20i			0.662504i	−0.943542	+	0.331252i	$0.892529\pi$
$152$	−2.25738e19	+	3.11874e20i	−0.0422758	+	0.584070i
$153$	−1.26641e20	−	7.45222e20i	−0.222846	−	1.31135i
$154$	1.30209e19	−	5.40517e20i	0.0215375	−	0.894052i
$155$	−7.69246e20			−1.19650
$156$	4.26574e19	+	1.18460e21i	0.0624181	+	1.73336i
$157$	−5.79313e20			−0.797749			−0.398875	−	0.917005i	$-0.630599\pi$
$157$	−5.79313e20			−0.797749			−0.398875	+	0.917005i	$0.630599\pi$
$158$	−5.31193e18	+	2.20506e20i	−0.00688668	+	0.285876i
$159$	−7.84558e20	+	6.61884e19i	−0.957971	+	0.0808181i
$160$	−1.31360e20	+	1.08552e21i	−0.151120	+	1.24881i
$161$			1.14564e21i			1.24223i
$162$	9.30727e20	−	3.00780e20i	0.951545	−	0.307508i
$163$			1.23113e21i			1.18719i	0.804762	+	0.593597i	$0.202293\pi$
$163$			1.23113e21i			1.18719i	−0.804762	+	0.593597i	$0.797707\pi$
$164$	−8.92505e18	+	1.85138e20i	−0.00812071	+	0.168453i
$165$	−1.32398e21	+	1.11696e20i	−1.13706	+	0.0959266i
$166$	1.11640e21	+	2.68937e19i	0.905299	+	0.0218084i
$167$	1.70826e21			1.30842			0.654212	−	0.756312i	$-0.273001\pi$
$167$	1.70826e21			1.30842			0.654212	+	0.756312i	$0.273001\pi$
$168$	1.36216e21	−	1.62232e19i	0.985802	−	0.0117408i
$169$	2.93615e21			2.00842
$170$	−2.58638e21	−	6.23052e19i	−1.67274	−	0.0402958i
$171$	−1.60387e20	−	9.43802e20i	−0.0981084	−	0.577322i
$172$	4.82387e19	−	1.00065e21i	0.0279174	−	0.579110i
$173$		−	3.79874e20i		−	0.208066i	−0.994574	−	0.104033i	$-0.966825\pi$
$173$		−	3.79874e20i		−	0.208066i	0.994574	−	0.104033i	$-0.0331748\pi$
$174$	−2.30431e21	+	1.38608e20i	−1.19487	+	0.0718740i
$175$		−	1.16919e21i		−	0.574146i
$176$	−1.94098e21	−	1.87575e20i	−0.902921	−	0.0872578i
$177$	2.08732e20	+	2.47419e21i	0.0920117	+	1.09065i
$178$	3.39579e19	−	1.40964e21i	0.0141890	−	0.589005i
$179$	5.62431e20			0.222826			0.111413	−	0.993774i	$-0.464462\pi$
$179$	5.62431e20			0.222826			0.111413	+	0.993774i	$0.464462\pi$
$180$	−4.01286e20	−	3.32354e21i	−0.150787	−	1.24885i
$181$	−1.64249e21			−0.585539			−0.292769	−	0.956183i	$-0.594577\pi$
$181$	−1.64249e21			−0.585539			−0.292769	+	0.956183i	$0.594577\pi$
$182$	1.21723e20	−	5.05291e21i	0.0411809	−	1.70948i
$183$	1.10915e20	+	1.31472e21i	0.0356207	+	0.422228i
$184$	4.12112e21	+	2.98292e20i	1.25674	+	0.0909646i
$185$			1.23519e21i			0.357769i
$186$	3.45023e21	−	2.07538e20i	0.949457	−	0.0571116i
$187$		−	4.61384e21i		−	1.20661i
$188$	−8.11045e20	−	3.90984e19i	−0.201625	−	0.00971985i
$189$	−4.03845e21	+	1.04192e21i	−0.954612	+	0.246290i
$190$	−3.27558e21	−	7.89078e19i	−0.736425	−	0.0177403i
$191$	5.73042e21			1.22566			0.612829	−	0.790216i	$-0.290031\pi$
$191$	5.73042e21			1.22566			0.612829	+	0.790216i	$0.290031\pi$
$192$	2.96310e20	−	4.90423e21i	0.0603093	−	0.998180i
$193$	−4.68313e20			−0.0907282			−0.0453641	−	0.998971i	$-0.514445\pi$
$193$	−4.68313e20			−0.0907282			−0.0453641	+	0.998971i	$0.514445\pi$
$194$	2.40838e20	+	5.80173e18i	0.0444231	+	0.00107014i
$195$	−1.23769e22	+	1.04416e21i	−2.17412	+	0.183417i
$196$	1.67479e20	+	8.07374e18i	0.0280239	+	0.00135096i
$197$			1.11167e22i			1.77234i	0.463359	+	0.886171i	$0.346644\pi$
$197$			1.11167e22i			1.77234i	−0.463359	+	0.886171i	$0.653356\pi$
$198$	5.90818e21	−	8.58180e20i	0.897707	−	0.130394i
$199$		−	7.45260e20i		−	0.107945i	−0.998542	−	0.0539726i	$-0.982812\pi$
$199$		−	7.45260e20i		−	0.107945i	0.998542	−	0.0539726i	$-0.0171884\pi$
$200$	−4.20583e21	−	3.04423e20i	−0.580854	−	0.0420429i
$201$	1.10948e22	−	9.36001e20i	1.46136	−	0.123286i
$202$	−2.49357e20	+	1.03512e22i	−0.0313317	+	1.30062i
$203$	9.84327e21			1.18012
$204$	1.16173e22	−	4.18338e20i	1.32928	−	0.0478675i
$205$	−1.94223e21			−0.212148
$206$	−1.54632e20	+	6.41898e21i	−0.0161272	+	0.669464i
$207$	−1.24715e22	+	2.11936e21i	−1.24222	+	0.211100i
$208$	−1.81448e22	−	1.75350e21i	−1.72644	−	0.166842i
$209$		−	5.84330e21i		−	0.531212i
$210$	8.57084e20	+	1.42487e22i	0.0744629	+	1.23791i
$211$			2.20994e22i			1.83525i	0.397442	+	0.917627i	$0.369898\pi$
$211$			2.20994e22i			1.83525i	−0.397442	+	0.917627i	$0.630102\pi$
$212$	5.83033e20	−	1.20943e22i	0.0462916	−	0.960259i
$213$	−3.93475e20	−	4.66402e21i	−0.0298752	−	0.354123i
$214$	1.05304e22	+	2.53675e20i	0.764742	+	0.0184224i
$215$	1.04975e22			0.729323
$216$	2.69652e21	+	1.47985e22i	0.179264	+	0.983801i
$217$	−1.47383e22			−0.937735
$218$	−2.68652e22	−	6.47176e20i	−1.63626	−	0.0394172i
$219$	−8.15021e20	−	9.66079e21i	−0.0475280	−	0.563370i
$220$	9.83894e20	−	2.04096e22i	0.0549456	−	1.13977i
$221$		−	4.31315e22i		−	2.30711i
$222$	−3.33248e20	−	5.54010e21i	−0.0170771	−	0.283899i
$223$		−	8.60037e21i		−	0.422300i	−0.977454	−	0.211150i	$-0.932279\pi$
$223$		−	8.60037e21i		−	0.422300i	0.977454	−	0.211150i	$-0.0677208\pi$
$224$	−2.51678e21	+	2.07979e22i	−0.118437	+	0.978732i
$225$	1.27278e22	−	2.16293e21i	0.574142	−	0.0975681i
$226$	−6.01592e20	+	2.49729e22i	−0.0260179	+	1.08004i
$227$	3.63110e22			1.50589			0.752944	−	0.658084i	$-0.228633\pi$
$227$	3.63110e22			1.50589			0.752944	+	0.658084i	$0.228633\pi$
$228$	1.47129e22	−	5.29812e20i	0.585219	−	0.0210737i
$229$	9.72721e20			0.0371151			0.0185576	−	0.999828i	$-0.494093\pi$
$229$	9.72721e20			0.0371151			0.0185576	+	0.999828i	$0.494093\pi$
$230$	−1.04269e21	+	4.32837e22i	−0.0381717	+	1.58456i
$231$	−2.53666e22	+	2.14003e21i	−0.891146	+	0.0751805i
$232$	2.56291e21	−	3.54085e22i	0.0864168	−	1.19391i
$233$			8.01140e21i			0.259315i	0.991559	+	0.129657i	$0.0413877\pi$
$233$			8.01140e21i			0.259315i	−0.991559	+	0.129657i	$0.958612\pi$
$234$	5.52314e22	−	8.02252e21i	1.71647	−	0.249322i
$235$		−	8.50841e21i		−	0.253924i
$236$	−3.81405e22	−	1.83866e21i	−1.09326	−	0.0527032i
$237$	1.03484e22	−	8.73031e20i	0.284947	−	0.0240392i
$238$	−4.95536e22	−	1.19373e21i	−1.31097	−	0.0315810i
$239$	−3.97416e22			−1.01033			−0.505167	−	0.863021i	$-0.668569\pi$
$239$	−3.97416e22			−1.01033			−0.505167	+	0.863021i	$0.668569\pi$
$240$	5.14789e22	+	6.26826e20i	1.25783	+	0.0153158i
$241$	1.06153e22			0.249327			0.124664	−	0.992199i	$-0.460215\pi$
$241$	1.06153e22			0.249327			0.124664	+	0.992199i	$0.460215\pi$
$242$	−7.84129e21	−	1.88895e20i	−0.177069	−	0.00426554i
$243$	−1.88133e22	−	4.20352e22i	−0.408512	−	0.912753i
$244$	−2.02668e22	−	9.77012e20i	−0.423236	−	0.0204031i
$245$			1.75697e21i			0.0352928i
$246$	8.71130e21	−	5.24001e20i	0.168345	−	0.0101263i
$247$		−	5.46248e22i		−	1.01571i
$248$	−3.83744e21	+	5.30171e22i	−0.0686675	+	0.948692i
$249$	−4.42006e21	−	5.23928e22i	−0.0761262	−	0.902356i
$250$	−7.63095e20	+	3.16772e22i	−0.0126517	+	0.525190i
$251$	3.89337e22			0.621478			0.310739	−	0.950495i	$-0.399424\pi$
$251$	3.89337e22			0.621478			0.310739	+	0.950495i	$0.399424\pi$
$252$	−7.68841e21	−	6.36770e22i	−0.118177	−	0.978763i
$253$	−7.72137e22			−1.14301
$254$	1.97887e21	−	8.21457e22i	0.0282161	−	1.17129i
$255$	1.02400e22	+	1.21379e23i	0.140660	+	1.66730i
$256$	7.41596e22	+	1.44686e22i	0.981494	+	0.191491i
$257$			2.70174e22i			0.344571i	0.985047	+	0.172286i	$0.0551152\pi$
$257$			2.70174e22i			0.344571i	−0.985047	+	0.172286i	$0.944885\pi$
$258$	−4.70834e22	+	2.83216e21i	−0.578737	+	0.0348121i
$259$			2.36656e22i			0.280394i
$260$	9.19773e21	−	1.90795e23i	0.105059	−	2.17931i
$261$	1.82095e22	+	1.07154e23i	0.200546	+	1.18012i
$262$	1.03771e23	+	2.49981e21i	1.10208	+	0.0265488i
$263$	6.60917e22			0.676966			0.338483	−	0.940972i	$-0.390086\pi$
$263$	6.60917e22			0.676966			0.338483	+	0.940972i	$0.390086\pi$
$264$	1.09341e21	+	9.18068e22i	0.0108030	+	0.907063i
$265$	1.26877e23			1.20934
$266$	−6.27581e22	−	1.51183e21i	−0.577158	−	0.0139036i
$267$	−6.61548e22	+	5.58108e21i	−0.587090	+	0.0495292i
$268$	−8.24495e21	+	1.71031e23i	−0.0706167	+	1.46485i
$269$			7.86477e22i			0.650188i	0.945682	+	0.325094i	$0.105396\pi$
$269$			7.86477e22i			0.650188i	−0.945682	+	0.325094i	$0.894604\pi$
$270$	−1.53526e23	+	3.56895e22i	−1.22525	+	0.284829i
$271$			1.20519e23i			0.928640i	0.885667	+	0.464320i	$0.153701\pi$
$271$			1.20519e23i			0.928640i	−0.885667	+	0.464320i	$0.846299\pi$
$272$	−1.71965e22	+	1.77945e23i	−0.127949	+	1.32398i
$273$	−2.37135e23	+	2.00056e22i	−1.70392	+	0.143749i
$274$	4.47497e21	−	1.85763e23i	0.0310571	−	1.28922i
$275$	7.88008e22			0.528287
$276$	−7.00097e21	−	1.94418e23i	−0.0453443	−	1.25921i
$277$	1.96276e23			1.22832			0.614158	−	0.789183i	$-0.289496\pi$
$277$	1.96276e23			1.22832			0.614158	+	0.789183i	$0.289496\pi$
$278$	3.72852e21	−	1.54776e23i	0.0225481	−	0.936006i
$279$	−2.72650e22	−	1.60442e23i	−0.159355	−	0.937730i
$280$	−2.18948e23	−	1.58478e22i	−1.23692	−	0.0895296i
$281$			2.87625e23i			1.57079i	0.618997	+	0.785393i	$0.287539\pi$
$281$			2.87625e23i			1.57079i	−0.618997	+	0.785393i	$0.712461\pi$
$282$	2.29552e21	+	3.81620e22i	0.0121203	+	0.201495i
$283$			1.05764e23i			0.539966i	0.962865	+	0.269983i	$0.0870181\pi$
$283$			1.05764e23i			0.539966i	−0.962865	+	0.269983i	$0.912982\pi$
$284$	7.18976e22	+	3.46600e21i	0.354969	+	0.0171121i
$285$	1.29687e22	+	1.53724e23i	0.0619257	+	0.734031i
$286$	3.40556e23	+	8.20391e21i	1.57294	+	0.0378917i
$287$	−3.72119e22			−0.166266
$288$	−2.31063e23	+	1.10772e22i	−0.998853	+	0.0478854i
$289$	−1.83915e23			−0.769287
$290$	3.71891e23	+	8.95877e21i	1.50534	+	0.0362633i
$291$	−9.53532e20	−	1.13026e22i	−0.00373553	−	0.0442787i
$292$	1.48925e23	+	7.17928e21i	0.564715	+	0.0272235i
$293$		−	3.59809e23i		−	1.32078i	−0.750924	−	0.660388i	$-0.770392\pi$
$293$		−	3.59809e23i		−	1.32078i	0.750924	−	0.660388i	$-0.229608\pi$
$294$	−4.74020e20	−	7.88039e21i	−0.00168460	−	0.0280058i
$295$		−	4.00120e23i		−	1.37683i
$296$	8.51305e22	+	6.16186e21i	0.283670	+	0.0205324i
$297$	−7.02232e22	−	2.72183e23i	−0.226618	−	0.878365i
$298$	1.31014e22	−	5.43858e23i	0.0409509	−	1.69993i
$299$	−7.21816e23			−2.18550
$300$	7.14488e21	+	1.98414e23i	0.0209577	+	0.581996i
$301$	2.01126e23			0.571592
$302$	−5.79376e21	+	2.40508e23i	−0.0159549	+	0.662312i
$303$	4.85783e23	−	4.09825e22i	1.29639	−	0.109369i
$304$	−2.17789e22	+	2.25362e23i	−0.0563295	+	0.582883i
$305$		−	2.12613e23i		−	0.533017i
$306$	−7.86762e22	−	5.41650e23i	−0.191201	−	1.31633i
$307$		−	1.03483e23i		−	0.243812i	−0.992542	−	0.121906i	$-0.961099\pi$
$307$		−	1.03483e23i		−	0.243812i	0.992542	−	0.121906i	$-0.0389007\pi$
$308$	1.88508e22	−	3.91036e23i	0.0430625	−	0.893274i
$309$	3.01244e23	−	2.54141e22i	0.667288	−	0.0562950i
$310$	−5.56832e23	−	1.34139e22i	−1.19616	−	0.0288151i
$311$	3.37742e23			0.703657			0.351829	−	0.936064i	$-0.385560\pi$
$311$	3.37742e23			0.703657			0.351829	+	0.936064i	$0.385560\pi$
$312$	1.02215e22	+	8.58236e23i	0.0206560	+	1.73436i
$313$	−3.96626e23			−0.777517			−0.388759	−	0.921340i	$-0.627096\pi$
$313$	−3.96626e23			−0.777517			−0.388759	+	0.921340i	$0.627096\pi$
$314$	−4.19346e23	−	1.01019e22i	−0.797518	−	0.0192120i
$315$	6.62587e23	−	1.12598e23i	1.22262	−	0.207769i
$316$	−7.69027e21	+	1.59524e23i	−0.0137694	+	0.285627i
$317$		−	1.29287e23i		−	0.224642i	−0.993672	−	0.112321i	$-0.964172\pi$
$317$		−	1.29287e23i		−	0.224642i	0.993672	−	0.112321i	$-0.0358285\pi$
$318$	−5.69070e23	+	3.42306e22i	−0.959640	+	0.0577241i
$319$			6.63417e23i			1.08586i
$320$	−1.14016e23	+	7.83481e23i	−0.181151	+	1.24481i
$321$	−4.16922e22	−	4.94195e23i	−0.0643069	−	0.762256i
$322$	−1.99774e22	+	8.29290e23i	−0.0299163	+	1.24187i
$323$	−5.35702e23			−0.778931
$324$	6.78968e23	−	2.01495e23i	0.958675	−	0.284503i
$325$	7.36652e23			1.01011
$326$	−2.14682e22	+	8.91175e23i	−0.0285909	+	1.18685i
$327$	1.06365e23	+	1.26079e24i	0.137593	+	1.63095i
$328$	−9.68895e21	+	1.33860e23i	−0.0121752	+	0.168209i
$329$		−	1.63016e23i		−	0.199008i
$330$	−9.60331e23	+	5.77657e22i	−1.13904	+	0.0685153i
$331$		−	9.53400e23i		−	1.09878i	−0.835567	−	0.549388i	$-0.814861\pi$
$331$		−	9.53400e23i		−	1.09878i	0.835567	−	0.549388i	$-0.185139\pi$
$332$	8.07654e23	+	3.89350e22i	0.904511	+	0.0436042i
$333$	−2.57624e23	+	4.37800e22i	−0.280393	+	0.0476492i
$334$	1.23656e24	+	2.97883e22i	1.30804	+	0.0315104i
$335$	−1.79423e24			−1.84481
$336$	9.86306e23	+	1.20096e22i	0.985799	+	0.0120034i
$337$	−1.21491e24			−1.18048			−0.590242	−	0.807227i	$-0.700967\pi$
$337$	−1.21491e24			−1.18048			−0.590242	+	0.807227i	$0.700967\pi$
$338$	2.12538e24	+	5.11999e22i	2.00784	+	0.0483682i
$339$	1.17199e24	−	9.88733e22i	1.07653	−	0.0908201i
$340$	−1.87111e24	−	9.02015e22i	−1.67128	−	0.0805682i
$341$		−	9.93332e23i		−	0.862835i
$342$	−9.96412e22	−	6.85984e23i	−0.0841765	−	0.579517i
$343$			1.23348e24i			1.01353i
$344$	5.23675e22	−	7.23495e23i	0.0418559	−	0.578270i
$345$	2.03131e24	−	1.71369e23i	1.57941	−	0.133245i
$346$	6.62416e21	−	2.74978e23i	0.00501081	−	0.208006i
$347$	−1.67024e23			−0.122927			−0.0614637	−	0.998109i	$-0.519577\pi$
$347$	−1.67024e23			−0.122927			−0.0614637	+	0.998109i	$0.519577\pi$
$348$	−1.67043e24	+	6.01521e22i	−1.19626	+	0.0430772i
$349$	−1.48635e24			−1.03581			−0.517903	−	0.855439i	$-0.673287\pi$
$349$	−1.48635e24			−1.03581			−0.517903	+	0.855439i	$0.673287\pi$
$350$	2.03880e22	−	8.46335e23i	0.0138270	−	0.573979i
$351$	−6.56467e23	−	2.54445e24i	−0.433307	−	1.67948i
$352$	−1.40174e24	−	1.69626e23i	−0.900558	−	0.108977i
$353$			1.33257e24i			0.833356i	0.909054	+	0.416678i	$0.136806\pi$
$353$			1.33257e24i			0.833356i	−0.909054	+	0.416678i	$0.863194\pi$
$354$	1.07950e23	+	1.79462e24i	0.0657191	+	1.09255i
$355$			7.54255e23i			0.447043i
$356$	4.91620e22	−	1.01980e24i	0.0283697	−	0.588492i
$357$	1.96193e23	+	2.32556e24i	0.110239	+	1.30671i
$358$	4.07125e23	+	9.80754e21i	0.222761	+	0.00536626i
$359$	8.93250e23			0.475966			0.237983	−	0.971269i	$-0.423514\pi$
$359$	8.93250e23			0.475966			0.237983	+	0.971269i	$0.423514\pi$
$360$	−2.32523e23	−	2.41280e24i	−0.120668	−	1.25212i
$361$	1.29997e24			0.657074
$362$	−1.18894e24	−	2.86413e22i	−0.585369	−	0.0141014i
$363$	3.10454e22	+	3.67994e23i	0.0148896	+	0.176493i
$364$	1.76223e23	−	3.65552e24i	0.0823379	−	1.70799i
$365$			1.56232e24i			0.711194i
$366$	5.73617e22	+	9.53614e23i	0.0254420	+	0.422963i
$367$		−	2.44161e24i		−	1.05523i	−0.849482	−	0.527617i	$-0.823086\pi$
$367$		−	2.44161e24i		−	1.05523i	0.849482	−	0.527617i	$-0.176914\pi$
$368$	2.97795e24	+	2.87787e23i	1.25419	+	0.121204i
$369$	−6.88400e22	−	4.05091e23i	−0.0282547	−	0.166265i
$370$	−2.15390e22	+	8.94116e23i	−0.00861607	+	0.357666i
$371$	2.43089e24			0.947792
$372$	2.50113e24	−	9.00656e22i	0.950557	−	0.0342295i
$373$	−2.28948e24			−0.848208			−0.424104	−	0.905614i	$-0.639411\pi$
$373$	−2.28948e24			−0.848208			−0.424104	+	0.905614i	$0.639411\pi$
$374$	8.04551e22	−	3.33981e24i	0.0290585	−	1.20626i
$375$	1.48662e24	−	1.25417e23i	0.523483	−	0.0441631i
$376$	−5.86407e23	−	4.24449e22i	−0.201333	−	0.0145727i
$377$			6.20181e24i			2.07623i
$378$	−2.94147e24	+	6.83789e23i	−0.960267	+	0.223229i
$379$		−	1.54554e24i		−	0.492049i	−0.969264	−	0.246024i	$-0.920876\pi$
$379$		−	1.54554e24i		−	0.492049i	0.969264	−	0.246024i	$-0.0791243\pi$
$380$	−2.36971e24	−	1.14238e23i	−0.735784	−	0.0354703i
$381$	−3.85512e24	+	3.25233e23i	−1.16748	+	0.0984934i
$382$	4.14806e24	+	9.99258e22i	1.22530	+	0.0295172i
$383$	−3.84431e24			−1.10772			−0.553860	−	0.832610i	$-0.686846\pi$
$383$	−3.84431e24			−1.10772			−0.553860	+	0.832610i	$0.686846\pi$
$384$	3.00008e23	−	3.54484e24i	0.0843307	−	0.996438i
$385$	4.10223e24			1.12498
$386$	−3.38997e23	−	8.16634e21i	−0.0907018	−	0.00218498i
$387$	3.72071e23	+	2.18946e24i	0.0971341	+	0.571588i
$388$	1.74234e23	+	8.39937e21i	0.0443845	+	0.00213966i
$389$		−	5.52482e24i		−	1.37340i	−0.726941	−	0.686700i	$-0.759059\pi$
$389$		−	5.52482e24i		−	1.37340i	0.726941	−	0.686700i	$-0.240941\pi$
$390$	−8.97745e24	+	5.40011e23i	−2.17791	+	0.131005i
$391$			7.07880e24i			1.67602i
$392$	1.21092e23	+	8.76478e21i	0.0279832	+	0.00202546i
$393$	−4.10851e23	−	4.86999e24i	−0.0926734	−	1.09850i
$394$	−1.93851e23	+	8.04703e24i	−0.0426829	+	1.77183i
$395$	−1.67352e24			−0.359715
$396$	4.29170e24	−	5.18183e23i	0.900587	−	0.108737i
$397$	2.18751e24			0.448168			0.224084	−	0.974570i	$-0.428061\pi$
$397$	2.18751e24			0.448168			0.224084	+	0.974570i	$0.428061\pi$
$398$	1.29957e22	−	5.39469e23i	0.00259962	−	0.107914i
$399$	2.48473e23	+	2.94526e24i	0.0485330	+	0.575282i
$400$	−3.03916e24	−	2.93702e23i	−0.579673	−	0.0560193i
$401$		−	1.51889e24i		−	0.282914i	−0.989944	−	0.141457i	$-0.954821\pi$
$401$		−	1.51889e24i		−	0.282914i	0.989944	−	0.141457i	$-0.0451786\pi$
$402$	8.04750e24	−	4.84072e23i	1.46391	−	0.0880567i
$403$		−	9.28596e24i		−	1.64979i
$404$	−3.61003e23	+	7.48852e24i	−0.0626451	+	1.29949i
$405$	2.45150e24	+	7.00465e24i	0.415536	+	1.18731i
$406$	7.12522e24	+	1.71645e23i	1.17978	+	0.0284206i
$407$	−1.59501e24			−0.257998
$408$	8.41666e24	−	1.00241e23i	1.33005	−	0.0158408i
$409$	3.51164e24			0.542174			0.271087	−	0.962555i	$-0.412617\pi$
$409$	3.51164e24			0.542174			0.271087	+	0.962555i	$0.412617\pi$
$410$	−1.40591e24	−	3.38681e22i	−0.212086	−	0.00510910i
$411$	−8.71789e24	+	7.35475e23i	−1.28503	+	0.108410i
$412$	−2.23865e23	+	4.64379e24i	−0.0322451	+	0.668882i
$413$		−	7.66607e24i		−	1.07906i
$414$	−9.06464e24	+	1.31666e24i	−1.24694	+	0.181122i
$415$			8.47284e24i			1.13913i
$416$	−1.31039e25	−	1.58571e24i	−1.72192	−	0.208371i
$417$	−7.26369e24	+	6.12793e23i	−0.932964	+	0.0787084i
$418$	1.01894e23	−	4.22977e24i	0.0127931	−	0.531058i
$419$	1.23815e25			1.51964			0.759818	−	0.650136i	$-0.225288\pi$
$419$	1.23815e25			1.51964			0.759818	+	0.650136i	$0.225288\pi$
$420$	3.71950e23	+	1.03291e25i	0.0446289	+	1.23935i
$421$	−5.94793e24			−0.697728			−0.348864	−	0.937173i	$-0.613433\pi$
$421$	−5.94793e24			−0.697728			−0.348864	+	0.937173i	$0.613433\pi$
$422$	−3.85364e23	+	1.59970e25i	−0.0441980	+	1.83472i
$423$	1.77460e24	−	3.01571e23i	0.199007	−	0.0338186i
$424$	6.32936e23	−	8.74447e24i	0.0694039	−	0.958866i
$425$		−	7.22430e24i		−	0.774641i
$426$	−2.03493e23	−	3.38299e24i	−0.0213383	−	0.354740i
$427$		−	4.07354e24i		−	0.417741i
$428$	7.61820e24	+	3.67254e23i	0.764076	+	0.0368342i
$429$	−1.34834e24	−	1.59824e25i	−0.132268	−	1.56782i
$430$	7.59878e24	+	1.83053e23i	0.729111	+	0.0175641i
$431$	1.64433e25			1.54331			0.771657	−	0.636039i	$-0.219428\pi$
$431$	1.64433e25			1.54331			0.771657	+	0.636039i	$0.219428\pi$
$432$	1.69387e24	+	1.07592e25i	0.155520	+	0.987833i
$433$	7.44009e24			0.668257			0.334128	−	0.942528i	$-0.391558\pi$
$433$	7.44009e24			0.668257			0.334128	+	0.942528i	$0.391558\pi$
$434$	−1.06686e25	−	2.57003e23i	−0.937463	−	0.0225832i
$435$	−1.47240e24	−	1.74530e25i	−0.126584	−	1.50045i
$436$	−1.94356e25	−	9.36939e23i	−1.63484	−	0.0788115i
$437$			8.96509e24i			0.737872i
$438$	−4.21505e23	−	7.00734e24i	−0.0339468	−	0.564351i
$439$		−	2.38017e24i		−	0.187583i	−0.995592	−	0.0937917i	$-0.970101\pi$
$439$		−	2.38017e24i		−	0.187583i	0.995592	−	0.0937917i	$-0.0298988\pi$
$440$	1.06811e24	−	1.47567e25i	0.0823786	−	1.13812i
$441$	−3.66452e23	+	6.22738e22i	−0.0276599	+	0.00470044i
$442$	7.52118e23	−	3.12215e25i	0.0555616	−	2.30644i
$443$	−1.57422e25			−1.13823			−0.569116	−	0.822257i	$-0.692715\pi$
$443$	−1.57422e25			−1.13823			−0.569116	+	0.822257i	$0.692715\pi$
$444$	−1.44620e23	−	4.01611e24i	−0.0102350	−	0.284228i
$445$	1.06984e25			0.741138
$446$	1.49971e23	−	6.22553e24i	0.0101701	−	0.422177i
$447$	−2.55234e25	+	2.15325e24i	−1.69441	+	0.142947i
$448$	−2.18448e24	+	1.50110e25i	−0.141974	+	0.975596i
$449$		−	9.43470e24i		−	0.600327i	−0.953888	−	0.300164i	$-0.902959\pi$
$449$		−	9.43470e24i		−	0.600327i	0.953888	−	0.300164i	$-0.0970413\pi$
$450$	9.25096e24	−	1.34373e24i	0.576325	−	0.0837129i
$451$		−	2.50801e24i		−	0.152986i
$452$	−8.70945e23	+	1.80666e25i	−0.0520207	+	1.07910i
$453$	1.12871e25	−	9.52222e23i	0.660159	−	0.0556936i
$454$	2.62844e25	+	6.33184e23i	1.50545	+	0.0362659i
$455$	3.83489e25			2.15102
$456$	1.06595e25	−	1.26953e23i	0.585557	−	0.00697391i
$457$	−1.53829e25			−0.827627			−0.413814	−	0.910362i	$-0.635803\pi$
$457$	−1.53829e25			−0.827627			−0.413814	+	0.910362i	$0.635803\pi$
$458$	7.04121e23	+	1.69621e22i	0.0371044	+	0.000893835i
$459$	−2.49532e25	+	6.43792e24i	−1.28797	+	0.332296i
$460$	−1.50954e24	+	3.13134e25i	−0.0763213	+	1.58318i
$461$			2.28093e25i			1.12967i	0.825203	+	0.564836i	$0.191061\pi$
$461$			2.28093e25i			1.12967i	−0.825203	+	0.564836i	$0.808939\pi$
$462$	−1.83994e25	+	1.10676e24i	−0.892698	+	0.0536975i
$463$			1.55149e25i			0.737445i	0.929540	+	0.368722i	$0.120205\pi$
$463$			1.55149e25i			0.737445i	−0.929540	+	0.368722i	$0.879795\pi$
$464$	2.47266e24	−	2.55864e25i	0.115144	−	1.19148i
$465$	2.20462e24	+	2.61323e25i	0.100584	+	1.19227i
$466$	−1.39701e23	+	5.79919e24i	−0.00624501	+	0.259239i
$467$	1.30353e25			0.570967			0.285483	−	0.958384i	$-0.407846\pi$
$467$	1.30353e25			0.570967			0.285483	+	0.958384i	$0.407846\pi$
$468$	4.01201e25	−	4.84413e24i	1.72197	−	0.207912i
$469$	−3.43764e25			−1.44583
$470$	1.48368e23	−	6.15896e24i	0.00611519	−	0.253850i
$471$	1.66028e24	+	1.96800e25i	0.0670630	+	0.794926i
$472$	−2.75766e25	−	1.99603e24i	−1.09167	−	0.0790166i
$473$			1.35555e25i			0.525937i
$474$	7.50609e24	−	4.51506e23i	0.285443	−	0.0171699i
$475$		−	9.14936e24i		−	0.341037i
$476$	−3.58494e25	−	1.72821e24i	−1.30983	−	0.0631437i
$477$	4.49701e24	+	2.64627e25i	0.161064	+	0.947786i
$478$	−2.87676e25	−	6.93005e23i	−1.01004	−	0.0243316i
$479$	−5.61374e25			−1.93226			−0.966128	−	0.258064i	$-0.916915\pi$
$479$	−5.61374e25			−1.93226			−0.966128	+	0.258064i	$0.916915\pi$
$480$	3.72529e25	+	1.35142e24i	1.25710	+	0.0456034i
$481$	−1.49106e25			−0.493308
$482$	7.68405e24	+	1.85107e23i	0.249255	+	0.00600448i
$483$	3.89188e25	−	3.28334e24i	1.23783	−	0.104428i
$484$	−5.67276e24	−	2.73469e23i	−0.176915	−	0.00852860i
$485$			1.82783e24i			0.0558972i
$486$	−1.28853e25	−	3.07560e25i	−0.386412	−	0.922326i
$487$			1.26544e25i			0.372149i	0.982536	+	0.186074i	$0.0595766\pi$
$487$			1.26544e25i			0.372149i	−0.982536	+	0.186074i	$0.940423\pi$
$488$	−1.46535e25	−	1.06064e24i	−0.422622	−	0.0305899i
$489$	4.18231e25	−	3.52836e24i	1.18299	−	0.0998017i
$490$	−3.06377e22	+	1.27181e24i	−0.000849949	+	0.0352826i
$491$	4.38161e25			1.19223			0.596114	−	0.802900i	$-0.296711\pi$
$491$	4.38161e25			1.19223			0.596114	+	0.802900i	$0.296711\pi$
$492$	6.31496e24	−	2.27402e23i	0.168540	−	0.00606911i
$493$	6.08207e25			1.59223
$494$	9.52536e23	−	3.95411e25i	0.0244611	−	1.01541i
$495$	7.58890e24	+	4.46571e25i	0.191174	+	1.12497i
$496$	−3.70230e24	+	3.83104e25i	−0.0914947	+	0.946763i
$497$			1.44511e25i			0.350360i
$498$	−2.28592e24	−	3.80025e25i	−0.0543729	−	0.903927i
$499$		−	3.41028e25i		−	0.795857i	−0.917416	−	0.397929i	$-0.869729\pi$
$499$		−	3.41028e25i		−	0.795857i	0.917416	−	0.397929i	$-0.130271\pi$
$500$	−1.10476e24	+	2.29168e25i	−0.0252961	+	0.524733i
$501$	−4.89579e24	−	5.80319e25i	−0.109993	−	1.30379i
$502$	2.81828e25	+	6.78918e23i	0.621297	+	0.0149669i
$503$	4.83016e24			0.104488			0.0522439	−	0.998634i	$-0.483363\pi$
$503$	4.83016e24			0.104488			0.0522439	+	0.998634i	$0.483363\pi$
$504$	−4.45500e24	−	4.62278e25i	−0.0945709	−	0.981326i
$505$	−7.85597e25			−1.63656
$506$	−5.58925e25	−	1.34643e24i	−1.14268	−	0.0275268i
$507$	−8.41485e24	−	9.97447e25i	−0.168838	−	2.00131i
$508$	2.86488e24	−	5.94281e25i	0.0564158	−	1.17027i
$509$			1.34104e25i			0.259192i	0.991567	+	0.129596i	$0.0413681\pi$
$509$			1.34104e25i			0.259192i	−0.991567	+	0.129596i	$0.958632\pi$
$510$	5.29584e24	+	8.80412e25i	0.100466	+	1.67020i
$511$			2.99332e25i			0.557383i
$512$	5.34294e25	+	1.17665e25i	0.976598	+	0.215072i
$513$	−3.16025e25	+	8.15344e24i	−0.567031	+	0.146294i
$514$	−4.71123e23	+	1.95570e25i	−0.00829822	+	0.344471i
$515$	−4.87166e25			−0.842380
$516$	−3.41316e25	+	1.22908e24i	−0.579407	+	0.0208644i
$517$	1.09870e25			0.183112
$518$	−4.12675e23	+	1.71307e25i	−0.00675267	+	0.280313i
$519$	−1.29048e25	+	1.08870e24i	−0.207330	+	0.0174911i
$520$	9.98497e24	−	1.37950e26i	0.157513	−	2.17615i
$521$		−	5.58594e25i		−	0.865242i	−0.901576	−	0.432621i	$-0.857589\pi$
$521$		−	5.58594e25i		−	0.865242i	0.901576	−	0.432621i	$-0.142411\pi$
$522$	1.13127e25	+	7.78830e25i	0.172067	+	1.18460i
$523$		−	7.02715e25i		−	1.04957i	−0.851233	−	0.524787i	$-0.824145\pi$
$523$		−	7.02715e25i		−	1.04957i	0.851233	−	0.524787i	$-0.175855\pi$
$524$	7.50726e25	+	3.61906e24i	1.10112	+	0.0530822i
$525$	−3.97187e25	+	3.35083e24i	−0.572113	+	0.0482657i
$526$	4.78416e25	+	1.15249e24i	0.676770	+	0.0163032i
$527$	−9.10667e25			−1.26520
$528$	−8.09424e23	+	6.64750e25i	−0.0110447	+	0.907060i
$529$	4.38498e25			0.587677
$530$	9.18421e25	+	2.21245e24i	1.20899	+	0.0291241i
$531$	8.34531e25	−	1.41818e25i	1.07906	−	0.183372i
$532$	−4.54022e25	−	2.18872e24i	−0.576655	−	0.0277991i
$533$		−	2.34456e25i		−	0.292518i
$534$	−4.79846e25	+	2.88637e24i	−0.588112	+	0.0353761i
$535$			7.99201e25i			0.962266i
$536$	−8.95065e24	+	1.23660e26i	−0.105874	+	1.46273i
$537$	−1.61190e24	−	1.91065e25i	−0.0187319	−	0.222037i
$538$	−1.37144e24	+	5.69305e25i	−0.0156583	+	0.650000i
$539$	−2.26879e24			−0.0254507
$540$	−1.11755e26	+	2.31573e25i	−1.23176	+	0.255239i
$541$	1.58666e26			1.71835			0.859174	−	0.511684i	$-0.170978\pi$
$541$	1.58666e26			1.71835			0.859174	+	0.511684i	$0.170978\pi$
$542$	−2.10158e24	+	8.72398e25i	−0.0223642	+	0.928371i
$543$	4.70729e24	+	5.57974e25i	0.0492235	+	0.583466i
$544$	−1.55509e25	+	1.28509e26i	−0.159796	+	1.32051i
$545$		−	2.03892e26i		−	2.05889i
$546$	−1.72003e26	+	1.03463e25i	−1.70689	+	0.102673i
$547$			2.32297e25i			0.226550i	0.993564	+	0.113275i	$0.0361341\pi$
$547$			2.32297e25i			0.226550i	−0.993564	+	0.113275i	$0.963866\pi$
$548$	6.47858e24	−	1.34389e26i	0.0620961	−	1.28810i
$549$	4.43447e25	−	7.53582e24i	0.417738	−	0.0709893i
$550$	5.70413e25	+	1.37411e24i	0.528134	+	0.0127226i
$551$	7.70277e25			0.700981
$552$	−1.67756e24	−	1.40855e26i	−0.0150058	−	1.25994i
$553$	−3.20637e25			−0.281919
$554$	1.42078e26	+	3.42262e24i	1.22796	+	0.0295812i
$555$	4.19611e25	−	3.54000e24i	0.356503	−	0.0300760i
$556$	5.39791e24	−	1.11972e26i	0.0450832	−	0.935192i
$557$			6.00718e25i			0.493226i	0.969114	+	0.246613i	$0.0793177\pi$
$557$			6.00718e25i			0.493226i	−0.969114	+	0.246613i	$0.920682\pi$
$558$	−1.69385e25	−	1.16614e26i	−0.136726	−	0.941295i
$559$			1.26720e26i			1.00562i
$560$	−1.58213e26	−	1.52896e25i	−1.23440	−	0.119292i
$561$	−1.56738e26	+	1.32230e25i	−1.20234	+	0.101434i
$562$	−5.01555e24	+	2.08203e26i	−0.0378289	+	1.57033i
$563$	−3.07397e25			−0.227966			−0.113983	−	0.993483i	$-0.536361\pi$
$563$	−3.07397e25			−0.227966			−0.113983	+	0.993483i	$0.536361\pi$
$564$	9.96190e23	+	2.76643e25i	0.00726425	+	0.201729i
$565$	−1.89531e26			−1.35900
$566$	−1.84429e24	+	7.65590e25i	−0.0130039	+	0.539809i
$567$	4.69693e25	+	1.34205e26i	0.325668	+	0.930529i
$568$	5.19839e25	+	3.76266e24i	0.354454	+	0.0256558i
$569$			9.86106e25i			0.661237i	0.943765	+	0.330618i	$0.107257\pi$
$569$			9.86106e25i			0.661237i	−0.943765	+	0.330618i	$0.892743\pi$
$570$	6.70703e24	+	1.11502e26i	0.0442302	+	0.735309i
$571$		−	2.92044e26i		−	1.89411i	−0.321075	−	0.947054i	$-0.604044\pi$
$571$		−	2.92044e26i		−	1.89411i	0.321075	−	0.947054i	$-0.395956\pi$
$572$	2.46374e26	+	1.18771e25i	1.57157	+	0.0757613i
$573$	−1.64231e25	−	1.94670e26i	−0.103035	−	1.22132i
$574$	−2.69365e25	−	6.48894e23i	−0.166218	−	0.00400415i
$575$	−1.20900e26			−0.733808
$576$	−1.67452e26	+	3.98923e24i	−0.999716	+	0.0238164i
$577$	2.73567e26			1.60655			0.803275	−	0.595609i	$-0.203089\pi$
$577$	2.73567e26			1.60655			0.803275	+	0.595609i	$0.203089\pi$
$578$	−1.33130e26	−	3.20707e24i	−0.769064	−	0.0185265i
$579$	1.34216e24	+	1.59092e25i	0.00762708	+	0.0904070i
$580$	2.69044e26	+	1.29699e25i	1.50403	+	0.0725056i
$581$			1.62335e26i			0.892768i
$582$	−4.93138e23	−	8.19822e24i	−0.00266809	−	0.0443559i
$583$			1.63837e26i			0.872089i
$584$	1.07676e26	+	7.79376e24i	0.563896	+	0.0408155i
$585$	7.09432e25	+	4.17467e26i	0.365536	+	2.15101i
$586$	6.27426e24	−	2.60454e26i	0.0318079	−	1.32039i
$587$	−3.14699e26			−1.56976			−0.784880	−	0.619647i	$-0.787276\pi$
$587$	−3.14699e26			−1.56976			−0.784880	+	0.619647i	$0.787276\pi$
$588$	−2.05711e23	−	5.71262e24i	−0.00100966	−	0.0280382i
$589$	−1.15333e26			−0.557006
$590$	6.97721e24	−	2.89634e26i	0.0331579	−	1.37643i
$591$	3.77649e26	−	3.18599e25i	1.76607	−	0.148992i
$592$	6.15158e25	+	5.94485e24i	0.283094	+	0.0273580i
$593$			3.21121e26i			1.45429i	0.686487	+	0.727143i	$0.259152\pi$
$593$			3.21121e26i			1.45429i	−0.686487	+	0.727143i	$0.740848\pi$
$594$	−4.60860e25	−	1.98249e26i	−0.205399	−	0.883567i
$595$		−	3.76084e26i		−	1.64958i
$596$	1.89674e25	−	3.93453e26i	0.0818781	−	1.69845i
$597$	−2.53174e25	+	2.13588e24i	−0.107563	+	0.00907445i
$598$	−5.22499e26	−	1.25869e25i	−2.18486	−	0.0526328i
$599$	−1.23579e26			−0.508616			−0.254308	−	0.967123i	$-0.581848\pi$
$599$	−1.23579e26			−0.508616			−0.254308	+	0.967123i	$0.581848\pi$
$600$	1.71204e24	+	1.43750e26i	0.00693551	+	0.582332i
$601$	2.80304e26			1.11769			0.558846	−	0.829272i	$-0.311244\pi$
$601$	2.80304e26			1.11769			0.558846	+	0.829272i	$0.311244\pi$
$602$	1.45588e26	+	3.50718e24i	0.571426	+	0.0137655i
$603$	−6.35943e25	−	3.74223e26i	−0.245699	−	1.44582i
$604$	−8.38783e24	+	1.73994e26i	−0.0319006	+	0.661736i
$605$		−	5.95111e25i		−	0.222804i
$606$	3.52357e26	−	2.11949e25i	1.29865	−	0.0781164i
$607$			1.20549e26i			0.437392i	0.975793	+	0.218696i	$0.0701802\pi$
$607$			1.20549e26i			0.437392i	−0.975793	+	0.218696i	$0.929820\pi$
$608$	−1.96948e25	+	1.62752e26i	−0.0703506	+	0.581357i
$609$	−2.82103e25	−	3.34389e26i	−0.0992073	−	1.17595i
$610$	3.70750e24	−	1.53903e26i	0.0128365	−	0.532862i
$611$	1.02709e26			0.350121
$612$	−4.75060e25	−	3.93455e26i	−0.159445	−	1.32055i
$613$	−5.12821e26			−1.69469			−0.847347	−	0.531040i	$-0.821802\pi$
$613$	−5.12821e26			−1.69469			−0.847347	+	0.531040i	$0.821802\pi$
$614$	1.80452e24	−	7.49082e25i	0.00587167	−	0.243742i
$615$	5.56632e24	+	6.59799e25i	0.0178342	+	0.211397i
$616$	2.04643e25	−	2.82729e26i	0.0645625	−	0.891978i
$617$		−	2.33232e26i		−	0.724568i	−0.932068	−	0.362284i	$-0.881997\pi$
$617$		−	2.33232e26i		−	0.724568i	0.932068	−	0.362284i	$-0.118003\pi$
$618$	2.18504e26	−	1.31434e25i	0.668450	−	0.0402085i
$619$			3.81573e26i			1.14952i	0.818322	+	0.574761i	$0.194905\pi$
$619$			3.81573e26i			1.14952i	−0.818322	+	0.574761i	$0.805095\pi$
$620$	−4.02839e26	−	1.94198e25i	−1.19512	−	0.0576135i
$621$	1.07740e26	+	4.17597e26i	0.314780	+	1.22008i
$622$	2.44480e26	+	5.88947e24i	0.703453	+	0.0169460i
$623$	2.04975e26			0.580852
$624$	−7.56673e24	+	6.21428e26i	−0.0211181	+	1.73435i
$625$	−4.52279e26			−1.24321
$626$	−2.87105e26	−	6.91628e24i	−0.777292	−	0.0187248i
$627$	−1.98504e26	+	1.67466e25i	−0.529332	+	0.0446565i
$628$	−3.03374e26	−	1.46249e25i	−0.796824	−	0.0384129i
$629$			1.46227e26i			0.378310i
$630$	4.81589e26	−	6.99522e25i	1.22727	−	0.178265i
$631$			4.50370e26i			1.13055i	0.824901	+	0.565277i	$0.191231\pi$
$631$			4.50370e26i			1.13055i	−0.824901	+	0.565277i	$0.808769\pi$
$632$	−8.34848e24	+	1.15340e26i	−0.0206441	+	0.285213i
$633$	7.50743e26	−	6.33356e25i	1.82876	−	0.154281i
$634$	2.25447e24	−	9.35864e25i	0.00541000	−	0.224577i
$635$	6.23441e26			1.47382
$636$	−4.12528e26	+	1.48551e25i	−0.960751	+	0.0345966i
$637$	−2.12093e25			−0.0486633
$638$	−1.15685e25	+	4.80226e26i	−0.0261506	+	1.08555i
$639$	−1.57315e26	+	2.67337e25i	−0.350358	+	0.0595389i
$640$	−9.61947e25	+	5.65148e26i	−0.211077	+	1.24009i
$641$		−	5.85256e25i		−	0.126530i	−0.997997	−	0.0632652i	$-0.979849\pi$
$641$		−	5.85256e25i		−	0.126530i	0.997997	−	0.0632652i	$-0.0201514\pi$
$642$	−2.15620e25	−	3.58459e26i	−0.0459310	−	0.763584i
$643$		−	7.20960e26i		−	1.51324i	−0.653856	−	0.756619i	$-0.726850\pi$
$643$		−	7.20960e26i		−	1.51324i	0.653856	−	0.756619i	$-0.273150\pi$
$644$	−2.89219e25	+	5.99947e26i	−0.0598152	+	1.24079i
$645$	−3.00852e25	−	3.56613e26i	−0.0613107	−	0.726741i
$646$	−3.87777e26	−	9.34145e24i	−0.778705	−	0.0187588i
$647$	−2.34600e26			−0.464235			−0.232118	−	0.972688i	$-0.574565\pi$
$647$	−2.34600e26			−0.464235			−0.232118	+	0.972688i	$0.574565\pi$
$648$	4.94996e26	−	1.34016e26i	0.965249	−	0.261333i
$649$	5.16678e26			0.992876
$650$	5.33239e26	+	1.28456e25i	1.00982	+	0.0243263i
$651$	4.22392e25	+	5.00679e26i	0.0788309	+	0.934416i
$652$	−3.10802e25	+	6.44718e26i	−0.0571652	+	1.18582i
$653$		−	5.12979e26i		−	0.929874i	−0.885344	−	0.464937i	$-0.846077\pi$
$653$		−	5.12979e26i		−	0.929874i	0.885344	−	0.464937i	$-0.153923\pi$
$654$	5.50089e25	+	9.14500e26i	0.0982753	+	1.63379i
$655$			7.87563e26i			1.38673i
$656$	−9.34773e24	+	9.67279e25i	−0.0162226	+	0.167867i
$657$	−3.25853e26	+	5.53746e25i	−0.557380	+	0.0947196i
$658$	2.84264e24	−	1.18002e26i	0.00479265	−	0.198950i
$659$	1.75891e25			0.0292303			0.0146151	−	0.999893i	$-0.495348\pi$
$659$	1.75891e25			0.0292303			0.0146151	+	0.999893i	$0.495348\pi$
$660$	−6.96159e26	+	2.50687e25i	−1.14036	+	0.0410643i
$661$	2.15333e26			0.347694			0.173847	−	0.984773i	$-0.444380\pi$
$661$	2.15333e26			0.347694			0.173847	+	0.984773i	$0.444380\pi$
$662$	1.66252e25	−	6.90135e26i	0.0264615	−	1.09846i
$663$	−1.46523e27	+	1.23613e26i	−2.29894	+	0.193948i
$664$	5.83956e26	+	4.22675e25i	0.903198	+	0.0653746i
$665$		−	4.76300e26i		−	0.726231i
$666$	−1.87249e26	+	2.71985e25i	−0.281459	+	0.0408827i
$667$		−	1.01785e27i		−	1.50830i
$668$	8.94583e26	+	4.31256e25i	1.30691	+	0.0630026i
$669$	−2.92166e26	+	2.46482e25i	−0.420805	+	0.0355007i
$670$	−1.29878e27	−	3.12874e25i	−1.84428	−	0.0444281i
$671$	2.74548e26			0.384375
$672$	7.13745e26	+	2.58923e25i	0.985224	+	0.0357407i
$673$	−1.14126e27			−1.55325			−0.776626	−	0.629961i	$-0.783071\pi$
$673$	−1.14126e27			−1.55325			−0.776626	+	0.629961i	$0.783071\pi$
$674$	−8.79433e26	−	2.11853e25i	−1.18014	−	0.0284293i
$675$	−1.09955e26	−	4.26181e26i	−0.145488	−	0.563908i
$676$	1.53760e27	+	7.41239e25i	2.00609	+	0.0967084i
$677$		−	1.06722e27i		−	1.37298i	−0.727141	−	0.686488i	$-0.759151\pi$
$677$		−	1.06722e27i		−	1.37298i	0.727141	−	0.686488i	$-0.240849\pi$
$678$	8.50087e26	−	5.11343e25i	1.07840	−	0.0648680i
$679$			3.50202e25i			0.0438082i
$680$	−1.35286e27	−	9.79219e25i	−1.66886	−	0.120794i
$681$	−1.04066e26	−	1.23353e27i	−0.126593	−	1.50056i
$682$	1.73215e25	−	7.19041e26i	0.0207795	−	0.862585i
$683$	1.20569e27			1.42640			0.713198	−	0.700963i	$-0.247246\pi$
$683$	1.20569e27			1.42640			0.713198	+	0.700963i	$0.247246\pi$
$684$	−6.01649e25	−	4.98299e26i	−0.0701957	−	0.581376i
$685$	1.40984e27			1.62222
$686$	−2.15091e25	+	8.92875e26i	−0.0244086	+	1.01324i
$687$	−2.78777e24	−	3.30446e25i	−0.00312009	−	0.0369838i
$688$	5.05233e25	−	5.22802e26i	0.0557701	−	0.577094i
$689$			1.53160e27i			1.66748i
$690$	1.47339e27	−	8.86272e25i	1.58216	−	0.0951701i
$691$		−	1.07225e27i		−	1.13567i	−0.823141	−	0.567836i	$-0.807781\pi$
$691$		−	1.07225e27i		−	1.13567i	0.823141	−	0.567836i	$-0.192219\pi$
$692$	9.59002e24	−	1.98932e26i	0.0100187	−	0.207825i
$693$	1.45399e26	+	8.55603e26i	0.149829	+	0.881671i
$694$	−1.20903e26	−	2.91253e24i	−0.122892	−	0.00296043i
$695$	1.17467e27			1.17777
$696$	−1.21022e27	+	1.44136e25i	−1.19695	+	0.0142555i
$697$	−2.29929e26			−0.224328
$698$	−1.07592e27	−	2.59186e25i	−1.03551	−	0.0249451i
$699$	2.72157e26	−	2.29603e25i	0.258397	−	0.0217993i
$700$	2.95164e25	−	6.12279e26i	0.0276460	−	0.573480i
$701$		−	2.03381e26i		−	0.187927i	−0.995576	−	0.0939633i	$-0.970046\pi$
$701$		−	2.03381e26i		−	0.187927i	0.995576	−	0.0939633i	$-0.0299536\pi$
$702$	−4.30825e26	−	1.85329e27i	−0.392734	−	1.68943i
$703$			1.85193e26i			0.166552i
$704$	−1.01171e27	−	1.47230e26i	−0.897672	−	0.130634i
$705$	−2.89042e26	+	2.43847e25i	−0.253025	+	0.0213462i
$706$	−2.32371e25	+	9.64605e26i	−0.0200695	+	0.833114i
$707$	−1.50516e27			−1.28262
$708$	4.68472e25	+	1.30095e27i	0.0393884	+	1.09382i
$709$	8.47362e26			0.702959			0.351479	−	0.936196i	$-0.385679\pi$
$709$	8.47362e26			0.702959			0.351479	+	0.936196i	$0.385679\pi$
$710$	−1.31525e25	+	5.45981e26i	−0.0107660	+	0.446913i
$711$	−5.93160e25	−	3.49046e26i	−0.0479083	−	0.281917i
$712$	5.33699e25	−	7.37344e26i	0.0425340	−	0.587638i
$713$			1.52402e27i			1.19851i
$714$	1.01465e26	+	1.68682e27i	0.0787380	+	1.30899i
$715$			2.58464e27i			1.97921i
$716$	2.94534e26	+	1.41987e25i	0.222567	+	0.0107294i
$717$	1.13897e26	+	1.35007e27i	0.0849340	+	1.00676i
$718$	6.46594e26	+	1.55763e25i	0.475828	+	0.0114626i
$719$	−2.90458e26			−0.210940			−0.105470	−	0.994422i	$-0.533635\pi$
$719$	−2.90458e26			−0.210940			−0.105470	+	0.994422i	$0.533635\pi$
$720$	−1.26242e26	−	1.75060e27i	−0.0904783	−	1.25467i
$721$	−9.33381e26			−0.660198
$722$	9.41005e26	+	2.26686e25i	0.656884	+	0.0158242i
$723$	−3.04228e25	−	3.60614e26i	−0.0209597	−	0.248444i
$724$	−8.60138e26	−	4.14651e25i	−0.584860	−	0.0281946i
$725$			1.03877e27i			0.697121i
$726$	1.60557e25	+	2.66920e26i	0.0106349	+	0.176800i
$727$		−	1.02847e27i		−	0.672378i	−0.941795	−	0.336189i	$-0.890862\pi$
$727$		−	1.02847e27i		−	0.672378i	0.941795	−	0.336189i	$-0.109138\pi$
$728$	1.91306e26	−	2.64304e27i	0.123447	−	1.70551i
$729$	−1.37407e27	+	7.59581e26i	−0.875181	+	0.483796i
$730$	−2.72434e25	+	1.13091e27i	−0.0171275	+	0.710987i
$731$	1.24274e27			0.771195
$732$	2.48933e25	+	6.91290e26i	0.0152485	+	0.423453i
$733$	−4.55528e25			−0.0275440			−0.0137720	−	0.999905i	$-0.504384\pi$
$733$	−4.55528e25			−0.0275440			−0.0137720	+	0.999905i	$0.504384\pi$
$734$	4.25763e25	−	1.76740e27i	0.0254129	−	1.05493i
$735$	5.96865e25	−	5.03539e24i	0.0351679	−	0.00296690i
$736$	2.15062e27	+	2.60248e26i	1.25090	+	0.151373i
$737$		−	2.31690e27i		−	1.33035i
$738$	−4.27671e25	−	2.94432e26i	−0.0242423	−	0.166898i
$739$			2.43457e27i			1.36238i	0.732105	+	0.681192i	$0.238538\pi$
$739$			2.43457e27i			1.36238i	−0.732105	+	0.681192i	$0.761462\pi$
$740$	−3.11828e25	+	6.46845e26i	−0.0172272	+	0.357354i
$741$	−1.85568e27	+	1.56552e26i	−1.01211	+	0.0853858i
$742$	1.75964e27	+	4.23893e25i	0.947517	+	0.0228254i
$743$	−1.32233e27			−0.702987			−0.351494	−	0.936190i	$-0.614326\pi$
$743$	−1.32233e27			−0.702987			−0.351494	+	0.936190i	$0.614326\pi$
$744$	1.81206e27	−	2.15814e25i	0.951106	−	0.0113276i
$745$	4.12759e27			2.13901
$746$	−1.65728e27	−	3.99234e25i	−0.847962	−	0.0204272i
$747$	−1.76718e27	+	3.00310e26i	−0.892762	+	0.151714i
$748$	1.16478e26	−	2.41618e27i	0.0581002	−	1.20521i
$749$			1.53122e27i			0.754156i
$750$	1.07830e27	−	6.48619e25i	0.524395	−	0.0315433i
$751$		−	7.24509e26i		−	0.347908i	−0.984754	−	0.173954i	$-0.944346\pi$
$751$		−	7.24509e26i		−	0.347908i	0.984754	−	0.173954i	$-0.0556544\pi$
$752$	−4.23741e26	−	4.09501e25i	−0.200924	−	0.0194171i
$753$	−1.11582e26	−	1.32263e27i	−0.0522447	−	0.619278i
$754$	−1.08146e26	+	4.48929e27i	−0.0500014	+	2.07563i
$755$	−1.82532e27			−0.833380
$756$	−2.14116e27	+	4.43680e26i	−0.965364	+	0.200038i
$757$	−1.00860e27			−0.449065			−0.224532	−	0.974467i	$-0.572085\pi$
$757$	−1.00860e27			−0.449065			−0.224532	+	0.974467i	$0.572085\pi$
$758$	2.69508e25	−	1.11877e27i	0.0118499	−	0.491906i
$759$	2.21290e26	+	2.62305e27i	0.0960872	+	1.13896i
$760$	−1.71336e27	−	1.24015e26i	−0.734716	−	0.0531797i
$761$			2.55491e27i			1.08199i	0.841027	+	0.540994i	$0.181952\pi$
$761$			2.55491e27i			1.08199i	−0.841027	+	0.540994i	$0.818048\pi$
$762$	−2.79627e27	+	1.68201e26i	−1.16952	+	0.0703486i
$763$		−	3.90646e27i		−	1.61362i
$764$	3.00090e27	+	1.44666e26i	1.22424	+	0.0590173i
$765$	4.09407e27	−	6.95735e26i	1.64957	−	0.280324i
$766$	−2.78277e27	−	6.70362e25i	−1.10740	−	0.0266769i
$767$	4.83005e27			1.89844
$768$	2.78980e26	−	2.56076e27i	0.108303	−	0.994118i
$769$	−4.50473e27			−1.72730			−0.863651	−	0.504090i	$-0.831828\pi$
$769$	−4.50473e27			−1.72730			−0.863651	+	0.504090i	$0.831828\pi$
$770$	2.96947e27	+	7.15338e25i	1.12465	+	0.0270925i
$771$	9.17816e26	−	7.74305e25i	0.343351	−	0.0289665i
$772$	−2.45246e26	−	1.18227e25i	−0.0906229	−	0.00436870i
$773$		−	2.41708e26i		−	0.0882238i	−0.999027	−	0.0441119i	$-0.985954\pi$
$773$		−	2.41708e26i		−	0.0882238i	0.999027	−	0.0441119i	$-0.0140458\pi$
$774$	2.31151e26	+	1.59137e27i	0.0833405	+	0.573762i
$775$		−	1.55535e27i		−	0.553938i
$776$	1.25976e26	+	9.11828e24i	0.0443201	+	0.00320794i
$777$	8.03950e26	−	6.78243e25i	0.279402	−	0.0235714i
$778$	9.63406e25	−	3.99924e27i	0.0330752	−	1.37300i
$779$	−2.91199e26			−0.0987606
$780$	−6.50790e27	+	2.34349e26i	−2.18043	+	0.0785172i
$781$	−9.73974e26			−0.322376
$782$	−1.23438e26	+	5.12411e27i	−0.0403633	+	1.67554i
$783$	3.58798e27	−	9.25698e26i	1.15908	−	0.299042i
$784$	8.75016e25	+	8.45611e24i	0.0279263	+	0.00269878i
$785$		−	3.18260e27i		−	1.00351i
$786$	−2.12480e26	−	3.53239e27i	−0.0661917	−	1.10041i
$787$			1.29742e27i			0.399319i	0.979865	+	0.199659i	$0.0639835\pi$
$787$			1.29742e27i			0.399319i	−0.979865	+	0.199659i	$0.936016\pi$
$788$	−2.80645e26	+	5.82160e27i	−0.0853410	+	1.77029i
$789$	−1.89415e26	−	2.24522e27i	−0.0569093	−	0.674570i
$790$	−1.21141e27	−	2.91825e25i	−0.359611	−	0.00866293i
$791$	−3.63131e27			−1.06509
$792$	3.11566e27	−	3.00258e26i	0.902944	−	0.0870172i
$793$	2.56656e27			0.734946
$794$	1.58347e27	+	3.81453e25i	0.448038	+	0.0107931i
$795$	−3.63623e26	−	4.31017e27i	−0.101663	−	1.20506i
$796$	1.88143e25	−	3.90278e26i	0.00519773	−	0.107820i
$797$		−	6.03779e27i		−	1.64825i	−0.566406	−	0.824126i	$-0.691667\pi$
$797$		−	6.03779e27i		−	1.64825i	0.566406	−	0.824126i	$-0.308333\pi$
$798$	1.28503e26	+	2.13631e27i	0.0346645	+	0.576283i
$799$		−	1.00726e27i		−	0.268503i
$800$	−2.19482e27	−	2.65598e26i	−0.578156	−	0.0699632i
$801$	3.79193e26	+	2.23137e27i	0.0987077	+	0.580848i
$802$	2.64860e25	−	1.09947e27i	0.00681334	−	0.282832i
$803$	−2.01743e27			−0.512863
$804$	5.83376e27	−	2.10073e26i	1.46560	−	0.0527763i
$805$	−6.29386e27			−1.56263
$806$	1.61926e26	−	6.72180e27i	0.0397315	−	1.64931i
$807$	2.67176e27	−	2.25400e26i	0.647887	−	0.0546582i
$808$	−3.91901e26	+	5.41440e27i	−0.0939223	+	1.29761i
$809$		−	1.32736e27i		−	0.314397i	−0.987567	−	0.157199i	$-0.949754\pi$
$809$		−	1.32736e27i		−	0.314397i	0.987567	−	0.157199i	$-0.0502463\pi$
$810$	1.65241e27	+	5.11319e27i	0.386822	+	1.19697i
$811$			4.63277e27i			1.07187i	0.844259	+	0.535935i	$0.180041\pi$
$811$			4.63277e27i			1.07187i	−0.844259	+	0.535935i	$0.819959\pi$
$812$	5.15472e27	+	2.48496e26i	1.17875	+	0.0568247i
$813$	4.09419e27	−	3.45401e26i	0.925353	−	0.0780664i
$814$	−1.15458e27	−	2.78135e25i	−0.257924	−	0.00621331i
$815$	−6.76353e27			−1.49340
$816$	6.09429e27	+	7.42064e25i	1.33005	+	0.0161951i
$817$	1.57389e27			0.339520
$818$	2.54196e27	+	6.12352e25i	0.542016	+	0.0130570i
$819$	1.35923e27	+	7.99843e27i	0.286481	+	1.68581i
$820$	−1.01710e27	−	4.90320e25i	−0.211902	−	0.0102152i
$821$		−	3.71388e27i		−	0.764835i	−0.923990	−	0.382417i	$-0.875092\pi$
$821$		−	3.71388e27i		−	0.764835i	0.923990	−	0.382417i	$-0.124908\pi$
$822$	−6.32342e27	+	3.80366e26i	−1.28727	+	0.0774317i
$823$		−	3.77683e27i		−	0.760028i	−0.924981	−	0.380014i	$-0.875919\pi$
$823$		−	3.77683e27i		−	0.760028i	0.924981	−	0.380014i	$-0.124081\pi$
$824$	−2.43026e26	+	3.35759e27i	−0.0483443	+	0.667911i
$825$	−2.25839e26	−	2.67696e27i	−0.0444106	−	0.526417i
$826$	1.33679e26	−	5.54922e27i	0.0259868	−	1.07875i
$827$	−1.85818e27			−0.357097			−0.178549	−	0.983931i	$-0.557140\pi$
$827$	−1.85818e27			−0.357097			−0.178549	+	0.983931i	$0.557140\pi$
$828$	−6.58456e27	+	7.95023e26i	−1.25095	+	0.151040i
$829$	5.72536e27			1.07531			0.537656	−	0.843164i	$-0.319310\pi$
$829$	5.72536e27			1.07531			0.537656	+	0.843164i	$0.319310\pi$
$830$	−1.47748e26	+	6.13322e27i	−0.0274333	+	1.13880i
$831$	−5.62518e26	−	6.66776e27i	−0.103259	−	1.22397i
$832$	−9.45780e27	−	1.37635e27i	−1.71640	−	0.249779i
$833$			2.07998e26i			0.0373191i
$834$	−5.26863e27	+	3.16918e26i	−0.934589	+	0.0562173i
$835$			9.38478e27i			1.64590i
$836$	1.47516e26	−	3.06002e27i	0.0255787	−	0.530596i
$837$	−5.37227e27	+	1.38605e27i	−0.921014	+	0.237622i
$838$	8.96256e27	+	2.15906e26i	1.51920	+	0.0365970i
$839$	−4.60447e27			−0.771687			−0.385844	−	0.922564i	$-0.626090\pi$
$839$	−4.60447e27			−0.771687			−0.385844	+	0.922564i	$0.626090\pi$
$840$	8.91261e25	+	7.48337e27i	0.0147690	+	1.24006i
$841$	−2.64205e27			−0.432891
$842$	−4.30552e27	−	1.03719e26i	−0.697526	−	0.0168032i
$843$	9.77100e27	−	8.24319e26i	1.56523	−	0.132048i
$844$	−5.57904e26	+	1.15730e28i	−0.0883703	+	1.83313i
$845$			1.61305e28i			2.52644i
$846$	1.28983e27	−	1.87352e26i	0.199763	−	0.0290162i
$847$		−	1.14020e27i		−	0.174618i
$848$	6.10645e26	−	6.31880e27i	0.0924759	−	0.956916i
$849$	3.59294e27	−	3.03114e26i	0.538055	−	0.0453924i
$850$	1.25976e26	−	5.22943e27i	0.0186555	−	0.774417i
$851$	2.44715e27			0.358368
$852$	−8.83104e25	−	2.45239e27i	−0.0127890	−	0.355151i
$853$	−3.96809e27			−0.568284			−0.284142	−	0.958782i	$-0.591709\pi$
$853$	−3.96809e27			−0.568284			−0.284142	+	0.958782i	$0.591709\pi$
$854$	7.10335e25	−	2.94870e27i	0.0100604	−	0.417620i
$855$	5.18502e27	−	8.81128e26i	0.726227	−	0.123413i
$856$	5.50816e27	+	3.98688e26i	0.762968	+	0.0552246i
$857$			7.93792e27i			1.08740i	0.839280	+	0.543700i	$0.182977\pi$
$857$			7.93792e27i			1.08740i	−0.839280	+	0.543700i	$0.817023\pi$
$858$	−6.97319e26	−	1.15926e28i	−0.0944718	−	1.57055i
$859$			1.20328e28i			1.61225i	0.591748	+	0.806123i	$0.298438\pi$
$859$			1.20328e28i			1.61225i	−0.591748	+	0.806123i	$0.701562\pi$
$860$	5.49732e27	+	2.65012e26i	0.728477	+	0.0351180i
$861$	1.06647e26	+	1.26414e27i	0.0139772	+	0.165678i
$862$	1.19028e28	+	2.86734e26i	1.54287	+	0.0371673i
$863$	1.84655e27			0.236732			0.118366	−	0.992970i	$-0.462234\pi$
$863$	1.84655e27			0.236732			0.118366	+	0.992970i	$0.462234\pi$
$864$	1.03852e27	+	7.81775e27i	0.131685	+	0.991292i
$865$	2.08694e27			0.261732
$866$	5.38564e27	+	1.29739e26i	0.668063	+	0.0160935i
$867$	5.27092e26	+	6.24784e27i	0.0646703	+	0.766564i
$868$	−7.71816e27	−	3.72073e26i	−0.936648	−	0.0451534i
$869$		−	2.16103e27i		−	0.259401i
$870$	−7.61481e26	−	1.26593e28i	−0.0904120	−	1.50306i
$871$		−	2.16590e28i		−	2.54370i
$872$	−1.40524e28	−	1.01713e27i	−1.63247	−	0.118160i
$873$	−3.81231e26	+	6.47854e25i	−0.0438080	+	0.00744461i
$874$	−1.56331e26	+	6.48954e27i	−0.0177700	+	0.737658i
$875$	−4.60617e27			−0.517921
$876$	−1.82921e26	−	5.07973e27i	−0.0203458	−	0.565005i
$877$	−3.21222e27			−0.353435			−0.176717	−	0.984262i	$-0.556548\pi$
$877$	−3.21222e27			−0.353435			−0.176717	+	0.984262i	$0.556548\pi$
$878$	4.15048e25	−	1.72292e27i	0.00451752	−	0.187529i
$879$	−1.22232e28	+	1.03119e27i	−1.31610	+	0.111031i
$880$	1.03049e27	−	1.06632e28i	0.109764	−	1.13581i
$881$		−	3.37235e27i		−	0.355354i	−0.984089	−	0.177677i	$-0.943142\pi$
$881$		−	3.37235e27i		−	0.355354i	0.984089	−	0.177677i	$-0.0568583\pi$
$882$	−2.66348e26	+	3.86878e25i	−0.0277650	+	0.00403295i
$883$		−	1.81243e28i		−	1.86911i	−0.355814	−	0.934557i	$-0.615796\pi$
$883$		−	1.81243e28i		−	1.86911i	0.355814	−	0.934557i	$-0.384204\pi$
$884$	1.08887e27	−	2.25871e28i	0.111091	−	2.30443i
$885$	−1.35926e28	+	1.14672e27i	−1.37196	+	0.115744i
$886$	−1.13953e28	−	2.74510e26i	−1.13790	−	0.0274118i
$887$	1.27964e28			1.26420			0.632098	−	0.774888i	$-0.282194\pi$
$887$	1.27964e28			1.26420			0.632098	+	0.774888i	$0.282194\pi$
$888$	−3.46536e25	−	2.90965e27i	−0.00338708	−	0.284392i
$889$	1.19448e28			1.15508
$890$	7.74423e27	+	1.86557e26i	0.740923	+	0.0178486i
$891$	−9.04515e27	+	3.16563e27i	−0.856205	+	0.299656i
$892$	2.17119e26	−	4.50384e27i	0.0203344	−	0.421810i
$893$		−	1.27567e27i		−	0.118209i
$894$	−1.85131e28	+	1.11360e27i	−1.69736	+	0.102099i
$895$			3.08986e27i			0.280298i
$896$	−1.84303e27	+	1.08279e28i	−0.165427	+	0.971894i
$897$	2.06869e27	+	2.45210e28i	0.183724	+	2.17776i
$898$	1.64520e26	−	6.82947e27i	0.0144575	−	0.600153i
$899$	1.30943e28			1.13859
$900$	6.71990e27	−	8.11365e26i	0.578174	−	0.0698091i
$901$	1.50202e28			1.27877
$902$	4.37341e25	−	1.81547e27i	0.00368433	−	0.152942i
$903$	−5.76416e26	−	6.83250e27i	−0.0480510	−	0.569568i
$904$	−9.45490e26	+	1.30626e28i	−0.0779933	+	1.07753i
$905$		−	9.02343e27i		−	0.736563i
$906$	8.18695e27	−	4.92461e26i	0.661309	−	0.0397790i
$907$			9.52978e27i			0.761752i	0.924626	+	0.380876i	$0.124378\pi$
$907$			9.52978e27i			0.761752i	−0.924626	+	0.380876i	$0.875622\pi$
$908$	1.90154e28	+	9.16682e26i	1.50414	+	0.0725109i
$909$	−2.78446e27	−	1.63852e28i	−0.217963	−	1.28261i
$910$	2.77595e28	+	6.68719e26i	2.15039	+	0.0518025i
$911$	−1.37925e28			−1.05735			−0.528673	−	0.848826i	$-0.677310\pi$
$911$	−1.37925e28			−1.05735			−0.528673	+	0.848826i	$0.677310\pi$
$912$	7.71825e27	+	9.39802e25i	0.585555	+	0.00712993i
$913$	−1.09410e28			−0.821459
$914$	−1.11352e28	−	2.68244e26i	−0.827387	−	0.0199315i
$915$	−7.22273e27	+	6.09337e26i	−0.531130	+	0.0448082i
$916$	5.09394e26	+	2.45566e25i	0.0370721	+	0.00178715i
$917$			1.50893e28i			1.08682i
$918$	−1.81751e28	+	4.22507e27i	−1.29560	+	0.301182i
$919$			1.45780e28i			1.02849i	0.857643	+	0.514246i	$0.171928\pi$
$919$			1.45780e28i			1.02849i	−0.857643	+	0.514246i	$0.828072\pi$
$920$	−1.63874e27	+	2.26405e28i	−0.114427	+	1.58089i
$921$	−3.51546e27	+	2.96578e26i	−0.242949	+	0.0204961i
$922$	−3.97743e26	+	1.65109e28i	−0.0272056	+	1.12934i
$923$	−9.10499e27			−0.616401
$924$	−1.33380e28	+	4.80301e26i	−0.893732	+	0.0321833i
$925$	−2.49745e27			−0.165634
$926$	−2.70545e26	+	1.12307e28i	−0.0177597	+	0.737231i
$927$	−1.72670e27	−	1.01608e28i	−0.112191	−	0.660194i
$928$	2.23604e27	−	1.84780e28i	0.143805	−	1.18837i
$929$		−	5.82827e27i		−	0.371014i	−0.982643	−	0.185507i	$-0.940607\pi$
$929$		−	5.82827e27i		−	0.371014i	0.982643	−	0.185507i	$-0.0593928\pi$
$930$	1.14016e27	+	1.89547e28i	0.0718421	+	1.19435i
$931$			2.63423e26i			0.0164298i
$932$	−2.02250e26	+	4.19541e27i	−0.0124864	+	0.259014i
$933$	−9.67950e26	−	1.14735e28i	−0.0591531	−	0.701166i
$934$	9.43583e27	+	2.27307e26i	0.570801	+	0.0137505i
$935$	2.53473e28			1.51783
$936$	2.91261e28	−	2.80690e27i	1.72648	−	0.166382i
$937$	1.40580e28			0.824894			0.412447	−	0.910982i	$-0.364674\pi$
$937$	1.40580e28			0.824894			0.412447	+	0.910982i	$0.364674\pi$
$938$	−2.48839e28	−	5.99448e26i	−1.44541	−	0.0348196i
$939$	1.13671e27	+	1.34739e28i	0.0653622	+	0.774765i
$940$	2.14797e26	−	4.45568e27i	0.0122268	−	0.253630i
$941$		−	4.94780e27i		−	0.278812i	−0.990235	−	0.139406i	$-0.955481\pi$
$941$		−	4.94780e27i		−	0.278812i	0.990235	−	0.139406i	$-0.0445193\pi$
$942$	8.58648e26	+	1.42747e28i	0.0478995	+	0.796310i
$943$			3.84792e27i			0.212503i
$944$	−1.99270e28	−	1.92574e27i	−1.08945	−	0.105284i
$945$	−5.72405e27	−	2.21862e28i	−0.309814	−	1.20083i
$946$	−2.36377e26	+	9.81236e27i	−0.0126660	+	0.525784i
$947$	1.84927e28			0.981014			0.490507	−	0.871437i	$-0.336812\pi$
$947$	1.84927e28			0.981014			0.490507	+	0.871437i	$0.336812\pi$
$948$	5.44129e27	−	1.95941e26i	0.285774	−	0.0102907i
$949$	−1.88596e28			−0.980624
$950$	1.59545e26	−	6.62292e27i	0.00821311	−	0.340938i
$951$	−4.39204e27	+	3.70529e26i	−0.223847	+	0.0188846i
$952$	−2.59201e28	−	1.87613e27i	−1.30793	−	0.0946697i
$953$		−	3.47008e28i		−	1.73363i	−0.498630	−	0.866815i	$-0.666163\pi$
$953$		−	3.47008e28i		−	1.73363i	0.498630	−	0.866815i	$-0.333837\pi$
$954$	2.79378e27	+	1.92339e28i	0.138192	+	0.951390i
$955$			3.14815e28i			1.54178i
$956$	−2.08119e28	−	1.00329e27i	−1.00916	−	0.0486492i
$957$	2.25371e28	−	1.90132e27i	1.08202	−	0.0912833i
$958$	−4.06360e28	−	9.78911e26i	−1.93170	−	0.0465340i
$959$	2.70117e28			1.27138
$960$	2.69426e28	+	1.62785e27i	1.25563	+	0.0758645i
$961$	2.06454e27			0.0952691
$962$	−1.07933e28	−	2.60008e26i	−0.493165	−	0.0118802i
$963$	−1.66690e28	+	2.83268e27i	−0.754152	+	0.128158i
$964$	5.55901e27	+	2.67986e26i	0.249038	+	0.0120055i
$965$		−	2.57280e27i		−	0.114129i
$966$	2.82293e28	−	1.69804e27i	1.23999	−	0.0745876i
$967$		−	3.20370e28i		−	1.39348i	−0.717324	−	0.696740i	$-0.754633\pi$
$967$		−	3.20370e28i		−	1.39348i	0.717324	−	0.696740i	$-0.245367\pi$
$968$	−4.10156e27	−	2.96876e26i	−0.176658	−	0.0127867i
$969$	1.53529e27	+	1.81985e28i	0.0654810	+	0.776174i
$970$	−3.18733e25	+	1.32311e27i	−0.00134616	+	0.0558809i
$971$	−4.05883e28			−1.69753			−0.848766	−	0.528768i	$-0.822654\pi$
$971$	−4.05883e28			−1.69753			−0.848766	+	0.528768i	$0.822654\pi$
$972$	−8.79094e27	−	2.24879e28i	−0.364087	−	0.931365i
$973$	2.25059e28			0.923050
$974$	−2.20665e26	+	9.16011e27i	−0.00896237	+	0.372041i
$975$	−2.11121e27	−	2.50250e28i	−0.0849155	−	1.00654i
$976$	−1.05887e28	−	1.02328e27i	−0.421763	−	0.0407589i
$977$			5.81513e27i			0.229383i	0.993401	+	0.114691i	$0.0365879\pi$
$977$			5.81513e27i			0.229383i	−0.993401	+	0.114691i	$0.963412\pi$
$978$	3.03359e28	−	1.82476e27i	1.18505	−	0.0712831i
$979$			1.38149e28i			0.534457i
$980$	−4.43552e25	+	9.20090e26i	−0.00169940	+	0.0352519i
$981$	4.25258e28	−	7.22672e27i	1.61361	−	0.274212i
$982$	3.17170e28	+	7.64055e26i	1.19188	+	0.0287121i
$983$	−7.37818e27			−0.274594			−0.137297	−	0.990530i	$-0.543841\pi$
$983$	−7.37818e27			−0.274594			−0.137297	+	0.990530i	$0.543841\pi$
$984$	4.57516e27	−	5.44896e25i	0.168637	−	0.00200845i
$985$	−6.10726e28			−2.22947
$986$	4.40261e28	+	1.06058e27i	1.59177	+	0.0383453i
$987$	−5.53787e27	+	4.67196e26i	−0.198303	+	0.0167296i
$988$	1.37902e27	−	2.86059e28i	0.0489079	−	1.01453i
$989$		−	2.07975e28i		−	0.730544i
$990$	4.71463e27	+	3.24581e28i	0.164026	+	1.12925i
$991$		−	5.06296e28i		−	1.74463i	−0.488940	−	0.872317i	$-0.662616\pi$
$991$		−	5.06296e28i		−	1.74463i	0.488940	−	0.872317i	$-0.337384\pi$
$992$	−3.34802e27	+	2.76671e28i	−0.114269	+	0.944285i
$993$	−3.23882e28	+	2.73239e27i	−1.09489	+	0.0923689i
$994$	−2.51995e26	+	1.04607e28i	−0.00843764	+	0.350259i
$995$	4.09428e27			0.135787
$996$	−9.92025e26	−	2.75486e28i	−0.0325881	−	0.904975i
$997$	−7.23025e27			−0.235261			−0.117630	−	0.993057i	$-0.537530\pi$
$997$	−7.23025e27			−0.235261			−0.117630	+	0.993057i	$0.537530\pi$
$998$	5.94678e26	−	2.46859e28i	0.0191664	−	0.795627i
$999$	2.22560e27	+	8.62636e27i	0.0710518	+	0.275395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.20.b.a.11.36	yes	36
3.2	odd	2	inner	12.20.b.a.11.1	✓	36
4.3	odd	2	inner	12.20.b.a.11.2	yes	36
12.11	even	2	inner	12.20.b.a.11.35	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.20.b.a.11.1	✓	36	3.2	odd	2	inner
12.20.b.a.11.2	yes	36	4.3	odd	2	inner
12.20.b.a.11.35	yes	36	12.11	even	2	inner
12.20.b.a.11.36	yes	36	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:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(723.867 + 17.4378i) q^{2} +(-2865.95 - 33971.3i) q^{3} +(523680. + 25245.3i) q^{4} +5.49376e6i q^{5} +(-1.48218e6 - 2.46407e7i) q^{6} +1.05257e8i q^{7} +(3.78635e8 + 2.74060e7i) q^{8} +(-1.14583e9 + 1.94720e8i) q^{9} +O(q^{10})\)	\(q+(723.867 + 17.4378i) q^{2} +(-2865.95 - 33971.3i) q^{3} +(523680. + 25245.3i) q^{4} +5.49376e6i q^{5} +(-1.48218e6 - 2.46407e7i) q^{6} +1.05257e8i q^{7} +(3.78635e8 + 2.74060e7i) q^{8} +(-1.14583e9 + 1.94720e8i) q^{9} +(-9.57989e7 + 3.97675e9i) q^{10} -7.09412e9 q^{11} +(-6.43225e8 - 1.78624e10i) q^{12} -6.63179e10 q^{13} +(-1.83545e9 + 7.61923e10i) q^{14} +(1.86630e11 - 1.57448e10i) q^{15} +(2.73603e11 + 2.64409e10i) q^{16} +6.50375e11i q^{17} +(-8.32827e11 + 1.20971e11i) q^{18} +8.23681e11i q^{19} +(-1.38691e11 + 2.87697e12i) q^{20} +(3.57572e12 - 3.01662e11i) q^{21} +(-5.13520e12 - 1.23706e11i) q^{22} +1.08842e13 q^{23} +(-1.54129e11 - 1.29412e13i) q^{24} -1.11079e13 q^{25} +(-4.80054e13 - 1.15644e12i) q^{26} +(9.89878e12 + 3.83674e13i) q^{27} +(-2.65725e12 + 5.51211e13i) q^{28} -9.35164e13i q^{29} +(1.35370e14 - 8.14275e12i) q^{30} +1.40022e14i q^{31} +(1.97591e14 + 2.39107e13i) q^{32} +(2.03314e13 + 2.40996e14i) q^{33} +(-1.13411e13 + 4.70785e14i) q^{34} -5.78258e14 q^{35} +(-6.04966e14 + 7.30440e13i) q^{36} +2.24836e14 q^{37} +(-1.43632e13 + 5.96236e14i) q^{38} +(1.90064e14 + 2.25290e15i) q^{39} +(-1.50562e14 + 2.08013e15i) q^{40} +3.53533e14i q^{41} +(2.59361e15 - 1.56010e14i) q^{42} -1.91080e15i q^{43} +(-3.71505e15 - 1.79093e14i) q^{44} +(-1.06974e15 - 6.29494e15i) q^{45} +(7.87870e15 + 1.89796e14i) q^{46} -1.54874e15 q^{47} +(1.14098e14 - 9.37043e15i) q^{48} +3.19812e14 q^{49} +(-8.04064e15 - 1.93697e14i) q^{50} +(2.20941e16 - 1.86394e15i) q^{51} +(-3.47294e16 - 1.67421e15i) q^{52} -2.30947e16i q^{53} +(6.49636e15 + 2.79455e16i) q^{54} -3.89734e16i q^{55} +(-2.88468e15 + 3.98540e16i) q^{56} +(2.79815e16 - 2.36063e15i) q^{57} +(1.63072e15 - 6.76934e16i) q^{58} -7.28318e16 q^{59} +(9.81318e16 - 3.53372e15i) q^{60} -3.87008e16 q^{61} +(-2.44167e15 + 1.01357e17i) q^{62} +(-2.04957e16 - 1.20607e17i) q^{63} +(1.42613e17 + 2.07537e16i) q^{64} -3.64335e17i q^{65} +(1.05148e16 + 1.74804e17i) q^{66} +3.26594e17i q^{67} +(-1.64189e16 + 3.40588e17i) q^{68} +(-3.11935e16 - 3.69749e17i) q^{69} +(-4.18582e17 - 1.00835e16i) q^{70} +1.37293e17 q^{71} +(-4.39189e17 + 4.23249e16i) q^{72} +2.84381e17 q^{73} +(1.62751e17 + 3.92063e15i) q^{74} +(3.18346e16 + 3.77349e17i) q^{75} +(-2.07941e16 + 4.31345e17i) q^{76} -7.46708e17i q^{77} +(9.82953e16 + 1.63412e18i) q^{78} +3.04622e17i q^{79} +(-1.45260e17 + 1.50311e18i) q^{80} +(1.27502e18 - 4.46233e17i) q^{81} +(-6.16484e15 + 2.55911e17i) q^{82} +1.54227e18 q^{83} +(1.88015e18 - 6.77041e16i) q^{84} -3.57300e18 q^{85} +(3.33201e16 - 1.38317e18i) q^{86} +(-3.17687e18 + 2.68013e17i) q^{87} +(-2.68608e18 - 1.94422e17i) q^{88} -1.94738e18i q^{89} +(-6.64583e17 - 4.57535e18i) q^{90} -6.98044e18i q^{91} +(5.69982e18 + 2.74774e17i) q^{92} +(4.75672e18 - 4.01295e17i) q^{93} +(-1.12108e18 - 2.70066e16i) q^{94} -4.52511e18 q^{95} +(2.45991e17 - 6.78096e18i) q^{96} +3.32711e17 q^{97} +(2.31502e17 + 5.57681e15i) q^{98} +(8.12869e18 - 1.38137e18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9}+O(q^{10}) \) 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9	\( 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9} - 4162950000 q^{10} - 2268767880 q^{12} - 25913431656 q^{13} + 791689296672 q^{16} + 2852271258192 q^{18} - 1650825908424 q^{21} + 7247870602416 q^{22} + 23719435803936 q^{24} - 118879690462380 q^{25} - 7629081673968 q^{28} + 37456727138640 q^{30} + 529254701828640 q^{33} - 248241675948480 q^{34} - 11\!\cdots\!16 q^{36}+ \cdots + 12\!\cdots\!88 q^{97}+O(q^{100}) \) 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9 - 4162950000 * q^10 - 2268767880 * q^12 - 25913431656 * q^13 + 791689296672 * q^16 + 2852271258192 * q^18 - 1650825908424 * q^21 + 7247870602416 * q^22 + 23719435803936 * q^24 - 118879690462380 * q^25 - 7629081673968 * q^28 + 37456727138640 * q^30 + 529254701828640 * q^33 - 248241675948480 * q^34 - 1177548745309416 * q^36 + 1847838600168120 * q^37 - 40433256181440 * q^40 - 2709671988768336 * q^42 - 4365410114088000 * q^45 + 17206125364795104 * q^46 + 1561106052682272 * q^48 - 49399737041580084 * q^49 + 16558671470242896 * q^52 + 40087412948587896 * q^54 + 44803667812766472 * q^57 - 34645536255764880 * q^58 + 50260381053157440 * q^60 + 174742350239997144 * q^61 - 139766490424918656 * q^64 - 87772097712685968 * q^66 - 957190369821780672 * q^69 + 244663962371376480 * q^70 + 54134736422921280 * q^72 - 1445122541399481432 * q^73 + 2744130151937256048 * q^76 + 1125465917961999024 * q^78 + 1033298241353042436 * q^81 + 1064985418859680800 * q^82 + 1920709484261873424 * q^84 - 1802899595088057600 * q^85 - 9209792381828477760 * q^88 - 5194944179528261040 * q^90 + 6719944190337314136 * q^93 - 3835186345170303552 * q^94 - 11947184361208227456 * q^96 + 12765226159947004488 * q^97

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