LMFDB - Embedded newform 325.4.c.f.51.1

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 = [14,0,12] 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} + 40708x^{8} + 309729x^{6} + 1120672x^{4} + 1546596x^{2} + 83136 $ x^14 + 84x^12 + 2674x^10 + 40708x^8 + 309729x^6 + 1120672x^4 + 1546596x^2 + 83136
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.1
Root			$-5.39779i$ of defining polynomial
Character	$\chi$	$=$	325.51
Dual form			325.4.c.f.51.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.39779i q^{2} +9.57032 q^{3} -21.1361 q^{4} -51.6586i q^{6} -19.5662i q^{7} +70.9061i q^{8} +64.5911 q^{9} -22.1851i q^{11} -202.280 q^{12} +(-41.2492 - 22.2600i) q^{13} -105.614 q^{14} +213.647 q^{16} -3.19819 q^{17} -348.649i q^{18} -79.9778i q^{19} -187.255i q^{21} -119.751 q^{22} -81.6896 q^{23} +678.595i q^{24} +(-120.155 + 222.654i) q^{26} +359.759 q^{27} +413.555i q^{28} +15.5101 q^{29} +27.4476i q^{31} -585.974i q^{32} -212.319i q^{33} +17.2632i q^{34} -1365.21 q^{36} +418.722i q^{37} -431.703 q^{38} +(-394.768 - 213.035i) q^{39} -253.693i q^{41} -1010.76 q^{42} +83.2815 q^{43} +468.908i q^{44} +440.943i q^{46} -388.997i q^{47} +2044.67 q^{48} -39.8376 q^{49} -30.6078 q^{51} +(871.848 + 470.490i) q^{52} -92.5015 q^{53} -1941.90i q^{54} +1387.37 q^{56} -765.413i q^{57} -83.7202i q^{58} +385.328i q^{59} +734.366 q^{61} +148.156 q^{62} -1263.80i q^{63} -1453.79 q^{64} -1146.05 q^{66} +138.626i q^{67} +67.5975 q^{68} -781.796 q^{69} +497.037i q^{71} +4579.90i q^{72} -716.898i q^{73} +2260.17 q^{74} +1690.42i q^{76} -434.079 q^{77} +(-1149.92 + 2130.87i) q^{78} +425.224 q^{79} +1699.05 q^{81} -1369.38 q^{82} +793.338i q^{83} +3957.85i q^{84} -449.536i q^{86} +148.436 q^{87} +1573.06 q^{88} -1007.38i q^{89} +(-435.544 + 807.091i) q^{91} +1726.60 q^{92} +262.682i q^{93} -2099.73 q^{94} -5607.96i q^{96} -740.271i q^{97} +215.035i q^{98} -1432.96i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 12 q^{3} - 56 q^{4} + 158 q^{9} - 300 q^{12} - 46 q^{13} - 92 q^{14} + 280 q^{16} - 106 q^{17} - 192 q^{22} - 148 q^{23} - 284 q^{26} + 456 q^{27} + 18 q^{29} - 2084 q^{36} - 740 q^{38} - 560 q^{39}+ \cdots - 5924 q^{94}+O(q^{100}) $ 14 * q + 12 * q^3 - 56 * q^4 + 158 * q^9 - 300 * q^12 - 46 * q^13 - 92 * q^14 + 280 * q^16 - 106 * q^17 - 192 * q^22 - 148 * q^23 - 284 * q^26 + 456 * q^27 + 18 * q^29 - 2084 * q^36 - 740 * q^38 - 560 * q^39 - 1088 * q^42 - 1132 * q^43 + 3932 * q^48 + 288 * q^49 + 536 * q^51 + 1680 * q^52 + 434 * q^53 + 2492 * q^56 + 130 * q^61 - 36 * q^62 - 2664 * q^64 - 1980 * q^66 + 104 * q^68 - 2140 * q^69 + 5352 * q^74 + 458 * q^77 - 1304 * q^78 + 1256 * q^79 + 4430 * q^81 - 5364 * q^82 + 1128 * q^87 + 1960 * q^88 + 976 * q^91 + 4280 * q^92 - 5924 * 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 $

$2$		−	5.39779i		−	1.90841i	−0.299158	−	0.954204i	$-0.596706\pi$
$2$		−	5.39779i		−	1.90841i	0.299158	−	0.954204i	$-0.403294\pi$
$3$	9.57032			1.84181			0.920905	−	0.389788i	$-0.127452\pi$
$3$	9.57032			1.84181			0.920905	+	0.389788i	$0.127452\pi$
$4$	−21.1361			−2.64202
$5$		0			0
$5$		0			0
$6$		−	51.6586i		−	3.51492i
$7$		−	19.5662i		−	1.05648i	−0.849096	−	0.528239i	$-0.822853\pi$
$7$		−	19.5662i		−	1.05648i	0.849096	−	0.528239i	$-0.177147\pi$
$8$			70.9061i			3.13364i
$9$	64.5911			2.39226
$10$		0			0
$11$		−	22.1851i		−	0.608097i	−0.952657	−	0.304049i	$-0.901662\pi$
$11$		−	22.1851i		−	0.608097i	0.952657	−	0.304049i	$-0.0983385\pi$
$12$	−202.280			−4.86609
$13$	−41.2492	−	22.2600i	−0.880035	−	0.474908i
$13$	−41.2492	−	22.2600i	−0.880035	−	0.474908i
$14$	−105.614			−2.01619
$15$		0			0
$16$	213.647			3.33824
$17$	−3.19819			−0.0456280			−0.0228140	−	0.999740i	$-0.507263\pi$
$17$	−3.19819			−0.0456280			−0.0228140	+	0.999740i	$0.507263\pi$
$18$		−	348.649i		−	4.56541i
$19$		−	79.9778i		−	0.965693i	−0.875705	−	0.482846i	$-0.839603\pi$
$19$		−	79.9778i		−	0.965693i	0.875705	−	0.482846i	$-0.160397\pi$
$20$		0			0
$21$		−	187.255i		−	1.94583i
$22$	−119.751			−1.16050
$23$	−81.6896			−0.740585			−0.370293	−	0.928915i	$-0.620743\pi$
$23$	−81.6896			−0.740585			−0.370293	+	0.928915i	$0.620743\pi$
$24$			678.595i			5.77156i
$25$		0			0
$26$	−120.155	+	222.654i	−0.906318	+	1.67947i
$27$	359.759			2.56428
$28$			413.555i			2.79123i
$29$	15.5101			0.0993155			0.0496577	−	0.998766i	$-0.484187\pi$
$29$	15.5101			0.0993155			0.0496577	+	0.998766i	$0.484187\pi$
$30$		0			0
$31$			27.4476i			0.159023i	0.996834	+	0.0795117i	$0.0253361\pi$
$31$			27.4476i			0.159023i	−0.996834	+	0.0795117i	$0.974664\pi$
$32$		−	585.974i		−	3.23708i
$33$		−	212.319i		−	1.12000i
$34$			17.2632i			0.0870768i
$35$		0			0
$36$	−1365.21			−6.32040
$37$			418.722i			1.86047i	0.366963	+	0.930236i	$0.380398\pi$
$37$			418.722i			1.86047i	−0.366963	+	0.930236i	$0.619602\pi$
$38$	−431.703			−1.84294
$39$	−394.768	−	213.035i	−1.62086	−	0.874690i
$40$		0			0
$41$		−	253.693i		−	0.966346i	−0.875525	−	0.483173i	$-0.839484\pi$
$41$		−	253.693i		−	0.966346i	0.875525	−	0.483173i	$-0.160516\pi$
$42$	−1010.76			−3.71344
$43$	83.2815			0.295356			0.147678	−	0.989035i	$-0.452820\pi$
$43$	83.2815			0.295356			0.147678	+	0.989035i	$0.452820\pi$
$44$			468.908i			1.60660i
$45$		0			0
$46$			440.943i			1.41334i
$47$		−	388.997i		−	1.20726i	−0.797266	−	0.603628i	$-0.793721\pi$
$47$		−	388.997i		−	1.20726i	0.797266	−	0.603628i	$-0.206279\pi$
$48$	2044.67			6.14840
$49$	−39.8376			−0.116145
$50$		0			0
$51$	−30.6078			−0.0840381
$52$	871.848	+	470.490i	2.32507	+	1.25472i
$53$	−92.5015			−0.239737			−0.119868	−	0.992790i	$-0.538247\pi$
$53$	−92.5015			−0.239737			−0.119868	+	0.992790i	$0.538247\pi$
$54$		−	1941.90i		−	4.89369i
$55$		0			0
$56$	1387.37			3.31062
$57$		−	765.413i		−	1.77862i
$58$		−	83.7202i		−	0.189534i
$59$			385.328i			0.850262i	0.905132	+	0.425131i	$0.139772\pi$
$59$			385.328i			0.850262i	−0.905132	+	0.425131i	$0.860228\pi$
$60$		0			0
$61$	734.366			1.54141			0.770704	−	0.637193i	$-0.219905\pi$
$61$	734.366			1.54141			0.770704	+	0.637193i	$0.219905\pi$
$62$	148.156			0.303482
$63$		−	1263.80i		−	2.52737i
$64$	−1453.79			−2.83943
$65$		0			0
$66$	−1146.05			−2.13741
$67$			138.626i			0.252774i	0.991981	+	0.126387i	$0.0403381\pi$
$67$			138.626i			0.252774i	−0.991981	+	0.126387i	$0.959662\pi$
$68$	67.5975			0.120550
$69$	−781.796			−1.36402
$70$		0			0
$71$			497.037i			0.830809i	0.909637	+	0.415404i	$0.136360\pi$
$71$			497.037i			0.830809i	−0.909637	+	0.415404i	$0.863640\pi$
$72$			4579.90i			7.49648i
$73$		−	716.898i		−	1.14941i	−0.818362	−	0.574703i	$-0.805118\pi$
$73$		−	716.898i		−	1.14941i	0.818362	−	0.574703i	$-0.194882\pi$
$74$	2260.17			3.55054
$75$		0			0
$76$			1690.42i			2.55138i
$77$	−434.079			−0.642441
$78$	−1149.92	+	2130.87i	−1.66926	+	3.09326i
$79$	425.224			0.605588			0.302794	−	0.953056i	$-0.402081\pi$
$79$	425.224			0.605588			0.302794	+	0.953056i	$0.402081\pi$
$80$		0			0
$81$	1699.05			2.33066
$82$	−1369.38			−1.84418
$83$			793.338i			1.04916i	0.851362	+	0.524579i	$0.175777\pi$
$83$			793.338i			1.04916i	−0.851362	+	0.524579i	$0.824223\pi$
$84$			3957.85i			5.14092i
$85$		0			0
$86$		−	449.536i		−	0.563659i
$87$	148.436			0.182920
$88$	1573.06			1.90556
$89$		−	1007.38i		−	1.19980i	−0.800074	−	0.599901i	$-0.795207\pi$
$89$		−	1007.38i		−	1.19980i	0.800074	−	0.599901i	$-0.204793\pi$
$90$		0			0
$91$	−435.544	+	807.091i	−0.501730	+	0.929738i
$92$	1726.60			1.95664
$93$			262.682i			0.292891i
$94$	−2099.73			−2.30394
$95$		0			0
$96$		−	5607.96i		−	5.96209i
$97$		−	740.271i		−	0.774878i	−0.921895	−	0.387439i	$-0.873360\pi$
$97$		−	740.271i		−	0.774878i	0.921895	−	0.387439i	$-0.126640\pi$
$98$			215.035i			0.221651i
$99$		−	1432.96i		−	1.45473i
$100$		0			0
$101$	1241.26			1.22287			0.611435	−	0.791295i	$-0.290593\pi$
$101$	1241.26			1.22287			0.611435	+	0.791295i	$0.290593\pi$
$102$			165.214i			0.160379i
$103$	539.693			0.516286			0.258143	−	0.966107i	$-0.416889\pi$
$103$	539.693			0.516286			0.258143	+	0.966107i	$0.416889\pi$
$104$	1578.37	−	2924.82i	1.48819	−	2.75771i
$105$		0			0
$106$			499.304i			0.457516i
$107$	1978.96			1.78798			0.893988	−	0.448092i	$-0.147896\pi$
$107$	1978.96			1.78798			0.893988	+	0.448092i	$0.147896\pi$
$108$	−7603.91			−6.77488
$109$			695.416i			0.611089i	0.952178	+	0.305545i	$0.0988386\pi$
$109$			695.416i			0.611089i	−0.952178	+	0.305545i	$0.901161\pi$
$110$		0			0
$111$			4007.30i			3.42663i
$112$		−	4180.27i		−	3.52677i
$113$	929.958			0.774187			0.387093	−	0.922041i	$-0.373479\pi$
$113$	929.958			0.774187			0.387093	+	0.922041i	$0.373479\pi$
$114$	−4131.54			−3.39434
$115$		0			0
$116$	−327.823			−0.262393
$117$	−2664.33	−	1437.80i	−2.10528	−	1.13610i
$118$	2079.92			1.62265
$119$			62.5766i			0.0482050i
$120$		0			0
$121$	838.820			0.630218
$122$		−	3963.95i		−	2.94164i
$123$		−	2427.92i		−	1.77982i
$124$		−	580.136i		−	0.420143i
$125$		0			0
$126$	−6821.75			−4.82325
$127$	−1018.39			−0.711558			−0.355779	−	0.934570i	$-0.615784\pi$
$127$	−1018.39			−0.711558			−0.355779	+	0.934570i	$0.615784\pi$
$128$			3159.45i			2.18171i
$129$	797.031			0.543989
$130$		0			0
$131$	181.321			0.120932			0.0604659	−	0.998170i	$-0.480741\pi$
$131$	181.321			0.120932			0.0604659	+	0.998170i	$0.480741\pi$
$132$			4487.60i			2.95906i
$133$	−1564.86			−1.02023
$134$	748.274			0.482395
$135$		0			0
$136$		−	226.772i		−	0.142982i
$137$			16.8451i			0.0105049i	0.999986	+	0.00525245i	$0.00167192\pi$
$137$			16.8451i			0.0105049i	−0.999986	+	0.00525245i	$0.998328\pi$
$138$			4219.97i			2.60310i
$139$	−303.101			−0.184954			−0.0924772	−	0.995715i	$-0.529479\pi$
$139$	−303.101			−0.184954			−0.0924772	+	0.995715i	$0.529479\pi$
$140$		0			0
$141$		−	3722.83i		−	2.22354i
$142$	2682.90			1.58552
$143$	−493.840	+	915.118i	−0.288790	+	0.535147i
$144$	13799.7			7.98594
$145$		0			0
$146$	−3869.67			−2.19353
$147$	−381.258			−0.213916
$148$		−	8850.16i		−	4.91540i
$149$			908.684i			0.499612i	0.968296	+	0.249806i	$0.0803669\pi$
$149$			908.684i			0.499612i	−0.968296	+	0.249806i	$0.919633\pi$
$150$		0			0
$151$		−	2598.33i		−	1.40032i	−0.713985	−	0.700161i	$-0.753111\pi$
$151$		−	2598.33i		−	1.40032i	0.713985	−	0.700161i	$-0.246889\pi$
$152$	5670.92			3.02613
$153$	−206.575			−0.109154
$154$			2343.07i			1.22604i
$155$		0			0
$156$	8343.87	+	4502.74i	4.28233	+	2.31095i
$157$	−2512.22			−1.27705			−0.638526	−	0.769600i	$-0.720456\pi$
$157$	−2512.22			−1.27705			−0.638526	+	0.769600i	$0.720456\pi$
$158$		−	2295.27i		−	1.15571i
$159$	−885.269			−0.441550
$160$		0			0
$161$			1598.36i			0.782412i
$162$		−	9171.11i		−	4.44784i
$163$		−	2128.77i		−	1.02293i	−0.859303	−	0.511467i	$-0.829102\pi$
$163$		−	2128.77i		−	1.02293i	0.859303	−	0.511467i	$-0.170898\pi$
$164$			5362.09i			2.55310i
$165$		0			0
$166$	4282.27			2.00222
$167$			1924.60i			0.891798i	0.895083	+	0.445899i	$0.147116\pi$
$167$			1924.60i			0.891798i	−0.895083	+	0.445899i	$0.852884\pi$
$168$	13277.5			6.09753
$169$	1205.99	+	1836.41i	0.548925	+	0.835872i
$170$		0			0
$171$		−	5165.85i		−	2.31019i
$172$	−1760.25			−0.780336
$173$	−3623.82			−1.59256			−0.796282	−	0.604926i	$-0.793203\pi$
$173$	−3623.82			−1.59256			−0.796282	+	0.604926i	$0.793203\pi$
$174$		−	801.229i		−	0.349086i
$175$		0			0
$176$		−	4739.79i		−	2.02997i
$177$			3687.71i			1.56602i
$178$	−5437.64			−2.28971
$179$	2895.47			1.20904			0.604518	−	0.796592i	$-0.293366\pi$
$179$	2895.47			1.20904			0.604518	+	0.796592i	$0.293366\pi$
$180$		0			0
$181$	−1833.42			−0.752913			−0.376457	−	0.926434i	$-0.622858\pi$
$181$	−1833.42			−0.752913			−0.376457	+	0.926434i	$0.622858\pi$
$182$	4356.51	+	2350.97i	1.77432	+	0.957504i
$183$	7028.12			2.83898
$184$		−	5792.29i		−	2.32073i
$185$		0			0
$186$	1417.90			0.558955
$187$			70.9524i			0.0277463i
$188$			8221.90i			3.18959i
$189$		−	7039.13i		−	2.70911i
$190$		0			0
$191$	−1377.00			−0.521654			−0.260827	−	0.965385i	$-0.583995\pi$
$191$	−1377.00			−0.521654			−0.260827	+	0.965385i	$0.583995\pi$
$192$	−13913.2			−5.22969
$193$		−	3493.38i		−	1.30290i	−0.758693	−	0.651449i	$-0.774162\pi$
$193$		−	3493.38i		−	1.30290i	0.758693	−	0.651449i	$-0.225838\pi$
$194$	−3995.83			−1.47878
$195$		0			0
$196$	842.012			0.306856
$197$			4698.05i			1.69910i	0.527510	+	0.849549i	$0.323126\pi$
$197$			4698.05i			1.69910i	−0.527510	+	0.849549i	$0.676874\pi$
$198$	−7734.82			−2.77621
$199$	−622.741			−0.221834			−0.110917	−	0.993830i	$-0.535379\pi$
$199$	−622.741			−0.221834			−0.110917	+	0.993830i	$0.535379\pi$
$200$		0			0
$201$			1326.69i			0.465561i
$202$		−	6700.05i		−	2.33373i
$203$		−	303.474i		−	0.104925i
$204$	646.930			0.222030
$205$		0			0
$206$		−	2913.15i		−	0.985284i
$207$	−5276.42			−1.77167
$208$	−8812.77	−	4755.78i	−2.93777	−	1.58536i
$209$	−1774.32			−0.587235
$210$		0			0
$211$	1343.25			0.438261			0.219131	−	0.975696i	$-0.429678\pi$
$211$	1343.25			0.438261			0.219131	+	0.975696i	$0.429678\pi$
$212$	1955.12			0.633389
$213$			4756.80i			1.53019i
$214$		−	10682.0i		−	3.41218i
$215$		0			0
$216$			25509.1i			8.03553i
$217$	537.045			0.168005
$218$	3753.71			1.16621
$219$		−	6860.95i		−	2.11699i
$220$		0			0
$221$	131.923	+	71.1917i	0.0401543	+	0.0216691i
$222$	21630.6			6.53941
$223$			1081.45i			0.324751i	0.986729	+	0.162375i	$0.0519155\pi$
$223$			1081.45i			0.324751i	−0.986729	+	0.162375i	$0.948084\pi$
$224$	−11465.3			−3.41990
$225$		0			0
$226$		−	5019.72i		−	1.47746i
$227$			4333.06i			1.26694i	0.773767	+	0.633470i	$0.218370\pi$
$227$			4333.06i			1.26694i	−0.773767	+	0.633470i	$0.781630\pi$
$228$			16177.9i			4.69915i
$229$			4091.36i			1.18063i	0.807172	+	0.590316i	$0.200997\pi$
$229$			4091.36i			1.18063i	−0.807172	+	0.590316i	$0.799003\pi$
$230$		0			0
$231$	−4154.28			−1.18325
$232$			1099.76i			0.311219i
$233$	−4921.94			−1.38389			−0.691946	−	0.721949i	$-0.743246\pi$
$233$	−4921.94			−1.38389			−0.691946	+	0.721949i	$0.743246\pi$
$234$	−7760.92	+	14381.5i	−2.16815	+	4.01772i
$235$		0			0
$236$		−	8144.35i		−	2.24641i
$237$	4069.53			1.11538
$238$	337.776			0.0919947
$239$			1848.41i			0.500265i	0.968212	+	0.250133i	$0.0804743\pi$
$239$			1848.41i			0.500265i	−0.968212	+	0.250133i	$0.919526\pi$
$240$		0			0
$241$		−	2033.42i		−	0.543501i	−0.962368	−	0.271751i	$-0.912397\pi$
$241$		−	2033.42i		−	0.543501i	0.962368	−	0.271751i	$-0.0876026\pi$
$242$		−	4527.78i		−	1.20271i
$243$	6546.96			1.72834
$244$	−15521.7			−4.07243
$245$		0			0
$246$	−13105.4			−3.39663
$247$	−1780.30	+	3299.02i	−0.458615	+	0.849844i
$248$	−1946.20			−0.498322
$249$			7592.50i			1.93235i
$250$		0			0
$251$	2624.85			0.660075			0.330038	−	0.943968i	$-0.392939\pi$
$251$	2624.85			0.660075			0.330038	+	0.943968i	$0.392939\pi$
$252$			26711.9i			6.67736i
$253$			1812.29i			0.450348i
$254$			5497.08i			1.35794i
$255$		0			0
$256$	5423.74			1.32415
$257$	−2704.07			−0.656323			−0.328162	−	0.944622i	$-0.606429\pi$
$257$	−2704.07			−0.656323			−0.328162	+	0.944622i	$0.606429\pi$
$258$		−	4302.20i		−	1.03815i
$259$	8192.81			1.96555
$260$		0			0
$261$	1001.81			0.237589
$262$		−	978.732i		−	0.230787i
$263$	7024.27			1.64690			0.823451	−	0.567387i	$-0.192046\pi$
$263$	7024.27			1.64690			0.823451	+	0.567387i	$0.192046\pi$
$264$	15054.7			3.50967
$265$		0			0
$266$			8446.81i			1.94702i
$267$		−	9640.98i		−	2.20981i
$268$		−	2930.02i		−	0.667833i
$269$	3126.72			0.708697			0.354348	−	0.935113i	$-0.384703\pi$
$269$	3126.72			0.708697			0.354348	+	0.935113i	$0.384703\pi$
$270$		0			0
$271$			7754.38i			1.73817i	0.494659	+	0.869087i	$0.335293\pi$
$271$			7754.38i			1.73817i	−0.494659	+	0.869087i	$0.664707\pi$
$272$	−683.286			−0.152317
$273$	−4168.29	+	7724.12i	−0.924090	+	1.71240i
$274$	90.9262			0.0200476
$275$		0			0
$276$	16524.2			3.60376
$277$	3379.40			0.733028			0.366514	−	0.930413i	$-0.380551\pi$
$277$	3379.40			0.733028			0.366514	+	0.930413i	$0.380551\pi$
$278$			1636.07i			0.352968i
$279$			1772.87i			0.380426i
$280$		0			0
$281$		−	3717.14i		−	0.789131i	−0.918868	−	0.394566i	$-0.870895\pi$
$281$		−	3717.14i		−	0.789131i	0.918868	−	0.394566i	$-0.129105\pi$
$282$	−20095.1			−4.24341
$283$	−3975.48			−0.835045			−0.417522	−	0.908667i	$-0.637102\pi$
$283$	−3975.48			−0.835045			−0.417522	+	0.908667i	$0.637102\pi$
$284$		−	10505.4i		−	2.19501i
$285$		0			0
$286$	4939.62	+	2665.65i	1.02128	+	0.551129i
$287$	−4963.81			−1.02092
$288$		−	37848.7i		−	7.74395i
$289$	−4902.77			−0.997918
$290$		0			0
$291$		−	7084.64i		−	1.42718i
$292$			15152.5i			3.03675i
$293$		−	7351.82i		−	1.46586i	−0.680302	−	0.732932i	$-0.738151\pi$
$293$		−	7351.82i		−	1.46586i	0.680302	−	0.732932i	$-0.261849\pi$
$294$			2057.95i			0.408239i
$295$		0			0
$296$	−29689.9			−5.83004
$297$		−	7981.29i		−	1.55933i
$298$	4904.88			0.953464
$299$	3369.63	+	1818.41i	0.651741	+	0.351710i
$300$		0			0
$301$		−	1629.50i		−	0.312037i
$302$	−14025.2			−2.67239
$303$	11879.2			2.25229
$304$		−	17087.0i		−	3.22371i
$305$		0			0
$306$			1115.05i			0.208311i
$307$		−	5822.03i		−	1.08235i	−0.840911	−	0.541174i	$-0.817980\pi$
$307$		−	5822.03i		−	1.08235i	0.840911	−	0.541174i	$-0.182020\pi$
$308$	9174.76			1.69734
$309$	5165.03			0.950901
$310$		0			0
$311$	8275.18			1.50882			0.754409	−	0.656405i	$-0.227924\pi$
$311$	8275.18			1.50882			0.754409	+	0.656405i	$0.227924\pi$
$312$	15105.5	−	27991.5i	2.74096	−	5.07918i
$313$	−4922.13			−0.888866			−0.444433	−	0.895812i	$-0.646595\pi$
$313$	−4922.13			−0.888866			−0.444433	+	0.895812i	$0.646595\pi$
$314$			13560.5i			2.43714i
$315$		0			0
$316$	−8987.60			−1.59997
$317$			2991.37i			0.530006i	0.964248	+	0.265003i	$0.0853730\pi$
$317$			2991.37i			0.530006i	−0.964248	+	0.265003i	$0.914627\pi$
$318$			4778.50i			0.842657i
$319$		−	344.093i		−	0.0603935i
$320$		0			0
$321$	18939.3			3.29311
$322$	8627.60			1.49316
$323$			255.785i			0.0440626i
$324$	−35911.3			−6.15764
$325$		0			0
$326$	−11490.7			−1.95217
$327$			6655.35i			1.12551i
$328$	17988.4			3.02818
$329$	−7611.21			−1.27544
$330$		0			0
$331$			5421.39i			0.900262i	0.892963	+	0.450131i	$0.148623\pi$
$331$			5421.39i			0.900262i	−0.892963	+	0.450131i	$0.851377\pi$
$332$		−	16768.1i		−	2.77190i
$333$			27045.7i			4.45074i
$334$	10388.6			1.70191
$335$		0			0
$336$		−	40006.6i		−	6.49565i
$337$	7639.38			1.23485			0.617424	−	0.786631i	$-0.288176\pi$
$337$	7639.38			1.23485			0.617424	+	0.786631i	$0.288176\pi$
$338$	9912.56	−	6509.67i	1.59518	−	1.04757i
$339$	8900.00			1.42590
$340$		0			0
$341$	608.928			0.0967017
$342$	−27884.2			−4.40878
$343$		−	5931.75i		−	0.933773i
$344$			5905.17i			0.925539i
$345$		0			0
$346$			19560.6i			3.03926i
$347$	10145.0			1.56948			0.784741	−	0.619823i	$-0.212796\pi$
$347$	10145.0			1.56948			0.784741	+	0.619823i	$0.212796\pi$
$348$	−3137.37			−0.483278
$349$			1126.84i			0.172831i	0.996259	+	0.0864157i	$0.0275413\pi$
$349$			1126.84i			0.172831i	−0.996259	+	0.0864157i	$0.972459\pi$
$350$		0			0
$351$	−14839.8	−	8008.22i	−2.25666	−	1.21780i
$352$	−12999.9			−1.96846
$353$			9532.90i			1.43735i	0.695345	+	0.718676i	$0.255251\pi$
$353$			9532.90i			1.43735i	−0.695345	+	0.718676i	$0.744749\pi$
$354$	19905.5			2.98860
$355$		0			0
$356$			21292.2i			3.16990i
$357$			598.879i			0.0887844i
$358$		−	15629.1i		−	2.30733i
$359$			6852.10i			1.00735i	0.863892	+	0.503677i	$0.168020\pi$
$359$			6852.10i			1.00735i	−0.863892	+	0.503677i	$0.831980\pi$
$360$		0			0
$361$	462.551			0.0674371
$362$			9896.44i			1.43686i
$363$	8027.78			1.16074
$364$	9205.71	−	17058.8i	1.32558	−	2.45638i
$365$		0			0
$366$		−	37936.3i		−	5.41793i
$367$	−2453.68			−0.348995			−0.174497	−	0.984658i	$-0.555830\pi$
$367$	−2453.68			−0.348995			−0.174497	+	0.984658i	$0.555830\pi$
$368$	−17452.8			−2.47225
$369$		−	16386.3i		−	2.31175i
$370$		0			0
$371$			1809.91i			0.253277i
$372$		−	5552.08i		−	0.773823i
$373$	−1900.82			−0.263862			−0.131931	−	0.991259i	$-0.542118\pi$
$373$	−1900.82			−0.263862			−0.131931	+	0.991259i	$0.542118\pi$
$374$	382.986			0.0529512
$375$		0			0
$376$	27582.3			3.78311
$377$	−639.778	−	345.254i	−0.0874012	−	0.0471657i
$378$	−37995.7			−5.17008
$379$			12116.2i			1.64213i	0.570831	+	0.821067i	$0.306621\pi$
$379$			12116.2i			1.64213i	−0.570831	+	0.821067i	$0.693379\pi$
$380$		0			0
$381$	−9746.36			−1.31055
$382$			7432.74i			0.995529i
$383$		−	6754.44i		−	0.901138i	−0.892742	−	0.450569i	$-0.851221\pi$
$383$		−	6754.44i		−	0.901138i	0.892742	−	0.450569i	$-0.148779\pi$
$384$			30236.9i			4.01829i
$385$		0			0
$386$	−18856.5			−2.48646
$387$	5379.24			0.706569
$388$			15646.5i			2.04724i
$389$	2535.39			0.330461			0.165231	−	0.986255i	$-0.447163\pi$
$389$	2535.39			0.330461			0.165231	+	0.986255i	$0.447163\pi$
$390$		0			0
$391$	261.259			0.0337914
$392$		−	2824.73i		−	0.363955i
$393$	1735.30			0.222733
$394$	25359.1			3.24257
$395$		0			0
$396$			30287.3i			3.84342i
$397$			3881.63i			0.490713i	0.969433	+	0.245357i	$0.0789051\pi$
$397$			3881.63i			0.490713i	−0.969433	+	0.245357i	$0.921095\pi$
$398$			3361.42i			0.423349i
$399$	−14976.3			−1.87907
$400$		0			0
$401$			10458.0i			1.30237i	0.758920	+	0.651184i	$0.225727\pi$
$401$			10458.0i			1.30237i	−0.758920	+	0.651184i	$0.774273\pi$
$402$	7161.22			0.888480
$403$	610.982	−	1132.19i	0.0755215	−	0.139946i
$404$	−26235.4			−3.23084
$405$		0			0
$406$	−1638.09			−0.200239
$407$	9289.40			1.13135
$408$		−	2170.28i		−	0.263345i
$409$			12296.3i			1.48658i	0.668970	+	0.743289i	$0.266735\pi$
$409$			12296.3i			1.48658i	−0.668970	+	0.743289i	$0.733265\pi$
$410$		0			0
$411$			161.213i			0.0193480i
$412$	−11407.0			−1.36404
$413$	7539.42			0.898282
$414$			28481.0i			3.38108i
$415$		0			0
$416$	−13043.8	+	24171.0i	−1.53732	+	2.84875i
$417$	−2900.77			−0.340651
$418$			9577.39i			1.12068i
$419$	−9401.01			−1.09611			−0.548054	−	0.836443i	$-0.684631\pi$
$419$	−9401.01			−1.09611			−0.548054	+	0.836443i	$0.684631\pi$
$420$		0			0
$421$		−	16241.2i		−	1.88016i	−0.340951	−	0.940081i	$-0.610749\pi$
$421$		−	16241.2i		−	1.88016i	0.340951	−	0.940081i	$-0.389251\pi$
$422$		−	7250.58i		−	0.836381i
$423$		−	25125.8i		−	2.88808i
$424$		−	6558.92i		−	0.751249i
$425$		0			0
$426$	25676.2			2.92023
$427$		−	14368.8i		−	1.62846i
$428$	−41827.6			−4.72386
$429$	−4726.21	+	8757.98i	−0.531896	+	0.985639i
$430$		0			0
$431$		−	2664.58i		−	0.297792i	−0.988853	−	0.148896i	$-0.952428\pi$
$431$		−	2664.58i		−	0.297792i	0.988853	−	0.148896i	$-0.0475720\pi$
$432$	76861.5			8.56019
$433$	−10804.1			−1.19910			−0.599551	−	0.800336i	$-0.704654\pi$
$433$	−10804.1			−1.19910			−0.599551	+	0.800336i	$0.704654\pi$
$434$		−	2898.86i		−	0.320621i
$435$		0			0
$436$		−	14698.4i		−	1.61451i
$437$			6533.36i			0.715178i
$438$	−37033.9			−4.04007
$439$	−8612.49			−0.936337			−0.468168	−	0.883639i	$-0.655086\pi$
$439$	−8612.49			−0.936337			−0.468168	+	0.883639i	$0.655086\pi$
$440$		0			0
$441$	−2573.15			−0.277848
$442$	384.278	−	712.092i	0.0413535	−	0.0766307i
$443$	2565.27			0.275123			0.137561	−	0.990493i	$-0.456074\pi$
$443$	2565.27			0.275123			0.137561	+	0.990493i	$0.456074\pi$
$444$		−	84698.9i		−	9.05323i
$445$		0			0
$446$	5837.45			0.619757
$447$			8696.40i			0.920191i
$448$			28445.2i			2.99979i
$449$		−	7527.86i		−	0.791229i	−0.918417	−	0.395614i	$-0.870532\pi$
$449$		−	7527.86i		−	0.791229i	0.918417	−	0.395614i	$-0.129468\pi$
$450$		0			0
$451$	−5628.21			−0.587632
$452$	−19655.7			−2.04541
$453$		−	24866.8i		−	2.57913i
$454$	23389.0			2.41784
$455$		0			0
$456$	54272.5			5.57356
$457$		−	6433.57i		−	0.658534i	−0.944237	−	0.329267i	$-0.893198\pi$
$457$		−	6433.57i		−	0.658534i	0.944237	−	0.329267i	$-0.106802\pi$
$458$	22084.3			2.25313
$459$	−1150.58			−0.117003
$460$		0			0
$461$		−	4993.42i		−	0.504483i	−0.967664	−	0.252242i	$-0.918832\pi$
$461$		−	4993.42i		−	0.504483i	0.967664	−	0.252242i	$-0.0811678\pi$
$462$			22423.9i			2.25813i
$463$			15182.4i			1.52395i	0.647608	+	0.761974i	$0.275770\pi$
$463$			15182.4i			1.52395i	−0.647608	+	0.761974i	$0.724230\pi$
$464$	3313.69			0.331539
$465$		0			0
$466$			26567.6i			2.64103i
$467$	−10748.1			−1.06502			−0.532509	−	0.846425i	$-0.678751\pi$
$467$	−10748.1			−1.06502			−0.532509	+	0.846425i	$0.678751\pi$
$468$	56313.6	+	30389.4i	5.56218	+	3.00161i
$469$	2712.39			0.267050
$470$		0			0
$471$	−24042.8			−2.35209
$472$	−27322.1			−2.66441
$473$		−	1847.61i		−	0.179605i
$474$		−	21966.5i		−	2.12860i
$475$		0			0
$476$		−	1322.63i		−	0.127358i
$477$	−5974.77			−0.573514
$478$	9977.31			0.954710
$479$			567.128i			0.0540976i	0.999634	+	0.0270488i	$0.00861095\pi$
$479$			567.128i			0.0540976i	−0.999634	+	0.0270488i	$0.991389\pi$
$480$		0			0
$481$	9320.73	−	17271.9i	0.883553	−	1.63728i
$482$	−10975.9			−1.03722
$483$			15296.8i			1.44105i
$484$	−17729.4			−1.66505
$485$		0			0
$486$		−	35339.1i		−	3.29838i
$487$			79.6868i			0.00741468i	0.999993	+	0.00370734i	$0.00118009\pi$
$487$			79.6868i			0.00741468i	−0.999993	+	0.00370734i	$0.998820\pi$
$488$			52071.1i			4.83022i
$489$		−	20373.0i		−	1.88405i
$490$		0			0
$491$	4638.66			0.426354			0.213177	−	0.977014i	$-0.431619\pi$
$491$	4638.66			0.426354			0.213177	+	0.977014i	$0.431619\pi$
$492$			51316.9i			4.70233i
$493$	−49.6043			−0.00453157
$494$	17807.4	+	9609.70i	1.62185	+	0.875225i
$495$		0			0
$496$			5864.10i			0.530858i
$497$	9725.14			0.877731
$498$	40982.7			3.68771
$499$		−	1508.55i		−	0.135334i	−0.997708	−	0.0676672i	$-0.978444\pi$
$499$		−	1508.55i		−	0.135334i	0.997708	−	0.0676672i	$-0.0215556\pi$
$500$		0			0
$501$			18419.1i			1.64252i
$502$		−	14168.4i		−	1.25969i
$503$	−6657.75			−0.590168			−0.295084	−	0.955471i	$-0.595348\pi$
$503$	−6657.75			−0.590168			−0.295084	+	0.955471i	$0.595348\pi$
$504$	89611.5			7.91987
$505$		0			0
$506$	9782.39			0.859447
$507$	11541.7	+	17575.0i	1.01101	+	1.53952i
$508$	21524.9			1.87995
$509$		−	11743.6i		−	1.02264i	−0.859390	−	0.511321i	$-0.829156\pi$
$509$		−	11743.6i		−	1.02264i	0.859390	−	0.511321i	$-0.170844\pi$
$510$		0			0
$511$	−14027.0			−1.21432
$512$		−	4000.61i		−	0.345319i
$513$		−	28772.7i		−	2.47631i
$514$			14596.0i			1.25253i
$515$		0			0
$516$	−16846.2			−1.43723
$517$	−8629.95			−0.734129
$518$		−	44223.1i		−	3.75106i
$519$	−34681.1			−2.93320
$520$		0			0
$521$	22239.4			1.87011			0.935054	−	0.354505i	$-0.115350\pi$
$521$	22239.4			1.87011			0.935054	+	0.354505i	$0.115350\pi$
$522$		−	5407.58i		−	0.453416i
$523$	−19668.3			−1.64443			−0.822214	−	0.569179i	$-0.807261\pi$
$523$	−19668.3			−1.64443			−0.822214	+	0.569179i	$0.807261\pi$
$524$	−3832.42			−0.319504
$525$		0			0
$526$		−	37915.6i		−	3.14296i
$527$		−	87.7827i		−	0.00725592i
$528$		−	45361.3i		−	3.73882i
$529$	−5493.81			−0.451533
$530$		0			0
$531$			24888.8i			2.03405i
$532$	33075.2			2.69547
$533$	−5647.20	+	10464.6i	−0.458925	+	0.850418i
$534$	−52040.0			−4.21721
$535$		0			0
$536$	−9829.43			−0.792102
$537$	27710.6			2.22681
$538$		−	16877.4i		−	1.35248i
$539$			883.802i			0.0706271i
$540$		0			0
$541$			13725.3i			1.09075i	0.838192	+	0.545375i	$0.183613\pi$
$541$			13725.3i			1.09075i	−0.838192	+	0.545375i	$0.816387\pi$
$542$	41856.5			3.31714
$543$	−17546.5			−1.38672
$544$			1874.06i			0.147702i
$545$		0			0
$546$	41693.2	+	22499.6i	3.26796	+	1.76354i
$547$	−16200.3			−1.26632			−0.633158	−	0.774022i	$-0.718242\pi$
$547$	−16200.3			−1.26632			−0.633158	+	0.774022i	$0.718242\pi$
$548$		−	356.040i		−	0.0277541i
$549$	47433.5			3.68745
$550$		0			0
$551$		−	1240.46i		−	0.0959083i
$552$		−	55434.1i		−	4.27434i
$553$		−	8320.04i		−	0.639790i
$554$		−	18241.3i		−	1.39892i
$555$		0			0
$556$	6406.38			0.488653
$557$		−	2529.48i		−	0.192419i	−0.995361	−	0.0962097i	$-0.969328\pi$
$557$		−	2529.48i		−	0.192419i	0.995361	−	0.0962097i	$-0.0306720\pi$
$558$	9569.57			0.726007
$559$	−3435.29	−	1853.84i	−0.259924	−	0.140267i
$560$		0			0
$561$			679.037i			0.0511033i
$562$	−20064.3			−1.50598
$563$	−3787.41			−0.283517			−0.141759	−	0.989901i	$-0.545276\pi$
$563$	−3787.41			−0.283517			−0.141759	+	0.989901i	$0.545276\pi$
$564$			78686.2i			5.87462i
$565$		0			0
$566$			21458.8i			1.59361i
$567$		−	33244.0i		−	2.46229i
$568$	−35243.0			−2.60345
$569$	12743.9			0.938933			0.469466	−	0.882950i	$-0.344446\pi$
$569$	12743.9			0.938933			0.469466	+	0.882950i	$0.344446\pi$
$570$		0			0
$571$	8991.11			0.658960			0.329480	−	0.944163i	$-0.393127\pi$
$571$	8991.11			0.658960			0.329480	+	0.944163i	$0.393127\pi$
$572$	10437.9	−	19342.1i	0.762989	−	1.41387i
$573$	−13178.3			−0.960788
$574$			26793.6i			1.94834i
$575$		0			0
$576$	−93901.7			−6.79266
$577$		−	17423.3i		−	1.25709i	−0.777774	−	0.628544i	$-0.783651\pi$
$577$		−	17423.3i		−	1.25709i	0.777774	−	0.628544i	$-0.216349\pi$
$578$			26464.1i			1.90443i
$579$		−	33432.8i		−	2.39969i
$580$		0			0
$581$	15522.6			1.10841
$582$	−38241.4			−2.72364
$583$			2052.16i			0.145783i
$584$	50832.5			3.60182
$585$		0			0
$586$	−39683.6			−2.79746
$587$			14511.5i			1.02036i	0.860067	+	0.510181i	$0.170422\pi$
$587$			14511.5i			1.02036i	−0.860067	+	0.510181i	$0.829578\pi$
$588$	8058.33			0.565170
$589$	2195.20			0.153568
$590$		0			0
$591$			44961.9i			3.12941i
$592$			89458.8i			6.21070i
$593$			267.436i			0.0185199i	0.999957	+	0.00925994i	$0.00294757\pi$
$593$			267.436i			0.0185199i	−0.999957	+	0.00925994i	$0.997052\pi$
$594$	−43081.4			−2.97584
$595$		0			0
$596$		−	19206.1i		−	1.31998i
$597$	−5959.83			−0.408576
$598$	9815.39	−	18188.5i	0.671206	−	1.24379i
$599$	5428.80			0.370308			0.185154	−	0.982709i	$-0.440722\pi$
$599$	5428.80			0.370308			0.185154	+	0.982709i	$0.440722\pi$
$600$		0			0
$601$	−25777.8			−1.74958			−0.874790	−	0.484502i	$-0.839001\pi$
$601$	−25777.8			−1.74958			−0.874790	+	0.484502i	$0.839001\pi$
$602$	−8795.73			−0.595493
$603$			8954.00i			0.604701i
$604$			54918.6i			3.69968i
$605$		0			0
$606$		−	64121.6i		−	4.29829i
$607$	−20383.4			−1.36299			−0.681497	−	0.731821i	$-0.738671\pi$
$607$	−20383.4			−1.36299			−0.681497	+	0.731821i	$0.738671\pi$
$608$	−46864.9			−3.12603
$609$		−	2904.34i		−	0.193251i
$610$		0			0
$611$	−8659.07	+	16045.8i	−0.573336	+	1.06243i
$612$	4366.20			0.288387
$613$			7433.13i			0.489757i	0.969554	+	0.244879i	$0.0787481\pi$
$613$			7433.13i			0.489757i	−0.969554	+	0.244879i	$0.921252\pi$
$614$	−31426.1			−2.06556
$615$		0			0
$616$		−	30778.9i		−	2.01318i
$617$		−	5540.71i		−	0.361524i	−0.983527	−	0.180762i	$-0.942144\pi$
$617$		−	5540.71i		−	0.361524i	0.983527	−	0.180762i	$-0.0578564\pi$
$618$		−	27879.8i		−	1.81471i
$619$			15878.2i			1.03101i	0.856886	+	0.515506i	$0.172396\pi$
$619$			15878.2i			1.03101i	−0.856886	+	0.515506i	$0.827604\pi$
$620$		0			0
$621$	−29388.6			−1.89907
$622$		−	44667.7i		−	2.87944i
$623$	−19710.7			−1.26756
$624$	−84341.1	−	45514.4i	−5.41081	−	2.91992i
$625$		0			0
$626$			26568.6i			1.69632i
$627$	−16980.8			−1.08158
$628$	53098.7			3.37400
$629$		−	1339.15i		−	0.0848896i
$630$		0			0
$631$		−	7809.85i		−	0.492718i	−0.969179	−	0.246359i	$-0.920766\pi$
$631$		−	7809.85i		−	0.492718i	0.969179	−	0.246359i	$-0.0792343\pi$
$632$			30151.0i			1.89769i
$633$	12855.3			0.807194
$634$	16146.8			1.01147
$635$		0			0
$636$	18711.2			1.16658
$637$	1643.27	+	886.783i	0.102211	+	0.0551580i
$638$	−1857.34			−0.115255
$639$			32104.1i			1.98751i
$640$		0			0
$641$	−3286.62			−0.202517			−0.101259	−	0.994860i	$-0.532287\pi$
$641$	−3286.62			−0.202517			−0.101259	+	0.994860i	$0.532287\pi$
$642$		−	102230.i		−	6.28459i
$643$		−	9976.67i		−	0.611884i	−0.952050	−	0.305942i	$-0.901029\pi$
$643$		−	9976.67i		−	0.611884i	0.952050	−	0.305942i	$-0.0989714\pi$
$644$		−	33783.1i		−	2.06715i
$645$		0			0
$646$	1380.67			0.0840895
$647$	−2603.91			−0.158223			−0.0791115	−	0.996866i	$-0.525208\pi$
$647$	−2603.91			−0.158223			−0.0791115	+	0.996866i	$0.525208\pi$
$648$			120473.i			7.30343i
$649$	8548.55			0.517042
$650$		0			0
$651$	5139.70			0.309433
$652$			44994.0i			2.70261i
$653$	−17296.8			−1.03657			−0.518283	−	0.855209i	$-0.673429\pi$
$653$	−17296.8			−1.03657			−0.518283	+	0.855209i	$0.673429\pi$
$654$	35924.2			2.14793
$655$		0			0
$656$		−	54200.8i		−	3.22589i
$657$		−	46305.2i		−	2.74968i
$658$			41083.7i			2.43406i
$659$	4108.13			0.242838			0.121419	−	0.992601i	$-0.461256\pi$
$659$	4108.13			0.242838			0.121419	+	0.992601i	$0.461256\pi$
$660$		0			0
$661$		−	5035.44i		−	0.296303i	−0.988965	−	0.148151i	$-0.952668\pi$
$661$		−	5035.44i		−	0.296303i	0.988965	−	0.148151i	$-0.0473323\pi$
$662$	29263.5			1.71807
$663$	1262.54	+	681.328i	0.0739565	+	0.0399104i
$664$	−56252.5			−3.28768
$665$		0			0
$666$	145987.			8.49381
$667$	−1267.01			−0.0735516
$668$		−	40678.7i		−	2.35615i
$669$			10349.8i			0.598129i
$670$		0			0
$671$		−	16292.0i		−	0.937326i
$672$	−109727.			−6.29881
$673$	29342.4			1.68063			0.840316	−	0.542097i	$-0.182369\pi$
$673$	29342.4			1.68063			0.840316	+	0.542097i	$0.182369\pi$
$674$		−	41235.8i		−	2.35659i
$675$		0			0
$676$	−25489.9	−	38814.6i	−1.45027	−	2.20839i
$677$	−15091.7			−0.856751			−0.428375	−	0.903601i	$-0.640914\pi$
$677$	−15091.7			−0.856751			−0.428375	+	0.903601i	$0.640914\pi$
$678$		−	48040.3i		−	2.72121i
$679$	−14484.3			−0.818641
$680$		0			0
$681$			41468.8i			2.33346i
$682$		−	3286.86i		−	0.184546i
$683$			15949.3i			0.893533i	0.894651	+	0.446767i	$0.147425\pi$
$683$			15949.3i			0.893533i	−0.894651	+	0.446767i	$0.852575\pi$
$684$			109186.i			6.10356i
$685$		0			0
$686$	−32018.3			−1.78202
$687$			39155.6i			2.17450i
$688$	17792.9			0.985969
$689$	3815.61	+	2059.08i	0.210977	+	0.113853i
$690$		0			0
$691$		−	9086.21i		−	0.500225i	−0.968217	−	0.250113i	$-0.919532\pi$
$691$		−	9086.21i		−	0.500225i	0.968217	−	0.250113i	$-0.0804677\pi$
$692$	76593.5			4.20758
$693$	−28037.7			−1.53689
$694$		−	54760.4i		−	2.99521i
$695$		0			0
$696$			10525.1i			0.573206i
$697$			811.359i			0.0440924i
$698$	6082.42			0.329832
$699$	−47104.5			−2.54887
$700$		0			0
$701$	−16228.1			−0.874359			−0.437179	−	0.899374i	$-0.644022\pi$
$701$	−16228.1			−0.874359			−0.437179	+	0.899374i	$0.644022\pi$
$702$	−43226.7	+	80101.9i	−2.32405	+	4.30662i
$703$	33488.4			1.79664
$704$			32252.5i			1.72665i
$705$		0			0
$706$	51456.6			2.74305
$707$		−	24286.7i		−	1.29193i
$708$		−	77944.0i		−	4.13745i
$709$		−	19425.5i		−	1.02897i	−0.857499	−	0.514485i	$-0.827983\pi$
$709$		−	19425.5i		−	1.02897i	0.857499	−	0.514485i	$-0.172017\pi$
$710$		0			0
$711$	27465.7			1.44873
$712$	71429.6			3.75975
$713$		−	2242.18i		−	0.117770i
$714$	3232.62			0.169437
$715$		0			0
$716$	−61199.0			−3.19429
$717$			17689.8i			0.921394i
$718$	36986.2			1.92244
$719$	548.566			0.0284535			0.0142268	−	0.999899i	$-0.495471\pi$
$719$	548.566			0.0284535			0.0142268	+	0.999899i	$0.495471\pi$
$720$		0			0
$721$		−	10559.8i		−	0.545445i
$722$		−	2496.75i		−	0.128697i
$723$		−	19460.4i		−	1.00103i
$724$	38751.5			1.98921
$725$		0			0
$726$		−	43332.3i		−	2.21517i
$727$	−10550.1			−0.538213			−0.269107	−	0.963110i	$-0.586728\pi$
$727$	−10550.1			−0.538213			−0.269107	+	0.963110i	$0.586728\pi$
$728$	−57227.7	−	30882.7i	−2.91346	−	1.57224i
$729$	16782.2			0.852623
$730$		0			0
$731$	−266.350			−0.0134765
$732$	−148547.			−7.50064
$733$			4007.86i			0.201956i	0.994889	+	0.100978i	$0.0321971\pi$
$733$			4007.86i			0.201956i	−0.994889	+	0.100978i	$0.967803\pi$
$734$			13244.4i			0.666024i
$735$		0			0
$736$			47868.0i			2.39734i
$737$	3075.43			0.153711
$738$	−88449.8			−4.41176
$739$		−	1960.69i		−	0.0975984i	−0.998809	−	0.0487992i	$-0.984461\pi$
$739$		−	1960.69i		−	0.0975984i	0.998809	−	0.0487992i	$-0.0155394\pi$
$740$		0			0
$741$	−17038.1	+	31572.7i	−0.844682	+	1.56525i
$742$	9769.49			0.483355
$743$			18597.5i			0.918272i	0.888366	+	0.459136i	$0.151841\pi$
$743$			18597.5i			0.918272i	−0.888366	+	0.459136i	$0.848159\pi$
$744$	−18625.8			−0.917814
$745$		0			0
$746$			10260.2i			0.503556i
$747$			51242.6i			2.50986i
$748$		−	1499.66i		−	0.0733061i
$749$		−	38720.8i		−	1.88896i
$750$		0			0
$751$	17920.4			0.870739			0.435369	−	0.900252i	$-0.356618\pi$
$751$	17920.4			0.870739			0.435369	+	0.900252i	$0.356618\pi$
$752$		−	83108.2i		−	4.03011i
$753$	25120.6			1.21573
$754$	−1863.61	+	3453.39i	−0.0900114	+	0.166797i
$755$		0			0
$756$			148780.i			7.15751i
$757$	−9391.11			−0.450893			−0.225446	−	0.974256i	$-0.572384\pi$
$757$	−9391.11			−0.450893			−0.225446	+	0.974256i	$0.572384\pi$
$758$	65400.9			3.13386
$759$			17344.2i			0.829455i
$760$		0			0
$761$			20548.2i			0.978805i	0.872058	+	0.489403i	$0.162785\pi$
$761$			20548.2i			0.978805i	−0.872058	+	0.489403i	$0.837215\pi$
$762$			52608.8i			2.50107i
$763$	13606.7			0.645602
$764$	29104.4			1.37822
$765$		0			0
$766$	−36459.1			−1.71974
$767$	8577.39	−	15894.5i	0.403796	−	0.748260i
$768$	51906.9			2.43884
$769$			10142.8i			0.475627i	0.971311	+	0.237813i	$0.0764307\pi$
$769$			10142.8i			0.475627i	−0.971311	+	0.237813i	$0.923569\pi$
$770$		0			0
$771$	−25878.8			−1.20882
$772$			73836.6i			3.44228i
$773$			213.912i			0.00995327i	0.999988	+	0.00497664i	$0.00158412\pi$
$773$			213.912i			0.00995327i	−0.999988	+	0.00497664i	$0.998416\pi$
$774$		−	29036.0i		−	1.34842i
$775$		0			0
$776$	52489.8			2.42819
$777$	78407.8			3.62016
$778$		−	13685.5i		−	0.630654i
$779$	−20289.8			−0.933193
$780$		0			0
$781$	11026.8			0.505212
$782$		−	1410.22i		−	0.0644878i
$783$	5579.89			0.254673
$784$	−8511.19			−0.387718
$785$		0			0
$786$		−	9366.78i		−	0.425066i
$787$			13315.9i			0.603127i	0.953446	+	0.301563i	$0.0975085\pi$
$787$			13315.9i			0.603127i	−0.953446	+	0.301563i	$0.902492\pi$
$788$		−	99298.7i		−	4.48905i
$789$	67224.6			3.03328
$790$		0			0
$791$		−	18195.8i		−	0.817911i
$792$	101606.			4.55859
$793$	−30292.0	−	16347.0i	−1.35649	−	0.732027i
$794$	20952.2			0.936481
$795$		0			0
$796$	13162.3			0.586089
$797$	−1432.22			−0.0636537			−0.0318268	−	0.999493i	$-0.510133\pi$
$797$	−1432.22			−0.0636537			−0.0318268	+	0.999493i	$0.510133\pi$
$798$			80838.7i			3.58604i
$799$			1244.09i			0.0550847i
$800$		0			0
$801$		−	65068.0i		−	2.87024i
$802$	56450.3			2.48545
$803$	−15904.5			−0.698950
$804$		−	28041.2i		−	1.23002i
$805$		0			0
$806$	−6111.32	−	3297.95i	−0.267075	−	0.144126i
$807$	29923.7			1.30528
$808$			88012.8i			3.83203i
$809$	−1717.53			−0.0746416			−0.0373208	−	0.999303i	$-0.511882\pi$
$809$	−1717.53			−0.0746416			−0.0373208	+	0.999303i	$0.511882\pi$
$810$		0			0
$811$		−	26684.7i		−	1.15539i	−0.816251	−	0.577697i	$-0.803951\pi$
$811$		−	26684.7i		−	1.15539i	0.816251	−	0.577697i	$-0.196049\pi$
$812$			6414.27i			0.277213i
$813$			74211.9i			3.20138i
$814$		−	50142.2i		−	2.15907i
$815$		0			0
$816$	−6539.27			−0.280539
$817$		−	6660.67i		−	0.285223i
$818$	66372.6			2.83700
$819$	−28132.2	+	52130.9i	−1.20027	+	2.22418i
$820$		0			0
$821$		−	28453.9i		−	1.20956i	−0.796394	−	0.604779i	$-0.793262\pi$
$821$		−	28453.9i		−	1.20956i	0.796394	−	0.604779i	$-0.206738\pi$
$822$	870.193			0.0369239
$823$	−24406.1			−1.03371			−0.516855	−	0.856073i	$-0.672898\pi$
$823$	−24406.1			−1.03371			−0.516855	+	0.856073i	$0.672898\pi$
$824$			38267.5i			1.61785i
$825$		0			0
$826$		−	40696.2i		−	1.71429i
$827$			23423.5i			0.984902i	0.870340	+	0.492451i	$0.163899\pi$
$827$			23423.5i			0.984902i	−0.870340	+	0.492451i	$0.836101\pi$
$828$	111523.			4.68079
$829$	−18813.3			−0.788193			−0.394097	−	0.919069i	$-0.628942\pi$
$829$	−18813.3			−0.788193			−0.394097	+	0.919069i	$0.628942\pi$
$830$		0			0
$831$	32342.0			1.35010
$832$	59967.6	+	32361.3i	2.49880	+	1.34847i
$833$	127.408			0.00529944
$834$			15657.7i			0.650100i
$835$		0			0
$836$	37502.2			1.55149
$837$			9874.50i			0.407781i
$838$			50744.7i			2.09182i
$839$		−	2274.01i		−	0.0935726i	−0.998905	−	0.0467863i	$-0.985102\pi$
$839$		−	2274.01i		−	0.0935726i	0.998905	−	0.0467863i	$-0.0148980\pi$
$840$		0			0
$841$	−24148.4			−0.990136
$842$	−87666.7			−3.58811
$843$		−	35574.2i		−	1.45343i
$844$	−28391.1			−1.15789
$845$		0			0
$846$	−135624.			−5.51162
$847$		−	16412.6i		−	0.665811i
$848$	−19762.7			−0.800299
$849$	−38046.6			−1.53799
$850$		0			0
$851$		−	34205.2i		−	1.37784i
$852$		−	100540.i		−	4.04279i
$853$		−	8197.12i		−	0.329032i	−0.986374	−	0.164516i	$-0.947394\pi$
$853$		−	8197.12i		−	0.329032i	0.986374	−	0.164516i	$-0.0526061\pi$
$854$	−77559.7			−3.10777
$855$		0			0
$856$			140320.i			5.60287i
$857$	43282.5			1.72521			0.862604	−	0.505879i	$-0.168832\pi$
$857$	43282.5			1.72521			0.862604	+	0.505879i	$0.168832\pi$
$858$	47273.7	+	25511.1i	1.88100	+	1.01507i
$859$	14884.8			0.591226			0.295613	−	0.955308i	$-0.404476\pi$
$859$	14884.8			0.591226			0.295613	+	0.955308i	$0.404476\pi$
$860$		0			0
$861$	−47505.3			−1.88034
$862$	−14382.9			−0.568309
$863$			29421.4i			1.16050i	0.814437	+	0.580252i	$0.197046\pi$
$863$			29421.4i			1.16050i	−0.814437	+	0.580252i	$0.802954\pi$
$864$		−	210809.i		−	8.30079i
$865$		0			0
$866$			58318.2i			2.28838i
$867$	−46921.1			−1.83798
$868$	−11351.1			−0.443871
$869$		−	9433.65i		−	0.368256i
$870$		0			0
$871$	3085.81	−	5718.20i	0.120044	−	0.222450i
$872$	−49309.2			−1.91493
$873$		−	47814.9i		−	1.85371i
$874$	35265.7			1.36485
$875$		0			0
$876$			145014.i			5.59311i
$877$		−	44242.4i		−	1.70349i	−0.523958	−	0.851744i	$-0.675545\pi$
$877$		−	44242.4i		−	1.70349i	0.523958	−	0.851744i	$-0.324455\pi$
$878$			46488.4i			1.78691i
$879$		−	70359.3i		−	2.69984i
$880$		0			0
$881$	6344.23			0.242614			0.121307	−	0.992615i	$-0.461292\pi$
$881$	6344.23			0.242614			0.121307	+	0.992615i	$0.461292\pi$
$882$			13889.3i			0.530247i
$883$	−31600.7			−1.20436			−0.602178	−	0.798362i	$-0.705700\pi$
$883$	−31600.7			−1.20436			−0.602178	+	0.798362i	$0.705700\pi$
$884$	−2788.34	−	1504.72i	−0.106088	−	0.0572502i
$885$		0			0
$886$		−	13846.8i		−	0.525047i
$887$	−22725.3			−0.860250			−0.430125	−	0.902769i	$-0.641531\pi$
$887$	−22725.3			−0.860250			−0.430125	+	0.902769i	$0.641531\pi$
$888$	−284142.			−10.7378
$889$			19926.1i			0.751745i
$890$		0			0
$891$		−	37693.6i		−	1.41727i
$892$		−	22857.7i		−	0.857997i
$893$	−31111.1			−1.16584
$894$	46941.3			1.75610
$895$		0			0
$896$	61818.5			2.30492
$897$	32248.4	+	17402.8i	1.20038	+	0.647783i
$898$	−40633.8			−1.50999
$899$			425.714i			0.0157935i
$900$		0			0
$901$	295.838			0.0109387
$902$			30379.9i			1.12144i
$903$		−	15594.9i		−	0.574713i
$904$			65939.7i			2.42602i
$905$		0			0
$906$	−134226.			−4.92203
$907$	−21217.0			−0.776736			−0.388368	−	0.921504i	$-0.626961\pi$
$907$	−21217.0			−0.776736			−0.388368	+	0.921504i	$0.626961\pi$
$908$		−	91584.2i		−	3.34728i
$909$	80174.2			2.92542
$910$		0			0
$911$	7009.14			0.254910			0.127455	−	0.991844i	$-0.459319\pi$
$911$	7009.14			0.254910			0.127455	+	0.991844i	$0.459319\pi$
$912$		−	163529.i		−	5.93747i
$913$	17600.3			0.637990
$914$	−34727.1			−1.25675
$915$		0			0
$916$		−	86475.6i		−	3.11925i
$917$		−	3547.77i		−	0.127762i
$918$			6210.58i			0.223290i
$919$	26748.5			0.960121			0.480061	−	0.877235i	$-0.340615\pi$
$919$	26748.5			0.960121			0.480061	+	0.877235i	$0.340615\pi$
$920$		0			0
$921$		−	55718.7i		−	1.99348i
$922$	−26953.4			−0.962759
$923$	11064.0	−	20502.4i	0.394558	−	0.731141i
$924$	87805.5			3.12618
$925$		0			0
$926$	81951.6			2.90831
$927$	34859.3			1.23509
$928$		−	9088.51i		−	0.321492i
$929$			18623.8i			0.657726i	0.944378	+	0.328863i	$0.106665\pi$
$929$			18623.8i			0.657726i	−0.944378	+	0.328863i	$0.893335\pi$
$930$		0			0
$931$			3186.12i			0.112160i
$932$	104031.			3.65627
$933$	79196.1			2.77895
$934$			58016.0i			2.03249i
$935$		0			0
$936$	101949.	−	188917.i	3.56014	−	6.59717i
$937$	40923.2			1.42679			0.713396	−	0.700761i	$-0.247156\pi$
$937$	40923.2			1.42679			0.713396	+	0.700761i	$0.247156\pi$
$938$		−	14640.9i		−	0.509640i
$939$	−47106.4			−1.63712
$940$		0			0
$941$			55098.3i			1.90877i	0.298576	+	0.954386i	$0.403488\pi$
$941$			55098.3i			1.90877i	−0.298576	+	0.954386i	$0.596512\pi$
$942$			129778.i			4.48874i
$943$			20724.1i			0.715661i
$944$			82324.3i			2.83838i
$945$		0			0
$946$	−9973.01			−0.342760
$947$			40418.2i			1.38692i	0.720495	+	0.693460i	$0.243915\pi$
$947$			40418.2i			1.38692i	−0.720495	+	0.693460i	$0.756085\pi$
$948$	−86014.2			−2.94685
$949$	−15958.1	+	29571.5i	−0.545862	+	1.01152i
$950$		0			0
$951$			28628.4i			0.976170i
$952$	−4437.07			−0.151057
$953$	11373.4			0.386591			0.193296	−	0.981141i	$-0.438082\pi$
$953$	11373.4			0.386591			0.193296	+	0.981141i	$0.438082\pi$
$954$			32250.6i			1.09450i
$955$		0			0
$956$		−	39068.2i		−	1.32171i
$957$		−	3293.08i		−	0.111233i
$958$	3061.24			0.103240
$959$	329.595			0.0110982
$960$		0			0
$961$	29037.6			0.974712
$962$	−93230.2	−	50311.4i	−3.12460	−	1.68618i
$963$	127823.			4.27731
$964$			42978.6i			1.43594i
$965$		0			0
$966$	82568.9			2.75012
$967$		−	12910.4i		−	0.429339i	−0.976687	−	0.214670i	$-0.931133\pi$
$967$		−	12910.4i		−	0.429339i	0.976687	−	0.214670i	$-0.0688675\pi$
$968$			59477.5i			1.97488i
$969$			2447.94i			0.0811550i
$970$		0			0
$971$	27002.5			0.892432			0.446216	−	0.894925i	$-0.352771\pi$
$971$	27002.5			0.892432			0.446216	+	0.894925i	$0.352771\pi$
$972$	−138377.			−4.56631
$973$			5930.54i			0.195400i
$974$	430.132			0.0141502
$975$		0			0
$976$	156895.			5.14559
$977$		−	8403.06i		−	0.275166i	−0.990490	−	0.137583i	$-0.956067\pi$
$977$		−	8403.06i		−	0.275166i	0.990490	−	0.137583i	$-0.0439334\pi$
$978$	−109969.			−3.59553
$979$	−22348.9			−0.729596
$980$		0			0
$981$			44917.7i			1.46189i
$982$		−	25038.5i		−	0.813656i
$983$			41927.2i			1.36040i	0.733028	+	0.680199i	$0.238106\pi$
$983$			41927.2i			1.36040i	−0.733028	+	0.680199i	$0.761894\pi$
$984$	172155.			5.57733
$985$		0			0
$986$			267.753i			0.00864808i
$987$	−72841.8			−2.34912
$988$	37628.7	−	69728.5i	1.21167	−	2.24530i
$989$	−6803.23			−0.218736
$990$		0			0
$991$	−21469.8			−0.688206			−0.344103	−	0.938932i	$-0.611817\pi$
$991$	−21469.8			−0.688206			−0.344103	+	0.938932i	$0.611817\pi$
$992$	16083.6			0.514772
$993$			51884.5i			1.65811i
$994$		−	52494.3i		−	1.67507i
$995$		0			0
$996$		−	160476.i		−	5.10530i
$997$	−24074.4			−0.764738			−0.382369	−	0.924010i	$-0.624892\pi$
$997$	−24074.4			−0.764738			−0.382369	+	0.924010i	$0.624892\pi$
$998$	−8142.82			−0.258273
$999$			150639.i			4.77077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.4.c.f.51.1	yes	14
5.2	odd	4		325.4.d.e.324.27		28
5.3	odd	4		325.4.d.e.324.2		28
5.4	even	2		325.4.c.d.51.14	yes	14
13.12	even	2	inner	325.4.c.f.51.14	yes	14
65.12	odd	4		325.4.d.e.324.1		28
65.38	odd	4		325.4.d.e.324.28		28
65.64	even	2		325.4.c.d.51.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.4.c.d.51.1	✓	14	65.64	even	2
325.4.c.d.51.14	yes	14	5.4	even	2
325.4.c.f.51.1	yes	14	1.1	even	1	trivial
325.4.c.f.51.14	yes	14	13.12	even	2	inner
325.4.d.e.324.1		28	65.12	odd	4
325.4.d.e.324.2		28	5.3	odd	4
325.4.d.e.324.27		28	5.2	odd	4
325.4.d.e.324.28		28	65.38	odd	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.39779i q^{2} +9.57032 q^{3} -21.1361 q^{4} -51.6586i q^{6} -19.5662i q^{7} +70.9061i q^{8} +64.5911 q^{9} -22.1851i q^{11} -202.280 q^{12} +(-41.2492 - 22.2600i) q^{13} -105.614 q^{14} +213.647 q^{16} -3.19819 q^{17} -348.649i q^{18} -79.9778i q^{19} -187.255i q^{21} -119.751 q^{22} -81.6896 q^{23} +678.595i q^{24} +(-120.155 + 222.654i) q^{26} +359.759 q^{27} +413.555i q^{28} +15.5101 q^{29} +27.4476i q^{31} -585.974i q^{32} -212.319i q^{33} +17.2632i q^{34} -1365.21 q^{36} +418.722i q^{37} -431.703 q^{38} +(-394.768 - 213.035i) q^{39} -253.693i q^{41} -1010.76 q^{42} +83.2815 q^{43} +468.908i q^{44} +440.943i q^{46} -388.997i q^{47} +2044.67 q^{48} -39.8376 q^{49} -30.6078 q^{51} +(871.848 + 470.490i) q^{52} -92.5015 q^{53} -1941.90i q^{54} +1387.37 q^{56} -765.413i q^{57} -83.7202i q^{58} +385.328i q^{59} +734.366 q^{61} +148.156 q^{62} -1263.80i q^{63} -1453.79 q^{64} -1146.05 q^{66} +138.626i q^{67} +67.5975 q^{68} -781.796 q^{69} +497.037i q^{71} +4579.90i q^{72} -716.898i q^{73} +2260.17 q^{74} +1690.42i q^{76} -434.079 q^{77} +(-1149.92 + 2130.87i) q^{78} +425.224 q^{79} +1699.05 q^{81} -1369.38 q^{82} +793.338i q^{83} +3957.85i q^{84} -449.536i q^{86} +148.436 q^{87} +1573.06 q^{88} -1007.38i q^{89} +(-435.544 + 807.091i) q^{91} +1726.60 q^{92} +262.682i q^{93} -2099.73 q^{94} -5607.96i q^{96} -740.271i q^{97} +215.035i q^{98} -1432.96i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 12 q^{3} - 56 q^{4} + 158 q^{9} - 300 q^{12} - 46 q^{13} - 92 q^{14} + 280 q^{16} - 106 q^{17} - 192 q^{22} - 148 q^{23} - 284 q^{26} + 456 q^{27} + 18 q^{29} - 2084 q^{36} - 740 q^{38} - 560 q^{39}+ \cdots - 5924 q^{94}+O(q^{100}) \) 14 * q + 12 * q^3 - 56 * q^4 + 158 * q^9 - 300 * q^12 - 46 * q^13 - 92 * q^14 + 280 * q^16 - 106 * q^17 - 192 * q^22 - 148 * q^23 - 284 * q^26 + 456 * q^27 + 18 * q^29 - 2084 * q^36 - 740 * q^38 - 560 * q^39 - 1088 * q^42 - 1132 * q^43 + 3932 * q^48 + 288 * q^49 + 536 * q^51 + 1680 * q^52 + 434 * q^53 + 2492 * q^56 + 130 * q^61 - 36 * q^62 - 2664 * q^64 - 1980 * q^66 + 104 * q^68 - 2140 * q^69 + 5352 * q^74 + 458 * q^77 - 1304 * q^78 + 1256 * q^79 + 4430 * q^81 - 5364 * q^82 + 1128 * q^87 + 1960 * q^88 + 976 * q^91 + 4280 * q^92 - 5924 * q^94

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