LMFDB - Embedded newform 48.9.l.a.43.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,9,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, 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:	$19.5541732829$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.20
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.16319 - 15.4489i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-221.336 - 128.633i) q^{4} +(-851.062 - 851.062i) q^{5} +(-648.534 + 373.196i) q^{6} -2002.62 q^{7} +(-2908.70 + 2883.86i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(4.16319 - 15.4489i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-221.336 - 128.633i) q^{4} +(-851.062 - 851.062i) q^{5} +(-648.534 + 373.196i) q^{6} -2002.62 q^{7} +(-2908.70 + 2883.86i) q^{8} +2187.00i q^{9} +(-16691.1 + 9604.82i) q^{10} +(18300.5 - 18300.5i) q^{11} +(3065.49 + 11572.8i) q^{12} +(16812.8 - 16812.8i) q^{13} +(-8337.29 + 30938.2i) q^{14} +56286.0i q^{15} +(32443.0 + 56942.3i) q^{16} -70830.1 q^{17} +(33786.7 + 9104.90i) q^{18} +(-87054.1 - 87054.1i) q^{19} +(78895.5 + 297845. i) q^{20} +(66222.9 + 66222.9i) q^{21} +(-206534. - 358911. i) q^{22} +201450. q^{23} +(191549. + 821.368i) q^{24} +1.05799e6i q^{25} +(-189745. - 329735. i) q^{26} +(72320.0 - 72320.0i) q^{27} +(443251. + 257604. i) q^{28} +(503996. - 503996. i) q^{29} +(869556. + 234329. i) q^{30} -680484. i q^{31} +(1.01476e6 - 264146. i) q^{32} -1.21033e6 q^{33} +(-294879. + 1.09425e6i) q^{34} +(1.70435e6 + 1.70435e6i) q^{35} +(281321. - 484061. i) q^{36} +(-126114. - 126114. i) q^{37} +(-1.70731e6 + 982466. i) q^{38} -1.11194e6 q^{39} +(4.92983e6 + 21139.3i) q^{40} -924105. i q^{41} +(1.29877e6 - 747371. i) q^{42} +(-4.25764e6 + 4.25764e6i) q^{43} +(-6.40462e6 + 1.69650e6i) q^{44} +(1.86127e6 - 1.86127e6i) q^{45} +(838673. - 3.11217e6i) q^{46} +1.66895e6i q^{47} +(810145. - 2.95580e6i) q^{48} -1.75431e6 q^{49} +(1.63447e7 + 4.40460e6i) q^{50} +(2.34222e6 + 2.34222e6i) q^{51} +(-5.88397e6 + 1.55859e6i) q^{52} +(2.78396e6 + 2.78396e6i) q^{53} +(-816180. - 1.41834e6i) q^{54} -3.11497e7 q^{55} +(5.82503e6 - 5.77528e6i) q^{56} +5.75743e6i q^{57} +(-5.68794e6 - 9.88441e6i) q^{58} +(-8.35450e6 + 8.35450e6i) q^{59} +(7.24025e6 - 1.24581e7i) q^{60} +(1.23431e7 - 1.23431e7i) q^{61} +(-1.05127e7 - 2.83299e6i) q^{62} -4.37973e6i q^{63} +(143880. - 1.67766e7i) q^{64} -2.86175e7 q^{65} +(-5.03882e6 + 1.86982e7i) q^{66} +(-2.18279e6 - 2.18279e6i) q^{67} +(1.56772e7 + 9.11111e6i) q^{68} +(-6.66156e6 - 6.66156e6i) q^{69} +(3.34259e7 - 1.92348e7i) q^{70} +9.22237e6 q^{71} +(-6.30701e6 - 6.36133e6i) q^{72} -2.91733e7i q^{73} +(-2.47336e6 + 1.42328e6i) q^{74} +(3.49856e7 - 3.49856e7i) q^{75} +(8.07013e6 + 3.04662e7i) q^{76} +(-3.66490e7 + 3.66490e7i) q^{77} +(-4.62921e6 + 1.71782e7i) q^{78} -2.44229e7i q^{79} +(2.08504e7 - 7.60723e7i) q^{80} -4.78297e6 q^{81} +(-1.42764e7 - 3.84722e6i) q^{82} +(-4.06740e7 - 4.06740e7i) q^{83} +(-6.13902e6 - 2.31759e7i) q^{84} +(6.02808e7 + 6.02808e7i) q^{85} +(4.80504e7 + 8.35011e7i) q^{86} -3.33324e7 q^{87} +(-454561. + 1.06007e8i) q^{88} +5.75928e7i q^{89} +(-2.10057e7 - 3.65034e7i) q^{90} +(-3.36697e7 + 3.36697e7i) q^{91} +(-4.45880e7 - 2.59131e7i) q^{92} +(-2.25023e7 + 2.25023e7i) q^{93} +(2.57835e7 + 6.94817e6i) q^{94} +1.48177e8i q^{95} +(-4.22910e7 - 2.48214e7i) q^{96} +1.01919e8 q^{97} +(-7.30354e6 + 2.71022e7i) q^{98} +(4.00232e7 + 4.00232e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) $ 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	4.16319	−	15.4489i	0.260199	−	0.965555i
$2$	4.16319	−	15.4489i	0.260199	−	0.965555i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$4$	−221.336	−	128.633i	−0.864593	−	0.502474i
$5$	−851.062	−	851.062i	−1.36170	−	1.36170i	−0.871753	−	0.489945i	$-0.837017\pi$
$5$	−851.062	−	851.062i	−1.36170	−	1.36170i	−0.489945	−	0.871753i	$-0.662983\pi$
$6$	−648.534	+	373.196i	−0.500412	+	0.287960i
$7$	−2002.62			−0.834077			−0.417039	−	0.908889i	$-0.636932\pi$
$7$	−2002.62			−0.834077			−0.417039	+	0.908889i	$0.636932\pi$
$8$	−2908.70	+	2883.86i	−0.710132	+	0.704068i
$9$			2187.00i			0.333333i
$10$	−16691.1	+	9604.82i	−1.66911	+	0.960482i
$11$	18300.5	−	18300.5i	1.24995	−	1.24995i	0.294210	−	0.955741i	$-0.404944\pi$
$11$	18300.5	−	18300.5i	1.24995	−	1.24995i	0.955741	−	0.294210i	$-0.0950564\pi$
$12$	3065.49	+	11572.8i	0.147834	+	0.558102i
$13$	16812.8	−	16812.8i	0.588664	−	0.588664i	−0.348605	−	0.937270i	$-0.613345\pi$
$13$	16812.8	−	16812.8i	0.588664	−	0.588664i	0.937270	+	0.348605i	$0.113345\pi$
$14$	−8337.29	+	30938.2i	−0.217026	+	0.805348i
$15$			56286.0i			1.11182i
$16$	32443.0	+	56942.3i	0.495040	+	0.868870i
$17$	−70830.1			−0.848051			−0.424026	−	0.905650i	$-0.639383\pi$
$17$	−70830.1			−0.848051			−0.424026	+	0.905650i	$0.639383\pi$
$18$	33786.7	+	9104.90i	0.321852	+	0.0867331i
$19$	−87054.1	−	87054.1i	−0.667998	−	0.667998i	0.289254	−	0.957252i	$-0.406593\pi$
$19$	−87054.1	−	87054.1i	−0.667998	−	0.667998i	−0.957252	+	0.289254i	$0.906593\pi$
$20$	78895.5	+	297845.i	0.493097	+	1.86153i
$21$	66222.9	+	66222.9i	0.340511	+	0.340511i
$22$	−206534.	−	358911.i	−0.881659	−	1.53213i
$23$	201450.			0.719872			0.359936	−	0.932977i	$-0.382799\pi$
$23$	201450.			0.719872			0.359936	+	0.932977i	$0.382799\pi$
$24$	191549.	+	821.368i	0.577345	+	0.00247567i
$25$			1.05799e6i			2.70845i
$26$	−189745.	−	329735.i	−0.415218	−	0.721558i
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$	443251.	+	257604.i	0.721137	+	0.419102i
$29$	503996.	−	503996.i	0.712583	−	0.712583i	−0.254492	−	0.967075i	$-0.581908\pi$
$29$	503996.	−	503996.i	0.712583	−	0.712583i	0.967075	+	0.254492i	$0.0819083\pi$
$30$	869556.	+	234329.i	1.07353	+	0.289295i
$31$		−	680484.i		−	0.736837i	−0.929660	−	0.368418i	$-0.879899\pi$
$31$		−	680484.i		−	0.736837i	0.929660	−	0.368418i	$-0.120101\pi$
$32$	1.01476e6	−	264146.i	0.967751	−	0.251909i
$33$	−1.21033e6			−1.02058
$34$	−294879.	+	1.09425e6i	−0.220662	+	0.818840i
$35$	1.70435e6	+	1.70435e6i	1.13576	+	1.13576i
$36$	281321.	−	484061.i	0.167491	−	0.288198i
$37$	−126114.	−	126114.i	−0.0672909	−	0.0672909i	0.672660	−	0.739951i	$-0.265151\pi$
$37$	−126114.	−	126114.i	−0.0672909	−	0.0672909i	−0.739951	+	0.672660i	$0.765151\pi$
$38$	−1.70731e6	+	982466.i	−0.818801	+	0.471176i
$39$	−1.11194e6			−0.480642
$40$	4.92983e6	+	21139.3i	1.92571	+	0.00825752i
$41$		−	924105.i		−	0.327029i	−0.986541	−	0.163514i	$-0.947717\pi$
$41$		−	924105.i		−	0.327029i	0.986541	−	0.163514i	$-0.0522830\pi$
$42$	1.29877e6	−	747371.i	0.417382	−	0.240181i
$43$	−4.25764e6	+	4.25764e6i	−1.24536	+	1.24536i	−0.287613	+	0.957747i	$0.592862\pi$
$43$	−4.25764e6	+	4.25764e6i	−1.24536	+	1.24536i	−0.957747	+	0.287613i	$0.907138\pi$
$44$	−6.40462e6	+	1.69650e6i	−1.70877	+	0.452631i
$45$	1.86127e6	−	1.86127e6i	0.453900	−	0.453900i
$46$	838673.	−	3.11217e6i	0.187310	−	0.695076i
$47$			1.66895e6i			0.342021i	0.985269	+	0.171011i	$0.0547032\pi$
$47$			1.66895e6i			0.342021i	−0.985269	+	0.171011i	$0.945297\pi$
$48$	810145.	−	2.95580e6i	0.152615	−	0.556814i
$49$	−1.75431e6			−0.304315
$50$	1.63447e7	+	4.40460e6i	2.61515	+	0.704736i
$51$	2.34222e6	+	2.34222e6i	0.346216	+	0.346216i
$52$	−5.88397e6	+	1.55859e6i	−0.804743	+	0.213167i
$53$	2.78396e6	+	2.78396e6i	0.352826	+	0.352826i	0.861160	−	0.508334i	$-0.169739\pi$
$53$	2.78396e6	+	2.78396e6i	0.352826	+	0.352826i	−0.508334	+	0.861160i	$0.669739\pi$
$54$	−816180.	−	1.41834e6i	−0.0959867	−	0.166804i
$55$	−3.11497e7			−3.40411
$56$	5.82503e6	−	5.77528e6i	0.592305	−	0.587247i
$57$			5.75743e6i			0.545418i
$58$	−5.68794e6	−	9.88441e6i	−0.502624	−	0.873451i
$59$	−8.35450e6	+	8.35450e6i	−0.689465	+	0.689465i	−0.962114	−	0.272648i	$-0.912100\pi$
$59$	−8.35450e6	+	8.35450e6i	−0.689465	+	0.689465i	0.272648	+	0.962114i	$0.412100\pi$
$60$	7.24025e6	−	1.24581e7i	0.558661	−	0.961273i
$61$	1.23431e7	−	1.23431e7i	0.891469	−	0.891469i	−0.103193	−	0.994661i	$-0.532906\pi$
$61$	1.23431e7	−	1.23431e7i	0.891469	−	0.891469i	0.994661	+	0.103193i	$0.0329059\pi$
$62$	−1.05127e7	−	2.83299e6i	−0.711457	−	0.191725i
$63$		−	4.37973e6i		−	0.278026i
$64$	143880.	−	1.67766e7i	0.00857590	−	0.999963i
$65$	−2.86175e7			−1.60317
$66$	−5.03882e6	+	1.86982e7i	−0.265554	+	0.985426i
$67$	−2.18279e6	−	2.18279e6i	−0.108321	−	0.108321i	0.650869	−	0.759190i	$-0.274405\pi$
$67$	−2.18279e6	−	2.18279e6i	−0.108321	−	0.108321i	−0.759190	+	0.650869i	$0.774405\pi$
$68$	1.56772e7	+	9.11111e6i	0.733219	+	0.426123i
$69$	−6.66156e6	−	6.66156e6i	−0.293886	−	0.293886i
$70$	3.34259e7	−	1.92348e7i	1.39217	−	0.801116i
$71$	9.22237e6			0.362919			0.181459	−	0.983398i	$-0.441918\pi$
$71$	9.22237e6			0.362919			0.181459	+	0.983398i	$0.441918\pi$
$72$	−6.30701e6	−	6.36133e6i	−0.234689	−	0.236711i
$73$		−	2.91733e7i		−	1.02729i	−0.858002	−	0.513647i	$-0.828294\pi$
$73$		−	2.91733e7i		−	1.02729i	0.858002	−	0.513647i	$-0.171706\pi$
$74$	−2.47336e6	+	1.42328e6i	−0.0824821	+	0.0474640i
$75$	3.49856e7	−	3.49856e7i	1.10572	−	1.10572i
$76$	8.07013e6	+	3.04662e7i	0.241895	+	0.913197i
$77$	−3.66490e7	+	3.66490e7i	−1.04256	+	1.04256i
$78$	−4.62921e6	+	1.71782e7i	−0.125063	+	0.464087i
$79$		−	2.44229e7i		−	0.627031i	−0.949583	−	0.313516i	$-0.898493\pi$
$79$		−	2.44229e7i		−	0.627031i	0.949583	−	0.313516i	$-0.101507\pi$
$80$	2.08504e7	−	7.60723e7i	0.509043	−	1.85723i
$81$	−4.78297e6			−0.111111
$82$	−1.42764e7	−	3.84722e6i	−0.315764	−	0.0850927i
$83$	−4.06740e7	−	4.06740e7i	−0.857046	−	0.857046i	0.133943	−	0.990989i	$-0.457236\pi$
$83$	−4.06740e7	−	4.06740e7i	−0.857046	−	0.857046i	−0.990989	+	0.133943i	$0.957236\pi$
$84$	−6.13902e6	−	2.31759e7i	−0.123305	−	0.465501i
$85$	6.02808e7	+	6.02808e7i	1.15479	+	1.15479i
$86$	4.80504e7	+	8.35011e7i	0.878422	+	1.52651i
$87$	−3.33324e7			−0.581821
$88$	−454561.	+	1.06007e8i	−0.00757986	+	1.76768i
$89$			5.75928e7i			0.917928i	0.888455	+	0.458964i	$0.151779\pi$
$89$			5.75928e7i			0.917928i	−0.888455	+	0.458964i	$0.848221\pi$
$90$	−2.10057e7	−	3.65034e7i	−0.320161	−	0.556369i
$91$	−3.36697e7	+	3.36697e7i	−0.490992	+	0.490992i
$92$	−4.45880e7	−	2.59131e7i	−0.622396	−	0.361717i
$93$	−2.25023e7	+	2.25023e7i	−0.300812	+	0.300812i
$94$	2.57835e7	+	6.94817e6i	0.330240	+	0.0889937i
$95$			1.48177e8i			1.81922i
$96$	−4.22910e7	−	2.48214e7i	−0.497924	−	0.292241i
$97$	1.01919e8			1.15125			0.575624	−	0.817714i	$-0.304759\pi$
$97$	1.01919e8			1.15125			0.575624	+	0.817714i	$0.304759\pi$
$98$	−7.30354e6	+	2.71022e7i	−0.0791825	+	0.293833i
$99$	4.00232e7	+	4.00232e7i	0.416650	+	0.416650i
$100$	1.36092e8	−	2.34170e8i	1.36092	−	2.34170i
$101$	3.46661e7	+	3.46661e7i	0.333134	+	0.333134i	0.853775	−	0.520641i	$-0.174307\pi$
$101$	3.46661e7	+	3.46661e7i	0.333134	+	0.333134i	−0.520641	+	0.853775i	$0.674307\pi$
$102$	4.59357e7	−	2.64335e7i	0.424375	−	0.244205i
$103$	−6.69800e7			−0.595109			−0.297554	−	0.954705i	$-0.596171\pi$
$103$	−6.69800e7			−0.595109			−0.297554	+	0.954705i	$0.596171\pi$
$104$	−417609.	+	9.73895e7i	−0.00356974	+	0.832490i
$105$		−	1.12719e8i		−	0.927346i
$106$	5.45993e7	−	3.14189e7i	0.432478	−	0.248868i
$107$	−8.13796e7	+	8.13796e7i	−0.620841	+	0.620841i	−0.945747	−	0.324905i	$-0.894668\pi$
$107$	−8.13796e7	+	8.13796e7i	−0.620841	+	0.620841i	0.324905	+	0.945747i	$0.394668\pi$
$108$	−2.53097e7	+	6.70424e6i	−0.186034	+	0.0492781i
$109$	5.47723e6	−	5.47723e6i	0.0388021	−	0.0388021i	−0.687440	−	0.726242i	$-0.741265\pi$
$109$	5.47723e6	−	5.47723e6i	0.0388021	−	0.0388021i	0.726242	+	0.687440i	$0.241265\pi$
$110$	−1.29682e8	+	4.81229e8i	−0.885748	+	3.28686i
$111$			8.34070e6i			0.0549428i
$112$	−6.49710e7	−	1.14034e8i	−0.412902	−	0.724705i
$113$	3.03378e8			1.86067			0.930336	−	0.366707i	$-0.119515\pi$
$113$	3.03378e8			1.86067			0.930336	+	0.366707i	$0.119515\pi$
$114$	8.89459e7	+	2.39693e7i	0.526631	+	0.141917i
$115$	−1.71446e8	−	1.71446e8i	−0.980248	−	0.980248i
$116$	−1.76383e8	+	4.67217e7i	−0.974148	+	0.258040i
$117$	3.67697e7	+	3.67697e7i	0.196221	+	0.196221i
$118$	9.42863e7	+	1.63849e8i	0.486318	+	0.845115i
$119$	1.41846e8			0.707341
$120$	−1.62321e8	−	1.63719e8i	−0.782799	−	0.789541i
$121$		−	4.55460e8i		−	2.12475i
$122$	−1.39301e8	−	2.42074e8i	−0.628802	−	1.09272i
$123$	−3.05584e7	+	3.05584e7i	−0.133509	+	0.133509i
$124$	−8.75329e7	+	1.50615e8i	−0.370241	+	0.637064i
$125$	5.67966e8	−	5.67966e8i	2.32639	−	2.32639i
$126$	−6.76619e7	−	1.82337e7i	−0.268449	−	0.0723422i
$127$		−	4.58415e7i		−	0.176215i	−0.996111	−	0.0881076i	$-0.971918\pi$
$127$		−	4.58415e7i		−	0.176215i	0.996111	−	0.0881076i	$-0.0280819\pi$
$128$	−2.58581e8	−	7.20670e7i	−0.963288	−	0.268470i
$129$	2.81584e8			1.01683
$130$	−1.19140e8	+	4.42109e8i	−0.417143	+	1.54795i
$131$	−1.84021e7	−	1.84021e7i	−0.0624860	−	0.0624860i	0.675173	−	0.737659i	$-0.264069\pi$
$131$	−1.84021e7	−	1.84021e7i	−0.0624860	−	0.0624860i	−0.737659	+	0.675173i	$0.764069\pi$
$132$	2.67889e8	+	1.55688e8i	0.882386	+	0.512815i
$133$	1.74336e8	+	1.74336e8i	0.557162	+	0.557162i
$134$	−4.28091e7	+	2.46343e7i	−0.132775	+	0.0764049i
$135$	−1.23097e8			−0.370607
$136$	2.06024e8	−	2.04264e8i	0.602229	−	0.597086i
$137$			6.91478e8i			1.96289i	0.191739	+	0.981446i	$0.438587\pi$
$137$			6.91478e8i			1.96289i	−0.191739	+	0.981446i	$0.561413\pi$
$138$	−1.30647e8	+	7.51803e7i	−0.360232	+	0.207294i
$139$	−5.75192e7	+	5.75192e7i	−0.154083	+	0.154083i	−0.779939	−	0.625856i	$-0.784750\pi$
$139$	−5.75192e7	+	5.75192e7i	−0.154083	+	0.154083i	0.625856	+	0.779939i	$0.284750\pi$
$140$	−1.57998e8	−	5.96471e8i	−0.411281	−	1.55266i
$141$	5.51892e7	−	5.51892e7i	0.139630	−	0.139630i
$142$	3.83945e7	−	1.42475e8i	0.0944312	−	0.350418i
$143$		−	6.15368e8i		−	1.47160i
$144$	−1.24533e8	+	7.09528e7i	−0.289623	+	0.165013i
$145$	−8.57864e8			−1.94065
$146$	−4.50695e8	−	1.21454e8i	−0.991909	−	0.267301i
$147$	5.80118e7	+	5.80118e7i	0.124236	+	0.124236i
$148$	1.16911e7	+	4.41360e7i	0.0243673	+	0.0919911i
$149$	−1.69448e8	−	1.69448e8i	−0.343788	−	0.343788i	0.514001	−	0.857789i	$-0.328163\pi$
$149$	−1.69448e8	−	1.69448e8i	−0.343788	−	0.343788i	−0.857789	+	0.514001i	$0.828163\pi$
$150$	−3.94837e8	−	6.86140e8i	−0.779925	−	1.35534i
$151$	−5.08305e8			−0.977725			−0.488863	−	0.872361i	$-0.662588\pi$
$151$	−5.08305e8			−0.977725			−0.488863	+	0.872361i	$0.662588\pi$
$152$	5.04267e8	+	2.16231e6i	0.944683	+	0.00405083i
$153$		−	1.54905e8i		−	0.282684i
$154$	4.13609e8	+	7.18763e8i	0.735372	+	1.27792i
$155$	−5.79134e8	+	5.79134e8i	−1.00335	+	1.00335i
$156$	2.46112e8	+	1.43032e8i	0.415560	+	0.241510i
$157$	−8.51485e7	+	8.51485e7i	−0.140145	+	0.140145i	−0.773699	−	0.633554i	$-0.781596\pi$
$157$	−8.51485e7	+	8.51485e7i	−0.140145	+	0.140145i	0.633554	+	0.773699i	$0.281596\pi$
$158$	−3.77307e8	−	1.01677e8i	−0.605433	−	0.163153i
$159$		−	1.84121e8i		−	0.288081i
$160$	−1.08843e9	−	6.38819e8i	−1.66081	−	0.974760i
$161$	−4.03427e8			−0.600429
$162$	−1.99124e7	+	7.38915e7i	−0.0289110	+	0.107284i
$163$	7.63635e8	+	7.63635e8i	1.08177	+	1.08177i	0.996344	+	0.0854267i	$0.0272253\pi$
$163$	7.63635e8	+	7.63635e8i	1.08177	+	1.08177i	0.0854267	+	0.996344i	$0.472775\pi$
$164$	−1.18871e8	+	2.04537e8i	−0.164323	+	0.282747i
$165$	1.03006e9	+	1.03006e9i	1.38972	+	1.38972i
$166$	−7.97701e8	+	4.59034e8i	−1.05053	+	0.604522i
$167$	1.05074e8			0.135092			0.0675460	−	0.997716i	$-0.478483\pi$
$167$	1.05074e8			0.135092			0.0675460	+	0.997716i	$0.478483\pi$
$168$	−3.83600e8	−	1.64489e6i	−0.481550	−	0.00206490i
$169$			2.50387e8i			0.306948i
$170$	1.18223e9	−	6.80310e8i	1.41549	−	0.814538i
$171$	1.90387e8	−	1.90387e8i	0.222666	−	0.222666i
$172$	1.49004e9	−	3.94693e8i	1.70249	−	0.450968i
$173$	1.00192e9	−	1.00192e9i	1.11853	−	1.11853i	0.126575	−	0.991957i	$-0.459601\pi$
$173$	1.00192e9	−	1.00192e9i	1.11853	−	1.11853i	0.991957	−	0.126575i	$-0.0403986\pi$
$174$	−1.38769e8	+	5.14948e8i	−0.151390	+	0.561781i
$175$		−	2.11875e9i		−	2.25905i
$176$	1.63580e9	+	4.48350e8i	1.70482	+	0.467268i
$177$	5.52535e8			0.562946
$178$	8.89745e8	+	2.39770e8i	0.886310	+	0.238844i
$179$	2.94932e8	+	2.94932e8i	0.287283	+	0.287283i	0.836005	−	0.548722i	$-0.184885\pi$
$179$	2.94932e8	+	2.94932e8i	0.287283	+	0.287283i	−0.548722	+	0.836005i	$0.684885\pi$
$180$	−6.51387e8	+	1.72544e8i	−0.620511	+	0.164366i
$181$	−4.36659e8	−	4.36659e8i	−0.406844	−	0.406844i	0.473792	−	0.880637i	$-0.342885\pi$
$181$	−4.36659e8	−	4.36659e8i	−0.406844	−	0.406844i	−0.880637	+	0.473792i	$0.842885\pi$
$182$	3.79986e8	+	6.60333e8i	0.346324	+	0.601835i
$183$	−8.16328e8			−0.727881
$184$	−5.85957e8	+	5.80953e8i	−0.511204	+	0.506839i
$185$			2.14662e8i			0.183260i
$186$	2.53954e8	+	4.41317e8i	0.212180	+	0.368722i
$187$	−1.29623e9	+	1.29623e9i	−1.06002	+	1.06002i
$188$	2.14683e8	−	3.69399e8i	0.171857	−	0.295709i
$189$	−1.44829e8	+	1.44829e8i	−0.113504	+	0.113504i
$190$	2.28917e9	+	6.16889e8i	1.75656	+	0.473361i
$191$			6.70633e8i			0.503908i	0.967739	+	0.251954i	$0.0810732\pi$
$191$			6.70633e8i			0.503908i	−0.967739	+	0.251954i	$0.918927\pi$
$192$	−5.59528e8	+	5.50013e8i	−0.411734	+	0.404732i
$193$	−3.31316e8			−0.238788			−0.119394	−	0.992847i	$-0.538095\pi$
$193$	−3.31316e8			−0.238788			−0.119394	+	0.992847i	$0.538095\pi$
$194$	4.24309e8	−	1.57454e9i	0.299554	−	1.11159i
$195$	9.46328e8	+	9.46328e8i	0.654490	+	0.654490i
$196$	3.88292e8	+	2.25663e8i	0.263108	+	0.152910i
$197$	4.31781e7	+	4.31781e7i	0.0286681	+	0.0286681i	0.721296	−	0.692627i	$-0.243547\pi$
$197$	4.31781e7	+	4.31781e7i	0.0286681	+	0.0286681i	−0.692627	+	0.721296i	$0.743547\pi$
$198$	7.84939e8	−	4.51690e8i	0.510711	−	0.293886i
$199$	−1.60456e9			−1.02316			−0.511579	−	0.859236i	$-0.670939\pi$
$199$	−1.60456e9			−1.02316			−0.511579	+	0.859236i	$0.670939\pi$
$200$	−3.05109e9	−	3.07737e9i	−1.90693	−	1.92335i
$201$			1.44362e8i			0.0884439i
$202$	6.79873e8	−	3.91230e8i	0.408341	−	0.234978i
$203$	−1.00931e9	+	1.00931e9i	−0.594349	+	0.594349i
$204$	−2.17129e8	−	8.19703e8i	−0.125371	−	0.473300i
$205$	−7.86470e8	+	7.86470e8i	−0.445314	+	0.445314i
$206$	−2.78851e8	+	1.03477e9i	−0.154847	+	0.574610i
$207$			4.40570e8i			0.239957i
$208$	1.50282e9	+	4.11903e8i	0.802886	+	0.220060i
$209$	−3.18627e9			−1.66993
$210$	−1.74139e9	−	4.69273e8i	−0.895403	−	0.241295i
$211$	−1.61635e9	−	1.61635e9i	−0.815465	−	0.815465i	0.169982	−	0.985447i	$-0.445629\pi$
$211$	−1.61635e9	−	1.61635e9i	−0.815465	−	0.815465i	−0.985447	+	0.169982i	$0.945629\pi$
$212$	−2.58080e8	−	9.74301e8i	−0.127765	−	0.482336i
$213$	−3.04966e8	−	3.04966e8i	−0.148161	−	0.148161i
$214$	9.18425e8	+	1.59602e9i	0.437914	+	0.760999i
$215$	7.24702e9			3.39161
$216$	−1.79633e6	+	4.18918e8i	−0.000825224	+	0.192448i
$217$			1.36275e9i			0.614579i
$218$	−6.18143e7	−	1.07420e8i	−0.0273693	−	0.0475618i
$219$	−9.64707e8	+	9.64707e8i	−0.419391	+	0.419391i
$220$	6.89455e9	+	4.00689e9i	2.94317	+	1.71048i
$221$	−1.19086e9	+	1.19086e9i	−0.499218	+	0.499218i
$222$	1.28854e8	+	3.47239e7i	0.0530503	+	0.0142961i
$223$			1.81261e9i			0.732968i	0.930424	+	0.366484i	$0.119439\pi$
$223$			1.81261e9i			0.732968i	−0.930424	+	0.366484i	$0.880561\pi$
$224$	−2.03218e9	+	5.28984e8i	−0.807179	+	0.210112i
$225$	−2.31382e9			−0.902815
$226$	1.26302e9	−	4.68685e9i	0.484146	−	1.79658i
$227$	−1.12740e9	−	1.12740e9i	−0.424595	−	0.424595i	0.462187	−	0.886782i	$-0.347065\pi$
$227$	−1.12740e9	−	1.12740e9i	−0.424595	−	0.424595i	−0.886782	+	0.462187i	$0.847065\pi$
$228$	7.40597e8	−	1.27433e9i	0.274058	−	0.471564i
$229$	1.10586e9	+	1.10586e9i	0.402121	+	0.402121i	0.878980	−	0.476859i	$-0.158225\pi$
$229$	1.10586e9	+	1.10586e9i	0.402121	+	0.402121i	−0.476859	+	0.878980i	$0.658225\pi$
$230$	−3.36241e9	+	1.93489e9i	−1.20154	+	0.691423i
$231$	2.42383e9			0.851243
$232$	−1.25186e7	+	2.91943e9i	−0.00432120	+	1.00774i
$233$		−	5.09400e9i		−	1.72836i	−0.503180	−	0.864182i	$-0.667837\pi$
$233$		−	5.09400e9i		−	1.72836i	0.503180	−	0.864182i	$-0.332163\pi$
$234$	7.21130e8	−	4.14971e8i	0.240519	−	0.138406i
$235$	1.42038e9	−	1.42038e9i	0.465730	−	0.465730i
$236$	2.92382e9	−	7.74483e8i	0.942545	−	0.249668i
$237$	−8.07619e8	+	8.07619e8i	−0.255984	+	0.255984i
$238$	5.90531e8	−	2.19136e9i	0.184050	−	0.682976i
$239$		−	4.96944e9i		−	1.52306i	−0.648132	−	0.761528i	$-0.724449\pi$
$239$		−	4.96944e9i		−	1.52306i	0.648132	−	0.761528i	$-0.275551\pi$
$240$	−3.20505e9	+	1.82609e9i	−0.966029	+	0.550397i
$241$	−4.69305e9			−1.39119			−0.695596	−	0.718433i	$-0.744860\pi$
$241$	−4.69305e9			−1.39119			−0.695596	+	0.718433i	$0.744860\pi$
$242$	−7.03634e9	−	1.89617e9i	−2.05157	−	0.552859i
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$	−4.31971e9	+	1.14424e9i	−1.21870	+	0.322818i
$245$	1.49303e9	+	1.49303e9i	0.414385	+	0.414385i
$246$	3.44873e8	+	5.99313e8i	0.0941712	+	0.163649i
$247$	−2.92726e9			−0.786453
$248$	1.96242e9	+	1.97933e9i	0.518783	+	0.523252i
$249$			2.69002e9i			0.699775i
$250$	−6.40989e9	−	1.11390e10i	−1.64093	−	2.85158i
$251$	1.76650e9	−	1.76650e9i	0.445061	−	0.445061i	−0.448647	−	0.893709i	$-0.648094\pi$
$251$	1.76650e9	−	1.76650e9i	0.445061	−	0.445061i	0.893709	+	0.448647i	$0.148094\pi$
$252$	−5.63379e8	+	9.69391e8i	−0.139701	+	0.240379i
$253$	3.68663e9	−	3.68663e9i	0.899804	−	0.899804i
$254$	−7.08199e8	−	1.90847e8i	−0.170146	−	0.0458511i
$255$		−	3.98674e9i		−	0.942882i
$256$	−2.18987e9	+	3.69475e9i	−0.509870	+	0.860252i
$257$	−2.32935e9			−0.533953			−0.266977	−	0.963703i	$-0.586025\pi$
$257$	−2.32935e9			−0.533953			−0.266977	+	0.963703i	$0.586025\pi$
$258$	1.17229e9	−	4.35016e9i	0.264579	−	0.981807i
$259$	2.52558e8	+	2.52558e8i	0.0561258	+	0.0561258i
$260$	6.33408e9	+	3.68117e9i	1.38609	+	0.805549i
$261$	1.10224e9	+	1.10224e9i	0.237528	+	0.237528i
$262$	−3.60904e8	+	2.07681e8i	−0.0765925	+	0.0440748i
$263$	−3.52881e9			−0.737574			−0.368787	−	0.929514i	$-0.620227\pi$
$263$	−3.52881e9			−0.737574			−0.368787	+	0.929514i	$0.620227\pi$
$264$	3.52048e9	−	3.49042e9i	0.724747	−	0.718558i
$265$		−	4.73865e9i		−	0.960884i
$266$	3.41910e9	−	1.96751e9i	0.682944	−	0.392997i
$267$	1.90449e9	−	1.90449e9i	0.374742	−	0.374742i
$268$	2.02350e8	+	7.63910e8i	0.0392251	+	0.148082i
$269$	−5.18285e9	+	5.18285e9i	−0.989828	+	0.989828i	−0.999949	−	0.0101204i	$-0.996779\pi$
$269$	−5.18285e9	+	5.18285e9i	−0.989828	+	0.989828i	0.0101204	+	0.999949i	$0.496779\pi$
$270$	−5.12478e8	+	1.90172e9i	−0.0964318	+	0.357842i
$271$		−	5.02039e9i		−	0.930808i	−0.885098	−	0.465404i	$-0.845909\pi$
$271$		−	5.02039e9i		−	0.930808i	0.885098	−	0.465404i	$-0.154091\pi$
$272$	−2.29794e9	−	4.03323e9i	−0.419820	−	0.736846i
$273$	2.22679e9			0.400893
$274$	1.06826e10	+	2.87876e9i	1.89528	+	0.510743i
$275$	1.93617e10	+	1.93617e10i	3.38542	+	3.38542i
$276$	6.17543e8	+	2.33134e9i	0.106422	+	0.401762i
$277$	1.35955e8	+	1.35955e8i	0.0230928	+	0.0230928i	0.718559	−	0.695466i	$-0.244802\pi$
$277$	1.35955e8	+	1.35955e8i	0.0230928	+	0.0230928i	−0.695466	+	0.718559i	$0.744802\pi$
$278$	6.49144e8	+	1.12807e9i	0.108683	+	0.188868i
$279$	1.48822e9			0.245612
$280$	−9.87258e9	−	4.23339e7i	−1.60620	−	0.00688741i
$281$		−	3.09049e9i		−	0.495680i	−0.968801	−	0.247840i	$-0.920279\pi$
$281$		−	3.09049e9i		−	0.495680i	0.968801	−	0.247840i	$-0.0797208\pi$
$282$	−6.22848e8	−	1.08237e9i	−0.0984885	−	0.171152i
$283$	−4.54485e9	+	4.54485e9i	−0.708555	+	0.708555i	−0.966231	−	0.257677i	$-0.917043\pi$
$283$	−4.54485e9	+	4.54485e9i	−0.708555	+	0.708555i	0.257677	+	0.966231i	$0.417043\pi$
$284$	−2.04124e9	−	1.18630e9i	−0.313777	−	0.182357i
$285$	4.89993e9	−	4.89993e9i	0.742695	−	0.742695i
$286$	−9.50674e9	−	2.56189e9i	−1.42091	−	0.382910i
$287$			1.85063e9i			0.272767i
$288$	5.77687e8	+	2.21928e9i	0.0839698	+	0.322584i
$289$	−1.95885e9			−0.280809
$290$	−3.57145e9	+	1.32530e10i	−0.504955	+	1.87380i
$291$	−3.37028e9	−	3.37028e9i	−0.469995	−	0.469995i
$292$	−3.75266e9	+	6.45710e9i	−0.516188	+	0.888191i
$293$	3.34725e9	+	3.34725e9i	0.454169	+	0.454169i	0.896736	−	0.442567i	$-0.145932\pi$
$293$	3.34725e9	+	3.34725e9i	0.454169	+	0.454169i	−0.442567	+	0.896736i	$0.645932\pi$
$294$	1.13773e9	−	6.54704e8i	0.152283	−	0.0876305i
$295$	1.42204e10			1.87769
$296$	7.30523e8	+	3.13251e6i	0.0951628	+	0.000408061i
$297$		−	2.64699e9i		−	0.340193i
$298$	−3.32322e9	+	1.91234e9i	−0.421400	+	0.242493i
$299$	3.38694e9	−	3.38694e9i	0.423763	−	0.423763i
$300$	−1.22439e10	+	3.24325e9i	−1.51159	+	0.400402i
$301$	8.52643e9	−	8.52643e9i	1.03873	−	1.03873i
$302$	−2.11617e9	+	7.85274e9i	−0.254403	+	0.944047i
$303$		−	2.29268e9i		−	0.272003i
$304$	2.13276e9	−	7.78136e9i	0.249717	−	0.911089i
$305$	−2.10095e10			−2.42782
$306$	−2.39312e9	−	6.44901e8i	−0.272947	−	0.0735542i
$307$	8.40561e8	+	8.40561e8i	0.0946271	+	0.0946271i	0.752836	−	0.658209i	$-0.228685\pi$
$307$	8.40561e8	+	8.40561e8i	0.0946271	+	0.0946271i	−0.658209	+	0.752836i	$0.728685\pi$
$308$	1.28260e10	−	3.39745e9i	1.42524	−	0.377529i
$309$	2.21490e9	+	2.21490e9i	0.242952	+	0.242952i
$310$	6.53593e9	+	1.13580e10i	0.707718	+	1.22986i
$311$	−1.32894e10			−1.42058			−0.710289	−	0.703910i	$-0.751436\pi$
$311$	−1.32894e10			−1.42058			−0.710289	+	0.703910i	$0.751436\pi$
$312$	3.23430e9	−	3.20668e9i	0.341320	−	0.338405i
$313$			1.70958e10i			1.78119i	0.454795	+	0.890596i	$0.349713\pi$
$313$			1.70958e10i			1.78119i	−0.454795	+	0.890596i	$0.650287\pi$
$314$	9.60959e8	+	1.66994e9i	0.0988522	+	0.171784i
$315$	−3.72742e9	+	3.72742e9i	−0.378587	+	0.378587i
$316$	−3.14160e9	+	5.40566e9i	−0.315067	+	0.542126i
$317$	1.11936e10	−	1.11936e10i	1.10849	−	1.10849i	0.115146	−	0.993349i	$-0.463266\pi$
$317$	1.11936e10	−	1.11936e10i	1.10849	−	1.10849i	0.993349	−	0.115146i	$-0.0367335\pi$
$318$	−2.84446e9	−	7.66530e8i	−0.278158	−	0.0749585i
$319$		−	1.84468e10i		−	1.78139i
$320$	−1.44004e10	+	1.41555e10i	−1.37333	+	1.34997i
$321$	5.38214e9			0.506915
$322$	−1.67954e9	+	6.23249e9i	−0.156231	+	0.579747i
$323$	6.16605e9	+	6.16605e9i	0.566497	+	0.566497i
$324$	1.05864e9	+	6.15249e8i	0.0960658	+	0.0558304i
$325$	1.77878e10	+	1.77878e10i	1.59437	+	1.59437i
$326$	1.49765e10	−	8.61815e9i	1.32599	−	0.763033i
$327$	−3.62243e8			−0.0316818
$328$	2.66499e9	+	2.68795e9i	0.230250	+	0.232234i
$329$		−	3.34228e9i		−	0.285272i
$330$	2.02017e10	−	1.16250e10i	1.70346	−	0.980249i
$331$	−8.34429e8	+	8.34429e8i	−0.0695148	+	0.0695148i	−0.741009	−	0.671495i	$-0.765653\pi$
$331$	−8.34429e8	+	8.34429e8i	−0.0695148	+	0.0695148i	0.671495	+	0.741009i	$0.265653\pi$
$332$	3.77058e9	+	1.42346e10i	0.310353	+	1.17164i
$333$	2.75811e8	−	2.75811e8i	0.0224303	−	0.0224303i
$334$	4.37443e8	−	1.62328e9i	0.0351509	−	0.130439i
$335$			3.71538e9i			0.295002i
$336$	−1.62241e9	+	5.91935e9i	−0.127293	+	0.464426i
$337$	−1.95173e10			−1.51321			−0.756606	−	0.653871i	$-0.773144\pi$
$337$	−1.95173e10			−1.51321			−0.756606	+	0.653871i	$0.773144\pi$
$338$	3.86820e9	+	1.04241e9i	0.296376	+	0.0798678i
$339$	−1.00321e10	−	1.00321e10i	−0.759616	−	0.759616i
$340$	−5.58818e9	−	2.10964e10i	−0.418171	−	1.57867i
$341$	−1.24532e10	−	1.24532e10i	−0.921010	−	0.921010i
$342$	−2.14865e9	−	3.73389e9i	−0.157059	−	0.272934i
$343$	1.50579e10			1.08790
$344$	1.05754e8	−	2.46626e10i	0.00755203	−	1.76119i
$345$			1.13388e10i			0.800369i
$346$	−1.13074e10	−	1.96497e10i	−0.788963	−	1.37105i
$347$	−2.24243e9	+	2.24243e9i	−0.154668	+	0.154668i	−0.780199	−	0.625531i	$-0.784882\pi$
$347$	−2.24243e9	+	2.24243e9i	−0.154668	+	0.154668i	0.625531	+	0.780199i	$0.284882\pi$
$348$	7.37765e9	+	4.28766e9i	0.503038	+	0.292350i
$349$	−8.32588e9	+	8.32588e9i	−0.561214	+	0.561214i	−0.929652	−	0.368438i	$-0.879893\pi$
$349$	−8.32588e9	+	8.32588e9i	−0.561214	+	0.561214i	0.368438	+	0.929652i	$0.379893\pi$
$350$	−3.27322e10	−	8.82074e9i	−2.18124	−	0.587804i
$351$		−	2.43181e9i		−	0.160214i
$352$	1.37366e10	−	2.34047e10i	0.894766	−	1.52451i
$353$	1.54706e10			0.996344			0.498172	−	0.867078i	$-0.334005\pi$
$353$	1.54706e10			0.996344			0.498172	+	0.867078i	$0.334005\pi$
$354$	2.30031e9	−	8.53605e9i	0.146478	−	0.543555i
$355$	−7.84881e9	−	7.84881e9i	−0.494186	−	0.494186i
$356$	7.40835e9	−	1.27474e10i	0.461234	−	0.793633i
$357$	−4.69057e9	−	4.69057e9i	−0.288771	−	0.288771i
$358$	5.78424e9	−	3.32852e9i	0.352139	−	0.202637i
$359$	7.65520e9			0.460870			0.230435	−	0.973088i	$-0.425985\pi$
$359$	7.65520e9			0.460870			0.230435	+	0.973088i	$0.425985\pi$
$360$	−4.62315e7	+	1.07815e10i	−0.00275251	+	0.641905i
$361$		−	1.82671e9i		−	0.107558i
$362$	−8.56379e9	+	4.92800e9i	−0.498691	+	0.286970i
$363$	−1.50612e10	+	1.50612e10i	−0.867427	+	0.867427i
$364$	1.17834e10	−	3.12127e9i	0.671218	−	0.177797i
$365$	−2.48283e10	+	2.48283e10i	−1.39886	+	1.39886i
$366$	−3.39853e9	+	1.26114e10i	−0.189394	+	0.702809i
$367$			1.13562e10i			0.625995i	0.949754	+	0.312997i	$0.101333\pi$
$367$			1.13562e10i			0.625995i	−0.949754	+	0.312997i	$0.898667\pi$
$368$	6.53562e9	+	1.14710e10i	0.356366	+	0.625475i
$369$	2.02102e9			0.109010
$370$	3.31628e9	+	8.93677e8i	0.176947	+	0.0476841i
$371$	−5.57522e9	−	5.57522e9i	−0.294284	−	0.294284i
$372$	7.87512e9	−	2.08602e9i	0.411231	−	0.108930i
$373$	−1.58175e10	−	1.58175e10i	−0.817152	−	0.817152i	0.168543	−	0.985694i	$-0.446094\pi$
$373$	−1.58175e10	−	1.58175e10i	−0.817152	−	0.817152i	−0.985694	+	0.168543i	$0.946094\pi$
$374$	1.46288e10	+	2.54217e10i	0.747693	+	1.29933i
$375$	−3.75631e10			−1.89949
$376$	−4.81304e9	−	4.85449e9i	−0.240806	−	0.242880i
$377$		−	1.69472e10i		−	0.838944i
$378$	1.63450e9	+	2.84040e9i	0.0800604	+	0.139127i
$379$	−3.09954e9	+	3.09954e9i	−0.150224	+	0.150224i	−0.778218	−	0.627994i	$-0.783876\pi$
$379$	−3.09954e9	+	3.09954e9i	−0.150224	+	0.150224i	0.627994	+	0.778218i	$0.283876\pi$
$380$	1.90605e10	−	3.27968e10i	0.914112	−	1.57289i
$381$	−1.51589e9	+	1.51589e9i	−0.0719396	+	0.0719396i
$382$	1.03605e10	+	2.79197e9i	0.486551	+	0.131117i
$383$		−	3.91035e9i		−	0.181727i	−0.995863	−	0.0908637i	$-0.971037\pi$
$383$		−	3.91035e9i		−	0.181727i	0.995863	−	0.0908637i	$-0.0289628\pi$
$384$	6.16766e9	+	1.09339e10i	0.283658	+	0.502863i
$385$	6.23811e10			2.83929
$386$	−1.37933e9	+	5.11846e9i	−0.0621326	+	0.230563i
$387$	−9.31145e9	−	9.31145e9i	−0.415120	−	0.415120i
$388$	−2.25584e10	−	1.31102e10i	−0.995361	−	0.578472i
$389$	−9.61248e9	−	9.61248e9i	−0.419795	−	0.419795i	0.465338	−	0.885133i	$-0.345933\pi$
$389$	−9.61248e9	−	9.61248e9i	−0.419795	−	0.419795i	−0.885133	+	0.465338i	$0.845933\pi$
$390$	1.85594e10	−	1.06800e10i	0.802244	−	0.461648i
$391$	−1.42687e10			−0.610488
$392$	5.10278e9	−	5.05920e9i	0.216104	−	0.214258i
$393$			1.21705e9i			0.0510196i
$394$	8.46812e8	−	4.87295e8i	0.0351400	−	0.0202212i
$395$	−2.07854e10	+	2.07854e10i	−0.853827	+	0.853827i
$396$	−3.71025e9	−	1.40069e10i	−0.150877	−	0.569588i
$397$	1.10734e10	−	1.10734e10i	0.445779	−	0.445779i	−0.448169	−	0.893949i	$-0.647924\pi$
$397$	1.10734e10	−	1.10734e10i	0.445779	−	0.445779i	0.893949	+	0.448169i	$0.147924\pi$
$398$	−6.68008e9	+	2.47886e10i	−0.266225	+	0.987916i
$399$		−	1.15299e10i		−	0.454921i
$400$	−6.02441e10	+	3.43242e10i	−2.35329	+	1.34079i
$401$	−3.78544e9			−0.146399			−0.0731996	−	0.997317i	$-0.523321\pi$
$401$	−3.78544e9			−0.146399			−0.0731996	+	0.997317i	$0.523321\pi$
$402$	2.23023e9	+	6.01005e8i	0.0853974	+	0.0230130i
$403$	−1.14409e10	−	1.14409e10i	−0.433750	−	0.433750i
$404$	−3.21363e9	−	1.21320e10i	−0.120634	−	0.455416i
$405$	4.07060e9	+	4.07060e9i	0.151300	+	0.151300i
$406$	1.13908e10	+	1.97947e10i	0.419228	+	0.728526i
$407$	−4.61590e9			−0.168221
$408$	−1.35674e10	−	5.81776e7i	−0.489618	−	0.00209950i
$409$			1.23802e10i			0.442421i	0.975226	+	0.221210i	$0.0710008\pi$
$409$			1.23802e10i			0.442421i	−0.975226	+	0.221210i	$0.928999\pi$
$410$	8.87586e9	+	1.54243e10i	0.314105	+	0.545846i
$411$	2.28659e10	−	2.28659e10i	0.801347	−	0.801347i
$412$	1.48251e10	+	8.61586e9i	0.514527	+	0.299026i
$413$	1.67309e10	−	1.67309e10i	0.575068	−	0.575068i
$414$	6.80632e9	+	1.83418e9i	0.231692	+	0.0624367i
$415$			6.92321e10i			2.33408i
$416$	1.26200e10	−	2.15021e10i	0.421390	−	0.717971i
$417$	3.80411e9			0.125808
$418$	−1.32651e10	+	4.92243e10i	−0.434514	+	1.61241i
$419$	−2.64630e10	−	2.64630e10i	−0.858585	−	0.858585i	0.132586	−	0.991171i	$-0.457672\pi$
$419$	−2.64630e10	−	2.64630e10i	−0.858585	−	0.858585i	−0.991171	+	0.132586i	$0.957672\pi$
$420$	−1.44995e10	+	2.49488e10i	−0.465967	+	0.801776i
$421$	3.95066e10	+	3.95066e10i	1.25760	+	1.25760i	0.952237	+	0.305360i	$0.0987769\pi$
$421$	3.95066e10	+	3.95066e10i	1.25760	+	1.25760i	0.305360	+	0.952237i	$0.401223\pi$
$422$	−3.17000e10	+	1.82416e10i	−0.999560	+	0.575193i
$423$	−3.65000e9			−0.114007
$424$	−1.61263e10	−	6.91500e7i	−0.498966	−	0.00213958i
$425$		−	7.49373e10i		−	2.29690i
$426$	−5.98102e9	+	3.44176e9i	−0.181609	+	0.104506i
$427$	−2.47186e10	+	2.47186e10i	−0.743554	+	0.743554i
$428$	2.84803e10	−	7.54409e9i	0.848731	−	0.224818i
$429$	−2.03491e10	+	2.03491e10i	−0.600779	+	0.600779i
$430$	3.01707e10	−	1.11958e11i	0.882495	−	3.27479i
$431$			4.42230e10i			1.28156i	0.767725	+	0.640780i	$0.221389\pi$
$431$			4.42230e10i			1.28156i	−0.767725	+	0.640780i	$0.778611\pi$
$432$	6.46434e9	+	1.77179e9i	0.185605	+	0.0508717i
$433$	1.90039e10			0.540618			0.270309	−	0.962774i	$-0.412874\pi$
$433$	1.90039e10			0.540618			0.270309	+	0.962774i	$0.412874\pi$
$434$	2.10530e10	+	5.67340e9i	0.593410	+	0.159913i
$435$	2.83679e10	+	2.83679e10i	0.792265	+	0.792265i
$436$	−1.91686e9	+	5.07753e8i	−0.0530450	+	0.0140510i
$437$	−1.75370e10	−	1.75370e10i	−0.480873	−	0.480873i
$438$	1.08874e10	+	1.89199e10i	0.295820	+	0.514070i
$439$	−2.53755e10			−0.683215			−0.341607	−	0.939843i	$-0.610971\pi$
$439$	−2.53755e10			−0.683215			−0.341607	+	0.939843i	$0.610971\pi$
$440$	9.06053e10	−	8.98316e10i	2.41737	−	2.39673i
$441$		−	3.83668e9i		−	0.101438i
$442$	1.34396e10	+	2.33551e10i	0.352126	+	0.611918i
$443$	2.27875e9	−	2.27875e9i	0.0591673	−	0.0591673i	−0.676904	−	0.736071i	$-0.736679\pi$
$443$	2.27875e9	−	2.27875e9i	0.0591673	−	0.0591673i	0.736071	+	0.676904i	$0.236679\pi$
$444$	1.07289e9	−	1.84610e9i	0.0276073	−	0.0475031i
$445$	4.90151e10	−	4.90151e10i	1.24994	−	1.24994i
$446$	2.80028e10	+	7.54624e9i	0.707721	+	0.190718i
$447$			1.12066e10i			0.280702i
$448$	−2.88136e8	+	3.35972e10i	−0.00715296	+	0.834047i
$449$	1.85538e10			0.456507			0.228253	−	0.973602i	$-0.426699\pi$
$449$	1.85538e10			0.456507			0.228253	+	0.973602i	$0.426699\pi$
$450$	−9.63286e9	+	3.57459e10i	−0.234912	+	0.871718i
$451$	−1.69116e10	−	1.69116e10i	−0.408770	−	0.408770i
$452$	−6.71483e10	−	3.90245e10i	−1.60872	−	0.934939i
$453$	1.68087e10	+	1.68087e10i	0.399155	+	0.399155i
$454$	−2.21107e10	+	1.27235e10i	−0.520449	+	0.299491i
$455$	5.73100e10			1.33717
$456$	−1.66036e10	−	1.67467e10i	−0.384011	−	0.387319i
$457$			5.51665e10i			1.26477i	0.774655	+	0.632384i	$0.217923\pi$
$457$			5.51665e10i			1.26477i	−0.774655	+	0.632384i	$0.782077\pi$
$458$	2.16881e10	−	1.24803e10i	0.492901	−	0.283638i
$459$	−5.12243e9	+	5.12243e9i	−0.115405	+	0.115405i
$460$	1.58935e10	+	6.00008e10i	0.354966	+	1.34006i
$461$	−2.88967e10	+	2.88967e10i	−0.639801	+	0.639801i	−0.950506	−	0.310705i	$-0.899435\pi$
$461$	−2.88967e10	+	2.88967e10i	−0.639801	+	0.639801i	0.310705	+	0.950506i	$0.399435\pi$
$462$	1.00909e10	−	3.74454e10i	0.221493	−	0.821922i
$463$		−	3.12068e10i		−	0.679086i	−0.940590	−	0.339543i	$-0.889728\pi$
$463$		−	3.12068e10i		−	0.679086i	0.940590	−	0.339543i	$-0.110272\pi$
$464$	4.50498e10	+	1.23475e10i	0.971899	+	0.266384i
$465$	3.83017e10			0.819232
$466$	−7.86966e10	−	2.12073e10i	−1.66883	−	0.449719i
$467$	2.13622e10	+	2.13622e10i	0.449137	+	0.449137i	0.895068	−	0.445931i	$-0.147127\pi$
$467$	2.13622e10	+	2.13622e10i	0.449137	+	0.449137i	−0.445931	+	0.895068i	$0.647127\pi$
$468$	−3.40864e9	−	1.28682e10i	−0.0710555	−	0.268248i
$469$	4.37131e9	+	4.37131e9i	0.0903483	+	0.0903483i
$470$	−1.60300e10	−	2.78566e10i	−0.328505	−	0.570870i
$471$	5.63140e9			0.114428
$472$	2.07515e8	−	4.83940e10i	0.00418101	−	0.975042i
$473$			1.55834e11i			3.11328i
$474$	9.11454e9	+	1.58391e10i	0.180560	+	0.313774i
$475$	9.21021e10	−	9.21021e10i	1.80924	−	1.80924i
$476$	−3.13955e10	−	1.82461e10i	−0.611561	−	0.355420i
$477$	−6.08853e9	+	6.08853e9i	−0.117609	+	0.117609i
$478$	−7.67723e10	−	2.06887e10i	−1.47059	−	0.396298i
$479$		−	4.49462e10i		−	0.853790i	−0.904301	−	0.426895i	$-0.859607\pi$
$479$		−	4.49462e10i		−	0.853790i	0.904301	−	0.426895i	$-0.140393\pi$
$480$	1.48677e10	+	5.71168e10i	0.280078	+	1.07597i
$481$	−4.24067e9			−0.0792235
$482$	−1.95381e10	+	7.25024e10i	−0.361987	+	1.34327i
$483$	1.33406e10	+	1.33406e10i	0.245124	+	0.245124i
$484$	−5.85872e10	+	1.00809e11i	−1.06763	+	1.83705i
$485$	−8.67395e10	−	8.67395e10i	−1.56765	−	1.56765i
$486$	3.10192e9	−	1.78499e9i	0.0556013	−	0.0319956i
$487$	−1.01271e11			−1.80040			−0.900198	−	0.435481i	$-0.856578\pi$
$487$	−1.01271e11			−1.80040			−0.900198	+	0.435481i	$0.856578\pi$
$488$	−3.06587e8	+	7.14984e10i	−0.00540598	+	1.26072i
$489$		−	5.05039e10i		−	0.883262i
$490$	2.92814e10	−	1.68499e10i	0.507934	−	0.292289i
$491$	6.76754e10	−	6.76754e10i	1.16441	−	1.16441i	0.180907	−	0.983500i	$-0.442097\pi$
$491$	6.76754e10	−	6.76754e10i	1.16441	−	1.16441i	0.983500	−	0.180907i	$-0.0579035\pi$
$492$	1.06945e10	−	2.83284e9i	0.182515	−	0.0483461i
$493$	−3.56981e10	+	3.56981e10i	−0.604307	+	0.604307i
$494$	−1.21867e10	+	4.52228e10i	−0.204635	+	0.759364i
$495$		−	6.81245e10i		−	1.13470i
$496$	3.87483e10	−	2.20769e10i	0.640215	−	0.364764i
$497$	−1.84689e10			−0.302702
$498$	4.15578e10	+	1.11991e10i	0.675671	+	0.182081i
$499$	−2.68207e10	−	2.68207e10i	−0.432581	−	0.432581i	0.456925	−	0.889505i	$-0.348951\pi$
$499$	−2.68207e10	−	2.68207e10i	−0.432581	−	0.432581i	−0.889505	+	0.456925i	$0.848951\pi$
$500$	−1.98770e11	+	5.26518e10i	−3.18033	+	0.842429i
$501$	−3.47460e9	−	3.47460e9i	−0.0551511	−	0.0551511i
$502$	−1.99362e10	−	3.46448e10i	−0.313926	−	0.545536i
$503$	9.46756e10			1.47899			0.739497	−	0.673160i	$-0.235064\pi$
$503$	9.46756e10			1.47899			0.739497	+	0.673160i	$0.235064\pi$
$504$	1.26305e10	+	1.27393e10i	0.195749	+	0.197435i
$505$		−	5.90059e10i		−	0.907256i
$506$	−4.16062e10	−	7.23025e10i	−0.634682	−	1.10294i
$507$	8.27983e9	−	8.27983e9i	0.125311	−	0.125311i
$508$	−5.89674e9	+	1.01464e10i	−0.0885435	+	0.152354i
$509$	5.87367e10	−	5.87367e10i	0.875061	−	0.875061i	−0.117958	−	0.993019i	$-0.537635\pi$
$509$	5.87367e10	−	5.87367e10i	0.875061	−	0.875061i	0.993019	+	0.117958i	$0.0376348\pi$
$510$	−6.15907e10	−	1.65976e10i	−0.910405	−	0.245337i
$511$			5.84231e10i			0.856843i
$512$	4.79629e10	+	4.92131e10i	0.697952	+	0.716144i
$513$	−1.25915e10			−0.181806
$514$	−9.69755e9	+	3.59859e10i	−0.138934	+	0.515561i
$515$	5.70041e10	+	5.70041e10i	0.810359	+	0.810359i
$516$	−6.23246e10	−	3.62211e10i	−0.879146	−	0.510931i
$517$	3.05427e10	+	3.05427e10i	0.427510	+	0.427510i
$518$	4.95319e9	−	2.85030e9i	0.0687965	−	0.0395887i
$519$	−6.62632e10			−0.913278
$520$	8.32399e10	−	8.25291e10i	1.13846	−	1.12874i
$521$		−	6.74113e10i		−	0.914917i	−0.889231	−	0.457459i	$-0.848760\pi$
$521$		−	6.74113e10i		−	0.914917i	0.889231	−	0.457459i	$-0.151240\pi$
$522$	2.16172e10	−	1.24395e10i	0.291150	−	0.167541i
$523$	4.65552e10	−	4.65552e10i	0.622246	−	0.622246i	−0.323860	−	0.946105i	$-0.604981\pi$
$523$	4.65552e10	−	4.65552e10i	0.622246	−	0.622246i	0.946105	+	0.323860i	$0.104981\pi$
$524$	1.70592e9	+	6.44017e9i	0.0226274	+	0.0854225i
$525$	−7.00629e10	+	7.00629e10i	−0.922255	+	0.922255i
$526$	−1.46911e10	+	5.45162e10i	−0.191916	+	0.712168i
$527$			4.81988e10i			0.624876i
$528$	−3.92666e10	−	6.89188e10i	−0.505229	−	0.886752i
$529$	−3.77290e10			−0.481785
$530$	−7.32068e10	−	1.97279e10i	−0.927787	−	0.250022i
$531$	−1.82713e10	−	1.82713e10i	−0.229822	−	0.229822i
$532$	−1.61614e10	−	6.10123e10i	−0.201759	−	0.761677i
$533$	−1.55368e10	−	1.55368e10i	−0.192510	−	0.192510i
$534$	−2.14934e10	−	3.73509e10i	−0.264327	−	0.459342i
$535$	1.38518e11			1.69080
$536$	1.26440e10	+	5.42177e7i	0.153188	+	0.000656874i
$537$		−	1.95057e10i		−	0.234566i
$538$	5.84921e10	+	1.01646e11i	0.698181	+	1.21329i
$539$	−3.21049e10	+	3.21049e10i	−0.380378	+	0.380378i
$540$	2.72459e10	+	1.58344e10i	0.320424	+	0.186220i
$541$	−1.22298e10	+	1.22298e10i	−0.142768	+	0.142768i	−0.774878	−	0.632110i	$-0.782189\pi$
$541$	−1.22298e10	+	1.22298e10i	−0.142768	+	0.142768i	0.632110	+	0.774878i	$0.282189\pi$
$542$	−7.75594e10	−	2.09008e10i	−0.898746	−	0.242196i
$543$			2.88790e10i			0.332187i
$544$	−7.18756e10	+	1.87095e10i	−0.820702	+	0.213632i
$545$	−9.32292e9			−0.105674
$546$	9.27055e9	−	3.44014e10i	0.104312	−	0.387084i
$547$	−5.75372e10	−	5.75372e10i	−0.642687	−	0.642687i	0.308528	−	0.951215i	$-0.400164\pi$
$547$	−5.75372e10	−	5.75372e10i	−0.642687	−	0.642687i	−0.951215	+	0.308528i	$0.900164\pi$
$548$	8.89471e10	−	1.53049e11i	0.986301	−	1.69710i
$549$	2.69944e10	+	2.69944e10i	0.297156	+	0.297156i
$550$	3.79723e11	−	2.18510e11i	4.14970	−	2.38793i
$551$	−8.77499e10			−0.952008
$552$	3.85875e10	+	1.65464e8i	0.415614	+	0.00178217i
$553$			4.89098e10i			0.522992i
$554$	2.66636e9	−	1.53435e9i	0.0283061	−	0.0162886i
$555$	7.09845e9	−	7.09845e9i	0.0748155	−	0.0748155i
$556$	2.01299e10	−	5.33217e9i	0.210641	−	0.0557963i
$557$	5.08435e9	−	5.08435e9i	0.0528220	−	0.0528220i	−0.680202	−	0.733024i	$-0.738108\pi$
$557$	5.08435e9	−	5.08435e9i	0.0528220	−	0.0528220i	0.733024	+	0.680202i	$0.238108\pi$
$558$	6.19574e9	−	2.29913e10i	0.0639082	−	0.237152i
$559$			1.43166e11i			1.46620i
$560$	−4.17554e10	+	1.52344e11i	−0.424581	+	1.54908i
$561$	8.57276e10			0.865505
$562$	−4.77446e10	−	1.28663e10i	−0.478607	−	0.128976i
$563$	−3.88406e10	−	3.88406e10i	−0.386592	−	0.386592i	0.486878	−	0.873470i	$-0.338136\pi$
$563$	−3.88406e10	−	3.88406e10i	−0.386592	−	0.386592i	−0.873470	+	0.486878i	$0.838136\pi$
$564$	−1.93145e10	+	5.11617e9i	−0.190883	+	0.0505625i
$565$	−2.58193e11	−	2.58193e11i	−2.53368	−	2.53368i
$566$	5.12917e10	+	8.91338e10i	0.499783	+	0.868514i
$567$	9.57847e9			0.0926753
$568$	−2.68251e10	+	2.65961e10i	−0.257720	+	0.255519i
$569$			3.39836e10i			0.324205i	0.986774	+	0.162103i	$0.0518276\pi$
$569$			3.39836e10i			0.324205i	−0.986774	+	0.162103i	$0.948172\pi$
$570$	−5.52991e10	−	9.60978e10i	−0.523864	−	0.910361i
$571$	4.14430e9	−	4.14430e9i	0.0389858	−	0.0389858i	−0.687345	−	0.726331i	$-0.741224\pi$
$571$	4.14430e9	−	4.14430e9i	0.0389858	−	0.0389858i	0.726331	+	0.687345i	$0.241224\pi$
$572$	−7.91568e10	+	1.36203e11i	−0.739442	+	1.27234i
$573$	2.21766e10	−	2.21766e10i	0.205720	−	0.205720i
$574$	2.85902e10	+	7.70453e9i	0.263372	+	0.0709739i
$575$			2.13131e11i			1.94973i
$576$	3.66904e10	+	3.14665e8i	0.333321	+	0.00285863i
$577$	3.11063e10			0.280637			0.140319	−	0.990106i	$-0.455187\pi$
$577$	3.11063e10			0.280637			0.140319	+	0.990106i	$0.455187\pi$
$578$	−8.15508e9	+	3.02621e10i	−0.0730663	+	0.271136i
$579$	1.09560e10	+	1.09560e10i	0.0974850	+	0.0974850i
$580$	1.89876e11	+	1.10350e11i	1.67787	+	0.975123i
$581$	8.14545e10	+	8.14545e10i	0.714843	+	0.714843i
$582$	−6.60981e10	+	3.80359e10i	−0.576099	+	0.331514i
$583$	1.01896e11			0.882029
$584$	8.41319e10	+	8.48566e10i	0.723285	+	0.729515i
$585$		−	6.25865e10i		−	0.534389i
$586$	6.56465e10	−	3.77760e10i	0.556700	−	0.320351i
$587$	6.02831e10	−	6.02831e10i	0.507742	−	0.507742i	−0.406091	−	0.913833i	$-0.633108\pi$
$587$	6.02831e10	−	6.02831e10i	0.507742	−	0.507742i	0.913833	+	0.406091i	$0.133108\pi$
$588$	−5.37784e9	−	2.03023e10i	−0.0449882	−	0.169839i
$589$	−5.92390e10	+	5.92390e10i	−0.492206	+	0.492206i
$590$	5.92022e10	−	2.19689e11i	0.488573	−	1.81301i
$591$		−	2.85564e9i		−	0.0234074i
$592$	3.08970e9	−	1.12727e10i	0.0251553	−	0.0917788i
$593$	1.93448e11			1.56440			0.782198	−	0.623030i	$-0.214099\pi$
$593$	1.93448e11			1.56440			0.782198	+	0.623030i	$0.214099\pi$
$594$	−4.08930e10	−	1.10199e10i	−0.328475	−	0.0885181i
$595$	−1.20719e11	−	1.20719e11i	−0.963185	−	0.963185i
$596$	1.57082e10	+	5.93015e10i	0.124492	+	0.469981i
$597$	5.30597e10	+	5.30597e10i	0.417703	+	0.417703i
$598$	−3.82240e10	−	6.64249e10i	−0.298903	−	0.519429i
$599$	−6.08320e10			−0.472525			−0.236262	−	0.971689i	$-0.575922\pi$
$599$	−6.08320e10			−0.472525			−0.236262	+	0.971689i	$0.575922\pi$
$600$	−8.68997e8	+	2.02656e11i	−0.00670522	+	1.56371i
$601$		−	7.06971e10i		−	0.541881i	−0.962596	−	0.270940i	$-0.912665\pi$
$601$		−	7.06971e10i		−	0.541881i	0.962596	−	0.270940i	$-0.0873346\pi$
$602$	−9.62266e10	−	1.67221e11i	−0.732672	−	1.27322i
$603$	4.77377e9	−	4.77377e9i	0.0361071	−	0.0361071i
$604$	1.12506e11	+	6.53849e10i	0.845334	+	0.491281i
$605$	−3.87624e11	+	3.87624e11i	−2.89327	+	2.89327i
$606$	−3.54194e10	−	9.54488e9i	−0.262634	−	0.0707750i
$607$		−	5.02258e9i		−	0.0369975i	−0.999829	−	0.0184988i	$-0.994111\pi$
$607$		−	5.02258e9i		−	0.0369975i	0.999829	−	0.0184988i	$-0.00588867\pi$
$608$	−1.11334e11	−	6.53441e10i	−0.814730	−	0.478181i
$609$	6.67522e10			0.485284
$610$	−8.74667e10	+	3.24574e11i	−0.631718	+	2.34420i
$611$	2.80599e10	+	2.80599e10i	0.201336	+	0.201336i
$612$	−1.99260e10	+	3.42861e10i	−0.142041	+	0.244406i
$613$	−1.34845e10	−	1.34845e10i	−0.0954977	−	0.0954977i	0.657744	−	0.753242i	$-0.271511\pi$
$613$	−1.34845e10	−	1.34845e10i	−0.0954977	−	0.0954977i	−0.753242	+	0.657744i	$0.771511\pi$
$614$	1.64851e10	−	9.48630e9i	0.115990	−	0.0667457i
$615$	5.20142e10			0.363598
$616$	9.10313e8	−	2.12292e11i	0.00632219	−	1.47438i
$617$			4.54381e10i			0.313530i	0.987636	+	0.156765i	$0.0501065\pi$
$617$			4.54381e10i			0.313530i	−0.987636	+	0.156765i	$0.949893\pi$
$618$	4.34388e10	−	2.49967e10i	0.297800	−	0.171368i
$619$	−5.45898e10	+	5.45898e10i	−0.371834	+	0.371834i	−0.868145	−	0.496311i	$-0.834688\pi$
$619$	−5.45898e10	+	5.45898e10i	−0.371834	+	0.371834i	0.496311	+	0.868145i	$0.334688\pi$
$620$	2.02679e11	−	5.36871e10i	1.37165	−	0.363332i
$621$	1.45688e10	−	1.45688e10i	0.0979621	−	0.0979621i
$622$	−5.53265e10	+	2.05307e11i	−0.369633	+	1.37165i
$623$		−	1.15337e11i		−	0.765623i
$624$	−3.60746e10	−	6.33163e10i	−0.237937	−	0.417616i
$625$	−5.53472e11			−3.62723
$626$	2.64110e11	+	7.11729e10i	1.71984	+	0.463465i
$627$	1.05364e11	+	1.05364e11i	0.681745	+	0.681745i
$628$	2.97993e10	−	7.89347e9i	0.191588	−	0.0507492i
$629$	8.93267e9	+	8.93267e9i	0.0570661	+	0.0570661i
$630$	4.20665e10	+	7.31024e10i	0.267039	+	0.464055i
$631$	2.58904e11			1.63313			0.816565	−	0.577253i	$-0.195876\pi$
$631$	2.58904e11			1.63313			0.816565	+	0.577253i	$0.195876\pi$
$632$	7.04323e10	+	7.10390e10i	0.441473	+	0.445275i
$633$			1.06899e11i			0.665825i
$634$	−1.26328e11	−	2.19530e11i	−0.781883	−	1.35874i
$635$	−3.90139e10	+	3.90139e10i	−0.239952	+	0.239952i
$636$	−2.36841e10	+	4.07525e10i	−0.144753	+	0.249073i
$637$	−2.94950e10	+	2.94950e10i	−0.179139	+	0.179139i
$638$	−2.84982e11	−	7.67975e10i	−1.72003	−	0.463516i
$639$			2.01693e10i			0.120973i
$640$	1.58735e11	+	2.81401e11i	0.946132	+	1.67728i
$641$	1.88775e11			1.11818			0.559091	−	0.829106i	$-0.311150\pi$
$641$	1.88775e11			1.11818			0.559091	+	0.829106i	$0.311150\pi$
$642$	2.24069e10	−	8.31480e10i	0.131899	−	0.489454i
$643$	−1.75249e10	−	1.75249e10i	−0.102521	−	0.102521i	0.653986	−	0.756507i	$-0.273095\pi$
$643$	−1.75249e10	−	1.75249e10i	−0.102521	−	0.102521i	−0.756507	+	0.653986i	$0.773095\pi$
$644$	8.92928e10	+	5.18941e10i	0.519126	+	0.301700i
$645$	−2.39645e11	−	2.39645e11i	−1.38462	−	1.38462i
$646$	1.20929e11	−	6.95882e10i	0.694386	−	0.399581i
$647$	−2.40941e11			−1.37497			−0.687487	−	0.726197i	$-0.741286\pi$
$647$	−2.40941e11			−1.37497			−0.687487	+	0.726197i	$0.741286\pi$
$648$	1.39122e10	−	1.37934e10i	0.0789036	−	0.0782298i
$649$			3.05784e11i			1.72360i
$650$	3.48855e11	−	2.00747e11i	1.95430	−	1.12459i
$651$	4.50636e10	−	4.50636e10i	0.250901	−	0.250901i
$652$	−7.07908e10	−	2.67249e11i	−0.391730	−	1.47885i
$653$	−3.11548e10	+	3.11548e10i	−0.171345	+	0.171345i	−0.787570	−	0.616225i	$-0.788661\pi$
$653$	−3.11548e10	+	3.11548e10i	−0.171345	+	0.171345i	0.616225	+	0.787570i	$0.288661\pi$
$654$	−1.50809e9	+	5.59626e9i	−0.00824358	+	0.0305905i
$655$			3.13227e10i			0.170174i
$656$	5.26206e10	−	2.99807e10i	0.284145	−	0.161892i
$657$	6.38021e10			0.342431
$658$	−5.16345e10	−	1.39146e10i	−0.275446	−	0.0742277i
$659$	1.26027e11	+	1.26027e11i	0.668224	+	0.668224i	0.957305	−	0.289081i	$-0.0933496\pi$
$659$	1.26027e11	+	1.26027e11i	0.668224	+	0.668224i	−0.289081	+	0.957305i	$0.593350\pi$
$660$	−9.54894e10	−	3.60490e11i	−0.503245	−	1.89984i
$661$	1.78384e11	+	1.78384e11i	0.934439	+	0.934439i	0.997979	−	0.0635400i	$-0.0202391\pi$
$661$	1.78384e11	+	1.78384e11i	0.934439	+	0.934439i	−0.0635400	+	0.997979i	$0.520239\pi$
$662$	9.41711e9	+	1.63649e10i	0.0490327	+	0.0852081i
$663$	7.87587e10			0.407610
$664$	2.35607e11	+	1.01029e9i	1.21204	+	0.00519724i
$665$		−	2.96742e11i		−	1.51737i
$666$	−3.11272e9	−	5.40923e9i	−0.0158213	−	0.0274940i
$667$	1.01530e11	−	1.01530e11i	0.512968	−	0.512968i
$668$	−2.32566e10	−	1.35160e10i	−0.116800	−	0.0678802i
$669$	5.99396e10	−	5.99396e10i	0.299233	−	0.299233i
$670$	5.73985e10	+	1.54678e10i	0.284840	+	0.0767592i
$671$		−	4.51772e11i		−	2.22858i
$672$	8.46928e10	+	4.97078e10i	0.415307	+	0.243752i
$673$	−1.57828e11			−0.769348			−0.384674	−	0.923052i	$-0.625686\pi$
$673$	−1.57828e11			−0.769348			−0.384674	+	0.923052i	$0.625686\pi$
$674$	−8.12542e10	+	3.01520e11i	−0.393737	+	1.46109i
$675$	7.65136e10	+	7.65136e10i	0.368573	+	0.368573i
$676$	3.22081e10	−	5.54196e10i	0.154233	−	0.265385i
$677$	2.52036e10	+	2.52036e10i	0.119980	+	0.119980i	0.764547	−	0.644568i	$-0.222963\pi$
$677$	2.52036e10	+	2.52036e10i	0.119980	+	0.119980i	−0.644568	+	0.764547i	$0.722963\pi$
$678$	−1.96751e11	+	1.13219e11i	−0.931103	+	0.535800i
$679$	−2.04106e11			−0.960231
$680$	−3.49180e11	−	1.49730e9i	−1.63311	−	0.00700280i
$681$			7.45621e10i			0.346681i
$682$	−2.44233e11	+	1.40543e11i	−1.12893	+	0.649639i
$683$	−1.09138e11	+	1.09138e11i	−0.501524	+	0.501524i	−0.911911	−	0.410387i	$-0.865393\pi$
$683$	−1.09138e11	+	1.09138e11i	−0.501524	+	0.501524i	0.410387	+	0.911911i	$0.365393\pi$
$684$	−6.66297e10	+	1.76494e10i	−0.304399	+	0.0806315i
$685$	5.88491e11	−	5.88491e11i	2.67287	−	2.67287i
$686$	6.26890e10	−	2.32628e11i	0.283071	−	1.05043i
$687$		−	7.31371e10i		−	0.328330i
$688$	−3.80570e11	−	1.04309e11i	−1.69856	−	0.465552i
$689$	9.36127e10			0.415392
$690$	1.75172e11	+	4.72056e10i	0.772800	+	0.208256i
$691$	−2.66428e11	−	2.66428e11i	−1.16860	−	1.16860i	−0.982537	−	0.186067i	$-0.940426\pi$
$691$	−2.66428e11	−	2.66428e11i	−1.16860	−	1.16860i	−0.186067	−	0.982537i	$-0.559574\pi$
$692$	−3.50641e11	+	9.28804e10i	−1.52911	+	0.405042i
$693$	−8.01514e10	−	8.01514e10i	−0.347519	−	0.347519i
$694$	2.53073e10	+	4.39786e10i	0.109096	+	0.189585i
$695$	9.79048e10			0.419628
$696$	9.69541e10	−	9.61261e10i	0.413170	−	0.409642i
$697$			6.54544e10i			0.277337i
$698$	9.39633e10	+	1.63288e11i	0.395855	+	0.687910i
$699$	−1.68449e11	+	1.68449e11i	−0.705602	+	0.705602i
$700$	−2.72541e11	+	4.68954e11i	−1.13511	+	1.95316i
$701$	3.03994e11	−	3.03994e11i	1.25891	−	1.25891i	0.307290	−	0.951616i	$-0.400578\pi$
$701$	3.03994e11	−	3.03994e11i	1.25891	−	1.25891i	0.951616	−	0.307290i	$-0.0994221\pi$
$702$	−3.75687e10	−	1.01241e10i	−0.154696	−	0.0416876i
$703$			2.19575e10i			0.0899003i
$704$	−3.04388e11	−	3.09654e11i	−1.23919	−	1.26062i
$705$	−9.39388e10			−0.380267
$706$	6.44072e10	−	2.39004e11i	0.259248	−	0.962025i
$707$	−6.94230e10	−	6.94230e10i	−0.277860	−	0.277860i
$708$	−1.22296e11	−	7.10744e10i	−0.486719	−	0.282866i
$709$	−1.64494e11	−	1.64494e11i	−0.650976	−	0.650976i	0.302252	−	0.953228i	$-0.402262\pi$
$709$	−1.64494e11	−	1.64494e11i	−0.650976	−	0.650976i	−0.953228	+	0.302252i	$0.902262\pi$
$710$	−1.53931e11	+	8.85792e10i	−0.605750	+	0.348577i
$711$	5.34129e10			0.209010
$712$	−1.66090e11	−	1.67520e11i	−0.646284	−	0.651850i
$713$		−	1.37083e11i		−	0.530428i
$714$	−9.19918e10	+	5.29363e10i	−0.353962	+	0.203686i
$715$	−5.23716e11	+	5.23716e11i	−2.00388	+	2.00388i
$716$	−2.73410e10	−	1.03217e11i	−0.104031	−	0.392735i
$717$	−1.64330e11	+	1.64330e11i	−0.621785	+	0.621785i
$718$	3.18701e10	−	1.18264e11i	0.119918	−	0.444996i
$719$		−	4.28683e11i		−	1.60406i	−0.597283	−	0.802030i	$-0.703753\pi$
$719$		−	4.28683e11i		−	1.60406i	0.597283	−	0.802030i	$-0.296247\pi$
$720$	1.66370e11	+	4.55998e10i	0.619078	+	0.169681i
$721$	1.34136e11			0.496367
$722$	−2.82207e10	−	7.60496e9i	−0.103853	−	0.0279865i
$723$	1.55190e11	+	1.55190e11i	0.567952	+	0.567952i
$724$	4.04793e10	+	1.52817e11i	0.147326	+	0.556183i
$725$	5.33221e11	+	5.33221e11i	1.92999	+	1.92999i
$726$	1.69976e11	+	2.95381e11i	0.611844	+	1.06325i
$727$	−4.99639e10			−0.178862			−0.0894312	−	0.995993i	$-0.528505\pi$
$727$	−4.99639e10			−0.178862			−0.0894312	+	0.995993i	$0.528505\pi$
$728$	8.36312e8	−	1.95034e11i	0.00297744	−	0.694361i
$729$		−	1.04604e10i		−	0.0370370i
$730$	2.80205e11	+	4.86934e11i	0.986697	+	1.71466i
$731$	3.01569e11	−	3.01569e11i	1.05613	−	1.05613i
$732$	1.80683e11	+	1.05007e11i	0.629321	+	0.365741i
$733$	3.12343e11	−	3.12343e11i	1.08197	−	1.08197i	0.0856458	−	0.996326i	$-0.472705\pi$
$733$	3.12343e11	−	3.12343e11i	1.08197	−	1.08197i	0.996326	−	0.0856458i	$-0.0272953\pi$
$734$	1.75441e11	+	4.72782e10i	0.604432	+	0.162883i
$735$		−	9.87433e10i		−	0.338344i
$736$	2.04423e11	−	5.32121e10i	0.696656	−	0.181342i
$737$	−7.98925e10			−0.270792
$738$	8.41388e9	−	3.12224e10i	0.0283642	−	0.105255i
$739$	4.73553e10	+	4.73553e10i	0.158778	+	0.158778i	0.782025	−	0.623247i	$-0.214187\pi$
$739$	4.73553e10	+	4.73553e10i	0.158778	+	0.158778i	−0.623247	+	0.782025i	$0.714187\pi$
$740$	2.76126e10	−	4.75123e10i	0.0920832	−	0.158445i
$741$	9.67988e10	+	9.67988e10i	0.321068	+	0.321068i
$742$	−1.09342e11	+	6.29202e10i	−0.360720	+	0.207575i
$743$	−4.46916e11			−1.46646			−0.733231	−	0.679980i	$-0.761989\pi$
$743$	−4.46916e11			−1.46646			−0.733231	+	0.679980i	$0.761989\pi$
$744$	5.58928e8	−	1.30346e11i	0.00182417	−	0.425409i
$745$			2.88421e11i			0.936272i
$746$	−3.10214e11	+	1.78511e11i	−1.00163	+	0.576383i
$747$	8.89540e10	−	8.89540e10i	0.285682	−	0.285682i
$748$	4.53640e11	−	1.20164e11i	1.44912	−	0.383854i
$749$	1.62972e11	−	1.62972e11i	0.517830	−	0.517830i
$750$	−1.56382e11	+	5.80308e11i	−0.494246	+	1.83406i
$751$			3.94868e11i			1.24134i	0.784071	+	0.620671i	$0.213140\pi$
$751$			3.94868e11i			1.24134i	−0.784071	+	0.620671i	$0.786860\pi$
$752$	−9.50340e10	+	5.41458e10i	−0.297172	+	0.169314i
$753$	−1.16830e11			−0.363391
$754$	−2.61816e11	−	7.05545e10i	−0.810047	−	0.218293i
$755$	4.32599e11	+	4.32599e11i	1.33137	+	1.33137i
$756$	5.06858e10	−	1.34260e10i	0.155167	−	0.0411018i
$757$	3.34882e11	+	3.34882e11i	1.01979	+	1.01979i	0.999800	+	0.0199847i	$0.00636176\pi$
$757$	3.34882e11	+	3.34882e11i	1.01979	+	1.01979i	0.0199847	+	0.999800i	$0.493638\pi$
$758$	3.49804e10	+	6.07884e10i	0.105962	+	0.184138i
$759$	−2.43820e11			−0.734687
$760$	−4.27322e11	−	4.31002e11i	−1.28086	−	1.29189i
$761$		−	6.49647e10i		−	0.193704i	−0.995299	−	0.0968520i	$-0.969123\pi$
$761$		−	6.49647e10i		−	0.193704i	0.995299	−	0.0968520i	$-0.0308773\pi$
$762$	1.71079e10	+	2.97298e10i	0.0507430	+	0.0881803i
$763$	−1.09688e10	+	1.09688e10i	−0.0323640	+	0.0323640i
$764$	8.62657e10	−	1.48435e11i	0.253201	−	0.435675i
$765$	−1.31834e11	+	1.31834e11i	−0.384930	+	0.384930i
$766$	−6.04105e10	−	1.62795e10i	−0.175468	−	0.0472854i
$767$			2.80926e11i			0.811728i
$768$	1.94593e11	−	4.97635e10i	0.559350	−	0.143043i
$769$	−2.18735e11			−0.625481			−0.312740	−	0.949839i	$-0.601247\pi$
$769$	−2.18735e11			−0.625481			−0.312740	+	0.949839i	$0.601247\pi$
$770$	2.59704e11	−	9.63718e11i	0.738782	−	2.74149i
$771$	7.70274e10	+	7.70274e10i	0.217985	+	0.217985i
$772$	7.33321e10	+	4.26183e10i	0.206455	+	0.119985i
$773$	−1.85211e11	−	1.85211e11i	−0.518739	−	0.518739i	0.398451	−	0.917190i	$-0.369548\pi$
$773$	−1.85211e11	−	1.85211e11i	−0.518739	−	0.518739i	−0.917190	+	0.398451i	$0.869548\pi$
$774$	−1.82617e11	+	1.05086e11i	−0.508835	+	0.292807i
$775$	7.19943e11			1.99568
$776$	−2.96453e11	+	2.93921e11i	−0.817539	+	0.810558i
$777$		−	1.67033e10i		−	0.0458265i
$778$	−1.88521e11	+	1.08483e11i	−0.514565	+	0.296105i
$779$	−8.04472e10	+	8.04472e10i	−0.218454	+	0.218454i
$780$	−8.77269e10	−	3.31185e11i	−0.237003	−	0.894731i
$781$	1.68774e11	−	1.68774e11i	0.453630	−	0.453630i
$782$	−5.94033e10	+	2.20435e11i	−0.158849	+	0.589460i
$783$		−	7.28980e10i		−	0.193940i
$784$	−5.69152e10	−	9.98946e10i	−0.150648	−	0.264410i
$785$	1.44933e11			0.381671
$786$	1.88020e10	+	5.06680e9i	0.0492622	+	0.0132753i
$787$	1.31282e11	+	1.31282e11i	0.342222	+	0.342222i	0.857202	−	0.514980i	$-0.172201\pi$
$787$	1.31282e11	+	1.31282e11i	0.342222	+	0.342222i	−0.514980	+	0.857202i	$0.672201\pi$
$788$	−4.00272e9	−	1.51110e10i	−0.0103813	−	0.0391912i
$789$	1.16691e11	+	1.16691e11i	0.301113	+	0.301113i
$790$	2.34578e11	+	4.07645e11i	0.602252	+	1.04658i
$791$	−6.07550e11			−1.55195
$792$	−2.31837e11	−	9.94125e8i	−0.589227	−	0.00252662i
$793$		−	4.15046e11i		−	1.04955i
$794$	−1.24971e11	−	2.17173e11i	−0.314433	−	0.546416i
$795$	−1.56698e11	+	1.56698e11i	−0.392279	+	0.392279i
$796$	3.55146e11	+	2.06400e11i	0.884616	+	0.514110i
$797$	−4.46507e11	+	4.46507e11i	−1.10661	+	1.10661i	−0.113019	+	0.993593i	$0.536052\pi$
$797$	−4.46507e11	+	4.46507e11i	−1.10661	+	1.10661i	−0.993593	+	0.113019i	$0.963948\pi$
$798$	−1.78125e11	−	4.80014e10i	−0.439251	−	0.118370i
$799$		−	1.18212e11i		−	0.290052i
$800$	2.79463e11	+	1.07360e12i	0.682283	+	2.62110i
$801$	−1.25956e11			−0.305976
$802$	−1.57595e10	+	5.84808e10i	−0.0380930	+	0.141356i
$803$	−5.33887e11	−	5.33887e11i	−1.28407	−	1.28407i
$804$	1.85697e10	−	3.19524e10i	0.0444407	−	0.0764679i
$805$	3.43341e11	+	3.43341e11i	0.817603	+	0.817603i
$806$	−2.24379e11	+	1.29118e11i	−0.531671	+	0.305948i
$807$	3.42774e11			0.808191
$808$	−2.00805e11	−	8.61060e8i	−0.471118	−	0.00202017i
$809$		−	1.08702e11i		−	0.253772i	−0.991917	−	0.126886i	$-0.959502\pi$
$809$		−	1.08702e11i		−	0.253772i	0.991917	−	0.126886i	$-0.0404982\pi$
$810$	7.98329e10	−	4.59395e10i	0.185456	−	0.106720i
$811$	2.78006e11	−	2.78006e11i	0.642644	−	0.642644i	−0.308561	−	0.951205i	$-0.599847\pi$
$811$	2.78006e11	−	2.78006e11i	0.642644	−	0.642644i	0.951205	+	0.308561i	$0.0998473\pi$
$812$	3.53228e11	−	9.35658e10i	0.812515	−	0.215225i
$813$	−1.66015e11	+	1.66015e11i	−0.380001	+	0.380001i
$814$	−1.92169e10	+	7.13105e10i	−0.0437709	+	0.162426i
$815$		−	1.29980e12i		−	2.94609i
$816$	−5.73827e10	+	2.09360e11i	−0.129426	+	0.472207i
$817$	7.41290e11			1.66380
$818$	1.91261e11	+	5.15413e10i	0.427182	+	0.115118i
$819$	−7.36357e10	−	7.36357e10i	−0.163664	−	0.163664i
$820$	2.75240e11	−	7.29077e10i	0.608774	−	0.161257i
$821$	5.15874e11	+	5.15874e11i	1.13546	+	1.13546i	0.989254	+	0.146205i	$0.0467058\pi$
$821$	5.15874e11	+	5.15874e11i	1.13546	+	1.13546i	0.146205	+	0.989254i	$0.453294\pi$
$822$	−2.58057e11	−	4.48447e11i	−0.565235	−	0.982255i
$823$	2.04831e11			0.446475			0.223237	−	0.974764i	$-0.428338\pi$
$823$	2.04831e11			0.446475			0.223237	+	0.974764i	$0.428338\pi$
$824$	1.94825e11	−	1.93161e11i	0.422606	−	0.418997i
$825$		−	1.28051e12i		−	2.76419i
$826$	−1.88820e11	−	3.28127e11i	−0.405627	−	0.704892i
$827$	−4.40214e11	+	4.40214e11i	−0.941113	+	0.941113i	−0.998360	−	0.0572466i	$-0.981768\pi$
$827$	−4.40214e11	+	4.40214e11i	−0.941113	+	0.941113i	0.0572466	+	0.998360i	$0.481768\pi$
$828$	5.66720e10	−	9.75139e10i	0.120572	−	0.207465i
$829$	−1.31620e11	+	1.31620e11i	−0.278679	+	0.278679i	−0.832581	−	0.553903i	$-0.813138\pi$
$829$	−1.31620e11	+	1.31620e11i	−0.278679	+	0.278679i	0.553903	+	0.832581i	$0.313138\pi$
$830$	1.06956e12	+	2.88226e11i	2.25368	+	0.607325i
$831$		−	8.99157e9i		−	0.0188552i
$832$	−2.79643e11	−	2.84481e11i	−0.583594	−	0.593691i
$833$	1.24258e11			0.258075
$834$	1.58372e10	−	5.87692e10i	0.0327352	−	0.121475i
$835$	−8.94245e10	−	8.94245e10i	−0.183955	−	0.183955i
$836$	7.05236e11	+	4.09861e11i	1.44381	+	0.839095i
$837$	−4.92126e10	−	4.92126e10i	−0.100271	−	0.100271i
$838$	−5.18995e11	+	2.98653e11i	−1.05241	+	0.605608i
$839$	−1.08257e11			−0.218478			−0.109239	−	0.994016i	$-0.534841\pi$
$839$	−1.08257e11			−0.218478			−0.109239	+	0.994016i	$0.534841\pi$
$840$	3.25068e11	+	3.27867e11i	0.652915	+	0.658538i
$841$		−	7.77811e9i		−	0.0155486i
$842$	7.74807e11	−	4.45859e11i	1.54151	−	0.887053i
$843$	−1.02197e11	+	1.02197e11i	−0.202361	+	0.202361i
$844$	1.49840e11	+	5.65672e11i	0.295295	+	1.11479i
$845$	2.13095e11	−	2.13095e11i	0.417971	−	0.417971i
$846$	−1.51957e10	+	5.63885e10i	−0.0296646	+	0.110080i
$847$			9.12112e11i			1.77221i
$848$	−6.82051e10	+	2.48845e11i	−0.131897	+	0.481223i
$849$	3.00579e11			0.578532
$850$	−1.15770e12	−	3.11978e11i	−2.21778	−	0.597652i
$851$	−2.54056e10	−	2.54056e10i	−0.0484408	−	0.0484408i
$852$	2.82711e10	+	1.06729e11i	0.0536519	+	0.202546i
$853$	1.79469e10	+	1.79469e10i	0.0338994	+	0.0338994i	0.723853	−	0.689954i	$-0.242369\pi$
$853$	1.79469e10	+	1.79469e10i	0.0338994	+	0.0338994i	−0.689954	+	0.723853i	$0.742369\pi$
$854$	2.78966e11	+	4.84783e11i	0.524470	+	0.911414i
$855$	−3.24063e11			−0.606408
$856$	2.02136e9	−	4.71397e11i	0.00376486	−	0.877994i
$857$			6.53199e11i			1.21094i	0.795869	+	0.605469i	$0.207015\pi$
$857$			6.53199e11i			1.21094i	−0.795869	+	0.605469i	$0.792985\pi$
$858$	2.29653e11	+	3.99087e11i	0.423763	+	0.736408i
$859$	5.64867e11	−	5.64867e11i	1.03747	−	1.03747i	0.0381958	−	0.999270i	$-0.487839\pi$
$859$	5.64867e11	−	5.64867e11i	1.03747	−	1.03747i	0.999270	−	0.0381958i	$-0.0121611\pi$
$860$	−1.60403e12	−	9.32208e11i	−2.93236	−	1.70419i
$861$	6.11969e10	−	6.11969e10i	0.111357	−	0.111357i
$862$	6.83195e11	+	1.84109e11i	1.23742	+	0.333461i
$863$			8.05296e11i			1.45182i	0.687790	+	0.725910i	$0.258581\pi$
$863$			8.05296e11i			1.45182i	−0.687790	+	0.725910i	$0.741419\pi$
$864$	5.42844e10	−	9.24905e10i	0.0974137	−	0.165975i
$865$	−1.70539e12			−3.04621
$866$	7.91167e10	−	2.93588e11i	0.140668	−	0.521996i
$867$	6.47756e10	+	6.47756e10i	0.114640	+	0.114640i
$868$	1.75295e11	−	3.01626e11i	0.308810	−	0.531361i
$869$	−4.46952e11	−	4.46952e11i	−0.783758	−	0.783758i
$870$	5.56354e11	−	3.20152e11i	0.971123	−	0.558829i
$871$	−7.33979e10			−0.127530
$872$	−1.36047e8	+	3.17272e10i	−0.000235301	+	0.0548739i
$873$			2.22897e11i			0.383750i
$874$	−3.43937e11	+	1.97917e11i	−0.589432	+	0.339186i
$875$	−1.13742e12	+	1.13742e12i	−1.94039	+	1.94039i
$876$	3.37618e11	−	8.94307e10i	0.573335	−	0.151869i
$877$	9.35590e10	−	9.35590e10i	0.158156	−	0.158156i	−0.623593	−	0.781749i	$-0.714328\pi$
$877$	9.35590e10	−	9.35590e10i	0.158156	−	0.158156i	0.781749	+	0.623593i	$0.214328\pi$
$878$	−1.05643e11	+	3.92024e11i	−0.177772	+	0.659682i
$879$		−	2.21374e11i		−	0.370827i
$880$	−1.01059e12	−	1.77374e12i	−1.68517	−	2.95773i
$881$	−2.27796e11			−0.378132			−0.189066	−	0.981964i	$-0.560546\pi$
$881$	−2.27796e11			−0.378132			−0.189066	+	0.981964i	$0.560546\pi$
$882$	−5.92725e10	−	1.59728e10i	−0.0979442	−	0.0263942i
$883$	1.11093e9	+	1.11093e9i	0.00182745	+	0.00182745i	0.708020	−	0.706192i	$-0.249589\pi$
$883$	1.11093e9	+	1.11093e9i	0.00182745	+	0.00182745i	−0.706192	+	0.708020i	$0.749589\pi$
$884$	4.16762e11	−	1.10395e11i	0.682464	−	0.180776i
$885$	−4.70241e11	−	4.70241e11i	−0.766563	−	0.766563i
$886$	−2.57173e10	−	4.46910e10i	−0.0417340	−	0.0725246i
$887$	−5.26042e11			−0.849819			−0.424909	−	0.905236i	$-0.639694\pi$
$887$	−5.26042e11			−0.849819			−0.424909	+	0.905236i	$0.639694\pi$
$888$	−2.40534e10	−	2.42606e10i	−0.0386835	−	0.0390167i
$889$			9.18030e10i			0.146977i
$890$	−5.53169e11	−	9.61287e11i	−0.881653	−	1.53212i
$891$	−8.75308e10	+	8.75308e10i	−0.138883	+	0.138883i
$892$	2.33162e11	−	4.01195e11i	0.368297	−	0.633719i
$893$	1.45289e11	−	1.45289e11i	0.228469	−	0.228469i
$894$	1.73130e11	+	4.66554e10i	0.271033	+	0.0730385i
$895$		−	5.02011e11i		−	0.782387i
$896$	5.17839e11	+	1.44323e11i	0.803457	+	0.223925i
$897$	−2.23999e11			−0.346001
$898$	7.72430e10	−	2.86635e11i	0.118783	−	0.440783i
$899$	−3.42962e11	−	3.42962e11i	−0.525057	−	0.525057i
$900$	5.12130e11	+	2.97634e11i	0.780567	+	0.453641i
$901$	−1.97188e11	−	1.97188e11i	−0.299214	−	0.299214i
$902$	−3.31672e11	+	1.90859e11i	−0.501051	+	0.288328i
$903$	−5.63906e11			−0.848117
$904$	−8.82436e11	+	8.74900e11i	−1.32132	+	1.31004i
$905$			7.43247e11i			1.10800i
$906$	3.29653e11	−	1.89698e11i	0.489265	−	0.281546i
$907$	−5.00955e11	+	5.00955e11i	−0.740235	+	0.740235i	−0.972623	−	0.232388i	$-0.925346\pi$
$907$	−5.00955e11	+	5.00955e11i	−0.740235	+	0.740235i	0.232388	+	0.972623i	$0.425346\pi$
$908$	1.04513e11	+	3.94555e11i	0.153754	+	0.580450i
$909$	−7.58147e10	+	7.58147e10i	−0.111045	+	0.111045i
$910$	2.38593e11	−	8.85376e11i	0.347930	−	1.29111i
$911$			9.77168e10i			0.141872i	0.997481	+	0.0709358i	$0.0225986\pi$
$911$			9.77168e10i			0.141872i	−0.997481	+	0.0709358i	$0.977401\pi$
$912$	−3.27841e11	+	1.86788e11i	−0.473897	+	0.270004i
$913$	−1.48871e12			−2.14253
$914$	8.52261e11	+	2.29669e11i	1.22120	+	0.329092i
$915$	6.94746e11	+	6.94746e11i	0.991155	+	0.991155i
$916$	−1.02516e11	−	3.87015e11i	−0.145616	−	0.549726i
$917$	3.68524e10	+	3.68524e10i	0.0521181	+	0.0521181i
$918$	5.78101e10	+	1.00461e11i	0.0814017	+	0.141458i
$919$	1.11051e12			1.55690			0.778450	−	0.627707i	$-0.216006\pi$
$919$	1.11051e12			1.55690			0.778450	+	0.627707i	$0.216006\pi$
$920$	9.93112e11	+	4.25849e9i	1.38627	+	0.00594435i
$921$		−	5.55915e10i		−	0.0772627i
$922$	3.26119e11	+	5.66724e11i	0.451287	+	0.784239i
$923$	1.55054e11	−	1.55054e11i	0.213637	−	0.213637i
$924$	−5.36479e11	−	3.11785e11i	−0.735978	−	0.427727i
$925$	1.33427e11	−	1.33427e11i	0.182254	−	0.182254i
$926$	−4.82110e11	−	1.29920e11i	−0.655695	−	0.176698i
$927$		−	1.46485e11i		−	0.198370i
$928$	3.78307e11	−	6.44564e11i	0.510096	−	0.869109i
$929$	−1.26338e10			−0.0169617			−0.00848086	−	0.999964i	$-0.502700\pi$
$929$	−1.26338e10			−0.0169617			−0.00848086	+	0.999964i	$0.502700\pi$
$930$	1.59457e11	−	5.91719e11i	0.213164	−	0.791013i
$931$	1.52720e11	+	1.52720e11i	0.203282	+	0.203282i
$932$	−6.55258e11	+	1.12748e12i	−0.868457	+	1.49433i
$933$	4.39457e11	+	4.39457e11i	0.579948	+	0.579948i
$934$	4.18957e11	−	2.41087e11i	0.550532	−	0.316801i
$935$	2.20634e12			2.88686
$936$	−2.12991e11	−	9.13311e8i	−0.277497	−	0.00118991i
$937$			1.26517e12i			1.64132i	0.571420	+	0.820658i	$0.306393\pi$
$937$			1.26517e12i			1.64132i	−0.571420	+	0.820658i	$0.693607\pi$
$938$	8.57303e10	−	4.93332e10i	0.110745	−	0.0637276i
$939$	5.65324e11	−	5.65324e11i	0.727169	−	0.727169i
$940$	−4.97090e11	+	1.31673e11i	−0.636683	+	0.168650i
$941$	2.66338e11	−	2.66338e11i	0.339683	−	0.339683i	−0.516565	−	0.856248i	$-0.672789\pi$
$941$	2.66338e11	−	2.66338e11i	0.339683	−	0.339683i	0.856248	+	0.516565i	$0.172789\pi$
$942$	2.34446e10	−	8.69988e10i	0.0297741	−	0.110487i
$943$		−	1.86161e11i		−	0.235419i
$944$	−7.46769e11	−	2.04679e11i	−0.940369	−	0.257742i
$945$	2.46517e11			0.309115
$946$	2.40746e12	+	6.48767e11i	3.00604	+	0.810073i
$947$	−3.02766e11	−	3.02766e11i	−0.376449	−	0.376449i	0.493370	−	0.869820i	$-0.335765\pi$
$947$	−3.02766e11	−	3.02766e11i	−0.376449	−	0.376449i	−0.869820	+	0.493370i	$0.835765\pi$
$948$	2.82642e11	−	7.48683e10i	0.349948	−	0.0926968i
$949$	−4.90487e11	−	4.90487e11i	−0.604731	−	0.604731i
$950$	−1.03944e12	−	1.80631e12i	−1.27615	−	2.21768i
$951$	−7.40304e11			−0.905082
$952$	−4.12587e11	+	4.09064e11i	−0.502305	+	0.498016i
$953$		−	6.40142e11i		−	0.776076i	−0.921643	−	0.388038i	$-0.873153\pi$
$953$		−	6.40142e11i		−	0.776076i	0.921643	−	0.388038i	$-0.126847\pi$
$954$	6.87132e10	+	1.19409e11i	0.0829558	+	0.144159i
$955$	5.70750e11	−	5.70750e11i	0.686171	−	0.686171i
$956$	−6.39235e11	+	1.09991e12i	−0.765296	+	1.31682i
$957$	−6.10001e11	+	6.10001e11i	−0.727248	+	0.727248i
$958$	−6.94368e11	−	1.87120e11i	−0.824381	−	0.222156i
$959$		−	1.38477e12i		−	1.63720i
$960$	9.44288e11	+	8.09841e9i	1.11178	+	0.00953487i
$961$	3.89832e11			0.457071
$962$	−1.76547e10	+	6.55136e10i	−0.0206139	+	0.0764947i
$963$	−1.77977e11	−	1.77977e11i	−0.206947	−	0.206947i
$964$	1.03874e12	+	6.03683e11i	1.20281	+	0.699038i
$965$	2.81970e11	+	2.81970e11i	0.325158	+	0.325158i
$966$	2.61636e11	−	1.50557e11i	0.300462	−	0.172900i
$967$	−1.07695e12			−1.23165			−0.615827	−	0.787882i	$-0.711178\pi$
$967$	−1.07695e12			−1.23165			−0.615827	+	0.787882i	$0.711178\pi$
$968$	1.31348e12	+	1.32480e12i	1.49597	+	1.50886i
$969$		−	4.07800e11i		−	0.462542i
$970$	−1.70114e12	+	9.78915e11i	−1.92156	+	1.10575i
$971$	1.14614e12	−	1.14614e12i	1.28932	−	1.28932i	0.354119	−	0.935201i	$-0.384781\pi$
$971$	1.14614e12	−	1.14614e12i	1.28932	−	1.28932i	0.935201	−	0.354119i	$-0.115219\pi$
$972$	−1.46622e10	−	5.53524e10i	−0.0164260	−	0.0620114i
$973$	1.15189e11	−	1.15189e11i	0.128517	−	0.128517i
$974$	−4.21609e11	+	1.56452e12i	−0.468462	+	1.73838i
$975$		−	1.17642e12i		−	1.30179i
$976$	1.10329e12	+	3.02398e11i	1.21588	+	0.333257i
$977$	−7.22995e11			−0.793519			−0.396759	−	0.917923i	$-0.629865\pi$
$977$	−7.22995e11			−0.793519			−0.396759	+	0.917923i	$0.629865\pi$
$978$	−7.80229e11	−	2.10257e11i	−0.852838	−	0.229824i
$979$	1.05398e12	+	1.05398e12i	1.14736	+	1.14736i
$980$	−1.38407e11	−	5.22514e11i	−0.150057	−	0.566492i
$981$	1.19787e10	+	1.19787e10i	0.0129340	+	0.0129340i
$982$	−7.63764e11	−	1.32726e12i	−0.821321	−	1.42728i
$983$	3.99184e11			0.427523			0.213761	−	0.976886i	$-0.431429\pi$
$983$	3.99184e11			0.427523			0.213761	+	0.976886i	$0.431429\pi$
$984$	7.59030e8	−	1.77012e11i	0.000809615	−	0.188808i
$985$		−	7.34944e10i		−	0.0780746i
$986$	4.02878e11	+	7.00114e11i	0.426251	+	0.740732i
$987$	−1.10523e11	+	1.10523e11i	−0.116462	+	0.116462i
$988$	6.47906e11	+	3.76542e11i	0.679962	+	0.395172i
$989$	−8.57699e11	+	8.57699e11i	−0.896499	+	0.896499i
$990$	−1.05245e12	−	2.83615e11i	−1.09562	−	0.295249i
$991$			9.09986e10i			0.0943496i	0.998887	+	0.0471748i	$0.0150218\pi$
$991$			9.09986e10i			0.0943496i	−0.998887	+	0.0471748i	$0.984978\pi$
$992$	−1.79747e11	−	6.90529e11i	−0.185616	−	0.713075i
$993$	5.51860e10			0.0567586
$994$	−7.68896e10	+	2.85324e11i	−0.0787629	+	0.292276i
$995$	1.36558e12	+	1.36558e12i	1.39323	+	1.39323i
$996$	3.46026e11	−	5.95398e11i	0.351619	−	0.605020i
$997$	−4.77092e11	−	4.77092e11i	−0.482860	−	0.482860i	0.423183	−	0.906044i	$-0.360913\pi$
$997$	−4.77092e11	−	4.77092e11i	−0.482860	−	0.482860i	−0.906044	+	0.423183i	$0.860913\pi$
$998$	−5.26009e11	+	3.02690e11i	−0.530238	+	0.305123i
$999$	−1.82411e10			−0.0183143

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.20	yes	64
4.3	odd	2		192.9.l.a.79.17		64
16.3	odd	4	inner	48.9.l.a.19.20	✓	64
16.13	even	4		192.9.l.a.175.17		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.20	✓	64	16.3	odd	4	inner
48.9.l.a.43.20	yes	64	1.1	even	1	trivial
192.9.l.a.79.17		64	4.3	odd	2
192.9.l.a.175.17		64	16.13	even	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.16319 - 15.4489i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-221.336 - 128.633i) q^{4} +(-851.062 - 851.062i) q^{5} +(-648.534 + 373.196i) q^{6} -2002.62 q^{7} +(-2908.70 + 2883.86i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(4.16319 - 15.4489i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-221.336 - 128.633i) q^{4} +(-851.062 - 851.062i) q^{5} +(-648.534 + 373.196i) q^{6} -2002.62 q^{7} +(-2908.70 + 2883.86i) q^{8} +2187.00i q^{9} +(-16691.1 + 9604.82i) q^{10} +(18300.5 - 18300.5i) q^{11} +(3065.49 + 11572.8i) q^{12} +(16812.8 - 16812.8i) q^{13} +(-8337.29 + 30938.2i) q^{14} +56286.0i q^{15} +(32443.0 + 56942.3i) q^{16} -70830.1 q^{17} +(33786.7 + 9104.90i) q^{18} +(-87054.1 - 87054.1i) q^{19} +(78895.5 + 297845. i) q^{20} +(66222.9 + 66222.9i) q^{21} +(-206534. - 358911. i) q^{22} +201450. q^{23} +(191549. + 821.368i) q^{24} +1.05799e6i q^{25} +(-189745. - 329735. i) q^{26} +(72320.0 - 72320.0i) q^{27} +(443251. + 257604. i) q^{28} +(503996. - 503996. i) q^{29} +(869556. + 234329. i) q^{30} -680484. i q^{31} +(1.01476e6 - 264146. i) q^{32} -1.21033e6 q^{33} +(-294879. + 1.09425e6i) q^{34} +(1.70435e6 + 1.70435e6i) q^{35} +(281321. - 484061. i) q^{36} +(-126114. - 126114. i) q^{37} +(-1.70731e6 + 982466. i) q^{38} -1.11194e6 q^{39} +(4.92983e6 + 21139.3i) q^{40} -924105. i q^{41} +(1.29877e6 - 747371. i) q^{42} +(-4.25764e6 + 4.25764e6i) q^{43} +(-6.40462e6 + 1.69650e6i) q^{44} +(1.86127e6 - 1.86127e6i) q^{45} +(838673. - 3.11217e6i) q^{46} +1.66895e6i q^{47} +(810145. - 2.95580e6i) q^{48} -1.75431e6 q^{49} +(1.63447e7 + 4.40460e6i) q^{50} +(2.34222e6 + 2.34222e6i) q^{51} +(-5.88397e6 + 1.55859e6i) q^{52} +(2.78396e6 + 2.78396e6i) q^{53} +(-816180. - 1.41834e6i) q^{54} -3.11497e7 q^{55} +(5.82503e6 - 5.77528e6i) q^{56} +5.75743e6i q^{57} +(-5.68794e6 - 9.88441e6i) q^{58} +(-8.35450e6 + 8.35450e6i) q^{59} +(7.24025e6 - 1.24581e7i) q^{60} +(1.23431e7 - 1.23431e7i) q^{61} +(-1.05127e7 - 2.83299e6i) q^{62} -4.37973e6i q^{63} +(143880. - 1.67766e7i) q^{64} -2.86175e7 q^{65} +(-5.03882e6 + 1.86982e7i) q^{66} +(-2.18279e6 - 2.18279e6i) q^{67} +(1.56772e7 + 9.11111e6i) q^{68} +(-6.66156e6 - 6.66156e6i) q^{69} +(3.34259e7 - 1.92348e7i) q^{70} +9.22237e6 q^{71} +(-6.30701e6 - 6.36133e6i) q^{72} -2.91733e7i q^{73} +(-2.47336e6 + 1.42328e6i) q^{74} +(3.49856e7 - 3.49856e7i) q^{75} +(8.07013e6 + 3.04662e7i) q^{76} +(-3.66490e7 + 3.66490e7i) q^{77} +(-4.62921e6 + 1.71782e7i) q^{78} -2.44229e7i q^{79} +(2.08504e7 - 7.60723e7i) q^{80} -4.78297e6 q^{81} +(-1.42764e7 - 3.84722e6i) q^{82} +(-4.06740e7 - 4.06740e7i) q^{83} +(-6.13902e6 - 2.31759e7i) q^{84} +(6.02808e7 + 6.02808e7i) q^{85} +(4.80504e7 + 8.35011e7i) q^{86} -3.33324e7 q^{87} +(-454561. + 1.06007e8i) q^{88} +5.75928e7i q^{89} +(-2.10057e7 - 3.65034e7i) q^{90} +(-3.36697e7 + 3.36697e7i) q^{91} +(-4.45880e7 - 2.59131e7i) q^{92} +(-2.25023e7 + 2.25023e7i) q^{93} +(2.57835e7 + 6.94817e6i) q^{94} +1.48177e8i q^{95} +(-4.22910e7 - 2.48214e7i) q^{96} +1.01919e8 q^{97} +(-7.30354e6 + 2.71022e7i) q^{98} +(4.00232e7 + 4.00232e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Introduction

L-functions

Modular forms

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Database

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