LMFDB - Embedded newform 325.4.d.c.324.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,4,Mod(324,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.324"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	325.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [14,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.1756207519$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 84x^{12} + 2674x^{10} + 40048x^{8} + 278769x^{6} + 727552x^{4} + 339456x^{2} + 9216 $ x^14 + 84x^12 + 2674x^10 + 40048x^8 + 278769x^6 + 727552x^4 + 339456x^2 + 9216
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			324.12
Root			$4.27643i$ of defining polynomial
Character	$\chi$	$=$	325.324
Dual form			325.4.d.c.324.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.27643 q^{2} +7.17327i q^{3} +10.2878 q^{4} +30.6760i q^{6} -5.20875 q^{7} +9.78383 q^{8} -24.4558 q^{9} +46.2698i q^{11} +73.7975i q^{12} +(-15.5139 + 44.2303i) q^{13} -22.2749 q^{14} -40.4629 q^{16} -14.9028i q^{17} -104.584 q^{18} -75.6973i q^{19} -37.3638i q^{21} +197.869i q^{22} +134.654i q^{23} +70.1820i q^{24} +(-66.3442 + 189.148i) q^{26} +18.2501i q^{27} -53.5869 q^{28} +236.857 q^{29} -65.0786i q^{31} -251.308 q^{32} -331.906 q^{33} -63.7309i q^{34} -251.598 q^{36} +311.148 q^{37} -323.714i q^{38} +(-317.276 - 111.286i) q^{39} -86.3371i q^{41} -159.784i q^{42} -299.321i q^{43} +476.016i q^{44} +575.840i q^{46} +108.671 q^{47} -290.252i q^{48} -315.869 q^{49} +106.902 q^{51} +(-159.605 + 455.035i) q^{52} +700.355i q^{53} +78.0454i q^{54} -50.9615 q^{56} +542.997 q^{57} +1012.90 q^{58} -287.115i q^{59} +59.0462 q^{61} -278.304i q^{62} +127.384 q^{63} -750.996 q^{64} -1419.37 q^{66} -304.295 q^{67} -153.318i q^{68} -965.912 q^{69} -274.262i q^{71} -239.271 q^{72} +835.177 q^{73} +1330.60 q^{74} -778.762i q^{76} -241.008i q^{77} +(-1356.81 - 475.905i) q^{78} +382.320 q^{79} -791.220 q^{81} -369.214i q^{82} +1493.88 q^{83} -384.393i q^{84} -1280.03i q^{86} +1699.04i q^{87} +452.695i q^{88} +1498.07i q^{89} +(80.8082 - 230.385i) q^{91} +1385.30i q^{92} +466.827 q^{93} +464.725 q^{94} -1802.70i q^{96} +1509.05 q^{97} -1350.79 q^{98} -1131.56i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{2} + 56 q^{4} + 108 q^{7} - 48 q^{8} - 158 q^{9} + 6 q^{13} + 152 q^{14} + 280 q^{16} - 272 q^{18} - 344 q^{26} + 572 q^{28} - 588 q^{29} - 1788 q^{32} + 248 q^{33} + 496 q^{36} + 940 q^{37}+ \cdots + 7364 q^{98}+O(q^{100}) $ 14 * q - 4 * q^2 + 56 * q^4 + 108 * q^7 - 48 * q^8 - 158 * q^9 + 6 * q^13 + 152 * q^14 + 280 * q^16 - 272 * q^18 - 344 * q^26 + 572 * q^28 - 588 * q^29 - 1788 * q^32 + 248 * q^33 + 496 * q^36 + 940 * q^37 + 260 * q^39 + 772 * q^47 + 1302 * q^49 + 176 * q^51 + 2068 * q^52 + 512 * q^56 + 1752 * q^57 + 3316 * q^58 - 1460 * q^61 - 5604 * q^63 - 1296 * q^64 - 600 * q^66 - 3292 * q^67 - 4160 * q^69 - 4572 * q^72 + 3220 * q^73 + 5928 * q^74 - 7636 * q^78 + 1024 * q^79 - 2890 * q^81 - 452 * q^83 + 916 * q^91 + 3936 * q^93 - 2656 * q^94 - 3964 * q^97 + 7364 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$-1$

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 $

$2$	4.27643			1.51195			0.755973	−	0.654603i	$-0.227164\pi$
$2$	4.27643			1.51195			0.755973	+	0.654603i	$0.227164\pi$
$3$			7.17327i			1.38050i	0.723573	+	0.690248i	$0.242499\pi$
$3$			7.17327i			1.38050i	−0.723573	+	0.690248i	$0.757501\pi$
$4$	10.2878			1.28598
$5$		0			0
$5$		0			0
$6$			30.6760i			2.08724i
$7$	−5.20875			−0.281246			−0.140623	−	0.990063i	$-0.544911\pi$
$7$	−5.20875			−0.281246			−0.140623	+	0.990063i	$0.544911\pi$
$8$	9.78383			0.432388
$9$	−24.4558			−0.905771
$10$		0			0
$11$			46.2698i			1.26826i	0.773227	+	0.634130i	$0.218642\pi$
$11$			46.2698i			1.26826i	−0.773227	+	0.634130i	$0.781358\pi$
$12$			73.7975i			1.77529i
$13$	−15.5139	+	44.2303i	−0.330984	+	0.943637i
$13$	−15.5139	+	44.2303i	−0.330984	+	0.943637i
$14$	−22.2749			−0.425229
$15$		0			0
$16$	−40.4629			−0.632234
$17$		−	14.9028i		−	0.212616i	−0.994333	−	0.106308i	$-0.966097\pi$
$17$		−	14.9028i		−	0.212616i	0.994333	−	0.106308i	$-0.0339029\pi$
$18$	−104.584			−1.36948
$19$		−	75.6973i		−	0.914008i	−0.889465	−	0.457004i	$-0.848923\pi$
$19$		−	75.6973i		−	0.914008i	0.889465	−	0.457004i	$-0.151077\pi$
$20$		0			0
$21$		−	37.3638i		−	0.388259i
$22$			197.869i			1.91754i
$23$			134.654i			1.22075i	0.792111	+	0.610377i	$0.208982\pi$
$23$			134.654i			1.22075i	−0.792111	+	0.610377i	$0.791018\pi$
$24$			70.1820i			0.596910i
$25$		0			0
$26$	−66.3442	+	189.148i	−0.500429	+	1.42673i
$27$			18.2501i			0.130083i
$28$	−53.5869			−0.361677
$29$	236.857			1.51666			0.758332	−	0.651868i	$-0.226014\pi$
$29$	236.857			1.51666			0.758332	+	0.651868i	$0.226014\pi$
$30$		0			0
$31$		−	65.0786i		−	0.377047i	−0.982069	−	0.188524i	$-0.939630\pi$
$31$		−	65.0786i		−	0.377047i	0.982069	−	0.188524i	$-0.0603702\pi$
$32$	−251.308			−1.38829
$33$	−331.906			−1.75083
$34$		−	63.7309i		−	0.321463i
$35$		0			0
$36$	−251.598			−1.16480
$37$	311.148			1.38250			0.691249	−	0.722617i	$-0.257061\pi$
$37$	311.148			1.38250			0.691249	+	0.722617i	$0.257061\pi$
$38$		−	323.714i		−	1.38193i
$39$	−317.276	−	111.286i	−1.30269	−	0.456922i
$40$		0			0
$41$		−	86.3371i		−	0.328868i	−0.986388	−	0.164434i	$-0.947420\pi$
$41$		−	86.3371i		−	0.328868i	0.986388	−	0.164434i	$-0.0525798\pi$
$42$		−	159.784i		−	0.587027i
$43$		−	299.321i		−	1.06154i	−0.847517	−	0.530768i	$-0.821903\pi$
$43$		−	299.321i		−	1.06154i	0.847517	−	0.530768i	$-0.178097\pi$
$44$			476.016i			1.63096i
$45$		0			0
$46$			575.840i			1.84572i
$47$	108.671			0.337263			0.168631	−	0.985679i	$-0.446065\pi$
$47$	108.671			0.337263			0.168631	+	0.985679i	$0.446065\pi$
$48$		−	290.252i		−	0.872796i
$49$	−315.869			−0.920901
$50$		0			0
$51$	106.902			0.293515
$52$	−159.605	+	455.035i	−0.425639	+	1.21350i
$53$			700.355i			1.81512i	0.419926	+	0.907558i	$0.362056\pi$
$53$			700.355i			1.81512i	−0.419926	+	0.907558i	$0.637944\pi$
$54$			78.0454i			0.196678i
$55$		0			0
$56$	−50.9615			−0.121608
$57$	542.997			1.26178
$58$	1012.90			2.29312
$59$		−	287.115i		−	0.633546i	−0.948501	−	0.316773i	$-0.897401\pi$
$59$		−	287.115i		−	0.633546i	0.948501	−	0.316773i	$-0.102599\pi$
$60$		0			0
$61$	59.0462			0.123936			0.0619680	−	0.998078i	$-0.480262\pi$
$61$	59.0462			0.123936			0.0619680	+	0.998078i	$0.480262\pi$
$62$		−	278.304i		−	0.570075i
$63$	127.384			0.254745
$64$	−750.996			−1.46679
$65$		0			0
$66$	−1419.37			−2.64716
$67$	−304.295			−0.554859			−0.277429	−	0.960746i	$-0.589482\pi$
$67$	−304.295			−0.554859			−0.277429	+	0.960746i	$0.589482\pi$
$68$		−	153.318i		−	0.273420i
$69$	−965.912			−1.68525
$70$		0			0
$71$		−	274.262i		−	0.458435i	−0.973375	−	0.229217i	$-0.926383\pi$
$71$		−	274.262i		−	0.458435i	0.973375	−	0.229217i	$-0.0736167\pi$
$72$	−239.271			−0.391645
$73$	835.177			1.33904			0.669521	−	0.742793i	$-0.266499\pi$
$73$	835.177			1.33904			0.669521	+	0.742793i	$0.266499\pi$
$74$	1330.60			2.09026
$75$		0			0
$76$		−	778.762i		−	1.17540i
$77$		−	241.008i		−	0.356693i
$78$	−1356.81	−	475.905i	−1.96959	−	0.690841i
$79$	382.320			0.544486			0.272243	−	0.962229i	$-0.412235\pi$
$79$	382.320			0.544486			0.272243	+	0.962229i	$0.412235\pi$
$80$		0			0
$81$	−791.220			−1.08535
$82$		−	369.214i		−	0.497231i
$83$	1493.88			1.97559			0.987797	−	0.155746i	$-0.0497782\pi$
$83$	1493.88			1.97559			0.987797	+	0.155746i	$0.0497782\pi$
$84$		−	384.393i		−	0.499294i
$85$		0			0
$86$		−	1280.03i		−	1.60499i
$87$			1699.04i			2.09375i
$88$			452.695i			0.548381i
$89$			1498.07i			1.78421i	0.451827	+	0.892106i	$0.350772\pi$
$89$			1498.07i			1.78421i	−0.451827	+	0.892106i	$0.649228\pi$
$90$		0			0
$91$	80.8082	−	230.385i	0.0930879	−	0.265394i
$92$			1385.30i			1.56987i
$93$	466.827			0.520513
$94$	464.725			0.509923
$95$		0			0
$96$		−	1802.70i		−	1.91653i
$97$	1509.05			1.57959			0.789797	−	0.613369i	$-0.210186\pi$
$97$	1509.05			1.57959			0.789797	+	0.613369i	$0.210186\pi$
$98$	−1350.79			−1.39235
$99$		−	1131.56i		−	1.14875i
$100$		0			0
$101$	1559.39			1.53629			0.768144	−	0.640277i	$-0.221180\pi$
$101$	1559.39			1.53629			0.768144	+	0.640277i	$0.221180\pi$
$102$	457.159			0.443779
$103$			519.651i			0.497114i	0.968617	+	0.248557i	$0.0799563\pi$
$103$			519.651i			0.497114i	−0.968617	+	0.248557i	$0.920044\pi$
$104$	−151.785	+	432.742i	−0.143113	+	0.408017i
$105$		0			0
$106$			2995.02i			2.74436i
$107$		−	1678.80i		−	1.51678i	−0.651801	−	0.758390i	$-0.725986\pi$
$107$		−	1678.80i		−	1.51678i	0.651801	−	0.758390i	$-0.274014\pi$
$108$			187.755i			0.167284i
$109$		−	484.862i		−	0.426068i	−0.977045	−	0.213034i	$-0.931666\pi$
$109$		−	484.862i		−	0.426068i	0.977045	−	0.213034i	$-0.0683344\pi$
$110$		0			0
$111$			2231.95i			1.90853i
$112$	210.762			0.177813
$113$			394.703i			0.328589i	0.986411	+	0.164294i	$0.0525347\pi$
$113$			394.703i			0.328589i	−0.986411	+	0.164294i	$0.947465\pi$
$114$	2322.09			1.90775
$115$		0			0
$116$	2436.75			1.95040
$117$	379.405	−	1081.69i	0.299795	−	0.854718i
$118$		−	1227.83i		−	0.957888i
$119$			77.6251i			0.0597973i
$120$		0			0
$121$	−809.891			−0.608483
$122$	252.507			0.187384
$123$	619.319			0.454001
$124$		−	669.519i		−	0.484876i
$125$		0			0
$126$	544.750			0.385160
$127$		−	887.714i		−	0.620251i	−0.950696	−	0.310125i	$-0.899629\pi$
$127$		−	887.714i		−	0.620251i	0.950696	−	0.310125i	$-0.100371\pi$
$128$	−1201.12			−0.829413
$129$	2147.11			1.46545
$130$		0			0
$131$	655.450			0.437152			0.218576	−	0.975820i	$-0.429859\pi$
$131$	655.450			0.437152			0.218576	+	0.975820i	$0.429859\pi$
$132$	−3414.59			−2.25153
$133$			394.289i			0.257061i
$134$	−1301.30			−0.838916
$135$		0			0
$136$		−	145.807i		−	0.0919325i
$137$	−2649.45			−1.65224			−0.826122	−	0.563492i	$-0.809458\pi$
$137$	−2649.45			−1.65224			−0.826122	+	0.563492i	$0.809458\pi$
$138$	−4130.65			−2.54800
$139$	−1580.06			−0.964165			−0.482082	−	0.876126i	$-0.660119\pi$
$139$	−1580.06			−0.964165			−0.482082	+	0.876126i	$0.660119\pi$
$140$		0			0
$141$			779.529i			0.465590i
$142$		−	1172.86i		−	0.693129i
$143$	−2046.52	−	717.825i	−1.19678	−	0.419773i
$144$	989.554			0.572659
$145$		0			0
$146$	3571.58			2.02456
$147$		−	2265.81i		−	1.27130i
$148$	3201.04			1.77787
$149$		−	1407.22i		−	0.773720i	−0.922138	−	0.386860i	$-0.873560\pi$
$149$		−	1407.22i		−	0.773720i	0.922138	−	0.386860i	$-0.126440\pi$
$150$		0			0
$151$		−	920.413i		−	0.496041i	−0.968755	−	0.248020i	$-0.920220\pi$
$151$		−	920.413i		−	0.496041i	0.968755	−	0.248020i	$-0.0797800\pi$
$152$		−	740.609i		−	0.395206i
$153$			364.461i			0.192581i
$154$		−	1030.65i		−	0.539301i
$155$		0			0
$156$	−3264.09	−	1144.89i	−1.67523	−	0.587593i
$157$			3431.29i			1.74425i	0.489285	+	0.872124i	$0.337258\pi$
$157$			3431.29i			1.74425i	−0.489285	+	0.872124i	$0.662742\pi$
$158$	1634.97			0.823233
$159$	−5023.84			−2.50576
$160$		0			0
$161$		−	701.381i		−	0.343333i
$162$	−3383.60			−1.64099
$163$	−1484.20			−0.713202			−0.356601	−	0.934257i	$-0.616064\pi$
$163$	−1484.20			−0.713202			−0.356601	+	0.934257i	$0.616064\pi$
$164$		−	888.223i		−	0.422918i
$165$		0			0
$166$	6388.46			2.98699
$167$	−1117.08			−0.517618			−0.258809	−	0.965928i	$-0.583330\pi$
$167$	−1117.08			−0.517618			−0.258809	+	0.965928i	$0.583330\pi$
$168$		−	365.561i		−	0.167879i
$169$	−1715.64	−	1372.37i	−0.780900	−	0.624656i
$170$		0			0
$171$			1851.24i			0.827882i
$172$		−	3079.37i		−	1.36512i
$173$			607.660i			0.267049i	0.991046	+	0.133525i	$0.0426295\pi$
$173$			607.660i			0.267049i	−0.991046	+	0.133525i	$0.957370\pi$
$174$			7265.83i			3.16564i
$175$		0			0
$176$		−	1872.21i		−	0.801836i
$177$	2059.56			0.874609
$178$			6406.38i			2.69763i
$179$	−1108.31			−0.462789			−0.231394	−	0.972860i	$-0.574329\pi$
$179$	−1108.31			−0.462789			−0.231394	+	0.972860i	$0.574329\pi$
$180$		0			0
$181$	−2128.97			−0.874282			−0.437141	−	0.899393i	$-0.644009\pi$
$181$	−2128.97			−0.874282			−0.437141	+	0.899393i	$0.644009\pi$
$182$	345.570	−	985.224i	0.140744	−	0.401262i
$183$			423.554i			0.171093i
$184$			1317.43i			0.527840i
$185$		0			0
$186$	1996.35			0.786987
$187$	689.550			0.269652
$188$	1117.99			0.433713
$189$		−	95.0605i		−	0.0365853i
$190$		0			0
$191$	−3817.85			−1.44634			−0.723168	−	0.690672i	$-0.757315\pi$
$191$	−3817.85			−1.44634			−0.723168	+	0.690672i	$0.757315\pi$
$192$		−	5387.09i		−	2.02490i
$193$	−2166.14			−0.807888			−0.403944	−	0.914784i	$-0.632361\pi$
$193$	−2166.14			−0.807888			−0.403944	+	0.914784i	$0.632361\pi$
$194$	6453.33			2.38826
$195$		0			0
$196$	−3249.61			−1.18426
$197$	2149.88			0.777528			0.388764	−	0.921337i	$-0.372902\pi$
$197$	2149.88			0.777528			0.388764	+	0.921337i	$0.372902\pi$
$198$		−	4839.06i		−	1.73685i
$199$	−1058.52			−0.377066			−0.188533	−	0.982067i	$-0.560373\pi$
$199$	−1058.52			−0.377066			−0.188533	+	0.982067i	$0.560373\pi$
$200$		0			0
$201$		−	2182.79i		−	0.765980i
$202$	6668.62			2.32279
$203$	−1233.73			−0.426556
$204$	1099.79			0.377455
$205$		0			0
$206$			2222.25i			0.751609i
$207$		−	3293.08i		−	1.10572i
$208$	627.739	−	1789.69i	0.209259	−	0.596599i
$209$	3502.50			1.15920
$210$		0			0
$211$	790.886			0.258042			0.129021	−	0.991642i	$-0.458817\pi$
$211$	790.886			0.258042			0.129021	+	0.991642i	$0.458817\pi$
$212$			7205.15i			2.33421i
$213$	1967.35			0.632868
$214$		−	7179.25i		−	2.29329i
$215$		0			0
$216$			178.556i			0.0562463i
$217$			338.979i			0.106043i
$218$		−	2073.48i		−	0.644191i
$219$			5990.95i			1.84854i
$220$		0			0
$221$	659.156	+	231.201i	0.200632	+	0.0703723i
$222$			9544.77i			2.88560i
$223$	5308.17			1.59400			0.796999	−	0.603981i	$-0.206420\pi$
$223$	5308.17			1.59400			0.796999	+	0.603981i	$0.206420\pi$
$224$	1309.00			0.390452
$225$		0			0
$226$			1687.92i			0.496808i
$227$	−2102.49			−0.614744			−0.307372	−	0.951589i	$-0.599450\pi$
$227$	−2102.49			−0.614744			−0.307372	+	0.951589i	$0.599450\pi$
$228$	5586.27			1.62263
$229$		−	4856.91i		−	1.40154i	−0.713385	−	0.700772i	$-0.752839\pi$
$229$		−	4856.91i		−	1.40154i	0.713385	−	0.700772i	$-0.247161\pi$
$230$		0			0
$231$	1728.81			0.492414
$232$	2317.37			0.655788
$233$			3496.48i			0.983100i	0.870849	+	0.491550i	$0.163569\pi$
$233$			3496.48i			0.983100i	−0.870849	+	0.491550i	$0.836431\pi$
$234$	1622.50	−	4625.76i	0.453274	−	1.29229i
$235$		0			0
$236$		−	2953.80i		−	0.814729i
$237$			2742.49i			0.751661i
$238$			331.958i			0.0904103i
$239$			702.746i			0.190196i	0.995468	+	0.0950980i	$0.0303165\pi$
$239$			702.746i			0.190196i	−0.995468	+	0.0950980i	$0.969684\pi$
$240$		0			0
$241$		−	5568.46i		−	1.48837i	−0.667976	−	0.744183i	$-0.732839\pi$
$241$		−	5568.46i		−	1.48837i	0.667976	−	0.744183i	$-0.267161\pi$
$242$	−3463.44			−0.919993
$243$		−	5182.88i		−	1.36824i
$244$	607.458			0.159379
$245$		0			0
$246$	2648.48			0.686425
$247$	3348.11	+	1174.36i	0.862491	+	0.302522i
$248$		−	636.718i		−	0.163031i
$249$			10716.0i			2.72730i
$250$		0			0
$251$	−5277.22			−1.32707			−0.663536	−	0.748144i	$-0.730945\pi$
$251$	−5277.22			−1.32707			−0.663536	+	0.748144i	$0.730945\pi$
$252$	1310.51			0.327597
$253$	−6230.42			−1.54823
$254$		−	3796.24i		−	0.937786i
$255$		0			0
$256$	871.464			0.212760
$257$			1979.47i			0.480451i	0.970717	+	0.240225i	$0.0772214\pi$
$257$			1979.47i			0.480451i	−0.970717	+	0.240225i	$0.922779\pi$
$258$	9181.98			2.21568
$259$	−1620.69			−0.388822
$260$		0			0
$261$	−5792.54			−1.37375
$262$	2802.99			0.660951
$263$		−	4482.39i		−	1.05094i	−0.850813	−	0.525468i	$-0.823890\pi$
$263$		−	4482.39i		−	1.05094i	0.850813	−	0.525468i	$-0.176110\pi$
$264$	−3247.31			−0.757037
$265$		0			0
$266$			1686.15i			0.388663i
$267$	−10746.0			−2.46310
$268$	−3130.54			−0.713538
$269$	4789.32			1.08554			0.542770	−	0.839881i	$-0.317376\pi$
$269$	4789.32			1.08554			0.542770	+	0.839881i	$0.317376\pi$
$270$		0			0
$271$		−	4617.30i		−	1.03499i	−0.855687	−	0.517493i	$-0.826865\pi$
$271$		−	4617.30i		−	1.03499i	0.855687	−	0.517493i	$-0.173135\pi$
$272$			603.012i			0.134423i
$273$	1652.61	+	579.659i	0.366376	+	0.128508i
$274$	−11330.2			−2.49810
$275$		0			0
$276$	−9937.15			−2.16720
$277$		−	4143.04i		−	0.898669i	−0.893364	−	0.449335i	$-0.851661\pi$
$277$		−	4143.04i		−	0.898669i	0.893364	−	0.449335i	$-0.148339\pi$
$278$	−6757.01			−1.45776
$279$			1591.55i			0.341519i
$280$		0			0
$281$			1563.53i			0.331929i	0.986132	+	0.165965i	$0.0530737\pi$
$281$			1563.53i			0.331929i	−0.986132	+	0.165965i	$0.946926\pi$
$282$			3333.60i			0.703947i
$283$			5234.56i			1.09951i	0.835325	+	0.549757i	$0.185280\pi$
$283$			5234.56i			1.09951i	−0.835325	+	0.549757i	$0.814720\pi$
$284$		−	2821.56i		−	0.589539i
$285$		0			0
$286$	−8751.82	−	3069.73i	−1.80946	−	0.634674i
$287$			449.709i			0.0924929i
$288$	6145.93			1.25747
$289$	4690.91			0.954795
$290$		0			0
$291$			10824.8i			2.18062i
$292$	8592.18			1.72198
$293$	4585.84			0.914360			0.457180	−	0.889374i	$-0.348860\pi$
$293$	4585.84			0.914360			0.457180	+	0.889374i	$0.348860\pi$
$294$		−	9689.59i		−	1.92214i
$295$		0			0
$296$	3044.22			0.597775
$297$	−844.429			−0.164979
$298$		−	6017.90i		−	1.16982i
$299$	−5955.80	−	2089.02i	−1.15195	−	0.404050i
$300$		0			0
$301$			1559.09i			0.298553i
$302$		−	3936.08i		−	0.749987i
$303$			11185.9i			2.12084i
$304$			3062.94i			0.577866i
$305$		0			0
$306$			1558.59i			0.291172i
$307$	−249.025			−0.0462951			−0.0231476	−	0.999732i	$-0.507369\pi$
$307$	−249.025			−0.0462951			−0.0231476	+	0.999732i	$0.507369\pi$
$308$		−	2479.45i		−	0.458701i
$309$	−3727.60			−0.686264
$310$		0			0
$311$	−2153.58			−0.392663			−0.196331	−	0.980538i	$-0.562903\pi$
$311$	−2153.58			−0.392663			−0.196331	+	0.980538i	$0.562903\pi$
$312$	−3104.17	−	1088.80i	−0.563266	−	0.197568i
$313$			2176.57i			0.393057i	0.980498	+	0.196529i	$0.0629669\pi$
$313$			2176.57i			0.393057i	−0.980498	+	0.196529i	$0.937033\pi$
$314$			14673.7i			2.63721i
$315$		0			0
$316$	3933.25			0.700199
$317$	−8235.91			−1.45923			−0.729614	−	0.683860i	$-0.760300\pi$
$317$	−8235.91			−1.45923			−0.729614	+	0.683860i	$0.760300\pi$
$318$	−21484.1			−3.78858
$319$			10959.3i			1.92353i
$320$		0			0
$321$	12042.5			2.09391
$322$		−	2999.41i		−	0.519101i
$323$	−1128.10			−0.194332
$324$	−8139.95			−1.39574
$325$		0			0
$326$	−6347.10			−1.07832
$327$	3478.05			0.588185
$328$		−	844.707i		−	0.142199i
$329$	−566.042			−0.0948538
$330$		0			0
$331$			6321.70i			1.04976i	0.851175	+	0.524882i	$0.175891\pi$
$331$			6321.70i			1.04976i	−0.851175	+	0.524882i	$0.824109\pi$
$332$	15368.8			2.54058
$333$	−7609.37			−1.25223
$334$	−4777.12			−0.782611
$335$		0			0
$336$			1511.85i			0.245471i
$337$			2558.47i			0.413558i	0.978388	+	0.206779i	$0.0662981\pi$
$337$			2558.47i			0.413558i	−0.978388	+	0.206779i	$0.933702\pi$
$338$	−7336.80	−	5868.84i	−1.18068	−	0.944447i
$339$	−2831.31			−0.453615
$340$		0			0
$341$	3011.17			0.478194
$342$			7916.69i			1.25171i
$343$	3431.89			0.540246
$344$		−	2928.51i		−	0.458996i
$345$		0			0
$346$			2598.61i			0.403764i
$347$			1820.72i			0.281675i	0.990033	+	0.140838i	$0.0449795\pi$
$347$			1820.72i			0.281675i	−0.990033	+	0.140838i	$0.955020\pi$
$348$			17479.5i			2.69252i
$349$			3806.77i			0.583873i	0.956438	+	0.291936i	$0.0942995\pi$
$349$			3806.77i			0.583873i	−0.956438	+	0.291936i	$0.905700\pi$
$350$		0			0
$351$	−807.209	−	283.131i	−0.122751	−	0.0430553i
$352$		−	11627.9i		−	1.76071i
$353$	4682.27			0.705983			0.352992	−	0.935626i	$-0.385164\pi$
$353$	4682.27			0.705983			0.352992	+	0.935626i	$0.385164\pi$
$354$	8807.55			1.32236
$355$		0			0
$356$			15411.9i			2.29446i
$357$	−556.826			−0.0825500
$358$	−4739.62			−0.699712
$359$		−	6697.05i		−	0.984560i	−0.870437	−	0.492280i	$-0.836164\pi$
$359$		−	6697.05i		−	0.984560i	0.870437	−	0.492280i	$-0.163836\pi$
$360$		0			0
$361$	1128.92			0.164590
$362$	−9104.38			−1.32187
$363$		−	5809.56i		−	0.840008i
$364$	831.342	−	2370.16i	0.119709	−	0.341292i
$365$		0			0
$366$			1811.30i			0.258684i
$367$		−	5163.48i		−	0.734418i	−0.930139	−	0.367209i	$-0.880313\pi$
$367$		−	5163.48i		−	0.734418i	0.930139	−	0.367209i	$-0.119687\pi$
$368$		−	5448.51i		−	0.771802i
$369$			2111.44i			0.297879i
$370$		0			0
$371$		−	3647.98i		−	0.510495i
$372$	4802.64			0.669370
$373$		−	5394.69i		−	0.748864i	−0.927254	−	0.374432i	$-0.877838\pi$
$373$		−	5394.69i		−	0.748864i	0.927254	−	0.374432i	$-0.122162\pi$
$374$	2948.81			0.407699
$375$		0			0
$376$	1063.22			0.145828
$377$	−3674.58	+	10476.3i	−0.501991	+	1.43118i
$378$		−	406.519i		−	0.0553151i
$379$		−	7982.32i		−	1.08186i	−0.841068	−	0.540929i	$-0.818073\pi$
$379$		−	7982.32i		−	1.08186i	0.841068	−	0.540929i	$-0.181927\pi$
$380$		0			0
$381$	6367.81			0.856254
$382$	−16326.8			−2.18678
$383$	−4886.18			−0.651886			−0.325943	−	0.945389i	$-0.605682\pi$
$383$	−4886.18			−0.651886			−0.325943	+	0.945389i	$0.605682\pi$
$384$		−	8615.95i		−	1.14500i
$385$		0			0
$386$	−9263.36			−1.22148
$387$			7320.15i			0.961509i
$388$	15524.9			2.03133
$389$	3376.51			0.440092			0.220046	−	0.975490i	$-0.429379\pi$
$389$	3376.51			0.440092			0.220046	+	0.975490i	$0.429379\pi$
$390$		0			0
$391$	2006.73			0.259552
$392$	−3090.41			−0.398187
$393$			4701.72i			0.603487i
$394$	9193.83			1.17558
$395$		0			0
$396$		−	11641.4i		−	1.47727i
$397$	−4446.60			−0.562137			−0.281069	−	0.959688i	$-0.590689\pi$
$397$	−4446.60			−0.562137			−0.281069	+	0.959688i	$0.590689\pi$
$398$	−4526.67			−0.570104
$399$	−2828.34			−0.354872
$400$		0			0
$401$			4546.80i			0.566225i	0.959087	+	0.283113i	$0.0913670\pi$
$401$			4546.80i			0.566225i	−0.959087	+	0.283113i	$0.908633\pi$
$402$		−	9334.54i		−	1.15812i
$403$	2878.45	+	1009.62i	0.355796	+	0.124797i
$404$	16042.8			1.97564
$405$		0			0
$406$	−5275.96			−0.644930
$407$			14396.7i			1.75337i
$408$	1045.91			0.126912
$409$		−	2879.96i		−	0.348179i	−0.984730	−	0.174089i	$-0.944302\pi$
$409$		−	2879.96i		−	0.348179i	0.984730	−	0.174089i	$-0.0556982\pi$
$410$		0			0
$411$		−	19005.2i		−	2.28092i
$412$			5346.09i			0.639279i
$413$			1495.51i			0.178183i
$414$		−	14082.6i		−	1.67180i
$415$		0			0
$416$	3898.76	−	11115.4i	0.459502	−	1.31004i
$417$		−	11334.2i		−	1.33103i
$418$	14978.2			1.75265
$419$	4060.33			0.473413			0.236706	−	0.971581i	$-0.423932\pi$
$419$	4060.33			0.473413			0.236706	+	0.971581i	$0.423932\pi$
$420$		0			0
$421$			6882.42i			0.796743i	0.917224	+	0.398371i	$0.130424\pi$
$421$			6882.42i			0.796743i	−0.917224	+	0.398371i	$0.869576\pi$
$422$	3382.17			0.390145
$423$	−2657.65			−0.305483
$424$			6852.15i			0.784835i
$425$		0			0
$426$	8413.25			0.956862
$427$	−307.557			−0.0348565
$428$		−	17271.2i		−	1.95055i
$429$	5149.15	−	14680.3i	0.579495	−	1.65215i
$430$		0			0
$431$		−	8472.47i		−	0.946878i	−0.880827	−	0.473439i	$-0.843012\pi$
$431$		−	8472.47i		−	0.946878i	0.880827	−	0.473439i	$-0.156988\pi$
$432$		−	738.454i		−	0.0822428i
$433$			5762.31i			0.639536i	0.947496	+	0.319768i	$0.103605\pi$
$433$			5762.31i			0.639536i	−0.947496	+	0.319768i	$0.896395\pi$
$434$			1449.62i			0.160332i
$435$		0			0
$436$		−	4988.19i		−	0.547915i
$437$	10193.0			1.11578
$438$			25619.9i			2.79490i
$439$	4537.20			0.493277			0.246638	−	0.969108i	$-0.420674\pi$
$439$	4537.20			0.493277			0.246638	+	0.969108i	$0.420674\pi$
$440$		0			0
$441$	7724.83			0.834125
$442$	2818.83	+	988.715i	0.303345	+	0.106399i
$443$		−	4500.12i		−	0.482635i	−0.970446	−	0.241317i	$-0.922421\pi$
$443$		−	4500.12i		−	0.482635i	0.970446	−	0.241317i	$-0.0775795\pi$
$444$			22961.9i			2.45434i
$445$		0			0
$446$	22700.0			2.41004
$447$	10094.4			1.06812
$448$	3911.75			0.412529
$449$			526.576i			0.0553467i	0.999617	+	0.0276733i	$0.00880983\pi$
$449$			526.576i			0.0553467i	−0.999617	+	0.0276733i	$0.991190\pi$
$450$		0			0
$451$	3994.80			0.417090
$452$			4060.64i			0.422559i
$453$	6602.37			0.684783
$454$	−8991.13			−0.929460
$455$		0			0
$456$	5312.59			0.545581
$457$	4385.91			0.448937			0.224468	−	0.974481i	$-0.427935\pi$
$457$	4385.91			0.448937			0.224468	+	0.974481i	$0.427935\pi$
$458$		−	20770.2i		−	2.11906i
$459$	271.979			0.0276577
$460$		0			0
$461$		−	3356.95i		−	0.339151i	−0.985517	−	0.169576i	$-0.945760\pi$
$461$		−	3356.95i		−	0.339151i	0.985517	−	0.169576i	$-0.0542397\pi$
$462$	7393.15			0.744503
$463$	−16274.1			−1.63353			−0.816764	−	0.576972i	$-0.804234\pi$
$463$	−16274.1			−1.63353			−0.816764	+	0.576972i	$0.804234\pi$
$464$	−9583.94			−0.958886
$465$		0			0
$466$			14952.5i			1.48639i
$467$		−	9804.73i		−	0.971539i	−0.874087	−	0.485770i	$-0.838539\pi$
$467$		−	9804.73i		−	0.971539i	0.874087	−	0.485770i	$-0.161461\pi$
$468$	3903.27	−	11128.2i	0.385531	−	1.09915i
$469$	1585.00			0.156052
$470$		0			0
$471$	−24613.6			−2.40793
$472$		−	2809.09i		−	0.273938i
$473$	13849.5			1.34630
$474$			11728.0i			1.13647i
$475$		0			0
$476$			798.596i			0.0768982i
$477$		−	17127.8i		−	1.64408i
$478$			3005.24i			0.287566i
$479$			16881.6i			1.61032i	0.593061	+	0.805158i	$0.297919\pi$
$479$			16881.6i			1.61032i	−0.593061	+	0.805158i	$0.702081\pi$
$480$		0			0
$481$	−4827.12	+	13762.2i	−0.457584	+	1.30457i
$482$		−	23813.1i		−	2.25033i
$483$	5031.20			0.473970
$484$	−8332.03			−0.782497
$485$		0			0
$486$		−	22164.2i		−	2.06870i
$487$	−1364.91			−0.127002			−0.0635009	−	0.997982i	$-0.520227\pi$
$487$	−1364.91			−0.127002			−0.0635009	+	0.997982i	$0.520227\pi$
$488$	577.698			0.0535884
$489$		−	10646.6i		−	0.984573i
$490$		0			0
$491$	6981.50			0.641692			0.320846	−	0.947131i	$-0.396033\pi$
$491$	6981.50			0.641692			0.320846	+	0.947131i	$0.396033\pi$
$492$	6371.46			0.583837
$493$		−	3529.84i		−	0.322467i
$494$	14318.0	+	5022.07i	1.30404	+	0.457396i
$495$		0			0
$496$			2633.27i			0.238382i
$497$			1428.56i			0.128933i
$498$			45826.2i			4.12353i
$499$			4600.22i			0.412694i	0.978479	+	0.206347i	$0.0661575\pi$
$499$			4600.22i			0.412694i	−0.978479	+	0.206347i	$0.933842\pi$
$500$		0			0
$501$		−	8013.12i		−	0.714571i
$502$	−22567.7			−2.00646
$503$		−	4447.14i		−	0.394211i	−0.980382	−	0.197106i	$-0.936846\pi$
$503$		−	4447.14i		−	0.394211i	0.980382	−	0.197106i	$-0.0631542\pi$
$504$	1246.31			0.110149
$505$		0			0
$506$	−26644.0			−2.34085
$507$	9844.38	−	12306.7i	0.862336	−	1.07803i
$508$		−	9132.66i		−	0.797631i
$509$		−	12304.7i		−	1.07150i	−0.844375	−	0.535752i	$-0.820028\pi$
$509$		−	12304.7i		−	1.07150i	0.844375	−	0.535752i	$-0.179972\pi$
$510$		0			0
$511$	−4350.23			−0.376601
$512$	13335.7			1.15109
$513$	1381.49			0.118897
$514$			8465.06i			0.726416i
$515$		0			0
$516$	22089.2			1.88454
$517$			5028.20i			0.427737i
$518$	−6930.78			−0.587878
$519$	−4358.91			−0.368660
$520$		0			0
$521$	21956.8			1.84634			0.923172	−	0.384388i	$-0.125587\pi$
$521$	21956.8			1.84634			0.923172	+	0.384388i	$0.125587\pi$
$522$	−24771.4			−2.07704
$523$			9329.17i			0.779993i	0.920816	+	0.389996i	$0.127524\pi$
$523$			9329.17i			0.779993i	−0.920816	+	0.389996i	$0.872476\pi$
$524$	6743.17			0.562169
$525$		0			0
$526$		−	19168.6i		−	1.58896i
$527$	−969.855			−0.0801662
$528$	13429.9			1.10693
$529$	−5964.78			−0.490242
$530$		0			0
$531$			7021.64i			0.573848i
$532$			4056.38i			0.330576i
$533$	3818.71	+	1339.43i	0.310332	+	0.108850i
$534$	−45954.7			−3.72407
$535$		0			0
$536$	−2977.17			−0.239914
$537$		−	7950.23i		−	0.638879i
$538$	20481.2			1.64128
$539$		−	14615.2i		−	1.16794i
$540$		0			0
$541$		−	14190.9i		−	1.12776i	−0.825858	−	0.563878i	$-0.809309\pi$
$541$		−	14190.9i		−	1.12776i	0.825858	−	0.563878i	$-0.190691\pi$
$542$		−	19745.6i		−	1.56484i
$543$		−	15271.7i		−	1.20694i
$544$			3745.19i			0.295172i
$545$		0			0
$546$	7067.28	+	2478.87i	0.553941	+	0.194296i
$547$			6080.89i			0.475320i	0.971348	+	0.237660i	$0.0763804\pi$
$547$			6080.89i			0.475320i	−0.971348	+	0.237660i	$0.923620\pi$
$548$	−27257.1			−2.12475
$549$	−1444.02			−0.112258
$550$		0			0
$551$		−	17929.5i		−	1.38624i
$552$	−9450.31			−0.728681
$553$	−1991.41			−0.153135
$554$		−	17717.4i		−	1.35874i
$555$		0			0
$556$	−16255.4			−1.23990
$557$	−4547.90			−0.345962			−0.172981	−	0.984925i	$-0.555340\pi$
$557$	−4547.90			−0.345962			−0.172981	+	0.984925i	$0.555340\pi$
$558$			6806.16i			0.516358i
$559$	13239.1	+	4643.65i	1.00170	+	0.351351i
$560$		0			0
$561$			4946.33i			0.372253i
$562$			6686.31i			0.501859i
$563$		−	8486.35i		−	0.635270i	−0.948213	−	0.317635i	$-0.897111\pi$
$563$		−	8486.35i		−	0.635270i	0.948213	−	0.317635i	$-0.102889\pi$
$564$			8019.68i			0.598740i
$565$		0			0
$566$			22385.2i			1.66241i
$567$	4121.27			0.305251
$568$		−	2683.33i		−	0.198222i
$569$	11315.7			0.833706			0.416853	−	0.908974i	$-0.363133\pi$
$569$	11315.7			0.833706			0.416853	+	0.908974i	$0.363133\pi$
$570$		0			0
$571$	−10804.4			−0.791855			−0.395927	−	0.918282i	$-0.629577\pi$
$571$	−10804.4			−0.791855			−0.395927	+	0.918282i	$0.629577\pi$
$572$	−21054.3	−	7384.88i	−1.53903	−	0.539820i
$573$		−	27386.5i		−	1.99666i
$574$			1923.15i			0.139844i
$575$		0			0
$576$	18366.2			1.32857
$577$	−16319.8			−1.17747			−0.588735	−	0.808326i	$-0.700374\pi$
$577$	−16319.8			−1.17747			−0.588735	+	0.808326i	$0.700374\pi$
$578$	20060.3			1.44360
$579$		−	15538.3i		−	1.11529i
$580$		0			0
$581$	−7781.24			−0.555628
$582$			46291.5i			3.29698i
$583$	−32405.3			−2.30204
$584$	8171.23			0.578986
$585$		0			0
$586$	19611.0			1.38246
$587$	25355.3			1.78284			0.891420	−	0.453179i	$-0.149710\pi$
$587$	25355.3			1.78284			0.891420	+	0.453179i	$0.149710\pi$
$588$		−	23310.3i		−	1.63487i
$589$	−4926.28			−0.344624
$590$		0			0
$591$			15421.7i			1.07337i
$592$	−12590.0			−0.874061
$593$	6158.04			0.426442			0.213221	−	0.977004i	$-0.431605\pi$
$593$	6158.04			0.426442			0.213221	+	0.977004i	$0.431605\pi$
$594$	−3611.14			−0.249439
$595$		0			0
$596$		−	14477.3i		−	0.994990i
$597$		−	7593.02i		−	0.520539i
$598$	−25469.6	−	8933.53i	−1.74168	−	0.610902i
$599$	23375.4			1.59448			0.797239	−	0.603664i	$-0.206293\pi$
$599$	23375.4			1.59448			0.797239	+	0.603664i	$0.206293\pi$
$600$		0			0
$601$	4871.29			0.330622			0.165311	−	0.986241i	$-0.447137\pi$
$601$	4871.29			0.330622			0.165311	+	0.986241i	$0.447137\pi$
$602$			6667.34i			0.451396i
$603$	7441.78			0.502575
$604$		−	9469.07i		−	0.637899i
$605$		0			0
$606$			47835.8i			3.20660i
$607$			9476.94i			0.633702i	0.948475	+	0.316851i	$0.102626\pi$
$607$			9476.94i			0.633702i	−0.948475	+	0.316851i	$0.897374\pi$
$608$			19023.3i			1.26891i
$609$		−	8849.89i		−	0.588860i
$610$		0			0
$611$	−1685.92	+	4806.56i	−0.111628	+	0.318253i
$612$			3749.52i			0.247656i
$613$	−25884.6			−1.70550			−0.852749	−	0.522322i	$-0.825066\pi$
$613$	−25884.6			−1.70550			−0.852749	+	0.522322i	$0.825066\pi$
$614$	−1064.94			−0.0699958
$615$		0			0
$616$		−	2357.98i		−	0.154230i
$617$	18011.5			1.17523			0.587614	−	0.809142i	$-0.300068\pi$
$617$	18011.5			1.17523			0.587614	+	0.809142i	$0.300068\pi$
$618$	−15940.8			−1.03759
$619$			9237.91i			0.599843i	0.953964	+	0.299922i	$0.0969606\pi$
$619$			9237.91i			0.599843i	−0.953964	+	0.299922i	$0.903039\pi$
$620$		0			0
$621$	−2457.46			−0.158799
$622$	−9209.62			−0.593685
$623$		−	7803.06i		−	0.501803i
$624$	12837.9	+	4502.94i	0.823602	+	0.288881i
$625$		0			0
$626$			9307.95i			0.594282i
$627$			25124.3i			1.60027i
$628$			35300.6i			2.24307i
$629$		−	4636.98i		−	0.293940i
$630$		0			0
$631$			26136.5i			1.64893i	0.565910	+	0.824467i	$0.308525\pi$
$631$			26136.5i			1.64893i	−0.565910	+	0.824467i	$0.691475\pi$
$632$	3740.55			0.235429
$633$			5673.24i			0.356226i
$634$	−35220.3			−2.20627
$635$		0			0
$636$	−51684.5			−3.22236
$637$	4900.36	−	13971.0i	0.304803	−	0.868995i
$638$			46866.8i			2.90827i
$639$			6707.29i			0.415237i
$640$		0			0
$641$	25457.6			1.56866			0.784332	−	0.620341i	$-0.213006\pi$
$641$	25457.6			1.56866			0.784332	+	0.620341i	$0.213006\pi$
$642$	51498.7			3.16588
$643$	24461.2			1.50024			0.750122	−	0.661299i	$-0.229995\pi$
$643$	24461.2			1.50024			0.750122	+	0.661299i	$0.229995\pi$
$644$		−	7215.70i		−	0.441519i
$645$		0			0
$646$	−4824.25			−0.293820
$647$		−	14409.2i		−	0.875552i	−0.899084	−	0.437776i	$-0.855766\pi$
$647$		−	14409.2i		−	0.875552i	0.899084	−	0.437776i	$-0.144234\pi$
$648$	−7741.16			−0.469293
$649$	13284.8			0.803501
$650$		0			0
$651$	−2431.59			−0.146392
$652$	−15269.3			−0.917164
$653$		−	30117.4i		−	1.80487i	−0.430821	−	0.902437i	$-0.641776\pi$
$653$		−	30117.4i		−	1.80487i	0.430821	−	0.902437i	$-0.358224\pi$
$654$	14873.6			0.889304
$655$		0			0
$656$			3493.45i			0.207921i
$657$	−20424.9			−1.21287
$658$	−2420.64			−0.143414
$659$	20622.9			1.21905			0.609524	−	0.792767i	$-0.291361\pi$
$659$	20622.9			1.21905			0.609524	+	0.792767i	$0.291361\pi$
$660$		0			0
$661$		−	6169.23i		−	0.363019i	−0.983389	−	0.181509i	$-0.941902\pi$
$661$		−	6169.23i		−	0.363019i	0.983389	−	0.181509i	$-0.0580983\pi$
$662$			27034.3i			1.58719i
$663$	−1658.47	+	4728.30i	−0.0971487	+	0.276972i
$664$	14615.8			0.854224
$665$		0			0
$666$	−32541.0			−1.89330
$667$			31893.8i			1.85148i
$668$	−11492.4			−0.665648
$669$			38077.0i			2.20051i
$670$		0			0
$671$			2732.05i			0.157183i
$672$			9389.80i			0.539017i
$673$			18705.5i			1.07139i	0.844413	+	0.535693i	$0.179949\pi$
$673$			18705.5i			1.07139i	−0.844413	+	0.535693i	$0.820051\pi$
$674$			10941.1i			0.625277i
$675$		0			0
$676$	−17650.2	−	14118.7i	−1.00422	−	0.803296i
$677$		−	13999.6i		−	0.794752i	−0.917656	−	0.397376i	$-0.869921\pi$
$677$		−	13999.6i		−	0.794752i	0.917656	−	0.397376i	$-0.130079\pi$
$678$	−12107.9			−0.685842
$679$	−7860.26			−0.444255
$680$		0			0
$681$		−	15081.7i		−	0.848652i
$682$	12877.1			0.723004
$683$	−26701.3			−1.49590			−0.747949	−	0.663756i	$-0.768961\pi$
$683$	−26701.3			−1.49590			−0.747949	+	0.663756i	$0.768961\pi$
$684$			19045.3i			1.06464i
$685$		0			0
$686$	14676.2			0.816823
$687$	34839.9			1.93483
$688$			12111.4i			0.671139i
$689$	−30976.9	−	10865.3i	−1.71281	−	0.600774i
$690$		0			0
$691$			30797.3i			1.69549i	0.530405	+	0.847745i	$0.322040\pi$
$691$			30797.3i			1.69549i	−0.530405	+	0.847745i	$0.677960\pi$
$692$			6251.51i			0.343420i
$693$			5894.04i			0.323082i
$694$			7786.17i			0.425878i
$695$		0			0
$696$			16623.1i			0.905313i
$697$	−1286.67			−0.0699225
$698$			16279.4i			0.882784i
$699$	−25081.2			−1.35717
$700$		0			0
$701$	−1914.30			−0.103141			−0.0515707	−	0.998669i	$-0.516423\pi$
$701$	−1914.30			−0.103141			−0.0515707	+	0.998669i	$0.516423\pi$
$702$	−3451.97	−	1210.79i	−0.185593	−	0.0650973i
$703$		−	23553.1i		−	1.26361i
$704$		−	34748.4i		−	1.86027i
$705$		0			0
$706$	20023.4			1.06741
$707$	−8122.48			−0.432075
$708$	21188.4			1.12473
$709$		−	119.977i		−	0.00635520i	−0.999995	−	0.00317760i	$-0.998989\pi$
$709$		−	119.977i		−	0.00635520i	0.999995	−	0.00317760i	$-0.00101146\pi$
$710$		0			0
$711$	−9349.95			−0.493179
$712$			14656.8i			0.771472i
$713$	8763.12			0.460282
$714$	−2381.23			−0.124811
$715$		0			0
$716$	−11402.2			−0.595138
$717$	−5040.99			−0.262565
$718$		−	28639.5i		−	1.48860i
$719$	−6043.22			−0.313455			−0.156727	−	0.987642i	$-0.550094\pi$
$719$	−6043.22			−0.313455			−0.156727	+	0.987642i	$0.550094\pi$
$720$		0			0
$721$		−	2706.73i		−	0.139811i
$722$	4827.75			0.248851
$723$	39944.1			2.05468
$724$	−21902.5			−1.12431
$725$		0			0
$726$		−	24844.2i		−	1.27005i
$727$			27917.4i			1.42421i	0.702074	+	0.712104i	$0.252257\pi$
$727$			27917.4i			1.42421i	−0.702074	+	0.712104i	$0.747743\pi$
$728$	790.613	−	2254.04i	0.0402501	−	0.114753i
$729$	15815.3			0.803499
$730$		0			0
$731$	−4460.73			−0.225699
$732$			4357.46i			0.220023i
$733$	−10871.2			−0.547801			−0.273900	−	0.961758i	$-0.588314\pi$
$733$	−10871.2			−0.547801			−0.273900	+	0.961758i	$0.588314\pi$
$734$		−	22081.2i		−	1.11040i
$735$		0			0
$736$		−	33839.6i		−	1.69476i
$737$		−	14079.6i		−	0.703705i
$738$			9029.44i			0.450377i
$739$		−	76.7079i		−	0.00381833i	−0.999998	−	0.00190916i	$-0.999392\pi$
$739$		−	76.7079i		−	0.00381833i	0.999998	−	0.00190916i	$-0.000607706\pi$
$740$		0			0
$741$	−8424.01	+	24016.9i	−0.417630	+	1.19067i
$742$		−	15600.3i		−	0.771840i
$743$	29467.6			1.45499			0.727497	−	0.686111i	$-0.240684\pi$
$743$	29467.6			1.45499			0.727497	+	0.686111i	$0.240684\pi$
$744$	4567.35			0.225064
$745$		0			0
$746$		−	23070.0i		−	1.13224i
$747$	−36534.0			−1.78944
$748$	7093.99			0.346767
$749$			8744.44i			0.426588i
$750$		0			0
$751$	−37540.9			−1.82409			−0.912043	−	0.410095i	$-0.865495\pi$
$751$	−37540.9			−1.82409			−0.912043	+	0.410095i	$0.865495\pi$
$752$	−4397.16			−0.213229
$753$		−	37854.9i		−	1.83202i
$754$	−15714.1	+	44801.0i	−0.758984	+	2.16387i
$755$		0			0
$756$		−	977.968i		−	0.0470481i
$757$		−	15276.6i		−	0.733472i	−0.930325	−	0.366736i	$-0.880475\pi$
$757$		−	15276.6i		−	0.733472i	0.930325	−	0.366736i	$-0.119525\pi$
$758$		−	34135.8i		−	1.63571i
$759$		−	44692.5i		−	2.13733i
$760$		0			0
$761$		−	28942.6i		−	1.37867i	−0.724441	−	0.689336i	$-0.757902\pi$
$761$		−	28942.6i		−	1.37867i	0.724441	−	0.689336i	$-0.242098\pi$
$762$	27231.5			1.29461
$763$			2525.53i			0.119830i
$764$	−39277.5			−1.85996
$765$		0			0
$766$	−20895.4			−0.985617
$767$	12699.2	+	4454.28i	0.597837	+	0.209693i
$768$			6251.25i			0.293714i
$769$		−	19643.6i		−	0.921151i	−0.887621	−	0.460575i	$-0.847643\pi$
$769$		−	19643.6i		−	0.921151i	0.887621	−	0.460575i	$-0.152357\pi$
$770$		0			0
$771$	−14199.3			−0.663261
$772$	−22285.0			−1.03893
$773$	−4746.94			−0.220874			−0.110437	−	0.993883i	$-0.535225\pi$
$773$	−4746.94			−0.220874			−0.110437	+	0.993883i	$0.535225\pi$
$774$			31304.1i			1.45375i
$775$		0			0
$776$	14764.3			0.682997
$777$		−	11625.7i		−	0.536768i
$778$	14439.4			0.665395
$779$	−6535.48			−0.300588
$780$		0			0
$781$	12690.0			0.581415
$782$	8581.63			0.392428
$783$			4322.68i			0.197292i
$784$	12781.0			0.582224
$785$		0			0
$786$			20106.6i			0.912440i
$787$	−7895.28			−0.357606			−0.178803	−	0.983885i	$-0.557223\pi$
$787$	−7895.28			−0.357606			−0.178803	+	0.983885i	$0.557223\pi$
$788$	22117.7			0.999886
$789$	32153.4			1.45081
$790$		0			0
$791$		−	2055.91i		−	0.0924143i
$792$		−	11071.0i		−	0.496707i
$793$	−916.038	+	2611.63i	−0.0410208	+	0.116950i
$794$	−19015.6			−0.849921
$795$		0			0
$796$	−10889.9			−0.484900
$797$		−	36729.0i		−	1.63238i	−0.577784	−	0.816190i	$-0.696082\pi$
$797$		−	36729.0i		−	1.63238i	0.577784	−	0.816190i	$-0.303918\pi$
$798$	−12095.2			−0.536548
$799$		−	1619.51i		−	0.0717073i
$800$		0			0
$801$		−	36636.4i		−	1.61609i
$802$			19444.1i			0.856102i
$803$			38643.4i			1.69825i
$804$		−	22456.2i		−	0.985036i
$805$		0			0
$806$	12309.5	+	4317.59i	0.537944	+	0.188686i
$807$			34355.1i			1.49858i
$808$	15256.8			0.664273
$809$	2008.18			0.0872729			0.0436364	−	0.999047i	$-0.486106\pi$
$809$	2008.18			0.0872729			0.0436364	+	0.999047i	$0.486106\pi$
$810$		0			0
$811$		−	2740.69i		−	0.118667i	−0.998238	−	0.0593334i	$-0.981103\pi$
$811$		−	2740.69i		−	0.118667i	0.998238	−	0.0593334i	$-0.0188975\pi$
$812$	−12692.4			−0.548543
$813$	33121.2			1.42880
$814$			61566.6i			2.65099i
$815$		0			0
$816$	−4325.57			−0.185570
$817$	−22657.8			−0.970253
$818$		−	12316.0i		−	0.526427i
$819$	−1976.23	+	5634.24i	−0.0843163	+	0.240386i
$820$		0			0
$821$		−	19064.1i		−	0.810405i	−0.914227	−	0.405203i	$-0.867201\pi$
$821$		−	19064.1i		−	0.810405i	0.914227	−	0.405203i	$-0.132799\pi$
$822$		−	81274.3i		−	3.44862i
$823$			31210.5i			1.32191i	0.750426	+	0.660954i	$0.229848\pi$
$823$			31210.5i			1.32191i	−0.750426	+	0.660954i	$0.770152\pi$
$824$			5084.18i			0.214946i
$825$		0			0
$826$			6395.46i			0.269402i
$827$	−19946.2			−0.838691			−0.419346	−	0.907827i	$-0.637740\pi$
$827$	−19946.2			−0.838691			−0.419346	+	0.907827i	$0.637740\pi$
$828$		−	33878.7i		−	1.42194i
$829$	26129.2			1.09470			0.547348	−	0.836905i	$-0.315637\pi$
$829$	26129.2			1.09470			0.547348	+	0.836905i	$0.315637\pi$
$830$		0			0
$831$	29719.2			1.24061
$832$	11650.9	−	33216.7i	0.485483	−	1.38411i
$833$			4707.34i			0.195798i
$834$		−	48469.9i		−	2.01244i
$835$		0			0
$836$	36033.1			1.49071
$837$	1187.69			0.0490475
$838$	17363.7			0.715775
$839$		−	19645.3i		−	0.808381i	−0.914675	−	0.404190i	$-0.867553\pi$
$839$		−	19645.3i		−	0.808381i	0.914675	−	0.404190i	$-0.132447\pi$
$840$		0			0
$841$	31712.3			1.30027
$842$			29432.2i			1.20463i
$843$	−11215.6			−0.458227
$844$	8136.51			0.331837
$845$		0			0
$846$	−11365.2			−0.461873
$847$	4218.52			0.171133
$848$		−	28338.4i		−	1.14758i
$849$	−37548.9			−1.51788
$850$		0			0
$851$			41897.4i			1.68769i
$852$	20239.8			0.813856
$853$	−22236.4			−0.892567			−0.446283	−	0.894892i	$-0.647253\pi$
$853$	−22236.4			−0.892567			−0.446283	+	0.894892i	$0.647253\pi$
$854$	−1315.25			−0.0527012
$855$		0			0
$856$		−	16425.1i		−	0.655837i
$857$			9147.58i			0.364615i	0.983242	+	0.182308i	$0.0583567\pi$
$857$			9147.58i			0.364615i	−0.983242	+	0.182308i	$0.941643\pi$
$858$	22020.0	−	62779.2i	0.876166	−	2.49796i
$859$	25810.6			1.02520			0.512599	−	0.858628i	$-0.328683\pi$
$859$	25810.6			1.02520			0.512599	+	0.858628i	$0.328683\pi$
$860$		0			0
$861$	−3225.88			−0.127686
$862$		−	36231.9i		−	1.43163i
$863$	−40079.9			−1.58092			−0.790461	−	0.612512i	$-0.790159\pi$
$863$	−40079.9			−1.58092			−0.790461	+	0.612512i	$0.790159\pi$
$864$		−	4586.40i		−	0.180593i
$865$		0			0
$866$			24642.1i			0.966943i
$867$			33649.1i			1.31809i
$868$			3487.36i			0.136370i
$869$			17689.9i			0.690549i
$870$		0			0
$871$	4720.80	−	13459.0i	0.183649	−	0.523585i
$872$		−	4743.81i		−	0.184227i
$873$	−36905.0			−1.43075
$874$	43589.5			1.68700
$875$		0			0
$876$			61634.0i			2.37719i
$877$	28881.1			1.11202			0.556012	−	0.831174i	$-0.312331\pi$
$877$	28881.1			1.11202			0.556012	+	0.831174i	$0.312331\pi$
$878$	19403.0			0.745808
$879$			32895.5i			1.26227i
$880$		0			0
$881$	30201.1			1.15494			0.577470	−	0.816412i	$-0.304040\pi$
$881$	30201.1			1.15494			0.577470	+	0.816412i	$0.304040\pi$
$882$	33034.7			1.26115
$883$		−	27307.5i		−	1.04074i	−0.853942	−	0.520369i	$-0.825795\pi$
$883$		−	27307.5i		−	1.04074i	0.853942	−	0.520369i	$-0.174205\pi$
$884$	6781.30	+	2378.56i	0.258009	+	0.0904974i
$885$		0			0
$886$		−	19244.5i		−	0.729718i
$887$			7353.93i			0.278378i	0.990266	+	0.139189i	$0.0444495\pi$
$887$			7353.93i			0.278378i	−0.990266	+	0.139189i	$0.955551\pi$
$888$			21837.0i			0.825227i
$889$			4623.88i			0.174443i
$890$		0			0
$891$		−	36609.6i		−	1.37651i
$892$	54609.7			2.04985
$893$		−	8226.13i		−	0.308261i
$894$	43168.0			1.61494
$895$		0			0
$896$	6256.33			0.233269
$897$	14985.1	−	42722.6i	0.557789	−	1.59026i
$898$			2251.87i			0.0836812i
$899$		−	15414.3i		−	0.571855i
$900$		0			0
$901$	10437.3			0.385922
$902$	17083.5			0.630618
$903$	−11183.8			−0.412152
$904$			3861.70i			0.142078i
$905$		0			0
$906$	28234.6			1.03535
$907$			20414.7i			0.747365i	0.927557	+	0.373682i	$0.121905\pi$
$907$			20414.7i			0.747365i	−0.927557	+	0.373682i	$0.878095\pi$
$908$	−21630.1			−0.790549
$909$	−38136.2			−1.39153
$910$		0			0
$911$	−12721.2			−0.462649			−0.231325	−	0.972877i	$-0.574306\pi$
$911$	−12721.2			−0.462649			−0.231325	+	0.972877i	$0.574306\pi$
$912$	−21971.3			−0.797743
$913$			69121.3i			2.50557i
$914$	18756.0			0.678768
$915$		0			0
$916$		−	49967.2i		−	1.80236i
$917$	−3414.08			−0.122947
$918$	1163.10			0.0418169
$919$	18000.9			0.646130			0.323065	−	0.946377i	$-0.395287\pi$
$919$	18000.9			0.646130			0.323065	+	0.946377i	$0.395287\pi$
$920$		0			0
$921$		−	1786.32i		−	0.0639103i
$922$		−	14355.7i		−	0.512778i
$923$	12130.7	+	4254.87i	0.432596	+	0.151734i
$924$	17785.8			0.633235
$925$		0			0
$926$	−69595.2			−2.46981
$927$		−	12708.5i		−	0.450271i
$928$	−59524.0			−2.10557
$929$			40583.7i			1.43327i	0.697448	+	0.716635i	$0.254319\pi$
$929$			40583.7i			1.43327i	−0.697448	+	0.716635i	$0.745681\pi$
$930$		0			0
$931$			23910.4i			0.841710i
$932$			35971.3i			1.26425i
$933$		−	15448.2i		−	0.542070i
$934$		−	41929.2i		−	1.46892i
$935$		0			0
$936$	3712.04	−	10583.0i	0.129628	−	0.369570i
$937$			17375.4i			0.605796i	0.953023	+	0.302898i	$0.0979541\pi$
$937$			17375.4i			0.605796i	−0.953023	+	0.302898i	$0.902046\pi$
$938$	6778.13			0.235942
$939$	−15613.1			−0.542615
$940$		0			0
$941$			14332.7i			0.496527i	0.968693	+	0.248264i	$0.0798599\pi$
$941$			14332.7i			0.496527i	−0.968693	+	0.248264i	$0.920140\pi$
$942$	−105258.			−3.64066
$943$	11625.7			0.401467
$944$			11617.5i			0.400549i
$945$		0			0
$946$	59226.5			2.03554
$947$	28957.6			0.993658			0.496829	−	0.867848i	$-0.334498\pi$
$947$	28957.6			0.993658			0.496829	+	0.867848i	$0.334498\pi$
$948$			28214.3i			0.966622i
$949$	−12956.9	+	36940.1i	−0.443201	+	1.26357i
$950$		0			0
$951$		−	59078.4i		−	2.01446i
$952$			759.471i			0.0258557i
$953$			34079.5i			1.15839i	0.815190	+	0.579194i	$0.196633\pi$
$953$			34079.5i			1.15839i	−0.815190	+	0.579194i	$0.803367\pi$
$954$		−	73245.6i		−	2.48576i
$955$		0			0
$956$			7229.74i			0.244589i
$957$	−78614.2			−2.65542
$958$			72193.1i			2.43471i
$959$	13800.3			0.464687
$960$		0			0
$961$	25555.8			0.857835
$962$	−20642.8	+	58852.9i	−0.691842	+	1.97245i
$963$			41056.3i			1.37385i
$964$		−	57287.5i		−	1.91401i
$965$		0			0
$966$	21515.6			0.716617
$967$	−51382.9			−1.70875			−0.854377	−	0.519654i	$-0.826061\pi$
$967$	−51382.9			−1.70875			−0.854377	+	0.519654i	$0.826061\pi$
$968$	−7923.83			−0.263101
$969$		−	8092.19i		−	0.268275i
$970$		0			0
$971$	−24450.8			−0.808097			−0.404049	−	0.914737i	$-0.632397\pi$
$971$	−24450.8			−0.808097			−0.404049	+	0.914737i	$0.632397\pi$
$972$		−	53320.7i		−	1.75953i
$973$	8230.14			0.271168
$974$	−5836.93			−0.192020
$975$		0			0
$976$	−2389.18			−0.0783564
$977$	−28371.3			−0.929047			−0.464523	−	0.885561i	$-0.653774\pi$
$977$	−28371.3			−0.929047			−0.464523	+	0.885561i	$0.653774\pi$
$978$		−	45529.4i		−	1.48862i
$979$	−69315.2			−2.26284
$980$		0			0
$981$			11857.7i			0.385920i
$982$	29855.9			0.970204
$983$	47296.1			1.53460			0.767300	−	0.641288i	$-0.221600\pi$
$983$	47296.1			1.53460			0.767300	+	0.641288i	$0.221600\pi$
$984$	6059.31			0.196305
$985$		0			0
$986$		−	15095.1i		−	0.487552i
$987$		−	4060.37i		−	0.130945i
$988$	34444.9	+	12081.7i	1.10915	+	0.389037i
$989$	40304.9			1.29588
$990$		0			0
$991$	16241.7			0.520620			0.260310	−	0.965525i	$-0.416175\pi$
$991$	16241.7			0.520620			0.260310	+	0.965525i	$0.416175\pi$
$992$			16354.8i			0.523452i
$993$	−45347.3			−1.44920
$994$			6109.14i			0.194940i
$995$		0			0
$996$			110244.i			3.50726i
$997$		−	1249.79i		−	0.0397004i	−0.999803	−	0.0198502i	$-0.993681\pi$
$997$		−	1249.79i		−	0.0397004i	0.999803	−	0.0198502i	$-0.00631894\pi$
$998$			19672.5i			0.623971i
$999$			5678.49i			0.179839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.4.d.c.324.12		14
5.2	odd	4		325.4.c.e.51.12		14
5.3	odd	4		65.4.c.a.51.3	✓	14
5.4	even	2		325.4.d.d.324.3		14
13.12	even	2		325.4.d.d.324.4		14
15.8	even	4		585.4.b.e.181.12		14
20.3	even	4		1040.4.k.d.961.12		14
65.8	even	4		845.4.a.i.1.6		7
65.12	odd	4		325.4.c.e.51.3		14
65.18	even	4		845.4.a.l.1.2		7
65.38	odd	4		65.4.c.a.51.12	yes	14
65.64	even	2	inner	325.4.d.c.324.11		14
195.38	even	4		585.4.b.e.181.3		14
260.103	even	4		1040.4.k.d.961.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.c.a.51.3	✓	14	5.3	odd	4
65.4.c.a.51.12	yes	14	65.38	odd	4
325.4.c.e.51.3		14	65.12	odd	4
325.4.c.e.51.12		14	5.2	odd	4
325.4.d.c.324.11		14	65.64	even	2	inner
325.4.d.c.324.12		14	1.1	even	1	trivial
325.4.d.d.324.3		14	5.4	even	2
325.4.d.d.324.4		14	13.12	even	2
585.4.b.e.181.3		14	195.38	even	4
585.4.b.e.181.12		14	15.8	even	4
845.4.a.i.1.6		7	65.8	even	4
845.4.a.l.1.2		7	65.18	even	4
1040.4.k.d.961.11		14	260.103	even	4
1040.4.k.d.961.12		14	20.3	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	325.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4.27643 q^{2} +7.17327i q^{3} +10.2878 q^{4} +30.6760i q^{6} -5.20875 q^{7} +9.78383 q^{8} -24.4558 q^{9} +46.2698i q^{11} +73.7975i q^{12} +(-15.5139 + 44.2303i) q^{13} -22.2749 q^{14} -40.4629 q^{16} -14.9028i q^{17} -104.584 q^{18} -75.6973i q^{19} -37.3638i q^{21} +197.869i q^{22} +134.654i q^{23} +70.1820i q^{24} +(-66.3442 + 189.148i) q^{26} +18.2501i q^{27} -53.5869 q^{28} +236.857 q^{29} -65.0786i q^{31} -251.308 q^{32} -331.906 q^{33} -63.7309i q^{34} -251.598 q^{36} +311.148 q^{37} -323.714i q^{38} +(-317.276 - 111.286i) q^{39} -86.3371i q^{41} -159.784i q^{42} -299.321i q^{43} +476.016i q^{44} +575.840i q^{46} +108.671 q^{47} -290.252i q^{48} -315.869 q^{49} +106.902 q^{51} +(-159.605 + 455.035i) q^{52} +700.355i q^{53} +78.0454i q^{54} -50.9615 q^{56} +542.997 q^{57} +1012.90 q^{58} -287.115i q^{59} +59.0462 q^{61} -278.304i q^{62} +127.384 q^{63} -750.996 q^{64} -1419.37 q^{66} -304.295 q^{67} -153.318i q^{68} -965.912 q^{69} -274.262i q^{71} -239.271 q^{72} +835.177 q^{73} +1330.60 q^{74} -778.762i q^{76} -241.008i q^{77} +(-1356.81 - 475.905i) q^{78} +382.320 q^{79} -791.220 q^{81} -369.214i q^{82} +1493.88 q^{83} -384.393i q^{84} -1280.03i q^{86} +1699.04i q^{87} +452.695i q^{88} +1498.07i q^{89} +(80.8082 - 230.385i) q^{91} +1385.30i q^{92} +466.827 q^{93} +464.725 q^{94} -1802.70i q^{96} +1509.05 q^{97} -1350.79 q^{98} -1131.56i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{2} + 56 q^{4} + 108 q^{7} - 48 q^{8} - 158 q^{9} + 6 q^{13} + 152 q^{14} + 280 q^{16} - 272 q^{18} - 344 q^{26} + 572 q^{28} - 588 q^{29} - 1788 q^{32} + 248 q^{33} + 496 q^{36} + 940 q^{37}+ \cdots + 7364 q^{98}+O(q^{100}) \) 14 * q - 4 * q^2 + 56 * q^4 + 108 * q^7 - 48 * q^8 - 158 * q^9 + 6 * q^13 + 152 * q^14 + 280 * q^16 - 272 * q^18 - 344 * q^26 + 572 * q^28 - 588 * q^29 - 1788 * q^32 + 248 * q^33 + 496 * q^36 + 940 * q^37 + 260 * q^39 + 772 * q^47 + 1302 * q^49 + 176 * q^51 + 2068 * q^52 + 512 * q^56 + 1752 * q^57 + 3316 * q^58 - 1460 * q^61 - 5604 * q^63 - 1296 * q^64 - 600 * q^66 - 3292 * q^67 - 4160 * q^69 - 4572 * q^72 + 3220 * q^73 + 5928 * q^74 - 7636 * q^78 + 1024 * q^79 - 2890 * q^81 - 452 * q^83 + 916 * q^91 + 3936 * q^93 - 2656 * q^94 - 3964 * q^97 + 7364 * q^98

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