LMFDB - Embedded newform 252.4.k.d.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(37,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("252.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.k (of order $3$, degree $2$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.2
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	252.109
Dual form			252.4.k.d.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.91238 + 8.50848i) q^{5} +(-16.3248 - 8.74657i) q^{7} +O(q^{10})$	$q+(4.91238 + 8.50848i) q^{5} +(-16.3248 - 8.74657i) q^{7} +(-7.08762 + 12.2761i) q^{11} -26.1238 q^{13} +(-39.2990 + 68.0679i) q^{17} +(-36.5876 - 63.3716i) q^{19} +(-48.0000 - 83.1384i) q^{23} +(14.2371 - 24.6594i) q^{25} -173.021 q^{29} +(-33.6238 + 58.2381i) q^{31} +(-5.77326 - 181.865i) q^{35} +(150.835 + 261.254i) q^{37} -472.042 q^{41} -463.670 q^{43} +(-45.5980 - 78.9781i) q^{47} +(189.995 + 285.571i) q^{49} +(-81.6341 + 141.394i) q^{53} -139.268 q^{55} +(-300.263 + 520.071i) q^{59} +(-285.846 - 495.099i) q^{61} +(-128.330 - 222.274i) q^{65} +(269.711 - 467.154i) q^{67} +1064.39 q^{71} +(221.340 - 383.372i) q^{73} +(223.078 - 138.412i) q^{77} +(22.8505 + 39.5782i) q^{79} +686.464 q^{83} -772.206 q^{85} +(330.072 + 571.702i) q^{89} +(426.464 + 228.493i) q^{91} +(359.464 - 622.610i) q^{95} +658.320 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{5} - 20 q^{7}+O(q^{10}) $ 4 * q - 3 * q^5 - 20 * q^7	$ 4 q - 3 q^{5} - 20 q^{7} - 51 q^{11} + 122 q^{13} + 24 q^{17} - 169 q^{19} - 192 q^{23} - 11 q^{25} + 78 q^{29} + 92 q^{31} + 294 q^{35} + 173 q^{37} - 348 q^{41} - 994 q^{43} + 180 q^{47} - 146 q^{49} + 285 q^{53} + 666 q^{55} - 1269 q^{59} - 328 q^{61} - 1374 q^{65} + 875 q^{67} + 2808 q^{71} + 1361 q^{73} - 897 q^{77} + 182 q^{79} + 798 q^{83} - 4176 q^{85} + 822 q^{89} + 1955 q^{91} - 510 q^{95} + 1682 q^{97}+O(q^{100}) $ 4 * q - 3 * q^5 - 20 * q^7 - 51 * q^11 + 122 * q^13 + 24 * q^17 - 169 * q^19 - 192 * q^23 - 11 * q^25 + 78 * q^29 + 92 * q^31 + 294 * q^35 + 173 * q^37 - 348 * q^41 - 994 * q^43 + 180 * q^47 - 146 * q^49 + 285 * q^53 + 666 * q^55 - 1269 * q^59 - 328 * q^61 - 1374 * q^65 + 875 * q^67 + 2808 * q^71 + 1361 * q^73 - 897 * q^77 + 182 * q^79 + 798 * q^83 - 4176 * q^85 + 822 * q^89 + 1955 * q^91 - 510 * q^95 + 1682 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	4.91238	+	8.50848i	0.439376	+	0.761022i	0.997641	−	0.0686406i	$-0.0218662\pi$
$5$	4.91238	+	8.50848i	0.439376	+	0.761022i	−0.558265	+	0.829663i	$0.688533\pi$
$6$		0			0
$7$	−16.3248	−	8.74657i	−0.881454	−	0.472270i
$7$	−16.3248	−	8.74657i	−0.881454	−	0.472270i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−7.08762	+	12.2761i	−0.194273	+	0.336490i	−0.946662	−	0.322229i	$-0.895568\pi$
$11$	−7.08762	+	12.2761i	−0.194273	+	0.336490i	0.752389	+	0.658719i	$0.228901\pi$
$12$		0			0
$13$	−26.1238			−0.557341			−0.278670	−	0.960387i	$-0.589894\pi$
$13$	−26.1238			−0.557341			−0.278670	+	0.960387i	$0.589894\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−39.2990	+	68.0679i	−0.560671	+	0.971111i	0.436767	+	0.899575i	$0.356123\pi$
$17$	−39.2990	+	68.0679i	−0.560671	+	0.971111i	−0.997438	+	0.0715361i	$0.977210\pi$
$18$		0			0
$19$	−36.5876	−	63.3716i	−0.441778	−	0.765181i	0.556044	−	0.831153i	$-0.312319\pi$
$19$	−36.5876	−	63.3716i	−0.441778	−	0.765181i	−0.997822	+	0.0659715i	$0.978985\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−48.0000	−	83.1384i	−0.435161	−	0.753720i	0.562148	−	0.827037i	$-0.309975\pi$
$23$	−48.0000	−	83.1384i	−0.435161	−	0.753720i	−0.997309	+	0.0733164i	$0.976642\pi$
$24$		0			0
$25$	14.2371	−	24.6594i	0.113897	−	0.197275i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−173.021			−1.10790			−0.553951	−	0.832549i	$-0.686880\pi$
$29$	−173.021			−1.10790			−0.553951	+	0.832549i	$0.686880\pi$
$30$		0			0
$31$	−33.6238	+	58.2381i	−0.194807	+	0.337415i	−0.946837	−	0.321713i	$-0.895741\pi$
$31$	−33.6238	+	58.2381i	−0.194807	+	0.337415i	0.752030	+	0.659128i	$0.229075\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.77326	−	181.865i	−0.0278817	−	0.878310i
$36$		0			0
$37$	150.835	+	261.254i	0.670193	+	1.16081i	0.977849	+	0.209311i	$0.0671221\pi$
$37$	150.835	+	261.254i	0.670193	+	1.16081i	−0.307656	+	0.951498i	$0.599545\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−472.042			−1.79806			−0.899031	−	0.437886i	$-0.855727\pi$
$41$	−472.042			−1.79806			−0.899031	+	0.437886i	$0.855727\pi$
$42$		0			0
$43$	−463.670			−1.64440			−0.822198	−	0.569201i	$-0.807253\pi$
$43$	−463.670			−1.64440			−0.822198	+	0.569201i	$0.807253\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−45.5980	−	78.9781i	−0.141514	−	0.245109i	0.786553	−	0.617523i	$-0.211864\pi$
$47$	−45.5980	−	78.9781i	−0.141514	−	0.245109i	−0.928067	+	0.372413i	$0.878530\pi$
$48$		0			0
$49$	189.995	+	285.571i	0.553921	+	0.832569i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−81.6341	+	141.394i	−0.211572	+	0.366453i	−0.952207	−	0.305455i	$-0.901192\pi$
$53$	−81.6341	+	141.394i	−0.211572	+	0.366453i	0.740635	+	0.671908i	$0.234525\pi$
$54$		0			0
$55$	−139.268			−0.341435
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−300.263	+	520.071i	−0.662558	+	1.14758i	0.317384	+	0.948297i	$0.397196\pi$
$59$	−300.263	+	520.071i	−0.662558	+	1.14758i	−0.979941	+	0.199286i	$0.936138\pi$
$60$		0			0
$61$	−285.846	−	495.099i	−0.599980	−	1.03920i	−0.992823	−	0.119590i	$-0.961842\pi$
$61$	−285.846	−	495.099i	−0.599980	−	1.03920i	0.392844	−	0.919605i	$-0.371491\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−128.330	−	222.274i	−0.244882	−	0.424148i
$66$		0			0
$67$	269.711	−	467.154i	0.491798	−	0.851820i	−0.508157	−	0.861264i	$-0.669673\pi$
$67$	269.711	−	467.154i	0.491798	−	0.851820i	0.999955	+	0.00944469i	$0.00300638\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1064.39			1.77916			0.889578	−	0.456783i	$-0.150998\pi$
$71$	1064.39			1.77916			0.889578	+	0.456783i	$0.150998\pi$
$72$		0			0
$73$	221.340	−	383.372i	0.354875	−	0.614662i	−0.632221	−	0.774788i	$-0.717857\pi$
$73$	221.340	−	383.372i	0.354875	−	0.614662i	0.987097	+	0.160126i	$0.0511900\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	223.078	−	138.412i	0.330157	−	0.204851i
$78$		0			0
$79$	22.8505	+	39.5782i	0.0325428	+	0.0563658i	0.881838	−	0.471552i	$-0.156306\pi$
$79$	22.8505	+	39.5782i	0.0325428	+	0.0563658i	−0.849295	+	0.527918i	$0.822973\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	686.464			0.907822			0.453911	−	0.891047i	$-0.350028\pi$
$83$	686.464			0.907822			0.453911	+	0.891047i	$0.350028\pi$
$84$		0			0
$85$	−772.206			−0.985382
$86$		0			0
$87$		0			0
$88$		0			0
$89$	330.072	+	571.702i	0.393119	+	0.680902i	0.992859	−	0.119293i	$-0.0380627\pi$
$89$	330.072	+	571.702i	0.393119	+	0.680902i	−0.599740	+	0.800195i	$0.704729\pi$
$90$		0			0
$91$	426.464	+	228.493i	0.491270	+	0.263215i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	359.464	−	622.610i	0.388213	−	0.672405i
$96$		0			0
$97$	658.320			0.689095			0.344548	−	0.938769i	$-0.388032\pi$
$97$	658.320			0.689095			0.344548	+	0.938769i	$0.388032\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−901.949	+	1562.22i	−0.888586	+	1.53908i	−0.0470394	+	0.998893i	$0.514979\pi$
$101$	−901.949	+	1562.22i	−0.888586	+	1.53908i	−0.841547	+	0.540184i	$0.818355\pi$
$102$		0			0
$103$	537.454	+	930.898i	0.514145	+	0.890525i	0.999865	+	0.0164107i	$0.00522392\pi$
$103$	537.454	+	930.898i	0.514145	+	0.890525i	−0.485721	+	0.874114i	$0.661443\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−829.676	−	1437.04i	−0.749605	−	1.29835i	−0.948012	−	0.318235i	$-0.896910\pi$
$107$	−829.676	−	1437.04i	−0.749605	−	1.29835i	0.198407	−	0.980120i	$-0.436423\pi$
$108$		0			0
$109$	−299.464	+	518.687i	−0.263151	+	0.455791i	−0.967077	−	0.254482i	$-0.918095\pi$
$109$	−299.464	+	518.687i	−0.263151	+	0.455791i	0.703927	+	0.710273i	$0.251428\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	781.650			0.650720			0.325360	−	0.945590i	$-0.394514\pi$
$113$	781.650			0.650720			0.325360	+	0.945590i	$0.394514\pi$
$114$		0			0
$115$	471.588	−	816.815i	0.382398	−	0.662333i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1236.91	−	767.460i	0.952833	−	0.591201i
$120$		0			0
$121$	565.031	+	978.663i	0.424516	+	0.735284i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1507.85			1.07893
$126$		0			0
$127$	25.3722			0.0177277			0.00886385	−	0.999961i	$-0.497179\pi$
$127$	25.3722			0.0177277			0.00886385	+	0.999961i	$0.497179\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−237.789	−	411.862i	−0.158593	−	0.274691i	0.775768	−	0.631018i	$-0.217362\pi$
$131$	−237.789	−	411.862i	−0.158593	−	0.274691i	−0.934362	+	0.356326i	$0.884029\pi$
$132$		0			0
$133$	42.9995	+	1354.54i	0.0280341	+	0.883111i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	529.268	−	916.720i	0.330062	−	0.571683i	−0.652462	−	0.757821i	$-0.726264\pi$
$137$	529.268	−	916.720i	0.330062	−	0.571683i	0.982524	+	0.186138i	$0.0595971\pi$
$138$		0			0
$139$	2580.99			1.57494			0.787470	−	0.616352i	$-0.211390\pi$
$139$	2580.99			1.57494			0.787470	+	0.616352i	$0.211390\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	185.155	−	320.699i	0.108276	−	0.187540i
$144$		0			0
$145$	−849.943	−	1472.14i	−0.486786	−	0.843138i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−50.9377	−	88.2266i	−0.0280066	−	0.0485088i	0.851682	−	0.524058i	$-0.175583\pi$
$149$	−50.9377	−	88.2266i	−0.0280066	−	0.0485088i	−0.879689	+	0.475549i	$0.842249\pi$
$150$		0			0
$151$	889.211	−	1540.16i	0.479225	−	0.830042i	−0.520491	−	0.853867i	$-0.674251\pi$
$151$	889.211	−	1540.16i	0.479225	−	0.830042i	0.999716	+	0.0238249i	$0.00758441\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−660.690			−0.342374
$156$		0			0
$157$	−699.629	+	1211.79i	−0.355646	+	0.615997i	−0.987228	−	0.159312i	$-0.949073\pi$
$157$	−699.629	+	1211.79i	−0.355646	+	0.615997i	0.631582	+	0.775309i	$0.282406\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	56.4119	+	1777.05i	0.0276142	+	0.869883i
$162$		0			0
$163$	−1807.71	−	3131.05i	−0.868656	−	1.50456i	−0.863370	−	0.504571i	$-0.831651\pi$
$163$	−1807.71	−	3131.05i	−0.868656	−	1.50456i	−0.00528615	−	0.999986i	$-0.501683\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1076.72			0.498917			0.249459	−	0.968385i	$-0.419747\pi$
$167$	1076.72			0.498917			0.249459	+	0.968385i	$0.419747\pi$
$168$		0			0
$169$	−1514.55			−0.689372
$170$		0			0
$171$		0			0
$172$		0			0
$173$	936.815	+	1622.61i	0.411704	+	0.713091i	0.995076	−	0.0991132i	$-0.0316006\pi$
$173$	936.815	+	1622.61i	0.411704	+	0.713091i	−0.583373	+	0.812205i	$0.698267\pi$
$174$		0			0
$175$	−448.103	+	278.033i	−0.193562	+	0.120099i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1346.15	+	2331.59i	−0.562099	+	0.973583i	0.435215	+	0.900327i	$0.356672\pi$
$179$	−1346.15	+	2331.59i	−0.562099	+	0.973583i	−0.997313	+	0.0732565i	$0.976661\pi$
$180$		0			0
$181$	461.670			0.189589			0.0947947	−	0.995497i	$-0.469781\pi$
$181$	461.670			0.189589			0.0947947	+	0.995497i	$0.469781\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1481.92	+	2566.76i	−0.588934	+	1.02006i
$186$		0			0
$187$	−557.073	−	964.879i	−0.217846	−	0.377321i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1882.41	−	3260.43i	−0.713124	−	1.23517i	−0.963679	−	0.267064i	$-0.913946\pi$
$191$	−1882.41	−	3260.43i	−0.713124	−	1.23517i	0.250555	−	0.968102i	$-0.419387\pi$
$192$		0			0
$193$	−1463.10	+	2534.16i	−0.545680	+	0.945145i	0.452884	+	0.891569i	$0.350395\pi$
$193$	−1463.10	+	2534.16i	−0.545680	+	0.945145i	−0.998564	+	0.0535755i	$0.982938\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5045.55			−1.82477			−0.912387	−	0.409330i	$-0.865763\pi$
$197$	−5045.55			−1.82477			−0.912387	+	0.409330i	$0.865763\pi$
$198$		0			0
$199$	−2146.12	+	3717.20i	−0.764496	+	1.32415i	0.176016	+	0.984387i	$0.443679\pi$
$199$	−2146.12	+	3717.20i	−0.764496	+	1.32415i	−0.940513	+	0.339759i	$0.889654\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2824.52	+	1513.34i	0.976564	+	0.523229i
$204$		0			0
$205$	−2318.85	−	4016.36i	−0.790025	−	1.36836i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1037.28			0.343301
$210$		0			0
$211$	3625.76			1.18297			0.591487	−	0.806315i	$-0.298541\pi$
$211$	3625.76			1.18297			0.591487	+	0.806315i	$0.298541\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2277.72	−	3945.13i	−0.722509	−	1.25142i
$216$		0			0
$217$	1058.28	−	656.629i	0.331064	−	0.205414i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1026.64	−	1778.19i	0.312485	−	0.541239i
$222$		0			0
$223$	−3145.00			−0.944417			−0.472208	−	0.881487i	$-0.656543\pi$
$223$	−3145.00			−0.944417			−0.472208	+	0.881487i	$0.656543\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−772.873	+	1338.65i	−0.225980	+	0.391408i	−0.956613	−	0.291362i	$-0.905892\pi$
$227$	−772.873	+	1338.65i	−0.225980	+	0.391408i	0.730633	+	0.682770i	$0.239225\pi$
$228$		0			0
$229$	2036.07	+	3526.58i	0.587544	+	1.01766i	0.994553	+	0.104232i	$0.0332383\pi$
$229$	2036.07	+	3526.58i	0.587544	+	1.01766i	−0.407009	+	0.913424i	$0.633428\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1507.86	−	2611.68i	−0.423961	−	0.734322i	0.572362	−	0.820001i	$-0.306027\pi$
$233$	−1507.86	−	2611.68i	−0.423961	−	0.734322i	−0.996323	+	0.0856790i	$0.972694\pi$
$234$		0			0
$235$	447.989	−	775.940i	0.124356	−	0.215390i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4647.38			−1.25780			−0.628900	−	0.777486i	$-0.716495\pi$
$239$	−4647.38			−1.25780			−0.628900	+	0.777486i	$0.716495\pi$
$240$		0			0
$241$	−559.138	+	968.456i	−0.149449	+	0.258854i	−0.931024	−	0.364958i	$-0.881083\pi$
$241$	−559.138	+	968.456i	−0.149449	+	0.258854i	0.781575	+	0.623812i	$0.214417\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1496.45	+	3019.40i	−0.390223	+	0.787357i
$246$		0			0
$247$	955.806	+	1655.50i	0.246221	+	0.426467i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−883.518			−0.222180			−0.111090	−	0.993810i	$-0.535434\pi$
$251$	−883.518			−0.222180			−0.111090	+	0.993810i	$0.535434\pi$
$252$		0			0
$253$	1360.82			0.338159
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2934.44	−	5082.61i	−0.712240	−	1.23364i	−0.964015	−	0.265849i	$-0.914348\pi$
$257$	−2934.44	−	5082.61i	−0.712240	−	1.23364i	0.251775	−	0.967786i	$-0.418986\pi$
$258$		0			0
$259$	−177.269	−	5584.20i	−0.0425287	−	1.33971i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2437.81	−	4222.41i	0.571565	−	0.989980i	−0.424841	−	0.905268i	$-0.639670\pi$
$263$	2437.81	−	4222.41i	0.571565	−	0.989980i	0.996406	−	0.0847114i	$-0.0269968\pi$
$264$		0			0
$265$	−1604.07			−0.371839
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2763.55	+	4786.61i	−0.626382	+	1.08493i	0.361890	+	0.932221i	$0.382132\pi$
$269$	−2763.55	+	4786.61i	−0.626382	+	1.08493i	−0.988272	+	0.152704i	$0.951202\pi$
$270$		0			0
$271$	1612.37	+	2792.70i	0.361418	+	0.625994i	0.988194	−	0.153205i	$-0.0489594\pi$
$271$	1612.37	+	2792.70i	0.361418	+	0.625994i	−0.626777	+	0.779199i	$0.715626\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	201.815	+	349.554i	0.0442542	+	0.0766504i
$276$		0			0
$277$	979.022	−	1695.72i	0.212360	−	0.367818i	−0.740093	−	0.672505i	$-0.765218\pi$
$277$	979.022	−	1695.72i	0.212360	−	0.367818i	0.952453	+	0.304687i	$0.0985517\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8531.16			−1.81113			−0.905563	−	0.424212i	$-0.860551\pi$
$281$	−8531.16			−1.81113			−0.905563	+	0.424212i	$0.860551\pi$
$282$		0			0
$283$	−3954.93	+	6850.14i	−0.830728	+	1.43886i	0.0667331	+	0.997771i	$0.478742\pi$
$283$	−3954.93	+	6850.14i	−0.830728	+	1.43886i	−0.897461	+	0.441093i	$0.854591\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7705.96	+	4128.74i	1.58491	+	0.849171i
$288$		0			0
$289$	−632.324	−	1095.22i	−0.128704	−	0.222922i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8321.41			1.65919			0.829594	−	0.558367i	$-0.188572\pi$
$293$	8321.41			1.65919			0.829594	+	0.558367i	$0.188572\pi$
$294$		0			0
$295$	−5900.02			−1.16445
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1253.94	+	2171.89i	0.242533	+	0.420079i
$300$		0			0
$301$	7569.30	+	4055.52i	1.44946	+	0.776600i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2808.36	−	4864.22i	0.527234	−	0.913196i
$306$		0			0
$307$	2541.79			0.472533			0.236267	−	0.971688i	$-0.424076\pi$
$307$	2541.79			0.472533			0.236267	+	0.971688i	$0.424076\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−303.855	+	526.292i	−0.0554020	+	0.0959590i	−0.892396	−	0.451253i	$-0.850977\pi$
$311$	−303.855	+	526.292i	−0.0554020	+	0.0959590i	0.836994	+	0.547212i	$0.184311\pi$
$312$		0			0
$313$	−5513.64	−	9549.90i	−0.995684	−	1.72458i	−0.578213	−	0.815886i	$-0.696250\pi$
$313$	−5513.64	−	9549.90i	−0.995684	−	1.72458i	−0.417471	−	0.908690i	$-0.637084\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3630.80	+	6288.73i	0.643300	+	1.11423i	0.984691	+	0.174307i	$0.0557685\pi$
$317$	3630.80	+	6288.73i	0.643300	+	1.11423i	−0.341391	+	0.939921i	$0.610898\pi$
$318$		0			0
$319$	1226.31	−	2124.02i	0.215235	−	0.372798i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	5751.43			0.990768
$324$		0			0
$325$	−371.927	+	644.197i	−0.0634794	+	0.109950i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	53.5890	+	1688.12i	0.00898011	+	0.282885i
$330$		0			0
$331$	−3316.36	−	5744.11i	−0.550706	−	0.953851i	−0.998224	−	0.0595761i	$-0.981025\pi$
$331$	−3316.36	−	5744.11i	−0.550706	−	0.953851i	0.447517	−	0.894275i	$-0.352308\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5299.69			0.864338
$336$		0			0
$337$	8104.59			1.31005			0.655023	−	0.755609i	$-0.272659\pi$
$337$	8104.59			1.31005			0.655023	+	0.755609i	$0.272659\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−476.625	−	825.539i	−0.0756912	−	0.131101i
$342$		0			0
$343$	−603.854	−	6323.68i	−0.0950584	−	0.995472i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2968.64	+	5141.83i	−0.459265	+	0.795470i	−0.998922	−	0.0464146i	$-0.985220\pi$
$347$	−2968.64	+	5141.83i	−0.459265	+	0.795470i	0.539657	+	0.841885i	$0.318554\pi$
$348$		0			0
$349$	268.472			0.0411775			0.0205888	−	0.999788i	$-0.493446\pi$
$349$	268.472			0.0411775			0.0205888	+	0.999788i	$0.493446\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1331.40	−	2306.06i	0.200747	−	0.347703i	−0.748023	−	0.663673i	$-0.768997\pi$
$353$	1331.40	−	2306.06i	0.200747	−	0.347703i	0.948769	+	0.315970i	$0.102330\pi$
$354$		0			0
$355$	5228.69	+	9056.36i	0.781719	+	1.35398i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−781.637	−	1353.83i	−0.114911	−	0.199032i	0.802833	−	0.596204i	$-0.203325\pi$
$359$	−781.637	−	1353.83i	−0.114911	−	0.199032i	−0.917744	+	0.397172i	$0.869992\pi$
$360$		0			0
$361$	752.192	−	1302.83i	0.109665	−	0.189945i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4349.22			0.623695
$366$		0			0
$367$	−605.408	+	1048.60i	−0.0861091	+	0.149145i	−0.905863	−	0.423570i	$-0.860777\pi$
$367$	−605.408	+	1048.60i	−0.0861091	+	0.149145i	0.819754	+	0.572716i	$0.194110\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2569.37	−	1594.21i	0.359556	−	0.223093i
$372$		0			0
$373$	2385.93	+	4132.55i	0.331203	+	0.573661i	0.982748	−	0.184949i	$-0.0592121\pi$
$373$	2385.93	+	4132.55i	0.331203	+	0.573661i	−0.651545	+	0.758610i	$0.725879\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4519.95			0.617479
$378$		0			0
$379$	−4118.66			−0.558209			−0.279104	−	0.960261i	$-0.590038\pi$
$379$	−4118.66			−0.558209			−0.279104	+	0.960261i	$0.590038\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1767.99	+	3062.25i	0.235875	+	0.408547i	0.959527	−	0.281618i	$-0.0908712\pi$
$383$	1767.99	+	3062.25i	0.235875	+	0.408547i	−0.723652	+	0.690165i	$0.757538\pi$
$384$		0			0
$385$	2273.52	+	1218.12i	0.300959	+	0.161250i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4803.23	−	8319.44i	0.626050	−	1.08435i	−0.362287	−	0.932067i	$-0.618004\pi$
$389$	4803.23	−	8319.44i	0.626050	−	1.08435i	0.988337	−	0.152284i	$-0.0486627\pi$
$390$		0			0
$391$	7545.41			0.975928
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−224.500	+	388.846i	−0.0285971	+	0.0495316i
$396$		0			0
$397$	−2683.54	−	4648.02i	−0.339252	−	0.587601i	0.645041	−	0.764148i	$-0.276840\pi$
$397$	−2683.54	−	4648.02i	−0.339252	−	0.587601i	−0.984292	+	0.176547i	$0.943507\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7032.91	−	12181.4i	−0.875828	−	1.51698i	−0.855878	−	0.517177i	$-0.826983\pi$
$401$	−7032.91	−	12181.4i	−0.875828	−	1.51698i	−0.0199492	−	0.999801i	$-0.506350\pi$
$402$		0			0
$403$	878.379	−	1521.40i	0.108574	−	0.188055i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4276.25			−0.520801
$408$		0			0
$409$	−1636.22	+	2834.02i	−0.197814	+	0.342624i	−0.947819	−	0.318808i	$-0.896718\pi$
$409$	−1636.22	+	2834.02i	−0.197814	+	0.342624i	0.750005	+	0.661432i	$0.230051\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	9450.55	−	5863.75i	1.12598	−	0.698635i
$414$		0			0
$415$	3372.17	+	5840.77i	0.398876	+	0.690873i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8077.07			−0.941744			−0.470872	−	0.882202i	$-0.656061\pi$
$419$	−8077.07			−0.941744			−0.470872	+	0.882202i	$0.656061\pi$
$420$		0			0
$421$	8051.68			0.932101			0.466051	−	0.884758i	$-0.345676\pi$
$421$	8051.68			0.932101			0.466051	+	0.884758i	$0.345676\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1119.01	+	1938.18i	0.127718	+	0.221213i
$426$		0			0
$427$	335.939	+	10582.5i	0.0380732	+	1.19936i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4950.11	+	8573.84i	−0.553221	+	0.958207i	0.444818	+	0.895621i	$0.353268\pi$
$431$	−4950.11	+	8573.84i	−0.553221	+	0.958207i	−0.998040	+	0.0625863i	$0.980065\pi$
$432$		0			0
$433$	−511.795			−0.0568021			−0.0284010	−	0.999597i	$-0.509042\pi$
$433$	−511.795			−0.0568021			−0.0284010	+	0.999597i	$0.509042\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3512.41	+	6083.68i	−0.384488	+	0.665954i
$438$		0			0
$439$	651.130	+	1127.79i	0.0707898	+	0.122612i	0.899248	−	0.437440i	$-0.144115\pi$
$439$	651.130	+	1127.79i	0.0707898	+	0.122612i	−0.828458	+	0.560051i	$0.810781\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4100.16	−	7101.69i	−0.439739	−	0.761651i	0.557930	−	0.829888i	$-0.311596\pi$
$443$	−4100.16	−	7101.69i	−0.439739	−	0.761651i	−0.997669	+	0.0682372i	$0.978263\pi$
$444$		0			0
$445$	−3242.88	+	5616.83i	−0.345454	+	0.598344i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	5788.12			0.608370			0.304185	−	0.952613i	$-0.401616\pi$
$449$	5788.12			0.608370			0.304185	+	0.952613i	$0.401616\pi$
$450$		0			0
$451$	3345.65	−	5794.84i	0.349314	−	0.605030i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	150.819	+	4751.01i	0.0155396	+	0.489518i
$456$		0			0
$457$	−3629.59	−	6286.63i	−0.371521	−	0.643493i	0.618279	−	0.785959i	$-0.287830\pi$
$457$	−3629.59	−	6286.63i	−0.371521	−	0.643493i	−0.989800	+	0.142466i	$0.954497\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5966.92			0.602835			0.301418	−	0.953492i	$-0.402540\pi$
$461$	5966.92			0.602835			0.301418	+	0.953492i	$0.402540\pi$
$462$		0			0
$463$	−8884.02			−0.891740			−0.445870	−	0.895098i	$-0.647106\pi$
$463$	−8884.02			−0.891740			−0.445870	+	0.895098i	$0.647106\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2014.68	−	3489.53i	−0.199632	−	0.345774i	0.748777	−	0.662822i	$-0.230641\pi$
$467$	−2014.68	−	3489.53i	−0.199632	−	0.345774i	−0.948409	+	0.317049i	$0.897308\pi$
$468$		0			0
$469$	−8488.96	+	5267.12i	−0.835787	+	0.518578i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3286.32	−	5692.07i	0.319461	−	0.553323i
$474$		0			0
$475$	−2083.61			−0.201269
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8720.33	+	15104.0i	−0.831820	+	1.44075i	0.0647733	+	0.997900i	$0.479368\pi$
$479$	−8720.33	+	15104.0i	−0.831820	+	1.44075i	−0.896593	+	0.442855i	$0.853966\pi$
$480$		0			0
$481$	−3940.38	−	6824.94i	−0.373526	−	0.646966i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3233.91	+	5601.30i	0.302772	+	0.524417i
$486$		0			0
$487$	2136.14	−	3699.90i	0.198763	−	0.344268i	−0.749364	−	0.662158i	$-0.769641\pi$
$487$	2136.14	−	3699.90i	0.198763	−	0.344268i	0.948128	+	0.317890i	$0.102974\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2013.29			−0.185048			−0.0925240	−	0.995710i	$-0.529493\pi$
$491$	−2013.29			−0.185048			−0.0925240	+	0.995710i	$0.529493\pi$
$492$		0			0
$493$	6799.54	−	11777.2i	0.621169	−	1.07590i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17375.9	−	9309.78i	−1.56824	−	0.840243i
$498$		0			0
$499$	2440.23	+	4226.60i	0.218917	+	0.379176i	0.954477	−	0.298284i	$-0.0964142\pi$
$499$	2440.23	+	4226.60i	0.218917	+	0.379176i	−0.735560	+	0.677460i	$0.763081\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12961.9			−1.14899			−0.574496	−	0.818508i	$-0.694802\pi$
$503$	−12961.9			−1.14899			−0.574496	+	0.818508i	$0.694802\pi$
$504$		0			0
$505$	−17722.8			−1.56170
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4077.69	+	7062.77i	0.355089	+	0.615033i	0.987133	−	0.159900i	$-0.0511172\pi$
$509$	4077.69	+	7062.77i	0.355089	+	0.615033i	−0.632044	+	0.774932i	$0.717784\pi$
$510$		0			0
$511$	−6966.51	+	4322.49i	−0.603093	+	0.374199i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5280.35	+	9145.84i	−0.451806	+	0.782551i
$516$		0			0
$517$	1292.73			0.109969
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−166.009	+	287.536i	−0.0139597	+	0.0241789i	−0.872921	−	0.487862i	$-0.837777\pi$
$521$	−166.009	+	287.536i	−0.0139597	+	0.0241789i	0.858961	+	0.512041i	$0.171110\pi$
$522$		0			0
$523$	−3627.42	−	6282.87i	−0.303281	−	0.525298i	0.673596	−	0.739099i	$-0.264749\pi$
$523$	−3627.42	−	6282.87i	−0.303281	−	0.525298i	−0.976877	+	0.213802i	$0.931415\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2642.76	−	4577.40i	−0.218445	−	0.378358i
$528$		0			0
$529$	1475.50	−	2555.64i	0.121271	−	0.210047i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12331.5			1.00213
$534$		0			0
$535$	8151.36	−	14118.6i	0.658718	−	1.14093i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4852.32	+	308.382i	−0.387763	+	0.0246437i
$540$		0			0
$541$	−2705.10	−	4685.36i	−0.214974	−	0.372347i	0.738290	−	0.674483i	$-0.235633\pi$
$541$	−2705.10	−	4685.36i	−0.214974	−	0.372347i	−0.953265	+	0.302137i	$0.902300\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5884.32			−0.462489
$546$		0			0
$547$	−18673.9			−1.45967			−0.729834	−	0.683625i	$-0.760403\pi$
$547$	−18673.9			−1.45967			−0.729834	+	0.683625i	$0.760403\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6330.42	+	10964.6i	0.489446	+	0.847746i
$552$		0			0
$553$	−26.8550	−	845.968i	−0.00206508	−	0.0650528i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4104.74	+	7109.62i	−0.312250	+	0.540833i	−0.978849	−	0.204583i	$-0.934416\pi$
$557$	−4104.74	+	7109.62i	−0.312250	+	0.540833i	0.666599	+	0.745417i	$0.267749\pi$
$558$		0			0
$559$	12112.8			0.916489
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8761.10	−	15174.7i	0.655837	−	1.13594i	−0.325846	−	0.945423i	$-0.605649\pi$
$563$	8761.10	−	15174.7i	0.655837	−	1.13594i	0.981683	−	0.190521i	$-0.0610176\pi$
$564$		0			0
$565$	3839.76	+	6650.65i	0.285911	+	0.495212i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4528.41	−	7843.44i	−0.333640	−	0.577881i	0.649583	−	0.760291i	$-0.274944\pi$
$569$	−4528.41	−	7843.44i	−0.333640	−	0.577881i	−0.983223	+	0.182410i	$0.941610\pi$
$570$		0			0
$571$	−5358.27	+	9280.80i	−0.392709	+	0.680191i	−0.992806	−	0.119736i	$-0.961795\pi$
$571$	−5358.27	+	9280.80i	−0.392709	+	0.680191i	0.600097	+	0.799927i	$0.295129\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2733.53			−0.198254
$576$		0			0
$577$	−1608.62	+	2786.21i	−0.116062	+	0.201025i	−0.918204	−	0.396109i	$-0.870360\pi$
$577$	−1608.62	+	2786.21i	−0.116062	+	0.201025i	0.802142	+	0.597133i	$0.203694\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−11206.4	−	6004.21i	−0.800203	−	0.428738i
$582$		0			0
$583$	−1157.18	−	2004.30i	−0.0822053	−	0.142384i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3248.45			−0.228412			−0.114206	−	0.993457i	$-0.536432\pi$
$587$	−3248.45			−0.228412			−0.114206	+	0.993457i	$0.536432\pi$
$588$		0			0
$589$	4920.85			0.344245
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10555.2	−	18282.1i	−0.730945	−	1.26603i	−0.956480	−	0.291799i	$-0.905746\pi$
$593$	−10555.2	−	18282.1i	−0.730945	−	1.26603i	0.225535	−	0.974235i	$-0.427587\pi$
$594$		0			0
$595$	12606.1	+	6754.15i	0.868569	+	0.465367i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7868.98	+	13629.5i	−0.536758	+	0.929692i	0.462318	+	0.886714i	$0.347018\pi$
$599$	−7868.98	+	13629.5i	−0.536758	+	0.929692i	−0.999076	+	0.0429777i	$0.986316\pi$
$600$		0			0
$601$	−4856.96			−0.329650			−0.164825	−	0.986323i	$-0.552706\pi$
$601$	−4856.96			−0.329650			−0.164825	+	0.986323i	$0.552706\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5551.29	+	9615.12i	−0.373045	+	0.646132i
$606$		0			0
$607$	8629.29	+	14946.4i	0.577022	+	0.999431i	0.995819	+	0.0913513i	$0.0291186\pi$
$607$	8629.29	+	14946.4i	0.577022	+	0.999431i	−0.418797	+	0.908080i	$0.637548\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1191.19	+	2063.20i	0.0788714	+	0.136609i
$612$		0			0
$613$	−8058.53	+	13957.8i	−0.530964	+	0.919657i	0.468383	+	0.883526i	$0.344837\pi$
$613$	−8058.53	+	13957.8i	−0.530964	+	0.919657i	−0.999347	+	0.0361315i	$0.988496\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17507.3			1.14233			0.571164	−	0.820836i	$-0.306492\pi$
$617$	17507.3			1.14233			0.571164	+	0.820836i	$0.306492\pi$
$618$		0			0
$619$	−4859.24	+	8416.46i	−0.315524	+	0.546504i	−0.979549	−	0.201207i	$-0.935514\pi$
$619$	−4859.24	+	8416.46i	−0.315524	+	0.546504i	0.664025	+	0.747711i	$0.268847\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−387.917	−	12219.9i	−0.0249463	−	0.785842i
$624$		0			0
$625$	5627.47	+	9747.06i	0.360158	+	0.623812i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−23710.7			−1.50303
$630$		0			0
$631$	5144.78			0.324580			0.162290	−	0.986743i	$-0.448112\pi$
$631$	5144.78			0.324580			0.162290	+	0.986743i	$0.448112\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	124.638	+	215.879i	0.00778913	+	0.0134912i
$636$		0			0
$637$	−4963.38	−	7460.19i	−0.308723	−	0.464024i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10843.0	−	18780.7i	0.668135	−	1.15724i	−0.310290	−	0.950642i	$-0.600426\pi$
$641$	10843.0	−	18780.7i	0.668135	−	1.15724i	0.978425	−	0.206602i	$-0.0662405\pi$
$642$		0			0
$643$	−14171.1			−0.869132			−0.434566	−	0.900640i	$-0.643098\pi$
$643$	−14171.1			−0.869132			−0.434566	+	0.900640i	$0.643098\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10026.6	−	17366.6i	0.609254	−	1.05526i	−0.382109	−	0.924117i	$-0.624802\pi$
$647$	10026.6	−	17366.6i	0.609254	−	1.05526i	0.991364	−	0.131142i	$-0.0418645\pi$
$648$		0			0
$649$	−4256.30	−	7372.13i	−0.257434	−	0.445888i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11820.6	+	20473.8i	0.708385	+	1.22696i	0.965456	+	0.260566i	$0.0839091\pi$
$653$	11820.6	+	20473.8i	0.708385	+	1.22696i	−0.257072	+	0.966392i	$0.582758\pi$
$654$		0			0
$655$	2336.21	−	4046.44i	0.139364	−	0.241386i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2367.34			−0.139937			−0.0699685	−	0.997549i	$-0.522290\pi$
$659$	−2367.34			−0.139937			−0.0699685	+	0.997549i	$0.522290\pi$
$660$		0			0
$661$	194.991	−	337.733i	0.0114739	−	0.0198734i	−0.860231	−	0.509904i	$-0.829681\pi$
$661$	194.991	−	337.733i	0.0114739	−	0.0198734i	0.871705	+	0.490030i	$0.163014\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−11313.9	+	7019.88i	−0.659749	+	0.409352i
$666$		0			0
$667$	8305.00	+	14384.7i	0.482115	+	0.835048i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	8103.86			0.466239
$672$		0			0
$673$	28764.5			1.64753			0.823766	−	0.566930i	$-0.191869\pi$
$673$	28764.5			1.64753			0.823766	+	0.566930i	$0.191869\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−881.061	−	1526.04i	−0.0500176	−	0.0866331i	0.839933	−	0.542691i	$-0.182594\pi$
$677$	−881.061	−	1526.04i	−0.0500176	−	0.0866331i	−0.889950	+	0.456058i	$0.849261\pi$
$678$		0			0
$679$	−10746.9	−	5758.04i	−0.607406	−	0.325439i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1114.44	+	1930.26i	−0.0624344	+	0.108140i	−0.895553	−	0.444955i	$-0.853220\pi$
$683$	−1114.44	+	1930.26i	−0.0624344	+	0.108140i	0.833119	+	0.553094i	$0.186553\pi$
$684$		0			0
$685$	10399.9			0.580085
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2132.59	−	3693.76i	0.117918	−	0.204239i
$690$		0			0
$691$	−8672.14	−	15020.6i	−0.477429	−	0.826932i	0.522236	−	0.852801i	$-0.325098\pi$
$691$	−8672.14	−	15020.6i	−0.477429	−	0.826932i	−0.999665	+	0.0258690i	$0.991765\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12678.8	+	21960.3i	0.691992	+	1.19856i
$696$		0			0
$697$	18550.8	−	32130.9i	1.00812	−	1.74612i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	23697.7			1.27682			0.638409	−	0.769697i	$-0.279593\pi$
$701$	23697.7			1.27682			0.638409	+	0.769697i	$0.279593\pi$
$702$		0			0
$703$	11037.4	−	19117.3i	0.592153	−	1.02564i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	28388.2	−	17613.9i	1.51011	−	0.936972i
$708$		0			0
$709$	11395.5	+	19737.6i	0.603620	+	1.04550i	0.992268	+	0.124114i	$0.0396088\pi$
$709$	11395.5	+	19737.6i	0.603620	+	1.04550i	−0.388648	+	0.921386i	$0.627058\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6455.76			0.339089
$714$		0			0
$715$	3638.21			0.190296
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15922.4	+	27578.4i	0.825876	+	1.43046i	0.901248	+	0.433304i	$0.142652\pi$
$719$	15922.4	+	27578.4i	0.825876	+	1.43046i	−0.0753721	+	0.997155i	$0.524014\pi$
$720$		0			0
$721$	−631.642	−	19897.5i	−0.0326263	−	1.02777i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2463.32	+	4266.59i	−0.126187	+	0.218562i
$726$		0			0
$727$	−22500.0			−1.14784			−0.573920	−	0.818912i	$-0.694578\pi$
$727$	−22500.0			−1.14784			−0.573920	+	0.818912i	$0.694578\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	18221.8	−	31561.1i	0.921966	−	1.59689i
$732$		0			0
$733$	1611.38	+	2790.99i	0.0811972	+	0.140638i	0.903764	−	0.428030i	$-0.140792\pi$
$733$	1611.38	+	2790.99i	0.0811972	+	0.140638i	−0.822567	+	0.568668i	$0.807459\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3823.23	+	6622.02i	0.191086	+	0.330971i
$738$		0			0
$739$	−9179.77	+	15899.8i	−0.456946	+	0.791454i	−0.998798	−	0.0490199i	$-0.984390\pi$
$739$	−9179.77	+	15899.8i	−0.456946	+	0.791454i	0.541851	+	0.840474i	$0.317724\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12890.4			−0.636478			−0.318239	−	0.948010i	$-0.603091\pi$
$743$	−12890.4			−0.636478			−0.318239	+	0.948010i	$0.603091\pi$
$744$		0			0
$745$	500.450	−	866.805i	0.0246108	−	0.0426272i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	975.075	+	30716.1i	0.0475680	+	1.49846i
$750$		0			0
$751$	−7695.10	−	13328.3i	−0.373899	−	0.647612i	0.616263	−	0.787541i	$-0.288646\pi$
$751$	−7695.10	−	13328.3i	−0.373899	−	0.647612i	−0.990162	+	0.139929i	$0.955313\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	17472.6			0.842241
$756$		0			0
$757$	13974.6			0.670957			0.335479	−	0.942048i	$-0.391102\pi$
$757$	13974.6			0.670957			0.335479	+	0.942048i	$0.391102\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1687.57	−	2922.96i	−0.0803868	−	0.139234i	0.823029	−	0.567999i	$-0.192282\pi$
$761$	−1687.57	−	2922.96i	−0.0803868	−	0.139234i	−0.903416	+	0.428765i	$0.858949\pi$
$762$		0			0
$763$	9425.40	−	5848.15i	0.447212	−	0.277480i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7843.99	−	13586.2i	0.369270	−	0.639595i
$768$		0			0
$769$	−31253.9			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$769$	−31253.9			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11581.8	−	20060.2i	0.538897	−	0.933396i	−0.460067	−	0.887884i	$-0.652175\pi$
$773$	11581.8	−	20060.2i	0.538897	−	0.933396i	0.998964	−	0.0455122i	$-0.0144920\pi$
$774$		0			0
$775$	957.411	+	1658.29i	0.0443758	+	0.0768611i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17270.9	+	29914.0i	0.794343	+	1.37584i
$780$		0			0
$781$	−7544.01	+	13066.6i	−0.345641	+	0.598668i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−13747.4			−0.625050
$786$		0			0
$787$	4951.47	−	8576.20i	0.224271	−	0.388448i	−0.731830	−	0.681488i	$-0.761333\pi$
$787$	4951.47	−	8576.20i	0.224271	−	0.388448i	0.956100	+	0.293039i	$0.0946667\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12760.2	−	6836.75i	−0.573580	−	0.307316i
$792$		0			0
$793$	7467.36	+	12933.8i	0.334393	+	0.579186i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16844.5			−0.748638			−0.374319	−	0.927300i	$-0.622123\pi$
$797$	−16844.5			−0.748638			−0.374319	+	0.927300i	$0.622123\pi$
$798$		0			0
$799$	7167.83			0.317371
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3137.55	+	5434.40i	0.137885	+	0.238824i
$804$		0			0
$805$	−14842.9	+	9209.52i	−0.649867	+	0.403221i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−17215.3	+	29817.8i	−0.748157	+	1.29585i	0.200549	+	0.979684i	$0.435728\pi$
$809$	−17215.3	+	29817.8i	−0.748157	+	1.29585i	−0.948705	+	0.316162i	$0.897606\pi$
$810$		0			0
$811$	−62.4498			−0.00270396			−0.00135198	−	0.999999i	$-0.500430\pi$
$811$	−62.4498			−0.00270396			−0.00135198	+	0.999999i	$0.500430\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	17760.3	−	30761.8i	0.763334	−	1.32213i
$816$		0			0
$817$	16964.6	+	29383.5i	0.726458	+	1.25826i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	19475.8	+	33733.1i	0.827906	+	1.43398i	0.899678	+	0.436555i	$0.143802\pi$
$821$	19475.8	+	33733.1i	0.827906	+	1.43398i	−0.0717711	+	0.997421i	$0.522865\pi$
$822$		0			0
$823$	17741.2	−	30728.6i	0.751420	−	1.30150i	−0.195715	−	0.980661i	$-0.562703\pi$
$823$	17741.2	−	30728.6i	0.751420	−	1.30150i	0.947135	−	0.320836i	$-0.103964\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7945.87			−0.334105			−0.167053	−	0.985948i	$-0.553425\pi$
$827$	−7945.87			−0.334105			−0.167053	+	0.985948i	$0.553425\pi$
$828$		0			0
$829$	−20318.2	+	35192.2i	−0.851243	+	1.47440i	0.0288439	+	0.999584i	$0.490817\pi$
$829$	−20318.2	+	35192.2i	−0.851243	+	1.47440i	−0.880087	+	0.474812i	$0.842516\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−26904.8	+	1709.90i	−1.11908	+	0.0711217i
$834$		0			0
$835$	5289.26	+	9161.26i	0.219212	+	0.379687i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−27723.5			−1.14079			−0.570394	−	0.821371i	$-0.693209\pi$
$839$	−27723.5			−1.14079			−0.570394	+	0.821371i	$0.693209\pi$
$840$		0			0
$841$	5547.19			0.227446
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−7440.04	−	12886.5i	−0.302893	−	0.524627i
$846$		0			0
$847$	−664.052	−	20918.5i	−0.0269387	−	0.848605i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	14480.2	−	25080.4i	0.583283	−	1.01028i
$852$		0			0
$853$	37599.1			1.50922			0.754612	−	0.656171i	$-0.227825\pi$
$853$	37599.1			1.50922			0.754612	+	0.656171i	$0.227825\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12805.0	−	22178.9i	0.510397	−	0.884034i	−0.489530	−	0.871986i	$-0.662832\pi$
$857$	12805.0	−	22178.9i	0.510397	−	0.884034i	0.999927	−	0.0120476i	$-0.00383496\pi$
$858$		0			0
$859$	1989.70	+	3446.26i	0.0790309	+	0.136886i	0.902832	−	0.429993i	$-0.141484\pi$
$859$	1989.70	+	3446.26i	0.0790309	+	0.136886i	−0.823801	+	0.566879i	$0.808151\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12410.2	−	21495.0i	−0.489510	−	0.847856i	0.510417	−	0.859927i	$-0.329491\pi$
$863$	−12410.2	−	21495.0i	−0.489510	−	0.847856i	−0.999927	+	0.0120708i	$0.996158\pi$
$864$		0			0
$865$	−9203.97	+	15941.7i	−0.361786	+	0.626631i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−647.823			−0.0252887
$870$		0			0
$871$	−7045.87	+	12203.8i	−0.274099	+	0.474754i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−24615.2	−	13188.5i	−0.951024	−	0.509545i
$876$		0			0
$877$	−25009.7	−	43318.1i	−0.962963	−	1.66790i	−0.714992	−	0.699133i	$-0.753570\pi$
$877$	−25009.7	−	43318.1i	−0.962963	−	1.66790i	−0.247971	−	0.968767i	$-0.579764\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	10386.4			0.397193			0.198596	−	0.980081i	$-0.436362\pi$
$881$	10386.4			0.397193			0.198596	+	0.980081i	$0.436362\pi$
$882$		0			0
$883$	36366.4			1.38599			0.692994	−	0.720944i	$-0.256291\pi$
$883$	36366.4			1.38599			0.692994	+	0.720944i	$0.256291\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3803.65	−	6588.12i	−0.143984	−	0.249388i	0.785009	−	0.619484i	$-0.212658\pi$
$887$	−3803.65	−	6588.12i	−0.143984	−	0.249388i	−0.928994	+	0.370096i	$0.879325\pi$
$888$		0			0
$889$	−414.195	−	221.920i	−0.0156261	−	0.00837227i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3336.65	+	5779.24i	−0.125035	+	0.216568i
$894$		0			0
$895$	−26451.1			−0.987891
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5817.61	−	10076.4i	0.215827	−	0.373823i
$900$		0			0
$901$	−6416.28	−	11113.3i	−0.237245	−	0.410920i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2267.90	+	3928.11i	0.0833011	+	0.144282i
$906$		0			0
$907$	−12901.5	+	22346.1i	−0.472314	+	0.818072i	−0.999498	−	0.0316794i	$-0.989914\pi$
$907$	−12901.5	+	22346.1i	−0.472314	+	0.818072i	0.527184	+	0.849751i	$0.323248\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−8165.21			−0.296954			−0.148477	−	0.988916i	$-0.547437\pi$
$911$	−8165.21			−0.296954			−0.148477	+	0.988916i	$0.547437\pi$
$912$		0			0
$913$	−4865.40	+	8427.12i	−0.176365	+	0.305473i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	279.461	+	8803.38i	0.0100639	+	0.317026i
$918$		0			0
$919$	−296.804	−	514.079i	−0.0106536	−	0.0184526i	0.860649	−	0.509198i	$-0.170058\pi$
$919$	−296.804	−	514.079i	−0.0106536	−	0.0184526i	−0.871303	+	0.490745i	$0.836725\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−27805.9			−0.991596
$924$		0			0
$925$	8589.84			0.305332
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16573.7	−	28706.5i	−0.585323	−	1.01381i	−0.994835	−	0.101504i	$-0.967635\pi$
$929$	−16573.7	−	28706.5i	−0.585323	−	1.01381i	0.409512	−	0.912305i	$-0.365699\pi$
$930$		0			0
$931$	11145.6	−	22488.7i	0.392356	−	0.791661i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5473.11	−	9479.70i	0.191433	−	0.331571i
$936$		0			0
$937$	−24883.8			−0.867575			−0.433788	−	0.901015i	$-0.642823\pi$
$937$	−24883.8			−0.867575			−0.433788	+	0.901015i	$0.642823\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13065.1	+	22629.5i	−0.452616	+	0.783954i	−0.998548	−	0.0538758i	$-0.982842\pi$
$941$	−13065.1	+	22629.5i	−0.452616	+	0.783954i	0.545932	+	0.837830i	$0.316176\pi$
$942$		0			0
$943$	22658.0	+	39244.8i	0.782445	+	1.35523i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3984.35	+	6901.09i	0.136720	+	0.236806i	0.926253	−	0.376902i	$-0.123011\pi$
$947$	3984.35	+	6901.09i	0.136720	+	0.236806i	−0.789533	+	0.613708i	$0.789677\pi$
$948$		0			0
$949$	−5782.24	+	10015.1i	−0.197786	+	0.342576i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6742.36			0.229178			0.114589	−	0.993413i	$-0.463445\pi$
$953$	6742.36			0.229178			0.114589	+	0.993413i	$0.463445\pi$
$954$		0			0
$955$	18494.2	−	32033.0i	0.626659	−	1.08541i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16658.3	+	10335.9i	−0.560923	+	0.348034i
$960$		0			0
$961$	12634.4	+	21883.4i	0.424101	+	0.734564i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−28749.2			−0.959035
$966$		0			0
$967$	−7202.50			−0.239521			−0.119760	−	0.992803i	$-0.538213\pi$
$967$	−7202.50			−0.239521			−0.119760	+	0.992803i	$0.538213\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6852.86	+	11869.5i	0.226487	+	0.392286i	0.956764	−	0.290864i	$-0.0939427\pi$
$971$	6852.86	+	11869.5i	0.226487	+	0.392286i	−0.730278	+	0.683150i	$0.760609\pi$
$972$		0			0
$973$	−42134.0	−	22574.8i	−1.38824	−	0.743798i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−28274.0	+	48972.0i	−0.925860	+	1.60364i	−0.135687	+	0.990752i	$0.543324\pi$
$977$	−28274.0	+	48972.0i	−0.925860	+	1.60364i	−0.790173	+	0.612884i	$0.790009\pi$
$978$		0			0
$979$	−9357.71			−0.305489
$980$		0			0
$981$		0			0
$982$		0			0
$983$	8681.87	−	15037.4i	0.281698	−	0.487914i	−0.690105	−	0.723709i	$-0.742436\pi$
$983$	8681.87	−	15037.4i	0.281698	−	0.487914i	0.971803	+	0.235794i	$0.0757692\pi$
$984$		0			0
$985$	−24785.6	−	42930.0i	−0.801762	−	1.38869i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	22256.2	+	38548.8i	0.715576	+	1.23941i
$990$		0			0
$991$	−24519.7	+	42469.4i	−0.785968	+	1.36134i	0.142451	+	0.989802i	$0.454502\pi$
$991$	−24519.7	+	42469.4i	−0.785968	+	1.36134i	−0.928419	+	0.371535i	$0.878832\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−42170.3			−1.34361
$996$		0			0
$997$	4558.30	−	7895.21i	0.144797	−	0.250796i	−0.784500	−	0.620129i	$-0.787080\pi$
$997$	4558.30	−	7895.21i	0.144797	−	0.250796i	0.929297	+	0.369333i	$0.120414\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.k.d.109.2		4
3.2	odd	2		84.4.i.b.25.1	✓	4
7.2	even	3	inner	252.4.k.d.37.2		4
7.3	odd	6		1764.4.a.p.1.2		2
7.4	even	3		1764.4.a.x.1.1		2
7.5	odd	6		1764.4.k.z.1549.1		4
7.6	odd	2		1764.4.k.z.361.1		4
12.11	even	2		336.4.q.h.193.1		4
21.2	odd	6		84.4.i.b.37.1	yes	4
21.5	even	6		588.4.i.i.373.2		4
21.11	odd	6		588.4.a.g.1.2		2
21.17	even	6		588.4.a.h.1.1		2
21.20	even	2		588.4.i.i.361.2		4
84.11	even	6		2352.4.a.cb.1.2		2
84.23	even	6		336.4.q.h.289.1		4
84.59	odd	6		2352.4.a.bp.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.i.b.25.1	✓	4	3.2	odd	2
84.4.i.b.37.1	yes	4	21.2	odd	6
252.4.k.d.37.2		4	7.2	even	3	inner
252.4.k.d.109.2		4	1.1	even	1	trivial
336.4.q.h.193.1		4	12.11	even	2
336.4.q.h.289.1		4	84.23	even	6
588.4.a.g.1.2		2	21.11	odd	6
588.4.a.h.1.1		2	21.17	even	6
588.4.i.i.361.2		4	21.20	even	2
588.4.i.i.373.2		4	21.5	even	6
1764.4.a.p.1.2		2	7.3	odd	6
1764.4.a.x.1.1		2	7.4	even	3
1764.4.k.z.361.1		4	7.6	odd	2
1764.4.k.z.1549.1		4	7.5	odd	6
2352.4.a.bp.1.1		2	84.59	odd	6
2352.4.a.cb.1.2		2	84.11	even	6

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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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.91238 + 8.50848i) q^{5} +(-16.3248 - 8.74657i) q^{7} +O(q^{10})\)	\(q+(4.91238 + 8.50848i) q^{5} +(-16.3248 - 8.74657i) q^{7} +(-7.08762 + 12.2761i) q^{11} -26.1238 q^{13} +(-39.2990 + 68.0679i) q^{17} +(-36.5876 - 63.3716i) q^{19} +(-48.0000 - 83.1384i) q^{23} +(14.2371 - 24.6594i) q^{25} -173.021 q^{29} +(-33.6238 + 58.2381i) q^{31} +(-5.77326 - 181.865i) q^{35} +(150.835 + 261.254i) q^{37} -472.042 q^{41} -463.670 q^{43} +(-45.5980 - 78.9781i) q^{47} +(189.995 + 285.571i) q^{49} +(-81.6341 + 141.394i) q^{53} -139.268 q^{55} +(-300.263 + 520.071i) q^{59} +(-285.846 - 495.099i) q^{61} +(-128.330 - 222.274i) q^{65} +(269.711 - 467.154i) q^{67} +1064.39 q^{71} +(221.340 - 383.372i) q^{73} +(223.078 - 138.412i) q^{77} +(22.8505 + 39.5782i) q^{79} +686.464 q^{83} -772.206 q^{85} +(330.072 + 571.702i) q^{89} +(426.464 + 228.493i) q^{91} +(359.464 - 622.610i) q^{95} +658.320 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{5} - 20 q^{7}+O(q^{10}) \) 4 * q - 3 * q^5 - 20 * q^7	\( 4 q - 3 q^{5} - 20 q^{7} - 51 q^{11} + 122 q^{13} + 24 q^{17} - 169 q^{19} - 192 q^{23} - 11 q^{25} + 78 q^{29} + 92 q^{31} + 294 q^{35} + 173 q^{37} - 348 q^{41} - 994 q^{43} + 180 q^{47} - 146 q^{49} + 285 q^{53} + 666 q^{55} - 1269 q^{59} - 328 q^{61} - 1374 q^{65} + 875 q^{67} + 2808 q^{71} + 1361 q^{73} - 897 q^{77} + 182 q^{79} + 798 q^{83} - 4176 q^{85} + 822 q^{89} + 1955 q^{91} - 510 q^{95} + 1682 q^{97}+O(q^{100}) \) 4 * q - 3 * q^5 - 20 * q^7 - 51 * q^11 + 122 * q^13 + 24 * q^17 - 169 * q^19 - 192 * q^23 - 11 * q^25 + 78 * q^29 + 92 * q^31 + 294 * q^35 + 173 * q^37 - 348 * q^41 - 994 * q^43 + 180 * q^47 - 146 * q^49 + 285 * q^53 + 666 * q^55 - 1269 * q^59 - 328 * q^61 - 1374 * q^65 + 875 * q^67 + 2808 * q^71 + 1361 * q^73 - 897 * q^77 + 182 * q^79 + 798 * q^83 - 4176 * q^85 + 822 * q^89 + 1955 * q^91 - 510 * q^95 + 1682 * q^97

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