LMFDB - Embedded newform 12.20.b.a.11.9

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			11.9
Character	$\chi$	$=$	12.11
Dual form			12.20.b.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-519.517 - 504.371i) q^{2} +(-19784.5 - 27763.9i) q^{3} +(15507.7 + 524059. i) q^{4} -1.34492e6i q^{5} +(-3.72492e6 + 2.44026e7i) q^{6} -1.72563e8i q^{7} +(2.56263e8 - 2.80079e8i) q^{8} +(-3.79408e8 + 1.09859e9i) q^{9} +O(q^{10})$	\(q+(-519.517 - 504.371i) q^{2} +(-19784.5 - 27763.9i) q^{3} +(15507.7 + 524059. i) q^{4} -1.34492e6i q^{5} +(-3.72492e6 + 2.44026e7i) q^{6} -1.72563e8i q^{7} +(2.56263e8 - 2.80079e8i) q^{8} +(-3.79408e8 + 1.09859e9i) q^{9} +(-6.78338e8 + 6.98708e8i) q^{10} -1.32949e10 q^{11} +(1.42431e10 - 1.07988e10i) q^{12} -2.84987e10 q^{13} +(-8.70355e10 + 8.96492e10i) q^{14} +(-3.73402e10 + 2.66085e10i) q^{15} +(-2.74397e11 + 1.62539e10i) q^{16} +1.96504e11i q^{17} +(7.51206e11 - 3.79374e11i) q^{18} -2.26261e12i q^{19} +(7.04816e11 - 2.08566e10i) q^{20} +(-4.79101e12 + 3.41407e12i) q^{21} +(6.90691e12 + 6.70555e12i) q^{22} -9.34021e12 q^{23} +(-1.28461e13 - 1.57365e12i) q^{24} +1.72647e13 q^{25} +(1.48056e13 + 1.43739e13i) q^{26} +(3.80076e13 - 1.12012e13i) q^{27} +(9.04329e13 - 2.67605e12i) q^{28} -1.66276e13i q^{29} +(3.28194e13 + 5.00971e12i) q^{30} +4.90603e13i q^{31} +(1.50752e14 + 1.29954e14i) q^{32} +(2.63032e14 + 3.69117e14i) q^{33} +(9.91108e13 - 1.02087e14i) q^{34} -2.32082e14 q^{35} +(-5.81610e14 - 1.81795e14i) q^{36} +9.66977e14 q^{37} +(-1.14119e15 + 1.17546e15i) q^{38} +(5.63833e14 + 7.91235e14i) q^{39} +(-3.76683e14 - 3.44653e14i) q^{40} +1.16915e15i q^{41} +(4.21097e15 + 6.42782e14i) q^{42} -3.53338e14i q^{43} +(-2.06173e14 - 6.96729e15i) q^{44} +(1.47751e15 + 5.10272e14i) q^{45} +(4.85240e15 + 4.71093e15i) q^{46} +2.94330e15 q^{47} +(5.88008e15 + 7.29675e15i) q^{48} -1.83789e16 q^{49} +(-8.96930e15 - 8.70781e15i) q^{50} +(5.45571e15 - 3.88773e15i) q^{51} +(-4.41950e14 - 1.49350e16i) q^{52} -9.59360e15i q^{53} +(-2.53952e16 - 1.33507e16i) q^{54} +1.78805e16i q^{55} +(-4.83311e16 - 4.42215e16i) q^{56} +(-6.28188e16 + 4.47646e16i) q^{57} +(-8.38648e15 + 8.63832e15i) q^{58} -1.43314e15 q^{59} +(-1.45235e16 - 1.91558e16i) q^{60} -1.36745e16 q^{61} +(2.47446e16 - 2.54876e16i) q^{62} +(1.89576e17 + 6.54715e16i) q^{63} +(-1.27733e16 - 1.43548e17i) q^{64} +3.83284e16i q^{65} +(4.95223e16 - 3.24429e17i) q^{66} +3.13017e17i q^{67} +(-1.02980e17 + 3.04733e15i) q^{68} +(1.84791e17 + 2.59321e17i) q^{69} +(1.20571e17 + 1.17056e17i) q^{70} +4.79155e17 q^{71} +(2.10464e17 + 3.87793e17i) q^{72} -3.71378e17 q^{73} +(-5.02361e17 - 4.87715e17i) q^{74} +(-3.41573e17 - 4.79335e17i) q^{75} +(1.18574e18 - 3.50879e16i) q^{76} +2.29420e18i q^{77} +(1.06155e17 - 6.95441e17i) q^{78} +5.54718e17i q^{79} +(2.18602e16 + 3.69041e17i) q^{80} +(-1.06295e18 - 8.33627e17i) q^{81} +(5.89686e17 - 6.07394e17i) q^{82} +1.99175e18 q^{83} +(-1.86347e18 - 2.45783e18i) q^{84} +2.64282e17 q^{85} +(-1.78213e17 + 1.83565e17i) q^{86} +(-4.61647e17 + 3.28969e17i) q^{87} +(-3.40699e18 + 3.72361e18i) q^{88} -2.47725e18i q^{89} +(-5.10227e17 - 1.01031e18i) q^{90} +4.91781e18i q^{91} +(-1.44845e17 - 4.89482e18i) q^{92} +(1.36210e18 - 9.70633e17i) q^{93} +(-1.52910e18 - 1.48452e18i) q^{94} -3.04302e18 q^{95} +(6.25470e17 - 6.75653e18i) q^{96} -5.09428e18 q^{97} +(9.54817e18 + 9.26980e18i) q^{98} +(5.04417e18 - 1.46056e19i) 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 $

$2$	−519.517	−	504.371i	−0.717488	−	0.696571i
$2$	−519.517	−	504.371i	−0.717488	−	0.696571i
$3$	−19784.5	−	27763.9i	−0.580328	−	0.814383i
$3$	−19784.5	−	27763.9i	−0.580328	−	0.814383i
$4$	15507.7	+	524059.i	0.0295787	+	0.999562i
$5$		−	1.34492e6i		−	0.307950i	−0.988075	−	0.153975i	$-0.950792\pi$
$5$		−	1.34492e6i		−	0.307950i	0.988075	−	0.153975i	$-0.0492076\pi$
$6$	−3.72492e6	+	2.44026e7i	−0.150897	+	0.988550i
$7$		−	1.72563e8i		−	1.61627i	−0.588994	−	0.808137i	$-0.700476\pi$
$7$		−	1.72563e8i		−	1.61627i	0.588994	−	0.808137i	$-0.299524\pi$
$8$	2.56263e8	−	2.80079e8i	0.675044	−	0.737778i
$9$	−3.79408e8	+	1.09859e9i	−0.326439	+	0.945218i
$10$	−6.78338e8	+	6.98708e8i	−0.214509	+	0.220951i
$11$	−1.32949e10			−1.70002			−0.850009	−	0.526768i	$-0.823404\pi$
$11$	−1.32949e10			−1.70002			−0.850009	+	0.526768i	$0.823404\pi$
$12$	1.42431e10	−	1.07988e10i	0.796861	−	0.604162i
$13$	−2.84987e10			−0.745355			−0.372678	−	0.927961i	$-0.621560\pi$
$13$	−2.84987e10			−0.745355			−0.372678	+	0.927961i	$0.621560\pi$
$14$	−8.70355e10	+	8.96492e10i	−1.12585	+	1.15966i
$15$	−3.73402e10	+	2.66085e10i	−0.250790	+	0.178712i
$16$	−2.74397e11	+	1.62539e10i	−0.998250	+	0.0591314i
$17$			1.96504e11i			0.401889i	0.979603	+	0.200945i	$0.0644011\pi$
$17$			1.96504e11i			0.401889i	−0.979603	+	0.200945i	$0.935599\pi$
$18$	7.51206e11	−	3.79374e11i	0.892627	−	0.450795i
$19$		−	2.26261e12i		−	1.60861i	−0.594219	−	0.804304i	$-0.702539\pi$
$19$		−	2.26261e12i		−	1.60861i	0.594219	−	0.804304i	$-0.297461\pi$
$20$	7.04816e11	−	2.08566e10i	0.307816	−	0.00910876i
$21$	−4.79101e12	+	3.41407e12i	−1.31627	+	0.937969i
$22$	6.90691e12	+	6.70555e12i	1.21974	+	1.18418i
$23$	−9.34021e12			−1.08129			−0.540645	−	0.841251i	$-0.681820\pi$
$23$	−9.34021e12			−1.08129			−0.540645	+	0.841251i	$0.681820\pi$
$24$	−1.28461e13	−	1.57365e12i	−0.992580	−	0.121591i
$25$	1.72647e13			0.905167
$26$	1.48056e13	+	1.43739e13i	0.534784	+	0.519192i
$27$	3.80076e13	−	1.12012e13i	0.959211	−	0.282690i
$28$	9.04329e13	−	2.67605e12i	1.61557	−	0.0478072i
$29$		−	1.66276e13i		−	0.212838i	−0.994321	−	0.106419i	$-0.966062\pi$
$29$		−	1.66276e13i		−	0.212838i	0.994321	−	0.106419i	$-0.0339384\pi$
$30$	3.28194e13	+	5.00971e12i	0.304424	+	0.0464687i
$31$			4.90603e13i			0.333268i	0.986019	+	0.166634i	$0.0532899\pi$
$31$			4.90603e13i			0.333268i	−0.986019	+	0.166634i	$0.946710\pi$
$32$	1.50752e14	+	1.29954e14i	0.757422	+	0.652926i
$33$	2.63032e14	+	3.69117e14i	0.986568	+	1.38447i
$34$	9.91108e13	−	1.02087e14i	0.279944	−	0.288351i
$35$	−2.32082e14			−0.497732
$36$	−5.81610e14	−	1.81795e14i	−0.954460	−	0.298338i
$37$	9.66977e14			1.22321			0.611603	−	0.791165i	$-0.290525\pi$
$37$	9.66977e14			1.22321			0.611603	+	0.791165i	$0.290525\pi$
$38$	−1.14119e15	+	1.17546e15i	−1.12051	+	1.15416i
$39$	5.63833e14	+	7.91235e14i	0.432550	+	0.607004i
$40$	−3.76683e14	−	3.44653e14i	−0.227199	−	0.207880i
$41$			1.16915e15i			0.557730i	0.960330	+	0.278865i	$0.0899582\pi$
$41$			1.16915e15i			0.557730i	−0.960330	+	0.278865i	$0.910042\pi$
$42$	4.21097e15	+	6.42782e14i	1.59777	+	0.243891i
$43$		−	3.53338e14i		−	0.107211i	−0.998562	−	0.0536055i	$-0.982929\pi$
$43$		−	3.53338e14i		−	0.107211i	0.998562	−	0.0536055i	$-0.0170714\pi$
$44$	−2.06173e14	−	6.96729e15i	−0.0502842	−	1.69927i
$45$	1.47751e15	+	5.10272e14i	0.291080	+	0.100527i
$46$	4.85240e15	+	4.71093e15i	0.775813	+	0.753195i
$47$	2.94330e15			0.383624			0.191812	−	0.981432i	$-0.438564\pi$
$47$	2.94330e15			0.383624			0.191812	+	0.981432i	$0.438564\pi$
$48$	5.88008e15	+	7.29675e15i	0.627468	+	0.778642i
$49$	−1.83789e16			−1.61234
$50$	−8.96930e15	−	8.70781e15i	−0.649446	−	0.630512i
$51$	5.45571e15	−	3.88773e15i	0.327292	−	0.233227i
$52$	−4.41950e14	−	1.49350e16i	−0.0220466	−	0.745029i
$53$		−	9.59360e15i		−	0.399357i	−0.979861	−	0.199678i	$-0.936010\pi$
$53$		−	9.59360e15i		−	0.399357i	0.979861	−	0.199678i	$-0.0639897\pi$
$54$	−2.53952e16	−	1.33507e16i	−0.885136	−	0.465332i
$55$			1.78805e16i			0.523521i
$56$	−4.83311e16	−	4.42215e16i	−1.19245	−	1.09106i
$57$	−6.28188e16	+	4.47646e16i	−1.31002	+	0.933520i
$58$	−8.38648e15	+	8.63832e15i	−0.148256	+	0.152709i
$59$	−1.43314e15			−0.0215374			−0.0107687	−	0.999942i	$-0.503428\pi$
$59$	−1.43314e15			−0.0215374			−0.0107687	+	0.999942i	$0.503428\pi$
$60$	−1.45235e16	−	1.91558e16i	−0.186052	−	0.245394i
$61$	−1.36745e16			−0.149719			−0.0748597	−	0.997194i	$-0.523851\pi$
$61$	−1.36745e16			−0.149719			−0.0748597	+	0.997194i	$0.523851\pi$
$62$	2.47446e16	−	2.54876e16i	0.232145	−	0.239116i
$63$	1.89576e17	+	6.54715e16i	1.52773	+	0.527615i
$64$	−1.27733e16	−	1.43548e17i	−0.0886324	−	0.996064i
$65$			3.83284e16i			0.229532i
$66$	4.95223e16	−	3.24429e17i	0.256527	−	1.68055i
$67$			3.13017e17i			1.40558i	0.711395	+	0.702792i	$0.248064\pi$
$67$			3.13017e17i			1.40558i	−0.711395	+	0.702792i	$0.751936\pi$
$68$	−1.02980e17	+	3.04733e15i	−0.401713	+	0.0118873i
$69$	1.84791e17	+	2.59321e17i	0.627503	+	0.880584i
$70$	1.20571e17	+	1.17056e17i	0.357117	+	0.346706i
$71$	4.79155e17			1.24029			0.620143	−	0.784489i	$-0.287075\pi$
$71$	4.79155e17			1.24029			0.620143	+	0.784489i	$0.287075\pi$
$72$	2.10464e17	+	3.87793e17i	0.477001	+	0.878903i
$73$	−3.71378e17			−0.738327			−0.369163	−	0.929365i	$-0.620356\pi$
$73$	−3.71378e17			−0.738327			−0.369163	+	0.929365i	$0.620356\pi$
$74$	−5.02361e17	−	4.87715e17i	−0.877636	−	0.852050i
$75$	−3.41573e17	−	4.79335e17i	−0.525293	−	0.737152i
$76$	1.18574e18	−	3.50879e16i	1.60790	−	0.0475804i
$77$			2.29420e18i			2.74770i
$78$	1.06155e17	−	6.95441e17i	0.112472	−	0.736820i
$79$			5.54718e17i			0.520733i	0.965510	+	0.260367i	$0.0838434\pi$
$79$			5.54718e17i			0.520733i	−0.965510	+	0.260367i	$0.916157\pi$
$80$	2.18602e16	+	3.69041e17i	0.0182095	+	0.307412i
$81$	−1.06295e18	−	8.33627e17i	−0.786875	−	0.617112i
$82$	5.89686e17	−	6.07394e17i	0.388498	−	0.400165i
$83$	1.99175e18			1.16948			0.584741	−	0.811220i	$-0.301196\pi$
$83$	1.99175e18			1.16948			0.584741	+	0.811220i	$0.301196\pi$
$84$	−1.86347e18	−	2.45783e18i	−0.976492	−	1.28795i
$85$	2.64282e17			0.123762
$86$	−1.78213e17	+	1.83565e17i	−0.0746801	+	0.0769227i
$87$	−4.61647e17	+	3.28969e17i	−0.173331	+	0.123516i
$88$	−3.40699e18	+	3.72361e18i	−1.14759	+	1.25424i
$89$		−	2.47725e18i		−	0.749488i	−0.927128	−	0.374744i	$-0.877731\pi$
$89$		−	2.47725e18i		−	0.749488i	0.927128	−	0.374744i	$-0.122269\pi$
$90$	−5.10227e17	−	1.01031e18i	−0.138823	−	0.274885i
$91$			4.91781e18i			1.20470i
$92$	−1.44845e17	−	4.89482e18i	−0.0319831	−	1.08082i
$93$	1.36210e18	−	9.70633e17i	0.271408	−	0.193405i
$94$	−1.52910e18	−	1.48452e18i	−0.275245	−	0.267221i
$95$	−3.04302e18			−0.495371
$96$	6.25470e17	−	6.75653e18i	0.0921785	−	0.995743i
$97$	−5.09428e18			−0.680380			−0.340190	−	0.940357i	$-0.610491\pi$
$97$	−5.09428e18			−0.680380			−0.340190	+	0.940357i	$0.610491\pi$
$98$	9.54817e18	+	9.26980e18i	1.15684	+	1.12311i
$99$	5.04417e18	−	1.46056e19i	0.554952	−	1.60689i
$100$	2.67736e17	+	9.04771e18i	0.0267736	+	0.904771i
$101$		−	1.23690e19i		−	1.12534i	−0.826683	−	0.562668i	$-0.809775\pi$
$101$		−	1.23690e19i		−	1.12534i	0.826683	−	0.562668i	$-0.190225\pi$
$102$	−4.79520e18	−	7.31961e17i	−0.397287	−	0.0606438i
$103$			5.70221e17i			0.0430615i	0.999768	+	0.0215308i	$0.00685399\pi$
$103$			5.70221e17i			0.0430615i	−0.999768	+	0.0215308i	$0.993146\pi$
$104$	−7.30318e18	+	7.98189e18i	−0.503147	+	0.549907i
$105$	4.59164e18	+	6.44352e18i	0.288848	+	0.405345i
$106$	−4.83874e18	+	4.98404e18i	−0.278180	+	0.286534i
$107$	−3.38232e19			−1.77856			−0.889280	−	0.457363i	$-0.848794\pi$
$107$	−3.38232e19			−1.77856			−0.889280	+	0.457363i	$0.848794\pi$
$108$	6.45952e18	+	1.97445e19i	0.310939	+	0.950430i
$109$	1.77659e19			0.783494			0.391747	−	0.920073i	$-0.371871\pi$
$109$	1.77659e19			0.783494			0.391747	+	0.920073i	$0.371871\pi$
$110$	9.01841e18	−	9.28923e18i	0.364670	−	0.375620i
$111$	−1.91312e19	−	2.68471e19i	−0.709861	−	0.996159i
$112$	2.80482e18	+	4.73506e19i	0.0955726	+	1.61345i
$113$			6.36977e18i			0.199470i	0.995014	+	0.0997352i	$0.0317996\pi$
$113$			6.36977e18i			0.199470i	−0.995014	+	0.0997352i	$0.968200\pi$
$114$	5.52134e19	+	8.42803e18i	1.59019	+	0.242734i
$115$			1.25618e19i			0.332984i
$116$	8.71384e18	−	2.57856e17i	0.212745	−	0.00629545i
$117$	1.08126e19	−	3.13084e19i	0.243313	−	0.704523i
$118$	7.44540e17	+	7.22834e17i	0.0154529	+	0.0150024i
$119$	3.39092e19			0.649563
$120$	−2.11643e18	+	1.72770e19i	−0.0374439	+	0.305665i
$121$	1.15594e20			1.89006
$122$	7.10413e18	+	6.89702e18i	0.107422	+	0.104290i
$123$	3.24602e19	−	2.31311e19i	0.454206	−	0.323666i
$124$	−2.57105e19	+	7.60814e17i	−0.333122	+	0.00985762i
$125$		−	4.88719e19i		−	0.586697i
$126$	−6.54658e19	−	1.29630e20i	−0.728608	−	1.44273i
$127$			9.93306e19i			1.02553i	0.858530	+	0.512764i	$0.171378\pi$
$127$			9.93306e19i			1.02553i	−0.858530	+	0.512764i	$0.828622\pi$
$128$	−6.57655e19	+	8.10181e19i	−0.630236	+	0.776403i
$129$	−9.81004e18	+	6.99061e18i	−0.0873109	+	0.0622176i
$130$	1.93317e19	−	1.99123e19i	0.159886	−	0.164687i
$131$	−1.27259e20			−0.978614			−0.489307	−	0.872111i	$-0.662750\pi$
$131$	−1.27259e20			−0.978614			−0.489307	+	0.872111i	$0.662750\pi$
$132$	−1.89360e20	+	1.43569e20i	−1.35468	+	1.02709i
$133$	−3.90441e20			−2.59995
$134$	1.57877e20	−	1.62618e20i	0.979089	−	1.00849i
$135$	−1.50648e19	−	5.11171e19i	−0.0870545	−	0.295389i
$136$	5.50366e19	+	5.03567e19i	0.296505	+	0.271293i
$137$			2.01832e20i			1.01425i	0.861873	+	0.507124i	$0.169291\pi$
$137$			2.01832e20i			1.01425i	−0.861873	+	0.507124i	$0.830709\pi$
$138$	3.47915e19	−	2.27925e20i	0.163163	−	1.06891i
$139$		−	1.99551e20i		−	0.873802i	−0.899510	−	0.436901i	$-0.856076\pi$
$139$		−	1.99551e20i		−	0.873802i	0.899510	−	0.436901i	$-0.143924\pi$
$140$	−3.59907e18	−	1.21625e20i	−0.0147223	−	0.497515i
$141$	−5.82318e19	−	8.17176e19i	−0.222628	−	0.312417i
$142$	−2.48929e20	−	2.41672e20i	−0.889890	−	0.863946i
$143$	3.78886e20			1.26712
$144$	8.62519e19	−	3.07617e20i	0.269976	−	0.962867i
$145$	−2.23628e19			−0.0655434
$146$	1.92937e20	+	1.87312e20i	0.529741	+	0.514297i
$147$	3.63618e20	+	5.10271e20i	0.935688	+	1.31306i
$148$	1.49956e19	+	5.06753e20i	0.0361808	+	1.22267i
$149$			3.15970e20i			0.715117i	0.933891	+	0.357558i	$0.116391\pi$
$149$			3.15970e20i			0.715117i	−0.933891	+	0.357558i	$0.883609\pi$
$150$	−6.43096e19	+	4.21302e20i	−0.136587	+	0.894802i
$151$			2.46468e20i			0.491450i	0.969340	+	0.245725i	$0.0790261\pi$
$151$			2.46468e20i			0.491450i	−0.969340	+	0.245725i	$0.920974\pi$
$152$	−6.33709e20	−	5.79824e20i	−1.18679	−	1.08588i
$153$	−2.15877e20	−	7.45550e19i	−0.379873	−	0.131192i
$154$	1.15713e21	−	1.19187e21i	1.91396	−	1.97144i
$155$	6.59820e19			0.102630
$156$	−4.05910e20	+	3.07752e20i	−0.593945	+	0.450315i
$157$	8.77508e20			1.20838			0.604191	−	0.796839i	$-0.293496\pi$
$157$	8.77508e20			1.20838			0.604191	+	0.796839i	$0.293496\pi$
$158$	2.79784e20	−	2.88186e20i	0.362727	−	0.373620i
$159$	−2.66356e20	+	1.89805e20i	−0.325229	+	0.231758i
$160$	1.74777e20	−	2.02749e20i	0.201069	−	0.233248i
$161$			1.61177e21i			1.74766i
$162$	1.31764e20	+	9.69205e20i	0.134711	+	0.990885i
$163$		−	2.49747e20i		−	0.240834i	−0.992723	−	0.120417i	$-0.961577\pi$
$163$		−	2.49747e20i		−	0.240834i	0.992723	−	0.120417i	$-0.0384232\pi$
$164$	−6.12704e20	+	1.81309e19i	−0.557486	+	0.0164969i
$165$	4.96433e20	−	3.53757e20i	0.426347	−	0.303814i
$166$	−1.03475e21	−	1.00458e21i	−0.839089	−	0.814627i
$167$	−1.13644e21			−0.870440			−0.435220	−	0.900324i	$-0.643329\pi$
$167$	−1.13644e21			−0.870440			−0.435220	+	0.900324i	$0.643329\pi$
$168$	−2.71553e20	+	2.21676e21i	−0.196524	+	1.60428i
$169$	−6.49744e20			−0.444446
$170$	−1.37299e20	−	1.33296e20i	−0.0887977	−	0.0862089i
$171$	2.48568e21	+	8.58450e20i	1.52048	+	0.525112i
$172$	1.85170e20	−	5.47947e18i	0.107164	−	0.00317116i
$173$		−	2.40894e21i		−	1.31944i	−0.751514	−	0.659718i	$-0.770676\pi$
$173$		−	2.40894e21i		−	1.31944i	0.751514	−	0.659718i	$-0.229324\pi$
$174$	4.05756e20	+	6.19365e19i	0.210401	+	0.0321165i
$175$		−	2.97924e21i		−	1.46300i
$176$	3.64807e21	−	2.16094e20i	1.69704	−	0.100524i
$177$	2.83540e19	+	3.97895e19i	0.0124988	+	0.0175397i
$178$	−1.24945e21	+	1.28697e21i	−0.522071	+	0.537749i
$179$	−4.71604e21			−1.86842			−0.934209	−	0.356727i	$-0.883893\pi$
$179$	−4.71604e21			−1.86842			−0.934209	+	0.356727i	$0.883893\pi$
$180$	−2.44500e20	+	7.82217e20i	−0.0918733	+	0.293926i
$181$	−9.39386e20			−0.334887			−0.167443	−	0.985882i	$-0.553551\pi$
$181$	−9.39386e20			−0.334887			−0.167443	+	0.985882i	$0.553551\pi$
$182$	2.48040e21	−	2.55488e21i	0.839158	−	0.864357i
$183$	2.70543e20	+	3.79658e20i	0.0868863	+	0.121929i
$184$	−2.39355e21	+	2.61600e21i	−0.729918	+	0.797752i
$185$		−	1.30051e21i		−	0.376687i
$186$	−1.19720e21	−	1.82746e20i	−0.329452	−	0.0502891i
$187$		−	2.61249e21i		−	0.683219i
$188$	4.56440e19	+	1.54246e21i	0.0113471	+	0.383456i
$189$	−1.93292e21	−	6.55868e21i	−0.456905	−	1.55035i
$190$	1.58090e21	+	1.53481e21i	0.355423	+	0.345061i
$191$	−2.28988e21			−0.489774			−0.244887	−	0.969552i	$-0.578751\pi$
$191$	−2.28988e21			−0.489774			−0.244887	+	0.969552i	$0.578751\pi$
$192$	−3.73274e21	+	3.19466e21i	−0.759742	+	0.650225i
$193$	3.21256e21			0.622381			0.311191	−	0.950348i	$-0.399272\pi$
$193$	3.21256e21			0.622381			0.311191	+	0.950348i	$0.399272\pi$
$194$	2.64656e21	+	2.56941e21i	0.488164	+	0.473932i
$195$	1.06415e21	−	7.58309e20i	0.186927	−	0.133204i
$196$	−2.85016e20	−	9.63164e21i	−0.0476909	−	1.61164i
$197$			3.88708e21i			0.619718i	0.950783	+	0.309859i	$0.100282\pi$
$197$			3.88708e21i			0.619718i	−0.950783	+	0.309859i	$0.899718\pi$
$198$	−9.98719e21	+	5.04373e21i	−1.51748	+	0.766360i
$199$			7.98638e21i			1.15677i	0.815765	+	0.578383i	$0.196316\pi$
$199$			7.98638e21i			1.15677i	−0.815765	+	0.578383i	$0.803684\pi$
$200$	4.42431e21	−	4.83547e21i	0.611027	−	0.667812i
$201$	8.69057e21	−	6.19288e21i	1.14468	−	0.815700i
$202$	−6.23858e21	+	6.42592e21i	−0.783876	+	0.807416i
$203$	−2.86930e21			−0.344004
$204$	2.12201e21	+	2.79882e21i	0.242806	+	0.320250i
$205$	1.57241e21			0.171753
$206$	2.87603e20	−	2.96239e20i	0.0299954	−	0.0308961i
$207$	3.54375e21	−	1.02611e22i	0.352975	−	1.02205i
$208$	7.81996e21	−	4.63216e20i	0.744051	−	0.0440739i
$209$			3.00811e22i			2.73466i
$210$	8.64489e20	−	5.66340e21i	0.0751062	−	0.492033i
$211$		−	2.89424e21i		−	0.240354i	−0.992752	−	0.120177i	$-0.961654\pi$
$211$		−	2.89424e21i		−	0.240354i	0.992752	−	0.120177i	$-0.0383462\pi$
$212$	5.02761e21	−	1.48775e20i	0.399182	−	0.0118124i
$213$	−9.47985e21	−	1.33032e22i	−0.719772	−	1.01007i
$214$	1.75717e22	+	1.70594e22i	1.27610	+	1.23889i
$215$	−4.75210e20			−0.0330157
$216$	6.60272e21	−	1.35156e22i	0.438947	−	0.898513i
$217$	8.46596e21			0.538653
$218$	−9.22970e21	−	8.96061e21i	−0.562148	−	0.545759i
$219$	7.34752e21	+	1.03109e22i	0.428471	+	0.601281i
$220$	−9.37043e21	+	2.77286e20i	−0.523292	+	0.0154851i
$221$		−	5.60010e21i		−	0.299550i
$222$	−3.60191e21	+	2.35967e22i	−0.184578	+	1.20920i
$223$			3.31609e22i			1.62828i	0.580667	+	0.814141i	$0.302792\pi$
$223$			3.31609e22i			1.62828i	−0.580667	+	0.814141i	$0.697208\pi$
$224$	2.24251e22	−	2.60141e22i	1.05531	−	1.22420i
$225$	−6.55035e21	+	1.89668e22i	−0.295482	+	0.855580i
$226$	3.21273e21	−	3.30920e21i	0.138945	−	0.143118i
$227$	−1.24463e21			−0.0516171			−0.0258085	−	0.999667i	$-0.508216\pi$
$227$	−1.24463e21			−0.0516171			−0.0258085	+	0.999667i	$0.508216\pi$
$228$	−2.44334e22	−	3.22265e22i	−0.971860	−	1.28184i
$229$	−4.26763e22			−1.62836			−0.814178	−	0.580615i	$-0.802812\pi$
$229$	−4.26763e22			−1.62836			−0.814178	+	0.580615i	$0.802812\pi$
$230$	6.33581e21	−	6.52607e21i	0.231947	−	0.238912i
$231$	6.36958e22	−	4.53895e22i	2.23768	−	1.59456i
$232$	−4.65704e21	−	4.26105e21i	−0.157027	−	0.143675i
$233$			1.68029e22i			0.543881i	0.962314	+	0.271941i	$0.0876654\pi$
$233$			1.68029e22i			0.543881i	−0.962314	+	0.271941i	$0.912335\pi$
$234$	−2.14084e22	+	1.08117e22i	−0.665324	+	0.336002i
$235$		−	3.95850e21i		−	0.118137i
$236$	−2.22247e19	−	7.51049e20i	−0.000637049	−	0.0215280i
$237$	1.54011e22	−	1.09748e22i	0.424076	−	0.302196i
$238$	−1.76164e22	−	1.71028e22i	−0.466054	−	0.452467i
$239$	−7.18116e22			−1.82564			−0.912818	−	0.408366i	$-0.866099\pi$
$239$	−7.18116e22			−1.82564			−0.912818	+	0.408366i	$0.866099\pi$
$240$	9.81354e21	−	7.90823e21i	0.239783	−	0.193229i
$241$	−3.21583e22			−0.755321			−0.377661	−	0.925944i	$-0.623271\pi$
$241$	−3.21583e22			−0.755321			−0.377661	+	0.925944i	$0.623271\pi$
$242$	−6.00533e22	−	5.83025e22i	−1.35610	−	1.31656i
$243$	−2.11478e21	+	4.60046e22i	−0.0459203	+	0.998945i
$244$	−2.12061e20	−	7.16624e21i	−0.00442850	−	0.149654i
$245$			2.47182e22i			0.496522i
$246$	−2.85303e22	−	4.35500e21i	−0.551344	−	0.0841597i
$247$			6.44814e22i			1.19898i
$248$	1.37407e22	+	1.25724e22i	0.245878	+	0.224971i
$249$	−3.94058e22	−	5.52988e22i	−0.678683	−	0.952406i
$250$	−2.46495e22	+	2.53898e22i	−0.408676	+	0.420948i
$251$	7.01962e22			1.12050			0.560252	−	0.828323i	$-0.310704\pi$
$251$	7.01962e22			1.12050			0.560252	+	0.828323i	$0.310704\pi$
$252$	−3.13710e22	+	1.00364e23i	−0.482196	+	1.54267i
$253$	1.24177e23			1.83821
$254$	5.00995e22	−	5.16039e22i	0.714353	−	0.735804i
$255$	−5.22868e21	−	7.33749e21i	−0.0718225	−	0.100790i
$256$	7.50295e22	−	8.92005e21i	0.993007	−	0.118056i
$257$		−	6.53328e22i		−	0.833233i	−0.909082	−	0.416617i	$-0.863216\pi$
$257$		−	6.53328e22i		−	0.833233i	0.909082	−	0.416617i	$-0.136784\pi$
$258$	8.62234e21	+	1.31615e21i	0.105983	+	0.0161778i
$259$		−	1.66864e23i		−	1.97704i
$260$	−2.00863e22	+	5.94387e20i	−0.229432	+	0.00678926i
$261$	1.82669e22	+	6.30864e21i	0.201178	+	0.0694785i
$262$	6.61133e22	+	6.41858e22i	0.702144	+	0.681674i
$263$	−3.76115e22			−0.385248			−0.192624	−	0.981273i	$-0.561700\pi$
$263$	−3.76115e22			−0.385248			−0.192624	+	0.981273i	$0.561700\pi$
$264$	1.70788e23	+	2.09214e22i	1.68740	+	0.206707i
$265$	−1.29026e22			−0.122982
$266$	2.02841e23	+	1.96927e23i	1.86543	+	1.81105i
$267$	−6.87781e22	+	4.90111e22i	−0.610370	+	0.434949i
$268$	−1.64039e23	+	4.85418e21i	−1.40497	+	0.0415753i
$269$			1.99972e23i			1.65319i	0.562796	+	0.826596i	$0.309726\pi$
$269$			1.99972e23i			1.65319i	−0.562796	+	0.826596i	$0.690274\pi$
$270$	−1.79556e22	+	3.41544e22i	−0.143299	+	0.272578i
$271$		−	1.05713e23i		−	0.814557i	−0.913304	−	0.407279i	$-0.866478\pi$
$271$		−	1.05713e23i		−	0.814557i	0.913304	−	0.407279i	$-0.133522\pi$
$272$	−3.19396e21	−	5.39200e22i	−0.0237643	−	0.401186i
$273$	1.36538e23	−	9.72964e22i	0.981086	−	0.699120i
$274$	1.01798e23	−	1.04855e23i	0.706496	−	0.727711i
$275$	−2.29532e23			−1.53880
$276$	−1.33034e23	+	1.00863e23i	−0.861638	+	0.653275i
$277$	−5.23245e22			−0.327452			−0.163726	−	0.986506i	$-0.552351\pi$
$277$	−5.23245e22			−0.327452			−0.163726	+	0.986506i	$0.552351\pi$
$278$	−1.00648e23	+	1.03670e23i	−0.608665	+	0.626942i
$279$	−5.38972e22	−	1.86138e22i	−0.315011	−	0.108792i
$280$	−5.94742e22	+	6.50014e22i	−0.335991	+	0.367216i
$281$		−	2.46223e23i		−	1.34468i	−0.740244	−	0.672339i	$-0.765290\pi$
$281$		−	2.46223e23i		−	1.34468i	0.740244	−	0.672339i	$-0.234710\pi$
$282$	−1.09636e22	+	7.18241e22i	−0.0578876	+	0.379231i
$283$		−	2.13125e21i		−	0.0108809i	−0.999985	−	0.00544043i	$-0.998268\pi$
$283$		−	2.13125e21i		−	0.0108809i	0.999985	−	0.00544043i	$-0.00173175\pi$
$284$	7.43061e21	+	2.51105e23i	0.0366860	+	1.23974i
$285$	6.02047e22	+	8.44862e22i	0.287478	+	0.403422i
$286$	−1.96838e23	−	1.91099e23i	−0.909142	−	0.882637i
$287$	2.01752e23			0.901445
$288$	−1.99962e23	+	1.16309e23i	−0.864409	+	0.502789i
$289$	2.00459e23			0.838485
$290$	1.16178e22	+	1.12791e22i	0.0470267	+	0.0456556i
$291$	1.00788e23	+	1.41437e23i	0.394843	+	0.554090i
$292$	−5.75922e21	−	1.94624e23i	−0.0218387	−	0.738003i
$293$		−	3.06405e23i		−	1.12474i	−0.826885	−	0.562371i	$-0.809889\pi$
$293$		−	3.06405e23i		−	1.12474i	0.826885	−	0.562371i	$-0.190111\pi$
$294$	6.84601e22	−	4.48493e23i	0.243297	−	1.59388i
$295$			1.92745e21i			0.00663246i
$296$	2.47801e23	−	2.70830e23i	0.825718	−	0.902455i
$297$	−5.05306e23	+	1.48919e23i	−1.63068	+	0.480578i
$298$	1.59366e23	−	1.64152e23i	0.498129	−	0.513088i
$299$	2.66184e23			0.805945
$300$	2.45903e23	−	1.86438e23i	0.721292	−	0.546868i
$301$	−6.09728e22			−0.173283
$302$	1.24311e23	−	1.28044e23i	0.342330	−	0.352610i
$303$	−3.43412e23	+	2.44715e23i	−0.916455	+	0.653064i
$304$	3.67762e22	+	6.20853e23i	0.0951192	+	1.60579i
$305$			1.83911e22i			0.0461061i
$306$	7.45485e22	+	1.47615e23i	0.181170	+	0.358737i
$307$		−	5.86296e22i		−	0.138135i	−0.997612	−	0.0690673i	$-0.977998\pi$
$307$		−	5.86296e22i		−	0.138135i	0.997612	−	0.0690673i	$-0.0220023\pi$
$308$	−1.20229e24	+	3.55778e22i	−2.74649	+	0.0812731i
$309$	1.58316e22	−	1.12815e22i	0.0350686	−	0.0249898i
$310$	−3.42788e22	−	3.32794e22i	−0.0736359	−	0.0714891i
$311$	2.84479e23			0.592689			0.296344	−	0.955081i	$-0.404232\pi$
$311$	2.84479e23			0.592689			0.296344	+	0.955081i	$0.404232\pi$
$312$	3.66098e23	+	4.48469e22i	0.739825	+	0.0906284i
$313$	−5.93941e23			−1.16432			−0.582160	−	0.813075i	$-0.697792\pi$
$313$	−5.93941e23			−1.16432			−0.582160	+	0.813075i	$0.697792\pi$
$314$	−4.55880e23	−	4.42590e23i	−0.867000	−	0.841724i
$315$	8.80538e22	−	2.54964e23i	0.162479	−	0.470466i
$316$	−2.90705e23	+	8.60242e21i	−0.520505	+	0.0154026i
$317$			5.66222e23i			0.983839i	0.870641	+	0.491919i	$0.163705\pi$
$317$			5.66222e23i			0.983839i	−0.870641	+	0.491919i	$0.836295\pi$
$318$	2.34108e23	+	3.57354e22i	0.394784	+	0.0602617i
$319$			2.21062e23i			0.361828i
$320$	−1.93060e23	+	1.71790e22i	−0.306738	+	0.0272944i
$321$	6.69175e23	+	9.39064e23i	1.03215	+	1.44843i
$322$	8.12930e23	−	8.37342e23i	1.21737	−	1.25393i
$323$	4.44611e23			0.646482
$324$	4.20386e23	−	5.69977e23i	0.593568	−	0.804784i
$325$	−4.92021e23			−0.674671
$326$	−1.25965e23	+	1.29748e23i	−0.167758	+	0.172796i
$327$	−3.51490e23	−	4.93251e23i	−0.454684	−	0.638064i
$328$	3.27455e23	+	2.99611e23i	0.411481	+	0.376492i
$329$		−	5.07904e23i		−	0.620041i
$330$	−4.36330e23	−	6.66035e22i	−0.517527	−	0.0789977i
$331$			8.00528e23i			0.922594i	0.887246	+	0.461297i	$0.152616\pi$
$331$			8.00528e23i			0.922594i	−0.887246	+	0.461297i	$0.847384\pi$
$332$	3.08876e22	+	1.04379e24i	0.0345917	+	1.16897i
$333$	−3.66879e23	+	1.06231e24i	−0.399303	+	1.15620i
$334$	5.90398e23	+	5.73186e23i	0.624530	+	0.606323i
$335$	4.20982e23			0.432850
$336$	1.25915e24	−	1.01468e24i	1.25850	−	1.01416i
$337$	1.11071e24			1.07924			0.539618	−	0.841910i	$-0.318569\pi$
$337$	1.11071e24			1.07924			0.539618	+	0.841910i	$0.318569\pi$
$338$	3.37553e23	+	3.27712e23i	0.318885	+	0.309588i
$339$	1.76850e23	−	1.26023e23i	0.162445	−	0.115758i
$340$	4.09841e21	+	1.38499e23i	0.00366071	+	0.123708i
$341$		−	6.52250e23i		−	0.566562i
$342$	−8.58375e23	−	1.69968e24i	−0.725152	−	1.43589i
$343$			1.20449e24i			0.989714i
$344$	−9.89625e22	−	9.05475e22i	−0.0790980	−	0.0723721i
$345$	3.48765e23	−	2.48529e23i	0.271176	−	0.193240i
$346$	−1.21500e24	+	1.25149e24i	−0.919080	+	0.946679i
$347$	6.08564e23			0.447895			0.223948	−	0.974601i	$-0.428106\pi$
$347$	6.08564e23			0.447895			0.223948	+	0.974601i	$0.428106\pi$
$348$	−1.79558e23	−	2.36829e23i	−0.128589	−	0.169602i
$349$	1.87965e24			1.30989			0.654945	−	0.755677i	$-0.272692\pi$
$349$	1.87965e24			1.30989			0.654945	+	0.755677i	$0.272692\pi$
$350$	−1.50264e24	+	1.54776e24i	−1.01908	+	1.04968i
$351$	−1.08317e24	+	3.19221e23i	−0.714953	+	0.210704i
$352$	−2.00423e24	−	1.72772e24i	−1.28763	−	1.10999i
$353$		−	1.85234e24i		−	1.15841i	−0.815182	−	0.579205i	$-0.803363\pi$
$353$		−	1.85234e24i		−	1.15841i	0.815182	−	0.579205i	$-0.196637\pi$
$354$	5.33833e21	−	3.49723e22i	0.00324993	−	0.0212908i
$355$		−	6.44424e23i		−	0.381946i
$356$	1.29822e24	−	3.84165e22i	0.749160	−	0.0221688i
$357$	−6.70877e23	−	9.41452e23i	−0.376960	−	0.528993i
$358$	2.45006e24	+	2.37864e24i	1.34057	+	1.30148i
$359$	1.68585e23			0.0898299			0.0449149	−	0.998991i	$-0.485698\pi$
$359$	1.68585e23			0.0898299			0.0449149	+	0.998991i	$0.485698\pi$
$360$	5.21549e23	−	2.83057e23i	0.270659	−	0.146892i
$361$	−3.14097e24			−1.58762
$362$	4.88027e23	+	4.73799e23i	0.240277	+	0.233272i
$363$	−2.28698e24	−	3.20935e24i	−1.09686	−	1.53923i
$364$	−2.57722e24	+	7.62641e22i	−1.20417	+	0.0356334i
$365$			4.99472e23i			0.227368i
$366$	5.09364e22	−	3.33693e23i	0.0225922	−	0.148005i
$367$		−	2.15406e24i		−	0.930957i	−0.885059	−	0.465478i	$-0.845882\pi$
$367$		−	2.15406e24i		−	0.930957i	0.885059	−	0.465478i	$-0.154118\pi$
$368$	2.56292e24	−	1.51815e23i	1.07940	−	0.0639382i
$369$	−1.28442e24	−	4.43585e23i	−0.527177	−	0.182065i
$370$	−6.55937e23	+	6.75634e23i	−0.262389	+	0.270268i
$371$	−1.65550e24			−0.645470
$372$	5.29792e23	+	6.98770e23i	0.201348	+	0.265568i
$373$	−3.67912e23			−0.136304			−0.0681522	−	0.997675i	$-0.521710\pi$
$373$	−3.67912e23			−0.136304			−0.0681522	+	0.997675i	$0.521710\pi$
$374$	−1.31767e24	+	1.35723e24i	−0.475910	+	0.490201i
$375$	−1.35687e24	+	9.66906e23i	−0.477796	+	0.340476i
$376$	7.54261e23	−	8.24357e23i	0.258963	−	0.283029i
$377$			4.73865e23i			0.158640i
$378$	−2.30383e24	+	4.38225e24i	−0.752104	+	1.43062i
$379$			7.64858e23i			0.243505i	0.992560	+	0.121753i	$0.0388514\pi$
$379$			7.64858e23i			0.243505i	−0.992560	+	0.121753i	$0.961149\pi$
$380$	−4.71904e22	−	1.59472e24i	−0.0146524	−	0.495154i
$381$	2.75781e24	−	1.96521e24i	0.835173	−	0.595143i
$382$	1.18963e24	+	1.15495e24i	0.351407	+	0.341162i
$383$	1.08282e24			0.312011			0.156005	−	0.987756i	$-0.450138\pi$
$383$	1.08282e24			0.312011			0.156005	+	0.987756i	$0.450138\pi$
$384$	3.55052e24	+	2.23004e23i	0.998033	+	0.0626854i
$385$	3.08551e24			0.846154
$386$	−1.66898e24	−	1.62032e24i	−0.446551	−	0.433532i
$387$	3.88174e23	+	1.34059e23i	0.101338	+	0.0349979i
$388$	−7.90007e22	−	2.66970e24i	−0.0201247	−	0.680082i
$389$		−	6.22083e24i		−	1.54642i	−0.634151	−	0.773210i	$-0.718650\pi$
$389$		−	6.22083e24i		−	1.54642i	0.634151	−	0.773210i	$-0.281350\pi$
$390$	−9.35311e23	−	1.42770e23i	−0.226904	−	0.0346357i
$391$		−	1.83539e24i		−	0.434559i
$392$	−4.70985e24	+	5.14755e24i	−1.08840	+	1.18955i
$393$	2.51776e24	+	3.53321e24i	0.567917	+	0.796967i
$394$	1.96053e24	−	2.01940e24i	0.431677	−	0.444640i
$395$	7.46051e23			0.160360
$396$	7.73242e24	+	2.41694e24i	1.62260	+	0.507180i
$397$	5.85498e23			0.119954			0.0599771	−	0.998200i	$-0.480897\pi$
$397$	5.85498e23			0.119954			0.0599771	+	0.998200i	$0.480897\pi$
$398$	4.02810e24	−	4.14906e24i	0.805770	−	0.829967i
$399$	7.72469e24	+	1.08402e25i	1.50882	+	2.11736i
$400$	−4.73738e24	+	2.80619e23i	−0.903583	+	0.0535238i
$401$			9.89454e24i			1.84299i	0.388385	+	0.921497i	$0.373033\pi$
$401$			9.89454e24i			1.84299i	−0.388385	+	0.921497i	$0.626967\pi$
$402$	−7.63841e24	−	1.16596e24i	−1.38949	−	0.212098i
$403$		−	1.39815e24i		−	0.248403i
$404$	6.48209e24	−	1.91816e23i	1.12484	−	0.0332859i
$405$	−1.12116e24	+	1.42958e24i	−0.190040	+	0.242318i
$406$	1.49065e24	+	1.44719e24i	0.246819	+	0.239623i
$407$	−1.28558e25			−2.07947
$408$	3.09228e23	−	2.52431e24i	0.0488660	−	0.398907i
$409$	5.98828e24			0.924551			0.462276	−	0.886736i	$-0.347033\pi$
$409$	5.98828e24			0.924551			0.462276	+	0.886736i	$0.347033\pi$
$410$	−8.16895e23	−	7.93079e23i	−0.123231	−	0.119638i
$411$	5.60364e24	−	3.99314e24i	0.825986	−	0.588597i
$412$	−2.98829e23	+	8.84283e21i	−0.0430427	+	0.00127370i
$413$			2.47306e23i			0.0348104i
$414$	−7.01642e24	+	3.54343e24i	−0.965189	+	0.487440i
$415$		−	2.67874e24i		−	0.360142i
$416$	−4.29623e24	−	3.70351e24i	−0.564548	−	0.486662i
$417$	−5.54031e24	+	3.94801e24i	−0.711609	+	0.507091i
$418$	1.51720e25	−	1.56276e25i	1.90488	−	1.96209i
$419$	1.45705e25			1.78830			0.894152	−	0.447764i	$-0.147780\pi$
$419$	1.45705e25			1.78830			0.894152	+	0.447764i	$0.147780\pi$
$420$	−3.30557e24	+	2.50621e24i	−0.396624	+	0.300711i
$421$	−1.57623e25			−1.84901			−0.924505	−	0.381171i	$-0.875521\pi$
$421$	−1.57623e25			−1.84901			−0.924505	+	0.381171i	$0.875521\pi$
$422$	−1.45977e24	+	1.50361e24i	−0.167423	+	0.172451i
$423$	−1.11671e24	+	3.23349e24i	−0.125230	+	0.362608i
$424$	−2.68697e24	−	2.45849e24i	−0.294637	−	0.269583i
$425$			3.39258e24i			0.363777i
$426$	−1.78481e24	+	1.16926e25i	−0.187155	+	1.22608i
$427$			2.35971e24i			0.241988i
$428$	−5.24521e23	−	1.77253e25i	−0.0526074	−	1.77778i
$429$	−7.49608e24	−	1.05194e25i	−0.735343	−	1.03192i
$430$	2.46880e23	+	2.39682e23i	0.0236884	+	0.0229978i
$431$	−9.19244e24			−0.862774			−0.431387	−	0.902167i	$-0.641976\pi$
$431$	−9.19244e24			−0.862774			−0.431387	+	0.902167i	$0.641976\pi$
$432$	−1.02471e25	+	3.69136e24i	−0.940817	+	0.338915i
$433$	−3.24019e24			−0.291028			−0.145514	−	0.989356i	$-0.546484\pi$
$433$	−3.24019e24			−0.291028			−0.145514	+	0.989356i	$0.546484\pi$
$434$	−4.39821e24	−	4.26999e24i	−0.386477	−	0.375210i
$435$	4.42436e23	+	6.20877e23i	0.0380367	+	0.0533775i
$436$	2.75509e23	+	9.31038e24i	0.0231747	+	0.783152i
$437$			2.11332e25i			1.73937i
$438$	1.38335e24	−	9.06256e24i	0.111411	−	0.729872i
$439$			7.31359e24i			0.576391i	0.957572	+	0.288196i	$0.0930553\pi$
$439$			7.31359e24i			0.576391i	−0.957572	+	0.288196i	$0.906945\pi$
$440$	5.00795e24	+	4.58212e24i	0.386242	+	0.353400i
$441$	6.97311e24	−	2.01909e25i	0.526332	−	1.52402i
$442$	−2.82453e24	+	2.90935e24i	−0.208658	+	0.214924i
$443$	3.64224e24			0.263350			0.131675	−	0.991293i	$-0.457964\pi$
$443$	3.64224e24			0.263350			0.131675	+	0.991293i	$0.457964\pi$
$444$	1.37728e25	−	1.04422e25i	0.974726	−	0.739015i
$445$	−3.33170e24			−0.230805
$446$	1.67254e25	−	1.72276e25i	1.13421	−	1.16827i
$447$	8.77257e24	−	6.25132e24i	0.582379	−	0.415002i
$448$	−2.47710e25	+	2.20419e24i	−1.60991	+	0.143254i
$449$		−	1.81510e24i		−	0.115494i	−0.998331	−	0.0577471i	$-0.981608\pi$
$449$		−	1.81510e24i		−	0.115494i	0.998331	−	0.0577471i	$-0.0183917\pi$
$450$	1.29693e25	−	6.54978e24i	0.807977	−	0.408045i
$451$		−	1.55437e25i		−	0.948151i
$452$	−3.33813e24	+	9.87807e22i	−0.199383	+	0.00590006i
$453$	6.84292e24	−	4.87625e24i	0.400229	−	0.285202i
$454$	6.46605e23	+	6.27754e23i	0.0370347	+	0.0359549i
$455$	6.61405e24			0.370987
$456$	−3.56055e24	+	2.90658e25i	−0.195592	+	1.59667i
$457$	3.30144e24			0.177623			0.0888117	−	0.996048i	$-0.471693\pi$
$457$	3.30144e24			0.177623			0.0888117	+	0.996048i	$0.471693\pi$
$458$	2.21710e25	+	2.15247e25i	1.16833	+	1.13427i
$459$	2.20109e24	+	7.46863e24i	0.113610	+	0.385497i
$460$	−6.58313e24	+	1.94805e23i	−0.332838	+	0.00984921i
$461$		−	5.99006e24i		−	0.296669i	−0.988937	−	0.148335i	$-0.952609\pi$
$461$		−	5.99006e24i		−	0.296669i	0.988937	−	0.148335i	$-0.0473913\pi$
$462$	−5.59842e25	−	8.54570e24i	−2.71623	−	0.414619i
$463$			3.87598e25i			1.84231i	0.389198	+	0.921154i	$0.372752\pi$
$463$			3.87598e25i			1.84231i	−0.389198	+	0.921154i	$0.627248\pi$
$464$	2.70264e23	+	4.56256e24i	0.0125854	+	0.212465i
$465$	−1.30542e24	−	1.83192e24i	−0.0595591	−	0.0835802i
$466$	8.47492e24	−	8.72941e24i	0.378852	−	0.390228i
$467$	−3.39957e25			−1.48907			−0.744533	−	0.667586i	$-0.767328\pi$
$467$	−3.39957e25			−1.48907			−0.744533	+	0.667586i	$0.767328\pi$
$468$	1.65751e25	+	5.18093e24i	0.711412	+	0.222368i
$469$	5.40150e25			2.27181
$470$	−1.99655e24	+	2.05651e24i	−0.0822908	+	0.0847619i
$471$	−1.73611e25	−	2.43630e25i	−0.701258	−	0.984086i
$472$	−3.67261e23	+	4.01392e23i	−0.0145387	+	0.0158899i
$473$			4.69758e24i			0.182261i
$474$	−1.35365e25	−	2.06628e24i	−0.514770	−	0.0785770i
$475$		−	3.90632e25i		−	1.45606i
$476$	5.25855e23	+	1.77704e25i	0.0192132	+	0.649279i
$477$	1.05394e25	+	3.63989e24i	0.377479	+	0.130366i
$478$	3.73073e25	+	3.62197e25i	1.30987	+	1.27169i
$479$	−5.21744e25			−1.79585			−0.897925	−	0.440149i	$-0.854926\pi$
$479$	−5.21744e25			−1.79585			−0.897925	+	0.440149i	$0.854926\pi$
$480$	−9.08698e24	−	8.41205e23i	−0.306639	−	0.0283864i
$481$	−2.75576e25			−0.911723
$482$	1.67068e25	+	1.62197e25i	0.541934	+	0.526135i
$483$	4.47490e25	−	3.18881e25i	1.42327	−	1.01422i
$484$	1.79261e24	+	6.05783e25i	0.0559055	+	1.88923i
$485$			6.85139e24i			0.209523i
$486$	2.43020e25	−	2.28335e25i	0.728783	−	0.684745i
$487$			3.79996e25i			1.11752i	0.829331	+	0.558758i	$0.188722\pi$
$487$			3.79996e25i			1.11752i	−0.829331	+	0.558758i	$0.811278\pi$
$488$	−3.50427e24	+	3.82994e24i	−0.101067	+	0.110460i
$489$	−6.93396e24	+	4.94113e24i	−0.196131	+	0.139763i
$490$	1.24671e25	−	1.28415e25i	0.345862	−	0.356248i
$491$	6.00488e24			0.163392			0.0816959	−	0.996657i	$-0.473966\pi$
$491$	6.00488e24			0.163392			0.0816959	+	0.996657i	$0.473966\pi$
$492$	1.26254e25	+	1.66523e25i	0.336960	+	0.444434i
$493$	3.26739e24			0.0855372
$494$	3.25225e25	−	3.34992e25i	0.835177	−	0.860257i
$495$	−1.96434e25	−	6.78400e24i	−0.494842	−	0.170898i
$496$	−7.97422e23	−	1.34620e25i	−0.0197066	−	0.332685i
$497$		−	8.26842e25i		−	2.00464i
$498$	−7.41912e24	+	4.86038e25i	−0.176471	+	1.15609i
$499$		−	3.97513e25i		−	0.927675i	−0.885920	−	0.463838i	$-0.846472\pi$
$499$		−	3.97513e25i		−	0.927675i	0.885920	−	0.463838i	$-0.153528\pi$
$500$	2.56117e25	−	7.57892e23i	0.586440	−	0.0173537i
$501$	2.24838e25	+	3.15519e25i	0.505141	+	0.708871i
$502$	−3.64681e25	−	3.54049e25i	−0.803948	−	0.780510i
$503$	5.75320e25			1.24455			0.622277	−	0.782797i	$-0.286208\pi$
$503$	5.75320e25			1.24455			0.622277	+	0.782797i	$0.286208\pi$
$504$	6.69185e25	−	3.63182e25i	1.42055	−	0.770964i
$505$	−1.66353e25			−0.346548
$506$	−6.45120e25	−	6.26312e25i	−1.31890	−	1.28044i
$507$	1.28549e25	+	1.80394e25i	0.257924	+	0.361949i
$508$	−5.20550e25	+	1.54039e24i	−1.02508	+	0.0303337i
$509$			2.80394e25i			0.541938i	0.962588	+	0.270969i	$0.0873440\pi$
$509$			2.80394e25i			0.541938i	−0.962588	+	0.270969i	$0.912656\pi$
$510$	−9.84428e23	+	6.44914e24i	−0.0186753	+	0.122345i
$511$			6.40858e25i			1.19334i
$512$	−4.34781e25	−	3.32086e25i	−0.794705	−	0.606996i
$513$	−2.53440e25	−	8.59962e25i	−0.454737	−	1.54299i
$514$	−3.29520e25	+	3.39415e25i	−0.580406	+	0.597835i
$515$	7.66900e23			0.0132608
$516$	−3.81562e24	−	5.03262e24i	−0.0647729	−	0.0854324i
$517$	−3.91308e25			−0.652167
$518$	−8.41614e25	+	8.66887e25i	−1.37715	+	1.41850i
$519$	−6.68816e25	+	4.76597e25i	−1.07453	+	0.765705i
$520$	1.07350e25	+	9.82217e24i	0.169344	+	0.154944i
$521$			6.80286e25i			1.05374i	0.849946	+	0.526870i	$0.176635\pi$
$521$			6.80286e25i			1.05374i	−0.849946	+	0.526870i	$0.823365\pi$
$522$	−6.30808e24	−	1.24908e25i	−0.0959462	−	0.189985i
$523$		−	4.08897e25i		−	0.610728i	−0.952236	−	0.305364i	$-0.901222\pi$
$523$		−	4.08897e25i		−	0.610728i	0.952236	−	0.305364i	$-0.0987781\pi$
$524$	−1.97350e24	−	6.66912e25i	−0.0289461	−	0.978186i
$525$	−8.27153e25	+	5.89428e25i	−1.19144	+	0.849018i
$526$	1.95398e25	+	1.89701e25i	0.276411	+	0.268353i
$527$	−9.64053e24			−0.133937
$528$	−7.81749e25	−	9.70094e25i	−1.06671	−	1.32371i
$529$	1.26240e25			0.169188
$530$	6.70312e24	+	6.50770e24i	0.0882382	+	0.0856657i
$531$	5.43744e23	−	1.57443e24i	0.00703066	−	0.0203576i
$532$	−6.05486e24	−	2.04614e26i	−0.0769030	−	2.59881i
$533$		−	3.33193e25i		−	0.415707i
$534$	6.04512e25	+	9.22755e24i	0.740906	+	0.113095i
$535$			4.54894e25i			0.547708i
$536$	8.76694e25	+	8.02148e25i	1.03701	+	0.948831i
$537$	9.33046e25	+	1.30936e26i	1.08429	+	1.52161i
$538$	1.00860e26	−	1.03889e26i	1.15156	−	1.18615i
$539$	2.44345e26			2.74101
$540$	2.65547e25	−	8.68752e24i	0.292685	−	0.0957536i
$541$	−5.32934e25			−0.577164			−0.288582	−	0.957455i	$-0.593184\pi$
$541$	−5.32934e25			−0.577164			−0.288582	+	0.957455i	$0.593184\pi$
$542$	−5.33188e25	+	5.49199e25i	−0.567397	+	0.584435i
$543$	1.85853e25	+	2.60810e25i	0.194344	+	0.272726i
$544$	−2.55364e25	+	2.96233e25i	−0.262404	+	0.304400i
$545$		−	2.38937e25i		−	0.241277i
$546$	−1.20007e26	−	1.83184e25i	−1.19090	−	0.181785i
$547$		−	5.95545e25i		−	0.580811i	−0.956904	−	0.290406i	$-0.906210\pi$
$547$		−	5.95545e25i		−	0.580811i	0.956904	−	0.290406i	$-0.0937902\pi$
$548$	−1.05772e26	+	3.12995e24i	−1.01380	+	0.0300001i
$549$	5.18821e24	−	1.50227e25i	0.0488743	−	0.141517i
$550$	1.19246e26	+	1.15769e26i	1.10407	+	1.07188i
$551$	−3.76217e25			−0.342372
$552$	1.19986e26	+	1.46982e25i	1.07327	+	0.131475i
$553$	9.57236e25			0.841648
$554$	2.71835e25	+	2.63910e25i	0.234943	+	0.228093i
$555$	−3.61071e25	+	2.57299e25i	−0.306767	+	0.218602i
$556$	1.04576e26	−	3.09458e24i	0.873419	−	0.0258459i
$557$			6.57624e24i			0.0539950i	0.999636	+	0.0269975i	$0.00859461\pi$
$557$			6.57624e24i			0.0539950i	−0.999636	+	0.0269975i	$0.991405\pi$
$558$	1.86122e25	+	3.68544e25i	0.150236	+	0.297484i
$559$			1.00697e25i			0.0799103i
$560$	6.36827e25	−	3.77225e24i	0.496861	−	0.0294316i
$561$	−7.25330e25	+	5.16869e25i	−0.556402	+	0.396491i
$562$	−1.24188e26	+	1.27917e26i	−0.936663	+	0.964790i
$563$	2.08374e25			0.154531			0.0772653	−	0.997011i	$-0.475381\pi$
$563$	2.08374e25			0.154531			0.0772653	+	0.997011i	$0.475381\pi$
$564$	4.19218e25	−	3.17841e25i	0.305695	−	0.231771i
$565$	8.56681e24			0.0614270
$566$	−1.07494e24	+	1.10722e24i	−0.00757928	+	0.00780688i
$567$	−1.43853e26	+	1.83426e26i	−0.997423	+	1.27181i
$568$	1.22790e26	−	1.34201e26i	0.837247	−	0.915055i
$569$			9.60683e25i			0.644189i	0.946707	+	0.322095i	$0.104387\pi$
$569$			9.60683e25i			0.644189i	−0.946707	+	0.322095i	$0.895613\pi$
$570$	1.13350e25	−	7.42575e25i	0.0747499	−	0.489699i
$571$		−	2.92701e26i		−	1.89837i	−0.314714	−	0.949187i	$-0.601909\pi$
$571$		−	2.92701e26i		−	1.89837i	0.314714	−	0.949187i	$-0.398091\pi$
$572$	5.87567e24	+	1.98559e26i	0.0374796	+	1.26656i
$573$	4.53041e25	+	6.35760e25i	0.284229	+	0.398863i
$574$	−1.04813e26	−	1.01758e26i	−0.646776	−	0.627920i
$575$	−1.61256e26			−0.978747
$576$	1.62547e26	+	4.04306e25i	0.970431	+	0.241377i
$577$	−2.35505e25			−0.138302			−0.0691512	−	0.997606i	$-0.522029\pi$
$577$	−2.35505e25			−0.138302			−0.0691512	+	0.997606i	$0.522029\pi$
$578$	−1.04142e26	−	1.01106e26i	−0.601603	−	0.584064i
$579$	−6.35589e25	−	8.91931e25i	−0.361185	−	0.506857i
$580$	−3.46796e23	−	1.17194e25i	−0.00193869	−	0.0655148i
$581$		−	3.43702e26i		−	1.89020i
$582$	1.89758e25	−	1.24313e26i	0.102667	−	0.672589i
$583$			1.27546e26i			0.678914i
$584$	−9.51705e25	+	1.04015e26i	−0.498403	+	0.544721i
$585$	−4.21072e25	−	1.45421e25i	−0.216958	−	0.0749283i
$586$	−1.54542e26	+	1.59182e26i	−0.783462	+	0.806989i
$587$	2.73283e26			1.36317			0.681586	−	0.731738i	$-0.261290\pi$
$587$	2.73283e26			1.36317			0.681586	+	0.731738i	$0.261290\pi$
$588$	−2.61773e26	+	1.98470e26i	−1.28481	+	0.974117i
$589$	1.11004e26			0.536098
$590$	9.72152e23	−	1.00135e24i	0.00461998	−	0.00475871i
$591$	1.07920e26	−	7.69039e25i	0.504688	−	0.359640i
$592$	−2.65336e26	+	1.57172e25i	−1.22107	+	0.0723300i
$593$		−	1.58679e26i		−	0.718621i	−0.933218	−	0.359310i	$-0.883012\pi$
$593$		−	1.58679e26i		−	0.718621i	0.933218	−	0.359310i	$-0.116988\pi$
$594$	3.37625e26	+	1.77496e26i	1.50475	+	0.791072i
$595$		−	4.56051e25i		−	0.200033i
$596$	−1.65587e26	+	4.89999e24i	−0.714804	+	0.0211522i
$597$	2.21733e26	−	1.58007e26i	0.942051	−	0.671304i
$598$	−1.38287e26	−	1.34255e26i	−0.578256	−	0.561398i
$599$	−1.42414e26			−0.586137			−0.293069	−	0.956091i	$-0.594676\pi$
$599$	−1.42414e26			−0.586137			−0.293069	+	0.956091i	$0.594676\pi$
$600$	−2.21784e26	−	2.71685e25i	−0.898451	−	0.110060i
$601$	−1.27474e26			−0.508293			−0.254146	−	0.967166i	$-0.581794\pi$
$601$	−1.27474e26			−0.508293			−0.254146	+	0.967166i	$0.581794\pi$
$602$	3.16764e25	+	3.07529e25i	0.124328	+	0.120704i
$603$	−3.43877e26	−	1.18761e26i	−1.32858	−	0.458838i
$604$	−1.29164e26	+	3.82216e24i	−0.491235	+	0.0145364i
$605$		−	1.55465e26i		−	0.582045i
$606$	3.01836e26	+	4.60736e25i	1.11245	+	0.169810i
$607$			3.23276e26i			1.17296i	0.809965	+	0.586478i	$0.199486\pi$
$607$			3.23276e26i			1.17296i	−0.809965	+	0.586478i	$0.800514\pi$
$608$	2.94034e26	−	3.41092e26i	1.05030	−	1.21839i
$609$	5.67677e25	+	7.96630e25i	0.199635	+	0.280151i
$610$	9.27593e24	−	9.55448e24i	0.0321162	−	0.0330806i
$611$	−8.38803e25			−0.285936
$612$	3.57234e25	−	1.14289e26i	0.119899	−	0.383587i
$613$	−1.95279e26			−0.645328			−0.322664	−	0.946514i	$-0.604578\pi$
$613$	−1.95279e26			−0.645328			−0.322664	+	0.946514i	$0.604578\pi$
$614$	−2.95711e25	+	3.04591e25i	−0.0962205	+	0.0991100i
$615$	−3.11094e25	−	4.36563e25i	−0.0996732	−	0.139873i
$616$	6.42556e26	+	5.87919e26i	2.02719	+	1.85481i
$617$		−	1.53509e26i		−	0.476898i	−0.971155	−	0.238449i	$-0.923361\pi$
$617$		−	1.53509e26i		−	0.476898i	0.971155	−	0.238449i	$-0.0766389\pi$
$618$	−1.39148e25	−	2.12403e24i	−0.0425685	−	0.00649785i
$619$		−	9.80949e25i		−	0.295519i	−0.989023	−	0.147759i	$-0.952794\pi$
$619$		−	9.80949e25i		−	0.295519i	0.989023	−	0.147759i	$-0.0472061\pi$
$620$	1.02323e24	+	3.45785e25i	0.00303566	+	0.102585i
$621$	−3.54999e26	+	1.04622e26i	−1.03719	+	0.305670i
$622$	−1.47792e26	−	1.43483e26i	−0.425247	−	0.412850i
$623$	−4.27480e26			−1.21138
$624$	−1.67575e26	−	2.07948e26i	−0.467687	−	0.580365i
$625$	2.63569e26			0.724493
$626$	3.08562e26	+	2.99567e26i	0.835385	+	0.811031i
$627$	8.35168e26	−	5.95139e26i	2.22706	−	1.58700i
$628$	1.36082e25	+	4.59866e26i	0.0357423	+	1.20785i
$629$			1.90015e26i			0.491594i
$630$	−1.74342e26	+	8.80461e25i	−0.444290	+	0.224375i
$631$		−	1.66032e26i		−	0.416787i	−0.978045	−	0.208393i	$-0.933177\pi$
$631$		−	1.66032e26i		−	0.416787i	0.978045	−	0.208393i	$-0.0668235\pi$
$632$	1.55365e26	+	1.42154e26i	0.384185	+	0.351518i
$633$	−8.03553e25	+	5.72611e25i	−0.195740	+	0.139484i
$634$	2.85586e26	−	2.94162e26i	0.685313	−	0.705893i
$635$	1.33591e26			0.315812
$636$	−1.03599e26	−	1.36643e26i	−0.241276	−	0.318232i
$637$	5.23776e26			1.20177
$638$	1.11497e26	−	1.14845e26i	0.252039	−	0.259607i
$639$	−1.81795e26	+	5.26395e26i	−0.404878	+	1.17234i
$640$	1.08963e26	+	8.84492e25i	0.239094	+	0.194082i
$641$			5.49273e26i			1.18751i	0.804647	+	0.593754i	$0.202355\pi$
$641$			5.49273e26i			1.18751i	−0.804647	+	0.593754i	$0.797645\pi$
$642$	1.25989e26	−	8.25372e26i	0.268379	−	1.75820i
$643$			5.99085e26i			1.25743i	0.777635	+	0.628716i	$0.216419\pi$
$643$			5.99085e26i			1.25743i	−0.777635	+	0.628716i	$0.783581\pi$
$644$	−8.44662e26	+	2.49949e25i	−1.74690	+	0.0516935i
$645$	9.40180e24	+	1.31937e25i	0.0191599	+	0.0268874i
$646$	−2.30983e26	−	2.24249e26i	−0.463843	−	0.450320i
$647$	1.22727e26			0.242855			0.121428	−	0.992600i	$-0.461253\pi$
$647$	1.22727e26			0.242855			0.121428	+	0.992600i	$0.461253\pi$
$648$	−5.05877e26	+	8.40821e25i	−0.986467	+	0.163961i
$649$	1.90534e25			0.0366140
$650$	2.55613e26	+	2.48161e26i	0.484068	+	0.469956i
$651$	−1.67495e26	−	2.35048e26i	−0.312595	−	0.438670i
$652$	1.30882e26	−	3.87301e24i	0.240729	−	0.00712355i
$653$			9.31026e26i			1.68767i	0.536606	+	0.843833i	$0.319706\pi$
$653$			9.31026e26i			1.68767i	−0.536606	+	0.843833i	$0.680294\pi$
$654$	−6.61766e25	+	4.33534e26i	−0.118227	+	0.774523i
$655$			1.71153e26i			0.301365i
$656$	−1.90033e25	−	3.20812e26i	−0.0329794	−	0.556754i
$657$	1.40903e26	−	4.07992e26i	0.241019	−	0.697880i
$658$	−2.56172e26	+	2.63865e26i	−0.431902	+	0.444872i
$659$	6.06156e26			1.00733			0.503666	−	0.863898i	$-0.331984\pi$
$659$	6.06156e26			1.00733			0.503666	+	0.863898i	$0.331984\pi$
$660$	1.93088e26	+	2.54674e26i	0.316292	+	0.417174i
$661$	−1.19806e27			−1.93448			−0.967239	−	0.253869i	$-0.918297\pi$
$661$	−1.19806e27			−1.93448			−0.967239	+	0.253869i	$0.918297\pi$
$662$	4.03763e26	−	4.15888e26i	0.642652	−	0.661951i
$663$	−1.55481e26	+	1.10795e26i	−0.243948	+	0.173837i
$664$	5.10413e26	−	5.57848e26i	0.789451	−	0.862818i
$665$			5.25111e26i			0.800656i
$666$	7.26399e26	−	3.66846e26i	1.09187	−	0.551416i
$667$			1.55305e26i			0.230139i
$668$	−1.76236e25	−	5.95559e26i	−0.0257464	−	0.870059i
$669$	9.20675e26	−	6.56072e26i	1.32605	−	0.944938i
$670$	−2.18707e26	−	2.12331e26i	−0.310565	−	0.301511i
$671$	1.81801e26			0.254526
$672$	−1.16592e27	−	1.07933e26i	−1.60939	−	0.148986i
$673$	−2.91934e26			−0.397321			−0.198661	−	0.980068i	$-0.563659\pi$
$673$	−2.91934e26			−0.397321			−0.198661	+	0.980068i	$0.563659\pi$
$674$	−5.77032e26	−	5.60209e26i	−0.774339	−	0.751764i
$675$	6.56189e26	−	1.93386e26i	0.868246	−	0.255882i
$676$	−1.00761e25	−	3.40504e26i	−0.0131461	−	0.444251i
$677$		−	4.63404e26i		−	0.596166i	−0.954540	−	0.298083i	$-0.903653\pi$
$677$		−	4.63404e26i		−	0.596166i	0.954540	−	0.298083i	$-0.0963473\pi$
$678$	−1.55439e26	−	2.37269e25i	−0.197186	−	0.0300994i
$679$			8.79082e26i			1.09968i
$680$	6.77257e25	−	7.40197e25i	0.0835447	−	0.0913088i
$681$	2.46243e25	+	3.45557e25i	0.0299548	+	0.0420361i
$682$	−3.28976e26	+	3.38855e26i	−0.394650	+	0.406501i
$683$	−5.52297e26			−0.653396			−0.326698	−	0.945129i	$-0.605936\pi$
$683$	−5.52297e26			−0.653396			−0.326698	+	0.945129i	$0.605936\pi$
$684$	−4.11331e26	+	1.31595e27i	−0.479909	+	1.53535i
$685$	2.71447e26			0.312338
$686$	6.07511e26	−	6.25754e26i	0.689406	−	0.710108i
$687$	8.44329e26	+	1.18486e27i	0.944980	+	1.32611i
$688$	5.74312e24	+	9.69548e25i	0.00633954	+	0.107023i
$689$			2.73405e26i			0.297663i
$690$	−3.06540e26	−	4.67918e25i	−0.329171	−	0.0502462i
$691$		−	1.21837e27i		−	1.29044i	−0.763997	−	0.645219i	$-0.776766\pi$
$691$		−	1.21837e27i		−	1.29044i	0.763997	−	0.645219i	$-0.223234\pi$
$692$	1.26243e27	−	3.73572e25i	1.31886	−	0.0390271i
$693$	−2.52038e27	−	8.70435e26i	−2.59717	−	0.896955i
$694$	−3.16159e26	−	3.06942e26i	−0.321359	−	0.311991i
$695$	−2.68379e26			−0.269088
$696$	−2.61660e25	+	2.13600e26i	−0.0258791	+	0.211259i
$697$	−2.29743e26			−0.224146
$698$	−9.76509e26	−	9.48040e26i	−0.939831	−	0.912431i
$699$	4.66515e26	−	3.32438e26i	0.442928	−	0.315629i
$700$	1.56129e27	−	4.62012e25i	1.46236	−	0.0432735i
$701$			2.66734e25i			0.0246467i	0.999924	+	0.0123233i	$0.00392274\pi$
$701$			2.66734e25i			0.0246467i	−0.999924	+	0.0123233i	$0.996077\pi$
$702$	7.23729e26	+	3.80477e26i	0.659741	+	0.346837i
$703$		−	2.18789e27i		−	1.96766i
$704$	1.69819e26	+	1.90845e27i	0.150677	+	1.69333i
$705$	−1.09903e26	+	7.83170e25i	−0.0962088	+	0.0685582i
$706$	−9.34269e26	+	9.62324e26i	−0.806914	+	0.831145i
$707$	−2.13443e27			−1.81885
$708$	−2.04123e25	+	1.54762e25i	−0.0171624	+	0.0130121i
$709$	1.00195e27			0.831205			0.415603	−	0.909546i	$-0.363571\pi$
$709$	1.00195e27			0.831205			0.415603	+	0.909546i	$0.363571\pi$
$710$	−3.25029e26	+	3.34789e26i	−0.266053	+	0.274042i
$711$	−6.09408e26	−	2.10464e26i	−0.492206	−	0.169988i
$712$	−6.93825e26	−	6.34828e26i	−0.552955	−	0.505937i
$713$		−	4.58233e26i		−	0.360359i
$714$	−1.26309e26	+	8.27471e26i	−0.0980170	+	0.642125i
$715$		−	5.09571e26i		−	0.390209i
$716$	−7.31351e25	−	2.47148e27i	−0.0552653	−	1.86760i
$717$	1.42076e27	+	1.99377e27i	1.05947	+	1.48677i
$718$	−8.75826e25	−	8.50292e25i	−0.0644519	−	0.0625728i
$719$	−1.66018e27			−1.20567			−0.602837	−	0.797865i	$-0.705963\pi$
$719$	−1.66018e27			−1.20567			−0.602837	+	0.797865i	$0.705963\pi$
$720$	−4.13719e26	−	1.16002e26i	−0.296515	−	0.0831392i
$721$	9.83988e25			0.0695993
$722$	1.63179e27	+	1.58422e27i	1.13910	+	1.10589i
$723$	6.36237e26	+	8.92841e26i	0.438334	+	0.615121i
$724$	−1.45677e25	−	4.92293e26i	−0.00990549	−	0.334740i
$725$		−	2.87070e26i		−	0.192654i
$726$	−4.30580e26	+	2.82080e27i	−0.285204	+	1.86842i
$727$			1.15179e27i			0.753001i	0.926416	+	0.376500i	$0.122873\pi$
$727$			1.15179e27i			0.753001i	−0.926416	+	0.376500i	$0.877127\pi$
$728$	1.37737e27	+	1.26025e27i	0.888800	+	0.813224i
$729$	1.31911e27	−	8.51464e26i	0.840173	−	0.542319i
$730$	2.51919e26	−	2.59484e26i	0.158378	−	0.163134i
$731$	6.94322e25			0.0430870
$732$	−1.94767e26	+	1.47668e26i	−0.119306	+	0.0904548i
$733$	1.45278e27			0.878441			0.439220	−	0.898379i	$-0.355255\pi$
$733$	1.45278e27			0.878441			0.439220	+	0.898379i	$0.355255\pi$
$734$	−1.08644e27	+	1.11907e27i	−0.648477	+	0.667950i
$735$	6.86272e26	−	4.89037e26i	0.404359	−	0.288145i
$736$	−1.40805e27	−	1.21379e27i	−0.818993	−	0.706002i
$737$		−	4.16152e27i		−	2.38952i
$738$	4.43546e26	+	8.78274e26i	0.251422	+	0.497845i
$739$			5.34107e25i			0.0298887i	0.999888	+	0.0149443i	$0.00475710\pi$
$739$			5.34107e25i			0.0298887i	−0.999888	+	0.0149443i	$0.995243\pi$
$740$	6.81541e26	−	2.01679e25i	0.376522	−	0.0111419i
$741$	1.79025e27	−	1.27573e27i	0.976432	−	0.695804i
$742$	8.60058e26	+	8.34984e26i	0.463117	+	0.449616i
$743$	2.17557e27			1.15659			0.578294	−	0.815828i	$-0.303719\pi$
$743$	2.17557e27			1.15659			0.578294	+	0.815828i	$0.303719\pi$
$744$	7.72036e25	−	6.30235e26i	0.0405224	−	0.330795i
$745$	4.24954e26			0.220220
$746$	1.91137e26	+	1.85564e26i	0.0977969	+	0.0949457i
$747$	−7.55686e26	+	2.18812e27i	−0.381765	+	1.10542i
$748$	1.36910e27	−	4.05138e25i	0.682920	−	0.0202087i
$749$			5.83662e27i			2.87464i
$750$	1.19260e27	+	1.82044e26i	0.579979	+	0.0885307i
$751$			4.88121e26i			0.234395i	0.993109	+	0.117197i	$0.0373910\pi$
$751$			4.88121e26i			0.234395i	−0.993109	+	0.117197i	$0.962609\pi$
$752$	−8.07633e26	+	4.78402e25i	−0.382952	+	0.0226842i
$753$	−1.38880e27	−	1.94892e27i	−0.650259	−	0.912519i
$754$	2.39004e26	−	2.46181e26i	0.110504	−	0.113822i
$755$	3.31479e26			0.151342
$756$	3.40716e27	−	1.11467e27i	1.53616	−	0.502562i
$757$	4.50904e26			0.200758			0.100379	−	0.994949i	$-0.467994\pi$
$757$	4.50904e26			0.200758			0.100379	+	0.994949i	$0.467994\pi$
$758$	3.85772e26	−	3.97356e26i	0.169619	−	0.174712i
$759$	−2.45678e27	−	3.44763e27i	−1.06677	−	1.49701i
$760$	−7.79815e26	+	8.52286e26i	−0.334397	+	0.365474i
$761$			8.15361e26i			0.345299i	0.984983	+	0.172650i	$0.0552328\pi$
$761$			8.15361e26i			0.345299i	−0.984983	+	0.172650i	$0.944767\pi$
$762$	−2.42392e27	−	3.69999e26i	−1.01379	−	0.154749i
$763$		−	3.06573e27i		−	1.26634i
$764$	−3.55108e25	−	1.20003e27i	−0.0144868	−	0.489559i
$765$	−1.00270e26	+	2.90337e26i	−0.0404007	+	0.116982i
$766$	−5.62545e26	−	5.46145e26i	−0.223864	−	0.217337i
$767$	4.08426e25			0.0160530
$768$	−1.73208e27	−	1.90663e27i	−0.672412	−	0.740177i
$769$	−9.01217e26			−0.345565			−0.172782	−	0.984960i	$-0.555276\pi$
$769$	−9.01217e26			−0.345565			−0.172782	+	0.984960i	$0.555276\pi$
$770$	−1.60297e27	−	1.55624e27i	−0.607105	−	0.589406i
$771$	−1.81389e27	+	1.29258e27i	−0.678571	+	0.483549i
$772$	4.98195e25	+	1.68357e27i	0.0184092	+	0.622109i
$773$		−	1.82382e27i		−	0.665696i	−0.942980	−	0.332848i	$-0.891990\pi$
$773$		−	1.82382e27i		−	0.665696i	0.942980	−	0.332848i	$-0.108010\pi$
$774$	−1.34047e26	−	2.65429e26i	−0.0483302	−	0.0956996i
$775$			8.47010e26i			0.301663i
$776$	−1.30548e27	+	1.42680e27i	−0.459286	+	0.501969i
$777$	−4.63280e27	+	3.30132e27i	−1.61007	+	1.14733i
$778$	−3.13761e27	+	3.23183e27i	−1.07719	+	1.10954i
$779$	2.64533e27			0.897169
$780$	4.13901e26	+	5.45916e26i	0.138675	+	0.182905i
$781$	−6.37030e27			−2.10851
$782$	−9.25716e26	+	9.53514e26i	−0.302701	+	0.311791i
$783$	−1.86250e26	−	6.31975e26i	−0.0601671	−	0.204156i
$784$	5.04312e27	−	2.98730e26i	1.60952	−	0.0953401i
$785$		−	1.18018e27i		−	0.372122i
$786$	4.74030e26	−	3.10545e27i	0.147670	−	0.967409i
$787$			4.33388e27i			1.33388i	0.745111	+	0.666940i	$0.232396\pi$
$787$			4.33388e27i			1.33388i	−0.745111	+	0.666940i	$0.767604\pi$
$788$	−2.03706e27	+	6.02798e25i	−0.619447	+	0.0183304i
$789$	7.44124e26	+	1.04424e27i	0.223570	+	0.313739i
$790$	−3.87586e26	−	3.76286e26i	−0.115056	−	0.111702i
$791$	1.09918e27			0.322399
$792$	−2.79809e27	−	5.15565e27i	−0.810909	−	1.49415i
$793$	3.89706e26			0.111594
$794$	−3.04176e26	−	2.95308e26i	−0.0860657	−	0.0835566i
$795$	2.55272e26	+	3.58227e26i	0.0713699	+	0.100154i
$796$	−4.18533e27	+	1.23851e26i	−1.15626	+	0.0342156i
$797$		−	4.23533e27i		−	1.15620i	−0.815966	−	0.578100i	$-0.803794\pi$
$797$		−	4.23533e27i		−	1.15620i	0.815966	−	0.578100i	$-0.196206\pi$
$798$	1.45436e27	−	9.52776e27i	0.392324	−	2.57018i
$799$			5.78370e26i			0.154174i
$800$	2.60268e27	+	2.24361e27i	0.685593	+	0.591007i
$801$	2.72148e27	+	9.39887e26i	0.708429	+	0.244662i
$802$	4.99052e27	−	5.14038e27i	1.28378	−	1.32233i
$803$	4.93742e27			1.25517
$804$	3.38021e27	+	4.45833e27i	0.849201	+	1.12006i
$805$	2.16770e27			0.538193
$806$	−7.05188e26	+	7.26365e26i	−0.173030	+	0.178226i
$807$	5.55201e27	−	3.95635e27i	1.34633	−	0.959393i
$808$	−3.46430e27	−	3.16973e27i	−0.830248	−	0.759651i
$809$			7.38409e27i			1.74899i	0.485038	+	0.874493i	$0.338806\pi$
$809$			7.38409e27i			1.74899i	−0.485038	+	0.874493i	$0.661194\pi$
$810$	1.30350e27	−	1.77212e26i	0.305143	−	0.0414844i
$811$			4.28620e27i			0.991686i	0.868412	+	0.495843i	$0.165141\pi$
$811$			4.28620e27i			0.991686i	−0.868412	+	0.495843i	$0.834859\pi$
$812$	−4.44963e25	−	1.50368e27i	−0.0101752	−	0.343854i
$813$	−2.93502e27	+	2.09149e27i	−0.663362	+	0.472710i
$814$	6.67882e27	+	6.48411e27i	1.49200	+	1.44850i
$815$	−3.35889e26			−0.0741650
$816$	−1.43384e27	+	1.15546e27i	−0.312928	+	0.252173i
$817$	−7.99464e26			−0.172461
$818$	−3.11102e27	−	3.02032e27i	−0.663355	−	0.644015i
$819$	−5.40266e27	−	1.86585e27i	−1.13870	−	0.393261i
$820$	2.43846e25	+	8.24036e26i	0.00508023	+	0.171678i
$821$		−	7.07227e27i		−	1.45646i	−0.685332	−	0.728231i	$-0.740343\pi$
$821$		−	7.07227e27i		−	1.45646i	0.685332	−	0.728231i	$-0.259657\pi$
$822$	−4.92521e27	−	7.51808e26i	−1.00263	−	0.153047i
$823$			6.69981e27i			1.34823i	0.738626	+	0.674115i	$0.235475\pi$
$823$			6.69981e27i			1.34823i	−0.738626	+	0.674115i	$0.764525\pi$
$824$	1.59707e26	+	1.46127e26i	0.0317699	+	0.0290684i
$825$	4.54117e27	+	6.37270e27i	0.893008	+	1.25317i
$826$	1.24734e26	−	1.28480e26i	0.0242479	−	0.0249761i
$827$	−1.77336e27			−0.340797			−0.170398	−	0.985375i	$-0.554505\pi$
$827$	−1.77336e27			−0.340797			−0.170398	+	0.985375i	$0.554505\pi$
$828$	5.43236e27	+	1.69800e27i	1.03205	+	0.322590i
$829$	3.45706e27			0.649290			0.324645	−	0.945836i	$-0.394755\pi$
$829$	3.45706e27			0.649290			0.324645	+	0.945836i	$0.394755\pi$
$830$	−1.35108e27	+	1.39165e27i	−0.250865	+	0.258398i
$831$	1.03521e27	+	1.45273e27i	0.190029	+	0.266671i
$832$	3.64022e26	+	4.09093e27i	0.0660626	+	0.742422i
$833$		−	3.61153e27i		−	0.647983i
$834$	4.86955e27	+	7.43311e26i	0.863796	+	0.131854i
$835$			1.52841e27i			0.268052i
$836$	−1.57642e28	+	4.66489e26i	−2.73346	+	0.0808876i
$837$	5.49536e26	+	1.86466e27i	0.0942116	+	0.319675i
$838$	−7.56962e27	−	7.34894e27i	−1.28309	−	1.24568i
$839$	5.29963e27			0.888193			0.444096	−	0.895979i	$-0.353525\pi$
$839$	5.29963e27			0.888193			0.444096	+	0.895979i	$0.353525\pi$
$840$	2.98136e27	+	3.65216e26i	0.494039	+	0.0605197i
$841$	5.82678e27			0.954700
$842$	8.18877e27	+	7.95004e27i	1.32664	+	1.28797i
$843$	−6.83611e27	+	4.87140e27i	−1.09508	+	0.780354i
$844$	1.51675e27	−	4.48831e25i	0.240249	−	0.00710934i
$845$			8.73853e26i			0.136867i
$846$	2.21103e27	−	1.11661e27i	0.342433	−	0.172936i
$847$		−	1.99473e28i		−	3.05486i
$848$	1.55934e26	+	2.63246e27i	0.0236145	+	0.398658i
$849$	−5.91718e25	+	4.21657e25i	−0.00886118	+	0.00631446i
$850$	1.71112e27	−	1.76250e27i	0.253396	−	0.261005i
$851$	−9.03177e27			−1.32264
$852$	6.82465e27	−	5.17430e27i	0.988336	−	0.749334i
$853$	−4.68710e27			−0.671256			−0.335628	−	0.941995i	$-0.608949\pi$
$853$	−4.68710e27			−0.671256			−0.335628	+	0.941995i	$0.608949\pi$
$854$	1.19017e27	−	1.22591e27i	0.168561	−	0.173623i
$855$	1.15455e27	−	3.34303e27i	0.161709	−	0.468234i
$856$	−8.66765e27	+	9.47316e27i	−1.20061	+	1.31218i
$857$			6.05364e27i			0.829275i	0.909987	+	0.414637i	$0.136092\pi$
$857$			6.05364e27i			0.829275i	−0.909987	+	0.414637i	$0.863908\pi$
$858$	−1.41132e27	+	9.24580e27i	−0.191204	+	1.25261i
$859$			3.36823e27i			0.451302i	0.974208	+	0.225651i	$0.0724508\pi$
$859$			3.36823e27i			0.451302i	−0.974208	+	0.225651i	$0.927549\pi$
$860$	−7.36943e24	−	2.49038e26i	−0.000976560	−	0.0330012i
$861$	−3.99156e27	−	5.60142e27i	−0.523134	−	0.734121i
$862$	4.77563e27	+	4.63640e27i	0.619030	+	0.600983i
$863$	9.00120e27			1.15398			0.576989	−	0.816752i	$-0.304227\pi$
$863$	9.00120e27			1.15398			0.576989	+	0.816752i	$0.304227\pi$
$864$	7.18535e27	+	3.25061e27i	0.911103	+	0.412178i
$865$	−3.23983e27			−0.406321
$866$	1.68333e27	+	1.63426e27i	0.208809	+	0.202722i
$867$	−3.96598e27	−	5.56552e27i	−0.486596	−	0.682848i
$868$	1.31288e26	+	4.43666e27i	0.0159326	+	0.538417i
$869$		−	7.37491e27i		−	0.885256i
$870$	8.32995e25	−	5.45708e26i	0.00989030	−	0.0647929i
$871$		−	8.92057e27i		−	1.04766i
$872$	4.55276e27	−	4.97586e27i	0.528893	−	0.578045i
$873$	1.93281e27	−	5.59653e27i	0.222103	−	0.643107i
$874$	1.06590e28	−	1.09791e28i	1.21159	−	1.24798i
$875$	−8.43345e27			−0.948263
$876$	−5.28957e27	+	4.01043e27i	−0.588344	+	0.446069i
$877$	−4.26350e27			−0.469105			−0.234553	−	0.972103i	$-0.575362\pi$
$877$	−4.26350e27			−0.469105			−0.234553	+	0.972103i	$0.575362\pi$
$878$	3.68876e27	−	3.79953e27i	0.401497	−	0.413554i
$879$	−8.50699e27	+	6.06206e27i	−0.915970	+	0.652719i
$880$	−2.90628e26	−	4.90636e27i	−0.0309566	−	0.522605i
$881$		−	9.60532e27i		−	1.01214i	−0.862492	−	0.506070i	$-0.831098\pi$
$881$		−	9.60532e27i		−	1.01214i	0.862492	−	0.506070i	$-0.168902\pi$
$882$	−1.38064e28	+	6.97249e27i	−1.43922	+	0.726836i
$883$			4.37756e27i			0.451446i	0.974192	+	0.225723i	$0.0724744\pi$
$883$			4.37756e27i			0.451446i	−0.974192	+	0.225723i	$0.927526\pi$
$884$	2.93478e27	−	8.68449e25i	0.299419	−	0.00886029i
$885$	5.35137e25	−	3.81337e25i	0.00540137	−	0.00384900i
$886$	−1.89221e27	−	1.83704e27i	−0.188950	−	0.183442i
$887$	−5.45183e27			−0.538602			−0.269301	−	0.963056i	$-0.586793\pi$
$887$	−5.45183e27			−0.538602			−0.269301	+	0.963056i	$0.586793\pi$
$888$	−1.24219e28	−	1.52168e27i	−1.21413	−	0.148731i
$889$	1.71407e28			1.65754
$890$	1.73087e27	+	1.68041e27i	0.165600	+	0.160772i
$891$	1.41318e28	+	1.10830e28i	1.33770	+	1.04910i
$892$	−1.73782e28	+	5.14250e26i	−1.62757	+	0.0481624i
$893$		−	6.65954e27i		−	0.617100i
$894$	−7.71049e27	−	1.17696e27i	−0.706928	−	0.107909i
$895$			6.34269e27i			0.575380i
$896$	1.39807e28	+	1.13487e28i	1.25488	+	1.01864i
$897$	−5.26632e27	−	7.39030e27i	−0.467712	−	0.656348i
$898$	−9.15484e26	+	9.42976e26i	−0.0804499	+	0.0828658i
$899$	8.15754e26			0.0709320
$900$	−1.00413e28	−	3.13864e27i	−0.863946	−	0.270046i
$901$	1.88518e27			0.160497
$902$	−7.83980e27	+	8.07522e27i	−0.660454	+	0.680287i
$903$	1.20632e27	+	1.69284e27i	0.100561	+	0.141118i
$904$	1.78404e27	+	1.63234e27i	0.147165	+	0.134651i
$905$			1.26340e27i			0.103128i
$906$	−6.01445e27	−	9.18074e26i	−0.485823	−	0.0741583i
$907$		−	1.25588e28i		−	1.00388i	−0.864904	−	0.501938i	$-0.832621\pi$
$907$		−	1.25588e28i		−	1.00388i	0.864904	−	0.501938i	$-0.167379\pi$
$908$	−1.93013e25	−	6.52257e26i	−0.00152676	−	0.0515945i
$909$	1.35885e28	+	4.69290e27i	1.06369	+	0.367354i
$910$	−3.43611e27	−	3.33593e27i	−0.266179	−	0.258419i
$911$	1.08131e28			0.828941			0.414471	−	0.910063i	$-0.363967\pi$
$911$	1.08131e28			0.828941			0.414471	+	0.910063i	$0.363967\pi$
$912$	1.65097e28	−	1.33043e28i	1.25253	−	1.00935i
$913$	−2.64801e28			−1.98814
$914$	−1.71516e27	−	1.66515e27i	−0.127443	−	0.123727i
$915$	5.10608e26	−	3.63859e26i	0.0375481	−	0.0267567i
$916$	−6.61812e26	−	2.23649e28i	−0.0481646	−	1.62764i
$917$			2.19602e28i			1.58171i
$918$	2.62346e27	−	4.99025e27i	0.187012	−	0.355727i
$919$		−	2.67527e28i		−	1.88743i	−0.330759	−	0.943715i	$-0.607305\pi$
$919$		−	2.67527e28i		−	1.88743i	0.330759	−	0.943715i	$-0.392695\pi$
$920$	3.51830e27	+	3.21913e27i	0.245668	+	0.224778i
$921$	−1.62779e27	+	1.15996e27i	−0.112494	+	0.0801634i
$922$	−3.02121e27	+	3.11194e27i	−0.206651	+	0.212857i
$923$	−1.36553e28			−0.924453
$924$	2.47746e28	+	3.26765e28i	1.66005	+	2.18953i
$925$	1.66946e28			1.10721
$926$	1.95493e28	−	2.01364e28i	1.28330	−	1.32183i
$927$	−6.26439e26	−	2.16346e26i	−0.0407025	−	0.0140570i
$928$	2.16082e27	−	2.50664e27i	0.138967	−	0.161208i
$929$			1.76575e28i			1.12404i	0.827125	+	0.562018i	$0.189975\pi$
$929$			1.76575e28i			1.12404i	−0.827125	+	0.562018i	$0.810025\pi$
$930$	−2.45778e26	+	1.61013e27i	−0.0154866	+	0.101455i
$931$			4.15843e28i			2.59363i
$932$	−8.80572e27	+	2.60575e26i	−0.543643	+	0.0160873i
$933$	−5.62828e27	−	7.89825e27i	−0.343954	−	0.482676i
$934$	1.76613e28	+	1.71465e28i	1.06839	+	1.03724i
$935$	−3.51359e27			−0.210397
$936$	−5.99795e27	−	1.10516e28i	−0.355535	−	0.655095i
$937$	−1.23556e28			−0.724999			−0.362500	−	0.931984i	$-0.618077\pi$
$937$	−1.23556e28			−0.724999			−0.362500	+	0.931984i	$0.618077\pi$
$938$	−2.80617e28	−	2.72436e28i	−1.63000	−	1.58248i
$939$	1.17508e28	+	1.64901e28i	0.675687	+	0.948202i
$940$	2.07449e27	−	6.13874e25i	0.118085	−	0.00349433i
$941$			2.16847e28i			1.22194i	0.791652	+	0.610972i	$0.209221\pi$
$941$			2.16847e28i			1.22194i	−0.791652	+	0.610972i	$0.790779\pi$
$942$	−3.26865e27	+	2.14134e28i	−0.182341	+	1.19455i
$943$		−	1.09201e28i		−	0.603068i
$944$	3.93249e26	−	2.32941e25i	0.0214998	−	0.00127354i
$945$	−8.82089e27	+	2.59961e27i	−0.477430	+	0.140704i
$946$	2.36932e27	−	2.44047e27i	0.126957	−	0.130770i
$947$	−9.35459e27			−0.496249			−0.248125	−	0.968728i	$-0.579814\pi$
$947$	−9.35459e27			−0.496249			−0.248125	+	0.968728i	$0.579814\pi$
$948$	5.99029e27	+	7.90091e27i	0.314607	+	0.414952i
$949$	1.05838e28			0.550315
$950$	−1.97023e28	+	2.02940e28i	−1.01425	+	1.04470i
$951$	1.57205e28	−	1.12024e28i	0.801221	−	0.570949i
$952$	8.68969e27	−	9.49725e27i	0.438483	−	0.479233i
$953$			2.00695e27i			0.100266i	0.998743	+	0.0501330i	$0.0159645\pi$
$953$			2.00695e27i			0.100266i	−0.998743	+	0.0501330i	$0.984035\pi$
$954$	−3.63957e27	−	7.20677e27i	−0.180028	−	0.356477i
$955$			3.07970e27i			0.150826i
$956$	−1.11363e27	−	3.76335e28i	−0.0539999	−	1.82484i
$957$	6.13754e27	−	4.37360e27i	0.294666	−	0.209979i
$958$	2.71055e28	+	2.63153e28i	1.28850	+	1.25094i
$959$	3.48286e28			1.63930
$960$	4.29656e27	+	5.02023e27i	0.200237	+	0.233963i
$961$	1.92638e28			0.888932
$962$	1.43166e28	+	1.38993e28i	0.654151	+	0.635080i
$963$	1.28328e28	−	3.71578e28i	0.580592	−	1.68113i
$964$	−4.98703e26	−	1.68529e28i	−0.0223414	−	0.754991i
$965$		−	4.32063e27i		−	0.191663i
$966$	−3.93313e28	−	6.00371e27i	−1.72765	−	0.263717i
$967$			2.45625e28i			1.06837i	0.845368	+	0.534184i	$0.179381\pi$
$967$			2.45625e28i			1.06837i	−0.845368	+	0.534184i	$0.820619\pi$
$968$	2.96226e28	−	3.23756e28i	1.27587	−	1.39445i
$969$	−8.79641e27	−	1.23441e28i	−0.375171	−	0.526484i
$970$	3.45564e27	−	3.55941e27i	0.145948	−	0.150330i
$971$	−1.15893e28			−0.484701			−0.242350	−	0.970189i	$-0.577918\pi$
$971$	−1.15893e28			−0.484701			−0.242350	+	0.970189i	$0.577918\pi$
$972$	−2.41419e28	−	3.94839e26i	−0.999866	−	0.0163528i
$973$	−3.44350e28			−1.41230
$974$	1.91659e28	−	1.97414e28i	0.778429	−	0.801805i
$975$	9.73440e27	+	1.36604e28i	0.391530	+	0.549440i
$976$	3.75224e27	−	2.22264e26i	0.149457	−	0.00885312i
$977$			8.58920e27i			0.338808i	0.985547	+	0.169404i	$0.0541843\pi$
$977$			8.58920e27i			0.338808i	−0.985547	+	0.169404i	$0.945816\pi$
$978$	6.09447e27	+	9.30288e26i	0.238077	+	0.0363411i
$979$			3.29347e28i			1.27414i
$980$	−1.29538e28	+	3.83322e26i	−0.496304	+	0.0146864i
$981$	−6.74052e27	+	1.95175e28i	−0.255763	+	0.740573i
$982$	−3.11964e27	−	3.02869e27i	−0.117232	−	0.113814i
$983$	−4.55404e28			−1.69488			−0.847440	−	0.530892i	$-0.821857\pi$
$983$	−4.55404e28			−1.69488			−0.847440	+	0.530892i	$0.821857\pi$
$984$	1.83983e27	−	1.50191e28i	0.0678149	−	0.553592i
$985$	5.22780e27			0.190842
$986$	−1.69746e27	−	1.64798e27i	−0.0613719	−	0.0595827i
$987$	−1.41014e28	+	1.00486e28i	−0.504951	+	0.359827i
$988$	−3.37920e28	+	9.99960e26i	−1.19846	+	0.0354643i
$989$			3.30025e27i			0.115926i
$990$	6.78340e27	+	1.34319e28i	0.236001	+	0.467309i
$991$		−	2.95548e28i		−	1.01842i	−0.860641	−	0.509212i	$-0.829937\pi$
$991$		−	2.95548e28i		−	1.01842i	0.860641	−	0.509212i	$-0.170063\pi$
$992$	−6.37556e27	+	7.39593e27i	−0.217599	+	0.252425i
$993$	2.22258e28	−	1.58381e28i	0.751345	−	0.535407i
$994$	−4.17035e28	+	4.29558e28i	−1.39637	+	1.43831i
$995$	1.07410e28			0.356227
$996$	2.83687e28	−	2.15085e28i	0.931915	−	0.706557i
$997$	−4.77596e28			−1.55402			−0.777010	−	0.629488i	$-0.783265\pi$
$997$	−4.77596e28			−1.55402			−0.777010	+	0.629488i	$0.783265\pi$
$998$	−2.00494e28	+	2.06515e28i	−0.646191	+	0.665596i
$999$	3.67525e28	−	1.08313e28i	1.17331	−	0.345788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.20.b.a.11.9	✓	36
3.2	odd	2	inner	12.20.b.a.11.28	yes	36
4.3	odd	2	inner	12.20.b.a.11.27	yes	36
12.11	even	2	inner	12.20.b.a.11.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.20.b.a.11.9	✓	36	1.1	even	1	trivial
12.20.b.a.11.10	yes	36	12.11	even	2	inner
12.20.b.a.11.27	yes	36	4.3	odd	2	inner
12.20.b.a.11.28	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-519.517 - 504.371i) q^{2} +(-19784.5 - 27763.9i) q^{3} +(15507.7 + 524059. i) q^{4} -1.34492e6i q^{5} +(-3.72492e6 + 2.44026e7i) q^{6} -1.72563e8i q^{7} +(2.56263e8 - 2.80079e8i) q^{8} +(-3.79408e8 + 1.09859e9i) q^{9} +O(q^{10})\)	\(q+(-519.517 - 504.371i) q^{2} +(-19784.5 - 27763.9i) q^{3} +(15507.7 + 524059. i) q^{4} -1.34492e6i q^{5} +(-3.72492e6 + 2.44026e7i) q^{6} -1.72563e8i q^{7} +(2.56263e8 - 2.80079e8i) q^{8} +(-3.79408e8 + 1.09859e9i) q^{9} +(-6.78338e8 + 6.98708e8i) q^{10} -1.32949e10 q^{11} +(1.42431e10 - 1.07988e10i) q^{12} -2.84987e10 q^{13} +(-8.70355e10 + 8.96492e10i) q^{14} +(-3.73402e10 + 2.66085e10i) q^{15} +(-2.74397e11 + 1.62539e10i) q^{16} +1.96504e11i q^{17} +(7.51206e11 - 3.79374e11i) q^{18} -2.26261e12i q^{19} +(7.04816e11 - 2.08566e10i) q^{20} +(-4.79101e12 + 3.41407e12i) q^{21} +(6.90691e12 + 6.70555e12i) q^{22} -9.34021e12 q^{23} +(-1.28461e13 - 1.57365e12i) q^{24} +1.72647e13 q^{25} +(1.48056e13 + 1.43739e13i) q^{26} +(3.80076e13 - 1.12012e13i) q^{27} +(9.04329e13 - 2.67605e12i) q^{28} -1.66276e13i q^{29} +(3.28194e13 + 5.00971e12i) q^{30} +4.90603e13i q^{31} +(1.50752e14 + 1.29954e14i) q^{32} +(2.63032e14 + 3.69117e14i) q^{33} +(9.91108e13 - 1.02087e14i) q^{34} -2.32082e14 q^{35} +(-5.81610e14 - 1.81795e14i) q^{36} +9.66977e14 q^{37} +(-1.14119e15 + 1.17546e15i) q^{38} +(5.63833e14 + 7.91235e14i) q^{39} +(-3.76683e14 - 3.44653e14i) q^{40} +1.16915e15i q^{41} +(4.21097e15 + 6.42782e14i) q^{42} -3.53338e14i q^{43} +(-2.06173e14 - 6.96729e15i) q^{44} +(1.47751e15 + 5.10272e14i) q^{45} +(4.85240e15 + 4.71093e15i) q^{46} +2.94330e15 q^{47} +(5.88008e15 + 7.29675e15i) q^{48} -1.83789e16 q^{49} +(-8.96930e15 - 8.70781e15i) q^{50} +(5.45571e15 - 3.88773e15i) q^{51} +(-4.41950e14 - 1.49350e16i) q^{52} -9.59360e15i q^{53} +(-2.53952e16 - 1.33507e16i) q^{54} +1.78805e16i q^{55} +(-4.83311e16 - 4.42215e16i) q^{56} +(-6.28188e16 + 4.47646e16i) q^{57} +(-8.38648e15 + 8.63832e15i) q^{58} -1.43314e15 q^{59} +(-1.45235e16 - 1.91558e16i) q^{60} -1.36745e16 q^{61} +(2.47446e16 - 2.54876e16i) q^{62} +(1.89576e17 + 6.54715e16i) q^{63} +(-1.27733e16 - 1.43548e17i) q^{64} +3.83284e16i q^{65} +(4.95223e16 - 3.24429e17i) q^{66} +3.13017e17i q^{67} +(-1.02980e17 + 3.04733e15i) q^{68} +(1.84791e17 + 2.59321e17i) q^{69} +(1.20571e17 + 1.17056e17i) q^{70} +4.79155e17 q^{71} +(2.10464e17 + 3.87793e17i) q^{72} -3.71378e17 q^{73} +(-5.02361e17 - 4.87715e17i) q^{74} +(-3.41573e17 - 4.79335e17i) q^{75} +(1.18574e18 - 3.50879e16i) q^{76} +2.29420e18i q^{77} +(1.06155e17 - 6.95441e17i) q^{78} +5.54718e17i q^{79} +(2.18602e16 + 3.69041e17i) q^{80} +(-1.06295e18 - 8.33627e17i) q^{81} +(5.89686e17 - 6.07394e17i) q^{82} +1.99175e18 q^{83} +(-1.86347e18 - 2.45783e18i) q^{84} +2.64282e17 q^{85} +(-1.78213e17 + 1.83565e17i) q^{86} +(-4.61647e17 + 3.28969e17i) q^{87} +(-3.40699e18 + 3.72361e18i) q^{88} -2.47725e18i q^{89} +(-5.10227e17 - 1.01031e18i) q^{90} +4.91781e18i q^{91} +(-1.44845e17 - 4.89482e18i) q^{92} +(1.36210e18 - 9.70633e17i) q^{93} +(-1.52910e18 - 1.48452e18i) q^{94} -3.04302e18 q^{95} +(6.25470e17 - 6.75653e18i) q^{96} -5.09428e18 q^{97} +(9.54817e18 + 9.26980e18i) q^{98} +(5.04417e18 - 1.46056e19i) 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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