LMFDB - Embedded newform 525.2.bf.e.32.4

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			32.4
Root			$-1.56717 - 0.737552i$ of defining polynomial
Character	$\chi$	$=$	525.32
Dual form			525.2.bf.e.443.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15988 + 0.578737i) q^{2} +(1.42232 + 0.988431i) q^{3} +(2.59808 + 1.50000i) q^{4} +(2.50000 + 2.95804i) q^{6} +(-2.55560 + 0.684771i) q^{7} +(1.58114 + 1.58114i) q^{8} +(1.04601 + 2.81174i) q^{9} +O(q^{10})$	\(q+(2.15988 + 0.578737i) q^{2} +(1.42232 + 0.988431i) q^{3} +(2.59808 + 1.50000i) q^{4} +(2.50000 + 2.95804i) q^{6} +(-2.55560 + 0.684771i) q^{7} +(1.58114 + 1.58114i) q^{8} +(1.04601 + 2.81174i) q^{9} +(2.21266 + 4.70150i) q^{12} +(3.74166 - 3.74166i) q^{13} -5.91608 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.15747 + 4.31975i) q^{17} +(0.631989 + 6.67837i) q^{18} +(-1.73205 + 1.00000i) q^{19} +(-4.31174 - 1.55207i) q^{21} +(1.73621 - 6.47963i) q^{23} +(0.686044 + 3.81174i) q^{24} +(10.2470 - 5.91608i) q^{26} +(-1.29145 + 5.03311i) q^{27} +(-7.66680 - 2.05431i) q^{28} -5.91608 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-1.73621 - 6.47963i) q^{32} +10.0000i q^{34} +(-1.50000 + 8.87412i) q^{36} +(2.73908 - 10.2224i) q^{37} +(-4.31975 + 1.15747i) q^{38} +(9.02022 - 1.62348i) q^{39} -5.91608i q^{41} +(-8.41458 - 5.84764i) q^{42} +(1.87083 - 1.87083i) q^{43} +(7.50000 - 12.9904i) q^{46} +(-8.63950 - 2.31495i) q^{47} +(0.144845 - 1.72598i) q^{48} +(6.06218 - 3.50000i) q^{49} +(-2.62348 + 7.28817i) q^{51} +(15.3336 - 4.10862i) q^{52} +(-4.31975 + 1.15747i) q^{53} +(-5.70221 + 10.1235i) q^{54} +(-5.12348 - 2.95804i) q^{56} +(-3.45197 - 0.289690i) q^{57} +(-12.7780 - 3.42385i) 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} +(2.55560 - 0.684771i) q^{67} +(-3.47242 + 12.9593i) q^{68} +(8.87412 - 7.50000i) q^{69} +11.8322i q^{71} +(-2.79186 + 6.09963i) q^{72} +(1.36954 + 5.11120i) q^{73} +(11.8322 - 20.4939i) q^{74} -6.00000 q^{76} +(20.4221 + 1.71383i) q^{78} +(-1.73205 + 1.00000i) q^{79} +(-6.81174 + 5.88220i) q^{81} +(3.42385 - 12.7780i) q^{82} +(1.58114 + 1.58114i) q^{83} +(-8.87412 - 10.5000i) q^{84} +(5.12348 - 2.95804i) q^{86} +(-8.41458 - 5.84764i) q^{87} +(2.95804 + 5.12348i) q^{89} +(-7.00000 + 12.1244i) q^{91} +(14.2302 - 14.2302i) q^{92} +(-3.13434 + 1.47510i) q^{93} +(-17.3205 - 10.0000i) q^{94} +(3.93521 - 10.9323i) q^{96} +(7.48331 + 7.48331i) q^{97} +(15.1191 - 4.05116i) 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.15988	+	0.578737i	1.52726	+	0.409229i	0.922125	−	0.386892i	$-0.126451\pi$
$2$	2.15988	+	0.578737i	1.52726	+	0.409229i	0.605138	+	0.796121i	$0.293118\pi$
$3$	1.42232	+	0.988431i	0.821179	+	0.570671i
$3$	1.42232	+	0.988431i	0.821179	+	0.570671i
$4$	2.59808	+	1.50000i	1.29904	+	0.750000i
$5$		0			0
$5$		0			0
$6$	2.50000	+	2.95804i	1.02062	+	1.20761i
$7$	−2.55560	+	0.684771i	−0.965926	+	0.258819i
$7$	−2.55560	+	0.684771i	−0.965926	+	0.258819i
$8$	1.58114	+	1.58114i	0.559017	+	0.559017i
$9$	1.04601	+	2.81174i	0.348669	+	0.937246i
$10$		0			0
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	2.21266	+	4.70150i	0.638739	+	1.35721i
$13$	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
$17$	1.15747	+	4.31975i	0.280729	+	1.04769i	0.951904	+	0.306395i	$0.0991229\pi$
$17$	1.15747	+	4.31975i	0.280729	+	1.04769i	−0.671176	+	0.741298i	$0.734210\pi$
$18$	0.631989	+	6.67837i	0.148961	+	1.57411i
$19$	−1.73205	+	1.00000i	−0.397360	+	0.229416i	−0.685344	−	0.728219i	$-0.740348\pi$
$19$	−1.73205	+	1.00000i	−0.397360	+	0.229416i	0.287984	+	0.957635i	$0.407015\pi$
$20$		0			0
$21$	−4.31174	−	1.55207i	−0.940898	−	0.338689i
$22$		0			0
$23$	1.73621	−	6.47963i	0.362025	−	1.35110i	−0.509384	−	0.860539i	$-0.670127\pi$
$23$	1.73621	−	6.47963i	0.362025	−	1.35110i	0.871409	−	0.490557i	$-0.163207\pi$
$24$	0.686044	+	3.81174i	0.140038	+	0.778068i
$25$		0			0
$26$	10.2470	−	5.91608i	2.00959	−	1.16024i
$27$	−1.29145	+	5.03311i	−0.248539	+	0.968622i
$28$	−7.66680	−	2.05431i	−1.44889	−	0.388229i
$29$	−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	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	−1.73621	−	6.47963i	−0.306922	−	1.14545i
$33$		0			0
$34$			10.0000i			1.71499i
$35$		0			0
$36$	−1.50000	+	8.87412i	−0.250000	+	1.47902i
$37$	2.73908	−	10.2224i	0.450303	−	1.68055i	−0.251240	−	0.967925i	$-0.580838\pi$
$37$	2.73908	−	10.2224i	0.450303	−	1.68055i	0.701543	−	0.712627i	$-0.252495\pi$
$38$	−4.31975	+	1.15747i	−0.700756	+	0.187767i
$39$	9.02022	−	1.62348i	1.44439	−	0.259964i
$40$		0			0
$41$		−	5.91608i		−	0.923936i	−0.886896	−	0.461968i	$-0.847143\pi$
$41$		−	5.91608i		−	0.923936i	0.886896	−	0.461968i	$-0.152857\pi$
$42$	−8.41458	−	5.84764i	−1.29840	−	0.902310i
$43$	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
$47$	−8.63950	−	2.31495i	−1.26020	−	0.337670i	−0.433932	−	0.900946i	$-0.642874\pi$
$47$	−8.63950	−	2.31495i	−1.26020	−	0.337670i	−0.826269	+	0.563276i	$0.809541\pi$
$48$	0.144845	−	1.72598i	0.0209066	−	0.249124i
$49$	6.06218	−	3.50000i	0.866025	−	0.500000i
$50$		0			0
$51$	−2.62348	+	7.28817i	−0.367360	+	1.02055i
$52$	15.3336	−	4.10862i	2.12639	−	0.569764i
$53$	−4.31975	+	1.15747i	−0.593364	+	0.158991i	−0.542990	−	0.839739i	$-0.682708\pi$
$53$	−4.31975	+	1.15747i	−0.593364	+	0.158991i	−0.0503735	+	0.998730i	$0.516041\pi$
$54$	−5.70221	+	10.1235i	−0.775973	+	1.37763i
$55$		0			0
$56$	−5.12348	−	2.95804i	−0.684653	−	0.395285i
$57$	−3.45197	−	0.289690i	−0.457224	−	0.0383704i
$58$	−12.7780	−	3.42385i	−1.67783	−	0.449574i
$59$	−5.91608	+	10.2470i	−0.770208	+	1.33404i	0.167241	+	0.985916i	$0.446514\pi$
$59$	−5.91608	+	10.2470i	−0.770208	+	1.33404i	−0.937449	+	0.348123i	$0.886819\pi$
$60$		0			0
$61$	5.50000	+	9.52628i	0.704203	+	1.21972i	0.966978	+	0.254858i	$0.0820288\pi$
$61$	5.50000	+	9.52628i	0.704203	+	1.21972i	−0.262776	+	0.964857i	$0.584638\pi$
$62$	−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
$67$	2.55560	−	0.684771i	0.312216	−	0.0836581i	−0.0993085	−	0.995057i	$-0.531663\pi$
$67$	2.55560	−	0.684771i	0.312216	−	0.0836581i	0.411525	+	0.911399i	$0.364996\pi$
$68$	−3.47242	+	12.9593i	−0.421093	+	1.57154i
$69$	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	$0.752242\pi$
$72$	−2.79186	+	6.09963i	−0.329024	+	0.718848i
$73$	1.36954	+	5.11120i	0.160293	+	0.598221i	0.998594	+	0.0530130i	$0.0168825\pi$
$73$	1.36954	+	5.11120i	0.160293	+	0.598221i	−0.838301	+	0.545208i	$0.816451\pi$
$74$	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	$-0.702555\pi$
$79$	−1.73205	+	1.00000i	−0.194871	+	0.112509i	0.399390	+	0.916781i	$0.369222\pi$
$80$		0			0
$81$	−6.81174	+	5.88220i	−0.756860	+	0.653577i
$82$	3.42385	−	12.7780i	0.378101	−	1.41109i
$83$	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
$87$	−8.41458	−	5.84764i	−0.902137	−	0.626933i
$88$		0			0
$89$	2.95804	+	5.12348i	0.313552	+	0.543087i	0.979129	−	0.203242i	$-0.0651478\pi$
$89$	2.95804	+	5.12348i	0.313552	+	0.543087i	−0.665577	+	0.746329i	$0.731814\pi$
$90$		0			0
$91$	−7.00000	+	12.1244i	−0.733799	+	1.27098i
$92$	14.2302	−	14.2302i	1.48361	−	1.48361i
$93$	−3.13434	+	1.47510i	−0.325016	+	0.152961i
$94$	−17.3205	−	10.0000i	−1.78647	−	1.03142i
$95$		0			0
$96$	3.93521	−	10.9323i	0.401636	−	1.11577i
$97$	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	$0.569455\pi$
$98$	15.1191	−	4.05116i	1.52726	−	0.409229i
$99$		0			0
$100$		0			0
$101$	−5.12348	−	2.95804i	−0.509805	−	0.294336i	0.222949	−	0.974830i	$-0.428432\pi$
$101$	−5.12348	−	2.95804i	−0.509805	−	0.294336i	−0.732753	+	0.680494i	$0.761765\pi$
$102$	−9.88431	+	14.2232i	−0.978693	+	1.40831i
$103$	7.66680	+	2.05431i	0.755432	+	0.202417i	0.615926	−	0.787804i	$-0.288782\pi$
$103$	7.66680	+	2.05431i	0.755432	+	0.202417i	0.139506	+	0.990221i	$0.455449\pi$
$104$	11.8322			1.16024
$105$		0			0
$106$	−10.0000			−0.971286
$107$	−2.15988	−	0.578737i	−0.208803	−	0.0559486i	0.152901	−	0.988241i	$-0.451138\pi$
$107$	−2.15988	−	0.578737i	−0.208803	−	0.0559486i	−0.361704	+	0.932293i	$0.617805\pi$
$108$	−10.9049	+	11.1392i	−1.04933	+	1.07187i
$109$	6.06218	+	3.50000i	0.580651	+	0.335239i	0.761392	−	0.648292i	$-0.224516\pi$
$109$	6.06218	+	3.50000i	0.580651	+	0.335239i	−0.180741	+	0.983531i	$0.557850\pi$
$110$		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	$0.817461\pi$
$114$	−7.28817	−	2.62348i	−0.682599	−	0.245711i
$115$		0			0
$116$	−15.3704	−	8.87412i	−1.42711	−	0.823941i
$117$	14.4344	+	6.60676i	1.33446	+	0.610795i
$118$	−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
$122$	6.36611	+	23.7586i	0.576360	+	2.15101i
$123$	5.84764	−	8.41458i	0.527264	−	0.758717i
$124$	−5.19615	+	3.00000i	−0.466628	+	0.269408i
$125$		0			0
$126$	−6.18826	−	16.6345i	−0.551294	−	1.48192i
$127$	−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	$0.998747\pi$
$128$	4.05116	−	15.1191i	0.358075	−	1.33635i
$129$	4.51011	−	0.811738i	0.397093	−	0.0714695i
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$		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
$137$	2.31495	+	8.63950i	0.197779	+	0.738123i	0.991530	+	0.129879i	$0.0414589\pi$
$137$	2.31495	+	8.63950i	0.197779	+	0.738123i	−0.793750	+	0.608243i	$0.791874\pi$
$138$	23.5075	−	11.0633i	2.00109	−	0.941770i
$139$			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
$142$	−6.84771	+	25.5560i	−0.574647	+	2.14461i
$143$		0			0
$144$	1.91203	−	2.31174i	0.159336	−	0.192645i
$145$		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	0.958147	+	0.286276i	$0.0924176\pi$
$149$	8.87412	+	15.3704i	0.726996	+	1.25919i	−0.231151	+	0.972918i	$0.574249\pi$
$150$		0			0
$151$	3.00000	−	5.19615i	0.244137	−	0.422857i	−0.717752	−	0.696299i	$-0.754829\pi$
$151$	3.00000	−	5.19615i	0.244137	−	0.422857i	0.961888	+	0.273442i	$0.0881622\pi$
$152$	−4.31975	−	1.15747i	−0.350378	−	0.0938835i
$153$	−10.9353	+	7.77300i	−0.884065	+	0.628410i
$154$		0			0
$155$		0			0
$156$	25.8704	+	9.31241i	2.07129	+	0.745590i
$157$	−10.2224	+	2.73908i	−0.815836	+	0.218603i	−0.642525	−	0.766265i	$-0.722113\pi$
$157$	−10.2224	+	2.73908i	−0.815836	+	0.218603i	−0.173311	+	0.984867i	$0.555447\pi$
$158$	−4.31975	+	1.15747i	−0.343661	+	0.0920837i
$159$	−7.28817	−	2.62348i	−0.577989	−	0.208055i
$160$		0			0
$161$			17.7482i			1.39876i
$162$	−18.1168	+	8.76261i	−1.42339	+	0.688456i
$163$	−5.11120	−	1.36954i	−0.400340	−	0.107271i	0.0530306	−	0.998593i	$-0.483112\pi$
$163$	−5.11120	−	1.36954i	−0.400340	−	0.107271i	−0.453371	+	0.891322i	$0.649779\pi$
$164$	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	$0.0429282\pi$
$168$	−4.36342	−	9.27149i	−0.336645	−	0.715311i
$169$		−	15.0000i		−	1.15385i
$170$		0			0
$171$	−4.62348	−	3.82407i	−0.353566	−	0.292434i
$172$	7.66680	−	2.05431i	0.584588	−	0.156640i
$173$	−2.31495	+	8.63950i	−0.176002	+	0.656849i	0.820377	+	0.571824i	$0.193764\pi$
$173$	−2.31495	+	8.63950i	−0.176002	+	0.656849i	−0.996379	+	0.0850256i	$0.972903\pi$
$174$	−14.7902	−	17.5000i	−1.12124	−	1.32667i
$175$		0			0
$176$		0			0
$177$	−18.5430	+	8.72684i	−1.39378	+	0.655949i
$178$	3.42385	+	12.7780i	0.256629	+	0.957751i
$179$	−5.91608	+	10.2470i	−0.442189	+	0.765893i	−0.997852	−	0.0655145i	$-0.979131\pi$
$179$	−5.91608	+	10.2470i	−0.442189	+	0.765893i	0.555663	+	0.831408i	$0.312464\pi$
$180$		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
$186$	−7.62348	+	1.37209i	−0.558980	+	0.100606i
$187$		0			0
$188$	−18.9737	−	18.9737i	−1.38380	−	1.38380i
$189$	−0.146098	−	13.7470i	−0.0106271	−	0.999944i
$190$		0			0
$191$	−20.4939	+	11.8322i	−1.48289	+	0.856145i	−0.999811	−	0.0194337i	$-0.993814\pi$
$191$	−20.4939	+	11.8322i	−1.48289	+	0.856145i	−0.483076	+	0.875579i	$0.660480\pi$
$192$	12.8496	−	18.4902i	0.927340	−	1.33442i
$193$	−2.73908	−	10.2224i	−0.197164	−	0.735824i	−0.991696	−	0.128603i	$-0.958951\pi$
$193$	−2.73908	−	10.2224i	−0.197164	−	0.735824i	0.794533	−	0.607221i	$-0.207716\pi$
$194$	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	$-0.424846\pi$
$199$	−6.92820	−	4.00000i	−0.491127	−	0.283552i	−0.725042	+	0.688705i	$0.758180\pi$
$200$		0			0
$201$	4.31174	+	1.55207i	0.304127	+	0.109475i
$202$	−9.35414	−	9.35414i	−0.658155	−	0.658155i
$203$	15.1191	−	4.05116i	1.06115	−	0.284336i
$204$	−17.7482	+	15.0000i	−1.24263	+	1.05021i
$205$		0			0
$206$	15.3704	+	8.87412i	1.07091	+	0.618289i
$207$	20.0351	−	1.89597i	1.39254	−	0.131779i
$208$	−5.11120	−	1.36954i	−0.354398	−	0.0949606i
$209$		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	$0.339947\pi$
$212$	−12.9593	−	3.47242i	−0.890045	−	0.238487i
$213$	−11.6953	+	16.8292i	−0.801347	+	1.15311i
$214$	−4.33013	−	2.50000i	−0.296001	−	0.170896i
$215$		0			0
$216$	−10.0000	+	5.91608i	−0.680414	+	0.402538i
$217$	1.36954	−	5.11120i	0.0929705	−	0.346971i
$218$	11.0680	+	11.0680i	0.749618	+	0.749618i
$219$	−3.10414	+	8.62348i	−0.209758	+	0.582720i
$220$		0			0
$221$	20.4939	+	11.8322i	1.37857	+	0.795917i
$222$	37.0860	−	17.4537i	2.48905	−	1.17141i
$223$	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		0.965926	−	0.258819i	$-0.0833333\pi$
$227$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$228$	−8.53394	−	5.93059i	−0.565174	−	0.392763i
$229$	15.5885	−	9.00000i	1.03011	−	0.594737i	0.113097	−	0.993584i	$-0.463923\pi$
$229$	15.5885	−	9.00000i	1.03011	−	0.594737i	0.917017	+	0.398847i	$0.130590\pi$
$230$		0			0
$231$		0			0
$232$	−9.35414	−	9.35414i	−0.614130	−	0.614130i
$233$	−5.78737	+	21.5988i	−0.379143	+	1.41498i	0.468052	+	0.883701i	$0.344956\pi$
$233$	−5.78737	+	21.5988i	−0.379143	+	1.41498i	−0.847196	+	0.531281i	$0.821711\pi$
$234$	27.3528	+	22.6235i	1.78811	+	1.47894i
$235$		0			0
$236$	−30.7409	+	17.7482i	−2.00106	+	1.15531i
$237$	−3.45197	−	0.289690i	−0.224229	−	0.0188174i
$238$	−6.84771	−	25.5560i	−0.443871	−	1.65655i
$239$	−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	−0.753077	−	0.657932i	$-0.771431\pi$
$241$	3.00000	−	5.19615i	0.193247	−	0.334714i	0.946324	+	0.323218i	$0.104765\pi$
$242$	−6.36611	−	23.7586i	−0.409229	−	1.52726i
$243$	−15.5026	+	1.63345i	−0.994495	+	0.104786i
$244$			33.0000i			2.11261i
$245$		0			0
$246$	17.5000	−	14.7902i	1.11576	−	0.942989i
$247$	−2.73908	+	10.2224i	−0.174284	+	0.650436i
$248$	−4.31975	+	1.15747i	−0.274305	+	0.0734997i
$249$	0.686044	+	3.81174i	0.0434762	+	0.241559i
$250$		0			0
$251$		−	11.8322i		−	0.746839i	−0.927663	−	0.373420i	$-0.878185\pi$
$251$		−	11.8322i		−	0.746839i	0.927663	−	0.373420i	$-0.121815\pi$
$252$	−2.24334	−	23.7059i	−0.141317	−	1.49333i
$253$		0			0
$254$	−17.7482	−	30.7409i	−1.11362	−	1.92885i
$255$		0			0
$256$	4.50000	−	7.79423i	0.281250	−	0.487139i
$257$	−25.9185	−	6.94484i	−1.61675	−	0.433207i	−0.666707	−	0.745320i	$-0.732297\pi$
$257$	−25.9185	−	6.94484i	−1.61675	−	0.433207i	−0.950045	+	0.312112i	$0.898963\pi$
$258$	10.2111	+	0.856914i	0.635713	+	0.0533491i
$259$			28.0000i			1.73984i
$260$		0			0
$261$	−6.18826	−	16.6345i	−0.383044	−	1.02965i
$262$		0			0
$263$	−6.47963	+	1.73621i	−0.399551	+	0.107059i	−0.452998	−	0.891511i	$-0.649646\pi$
$263$	−6.47963	+	1.73621i	−0.399551	+	0.107059i	0.0534475	+	0.998571i	$0.482979\pi$
$264$		0			0
$265$		0			0
$266$	10.2470	−	5.91608i	0.628281	−	0.362738i
$267$	−0.856914	+	10.2111i	−0.0524423	+	0.624907i
$268$	7.66680	+	2.05431i	0.468324	+	0.125487i
$269$	−2.95804	+	5.12348i	−0.180355	+	0.312384i	−0.942001	−	0.335609i	$-0.891058\pi$
$269$	−2.95804	+	5.12348i	−0.180355	+	0.312384i	0.761647	+	0.647993i	$0.224391\pi$
$270$		0			0
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$	3.16228	−	3.16228i	0.191741	−	0.191741i
$273$	−21.9404	+	10.3257i	−1.32789	+	0.624942i
$274$			20.0000i			1.20824i
$275$		0			0
$276$	34.3056	−	6.17439i	2.06496	−	0.371655i
$277$	15.3336	−	4.10862i	0.921307	−	0.246863i	0.233163	−	0.972438i	$-0.425092\pi$
$277$	15.3336	−	4.10862i	0.921307	−	0.246863i	0.688144	+	0.725574i	$0.258426\pi$
$278$	−4.62990	+	17.2790i	−0.277683	+	1.03633i
$279$	−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	$-0.249434\pi$
$282$	−14.7510	−	31.3434i	−0.878412	−	1.86647i
$283$	1.36954	+	5.11120i	0.0814108	+	0.303829i	0.994610	−	0.103683i	$-0.0330629\pi$
$283$	1.36954	+	5.11120i	0.0814108	+	0.303829i	−0.913200	+	0.407513i	$0.866396\pi$
$284$	−17.7482	+	30.7409i	−1.05316	+	1.82413i
$285$		0			0
$286$		0			0
$287$	4.05116	+	15.1191i	0.239132	+	0.892454i
$288$	16.4029	−	11.6595i	0.966552	−	0.687043i
$289$	−2.59808	+	1.50000i	−0.152828	+	0.0882353i
$290$		0			0
$291$	3.24695	+	18.0404i	0.190340	+	1.05755i
$292$	−4.10862	+	15.3336i	−0.240439	+	0.897331i
$293$	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	$0.665860\pi$
$294$	25.5086	+	9.18216i	1.48769	+	0.535515i
$295$		0			0
$296$	20.4939	−	11.8322i	1.19118	−	0.687730i
$297$		0			0
$298$	10.2716	+	38.3340i	0.595016	+	2.22063i
$299$	−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
$303$	−4.36342	−	9.27149i	−0.250672	−	0.532633i
$304$	1.73205	+	1.00000i	0.0993399	+	0.0573539i
$305$		0			0
$306$	−28.1174	+	10.4601i	−1.60736	+	0.597963i
$307$	−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	$-0.224438\pi$
$311$	10.2470	+	5.91608i	0.581051	+	0.335470i	−0.180500	+	0.983575i	$0.557772\pi$
$312$	16.8292	+	11.6953i	0.952763	+	0.662115i
$313$	10.2224	+	2.73908i	0.577804	+	0.154822i	0.535873	−	0.844298i	$-0.319982\pi$
$313$	10.2224	+	2.73908i	0.577804	+	0.154822i	0.0419307	+	0.999121i	$0.486649\pi$
$314$	−23.6643			−1.33545
$315$		0			0
$316$	−6.00000			−0.337526
$317$	21.5988	+	5.78737i	1.21311	+	0.325051i	0.807980	−	0.589209i	$-0.200561\pi$
$317$	21.5988	+	5.78737i	1.21311	+	0.325051i	0.405127	+	0.914261i	$0.367227\pi$
$318$	−14.2232	−	9.88431i	−0.797599	−	0.554285i
$319$		0			0
$320$		0			0
$321$	−2.50000	−	2.95804i	−0.139536	−	0.165102i
$322$	−10.2716	+	38.3340i	−0.572412	+	2.13627i
$323$	−6.32456	−	6.32456i	−0.351908	−	0.351908i
$324$	−26.5207	+	5.06479i	−1.47337	+	0.281377i
$325$		0			0
$326$	−10.2470	−	5.91608i	−0.567526	−	0.327661i
$327$	5.16287	+	10.9702i	0.285507	+	0.606652i
$328$	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	0.606980	−	0.794717i	$-0.292381\pi$
$331$	−7.00000	−	12.1244i	−0.384755	−	0.666415i	−0.991735	+	0.128302i	$0.959047\pi$
$332$	1.73621	+	6.47963i	0.0952870	+	0.355616i
$333$	31.6078	−	2.99112i	1.73210	−	0.163912i
$334$	30.3109	−	17.5000i	1.65854	−	0.957557i
$335$		0			0
$336$	0.811738	+	4.51011i	0.0442839	+	0.246047i
$337$	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	$0.703964\pi$
$338$	8.68105	−	32.3981i	0.472187	−	1.76223i
$339$	−1.37209	−	7.62348i	−0.0745215	−	0.414050i
$340$		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
$347$	2.89368	+	10.7994i	0.155341	+	0.579741i	0.999076	+	0.0429807i	$0.0136854\pi$
$347$	2.89368	+	10.7994i	0.155341	+	0.579741i	−0.843735	+	0.536760i	$0.819648\pi$
$348$	−13.0903	−	27.8145i	−0.701711	−	1.49101i
$349$		−	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
$353$	12.9593	−	3.47242i	0.689752	−	0.184818i	0.103116	−	0.994669i	$-0.467119\pi$
$353$	12.9593	−	3.47242i	0.689752	−	0.184818i	0.586636	+	0.809851i	$0.300452\pi$
$354$	−45.1011	+	8.11738i	−2.39710	+	0.431434i
$355$		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	0.978847	−	0.204595i	$-0.0655878\pi$
$359$	5.91608	+	10.2470i	0.312239	+	0.540813i	−0.666608	+	0.745409i	$0.732254\pi$
$360$		0			0
$361$	−7.50000	+	12.9904i	−0.394737	+	0.683704i
$362$	−6.47963	−	1.73621i	−0.340562	−	0.0912532i
$363$	1.59329	−	18.9858i	0.0836263	−	0.996497i
$364$	−36.3731	+	21.0000i	−1.90647	+	1.10070i
$365$		0			0
$366$	−14.4291	+	40.0849i	−0.754222	+	2.09527i
$367$	7.66680	−	2.05431i	0.400204	−	0.107234i	−0.0531027	−	0.998589i	$-0.516911\pi$
$367$	7.66680	−	2.05431i	0.400204	−	0.107234i	0.453306	+	0.891355i	$0.350244\pi$
$368$	−6.47963	+	1.73621i	−0.337774	+	0.0905063i
$369$	16.6345	−	6.18826i	0.865956	−	0.322148i
$370$		0			0
$371$	10.2470	−	5.91608i	0.531995	−	0.307148i
$372$	−10.3559	−	0.869070i	−0.536929	−	0.0450592i
$373$	20.4448	+	5.47817i	1.05859	+	0.283649i	0.745798	−	0.666172i	$-0.232069\pi$
$373$	20.4448	+	5.47817i	1.05859	+	0.283649i	0.312794	+	0.949821i	$0.398735\pi$
$374$		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
$381$	−4.87043	−	27.0607i	−0.249519	−	1.38636i
$382$	−51.1120	+	13.6954i	−2.61512	+	0.700718i
$383$	−1.73621	+	6.47963i	−0.0887162	+	0.331093i	−0.995992	−	0.0894428i	$-0.971491\pi$
$383$	−1.73621	+	6.47963i	−0.0887162	+	0.331093i	0.907276	+	0.420536i	$0.138158\pi$
$384$	20.7063	−	17.5000i	1.05666	−	0.893043i
$385$		0			0
$386$		−	23.6643i		−	1.20448i
$387$	7.21718	+	3.30338i	0.366870	+	0.167920i
$388$	8.21725	+	30.6672i	0.417168	+	1.55689i
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$		0			0
$391$	30.0000			1.51717
$392$	15.1191	+	4.05116i	0.763631	+	0.204614i
$393$		0			0
$394$	51.9615	−	30.0000i	2.61778	−	1.51138i
$395$		0			0
$396$		0			0
$397$	−5.47817	+	20.4448i	−0.274941	+	1.02609i	0.680939	+	0.732340i	$0.261572\pi$
$397$	−5.47817	+	20.4448i	−0.274941	+	1.02609i	−0.955881	+	0.293755i	$0.905095\pi$
$398$	−12.6491	−	12.6491i	−0.634043	−	0.634043i
$399$	9.02022	−	1.62348i	0.451576	−	0.0812754i
$400$		0			0
$401$	15.3704	−	8.87412i	0.767562	−	0.443152i	−0.0644419	−	0.997921i	$-0.520527\pi$
$401$	15.3704	−	8.87412i	0.767562	−	0.443152i	0.832004	+	0.554769i	$0.187193\pi$
$402$	8.41458	+	5.84764i	0.419681	+	0.291654i
$403$	2.73908	+	10.2224i	0.136443	+	0.509214i
$404$	−8.87412	−	15.3704i	−0.441504	−	0.764707i
$405$		0			0
$406$	35.0000			1.73702
$407$		0			0
$408$	−15.6717	+	7.37552i	−0.775864	+	0.365143i
$409$	−11.2583	−	6.50000i	−0.556689	−	0.321404i	0.195127	−	0.980778i	$-0.437488\pi$
$409$	−11.2583	−	6.50000i	−0.556689	−	0.321404i	−0.751815	+	0.659374i	$0.770822\pi$
$410$		0			0
$411$	−5.24695	+	14.5763i	−0.258813	+	0.718998i
$412$	16.8375	+	16.8375i	0.829522	+	0.829522i
$413$	8.10232	−	30.2383i	0.398689	−	1.48793i
$414$	44.3706	+	7.50000i	2.18070	+	0.368605i
$415$		0			0
$416$	−30.7409	−	17.7482i	−1.50719	−	0.870179i
$417$	−7.90745	+	11.3786i	−0.387230	+	0.557212i
$418$		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	$0.586380\pi$
$422$	30.2383	+	8.10232i	1.47198	+	0.394415i
$423$	−2.52796	−	26.7135i	−0.122913	−	1.29885i
$424$	−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	$-0.140302\pi$
$431$	20.4939	+	11.8322i	0.987157	+	0.569935i	0.0827334	+	0.996572i	$0.473635\pi$
$432$	5.00452	−	1.39813i	0.240780	−	0.0672673i
$433$	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
$437$	3.47242	+	12.9593i	0.166108	+	0.619925i
$438$	−11.6953	+	16.8292i	−0.558822	+	0.804128i
$439$	−27.7128	+	16.0000i	−1.32266	+	0.763638i	−0.984152	−	0.177325i	$-0.943256\pi$
$439$	−27.7128	+	16.0000i	−1.32266	+	0.763638i	−0.338508	+	0.940963i	$0.609922\pi$
$440$		0			0
$441$	16.1822	+	13.3842i	0.770579	+	0.637344i
$442$	37.4166	+	37.4166i	1.77972	+	1.77972i
$443$	0.578737	−	2.15988i	0.0274966	−	0.102619i	−0.950814	−	0.309763i	$-0.899750\pi$
$443$	0.578737	−	2.15988i	0.0274966	−	0.102619i	0.978310	+	0.207144i	$0.0664169\pi$
$444$	54.1213	−	9.74085i	2.56848	−	0.462280i
$445$		0			0
$446$	10.2470	−	5.91608i	0.485207	−	0.280134i
$447$	−2.57074	+	30.6332i	−0.121592	+	1.44890i
$448$	8.90202	+	33.2228i	0.420581	+	1.56963i
$449$	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
$452$	−3.47242	−	12.9593i	−0.163329	−	0.609552i
$453$	9.40301	−	4.42531i	0.441792	−	0.207919i
$454$		0			0
$455$		0			0
$456$	−5.00000	−	5.91608i	−0.234146	−	0.277046i
$457$	2.73908	−	10.2224i	0.128129	−	0.478184i	−0.871803	−	0.489857i	$-0.837049\pi$
$457$	2.73908	−	10.2224i	0.128129	−	0.478184i	0.999932	+	0.0116731i	$0.00371575\pi$
$458$	38.8778	−	10.4173i	1.81664	−	0.486767i
$459$	−23.2366	+	0.246951i	−1.08459	+	0.0115267i
$460$		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
$467$	−15.1191	−	4.05116i	−0.699630	−	0.187465i	−0.108565	−	0.994089i	$-0.534626\pi$
$467$	−15.1191	−	4.05116i	−0.699630	−	0.187465i	−0.591065	+	0.806624i	$0.701292\pi$
$468$	27.5914	+	38.8164i	1.27541	+	1.79429i
$469$	−6.06218	+	3.50000i	−0.279925	+	0.161615i
$470$		0			0
$471$	−17.2470	−	6.20828i	−0.794698	−	0.286062i
$472$	−25.5560	+	6.84771i	−1.17631	+	0.315191i
$473$		0			0
$474$	−7.28817	−	2.62348i	−0.334757	−	0.120500i
$475$		0			0
$476$		−	35.4965i		−	1.62698i
$477$	−7.77300	−	10.9353i	−0.355901	−	0.500692i
$478$	−25.5560	−	6.84771i	−1.16890	−	0.313207i
$479$	17.7482	−	30.7409i	0.810938	−	1.40459i	−0.101271	−	0.994859i	$-0.532291\pi$
$479$	17.7482	−	30.7409i	0.810938	−	1.40459i	0.912208	−	0.409726i	$-0.134376\pi$
$480$		0			0
$481$	−28.0000	−	48.4974i	−1.27669	−	2.21129i
$482$	9.48683	−	9.48683i	0.432113	−	0.432113i
$483$	−17.5429	+	25.2437i	−0.798230	+	1.14863i
$484$		−	33.0000i		−	1.50000i
$485$		0			0
$486$	−34.4291	−	5.44390i	−1.56174	−	0.246940i
$487$	−5.11120	+	1.36954i	−0.231611	+	0.0620599i	−0.372757	−	0.927929i	$-0.621588\pi$
$487$	−5.11120	+	1.36954i	−0.231611	+	0.0620599i	0.141147	+	0.989989i	$0.454921\pi$
$488$	−6.36611	+	23.7586i	−0.288180	+	1.07550i
$489$	−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	$-0.0860287\pi$
$492$	27.8145	−	13.0903i	1.25397	−	0.590154i
$493$	−6.84771	−	25.5560i	−0.308405	−	1.15098i
$494$	−11.8322	+	20.4939i	−0.532354	+	0.922064i
$495$		0			0
$496$	2.00000			0.0898027
$497$	−8.10232	−	30.2383i	−0.363439	−	1.35637i
$498$	−0.724225	+	8.62992i	−0.0324533	+	0.386716i
$499$	−10.3923	+	6.00000i	−0.465223	+	0.268597i	−0.714238	−	0.699903i	$-0.753227\pi$
$499$	−10.3923	+	6.00000i	−0.465223	+	0.268597i	0.249015	+	0.968500i	$0.419893\pi$
$500$		0			0
$501$	26.6822	−	4.80230i	1.19207	−	0.214551i
$502$	6.84771	−	25.5560i	0.305628	−	1.14062i
$503$	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
$507$	14.8265	−	21.3348i	0.658467	−	0.947514i
$508$	−12.3259	−	46.0008i	−0.546872	−	2.04096i
$509$	−8.87412	−	15.3704i	−0.393338	−	0.681282i	0.599549	−	0.800338i	$-0.295347\pi$
$509$	−8.87412	−	15.3704i	−0.393338	−	0.681282i	−0.992888	+	0.119056i	$0.962013\pi$
$510$		0			0
$511$	−7.00000	−	12.1244i	−0.309662	−	0.536350i
$512$	−7.90569	+	7.90569i	−0.349386	+	0.349386i
$513$	−2.79625	−	10.0090i	−0.123458	−	0.441910i
$514$	−51.9615	−	30.0000i	−2.29192	−	1.32324i
$515$		0			0
$516$	12.9352	+	4.65621i	0.569441	+	0.204978i
$517$		0			0
$518$	−16.2046	+	60.4765i	−0.711991	+	2.65719i
$519$	−11.8322	+	10.0000i	−0.519374	+	0.438951i
$520$		0			0
$521$	−20.4939	−	11.8322i	−0.897854	−	0.518376i	−0.0213508	−	0.999772i	$-0.506797\pi$
$521$	−20.4939	−	11.8322i	−0.897854	−	0.518376i	−0.876503	+	0.481396i	$0.840130\pi$
$522$	−3.73890	−	39.5098i	−0.163647	−	1.72929i
$523$	35.7784	+	9.58679i	1.56448	+	0.419201i	0.934078	−	0.357068i	$-0.116224\pi$
$523$	35.7784	+	9.58679i	1.56448	+	0.419201i	0.630402	+	0.776269i	$0.282890\pi$
$524$		0			0
$525$		0			0
$526$	−15.0000			−0.654031
$527$	−8.63950	−	2.31495i	−0.376343	−	0.100841i
$528$		0			0
$529$	−19.0526	−	11.0000i	−0.828372	−	0.478261i
$530$		0			0
$531$	−35.0000	−	5.91608i	−1.51887	−	0.256736i
$532$	15.3336	−	4.10862i	0.664796	−	0.178131i
$533$	−22.1359	−	22.1359i	−0.958814	−	0.958814i
$534$	−7.76034	+	21.5587i	−0.335823	+	0.932936i
$535$		0			0
$536$	5.12348	+	2.95804i	0.221300	+	0.127768i
$537$	−18.5430	+	8.72684i	−0.800189	+	0.376591i
$538$	−9.35414	+	9.35414i	−0.403286	+	0.403286i
$539$		0			0
$540$		0			0
$541$	−9.50000	−	16.4545i	−0.408437	−	0.707433i	0.586278	−	0.810110i	$-0.300593\pi$
$541$	−9.50000	−	16.4545i	−0.408437	−	0.707433i	−0.994715	+	0.102677i	$0.967259\pi$
$542$	−1.15747	−	4.31975i	−0.0497178	−	0.185549i
$543$	−4.26697	−	2.96529i	−0.183113	−	0.127253i
$544$	25.9808	−	15.0000i	1.11392	−	0.643120i
$545$		0			0
$546$	−53.3643	+	9.60461i	−2.28378	+	0.411039i
$547$	−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	$-0.512962\pi$
$548$	−6.94484	+	25.9185i	−0.296669	+	1.10718i
$549$	−21.0324	+	25.4291i	−0.897639	+	1.08529i
$550$		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
$557$	−2.31495	−	8.63950i	−0.0980875	−	0.366068i	0.899382	−	0.437164i	$-0.144017\pi$
$557$	−2.31495	−	8.63950i	−0.0980875	−	0.366068i	−0.997469	+	0.0710962i	$0.977350\pi$
$558$	−12.1993	−	5.58373i	−0.516436	−	0.236378i
$559$		−	14.0000i		−	0.592137i
$560$		0			0
$561$		0			0
$562$	13.6954	−	51.1120i	0.577706	−	2.15603i
$563$	−41.0376	+	10.9960i	−1.72953	+	0.463426i	−0.980075	−	0.198628i	$-0.936351\pi$
$563$	−41.0376	+	10.9960i	−1.72953	+	0.463426i	−0.749455	+	0.662055i	$0.769685\pi$
$564$	−8.23252	−	45.7409i	−0.346652	−	1.92604i
$565$		0			0
$566$			11.8322i			0.497343i
$567$	13.3801	−	19.6970i	0.561912	−	0.827197i
$568$	−18.7083	+	18.7083i	−0.784982	+	0.784982i
$569$	−11.8322	−	20.4939i	−0.496030	−	0.859149i	0.503960	−	0.863727i	$-0.331876\pi$
$569$	−11.8322	−	20.4939i	−0.496030	−	0.859149i	−0.999990	+	0.00457819i	$0.998543\pi$
$570$		0			0
$571$	−7.00000	+	12.1244i	−0.292941	+	0.507388i	−0.974504	−	0.224371i	$-0.927967\pi$
$571$	−7.00000	+	12.1244i	−0.292941	+	0.507388i	0.681563	+	0.731760i	$0.261301\pi$
$572$		0			0
$573$	−40.8442	−	3.42766i	−1.70629	−	0.143192i
$574$			35.0000i			1.46087i
$575$		0			0
$576$	36.5526	−	13.5981i	1.52302	−	0.566587i
$577$	20.4448	−	5.47817i	0.851128	−	0.228059i	0.193218	−	0.981156i	$-0.438107\pi$
$577$	20.4448	−	5.47817i	0.851128	−	0.228059i	0.657910	+	0.753097i	$0.271441\pi$
$578$	−6.47963	+	1.73621i	−0.269517	+	0.0722169i
$579$	6.20828	−	17.2470i	0.258007	−	0.716759i
$580$		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	$0.129642\pi$
$588$	29.8688	+	20.7571i	1.23177	+	0.856007i
$589$		−	4.00000i		−	0.164817i
$590$		0			0
$591$	45.7409	−	8.23252i	1.88153	−	0.338641i
$592$	−10.2224	+	2.73908i	−0.420138	+	0.112576i
$593$	8.10232	−	30.2383i	0.332722	−	1.24174i	−0.573595	−	0.819139i	$-0.694452\pi$
$593$	8.10232	−	30.2383i	0.332722	−	1.24174i	0.906317	−	0.422598i	$-0.138882\pi$
$594$		0			0
$595$		0			0
$596$			53.2447i			2.18099i
$597$	−5.90042	−	12.5373i	−0.241488	−	0.513119i
$598$	−20.5431	−	76.6680i	−0.840071	−	3.13519i
$599$	11.8322	−	20.4939i	0.483449	−	0.837358i	−0.516370	−	0.856365i	$-0.672717\pi$
$599$	11.8322	−	20.4939i	0.483449	−	0.837358i	0.999819	+	0.0190072i	$0.00605055\pi$
$600$		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
$606$	−4.05869	−	22.5505i	−0.164873	−	0.916053i
$607$	−0.684771	+	2.55560i	−0.0277940	+	0.103729i	−0.978429	−	0.206581i	$-0.933766\pi$
$607$	−0.684771	+	2.55560i	−0.0277940	+	0.103729i	0.950635	+	0.310310i	$0.100433\pi$
$608$	9.48683	+	9.48683i	0.384742	+	0.384742i
$609$	25.5086	+	9.18216i	1.03366	+	0.372080i
$610$		0			0
$611$	−40.9878	+	23.6643i	−1.65819	+	0.957356i
$612$	−40.0702	+	3.79193i	−1.61974	+	0.153280i
$613$	−9.58679	−	35.7784i	−0.387207	−	1.44508i	−0.834659	−	0.550768i	$-0.814335\pi$
$613$	−9.58679	−	35.7784i	−0.387207	−	1.44508i	0.447452	−	0.894308i	$-0.352332\pi$
$614$	−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	$0.367252\pi$
$618$	13.0903	+	27.8145i	0.526567	+	1.11886i
$619$	31.1769	+	18.0000i	1.25311	+	0.723481i	0.971725	−	0.236115i	$-0.0758742\pi$
$619$	31.1769	+	18.0000i	1.25311	+	0.723481i	0.281381	+	0.959596i	$0.409208\pi$
$620$		0			0
$621$	30.3704	+	17.1066i	1.21872	+	0.686466i
$622$	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
$628$	−30.6672	−	8.21725i	−1.22375	−	0.327904i
$629$	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	$0.341466\pi$
$632$	−4.31975	−	1.15747i	−0.171830	−	0.0460418i
$633$	19.9125	+	13.8380i	0.791452	+	0.550013i
$634$	43.3013	+	25.0000i	1.71971	+	0.992877i
$635$		0			0
$636$	−15.0000	−	17.7482i	−0.594789	−	0.703763i
$637$	9.58679	−	35.7784i	0.379843	−	1.41759i
$638$		0			0
$639$	−33.2689	+	12.3765i	−1.31610	+	0.489608i
$640$		0			0
$641$	−5.12348	−	2.95804i	−0.202365	−	0.116836i	0.395393	−	0.918512i	$-0.370608\pi$
$641$	−5.12348	−	2.95804i	−0.202365	−	0.116836i	−0.597758	+	0.801676i	$0.703942\pi$
$642$	−3.68776	−	7.83584i	−0.145544	−	0.309256i
$643$	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
$647$	−4.05116	−	15.1191i	−0.159267	−	0.594394i	−0.998702	−	0.0509336i	$-0.983780\pi$
$647$	−4.05116	−	15.1191i	−0.159267	−	0.594394i	0.839435	−	0.543461i	$-0.182886\pi$
$648$	−20.0709	−	1.46973i	−0.788458	−	0.0577366i
$649$		0			0
$650$		0			0
$651$	7.00000	−	5.91608i	0.274352	−	0.231869i
$652$	−11.2250	−	11.2250i	−0.439604	−	0.439604i
$653$	3.47242	−	12.9593i	0.135886	−	0.507135i	−0.864106	−	0.503309i	$-0.832116\pi$
$653$	3.47242	−	12.9593i	0.135886	−	0.507135i	0.999993	−	0.00382551i	$-0.00121770\pi$
$654$	4.80230	+	26.6822i	0.187785	+	1.04336i
$655$		0			0
$656$	−5.12348	+	2.95804i	−0.200038	+	0.115492i
$657$	−12.9388	+	9.19714i	−0.504791	+	0.358815i
$658$	51.1120	+	13.6954i	1.99255	+	0.533903i
$659$	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	−0.989489	−	0.144611i	$-0.953807\pi$
$661$	−9.50000	+	16.4545i	−0.369507	+	0.640005i	0.619981	+	0.784617i	$0.287140\pi$
$662$	−8.10232	−	30.2383i	−0.314906	−	1.17524i
$663$	17.4537	+	37.0860i	0.677845	+	1.44030i
$664$			5.00000i			0.194038i
$665$		0			0
$666$	70.0000	+	11.8322i	2.71244	+	0.458487i
$667$	−10.2716	+	38.3340i	−0.397716	+	1.48430i
$668$	45.3574	−	12.1535i	1.75493	−	0.470232i
$669$	9.02022	−	1.62348i	0.348742	−	0.0627672i
$670$		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
$677$	−4.31975	−	1.15747i	−0.166022	−	0.0444853i	0.174851	−	0.984595i	$-0.444056\pi$
$677$	−4.31975	−	1.15747i	−0.166022	−	0.0444853i	−0.340872	+	0.940110i	$0.610722\pi$
$678$	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
$683$	−10.7994	+	2.89368i	−0.413227	+	0.110724i	−0.459442	−	0.888208i	$-0.651951\pi$
$683$	−10.7994	+	2.89368i	−0.413227	+	0.110724i	0.0462153	+	0.998932i	$0.485284\pi$
$684$	−6.27604	−	16.8704i	−0.239971	−	0.645057i
$685$		0			0
$686$	−35.8643	+	20.7063i	−1.36931	+	0.790569i
$687$	31.0677	+	2.60721i	1.18531	+	0.0994712i
$688$	−2.55560	−	0.684771i	−0.0974313	−	0.0261066i
$689$	−11.8322	+	20.4939i	−0.450769	+	0.780755i
$690$		0			0
$691$	8.00000	+	13.8564i	0.304334	+	0.527123i	0.977113	−	0.212721i	$-0.0682327\pi$
$691$	8.00000	+	13.8564i	0.304334	+	0.527123i	−0.672779	+	0.739844i	$0.734899\pi$
$692$	−18.9737	+	18.9737i	−0.721271	+	0.721271i
$693$		0			0
$694$			25.0000i			0.948987i
$695$		0			0
$696$	−4.05869	−	22.5505i	−0.153844	−	0.854776i
$697$	25.5560	−	6.84771i	0.968002	−	0.259375i
$698$	17.9408	−	66.9562i	0.679071	−	2.53433i
$699$	−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	$0.891206\pi$
$702$	16.5428	+	59.2143i	0.624369	+	2.23490i
$703$	5.47817	+	20.4448i	0.206613	+	0.771090i
$704$		0			0
$705$		0			0
$706$	30.0000			1.12906
$707$	15.1191	+	4.05116i	0.568613	+	0.152360i
$708$	−61.2663	−	5.14149i	−2.30253	−	0.193229i
$709$	19.9186	−	11.5000i	0.748058	−	0.431892i	−0.0769337	−	0.997036i	$-0.524513\pi$
$709$	19.9186	−	11.5000i	0.748058	−	0.431892i	0.824992	+	0.565145i	$0.191180\pi$
$710$		0			0
$711$	−4.62348	−	3.82407i	−0.173394	−	0.143414i
$712$	−3.42385	+	12.7780i	−0.128314	+	0.478876i
$713$	9.48683	+	9.48683i	0.355285	+	0.355285i
$714$	15.5207	−	43.1174i	0.580847	−	1.61363i
$715$		0			0
$716$	−30.7409	+	17.7482i	−1.14884	+	0.663283i
$717$	−16.8292	−	11.6953i	−0.628496	−	0.436768i
$718$	6.84771	+	25.5560i	0.255554	+	0.953741i
$719$	23.6643	+	40.9878i	0.882530	+	1.52859i	0.848519	+	0.529166i	$0.177495\pi$
$719$	23.6643	+	40.9878i	0.882530	+	1.52859i	0.0340117	+	0.999421i	$0.489172\pi$
$720$		0			0
$721$	−21.0000			−0.782081
$722$	−23.7171	+	23.7171i	−0.882658	+	0.882658i
$723$	9.40301	−	4.42531i	0.349702	−	0.164579i
$724$	−7.79423	−	4.50000i	−0.289670	−	0.167241i
$725$		0			0
$726$	14.4291	−	40.0849i	0.535515	−	1.48769i
$727$	−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	$0.931459\pi$
$728$	−30.2383	+	8.10232i	−1.12070	+	0.300292i
$729$	−23.6643	−	13.0000i	−0.876456	−	0.481481i
$730$		0			0
$731$	10.2470	+	5.91608i	0.378997	+	0.218814i
$732$	−32.6182	+	46.9367i	−1.20560	+	1.73483i
$733$	−30.6672	−	8.21725i	−1.13272	−	0.303511i	−0.356699	−	0.934219i	$-0.616098\pi$
$733$	−30.6672	−	8.21725i	−1.13272	−	0.303511i	−0.776020	+	0.630708i	$0.782764\pi$
$734$	17.7482			0.655099
$735$		0			0
$736$	−45.0000			−1.65872
$737$		0			0
$738$	39.5098	−	3.73890i	1.45437	−	0.137631i
$739$	27.7128	+	16.0000i	1.01943	+	0.588570i	0.913939	−	0.405851i	$-0.133025\pi$
$739$	27.7128	+	16.0000i	1.01943	+	0.588570i	0.105493	+	0.994420i	$0.466358\pi$
$740$		0			0
$741$	−14.0000	+	11.8322i	−0.514303	+	0.434665i
$742$	25.5560	−	6.84771i	0.938190	−	0.251387i
$743$	−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	$0.929017\pi$
$744$	−7.28817	−	2.62348i	−0.267197	−	0.0961813i
$745$		0			0
$746$	40.9878	+	23.6643i	1.50067	+	0.866412i
$747$	−2.79186	+	6.09963i	−0.102149	+	0.223174i
$748$		0			0
$749$	5.91608			0.216169
$750$		0			0
$751$	18.0000	+	31.1769i	0.656829	+	1.13766i	0.981432	+	0.191811i	$0.0614361\pi$
$751$	18.0000	+	31.1769i	0.656829	+	1.13766i	−0.324603	+	0.945851i	$0.605231\pi$
$752$	2.31495	+	8.63950i	0.0844175	+	0.315050i
$753$	11.6953	−	16.8292i	0.426200	−	0.613289i
$754$	−60.6218	+	35.0000i	−2.20771	+	1.27462i
$755$		0			0
$756$	20.2409	−	35.9348i	0.736153	−	1.30694i
$757$	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	$0.514949\pi$
$758$	−10.4173	+	38.8778i	−0.378372	+	1.41210i
$759$		0			0
$760$		0			0
$761$	20.4939	−	11.8322i	0.742903	−	0.428915i	−0.0802206	−	0.996777i	$-0.525562\pi$
$761$	20.4939	−	11.8322i	0.742903	−	0.428915i	0.823124	+	0.567862i	$0.192229\pi$
$762$	5.14149	−	61.2663i	0.186256	−	2.21945i
$763$	−17.8892	−	4.79340i	−0.647632	−	0.173533i
$764$	−70.9930			−2.56844
$765$		0			0
$766$	−7.50000	+	12.9904i	−0.270986	+	0.469362i
$767$	16.2046	+	60.4765i	0.585115	+	2.18368i
$768$	14.1045	−	6.63797i	0.508953	−	0.239527i
$769$			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
$772$	8.21725	−	30.6672i	0.295745	−	1.10374i
$773$	−4.31975	+	1.15747i	−0.155371	+	0.0416314i	−0.335666	−	0.941981i	$-0.608961\pi$
$773$	−4.31975	+	1.15747i	−0.155371	+	0.0416314i	0.180295	+	0.983613i	$0.442295\pi$
$774$	13.6764	+	11.3117i	0.491589	+	0.406592i
$775$		0			0
$776$			23.6643i			0.849500i
$777$	−27.6761	+	39.8251i	−0.992874	+	1.42872i
$778$		0			0
$779$	5.91608	+	10.2470i	0.211966	+	0.367135i
$780$		0			0
$781$		0			0
$782$	64.7963	+	17.3621i	2.31711	+	0.620868i
$783$	7.64032	−	29.7763i	0.273043	−	1.06412i
$784$	−6.06218	−	3.50000i	−0.216506	−	0.125000i
$785$		0			0
$786$		0			0
$787$	−48.5564	+	13.0106i	−1.73085	+	0.463779i	−0.980378	−	0.197125i	$-0.936840\pi$
$787$	−48.5564	+	13.0106i	−1.73085	+	0.463779i	−0.750470	+	0.660904i	$0.770173\pi$
$788$	77.7555	−	20.8345i	2.76993	−	0.742199i
$789$	−10.9323	−	3.93521i	−0.389198	−	0.140097i
$790$		0			0
$791$	10.2470	+	5.91608i	0.364340	+	0.210352i
$792$		0			0
$793$	56.2232	+	15.0650i	1.99654	+	0.534972i
$794$	−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
$801$	−11.3117	+	13.6764i	−0.399681	+	0.483233i
$802$	38.3340	−	10.2716i	1.35362	−	0.362701i
$803$		0			0
$804$	8.87412	+	10.5000i	0.312966	+	0.370306i
$805$		0			0
$806$			23.6643i			0.833540i
$807$	−9.27149	+	4.36342i	−0.326372	+	0.153600i
$808$	−3.42385	−	12.7780i	−0.120451	−	0.449528i
$809$	20.7063	−	35.8643i	0.727994	−	1.26092i	−0.229736	−	0.973253i	$-0.573786\pi$
$809$	20.7063	−	35.8643i	0.727994	−	1.26092i	0.957730	−	0.287670i	$-0.0928805\pi$
$810$		0			0
$811$	−6.00000			−0.210688			−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000			−0.210688			−0.105344	+	0.994436i	$0.533594\pi$
$812$	45.3574	+	12.1535i	1.59173	+	0.426503i
$813$	0.289690	−	3.45197i	0.0101599	−	0.121066i
$814$		0			0
$815$		0			0
$816$	7.62348	−	1.37209i	0.266875	−	0.0480327i
$817$	−1.36954	+	5.11120i	−0.0479142	+	0.178818i
$818$	−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	$-0.531167\pi$
$821$	20.4939	−	11.8322i	0.715242	−	0.412945i	0.812999	+	0.582265i	$0.197833\pi$
$822$	−19.7686	+	28.4465i	−0.689510	+	0.992184i
$823$	4.79340	+	17.8892i	0.167087	+	0.623578i	0.997765	+	0.0668243i	$0.0212867\pi$
$823$	4.79340	+	17.8892i	0.167087	+	0.623578i	−0.830677	+	0.556754i	$0.812047\pi$
$824$	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	$0.136215\pi$
$828$	54.8967	+	25.1268i	1.90779	+	0.873216i
$829$	1.73205	+	1.00000i	0.0601566	+	0.0347314i	0.529777	−	0.848137i	$-0.322276\pi$
$829$	1.73205	+	1.00000i	0.0601566	+	0.0347314i	−0.469620	+	0.882869i	$0.655609\pi$
$830$		0			0
$831$	25.8704	+	9.31241i	0.897435	+	0.323044i
$832$	−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
$837$	−7.42615	−	7.26996i	−0.256685	−	0.251287i
$838$	−51.1120	−	13.6954i	−1.76563	−	0.473100i
$839$	−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
$842$	−23.7586	−	6.36611i	−0.818777	−	0.219391i
$843$	23.3906	−	33.6583i	0.805613	−	1.15925i
$844$	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
$849$	−3.10414	+	8.62348i	−0.106534	+	0.295957i
$850$		0			0
$851$	−61.4817	−	35.4965i	−2.10757	−	1.21680i
$852$	−55.6290	+	26.1805i	−1.90582	+	0.896930i
$853$	−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
$857$	−6.94484	−	25.9185i	−0.237231	−	0.885359i	−0.977130	−	0.212641i	$-0.931793\pi$
$857$	−6.94484	−	25.9185i	−0.237231	−	0.885359i	0.739899	−	0.672718i	$-0.234873\pi$
$858$		0			0
$859$	3.46410	−	2.00000i	0.118194	−	0.0682391i	−0.439738	−	0.898126i	$-0.644929\pi$
$859$	3.46410	−	2.00000i	0.118194	−	0.0682391i	0.557931	+	0.829887i	$0.311595\pi$
$860$		0			0
$861$	−9.18216	+	25.5086i	−0.312927	+	0.869330i
$862$	37.4166	+	37.4166i	1.27441	+	1.27441i
$863$	−7.52358	+	28.0784i	−0.256106	+	0.955799i	0.711366	+	0.702821i	$0.248077\pi$
$863$	−7.52358	+	28.0784i	−0.256106	+	0.955799i	−0.967472	+	0.252978i	$0.918590\pi$
$864$	34.8549	−	0.370426i	1.18579	−	0.0126022i
$865$		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
$872$	4.05116	+	15.1191i	0.137190	+	0.511998i
$873$	−13.2135	+	28.8687i	−0.447210	+	0.977058i
$874$			30.0000i			1.01477i
$875$		0			0
$876$	−21.0000	+	17.7482i	−0.709524	+	0.599657i
$877$	−4.10862	+	15.3336i	−0.138738	+	0.517779i	0.861216	+	0.508239i	$0.169703\pi$
$877$	−4.10862	+	15.3336i	−0.138738	+	0.517779i	−0.999954	+	0.00953982i	$0.996963\pi$
$878$	−69.1160	+	18.5196i	−2.33255	+	0.625006i
$879$	2.74417	+	15.2470i	0.0925587	+	0.514267i
$880$		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
$887$	−6.47963	−	1.73621i	−0.217565	−	0.0582963i	0.148390	−	0.988929i	$-0.452591\pi$
$887$	−6.47963	−	1.73621i	−0.217565	−	0.0582963i	−0.365955	+	0.930633i	$0.619258\pi$
$888$	40.8442	+	3.42766i	1.37064	+	0.115025i
$889$	36.3731	+	21.0000i	1.21991	+	0.704317i
$890$		0			0
$891$		0			0
$892$	15.3336	−	4.10862i	0.513407	−	0.137567i
$893$	17.2790	−	4.62990i	0.578220	−	0.154934i
$894$	−23.2810	+	64.6761i	−0.778634	+	2.16309i
$895$		0			0
$896$			41.4126i			1.38350i
$897$	5.14149	−	61.2663i	0.171669	−	2.04562i
$898$	38.3340	+	10.2716i	1.27922	+	0.342766i
$899$	5.91608	−	10.2470i	0.197312	−	0.341755i
$900$		0			0
$901$	−10.0000	−	17.3205i	−0.333148	−	0.577030i
$902$		0			0
$903$	−10.9702	+	5.16287i	−0.365065	+	0.171809i
$904$		−	10.0000i		−	0.332595i
$905$		0			0
$906$	22.8704	−	4.11626i	0.759819	−	0.136754i
$907$	53.6676	−	14.3802i	1.78200	−	0.477486i	0.791057	−	0.611743i	$-0.209531\pi$
$907$	53.6676	−	14.3802i	1.78200	−	0.477486i	0.990947	+	0.134257i	$0.0428647\pi$
$908$		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	$0.871777\pi$
$912$	1.47510	+	3.13434i	0.0488456	+	0.103788i
$913$		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	$-0.592497\pi$
$919$	12.1244	−	7.00000i	0.399946	−	0.230909i	0.686461	+	0.727167i	$0.259163\pi$
$920$		0			0
$921$	−2.43521	−	13.5303i	−0.0802430	−	0.445839i
$922$	13.6954	−	51.1120i	0.451035	−	1.68328i
$923$	44.2719	+	44.2719i	1.45723	+	1.45723i
$924$		0			0
$925$		0			0
$926$	35.8643	−	20.7063i	1.17857	−	0.680451i
$927$	2.24334	+	23.7059i	0.0736809	+	0.778602i
$928$	10.2716	+	38.3340i	0.337181	+	1.25837i
$929$	20.7063	+	35.8643i	0.679351	+	1.17667i	0.975177	+	0.221428i	$0.0710719\pi$
$929$	20.7063	+	35.8643i	0.679351	+	1.17667i	−0.295826	+	0.955242i	$0.595595\pi$
$930$		0			0
$931$	−7.00000	+	12.1244i	−0.229416	+	0.397360i
$932$	−47.4342	+	47.4342i	−1.55376	+	1.55376i
$933$	8.72684	+	18.5430i	0.285704	+	0.607070i
$934$	−30.3109	−	17.5000i	−0.991803	−	0.572617i
$935$		0			0
$936$	12.3765	+	33.2689i	0.404539	+	1.08743i
$937$	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	$0.576454\pi$
$938$	−15.1191	+	4.05116i	−0.493657	+	0.132275i
$939$	11.8322	+	14.0000i	0.386128	+	0.456873i
$940$		0			0
$941$	−40.9878	−	23.6643i	−1.33616	−	0.771435i	−0.349928	−	0.936777i	$-0.613794\pi$
$941$	−40.9878	−	23.6643i	−1.33616	−	0.771435i	−0.986236	+	0.165342i	$0.947127\pi$
$942$	−33.6583	−	23.3906i	−1.09665	−	0.762105i
$943$	−38.3340	−	10.2716i	−1.24833	−	0.334488i
$944$	11.8322			0.385104
$945$		0			0
$946$		0			0
$947$	−28.0784	−	7.52358i	−0.912425	−	0.244484i	−0.228080	−	0.973642i	$-0.573245\pi$
$947$	−28.0784	−	7.52358i	−0.912425	−	0.244484i	−0.684345	+	0.729159i	$0.739912\pi$
$948$	−8.53394	−	5.93059i	−0.277169	−	0.192617i
$949$	24.2487	+	14.0000i	0.787146	+	0.454459i
$950$		0			0
$951$	25.0000	+	29.5804i	0.810681	+	0.959210i
$952$	6.84771	−	25.5560i	0.221936	−	0.828275i
$953$	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	$0.606890\pi$
$954$	−10.4601	−	28.1174i	−0.338657	−	0.910334i
$955$		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
$962$	−32.4093	−	120.953i	−1.04492	−	3.89968i
$963$	−0.631989	−	6.67837i	−0.0203656	−	0.215207i
$964$	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	$0.905007\pi$
$968$	6.36611	−	23.7586i	0.204614	−	0.763631i
$969$	−2.74417	−	15.2470i	−0.0881556	−	0.489803i
$970$		0			0
$971$	−40.9878	+	23.6643i	−1.31536	+	0.759424i	−0.982979	−	0.183720i	$-0.941186\pi$
$971$	−40.9878	+	23.6643i	−1.31536	+	0.759424i	−0.332383	+	0.943145i	$0.607853\pi$
$972$	−42.7272	−	19.0101i	−1.37048	−	0.609750i
$973$	−5.47817	−	20.4448i	−0.175622	−	0.655430i
$974$	−11.8322			−0.379127
$975$		0			0
$976$	5.50000	−	9.52628i	0.176051	−	0.304929i
$977$	9.25979	+	34.5580i	0.296247	+	1.10561i	0.940222	+	0.340562i	$0.110617\pi$
$977$	9.25979	+	34.5580i	0.296247	+	1.10561i	−0.643975	+	0.765047i	$0.722716\pi$
$978$	−8.72684	−	18.5430i	−0.279054	−	0.592939i
$979$		0			0
$980$		0			0
$981$	−3.50000	+	20.7063i	−0.111746	+	0.661101i
$982$	6.84771	−	25.5560i	0.218519	−	0.815525i
$983$	32.3981	−	8.68105i	1.03334	−	0.276883i	0.297989	−	0.954569i	$-0.403684\pi$
$983$	32.3981	−	8.68105i	1.03334	−	0.276883i	0.735351	+	0.677687i	$0.237017\pi$
$984$	22.5505	−	4.05869i	0.718885	−	0.129386i
$985$		0			0
$986$		−	59.1608i		−	1.88406i
$987$	33.6583	+	23.3906i	1.07136	+	0.744530i
$988$	−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	−0.388723	−	0.921355i	$-0.627084\pi$
$991$	19.0000	−	32.9090i	0.603555	−	1.04539i	0.992278	−	0.124033i	$-0.0395829\pi$
$992$	12.9593	+	3.47242i	0.411457	+	0.110250i
$993$	2.02783	−	24.1638i	0.0643512	−	0.766814i
$994$		−	70.0000i		−	2.22027i
$995$		0			0
$996$	−3.93521	+	10.9323i	−0.124692	+	0.346402i
$997$	15.3336	−	4.10862i	0.485620	−	0.130121i	−0.00769834	−	0.999970i	$-0.502450\pi$
$997$	15.3336	−	4.10862i	0.485620	−	0.130121i	0.493318	+	0.869849i	$0.335784\pi$
$998$	−25.9185	+	6.94484i	−0.820436	+	0.219835i
$999$	47.9130	+	26.9878i	1.51590	+	0.853856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bf.e.32.4	yes	16
3.2	odd	2	inner	525.2.bf.e.32.2	yes	16
5.2	odd	4	inner	525.2.bf.e.368.2	yes	16
5.3	odd	4	inner	525.2.bf.e.368.3	yes	16
5.4	even	2	inner	525.2.bf.e.32.1	✓	16
7.2	even	3	inner	525.2.bf.e.107.1	yes	16
15.2	even	4	inner	525.2.bf.e.368.4	yes	16
15.8	even	4	inner	525.2.bf.e.368.1	yes	16
15.14	odd	2	inner	525.2.bf.e.32.3	yes	16
21.2	odd	6	inner	525.2.bf.e.107.3	yes	16
35.2	odd	12	inner	525.2.bf.e.443.3	yes	16
35.9	even	6	inner	525.2.bf.e.107.4	yes	16
35.23	odd	12	inner	525.2.bf.e.443.2	yes	16
105.2	even	12	inner	525.2.bf.e.443.1	yes	16
105.23	even	12	inner	525.2.bf.e.443.4	yes	16
105.44	odd	6	inner	525.2.bf.e.107.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bf.e.32.1	✓	16	5.4	even	2	inner
525.2.bf.e.32.2	yes	16	3.2	odd	2	inner
525.2.bf.e.32.3	yes	16	15.14	odd	2	inner
525.2.bf.e.32.4	yes	16	1.1	even	1	trivial
525.2.bf.e.107.1	yes	16	7.2	even	3	inner
525.2.bf.e.107.2	yes	16	105.44	odd	6	inner
525.2.bf.e.107.3	yes	16	21.2	odd	6	inner
525.2.bf.e.107.4	yes	16	35.9	even	6	inner
525.2.bf.e.368.1	yes	16	15.8	even	4	inner
525.2.bf.e.368.2	yes	16	5.2	odd	4	inner
525.2.bf.e.368.3	yes	16	5.3	odd	4	inner
525.2.bf.e.368.4	yes	16	15.2	even	4	inner
525.2.bf.e.443.1	yes	16	105.2	even	12	inner
525.2.bf.e.443.2	yes	16	35.23	odd	12	inner
525.2.bf.e.443.3	yes	16	35.2	odd	12	inner
525.2.bf.e.443.4	yes	16	105.23	even	12	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)

\(f(q)\)	\(=\)	\(q+(2.15988 + 0.578737i) q^{2} +(1.42232 + 0.988431i) q^{3} +(2.59808 + 1.50000i) q^{4} +(2.50000 + 2.95804i) q^{6} +(-2.55560 + 0.684771i) q^{7} +(1.58114 + 1.58114i) q^{8} +(1.04601 + 2.81174i) q^{9} +O(q^{10})\)	\(q+(2.15988 + 0.578737i) q^{2} +(1.42232 + 0.988431i) q^{3} +(2.59808 + 1.50000i) q^{4} +(2.50000 + 2.95804i) q^{6} +(-2.55560 + 0.684771i) q^{7} +(1.58114 + 1.58114i) q^{8} +(1.04601 + 2.81174i) q^{9} +(2.21266 + 4.70150i) q^{12} +(3.74166 - 3.74166i) q^{13} -5.91608 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.15747 + 4.31975i) q^{17} +(0.631989 + 6.67837i) q^{18} +(-1.73205 + 1.00000i) q^{19} +(-4.31174 - 1.55207i) q^{21} +(1.73621 - 6.47963i) q^{23} +(0.686044 + 3.81174i) q^{24} +(10.2470 - 5.91608i) q^{26} +(-1.29145 + 5.03311i) q^{27} +(-7.66680 - 2.05431i) q^{28} -5.91608 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-1.73621 - 6.47963i) q^{32} +10.0000i q^{34} +(-1.50000 + 8.87412i) q^{36} +(2.73908 - 10.2224i) q^{37} +(-4.31975 + 1.15747i) q^{38} +(9.02022 - 1.62348i) q^{39} -5.91608i q^{41} +(-8.41458 - 5.84764i) q^{42} +(1.87083 - 1.87083i) q^{43} +(7.50000 - 12.9904i) q^{46} +(-8.63950 - 2.31495i) q^{47} +(0.144845 - 1.72598i) q^{48} +(6.06218 - 3.50000i) q^{49} +(-2.62348 + 7.28817i) q^{51} +(15.3336 - 4.10862i) q^{52} +(-4.31975 + 1.15747i) q^{53} +(-5.70221 + 10.1235i) q^{54} +(-5.12348 - 2.95804i) q^{56} +(-3.45197 - 0.289690i) q^{57} +(-12.7780 - 3.42385i) 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} +(2.55560 - 0.684771i) q^{67} +(-3.47242 + 12.9593i) q^{68} +(8.87412 - 7.50000i) q^{69} +11.8322i q^{71} +(-2.79186 + 6.09963i) q^{72} +(1.36954 + 5.11120i) q^{73} +(11.8322 - 20.4939i) q^{74} -6.00000 q^{76} +(20.4221 + 1.71383i) q^{78} +(-1.73205 + 1.00000i) q^{79} +(-6.81174 + 5.88220i) q^{81} +(3.42385 - 12.7780i) q^{82} +(1.58114 + 1.58114i) q^{83} +(-8.87412 - 10.5000i) q^{84} +(5.12348 - 2.95804i) q^{86} +(-8.41458 - 5.84764i) q^{87} +(2.95804 + 5.12348i) q^{89} +(-7.00000 + 12.1244i) q^{91} +(14.2302 - 14.2302i) q^{92} +(-3.13434 + 1.47510i) q^{93} +(-17.3205 - 10.0000i) q^{94} +(3.93521 - 10.9323i) q^{96} +(7.48331 + 7.48331i) q^{97} +(15.1191 - 4.05116i) 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

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