LMFDB - Embedded newform 128.4.g.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	128.49
Dual form			128.4.g.a.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.57022 + 3.13569i) q^{3} +(-8.03744 + 19.4041i) q^{5} +(1.85119 + 1.85119i) q^{7} +(28.3838 - 28.3838i) q^{9} +O(q^{10})$	\(q+(-7.57022 + 3.13569i) q^{3} +(-8.03744 + 19.4041i) q^{5} +(1.85119 + 1.85119i) q^{7} +(28.3838 - 28.3838i) q^{9} +(-8.63132 - 3.57521i) q^{11} +(-11.5947 - 27.9922i) q^{13} -172.096i q^{15} +7.99555i q^{17} +(-5.76123 - 13.9088i) q^{19} +(-19.8187 - 8.20916i) q^{21} +(-60.2483 + 60.2483i) q^{23} +(-223.530 - 223.530i) q^{25} +(-41.2051 + 99.4779i) q^{27} +(167.485 - 69.3746i) q^{29} +225.749 q^{31} +76.5517 q^{33} +(-50.7995 + 21.0419i) q^{35} +(0.431507 - 1.04175i) q^{37} +(175.549 + 175.549i) q^{39} +(-275.430 + 275.430i) q^{41} +(-257.686 - 106.737i) q^{43} +(322.629 + 778.894i) q^{45} +51.3926i q^{47} -336.146i q^{49} +(-25.0715 - 60.5281i) q^{51} +(-2.98375 - 1.23591i) q^{53} +(138.747 - 138.747i) q^{55} +(87.2275 + 87.2275i) q^{57} +(-101.242 + 244.419i) q^{59} +(-270.238 + 111.936i) q^{61} +105.087 q^{63} +636.355 q^{65} +(-778.765 + 322.575i) q^{67} +(267.173 - 645.012i) q^{69} +(-484.526 - 484.526i) q^{71} +(-212.413 + 212.413i) q^{73} +(2393.10 + 991.252i) q^{75} +(-9.35982 - 22.5966i) q^{77} -593.194i q^{79} +201.524i q^{81} +(-320.510 - 773.780i) q^{83} +(-155.147 - 64.2638i) q^{85} +(-1050.36 + 1050.36i) q^{87} +(435.716 + 435.716i) q^{89} +(30.3548 - 73.2829i) q^{91} +(-1708.97 + 707.879i) q^{93} +316.194 q^{95} -570.125 q^{97} +(-346.467 + 143.511i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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
$3$	−7.57022	+	3.13569i	−1.45689	+	0.603463i	−0.963826	−	0.266531i	$-0.914123\pi$
$3$	−7.57022	+	3.13569i	−1.45689	+	0.603463i	−0.493062	+	0.869994i	$0.664123\pi$
$4$		0			0
$5$	−8.03744	+	19.4041i	−0.718891	+	1.73556i	−0.0424048	+	0.999101i	$0.513502\pi$
$5$	−8.03744	+	19.4041i	−0.718891	+	1.73556i	−0.676486	+	0.736455i	$0.736498\pi$
$6$		0			0
$7$	1.85119	+	1.85119i	0.0999549	+	0.0999549i	0.755316	−	0.655361i	$-0.227483\pi$
$7$	1.85119	+	1.85119i	0.0999549	+	0.0999549i	−0.655361	+	0.755316i	$0.727483\pi$
$8$		0			0
$9$	28.3838	−	28.3838i	1.05125	−	1.05125i
$10$		0			0
$11$	−8.63132	−	3.57521i	−0.236585	−	0.0979969i	0.261241	−	0.965274i	$-0.415868\pi$
$11$	−8.63132	−	3.57521i	−0.236585	−	0.0979969i	−0.497826	+	0.867277i	$0.665868\pi$
$12$		0			0
$13$	−11.5947	−	27.9922i	−0.247369	−	0.597202i	0.750610	−	0.660746i	$-0.229760\pi$
$13$	−11.5947	−	27.9922i	−0.247369	−	0.597202i	−0.997979	+	0.0635434i	$0.979760\pi$
$14$		0			0
$15$		−	172.096i		−	2.96234i
$16$		0			0
$17$			7.99555i			0.114071i	0.998372	+	0.0570355i	$0.0181648\pi$
$17$			7.99555i			0.114071i	−0.998372	+	0.0570355i	$0.981835\pi$
$18$		0			0
$19$	−5.76123	−	13.9088i	−0.0695641	−	0.167942i	0.885274	−	0.465071i	$-0.153971\pi$
$19$	−5.76123	−	13.9088i	−0.0695641	−	0.167942i	−0.954838	+	0.297128i	$0.903971\pi$
$20$		0			0
$21$	−19.8187	−	8.20916i	−0.205942	−	0.0853041i
$22$		0			0
$23$	−60.2483	+	60.2483i	−0.546202	+	0.546202i	−0.925340	−	0.379138i	$-0.876220\pi$
$23$	−60.2483	+	60.2483i	−0.546202	+	0.546202i	0.379138	+	0.925340i	$0.376220\pi$
$24$		0			0
$25$	−223.530	−	223.530i	−1.78824	−	1.78824i
$26$		0			0
$27$	−41.2051	+	99.4779i	−0.293701	+	0.709056i
$28$		0			0
$29$	167.485	−	69.3746i	1.07245	−	0.444225i	0.224598	−	0.974451i	$-0.427893\pi$
$29$	167.485	−	69.3746i	1.07245	−	0.444225i	0.847856	+	0.530226i	$0.177893\pi$
$30$		0			0
$31$	225.749			1.30793			0.653964	−	0.756526i	$-0.273105\pi$
$31$	225.749			1.30793			0.653964	+	0.756526i	$0.273105\pi$
$32$		0			0
$33$	76.5517			0.403816
$34$		0			0
$35$	−50.7995	+	21.0419i	−0.245334	+	0.101621i
$36$		0			0
$37$	0.431507	−	1.04175i	0.00191728	−	0.00462872i	−0.922918	−	0.384997i	$-0.874203\pi$
$37$	0.431507	−	1.04175i	0.00191728	−	0.00462872i	0.924835	+	0.380368i	$0.124203\pi$
$38$		0			0
$39$	175.549	+	175.549i	0.720779	+	0.720779i
$40$		0			0
$41$	−275.430	+	275.430i	−1.04914	+	1.04914i	−0.0504150	+	0.998728i	$0.516054\pi$
$41$	−275.430	+	275.430i	−1.04914	+	1.04914i	−0.998728	+	0.0504150i	$0.983946\pi$
$42$		0			0
$43$	−257.686	−	106.737i	−0.913877	−	0.378540i	−0.124338	−	0.992240i	$-0.539681\pi$
$43$	−257.686	−	106.737i	−0.913877	−	0.378540i	−0.789540	+	0.613700i	$0.789681\pi$
$44$		0			0
$45$	322.629	+	778.894i	1.06877	+	2.58024i
$46$		0			0
$47$			51.3926i			0.159497i	0.996815	+	0.0797487i	$0.0254118\pi$
$47$			51.3926i			0.159497i	−0.996815	+	0.0797487i	$0.974588\pi$
$48$		0			0
$49$		−	336.146i		−	0.980018i
$50$		0			0
$51$	−25.0715	−	60.5281i	−0.0688376	−	0.166189i
$52$		0			0
$53$	−2.98375	−	1.23591i	−0.00773301	−	0.00320312i	0.378814	−	0.925473i	$-0.376332\pi$
$53$	−2.98375	−	1.23591i	−0.00773301	−	0.00320312i	−0.386547	+	0.922270i	$0.626332\pi$
$54$		0			0
$55$	138.747	−	138.747i	0.340158	−	0.340158i
$56$		0			0
$57$	87.2275	+	87.2275i	0.202694	+	0.202694i
$58$		0			0
$59$	−101.242	+	244.419i	−0.223399	+	0.539334i	−0.995347	−	0.0963518i	$-0.969283\pi$
$59$	−101.242	+	244.419i	−0.223399	+	0.539334i	0.771948	+	0.635686i	$0.219283\pi$
$60$		0			0
$61$	−270.238	+	111.936i	−0.567219	+	0.234950i	−0.647816	−	0.761797i	$-0.724317\pi$
$61$	−270.238	+	111.936i	−0.567219	+	0.234950i	0.0805967	+	0.996747i	$0.474317\pi$
$62$		0			0
$63$	105.087			0.210155
$64$		0			0
$65$	636.355			1.21431
$66$		0			0
$67$	−778.765	+	322.575i	−1.42002	+	0.588191i	−0.954866	−	0.297038i	$-0.904001\pi$
$67$	−778.765	+	322.575i	−1.42002	+	0.588191i	−0.465154	+	0.885230i	$0.654001\pi$
$68$		0			0
$69$	267.173	−	645.012i	0.466142	−	1.12537i
$70$		0			0
$71$	−484.526	−	484.526i	−0.809897	−	0.809897i	0.174721	−	0.984618i	$-0.444098\pi$
$71$	−484.526	−	484.526i	−0.809897	−	0.809897i	−0.984618	+	0.174721i	$0.944098\pi$
$72$		0			0
$73$	−212.413	+	212.413i	−0.340563	+	0.340563i	−0.856579	−	0.516016i	$-0.827414\pi$
$73$	−212.413	+	212.413i	−0.340563	+	0.340563i	0.516016	+	0.856579i	$0.327414\pi$
$74$		0			0
$75$	2393.10	+	991.252i	3.68441	+	1.52613i
$76$		0			0
$77$	−9.35982	−	22.5966i	−0.0138526	−	0.0334432i
$78$		0			0
$79$		−	593.194i		−	0.844804i	−0.906409	−	0.422402i	$-0.861187\pi$
$79$		−	593.194i		−	0.844804i	0.906409	−	0.422402i	$-0.138813\pi$
$80$		0			0
$81$			201.524i			0.276438i
$82$		0			0
$83$	−320.510	−	773.780i	−0.423862	−	1.02329i	−0.981197	−	0.193007i	$-0.938176\pi$
$83$	−320.510	−	773.780i	−0.423862	−	1.02329i	0.557335	−	0.830288i	$-0.311824\pi$
$84$		0			0
$85$	−155.147	−	64.2638i	−0.197977	−	0.0820046i
$86$		0			0
$87$	−1050.36	+	1050.36i	−1.29437	+	1.29437i
$88$		0			0
$89$	435.716	+	435.716i	0.518941	+	0.518941i	0.917251	−	0.398310i	$-0.130403\pi$
$89$	435.716	+	435.716i	0.518941	+	0.518941i	−0.398310	+	0.917251i	$0.630403\pi$
$90$		0			0
$91$	30.3548	−	73.2829i	0.0349675	−	0.0844191i
$92$		0			0
$93$	−1708.97	+	707.879i	−1.90551	+	0.789286i
$94$		0			0
$95$	316.194			0.341483
$96$		0			0
$97$	−570.125			−0.596777			−0.298389	−	0.954444i	$-0.596449\pi$
$97$	−570.125			−0.596777			−0.298389	+	0.954444i	$0.596449\pi$
$98$		0			0
$99$	−346.467	+	143.511i	−0.351730	+	0.145691i
$100$		0			0
$101$	356.049	−	859.577i	0.350774	−	0.846843i	−0.645751	−	0.763548i	$-0.723456\pi$
$101$	356.049	−	859.577i	0.350774	−	0.846843i	0.996525	−	0.0832951i	$-0.0265444\pi$
$102$		0			0
$103$	1047.19	+	1047.19i	1.00177	+	1.00177i	0.999998	+	0.00177476i	$0.000564924\pi$
$103$	1047.19	+	1047.19i	1.00177	+	1.00177i	0.00177476	+	0.999998i	$0.499435\pi$
$104$		0			0
$105$	318.583	−	318.583i	0.296100	−	0.296100i
$106$		0			0
$107$	−957.653	−	396.673i	−0.865232	−	0.358391i	−0.0944807	−	0.995527i	$-0.530119\pi$
$107$	−957.653	−	396.673i	−0.865232	−	0.358391i	−0.770752	+	0.637136i	$0.780119\pi$
$108$		0			0
$109$	−283.303	−	683.954i	−0.248950	−	0.601017i	0.749166	−	0.662382i	$-0.230455\pi$
$109$	−283.303	−	683.954i	−0.248950	−	0.601017i	−0.998115	+	0.0613651i	$0.980455\pi$
$110$		0			0
$111$			9.23934i			0.00790054i
$112$		0			0
$113$		−	984.044i		−	0.819213i	−0.912262	−	0.409606i	$-0.865666\pi$
$113$		−	984.044i		−	0.819213i	0.912262	−	0.409606i	$-0.134334\pi$
$114$		0			0
$115$	−684.822	−	1653.31i	−0.555304	−	1.34062i
$116$		0			0
$117$	−1123.63	−	465.421i	−0.887856	−	0.367762i
$118$		0			0
$119$	−14.8013	+	14.8013i	−0.0114020	+	0.0114020i
$120$		0			0
$121$	−879.442	−	879.442i	−0.660737	−	0.660737i
$122$		0			0
$123$	1221.40	−	2948.72i	0.895366	−	2.16160i
$124$		0			0
$125$	3708.51	−	1536.11i	2.65359	−	1.09915i
$126$		0			0
$127$	−1313.80			−0.917962			−0.458981	−	0.888446i	$-0.651785\pi$
$127$	−1313.80			−0.917962			−0.458981	+	0.888446i	$0.651785\pi$
$128$		0			0
$129$	2285.43			1.55985
$130$		0			0
$131$	2259.39	−	935.870i	1.50690	−	0.624178i	0.531984	−	0.846755i	$-0.321447\pi$
$131$	2259.39	−	935.870i	1.50690	−	0.624178i	0.974915	+	0.222577i	$0.0714467\pi$
$132$		0			0
$133$	15.0828	−	36.4131i	0.00983341	−	0.0237399i
$134$		0			0
$135$	−1599.10	−	1599.10i	−1.01947	−	1.01947i
$136$		0			0
$137$	−1675.97	+	1675.97i	−1.04516	+	1.04516i	−0.0462334	+	0.998931i	$0.514722\pi$
$137$	−1675.97	+	1675.97i	−1.04516	+	1.04516i	−0.998931	+	0.0462334i	$0.985278\pi$
$138$		0			0
$139$	−1548.84	−	641.550i	−0.945114	−	0.391479i	−0.143722	−	0.989618i	$-0.545907\pi$
$139$	−1548.84	−	641.550i	−0.945114	−	0.391479i	−0.801392	+	0.598139i	$0.795907\pi$
$140$		0			0
$141$	−161.151	−	389.053i	−0.0962508	−	0.232370i
$142$		0			0
$143$			283.063i			0.165531i
$144$		0			0
$145$			3807.49i			2.18065i
$146$		0			0
$147$	1054.05	+	2544.70i	0.591405	+	1.42778i
$148$		0			0
$149$	−1185.43	−	491.023i	−0.651775	−	0.269974i	0.0321978	−	0.999482i	$-0.489749\pi$
$149$	−1185.43	−	491.023i	−0.651775	−	0.269974i	−0.683973	+	0.729507i	$0.739749\pi$
$150$		0			0
$151$	−1122.70	+	1122.70i	−0.605061	+	0.605061i	−0.941651	−	0.336590i	$-0.890726\pi$
$151$	−1122.70	+	1122.70i	−0.605061	+	0.605061i	0.336590	+	0.941651i	$0.390726\pi$
$152$		0			0
$153$	226.944	+	226.944i	0.119917	+	0.119917i
$154$		0			0
$155$	−1814.45	+	4380.46i	−0.940257	+	2.26998i
$156$		0			0
$157$	−1738.24	+	720.001i	−0.883608	+	0.366002i	−0.777895	−	0.628394i	$-0.783712\pi$
$157$	−1738.24	+	720.001i	−0.883608	+	0.366002i	−0.105713	+	0.994397i	$0.533712\pi$
$158$		0			0
$159$	26.4630			0.0131991
$160$		0			0
$161$	−223.062			−0.109191
$162$		0			0
$163$	2535.60	−	1050.28i	1.21843	−	0.504690i	0.321519	−	0.946903i	$-0.395807\pi$
$163$	2535.60	−	1050.28i	1.21843	−	0.504690i	0.896910	+	0.442214i	$0.145807\pi$
$164$		0			0
$165$	−615.280	+	1485.42i	−0.290300	+	0.700846i
$166$		0			0
$167$	1815.07	+	1815.07i	0.841042	+	0.841042i	0.988995	−	0.147952i	$-0.0472682\pi$
$167$	1815.07	+	1815.07i	0.841042	+	0.841042i	−0.147952	+	0.988995i	$0.547268\pi$
$168$		0			0
$169$	904.390	−	904.390i	0.411648	−	0.411648i
$170$		0			0
$171$	−558.311	−	231.260i	−0.249679	−	0.103420i
$172$		0			0
$173$	1289.74	+	3113.71i	0.566805	+	1.36839i	0.904234	+	0.427037i	$0.140443\pi$
$173$	1289.74	+	3113.71i	0.566805	+	1.36839i	−0.337429	+	0.941351i	$0.609557\pi$
$174$		0			0
$175$		−	827.595i		−	0.357488i
$176$		0			0
$177$		−	2167.77i		−	0.920563i
$178$		0			0
$179$	1147.04	+	2769.21i	0.478961	+	1.15631i	0.960097	+	0.279668i	$0.0902244\pi$
$179$	1147.04	+	2769.21i	0.478961	+	1.15631i	−0.481136	+	0.876646i	$0.659776\pi$
$180$		0			0
$181$	979.116	+	405.563i	0.402083	+	0.166548i	0.574555	−	0.818466i	$-0.305175\pi$
$181$	979.116	+	405.563i	0.402083	+	0.166548i	−0.172471	+	0.985015i	$0.555175\pi$
$182$		0			0
$183$	1694.76	−	1694.76i	0.684592	−	0.684592i
$184$		0			0
$185$	16.7460	+	16.7460i	0.00665509	+	0.00665509i
$186$		0			0
$187$	28.5858	−	69.0122i	0.0111786	−	0.0269875i
$188$		0			0
$189$	−260.431	+	107.874i	−0.100231	+	0.0415168i
$190$		0			0
$191$	2800.50			1.06093			0.530464	−	0.847707i	$-0.322018\pi$
$191$	2800.50			1.06093			0.530464	+	0.847707i	$0.322018\pi$
$192$		0			0
$193$	301.516			0.112454			0.0562269	−	0.998418i	$-0.482093\pi$
$193$	301.516			0.112454			0.0562269	+	0.998418i	$0.482093\pi$
$194$		0			0
$195$	−4817.34	+	1995.41i	−1.76911	+	0.732791i
$196$		0			0
$197$	−1800.02	+	4345.63i	−0.650995	+	1.57164i	0.160342	+	0.987061i	$0.448740\pi$
$197$	−1800.02	+	4345.63i	−0.650995	+	1.57164i	−0.811337	+	0.584579i	$0.801260\pi$
$198$		0			0
$199$	−437.430	−	437.430i	−0.155822	−	0.155822i	0.624890	−	0.780713i	$-0.285144\pi$
$199$	−437.430	−	437.430i	−0.155822	−	0.155822i	−0.780713	+	0.624890i	$0.785144\pi$
$200$		0			0
$201$	4883.93	−	4883.93i	1.71386	−	1.71386i
$202$		0			0
$203$	438.472	+	181.621i	0.151600	+	0.0627946i
$204$		0			0
$205$	−3130.72	−	7558.22i	−1.06663	−	2.57507i
$206$		0			0
$207$			3420.15i			1.14839i
$208$		0			0
$209$			140.649i			0.0465498i
$210$		0			0
$211$	188.416	+	454.876i	0.0614744	+	0.148412i	0.951632	−	0.307241i	$-0.0994057\pi$
$211$	188.416	+	454.876i	0.0614744	+	0.148412i	−0.890157	+	0.455653i	$0.849406\pi$
$212$		0			0
$213$	5187.29	+	2148.65i	1.66867	+	0.691187i
$214$		0			0
$215$	4142.27	−	4142.27i	1.31396	−	1.31396i
$216$		0			0
$217$	417.905	+	417.905i	0.130734	+	0.130734i
$218$		0			0
$219$	941.952	−	2274.07i	0.290645	−	0.701679i
$220$		0			0
$221$	223.813	−	92.7063i	0.0681235	−	0.0282177i
$222$		0			0
$223$	−4202.52			−1.26198			−0.630990	−	0.775791i	$-0.717351\pi$
$223$	−4202.52			−1.26198			−0.630990	+	0.775791i	$0.717351\pi$
$224$		0			0
$225$	−12689.3			−3.75978
$226$		0			0
$227$	−1291.98	+	535.157i	−0.377762	+	0.156474i	−0.563482	−	0.826129i	$-0.690538\pi$
$227$	−1291.98	+	535.157i	−0.377762	+	0.156474i	0.185719	+	0.982603i	$0.440538\pi$
$228$		0			0
$229$	−336.893	+	813.331i	−0.0972161	+	0.234700i	−0.965004	−	0.262234i	$-0.915541\pi$
$229$	−336.893	+	813.331i	−0.0972161	+	0.234700i	0.867788	+	0.496934i	$0.165541\pi$
$230$		0			0
$231$	141.712	+	141.712i	0.0403634	+	0.0403634i
$232$		0			0
$233$	−2104.79	+	2104.79i	−0.591799	+	0.591799i	−0.938117	−	0.346318i	$-0.887432\pi$
$233$	−2104.79	+	2104.79i	−0.591799	+	0.591799i	0.346318	+	0.938117i	$0.387432\pi$
$234$		0			0
$235$	−997.227	−	413.065i	−0.276817	−	0.114661i
$236$		0			0
$237$	1860.07	+	4490.60i	0.509808	+	1.23079i
$238$		0			0
$239$		−	1907.72i		−	0.516317i	−0.966103	−	0.258159i	$-0.916884\pi$
$239$		−	1907.72i		−	0.516317i	0.966103	−	0.258159i	$-0.0831157\pi$
$240$		0			0
$241$		−	2893.81i		−	0.773472i	−0.922190	−	0.386736i	$-0.873602\pi$
$241$		−	2893.81i		−	0.773472i	0.922190	−	0.386736i	$-0.126398\pi$
$242$		0			0
$243$	−1744.45	−	4211.48i	−0.460521	−	1.11180i
$244$		0			0
$245$	6522.62	+	2701.76i	1.70088	+	0.704526i
$246$		0			0
$247$	−322.539	+	322.539i	−0.0830876	+	0.0830876i
$248$		0			0
$249$	4852.66	+	4852.66i	1.23504	+	1.23504i
$250$		0			0
$251$	−299.796	+	723.771i	−0.0753902	+	0.182008i	−0.957082	−	0.289818i	$-0.906405\pi$
$251$	−299.796	+	723.771i	−0.0753902	+	0.182008i	0.881691	+	0.471826i	$0.156405\pi$
$252$		0			0
$253$	735.422	−	304.622i	0.182749	−	0.0756973i
$254$		0			0
$255$	1376.00			0.337917
$256$		0			0
$257$	−1327.65			−0.322243			−0.161122	−	0.986935i	$-0.551511\pi$
$257$	−1327.65			−0.322243			−0.161122	+	0.986935i	$0.551511\pi$
$258$		0			0
$259$	2.72728	−	1.12968i	0.000654305	−	0.000271022i
$260$		0			0
$261$	2784.74	−	6722.96i	0.660426	−	1.59441i
$262$		0			0
$263$	−2807.57	−	2807.57i	−0.658258	−	0.658258i	0.296710	−	0.954968i	$-0.404111\pi$
$263$	−2807.57	−	2807.57i	−0.658258	−	0.658258i	−0.954968	+	0.296710i	$0.904111\pi$
$264$		0			0
$265$	47.9634	−	47.9634i	0.0111184	−	0.0111184i
$266$		0			0
$267$	−4664.73	−	1932.19i	−1.06920	−	0.442878i
$268$		0			0
$269$	−916.467	−	2212.55i	−0.207725	−	0.501492i	0.785339	−	0.619065i	$-0.212488\pi$
$269$	−916.467	−	2212.55i	−0.207725	−	0.501492i	−0.993064	+	0.117573i	$0.962488\pi$
$270$		0			0
$271$			6184.98i			1.38639i	0.720752	+	0.693193i	$0.243797\pi$
$271$			6184.98i			1.38639i	−0.720752	+	0.693193i	$0.756203\pi$
$272$		0			0
$273$			649.951i			0.144091i
$274$		0			0
$275$	1130.19	+	2728.53i	0.247830	+	0.598315i
$276$		0			0
$277$	−2920.62	−	1209.76i	−0.633512	−	0.262409i	0.0427323	−	0.999087i	$-0.486394\pi$
$277$	−2920.62	−	1209.76i	−0.633512	−	0.262409i	−0.676245	+	0.736677i	$0.736394\pi$
$278$		0			0
$279$	6407.61	−	6407.61i	1.37496	−	1.37496i
$280$		0			0
$281$	−6139.54	−	6139.54i	−1.30340	−	1.30340i	−0.926087	−	0.377309i	$-0.876849\pi$
$281$	−6139.54	−	6139.54i	−1.30340	−	1.30340i	−0.377309	−	0.926087i	$-0.623151\pi$
$282$		0			0
$283$	511.714	−	1235.39i	0.107485	−	0.259492i	−0.860981	−	0.508637i	$-0.830150\pi$
$283$	511.714	−	1235.39i	0.107485	−	0.259492i	0.968466	+	0.249145i	$0.0801496\pi$
$284$		0			0
$285$	−2393.66	+	991.486i	−0.497502	+	0.206072i
$286$		0			0
$287$	−1019.75			−0.209734
$288$		0			0
$289$	4849.07			0.986988
$290$		0			0
$291$	4315.97	−	1787.73i	0.869438	−	0.360133i
$292$		0			0
$293$	15.2449	−	36.8044i	0.00303964	−	0.00733835i	−0.922352	−	0.386350i	$-0.873736\pi$
$293$	15.2449	−	36.8044i	0.00303964	−	0.00733835i	0.925392	+	0.379011i	$0.123736\pi$
$294$		0			0
$295$	−3929.02	−	3929.02i	−0.775445	−	0.775445i
$296$		0			0
$297$	711.308	−	711.308i	0.138971	−	0.138971i
$298$		0			0
$299$	2385.04	+	987.917i	0.461306	+	0.191079i
$300$		0			0
$301$	−279.435	−	674.616i	−0.0535095	−	0.129183i
$302$		0			0
$303$			7623.64i			1.44544i
$304$		0			0
$305$		−	6143.40i		−	1.15334i
$306$		0			0
$307$	44.0533	+	106.354i	0.00818976	+	0.0197718i	0.927922	−	0.372776i	$-0.121594\pi$
$307$	44.0533	+	106.354i	0.00818976	+	0.0197718i	−0.919732	+	0.392547i	$0.871594\pi$
$308$		0			0
$309$	−11211.1	−	4643.79i	−2.06401	−	0.854939i
$310$		0			0
$311$	−3248.93	+	3248.93i	−0.592379	+	0.592379i	−0.938273	−	0.345895i	$-0.887575\pi$
$311$	−3248.93	+	3248.93i	−0.592379	+	0.592379i	0.345895	+	0.938273i	$0.387575\pi$
$312$		0			0
$313$	−1997.72	−	1997.72i	−0.360760	−	0.360760i	0.503333	−	0.864093i	$-0.332107\pi$
$313$	−1997.72	−	1997.72i	−0.360760	−	0.360760i	−0.864093	+	0.503333i	$0.832107\pi$
$314$		0			0
$315$	−844.635	+	2039.13i	−0.151079	+	0.364736i
$316$		0			0
$317$	2070.39	−	857.583i	0.366829	−	0.151945i	−0.191652	−	0.981463i	$-0.561385\pi$
$317$	2070.39	−	857.583i	0.366829	−	0.151945i	0.558481	+	0.829518i	$0.311385\pi$
$318$		0			0
$319$	−1693.64			−0.297260
$320$		0			0
$321$	8493.48			1.47682
$322$		0			0
$323$	111.209	−	46.0642i	0.0191574	−	0.00793524i
$324$		0			0
$325$	−3665.33	+	8848.88i	−0.625587	+	1.51030i
$326$		0			0
$327$	4289.33	+	4289.33i	0.725384	+	0.725384i
$328$		0			0
$329$	−95.1375	+	95.1375i	−0.0159425	+	0.0159425i
$330$		0			0
$331$	−8070.63	−	3342.97i	−1.34019	−	0.555124i	−0.406644	−	0.913587i	$-0.633301\pi$
$331$	−8070.63	−	3342.97i	−1.34019	−	0.555124i	−0.933544	+	0.358463i	$0.883301\pi$
$332$		0			0
$333$	−17.3210	−	41.8166i	−0.00285040	−	0.00688148i
$334$		0			0
$335$		−	17703.9i		−	2.88737i
$336$		0			0
$337$			4867.88i			0.786856i	0.919356	+	0.393428i	$0.128711\pi$
$337$			4867.88i			0.786856i	−0.919356	+	0.393428i	$0.871289\pi$
$338$		0			0
$339$	3085.65	+	7449.42i	0.494365	+	1.19350i
$340$		0			0
$341$	−1948.51	−	807.101i	−0.309437	−	0.128173i
$342$		0			0
$343$	1257.23	−	1257.23i	0.197913	−	0.197913i
$344$		0			0
$345$	10368.5	+	10368.5i	1.61803	+	1.61803i
$346$		0			0
$347$	1842.65	−	4448.54i	0.285067	−	0.688214i	−0.714872	−	0.699256i	$-0.753515\pi$
$347$	1842.65	−	4448.54i	0.285067	−	0.688214i	0.999939	+	0.0110421i	$0.00351487\pi$
$348$		0			0
$349$	−2708.99	+	1122.10i	−0.415498	+	0.172105i	−0.580632	−	0.814166i	$-0.697194\pi$
$349$	−2708.99	+	1122.10i	−0.415498	+	0.172105i	0.165134	+	0.986271i	$0.447194\pi$
$350$		0			0
$351$	3262.36			0.496103
$352$		0			0
$353$	−906.516			−0.136683			−0.0683413	−	0.997662i	$-0.521771\pi$
$353$	−906.516			−0.136683			−0.0683413	+	0.997662i	$0.521771\pi$
$354$		0			0
$355$	13296.2	−	5507.45i	1.98785	−	0.823394i
$356$		0			0
$357$	65.6368	−	158.461i	0.00973072	−	0.0234920i
$358$		0			0
$359$	5648.41	+	5648.41i	0.830395	+	0.830395i	0.987571	−	0.157176i	$-0.0502389\pi$
$359$	5648.41	+	5648.41i	0.830395	+	0.830395i	−0.157176	+	0.987571i	$0.550239\pi$
$360$		0			0
$361$	4689.78	−	4689.78i	0.683741	−	0.683741i
$362$		0			0
$363$	9415.22	+	3899.91i	1.36135	+	0.563890i
$364$		0			0
$365$	−2414.43	−	5828.94i	−0.346238	−	0.835893i
$366$		0			0
$367$			1805.15i			0.256752i	0.991726	+	0.128376i	$0.0409765\pi$
$367$			1805.15i			0.256752i	−0.991726	+	0.128376i	$0.959024\pi$
$368$		0			0
$369$			15635.5i			2.20582i
$370$		0			0
$371$	−3.23558	−	7.81139i	−0.000452785	−	0.00109312i
$372$		0			0
$373$	6690.32	+	2771.22i	0.928718	+	0.384688i	0.795192	−	0.606358i	$-0.207370\pi$
$373$	6690.32	+	2771.22i	0.928718	+	0.384688i	0.133526	+	0.991045i	$0.457370\pi$
$374$		0			0
$375$	−23257.4	+	23257.4i	−3.20269	+	3.20269i
$376$		0			0
$377$	−3883.89	−	3883.89i	−0.530585	−	0.530585i
$378$		0			0
$379$	−4596.66	+	11097.3i	−0.622993	+	1.50404i	0.225179	+	0.974317i	$0.427703\pi$
$379$	−4596.66	+	11097.3i	−0.622993	+	1.50404i	−0.848172	+	0.529721i	$0.822297\pi$
$380$		0			0
$381$	9945.77	−	4119.67i	1.33737	−	0.553956i
$382$		0			0
$383$	−13606.3			−1.81528			−0.907639	−	0.419751i	$-0.862117\pi$
$383$	−13606.3			−1.81528			−0.907639	+	0.419751i	$0.862117\pi$
$384$		0			0
$385$	513.696			0.0680010
$386$		0			0
$387$	−10343.7	+	4284.49i	−1.35865	+	0.562773i
$388$		0			0
$389$	1595.62	−	3852.17i	0.207972	−	0.502090i	−0.785131	−	0.619329i	$-0.787405\pi$
$389$	1595.62	−	3852.17i	0.207972	−	0.502090i	0.993104	+	0.117240i	$0.0374046\pi$
$390$		0			0
$391$	−481.718	−	481.718i	−0.0623058	−	0.0623058i
$392$		0			0
$393$	−14169.5	+	14169.5i	−1.81872	+	1.81872i
$394$		0			0
$395$	11510.4	+	4767.76i	1.46620	+	0.607322i
$396$		0			0
$397$	2917.91	+	7044.45i	0.368881	+	0.890557i	0.993934	+	0.109975i	$0.0350770\pi$
$397$	2917.91	+	7044.45i	0.368881	+	0.890557i	−0.625054	+	0.780582i	$0.714923\pi$
$398$		0			0
$399$			322.950i			0.0405206i
$400$		0			0
$401$			11807.9i			1.47047i	0.677810	+	0.735237i	$0.262929\pi$
$401$			11807.9i			1.47047i	−0.677810	+	0.735237i	$0.737071\pi$
$402$		0			0
$403$	−2617.50	−	6319.21i	−0.323541	−	0.781098i
$404$		0			0
$405$	−3910.38	−	1619.73i	−0.479774	−	0.198729i
$406$		0			0
$407$	−7.44895	+	7.44895i	−0.000907200	+	0.000907200i
$408$		0			0
$409$	−1683.88	−	1683.88i	−0.203576	−	0.203576i	0.597954	−	0.801530i	$-0.295980\pi$
$409$	−1683.88	−	1683.88i	−0.203576	−	0.203576i	−0.801530	+	0.597954i	$0.795980\pi$
$410$		0			0
$411$	7432.12	−	17942.7i	0.891970	−	2.15341i
$412$		0			0
$413$	−639.885	+	265.049i	−0.0762390	+	0.0315792i
$414$		0			0
$415$	17590.6			2.08070
$416$		0			0
$417$	13736.8			1.61317
$418$		0			0
$419$	−8440.17	+	3496.03i	−0.984080	+	0.407619i	−0.815935	−	0.578143i	$-0.803778\pi$
$419$	−8440.17	+	3496.03i	−0.984080	+	0.407619i	−0.168145	+	0.985762i	$0.553778\pi$
$420$		0			0
$421$	919.284	−	2219.35i	0.106421	−	0.256922i	−0.861695	−	0.507427i	$-0.830597\pi$
$421$	919.284	−	2219.35i	0.106421	−	0.256922i	0.968115	+	0.250505i	$0.0805966\pi$
$422$		0			0
$423$	1458.71	+	1458.71i	0.167672	+	0.167672i
$424$		0			0
$425$	1787.25	−	1787.25i	0.203987	−	0.203987i
$426$		0			0
$427$	−707.476	−	293.046i	−0.0801807	−	0.0332120i
$428$		0			0
$429$	−887.596	−	2142.85i	−0.0998917	−	0.241160i
$430$		0			0
$431$		−	8878.13i		−	0.992215i	−0.868261	−	0.496107i	$-0.834762\pi$
$431$		−	8878.13i		−	0.992215i	0.868261	−	0.496107i	$-0.165238\pi$
$432$		0			0
$433$		−	6784.43i		−	0.752977i	−0.926421	−	0.376489i	$-0.877131\pi$
$433$		−	6784.43i		−	0.752977i	0.926421	−	0.376489i	$-0.122869\pi$
$434$		0			0
$435$	−11939.1	−	28823.5i	−1.31594	−	3.17697i
$436$		0			0
$437$	1185.09	+	490.880i	0.129726	+	0.0537345i
$438$		0			0
$439$	832.203	−	832.203i	0.0904758	−	0.0904758i	−0.660420	−	0.750896i	$-0.729622\pi$
$439$	832.203	−	832.203i	0.0904758	−	0.0904758i	0.750896	+	0.660420i	$0.229622\pi$
$440$		0			0
$441$	−9541.09	−	9541.09i	−1.03024	−	1.03024i
$442$		0			0
$443$	−1698.13	+	4099.65i	−0.182123	+	0.439685i	−0.988404	−	0.151849i	$-0.951477\pi$
$443$	−1698.13	+	4099.65i	−0.182123	+	0.439685i	0.806280	+	0.591534i	$0.201477\pi$
$444$		0			0
$445$	−11956.7	+	4952.63i	−1.27371	+	0.527590i
$446$		0			0
$447$	10513.7			1.11248
$448$		0			0
$449$	−8435.82			−0.886661			−0.443331	−	0.896358i	$-0.646203\pi$
$449$	−8435.82			−0.886661			−0.443331	+	0.896358i	$0.646203\pi$
$450$		0			0
$451$	3362.04	−	1392.60i	0.351025	−	0.145399i
$452$		0			0
$453$	4978.66	−	12019.5i	0.516375	−	1.24664i
$454$		0			0
$455$	1178.01	+	1178.01i	0.121376	+	0.121376i
$456$		0			0
$457$	8504.55	−	8504.55i	0.870517	−	0.870517i	−0.122012	−	0.992529i	$-0.538935\pi$
$457$	8504.55	−	8504.55i	0.870517	−	0.870517i	0.992529	+	0.122012i	$0.0389346\pi$
$458$		0			0
$459$	−795.381	−	329.457i	−0.0808828	−	0.0335027i
$460$		0			0
$461$	6333.87	+	15291.3i	0.639908	+	1.54487i	0.826801	+	0.562494i	$0.190158\pi$
$461$	6333.87	+	15291.3i	0.639908	+	1.54487i	−0.186893	+	0.982380i	$0.559842\pi$
$462$		0			0
$463$			9928.12i			0.996542i	0.867021	+	0.498271i	$0.166031\pi$
$463$			9928.12i			0.996542i	−0.867021	+	0.498271i	$0.833969\pi$
$464$		0			0
$465$		−	38850.6i		−	3.87452i
$466$		0			0
$467$	4268.66	+	10305.4i	0.422976	+	1.02115i	0.981465	+	0.191643i	$0.0613815\pi$
$467$	4268.66	+	10305.4i	0.422976	+	1.02115i	−0.558489	+	0.829512i	$0.688619\pi$
$468$		0			0
$469$	−2038.79	−	844.495i	−0.200731	−	0.0831453i
$470$		0			0
$471$	10901.1	−	10901.1i	1.06645	−	1.06645i
$472$		0			0
$473$	1842.56	+	1842.56i	0.179114	+	0.179114i
$474$		0			0
$475$	−1821.24	+	4396.86i	−0.175925	+	0.424720i
$476$		0			0
$477$	−119.770	+	49.6102i	−0.0114966	+	0.00476205i
$478$		0			0
$479$	−11404.9			−1.08790			−0.543949	−	0.839118i	$-0.683072\pi$
$479$	−11404.9			−1.08790			−0.543949	+	0.839118i	$0.683072\pi$
$480$		0			0
$481$	−34.1640			−0.00323856
$482$		0			0
$483$	1688.63	−	699.453i	0.159079	−	0.0658928i
$484$		0			0
$485$	4582.35	−	11062.8i	0.429018	−	1.03574i
$486$		0			0
$487$	−821.653	−	821.653i	−0.0764531	−	0.0764531i	0.667846	−	0.744299i	$-0.267216\pi$
$487$	−821.653	−	821.653i	−0.0764531	−	0.0764531i	−0.744299	+	0.667846i	$0.767216\pi$
$488$		0			0
$489$	−15901.7	+	15901.7i	−1.47055	+	1.47055i
$490$		0			0
$491$	3012.33	+	1247.75i	0.276873	+	0.114685i	0.516800	−	0.856106i	$-0.327123\pi$
$491$	3012.33	+	1247.75i	0.276873	+	0.114685i	−0.239926	+	0.970791i	$0.577123\pi$
$492$		0			0
$493$	554.688	+	1339.14i	0.0506732	+	0.122336i
$494$		0			0
$495$		−	7876.35i		−	0.715183i
$496$		0			0
$497$		−	1793.90i		−	0.161906i
$498$		0			0
$499$	3857.50	+	9312.83i	0.346063	+	0.835470i	0.997077	+	0.0764045i	$0.0243440\pi$
$499$	3857.50	+	9312.83i	0.346063	+	0.835470i	−0.651014	+	0.759066i	$0.725656\pi$
$500$		0			0
$501$	−19431.9	−	8048.97i	−1.73284	−	0.717767i
$502$		0			0
$503$	668.327	−	668.327i	0.0592430	−	0.0592430i	−0.676865	−	0.736108i	$-0.736662\pi$
$503$	668.327	−	668.327i	0.0592430	−	0.0592430i	0.736108	+	0.676865i	$0.236662\pi$
$504$		0			0
$505$	13817.6	+	13817.6i	1.21758	+	1.21758i
$506$		0			0
$507$	−4010.54	+	9682.31i	−0.351311	+	0.848139i
$508$		0			0
$509$	−9826.87	+	4070.42i	−0.855733	+	0.354456i	−0.767037	−	0.641602i	$-0.778270\pi$
$509$	−9826.87	+	4070.42i	−0.855733	+	0.354456i	−0.0886960	+	0.996059i	$0.528270\pi$
$510$		0			0
$511$	−786.434			−0.0680818
$512$		0			0
$513$	1621.01			0.139512
$514$		0			0
$515$	−28736.5	+	11903.0i	−2.45880	+	1.01847i
$516$		0			0
$517$	183.739	−	443.586i	0.0156302	−	0.0377348i
$518$		0			0
$519$	−19527.2	−	19527.2i	−1.65154	−	1.65154i
$520$		0			0
$521$	−4723.06	+	4723.06i	−0.397161	+	0.397161i	−0.877231	−	0.480069i	$-0.840612\pi$
$521$	−4723.06	+	4723.06i	−0.397161	+	0.397161i	0.480069	+	0.877231i	$0.340612\pi$
$522$		0			0
$523$	9785.16	+	4053.14i	0.818117	+	0.338875i	0.752187	−	0.658949i	$-0.228999\pi$
$523$	9785.16	+	4053.14i	0.818117	+	0.338875i	0.0659293	+	0.997824i	$0.478999\pi$
$524$		0			0
$525$	2595.08	+	6265.07i	0.215730	+	0.520819i
$526$		0			0
$527$			1804.99i			0.149197i
$528$		0			0
$529$			4907.29i			0.403328i
$530$		0			0
$531$	4063.92	+	9811.17i	0.332126	+	0.801824i
$532$		0			0
$533$	10903.4	+	4516.34i	0.886077	+	0.367025i
$534$		0			0
$535$	15394.2	−	15394.2i	1.24402	−	1.24402i
$536$		0			0
$537$	−17366.7	−	17366.7i	−1.39559	−	1.39559i
$538$		0			0
$539$	−1201.79	+	2901.38i	−0.0960387	+	0.231858i
$540$		0			0
$541$	16214.3	−	6716.19i	1.28855	−	0.533737i	0.370000	−	0.929032i	$-0.379358\pi$
$541$	16214.3	−	6716.19i	1.28855	−	0.533737i	0.918554	+	0.395295i	$0.129358\pi$
$542$		0			0
$543$	−8683.83			−0.686297
$544$		0			0
$545$	15548.5			1.22207
$546$		0			0
$547$	10437.6	−	4323.38i	0.815865	−	0.337942i	0.0645734	−	0.997913i	$-0.479431\pi$
$547$	10437.6	−	4323.38i	0.815865	−	0.337942i	0.751291	+	0.659971i	$0.229431\pi$
$548$		0			0
$549$	−4493.19	+	10847.5i	−0.349298	+	0.843280i
$550$		0			0
$551$	−1929.84	−	1929.84i	−0.149209	−	0.149209i
$552$		0			0
$553$	1098.11	−	1098.11i	0.0844423	−	0.0844423i
$554$		0			0
$555$	−179.281	−	74.2607i	−0.0137118	−	0.00567962i
$556$		0			0
$557$	4647.08	+	11219.0i	0.353506	+	0.853440i	0.996182	+	0.0873013i	$0.0278243\pi$
$557$	4647.08	+	11219.0i	0.353506	+	0.853440i	−0.642676	+	0.766138i	$0.722176\pi$
$558$		0			0
$559$			8450.77i			0.639409i
$560$		0			0
$561$			612.073i			0.0460637i
$562$		0			0
$563$	−8530.33	−	20594.0i	−0.638563	−	1.54163i	−0.828595	−	0.559849i	$-0.810859\pi$
$563$	−8530.33	−	20594.0i	−0.638563	−	1.54163i	0.190032	−	0.981778i	$-0.439141\pi$
$564$		0			0
$565$	19094.5	+	7909.19i	1.42179	+	0.588924i
$566$		0			0
$567$	−373.059	+	373.059i	−0.0276314	+	0.0276314i
$568$		0			0
$569$	1310.30	+	1310.30i	0.0965389	+	0.0965389i	0.753727	−	0.657188i	$-0.228254\pi$
$569$	1310.30	+	1310.30i	0.0965389	+	0.0965389i	−0.657188	+	0.753727i	$0.728254\pi$
$570$		0			0
$571$	6582.43	−	15891.4i	0.482427	−	1.16468i	−0.476026	−	0.879431i	$-0.657923\pi$
$571$	6582.43	−	15891.4i	0.482427	−	1.16468i	0.958453	−	0.285251i	$-0.0920769\pi$
$572$		0			0
$573$	−21200.4	+	8781.50i	−1.54565	+	0.640231i
$574$		0			0
$575$	26934.7			1.95348
$576$		0			0
$577$	−16870.7			−1.21722			−0.608609	−	0.793470i	$-0.708272\pi$
$577$	−16870.7			−1.21722			−0.608609	+	0.793470i	$0.708272\pi$
$578$		0			0
$579$	−2282.54	+	945.458i	−0.163833	+	0.0678617i
$580$		0			0
$581$	839.089	−	2025.74i	0.0599162	−	0.144650i
$582$		0			0
$583$	21.3350	+	21.3350i	0.00151562	+	0.00151562i
$584$		0			0
$585$	18062.1	−	18062.1i	1.27654	−	1.27654i
$586$		0			0
$587$	−12653.1	−	5241.10i	−0.889694	−	0.368523i	−0.109445	−	0.993993i	$-0.534908\pi$
$587$	−12653.1	−	5241.10i	−0.889694	−	0.368523i	−0.780249	+	0.625469i	$0.784908\pi$
$588$		0			0
$589$	−1300.59	−	3139.91i	−0.0909848	−	0.219657i
$590$		0			0
$591$		−	38541.6i		−	2.68256i
$592$		0			0
$593$		−	14304.6i		−	0.990586i	−0.868726	−	0.495293i	$-0.835061\pi$
$593$		−	14304.6i		−	0.990586i	0.868726	−	0.495293i	$-0.164939\pi$
$594$		0			0
$595$	−168.241	−	406.171i	−0.0115920	−	0.0279855i
$596$		0			0
$597$	4683.09	+	1939.80i	0.321049	+	0.132983i
$598$		0			0
$599$	−14071.7	+	14071.7i	−0.959857	+	0.959857i	−0.999225	−	0.0393679i	$-0.987466\pi$
$599$	−14071.7	+	14071.7i	−0.959857	+	0.959857i	0.0393679	+	0.999225i	$0.487466\pi$
$600$		0			0
$601$	249.222	+	249.222i	0.0169151	+	0.0169151i	0.715514	−	0.698599i	$-0.246193\pi$
$601$	249.222	+	249.222i	0.0169151	+	0.0169151i	−0.698599	+	0.715514i	$0.746193\pi$
$602$		0			0
$603$	−12948.4	+	31260.2i	−0.874460	+	2.11113i
$604$		0			0
$605$	24133.2	−	9996.32i	1.62175	−	0.671749i
$606$		0			0
$607$	14155.5			0.946545			0.473273	−	0.880916i	$-0.343073\pi$
$607$	14155.5			0.946545			0.473273	+	0.880916i	$0.343073\pi$
$608$		0			0
$609$	−3888.84			−0.258758
$610$		0			0
$611$	1438.59	−	595.883i	0.0952522	−	0.0394548i
$612$		0			0
$613$	924.686	−	2232.39i	0.0609261	−	0.147089i	−0.890485	−	0.455013i	$-0.849634\pi$
$613$	924.686	−	2232.39i	0.0609261	−	0.147089i	0.951411	+	0.307925i	$0.0996345\pi$
$614$		0			0
$615$	47400.4	+	47400.4i	3.10792	+	3.10792i
$616$		0			0
$617$	−1676.58	+	1676.58i	−0.109395	+	0.109395i	−0.759686	−	0.650291i	$-0.774647\pi$
$617$	−1676.58	+	1676.58i	−0.109395	+	0.109395i	0.650291	+	0.759686i	$0.274647\pi$
$618$		0			0
$619$	−7185.77	−	2976.44i	−0.466592	−	0.193269i	0.136985	−	0.990573i	$-0.456259\pi$
$619$	−7185.77	−	2976.44i	−0.466592	−	0.193269i	−0.603578	+	0.797304i	$0.706259\pi$
$620$		0			0
$621$	−3510.84	−	8475.91i	−0.226868	−	0.547708i
$622$		0			0
$623$			1613.19i			0.103741i
$624$		0			0
$625$			44791.8i			2.86667i
$626$		0			0
$627$	−441.032	−	1064.75i	−0.0280911	−	0.0678179i
$628$		0			0
$629$	8.32937	+	3.45014i	0.000528003	+	0.000218706i
$630$		0			0
$631$	−18919.9	+	18919.9i	−1.19364	+	1.19364i	−0.217608	+	0.976036i	$0.569826\pi$
$631$	−18919.9	+	18919.9i	−1.19364	+	1.19364i	−0.976036	+	0.217608i	$0.930174\pi$
$632$		0			0
$633$	−2852.70	−	2852.70i	−0.179123	−	0.179123i
$634$		0			0
$635$	10559.6	−	25493.2i	0.659914	−	1.59317i
$636$		0			0
$637$	−9409.46	+	3897.53i	−0.585269	+	0.242426i
$638$		0			0
$639$	−27505.4			−1.70281
$640$		0			0
$641$	−25369.4			−1.56323			−0.781616	−	0.623760i	$-0.785604\pi$
$641$	−25369.4			−1.56323			−0.781616	+	0.623760i	$0.785604\pi$
$642$		0			0
$643$	−2482.19	+	1028.16i	−0.152236	+	0.0630584i	−0.457501	−	0.889209i	$-0.651255\pi$
$643$	−2482.19	+	1028.16i	−0.152236	+	0.0630584i	0.305264	+	0.952268i	$0.401255\pi$
$644$		0			0
$645$	−18369.0	+	44346.7i	−1.12136	+	2.70721i
$646$		0			0
$647$	−8859.24	−	8859.24i	−0.538319	−	0.538319i	0.384716	−	0.923035i	$-0.374299\pi$
$647$	−8859.24	−	8859.24i	−0.538319	−	0.538319i	−0.923035	+	0.384716i	$0.874299\pi$
$648$		0			0
$649$	1747.70	−	1747.70i	0.105706	−	0.105706i
$650$		0			0
$651$	−4474.05	−	1853.21i	−0.269358	−	0.111572i
$652$		0			0
$653$	−3943.50	−	9520.46i	−0.236327	−	0.570543i	0.760571	−	0.649255i	$-0.224919\pi$
$653$	−3943.50	−	9520.46i	−0.236327	−	0.570543i	−0.996897	+	0.0787121i	$0.974919\pi$
$654$		0			0
$655$			51363.4i			3.06402i
$656$		0			0
$657$			12058.2i			0.716033i
$658$		0			0
$659$	9236.28	+	22298.4i	0.545970	+	1.31809i	0.920452	+	0.390855i	$0.127821\pi$
$659$	9236.28	+	22298.4i	0.545970	+	1.31809i	−0.374482	+	0.927234i	$0.622179\pi$
$660$		0			0
$661$	9897.03	+	4099.48i	0.582375	+	0.241228i	0.654366	−	0.756178i	$-0.272935\pi$
$661$	9897.03	+	4099.48i	0.582375	+	0.241228i	−0.0719914	+	0.997405i	$0.522935\pi$
$662$		0			0
$663$	−1403.61	+	1403.61i	−0.0822200	+	0.0822200i
$664$		0			0
$665$	585.336	+	585.336i	0.0341329	+	0.0341329i
$666$		0			0
$667$	−5910.99	+	14270.4i	−0.343140	+	0.828413i
$668$		0			0
$669$	31814.0	−	13177.8i	1.83857	−	0.761559i
$670$		0			0
$671$	2732.70			0.157220
$672$		0			0
$673$	10568.7			0.605338			0.302669	−	0.953096i	$-0.402122\pi$
$673$	10568.7			0.605338			0.302669	+	0.953096i	$0.402122\pi$
$674$		0			0
$675$	31446.9	−	13025.7i	1.79317	−	0.742757i
$676$		0			0
$677$	−6662.42	+	16084.5i	−0.378224	+	0.913114i	0.614075	+	0.789248i	$0.289529\pi$
$677$	−6662.42	+	16084.5i	−0.378224	+	0.913114i	−0.992299	+	0.123866i	$0.960471\pi$
$678$		0			0
$679$	−1055.41	−	1055.41i	−0.0596508	−	0.0596508i
$680$		0			0
$681$	8102.51	−	8102.51i	0.455931	−	0.455931i
$682$		0			0
$683$	−1440.76	−	596.782i	−0.0807162	−	0.0334337i	0.341960	−	0.939714i	$-0.388909\pi$
$683$	−1440.76	−	596.782i	−0.0807162	−	0.0334337i	−0.422676	+	0.906281i	$0.638909\pi$
$684$		0			0
$685$	−19050.1	−	45991.1i	−1.06258	−	2.56530i
$686$		0			0
$687$		−	7213.48i		−	0.400599i
$688$		0			0
$689$			97.8516i			0.00541052i
$690$		0			0
$691$	10768.2	+	25996.8i	0.592825	+	1.43121i	0.880763	+	0.473558i	$0.157031\pi$
$691$	10768.2	+	25996.8i	0.592825	+	1.43121i	−0.287937	+	0.957649i	$0.592969\pi$
$692$		0			0
$693$	−907.043	−	375.710i	−0.0497197	−	0.0205946i
$694$		0			0
$695$	24897.4	−	24897.4i	1.35887	−	1.35887i
$696$		0			0
$697$	−2202.21	−	2202.21i	−0.119677	−	0.119677i
$698$		0			0
$699$	9333.74	−	22533.6i	0.505056	−	1.21931i
$700$		0			0
$701$	13321.0	−	5517.74i	0.717727	−	0.297292i	0.00622949	−	0.999981i	$-0.498017\pi$
$701$	13321.0	−	5517.74i	0.717727	−	0.297292i	0.711498	+	0.702688i	$0.248017\pi$
$702$		0			0
$703$	−16.9755			−0.000910732
$704$		0			0
$705$	8844.46			0.472485
$706$		0			0
$707$	2250.36	−	932.128i	0.119708	−	0.0495846i
$708$		0			0
$709$	9438.27	−	22786.0i	0.499946	−	1.20698i	−0.449566	−	0.893247i	$-0.648421\pi$
$709$	9438.27	−	22786.0i	0.499946	−	1.20698i	0.949512	−	0.313730i	$-0.101579\pi$
$710$		0			0
$711$	−16837.1	−	16837.1i	−0.888100	−	0.888100i
$712$		0			0
$713$	−13601.0	+	13601.0i	−0.714392	+	0.714392i
$714$		0			0
$715$	−5492.58	−	2275.10i	−0.287288	−	0.118999i
$716$		0			0
$717$	5982.00	+	14441.8i	0.311578	+	0.752217i
$718$		0			0
$719$		−	570.471i		−	0.0295897i	−0.999891	−	0.0147948i	$-0.995290\pi$
$719$		−	570.471i		−	0.0295897i	0.999891	−	0.0147948i	$-0.00470952\pi$
$720$		0			0
$721$			3877.10i			0.200264i
$722$		0			0
$723$	9074.09	+	21906.8i	0.466762	+	1.12686i
$724$		0			0
$725$	−52945.3	−	21930.7i	−2.71219	−	1.12343i
$726$		0			0
$727$	9995.37	−	9995.37i	0.509914	−	0.509914i	−0.404586	−	0.914500i	$-0.632584\pi$
$727$	9995.37	−	9995.37i	0.509914	−	0.509914i	0.914500	+	0.404586i	$0.132584\pi$
$728$		0			0
$729$	22564.3	+	22564.3i	1.14638	+	1.14638i
$730$		0			0
$731$	853.421	−	2060.34i	0.0431805	−	0.104247i
$732$		0			0
$733$	−33049.1	+	13689.4i	−1.66535	+	0.689809i	−0.998467	−	0.0553575i	$-0.982370\pi$
$733$	−33049.1	+	13689.4i	−1.66535	+	0.689809i	−0.666879	+	0.745166i	$0.732370\pi$
$734$		0			0
$735$	−57849.5			−2.90314
$736$		0			0
$737$	7875.04			0.393597
$738$		0			0
$739$	32820.7	−	13594.8i	1.63373	−	0.676715i	0.638091	−	0.769961i	$-0.279725\pi$
$739$	32820.7	−	13594.8i	1.63373	−	0.676715i	0.995643	+	0.0932466i	$0.0297245\pi$
$740$		0			0
$741$	1430.31	−	3453.07i	0.0709091	−	0.171190i
$742$		0			0
$743$	−2806.83	−	2806.83i	−0.138590	−	0.138590i	0.634408	−	0.772998i	$-0.281244\pi$
$743$	−2806.83	−	2806.83i	−0.138590	−	0.138590i	−0.772998	+	0.634408i	$0.781244\pi$
$744$		0			0
$745$	19055.7	−	19055.7i	0.937110	−	0.937110i
$746$		0			0
$747$	−31060.1	−	12865.5i	−1.52132	−	0.630153i
$748$		0			0
$749$	−1038.48	−	2507.12i	−0.0506613	−	0.122307i
$750$		0			0
$751$		−	16498.0i		−	0.801625i	−0.916160	−	0.400813i	$-0.868728\pi$
$751$		−	16498.0i		−	0.801625i	0.916160	−	0.400813i	$-0.131272\pi$
$752$		0			0
$753$		−	6419.17i		−	0.310661i
$754$		0			0
$755$	−12761.4	−	30808.7i	−0.615145	−	1.48509i
$756$		0			0
$757$	6971.70	+	2887.77i	0.334730	+	0.138650i	0.543717	−	0.839269i	$-0.317017\pi$
$757$	6971.70	+	2887.77i	0.334730	+	0.138650i	−0.208987	+	0.977919i	$0.567017\pi$
$758$		0			0
$759$	−4612.11	+	4612.11i	−0.220565	+	0.220565i
$760$		0			0
$761$	14465.4	+	14465.4i	0.689052	+	0.689052i	0.962022	−	0.272970i	$-0.0880061\pi$
$761$	14465.4	+	14465.4i	0.689052	+	0.689052i	−0.272970	+	0.962022i	$0.588006\pi$
$762$		0			0
$763$	741.681	−	1790.58i	0.0351909	−	0.0849584i
$764$		0			0
$765$	−6227.69	+	2579.59i	−0.294330	+	0.121916i
$766$		0			0
$767$	8015.70			0.377354
$768$		0			0
$769$	−18245.8			−0.855605			−0.427803	−	0.903872i	$-0.640712\pi$
$769$	−18245.8			−0.855605			−0.427803	+	0.903872i	$0.640712\pi$
$770$		0			0
$771$	10050.6	−	4163.09i	0.469473	−	0.194462i
$772$		0			0
$773$	10869.6	−	26241.5i	0.505760	−	1.22101i	−0.440543	−	0.897732i	$-0.645214\pi$
$773$	10869.6	−	26241.5i	0.505760	−	1.22101i	0.946303	−	0.323281i	$-0.104786\pi$
$774$		0			0
$775$	−50461.8	−	50461.8i	−2.33889	−	2.33889i
$776$		0			0
$777$	−17.1038	+	17.1038i	−0.000789697	+	0.000789697i
$778$		0			0
$779$	5417.72	+	2244.09i	0.249178	+	0.103213i
$780$		0			0
$781$	2449.82	+	5914.38i	0.112242	+	0.270977i
$782$		0			0
$783$			19519.6i			0.890900i
$784$		0			0
$785$		−	39515.9i		−	1.79667i
$786$		0			0
$787$	−5885.08	−	14207.8i	−0.266557	−	0.643525i	0.732760	−	0.680487i	$-0.238232\pi$
$787$	−5885.08	−	14207.8i	−0.266557	−	0.643525i	−0.999317	+	0.0369621i	$0.988232\pi$
$788$		0			0
$789$	30057.5	+	12450.2i	1.35624	+	0.561774i
$790$		0			0
$791$	1821.65	−	1821.65i	0.0818843	−	0.0818843i
$792$		0			0
$793$	6266.67	+	6266.67i	0.280625	+	0.280625i
$794$		0			0
$795$	−212.695	+	513.492i	−0.00948871	+	0.0229078i
$796$		0			0
$797$	−31983.9	+	13248.2i	−1.42149	+	0.588801i	−0.955235	−	0.295848i	$-0.904398\pi$
$797$	−31983.9	+	13248.2i	−1.42149	+	0.588801i	−0.466257	+	0.884649i	$0.654398\pi$
$798$		0			0
$799$	−410.912			−0.0181940
$800$		0			0
$801$	24734.5			1.09107
$802$		0			0
$803$	2592.83	−	1073.98i	0.113946	−	0.0471981i
$804$		0			0
$805$	1792.85	−	4328.32i	0.0784965	−	0.189507i
$806$		0			0
$807$	13875.7	+	13875.7i	0.605264	+	0.605264i
$808$		0			0
$809$	6907.25	−	6907.25i	0.300180	−	0.300180i	−0.540904	−	0.841084i	$-0.681918\pi$
$809$	6907.25	−	6907.25i	0.300180	−	0.300180i	0.841084	+	0.540904i	$0.181918\pi$
$810$		0			0
$811$	−24959.9	−	10338.7i	−1.08072	−	0.447647i	−0.229955	−	0.973201i	$-0.573858\pi$
$811$	−24959.9	−	10338.7i	−1.08072	−	0.447647i	−0.850760	+	0.525554i	$0.823858\pi$
$812$		0			0
$813$	−19394.2	−	46821.6i	−0.836633	−	2.01981i
$814$		0			0
$815$			57642.7i			2.47747i
$816$		0			0
$817$			4199.05i			0.179812i
$818$		0			0
$819$	−1218.46	−	2941.63i	−0.0519860	−	0.125505i
$820$		0			0
$821$	−26816.1	−	11107.6i	−1.13994	−	0.472177i	−0.268789	−	0.963199i	$-0.586624\pi$
$821$	−26816.1	−	11107.6i	−1.13994	−	0.472177i	−0.871147	+	0.491022i	$0.836624\pi$
$822$		0			0
$823$	26943.0	−	26943.0i	1.14116	−	1.14116i	0.152920	−	0.988239i	$-0.451132\pi$
$823$	26943.0	−	26943.0i	1.14116	−	1.14116i	0.988239	−	0.152920i	$-0.0488675\pi$
$824$		0			0
$825$	−17111.6	−	17111.6i	−0.722122	−	0.722122i
$826$		0			0
$827$	−1442.00	+	3481.31i	−0.0606329	+	0.146381i	−0.951292	−	0.308290i	$-0.900243\pi$
$827$	−1442.00	+	3481.31i	−0.0606329	+	0.146381i	0.890659	+	0.454671i	$0.150243\pi$
$828$		0			0
$829$	14452.8	−	5986.56i	0.605510	−	0.250810i	−0.0587974	−	0.998270i	$-0.518727\pi$
$829$	14452.8	−	5986.56i	0.605510	−	0.250810i	0.664307	+	0.747459i	$0.268727\pi$
$830$		0			0
$831$	25903.1			1.08131
$832$		0			0
$833$	2687.68			0.111792
$834$		0			0
$835$	−49808.2	+	20631.2i	−2.06429	+	0.855058i
$836$		0			0
$837$	−9302.02	+	22457.1i	−0.384139	+	0.927395i
$838$		0			0
$839$	16946.0	+	16946.0i	0.697305	+	0.697305i	0.963829	−	0.266523i	$-0.0858749\pi$
$839$	16946.0	+	16946.0i	0.697305	+	0.697305i	−0.266523	+	0.963829i	$0.585875\pi$
$840$		0			0
$841$	5992.77	−	5992.77i	0.245716	−	0.245716i
$842$		0			0
$843$	65729.3	+	27226.0i	2.68546	+	1.11235i
$844$		0			0
$845$	10279.9	+	24817.9i	0.418508	+	1.01037i
$846$		0			0
$847$		−	3256.03i		−	0.132088i
$848$		0			0
$849$			10956.7i			0.442913i
$850$		0			0
$851$	36.7661	+	88.7612i	0.00148099	+	0.00357543i
$852$		0			0
$853$	25114.9	+	10402.9i	1.00811	+	0.417572i	0.824764	−	0.565477i	$-0.191308\pi$
$853$	25114.9	+	10402.9i	1.00811	+	0.417572i	0.183344	+	0.983049i	$0.441308\pi$
$854$		0			0
$855$	8974.78	−	8974.78i	0.358984	−	0.358984i
$856$		0			0
$857$	17004.0	+	17004.0i	0.677765	+	0.677765i	0.959494	−	0.281729i	$-0.0909079\pi$
$857$	17004.0	+	17004.0i	0.677765	+	0.677765i	−0.281729	+	0.959494i	$0.590908\pi$
$858$		0			0
$859$	14867.5	−	35893.4i	0.590539	−	1.42569i	−0.292444	−	0.956283i	$-0.594469\pi$
$859$	14867.5	−	35893.4i	0.590539	−	1.42569i	0.882983	−	0.469405i	$-0.155531\pi$
$860$		0			0
$861$	7719.69	−	3197.60i	0.305559	−	0.126567i
$862$		0			0
$863$	9227.90			0.363988			0.181994	−	0.983300i	$-0.441745\pi$
$863$	9227.90			0.363988			0.181994	+	0.983300i	$0.441745\pi$
$864$		0			0
$865$	−70785.0			−2.78238
$866$		0			0
$867$	−36708.5	+	15205.2i	−1.43793	+	0.595611i
$868$		0			0
$869$	−2120.79	+	5120.04i	−0.0827882	+	0.199868i
$870$		0			0
$871$	18059.2	+	18059.2i	0.702539	+	0.702539i
$872$		0			0
$873$	−16182.3	+	16182.3i	−0.627362	+	0.627362i
$874$		0			0
$875$	9708.80	+	4021.52i	0.375106	+	0.155374i
$876$		0			0
$877$	9943.41	+	24005.5i	0.382857	+	0.924298i	0.991411	+	0.130785i	$0.0417498\pi$
$877$	9943.41	+	24005.5i	0.382857	+	0.924298i	−0.608554	+	0.793512i	$0.708250\pi$
$878$		0			0
$879$			326.420i			0.0125255i
$880$		0			0
$881$			6688.49i			0.255779i	0.991788	+	0.127889i	$0.0408202\pi$
$881$			6688.49i			0.255779i	−0.991788	+	0.127889i	$0.959180\pi$
$882$		0			0
$883$	−10114.2	−	24417.8i	−0.385470	−	0.930606i	−0.990887	−	0.134698i	$-0.956994\pi$
$883$	−10114.2	−	24417.8i	−0.385470	−	0.930606i	0.605417	−	0.795908i	$-0.293006\pi$
$884$		0			0
$885$	42063.7	+	17423.3i	1.59769	+	0.661784i
$886$		0			0
$887$	−34103.3	+	34103.3i	−1.29096	+	1.29096i	−0.356760	+	0.934196i	$0.616119\pi$
$887$	−34103.3	+	34103.3i	−1.29096	+	1.29096i	−0.934196	+	0.356760i	$0.883881\pi$
$888$		0			0
$889$	−2432.10	−	2432.10i	−0.0917548	−	0.0917548i
$890$		0			0
$891$	720.489	−	1739.41i	0.0270901	−	0.0654013i
$892$		0			0
$893$	714.811	−	296.084i	0.0267864	−	0.0110953i
$894$		0			0
$895$	−62953.3			−2.35117
$896$		0			0
$897$	−21153.1			−0.787381
$898$		0			0
$899$	37809.6	−	15661.3i	1.40269	−	0.581015i
$900$		0			0
$901$	9.88178	−	23.8567i	0.000365383	−	0.000882112i
$902$		0			0
$903$	4230.77	+	4230.77i	0.155915	+	0.155915i
$904$		0			0
$905$	−15739.2	+	15739.2i	−0.578108	+	0.578108i
$906$		0			0
$907$	−16994.3	−	7039.26i	−0.622145	−	0.257701i	0.0492664	−	0.998786i	$-0.484312\pi$
$907$	−16994.3	−	7039.26i	−0.622145	−	0.257701i	−0.671412	+	0.741085i	$0.734312\pi$
$908$		0			0
$909$	−14292.0	−	34504.0i	−0.521493	−	1.25900i
$910$		0			0
$911$		−	838.960i		−	0.0305115i	−0.999884	−	0.0152558i	$-0.995144\pi$
$911$		−	838.960i		−	0.0305115i	0.999884	−	0.0152558i	$-0.00485625\pi$
$912$		0			0
$913$			7824.63i			0.283634i
$914$		0			0
$915$	19263.8	+	46506.8i	0.696001	+	1.68029i
$916$		0			0
$917$	5915.03	+	2450.09i	0.213012	+	0.0882323i
$918$		0			0
$919$	3442.04	−	3442.04i	0.123550	−	0.123550i	−0.642628	−	0.766178i	$-0.722156\pi$
$919$	3442.04	−	3442.04i	0.123550	−	0.123550i	0.766178	+	0.642628i	$0.222156\pi$
$920$		0			0
$921$	−666.986	−	666.986i	−0.0238631	−	0.0238631i
$922$		0			0
$923$	−7944.99	+	19180.9i	−0.283329	+	0.684016i
$924$		0			0
$925$	−329.318	+	136.408i	−0.0117058	+	0.00484872i
$926$		0			0
$927$	59446.3			2.10623
$928$		0			0
$929$	−25973.4			−0.917288			−0.458644	−	0.888620i	$-0.651665\pi$
$929$	−25973.4			−0.917288			−0.458644	+	0.888620i	$0.651665\pi$
$930$		0			0
$931$	−4675.40	+	1936.62i	−0.164587	+	0.0681740i
$932$		0			0
$933$	14407.5	−	34782.7i	0.505551	−	1.22051i
$934$		0			0
$935$	1109.36	+	1109.36i	0.0388022	+	0.0388022i
$936$		0			0
$937$	18508.1	−	18508.1i	0.645288	−	0.645288i	−0.306563	−	0.951850i	$-0.599179\pi$
$937$	18508.1	−	18508.1i	0.645288	−	0.645288i	0.951850	+	0.306563i	$0.0991790\pi$
$938$		0			0
$939$	21387.4	+	8858.96i	0.743293	+	0.307882i
$940$		0			0
$941$	4577.98	+	11052.2i	0.158595	+	0.382882i	0.983125	−	0.182936i	$-0.0585602\pi$
$941$	4577.98	+	11052.2i	0.158595	+	0.382882i	−0.824530	+	0.565819i	$0.808560\pi$
$942$		0			0
$943$		−	33188.3i		−	1.14609i
$944$		0			0
$945$		−	5920.46i		−	0.203802i
$946$		0			0
$947$	−1155.16	−	2788.81i	−0.0396387	−	0.0956962i	0.902820	−	0.430018i	$-0.141493\pi$
$947$	−1155.16	−	2788.81i	−0.0396387	−	0.0956962i	−0.942459	+	0.334322i	$0.891493\pi$
$948$		0			0
$949$	8408.77	+	3483.03i	0.287629	+	0.119140i
$950$		0			0
$951$	−12984.2	+	12984.2i	−0.442735	+	0.442735i
$952$		0			0
$953$	24724.8	+	24724.8i	0.840416	+	0.840416i	0.988913	−	0.148497i	$-0.0474435\pi$
$953$	24724.8	+	24724.8i	0.840416	+	0.840416i	−0.148497	+	0.988913i	$0.547444\pi$
$954$		0			0
$955$	−22508.9	+	54341.3i	−0.762692	+	1.84130i
$956$		0			0
$957$	12821.3	−	5310.74i	0.433075	−	0.179385i
$958$		0			0
$959$	−6205.07			−0.208939
$960$		0			0
$961$	21171.7			0.710675
$962$		0			0
$963$	−38440.9	+	15922.7i	−1.28633	+	0.532817i
$964$		0			0
$965$	−2423.41	+	5850.64i	−0.0808419	+	0.195170i
$966$		0			0
$967$	13376.9	+	13376.9i	0.444853	+	0.444853i	0.893639	−	0.448786i	$-0.148144\pi$
$967$	13376.9	+	13376.9i	0.444853	+	0.444853i	−0.448786	+	0.893639i	$0.648144\pi$
$968$		0			0
$969$	−697.432	+	697.432i	−0.0231215	+	0.0231215i
$970$		0			0
$971$	5449.59	+	2257.30i	0.180109	+	0.0746036i	0.470916	−	0.882178i	$-0.343924\pi$
$971$	5449.59	+	2257.30i	0.180109	+	0.0746036i	−0.290807	+	0.956782i	$0.593924\pi$
$972$		0			0
$973$	−1679.57	−	4054.83i	−0.0553385	−	0.133599i
$974$		0			0
$975$		−	78481.2i		−	2.57786i
$976$		0			0
$977$			4626.40i			0.151496i	0.997127	+	0.0757480i	$0.0241344\pi$
$977$			4626.40i			0.151496i	−0.997127	+	0.0757480i	$0.975866\pi$
$978$		0			0
$979$	−2203.03	−	5318.58i	−0.0719193	−	0.173629i
$980$		0			0
$981$	−27454.4	−	11372.0i	−0.893528	−	0.370111i
$982$		0			0
$983$	−627.537	+	627.537i	−0.0203615	+	0.0203615i	−0.717214	−	0.696853i	$-0.754583\pi$
$983$	−627.537	+	627.537i	−0.0203615	+	0.0203615i	0.696853	+	0.717214i	$0.254583\pi$
$984$		0			0
$985$	−69855.5	−	69855.5i	−2.25968	−	2.25968i
$986$		0			0
$987$	421.890	−	1018.53i	0.0136058	−	0.0328473i
$988$		0			0
$989$	21955.8	−	9094.41i	0.705920	−	0.292402i
$990$		0			0
$991$	59928.1			1.92097			0.960484	−	0.278336i	$-0.0897827\pi$
$991$	59928.1			1.92097			0.960484	+	0.278336i	$0.0897827\pi$
$992$		0			0
$993$	71578.9			2.28750
$994$		0			0
$995$	12003.8	−	4972.12i	0.382457	−	0.158419i
$996$		0			0
$997$	−19960.9	+	48190.0i	−0.634072	+	1.53078i	0.200389	+	0.979716i	$0.435780\pi$
$997$	−19960.9	+	48190.0i	−0.634072	+	1.53078i	−0.834460	+	0.551068i	$0.814220\pi$
$998$		0			0
$999$	85.8508	+	85.8508i	0.00271892	+	0.00271892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.49.1		44
4.3	odd	2		32.4.g.a.21.7	✓	44
8.3	odd	2		256.4.g.b.97.1		44
8.5	even	2		256.4.g.a.97.11		44
32.3	odd	8		32.4.g.a.29.7	yes	44
32.13	even	8		256.4.g.a.161.11		44
32.19	odd	8		256.4.g.b.161.1		44
32.29	even	8	inner	128.4.g.a.81.1		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.7	✓	44	4.3	odd	2
32.4.g.a.29.7	yes	44	32.3	odd	8
128.4.g.a.49.1		44	1.1	even	1	trivial
128.4.g.a.81.1		44	32.29	even	8	inner
256.4.g.a.97.11		44	8.5	even	2
256.4.g.a.161.11		44	32.13	even	8
256.4.g.b.97.1		44	8.3	odd	2
256.4.g.b.161.1		44	32.19	odd	8

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-7.57022 + 3.13569i) q^{3} +(-8.03744 + 19.4041i) q^{5} +(1.85119 + 1.85119i) q^{7} +(28.3838 - 28.3838i) q^{9} +O(q^{10})\)	\(q+(-7.57022 + 3.13569i) q^{3} +(-8.03744 + 19.4041i) q^{5} +(1.85119 + 1.85119i) q^{7} +(28.3838 - 28.3838i) q^{9} +(-8.63132 - 3.57521i) q^{11} +(-11.5947 - 27.9922i) q^{13} -172.096i q^{15} +7.99555i q^{17} +(-5.76123 - 13.9088i) q^{19} +(-19.8187 - 8.20916i) q^{21} +(-60.2483 + 60.2483i) q^{23} +(-223.530 - 223.530i) q^{25} +(-41.2051 + 99.4779i) q^{27} +(167.485 - 69.3746i) q^{29} +225.749 q^{31} +76.5517 q^{33} +(-50.7995 + 21.0419i) q^{35} +(0.431507 - 1.04175i) q^{37} +(175.549 + 175.549i) q^{39} +(-275.430 + 275.430i) q^{41} +(-257.686 - 106.737i) q^{43} +(322.629 + 778.894i) q^{45} +51.3926i q^{47} -336.146i q^{49} +(-25.0715 - 60.5281i) q^{51} +(-2.98375 - 1.23591i) q^{53} +(138.747 - 138.747i) q^{55} +(87.2275 + 87.2275i) q^{57} +(-101.242 + 244.419i) q^{59} +(-270.238 + 111.936i) q^{61} +105.087 q^{63} +636.355 q^{65} +(-778.765 + 322.575i) q^{67} +(267.173 - 645.012i) q^{69} +(-484.526 - 484.526i) q^{71} +(-212.413 + 212.413i) q^{73} +(2393.10 + 991.252i) q^{75} +(-9.35982 - 22.5966i) q^{77} -593.194i q^{79} +201.524i q^{81} +(-320.510 - 773.780i) q^{83} +(-155.147 - 64.2638i) q^{85} +(-1050.36 + 1050.36i) q^{87} +(435.716 + 435.716i) q^{89} +(30.3548 - 73.2829i) q^{91} +(-1708.97 + 707.879i) q^{93} +316.194 q^{95} -570.125 q^{97} +(-346.467 + 143.511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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