LMFDB - Embedded newform 1850.2.d.i.1701.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(1701,1850)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1850.1701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 48 x^{18} + 878 x^{16} + 8102 x^{14} + 41081 x^{12} + 115688 x^{10} + 175041 x^{8} + 134990 x^{6} + \cdots + 1 $ x^20 + 48x^18 + 878x^16 + 8102x^14 + 41081x^12 + 115688x^10 + 175041x^8 + 134990x^6 + 49782x^4 + 6932*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1701.13
Root			$0.762160i$ of defining polynomial
Character	$\chi$	$=$	1850.1701
Dual form			1850.2.d.i.1701.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.76216 q^{3} -1.00000 q^{4} -1.76216i q^{6} -1.22131 q^{7} -1.00000i q^{8} +0.105209 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.76216 q^{3} -1.00000 q^{4} -1.76216i q^{6} -1.22131 q^{7} -1.00000i q^{8} +0.105209 q^{9} +1.87120 q^{11} +1.76216 q^{12} +6.50491i q^{13} -1.22131i q^{14} +1.00000 q^{16} +0.765994i q^{17} +0.105209i q^{18} -3.34507i q^{19} +2.15215 q^{21} +1.87120i q^{22} +1.38964i q^{23} +1.76216i q^{24} -6.50491 q^{26} +5.10109 q^{27} +1.22131 q^{28} +1.72909i q^{29} +4.11288i q^{31} +1.00000i q^{32} -3.29736 q^{33} -0.765994 q^{34} -0.105209 q^{36} +(-5.82076 - 1.76599i) q^{37} +3.34507 q^{38} -11.4627i q^{39} +3.73892 q^{41} +2.15215i q^{42} +4.91814i q^{43} -1.87120 q^{44} -1.38964 q^{46} -6.30775 q^{47} -1.76216 q^{48} -5.50840 q^{49} -1.34980i q^{51} -6.50491i q^{52} +2.57768 q^{53} +5.10109i q^{54} +1.22131i q^{56} +5.89455i q^{57} -1.72909 q^{58} -10.5664i q^{59} -11.1550i q^{61} -4.11288 q^{62} -0.128493 q^{63} -1.00000 q^{64} -3.29736i q^{66} -11.1219 q^{67} -0.765994i q^{68} -2.44877i q^{69} +0.963126 q^{71} -0.105209i q^{72} -9.03119 q^{73} +(1.76599 - 5.82076i) q^{74} +3.34507i q^{76} -2.28532 q^{77} +11.4627 q^{78} -10.3333i q^{79} -9.30456 q^{81} +3.73892i q^{82} +0.00656819 q^{83} -2.15215 q^{84} -4.91814 q^{86} -3.04694i q^{87} -1.87120i q^{88} +4.70144i q^{89} -7.94452i q^{91} -1.38964i q^{92} -7.24756i q^{93} -6.30775i q^{94} -1.76216i q^{96} +0.403430i q^{97} -5.50840i q^{98} +0.196867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} + 16 q^{9}+O(q^{10}) $ 20 * q - 20 * q^4 + 16 * q^9	$ 20 q - 20 q^{4} + 16 q^{9} + 20 q^{16} - 24 q^{21} + 4 q^{26} + 36 q^{34} - 16 q^{36} - 8 q^{41} - 20 q^{46} + 16 q^{49} - 20 q^{64} - 40 q^{71} - 16 q^{74} + 116 q^{81} + 24 q^{84} + 20 q^{86} + 164 q^{99}+O(q^{100}) $ 20 * q - 20 * q^4 + 16 * q^9 + 20 * q^16 - 24 * q^21 + 4 * q^26 + 36 * q^34 - 16 * q^36 - 8 * q^41 - 20 * q^46 + 16 * q^49 - 20 * q^64 - 40 * q^71 - 16 * q^74 + 116 * q^81 + 24 * q^84 + 20 * q^86 + 164 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.76216			−1.01738			−0.508692	−	0.860949i	$-0.669871\pi$
$3$	−1.76216			−1.01738			−0.508692	+	0.860949i	$0.669871\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	1.76216i		−	0.719399i
$7$	−1.22131			−0.461612			−0.230806	−	0.973000i	$-0.574136\pi$
$7$	−1.22131			−0.461612			−0.230806	+	0.973000i	$0.574136\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.105209			0.0350696
$10$		0			0
$11$	1.87120			0.564189			0.282094	−	0.959387i	$-0.408971\pi$
$11$	1.87120			0.564189			0.282094	+	0.959387i	$0.408971\pi$
$12$	1.76216			0.508692
$13$			6.50491i			1.80414i	0.431592	+	0.902069i	$0.357952\pi$
$13$			6.50491i			1.80414i	−0.431592	+	0.902069i	$0.642048\pi$
$14$		−	1.22131i		−	0.326409i
$15$		0			0
$16$	1.00000			0.250000
$17$			0.765994i			0.185781i	0.995676	+	0.0928904i	$0.0296106\pi$
$17$			0.765994i			0.185781i	−0.995676	+	0.0928904i	$0.970389\pi$
$18$			0.105209i			0.0247979i
$19$		−	3.34507i		−	0.767412i	−0.923455	−	0.383706i	$-0.874648\pi$
$19$		−	3.34507i		−	0.767412i	0.923455	−	0.383706i	$-0.125352\pi$
$20$		0			0
$21$	2.15215			0.469637
$22$			1.87120i			0.398942i
$23$			1.38964i			0.289760i	0.989449	+	0.144880i	$0.0462796\pi$
$23$			1.38964i			0.289760i	−0.989449	+	0.144880i	$0.953720\pi$
$24$			1.76216i			0.359699i
$25$		0			0
$26$	−6.50491			−1.27572
$27$	5.10109			0.981704
$28$	1.22131			0.230806
$29$			1.72909i			0.321084i	0.987029	+	0.160542i	$0.0513243\pi$
$29$			1.72909i			0.321084i	−0.987029	+	0.160542i	$0.948676\pi$
$30$		0			0
$31$			4.11288i			0.738695i	0.929291	+	0.369348i	$0.120419\pi$
$31$			4.11288i			0.738695i	−0.929291	+	0.369348i	$0.879581\pi$
$32$			1.00000i			0.176777i
$33$	−3.29736			−0.573996
$34$	−0.765994			−0.131367
$35$		0			0
$36$	−0.105209			−0.0175348
$37$	−5.82076	−	1.76599i	−0.956927	−	0.290328i
$37$	−5.82076	−	1.76599i	−0.956927	−	0.290328i
$38$	3.34507			0.542642
$39$		−	11.4627i		−	1.83550i
$40$		0			0
$41$	3.73892			0.583921			0.291960	−	0.956430i	$-0.405692\pi$
$41$	3.73892			0.583921			0.291960	+	0.956430i	$0.405692\pi$
$42$			2.15215i			0.332083i
$43$			4.91814i			0.750009i	0.927023	+	0.375005i	$0.122359\pi$
$43$			4.91814i			0.750009i	−0.927023	+	0.375005i	$0.877641\pi$
$44$	−1.87120			−0.282094
$45$		0			0
$46$	−1.38964			−0.204891
$47$	−6.30775			−0.920080			−0.460040	−	0.887898i	$-0.652165\pi$
$47$	−6.30775			−0.920080			−0.460040	+	0.887898i	$0.652165\pi$
$48$	−1.76216			−0.254346
$49$	−5.50840			−0.786914
$50$		0			0
$51$		−	1.34980i		−	0.189010i
$52$		−	6.50491i		−	0.902069i
$53$	2.57768			0.354072			0.177036	−	0.984204i	$-0.443349\pi$
$53$	2.57768			0.354072			0.177036	+	0.984204i	$0.443349\pi$
$54$			5.10109i			0.694170i
$55$		0			0
$56$			1.22131i			0.163205i
$57$			5.89455i			0.780752i
$58$	−1.72909			−0.227041
$59$		−	10.5664i		−	1.37563i	−0.725887	−	0.687814i	$-0.758571\pi$
$59$		−	10.5664i		−	1.37563i	0.725887	−	0.687814i	$-0.241429\pi$
$60$		0			0
$61$		−	11.1550i		−	1.42825i	−0.700020	−	0.714123i	$-0.746826\pi$
$61$		−	11.1550i		−	1.42825i	0.700020	−	0.714123i	$-0.253174\pi$
$62$	−4.11288			−0.522337
$63$	−0.128493			−0.0161886
$64$	−1.00000			−0.125000
$65$		0			0
$66$		−	3.29736i		−	0.405877i
$67$	−11.1219			−1.35875			−0.679377	−	0.733789i	$-0.737750\pi$
$67$	−11.1219			−1.35875			−0.679377	+	0.733789i	$0.737750\pi$
$68$		−	0.765994i		−	0.0928904i
$69$		−	2.44877i		−	0.294797i
$70$		0			0
$71$	0.963126			0.114302			0.0571510	−	0.998366i	$-0.481798\pi$
$71$	0.963126			0.114302			0.0571510	+	0.998366i	$0.481798\pi$
$72$		−	0.105209i		−	0.0123990i
$73$	−9.03119			−1.05702			−0.528511	−	0.848927i	$-0.677249\pi$
$73$	−9.03119			−1.05702			−0.528511	+	0.848927i	$0.677249\pi$
$74$	1.76599	−	5.82076i	0.205293	−	0.676650i
$75$		0			0
$76$			3.34507i			0.383706i
$77$	−2.28532			−0.260436
$78$	11.4627			1.29789
$79$		−	10.3333i		−	1.16259i	−0.813694	−	0.581293i	$-0.802547\pi$
$79$		−	10.3333i		−	1.16259i	0.813694	−	0.581293i	$-0.197453\pi$
$80$		0			0
$81$	−9.30456			−1.03384
$82$			3.73892i			0.412894i
$83$	0.00656819			0.000720953			0.000360477	−	1.00000i	$-0.499885\pi$
$83$	0.00656819			0.000720953			0.000360477		1.00000i	$0.499885\pi$
$84$	−2.15215			−0.234818
$85$		0			0
$86$	−4.91814			−0.530337
$87$		−	3.04694i		−	0.326666i
$88$		−	1.87120i		−	0.199471i
$89$			4.70144i			0.498352i	0.968458	+	0.249176i	$0.0801598\pi$
$89$			4.70144i			0.498352i	−0.968458	+	0.249176i	$0.919840\pi$
$90$		0			0
$91$		−	7.94452i		−	0.832812i
$92$		−	1.38964i		−	0.144880i
$93$		−	7.24756i		−	0.751537i
$94$		−	6.30775i		−	0.650595i
$95$		0			0
$96$		−	1.76216i		−	0.179850i
$97$			0.403430i			0.0409621i	0.999790	+	0.0204811i	$0.00651978\pi$
$97$			0.403430i			0.0409621i	−0.999790	+	0.0204811i	$0.993480\pi$
$98$		−	5.50840i		−	0.556432i
$99$	0.196867			0.0197859
$100$		0			0
$101$	−19.3724			−1.92762			−0.963812	−	0.266582i	$-0.914106\pi$
$101$	−19.3724			−1.92762			−0.963812	+	0.266582i	$0.914106\pi$
$102$	1.34980			0.133650
$103$		−	5.56165i		−	0.548005i	−0.961729	−	0.274003i	$-0.911652\pi$
$103$		−	5.56165i		−	0.548005i	0.961729	−	0.274003i	$-0.0883477\pi$
$104$	6.50491			0.637859
$105$		0			0
$106$			2.57768i			0.250367i
$107$	1.93484			0.187048			0.0935241	−	0.995617i	$-0.470187\pi$
$107$	1.93484			0.187048			0.0935241	+	0.995617i	$0.470187\pi$
$108$	−5.10109			−0.490852
$109$			8.70619i			0.833901i	0.908929	+	0.416951i	$0.136901\pi$
$109$			8.70619i			0.833901i	−0.908929	+	0.416951i	$0.863099\pi$
$110$		0			0
$111$	10.2571	+	3.11196i	0.973562	+	0.295375i
$112$	−1.22131			−0.115403
$113$		−	14.7585i		−	1.38837i	−0.719798	−	0.694183i	$-0.755766\pi$
$113$		−	14.7585i		−	1.38837i	0.719798	−	0.694183i	$-0.244234\pi$
$114$	−5.89455			−0.552075
$115$		0			0
$116$		−	1.72909i		−	0.160542i
$117$			0.684374i			0.0632704i
$118$	10.5664			0.972715
$119$		−	0.935517i		−	0.0857587i
$120$		0			0
$121$	−7.49860			−0.681691
$122$	11.1550			1.00992
$123$	−6.58857			−0.594072
$124$		−	4.11288i		−	0.369348i
$125$		0			0
$126$		−	0.128493i		−	0.0114470i
$127$	11.1280			0.987453			0.493727	−	0.869617i	$-0.335634\pi$
$127$	11.1280			0.987453			0.493727	+	0.869617i	$0.335634\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		−	8.66655i		−	0.763047i
$130$		0			0
$131$		−	12.8363i		−	1.12152i	−0.827980	−	0.560758i	$-0.810510\pi$
$131$		−	12.8363i		−	1.12152i	0.827980	−	0.560758i	$-0.189490\pi$
$132$	3.29736			0.286998
$133$			4.08537i			0.354247i
$134$		−	11.1219i		−	0.960785i
$135$		0			0
$136$	0.765994			0.0656834
$137$	−12.0355			−1.02826			−0.514129	−	0.857713i	$-0.671885\pi$
$137$	−12.0355			−1.02826			−0.514129	+	0.857713i	$0.671885\pi$
$138$	2.44877			0.208453
$139$	9.78562			0.830005			0.415003	−	0.909820i	$-0.363781\pi$
$139$	9.78562			0.830005			0.415003	+	0.909820i	$0.363781\pi$
$140$		0			0
$141$	11.1153			0.936075
$142$			0.963126i			0.0808237i
$143$			12.1720i			1.01787i
$144$	0.105209			0.00876740
$145$		0			0
$146$		−	9.03119i		−	0.747427i
$147$	9.70668			0.800594
$148$	5.82076	+	1.76599i	0.478464	+	0.145164i
$149$	11.8876			0.973868			0.486934	−	0.873439i	$-0.338115\pi$
$149$	11.8876			0.973868			0.486934	+	0.873439i	$0.338115\pi$
$150$		0			0
$151$	21.3141			1.73452			0.867259	−	0.497857i	$-0.165880\pi$
$151$	21.3141			1.73452			0.867259	+	0.497857i	$0.165880\pi$
$152$	−3.34507			−0.271321
$153$			0.0805893i			0.00651526i
$154$		−	2.28532i		−	0.184156i
$155$		0			0
$156$			11.4627i			0.917750i
$157$	15.3009			1.22115			0.610573	−	0.791960i	$-0.290939\pi$
$157$	15.3009			1.22115			0.610573	+	0.791960i	$0.290939\pi$
$158$	10.3333			0.822072
$159$	−4.54229			−0.360227
$160$		0			0
$161$		−	1.69718i		−	0.133757i
$162$		−	9.30456i		−	0.731035i
$163$		−	14.9177i		−	1.16844i	−0.811595	−	0.584221i	$-0.801400\pi$
$163$		−	14.9177i		−	1.16844i	0.811595	−	0.584221i	$-0.198600\pi$
$164$	−3.73892			−0.291960
$165$		0			0
$166$			0.00656819i			0.000509791i
$167$		−	17.3041i		−	1.33903i	−0.742800	−	0.669514i	$-0.766502\pi$
$167$		−	17.3041i		−	1.33903i	0.742800	−	0.669514i	$-0.233498\pi$
$168$		−	2.15215i		−	0.166042i
$169$	−29.3139			−2.25491
$170$		0			0
$171$		−	0.351931i		−	0.0269128i
$172$		−	4.91814i		−	0.375005i
$173$	−19.7322			−1.50021			−0.750107	−	0.661317i	$-0.769998\pi$
$173$	−19.7322			−1.50021			−0.750107	+	0.661317i	$0.769998\pi$
$174$	3.04694			0.230988
$175$		0			0
$176$	1.87120			0.141047
$177$			18.6197i			1.39954i
$178$	−4.70144			−0.352388
$179$			3.70357i			0.276818i	0.990375	+	0.138409i	$0.0441988\pi$
$179$			3.70357i			0.276818i	−0.990375	+	0.138409i	$0.955801\pi$
$180$		0			0
$181$	−10.4093			−0.773714			−0.386857	−	0.922140i	$-0.626439\pi$
$181$	−10.4093			−0.773714			−0.386857	+	0.922140i	$0.626439\pi$
$182$	7.94452			0.588887
$183$			19.6568i			1.45307i
$184$	1.38964			0.102446
$185$		0			0
$186$	7.24756			0.531417
$187$			1.43333i			0.104815i
$188$	6.30775			0.460040
$189$	−6.23001			−0.453167
$190$		0			0
$191$			23.0954i			1.67113i	0.549395	+	0.835563i	$0.314858\pi$
$191$			23.0954i			1.67113i	−0.549395	+	0.835563i	$0.685142\pi$
$192$	1.76216			0.127173
$193$		−	12.4951i		−	0.899418i	−0.893175	−	0.449709i	$-0.851528\pi$
$193$		−	12.4951i		−	0.899418i	0.893175	−	0.449709i	$-0.148472\pi$
$194$	−0.403430			−0.0289646
$195$		0			0
$196$	5.50840			0.393457
$197$	−5.51302			−0.392786			−0.196393	−	0.980525i	$-0.562923\pi$
$197$	−5.51302			−0.392786			−0.196393	+	0.980525i	$0.562923\pi$
$198$			0.196867i			0.0139907i
$199$			18.8033i			1.33293i	0.745537	+	0.666464i	$0.232193\pi$
$199$			18.8033i			1.33293i	−0.745537	+	0.666464i	$0.767807\pi$
$200$		0			0
$201$	19.5985			1.38237
$202$		−	19.3724i		−	1.36304i
$203$		−	2.11176i		−	0.148216i
$204$			1.34980i			0.0945052i
$205$		0			0
$206$	5.56165			0.387498
$207$			0.146202i			0.0101618i
$208$			6.50491i			0.451034i
$209$		−	6.25931i		−	0.432965i
$210$		0			0
$211$	−26.6632			−1.83557			−0.917784	−	0.397081i	$-0.870023\pi$
$211$	−26.6632			−1.83557			−0.917784	+	0.397081i	$0.870023\pi$
$212$	−2.57768			−0.177036
$213$	−1.69718			−0.116289
$214$			1.93484i			0.132263i
$215$		0			0
$216$		−	5.10109i		−	0.347085i
$217$		−	5.02311i		−	0.340991i
$218$	−8.70619			−0.589657
$219$	15.9144			1.07540
$220$		0			0
$221$	−4.98272			−0.335174
$222$	−3.11196	+	10.2571i	−0.208861	+	0.688412i
$223$	−10.8630			−0.727441			−0.363721	−	0.931508i	$-0.618494\pi$
$223$	−10.8630			−0.727441			−0.363721	+	0.931508i	$0.618494\pi$
$224$		−	1.22131i		−	0.0816023i
$225$		0			0
$226$	14.7585			0.981723
$227$		−	6.82427i		−	0.452942i	−0.974018	−	0.226471i	$-0.927281\pi$
$227$		−	6.82427i		−	0.452942i	0.974018	−	0.226471i	$-0.0727189\pi$
$228$		−	5.89455i		−	0.390376i
$229$	−2.56189			−0.169294			−0.0846471	−	0.996411i	$-0.526976\pi$
$229$	−2.56189			−0.169294			−0.0846471	+	0.996411i	$0.526976\pi$
$230$		0			0
$231$	4.02710			0.264964
$232$	1.72909			0.113520
$233$	−23.3423			−1.52921			−0.764603	−	0.644502i	$-0.777065\pi$
$233$	−23.3423			−1.52921			−0.764603	+	0.644502i	$0.777065\pi$
$234$	−0.684374			−0.0447389
$235$		0			0
$236$			10.5664i			0.687814i
$237$			18.2089i			1.18280i
$238$	0.935517			0.0606405
$239$			5.19256i			0.335879i	0.985797	+	0.167940i	$0.0537113\pi$
$239$			5.19256i			0.335879i	−0.985797	+	0.167940i	$0.946289\pi$
$240$		0			0
$241$		−	15.5243i		−	1.00001i	−0.866022	−	0.500005i	$-0.833331\pi$
$241$		−	15.5243i		−	1.00001i	0.866022	−	0.500005i	$-0.166669\pi$
$242$		−	7.49860i		−	0.482028i
$243$	1.09286			0.0701072
$244$			11.1550i			0.714123i
$245$		0			0
$246$		−	6.58857i		−	0.420072i
$247$	21.7594			1.38452
$248$	4.11288			0.261168
$249$	−0.0115742			−0.000733486
$250$		0			0
$251$			3.85199i			0.243136i	0.992583	+	0.121568i	$0.0387922\pi$
$251$			3.85199i			0.243136i	−0.992583	+	0.121568i	$0.961208\pi$
$252$	0.128493			0.00809428
$253$			2.60030i			0.163479i
$254$			11.1280i			0.698235i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	3.34529i		−	0.208673i	−0.994542	−	0.104337i	$-0.966728\pi$
$257$		−	3.34529i		−	0.208673i	0.994542	−	0.104337i	$-0.0332719\pi$
$258$	8.66655			0.539556
$259$	7.10896	+	2.15683i	0.441729	+	0.134019i
$260$		0			0
$261$			0.181916i			0.0112603i
$262$	12.8363			0.793031
$263$	−1.14405			−0.0705454			−0.0352727	−	0.999378i	$-0.511230\pi$
$263$	−1.14405			−0.0705454			−0.0352727	+	0.999378i	$0.511230\pi$
$264$			3.29736i			0.202938i
$265$		0			0
$266$	−4.08537			−0.250490
$267$		−	8.28470i		−	0.507015i
$268$	11.1219			0.679377
$269$	−15.1344			−0.922760			−0.461380	−	0.887203i	$-0.652645\pi$
$269$	−15.1344			−0.922760			−0.461380	+	0.887203i	$0.652645\pi$
$270$		0			0
$271$	−18.2842			−1.11069			−0.555344	−	0.831621i	$-0.687413\pi$
$271$	−18.2842			−1.11069			−0.555344	+	0.831621i	$0.687413\pi$
$272$			0.765994i			0.0464452i
$273$			13.9995i			0.847289i
$274$		−	12.0355i		−	0.727088i
$275$		0			0
$276$			2.44877i			0.147398i
$277$		−	2.58352i		−	0.155229i	−0.996983	−	0.0776145i	$-0.975270\pi$
$277$		−	2.58352i		−	0.155229i	0.996983	−	0.0776145i	$-0.0247303\pi$
$278$			9.78562i			0.586902i
$279$			0.432711i			0.0259057i
$280$		0			0
$281$			19.3056i			1.15168i	0.817563	+	0.575839i	$0.195325\pi$
$281$			19.3056i			1.15168i	−0.817563	+	0.575839i	$0.804675\pi$
$282$			11.1153i			0.661905i
$283$			9.02942i			0.536743i	0.963315	+	0.268372i	$0.0864855\pi$
$283$			9.02942i			0.536743i	−0.963315	+	0.268372i	$0.913514\pi$
$284$	−0.963126			−0.0571510
$285$		0			0
$286$	−12.1720			−0.719746
$287$	−4.56638			−0.269545
$288$			0.105209i			0.00619949i
$289$	16.4133			0.965485
$290$		0			0
$291$		−	0.710909i		−	0.0416742i
$292$	9.03119			0.528511
$293$	13.0845			0.764405			0.382203	−	0.924079i	$-0.375166\pi$
$293$	13.0845			0.764405			0.382203	+	0.924079i	$0.375166\pi$
$294$			9.70668i			0.566105i
$295$		0			0
$296$	−1.76599	+	5.82076i	−0.102646	+	0.338325i
$297$	9.54517			0.553867
$298$			11.8876i			0.688629i
$299$	−9.03948			−0.522767
$300$		0			0
$301$		−	6.00658i		−	0.346213i
$302$			21.3141i			1.22649i
$303$	34.1373			1.96113
$304$		−	3.34507i		−	0.191853i
$305$		0			0
$306$	−0.0805893			−0.00460698
$307$	7.60942			0.434293			0.217146	−	0.976139i	$-0.430325\pi$
$307$	7.60942			0.434293			0.217146	+	0.976139i	$0.430325\pi$
$308$	2.28532			0.130218
$309$			9.80051i			0.557532i
$310$		0			0
$311$			15.2359i			0.863950i	0.901886	+	0.431975i	$0.142183\pi$
$311$			15.2359i			0.863950i	−0.901886	+	0.431975i	$0.857817\pi$
$312$	−11.4627			−0.648947
$313$		−	10.0000i		−	0.565233i	−0.959233	−	0.282617i	$-0.908798\pi$
$313$		−	10.0000i		−	0.565233i	0.959233	−	0.282617i	$-0.0912024\pi$
$314$			15.3009i			0.863480i
$315$		0			0
$316$			10.3333i			0.581293i
$317$	−34.1403			−1.91751			−0.958756	−	0.284230i	$-0.908262\pi$
$317$	−34.1403			−1.91751			−0.958756	+	0.284230i	$0.908262\pi$
$318$		−	4.54229i		−	0.254719i
$319$			3.23548i			0.181152i
$320$		0			0
$321$	−3.40950			−0.190300
$322$	1.69718			0.0945803
$323$	2.56230			0.142570
$324$	9.30456			0.516920
$325$		0			0
$326$	14.9177			0.826213
$327$		−	15.3417i		−	0.848398i
$328$		−	3.73892i		−	0.206447i
$329$	7.70373			0.424720
$330$		0			0
$331$		−	27.2567i		−	1.49817i	−0.662476	−	0.749083i	$-0.730494\pi$
$331$		−	27.2567i		−	1.49817i	0.662476	−	0.749083i	$-0.269506\pi$
$332$	−0.00656819			−0.000360477
$333$	−0.612395	−	0.185798i	−0.0335590	−	0.0101817i
$334$	17.3041			0.946836
$335$		0			0
$336$	2.15215			0.117409
$337$	−22.5315			−1.22737			−0.613683	−	0.789552i	$-0.710313\pi$
$337$	−22.5315			−1.22737			−0.613683	+	0.789552i	$0.710313\pi$
$338$		−	29.3139i		−	1.59446i
$339$			26.0069i			1.41250i
$340$		0			0
$341$			7.69603i			0.416764i
$342$	0.351931			0.0190302
$343$	15.2766			0.824861
$344$	4.91814			0.265168
$345$		0			0
$346$		−	19.7322i		−	1.06081i
$347$			34.7252i			1.86415i	0.362272	+	0.932073i	$0.382001\pi$
$347$			34.7252i			1.86415i	−0.362272	+	0.932073i	$0.617999\pi$
$348$			3.04694i			0.163333i
$349$	−15.9343			−0.852942			−0.426471	−	0.904501i	$-0.640243\pi$
$349$	−15.9343			−0.852942			−0.426471	+	0.904501i	$0.640243\pi$
$350$		0			0
$351$			33.1821i			1.77113i
$352$			1.87120i			0.0997354i
$353$			20.1925i			1.07474i	0.843347	+	0.537370i	$0.180582\pi$
$353$			20.1925i			1.07474i	−0.843347	+	0.537370i	$0.819418\pi$
$354$	−18.6197			−0.989625
$355$		0			0
$356$		−	4.70144i		−	0.249176i
$357$			1.64853i			0.0872495i
$358$	−3.70357			−0.195740
$359$	30.8657			1.62903			0.814515	−	0.580143i	$-0.197003\pi$
$359$	30.8657			1.62903			0.814515	+	0.580143i	$0.197003\pi$
$360$		0			0
$361$	7.81050			0.411079
$362$		−	10.4093i		−	0.547099i
$363$	13.2137			0.693541
$364$			7.94452i			0.416406i
$365$		0			0
$366$	−19.6568			−1.02748
$367$	28.9254			1.50989			0.754947	−	0.655786i	$-0.227663\pi$
$367$	28.9254			1.50989			0.754947	+	0.655786i	$0.227663\pi$
$368$			1.38964i			0.0724400i
$369$	0.393367			0.0204779
$370$		0			0
$371$	−3.14815			−0.163444
$372$			7.24756i			0.375768i
$373$	27.8899			1.44408			0.722042	−	0.691849i	$-0.243204\pi$
$373$	27.8899			1.44408			0.722042	+	0.691849i	$0.243204\pi$
$374$	−1.43333			−0.0741157
$375$		0			0
$376$			6.30775i			0.325298i
$377$	−11.2476			−0.579280
$378$		−	6.23001i		−	0.320437i
$379$	5.73365			0.294518			0.147259	−	0.989098i	$-0.452955\pi$
$379$	5.73365			0.294518			0.147259	+	0.989098i	$0.452955\pi$
$380$		0			0
$381$	−19.6094			−1.00462
$382$	−23.0954			−1.18166
$383$			17.8363i			0.911391i	0.890136	+	0.455696i	$0.150609\pi$
$383$			17.8363i			0.911391i	−0.890136	+	0.455696i	$0.849391\pi$
$384$			1.76216i			0.0899249i
$385$		0			0
$386$	12.4951			0.635985
$387$			0.517431i			0.0263025i
$388$		−	0.403430i		−	0.0204811i
$389$			29.8974i			1.51586i	0.652337	+	0.757929i	$0.273789\pi$
$389$			29.8974i			1.51586i	−0.652337	+	0.757929i	$0.726211\pi$
$390$		0			0
$391$	−1.06446			−0.0538318
$392$			5.50840i			0.278216i
$393$			22.6197i			1.14101i
$394$		−	5.51302i		−	0.277742i
$395$		0			0
$396$	−0.196867			−0.00989293
$397$	−13.2064			−0.662812			−0.331406	−	0.943488i	$-0.607523\pi$
$397$	−13.2064			−0.662812			−0.331406	+	0.943488i	$0.607523\pi$
$398$	−18.8033			−0.942523
$399$		−	7.19908i		−	0.360405i
$400$		0			0
$401$			23.0269i			1.14991i	0.818185	+	0.574954i	$0.194980\pi$
$401$			23.0269i			1.14991i	−0.818185	+	0.574954i	$0.805020\pi$
$402$			19.5985i			0.977487i
$403$	−26.7539			−1.33271
$404$	19.3724			0.963812
$405$		0			0
$406$	2.11176			0.104805
$407$	−10.8918	−	3.30453i	−0.539888	−	0.163800i
$408$	−1.34980			−0.0668252
$409$			9.77049i			0.483120i	0.970386	+	0.241560i	$0.0776590\pi$
$409$			9.77049i			0.483120i	−0.970386	+	0.241560i	$0.922341\pi$
$410$		0			0
$411$	21.2084			1.04613
$412$			5.56165i			0.274003i
$413$			12.9049i			0.635006i
$414$	−0.146202			−0.00718545
$415$		0			0
$416$	−6.50491			−0.318930
$417$	−17.2438			−0.844434
$418$	6.25931			0.306153
$419$	−2.06109			−0.100691			−0.0503455	−	0.998732i	$-0.516032\pi$
$419$	−2.06109			−0.100691			−0.0503455	+	0.998732i	$0.516032\pi$
$420$		0			0
$421$			12.8910i			0.628271i	0.949378	+	0.314135i	$0.101715\pi$
$421$			12.8910i			0.628271i	−0.949378	+	0.314135i	$0.898285\pi$
$422$		−	26.6632i		−	1.29794i
$423$	−0.663631			−0.0322668
$424$		−	2.57768i		−	0.125183i
$425$		0			0
$426$		−	1.69718i		−	0.0822288i
$427$			13.6237i			0.659296i
$428$	−1.93484			−0.0935241
$429$		−	21.4490i		−	1.03557i
$430$		0			0
$431$		−	9.41662i		−	0.453582i	−0.973943	−	0.226791i	$-0.927176\pi$
$431$		−	9.41662i		−	0.453582i	0.973943	−	0.226791i	$-0.0728235\pi$
$432$	5.10109			0.245426
$433$	3.07581			0.147814			0.0739069	−	0.997265i	$-0.476453\pi$
$433$	3.07581			0.147814			0.0739069	+	0.997265i	$0.476453\pi$
$434$	5.02311			0.241117
$435$		0			0
$436$		−	8.70619i		−	0.416951i
$437$	4.64844			0.222365
$438$			15.9144i			0.760420i
$439$		−	1.93763i		−	0.0924780i	−0.998930	−	0.0462390i	$-0.985276\pi$
$439$		−	1.93763i		−	0.0924780i	0.998930	−	0.0462390i	$-0.0147236\pi$
$440$		0			0
$441$	−0.579532			−0.0275968
$442$		−	4.98272i		−	0.237004i
$443$	−26.5690			−1.26233			−0.631165	−	0.775649i	$-0.717423\pi$
$443$	−26.5690			−1.26233			−0.631165	+	0.775649i	$0.717423\pi$
$444$	−10.2571	−	3.11196i	−0.486781	−	0.147687i
$445$		0			0
$446$		−	10.8630i		−	0.514379i
$447$	−20.9478			−0.990798
$448$	1.22131			0.0577015
$449$			0.777045i			0.0366710i	0.999832	+	0.0183355i	$0.00583670\pi$
$449$			0.777045i			0.0366710i	−0.999832	+	0.0183355i	$0.994163\pi$
$450$		0			0
$451$	6.99627			0.329442
$452$			14.7585i			0.694183i
$453$	−37.5589			−1.76467
$454$	6.82427			0.320279
$455$		0			0
$456$	5.89455			0.276038
$457$		−	21.1753i		−	0.990537i	−0.868740	−	0.495268i	$-0.835070\pi$
$457$		−	21.1753i		−	0.990537i	0.868740	−	0.495268i	$-0.164930\pi$
$458$		−	2.56189i		−	0.119709i
$459$			3.90740i			0.182382i
$460$		0			0
$461$			23.9797i			1.11685i	0.829556	+	0.558424i	$0.188594\pi$
$461$			23.9797i			1.11685i	−0.829556	+	0.558424i	$0.811406\pi$
$462$			4.02710i			0.187358i
$463$		−	25.1591i		−	1.16924i	−0.811306	−	0.584622i	$-0.801243\pi$
$463$		−	25.1591i		−	1.16924i	0.811306	−	0.584622i	$-0.198757\pi$
$464$			1.72909i			0.0802711i
$465$		0			0
$466$		−	23.3423i		−	1.08131i
$467$		−	15.6162i		−	0.722632i	−0.932443	−	0.361316i	$-0.882328\pi$
$467$		−	15.6162i		−	0.722632i	0.932443	−	0.361316i	$-0.117672\pi$
$468$		−	0.684374i		−	0.0316352i
$469$	13.5833			0.627218
$470$		0			0
$471$	−26.9626			−1.24237
$472$	−10.5664			−0.486358
$473$			9.20284i			0.423147i
$474$	−18.2089			−0.836363
$475$		0			0
$476$			0.935517i			0.0428793i
$477$	0.271195			0.0124172
$478$	−5.19256			−0.237502
$479$		−	31.4974i		−	1.43915i	−0.694414	−	0.719576i	$-0.744336\pi$
$479$		−	31.4974i		−	1.43915i	0.694414	−	0.719576i	$-0.255664\pi$
$480$		0			0
$481$	11.4876	−	37.8635i	0.523791	−	1.72643i
$482$	15.5243			0.707114
$483$			2.99071i			0.136082i
$484$	7.49860			0.340845
$485$		0			0
$486$			1.09286i			0.0495733i
$487$		−	24.2768i		−	1.10009i	−0.835137	−	0.550043i	$-0.814611\pi$
$487$		−	24.2768i		−	1.10009i	0.835137	−	0.550043i	$-0.185389\pi$
$488$	−11.1550			−0.504961
$489$			26.2873i			1.18875i
$490$		0			0
$491$	16.5129			0.745218			0.372609	−	0.927988i	$-0.378463\pi$
$491$	16.5129			0.745218			0.372609	+	0.927988i	$0.378463\pi$
$492$	6.58857			0.297036
$493$	−1.32447			−0.0596513
$494$			21.7594i			0.979001i
$495$		0			0
$496$			4.11288i			0.184674i
$497$	−1.17628			−0.0527632
$498$		−	0.0115742i		−	0.000518653i
$499$			22.8436i			1.02262i	0.859397	+	0.511310i	$0.170839\pi$
$499$			22.8436i			1.02262i	−0.859397	+	0.511310i	$0.829161\pi$
$500$		0			0
$501$			30.4925i			1.36231i
$502$	−3.85199			−0.171923
$503$		−	37.0666i		−	1.65272i	−0.563144	−	0.826359i	$-0.690408\pi$
$503$		−	37.0666i		−	1.65272i	0.563144	−	0.826359i	$-0.309592\pi$
$504$			0.128493i			0.00572352i
$505$		0			0
$506$	−2.60030			−0.115597
$507$	51.6557			2.29411
$508$	−11.1280			−0.493727
$509$	−20.0939			−0.890645			−0.445323	−	0.895370i	$-0.646911\pi$
$509$	−20.0939			−0.890645			−0.445323	+	0.895370i	$0.646911\pi$
$510$		0			0
$511$	11.0299			0.487934
$512$			1.00000i			0.0441942i
$513$		−	17.0635i		−	0.753372i
$514$	3.34529			0.147554
$515$		0			0
$516$			8.66655i			0.381524i
$517$	−11.8031			−0.519099
$518$	−2.15683	+	7.10896i	−0.0947656	+	0.312350i
$519$	34.7713			1.52629
$520$		0			0
$521$	32.3101			1.41553			0.707766	−	0.706447i	$-0.249703\pi$
$521$	32.3101			1.41553			0.707766	+	0.706447i	$0.249703\pi$
$522$	−0.181916			−0.00796223
$523$		−	38.5348i		−	1.68501i	−0.538688	−	0.842505i	$-0.681080\pi$
$523$		−	38.5348i		−	1.68501i	0.538688	−	0.842505i	$-0.318920\pi$
$524$			12.8363i			0.560758i
$525$		0			0
$526$		−	1.14405i		−	0.0498831i
$527$	−3.15044			−0.137235
$528$	−3.29736			−0.143499
$529$	21.0689			0.916039
$530$		0			0
$531$		−	1.11168i		−	0.0482427i
$532$		−	4.08537i		−	0.177123i
$533$			24.3213i			1.05347i
$534$	8.28470			0.358514
$535$		0			0
$536$			11.1219i			0.480392i
$537$		−	6.52628i		−	0.281630i
$538$		−	15.1344i		−	0.652490i
$539$	−10.3073			−0.443968
$540$		0			0
$541$		−	40.6354i		−	1.74705i	−0.486776	−	0.873527i	$-0.661827\pi$
$541$		−	40.6354i		−	1.74705i	0.486776	−	0.873527i	$-0.338173\pi$
$542$		−	18.2842i		−	0.785374i
$543$	18.3428			0.787164
$544$	−0.765994			−0.0328417
$545$		0			0
$546$	−13.9995			−0.599124
$547$			26.6260i			1.13845i	0.822183	+	0.569223i	$0.192756\pi$
$547$			26.6260i			1.13845i	−0.822183	+	0.569223i	$0.807244\pi$
$548$	12.0355			0.514129
$549$		−	1.17360i		−	0.0500880i
$550$		0			0
$551$	5.78394			0.246404
$552$	−2.44877			−0.104226
$553$			12.6202i			0.536664i
$554$	2.58352			0.109763
$555$		0			0
$556$	−9.78562			−0.415003
$557$			31.8613i			1.35001i	0.737814	+	0.675004i	$0.235858\pi$
$557$			31.8613i			1.35001i	−0.737814	+	0.675004i	$0.764142\pi$
$558$	−0.432711			−0.0183181
$559$	−31.9921			−1.35312
$560$		0			0
$561$		−	2.52576i		−	0.106638i
$562$	−19.3056			−0.814360
$563$		−	0.477178i		−	0.0201107i	−0.999949	−	0.0100553i	$-0.996799\pi$
$563$		−	0.477178i		−	0.0201107i	0.999949	−	0.0100553i	$-0.00320077\pi$
$564$	−11.1153			−0.468037
$565$		0			0
$566$	−9.02942			−0.379535
$567$	11.3638			0.477233
$568$		−	0.963126i		−	0.0404119i
$569$			10.3567i			0.434175i	0.976152	+	0.217087i	$0.0696557\pi$
$569$			10.3567i			0.434175i	−0.976152	+	0.217087i	$0.930344\pi$
$570$		0			0
$571$	−1.56306			−0.0654119			−0.0327059	−	0.999465i	$-0.510412\pi$
$571$	−1.56306			−0.0654119			−0.0327059	+	0.999465i	$0.510412\pi$
$572$		−	12.1720i		−	0.508937i
$573$		−	40.6978i		−	1.70018i
$574$		−	4.56638i		−	0.190597i
$575$		0			0
$576$	−0.105209			−0.00438370
$577$			19.1344i			0.796575i	0.917261	+	0.398287i	$0.130395\pi$
$577$			19.1344i			0.796575i	−0.917261	+	0.398287i	$0.869605\pi$
$578$			16.4133i			0.682701i
$579$			22.0184i			0.915053i
$580$		0			0
$581$	−0.00802181			−0.000332801
$582$	0.710909			0.0294681
$583$	4.82337			0.199763
$584$			9.03119i			0.373713i
$585$		0			0
$586$			13.0845i			0.540516i
$587$		−	7.16828i		−	0.295867i	−0.988997	−	0.147933i	$-0.952738\pi$
$587$		−	7.16828i		−	0.295867i	0.988997	−	0.147933i	$-0.0472621\pi$
$588$	−9.70668			−0.400297
$589$	13.7579			0.566884
$590$		0			0
$591$	9.71482			0.399614
$592$	−5.82076	−	1.76599i	−0.239232	−	0.0725819i
$593$	−36.6287			−1.50416			−0.752081	−	0.659071i	$-0.770950\pi$
$593$	−36.6287			−1.50416			−0.752081	+	0.659071i	$0.770950\pi$
$594$			9.54517i			0.391643i
$595$		0			0
$596$	−11.8876			−0.486934
$597$		−	33.1344i		−	1.35610i
$598$		−	9.03948i		−	0.369652i
$599$	−38.3505			−1.56696			−0.783480	−	0.621417i	$-0.786557\pi$
$599$	−38.3505			−1.56696			−0.783480	+	0.621417i	$0.786557\pi$
$600$		0			0
$601$	−20.5311			−0.837480			−0.418740	−	0.908106i	$-0.637528\pi$
$601$	−20.5311			−0.837480			−0.418740	+	0.908106i	$0.637528\pi$
$602$	6.00658			0.244810
$603$	−1.17012			−0.0476510
$604$	−21.3141			−0.867259
$605$		0			0
$606$			34.1373i			1.38673i
$607$			35.3953i			1.43665i	0.695706	+	0.718326i	$0.255091\pi$
$607$			35.3953i			1.43665i	−0.695706	+	0.718326i	$0.744909\pi$
$608$	3.34507			0.135661
$609$			3.72126i			0.150793i
$610$		0			0
$611$		−	41.0314i		−	1.65995i
$612$		−	0.0805893i		−	0.00325763i
$613$	10.3293			0.417198			0.208599	−	0.978001i	$-0.433110\pi$
$613$	10.3293			0.417198			0.208599	+	0.978001i	$0.433110\pi$
$614$			7.60942i			0.307091i
$615$		0			0
$616$			2.28532i			0.0920782i
$617$	−2.91338			−0.117288			−0.0586441	−	0.998279i	$-0.518678\pi$
$617$	−2.91338			−0.117288			−0.0586441	+	0.998279i	$0.518678\pi$
$618$	−9.80051			−0.394234
$619$	−30.7715			−1.23681			−0.618405	−	0.785860i	$-0.712221\pi$
$619$	−30.7715			−1.23681			−0.618405	+	0.785860i	$0.712221\pi$
$620$		0			0
$621$			7.08867i			0.284459i
$622$	−15.2359			−0.610905
$623$		−	5.74193i		−	0.230045i
$624$		−	11.4627i		−	0.458875i
$625$		0			0
$626$	10.0000			0.399680
$627$			11.0299i			0.440492i
$628$	−15.3009			−0.610573
$629$	1.35274	−	4.45867i	0.0539373	−	0.177779i
$630$		0			0
$631$		−	12.8167i		−	0.510225i	−0.966911	−	0.255113i	$-0.917887\pi$
$631$		−	12.8167i		−	0.510225i	0.966911	−	0.255113i	$-0.0821126\pi$
$632$	−10.3333			−0.411036
$633$	46.9847			1.86748
$634$		−	34.1403i		−	1.35589i
$635$		0			0
$636$	4.54229			0.180114
$637$		−	35.8316i		−	1.41970i
$638$	−3.23548			−0.128094
$639$	0.101329			0.00400853
$640$		0			0
$641$	39.8277			1.57310			0.786550	−	0.617527i	$-0.211865\pi$
$641$	39.8277			1.57310			0.786550	+	0.617527i	$0.211865\pi$
$642$		−	3.40950i		−	0.134562i
$643$		−	15.9821i		−	0.630273i	−0.949046	−	0.315137i	$-0.897950\pi$
$643$		−	15.9821i		−	0.630273i	0.949046	−	0.315137i	$-0.102050\pi$
$644$			1.69718i			0.0668784i
$645$		0			0
$646$			2.56230i			0.100812i
$647$		−	37.8647i		−	1.48861i	−0.667838	−	0.744307i	$-0.732780\pi$
$647$		−	37.8647i		−	1.48861i	0.667838	−	0.744307i	$-0.267220\pi$
$648$			9.30456i			0.365518i
$649$		−	19.7719i		−	0.776113i
$650$		0			0
$651$			8.85152i			0.346919i
$652$			14.9177i			0.584221i
$653$		−	9.60006i		−	0.375679i	−0.982200	−	0.187840i	$-0.939851\pi$
$653$		−	9.60006i		−	0.375679i	0.982200	−	0.187840i	$-0.0601485\pi$
$654$	15.3417			0.599908
$655$		0			0
$656$	3.73892			0.145980
$657$	−0.950161			−0.0370693
$658$			7.70373i			0.300323i
$659$	−30.3448			−1.18207			−0.591033	−	0.806647i	$-0.701280\pi$
$659$	−30.3448			−1.18207			−0.591033	+	0.806647i	$0.701280\pi$
$660$		0			0
$661$			28.0304i			1.09026i	0.838353	+	0.545128i	$0.183519\pi$
$661$			28.0304i			1.09026i	−0.838353	+	0.545128i	$0.816481\pi$
$662$	27.2567			1.05936
$663$	8.78035			0.341001
$664$		−	0.00656819i		−	0.000254895i
$665$		0			0
$666$	0.185798	−	0.612395i	0.00719953	−	0.0237298i
$667$	−2.40281			−0.0930374
$668$			17.3041i			0.669514i
$669$	19.1424			0.740087
$670$		0			0
$671$		−	20.8732i		−	0.805800i
$672$			2.15215i			0.0830208i
$673$	−1.70175			−0.0655975			−0.0327987	−	0.999462i	$-0.510442\pi$
$673$	−1.70175			−0.0655975			−0.0327987	+	0.999462i	$0.510442\pi$
$674$		−	22.5315i		−	0.867879i
$675$		0			0
$676$	29.3139			1.12746
$677$	−3.49272			−0.134236			−0.0671180	−	0.997745i	$-0.521380\pi$
$677$	−3.49272			−0.134236			−0.0671180	+	0.997745i	$0.521380\pi$
$678$	−26.0069			−0.998789
$679$		−	0.492714i		−	0.0189086i
$680$		0			0
$681$			12.0254i			0.460816i
$682$	−7.69603			−0.294696
$683$		−	18.9186i		−	0.723901i	−0.932197	−	0.361950i	$-0.882111\pi$
$683$		−	18.9186i		−	0.723901i	0.932197	−	0.361950i	$-0.117889\pi$
$684$			0.351931i			0.0134564i
$685$		0			0
$686$			15.2766i			0.583265i
$687$	4.51446			0.172237
$688$			4.91814i			0.187502i
$689$			16.7676i			0.638795i
$690$		0			0
$691$	4.56018			0.173477			0.0867386	−	0.996231i	$-0.472355\pi$
$691$	4.56018			0.173477			0.0867386	+	0.996231i	$0.472355\pi$
$692$	19.7322			0.750107
$693$	−0.240436			−0.00913340
$694$	−34.7252			−1.31815
$695$		0			0
$696$	−3.04694			−0.115494
$697$			2.86399i			0.108481i
$698$		−	15.9343i		−	0.603121i
$699$	41.1329			1.55579
$700$		0			0
$701$		−	18.9895i		−	0.717224i	−0.933487	−	0.358612i	$-0.883250\pi$
$701$		−	18.9895i		−	0.717224i	0.933487	−	0.358612i	$-0.116750\pi$
$702$	−33.1821			−1.25238
$703$	−5.90737	+	19.4709i	−0.222801	+	0.734357i
$704$	−1.87120			−0.0705236
$705$		0			0
$706$	−20.1925			−0.759956
$707$	23.6597			0.889815
$708$		−	18.6197i		−	0.699770i
$709$			10.8195i			0.406336i	0.979144	+	0.203168i	$0.0651238\pi$
$709$			10.8195i			0.406336i	−0.979144	+	0.203168i	$0.934876\pi$
$710$		0			0
$711$		−	1.08715i		−	0.0407714i
$712$	4.70144			0.176194
$713$	−5.71542			−0.214044
$714$	−1.64853			−0.0616947
$715$		0			0
$716$		−	3.70357i		−	0.138409i
$717$		−	9.15013i		−	0.341718i
$718$			30.8657i			1.15190i
$719$	8.43399			0.314535			0.157267	−	0.987556i	$-0.449732\pi$
$719$	8.43399			0.314535			0.157267	+	0.987556i	$0.449732\pi$
$720$		0			0
$721$			6.79250i			0.252966i
$722$			7.81050i			0.290677i
$723$			27.3564i			1.01739i
$724$	10.4093			0.386857
$725$		0			0
$726$			13.2137i			0.490408i
$727$			16.7156i			0.619947i	0.950745	+	0.309974i	$0.100320\pi$
$727$			16.7156i			0.619947i	−0.950745	+	0.309974i	$0.899680\pi$
$728$	−7.94452			−0.294444
$729$	25.9879			0.962514
$730$		0			0
$731$	−3.76726			−0.139337
$732$		−	19.6568i		−	0.726537i
$733$	10.4157			0.384711			0.192356	−	0.981325i	$-0.438387\pi$
$733$	10.4157			0.384711			0.192356	+	0.981325i	$0.438387\pi$
$734$			28.9254i			1.06766i
$735$		0			0
$736$	−1.38964			−0.0512228
$737$	−20.8113			−0.766594
$738$			0.393367i			0.0144800i
$739$	19.7975			0.728261			0.364131	−	0.931348i	$-0.381366\pi$
$739$	19.7975			0.728261			0.364131	+	0.931348i	$0.381366\pi$
$740$		0			0
$741$	−38.3435			−1.40858
$742$		−	3.14815i		−	0.115572i
$743$	34.4142			1.26253			0.631267	−	0.775566i	$-0.282535\pi$
$743$	34.4142			1.26253			0.631267	+	0.775566i	$0.282535\pi$
$744$	−7.24756			−0.265708
$745$		0			0
$746$			27.8899i			1.02112i
$747$	0.000691032	0		2.52835e−5	0
$748$		−	1.43333i		−	0.0524077i
$749$	−2.36304			−0.0863437
$750$		0			0
$751$	−40.7020			−1.48524			−0.742618	−	0.669715i	$-0.766416\pi$
$751$	−40.7020			−1.48524			−0.742618	+	0.669715i	$0.766416\pi$
$752$	−6.30775			−0.230020
$753$		−	6.78783i		−	0.247362i
$754$		−	11.2476i		−	0.409613i
$755$		0			0
$756$	6.23001			0.226583
$757$		−	2.06470i		−	0.0750426i	−0.999296	−	0.0375213i	$-0.988054\pi$
$757$		−	2.06470i		−	0.0750426i	0.999296	−	0.0375213i	$-0.0119462\pi$
$758$			5.73365i			0.208256i
$759$		−	4.58214i		−	0.166321i
$760$		0			0
$761$	9.07263			0.328883			0.164441	−	0.986387i	$-0.447418\pi$
$761$	9.07263			0.328883			0.164441	+	0.986387i	$0.447418\pi$
$762$		−	19.6094i		−	0.710373i
$763$		−	10.6330i		−	0.384939i
$764$		−	23.0954i		−	0.835563i
$765$		0			0
$766$	−17.8363			−0.644451
$767$	68.7335			2.48182
$768$	−1.76216			−0.0635865
$769$		−	50.9991i		−	1.83907i	−0.393002	−	0.919537i	$-0.628564\pi$
$769$		−	50.9991i		−	1.83907i	0.393002	−	0.919537i	$-0.371436\pi$
$770$		0			0
$771$			5.89493i			0.212301i
$772$			12.4951i			0.449709i
$773$	−40.9981			−1.47460			−0.737300	−	0.675565i	$-0.763900\pi$
$773$	−40.9981			−1.47460			−0.737300	+	0.675565i	$0.763900\pi$
$774$	−0.517431			−0.0185987
$775$		0			0
$776$	0.403430			0.0144823
$777$	−12.5271	−	3.80068i	−0.449408	−	0.136349i
$778$	−29.8974			−1.07187
$779$		−	12.5069i		−	0.448108i
$780$		0			0
$781$	1.80220			0.0644879
$782$		−	1.06446i		−	0.0380648i
$783$			8.82025i			0.315210i
$784$	−5.50840			−0.196729
$785$		0			0
$786$	−22.6197			−0.806817
$787$	−30.4357			−1.08492			−0.542458	−	0.840083i	$-0.682506\pi$
$787$	−30.4357			−1.08492			−0.542458	+	0.840083i	$0.682506\pi$
$788$	5.51302			0.196393
$789$	2.01601			0.0717718
$790$		0			0
$791$			18.0248i			0.640887i
$792$		−	0.196867i		−	0.00699536i
$793$	72.5620			2.57675
$794$		−	13.2064i		−	0.468679i
$795$		0			0
$796$		−	18.8033i		−	0.666464i
$797$		−	0.999495i		−	0.0354039i	−0.999843	−	0.0177020i	$-0.994365\pi$
$797$		−	0.999495i		−	0.0354039i	0.999843	−	0.0177020i	$-0.00563500\pi$
$798$	7.19908			0.254845
$799$		−	4.83170i		−	0.170933i
$800$		0			0
$801$			0.494633i			0.0174770i
$802$	−23.0269			−0.813108
$803$	−16.8992			−0.596360
$804$	−19.5985			−0.691187
$805$		0			0
$806$		−	26.7539i		−	0.942367i
$807$	26.6692			0.938801
$808$			19.3724i			0.681518i
$809$			21.8030i			0.766552i	0.923634	+	0.383276i	$0.125204\pi$
$809$			21.8030i			0.766552i	−0.923634	+	0.383276i	$0.874796\pi$
$810$		0			0
$811$	−40.9653			−1.43848			−0.719242	−	0.694759i	$-0.755511\pi$
$811$	−40.9653			−1.43848			−0.719242	+	0.694759i	$0.755511\pi$
$812$			2.11176i			0.0741082i
$813$	32.2197			1.12999
$814$	3.30453	−	10.8918i	0.115824	−	0.381758i
$815$		0			0
$816$		−	1.34980i		−	0.0472526i
$817$	16.4515			0.575566
$818$	−9.77049			−0.341617
$819$		−	0.835833i		−	0.0292064i
$820$		0			0
$821$	36.2693			1.26581			0.632904	−	0.774230i	$-0.281863\pi$
$821$	36.2693			1.26581			0.632904	+	0.774230i	$0.281863\pi$
$822$			21.2084i			0.739728i
$823$	48.5397			1.69199			0.845993	−	0.533194i	$-0.179008\pi$
$823$	48.5397			1.69199			0.845993	+	0.533194i	$0.179008\pi$
$824$	−5.56165			−0.193749
$825$		0			0
$826$	−12.9049			−0.449017
$827$			39.6895i			1.38014i	0.723743	+	0.690069i	$0.242420\pi$
$827$			39.6895i			1.38014i	−0.723743	+	0.690069i	$0.757580\pi$
$828$		−	0.146202i		−	0.00508088i
$829$		−	53.4506i		−	1.85641i	−0.372064	−	0.928207i	$-0.621350\pi$
$829$		−	53.4506i		−	1.85641i	0.372064	−	0.928207i	$-0.378650\pi$
$830$		0			0
$831$			4.55258i			0.157927i
$832$		−	6.50491i		−	0.225517i
$833$		−	4.21940i		−	0.146194i
$834$		−	17.2438i		−	0.597105i
$835$		0			0
$836$			6.25931i			0.216483i
$837$			20.9802i			0.725181i
$838$		−	2.06109i		−	0.0711993i
$839$	33.5857			1.15951			0.579753	−	0.814792i	$-0.303149\pi$
$839$	33.5857			1.15951			0.579753	+	0.814792i	$0.303149\pi$
$840$		0			0
$841$	26.0102			0.896905
$842$	−12.8910			−0.444255
$843$		−	34.0196i		−	1.17170i
$844$	26.6632			0.917784
$845$		0			0
$846$		−	0.663631i		−	0.0228161i
$847$	9.15813			0.314677
$848$	2.57768			0.0885180
$849$		−	15.9113i		−	0.546074i
$850$		0			0
$851$	2.45409	−	8.08876i	0.0841253	−	0.277279i
$852$	1.69718			0.0581445
$853$		−	0.641846i		−	0.0219764i	−0.999940	−	0.0109882i	$-0.996502\pi$
$853$		−	0.641846i		−	0.0219764i	0.999940	−	0.0109882i	$-0.00349772\pi$
$854$	−13.6237			−0.466192
$855$		0			0
$856$		−	1.93484i		−	0.0661315i
$857$			20.5938i			0.703470i	0.936100	+	0.351735i	$0.114408\pi$
$857$			20.5938i			0.703470i	−0.936100	+	0.351735i	$0.885592\pi$
$858$	21.4490			0.732258
$859$			6.18892i			0.211163i	0.994411	+	0.105582i	$0.0336704\pi$
$859$			6.18892i			0.211163i	−0.994411	+	0.105582i	$0.966330\pi$
$860$		0			0
$861$	8.04670			0.274231
$862$	9.41662			0.320731
$863$	48.8873			1.66414			0.832071	−	0.554669i	$-0.187155\pi$
$863$	48.8873			1.66414			0.832071	+	0.554669i	$0.187155\pi$
$864$			5.10109i			0.173542i
$865$		0			0
$866$			3.07581i			0.104520i
$867$	−28.9228			−0.982269
$868$			5.02311i			0.170495i
$869$		−	19.3357i		−	0.655918i
$870$		0			0
$871$		−	72.3469i		−	2.45138i
$872$	8.70619			0.294829
$873$			0.0424444i			0.00143653i
$874$			4.64844i			0.157236i
$875$		0			0
$876$	−15.9144			−0.537698
$877$	−2.65696			−0.0897190			−0.0448595	−	0.998993i	$-0.514284\pi$
$877$	−2.65696			−0.0897190			−0.0448595	+	0.998993i	$0.514284\pi$
$878$	1.93763			0.0653918
$879$	−23.0570			−0.777693
$880$		0			0
$881$	−1.97718			−0.0666130			−0.0333065	−	0.999445i	$-0.510604\pi$
$881$	−1.97718			−0.0666130			−0.0333065	+	0.999445i	$0.510604\pi$
$882$		−	0.579532i		−	0.0195139i
$883$			35.6965i			1.20128i	0.799519	+	0.600641i	$0.205088\pi$
$883$			35.6965i			1.20128i	−0.799519	+	0.600641i	$0.794912\pi$
$884$	4.98272			0.167587
$885$		0			0
$886$		−	26.5690i		−	0.892602i
$887$	−0.181192			−0.00608382			−0.00304191	−	0.999995i	$-0.500968\pi$
$887$	−0.181192			−0.00608382			−0.00304191	+	0.999995i	$0.500968\pi$
$888$	3.11196	−	10.2571i	0.104431	−	0.344206i
$889$	−13.5908			−0.455820
$890$		0			0
$891$	−17.4107			−0.583281
$892$	10.8630			0.363721
$893$			21.0999i			0.706081i
$894$		−	20.9478i		−	0.700600i
$895$		0			0
$896$			1.22131i			0.0408011i
$897$	15.9290			0.531854
$898$	−0.777045			−0.0259303
$899$	−7.11155			−0.237184
$900$		0			0
$901$			1.97449i			0.0657798i
$902$			6.99627i			0.232950i
$903$			10.5846i			0.352232i
$904$	−14.7585			−0.490862
$905$		0			0
$906$		−	37.5589i		−	1.24781i
$907$		−	28.0542i		−	0.931525i	−0.884910	−	0.465762i	$-0.845780\pi$
$907$		−	28.0542i		−	0.931525i	0.884910	−	0.465762i	$-0.154220\pi$
$908$			6.82427i			0.226471i
$909$	−2.03814			−0.0676010
$910$		0			0
$911$			33.0379i			1.09459i	0.836939	+	0.547297i	$0.184343\pi$
$911$			33.0379i			1.09459i	−0.836939	+	0.547297i	$0.815657\pi$
$912$			5.89455i			0.195188i
$913$	0.0122904			0.000406754
$914$	21.1753			0.700415
$915$		0			0
$916$	2.56189			0.0846471
$917$			15.6772i			0.517705i
$918$	−3.90740			−0.128963
$919$		−	24.1489i		−	0.796600i	−0.917255	−	0.398300i	$-0.869600\pi$
$919$		−	24.1489i		−	0.796600i	0.917255	−	0.398300i	$-0.130400\pi$
$920$		0			0
$921$	−13.4090			−0.441842
$922$	−23.9797			−0.789731
$923$			6.26505i			0.206217i
$924$	−4.02710			−0.132482
$925$		0			0
$926$	25.1591			0.826781
$927$		−	0.585134i		−	0.0192183i
$928$	−1.72909			−0.0567602
$929$	−30.9086			−1.01408			−0.507039	−	0.861923i	$-0.669260\pi$
$929$	−30.9086			−1.01408			−0.507039	+	0.861923i	$0.669260\pi$
$930$		0			0
$931$			18.4260i			0.603887i
$932$	23.3423			0.764603
$933$		−	26.8481i		−	0.878969i
$934$	15.6162			0.510978
$935$		0			0
$936$	0.684374			0.0223695
$937$	33.6530			1.09940			0.549698	−	0.835363i	$-0.314743\pi$
$937$	33.6530			1.09940			0.549698	+	0.835363i	$0.314743\pi$
$938$			13.5833i			0.443510i
$939$			17.6216i			0.575059i
$940$		0			0
$941$	−33.8242			−1.10264			−0.551319	−	0.834294i	$-0.685875\pi$
$941$	−33.8242			−1.10264			−0.551319	+	0.834294i	$0.685875\pi$
$942$		−	26.9626i		−	0.878490i
$943$			5.19575i			0.169197i
$944$		−	10.5664i		−	0.343907i
$945$		0			0
$946$	−9.20284			−0.299210
$947$		−	17.3591i		−	0.564095i	−0.959400	−	0.282048i	$-0.908986\pi$
$947$		−	17.3591i		−	0.564095i	0.959400	−	0.282048i	$-0.0910136\pi$
$948$		−	18.2089i		−	0.591398i
$949$		−	58.7471i		−	1.90701i
$950$		0			0
$951$	60.1607			1.95085
$952$	−0.935517			−0.0303203
$953$	−15.0520			−0.487582			−0.243791	−	0.969828i	$-0.578391\pi$
$953$	−15.0520			−0.487582			−0.243791	+	0.969828i	$0.578391\pi$
$954$			0.271195i			0.00878026i
$955$		0			0
$956$		−	5.19256i		−	0.167940i
$957$		−	5.70144i		−	0.184301i
$958$	31.4974			1.01763
$959$	14.6990			0.474657
$960$		0			0
$961$	14.0842			0.454329
$962$	37.8635	+	11.4876i	1.22077	+	0.370376i
$963$	0.203562			0.00655970
$964$			15.5243i			0.500005i
$965$		0			0
$966$	−2.99071			−0.0962244
$967$		−	23.3045i		−	0.749423i	−0.927141	−	0.374712i	$-0.877742\pi$
$967$		−	23.3045i		−	0.749423i	0.927141	−	0.374712i	$-0.122258\pi$
$968$			7.49860i			0.241014i
$969$	−4.51519			−0.145049
$970$		0			0
$971$	−40.7911			−1.30905			−0.654524	−	0.756041i	$-0.727131\pi$
$971$	−40.7911			−1.30905			−0.654524	+	0.756041i	$0.727131\pi$
$972$	−1.09286			−0.0350536
$973$	−11.9513			−0.383140
$974$	24.2768			0.777878
$975$		0			0
$976$		−	11.1550i		−	0.357061i
$977$			2.64739i			0.0846976i	0.999103	+	0.0423488i	$0.0134841\pi$
$977$			2.64739i			0.0846976i	−0.999103	+	0.0423488i	$0.986516\pi$
$978$	−26.2873			−0.840575
$979$			8.79735i			0.281165i
$980$		0			0
$981$			0.915967i			0.0292446i
$982$			16.5129i			0.526949i
$983$	27.8528			0.888367			0.444183	−	0.895936i	$-0.353494\pi$
$983$	27.8528			0.888367			0.444183	+	0.895936i	$0.353494\pi$
$984$			6.58857i			0.210036i
$985$		0			0
$986$		−	1.32447i		−	0.0421798i
$987$	−13.5752			−0.432104
$988$	−21.7594			−0.692258
$989$	−6.83444			−0.217323
$990$		0			0
$991$		−	47.8484i		−	1.51995i	−0.649950	−	0.759977i	$-0.725210\pi$
$991$		−	47.8484i		−	1.51995i	0.649950	−	0.759977i	$-0.274790\pi$
$992$	−4.11288			−0.130584
$993$			48.0307i			1.52421i
$994$		−	1.17628i		−	0.0373092i
$995$		0			0
$996$	0.0115742			0.000366743
$997$			3.95282i			0.125187i	0.998039	+	0.0625936i	$0.0199372\pi$
$997$			3.95282i			0.125187i	−0.998039	+	0.0625936i	$0.980063\pi$
$998$	−22.8436			−0.723101
$999$	−29.6922	−	9.00849i	−0.939420	−	0.285016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.d.i.1701.13		20
5.2	odd	4		370.2.c.a.369.8	yes	10
5.3	odd	4		370.2.c.b.369.3	yes	10
5.4	even	2	inner	1850.2.d.i.1701.8		20
15.2	even	4		3330.2.e.d.739.8		10
15.8	even	4		3330.2.e.c.739.4		10
37.36	even	2	inner	1850.2.d.i.1701.3		20
185.73	odd	4		370.2.c.a.369.3	✓	10
185.147	odd	4		370.2.c.b.369.8	yes	10
185.184	even	2	inner	1850.2.d.i.1701.18		20
555.332	even	4		3330.2.e.c.739.3		10
555.443	even	4		3330.2.e.d.739.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.3	✓	10	185.73	odd	4
370.2.c.a.369.8	yes	10	5.2	odd	4
370.2.c.b.369.3	yes	10	5.3	odd	4
370.2.c.b.369.8	yes	10	185.147	odd	4
1850.2.d.i.1701.3		20	37.36	even	2	inner
1850.2.d.i.1701.8		20	5.4	even	2	inner
1850.2.d.i.1701.13		20	1.1	even	1	trivial
1850.2.d.i.1701.18		20	185.184	even	2	inner
3330.2.e.c.739.3		10	555.332	even	4
3330.2.e.c.739.4		10	15.8	even	4
3330.2.e.d.739.7		10	555.443	even	4
3330.2.e.d.739.8		10	15.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.76216 q^{3} -1.00000 q^{4} -1.76216i q^{6} -1.22131 q^{7} -1.00000i q^{8} +0.105209 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.76216 q^{3} -1.00000 q^{4} -1.76216i q^{6} -1.22131 q^{7} -1.00000i q^{8} +0.105209 q^{9} +1.87120 q^{11} +1.76216 q^{12} +6.50491i q^{13} -1.22131i q^{14} +1.00000 q^{16} +0.765994i q^{17} +0.105209i q^{18} -3.34507i q^{19} +2.15215 q^{21} +1.87120i q^{22} +1.38964i q^{23} +1.76216i q^{24} -6.50491 q^{26} +5.10109 q^{27} +1.22131 q^{28} +1.72909i q^{29} +4.11288i q^{31} +1.00000i q^{32} -3.29736 q^{33} -0.765994 q^{34} -0.105209 q^{36} +(-5.82076 - 1.76599i) q^{37} +3.34507 q^{38} -11.4627i q^{39} +3.73892 q^{41} +2.15215i q^{42} +4.91814i q^{43} -1.87120 q^{44} -1.38964 q^{46} -6.30775 q^{47} -1.76216 q^{48} -5.50840 q^{49} -1.34980i q^{51} -6.50491i q^{52} +2.57768 q^{53} +5.10109i q^{54} +1.22131i q^{56} +5.89455i q^{57} -1.72909 q^{58} -10.5664i q^{59} -11.1550i q^{61} -4.11288 q^{62} -0.128493 q^{63} -1.00000 q^{64} -3.29736i q^{66} -11.1219 q^{67} -0.765994i q^{68} -2.44877i q^{69} +0.963126 q^{71} -0.105209i q^{72} -9.03119 q^{73} +(1.76599 - 5.82076i) q^{74} +3.34507i q^{76} -2.28532 q^{77} +11.4627 q^{78} -10.3333i q^{79} -9.30456 q^{81} +3.73892i q^{82} +0.00656819 q^{83} -2.15215 q^{84} -4.91814 q^{86} -3.04694i q^{87} -1.87120i q^{88} +4.70144i q^{89} -7.94452i q^{91} -1.38964i q^{92} -7.24756i q^{93} -6.30775i q^{94} -1.76216i q^{96} +0.403430i q^{97} -5.50840i q^{98} +0.196867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 20 * q - 20 * q^4 + 16 * q^9	\( 20 q - 20 q^{4} + 16 q^{9} + 20 q^{16} - 24 q^{21} + 4 q^{26} + 36 q^{34} - 16 q^{36} - 8 q^{41} - 20 q^{46} + 16 q^{49} - 20 q^{64} - 40 q^{71} - 16 q^{74} + 116 q^{81} + 24 q^{84} + 20 q^{86} + 164 q^{99}+O(q^{100}) \) 20 * q - 20 * q^4 + 16 * q^9 + 20 * q^16 - 24 * q^21 + 4 * q^26 + 36 * q^34 - 16 * q^36 - 8 * q^41 - 20 * q^46 + 16 * q^49 - 20 * q^64 - 40 * q^71 - 16 * q^74 + 116 * q^81 + 24 * q^84 + 20 * q^86 + 164 * q^99

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