LMFDB - Embedded newform 525.2.bf.e.443.2

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			443.2
Root			$-0.988431 - 1.42232i$ of defining polynomial
Character	$\chi$	$=$	525.443
Dual form			525.2.bf.e.32.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15988 + 0.578737i) q^{2} +(-0.737552 - 1.56717i) q^{3} +(2.59808 - 1.50000i) q^{4} +(2.50000 + 2.95804i) q^{6} +(-2.55560 - 0.684771i) q^{7} +(-1.58114 + 1.58114i) q^{8} +(-1.91203 + 2.31174i) q^{9} +O(q^{10})$	\(q+(-2.15988 + 0.578737i) q^{2} +(-0.737552 - 1.56717i) 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} +(-1.91203 + 2.31174i) q^{9} +(-4.26697 - 2.96529i) q^{12} +(3.74166 + 3.74166i) q^{13} +5.91608 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.15747 + 4.31975i) q^{17} +(2.79186 - 6.09963i) q^{18} +(-1.73205 - 1.00000i) q^{19} +(0.811738 + 4.51011i) q^{21} +(-1.73621 - 6.47963i) q^{23} +(3.64408 + 1.31174i) q^{24} +(-10.2470 - 5.91608i) q^{26} +(5.03311 + 1.29145i) 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} +(3.10414 - 8.62348i) q^{39} -5.91608i q^{41} +(-4.36342 - 9.27149i) q^{42} +(1.87083 + 1.87083i) q^{43} +(7.50000 + 12.9904i) q^{46} +(8.63950 - 2.31495i) q^{47} +(1.72598 + 0.144845i) q^{48} +(6.06218 + 3.50000i) q^{49} +(7.62348 - 1.37209i) q^{51} +(15.3336 + 4.10862i) q^{52} +(4.31975 + 1.15747i) q^{53} +(-11.6183 + 0.123475i) q^{54} +(5.12348 - 2.95804i) q^{56} +(-0.289690 + 3.45197i) 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} +(6.46940 - 4.59857i) 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} +(-0.631989 - 6.67837i) q^{72} +(1.36954 - 5.11120i) q^{73} +(-11.8322 - 20.4939i) q^{74} -6.00000 q^{76} +(-1.71383 + 20.4221i) q^{78} +(-1.73205 - 1.00000i) q^{79} +(-1.68826 - 8.84024i) 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} +(-4.36342 - 9.27149i) q^{87} +(-2.95804 + 5.12348i) q^{89} +(-7.00000 - 12.1244i) q^{91} +(-14.2302 - 14.2302i) q^{92} +(-1.97686 + 2.84465i) q^{93} +(-17.3205 + 10.0000i) q^{94} +(-11.4352 + 2.05813i) 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.15988	+	0.578737i	−1.52726	+	0.409229i	−0.922125	−	0.386892i	$-0.873549\pi$
$2$	−2.15988	+	0.578737i	−1.52726	+	0.409229i	−0.605138	+	0.796121i	$0.706882\pi$
$3$	−0.737552	−	1.56717i	−0.425826	−	0.904805i
$3$	−0.737552	−	1.56717i	−0.425826	−	0.904805i
$4$	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
$9$	−1.91203	+	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	$0.333333\pi$
$12$	−4.26697	−	2.96529i	−1.23177	−	0.856007i
$13$	3.74166	+	3.74166i	1.03775	+	1.03775i	0.999259	+	0.0384901i	$0.0122548\pi$
$13$	3.74166	+	3.74166i	1.03775	+	1.03775i	0.0384901	+	0.999259i	$0.487745\pi$
$14$	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	0.671176	+	0.741298i	$0.265790\pi$
$17$	−1.15747	+	4.31975i	−0.280729	+	1.04769i	−0.951904	+	0.306395i	$0.900877\pi$
$18$	2.79186	−	6.09963i	0.658049	−	1.43770i
$19$	−1.73205	−	1.00000i	−0.397360	−	0.229416i	0.287984	−	0.957635i	$-0.407015\pi$
$19$	−1.73205	−	1.00000i	−0.397360	−	0.229416i	−0.685344	+	0.728219i	$0.740348\pi$
$20$		0			0
$21$	0.811738	+	4.51011i	0.177136	+	0.984186i
$22$		0			0
$23$	−1.73621	−	6.47963i	−0.362025	−	1.35110i	−0.871409	−	0.490557i	$-0.836793\pi$
$23$	−1.73621	−	6.47963i	−0.362025	−	1.35110i	0.509384	−	0.860539i	$-0.329873\pi$
$24$	3.64408	+	1.31174i	0.743845	+	0.267757i
$25$		0			0
$26$	−10.2470	−	5.91608i	−2.00959	−	1.16024i
$27$	5.03311	+	1.29145i	0.968622	+	0.248539i
$28$	−7.66680	+	2.05431i	−1.44889	+	0.388229i
$29$	5.91608			1.09859			0.549294	−	0.835629i	$-0.314897\pi$
$29$	5.91608			1.09859			0.549294	+	0.835629i	$0.314897\pi$
$30$		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	$0.890815\pi$
$32$	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	0.701543	+	0.712627i	$0.252495\pi$
$37$	2.73908	+	10.2224i	0.450303	+	1.68055i	−0.251240	+	0.967925i	$0.580838\pi$
$38$	4.31975	+	1.15747i	0.700756	+	0.187767i
$39$	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	$-0.152857\pi$
$42$	−4.36342	−	9.27149i	−0.673290	−	1.43062i
$43$	1.87083	+	1.87083i	0.285299	+	0.285299i	0.835218	−	0.549919i	$-0.185341\pi$
$43$	1.87083	+	1.87083i	0.285299	+	0.285299i	−0.549919	+	0.835218i	$0.685341\pi$
$44$		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	$-0.357126\pi$
$47$	8.63950	−	2.31495i	1.26020	−	0.337670i	0.826269	+	0.563276i	$0.190459\pi$
$48$	1.72598	+	0.144845i	0.249124	+	0.0209066i
$49$	6.06218	+	3.50000i	0.866025	+	0.500000i
$50$		0			0
$51$	7.62348	−	1.37209i	1.06750	−	0.192131i
$52$	15.3336	+	4.10862i	2.12639	+	0.569764i
$53$	4.31975	+	1.15747i	0.593364	+	0.158991i	0.542990	−	0.839739i	$-0.317292\pi$
$53$	4.31975	+	1.15747i	0.593364	+	0.158991i	0.0503735	+	0.998730i	$0.483959\pi$
$54$	−11.6183	+	0.123475i	−1.58105	+	0.0168029i
$55$		0			0
$56$	5.12348	−	2.95804i	0.684653	−	0.395285i
$57$	−0.289690	+	3.45197i	−0.0383704	+	0.457224i
$58$	−12.7780	+	3.42385i	−1.67783	+	0.449574i
$59$	5.91608	+	10.2470i	0.770208	+	1.33404i	0.937449	+	0.348123i	$0.113181\pi$
$59$	5.91608	+	10.2470i	0.770208	+	1.33404i	−0.167241	+	0.985916i	$0.553486\pi$
$60$		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
$63$	6.46940	−	4.59857i	0.815068	−	0.579366i
$64$			13.0000i			1.62500i
$65$		0			0
$66$		0			0
$67$	2.55560	+	0.684771i	0.312216	+	0.0836581i	0.411525	−	0.911399i	$-0.364996\pi$
$67$	2.55560	+	0.684771i	0.312216	+	0.0836581i	−0.0993085	+	0.995057i	$0.531663\pi$
$68$	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	$0.752242\pi$
$72$	−0.631989	−	6.67837i	−0.0744806	−	0.787053i
$73$	1.36954	−	5.11120i	0.160293	−	0.598221i	−0.838301	−	0.545208i	$-0.816451\pi$
$73$	1.36954	−	5.11120i	0.160293	−	0.598221i	0.998594	−	0.0530130i	$-0.0168825\pi$
$74$	−11.8322	−	20.4939i	−1.37546	−	2.38237i
$75$		0			0
$76$	−6.00000			−0.688247
$77$		0			0
$78$	−1.71383	+	20.4221i	−0.194053	+	2.31235i
$79$	−1.73205	−	1.00000i	−0.194871	−	0.112509i	0.399390	−	0.916781i	$-0.369222\pi$
$79$	−1.73205	−	1.00000i	−0.194871	−	0.112509i	−0.594261	+	0.804272i	$0.702555\pi$
$80$		0			0
$81$	−1.68826	−	8.84024i	−0.187585	−	0.982248i
$82$	3.42385	+	12.7780i	0.378101	+	1.41109i
$83$	−1.58114	+	1.58114i	−0.173553	+	0.173553i	−0.788538	−	0.614986i	$-0.789162\pi$
$83$	−1.58114	+	1.58114i	−0.173553	+	0.173553i	0.614986	+	0.788538i	$0.289162\pi$
$84$	8.87412	+	10.5000i	0.968246	+	1.14564i
$85$		0			0
$86$	−5.12348	−	2.95804i	−0.552479	−	0.318974i
$87$	−4.36342	−	9.27149i	−0.467808	−	0.994008i
$88$		0			0
$89$	−2.95804	+	5.12348i	−0.313552	+	0.543087i	−0.979129	−	0.203242i	$-0.934852\pi$
$89$	−2.95804	+	5.12348i	−0.313552	+	0.543087i	0.665577	+	0.746329i	$0.268186\pi$
$90$		0			0
$91$	−7.00000	−	12.1244i	−0.733799	−	1.27098i
$92$	−14.2302	−	14.2302i	−1.48361	−	1.48361i
$93$	−1.97686	+	2.84465i	−0.204991	+	0.294976i
$94$	−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	−0.216473	−	0.976289i	$-0.569455\pi$
$97$	7.48331	−	7.48331i	0.759815	−	0.759815i	0.976289	+	0.216473i	$0.0694554\pi$
$98$	−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	$-0.571568\pi$
$101$	5.12348	−	2.95804i	0.509805	−	0.294336i	0.732753	+	0.680494i	$0.238235\pi$
$102$	−15.6717	+	7.37552i	−1.55173	+	0.730286i
$103$	7.66680	−	2.05431i	0.755432	−	0.202417i	0.139506	−	0.990221i	$-0.455449\pi$
$103$	7.66680	−	2.05431i	0.755432	−	0.202417i	0.615926	+	0.787804i	$0.288782\pi$
$104$	−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	$-0.548862\pi$
$107$	2.15988	−	0.578737i	0.208803	−	0.0559486i	0.361704	+	0.932293i	$0.382195\pi$
$108$	15.0136	−	4.19438i	1.44468	−	0.403604i
$109$	6.06218	−	3.50000i	0.580651	−	0.335239i	−0.180741	−	0.983531i	$-0.557850\pi$
$109$	6.06218	−	3.50000i	0.580651	−	0.335239i	0.761392	+	0.648292i	$0.224516\pi$
$110$		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	$-0.682539\pi$
$113$	3.16228	−	3.16228i	0.297482	−	0.297482i	0.840027	+	0.542545i	$0.182539\pi$
$114$	−1.37209	−	7.62348i	−0.128508	−	0.714004i
$115$		0			0
$116$	15.3704	−	8.87412i	1.42711	−	0.823941i
$117$	−15.8039	+	1.49556i	−1.46107	+	0.138265i
$118$	−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
$123$	−9.27149	+	4.36342i	−0.835982	+	0.393436i
$124$	−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	−0.999992	−	0.00393704i	$-0.998747\pi$
$127$	−11.2250	+	11.2250i	−0.996055	+	0.996055i	0.00393704	+	0.999992i	$0.498747\pi$
$128$	−4.05116	−	15.1191i	−0.358075	−	1.33635i
$129$	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
$137$	−2.31495	+	8.63950i	−0.197779	+	0.738123i	0.793750	+	0.608243i	$0.208126\pi$
$137$	−2.31495	+	8.63950i	−0.197779	+	0.738123i	−0.991530	+	0.129879i	$0.958541\pi$
$138$	14.8265	−	21.3348i	1.26211	−	1.81614i
$139$		−	8.00000i		−	0.678551i	−0.940687	−	0.339276i	$-0.889818\pi$
$139$		−	8.00000i		−	0.678551i	0.940687	−	0.339276i	$-0.110182\pi$
$140$		0			0
$141$	−10.0000	−	11.8322i	−0.842152	−	0.996448i
$142$	−6.84771	−	25.5560i	−0.574647	−	2.14461i
$143$		0			0
$144$	−1.04601	−	2.81174i	−0.0871673	−	0.234311i
$145$		0			0
$146$			11.8322i			0.979236i
$147$	1.01391	−	12.0819i	0.0836263	−	0.996497i
$148$	22.4499	+	22.4499i	1.84537	+	1.84537i
$149$	−8.87412	+	15.3704i	−0.726996	+	1.25919i	0.231151	+	0.972918i	$0.425751\pi$
$149$	−8.87412	+	15.3704i	−0.726996	+	1.25919i	−0.958147	+	0.286276i	$0.907582\pi$
$150$		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	$0.754829\pi$
$152$	4.31975	−	1.15747i	0.350378	−	0.0938835i
$153$	−7.77300	−	10.9353i	−0.628410	−	0.884065i
$154$		0			0
$155$		0			0
$156$	−4.87043	−	27.0607i	−0.389946	−	2.16659i
$157$	−10.2224	−	2.73908i	−0.815836	−	0.218603i	−0.173311	−	0.984867i	$-0.555447\pi$
$157$	−10.2224	−	2.73908i	−0.815836	−	0.218603i	−0.642525	+	0.766265i	$0.722113\pi$
$158$	4.31975	+	1.15747i	0.343661	+	0.0920837i
$159$	−1.37209	−	7.62348i	−0.108814	−	0.604581i
$160$		0			0
$161$			17.7482i			1.39876i
$162$	8.76261	+	18.1168i	0.688456	+	1.42339i
$163$	−5.11120	+	1.36954i	−0.400340	+	0.107271i	−0.453371	−	0.891322i	$-0.649779\pi$
$163$	−5.11120	+	1.36954i	−0.400340	+	0.107271i	0.0530306	+	0.998593i	$0.483112\pi$
$164$	−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	$-0.457072\pi$
$167$	−11.0680	−	11.0680i	−0.856465	−	0.856465i	−0.990920	+	0.134454i	$0.957072\pi$
$168$	−8.41458	−	5.84764i	−0.649199	−	0.451155i
$169$			15.0000i			1.15385i
$170$		0			0
$171$	5.62348	−	2.09201i	0.430038	−	0.159980i
$172$	7.66680	+	2.05431i	0.584588	+	0.156640i
$173$	2.31495	+	8.63950i	0.176002	+	0.656849i	0.996379	+	0.0850256i	$0.0270972\pi$
$173$	2.31495	+	8.63950i	0.176002	+	0.656849i	−0.820377	+	0.571824i	$0.806236\pi$
$174$	14.7902	+	17.5000i	1.12124	+	1.32667i
$175$		0			0
$176$		0			0
$177$	11.6953	−	16.8292i	0.879071	−	1.26496i
$178$	3.42385	−	12.7780i	0.256629	−	0.957751i
$179$	5.91608	+	10.2470i	0.442189	+	0.765893i	0.997852	−	0.0655145i	$-0.0208689\pi$
$179$	5.91608	+	10.2470i	0.442189	+	0.765893i	−0.555663	+	0.831408i	$0.687536\pi$
$180$		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
$183$	−18.9858	−	1.59329i	−1.40347	−	0.117780i
$184$	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	$0.339520\pi$
$192$	20.3732	−	9.58818i	1.47031	−	0.691967i
$193$	−2.73908	+	10.2224i	−0.197164	+	0.735824i	0.794533	+	0.607221i	$0.207716\pi$
$193$	−2.73908	+	10.2224i	−0.197164	+	0.735824i	−0.991696	+	0.128603i	$0.958951\pi$
$194$	−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	−0.883628	−	0.468190i	$-0.844906\pi$
$197$	−18.9737	−	18.9737i	−1.35182	−	1.35182i	−0.468190	−	0.883628i	$-0.655094\pi$
$198$		0			0
$199$	−6.92820	+	4.00000i	−0.491127	+	0.283552i	−0.725042	−	0.688705i	$-0.758180\pi$
$199$	−6.92820	+	4.00000i	−0.491127	+	0.283552i	0.233915	+	0.972257i	$0.424846\pi$
$200$		0			0
$201$	−0.811738	−	4.51011i	−0.0572556	−	0.318119i
$202$	−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
$207$	18.2989	+	8.37559i	1.27186	+	0.582144i
$208$	−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
$213$	18.5430	−	8.72684i	1.27054	−	0.597953i
$214$	−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
$219$	−9.02022	+	1.62348i	−0.609530	+	0.109704i
$220$		0			0
$221$	−20.4939	+	11.8322i	−1.37857	+	0.795917i
$222$	−23.3906	+	33.6583i	−1.56987	+	2.25900i
$223$	3.74166	+	3.74166i	0.250560	+	0.250560i	0.821200	−	0.570640i	$-0.193305\pi$
$223$	3.74166	+	3.74166i	0.250560	+	0.250560i	−0.570640	+	0.821200i	$0.693305\pi$
$224$	−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	$-0.916667\pi$
$227$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$228$	4.42531	+	9.40301i	0.293074	+	0.622730i
$229$	15.5885	+	9.00000i	1.03011	+	0.594737i	0.917017	−	0.398847i	$-0.130590\pi$
$229$	15.5885	+	9.00000i	1.03011	+	0.594737i	0.113097	+	0.993584i	$0.463923\pi$
$230$		0			0
$231$		0			0
$232$	−9.35414	+	9.35414i	−0.614130	+	0.614130i
$233$	5.78737	+	21.5988i	0.379143	+	1.41498i	0.847196	+	0.531281i	$0.178289\pi$
$233$	5.78737	+	21.5988i	0.379143	+	1.41498i	−0.468052	+	0.883701i	$0.655044\pi$
$234$	33.2689	−	12.3765i	2.17486	−	0.809079i
$235$		0			0
$236$	30.7409	+	17.7482i	2.00106	+	1.15531i
$237$	−0.289690	+	3.45197i	−0.0188174	+	0.224229i
$238$	−6.84771	+	25.5560i	−0.443871	+	1.65655i
$239$	11.8322			0.765359			0.382679	−	0.923881i	$-0.375001\pi$
$239$	11.8322			0.765359			0.382679	+	0.923881i	$0.375001\pi$
$240$		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	$0.771431\pi$
$242$	6.36611	−	23.7586i	0.409229	−	1.52726i
$243$	−12.6090	+	9.16593i	−0.808865	+	0.587995i
$244$		−	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
$249$	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	$-0.121815\pi$
$252$	9.91014	−	21.6515i	0.624280	−	1.36392i
$253$		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	$-0.267703\pi$
$257$	25.9185	−	6.94484i	1.61675	−	0.433207i	0.950045	+	0.312112i	$0.101037\pi$
$258$	−0.856914	+	10.2111i	−0.0533491	+	0.635713i
$259$		−	28.0000i		−	1.73984i
$260$		0			0
$261$	−11.3117	+	13.6764i	−0.700179	+	0.846549i
$262$		0			0
$263$	6.47963	+	1.73621i	0.399551	+	0.107059i	0.452998	−	0.891511i	$-0.350354\pi$
$263$	6.47963	+	1.73621i	0.399551	+	0.107059i	−0.0534475	+	0.998571i	$0.517021\pi$
$264$		0			0
$265$		0			0
$266$	−10.2470	−	5.91608i	−0.628281	−	0.362738i
$267$	10.2111	+	0.856914i	0.624907	+	0.0524423i
$268$	7.66680	−	2.05431i	0.468324	−	0.125487i
$269$	2.95804	+	5.12348i	0.180355	+	0.312384i	0.942001	−	0.335609i	$-0.108942\pi$
$269$	2.95804	+	5.12348i	0.180355	+	0.312384i	−0.761647	+	0.647993i	$0.775609\pi$
$270$		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
$273$	−13.8380	+	19.9125i	−0.837516	+	1.20516i
$274$		−	20.0000i		−	1.20824i
$275$		0			0
$276$	−11.8056	+	32.7968i	−0.710616	+	1.97413i
$277$	15.3336	+	4.10862i	0.921307	+	0.246863i	0.688144	−	0.725574i	$-0.258426\pi$
$277$	15.3336	+	4.10862i	0.921307	+	0.246863i	0.233163	+	0.972438i	$0.425092\pi$
$278$	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	$-0.249434\pi$
$282$	28.4465	+	19.7686i	1.69396	+	1.17720i
$283$	1.36954	−	5.11120i	0.0814108	−	0.303829i	−0.913200	−	0.407513i	$-0.866396\pi$
$283$	1.36954	−	5.11120i	0.0814108	−	0.303829i	0.994610	+	0.103683i	$0.0330629\pi$
$284$	17.7482	+	30.7409i	1.05316	+	1.82413i
$285$		0			0
$286$		0			0
$287$	−4.05116	+	15.1191i	−0.239132	+	0.892454i
$288$	11.6595	+	16.4029i	0.687043	+	0.966552i
$289$	−2.59808	−	1.50000i	−0.152828	−	0.0882353i
$290$		0			0
$291$	−17.2470	−	6.20828i	−1.01103	−	0.363936i
$292$	−4.10862	−	15.3336i	−0.240439	−	0.897331i
$293$	−6.32456	+	6.32456i	−0.369484	+	0.369484i	−0.867289	−	0.497805i	$-0.834140\pi$
$293$	−6.32456	+	6.32456i	−0.369484	+	0.369484i	0.497805	+	0.867289i	$0.334140\pi$
$294$	4.80230	+	26.6822i	0.280076	+	1.55614i
$295$		0			0
$296$	−20.4939	−	11.8322i	−1.19118	−	0.687730i
$297$		0			0
$298$	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
$303$	−8.41458	−	5.84764i	−0.483405	−	0.335938i
$304$	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	−0.848890	−	0.528569i	$-0.822729\pi$
$307$	−5.61249	+	5.61249i	−0.320321	+	0.320321i	0.528569	+	0.848890i	$0.322729\pi$
$308$		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	$0.442228\pi$
$312$	8.72684	+	18.5430i	0.494060	+	1.04979i
$313$	10.2224	−	2.73908i	0.577804	−	0.154822i	0.0419307	−	0.999121i	$-0.486649\pi$
$313$	10.2224	−	2.73908i	0.577804	−	0.154822i	0.535873	+	0.844298i	$0.319982\pi$
$314$	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	$-0.799439\pi$
$317$	−21.5988	+	5.78737i	−1.21311	+	0.325051i	−0.405127	+	0.914261i	$0.632773\pi$
$318$	7.37552	+	15.6717i	0.413599	+	0.878824i
$319$		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
$324$	−17.6466	−	20.4352i	−0.980366	−	1.13529i
$325$		0			0
$326$	10.2470	−	5.91608i	0.567526	−	0.327661i
$327$	−9.95626	−	6.91902i	−0.550583	−	0.382623i
$328$	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	$0.292381\pi$
$332$	−1.73621	+	6.47963i	−0.0952870	+	0.355616i
$333$	−28.8687	−	13.2135i	−1.58200	−	0.724096i
$334$	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	−0.597814	−	0.801635i	$-0.703964\pi$
$337$	3.74166	−	3.74166i	0.203821	−	0.203821i	0.801635	+	0.597814i	$0.203964\pi$
$338$	−8.68105	−	32.3981i	−0.472187	−	1.76223i
$339$	−7.28817	−	2.62348i	−0.395839	−	0.142488i
$340$		0			0
$341$		0			0
$342$	−10.9353	+	7.77300i	−0.591312	+	0.420316i
$343$	−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	0.843735	+	0.536760i	$0.180352\pi$
$347$	−2.89368	+	10.7994i	−0.155341	+	0.579741i	−0.999076	+	0.0429807i	$0.986315\pi$
$348$	−25.2437	−	17.5429i	−1.35321	−	0.940399i
$349$			31.0000i			1.65939i	0.558216	+	0.829696i	$0.311486\pi$
$349$			31.0000i			1.65939i	−0.558216	+	0.829696i	$0.688514\pi$
$350$		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	$-0.532881\pi$
$353$	−12.9593	−	3.47242i	−0.689752	−	0.184818i	−0.586636	+	0.809851i	$0.699548\pi$
$354$	−15.5207	+	43.1174i	−0.824915	+	2.29166i
$355$		0			0
$356$			17.7482i			0.940655i
$357$	−20.4221	−	1.71383i	−1.08085	−	0.0907054i
$358$	−18.7083	−	18.7083i	−0.988764	−	0.988764i
$359$	−5.91608	+	10.2470i	−0.312239	+	0.540813i	−0.978847	−	0.204595i	$-0.934412\pi$
$359$	−5.91608	+	10.2470i	−0.312239	+	0.540813i	0.666608	+	0.745409i	$0.267746\pi$
$360$		0			0
$361$	−7.50000	−	12.9904i	−0.394737	−	0.683704i
$362$	6.47963	−	1.73621i	0.340562	−	0.0912532i
$363$	18.9858	+	1.59329i	0.996497	+	0.0836263i
$364$	−36.3731	−	21.0000i	−1.90647	−	1.10070i
$365$		0			0
$366$	41.9291	−	7.54648i	2.19167	−	0.394461i
$367$	7.66680	+	2.05431i	0.400204	+	0.107234i	0.453306	−	0.891355i	$-0.350244\pi$
$367$	7.66680	+	2.05431i	0.400204	+	0.107234i	−0.0531027	+	0.998589i	$0.516911\pi$
$368$	6.47963	+	1.73621i	0.337774	+	0.0905063i
$369$	13.6764	+	11.3117i	0.711966	+	0.588866i
$370$		0			0
$371$	−10.2470	−	5.91608i	−0.531995	−	0.307148i
$372$	−0.869070	+	10.3559i	−0.0450592	+	0.536929i
$373$	20.4448	−	5.47817i	1.05859	−	0.283649i	0.312794	−	0.949821i	$-0.398735\pi$
$373$	20.4448	−	5.47817i	1.05859	−	0.283649i	0.745798	+	0.666172i	$0.232069\pi$
$374$		0			0
$375$		0			0
$376$	−10.0000	+	17.3205i	−0.515711	+	0.893237i
$377$	22.1359	+	22.1359i	1.14006	+	1.14006i
$378$	29.7763	+	7.64032i	1.53153	+	0.392975i
$379$		−	18.0000i		−	0.924598i	−0.886724	−	0.462299i	$-0.847025\pi$
$379$		−	18.0000i		−	0.924598i	0.886724	−	0.462299i	$-0.152975\pi$
$380$		0			0
$381$	25.8704	+	9.31241i	1.32538	+	0.477089i
$382$	−51.1120	−	13.6954i	−2.61512	−	0.700718i
$383$	1.73621	+	6.47963i	0.0887162	+	0.331093i	0.995992	−	0.0894428i	$-0.0285086\pi$
$383$	1.73621	+	6.47963i	0.0887162	+	0.331093i	−0.907276	+	0.420536i	$0.861842\pi$
$384$	−20.7063	+	17.5000i	−1.05666	+	0.893043i
$385$		0			0
$386$		−	23.6643i		−	1.20448i
$387$	−7.90195	+	0.747780i	−0.401679	+	0.0380118i
$388$	8.21725	−	30.6672i	0.417168	−	1.55689i
$389$		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
$392$	−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	−0.955881	−	0.293755i	$-0.905095\pi$
$397$	−5.47817	−	20.4448i	−0.274941	−	1.02609i	0.680939	−	0.732340i	$-0.261572\pi$
$398$	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	$0.812807\pi$
$402$	4.36342	+	9.27149i	0.217628	+	0.462420i
$403$	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
$408$	−9.88431	+	14.2232i	−0.489346	+	0.704155i
$409$	−11.2583	+	6.50000i	−0.556689	+	0.321404i	−0.751815	−	0.659374i	$-0.770822\pi$
$409$	−11.2583	+	6.50000i	−0.556689	+	0.321404i	0.195127	+	0.980778i	$0.437488\pi$
$410$		0			0
$411$	15.2470	−	2.74417i	0.752077	−	0.135360i
$412$	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
$417$	−12.5373	+	5.90042i	−0.613956	+	0.288945i
$418$		0			0
$419$	23.6643			1.15608			0.578039	−	0.816009i	$-0.303818\pi$
$419$	23.6643			1.15608			0.578039	+	0.816009i	$0.303818\pi$
$420$		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
$423$	−11.1675	+	24.3985i	−0.542980	+	1.18630i
$424$	−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	$0.526365\pi$
$432$	−3.63498	+	3.71307i	−0.174888	+	0.178645i
$433$	11.2250	+	11.2250i	0.539438	+	0.539438i	0.923364	−	0.383926i	$-0.125428\pi$
$433$	11.2250	+	11.2250i	0.539438	+	0.539438i	−0.383926	+	0.923364i	$0.625428\pi$
$434$	−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
$438$	18.5430	−	8.72684i	0.886018	−	0.416984i
$439$	−27.7128	−	16.0000i	−1.32266	−	0.763638i	−0.338508	−	0.940963i	$-0.609922\pi$
$439$	−27.7128	−	16.0000i	−1.32266	−	0.763638i	−0.984152	+	0.177325i	$0.943256\pi$
$440$		0			0
$441$	−19.6822	+	7.32205i	−0.937246	+	0.348669i
$442$	37.4166	−	37.4166i	1.77972	−	1.77972i
$443$	−0.578737	−	2.15988i	−0.0274966	−	0.102619i	0.950814	−	0.309763i	$-0.100250\pi$
$443$	−0.578737	−	2.15988i	−0.0274966	−	0.102619i	−0.978310	+	0.207144i	$0.933583\pi$
$444$	18.6248	−	51.7409i	0.883895	−	2.45551i
$445$		0			0
$446$	−10.2470	−	5.91608i	−0.485207	−	0.280134i
$447$	30.6332	+	2.57074i	1.44890	+	0.121592i
$448$	8.90202	−	33.2228i	0.420581	−	1.56963i
$449$	−17.7482			−0.837591			−0.418796	−	0.908081i	$-0.637548\pi$
$449$	−17.7482			−0.837591			−0.418796	+	0.908081i	$0.637548\pi$
$450$		0			0
$451$		0			0
$452$	3.47242	−	12.9593i	0.163329	−	0.609552i
$453$	5.93059	−	8.53394i	0.278643	−	0.400959i
$454$		0			0
$455$		0			0
$456$	−5.00000	−	5.91608i	−0.234146	−	0.277046i
$457$	2.73908	+	10.2224i	0.128129	+	0.478184i	0.999932	−	0.0116731i	$-0.00371575\pi$
$457$	2.73908	+	10.2224i	0.128129	+	0.478184i	−0.871803	+	0.489857i	$0.837049\pi$
$458$	−38.8778	−	10.4173i	−1.81664	−	0.486767i
$459$	−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	0.942584	−	0.333970i	$-0.108388\pi$
$463$	13.0958	+	13.0958i	0.608613	+	0.608613i	−0.333970	+	0.942584i	$0.608388\pi$
$464$	−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	$-0.465374\pi$
$467$	15.1191	−	4.05116i	0.699630	−	0.187465i	0.591065	+	0.806624i	$0.298708\pi$
$468$	−38.8164	+	27.5914i	−1.79429	+	1.27541i
$469$	−6.06218	−	3.50000i	−0.279925	−	0.161615i
$470$		0			0
$471$	3.24695	+	18.0404i	0.149612	+	0.831259i
$472$	−25.5560	−	6.84771i	−1.17631	−	0.315191i
$473$		0			0
$474$	−1.37209	−	7.62348i	−0.0630220	−	0.350158i
$475$		0			0
$476$		−	35.4965i		−	1.62698i
$477$	−10.9353	+	7.77300i	−0.500692	+	0.355901i
$478$	−25.5560	+	6.84771i	−1.16890	+	0.313207i
$479$	−17.7482	−	30.7409i	−0.810938	−	1.40459i	−0.912208	−	0.409726i	$-0.865624\pi$
$479$	−17.7482	−	30.7409i	−0.810938	−	1.40459i	0.101271	−	0.994859i	$-0.467709\pi$
$480$		0			0
$481$	−28.0000	+	48.4974i	−1.27669	+	2.21129i
$482$	−9.48683	−	9.48683i	−0.432113	−	0.432113i
$483$	27.8145	−	13.0903i	1.26560	−	0.595627i
$484$			33.0000i			1.50000i
$485$		0			0
$486$	21.9291	−	27.0945i	0.994725	−	1.22903i
$487$	−5.11120	−	1.36954i	−0.231611	−	0.0620599i	0.141147	−	0.989989i	$-0.454921\pi$
$487$	−5.11120	−	1.36954i	−0.231611	−	0.0620599i	−0.372757	+	0.927929i	$0.621588\pi$
$488$	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	$-0.0860287\pi$
$492$	−17.5429	+	25.2437i	−0.790896	+	1.13808i
$493$	−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
$498$	−8.62992	−	0.724225i	−0.386716	−	0.0324533i
$499$	−10.3923	−	6.00000i	−0.465223	−	0.268597i	0.249015	−	0.968500i	$-0.419893\pi$
$499$	−10.3923	−	6.00000i	−0.465223	−	0.268597i	−0.714238	+	0.699903i	$0.753227\pi$
$500$		0			0
$501$	−9.18216	+	25.5086i	−0.410229	+	1.13964i
$502$	6.84771	+	25.5560i	0.305628	+	1.14062i
$503$	−23.7171	+	23.7171i	−1.05749	+	1.05749i	−0.0592492	+	0.998243i	$0.518871\pi$
$503$	−23.7171	+	23.7171i	−1.05749	+	1.05749i	−0.998243	+	0.0592492i	$0.981129\pi$
$504$	−2.95804	+	17.5000i	−0.131762	+	0.779512i
$505$		0			0
$506$		0			0
$507$	23.5075	−	11.0633i	1.04401	−	0.491338i
$508$	−12.3259	+	46.0008i	−0.546872	+	2.04096i
$509$	8.87412	−	15.3704i	0.393338	−	0.681282i	−0.599549	−	0.800338i	$-0.704653\pi$
$509$	8.87412	−	15.3704i	0.393338	−	0.681282i	0.992888	+	0.119056i	$0.0379867\pi$
$510$		0			0
$511$	−7.00000	+	12.1244i	−0.309662	+	0.536350i
$512$	7.90569	+	7.90569i	0.349386	+	0.349386i
$513$	−7.42615	−	7.26996i	−0.327872	−	0.320977i
$514$	−51.9615	+	30.0000i	−2.29192	+	1.32324i
$515$		0			0
$516$	−2.43521	−	13.5303i	−0.107204	−	0.595639i
$517$		0			0
$518$	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	$-0.493203\pi$
$521$	20.4939	−	11.8322i	0.897854	−	0.518376i	0.876503	+	0.481396i	$0.159870\pi$
$522$	16.5169	−	36.0859i	0.722925	−	1.57944i
$523$	35.7784	−	9.58679i	1.56448	−	0.419201i	0.630402	−	0.776269i	$-0.282890\pi$
$523$	35.7784	−	9.58679i	1.56448	−	0.419201i	0.934078	+	0.357068i	$0.116224\pi$
$524$		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
$534$	−22.5505	+	4.05869i	−0.975857	+	0.175637i
$535$		0			0
$536$	−5.12348	+	2.95804i	−0.221300	+	0.127768i
$537$	11.6953	−	16.8292i	0.504688	−	0.726232i
$538$	−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	$0.300593\pi$
$542$	1.15747	−	4.31975i	0.0497178	−	0.185549i
$543$	2.21266	+	4.70150i	0.0949542	+	0.201761i
$544$	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	−0.0407102	+	0.999171i	$0.512962\pi$
$547$	−24.3208	+	24.3208i	−1.03988	+	1.03988i	−0.999171	+	0.0407102i	$0.987038\pi$
$548$	6.94484	+	25.9185i	0.296669	+	1.10718i
$549$	11.5061	+	30.9291i	0.491068	+	1.32002i
$550$		0			0
$551$	−10.2470	−	5.91608i	−0.436535	−	0.252033i
$552$	2.17267	−	25.8898i	0.0924751	−	1.10194i
$553$	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	$-0.855983\pi$
$557$	2.31495	−	8.63950i	0.0980875	−	0.366068i	0.997469	+	0.0710962i	$0.0226497\pi$
$558$	−13.3567	+	1.26398i	−0.565436	+	0.0535085i
$559$			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	$-0.0636487\pi$
$563$	41.0376	+	10.9960i	1.72953	+	0.463426i	0.749455	+	0.662055i	$0.230315\pi$
$564$	−43.7290	−	15.7409i	−1.84132	−	0.662809i
$565$		0			0
$566$			11.8322i			0.497343i
$567$	−1.73901	+	23.7482i	−0.0730317	+	0.997330i
$568$	−18.7083	−	18.7083i	−0.784982	−	0.784982i
$569$	11.8322	−	20.4939i	0.496030	−	0.859149i	−0.503960	−	0.863727i	$-0.668124\pi$
$569$	11.8322	−	20.4939i	0.496030	−	0.859149i	0.999990	+	0.00457819i	$0.00145729\pi$
$570$		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
$573$	3.42766	−	40.8442i	0.143192	−	1.70629i
$574$		−	35.0000i		−	1.46087i
$575$		0			0
$576$	−30.0526	−	24.8564i	−1.25219	−	1.03568i
$577$	20.4448	+	5.47817i	0.851128	+	0.228059i	0.657910	−	0.753097i	$-0.271441\pi$
$577$	20.4448	+	5.47817i	0.851128	+	0.228059i	0.193218	+	0.981156i	$0.438107\pi$
$578$	6.47963	+	1.73621i	0.269517	+	0.0722169i
$579$	18.0404	−	3.24695i	0.749735	−	0.134939i
$580$		0			0
$581$	5.12348	−	2.95804i	0.212558	−	0.122720i
$582$	40.8442	+	3.42766i	1.69305	+	0.142081i
$583$		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	$-0.370358\pi$
$587$	−12.6491	−	12.6491i	−0.522085	−	0.522085i	−0.918201	+	0.396116i	$0.870358\pi$
$588$	−15.4886	−	32.9105i	−0.638739	−	1.35721i
$589$			4.00000i			0.164817i
$590$		0			0
$591$	−15.7409	+	43.7290i	−0.647492	+	1.79877i
$592$	−10.2224	−	2.73908i	−0.420138	−	0.112576i
$593$	−8.10232	−	30.2383i	−0.332722	−	1.24174i	−0.906317	−	0.422598i	$-0.861118\pi$
$593$	−8.10232	−	30.2383i	−0.332722	−	1.24174i	0.573595	−	0.819139i	$-0.305548\pi$
$594$		0			0
$595$		0			0
$596$			53.2447i			2.18099i
$597$	11.3786	+	7.90745i	0.465695	+	0.323630i
$598$	−20.5431	+	76.6680i	−0.840071	+	3.13519i
$599$	−11.8322	−	20.4939i	−0.483449	−	0.837358i	0.516370	−	0.856365i	$-0.327283\pi$
$599$	−11.8322	−	20.4939i	−0.483449	−	0.837358i	−0.999819	+	0.0190072i	$0.993949\pi$
$600$		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
$603$	−6.46940	+	4.59857i	−0.263454	+	0.187268i
$604$	15.5885	+	9.00000i	0.634285	+	0.366205i
$605$		0			0
$606$	21.5587	+	7.76034i	0.875762	+	0.315242i
$607$	−0.684771	−	2.55560i	−0.0277940	−	0.103729i	0.950635	−	0.310310i	$-0.100433\pi$
$607$	−0.684771	−	2.55560i	−0.0277940	−	0.103729i	−0.978429	+	0.206581i	$0.933766\pi$
$608$	−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
$612$	−36.5978	−	16.7512i	−1.47938	−	0.677127i
$613$	−9.58679	+	35.7784i	−0.387207	+	1.44508i	0.447452	+	0.894308i	$0.352332\pi$
$613$	−9.58679	+	35.7784i	−0.387207	+	1.44508i	−0.834659	+	0.550768i	$0.814335\pi$
$614$	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	$-0.132748\pi$
$617$	12.6491	+	12.6491i	0.509234	+	0.509234i	−0.405057	+	0.914291i	$0.632748\pi$
$618$	25.2437	+	17.5429i	1.01545	+	0.705680i
$619$	31.1769	−	18.0000i	1.25311	−	0.723481i	0.281381	−	0.959596i	$-0.409208\pi$
$619$	31.1769	−	18.0000i	1.25311	−	0.723481i	0.971725	+	0.236115i	$0.0758742\pi$
$620$		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
$628$	−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
$633$	−10.3257	−	21.9404i	−0.410411	−	0.872051i
$634$	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
$639$	−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	$0.296058\pi$
$642$	7.11162	+	4.94216i	0.280673	+	0.195051i
$643$	3.74166	+	3.74166i	0.147557	+	0.147557i	0.777026	−	0.629469i	$-0.216728\pi$
$643$	3.74166	+	3.74166i	0.147557	+	0.147557i	−0.629469	+	0.777026i	$0.716728\pi$
$644$	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	−0.839435	−	0.543461i	$-0.817114\pi$
$647$	4.05116	−	15.1191i	0.159267	−	0.594394i	0.998702	−	0.0509336i	$-0.0162197\pi$
$648$	16.6470	+	11.3083i	0.653957	+	0.444231i
$649$		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	−0.999993	−	0.00382551i	$-0.998782\pi$
$653$	−3.47242	−	12.9593i	−0.135886	−	0.507135i	0.864106	−	0.503309i	$-0.167884\pi$
$654$	25.5086	+	9.18216i	0.997465	+	0.359051i
$655$		0			0
$656$	5.12348	+	2.95804i	0.200038	+	0.115492i
$657$	9.19714	+	12.9388i	0.358815	+	0.504791i
$658$	51.1120	−	13.6954i	1.99255	−	0.533903i
$659$	−11.8322			−0.460915			−0.230458	−	0.973082i	$-0.574022\pi$
$659$	−11.8322			−0.460915			−0.230458	+	0.973082i	$0.574022\pi$
$660$		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	$0.953807\pi$
$662$	8.10232	−	30.2383i	0.314906	−	1.17524i
$663$	33.6583	+	23.3906i	1.30718	+	0.908414i
$664$		−	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
$669$	3.10414	−	8.62348i	0.120013	−	0.333403i
$670$		0			0
$671$		0			0
$672$	30.6332	+	2.57074i	1.18170	+	0.0991685i
$673$	−14.9666	−	14.9666i	−0.576921	−	0.576921i	0.357133	−	0.934054i	$-0.383754\pi$
$673$	−14.9666	−	14.9666i	−0.576921	−	0.576921i	−0.934054	+	0.357133i	$0.883754\pi$
$674$	−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	$-0.555944\pi$
$677$	4.31975	−	1.15747i	0.166022	−	0.0444853i	0.340872	+	0.940110i	$0.389278\pi$
$678$	17.2598	+	1.44845i	0.662860	+	0.0556274i
$679$	−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	$-0.348049\pi$
$683$	10.7994	+	2.89368i	0.413227	+	0.110724i	−0.0462153	+	0.998932i	$0.514716\pi$
$684$	11.4722	−	13.8704i	0.438650	−	0.530349i
$685$		0			0
$686$	35.8643	+	20.7063i	1.36931	+	0.790569i
$687$	2.60721	−	31.0677i	0.0994712	−	1.18531i
$688$	−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	−0.672779	−	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
$697$	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	$0.891206\pi$
$702$	−43.9337	−	43.0097i	−1.65817	−	1.62330i
$703$	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
$708$	5.14149	−	61.2663i	0.193229	−	2.30253i
$709$	19.9186	+	11.5000i	0.748058	+	0.431892i	0.824992	−	0.565145i	$-0.191180\pi$
$709$	19.9186	+	11.5000i	0.748058	+	0.431892i	−0.0769337	+	0.997036i	$0.524513\pi$
$710$		0			0
$711$	5.62348	−	2.09201i	0.210897	−	0.0784567i
$712$	−3.42385	−	12.7780i	−0.128314	−	0.478876i
$713$	−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
$717$	−8.72684	−	18.5430i	−0.325910	−	0.692500i
$718$	6.84771	−	25.5560i	0.255554	−	0.953741i
$719$	−23.6643	+	40.9878i	−0.882530	+	1.52859i	−0.0340117	+	0.999421i	$0.510828\pi$
$719$	−23.6643	+	40.9878i	−0.882530	+	1.52859i	−0.848519	+	0.529166i	$0.822505\pi$
$720$		0			0
$721$	−21.0000			−0.782081
$722$	23.7171	+	23.7171i	0.882658	+	0.882658i
$723$	5.93059	−	8.53394i	0.220561	−	0.317381i
$724$	−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	−0.976906	−	0.213669i	$-0.931459\pi$
$727$	−20.5791	+	20.5791i	−0.763237	+	0.763237i	0.213669	+	0.976906i	$0.431459\pi$
$728$	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
$732$	−51.7166	+	24.3392i	−1.91150	+	0.899604i
$733$	−30.6672	+	8.21725i	−1.13272	+	0.303511i	−0.776020	−	0.630708i	$-0.782764\pi$
$733$	−30.6672	+	8.21725i	−1.13272	+	0.303511i	−0.356699	+	0.934219i	$0.616098\pi$
$734$	−17.7482			−0.655099
$735$		0			0
$736$	−45.0000			−1.65872
$737$		0			0
$738$	−36.0859	−	16.5169i	−1.32834	−	0.607995i
$739$	27.7128	−	16.0000i	1.01943	−	0.588570i	0.105493	−	0.994420i	$-0.466358\pi$
$739$	27.7128	−	16.0000i	1.01943	−	0.588570i	0.913939	+	0.405851i	$0.133025\pi$
$740$		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	$-0.570983\pi$
$743$	20.5548	−	20.5548i	0.754083	−	0.754083i	0.975238	+	0.221156i	$0.0709829\pi$
$744$	−1.37209	−	7.62348i	−0.0503032	−	0.279490i
$745$		0			0
$746$	−40.9878	+	23.6643i	−1.50067	+	0.866412i
$747$	−0.631989	−	6.67837i	−0.0231233	−	0.244349i
$748$		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	$-0.0614361\pi$
$752$	−2.31495	+	8.63950i	−0.0844175	+	0.315050i
$753$	−18.5430	+	8.72684i	−0.675744	+	0.318024i
$754$	−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	−0.0469474	−	0.998897i	$-0.514949\pi$
$757$	26.1916	−	26.1916i	0.951950	−	0.951950i	0.998897	+	0.0469474i	$0.0149493\pi$
$758$	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	$-0.474438\pi$
$761$	−20.4939	−	11.8322i	−0.742903	−	0.428915i	−0.823124	+	0.567862i	$0.807771\pi$
$762$	−61.2663	−	5.14149i	−2.21945	−	0.186256i
$763$	−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
$768$	8.89588	−	12.8009i	0.321002	−	0.461913i
$769$		−	34.0000i		−	1.22607i	−0.790055	−	0.613036i	$-0.789948\pi$
$769$		−	34.0000i		−	1.22607i	0.790055	−	0.613036i	$-0.210052\pi$
$770$		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	$-0.391039\pi$
$773$	4.31975	+	1.15747i	0.155371	+	0.0416314i	−0.180295	+	0.983613i	$0.557705\pi$
$774$	16.6345	−	6.18826i	0.597913	−	0.222432i
$775$		0			0
$776$			23.6643i			0.849500i
$777$	−43.8807	+	20.6515i	−1.57421	+	0.740867i
$778$		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
$783$	29.7763	+	7.64032i	1.06412	+	0.273043i
$784$	−6.06218	+	3.50000i	−0.216506	+	0.125000i
$785$		0			0
$786$		0			0
$787$	−48.5564	−	13.0106i	−1.73085	−	0.463779i	−0.750470	−	0.660904i	$-0.770173\pi$
$787$	−48.5564	−	13.0106i	−1.73085	−	0.463779i	−0.980378	+	0.197125i	$0.936840\pi$
$788$	−77.7555	−	20.8345i	−2.76993	−	0.742199i
$789$	−2.05813	−	11.4352i	−0.0732714	−	0.407104i
$790$		0			0
$791$	−10.2470	+	5.91608i	−0.364340	+	0.210352i
$792$		0			0
$793$	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	−0.991720	−	0.128416i	$-0.959011\pi$
$797$	−31.6228	−	31.6228i	−1.12014	−	1.12014i	−0.128416	−	0.991720i	$-0.540989\pi$
$798$	−1.71383	+	20.4221i	−0.0606689	+	0.722935i
$799$			40.0000i			1.41510i
$800$		0			0
$801$	−6.18826	−	16.6345i	−0.218651	−	0.587750i
$802$	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
$807$	5.84764	−	8.41458i	0.205847	−	0.296207i
$808$	−3.42385	+	12.7780i	−0.120451	+	0.449528i
$809$	−20.7063	−	35.8643i	−0.727994	−	1.26092i	−0.957730	−	0.287670i	$-0.907120\pi$
$809$	−20.7063	−	35.8643i	−0.727994	−	1.26092i	0.229736	−	0.973253i	$-0.426214\pi$
$810$		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
$813$	3.45197	+	0.289690i	0.121066	+	0.0101599i
$814$		0			0
$815$		0			0
$816$	−2.62348	+	7.28817i	−0.0918400	+	0.255137i
$817$	−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	$-0.468833\pi$
$821$	−20.4939	−	11.8322i	−0.715242	−	0.412945i	−0.812999	+	0.582265i	$0.802167\pi$
$822$	−31.3434	+	14.7510i	−1.09323	+	0.514502i
$823$	4.79340	−	17.8892i	0.167087	−	0.623578i	−0.830677	−	0.556754i	$-0.812047\pi$
$823$	4.79340	−	17.8892i	0.167087	−	0.623578i	0.997765	−	0.0668243i	$-0.0212867\pi$
$824$	−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	$-0.363785\pi$
$827$	−14.2302	−	14.2302i	−0.494834	−	0.494834i	−0.909825	+	0.414991i	$0.863785\pi$
$828$	60.1053	−	5.68790i	2.08880	−	0.197668i
$829$	1.73205	−	1.00000i	0.0601566	−	0.0347314i	−0.469620	−	0.882869i	$-0.655609\pi$
$829$	1.73205	−	1.00000i	0.0601566	−	0.0347314i	0.529777	+	0.848137i	$0.322276\pi$
$830$		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
$837$	−2.79625	−	10.0090i	−0.0966526	−	0.345963i
$838$	−51.1120	+	13.6954i	−1.76563	+	0.473100i
$839$	23.6643			0.816983			0.408492	−	0.912762i	$-0.366055\pi$
$839$	23.6643			0.816983			0.408492	+	0.912762i	$0.366055\pi$
$840$		0			0
$841$	6.00000			0.206897
$842$	23.7586	−	6.36611i	0.818777	−	0.219391i
$843$	−37.0860	+	17.4537i	−1.27731	+	0.601137i
$844$	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
$852$	35.0858	−	50.4875i	1.20202	−	1.72967i
$853$	−26.1916	−	26.1916i	−0.896783	−	0.896783i	0.0983669	−	0.995150i	$-0.468638\pi$
$853$	−26.1916	−	26.1916i	−0.896783	−	0.896783i	−0.995150	+	0.0983669i	$0.968638\pi$
$854$	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	−0.739899	−	0.672718i	$-0.765127\pi$
$857$	6.94484	−	25.9185i	0.237231	−	0.885359i	0.977130	−	0.212641i	$-0.0682066\pi$
$858$		0			0
$859$	3.46410	+	2.00000i	0.118194	+	0.0682391i	0.557931	−	0.829887i	$-0.311595\pi$
$859$	3.46410	+	2.00000i	0.118194	+	0.0682391i	−0.439738	+	0.898126i	$0.644929\pi$
$860$		0			0
$861$	26.6822	−	4.80230i	0.909326	−	0.163662i
$862$	37.4166	−	37.4166i	1.27441	−	1.27441i
$863$	7.52358	+	28.0784i	0.256106	+	0.955799i	0.967472	+	0.252978i	$0.0814100\pi$
$863$	7.52358	+	28.0784i	0.256106	+	0.955799i	−0.711366	+	0.702821i	$0.751923\pi$
$864$	17.1066	−	30.3704i	0.581980	−	1.03322i
$865$		0			0
$866$	−30.7409	−	17.7482i	−1.04462	−	0.603110i
$867$	−0.434535	+	5.17795i	−0.0147576	+	0.175852i
$868$	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
$873$	2.99112	+	31.6078i	0.101234	+	1.06976i
$874$		−	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	−0.999954	−	0.00953982i	$-0.996963\pi$
$877$	−4.10862	−	15.3336i	−0.138738	−	0.517779i	0.861216	−	0.508239i	$-0.169703\pi$
$878$	69.1160	+	18.5196i	2.33255	+	0.625006i
$879$	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	$0.645792\pi$
$882$	38.2735	−	27.2055i	1.28874	−	0.916057i
$883$	−33.6749	−	33.6749i	−1.13325	−	1.13325i	−0.989633	−	0.143618i	$-0.954126\pi$
$883$	−33.6749	−	33.6749i	−1.13325	−	1.13325i	−0.143618	−	0.989633i	$-0.545874\pi$
$884$	−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	$-0.547409\pi$
$887$	6.47963	−	1.73621i	0.217565	−	0.0582963i	0.365955	+	0.930633i	$0.380742\pi$
$888$	−3.42766	+	40.8442i	−0.115025	+	1.37064i
$889$	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
$894$	−67.6516	+	12.1761i	−2.26261	+	0.407229i
$895$		0			0
$896$			41.4126i			1.38350i
$897$	−61.2663	−	5.14149i	−2.04562	−	0.171669i
$898$	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
$903$	−6.91902	+	9.95626i	−0.230251	+	0.331324i
$904$			10.0000i			0.332595i
$905$		0			0
$906$	−7.87043	+	21.8645i	−0.261477	+	0.726399i
$907$	53.6676	+	14.3802i	1.78200	+	0.477486i	0.990947	−	0.134257i	$-0.0428647\pi$
$907$	53.6676	+	14.3802i	1.78200	+	0.477486i	0.791057	+	0.611743i	$0.209531\pi$
$908$		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	$0.871777\pi$
$912$	−2.84465	−	1.97686i	−0.0941957	−	0.0654605i
$913$		0			0
$914$	−11.8322	−	20.4939i	−0.391373	−	0.677878i
$915$		0			0
$916$	54.0000			1.78421
$917$		0			0
$918$	12.9145	−	50.3311i	0.426242	−	1.66117i
$919$	12.1244	+	7.00000i	0.399946	+	0.230909i	0.686461	−	0.727167i	$-0.259163\pi$
$919$	12.1244	+	7.00000i	0.399946	+	0.230909i	−0.286515	+	0.958076i	$0.592497\pi$
$920$		0			0
$921$	12.9352	+	4.65621i	0.426230	+	0.153427i
$922$	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
$927$	−9.91014	+	21.6515i	−0.325492	+	0.711130i
$928$	10.2716	−	38.3340i	0.337181	−	1.25837i
$929$	−20.7063	+	35.8643i	−0.679351	+	1.17667i	0.295826	+	0.955242i	$0.404405\pi$
$929$	−20.7063	+	35.8643i	−0.679351	+	1.17667i	−0.975177	+	0.221428i	$0.928928\pi$
$930$		0			0
$931$	−7.00000	−	12.1244i	−0.229416	−	0.397360i
$932$	47.4342	+	47.4342i	1.55376	+	1.55376i
$933$	16.8292	+	11.6953i	0.550962	+	0.382886i
$934$	−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	−0.237885	−	0.971293i	$-0.576454\pi$
$937$	22.4499	−	22.4499i	0.733408	−	0.733408i	0.971293	+	0.237885i	$0.0764543\pi$
$938$	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	$-0.386206\pi$
$941$	40.9878	−	23.6643i	1.33616	−	0.771435i	0.986236	+	0.165342i	$0.0528728\pi$
$942$	−17.4537	−	37.0860i	−0.568672	−	1.20833i
$943$	−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	$-0.426755\pi$
$947$	28.0784	−	7.52358i	0.912425	−	0.244484i	0.684345	+	0.729159i	$0.260088\pi$
$948$	4.42531	+	9.40301i	0.143728	+	0.305396i
$949$	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	$-0.893110\pi$
$953$	−18.9737	+	18.9737i	−0.614617	+	0.614617i	0.329528	+	0.944146i	$0.393110\pi$
$954$	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
$962$	32.4093	−	120.953i	1.04492	−	3.89968i
$963$	−2.79186	+	6.09963i	−0.0899666	+	0.196558i
$964$	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	−0.955799	−	0.294020i	$-0.905007\pi$
$967$	−20.5791	+	20.5791i	−0.661780	+	0.661780i	0.294020	+	0.955799i	$0.405007\pi$
$968$	−6.36611	−	23.7586i	−0.204614	−	0.763631i
$969$	−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	$0.392147\pi$
$972$	−19.0101	+	42.7272i	−0.609750	+	1.37048i
$973$	−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	0.643975	+	0.765047i	$0.277284\pi$
$977$	−9.25979	+	34.5580i	−0.296247	+	1.10561i	−0.940222	+	0.340562i	$0.889383\pi$
$978$	−16.8292	−	11.6953i	−0.538137	−	0.373974i
$979$		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	$-0.596316\pi$
$983$	−32.3981	−	8.68105i	−1.03334	−	0.276883i	−0.735351	+	0.677687i	$0.762983\pi$
$984$	7.76034	−	21.5587i	0.247391	−	0.687266i
$985$		0			0
$986$		−	59.1608i		−	1.88406i
$987$	17.4537	+	37.0860i	0.555557	+	1.18046i
$988$	−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	$0.627084\pi$
$992$	−12.9593	+	3.47242i	−0.411457	+	0.110250i
$993$	24.1638	+	2.02783i	0.766814	+	0.0643512i
$994$			70.0000i			2.22027i
$995$		0			0
$996$	11.4352	−	2.05813i	0.362339	−	0.0652144i
$997$	15.3336	+	4.10862i	0.485620	+	0.130121i	0.493318	−	0.869849i	$-0.335784\pi$
$997$	15.3336	+	4.10862i	0.485620	+	0.130121i	−0.00769834	+	0.999970i	$0.502450\pi$
$998$	25.9185	+	6.94484i	0.820436	+	0.219835i
$999$	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.443.2	yes	16
3.2	odd	2	inner	525.2.bf.e.443.4	yes	16
5.2	odd	4	inner	525.2.bf.e.107.1	yes	16
5.3	odd	4	inner	525.2.bf.e.107.4	yes	16
5.4	even	2	inner	525.2.bf.e.443.3	yes	16
7.4	even	3	inner	525.2.bf.e.368.3	yes	16
15.2	even	4	inner	525.2.bf.e.107.3	yes	16
15.8	even	4	inner	525.2.bf.e.107.2	yes	16
15.14	odd	2	inner	525.2.bf.e.443.1	yes	16
21.11	odd	6	inner	525.2.bf.e.368.1	yes	16
35.4	even	6	inner	525.2.bf.e.368.2	yes	16
35.18	odd	12	inner	525.2.bf.e.32.1	✓	16
35.32	odd	12	inner	525.2.bf.e.32.4	yes	16
105.32	even	12	inner	525.2.bf.e.32.2	yes	16
105.53	even	12	inner	525.2.bf.e.32.3	yes	16
105.74	odd	6	inner	525.2.bf.e.368.4	yes	16

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

\(f(q)\)	\(=\)	\(q+(-2.15988 + 0.578737i) q^{2} +(-0.737552 - 1.56717i) q^{3} +(2.59808 - 1.50000i) q^{4} +(2.50000 + 2.95804i) q^{6} +(-2.55560 - 0.684771i) q^{7} +(-1.58114 + 1.58114i) q^{8} +(-1.91203 + 2.31174i) q^{9} +O(q^{10})\)	\(q+(-2.15988 + 0.578737i) q^{2} +(-0.737552 - 1.56717i) 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} +(-1.91203 + 2.31174i) q^{9} +(-4.26697 - 2.96529i) q^{12} +(3.74166 + 3.74166i) q^{13} +5.91608 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.15747 + 4.31975i) q^{17} +(2.79186 - 6.09963i) q^{18} +(-1.73205 - 1.00000i) q^{19} +(0.811738 + 4.51011i) q^{21} +(-1.73621 - 6.47963i) q^{23} +(3.64408 + 1.31174i) q^{24} +(-10.2470 - 5.91608i) q^{26} +(5.03311 + 1.29145i) 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} +(3.10414 - 8.62348i) q^{39} -5.91608i q^{41} +(-4.36342 - 9.27149i) q^{42} +(1.87083 + 1.87083i) q^{43} +(7.50000 + 12.9904i) q^{46} +(8.63950 - 2.31495i) q^{47} +(1.72598 + 0.144845i) q^{48} +(6.06218 + 3.50000i) q^{49} +(7.62348 - 1.37209i) q^{51} +(15.3336 + 4.10862i) q^{52} +(4.31975 + 1.15747i) q^{53} +(-11.6183 + 0.123475i) q^{54} +(5.12348 - 2.95804i) q^{56} +(-0.289690 + 3.45197i) 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} +(6.46940 - 4.59857i) 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} +(-0.631989 - 6.67837i) q^{72} +(1.36954 - 5.11120i) q^{73} +(-11.8322 - 20.4939i) q^{74} -6.00000 q^{76} +(-1.71383 + 20.4221i) q^{78} +(-1.73205 - 1.00000i) q^{79} +(-1.68826 - 8.84024i) 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} +(-4.36342 - 9.27149i) q^{87} +(-2.95804 + 5.12348i) q^{89} +(-7.00000 - 12.1244i) q^{91} +(-14.2302 - 14.2302i) q^{92} +(-1.97686 + 2.84465i) q^{93} +(-17.3205 + 10.0000i) q^{94} +(-11.4352 + 2.05813i) 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

L-functions

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