LMFDB - Embedded newform 525.2.bf.e.32.2

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			32.2
Root			$-0.988431 + 1.42232i$ of defining polynomial
Character	$\chi$	$=$	525.32
Dual form			525.2.bf.e.443.2

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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	−0.605138	−	0.796121i	$-0.706882\pi$
$2$	−2.15988	−	0.578737i	−1.52726	−	0.409229i	−0.922125	+	0.386892i	$0.873549\pi$
$3$	−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	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	−4.26697	+	2.96529i	−1.23177	+	0.856007i
$13$	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	$-0.900877\pi$
$17$	−1.15747	−	4.31975i	−0.280729	−	1.04769i	0.671176	−	0.741298i	$-0.265790\pi$
$18$	2.79186	+	6.09963i	0.658049	+	1.43770i
$19$	−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
$21$	0.811738	−	4.51011i	0.177136	−	0.984186i
$22$		0			0
$23$	−1.73621	+	6.47963i	−0.362025	+	1.35110i	0.509384	+	0.860539i	$0.329873\pi$
$23$	−1.73621	+	6.47963i	−0.362025	+	1.35110i	−0.871409	+	0.490557i	$0.836793\pi$
$24$	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	−0.941745	−	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
$39$	3.10414	+	8.62348i	0.497060	+	1.38086i
$40$		0			0
$41$			5.91608i			0.923936i	0.886896	+	0.461968i	$0.152857\pi$
$41$			5.91608i			0.923936i	−0.886896	+	0.461968i	$0.847143\pi$
$42$	−4.36342	+	9.27149i	−0.673290	+	1.43062i
$43$	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	0.826269	−	0.563276i	$-0.190459\pi$
$47$	8.63950	+	2.31495i	1.26020	+	0.337670i	0.433932	+	0.900946i	$0.357126\pi$
$48$	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	0.0503735	−	0.998730i	$-0.483959\pi$
$53$	4.31975	−	1.15747i	0.593364	−	0.158991i	0.542990	+	0.839739i	$0.317292\pi$
$54$	−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	−0.167241	−	0.985916i	$-0.553486\pi$
$59$	5.91608	−	10.2470i	0.770208	−	1.33404i	0.937449	−	0.348123i	$-0.113181\pi$
$60$		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
$63$	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	−0.0993085	−	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	$-0.752242\pi$
$71$		−	11.8322i		−	1.40422i	0.712069	−	0.702109i	$-0.247758\pi$
$72$	−0.631989	+	6.67837i	−0.0744806	+	0.787053i
$73$	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
$78$	−1.71383	−	20.4221i	−0.194053	−	2.31235i
$79$	−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
$81$	−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	0.614986	−	0.788538i	$-0.289162\pi$
$83$	−1.58114	−	1.58114i	−0.173553	−	0.173553i	−0.788538	+	0.614986i	$0.789162\pi$
$84$	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	0.665577	−	0.746329i	$-0.268186\pi$
$89$	−2.95804	−	5.12348i	−0.313552	−	0.543087i	−0.979129	+	0.203242i	$0.934852\pi$
$90$		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	0.976289	−	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	0.732753	−	0.680494i	$-0.238235\pi$
$101$	5.12348	+	2.95804i	0.509805	+	0.294336i	−0.222949	+	0.974830i	$0.571568\pi$
$102$	−15.6717	−	7.37552i	−1.55173	−	0.730286i
$103$	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	0.361704	−	0.932293i	$-0.382195\pi$
$107$	2.15988	+	0.578737i	0.208803	+	0.0559486i	−0.152901	+	0.988241i	$0.548862\pi$
$108$	15.0136	+	4.19438i	1.44468	+	0.403604i
$109$	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	0.840027	−	0.542545i	$-0.182539\pi$
$113$	3.16228	+	3.16228i	0.297482	+	0.297482i	−0.542545	+	0.840027i	$0.682539\pi$
$114$	−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	0.00393704	−	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
$129$	1.55207	+	4.31174i	0.136652	+	0.379627i
$130$		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	$-0.958541\pi$
$137$	−2.31495	−	8.63950i	−0.197779	−	0.738123i	0.793750	−	0.608243i	$-0.208126\pi$
$138$	14.8265	+	21.3348i	1.26211	+	1.81614i
$139$			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
$144$	−1.04601	+	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	−0.958147	−	0.286276i	$-0.907582\pi$
$149$	−8.87412	−	15.3704i	−0.726996	−	1.25919i	0.231151	−	0.972918i	$-0.425751\pi$
$150$		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
$153$	−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	−0.642525	−	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
$159$	−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	0.0530306	−	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	−0.990920	−	0.134454i	$-0.957072\pi$
$167$	−11.0680	+	11.0680i	−0.856465	+	0.856465i	0.134454	+	0.990920i	$0.457072\pi$
$168$	−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	−0.820377	−	0.571824i	$-0.806236\pi$
$173$	2.31495	−	8.63950i	0.176002	−	0.656849i	0.996379	−	0.0850256i	$-0.0270972\pi$
$174$	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	−0.555663	−	0.831408i	$-0.687536\pi$
$179$	5.91608	−	10.2470i	0.442189	−	0.765893i	0.997852	+	0.0655145i	$0.0208689\pi$
$180$		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	0.483076	−	0.875579i	$-0.339520\pi$
$191$	20.4939	−	11.8322i	1.48289	−	0.856145i	0.999811	+	0.0194337i	$0.00618632\pi$
$192$	20.3732	+	9.58818i	1.47031	+	0.691967i
$193$	−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	$0.655094\pi$
$197$	−18.9737	+	18.9737i	−1.35182	+	1.35182i	−0.883628	+	0.468190i	$0.844906\pi$
$198$		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
$201$	−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	−0.570640	−	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	$0.916667\pi$
$228$	4.42531	−	9.40301i	0.293074	−	0.622730i
$229$	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	$-0.655044\pi$
$233$	5.78737	−	21.5988i	0.379143	−	1.41498i	0.847196	−	0.531281i	$-0.178289\pi$
$234$	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	−0.753077	−	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
$243$	−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	$0.121815\pi$
$251$			11.8322i			0.746839i	−0.927663	+	0.373420i	$0.878185\pi$
$252$	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	0.950045	−	0.312112i	$-0.101037\pi$
$257$	25.9185	+	6.94484i	1.61675	+	0.433207i	0.666707	+	0.745320i	$0.267703\pi$
$258$	−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	−0.0534475	−	0.998571i	$-0.517021\pi$
$263$	6.47963	−	1.73621i	0.399551	−	0.107059i	0.452998	+	0.891511i	$0.350354\pi$
$264$		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	−0.761647	−	0.647993i	$-0.775609\pi$
$269$	2.95804	−	5.12348i	0.180355	−	0.312384i	0.942001	+	0.335609i	$0.108942\pi$
$270$		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
$273$	−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	0.233163	−	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	$0.249434\pi$
$281$			23.6643i			1.41169i	−0.708364	+	0.705847i	$0.750566\pi$
$282$	28.4465	−	19.7686i	1.69396	−	1.17720i
$283$	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
$288$	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	0.497805	−	0.867289i	$-0.334140\pi$
$293$	−6.32456	−	6.32456i	−0.369484	−	0.369484i	−0.867289	+	0.497805i	$0.834140\pi$
$294$	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	0.528569	−	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	0.180500	−	0.983575i	$-0.442228\pi$
$311$	−10.2470	−	5.91608i	−0.581051	−	0.335470i	−0.761551	+	0.648105i	$0.775562\pi$
$312$	8.72684	−	18.5430i	0.494060	−	1.04979i
$313$	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	−0.405127	−	0.914261i	$-0.632773\pi$
$317$	−21.5988	−	5.78737i	−1.21311	−	0.325051i	−0.807980	+	0.589209i	$0.799439\pi$
$318$	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	0.606980	−	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
$333$	−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	0.801635	−	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
$339$	−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	−0.999076	−	0.0429807i	$-0.986315\pi$
$347$	−2.89368	−	10.7994i	−0.155341	−	0.579741i	0.843735	−	0.536760i	$-0.180352\pi$
$348$	−25.2437	+	17.5429i	−1.35321	+	0.940399i
$349$		−	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	−0.586636	−	0.809851i	$-0.699548\pi$
$353$	−12.9593	+	3.47242i	−0.689752	+	0.184818i	−0.103116	+	0.994669i	$0.532881\pi$
$354$	−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	0.666608	−	0.745409i	$-0.267746\pi$
$359$	−5.91608	−	10.2470i	−0.312239	−	0.540813i	−0.978847	+	0.204595i	$0.934412\pi$
$360$		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	−0.0531027	−	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
$369$	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	0.745798	−	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
$378$	29.7763	−	7.64032i	1.53153	−	0.392975i
$379$			18.0000i			0.924598i	0.886724	+	0.462299i	$0.152975\pi$
$379$			18.0000i			0.924598i	−0.886724	+	0.462299i	$0.847025\pi$
$380$		0			0
$381$	25.8704	−	9.31241i	1.32538	−	0.477089i
$382$	−51.1120	+	13.6954i	−2.61512	+	0.700718i
$383$	1.73621	−	6.47963i	0.0887162	−	0.331093i	−0.907276	−	0.420536i	$-0.861842\pi$
$383$	1.73621	−	6.47963i	0.0887162	−	0.331093i	0.995992	+	0.0894428i	$0.0285086\pi$
$384$	−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	$-0.833333\pi$
$389$		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
$399$	3.10414	+	8.62348i	0.155401	+	0.431714i
$400$		0			0
$401$	−15.3704	+	8.87412i	−0.767562	+	0.443152i	−0.832004	−	0.554769i	$-0.812807\pi$
$401$	−15.3704	+	8.87412i	−0.767562	+	0.443152i	0.0644419	+	0.997921i	$0.479473\pi$
$402$	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	0.195127	−	0.980778i	$-0.437488\pi$
$409$	−11.2583	−	6.50000i	−0.556689	−	0.321404i	−0.751815	+	0.659374i	$0.770822\pi$
$410$		0			0
$411$	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	−0.0827334	−	0.996572i	$-0.526365\pi$
$431$	−20.4939	−	11.8322i	−0.987157	−	0.569935i	−0.904423	+	0.426637i	$0.859698\pi$
$432$	−3.63498	−	3.71307i	−0.174888	−	0.178645i
$433$	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
$438$	18.5430	+	8.72684i	0.886018	+	0.416984i
$439$	−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
$441$	−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	−0.978310	−	0.207144i	$-0.933583\pi$
$443$	−0.578737	+	2.15988i	−0.0274966	+	0.102619i	0.950814	+	0.309763i	$0.100250\pi$
$444$	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	−0.871803	−	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
$459$	−11.4044	−	20.2470i	−0.532313	−	0.945047i
$460$		0			0
$461$			23.6643i			1.10216i	0.834453	+	0.551079i	$0.185784\pi$
$461$			23.6643i			1.10216i	−0.834453	+	0.551079i	$0.814216\pi$
$462$		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	0.591065	−	0.806624i	$-0.298708\pi$
$467$	15.1191	+	4.05116i	0.699630	+	0.187465i	0.108565	+	0.994089i	$0.465374\pi$
$468$	−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	0.101271	+	0.994859i	$0.467709\pi$
$479$	−17.7482	+	30.7409i	−0.810938	+	1.40459i	−0.912208	+	0.409726i	$0.865624\pi$
$480$		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	−0.372757	−	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	$0.0860287\pi$
$491$			11.8322i			0.533978i	−0.963700	+	0.266989i	$0.913971\pi$
$492$	−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	−0.714238	−	0.699903i	$-0.753227\pi$
$499$	−10.3923	+	6.00000i	−0.465223	+	0.268597i	0.249015	+	0.968500i	$0.419893\pi$
$500$		0			0
$501$	−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	−0.998243	−	0.0592492i	$-0.981129\pi$
$503$	−23.7171	−	23.7171i	−1.05749	−	1.05749i	−0.0592492	−	0.998243i	$-0.518871\pi$
$504$	−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	0.992888	−	0.119056i	$-0.0379867\pi$
$509$	8.87412	+	15.3704i	0.393338	+	0.681282i	−0.599549	+	0.800338i	$0.704653\pi$
$510$		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	0.876503	−	0.481396i	$-0.159870\pi$
$521$	20.4939	+	11.8322i	0.897854	+	0.518376i	0.0213508	+	0.999772i	$0.493203\pi$
$522$	16.5169	+	36.0859i	0.722925	+	1.57944i
$523$	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
$534$	−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	0.586278	−	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
$543$	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	−0.999171	−	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
$549$	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	0.997469	−	0.0710962i	$-0.0226497\pi$
$557$	2.31495	+	8.63950i	0.0980875	+	0.366068i	−0.899382	+	0.437164i	$0.855983\pi$
$558$	−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	0.749455	−	0.662055i	$-0.230315\pi$
$563$	41.0376	−	10.9960i	1.72953	−	0.463426i	0.980075	+	0.198628i	$0.0636487\pi$
$564$	−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	0.999990	−	0.00457819i	$-0.00145729\pi$
$569$	11.8322	+	20.4939i	0.496030	+	0.859149i	−0.503960	+	0.863727i	$0.668124\pi$
$570$		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
$573$	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	0.193218	−	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
$579$	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	−0.918201	−	0.396116i	$-0.870358\pi$
$587$	−12.6491	+	12.6491i	−0.522085	+	0.522085i	0.396116	+	0.918201i	$0.370358\pi$
$588$	−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	0.573595	+	0.819139i	$0.305548\pi$
$593$	−8.10232	+	30.2383i	−0.332722	+	1.24174i	−0.906317	+	0.422598i	$0.861118\pi$
$594$		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	−0.999819	−	0.0190072i	$-0.993949\pi$
$599$	−11.8322	+	20.4939i	−0.483449	+	0.837358i	0.516370	+	0.856365i	$0.327283\pi$
$600$		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	−0.978429	−	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
$609$	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	−0.834659	−	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	−0.405057	−	0.914291i	$-0.632748\pi$
$617$	12.6491	−	12.6491i	0.509234	−	0.509234i	0.914291	+	0.405057i	$0.132748\pi$
$618$	25.2437	−	17.5429i	1.01545	−	0.705680i
$619$	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
$621$	−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	0.597758	−	0.801676i	$-0.296058\pi$
$641$	5.12348	+	2.95804i	0.202365	+	0.116836i	−0.395393	+	0.918512i	$0.629392\pi$
$642$	7.11162	−	4.94216i	0.280673	−	0.195051i
$643$	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	$0.0162197\pi$
$647$	4.05116	+	15.1191i	0.159267	+	0.594394i	−0.839435	+	0.543461i	$0.817114\pi$
$648$	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	0.864106	+	0.503309i	$0.167884\pi$
$653$	−3.47242	+	12.9593i	−0.135886	+	0.507135i	−0.999993	+	0.00382551i	$0.998782\pi$
$654$	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	−0.989489	−	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
$663$	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	−0.934054	−	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	0.340872	−	0.940110i	$-0.389278\pi$
$677$	4.31975	+	1.15747i	0.166022	+	0.0444853i	−0.174851	+	0.984595i	$0.555944\pi$
$678$	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	−0.0462153	−	0.998932i	$-0.514716\pi$
$683$	10.7994	−	2.89368i	0.413227	−	0.110724i	0.459442	+	0.888208i	$0.348049\pi$
$684$	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	0.977113	−	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
$696$	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	$-0.891206\pi$
$701$		−	17.7482i		−	0.670342i	0.942157	−	0.335171i	$-0.108794\pi$
$702$	−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	−0.0769337	−	0.997036i	$-0.524513\pi$
$709$	19.9186	−	11.5000i	0.748058	−	0.431892i	0.824992	+	0.565145i	$0.191180\pi$
$710$		0			0
$711$	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	−0.848519	−	0.529166i	$-0.822505\pi$
$719$	−23.6643	−	40.9878i	−0.882530	−	1.52859i	−0.0340117	−	0.999421i	$-0.510828\pi$
$720$		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	0.213669	−	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
$732$	−51.7166	−	24.3392i	−1.91150	−	0.899604i
$733$	−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
$738$	−36.0859	+	16.5169i	−1.32834	+	0.607995i
$739$	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	0.975238	−	0.221156i	$-0.0709829\pi$
$743$	20.5548	+	20.5548i	0.754083	+	0.754083i	−0.221156	+	0.975238i	$0.570983\pi$
$744$	−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	0.981432	+	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
$753$	−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	0.998897	−	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	−0.823124	−	0.567862i	$-0.807771\pi$
$761$	−20.4939	+	11.8322i	−0.742903	+	0.428915i	0.0802206	+	0.996777i	$0.474438\pi$
$762$	−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	$0.210052\pi$
$769$			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	−0.180295	−	0.983613i	$-0.557705\pi$
$773$	4.31975	−	1.15747i	0.155371	−	0.0416314i	0.335666	+	0.941981i	$0.391039\pi$
$774$	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	−0.980378	−	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
$789$	−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	−0.128416	+	0.991720i	$0.540989\pi$
$797$	−31.6228	+	31.6228i	−1.12014	+	1.12014i	−0.991720	+	0.128416i	$0.959011\pi$
$798$	−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	0.229736	+	0.973253i	$0.426214\pi$
$809$	−20.7063	+	35.8643i	−0.727994	+	1.26092i	−0.957730	+	0.287670i	$0.907120\pi$
$810$		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	−0.812999	−	0.582265i	$-0.802167\pi$
$821$	−20.4939	+	11.8322i	−0.715242	+	0.412945i	0.0977569	+	0.995210i	$0.468833\pi$
$822$	−31.3434	−	14.7510i	−1.09323	−	0.514502i
$823$	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	−0.909825	−	0.414991i	$-0.863785\pi$
$827$	−14.2302	+	14.2302i	−0.494834	+	0.494834i	0.414991	+	0.909825i	$0.363785\pi$
$828$	60.1053	+	5.68790i	2.08880	+	0.197668i
$829$	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
$831$	−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	−0.995150	−	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	$0.0682066\pi$
$857$	6.94484	+	25.9185i	0.237231	+	0.885359i	−0.739899	+	0.672718i	$0.765127\pi$
$858$		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
$861$	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	−0.711366	−	0.702821i	$-0.751923\pi$
$863$	7.52358	−	28.0784i	0.256106	−	0.955799i	0.967472	−	0.252978i	$-0.0814100\pi$
$864$	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	0.861216	+	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
$879$	14.5763	−	5.24695i	0.491648	−	0.176975i
$880$		0			0
$881$		−	53.2447i		−	1.79386i	−0.442172	−	0.896930i	$-0.645792\pi$
$881$		−	53.2447i		−	1.79386i	0.442172	−	0.896930i	$-0.354208\pi$
$882$	38.2735	+	27.2055i	1.28874	+	0.916057i
$883$	−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	0.365955	−	0.930633i	$-0.380742\pi$
$887$	6.47963	+	1.73621i	0.217565	+	0.0582963i	−0.148390	+	0.988929i	$0.547409\pi$
$888$	−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	0.791057	−	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	$-0.871777\pi$
$911$		−	23.6643i		−	0.784034i	0.919958	−	0.392017i	$-0.128223\pi$
$912$	−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	−0.286515	−	0.958076i	$-0.592497\pi$
$919$	12.1244	−	7.00000i	0.399946	−	0.230909i	0.686461	+	0.727167i	$0.259163\pi$
$920$		0			0
$921$	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	−0.975177	−	0.221428i	$-0.928928\pi$
$929$	−20.7063	−	35.8643i	−0.679351	−	1.17667i	0.295826	−	0.955242i	$-0.404405\pi$
$930$		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	0.971293	−	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	0.986236	−	0.165342i	$-0.0528728\pi$
$941$	40.9878	+	23.6643i	1.33616	+	0.771435i	0.349928	+	0.936777i	$0.386206\pi$
$942$	−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	0.684345	−	0.729159i	$-0.260088\pi$
$947$	28.0784	+	7.52358i	0.912425	+	0.244484i	0.228080	+	0.973642i	$0.426755\pi$
$948$	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	0.329528	−	0.944146i	$-0.393110\pi$
$953$	−18.9737	−	18.9737i	−0.614617	−	0.614617i	−0.944146	+	0.329528i	$0.893110\pi$
$954$	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	0.294020	−	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
$969$	−14.5763	+	5.24695i	−0.468259	+	0.168556i
$970$		0			0
$971$	40.9878	−	23.6643i	1.31536	−	0.759424i	0.332383	−	0.943145i	$-0.392147\pi$
$971$	40.9878	−	23.6643i	1.31536	−	0.759424i	0.982979	+	0.183720i	$0.0588141\pi$
$972$	−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	−0.940222	−	0.340562i	$-0.889383\pi$
$977$	−9.25979	−	34.5580i	−0.296247	−	1.10561i	0.643975	−	0.765047i	$-0.277284\pi$
$978$	−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	−0.735351	−	0.677687i	$-0.762983\pi$
$983$	−32.3981	+	8.68105i	−1.03334	+	0.276883i	−0.297989	+	0.954569i	$0.596316\pi$
$984$	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	−0.388723	−	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
$993$	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	−0.00769834	−	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
$999$	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.32.2	yes	16
3.2	odd	2	inner	525.2.bf.e.32.4	yes	16
5.2	odd	4	inner	525.2.bf.e.368.4	yes	16
5.3	odd	4	inner	525.2.bf.e.368.1	yes	16
5.4	even	2	inner	525.2.bf.e.32.3	yes	16
7.2	even	3	inner	525.2.bf.e.107.3	yes	16
15.2	even	4	inner	525.2.bf.e.368.2	yes	16
15.8	even	4	inner	525.2.bf.e.368.3	yes	16
15.14	odd	2	inner	525.2.bf.e.32.1	✓	16
21.2	odd	6	inner	525.2.bf.e.107.1	yes	16
35.2	odd	12	inner	525.2.bf.e.443.1	yes	16
35.9	even	6	inner	525.2.bf.e.107.2	yes	16
35.23	odd	12	inner	525.2.bf.e.443.4	yes	16
105.2	even	12	inner	525.2.bf.e.443.3	yes	16
105.23	even	12	inner	525.2.bf.e.443.2	yes	16
105.44	odd	6	inner	525.2.bf.e.107.4	yes	16

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

\(f(q)\)	\(=\)	\(q+(-2.15988 - 0.578737i) q^{2} +(-0.737552 + 1.56717i) q^{3} +(2.59808 + 1.50000i) q^{4} +(2.50000 - 2.95804i) q^{6} +(-2.55560 + 0.684771i) q^{7} +(-1.58114 - 1.58114i) q^{8} +(-1.91203 - 2.31174i) q^{9} +O(q^{10})\)	\(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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more