LMFDB - Embedded newform 128.12.e.b.33.20

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			33.20
Character	$\chi$	$=$	128.33
Dual form			128.12.e.b.97.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(491.248 + 491.248i) q^{3} +(-6777.57 + 6777.57i) q^{5} +47511.7i q^{7} +305503. i q^{9} +O(q^{10})$	\(q+(491.248 + 491.248i) q^{3} +(-6777.57 + 6777.57i) q^{5} +47511.7i q^{7} +305503. i q^{9} +(348627. - 348627. i) q^{11} +(-623712. - 623712. i) q^{13} -6.65894e6 q^{15} -447898. q^{17} +(-1.39118e7 - 1.39118e7i) q^{19} +(-2.33400e7 + 2.33400e7i) q^{21} +4.84106e7i q^{23} -4.30427e7i q^{25} +(-6.30548e7 + 6.30548e7i) q^{27} +(4.44473e6 + 4.44473e6i) q^{29} -1.41505e8 q^{31} +3.42525e8 q^{33} +(-3.22014e8 - 3.22014e8i) q^{35} +(-4.51599e7 + 4.51599e7i) q^{37} -6.12795e8i q^{39} -3.91782e8i q^{41} +(-8.76450e8 + 8.76450e8i) q^{43} +(-2.07057e9 - 2.07057e9i) q^{45} -1.57121e9 q^{47} -2.80034e8 q^{49} +(-2.20029e8 - 2.20029e8i) q^{51} +(3.45392e9 - 3.45392e9i) q^{53} +4.72568e9i q^{55} -1.36683e10i q^{57} +(5.84309e9 - 5.84309e9i) q^{59} +(-1.80673e9 - 1.80673e9i) q^{61} -1.45150e10 q^{63} +8.45450e9 q^{65} +(5.33925e9 + 5.33925e9i) q^{67} +(-2.37816e10 + 2.37816e10i) q^{69} -6.24617e9i q^{71} +2.44700e10i q^{73} +(2.11447e10 - 2.11447e10i) q^{75} +(1.65638e10 + 1.65638e10i) q^{77} -2.55656e8 q^{79} -7.83214e9 q^{81} +(-5.06400e8 - 5.06400e8i) q^{83} +(3.03566e9 - 3.03566e9i) q^{85} +4.36694e9i q^{87} +4.97326e10i q^{89} +(2.96336e10 - 2.96336e10i) q^{91} +(-6.95139e10 - 6.95139e10i) q^{93} +1.88576e11 q^{95} +5.39948e10 q^{97} +(1.06507e11 + 1.06507e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	491.248	+	491.248i	1.16717	+	1.16717i	0.982870	+	0.184301i	$0.0590020\pi$
$3$	491.248	+	491.248i	1.16717	+	1.16717i	0.184301	+	0.982870i	$0.440998\pi$
$4$		0			0
$5$	−6777.57	+	6777.57i	−0.969927	+	0.969927i	−0.999561	−	0.0296343i	$-0.990566\pi$
$5$	−6777.57	+	6777.57i	−0.969927	+	0.969927i	0.0296343	+	0.999561i	$0.490566\pi$
$6$		0			0
$7$			47511.7i			1.06847i	0.845337	+	0.534234i	$0.179400\pi$
$7$			47511.7i			1.06847i	−0.845337	+	0.534234i	$0.820600\pi$
$8$		0			0
$9$			305503.i			1.72457i
$10$		0			0
$11$	348627.	−	348627.i	0.652681	−	0.652681i	−0.300957	−	0.953638i	$-0.597306\pi$
$11$	348627.	−	348627.i	0.652681	−	0.652681i	0.953638	+	0.300957i	$0.0973061\pi$
$12$		0			0
$13$	−623712.	−	623712.i	−0.465903	−	0.465903i	0.434681	−	0.900584i	$-0.356861\pi$
$13$	−623712.	−	623712.i	−0.465903	−	0.465903i	−0.900584	+	0.434681i	$0.856861\pi$
$14$		0			0
$15$	−6.65894e6			−2.26414
$16$		0			0
$17$	−447898.			−0.0765085			−0.0382543	−	0.999268i	$-0.512180\pi$
$17$	−447898.			−0.0765085			−0.0382543	+	0.999268i	$0.512180\pi$
$18$		0			0
$19$	−1.39118e7	−	1.39118e7i	−1.28895	−	1.28895i	−0.935423	−	0.353529i	$-0.884981\pi$
$19$	−1.39118e7	−	1.39118e7i	−1.28895	−	1.28895i	−0.353529	−	0.935423i	$-0.615019\pi$
$20$		0			0
$21$	−2.33400e7	+	2.33400e7i	−1.24708	+	1.24708i
$22$		0			0
$23$			4.84106e7i			1.56833i	0.620553	+	0.784165i	$0.286908\pi$
$23$			4.84106e7i			1.56833i	−0.620553	+	0.784165i	$0.713092\pi$
$24$		0			0
$25$		−	4.30427e7i		−	0.881515i
$26$		0			0
$27$	−6.30548e7	+	6.30548e7i	−0.845702	+	0.845702i
$28$		0			0
$29$	4.44473e6	+	4.44473e6i	0.0402399	+	0.0402399i	0.726940	−	0.686701i	$-0.240942\pi$
$29$	4.44473e6	+	4.44473e6i	0.0402399	+	0.0402399i	−0.686701	+	0.726940i	$0.740942\pi$
$30$		0			0
$31$	−1.41505e8			−0.887731			−0.443865	−	0.896094i	$-0.646393\pi$
$31$	−1.41505e8			−0.887731			−0.443865	+	0.896094i	$0.646393\pi$
$32$		0			0
$33$	3.42525e8			1.52358
$34$		0			0
$35$	−3.22014e8	−	3.22014e8i	−1.03633	−	1.03633i
$36$		0			0
$37$	−4.51599e7	+	4.51599e7i	−0.107064	+	0.107064i	−0.758610	−	0.651546i	$-0.774121\pi$
$37$	−4.51599e7	+	4.51599e7i	−0.107064	+	0.107064i	0.651546	+	0.758610i	$0.274121\pi$
$38$		0			0
$39$		−	6.12795e8i		−	1.08758i
$40$		0			0
$41$		−	3.91782e8i		−	0.528121i	−0.964506	−	0.264060i	$-0.914938\pi$
$41$		−	3.91782e8i		−	0.528121i	0.964506	−	0.264060i	$-0.0850618\pi$
$42$		0			0
$43$	−8.76450e8	+	8.76450e8i	−0.909182	+	0.909182i	−0.996206	−	0.0870244i	$-0.972264\pi$
$43$	−8.76450e8	+	8.76450e8i	−0.909182	+	0.909182i	0.0870244	+	0.996206i	$0.472264\pi$
$44$		0			0
$45$	−2.07057e9	−	2.07057e9i	−1.67271	−	1.67271i
$46$		0			0
$47$	−1.57121e9			−0.999300			−0.499650	−	0.866227i	$-0.666538\pi$
$47$	−1.57121e9			−0.999300			−0.499650	+	0.866227i	$0.666538\pi$
$48$		0			0
$49$	−2.80034e8			−0.141622
$50$		0			0
$51$	−2.20029e8	−	2.20029e8i	−0.0892985	−	0.0892985i
$52$		0			0
$53$	3.45392e9	−	3.45392e9i	1.13448	−	1.13448i	0.145052	−	0.989424i	$-0.453665\pi$
$53$	3.45392e9	−	3.45392e9i	1.13448	−	1.13448i	0.989424	−	0.145052i	$-0.0463348\pi$
$54$		0			0
$55$			4.72568e9i			1.26610i
$56$		0			0
$57$		−	1.36683e10i		−	3.00886i
$58$		0			0
$59$	5.84309e9	−	5.84309e9i	1.06404	−	1.06404i	0.0662320	−	0.997804i	$-0.478902\pi$
$59$	5.84309e9	−	5.84309e9i	1.06404	−	1.06404i	0.997804	−	0.0662320i	$-0.0210978\pi$
$60$		0			0
$61$	−1.80673e9	−	1.80673e9i	−0.273891	−	0.273891i	0.556773	−	0.830665i	$-0.312039\pi$
$61$	−1.80673e9	−	1.80673e9i	−0.273891	−	0.273891i	−0.830665	+	0.556773i	$0.812039\pi$
$62$		0			0
$63$	−1.45150e10			−1.84265
$64$		0			0
$65$	8.45450e9			0.903783
$66$		0			0
$67$	5.33925e9	+	5.33925e9i	0.483135	+	0.483135i	0.906131	−	0.422996i	$-0.139022\pi$
$67$	5.33925e9	+	5.33925e9i	0.483135	+	0.483135i	−0.422996	+	0.906131i	$0.639022\pi$
$68$		0			0
$69$	−2.37816e10	+	2.37816e10i	−1.83051	+	1.83051i
$70$		0			0
$71$		−	6.24617e9i		−	0.410859i	−0.978672	−	0.205430i	$-0.934141\pi$
$71$		−	6.24617e9i		−	0.410859i	0.978672	−	0.205430i	$-0.0658592\pi$
$72$		0			0
$73$			2.44700e10i			1.38152i	0.723084	+	0.690760i	$0.242724\pi$
$73$			2.44700e10i			1.38152i	−0.723084	+	0.690760i	$0.757276\pi$
$74$		0			0
$75$	2.11447e10	−	2.11447e10i	1.02888	−	1.02888i
$76$		0			0
$77$	1.65638e10	+	1.65638e10i	0.697368	+	0.697368i
$78$		0			0
$79$	−2.55656e8			−0.00934773			−0.00467387	−	0.999989i	$-0.501488\pi$
$79$	−2.55656e8			−0.00934773			−0.00467387	+	0.999989i	$0.501488\pi$
$80$		0			0
$81$	−7.83214e9			−0.249582
$82$		0			0
$83$	−5.06400e8	−	5.06400e8i	−0.0141112	−	0.0141112i	0.700016	−	0.714127i	$-0.253176\pi$
$83$	−5.06400e8	−	5.06400e8i	−0.0141112	−	0.0141112i	−0.714127	+	0.700016i	$0.753176\pi$
$84$		0			0
$85$	3.03566e9	−	3.03566e9i	0.0742076	−	0.0742076i
$86$		0			0
$87$			4.36694e9i			0.0939336i
$88$		0			0
$89$			4.97326e10i			0.944053i	0.881584	+	0.472026i	$0.156477\pi$
$89$			4.97326e10i			0.944053i	−0.881584	+	0.472026i	$0.843523\pi$
$90$		0			0
$91$	2.96336e10	−	2.96336e10i	0.497802	−	0.497802i
$92$		0			0
$93$	−6.95139e10	−	6.95139e10i	−1.03613	−	1.03613i
$94$		0			0
$95$	1.88576e11			2.50038
$96$		0			0
$97$	5.39948e10			0.638421			0.319211	−	0.947684i	$-0.396582\pi$
$97$	5.39948e10			0.638421			0.319211	+	0.947684i	$0.396582\pi$
$98$		0			0
$99$	1.06507e11	+	1.06507e11i	1.12560	+	1.12560i
$100$		0			0
$101$	−8.42977e10	+	8.42977e10i	−0.798083	+	0.798083i	−0.982793	−	0.184710i	$-0.940865\pi$
$101$	−8.42977e10	+	8.42977e10i	−0.798083	+	0.798083i	0.184710	+	0.982793i	$0.440865\pi$
$102$		0			0
$103$		−	1.11053e11i		−	0.943903i	−0.881625	−	0.471951i	$-0.843550\pi$
$103$		−	1.11053e11i		−	0.943903i	0.881625	−	0.471951i	$-0.156450\pi$
$104$		0			0
$105$		−	3.16377e11i		−	2.41916i
$106$		0			0
$107$	6.29435e10	−	6.29435e10i	0.433851	−	0.433851i	−0.456085	−	0.889936i	$-0.650749\pi$
$107$	6.29435e10	−	6.29435e10i	0.433851	−	0.433851i	0.889936	+	0.456085i	$0.150749\pi$
$108$		0			0
$109$	−9.16501e10	−	9.16501e10i	−0.570541	−	0.570541i	0.361738	−	0.932280i	$-0.382183\pi$
$109$	−9.16501e10	−	9.16501e10i	−0.570541	−	0.570541i	−0.932280	+	0.361738i	$0.882183\pi$
$110$		0			0
$111$	−4.43694e10			−0.249924
$112$		0			0
$113$	−2.46974e11			−1.26101			−0.630507	−	0.776184i	$-0.717153\pi$
$113$	−2.46974e11			−1.26101			−0.630507	+	0.776184i	$0.717153\pi$
$114$		0			0
$115$	−3.28106e11	−	3.28106e11i	−1.52116	−	1.52116i
$116$		0			0
$117$	1.90546e11	−	1.90546e11i	0.803484	−	0.803484i
$118$		0			0
$119$		−	2.12804e10i		−	0.0817469i
$120$		0			0
$121$			4.22307e10i			0.148016i
$122$		0			0
$123$	1.92462e11	−	1.92462e11i	0.616407	−	0.616407i
$124$		0			0
$125$	−3.92110e10	−	3.92110e10i	−0.114922	−	0.114922i
$126$		0			0
$127$	1.69815e11			0.456094			0.228047	−	0.973650i	$-0.426766\pi$
$127$	1.69815e11			0.456094			0.228047	+	0.973650i	$0.426766\pi$
$128$		0			0
$129$	−8.61110e11			−2.12234
$130$		0			0
$131$	8.41543e10	+	8.41543e10i	0.190583	+	0.190583i	0.795948	−	0.605365i	$-0.206973\pi$
$131$	8.41543e10	+	8.41543e10i	0.190583	+	0.190583i	−0.605365	+	0.795948i	$0.706973\pi$
$132$		0			0
$133$	6.60971e11	−	6.60971e11i	1.37720	−	1.37720i
$134$		0			0
$135$		−	8.54716e11i		−	1.64054i
$136$		0			0
$137$		−	5.08070e11i		−	0.899416i	−0.893176	−	0.449708i	$-0.851528\pi$
$137$		−	5.08070e11i		−	0.899416i	0.893176	−	0.449708i	$-0.148472\pi$
$138$		0			0
$139$	−7.20709e11	+	7.20709e11i	−1.17809	+	1.17809i	−0.197860	+	0.980230i	$0.563399\pi$
$139$	−7.20709e11	+	7.20709e11i	−1.17809	+	1.17809i	−0.980230	+	0.197860i	$0.936601\pi$
$140$		0			0
$141$	−7.71854e11	−	7.71854e11i	−1.16635	−	1.16635i
$142$		0			0
$143$	−4.34885e11			−0.608172
$144$		0			0
$145$	−6.02490e10			−0.0780595
$146$		0			0
$147$	−1.37566e11	−	1.37566e11i	−0.165297	−	0.165297i
$148$		0			0
$149$	−3.75941e10	+	3.75941e10i	−0.0419367	+	0.0419367i	−0.727764	−	0.685827i	$-0.759440\pi$
$149$	−3.75941e10	+	3.75941e10i	−0.0419367	+	0.0419367i	0.685827	+	0.727764i	$0.259440\pi$
$150$		0			0
$151$		−	6.61826e11i		−	0.686073i	−0.939322	−	0.343037i	$-0.888544\pi$
$151$		−	6.61826e11i		−	0.686073i	0.939322	−	0.343037i	$-0.111456\pi$
$152$		0			0
$153$		−	1.36834e11i		−	0.131945i
$154$		0			0
$155$	9.59057e11	−	9.59057e11i	0.861034	−	0.861034i
$156$		0			0
$157$	−6.21614e11	−	6.21614e11i	−0.520083	−	0.520083i	0.397513	−	0.917596i	$-0.369873\pi$
$157$	−6.21614e11	−	6.21614e11i	−0.520083	−	0.520083i	−0.917596	+	0.397513i	$0.869873\pi$
$158$		0			0
$159$	3.39347e12			2.64825
$160$		0			0
$161$	−2.30007e12			−1.67571
$162$		0			0
$163$	2.56324e11	+	2.56324e11i	0.174485	+	0.174485i	0.788947	−	0.614462i	$-0.210627\pi$
$163$	2.56324e11	+	2.56324e11i	0.174485	+	0.174485i	−0.614462	+	0.788947i	$0.710627\pi$
$164$		0			0
$165$	−2.32148e12	+	2.32148e12i	−1.47776	+	1.47776i
$166$		0			0
$167$			5.24193e11i			0.312285i	0.987735	+	0.156142i	$0.0499059\pi$
$167$			5.24193e11i			0.312285i	−0.987735	+	0.156142i	$0.950094\pi$
$168$		0			0
$169$		−	1.01413e12i		−	0.565869i
$170$		0			0
$171$	4.25008e12	−	4.25008e12i	2.22289	−	2.22289i
$172$		0			0
$173$	8.62237e11	+	8.62237e11i	0.423032	+	0.423032i	0.886246	−	0.463214i	$-0.153304\pi$
$173$	8.62237e11	+	8.62237e11i	0.423032	+	0.423032i	−0.463214	+	0.886246i	$0.653304\pi$
$174$		0			0
$175$	2.04503e12			0.941870
$176$		0			0
$177$	5.74082e12			2.48382
$178$		0			0
$179$	4.27653e11	+	4.27653e11i	0.173940	+	0.173940i	0.788708	−	0.614768i	$-0.210750\pi$
$179$	4.27653e11	+	4.27653e11i	0.173940	+	0.173940i	−0.614768	+	0.788708i	$0.710750\pi$
$180$		0			0
$181$	7.91066e11	−	7.91066e11i	0.302678	−	0.302678i	−0.539383	−	0.842061i	$-0.681342\pi$
$181$	7.91066e11	−	7.91066e11i	0.302678	−	0.302678i	0.842061	+	0.539383i	$0.181342\pi$
$182$		0			0
$183$		−	1.77510e12i		−	0.639356i
$184$		0			0
$185$		−	6.12148e11i		−	0.207688i
$186$		0			0
$187$	−1.56149e11	+	1.56149e11i	−0.0499356	+	0.0499356i
$188$		0			0
$189$	−2.99584e12	−	2.99584e12i	−0.903605	−	0.903605i
$190$		0			0
$191$	−9.78732e11			−0.278599			−0.139300	−	0.990250i	$-0.544485\pi$
$191$	−9.78732e11			−0.278599			−0.139300	+	0.990250i	$0.544485\pi$
$192$		0			0
$193$	−1.02121e12			−0.274504			−0.137252	−	0.990536i	$-0.543827\pi$
$193$	−1.02121e12			−0.274504			−0.137252	+	0.990536i	$0.543827\pi$
$194$		0			0
$195$	4.15326e12	+	4.15326e12i	1.05487	+	1.05487i
$196$		0			0
$197$	−3.26974e12	+	3.26974e12i	−0.785144	+	0.785144i	−0.980694	−	0.195550i	$-0.937351\pi$
$197$	−3.26974e12	+	3.26974e12i	−0.785144	+	0.785144i	0.195550	+	0.980694i	$0.437351\pi$
$198$		0			0
$199$			5.94516e12i			1.35043i	0.737622	+	0.675214i	$0.235949\pi$
$199$			5.94516e12i			1.35043i	−0.737622	+	0.675214i	$0.764051\pi$
$200$		0			0
$201$			5.24579e12i			1.12780i
$202$		0			0
$203$	−2.11177e11	+	2.11177e11i	−0.0429950	+	0.0429950i
$204$		0			0
$205$	2.65533e12	+	2.65533e12i	0.512238	+	0.512238i
$206$		0			0
$207$	−1.47896e13			−2.70470
$208$		0			0
$209$	−9.70001e12			−1.68255
$210$		0			0
$211$	−6.50187e12	−	6.50187e12i	−1.07025	−	1.07025i	−0.997338	−	0.0729105i	$-0.976771\pi$
$211$	−6.50187e12	−	6.50187e12i	−1.07025	−	1.07025i	−0.0729105	−	0.997338i	$-0.523229\pi$
$212$		0			0
$213$	3.06842e12	−	3.06842e12i	0.479543	−	0.479543i
$214$		0			0
$215$		−	1.18804e13i		−	1.76368i
$216$		0			0
$217$		−	6.72312e12i		−	0.948511i
$218$		0			0
$219$	−1.20208e13	+	1.20208e13i	−1.61247	+	1.61247i
$220$		0			0
$221$	2.79359e11	+	2.79359e11i	0.0356455	+	0.0356455i
$222$		0			0
$223$	−6.38459e12			−0.775275			−0.387638	−	0.921812i	$-0.626709\pi$
$223$	−6.38459e12			−0.775275			−0.387638	+	0.921812i	$0.626709\pi$
$224$		0			0
$225$	1.31497e13			1.52024
$226$		0			0
$227$	−3.98249e12	−	3.98249e12i	−0.438543	−	0.438543i	0.452978	−	0.891522i	$-0.350362\pi$
$227$	−3.98249e12	−	3.98249e12i	−0.438543	−	0.438543i	−0.891522	+	0.452978i	$0.850362\pi$
$228$		0			0
$229$	6.19174e12	−	6.19174e12i	0.649707	−	0.649707i	−0.303215	−	0.952922i	$-0.598060\pi$
$229$	6.19174e12	−	6.19174e12i	0.649707	−	0.649707i	0.952922	+	0.303215i	$0.0980602\pi$
$230$		0			0
$231$			1.62739e13i			1.62789i
$232$		0			0
$233$		−	5.61999e12i		−	0.536140i	−0.963399	−	0.268070i	$-0.913614\pi$
$233$		−	5.61999e12i		−	0.536140i	0.963399	−	0.268070i	$-0.0863858\pi$
$234$		0			0
$235$	1.06490e13	−	1.06490e13i	0.969247	−	0.969247i
$236$		0			0
$237$	−1.25590e11	−	1.25590e11i	−0.0109104	−	0.0109104i
$238$		0			0
$239$	1.23308e13			1.02283			0.511414	−	0.859335i	$-0.329122\pi$
$239$	1.23308e13			1.02283			0.511414	+	0.859335i	$0.329122\pi$
$240$		0			0
$241$	1.52533e13			1.20856			0.604281	−	0.796771i	$-0.293460\pi$
$241$	1.52533e13			1.20856			0.604281	+	0.796771i	$0.293460\pi$
$242$		0			0
$243$	7.32243e12	+	7.32243e12i	0.554397	+	0.554397i
$244$		0			0
$245$	1.89795e12	−	1.89795e12i	0.137363	−	0.137363i
$246$		0			0
$247$			1.73538e13i			1.20105i
$248$		0			0
$249$		−	4.97537e11i		−	0.0329404i
$250$		0			0
$251$	−1.60987e13	+	1.60987e13i	−1.01997	+	1.01997i	−0.0201706	+	0.999797i	$0.506421\pi$
$251$	−1.60987e13	+	1.60987e13i	−1.01997	+	1.01997i	−0.999797	+	0.0201706i	$0.993579\pi$
$252$		0			0
$253$	1.68772e13	+	1.68772e13i	1.02362	+	1.02362i
$254$		0			0
$255$	2.98252e12			0.173226
$256$		0			0
$257$	−2.30607e13			−1.28304			−0.641519	−	0.767107i	$-0.721696\pi$
$257$	−2.30607e13			−1.28304			−0.641519	+	0.767107i	$0.721696\pi$
$258$		0			0
$259$	−2.14562e12	−	2.14562e12i	−0.114394	−	0.114394i
$260$		0			0
$261$	−1.35788e12	+	1.35788e12i	−0.0693967	+	0.0693967i
$262$		0			0
$263$		−	1.05327e13i		−	0.516159i	−0.966124	−	0.258080i	$-0.916910\pi$
$263$		−	1.05327e13i		−	0.516159i	0.966124	−	0.258080i	$-0.0830897\pi$
$264$		0			0
$265$			4.68184e13i			2.20072i
$266$		0			0
$267$	−2.44311e13	+	2.44311e13i	−1.10187	+	1.10187i
$268$		0			0
$269$	−1.61223e13	−	1.61223e13i	−0.697895	−	0.697895i	0.266062	−	0.963956i	$-0.414278\pi$
$269$	−1.61223e13	−	1.61223e13i	−0.697895	−	0.697895i	−0.963956	+	0.266062i	$0.914278\pi$
$270$		0			0
$271$	1.25041e13			0.519662			0.259831	−	0.965654i	$-0.416333\pi$
$271$	1.25041e13			0.519662			0.259831	+	0.965654i	$0.416333\pi$
$272$		0			0
$273$	2.91149e13			1.16204
$274$		0			0
$275$	−1.50058e13	−	1.50058e13i	−0.575348	−	0.575348i
$276$		0			0
$277$	1.36829e12	−	1.36829e12i	0.0504125	−	0.0504125i	−0.681451	−	0.731864i	$-0.738651\pi$
$277$	1.36829e12	−	1.36829e12i	0.0504125	−	0.0504125i	0.731864	+	0.681451i	$0.238651\pi$
$278$		0			0
$279$		−	4.32301e13i		−	1.53096i
$280$		0			0
$281$			3.42090e13i			1.16481i	0.812898	+	0.582406i	$0.197888\pi$
$281$			3.42090e13i			1.16481i	−0.812898	+	0.582406i	$0.802112\pi$
$282$		0			0
$283$	−3.26611e13	+	3.26611e13i	−1.06956	+	1.06956i	−0.0721666	+	0.997393i	$0.522991\pi$
$283$	−3.26611e13	+	3.26611e13i	−1.06956	+	1.06956i	−0.997393	+	0.0721666i	$0.977009\pi$
$284$		0			0
$285$	9.26375e13	+	9.26375e13i	2.91837	+	2.91837i
$286$		0			0
$287$	1.86142e13			0.564280
$288$		0			0
$289$	−3.40713e13			−0.994146
$290$		0			0
$291$	2.65249e13	+	2.65249e13i	0.745147	+	0.745147i
$292$		0			0
$293$	−3.33163e13	+	3.33163e13i	−0.901333	+	0.901333i	−0.995552	−	0.0942188i	$-0.969965\pi$
$293$	−3.33163e13	+	3.33163e13i	−0.901333	+	0.901333i	0.0942188	+	0.995552i	$0.469965\pi$
$294$		0			0
$295$			7.92039e13i			2.06407i
$296$		0			0
$297$			4.39651e13i			1.10395i
$298$		0			0
$299$	3.01942e13	−	3.01942e13i	0.730689	−	0.730689i
$300$		0			0
$301$	−4.16416e13	−	4.16416e13i	−0.971431	−	0.971431i
$302$		0			0
$303$	−8.28222e13			−1.86300
$304$		0			0
$305$	2.44904e13			0.531309
$306$		0			0
$307$	2.22569e13	+	2.22569e13i	0.465805	+	0.465805i	0.900552	−	0.434747i	$-0.143162\pi$
$307$	2.22569e13	+	2.22569e13i	0.465805	+	0.465805i	−0.434747	+	0.900552i	$0.643162\pi$
$308$		0			0
$309$	5.45548e13	−	5.45548e13i	1.10170	−	1.10170i
$310$		0			0
$311$			3.81764e13i			0.744069i	0.928219	+	0.372035i	$0.121340\pi$
$311$			3.81764e13i			0.744069i	−0.928219	+	0.372035i	$0.878660\pi$
$312$		0			0
$313$		−	5.77077e13i		−	1.08577i	−0.839805	−	0.542887i	$-0.817331\pi$
$313$		−	5.77077e13i		−	1.08577i	0.839805	−	0.542887i	$-0.182669\pi$
$314$		0			0
$315$	9.83762e13	−	9.83762e13i	1.78724	−	1.78724i
$316$		0			0
$317$	−1.12780e13	−	1.12780e13i	−0.197881	−	0.197881i	0.601210	−	0.799091i	$-0.294686\pi$
$317$	−1.12780e13	−	1.12780e13i	−0.197881	−	0.197881i	−0.799091	+	0.601210i	$0.794686\pi$
$318$		0			0
$319$	3.09910e12			0.0525276
$320$		0			0
$321$	6.18418e13			1.01276
$322$		0			0
$323$	6.23104e12	+	6.23104e12i	0.0986159	+	0.0986159i
$324$		0			0
$325$	−2.68462e13	+	2.68462e13i	−0.410700	+	0.410700i
$326$		0			0
$327$		−	9.00459e13i		−	1.33184i
$328$		0			0
$329$		−	7.46508e13i		−	1.06772i
$330$		0			0
$331$	−3.48998e13	+	3.48998e13i	−0.482802	+	0.482802i	−0.906025	−	0.423223i	$-0.860899\pi$
$331$	−3.48998e13	+	3.48998e13i	−0.482802	+	0.482802i	0.423223	+	0.906025i	$0.360899\pi$
$332$		0			0
$333$	−1.37965e13	−	1.37965e13i	−0.184640	−	0.184640i
$334$		0			0
$335$	−7.23742e13			−0.937211
$336$		0			0
$337$	−3.04682e13			−0.381841			−0.190920	−	0.981606i	$-0.561147\pi$
$337$	−3.04682e13			−0.381841			−0.190920	+	0.981606i	$0.561147\pi$
$338$		0			0
$339$	−1.21326e14	−	1.21326e14i	−1.47182	−	1.47182i
$340$		0			0
$341$	−4.93323e13	+	4.93323e13i	−0.579405	+	0.579405i
$342$		0			0
$343$			8.06413e13i			0.917148i
$344$		0			0
$345$		−	3.22363e14i		−	3.55092i
$346$		0			0
$347$	−4.49902e13	+	4.49902e13i	−0.480071	+	0.480071i	−0.905154	−	0.425083i	$-0.860245\pi$
$347$	−4.49902e13	+	4.49902e13i	−0.480071	+	0.480071i	0.425083	+	0.905154i	$0.360245\pi$
$348$		0			0
$349$	−1.26485e14	−	1.26485e14i	−1.30767	−	1.30767i	−0.923090	−	0.384584i	$-0.874345\pi$
$349$	−1.26485e14	−	1.26485e14i	−1.30767	−	1.30767i	−0.384584	−	0.923090i	$-0.625655\pi$
$350$		0			0
$351$	7.86560e13			0.788030
$352$		0			0
$353$	−6.13312e13			−0.595554			−0.297777	−	0.954636i	$-0.596245\pi$
$353$	−6.13312e13			−0.595554			−0.297777	+	0.954636i	$0.596245\pi$
$354$		0			0
$355$	4.23339e13	+	4.23339e13i	0.398503	+	0.398503i
$356$		0			0
$357$	1.04540e13	−	1.04540e13i	0.0954125	−	0.0954125i
$358$		0			0
$359$		−	1.56749e14i		−	1.38734i	−0.720291	−	0.693672i	$-0.755992\pi$
$359$		−	1.56749e14i		−	1.38734i	0.720291	−	0.693672i	$-0.244008\pi$
$360$		0			0
$361$			2.70583e14i			2.32280i
$362$		0			0
$363$	−2.07458e13	+	2.07458e13i	−0.172760	+	0.172760i
$364$		0			0
$365$	−1.65847e14	−	1.65847e14i	−1.33997	−	1.33997i
$366$		0			0
$367$	2.36073e13			0.185090			0.0925452	−	0.995708i	$-0.470500\pi$
$367$	2.36073e13			0.185090			0.0925452	+	0.995708i	$0.470500\pi$
$368$		0			0
$369$	1.19691e14			0.910783
$370$		0			0
$371$	1.64102e14	+	1.64102e14i	1.21215	+	1.21215i
$372$		0			0
$373$	1.23900e14	−	1.23900e14i	0.888533	−	0.888533i	−0.105849	−	0.994382i	$-0.533756\pi$
$373$	1.23900e14	−	1.23900e14i	0.888533	−	0.888533i	0.994382	+	0.105849i	$0.0337562\pi$
$374$		0			0
$375$		−	3.85247e13i		−	0.268267i
$376$		0			0
$377$		−	5.54446e12i		−	0.0374958i
$378$		0			0
$379$	1.89125e14	−	1.89125e14i	1.24232	−	1.24232i	0.283279	−	0.959037i	$-0.408578\pi$
$379$	1.89125e14	−	1.89125e14i	1.24232	−	1.24232i	0.959037	−	0.283279i	$-0.0914223\pi$
$380$		0			0
$381$	8.34212e13	+	8.34212e13i	0.532340	+	0.532340i
$382$		0			0
$383$	−1.18647e14			−0.735640			−0.367820	−	0.929897i	$-0.619896\pi$
$383$	−1.18647e14			−0.735640			−0.367820	+	0.929897i	$0.619896\pi$
$384$		0			0
$385$	−2.24525e14			−1.35279
$386$		0			0
$387$	−2.67758e14	−	2.67758e14i	−1.56795	−	1.56795i
$388$		0			0
$389$	−1.64051e14	+	1.64051e14i	−0.933807	+	0.933807i	−0.997941	−	0.0641342i	$-0.979571\pi$
$389$	−1.64051e14	+	1.64051e14i	−0.933807	+	0.933807i	0.0641342	+	0.997941i	$0.479571\pi$
$390$		0			0
$391$		−	2.16830e13i		−	0.119991i
$392$		0			0
$393$			8.26813e13i			0.444886i
$394$		0			0
$395$	1.73272e12	−	1.73272e12i	0.00906661	−	0.00906661i
$396$		0			0
$397$	1.00961e14	+	1.00961e14i	0.513814	+	0.513814i	0.915693	−	0.401879i	$-0.131643\pi$
$397$	1.00961e14	+	1.00961e14i	0.513814	+	0.513814i	−0.401879	+	0.915693i	$0.631643\pi$
$398$		0			0
$399$	6.49402e14			3.21486
$400$		0			0
$401$	8.85961e13			0.426698			0.213349	−	0.976976i	$-0.431563\pi$
$401$	8.85961e13			0.426698			0.213349	+	0.976976i	$0.431563\pi$
$402$		0			0
$403$	8.82581e13	+	8.82581e13i	0.413596	+	0.413596i
$404$		0			0
$405$	5.30829e13	−	5.30829e13i	0.242076	−	0.242076i
$406$		0			0
$407$			3.14879e13i			0.139757i
$408$		0			0
$409$		−	6.09716e13i		−	0.263421i	−0.991288	−	0.131710i	$-0.957953\pi$
$409$		−	6.09716e13i		−	0.263421i	0.991288	−	0.131710i	$-0.0420469\pi$
$410$		0			0
$411$	2.49589e14	−	2.49589e14i	1.04977	−	1.04977i
$412$		0			0
$413$	2.77615e14	+	2.77615e14i	1.13689	+	1.13689i
$414$		0			0
$415$	6.86432e12			0.0273737
$416$		0			0
$417$	−7.08094e14			−2.75006
$418$		0			0
$419$	2.16284e14	+	2.16284e14i	0.818176	+	0.818176i	0.985844	−	0.167668i	$-0.0536235\pi$
$419$	2.16284e14	+	2.16284e14i	0.818176	+	0.818176i	−0.167668	+	0.985844i	$0.553624\pi$
$420$		0			0
$421$	−3.49912e14	+	3.49912e14i	−1.28946	+	1.28946i	−0.354345	+	0.935115i	$0.615296\pi$
$421$	−3.49912e14	+	3.49912e14i	−1.28946	+	1.28946i	−0.935115	+	0.354345i	$0.884704\pi$
$422$		0			0
$423$		−	4.80009e14i		−	1.72337i
$424$		0			0
$425$			1.92787e13i			0.0674434i
$426$		0			0
$427$	8.58406e13	−	8.58406e13i	0.292644	−	0.292644i
$428$		0			0
$429$	−2.13637e14	−	2.13637e14i	−0.709840	−	0.709840i
$430$		0			0
$431$	4.11853e13			0.133388			0.0666941	−	0.997773i	$-0.478755\pi$
$431$	4.11853e13			0.133388			0.0666941	+	0.997773i	$0.478755\pi$
$432$		0			0
$433$	1.87442e14			0.591810			0.295905	−	0.955217i	$-0.404379\pi$
$433$	1.87442e14			0.591810			0.295905	+	0.955217i	$0.404379\pi$
$434$		0			0
$435$	−2.95972e13	−	2.95972e13i	−0.0911087	−	0.0911087i
$436$		0			0
$437$	6.73476e14	−	6.73476e14i	2.02150	−	2.02150i
$438$		0			0
$439$			2.44174e14i			0.714734i	0.933964	+	0.357367i	$0.116325\pi$
$439$			2.44174e14i			0.714734i	−0.933964	+	0.357367i	$0.883675\pi$
$440$		0			0
$441$		−	8.55511e13i		−	0.244238i
$442$		0			0
$443$	−3.95338e14	+	3.95338e14i	−1.10090	+	1.10090i	−0.106599	+	0.994302i	$0.533996\pi$
$443$	−3.95338e14	+	3.95338e14i	−1.10090	+	1.10090i	−0.994302	+	0.106599i	$0.966004\pi$
$444$		0			0
$445$	−3.37066e14	−	3.37066e14i	−0.915662	−	0.915662i
$446$		0			0
$447$	−3.69361e13			−0.0978947
$448$		0			0
$449$	−3.39123e14			−0.877005			−0.438503	−	0.898730i	$-0.644491\pi$
$449$	−3.39123e14			−0.877005			−0.438503	+	0.898730i	$0.644491\pi$
$450$		0			0
$451$	−1.36586e14	−	1.36586e14i	−0.344694	−	0.344694i
$452$		0			0
$453$	3.25121e14	−	3.25121e14i	0.800765	−	0.800765i
$454$		0			0
$455$			4.01687e14i			0.965663i
$456$		0			0
$457$		−	3.62436e14i		−	0.850535i	−0.905068	−	0.425267i	$-0.860180\pi$
$457$		−	3.62436e14i		−	0.850535i	0.905068	−	0.425267i	$-0.139820\pi$
$458$		0			0
$459$	2.82421e13	−	2.82421e13i	0.0647034	−	0.0647034i
$460$		0			0
$461$	−4.25739e14	−	4.25739e14i	−0.952333	−	0.952333i	0.0465818	−	0.998914i	$-0.485167\pi$
$461$	−4.25739e14	−	4.25739e14i	−0.952333	−	0.952333i	−0.998914	+	0.0465818i	$0.985167\pi$
$462$		0			0
$463$	1.92004e14			0.419387			0.209693	−	0.977767i	$-0.432753\pi$
$463$	1.92004e14			0.419387			0.209693	+	0.977767i	$0.432753\pi$
$464$		0			0
$465$	9.42271e14			2.00995
$466$		0			0
$467$	5.47493e14	+	5.47493e14i	1.14061	+	1.14061i	0.988339	+	0.152266i	$0.0486572\pi$
$467$	5.47493e14	+	5.47493e14i	1.14061	+	1.14061i	0.152266	+	0.988339i	$0.451343\pi$
$468$		0			0
$469$	−2.53677e14	+	2.53677e14i	−0.516214	+	0.516214i
$470$		0			0
$471$		−	6.10734e14i		−	1.21405i
$472$		0			0
$473$			6.11108e14i			1.18681i
$474$		0			0
$475$	−5.98800e14	+	5.98800e14i	−1.13623	+	1.13623i
$476$		0			0
$477$	1.05518e15	+	1.05518e15i	1.95649	+	1.95649i
$478$		0			0
$479$	−4.71009e14			−0.853461			−0.426730	−	0.904379i	$-0.640335\pi$
$479$	−4.71009e14			−0.853461			−0.426730	+	0.904379i	$0.640335\pi$
$480$		0			0
$481$	5.63335e13			0.0997628
$482$		0			0
$483$	−1.12991e15	−	1.12991e15i	−1.95584	−	1.95584i
$484$		0			0
$485$	−3.65953e14	+	3.65953e14i	−0.619222	+	0.619222i
$486$		0			0
$487$			3.48163e14i			0.575934i	0.957640	+	0.287967i	$0.0929794\pi$
$487$			3.48163e14i			0.575934i	−0.957640	+	0.287967i	$0.907021\pi$
$488$		0			0
$489$			2.51838e14i			0.407308i
$490$		0			0
$491$	−3.92493e14	+	3.92493e14i	−0.620703	+	0.620703i	−0.945711	−	0.325008i	$-0.894633\pi$
$491$	−3.92493e14	+	3.92493e14i	−0.620703	+	0.620703i	0.325008	+	0.945711i	$0.394633\pi$
$492$		0			0
$493$	−1.99079e12	−	1.99079e12i	−0.00307869	−	0.00307869i
$494$		0			0
$495$	−1.44371e15			−2.18349
$496$		0			0
$497$	2.96766e14			0.438990
$498$		0			0
$499$	−8.56521e14	−	8.56521e14i	−1.23932	−	1.23932i	−0.960278	−	0.279047i	$-0.909982\pi$
$499$	−8.56521e14	−	8.56521e14i	−1.23932	−	1.23932i	−0.279047	−	0.960278i	$-0.590018\pi$
$500$		0			0
$501$	−2.57509e14	+	2.57509e14i	−0.364490	+	0.364490i
$502$		0			0
$503$			6.57746e14i			0.910823i	0.890281	+	0.455412i	$0.150508\pi$
$503$			6.57746e14i			0.910823i	−0.890281	+	0.455412i	$0.849492\pi$
$504$		0			0
$505$		−	1.14267e15i		−	1.54816i
$506$		0			0
$507$	4.98189e14	−	4.98189e14i	0.660466	−	0.660466i
$508$		0			0
$509$	−6.23390e14	−	6.23390e14i	−0.808746	−	0.808746i	0.175698	−	0.984444i	$-0.443782\pi$
$509$	−6.23390e14	−	6.23390e14i	−0.808746	−	0.808746i	−0.984444	+	0.175698i	$0.943782\pi$
$510$		0			0
$511$	−1.16261e15			−1.47611
$512$		0			0
$513$	1.75440e15			2.18014
$514$		0			0
$515$	7.52672e14	+	7.52672e14i	0.915516	+	0.915516i
$516$		0			0
$517$	−5.47765e14	+	5.47765e14i	−0.652223	+	0.652223i
$518$		0			0
$519$			8.47145e14i			0.987501i
$520$		0			0
$521$			7.57107e14i			0.864072i	0.901856	+	0.432036i	$0.142205\pi$
$521$			7.57107e14i			0.864072i	−0.901856	+	0.432036i	$0.857795\pi$
$522$		0			0
$523$	1.25634e14	−	1.25634e14i	0.140394	−	0.140394i	−0.633417	−	0.773811i	$-0.718348\pi$
$523$	1.25634e14	−	1.25634e14i	0.140394	−	0.140394i	0.773811	+	0.633417i	$0.218348\pi$
$524$		0			0
$525$	1.00462e15	+	1.00462e15i	1.09932	+	1.09932i
$526$		0			0
$527$	6.33796e13			0.0679190
$528$		0			0
$529$	−1.39077e15			−1.45966
$530$		0			0
$531$	1.78508e15	+	1.78508e15i	1.83501	+	1.83501i
$532$		0			0
$533$	−2.44359e14	+	2.44359e14i	−0.246053	+	0.246053i
$534$		0			0
$535$			8.53208e14i			0.841607i
$536$		0			0
$537$			4.20168e14i			0.406035i
$538$		0			0
$539$	−9.76271e13	+	9.76271e13i	−0.0924341	+	0.0924341i
$540$		0			0
$541$	6.24928e14	+	6.24928e14i	0.579756	+	0.579756i	0.934836	−	0.355080i	$-0.115546\pi$
$541$	6.24928e14	+	6.24928e14i	0.579756	+	0.579756i	−0.355080	+	0.934836i	$0.615546\pi$
$542$		0			0
$543$	7.77220e14			0.706554
$544$		0			0
$545$	1.24233e15			1.10677
$546$		0			0
$547$	9.63322e14	+	9.63322e14i	0.841087	+	0.841087i	0.989000	−	0.147913i	$-0.0472555\pi$
$547$	9.63322e14	+	9.63322e14i	0.841087	+	0.841087i	−0.147913	+	0.989000i	$0.547256\pi$
$548$		0			0
$549$	5.51960e14	−	5.51960e14i	0.472346	−	0.472346i
$550$		0			0
$551$		−	1.23668e14i		−	0.103735i
$552$		0			0
$553$		−	1.21466e13i		−	0.00998775i
$554$		0			0
$555$	3.00717e14	−	3.00717e14i	0.242408	−	0.242408i
$556$		0			0
$557$	2.17103e14	+	2.17103e14i	0.171579	+	0.171579i	0.787673	−	0.616094i	$-0.211286\pi$
$557$	2.17103e14	+	2.17103e14i	0.171579	+	0.171579i	−0.616094	+	0.787673i	$0.711286\pi$
$558$		0			0
$559$	1.09330e15			0.847181
$560$		0			0
$561$	−1.53416e14			−0.116567
$562$		0			0
$563$	−1.35181e15	−	1.35181e15i	−1.00721	−	1.00721i	−0.999974	−	0.00723157i	$-0.997698\pi$
$563$	−1.35181e15	−	1.35181e15i	−1.00721	−	1.00721i	−0.00723157	−	0.999974i	$-0.502302\pi$
$564$		0			0
$565$	1.67388e15	−	1.67388e15i	1.22309	−	1.22309i
$566$		0			0
$567$		−	3.72118e14i		−	0.266670i
$568$		0			0
$569$			1.98028e15i			1.39190i	0.718090	+	0.695951i	$0.245017\pi$
$569$			1.98028e15i			1.39190i	−0.718090	+	0.695951i	$0.754983\pi$
$570$		0			0
$571$	4.03386e13	−	4.03386e13i	0.0278114	−	0.0278114i	−0.693064	−	0.720876i	$-0.743740\pi$
$571$	4.03386e13	−	4.03386e13i	0.0278114	−	0.0278114i	0.720876	+	0.693064i	$0.243740\pi$
$572$		0			0
$573$	−4.80801e14	−	4.80801e14i	−0.325173	−	0.325173i
$574$		0			0
$575$	2.08372e15			1.38251
$576$		0			0
$577$	−1.24036e15			−0.807384			−0.403692	−	0.914895i	$-0.632273\pi$
$577$	−1.24036e15			−0.807384			−0.403692	+	0.914895i	$0.632273\pi$
$578$		0			0
$579$	−5.01666e14	−	5.01666e14i	−0.320393	−	0.320393i
$580$		0			0
$581$	2.40599e13	−	2.40599e13i	0.0150774	−	0.0150774i
$582$		0			0
$583$		−	2.40826e15i		−	1.48090i
$584$		0			0
$585$			2.58287e15i			1.55864i
$586$		0			0
$587$	2.42607e13	−	2.42607e13i	0.0143679	−	0.0143679i	−0.699886	−	0.714254i	$-0.746766\pi$
$587$	2.42607e13	−	2.42607e13i	0.0143679	−	0.0143679i	0.714254	+	0.699886i	$0.246766\pi$
$588$		0			0
$589$	1.96858e15	+	1.96858e15i	1.14424	+	1.14424i
$590$		0			0
$591$	−3.21251e15			−1.83279
$592$		0			0
$593$	−1.06516e15			−0.596504			−0.298252	−	0.954487i	$-0.596404\pi$
$593$	−1.06516e15			−0.596504			−0.298252	+	0.954487i	$0.596404\pi$
$594$		0			0
$595$	1.44229e14	+	1.44229e14i	0.0792884	+	0.0792884i
$596$		0			0
$597$	−2.92055e15	+	2.92055e15i	−1.57618	+	1.57618i
$598$		0			0
$599$		−	1.54332e14i		−	0.0817729i	−0.999164	−	0.0408865i	$-0.986982\pi$
$599$		−	1.54332e14i		−	0.0817729i	0.999164	−	0.0408865i	$-0.0130182\pi$
$600$		0			0
$601$		−	6.03222e14i		−	0.313811i	−0.987614	−	0.156905i	$-0.949848\pi$
$601$		−	6.03222e14i		−	0.313811i	0.987614	−	0.156905i	$-0.0501518\pi$
$602$		0			0
$603$	−1.63116e15	+	1.63116e15i	−0.833202	+	0.833202i
$604$		0			0
$605$	−2.86222e14	−	2.86222e14i	−0.143565	−	0.143565i
$606$		0			0
$607$	3.40313e15			1.67626			0.838128	−	0.545474i	$-0.183650\pi$
$607$	3.40313e15			1.67626			0.838128	+	0.545474i	$0.183650\pi$
$608$		0			0
$609$	−2.07481e14			−0.100365
$610$		0			0
$611$	9.79981e14	+	9.79981e14i	0.465577	+	0.465577i
$612$		0			0
$613$	4.01340e14	−	4.01340e14i	0.187275	−	0.187275i	−0.607242	−	0.794517i	$-0.707724\pi$
$613$	4.01340e14	−	4.01340e14i	0.187275	−	0.187275i	0.794517	+	0.607242i	$0.207724\pi$
$614$		0			0
$615$			2.60885e15i			1.19574i
$616$		0			0
$617$		−	2.48564e15i		−	1.11910i	−0.828796	−	0.559552i	$-0.810973\pi$
$617$		−	2.48564e15i		−	1.11910i	0.828796	−	0.559552i	$-0.189027\pi$
$618$		0			0
$619$	−1.37578e15	+	1.37578e15i	−0.608484	+	0.608484i	−0.942550	−	0.334066i	$-0.891579\pi$
$619$	−1.37578e15	+	1.37578e15i	−0.608484	+	0.608484i	0.334066	+	0.942550i	$0.391579\pi$
$620$		0			0
$621$	−3.05252e15	−	3.05252e15i	−1.32634	−	1.32634i
$622$		0			0
$623$	−2.36288e15			−1.00869
$624$		0			0
$625$	2.63321e15			1.10445
$626$		0			0
$627$	−4.76512e15	−	4.76512e15i	−1.96382	−	1.96382i
$628$		0			0
$629$	2.02270e13	−	2.02270e13i	0.00819130	−	0.00819130i
$630$		0			0
$631$			1.74122e14i			0.0692933i	0.999400	+	0.0346467i	$0.0110306\pi$
$631$			1.74122e14i			0.0692933i	−0.999400	+	0.0346467i	$0.988969\pi$
$632$		0			0
$633$		−	6.38807e15i		−	2.49833i
$634$		0			0
$635$	−1.15093e15	+	1.15093e15i	−0.442378	+	0.442378i
$636$		0			0
$637$	1.74660e14	+	1.74660e14i	0.0659822	+	0.0659822i
$638$		0			0
$639$	1.90823e15			0.708557
$640$		0			0
$641$	5.21652e14			0.190398			0.0951988	−	0.995458i	$-0.469651\pi$
$641$	5.21652e14			0.190398			0.0951988	+	0.995458i	$0.469651\pi$
$642$		0			0
$643$	2.06632e14	+	2.06632e14i	0.0741372	+	0.0741372i	0.743203	−	0.669066i	$-0.233306\pi$
$643$	2.06632e14	+	2.06632e14i	0.0741372	+	0.0741372i	−0.669066	+	0.743203i	$0.733306\pi$
$644$		0			0
$645$	5.83623e15	−	5.83623e15i	2.05851	−	2.05851i
$646$		0			0
$647$		−	4.78314e15i		−	1.65859i	−0.558809	−	0.829297i	$-0.688741\pi$
$647$		−	4.78314e15i		−	1.65859i	0.558809	−	0.829297i	$-0.311259\pi$
$648$		0			0
$649$		−	4.07411e15i		−	1.38895i
$650$		0			0
$651$	3.30272e15	−	3.30272e15i	1.10707	−	1.10707i
$652$		0			0
$653$	−2.83678e15	−	2.83678e15i	−0.934981	−	0.934981i	0.0630307	−	0.998012i	$-0.479923\pi$
$653$	−2.83678e15	−	2.83678e15i	−0.934981	−	0.934981i	−0.998012	+	0.0630307i	$0.979923\pi$
$654$		0			0
$655$	−1.14072e15			−0.369703
$656$		0			0
$657$	−7.47565e15			−2.38253
$658$		0			0
$659$	−4.97751e14	−	4.97751e14i	−0.156006	−	0.156006i	0.624788	−	0.780794i	$-0.285185\pi$
$659$	−4.97751e14	−	4.97751e14i	−0.156006	−	0.156006i	−0.780794	+	0.624788i	$0.785185\pi$
$660$		0			0
$661$	−2.20684e15	+	2.20684e15i	−0.680242	+	0.680242i	−0.960055	−	0.279813i	$-0.909728\pi$
$661$	−2.20684e15	+	2.20684e15i	−0.680242	+	0.680242i	0.279813	+	0.960055i	$0.409728\pi$
$662$		0			0
$663$			2.74469e14i			0.0832089i
$664$		0			0
$665$			8.95955e15i			2.67157i
$666$		0			0
$667$	−2.15172e14	+	2.15172e14i	−0.0631094	+	0.0631094i
$668$		0			0
$669$	−3.13642e15	−	3.13642e15i	−0.904879	−	0.904879i
$670$		0			0
$671$	−1.25975e15			−0.357527
$672$		0			0
$673$	−3.47072e15			−0.969028			−0.484514	−	0.874783i	$-0.661004\pi$
$673$	−3.47072e15			−0.969028			−0.484514	+	0.874783i	$0.661004\pi$
$674$		0			0
$675$	2.71405e15	+	2.71405e15i	0.745499	+	0.745499i
$676$		0			0
$677$	3.88738e15	−	3.88738e15i	1.05056	−	1.05056i	0.0519033	−	0.998652i	$-0.483471\pi$
$677$	3.88738e15	−	3.88738e15i	1.05056	−	1.05056i	0.998652	−	0.0519033i	$-0.0165288\pi$
$678$		0			0
$679$			2.56538e15i			0.682132i
$680$		0			0
$681$		−	3.91278e15i		−	1.02371i
$682$		0			0
$683$	5.25838e15	−	5.25838e15i	1.35375	−	1.35375i	0.472321	−	0.881426i	$-0.343416\pi$
$683$	5.25838e15	−	5.25838e15i	1.35375	−	1.35375i	0.881426	−	0.472321i	$-0.156584\pi$
$684$		0			0
$685$	3.44348e15	+	3.44348e15i	0.872367	+	0.872367i
$686$		0			0
$687$	6.08336e15			1.51664
$688$		0			0
$689$	−4.30850e15			−1.05711
$690$		0			0
$691$	5.14710e15	+	5.14710e15i	1.24289	+	1.24289i	0.958795	+	0.284098i	$0.0916940\pi$
$691$	5.14710e15	+	5.14710e15i	1.24289	+	1.24289i	0.284098	+	0.958795i	$0.408306\pi$
$692$		0			0
$693$	−5.06030e15	+	5.06030e15i	−1.20266	+	1.20266i
$694$		0			0
$695$		−	9.76931e15i		−	2.28532i
$696$		0			0
$697$			1.75478e14i			0.0404057i
$698$		0			0
$699$	2.76081e15	−	2.76081e15i	0.625767	−	0.625767i
$700$		0			0
$701$	−5.46695e15	−	5.46695e15i	−1.21982	−	1.21982i	−0.967695	−	0.252125i	$-0.918870\pi$
$701$	−5.46695e15	−	5.46695e15i	−1.21982	−	1.21982i	−0.252125	−	0.967695i	$-0.581130\pi$
$702$		0			0
$703$	1.25651e15			0.276001
$704$		0			0
$705$	1.04626e16			2.26255
$706$		0			0
$707$	−4.00512e15	−	4.00512e15i	−0.852725	−	0.852725i
$708$		0			0
$709$	−2.91858e15	+	2.91858e15i	−0.611811	+	0.611811i	−0.943418	−	0.331607i	$-0.892409\pi$
$709$	−2.91858e15	+	2.91858e15i	−0.611811	+	0.611811i	0.331607	+	0.943418i	$0.392409\pi$
$710$		0			0
$711$		−	7.81036e13i		−	0.0161209i
$712$		0			0
$713$		−	6.85032e15i		−	1.39225i
$714$		0			0
$715$	2.94746e15	−	2.94746e15i	0.589882	−	0.589882i
$716$		0			0
$717$	6.05748e15	+	6.05748e15i	1.19381	+	1.19381i
$718$		0			0
$719$	−3.53754e15			−0.686582			−0.343291	−	0.939229i	$-0.611542\pi$
$719$	−3.53754e15			−0.686582			−0.343291	+	0.939229i	$0.611542\pi$
$720$		0			0
$721$	5.27634e15			1.00853
$722$		0			0
$723$	7.49315e15	+	7.49315e15i	1.41060	+	1.41060i
$724$		0			0
$725$	1.91313e14	−	1.91313e14i	0.0354721	−	0.0354721i
$726$		0			0
$727$			6.70485e15i			1.22447i	0.790674	+	0.612237i	$0.209730\pi$
$727$			6.70485e15i			1.22447i	−0.790674	+	0.612237i	$0.790270\pi$
$728$		0			0
$729$			8.58171e15i			1.54373i
$730$		0			0
$731$	3.92560e14	−	3.92560e14i	0.0695602	−	0.0695602i
$732$		0			0
$733$	−1.66881e15	−	1.66881e15i	−0.291297	−	0.291297i	0.546295	−	0.837593i	$-0.316038\pi$
$733$	−1.66881e15	−	1.66881e15i	−0.291297	−	0.291297i	−0.837593	+	0.546295i	$0.816038\pi$
$734$		0			0
$735$	1.86473e15			0.320653
$736$		0			0
$737$	3.72281e15			0.630666
$738$		0			0
$739$	−5.34409e15	−	5.34409e15i	−0.891928	−	0.891928i	0.102777	−	0.994704i	$-0.467227\pi$
$739$	−5.34409e15	−	5.34409e15i	−0.891928	−	0.891928i	−0.994704	+	0.102777i	$0.967227\pi$
$740$		0			0
$741$	−8.52505e15	+	8.52505e15i	−1.40183	+	1.40183i
$742$		0			0
$743$		−	4.45245e15i		−	0.721374i	−0.932687	−	0.360687i	$-0.882542\pi$
$743$		−	4.45245e15i		−	0.721374i	0.932687	−	0.360687i	$-0.117458\pi$
$744$		0			0
$745$		−	5.09593e14i		−	0.0813511i
$746$		0			0
$747$	1.54707e14	−	1.54707e14i	0.0243358	−	0.0243358i
$748$		0			0
$749$	2.99055e15	+	2.99055e15i	0.463555	+	0.463555i
$750$		0			0
$751$	2.33457e15			0.356605			0.178302	−	0.983976i	$-0.442939\pi$
$751$	2.33457e15			0.356605			0.178302	+	0.983976i	$0.442939\pi$
$752$		0			0
$753$	−1.58170e16			−2.38095
$754$		0			0
$755$	4.48557e15	+	4.48557e15i	0.665441	+	0.665441i
$756$		0			0
$757$	2.83109e15	−	2.83109e15i	0.413930	−	0.413930i	−0.469175	−	0.883105i	$-0.655449\pi$
$757$	2.83109e15	−	2.83109e15i	0.413930	−	0.413930i	0.883105	+	0.469175i	$0.155449\pi$
$758$		0			0
$759$			1.65818e16i			2.38947i
$760$		0			0
$761$			2.83306e15i			0.402383i	0.979552	+	0.201192i	$0.0644814\pi$
$761$			2.83306e15i			0.402383i	−0.979552	+	0.201192i	$0.935519\pi$
$762$		0			0
$763$	4.35445e15	−	4.35445e15i	0.609605	−	0.609605i
$764$		0			0
$765$	9.27403e14	+	9.27403e14i	0.127977	+	0.127977i
$766$		0			0
$767$	−7.28881e15			−0.991475
$768$		0			0
$769$	9.11818e15			1.22268			0.611341	−	0.791367i	$-0.290630\pi$
$769$	9.11818e15			1.22268			0.611341	+	0.791367i	$0.290630\pi$
$770$		0			0
$771$	−1.13285e16	−	1.13285e16i	−1.49752	−	1.49752i
$772$		0			0
$773$	−7.27074e15	+	7.27074e15i	−0.947527	+	0.947527i	−0.998690	−	0.0511632i	$-0.983707\pi$
$773$	−7.27074e15	+	7.27074e15i	−0.947527	+	0.947527i	0.0511632	+	0.998690i	$0.483707\pi$
$774$		0			0
$775$			6.09074e15i			0.782548i
$776$		0			0
$777$		−	2.10807e15i		−	0.267035i
$778$		0			0
$779$	−5.45037e15	+	5.45037e15i	−0.680722	+	0.680722i
$780$		0			0
$781$	−2.17758e15	−	2.17758e15i	−0.268160	−	0.268160i
$782$		0			0
$783$	−5.60523e14			−0.0680619
$784$		0			0
$785$	8.42607e15			1.00889
$786$		0			0
$787$	−6.22508e15	−	6.22508e15i	−0.734995	−	0.734995i	0.236610	−	0.971605i	$-0.423964\pi$
$787$	−6.22508e15	−	6.22508e15i	−0.734995	−	0.734995i	−0.971605	+	0.236610i	$0.923964\pi$
$788$		0			0
$789$	5.17418e15	−	5.17418e15i	0.602446	−	0.602446i
$790$		0			0
$791$		−	1.17342e16i		−	1.34735i
$792$		0			0
$793$			2.25375e15i			0.255213i
$794$		0			0
$795$	−2.29995e16	+	2.29995e16i	−2.56861	+	2.56861i
$796$		0			0
$797$	−5.53204e15	−	5.53204e15i	−0.609347	−	0.609347i	0.333429	−	0.942775i	$-0.391794\pi$
$797$	−5.53204e15	−	5.53204e15i	−0.609347	−	0.609347i	−0.942775	+	0.333429i	$0.891794\pi$
$798$		0			0
$799$	7.03741e14			0.0764549
$800$		0			0
$801$	−1.51935e16			−1.62809
$802$		0			0
$803$	8.53088e15	+	8.53088e15i	0.901692	+	0.901692i
$804$		0			0
$805$	1.55889e16	−	1.55889e16i	1.62531	−	1.62531i
$806$		0			0
$807$		−	1.58401e16i		−	1.62912i
$808$		0			0
$809$			1.10193e16i			1.11799i	0.829171	+	0.558995i	$0.188813\pi$
$809$			1.10193e16i			1.11799i	−0.829171	+	0.558995i	$0.811187\pi$
$810$		0			0
$811$	3.08512e15	−	3.08512e15i	0.308786	−	0.308786i	−0.535653	−	0.844438i	$-0.679934\pi$
$811$	3.08512e15	−	3.08512e15i	0.308786	−	0.308786i	0.844438	+	0.535653i	$0.179934\pi$
$812$		0			0
$813$	6.14262e15	+	6.14262e15i	0.606534	+	0.606534i
$814$		0			0
$815$	−3.47451e15			−0.338475
$816$		0			0
$817$	2.43859e16			2.34378
$818$		0			0
$819$	9.05316e15	+	9.05316e15i	0.858496	+	0.858496i
$820$		0			0
$821$	3.34565e15	−	3.34565e15i	0.313035	−	0.313035i	−0.533049	−	0.846084i	$-0.678954\pi$
$821$	3.34565e15	−	3.34565e15i	0.313035	−	0.313035i	0.846084	+	0.533049i	$0.178954\pi$
$822$		0			0
$823$		−	9.30189e15i		−	0.858760i	−0.903124	−	0.429380i	$-0.858732\pi$
$823$		−	9.30189e15i		−	0.858760i	0.903124	−	0.429380i	$-0.141268\pi$
$824$		0			0
$825$		−	1.47432e16i		−	1.34306i
$826$		0			0
$827$	3.80483e15	−	3.80483e15i	0.342023	−	0.342023i	−0.515104	−	0.857127i	$-0.672247\pi$
$827$	3.80483e15	−	3.80483e15i	0.342023	−	0.342023i	0.857127	+	0.515104i	$0.172247\pi$
$828$		0			0
$829$	1.95488e15	+	1.95488e15i	0.173408	+	0.173408i	0.788475	−	0.615067i	$-0.210871\pi$
$829$	1.95488e15	+	1.95488e15i	0.173408	+	0.173408i	−0.615067	+	0.788475i	$0.710871\pi$
$830$		0			0
$831$	1.34434e15			0.117680
$832$		0			0
$833$	1.25426e14			0.0108353
$834$		0			0
$835$	−3.55276e15	−	3.55276e15i	−0.302893	−	0.302893i
$836$		0			0
$837$	8.92254e15	−	8.92254e15i	0.750755	−	0.750755i
$838$		0			0
$839$			6.01775e15i			0.499739i	0.968280	+	0.249869i	$0.0803877\pi$
$839$			6.01775e15i			0.499739i	−0.968280	+	0.249869i	$0.919612\pi$
$840$		0			0
$841$		−	1.21610e16i		−	0.996762i
$842$		0			0
$843$	−1.68051e16	+	1.68051e16i	−1.35953	+	1.35953i
$844$		0			0
$845$	6.87332e15	+	6.87332e15i	0.548851	+	0.548851i
$846$		0			0
$847$	−2.00645e15			−0.158150
$848$		0			0
$849$	−3.20894e16			−2.49672
$850$		0			0
$851$	−2.18622e15	−	2.18622e15i	−0.167912	−	0.167912i
$852$		0			0
$853$	1.15272e16	−	1.15272e16i	0.873986	−	0.873986i	−0.118918	−	0.992904i	$-0.537943\pi$
$853$	1.15272e16	−	1.15272e16i	0.873986	−	0.873986i	0.992904	+	0.118918i	$0.0379425\pi$
$854$		0			0
$855$			5.76105e16i			4.31209i
$856$		0			0
$857$			1.19721e16i			0.884660i	0.896852	+	0.442330i	$0.145848\pi$
$857$			1.19721e16i			0.884660i	−0.896852	+	0.442330i	$0.854152\pi$
$858$		0			0
$859$	−3.69376e14	+	3.69376e14i	−0.0269468	+	0.0269468i	−0.720452	−	0.693505i	$-0.756066\pi$
$859$	−3.69376e14	+	3.69376e14i	−0.0269468	+	0.0269468i	0.693505	+	0.720452i	$0.256066\pi$
$860$		0			0
$861$	9.14420e15	+	9.14420e15i	0.658610	+	0.658610i
$862$		0			0
$863$	6.17590e14			0.0439178			0.0219589	−	0.999759i	$-0.493010\pi$
$863$	6.17590e14			0.0439178			0.0219589	+	0.999759i	$0.493010\pi$
$864$		0			0
$865$	−1.16877e16			−0.820620
$866$		0			0
$867$	−1.67375e16	−	1.67375e16i	−1.16034	−	1.16034i
$868$		0			0
$869$	−8.91283e13	+	8.91283e13i	−0.00610108	+	0.00610108i
$870$		0			0
$871$		−	6.66030e15i		−	0.450188i
$872$		0			0
$873$			1.64956e16i			1.10101i
$874$		0			0
$875$	1.86298e15	−	1.86298e15i	0.122790	−	0.122790i
$876$		0			0
$877$	2.06088e15	+	2.06088e15i	0.134139	+	0.134139i	0.770988	−	0.636849i	$-0.219763\pi$
$877$	2.06088e15	+	2.06088e15i	0.134139	+	0.134139i	−0.636849	+	0.770988i	$0.719763\pi$
$878$		0			0
$879$	−3.27332e16			−2.10402
$880$		0			0
$881$	2.09278e16			1.32848			0.664242	−	0.747517i	$-0.268754\pi$
$881$	2.09278e16			1.32848			0.664242	+	0.747517i	$0.268754\pi$
$882$		0			0
$883$	7.02998e15	+	7.02998e15i	0.440728	+	0.440728i	0.892257	−	0.451529i	$-0.149121\pi$
$883$	7.02998e15	+	7.02998e15i	0.440728	+	0.440728i	−0.451529	+	0.892257i	$0.649121\pi$
$884$		0			0
$885$	−3.89088e16	+	3.89088e16i	−2.40913	+	2.40913i
$886$		0			0
$887$		−	4.94125e15i		−	0.302174i	−0.988520	−	0.151087i	$-0.951723\pi$
$887$		−	4.94125e15i		−	0.302174i	0.988520	−	0.151087i	$-0.0482773\pi$
$888$		0			0
$889$			8.06818e15i			0.487322i
$890$		0			0
$891$	−2.73049e15	+	2.73049e15i	−0.162897	+	0.162897i
$892$		0			0
$893$	2.18583e16	+	2.18583e16i	1.28805	+	1.28805i
$894$		0			0
$895$	−5.79689e15			−0.337418
$896$		0			0
$897$	2.96658e16			1.70568
$898$		0			0
$899$	−6.28950e14	−	6.28950e14i	−0.0357222	−	0.0357222i
$900$		0			0
$901$	−1.54700e15	+	1.54700e15i	−0.0867971	+	0.0867971i
$902$		0			0
$903$		−	4.09128e16i		−	2.26765i
$904$		0			0
$905$			1.07230e16i			0.587151i
$906$		0			0
$907$	4.99180e15	−	4.99180e15i	0.270033	−	0.270033i	−0.559080	−	0.829113i	$-0.688846\pi$
$907$	4.99180e15	−	4.99180e15i	0.270033	−	0.270033i	0.829113	+	0.559080i	$0.188846\pi$
$908$		0			0
$909$	−2.57532e16	−	2.57532e16i	−1.37635	−	1.37635i
$910$		0			0
$911$	1.44152e16			0.761147			0.380574	−	0.924751i	$-0.375727\pi$
$911$	1.44152e16			0.761147			0.380574	+	0.924751i	$0.375727\pi$
$912$		0			0
$913$	−3.53089e14			−0.0184202
$914$		0			0
$915$	1.20309e16	+	1.20309e16i	0.620128	+	0.620128i
$916$		0			0
$917$	−3.99831e15	+	3.99831e15i	−0.203632	+	0.203632i
$918$		0			0
$919$			3.26840e16i			1.64475i	0.568947	+	0.822374i	$0.307351\pi$
$919$			3.26840e16i			1.64475i	−0.568947	+	0.822374i	$0.692649\pi$
$920$		0			0
$921$			2.18674e16i			1.08735i
$922$		0			0
$923$	−3.89581e15	+	3.89581e15i	−0.191420	+	0.191420i
$924$		0			0
$925$	1.94380e15	+	1.94380e15i	0.0943785	+	0.0943785i
$926$		0			0
$927$	3.39272e16			1.62783
$928$		0			0
$929$	−1.75221e16			−0.830806			−0.415403	−	0.909637i	$-0.636359\pi$
$929$	−1.75221e16			−0.830806			−0.415403	+	0.909637i	$0.636359\pi$
$930$		0			0
$931$	3.89576e15	+	3.89576e15i	0.182544	+	0.182544i
$932$		0			0
$933$	−1.87541e16	+	1.87541e16i	−0.868456	+	0.868456i
$934$		0			0
$935$		−	2.11662e15i		−	0.0968678i
$936$		0			0
$937$			7.77977e15i			0.351884i	0.984401	+	0.175942i	$0.0562971\pi$
$937$			7.77977e15i			0.351884i	−0.984401	+	0.175942i	$0.943703\pi$
$938$		0			0
$939$	2.83488e16	−	2.83488e16i	1.26728	−	1.26728i
$940$		0			0
$941$	1.69296e16	+	1.69296e16i	0.748002	+	0.748002i	0.974104	−	0.226101i	$-0.0725981\pi$
$941$	1.69296e16	+	1.69296e16i	0.748002	+	0.748002i	−0.226101	+	0.974104i	$0.572598\pi$
$942$		0			0
$943$	1.89664e16			0.828267
$944$		0			0
$945$	4.06090e16			1.75286
$946$		0			0
$947$	−5.72030e14	−	5.72030e14i	−0.0244058	−	0.0244058i	0.694799	−	0.719204i	$-0.255494\pi$
$947$	−5.72030e14	−	5.72030e14i	−0.0244058	−	0.0244058i	−0.719204	+	0.694799i	$0.755494\pi$
$948$		0			0
$949$	1.52622e16	−	1.52622e16i	0.643654	−	0.643654i
$950$		0			0
$951$		−	1.10806e16i		−	0.461923i
$952$		0			0
$953$		−	4.63612e16i		−	1.91048i	−0.295826	−	0.955242i	$-0.595595\pi$
$953$		−	4.63612e16i		−	1.91048i	0.295826	−	0.955242i	$-0.404405\pi$
$954$		0			0
$955$	6.63342e15	−	6.63342e15i	0.270221	−	0.270221i
$956$		0			0
$957$	1.52243e15	+	1.52243e15i	0.0613086	+	0.0613086i
$958$		0			0
$959$	2.41393e16			0.960996
$960$		0			0
$961$	−5.38493e15			−0.211934
$962$		0			0
$963$	1.92294e16	+	1.92294e16i	0.748208	+	0.748208i
$964$		0			0
$965$	6.92129e15	−	6.92129e15i	0.266248	−	0.266248i
$966$		0			0
$967$		−	3.34077e16i		−	1.27058i	−0.772274	−	0.635289i	$-0.780881\pi$
$967$		−	3.34077e16i		−	1.27058i	0.772274	−	0.635289i	$-0.219119\pi$
$968$		0			0
$969$			6.12198e15i			0.230203i
$970$		0			0
$971$	−1.02287e16	+	1.02287e16i	−0.380288	+	0.380288i	−0.871206	−	0.490918i	$-0.836662\pi$
$971$	−1.02287e16	+	1.02287e16i	−0.380288	+	0.380288i	0.490918	+	0.871206i	$0.336662\pi$
$972$		0			0
$973$	−3.42421e16	−	3.42421e16i	−1.25875	−	1.25875i
$974$		0			0
$975$	−2.63764e16			−0.958715
$976$		0			0
$977$	8.50132e14			0.0305539			0.0152769	−	0.999883i	$-0.495137\pi$
$977$	8.50132e14			0.0305539			0.0152769	+	0.999883i	$0.495137\pi$
$978$		0			0
$979$	1.73381e16	+	1.73381e16i	0.616165	+	0.616165i
$980$		0			0
$981$	2.79994e16	−	2.79994e16i	0.983941	−	0.983941i
$982$		0			0
$983$			3.30602e16i			1.14885i	0.818559	+	0.574423i	$0.194773\pi$
$983$			3.30602e16i			1.14885i	−0.818559	+	0.574423i	$0.805227\pi$
$984$		0			0
$985$		−	4.43218e16i		−	1.52306i
$986$		0			0
$987$	3.66721e16	−	3.66721e16i	1.24621	−	1.24621i
$988$		0			0
$989$	−4.24295e16	−	4.24295e16i	−1.42590	−	1.42590i
$990$		0			0
$991$	2.80284e16			0.931522			0.465761	−	0.884910i	$-0.345781\pi$
$991$	2.80284e16			0.931522			0.465761	+	0.884910i	$0.345781\pi$
$992$		0			0
$993$	−3.42889e16			−1.12702
$994$		0			0
$995$	−4.02937e16	−	4.02937e16i	−1.30982	−	1.30982i
$996$		0			0
$997$	−1.58658e16	+	1.58658e16i	−0.510079	+	0.510079i	−0.914551	−	0.404471i	$-0.867456\pi$
$997$	−1.58658e16	+	1.58658e16i	−0.510079	+	0.510079i	0.404471	+	0.914551i	$0.367456\pi$
$998$		0			0
$999$		−	5.69509e15i		−	0.181088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.12.e.b.33.20		42
4.3	odd	2		128.12.e.a.33.2		42
8.3	odd	2		64.12.e.a.17.20		42
8.5	even	2		16.12.e.a.13.13	yes	42
16.3	odd	4		64.12.e.a.49.20		42
16.5	even	4	inner	128.12.e.b.97.20		42
16.11	odd	4		128.12.e.a.97.2		42
16.13	even	4		16.12.e.a.5.13	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.13	✓	42	16.13	even	4
16.12.e.a.13.13	yes	42	8.5	even	2
64.12.e.a.17.20		42	8.3	odd	2
64.12.e.a.49.20		42	16.3	odd	4
128.12.e.a.33.2		42	4.3	odd	2
128.12.e.a.97.2		42	16.11	odd	4
128.12.e.b.33.20		42	1.1	even	1	trivial
128.12.e.b.97.20		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)

\(f(q)\)	\(=\)	\(q+(491.248 + 491.248i) q^{3} +(-6777.57 + 6777.57i) q^{5} +47511.7i q^{7} +305503. i q^{9} +O(q^{10})\)	\(q+(491.248 + 491.248i) q^{3} +(-6777.57 + 6777.57i) q^{5} +47511.7i q^{7} +305503. i q^{9} +(348627. - 348627. i) q^{11} +(-623712. - 623712. i) q^{13} -6.65894e6 q^{15} -447898. q^{17} +(-1.39118e7 - 1.39118e7i) q^{19} +(-2.33400e7 + 2.33400e7i) q^{21} +4.84106e7i q^{23} -4.30427e7i q^{25} +(-6.30548e7 + 6.30548e7i) q^{27} +(4.44473e6 + 4.44473e6i) q^{29} -1.41505e8 q^{31} +3.42525e8 q^{33} +(-3.22014e8 - 3.22014e8i) q^{35} +(-4.51599e7 + 4.51599e7i) q^{37} -6.12795e8i q^{39} -3.91782e8i q^{41} +(-8.76450e8 + 8.76450e8i) q^{43} +(-2.07057e9 - 2.07057e9i) q^{45} -1.57121e9 q^{47} -2.80034e8 q^{49} +(-2.20029e8 - 2.20029e8i) q^{51} +(3.45392e9 - 3.45392e9i) q^{53} +4.72568e9i q^{55} -1.36683e10i q^{57} +(5.84309e9 - 5.84309e9i) q^{59} +(-1.80673e9 - 1.80673e9i) q^{61} -1.45150e10 q^{63} +8.45450e9 q^{65} +(5.33925e9 + 5.33925e9i) q^{67} +(-2.37816e10 + 2.37816e10i) q^{69} -6.24617e9i q^{71} +2.44700e10i q^{73} +(2.11447e10 - 2.11447e10i) q^{75} +(1.65638e10 + 1.65638e10i) q^{77} -2.55656e8 q^{79} -7.83214e9 q^{81} +(-5.06400e8 - 5.06400e8i) q^{83} +(3.03566e9 - 3.03566e9i) q^{85} +4.36694e9i q^{87} +4.97326e10i q^{89} +(2.96336e10 - 2.96336e10i) q^{91} +(-6.95139e10 - 6.95139e10i) q^{93} +1.88576e11 q^{95} +5.39948e10 q^{97} +(1.06507e11 + 1.06507e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 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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