LMFDB - Embedded newform 325.4.d.c.324.3

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			324.3
Root			$-3.65500i$ of defining polynomial
Character	$\chi$	$=$	325.324
Dual form			325.4.d.c.324.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.65500 q^{2} -8.59394i q^{3} +5.35901 q^{4} +31.4108i q^{6} +19.4590 q^{7} +9.65282 q^{8} -46.8559 q^{9} -20.0770i q^{11} -46.0550i q^{12} +(0.655046 + 46.8676i) q^{13} -71.1227 q^{14} -78.1531 q^{16} -89.4229i q^{17} +171.258 q^{18} +11.7815i q^{19} -167.230i q^{21} +73.3816i q^{22} -157.627i q^{23} -82.9558i q^{24} +(-2.39419 - 171.301i) q^{26} +170.640i q^{27} +104.281 q^{28} -116.112 q^{29} -245.999i q^{31} +208.427 q^{32} -172.541 q^{33} +326.840i q^{34} -251.101 q^{36} -213.834 q^{37} -43.0613i q^{38} +(402.777 - 5.62943i) q^{39} +442.192i q^{41} +611.224i q^{42} -184.625i q^{43} -107.593i q^{44} +576.126i q^{46} +247.157 q^{47} +671.643i q^{48} +35.6534 q^{49} -768.495 q^{51} +(3.51040 + 251.164i) q^{52} -14.9253i q^{53} -623.689i q^{54} +187.834 q^{56} +101.250 q^{57} +424.389 q^{58} +416.520i q^{59} -898.135 q^{61} +899.127i q^{62} -911.769 q^{63} -136.575 q^{64} +630.637 q^{66} -847.535 q^{67} -479.218i q^{68} -1354.64 q^{69} -512.385i q^{71} -452.291 q^{72} +533.502 q^{73} +781.564 q^{74} +63.1371i q^{76} -390.680i q^{77} +(-1472.15 + 20.5756i) q^{78} +90.0657 q^{79} +201.363 q^{81} -1616.21i q^{82} +1092.74 q^{83} -896.185i q^{84} +674.804i q^{86} +997.859i q^{87} -193.800i q^{88} +117.323i q^{89} +(12.7466 + 911.997i) q^{91} -844.724i q^{92} -2114.11 q^{93} -903.360 q^{94} -1791.21i q^{96} -895.447 q^{97} -130.313 q^{98} +940.727i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.65500			−1.29224			−0.646118	−	0.763237i	$-0.723609\pi$
$2$	−3.65500			−1.29224			−0.646118	+	0.763237i	$0.723609\pi$
$3$		−	8.59394i		−	1.65391i	−0.562272	−	0.826953i	$-0.690072\pi$
$3$		−	8.59394i		−	1.65391i	0.562272	−	0.826953i	$-0.309928\pi$
$4$	5.35901			0.669876
$5$		0			0
$5$		0			0
$6$			31.4108i			2.13724i
$7$	19.4590			1.05069			0.525344	−	0.850890i	$-0.323937\pi$
$7$	19.4590			1.05069			0.525344	+	0.850890i	$0.323937\pi$
$8$	9.65282			0.426599
$9$	−46.8559			−1.73540
$10$		0			0
$11$		−	20.0770i		−	0.550314i	−0.961399	−	0.275157i	$-0.911270\pi$
$11$		−	20.0770i		−	0.550314i	0.961399	−	0.275157i	$-0.0887299\pi$
$12$		−	46.0550i		−	1.10791i
$13$	0.655046	+	46.8676i	0.0139752	+	0.999902i
$13$	0.655046	+	46.8676i	0.0139752	+	0.999902i
$14$	−71.1227			−1.35774
$15$		0			0
$16$	−78.1531			−1.22114
$17$		−	89.4229i		−	1.27578i	−0.770128	−	0.637889i	$-0.779808\pi$
$17$		−	89.4229i		−	1.27578i	0.770128	−	0.637889i	$-0.220192\pi$
$18$	171.258			2.24255
$19$			11.7815i			0.142256i	0.997467	+	0.0711279i	$0.0226599\pi$
$19$			11.7815i			0.142256i	−0.997467	+	0.0711279i	$0.977340\pi$
$20$		0			0
$21$		−	167.230i		−	1.73774i
$22$			73.3816i			0.711136i
$23$		−	157.627i		−	1.42902i	−0.699624	−	0.714511i	$-0.746649\pi$
$23$		−	157.627i		−	1.42902i	0.699624	−	0.714511i	$-0.253351\pi$
$24$		−	82.9558i		−	0.705554i
$25$		0			0
$26$	−2.39419	−	171.301i	−0.0180592	−	1.29211i
$27$			170.640i			1.21629i
$28$	104.281			0.703831
$29$	−116.112			−0.743498			−0.371749	−	0.928333i	$-0.621242\pi$
$29$	−116.112			−0.743498			−0.371749	+	0.928333i	$0.621242\pi$
$30$		0			0
$31$		−	245.999i		−	1.42525i	−0.701544	−	0.712626i	$-0.747506\pi$
$31$		−	245.999i		−	1.42525i	0.701544	−	0.712626i	$-0.252494\pi$
$32$	208.427			1.15141
$33$	−172.541			−0.910168
$34$			326.840i			1.64861i
$35$		0			0
$36$	−251.101			−1.16250
$37$	−213.834			−0.950112			−0.475056	−	0.879956i	$-0.657572\pi$
$37$	−213.834			−0.950112			−0.475056	+	0.879956i	$0.657572\pi$
$38$		−	43.0613i		−	0.183828i
$39$	402.777	−	5.62943i	1.65374	−	0.0231136i
$40$		0			0
$41$			442.192i			1.68436i	0.539196	+	0.842180i	$0.318728\pi$
$41$			442.192i			1.68436i	−0.539196	+	0.842180i	$0.681272\pi$
$42$			611.224i			2.24557i
$43$		−	184.625i		−	0.654768i	−0.944891	−	0.327384i	$-0.893833\pi$
$43$		−	184.625i		−	0.654768i	0.944891	−	0.327384i	$-0.106167\pi$
$44$		−	107.593i		−	0.368642i
$45$		0			0
$46$			576.126i			1.84663i
$47$	247.157			0.767056			0.383528	−	0.923529i	$-0.374709\pi$
$47$	247.157			0.767056			0.383528	+	0.923529i	$0.374709\pi$
$48$			671.643i			2.01965i
$49$	35.6534			0.103946
$50$		0			0
$51$	−768.495			−2.11002
$52$	3.51040	+	251.164i	0.00936162	+	0.669810i
$53$		−	14.9253i		−	0.0386821i	−0.999813	−	0.0193410i	$-0.993843\pi$
$53$		−	14.9253i		−	0.0386821i	0.999813	−	0.0193410i	$-0.00615683\pi$
$54$		−	623.689i		−	1.57173i
$55$		0			0
$56$	187.834			0.448222
$57$	101.250			0.235278
$58$	424.389			0.960776
$59$			416.520i			0.919090i	0.888155	+	0.459545i	$0.151987\pi$
$59$			416.520i			0.919090i	−0.888155	+	0.459545i	$0.848013\pi$
$60$		0			0
$61$	−898.135			−1.88515			−0.942577	−	0.333989i	$-0.891605\pi$
$61$	−898.135			−1.88515			−0.942577	+	0.333989i	$0.891605\pi$
$62$			899.127i			1.84176i
$63$	−911.769			−1.82337
$64$	−136.575			−0.266747
$65$		0			0
$66$	630.637			1.17615
$67$	−847.535			−1.54542			−0.772708	−	0.634761i	$-0.781098\pi$
$67$	−847.535			−1.54542			−0.772708	+	0.634761i	$0.781098\pi$
$68$		−	479.218i		−	0.854613i
$69$	−1354.64			−2.36347
$70$		0			0
$71$		−	512.385i		−	0.856463i	−0.903669	−	0.428232i	$-0.859137\pi$
$71$		−	512.385i		−	0.856463i	0.903669	−	0.428232i	$-0.140863\pi$
$72$	−452.291			−0.740320
$73$	533.502			0.855365			0.427683	−	0.903929i	$-0.359330\pi$
$73$	533.502			0.855365			0.427683	+	0.903929i	$0.359330\pi$
$74$	781.564			1.22777
$75$		0			0
$76$			63.1371i			0.0952938i
$77$		−	390.680i		−	0.578209i
$78$	−1472.15	+	20.5756i	−2.13703	+	0.0298682i
$79$	90.0657			0.128268			0.0641341	−	0.997941i	$-0.479571\pi$
$79$	90.0657			0.128268			0.0641341	+	0.997941i	$0.479571\pi$
$80$		0			0
$81$	201.363			0.276218
$82$		−	1616.21i		−	2.17659i
$83$	1092.74			1.44510			0.722551	−	0.691318i	$-0.242970\pi$
$83$	1092.74			1.44510			0.722551	+	0.691318i	$0.242970\pi$
$84$		−	896.185i		−	1.16407i
$85$		0			0
$86$			674.804i			0.846116i
$87$			997.859i			1.22968i
$88$		−	193.800i		−	0.234763i
$89$			117.323i			0.139733i	0.997556	+	0.0698666i	$0.0222574\pi$
$89$			117.323i			0.139733i	−0.997556	+	0.0698666i	$0.977743\pi$
$90$		0			0
$91$	12.7466	+	911.997i	0.0146835	+	1.05059i
$92$		−	844.724i		−	0.957267i
$93$	−2114.11			−2.35723
$94$	−903.360			−0.991217
$95$		0			0
$96$		−	1791.21i		−	1.90432i
$97$	−895.447			−0.937308			−0.468654	−	0.883382i	$-0.655261\pi$
$97$	−895.447			−0.937308			−0.468654	+	0.883382i	$0.655261\pi$
$98$	−130.313			−0.134323
$99$			940.727i			0.955017i
$100$		0			0
$101$	−240.227			−0.236668			−0.118334	−	0.992974i	$-0.537755\pi$
$101$	−240.227			−0.236668			−0.118334	+	0.992974i	$0.537755\pi$
$102$	2808.85			2.72664
$103$			123.954i			0.118578i	0.998241	+	0.0592891i	$0.0188834\pi$
$103$			123.954i			0.118578i	−0.998241	+	0.0592891i	$0.981117\pi$
$104$	6.32305	+	452.405i	0.00596178	+	0.426557i
$105$		0			0
$106$			54.5520i			0.0499864i
$107$		−	1223.36i		−	1.10530i	−0.833414	−	0.552649i	$-0.813617\pi$
$107$		−	1223.36i		−	1.10530i	0.833414	−	0.552649i	$-0.186383\pi$
$108$			914.461i			0.814760i
$109$			1738.02i			1.52727i	0.645648	+	0.763635i	$0.276587\pi$
$109$			1738.02i			1.52727i	−0.645648	+	0.763635i	$0.723413\pi$
$110$		0			0
$111$			1837.68i			1.57139i
$112$	−1520.78			−1.28304
$113$		−	633.634i		−	0.527498i	−0.964591	−	0.263749i	$-0.915041\pi$
$113$		−	633.634i		−	0.527498i	0.964591	−	0.263749i	$-0.0849590\pi$
$114$	−370.067			−0.304034
$115$		0			0
$116$	−622.245			−0.498051
$117$	−30.6927	−	2196.02i	−0.0242525	−	1.73523i
$118$		−	1522.38i		−	1.18768i
$119$		−	1740.08i		−	1.34045i
$120$		0			0
$121$	927.912			0.697154
$122$	3282.68			2.43607
$123$	3800.17			2.78577
$124$		−	1318.31i		−	0.954742i
$125$		0			0
$126$	3332.51			2.35622
$127$			1731.65i			1.20991i	0.796259	+	0.604955i	$0.206809\pi$
$127$			1731.65i			1.20991i	−0.796259	+	0.604955i	$0.793191\pi$
$128$	−1168.23			−0.806706
$129$	−1586.66			−1.08292
$130$		0			0
$131$	2334.08			1.55671			0.778357	−	0.627822i	$-0.216053\pi$
$131$	2334.08			1.55671			0.778357	+	0.627822i	$0.216053\pi$
$132$	−924.648			−0.609699
$133$			229.256i			0.149467i
$134$	3097.74			1.99704
$135$		0			0
$136$		−	863.183i		−	0.544245i
$137$	−1528.05			−0.952922			−0.476461	−	0.879196i	$-0.658081\pi$
$137$	−1528.05			−0.952922			−0.476461	+	0.879196i	$0.658081\pi$
$138$	4951.20			3.05416
$139$	2246.04			1.37055			0.685274	−	0.728285i	$-0.259682\pi$
$139$	2246.04			1.37055			0.685274	+	0.728285i	$0.259682\pi$
$140$		0			0
$141$		−	2124.06i		−	1.26864i
$142$			1872.77i			1.10675i
$143$	940.963	−	13.1514i	0.550261	−	0.00769073i
$144$	3661.93			2.11917
$145$		0			0
$146$	−1949.95			−1.10533
$147$		−	306.403i		−	0.171917i
$148$	−1145.94			−0.636457
$149$		−	710.547i		−	0.390673i	−0.980736	−	0.195337i	$-0.937420\pi$
$149$		−	710.547i		−	0.390673i	0.980736	−	0.195337i	$-0.0625799\pi$
$150$		0			0
$151$		−	1201.89i		−	0.647738i	−0.946102	−	0.323869i	$-0.895016\pi$
$151$		−	1201.89i		−	0.647738i	0.946102	−	0.323869i	$-0.104984\pi$
$152$			113.725i			0.0606861i
$153$			4189.99i			2.21399i
$154$			1427.93i			0.747183i
$155$		0			0
$156$	2158.49	−	30.1682i	1.10780	−	0.0154832i
$157$		−	677.363i		−	0.344328i	−0.985068	−	0.172164i	$-0.944924\pi$
$157$		−	677.363i		−	0.344328i	0.985068	−	0.172164i	$-0.0550758\pi$
$158$	−329.190			−0.165753
$159$	−128.267			−0.0639765
$160$		0			0
$161$		−	3067.27i		−	1.50146i
$162$	−735.981			−0.356939
$163$	−2043.08			−0.981756			−0.490878	−	0.871228i	$-0.663324\pi$
$163$	−2043.08			−0.981756			−0.490878	+	0.871228i	$0.663324\pi$
$164$			2369.71i			1.12831i
$165$		0			0
$166$	−3993.95			−1.86741
$167$	−2590.58			−1.20039			−0.600195	−	0.799854i	$-0.704910\pi$
$167$	−2590.58			−1.20039			−0.600195	+	0.799854i	$0.704910\pi$
$168$		−	1614.24i		−	0.741317i
$169$	−2196.14	+	61.4009i	−0.999609	+	0.0279476i
$170$		0			0
$171$		−	552.032i		−	0.246871i
$172$		−	989.407i		−	0.438614i
$173$		−	1092.54i		−	0.480140i	−0.970756	−	0.240070i	$-0.922830\pi$
$173$		−	1092.54i		−	0.480140i	0.970756	−	0.240070i	$-0.0771703\pi$
$174$		−	3647.17i		−	1.58903i
$175$		0			0
$176$			1569.08i			0.672012i
$177$	3579.55			1.52009
$178$		−	428.817i		−	0.180568i
$179$	−2643.64			−1.10388			−0.551942	−	0.833883i	$-0.686113\pi$
$179$	−2643.64			−1.10388			−0.551942	+	0.833883i	$0.686113\pi$
$180$		0			0
$181$	113.656			0.0466739			0.0233370	−	0.999728i	$-0.492571\pi$
$181$	113.656			0.0466739			0.0233370	+	0.999728i	$0.492571\pi$
$182$	−46.5886	−	3333.35i	−0.0189746	−	1.35761i
$183$			7718.52i			3.11787i
$184$		−	1521.55i		−	0.609619i
$185$		0			0
$186$	7727.05			3.04610
$187$	−1795.35			−0.702079
$188$	1324.52			0.513832
$189$			3320.49i			1.27794i
$190$		0			0
$191$	−1586.92			−0.601181			−0.300590	−	0.953753i	$-0.597184\pi$
$191$	−1586.92			−0.601181			−0.300590	+	0.953753i	$0.597184\pi$
$192$			1173.71i			0.441175i
$193$	−2480.87			−0.925270			−0.462635	−	0.886549i	$-0.653096\pi$
$193$	−2480.87			−0.925270			−0.462635	+	0.886549i	$0.653096\pi$
$194$	3272.86			1.21122
$195$		0			0
$196$	191.067			0.0696308
$197$	4720.28			1.70714			0.853568	−	0.520981i	$-0.174434\pi$
$197$	4720.28			1.70714			0.853568	+	0.520981i	$0.174434\pi$
$198$		−	3438.36i		−	1.23411i
$199$	−849.011			−0.302436			−0.151218	−	0.988500i	$-0.548320\pi$
$199$	−849.011			−0.302436			−0.151218	+	0.988500i	$0.548320\pi$
$200$		0			0
$201$			7283.67i			2.55597i
$202$	878.028			0.305831
$203$	−2259.42			−0.781185
$204$	−4118.37			−1.41345
$205$		0			0
$206$		−	453.051i		−	0.153231i
$207$			7385.75i			2.47993i
$208$	−51.1939	−	3662.85i	−0.0170657	−	1.22102i
$209$	236.538			0.0782854
$210$		0			0
$211$	−3094.07			−1.00950			−0.504751	−	0.863265i	$-0.668416\pi$
$211$	−3094.07			−1.00950			−0.504751	+	0.863265i	$0.668416\pi$
$212$		−	79.9849i		−	0.0259122i
$213$	−4403.41			−1.41651
$214$			4471.38i			1.42831i
$215$		0			0
$216$			1647.16i			0.518865i
$217$		−	4786.91i		−	1.49750i
$218$		−	6352.47i		−	1.97359i
$219$		−	4584.88i		−	1.41469i
$220$		0			0
$221$	4191.04	−	58.5761i	1.27565	−	0.0178292i
$222$		−	6716.71i		−	2.03061i
$223$	923.125			0.277206			0.138603	−	0.990348i	$-0.455739\pi$
$223$	923.125			0.277206			0.138603	+	0.990348i	$0.455739\pi$
$224$	4055.78			1.20977
$225$		0			0
$226$			2315.93i			0.681652i
$227$	652.853			0.190887			0.0954435	−	0.995435i	$-0.469573\pi$
$227$	652.853			0.190887			0.0954435	+	0.995435i	$0.469573\pi$
$228$	542.597			0.157607
$229$			3450.44i			0.995685i	0.867268	+	0.497842i	$0.165874\pi$
$229$			3450.44i			0.995685i	−0.867268	+	0.497842i	$0.834126\pi$
$230$		0			0
$231$	−3357.48			−0.956302
$232$	−1120.81			−0.317175
$233$		−	2746.83i		−	0.772320i	−0.922432	−	0.386160i	$-0.873801\pi$
$233$		−	2746.83i		−	0.772320i	0.922432	−	0.386160i	$-0.126199\pi$
$234$	112.182	+	8026.45i	0.0313400	+	2.24233i
$235$		0			0
$236$			2232.13i			0.615676i
$237$		−	774.020i		−	0.212143i
$238$			6359.99i			1.73217i
$239$		−	6624.49i		−	1.79290i	−0.443148	−	0.896448i	$-0.646138\pi$
$239$		−	6624.49i		−	1.79290i	0.443148	−	0.896448i	$-0.353862\pi$
$240$		0			0
$241$		−	3220.25i		−	0.860725i	−0.902656	−	0.430362i	$-0.858386\pi$
$241$		−	3220.25i		−	0.860725i	0.902656	−	0.430362i	$-0.141614\pi$
$242$	−3391.52			−0.900888
$243$			2876.78i			0.759447i
$244$	−4813.11			−1.26282
$245$		0			0
$246$	−13889.6			−3.59988
$247$	−552.170	+	7.71743i	−0.142242	+	0.00198805i
$248$		−	2374.59i		−	0.608010i
$249$		−	9390.91i		−	2.39006i
$250$		0			0
$251$	−410.078			−0.103123			−0.0515615	−	0.998670i	$-0.516420\pi$
$251$	−410.078			−0.103123			−0.0515615	+	0.998670i	$0.516420\pi$
$252$	−4886.18			−1.22143
$253$	−3164.68			−0.786411
$254$		−	6329.16i		−	1.56349i
$255$		0			0
$256$	5362.49			1.30920
$257$			117.117i			0.0284262i	0.999899	+	0.0142131i	$0.00452433\pi$
$257$			117.117i			0.0284262i	−0.999899	+	0.0142131i	$0.995476\pi$
$258$	5799.23			1.39940
$259$	−4161.00			−0.998271
$260$		0			0
$261$	5440.52			1.29027
$262$	−8531.06			−2.01164
$263$		−	2511.96i		−	0.588950i	−0.955659	−	0.294475i	$-0.904855\pi$
$263$		−	2511.96i		−	0.588950i	0.955659	−	0.294475i	$-0.0951448\pi$
$264$	−1665.51			−0.388276
$265$		0			0
$266$		−	837.932i		−	0.193146i
$267$	1008.27			0.231105
$268$	−4541.95			−1.03524
$269$	−5896.91			−1.33658			−0.668292	−	0.743899i	$-0.732974\pi$
$269$	−5896.91			−1.33658			−0.668292	+	0.743899i	$0.732974\pi$
$270$		0			0
$271$		−	3452.44i		−	0.773877i	−0.922106	−	0.386938i	$-0.873533\pi$
$271$		−	3452.44i		−	0.773877i	0.922106	−	0.386938i	$-0.126467\pi$
$272$			6988.68i			1.55791i
$273$	7837.65	−	109.543i	1.73757	−	0.0242852i
$274$	5585.03			1.23140
$275$		0			0
$276$	−7259.51			−1.58323
$277$		−	2430.98i		−	0.527304i	−0.964618	−	0.263652i	$-0.915073\pi$
$277$		−	2430.98i		−	0.527304i	0.964618	−	0.263652i	$-0.0849270\pi$
$278$	−8209.26			−1.77107
$279$			11526.5i			2.47338i
$280$		0			0
$281$			3512.86i			0.745763i	0.927879	+	0.372882i	$0.121630\pi$
$281$			3512.86i			0.745763i	−0.927879	+	0.372882i	$0.878370\pi$
$282$			7763.42i			1.63938i
$283$			3590.13i			0.754103i	0.926192	+	0.377051i	$0.123062\pi$
$283$			3590.13i			0.754103i	−0.926192	+	0.377051i	$0.876938\pi$
$284$		−	2745.87i		−	0.573724i
$285$		0			0
$286$	−3439.22	+	48.0683i	−0.711067	+	0.00993825i
$287$			8604.62i			1.76974i
$288$	−9766.02			−1.99815
$289$	−3083.45			−0.627611
$290$		0			0
$291$			7695.42i			1.55022i
$292$	2859.04			0.572989
$293$	9311.11			1.85652			0.928260	−	0.371931i	$-0.121304\pi$
$293$	9311.11			1.85652			0.928260	+	0.371931i	$0.121304\pi$
$294$			1119.90i			0.222157i
$295$		0			0
$296$	−2064.10			−0.405316
$297$	3425.95			0.669339
$298$			2597.05i			0.504842i
$299$	7387.60	−	103.253i	1.42888	−	0.0199708i
$300$		0			0
$301$		−	3592.62i		−	0.687958i
$302$			4392.90i			0.837030i
$303$			2064.49i			0.391426i
$304$		−	920.761i		−	0.173715i
$305$		0			0
$306$		−	15314.4i		−	2.86100i
$307$	2634.13			0.489699			0.244849	−	0.969561i	$-0.421261\pi$
$307$	2634.13			0.489699			0.244849	+	0.969561i	$0.421261\pi$
$308$		−	2093.65i		−	0.387328i
$309$	1065.25			0.196117
$310$		0			0
$311$	−1976.39			−0.360356			−0.180178	−	0.983634i	$-0.557667\pi$
$311$	−1976.39			−0.360356			−0.180178	+	0.983634i	$0.557667\pi$
$312$	3887.94	−	54.3399i	0.705485	−	0.00986023i
$313$		−	4099.30i		−	0.740276i	−0.928977	−	0.370138i	$-0.879310\pi$
$313$		−	4099.30i		−	0.740276i	0.928977	−	0.370138i	$-0.120690\pi$
$314$			2475.76i			0.444953i
$315$		0			0
$316$	482.663			0.0859238
$317$	619.492			0.109761			0.0548804	−	0.998493i	$-0.482522\pi$
$317$	619.492			0.109761			0.0548804	+	0.998493i	$0.482522\pi$
$318$	468.817			0.0826728
$319$			2331.18i			0.409158i
$320$		0			0
$321$	−10513.5			−1.82806
$322$			11210.9i			1.94024i
$323$	1053.54			0.181487
$324$	1079.11			0.185032
$325$		0			0
$326$	7467.45			1.26866
$327$	14936.5			2.52596
$328$			4268.40i			0.718546i
$329$	4809.44			0.805936
$330$		0			0
$331$		−	4249.98i		−	0.705741i	−0.935672	−	0.352870i	$-0.885206\pi$
$331$		−	4249.98i		−	0.705741i	0.935672	−	0.352870i	$-0.114794\pi$
$332$	5855.98			0.968038
$333$	10019.4			1.64883
$334$	9468.56			1.55119
$335$		0			0
$336$			13069.5i			2.12203i
$337$		−	6965.45i		−	1.12591i	−0.826487	−	0.562956i	$-0.809664\pi$
$337$		−	6965.45i		−	1.12591i	0.826487	−	0.562956i	$-0.190336\pi$
$338$	8026.89	−	224.420i	1.29173	−	0.0361149i
$339$	−5445.41			−0.872431
$340$		0			0
$341$	−4938.94			−0.784336
$342$			2017.68i			0.319016i
$343$	−5980.66			−0.941474
$344$		−	1782.15i		−	0.279323i
$345$		0			0
$346$			3993.22i			0.620454i
$347$		−	4287.03i		−	0.663227i	−0.943415	−	0.331613i	$-0.892407\pi$
$347$		−	4287.03i		−	0.663227i	0.943415	−	0.331613i	$-0.107593\pi$
$348$			5347.53i			0.823730i
$349$			10344.2i			1.58657i	0.608848	+	0.793287i	$0.291632\pi$
$349$			10344.2i			1.58657i	−0.608848	+	0.793287i	$0.708368\pi$
$350$		0			0
$351$	−7997.49	+	111.777i	−1.21617	+	0.0169978i
$352$		−	4184.59i		−	0.633635i
$353$	1570.76			0.236835			0.118418	−	0.992964i	$-0.462218\pi$
$353$	1570.76			0.236835			0.118418	+	0.992964i	$0.462218\pi$
$354$	−13083.2			−1.96431
$355$		0			0
$356$			628.737i			0.0936039i
$357$	−14954.2			−2.21697
$358$	9662.51			1.42648
$359$			4580.91i			0.673458i	0.941602	+	0.336729i	$0.109321\pi$
$359$			4580.91i			0.673458i	−0.941602	+	0.336729i	$0.890679\pi$
$360$		0			0
$361$	6720.20			0.979763
$362$	−415.412			−0.0603138
$363$		−	7974.42i		−	1.15303i
$364$	68.3089	+	4887.40i	0.00983615	+	0.703762i
$365$		0			0
$366$		−	28211.2i		−	4.02902i
$367$			7725.22i			1.09878i	0.835565	+	0.549392i	$0.185140\pi$
$367$			7725.22i			1.09878i	−0.835565	+	0.549392i	$0.814860\pi$
$368$			12319.0i			1.74504i
$369$		−	20719.3i		−	2.92304i
$370$		0			0
$371$		−	290.432i		−	0.0406428i
$372$	−11329.5			−1.57905
$373$			8286.80i			1.15033i	0.818036	+	0.575166i	$0.195063\pi$
$373$			8286.80i			1.15033i	−0.818036	+	0.575166i	$0.804937\pi$
$374$	6561.99			0.907253
$375$		0			0
$376$	2385.77			0.327225
$377$	−76.0587	−	5441.89i	−0.0103905	−	0.743425i
$378$		−	12136.4i		−	1.65140i
$379$		−	8496.27i		−	1.15151i	−0.817621	−	0.575757i	$-0.804707\pi$
$379$		−	8496.27i		−	1.15151i	0.817621	−	0.575757i	$-0.195293\pi$
$380$		0			0
$381$	14881.7			2.00108
$382$	5800.19			0.776868
$383$	−2814.87			−0.375544			−0.187772	−	0.982213i	$-0.560127\pi$
$383$	−2814.87			−0.375544			−0.187772	+	0.982213i	$0.560127\pi$
$384$			10039.7i			1.33421i
$385$		0			0
$386$	9067.58			1.19567
$387$			8650.76i			1.13629i
$388$	−4798.70			−0.627880
$389$	1795.14			0.233977			0.116989	−	0.993133i	$-0.462676\pi$
$389$	1795.14			0.233977			0.116989	+	0.993133i	$0.462676\pi$
$390$		0			0
$391$	−14095.5			−1.82312
$392$	344.156			0.0443431
$393$		−	20059.0i		−	2.57466i
$394$	−17252.6			−2.20602
$395$		0			0
$396$			5041.36i			0.639743i
$397$	−3046.79			−0.385174			−0.192587	−	0.981280i	$-0.561688\pi$
$397$	−3046.79			−0.385174			−0.192587	+	0.981280i	$0.561688\pi$
$398$	3103.13			0.390819
$399$	1970.22			0.247203
$400$		0			0
$401$		−	6060.07i		−	0.754677i	−0.926075	−	0.377339i	$-0.876839\pi$
$401$		−	6060.07i		−	0.754677i	0.926075	−	0.377339i	$-0.123161\pi$
$402$		−	26621.8i		−	3.30292i
$403$	11529.4	−	161.141i	1.42511	−	0.0199181i
$404$	−1287.38			−0.158538
$405$		0			0
$406$	8258.19			1.00948
$407$			4293.16i			0.522860i
$408$	−7418.15			−0.900130
$409$			5020.20i			0.606927i	0.952843	+	0.303463i	$0.0981430\pi$
$409$			5020.20i			0.606927i	−0.952843	+	0.303463i	$0.901857\pi$
$410$		0			0
$411$			13132.0i			1.57604i
$412$			664.270i			0.0794326i
$413$			8105.07i			0.965677i
$414$		−	26994.9i		−	3.20465i
$415$		0			0
$416$	136.529	+	9768.46i	0.0160911	+	1.15129i
$417$		−	19302.3i		−	2.26676i
$418$	−864.545			−0.101163
$419$	9083.45			1.05908			0.529541	−	0.848284i	$-0.322364\pi$
$419$	9083.45			1.05908			0.529541	+	0.848284i	$0.322364\pi$
$420$		0			0
$421$		−	1928.90i		−	0.223299i	−0.993748	−	0.111650i	$-0.964387\pi$
$421$		−	1928.90i		−	0.223299i	0.993748	−	0.111650i	$-0.0356135\pi$
$422$	11308.8			1.30452
$423$	−11580.8			−1.33115
$424$		−	144.072i		−	0.0165017i
$425$		0			0
$426$	16094.4			1.83047
$427$	−17476.8			−1.98071
$428$		−	6556.00i		−	0.740412i
$429$	−113.022	−	8086.58i	−0.0127197	−	0.910079i
$430$		0			0
$431$		−	3177.44i		−	0.355109i	−0.984111	−	0.177554i	$-0.943181\pi$
$431$		−	3177.44i		−	0.355109i	0.984111	−	0.177554i	$-0.0568185\pi$
$432$		−	13336.1i		−	1.48526i
$433$		−	9465.37i		−	1.05052i	−0.850941	−	0.525262i	$-0.823967\pi$
$433$		−	9465.37i		−	1.05052i	0.850941	−	0.525262i	$-0.176033\pi$
$434$			17496.1i			1.93512i
$435$		0			0
$436$			9314.08i			1.02308i
$437$	1857.08			0.203287
$438$			16757.7i			1.82812i
$439$	768.174			0.0835146			0.0417573	−	0.999128i	$-0.486704\pi$
$439$	768.174			0.0835146			0.0417573	+	0.999128i	$0.486704\pi$
$440$		0			0
$441$	−1670.57			−0.180388
$442$	−15318.2	+	214.096i	−1.64845	+	0.0230396i
$443$		−	1368.96i		−	0.146820i	−0.997302	−	0.0734099i	$-0.976612\pi$
$443$		−	1368.96i		−	0.146820i	0.997302	−	0.0734099i	$-0.0233881\pi$
$444$			9848.14i			1.05264i
$445$		0			0
$446$	−3374.02			−0.358216
$447$	−6106.40			−0.646136
$448$	−2657.61			−0.280268
$449$		−	2152.16i		−	0.226206i	−0.993583	−	0.113103i	$-0.963921\pi$
$449$		−	2152.16i		−	0.226206i	0.993583	−	0.113103i	$-0.0360790\pi$
$450$		0			0
$451$	8877.91			0.926927
$452$		−	3395.65i		−	0.353358i
$453$	−10329.0			−1.07130
$454$	−2386.18			−0.246671
$455$		0			0
$456$	977.344			0.100369
$457$	10468.5			1.07154			0.535771	−	0.844363i	$-0.320021\pi$
$457$	10468.5			1.07154			0.535771	+	0.844363i	$0.320021\pi$
$458$		−	12611.4i		−	1.28666i
$459$	15259.1			1.55171
$460$		0			0
$461$			6737.46i			0.680683i	0.940302	+	0.340341i	$0.110543\pi$
$461$			6737.46i			0.680683i	−0.940302	+	0.340341i	$0.889457\pi$
$462$	12271.6			1.23577
$463$	6896.27			0.692218			0.346109	−	0.938194i	$-0.387503\pi$
$463$	6896.27			0.692218			0.346109	+	0.938194i	$0.387503\pi$
$464$	9074.51			0.907917
$465$		0			0
$466$			10039.6i			0.998021i
$467$		−	11356.8i		−	1.12533i	−0.826685	−	0.562664i	$-0.809776\pi$
$467$		−	11356.8i		−	1.12533i	0.826685	−	0.562664i	$-0.190224\pi$
$468$	−164.483	−	11768.5i	−0.0162462	−	1.16239i
$469$	−16492.2			−1.62375
$470$		0			0
$471$	−5821.22			−0.569485
$472$			4020.59i			0.392082i
$473$	−3706.72			−0.360328
$474$			2829.04i			0.274139i
$475$		0			0
$476$		−	9325.11i		−	0.897932i
$477$			699.339i			0.0671290i
$478$			24212.5i			2.31685i
$479$			7739.00i			0.738213i	0.929387	+	0.369106i	$0.120336\pi$
$479$			7739.00i			0.738213i	−0.929387	+	0.369106i	$0.879664\pi$
$480$		0			0
$481$	−140.071	−	10021.9i	−0.0132780	−	0.950019i
$482$			11770.0i			1.11226i
$483$	−26359.9			−2.48327
$484$	4972.69			0.467007
$485$		0			0
$486$		−	10514.6i		−	0.981385i
$487$	21347.3			1.98632			0.993162	−	0.116748i	$-0.0372471\pi$
$487$	21347.3			1.98632			0.993162	+	0.116748i	$0.0372471\pi$
$488$	−8669.54			−0.804204
$489$			17558.1i			1.62373i
$490$		0			0
$491$	11452.5			1.05264			0.526319	−	0.850287i	$-0.323572\pi$
$491$	11452.5			1.05264			0.526319	+	0.850287i	$0.323572\pi$
$492$	20365.1			1.86612
$493$			10383.1i			0.948539i
$494$	2018.18	−	28.2072i	0.183810	−	0.00256903i
$495$		0			0
$496$			19225.6i			1.74043i
$497$		−	9970.51i		−	0.899876i
$498$			34323.8i			3.08852i
$499$		−	8778.37i		−	0.787522i	−0.919213	−	0.393761i	$-0.871174\pi$
$499$		−	8778.37i		−	0.787522i	0.919213	−	0.393761i	$-0.128826\pi$
$500$		0			0
$501$			22263.3i			1.98533i
$502$	1498.83			0.133259
$503$		−	20459.6i		−	1.81362i	−0.421540	−	0.906810i	$-0.638510\pi$
$503$		−	20459.6i		−	1.81362i	0.421540	−	0.906810i	$-0.361490\pi$
$504$	−8801.14			−0.777846
$505$		0			0
$506$	11566.9			1.01623
$507$	527.676	+	18873.5i	0.0462227	+	1.65326i
$508$			9279.90i			0.810490i
$509$		−	6203.63i		−	0.540218i	−0.962830	−	0.270109i	$-0.912940\pi$
$509$		−	6203.63i		−	0.540218i	0.962830	−	0.270109i	$-0.0870598\pi$
$510$		0			0
$511$	10381.4			0.898722
$512$	−10254.0			−0.885093
$513$	−2010.40			−0.173024
$514$		−	428.062i		−	0.0367334i
$515$		0			0
$516$	−8502.90			−0.725425
$517$		−	4962.19i		−	0.422122i
$518$	15208.5			1.29000
$519$	−9389.21			−0.794105
$520$		0			0
$521$	9308.04			0.782711			0.391356	−	0.920240i	$-0.372006\pi$
$521$	9308.04			0.782711			0.391356	+	0.920240i	$0.372006\pi$
$522$	−19885.1			−1.66733
$523$		−	1285.95i		−	0.107515i	−0.998554	−	0.0537577i	$-0.982880\pi$
$523$		−	1285.95i		−	0.107515i	0.998554	−	0.0537577i	$-0.0171199\pi$
$524$	12508.4			1.04281
$525$		0			0
$526$			9181.20i			0.761063i
$527$	−21998.0			−1.81831
$528$	13484.6			1.11144
$529$	−12679.3			−1.04210
$530$		0			0
$531$		−	19516.4i		−	1.59499i
$532$			1228.59i			0.100124i
$533$	−20724.5	+	289.656i	−1.68420	+	0.0235392i
$534$	−3685.23			−0.298643
$535$		0			0
$536$	−8181.11			−0.659272
$537$			22719.3i			1.82572i
$538$	21553.2			1.72718
$539$		−	715.815i		−	0.0572029i
$540$		0			0
$541$		−	10504.9i		−	0.834824i	−0.908717	−	0.417412i	$-0.862937\pi$
$541$		−	10504.9i		−	0.834824i	0.908717	−	0.417412i	$-0.137063\pi$
$542$			12618.6i			1.00003i
$543$		−	976.753i		−	0.0771943i
$544$		−	18638.1i		−	1.46894i
$545$		0			0
$546$	−28646.6	+	400.380i	−2.24535	+	0.0313822i
$547$			1017.35i			0.0795227i	0.999209	+	0.0397614i	$0.0126598\pi$
$547$			1017.35i			0.0795227i	−0.999209	+	0.0397614i	$0.987340\pi$
$548$	−8188.84			−0.638339
$549$	42082.9			3.27150
$550$		0			0
$551$		−	1367.97i		−	0.105767i
$552$	−13076.1			−1.00825
$553$	1752.59			0.134770
$554$			8885.21i			0.681401i
$555$		0			0
$556$	12036.5			0.918098
$557$	−15058.6			−1.14551			−0.572757	−	0.819725i	$-0.694126\pi$
$557$	−15058.6			−1.14551			−0.572757	+	0.819725i	$0.694126\pi$
$558$		−	42129.4i		−	3.19620i
$559$	8652.93	−	120.938i	0.654705	−	0.00915050i
$560$		0			0
$561$			15429.1i			1.16117i
$562$		−	12839.5i		−	0.963703i
$563$			6892.23i			0.515938i	0.966153	+	0.257969i	$0.0830532\pi$
$563$			6892.23i			0.515938i	−0.966153	+	0.257969i	$0.916947\pi$
$564$		−	11382.8i		−	0.849829i
$565$		0			0
$566$		−	13121.9i		−	0.974479i
$567$	3918.33			0.290219
$568$		−	4945.96i		−	0.365366i
$569$	23546.3			1.73482			0.867409	−	0.497595i	$-0.165783\pi$
$569$	23546.3			1.73482			0.867409	+	0.497595i	$0.165783\pi$
$570$		0			0
$571$	−4737.30			−0.347198			−0.173599	−	0.984816i	$-0.555540\pi$
$571$	−4737.30			−0.347198			−0.173599	+	0.984816i	$0.555540\pi$
$572$	5042.63	−	70.4784i	0.368606	−	0.00515184i
$573$			13637.9i			0.994296i
$574$		−	31449.9i		−	2.28692i
$575$		0			0
$576$	6399.32			0.462914
$577$	2000.42			0.144330			0.0721652	−	0.997393i	$-0.477009\pi$
$577$	2000.42			0.144330			0.0721652	+	0.997393i	$0.477009\pi$
$578$	11270.0			0.811022
$579$			21320.5i			1.53031i
$580$		0			0
$581$	21263.6			1.51835
$582$		−	28126.7i		−	2.00325i
$583$	−299.656			−0.0212873
$584$	5149.80			0.364898
$585$		0			0
$586$	−34032.1			−2.39906
$587$	5961.64			0.419188			0.209594	−	0.977789i	$-0.432786\pi$
$587$	5961.64			0.419188			0.209594	+	0.977789i	$0.432786\pi$
$588$		−	1642.02i		−	0.115163i
$589$	2898.24			0.202750
$590$		0			0
$591$		−	40565.8i		−	2.82344i
$592$	16711.8			1.16022
$593$	9517.01			0.659050			0.329525	−	0.944147i	$-0.393111\pi$
$593$	9517.01			0.659050			0.329525	+	0.944147i	$0.393111\pi$
$594$	−12521.8			−0.864945
$595$		0			0
$596$		−	3807.83i		−	0.261703i
$597$			7296.35i			0.500201i
$598$	−27001.7	+	377.389i	−1.84645	+	0.0258070i
$599$	−8822.25			−0.601782			−0.300891	−	0.953659i	$-0.597284\pi$
$599$	−8822.25			−0.601782			−0.300891	+	0.953659i	$0.597284\pi$
$600$		0			0
$601$	−388.522			−0.0263696			−0.0131848	−	0.999913i	$-0.504197\pi$
$601$	−388.522			−0.0263696			−0.0131848	+	0.999913i	$0.504197\pi$
$602$			13131.0i			0.889004i
$603$	39712.0			2.68192
$604$		−	6440.93i		−	0.433904i
$605$		0			0
$606$		−	7545.72i		−	0.505815i
$607$		−	2729.75i		−	0.182532i	−0.995827	−	0.0912662i	$-0.970909\pi$
$607$		−	2729.75i		−	0.182532i	0.995827	−	0.0912662i	$-0.0290914\pi$
$608$			2455.58i			0.163794i
$609$			19417.4i			1.29201i
$610$		0			0
$611$	161.900	+	11583.7i	0.0107197	+	0.766981i
$612$			22454.2i			1.48310i
$613$	27578.2			1.81708			0.908542	−	0.417794i	$-0.137197\pi$
$613$	27578.2			1.81708			0.908542	+	0.417794i	$0.137197\pi$
$614$	−9627.72			−0.632807
$615$		0			0
$616$		−	3771.16i		−	0.246663i
$617$	247.197			0.0161293			0.00806464	−	0.999967i	$-0.497433\pi$
$617$	247.197			0.0161293			0.00806464	+	0.999967i	$0.497433\pi$
$618$	−3893.50			−0.253430
$619$		−	6035.92i		−	0.391929i	−0.980611	−	0.195965i	$-0.937216\pi$
$619$		−	6035.92i		−	0.391929i	0.980611	−	0.195965i	$-0.0627838\pi$
$620$		0			0
$621$	26897.5			1.73810
$622$	7223.70			0.465665
$623$			2283.00i			0.146816i
$624$	−31478.3	+	439.957i	−2.01946	+	0.0282250i
$625$		0			0
$626$			14982.9i			0.956611i
$627$		−	2032.79i		−	0.129477i
$628$		−	3629.99i		−	0.230657i
$629$			19121.7i			1.21213i
$630$		0			0
$631$			16570.3i			1.04541i	0.852514	+	0.522705i	$0.175077\pi$
$631$			16570.3i			1.04541i	−0.852514	+	0.522705i	$0.824923\pi$
$632$	869.389			0.0547190
$633$			26590.3i			1.66962i
$634$	−2264.24			−0.141837
$635$		0			0
$636$	−687.386			−0.0428563
$637$	23.3546	+	1670.99i	0.00145266	+	0.103936i
$638$		−	8520.47i		−	0.528729i
$639$			24008.2i			1.48631i
$640$		0			0
$641$	−7610.28			−0.468936			−0.234468	−	0.972124i	$-0.575335\pi$
$641$	−7610.28			−0.468936			−0.234468	+	0.972124i	$0.575335\pi$
$642$	38426.8			2.36228
$643$	15468.4			0.948699			0.474350	−	0.880337i	$-0.342683\pi$
$643$	15468.4			0.948699			0.474350	+	0.880337i	$0.342683\pi$
$644$		−	16437.5i		−	1.00579i
$645$		0			0
$646$	−3850.67			−0.234524
$647$		−	25669.6i		−	1.55978i	−0.625917	−	0.779889i	$-0.715275\pi$
$647$		−	25669.6i		−	1.55978i	0.625917	−	0.779889i	$-0.284725\pi$
$648$	1943.72			0.117834
$649$	8362.49			0.505788
$650$		0			0
$651$	−41138.4			−2.47671
$652$	−10948.9			−0.657655
$653$		−	3691.09i		−	0.221200i	−0.993865	−	0.110600i	$-0.964723\pi$
$653$		−	3691.09i		−	0.221200i	0.993865	−	0.110600i	$-0.0352772\pi$
$654$	−54592.8			−3.26414
$655$		0			0
$656$		−	34558.7i		−	2.05684i
$657$	−24997.7			−1.48440
$658$	−17578.5			−1.04146
$659$	−23260.7			−1.37497			−0.687487	−	0.726197i	$-0.741286\pi$
$659$	−23260.7			−1.37497			−0.687487	+	0.726197i	$0.741286\pi$
$660$		0			0
$661$			93.6601i			0.00551128i	0.999996	+	0.00275564i	$0.000877149\pi$
$661$			93.6601i			0.00551128i	−0.999996	+	0.00275564i	$0.999123\pi$
$662$			15533.7i			0.911984i
$663$	−503.400	−	36017.5i	−0.0294878	−	2.10981i
$664$	10548.0			0.616478
$665$		0			0
$666$	−36620.8			−2.13067
$667$			18302.4i			1.06247i
$668$	−13882.9			−0.804112
$669$		−	7933.29i		−	0.458473i
$670$		0			0
$671$			18031.9i			1.03743i
$672$		−	34855.2i		−	2.00084i
$673$		−	15681.6i		−	0.898191i	−0.893484	−	0.449096i	$-0.851746\pi$
$673$		−	15681.6i		−	0.898191i	0.893484	−	0.449096i	$-0.148254\pi$
$674$			25458.7i			1.45494i
$675$		0			0
$676$	−11769.1	+	329.048i	−0.669614	+	0.0187214i
$677$			6692.61i			0.379938i	0.981790	+	0.189969i	$0.0608387\pi$
$677$			6692.61i			0.379938i	−0.981790	+	0.189969i	$0.939161\pi$
$678$	19903.0			1.12739
$679$	−17424.5			−0.984818
$680$		0			0
$681$		−	5610.58i		−	0.315709i
$682$	18051.8			1.01355
$683$	−5093.28			−0.285342			−0.142671	−	0.989770i	$-0.545569\pi$
$683$	−5093.28			−0.285342			−0.142671	+	0.989770i	$0.545569\pi$
$684$		−	2958.34i		−	0.165373i
$685$		0			0
$686$	21859.3			1.21661
$687$	29652.9			1.64677
$688$			14429.0i			0.799565i
$689$	699.514	−	9.77678i	0.0386783	−	0.000540589i
$690$		0			0
$691$		−	16747.8i		−	0.922020i	−0.887395	−	0.461010i	$-0.847487\pi$
$691$		−	16747.8i		−	0.922020i	0.887395	−	0.461010i	$-0.152513\pi$
$692$		−	5854.92i		−	0.321634i
$693$			18305.6i			1.00342i
$694$			15669.1i			0.857046i
$695$		0			0
$696$			9632.16i			0.524578i
$697$	39542.1			2.14887
$698$		−	37808.2i		−	2.05023i
$699$	−23606.1			−1.27734
$700$		0			0
$701$	18385.1			0.990580			0.495290	−	0.868728i	$-0.335062\pi$
$701$	18385.1			0.990580			0.495290	+	0.868728i	$0.335062\pi$
$702$	29230.8	−	408.545i	1.57157	−	0.0219652i
$703$		−	2519.29i		−	0.135159i
$704$			2742.02i			0.146795i
$705$		0			0
$706$	−5741.11			−0.306047
$707$	−4674.58			−0.248664
$708$	19182.8			1.01827
$709$		−	18930.7i		−	1.00276i	−0.865227	−	0.501380i	$-0.832826\pi$
$709$		−	18930.7i		−	1.00276i	0.865227	−	0.501380i	$-0.167174\pi$
$710$		0			0
$711$	−4220.11			−0.222597
$712$			1132.50i			0.0596100i
$713$	−38776.2			−2.03672
$714$	54657.4			2.86485
$715$		0			0
$716$	−14167.3			−0.739465
$717$	−56930.5			−2.96528
$718$		−	16743.2i		−	0.870267i
$719$	12492.1			0.647951			0.323975	−	0.946066i	$-0.394981\pi$
$719$	12492.1			0.647951			0.323975	+	0.946066i	$0.394981\pi$
$720$		0			0
$721$			2412.02i			0.124589i
$722$	−24562.3			−1.26609
$723$	−27674.7			−1.42356
$724$	609.083			0.0312657
$725$		0			0
$726$			29146.5i			1.48998i
$727$		−	20599.5i		−	1.05088i	−0.850829	−	0.525442i	$-0.823900\pi$
$727$		−	20599.5i		−	1.05088i	0.850829	−	0.525442i	$-0.176100\pi$
$728$	123.040	+	8803.35i	0.00626398	+	0.448178i
$729$	30159.7			1.53227
$730$		0			0
$731$	−16509.7			−0.835340
$732$			41363.6i			2.08858i
$733$	10452.1			0.526683			0.263342	−	0.964703i	$-0.415175\pi$
$733$	10452.1			0.526683			0.263342	+	0.964703i	$0.415175\pi$
$734$		−	28235.7i		−	1.41989i
$735$		0			0
$736$		−	32853.7i		−	1.64538i
$737$			17016.0i			0.850465i
$738$			75728.9i			3.77726i
$739$		−	15791.4i		−	0.786059i	−0.919526	−	0.393030i	$-0.871427\pi$
$739$		−	15791.4i		−	0.786059i	0.919526	−	0.393030i	$-0.128573\pi$
$740$		0			0
$741$	66.3231	+	4745.32i	0.00328804	+	0.235255i
$742$			1061.53i			0.0525201i
$743$	−16295.2			−0.804592			−0.402296	−	0.915510i	$-0.631788\pi$
$743$	−16295.2			−0.804592			−0.402296	+	0.915510i	$0.631788\pi$
$744$	−20407.1			−1.00559
$745$		0			0
$746$		−	30288.2i		−	1.48650i
$747$	−51201.1			−2.50783
$748$	−9621.28			−0.470306
$749$		−	23805.4i		−	1.16132i
$750$		0			0
$751$	−2781.04			−0.135129			−0.0675643	−	0.997715i	$-0.521523\pi$
$751$	−2781.04			−0.135129			−0.0675643	+	0.997715i	$0.521523\pi$
$752$	−19316.1			−0.936684
$753$			3524.19i			0.170556i
$754$	277.994	+	19890.1i	0.0134270	+	0.960682i
$755$		0			0
$756$			17794.5i			0.856059i
$757$			25968.3i			1.24681i	0.781901	+	0.623403i	$0.214250\pi$
$757$			25968.3i			1.24681i	−0.781901	+	0.623403i	$0.785750\pi$
$758$			31053.8i			1.48803i
$759$			27197.1i			1.30065i
$760$		0			0
$761$			6582.16i			0.313539i	0.987635	+	0.156769i	$0.0501080\pi$
$761$			6582.16i			0.313539i	−0.987635	+	0.156769i	$0.949892\pi$
$762$	−54392.4			−2.58587
$763$			33820.2i			1.60468i
$764$	−8504.32			−0.402716
$765$		0			0
$766$	10288.4			0.485292
$767$	−19521.3	+	272.840i	−0.919000	+	0.0128444i
$768$		−	46084.9i		−	2.16530i
$769$		−	7980.32i		−	0.374223i	−0.982339	−	0.187112i	$-0.940087\pi$
$769$		−	7980.32i		−	0.374223i	0.982339	−	0.187112i	$-0.0599126\pi$
$770$		0			0
$771$	1006.49			0.0470143
$772$	−13295.0			−0.619816
$773$	14633.6			0.680899			0.340450	−	0.940263i	$-0.389421\pi$
$773$	14633.6			0.680899			0.340450	+	0.940263i	$0.389421\pi$
$774$		−	31618.5i		−	1.46835i
$775$		0			0
$776$	−8643.59			−0.399854
$777$			35759.4i			1.65105i
$778$	−6561.23			−0.302354
$779$	−5209.68			−0.239610
$780$		0			0
$781$	−10287.2			−0.471324
$782$	51518.9			2.35590
$783$		−	19813.3i		−	0.904306i
$784$	−2786.43			−0.126933
$785$		0			0
$786$			73315.4i			3.32707i
$787$	32406.4			1.46780			0.733902	−	0.679255i	$-0.237697\pi$
$787$	32406.4			1.46780			0.733902	+	0.679255i	$0.237697\pi$
$788$	25296.0			1.14357
$789$	−21587.6			−0.974068
$790$		0			0
$791$		−	12329.9i		−	0.554236i
$792$			9080.67i			0.407409i
$793$	−588.320	−	42093.4i	−0.0263453	−	1.88497i
$794$	11136.0			0.497736
$795$		0			0
$796$	−4549.85			−0.202595
$797$		−	43761.2i		−	1.94492i	−0.233066	−	0.972461i	$-0.574876\pi$
$797$		−	43761.2i		−	1.94492i	0.233066	−	0.972461i	$-0.425124\pi$
$798$	−7201.14			−0.319445
$799$		−	22101.5i		−	0.978593i
$800$		0			0
$801$		−	5497.29i		−	0.242493i
$802$			22149.6i			0.975222i
$803$		−	10711.1i		−	0.470720i
$804$			39033.2i			1.71218i
$805$		0			0
$806$	−42139.9	+	588.970i	−1.84158	+	0.0257389i
$807$			50677.7i			2.21058i
$808$	−2318.87			−0.100962
$809$	20194.7			0.877638			0.438819	−	0.898576i	$-0.355397\pi$
$809$	20194.7			0.877638			0.438819	+	0.898576i	$0.355397\pi$
$810$		0			0
$811$			35223.5i			1.52511i	0.646924	+	0.762554i	$0.276055\pi$
$811$			35223.5i			1.52511i	−0.646924	+	0.762554i	$0.723945\pi$
$812$	−12108.3			−0.523297
$813$	−29670.0			−1.27992
$814$		−	15691.5i		−	0.675659i
$815$		0			0
$816$	60060.3			2.57663
$817$	2175.16			0.0931446
$818$		−	18348.8i		−	0.784293i
$819$	−597.251	−	42732.4i	−0.0254818	−	1.82319i
$820$		0			0
$821$			21772.3i			0.925527i	0.886482	+	0.462764i	$0.153142\pi$
$821$			21772.3i			0.925527i	−0.886482	+	0.462764i	$0.846858\pi$
$822$		−	47997.4i		−	2.03662i
$823$			12117.3i			0.513224i	0.966514	+	0.256612i	$0.0826063\pi$
$823$			12117.3i			0.513224i	−0.966514	+	0.256612i	$0.917394\pi$
$824$			1196.51i			0.0505852i
$825$		0			0
$826$		−	29624.0i		−	1.24788i
$827$	17732.9			0.745628			0.372814	−	0.927906i	$-0.378393\pi$
$827$	17732.9			0.745628			0.372814	+	0.927906i	$0.378393\pi$
$828$			39580.3i			1.66124i
$829$	42202.5			1.76810			0.884050	−	0.467392i	$-0.154806\pi$
$829$	42202.5			1.76810			0.884050	+	0.467392i	$0.154806\pi$
$830$		0			0
$831$	−20891.7			−0.872110
$832$	−89.4627	−	6400.92i	−0.00372784	−	0.266721i
$833$		−	3188.23i		−	0.132612i
$834$			70549.9i			2.92919i
$835$		0			0
$836$	1267.61			0.0524415
$837$	41977.4			1.73351
$838$	−33200.0			−1.36859
$839$			24334.6i			1.00134i	0.865639	+	0.500669i	$0.166913\pi$
$839$			24334.6i			1.00134i	−0.865639	+	0.500669i	$0.833087\pi$
$840$		0			0
$841$	−10907.0			−0.447211
$842$			7050.14i			0.288556i
$843$	30189.3			1.23342
$844$	−16581.2			−0.676241
$845$		0			0
$846$	42327.7			1.72016
$847$	18056.3			0.732492
$848$			1166.46i			0.0472363i
$849$	30853.4			1.24721
$850$		0			0
$851$			33706.0i			1.35773i
$852$	−23597.9			−0.948885
$853$	−40903.4			−1.64186			−0.820929	−	0.571031i	$-0.806544\pi$
$853$	−40903.4			−1.64186			−0.820929	+	0.571031i	$0.806544\pi$
$854$	63877.8			2.55955
$855$		0			0
$856$		−	11808.9i		−	0.471518i
$857$		−	34239.0i		−	1.36474i	−0.731007	−	0.682370i	$-0.760949\pi$
$857$		−	34239.0i		−	1.36474i	0.731007	−	0.682370i	$-0.239051\pi$
$858$	413.096	+	29556.4i	0.0164369	+	1.17604i
$859$	−46008.6			−1.82747			−0.913734	−	0.406314i	$-0.866814\pi$
$859$	−46008.6			−1.82747			−0.913734	+	0.406314i	$0.866814\pi$
$860$		0			0
$861$	73947.6			2.92698
$862$			11613.5i			0.458884i
$863$	1552.40			0.0612331			0.0306166	−	0.999531i	$-0.490253\pi$
$863$	1552.40			0.0612331			0.0306166	+	0.999531i	$0.490253\pi$
$864$			35566.0i			1.40044i
$865$		0			0
$866$			34595.9i			1.35752i
$867$			26499.0i			1.03801i
$868$		−	25653.1i		−	1.00314i
$869$		−	1808.25i		−	0.0705878i
$870$		0			0
$871$	−555.175	−	39721.9i	−0.0215974	−	1.54527i
$872$			16776.8i			0.651531i
$873$	41956.9			1.62661
$874$	−6787.63			−0.262695
$875$		0			0
$876$		−	24570.4i		−	0.947669i
$877$	5802.07			0.223400			0.111700	−	0.993742i	$-0.464370\pi$
$877$	5802.07			0.223400			0.111700	+	0.993742i	$0.464370\pi$
$878$	−2807.67			−0.107921
$879$		−	80019.1i		−	3.07051i
$880$		0			0
$881$	−991.228			−0.0379062			−0.0189531	−	0.999820i	$-0.506033\pi$
$881$	−991.228			−0.0379062			−0.0189531	+	0.999820i	$0.506033\pi$
$882$	6105.93			0.233104
$883$		−	17576.6i		−	0.669874i	−0.942241	−	0.334937i	$-0.891285\pi$
$883$		−	17576.6i		−	0.669874i	0.942241	−	0.334937i	$-0.108715\pi$
$884$	22459.8	−	313.910i	0.854530	−	0.0119434i
$885$		0			0
$886$			5003.54i			0.189726i
$887$		−	27370.0i		−	1.03607i	−0.855360	−	0.518035i	$-0.826664\pi$
$887$		−	27370.0i		−	1.03607i	0.855360	−	0.518035i	$-0.173336\pi$
$888$			17738.8i			0.670355i
$889$			33696.1i			1.27124i
$890$		0			0
$891$		−	4042.78i		−	0.152007i
$892$	4947.03			0.185694
$893$			2911.88i			0.109118i
$894$	22318.9			0.834961
$895$		0			0
$896$	−22732.7			−0.847596
$897$	−887.350	−	63488.6i	−0.0330298	−	2.36324i
$898$			7866.13i			0.292312i
$899$			28563.5i			1.05967i
$900$		0			0
$901$	−1334.67			−0.0493498
$902$	−32448.7			−1.19781
$903$	−30874.8			−1.13782
$904$		−	6116.35i		−	0.225030i
$905$		0			0
$906$	37752.4			1.38437
$907$		−	28779.1i		−	1.05358i	−0.849997	−	0.526788i	$-0.823396\pi$
$907$		−	28779.1i		−	1.05358i	0.849997	−	0.526788i	$-0.176604\pi$
$908$	3498.64			0.127871
$909$	11256.0			0.410714
$910$		0			0
$911$	812.241			0.0295398			0.0147699	−	0.999891i	$-0.495298\pi$
$911$	812.241			0.0295398			0.0147699	+	0.999891i	$0.495298\pi$
$912$	−7912.96			−0.287307
$913$		−	21938.9i		−	0.795260i
$914$	−38262.3			−1.38469
$915$		0			0
$916$			18491.0i			0.666985i
$917$	45418.9			1.63562
$918$	−55772.1			−2.00518
$919$	7982.53			0.286528			0.143264	−	0.989685i	$-0.454240\pi$
$919$	7982.53			0.286528			0.143264	+	0.989685i	$0.454240\pi$
$920$		0			0
$921$		−	22637.5i		−	0.809915i
$922$		−	24625.4i		−	0.879604i
$923$	24014.2	−	335.636i	0.856380	−	0.0119692i
$924$	−17992.8			−0.640604
$925$		0			0
$926$	−25205.9			−0.894510
$927$		−	5807.97i		−	0.205781i
$928$	−24200.8			−0.856068
$929$		−	52612.3i		−	1.85808i	−0.369984	−	0.929038i	$-0.620637\pi$
$929$		−	52612.3i		−	1.85808i	0.369984	−	0.929038i	$-0.379363\pi$
$930$		0			0
$931$			420.051i			0.0147869i
$932$		−	14720.3i		−	0.517359i
$933$			16985.0i			0.595995i
$934$			41509.0i			1.45419i
$935$		0			0
$936$	−296.272	−	21197.8i	−0.0103461	−	0.740248i
$937$		−	34900.3i		−	1.21680i	−0.793630	−	0.608401i	$-0.791811\pi$
$937$		−	34900.3i		−	1.21680i	0.793630	−	0.608401i	$-0.208189\pi$
$938$	60279.0			2.09827
$939$	−35229.2			−1.22435
$940$		0			0
$941$			4626.31i			0.160269i	0.996784	+	0.0801346i	$0.0255350\pi$
$941$			4626.31i			0.160269i	−0.996784	+	0.0801346i	$0.974465\pi$
$942$	21276.5			0.735909
$943$	69701.4			2.40699
$944$		−	32552.3i		−	1.12234i
$945$		0			0
$946$	13548.1			0.465630
$947$	−22103.4			−0.758463			−0.379232	−	0.925302i	$-0.623812\pi$
$947$	−22103.4			−0.758463			−0.379232	+	0.925302i	$0.623812\pi$
$948$		−	4147.98i		−	0.142110i
$949$	349.468	+	25003.9i	0.0119539	+	0.855282i
$950$		0			0
$951$		−	5323.88i		−	0.181534i
$952$		−	16796.7i		−	0.571832i
$953$		−	41498.1i		−	1.41055i	−0.708933	−	0.705276i	$-0.750823\pi$
$953$		−	41498.1i		−	1.41055i	0.708933	−	0.705276i	$-0.249177\pi$
$954$		−	2556.08i		−	0.0867465i
$955$		0			0
$956$		−	35500.7i		−	1.20102i
$957$	20034.1			0.676708
$958$		−	28286.0i		−	0.953946i
$959$	−29734.4			−1.00122
$960$		0			0
$961$	−30724.7			−1.03134
$962$	511.960	+	36630.0i	0.0171583	+	1.22765i
$963$			57321.7i			1.91814i
$964$		−	17257.4i		−	0.576579i
$965$		0			0
$966$	96345.4			3.20897
$967$	−42191.4			−1.40309			−0.701543	−	0.712627i	$-0.747505\pi$
$967$	−42191.4			−1.40309			−0.701543	+	0.712627i	$0.747505\pi$
$968$	8956.97			0.297405
$969$		−	9054.03i		−	0.300162i
$970$		0			0
$971$	−10472.7			−0.346123			−0.173061	−	0.984911i	$-0.555366\pi$
$971$	−10472.7			−0.346123			−0.173061	+	0.984911i	$0.555366\pi$
$972$			15416.7i			0.508735i
$973$	43705.7			1.44002
$974$	−78024.4			−2.56680
$975$		0			0
$976$	70192.0			2.30204
$977$	34586.0			1.13255			0.566276	−	0.824216i	$-0.308384\pi$
$977$	34586.0			1.13255			0.566276	+	0.824216i	$0.308384\pi$
$978$		−	64174.8i		−	2.09825i
$979$	2355.51			0.0768972
$980$		0			0
$981$		−	81436.5i		−	2.65043i
$982$	−41858.9			−1.36026
$983$	−53923.9			−1.74965			−0.874825	−	0.484439i	$-0.839024\pi$
$983$	−53923.9			−1.74965			−0.874825	+	0.484439i	$0.839024\pi$
$984$	36682.4			1.18841
$985$		0			0
$986$		−	37950.1i		−	1.22574i
$987$		−	41332.1i		−	1.33294i
$988$	−2959.09	+	41.3577i	−0.0952845	+	0.00133175i
$989$	−29101.9			−0.935678
$990$		0			0
$991$	−2349.40			−0.0753090			−0.0376545	−	0.999291i	$-0.511989\pi$
$991$	−2349.40			−0.0753090			−0.0376545	+	0.999291i	$0.511989\pi$
$992$		−	51272.9i		−	1.64104i
$993$	−36524.1			−1.16723
$994$			36442.2i			1.16285i
$995$		0			0
$996$		−	50326.0i		−	1.60104i
$997$		−	10949.2i		−	0.347807i	−0.984763	−	0.173903i	$-0.944362\pi$
$997$		−	10949.2i		−	0.347807i	0.984763	−	0.173903i	$-0.0556381\pi$
$998$			32084.9i			1.01767i
$999$		−	36488.7i		−	1.15561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.4.d.c.324.3		14
5.2	odd	4		325.4.c.e.51.4		14
5.3	odd	4		65.4.c.a.51.11	yes	14
5.4	even	2		325.4.d.d.324.12		14
13.12	even	2		325.4.d.d.324.11		14
15.8	even	4		585.4.b.e.181.4		14
20.3	even	4		1040.4.k.d.961.2		14
65.8	even	4		845.4.a.i.1.2		7
65.12	odd	4		325.4.c.e.51.11		14
65.18	even	4		845.4.a.l.1.6		7
65.38	odd	4		65.4.c.a.51.4	✓	14
65.64	even	2	inner	325.4.d.c.324.4		14
195.38	even	4		585.4.b.e.181.11		14
260.103	even	4		1040.4.k.d.961.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.c.a.51.4	✓	14	65.38	odd	4
65.4.c.a.51.11	yes	14	5.3	odd	4
325.4.c.e.51.4		14	5.2	odd	4
325.4.c.e.51.11		14	65.12	odd	4
325.4.d.c.324.3		14	1.1	even	1	trivial
325.4.d.c.324.4		14	65.64	even	2	inner
325.4.d.d.324.11		14	13.12	even	2
325.4.d.d.324.12		14	5.4	even	2
585.4.b.e.181.4		14	15.8	even	4
585.4.b.e.181.11		14	195.38	even	4
845.4.a.i.1.2		7	65.8	even	4
845.4.a.l.1.6		7	65.18	even	4
1040.4.k.d.961.1		14	260.103	even	4
1040.4.k.d.961.2		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)

\(f(q)\)	\(=\)	\(q-3.65500 q^{2} -8.59394i q^{3} +5.35901 q^{4} +31.4108i q^{6} +19.4590 q^{7} +9.65282 q^{8} -46.8559 q^{9} -20.0770i q^{11} -46.0550i q^{12} +(0.655046 + 46.8676i) q^{13} -71.1227 q^{14} -78.1531 q^{16} -89.4229i q^{17} +171.258 q^{18} +11.7815i q^{19} -167.230i q^{21} +73.3816i q^{22} -157.627i q^{23} -82.9558i q^{24} +(-2.39419 - 171.301i) q^{26} +170.640i q^{27} +104.281 q^{28} -116.112 q^{29} -245.999i q^{31} +208.427 q^{32} -172.541 q^{33} +326.840i q^{34} -251.101 q^{36} -213.834 q^{37} -43.0613i q^{38} +(402.777 - 5.62943i) q^{39} +442.192i q^{41} +611.224i q^{42} -184.625i q^{43} -107.593i q^{44} +576.126i q^{46} +247.157 q^{47} +671.643i q^{48} +35.6534 q^{49} -768.495 q^{51} +(3.51040 + 251.164i) q^{52} -14.9253i q^{53} -623.689i q^{54} +187.834 q^{56} +101.250 q^{57} +424.389 q^{58} +416.520i q^{59} -898.135 q^{61} +899.127i q^{62} -911.769 q^{63} -136.575 q^{64} +630.637 q^{66} -847.535 q^{67} -479.218i q^{68} -1354.64 q^{69} -512.385i q^{71} -452.291 q^{72} +533.502 q^{73} +781.564 q^{74} +63.1371i q^{76} -390.680i q^{77} +(-1472.15 + 20.5756i) q^{78} +90.0657 q^{79} +201.363 q^{81} -1616.21i q^{82} +1092.74 q^{83} -896.185i q^{84} +674.804i q^{86} +997.859i q^{87} -193.800i q^{88} +117.323i q^{89} +(12.7466 + 911.997i) q^{91} -844.724i q^{92} -2114.11 q^{93} -903.360 q^{94} -1791.21i q^{96} -895.447 q^{97} -130.313 q^{98} +940.727i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{2} + 56 q^{4} + 108 q^{7} - 48 q^{8} - 158 q^{9} + 6 q^{13} + 152 q^{14} + 280 q^{16} - 272 q^{18} - 344 q^{26} + 572 q^{28} - 588 q^{29} - 1788 q^{32} + 248 q^{33} + 496 q^{36} + 940 q^{37}+ \cdots + 7364 q^{98}+O(q^{100}) \) 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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