LMFDB - Embedded newform 64.12.e.a.17.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("64.17");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	64.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$49.1739635558$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.12
Character	$\chi$	$=$	64.17
Dual form			64.12.e.a.49.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(56.4628 + 56.4628i) q^{3} +(6260.45 - 6260.45i) q^{5} -32944.0i q^{7} -170771. i q^{9} +O(q^{10})$	\(q+(56.4628 + 56.4628i) q^{3} +(6260.45 - 6260.45i) q^{5} -32944.0i q^{7} -170771. i q^{9} +(151744. - 151744. i) q^{11} +(-1.05140e6 - 1.05140e6i) q^{13} +706965. q^{15} -1.95797e6 q^{17} +(-5.25340e6 - 5.25340e6i) q^{19} +(1.86011e6 - 1.86011e6i) q^{21} +4.62502e7i q^{23} -2.95583e7i q^{25} +(1.96444e7 - 1.96444e7i) q^{27} +(1.16274e8 + 1.16274e8i) q^{29} -2.86231e8 q^{31} +1.71358e7 q^{33} +(-2.06244e8 - 2.06244e8i) q^{35} +(3.33901e8 - 3.33901e8i) q^{37} -1.18730e8i q^{39} -1.31100e8i q^{41} +(-5.60465e8 + 5.60465e8i) q^{43} +(-1.06910e9 - 1.06910e9i) q^{45} -1.10264e8 q^{47} +8.92021e8 q^{49} +(-1.10553e8 - 1.10553e8i) q^{51} +(-2.81385e9 + 2.81385e9i) q^{53} -1.89998e9i q^{55} -5.93243e8i q^{57} +(3.57157e8 - 3.57157e8i) q^{59} +(-6.15858e9 - 6.15858e9i) q^{61} -5.62587e9 q^{63} -1.31645e10 q^{65} +(-8.27855e9 - 8.27855e9i) q^{67} +(-2.61142e9 + 2.61142e9i) q^{69} -1.51270e10i q^{71} -1.11074e10i q^{73} +(1.66895e9 - 1.66895e9i) q^{75} +(-4.99907e9 - 4.99907e9i) q^{77} -1.68275e10 q^{79} -2.80332e10 q^{81} +(1.04553e10 + 1.04553e10i) q^{83} +(-1.22578e10 + 1.22578e10i) q^{85} +1.31303e10i q^{87} -3.00687e10i q^{89} +(-3.46373e10 + 3.46373e10i) q^{91} +(-1.61614e10 - 1.61614e10i) q^{93} -6.57772e10 q^{95} +1.53440e11 q^{97} +(-2.59135e10 - 2.59135e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} - 2 q^{5}+O(q^{10}) $ 42 * q + 2 * q^3 - 2 * q^5	$ 42 q + 2 q^{3} - 2 q^{5} + 540846 q^{11} - 2 q^{13} + 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} + 354292 q^{21} + 66463304 q^{27} + 77673206 q^{29} - 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} - 522762058 q^{37} - 3824193658 q^{43} + 97301954 q^{45} + 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} - 2100608058 q^{53} - 955824746 q^{59} + 2150827022 q^{61} - 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} - 16193060732 q^{69} - 28890034486 q^{75} - 22711870540 q^{77} - 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} - 84575506252 q^{85} + 147369662716 q^{91} - 69689773328 q^{93} - 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) $ 42 * q + 2 * q^3 - 2 * q^5 + 540846 * q^11 - 2 * q^13 + 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 + 354292 * q^21 + 66463304 * q^27 + 77673206 * q^29 - 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 - 522762058 * q^37 - 3824193658 * q^43 + 97301954 * q^45 + 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 - 2100608058 * q^53 - 955824746 * q^59 + 2150827022 * q^61 - 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 - 16193060732 * q^69 - 28890034486 * q^75 - 22711870540 * q^77 - 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 - 84575506252 * q^85 + 147369662716 * q^91 - 69689773328 * q^93 - 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	56.4628	+	56.4628i	0.134151	+	0.134151i	0.770994	−	0.636842i	$-0.219760\pi$
$3$	56.4628	+	56.4628i	0.134151	+	0.134151i	−0.636842	+	0.770994i	$0.719760\pi$
$4$		0			0
$5$	6260.45	−	6260.45i	0.895922	−	0.895922i	−0.0991500	−	0.995072i	$-0.531612\pi$
$5$	6260.45	−	6260.45i	0.895922	−	0.895922i	0.995072	+	0.0991500i	$0.0316124\pi$
$6$		0			0
$7$		−	32944.0i		−	0.740861i	−0.928860	−	0.370431i	$-0.879210\pi$
$7$		−	32944.0i		−	0.740861i	0.928860	−	0.370431i	$-0.120790\pi$
$8$		0			0
$9$		−	170771.i		−	0.964007i
$10$		0			0
$11$	151744.	−	151744.i	0.284088	−	0.284088i	−0.550649	−	0.834737i	$-0.685620\pi$
$11$	151744.	−	151744.i	0.284088	−	0.284088i	0.834737	+	0.550649i	$0.185620\pi$
$12$		0			0
$13$	−1.05140e6	−	1.05140e6i	−0.785380	−	0.785380i	0.195353	−	0.980733i	$-0.437415\pi$
$13$	−1.05140e6	−	1.05140e6i	−0.785380	−	0.785380i	−0.980733	+	0.195353i	$0.937415\pi$
$14$		0			0
$15$	706965.			0.240379
$16$		0			0
$17$	−1.95797e6			−0.334455			−0.167228	−	0.985918i	$-0.553481\pi$
$17$	−1.95797e6			−0.334455			−0.167228	+	0.985918i	$0.553481\pi$
$18$		0			0
$19$	−5.25340e6	−	5.25340e6i	−0.486738	−	0.486738i	0.420537	−	0.907275i	$-0.361842\pi$
$19$	−5.25340e6	−	5.25340e6i	−0.486738	−	0.486738i	−0.907275	+	0.420537i	$0.861842\pi$
$20$		0			0
$21$	1.86011e6	−	1.86011e6i	0.0993876	−	0.0993876i
$22$		0			0
$23$			4.62502e7i			1.49834i	0.662377	+	0.749170i	$0.269548\pi$
$23$			4.62502e7i			1.49834i	−0.662377	+	0.749170i	$0.730452\pi$
$24$		0			0
$25$		−	2.95583e7i		−	0.605354i
$26$		0			0
$27$	1.96444e7	−	1.96444e7i	0.263474	−	0.263474i
$28$		0			0
$29$	1.16274e8	+	1.16274e8i	1.05267	+	1.05267i	0.998533	+	0.0541405i	$0.0172419\pi$
$29$	1.16274e8	+	1.16274e8i	1.05267	+	1.05267i	0.0541405	+	0.998533i	$0.482758\pi$
$30$		0			0
$31$	−2.86231e8			−1.79567			−0.897836	−	0.440331i	$-0.854861\pi$
$31$	−2.86231e8			−1.79567			−0.897836	+	0.440331i	$0.854861\pi$
$32$		0			0
$33$	1.71358e7			0.0762217
$34$		0			0
$35$	−2.06244e8	−	2.06244e8i	−0.663754	−	0.663754i
$36$		0			0
$37$	3.33901e8	−	3.33901e8i	0.791606	−	0.791606i	−0.190150	−	0.981755i	$-0.560897\pi$
$37$	3.33901e8	−	3.33901e8i	0.791606	−	0.791606i	0.981755	+	0.190150i	$0.0608973\pi$
$38$		0			0
$39$		−	1.18730e8i		−	0.210720i
$40$		0			0
$41$		−	1.31100e8i		−	0.176722i	−0.996089	−	0.0883610i	$-0.971837\pi$
$41$		−	1.31100e8i		−	0.176722i	0.996089	−	0.0883610i	$-0.0281629\pi$
$42$		0			0
$43$	−5.60465e8	+	5.60465e8i	−0.581396	+	0.581396i	−0.935287	−	0.353891i	$-0.884859\pi$
$43$	−5.60465e8	+	5.60465e8i	−0.581396	+	0.581396i	0.353891	+	0.935287i	$0.384859\pi$
$44$		0			0
$45$	−1.06910e9	−	1.06910e9i	−0.863675	−	0.863675i
$46$		0			0
$47$	−1.10264e8			−0.0701288			−0.0350644	−	0.999385i	$-0.511164\pi$
$47$	−1.10264e8			−0.0701288			−0.0350644	+	0.999385i	$0.511164\pi$
$48$		0			0
$49$	8.92021e8			0.451125
$50$		0			0
$51$	−1.10553e8	−	1.10553e8i	−0.0448677	−	0.0448677i
$52$		0			0
$53$	−2.81385e9	+	2.81385e9i	−0.924238	+	0.924238i	−0.997326	−	0.0730872i	$-0.976715\pi$
$53$	−2.81385e9	+	2.81385e9i	−0.924238	+	0.924238i	0.0730872	+	0.997326i	$0.476715\pi$
$54$		0			0
$55$		−	1.89998e9i		−	0.509042i
$56$		0			0
$57$		−	5.93243e8i		−	0.130593i
$58$		0			0
$59$	3.57157e8	−	3.57157e8i	0.0650389	−	0.0650389i	−0.673839	−	0.738878i	$-0.735356\pi$
$59$	3.57157e8	−	3.57157e8i	0.0650389	−	0.0650389i	0.738878	+	0.673839i	$0.235356\pi$
$60$		0			0
$61$	−6.15858e9	−	6.15858e9i	−0.933612	−	0.933612i	0.0643176	−	0.997929i	$-0.479513\pi$
$61$	−6.15858e9	−	6.15858e9i	−0.933612	−	0.933612i	−0.997929	+	0.0643176i	$0.979513\pi$
$62$		0			0
$63$	−5.62587e9			−0.714195
$64$		0			0
$65$	−1.31645e10			−1.40728
$66$		0			0
$67$	−8.27855e9	−	8.27855e9i	−0.749106	−	0.749106i	0.225206	−	0.974311i	$-0.427695\pi$
$67$	−8.27855e9	−	8.27855e9i	−0.749106	−	0.749106i	−0.974311	+	0.225206i	$0.927695\pi$
$68$		0			0
$69$	−2.61142e9	+	2.61142e9i	−0.201005	+	0.201005i
$70$		0			0
$71$		−	1.51270e10i		−	0.995020i	−0.867458	−	0.497510i	$-0.834248\pi$
$71$		−	1.51270e10i		−	0.995020i	0.867458	−	0.497510i	$-0.165752\pi$
$72$		0			0
$73$		−	1.11074e10i		−	0.627100i	−0.949572	−	0.313550i	$-0.898482\pi$
$73$		−	1.11074e10i		−	0.627100i	0.949572	−	0.313550i	$-0.101518\pi$
$74$		0			0
$75$	1.66895e9	−	1.66895e9i	0.0812092	−	0.0812092i
$76$		0			0
$77$	−4.99907e9	−	4.99907e9i	−0.210470	−	0.210470i
$78$		0			0
$79$	−1.68275e10			−0.615275			−0.307638	−	0.951504i	$-0.599538\pi$
$79$	−1.68275e10			−0.615275			−0.307638	+	0.951504i	$0.599538\pi$
$80$		0			0
$81$	−2.80332e10			−0.893316
$82$		0			0
$83$	1.04553e10	+	1.04553e10i	0.291345	+	0.291345i	0.837611	−	0.546267i	$-0.183951\pi$
$83$	1.04553e10	+	1.04553e10i	0.291345	+	0.291345i	−0.546267	+	0.837611i	$0.683951\pi$
$84$		0			0
$85$	−1.22578e10	+	1.22578e10i	−0.299646	+	0.299646i
$86$		0			0
$87$			1.31303e10i			0.282436i
$88$		0			0
$89$		−	3.00687e10i		−	0.570781i	−0.958411	−	0.285391i	$-0.907877\pi$
$89$		−	3.00687e10i		−	0.570781i	0.958411	−	0.285391i	$-0.0921233\pi$
$90$		0			0
$91$	−3.46373e10	+	3.46373e10i	−0.581858	+	0.581858i
$92$		0			0
$93$	−1.61614e10	−	1.61614e10i	−0.240892	−	0.240892i
$94$		0			0
$95$	−6.57772e10			−0.872159
$96$		0			0
$97$	1.53440e11			1.81423			0.907117	−	0.420878i	$-0.138278\pi$
$97$	1.53440e11			1.81423			0.907117	+	0.420878i	$0.138278\pi$
$98$		0			0
$99$	−2.59135e10	−	2.59135e10i	−0.273863	−	0.273863i
$100$		0			0
$101$	−1.83207e10	+	1.83207e10i	−0.173450	+	0.173450i	−0.788493	−	0.615043i	$-0.789138\pi$
$101$	−1.83207e10	+	1.83207e10i	−0.173450	+	0.173450i	0.615043	+	0.788493i	$0.289138\pi$
$102$		0			0
$103$		−	2.26120e11i		−	1.92192i	−0.276688	−	0.960960i	$-0.589237\pi$
$103$		−	2.26120e11i		−	1.92192i	0.276688	−	0.960960i	$-0.410763\pi$
$104$		0			0
$105$		−	2.32902e10i		−	0.178087i
$106$		0			0
$107$	−8.60250e10	+	8.60250e10i	−0.592945	+	0.592945i	−0.938426	−	0.345481i	$-0.887716\pi$
$107$	−8.60250e10	+	8.60250e10i	−0.592945	+	0.592945i	0.345481	+	0.938426i	$0.387716\pi$
$108$		0			0
$109$	−5.61060e10	−	5.61060e10i	−0.349272	−	0.349272i	0.510567	−	0.859838i	$-0.329436\pi$
$109$	−5.61060e10	−	5.61060e10i	−0.349272	−	0.349272i	−0.859838	+	0.510567i	$0.829436\pi$
$110$		0			0
$111$	3.77060e10			0.212390
$112$		0			0
$113$	2.67377e11			1.36519			0.682595	−	0.730797i	$-0.260851\pi$
$113$	2.67377e11			1.36519			0.682595	+	0.730797i	$0.260851\pi$
$114$		0			0
$115$	2.89547e11	+	2.89547e11i	1.34240	+	1.34240i
$116$		0			0
$117$	−1.79549e11	+	1.79549e11i	−0.757112	+	0.757112i
$118$		0			0
$119$			6.45034e10i			0.247785i
$120$		0			0
$121$			2.39259e11i			0.838588i
$122$		0			0
$123$	7.40226e9	−	7.40226e9i	0.0237075	−	0.0237075i
$124$		0			0
$125$	1.20638e11	+	1.20638e11i	0.353572	+	0.353572i
$126$		0			0
$127$	3.39115e11			0.910807			0.455404	−	0.890285i	$-0.349495\pi$
$127$	3.39115e11			0.910807			0.455404	+	0.890285i	$0.349495\pi$
$128$		0			0
$129$	−6.32909e10			−0.155990
$130$		0			0
$131$	5.87379e11	+	5.87379e11i	1.33023	+	1.33023i	0.905162	+	0.425068i	$0.139750\pi$
$131$	5.87379e11	+	5.87379e11i	1.33023	+	1.33023i	0.425068	+	0.905162i	$0.360250\pi$
$132$		0			0
$133$	−1.73068e11	+	1.73068e11i	−0.360605	+	0.360605i
$134$		0			0
$135$		−	2.45966e11i		−	0.472105i
$136$		0			0
$137$		−	6.79735e11i		−	1.20331i	−0.798757	−	0.601654i	$-0.794509\pi$
$137$		−	6.79735e11i		−	1.20331i	0.798757	−	0.601654i	$-0.205491\pi$
$138$		0			0
$139$	7.49060e11	−	7.49060e11i	1.22443	−	1.22443i	0.258393	−	0.966040i	$-0.416807\pi$
$139$	7.49060e11	−	7.49060e11i	1.22443	−	1.22443i	0.966040	−	0.258393i	$-0.0831929\pi$
$140$		0			0
$141$	−6.22582e9	−	6.22582e9i	−0.00940788	−	0.00940788i
$142$		0			0
$143$	−3.19089e11			−0.446235
$144$		0			0
$145$	1.45586e12			1.88623
$146$		0			0
$147$	5.03660e10	+	5.03660e10i	0.0605191	+	0.0605191i
$148$		0			0
$149$	−7.36973e11	+	7.36973e11i	−0.822105	+	0.822105i	−0.986410	−	0.164305i	$-0.947462\pi$
$149$	−7.36973e11	+	7.36973e11i	−0.822105	+	0.822105i	0.164305	+	0.986410i	$0.447462\pi$
$150$		0			0
$151$		−	5.40219e11i		−	0.560011i	−0.959998	−	0.280006i	$-0.909664\pi$
$151$		−	5.40219e11i		−	0.560011i	0.959998	−	0.280006i	$-0.0903363\pi$
$152$		0			0
$153$			3.34365e11i			0.322417i
$154$		0			0
$155$	−1.79193e12	+	1.79193e12i	−1.60878	+	1.60878i
$156$		0			0
$157$	−1.25630e11	−	1.25630e11i	−0.105110	−	0.105110i	0.652596	−	0.757706i	$-0.273680\pi$
$157$	−1.25630e11	−	1.25630e11i	−0.105110	−	0.105110i	−0.757706	+	0.652596i	$0.773680\pi$
$158$		0			0
$159$	−3.17756e11			−0.247976
$160$		0			0
$161$	1.52367e12			1.11006
$162$		0			0
$163$	8.92563e11	+	8.92563e11i	0.607585	+	0.607585i	0.942314	−	0.334729i	$-0.108645\pi$
$163$	8.92563e11	+	8.92563e11i	0.607585	+	0.607585i	−0.334729	+	0.942314i	$0.608645\pi$
$164$		0			0
$165$	1.07278e11	−	1.07278e11i	0.0682887	−	0.0682887i
$166$		0			0
$167$		−	2.53237e12i		−	1.50864i	−0.656506	−	0.754321i	$-0.727966\pi$
$167$		−	2.53237e12i		−	1.50864i	0.656506	−	0.754321i	$-0.272034\pi$
$168$		0			0
$169$			4.18729e11i			0.233645i
$170$		0			0
$171$	−8.97127e11	+	8.97127e11i	−0.469219	+	0.469219i
$172$		0			0
$173$	−1.51275e12	−	1.51275e12i	−0.742188	−	0.742188i	0.230810	−	0.972999i	$-0.425862\pi$
$173$	−1.51275e12	−	1.51275e12i	−0.742188	−	0.742188i	−0.972999	+	0.230810i	$0.925862\pi$
$174$		0			0
$175$	−9.73768e11			−0.448483
$176$		0			0
$177$	4.03322e10			0.0174501
$178$		0			0
$179$	6.66463e8	+	6.66463e8i	0.000271072	+	0.000271072i	0.707242	−	0.706971i	$-0.249939\pi$
$179$	6.66463e8	+	6.66463e8i	0.000271072	+	0.000271072i	−0.706971	+	0.707242i	$0.749939\pi$
$180$		0			0
$181$	−8.79540e11	+	8.79540e11i	−0.336530	+	0.336530i	−0.855060	−	0.518530i	$-0.826480\pi$
$181$	−8.79540e11	+	8.79540e11i	−0.336530	+	0.336530i	0.518530	+	0.855060i	$0.326480\pi$
$182$		0			0
$183$		−	6.95461e11i		−	0.250491i
$184$		0			0
$185$		−	4.18075e12i		−	1.41843i
$186$		0			0
$187$	−2.97112e11	+	2.97112e11i	−0.0950147	+	0.0950147i
$188$		0			0
$189$	−6.47165e11	−	6.47165e11i	−0.195198	−	0.195198i
$190$		0			0
$191$	−5.27207e12			−1.50071			−0.750357	−	0.661033i	$-0.770118\pi$
$191$	−5.27207e12			−1.50071			−0.750357	+	0.661033i	$0.770118\pi$
$192$		0			0
$193$	−4.42702e12			−1.19000			−0.595000	−	0.803726i	$-0.702848\pi$
$193$	−4.42702e12			−1.19000			−0.595000	+	0.803726i	$0.702848\pi$
$194$		0			0
$195$	−7.43304e11	−	7.43304e11i	−0.188789	−	0.188789i
$196$		0			0
$197$	−1.55303e12	+	1.55303e12i	−0.372920	+	0.372920i	−0.868540	−	0.495620i	$-0.834941\pi$
$197$	−1.55303e12	+	1.55303e12i	−0.372920	+	0.372920i	0.495620	+	0.868540i	$0.334941\pi$
$198$		0			0
$199$		−	9.09713e11i		−	0.206639i	−0.994648	−	0.103320i	$-0.967054\pi$
$199$		−	9.09713e11i		−	0.206639i	0.994648	−	0.103320i	$-0.0329464\pi$
$200$		0			0
$201$		−	9.34861e11i		−	0.200987i
$202$		0			0
$203$	3.83053e12	−	3.83053e12i	0.779885	−	0.779885i
$204$		0			0
$205$	−8.20744e11	−	8.20744e11i	−0.158329	−	0.158329i
$206$		0			0
$207$	7.89819e12			1.44441
$208$		0			0
$209$	−1.59435e12			−0.276553
$210$		0			0
$211$	−7.96643e12	−	7.96643e12i	−1.31132	−	1.31132i	−0.920440	−	0.390884i	$-0.872169\pi$
$211$	−7.96643e12	−	7.96643e12i	−1.31132	−	1.31132i	−0.390884	−	0.920440i	$-0.627831\pi$
$212$		0			0
$213$	8.54112e11	−	8.54112e11i	0.133483	−	0.133483i
$214$		0			0
$215$			7.01753e12i			1.04177i
$216$		0			0
$217$			9.42957e12i			1.33034i
$218$		0			0
$219$	6.27155e11	−	6.27155e11i	0.0841263	−	0.0841263i
$220$		0			0
$221$	2.05862e12	+	2.05862e12i	0.262675	+	0.262675i
$222$		0			0
$223$	−6.00097e12			−0.728693			−0.364346	−	0.931263i	$-0.618708\pi$
$223$	−6.00097e12			−0.728693			−0.364346	+	0.931263i	$0.618708\pi$
$224$		0			0
$225$	−5.04770e12			−0.583566
$226$		0			0
$227$	9.49853e12	+	9.49853e12i	1.04596	+	1.04596i	0.998892	+	0.0470662i	$0.0149872\pi$
$227$	9.49853e12	+	9.49853e12i	1.04596	+	1.04596i	0.0470662	+	0.998892i	$0.485013\pi$
$228$		0			0
$229$	3.57204e12	−	3.57204e12i	0.374819	−	0.374819i	−0.494410	−	0.869229i	$-0.664616\pi$
$229$	3.57204e12	−	3.57204e12i	0.374819	−	0.374819i	0.869229	+	0.494410i	$0.164616\pi$
$230$		0			0
$231$		−	5.64522e11i		−	0.0564697i
$232$		0			0
$233$		−	5.68541e12i		−	0.542380i	−0.962526	−	0.271190i	$-0.912583\pi$
$233$		−	5.68541e12i		−	0.542380i	0.962526	−	0.271190i	$-0.0874172\pi$
$234$		0			0
$235$	−6.90303e11	+	6.90303e11i	−0.0628299	+	0.0628299i
$236$		0			0
$237$	−9.50126e11	−	9.50126e11i	−0.0825401	−	0.0825401i
$238$		0			0
$239$	1.23973e13			1.02834			0.514171	−	0.857688i	$-0.328100\pi$
$239$	1.23973e13			1.02834			0.514171	+	0.857688i	$0.328100\pi$
$240$		0			0
$241$	−2.15671e12			−0.170883			−0.0854414	−	0.996343i	$-0.527230\pi$
$241$	−2.15671e12			−0.170883			−0.0854414	+	0.996343i	$0.527230\pi$
$242$		0			0
$243$	−5.06278e12	−	5.06278e12i	−0.383314	−	0.383314i
$244$		0			0
$245$	5.58445e12	−	5.58445e12i	0.404173	−	0.404173i
$246$		0			0
$247$			1.10469e13i			0.764549i
$248$		0			0
$249$			1.18067e12i			0.0781687i
$250$		0			0
$251$	2.78742e11	−	2.78742e11i	0.0176603	−	0.0176603i	−0.698222	−	0.715882i	$-0.746025\pi$
$251$	2.78742e11	−	2.78742e11i	0.0176603	−	0.0176603i	0.715882	+	0.698222i	$0.246025\pi$
$252$		0			0
$253$	7.01821e12	+	7.01821e12i	0.425661	+	0.425661i
$254$		0			0
$255$	−1.38422e12			−0.0803959
$256$		0			0
$257$	1.43940e13			0.800844			0.400422	−	0.916331i	$-0.368864\pi$
$257$	1.43940e13			0.800844			0.400422	+	0.916331i	$0.368864\pi$
$258$		0			0
$259$	−1.10000e13	−	1.10000e13i	−0.586470	−	0.586470i
$260$		0			0
$261$	1.98562e13	−	1.98562e13i	1.01478	−	1.01478i
$262$		0			0
$263$			1.03878e13i			0.509057i	0.967065	+	0.254529i	$0.0819203\pi$
$263$			1.03878e13i			0.509057i	−0.967065	+	0.254529i	$0.918080\pi$
$264$		0			0
$265$			3.52320e13i			1.65609i
$266$		0			0
$267$	1.69776e12	−	1.69776e12i	0.0765711	−	0.0765711i
$268$		0			0
$269$	2.99941e13	+	2.99941e13i	1.29837	+	1.29837i	0.929468	+	0.368903i	$0.120266\pi$
$269$	2.99941e13	+	2.99941e13i	1.29837	+	1.29837i	0.368903	+	0.929468i	$0.379734\pi$
$270$		0			0
$271$	2.44910e13			1.01783			0.508915	−	0.860817i	$-0.330047\pi$
$271$	2.44910e13			1.01783			0.508915	+	0.860817i	$0.330047\pi$
$272$		0			0
$273$	−3.91144e12			−0.156114
$274$		0			0
$275$	−4.48531e12	−	4.48531e12i	−0.171974	−	0.171974i
$276$		0			0
$277$	1.19102e13	−	1.19102e13i	0.438815	−	0.438815i	−0.452798	−	0.891613i	$-0.649574\pi$
$277$	1.19102e13	−	1.19102e13i	0.438815	−	0.438815i	0.891613	+	0.452798i	$0.149574\pi$
$278$		0			0
$279$			4.88799e13i			1.73104i
$280$		0			0
$281$		−	1.77505e13i		−	0.604403i	−0.953244	−	0.302201i	$-0.902279\pi$
$281$		−	1.77505e13i		−	0.604403i	0.953244	−	0.302201i	$-0.0977215\pi$
$282$		0			0
$283$	6.56292e12	−	6.56292e12i	0.214917	−	0.214917i	−0.591435	−	0.806353i	$-0.701438\pi$
$283$	6.56292e12	−	6.56292e12i	0.214917	−	0.214917i	0.806353	+	0.591435i	$0.201438\pi$
$284$		0			0
$285$	−3.71397e12	−	3.71397e12i	−0.117001	−	0.117001i
$286$		0			0
$287$	−4.31895e12			−0.130927
$288$		0			0
$289$	−3.04382e13			−0.888140
$290$		0			0
$291$	8.66364e12	+	8.66364e12i	0.243382	+	0.243382i
$292$		0			0
$293$	−1.28607e13	+	1.28607e13i	−0.347931	+	0.347931i	−0.859338	−	0.511408i	$-0.829124\pi$
$293$	−1.28607e13	+	1.28607e13i	−0.347931	+	0.347931i	0.511408	+	0.859338i	$0.329124\pi$
$294$		0			0
$295$		−	4.47193e12i		−	0.116540i
$296$		0			0
$297$		−	5.96186e12i		−	0.149700i
$298$		0			0
$299$	4.86275e13	−	4.86275e13i	1.17677	−	1.17677i
$300$		0			0
$301$	1.84640e13	+	1.84640e13i	0.430734	+	0.430734i
$302$		0			0
$303$	−2.06887e12			−0.0465371
$304$		0			0
$305$	−7.71109e13			−1.67289
$306$		0			0
$307$	−2.49037e13	−	2.49037e13i	−0.521199	−	0.521199i	0.396735	−	0.917933i	$-0.370143\pi$
$307$	−2.49037e13	−	2.49037e13i	−0.521199	−	0.521199i	−0.917933	+	0.396735i	$0.870143\pi$
$308$		0			0
$309$	1.27674e13	−	1.27674e13i	0.257828	−	0.257828i
$310$		0			0
$311$		−	4.08332e13i		−	0.795851i	−0.917418	−	0.397925i	$-0.869730\pi$
$311$		−	4.08332e13i		−	0.795851i	0.917418	−	0.397925i	$-0.130270\pi$
$312$		0			0
$313$		−	1.00390e13i		−	0.188885i	−0.995530	−	0.0944423i	$-0.969893\pi$
$313$		−	1.00390e13i		−	0.188885i	0.995530	−	0.0944423i	$-0.0301068\pi$
$314$		0			0
$315$	−3.52205e13	+	3.52205e13i	−0.639863	+	0.639863i
$316$		0			0
$317$	−6.71251e13	−	6.71251e13i	−1.17777	−	1.17777i	−0.980312	−	0.197455i	$-0.936732\pi$
$317$	−6.71251e13	−	6.71251e13i	−1.17777	−	1.17777i	−0.197455	−	0.980312i	$-0.563268\pi$
$318$		0			0
$319$	3.52879e13			0.598104
$320$		0			0
$321$	−9.71443e12			−0.159089
$322$		0			0
$323$	1.02860e13	+	1.02860e13i	0.162792	+	0.162792i
$324$		0			0
$325$	−3.10776e13	+	3.10776e13i	−0.475433	+	0.475433i
$326$		0			0
$327$		−	6.33580e12i		−	0.0937106i
$328$		0			0
$329$			3.63254e12i			0.0519557i
$330$		0			0
$331$	−3.21941e13	+	3.21941e13i	−0.445371	+	0.445371i	−0.893812	−	0.448441i	$-0.851979\pi$
$331$	−3.21941e13	+	3.21941e13i	−0.445371	+	0.445371i	0.448441	+	0.893812i	$0.351979\pi$
$332$		0			0
$333$	−5.70207e13	−	5.70207e13i	−0.763113	−	0.763113i
$334$		0			0
$335$	−1.03655e14			−1.34228
$336$		0			0
$337$	1.17704e14			1.47512			0.737562	−	0.675279i	$-0.235977\pi$
$337$	1.17704e14			1.47512			0.737562	+	0.675279i	$0.235977\pi$
$338$		0			0
$339$	1.50969e13	+	1.50969e13i	0.183142	+	0.183142i
$340$		0			0
$341$	−4.34339e13	+	4.34339e13i	−0.510129	+	0.510129i
$342$		0			0
$343$		−	9.45277e13i		−	1.07508i
$344$		0			0
$345$			3.26973e13i			0.360169i
$346$		0			0
$347$	−6.26543e13	+	6.26543e13i	−0.668558	+	0.668558i	−0.957382	−	0.288824i	$-0.906736\pi$
$347$	−6.26543e13	+	6.26543e13i	−0.668558	+	0.668558i	0.288824	+	0.957382i	$0.406736\pi$
$348$		0			0
$349$	4.36968e13	+	4.36968e13i	0.451762	+	0.451762i	0.895939	−	0.444177i	$-0.146504\pi$
$349$	4.36968e13	+	4.36968e13i	0.451762	+	0.451762i	−0.444177	+	0.895939i	$0.646504\pi$
$350$		0			0
$351$	−4.13083e13			−0.413855
$352$		0			0
$353$	1.05748e14			1.02686			0.513431	−	0.858131i	$-0.328374\pi$
$353$	1.05748e14			1.02686			0.513431	+	0.858131i	$0.328374\pi$
$354$		0			0
$355$	−9.47017e13	−	9.47017e13i	−0.891460	−	0.891460i
$356$		0			0
$357$	−3.64205e12	+	3.64205e12i	−0.0332407	+	0.0332407i
$358$		0			0
$359$		−	2.59583e13i		−	0.229751i	−0.993380	−	0.114875i	$-0.963353\pi$
$359$		−	2.59583e13i		−	0.229751i	0.993380	−	0.114875i	$-0.0366469\pi$
$360$		0			0
$361$		−	6.12939e13i		−	0.526172i
$362$		0			0
$363$	−1.35092e13	+	1.35092e13i	−0.112498	+	0.112498i
$364$		0			0
$365$	−6.95373e13	−	6.95373e13i	−0.561833	−	0.561833i
$366$		0			0
$367$	−1.12895e14			−0.885137			−0.442568	−	0.896735i	$-0.645933\pi$
$367$	−1.12895e14			−0.885137			−0.442568	+	0.896735i	$0.645933\pi$
$368$		0			0
$369$	−2.23880e13			−0.170361
$370$		0			0
$371$	9.26995e13	+	9.26995e13i	0.684732	+	0.684732i
$372$		0			0
$373$	−4.27445e13	+	4.27445e13i	−0.306536	+	0.306536i	−0.843564	−	0.537028i	$-0.819547\pi$
$373$	−4.27445e13	+	4.27445e13i	−0.306536	+	0.306536i	0.537028	+	0.843564i	$0.319547\pi$
$374$		0			0
$375$			1.36231e13i			0.0948644i
$376$		0			0
$377$		−	2.44501e14i		−	1.65350i
$378$		0			0
$379$	1.18007e14	−	1.18007e14i	0.775162	−	0.775162i	−0.203842	−	0.979004i	$-0.565343\pi$
$379$	1.18007e14	−	1.18007e14i	0.775162	−	0.775162i	0.979004	+	0.203842i	$0.0653429\pi$
$380$		0			0
$381$	1.91474e13	+	1.91474e13i	0.122186	+	0.122186i
$382$		0			0
$383$	7.83589e13			0.485842			0.242921	−	0.970046i	$-0.421894\pi$
$383$	7.83589e13			0.485842			0.242921	+	0.970046i	$0.421894\pi$
$384$		0			0
$385$	−6.25928e13			−0.377129
$386$		0			0
$387$	9.57112e13	+	9.57112e13i	0.560470	+	0.560470i
$388$		0			0
$389$	5.66527e13	−	5.66527e13i	0.322476	−	0.322476i	−0.527240	−	0.849716i	$-0.676773\pi$
$389$	5.66527e13	−	5.66527e13i	0.322476	−	0.322476i	0.849716	+	0.527240i	$0.176773\pi$
$390$		0			0
$391$		−	9.05567e13i		−	0.501128i
$392$		0			0
$393$			6.63302e13i			0.356904i
$394$		0			0
$395$	−1.05347e14	+	1.05347e14i	−0.551239	+	0.551239i
$396$		0			0
$397$	1.13353e14	+	1.13353e14i	0.576881	+	0.576881i	0.934043	−	0.357161i	$-0.116255\pi$
$397$	1.13353e14	+	1.13353e14i	0.576881	+	0.576881i	−0.357161	+	0.934043i	$0.616255\pi$
$398$		0			0
$399$	−1.95438e13			−0.0967515
$400$		0			0
$401$	2.11807e14			1.02011			0.510054	−	0.860142i	$-0.329625\pi$
$401$	2.11807e14			1.02011			0.510054	+	0.860142i	$0.329625\pi$
$402$		0			0
$403$	3.00943e14	+	3.00943e14i	1.41029	+	1.41029i
$404$		0			0
$405$	−1.75500e14	+	1.75500e14i	−0.800342	+	0.800342i
$406$		0			0
$407$		−	1.01335e14i		−	0.449771i
$408$		0			0
$409$			3.06014e14i			1.32210i	0.750343	+	0.661049i	$0.229888\pi$
$409$			3.06014e14i			1.32210i	−0.750343	+	0.661049i	$0.770112\pi$
$410$		0			0
$411$	3.83797e13	−	3.83797e13i	0.161425	−	0.161425i
$412$		0			0
$413$	−1.17662e13	−	1.17662e13i	−0.0481848	−	0.0481848i
$414$		0			0
$415$	1.30910e14			0.522045
$416$		0			0
$417$	8.45880e13			0.328519
$418$		0			0
$419$	−4.57305e13	−	4.57305e13i	−0.172993	−	0.172993i	0.615300	−	0.788293i	$-0.289035\pi$
$419$	−4.57305e13	−	4.57305e13i	−0.172993	−	0.172993i	−0.788293	+	0.615300i	$0.789035\pi$
$420$		0			0
$421$	−2.12318e14	+	2.12318e14i	−0.782412	+	0.782412i	−0.980237	−	0.197825i	$-0.936612\pi$
$421$	−2.12318e14	+	2.12318e14i	−0.782412	+	0.782412i	0.197825	+	0.980237i	$0.436612\pi$
$422$		0			0
$423$			1.88299e13i			0.0676046i
$424$		0			0
$425$			5.78744e13i			0.202464i
$426$		0			0
$427$	−2.02888e14	+	2.02888e14i	−0.691677	+	0.691677i
$428$		0			0
$429$	−1.80166e13	−	1.80166e13i	−0.0598630	−	0.0598630i
$430$		0			0
$431$	4.65703e14			1.50829			0.754143	−	0.656710i	$-0.228052\pi$
$431$	4.65703e14			1.50829			0.754143	+	0.656710i	$0.228052\pi$
$432$		0			0
$433$	3.52107e14			1.11171			0.555855	−	0.831280i	$-0.312391\pi$
$433$	3.52107e14			1.11171			0.555855	+	0.831280i	$0.312391\pi$
$434$		0			0
$435$	8.22017e13	+	8.22017e13i	0.253040	+	0.253040i
$436$		0			0
$437$	2.42971e14	−	2.42971e14i	0.729300	−	0.729300i
$438$		0			0
$439$		−	3.34946e14i		−	0.980438i	−0.871599	−	0.490219i	$-0.836917\pi$
$439$		−	3.34946e14i		−	0.980438i	0.871599	−	0.490219i	$-0.163083\pi$
$440$		0			0
$441$		−	1.52331e14i		−	0.434887i
$442$		0			0
$443$	2.92942e14	−	2.92942e14i	0.815758	−	0.815758i	−0.169732	−	0.985490i	$-0.554290\pi$
$443$	2.92942e14	−	2.92942e14i	0.815758	−	0.815758i	0.985490	+	0.169732i	$0.0542903\pi$
$444$		0			0
$445$	−1.88244e14	−	1.88244e14i	−0.511376	−	0.511376i
$446$		0			0
$447$	−8.32231e13			−0.220573
$448$		0			0
$449$	9.79517e13			0.253313			0.126656	−	0.991947i	$-0.459575\pi$
$449$	9.79517e13			0.253313			0.126656	+	0.991947i	$0.459575\pi$
$450$		0			0
$451$	−1.98937e13	−	1.98937e13i	−0.0502046	−	0.0502046i
$452$		0			0
$453$	3.05023e13	−	3.05023e13i	0.0751263	−	0.0751263i
$454$		0			0
$455$			4.33691e14i			1.04260i
$456$		0			0
$457$		−	2.00143e14i		−	0.469679i	−0.972034	−	0.234840i	$-0.924544\pi$
$457$		−	2.00143e14i		−	0.469679i	0.972034	−	0.234840i	$-0.0754565\pi$
$458$		0			0
$459$	−3.84633e13	+	3.84633e13i	−0.0881204	+	0.0881204i
$460$		0			0
$461$	1.05469e14	+	1.05469e14i	0.235923	+	0.235923i	0.815159	−	0.579237i	$-0.196649\pi$
$461$	1.05469e14	+	1.05469e14i	0.235923	+	0.235923i	−0.579237	+	0.815159i	$0.696649\pi$
$462$		0			0
$463$	−4.68208e14			−1.02269			−0.511345	−	0.859376i	$-0.670852\pi$
$463$	−4.68208e14			−1.02269			−0.511345	+	0.859376i	$0.670852\pi$
$464$		0			0
$465$	−2.02355e14			−0.431641
$466$		0			0
$467$	−2.01214e14	−	2.01214e14i	−0.419193	−	0.419193i	0.465732	−	0.884926i	$-0.345791\pi$
$467$	−2.01214e14	−	2.01214e14i	−0.419193	−	0.419193i	−0.884926	+	0.465732i	$0.845791\pi$
$468$		0			0
$469$	−2.72728e14	+	2.72728e14i	−0.554983	+	0.554983i
$470$		0			0
$471$		−	1.41869e13i		−	0.0282015i
$472$		0			0
$473$			1.70095e14i			0.330335i
$474$		0			0
$475$	−1.55282e14	+	1.55282e14i	−0.294649	+	0.294649i
$476$		0			0
$477$	4.80524e14	+	4.80524e14i	0.890972	+	0.890972i
$478$		0			0
$479$	3.21690e13			0.0582897			0.0291449	−	0.999575i	$-0.490722\pi$
$479$	3.21690e13			0.0582897			0.0291449	+	0.999575i	$0.490722\pi$
$480$		0			0
$481$	−7.02129e14			−1.24342
$482$		0			0
$483$	8.60304e13	+	8.60304e13i	0.148917	+	0.148917i
$484$		0			0
$485$	9.60602e14	−	9.60602e14i	1.62541	−	1.62541i
$486$		0			0
$487$			1.04866e15i			1.73470i	0.497699	+	0.867350i	$0.334179\pi$
$487$			1.04866e15i			1.73470i	−0.497699	+	0.867350i	$0.665821\pi$
$488$		0			0
$489$			1.00793e14i			0.163017i
$490$		0			0
$491$	1.74910e14	−	1.74910e14i	0.276609	−	0.276609i	−0.555145	−	0.831754i	$-0.687337\pi$
$491$	1.74910e14	−	1.74910e14i	0.276609	−	0.276609i	0.831754	+	0.555145i	$0.187337\pi$
$492$		0			0
$493$	−2.27662e14	−	2.27662e14i	−0.352072	−	0.352072i
$494$		0			0
$495$	−3.24461e14			−0.490720
$496$		0			0
$497$	−4.98343e14			−0.737171
$498$		0			0
$499$	−7.23474e14	−	7.23474e14i	−1.04681	−	1.04681i	−0.998849	−	0.0479657i	$-0.984726\pi$
$499$	−7.23474e14	−	7.23474e14i	−1.04681	−	1.04681i	−0.0479657	−	0.998849i	$-0.515274\pi$
$500$		0			0
$501$	1.42985e14	−	1.42985e14i	0.202387	−	0.202387i
$502$		0			0
$503$		−	3.28578e14i		−	0.455004i	−0.973778	−	0.227502i	$-0.926944\pi$
$503$		−	3.28578e14i		−	0.455004i	0.973778	−	0.227502i	$-0.0730557\pi$
$504$		0			0
$505$			2.29391e14i			0.310795i
$506$		0			0
$507$	−2.36426e13	+	2.36426e13i	−0.0313438	+	0.0313438i
$508$		0			0
$509$	−1.04845e14	−	1.04845e14i	−0.136019	−	0.136019i	0.635819	−	0.771838i	$-0.280662\pi$
$509$	−1.04845e14	−	1.04845e14i	−0.136019	−	0.136019i	−0.771838	+	0.635819i	$0.780662\pi$
$510$		0			0
$511$	−3.65922e14			−0.464594
$512$		0			0
$513$	−2.06400e14			−0.256486
$514$		0			0
$515$	−1.41562e15	−	1.41562e15i	−1.72189	−	1.72189i
$516$		0			0
$517$	−1.67320e13	+	1.67320e13i	−0.0199227	+	0.0199227i
$518$		0			0
$519$		−	1.70828e14i		−	0.199131i
$520$		0			0
$521$		−	5.46017e14i		−	0.623158i	−0.950220	−	0.311579i	$-0.899142\pi$
$521$		−	5.46017e14i		−	0.623158i	0.950220	−	0.311579i	$-0.100858\pi$
$522$		0			0
$523$	3.73217e14	−	3.73217e14i	0.417063	−	0.417063i	−0.467127	−	0.884190i	$-0.654711\pi$
$523$	3.73217e14	−	3.73217e14i	0.417063	−	0.417063i	0.884190	+	0.467127i	$0.154711\pi$
$524$		0			0
$525$	−5.49817e13	−	5.49817e13i	−0.0601647	−	0.0601647i
$526$		0			0
$527$	5.60432e14			0.600571
$528$		0			0
$529$	−1.18627e15			−1.24503
$530$		0			0
$531$	−6.09921e13	−	6.09921e13i	−0.0626980	−	0.0626980i
$532$		0			0
$533$	−1.37839e14	+	1.37839e14i	−0.138794	+	0.138794i
$534$		0			0
$535$			1.07711e15i			1.06246i
$536$		0			0
$537$			7.52607e10i			7.27294e-5i
$538$		0			0
$539$	1.35359e14	−	1.35359e14i	0.128159	−	0.128159i
$540$		0			0
$541$	−4.09581e14	−	4.09581e14i	−0.379974	−	0.379974i	0.491118	−	0.871093i	$-0.336588\pi$
$541$	−4.09581e14	−	4.09581e14i	−0.379974	−	0.379974i	−0.871093	+	0.491118i	$0.836588\pi$
$542$		0			0
$543$	−9.93226e13			−0.0902919
$544$		0			0
$545$	−7.02497e14			−0.625841
$546$		0			0
$547$	1.12176e15	+	1.12176e15i	0.979419	+	0.979419i	0.999792	−	0.0203735i	$-0.00648554\pi$
$547$	1.12176e15	+	1.12176e15i	0.979419	+	0.979419i	−0.0203735	+	0.999792i	$0.506486\pi$
$548$		0			0
$549$	−1.05171e15	+	1.05171e15i	−0.900008	+	0.900008i
$550$		0			0
$551$		−	1.22167e15i		−	1.02475i
$552$		0			0
$553$			5.54363e14i			0.455834i
$554$		0			0
$555$	2.36057e14	−	2.36057e14i	0.190285	−	0.190285i
$556$		0			0
$557$	−4.15223e13	−	4.15223e13i	−0.0328154	−	0.0328154i	0.690509	−	0.723324i	$-0.257387\pi$
$557$	−4.15223e13	−	4.15223e13i	−0.0328154	−	0.0328154i	−0.723324	+	0.690509i	$0.757387\pi$
$558$		0			0
$559$	1.17855e15			0.913234
$560$		0			0
$561$	−3.35515e13			−0.0254927
$562$		0			0
$563$	3.90578e13	+	3.90578e13i	0.0291013	+	0.0291013i	0.721508	−	0.692406i	$-0.243449\pi$
$563$	3.90578e13	+	3.90578e13i	0.0291013	+	0.0291013i	−0.692406	+	0.721508i	$0.743449\pi$
$564$		0			0
$565$	1.67390e15	−	1.67390e15i	1.22311	−	1.22311i
$566$		0			0
$567$			9.23525e14i			0.661823i
$568$		0			0
$569$		−	1.33180e14i		−	0.0936100i	−0.998904	−	0.0468050i	$-0.985096\pi$
$569$		−	1.33180e14i		−	0.0936100i	0.998904	−	0.0468050i	$-0.0149039\pi$
$570$		0			0
$571$	−1.12590e15	+	1.12590e15i	−0.776252	+	0.776252i	−0.979191	−	0.202939i	$-0.934951\pi$
$571$	−1.12590e15	+	1.12590e15i	−0.776252	+	0.776252i	0.202939	+	0.979191i	$0.434951\pi$
$572$		0			0
$573$	−2.97676e14	−	2.97676e14i	−0.201323	−	0.201323i
$574$		0			0
$575$	1.36708e15			0.907027
$576$		0			0
$577$	1.08744e15			0.707846			0.353923	−	0.935275i	$-0.384848\pi$
$577$	1.08744e15			0.707846			0.353923	+	0.935275i	$0.384848\pi$
$578$		0			0
$579$	−2.49962e14	−	2.49962e14i	−0.159640	−	0.159640i
$580$		0			0
$581$	3.44439e14	−	3.44439e14i	0.215846	−	0.215846i
$582$		0			0
$583$			8.53973e14i			0.525130i
$584$		0			0
$585$			2.24811e15i			1.35663i
$586$		0			0
$587$	1.48568e15	−	1.48568e15i	0.879865	−	0.879865i	−0.113655	−	0.993520i	$-0.536256\pi$
$587$	1.48568e15	−	1.48568e15i	0.879865	−	0.879865i	0.993520	+	0.113655i	$0.0362559\pi$
$588$		0			0
$589$	1.50368e15	+	1.50368e15i	0.874022	+	0.874022i
$590$		0			0
$591$	−1.75377e14			−0.100055
$592$		0			0
$593$	8.96247e13			0.0501911			0.0250956	−	0.999685i	$-0.492011\pi$
$593$	8.96247e13			0.0501911			0.0250956	+	0.999685i	$0.492011\pi$
$594$		0			0
$595$	4.03821e14	+	4.03821e14i	0.221996	+	0.221996i
$596$		0			0
$597$	5.13650e13	−	5.13650e13i	0.0277209	−	0.0277209i
$598$		0			0
$599$		−	1.01799e15i		−	0.539382i	−0.962947	−	0.269691i	$-0.913078\pi$
$599$		−	1.01799e15i		−	0.539382i	0.962947	−	0.269691i	$-0.0869215\pi$
$600$		0			0
$601$		−	1.26276e15i		−	0.656918i	−0.944518	−	0.328459i	$-0.893471\pi$
$601$		−	1.26276e15i		−	0.656918i	0.944518	−	0.328459i	$-0.106529\pi$
$602$		0			0
$603$	−1.41374e15	+	1.41374e15i	−0.722143	+	0.722143i
$604$		0			0
$605$	1.49787e15	+	1.49787e15i	0.751310	+	0.751310i
$606$		0			0
$607$	−1.97399e15			−0.972315			−0.486158	−	0.873871i	$-0.661602\pi$
$607$	−1.97399e15			−0.972315			−0.486158	+	0.873871i	$0.661602\pi$
$608$		0			0
$609$	4.32565e14			0.209245
$610$		0			0
$611$	1.15932e14	+	1.15932e14i	0.0550778	+	0.0550778i
$612$		0			0
$613$	5.25981e13	−	5.25981e13i	0.0245436	−	0.0245436i	−0.694729	−	0.719272i	$-0.744475\pi$
$613$	5.25981e13	−	5.25981e13i	0.0245436	−	0.0245436i	0.719272	+	0.694729i	$0.244475\pi$
$614$		0			0
$615$		−	9.26830e13i		−	0.0424802i
$616$		0			0
$617$		−	1.26267e15i		−	0.568490i	−0.958752	−	0.284245i	$-0.908257\pi$
$617$		−	1.26267e15i		−	0.568490i	0.958752	−	0.284245i	$-0.0917429\pi$
$618$		0			0
$619$	3.09325e14	−	3.09325e14i	0.136810	−	0.136810i	−0.635386	−	0.772195i	$-0.719159\pi$
$619$	3.09325e14	−	3.09325e14i	0.136810	−	0.136810i	0.772195	+	0.635386i	$0.219159\pi$
$620$		0			0
$621$	9.08559e14	+	9.08559e14i	0.394775	+	0.394775i
$622$		0			0
$623$	−9.90582e14			−0.422870
$624$		0			0
$625$	2.95377e15			1.23890
$626$		0			0
$627$	−9.00213e13	−	9.00213e13i	−0.0371000	−	0.0371000i
$628$		0			0
$629$	−6.53770e14	+	6.53770e14i	−0.264757	+	0.264757i
$630$		0			0
$631$			3.14311e15i			1.25083i	0.780293	+	0.625414i	$0.215070\pi$
$631$			3.14311e15i			1.25083i	−0.780293	+	0.625414i	$0.784930\pi$
$632$		0			0
$633$		−	8.99613e14i		−	0.351832i
$634$		0			0
$635$	2.12301e15	−	2.12301e15i	0.816013	−	0.816013i
$636$		0			0
$637$	−9.37872e14	−	9.37872e14i	−0.354305	−	0.354305i
$638$		0			0
$639$	−2.58325e15			−0.959206
$640$		0			0
$641$	4.51734e15			1.64878			0.824392	−	0.566019i	$-0.191517\pi$
$641$	4.51734e15			1.64878			0.824392	+	0.566019i	$0.191517\pi$
$642$		0			0
$643$	1.65387e15	+	1.65387e15i	0.593392	+	0.593392i	0.938546	−	0.345154i	$-0.112173\pi$
$643$	1.65387e15	+	1.65387e15i	0.593392	+	0.593392i	−0.345154	+	0.938546i	$0.612173\pi$
$644$		0			0
$645$	−3.96229e14	+	3.96229e14i	−0.139755	+	0.139755i
$646$		0			0
$647$		−	3.33623e15i		−	1.15687i	−0.815730	−	0.578433i	$-0.803665\pi$
$647$		−	3.33623e15i		−	1.15687i	0.815730	−	0.578433i	$-0.196335\pi$
$648$		0			0
$649$		−	1.08393e14i		−	0.0369536i
$650$		0			0
$651$	−5.32420e14	+	5.32420e14i	−0.178467	+	0.178467i
$652$		0			0
$653$	−2.00196e15	−	2.00196e15i	−0.659832	−	0.659832i	0.295508	−	0.955340i	$-0.404511\pi$
$653$	−2.00196e15	−	2.00196e15i	−0.659832	−	0.659832i	−0.955340	+	0.295508i	$0.904511\pi$
$654$		0			0
$655$	7.35452e15			2.38356
$656$		0			0
$657$	−1.89682e15			−0.604528
$658$		0			0
$659$	4.02032e15	+	4.02032e15i	1.26006	+	1.26006i	0.951064	+	0.308994i	$0.0999922\pi$
$659$	4.02032e15	+	4.02032e15i	1.26006	+	1.26006i	0.308994	+	0.951064i	$0.400008\pi$
$660$		0			0
$661$	−2.33815e15	+	2.33815e15i	−0.720716	+	0.720716i	−0.968751	−	0.248035i	$-0.920215\pi$
$661$	−2.33815e15	+	2.33815e15i	−0.720716	+	0.720716i	0.248035	+	0.968751i	$0.420215\pi$
$662$		0			0
$663$			2.32471e14i			0.0704764i
$664$		0			0
$665$			2.16696e15i			0.646149i
$666$		0			0
$667$	−5.37770e15	+	5.37770e15i	−1.57726	+	1.57726i
$668$		0			0
$669$	−3.38831e14	−	3.38831e14i	−0.0977552	−	0.0977552i
$670$		0			0
$671$	−1.86906e15			−0.530456
$672$		0			0
$673$	−2.38810e15			−0.666761			−0.333380	−	0.942792i	$-0.608189\pi$
$673$	−2.38810e15			−0.666761			−0.333380	+	0.942792i	$0.608189\pi$
$674$		0			0
$675$	−5.80656e14	−	5.80656e14i	−0.159495	−	0.159495i
$676$		0			0
$677$	−2.44961e15	+	2.44961e15i	−0.662001	+	0.662001i	−0.955851	−	0.293851i	$-0.905063\pi$
$677$	−2.44961e15	+	2.44961e15i	−0.662001	+	0.662001i	0.293851	+	0.955851i	$0.405063\pi$
$678$		0			0
$679$		−	5.05492e15i		−	1.34410i
$680$		0			0
$681$			1.07263e15i			0.280634i
$682$		0			0
$683$	1.97634e15	−	1.97634e15i	0.508801	−	0.508801i	−0.405358	−	0.914158i	$-0.632853\pi$
$683$	1.97634e15	−	1.97634e15i	0.508801	−	0.508801i	0.914158	+	0.405358i	$0.132853\pi$
$684$		0			0
$685$	−4.25545e15	−	4.25545e15i	−1.07807	−	1.07807i
$686$		0			0
$687$	4.03375e14			0.100565
$688$		0			0
$689$	5.91698e15			1.45176
$690$		0			0
$691$	−7.91531e14	−	7.91531e14i	−0.191134	−	0.191134i	0.605052	−	0.796186i	$-0.293152\pi$
$691$	−7.91531e14	−	7.91531e14i	−0.191134	−	0.191134i	−0.796186	+	0.605052i	$0.793152\pi$
$692$		0			0
$693$	−8.53695e14	+	8.53695e14i	−0.202894	+	0.202894i
$694$		0			0
$695$		−	9.37890e15i		−	2.19399i
$696$		0			0
$697$			2.56690e14i			0.0591056i
$698$		0			0
$699$	3.21014e14	−	3.21014e14i	0.0727611	−	0.0727611i
$700$		0			0
$701$	−1.40321e15	−	1.40321e15i	−0.313092	−	0.313092i	0.533014	−	0.846106i	$-0.321059\pi$
$701$	−1.40321e15	−	1.40321e15i	−0.313092	−	0.313092i	−0.846106	+	0.533014i	$0.821059\pi$
$702$		0			0
$703$	−3.50823e15			−0.770609
$704$		0			0
$705$	−7.79529e13			−0.0168575
$706$		0			0
$707$	6.03556e14	+	6.03556e14i	0.128502	+	0.128502i
$708$		0			0
$709$	−2.29645e15	+	2.29645e15i	−0.481397	+	0.481397i	−0.905578	−	0.424181i	$-0.860562\pi$
$709$	−2.29645e15	+	2.29645e15i	−0.481397	+	0.481397i	0.424181	+	0.905578i	$0.360562\pi$
$710$		0			0
$711$			2.87364e15i			0.593130i
$712$		0			0
$713$		−	1.32382e16i		−	2.69053i
$714$		0			0
$715$	−1.99764e15	+	1.99764e15i	−0.399792	+	0.399792i
$716$		0			0
$717$	6.99985e14	+	6.99985e14i	0.137954	+	0.137954i
$718$		0			0
$719$	−6.67854e15			−1.29620			−0.648101	−	0.761555i	$-0.724436\pi$
$719$	−6.67854e15			−1.29620			−0.648101	+	0.761555i	$0.724436\pi$
$720$		0			0
$721$	−7.44931e15			−1.42388
$722$		0			0
$723$	−1.21774e14	−	1.21774e14i	−0.0229242	−	0.0229242i
$724$		0			0
$725$	3.43686e15	−	3.43686e15i	0.637241	−	0.637241i
$726$		0			0
$727$		−	5.13449e15i		−	0.937687i	−0.883281	−	0.468844i	$-0.844671\pi$
$727$		−	5.13449e15i		−	0.937687i	0.883281	−	0.468844i	$-0.155329\pi$
$728$		0			0
$729$			4.39428e15i			0.790471i
$730$		0			0
$731$	1.09738e15	−	1.09738e15i	0.194451	−	0.194451i
$732$		0			0
$733$	2.05664e14	+	2.05664e14i	0.0358993	+	0.0358993i	0.724829	−	0.688929i	$-0.241919\pi$
$733$	2.05664e14	+	2.05664e14i	0.0358993	+	0.0358993i	−0.688929	+	0.724829i	$0.741919\pi$
$734$		0			0
$735$	6.30628e14			0.108441
$736$		0			0
$737$	−2.51245e15			−0.425624
$738$		0			0
$739$	−3.42273e15	−	3.42273e15i	−0.571252	−	0.571252i	0.361226	−	0.932478i	$-0.382358\pi$
$739$	−3.42273e15	−	3.42273e15i	−0.571252	−	0.571252i	−0.932478	+	0.361226i	$0.882358\pi$
$740$		0			0
$741$	−6.23737e14	+	6.23737e14i	−0.102565	+	0.102565i
$742$		0			0
$743$			1.18217e16i			1.91533i	0.287891	+	0.957663i	$0.407046\pi$
$743$			1.18217e16i			1.91533i	−0.287891	+	0.957663i	$0.592954\pi$
$744$		0			0
$745$			9.22756e15i			1.47308i
$746$		0			0
$747$	1.78546e15	−	1.78546e15i	0.280858	−	0.280858i
$748$		0			0
$749$	2.83401e15	+	2.83401e15i	0.439289	+	0.439289i
$750$		0			0
$751$	−1.82477e15			−0.278734			−0.139367	−	0.990241i	$-0.544507\pi$
$751$	−1.82477e15			−0.278734			−0.139367	+	0.990241i	$0.544507\pi$
$752$		0			0
$753$	3.14771e13			0.00473830
$754$		0			0
$755$	−3.38201e15	−	3.38201e15i	−0.501726	−	0.501726i
$756$		0			0
$757$	−3.85298e15	+	3.85298e15i	−0.563339	+	0.563339i	−0.930254	−	0.366916i	$-0.880414\pi$
$757$	−3.85298e15	+	3.85298e15i	−0.563339	+	0.563339i	0.366916	+	0.930254i	$0.380414\pi$
$758$		0			0
$759$			7.92536e14i			0.114206i
$760$		0			0
$761$		−	1.29389e16i		−	1.83774i	−0.394564	−	0.918868i	$-0.629104\pi$
$761$		−	1.29389e16i		−	1.83774i	0.394564	−	0.918868i	$-0.370896\pi$
$762$		0			0
$763$	−1.84835e15	+	1.84835e15i	−0.258762	+	0.258762i
$764$		0			0
$765$	2.09328e15	+	2.09328e15i	0.288861	+	0.288861i
$766$		0			0
$767$	−7.51031e14			−0.102161
$768$		0			0
$769$	6.01579e15			0.806674			0.403337	−	0.915052i	$-0.367850\pi$
$769$	6.01579e15			0.806674			0.403337	+	0.915052i	$0.367850\pi$
$770$		0			0
$771$	8.12723e14	+	8.12723e14i	0.107434	+	0.107434i
$772$		0			0
$773$	7.15970e15	−	7.15970e15i	0.933055	−	0.933055i	−0.0648402	−	0.997896i	$-0.520654\pi$
$773$	7.15970e15	−	7.15970e15i	0.933055	−	0.933055i	0.997896	+	0.0648402i	$0.0206538\pi$
$774$		0			0
$775$			8.46049e15i			1.08702i
$776$		0			0
$777$		−	1.24219e15i		−	0.157352i
$778$		0			0
$779$	−6.88719e14	+	6.88719e14i	−0.0860174	+	0.0860174i
$780$		0			0
$781$	−2.29544e15	−	2.29544e15i	−0.282673	−	0.282673i
$782$		0			0
$783$	4.56827e15			0.554705
$784$		0			0
$785$	−1.57300e15			−0.188342
$786$		0			0
$787$	7.18804e14	+	7.18804e14i	0.0848691	+	0.0848691i	0.748267	−	0.663398i	$-0.230886\pi$
$787$	7.18804e14	+	7.18804e14i	0.0848691	+	0.0848691i	−0.663398	+	0.748267i	$0.730886\pi$
$788$		0			0
$789$	−5.86524e14	+	5.86524e14i	−0.0682908	+	0.0682908i
$790$		0			0
$791$		−	8.80848e15i		−	1.01142i
$792$		0			0
$793$			1.29503e16i			1.46648i
$794$		0			0
$795$	−1.98929e15	+	1.98929e15i	−0.222167	+	0.222167i
$796$		0			0
$797$	−1.46538e15	−	1.46538e15i	−0.161409	−	0.161409i	0.621781	−	0.783191i	$-0.286409\pi$
$797$	−1.46538e15	−	1.46538e15i	−0.161409	−	0.161409i	−0.783191	+	0.621781i	$0.786409\pi$
$798$		0			0
$799$	2.15894e14			0.0234549
$800$		0			0
$801$	−5.13486e15			−0.550237
$802$		0			0
$803$	−1.68549e15	−	1.68549e15i	−0.178152	−	0.178152i
$804$		0			0
$805$	9.53883e15	−	9.53883e15i	0.994530	−	0.994530i
$806$		0			0
$807$			3.38711e15i			0.348357i
$808$		0			0
$809$			9.80373e14i			0.0994659i	0.998763	+	0.0497330i	$0.0158370\pi$
$809$			9.80373e14i			0.0994659i	−0.998763	+	0.0497330i	$0.984163\pi$
$810$		0			0
$811$	2.61388e15	−	2.61388e15i	0.261620	−	0.261620i	−0.564092	−	0.825712i	$-0.690774\pi$
$811$	2.61388e15	−	2.61388e15i	0.261620	−	0.261620i	0.825712	+	0.564092i	$0.190774\pi$
$812$		0			0
$813$	1.38283e15	+	1.38283e15i	0.136543	+	0.136543i
$814$		0			0
$815$	1.11757e16			1.08870
$816$		0			0
$817$	5.88869e15			0.565975
$818$		0			0
$819$	5.91505e15	+	5.91505e15i	0.560915	+	0.560915i
$820$		0			0
$821$	3.88644e15	−	3.88644e15i	0.363634	−	0.363634i	−0.501515	−	0.865149i	$-0.667224\pi$
$821$	3.88644e15	−	3.88644e15i	0.363634	−	0.363634i	0.865149	+	0.501515i	$0.167224\pi$
$822$		0			0
$823$		−	1.53461e15i		−	0.141677i	−0.997488	−	0.0708386i	$-0.977432\pi$
$823$		−	1.53461e15i		−	0.141677i	0.997488	−	0.0708386i	$-0.0225675\pi$
$824$		0			0
$825$		−	5.06506e14i		−	0.0461411i
$826$		0			0
$827$	7.82916e15	−	7.82916e15i	0.703776	−	0.703776i	−0.261443	−	0.965219i	$-0.584198\pi$
$827$	7.82916e15	−	7.82916e15i	0.703776	−	0.703776i	0.965219	+	0.261443i	$0.0841982\pi$
$828$		0			0
$829$	1.11549e16	+	1.11549e16i	0.989502	+	0.989502i	0.999945	−	0.0104437i	$-0.00332438\pi$
$829$	1.11549e16	+	1.11549e16i	0.989502	+	0.989502i	−0.0104437	+	0.999945i	$0.503324\pi$
$830$		0			0
$831$	1.34497e15			0.117735
$832$		0			0
$833$	−1.74655e15			−0.150881
$834$		0			0
$835$	−1.58538e16	−	1.58538e16i	−1.35163	−	1.35163i
$836$		0			0
$837$	−5.62283e15	+	5.62283e15i	−0.473113	+	0.473113i
$838$		0			0
$839$			9.71424e15i			0.806711i	0.915043	+	0.403356i	$0.132156\pi$
$839$			9.71424e15i			0.806711i	−0.915043	+	0.403356i	$0.867844\pi$
$840$		0			0
$841$			1.48388e16i			1.21624i
$842$		0			0
$843$	1.00224e15	−	1.00224e15i	0.0810815	−	0.0810815i
$844$		0			0
$845$	2.62143e15	+	2.62143e15i	0.209328	+	0.209328i
$846$		0			0
$847$	7.88214e15			0.621277
$848$		0			0
$849$	7.41121e14			0.0576630
$850$		0			0
$851$	1.54430e16	+	1.54430e16i	1.18610	+	1.18610i
$852$		0			0
$853$	3.75088e15	−	3.75088e15i	0.284389	−	0.284389i	−0.550467	−	0.834857i	$-0.685550\pi$
$853$	3.75088e15	−	3.75088e15i	0.284389	−	0.284389i	0.834857	+	0.550467i	$0.185550\pi$
$854$		0			0
$855$			1.12328e16i			0.840768i
$856$		0			0
$857$			1.75963e16i			1.30025i	0.759827	+	0.650125i	$0.225284\pi$
$857$			1.75963e16i			1.30025i	−0.759827	+	0.650125i	$0.774716\pi$
$858$		0			0
$859$	5.44329e15	−	5.44329e15i	0.397100	−	0.397100i	−0.480109	−	0.877209i	$-0.659403\pi$
$859$	5.44329e15	−	5.44329e15i	0.397100	−	0.397100i	0.877209	+	0.480109i	$0.159403\pi$
$860$		0			0
$861$	−2.43860e14	−	2.43860e14i	−0.0175640	−	0.0175640i
$862$		0			0
$863$	1.34935e16			0.959545			0.479773	−	0.877393i	$-0.340719\pi$
$863$	1.34935e16			0.959545			0.479773	+	0.877393i	$0.340719\pi$
$864$		0			0
$865$	−1.89410e16			−1.32989
$866$		0			0
$867$	−1.71863e15	−	1.71863e15i	−0.119145	−	0.119145i
$868$		0			0
$869$	−2.55347e15	+	2.55347e15i	−0.174792	+	0.174792i
$870$		0			0
$871$			1.74082e16i			1.17667i
$872$		0			0
$873$		−	2.62031e16i		−	1.74893i
$874$		0			0
$875$	3.97428e15	−	3.97428e15i	0.261948	−	0.261948i
$876$		0			0
$877$	6.53286e14	+	6.53286e14i	0.0425212	+	0.0425212i	0.728048	−	0.685526i	$-0.240428\pi$
$877$	6.53286e14	+	6.53286e14i	0.0425212	+	0.0425212i	−0.685526	+	0.728048i	$0.740428\pi$
$878$		0			0
$879$	−1.45230e15			−0.0933508
$880$		0			0
$881$	−1.19301e16			−0.757313			−0.378657	−	0.925537i	$-0.623614\pi$
$881$	−1.19301e16			−0.757313			−0.378657	+	0.925537i	$0.623614\pi$
$882$		0			0
$883$	9.60474e15	+	9.60474e15i	0.602146	+	0.602146i	0.940882	−	0.338736i	$-0.109999\pi$
$883$	9.60474e15	+	9.60474e15i	0.602146	+	0.602146i	−0.338736	+	0.940882i	$0.609999\pi$
$884$		0			0
$885$	2.52498e14	−	2.52498e14i	0.0156340	−	0.0156340i
$886$		0			0
$887$			9.67854e15i			0.591875i	0.955207	+	0.295937i	$0.0956320\pi$
$887$			9.67854e15i			0.591875i	−0.955207	+	0.295937i	$0.904368\pi$
$888$		0			0
$889$		−	1.11718e16i		−	0.674782i
$890$		0			0
$891$	−4.25388e15	+	4.25388e15i	−0.253780	+	0.253780i
$892$		0			0
$893$	5.79261e14	+	5.79261e14i	0.0341343	+	0.0341343i
$894$		0			0
$895$	8.34471e12			0.000485719
$896$		0			0
$897$	5.49129e15			0.315730
$898$		0			0
$899$	−3.32812e16	−	3.32812e16i	−1.89026	−	1.89026i
$900$		0			0
$901$	5.50945e15	−	5.50945e15i	0.309116	−	0.309116i
$902$		0			0
$903$			2.08505e15i			0.115567i
$904$		0			0
$905$			1.10126e16i			0.603009i
$906$		0			0
$907$	1.20741e16	−	1.20741e16i	0.653153	−	0.653153i	−0.300598	−	0.953751i	$-0.597186\pi$
$907$	1.20741e16	−	1.20741e16i	0.653153	−	0.653153i	0.953751	+	0.300598i	$0.0971863\pi$
$908$		0			0
$909$	3.12864e15	+	3.12864e15i	0.167207	+	0.167207i
$910$		0			0
$911$	−5.70446e15			−0.301206			−0.150603	−	0.988594i	$-0.548121\pi$
$911$	−5.70446e15			−0.301206			−0.150603	+	0.988594i	$0.548121\pi$
$912$		0			0
$913$	3.17307e15			0.165535
$914$		0			0
$915$	−4.35390e15	−	4.35390e15i	−0.224420	−	0.224420i
$916$		0			0
$917$	1.93506e16	−	1.93506e16i	0.985515	−	0.985515i
$918$		0			0
$919$		−	3.83830e16i		−	1.93154i	−0.259400	−	0.965770i	$-0.583525\pi$
$919$		−	3.83830e16i		−	1.93154i	0.259400	−	0.965770i	$-0.416475\pi$
$920$		0			0
$921$		−	2.81227e15i		−	0.139839i
$922$		0			0
$923$	−1.59045e16	+	1.59045e16i	−0.781469	+	0.781469i
$924$		0			0
$925$	−9.86956e15	−	9.86956e15i	−0.479202	−	0.479202i
$926$		0			0
$927$	−3.86148e16			−1.85274
$928$		0			0
$929$	−1.43607e16			−0.680907			−0.340454	−	0.940261i	$-0.610581\pi$
$929$	−1.43607e16			−0.680907			−0.340454	+	0.940261i	$0.610581\pi$
$930$		0			0
$931$	−4.68614e15	−	4.68614e15i	−0.219580	−	0.219580i
$932$		0			0
$933$	2.30556e15	−	2.30556e15i	0.106765	−	0.106765i
$934$		0			0
$935$			3.72011e15i			0.170252i
$936$		0			0
$937$			1.63980e16i			0.741689i	0.928695	+	0.370845i	$0.120932\pi$
$937$			1.63980e16i			0.741689i	−0.928695	+	0.370845i	$0.879068\pi$
$938$		0			0
$939$	5.66830e14	−	5.66830e14i	0.0253392	−	0.0253392i
$940$		0			0
$941$	9.98449e15	+	9.98449e15i	0.441147	+	0.441147i	0.892397	−	0.451251i	$-0.149022\pi$
$941$	9.98449e15	+	9.98449e15i	0.441147	+	0.441147i	−0.451251	+	0.892397i	$0.649022\pi$
$942$		0			0
$943$	6.06339e15			0.264790
$944$		0			0
$945$	−8.10309e15			−0.349764
$946$		0			0
$947$	1.46577e16	+	1.46577e16i	0.625376	+	0.625376i	0.946901	−	0.321525i	$-0.104195\pi$
$947$	1.46577e16	+	1.46577e16i	0.625376	+	0.625376i	−0.321525	+	0.946901i	$0.604195\pi$
$948$		0			0
$949$	−1.16783e16	+	1.16783e16i	−0.492512	+	0.492512i
$950$		0			0
$951$		−	7.58015e15i		−	0.315998i
$952$		0			0
$953$		−	4.21764e16i		−	1.73803i	−0.494783	−	0.869017i	$-0.664752\pi$
$953$		−	4.21764e16i		−	1.73803i	0.494783	−	0.869017i	$-0.335248\pi$
$954$		0			0
$955$	−3.30055e16	+	3.30055e16i	−1.34452	+	1.34452i
$956$		0			0
$957$	1.99245e15	+	1.99245e15i	0.0802366	+	0.0802366i
$958$		0			0
$959$	−2.23932e16			−0.891483
$960$		0			0
$961$	5.65195e16			2.22443
$962$		0			0
$963$	1.46906e16	+	1.46906e16i	0.571603	+	0.571603i
$964$		0			0
$965$	−2.77152e16	+	2.77152e16i	−1.06615	+	1.06615i
$966$		0			0
$967$		−	1.35622e16i		−	0.515803i	−0.966171	−	0.257902i	$-0.916969\pi$
$967$		−	1.35622e16i		−	0.515803i	0.966171	−	0.257902i	$-0.0830310\pi$
$968$		0			0
$969$			1.16155e15i			0.0436776i
$970$		0			0
$971$	5.96160e15	−	5.96160e15i	0.221645	−	0.221645i	−0.587546	−	0.809191i	$-0.699906\pi$
$971$	5.96160e15	−	5.96160e15i	0.221645	−	0.221645i	0.809191	+	0.587546i	$0.199906\pi$
$972$		0			0
$973$	−2.46770e16	−	2.46770e16i	−0.907135	−	0.907135i
$974$		0			0
$975$	−3.50946e15			−0.127560
$976$		0			0
$977$	−1.03993e16			−0.373753			−0.186877	−	0.982383i	$-0.559836\pi$
$977$	−1.03993e16			−0.373753			−0.186877	+	0.982383i	$0.559836\pi$
$978$		0			0
$979$	−4.56276e15	−	4.56276e15i	−0.162152	−	0.162152i
$980$		0			0
$981$	−9.58127e15	+	9.58127e15i	−0.336700	+	0.336700i
$982$		0			0
$983$		−	1.51148e16i		−	0.525240i	−0.964899	−	0.262620i	$-0.915414\pi$
$983$		−	1.51148e16i		−	0.525240i	0.964899	−	0.262620i	$-0.0845865\pi$
$984$		0			0
$985$			1.94453e16i			0.668214i
$986$		0			0
$987$	−2.05103e14	+	2.05103e14i	−0.00696993	+	0.00696993i
$988$		0			0
$989$	−2.59216e16	−	2.59216e16i	−0.871130	−	0.871130i
$990$		0			0
$991$	4.92652e15			0.163733			0.0818663	−	0.996643i	$-0.473912\pi$
$991$	4.92652e15			0.163733			0.0818663	+	0.996643i	$0.473912\pi$
$992$		0			0
$993$	−3.63554e15			−0.119494
$994$		0			0
$995$	−5.69521e15	−	5.69521e15i	−0.185133	−	0.185133i
$996$		0			0
$997$	−3.32641e15	+	3.32641e15i	−0.106943	+	0.106943i	−0.758554	−	0.651611i	$-0.774094\pi$
$997$	−3.32641e15	+	3.32641e15i	−0.106943	+	0.106943i	0.651611	+	0.758554i	$0.274094\pi$
$998$		0			0
$999$		−	1.31186e16i		−	0.417136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.12.e.a.17.12		42
4.3	odd	2		16.12.e.a.13.16	yes	42
8.3	odd	2		128.12.e.b.33.12		42
8.5	even	2		128.12.e.a.33.10		42
16.3	odd	4		128.12.e.b.97.12		42
16.5	even	4	inner	64.12.e.a.49.12		42
16.11	odd	4		16.12.e.a.5.16	✓	42
16.13	even	4		128.12.e.a.97.10		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.16	✓	42	16.11	odd	4
16.12.e.a.13.16	yes	42	4.3	odd	2
64.12.e.a.17.12		42	1.1	even	1	trivial
64.12.e.a.49.12		42	16.5	even	4	inner
128.12.e.a.33.10		42	8.5	even	2
128.12.e.a.97.10		42	16.13	even	4
128.12.e.b.33.12		42	8.3	odd	2
128.12.e.b.97.12		42	16.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(56.4628 + 56.4628i) q^{3} +(6260.45 - 6260.45i) q^{5} -32944.0i q^{7} -170771. i q^{9} +O(q^{10})\)	\(q+(56.4628 + 56.4628i) q^{3} +(6260.45 - 6260.45i) q^{5} -32944.0i q^{7} -170771. i q^{9} +(151744. - 151744. i) q^{11} +(-1.05140e6 - 1.05140e6i) q^{13} +706965. q^{15} -1.95797e6 q^{17} +(-5.25340e6 - 5.25340e6i) q^{19} +(1.86011e6 - 1.86011e6i) q^{21} +4.62502e7i q^{23} -2.95583e7i q^{25} +(1.96444e7 - 1.96444e7i) q^{27} +(1.16274e8 + 1.16274e8i) q^{29} -2.86231e8 q^{31} +1.71358e7 q^{33} +(-2.06244e8 - 2.06244e8i) q^{35} +(3.33901e8 - 3.33901e8i) q^{37} -1.18730e8i q^{39} -1.31100e8i q^{41} +(-5.60465e8 + 5.60465e8i) q^{43} +(-1.06910e9 - 1.06910e9i) q^{45} -1.10264e8 q^{47} +8.92021e8 q^{49} +(-1.10553e8 - 1.10553e8i) q^{51} +(-2.81385e9 + 2.81385e9i) q^{53} -1.89998e9i q^{55} -5.93243e8i q^{57} +(3.57157e8 - 3.57157e8i) q^{59} +(-6.15858e9 - 6.15858e9i) q^{61} -5.62587e9 q^{63} -1.31645e10 q^{65} +(-8.27855e9 - 8.27855e9i) q^{67} +(-2.61142e9 + 2.61142e9i) q^{69} -1.51270e10i q^{71} -1.11074e10i q^{73} +(1.66895e9 - 1.66895e9i) q^{75} +(-4.99907e9 - 4.99907e9i) q^{77} -1.68275e10 q^{79} -2.80332e10 q^{81} +(1.04553e10 + 1.04553e10i) q^{83} +(-1.22578e10 + 1.22578e10i) q^{85} +1.31303e10i q^{87} -3.00687e10i q^{89} +(-3.46373e10 + 3.46373e10i) q^{91} +(-1.61614e10 - 1.61614e10i) q^{93} -6.57772e10 q^{95} +1.53440e11 q^{97} +(-2.59135e10 - 2.59135e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) 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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