LMFDB - Embedded newform 128.12.e.b.33.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,12,Mod(33,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, 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("128.33");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	128.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:	$98.3479271116$
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			33.9
Character	$\chi$	$=$	128.33
Dual form			128.12.e.b.97.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-137.041 - 137.041i) q^{3} +(-3899.66 + 3899.66i) q^{5} -37938.5i q^{7} -139586. i q^{9} +O(q^{10})$	\(q+(-137.041 - 137.041i) q^{3} +(-3899.66 + 3899.66i) q^{5} -37938.5i q^{7} -139586. i q^{9} +(68184.4 - 68184.4i) q^{11} +(109818. + 109818. i) q^{13} +1.06883e6 q^{15} +8.85033e6 q^{17} +(712421. + 712421. i) q^{19} +(-5.19914e6 + 5.19914e6i) q^{21} -2.69728e7i q^{23} +1.84134e7i q^{25} +(-4.34056e7 + 4.34056e7i) q^{27} +(1.10441e8 + 1.10441e8i) q^{29} -1.15699e8 q^{31} -1.86882e7 q^{33} +(1.47947e8 + 1.47947e8i) q^{35} +(-3.15546e8 + 3.15546e8i) q^{37} -3.00993e7i q^{39} -8.66621e8i q^{41} +(3.13940e8 - 3.13940e8i) q^{43} +(5.44339e8 + 5.44339e8i) q^{45} +1.93131e9 q^{47} +5.37998e8 q^{49} +(-1.21286e9 - 1.21286e9i) q^{51} +(-8.24466e8 + 8.24466e8i) q^{53} +5.31792e8i q^{55} -1.95262e8i q^{57} +(7.47540e9 - 7.47540e9i) q^{59} +(6.44620e8 + 6.44620e8i) q^{61} -5.29570e9 q^{63} -8.56508e8 q^{65} +(-5.39064e9 - 5.39064e9i) q^{67} +(-3.69638e9 + 3.69638e9i) q^{69} +2.90073e10i q^{71} -1.12038e10i q^{73} +(2.52340e9 - 2.52340e9i) q^{75} +(-2.58681e9 - 2.58681e9i) q^{77} -2.03542e7 q^{79} -1.28306e10 q^{81} +(-2.10772e10 - 2.10772e10i) q^{83} +(-3.45133e10 + 3.45133e10i) q^{85} -3.02699e10i q^{87} -7.01544e10i q^{89} +(4.16634e9 - 4.16634e9i) q^{91} +(1.58556e10 + 1.58556e10i) q^{93} -5.55640e9 q^{95} -3.85844e10 q^{97} +(-9.51762e9 - 9.51762e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−137.041	−	137.041i	−0.325600	−	0.325600i	0.525310	−	0.850911i	$-0.323949\pi$
$3$	−137.041	−	137.041i	−0.325600	−	0.325600i	−0.850911	+	0.525310i	$0.823949\pi$
$4$		0			0
$5$	−3899.66	+	3899.66i	−0.558074	+	0.558074i	−0.928759	−	0.370685i	$-0.879123\pi$
$5$	−3899.66	+	3899.66i	−0.558074	+	0.558074i	0.370685	+	0.928759i	$0.379123\pi$
$6$		0			0
$7$		−	37938.5i		−	0.853180i	−0.904445	−	0.426590i	$-0.859715\pi$
$7$		−	37938.5i		−	0.853180i	0.904445	−	0.426590i	$-0.140285\pi$
$8$		0			0
$9$		−	139586.i		−	0.787969i
$10$		0			0
$11$	68184.4	−	68184.4i	0.127651	−	0.127651i	−0.640395	−	0.768046i	$-0.721229\pi$
$11$	68184.4	−	68184.4i	0.127651	−	0.127651i	0.768046	+	0.640395i	$0.221229\pi$
$12$		0			0
$13$	109818.	+	109818.i	0.0820325	+	0.0820325i	0.746932	−	0.664900i	$-0.231526\pi$
$13$	109818.	+	109818.i	0.0820325	+	0.0820325i	−0.664900	+	0.746932i	$0.731526\pi$
$14$		0			0
$15$	1.06883e6			0.363418
$16$		0			0
$17$	8.85033e6			1.51179			0.755893	−	0.654695i	$-0.227203\pi$
$17$	8.85033e6			1.51179			0.755893	+	0.654695i	$0.227203\pi$
$18$		0			0
$19$	712421.	+	712421.i	0.0660073	+	0.0660073i	0.739340	−	0.673333i	$-0.235138\pi$
$19$	712421.	+	712421.i	0.0660073	+	0.0660073i	−0.673333	+	0.739340i	$0.735138\pi$
$20$		0			0
$21$	−5.19914e6	+	5.19914e6i	−0.277796	+	0.277796i
$22$		0			0
$23$		−	2.69728e7i		−	0.873821i	−0.899505	−	0.436910i	$-0.856073\pi$
$23$		−	2.69728e7i		−	0.873821i	0.899505	−	0.436910i	$-0.143927\pi$
$24$		0			0
$25$			1.84134e7i			0.377107i
$26$		0			0
$27$	−4.34056e7	+	4.34056e7i	−0.582163	+	0.582163i
$28$		0			0
$29$	1.10441e8	+	1.10441e8i	0.999862	+	0.999862i	1.00000		0.000137853i	$-4.38800e-5\pi$
$29$	1.10441e8	+	1.10441e8i	0.999862	+	0.999862i	−0.000137853		1.00000i	$0.500044\pi$
$30$		0			0
$31$	−1.15699e8			−0.725842			−0.362921	−	0.931820i	$-0.618221\pi$
$31$	−1.15699e8			−0.725842			−0.362921	+	0.931820i	$0.618221\pi$
$32$		0			0
$33$	−1.86882e7			−0.0831266
$34$		0			0
$35$	1.47947e8	+	1.47947e8i	0.476138	+	0.476138i
$36$		0			0
$37$	−3.15546e8	+	3.15546e8i	−0.748088	+	0.748088i	−0.974120	−	0.226032i	$-0.927425\pi$
$37$	−3.15546e8	+	3.15546e8i	−0.748088	+	0.748088i	0.226032	+	0.974120i	$0.427425\pi$
$38$		0			0
$39$		−	3.00993e7i		−	0.0534196i
$40$		0			0
$41$		−	8.66621e8i		−	1.16820i	−0.811681	−	0.584101i	$-0.801447\pi$
$41$		−	8.66621e8i		−	1.16820i	0.811681	−	0.584101i	$-0.198553\pi$
$42$		0			0
$43$	3.13940e8	−	3.13940e8i	0.325665	−	0.325665i	−0.525271	−	0.850935i	$-0.676036\pi$
$43$	3.13940e8	−	3.13940e8i	0.325665	−	0.325665i	0.850935	+	0.525271i	$0.176036\pi$
$44$		0			0
$45$	5.44339e8	+	5.44339e8i	0.439745	+	0.439745i
$46$		0			0
$47$	1.93131e9			1.22833			0.614164	−	0.789179i	$-0.289493\pi$
$47$	1.93131e9			1.22833			0.614164	+	0.789179i	$0.289493\pi$
$48$		0			0
$49$	5.37998e8			0.272083
$50$		0			0
$51$	−1.21286e9	−	1.21286e9i	−0.492238	−	0.492238i
$52$		0			0
$53$	−8.24466e8	+	8.24466e8i	−0.270804	+	0.270804i	−0.829424	−	0.558620i	$-0.811331\pi$
$53$	−8.24466e8	+	8.24466e8i	−0.270804	+	0.270804i	0.558620	+	0.829424i	$0.311331\pi$
$54$		0			0
$55$			5.31792e8i			0.142478i
$56$		0			0
$57$		−	1.95262e8i		−	0.0429840i
$58$		0			0
$59$	7.47540e9	−	7.47540e9i	1.36128	−	1.36128i	0.488998	−	0.872285i	$-0.337363\pi$
$59$	7.47540e9	−	7.47540e9i	1.36128	−	1.36128i	0.872285	−	0.488998i	$-0.162637\pi$
$60$		0			0
$61$	6.44620e8	+	6.44620e8i	0.0977215	+	0.0977215i	0.754277	−	0.656556i	$-0.227987\pi$
$61$	6.44620e8	+	6.44620e8i	0.0977215	+	0.0977215i	−0.656556	+	0.754277i	$0.727987\pi$
$62$		0			0
$63$	−5.29570e9			−0.672280
$64$		0			0
$65$	−8.56508e8			−0.0915605
$66$		0			0
$67$	−5.39064e9	−	5.39064e9i	−0.487786	−	0.487786i	0.419821	−	0.907607i	$-0.362093\pi$
$67$	−5.39064e9	−	5.39064e9i	−0.487786	−	0.487786i	−0.907607	+	0.419821i	$0.862093\pi$
$68$		0			0
$69$	−3.69638e9	+	3.69638e9i	−0.284516	+	0.284516i
$70$		0			0
$71$			2.90073e10i			1.90804i	0.299747	+	0.954019i	$0.403098\pi$
$71$			2.90073e10i			1.90804i	−0.299747	+	0.954019i	$0.596902\pi$
$72$		0			0
$73$		−	1.12038e10i		−	0.632540i	−0.948669	−	0.316270i	$-0.897569\pi$
$73$		−	1.12038e10i		−	0.632540i	0.948669	−	0.316270i	$-0.102431\pi$
$74$		0			0
$75$	2.52340e9	−	2.52340e9i	0.122786	−	0.122786i
$76$		0			0
$77$	−2.58681e9	−	2.58681e9i	−0.108910	−	0.108910i
$78$		0			0
$79$	−2.03542e7			−0.000744226			−0.000372113	−	1.00000i	$-0.500118\pi$
$79$	−2.03542e7			−0.000744226			−0.000372113		1.00000i	$0.500118\pi$
$80$		0			0
$81$	−1.28306e10			−0.408864
$82$		0			0
$83$	−2.10772e10	−	2.10772e10i	−0.587330	−	0.587330i	0.349577	−	0.936908i	$-0.386325\pi$
$83$	−2.10772e10	−	2.10772e10i	−0.587330	−	0.587330i	−0.936908	+	0.349577i	$0.886325\pi$
$84$		0			0
$85$	−3.45133e10	+	3.45133e10i	−0.843689	+	0.843689i
$86$		0			0
$87$		−	3.02699e10i		−	0.651111i
$88$		0			0
$89$		−	7.01544e10i		−	1.33171i	−0.746081	−	0.665855i	$-0.768067\pi$
$89$		−	7.01544e10i		−	1.33171i	0.746081	−	0.665855i	$-0.231933\pi$
$90$		0			0
$91$	4.16634e9	−	4.16634e9i	0.0699886	−	0.0699886i
$92$		0			0
$93$	1.58556e10	+	1.58556e10i	0.236334	+	0.236334i
$94$		0			0
$95$	−5.55640e9			−0.0736739
$96$		0			0
$97$	−3.85844e10			−0.456213			−0.228107	−	0.973636i	$-0.573253\pi$
$97$	−3.85844e10			−0.456213			−0.228107	+	0.973636i	$0.573253\pi$
$98$		0			0
$99$	−9.51762e9	−	9.51762e9i	−0.100585	−	0.100585i
$100$		0			0
$101$	−7.64448e9	+	7.64448e9i	−0.0723736	+	0.0723736i	−0.742367	−	0.669993i	$-0.766297\pi$
$101$	−7.64448e9	+	7.64448e9i	−0.0723736	+	0.0723736i	0.669993	+	0.742367i	$0.266297\pi$
$102$		0			0
$103$		−	1.42256e11i		−	1.20911i	−0.796562	−	0.604557i	$-0.793350\pi$
$103$		−	1.42256e11i		−	1.20911i	0.796562	−	0.604557i	$-0.206650\pi$
$104$		0			0
$105$		−	4.05498e10i		−	0.310061i
$106$		0			0
$107$	1.42681e11	−	1.42681e11i	0.983455	−	0.983455i	−0.0164100	−	0.999865i	$-0.505224\pi$
$107$	1.42681e11	−	1.42681e11i	0.983455	−	0.983455i	0.999865	+	0.0164100i	$0.00522370\pi$
$108$		0			0
$109$	−1.77386e11	−	1.77386e11i	−1.10427	−	1.10427i	−0.993890	−	0.110376i	$-0.964794\pi$
$109$	−1.77386e11	−	1.77386e11i	−1.10427	−	1.10427i	−0.110376	−	0.993890i	$-0.535206\pi$
$110$		0			0
$111$	8.64856e10			0.487155
$112$		0			0
$113$	−2.63766e11			−1.34675			−0.673376	−	0.739300i	$-0.735156\pi$
$113$	−2.63766e11			−1.34675			−0.673376	+	0.739300i	$0.735156\pi$
$114$		0			0
$115$	1.05185e11	+	1.05185e11i	0.487657	+	0.487657i
$116$		0			0
$117$	1.53291e10	−	1.53291e10i	0.0646391	−	0.0646391i
$118$		0			0
$119$		−	3.35768e11i		−	1.28983i
$120$		0			0
$121$			2.76013e11i			0.967410i
$122$		0			0
$123$	−1.18763e11	+	1.18763e11i	−0.380367	+	0.380367i
$124$		0			0
$125$	−2.62219e11	−	2.62219e11i	−0.768528	−	0.768528i
$126$		0			0
$127$	2.05563e11			0.552109			0.276055	−	0.961142i	$-0.410973\pi$
$127$	2.05563e11			0.552109			0.276055	+	0.961142i	$0.410973\pi$
$128$		0			0
$129$	−8.60456e10			−0.212073
$130$		0			0
$131$	−4.20410e11	−	4.20410e11i	−0.952097	−	0.952097i	0.0468069	−	0.998904i	$-0.485095\pi$
$131$	−4.20410e11	−	4.20410e11i	−0.952097	−	0.952097i	−0.998904	+	0.0468069i	$0.985095\pi$
$132$		0			0
$133$	2.70282e10	−	2.70282e10i	0.0563161	−	0.0563161i
$134$		0			0
$135$		−	3.38534e11i		−	0.649780i
$136$		0			0
$137$			8.28024e11i			1.46582i	0.680327	+	0.732909i	$0.261838\pi$
$137$			8.28024e11i			1.46582i	−0.680327	+	0.732909i	$0.738162\pi$
$138$		0			0
$139$	5.46403e11	−	5.46403e11i	0.893165	−	0.893165i	−0.101654	−	0.994820i	$-0.532414\pi$
$139$	5.46403e11	−	5.46403e11i	0.893165	−	0.893165i	0.994820	+	0.101654i	$0.0324136\pi$
$140$		0			0
$141$	−2.64670e11	−	2.64670e11i	−0.399944	−	0.399944i
$142$		0			0
$143$	1.49758e10			0.0209431
$144$		0			0
$145$	−8.61363e11			−1.11599
$146$		0			0
$147$	−7.37279e10	−	7.37279e10i	−0.0885904	−	0.0885904i
$148$		0			0
$149$	−2.56398e11	+	2.56398e11i	−0.286016	+	0.286016i	−0.835503	−	0.549486i	$-0.814823\pi$
$149$	−2.56398e11	+	2.56398e11i	−0.286016	+	0.286016i	0.549486	+	0.835503i	$0.314823\pi$
$150$		0			0
$151$		−	1.65411e12i		−	1.71471i	−0.514724	−	0.857356i	$-0.672106\pi$
$151$		−	1.65411e12i		−	1.71471i	0.514724	−	0.857356i	$-0.327894\pi$
$152$		0			0
$153$		−	1.23539e12i		−	1.19124i
$154$		0			0
$155$	4.51189e11	−	4.51189e11i	0.405074	−	0.405074i
$156$		0			0
$157$	−3.88138e11	−	3.88138e11i	−0.324742	−	0.324742i	0.525841	−	0.850583i	$-0.323751\pi$
$157$	−3.88138e11	−	3.88138e11i	−0.324742	−	0.324742i	−0.850583	+	0.525841i	$0.823751\pi$
$158$		0			0
$159$	2.25972e11			0.176348
$160$		0			0
$161$	−1.02331e12			−0.745527
$162$		0			0
$163$	7.23237e11	+	7.23237e11i	0.492321	+	0.492321i	0.909037	−	0.416716i	$-0.136819\pi$
$163$	7.23237e11	+	7.23237e11i	0.492321	+	0.492321i	−0.416716	+	0.909037i	$0.636819\pi$
$164$		0			0
$165$	7.28775e10	−	7.28775e10i	0.0463908	−	0.0463908i
$166$		0			0
$167$		−	5.49609e11i		−	0.327426i	−0.986508	−	0.163713i	$-0.947653\pi$
$167$		−	5.49609e11i		−	0.327426i	0.986508	−	0.163713i	$-0.0523471\pi$
$168$		0			0
$169$		−	1.76804e12i		−	0.986541i
$170$		0			0
$171$	9.94442e10	−	9.94442e10i	0.0520117	−	0.0520117i
$172$		0			0
$173$	−1.95564e12	−	1.95564e12i	−0.959477	−	0.959477i	0.0397338	−	0.999210i	$-0.487349\pi$
$173$	−1.95564e12	−	1.95564e12i	−0.959477	−	0.959477i	−0.999210	+	0.0397338i	$0.987349\pi$
$174$		0			0
$175$	6.98577e11			0.321740
$176$		0			0
$177$	−2.04888e12			−0.886468
$178$		0			0
$179$	−2.41737e12	−	2.41737e12i	−0.983220	−	0.983220i	0.0166415	−	0.999862i	$-0.494703\pi$
$179$	−2.41737e12	−	2.41737e12i	−0.983220	−	0.983220i	−0.999862	+	0.0166415i	$0.994703\pi$
$180$		0			0
$181$	−3.47137e12	+	3.47137e12i	−1.32822	+	1.32822i	−0.421289	+	0.906926i	$0.638422\pi$
$181$	−3.47137e12	+	3.47137e12i	−1.32822	+	1.32822i	−0.906926	+	0.421289i	$0.861578\pi$
$182$		0			0
$183$		−	1.76679e11i		−	0.0636362i
$184$		0			0
$185$		−	2.46104e12i		−	0.834977i
$186$		0			0
$187$	6.03455e11	−	6.03455e11i	0.192982	−	0.192982i
$188$		0			0
$189$	1.64674e12	+	1.64674e12i	0.496690	+	0.496690i
$190$		0			0
$191$	−1.42722e12			−0.406264			−0.203132	−	0.979151i	$-0.565112\pi$
$191$	−1.42722e12			−0.406264			−0.203132	+	0.979151i	$0.565112\pi$
$192$		0			0
$193$	2.73266e12			0.734550			0.367275	−	0.930112i	$-0.380291\pi$
$193$	2.73266e12			0.734550			0.367275	+	0.930112i	$0.380291\pi$
$194$		0			0
$195$	1.17377e11	+	1.17377e11i	0.0298121	+	0.0298121i
$196$		0			0
$197$	6.90303e11	−	6.90303e11i	0.165758	−	0.165758i	−0.619354	−	0.785112i	$-0.712605\pi$
$197$	6.90303e11	−	6.90303e11i	0.165758	−	0.165758i	0.785112	+	0.619354i	$0.212605\pi$
$198$		0			0
$199$			6.35449e12i			1.44341i	0.692202	+	0.721704i	$0.256641\pi$
$199$			6.35449e12i			1.44341i	−0.692202	+	0.721704i	$0.743359\pi$
$200$		0			0
$201$			1.47748e12i			0.317646i
$202$		0			0
$203$	4.18995e12	−	4.18995e12i	0.853063	−	0.853063i
$204$		0			0
$205$	3.37953e12	+	3.37953e12i	0.651944	+	0.651944i
$206$		0			0
$207$	−3.76503e12			−0.688544
$208$		0			0
$209$	9.71520e10			0.0168518
$210$		0			0
$211$	−3.30209e12	−	3.30209e12i	−0.543545	−	0.543545i	0.381021	−	0.924566i	$-0.375573\pi$
$211$	−3.30209e12	−	3.30209e12i	−0.543545	−	0.543545i	−0.924566	+	0.381021i	$0.875573\pi$
$212$		0			0
$213$	3.97520e12	−	3.97520e12i	0.621257	−	0.621257i
$214$		0			0
$215$			2.44852e12i			0.363490i
$216$		0			0
$217$			4.38946e12i			0.619274i
$218$		0			0
$219$	−1.53538e12	+	1.53538e12i	−0.205955	+	0.205955i
$220$		0			0
$221$	9.71928e11	+	9.71928e11i	0.124016	+	0.124016i
$222$		0			0
$223$	1.22014e13			1.48161			0.740806	−	0.671719i	$-0.234444\pi$
$223$	1.22014e13			1.48161			0.740806	+	0.671719i	$0.234444\pi$
$224$		0			0
$225$	2.57026e12			0.297148
$226$		0			0
$227$	4.44935e12	+	4.44935e12i	0.489953	+	0.489953i	0.908291	−	0.418338i	$-0.137387\pi$
$227$	4.44935e12	+	4.44935e12i	0.489953	+	0.489953i	−0.418338	+	0.908291i	$0.637387\pi$
$228$		0			0
$229$	−2.35262e11	+	2.35262e11i	−0.0246864	+	0.0246864i	−0.719342	−	0.694656i	$-0.755557\pi$
$229$	−2.35262e11	+	2.35262e11i	−0.0246864	+	0.0246864i	0.694656	+	0.719342i	$0.255557\pi$
$230$		0			0
$231$			7.09001e11i			0.0709220i
$232$		0			0
$233$			1.95717e12i			0.186711i	0.995633	+	0.0933555i	$0.0297593\pi$
$233$			1.95717e12i			0.186711i	−0.995633	+	0.0933555i	$0.970241\pi$
$234$		0			0
$235$	−7.53146e12	+	7.53146e12i	−0.685498	+	0.685498i
$236$		0			0
$237$	2.78937e9	+	2.78937e9i	0.000242320	+	0.000242320i
$238$		0			0
$239$	−1.55805e13			−1.29239			−0.646195	−	0.763172i	$-0.723641\pi$
$239$	−1.55805e13			−1.29239			−0.646195	+	0.763172i	$0.723641\pi$
$240$		0			0
$241$	1.49774e13			1.18670			0.593352	−	0.804943i	$-0.297804\pi$
$241$	1.49774e13			1.18670			0.593352	+	0.804943i	$0.297804\pi$
$242$		0			0
$243$	9.44749e12	+	9.44749e12i	0.715289	+	0.715289i
$244$		0			0
$245$	−2.09801e12	+	2.09801e12i	−0.151843	+	0.151843i
$246$		0			0
$247$			1.56474e11i			0.0108295i
$248$		0			0
$249$			5.77688e12i			0.382470i
$250$		0			0
$251$	−1.35422e13	+	1.35422e13i	−0.857996	+	0.857996i	−0.991102	−	0.133106i	$-0.957505\pi$
$251$	−1.35422e13	+	1.35422e13i	−0.857996	+	0.857996i	0.133106	+	0.991102i	$0.457505\pi$
$252$		0			0
$253$	−1.83912e12	−	1.83912e12i	−0.111544	−	0.111544i
$254$		0			0
$255$	9.45950e12			0.549411
$256$		0			0
$257$	1.84308e12			0.102545			0.0512723	−	0.998685i	$-0.483672\pi$
$257$	1.84308e12			0.102545			0.0512723	+	0.998685i	$0.483672\pi$
$258$		0			0
$259$	1.19713e13	+	1.19713e13i	0.638254	+	0.638254i
$260$		0			0
$261$	1.54160e13	−	1.54160e13i	0.787860	−	0.787860i
$262$		0			0
$263$		−	1.20322e13i		−	0.589642i	−0.955553	−	0.294821i	$-0.904740\pi$
$263$		−	1.20322e13i		−	0.589642i	0.955553	−	0.294821i	$-0.0952600\pi$
$264$		0			0
$265$		−	6.43028e12i		−	0.302258i
$266$		0			0
$267$	−9.61405e12	+	9.61405e12i	−0.433605	+	0.433605i
$268$		0			0
$269$	2.45811e13	+	2.45811e13i	1.06405	+	1.06405i	0.997803	+	0.0662507i	$0.0211037\pi$
$269$	2.45811e13	+	2.45811e13i	1.06405	+	1.06405i	0.0662507	+	0.997803i	$0.478896\pi$
$270$		0			0
$271$	−1.50612e12			−0.0625935			−0.0312967	−	0.999510i	$-0.509964\pi$
$271$	−1.50612e12			−0.0625935			−0.0312967	+	0.999510i	$0.509964\pi$
$272$		0			0
$273$	−1.14192e12			−0.0455766
$274$		0			0
$275$	1.25551e12	+	1.25551e12i	0.0481382	+	0.0481382i
$276$		0			0
$277$	2.54745e13	−	2.54745e13i	0.938570	−	0.938570i	−0.0596494	−	0.998219i	$-0.518998\pi$
$277$	2.54745e13	−	2.54745e13i	0.938570	−	0.938570i	0.998219	+	0.0596494i	$0.0189983\pi$
$278$		0			0
$279$			1.61501e13i			0.571941i
$280$		0			0
$281$			2.86124e13i			0.974249i	0.873332	+	0.487125i	$0.161954\pi$
$281$			2.86124e13i			0.974249i	−0.873332	+	0.487125i	$0.838046\pi$
$282$		0			0
$283$	−2.53014e13	+	2.53014e13i	−0.828550	+	0.828550i	−0.987316	−	0.158766i	$-0.949248\pi$
$283$	−2.53014e13	+	2.53014e13i	−0.828550	+	0.828550i	0.158766	+	0.987316i	$0.449248\pi$
$284$		0			0
$285$	7.61456e11	+	7.61456e11i	0.0239882	+	0.0239882i
$286$		0			0
$287$	−3.28783e13			−0.996687
$288$		0			0
$289$	4.40565e13			1.28550
$290$		0			0
$291$	5.28766e12	+	5.28766e12i	0.148543	+	0.148543i
$292$		0			0
$293$	−1.19988e13	+	1.19988e13i	−0.324614	+	0.324614i	−0.850534	−	0.525920i	$-0.823721\pi$
$293$	−1.19988e13	+	1.19988e13i	−0.324614	+	0.324614i	0.525920	+	0.850534i	$0.323721\pi$
$294$		0			0
$295$			5.83031e13i			1.51939i
$296$		0			0
$297$			5.91917e12i			0.148628i
$298$		0			0
$299$	2.96210e12	−	2.96210e12i	0.0716818	−	0.0716818i
$300$		0			0
$301$	−1.19104e13	−	1.19104e13i	−0.277851	−	0.277851i
$302$		0			0
$303$	2.09522e12			0.0471297
$304$		0			0
$305$	−5.02760e12			−0.109072
$306$		0			0
$307$	−3.56171e13	−	3.56171e13i	−0.745414	−	0.745414i	0.228200	−	0.973614i	$-0.426716\pi$
$307$	−3.56171e13	−	3.56171e13i	−0.745414	−	0.745414i	−0.973614	+	0.228200i	$0.926716\pi$
$308$		0			0
$309$	−1.94950e13	+	1.94950e13i	−0.393687	+	0.393687i
$310$		0			0
$311$		−	5.85014e12i		−	0.114021i	−0.998374	−	0.0570104i	$-0.981843\pi$
$311$		−	5.85014e12i		−	0.114021i	0.998374	−	0.0570104i	$-0.0181568\pi$
$312$		0			0
$313$			7.17988e12i			0.135090i	0.997716	+	0.0675450i	$0.0215166\pi$
$313$			7.17988e12i			0.135090i	−0.997716	+	0.0675450i	$0.978483\pi$
$314$		0			0
$315$	2.06514e13	−	2.06514e13i	0.375182	−	0.375182i
$316$		0			0
$317$	−1.76432e13	−	1.76432e13i	−0.309564	−	0.309564i	0.535176	−	0.844740i	$-0.320245\pi$
$317$	−1.76432e13	−	1.76432e13i	−0.309564	−	0.309564i	−0.844740	+	0.535176i	$0.820245\pi$
$318$		0			0
$319$	1.50607e13			0.255268
$320$		0			0
$321$	−3.91063e13			−0.640426
$322$		0			0
$323$	6.30516e12	+	6.30516e12i	0.0997889	+	0.0997889i
$324$		0			0
$325$	−2.02213e12	+	2.02213e12i	−0.0309350	+	0.0309350i
$326$		0			0
$327$			4.86184e13i			0.719099i
$328$		0			0
$329$		−	7.32711e13i		−	1.04798i
$330$		0			0
$331$	3.82241e13	−	3.82241e13i	0.528790	−	0.528790i	−0.391422	−	0.920211i	$-0.628017\pi$
$331$	3.82241e13	−	3.82241e13i	0.528790	−	0.528790i	0.920211	+	0.391422i	$0.128017\pi$
$332$		0			0
$333$	4.40459e13	+	4.40459e13i	0.589470	+	0.589470i
$334$		0			0
$335$	4.20434e13			0.544441
$336$		0			0
$337$	2.67134e13			0.334784			0.167392	−	0.985890i	$-0.446465\pi$
$337$	2.67134e13			0.334784			0.167392	+	0.985890i	$0.446465\pi$
$338$		0			0
$339$	3.61469e13	+	3.61469e13i	0.438503	+	0.438503i
$340$		0			0
$341$	−7.88890e12	+	7.88890e12i	−0.0926547	+	0.0926547i
$342$		0			0
$343$		−	9.54276e13i		−	1.08532i
$344$		0			0
$345$		−	2.88293e13i		−	0.317562i
$346$		0			0
$347$	1.05470e14	−	1.05470e14i	1.12543	−	1.12543i	0.134515	−	0.990912i	$-0.457052\pi$
$347$	1.05470e14	−	1.05470e14i	1.12543	−	1.12543i	0.990912	−	0.134515i	$-0.0429477\pi$
$348$		0			0
$349$	−2.45469e13	−	2.45469e13i	−0.253780	−	0.253780i	0.568738	−	0.822518i	$-0.307432\pi$
$349$	−2.45469e13	−	2.45469e13i	−0.253780	−	0.253780i	−0.822518	+	0.568738i	$0.807432\pi$
$350$		0			0
$351$	−9.53345e12			−0.0955126
$352$		0			0
$353$	−5.54612e13			−0.538553			−0.269276	−	0.963063i	$-0.586785\pi$
$353$	−5.54612e13			−0.538553			−0.269276	+	0.963063i	$0.586785\pi$
$354$		0			0
$355$	−1.13119e14	−	1.13119e14i	−1.06483	−	1.06483i
$356$		0			0
$357$	−4.60141e13	+	4.60141e13i	−0.419968	+	0.419968i
$358$		0			0
$359$		−	1.17444e14i		−	1.03947i	−0.854328	−	0.519734i	$-0.826031\pi$
$359$		−	1.17444e14i		−	1.03947i	0.854328	−	0.519734i	$-0.173969\pi$
$360$		0			0
$361$		−	1.15475e14i		−	0.991286i
$362$		0			0
$363$	3.78252e13	−	3.78252e13i	0.314989	−	0.314989i
$364$		0			0
$365$	4.36908e13	+	4.36908e13i	0.353004	+	0.353004i
$366$		0			0
$367$	6.53804e13			0.512607			0.256303	−	0.966596i	$-0.417495\pi$
$367$	6.53804e13			0.512607			0.256303	+	0.966596i	$0.417495\pi$
$368$		0			0
$369$	−1.20969e14			−0.920507
$370$		0			0
$371$	3.12790e13	+	3.12790e13i	0.231045	+	0.231045i
$372$		0			0
$373$	−1.53272e14	+	1.53272e14i	−1.09917	+	1.09917i	−0.104658	+	0.994508i	$0.533375\pi$
$373$	−1.53272e14	+	1.53272e14i	−1.09917	+	1.09917i	−0.994508	+	0.104658i	$0.966625\pi$
$374$		0			0
$375$			7.18697e13i			0.500465i
$376$		0			0
$377$			2.42568e13i			0.164042i
$378$		0			0
$379$	−1.21627e14	+	1.21627e14i	−0.798940	+	0.798940i	−0.982928	−	0.183988i	$-0.941099\pi$
$379$	−1.21627e14	+	1.21627e14i	−0.798940	+	0.798940i	0.183988	+	0.982928i	$0.441099\pi$
$380$		0			0
$381$	−2.81707e13	−	2.81707e13i	−0.179767	−	0.179767i
$382$		0			0
$383$	−9.93966e13			−0.616280			−0.308140	−	0.951341i	$-0.599707\pi$
$383$	−9.93966e13			−0.616280			−0.308140	+	0.951341i	$0.599707\pi$
$384$		0			0
$385$	2.01754e13			0.121559
$386$		0			0
$387$	−4.38218e13	−	4.38218e13i	−0.256614	−	0.256614i
$388$		0			0
$389$	5.20938e13	−	5.20938e13i	0.296526	−	0.296526i	−0.543125	−	0.839652i	$-0.682759\pi$
$389$	5.20938e13	−	5.20938e13i	0.296526	−	0.296526i	0.839652	+	0.543125i	$0.182759\pi$
$390$		0			0
$391$		−	2.38718e14i		−	1.32103i
$392$		0			0
$393$			1.15227e14i			0.620006i
$394$		0			0
$395$	7.93745e10	−	7.93745e10i	0.000415333	−	0.000415333i
$396$		0			0
$397$	−2.43146e14	−	2.43146e14i	−1.23743	−	1.23743i	−0.961050	−	0.276376i	$-0.910866\pi$
$397$	−2.43146e14	−	2.43146e14i	−1.23743	−	1.23743i	−0.276376	−	0.961050i	$-0.589134\pi$
$398$		0			0
$399$	−7.40795e12			−0.0366731
$400$		0			0
$401$	−1.60446e14			−0.772744			−0.386372	−	0.922343i	$-0.626272\pi$
$401$	−1.60446e14			−0.772744			−0.386372	+	0.922343i	$0.626272\pi$
$402$		0			0
$403$	−1.27059e13	−	1.27059e13i	−0.0595427	−	0.0595427i
$404$		0			0
$405$	5.00350e13	−	5.00350e13i	0.228177	−	0.228177i
$406$		0			0
$407$			4.30306e13i			0.190989i
$408$		0			0
$409$			8.28735e13i			0.358045i	0.983845	+	0.179022i	$0.0572935\pi$
$409$			8.28735e13i			0.358045i	−0.983845	+	0.179022i	$0.942707\pi$
$410$		0			0
$411$	1.13474e14	−	1.13474e14i	0.477270	−	0.477270i
$412$		0			0
$413$	−2.83605e14	−	2.83605e14i	−1.16142	−	1.16142i
$414$		0			0
$415$	1.64388e14			0.655548
$416$		0			0
$417$	−1.49760e14			−0.581630
$418$		0			0
$419$	7.37301e11	+	7.37301e11i	0.00278912	+	0.00278912i	0.708500	−	0.705711i	$-0.249372\pi$
$419$	7.37301e11	+	7.37301e11i	0.00278912	+	0.00278912i	−0.705711	+	0.708500i	$0.749372\pi$
$420$		0			0
$421$	2.94206e14	−	2.94206e14i	1.08418	−	1.08418i	0.0880630	−	0.996115i	$-0.471932\pi$
$421$	2.94206e14	−	2.94206e14i	1.08418	−	1.08418i	0.996115	−	0.0880630i	$-0.0280677\pi$
$422$		0			0
$423$		−	2.69585e14i		−	0.967884i
$424$		0			0
$425$			1.62965e14i			0.570105i
$426$		0			0
$427$	2.44559e13	−	2.44559e13i	0.0833740	−	0.0833740i
$428$		0			0
$429$	−2.05230e12	−	2.05230e12i	−0.00681909	−	0.00681909i
$430$		0			0
$431$	−1.13680e14			−0.368180			−0.184090	−	0.982909i	$-0.558934\pi$
$431$	−1.13680e14			−0.368180			−0.184090	+	0.982909i	$0.558934\pi$
$432$		0			0
$433$	−3.36153e14			−1.06134			−0.530669	−	0.847579i	$-0.678059\pi$
$433$	−3.36153e14			−1.06134			−0.530669	+	0.847579i	$0.678059\pi$
$434$		0			0
$435$	1.18042e14	+	1.18042e14i	0.363368	+	0.363368i
$436$		0			0
$437$	1.92160e13	−	1.92160e13i	0.0576785	−	0.0576785i
$438$		0			0
$439$		−	1.16264e14i		−	0.340323i	−0.985416	−	0.170162i	$-0.945571\pi$
$439$		−	1.16264e14i		−	0.340323i	0.985416	−	0.170162i	$-0.0544290\pi$
$440$		0			0
$441$		−	7.50971e13i		−	0.214393i
$442$		0			0
$443$	1.78673e14	−	1.78673e14i	0.497551	−	0.497551i	−0.413124	−	0.910675i	$-0.635562\pi$
$443$	1.78673e14	−	1.78673e14i	0.497551	−	0.497551i	0.910675	+	0.413124i	$0.135562\pi$
$444$		0			0
$445$	2.73578e14	+	2.73578e14i	0.743193	+	0.743193i
$446$		0			0
$447$	7.02743e13			0.186254
$448$		0			0
$449$	7.06977e14			1.82831			0.914156	−	0.405363i	$-0.132855\pi$
$449$	7.06977e14			1.82831			0.914156	+	0.405363i	$0.132855\pi$
$450$		0			0
$451$	−5.90901e13	−	5.90901e13i	−0.149123	−	0.149123i
$452$		0			0
$453$	−2.26681e14	+	2.26681e14i	−0.558311	+	0.558311i
$454$		0			0
$455$			3.24946e13i			0.0781176i
$456$		0			0
$457$		−	1.46033e13i		−	0.0342698i	−0.999853	−	0.0171349i	$-0.994546\pi$
$457$		−	1.46033e13i		−	0.0342698i	0.999853	−	0.0171349i	$-0.00545448\pi$
$458$		0			0
$459$	−3.84154e14	+	3.84154e14i	−0.880106	+	0.880106i
$460$		0			0
$461$	−9.16736e13	−	9.16736e13i	−0.205064	−	0.205064i	0.597102	−	0.802166i	$-0.296319\pi$
$461$	−9.16736e13	−	9.16736e13i	−0.205064	−	0.205064i	−0.802166	+	0.597102i	$0.796319\pi$
$462$		0			0
$463$	2.43203e14			0.531219			0.265610	−	0.964081i	$-0.414427\pi$
$463$	2.43203e14			0.531219			0.265610	+	0.964081i	$0.414427\pi$
$464$		0			0
$465$	−1.23663e14			−0.263784
$466$		0			0
$467$	−7.14887e13	−	7.14887e13i	−0.148934	−	0.148934i	0.628708	−	0.777642i	$-0.283584\pi$
$467$	−7.14887e13	−	7.14887e13i	−0.148934	−	0.148934i	−0.777642	+	0.628708i	$0.783584\pi$
$468$		0			0
$469$	−2.04513e14	+	2.04513e14i	−0.416169	+	0.416169i
$470$		0			0
$471$			1.06382e14i			0.211472i
$472$		0			0
$473$		−	4.28117e13i		−	0.0831431i
$474$		0			0
$475$	−1.31181e13	+	1.31181e13i	−0.0248918	+	0.0248918i
$476$		0			0
$477$	1.15084e14	+	1.15084e14i	0.213385	+	0.213385i
$478$		0			0
$479$	−2.74810e14			−0.497951			−0.248975	−	0.968510i	$-0.580094\pi$
$479$	−2.74810e14			−0.497951			−0.248975	+	0.968510i	$0.580094\pi$
$480$		0			0
$481$	−6.93054e13			−0.122735
$482$		0			0
$483$	1.40235e14	+	1.40235e14i	0.242744	+	0.242744i
$484$		0			0
$485$	1.50466e14	−	1.50466e14i	0.254601	−	0.254601i
$486$		0			0
$487$			4.74099e14i			0.784260i	0.919910	+	0.392130i	$0.128262\pi$
$487$			4.74099e14i			0.784260i	−0.919910	+	0.392130i	$0.871738\pi$
$488$		0			0
$489$		−	1.98227e14i		−	0.320600i
$490$		0			0
$491$	−3.34687e14	+	3.34687e14i	−0.529287	+	0.529287i	−0.920360	−	0.391073i	$-0.872104\pi$
$491$	−3.34687e14	+	3.34687e14i	−0.529287	+	0.529287i	0.391073	+	0.920360i	$0.372104\pi$
$492$		0			0
$493$	9.77437e14	+	9.77437e14i	1.51158	+	1.51158i
$494$		0			0
$495$	7.42310e13			0.112268
$496$		0			0
$497$	1.10049e15			1.62790
$498$		0			0
$499$	3.00431e14	+	3.00431e14i	0.434702	+	0.434702i	0.890224	−	0.455523i	$-0.150548\pi$
$499$	3.00431e14	+	3.00431e14i	0.434702	+	0.434702i	−0.455523	+	0.890224i	$0.650548\pi$
$500$		0			0
$501$	−7.53192e13	+	7.53192e13i	−0.106610	+	0.106610i
$502$		0			0
$503$			7.90668e14i			1.09489i	0.836842	+	0.547444i	$0.184399\pi$
$503$			7.90668e14i			1.09489i	−0.836842	+	0.547444i	$0.815601\pi$
$504$		0			0
$505$		−	5.96217e13i		−	0.0807796i
$506$		0			0
$507$	−2.42295e14	+	2.42295e14i	−0.321218	+	0.321218i
$508$		0			0
$509$	3.74275e14	+	3.74275e14i	0.485560	+	0.485560i	0.906902	−	0.421342i	$-0.138441\pi$
$509$	3.74275e14	+	3.74275e14i	0.485560	+	0.485560i	−0.421342	+	0.906902i	$0.638441\pi$
$510$		0			0
$511$	−4.25054e14			−0.539671
$512$		0			0
$513$	−6.18461e13			−0.0768540
$514$		0			0
$515$	5.54752e14	+	5.54752e14i	0.674775	+	0.674775i
$516$		0			0
$517$	1.31685e14	−	1.31685e14i	0.156798	−	0.156798i
$518$		0			0
$519$			5.36006e14i			0.624811i
$520$		0			0
$521$		−	3.28240e14i		−	0.374614i	−0.982301	−	0.187307i	$-0.940024\pi$
$521$		−	3.28240e14i		−	0.374614i	0.982301	−	0.187307i	$-0.0599759\pi$
$522$		0			0
$523$	7.89619e14	−	7.89619e14i	0.882385	−	0.882385i	−0.111392	−	0.993777i	$-0.535531\pi$
$523$	7.89619e14	−	7.89619e14i	0.882385	−	0.882385i	0.993777	+	0.111392i	$0.0355308\pi$
$524$		0			0
$525$	−9.57339e13	−	9.57339e13i	−0.104759	−	0.104759i
$526$		0			0
$527$	−1.02398e15			−1.09732
$528$		0			0
$529$	2.25279e14			0.236437
$530$		0			0
$531$	−1.04346e15	−	1.04346e15i	−1.07265	−	1.07265i
$532$		0			0
$533$	9.51709e13	−	9.51709e13i	0.0958306	−	0.0958306i
$534$		0			0
$535$			1.11281e15i			1.09768i
$536$		0			0
$537$			6.62558e14i			0.640273i
$538$		0			0
$539$	3.66831e13	−	3.66831e13i	0.0347318	−	0.0347318i
$540$		0			0
$541$	−3.87444e13	−	3.87444e13i	−0.0359438	−	0.0359438i	0.688906	−	0.724850i	$-0.258091\pi$
$541$	−3.87444e13	−	3.87444e13i	−0.0359438	−	0.0359438i	−0.724850	+	0.688906i	$0.758091\pi$
$542$		0			0
$543$	9.51442e14			0.864934
$544$		0			0
$545$	1.38349e15			1.23252
$546$		0			0
$547$	−7.46902e14	−	7.46902e14i	−0.652129	−	0.652129i	0.301377	−	0.953505i	$-0.402554\pi$
$547$	−7.46902e14	−	7.46902e14i	−0.652129	−	0.652129i	−0.953505	+	0.301377i	$0.902554\pi$
$548$		0			0
$549$	8.99802e13	−	8.99802e13i	0.0770015	−	0.0770015i
$550$		0			0
$551$			1.57361e14i			0.131996i
$552$		0			0
$553$			7.72208e11i			0.000634959i
$554$		0			0
$555$	−3.37264e14	+	3.37264e14i	−0.271869	+	0.271869i
$556$		0			0
$557$	−3.84096e14	−	3.84096e14i	−0.303554	−	0.303554i	0.538849	−	0.842403i	$-0.318859\pi$
$557$	−3.84096e14	−	3.84096e14i	−0.303554	−	0.303554i	−0.842403	+	0.538849i	$0.818859\pi$
$558$		0			0
$559$	6.89528e13			0.0534302
$560$		0			0
$561$	−1.65397e14			−0.125670
$562$		0			0
$563$	1.33405e15	+	1.33405e15i	0.993979	+	0.993979i	0.999982	−	0.00600253i	$-0.00191068\pi$
$563$	1.33405e15	+	1.33405e15i	0.993979	+	0.993979i	−0.00600253	+	0.999982i	$0.501911\pi$
$564$		0			0
$565$	1.02860e15	−	1.02860e15i	0.751587	−	0.751587i
$566$		0			0
$567$			4.86773e14i			0.348835i
$568$		0			0
$569$		−	6.39918e14i		−	0.449787i	−0.974383	−	0.224893i	$-0.927797\pi$
$569$		−	6.39918e14i		−	0.449787i	0.974383	−	0.224893i	$-0.0722034\pi$
$570$		0			0
$571$	−1.74958e15	+	1.74958e15i	−1.20625	+	1.20625i	−0.234014	+	0.972233i	$0.575186\pi$
$571$	−1.74958e15	+	1.74958e15i	−1.20625	+	1.20625i	−0.972233	+	0.234014i	$0.924814\pi$
$572$		0			0
$573$	1.95589e14	+	1.95589e14i	0.132280	+	0.132280i
$574$		0			0
$575$	4.96661e14			0.329524
$576$		0			0
$577$	−1.55990e15			−1.01538			−0.507690	−	0.861540i	$-0.669501\pi$
$577$	−1.55990e15			−1.01538			−0.507690	+	0.861540i	$0.669501\pi$
$578$		0			0
$579$	−3.74488e14	−	3.74488e14i	−0.239169	−	0.239169i
$580$		0			0
$581$	−7.99636e14	+	7.99636e14i	−0.501099	+	0.501099i
$582$		0			0
$583$			1.12432e14i			0.0691371i
$584$		0			0
$585$			1.19557e14i			0.0721468i
$586$		0			0
$587$	5.95871e14	−	5.95871e14i	0.352893	−	0.352893i	−0.508292	−	0.861185i	$-0.669723\pi$
$587$	5.95871e14	−	5.95871e14i	0.352893	−	0.352893i	0.861185	+	0.508292i	$0.169723\pi$
$588$		0			0
$589$	−8.24267e13	−	8.24267e13i	−0.0479109	−	0.0479109i
$590$		0			0
$591$	−1.89200e14			−0.107942
$592$		0			0
$593$	4.06287e14			0.227526			0.113763	−	0.993508i	$-0.463709\pi$
$593$	4.06287e14			0.227526			0.113763	+	0.993508i	$0.463709\pi$
$594$		0			0
$595$	1.30938e15	+	1.30938e15i	0.719819	+	0.719819i
$596$		0			0
$597$	8.70828e14	−	8.70828e14i	0.469974	−	0.469974i
$598$		0			0
$599$		−	2.58399e15i		−	1.36913i	−0.728953	−	0.684563i	$-0.759993\pi$
$599$		−	2.58399e15i		−	1.36913i	0.728953	−	0.684563i	$-0.240007\pi$
$600$		0			0
$601$			8.49105e14i			0.441725i	0.975305	+	0.220862i	$0.0708872\pi$
$601$			8.49105e14i			0.441725i	−0.975305	+	0.220862i	$0.929113\pi$
$602$		0			0
$603$	−7.52460e14	+	7.52460e14i	−0.384360	+	0.384360i
$604$		0			0
$605$	−1.07636e15	−	1.07636e15i	−0.539887	−	0.539887i
$606$		0			0
$607$	−9.22193e14			−0.454238			−0.227119	−	0.973867i	$-0.572931\pi$
$607$	−9.22193e14			−0.454238			−0.227119	+	0.973867i	$0.572931\pi$
$608$		0			0
$609$	−1.14839e15			−0.555515
$610$		0			0
$611$	2.12093e14	+	2.12093e14i	0.100763	+	0.100763i
$612$		0			0
$613$	4.49009e14	−	4.49009e14i	0.209518	−	0.209518i	−0.594544	−	0.804063i	$-0.702668\pi$
$613$	4.49009e14	−	4.49009e14i	0.209518	−	0.209518i	0.804063	+	0.594544i	$0.202668\pi$
$614$		0			0
$615$		−	9.26270e14i		−	0.424546i
$616$		0			0
$617$			1.59922e15i			0.720014i	0.932950	+	0.360007i	$0.117226\pi$
$617$			1.59922e15i			0.720014i	−0.932950	+	0.360007i	$0.882774\pi$
$618$		0			0
$619$	9.83868e14	−	9.83868e14i	0.435149	−	0.435149i	−0.455226	−	0.890376i	$-0.650442\pi$
$619$	9.83868e14	−	9.83868e14i	0.435149	−	0.435149i	0.890376	+	0.455226i	$0.150442\pi$
$620$		0			0
$621$	1.17077e15	+	1.17077e15i	0.508706	+	0.508706i
$622$		0			0
$623$	−2.66155e15			−1.13619
$624$		0			0
$625$	1.14604e15			0.480684
$626$		0			0
$627$	−1.33138e13	−	1.33138e13i	−0.00548696	−	0.00548696i
$628$		0			0
$629$	−2.79268e15	+	2.79268e15i	−1.13095	+	1.13095i
$630$		0			0
$631$		−	3.81351e15i		−	1.51762i	−0.651311	−	0.758811i	$-0.725780\pi$
$631$		−	3.81351e15i		−	1.51762i	0.651311	−	0.758811i	$-0.274220\pi$
$632$		0			0
$633$			9.05046e14i			0.353957i
$634$		0			0
$635$	−8.01627e14	+	8.01627e14i	−0.308118	+	0.308118i
$636$		0			0
$637$	5.90820e13	+	5.90820e13i	0.0223197	+	0.0223197i
$638$		0			0
$639$	4.04903e15			1.50347
$640$		0			0
$641$	8.09256e13			0.0295370			0.0147685	−	0.999891i	$-0.495299\pi$
$641$	8.09256e13			0.0295370			0.0147685	+	0.999891i	$0.495299\pi$
$642$		0			0
$643$	4.31419e14	+	4.31419e14i	0.154788	+	0.154788i	0.780253	−	0.625464i	$-0.215090\pi$
$643$	4.31419e14	+	4.31419e14i	0.154788	+	0.154788i	−0.625464	+	0.780253i	$0.715090\pi$
$644$		0			0
$645$	3.35549e14	−	3.35549e14i	0.118352	−	0.118352i
$646$		0			0
$647$		−	2.56351e15i		−	0.888918i	−0.895799	−	0.444459i	$-0.853396\pi$
$647$		−	2.56351e15i		−	0.888918i	0.895799	−	0.444459i	$-0.146604\pi$
$648$		0			0
$649$		−	1.01941e15i		−	0.347539i
$650$		0			0
$651$	6.01538e14	−	6.01538e14i	0.201636	−	0.201636i
$652$		0			0
$653$	−1.70508e15	−	1.70508e15i	−0.561983	−	0.561983i	0.367887	−	0.929870i	$-0.380081\pi$
$653$	−1.70508e15	−	1.70508e15i	−0.561983	−	0.561983i	−0.929870	+	0.367887i	$0.880081\pi$
$654$		0			0
$655$	3.27892e15			1.06268
$656$		0			0
$657$	−1.56389e15			−0.498422
$658$		0			0
$659$	−3.27825e15	−	3.27825e15i	−1.02748	−	1.02748i	−0.999612	−	0.0278658i	$-0.991129\pi$
$659$	−3.27825e15	−	3.27825e15i	−1.02748	−	1.02748i	−0.0278658	−	0.999612i	$-0.508871\pi$
$660$		0			0
$661$	3.34786e15	−	3.34786e15i	1.03195	−	1.03195i	0.0324779	−	0.999472i	$-0.489660\pi$
$661$	3.34786e15	−	3.34786e15i	1.03195	−	1.03195i	0.999472	−	0.0324779i	$-0.0103399\pi$
$662$		0			0
$663$		−	2.66389e14i		−	0.0807591i
$664$		0			0
$665$			2.10801e14i			0.0628571i
$666$		0			0
$667$	2.97889e15	−	2.97889e15i	0.873700	−	0.873700i
$668$		0			0
$669$	−1.67210e15	−	1.67210e15i	−0.482413	−	0.482413i
$670$		0			0
$671$	8.79061e13			0.0249486
$672$		0			0
$673$	−6.35604e15			−1.77461			−0.887307	−	0.461180i	$-0.847426\pi$
$673$	−6.35604e15			−1.77461			−0.887307	+	0.461180i	$0.847426\pi$
$674$		0			0
$675$	−7.99244e14	−	7.99244e14i	−0.219538	−	0.219538i
$676$		0			0
$677$	−4.38761e15	+	4.38761e15i	−1.18574	+	1.18574i	−0.207509	+	0.978233i	$0.566536\pi$
$677$	−4.38761e15	+	4.38761e15i	−1.18574	+	1.18574i	−0.978233	+	0.207509i	$0.933464\pi$
$678$		0			0
$679$			1.46384e15i			0.389232i
$680$		0			0
$681$		−	1.21949e15i		−	0.319058i
$682$		0			0
$683$	4.43219e15	−	4.43219e15i	1.14105	−	1.14105i	0.152790	−	0.988259i	$-0.451174\pi$
$683$	4.43219e15	−	4.43219e15i	1.14105	−	1.14105i	0.988259	−	0.152790i	$-0.0488258\pi$
$684$		0			0
$685$	−3.22901e15	−	3.22901e15i	−0.818035	−	0.818035i
$686$		0			0
$687$	6.44814e13			0.0160758
$688$		0			0
$689$	−1.81083e14			−0.0444295
$690$		0			0
$691$	−2.89530e14	−	2.89530e14i	−0.0699139	−	0.0699139i	0.671285	−	0.741199i	$-0.265743\pi$
$691$	−2.89530e14	−	2.89530e14i	−0.0699139	−	0.0699139i	−0.741199	+	0.671285i	$0.765743\pi$
$692$		0			0
$693$	−3.61084e14	+	3.61084e14i	−0.0858174	+	0.0858174i
$694$		0			0
$695$			4.26157e15i			0.996905i
$696$		0			0
$697$		−	7.66989e15i		−	1.76607i
$698$		0			0
$699$	2.68213e14	−	2.68213e14i	0.0607932	−	0.0607932i
$700$		0			0
$701$	−1.61287e15	−	1.61287e15i	−0.359874	−	0.359874i	0.503892	−	0.863766i	$-0.331901\pi$
$701$	−1.61287e15	−	1.61287e15i	−0.359874	−	0.359874i	−0.863766	+	0.503892i	$0.831901\pi$
$702$		0			0
$703$	−4.49603e14			−0.0987585
$704$		0			0
$705$	2.06424e15			0.446396
$706$		0			0
$707$	2.90020e14	+	2.90020e14i	0.0617477	+	0.0617477i
$708$		0			0
$709$	−1.86537e14	+	1.86537e14i	−0.0391030	+	0.0391030i	−0.726388	−	0.687285i	$-0.758802\pi$
$709$	−1.86537e14	+	1.86537e14i	−0.0391030	+	0.0391030i	0.687285	+	0.726388i	$0.258802\pi$
$710$		0			0
$711$			2.84117e12i			0.000586427i
$712$		0			0
$713$			3.12074e15i			0.634256i
$714$		0			0
$715$	−5.84005e13	+	5.84005e13i	−0.0116878	+	0.0116878i
$716$		0			0
$717$	2.13518e15	+	2.13518e15i	0.420802	+	0.420802i
$718$		0			0
$719$	−6.94242e15			−1.34742			−0.673709	−	0.738997i	$-0.735300\pi$
$719$	−6.94242e15			−1.34742			−0.673709	+	0.738997i	$0.735300\pi$
$720$		0			0
$721$	−5.39699e15			−1.03159
$722$		0			0
$723$	−2.05252e15	−	2.05252e15i	−0.386391	−	0.386391i
$724$		0			0
$725$	−2.03359e15	+	2.03359e15i	−0.377055	+	0.377055i
$726$		0			0
$727$			4.03478e15i			0.736853i	0.929657	+	0.368426i	$0.120103\pi$
$727$			4.03478e15i			0.736853i	−0.929657	+	0.368426i	$0.879897\pi$
$728$		0			0
$729$		−	3.16490e14i		−	0.0569323i
$730$		0			0
$731$	2.77848e15	−	2.77848e15i	0.492335	−	0.492335i
$732$		0			0
$733$	5.85001e15	+	5.85001e15i	1.02114	+	1.02114i	0.999772	+	0.0213673i	$0.00680193\pi$
$733$	5.85001e15	+	5.85001e15i	1.02114	+	1.02114i	0.0213673	+	0.999772i	$0.493198\pi$
$734$		0			0
$735$	5.75028e14			0.0988800
$736$		0			0
$737$	−7.35116e14			−0.124533
$738$		0			0
$739$	−6.33201e15	−	6.33201e15i	−1.05681	−	1.05681i	−0.998286	−	0.0585244i	$-0.981360\pi$
$739$	−6.33201e15	−	6.33201e15i	−1.05681	−	1.05681i	−0.0585244	−	0.998286i	$-0.518640\pi$
$740$		0			0
$741$	2.14434e13	−	2.14434e13i	0.00352608	−	0.00352608i
$742$		0			0
$743$		−	7.78552e15i		−	1.26139i	−0.776031	−	0.630695i	$-0.782770\pi$
$743$		−	7.78552e15i		−	1.26139i	0.776031	−	0.630695i	$-0.217230\pi$
$744$		0			0
$745$		−	1.99973e15i		−	0.319236i
$746$		0			0
$747$	−2.94208e15	+	2.94208e15i	−0.462798	+	0.462798i
$748$		0			0
$749$	−5.41309e15	−	5.41309e15i	−0.839065	−	0.839065i
$750$		0			0
$751$	2.79527e15			0.426976			0.213488	−	0.976946i	$-0.431518\pi$
$751$	2.79527e15			0.426976			0.213488	+	0.976946i	$0.431518\pi$
$752$		0			0
$753$	3.71169e15			0.558727
$754$		0			0
$755$	6.45047e15	+	6.45047e15i	0.956936	+	0.956936i
$756$		0			0
$757$	−2.93505e15	+	2.93505e15i	−0.429130	+	0.429130i	−0.888332	−	0.459202i	$-0.848135\pi$
$757$	−2.93505e15	+	2.93505e15i	−0.429130	+	0.429130i	0.459202	+	0.888332i	$0.348135\pi$
$758$		0			0
$759$			5.04072e14i			0.0726378i
$760$		0			0
$761$		−	8.83693e14i		−	0.125512i	−0.998029	−	0.0627561i	$-0.980011\pi$
$761$		−	8.83693e14i		−	0.125512i	0.998029	−	0.0627561i	$-0.0199890\pi$
$762$		0			0
$763$	−6.72976e15	+	6.72976e15i	−0.942138	+	0.942138i
$764$		0			0
$765$	4.81759e15	+	4.81759e15i	0.664801	+	0.664801i
$766$		0			0
$767$	1.64187e15			0.223339
$768$		0			0
$769$	1.16185e16			1.55796			0.778979	−	0.627049i	$-0.215738\pi$
$769$	1.16185e16			1.55796			0.778979	+	0.627049i	$0.215738\pi$
$770$		0			0
$771$	−2.52578e14	−	2.52578e14i	−0.0333885	−	0.0333885i
$772$		0			0
$773$	2.72914e15	−	2.72914e15i	0.355663	−	0.355663i	−0.506548	−	0.862212i	$-0.669079\pi$
$773$	2.72914e15	−	2.72914e15i	0.355663	−	0.355663i	0.862212	+	0.506548i	$0.169079\pi$
$774$		0			0
$775$		−	2.13042e15i		−	0.273720i
$776$		0			0
$777$		−	3.28113e15i		−	0.415631i
$778$		0			0
$779$	6.17399e14	−	6.17399e14i	0.0771099	−	0.0771099i
$780$		0			0
$781$	1.97785e15	+	1.97785e15i	0.243564	+	0.243564i
$782$		0			0
$783$	−9.58748e15			−1.16417
$784$		0			0
$785$	3.02721e15			0.362460
$786$		0			0
$787$	8.50494e15	+	8.50494e15i	1.00418	+	1.00418i	0.999991	+	0.00418577i	$0.00133238\pi$
$787$	8.50494e15	+	8.50494e15i	1.00418	+	1.00418i	0.00418577	+	0.999991i	$0.498668\pi$
$788$		0			0
$789$	−1.64891e15	+	1.64891e15i	−0.191987	+	0.191987i
$790$		0			0
$791$			1.00069e16i			1.14902i
$792$		0			0
$793$			1.41582e14i			0.0160327i
$794$		0			0
$795$	−8.81213e14	+	8.81213e14i	−0.0984151	+	0.0984151i
$796$		0			0
$797$	2.28772e15	+	2.28772e15i	0.251990	+	0.251990i	0.821786	−	0.569796i	$-0.192978\pi$
$797$	2.28772e15	+	2.28772e15i	0.251990	+	0.251990i	−0.569796	+	0.821786i	$0.692978\pi$
$798$		0			0
$799$	1.70928e16			1.85697
$800$		0			0
$801$	−9.79259e15			−1.04935
$802$		0			0
$803$	−7.63922e14	−	7.63922e14i	−0.0807446	−	0.0807446i
$804$		0			0
$805$	3.99055e15	−	3.99055e15i	0.416059	−	0.416059i
$806$		0			0
$807$		−	6.73725e15i		−	0.692912i
$808$		0			0
$809$			1.18390e16i			1.20115i	0.799568	+	0.600576i	$0.205062\pi$
$809$			1.18390e16i			1.20115i	−0.799568	+	0.600576i	$0.794938\pi$
$810$		0			0
$811$	6.73923e14	−	6.73923e14i	0.0674521	−	0.0674521i	−0.672576	−	0.740028i	$-0.734812\pi$
$811$	6.73923e14	−	6.73923e14i	0.0674521	−	0.0674521i	0.740028	+	0.672576i	$0.234812\pi$
$812$		0			0
$813$	2.06401e14	+	2.06401e14i	0.0203804	+	0.0203804i
$814$		0			0
$815$	−5.64076e15			−0.549504
$816$		0			0
$817$	4.47315e14			0.0429925
$818$		0			0
$819$	−5.81564e14	−	5.81564e14i	−0.0551488	−	0.0551488i
$820$		0			0
$821$	8.52198e15	−	8.52198e15i	0.797357	−	0.797357i	−0.185321	−	0.982678i	$-0.559332\pi$
$821$	8.52198e15	−	8.52198e15i	0.797357	−	0.797357i	0.982678	+	0.185321i	$0.0593324\pi$
$822$		0			0
$823$			1.25677e16i			1.16027i	0.814521	+	0.580134i	$0.197000\pi$
$823$			1.25677e16i			1.16027i	−0.814521	+	0.580134i	$0.803000\pi$
$824$		0			0
$825$		−	3.44113e14i		−	0.0313476i
$826$		0			0
$827$	−7.22965e15	+	7.22965e15i	−0.649886	+	0.649886i	−0.952965	−	0.303080i	$-0.901985\pi$
$827$	−7.22965e15	+	7.22965e15i	−0.649886	+	0.649886i	0.303080	+	0.952965i	$0.401985\pi$
$828$		0			0
$829$	−6.78362e15	−	6.78362e15i	−0.601744	−	0.601744i	0.339031	−	0.940775i	$-0.389901\pi$
$829$	−6.78362e15	−	6.78362e15i	−0.601744	−	0.601744i	−0.940775	+	0.339031i	$0.889901\pi$
$830$		0			0
$831$	−6.98211e15			−0.611197
$832$		0			0
$833$	4.76146e15			0.411332
$834$		0			0
$835$	2.14329e15	+	2.14329e15i	0.182728	+	0.182728i
$836$		0			0
$837$	5.02200e15	−	5.02200e15i	0.422558	−	0.422558i
$838$		0			0
$839$		−	2.46633e15i		−	0.204814i	−0.994743	−	0.102407i	$-0.967346\pi$
$839$		−	2.46633e15i		−	0.204814i	0.994743	−	0.102407i	$-0.0326545\pi$
$840$		0			0
$841$			1.21938e16i			0.999449i
$842$		0			0
$843$	3.92109e15	−	3.92109e15i	0.317216	−	0.317216i
$844$		0			0
$845$	6.89476e15	+	6.89476e15i	0.550563	+	0.550563i
$846$		0			0
$847$	1.04715e16			0.825375
$848$		0			0
$849$	6.93467e15			0.539552
$850$		0			0
$851$	8.51114e15	+	8.51114e15i	0.653695	+	0.653695i
$852$		0			0
$853$	5.10449e15	−	5.10449e15i	0.387019	−	0.387019i	−0.486604	−	0.873623i	$-0.661764\pi$
$853$	5.10449e15	−	5.10449e15i	0.387019	−	0.387019i	0.873623	+	0.486604i	$0.161764\pi$
$854$		0			0
$855$			7.75598e14i			0.0580528i
$856$		0			0
$857$			1.88606e16i			1.39367i	0.717230	+	0.696836i	$0.245410\pi$
$857$			1.88606e16i			1.39367i	−0.717230	+	0.696836i	$0.754590\pi$
$858$		0			0
$859$	−9.36000e15	+	9.36000e15i	−0.682831	+	0.682831i	−0.960637	−	0.277806i	$-0.910393\pi$
$859$	−9.36000e15	+	9.36000e15i	−0.682831	+	0.682831i	0.277806	+	0.960637i	$0.410393\pi$
$860$		0			0
$861$	4.50569e15	+	4.50569e15i	0.324522	+	0.324522i
$862$		0			0
$863$	−1.77662e16			−1.26338			−0.631690	−	0.775221i	$-0.717639\pi$
$863$	−1.77662e16			−1.26338			−0.631690	+	0.775221i	$0.717639\pi$
$864$		0			0
$865$	1.52526e16			1.07092
$866$		0			0
$867$	−6.03756e15	−	6.03756e15i	−0.418559	−	0.418559i
$868$		0			0
$869$	−1.38784e12	+	1.38784e12i	−9.50015e−5	+	9.50015e-5i
$870$		0			0
$871$		−	1.18398e15i		−	0.0800286i
$872$		0			0
$873$			5.38586e15i			0.359482i
$874$		0			0
$875$	−9.94820e15	+	9.94820e15i	−0.655693	+	0.655693i
$876$		0			0
$877$	−5.61984e14	−	5.61984e14i	−0.0365785	−	0.0365785i	0.688581	−	0.725159i	$-0.258234\pi$
$877$	−5.61984e14	−	5.61984e14i	−0.0365785	−	0.0365785i	−0.725159	+	0.688581i	$0.758234\pi$
$878$		0			0
$879$	3.28867e15			0.211389
$880$		0			0
$881$	9.89236e15			0.627961			0.313980	−	0.949430i	$-0.398337\pi$
$881$	9.89236e15			0.627961			0.313980	+	0.949430i	$0.398337\pi$
$882$		0			0
$883$	1.07380e16	+	1.07380e16i	0.673196	+	0.673196i	0.958451	−	0.285256i	$-0.0920785\pi$
$883$	1.07380e16	+	1.07380e16i	0.673196	+	0.673196i	−0.285256	+	0.958451i	$0.592079\pi$
$884$		0			0
$885$	7.98993e15	−	7.98993e15i	0.494715	−	0.494715i
$886$		0			0
$887$			9.63733e15i			0.589355i	0.955597	+	0.294678i	$0.0952122\pi$
$887$			9.63733e15i			0.589355i	−0.955597	+	0.294678i	$0.904788\pi$
$888$		0			0
$889$		−	7.79876e15i		−	0.471049i
$890$		0			0
$891$	−8.74847e14	+	8.74847e14i	−0.0521921	+	0.0521921i
$892$		0			0
$893$	1.37591e15	+	1.37591e15i	0.0810786	+	0.0810786i
$894$		0			0
$895$	1.88538e16			1.09742
$896$		0			0
$897$	−8.11861e14			−0.0466792
$898$		0			0
$899$	−1.27779e16	−	1.27779e16i	−0.725742	−	0.725742i
$900$		0			0
$901$	−7.29680e15	+	7.29680e15i	−0.409398	+	0.409398i
$902$		0			0
$903$			3.26444e15i			0.180936i
$904$		0			0
$905$		−	2.70743e16i		−	1.48249i
$906$		0			0
$907$	3.59486e15	−	3.59486e15i	0.194465	−	0.194465i	−0.603157	−	0.797622i	$-0.706091\pi$
$907$	3.59486e15	−	3.59486e15i	0.194465	−	0.194465i	0.797622	+	0.603157i	$0.206091\pi$
$908$		0			0
$909$	1.06706e15	+	1.06706e15i	0.0570281	+	0.0570281i
$910$		0			0
$911$	−1.25477e16			−0.662540			−0.331270	−	0.943536i	$-0.607477\pi$
$911$	−1.25477e16			−0.662540			−0.331270	+	0.943536i	$0.607477\pi$
$912$		0			0
$913$	−2.87427e15			−0.149947
$914$		0			0
$915$	6.88989e14	+	6.88989e14i	0.0355137	+	0.0355137i
$916$		0			0
$917$	−1.59497e16	+	1.59497e16i	−0.812311	+	0.812311i
$918$		0			0
$919$			5.50344e15i			0.276949i	0.990366	+	0.138474i	$0.0442198\pi$
$919$			5.50344e15i			0.276949i	−0.990366	+	0.138474i	$0.955780\pi$
$920$		0			0
$921$			9.76203e15i			0.485414i
$922$		0			0
$923$	−3.18554e15	+	3.18554e15i	−0.156521	+	0.156521i
$924$		0			0
$925$	−5.81027e15	−	5.81027e15i	−0.282109	−	0.282109i
$926$		0			0
$927$	−1.98570e16			−0.952744
$928$		0			0
$929$	−8.00447e15			−0.379530			−0.189765	−	0.981830i	$-0.560773\pi$
$929$	−8.00447e15			−0.379530			−0.189765	+	0.981830i	$0.560773\pi$
$930$		0			0
$931$	3.83281e14	+	3.83281e14i	0.0179595	+	0.0179595i
$932$		0			0
$933$	−8.01710e14	+	8.01710e14i	−0.0371252	+	0.0371252i
$934$		0			0
$935$			4.70654e15i			0.215396i
$936$		0			0
$937$		−	2.07607e16i		−	0.939017i	−0.882928	−	0.469509i	$-0.844431\pi$
$937$		−	2.07607e16i		−	0.939017i	0.882928	−	0.469509i	$-0.155569\pi$
$938$		0			0
$939$	9.83940e14	−	9.83940e14i	0.0439853	−	0.0439853i
$940$		0			0
$941$	2.43338e16	+	2.43338e16i	1.07514	+	1.07514i	0.996937	+	0.0782075i	$0.0249197\pi$
$941$	2.43338e16	+	2.43338e16i	1.07514	+	1.07514i	0.0782075	+	0.996937i	$0.475080\pi$
$942$		0			0
$943$	−2.33752e16			−1.02080
$944$		0			0
$945$	−1.28435e16			−0.554380
$946$		0			0
$947$	1.37491e16	+	1.37491e16i	0.586609	+	0.586609i	0.936711	−	0.350103i	$-0.113853\pi$
$947$	1.37491e16	+	1.37491e16i	0.586609	+	0.586609i	−0.350103	+	0.936711i	$0.613853\pi$
$948$		0			0
$949$	1.23038e15	−	1.23038e15i	0.0518889	−	0.0518889i
$950$		0			0
$951$			4.83568e15i			0.201588i
$952$		0			0
$953$		−	3.61839e16i		−	1.49109i	−0.666454	−	0.745546i	$-0.732189\pi$
$953$		−	3.61839e16i		−	1.49109i	0.666454	−	0.745546i	$-0.267811\pi$
$954$		0			0
$955$	5.56569e15	−	5.56569e15i	0.226726	−	0.226726i
$956$		0			0
$957$	−2.06393e15	−	2.06393e15i	−0.0831152	−	0.0831152i
$958$		0			0
$959$	3.14140e16			1.25061
$960$		0			0
$961$	−1.20221e16			−0.473153
$962$		0			0
$963$	−1.99163e16	−	1.99163e16i	−0.774932	−	0.774932i
$964$		0			0
$965$	−1.06565e16	+	1.06565e16i	−0.409933	+	0.409933i
$966$		0			0
$967$		−	1.91870e16i		−	0.729731i	−0.931060	−	0.364865i	$-0.881115\pi$
$967$		−	1.91870e16i		−	0.729731i	0.931060	−	0.364865i	$-0.118885\pi$
$968$		0			0
$969$		−	1.72814e15i		−	0.0649826i
$970$		0			0
$971$	2.73115e16	−	2.73115e16i	1.01541	−	1.01541i	0.0155257	−	0.999879i	$-0.495058\pi$
$971$	2.73115e16	−	2.73115e16i	1.01541	−	1.01541i	0.999879	−	0.0155257i	$-0.00494219\pi$
$972$		0			0
$973$	−2.07297e16	−	2.07297e16i	−0.762031	−	0.762031i
$974$		0			0
$975$	5.54230e14			0.0201449
$976$		0			0
$977$	−3.28279e16			−1.17984			−0.589919	−	0.807462i	$-0.700840\pi$
$977$	−3.28279e16			−1.17984			−0.589919	+	0.807462i	$0.700840\pi$
$978$		0			0
$979$	−4.78344e15	−	4.78344e15i	−0.169995	−	0.169995i
$980$		0			0
$981$	−2.47607e16	+	2.47607e16i	−0.870128	+	0.870128i
$982$		0			0
$983$		−	6.37843e15i		−	0.221651i	−0.993840	−	0.110825i	$-0.964651\pi$
$983$		−	6.37843e15i		−	0.221651i	0.993840	−	0.110825i	$-0.0353494\pi$
$984$		0			0
$985$			5.38389e15i			0.185011i
$986$		0			0
$987$	−1.00412e16	+	1.00412e16i	−0.341224	+	0.341224i
$988$		0			0
$989$	−8.46784e15	−	8.46784e15i	−0.284573	−	0.284573i
$990$		0			0
$991$	4.94195e16			1.64245			0.821227	−	0.570602i	$-0.193290\pi$
$991$	4.94195e16			1.64245			0.821227	+	0.570602i	$0.193290\pi$
$992$		0			0
$993$	−1.04766e16			−0.344348
$994$		0			0
$995$	−2.47804e16	−	2.47804e16i	−0.805528	−	0.805528i
$996$		0			0
$997$	9.89761e15	−	9.89761e15i	0.318205	−	0.318205i	−0.529872	−	0.848077i	$-0.677760\pi$
$997$	9.89761e15	−	9.89761e15i	0.318205	−	0.318205i	0.848077	+	0.529872i	$0.177760\pi$
$998$		0			0
$999$		−	2.73929e16i		−	0.871018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.12.e.b.33.9		42
4.3	odd	2		128.12.e.a.33.13		42
8.3	odd	2		64.12.e.a.17.9		42
8.5	even	2		16.12.e.a.13.10	yes	42
16.3	odd	4		64.12.e.a.49.9		42
16.5	even	4	inner	128.12.e.b.97.9		42
16.11	odd	4		128.12.e.a.97.13		42
16.13	even	4		16.12.e.a.5.10	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.10	✓	42	16.13	even	4
16.12.e.a.13.10	yes	42	8.5	even	2
64.12.e.a.17.9		42	8.3	odd	2
64.12.e.a.49.9		42	16.3	odd	4
128.12.e.a.33.13		42	4.3	odd	2
128.12.e.a.97.13		42	16.11	odd	4
128.12.e.b.33.9		42	1.1	even	1	trivial
128.12.e.b.97.9		42	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-137.041 - 137.041i) q^{3} +(-3899.66 + 3899.66i) q^{5} -37938.5i q^{7} -139586. i q^{9} +O(q^{10})\)	\(q+(-137.041 - 137.041i) q^{3} +(-3899.66 + 3899.66i) q^{5} -37938.5i q^{7} -139586. i q^{9} +(68184.4 - 68184.4i) q^{11} +(109818. + 109818. i) q^{13} +1.06883e6 q^{15} +8.85033e6 q^{17} +(712421. + 712421. i) q^{19} +(-5.19914e6 + 5.19914e6i) q^{21} -2.69728e7i q^{23} +1.84134e7i q^{25} +(-4.34056e7 + 4.34056e7i) q^{27} +(1.10441e8 + 1.10441e8i) q^{29} -1.15699e8 q^{31} -1.86882e7 q^{33} +(1.47947e8 + 1.47947e8i) q^{35} +(-3.15546e8 + 3.15546e8i) q^{37} -3.00993e7i q^{39} -8.66621e8i q^{41} +(3.13940e8 - 3.13940e8i) q^{43} +(5.44339e8 + 5.44339e8i) q^{45} +1.93131e9 q^{47} +5.37998e8 q^{49} +(-1.21286e9 - 1.21286e9i) q^{51} +(-8.24466e8 + 8.24466e8i) q^{53} +5.31792e8i q^{55} -1.95262e8i q^{57} +(7.47540e9 - 7.47540e9i) q^{59} +(6.44620e8 + 6.44620e8i) q^{61} -5.29570e9 q^{63} -8.56508e8 q^{65} +(-5.39064e9 - 5.39064e9i) q^{67} +(-3.69638e9 + 3.69638e9i) q^{69} +2.90073e10i q^{71} -1.12038e10i q^{73} +(2.52340e9 - 2.52340e9i) q^{75} +(-2.58681e9 - 2.58681e9i) q^{77} -2.03542e7 q^{79} -1.28306e10 q^{81} +(-2.10772e10 - 2.10772e10i) q^{83} +(-3.45133e10 + 3.45133e10i) q^{85} -3.02699e10i q^{87} -7.01544e10i q^{89} +(4.16634e9 - 4.16634e9i) q^{91} +(1.58556e10 + 1.58556e10i) q^{93} -5.55640e9 q^{95} -3.85844e10 q^{97} +(-9.51762e9 - 9.51762e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 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

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Database

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