LMFDB - Embedded newform 325.4.c.e.51.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,4,Mod(51,325)] 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([0, 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("325.51"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	325.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == 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^{4}\cdot 3^{2}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.13
Root			$4.29153i$ of defining polynomial
Character	$\chi$	$=$	325.51
Dual form			325.4.c.e.51.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.29153i q^{2} -5.89541 q^{3} -10.4172 q^{4} -25.3003i q^{6} +34.1818i q^{7} -10.3735i q^{8} +7.75582 q^{9} +20.2972i q^{11} +61.4137 q^{12} +(-37.3790 - 28.2809i) q^{13} -146.692 q^{14} -38.8194 q^{16} -75.8275 q^{17} +33.2843i q^{18} +106.383i q^{19} -201.516i q^{21} -87.1059 q^{22} -11.7556 q^{23} +61.1562i q^{24} +(121.368 - 160.413i) q^{26} +113.452 q^{27} -356.079i q^{28} +224.787 q^{29} +126.246i q^{31} -249.583i q^{32} -119.660i q^{33} -325.416i q^{34} -80.7940 q^{36} +9.49313i q^{37} -456.544 q^{38} +(220.365 + 166.727i) q^{39} -214.584i q^{41} +864.810 q^{42} +308.118 q^{43} -211.440i q^{44} -50.4494i q^{46} +42.4480i q^{47} +228.856 q^{48} -825.396 q^{49} +447.034 q^{51} +(389.385 + 294.608i) q^{52} +112.704 q^{53} +486.884i q^{54} +354.586 q^{56} -627.169i q^{57} +964.678i q^{58} -437.774i q^{59} +440.774 q^{61} -541.787 q^{62} +265.108i q^{63} +760.536 q^{64} +513.525 q^{66} -758.560i q^{67} +789.911 q^{68} +69.3040 q^{69} +693.631i q^{71} -80.4553i q^{72} -113.362i q^{73} -40.7400 q^{74} -1108.21i q^{76} -693.795 q^{77} +(-715.515 + 945.700i) q^{78} -1216.88 q^{79} -878.254 q^{81} +920.893 q^{82} +1117.77i q^{83} +2099.23i q^{84} +1322.30i q^{86} -1325.21 q^{87} +210.554 q^{88} -151.740i q^{89} +(966.692 - 1277.68i) q^{91} +122.460 q^{92} -744.270i q^{93} -182.167 q^{94} +1471.39i q^{96} +179.668i q^{97} -3542.21i q^{98} +157.421i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 56 q^{4} + 158 q^{9} + 108 q^{12} + 4 q^{13} - 152 q^{14} + 280 q^{16} + 100 q^{17} - 648 q^{22} + 532 q^{23} - 344 q^{26} + 48 q^{27} + 588 q^{29} + 496 q^{36} - 148 q^{38} - 260 q^{39} + 620 q^{42}+ \cdots + 2656 q^{94}+O(q^{100}) $ 14 * q - 56 * q^4 + 158 * q^9 + 108 * q^12 + 4 * q^13 - 152 * q^14 + 280 * q^16 + 100 * q^17 - 648 * q^22 + 532 * q^23 - 344 * q^26 + 48 * q^27 + 588 * q^29 + 496 * q^36 - 148 * q^38 - 260 * q^39 + 620 * q^42 - 728 * q^43 + 2008 * q^48 - 1302 * q^49 + 176 * q^51 + 528 * q^52 - 1040 * q^53 + 512 * q^56 - 1460 * q^61 - 2964 * q^62 + 1296 * q^64 - 600 * q^66 - 1604 * q^68 + 4160 * q^69 - 5928 * q^74 + 3568 * q^77 - 2560 * q^78 - 1024 * q^79 - 2890 * q^81 + 6660 * q^82 - 5256 * q^87 - 1132 * q^88 + 916 * q^91 - 6044 * q^92 + 2656 * q^94

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 $

$2$			4.29153i			1.51728i	0.651508	+	0.758642i	$0.274137\pi$
$2$			4.29153i			1.51728i	−0.651508	+	0.758642i	$0.725863\pi$
$3$	−5.89541			−1.13457			−0.567286	−	0.823521i	$-0.692007\pi$
$3$	−5.89541			−1.13457			−0.567286	+	0.823521i	$0.692007\pi$
$4$	−10.4172			−1.30215
$5$		0			0
$5$		0			0
$6$		−	25.3003i		−	1.72147i
$7$			34.1818i			1.84564i	0.385226	+	0.922822i	$0.374123\pi$
$7$			34.1818i			1.84564i	−0.385226	+	0.922822i	$0.625877\pi$
$8$		−	10.3735i		−	0.458450i
$9$	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	$0.910271\pi$
$12$	61.4137			1.47738
$13$	−37.3790	−	28.2809i	−0.797467	−	0.603362i
$13$	−37.3790	−	28.2809i	−0.797467	−	0.603362i
$14$	−146.692			−2.80037
$15$		0			0
$16$	−38.8194			−0.606553
$17$	−75.8275			−1.08182			−0.540908	−	0.841082i	$-0.681919\pi$
$17$	−75.8275			−1.08182			−0.540908	+	0.841082i	$0.681919\pi$
$18$			33.2843i			0.435844i
$19$			106.383i			1.28452i	0.766487	+	0.642259i	$0.222003\pi$
$19$			106.383i			1.28452i	−0.766487	+	0.642259i	$0.777997\pi$
$20$		0			0
$21$		−	201.516i		−	2.09402i
$22$	−87.1059			−0.844139
$23$	−11.7556			−0.106574			−0.0532872	−	0.998579i	$-0.516970\pi$
$23$	−11.7556			−0.106574			−0.0532872	+	0.998579i	$0.516970\pi$
$24$			61.1562i			0.520144i
$25$		0			0
$26$	121.368	−	160.413i	0.915472	−	1.20998i
$27$	113.452			0.808663
$28$		−	356.079i		−	2.40331i
$29$	224.787			1.43937			0.719686	−	0.694299i	$-0.244286\pi$
$29$	224.787			1.43937			0.719686	+	0.694299i	$0.244286\pi$
$30$		0			0
$31$			126.246i			0.731432i	0.930726	+	0.365716i	$0.119176\pi$
$31$			126.246i			0.731432i	−0.930726	+	0.365716i	$0.880824\pi$
$32$		−	249.583i		−	1.37876i
$33$		−	119.660i		−	0.631217i
$34$		−	325.416i		−	1.64142i
$35$		0			0
$36$	−80.7940			−0.374046
$37$			9.49313i			0.0421800i	0.999778	+	0.0210900i	$0.00671366\pi$
$37$			9.49313i			0.0421800i	−0.999778	+	0.0210900i	$0.993286\pi$
$38$	−456.544			−1.94898
$39$	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	$-0.134013\pi$
$42$	864.810			3.17722
$43$	308.118			1.09273			0.546367	−	0.837546i	$-0.316010\pi$
$43$	308.118			1.09273			0.546367	+	0.837546i	$0.316010\pi$
$44$		−	211.440i		−	0.724450i
$45$		0			0
$46$		−	50.4494i		−	0.161704i
$47$			42.4480i			0.131738i	0.997828	+	0.0658689i	$0.0209819\pi$
$47$			42.4480i			0.131738i	−0.997828	+	0.0658689i	$0.979018\pi$
$48$	228.856			0.688178
$49$	−825.396			−2.40640
$50$		0			0
$51$	447.034			1.22740
$52$	389.385	+	294.608i	1.03842	+	0.785669i
$53$	112.704			0.292097			0.146048	−	0.989277i	$-0.453344\pi$
$53$	112.704			0.292097			0.146048	+	0.989277i	$0.453344\pi$
$54$			486.884i			1.22697i
$55$		0			0
$56$	354.586			0.846135
$57$		−	627.169i		−	1.45738i
$58$			964.678i			2.18394i
$59$		−	437.774i		−	0.965989i	−0.875623	−	0.482994i	$-0.839549\pi$
$59$		−	437.774i		−	0.965989i	0.875623	−	0.482994i	$-0.160451\pi$
$60$		0			0
$61$	440.774			0.925170			0.462585	−	0.886575i	$-0.346922\pi$
$61$	440.774			0.925170			0.462585	+	0.886575i	$0.346922\pi$
$62$	−541.787			−1.10979
$63$			265.108i			0.530166i
$64$	760.536			1.48542
$65$		0			0
$66$	513.525			0.957736
$67$		−	758.560i		−	1.38318i	−0.722292	−	0.691588i	$-0.756911\pi$
$67$		−	758.560i		−	1.38318i	0.722292	−	0.691588i	$-0.243089\pi$
$68$	789.911			1.40869
$69$	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	$0.803166\pi$
$72$		−	80.4553i		−	0.131691i
$73$		−	113.362i		−	0.181754i	−0.995862	−	0.0908772i	$-0.971033\pi$
$73$		−	113.362i		−	0.181754i	0.995862	−	0.0908772i	$-0.0289671\pi$
$74$	−40.7400			−0.0639991
$75$		0			0
$76$		−	1108.21i		−	1.67264i
$77$	−693.795			−1.02682
$78$	−715.515	+	945.700i	−1.03867	+	1.37281i
$79$	−1216.88			−1.73304			−0.866520	−	0.499143i	$-0.833648\pi$
$79$	−1216.88			−1.73304			−0.866520	+	0.499143i	$0.833648\pi$
$80$		0			0
$81$	−878.254			−1.20474
$82$	920.893			1.24019
$83$			1117.77i			1.47821i	0.673591	+	0.739105i	$0.264751\pi$
$83$			1117.77i			1.47821i	−0.673591	+	0.739105i	$0.735249\pi$
$84$			2099.23i			2.72673i
$85$		0			0
$86$			1322.30i			1.65799i
$87$	−1325.21			−1.63307
$88$	210.554			0.255058
$89$		−	151.740i		−	0.180724i	−0.995909	−	0.0903621i	$-0.971198\pi$
$89$		−	151.740i		−	0.180724i	0.995909	−	0.0903621i	$-0.0288024\pi$
$90$		0			0
$91$	966.692	−	1277.68i	1.11359	−	1.47184i
$92$	122.460			0.138776
$93$		−	744.270i		−	0.829862i
$94$	−182.167			−0.199884
$95$		0			0
$96$			1471.39i			1.56431i
$97$			179.668i			0.188067i	0.995569	+	0.0940337i	$0.0299761\pi$
$97$			179.668i			0.188067i	−0.995569	+	0.0940337i	$0.970024\pi$
$98$		−	3542.21i		−	3.65120i
$99$			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	$0.534468\pi$
$102$			1918.46i			1.86231i
$103$	1010.41			0.966591			0.483295	−	0.875457i	$-0.339440\pi$
$103$	1010.41			0.966591			0.483295	+	0.875457i	$0.339440\pi$
$104$	−293.373	+	387.752i	−0.276611	+	0.365599i
$105$		0			0
$106$			483.674i			0.443194i
$107$	−694.878			−0.627817			−0.313908	−	0.949453i	$-0.601638\pi$
$107$	−694.878			−0.627817			−0.313908	+	0.949453i	$0.601638\pi$
$108$	−1181.86			−1.05300
$109$		−	1189.96i		−	1.04567i	−0.852435	−	0.522833i	$-0.824875\pi$
$109$		−	1189.96i		−	1.04567i	0.852435	−	0.522833i	$-0.175125\pi$
$110$		0			0
$111$		−	55.9659i		−	0.0478563i
$112$		−	1326.92i		−	1.11948i
$113$	93.2049			0.0775927			0.0387964	−	0.999247i	$-0.487648\pi$
$113$	93.2049			0.0775927			0.0387964	+	0.999247i	$0.487648\pi$
$114$	2691.51			2.21126
$115$		0			0
$116$	−2341.65			−1.87428
$117$	−289.905	−	219.342i	−0.229075	−	0.173317i
$118$	1878.72			1.46568
$119$		−	2591.92i		−	1.99665i
$120$		0			0
$121$	919.024			0.690476
$122$			1891.60i			1.40375i
$123$			1265.06i			0.927370i
$124$		−	1315.13i		−	0.952436i
$125$		0			0
$126$	−1137.72			−0.804413
$127$	779.785			0.544841			0.272420	−	0.962178i	$-0.412176\pi$
$127$	779.785			0.544841			0.272420	+	0.962178i	$0.412176\pi$
$128$			1267.20i			0.875045i
$129$	−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	$0.697097\pi$
$132$			1246.53i			0.821940i
$133$	−3636.35			−2.37076
$134$	3255.38			2.09867
$135$		0			0
$136$			786.599i			0.495958i
$137$			932.185i			0.581328i	0.956825	+	0.290664i	$0.0938762\pi$
$137$			932.185i			0.581328i	−0.956825	+	0.290664i	$0.906124\pi$
$138$			297.420i			0.183464i
$139$	−1445.62			−0.882131			−0.441065	−	0.897475i	$-0.645399\pi$
$139$	−1445.62			−0.882131			−0.441065	+	0.897475i	$0.645399\pi$
$140$		0			0
$141$		−	250.248i		−	0.149466i
$142$	−2976.74			−1.75917
$143$	574.023	−	758.689i	0.335680	−	0.443670i
$144$	−301.076			−0.174234
$145$		0			0
$146$	486.498			0.275773
$147$	4866.05			2.73024
$148$		−	98.8920i		−	0.0549248i
$149$			3510.93i			1.93038i	0.261545	+	0.965191i	$0.415768\pi$
$149$			3510.93i			1.93038i	−0.261545	+	0.965191i	$0.584232\pi$
$150$		0			0
$151$		−	1521.55i		−	0.820013i	−0.912083	−	0.410007i	$-0.865526\pi$
$151$		−	1521.55i		−	0.820013i	0.912083	−	0.410007i	$-0.134474\pi$
$152$	1103.56			0.588887
$153$	−588.105			−0.310755
$154$		−	2977.44i		−	1.55798i
$155$		0			0
$156$	−2295.58	−	1736.83i	−1.17817	−	0.891398i
$157$	−3196.37			−1.62483			−0.812413	−	0.583082i	$-0.801847\pi$
$157$	−3196.37			−1.62483			−0.812413	+	0.583082i	$0.801847\pi$
$158$		−	5222.29i		−	2.62951i
$159$	−664.438			−0.331405
$160$		0			0
$161$		−	401.827i		−	0.196698i
$162$		−	3769.05i		−	1.82793i
$163$			1363.46i			0.655179i	0.944820	+	0.327590i	$0.106236\pi$
$163$			1363.46i			0.655179i	−0.944820	+	0.327590i	$0.893764\pi$
$164$			2235.37i			1.06435i
$165$		0			0
$166$	−4796.95			−2.24286
$167$		−	922.250i		−	0.427340i	−0.976906	−	0.213670i	$-0.931458\pi$
$167$		−	922.250i		−	0.427340i	0.976906	−	0.213670i	$-0.0685418\pi$
$168$	−2090.43			−0.960001
$169$	597.382	+	2114.22i	0.271908	+	0.962323i
$170$		0			0
$171$			825.085i			0.368981i
$172$	−3209.73			−1.42291
$173$	−1361.55			−0.598362			−0.299181	−	0.954196i	$-0.596713\pi$
$173$	−1361.55			−0.598362			−0.299181	+	0.954196i	$0.596713\pi$
$174$		−	5687.17i		−	2.47783i
$175$		0			0
$176$		−	787.925i		−	0.337455i
$177$			2580.86i			1.09598i
$178$	651.198			0.274210
$179$	4222.14			1.76300			0.881501	−	0.472182i	$-0.156534\pi$
$179$	4222.14			1.76300			0.881501	+	0.472182i	$0.156534\pi$
$180$		0			0
$181$	−3487.32			−1.43210			−0.716051	−	0.698048i	$-0.754052\pi$
$181$	−3487.32			−1.43210			−0.716051	+	0.698048i	$0.754052\pi$
$182$	5483.21	+	4148.59i	2.23320	+	1.68964i
$183$	−2598.54			−1.04967
$184$			121.947i			0.0488589i
$185$		0			0
$186$	3194.06			1.25914
$187$		−	1539.09i		−	0.601867i
$188$		−	442.190i		−	0.171543i
$189$			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	$0.412592\pi$
$192$	−4483.67			−1.68532
$193$			131.553i			0.0490641i	0.999699	+	0.0245321i	$0.00780958\pi$
$193$			131.553i			0.0490641i	−0.999699	+	0.0245321i	$0.992190\pi$
$194$	−771.051			−0.285352
$195$		0			0
$196$	8598.33			3.13350
$197$		−	898.804i		−	0.325062i	−0.986703	−	0.162531i	$-0.948034\pi$
$197$		−	898.804i		−	0.325062i	0.986703	−	0.162531i	$-0.0519657\pi$
$198$	−675.578			−0.242481
$199$	−2240.52			−0.798124			−0.399062	−	0.916924i	$-0.630664\pi$
$199$	−2240.52			−0.798124			−0.399062	+	0.916924i	$0.630664\pi$
$200$		0			0
$201$			4472.02i			1.56931i
$202$		−	941.539i		−	0.327953i
$203$			7683.61i			2.65657i
$204$	−4656.85			−1.59826
$205$		0			0
$206$			4336.21i			1.46659i
$207$	−91.1742			−0.0306138
$208$	1451.03	+	1097.85i	0.483706	+	0.365971i
$209$	−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	$0.657550\pi$
$212$	−1174.07			−0.380354
$213$		−	4089.24i		−	1.31544i
$214$		−	2982.09i		−	0.952576i
$215$		0			0
$216$		−	1176.90i		−	0.370731i
$217$	−4315.31			−1.34996
$218$	5106.75			1.58657
$219$			668.318i			0.206213i
$220$		0			0
$221$	2834.36	+	2144.47i	0.862713	+	0.652727i
$222$	240.179			0.0726116
$223$		−	1492.95i		−	0.448321i	−0.974552	−	0.224160i	$-0.928036\pi$
$223$		−	1492.95i		−	0.448321i	0.974552	−	0.224160i	$-0.0719640\pi$
$224$	8531.19			2.54471
$225$		0			0
$226$			399.991i			0.117730i
$227$			3318.55i			0.970309i	0.874428	+	0.485155i	$0.161237\pi$
$227$			3318.55i			0.970309i	−0.874428	+	0.485155i	$0.838763\pi$
$228$			6533.35i			1.89773i
$229$			3754.91i			1.08354i	0.840526	+	0.541772i	$0.182246\pi$
$229$			3754.91i			1.08354i	−0.840526	+	0.541772i	$0.817754\pi$
$230$		0			0
$231$	4090.20			1.16500
$232$		−	2331.83i		−	0.659880i
$233$	6098.90			1.71482			0.857408	−	0.514636i	$-0.172073\pi$
$233$	6098.90			1.71482			0.857408	+	0.514636i	$0.172073\pi$
$234$	941.311	−	1244.14i	0.262972	−	0.347571i
$235$		0			0
$236$			4560.39i			1.25786i
$237$	7174.02			1.96626
$238$	11123.3			3.02948
$239$			2603.41i			0.704606i	0.935886	+	0.352303i	$0.114601\pi$
$239$			2603.41i			0.704606i	−0.935886	+	0.352303i	$0.885399\pi$
$240$		0			0
$241$		−	73.6905i		−	0.0196963i	−0.999952	−	0.00984817i	$-0.996865\pi$
$241$		−	73.6905i		−	0.0196963i	0.999952	−	0.00984817i	$-0.00313482\pi$
$242$			3944.02i			1.04765i
$243$	2114.46			0.558199
$244$	−4591.64			−1.20471
$245$		0			0
$246$	−5429.04			−1.40708
$247$	3008.60	−	3976.48i	0.775030	−	1.02436i
$248$	1309.61			0.335325
$249$		−	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	$0.428792\pi$
$252$		−	2761.69i		−	0.690357i
$253$		−	238.605i		−	0.0592924i
$254$			3346.47i			0.826678i
$255$		0			0
$256$	646.064			0.157731
$257$	−6778.90			−1.64535			−0.822677	−	0.568508i	$-0.807521\pi$
$257$	−6778.90			−1.64535			−0.822677	+	0.568508i	$0.807521\pi$
$258$		−	7795.48i		−	1.88111i
$259$	−324.492			−0.0778493
$260$		0			0
$261$	1743.40			0.413464
$262$		−	7469.01i		−	1.76121i
$263$	−5829.83			−1.36686			−0.683428	−	0.730018i	$-0.739512\pi$
$263$	−5829.83			−1.36686			−0.683428	+	0.730018i	$0.739512\pi$
$264$	−1241.30			−0.289381
$265$		0			0
$266$		−	15605.5i		−	3.59712i
$267$			894.572i			0.205045i
$268$			7902.08i			1.80111i
$269$	1701.60			0.385682			0.192841	−	0.981230i	$-0.438230\pi$
$269$	1701.60			0.385682			0.192841	+	0.981230i	$0.438230\pi$
$270$		0			0
$271$		−	5238.97i		−	1.17434i	−0.809465	−	0.587168i	$-0.800243\pi$
$271$		−	5238.97i		−	1.17434i	0.809465	−	0.587168i	$-0.199757\pi$
$272$	2943.58			0.656179
$273$	−5699.04	+	7532.46i	−1.26345	+	1.66991i
$274$	−4000.50			−0.882040
$275$		0			0
$276$	−721.954			−0.157451
$277$	−3327.15			−0.721694			−0.360847	−	0.932625i	$-0.617512\pi$
$277$	−3327.15			−0.721694			−0.360847	+	0.932625i	$0.617512\pi$
$278$		−	6203.93i		−	1.33844i
$279$			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	$-0.290970\pi$
$282$	1073.95			0.226782
$283$	−8288.85			−1.74106			−0.870532	−	0.492112i	$-0.836225\pi$
$283$	−8288.85			−1.74106			−0.870532	+	0.492112i	$0.836225\pi$
$284$		−	7225.70i		−	1.50974i
$285$		0			0
$286$	3255.93	+	2463.43i	0.673173	+	0.509321i
$287$	7334.87			1.50858
$288$		−	1935.72i		−	0.396053i
$289$	836.812			0.170326
$290$		0			0
$291$		−	1059.22i		−	0.213376i
$292$			1180.92i			0.236672i
$293$		−	940.431i		−	0.187510i	−0.995595	−	0.0937552i	$-0.970113\pi$
$293$		−	940.431i		−	0.187510i	0.995595	−	0.0937552i	$-0.0298871\pi$
$294$			20882.8i			4.14254i
$295$		0			0
$296$	98.4773			0.0193374
$297$			2302.76i			0.449898i
$298$	−15067.3			−2.92894
$299$	439.412	+	332.458i	0.0849895	+	0.0643029i
$300$		0			0
$301$			10532.0i			2.01680i
$302$	6529.78			1.24419
$303$	1293.42			0.245231
$304$		−	4129.71i		−	0.779129i
$305$		0			0
$306$		−	2523.87i		−	0.471503i
$307$		−	7526.42i		−	1.39920i	−0.714533	−	0.699602i	$-0.753361\pi$
$307$		−	7526.42i		−	1.39920i	0.714533	−	0.699602i	$-0.246639\pi$
$308$	7227.41			1.33708
$309$	−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	$0.390004\pi$
$312$	1729.55	−	2285.96i	0.313835	−	0.414798i
$313$	5715.69			1.03217			0.516086	−	0.856536i	$-0.327388\pi$
$313$	5715.69			1.03217			0.516086	+	0.856536i	$0.327388\pi$
$314$		−	13717.3i		−	2.46532i
$315$		0			0
$316$	12676.5			2.25668
$317$			3825.01i			0.677709i	0.940839	+	0.338855i	$0.110040\pi$
$317$			3825.01i			0.677709i	−0.940839	+	0.338855i	$0.889960\pi$
$318$		−	2851.45i		−	0.502835i
$319$			4562.53i			0.800793i
$320$		0			0
$321$	4096.59			0.712303
$322$	1724.45			0.298447
$323$		−	8066.73i		−	1.38961i
$324$	9148.96			1.56875
$325$		0			0
$326$	−5851.31			−0.994093
$327$			7015.31i			1.18638i
$328$	−2225.99			−0.374725
$329$	−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	$-0.105361\pi$
$332$		−	11644.1i		−	1.92485i
$333$			73.6270i			0.0121163i
$334$	3957.86			0.648397
$335$		0			0
$336$			7822.72i			1.27013i
$337$	4622.42			0.747179			0.373589	−	0.927594i	$-0.378127\pi$
$337$	4622.42			0.747179			0.373589	+	0.927594i	$0.378127\pi$
$338$	−9073.25	+	2563.68i	−1.46012	+	0.412562i
$339$	−549.481			−0.0880345
$340$		0			0
$341$	−2562.43			−0.406931
$342$	−3540.88			−0.559850
$343$		−	16489.2i		−	2.59572i
$344$		−	3196.27i		−	0.500964i
$345$		0			0
$346$		−	5843.12i		−	0.907885i
$347$	8192.01			1.26735			0.633674	−	0.773600i	$-0.281546\pi$
$347$	8192.01			1.26735			0.633674	+	0.773600i	$0.281546\pi$
$348$	13805.0			2.12651
$349$			243.024i			0.0372744i	0.999826	+	0.0186372i	$0.00593275\pi$
$349$			243.024i			0.0372744i	−0.999826	+	0.0186372i	$0.994067\pi$
$350$		0			0
$351$	−4240.73	−	3208.53i	−0.644882	−	0.487917i
$352$	5065.83			0.767073
$353$			2766.97i			0.417198i	0.978001	+	0.208599i	$0.0668904\pi$
$353$			2766.97i			0.417198i	−0.978001	+	0.208599i	$0.933110\pi$
$354$	−11075.8			−1.66292
$355$		0			0
$356$			1580.71i			0.235330i
$357$			15280.4i			2.26534i
$358$			18119.4i			2.67497i
$359$			2472.79i			0.363535i	0.983342	+	0.181768i	$0.0581818\pi$
$359$			2472.79i			0.363535i	−0.983342	+	0.181768i	$0.941818\pi$
$360$		0			0
$361$	−4458.27			−0.649988
$362$		−	14965.9i		−	2.17291i
$363$	−5418.02			−0.783395
$364$	−10070.2	+	13309.9i	−1.45007	+	1.91656i
$365$		0			0
$366$		−	11151.7i		−	1.59265i
$367$	−5263.61			−0.748660			−0.374330	−	0.927296i	$-0.622127\pi$
$367$	−5263.61			−0.748660			−0.374330	+	0.927296i	$0.622127\pi$
$368$	456.345			0.0646430
$369$		−	1664.27i		−	0.234793i
$370$		0			0
$371$			3852.44i			0.539107i
$372$			7753.22i			1.08061i
$373$	−5633.17			−0.781969			−0.390984	−	0.920397i	$-0.627865\pi$
$373$	−5633.17			−0.781969			−0.390984	+	0.920397i	$0.627865\pi$
$374$	6605.03			0.913203
$375$		0			0
$376$	440.336			0.0603952
$377$	−8402.30	−	6357.16i	−1.14785	−	0.868463i
$378$	−16642.6			−2.26455
$379$		−	9079.61i		−	1.23058i	−0.788302	−	0.615288i	$-0.789040\pi$
$379$		−	9079.61i		−	1.23058i	0.788302	−	0.615288i	$-0.210960\pi$
$380$		0			0
$381$	−4597.15			−0.618161
$382$			6143.58i			0.822861i
$383$		−	1196.31i		−	0.159604i	−0.996811	−	0.0798022i	$-0.974571\pi$
$383$		−	1196.31i		−	0.159604i	0.996811	−	0.0798022i	$-0.0254289\pi$
$384$		−	7470.66i		−	0.992801i
$385$		0			0
$386$	−564.562			−0.0744442
$387$	2389.71			0.313891
$388$		−	1871.64i		−	0.244892i
$389$	1888.94			0.246203			0.123102	−	0.992394i	$-0.460716\pi$
$389$	1888.94			0.246203			0.123102	+	0.992394i	$0.460716\pi$
$390$		0			0
$391$	891.397			0.115294
$392$			8562.27i			1.10321i
$393$	10260.4			1.31697
$394$	3857.24			0.493211
$395$		0			0
$396$		−	1639.89i		−	0.208100i
$397$			9297.50i			1.17539i	0.809084	+	0.587693i	$0.199964\pi$
$397$			9297.50i			1.17539i	−0.809084	+	0.587693i	$0.800036\pi$
$398$		−	9615.27i		−	1.21098i
$399$	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	$-0.0553379\pi$
$402$	−19191.8			−2.38109
$403$	3570.34	−	4718.94i	0.441319	−	0.583293i
$404$	2285.48			0.281453
$405$		0			0
$406$	−32974.4			−4.03077
$407$	−192.684			−0.0234668
$408$		−	4637.32i		−	0.562700i
$409$		−	202.305i		−	0.0244581i	−0.999925	−	0.0122290i	$-0.996107\pi$
$409$		−	202.305i		−	0.0244581i	0.999925	−	0.0122290i	$-0.00389272\pi$
$410$		0			0
$411$		−	5495.61i		−	0.659558i
$412$	−10525.7			−1.25865
$413$	14963.9			1.78287
$414$		−	391.277i		−	0.0464498i
$415$		0			0
$416$	−7058.42	+	9329.16i	−0.831894	+	1.09952i
$417$	8522.54			1.00084
$418$		−	9266.56i		−	1.08431i
$419$	−14295.5			−1.66678			−0.833390	−	0.552685i	$-0.813603\pi$
$419$	−14295.5			−1.66678			−0.833390	+	0.552685i	$0.813603\pi$
$420$		0			0
$421$		−	3873.61i		−	0.448428i	−0.974540	−	0.224214i	$-0.928019\pi$
$421$		−	3873.61i		−	0.448428i	0.974540	−	0.224214i	$-0.0719815\pi$
$422$		−	12495.5i		−	1.44140i
$423$			329.219i			0.0378421i
$424$		−	1169.14i		−	0.133912i
$425$		0			0
$426$	17549.1			1.99590
$427$			15066.5i			1.70753i
$428$	7238.69			0.817512
$429$	−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	$-0.0291322\pi$
$432$	−4404.15			−0.490497
$433$	5504.75			0.610950			0.305475	−	0.952200i	$-0.401185\pi$
$433$	5504.75			0.610950			0.305475	+	0.952200i	$0.401185\pi$
$434$		−	18519.3i		−	2.04828i
$435$		0			0
$436$			12396.1i			1.36162i
$437$		−	1250.59i		−	0.136897i
$438$	−2868.10			−0.312884
$439$	4613.62			0.501585			0.250793	−	0.968041i	$-0.419309\pi$
$439$	4613.62			0.501585			0.250793	+	0.968041i	$0.419309\pi$
$440$		0			0
$441$	−6401.63			−0.691246
$442$	−9203.05	+	12163.7i	−0.990372	+	1.30898i
$443$	13293.5			1.42572			0.712862	−	0.701305i	$-0.247399\pi$
$443$	13293.5			1.42572			0.712862	+	0.701305i	$0.247399\pi$
$444$			583.008i			0.0623161i
$445$		0			0
$446$	6407.05			0.680230
$447$		−	20698.4i		−	2.19016i
$448$			25996.5i			2.74156i
$449$			7629.93i			0.801957i	0.916088	+	0.400978i	$0.131330\pi$
$449$			7629.93i			0.801957i	−0.916088	+	0.400978i	$0.868670\pi$
$450$		0			0
$451$	4355.45			0.454745
$452$	−970.935			−0.101037
$453$			8970.16i			0.930364i
$454$	−14241.7			−1.47223
$455$		0			0
$456$	−6505.96			−0.668135
$457$		−	13439.5i		−	1.37566i	−0.725873	−	0.687829i	$-0.758564\pi$
$457$		−	13439.5i		−	1.37566i	0.725873	−	0.687829i	$-0.241436\pi$
$458$	−16114.3			−1.64404
$459$	−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	$0.703688\pi$
$462$			17553.2i			1.76764i
$463$			14962.5i			1.50187i	0.660374	+	0.750937i	$0.270398\pi$
$463$			14962.5i			1.50187i	−0.660374	+	0.750937i	$0.729602\pi$
$464$	−8726.08			−0.873056
$465$		0			0
$466$			26173.6i			2.60186i
$467$	7204.07			0.713843			0.356922	−	0.934134i	$-0.383826\pi$
$467$	7204.07			0.713843			0.356922	+	0.934134i	$0.383826\pi$
$468$	3020.00	+	2284.93i	0.298290	+	0.225686i
$469$	25929.0			2.55285
$470$		0			0
$471$	18843.9			1.84348
$472$	−4541.26			−0.442857
$473$			6253.93i			0.607941i
$474$			30787.5i			2.98337i
$475$		0			0
$476$			27000.6i			2.59994i
$477$	874.115			0.0839056
$478$	−11172.6			−1.06909
$479$			11072.8i			1.05621i	0.849178	+	0.528107i	$0.177098\pi$
$479$			11072.8i			1.05621i	−0.849178	+	0.528107i	$0.822902\pi$
$480$		0			0
$481$	268.474	−	354.844i	0.0254498	−	0.0336372i
$482$	316.245			0.0298850
$483$			2368.93i			0.223168i
$484$	−9573.67			−0.899105
$485$		0			0
$486$			9074.25i			0.846947i
$487$			6559.96i			0.610391i	0.952290	+	0.305195i	$0.0987218\pi$
$487$			6559.96i			0.610391i	−0.952290	+	0.305195i	$0.901278\pi$
$488$		−	4572.39i		−	0.424144i
$489$		−	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	$0.411816\pi$
$492$		−	13178.4i		−	1.20758i
$493$	−17045.0			−1.55714
$494$	17065.2	+	12911.5i	1.55425	+	1.17594i
$495$		0			0
$496$		−	4900.78i		−	0.443653i
$497$	−23709.6			−2.13988
$498$	28280.0			2.54469
$499$			203.291i			0.0182376i	0.999958	+	0.00911880i	$0.00290264\pi$
$499$			203.291i			0.0182376i	−0.999958	+	0.00911880i	$0.997097\pi$
$500$		0			0
$501$			5437.04i			0.484848i
$502$			7571.84i			0.673203i
$503$	−4109.83			−0.364311			−0.182155	−	0.983270i	$-0.558307\pi$
$503$	−4109.83			−0.364311			−0.182155	+	0.983270i	$0.558307\pi$
$504$	2750.11			0.243055
$505$		0			0
$506$	1023.98			0.0899635
$507$	−3521.81	−	12464.2i	−0.308499	−	1.09182i
$508$	−8123.19			−0.709465
$509$		−	19836.8i		−	1.72741i	−0.503997	−	0.863705i	$-0.668138\pi$
$509$		−	19836.8i		−	1.72741i	0.503997	−	0.863705i	$-0.331862\pi$
$510$		0			0
$511$	3874.93			0.335454
$512$			12910.2i			1.11437i
$513$			12069.4i			1.03874i
$514$		−	29091.8i		−	2.49647i
$515$		0			0
$516$	18922.7			1.61439
$517$	−861.575			−0.0732922
$518$		−	1392.57i		−	0.118120i
$519$	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	$0.759950\pi$
$522$			7481.87i			0.627342i
$523$	−2886.27			−0.241315			−0.120658	−	0.992694i	$-0.538500\pi$
$523$	−2886.27			−0.241315			−0.120658	+	0.992694i	$0.538500\pi$
$524$	18130.2			1.51149
$525$		0			0
$526$		−	25018.9i		−	2.07391i
$527$		−	9572.90i		−	0.791275i
$528$			4645.14i			0.382867i
$529$	−12028.8			−0.988642
$530$		0			0
$531$		−	3395.30i		−	0.277483i
$532$	37880.6			3.08709
$533$	−6068.62	+	8020.94i	−0.493173	+	0.651830i
$534$	−3839.08			−0.311111
$535$		0			0
$536$	−7868.94			−0.634117
$537$	−24891.2			−2.00025
$538$			7302.47i			0.585190i
$539$		−	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	$-0.194342\pi$
$542$	22483.2			1.78180
$543$	20559.2			1.62482
$544$			18925.2i			1.49157i
$545$		0			0
$546$	−32325.8	−	24457.6i	−2.53373	−	1.91701i
$547$	−17024.1			−1.33071			−0.665353	−	0.746529i	$-0.731719\pi$
$547$	−17024.1			−1.33071			−0.665353	+	0.746529i	$0.731719\pi$
$548$		−	9710.77i		−	0.756977i
$549$	3418.57			0.265758
$550$		0			0
$551$			23913.4i			1.84890i
$552$		−	718.927i		−	0.0554340i
$553$		−	41595.3i		−	3.19857i
$554$		−	14278.6i		−	1.09502i
$555$		0			0
$556$	15059.4			1.14867
$557$			12087.4i			0.919498i	0.888049	+	0.459749i	$0.152061\pi$
$557$			12087.4i			0.919498i	−0.888049	+	0.459749i	$0.847939\pi$
$558$	−4202.00			−0.318790
$559$	−11517.2	−	8713.86i	−0.871420	−	0.659315i
$560$		0			0
$561$			9073.53i			0.682861i
$562$	32021.2			2.40344
$563$	2618.53			0.196017			0.0980086	−	0.995186i	$-0.468753\pi$
$563$	2618.53			0.196017			0.0980086	+	0.995186i	$0.468753\pi$
$564$			2606.89i			0.194627i
$565$		0			0
$566$		−	35571.8i		−	2.64169i
$567$		−	30020.3i		−	2.22352i
$568$	7195.40			0.531536
$569$	6859.30			0.505372			0.252686	−	0.967548i	$-0.418686\pi$
$569$	6859.30			0.505372			0.252686	+	0.967548i	$0.418686\pi$
$570$		0			0
$571$	−15207.9			−1.11459			−0.557297	−	0.830314i	$-0.688161\pi$
$571$	−15207.9			−1.11459			−0.557297	+	0.830314i	$0.688161\pi$
$572$	−5979.72	+	7903.42i	−0.437106	+	0.577725i
$573$	−8439.63			−0.615306
$574$			31477.8i			2.28895i
$575$		0			0
$576$	5898.58			0.426692
$577$		−	17531.0i		−	1.26486i	−0.774618	−	0.632429i	$-0.782058\pi$
$577$		−	17531.0i		−	1.26486i	0.774618	−	0.632429i	$-0.217942\pi$
$578$			3591.20i			0.258433i
$579$		−	775.557i		−	0.0556668i
$580$		0			0
$581$	−38207.5			−2.72825
$582$	4545.66			0.323752
$583$			2287.58i			0.162508i
$584$	−1175.97			−0.0833252
$585$		0			0
$586$	4035.89			0.284507
$587$			5988.25i			0.421059i	0.977588	+	0.210529i	$0.0675188\pi$
$587$			5988.25i			0.421059i	−0.977588	+	0.210529i	$0.932481\pi$
$588$	−50690.6			−3.55518
$589$	−13430.4			−0.939539
$590$		0			0
$591$			5298.82i			0.368806i
$592$		−	368.518i		−	0.0255844i
$593$		−	15990.9i		−	1.10737i	−0.832728	−	0.553683i	$-0.813222\pi$
$593$		−	15990.9i		−	1.10737i	0.832728	−	0.553683i	$-0.186778\pi$
$594$	−9882.37			−0.682624
$595$		0			0
$596$		−	36574.1i		−	2.51365i
$597$	13208.8			0.905528
$598$	−1426.75	+	1885.75i	−0.0975658	+	0.128953i
$599$	8103.88			0.552781			0.276390	−	0.961045i	$-0.410862\pi$
$599$	8103.88			0.552781			0.276390	+	0.961045i	$0.410862\pi$
$600$		0			0
$601$	5291.20			0.359122			0.179561	−	0.983747i	$-0.442532\pi$
$601$	5291.20			0.359122			0.179561	+	0.983747i	$0.442532\pi$
$602$	−45198.5			−3.06006
$603$		−	5883.26i		−	0.397321i
$604$			15850.3i			1.06778i
$605$		0			0
$606$			5550.75i			0.372086i
$607$	11506.8			0.769431			0.384715	−	0.923035i	$-0.374300\pi$
$607$	11506.8			0.769431			0.384715	+	0.923035i	$0.374300\pi$
$608$	26551.3			1.77105
$609$		−	45298.0i		−	3.01407i
$610$		0			0
$611$	1200.47	−	1586.67i	0.0794857	−	0.105057i
$612$	6126.41			0.404650
$613$		−	4997.20i		−	0.329258i	−0.986356	−	0.164629i	$-0.947357\pi$
$613$		−	4997.20i		−	0.329258i	0.986356	−	0.164629i	$-0.0526426\pi$
$614$	32299.9			2.12299
$615$		0			0
$616$			7197.10i			0.470746i
$617$		−	1546.06i		−	0.100878i	−0.998727	−	0.0504392i	$-0.983938\pi$
$617$		−	1546.06i		−	0.100878i	0.998727	−	0.0504392i	$-0.0160621\pi$
$618$		−	25563.7i		−	1.66395i
$619$			7719.68i			0.501260i	0.968083	+	0.250630i	$0.0806378\pi$
$619$			7719.68i			0.501260i	−0.968083	+	0.250630i	$0.919362\pi$
$620$		0			0
$621$	−1333.70			−0.0861827
$622$			15945.3i			1.02789i
$623$	5186.76			0.333553
$624$	−8554.42	−	6472.26i	−0.548799	−	0.415221i
$625$		0			0
$626$			24529.1i			1.56610i
$627$	12729.8			0.810810
$628$	33297.2			2.11577
$629$		−	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	$-0.0709676\pi$
$632$			12623.4i			0.794511i
$633$	17165.5			1.07783
$634$	−16415.1			−1.02828
$635$		0			0
$636$	6921.59			0.431539
$637$	30852.5	+	23342.9i	1.91903	+	1.45193i
$638$	−19580.2			−1.21503
$639$			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	$0.469635\pi$
$642$			17580.6i			1.08077i
$643$			5872.84i			0.360190i	0.983649	+	0.180095i	$0.0576405\pi$
$643$			5872.84i			0.360190i	−0.983649	+	0.180095i	$0.942359\pi$
$644$			4185.92i			0.256131i
$645$		0			0
$646$	34618.6			2.10844
$647$	−7029.20			−0.427120			−0.213560	−	0.976930i	$-0.568506\pi$
$647$	−7029.20			−0.427120			−0.213560	+	0.976930i	$0.568506\pi$
$648$			9110.60i			0.552312i
$649$	8885.59			0.537426
$650$		0			0
$651$	25440.5			1.53163
$652$		−	14203.4i		−	0.853142i
$653$	−4151.74			−0.248806			−0.124403	−	0.992232i	$-0.539701\pi$
$653$	−4151.74			−0.248806			−0.124403	+	0.992232i	$0.539701\pi$
$654$	−30106.4			−1.80008
$655$		0			0
$656$			8330.02i			0.495781i
$657$		−	879.219i		−	0.0522094i
$658$		−	6226.79i		−	0.368914i
$659$	5191.50			0.306877			0.153439	−	0.988158i	$-0.450965\pi$
$659$	5191.50			0.306877			0.153439	+	0.988158i	$0.450965\pi$
$660$		0			0
$661$			787.020i			0.0463109i	0.999732	+	0.0231555i	$0.00737127\pi$
$661$			787.020i			0.0463109i	−0.999732	+	0.0231555i	$0.992629\pi$
$662$	16797.9			0.986206
$663$	−16709.7	−	12642.5i	−0.978810	−	0.740565i
$664$	11595.2			0.677685
$665$		0			0
$666$	−315.973			−0.0183839
$667$	−2642.50			−0.153400
$668$			9607.27i			0.556462i
$669$			8801.57i			0.508652i
$670$		0			0
$671$			8946.48i			0.514717i
$672$	−50294.8			−2.88715
$673$	−10073.1			−0.576952			−0.288476	−	0.957487i	$-0.593149\pi$
$673$	−10073.1			−0.576952			−0.288476	+	0.957487i	$0.593149\pi$
$674$			19837.2i			1.13368i
$675$		0			0
$676$	−6223.06	−	22024.3i	−0.354065	−	1.25309i
$677$	−6795.48			−0.385778			−0.192889	−	0.981221i	$-0.561786\pi$
$677$	−6795.48			−0.385778			−0.192889	+	0.981221i	$0.561786\pi$
$678$		−	2358.11i		−	0.133573i
$679$	−6141.38			−0.347105
$680$		0			0
$681$		−	19564.2i		−	1.10089i
$682$		−	10996.8i		−	0.617430i
$683$			8789.65i			0.492426i	0.969216	+	0.246213i	$0.0791862\pi$
$683$			8789.65i			0.492426i	−0.969216	+	0.246213i	$0.920814\pi$
$684$		−	8595.09i		−	0.480470i
$685$		0			0
$686$	70763.7			3.93844
$687$		−	22136.7i		−	1.22936i
$688$	−11961.0			−0.662801
$689$	−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	$-0.453461\pi$
$692$	14183.5			0.779158
$693$	−5380.95			−0.294957
$694$			35156.2i			1.92293i
$695$		0			0
$696$			13747.1i			0.748681i
$697$			16271.4i			0.884249i
$698$	−1042.94			−0.0565559
$699$	−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	$0.426159\pi$
$702$	13769.5	−	18199.2i	0.740308	−	0.978470i
$703$	−1009.90			−0.0541810
$704$			15436.7i			0.826412i
$705$		0			0
$706$	−11874.5			−0.633009
$707$		−	7499.31i		−	0.398926i
$708$		−	26885.3i		−	1.42714i
$709$			16404.0i			0.868923i	0.900690	+	0.434462i	$0.143061\pi$
$709$			16404.0i			0.868923i	−0.900690	+	0.434462i	$0.856939\pi$
$710$		0			0
$711$	−9437.93			−0.497820
$712$	−1574.08			−0.0828529
$713$		−	1484.09i		−	0.0779519i
$714$	−65576.4			−3.43716
$715$		0			0
$716$	−43982.9			−2.29570
$717$		−	15348.2i		−	0.799426i
$718$	−10612.1			−0.551586
$719$	1640.70			0.0851012			0.0425506	−	0.999094i	$-0.486452\pi$
$719$	1640.70			0.0851012			0.0425506	+	0.999094i	$0.486452\pi$
$720$		0			0
$721$			34537.7i			1.78398i
$722$		−	19132.8i		−	0.986217i
$723$			434.435i			0.0223469i
$724$	36328.2			1.86481
$725$		0			0
$726$		−	23251.6i		−	1.18863i
$727$	3373.78			0.172114			0.0860569	−	0.996290i	$-0.472573\pi$
$727$	3373.78			0.172114			0.0860569	+	0.996290i	$0.472573\pi$
$728$	−13254.1	−	10028.0i	−0.674765	−	0.510526i
$729$	11247.3			0.571422
$730$		0			0
$731$	−23363.8			−1.18214
$732$	27069.6			1.36683
$733$			26029.1i			1.31161i	0.754932	+	0.655803i	$0.227670\pi$
$733$			26029.1i			1.31161i	−0.754932	+	0.655803i	$0.772330\pi$
$734$		−	22588.9i		−	1.13593i
$735$		0			0
$736$			2933.99i			0.146941i
$737$	15396.6			0.769528
$738$	7142.28			0.356248
$739$			32836.8i			1.63454i	0.576258	+	0.817268i	$0.304512\pi$
$739$			32836.8i			1.63454i	−0.576258	+	0.817268i	$0.695488\pi$
$740$		0			0
$741$	−17736.9	+	23443.0i	−0.879327	+	1.16221i
$742$	−16532.8			−0.817978
$743$			7026.50i			0.346941i	0.984839	+	0.173471i	$0.0554982\pi$
$743$			7026.50i			0.346941i	−0.984839	+	0.173471i	$0.944502\pi$
$744$	−7720.71			−0.380450
$745$		0			0
$746$		−	24174.9i		−	1.18647i
$747$			8669.24i			0.424620i
$748$			16033.0i			0.783722i
$749$		−	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	$0.346278\pi$
$752$		−	1647.81i		−	0.0799060i
$753$	−10401.7			−0.503397
$754$	27281.9	−	36058.7i	1.31771	−	1.74162i
$755$		0			0
$756$		−	40398.0i		−	1.94347i
$757$	1293.50			0.0621046			0.0310523	−	0.999518i	$-0.490114\pi$
$757$	1293.50			0.0621046			0.0310523	+	0.999518i	$0.490114\pi$
$758$	38965.4			1.86713
$759$			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	$-0.237593\pi$
$762$		−	19728.8i		−	0.937926i
$763$	40675.0			1.92993
$764$	−14912.9			−0.706189
$765$		0			0
$766$	5133.99			0.242165
$767$	−12380.6	+	16363.6i	−0.582841	+	0.770345i
$768$	−3808.81			−0.178957
$769$			2327.55i			0.109147i	0.998510	+	0.0545733i	$0.0173798\pi$
$769$			2327.55i			0.109147i	−0.998510	+	0.0545733i	$0.982620\pi$
$770$		0			0
$771$	39964.4			1.86677
$772$		−	1370.41i		−	0.0638889i
$773$		−	2598.20i		−	0.120893i	−0.998171	−	0.0604467i	$-0.980747\pi$
$773$		−	2598.20i		−	0.120893i	0.998171	−	0.0604467i	$-0.0192525\pi$
$774$			10255.5i			0.476262i
$775$		0			0
$776$	1863.79			0.0862194
$777$	1913.01			0.0883256
$778$			8106.43i			0.373560i
$779$	22828.0			1.04993
$780$		0			0
$781$	−14078.8			−0.645041
$782$			3825.45i			0.174933i
$783$	25502.5			1.16397
$784$	32041.4			1.45961
$785$		0			0
$786$			44032.8i			1.99822i
$787$		−	1799.68i		−	0.0815140i	−0.999169	−	0.0407570i	$-0.987023\pi$
$787$		−	1799.68i		−	0.0815140i	0.999169	−	0.0407570i	$-0.0129769\pi$
$788$			9363.03i			0.423280i
$789$	34369.2			1.55080
$790$		0			0
$791$			3185.91i			0.143209i
$792$	1633.02			0.0732660
$793$	−16475.7	−	12465.5i	−0.737793	−	0.558213i
$794$	−39900.5			−1.78339
$795$		0			0
$796$	23340.0			1.03928
$797$	13328.9			0.592388			0.296194	−	0.955128i	$-0.404283\pi$
$797$	13328.9			0.592388			0.296194	+	0.955128i	$0.404283\pi$
$798$			92000.8i			4.08119i
$799$		−	3218.73i		−	0.142516i
$800$		0			0
$801$		−	1176.87i		−	0.0519135i
$802$	11921.8			0.524904
$803$	2300.94			0.101119
$804$		−	46586.0i		−	2.04348i
$805$		0			0
$806$	20251.5	+	15322.2i	0.885022	+	0.669606i
$807$	−10031.6			−0.437584
$808$			2275.90i			0.0990914i
$809$	−6514.79			−0.283125			−0.141562	−	0.989929i	$-0.545213\pi$
$809$	−6514.79			−0.283125			−0.141562	+	0.989929i	$0.545213\pi$
$810$		0			0
$811$		−	7474.15i		−	0.323617i	−0.986822	−	0.161808i	$-0.948267\pi$
$811$		−	7474.15i		−	0.323617i	0.986822	−	0.161808i	$-0.0517326\pi$
$812$		−	80041.8i		−	3.45926i
$813$			30885.9i			1.33237i
$814$		−	826.908i		−	0.0356058i
$815$		0			0
$816$	−17353.6			−0.744482
$817$			32778.4i			1.40364i
$818$	868.199			0.0371099
$819$	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	$0.857292\pi$
$822$	23584.6			1.00074
$823$	−32999.0			−1.39766			−0.698829	−	0.715288i	$-0.746295\pi$
$823$	−32999.0			−1.39766			−0.698829	+	0.715288i	$0.746295\pi$
$824$		−	10481.5i		−	0.443133i
$825$		0			0
$826$			64218.1i			2.70512i
$827$			9715.21i			0.408502i	0.978919	+	0.204251i	$0.0654758\pi$
$827$			9715.21i			0.408502i	−0.978919	+	0.204251i	$0.934524\pi$
$828$	949.781			0.0398637
$829$	29994.8			1.25665			0.628324	−	0.777951i	$-0.283741\pi$
$829$	29994.8			1.25665			0.628324	+	0.777951i	$0.283741\pi$
$830$		0			0
$831$	19614.9			0.818814
$832$	−28428.1	−	21508.6i	−1.18458	−	0.896248i
$833$	62587.7			2.60328
$834$			36574.7i			1.51856i
$835$		0			0
$836$	22493.6			0.930569
$837$			14322.9i			0.591482i
$838$		−	61349.5i		−	2.52898i
$839$			7057.85i			0.290422i	0.989401	+	0.145211i	$0.0463861\pi$
$839$			7057.85i			0.290422i	−0.989401	+	0.145211i	$0.953614\pi$
$840$		0			0
$841$	26140.0			1.07179
$842$	16623.7			0.680393
$843$			43988.5i			1.79721i
$844$	30331.5			1.23703
$845$		0			0
$846$	−1412.85			−0.0574172
$847$			31413.9i			1.27437i
$848$	−4375.11			−0.177172
$849$	48866.2			1.97536
$850$		0			0
$851$		−	111.597i		−	0.00449531i
$852$			42598.4i			1.71291i
$853$		−	9202.00i		−	0.369368i	−0.982798	−	0.184684i	$-0.940874\pi$
$853$		−	9202.00i		−	0.369368i	0.982798	−	0.184684i	$-0.0591261\pi$
$854$	−64658.1			−2.59082
$855$		0			0
$856$			7208.34i			0.287822i
$857$	−41288.6			−1.64573			−0.822866	−	0.568235i	$-0.807626\pi$
$857$	−41288.6			−1.64573			−0.822866	+	0.568235i	$0.807626\pi$
$858$	−19195.1	−	14522.9i	−0.763763	−	0.577862i
$859$	−33717.1			−1.33925			−0.669623	−	0.742702i	$-0.733544\pi$
$859$	−33717.1			−1.33925			−0.669623	+	0.742702i	$0.733544\pi$
$860$		0			0
$861$	−43242.0			−1.71160
$862$	7018.98			0.277341
$863$		−	8063.90i		−	0.318075i	−0.987273	−	0.159037i	$-0.949161\pi$
$863$		−	8063.90i		−	0.318075i	0.987273	−	0.159037i	$-0.0508390\pi$
$864$		−	28315.7i		−	1.11495i
$865$		0			0
$866$			23623.8i			0.926985i
$867$	−4933.35			−0.193247
$868$	44953.5			1.75786
$869$		−	24699.3i		−	0.964174i
$870$		0			0
$871$	−21452.8	+	28354.2i	−0.834557	+	1.10304i
$872$	−12344.1			−0.479386
$873$			1393.47i			0.0540229i
$874$	5366.94			0.207711
$875$		0			0
$876$		−	6962.01i		−	0.268521i
$877$		−	16211.6i		−	0.624203i	−0.950049	−	0.312102i	$-0.898967\pi$
$877$		−	16211.6i		−	0.624203i	0.950049	−	0.312102i	$-0.101033\pi$
$878$			19799.5i			0.761047i
$879$			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	$0.443962\pi$
$882$		−	27472.8i		−	1.04882i
$883$	20476.8			0.780408			0.390204	−	0.920728i	$-0.372405\pi$
$883$	20476.8			0.780408			0.390204	+	0.920728i	$0.372405\pi$
$884$	−29526.1	−	22339.4i	−1.12338	−	0.849949i
$885$		0			0
$886$			57049.6i			2.16323i
$887$	7491.56			0.283587			0.141794	−	0.989896i	$-0.454713\pi$
$887$	7491.56			0.283587			0.141794	+	0.989896i	$0.454713\pi$
$888$	−580.564			−0.0219397
$889$			26654.5i			1.00558i
$890$		0			0
$891$		−	17826.1i		−	0.670254i
$892$			15552.4i			0.583782i
$893$	−4515.73			−0.169220
$894$	88827.7			3.32309
$895$		0			0
$896$	−43315.2			−1.61502
$897$	−2590.51	−	1959.98i	−0.0964267	−	0.0729563i
$898$	−32744.0			−1.21680
$899$			28378.3i			1.05280i
$900$		0			0
$901$	−8546.09			−0.315995
$902$			18691.5i			0.689978i
$903$		−	62090.6i		−	2.28820i
$904$		−	966.864i		−	0.0355724i
$905$		0			0
$906$	−38495.7			−1.41163
$907$	50090.1			1.83375			0.916877	−	0.399170i	$-0.130702\pi$
$907$	50090.1			1.83375			0.916877	+	0.399170i	$0.130702\pi$
$908$		−	34570.1i		−	1.26349i
$909$	−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	$0.507819\pi$
$912$			24346.3i			0.883977i
$913$	−22687.6			−0.822399
$914$	57676.2			2.08726
$915$		0			0
$916$		−	39115.7i		−	1.41094i
$917$		−	59490.3i		−	2.14236i
$918$		−	36919.2i		−	1.32736i
$919$	−38062.2			−1.36622			−0.683111	−	0.730315i	$-0.739373\pi$
$919$	−38062.2			−1.36622			−0.683111	+	0.730315i	$0.739373\pi$
$920$		0			0
$921$			44371.3i			1.58750i
$922$	−68147.6			−2.43419
$923$	19616.5	−	25927.2i	0.699550	−	0.924599i
$924$	−42608.5			−1.51701
$925$		0			0
$926$	−64212.1			−2.27877
$927$	7836.57			0.277656
$928$		−	56102.8i		−	1.98455i
$929$		−	18698.6i		−	0.660366i	−0.943917	−	0.330183i	$-0.892890\pi$
$929$		−	18698.6i		−	0.660366i	0.943917	−	0.330183i	$-0.107110\pi$
$930$		0			0
$931$		−	87807.8i		−	3.09107i
$932$	−63533.6			−2.23295
$933$	−21904.5			−0.768620
$934$			30916.5i			1.08310i
$935$		0			0
$936$	−2275.35	+	3007.34i	−0.0794573	+	0.105019i
$937$	−8664.13			−0.302076			−0.151038	−	0.988528i	$-0.548262\pi$
$937$	−8664.13			−0.302076			−0.151038	+	0.988528i	$0.548262\pi$
$938$			111275.i			3.87340i
$939$	−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	$-0.0996951\pi$
$942$			80869.0i			2.79709i
$943$			2522.56i			0.0871112i
$944$			16994.1i			0.585924i
$945$		0			0
$946$	−26838.9			−0.922419
$947$			48570.3i			1.66665i	0.552780	+	0.833327i	$0.313567\pi$
$947$			48570.3i			1.66665i	−0.552780	+	0.833327i	$0.686433\pi$
$948$	−74733.3			−2.56036
$949$	−3205.99	+	4237.38i	−0.109664	+	0.144943i
$950$		0			0
$951$		−	22550.0i		−	0.768910i
$952$	−26887.4			−0.915362
$953$	−33701.1			−1.14553			−0.572763	−	0.819721i	$-0.694128\pi$
$953$	−33701.1			−1.14553			−0.572763	+	0.819721i	$0.694128\pi$
$954$			3751.29i			0.127309i
$955$		0			0
$956$		−	27120.3i		−	0.917503i
$957$		−	26898.0i		−	0.908557i
$958$	−47519.0			−1.60258
$959$	−31863.8			−1.07292
$960$		0			0
$961$	13853.0			0.465007
$962$	1522.82	+	1152.16i	0.0510372	+	0.0386146i
$963$	−5389.35			−0.180342
$964$			767.649i			0.0256476i
$965$		0			0
$966$	−10166.3			−0.338610
$967$			11377.7i			0.378367i	0.981942	+	0.189183i	$0.0605841\pi$
$967$			11377.7i			0.378367i	−0.981942	+	0.189183i	$0.939416\pi$
$968$		−	9533.53i		−	0.316549i
$969$			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	$0.340764\pi$
$972$	−22026.7			−0.726860
$973$		−	49414.0i		−	1.62810i
$974$	−28152.3			−0.926136
$975$		0			0
$976$	−17110.6			−0.561165
$977$			2482.90i			0.0813051i	0.999173	+	0.0406525i	$0.0129437\pi$
$977$			2482.90i			0.0813051i	−0.999173	+	0.0406525i	$0.987056\pi$
$978$	34495.9			1.12787
$979$	3079.90			0.100546
$980$		0			0
$981$		−	9229.13i		−	0.300371i
$982$			25540.7i			0.829976i
$983$		−	38919.6i		−	1.26281i	−0.775453	−	0.631405i	$-0.782479\pi$
$983$		−	38919.6i		−	1.26281i	0.775453	−	0.631405i	$-0.217521\pi$
$984$	13123.1			0.425153
$985$		0			0
$986$		−	73149.1i		−	2.36262i
$987$	8553.94			0.275861
$988$	−31341.2	+	41423.8i	−1.00921	+	1.33387i
$989$	−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	$0.395636\pi$
$992$	31508.8			1.00847
$993$			23075.8i			0.737450i
$994$		−	101750.i		−	3.24680i
$995$		0			0
$996$			68646.5i			2.18388i
$997$	−54046.2			−1.71681			−0.858405	−	0.512973i	$-0.828544\pi$
$997$	−54046.2			−1.71681			−0.858405	+	0.512973i	$0.828544\pi$
$998$	−872.430			−0.0276716
$999$			1077.02i			0.0341094i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.c.a.51.2	✓	14	5.4	even	2
65.4.c.a.51.13	yes	14	65.64	even	2
325.4.c.e.51.2		14	13.12	even	2	inner
325.4.c.e.51.13		14	1.1	even	1	trivial
325.4.d.c.324.13		14	5.3	odd	4
325.4.d.c.324.14		14	65.12	odd	4
325.4.d.d.324.1		14	65.38	odd	4
325.4.d.d.324.2		14	5.2	odd	4
585.4.b.e.181.2		14	195.194	odd	2
585.4.b.e.181.13		14	15.14	odd	2
845.4.a.i.1.7		7	65.34	odd	4
845.4.a.l.1.1		7	65.44	odd	4
1040.4.k.d.961.3		14	260.259	odd	2
1040.4.k.d.961.4		14	20.19	odd	2

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.29153i q^{2} -5.89541 q^{3} -10.4172 q^{4} -25.3003i q^{6} +34.1818i q^{7} -10.3735i q^{8} +7.75582 q^{9} +20.2972i q^{11} +61.4137 q^{12} +(-37.3790 - 28.2809i) q^{13} -146.692 q^{14} -38.8194 q^{16} -75.8275 q^{17} +33.2843i q^{18} +106.383i q^{19} -201.516i q^{21} -87.1059 q^{22} -11.7556 q^{23} +61.1562i q^{24} +(121.368 - 160.413i) q^{26} +113.452 q^{27} -356.079i q^{28} +224.787 q^{29} +126.246i q^{31} -249.583i q^{32} -119.660i q^{33} -325.416i q^{34} -80.7940 q^{36} +9.49313i q^{37} -456.544 q^{38} +(220.365 + 166.727i) q^{39} -214.584i q^{41} +864.810 q^{42} +308.118 q^{43} -211.440i q^{44} -50.4494i q^{46} +42.4480i q^{47} +228.856 q^{48} -825.396 q^{49} +447.034 q^{51} +(389.385 + 294.608i) q^{52} +112.704 q^{53} +486.884i q^{54} +354.586 q^{56} -627.169i q^{57} +964.678i q^{58} -437.774i q^{59} +440.774 q^{61} -541.787 q^{62} +265.108i q^{63} +760.536 q^{64} +513.525 q^{66} -758.560i q^{67} +789.911 q^{68} +69.3040 q^{69} +693.631i q^{71} -80.4553i q^{72} -113.362i q^{73} -40.7400 q^{74} -1108.21i q^{76} -693.795 q^{77} +(-715.515 + 945.700i) q^{78} -1216.88 q^{79} -878.254 q^{81} +920.893 q^{82} +1117.77i q^{83} +2099.23i q^{84} +1322.30i q^{86} -1325.21 q^{87} +210.554 q^{88} -151.740i q^{89} +(966.692 - 1277.68i) q^{91} +122.460 q^{92} -744.270i q^{93} -182.167 q^{94} +1471.39i q^{96} +179.668i q^{97} -3542.21i q^{98} +157.421i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 56 q^{4} + 158 q^{9} + 108 q^{12} + 4 q^{13} - 152 q^{14} + 280 q^{16} + 100 q^{17} - 648 q^{22} + 532 q^{23} - 344 q^{26} + 48 q^{27} + 588 q^{29} + 496 q^{36} - 148 q^{38} - 260 q^{39} + 620 q^{42}+ \cdots + 2656 q^{94}+O(q^{100}) \) 14 * q - 56 * q^4 + 158 * q^9 + 108 * q^12 + 4 * q^13 - 152 * q^14 + 280 * q^16 + 100 * q^17 - 648 * q^22 + 532 * q^23 - 344 * q^26 + 48 * q^27 + 588 * q^29 + 496 * q^36 - 148 * q^38 - 260 * q^39 + 620 * q^42 - 728 * q^43 + 2008 * q^48 - 1302 * q^49 + 176 * q^51 + 528 * q^52 - 1040 * q^53 + 512 * q^56 - 1460 * q^61 - 2964 * q^62 + 1296 * q^64 - 600 * q^66 - 1604 * q^68 + 4160 * q^69 - 5928 * q^74 + 3568 * q^77 - 2560 * q^78 - 1024 * q^79 - 2890 * q^81 + 6660 * q^82 - 5256 * q^87 - 1132 * q^88 + 916 * q^91 - 6044 * q^92 + 2656 * q^94

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