LMFDB - Embedded newform 325.4.d.c.324.13

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			324.13
Root			$4.29153i$ of defining polynomial
Character	$\chi$	$=$	325.324
Dual form			325.4.d.c.324.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.29153 q^{2} -5.89541i q^{3} +10.4172 q^{4} -25.3003i q^{6} +34.1818 q^{7} +10.3735 q^{8} -7.75582 q^{9} +20.2972i q^{11} -61.4137i q^{12} +(28.2809 - 37.3790i) q^{13} +146.692 q^{14} -38.8194 q^{16} +75.8275i q^{17} -33.2843 q^{18} -106.383i q^{19} -201.516i q^{21} +87.1059i q^{22} -11.7556i q^{23} -61.1562i q^{24} +(121.368 - 160.413i) q^{26} -113.452i q^{27} +356.079 q^{28} -224.787 q^{29} +126.246i q^{31} -249.583 q^{32} +119.660 q^{33} +325.416i q^{34} -80.7940 q^{36} +9.49313 q^{37} -456.544i q^{38} +(-220.365 - 166.727i) q^{39} -214.584i q^{41} -864.810i q^{42} +308.118i q^{43} +211.440i q^{44} -50.4494i q^{46} +42.4480 q^{47} +228.856i q^{48} +825.396 q^{49} +447.034 q^{51} +(294.608 - 389.385i) q^{52} +112.704i q^{53} -486.884i q^{54} +354.586 q^{56} -627.169 q^{57} -964.678 q^{58} +437.774i q^{59} +440.774 q^{61} +541.787i q^{62} -265.108 q^{63} -760.536 q^{64} +513.525 q^{66} -758.560 q^{67} +789.911i q^{68} -69.3040 q^{69} +693.631i q^{71} -80.4553 q^{72} +113.362 q^{73} +40.7400 q^{74} -1108.21i q^{76} +693.795i q^{77} +(-945.700 - 715.515i) q^{78} +1216.88 q^{79} -878.254 q^{81} -920.893i q^{82} -1117.77 q^{83} -2099.23i q^{84} +1322.30i q^{86} +1325.21i q^{87} +210.554i q^{88} +151.740i q^{89} +(966.692 - 1277.68i) q^{91} -122.460i q^{92} +744.270 q^{93} +182.167 q^{94} +1471.39i q^{96} +179.668 q^{97} +3542.21 q^{98} -157.421i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.29153			1.51728			0.758642	−	0.651508i	$-0.225863\pi$
$2$	4.29153			1.51728			0.758642	+	0.651508i	$0.225863\pi$
$3$		−	5.89541i		−	1.13457i	−0.823521	−	0.567286i	$-0.807993\pi$
$3$		−	5.89541i		−	1.13457i	0.823521	−	0.567286i	$-0.192007\pi$
$4$	10.4172			1.30215
$5$		0			0
$5$		0			0
$6$		−	25.3003i		−	1.72147i
$7$	34.1818			1.84564			0.922822	−	0.385226i	$-0.125877\pi$
$7$	34.1818			1.84564			0.922822	+	0.385226i	$0.125877\pi$
$8$	10.3735			0.458450
$9$	−7.75582			−0.287253
$10$		0			0
$11$			20.2972i			0.556348i	0.960531	+	0.278174i	$0.0897293\pi$
$11$			20.2972i			0.556348i	−0.960531	+	0.278174i	$0.910271\pi$
$12$		−	61.4137i		−	1.47738i
$13$	28.2809	−	37.3790i	0.603362	−	0.797467i
$13$	28.2809	−	37.3790i	0.603362	−	0.797467i
$14$	146.692			2.80037
$15$		0			0
$16$	−38.8194			−0.606553
$17$			75.8275i			1.08182i	0.841082	+	0.540908i	$0.181919\pi$
$17$			75.8275i			1.08182i	−0.841082	+	0.540908i	$0.818081\pi$
$18$	−33.2843			−0.435844
$19$		−	106.383i		−	1.28452i	−0.766487	−	0.642259i	$-0.777997\pi$
$19$		−	106.383i		−	1.28452i	0.766487	−	0.642259i	$-0.222003\pi$
$20$		0			0
$21$		−	201.516i		−	2.09402i
$22$			87.1059i			0.844139i
$23$		−	11.7556i		−	0.106574i	−0.998579	−	0.0532872i	$-0.983030\pi$
$23$		−	11.7556i		−	0.106574i	0.998579	−	0.0532872i	$-0.0169699\pi$
$24$		−	61.1562i		−	0.520144i
$25$		0			0
$26$	121.368	−	160.413i	0.915472	−	1.20998i
$27$		−	113.452i		−	0.808663i
$28$	356.079			2.40331
$29$	−224.787			−1.43937			−0.719686	−	0.694299i	$-0.755714\pi$
$29$	−224.787			−1.43937			−0.719686	+	0.694299i	$0.755714\pi$
$30$		0			0
$31$			126.246i			0.731432i	0.930726	+	0.365716i	$0.119176\pi$
$31$			126.246i			0.731432i	−0.930726	+	0.365716i	$0.880824\pi$
$32$	−249.583			−1.37876
$33$	119.660			0.631217
$34$			325.416i			1.64142i
$35$		0			0
$36$	−80.7940			−0.374046
$37$	9.49313			0.0421800			0.0210900	−	0.999778i	$-0.493286\pi$
$37$	9.49313			0.0421800			0.0210900	+	0.999778i	$0.493286\pi$
$38$		−	456.544i		−	1.94898i
$39$	−220.365	−	166.727i	−0.904784	−	0.684558i
$40$		0			0
$41$		−	214.584i		−	0.817375i	−0.912674	−	0.408687i	$-0.865987\pi$
$41$		−	214.584i		−	0.817375i	0.912674	−	0.408687i	$-0.134013\pi$
$42$		−	864.810i		−	3.17722i
$43$			308.118i			1.09273i	0.837546	+	0.546367i	$0.183990\pi$
$43$			308.118i			1.09273i	−0.837546	+	0.546367i	$0.816010\pi$
$44$			211.440i			0.724450i
$45$		0			0
$46$		−	50.4494i		−	0.161704i
$47$	42.4480			0.131738			0.0658689	−	0.997828i	$-0.479018\pi$
$47$	42.4480			0.131738			0.0658689	+	0.997828i	$0.479018\pi$
$48$			228.856i			0.688178i
$49$	825.396			2.40640
$50$		0			0
$51$	447.034			1.22740
$52$	294.608	−	389.385i	0.785669	−	1.03842i
$53$			112.704i			0.292097i	0.989277	+	0.146048i	$0.0466555\pi$
$53$			112.704i			0.292097i	−0.989277	+	0.146048i	$0.953344\pi$
$54$		−	486.884i		−	1.22697i
$55$		0			0
$56$	354.586			0.846135
$57$	−627.169			−1.45738
$58$	−964.678			−2.18394
$59$			437.774i			0.965989i	0.875623	+	0.482994i	$0.160451\pi$
$59$			437.774i			0.965989i	−0.875623	+	0.482994i	$0.839549\pi$
$60$		0			0
$61$	440.774			0.925170			0.462585	−	0.886575i	$-0.346922\pi$
$61$	440.774			0.925170			0.462585	+	0.886575i	$0.346922\pi$
$62$			541.787i			1.10979i
$63$	−265.108			−0.530166
$64$	−760.536			−1.48542
$65$		0			0
$66$	513.525			0.957736
$67$	−758.560			−1.38318			−0.691588	−	0.722292i	$-0.743089\pi$
$67$	−758.560			−1.38318			−0.691588	+	0.722292i	$0.743089\pi$
$68$			789.911i			1.40869i
$69$	−69.3040			−0.120916
$70$		0			0
$71$			693.631i			1.15942i	0.814823	+	0.579710i	$0.196834\pi$
$71$			693.631i			1.15942i	−0.814823	+	0.579710i	$0.803166\pi$
$72$	−80.4553			−0.131691
$73$	113.362			0.181754			0.0908772	−	0.995862i	$-0.471033\pi$
$73$	113.362			0.181754			0.0908772	+	0.995862i	$0.471033\pi$
$74$	40.7400			0.0639991
$75$		0			0
$76$		−	1108.21i		−	1.67264i
$77$			693.795i			1.02682i
$78$	−945.700	−	715.515i	−1.37281	−	1.03867i
$79$	1216.88			1.73304			0.866520	−	0.499143i	$-0.166352\pi$
$79$	1216.88			1.73304			0.866520	+	0.499143i	$0.166352\pi$
$80$		0			0
$81$	−878.254			−1.20474
$82$		−	920.893i		−	1.24019i
$83$	−1117.77			−1.47821			−0.739105	−	0.673591i	$-0.764751\pi$
$83$	−1117.77			−1.47821			−0.739105	+	0.673591i	$0.764751\pi$
$84$		−	2099.23i		−	2.72673i
$85$		0			0
$86$			1322.30i			1.65799i
$87$			1325.21i			1.63307i
$88$			210.554i			0.255058i
$89$			151.740i			0.180724i	0.995909	+	0.0903621i	$0.0288024\pi$
$89$			151.740i			0.180724i	−0.995909	+	0.0903621i	$0.971198\pi$
$90$		0			0
$91$	966.692	−	1277.68i	1.11359	−	1.47184i
$92$		−	122.460i		−	0.138776i
$93$	744.270			0.829862
$94$	182.167			0.199884
$95$		0			0
$96$			1471.39i			1.56431i
$97$	179.668			0.188067			0.0940337	−	0.995569i	$-0.470024\pi$
$97$	179.668			0.188067			0.0940337	+	0.995569i	$0.470024\pi$
$98$	3542.21			3.65120
$99$		−	157.421i		−	0.159813i
$100$		0			0
$101$	−219.395			−0.216145			−0.108072	−	0.994143i	$-0.534468\pi$
$101$	−219.395			−0.216145			−0.108072	+	0.994143i	$0.534468\pi$
$102$	1918.46			1.86231
$103$			1010.41i			0.966591i	0.875457	+	0.483295i	$0.160560\pi$
$103$			1010.41i			0.966591i	−0.875457	+	0.483295i	$0.839440\pi$
$104$	293.373	−	387.752i	0.276611	−	0.365599i
$105$		0			0
$106$			483.674i			0.443194i
$107$			694.878i			0.627817i	0.949453	+	0.313908i	$0.101638\pi$
$107$			694.878i			0.627817i	−0.949453	+	0.313908i	$0.898362\pi$
$108$		−	1181.86i		−	1.05300i
$109$			1189.96i			1.04567i	0.852435	+	0.522833i	$0.175125\pi$
$109$			1189.96i			1.04567i	−0.852435	+	0.522833i	$0.824875\pi$
$110$		0			0
$111$		−	55.9659i		−	0.0478563i
$112$	−1326.92			−1.11948
$113$			93.2049i			0.0775927i	0.999247	+	0.0387964i	$0.0123524\pi$
$113$			93.2049i			0.0775927i	−0.999247	+	0.0387964i	$0.987648\pi$
$114$	−2691.51			−2.21126
$115$		0			0
$116$	−2341.65			−1.87428
$117$	−219.342	+	289.905i	−0.173317	+	0.229075i
$118$			1878.72i			1.46568i
$119$			2591.92i			1.99665i
$120$		0			0
$121$	919.024			0.690476
$122$	1891.60			1.40375
$123$	−1265.06			−0.927370
$124$			1315.13i			0.952436i
$125$		0			0
$126$	−1137.72			−0.804413
$127$		−	779.785i		−	0.544841i	−0.962178	−	0.272420i	$-0.912176\pi$
$127$		−	779.785i		−	0.544841i	0.962178	−	0.272420i	$-0.0878241\pi$
$128$	−1267.20			−0.875045
$129$	1816.48			1.23979
$130$		0			0
$131$	−1740.41			−1.16076			−0.580382	−	0.814344i	$-0.697097\pi$
$131$	−1740.41			−1.16076			−0.580382	+	0.814344i	$0.697097\pi$
$132$	1246.53			0.821940
$133$		−	3636.35i		−	2.37076i
$134$	−3255.38			−2.09867
$135$		0			0
$136$			786.599i			0.495958i
$137$	932.185			0.581328			0.290664	−	0.956825i	$-0.406124\pi$
$137$	932.185			0.581328			0.290664	+	0.956825i	$0.406124\pi$
$138$	−297.420			−0.183464
$139$	1445.62			0.882131			0.441065	−	0.897475i	$-0.354601\pi$
$139$	1445.62			0.882131			0.441065	+	0.897475i	$0.354601\pi$
$140$		0			0
$141$		−	250.248i		−	0.149466i
$142$			2976.74i			1.75917i
$143$	758.689	+	574.023i	0.443670	+	0.335680i
$144$	301.076			0.174234
$145$		0			0
$146$	486.498			0.275773
$147$		−	4866.05i		−	2.73024i
$148$	98.8920			0.0549248
$149$		−	3510.93i		−	1.93038i	−0.261545	−	0.965191i	$-0.584232\pi$
$149$		−	3510.93i		−	1.93038i	0.261545	−	0.965191i	$-0.415768\pi$
$150$		0			0
$151$		−	1521.55i		−	0.820013i	−0.912083	−	0.410007i	$-0.865526\pi$
$151$		−	1521.55i		−	0.820013i	0.912083	−	0.410007i	$-0.134474\pi$
$152$		−	1103.56i		−	0.588887i
$153$		−	588.105i		−	0.310755i
$154$			2977.44i			1.55798i
$155$		0			0
$156$	−2295.58	−	1736.83i	−1.17817	−	0.891398i
$157$			3196.37i			1.62483i	0.583082	+	0.812413i	$0.301847\pi$
$157$			3196.37i			1.62483i	−0.583082	+	0.812413i	$0.698153\pi$
$158$	5222.29			2.62951
$159$	664.438			0.331405
$160$		0			0
$161$		−	401.827i		−	0.196698i
$162$	−3769.05			−1.82793
$163$	−1363.46			−0.655179			−0.327590	−	0.944820i	$-0.606236\pi$
$163$	−1363.46			−0.655179			−0.327590	+	0.944820i	$0.606236\pi$
$164$		−	2235.37i		−	1.06435i
$165$		0			0
$166$	−4796.95			−2.24286
$167$	−922.250			−0.427340			−0.213670	−	0.976906i	$-0.568542\pi$
$167$	−922.250			−0.427340			−0.213670	+	0.976906i	$0.568542\pi$
$168$		−	2090.43i		−	0.960001i
$169$	−597.382	−	2114.22i	−0.271908	−	0.962323i
$170$		0			0
$171$			825.085i			0.368981i
$172$			3209.73i			1.42291i
$173$		−	1361.55i		−	0.598362i	−0.954196	−	0.299181i	$-0.903287\pi$
$173$		−	1361.55i		−	0.598362i	0.954196	−	0.299181i	$-0.0967134\pi$
$174$			5687.17i			2.47783i
$175$		0			0
$176$		−	787.925i		−	0.337455i
$177$	2580.86			1.09598
$178$			651.198i			0.274210i
$179$	−4222.14			−1.76300			−0.881501	−	0.472182i	$-0.843466\pi$
$179$	−4222.14			−1.76300			−0.881501	+	0.472182i	$0.843466\pi$
$180$		0			0
$181$	−3487.32			−1.43210			−0.716051	−	0.698048i	$-0.754052\pi$
$181$	−3487.32			−1.43210			−0.716051	+	0.698048i	$0.754052\pi$
$182$	4148.59	−	5483.21i	1.68964	−	2.23320i
$183$		−	2598.54i		−	1.04967i
$184$		−	121.947i		−	0.0488589i
$185$		0			0
$186$	3194.06			1.25914
$187$	−1539.09			−0.601867
$188$	442.190			0.171543
$189$		−	3878.00i		−	1.49250i
$190$		0			0
$191$	1431.56			0.542325			0.271162	−	0.962534i	$-0.412592\pi$
$191$	1431.56			0.542325			0.271162	+	0.962534i	$0.412592\pi$
$192$			4483.67i			1.68532i
$193$	−131.553			−0.0490641			−0.0245321	−	0.999699i	$-0.507810\pi$
$193$	−131.553			−0.0490641			−0.0245321	+	0.999699i	$0.507810\pi$
$194$	771.051			0.285352
$195$		0			0
$196$	8598.33			3.13350
$197$	−898.804			−0.325062			−0.162531	−	0.986703i	$-0.551966\pi$
$197$	−898.804			−0.325062			−0.162531	+	0.986703i	$0.551966\pi$
$198$		−	675.578i		−	0.242481i
$199$	2240.52			0.798124			0.399062	−	0.916924i	$-0.369336\pi$
$199$	2240.52			0.798124			0.399062	+	0.916924i	$0.369336\pi$
$200$		0			0
$201$			4472.02i			1.56931i
$202$	−941.539			−0.327953
$203$	−7683.61			−2.65657
$204$	4656.85			1.59826
$205$		0			0
$206$			4336.21i			1.46659i
$207$			91.1742i			0.0306138i
$208$	−1097.85	+	1451.03i	−0.365971	+	0.483706i
$209$	2159.27			0.714640
$210$		0			0
$211$	−2911.67			−0.949989			−0.474995	−	0.879989i	$-0.657550\pi$
$211$	−2911.67			−0.949989			−0.474995	+	0.879989i	$0.657550\pi$
$212$			1174.07i			0.380354i
$213$	4089.24			1.31544
$214$			2982.09i			0.952576i
$215$		0			0
$216$		−	1176.90i		−	0.370731i
$217$			4315.31i			1.34996i
$218$			5106.75i			1.58657i
$219$		−	668.318i		−	0.206213i
$220$		0			0
$221$	2834.36	+	2144.47i	0.862713	+	0.652727i
$222$		−	240.179i		−	0.0726116i
$223$	1492.95			0.448321			0.224160	−	0.974552i	$-0.428036\pi$
$223$	1492.95			0.448321			0.224160	+	0.974552i	$0.428036\pi$
$224$	−8531.19			−2.54471
$225$		0			0
$226$			399.991i			0.117730i
$227$	3318.55			0.970309			0.485155	−	0.874428i	$-0.338763\pi$
$227$	3318.55			0.970309			0.485155	+	0.874428i	$0.338763\pi$
$228$	−6533.35			−1.89773
$229$		−	3754.91i		−	1.08354i	−0.840526	−	0.541772i	$-0.817754\pi$
$229$		−	3754.91i		−	1.08354i	0.840526	−	0.541772i	$-0.182246\pi$
$230$		0			0
$231$	4090.20			1.16500
$232$	−2331.83			−0.659880
$233$			6098.90i			1.71482i	0.514636	+	0.857408i	$0.327927\pi$
$233$			6098.90i			1.71482i	−0.514636	+	0.857408i	$0.672073\pi$
$234$	−941.311	+	1244.14i	−0.262972	+	0.347571i
$235$		0			0
$236$			4560.39i			1.25786i
$237$		−	7174.02i		−	1.96626i
$238$			11123.3i			3.02948i
$239$		−	2603.41i		−	0.704606i	−0.935886	−	0.352303i	$-0.885399\pi$
$239$		−	2603.41i		−	0.704606i	0.935886	−	0.352303i	$-0.114601\pi$
$240$		0			0
$241$		−	73.6905i		−	0.0196963i	−0.999952	−	0.00984817i	$-0.996865\pi$
$241$		−	73.6905i		−	0.0196963i	0.999952	−	0.00984817i	$-0.00313482\pi$
$242$	3944.02			1.04765
$243$			2114.46i			0.558199i
$244$	4591.64			1.20471
$245$		0			0
$246$	−5429.04			−1.40708
$247$	−3976.48	−	3008.60i	−1.02436	−	0.775030i
$248$			1309.61i			0.335325i
$249$			6589.72i			1.67713i
$250$		0			0
$251$	1764.37			0.443689			0.221845	−	0.975082i	$-0.428792\pi$
$251$	1764.37			0.443689			0.221845	+	0.975082i	$0.428792\pi$
$252$	−2761.69			−0.690357
$253$	238.605			0.0592924
$254$		−	3346.47i		−	0.826678i
$255$		0			0
$256$	646.064			0.157731
$257$			6778.90i			1.64535i	0.568508	+	0.822677i	$0.307521\pi$
$257$			6778.90i			1.64535i	−0.568508	+	0.822677i	$0.692479\pi$
$258$	7795.48			1.88111
$259$	324.492			0.0778493
$260$		0			0
$261$	1743.40			0.413464
$262$	−7469.01			−1.76121
$263$		−	5829.83i		−	1.36686i	−0.730018	−	0.683428i	$-0.760488\pi$
$263$		−	5829.83i		−	1.36686i	0.730018	−	0.683428i	$-0.239512\pi$
$264$	1241.30			0.289381
$265$		0			0
$266$		−	15605.5i		−	3.59712i
$267$	894.572			0.205045
$268$	−7902.08			−1.80111
$269$	−1701.60			−0.385682			−0.192841	−	0.981230i	$-0.561770\pi$
$269$	−1701.60			−0.385682			−0.192841	+	0.981230i	$0.561770\pi$
$270$		0			0
$271$		−	5238.97i		−	1.17434i	−0.809465	−	0.587168i	$-0.800243\pi$
$271$		−	5238.97i		−	1.17434i	0.809465	−	0.587168i	$-0.199757\pi$
$272$		−	2943.58i		−	0.656179i
$273$	−7532.46	−	5699.04i	−1.66991	−	1.26345i
$274$	4000.50			0.882040
$275$		0			0
$276$	−721.954			−0.157451
$277$			3327.15i			0.721694i	0.932625	+	0.360847i	$0.117512\pi$
$277$			3327.15i			0.721694i	−0.932625	+	0.360847i	$0.882488\pi$
$278$	6203.93			1.33844
$279$		−	979.139i		−	0.210106i
$280$		0			0
$281$		−	7461.49i		−	1.58404i	−0.610495	−	0.792020i	$-0.709030\pi$
$281$		−	7461.49i		−	1.58404i	0.610495	−	0.792020i	$-0.290970\pi$
$282$		−	1073.95i		−	0.226782i
$283$		−	8288.85i		−	1.74106i	−0.492112	−	0.870532i	$-0.663775\pi$
$283$		−	8288.85i		−	1.74106i	0.492112	−	0.870532i	$-0.336225\pi$
$284$			7225.70i			1.50974i
$285$		0			0
$286$	3255.93	+	2463.43i	0.673173	+	0.509321i
$287$		−	7334.87i		−	1.50858i
$288$	1935.72			0.396053
$289$	−836.812			−0.170326
$290$		0			0
$291$		−	1059.22i		−	0.213376i
$292$	1180.92			0.236672
$293$	940.431			0.187510			0.0937552	−	0.995595i	$-0.470113\pi$
$293$	940.431			0.187510			0.0937552	+	0.995595i	$0.470113\pi$
$294$		−	20882.8i		−	4.14254i
$295$		0			0
$296$	98.4773			0.0193374
$297$	2302.76			0.449898
$298$		−	15067.3i		−	2.92894i
$299$	−439.412	−	332.458i	−0.0849895	−	0.0643029i
$300$		0			0
$301$			10532.0i			2.01680i
$302$		−	6529.78i		−	1.24419i
$303$			1293.42i			0.245231i
$304$			4129.71i			0.779129i
$305$		0			0
$306$		−	2523.87i		−	0.471503i
$307$	−7526.42			−1.39920			−0.699602	−	0.714533i	$-0.746639\pi$
$307$	−7526.42			−1.39920			−0.699602	+	0.714533i	$0.746639\pi$
$308$			7227.41i			1.33708i
$309$	5956.79			1.09667
$310$		0			0
$311$	3715.53			0.677454			0.338727	−	0.940885i	$-0.390004\pi$
$311$	3715.53			0.677454			0.338727	+	0.940885i	$0.390004\pi$
$312$	−2285.96	−	1729.55i	−0.414798	−	0.313835i
$313$			5715.69i			1.03217i	0.856536	+	0.516086i	$0.172612\pi$
$313$			5715.69i			1.03217i	−0.856536	+	0.516086i	$0.827388\pi$
$314$			13717.3i			2.46532i
$315$		0			0
$316$	12676.5			2.25668
$317$	3825.01			0.677709			0.338855	−	0.940839i	$-0.389960\pi$
$317$	3825.01			0.677709			0.338855	+	0.940839i	$0.389960\pi$
$318$	2851.45			0.502835
$319$		−	4562.53i		−	0.800793i
$320$		0			0
$321$	4096.59			0.712303
$322$		−	1724.45i		−	0.298447i
$323$	8066.73			1.38961
$324$	−9148.96			−1.56875
$325$		0			0
$326$	−5851.31			−0.994093
$327$	7015.31			1.18638
$328$		−	2225.99i		−	0.374725i
$329$	1450.95			0.243141
$330$		0			0
$331$		−	3914.20i		−	0.649981i	−0.945717	−	0.324991i	$-0.894639\pi$
$331$		−	3914.20i		−	0.649981i	0.945717	−	0.324991i	$-0.105361\pi$
$332$	−11644.1			−1.92485
$333$	−73.6270			−0.0121163
$334$	−3957.86			−0.648397
$335$		0			0
$336$			7822.72i			1.27013i
$337$		−	4622.42i		−	0.747179i	−0.927594	−	0.373589i	$-0.878127\pi$
$337$		−	4622.42i		−	0.747179i	0.927594	−	0.373589i	$-0.121873\pi$
$338$	−2563.68	−	9073.25i	−0.412562	−	1.46012i
$339$	549.481			0.0880345
$340$		0			0
$341$	−2562.43			−0.406931
$342$			3540.88i			0.559850i
$343$	16489.2			2.59572
$344$			3196.27i			0.500964i
$345$		0			0
$346$		−	5843.12i		−	0.907885i
$347$		−	8192.01i		−	1.26735i	−0.773600	−	0.633674i	$-0.781546\pi$
$347$		−	8192.01i		−	1.26735i	0.773600	−	0.633674i	$-0.218454\pi$
$348$			13805.0i			2.12651i
$349$		−	243.024i		−	0.0372744i	−0.999826	−	0.0186372i	$-0.994067\pi$
$349$		−	243.024i		−	0.0372744i	0.999826	−	0.0186372i	$-0.00593275\pi$
$350$		0			0
$351$	−4240.73	−	3208.53i	−0.644882	−	0.487917i
$352$		−	5065.83i		−	0.767073i
$353$	−2766.97			−0.417198			−0.208599	−	0.978001i	$-0.566890\pi$
$353$	−2766.97			−0.417198			−0.208599	+	0.978001i	$0.566890\pi$
$354$	11075.8			1.66292
$355$		0			0
$356$			1580.71i			0.235330i
$357$	15280.4			2.26534
$358$	−18119.4			−2.67497
$359$		−	2472.79i		−	0.363535i	−0.983342	−	0.181768i	$-0.941818\pi$
$359$		−	2472.79i		−	0.363535i	0.983342	−	0.181768i	$-0.0581818\pi$
$360$		0			0
$361$	−4458.27			−0.649988
$362$	−14965.9			−2.17291
$363$		−	5418.02i		−	0.783395i
$364$	10070.2	−	13309.9i	1.45007	−	1.91656i
$365$		0			0
$366$		−	11151.7i		−	1.59265i
$367$			5263.61i			0.748660i	0.927296	+	0.374330i	$0.122127\pi$
$367$			5263.61i			0.748660i	−0.927296	+	0.374330i	$0.877873\pi$
$368$			456.345i			0.0646430i
$369$			1664.27i			0.234793i
$370$		0			0
$371$			3852.44i			0.539107i
$372$	7753.22			1.08061
$373$		−	5633.17i		−	0.781969i	−0.920397	−	0.390984i	$-0.872135\pi$
$373$		−	5633.17i		−	0.781969i	0.920397	−	0.390984i	$-0.127865\pi$
$374$	−6605.03			−0.913203
$375$		0			0
$376$	440.336			0.0603952
$377$	−6357.16	+	8402.30i	−0.868463	+	1.14785i
$378$		−	16642.6i		−	2.26455i
$379$			9079.61i			1.23058i	0.788302	+	0.615288i	$0.210960\pi$
$379$			9079.61i			1.23058i	−0.788302	+	0.615288i	$0.789040\pi$
$380$		0			0
$381$	−4597.15			−0.618161
$382$	6143.58			0.822861
$383$	1196.31			0.159604			0.0798022	−	0.996811i	$-0.474571\pi$
$383$	1196.31			0.159604			0.0798022	+	0.996811i	$0.474571\pi$
$384$			7470.66i			0.992801i
$385$		0			0
$386$	−564.562			−0.0744442
$387$		−	2389.71i		−	0.313891i
$388$	1871.64			0.244892
$389$	−1888.94			−0.246203			−0.123102	−	0.992394i	$-0.539284\pi$
$389$	−1888.94			−0.246203			−0.123102	+	0.992394i	$0.539284\pi$
$390$		0			0
$391$	891.397			0.115294
$392$	8562.27			1.10321
$393$			10260.4i			1.31697i
$394$	−3857.24			−0.493211
$395$		0			0
$396$		−	1639.89i		−	0.208100i
$397$	9297.50			1.17539			0.587693	−	0.809084i	$-0.300036\pi$
$397$	9297.50			1.17539			0.587693	+	0.809084i	$0.300036\pi$
$398$	9615.27			1.21098
$399$	−21437.8			−2.68980
$400$		0			0
$401$		−	2777.98i		−	0.345949i	−0.984926	−	0.172975i	$-0.944662\pi$
$401$		−	2777.98i		−	0.345949i	0.984926	−	0.172975i	$-0.0553379\pi$
$402$			19191.8i			2.38109i
$403$	4718.94	+	3570.34i	0.583293	+	0.441319i
$404$	−2285.48			−0.281453
$405$		0			0
$406$	−32974.4			−4.03077
$407$			192.684i			0.0234668i
$408$	4637.32			0.562700
$409$			202.305i			0.0244581i	0.999925	+	0.0122290i	$0.00389272\pi$
$409$			202.305i			0.0244581i	−0.999925	+	0.0122290i	$0.996107\pi$
$410$		0			0
$411$		−	5495.61i		−	0.659558i
$412$			10525.7i			1.25865i
$413$			14963.9i			1.78287i
$414$			391.277i			0.0464498i
$415$		0			0
$416$	−7058.42	+	9329.16i	−0.831894	+	1.09952i
$417$		−	8522.54i		−	1.00084i
$418$	9266.56			1.08431
$419$	14295.5			1.66678			0.833390	−	0.552685i	$-0.186397\pi$
$419$	14295.5			1.66678			0.833390	+	0.552685i	$0.186397\pi$
$420$		0			0
$421$		−	3873.61i		−	0.448428i	−0.974540	−	0.224214i	$-0.928019\pi$
$421$		−	3873.61i		−	0.448428i	0.974540	−	0.224214i	$-0.0719815\pi$
$422$	−12495.5			−1.44140
$423$	−329.219			−0.0378421
$424$			1169.14i			0.133912i
$425$		0			0
$426$	17549.1			1.99590
$427$	15066.5			1.70753
$428$			7238.69i			0.817512i
$429$	3384.10	−	4472.78i	0.380853	−	0.503375i
$430$		0			0
$431$		−	1635.54i		−	0.182787i	−0.995815	−	0.0913937i	$-0.970868\pi$
$431$		−	1635.54i		−	0.182787i	0.995815	−	0.0913937i	$-0.0291322\pi$
$432$			4404.15i			0.490497i
$433$			5504.75i			0.610950i	0.952200	+	0.305475i	$0.0988152\pi$
$433$			5504.75i			0.610950i	−0.952200	+	0.305475i	$0.901185\pi$
$434$			18519.3i			2.04828i
$435$		0			0
$436$			12396.1i			1.36162i
$437$	−1250.59			−0.136897
$438$		−	2868.10i		−	0.312884i
$439$	−4613.62			−0.501585			−0.250793	−	0.968041i	$-0.580691\pi$
$439$	−4613.62			−0.501585			−0.250793	+	0.968041i	$0.580691\pi$
$440$		0			0
$441$	−6401.63			−0.691246
$442$	12163.7	+	9203.05i	1.30898	+	0.990372i
$443$			13293.5i			1.42572i	0.701305	+	0.712862i	$0.252601\pi$
$443$			13293.5i			1.42572i	−0.701305	+	0.712862i	$0.747399\pi$
$444$		−	583.008i		−	0.0623161i
$445$		0			0
$446$	6407.05			0.680230
$447$	−20698.4			−2.19016
$448$	−25996.5			−2.74156
$449$		−	7629.93i		−	0.801957i	−0.916088	−	0.400978i	$-0.868670\pi$
$449$		−	7629.93i		−	0.801957i	0.916088	−	0.400978i	$-0.131330\pi$
$450$		0			0
$451$	4355.45			0.454745
$452$			970.935i			0.101037i
$453$	−8970.16			−0.930364
$454$	14241.7			1.47223
$455$		0			0
$456$	−6505.96			−0.668135
$457$	−13439.5			−1.37566			−0.687829	−	0.725873i	$-0.741436\pi$
$457$	−13439.5			−1.37566			−0.687829	+	0.725873i	$0.741436\pi$
$458$		−	16114.3i		−	1.64404i
$459$	8602.80			0.874825
$460$		0			0
$461$			15879.6i			1.60430i	0.597119	+	0.802152i	$0.296312\pi$
$461$			15879.6i			1.60430i	−0.597119	+	0.802152i	$0.703688\pi$
$462$	17553.2			1.76764
$463$	−14962.5			−1.50187			−0.750937	−	0.660374i	$-0.770398\pi$
$463$	−14962.5			−1.50187			−0.750937	+	0.660374i	$0.770398\pi$
$464$	8726.08			0.873056
$465$		0			0
$466$			26173.6i			2.60186i
$467$		−	7204.07i		−	0.713843i	−0.934134	−	0.356922i	$-0.883826\pi$
$467$		−	7204.07i		−	0.713843i	0.934134	−	0.356922i	$-0.116174\pi$
$468$	−2284.93	+	3020.00i	−0.225686	+	0.298290i
$469$	−25929.0			−2.55285
$470$		0			0
$471$	18843.9			1.84348
$472$			4541.26i			0.442857i
$473$	−6253.93			−0.607941
$474$		−	30787.5i		−	2.98337i
$475$		0			0
$476$			27000.6i			2.59994i
$477$		−	874.115i		−	0.0839056i
$478$		−	11172.6i		−	1.06909i
$479$		−	11072.8i		−	1.05621i	−0.849178	−	0.528107i	$-0.822902\pi$
$479$		−	11072.8i		−	1.05621i	0.849178	−	0.528107i	$-0.177098\pi$
$480$		0			0
$481$	268.474	−	354.844i	0.0254498	−	0.0336372i
$482$		−	316.245i		−	0.0298850i
$483$	−2368.93			−0.223168
$484$	9573.67			0.899105
$485$		0			0
$486$			9074.25i			0.846947i
$487$	6559.96			0.610391			0.305195	−	0.952290i	$-0.401278\pi$
$487$	6559.96			0.610391			0.305195	+	0.952290i	$0.401278\pi$
$488$	4572.39			0.424144
$489$			8038.13i			0.743348i
$490$		0			0
$491$	5951.42			0.547014			0.273507	−	0.961870i	$-0.411816\pi$
$491$	5951.42			0.547014			0.273507	+	0.961870i	$0.411816\pi$
$492$	−13178.4			−1.20758
$493$		−	17045.0i		−	1.55714i
$494$	−17065.2	−	12911.5i	−1.55425	−	1.17594i
$495$		0			0
$496$		−	4900.78i		−	0.443653i
$497$			23709.6i			2.13988i
$498$			28280.0i			2.54469i
$499$		−	203.291i		−	0.0182376i	−0.999958	−	0.00911880i	$-0.997097\pi$
$499$		−	203.291i		−	0.0182376i	0.999958	−	0.00911880i	$-0.00290264\pi$
$500$		0			0
$501$			5437.04i			0.484848i
$502$	7571.84			0.673203
$503$		−	4109.83i		−	0.364311i	−0.983270	−	0.182155i	$-0.941693\pi$
$503$		−	4109.83i		−	0.364311i	0.983270	−	0.182155i	$-0.0583074\pi$
$504$	−2750.11			−0.243055
$505$		0			0
$506$	1023.98			0.0899635
$507$	−12464.2	+	3521.81i	−1.09182	+	0.308499i
$508$		−	8123.19i		−	0.709465i
$509$			19836.8i			1.72741i	0.503997	+	0.863705i	$0.331862\pi$
$509$			19836.8i			1.72741i	−0.503997	+	0.863705i	$0.668138\pi$
$510$		0			0
$511$	3874.93			0.335454
$512$	12910.2			1.11437
$513$	−12069.4			−1.03874
$514$			29091.8i			2.49647i
$515$		0			0
$516$	18922.7			1.61439
$517$			861.575i			0.0732922i
$518$	1392.57			0.118120
$519$	−8026.88			−0.678884
$520$		0			0
$521$	−17335.3			−1.45772			−0.728861	−	0.684661i	$-0.759950\pi$
$521$	−17335.3			−1.45772			−0.728861	+	0.684661i	$0.759950\pi$
$522$	7481.87			0.627342
$523$		−	2886.27i		−	0.241315i	−0.992694	−	0.120658i	$-0.961500\pi$
$523$		−	2886.27i		−	0.241315i	0.992694	−	0.120658i	$-0.0385003\pi$
$524$	−18130.2			−1.51149
$525$		0			0
$526$		−	25018.9i		−	2.07391i
$527$	−9572.90			−0.791275
$528$	−4645.14			−0.382867
$529$	12028.8			0.988642
$530$		0			0
$531$		−	3395.30i		−	0.277483i
$532$		−	37880.6i		−	3.08709i
$533$	−8020.94	−	6068.62i	−0.651830	−	0.493173i
$534$	3839.08			0.311111
$535$		0			0
$536$	−7868.94			−0.634117
$537$			24891.2i			2.00025i
$538$	−7302.47			−0.585190
$539$			16753.2i			1.33880i
$540$		0			0
$541$		−	14428.4i		−	1.14663i	−0.819336	−	0.573314i	$-0.805658\pi$
$541$		−	14428.4i		−	1.14663i	0.819336	−	0.573314i	$-0.194342\pi$
$542$		−	22483.2i		−	1.78180i
$543$			20559.2i			1.62482i
$544$		−	18925.2i		−	1.49157i
$545$		0			0
$546$	−32325.8	−	24457.6i	−2.53373	−	1.91701i
$547$			17024.1i			1.33071i	0.746529	+	0.665353i	$0.231719\pi$
$547$			17024.1i			1.33071i	−0.746529	+	0.665353i	$0.768281\pi$
$548$	9710.77			0.756977
$549$	−3418.57			−0.265758
$550$		0			0
$551$			23913.4i			1.84890i
$552$	−718.927			−0.0554340
$553$	41595.3			3.19857
$554$			14278.6i			1.09502i
$555$		0			0
$556$	15059.4			1.14867
$557$	12087.4			0.919498			0.459749	−	0.888049i	$-0.347939\pi$
$557$	12087.4			0.919498			0.459749	+	0.888049i	$0.347939\pi$
$558$		−	4202.00i		−	0.318790i
$559$	11517.2	+	8713.86i	0.871420	+	0.659315i
$560$		0			0
$561$			9073.53i			0.682861i
$562$		−	32021.2i		−	2.40344i
$563$			2618.53i			0.196017i	0.995186	+	0.0980086i	$0.0312473\pi$
$563$			2618.53i			0.196017i	−0.995186	+	0.0980086i	$0.968753\pi$
$564$		−	2606.89i		−	0.194627i
$565$		0			0
$566$		−	35571.8i		−	2.64169i
$567$	−30020.3			−2.22352
$568$			7195.40i			0.531536i
$569$	−6859.30			−0.505372			−0.252686	−	0.967548i	$-0.581314\pi$
$569$	−6859.30			−0.505372			−0.252686	+	0.967548i	$0.581314\pi$
$570$		0			0
$571$	−15207.9			−1.11459			−0.557297	−	0.830314i	$-0.688161\pi$
$571$	−15207.9			−1.11459			−0.557297	+	0.830314i	$0.688161\pi$
$572$	7903.42	+	5979.72i	0.577725	+	0.437106i
$573$		−	8439.63i		−	0.615306i
$574$		−	31477.8i		−	2.28895i
$575$		0			0
$576$	5898.58			0.426692
$577$	−17531.0			−1.26486			−0.632429	−	0.774618i	$-0.717942\pi$
$577$	−17531.0			−1.26486			−0.632429	+	0.774618i	$0.717942\pi$
$578$	−3591.20			−0.258433
$579$			775.557i			0.0556668i
$580$		0			0
$581$	−38207.5			−2.72825
$582$		−	4545.66i		−	0.323752i
$583$	−2287.58			−0.162508
$584$	1175.97			0.0833252
$585$		0			0
$586$	4035.89			0.284507
$587$	5988.25			0.421059			0.210529	−	0.977588i	$-0.432481\pi$
$587$	5988.25			0.421059			0.210529	+	0.977588i	$0.432481\pi$
$588$		−	50690.6i		−	3.55518i
$589$	13430.4			0.939539
$590$		0			0
$591$			5298.82i			0.368806i
$592$	−368.518			−0.0255844
$593$	15990.9			1.10737			0.553683	−	0.832728i	$-0.313222\pi$
$593$	15990.9			1.10737			0.553683	+	0.832728i	$0.313222\pi$
$594$	9882.37			0.682624
$595$		0			0
$596$		−	36574.1i		−	2.51365i
$597$		−	13208.8i		−	0.905528i
$598$	−1885.75	−	1426.75i	−0.128953	−	0.0975658i
$599$	−8103.88			−0.552781			−0.276390	−	0.961045i	$-0.589138\pi$
$599$	−8103.88			−0.552781			−0.276390	+	0.961045i	$0.589138\pi$
$600$		0			0
$601$	5291.20			0.359122			0.179561	−	0.983747i	$-0.442532\pi$
$601$	5291.20			0.359122			0.179561	+	0.983747i	$0.442532\pi$
$602$			45198.5i			3.06006i
$603$	5883.26			0.397321
$604$		−	15850.3i		−	1.06778i
$605$		0			0
$606$			5550.75i			0.372086i
$607$		−	11506.8i		−	0.769431i	−0.923035	−	0.384715i	$-0.874300\pi$
$607$		−	11506.8i		−	0.769431i	0.923035	−	0.384715i	$-0.125700\pi$
$608$			26551.3i			1.77105i
$609$			45298.0i			3.01407i
$610$		0			0
$611$	1200.47	−	1586.67i	0.0794857	−	0.105057i
$612$		−	6126.41i		−	0.404650i
$613$	4997.20			0.329258			0.164629	−	0.986356i	$-0.447357\pi$
$613$	4997.20			0.329258			0.164629	+	0.986356i	$0.447357\pi$
$614$	−32299.9			−2.12299
$615$		0			0
$616$			7197.10i			0.470746i
$617$	−1546.06			−0.100878			−0.0504392	−	0.998727i	$-0.516062\pi$
$617$	−1546.06			−0.100878			−0.0504392	+	0.998727i	$0.516062\pi$
$618$	25563.7			1.66395
$619$		−	7719.68i		−	0.501260i	−0.968083	−	0.250630i	$-0.919362\pi$
$619$		−	7719.68i		−	0.501260i	0.968083	−	0.250630i	$-0.0806378\pi$
$620$		0			0
$621$	−1333.70			−0.0861827
$622$	15945.3			1.02789
$623$			5186.76i			0.333553i
$624$	8554.42	+	6472.26i	0.548799	+	0.415221i
$625$		0			0
$626$			24529.1i			1.56610i
$627$		−	12729.8i		−	0.810810i
$628$			33297.2i			2.11577i
$629$			719.841i			0.0456310i
$630$		0			0
$631$		−	7009.39i		−	0.442218i	−0.975249	−	0.221109i	$-0.929032\pi$
$631$		−	7009.39i		−	0.442218i	0.975249	−	0.221109i	$-0.0709676\pi$
$632$	12623.4			0.794511
$633$			17165.5i			1.07783i
$634$	16415.1			1.02828
$635$		0			0
$636$	6921.59			0.431539
$637$	23342.9	−	30852.5i	1.45193	−	1.91903i
$638$		−	19580.2i		−	1.21503i
$639$		−	5379.68i		−	0.333046i
$640$		0			0
$641$	3091.60			0.190501			0.0952504	−	0.995453i	$-0.469635\pi$
$641$	3091.60			0.190501			0.0952504	+	0.995453i	$0.469635\pi$
$642$	17580.6			1.08077
$643$	−5872.84			−0.360190			−0.180095	−	0.983649i	$-0.557641\pi$
$643$	−5872.84			−0.360190			−0.180095	+	0.983649i	$0.557641\pi$
$644$		−	4185.92i		−	0.256131i
$645$		0			0
$646$	34618.6			2.10844
$647$			7029.20i			0.427120i	0.976930	+	0.213560i	$0.0685058\pi$
$647$			7029.20i			0.427120i	−0.976930	+	0.213560i	$0.931494\pi$
$648$	−9110.60			−0.552312
$649$	−8885.59			−0.537426
$650$		0			0
$651$	25440.5			1.53163
$652$	−14203.4			−0.853142
$653$		−	4151.74i		−	0.248806i	−0.992232	−	0.124403i	$-0.960299\pi$
$653$		−	4151.74i		−	0.248806i	0.992232	−	0.124403i	$-0.0397015\pi$
$654$	30106.4			1.80008
$655$		0			0
$656$			8330.02i			0.495781i
$657$	−879.219			−0.0522094
$658$	6226.79			0.368914
$659$	−5191.50			−0.306877			−0.153439	−	0.988158i	$-0.549035\pi$
$659$	−5191.50			−0.306877			−0.153439	+	0.988158i	$0.549035\pi$
$660$		0			0
$661$			787.020i			0.0463109i	0.999732	+	0.0231555i	$0.00737127\pi$
$661$			787.020i			0.0463109i	−0.999732	+	0.0231555i	$0.992629\pi$
$662$		−	16797.9i		−	0.986206i
$663$	12642.5	−	16709.7i	0.740565	−	0.978810i
$664$	−11595.2			−0.677685
$665$		0			0
$666$	−315.973			−0.0183839
$667$			2642.50i			0.153400i
$668$	−9607.27			−0.556462
$669$		−	8801.57i		−	0.508652i
$670$		0			0
$671$			8946.48i			0.514717i
$672$			50294.8i			2.88715i
$673$		−	10073.1i		−	0.576952i	−0.957487	−	0.288476i	$-0.906851\pi$
$673$		−	10073.1i		−	0.576952i	0.957487	−	0.288476i	$-0.0931486\pi$
$674$		−	19837.2i		−	1.13368i
$675$		0			0
$676$	−6223.06	−	22024.3i	−0.354065	−	1.25309i
$677$			6795.48i			0.385778i	0.981221	+	0.192889i	$0.0617857\pi$
$677$			6795.48i			0.385778i	−0.981221	+	0.192889i	$0.938214\pi$
$678$	2358.11			0.133573
$679$	6141.38			0.347105
$680$		0			0
$681$		−	19564.2i		−	1.10089i
$682$	−10996.8			−0.617430
$683$	−8789.65			−0.492426			−0.246213	−	0.969216i	$-0.579186\pi$
$683$	−8789.65			−0.492426			−0.246213	+	0.969216i	$0.579186\pi$
$684$			8595.09i			0.480470i
$685$		0			0
$686$	70763.7			3.93844
$687$	−22136.7			−1.22936
$688$		−	11961.0i		−	0.662801i
$689$	4212.78	+	3187.38i	0.232938	+	0.176240i
$690$		0			0
$691$		−	35940.9i		−	1.97866i	−0.145687	−	0.989331i	$-0.546539\pi$
$691$		−	35940.9i		−	1.97866i	0.145687	−	0.989331i	$-0.453461\pi$
$692$		−	14183.5i		−	0.779158i
$693$		−	5380.95i		−	0.294957i
$694$		−	35156.2i		−	1.92293i
$695$		0			0
$696$			13747.1i			0.748681i
$697$	16271.4			0.884249
$698$		−	1042.94i		−	0.0565559i
$699$	35955.5			1.94558
$700$		0			0
$701$	8533.98			0.459806			0.229903	−	0.973214i	$-0.426159\pi$
$701$	8533.98			0.459806			0.229903	+	0.973214i	$0.426159\pi$
$702$	−18199.2	−	13769.5i	−0.978470	−	0.740308i
$703$		−	1009.90i		−	0.0541810i
$704$		−	15436.7i		−	0.826412i
$705$		0			0
$706$	−11874.5			−0.633009
$707$	−7499.31			−0.398926
$708$	26885.3			1.42714
$709$		−	16404.0i		−	0.868923i	−0.900690	−	0.434462i	$-0.856939\pi$
$709$		−	16404.0i		−	0.868923i	0.900690	−	0.434462i	$-0.143061\pi$
$710$		0			0
$711$	−9437.93			−0.497820
$712$			1574.08i			0.0828529i
$713$	1484.09			0.0779519
$714$	65576.4			3.43716
$715$		0			0
$716$	−43982.9			−2.29570
$717$	−15348.2			−0.799426
$718$		−	10612.1i		−	0.551586i
$719$	−1640.70			−0.0851012			−0.0425506	−	0.999094i	$-0.513548\pi$
$719$	−1640.70			−0.0851012			−0.0425506	+	0.999094i	$0.513548\pi$
$720$		0			0
$721$			34537.7i			1.78398i
$722$	−19132.8			−0.986217
$723$	−434.435			−0.0223469
$724$	−36328.2			−1.86481
$725$		0			0
$726$		−	23251.6i		−	1.18863i
$727$		−	3373.78i		−	0.172114i	−0.996290	−	0.0860569i	$-0.972573\pi$
$727$		−	3373.78i		−	0.172114i	0.996290	−	0.0860569i	$-0.0274267\pi$
$728$	10028.0	−	13254.1i	0.510526	−	0.674765i
$729$	−11247.3			−0.571422
$730$		0			0
$731$	−23363.8			−1.18214
$732$		−	27069.6i		−	1.36683i
$733$	−26029.1			−1.31161			−0.655803	−	0.754932i	$-0.727670\pi$
$733$	−26029.1			−1.31161			−0.655803	+	0.754932i	$0.727670\pi$
$734$			22588.9i			1.13593i
$735$		0			0
$736$			2933.99i			0.146941i
$737$		−	15396.6i		−	0.769528i
$738$			7142.28i			0.356248i
$739$		−	32836.8i		−	1.63454i	−0.576258	−	0.817268i	$-0.695488\pi$
$739$		−	32836.8i		−	1.63454i	0.576258	−	0.817268i	$-0.304512\pi$
$740$		0			0
$741$	−17736.9	+	23443.0i	−0.879327	+	1.16221i
$742$			16532.8i			0.817978i
$743$	−7026.50			−0.346941			−0.173471	−	0.984839i	$-0.555498\pi$
$743$	−7026.50			−0.346941			−0.173471	+	0.984839i	$0.555498\pi$
$744$	7720.71			0.380450
$745$		0			0
$746$		−	24174.9i		−	1.18647i
$747$	8669.24			0.424620
$748$	−16033.0			−0.783722
$749$			23752.2i			1.15873i
$750$		0			0
$751$	19114.4			0.928756			0.464378	−	0.885637i	$-0.346278\pi$
$751$	19114.4			0.928756			0.464378	+	0.885637i	$0.346278\pi$
$752$	−1647.81			−0.0799060
$753$		−	10401.7i		−	0.503397i
$754$	−27281.9	+	36058.7i	−1.31771	+	1.74162i
$755$		0			0
$756$		−	40398.0i		−	1.94347i
$757$		−	1293.50i		−	0.0621046i	−0.999518	−	0.0310523i	$-0.990114\pi$
$757$		−	1293.50i		−	0.0621046i	0.999518	−	0.0310523i	$-0.00988584\pi$
$758$			38965.4i			1.86713i
$759$		−	1406.68i		−	0.0672715i
$760$		0			0
$761$		−	28509.3i		−	1.35803i	−0.734125	−	0.679014i	$-0.762407\pi$
$761$		−	28509.3i		−	1.35803i	0.734125	−	0.679014i	$-0.237593\pi$
$762$	−19728.8			−0.937926
$763$			40675.0i			1.92993i
$764$	14912.9			0.706189
$765$		0			0
$766$	5133.99			0.242165
$767$	16363.6	+	12380.6i	0.770345	+	0.582841i
$768$		−	3808.81i		−	0.178957i
$769$		−	2327.55i		−	0.109147i	−0.998510	−	0.0545733i	$-0.982620\pi$
$769$		−	2327.55i		−	0.109147i	0.998510	−	0.0545733i	$-0.0173798\pi$
$770$		0			0
$771$	39964.4			1.86677
$772$	−1370.41			−0.0638889
$773$	2598.20			0.120893			0.0604467	−	0.998171i	$-0.480747\pi$
$773$	2598.20			0.120893			0.0604467	+	0.998171i	$0.480747\pi$
$774$		−	10255.5i		−	0.476262i
$775$		0			0
$776$	1863.79			0.0862194
$777$		−	1913.01i		−	0.0883256i
$778$	−8106.43			−0.373560
$779$	−22828.0			−1.04993
$780$		0			0
$781$	−14078.8			−0.645041
$782$	3825.45			0.174933
$783$			25502.5i			1.16397i
$784$	−32041.4			−1.45961
$785$		0			0
$786$			44032.8i			1.99822i
$787$	−1799.68			−0.0815140			−0.0407570	−	0.999169i	$-0.512977\pi$
$787$	−1799.68			−0.0815140			−0.0407570	+	0.999169i	$0.512977\pi$
$788$	−9363.03			−0.423280
$789$	−34369.2			−1.55080
$790$		0			0
$791$			3185.91i			0.143209i
$792$		−	1633.02i		−	0.0732660i
$793$	12465.5	−	16475.7i	0.558213	−	0.737793i
$794$	39900.5			1.78339
$795$		0			0
$796$	23340.0			1.03928
$797$		−	13328.9i		−	0.592388i	−0.955128	−	0.296194i	$-0.904283\pi$
$797$		−	13328.9i		−	0.592388i	0.955128	−	0.296194i	$-0.0957174\pi$
$798$	−92000.8			−4.08119
$799$			3218.73i			0.142516i
$800$		0			0
$801$		−	1176.87i		−	0.0519135i
$802$		−	11921.8i		−	0.524904i
$803$			2300.94i			0.101119i
$804$			46586.0i			2.04348i
$805$		0			0
$806$	20251.5	+	15322.2i	0.885022	+	0.669606i
$807$			10031.6i			0.437584i
$808$	−2275.90			−0.0990914
$809$	6514.79			0.283125			0.141562	−	0.989929i	$-0.454787\pi$
$809$	6514.79			0.283125			0.141562	+	0.989929i	$0.454787\pi$
$810$		0			0
$811$		−	7474.15i		−	0.323617i	−0.986822	−	0.161808i	$-0.948267\pi$
$811$		−	7474.15i		−	0.323617i	0.986822	−	0.161808i	$-0.0517326\pi$
$812$	−80041.8			−3.45926
$813$	−30885.9			−1.33237
$814$			826.908i			0.0356058i
$815$		0			0
$816$	−17353.6			−0.744482
$817$	32778.4			1.40364
$818$			868.199i			0.0371099i
$819$	−7497.49	+	9909.48i	−0.319882	+	0.422790i
$820$		0			0
$821$			20393.6i			0.866922i	0.901172	+	0.433461i	$0.142708\pi$
$821$			20393.6i			0.866922i	−0.901172	+	0.433461i	$0.857292\pi$
$822$		−	23584.6i		−	1.00074i
$823$		−	32999.0i		−	1.39766i	−0.715288	−	0.698829i	$-0.753705\pi$
$823$		−	32999.0i		−	1.39766i	0.715288	−	0.698829i	$-0.246295\pi$
$824$			10481.5i			0.443133i
$825$		0			0
$826$			64218.1i			2.70512i
$827$	9715.21			0.408502			0.204251	−	0.978919i	$-0.434524\pi$
$827$	9715.21			0.408502			0.204251	+	0.978919i	$0.434524\pi$
$828$			949.781i			0.0398637i
$829$	−29994.8			−1.25665			−0.628324	−	0.777951i	$-0.716259\pi$
$829$	−29994.8			−1.25665			−0.628324	+	0.777951i	$0.716259\pi$
$830$		0			0
$831$	19614.9			0.818814
$832$	−21508.6	+	28428.1i	−0.896248	+	1.18458i
$833$			62587.7i			2.60328i
$834$		−	36574.7i		−	1.51856i
$835$		0			0
$836$	22493.6			0.930569
$837$	14322.9			0.591482
$838$	61349.5			2.52898
$839$		−	7057.85i		−	0.290422i	−0.989401	−	0.145211i	$-0.953614\pi$
$839$		−	7057.85i		−	0.290422i	0.989401	−	0.145211i	$-0.0463861\pi$
$840$		0			0
$841$	26140.0			1.07179
$842$		−	16623.7i		−	0.680393i
$843$	−43988.5			−1.79721
$844$	−30331.5			−1.23703
$845$		0			0
$846$	−1412.85			−0.0574172
$847$	31413.9			1.27437
$848$		−	4375.11i		−	0.177172i
$849$	−48866.2			−1.97536
$850$		0			0
$851$		−	111.597i		−	0.00449531i
$852$	42598.4			1.71291
$853$	9202.00			0.369368			0.184684	−	0.982798i	$-0.440874\pi$
$853$	9202.00			0.369368			0.184684	+	0.982798i	$0.440874\pi$
$854$	64658.1			2.59082
$855$		0			0
$856$			7208.34i			0.287822i
$857$			41288.6i			1.64573i	0.568235	+	0.822866i	$0.307626\pi$
$857$			41288.6i			1.64573i	−0.568235	+	0.822866i	$0.692374\pi$
$858$	14522.9	−	19195.1i	0.577862	−	0.763763i
$859$	33717.1			1.33925			0.669623	−	0.742702i	$-0.266456\pi$
$859$	33717.1			1.33925			0.669623	+	0.742702i	$0.266456\pi$
$860$		0			0
$861$	−43242.0			−1.71160
$862$		−	7018.98i		−	0.277341i
$863$	8063.90			0.318075			0.159037	−	0.987273i	$-0.449161\pi$
$863$	8063.90			0.318075			0.159037	+	0.987273i	$0.449161\pi$
$864$			28315.7i			1.11495i
$865$		0			0
$866$			23623.8i			0.926985i
$867$			4933.35i			0.193247i
$868$			44953.5i			1.75786i
$869$			24699.3i			0.964174i
$870$		0			0
$871$	−21452.8	+	28354.2i	−0.834557	+	1.10304i
$872$			12344.1i			0.479386i
$873$	−1393.47			−0.0540229
$874$	−5366.94			−0.207711
$875$		0			0
$876$		−	6962.01i		−	0.268521i
$877$	−16211.6			−0.624203			−0.312102	−	0.950049i	$-0.601033\pi$
$877$	−16211.6			−0.624203			−0.312102	+	0.950049i	$0.601033\pi$
$878$	−19799.5			−0.761047
$879$		−	5544.22i		−	0.212744i
$880$		0			0
$881$	9159.69			0.350281			0.175141	−	0.984543i	$-0.443962\pi$
$881$	9159.69			0.350281			0.175141	+	0.984543i	$0.443962\pi$
$882$	−27472.8			−1.04882
$883$			20476.8i			0.780408i	0.920728	+	0.390204i	$0.127595\pi$
$883$			20476.8i			0.780408i	−0.920728	+	0.390204i	$0.872405\pi$
$884$	29526.1	+	22339.4i	1.12338	+	0.849949i
$885$		0			0
$886$			57049.6i			2.16323i
$887$		−	7491.56i		−	0.283587i	−0.989896	−	0.141794i	$-0.954713\pi$
$887$		−	7491.56i		−	0.283587i	0.989896	−	0.141794i	$-0.0452869\pi$
$888$		−	580.564i		−	0.0219397i
$889$		−	26654.5i		−	1.00558i
$890$		0			0
$891$		−	17826.1i		−	0.670254i
$892$	15552.4			0.583782
$893$		−	4515.73i		−	0.169220i
$894$	−88827.7			−3.32309
$895$		0			0
$896$	−43315.2			−1.61502
$897$	−1959.98	+	2590.51i	−0.0729563	+	0.0964267i
$898$		−	32744.0i		−	1.21680i
$899$		−	28378.3i		−	1.05280i
$900$		0			0
$901$	−8546.09			−0.315995
$902$	18691.5			0.689978
$903$	62090.6			2.28820
$904$			966.864i			0.0355724i
$905$		0			0
$906$	−38495.7			−1.41163
$907$		−	50090.1i		−	1.83375i	−0.399170	−	0.916877i	$-0.630702\pi$
$907$		−	50090.1i		−	1.83375i	0.399170	−	0.916877i	$-0.369298\pi$
$908$	34570.1			1.26349
$909$	1701.59			0.0620881
$910$		0			0
$911$	−1350.63			−0.0491202			−0.0245601	−	0.999698i	$-0.507819\pi$
$911$	−1350.63			−0.0491202			−0.0245601	+	0.999698i	$0.507819\pi$
$912$	24346.3			0.883977
$913$		−	22687.6i		−	0.822399i
$914$	−57676.2			−2.08726
$915$		0			0
$916$		−	39115.7i		−	1.41094i
$917$	−59490.3			−2.14236
$918$	36919.2			1.32736
$919$	38062.2			1.36622			0.683111	−	0.730315i	$-0.260627\pi$
$919$	38062.2			1.36622			0.683111	+	0.730315i	$0.260627\pi$
$920$		0			0
$921$			44371.3i			1.58750i
$922$			68147.6i			2.43419i
$923$	25927.2	+	19616.5i	0.924599	+	0.699550i
$924$	42608.5			1.51701
$925$		0			0
$926$	−64212.1			−2.27877
$927$		−	7836.57i		−	0.277656i
$928$	56102.8			1.98455
$929$			18698.6i			0.660366i	0.943917	+	0.330183i	$0.107110\pi$
$929$			18698.6i			0.660366i	−0.943917	+	0.330183i	$0.892890\pi$
$930$		0			0
$931$		−	87807.8i		−	3.09107i
$932$			63533.6i			2.23295i
$933$		−	21904.5i		−	0.768620i
$934$		−	30916.5i		−	1.08310i
$935$		0			0
$936$	−2275.35	+	3007.34i	−0.0794573	+	0.105019i
$937$			8664.13i			0.302076i	0.988528	+	0.151038i	$0.0482615\pi$
$937$			8664.13i			0.302076i	−0.988528	+	0.151038i	$0.951738\pi$
$938$	−111275.			−3.87340
$939$	33696.3			1.17107
$940$		0			0
$941$		−	17787.5i		−	0.616212i	−0.951352	−	0.308106i	$-0.900305\pi$
$941$		−	17787.5i		−	0.616212i	0.951352	−	0.308106i	$-0.0996951\pi$
$942$	80869.0			2.79709
$943$	−2522.56			−0.0871112
$944$		−	16994.1i		−	0.585924i
$945$		0			0
$946$	−26838.9			−0.922419
$947$	48570.3			1.66665			0.833327	−	0.552780i	$-0.186433\pi$
$947$	48570.3			1.66665			0.833327	+	0.552780i	$0.186433\pi$
$948$		−	74733.3i		−	2.56036i
$949$	3205.99	−	4237.38i	0.109664	−	0.144943i
$950$		0			0
$951$		−	22550.0i		−	0.768910i
$952$			26887.4i			0.915362i
$953$		−	33701.1i		−	1.14553i	−0.819721	−	0.572763i	$-0.805872\pi$
$953$		−	33701.1i		−	1.14553i	0.819721	−	0.572763i	$-0.194128\pi$
$954$		−	3751.29i		−	0.127309i
$955$		0			0
$956$		−	27120.3i		−	0.917503i
$957$	−26898.0			−0.908557
$958$		−	47519.0i		−	1.60258i
$959$	31863.8			1.07292
$960$		0			0
$961$	13853.0			0.465007
$962$	1152.16	−	1522.82i	0.0386146	−	0.0510372i
$963$		−	5389.35i		−	0.180342i
$964$		−	767.649i		−	0.0256476i
$965$		0			0
$966$	−10166.3			−0.338610
$967$	11377.7			0.378367			0.189183	−	0.981942i	$-0.439416\pi$
$967$	11377.7			0.378367			0.189183	+	0.981942i	$0.439416\pi$
$968$	9533.53			0.316549
$969$		−	47556.7i		−	1.57662i
$970$		0			0
$971$	29025.7			0.959299			0.479650	−	0.877460i	$-0.340764\pi$
$971$	29025.7			0.959299			0.479650	+	0.877460i	$0.340764\pi$
$972$			22026.7i			0.726860i
$973$	49414.0			1.62810
$974$	28152.3			0.926136
$975$		0			0
$976$	−17110.6			−0.561165
$977$	2482.90			0.0813051			0.0406525	−	0.999173i	$-0.487056\pi$
$977$	2482.90			0.0813051			0.0406525	+	0.999173i	$0.487056\pi$
$978$			34495.9i			1.12787i
$979$	−3079.90			−0.100546
$980$		0			0
$981$		−	9229.13i		−	0.300371i
$982$	25540.7			0.829976
$983$	38919.6			1.26281			0.631405	−	0.775453i	$-0.282479\pi$
$983$	38919.6			1.26281			0.631405	+	0.775453i	$0.282479\pi$
$984$	−13123.1			−0.425153
$985$		0			0
$986$		−	73149.1i		−	2.36262i
$987$		−	8553.94i		−	0.275861i
$988$	−41423.8	−	31341.2i	−1.33387	−	1.00921i
$989$	3622.11			0.116457
$990$		0			0
$991$	20092.5			0.644054			0.322027	−	0.946730i	$-0.395636\pi$
$991$	20092.5			0.644054			0.322027	+	0.946730i	$0.395636\pi$
$992$		−	31508.8i		−	1.00847i
$993$	−23075.8			−0.737450
$994$			101750.i			3.24680i
$995$		0			0
$996$			68646.5i			2.18388i
$997$			54046.2i			1.71681i	0.512973	+	0.858405i	$0.328544\pi$
$997$			54046.2i			1.71681i	−0.512973	+	0.858405i	$0.671456\pi$
$998$		−	872.430i		−	0.0276716i
$999$		−	1077.02i		−	0.0341094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.4.d.c.324.13		14
5.2	odd	4		325.4.c.e.51.13		14
5.3	odd	4		65.4.c.a.51.2	✓	14
5.4	even	2		325.4.d.d.324.2		14
13.12	even	2		325.4.d.d.324.1		14
15.8	even	4		585.4.b.e.181.13		14
20.3	even	4		1040.4.k.d.961.4		14
65.8	even	4		845.4.a.i.1.7		7
65.12	odd	4		325.4.c.e.51.2		14
65.18	even	4		845.4.a.l.1.1		7
65.38	odd	4		65.4.c.a.51.13	yes	14
65.64	even	2	inner	325.4.d.c.324.14		14
195.38	even	4		585.4.b.e.181.2		14
260.103	even	4		1040.4.k.d.961.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.c.a.51.2	✓	14	5.3	odd	4
65.4.c.a.51.13	yes	14	65.38	odd	4
325.4.c.e.51.2		14	65.12	odd	4
325.4.c.e.51.13		14	5.2	odd	4
325.4.d.c.324.13		14	1.1	even	1	trivial
325.4.d.c.324.14		14	65.64	even	2	inner
325.4.d.d.324.1		14	13.12	even	2
325.4.d.d.324.2		14	5.4	even	2
585.4.b.e.181.2		14	195.38	even	4
585.4.b.e.181.13		14	15.8	even	4
845.4.a.i.1.7		7	65.8	even	4
845.4.a.l.1.1		7	65.18	even	4
1040.4.k.d.961.3		14	260.103	even	4
1040.4.k.d.961.4		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)

\(f(q)\)	\(=\)	\(q+4.29153 q^{2} -5.89541i q^{3} +10.4172 q^{4} -25.3003i q^{6} +34.1818 q^{7} +10.3735 q^{8} -7.75582 q^{9} +20.2972i q^{11} -61.4137i q^{12} +(28.2809 - 37.3790i) q^{13} +146.692 q^{14} -38.8194 q^{16} +75.8275i q^{17} -33.2843 q^{18} -106.383i q^{19} -201.516i q^{21} +87.1059i q^{22} -11.7556i q^{23} -61.1562i q^{24} +(121.368 - 160.413i) q^{26} -113.452i q^{27} +356.079 q^{28} -224.787 q^{29} +126.246i q^{31} -249.583 q^{32} +119.660 q^{33} +325.416i q^{34} -80.7940 q^{36} +9.49313 q^{37} -456.544i q^{38} +(-220.365 - 166.727i) q^{39} -214.584i q^{41} -864.810i q^{42} +308.118i q^{43} +211.440i q^{44} -50.4494i q^{46} +42.4480 q^{47} +228.856i q^{48} +825.396 q^{49} +447.034 q^{51} +(294.608 - 389.385i) q^{52} +112.704i q^{53} -486.884i q^{54} +354.586 q^{56} -627.169 q^{57} -964.678 q^{58} +437.774i q^{59} +440.774 q^{61} +541.787i q^{62} -265.108 q^{63} -760.536 q^{64} +513.525 q^{66} -758.560 q^{67} +789.911i q^{68} -69.3040 q^{69} +693.631i q^{71} -80.4553 q^{72} +113.362 q^{73} +40.7400 q^{74} -1108.21i q^{76} +693.795i q^{77} +(-945.700 - 715.515i) q^{78} +1216.88 q^{79} -878.254 q^{81} -920.893i q^{82} -1117.77 q^{83} -2099.23i q^{84} +1322.30i q^{86} +1325.21i q^{87} +210.554i q^{88} +151.740i q^{89} +(966.692 - 1277.68i) q^{91} -122.460i q^{92} +744.270 q^{93} +182.167 q^{94} +1471.39i q^{96} +179.668 q^{97} +3542.21 q^{98} -157.421i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{2} + 56 q^{4} + 108 q^{7} - 48 q^{8} - 158 q^{9} + 6 q^{13} + 152 q^{14} + 280 q^{16} - 272 q^{18} - 344 q^{26} + 572 q^{28} - 588 q^{29} - 1788 q^{32} + 248 q^{33} + 496 q^{36} + 940 q^{37}+ \cdots + 7364 q^{98}+O(q^{100}) \) 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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