LMFDB - Embedded newform 64.12.e.a.17.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,12,Mod(17,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("64.17");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	64.e (of order $4$, degree $2$, not 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:	$49.1739635558$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.19
Character	$\chi$	$=$	64.17
Dual form			64.12.e.a.49.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(475.976 + 475.976i) q^{3} +(2805.14 - 2805.14i) q^{5} +76033.6i q^{7} +275960. i q^{9} +O(q^{10})$	\(q+(475.976 + 475.976i) q^{3} +(2805.14 - 2805.14i) q^{5} +76033.6i q^{7} +275960. i q^{9} +(-409752. + 409752. i) q^{11} +(-1.80631e6 - 1.80631e6i) q^{13} +2.67036e6 q^{15} -1.50853e6 q^{17} +(-5.45825e6 - 5.45825e6i) q^{19} +(-3.61902e7 + 3.61902e7i) q^{21} +2.28696e6i q^{23} +3.30905e7i q^{25} +(-4.70326e7 + 4.70326e7i) q^{27} +(4.38084e7 + 4.38084e7i) q^{29} -2.76655e7 q^{31} -3.90064e8 q^{33} +(2.13285e8 + 2.13285e8i) q^{35} +(2.40566e8 - 2.40566e8i) q^{37} -1.71953e9i q^{39} +1.08336e8i q^{41} +(-1.91015e8 + 1.91015e8i) q^{43} +(7.74106e8 + 7.74106e8i) q^{45} +1.72497e9 q^{47} -3.80378e9 q^{49} +(-7.18026e8 - 7.18026e8i) q^{51} +(-8.00868e7 + 8.00868e7i) q^{53} +2.29882e9i q^{55} -5.19599e9i q^{57} +(-6.70345e9 + 6.70345e9i) q^{59} +(9.82284e7 + 9.82284e7i) q^{61} -2.09822e10 q^{63} -1.01339e10 q^{65} +(-6.92288e9 - 6.92288e9i) q^{67} +(-1.08854e9 + 1.08854e9i) q^{69} +1.20473e9i q^{71} +2.00681e10i q^{73} +(-1.57503e10 + 1.57503e10i) q^{75} +(-3.11549e10 - 3.11549e10i) q^{77} +1.65053e10 q^{79} +4.11263e9 q^{81} +(-2.19541e10 - 2.19541e10i) q^{83} +(-4.23165e9 + 4.23165e9i) q^{85} +4.17036e10i q^{87} -3.11065e10i q^{89} +(1.37341e11 - 1.37341e11i) q^{91} +(-1.31681e10 - 1.31681e10i) q^{93} -3.06223e10 q^{95} -1.12128e9 q^{97} +(-1.13075e11 - 1.13075e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} - 2 q^{5}+O(q^{10}) $ 42 * q + 2 * q^3 - 2 * q^5	$ 42 q + 2 q^{3} - 2 q^{5} + 540846 q^{11} - 2 q^{13} + 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} + 354292 q^{21} + 66463304 q^{27} + 77673206 q^{29} - 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} - 522762058 q^{37} - 3824193658 q^{43} + 97301954 q^{45} + 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} - 2100608058 q^{53} - 955824746 q^{59} + 2150827022 q^{61} - 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} - 16193060732 q^{69} - 28890034486 q^{75} - 22711870540 q^{77} - 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} - 84575506252 q^{85} + 147369662716 q^{91} - 69689773328 q^{93} - 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) $ 42 * q + 2 * q^3 - 2 * q^5 + 540846 * q^11 - 2 * q^13 + 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 + 354292 * q^21 + 66463304 * q^27 + 77673206 * q^29 - 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 - 522762058 * q^37 - 3824193658 * q^43 + 97301954 * q^45 + 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 - 2100608058 * q^53 - 955824746 * q^59 + 2150827022 * q^61 - 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 - 16193060732 * q^69 - 28890034486 * q^75 - 22711870540 * q^77 - 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 - 84575506252 * q^85 + 147369662716 * q^91 - 69689773328 * q^93 - 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	475.976	+	475.976i	1.13089	+	1.13089i	0.990030	+	0.140855i	$0.0449851\pi$
$3$	475.976	+	475.976i	1.13089	+	1.13089i	0.140855	+	0.990030i	$0.455015\pi$
$4$		0			0
$5$	2805.14	−	2805.14i	0.401439	−	0.401439i	−0.477301	−	0.878740i	$-0.658385\pi$
$5$	2805.14	−	2805.14i	0.401439	−	0.401439i	0.878740	+	0.477301i	$0.158385\pi$
$6$		0			0
$7$			76033.6i			1.70988i	0.518725	+	0.854941i	$0.326407\pi$
$7$			76033.6i			1.70988i	−0.518725	+	0.854941i	$0.673593\pi$
$8$		0			0
$9$			275960.i			1.55780i
$10$		0			0
$11$	−409752.	+	409752.i	−0.767116	+	0.767116i	−0.977598	−	0.210482i	$-0.932497\pi$
$11$	−409752.	+	409752.i	−0.767116	+	0.767116i	0.210482	+	0.977598i	$0.432497\pi$
$12$		0			0
$13$	−1.80631e6	−	1.80631e6i	−1.34929	−	1.34929i	−0.886435	−	0.462853i	$-0.846826\pi$
$13$	−1.80631e6	−	1.80631e6i	−1.34929	−	1.34929i	−0.462853	−	0.886435i	$-0.653174\pi$
$14$		0			0
$15$	2.67036e6			0.907962
$16$		0			0
$17$	−1.50853e6			−0.257683			−0.128842	−	0.991665i	$-0.541126\pi$
$17$	−1.50853e6			−0.257683			−0.128842	+	0.991665i	$0.541126\pi$
$18$		0			0
$19$	−5.45825e6	−	5.45825e6i	−0.505718	−	0.505718i	0.407491	−	0.913209i	$-0.366404\pi$
$19$	−5.45825e6	−	5.45825e6i	−0.505718	−	0.505718i	−0.913209	+	0.407491i	$0.866404\pi$
$20$		0			0
$21$	−3.61902e7	+	3.61902e7i	−1.93368	+	1.93368i
$22$		0			0
$23$			2.28696e6i			0.0740893i	0.999314	+	0.0370446i	$0.0117944\pi$
$23$			2.28696e6i			0.0740893i	−0.999314	+	0.0370446i	$0.988206\pi$
$24$		0			0
$25$			3.30905e7i			0.677694i
$26$		0			0
$27$	−4.70326e7	+	4.70326e7i	−0.630810	+	0.630810i
$28$		0			0
$29$	4.38084e7	+	4.38084e7i	0.396615	+	0.396615i	0.877037	−	0.480422i	$-0.159517\pi$
$29$	4.38084e7	+	4.38084e7i	0.396615	+	0.396615i	−0.480422	+	0.877037i	$0.659517\pi$
$30$		0			0
$31$	−2.76655e7			−0.173560			−0.0867798	−	0.996228i	$-0.527658\pi$
$31$	−2.76655e7			−0.173560			−0.0867798	+	0.996228i	$0.527658\pi$
$32$		0			0
$33$	−3.90064e8			−1.73504
$34$		0			0
$35$	2.13285e8	+	2.13285e8i	0.686413	+	0.686413i
$36$		0			0
$37$	2.40566e8	−	2.40566e8i	0.570327	−	0.570327i	−0.361893	−	0.932220i	$-0.617869\pi$
$37$	2.40566e8	−	2.40566e8i	0.570327	−	0.570327i	0.932220	+	0.361893i	$0.117869\pi$
$38$		0			0
$39$		−	1.71953e9i		−	3.05178i
$40$		0			0
$41$			1.08336e8i			0.146037i	0.997331	+	0.0730184i	$0.0232632\pi$
$41$			1.08336e8i			0.146037i	−0.997331	+	0.0730184i	$0.976737\pi$
$42$		0			0
$43$	−1.91015e8	+	1.91015e8i	−0.198149	+	0.198149i	−0.799206	−	0.601057i	$-0.794746\pi$
$43$	−1.91015e8	+	1.91015e8i	−0.198149	+	0.198149i	0.601057	+	0.799206i	$0.294746\pi$
$44$		0			0
$45$	7.74106e8	+	7.74106e8i	0.625362	+	0.625362i
$46$		0			0
$47$	1.72497e9			1.09709			0.548547	−	0.836120i	$-0.315181\pi$
$47$	1.72497e9			1.09709			0.548547	+	0.836120i	$0.315181\pi$
$48$		0			0
$49$	−3.80378e9			−1.92370
$50$		0			0
$51$	−7.18026e8	−	7.18026e8i	−0.291410	−	0.291410i
$52$		0			0
$53$	−8.00868e7	+	8.00868e7i	−0.0263053	+	0.0263053i	−0.720137	−	0.693832i	$-0.755921\pi$
$53$	−8.00868e7	+	8.00868e7i	−0.0263053	+	0.0263053i	0.693832	+	0.720137i	$0.255921\pi$
$54$		0			0
$55$			2.29882e9i			0.615900i
$56$		0			0
$57$		−	5.19599e9i		−	1.14382i
$58$		0			0
$59$	−6.70345e9	+	6.70345e9i	−1.22071	+	1.22071i	−0.253328	+	0.967380i	$0.581525\pi$
$59$	−6.70345e9	+	6.70345e9i	−1.22071	+	1.22071i	−0.967380	+	0.253328i	$0.918475\pi$
$60$		0			0
$61$	9.82284e7	+	9.82284e7i	0.0148910	+	0.0148910i	0.714513	−	0.699622i	$-0.246648\pi$
$61$	9.82284e7	+	9.82284e7i	0.0148910	+	0.0148910i	−0.699622	+	0.714513i	$0.746648\pi$
$62$		0			0
$63$	−2.09822e10			−2.66366
$64$		0			0
$65$	−1.01339e10			−1.08331
$66$		0			0
$67$	−6.92288e9	−	6.92288e9i	−0.626434	−	0.626434i	0.320735	−	0.947169i	$-0.396070\pi$
$67$	−6.92288e9	−	6.92288e9i	−0.626434	−	0.626434i	−0.947169	+	0.320735i	$0.896070\pi$
$68$		0			0
$69$	−1.08854e9	+	1.08854e9i	−0.0837865	+	0.0837865i
$70$		0			0
$71$			1.20473e9i			0.0792443i	0.999215	+	0.0396221i	$0.0126154\pi$
$71$			1.20473e9i			0.0792443i	−0.999215	+	0.0396221i	$0.987385\pi$
$72$		0			0
$73$			2.00681e10i			1.13300i	0.824061	+	0.566501i	$0.191703\pi$
$73$			2.00681e10i			1.13300i	−0.824061	+	0.566501i	$0.808297\pi$
$74$		0			0
$75$	−1.57503e10	+	1.57503e10i	−0.766394	+	0.766394i
$76$		0			0
$77$	−3.11549e10	−	3.11549e10i	−1.31168	−	1.31168i
$78$		0			0
$79$	1.65053e10			0.603497			0.301748	−	0.953388i	$-0.402430\pi$
$79$	1.65053e10			0.603497			0.301748	+	0.953388i	$0.402430\pi$
$80$		0			0
$81$	4.11263e9			0.131054
$82$		0			0
$83$	−2.19541e10	−	2.19541e10i	−0.611768	−	0.611768i	0.331638	−	0.943407i	$-0.392399\pi$
$83$	−2.19541e10	−	2.19541e10i	−0.611768	−	0.611768i	−0.943407	+	0.331638i	$0.892399\pi$
$84$		0			0
$85$	−4.23165e9	+	4.23165e9i	−0.103444	+	0.103444i
$86$		0			0
$87$			4.17036e10i			0.897051i
$88$		0			0
$89$		−	3.11065e10i		−	0.590482i	−0.955423	−	0.295241i	$-0.904600\pi$
$89$		−	3.11065e10i		−	0.590482i	0.955423	−	0.295241i	$-0.0953999\pi$
$90$		0			0
$91$	1.37341e11	−	1.37341e11i	2.30712	−	2.30712i
$92$		0			0
$93$	−1.31681e10	−	1.31681e10i	−0.196276	−	0.196276i
$94$		0			0
$95$	−3.06223e10			−0.406030
$96$		0			0
$97$	−1.12128e9			−0.0132577			−0.00662884	−	0.999978i	$-0.502110\pi$
$97$	−1.12128e9			−0.0132577			−0.00662884	+	0.999978i	$0.502110\pi$
$98$		0			0
$99$	−1.13075e11	−	1.13075e11i	−1.19502	−	1.19502i
$100$		0			0
$101$	−6.44136e10	+	6.44136e10i	−0.609831	+	0.609831i	−0.942902	−	0.333071i	$-0.891915\pi$
$101$	−6.44136e10	+	6.44136e10i	−0.609831	+	0.609831i	0.333071	+	0.942902i	$0.391915\pi$
$102$		0			0
$103$			1.57692e11i			1.34031i	0.742220	+	0.670156i	$0.233773\pi$
$103$			1.57692e11i			1.34031i	−0.742220	+	0.670156i	$0.766227\pi$
$104$		0			0
$105$			2.03037e11i			1.55251i
$106$		0			0
$107$	−1.50680e11	+	1.50680e11i	−1.03859	+	1.03859i	−0.0393645	+	0.999225i	$0.512533\pi$
$107$	−1.50680e11	+	1.50680e11i	−1.03859	+	1.03859i	−0.999225	+	0.0393645i	$0.987467\pi$
$108$		0			0
$109$	1.00044e11	+	1.00044e11i	0.622793	+	0.622793i	0.946245	−	0.323452i	$-0.104843\pi$
$109$	1.00044e11	+	1.00044e11i	0.622793	+	0.622793i	−0.323452	+	0.946245i	$0.604843\pi$
$110$		0			0
$111$	2.29007e11			1.28995
$112$		0			0
$113$	−3.10659e11			−1.58618			−0.793090	−	0.609105i	$-0.791529\pi$
$113$	−3.10659e11			−1.58618			−0.793090	+	0.609105i	$0.791529\pi$
$114$		0			0
$115$	6.41524e9	+	6.41524e9i	0.0297423	+	0.0297423i
$116$		0			0
$117$	4.98470e11	−	4.98470e11i	2.10192	−	2.10192i
$118$		0			0
$119$		−	1.14699e11i		−	0.440608i
$120$		0			0
$121$		−	5.04814e10i		−	0.176934i
$122$		0			0
$123$	−5.15655e10	+	5.15655e10i	−0.165151	+	0.165151i
$124$		0			0
$125$	2.29793e11	+	2.29793e11i	0.673491	+	0.673491i
$126$		0			0
$127$	1.13068e11			0.303683			0.151842	−	0.988405i	$-0.451480\pi$
$127$	1.13068e11			0.303683			0.151842	+	0.988405i	$0.451480\pi$
$128$		0			0
$129$	−1.81837e11			−0.448167
$130$		0			0
$131$	4.98223e11	+	4.98223e11i	1.12832	+	1.12832i	0.990451	+	0.137868i	$0.0440249\pi$
$131$	4.98223e11	+	4.98223e11i	1.12832	+	1.12832i	0.137868	+	0.990451i	$0.455975\pi$
$132$		0			0
$133$	4.15010e11	−	4.15010e11i	0.864718	−	0.864718i
$134$		0			0
$135$			2.63866e11i			0.506463i
$136$		0			0
$137$			1.09163e11i			0.193246i	0.995321	+	0.0966231i	$0.0308041\pi$
$137$			1.09163e11i			0.193246i	−0.995321	+	0.0966231i	$0.969196\pi$
$138$		0			0
$139$	3.81502e11	−	3.81502e11i	0.623614	−	0.623614i	−0.322840	−	0.946454i	$-0.604638\pi$
$139$	3.81502e11	−	3.81502e11i	0.623614	−	0.623614i	0.946454	+	0.322840i	$0.104638\pi$
$140$		0			0
$141$	8.21045e11	+	8.21045e11i	1.24069	+	1.24069i
$142$		0			0
$143$	1.48028e12			2.07012
$144$		0			0
$145$	2.45777e11			0.318433
$146$		0			0
$147$	−1.81051e12	−	1.81051e12i	−2.17548	−	2.17548i
$148$		0			0
$149$	9.96155e11	−	9.96155e11i	1.11123	−	1.11123i	0.118241	−	0.992985i	$-0.462274\pi$
$149$	9.96155e11	−	9.96155e11i	1.11123	−	1.11123i	0.992985	−	0.118241i	$-0.0377256\pi$
$150$		0			0
$151$			7.33435e11i			0.760306i	0.924924	+	0.380153i	$0.124129\pi$
$151$			7.33435e11i			0.760306i	−0.924924	+	0.380153i	$0.875871\pi$
$152$		0			0
$153$		−	4.16295e11i		−	0.401419i
$154$		0			0
$155$	−7.76054e10	+	7.76054e10i	−0.0696735	+	0.0696735i
$156$		0			0
$157$	−1.44765e12	−	1.44765e12i	−1.21120	−	1.21120i	−0.970632	−	0.240569i	$-0.922666\pi$
$157$	−1.44765e12	−	1.44765e12i	−1.21120	−	1.21120i	−0.240569	−	0.970632i	$-0.577334\pi$
$158$		0			0
$159$	−7.62388e10			−0.0594966
$160$		0			0
$161$	−1.73886e11			−0.126684
$162$		0			0
$163$	3.22436e11	+	3.22436e11i	0.219488	+	0.219488i	0.808283	−	0.588795i	$-0.200397\pi$
$163$	3.22436e11	+	3.22436e11i	0.219488	+	0.219488i	−0.588795	+	0.808283i	$0.700397\pi$
$164$		0			0
$165$	−1.09418e12	+	1.09418e12i	−0.696512	+	0.696512i
$166$		0			0
$167$			2.78508e12i			1.65920i	0.558361	+	0.829598i	$0.311430\pi$
$167$			2.78508e12i			1.65920i	−0.558361	+	0.829598i	$0.688570\pi$
$168$		0			0
$169$			4.73338e12i			2.64116i
$170$		0			0
$171$	1.50626e12	−	1.50626e12i	0.787809	−	0.787809i
$172$		0			0
$173$	1.03081e12	+	1.03081e12i	0.505740	+	0.505740i	0.913216	−	0.407476i	$-0.133591\pi$
$173$	1.03081e12	+	1.03081e12i	0.505740	+	0.505740i	−0.407476	+	0.913216i	$0.633591\pi$
$174$		0			0
$175$	−2.51599e12			−1.15878
$176$		0			0
$177$	−6.38136e12			−2.76096
$178$		0			0
$179$	−1.53907e12	−	1.53907e12i	−0.625990	−	0.625990i	0.321066	−	0.947057i	$-0.395959\pi$
$179$	−1.53907e12	−	1.53907e12i	−0.625990	−	0.625990i	−0.947057	+	0.321066i	$0.895959\pi$
$180$		0			0
$181$	−1.04299e12	+	1.04299e12i	−0.399070	+	0.399070i	−0.877905	−	0.478835i	$-0.841059\pi$
$181$	−1.04299e12	+	1.04299e12i	−0.399070	+	0.399070i	0.478835	+	0.877905i	$0.341059\pi$
$182$		0			0
$183$			9.35088e10i			0.0336799i
$184$		0			0
$185$		−	1.34964e12i		−	0.457903i
$186$		0			0
$187$	6.18124e11	−	6.18124e11i	0.197673	−	0.197673i
$188$		0			0
$189$	−3.57606e12	−	3.57606e12i	−1.07861	−	1.07861i
$190$		0			0
$191$	5.44868e11			0.155099			0.0775494	−	0.996989i	$-0.475290\pi$
$191$	5.44868e11			0.155099			0.0775494	+	0.996989i	$0.475290\pi$
$192$		0			0
$193$	4.82936e12			1.29815			0.649074	−	0.760725i	$-0.275157\pi$
$193$	4.82936e12			1.29815			0.649074	+	0.760725i	$0.275157\pi$
$194$		0			0
$195$	−4.82350e12	−	4.82350e12i	−1.22510	−	1.22510i
$196$		0			0
$197$	1.97463e12	−	1.97463e12i	0.474156	−	0.474156i	−0.429101	−	0.903257i	$-0.641169\pi$
$197$	1.97463e12	−	1.97463e12i	0.474156	−	0.474156i	0.903257	+	0.429101i	$0.141169\pi$
$198$		0			0
$199$		−	8.29074e11i		−	0.188322i	−0.995557	−	0.0941610i	$-0.969983\pi$
$199$		−	8.29074e11i		−	0.188322i	0.995557	−	0.0941610i	$-0.0300169\pi$
$200$		0			0
$201$		−	6.59026e12i		−	1.41685i
$202$		0			0
$203$	−3.33091e12	+	3.33091e12i	−0.678165	+	0.678165i
$204$		0			0
$205$	3.03898e11	+	3.03898e11i	0.0586248	+	0.0586248i
$206$		0			0
$207$	−6.31109e11			−0.115416
$208$		0			0
$209$	4.47305e12			0.775889
$210$		0			0
$211$	6.62494e12	+	6.62494e12i	1.09051	+	1.09051i	0.995474	+	0.0950325i	$0.0302955\pi$
$211$	6.62494e12	+	6.62494e12i	1.09051	+	1.09051i	0.0950325	+	0.995474i	$0.469704\pi$
$212$		0			0
$213$	−5.73422e11	+	5.73422e11i	−0.0896162	+	0.0896162i
$214$		0			0
$215$			1.07165e12i			0.159089i
$216$		0			0
$217$		−	2.10350e12i		−	0.296767i
$218$		0			0
$219$	−9.55194e12	+	9.55194e12i	−1.28129	+	1.28129i
$220$		0			0
$221$	2.72488e12	+	2.72488e12i	0.347689	+	0.347689i
$222$		0			0
$223$	−4.00358e12			−0.486152			−0.243076	−	0.970007i	$-0.578156\pi$
$223$	−4.00358e12			−0.486152			−0.243076	+	0.970007i	$0.578156\pi$
$224$		0			0
$225$	−9.13166e12			−1.05571
$226$		0			0
$227$	3.84203e12	+	3.84203e12i	0.423076	+	0.423076i	0.886261	−	0.463185i	$-0.153294\pi$
$227$	3.84203e12	+	3.84203e12i	0.423076	+	0.423076i	−0.463185	+	0.886261i	$0.653294\pi$
$228$		0			0
$229$	2.03856e12	−	2.03856e12i	0.213909	−	0.213909i	−0.592017	−	0.805926i	$-0.701668\pi$
$229$	2.03856e12	−	2.03856e12i	0.213909	−	0.213909i	0.805926	+	0.592017i	$0.201668\pi$
$230$		0			0
$231$		−	2.96580e13i		−	2.96672i
$232$		0			0
$233$			1.18553e13i			1.13098i	0.824754	+	0.565491i	$0.191313\pi$
$233$			1.18553e13i			1.13098i	−0.824754	+	0.565491i	$0.808687\pi$
$234$		0			0
$235$	4.83878e12	−	4.83878e12i	0.440416	−	0.440416i
$236$		0			0
$237$	7.85614e12	+	7.85614e12i	0.682485	+	0.682485i
$238$		0			0
$239$	4.13763e11			0.0343213			0.0171606	−	0.999853i	$-0.494537\pi$
$239$	4.13763e11			0.0343213			0.0171606	+	0.999853i	$0.494537\pi$
$240$		0			0
$241$	−6.66336e12			−0.527958			−0.263979	−	0.964528i	$-0.585035\pi$
$241$	−6.66336e12			−0.527958			−0.263979	+	0.964528i	$0.585035\pi$
$242$		0			0
$243$	1.02892e13	+	1.02892e13i	0.779018	+	0.779018i
$244$		0			0
$245$	−1.06701e13	+	1.06701e13i	−0.772247	+	0.772247i
$246$		0			0
$247$			1.97186e13i			1.36472i
$248$		0			0
$249$		−	2.08993e13i		−	1.38368i
$250$		0			0
$251$	4.35293e12	−	4.35293e12i	0.275788	−	0.275788i	−0.555637	−	0.831425i	$-0.687525\pi$
$251$	4.35293e12	−	4.35293e12i	0.275788	−	0.275788i	0.831425	+	0.555637i	$0.187525\pi$
$252$		0			0
$253$	−9.37086e11	−	9.37086e11i	−0.0568351	−	0.0568351i
$254$		0			0
$255$	−4.02833e12			−0.233966
$256$		0			0
$257$	8.08461e12			0.449808			0.224904	−	0.974381i	$-0.427793\pi$
$257$	8.08461e12			0.449808			0.224904	+	0.974381i	$0.427793\pi$
$258$		0			0
$259$	1.82911e13	+	1.82911e13i	0.975193	+	0.975193i
$260$		0			0
$261$	−1.20894e13	+	1.20894e13i	−0.617847	+	0.617847i
$262$		0			0
$263$		−	1.83271e13i		−	0.898127i	−0.893500	−	0.449064i	$-0.851758\pi$
$263$		−	1.83271e13i		−	0.898127i	0.893500	−	0.449064i	$-0.148242\pi$
$264$		0			0
$265$			4.49309e11i			0.0211199i
$266$		0			0
$267$	1.48060e13	−	1.48060e13i	0.667767	−	0.667767i
$268$		0			0
$269$	−8.88707e12	−	8.88707e12i	−0.384699	−	0.384699i	0.488093	−	0.872792i	$-0.337693\pi$
$269$	−8.88707e12	−	8.88707e12i	−0.384699	−	0.384699i	−0.872792	+	0.488093i	$0.837693\pi$
$270$		0			0
$271$	3.04500e13			1.26548			0.632742	−	0.774363i	$-0.281929\pi$
$271$	3.04500e13			1.26548			0.632742	+	0.774363i	$0.281929\pi$
$272$		0			0
$273$	1.30742e14			5.21819
$274$		0			0
$275$	−1.35589e13	−	1.35589e13i	−0.519870	−	0.519870i
$276$		0			0
$277$	−1.57011e13	+	1.57011e13i	−0.578486	+	0.578486i	−0.934486	−	0.356000i	$-0.884140\pi$
$277$	−1.57011e13	+	1.57011e13i	−0.578486	+	0.578486i	0.356000	+	0.934486i	$0.384140\pi$
$278$		0			0
$279$		−	7.63456e12i		−	0.270371i
$280$		0			0
$281$			2.15542e13i			0.733919i	0.930237	+	0.366959i	$0.119601\pi$
$281$			2.15542e13i			0.733919i	−0.930237	+	0.366959i	$0.880399\pi$
$282$		0			0
$283$	9.93257e12	−	9.93257e12i	0.325264	−	0.325264i	−0.525518	−	0.850782i	$-0.676129\pi$
$283$	9.93257e12	−	9.93257e12i	0.325264	−	0.325264i	0.850782	+	0.525518i	$0.176129\pi$
$284$		0			0
$285$	−1.45755e13	−	1.45755e13i	−0.459173	−	0.459173i
$286$		0			0
$287$	−8.23719e12			−0.249706
$288$		0			0
$289$	−3.19962e13			−0.933599
$290$		0			0
$291$	−5.33701e11	−	5.33701e11i	−0.0149929	−	0.0149929i
$292$		0			0
$293$	3.63841e13	−	3.63841e13i	0.984327	−	0.984327i	−0.0155521	−	0.999879i	$-0.504951\pi$
$293$	3.63841e13	−	3.63841e13i	0.984327	−	0.984327i	0.999879	+	0.0155521i	$0.00495060\pi$
$294$		0			0
$295$			3.76082e13i			0.980079i
$296$		0			0
$297$		−	3.85434e13i		−	0.967809i
$298$		0			0
$299$	4.13097e12	−	4.13097e12i	0.0999678	−	0.0999678i
$300$		0			0
$301$	−1.45236e13	−	1.45236e13i	−0.338811	−	0.338811i
$302$		0			0
$303$	−6.13187e13			−1.37930
$304$		0			0
$305$	5.51088e11			0.0119556
$306$		0			0
$307$	4.26294e13	+	4.26294e13i	0.892171	+	0.892171i	0.994727	−	0.102556i	$-0.0327022\pi$
$307$	4.26294e13	+	4.26294e13i	0.892171	+	0.892171i	−0.102556	+	0.994727i	$0.532702\pi$
$308$		0			0
$309$	−7.50578e13	+	7.50578e13i	−1.51574	+	1.51574i
$310$		0			0
$311$		−	5.98356e13i		−	1.16621i	−0.812396	−	0.583106i	$-0.801837\pi$
$311$		−	5.98356e13i		−	1.16621i	0.812396	−	0.583106i	$-0.198163\pi$
$312$		0			0
$313$		−	6.26571e13i		−	1.17890i	−0.807805	−	0.589449i	$-0.799345\pi$
$313$		−	6.26571e13i		−	1.17890i	0.807805	−	0.589449i	$-0.200655\pi$
$314$		0			0
$315$	−5.88581e13	+	5.88581e13i	−1.06930	+	1.06930i
$316$		0			0
$317$	8.32656e12	+	8.32656e12i	0.146096	+	0.146096i	0.776372	−	0.630275i	$-0.217058\pi$
$317$	8.32656e12	+	8.32656e12i	0.146096	+	0.146096i	−0.630275	+	0.776372i	$0.717058\pi$
$318$		0			0
$319$	−3.59012e13			−0.608499
$320$		0			0
$321$	−1.43440e14			−2.34905
$322$		0			0
$323$	8.23395e12	+	8.23395e12i	0.130315	+	0.130315i
$324$		0			0
$325$	5.97719e13	−	5.97719e13i	0.914404	−	0.914404i
$326$		0			0
$327$			9.52368e13i			1.40862i
$328$		0			0
$329$			1.31156e14i			1.87590i
$330$		0			0
$331$	−8.11137e13	+	8.11137e13i	−1.12212	+	1.12212i	−0.130701	+	0.991422i	$0.541723\pi$
$331$	−8.11137e13	+	8.11137e13i	−1.12212	+	1.12212i	−0.991422	+	0.130701i	$0.958277\pi$
$332$		0			0
$333$	6.63865e13	+	6.63865e13i	0.888457	+	0.888457i
$334$		0			0
$335$	−3.88393e13			−0.502950
$336$		0			0
$337$	−5.00143e13			−0.626801			−0.313401	−	0.949621i	$-0.601468\pi$
$337$	−5.00143e13			−0.626801			−0.313401	+	0.949621i	$0.601468\pi$
$338$		0			0
$339$	−1.47866e14	−	1.47866e14i	−1.79379	−	1.79379i
$340$		0			0
$341$	1.13360e13	−	1.13360e13i	0.133140	−	0.133140i
$342$		0			0
$343$		−	1.38872e14i		−	1.57942i
$344$		0			0
$345$			6.10700e12i			0.0672703i
$346$		0			0
$347$	7.02184e13	−	7.02184e13i	0.749271	−	0.749271i	−0.225072	−	0.974342i	$-0.572262\pi$
$347$	7.02184e13	−	7.02184e13i	0.749271	−	0.749271i	0.974342	+	0.225072i	$0.0722616\pi$
$348$		0			0
$349$	−8.07392e13	−	8.07392e13i	−0.834728	−	0.834728i	0.153432	−	0.988159i	$-0.450968\pi$
$349$	−8.07392e13	−	8.07392e13i	−0.834728	−	0.834728i	−0.988159	+	0.153432i	$0.950968\pi$
$350$		0			0
$351$	1.69911e14			1.70229
$352$		0			0
$353$	−5.65562e13			−0.549186			−0.274593	−	0.961561i	$-0.588543\pi$
$353$	−5.65562e13			−0.549186			−0.274593	+	0.961561i	$0.588543\pi$
$354$		0			0
$355$	3.37943e12	+	3.37943e12i	0.0318117	+	0.0318117i
$356$		0			0
$357$	5.45941e13	−	5.45941e13i	0.498277	−	0.498277i
$358$		0			0
$359$		−	1.91411e13i		−	0.169413i	−0.996406	−	0.0847065i	$-0.973005\pi$
$359$		−	1.91411e13i		−	0.169413i	0.996406	−	0.0847065i	$-0.0269953\pi$
$360$		0			0
$361$		−	5.69053e13i		−	0.488499i
$362$		0			0
$363$	2.40280e13	−	2.40280e13i	0.200092	−	0.200092i
$364$		0			0
$365$	5.62938e13	+	5.62938e13i	0.454831	+	0.454831i
$366$		0			0
$367$	1.09458e14			0.858189			0.429095	−	0.903260i	$-0.358833\pi$
$367$	1.09458e14			0.858189			0.429095	+	0.903260i	$0.358833\pi$
$368$		0			0
$369$	−2.98965e13			−0.227496
$370$		0			0
$371$	−6.08929e12	−	6.08929e12i	−0.0449790	−	0.0449790i
$372$		0			0
$373$	−8.82988e13	+	8.82988e13i	−0.633222	+	0.633222i	−0.948875	−	0.315652i	$-0.897777\pi$
$373$	−8.82988e13	+	8.82988e13i	−0.633222	+	0.633222i	0.315652	+	0.948875i	$0.397777\pi$
$374$		0			0
$375$			2.18752e14i			1.52328i
$376$		0			0
$377$		−	1.58264e14i		−	1.07029i
$378$		0			0
$379$	8.73807e13	−	8.73807e13i	0.573984	−	0.573984i	−0.359255	−	0.933239i	$-0.616969\pi$
$379$	8.73807e13	−	8.73807e13i	0.573984	−	0.573984i	0.933239	+	0.359255i	$0.116969\pi$
$380$		0			0
$381$	5.38179e13	+	5.38179e13i	0.343431	+	0.343431i
$382$		0			0
$383$	−2.54041e14			−1.57511			−0.787555	−	0.616245i	$-0.788653\pi$
$383$	−2.54041e14			−1.57511			−0.787555	+	0.616245i	$0.788653\pi$
$384$		0			0
$385$	−1.74788e14			−1.05312
$386$		0			0
$387$	−5.27126e13	−	5.27126e13i	−0.308677	−	0.308677i
$388$		0			0
$389$	2.20478e14	−	2.20478e14i	1.25499	−	1.25499i	0.301540	−	0.953453i	$-0.402499\pi$
$389$	2.20478e14	−	2.20478e14i	1.25499	−	1.25499i	0.953453	−	0.301540i	$-0.0975008\pi$
$390$		0			0
$391$		−	3.44996e12i		−	0.0190916i
$392$		0			0
$393$			4.74285e14i			2.55200i
$394$		0			0
$395$	4.62997e13	−	4.62997e13i	0.242267	−	0.242267i
$396$		0			0
$397$	3.45645e13	+	3.45645e13i	0.175907	+	0.175907i	0.789569	−	0.613662i	$-0.210304\pi$
$397$	3.45645e13	+	3.45645e13i	0.175907	+	0.175907i	−0.613662	+	0.789569i	$0.710304\pi$
$398$		0			0
$399$	3.95070e14			1.95579
$400$		0			0
$401$	1.54405e14			0.743646			0.371823	−	0.928304i	$-0.378733\pi$
$401$	1.54405e14			0.743646			0.371823	+	0.928304i	$0.378733\pi$
$402$		0			0
$403$	4.99725e13	+	4.99725e13i	0.234182	+	0.234182i
$404$		0			0
$405$	1.15365e13	−	1.15365e13i	0.0526103	−	0.0526103i
$406$		0			0
$407$			1.97144e14i			0.875014i
$408$		0			0
$409$			2.08138e14i			0.899236i	0.893221	+	0.449618i	$0.148440\pi$
$409$			2.08138e14i			0.899236i	−0.893221	+	0.449618i	$0.851560\pi$
$410$		0			0
$411$	−5.19588e13	+	5.19588e13i	−0.218539	+	0.218539i
$412$		0			0
$413$	−5.09687e14	−	5.09687e14i	−2.08727	−	2.08727i
$414$		0			0
$415$	−1.23169e14			−0.491175
$416$		0			0
$417$	3.63172e14			1.41047
$418$		0			0
$419$	−2.92778e14	−	2.92778e14i	−1.10755	−	1.10755i	−0.993472	−	0.114073i	$-0.963610\pi$
$419$	−2.92778e14	−	2.92778e14i	−1.10755	−	1.10755i	−0.114073	−	0.993472i	$-0.536390\pi$
$420$		0			0
$421$	1.64588e14	−	1.64588e14i	0.606521	−	0.606521i	−0.335515	−	0.942035i	$-0.608910\pi$
$421$	1.64588e14	−	1.64588e14i	0.606521	−	0.606521i	0.942035	+	0.335515i	$0.108910\pi$
$422$		0			0
$423$			4.76023e14i			1.70905i
$424$		0			0
$425$		−	4.99182e13i		−	0.174630i
$426$		0			0
$427$	−7.46866e12	+	7.46866e12i	−0.0254618	+	0.0254618i
$428$		0			0
$429$	7.04578e14	+	7.04578e14i	2.34107	+	2.34107i
$430$		0			0
$431$	−2.93359e14			−0.950113			−0.475056	−	0.879955i	$-0.657572\pi$
$431$	−2.93359e14			−0.950113			−0.475056	+	0.879955i	$0.657572\pi$
$432$		0			0
$433$	2.65581e14			0.838519			0.419260	−	0.907866i	$-0.362290\pi$
$433$	2.65581e14			0.838519			0.419260	+	0.907866i	$0.362290\pi$
$434$		0			0
$435$	1.16984e14	+	1.16984e14i	0.360111	+	0.360111i
$436$		0			0
$437$	1.24828e13	−	1.24828e13i	0.0374683	−	0.0374683i
$438$		0			0
$439$			4.88728e14i			1.43058i	0.698828	+	0.715290i	$0.253705\pi$
$439$			4.88728e14i			1.43058i	−0.698828	+	0.715290i	$0.746295\pi$
$440$		0			0
$441$		−	1.04969e15i		−	2.99674i
$442$		0			0
$443$	2.17621e14	−	2.17621e14i	0.606010	−	0.606010i	−0.335891	−	0.941901i	$-0.609037\pi$
$443$	2.17621e14	−	2.17621e14i	0.606010	−	0.606010i	0.941901	+	0.335891i	$0.109037\pi$
$444$		0			0
$445$	−8.72581e13	−	8.72581e13i	−0.237042	−	0.237042i
$446$		0			0
$447$	9.48293e14			2.51334
$448$		0			0
$449$	−2.88213e14			−0.745346			−0.372673	−	0.927963i	$-0.621559\pi$
$449$	−2.88213e14			−0.745346			−0.372673	+	0.927963i	$0.621559\pi$
$450$		0			0
$451$	−4.43909e13	−	4.43909e13i	−0.112027	−	0.112027i
$452$		0			0
$453$	−3.49098e14	+	3.49098e14i	−0.859818	+	0.859818i
$454$		0			0
$455$		−	7.70518e14i		−	1.85234i
$456$		0			0
$457$			7.33246e14i			1.72072i	0.509685	+	0.860361i	$0.329762\pi$
$457$			7.33246e14i			1.72072i	−0.509685	+	0.860361i	$0.670238\pi$
$458$		0			0
$459$	7.09503e13	−	7.09503e13i	0.162549	−	0.162549i
$460$		0			0
$461$	1.64165e13	+	1.64165e13i	0.0367220	+	0.0367220i	0.725229	−	0.688507i	$-0.241734\pi$
$461$	1.64165e13	+	1.64165e13i	0.0367220	+	0.0367220i	−0.688507	+	0.725229i	$0.741734\pi$
$462$		0			0
$463$	−5.07863e14			−1.10931			−0.554653	−	0.832082i	$-0.687149\pi$
$463$	−5.07863e14			−1.10931			−0.554653	+	0.832082i	$0.687149\pi$
$464$		0			0
$465$	−7.38767e13			−0.157585
$466$		0			0
$467$	5.51057e14	+	5.51057e14i	1.14803	+	1.14803i	0.986939	+	0.161093i	$0.0515018\pi$
$467$	5.51057e14	+	5.51057e14i	1.14803	+	1.14803i	0.161093	+	0.986939i	$0.448498\pi$
$468$		0			0
$469$	5.26372e14	−	5.26372e14i	1.07113	−	1.07113i
$470$		0			0
$471$		−	1.37810e15i		−	2.73946i
$472$		0			0
$473$		−	1.56538e14i		−	0.304006i
$474$		0			0
$475$	1.80616e14	−	1.80616e14i	0.342722	−	0.342722i
$476$		0			0
$477$	−2.21007e13	−	2.21007e13i	−0.0409785	−	0.0409785i
$478$		0			0
$479$	3.92439e14			0.711094			0.355547	−	0.934658i	$-0.384295\pi$
$479$	3.92439e14			0.711094			0.355547	+	0.934658i	$0.384295\pi$
$480$		0			0
$481$	−8.69074e14			−1.53907
$482$		0			0
$483$	−8.27655e13	−	8.27655e13i	−0.143265	−	0.143265i
$484$		0			0
$485$	−3.14533e12	+	3.14533e12i	−0.00532215	+	0.00532215i
$486$		0			0
$487$		−	3.30426e14i		−	0.546594i	−0.961930	−	0.273297i	$-0.911886\pi$
$487$		−	3.30426e14i		−	0.546594i	0.961930	−	0.273297i	$-0.0881141\pi$
$488$		0			0
$489$			3.06944e14i			0.496432i
$490$		0			0
$491$	−4.42264e14	+	4.42264e14i	−0.699412	+	0.699412i	−0.964284	−	0.264871i	$-0.914670\pi$
$491$	−4.42264e14	+	4.42264e14i	−0.699412	+	0.699412i	0.264871	+	0.964284i	$0.414670\pi$
$492$		0			0
$493$	−6.60865e13	−	6.60865e13i	−0.102201	−	0.102201i
$494$		0			0
$495$	−6.34383e14			−0.959451
$496$		0			0
$497$	−9.15998e13			−0.135498
$498$		0			0
$499$	5.81971e14	+	5.81971e14i	0.842071	+	0.842071i	0.989128	−	0.147057i	$-0.0469802\pi$
$499$	5.81971e14	+	5.81971e14i	0.842071	+	0.842071i	−0.147057	+	0.989128i	$0.546980\pi$
$500$		0			0
$501$	−1.32563e15	+	1.32563e15i	−1.87636	+	1.87636i
$502$		0			0
$503$		−	5.90788e14i		−	0.818102i	−0.912512	−	0.409051i	$-0.865860\pi$
$503$		−	5.90788e14i		−	0.818102i	0.912512	−	0.409051i	$-0.134140\pi$
$504$		0			0
$505$			3.61378e14i			0.489620i
$506$		0			0
$507$	−2.25298e15	+	2.25298e15i	−2.98684	+	2.98684i
$508$		0			0
$509$	1.70291e14	+	1.70291e14i	0.220924	+	0.220924i	0.808887	−	0.587963i	$-0.200070\pi$
$509$	1.70291e14	+	1.70291e14i	0.220924	+	0.220924i	−0.587963	+	0.808887i	$0.700070\pi$
$510$		0			0
$511$	−1.52585e15			−1.93730
$512$		0			0
$513$	5.13432e14			0.638024
$514$		0			0
$515$	4.42349e14	+	4.42349e14i	0.538053	+	0.538053i
$516$		0			0
$517$	−7.06810e14	+	7.06810e14i	−0.841598	+	0.841598i
$518$		0			0
$519$			9.81287e14i			1.14387i
$520$		0			0
$521$		−	1.56998e15i		−	1.79179i	−0.444266	−	0.895895i	$-0.646535\pi$
$521$		−	1.56998e15i		−	1.79179i	0.444266	−	0.895895i	$-0.353465\pi$
$522$		0			0
$523$	8.14707e14	−	8.14707e14i	0.910421	−	0.910421i	−0.0858840	−	0.996305i	$-0.527371\pi$
$523$	8.14707e14	−	8.14707e14i	0.910421	−	0.910421i	0.996305	+	0.0858840i	$0.0273715\pi$
$524$		0			0
$525$	−1.19755e15	−	1.19755e15i	−1.31044	−	1.31044i
$526$		0			0
$527$	4.17343e13			0.0447234
$528$		0			0
$529$	9.47580e14			0.994511
$530$		0			0
$531$	−1.84988e15	−	1.84988e15i	−1.90162	−	1.90162i
$532$		0			0
$533$	1.95689e14	−	1.95689e14i	0.197046	−	0.197046i
$534$		0			0
$535$			8.45355e14i			0.833860i
$536$		0			0
$537$		−	1.46513e15i		−	1.41585i
$538$		0			0
$539$	1.55861e15	−	1.55861e15i	1.47570	−	1.47570i
$540$		0			0
$541$	−1.62507e14	−	1.62507e14i	−0.150760	−	0.150760i	0.627697	−	0.778458i	$-0.283998\pi$
$541$	−1.62507e14	−	1.62507e14i	−0.150760	−	0.150760i	−0.778458	+	0.627697i	$0.783998\pi$
$542$		0			0
$543$	−9.92880e14			−0.902605
$544$		0			0
$545$	5.61273e14			0.500026
$546$		0			0
$547$	3.52073e14	+	3.52073e14i	0.307399	+	0.307399i	0.843900	−	0.536501i	$-0.180254\pi$
$547$	3.52073e14	+	3.52073e14i	0.307399	+	0.307399i	−0.536501	+	0.843900i	$0.680254\pi$
$548$		0			0
$549$	−2.71071e13	+	2.71071e13i	−0.0231972	+	0.0231972i
$550$		0			0
$551$		−	4.78235e14i		−	0.401150i
$552$		0			0
$553$			1.25496e15i			1.03191i
$554$		0			0
$555$	6.42397e14	−	6.42397e14i	0.517835	−	0.517835i
$556$		0			0
$557$	−8.52294e13	−	8.52294e13i	−0.0673575	−	0.0673575i	0.672626	−	0.739983i	$-0.265166\pi$
$557$	−8.52294e13	−	8.52294e13i	−0.0673575	−	0.0673575i	−0.739983	+	0.672626i	$0.765166\pi$
$558$		0			0
$559$	6.90067e14			0.534720
$560$		0			0
$561$	5.88425e14			0.447091
$562$		0			0
$563$	6.50742e14	+	6.50742e14i	0.484856	+	0.484856i	0.906678	−	0.421823i	$-0.138610\pi$
$563$	6.50742e14	+	6.50742e14i	0.484856	+	0.484856i	−0.421823	+	0.906678i	$0.638610\pi$
$564$		0			0
$565$	−8.71441e14	+	8.71441e14i	−0.636754	+	0.636754i
$566$		0			0
$567$			3.12698e14i			0.224088i
$568$		0			0
$569$			1.48183e15i			1.04155i	0.853693	+	0.520777i	$0.174358\pi$
$569$			1.48183e15i			1.04155i	−0.853693	+	0.520777i	$0.825642\pi$
$570$		0			0
$571$	−8.55470e14	+	8.55470e14i	−0.589802	+	0.589802i	−0.937578	−	0.347776i	$-0.886937\pi$
$571$	−8.55470e14	+	8.55470e14i	−0.589802	+	0.589802i	0.347776	+	0.937578i	$0.386937\pi$
$572$		0			0
$573$	2.59345e14	+	2.59345e14i	0.175399	+	0.175399i
$574$		0			0
$575$	−7.56767e13			−0.0502099
$576$		0			0
$577$	2.53819e15			1.65218			0.826089	−	0.563539i	$-0.190561\pi$
$577$	2.53819e15			1.65218			0.826089	+	0.563539i	$0.190561\pi$
$578$		0			0
$579$	2.29866e15	+	2.29866e15i	1.46806	+	1.46806i
$580$		0			0
$581$	1.66925e15	−	1.66925e15i	1.04605	−	1.04605i
$582$		0			0
$583$		−	6.56314e13i		−	0.0403585i
$584$		0			0
$585$		−	2.79656e15i		−	1.68759i
$586$		0			0
$587$	−1.49682e14	+	1.49682e14i	−0.0886464	+	0.0886464i	−0.750039	−	0.661393i	$-0.769966\pi$
$587$	−1.49682e14	+	1.49682e14i	−0.0886464	+	0.0886464i	0.661393	+	0.750039i	$0.269966\pi$
$588$		0			0
$589$	1.51005e14	+	1.51005e14i	0.0877722	+	0.0877722i
$590$		0			0
$591$	1.87975e15			1.07243
$592$		0			0
$593$	−2.51255e14			−0.140706			−0.0703532	−	0.997522i	$-0.522413\pi$
$593$	−2.51255e14			−0.140706			−0.0703532	+	0.997522i	$0.522413\pi$
$594$		0			0
$595$	−3.21747e14	−	3.21747e14i	−0.176877	−	0.176877i
$596$		0			0
$597$	3.94619e14	−	3.94619e14i	0.212971	−	0.212971i
$598$		0			0
$599$		−	1.70110e15i		−	0.901329i	−0.892693	−	0.450665i	$-0.851187\pi$
$599$		−	1.70110e15i		−	0.901329i	0.892693	−	0.450665i	$-0.148813\pi$
$600$		0			0
$601$			2.33302e15i			1.21369i	0.794819	+	0.606847i	$0.207566\pi$
$601$			2.33302e15i			1.21369i	−0.794819	+	0.606847i	$0.792434\pi$
$602$		0			0
$603$	1.91044e15	−	1.91044e15i	0.975861	−	0.975861i
$604$		0			0
$605$	−1.41607e14	−	1.41607e14i	−0.0710283	−	0.0710283i
$606$		0			0
$607$	−1.91749e14			−0.0944486			−0.0472243	−	0.998884i	$-0.515038\pi$
$607$	−1.91749e14			−0.0944486			−0.0472243	+	0.998884i	$0.515038\pi$
$608$		0			0
$609$	−3.17087e15			−1.53385
$610$		0			0
$611$	−3.11584e15	−	3.11584e15i	−1.48029	−	1.48029i
$612$		0			0
$613$	−1.21713e14	+	1.21713e14i	−0.0567944	+	0.0567944i	−0.734934	−	0.678139i	$-0.762787\pi$
$613$	−1.21713e14	+	1.21713e14i	−0.0567944	+	0.0567944i	0.678139	+	0.734934i	$0.262787\pi$
$614$		0			0
$615$			2.89296e14i			0.132596i
$616$		0			0
$617$		−	5.95192e14i		−	0.267972i	−0.990983	−	0.133986i	$-0.957222\pi$
$617$		−	5.95192e14i		−	0.267972i	0.990983	−	0.133986i	$-0.0427777\pi$
$618$		0			0
$619$	−2.40823e15	+	2.40823e15i	−1.06512	+	1.06512i	−0.0673975	+	0.997726i	$0.521470\pi$
$619$	−2.40823e15	+	2.40823e15i	−1.06512	+	1.06512i	−0.997726	+	0.0673975i	$0.978530\pi$
$620$		0			0
$621$	−1.07562e14	−	1.07562e14i	−0.0467363	−	0.0467363i
$622$		0			0
$623$	2.36514e15			1.00965
$624$		0			0
$625$	−3.26546e14			−0.136963
$626$		0			0
$627$	2.12907e15	+	2.12907e15i	0.877441	+	0.877441i
$628$		0			0
$629$	−3.62901e14	+	3.62901e14i	−0.146964	+	0.146964i
$630$		0			0
$631$		−	4.59339e14i		−	0.182798i	−0.995814	−	0.0913991i	$-0.970866\pi$
$631$		−	4.59339e14i		−	0.182798i	0.995814	−	0.0913991i	$-0.0291339\pi$
$632$		0			0
$633$			6.30663e15i			2.46648i
$634$		0			0
$635$	3.17172e14	−	3.17172e14i	0.121910	−	0.121910i
$636$		0			0
$637$	6.87082e15	+	6.87082e15i	2.59562	+	2.59562i
$638$		0			0
$639$	−3.32457e14			−0.123447
$640$		0			0
$641$	−1.14966e14			−0.0419613			−0.0209807	−	0.999780i	$-0.506679\pi$
$641$	−1.14966e14			−0.0419613			−0.0209807	+	0.999780i	$0.506679\pi$
$642$		0			0
$643$	−1.76444e14	−	1.76444e14i	−0.0633061	−	0.0633061i	0.674745	−	0.738051i	$-0.264254\pi$
$643$	−1.76444e14	−	1.76444e14i	−0.0633061	−	0.0633061i	−0.738051	+	0.674745i	$0.764254\pi$
$644$		0			0
$645$	−5.10079e14	+	5.10079e14i	−0.179912	+	0.179912i
$646$		0			0
$647$			2.12407e15i			0.736540i	0.929719	+	0.368270i	$0.120050\pi$
$647$			2.12407e15i			0.736540i	−0.929719	+	0.368270i	$0.879950\pi$
$648$		0			0
$649$		−	5.49350e15i		−	1.87285i
$650$		0			0
$651$	1.00122e15	−	1.00122e15i	0.335609	−	0.335609i
$652$		0			0
$653$	−2.15088e15	−	2.15088e15i	−0.708913	−	0.708913i	0.257393	−	0.966307i	$-0.417136\pi$
$653$	−2.15088e15	−	2.15088e15i	−0.708913	−	0.708913i	−0.966307	+	0.257393i	$0.917136\pi$
$654$		0			0
$655$	2.79517e15			0.905901
$656$		0			0
$657$	−5.53799e15			−1.76499
$658$		0			0
$659$	−3.09422e14	−	3.09422e14i	−0.0969797	−	0.0969797i	0.656952	−	0.753932i	$-0.271845\pi$
$659$	−3.09422e14	−	3.09422e14i	−0.0969797	−	0.0969797i	−0.753932	+	0.656952i	$0.771845\pi$
$660$		0			0
$661$	3.62461e15	−	3.62461e15i	1.11726	−	1.11726i	0.125115	−	0.992142i	$-0.460070\pi$
$661$	3.62461e15	−	3.62461e15i	1.11726	−	1.11726i	0.992142	−	0.125115i	$-0.0399301\pi$
$662$		0			0
$663$			2.59396e15i			0.786392i
$664$		0			0
$665$		−	2.32832e15i		−	0.694263i
$666$		0			0
$667$	−1.00188e14	+	1.00188e14i	−0.0293849	+	0.0293849i
$668$		0			0
$669$	−1.90561e15	−	1.90561e15i	−0.549782	−	0.549782i
$670$		0			0
$671$	−8.04985e13			−0.0228462
$672$		0			0
$673$	−3.77117e14			−0.105291			−0.0526457	−	0.998613i	$-0.516765\pi$
$673$	−3.77117e14			−0.105291			−0.0526457	+	0.998613i	$0.516765\pi$
$674$		0			0
$675$	−1.55634e15	−	1.55634e15i	−0.427496	−	0.427496i
$676$		0			0
$677$	2.32594e15	−	2.32594e15i	0.628581	−	0.628581i	−0.319130	−	0.947711i	$-0.603391\pi$
$677$	2.32594e15	−	2.32594e15i	0.628581	−	0.628581i	0.947711	+	0.319130i	$0.103391\pi$
$678$		0			0
$679$		−	8.52546e13i		−	0.0226691i
$680$		0			0
$681$			3.65743e15i			0.956901i
$682$		0			0
$683$	1.34268e15	−	1.34268e15i	0.345669	−	0.345669i	−0.512825	−	0.858493i	$-0.671401\pi$
$683$	1.34268e15	−	1.34268e15i	0.345669	−	0.345669i	0.858493	+	0.512825i	$0.171401\pi$
$684$		0			0
$685$	3.06216e14	+	3.06216e14i	0.0775765	+	0.0775765i
$686$		0			0
$687$	1.94061e15			0.483812
$688$		0			0
$689$	2.89324e14			0.0709869
$690$		0			0
$691$	−1.81110e15	−	1.81110e15i	−0.437333	−	0.437333i	0.453781	−	0.891113i	$-0.350075\pi$
$691$	−1.81110e15	−	1.81110e15i	−0.437333	−	0.437333i	−0.891113	+	0.453781i	$0.850075\pi$
$692$		0			0
$693$	8.59751e15	−	8.59751e15i	2.04334	−	2.04334i
$694$		0			0
$695$		−	2.14033e15i		−	0.500685i
$696$		0			0
$697$		−	1.63429e14i		−	0.0376312i
$698$		0			0
$699$	−5.64286e15	+	5.64286e15i	−1.27901	+	1.27901i
$700$		0			0
$701$	−3.18446e15	−	3.18446e15i	−0.710537	−	0.710537i	0.256110	−	0.966648i	$-0.417559\pi$
$701$	−3.18446e15	−	3.18446e15i	−0.710537	−	0.710537i	−0.966648	+	0.256110i	$0.917559\pi$
$702$		0			0
$703$	−2.62613e15			−0.576850
$704$		0			0
$705$	4.60629e15			0.996119
$706$		0			0
$707$	−4.89760e15	−	4.89760e15i	−1.04274	−	1.04274i
$708$		0			0
$709$	−6.07734e15	+	6.07734e15i	−1.27397	+	1.27397i	−0.329982	+	0.943987i	$0.607043\pi$
$709$	−6.07734e15	+	6.07734e15i	−1.27397	+	1.27397i	−0.943987	+	0.329982i	$0.892957\pi$
$710$		0			0
$711$			4.55481e15i			0.940128i
$712$		0			0
$713$		−	6.32698e13i		−	0.0128589i
$714$		0			0
$715$	4.15239e15	−	4.15239e15i	0.831027	−	0.831027i
$716$		0			0
$717$	1.96941e14	+	1.96941e14i	0.0388134	+	0.0388134i
$718$		0			0
$719$	−6.62588e15			−1.28598			−0.642990	−	0.765874i	$-0.722306\pi$
$719$	−6.62588e15			−1.28598			−0.642990	+	0.765874i	$0.722306\pi$
$720$		0			0
$721$	−1.19899e16			−2.29178
$722$		0			0
$723$	−3.17160e15	−	3.17160e15i	−0.597060	−	0.597060i
$724$		0			0
$725$	−1.44964e15	+	1.44964e15i	−0.268783	+	0.268783i
$726$		0			0
$727$			9.23539e15i			1.68662i	0.537431	+	0.843308i	$0.319395\pi$
$727$			9.23539e15i			1.68662i	−0.537431	+	0.843308i	$0.680605\pi$
$728$		0			0
$729$			9.06630e15i			1.63090i
$730$		0			0
$731$	2.88153e14	−	2.88153e14i	0.0510596	−	0.0510596i
$732$		0			0
$733$	3.31578e15	+	3.31578e15i	0.578781	+	0.578781i	0.934567	−	0.355787i	$-0.115787\pi$
$733$	3.31578e15	+	3.31578e15i	0.578781	+	0.578781i	−0.355787	+	0.934567i	$0.615787\pi$
$734$		0			0
$735$	−1.01575e16			−1.74665
$736$		0			0
$737$	5.67333e15			0.961096
$738$		0			0
$739$	3.68264e14	+	3.68264e14i	0.0614632	+	0.0614632i	0.737170	−	0.675707i	$-0.236162\pi$
$739$	3.68264e14	+	3.68264e14i	0.0614632	+	0.0614632i	−0.675707	+	0.737170i	$0.736162\pi$
$740$		0			0
$741$	−9.38559e15	+	9.38559e15i	−1.54334	+	1.54334i
$742$		0			0
$743$			1.47188e15i			0.238469i	0.992866	+	0.119235i	$0.0380441\pi$
$743$			1.47188e15i			0.238469i	−0.992866	+	0.119235i	$0.961956\pi$
$744$		0			0
$745$		−	5.58870e15i		−	0.892178i
$746$		0			0
$747$	6.05847e15	−	6.05847e15i	0.953014	−	0.953014i
$748$		0			0
$749$	−1.14567e16	−	1.14567e16i	−1.77587	−	1.77587i
$750$		0			0
$751$	−3.16182e14			−0.0482966			−0.0241483	−	0.999708i	$-0.507687\pi$
$751$	−3.16182e14			−0.0482966			−0.0241483	+	0.999708i	$0.507687\pi$
$752$		0			0
$753$	4.14378e15			0.623770
$754$		0			0
$755$	2.05739e15	+	2.05739e15i	0.305216	+	0.305216i
$756$		0			0
$757$	−6.85861e15	+	6.85861e15i	−1.00279	+	1.00279i	−0.00279044	+	0.999996i	$0.500888\pi$
$757$	−6.85861e15	+	6.85861e15i	−1.00279	+	1.00279i	−0.999996	+	0.00279044i	$0.999112\pi$
$758$		0			0
$759$		−	8.92062e14i		−	0.128548i
$760$		0			0
$761$		−	1.01455e16i		−	1.44098i	−0.693465	−	0.720490i	$-0.743917\pi$
$761$		−	1.01455e16i		−	1.44098i	0.693465	−	0.720490i	$-0.256083\pi$
$762$		0			0
$763$	−7.60668e15	+	7.60668e15i	−1.06490	+	1.06490i
$764$		0			0
$765$	−1.16776e15	−	1.16776e15i	−0.161145	−	0.161145i
$766$		0			0
$767$	2.42170e16			3.29418
$768$		0			0
$769$	5.34284e14			0.0716436			0.0358218	−	0.999358i	$-0.488595\pi$
$769$	5.34284e14			0.0716436			0.0358218	+	0.999358i	$0.488595\pi$
$770$		0			0
$771$	3.84808e15	+	3.84808e15i	0.508681	+	0.508681i
$772$		0			0
$773$	5.03391e14	−	5.03391e14i	0.0656022	−	0.0656022i	−0.673545	−	0.739147i	$-0.735229\pi$
$773$	5.03391e14	−	5.03391e14i	0.0656022	−	0.0656022i	0.739147	+	0.673545i	$0.235229\pi$
$774$		0			0
$775$		−	9.15465e14i		−	0.117620i
$776$		0			0
$777$			1.74122e16i			2.20566i
$778$		0			0
$779$	5.91326e14	−	5.91326e14i	0.0738534	−	0.0738534i
$780$		0			0
$781$	−4.93639e14	−	4.93639e14i	−0.0607896	−	0.0607896i
$782$		0			0
$783$	−4.12085e15			−0.500377
$784$		0			0
$785$	−8.12173e15			−0.972446
$786$		0			0
$787$	−2.82819e15	−	2.82819e15i	−0.333924	−	0.333924i	0.520151	−	0.854075i	$-0.325876\pi$
$787$	−2.82819e15	−	2.82819e15i	−0.333924	−	0.333924i	−0.854075	+	0.520151i	$0.825876\pi$
$788$		0			0
$789$	8.72328e15	−	8.72328e15i	1.01568	−	1.01568i
$790$		0			0
$791$		−	2.36205e16i		−	2.71218i
$792$		0			0
$793$		−	3.54863e14i		−	0.0401844i
$794$		0			0
$795$	−2.13860e14	+	2.13860e14i	−0.0238842	+	0.0238842i
$796$		0			0
$797$	1.08811e16	+	1.08811e16i	1.19854	+	1.19854i	0.974604	+	0.223934i	$0.0718899\pi$
$797$	1.08811e16	+	1.08811e16i	1.19854	+	1.19854i	0.223934	+	0.974604i	$0.428110\pi$
$798$		0			0
$799$	−2.60218e15			−0.282702
$800$		0			0
$801$	8.58415e15			0.919854
$802$		0			0
$803$	−8.22294e15	−	8.22294e15i	−0.869144	−	0.869144i
$804$		0			0
$805$	−4.87774e14	+	4.87774e14i	−0.0508559	+	0.0508559i
$806$		0			0
$807$		−	8.46007e15i		−	0.870101i
$808$		0			0
$809$		−	1.10309e16i		−	1.11916i	−0.828776	−	0.559580i	$-0.810962\pi$
$809$		−	1.10309e16i		−	1.11916i	0.828776	−	0.559580i	$-0.189038\pi$
$810$		0			0
$811$	3.68941e15	−	3.68941e15i	0.369269	−	0.369269i	−0.497942	−	0.867211i	$-0.665911\pi$
$811$	3.68941e15	−	3.68941e15i	0.369269	−	0.369269i	0.867211	+	0.497942i	$0.165911\pi$
$812$		0			0
$813$	1.44935e16	+	1.44935e16i	1.43112	+	1.43112i
$814$		0			0
$815$	1.80895e15			0.176222
$816$		0			0
$817$	2.08522e15			0.200415
$818$		0			0
$819$	3.79005e16	+	3.79005e16i	3.59404	+	3.59404i
$820$		0			0
$821$	1.29997e16	−	1.29997e16i	1.21632	−	1.21632i	0.247406	−	0.968912i	$-0.420422\pi$
$821$	1.29997e16	−	1.29997e16i	1.21632	−	1.21632i	0.968912	−	0.247406i	$-0.0795780\pi$
$822$		0			0
$823$		−	9.57009e15i		−	0.883521i	−0.897133	−	0.441760i	$-0.854354\pi$
$823$		−	9.57009e15i		−	0.883521i	0.897133	−	0.441760i	$-0.145646\pi$
$824$		0			0
$825$		−	1.29074e16i		−	1.17583i
$826$		0			0
$827$	−2.06170e15	+	2.06170e15i	−0.185330	+	0.185330i	−0.793674	−	0.608344i	$-0.791834\pi$
$827$	−2.06170e15	+	2.06170e15i	−0.185330	+	0.185330i	0.608344	+	0.793674i	$0.291834\pi$
$828$		0			0
$829$	−9.19446e15	−	9.19446e15i	−0.815598	−	0.815598i	0.169869	−	0.985467i	$-0.445666\pi$
$829$	−9.19446e15	−	9.19446e15i	−0.815598	−	0.815598i	−0.985467	+	0.169869i	$0.945666\pi$
$830$		0			0
$831$	−1.49467e16			−1.30840
$832$		0			0
$833$	5.73813e15			0.495705
$834$		0			0
$835$	7.81254e15	+	7.81254e15i	0.666065	+	0.666065i
$836$		0			0
$837$	1.30118e15	−	1.30118e15i	0.109483	−	0.109483i
$838$		0			0
$839$			1.17712e16i			0.977528i	0.872416	+	0.488764i	$0.162552\pi$
$839$			1.17712e16i			0.977528i	−0.872416	+	0.488764i	$0.837448\pi$
$840$		0			0
$841$		−	8.36215e15i		−	0.685394i
$842$		0			0
$843$	−1.02593e16	+	1.02593e16i	−0.829978	+	0.829978i
$844$		0			0
$845$	1.32778e16	+	1.32778e16i	1.06026	+	1.06026i
$846$		0			0
$847$	3.83828e15			0.302537
$848$		0			0
$849$	9.45533e15			0.735673
$850$		0			0
$851$	5.50164e14	+	5.50164e14i	0.0422551	+	0.0422551i
$852$		0			0
$853$	−9.41578e15	+	9.41578e15i	−0.713899	+	0.713899i	−0.967349	−	0.253450i	$-0.918435\pi$
$853$	−9.41578e15	+	9.41578e15i	−0.713899	+	0.713899i	0.253450	+	0.967349i	$0.418435\pi$
$854$		0			0
$855$		−	8.45052e15i		−	0.632514i
$856$		0			0
$857$		−	3.55343e14i		−	0.0262575i	−0.999914	−	0.0131287i	$-0.995821\pi$
$857$		−	3.55343e14i		−	0.0262575i	0.999914	−	0.0131287i	$-0.00417913\pi$
$858$		0			0
$859$	1.10513e16	−	1.10513e16i	0.806216	−	0.806216i	−0.177843	−	0.984059i	$-0.556912\pi$
$859$	1.10513e16	−	1.10513e16i	0.806216	−	0.806216i	0.984059	+	0.177843i	$0.0569118\pi$
$860$		0			0
$861$	−3.92071e15	−	3.92071e15i	−0.282389	−	0.282389i
$862$		0			0
$863$	−1.12704e16			−0.801460			−0.400730	−	0.916196i	$-0.631243\pi$
$863$	−1.12704e16			−0.801460			−0.400730	+	0.916196i	$0.631243\pi$
$864$		0			0
$865$	5.78315e15			0.406047
$866$		0			0
$867$	−1.52294e16	−	1.52294e16i	−1.05579	−	1.05579i
$868$		0			0
$869$	−6.76308e15	+	6.76308e15i	−0.462952	+	0.462952i
$870$		0			0
$871$			2.50098e16i			1.69048i
$872$		0			0
$873$		−	3.09427e14i		−	0.0206529i
$874$		0			0
$875$	−1.74720e16	+	1.74720e16i	−1.15159	+	1.15159i
$876$		0			0
$877$	−1.18211e16	−	1.18211e16i	−0.769414	−	0.769414i	0.208589	−	0.978003i	$-0.433113\pi$
$877$	−1.18211e16	−	1.18211e16i	−0.769414	−	0.769414i	−0.978003	+	0.208589i	$0.933113\pi$
$878$		0			0
$879$	3.46359e16			2.22632
$880$		0			0
$881$	1.37908e16			0.875430			0.437715	−	0.899114i	$-0.355788\pi$
$881$	1.37908e16			0.875430			0.437715	+	0.899114i	$0.355788\pi$
$882$		0			0
$883$	−2.35176e15	−	2.35176e15i	−0.147438	−	0.147438i	0.629534	−	0.776973i	$-0.283246\pi$
$883$	−2.35176e15	−	2.35176e15i	−0.147438	−	0.147438i	−0.776973	+	0.629534i	$0.783246\pi$
$884$		0			0
$885$	−1.79006e16	+	1.79006e16i	−1.10836	+	1.10836i
$886$		0			0
$887$		−	7.28863e15i		−	0.445724i	−0.974850	−	0.222862i	$-0.928460\pi$
$887$		−	7.28863e15i		−	0.445724i	0.974850	−	0.222862i	$-0.0715399\pi$
$888$		0			0
$889$			8.59700e15i			0.519263i
$890$		0			0
$891$	−1.68516e15	+	1.68516e15i	−0.100534	+	0.100534i
$892$		0			0
$893$	−9.41532e15	−	9.41532e15i	−0.554820	−	0.554820i
$894$		0			0
$895$	−8.63463e15			−0.502593
$896$		0			0
$897$	3.93248e15			0.226104
$898$		0			0
$899$	−1.21198e15	−	1.21198e15i	−0.0688363	−	0.0688363i
$900$		0			0
$901$	1.20814e14	−	1.20814e14i	0.00677844	−	0.00677844i
$902$		0			0
$903$		−	1.38258e16i		−	0.766313i
$904$		0			0
$905$			5.85148e15i			0.320404i
$906$		0			0
$907$	1.38649e16	−	1.38649e16i	0.750026	−	0.750026i	−0.224457	−	0.974484i	$-0.572061\pi$
$907$	1.38649e16	−	1.38649e16i	0.750026	−	0.750026i	0.974484	+	0.224457i	$0.0720610\pi$
$908$		0			0
$909$	−1.77756e16	−	1.77756e16i	−0.949997	−	0.949997i
$910$		0			0
$911$	−4.60466e15			−0.243134			−0.121567	−	0.992583i	$-0.538792\pi$
$911$	−4.60466e15			−0.243134			−0.121567	+	0.992583i	$0.538792\pi$
$912$		0			0
$913$	1.79915e16			0.938595
$914$		0			0
$915$	2.62305e14	+	2.62305e14i	0.0135204	+	0.0135204i
$916$		0			0
$917$	−3.78817e16	+	3.78817e16i	−1.92929	+	1.92929i
$918$		0			0
$919$			3.57692e15i			0.180000i	0.995942	+	0.0900002i	$0.0286868\pi$
$919$			3.57692e15i			0.180000i	−0.995942	+	0.0900002i	$0.971313\pi$
$920$		0			0
$921$			4.05812e16i			2.01789i
$922$		0			0
$923$	2.17612e15	−	2.17612e15i	0.106923	−	0.106923i
$924$		0			0
$925$	7.96044e15	+	7.96044e15i	0.386507	+	0.386507i
$926$		0			0
$927$	−4.35168e16			−2.08794
$928$		0			0
$929$	−2.60435e16			−1.23484			−0.617422	−	0.786632i	$-0.711823\pi$
$929$	−2.60435e16			−1.23484			−0.617422	+	0.786632i	$0.711823\pi$
$930$		0			0
$931$	2.07620e16	+	2.07620e16i	0.972849	+	0.972849i
$932$		0			0
$933$	2.84804e16	−	2.84804e16i	1.31885	−	1.31885i
$934$		0			0
$935$		−	3.46785e15i		−	0.158707i
$936$		0			0
$937$		−	3.91020e16i		−	1.76861i	−0.466912	−	0.884304i	$-0.654633\pi$
$937$		−	3.91020e16i		−	1.76861i	0.466912	−	0.884304i	$-0.345367\pi$
$938$		0			0
$939$	2.98233e16	−	2.98233e16i	1.33320	−	1.33320i
$940$		0			0
$941$	3.89415e15	+	3.89415e15i	0.172056	+	0.172056i	0.787882	−	0.615826i	$-0.211178\pi$
$941$	3.89415e15	+	3.89415e15i	0.172056	+	0.172056i	−0.615826	+	0.787882i	$0.711178\pi$
$942$		0			0
$943$	−2.47760e14			−0.0108198
$944$		0			0
$945$	−2.00627e16			−0.865993
$946$		0			0
$947$	−2.18994e16	−	2.18994e16i	−0.934346	−	0.934346i	0.0636279	−	0.997974i	$-0.479733\pi$
$947$	−2.18994e16	−	2.18994e16i	−0.934346	−	0.934346i	−0.997974	+	0.0636279i	$0.979733\pi$
$948$		0			0
$949$	3.62493e16	−	3.62493e16i	1.52875	−	1.52875i
$950$		0			0
$951$			7.92649e15i			0.330436i
$952$		0			0
$953$		−	1.83361e16i		−	0.755607i	−0.925886	−	0.377803i	$-0.876680\pi$
$953$		−	1.83361e16i		−	0.755607i	0.925886	−	0.377803i	$-0.123320\pi$
$954$		0			0
$955$	1.52843e15	−	1.52843e15i	0.0622626	−	0.0622626i
$956$		0			0
$957$	−1.70881e16	−	1.70881e16i	−0.688143	−	0.688143i
$958$		0			0
$959$	−8.30003e15			−0.330428
$960$		0			0
$961$	−2.46431e16			−0.969877
$962$		0			0
$963$	−4.15816e16	−	4.15816e16i	−1.61792	−	1.61792i
$964$		0			0
$965$	1.35470e16	−	1.35470e16i	0.521127	−	0.521127i
$966$		0			0
$967$			4.02755e16i			1.53178i	0.642974	+	0.765888i	$0.277700\pi$
$967$			4.02755e16i			1.53178i	−0.642974	+	0.765888i	$0.722300\pi$
$968$		0			0
$969$			7.83833e15i			0.294743i
$970$		0			0
$971$	6.03111e15	−	6.03111e15i	0.224229	−	0.224229i	−0.586048	−	0.810276i	$-0.699317\pi$
$971$	6.03111e15	−	6.03111e15i	0.224229	−	0.224229i	0.810276	+	0.586048i	$0.199317\pi$
$972$		0			0
$973$	2.90070e16	+	2.90070e16i	1.06631	+	1.06631i
$974$		0			0
$975$	5.69000e16			2.06817
$976$		0			0
$977$	4.37405e16			1.57204			0.786020	−	0.618201i	$-0.212138\pi$
$977$	4.37405e16			1.57204			0.786020	+	0.618201i	$0.212138\pi$
$978$		0			0
$979$	1.27460e16	+	1.27460e16i	0.452968	+	0.452968i
$980$		0			0
$981$	−2.76080e16	+	2.76080e16i	−0.970189	+	0.970189i
$982$		0			0
$983$		−	4.47204e16i		−	1.55404i	−0.629477	−	0.777019i	$-0.716731\pi$
$983$		−	4.47204e16i		−	1.55404i	0.629477	−	0.777019i	$-0.283269\pi$
$984$		0			0
$985$		−	1.10782e16i		−	0.380689i
$986$		0			0
$987$	−6.24270e16	+	6.24270e16i	−2.12143	+	2.12143i
$988$		0			0
$989$	−4.36844e14	−	4.36844e14i	−0.0146807	−	0.0146807i
$990$		0			0
$991$	−6.29973e15			−0.209371			−0.104686	−	0.994505i	$-0.533384\pi$
$991$	−6.29973e15			−0.209371			−0.104686	+	0.994505i	$0.533384\pi$
$992$		0			0
$993$	−7.72164e16			−2.53798
$994$		0			0
$995$	−2.32567e15	−	2.32567e15i	−0.0755997	−	0.0755997i
$996$		0			0
$997$	−1.47683e16	+	1.47683e16i	−0.474796	+	0.474796i	−0.903463	−	0.428666i	$-0.858984\pi$
$997$	−1.47683e16	+	1.47683e16i	−0.474796	+	0.474796i	0.428666	+	0.903463i	$0.358984\pi$
$998$		0			0
$999$			2.26289e16i			0.719537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.12.e.a.17.19		42
4.3	odd	2		16.12.e.a.13.4	yes	42
8.3	odd	2		128.12.e.b.33.19		42
8.5	even	2		128.12.e.a.33.3		42
16.3	odd	4		128.12.e.b.97.19		42
16.5	even	4	inner	64.12.e.a.49.19		42
16.11	odd	4		16.12.e.a.5.4	✓	42
16.13	even	4		128.12.e.a.97.3		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.4	✓	42	16.11	odd	4
16.12.e.a.13.4	yes	42	4.3	odd	2
64.12.e.a.17.19		42	1.1	even	1	trivial
64.12.e.a.49.19		42	16.5	even	4	inner
128.12.e.a.33.3		42	8.5	even	2
128.12.e.a.97.3		42	16.13	even	4
128.12.e.b.33.19		42	8.3	odd	2
128.12.e.b.97.19		42	16.3	odd	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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(475.976 + 475.976i) q^{3} +(2805.14 - 2805.14i) q^{5} +76033.6i q^{7} +275960. i q^{9} +O(q^{10})\)	\(q+(475.976 + 475.976i) q^{3} +(2805.14 - 2805.14i) q^{5} +76033.6i q^{7} +275960. i q^{9} +(-409752. + 409752. i) q^{11} +(-1.80631e6 - 1.80631e6i) q^{13} +2.67036e6 q^{15} -1.50853e6 q^{17} +(-5.45825e6 - 5.45825e6i) q^{19} +(-3.61902e7 + 3.61902e7i) q^{21} +2.28696e6i q^{23} +3.30905e7i q^{25} +(-4.70326e7 + 4.70326e7i) q^{27} +(4.38084e7 + 4.38084e7i) q^{29} -2.76655e7 q^{31} -3.90064e8 q^{33} +(2.13285e8 + 2.13285e8i) q^{35} +(2.40566e8 - 2.40566e8i) q^{37} -1.71953e9i q^{39} +1.08336e8i q^{41} +(-1.91015e8 + 1.91015e8i) q^{43} +(7.74106e8 + 7.74106e8i) q^{45} +1.72497e9 q^{47} -3.80378e9 q^{49} +(-7.18026e8 - 7.18026e8i) q^{51} +(-8.00868e7 + 8.00868e7i) q^{53} +2.29882e9i q^{55} -5.19599e9i q^{57} +(-6.70345e9 + 6.70345e9i) q^{59} +(9.82284e7 + 9.82284e7i) q^{61} -2.09822e10 q^{63} -1.01339e10 q^{65} +(-6.92288e9 - 6.92288e9i) q^{67} +(-1.08854e9 + 1.08854e9i) q^{69} +1.20473e9i q^{71} +2.00681e10i q^{73} +(-1.57503e10 + 1.57503e10i) q^{75} +(-3.11549e10 - 3.11549e10i) q^{77} +1.65053e10 q^{79} +4.11263e9 q^{81} +(-2.19541e10 - 2.19541e10i) q^{83} +(-4.23165e9 + 4.23165e9i) q^{85} +4.17036e10i q^{87} -3.11065e10i q^{89} +(1.37341e11 - 1.37341e11i) q^{91} +(-1.31681e10 - 1.31681e10i) q^{93} -3.06223e10 q^{95} -1.12128e9 q^{97} +(-1.13075e11 - 1.13075e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) 42 * q + 2 * q^3 - 2 * q^5	\( 42 q + 2 q^{3} - 2 q^{5} + 540846 q^{11} - 2 q^{13} + 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} + 354292 q^{21} + 66463304 q^{27} + 77673206 q^{29} - 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} - 522762058 q^{37} - 3824193658 q^{43} + 97301954 q^{45} + 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} - 2100608058 q^{53} - 955824746 q^{59} + 2150827022 q^{61} - 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} - 16193060732 q^{69} - 28890034486 q^{75} - 22711870540 q^{77} - 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} - 84575506252 q^{85} + 147369662716 q^{91} - 69689773328 q^{93} - 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) \) 42 * q + 2 * q^3 - 2 * q^5 + 540846 * q^11 - 2 * q^13 + 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 + 354292 * q^21 + 66463304 * q^27 + 77673206 * q^29 - 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 - 522762058 * q^37 - 3824193658 * q^43 + 97301954 * q^45 + 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 - 2100608058 * q^53 - 955824746 * q^59 + 2150827022 * q^61 - 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 - 16193060732 * q^69 - 28890034486 * q^75 - 22711870540 * q^77 - 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 - 84575506252 * q^85 + 147369662716 * q^91 - 69689773328 * q^93 - 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more