LMFDB - Embedded newform 43.11.d.a.37.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,11,Mod(7,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, 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:	$27.3203618650$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.23
Character	$\chi$	$=$	43.37
Dual form			43.11.d.a.7.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+20.4162i q^{2} +(-201.640 - 116.417i) q^{3} +607.178 q^{4} +(4872.92 + 2813.38i) q^{5} +(2376.79 - 4116.72i) q^{6} +(-6546.27 + 3779.49i) q^{7} +33302.5i q^{8} +(-2418.78 - 4189.45i) q^{9} +O(q^{10})$	\(q+20.4162i q^{2} +(-201.640 - 116.417i) q^{3} +607.178 q^{4} +(4872.92 + 2813.38i) q^{5} +(2376.79 - 4116.72i) q^{6} +(-6546.27 + 3779.49i) q^{7} +33302.5i q^{8} +(-2418.78 - 4189.45i) q^{9} +(-57438.7 + 99486.7i) q^{10} +309963. q^{11} +(-122431. - 70685.7i) q^{12} +(-168451. - 291765. i) q^{13} +(-77162.9 - 133650. i) q^{14} +(-655050. - 1.13458e6i) q^{15} -58159.9 q^{16} +(117678. + 203824. i) q^{17} +(85532.8 - 49382.4i) q^{18} +(-737457. - 425771. i) q^{19} +(2.95873e6 + 1.70823e6i) q^{20} +1.75998e6 q^{21} +6.32827e6i q^{22} +(2.63431e6 - 4.56276e6i) q^{23} +(3.87697e6 - 6.71510e6i) q^{24} +(1.09475e7 + 1.89615e7i) q^{25} +(5.95674e6 - 3.43913e6i) q^{26} +1.48749e7i q^{27} +(-3.97475e6 + 2.29482e6i) q^{28} +(5.47605e6 - 3.16160e6i) q^{29} +(2.31638e7 - 1.33736e7i) q^{30} +(-1.79685e7 + 3.11224e7i) q^{31} +3.29143e7i q^{32} +(-6.25009e7 - 3.60849e7i) q^{33} +(-4.16132e6 + 2.40254e6i) q^{34} -4.25326e7 q^{35} +(-1.46863e6 - 2.54375e6i) q^{36} +(5.89077e7 + 3.40104e7i) q^{37} +(8.69263e6 - 1.50561e7i) q^{38} +7.84420e7i q^{39} +(-9.36927e7 + 1.62280e8i) q^{40} +1.60791e8 q^{41} +3.59322e7i q^{42} +(-1.41723e8 - 3.90667e7i) q^{43} +1.88203e8 q^{44} -2.72199e7i q^{45} +(9.31542e7 + 5.37826e7i) q^{46} +1.69879e8 q^{47} +(1.17273e7 + 6.77078e6i) q^{48} +(-1.12669e8 + 1.95148e8i) q^{49} +(-3.87123e8 + 2.23505e8i) q^{50} -5.47988e7i q^{51} +(-1.02280e8 - 1.77154e8i) q^{52} +(-6.07591e7 + 1.05238e8i) q^{53} -3.03690e8 q^{54} +(1.51043e9 + 8.72045e8i) q^{55} +(-1.25866e8 - 2.18007e8i) q^{56} +(9.91338e7 + 1.71705e8i) q^{57} +(6.45479e7 + 1.11800e8i) q^{58} +7.67422e8 q^{59} +(-3.97732e8 - 6.88892e8i) q^{60} +(6.41857e8 - 3.70576e8i) q^{61} +(-6.35401e8 - 3.66849e8i) q^{62} +(3.16680e7 + 1.82835e7i) q^{63} -7.31542e8 q^{64} -1.89567e9i q^{65} +(7.36717e8 - 1.27603e9i) q^{66} +(-8.44456e8 + 1.46264e9i) q^{67} +(7.14516e7 + 1.23758e8i) q^{68} +(-1.06236e9 + 6.13355e8i) q^{69} -8.68355e8i q^{70} +(-1.33181e9 + 7.68923e8i) q^{71} +(1.39519e8 - 8.05515e7i) q^{72} +(5.28559e8 - 3.05163e8i) q^{73} +(-6.94363e8 + 1.20267e9i) q^{74} -5.09787e9i q^{75} +(-4.47768e8 - 2.58519e8i) q^{76} +(-2.02910e9 + 1.17150e9i) q^{77} -1.60149e9 q^{78} +(-2.40203e9 - 4.16043e9i) q^{79} +(-2.83409e8 - 1.63626e8i) q^{80} +(1.58886e9 - 2.75199e9i) q^{81} +3.28274e9i q^{82} +(2.27518e8 - 3.94072e8i) q^{83} +1.06862e9 q^{84} +1.32429e9i q^{85} +(7.97594e8 - 2.89344e9i) q^{86} -1.47225e9 q^{87} +1.03225e10i q^{88} +(4.12432e9 + 2.38118e9i) q^{89} +5.55726e8 q^{90} +(2.20545e9 + 1.27332e9i) q^{91} +(1.59950e9 - 2.77041e9i) q^{92} +(7.24633e9 - 4.18367e9i) q^{93} +3.46829e9i q^{94} +(-2.39572e9 - 4.14950e9i) q^{95} +(3.83178e9 - 6.63684e9i) q^{96} -1.08534e10 q^{97} +(-3.98418e9 - 2.30026e9i) q^{98} +(-7.49733e8 - 1.29858e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) $ 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9} - 127061 q^{10} + 521524 q^{11} - 606618 q^{12} + 796742 q^{13} - 865794 q^{14} - 433513 q^{15} + 22423366 q^{16} - 1768471 q^{17} - 11957547 q^{18} - 122844 q^{19} + 419841 q^{20} - 26778860 q^{21} + 16414886 q^{23} + 8684578 q^{24} + 70516989 q^{25} + 3069 q^{26} - 97624092 q^{28} + 118701393 q^{29} - 1455921 q^{30} + 10824883 q^{31} + 315141798 q^{33} + 47529561 q^{34} - 333788722 q^{35} - 597728908 q^{36} - 169881246 q^{37} - 88887452 q^{38} + 570788831 q^{40} - 543049070 q^{41} + 408159179 q^{43} - 754130886 q^{44} + 270181896 q^{46} + 348527658 q^{47} + 175039227 q^{48} + 781091547 q^{49} - 663244398 q^{50} - 1853993086 q^{52} + 219922736 q^{53} + 3104867360 q^{54} + 2154394182 q^{55} + 2010912675 q^{56} + 349107351 q^{57} + 2023447828 q^{58} + 2247595680 q^{59} - 2906780465 q^{60} + 508093974 q^{61} - 3451752063 q^{62} + 158921973 q^{63} - 13473879716 q^{64} + 1277847051 q^{66} - 2812410281 q^{67} + 13614613118 q^{68} - 5113655829 q^{69} + 2418191196 q^{71} + 26243329290 q^{72} - 6537901611 q^{73} - 2632816966 q^{74} - 10170994206 q^{76} - 16936463889 q^{77} - 24146069696 q^{78} + 5397136602 q^{79} + 7242149661 q^{80} - 15745886176 q^{81} + 4998656042 q^{83} + 44726677232 q^{84} - 27688564866 q^{86} + 37895576172 q^{87} - 12151857357 q^{89} - 96024912764 q^{90} + 36633770214 q^{91} - 31643971023 q^{92} + 59768940153 q^{93} - 19802964089 q^{95} - 3289705262 q^{96} - 40329658574 q^{97} + 19243888221 q^{98} + 18506221111 q^{99}+O(q^{100}) \) 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9 - 127061 * q^10 + 521524 * q^11 - 606618 * q^12 + 796742 * q^13 - 865794 * q^14 - 433513 * q^15 + 22423366 * q^16 - 1768471 * q^17 - 11957547 * q^18 - 122844 * q^19 + 419841 * q^20 - 26778860 * q^21 + 16414886 * q^23 + 8684578 * q^24 + 70516989 * q^25 + 3069 * q^26 - 97624092 * q^28 + 118701393 * q^29 - 1455921 * q^30 + 10824883 * q^31 + 315141798 * q^33 + 47529561 * q^34 - 333788722 * q^35 - 597728908 * q^36 - 169881246 * q^37 - 88887452 * q^38 + 570788831 * q^40 - 543049070 * q^41 + 408159179 * q^43 - 754130886 * q^44 + 270181896 * q^46 + 348527658 * q^47 + 175039227 * q^48 + 781091547 * q^49 - 663244398 * q^50 - 1853993086 * q^52 + 219922736 * q^53 + 3104867360 * q^54 + 2154394182 * q^55 + 2010912675 * q^56 + 349107351 * q^57 + 2023447828 * q^58 + 2247595680 * q^59 - 2906780465 * q^60 + 508093974 * q^61 - 3451752063 * q^62 + 158921973 * q^63 - 13473879716 * q^64 + 1277847051 * q^66 - 2812410281 * q^67 + 13614613118 * q^68 - 5113655829 * q^69 + 2418191196 * q^71 + 26243329290 * q^72 - 6537901611 * q^73 - 2632816966 * q^74 - 10170994206 * q^76 - 16936463889 * q^77 - 24146069696 * q^78 + 5397136602 * q^79 + 7242149661 * q^80 - 15745886176 * q^81 + 4998656042 * q^83 + 44726677232 * q^84 - 27688564866 * q^86 + 37895576172 * q^87 - 12151857357 * q^89 - 96024912764 * q^90 + 36633770214 * q^91 - 31643971023 * q^92 + 59768940153 * q^93 - 19802964089 * q^95 - 3289705262 * q^96 - 40329658574 * q^97 + 19243888221 * q^98 + 18506221111 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			20.4162i			0.638007i	0.947754	+	0.319003i	$0.103348\pi$
$2$			20.4162i			0.638007i	−0.947754	+	0.319003i	$0.896652\pi$
$3$	−201.640	−	116.417i	−0.829793	−	0.479081i	0.0239887	−	0.999712i	$-0.492363\pi$
$3$	−201.640	−	116.417i	−0.829793	−	0.479081i	−0.853782	+	0.520631i	$0.825697\pi$
$4$	607.178			0.592948
$5$	4872.92	+	2813.38i	1.55934	+	0.900283i	0.997320	+	0.0731563i	$0.0233072\pi$
$5$	4872.92	+	2813.38i	1.55934	+	0.900283i	0.562015	+	0.827127i	$0.310026\pi$
$6$	2376.79	−	4116.72i	0.305657	−	0.529413i
$7$	−6546.27	+	3779.49i	−0.389497	+	0.224876i	−0.681942	−	0.731406i	$-0.738864\pi$
$7$	−6546.27	+	3779.49i	−0.389497	+	0.224876i	0.292445	+	0.956282i	$0.405531\pi$
$8$			33302.5i			1.01631i
$9$	−2418.78	−	4189.45i	−0.0409623	−	0.0709488i
$10$	−57438.7	+	99486.7i	−0.574387	+	0.994867i
$11$	309963.			1.92463			0.962313	−	0.271943i	$-0.0876661\pi$
$11$	309963.			1.92463			0.962313	+	0.271943i	$0.0876661\pi$
$12$	−122431.	−	70685.7i	−0.492024	−	0.284070i
$13$	−168451.	−	291765.i	−0.453687	−	0.785809i	0.544925	−	0.838485i	$-0.316558\pi$
$13$	−168451.	−	291765.i	−0.453687	−	0.785809i	−0.998612	+	0.0526760i	$0.983225\pi$
$14$	−77162.9	−	133650.i	−0.143472	−	0.248501i
$15$	−655050.	−	1.13458e6i	−0.862617	−	1.49410i
$16$	−58159.9			−0.0554656
$17$	117678.	+	203824.i	0.0828802	+	0.143553i	0.904486	−	0.426503i	$-0.140255\pi$
$17$	117678.	+	203824.i	0.0828802	+	0.143553i	−0.821606	+	0.570056i	$0.806921\pi$
$18$	85532.8	−	49382.4i	0.0452658	−	0.0261342i
$19$	−737457.	−	425771.i	−0.297830	−	0.171952i	0.343637	−	0.939102i	$-0.388341\pi$
$19$	−737457.	−	425771.i	−0.297830	−	0.171952i	−0.641468	+	0.767150i	$0.721674\pi$
$20$	2.95873e6	+	1.70823e6i	0.924604	+	0.533821i
$21$	1.75998e6			0.430935
$22$			6.32827e6i			1.22792i
$23$	2.63431e6	−	4.56276e6i	0.409287	−	0.708905i	−0.585523	−	0.810655i	$-0.699111\pi$
$23$	2.63431e6	−	4.56276e6i	0.409287	−	0.708905i	0.994810	+	0.101750i	$0.0324443\pi$
$24$	3.87697e6	−	6.71510e6i	0.486896	−	0.843328i
$25$	1.09475e7	+	1.89615e7i	1.12102	+	1.94166i
$26$	5.95674e6	−	3.43913e6i	0.501351	−	0.289455i
$27$			1.48749e7i			1.03666i
$28$	−3.97475e6	+	2.29482e6i	−0.230951	+	0.133340i
$29$	5.47605e6	−	3.16160e6i	0.266979	−	0.154141i	−0.360535	−	0.932746i	$-0.617406\pi$
$29$	5.47605e6	−	3.16160e6i	0.266979	−	0.154141i	0.627514	+	0.778605i	$0.284072\pi$
$30$	2.31638e7	−	1.33736e7i	0.953244	−	0.550356i
$31$	−1.79685e7	+	3.11224e7i	−0.627630	+	1.08709i	0.360396	+	0.932799i	$0.382642\pi$
$31$	−1.79685e7	+	3.11224e7i	−0.627630	+	1.08709i	−0.988026	+	0.154288i	$0.950692\pi$
$32$			3.29143e7i			0.980924i
$33$	−6.25009e7	−	3.60849e7i	−1.59704	−	0.922053i
$34$	−4.16132e6	+	2.40254e6i	−0.0915876	+	0.0528781i
$35$	−4.25326e7			−0.809808
$36$	−1.46863e6	−	2.54375e6i	−0.0242885	−	0.0420689i
$37$	5.89077e7	+	3.40104e7i	0.849499	+	0.490459i	0.860482	−	0.509481i	$-0.170163\pi$
$37$	5.89077e7	+	3.40104e7i	0.849499	+	0.490459i	−0.0109825	+	0.999940i	$0.503496\pi$
$38$	8.69263e6	−	1.50561e7i	0.109707	−	0.190018i
$39$			7.84420e7i			0.869412i
$40$	−9.36927e7	+	1.62280e8i	−0.914968	+	1.58477i
$41$	1.60791e8			1.38785			0.693924	−	0.720048i	$-0.255880\pi$
$41$	1.60791e8			1.38785			0.693924	+	0.720048i	$0.255880\pi$
$42$			3.59322e7i			0.274940i
$43$	−1.41723e8	−	3.90667e7i	−0.964043	−	0.265745i
$43$	−1.41723e8	−	3.90667e7i	−0.964043	−	0.265745i
$44$	1.88203e8			1.14120
$45$		−	2.72199e7i		−	0.147511i
$46$	9.31542e7	+	5.37826e7i	0.452286	+	0.261128i
$47$	1.69879e8			0.740714			0.370357	−	0.928889i	$-0.379235\pi$
$47$	1.69879e8			0.740714			0.370357	+	0.928889i	$0.379235\pi$
$48$	1.17273e7	+	6.77078e6i	0.0460250	+	0.0265725i
$49$	−1.12669e8	+	1.95148e8i	−0.398862	+	0.690849i
$50$	−3.87123e8	+	2.23505e8i	−1.23879	+	0.715218i
$51$		−	5.47988e7i		−	0.158825i
$52$	−1.02280e8	−	1.77154e8i	−0.269013	−	0.465944i
$53$	−6.07591e7	+	1.05238e8i	−0.145289	+	0.251647i	−0.929481	−	0.368871i	$-0.879744\pi$
$53$	−6.07591e7	+	1.05238e8i	−0.145289	+	0.251647i	0.784192	+	0.620518i	$0.213078\pi$
$54$	−3.03690e8			−0.661396
$55$	1.51043e9	+	8.72045e8i	3.00114	+	1.73271i
$56$	−1.25866e8	−	2.18007e8i	−0.228544	−	0.395850i
$57$	9.91338e7	+	1.71705e8i	0.164758	+	0.285370i
$58$	6.45479e7	+	1.11800e8i	0.0983427	+	0.170334i
$59$	7.67422e8			1.07343			0.536716	−	0.843763i	$-0.319665\pi$
$59$	7.67422e8			1.07343			0.536716	+	0.843763i	$0.319665\pi$
$60$	−3.97732e8	−	6.88892e8i	−0.511487	−	0.885921i
$61$	6.41857e8	−	3.70576e8i	0.759957	−	0.438761i	−0.0693235	−	0.997594i	$-0.522084\pi$
$61$	6.41857e8	−	3.70576e8i	0.759957	−	0.438761i	0.829280	+	0.558833i	$0.188751\pi$
$62$	−6.35401e8	−	3.66849e8i	−0.693569	−	0.400432i
$63$	3.16680e7	+	1.82835e7i	0.0319093	+	0.0184229i
$64$	−7.31542e8			−0.681301
$65$		−	1.89567e9i		−	1.63379i
$66$	7.36717e8	−	1.27603e9i	0.588276	−	1.01892i
$67$	−8.44456e8	+	1.46264e9i	−0.625465	+	1.08334i	0.362986	+	0.931795i	$0.381757\pi$
$67$	−8.44456e8	+	1.46264e9i	−0.625465	+	1.08334i	−0.988451	+	0.151542i	$0.951576\pi$
$68$	7.14516e7	+	1.23758e8i	0.0491436	+	0.0851193i
$69$	−1.06236e9	+	6.13355e8i	−0.679246	+	0.392163i
$70$		−	8.68355e8i		−	0.516663i
$71$	−1.33181e9	+	7.68923e8i	−0.738162	+	0.426178i	−0.821401	−	0.570352i	$-0.806807\pi$
$71$	−1.33181e9	+	7.68923e8i	−0.738162	+	0.426178i	0.0832387	+	0.996530i	$0.473474\pi$
$72$	1.39519e8	−	8.05515e7i	0.0721060	−	0.0416304i
$73$	5.28559e8	−	3.05163e8i	0.254964	−	0.147204i	−0.367071	−	0.930193i	$-0.619639\pi$
$73$	5.28559e8	−	3.05163e8i	0.254964	−	0.147204i	0.622035	+	0.782989i	$0.286306\pi$
$74$	−6.94363e8	+	1.20267e9i	−0.312916	+	0.541986i
$75$		−	5.09787e9i		−	2.14824i
$76$	−4.47768e8	−	2.58519e8i	−0.176598	−	0.101959i
$77$	−2.02910e9	+	1.17150e9i	−0.749635	+	0.432802i
$78$	−1.60149e9			−0.554691
$79$	−2.40203e9	−	4.16043e9i	−0.780625	−	1.35208i	−0.931578	−	0.363541i	$-0.881568\pi$
$79$	−2.40203e9	−	4.16043e9i	−0.780625	−	1.35208i	0.150954	−	0.988541i	$-0.451766\pi$
$80$	−2.83409e8	−	1.63626e8i	−0.0864895	−	0.0499347i
$81$	1.58886e9	−	2.75199e9i	0.455682	−	0.789264i
$82$			3.28274e9i			0.885456i
$83$	2.27518e8	−	3.94072e8i	0.0577596	−	0.100043i	−0.835700	−	0.549187i	$-0.814938\pi$
$83$	2.27518e8	−	3.94072e8i	0.0577596	−	0.100043i	0.893459	+	0.449144i	$0.148271\pi$
$84$	1.06862e9			0.255522
$85$			1.32429e9i			0.298463i
$86$	7.97594e8	−	2.89344e9i	0.169547	−	0.615066i
$87$	−1.47225e9			−0.295383
$88$			1.03225e10i			1.95602i
$89$	4.12432e9	+	2.38118e9i	0.738589	+	0.426424i	0.821556	−	0.570128i	$-0.193106\pi$
$89$	4.12432e9	+	2.38118e9i	0.738589	+	0.426424i	−0.0829672	+	0.996552i	$0.526440\pi$
$90$	5.55726e8			0.0941128
$91$	2.20545e9	+	1.27332e9i	0.353419	+	0.204047i
$92$	1.59950e9	−	2.77041e9i	0.242685	−	0.420344i
$93$	7.24633e9	−	4.18367e9i	1.04161	−	0.601371i
$94$			3.46829e9i			0.472581i
$95$	−2.39572e9	−	4.14950e9i	−0.309612	−	0.536263i
$96$	3.83178e9	−	6.63684e9i	0.469942	−	0.813964i
$97$	−1.08534e10			−1.26389			−0.631944	−	0.775014i	$-0.717743\pi$
$97$	−1.08534e10			−1.26389			−0.631944	+	0.775014i	$0.717743\pi$
$98$	−3.98418e9	−	2.30026e9i	−0.440766	−	0.254476i
$99$	−7.49733e8	−	1.29858e9i	−0.0788371	−	0.136550i
$100$	6.64706e9	+	1.15130e10i	0.664706	+	1.15130i
$101$	5.78487e8	+	1.00197e9i	0.0550410	+	0.0953338i	0.892233	−	0.451575i	$-0.149138\pi$
$101$	5.78487e8	+	1.00197e9i	0.0550410	+	0.0953338i	−0.837192	+	0.546909i	$0.815804\pi$
$102$	1.11878e9			0.101332
$103$	−1.01105e10	−	1.75120e10i	−0.872145	−	1.51060i	−0.859774	−	0.510675i	$-0.829395\pi$
$103$	−1.01105e10	−	1.75120e10i	−0.872145	−	1.51060i	−0.0123712	−	0.999923i	$-0.503938\pi$
$104$	9.71651e9	−	5.60983e9i	0.798626	−	0.461087i
$105$	8.57627e9	+	4.95151e9i	0.671973	+	0.387964i
$106$	−2.14856e9	−	1.24047e9i	−0.160553	−	0.0926952i
$107$	−4.83969e9			−0.345063			−0.172532	−	0.985004i	$-0.555195\pi$
$107$	−4.83969e9			−0.345063			−0.172532	+	0.985004i	$0.555195\pi$
$108$			9.03174e9i			0.614685i
$109$	−3.09935e9	+	5.36823e9i	−0.201436	+	0.348898i	−0.948991	−	0.315302i	$-0.897894\pi$
$109$	−3.09935e9	+	5.36823e9i	−0.201436	+	0.348898i	0.747555	+	0.664200i	$0.231228\pi$
$110$	−1.78039e10	+	3.08372e10i	−1.10548	+	1.91475i
$111$	−7.91875e9	−	1.37157e10i	−0.469939	−	0.813959i
$112$	3.80730e8	−	2.19815e8i	0.0216036	−	0.0124729i
$113$			2.50479e10i			1.35950i	0.733445	+	0.679749i	$0.237911\pi$
$113$			2.50479e10i			1.35950i	−0.733445	+	0.679749i	$0.762089\pi$
$114$	−3.50556e9	+	2.02394e9i	−0.182068	+	0.105117i
$115$	2.56736e10	−	1.48226e10i	1.27643	−	0.736947i
$116$	3.32494e9	−	1.91965e9i	0.158305	−	0.0913972i
$117$	−8.14892e8	+	1.41143e9i	−0.0371681	+	0.0643771i
$118$			1.56679e10i			0.684856i
$119$	−1.54070e9	−	8.89526e8i	−0.0645631	−	0.0372755i
$120$	3.77843e10	−	2.18148e10i	1.51847	−	0.876688i
$121$	7.01397e10			2.70419
$122$	7.56576e9	+	1.31043e10i	0.279933	+	0.484857i
$123$	−3.24218e10	−	1.87187e10i	−1.15163	−	0.664892i
$124$	−1.09101e10	+	1.88968e10i	−0.372152	+	0.644586i
$125$			6.82486e10i			2.23637i
$126$	−3.73280e8	+	6.46541e8i	−0.0117539	+	0.0203584i
$127$	−5.89572e10			−1.78451			−0.892254	−	0.451534i	$-0.850877\pi$
$127$	−5.89572e10			−1.78451			−0.892254	+	0.451534i	$0.850877\pi$
$128$			1.87690e10i			0.546249i
$129$	2.40289e10	+	2.43763e10i	0.672643	+	0.682368i
$130$	3.87024e10			1.04237
$131$			4.87930e9i			0.126474i	0.997999	+	0.0632370i	$0.0201424\pi$
$131$			4.87930e9i			0.126474i	−0.997999	+	0.0632370i	$0.979858\pi$
$132$	−3.79492e10	−	2.19100e10i	−0.946962	−	0.546729i
$133$	6.43679e9			0.154672
$134$	−2.98616e10	−	1.72406e10i	−0.691176	−	0.399051i
$135$	−4.18489e10	+	7.24844e10i	−0.933287	+	1.61650i
$136$	−6.78786e9	+	3.91897e9i	−0.145894	+	0.0842321i
$137$		−	6.53754e10i		−	1.35460i	−0.735706	−	0.677301i	$-0.763149\pi$
$137$		−	6.53754e10i		−	1.35460i	0.735706	−	0.677301i	$-0.236851\pi$
$138$	−1.25224e10	−	2.16894e10i	−0.250203	−	0.433364i
$139$	2.81957e10	−	4.88364e10i	0.543387	−	0.941174i	−0.455319	−	0.890328i	$-0.650475\pi$
$139$	2.81957e10	−	4.88364e10i	0.543387	−	0.941174i	0.998707	−	0.0508458i	$-0.0161917\pi$
$140$	−2.58249e10			−0.480174
$141$	−3.42544e10	−	1.97768e10i	−0.614640	−	0.354862i
$142$	−1.56985e10	−	2.71906e10i	−0.271904	−	0.470952i
$143$	−5.22135e10	−	9.04365e10i	−0.873178	−	1.51239i
$144$	1.40676e8	+	2.43658e8i	0.00227200	+	0.00393522i
$145$	3.55792e10			0.555080
$146$	6.23028e9	+	1.07912e10i	0.0939168	+	0.162669i
$147$	4.54369e10	−	2.62330e10i	0.661945	−	0.382174i
$148$	3.57675e10	+	2.06503e10i	0.503709	+	0.290816i
$149$	−8.30959e9	−	4.79755e9i	−0.113148	−	0.0653263i	0.442358	−	0.896839i	$-0.354142\pi$
$149$	−8.30959e9	−	4.79755e9i	−0.113148	−	0.0653263i	−0.555506	+	0.831512i	$0.687475\pi$
$150$	1.04079e11			1.37059
$151$		−	3.72126e10i		−	0.474029i	−0.971506	−	0.237015i	$-0.923831\pi$
$151$		−	3.72126e10i		−	0.474029i	0.971506	−	0.237015i	$-0.0761689\pi$
$152$	1.41792e10	−	2.45592e10i	0.174757	−	0.302688i
$153$	5.69276e8	−	9.86014e8i	0.00678993	−	0.0117605i
$154$	−2.39176e10	−	4.14266e10i	−0.276131	−	0.478272i
$155$	−1.75118e11	+	1.01105e11i	−1.95737	+	1.13009i
$156$			4.76283e10i			0.515516i
$157$	1.46982e10	−	8.48600e9i	0.154087	−	0.0889621i	−0.420974	−	0.907073i	$-0.638312\pi$
$157$	1.46982e10	−	8.48600e9i	0.154087	−	0.0889621i	0.575061	+	0.818111i	$0.304978\pi$
$158$	8.49402e10	−	4.90403e10i	0.862637	−	0.498044i
$159$	2.45029e10	−	1.41468e10i	0.241119	−	0.139210i
$160$	−9.26007e10	+	1.60389e11i	−0.883109	+	1.52959i
$161$			3.98254e10i			0.368155i
$162$	5.61853e10	+	3.24386e10i	0.503556	+	0.290728i
$163$	8.93459e10	−	5.15839e10i	0.776491	−	0.448307i	−0.0586942	−	0.998276i	$-0.518694\pi$
$163$	8.93459e10	−	5.15839e10i	0.776491	−	0.448307i	0.835185	+	0.549969i	$0.185360\pi$
$164$	9.76287e10			0.822921
$165$	−2.03041e11	−	3.51678e11i	−1.66022	−	2.87558i
$166$	8.04545e9	+	4.64505e9i	0.0638278	+	0.0368510i
$167$	8.23346e10	−	1.42608e11i	0.633870	−	1.09789i	−0.352883	−	0.935667i	$-0.614799\pi$
$167$	8.23346e10	−	1.42608e11i	0.633870	−	1.09789i	0.986753	−	0.162228i	$-0.0518679\pi$
$168$			5.86118e10i			0.437964i
$169$	1.21779e10	−	2.10927e10i	0.0883361	−	0.153003i
$170$	−2.70371e10			−0.190421
$171$			4.11939e9i			0.0281743i
$172$	−8.60508e10	−	2.37205e10i	−0.571627	−	0.157573i
$173$	6.13089e10			0.395633			0.197817	−	0.980239i	$-0.436615\pi$
$173$	6.13089e10			0.395633			0.197817	+	0.980239i	$0.436615\pi$
$174$		−	3.00578e10i		−	0.188456i
$175$	−1.43330e11	−	8.27516e10i	−0.873266	−	0.504180i
$176$	−1.80274e10			−0.106751
$177$	−1.54743e11	−	8.93408e10i	−0.890726	−	0.514261i
$178$	−4.86147e10	+	8.42031e10i	−0.272062	+	0.471224i
$179$	2.02221e11	−	1.16753e11i	1.10043	−	0.635333i	0.164095	−	0.986445i	$-0.447530\pi$
$179$	2.02221e11	−	1.16753e11i	1.10043	−	0.635333i	0.936334	+	0.351112i	$0.114196\pi$
$180$		−	1.65273e10i		−	0.0874661i
$181$	8.26646e10	+	1.43179e11i	0.425527	+	0.737034i	0.996469	−	0.0839560i	$-0.0267555\pi$
$181$	8.26646e10	+	1.43179e11i	0.425527	+	0.737034i	−0.570943	+	0.820990i	$0.693422\pi$
$182$	−2.59963e10	+	4.50269e10i	−0.130183	+	0.225484i
$183$	−1.72565e11			−0.840809
$184$	1.51951e11	+	8.77290e10i	0.720468	+	0.415962i
$185$	1.91368e11	+	3.31460e11i	0.883103	+	1.52958i
$186$	8.54147e10	+	1.47943e11i	0.383679	+	0.664551i
$187$	3.64759e10	+	6.31781e10i	0.159514	+	0.276286i
$188$	1.03147e11			0.439205
$189$	−5.62196e10	−	9.73753e10i	−0.233120	−	0.403775i
$190$	8.47171e10	−	4.89114e10i	0.342139	−	0.197534i
$191$	−2.18596e11	−	1.26207e11i	−0.859955	−	0.496495i	0.00404226	−	0.999992i	$-0.498713\pi$
$191$	−2.18596e11	−	1.26207e11i	−0.859955	−	0.496495i	−0.863997	+	0.503497i	$0.832047\pi$
$192$	1.47508e11	+	8.51637e10i	0.565339	+	0.326399i
$193$	−3.16793e11			−1.18301			−0.591507	−	0.806300i	$-0.701467\pi$
$193$	−3.16793e11			−1.18301			−0.591507	+	0.806300i	$0.701467\pi$
$194$		−	2.21586e11i		−	0.806369i
$195$	−2.20687e11	+	3.82242e11i	−0.782717	+	1.35571i
$196$	−6.84099e10	+	1.18489e11i	−0.236504	+	0.409637i
$197$	8.09685e10	+	1.40241e11i	0.272888	+	0.472656i	0.969600	−	0.244695i	$-0.0786878\pi$
$197$	8.09685e10	+	1.40241e11i	0.272888	+	0.472656i	−0.696712	+	0.717351i	$0.745354\pi$
$198$	2.65120e10	−	1.53067e10i	0.0871198	−	0.0502986i
$199$		−	9.52483e9i		−	0.0305205i	−0.999884	−	0.0152603i	$-0.995142\pi$
$199$		−	9.52483e9i		−	0.0305205i	0.999884	−	0.0152603i	$-0.00485768\pi$
$200$	−6.31466e11	+	3.64577e11i	−1.97333	+	1.13930i
$201$	3.40552e11	−	1.96618e11i	1.03801	−	0.599297i
$202$	−2.04564e10	+	1.18105e10i	−0.0608236	+	0.0351165i
$203$	−2.38985e10	+	4.13933e10i	−0.0693250	+	0.120074i
$204$		−	3.32726e10i		−	0.0941752i
$205$	7.83521e11	+	4.52366e11i	2.16412	+	1.24946i
$206$	3.57528e11	−	2.06419e11i	0.963772	−	0.556434i
$207$	−2.54873e10			−0.0670613
$208$	9.79708e9	+	1.69690e10i	0.0251640	+	0.0435854i
$209$	−2.28585e11	−	1.31973e11i	−0.573212	−	0.330944i
$210$	−1.01091e11	+	1.75095e11i	−0.247523	+	0.428723i
$211$			4.69015e11i			1.12144i	0.828007	+	0.560718i	$0.189475\pi$
$211$			4.69015e11i			1.12144i	−0.828007	+	0.560718i	$0.810525\pi$
$212$	−3.68916e10	+	6.38981e10i	−0.0861486	+	0.149214i
$213$	3.58062e11			0.816696
$214$		−	9.88082e10i		−	0.220153i
$215$	−5.80694e11	−	5.89089e11i	−1.26402	−	1.28230i
$216$	−4.95372e11			−1.05357
$217$		−	2.71647e11i		−	0.564555i
$218$	−1.09599e11	−	6.32769e10i	−0.222599	−	0.128518i
$219$	−1.42105e11			−0.282090
$220$	9.17098e11	+	5.29487e11i	1.77952	+	1.02741i
$221$	3.96459e10	−	6.86688e10i	0.0752034	−	0.130256i
$222$	2.80022e11	−	1.61671e11i	0.519311	−	0.299824i
$223$		−	6.51582e11i		−	1.18153i	−0.806844	−	0.590765i	$-0.798826\pi$
$223$		−	6.51582e11i		−	1.18153i	0.806844	−	0.590765i	$-0.201174\pi$
$224$	−1.24399e11	−	2.15466e11i	−0.220586	−	0.382066i
$225$	5.29590e10	−	9.17277e10i	0.0918390	−	0.159070i
$226$	−5.11383e11			−0.867369
$227$	2.13003e11	+	1.22977e11i	0.353392	+	0.204031i	0.666178	−	0.745793i	$-0.267929\pi$
$227$	2.13003e11	+	1.22977e11i	0.353392	+	0.204031i	−0.312786	+	0.949824i	$0.601262\pi$
$228$	6.01919e10	+	1.04255e11i	0.0976931	+	0.169209i
$229$	−1.72791e11	−	2.99282e11i	−0.274374	−	0.475229i	0.695603	−	0.718426i	$-0.255137\pi$
$229$	−1.72791e11	−	2.99282e11i	−0.274374	−	0.475229i	−0.969977	+	0.243197i	$0.921804\pi$
$230$	3.02622e11	+	5.24157e11i	0.470177	+	0.814371i
$231$	5.45530e11			0.829390
$232$	1.05289e11	+	1.82366e11i	0.156655	+	0.271334i
$233$	−7.25021e11	+	4.18591e11i	−1.05577	+	0.609552i	−0.924260	−	0.381763i	$-0.875317\pi$
$233$	−7.25021e11	+	4.18591e11i	−1.05577	+	0.609552i	−0.131514	+	0.991314i	$0.541984\pi$
$234$	−2.88161e10	−	1.66370e10i	−0.0410730	−	0.0237135i
$235$	8.27808e11	+	4.77935e11i	1.15502	+	0.666852i
$236$	4.65962e11			0.636489
$237$			1.11854e12i			1.49593i
$238$	1.81608e10	−	3.14554e10i	0.0237820	−	0.0411917i
$239$	4.80355e11	−	8.31999e11i	0.615988	−	1.06692i	−0.374222	−	0.927339i	$-0.622090\pi$
$239$	4.80355e11	−	8.31999e11i	0.615988	−	1.06692i	0.990210	−	0.139584i	$-0.0445765\pi$
$240$	3.80976e10	+	6.59870e10i	0.0478456	+	0.0828710i
$241$	9.35190e11	−	5.39932e11i	1.15031	−	0.664131i	0.201346	−	0.979520i	$-0.435468\pi$
$241$	9.35190e11	−	5.39932e11i	1.15031	−	0.664131i	0.948962	+	0.315389i	$0.102135\pi$
$242$			1.43199e12i			1.72529i
$243$	1.19917e11	−	6.92341e10i	0.141530	−	0.0817125i
$244$	3.89721e11	−	2.25006e11i	0.450615	−	0.260162i
$245$	−1.09805e12	+	6.33960e11i	−1.24392	+	0.718177i
$246$	3.82166e11	−	6.61930e11i	0.424205	−	0.734745i
$247$			2.86886e11i			0.312050i
$248$	−1.03645e12	−	5.98396e11i	−1.10482	−	0.637867i
$249$	−9.17531e10	+	5.29737e10i	−0.0958571	+	0.0553431i
$250$	−1.39338e12			−1.42682
$251$	−6.83880e11	−	1.18451e12i	−0.686454	−	1.18897i	−0.972978	−	0.230900i	$-0.925833\pi$
$251$	−6.83880e11	−	1.18451e12i	−0.686454	−	1.18897i	0.286524	−	0.958073i	$-0.407500\pi$
$252$	1.92281e10	+	1.11014e10i	0.0189206	+	0.0109238i
$253$	8.16538e11	−	1.41429e12i	0.787724	−	1.36438i
$254$		−	1.20368e12i		−	1.13853i
$255$	1.54170e11	−	2.67030e11i	0.142988	−	0.247662i
$256$	−1.13229e12			−1.02981
$257$			5.43433e11i			0.484708i	0.970188	+	0.242354i	$0.0779196\pi$
$257$			5.43433e11i			0.484708i	−0.970188	+	0.242354i	$0.922080\pi$
$258$	−4.97671e11	+	4.90579e11i	−0.435355	+	0.429151i
$259$	−5.14167e11			−0.441169
$260$		−	1.15101e12i		−	0.968750i
$261$	−2.64908e10	−	1.52944e10i	−0.0218722	−	0.0126279i
$262$	−9.96169e10			−0.0806913
$263$	−9.84382e10	−	5.68333e10i	−0.0782321	−	0.0451673i	0.460374	−	0.887725i	$-0.347715\pi$
$263$	−9.84382e10	−	5.68333e10i	−0.0782321	−	0.0451673i	−0.538606	+	0.842558i	$0.681049\pi$
$264$	1.20172e12	−	2.08143e12i	0.937092	−	1.62309i
$265$	−5.92149e11	+	3.41877e11i	−0.453108	+	0.261602i
$266$			1.31415e11i			0.0986816i
$267$	−5.54418e11	−	9.60281e11i	−0.408584	−	0.707688i
$268$	−5.12735e11	+	8.88084e11i	−0.370868	+	0.642362i
$269$	−2.42148e12			−1.71918			−0.859588	−	0.510988i	$-0.829280\pi$
$269$	−2.42148e12			−1.71918			−0.859588	+	0.510988i	$0.829280\pi$
$270$	−1.47986e12	−	8.54396e11i	−1.03134	−	0.595443i
$271$	−1.31493e12	−	2.27752e12i	−0.899612	−	1.55817i	−0.827991	−	0.560742i	$-0.810516\pi$
$271$	−1.31493e12	−	2.27752e12i	−0.899612	−	1.55817i	−0.0716210	−	0.997432i	$-0.522817\pi$
$272$	−6.84414e9	−	1.18544e10i	−0.00459700	−	0.00796224i
$273$	−2.96471e11	−	5.13502e11i	−0.195510	−	0.338633i
$274$	1.33472e12			0.864245
$275$	3.39331e12	+	5.87738e12i	2.15754	+	3.73697i
$276$	−6.45043e11	+	3.72416e11i	−0.402757	+	0.232532i
$277$	−1.53079e12	−	8.83800e11i	−0.938676	−	0.541945i	−0.0491311	−	0.998792i	$-0.515645\pi$
$277$	−1.53079e12	−	8.83800e11i	−0.938676	−	0.541945i	−0.889545	+	0.456847i	$0.848979\pi$
$278$	9.97055e11	+	5.75650e11i	0.600475	+	0.346685i
$279$	1.73848e11			0.102837
$280$		−	1.41644e12i		−	0.823017i
$281$	2.58249e11	−	4.47301e11i	0.147403	−	0.255310i	−0.782864	−	0.622193i	$-0.786242\pi$
$281$	2.58249e11	−	4.47301e11i	0.147403	−	0.255310i	0.930267	+	0.366883i	$0.119575\pi$
$282$	4.03767e11	−	6.99345e11i	0.226405	−	0.392144i
$283$	−6.03889e11	−	1.04597e12i	−0.332679	−	0.576216i	0.650358	−	0.759628i	$-0.274619\pi$
$283$	−6.03889e11	−	1.04597e12i	−0.332679	−	0.576216i	−0.983036	+	0.183412i	$0.941286\pi$
$284$	−8.08648e11	+	4.66873e11i	−0.437691	+	0.252701i
$285$			1.11561e12i			0.593317i
$286$	1.84637e12	−	1.06600e12i	0.964914	−	0.557094i
$287$	−1.05258e12	+	6.07707e11i	−0.540562	+	0.312094i
$288$	1.37893e11	−	7.96126e10i	0.0695953	−	0.0401809i
$289$	9.80301e11	−	1.69793e12i	0.486262	−	0.842230i
$290$			7.26392e11i			0.354145i
$291$	2.18848e12	+	1.26352e12i	1.04877	+	0.605505i
$292$	3.20929e11	−	1.85289e11i	0.151180	−	0.0872840i
$293$	2.59734e12			1.20279			0.601395	−	0.798952i	$-0.294612\pi$
$293$	2.59734e12			1.20279			0.601395	+	0.798952i	$0.294612\pi$
$294$	5.35579e11	+	9.27649e11i	0.243830	+	0.422325i
$295$	3.73959e12	+	2.15905e12i	1.67384	+	0.966392i
$296$	−1.13263e12	+	1.96177e12i	−0.498459	+	0.863356i
$297$			4.61068e12i			1.99518i
$298$	9.79477e10	−	1.69650e11i	0.0416786	−	0.0721894i
$299$	−1.77501e12			−0.742752
$300$		−	3.09531e12i		−	1.27379i
$301$	1.07541e12	−	2.79898e11i	0.435251	−	0.113284i
$302$	7.59740e11			0.302434
$303$		−	2.69382e11i		−	0.105476i
$304$	4.28904e10	+	2.47628e10i	0.0165193	+	0.00953744i
$305$	4.17029e12			1.58004
$306$	2.01307e10	+	1.16224e10i	0.00750328	+	0.00433202i
$307$	1.18310e11	−	2.04919e11i	0.0433840	−	0.0751433i	−0.843518	−	0.537101i	$-0.819519\pi$
$307$	1.18310e11	−	2.04919e11i	0.0433840	−	0.0751433i	0.886902	+	0.461958i	$0.152853\pi$
$308$	−1.23203e12	+	7.11311e11i	−0.444495	+	0.256629i
$309$			4.70815e12i			1.67131i
$310$	−2.06417e12	−	3.57525e12i	−0.721004	−	1.24882i
$311$	−2.30458e12	+	3.99165e12i	−0.792117	+	1.37199i	0.132536	+	0.991178i	$0.457688\pi$
$311$	−2.30458e12	+	3.99165e12i	−0.792117	+	1.37199i	−0.924654	+	0.380809i	$0.875645\pi$
$312$	−2.61231e12			−0.883593
$313$	−1.63573e12	−	9.44387e11i	−0.544489	−	0.314361i	0.202407	−	0.979301i	$-0.435124\pi$
$313$	−1.63573e12	−	9.44387e11i	−0.544489	−	0.314361i	−0.746896	+	0.664941i	$0.768457\pi$
$314$	1.73252e11	+	3.00081e11i	0.0567584	+	0.0983084i
$315$	1.02877e11	+	1.78189e11i	0.0331716	+	0.0574549i
$316$	−1.45846e12	−	2.52612e12i	−0.462869	−	0.801713i
$317$	−4.24180e11			−0.132512			−0.0662558	−	0.997803i	$-0.521105\pi$
$317$	−4.24180e11			−0.132512			−0.0662558	+	0.997803i	$0.521105\pi$
$318$	2.88823e11	+	5.00256e11i	0.0888170	+	0.153836i
$319$	1.69737e12	−	9.79979e11i	0.513835	−	0.296663i
$320$	−3.56475e12	−	2.05811e12i	−1.06238	−	0.613364i
$321$	9.75874e11	+	5.63421e11i	0.286331	+	0.165313i
$322$	−8.13083e11			−0.234885
$323$		−	2.00416e11i		−	0.0570058i
$324$	9.64724e11	−	1.67095e12i	0.270195	−	0.467992i
$325$	3.68821e12	−	6.38818e12i	1.01718	−	1.76181i
$326$	1.05315e12	+	1.82410e12i	0.286023	+	0.495406i
$327$	1.24990e12	−	7.21632e11i	0.334301	−	0.193009i
$328$			5.35473e12i			1.41049i
$329$	−1.11207e12	+	6.42056e11i	−0.288506	+	0.166569i
$330$	7.17993e12	−	4.14534e12i	1.83464	−	1.05923i
$331$	−5.99802e12	+	3.46296e12i	−1.50962	+	0.871580i	−0.509683	+	0.860362i	$0.670237\pi$
$331$	−5.99802e12	+	3.46296e12i	−1.50962	+	0.871580i	−0.999937	+	0.0112174i	$0.996429\pi$
$332$	1.38144e11	−	2.39272e11i	0.0342484	−	0.0593200i
$333$		−	3.29055e11i		−	0.0803613i
$334$	2.91151e12	+	1.68096e12i	0.700464	+	0.404413i
$335$	−8.22994e12	+	4.75156e12i	−1.95062	+	1.12619i
$336$	−1.02360e11			−0.0239021
$337$	2.99747e12	+	5.19178e12i	0.689614	+	1.19445i	0.971963	+	0.235135i	$0.0755531\pi$
$337$	2.99747e12	+	5.19178e12i	0.689614	+	1.19445i	−0.282349	+	0.959312i	$0.591114\pi$
$338$	4.30633e11	+	2.48626e11i	0.0976167	+	0.0563590i
$339$	2.91599e12	−	5.05065e12i	0.651310	−	1.12810i
$340$			8.04083e11i			0.176973i
$341$	−5.56958e12	+	9.64679e12i	−1.20795	+	2.09224i
$342$	−8.41024e10			−0.0179754
$343$		−	3.83854e12i		−	0.808529i
$344$	1.30102e12	−	4.71971e12i	0.270079	−	0.979768i
$345$	−6.90242e12			−1.41223
$346$			1.25170e12i			0.252417i
$347$	3.98487e12	+	2.30067e12i	0.792076	+	0.457305i	0.840693	−	0.541512i	$-0.182148\pi$
$347$	3.98487e12	+	2.30067e12i	0.792076	+	0.457305i	−0.0486171	+	0.998817i	$0.515481\pi$
$348$	−8.93920e11			−0.175147
$349$	5.49473e12	+	3.17239e12i	1.06125	+	0.612716i	0.925779	−	0.378065i	$-0.123410\pi$
$349$	5.49473e12	+	3.17239e12i	1.06125	+	0.612716i	0.135476	+	0.990781i	$0.456744\pi$
$350$	1.68947e12	−	2.92625e12i	0.321670	−	0.557149i
$351$	4.33999e12	−	2.50569e12i	0.814617	−	0.470319i
$352$			1.02022e13i			1.88791i
$353$	−2.19168e12	−	3.79609e12i	−0.399855	−	0.692570i	0.593853	−	0.804574i	$-0.297606\pi$
$353$	−2.19168e12	−	3.79609e12i	−0.399855	−	0.692570i	−0.993708	+	0.112004i	$0.964273\pi$
$354$	1.82400e12	−	3.15926e12i	0.328102	−	0.568289i
$355$	−8.65310e12			−1.53472
$356$	2.50420e12	+	1.44580e12i	0.437944	+	0.252847i
$357$	2.07112e11	+	3.58728e11i	0.0357160	+	0.0618620i
$358$	2.38365e12	+	4.12859e12i	0.405347	+	0.702081i
$359$	3.36078e11	+	5.82104e11i	0.0563596	+	0.0976177i	0.892829	−	0.450396i	$-0.148717\pi$
$359$	3.36078e11	+	5.82104e11i	0.0563596	+	0.0976177i	−0.836469	+	0.548014i	$0.815384\pi$
$360$	9.06489e11			0.149917
$361$	−2.70297e12	−	4.68168e12i	−0.440865	−	0.763600i
$362$	−2.92318e12	+	1.68770e12i	−0.470232	+	0.271489i
$363$	−1.41429e13	−	8.16543e12i	−2.24392	−	1.29553i
$364$	1.33910e12	+	7.73130e11i	0.209559	+	0.120989i
$365$	3.43417e12			0.530099
$366$		−	3.52312e12i		−	0.536442i
$367$	2.76464e12	−	4.78850e12i	0.415249	−	0.719232i	−0.580206	−	0.814470i	$-0.697028\pi$
$367$	2.76464e12	−	4.78850e12i	0.415249	−	0.719232i	0.995455	+	0.0952382i	$0.0303613\pi$
$368$	−1.53211e11	+	2.65369e11i	−0.0227013	+	0.0393198i
$369$	−3.88918e11	−	6.73626e11i	−0.0568494	−	0.0984661i
$370$	−6.76715e12	+	3.90702e12i	−0.975882	+	0.563426i
$371$		−	9.18553e11i		−	0.130688i
$372$	4.39982e12	−	2.54023e12i	0.617618	−	0.356582i
$373$	9.89376e12	−	5.71217e12i	1.37031	−	0.791146i	0.379339	−	0.925258i	$-0.376151\pi$
$373$	9.89376e12	−	5.71217e12i	1.37031	−	0.791146i	0.990966	+	0.134112i	$0.0428181\pi$
$374$	−1.28986e12	+	7.44699e11i	−0.176272	+	0.101771i
$375$	7.94529e12	−	1.37616e13i	1.07140	−	1.85573i
$376$			5.65740e12i			0.752796i
$377$	−1.84489e12	−	1.06515e12i	−0.242250	−	0.139863i
$378$	1.98803e12	−	1.14779e12i	0.257611	−	0.148732i
$379$	−5.88199e12			−0.752192			−0.376096	−	0.926581i	$-0.622734\pi$
$379$	−5.88199e12			−0.752192			−0.376096	+	0.926581i	$0.622734\pi$
$380$	−1.45463e12	−	2.51949e12i	−0.183583	−	0.317976i
$381$	1.18881e13	+	6.86361e12i	1.48077	+	0.854924i
$382$	2.57666e12	−	4.46291e12i	0.316767	−	0.548657i
$383$			9.57534e12i			1.16188i	0.813947	+	0.580938i	$0.197314\pi$
$383$			9.57534e12i			1.16188i	−0.813947	+	0.580938i	$0.802686\pi$
$384$	2.18502e12	−	3.78457e12i	0.261698	−	0.453274i
$385$	−1.31835e13			−1.55858
$386$		−	6.46772e12i		−	0.754770i
$387$	1.79128e11	+	6.88234e11i	0.0206352	+	0.0792832i
$388$	−6.58997e12			−0.749419
$389$			1.09945e13i			1.23432i	0.786837	+	0.617161i	$0.211717\pi$
$389$			1.09945e13i			1.23432i	−0.786837	+	0.617161i	$0.788283\pi$
$390$	−7.80393e12	−	4.50560e12i	−0.864949	−	0.499378i
$391$	1.24000e12			0.135687
$392$	−6.49890e12	−	3.75214e12i	−0.702117	−	0.405368i
$393$	5.68033e11	−	9.83861e11i	0.0605913	−	0.104947i
$394$	−2.86320e12	+	1.65307e12i	−0.301558	+	0.174104i
$395$		−	2.70313e13i		−	2.81113i
$396$	−4.55222e11	−	7.88467e11i	−0.0467463	−	0.0809670i
$397$	−4.01951e12	+	6.96199e12i	−0.407587	+	0.705961i	−0.994619	−	0.103603i	$-0.966963\pi$
$397$	−4.01951e12	+	6.96199e12i	−0.407587	+	0.705961i	0.587032	+	0.809564i	$0.300296\pi$
$398$	1.94461e11			0.0194723
$399$	−1.29791e12	−	7.49350e11i	−0.128346	−	0.0741004i
$400$	−6.36702e11	−	1.10280e12i	−0.0621780	−	0.107695i
$401$	−2.35903e12	−	4.08595e12i	−0.227515	−	0.394068i	0.729556	−	0.683921i	$-0.239727\pi$
$401$	−2.35903e12	−	4.08595e12i	−0.227515	−	0.394068i	−0.957071	+	0.289853i	$0.906394\pi$
$402$	4.01419e12	+	6.95278e12i	0.382355	+	0.662259i
$403$	1.21072e13			1.13899
$404$	3.51245e11	+	6.08373e11i	0.0326364	+	0.0565280i
$405$	1.54848e13	−	8.94017e12i	1.42112	−	0.820485i
$406$	−8.45095e11	−	4.87916e11i	−0.0766082	−	0.0442298i
$407$	1.82592e13	+	1.05420e13i	1.63497	+	0.943950i
$408$	1.82494e12			0.161416
$409$		−	2.08648e13i		−	1.82305i	−0.411245	−	0.911525i	$-0.634906\pi$
$409$		−	2.08648e13i		−	1.82305i	0.411245	−	0.911525i	$-0.365094\pi$
$410$	−9.23561e12	+	1.59965e13i	−0.797161	+	1.38072i
$411$	−7.61080e12	+	1.31823e13i	−0.648965	+	1.12404i
$412$	−6.13891e12	−	1.06329e13i	−0.517136	−	0.895706i
$413$	−5.02375e12	+	2.90046e12i	−0.418098	+	0.241389i
$414$		−	5.20354e11i		−	0.0427855i
$415$	2.21735e12	−	1.28019e12i	0.180133	−	0.104000i
$416$	9.60326e12	−	5.54445e12i	0.770819	−	0.445032i
$417$	−1.13708e13	+	6.56491e12i	−0.901798	+	0.520653i
$418$	2.69440e12	−	4.66683e12i	0.211145	−	0.365713i
$419$			1.69603e12i			0.131330i	0.997842	+	0.0656651i	$0.0209169\pi$
$419$			1.69603e12i			0.131330i	−0.997842	+	0.0656651i	$0.979083\pi$
$420$	5.20732e12	+	3.00645e12i	0.398445	+	0.230042i
$421$	1.38719e13	−	8.00892e12i	1.04888	−	0.605569i	0.126542	−	0.991961i	$-0.459612\pi$
$421$	1.38719e13	−	8.00892e12i	1.04888	−	0.605569i	0.922335	+	0.386392i	$0.126279\pi$
$422$	−9.57550e12			−0.715483
$423$	−4.10901e11	−	7.11701e11i	−0.0303414	−	0.0525528i
$424$	−3.50468e12	−	2.02343e12i	−0.255752	−	0.147659i
$425$	−2.57655e12	+	4.46272e12i	−0.185821	+	0.321851i
$426$			7.31027e12i			0.521057i
$427$	−2.80118e12	+	4.85178e12i	−0.197334	+	0.341792i
$428$	−2.93856e12			−0.204605
$429$			2.43141e13i			1.67329i
$430$	1.20270e13	−	1.18556e13i	0.818114	−	0.806455i
$431$	−5.63058e12			−0.378588			−0.189294	−	0.981920i	$-0.560620\pi$
$431$	−5.63058e12			−0.378588			−0.189294	+	0.981920i	$0.560620\pi$
$432$		−	8.65124e11i		−	0.0574989i
$433$	−2.18593e13	−	1.26205e13i	−1.43614	−	0.829157i	−0.438564	−	0.898700i	$-0.644513\pi$
$433$	−2.18593e13	−	1.26205e13i	−1.43614	−	0.829157i	−0.997579	+	0.0695425i	$0.977846\pi$
$434$	5.54601e12			0.360190
$435$	−7.17417e12	−	4.14201e12i	−0.460602	−	0.265929i
$436$	−1.88186e12	+	3.25947e12i	−0.119441	+	0.206878i
$437$	−3.88538e12	+	2.24323e12i	−0.243796	+	0.140756i
$438$		−	2.90124e12i		−	0.179975i
$439$	−1.24804e12	−	2.16167e12i	−0.0765430	−	0.132576i	0.825213	−	0.564821i	$-0.191055\pi$
$439$	−1.24804e12	−	2.16167e12i	−0.0765430	−	0.132576i	−0.901756	+	0.432245i	$0.857722\pi$
$440$	−2.90413e13	+	5.03010e13i	−1.76097	+	3.05009i
$441$	1.09008e12			0.0653532
$442$	1.40196e12	+	8.09420e11i	0.0831043	+	0.0479803i
$443$	4.78878e12	+	8.29441e12i	0.280677	+	0.486146i	0.971552	−	0.236828i	$-0.0761079\pi$
$443$	4.78878e12	+	8.29441e12i	0.280677	+	0.486146i	−0.690875	+	0.722974i	$0.742775\pi$
$444$	−4.80809e12	−	8.32786e12i	−0.278649	−	0.482635i
$445$	1.33983e13	+	2.32066e13i	0.767805	+	1.32988i
$446$	1.33028e13			0.753824
$447$	1.11703e12	+	1.93475e12i	0.0625932	+	0.108415i
$448$	4.78887e12	−	2.76485e12i	0.265364	−	0.153208i
$449$	−1.72326e12	−	9.94923e11i	−0.0944318	−	0.0545202i	0.452040	−	0.891997i	$-0.350696\pi$
$449$	−1.72326e12	−	9.94923e11i	−0.0944318	−	0.0545202i	−0.546472	+	0.837477i	$0.684030\pi$
$450$	1.87273e12	+	1.08122e12i	0.101488	+	0.0585939i
$451$	4.98392e13			2.67109
$452$			1.52085e13i			0.806111i
$453$	−4.33217e12	+	7.50353e12i	−0.227098	+	0.393346i
$454$	−2.51073e12	+	4.34872e12i	−0.130173	+	0.225466i
$455$	7.16466e12	+	1.24095e13i	0.367399	+	0.636354i
$456$	−5.71819e12	+	3.30140e12i	−0.290025	+	0.167446i
$457$			1.80401e13i			0.905020i	0.891759	+	0.452510i	$0.149471\pi$
$457$			1.80401e13i			0.905020i	−0.891759	+	0.452510i	$0.850529\pi$
$458$	6.11021e12	−	3.52773e12i	0.303200	−	0.175052i
$459$	−3.03187e12	+	1.75045e12i	−0.148815	+	0.0859186i
$460$	1.55884e13	−	8.99999e12i	0.756856	−	0.436971i
$461$	1.55121e13	−	2.68678e13i	0.745018	−	1.29041i	−0.205168	−	0.978727i	$-0.565774\pi$
$461$	1.55121e13	−	2.68678e13i	0.745018	−	1.29041i	0.950186	−	0.311683i	$-0.100893\pi$
$462$			1.11377e13i			0.529156i
$463$	−2.18863e13	−	1.26360e13i	−1.02865	−	0.593890i	−0.112051	−	0.993702i	$-0.535742\pi$
$463$	−2.18863e13	−	1.26360e13i	−1.02865	−	0.593890i	−0.916597	+	0.399812i	$0.869075\pi$
$464$	−3.18486e11	+	1.83878e11i	−0.0148082	+	0.00854949i
$465$	4.70811e13			2.16562
$466$	−8.54605e12	−	1.48022e13i	−0.388898	−	0.673591i
$467$	−1.18011e13	−	6.81335e12i	−0.531296	−	0.306744i	0.210248	−	0.977648i	$-0.432573\pi$
$467$	−1.18011e13	−	6.81335e12i	−0.531296	−	0.306744i	−0.741544	+	0.670904i	$0.765906\pi$
$468$	−4.94785e11	+	8.56992e11i	−0.0220388	+	0.0381722i
$469$		−	1.27664e13i		−	0.562608i
$470$	−9.75763e12	+	1.69007e13i	−0.425456	+	0.736912i
$471$	−3.95165e12			−0.170480
$472$			2.55571e13i			1.09094i
$473$	−4.39288e13	−	1.21092e13i	−1.85542	−	0.511459i
$474$	−2.28364e13			−0.954413
$475$		−	1.86444e13i		−	0.771048i
$476$	−9.35483e11	−	5.40101e11i	−0.0382826	−	0.0221024i
$477$	5.87852e11			0.0238054
$478$	1.69863e13	+	9.80702e12i	0.680704	+	0.393005i
$479$	−1.33428e13	+	2.31104e13i	−0.529139	+	0.916496i	0.470283	+	0.882516i	$0.344152\pi$
$479$	−1.33428e13	+	2.31104e13i	−0.529139	+	0.916496i	−0.999422	+	0.0339807i	$0.989182\pi$
$480$	3.73440e13	−	2.15605e13i	1.46560	−	0.846162i
$481$		−	2.29163e13i		−	0.890059i
$482$	1.10234e13	+	1.90930e13i	0.423720	+	0.733905i
$483$	4.63634e12	−	8.03038e12i	0.176376	−	0.305492i
$484$	4.25873e13			1.60344
$485$	−5.28880e13	−	3.05349e13i	−1.97083	−	1.13786i
$486$	1.41350e12	+	2.44825e12i	0.0521331	+	0.0902972i
$487$	−4.59246e12	−	7.95437e12i	−0.167649	−	0.290376i	0.769944	−	0.638111i	$-0.220284\pi$
$487$	−4.59246e12	−	7.95437e12i	−0.167649	−	0.290376i	−0.937593	+	0.347735i	$0.886951\pi$
$488$	1.23411e13	+	2.13754e13i	0.445918	+	0.772352i
$489$	−2.40209e13			−0.859103
$490$	−1.29431e13	−	2.24180e13i	−0.458201	−	0.793628i
$491$	1.27770e13	−	7.37678e12i	0.447734	−	0.258499i	−0.259139	−	0.965840i	$-0.583439\pi$
$491$	1.27770e13	−	7.37678e12i	0.447734	−	0.258499i	0.706873	+	0.707341i	$0.250105\pi$
$492$	−1.96858e13	−	1.13656e13i	−0.682854	−	0.394246i
$493$	1.28882e12	+	7.44102e11i	0.0442546	+	0.0255504i
$494$	−5.85713e12			−0.199090
$495$		−	8.43715e12i		−	0.283903i
$496$	1.04505e12	−	1.81007e12i	0.0348119	−	0.0602959i
$497$	5.81227e12	−	1.00671e13i	0.191674	−	0.331990i
$498$	−1.08152e12	−	1.87325e12i	−0.0353093	−	0.0611574i
$499$	−3.10036e13	+	1.78999e13i	−1.00210	+	0.578560i	−0.908868	−	0.417084i	$-0.863052\pi$
$499$	−3.10036e13	+	1.78999e13i	−1.00210	+	0.578560i	−0.0932281	+	0.995645i	$0.529719\pi$
$500$			4.14391e13i			1.32605i
$501$	−3.32039e13	+	1.91703e13i	−1.05196	+	0.607350i
$502$	2.41833e13	−	1.39622e13i	0.758572	−	0.437962i
$503$	2.01221e13	−	1.16175e13i	0.624933	−	0.360805i	−0.153854	−	0.988094i	$-0.549169\pi$
$503$	2.01221e13	−	1.16175e13i	0.624933	−	0.360805i	0.778787	+	0.627288i	$0.215835\pi$
$504$	−6.08887e11	+	1.05462e12i	−0.0187234	+	0.0324298i
$505$			6.51002e12i			0.198210i
$506$	2.88744e13	+	1.66706e13i	0.870482	+	0.502573i
$507$	−4.91109e12	+	2.83542e12i	−0.146601	+	0.0846403i
$508$	−3.57976e13			−1.05812
$509$	−2.44958e12	−	4.24280e12i	−0.0716974	−	0.124183i	0.827948	−	0.560805i	$-0.189508\pi$
$509$	−2.44958e12	−	4.24280e12i	−0.0716974	−	0.124183i	−0.899645	+	0.436621i	$0.856175\pi$
$510$	5.45175e12	+	3.14757e12i	0.158010	+	0.0912272i
$511$	−2.30672e12	+	3.99536e12i	−0.0662051	+	0.114671i
$512$		−	3.89765e12i		−	0.110778i
$513$	6.33332e12	−	1.09696e13i	0.178256	−	0.308749i
$514$	−1.10948e13			−0.309247
$515$		−	1.13779e14i		−	3.14071i
$516$	1.45898e13	+	1.48007e13i	0.398842	+	0.404609i
$517$	5.26563e13			1.42560
$518$		−	1.04973e13i		−	0.281469i
$519$	−1.23623e13	−	7.13738e12i	−0.328294	−	0.189541i
$520$	6.31304e13			1.66044
$521$	4.53273e13	+	2.61697e13i	1.18079	+	0.681727i	0.956196	−	0.292726i	$-0.0945625\pi$
$521$	4.53273e13	+	2.61697e13i	1.18079	+	0.681727i	0.224590	+	0.974453i	$0.427896\pi$
$522$	3.12255e11	−	5.40841e11i	0.00805668	−	0.0139546i
$523$	−1.47439e13	+	8.51237e12i	−0.376793	+	0.217541i	−0.676422	−	0.736514i	$-0.736470\pi$
$523$	−1.47439e13	+	8.51237e12i	−0.376793	+	0.217541i	0.299629	+	0.954056i	$0.403137\pi$
$524$			2.96261e12i			0.0749925i
$525$	1.92673e13	+	3.33720e13i	0.483087	+	0.836731i
$526$	1.16032e12	−	2.00974e12i	0.0288171	−	0.0499126i
$527$	−8.45800e12			−0.208072
$528$	3.63504e12	+	2.09869e12i	0.0885809	+	0.0511422i
$529$	6.83409e12	+	1.18370e13i	0.164969	+	0.285735i
$530$	−6.97984e12	−	1.20894e13i	−0.166904	−	0.289086i
$531$	−1.85623e12	−	3.21508e12i	−0.0439702	−	0.0761587i
$532$	3.90828e12			0.0917123
$533$	−2.70853e13	−	4.69132e13i	−0.629649	−	1.09058i
$534$	1.96053e13	−	1.13191e13i	0.451510	−	0.260679i
$535$	−2.35835e13	−	1.36159e13i	−0.538070	−	0.310655i
$536$	−4.87096e13	−	2.81225e13i	−1.10101	−	0.635667i
$537$	−5.43678e13			−1.21750
$538$		−	4.94375e13i		−	1.09685i
$539$	−3.49231e13	+	6.04886e13i	−0.767660	+	1.32963i
$540$	−2.54097e13	+	4.40110e13i	−0.553390	+	0.958500i
$541$	2.60620e13	+	4.51408e13i	0.562370	+	0.974053i	0.997289	+	0.0735834i	$0.0234435\pi$
$541$	2.60620e13	+	4.51408e13i	0.562370	+	0.974053i	−0.434919	+	0.900469i	$0.643223\pi$
$542$	4.64983e13	−	2.68458e13i	0.994125	−	0.573958i
$543$		−	3.84942e13i		−	0.815447i
$544$	−6.70875e12	+	3.87330e12i	−0.140814	+	0.0812992i
$545$	−3.02058e13	+	1.74393e13i	−0.628214	+	0.362699i
$546$	1.04838e13	−	6.05281e12i	0.216050	−	0.124737i
$547$	4.42892e12	−	7.67112e12i	0.0904402	−	0.156647i	−0.817256	−	0.576274i	$-0.804506\pi$
$547$	4.42892e12	−	7.67112e12i	0.0904402	−	0.156647i	0.907696	+	0.419627i	$0.137839\pi$
$548$		−	3.96946e13i		−	0.803208i
$549$	−3.10502e12	−	1.79269e12i	−0.0622592	−	0.0359453i
$550$	−1.19994e14	+	6.92784e13i	−2.38421	+	1.37653i
$551$	−5.38447e12			−0.106019
$552$	−2.04263e13	−	3.53793e13i	−0.398560	−	0.690326i
$553$	3.14486e13	+	1.81569e13i	0.608101	+	0.351087i
$554$	1.80438e13	−	3.12529e13i	0.345764	−	0.598882i
$555$		−	8.91139e13i		−	1.69231i
$556$	1.71198e13	−	2.96524e13i	0.322200	−	0.558067i
$557$	−6.19587e13			−1.15565			−0.577825	−	0.816161i	$-0.696098\pi$
$557$	−6.19587e13			−1.15565			−0.577825	+	0.816161i	$0.696098\pi$
$558$			3.54931e12i			0.0656105i
$559$	1.24750e13	+	4.79305e13i	0.228549	+	0.878119i
$560$	2.47369e12			0.0449165
$561$		−	1.69856e13i		−	0.305680i
$562$	9.13219e12	+	5.27247e12i	0.162890	+	0.0940443i
$563$	−1.51715e13			−0.268218			−0.134109	−	0.990967i	$-0.542817\pi$
$563$	−1.51715e13			−0.268218			−0.134109	+	0.990967i	$0.542817\pi$
$564$	−2.07985e13	−	1.20080e13i	−0.364449	−	0.210415i
$565$	−7.04693e13	+	1.22056e14i	−1.22393	+	2.11991i
$566$	2.13547e13	−	1.23291e13i	0.367630	−	0.212251i
$567$			2.40204e13i			0.409888i
$568$	−2.56070e13	−	4.43527e13i	−0.433129	−	0.750202i
$569$	3.95492e13	−	6.85013e13i	0.663097	−	1.14852i	−0.316701	−	0.948525i	$-0.602575\pi$
$569$	3.95492e13	−	6.85013e13i	0.663097	−	1.14852i	0.979798	−	0.199992i	$-0.0640915\pi$
$570$	−2.27764e13			−0.378540
$571$	−1.69343e12	−	9.77704e11i	−0.0278989	−	0.0161074i	0.485986	−	0.873967i	$-0.338461\pi$
$571$	−1.69343e12	−	9.77704e11i	−0.0278989	−	0.0161074i	−0.513885	+	0.857859i	$0.671794\pi$
$572$	−3.17029e13	−	5.49111e13i	−0.517749	−	0.896768i
$573$	2.93851e13	+	5.08965e13i	0.475723	+	0.823977i
$574$	−1.24071e13	−	2.14897e13i	−0.199118	−	0.344882i
$575$	1.15356e14			1.83527
$576$	1.76944e12	+	3.06476e12i	0.0279077	+	0.0483375i
$577$	−8.27116e12	+	4.77536e12i	−0.129326	+	0.0746667i	−0.563268	−	0.826275i	$-0.690456\pi$
$577$	−8.27116e12	+	4.77536e12i	−0.129326	+	0.0746667i	0.433941	+	0.900941i	$0.357123\pi$
$578$	3.46653e13	+	2.00140e13i	0.537348	+	0.310238i
$579$	6.38781e13	+	3.68801e13i	0.981656	+	0.566759i
$580$	2.16029e13			0.329134
$581$			3.43960e12i			0.0519550i
$582$	−2.57963e13	+	4.46805e13i	−0.386316	+	0.669119i
$583$	−1.88331e13	+	3.26198e13i	−0.279627	+	0.484327i
$584$	1.01627e13	+	1.76023e13i	0.149605	+	0.259123i
$585$	−7.94181e12	+	4.58521e12i	−0.115915	+	0.0669237i
$586$			5.30278e13i			0.767388i
$587$	9.83652e13	−	5.67912e13i	1.41140	−	0.814874i	0.415882	−	0.909418i	$-0.363473\pi$
$587$	9.83652e13	−	5.67912e13i	1.41140	−	0.814874i	0.995521	+	0.0945445i	$0.0301395\pi$
$588$	2.75883e13	−	1.59281e13i	0.392499	−	0.226609i
$589$	2.65020e13	−	1.53009e13i	0.373854	−	0.215845i
$590$	−4.40797e13	+	7.63483e13i	−0.616565	+	1.06792i
$591$		−	3.77043e13i		−	0.522942i
$592$	−3.42606e12	−	1.97804e12i	−0.0471180	−	0.0272036i
$593$	−7.07041e13	+	4.08210e13i	−0.964209	+	0.556686i	−0.897466	−	0.441084i	$-0.854594\pi$
$593$	−7.07041e13	+	4.08210e13i	−0.964209	+	0.556686i	−0.0667431	+	0.997770i	$0.521261\pi$
$594$	−9.41326e13			−1.27294
$595$	−5.00516e12	−	8.66919e12i	−0.0671171	−	0.116250i
$596$	−5.04541e12	−	2.91297e12i	−0.0670911	−	0.0387351i
$597$	−1.10885e12	+	1.92058e12i	−0.0146218	+	0.0253257i
$598$		−	3.62389e13i		−	0.473881i
$599$	−2.58457e13	+	4.47661e13i	−0.335161	+	0.580517i	−0.983516	−	0.180822i	$-0.942124\pi$
$599$	−2.58457e13	+	4.47661e13i	−0.335161	+	0.580517i	0.648354	+	0.761339i	$0.275458\pi$
$600$	1.69772e14			2.18328
$601$			5.62780e13i			0.717739i	0.933388	+	0.358870i	$0.116838\pi$
$601$			5.62780e13i			0.717739i	−0.933388	+	0.358870i	$0.883162\pi$
$602$	5.71445e12	+	2.19557e13i	0.0722756	+	0.277693i
$603$	8.17022e12			0.102482
$604$		−	2.25947e13i		−	0.281074i
$605$	3.41785e14	+	1.97330e14i	4.21674	+	2.43454i
$606$	5.49976e12			0.0672947
$607$	2.60087e13	+	1.50161e13i	0.315628	+	0.182228i	0.649442	−	0.760411i	$-0.275002\pi$
$607$	2.60087e13	+	1.50161e13i	0.315628	+	0.182228i	−0.333814	+	0.942639i	$0.608336\pi$
$608$	1.40140e13	−	2.42729e13i	0.168672	−	0.292149i
$609$	9.63776e12	−	5.56436e12i	0.115051	−	0.0664246i
$610$			8.51416e13i			1.00807i
$611$	−2.86163e13	−	4.95649e13i	−0.336052	−	0.582060i
$612$	3.45652e11	−	5.98686e11i	0.00402607	−	0.00697336i
$613$	1.27347e14			1.47125			0.735626	−	0.677388i	$-0.236888\pi$
$613$	1.27347e14			1.47125			0.735626	+	0.677388i	$0.236888\pi$
$614$	4.18367e12	+	2.41544e12i	0.0479419	+	0.0276793i
$615$	−1.05326e14	−	1.82430e14i	−1.19718	−	2.07358i
$616$	−3.90139e13	−	6.75741e13i	−0.439862	−	0.761863i
$617$	6.47647e11	+	1.12176e12i	0.00724290	+	0.0125451i	0.869624	−	0.493714i	$-0.164361\pi$
$617$	6.47647e11	+	1.12176e12i	0.00724290	+	0.0125451i	−0.862381	+	0.506259i	$0.831028\pi$
$618$	−9.61225e13			−1.06631
$619$	4.15477e13	+	7.19627e13i	0.457186	+	0.791870i	0.998811	−	0.0487503i	$-0.0155239\pi$
$619$	4.15477e13	+	7.19627e13i	0.457186	+	0.791870i	−0.541625	+	0.840621i	$0.682191\pi$
$620$	−1.06328e14	+	6.13886e13i	−1.16062	+	0.670084i
$621$	6.78707e13	+	3.91852e13i	0.734893	+	0.424291i
$622$	−8.14943e13	−	4.70508e13i	−0.875337	−	0.505376i
$623$	−3.59986e13			−0.383570
$624$		−	4.56218e12i		−	0.0482224i
$625$	−8.51010e13	+	1.47399e14i	−0.892348	+	1.54559i
$626$	1.92808e13	−	3.33953e13i	0.200564	−	0.347388i
$627$	3.07278e13	+	5.32221e13i	0.317098	+	0.549230i
$628$	8.92442e12	−	5.15252e12i	0.0913654	−	0.0527499i
$629$			1.60091e13i			0.162597i
$630$	−3.63793e12	+	2.10036e12i	−0.0366566	+	0.0211637i
$631$	−1.31143e14	+	7.57153e13i	−1.31098	+	0.756897i	−0.982259	−	0.187529i	$-0.939952\pi$
$631$	−1.31143e14	+	7.57153e13i	−1.31098	+	0.756897i	−0.328724	+	0.944426i	$0.606619\pi$
$632$	1.38553e14	−	7.99934e13i	1.37414	−	0.793357i
$633$	5.46012e13	−	9.45720e13i	0.537259	−	0.930559i
$634$		−	8.66015e12i		−	0.0845432i
$635$	−2.87294e14	−	1.65869e14i	−2.78265	−	1.60656i
$636$	1.48776e13	−	8.58960e12i	0.142971	−	0.0825444i
$637$	7.59164e13			0.723833
$638$	2.00075e13	+	3.46539e13i	0.189273	+	0.327830i
$639$	6.44273e12	+	3.71971e12i	0.0604736	+	0.0349145i
$640$	−5.28043e13	+	9.14598e13i	−0.491779	+	0.851786i
$641$		−	4.52084e13i		−	0.417762i	−0.977941	−	0.208881i	$-0.933018\pi$
$641$		−	4.52084e13i		−	0.417762i	0.977941	−	0.208881i	$-0.0669821\pi$
$642$	−1.15029e13	+	1.99237e13i	−0.105471	+	0.182681i
$643$	−1.89322e14			−1.72245			−0.861223	−	0.508227i	$-0.830301\pi$
$643$	−1.89322e14			−1.72245			−0.861223	+	0.508227i	$0.830301\pi$
$644$			2.41811e13i			0.218296i
$645$	4.85111e13	+	1.86386e14i	0.434552	+	1.66961i
$646$	4.09173e12			0.0363701
$647$		−	1.96565e14i		−	1.73374i	−0.498534	−	0.866870i	$-0.666128\pi$
$647$		−	1.96565e14i		−	1.73374i	0.498534	−	0.866870i	$-0.333872\pi$
$648$	9.16482e13	+	5.29131e13i	0.802138	+	0.463115i
$649$	2.37873e14			2.06596
$650$	1.30422e14	+	7.52994e13i	1.12405	+	0.648970i
$651$	−3.16243e13	+	5.47749e13i	−0.270468	+	0.468464i
$652$	5.42489e13	−	3.13206e13i	0.460418	−	0.265823i
$653$			6.87492e13i			0.579031i	0.957173	+	0.289515i	$0.0934942\pi$
$653$			6.87492e13i			0.579031i	−0.957173	+	0.289515i	$0.906506\pi$
$654$	1.47330e13	+	2.55183e13i	0.123141	+	0.213286i
$655$	−1.37274e13	+	2.37765e13i	−0.113862	+	0.197215i
$656$	−9.35157e12			−0.0769778
$657$	−2.55694e12	−	1.47625e12i	−0.0208878	−	0.0120596i
$658$	−1.31084e13	−	2.27043e13i	−0.106272	−	0.184068i
$659$	−6.08809e13	−	1.05449e14i	−0.489840	−	0.848427i	0.510092	−	0.860120i	$-0.329611\pi$
$659$	−6.08809e13	−	1.05449e14i	−0.489840	−	0.848427i	−0.999932	+	0.0116926i	$0.996278\pi$
$660$	−1.23282e14	−	2.13531e14i	−0.984421	−	1.70507i
$661$	−6.68969e13			−0.530150			−0.265075	−	0.964228i	$-0.585397\pi$
$661$	−6.68969e13			−0.530150			−0.265075	+	0.964228i	$0.585397\pi$
$662$	−7.07005e13	−	1.22457e14i	−0.556074	−	0.963148i
$663$	−1.59884e13	+	9.23090e12i	−0.124807	+	0.0720571i
$664$	1.31236e13	+	7.57690e12i	0.101674	+	0.0587017i
$665$	3.13660e13	+	1.81092e13i	0.241185	+	0.139248i
$666$	6.71805e12			0.0512710
$667$		−	3.33145e13i		−	0.252351i
$668$	4.99918e13	−	8.65883e13i	0.375852	−	0.650994i
$669$	−7.58550e13	+	1.31385e14i	−0.566049	+	0.980425i
$670$	−9.70088e13	−	1.68024e14i	−0.718517	−	1.24451i
$671$	1.98952e14	−	1.14865e14i	1.46263	−	0.844452i
$672$			5.79287e13i			0.422715i
$673$	−1.26888e14	+	7.32589e13i	−0.919063	+	0.530621i	−0.883336	−	0.468740i	$-0.844708\pi$
$673$	−1.26888e14	+	7.32589e13i	−0.919063	+	0.530621i	−0.0357272	+	0.999362i	$0.511375\pi$
$674$	−1.05996e14	+	6.11971e13i	−0.762065	+	0.439978i
$675$	−2.82052e14	+	1.62843e14i	−2.01284	+	1.16212i
$676$	7.39414e12	−	1.28070e13i	0.0523787	−	0.0907225i
$677$			8.83561e13i			0.621289i	0.950526	+	0.310644i	$0.100545\pi$
$677$			8.83561e13i			0.621289i	−0.950526	+	0.310644i	$0.899455\pi$
$678$	1.03115e14	+	5.95335e13i	0.719737	+	0.415540i
$679$	7.10495e13	−	4.10204e13i	0.492280	−	0.284218i
$680$	−4.41023e13			−0.303331
$681$	−2.86333e13	−	4.95943e13i	−0.195495	−	0.338607i
$682$	−1.96951e14	−	1.13710e14i	−1.33486	−	0.770682i
$683$	−8.68203e13	+	1.50377e14i	−0.584141	+	1.01176i	0.410841	+	0.911707i	$0.365235\pi$
$683$	−8.68203e13	+	1.50377e14i	−0.584141	+	1.01176i	−0.994982	+	0.100055i	$0.968098\pi$
$684$			2.50121e12i			0.0167059i
$685$	1.83926e14	−	3.18570e14i	1.21953	−	2.11228i
$686$	7.83685e13			0.515847
$687$			8.04629e13i			0.525789i
$688$	8.24256e12	+	2.27211e12i	0.0534712	+	0.0147397i
$689$	4.09397e13			0.263662
$690$		−	1.40921e14i		−	0.901013i
$691$	3.35052e13	+	1.93442e13i	0.212678	+	0.122790i	0.602555	−	0.798077i	$-0.294149\pi$
$691$	3.35052e13	+	1.93442e13i	0.212678	+	0.122790i	−0.389878	+	0.920867i	$0.627483\pi$
$692$	3.72254e13			0.234590
$693$	9.81591e12	+	5.66722e12i	0.0614136	+	0.0354571i
$694$	−4.69709e13	+	8.13559e13i	−0.291764	+	0.505350i
$695$	2.74791e14	−	1.58651e14i	1.69465	−	0.978404i
$696$		−	4.90296e13i		−	0.300201i
$697$	1.89216e13	+	3.27731e13i	0.115025	+	0.199229i
$698$	−6.47681e13	+	1.12182e14i	−0.390917	+	0.677087i
$699$	1.94924e14			1.16810
$700$	−8.70268e13	−	5.02450e13i	−0.517801	−	0.298953i
$701$	−3.15498e13	−	5.46459e13i	−0.186383	−	0.322825i	0.757658	−	0.652651i	$-0.226343\pi$
$701$	−3.15498e13	−	5.46459e13i	−0.186383	−	0.322825i	−0.944042	+	0.329826i	$0.893010\pi$
$702$	5.11568e13	+	8.86062e13i	0.300067	+	0.519731i
$703$	−2.89613e13	−	5.01624e13i	−0.168671	−	0.292147i
$704$	−2.26751e14			−1.31125
$705$	−1.11279e14	−	1.92741e14i	−0.638953	−	1.10670i
$706$	7.75018e13	−	4.47457e13i	0.441864	−	0.255110i
$707$	−7.57386e12	−	4.37277e12i	−0.0428766	−	0.0247548i
$708$	−9.39565e13	−	5.42458e13i	−0.528154	−	0.304930i
$709$	8.08089e13			0.451054			0.225527	−	0.974237i	$-0.427590\pi$
$709$	8.08089e13			0.451054			0.225527	+	0.974237i	$0.427590\pi$
$710$		−	1.76664e14i		−	0.979163i
$711$	−1.16200e13	+	2.01264e13i	−0.0639524	+	0.110769i
$712$	−7.92992e13	+	1.37350e14i	−0.433380	+	0.750636i
$713$	9.46692e13	+	1.63972e14i	0.513761	+	0.889860i
$714$	−7.32386e12	+	4.22843e12i	−0.0394683	+	0.0227871i
$715$		−	5.87587e14i		−	3.14443i
$716$	1.22784e14	−	7.08896e13i	0.652497	−	0.376719i
$717$	−1.93717e14	+	1.11843e14i	−1.02229	+	0.590217i
$718$	−1.18844e13	+	6.86144e12i	−0.0622807	+	0.0359578i
$719$	4.78085e11	−	8.28067e11i	0.00248806	−	0.00430944i	−0.864779	−	0.502153i	$-0.832541\pi$
$719$	4.78085e11	−	8.28067e11i	0.00248806	−	0.00430944i	0.867267	+	0.497844i	$0.165875\pi$
$720$			1.58310e12i			0.00818176i
$721$	1.32373e14	+	7.64254e13i	0.679395	+	0.392249i
$722$	9.55822e13	−	5.51844e13i	0.487182	−	0.281275i
$723$	−2.51428e14			−1.27269
$724$	5.01922e13	+	8.69354e13i	0.252315	+	0.437022i
$725$	1.19898e14	+	6.92229e13i	0.598577	+	0.345589i
$726$	1.66707e14	−	2.88745e14i	0.826554	−	1.43163i
$727$		−	8.46647e13i		−	0.416899i	−0.978033	−	0.208449i	$-0.933158\pi$
$727$		−	8.46647e13i		−	0.416899i	0.978033	−	0.208449i	$-0.0668416\pi$
$728$	−4.24046e13	+	7.34469e13i	−0.207375	+	0.359184i
$729$	−2.19882e14			−1.06795
$730$			7.01127e13i			0.338207i
$731$	−8.71489e12	−	3.34838e13i	−0.0417518	−	0.160416i
$732$	−1.04778e14			−0.498556
$733$		−	2.72995e13i		−	0.129013i	−0.997917	−	0.0645066i	$-0.979453\pi$
$733$		−	2.72995e13i		−	0.129013i	0.997917	−	0.0645066i	$-0.0205474\pi$
$734$	9.77629e13	+	5.64435e13i	0.458874	+	0.264931i
$735$	2.95214e14			1.37626
$736$	1.50180e14	+	8.67065e13i	0.695382	+	0.401479i
$737$	−2.61750e14	+	4.53365e14i	−1.20379	+	2.08502i
$738$	1.37529e13	−	7.94023e12i	0.0628220	−	0.0362703i
$739$		−	1.19670e14i		−	0.542954i	−0.962445	−	0.271477i	$-0.912488\pi$
$739$		−	1.19670e14i		−	0.542954i	0.962445	−	0.271477i	$-0.0875121\pi$
$740$	1.16195e14	+	2.01255e14i	0.523634	+	0.906961i
$741$	3.33983e13	−	5.78476e13i	0.149497	−	0.258937i
$742$	1.87534e13			0.0833796
$743$	4.11804e13	+	2.37755e13i	0.181864	+	0.104999i	0.588168	−	0.808739i	$-0.299849\pi$
$743$	4.11804e13	+	2.37755e13i	0.181864	+	0.104999i	−0.406304	+	0.913738i	$0.633183\pi$
$744$	1.39327e14	+	2.41321e14i	0.611180	+	1.05860i
$745$	−2.69947e13	−	4.67562e13i	−0.117624	−	0.203731i
$746$	1.16621e14	+	2.01993e14i	0.504756	+	0.874264i
$747$	−2.20126e12			−0.00946387
$748$	2.21474e13	+	3.83603e13i	0.0945832	+	0.163823i
$749$	3.16819e13	−	1.82916e13i	0.134401	−	0.0775965i
$750$	2.80960e14	+	1.62213e14i	1.18397	+	0.683563i
$751$	1.52262e14	+	8.79088e13i	0.637372	+	0.367987i	0.783602	−	0.621264i	$-0.213380\pi$
$751$	1.52262e14	+	8.79088e13i	0.637372	+	0.367987i	−0.146229	+	0.989251i	$0.546714\pi$
$752$	−9.88015e12			−0.0410841
$753$			3.18460e14i			1.31547i
$754$	2.17463e13	−	3.76657e13i	0.0892336	−	0.154557i
$755$	1.04693e14	−	1.81334e14i	0.426760	−	0.739171i
$756$	−3.41354e13	−	5.91242e13i	−0.138228	−	0.239418i
$757$	−1.08799e14	+	6.28151e13i	−0.437668	+	0.252688i	−0.702608	−	0.711577i	$-0.747981\pi$
$757$	−1.08799e14	+	6.28151e13i	−0.437668	+	0.252688i	0.264940	+	0.964265i	$0.414648\pi$
$758$		−	1.20088e14i		−	0.479903i
$759$	−3.29293e14	+	1.90117e14i	−1.30730	+	0.754767i
$760$	1.38189e14	−	7.97833e13i	0.545010	−	0.314662i
$761$	3.15456e14	−	1.82129e14i	1.23599	−	0.713601i	0.267720	−	0.963497i	$-0.413730\pi$
$761$	3.15456e14	−	1.82129e14i	1.23599	−	0.713601i	0.968273	+	0.249896i	$0.0803965\pi$
$762$	−1.40129e14	+	2.42710e14i	−0.545447	+	0.944743i
$763$		−	4.68558e13i		−	0.181193i
$764$	−1.32727e14	−	7.66299e13i	−0.509908	−	0.294396i
$765$	5.54807e12	−	3.20318e12i	0.0211756	−	0.0122257i
$766$	−1.95492e14			−0.741285
$767$	−1.29273e14	−	2.23907e14i	−0.487002	−	0.843512i
$768$	2.28315e14	+	1.31818e14i	0.854531	+	0.493364i
$769$	−1.73098e14	+	2.99815e14i	−0.643666	+	1.11486i	0.340942	+	0.940084i	$0.389254\pi$
$769$	−1.73098e14	+	2.99815e14i	−0.643666	+	1.11486i	−0.984608	+	0.174778i	$0.944079\pi$
$770$		−	2.69158e14i		−	0.994383i
$771$	6.32647e13	−	1.09578e14i	0.232215	−	0.402208i
$772$	−1.92350e14			−0.701465
$773$		−	2.22273e14i		−	0.805360i	−0.915341	−	0.402680i	$-0.868079\pi$
$773$		−	2.22273e14i		−	0.805360i	0.915341	−	0.402680i	$-0.131921\pi$
$774$	−1.40511e13	+	3.65711e12i	−0.0505832	+	0.0131654i
$775$	−7.86838e14			−2.81434
$776$		−	3.61446e14i		−	1.28450i
$777$	1.03676e14	+	5.98577e13i	0.366079	+	0.211356i
$778$	−2.24467e14			−0.787506
$779$	−1.18576e14	−	6.84601e13i	−0.413343	−	0.238644i
$780$	−1.33997e14	+	2.32089e14i	−0.464110	+	0.803862i
$781$	−4.12813e14	+	2.38338e14i	−1.42069	+	0.820234i
$782$			2.53161e13i			0.0865693i
$783$	4.70286e13	+	8.14559e13i	0.159791	+	0.276767i
$784$	6.55279e12	−	1.13498e13i	0.0221231	−	0.0383183i
$785$	9.54976e13			0.320364
$786$	2.00867e13	+	1.15971e13i	0.0669570	+	0.0386577i
$787$	1.85595e14	+	3.21459e14i	0.614740	+	1.06476i	0.990430	+	0.138016i	$0.0440724\pi$
$787$	1.85595e14	+	3.21459e14i	0.614740	+	1.06476i	−0.375690	+	0.926745i	$0.622594\pi$
$788$	4.91623e13	+	8.51516e13i	0.161808	+	0.280260i
$789$	1.32327e13	+	2.29197e13i	0.0432776	+	0.0749591i
$790$	5.51876e14			1.79352
$791$	−9.46682e13	−	1.63970e14i	−0.305718	−	0.529520i
$792$	4.32458e13	−	2.49680e13i	0.138777	−	0.0801231i
$793$	−2.16243e14	−	1.24848e14i	−0.689565	−	0.398121i
$794$	−1.42137e14	−	8.20631e13i	−0.450408	−	0.260043i
$795$	1.59201e14			0.501314
$796$		−	5.78327e12i		−	0.0180971i
$797$	1.83211e14	−	3.17330e14i	0.569717	−	0.986778i	−0.426877	−	0.904310i	$-0.640386\pi$
$797$	1.83211e14	−	3.17330e14i	0.569717	−	0.986778i	0.996594	−	0.0824687i	$-0.0262804\pi$
$798$	1.52989e13	−	2.64985e13i	0.0472765	−	0.0818853i
$799$	1.99911e13	+	3.46255e13i	0.0613906	+	0.106332i
$800$	−6.24107e14	+	3.60328e14i	−1.90462	+	1.09963i
$801$		−	2.30382e13i		−	0.0698693i
$802$	8.34197e13	−	4.81624e13i	0.251418	−	0.145156i
$803$	1.63834e14	−	9.45894e13i	0.490711	−	0.283312i
$804$	2.06776e14	−	1.19382e14i	0.615487	−	0.355352i
$805$	−1.12044e14	+	1.94066e14i	−0.331443	+	0.574077i
$806$			2.47184e14i			0.726683i
$807$	4.88267e14	+	2.81901e14i	1.42656	+	0.823625i
$808$	−3.33680e13	+	1.92650e13i	−0.0968888	+	0.0559388i
$809$	9.90944e13			0.285961			0.142980	−	0.989726i	$-0.454331\pi$
$809$	9.90944e13			0.285961			0.142980	+	0.989726i	$0.454331\pi$
$810$	1.82524e14	+	3.16142e14i	0.523475	+	0.906685i
$811$	−2.99387e14	−	1.72851e14i	−0.853354	−	0.492684i	0.00842720	−	0.999964i	$-0.497318\pi$
$811$	−2.99387e14	−	1.72851e14i	−0.853354	−	0.492684i	−0.861781	+	0.507280i	$0.830651\pi$
$812$	−1.45106e13	+	2.51331e13i	−0.0411061	+	0.0711978i
$813$			6.12318e14i			1.72395i
$814$	−2.15227e14	+	3.72784e14i	−0.602246	+	1.04312i
$815$	5.80501e14			1.61441
$816$			3.18709e12i			0.00880935i
$817$	8.78808e13	+	8.91514e13i	0.241426	+	0.244916i
$818$	4.25981e14			1.16312
$819$		−	1.23195e13i		−	0.0334329i
$820$	4.75737e14	+	2.74667e14i	1.28321	+	0.740862i
$821$	−2.93777e14			−0.787593			−0.393797	−	0.919198i	$-0.628839\pi$
$821$	−2.93777e14			−0.787593			−0.393797	+	0.919198i	$0.628839\pi$
$822$	−2.69132e14	−	1.55384e14i	−0.717145	−	0.414044i
$823$	−9.45974e13	+	1.63847e14i	−0.250542	+	0.433951i	−0.963675	−	0.267078i	$-0.913942\pi$
$823$	−9.45974e13	+	1.63847e14i	−0.250542	+	0.433951i	0.713133	+	0.701028i	$0.247275\pi$
$824$	5.83192e14	−	3.36706e14i	1.53524	−	0.886370i
$825$		−	1.58015e15i		−	4.13455i
$826$	−5.92165e13	−	1.02566e14i	−0.154008	−	0.266749i
$827$	−3.36440e14	+	5.82731e14i	−0.869721	+	1.50640i	−0.00743904	+	0.999972i	$0.502368\pi$
$827$	−3.36440e14	+	5.82731e14i	−0.869721	+	1.50640i	−0.862282	+	0.506429i	$0.830965\pi$
$828$	−1.54753e13			−0.0397638
$829$	3.31873e14	+	1.91607e14i	0.847617	+	0.489372i	0.859846	−	0.510554i	$-0.170559\pi$
$829$	3.31873e14	+	1.91607e14i	0.847617	+	0.489372i	−0.0122294	+	0.999925i	$0.503893\pi$
$830$	2.61366e13	+	4.52699e13i	0.0663527	+	0.114926i
$831$	2.05778e14	+	3.56418e14i	0.519271	+	0.899404i
$832$	1.23229e14	+	2.13439e14i	0.309098	+	0.535373i
$833$	−5.30345e13			−0.132231
$834$	−1.34031e14	−	2.32148e14i	−0.332180	−	0.575353i
$835$	8.02421e14	−	4.63278e14i	1.97683	−	1.14132i
$836$	−1.38792e14	−	8.01314e13i	−0.339885	−	0.196233i
$837$	−4.62943e14	−	2.67280e14i	−1.12694	−	0.650639i
$838$	−3.46266e13			−0.0837895
$839$		−	1.10486e13i		−	0.0265765i	−0.999912	−	0.0132883i	$-0.995770\pi$
$839$		−	1.10486e13i		−	0.0265765i	0.999912	−	0.0132883i	$-0.00422991\pi$
$840$	−1.64898e14	+	2.85611e14i	−0.394292	+	0.682934i
$841$	−1.90362e14	+	3.29717e14i	−0.452481	+	0.783721i
$842$	1.63512e14	+	2.83211e14i	0.386357	+	0.669190i
$843$	−1.04147e14	+	6.01291e13i	−0.244629	+	0.141236i
$844$			2.84776e14i			0.664952i
$845$	1.18684e14	−	6.85221e13i	0.275491	−	0.159055i
$846$	1.45302e13	−	8.38904e12i	0.0335290	−	0.0193580i
$847$	−4.59153e14	+	2.65092e14i	−1.05327	+	0.608107i
$848$	3.53374e12	−	6.12062e12i	0.00805852	−	0.0139578i
$849$			2.81211e14i			0.637520i
$850$	−9.11118e13	−	5.26034e13i	−0.205343	−	0.118555i
$851$	3.10362e14	−	1.79188e14i	0.695377	−	0.401476i
$852$	2.17407e14			0.484258
$853$	−2.14967e14	−	3.72333e14i	−0.476021	−	0.824493i	0.523601	−	0.851963i	$-0.324588\pi$
$853$	−2.14967e14	−	3.72333e14i	−0.476021	−	0.824493i	−0.999623	+	0.0274704i	$0.991255\pi$
$854$	−9.90550e13	−	5.71894e13i	−0.218066	−	0.125900i
$855$	−1.15894e13	+	2.00735e13i	−0.0253648	+	0.0439331i
$856$		−	1.61174e14i		−	0.350692i
$857$	2.29731e14	−	3.97906e14i	0.496954	−	0.860749i	−0.503040	−	0.864263i	$-0.667785\pi$
$857$	2.29731e14	−	3.97906e14i	0.496954	−	0.860749i	0.999994	+	0.00351406i	$0.00111856\pi$
$858$	−4.96402e14			−1.06757
$859$			3.36800e13i			0.0720123i	0.999352	+	0.0360061i	$0.0114636\pi$
$859$			3.36800e13i			0.0720123i	−0.999352	+	0.0360061i	$0.988536\pi$
$860$	−3.52585e14	−	3.57682e14i	−0.749499	−	0.760335i
$861$	2.82989e14			0.598073
$862$		−	1.14955e14i		−	0.241542i
$863$	−2.55503e13	−	1.47515e13i	−0.0533756	−	0.0308164i	0.473075	−	0.881022i	$-0.343144\pi$
$863$	−2.55503e13	−	1.47515e13i	−0.0533756	−	0.0308164i	−0.526450	+	0.850206i	$0.676477\pi$
$864$	−4.89599e14			−1.01688
$865$	2.98754e14	+	1.72485e14i	0.616925	+	0.356182i
$866$	2.57663e14	−	4.46285e14i	0.529008	−	0.916269i
$867$	−3.95335e14	+	2.28247e14i	−0.806993	+	0.465918i
$868$		−	1.64938e14i		−	0.334752i
$869$	−7.44539e14	−	1.28958e15i	−1.50241	−	2.60225i
$870$	8.45642e13	−	1.46469e14i	0.169664	−	0.293867i
$871$	5.68997e14			1.13506
$872$	−1.78775e14	−	1.03216e14i	−0.354589	−	0.204722i
$873$	2.62521e13	+	4.54700e13i	0.0517717	+	0.0896713i
$874$	−4.57982e13	−	7.93247e13i	−0.0898030	−	0.155543i
$875$	−2.57945e14	−	4.46774e14i	−0.502906	−	0.871059i
$876$	−8.62828e13			−0.167264
$877$	−7.88651e13	−	1.36598e14i	−0.152015	−	0.263298i	0.779953	−	0.625838i	$-0.215243\pi$
$877$	−7.88651e13	−	1.36598e14i	−0.152015	−	0.263298i	−0.931968	+	0.362540i	$0.881910\pi$
$878$	4.41330e13	−	2.54802e13i	0.0845845	−	0.0488349i
$879$	−5.23726e14	−	3.02373e14i	−0.998067	−	0.576234i
$880$	−8.78462e13	−	5.07180e13i	−0.166460	−	0.0961057i
$881$	−1.95173e14			−0.367739			−0.183869	−	0.982951i	$-0.558862\pi$
$881$	−1.95173e14			−0.367739			−0.183869	+	0.982951i	$0.558862\pi$
$882$			2.22554e13i			0.0416957i
$883$	2.64247e14	−	4.57689e14i	0.492273	−	0.852642i	−0.507687	−	0.861542i	$-0.669499\pi$
$883$	2.64247e14	−	4.57689e14i	0.492273	−	0.852642i	0.999960	+	0.00889909i	$0.00283271\pi$
$884$	2.40722e13	−	4.16942e13i	0.0445917	−	0.0772350i
$885$	−5.02700e14	−	8.70702e14i	−0.925961	−	1.60381i
$886$	−1.69340e14	+	9.77687e13i	−0.310164	+	0.179073i
$887$			6.58110e14i			1.19862i	0.800518	+	0.599308i	$0.204558\pi$
$887$			6.58110e14i			1.19862i	−0.800518	+	0.599308i	$0.795442\pi$
$888$	4.56766e14	−	2.63714e14i	0.827235	−	0.477604i
$889$	3.85950e14	−	2.22828e14i	0.695060	−	0.401293i
$890$	−4.73791e14	+	2.73543e14i	−0.848471	+	0.489865i
$891$	4.92489e14	−	8.53017e14i	0.877018	−	1.51904i
$892$		−	3.95626e14i		−	0.700585i
$893$	−1.25279e14	−	7.23296e13i	−0.220607	−	0.127368i
$894$	−3.95003e13	+	2.28055e13i	−0.0691692	+	0.0399349i
$895$	1.31388e15			2.28792
$896$	−7.09371e13	−	1.22867e14i	−0.122838	−	0.212762i
$897$	3.57912e14	+	2.06640e14i	0.616331	+	0.355839i
$898$	2.03126e13	−	3.51824e13i	0.0347843	−	0.0602481i
$899$			2.27237e14i			0.386973i
$900$	3.21556e13	−	5.56951e13i	0.0544557	−	0.0943201i
$901$	−2.86001e13			−0.0481663
$902$			1.01753e15i			1.70417i
$903$	−2.49429e14	−	6.87568e13i	−0.415440	−	0.114519i
$904$	−8.34156e14			−1.38167
$905$			9.30269e14i			1.53238i
$906$	−1.53194e14	−	8.84464e13i	−0.250957	−	0.144890i
$907$	−7.07765e14			−1.15306			−0.576531	−	0.817076i	$-0.695594\pi$
$907$	−7.07765e14			−1.15306			−0.576531	+	0.817076i	$0.695594\pi$
$908$	1.29331e14	+	7.46692e13i	0.209543	+	0.120980i
$909$	2.79847e12	−	4.84709e12i	0.00450921	−	0.00781019i
$910$	−2.53356e14	+	1.46275e14i	−0.405998	+	0.234403i
$911$			8.72188e14i			1.39001i	0.719004	+	0.695006i	$0.244598\pi$
$911$			8.72188e14i			1.39001i	−0.719004	+	0.695006i	$0.755402\pi$
$912$	−5.76561e12	−	9.98633e12i	−0.00913842	−	0.0158282i
$913$	7.05220e13	−	1.22148e14i	0.111166	−	0.192545i
$914$	−3.68311e14			−0.577408
$915$	−8.40897e14	−	4.85492e14i	−1.31110	−	0.756966i
$916$	−1.04915e14	−	1.81718e14i	−0.162689	−	0.281786i
$917$	−1.84413e13	−	3.19412e13i	−0.0284410	−	0.0492612i
$918$	−3.57376e13	−	6.18994e13i	−0.0548166	−	0.0949452i
$919$	4.09282e14			0.624375			0.312187	−	0.950021i	$-0.398938\pi$
$919$	4.09282e14			0.624375			0.312187	+	0.950021i	$0.398938\pi$
$920$	4.93631e14	+	8.54994e14i	0.748968	+	1.29725i
$921$	−4.77120e13	+	2.75465e13i	−0.0719995	+	0.0415689i
$922$	5.48539e14	+	3.16699e14i	0.823290	+	0.475327i
$923$	4.48690e14	+	2.59051e14i	0.669789	+	0.386703i
$924$	3.31234e14			0.491785
$925$			1.48931e15i			2.19925i
$926$	2.57980e14	−	4.46835e14i	0.378906	−	0.656284i
$927$	−4.89104e13	+	8.47154e13i	−0.0714501	+	0.123755i
$928$	1.04062e14	+	1.80241e14i	0.151200	+	0.261886i
$929$	−4.29264e14	+	2.47836e14i	−0.620363	+	0.358167i	−0.777010	−	0.629488i	$-0.783265\pi$
$929$	−4.29264e14	+	2.47836e14i	−0.620363	+	0.358167i	0.156647	+	0.987655i	$0.449931\pi$
$930$			9.61218e14i			1.38168i
$931$	1.66176e14	−	9.59420e13i	0.237586	−	0.137170i
$932$	−4.40217e14	+	2.54159e14i	−0.626019	+	0.361432i
$933$	9.29389e14	−	5.36583e14i	1.31459	−	0.758977i
$934$	1.39103e14	−	2.40933e14i	0.195705	−	0.338970i
$935$			4.10483e14i			0.574429i
$936$	−4.70043e13	−	2.71379e13i	−0.0654272	−	0.0377744i
$937$	−5.17410e14	+	2.98727e14i	−0.716369	+	0.413596i	−0.813415	−	0.581684i	$-0.802394\pi$
$937$	−5.17410e14	+	2.98727e14i	−0.716369	+	0.413596i	0.0970460	+	0.995280i	$0.469061\pi$
$938$	2.60642e14			0.358948
$939$	2.19885e14	+	3.80852e14i	0.301209	+	0.521709i
$940$	5.02627e14	+	2.90192e14i	0.684868	+	0.395409i
$941$	6.20477e14	−	1.07470e15i	0.840964	−	1.45659i	−0.0481162	−	0.998842i	$-0.515322\pi$
$941$	6.20477e14	−	1.07470e15i	0.840964	−	1.45659i	0.889080	−	0.457751i	$-0.151345\pi$
$942$		−	8.06778e13i		−	0.108768i
$943$	4.23573e14	−	7.33649e14i	0.568027	−	0.983852i
$944$	−4.46332e13			−0.0595385
$945$		−	6.32670e14i		−	0.839495i
$946$	2.47225e14	−	8.96859e14i	0.326314	−	1.18377i
$947$	−1.48323e15			−1.94742			−0.973708	−	0.227800i	$-0.926847\pi$
$947$	−1.48323e15			−1.94742			−0.973708	+	0.227800i	$0.926847\pi$
$948$			6.79156e14i			0.887008i
$949$	−1.78072e14	−	1.02810e14i	−0.231348	−	0.133569i
$950$	3.80649e14			0.491934
$951$	8.55315e13	+	4.93816e13i	0.109957	+	0.0634838i
$952$	2.96234e13	−	5.13093e13i	0.0378835	−	0.0656162i
$953$	−3.39095e14	+	1.95776e14i	−0.431377	+	0.249055i	−0.699933	−	0.714209i	$-0.746787\pi$
$953$	−3.39095e14	+	1.95776e14i	−0.431377	+	0.249055i	0.268556	+	0.963264i	$0.413453\pi$
$954$			1.20017e13i			0.0151880i
$955$	−7.10135e14	−	1.22999e15i	−0.893972	−	1.54841i
$956$	2.91661e14	−	5.05172e14i	0.365249	−	0.632630i
$957$	−4.56344e14			−0.568503
$958$	−4.71828e14	−	2.72410e14i	−0.584731	−	0.337594i
$959$	2.47086e14	+	4.27965e14i	0.304617	+	0.527613i
$960$	4.79197e14	+	8.29993e14i	0.587702	+	1.01793i
$961$	−2.35921e14	−	4.08627e14i	−0.287839	−	0.498551i
$962$	4.67864e14			0.567864
$963$	1.17062e13	+	2.02757e13i	0.0141346	+	0.0244818i
$964$	5.67827e14	−	3.27835e14i	0.682073	−	0.393795i
$965$	−1.54371e15	−	8.91262e14i	−1.84471	−	1.06505i
$966$	1.63950e14	+	9.46565e13i	0.194906	+	0.112529i
$967$	1.33114e14			0.157432			0.0787160	−	0.996897i	$-0.474918\pi$
$967$	1.33114e14			0.157432			0.0787160	+	0.996897i	$0.474918\pi$
$968$			2.33583e15i			2.74830i
$969$	−2.33318e13	+	4.04118e13i	−0.0273104	+	0.0473030i
$970$	6.23407e14	−	1.07977e15i	0.725960	−	1.25740i
$971$	2.67739e14	+	4.63738e14i	0.310181	+	0.537250i	0.978401	−	0.206714i	$-0.0662769\pi$
$971$	2.67739e14	+	4.63738e14i	0.310181	+	0.537250i	−0.668220	+	0.743964i	$0.732944\pi$
$972$	7.28110e13	−	4.20374e13i	0.0839200	−	0.0484512i
$973$			4.26262e14i			0.488779i
$974$	1.62398e14	−	9.37606e13i	0.185262	−	0.106961i
$975$	−1.48738e15	+	8.58740e14i	−1.68810	+	0.974627i
$976$	−3.73303e13	+	2.15527e13i	−0.0421514	+	0.0243361i
$977$	−2.99838e14	+	5.19334e14i	−0.336832	+	0.583411i	−0.983835	−	0.179077i	$-0.942689\pi$
$977$	−2.99838e14	+	5.19334e14i	−0.336832	+	0.583411i	0.647003	+	0.762488i	$0.276022\pi$
$978$		−	4.90416e14i		−	0.548113i
$979$	1.27839e15	+	7.38078e14i	1.42151	+	0.820708i
$980$	−6.66713e14	+	3.84927e14i	−0.737579	+	0.425841i
$981$	2.99866e13			0.0330052
$982$	1.50606e14	+	2.60857e14i	0.164924	+	0.285657i
$983$	7.07767e14	+	4.08629e14i	0.771121	+	0.445207i	0.833274	−	0.552860i	$-0.186463\pi$
$983$	7.07767e14	+	4.08629e14i	0.771121	+	0.445207i	−0.0621532	+	0.998067i	$0.519797\pi$
$984$	6.23380e14	−	1.07973e15i	0.675737	−	1.17041i
$985$			9.11182e14i			0.982706i
$986$	−1.51917e13	+	2.63129e13i	−0.0163013	+	0.0282347i
$987$	2.98984e14			0.319200
$988$			1.74191e14i			0.185029i
$989$	−5.51593e14	+	5.43732e14i	−0.582958	+	0.574650i
$990$	1.72255e14			0.181132
$991$		−	1.11243e15i		−	1.16387i	−0.813237	−	0.581933i	$-0.802297\pi$
$991$		−	1.11243e15i		−	1.16387i	0.813237	−	0.581933i	$-0.197703\pi$
$992$	−1.02437e15	−	5.91422e14i	−1.06635	−	0.615657i
$993$	1.61258e15			1.67023
$994$	2.05533e14	+	1.18665e14i	0.211812	+	0.122289i
$995$	2.67970e13	−	4.64138e13i	0.0274771	−	0.0475917i
$996$	−5.57105e13	+	3.21645e13i	−0.0568382	+	0.0328156i
$997$			1.27166e15i			1.29090i	0.763801	+	0.645452i	$0.223331\pi$
$997$			1.27166e15i			1.29090i	−0.763801	+	0.645452i	$0.776669\pi$
$998$	−3.65449e14	−	6.32976e14i	−0.369125	−	0.639344i
$999$	−5.05902e14	+	8.76247e14i	−0.508439	+	0.880642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.37.23	yes	72
43.7	odd	6	inner	43.11.d.a.7.14	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.14	✓	72	43.7	odd	6	inner
43.11.d.a.37.23	yes	72	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+20.4162i q^{2} +(-201.640 - 116.417i) q^{3} +607.178 q^{4} +(4872.92 + 2813.38i) q^{5} +(2376.79 - 4116.72i) q^{6} +(-6546.27 + 3779.49i) q^{7} +33302.5i q^{8} +(-2418.78 - 4189.45i) q^{9} +O(q^{10})\)	\(q+20.4162i q^{2} +(-201.640 - 116.417i) q^{3} +607.178 q^{4} +(4872.92 + 2813.38i) q^{5} +(2376.79 - 4116.72i) q^{6} +(-6546.27 + 3779.49i) q^{7} +33302.5i q^{8} +(-2418.78 - 4189.45i) q^{9} +(-57438.7 + 99486.7i) q^{10} +309963. q^{11} +(-122431. - 70685.7i) q^{12} +(-168451. - 291765. i) q^{13} +(-77162.9 - 133650. i) q^{14} +(-655050. - 1.13458e6i) q^{15} -58159.9 q^{16} +(117678. + 203824. i) q^{17} +(85532.8 - 49382.4i) q^{18} +(-737457. - 425771. i) q^{19} +(2.95873e6 + 1.70823e6i) q^{20} +1.75998e6 q^{21} +6.32827e6i q^{22} +(2.63431e6 - 4.56276e6i) q^{23} +(3.87697e6 - 6.71510e6i) q^{24} +(1.09475e7 + 1.89615e7i) q^{25} +(5.95674e6 - 3.43913e6i) q^{26} +1.48749e7i q^{27} +(-3.97475e6 + 2.29482e6i) q^{28} +(5.47605e6 - 3.16160e6i) q^{29} +(2.31638e7 - 1.33736e7i) q^{30} +(-1.79685e7 + 3.11224e7i) q^{31} +3.29143e7i q^{32} +(-6.25009e7 - 3.60849e7i) q^{33} +(-4.16132e6 + 2.40254e6i) q^{34} -4.25326e7 q^{35} +(-1.46863e6 - 2.54375e6i) q^{36} +(5.89077e7 + 3.40104e7i) q^{37} +(8.69263e6 - 1.50561e7i) q^{38} +7.84420e7i q^{39} +(-9.36927e7 + 1.62280e8i) q^{40} +1.60791e8 q^{41} +3.59322e7i q^{42} +(-1.41723e8 - 3.90667e7i) q^{43} +1.88203e8 q^{44} -2.72199e7i q^{45} +(9.31542e7 + 5.37826e7i) q^{46} +1.69879e8 q^{47} +(1.17273e7 + 6.77078e6i) q^{48} +(-1.12669e8 + 1.95148e8i) q^{49} +(-3.87123e8 + 2.23505e8i) q^{50} -5.47988e7i q^{51} +(-1.02280e8 - 1.77154e8i) q^{52} +(-6.07591e7 + 1.05238e8i) q^{53} -3.03690e8 q^{54} +(1.51043e9 + 8.72045e8i) q^{55} +(-1.25866e8 - 2.18007e8i) q^{56} +(9.91338e7 + 1.71705e8i) q^{57} +(6.45479e7 + 1.11800e8i) q^{58} +7.67422e8 q^{59} +(-3.97732e8 - 6.88892e8i) q^{60} +(6.41857e8 - 3.70576e8i) q^{61} +(-6.35401e8 - 3.66849e8i) q^{62} +(3.16680e7 + 1.82835e7i) q^{63} -7.31542e8 q^{64} -1.89567e9i q^{65} +(7.36717e8 - 1.27603e9i) q^{66} +(-8.44456e8 + 1.46264e9i) q^{67} +(7.14516e7 + 1.23758e8i) q^{68} +(-1.06236e9 + 6.13355e8i) q^{69} -8.68355e8i q^{70} +(-1.33181e9 + 7.68923e8i) q^{71} +(1.39519e8 - 8.05515e7i) q^{72} +(5.28559e8 - 3.05163e8i) q^{73} +(-6.94363e8 + 1.20267e9i) q^{74} -5.09787e9i q^{75} +(-4.47768e8 - 2.58519e8i) q^{76} +(-2.02910e9 + 1.17150e9i) q^{77} -1.60149e9 q^{78} +(-2.40203e9 - 4.16043e9i) q^{79} +(-2.83409e8 - 1.63626e8i) q^{80} +(1.58886e9 - 2.75199e9i) q^{81} +3.28274e9i q^{82} +(2.27518e8 - 3.94072e8i) q^{83} +1.06862e9 q^{84} +1.32429e9i q^{85} +(7.97594e8 - 2.89344e9i) q^{86} -1.47225e9 q^{87} +1.03225e10i q^{88} +(4.12432e9 + 2.38118e9i) q^{89} +5.55726e8 q^{90} +(2.20545e9 + 1.27332e9i) q^{91} +(1.59950e9 - 2.77041e9i) q^{92} +(7.24633e9 - 4.18367e9i) q^{93} +3.46829e9i q^{94} +(-2.39572e9 - 4.14950e9i) q^{95} +(3.83178e9 - 6.63684e9i) q^{96} -1.08534e10 q^{97} +(-3.98418e9 - 2.30026e9i) q^{98} +(-7.49733e8 - 1.29858e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \) 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9} - 127061 q^{10} + 521524 q^{11} - 606618 q^{12} + 796742 q^{13} - 865794 q^{14} - 433513 q^{15} + 22423366 q^{16} - 1768471 q^{17} - 11957547 q^{18} - 122844 q^{19} + 419841 q^{20} - 26778860 q^{21} + 16414886 q^{23} + 8684578 q^{24} + 70516989 q^{25} + 3069 q^{26} - 97624092 q^{28} + 118701393 q^{29} - 1455921 q^{30} + 10824883 q^{31} + 315141798 q^{33} + 47529561 q^{34} - 333788722 q^{35} - 597728908 q^{36} - 169881246 q^{37} - 88887452 q^{38} + 570788831 q^{40} - 543049070 q^{41} + 408159179 q^{43} - 754130886 q^{44} + 270181896 q^{46} + 348527658 q^{47} + 175039227 q^{48} + 781091547 q^{49} - 663244398 q^{50} - 1853993086 q^{52} + 219922736 q^{53} + 3104867360 q^{54} + 2154394182 q^{55} + 2010912675 q^{56} + 349107351 q^{57} + 2023447828 q^{58} + 2247595680 q^{59} - 2906780465 q^{60} + 508093974 q^{61} - 3451752063 q^{62} + 158921973 q^{63} - 13473879716 q^{64} + 1277847051 q^{66} - 2812410281 q^{67} + 13614613118 q^{68} - 5113655829 q^{69} + 2418191196 q^{71} + 26243329290 q^{72} - 6537901611 q^{73} - 2632816966 q^{74} - 10170994206 q^{76} - 16936463889 q^{77} - 24146069696 q^{78} + 5397136602 q^{79} + 7242149661 q^{80} - 15745886176 q^{81} + 4998656042 q^{83} + 44726677232 q^{84} - 27688564866 q^{86} + 37895576172 q^{87} - 12151857357 q^{89} - 96024912764 q^{90} + 36633770214 q^{91} - 31643971023 q^{92} + 59768940153 q^{93} - 19802964089 q^{95} - 3289705262 q^{96} - 40329658574 q^{97} + 19243888221 q^{98} + 18506221111 q^{99}+O(q^{100}) \) 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9 - 127061 * q^10 + 521524 * q^11 - 606618 * q^12 + 796742 * q^13 - 865794 * q^14 - 433513 * q^15 + 22423366 * q^16 - 1768471 * q^17 - 11957547 * q^18 - 122844 * q^19 + 419841 * q^20 - 26778860 * q^21 + 16414886 * q^23 + 8684578 * q^24 + 70516989 * q^25 + 3069 * q^26 - 97624092 * q^28 + 118701393 * q^29 - 1455921 * q^30 + 10824883 * q^31 + 315141798 * q^33 + 47529561 * q^34 - 333788722 * q^35 - 597728908 * q^36 - 169881246 * q^37 - 88887452 * q^38 + 570788831 * q^40 - 543049070 * q^41 + 408159179 * q^43 - 754130886 * q^44 + 270181896 * q^46 + 348527658 * q^47 + 175039227 * q^48 + 781091547 * q^49 - 663244398 * q^50 - 1853993086 * q^52 + 219922736 * q^53 + 3104867360 * q^54 + 2154394182 * q^55 + 2010912675 * q^56 + 349107351 * q^57 + 2023447828 * q^58 + 2247595680 * q^59 - 2906780465 * q^60 + 508093974 * q^61 - 3451752063 * q^62 + 158921973 * q^63 - 13473879716 * q^64 + 1277847051 * q^66 - 2812410281 * q^67 + 13614613118 * q^68 - 5113655829 * q^69 + 2418191196 * q^71 + 26243329290 * q^72 - 6537901611 * q^73 - 2632816966 * q^74 - 10170994206 * q^76 - 16936463889 * q^77 - 24146069696 * q^78 + 5397136602 * q^79 + 7242149661 * q^80 - 15745886176 * q^81 + 4998656042 * q^83 + 44726677232 * q^84 - 27688564866 * q^86 + 37895576172 * q^87 - 12151857357 * q^89 - 96024912764 * q^90 + 36633770214 * q^91 - 31643971023 * q^92 + 59768940153 * q^93 - 19802964089 * q^95 - 3289705262 * q^96 - 40329658574 * q^97 + 19243888221 * q^98 + 18506221111 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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