LMFDB - Embedded newform 525.2.bf.e.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(32,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("525.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bf (of order $12$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.63456228123711897600000000.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 17x^{12} + 208x^{8} + 1377x^{4} + 6561 $ x^16 + 17x^12 + 208x^8 + 1377*x^4 + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.1
Root			$1.42232 - 0.988431i$ of defining polynomial
Character	$\chi$	$=$	525.107
Dual form			525.2.bf.e.368.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.578737 - 2.15988i) q^{2} +(-1.56717 + 0.737552i) q^{3} +(-2.59808 + 1.50000i) q^{4} +(2.50000 + 2.95804i) q^{6} +(0.684771 - 2.55560i) q^{7} +(1.58114 + 1.58114i) q^{8} +(1.91203 - 2.31174i) q^{9} +O(q^{10})$	\(q+(-0.578737 - 2.15988i) q^{2} +(-1.56717 + 0.737552i) q^{3} +(-2.59808 + 1.50000i) q^{4} +(2.50000 + 2.95804i) q^{6} +(0.684771 - 2.55560i) q^{7} +(1.58114 + 1.58114i) q^{8} +(1.91203 - 2.31174i) q^{9} +(2.96529 - 4.26697i) q^{12} +(3.74166 - 3.74166i) q^{13} -5.91608 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.31975 - 1.15747i) q^{17} +(-6.09963 - 2.79186i) q^{18} +(1.73205 + 1.00000i) q^{19} +(0.811738 + 4.51011i) q^{21} +(-6.47963 + 1.73621i) q^{23} +(-3.64408 - 1.31174i) q^{24} +(-10.2470 - 5.91608i) q^{26} +(-1.29145 + 5.03311i) q^{27} +(2.05431 + 7.66680i) q^{28} -5.91608 q^{29} +(-1.00000 - 1.73205i) q^{31} +(6.47963 + 1.73621i) q^{32} +10.0000i q^{34} +(-1.50000 + 8.87412i) q^{36} +(-10.2224 + 2.73908i) q^{37} +(1.15747 - 4.31975i) q^{38} +(-3.10414 + 8.62348i) q^{39} -5.91608i q^{41} +(9.27149 - 4.36342i) q^{42} +(1.87083 - 1.87083i) q^{43} +(7.50000 + 12.9904i) q^{46} +(2.31495 + 8.63950i) q^{47} +(0.144845 - 1.72598i) q^{48} +(-6.06218 - 3.50000i) q^{49} +(7.62348 - 1.37209i) q^{51} +(-4.10862 + 15.3336i) q^{52} +(1.15747 - 4.31975i) q^{53} +(11.6183 - 0.123475i) q^{54} +(5.12348 - 2.95804i) q^{56} +(-3.45197 - 0.289690i) q^{57} +(3.42385 + 12.7780i) q^{58} +(-5.91608 - 10.2470i) q^{59} +(5.50000 - 9.52628i) q^{61} +(-3.16228 + 3.16228i) q^{62} +(-4.59857 - 6.46940i) q^{63} -13.0000i q^{64} +(-0.684771 + 2.55560i) q^{67} +(12.9593 - 3.47242i) q^{68} +(8.87412 - 7.50000i) q^{69} +11.8322i q^{71} +(6.67837 - 0.631989i) q^{72} +(-5.11120 - 1.36954i) q^{73} +(11.8322 + 20.4939i) q^{74} -6.00000 q^{76} +(20.4221 + 1.71383i) q^{78} +(1.73205 + 1.00000i) q^{79} +(-1.68826 - 8.84024i) q^{81} +(-12.7780 + 3.42385i) q^{82} +(1.58114 + 1.58114i) q^{83} +(-8.87412 - 10.5000i) q^{84} +(-5.12348 - 2.95804i) q^{86} +(9.27149 - 4.36342i) q^{87} +(2.95804 - 5.12348i) q^{89} +(-7.00000 - 12.1244i) q^{91} +(14.2302 - 14.2302i) q^{92} +(2.84465 + 1.97686i) q^{93} +(17.3205 - 10.0000i) q^{94} +(-11.4352 + 2.05813i) q^{96} +(7.48331 + 7.48331i) q^{97} +(-4.05116 + 15.1191i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 40 q^{6}+O(q^{10}) $ 16 * q + 40 * q^6	$ 16 q + 40 q^{6} - 8 q^{16} - 28 q^{21} - 16 q^{31} - 24 q^{36} + 120 q^{46} + 40 q^{51} + 88 q^{61} - 96 q^{76} - 68 q^{81} - 112 q^{91} - 60 q^{96}+O(q^{100}) $ 16 * q + 40 * q^6 - 8 * q^16 - 28 * q^21 - 16 * q^31 - 24 * q^36 + 120 * q^46 + 40 * q^51 + 88 * q^61 - 96 * q^76 - 68 * q^81 - 112 * q^91 - 60 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.578737	−	2.15988i	−0.409229	−	1.52726i	−0.796121	−	0.605138i	$-0.793118\pi$
$2$	−0.578737	−	2.15988i	−0.409229	−	1.52726i	0.386892	−	0.922125i	$-0.373549\pi$
$3$	−1.56717	+	0.737552i	−0.904805	+	0.425826i
$3$	−1.56717	+	0.737552i	−0.904805	+	0.425826i
$4$	−2.59808	+	1.50000i	−1.29904	+	0.750000i
$5$		0			0
$5$		0			0
$6$	2.50000	+	2.95804i	1.02062	+	1.20761i
$7$	0.684771	−	2.55560i	0.258819	−	0.965926i
$7$	0.684771	−	2.55560i	0.258819	−	0.965926i
$8$	1.58114	+	1.58114i	0.559017	+	0.559017i
$9$	1.91203	−	2.31174i	0.637344	−	0.770579i
$10$		0			0
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	2.96529	−	4.26697i	0.856007	−	1.23177i
$13$	3.74166	−	3.74166i	1.03775	−	1.03775i	0.0384901	−	0.999259i	$-0.487745\pi$
$13$	3.74166	−	3.74166i	1.03775	−	1.03775i	0.999259	−	0.0384901i	$-0.0122548\pi$
$14$	−5.91608			−1.58114
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.31975	−	1.15747i	−1.04769	−	0.280729i	−0.306395	−	0.951904i	$-0.599123\pi$
$17$	−4.31975	−	1.15747i	−1.04769	−	0.280729i	−0.741298	+	0.671176i	$0.765790\pi$
$18$	−6.09963	−	2.79186i	−1.43770	−	0.658049i
$19$	1.73205	+	1.00000i	0.397360	+	0.229416i	0.685344	−	0.728219i	$-0.259652\pi$
$19$	1.73205	+	1.00000i	0.397360	+	0.229416i	−0.287984	+	0.957635i	$0.592985\pi$
$20$		0			0
$21$	0.811738	+	4.51011i	0.177136	+	0.984186i
$22$		0			0
$23$	−6.47963	+	1.73621i	−1.35110	+	0.362025i	−0.860539	−	0.509384i	$-0.829873\pi$
$23$	−6.47963	+	1.73621i	−1.35110	+	0.362025i	−0.490557	+	0.871409i	$0.663207\pi$
$24$	−3.64408	−	1.31174i	−0.743845	−	0.267757i
$25$		0			0
$26$	−10.2470	−	5.91608i	−2.00959	−	1.16024i
$27$	−1.29145	+	5.03311i	−0.248539	+	0.968622i
$28$	2.05431	+	7.66680i	0.388229	+	1.44889i
$29$	−5.91608			−1.09859			−0.549294	−	0.835629i	$-0.685103\pi$
$29$	−5.91608			−1.09859			−0.549294	+	0.835629i	$0.685103\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	6.47963	+	1.73621i	1.14545	+	0.306922i
$33$		0			0
$34$			10.0000i			1.71499i
$35$		0			0
$36$	−1.50000	+	8.87412i	−0.250000	+	1.47902i
$37$	−10.2224	+	2.73908i	−1.68055	+	0.450303i	−0.967925	−	0.251240i	$-0.919162\pi$
$37$	−10.2224	+	2.73908i	−1.68055	+	0.450303i	−0.712627	+	0.701543i	$0.752495\pi$
$38$	1.15747	−	4.31975i	0.187767	−	0.700756i
$39$	−3.10414	+	8.62348i	−0.497060	+	1.38086i
$40$		0			0
$41$		−	5.91608i		−	0.923936i	−0.886896	−	0.461968i	$-0.847143\pi$
$41$		−	5.91608i		−	0.923936i	0.886896	−	0.461968i	$-0.152857\pi$
$42$	9.27149	−	4.36342i	1.43062	−	0.673290i
$43$	1.87083	−	1.87083i	0.285299	−	0.285299i	−0.549919	−	0.835218i	$-0.685341\pi$
$43$	1.87083	−	1.87083i	0.285299	−	0.285299i	0.835218	+	0.549919i	$0.185341\pi$
$44$		0			0
$45$		0			0
$46$	7.50000	+	12.9904i	1.10581	+	1.91533i
$47$	2.31495	+	8.63950i	0.337670	+	1.26020i	0.900946	+	0.433932i	$0.142874\pi$
$47$	2.31495	+	8.63950i	0.337670	+	1.26020i	−0.563276	+	0.826269i	$0.690459\pi$
$48$	0.144845	−	1.72598i	0.0209066	−	0.249124i
$49$	−6.06218	−	3.50000i	−0.866025	−	0.500000i
$50$		0			0
$51$	7.62348	−	1.37209i	1.06750	−	0.192131i
$52$	−4.10862	+	15.3336i	−0.569764	+	2.12639i
$53$	1.15747	−	4.31975i	0.158991	−	0.593364i	−0.839739	−	0.542990i	$-0.817292\pi$
$53$	1.15747	−	4.31975i	0.158991	−	0.593364i	0.998730	−	0.0503735i	$-0.0160412\pi$
$54$	11.6183	−	0.123475i	1.58105	−	0.0168029i
$55$		0			0
$56$	5.12348	−	2.95804i	0.684653	−	0.395285i
$57$	−3.45197	−	0.289690i	−0.457224	−	0.0383704i
$58$	3.42385	+	12.7780i	0.449574	+	1.67783i
$59$	−5.91608	−	10.2470i	−0.770208	−	1.33404i	−0.937449	−	0.348123i	$-0.886819\pi$
$59$	−5.91608	−	10.2470i	−0.770208	−	1.33404i	0.167241	−	0.985916i	$-0.446514\pi$
$60$		0			0
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	−0.262776	−	0.964857i	$-0.584638\pi$
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	0.966978	−	0.254858i	$-0.0820288\pi$
$62$	−3.16228	+	3.16228i	−0.401610	+	0.401610i
$63$	−4.59857	−	6.46940i	−0.579366	−	0.815068i
$64$		−	13.0000i		−	1.62500i
$65$		0			0
$66$		0			0
$67$	−0.684771	+	2.55560i	−0.0836581	+	0.312216i	−0.995057	−	0.0993085i	$-0.968337\pi$
$67$	−0.684771	+	2.55560i	−0.0836581	+	0.312216i	0.911399	+	0.411525i	$0.135004\pi$
$68$	12.9593	−	3.47242i	1.57154	−	0.421093i
$69$	8.87412	−	7.50000i	1.06832	−	0.902894i
$70$		0			0
$71$			11.8322i			1.40422i	0.712069	+	0.702109i	$0.247758\pi$
$71$			11.8322i			1.40422i	−0.712069	+	0.702109i	$0.752242\pi$
$72$	6.67837	−	0.631989i	0.787053	−	0.0744806i
$73$	−5.11120	−	1.36954i	−0.598221	−	0.160293i	−0.0530130	−	0.998594i	$-0.516882\pi$
$73$	−5.11120	−	1.36954i	−0.598221	−	0.160293i	−0.545208	+	0.838301i	$0.683549\pi$
$74$	11.8322	+	20.4939i	1.37546	+	2.38237i
$75$		0			0
$76$	−6.00000			−0.688247
$77$		0			0
$78$	20.4221	+	1.71383i	2.31235	+	0.194053i
$79$	1.73205	+	1.00000i	0.194871	+	0.112509i	0.594261	−	0.804272i	$-0.297445\pi$
$79$	1.73205	+	1.00000i	0.194871	+	0.112509i	−0.399390	+	0.916781i	$0.630778\pi$
$80$		0			0
$81$	−1.68826	−	8.84024i	−0.187585	−	0.982248i
$82$	−12.7780	+	3.42385i	−1.41109	+	0.378101i
$83$	1.58114	+	1.58114i	0.173553	+	0.173553i	0.788538	−	0.614986i	$-0.210838\pi$
$83$	1.58114	+	1.58114i	0.173553	+	0.173553i	−0.614986	+	0.788538i	$0.710838\pi$
$84$	−8.87412	−	10.5000i	−0.968246	−	1.14564i
$85$		0			0
$86$	−5.12348	−	2.95804i	−0.552479	−	0.318974i
$87$	9.27149	−	4.36342i	0.994008	−	0.467808i
$88$		0			0
$89$	2.95804	−	5.12348i	0.313552	−	0.543087i	−0.665577	−	0.746329i	$-0.731814\pi$
$89$	2.95804	−	5.12348i	0.313552	−	0.543087i	0.979129	+	0.203242i	$0.0651478\pi$
$90$		0			0
$91$	−7.00000	−	12.1244i	−0.733799	−	1.27098i
$92$	14.2302	−	14.2302i	1.48361	−	1.48361i
$93$	2.84465	+	1.97686i	0.294976	+	0.204991i
$94$	17.3205	−	10.0000i	1.78647	−	1.03142i
$95$		0			0
$96$	−11.4352	+	2.05813i	−1.16710	+	0.210057i
$97$	7.48331	+	7.48331i	0.759815	+	0.759815i	0.976289	−	0.216473i	$-0.0694554\pi$
$97$	7.48331	+	7.48331i	0.759815	+	0.759815i	−0.216473	+	0.976289i	$0.569455\pi$
$98$	−4.05116	+	15.1191i	−0.409229	+	1.52726i
$99$		0			0
$100$		0			0
$101$	5.12348	−	2.95804i	0.509805	−	0.294336i	−0.222949	−	0.974830i	$-0.571568\pi$
$101$	5.12348	−	2.95804i	0.509805	−	0.294336i	0.732753	+	0.680494i	$0.238235\pi$
$102$	−7.37552	−	15.6717i	−0.730286	−	1.55173i
$103$	−2.05431	−	7.66680i	−0.202417	−	0.755432i	−0.990221	−	0.139506i	$-0.955449\pi$
$103$	−2.05431	−	7.66680i	−0.202417	−	0.755432i	0.787804	−	0.615926i	$-0.211218\pi$
$104$	11.8322			1.16024
$105$		0			0
$106$	−10.0000			−0.971286
$107$	0.578737	+	2.15988i	0.0559486	+	0.208803i	0.988241	−	0.152901i	$-0.0488617\pi$
$107$	0.578737	+	2.15988i	0.0559486	+	0.208803i	−0.932293	+	0.361704i	$0.882195\pi$
$108$	−4.19438	−	15.0136i	−0.403604	−	1.44468i
$109$	−6.06218	+	3.50000i	−0.580651	+	0.335239i	−0.761392	−	0.648292i	$-0.775484\pi$
$109$	−6.06218	+	3.50000i	−0.580651	+	0.335239i	0.180741	+	0.983531i	$0.442150\pi$
$110$		0			0
$111$	14.0000	−	11.8322i	1.32882	−	1.12306i
$112$	1.87083	+	1.87083i	0.176777	+	0.176777i
$113$	−3.16228	−	3.16228i	−0.297482	−	0.297482i	0.542545	−	0.840027i	$-0.317461\pi$
$113$	−3.16228	−	3.16228i	−0.297482	−	0.297482i	−0.840027	+	0.542545i	$0.817461\pi$
$114$	1.37209	+	7.62348i	0.128508	+	0.714004i
$115$		0			0
$116$	15.3704	−	8.87412i	1.42711	−	0.823941i
$117$	−1.49556	−	15.8039i	−0.138265	−	1.46107i
$118$	−18.7083	+	18.7083i	−1.72224	+	1.72224i
$119$	−5.91608	+	10.2470i	−0.542326	+	0.939336i
$120$		0			0
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$	−23.7586	−	6.36611i	−2.15101	−	0.576360i
$123$	4.36342	+	9.27149i	0.393436	+	0.835982i
$124$	5.19615	+	3.00000i	0.466628	+	0.269408i
$125$		0			0
$126$	−11.3117	+	13.6764i	−1.00773	+	1.21839i
$127$	−11.2250	−	11.2250i	−0.996055	−	0.996055i	0.00393704	−	0.999992i	$-0.498747\pi$
$127$	−11.2250	−	11.2250i	−0.996055	−	0.996055i	−0.999992	+	0.00393704i	$0.998747\pi$
$128$	−15.1191	+	4.05116i	−1.33635	+	0.358075i
$129$	−1.55207	+	4.31174i	−0.136652	+	0.379627i
$130$		0			0
$131$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$131$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$132$		0			0
$133$	3.74166	−	3.74166i	0.324443	−	0.324443i
$134$	5.91608			0.511071
$135$		0			0
$136$	−5.00000	−	8.66025i	−0.428746	−	0.742611i
$137$	−8.63950	−	2.31495i	−0.738123	−	0.197779i	−0.129879	−	0.991530i	$-0.541459\pi$
$137$	−8.63950	−	2.31495i	−0.738123	−	0.197779i	−0.608243	+	0.793750i	$0.708126\pi$
$138$	−21.3348	−	14.8265i	−1.81614	−	1.26211i
$139$			8.00000i			0.678551i	0.940687	+	0.339276i	$0.110182\pi$
$139$			8.00000i			0.678551i	−0.940687	+	0.339276i	$0.889818\pi$
$140$		0			0
$141$	−10.0000	−	11.8322i	−0.842152	−	0.996448i
$142$	25.5560	−	6.84771i	2.14461	−	0.574647i
$143$		0			0
$144$	1.04601	+	2.81174i	0.0871673	+	0.234311i
$145$		0			0
$146$			11.8322i			0.979236i
$147$	12.0819	+	1.01391i	0.996497	+	0.0836263i
$148$	22.4499	−	22.4499i	1.84537	−	1.84537i
$149$	8.87412	−	15.3704i	0.726996	−	1.25919i	−0.231151	−	0.972918i	$-0.574249\pi$
$149$	8.87412	−	15.3704i	0.726996	−	1.25919i	0.958147	−	0.286276i	$-0.0924176\pi$
$150$		0			0
$151$	3.00000	+	5.19615i	0.244137	+	0.422857i	0.961888	−	0.273442i	$-0.0881622\pi$
$151$	3.00000	+	5.19615i	0.244137	+	0.422857i	−0.717752	+	0.696299i	$0.754829\pi$
$152$	1.15747	+	4.31975i	0.0938835	+	0.350378i
$153$	−10.9353	+	7.77300i	−0.884065	+	0.628410i
$154$		0			0
$155$		0			0
$156$	−4.87043	−	27.0607i	−0.389946	−	2.16659i
$157$	2.73908	−	10.2224i	0.218603	−	0.815836i	−0.766265	−	0.642525i	$-0.777887\pi$
$157$	2.73908	−	10.2224i	0.218603	−	0.815836i	0.984867	−	0.173311i	$-0.0554466\pi$
$158$	1.15747	−	4.31975i	0.0920837	−	0.343661i
$159$	1.37209	+	7.62348i	0.108814	+	0.604581i
$160$		0			0
$161$			17.7482i			1.39876i
$162$	−18.1168	+	8.76261i	−1.42339	+	0.688456i
$163$	1.36954	+	5.11120i	0.107271	+	0.400340i	0.998593	−	0.0530306i	$-0.0168881\pi$
$163$	1.36954	+	5.11120i	0.107271	+	0.400340i	−0.891322	+	0.453371i	$0.850221\pi$
$164$	8.87412	+	15.3704i	0.692952	+	1.20023i
$165$		0			0
$166$	2.50000	−	4.33013i	0.194038	−	0.336083i
$167$	11.0680	−	11.0680i	0.856465	−	0.856465i	−0.134454	−	0.990920i	$-0.542928\pi$
$167$	11.0680	−	11.0680i	0.856465	−	0.856465i	0.990920	+	0.134454i	$0.0429282\pi$
$168$	−5.84764	+	8.41458i	−0.451155	+	0.649199i
$169$		−	15.0000i		−	1.15385i
$170$		0			0
$171$	5.62348	−	2.09201i	0.430038	−	0.159980i
$172$	−2.05431	+	7.66680i	−0.156640	+	0.584588i
$173$	8.63950	−	2.31495i	0.656849	−	0.176002i	0.0850256	−	0.996379i	$-0.472903\pi$
$173$	8.63950	−	2.31495i	0.656849	−	0.176002i	0.571824	+	0.820377i	$0.306236\pi$
$174$	−14.7902	−	17.5000i	−1.12124	−	1.32667i
$175$		0			0
$176$		0			0
$177$	16.8292	+	11.6953i	1.26496	+	0.879071i
$178$	−12.7780	−	3.42385i	−0.957751	−	0.256629i
$179$	−5.91608	−	10.2470i	−0.442189	−	0.765893i	0.555663	−	0.831408i	$-0.312464\pi$
$179$	−5.91608	−	10.2470i	−0.442189	−	0.765893i	−0.997852	+	0.0655145i	$0.979131\pi$
$180$		0			0
$181$	−3.00000			−0.222988			−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000			−0.222988			−0.111494	+	0.993765i	$0.535564\pi$
$182$	−22.1359	+	22.1359i	−1.64083	+	1.64083i
$183$	−1.59329	+	18.9858i	−0.117780	+	1.40347i
$184$	−12.9904	−	7.50000i	−0.957664	−	0.552907i
$185$		0			0
$186$	2.62348	−	7.28817i	0.192363	−	0.534394i
$187$		0			0
$188$	−18.9737	−	18.9737i	−1.38380	−	1.38380i
$189$	11.9783	+	6.74695i	0.871290	+	0.490768i
$190$		0			0
$191$	20.4939	+	11.8322i	1.48289	+	0.856145i	0.999811	−	0.0194337i	$-0.00618632\pi$
$191$	20.4939	+	11.8322i	1.48289	+	0.856145i	0.483076	+	0.875579i	$0.339520\pi$
$192$	9.58818	+	20.3732i	0.691967	+	1.47031i
$193$	10.2224	+	2.73908i	0.735824	+	0.197164i	0.607221	−	0.794533i	$-0.292284\pi$
$193$	10.2224	+	2.73908i	0.735824	+	0.197164i	0.128603	+	0.991696i	$0.458951\pi$
$194$	11.8322	−	20.4939i	0.849500	−	1.47138i
$195$		0			0
$196$	21.0000			1.50000
$197$	18.9737	−	18.9737i	1.35182	−	1.35182i	0.468190	−	0.883628i	$-0.344906\pi$
$197$	18.9737	−	18.9737i	1.35182	−	1.35182i	0.883628	−	0.468190i	$-0.155094\pi$
$198$		0			0
$199$	6.92820	−	4.00000i	0.491127	−	0.283552i	−0.233915	−	0.972257i	$-0.575154\pi$
$199$	6.92820	−	4.00000i	0.491127	−	0.283552i	0.725042	+	0.688705i	$0.241820\pi$
$200$		0			0
$201$	−0.811738	−	4.51011i	−0.0572556	−	0.318119i
$202$	−9.35414	−	9.35414i	−0.658155	−	0.658155i
$203$	−4.05116	+	15.1191i	−0.284336	+	1.06115i
$204$	−17.7482	+	15.0000i	−1.24263	+	1.05021i
$205$		0			0
$206$	−15.3704	+	8.87412i	−1.07091	+	0.618289i
$207$	−8.37559	+	18.2989i	−0.582144	+	1.27186i
$208$	1.36954	+	5.11120i	0.0949606	+	0.354398i
$209$		0			0
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	3.47242	+	12.9593i	0.238487	+	0.890045i
$213$	−8.72684	−	18.5430i	−0.597953	−	1.27054i
$214$	4.33013	−	2.50000i	0.296001	−	0.170896i
$215$		0			0
$216$	−10.0000	+	5.91608i	−0.680414	+	0.402538i
$217$	−5.11120	+	1.36954i	−0.346971	+	0.0929705i
$218$	11.0680	+	11.0680i	0.749618	+	0.749618i
$219$	9.02022	−	1.62348i	0.609530	−	0.109704i
$220$		0			0
$221$	−20.4939	+	11.8322i	−1.37857	+	0.795917i
$222$	−33.6583	−	23.3906i	−2.25900	−	1.56987i
$223$	3.74166	−	3.74166i	0.250560	−	0.250560i	−0.570640	−	0.821200i	$-0.693305\pi$
$223$	3.74166	−	3.74166i	0.250560	−	0.250560i	0.821200	+	0.570640i	$0.193305\pi$
$224$	8.87412	−	15.3704i	0.592927	−	1.02698i
$225$		0			0
$226$	−5.00000	+	8.66025i	−0.332595	+	0.576072i
$227$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$227$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$228$	9.40301	−	4.42531i	0.622730	−	0.293074i
$229$	−15.5885	−	9.00000i	−1.03011	−	0.594737i	−0.113097	−	0.993584i	$-0.536077\pi$
$229$	−15.5885	−	9.00000i	−1.03011	−	0.594737i	−0.917017	+	0.398847i	$0.869410\pi$
$230$		0			0
$231$		0			0
$232$	−9.35414	−	9.35414i	−0.614130	−	0.614130i
$233$	21.5988	−	5.78737i	1.41498	−	0.379143i	0.531281	−	0.847196i	$-0.321711\pi$
$233$	21.5988	−	5.78737i	1.41498	−	0.379143i	0.883701	+	0.468052i	$0.155044\pi$
$234$	−33.2689	+	12.3765i	−2.17486	+	0.809079i
$235$		0			0
$236$	30.7409	+	17.7482i	2.00106	+	1.15531i
$237$	−3.45197	−	0.289690i	−0.224229	−	0.0188174i
$238$	25.5560	+	6.84771i	1.65655	+	0.443871i
$239$	−11.8322			−0.765359			−0.382679	−	0.923881i	$-0.624999\pi$
$239$	−11.8322			−0.765359			−0.382679	+	0.923881i	$0.624999\pi$
$240$		0			0
$241$	3.00000	+	5.19615i	0.193247	+	0.334714i	0.946324	−	0.323218i	$-0.104765\pi$
$241$	3.00000	+	5.19615i	0.193247	+	0.334714i	−0.753077	+	0.657932i	$0.771431\pi$
$242$	23.7586	+	6.36611i	1.52726	+	0.409229i
$243$	9.16593	+	12.6090i	0.587995	+	0.808865i
$244$			33.0000i			2.11261i
$245$		0			0
$246$	17.5000	−	14.7902i	1.11576	−	0.942989i
$247$	10.2224	−	2.73908i	0.650436	−	0.174284i
$248$	1.15747	−	4.31975i	0.0734997	−	0.274305i
$249$	−3.64408	−	1.31174i	−0.230934	−	0.0831280i
$250$		0			0
$251$		−	11.8322i		−	0.746839i	−0.927663	−	0.373420i	$-0.878185\pi$
$251$		−	11.8322i		−	0.746839i	0.927663	−	0.373420i	$-0.121815\pi$
$252$	21.6515	+	9.91014i	1.36392	+	0.624280i
$253$		0			0
$254$	−17.7482	+	30.7409i	−1.11362	+	1.92885i
$255$		0			0
$256$	4.50000	+	7.79423i	0.281250	+	0.487139i
$257$	6.94484	+	25.9185i	0.433207	+	1.61675i	0.745320	+	0.666707i	$0.232297\pi$
$257$	6.94484	+	25.9185i	0.433207	+	1.61675i	−0.312112	+	0.950045i	$0.601037\pi$
$258$	10.2111	+	0.856914i	0.635713	+	0.0533491i
$259$			28.0000i			1.73984i
$260$		0			0
$261$	−11.3117	+	13.6764i	−0.700179	+	0.846549i
$262$		0			0
$263$	1.73621	−	6.47963i	0.107059	−	0.399551i	−0.891511	−	0.452998i	$-0.850354\pi$
$263$	1.73621	−	6.47963i	0.107059	−	0.399551i	0.998571	+	0.0534475i	$0.0170210\pi$
$264$		0			0
$265$		0			0
$266$	−10.2470	−	5.91608i	−0.628281	−	0.362738i
$267$	−0.856914	+	10.2111i	−0.0524423	+	0.624907i
$268$	−2.05431	−	7.66680i	−0.125487	−	0.468324i
$269$	−2.95804	−	5.12348i	−0.180355	−	0.312384i	0.761647	−	0.647993i	$-0.224391\pi$
$269$	−2.95804	−	5.12348i	−0.180355	−	0.312384i	−0.942001	+	0.335609i	$0.891058\pi$
$270$		0			0
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$	3.16228	−	3.16228i	0.191741	−	0.191741i
$273$	19.9125	+	13.8380i	1.20516	+	0.837516i
$274$			20.0000i			1.20824i
$275$		0			0
$276$	−11.8056	+	32.7968i	−0.710616	+	1.97413i
$277$	−4.10862	+	15.3336i	−0.246863	+	0.921307i	0.725574	+	0.688144i	$0.241574\pi$
$277$	−4.10862	+	15.3336i	−0.246863	+	0.921307i	−0.972438	+	0.233163i	$0.925092\pi$
$278$	17.2790	−	4.62990i	1.03633	−	0.277683i
$279$	−5.91608	−	1.00000i	−0.354186	−	0.0598684i
$280$		0			0
$281$		−	23.6643i		−	1.41169i	−0.708364	−	0.705847i	$-0.750566\pi$
$281$		−	23.6643i		−	1.41169i	0.708364	−	0.705847i	$-0.249434\pi$
$282$	−19.7686	+	28.4465i	−1.17720	+	1.69396i
$283$	−5.11120	−	1.36954i	−0.303829	−	0.0814108i	0.103683	−	0.994610i	$-0.466937\pi$
$283$	−5.11120	−	1.36954i	−0.303829	−	0.0814108i	−0.407513	+	0.913200i	$0.633604\pi$
$284$	−17.7482	−	30.7409i	−1.05316	−	1.82413i
$285$		0			0
$286$		0			0
$287$	−15.1191	−	4.05116i	−0.892454	−	0.239132i
$288$	16.4029	−	11.6595i	0.966552	−	0.687043i
$289$	2.59808	+	1.50000i	0.152828	+	0.0882353i
$290$		0			0
$291$	−17.2470	−	6.20828i	−1.01103	−	0.363936i
$292$	15.3336	−	4.10862i	0.897331	−	0.240439i
$293$	6.32456	+	6.32456i	0.369484	+	0.369484i	0.867289	−	0.497805i	$-0.165860\pi$
$293$	6.32456	+	6.32456i	0.369484	+	0.369484i	−0.497805	+	0.867289i	$0.665860\pi$
$294$	−4.80230	−	26.6822i	−0.280076	−	1.55614i
$295$		0			0
$296$	−20.4939	−	11.8322i	−1.19118	−	0.687730i
$297$		0			0
$298$	−38.3340	−	10.2716i	−2.22063	−	0.595016i
$299$	−17.7482	+	30.7409i	−1.02641	+	1.77779i
$300$		0			0
$301$	−3.50000	−	6.06218i	−0.201737	−	0.349418i
$302$	9.48683	−	9.48683i	0.545906	−	0.545906i
$303$	−5.84764	+	8.41458i	−0.335938	+	0.483405i
$304$	−1.73205	+	1.00000i	−0.0993399	+	0.0573539i
$305$		0			0
$306$	23.1174	+	19.1203i	1.32153	+	1.09304i
$307$	−5.61249	−	5.61249i	−0.320321	−	0.320321i	0.528569	−	0.848890i	$-0.322729\pi$
$307$	−5.61249	−	5.61249i	−0.320321	−	0.320321i	−0.848890	+	0.528569i	$0.822729\pi$
$308$		0			0
$309$	8.87412	+	10.5000i	0.504831	+	0.597324i
$310$		0			0
$311$	−10.2470	+	5.91608i	−0.581051	+	0.335470i	−0.761551	−	0.648105i	$-0.775562\pi$
$311$	−10.2470	+	5.91608i	−0.581051	+	0.335470i	0.180500	+	0.983575i	$0.442228\pi$
$312$	−18.5430	+	8.72684i	−1.04979	+	0.494060i
$313$	−2.73908	−	10.2224i	−0.154822	−	0.577804i	−0.999121	−	0.0419307i	$-0.986649\pi$
$313$	−2.73908	−	10.2224i	−0.154822	−	0.577804i	0.844298	−	0.535873i	$-0.180018\pi$
$314$	−23.6643			−1.33545
$315$		0			0
$316$	−6.00000			−0.337526
$317$	−5.78737	−	21.5988i	−0.325051	−	1.21311i	−0.914261	−	0.405127i	$-0.867227\pi$
$317$	−5.78737	−	21.5988i	−0.325051	−	1.21311i	0.589209	−	0.807980i	$-0.299439\pi$
$318$	15.6717	−	7.37552i	0.878824	−	0.413599i
$319$		0			0
$320$		0			0
$321$	−2.50000	−	2.95804i	−0.139536	−	0.165102i
$322$	38.3340	−	10.2716i	2.13627	−	0.572412i
$323$	−6.32456	−	6.32456i	−0.351908	−	0.351908i
$324$	17.6466	+	20.4352i	0.980366	+	1.13529i
$325$		0			0
$326$	10.2470	−	5.91608i	0.567526	−	0.327661i
$327$	6.91902	−	9.95626i	0.382623	−	0.550583i
$328$	9.35414	−	9.35414i	0.516496	−	0.516496i
$329$	23.6643			1.30466
$330$		0			0
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	−0.991735	−	0.128302i	$-0.959047\pi$
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	0.606980	+	0.794717i	$0.292381\pi$
$332$	−6.47963	−	1.73621i	−0.355616	−	0.0952870i
$333$	−13.2135	+	28.8687i	−0.724096	+	1.58200i
$334$	−30.3109	−	17.5000i	−1.65854	−	0.957557i
$335$		0			0
$336$	−4.31174	−	1.55207i	−0.235225	−	0.0846723i
$337$	3.74166	+	3.74166i	0.203821	+	0.203821i	0.801635	−	0.597814i	$-0.203964\pi$
$337$	3.74166	+	3.74166i	0.203821	+	0.203821i	−0.597814	+	0.801635i	$0.703964\pi$
$338$	−32.3981	+	8.68105i	−1.76223	+	0.472187i
$339$	7.28817	+	2.62348i	0.395839	+	0.142488i
$340$		0			0
$341$		0			0
$342$	−7.77300	−	10.9353i	−0.420316	−	0.591312i
$343$	−13.0958	+	13.0958i	−0.707107	+	0.707107i
$344$	5.91608			0.318974
$345$		0			0
$346$	−10.0000	−	17.3205i	−0.537603	−	0.931156i
$347$	−10.7994	−	2.89368i	−0.579741	−	0.155341i	−0.0429807	−	0.999076i	$-0.513685\pi$
$347$	−10.7994	−	2.89368i	−0.579741	−	0.155341i	−0.536760	+	0.843735i	$0.680352\pi$
$348$	−17.5429	+	25.2437i	−0.940399	+	1.35321i
$349$		−	31.0000i		−	1.65939i	−0.558216	−	0.829696i	$-0.688514\pi$
$349$		−	31.0000i		−	1.65939i	0.558216	−	0.829696i	$-0.311486\pi$
$350$		0			0
$351$	14.0000	+	23.6643i	0.747265	+	1.26311i
$352$		0			0
$353$	−3.47242	+	12.9593i	−0.184818	+	0.689752i	0.809851	+	0.586636i	$0.199548\pi$
$353$	−3.47242	+	12.9593i	−0.184818	+	0.689752i	−0.994669	+	0.103116i	$0.967119\pi$
$354$	15.5207	−	43.1174i	0.824915	−	2.29166i
$355$		0			0
$356$			17.7482i			0.940655i
$357$	1.71383	−	20.4221i	0.0907054	−	1.08085i
$358$	−18.7083	+	18.7083i	−0.988764	+	0.988764i
$359$	5.91608	−	10.2470i	0.312239	−	0.540813i	−0.666608	−	0.745409i	$-0.732254\pi$
$359$	5.91608	−	10.2470i	0.312239	−	0.540813i	0.978847	+	0.204595i	$0.0655878\pi$
$360$		0			0
$361$	−7.50000	−	12.9904i	−0.394737	−	0.683704i
$362$	1.73621	+	6.47963i	0.0912532	+	0.340562i
$363$	1.59329	−	18.9858i	0.0836263	−	0.996497i
$364$	36.3731	+	21.0000i	1.90647	+	1.10070i
$365$		0			0
$366$	41.9291	−	7.54648i	2.19167	−	0.394461i
$367$	−2.05431	+	7.66680i	−0.107234	+	0.400204i	−0.998589	−	0.0531027i	$-0.983089\pi$
$367$	−2.05431	+	7.66680i	−0.107234	+	0.400204i	0.891355	+	0.453306i	$0.149756\pi$
$368$	1.73621	−	6.47963i	0.0905063	−	0.337774i
$369$	−13.6764	−	11.3117i	−0.711966	−	0.588866i
$370$		0			0
$371$	−10.2470	−	5.91608i	−0.531995	−	0.307148i
$372$	−10.3559	−	0.869070i	−0.536929	−	0.0450592i
$373$	−5.47817	−	20.4448i	−0.283649	−	1.05859i	−0.949821	−	0.312794i	$-0.898735\pi$
$373$	−5.47817	−	20.4448i	−0.283649	−	1.05859i	0.666172	−	0.745798i	$-0.267931\pi$
$374$		0			0
$375$		0			0
$376$	−10.0000	+	17.3205i	−0.515711	+	0.893237i
$377$	−22.1359	+	22.1359i	−1.14006	+	1.14006i
$378$	7.64032	−	29.7763i	0.392975	−	1.53153i
$379$			18.0000i			0.924598i	0.886724	+	0.462299i	$0.152975\pi$
$379$			18.0000i			0.924598i	−0.886724	+	0.462299i	$0.847025\pi$
$380$		0			0
$381$	25.8704	+	9.31241i	1.32538	+	0.477089i
$382$	13.6954	−	51.1120i	0.700718	−	2.61512i
$383$	6.47963	−	1.73621i	0.331093	−	0.0887162i	−0.0894428	−	0.995992i	$-0.528509\pi$
$383$	6.47963	−	1.73621i	0.331093	−	0.0887162i	0.420536	+	0.907276i	$0.361842\pi$
$384$	20.7063	−	17.5000i	1.05666	−	0.893043i
$385$		0			0
$386$		−	23.6643i		−	1.20448i
$387$	−0.747780	−	7.90195i	−0.0380118	−	0.401679i
$388$	−30.6672	−	8.21725i	−1.55689	−	0.417168i
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$		0			0
$391$	30.0000			1.51717
$392$	−4.05116	−	15.1191i	−0.204614	−	0.763631i
$393$		0			0
$394$	−51.9615	−	30.0000i	−2.61778	−	1.51138i
$395$		0			0
$396$		0			0
$397$	20.4448	−	5.47817i	1.02609	−	0.274941i	0.293755	−	0.955881i	$-0.405095\pi$
$397$	20.4448	−	5.47817i	1.02609	−	0.274941i	0.732340	+	0.680939i	$0.238428\pi$
$398$	−12.6491	−	12.6491i	−0.634043	−	0.634043i
$399$	−3.10414	+	8.62348i	−0.155401	+	0.431714i
$400$		0			0
$401$	−15.3704	−	8.87412i	−0.767562	−	0.443152i	0.0644419	−	0.997921i	$-0.479473\pi$
$401$	−15.3704	−	8.87412i	−0.767562	−	0.443152i	−0.832004	+	0.554769i	$0.812807\pi$
$402$	−9.27149	+	4.36342i	−0.462420	+	0.217628i
$403$	−10.2224	−	2.73908i	−0.509214	−	0.136443i
$404$	−8.87412	+	15.3704i	−0.441504	+	0.764707i
$405$		0			0
$406$	35.0000			1.73702
$407$		0			0
$408$	14.2232	+	9.88431i	0.704155	+	0.489346i
$409$	11.2583	−	6.50000i	0.556689	−	0.321404i	−0.195127	−	0.980778i	$-0.562512\pi$
$409$	11.2583	−	6.50000i	0.556689	−	0.321404i	0.751815	+	0.659374i	$0.229178\pi$
$410$		0			0
$411$	15.2470	−	2.74417i	0.752077	−	0.135360i
$412$	16.8375	+	16.8375i	0.829522	+	0.829522i
$413$	−30.2383	+	8.10232i	−1.48793	+	0.398689i
$414$	44.3706	+	7.50000i	2.18070	+	0.368605i
$415$		0			0
$416$	30.7409	−	17.7482i	1.50719	−	0.870179i
$417$	−5.90042	−	12.5373i	−0.288945	−	0.613956i
$418$		0			0
$419$	−23.6643			−1.15608			−0.578039	−	0.816009i	$-0.696182\pi$
$419$	−23.6643			−1.15608			−0.578039	+	0.816009i	$0.696182\pi$
$420$		0			0
$421$	−11.0000			−0.536107			−0.268054	−	0.963404i	$-0.586380\pi$
$421$	−11.0000			−0.536107			−0.268054	+	0.963404i	$0.586380\pi$
$422$	−8.10232	−	30.2383i	−0.394415	−	1.47198i
$423$	24.3985	+	11.1675i	1.18630	+	0.542980i
$424$	8.66025	−	5.00000i	0.420579	−	0.242821i
$425$		0			0
$426$	−35.0000	+	29.5804i	−1.69576	+	1.43318i
$427$	−20.5791	−	20.5791i	−0.995893	−	0.995893i
$428$	−4.74342	−	4.74342i	−0.229282	−	0.229282i
$429$		0			0
$430$		0			0
$431$	−20.4939	+	11.8322i	−0.987157	+	0.569935i	−0.904423	−	0.426637i	$-0.859698\pi$
$431$	−20.4939	+	11.8322i	−0.987157	+	0.569935i	−0.0827334	+	0.996572i	$0.526365\pi$
$432$	−3.71307	−	3.63498i	−0.178645	−	0.174888i
$433$	11.2250	−	11.2250i	0.539438	−	0.539438i	−0.383926	−	0.923364i	$-0.625428\pi$
$433$	11.2250	−	11.2250i	0.539438	−	0.539438i	0.923364	+	0.383926i	$0.125428\pi$
$434$	5.91608	+	10.2470i	0.283981	+	0.491869i
$435$		0			0
$436$	10.5000	−	18.1865i	0.502859	−	0.870977i
$437$	−12.9593	−	3.47242i	−0.619925	−	0.166108i
$438$	−8.72684	−	18.5430i	−0.416984	−	0.886018i
$439$	27.7128	+	16.0000i	1.32266	+	0.763638i	0.984152	−	0.177325i	$-0.0567444\pi$
$439$	27.7128	+	16.0000i	1.32266	+	0.763638i	0.338508	+	0.940963i	$0.390078\pi$
$440$		0			0
$441$	−19.6822	+	7.32205i	−0.937246	+	0.348669i
$442$	37.4166	+	37.4166i	1.77972	+	1.77972i
$443$	−2.15988	+	0.578737i	−0.102619	+	0.0274966i	−0.309763	−	0.950814i	$-0.600250\pi$
$443$	−2.15988	+	0.578737i	−0.102619	+	0.0274966i	0.207144	+	0.978310i	$0.433583\pi$
$444$	−18.6248	+	51.7409i	−0.883895	+	2.45551i
$445$		0			0
$446$	−10.2470	−	5.91608i	−0.485207	−	0.280134i
$447$	−2.57074	+	30.6332i	−0.121592	+	1.44890i
$448$	−33.2228	−	8.90202i	−1.56963	−	0.420581i
$449$	17.7482			0.837591			0.418796	−	0.908081i	$-0.362452\pi$
$449$	17.7482			0.837591			0.418796	+	0.908081i	$0.362452\pi$
$450$		0			0
$451$		0			0
$452$	12.9593	+	3.47242i	0.609552	+	0.163329i
$453$	−8.53394	−	5.93059i	−0.400959	−	0.278643i
$454$		0			0
$455$		0			0
$456$	−5.00000	−	5.91608i	−0.234146	−	0.277046i
$457$	−10.2224	+	2.73908i	−0.478184	+	0.128129i	−0.489857	−	0.871803i	$-0.662951\pi$
$457$	−10.2224	+	2.73908i	−0.478184	+	0.128129i	0.0116731	+	0.999932i	$0.496284\pi$
$458$	−10.4173	+	38.8778i	−0.486767	+	1.81664i
$459$	11.4044	−	20.2470i	0.532313	−	0.945047i
$460$		0			0
$461$		−	23.6643i		−	1.10216i	−0.834453	−	0.551079i	$-0.814216\pi$
$461$		−	23.6643i		−	1.10216i	0.834453	−	0.551079i	$-0.185784\pi$
$462$		0			0
$463$	13.0958	−	13.0958i	0.608613	−	0.608613i	−0.333970	−	0.942584i	$-0.608388\pi$
$463$	13.0958	−	13.0958i	0.608613	−	0.608613i	0.942584	+	0.333970i	$0.108388\pi$
$464$	2.95804	−	5.12348i	0.137324	−	0.237851i
$465$		0			0
$466$	−25.0000	−	43.3013i	−1.15810	−	2.00589i
$467$	4.05116	+	15.1191i	0.187465	+	0.699630i	0.994089	+	0.108565i	$0.0346256\pi$
$467$	4.05116	+	15.1191i	0.187465	+	0.699630i	−0.806624	+	0.591065i	$0.798708\pi$
$468$	27.5914	+	38.8164i	1.27541	+	1.79429i
$469$	6.06218	+	3.50000i	0.279925	+	0.161615i
$470$		0			0
$471$	3.24695	+	18.0404i	0.149612	+	0.831259i
$472$	6.84771	−	25.5560i	0.315191	−	1.17631i
$473$		0			0
$474$	1.37209	+	7.62348i	0.0630220	+	0.350158i
$475$		0			0
$476$		−	35.4965i		−	1.62698i
$477$	−7.77300	−	10.9353i	−0.355901	−	0.500692i
$478$	6.84771	+	25.5560i	0.313207	+	1.16890i
$479$	17.7482	+	30.7409i	0.810938	+	1.40459i	0.912208	+	0.409726i	$0.134376\pi$
$479$	17.7482	+	30.7409i	0.810938	+	1.40459i	−0.101271	+	0.994859i	$0.532291\pi$
$480$		0			0
$481$	−28.0000	+	48.4974i	−1.27669	+	2.21129i
$482$	9.48683	−	9.48683i	0.432113	−	0.432113i
$483$	−13.0903	−	27.8145i	−0.595627	−	1.26560i
$484$		−	33.0000i		−	1.50000i
$485$		0			0
$486$	21.9291	−	27.0945i	0.994725	−	1.22903i
$487$	1.36954	−	5.11120i	0.0620599	−	0.231611i	−0.927929	−	0.372757i	$-0.878412\pi$
$487$	1.36954	−	5.11120i	0.0620599	−	0.231611i	0.989989	+	0.141147i	$0.0450790\pi$
$488$	23.7586	−	6.36611i	1.07550	−	0.288180i
$489$	−5.91608	−	7.00000i	−0.267534	−	0.316551i
$490$		0			0
$491$		−	11.8322i		−	0.533978i	−0.963700	−	0.266989i	$-0.913971\pi$
$491$		−	11.8322i		−	0.533978i	0.963700	−	0.266989i	$-0.0860287\pi$
$492$	−25.2437	−	17.5429i	−1.13808	−	0.790896i
$493$	25.5560	+	6.84771i	1.15098	+	0.308405i
$494$	−11.8322	−	20.4939i	−0.532354	−	0.922064i
$495$		0			0
$496$	2.00000			0.0898027
$497$	30.2383	+	8.10232i	1.35637	+	0.363439i
$498$	−0.724225	+	8.62992i	−0.0324533	+	0.386716i
$499$	10.3923	+	6.00000i	0.465223	+	0.268597i	0.714238	−	0.699903i	$-0.246773\pi$
$499$	10.3923	+	6.00000i	0.465223	+	0.268597i	−0.249015	+	0.968500i	$0.580107\pi$
$500$		0			0
$501$	−9.18216	+	25.5086i	−0.410229	+	1.13964i
$502$	−25.5560	+	6.84771i	−1.14062	+	0.305628i
$503$	23.7171	+	23.7171i	1.05749	+	1.05749i	0.998243	+	0.0592492i	$0.0188707\pi$
$503$	23.7171	+	23.7171i	1.05749	+	1.05749i	0.0592492	+	0.998243i	$0.481129\pi$
$504$	2.95804	−	17.5000i	0.131762	−	0.779512i
$505$		0			0
$506$		0			0
$507$	11.0633	+	23.5075i	0.491338	+	1.04401i
$508$	46.0008	+	12.3259i	2.04096	+	0.546872i
$509$	−8.87412	+	15.3704i	−0.393338	+	0.681282i	−0.992888	−	0.119056i	$-0.962013\pi$
$509$	−8.87412	+	15.3704i	−0.393338	+	0.681282i	0.599549	+	0.800338i	$0.295347\pi$
$510$		0			0
$511$	−7.00000	+	12.1244i	−0.309662	+	0.536350i
$512$	−7.90569	+	7.90569i	−0.349386	+	0.349386i
$513$	−7.26996	+	7.42615i	−0.320977	+	0.327872i
$514$	51.9615	−	30.0000i	2.29192	−	1.32324i
$515$		0			0
$516$	−2.43521	−	13.5303i	−0.107204	−	0.595639i
$517$		0			0
$518$	60.4765	−	16.2046i	2.65719	−	0.711991i
$519$	−11.8322	+	10.0000i	−0.519374	+	0.438951i
$520$		0			0
$521$	20.4939	−	11.8322i	0.897854	−	0.518376i	0.0213508	−	0.999772i	$-0.493203\pi$
$521$	20.4939	−	11.8322i	0.897854	−	0.518376i	0.876503	+	0.481396i	$0.159870\pi$
$522$	36.0859	+	16.5169i	1.57944	+	0.722925i
$523$	−9.58679	−	35.7784i	−0.419201	−	1.56448i	−0.776269	−	0.630402i	$-0.782890\pi$
$523$	−9.58679	−	35.7784i	−0.419201	−	1.56448i	0.357068	−	0.934078i	$-0.383776\pi$
$524$		0			0
$525$		0			0
$526$	−15.0000			−0.654031
$527$	2.31495	+	8.63950i	0.100841	+	0.376343i
$528$		0			0
$529$	19.0526	−	11.0000i	0.828372	−	0.478261i
$530$		0			0
$531$	−35.0000	−	5.91608i	−1.51887	−	0.256736i
$532$	−4.10862	+	15.3336i	−0.178131	+	0.664796i
$533$	−22.1359	−	22.1359i	−0.958814	−	0.958814i
$534$	22.5505	−	4.05869i	0.975857	−	0.175637i
$535$		0			0
$536$	−5.12348	+	2.95804i	−0.221300	+	0.127768i
$537$	16.8292	+	11.6953i	0.726232	+	0.504688i
$538$	−9.35414	+	9.35414i	−0.403286	+	0.403286i
$539$		0			0
$540$		0			0
$541$	−9.50000	+	16.4545i	−0.408437	+	0.707433i	−0.994715	−	0.102677i	$-0.967259\pi$
$541$	−9.50000	+	16.4545i	−0.408437	+	0.707433i	0.586278	+	0.810110i	$0.300593\pi$
$542$	4.31975	+	1.15747i	0.185549	+	0.0497178i
$543$	4.70150	−	2.21266i	0.201761	−	0.0949542i
$544$	−25.9808	−	15.0000i	−1.11392	−	0.643120i
$545$		0			0
$546$	18.3643	−	51.0172i	0.785921	−	2.18333i
$547$	−24.3208	−	24.3208i	−1.03988	−	1.03988i	−0.999171	−	0.0407102i	$-0.987038\pi$
$547$	−24.3208	−	24.3208i	−1.03988	−	1.03988i	−0.0407102	−	0.999171i	$-0.512962\pi$
$548$	25.9185	−	6.94484i	1.10718	−	0.296669i
$549$	−11.5061	−	30.9291i	−0.491068	−	1.32002i
$550$		0			0
$551$	−10.2470	−	5.91608i	−0.436535	−	0.252033i
$552$	25.8898	+	2.17267i	1.10194	+	0.0924751i
$553$	3.74166	−	3.74166i	0.159111	−	0.159111i
$554$	35.4965			1.50810
$555$		0			0
$556$	−12.0000	−	20.7846i	−0.508913	−	0.881464i
$557$	8.63950	+	2.31495i	0.366068	+	0.0980875i	0.437164	−	0.899382i	$-0.355983\pi$
$557$	8.63950	+	2.31495i	0.366068	+	0.0980875i	−0.0710962	+	0.997469i	$0.522650\pi$
$558$	1.26398	+	13.3567i	0.0535085	+	0.565436i
$559$		−	14.0000i		−	0.592137i
$560$		0			0
$561$		0			0
$562$	−51.1120	+	13.6954i	−2.15603	+	0.577706i
$563$	10.9960	−	41.0376i	0.463426	−	1.72953i	−0.198628	−	0.980075i	$-0.563649\pi$
$563$	10.9960	−	41.0376i	0.463426	−	1.72953i	0.662055	−	0.749455i	$-0.269685\pi$
$564$	43.7290	+	15.7409i	1.84132	+	0.662809i
$565$		0			0
$566$			11.8322i			0.497343i
$567$	−23.7482	−	1.73901i	−0.997330	−	0.0730317i
$568$	−18.7083	+	18.7083i	−0.784982	+	0.784982i
$569$	−11.8322	+	20.4939i	−0.496030	+	0.859149i	−0.999990	−	0.00457819i	$-0.998543\pi$
$569$	−11.8322	+	20.4939i	−0.496030	+	0.859149i	0.503960	+	0.863727i	$0.331876\pi$
$570$		0			0
$571$	−7.00000	−	12.1244i	−0.292941	−	0.507388i	0.681563	−	0.731760i	$-0.261301\pi$
$571$	−7.00000	−	12.1244i	−0.292941	−	0.507388i	−0.974504	+	0.224371i	$0.927967\pi$
$572$		0			0
$573$	−40.8442	−	3.42766i	−1.70629	−	0.143192i
$574$			35.0000i			1.46087i
$575$		0			0
$576$	−30.0526	−	24.8564i	−1.25219	−	1.03568i
$577$	−5.47817	+	20.4448i	−0.228059	+	0.851128i	0.753097	+	0.657910i	$0.228559\pi$
$577$	−5.47817	+	20.4448i	−0.228059	+	0.851128i	−0.981156	+	0.193218i	$0.938107\pi$
$578$	1.73621	−	6.47963i	0.0722169	−	0.269517i
$579$	−18.0404	+	3.24695i	−0.749735	+	0.134939i
$580$		0			0
$581$	5.12348	−	2.95804i	0.212558	−	0.122720i
$582$	−3.42766	+	40.8442i	−0.142081	+	1.69305i
$583$		0			0
$584$	−5.91608	−	10.2470i	−0.244809	−	0.424022i
$585$		0			0
$586$	10.0000	−	17.3205i	0.413096	−	0.715504i
$587$	12.6491	−	12.6491i	0.522085	−	0.522085i	−0.396116	−	0.918201i	$-0.629642\pi$
$587$	12.6491	−	12.6491i	0.522085	−	0.522085i	0.918201	+	0.396116i	$0.129642\pi$
$588$	−32.9105	+	15.4886i	−1.35721	+	0.638739i
$589$		−	4.00000i		−	0.164817i
$590$		0			0
$591$	−15.7409	+	43.7290i	−0.647492	+	1.79877i
$592$	2.73908	−	10.2224i	0.112576	−	0.420138i
$593$	−30.2383	+	8.10232i	−1.24174	+	0.332722i	−0.819139	−	0.573595i	$-0.805548\pi$
$593$	−30.2383	+	8.10232i	−1.24174	+	0.332722i	−0.422598	+	0.906317i	$0.638882\pi$
$594$		0			0
$595$		0			0
$596$			53.2447i			2.18099i
$597$	−7.90745	+	11.3786i	−0.323630	+	0.465695i
$598$	76.6680	+	20.5431i	3.13519	+	0.840071i
$599$	11.8322	+	20.4939i	0.483449	+	0.837358i	0.999819	−	0.0190072i	$-0.00605055\pi$
$599$	11.8322	+	20.4939i	0.483449	+	0.837358i	−0.516370	+	0.856365i	$0.672717\pi$
$600$		0			0
$601$	34.0000			1.38689			0.693444	−	0.720510i	$-0.256092\pi$
$601$	34.0000			1.38689			0.693444	+	0.720510i	$0.256092\pi$
$602$	−11.0680	+	11.0680i	−0.451097	+	0.451097i
$603$	4.59857	+	6.46940i	0.187268	+	0.263454i
$604$	−15.5885	−	9.00000i	−0.634285	−	0.366205i
$605$		0			0
$606$	21.5587	+	7.76034i	0.875762	+	0.315242i
$607$	2.55560	−	0.684771i	0.103729	−	0.0277940i	−0.206581	−	0.978429i	$-0.566234\pi$
$607$	2.55560	−	0.684771i	0.103729	−	0.0277940i	0.310310	+	0.950635i	$0.399567\pi$
$608$	9.48683	+	9.48683i	0.384742	+	0.384742i
$609$	−4.80230	−	26.6822i	−0.194599	−	1.08122i
$610$		0			0
$611$	40.9878	+	23.6643i	1.65819	+	0.957356i
$612$	16.7512	−	36.5978i	0.677127	−	1.47938i
$613$	35.7784	+	9.58679i	1.44508	+	0.387207i	0.894308	−	0.447452i	$-0.147668\pi$
$613$	35.7784	+	9.58679i	1.44508	+	0.387207i	0.550768	+	0.834659i	$0.314335\pi$
$614$	−8.87412	+	15.3704i	−0.358130	+	0.620300i
$615$		0			0
$616$		0			0
$617$	−12.6491	+	12.6491i	−0.509234	+	0.509234i	−0.914291	−	0.405057i	$-0.867252\pi$
$617$	−12.6491	+	12.6491i	−0.509234	+	0.509234i	0.405057	+	0.914291i	$0.367252\pi$
$618$	17.5429	−	25.2437i	0.705680	−	1.01545i
$619$	−31.1769	+	18.0000i	−1.25311	+	0.723481i	−0.971725	−	0.236115i	$-0.924126\pi$
$619$	−31.1769	+	18.0000i	−1.25311	+	0.723481i	−0.281381	+	0.959596i	$0.590792\pi$
$620$		0			0
$621$	−0.370426	−	34.8549i	−0.0148647	−	1.39868i
$622$	18.7083	+	18.7083i	0.750134	+	0.750134i
$623$	−11.0680	−	11.0680i	−0.443429	−	0.443429i
$624$	−5.91608	−	7.00000i	−0.236833	−	0.280224i
$625$		0			0
$626$	−20.4939	+	11.8322i	−0.819101	+	0.472908i
$627$		0			0
$628$	8.21725	+	30.6672i	0.327904	+	1.22375i
$629$	47.3286			1.88712
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$	1.15747	+	4.31975i	0.0460418	+	0.171830i
$633$	−21.9404	+	10.3257i	−0.872051	+	0.410411i
$634$	−43.3013	+	25.0000i	−1.71971	+	0.992877i
$635$		0			0
$636$	−15.0000	−	17.7482i	−0.594789	−	0.703763i
$637$	−35.7784	+	9.58679i	−1.41759	+	0.379843i
$638$		0			0
$639$	27.3528	+	22.6235i	1.08206	+	0.894971i
$640$		0			0
$641$	5.12348	−	2.95804i	0.202365	−	0.116836i	−0.395393	−	0.918512i	$-0.629392\pi$
$641$	5.12348	−	2.95804i	0.202365	−	0.116836i	0.597758	+	0.801676i	$0.296058\pi$
$642$	−4.94216	+	7.11162i	−0.195051	+	0.280673i
$643$	3.74166	−	3.74166i	0.147557	−	0.147557i	−0.629469	−	0.777026i	$-0.716728\pi$
$643$	3.74166	−	3.74166i	0.147557	−	0.147557i	0.777026	+	0.629469i	$0.216728\pi$
$644$	−26.6224	−	46.1113i	−1.04907	−	1.81704i
$645$		0			0
$646$	−10.0000	+	17.3205i	−0.393445	+	0.681466i
$647$	15.1191	+	4.05116i	0.594394	+	0.159267i	0.543461	−	0.839435i	$-0.317114\pi$
$647$	15.1191	+	4.05116i	0.594394	+	0.159267i	0.0509336	+	0.998702i	$0.483780\pi$
$648$	11.3083	−	16.6470i	0.444231	−	0.653957i
$649$		0			0
$650$		0			0
$651$	7.00000	−	5.91608i	0.274352	−	0.231869i
$652$	−11.2250	−	11.2250i	−0.439604	−	0.439604i
$653$	−12.9593	+	3.47242i	−0.507135	+	0.135886i	−0.503309	−	0.864106i	$-0.667884\pi$
$653$	−12.9593	+	3.47242i	−0.507135	+	0.135886i	−0.00382551	+	0.999993i	$0.501218\pi$
$654$	−25.5086	−	9.18216i	−0.997465	−	0.359051i
$655$		0			0
$656$	5.12348	+	2.95804i	0.200038	+	0.115492i
$657$	−12.9388	+	9.19714i	−0.504791	+	0.358815i
$658$	−13.6954	−	51.1120i	−0.533903	−	1.99255i
$659$	11.8322			0.460915			0.230458	−	0.973082i	$-0.425978\pi$
$659$	11.8322			0.460915			0.230458	+	0.973082i	$0.425978\pi$
$660$		0			0
$661$	−9.50000	−	16.4545i	−0.369507	−	0.640005i	0.619981	−	0.784617i	$-0.287140\pi$
$661$	−9.50000	−	16.4545i	−0.369507	−	0.640005i	−0.989489	+	0.144611i	$0.953807\pi$
$662$	30.2383	+	8.10232i	1.17524	+	0.314906i
$663$	23.3906	−	33.6583i	0.908414	−	1.30718i
$664$			5.00000i			0.194038i
$665$		0			0
$666$	70.0000	+	11.8322i	2.71244	+	0.458487i
$667$	38.3340	−	10.2716i	1.48430	−	0.397716i
$668$	−12.1535	+	45.3574i	−0.470232	+	1.75493i
$669$	−3.10414	+	8.62348i	−0.120013	+	0.333403i
$670$		0			0
$671$		0			0
$672$	−2.57074	+	30.6332i	−0.0991685	+	1.18170i
$673$	−14.9666	+	14.9666i	−0.576921	+	0.576921i	−0.934054	−	0.357133i	$-0.883754\pi$
$673$	−14.9666	+	14.9666i	−0.576921	+	0.576921i	0.357133	+	0.934054i	$0.383754\pi$
$674$	5.91608	−	10.2470i	0.227879	−	0.394698i
$675$		0			0
$676$	22.5000	+	38.9711i	0.865385	+	1.49889i
$677$	1.15747	+	4.31975i	0.0444853	+	0.166022i	0.984595	−	0.174851i	$-0.0559443\pi$
$677$	1.15747	+	4.31975i	0.0444853	+	0.166022i	−0.940110	+	0.340872i	$0.889278\pi$
$678$	1.44845	−	17.2598i	0.0556274	−	0.662860i
$679$	24.2487	−	14.0000i	0.930580	−	0.537271i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	2.89368	−	10.7994i	0.110724	−	0.413227i	−0.888208	−	0.459442i	$-0.848049\pi$
$683$	2.89368	−	10.7994i	0.110724	−	0.413227i	0.998932	+	0.0462153i	$0.0147160\pi$
$684$	−11.4722	+	13.8704i	−0.438650	+	0.530349i
$685$		0			0
$686$	35.8643	+	20.7063i	1.36931	+	0.790569i
$687$	31.0677	+	2.60721i	1.18531	+	0.0994712i
$688$	0.684771	+	2.55560i	0.0261066	+	0.0974313i
$689$	−11.8322	−	20.4939i	−0.450769	−	0.780755i
$690$		0			0
$691$	8.00000	−	13.8564i	0.304334	−	0.527123i	−0.672779	−	0.739844i	$-0.734899\pi$
$691$	8.00000	−	13.8564i	0.304334	−	0.527123i	0.977113	+	0.212721i	$0.0682327\pi$
$692$	−18.9737	+	18.9737i	−0.721271	+	0.721271i
$693$		0			0
$694$			25.0000i			0.948987i
$695$		0			0
$696$	21.5587	+	7.76034i	0.817180	+	0.294155i
$697$	−6.84771	+	25.5560i	−0.259375	+	0.968002i
$698$	−66.9562	+	17.9408i	−2.53433	+	0.679071i
$699$	−29.5804	+	25.0000i	−1.11883	+	0.945587i
$700$		0			0
$701$			17.7482i			0.670342i	0.942157	+	0.335171i	$0.108794\pi$
$701$			17.7482i			0.670342i	−0.942157	+	0.335171i	$0.891206\pi$
$702$	43.0097	−	43.9337i	1.62330	−	1.65817i
$703$	−20.4448	−	5.47817i	−0.771090	−	0.206613i
$704$		0			0
$705$		0			0
$706$	30.0000			1.12906
$707$	−4.05116	−	15.1191i	−0.152360	−	0.568613i
$708$	−61.2663	−	5.14149i	−2.30253	−	0.193229i
$709$	−19.9186	−	11.5000i	−0.748058	−	0.431892i	0.0769337	−	0.997036i	$-0.475487\pi$
$709$	−19.9186	−	11.5000i	−0.748058	−	0.431892i	−0.824992	+	0.565145i	$0.808820\pi$
$710$		0			0
$711$	5.62348	−	2.09201i	0.210897	−	0.0784567i
$712$	12.7780	−	3.42385i	0.478876	−	0.128314i
$713$	9.48683	+	9.48683i	0.355285	+	0.355285i
$714$	−45.1011	+	8.11738i	−1.68787	+	0.303785i
$715$		0			0
$716$	30.7409	+	17.7482i	1.14884	+	0.663283i
$717$	18.5430	−	8.72684i	0.692500	−	0.325910i
$718$	−25.5560	−	6.84771i	−0.953741	−	0.255554i
$719$	23.6643	−	40.9878i	0.882530	−	1.52859i	0.0340117	−	0.999421i	$-0.489172\pi$
$719$	23.6643	−	40.9878i	0.882530	−	1.52859i	0.848519	−	0.529166i	$-0.177495\pi$
$720$		0			0
$721$	−21.0000			−0.782081
$722$	−23.7171	+	23.7171i	−0.882658	+	0.882658i
$723$	−8.53394	−	5.93059i	−0.317381	−	0.220561i
$724$	7.79423	−	4.50000i	0.289670	−	0.167241i
$725$		0			0
$726$	−41.9291	+	7.54648i	−1.55614	+	0.280076i
$727$	−20.5791	−	20.5791i	−0.763237	−	0.763237i	0.213669	−	0.976906i	$-0.431459\pi$
$727$	−20.5791	−	20.5791i	−0.763237	−	0.763237i	−0.976906	+	0.213669i	$0.931459\pi$
$728$	8.10232	−	30.2383i	0.300292	−	1.12070i
$729$	−23.6643	−	13.0000i	−0.876456	−	0.481481i
$730$		0			0
$731$	−10.2470	+	5.91608i	−0.378997	+	0.218814i
$732$	−24.3392	−	51.7166i	−0.899604	−	1.91150i
$733$	8.21725	+	30.6672i	0.303511	+	1.13272i	0.934219	+	0.356699i	$0.116098\pi$
$733$	8.21725	+	30.6672i	0.303511	+	1.13272i	−0.630708	+	0.776020i	$0.717236\pi$
$734$	17.7482			0.655099
$735$		0			0
$736$	−45.0000			−1.65872
$737$		0			0
$738$	−16.5169	+	36.0859i	−0.607995	+	1.32834i
$739$	−27.7128	+	16.0000i	−1.01943	+	0.588570i	−0.913939	−	0.405851i	$-0.866975\pi$
$739$	−27.7128	+	16.0000i	−1.01943	+	0.588570i	−0.105493	+	0.994420i	$0.533642\pi$
$740$		0			0
$741$	−14.0000	+	11.8322i	−0.514303	+	0.434665i
$742$	−6.84771	+	25.5560i	−0.251387	+	0.938190i
$743$	−20.5548	−	20.5548i	−0.754083	−	0.754083i	0.221156	−	0.975238i	$-0.429017\pi$
$743$	−20.5548	−	20.5548i	−0.754083	−	0.754083i	−0.975238	+	0.221156i	$0.929017\pi$
$744$	1.37209	+	7.62348i	0.0503032	+	0.279490i
$745$		0			0
$746$	−40.9878	+	23.6643i	−1.50067	+	0.866412i
$747$	6.67837	−	0.631989i	0.244349	−	0.0231233i
$748$		0			0
$749$	5.91608			0.216169
$750$		0			0
$751$	18.0000	−	31.1769i	0.656829	−	1.13766i	−0.324603	−	0.945851i	$-0.605231\pi$
$751$	18.0000	−	31.1769i	0.656829	−	1.13766i	0.981432	−	0.191811i	$-0.0614361\pi$
$752$	−8.63950	−	2.31495i	−0.315050	−	0.0844175i
$753$	8.72684	+	18.5430i	0.318024	+	0.675744i
$754$	60.6218	+	35.0000i	2.20771	+	1.27462i
$755$		0			0
$756$	−41.2409	+	0.438294i	−1.49992	+	0.0159406i
$757$	26.1916	+	26.1916i	0.951950	+	0.951950i	0.998897	−	0.0469474i	$-0.0149493\pi$
$757$	26.1916	+	26.1916i	0.951950	+	0.951950i	−0.0469474	+	0.998897i	$0.514949\pi$
$758$	38.8778	−	10.4173i	1.41210	−	0.378372i
$759$		0			0
$760$		0			0
$761$	−20.4939	−	11.8322i	−0.742903	−	0.428915i	0.0802206	−	0.996777i	$-0.474438\pi$
$761$	−20.4939	−	11.8322i	−0.742903	−	0.428915i	−0.823124	+	0.567862i	$0.807771\pi$
$762$	5.14149	−	61.2663i	0.186256	−	2.21945i
$763$	4.79340	+	17.8892i	0.173533	+	0.647632i
$764$	−70.9930			−2.56844
$765$		0			0
$766$	−7.50000	−	12.9904i	−0.270986	−	0.469362i
$767$	−60.4765	−	16.2046i	−2.18368	−	0.585115i
$768$	−12.8009	−	8.89588i	−0.461913	−	0.321002i
$769$			34.0000i			1.22607i	0.790055	+	0.613036i	$0.210052\pi$
$769$			34.0000i			1.22607i	−0.790055	+	0.613036i	$0.789948\pi$
$770$		0			0
$771$	−30.0000	−	35.4965i	−1.08042	−	1.27837i
$772$	−30.6672	+	8.21725i	−1.10374	+	0.295745i
$773$	1.15747	−	4.31975i	0.0416314	−	0.155371i	−0.941981	−	0.335666i	$-0.891039\pi$
$773$	1.15747	−	4.31975i	0.0416314	−	0.155371i	0.983613	+	0.180295i	$0.0577053\pi$
$774$	−16.6345	+	6.18826i	−0.597913	+	0.222432i
$775$		0			0
$776$			23.6643i			0.849500i
$777$	−20.6515	−	43.8807i	−0.740867	−	1.57421i
$778$		0			0
$779$	5.91608	−	10.2470i	0.211966	−	0.367135i
$780$		0			0
$781$		0			0
$782$	−17.3621	−	64.7963i	−0.620868	−	2.31711i
$783$	7.64032	−	29.7763i	0.273043	−	1.06412i
$784$	6.06218	−	3.50000i	0.216506	−	0.125000i
$785$		0			0
$786$		0			0
$787$	13.0106	−	48.5564i	0.463779	−	1.73085i	−0.197125	−	0.980378i	$-0.563160\pi$
$787$	13.0106	−	48.5564i	0.463779	−	1.73085i	0.660904	−	0.750470i	$-0.270173\pi$
$788$	−20.8345	+	77.7555i	−0.742199	+	2.76993i
$789$	2.05813	+	11.4352i	0.0732714	+	0.407104i
$790$		0			0
$791$	−10.2470	+	5.91608i	−0.364340	+	0.210352i
$792$		0			0
$793$	−15.0650	−	56.2232i	−0.534972	−	1.99654i
$794$	−23.6643	−	40.9878i	−0.839815	−	1.45460i
$795$		0			0
$796$	−12.0000	+	20.7846i	−0.425329	+	0.736691i
$797$	31.6228	−	31.6228i	1.12014	−	1.12014i	0.128416	−	0.991720i	$-0.459011\pi$
$797$	31.6228	−	31.6228i	1.12014	−	1.12014i	0.991720	−	0.128416i	$-0.0409892\pi$
$798$	20.4221	+	1.71383i	0.722935	+	0.0606689i
$799$		−	40.0000i		−	1.41510i
$800$		0			0
$801$	−6.18826	−	16.6345i	−0.218651	−	0.587750i
$802$	−10.2716	+	38.3340i	−0.362701	+	1.35362i
$803$		0			0
$804$	8.87412	+	10.5000i	0.312966	+	0.370306i
$805$		0			0
$806$			23.6643i			0.833540i
$807$	8.41458	+	5.84764i	0.296207	+	0.205847i
$808$	12.7780	+	3.42385i	0.449528	+	0.120451i
$809$	20.7063	+	35.8643i	0.727994	+	1.26092i	0.957730	+	0.287670i	$0.0928805\pi$
$809$	20.7063	+	35.8643i	0.727994	+	1.26092i	−0.229736	+	0.973253i	$0.573786\pi$
$810$		0			0
$811$	−6.00000			−0.210688			−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000			−0.210688			−0.105344	+	0.994436i	$0.533594\pi$
$812$	−12.1535	−	45.3574i	−0.426503	−	1.59173i
$813$	0.289690	−	3.45197i	0.0101599	−	0.121066i
$814$		0			0
$815$		0			0
$816$	−2.62348	+	7.28817i	−0.0918400	+	0.255137i
$817$	5.11120	−	1.36954i	0.178818	−	0.0479142i
$818$	−20.5548	−	20.5548i	−0.718682	−	0.718682i
$819$	−41.4126	−	7.00000i	−1.44707	−	0.244600i
$820$		0			0
$821$	−20.4939	−	11.8322i	−0.715242	−	0.412945i	0.0977569	−	0.995210i	$-0.468833\pi$
$821$	−20.4939	−	11.8322i	−0.715242	−	0.412945i	−0.812999	+	0.582265i	$0.802167\pi$
$822$	−14.7510	−	31.3434i	−0.514502	−	1.09323i
$823$	−17.8892	−	4.79340i	−0.623578	−	0.167087i	−0.0668243	−	0.997765i	$-0.521287\pi$
$823$	−17.8892	−	4.79340i	−0.623578	−	0.167087i	−0.556754	+	0.830677i	$0.687953\pi$
$824$	8.87412	−	15.3704i	0.309145	−	0.535454i
$825$		0			0
$826$	35.0000	+	60.6218i	1.21781	+	2.10930i
$827$	14.2302	−	14.2302i	0.494834	−	0.494834i	−0.414991	−	0.909825i	$-0.636215\pi$
$827$	14.2302	−	14.2302i	0.494834	−	0.494834i	0.909825	+	0.414991i	$0.136215\pi$
$828$	−5.68790	−	60.1053i	−0.197668	−	2.08880i
$829$	−1.73205	+	1.00000i	−0.0601566	+	0.0347314i	−0.529777	−	0.848137i	$-0.677724\pi$
$829$	−1.73205	+	1.00000i	−0.0601566	+	0.0347314i	0.469620	+	0.882869i	$0.344391\pi$
$830$		0			0
$831$	−4.87043	−	27.0607i	−0.168953	−	0.938724i
$832$	−48.6415	−	48.6415i	−1.68634	−	1.68634i
$833$	22.1359	+	22.1359i	0.766965	+	0.766965i
$834$	−23.6643	+	20.0000i	−0.819428	+	0.692543i
$835$		0			0
$836$		0			0
$837$	10.0090	−	2.79625i	0.345963	−	0.0966526i
$838$	13.6954	+	51.1120i	0.473100	+	1.76563i
$839$	−23.6643			−0.816983			−0.408492	−	0.912762i	$-0.633945\pi$
$839$	−23.6643			−0.816983			−0.408492	+	0.912762i	$0.633945\pi$
$840$		0			0
$841$	6.00000			0.206897
$842$	6.36611	+	23.7586i	0.219391	+	0.818777i
$843$	17.4537	+	37.0860i	0.601137	+	1.27731i
$844$	−36.3731	+	21.0000i	−1.25201	+	0.722850i
$845$		0			0
$846$	10.0000	−	59.1608i	0.343807	−	2.03399i
$847$	20.5791	+	20.5791i	0.707107	+	0.707107i
$848$	3.16228	+	3.16228i	0.108593	+	0.108593i
$849$	9.02022	−	1.62348i	0.309573	−	0.0557175i
$850$		0			0
$851$	61.4817	−	35.4965i	2.10757	−	1.21680i
$852$	50.4875	+	35.0858i	1.72967	+	1.20202i
$853$	−26.1916	+	26.1916i	−0.896783	+	0.896783i	−0.995150	−	0.0983669i	$-0.968638\pi$
$853$	−26.1916	+	26.1916i	−0.896783	+	0.896783i	0.0983669	+	0.995150i	$0.468638\pi$
$854$	−32.5384	+	56.3582i	−1.11344	+	1.92854i
$855$		0			0
$856$	−2.50000	+	4.33013i	−0.0854482	+	0.148001i
$857$	25.9185	+	6.94484i	0.885359	+	0.237231i	0.672718	−	0.739899i	$-0.265127\pi$
$857$	25.9185	+	6.94484i	0.885359	+	0.237231i	0.212641	+	0.977130i	$0.431793\pi$
$858$		0			0
$859$	−3.46410	−	2.00000i	−0.118194	−	0.0682391i	0.439738	−	0.898126i	$-0.355071\pi$
$859$	−3.46410	−	2.00000i	−0.118194	−	0.0682391i	−0.557931	+	0.829887i	$0.688405\pi$
$860$		0			0
$861$	26.6822	−	4.80230i	0.909326	−	0.163662i
$862$	37.4166	+	37.4166i	1.27441	+	1.27441i
$863$	28.0784	−	7.52358i	0.955799	−	0.256106i	0.252978	−	0.967472i	$-0.418590\pi$
$863$	28.0784	−	7.52358i	0.955799	−	0.256106i	0.702821	+	0.711366i	$0.251923\pi$
$864$	−17.1066	+	30.3704i	−0.581980	+	1.03322i
$865$		0			0
$866$	−30.7409	−	17.7482i	−1.04462	−	0.603110i
$867$	−5.17795	−	0.434535i	−0.175852	−	0.0147576i
$868$	11.2250	−	11.2250i	0.381000	−	0.381000i
$869$		0			0
$870$		0			0
$871$	7.00000	+	12.1244i	0.237186	+	0.410818i
$872$	−15.1191	−	4.05116i	−0.511998	−	0.137190i
$873$	31.6078	−	2.99112i	1.06976	−	0.101234i
$874$			30.0000i			1.01477i
$875$		0			0
$876$	−21.0000	+	17.7482i	−0.709524	+	0.599657i
$877$	15.3336	−	4.10862i	0.517779	−	0.138738i	0.00953982	−	0.999954i	$-0.496963\pi$
$877$	15.3336	−	4.10862i	0.517779	−	0.138738i	0.508239	+	0.861216i	$0.330297\pi$
$878$	18.5196	−	69.1160i	0.625006	−	2.33255i
$879$	−14.5763	−	5.24695i	−0.491648	−	0.176975i
$880$		0			0
$881$			53.2447i			1.79386i	0.442172	+	0.896930i	$0.354208\pi$
$881$			53.2447i			1.79386i	−0.442172	+	0.896930i	$0.645792\pi$
$882$	27.2055	+	38.2735i	0.916057	+	1.28874i
$883$	−33.6749	+	33.6749i	−1.13325	+	1.13325i	−0.143618	+	0.989633i	$0.545874\pi$
$883$	−33.6749	+	33.6749i	−1.13325	+	1.13325i	−0.989633	+	0.143618i	$0.954126\pi$
$884$	35.4965	−	61.4817i	1.19388	−	2.06785i
$885$		0			0
$886$	2.50000	+	4.33013i	0.0839891	+	0.145473i
$887$	1.73621	+	6.47963i	0.0582963	+	0.217565i	0.988929	−	0.148390i	$-0.0474091\pi$
$887$	1.73621	+	6.47963i	0.0582963	+	0.217565i	−0.930633	+	0.365955i	$0.880742\pi$
$888$	40.8442	+	3.42766i	1.37064	+	0.115025i
$889$	−36.3731	+	21.0000i	−1.21991	+	0.704317i
$890$		0			0
$891$		0			0
$892$	−4.10862	+	15.3336i	−0.137567	+	0.513407i
$893$	−4.62990	+	17.2790i	−0.154934	+	0.578220i
$894$	67.6516	−	12.1761i	2.26261	−	0.407229i
$895$		0			0
$896$			41.4126i			1.38350i
$897$	5.14149	−	61.2663i	0.171669	−	2.04562i
$898$	−10.2716	−	38.3340i	−0.342766	−	1.27922i
$899$	5.91608	+	10.2470i	0.197312	+	0.341755i
$900$		0			0
$901$	−10.0000	+	17.3205i	−0.333148	+	0.577030i
$902$		0			0
$903$	9.95626	+	6.91902i	0.331324	+	0.230251i
$904$		−	10.0000i		−	0.332595i
$905$		0			0
$906$	−7.87043	+	21.8645i	−0.261477	+	0.726399i
$907$	−14.3802	+	53.6676i	−0.477486	+	1.78200i	0.134257	+	0.990947i	$0.457135\pi$
$907$	−14.3802	+	53.6676i	−0.477486	+	1.78200i	−0.611743	+	0.791057i	$0.709531\pi$
$908$		0			0
$909$	2.95804	−	17.5000i	0.0981120	−	0.580438i
$910$		0			0
$911$			23.6643i			0.784034i	0.919958	+	0.392017i	$0.128223\pi$
$911$			23.6643i			0.784034i	−0.919958	+	0.392017i	$0.871777\pi$
$912$	1.97686	−	2.84465i	0.0654605	−	0.0941957i
$913$		0			0
$914$	11.8322	+	20.4939i	0.391373	+	0.677878i
$915$		0			0
$916$	54.0000			1.78421
$917$		0			0
$918$	−50.3311	−	12.9145i	−1.66117	−	0.426242i
$919$	−12.1244	−	7.00000i	−0.399946	−	0.230909i	0.286515	−	0.958076i	$-0.407503\pi$
$919$	−12.1244	−	7.00000i	−0.399946	−	0.230909i	−0.686461	+	0.727167i	$0.740837\pi$
$920$		0			0
$921$	12.9352	+	4.65621i	0.426230	+	0.153427i
$922$	−51.1120	+	13.6954i	−1.68328	+	0.451035i
$923$	44.2719	+	44.2719i	1.45723	+	1.45723i
$924$		0			0
$925$		0			0
$926$	−35.8643	−	20.7063i	−1.17857	−	0.680451i
$927$	−21.6515	−	9.91014i	−0.711130	−	0.325492i
$928$	−38.3340	−	10.2716i	−1.25837	−	0.337181i
$929$	20.7063	−	35.8643i	0.679351	−	1.17667i	−0.295826	−	0.955242i	$-0.595595\pi$
$929$	20.7063	−	35.8643i	0.679351	−	1.17667i	0.975177	−	0.221428i	$-0.0710719\pi$
$930$		0			0
$931$	−7.00000	−	12.1244i	−0.229416	−	0.397360i
$932$	−47.4342	+	47.4342i	−1.55376	+	1.55376i
$933$	11.6953	−	16.8292i	0.382886	−	0.550962i
$934$	30.3109	−	17.5000i	0.991803	−	0.572617i
$935$		0			0
$936$	22.6235	−	27.3528i	0.739471	−	0.894056i
$937$	22.4499	+	22.4499i	0.733408	+	0.733408i	0.971293	−	0.237885i	$-0.0764543\pi$
$937$	22.4499	+	22.4499i	0.733408	+	0.733408i	−0.237885	+	0.971293i	$0.576454\pi$
$938$	4.05116	−	15.1191i	0.132275	−	0.493657i
$939$	11.8322	+	14.0000i	0.386128	+	0.456873i
$940$		0			0
$941$	40.9878	−	23.6643i	1.33616	−	0.771435i	0.349928	−	0.936777i	$-0.386206\pi$
$941$	40.9878	−	23.6643i	1.33616	−	0.771435i	0.986236	+	0.165342i	$0.0528728\pi$
$942$	37.0860	−	17.4537i	1.20833	−	0.568672i
$943$	10.2716	+	38.3340i	0.334488	+	1.24833i
$944$	11.8322			0.385104
$945$		0			0
$946$		0			0
$947$	7.52358	+	28.0784i	0.244484	+	0.912425i	0.973642	+	0.228080i	$0.0732449\pi$
$947$	7.52358	+	28.0784i	0.244484	+	0.912425i	−0.729159	+	0.684345i	$0.760088\pi$
$948$	9.40301	−	4.42531i	0.305396	−	0.143728i
$949$	−24.2487	+	14.0000i	−0.787146	+	0.454459i
$950$		0			0
$951$	25.0000	+	29.5804i	0.810681	+	0.959210i
$952$	−25.5560	+	6.84771i	−0.828275	+	0.221936i
$953$	18.9737	+	18.9737i	0.614617	+	0.614617i	0.944146	−	0.329528i	$-0.106890\pi$
$953$	18.9737	+	18.9737i	0.614617	+	0.614617i	−0.329528	+	0.944146i	$0.606890\pi$
$954$	−19.1203	+	23.1174i	−0.619043	+	0.748453i
$955$		0			0
$956$	30.7409	−	17.7482i	0.994230	−	0.574019i
$957$		0			0
$958$	56.1249	−	56.1249i	1.81331	−	1.81331i
$959$	−11.8322	+	20.4939i	−0.382080	+	0.661783i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	120.953	+	32.4093i	3.89968	+	1.04492i
$963$	6.09963	+	2.79186i	0.196558	+	0.0899666i
$964$	−15.5885	−	9.00000i	−0.502070	−	0.289870i
$965$		0			0
$966$	−52.5000	+	44.3706i	−1.68916	+	1.42760i
$967$	−20.5791	−	20.5791i	−0.661780	−	0.661780i	0.294020	−	0.955799i	$-0.405007\pi$
$967$	−20.5791	−	20.5791i	−0.661780	−	0.661780i	−0.955799	+	0.294020i	$0.905007\pi$
$968$	−23.7586	+	6.36611i	−0.763631	+	0.204614i
$969$	14.5763	+	5.24695i	0.468259	+	0.168556i
$970$		0			0
$971$	40.9878	+	23.6643i	1.31536	+	0.759424i	0.982979	−	0.183720i	$-0.0588141\pi$
$971$	40.9878	+	23.6643i	1.31536	+	0.759424i	0.332383	+	0.943145i	$0.392147\pi$
$972$	−42.7272	−	19.0101i	−1.37048	−	0.609750i
$973$	20.4448	+	5.47817i	0.655430	+	0.175622i
$974$	−11.8322			−0.379127
$975$		0			0
$976$	5.50000	+	9.52628i	0.176051	+	0.304929i
$977$	−34.5580	−	9.25979i	−1.10561	−	0.296247i	−0.340562	−	0.940222i	$-0.610617\pi$
$977$	−34.5580	−	9.25979i	−1.10561	−	0.296247i	−0.765047	+	0.643975i	$0.777284\pi$
$978$	−11.6953	+	16.8292i	−0.373974	+	0.538137i
$979$		0			0
$980$		0			0
$981$	−3.50000	+	20.7063i	−0.111746	+	0.661101i
$982$	−25.5560	+	6.84771i	−0.815525	+	0.218519i
$983$	−8.68105	+	32.3981i	−0.276883	+	1.03334i	0.677687	+	0.735351i	$0.262983\pi$
$983$	−8.68105	+	32.3981i	−0.276883	+	1.03334i	−0.954569	+	0.297989i	$0.903684\pi$
$984$	−7.76034	+	21.5587i	−0.247391	+	0.687266i
$985$		0			0
$986$		−	59.1608i		−	1.88406i
$987$	−37.0860	+	17.4537i	−1.18046	+	0.555557i
$988$	−22.4499	+	22.4499i	−0.714228	+	0.714228i
$989$	−8.87412	+	15.3704i	−0.282181	+	0.488751i
$990$		0			0
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	0.992278	+	0.124033i	$0.0395829\pi$
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	−0.388723	+	0.921355i	$0.627084\pi$
$992$	−3.47242	−	12.9593i	−0.110250	−	0.411457i
$993$	2.02783	−	24.1638i	0.0643512	−	0.766814i
$994$		−	70.0000i		−	2.22027i
$995$		0			0
$996$	11.4352	−	2.05813i	0.362339	−	0.0652144i
$997$	−4.10862	+	15.3336i	−0.130121	+	0.485620i	−0.999970	−	0.00769834i	$-0.997550\pi$
$997$	−4.10862	+	15.3336i	−0.130121	+	0.485620i	0.869849	+	0.493318i	$0.164216\pi$
$998$	6.94484	−	25.9185i	0.219835	−	0.820436i
$999$	−0.584392	−	54.9878i	−0.0184894	−	1.73974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bf.e.107.1	yes	16
3.2	odd	2	inner	525.2.bf.e.107.3	yes	16
5.2	odd	4	inner	525.2.bf.e.443.3	yes	16
5.3	odd	4	inner	525.2.bf.e.443.2	yes	16
5.4	even	2	inner	525.2.bf.e.107.4	yes	16
7.4	even	3	inner	525.2.bf.e.32.4	yes	16
15.2	even	4	inner	525.2.bf.e.443.1	yes	16
15.8	even	4	inner	525.2.bf.e.443.4	yes	16
15.14	odd	2	inner	525.2.bf.e.107.2	yes	16
21.11	odd	6	inner	525.2.bf.e.32.2	yes	16
35.4	even	6	inner	525.2.bf.e.32.1	✓	16
35.18	odd	12	inner	525.2.bf.e.368.3	yes	16
35.32	odd	12	inner	525.2.bf.e.368.2	yes	16
105.32	even	12	inner	525.2.bf.e.368.4	yes	16
105.53	even	12	inner	525.2.bf.e.368.1	yes	16
105.74	odd	6	inner	525.2.bf.e.32.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bf.e.32.1	✓	16	35.4	even	6	inner
525.2.bf.e.32.2	yes	16	21.11	odd	6	inner
525.2.bf.e.32.3	yes	16	105.74	odd	6	inner
525.2.bf.e.32.4	yes	16	7.4	even	3	inner
525.2.bf.e.107.1	yes	16	1.1	even	1	trivial
525.2.bf.e.107.2	yes	16	15.14	odd	2	inner
525.2.bf.e.107.3	yes	16	3.2	odd	2	inner
525.2.bf.e.107.4	yes	16	5.4	even	2	inner
525.2.bf.e.368.1	yes	16	105.53	even	12	inner
525.2.bf.e.368.2	yes	16	35.32	odd	12	inner
525.2.bf.e.368.3	yes	16	35.18	odd	12	inner
525.2.bf.e.368.4	yes	16	105.32	even	12	inner
525.2.bf.e.443.1	yes	16	15.2	even	4	inner
525.2.bf.e.443.2	yes	16	5.3	odd	4	inner
525.2.bf.e.443.3	yes	16	5.2	odd	4	inner
525.2.bf.e.443.4	yes	16	15.8	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.578737 - 2.15988i) q^{2} +(-1.56717 + 0.737552i) q^{3} +(-2.59808 + 1.50000i) q^{4} +(2.50000 + 2.95804i) q^{6} +(0.684771 - 2.55560i) q^{7} +(1.58114 + 1.58114i) q^{8} +(1.91203 - 2.31174i) q^{9} +O(q^{10})\)	\(q+(-0.578737 - 2.15988i) q^{2} +(-1.56717 + 0.737552i) q^{3} +(-2.59808 + 1.50000i) q^{4} +(2.50000 + 2.95804i) q^{6} +(0.684771 - 2.55560i) q^{7} +(1.58114 + 1.58114i) q^{8} +(1.91203 - 2.31174i) q^{9} +(2.96529 - 4.26697i) q^{12} +(3.74166 - 3.74166i) q^{13} -5.91608 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.31975 - 1.15747i) q^{17} +(-6.09963 - 2.79186i) q^{18} +(1.73205 + 1.00000i) q^{19} +(0.811738 + 4.51011i) q^{21} +(-6.47963 + 1.73621i) q^{23} +(-3.64408 - 1.31174i) q^{24} +(-10.2470 - 5.91608i) q^{26} +(-1.29145 + 5.03311i) q^{27} +(2.05431 + 7.66680i) q^{28} -5.91608 q^{29} +(-1.00000 - 1.73205i) q^{31} +(6.47963 + 1.73621i) q^{32} +10.0000i q^{34} +(-1.50000 + 8.87412i) q^{36} +(-10.2224 + 2.73908i) q^{37} +(1.15747 - 4.31975i) q^{38} +(-3.10414 + 8.62348i) q^{39} -5.91608i q^{41} +(9.27149 - 4.36342i) q^{42} +(1.87083 - 1.87083i) q^{43} +(7.50000 + 12.9904i) q^{46} +(2.31495 + 8.63950i) q^{47} +(0.144845 - 1.72598i) q^{48} +(-6.06218 - 3.50000i) q^{49} +(7.62348 - 1.37209i) q^{51} +(-4.10862 + 15.3336i) q^{52} +(1.15747 - 4.31975i) q^{53} +(11.6183 - 0.123475i) q^{54} +(5.12348 - 2.95804i) q^{56} +(-3.45197 - 0.289690i) q^{57} +(3.42385 + 12.7780i) q^{58} +(-5.91608 - 10.2470i) q^{59} +(5.50000 - 9.52628i) q^{61} +(-3.16228 + 3.16228i) q^{62} +(-4.59857 - 6.46940i) q^{63} -13.0000i q^{64} +(-0.684771 + 2.55560i) q^{67} +(12.9593 - 3.47242i) q^{68} +(8.87412 - 7.50000i) q^{69} +11.8322i q^{71} +(6.67837 - 0.631989i) q^{72} +(-5.11120 - 1.36954i) q^{73} +(11.8322 + 20.4939i) q^{74} -6.00000 q^{76} +(20.4221 + 1.71383i) q^{78} +(1.73205 + 1.00000i) q^{79} +(-1.68826 - 8.84024i) q^{81} +(-12.7780 + 3.42385i) q^{82} +(1.58114 + 1.58114i) q^{83} +(-8.87412 - 10.5000i) q^{84} +(-5.12348 - 2.95804i) q^{86} +(9.27149 - 4.36342i) q^{87} +(2.95804 - 5.12348i) q^{89} +(-7.00000 - 12.1244i) q^{91} +(14.2302 - 14.2302i) q^{92} +(2.84465 + 1.97686i) q^{93} +(17.3205 - 10.0000i) q^{94} +(-11.4352 + 2.05813i) q^{96} +(7.48331 + 7.48331i) q^{97} +(-4.05116 + 15.1191i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 40 q^{6}+O(q^{10}) \) 16 * q + 40 * q^6	\( 16 q + 40 q^{6} - 8 q^{16} - 28 q^{21} - 16 q^{31} - 24 q^{36} + 120 q^{46} + 40 q^{51} + 88 q^{61} - 96 q^{76} - 68 q^{81} - 112 q^{91} - 60 q^{96}+O(q^{100}) \) 16 * q + 40 * q^6 - 8 * q^16 - 28 * q^21 - 16 * q^31 - 24 * q^36 + 120 * q^46 + 40 * q^51 + 88 * q^61 - 96 * q^76 - 68 * q^81 - 112 * q^91 - 60 * q^96

Introduction

L-functions

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