LMFDB - Embedded newform 128.12.e.b.33.18

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			33.18
Character	$\chi$	$=$	128.33
Dual form			128.12.e.b.97.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(435.014 + 435.014i) q^{3} +(1517.34 - 1517.34i) q^{5} +59722.7i q^{7} +201326. i q^{9} +O(q^{10})$	\(q+(435.014 + 435.014i) q^{3} +(1517.34 - 1517.34i) q^{5} +59722.7i q^{7} +201326. i q^{9} +(-56196.6 + 56196.6i) q^{11} +(315796. + 315796. i) q^{13} +1.32013e6 q^{15} +8.11170e6 q^{17} +(1.33811e7 + 1.33811e7i) q^{19} +(-2.59802e7 + 2.59802e7i) q^{21} -2.84613e7i q^{23} +4.42235e7i q^{25} +(-1.05184e7 + 1.05184e7i) q^{27} +(-7.59695e7 - 7.59695e7i) q^{29} +5.67278e7 q^{31} -4.88926e7 q^{33} +(9.06196e7 + 9.06196e7i) q^{35} +(-3.75680e8 + 3.75680e8i) q^{37} +2.74751e8i q^{39} +1.51696e7i q^{41} +(-1.08339e9 + 1.08339e9i) q^{43} +(3.05481e8 + 3.05481e8i) q^{45} +2.79798e9 q^{47} -1.58947e9 q^{49} +(3.52870e9 + 3.52870e9i) q^{51} +(-2.03657e9 + 2.03657e9i) q^{53} +1.70539e8i q^{55} +1.16419e10i q^{57} +(4.23123e9 - 4.23123e9i) q^{59} +(-6.54407e9 - 6.54407e9i) q^{61} -1.20238e10 q^{63} +9.58341e8 q^{65} +(8.01903e9 + 8.01903e9i) q^{67} +(1.23810e10 - 1.23810e10i) q^{69} -1.40718e10i q^{71} +6.29343e9i q^{73} +(-1.92378e10 + 1.92378e10i) q^{75} +(-3.35621e9 - 3.35621e9i) q^{77} -3.46459e10 q^{79} +2.65131e10 q^{81} +(-4.29998e10 - 4.29998e10i) q^{83} +(1.23082e10 - 1.23082e10i) q^{85} -6.60955e10i q^{87} +3.39308e9i q^{89} +(-1.88602e10 + 1.88602e10i) q^{91} +(2.46773e10 + 2.46773e10i) q^{93} +4.06073e10 q^{95} +1.55551e10 q^{97} +(-1.13139e10 - 1.13139e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	435.014	+	435.014i	1.03356	+	1.03356i	0.999417	+	0.0341434i	$0.0108703\pi$
$3$	435.014	+	435.014i	1.03356	+	1.03356i	0.0341434	+	0.999417i	$0.489130\pi$
$4$		0			0
$5$	1517.34	−	1517.34i	0.217144	−	0.217144i	−0.590150	−	0.807294i	$-0.700931\pi$
$5$	1517.34	−	1517.34i	0.217144	−	0.217144i	0.807294	+	0.590150i	$0.200931\pi$
$6$		0			0
$7$			59722.7i			1.34307i	0.740971	+	0.671537i	$0.234366\pi$
$7$			59722.7i			1.34307i	−0.740971	+	0.671537i	$0.765634\pi$
$8$		0			0
$9$			201326.i			1.13649i
$10$		0			0
$11$	−56196.6	+	56196.6i	−0.105208	+	0.105208i	−0.757752	−	0.652543i	$-0.773702\pi$
$11$	−56196.6	+	56196.6i	−0.105208	+	0.105208i	0.652543	+	0.757752i	$0.273702\pi$
$12$		0			0
$13$	315796.	+	315796.i	0.235895	+	0.235895i	0.815148	−	0.579253i	$-0.196656\pi$
$13$	315796.	+	315796.i	0.235895	+	0.235895i	−0.579253	+	0.815148i	$0.696656\pi$
$14$		0			0
$15$	1.32013e6			0.448863
$16$		0			0
$17$	8.11170e6			1.38562			0.692808	−	0.721122i	$-0.256373\pi$
$17$	8.11170e6			1.38562			0.692808	+	0.721122i	$0.256373\pi$
$18$		0			0
$19$	1.33811e7	+	1.33811e7i	1.23978	+	1.23978i	0.960089	+	0.279695i	$0.0902334\pi$
$19$	1.33811e7	+	1.33811e7i	1.23978	+	1.23978i	0.279695	+	0.960089i	$0.409767\pi$
$20$		0			0
$21$	−2.59802e7	+	2.59802e7i	−1.38815	+	1.38815i
$22$		0			0
$23$		−	2.84613e7i		−	0.922043i	−0.887389	−	0.461022i	$-0.847483\pi$
$23$		−	2.84613e7i		−	0.922043i	0.887389	−	0.461022i	$-0.152517\pi$
$24$		0			0
$25$			4.42235e7i			0.905697i
$26$		0			0
$27$	−1.05184e7	+	1.05184e7i	−0.141075	+	0.141075i
$28$		0			0
$29$	−7.59695e7	−	7.59695e7i	−0.687781	−	0.687781i	0.273960	−	0.961741i	$-0.411666\pi$
$29$	−7.59695e7	−	7.59695e7i	−0.687781	−	0.687781i	−0.961741	+	0.273960i	$0.911666\pi$
$30$		0			0
$31$	5.67278e7			0.355882			0.177941	−	0.984041i	$-0.443056\pi$
$31$	5.67278e7			0.355882			0.177941	+	0.984041i	$0.443056\pi$
$32$		0			0
$33$	−4.88926e7			−0.217479
$34$		0			0
$35$	9.06196e7	+	9.06196e7i	0.291641	+	0.291641i
$36$		0			0
$37$	−3.75680e8	+	3.75680e8i	−0.890654	+	0.890654i	−0.994585	−	0.103931i	$-0.966858\pi$
$37$	−3.75680e8	+	3.75680e8i	−0.890654	+	0.890654i	0.103931	+	0.994585i	$0.466858\pi$
$38$		0			0
$39$			2.74751e8i			0.487623i
$40$		0			0
$41$			1.51696e7i			0.0204486i	0.999948	+	0.0102243i	$0.00325455\pi$
$41$			1.51696e7i			0.0204486i	−0.999948	+	0.0102243i	$0.996745\pi$
$42$		0			0
$43$	−1.08339e9	+	1.08339e9i	−1.12385	+	1.12385i	−0.132689	+	0.991158i	$0.542361\pi$
$43$	−1.08339e9	+	1.08339e9i	−1.12385	+	1.12385i	−0.991158	+	0.132689i	$0.957639\pi$
$44$		0			0
$45$	3.05481e8	+	3.05481e8i	0.246783	+	0.246783i
$46$		0			0
$47$	2.79798e9			1.77954			0.889768	−	0.456414i	$-0.150866\pi$
$47$	2.79798e9			1.77954			0.889768	+	0.456414i	$0.150866\pi$
$48$		0			0
$49$	−1.58947e9			−0.803848
$50$		0			0
$51$	3.52870e9	+	3.52870e9i	1.43212	+	1.43212i
$52$		0			0
$53$	−2.03657e9	+	2.03657e9i	−0.668932	+	0.668932i	−0.957469	−	0.288537i	$-0.906831\pi$
$53$	−2.03657e9	+	2.03657e9i	−0.668932	+	0.668932i	0.288537	+	0.957469i	$0.406831\pi$
$54$		0			0
$55$			1.70539e8i			0.0456908i
$56$		0			0
$57$			1.16419e10i			2.56278i
$58$		0			0
$59$	4.23123e9	−	4.23123e9i	0.770513	−	0.770513i	−0.207683	−	0.978196i	$-0.566592\pi$
$59$	4.23123e9	−	4.23123e9i	0.770513	−	0.770513i	0.978196	+	0.207683i	$0.0665922\pi$
$60$		0			0
$61$	−6.54407e9	−	6.54407e9i	−0.992051	−	0.992051i	0.00791726	−	0.999969i	$-0.497480\pi$
$61$	−6.54407e9	−	6.54407e9i	−0.992051	−	0.992051i	−0.999969	+	0.00791726i	$0.997480\pi$
$62$		0			0
$63$	−1.20238e10			−1.52640
$64$		0			0
$65$	9.58341e8			0.102446
$66$		0			0
$67$	8.01903e9	+	8.01903e9i	0.725622	+	0.725622i	0.969744	−	0.244122i	$-0.0784998\pi$
$67$	8.01903e9	+	8.01903e9i	0.725622	+	0.725622i	−0.244122	+	0.969744i	$0.578500\pi$
$68$		0			0
$69$	1.23810e10	−	1.23810e10i	0.952987	−	0.952987i
$70$		0			0
$71$		−	1.40718e10i		−	0.925608i	−0.886461	−	0.462804i	$-0.846843\pi$
$71$		−	1.40718e10i		−	0.925608i	0.886461	−	0.462804i	$-0.153157\pi$
$72$		0			0
$73$			6.29343e9i			0.355314i	0.984093	+	0.177657i	$0.0568517\pi$
$73$			6.29343e9i			0.355314i	−0.984093	+	0.177657i	$0.943148\pi$
$74$		0			0
$75$	−1.92378e10	+	1.92378e10i	−0.936092	+	0.936092i
$76$		0			0
$77$	−3.35621e9	−	3.35621e9i	−0.141303	−	0.141303i
$78$		0			0
$79$	−3.46459e10			−1.26678			−0.633392	−	0.773831i	$-0.718338\pi$
$79$	−3.46459e10			−1.26678			−0.633392	+	0.773831i	$0.718338\pi$
$80$		0			0
$81$	2.65131e10			0.844875
$82$		0			0
$83$	−4.29998e10	−	4.29998e10i	−1.19822	−	1.19822i	−0.974699	−	0.223521i	$-0.928245\pi$
$83$	−4.29998e10	−	4.29998e10i	−1.19822	−	1.19822i	−0.223521	−	0.974699i	$-0.571755\pi$
$84$		0			0
$85$	1.23082e10	−	1.23082e10i	0.300878	−	0.300878i
$86$		0			0
$87$		−	6.60955e10i		−	1.42173i
$88$		0			0
$89$			3.39308e9i			0.0644093i	0.999481	+	0.0322047i	$0.0102528\pi$
$89$			3.39308e9i			0.0644093i	−0.999481	+	0.0322047i	$0.989747\pi$
$90$		0			0
$91$	−1.88602e10	+	1.88602e10i	−0.316824	+	0.316824i
$92$		0			0
$93$	2.46773e10	+	2.46773e10i	0.367826	+	0.367826i
$94$		0			0
$95$	4.06073e10			0.538423
$96$		0			0
$97$	1.55551e10			0.183920			0.0919601	−	0.995763i	$-0.470687\pi$
$97$	1.55551e10			0.183920			0.0919601	+	0.995763i	$0.470687\pi$
$98$		0			0
$99$	−1.13139e10	−	1.13139e10i	−0.119569	−	0.119569i
$100$		0			0
$101$	−8.04221e10	+	8.04221e10i	−0.761391	+	0.761391i	−0.976574	−	0.215183i	$-0.930965\pi$
$101$	−8.04221e10	+	8.04221e10i	−0.761391	+	0.761391i	0.215183	+	0.976574i	$0.430965\pi$
$102$		0			0
$103$		−	2.48411e10i		−	0.211138i	−0.994412	−	0.105569i	$-0.966334\pi$
$103$		−	2.48411e10i		−	0.211138i	0.994412	−	0.105569i	$-0.0336663\pi$
$104$		0			0
$105$			7.88415e10i			0.602856i
$106$		0			0
$107$	−5.76499e10	+	5.76499e10i	−0.397363	+	0.397363i	−0.877302	−	0.479939i	$-0.840659\pi$
$107$	−5.76499e10	+	5.76499e10i	−0.397363	+	0.397363i	0.479939	+	0.877302i	$0.340659\pi$
$108$		0			0
$109$	5.69123e10	+	5.69123e10i	0.354291	+	0.354291i	0.861704	−	0.507412i	$-0.169398\pi$
$109$	5.69123e10	+	5.69123e10i	0.354291	+	0.354291i	−0.507412	+	0.861704i	$0.669398\pi$
$110$		0			0
$111$	−3.26852e11			−1.84109
$112$		0			0
$113$	1.29979e11			0.663653			0.331826	−	0.943340i	$-0.392335\pi$
$113$	1.29979e11			0.663653			0.331826	+	0.943340i	$0.392335\pi$
$114$		0			0
$115$	−4.31854e10	−	4.31854e10i	−0.200216	−	0.200216i
$116$		0			0
$117$	−6.35782e10	+	6.35782e10i	−0.268093	+	0.268093i
$118$		0			0
$119$			4.84453e11i			1.86099i
$120$		0			0
$121$			2.78996e11i			0.977862i
$122$		0			0
$123$	−6.59899e9	+	6.59899e9i	−0.0211348	+	0.0211348i
$124$		0			0
$125$	1.41191e11	+	1.41191e11i	0.413811	+	0.413811i
$126$		0			0
$127$	−9.81625e9			−0.0263648			−0.0131824	−	0.999913i	$-0.504196\pi$
$127$	−9.81625e9			−0.0263648			−0.0131824	+	0.999913i	$0.504196\pi$
$128$		0			0
$129$	−9.42576e11			−2.32313
$130$		0			0
$131$	−3.01725e11	−	3.01725e11i	−0.683312	−	0.683312i	0.277433	−	0.960745i	$-0.410516\pi$
$131$	−3.01725e11	−	3.01725e11i	−0.683312	−	0.683312i	−0.960745	+	0.277433i	$0.910516\pi$
$132$		0			0
$133$	−7.99153e11	+	7.99153e11i	−1.66512	+	1.66512i
$134$		0			0
$135$			3.19200e10i			0.0612671i
$136$		0			0
$137$			2.21227e11i			0.391629i	0.980641	+	0.195814i	$0.0627350\pi$
$137$			2.21227e11i			0.391629i	−0.980641	+	0.195814i	$0.937265\pi$
$138$		0			0
$139$	−1.76441e11	+	1.76441e11i	−0.288415	+	0.288415i	−0.836453	−	0.548038i	$-0.815375\pi$
$139$	−1.76441e11	+	1.76441e11i	−0.288415	+	0.288415i	0.548038	+	0.836453i	$0.315375\pi$
$140$		0			0
$141$	1.21716e12	+	1.21716e12i	1.83926	+	1.83926i
$142$		0			0
$143$	−3.54934e10			−0.0496363
$144$		0			0
$145$	−2.30543e11			−0.298695
$146$		0			0
$147$	−6.91441e11	−	6.91441e11i	−0.830825	−	0.830825i
$148$		0			0
$149$	−1.96547e10	+	1.96547e10i	−0.0219251	+	0.0219251i	−0.717984	−	0.696059i	$-0.754935\pi$
$149$	−1.96547e10	+	1.96547e10i	−0.0219251	+	0.0219251i	0.696059	+	0.717984i	$0.254935\pi$
$150$		0			0
$151$			1.18330e12i			1.22666i	0.789828	+	0.613329i	$0.210170\pi$
$151$			1.18330e12i			1.22666i	−0.789828	+	0.613329i	$0.789830\pi$
$152$		0			0
$153$			1.63310e12i			1.57474i
$154$		0			0
$155$	8.60753e10	−	8.60753e10i	0.0772777	−	0.0772777i
$156$		0			0
$157$	−4.40152e11	−	4.40152e11i	−0.368260	−	0.368260i	0.498582	−	0.866842i	$-0.333854\pi$
$157$	−4.40152e11	−	4.40152e11i	−0.368260	−	0.368260i	−0.866842	+	0.498582i	$0.833854\pi$
$158$		0			0
$159$	−1.77187e12			−1.38276
$160$		0			0
$161$	1.69978e12			1.23837
$162$		0			0
$163$	−1.90450e11	−	1.90450e11i	−0.129643	−	0.129643i	0.639308	−	0.768951i	$-0.279221\pi$
$163$	−1.90450e11	−	1.90450e11i	−0.129643	−	0.129643i	−0.768951	+	0.639308i	$0.779221\pi$
$164$		0			0
$165$	−7.41867e10	+	7.41867e10i	−0.0472242	+	0.0472242i
$166$		0			0
$167$		−	2.80229e12i		−	1.66945i	−0.550669	−	0.834723i	$-0.685628\pi$
$167$		−	2.80229e12i		−	1.66945i	0.550669	−	0.834723i	$-0.314372\pi$
$168$		0			0
$169$		−	1.59271e12i		−	0.888707i
$170$		0			0
$171$	−2.69396e12	+	2.69396e12i	−1.40901	+	1.40901i
$172$		0			0
$173$	−4.15917e11	−	4.15917e11i	−0.204058	−	0.204058i	0.597678	−	0.801736i	$-0.296090\pi$
$173$	−4.15917e11	−	4.15917e11i	−0.204058	−	0.204058i	−0.801736	+	0.597678i	$0.796090\pi$
$174$		0			0
$175$	−2.64114e12			−1.21642
$176$		0			0
$177$	3.68128e12			1.59274
$178$		0			0
$179$	−1.25777e12	−	1.25777e12i	−0.511575	−	0.511575i	0.403434	−	0.915009i	$-0.367817\pi$
$179$	−1.25777e12	−	1.25777e12i	−0.511575	−	0.511575i	−0.915009	+	0.403434i	$0.867817\pi$
$180$		0			0
$181$	7.02645e11	−	7.02645e11i	0.268846	−	0.268846i	−0.559789	−	0.828635i	$-0.689118\pi$
$181$	7.02645e11	−	7.02645e11i	0.268846	−	0.268846i	0.828635	+	0.559789i	$0.189118\pi$
$182$		0			0
$183$		−	5.69352e12i		−	2.05069i
$184$		0			0
$185$			1.14007e12i			0.386800i
$186$		0			0
$187$	−4.55850e11	+	4.55850e11i	−0.145779	+	0.145779i
$188$		0			0
$189$	−6.28187e11	−	6.28187e11i	−0.189474	−	0.189474i
$190$		0			0
$191$	−1.55093e12			−0.441478			−0.220739	−	0.975333i	$-0.570847\pi$
$191$	−1.55093e12			−0.441478			−0.220739	+	0.975333i	$0.570847\pi$
$192$		0			0
$193$	−4.58114e12			−1.23143			−0.615713	−	0.787971i	$-0.711132\pi$
$193$	−4.58114e12			−1.23143			−0.615713	+	0.787971i	$0.711132\pi$
$194$		0			0
$195$	4.16891e11	+	4.16891e11i	0.105885	+	0.105885i
$196$		0			0
$197$	−8.42541e11	+	8.42541e11i	−0.202315	+	0.202315i	−0.800991	−	0.598676i	$-0.795694\pi$
$197$	−8.42541e11	+	8.42541e11i	−0.202315	+	0.202315i	0.598676	+	0.800991i	$0.295694\pi$
$198$		0			0
$199$			6.45938e12i			1.46723i	0.679564	+	0.733616i	$0.262169\pi$
$199$			6.45938e12i			1.46723i	−0.679564	+	0.733616i	$0.737831\pi$
$200$		0			0
$201$			6.97677e12i			1.49995i
$202$		0			0
$203$	4.53710e12	−	4.53710e12i	0.923741	−	0.923741i
$204$		0			0
$205$	2.30175e10	+	2.30175e10i	0.00444029	+	0.00444029i
$206$		0			0
$207$	5.73001e12			1.04790
$208$		0			0
$209$	−1.50394e12			−0.260871
$210$		0			0
$211$	5.66233e12	+	5.66233e12i	0.932055	+	0.932055i	0.997834	−	0.0657787i	$-0.0209532\pi$
$211$	5.66233e12	+	5.66233e12i	0.932055	+	0.932055i	−0.0657787	+	0.997834i	$0.520953\pi$
$212$		0			0
$213$	6.12140e12	−	6.12140e12i	0.956672	−	0.956672i
$214$		0			0
$215$			3.28773e12i			0.488073i
$216$		0			0
$217$			3.38793e12i			0.477976i
$218$		0			0
$219$	−2.73773e12	+	2.73773e12i	−0.367238	+	0.367238i
$220$		0			0
$221$	2.56165e12	+	2.56165e12i	0.326860	+	0.326860i
$222$		0			0
$223$	2.46919e12			0.299832			0.149916	−	0.988699i	$-0.452100\pi$
$223$	2.46919e12			0.299832			0.149916	+	0.988699i	$0.452100\pi$
$224$		0			0
$225$	−8.90336e12			−1.02932
$226$		0			0
$227$	2.54818e12	+	2.54818e12i	0.280600	+	0.280600i	0.833348	−	0.552748i	$-0.186421\pi$
$227$	2.54818e12	+	2.54818e12i	0.280600	+	0.280600i	−0.552748	+	0.833348i	$0.686421\pi$
$228$		0			0
$229$	−8.81027e12	+	8.81027e12i	−0.924473	+	0.924473i	−0.997342	−	0.0728690i	$-0.976785\pi$
$229$	−8.81027e12	+	8.81027e12i	−0.924473	+	0.924473i	0.0728690	+	0.997342i	$0.476785\pi$
$230$		0			0
$231$		−	2.92000e12i		−	0.292090i
$232$		0			0
$233$		−	1.10524e13i		−	1.05438i	−0.849747	−	0.527191i	$-0.823245\pi$
$233$		−	1.10524e13i		−	1.05438i	0.849747	−	0.527191i	$-0.176755\pi$
$234$		0			0
$235$	4.24549e12	−	4.24549e12i	0.386415	−	0.386415i
$236$		0			0
$237$	−1.50714e13	−	1.50714e13i	−1.30930	−	1.30930i
$238$		0			0
$239$	8.37084e12			0.694353			0.347177	−	0.937800i	$-0.387140\pi$
$239$	8.37084e12			0.694353			0.347177	+	0.937800i	$0.387140\pi$
$240$		0			0
$241$	1.48928e13			1.18000			0.590002	−	0.807402i	$-0.299127\pi$
$241$	1.48928e13			1.18000			0.590002	+	0.807402i	$0.299127\pi$
$242$		0			0
$243$	1.33969e13	+	1.33969e13i	1.01430	+	1.01430i
$244$		0			0
$245$	−2.41177e12	+	2.41177e12i	−0.174551	+	0.174551i
$246$		0			0
$247$			8.45139e12i			0.584918i
$248$		0			0
$249$		−	3.74110e13i		−	2.47687i
$250$		0			0
$251$	7.98403e12	−	7.98403e12i	0.505844	−	0.505844i	−0.407404	−	0.913248i	$-0.633566\pi$
$251$	7.98403e12	−	7.98403e12i	0.505844	−	0.505844i	0.913248	+	0.407404i	$0.133566\pi$
$252$		0			0
$253$	1.59943e12	+	1.59943e12i	0.0970067	+	0.0970067i
$254$		0			0
$255$	1.07085e13			0.621952
$256$		0			0
$257$	2.70752e12			0.150640			0.0753200	−	0.997159i	$-0.476002\pi$
$257$	2.70752e12			0.150640			0.0753200	+	0.997159i	$0.476002\pi$
$258$		0			0
$259$	−2.24366e13	−	2.24366e13i	−1.19621	−	1.19621i
$260$		0			0
$261$	1.52947e13	−	1.52947e13i	0.781659	−	0.781659i
$262$		0			0
$263$		−	9.34160e11i		−	0.0457788i	−0.999738	−	0.0228894i	$-0.992713\pi$
$263$		−	9.34160e11i		−	0.0457788i	0.999738	−	0.0228894i	$-0.00728656\pi$
$264$		0			0
$265$			6.18034e12i			0.290509i
$266$		0			0
$267$	−1.47603e12	+	1.47603e12i	−0.0665709	+	0.0665709i
$268$		0			0
$269$	1.46911e13	+	1.46911e13i	0.635942	+	0.635942i	0.949552	−	0.313610i	$-0.101538\pi$
$269$	1.46911e13	+	1.46911e13i	0.635942	+	0.635942i	−0.313610	+	0.949552i	$0.601538\pi$
$270$		0			0
$271$	3.98105e13			1.65450			0.827249	−	0.561835i	$-0.189905\pi$
$271$	3.98105e13			1.65450			0.827249	+	0.561835i	$0.189905\pi$
$272$		0			0
$273$	−1.64089e13			−0.654914
$274$		0			0
$275$	−2.48521e12	−	2.48521e12i	−0.0952869	−	0.0952869i
$276$		0			0
$277$	1.57182e13	−	1.57182e13i	0.579114	−	0.579114i	−0.355545	−	0.934659i	$-0.615705\pi$
$277$	1.57182e13	−	1.57182e13i	0.579114	−	0.579114i	0.934659	+	0.355545i	$0.115705\pi$
$278$		0			0
$279$			1.14208e13i			0.404458i
$280$		0			0
$281$		−	5.65668e13i		−	1.92609i	−0.269339	−	0.963045i	$-0.586805\pi$
$281$		−	5.65668e13i		−	1.92609i	0.269339	−	0.963045i	$-0.413195\pi$
$282$		0			0
$283$	2.30718e13	−	2.30718e13i	0.755538	−	0.755538i	−0.219969	−	0.975507i	$-0.570596\pi$
$283$	2.30718e13	−	2.30718e13i	0.755538	−	0.755538i	0.975507	+	0.219969i	$0.0705957\pi$
$284$		0			0
$285$	1.76647e13	+	1.76647e13i	0.556493	+	0.556493i
$286$		0			0
$287$	−9.05970e11			−0.0274640
$288$		0			0
$289$	3.15279e13			0.919933
$290$		0			0
$291$	6.76670e12	+	6.76670e12i	0.190093	+	0.190093i
$292$		0			0
$293$	1.47734e13	−	1.47734e13i	0.399675	−	0.399675i	−0.478443	−	0.878118i	$-0.658799\pi$
$293$	1.47734e13	−	1.47734e13i	0.399675	−	0.399675i	0.878118	+	0.478443i	$0.158799\pi$
$294$		0			0
$295$		−	1.28404e13i		−	0.334625i
$296$		0			0
$297$		−	1.18220e12i		−	0.0296845i
$298$		0			0
$299$	8.98797e12	−	8.98797e12i	0.217505	−	0.217505i
$300$		0			0
$301$	−6.47027e13	−	6.47027e13i	−1.50941	−	1.50941i
$302$		0			0
$303$	−6.99694e13			−1.57389
$304$		0			0
$305$	−1.98592e13			−0.430836
$306$		0			0
$307$	−3.74033e13	−	3.74033e13i	−0.782796	−	0.782796i	0.197506	−	0.980302i	$-0.436716\pi$
$307$	−3.74033e13	−	3.74033e13i	−0.782796	−	0.782796i	−0.980302	+	0.197506i	$0.936716\pi$
$308$		0			0
$309$	1.08062e13	−	1.08062e13i	0.218223	−	0.218223i
$310$		0			0
$311$		−	5.07867e13i		−	0.989847i	−0.868937	−	0.494924i	$-0.835196\pi$
$311$		−	5.07867e13i		−	0.989847i	0.868937	−	0.494924i	$-0.164804\pi$
$312$		0			0
$313$			1.06893e13i			0.201120i	0.994931	+	0.100560i	$0.0320634\pi$
$313$			1.06893e13i			0.201120i	−0.994931	+	0.100560i	$0.967937\pi$
$314$		0			0
$315$	−1.82441e13	+	1.82441e13i	−0.331448	+	0.331448i
$316$		0			0
$317$	1.50024e13	+	1.50024e13i	0.263229	+	0.263229i	0.826365	−	0.563135i	$-0.190405\pi$
$317$	1.50024e13	+	1.50024e13i	0.263229	+	0.263229i	−0.563135	+	0.826365i	$0.690405\pi$
$318$		0			0
$319$	8.53846e12			0.144721
$320$		0			0
$321$	−5.01569e13			−0.821398
$322$		0			0
$323$	1.08543e14	+	1.08543e14i	1.71787	+	1.71787i
$324$		0			0
$325$	−1.39656e13	+	1.39656e13i	−0.213649	+	0.213649i
$326$		0			0
$327$			4.95153e13i			0.732363i
$328$		0			0
$329$			1.67103e14i			2.39005i
$330$		0			0
$331$	−1.15849e12	+	1.15849e12i	−0.0160265	+	0.0160265i	−0.715075	−	0.699048i	$-0.753607\pi$
$331$	−1.15849e12	+	1.15849e12i	−0.0160265	+	0.0160265i	0.699048	+	0.715075i	$0.253607\pi$
$332$		0			0
$333$	−7.56344e13	−	7.56344e13i	−1.01222	−	1.01222i
$334$		0			0
$335$	2.43352e13			0.315129
$336$		0			0
$337$	1.54894e14			1.94120			0.970602	−	0.240691i	$-0.0773741\pi$
$337$	1.54894e14			1.94120			0.970602	+	0.240691i	$0.0773741\pi$
$338$		0			0
$339$	5.65425e13	+	5.65425e13i	0.685925	+	0.685925i
$340$		0			0
$341$	−3.18791e12	+	3.18791e12i	−0.0374418	+	0.0374418i
$342$		0			0
$343$			2.31639e13i			0.263447i
$344$		0			0
$345$		−	3.75725e13i		−	0.413871i
$346$		0			0
$347$	−4.18262e13	+	4.18262e13i	−0.446309	+	0.446309i	−0.894126	−	0.447816i	$-0.852202\pi$
$347$	−4.18262e13	+	4.18262e13i	−0.446309	+	0.446309i	0.447816	+	0.894126i	$0.352202\pi$
$348$		0			0
$349$	1.30512e14	+	1.30512e14i	1.34931	+	1.34931i	0.886412	+	0.462897i	$0.153190\pi$
$349$	1.30512e14	+	1.30512e14i	1.34931	+	1.34931i	0.462897	+	0.886412i	$0.346810\pi$
$350$		0			0
$351$	−6.64335e12			−0.0665576
$352$		0			0
$353$	−1.77057e14			−1.71930			−0.859652	−	0.510880i	$-0.829320\pi$
$353$	−1.77057e14			−1.71930			−0.859652	+	0.510880i	$0.829320\pi$
$354$		0			0
$355$	−2.13516e13	−	2.13516e13i	−0.200990	−	0.200990i
$356$		0			0
$357$	−2.10743e14	+	2.10743e14i	−1.92344	+	1.92344i
$358$		0			0
$359$		−	1.06853e14i		−	0.945727i	−0.881136	−	0.472863i	$-0.843220\pi$
$359$		−	1.06853e14i		−	0.945727i	0.881136	−	0.472863i	$-0.156780\pi$
$360$		0			0
$361$			2.41616e14i			2.07413i
$362$		0			0
$363$	−1.21367e14	+	1.21367e14i	−1.01068	+	1.01068i
$364$		0			0
$365$	9.54928e12	+	9.54928e12i	0.0771542	+	0.0771542i
$366$		0			0
$367$	4.42951e13			0.347290			0.173645	−	0.984808i	$-0.444446\pi$
$367$	4.42951e13			0.347290			0.173645	+	0.984808i	$0.444446\pi$
$368$		0			0
$369$	−3.05404e12			−0.0232397
$370$		0			0
$371$	−1.21629e14	−	1.21629e14i	−0.898425	−	0.898425i
$372$		0			0
$373$	9.20225e13	−	9.20225e13i	0.659926	−	0.659926i	−0.295436	−	0.955362i	$-0.595465\pi$
$373$	9.20225e13	−	9.20225e13i	0.659926	−	0.659926i	0.955362	+	0.295436i	$0.0954650\pi$
$374$		0			0
$375$			1.22840e14i			0.855397i
$376$		0			0
$377$		−	4.79818e13i		−	0.324488i
$378$		0			0
$379$	4.11973e13	−	4.11973e13i	0.270616	−	0.270616i	−0.558732	−	0.829348i	$-0.688712\pi$
$379$	4.11973e13	−	4.11973e13i	0.270616	−	0.270616i	0.829348	+	0.558732i	$0.188712\pi$
$380$		0			0
$381$	−4.27020e12	−	4.27020e12i	−0.0272496	−	0.0272496i
$382$		0			0
$383$	−2.44621e13			−0.151670			−0.0758351	−	0.997120i	$-0.524162\pi$
$383$	−2.44621e13			−0.151670			−0.0758351	+	0.997120i	$0.524162\pi$
$384$		0			0
$385$	−1.01850e13			−0.0613661
$386$		0			0
$387$	−2.18114e14	−	2.18114e14i	−1.27724	−	1.27724i
$388$		0			0
$389$	−4.33424e13	+	4.33424e13i	−0.246712	+	0.246712i	−0.819620	−	0.572908i	$-0.805815\pi$
$389$	−4.33424e13	+	4.33424e13i	−0.246712	+	0.246712i	0.572908	+	0.819620i	$0.305815\pi$
$390$		0			0
$391$		−	2.30870e14i		−	1.27760i
$392$		0			0
$393$		−	2.62509e14i		−	1.41249i
$394$		0			0
$395$	−5.25696e13	+	5.25696e13i	−0.275075	+	0.275075i
$396$		0			0
$397$	2.24044e13	+	2.24044e13i	0.114021	+	0.114021i	0.761815	−	0.647794i	$-0.224308\pi$
$397$	2.24044e13	+	2.24044e13i	0.114021	+	0.114021i	−0.647794	+	0.761815i	$0.724308\pi$
$398$		0			0
$399$	−6.95285e14			−3.44201
$400$		0			0
$401$	3.28823e14			1.58368			0.791842	−	0.610727i	$-0.209123\pi$
$401$	3.28823e14			1.58368			0.791842	+	0.610727i	$0.209123\pi$
$402$		0			0
$403$	1.79144e13	+	1.79144e13i	0.0839508	+	0.0839508i
$404$		0			0
$405$	4.02294e13	−	4.02294e13i	0.183460	−	0.183460i
$406$		0			0
$407$		−	4.22239e13i		−	0.187409i
$408$		0			0
$409$			1.11279e14i			0.480767i	0.970678	+	0.240384i	$0.0772732\pi$
$409$			1.11279e14i			0.480767i	−0.970678	+	0.240384i	$0.922727\pi$
$410$		0			0
$411$	−9.62366e13	+	9.62366e13i	−0.404772	+	0.404772i
$412$		0			0
$413$	2.52700e14	+	2.52700e14i	1.03486	+	1.03486i
$414$		0			0
$415$	−1.30491e14			−0.520373
$416$		0			0
$417$	−1.53508e14			−0.596188
$418$		0			0
$419$	−1.31929e14	−	1.31929e14i	−0.499072	−	0.499072i	0.412077	−	0.911149i	$-0.364803\pi$
$419$	−1.31929e14	−	1.31929e14i	−0.499072	−	0.499072i	−0.911149	+	0.412077i	$0.864803\pi$
$420$		0			0
$421$	−1.11228e13	+	1.11228e13i	−0.0409887	+	0.0409887i	−0.727304	−	0.686315i	$-0.759227\pi$
$421$	−1.11228e13	+	1.11228e13i	−0.0409887	+	0.0409887i	0.686315	+	0.727304i	$0.259227\pi$
$422$		0			0
$423$			5.63308e14i			2.02243i
$424$		0			0
$425$			3.58728e14i			1.25495i
$426$		0			0
$427$	3.90830e14	−	3.90830e14i	1.33240	−	1.33240i
$428$		0			0
$429$	−1.54401e13	−	1.54401e13i	−0.0513021	−	0.0513021i
$430$		0			0
$431$	4.45018e14			1.44129			0.720647	−	0.693302i	$-0.243845\pi$
$431$	4.45018e14			1.44129			0.720647	+	0.693302i	$0.243845\pi$
$432$		0			0
$433$	−1.12463e13			−0.0355080			−0.0177540	−	0.999842i	$-0.505652\pi$
$433$	−1.12463e13			−0.0355080			−0.0177540	+	0.999842i	$0.505652\pi$
$434$		0			0
$435$	−1.00289e14	−	1.00289e14i	−0.308720	−	0.308720i
$436$		0			0
$437$	3.80842e14	−	3.80842e14i	1.14313	−	1.14313i
$438$		0			0
$439$		−	5.67001e13i		−	0.165970i	−0.996551	−	0.0829849i	$-0.973555\pi$
$439$		−	5.67001e13i		−	0.165970i	0.996551	−	0.0829849i	$-0.0264453\pi$
$440$		0			0
$441$		−	3.20002e14i		−	0.913568i
$442$		0			0
$443$	2.60481e13	−	2.60481e13i	0.0725362	−	0.0725362i	−0.669908	−	0.742444i	$-0.733666\pi$
$443$	2.60481e13	−	2.60481e13i	0.0725362	−	0.0725362i	0.742444	+	0.669908i	$0.233666\pi$
$444$		0			0
$445$	5.14845e12	+	5.14845e12i	0.0139861	+	0.0139861i
$446$		0			0
$447$	−1.71001e13			−0.0453219
$448$		0			0
$449$	−3.91719e14			−1.01302			−0.506512	−	0.862233i	$-0.669065\pi$
$449$	−3.91719e14			−1.01302			−0.506512	+	0.862233i	$0.669065\pi$
$450$		0			0
$451$	−8.52481e11	−	8.52481e11i	−0.00215136	−	0.00215136i
$452$		0			0
$453$	−5.14753e14	+	5.14753e14i	−1.26782	+	1.26782i
$454$		0			0
$455$			5.72347e13i			0.137593i
$456$		0			0
$457$		−	1.98305e14i		−	0.465365i	−0.972553	−	0.232683i	$-0.925250\pi$
$457$		−	1.98305e14i		−	0.465365i	0.972553	−	0.232683i	$-0.0747504\pi$
$458$		0			0
$459$	−8.53222e13	+	8.53222e13i	−0.195475	+	0.195475i
$460$		0			0
$461$	2.94593e14	+	2.94593e14i	0.658972	+	0.658972i	0.955137	−	0.296165i	$-0.0957079\pi$
$461$	2.94593e14	+	2.94593e14i	0.658972	+	0.658972i	−0.296165	+	0.955137i	$0.595708\pi$
$462$		0			0
$463$	5.44141e14			1.18855			0.594273	−	0.804263i	$-0.297440\pi$
$463$	5.44141e14			1.18855			0.594273	+	0.804263i	$0.297440\pi$
$464$		0			0
$465$	7.48878e13			0.159742
$466$		0			0
$467$	6.92417e13	+	6.92417e13i	0.144253	+	0.144253i	0.775545	−	0.631292i	$-0.217475\pi$
$467$	6.92417e13	+	6.92417e13i	0.144253	+	0.144253i	−0.631292	+	0.775545i	$0.717475\pi$
$468$		0			0
$469$	−4.78918e14	+	4.78918e14i	−0.974564	+	0.974564i
$470$		0			0
$471$		−	3.82944e14i		−	0.761238i
$472$		0			0
$473$		−	1.21765e14i		−	0.236476i
$474$		0			0
$475$	−5.91757e14	+	5.91757e14i	−1.12287	+	1.12287i
$476$		0			0
$477$	−4.10015e14	−	4.10015e14i	−0.760237	−	0.760237i
$478$		0			0
$479$	5.45377e14			0.988216			0.494108	−	0.869401i	$-0.335495\pi$
$479$	5.45377e14			0.988216			0.494108	+	0.869401i	$0.335495\pi$
$480$		0			0
$481$	−2.37277e14			−0.420201
$482$		0			0
$483$	7.39429e14	+	7.39429e14i	1.27993	+	1.27993i
$484$		0			0
$485$	2.36025e13	−	2.36025e13i	0.0399372	−	0.0399372i
$486$		0			0
$487$			2.73024e14i			0.451640i	0.974169	+	0.225820i	$0.0725061\pi$
$487$			2.73024e14i			0.451640i	−0.974169	+	0.225820i	$0.927494\pi$
$488$		0			0
$489$		−	1.65696e14i		−	0.267987i
$490$		0			0
$491$	−2.44712e13	+	2.44712e13i	−0.0386996	+	0.0386996i	−0.726192	−	0.687492i	$-0.758712\pi$
$491$	−2.44712e13	+	2.44712e13i	−0.0386996	+	0.0386996i	0.687492	+	0.726192i	$0.258712\pi$
$492$		0			0
$493$	−6.16242e14	−	6.16242e14i	−0.953001	−	0.953001i
$494$		0			0
$495$	−3.43340e13			−0.0519273
$496$		0			0
$497$	8.40402e14			1.24316
$498$		0			0
$499$	5.44937e14	+	5.44937e14i	0.788484	+	0.788484i	0.981246	−	0.192762i	$-0.0617444\pi$
$499$	5.44937e14	+	5.44937e14i	0.788484	+	0.788484i	−0.192762	+	0.981246i	$0.561744\pi$
$500$		0			0
$501$	1.21903e15	−	1.21903e15i	1.72547	−	1.72547i
$502$		0			0
$503$		−	2.12390e14i		−	0.294110i	−0.989128	−	0.147055i	$-0.953021\pi$
$503$		−	2.12390e14i		−	0.294110i	0.989128	−	0.147055i	$-0.0469794\pi$
$504$		0			0
$505$			2.44055e14i			0.330663i
$506$		0			0
$507$	6.92848e14	−	6.92848e14i	0.918532	−	0.918532i
$508$		0			0
$509$	−2.91460e14	−	2.91460e14i	−0.378121	−	0.378121i	0.492303	−	0.870424i	$-0.336155\pi$
$509$	−2.91460e14	−	2.91460e14i	−0.378121	−	0.378121i	−0.870424	+	0.492303i	$0.836155\pi$
$510$		0			0
$511$	−3.75861e14			−0.477212
$512$		0			0
$513$	−2.81495e14			−0.349804
$514$		0			0
$515$	−3.76924e13	−	3.76924e13i	−0.0458473	−	0.0458473i
$516$		0			0
$517$	−1.57237e14	+	1.57237e14i	−0.187222	+	0.187222i
$518$		0			0
$519$		−	3.61859e14i		−	0.421812i
$520$		0			0
$521$			1.21124e15i			1.38236i	0.722681	+	0.691182i	$0.242910\pi$
$521$			1.21124e15i			1.38236i	−0.722681	+	0.691182i	$0.757090\pi$
$522$		0			0
$523$	7.39703e14	−	7.39703e14i	0.826605	−	0.826605i	−0.160440	−	0.987046i	$-0.551291\pi$
$523$	7.39703e14	−	7.39703e14i	0.826605	−	0.826605i	0.987046	+	0.160440i	$0.0512914\pi$
$524$		0			0
$525$	−1.14893e15	−	1.14893e15i	−1.25724	−	1.25724i
$526$		0			0
$527$	4.60159e14			0.493116
$528$		0			0
$529$	1.42765e14			0.149836
$530$		0			0
$531$	8.51858e14	+	8.51858e14i	0.875684	+	0.875684i
$532$		0			0
$533$	−4.79051e12	+	4.79051e12i	−0.00482372	+	0.00482372i
$534$		0			0
$535$			1.74949e14i			0.172570i
$536$		0			0
$537$		−	1.09429e15i		−	1.05749i
$538$		0			0
$539$	8.93228e13	−	8.93228e13i	0.0845716	−	0.0845716i
$540$		0			0
$541$	9.36873e14	+	9.36873e14i	0.869152	+	0.869152i	0.992379	−	0.123227i	$-0.0393242\pi$
$541$	9.36873e14	+	9.36873e14i	0.869152	+	0.869152i	−0.123227	+	0.992379i	$0.539324\pi$
$542$		0			0
$543$	6.11320e14			0.555737
$544$		0			0
$545$	1.72711e14			0.153865
$546$		0			0
$547$	7.01752e13	+	7.01752e13i	0.0612708	+	0.0612708i	0.737078	−	0.675807i	$-0.236205\pi$
$547$	7.01752e13	+	7.01752e13i	0.0612708	+	0.0612708i	−0.675807	+	0.737078i	$0.736205\pi$
$548$		0			0
$549$	1.31750e15	−	1.31750e15i	1.12746	−	1.12746i
$550$		0			0
$551$		−	2.03311e15i		−	1.70540i
$552$		0			0
$553$		−	2.06914e15i		−	1.70138i
$554$		0			0
$555$	−4.95946e14	+	4.95946e14i	−0.399781	+	0.399781i
$556$		0			0
$557$	4.21492e14	+	4.21492e14i	0.333109	+	0.333109i	0.853766	−	0.520657i	$-0.174313\pi$
$557$	4.21492e14	+	4.21492e14i	0.333109	+	0.333109i	−0.520657	+	0.853766i	$0.674313\pi$
$558$		0			0
$559$	−6.84259e14			−0.530219
$560$		0			0
$561$	−3.96602e14			−0.301342
$562$		0			0
$563$	−1.18164e15	−	1.18164e15i	−0.880416	−	0.880416i	0.113160	−	0.993577i	$-0.463903\pi$
$563$	−1.18164e15	−	1.18164e15i	−0.880416	−	0.880416i	−0.993577	+	0.113160i	$0.963903\pi$
$564$		0			0
$565$	1.97222e14	−	1.97222e14i	0.144108	−	0.144108i
$566$		0			0
$567$			1.58343e15i			1.13473i
$568$		0			0
$569$		−	9.73112e14i		−	0.683983i	−0.939703	−	0.341992i	$-0.888899\pi$
$569$		−	9.73112e14i		−	0.683983i	0.939703	−	0.341992i	$-0.111101\pi$
$570$		0			0
$571$	1.00987e15	−	1.00987e15i	0.696253	−	0.696253i	−0.267347	−	0.963600i	$-0.586147\pi$
$571$	1.00987e15	−	1.00987e15i	0.696253	−	0.696253i	0.963600	+	0.267347i	$0.0861470\pi$
$572$		0			0
$573$	−6.74676e14	−	6.74676e14i	−0.456294	−	0.456294i
$574$		0			0
$575$	1.25866e15			0.835092
$576$		0			0
$577$	1.63029e15			1.06120			0.530602	−	0.847621i	$-0.321966\pi$
$577$	1.63029e15			1.06120			0.530602	+	0.847621i	$0.321966\pi$
$578$		0			0
$579$	−1.99286e15	−	1.99286e15i	−1.27275	−	1.27275i
$580$		0			0
$581$	2.56806e15	−	2.56806e15i	1.60930	−	1.60930i
$582$		0			0
$583$		−	2.28897e14i		−	0.140755i
$584$		0			0
$585$			1.92939e14i			0.116430i
$586$		0			0
$587$	−7.41304e14	+	7.41304e14i	−0.439022	+	0.439022i	−0.891683	−	0.452661i	$-0.850475\pi$
$587$	−7.41304e14	+	7.41304e14i	−0.439022	+	0.439022i	0.452661	+	0.891683i	$0.350475\pi$
$588$		0			0
$589$	7.59078e14	+	7.59078e14i	0.441217	+	0.441217i
$590$		0			0
$591$	−7.33034e14			−0.418209
$592$		0			0
$593$	−3.32085e15			−1.85972			−0.929861	−	0.367910i	$-0.880073\pi$
$593$	−3.32085e15			−1.85972			−0.929861	+	0.367910i	$0.880073\pi$
$594$		0			0
$595$	7.35079e14	+	7.35079e14i	0.404102	+	0.404102i
$596$		0			0
$597$	−2.80992e15	+	2.80992e15i	−1.51647	+	1.51647i
$598$		0			0
$599$			2.87597e15i			1.52383i	0.647675	+	0.761916i	$0.275741\pi$
$599$			2.87597e15i			1.52383i	−0.647675	+	0.761916i	$0.724259\pi$
$600$		0			0
$601$		−	3.01761e14i		−	0.156984i	−0.996915	−	0.0784918i	$-0.974990\pi$
$601$		−	3.01761e14i		−	0.156984i	0.996915	−	0.0784918i	$-0.0250104\pi$
$602$		0			0
$603$	−1.61444e15	+	1.61444e15i	−0.824665	+	0.824665i
$604$		0			0
$605$	4.23331e14	+	4.23331e14i	0.212337	+	0.212337i
$606$		0			0
$607$	−1.10741e15			−0.545470			−0.272735	−	0.962089i	$-0.587928\pi$
$607$	−1.10741e15			−0.545470			−0.272735	+	0.962089i	$0.587928\pi$
$608$		0			0
$609$	3.94740e15			1.90948
$610$		0			0
$611$	8.83592e14	+	8.83592e14i	0.419783	+	0.419783i
$612$		0			0
$613$	−2.34187e15	+	2.34187e15i	−1.09277	+	1.09277i	−0.0975435	+	0.995231i	$0.531098\pi$
$613$	−2.34187e15	+	2.34187e15i	−1.09277	+	1.09277i	−0.995231	+	0.0975435i	$0.968902\pi$
$614$		0			0
$615$			2.00258e13i			0.00917861i
$616$		0			0
$617$		−	6.98011e14i		−	0.314264i	−0.987578	−	0.157132i	$-0.949775\pi$
$617$		−	6.98011e14i		−	0.314264i	0.987578	−	0.157132i	$-0.0502248\pi$
$618$		0			0
$619$	2.28130e15	−	2.28130e15i	1.00898	−	1.00898i	0.00902486	−	0.999959i	$-0.497127\pi$
$619$	2.28130e15	−	2.28130e15i	1.00898	−	1.00898i	0.999959	−	0.00902486i	$-0.00287274\pi$
$620$		0			0
$621$	2.99367e14	+	2.99367e14i	0.130077	+	0.130077i
$622$		0			0
$623$	−2.02644e14			−0.0865065
$624$		0			0
$625$	−1.73088e15			−0.725984
$626$		0			0
$627$	−6.54235e14	−	6.54235e14i	−0.269626	−	0.269626i
$628$		0			0
$629$	−3.04741e15	+	3.04741e15i	−1.23410	+	1.23410i
$630$		0			0
$631$		−	3.06944e15i		−	1.22151i	−0.791819	−	0.610755i	$-0.790866\pi$
$631$		−	3.06944e15i		−	1.22151i	0.791819	−	0.610755i	$-0.209134\pi$
$632$		0			0
$633$			4.92638e15i			1.92667i
$634$		0			0
$635$	−1.48946e13	+	1.48946e13i	−0.00572497	+	0.00572497i
$636$		0			0
$637$	−5.01949e14	−	5.01949e14i	−0.189624	−	0.189624i
$638$		0			0
$639$	2.83302e15			1.05195
$640$		0			0
$641$	−2.26554e15			−0.826899			−0.413449	−	0.910527i	$-0.635676\pi$
$641$	−2.26554e15			−0.826899			−0.413449	+	0.910527i	$0.635676\pi$
$642$		0			0
$643$	4.93160e14	+	4.93160e14i	0.176941	+	0.176941i	0.790021	−	0.613080i	$-0.210070\pi$
$643$	4.93160e14	+	4.93160e14i	0.176941	+	0.176941i	−0.613080	+	0.790021i	$0.710070\pi$
$644$		0			0
$645$	−1.43021e15	+	1.43021e15i	−0.504453	+	0.504453i
$646$		0			0
$647$			2.61317e15i			0.906139i	0.891475	+	0.453069i	$0.149671\pi$
$647$			2.61317e15i			0.906139i	−0.891475	+	0.453069i	$0.850329\pi$
$648$		0			0
$649$			4.75561e14i			0.162129i
$650$		0			0
$651$	−1.47380e15	+	1.47380e15i	−0.494017	+	0.494017i
$652$		0			0
$653$	3.24689e15	+	3.24689e15i	1.07015	+	1.07015i	0.997346	+	0.0728038i	$0.0231947\pi$
$653$	3.24689e15	+	3.24689e15i	1.07015	+	1.07015i	0.0728038	+	0.997346i	$0.476805\pi$
$654$		0			0
$655$	−9.15639e14			−0.296754
$656$		0			0
$657$	−1.26703e15			−0.403812
$658$		0			0
$659$	8.89857e13	+	8.89857e13i	0.0278901	+	0.0278901i	0.720914	−	0.693024i	$-0.243722\pi$
$659$	8.89857e13	+	8.89857e13i	0.0278901	+	0.0278901i	−0.693024	+	0.720914i	$0.743722\pi$
$660$		0			0
$661$	−2.37602e14	+	2.37602e14i	−0.0732388	+	0.0732388i	−0.742777	−	0.669539i	$-0.766492\pi$
$661$	−2.37602e14	+	2.37602e14i	−0.0732388	+	0.0732388i	0.669539	+	0.742777i	$0.266492\pi$
$662$		0			0
$663$			2.22870e15i			0.675659i
$664$		0			0
$665$			2.42517e15i			0.723142i
$666$		0			0
$667$	−2.16219e15	+	2.16219e15i	−0.634164	+	0.634164i
$668$		0			0
$669$	1.07413e15	+	1.07413e15i	0.309894	+	0.309894i
$670$		0			0
$671$	7.35510e14			0.208744
$672$		0			0
$673$	4.98817e14			0.139270			0.0696352	−	0.997573i	$-0.477816\pi$
$673$	4.98817e14			0.139270			0.0696352	+	0.997573i	$0.477816\pi$
$674$		0			0
$675$	−4.65160e14	−	4.65160e14i	−0.127771	−	0.127771i
$676$		0			0
$677$	3.03419e15	−	3.03419e15i	0.819984	−	0.819984i	−0.166121	−	0.986105i	$-0.553124\pi$
$677$	3.03419e15	−	3.03419e15i	0.819984	−	0.819984i	0.986105	+	0.166121i	$0.0531243\pi$
$678$		0			0
$679$			9.28995e14i			0.247019i
$680$		0			0
$681$			2.21698e15i			0.580034i
$682$		0			0
$683$	−3.12787e15	+	3.12787e15i	−0.805257	+	0.805257i	−0.983912	−	0.178655i	$-0.942825\pi$
$683$	−3.12787e15	+	3.12787e15i	−0.805257	+	0.805257i	0.178655	+	0.983912i	$0.442825\pi$
$684$		0			0
$685$	3.35676e14	+	3.35676e14i	0.0850398	+	0.0850398i
$686$		0			0
$687$	−7.66517e15			−1.91100
$688$		0			0
$689$	−1.28628e15			−0.315595
$690$		0			0
$691$	−2.77334e15	−	2.77334e15i	−0.669689	−	0.669689i	0.287955	−	0.957644i	$-0.407025\pi$
$691$	−2.77334e15	−	2.77334e15i	−0.669689	−	0.669689i	−0.957644	+	0.287955i	$0.907025\pi$
$692$		0			0
$693$	6.75694e14	−	6.75694e14i	0.160590	−	0.160590i
$694$		0			0
$695$			5.35441e14i			0.125255i
$696$		0			0
$697$			1.23051e14i			0.0283339i
$698$		0			0
$699$	4.80793e15	−	4.80793e15i	1.08977	−	1.08977i
$700$		0			0
$701$	−3.58804e15	−	3.58804e15i	−0.800587	−	0.800587i	0.182600	−	0.983187i	$-0.441549\pi$
$701$	−3.58804e15	−	3.58804e15i	−0.800587	−	0.800587i	−0.983187	+	0.182600i	$0.941549\pi$
$702$		0			0
$703$	−1.00540e16			−2.20844
$704$		0			0
$705$	3.69369e15			0.798767
$706$		0			0
$707$	−4.80302e15	−	4.80302e15i	−1.02260	−	1.02260i
$708$		0			0
$709$	2.93575e15	−	2.93575e15i	0.615410	−	0.615410i	−0.328940	−	0.944351i	$-0.606692\pi$
$709$	2.93575e15	−	2.93575e15i	0.615410	−	0.615410i	0.944351	+	0.328940i	$0.106692\pi$
$710$		0			0
$711$		−	6.97513e15i		−	1.43969i
$712$		0			0
$713$		−	1.61454e15i		−	0.328139i
$714$		0			0
$715$	−5.38555e13	+	5.38555e13i	−0.0107782	+	0.0107782i
$716$		0			0
$717$	3.64143e15	+	3.64143e15i	0.717656	+	0.717656i
$718$		0			0
$719$	4.19879e15			0.814920			0.407460	−	0.913223i	$-0.366415\pi$
$719$	4.19879e15			0.814920			0.407460	+	0.913223i	$0.366415\pi$
$720$		0			0
$721$	1.48357e15			0.283573
$722$		0			0
$723$	6.47858e15	+	6.47858e15i	1.21960	+	1.21960i
$724$		0			0
$725$	3.35964e15	−	3.35964e15i	0.622922	−	0.622922i
$726$		0			0
$727$		−	4.12785e15i		−	0.753849i	−0.926244	−	0.376925i	$-0.876982\pi$
$727$		−	4.12785e15i		−	0.753849i	0.926244	−	0.376925i	$-0.123018\pi$
$728$		0			0
$729$			6.95891e15i			1.25181i
$730$		0			0
$731$	−8.78811e15	+	8.78811e15i	−1.55722	+	1.55722i
$732$		0			0
$733$	−4.75984e15	−	4.75984e15i	−0.830845	−	0.830845i	0.156787	−	0.987632i	$-0.449886\pi$
$733$	−4.75984e15	−	4.75984e15i	−0.830845	−	0.830845i	−0.987632	+	0.156787i	$0.949886\pi$
$734$		0			0
$735$	−2.09830e15			−0.360817
$736$		0			0
$737$	−9.01285e14			−0.152683
$738$		0			0
$739$	−3.24543e15	−	3.24543e15i	−0.541661	−	0.541661i	0.382355	−	0.924016i	$-0.375113\pi$
$739$	−3.24543e15	−	3.24543e15i	−0.541661	−	0.541661i	−0.924016	+	0.382355i	$0.875113\pi$
$740$		0			0
$741$	−3.67647e15	+	3.67647e15i	−0.604548	+	0.604548i
$742$		0			0
$743$		−	9.92853e15i		−	1.60859i	−0.594227	−	0.804297i	$-0.702542\pi$
$743$		−	9.92853e15i		−	1.60859i	0.594227	−	0.804297i	$-0.297458\pi$
$744$		0			0
$745$			5.96457e13i			0.00952182i
$746$		0			0
$747$	8.65699e15	−	8.65699e15i	1.36177	−	1.36177i
$748$		0			0
$749$	−3.44300e15	−	3.44300e15i	−0.533688	−	0.533688i
$750$		0			0
$751$	2.11436e14			0.0322969			0.0161484	−	0.999870i	$-0.494860\pi$
$751$	2.11436e14			0.0322969			0.0161484	+	0.999870i	$0.494860\pi$
$752$		0			0
$753$	6.94632e15			1.04564
$754$		0			0
$755$	1.79548e15	+	1.79548e15i	0.266361	+	0.266361i
$756$		0			0
$757$	−7.13066e15	+	7.13066e15i	−1.04256	+	1.04256i	−0.0435106	+	0.999053i	$0.513854\pi$
$757$	−7.13066e15	+	7.13066e15i	−1.04256	+	1.04256i	−0.999053	+	0.0435106i	$0.986146\pi$
$758$		0			0
$759$			1.39155e15i			0.200525i
$760$		0			0
$761$			7.63959e15i			1.08506i	0.840036	+	0.542531i	$0.182534\pi$
$761$			7.63959e15i			1.08506i	−0.840036	+	0.542531i	$0.817466\pi$
$762$		0			0
$763$	−3.39896e15	+	3.39896e15i	−0.475840	+	0.475840i
$764$		0			0
$765$	2.47797e15	+	2.47797e15i	0.341946	+	0.341946i
$766$		0			0
$767$	2.67241e15			0.363521
$768$		0			0
$769$	5.21778e15			0.699667			0.349833	−	0.936812i	$-0.386238\pi$
$769$	5.21778e15			0.699667			0.349833	+	0.936812i	$0.386238\pi$
$770$		0			0
$771$	1.17781e15	+	1.17781e15i	0.155696	+	0.155696i
$772$		0			0
$773$	3.63573e15	−	3.63573e15i	0.473811	−	0.473811i	−0.429335	−	0.903145i	$-0.641252\pi$
$773$	3.63573e15	−	3.63573e15i	0.473811	−	0.473811i	0.903145	+	0.429335i	$0.141252\pi$
$774$		0			0
$775$			2.50870e15i			0.322321i
$776$		0			0
$777$		−	1.95205e16i		−	2.47272i
$778$		0			0
$779$	−2.02986e14	+	2.02986e14i	−0.0253518	+	0.0253518i
$780$		0			0
$781$	7.90785e14	+	7.90785e14i	0.0973818	+	0.0973818i
$782$		0			0
$783$	1.59816e15			0.194057
$784$		0			0
$785$	−1.33572e15			−0.159931
$786$		0			0
$787$	6.27028e15	+	6.27028e15i	0.740331	+	0.740331i	0.972642	−	0.232311i	$-0.0746286\pi$
$787$	6.27028e15	+	6.27028e15i	0.740331	+	0.740331i	−0.232311	+	0.972642i	$0.574629\pi$
$788$		0			0
$789$	4.06372e14	−	4.06372e14i	0.0473152	−	0.0473152i
$790$		0			0
$791$			7.76268e15i			0.891335i
$792$		0			0
$793$		−	4.13319e15i		−	0.468040i
$794$		0			0
$795$	−2.68853e15	+	2.68853e15i	−0.300259	+	0.300259i
$796$		0			0
$797$	−5.11428e15	−	5.11428e15i	−0.563331	−	0.563331i	0.366921	−	0.930252i	$-0.380412\pi$
$797$	−5.11428e15	−	5.11428e15i	−0.563331	−	0.563331i	−0.930252	+	0.366921i	$0.880412\pi$
$798$		0			0
$799$	2.26964e16			2.46575
$800$		0			0
$801$	−6.83116e14			−0.0732008
$802$		0			0
$803$	−3.53670e14	−	3.53670e14i	−0.0373820	−	0.0373820i
$804$		0			0
$805$	2.57915e15	−	2.57915e15i	0.268905	−	0.268905i
$806$		0			0
$807$			1.27817e16i			1.31457i
$808$		0			0
$809$		−	5.91750e15i		−	0.600373i	−0.953881	−	0.300187i	$-0.902951\pi$
$809$		−	5.91750e15i		−	0.600373i	0.953881	−	0.300187i	$-0.0970489\pi$
$810$		0			0
$811$	5.44663e15	−	5.44663e15i	0.545147	−	0.545147i	−0.379886	−	0.925033i	$-0.624037\pi$
$811$	5.44663e15	−	5.44663e15i	0.545147	−	0.545147i	0.925033	+	0.379886i	$0.124037\pi$
$812$		0			0
$813$	1.73181e16	+	1.73181e16i	1.71002	+	1.71002i
$814$		0			0
$815$	−5.77954e14			−0.0563023
$816$		0			0
$817$	−2.89937e16			−2.78665
$818$		0			0
$819$	−3.79706e15	−	3.79706e15i	−0.360069	−	0.360069i
$820$		0			0
$821$	7.94880e14	−	7.94880e14i	0.0743728	−	0.0743728i	−0.668942	−	0.743315i	$-0.733253\pi$
$821$	7.94880e14	−	7.94880e14i	0.0743728	−	0.0743728i	0.743315	+	0.668942i	$0.233253\pi$
$822$		0			0
$823$			5.95135e15i			0.549435i	0.961525	+	0.274717i	$0.0885843\pi$
$823$			5.95135e15i			0.549435i	−0.961525	+	0.274717i	$0.911416\pi$
$824$		0			0
$825$		−	2.16220e15i		−	0.196970i
$826$		0			0
$827$	−2.73320e15	+	2.73320e15i	−0.245692	+	0.245692i	−0.819200	−	0.573508i	$-0.805582\pi$
$827$	−2.73320e15	+	2.73320e15i	−0.245692	+	0.245692i	0.573508	+	0.819200i	$0.305582\pi$
$828$		0			0
$829$	−1.31586e16	−	1.31586e16i	−1.16724	−	1.16724i	−0.982855	−	0.184382i	$-0.940971\pi$
$829$	−1.31586e16	−	1.31586e16i	−1.16724	−	1.16724i	−0.184382	−	0.982855i	$-0.559029\pi$
$830$		0			0
$831$	1.36753e16			1.19710
$832$		0			0
$833$	−1.28933e16			−1.11382
$834$		0			0
$835$	−4.25203e15	−	4.25203e15i	−0.362510	−	0.362510i
$836$		0			0
$837$	−5.96686e14	+	5.96686e14i	−0.0502060	+	0.0502060i
$838$		0			0
$839$			1.78995e15i			0.148645i	0.997234	+	0.0743226i	$0.0236795\pi$
$839$			1.78995e15i			0.148645i	−0.997234	+	0.0743226i	$0.976321\pi$
$840$		0			0
$841$		−	6.57772e14i		−	0.0539135i
$842$		0			0
$843$	2.46073e16	−	2.46073e16i	1.99073	−	1.99073i
$844$		0			0
$845$	−2.41668e15	−	2.41668e15i	−0.192977	−	0.192977i
$846$		0			0
$847$	−1.66624e16			−1.31334
$848$		0			0
$849$	2.00731e16			1.56179
$850$		0			0
$851$	1.06923e16	+	1.06923e16i	0.821221	+	0.821221i
$852$		0			0
$853$	3.28258e15	−	3.28258e15i	0.248883	−	0.248883i	−0.571629	−	0.820512i	$-0.693688\pi$
$853$	3.28258e15	−	3.28258e15i	0.248883	−	0.248883i	0.820512	+	0.571629i	$0.193688\pi$
$854$		0			0
$855$			8.17532e15i			0.611915i
$856$		0			0
$857$		−	9.76700e15i		−	0.721717i	−0.932621	−	0.360858i	$-0.882484\pi$
$857$		−	9.76700e15i		−	0.721717i	0.932621	−	0.360858i	$-0.117516\pi$
$858$		0			0
$859$	1.01771e16	−	1.01771e16i	0.742439	−	0.742439i	−0.230608	−	0.973047i	$-0.574071\pi$
$859$	1.01771e16	−	1.01771e16i	0.742439	−	0.742439i	0.973047	+	0.230608i	$0.0740714\pi$
$860$		0			0
$861$	−3.94109e14	−	3.94109e14i	−0.0283857	−	0.0283857i
$862$		0			0
$863$	1.35368e16			0.962627			0.481314	−	0.876548i	$-0.340160\pi$
$863$	1.35368e16			0.962627			0.481314	+	0.876548i	$0.340160\pi$
$864$		0			0
$865$	−1.26217e15			−0.0886198
$866$		0			0
$867$	1.37150e16	+	1.37150e16i	0.950807	+	0.950807i
$868$		0			0
$869$	1.94698e15	−	1.94698e15i	0.133276	−	0.133276i
$870$		0			0
$871$			5.06476e15i			0.342341i
$872$		0			0
$873$			3.13166e15i			0.209024i
$874$		0			0
$875$	−8.43230e15	+	8.43230e15i	−0.555778	+	0.555778i
$876$		0			0
$877$	−1.80704e16	−	1.80704e16i	−1.17617	−	1.17617i	−0.980713	−	0.195454i	$-0.937382\pi$
$877$	−1.80704e16	−	1.80704e16i	−1.17617	−	1.17617i	−0.195454	−	0.980713i	$-0.562618\pi$
$878$		0			0
$879$	1.28532e16			0.826177
$880$		0			0
$881$	1.07538e16			0.682642			0.341321	−	0.939947i	$-0.389126\pi$
$881$	1.07538e16			0.682642			0.341321	+	0.939947i	$0.389126\pi$
$882$		0			0
$883$	−1.44950e15	−	1.44950e15i	−0.0908731	−	0.0908731i	0.660209	−	0.751082i	$-0.270468\pi$
$883$	−1.44950e15	−	1.44950e15i	−0.0908731	−	0.0908731i	−0.751082	+	0.660209i	$0.770468\pi$
$884$		0			0
$885$	5.58576e15	−	5.58576e15i	0.345855	−	0.345855i
$886$		0			0
$887$		−	2.98383e14i		−	0.0182471i	−0.999958	−	0.00912354i	$-0.997096\pi$
$887$		−	2.98383e14i		−	0.0182471i	0.999958	−	0.00912354i	$-0.00290415\pi$
$888$		0			0
$889$		−	5.86252e14i		−	0.0354099i
$890$		0			0
$891$	−1.48995e15	+	1.48995e15i	−0.0888880	+	0.0888880i
$892$		0			0
$893$	3.74400e16	+	3.74400e16i	2.20624	+	2.20624i
$894$		0			0
$895$	−3.81693e15			−0.222171
$896$		0			0
$897$	7.81978e15			0.449610
$898$		0			0
$899$	−4.30958e15	−	4.30958e15i	−0.244769	−	0.244769i
$900$		0			0
$901$	−1.65201e16	+	1.65201e16i	−0.926883	+	0.926883i
$902$		0			0
$903$		−	5.62931e16i		−	3.12013i
$904$		0			0
$905$		−	2.13230e15i		−	0.116757i
$906$		0			0
$907$	−1.80050e16	+	1.80050e16i	−0.973986	+	0.973986i	−0.999670	−	0.0256843i	$-0.991824\pi$
$907$	−1.80050e16	+	1.80050e16i	−0.973986	+	0.973986i	0.0256843	+	0.999670i	$0.491824\pi$
$908$		0			0
$909$	−1.61911e16	−	1.61911e16i	−0.865316	−	0.865316i
$910$		0			0
$911$	−2.73035e16			−1.44168			−0.720838	−	0.693104i	$-0.756243\pi$
$911$	−2.73035e16			−1.44168			−0.720838	+	0.693104i	$0.756243\pi$
$912$		0			0
$913$	4.83289e15			0.252126
$914$		0			0
$915$	−8.63901e15	−	8.63901e15i	−0.445295	−	0.445295i
$916$		0			0
$917$	1.80198e16	−	1.80198e16i	0.917739	−	0.917739i
$918$		0			0
$919$			5.96410e15i			0.300130i	0.988676	+	0.150065i	$0.0479483\pi$
$919$			5.96410e15i			0.300130i	−0.988676	+	0.150065i	$0.952052\pi$
$920$		0			0
$921$		−	3.25418e16i		−	1.61813i
$922$		0			0
$923$	4.44381e15	−	4.44381e15i	0.218346	−	0.218346i
$924$		0			0
$925$	−1.66139e16	−	1.66139e16i	−0.806662	−	0.806662i
$926$		0			0
$927$	5.00117e15			0.239957
$928$		0			0
$929$	1.74073e16			0.825365			0.412683	−	0.910875i	$-0.364592\pi$
$929$	1.74073e16			0.825365			0.412683	+	0.910875i	$0.364592\pi$
$930$		0			0
$931$	−2.12688e16	−	2.12688e16i	−0.996598	−	0.996598i
$932$		0			0
$933$	2.20929e16	−	2.20929e16i	1.02307	−	1.02307i
$934$		0			0
$935$			1.38336e15i			0.0633099i
$936$		0			0
$937$			8.96273e15i			0.405390i	0.979242	+	0.202695i	$0.0649699\pi$
$937$			8.96273e15i			0.405390i	−0.979242	+	0.202695i	$0.935030\pi$
$938$		0			0
$939$	−4.64999e15	+	4.64999e15i	−0.207870	+	0.207870i
$940$		0			0
$941$	−4.72270e15	−	4.72270e15i	−0.208664	−	0.208664i	0.595036	−	0.803699i	$-0.297138\pi$
$941$	−4.72270e15	−	4.72270e15i	−0.208664	−	0.208664i	−0.803699	+	0.595036i	$0.797138\pi$
$942$		0			0
$943$	4.31747e14			0.0188545
$944$		0			0
$945$	−1.90635e15			−0.0822862
$946$		0			0
$947$	1.11972e16	+	1.11972e16i	0.477732	+	0.477732i	0.904406	−	0.426674i	$-0.140315\pi$
$947$	1.11972e16	+	1.11972e16i	0.477732	+	0.477732i	−0.426674	+	0.904406i	$0.640315\pi$
$948$		0			0
$949$	−1.98744e15	+	1.98744e15i	−0.0838167	+	0.0838167i
$950$		0			0
$951$			1.30525e16i			0.544127i
$952$		0			0
$953$		−	1.58414e16i		−	0.652804i	−0.945231	−	0.326402i	$-0.894164\pi$
$953$		−	1.58414e16i		−	0.652804i	0.945231	−	0.326402i	$-0.105836\pi$
$954$		0			0
$955$	−2.35329e15	+	2.35329e15i	−0.0958642	+	0.0958642i
$956$		0			0
$957$	3.71435e15	+	3.71435e15i	0.149578	+	0.149578i
$958$		0			0
$959$	−1.32122e16			−0.525986
$960$		0			0
$961$	−2.21904e16			−0.873348
$962$		0			0
$963$	−1.16064e16	−	1.16064e16i	−0.451601	−	0.451601i
$964$		0			0
$965$	−6.95115e15	+	6.95115e15i	−0.267397	+	0.267397i
$966$		0			0
$967$		−	3.29506e16i		−	1.25319i	−0.779345	−	0.626596i	$-0.784448\pi$
$967$		−	3.29506e16i		−	1.25319i	0.779345	−	0.626596i	$-0.215552\pi$
$968$		0			0
$969$			9.44356e16i			3.55103i
$970$		0			0
$971$	1.54480e16	−	1.54480e16i	0.574335	−	0.574335i	−0.359002	−	0.933337i	$-0.616883\pi$
$971$	1.54480e16	−	1.54480e16i	0.574335	−	0.574335i	0.933337	+	0.359002i	$0.116883\pi$
$972$		0			0
$973$	−1.05375e16	−	1.05375e16i	−0.387362	−	0.387362i
$974$		0			0
$975$	−1.21505e16			−0.441639
$976$		0			0
$977$	−4.75813e15			−0.171008			−0.0855040	−	0.996338i	$-0.527250\pi$
$977$	−4.75813e15			−0.171008			−0.0855040	+	0.996338i	$0.527250\pi$
$978$		0			0
$979$	−1.90679e14	−	1.90679e14i	−0.00677640	−	0.00677640i
$980$		0			0
$981$	−1.14580e16	+	1.14580e16i	−0.402650	+	0.402650i
$982$		0			0
$983$			1.45977e16i			0.507270i	0.967300	+	0.253635i	$0.0816262\pi$
$983$			1.45977e16i			0.507270i	−0.967300	+	0.253635i	$0.918374\pi$
$984$		0			0
$985$			2.55684e15i			0.0878628i
$986$		0			0
$987$	−7.26920e16	+	7.26920e16i	−2.47026	+	2.47026i
$988$		0			0
$989$	3.08346e16	+	3.08346e16i	1.03623	+	1.03623i
$990$		0			0
$991$	3.14429e16			1.04500			0.522501	−	0.852639i	$-0.324999\pi$
$991$	3.14429e16			1.04500			0.522501	+	0.852639i	$0.324999\pi$
$992$		0			0
$993$	−1.00792e15			−0.0331286
$994$		0			0
$995$	9.80108e15	+	9.80108e15i	0.318601	+	0.318601i
$996$		0			0
$997$	−1.86303e16	+	1.86303e16i	−0.598958	+	0.598958i	−0.940035	−	0.341077i	$-0.889208\pi$
$997$	−1.86303e16	+	1.86303e16i	−0.598958	+	0.598958i	0.341077	+	0.940035i	$0.389208\pi$
$998$		0			0
$999$		−	7.90311e15i		−	0.251297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.12.e.b.33.18		42
4.3	odd	2		128.12.e.a.33.4		42
8.3	odd	2		64.12.e.a.17.18		42
8.5	even	2		16.12.e.a.13.3	yes	42
16.3	odd	4		64.12.e.a.49.18		42
16.5	even	4	inner	128.12.e.b.97.18		42
16.11	odd	4		128.12.e.a.97.4		42
16.13	even	4		16.12.e.a.5.3	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.3	✓	42	16.13	even	4
16.12.e.a.13.3	yes	42	8.5	even	2
64.12.e.a.17.18		42	8.3	odd	2
64.12.e.a.49.18		42	16.3	odd	4
128.12.e.a.33.4		42	4.3	odd	2
128.12.e.a.97.4		42	16.11	odd	4
128.12.e.b.33.18		42	1.1	even	1	trivial
128.12.e.b.97.18		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)

\(f(q)\)	\(=\)	\(q+(435.014 + 435.014i) q^{3} +(1517.34 - 1517.34i) q^{5} +59722.7i q^{7} +201326. i q^{9} +O(q^{10})\)	\(q+(435.014 + 435.014i) q^{3} +(1517.34 - 1517.34i) q^{5} +59722.7i q^{7} +201326. i q^{9} +(-56196.6 + 56196.6i) q^{11} +(315796. + 315796. i) q^{13} +1.32013e6 q^{15} +8.11170e6 q^{17} +(1.33811e7 + 1.33811e7i) q^{19} +(-2.59802e7 + 2.59802e7i) q^{21} -2.84613e7i q^{23} +4.42235e7i q^{25} +(-1.05184e7 + 1.05184e7i) q^{27} +(-7.59695e7 - 7.59695e7i) q^{29} +5.67278e7 q^{31} -4.88926e7 q^{33} +(9.06196e7 + 9.06196e7i) q^{35} +(-3.75680e8 + 3.75680e8i) q^{37} +2.74751e8i q^{39} +1.51696e7i q^{41} +(-1.08339e9 + 1.08339e9i) q^{43} +(3.05481e8 + 3.05481e8i) q^{45} +2.79798e9 q^{47} -1.58947e9 q^{49} +(3.52870e9 + 3.52870e9i) q^{51} +(-2.03657e9 + 2.03657e9i) q^{53} +1.70539e8i q^{55} +1.16419e10i q^{57} +(4.23123e9 - 4.23123e9i) q^{59} +(-6.54407e9 - 6.54407e9i) q^{61} -1.20238e10 q^{63} +9.58341e8 q^{65} +(8.01903e9 + 8.01903e9i) q^{67} +(1.23810e10 - 1.23810e10i) q^{69} -1.40718e10i q^{71} +6.29343e9i q^{73} +(-1.92378e10 + 1.92378e10i) q^{75} +(-3.35621e9 - 3.35621e9i) q^{77} -3.46459e10 q^{79} +2.65131e10 q^{81} +(-4.29998e10 - 4.29998e10i) q^{83} +(1.23082e10 - 1.23082e10i) q^{85} -6.60955e10i q^{87} +3.39308e9i q^{89} +(-1.88602e10 + 1.88602e10i) q^{91} +(2.46773e10 + 2.46773e10i) q^{93} +4.06073e10 q^{95} +1.55551e10 q^{97} +(-1.13139e10 - 1.13139e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 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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