LMFDB - Embedded newform 693.2.i.i.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(100,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("693.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.i (of order $3$, degree $2$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.10423593216.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$-0.758290 + 1.31340i$ of defining polynomial
Character	$\chi$	$=$	693.100
Dual form			693.2.i.i.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.758290 + 1.31340i) q^{2} +(-0.150007 - 0.259820i) q^{4} +(-1.16659 + 2.02059i) q^{5} +(-2.28580 - 1.33233i) q^{7} -2.57816 q^{8} +O(q^{10})$	\(q+(-0.758290 + 1.31340i) q^{2} +(-0.150007 - 0.259820i) q^{4} +(-1.16659 + 2.02059i) q^{5} +(-2.28580 - 1.33233i) q^{7} -2.57816 q^{8} +(-1.76922 - 3.06438i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.53844 q^{13} +(3.48318 - 1.99187i) q^{14} +(2.25501 - 3.90579i) q^{16} +(-0.0583043 - 0.100986i) q^{17} +(1.80566 - 3.12750i) q^{19} +0.699986 q^{20} +1.51658 q^{22} +(3.55502 - 6.15748i) q^{23} +(-0.221850 - 0.384256i) q^{25} +(1.16659 - 2.02059i) q^{26} +(-0.00327987 + 0.793757i) q^{28} -5.05502 q^{29} +(2.18845 + 3.79051i) q^{31} +(0.841739 + 1.45793i) q^{32} +0.176846 q^{34} +(5.35868 - 3.06438i) q^{35} +(0.150007 - 0.259820i) q^{37} +(2.73843 + 4.74310i) q^{38} +(3.00765 - 5.20941i) q^{40} -8.20479 q^{41} -4.18293 q^{43} +(-0.150007 + 0.259820i) q^{44} +(5.39148 + 9.33831i) q^{46} +(1.15001 - 1.99187i) q^{47} +(3.44978 + 6.09089i) q^{49} +0.672908 q^{50} +(0.230778 + 0.399719i) q^{52} +(-5.94346 - 10.2944i) q^{53} +2.33317 q^{55} +(5.89317 + 3.43497i) q^{56} +(3.83317 - 6.63925i) q^{58} +(2.47814 + 4.29226i) q^{59} +(2.28580 - 3.95913i) q^{61} -6.63792 q^{62} +6.46691 q^{64} +(1.79473 - 3.10856i) q^{65} +(-6.14472 - 10.6430i) q^{67} +(-0.0174921 + 0.0302972i) q^{68} +(-0.0386836 + 9.36176i) q^{70} -4.25628 q^{71} +(-5.21900 - 9.03958i) q^{73} +(0.227498 + 0.394038i) q^{74} -1.08345 q^{76} +(-0.0109324 + 2.64573i) q^{77} +(-7.15742 + 12.3970i) q^{79} +(5.26133 + 9.11289i) q^{80} +(6.22161 - 10.7761i) q^{82} +11.1869 q^{83} +0.272068 q^{85} +(3.17187 - 5.49384i) q^{86} +(1.28908 + 2.23276i) q^{88} +(6.96636 - 12.0661i) q^{89} +(3.51658 + 2.04972i) q^{91} -2.13312 q^{92} +(1.74408 + 3.02083i) q^{94} +(4.21292 + 7.29700i) q^{95} -16.4101 q^{97} +(-10.6157 - 0.0877314i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8	$ 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8} - 10 q^{10} - 4 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{17} - 4 q^{22} + 4 q^{23} - 4 q^{25} - 4 q^{26} - 22 q^{28} - 16 q^{29} + 12 q^{31} + 26 q^{32} - 32 q^{34} + 2 q^{35} + 4 q^{37} + 8 q^{38} + 6 q^{40} - 4 q^{41} + 36 q^{43} - 4 q^{44} + 14 q^{46} + 12 q^{47} - 4 q^{49} - 4 q^{50} + 6 q^{52} - 12 q^{53} - 8 q^{55} - 48 q^{56} + 4 q^{58} + 12 q^{59} - 2 q^{61} + 52 q^{62} + 112 q^{64} - 4 q^{65} - 28 q^{67} - 48 q^{68} - 32 q^{70} - 24 q^{71} - 6 q^{73} - 16 q^{74} - 36 q^{76} - 4 q^{77} - 2 q^{79} + 16 q^{80} + 12 q^{82} + 24 q^{83} + 36 q^{85} + 36 q^{86} + 12 q^{88} + 8 q^{89} + 12 q^{91} + 32 q^{92} - 20 q^{94} + 34 q^{95} - 88 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8 - 10 * q^10 - 4 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^17 - 4 * q^22 + 4 * q^23 - 4 * q^25 - 4 * q^26 - 22 * q^28 - 16 * q^29 + 12 * q^31 + 26 * q^32 - 32 * q^34 + 2 * q^35 + 4 * q^37 + 8 * q^38 + 6 * q^40 - 4 * q^41 + 36 * q^43 - 4 * q^44 + 14 * q^46 + 12 * q^47 - 4 * q^49 - 4 * q^50 + 6 * q^52 - 12 * q^53 - 8 * q^55 - 48 * q^56 + 4 * q^58 + 12 * q^59 - 2 * q^61 + 52 * q^62 + 112 * q^64 - 4 * q^65 - 28 * q^67 - 48 * q^68 - 32 * q^70 - 24 * q^71 - 6 * q^73 - 16 * q^74 - 36 * q^76 - 4 * q^77 - 2 * q^79 + 16 * q^80 + 12 * q^82 + 24 * q^83 + 36 * q^85 + 36 * q^86 + 12 * q^88 + 8 * q^89 + 12 * q^91 + 32 * q^92 - 20 * q^94 + 34 * q^95 - 88 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.758290	+	1.31340i	−0.536192	+	0.928712i	0.462913	+	0.886404i	$0.346804\pi$
$2$	−0.758290	+	1.31340i	−0.536192	+	0.928712i	−0.999105	+	0.0423078i	$0.986529\pi$
$3$		0			0
$3$		0			0
$4$	−0.150007	−	0.259820i	−0.0750036	−	0.129910i
$5$	−1.16659	+	2.02059i	−0.521714	+	0.903634i	0.477967	+	0.878378i	$0.341374\pi$
$5$	−1.16659	+	2.02059i	−0.521714	+	0.903634i	−0.999681	+	0.0252568i	$0.991960\pi$
$6$		0			0
$7$	−2.28580	−	1.33233i	−0.863952	−	0.503574i
$7$	−2.28580	−	1.33233i	−0.863952	−	0.503574i
$8$	−2.57816			−0.911519
$9$		0			0
$10$	−1.76922	−	3.06438i	−0.559477	−	0.969043i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−1.53844			−0.426688			−0.213344	−	0.976977i	$-0.568435\pi$
$13$	−1.53844			−0.426688			−0.213344	+	0.976977i	$0.568435\pi$
$14$	3.48318	−	1.99187i	0.930919	−	0.532350i
$15$		0			0
$16$	2.25501	−	3.90579i	0.563753	−	0.976448i
$17$	−0.0583043	−	0.100986i	−0.0141409	−	0.0244927i	0.858868	−	0.512196i	$-0.171168\pi$
$17$	−0.0583043	−	0.100986i	−0.0141409	−	0.0244927i	−0.873009	+	0.487704i	$0.837835\pi$
$18$		0			0
$19$	1.80566	−	3.12750i	0.414247	−	0.717497i	−0.581102	−	0.813831i	$-0.697378\pi$
$19$	1.80566	−	3.12750i	0.414247	−	0.717497i	0.995349	+	0.0963336i	$0.0307116\pi$
$20$	0.699986			0.156522
$21$		0			0
$22$	1.51658			0.323336
$23$	3.55502	−	6.15748i	0.741274	−	1.28392i	−0.210642	−	0.977563i	$-0.567555\pi$
$23$	3.55502	−	6.15748i	0.741274	−	1.28392i	0.951916	−	0.306361i	$-0.0991113\pi$
$24$		0			0
$25$	−0.221850	−	0.384256i	−0.0443701	−	0.0768512i
$26$	1.16659	−	2.02059i	0.228787	−	0.396270i
$27$		0			0
$28$	−0.00327987	+	0.793757i	−0.000619837	+	0.150006i
$29$	−5.05502			−0.938694			−0.469347	−	0.883014i	$-0.655511\pi$
$29$	−5.05502			−0.938694			−0.469347	+	0.883014i	$0.655511\pi$
$30$		0			0
$31$	2.18845	+	3.79051i	0.393058	+	0.680796i	0.992851	−	0.119359i	$-0.0380840\pi$
$31$	2.18845	+	3.79051i	0.393058	+	0.680796i	−0.599794	+	0.800155i	$0.704751\pi$
$32$	0.841739	+	1.45793i	0.148800	+	0.257729i
$33$		0			0
$34$	0.176846			0.0303289
$35$	5.35868	−	3.06438i	0.905782	−	0.517975i
$36$		0			0
$37$	0.150007	−	0.259820i	0.0246610	−	0.0427142i	−0.853432	−	0.521205i	$-0.825483\pi$
$37$	0.150007	−	0.259820i	0.0246610	−	0.0427142i	0.878093	+	0.478491i	$0.158816\pi$
$38$	2.73843	+	4.74310i	0.444232	+	0.769432i
$39$		0			0
$40$	3.00765	−	5.20941i	0.475552	−	0.823680i
$41$	−8.20479			−1.28137			−0.640687	−	0.767802i	$-0.721350\pi$
$41$	−8.20479			−1.28137			−0.640687	+	0.767802i	$0.721350\pi$
$42$		0			0
$43$	−4.18293			−0.637891			−0.318945	−	0.947773i	$-0.603329\pi$
$43$	−4.18293			−0.637891			−0.318945	+	0.947773i	$0.603329\pi$
$44$	−0.150007	+	0.259820i	−0.0226144	+	0.0391693i
$45$		0			0
$46$	5.39148	+	9.33831i	0.794930	+	1.37686i
$47$	1.15001	−	1.99187i	0.167746	−	0.290544i	−0.769881	−	0.638187i	$-0.779685\pi$
$47$	1.15001	−	1.99187i	0.167746	−	0.290544i	0.937627	+	0.347643i	$0.113018\pi$
$48$		0			0
$49$	3.44978	+	6.09089i	0.492826	+	0.870128i
$50$	0.672908			0.0951635
$51$		0			0
$52$	0.230778	+	0.399719i	0.0320031	+	0.0554310i
$53$	−5.94346	−	10.2944i	−0.816397	−	1.41404i	−0.908320	−	0.418275i	$-0.862635\pi$
$53$	−5.94346	−	10.2944i	−0.816397	−	1.41404i	0.0919230	−	0.995766i	$-0.470699\pi$
$54$		0			0
$55$	2.33317			0.314605
$56$	5.89317	+	3.43497i	0.787508	+	0.459017i
$57$		0			0
$58$	3.83317	−	6.63925i	0.503320	−	0.871777i
$59$	2.47814	+	4.29226i	0.322626	+	0.558804i	0.981029	−	0.193861i	$-0.0621012\pi$
$59$	2.47814	+	4.29226i	0.322626	+	0.558804i	−0.658403	+	0.752665i	$0.728768\pi$
$60$		0			0
$61$	2.28580	−	3.95913i	0.292667	−	0.506914i	−0.681773	−	0.731564i	$-0.738791\pi$
$61$	2.28580	−	3.95913i	0.292667	−	0.506914i	0.974439	+	0.224650i	$0.0721239\pi$
$62$	−6.63792			−0.843017
$63$		0			0
$64$	6.46691			0.808364
$65$	1.79473	−	3.10856i	0.222609	−	0.385570i
$66$		0			0
$67$	−6.14472	−	10.6430i	−0.750697	−	1.30025i	−0.947485	−	0.319800i	$-0.896384\pi$
$67$	−6.14472	−	10.6430i	−0.750697	−	1.30025i	0.196788	−	0.980446i	$-0.436949\pi$
$68$	−0.0174921	+	0.0302972i	−0.00212123	+	0.00367408i
$69$		0			0
$70$	−0.0386836	+	9.36176i	−0.00462357	+	1.11894i
$71$	−4.25628			−0.505128			−0.252564	−	0.967580i	$-0.581274\pi$
$71$	−4.25628			−0.505128			−0.252564	+	0.967580i	$0.581274\pi$
$72$		0			0
$73$	−5.21900	−	9.03958i	−0.610838	−	1.05800i	−0.991099	−	0.133124i	$-0.957499\pi$
$73$	−5.21900	−	9.03958i	−0.610838	−	1.05800i	0.380261	−	0.924879i	$-0.375834\pi$
$74$	0.227498	+	0.394038i	0.0264461	+	0.0458060i
$75$		0			0
$76$	−1.08345			−0.124280
$77$	−0.0109324	+	2.64573i	−0.00124586	+	0.301509i
$78$		0			0
$79$	−7.15742	+	12.3970i	−0.805273	+	1.39477i	0.110834	+	0.993839i	$0.464648\pi$
$79$	−7.15742	+	12.3970i	−0.805273	+	1.39477i	−0.916107	+	0.400934i	$0.868686\pi$
$80$	5.26133	+	9.11289i	0.588235	+	1.01885i
$81$		0			0
$82$	6.22161	−	10.7761i	0.687062	−	1.19003i
$83$	11.1869			1.22793			0.613963	−	0.789335i	$-0.289574\pi$
$83$	11.1869			1.22793			0.613963	+	0.789335i	$0.289574\pi$
$84$		0			0
$85$	0.272068			0.0295099
$86$	3.17187	−	5.49384i	0.342032	−	0.592416i
$87$		0			0
$88$	1.28908	+	2.23276i	0.137417	+	0.238013i
$89$	6.96636	−	12.0661i	0.738433	−	1.27900i	−0.214768	−	0.976665i	$-0.568899\pi$
$89$	6.96636	−	12.0661i	0.738433	−	1.27900i	0.953201	−	0.302338i	$-0.0977672\pi$
$90$		0			0
$91$	3.51658	+	2.04972i	0.368638	+	0.214869i
$92$	−2.13312			−0.222393
$93$		0			0
$94$	1.74408	+	3.02083i	0.179888	+	0.311575i
$95$	4.21292	+	7.29700i	0.432237	+	0.748656i
$96$		0			0
$97$	−16.4101			−1.66619			−0.833095	−	0.553130i	$-0.813433\pi$
$97$	−16.4101			−1.66619			−0.833095	+	0.553130i	$0.813433\pi$
$98$	−10.6157	−	0.0877314i	−1.07235	−	0.00886221i
$99$		0			0
$100$	−0.0665583	+	0.115282i	−0.00665583	+	0.0115282i
$101$	4.82753	+	8.36152i	0.480357	+	0.832002i	0.999746	−	0.0225353i	$-0.00717383\pi$
$101$	4.82753	+	8.36152i	0.480357	+	0.832002i	−0.519389	+	0.854538i	$0.673840\pi$
$102$		0			0
$103$	−4.41006	+	7.63845i	−0.434536	+	0.752639i	−0.997258	−	0.0740075i	$-0.976421\pi$
$103$	−4.41006	+	7.63845i	−0.434536	+	0.752639i	0.562721	+	0.826647i	$0.309754\pi$
$104$	3.96636			0.388934
$105$		0			0
$106$	18.0275			1.75098
$107$	5.24207	−	9.07954i	0.506770	−	0.877752i	−0.493199	−	0.869917i	$-0.664173\pi$
$107$	5.24207	−	9.07954i	0.506770	−	0.877752i	0.999969	−	0.00783538i	$-0.00249410\pi$
$108$		0			0
$109$	−5.26394	−	9.11741i	−0.504194	−	0.873289i	−0.999988	−	0.00484932i	$-0.998456\pi$
$109$	−5.26394	−	9.11741i	−0.504194	−	0.873289i	0.495794	−	0.868440i	$-0.334877\pi$
$110$	−1.76922	+	3.06438i	−0.168689	+	0.292177i
$111$		0			0
$112$	−10.3583	+	5.92345i	−0.978769	+	0.559713i
$113$	−11.4327			−1.07549			−0.537747	−	0.843106i	$-0.680724\pi$
$113$	−11.4327			−1.07549			−0.537747	+	0.843106i	$0.680724\pi$
$114$		0			0
$115$	8.29449	+	14.3665i	0.773465	+	1.33968i
$116$	0.758290	+	1.31340i	0.0704055	+	0.121946i
$117$		0			0
$118$	−7.51658			−0.691957
$119$	−0.00127481	+	0.308514i	−0.000116861	+	0.0282815i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	3.46660	+	6.00433i	0.313851	+	0.543606i
$123$		0			0
$124$	0.656567	−	1.13721i	0.0589614	−	0.102124i
$125$	−10.6306			−0.950833
$126$		0			0
$127$	0.234898			0.0208438			0.0104219	−	0.999946i	$-0.496683\pi$
$127$	0.234898			0.0208438			0.0104219	+	0.999946i	$0.496683\pi$
$128$	−6.58727	+	11.4095i	−0.582238	+	1.00847i
$129$		0			0
$130$	2.72185	+	4.71438i	0.238722	+	0.413479i
$131$	−2.87927	+	4.98704i	−0.251563	+	0.435720i	−0.963956	−	0.266060i	$-0.914278\pi$
$131$	−2.87927	+	4.98704i	−0.251563	+	0.435720i	0.712393	+	0.701780i	$0.247611\pi$
$132$		0			0
$133$	−8.29425	+	4.74310i	−0.719203	+	0.411279i
$134$	18.6379			1.61007
$135$		0			0
$136$	0.150318	+	0.260358i	0.0128897	+	0.0223255i
$137$	8.04325	+	13.9313i	0.687181	+	1.19023i	0.972746	+	0.231874i	$0.0744856\pi$
$137$	8.04325	+	13.9313i	0.687181	+	1.19023i	−0.285565	+	0.958359i	$0.592181\pi$
$138$		0			0
$139$	−14.2930			−1.21231			−0.606157	−	0.795345i	$-0.707290\pi$
$139$	−14.2930			−1.21231			−0.606157	+	0.795345i	$0.707290\pi$
$140$	−1.60003	−	0.932613i	−0.135227	−	0.0788202i
$141$		0			0
$142$	3.22750	−	5.59019i	0.270846	−	0.469118i
$143$	0.769222	+	1.33233i	0.0643256	+	0.111415i
$144$		0			0
$145$	5.89713	−	10.2141i	0.489730	−	0.848237i
$146$	15.8301			1.31011
$147$		0			0
$148$	−0.0900086			−0.00739866
$149$	−0.336454	+	0.582755i	−0.0275634	+	0.0477412i	−0.879478	−	0.475939i	$-0.842108\pi$
$149$	−0.336454	+	0.582755i	−0.0275634	+	0.0477412i	0.851915	+	0.523681i	$0.175441\pi$
$150$		0			0
$151$	−11.8862	−	20.5875i	−0.967285	−	1.67539i	−0.703347	−	0.710846i	$-0.748312\pi$
$151$	−11.8862	−	20.5875i	−0.967285	−	1.67539i	−0.263937	−	0.964540i	$-0.585021\pi$
$152$	−4.65529	+	8.06320i	−0.377594	+	0.654012i
$153$		0			0
$154$	−3.46660	−	2.02059i	−0.279347	−	0.162824i
$155$	−10.2121			−0.820254
$156$		0			0
$157$	7.62790	+	13.2119i	0.608773	+	1.05443i	0.991443	+	0.130541i	$0.0416713\pi$
$157$	7.62790	+	13.2119i	0.608773	+	1.05443i	−0.382670	+	0.923885i	$0.624995\pi$
$158$	−10.8548	−	18.8011i	−0.863561	−	1.49573i
$159$		0			0
$160$	−3.92785			−0.310523
$161$	−16.3299	+	9.33831i	−1.28698	+	0.735962i
$162$		0			0
$163$	−0.210316	+	0.364279i	−0.0164733	+	0.0285325i	−0.874145	−	0.485666i	$-0.838577\pi$
$163$	−0.210316	+	0.364279i	−0.0164733	+	0.0285325i	0.857671	+	0.514198i	$0.171911\pi$
$164$	1.23078	+	2.13177i	0.0961076	+	0.166463i
$165$		0			0
$166$	−8.48294	+	14.6929i	−0.658404	+	1.14039i
$167$	−16.4331			−1.27163			−0.635817	−	0.771840i	$-0.719337\pi$
$167$	−16.4331			−1.27163			−0.635817	+	0.771840i	$0.719337\pi$
$168$		0			0
$169$	−10.6332			−0.817938
$170$	−0.206306	+	0.357333i	−0.0158230	+	0.0274062i
$171$		0			0
$172$	0.627469	+	1.08681i	0.0478441	+	0.0828684i
$173$	1.93076	−	3.34418i	0.146793	−	0.254253i	−0.783247	−	0.621710i	$-0.786438\pi$
$173$	1.93076	−	3.34418i	0.146793	−	0.254253i	0.930041	+	0.367457i	$0.119771\pi$
$174$		0			0
$175$	−0.00485070	+	1.17391i	−0.000366679	+	0.0887394i
$176$	−4.51002			−0.339956
$177$		0			0
$178$	10.5650	+	18.2992i	0.791884	+	1.37158i
$179$	−6.35480	−	11.0068i	−0.474980	−	0.822690i	0.524609	−	0.851343i	$-0.324211\pi$
$179$	−6.35480	−	11.0068i	−0.474980	−	0.822690i	−0.999589	+	0.0286535i	$0.990878\pi$
$180$		0			0
$181$	16.5196			1.22789			0.613947	−	0.789347i	$-0.289581\pi$
$181$	16.5196			1.22789			0.613947	+	0.789347i	$0.289581\pi$
$182$	−5.35868	+	3.06438i	−0.397212	+	0.227147i
$183$		0			0
$184$	−9.16544	+	15.8750i	−0.675685	+	1.17032i
$185$	0.349993	+	0.606205i	0.0257320	+	0.0445691i
$186$		0			0
$187$	−0.0583043	+	0.100986i	−0.00426363	+	0.00738482i
$188$	−0.690037			−0.0503261
$189$		0			0
$190$	−12.7785			−0.927048
$191$	−8.20479	+	14.2111i	−0.593678	+	1.02828i	0.400054	+	0.916492i	$0.368991\pi$
$191$	−8.20479	+	14.2111i	−0.593678	+	1.02828i	−0.993732	+	0.111789i	$0.964342\pi$
$192$		0			0
$193$	−10.3266	−	17.8862i	−0.743326	−	1.28748i	−0.950973	−	0.309274i	$-0.899914\pi$
$193$	−10.3266	−	17.8862i	−0.743326	−	1.28748i	0.207647	−	0.978204i	$-0.433420\pi$
$194$	12.4436	−	21.5529i	0.893397	−	1.54741i
$195$		0			0
$196$	1.06504	−	1.81000i	0.0760746	−	0.129286i
$197$	−26.3132			−1.87474			−0.937368	−	0.348342i	$-0.886745\pi$
$197$	−26.3132			−1.87474			−0.937368	+	0.348342i	$0.886745\pi$
$198$		0			0
$199$	5.50528	+	9.53543i	0.390259	+	0.675949i	0.992484	−	0.122378i	$-0.0390520\pi$
$199$	5.50528	+	9.53543i	0.390259	+	0.675949i	−0.602224	+	0.798327i	$0.705719\pi$
$200$	0.571967	+	0.990675i	0.0404442	+	0.0700513i
$201$		0			0
$202$	−14.6427			−1.03025
$203$	11.5548	+	6.73497i	0.810987	+	0.472702i
$204$		0			0
$205$	9.57160	−	16.5785i	0.668510	−	1.15789i
$206$	−6.68821	−	11.5843i	−0.465990	−	0.807118i
$207$		0			0
$208$	−3.46921	+	6.00884i	−0.240546	+	0.416638i
$209$	−3.61132			−0.249800
$210$		0			0
$211$	22.2476			1.53159			0.765793	−	0.643087i	$-0.222347\pi$
$211$	22.2476			1.53159			0.765793	+	0.643087i	$0.222347\pi$
$212$	−1.78312	+	3.08846i	−0.122465	+	0.212116i
$213$		0			0
$214$	7.95002	+	13.7698i	0.543452	+	0.941287i
$215$	4.87975	−	8.45197i	0.332796	−	0.576420i
$216$		0			0
$217$	0.0478499	−	11.5801i	0.00324827	−	0.786108i
$218$	15.9664			1.08138
$219$		0			0
$220$	−0.349993	−	0.606205i	−0.0235965	−	0.0408704i
$221$	0.0896979	+	0.155361i	0.00603373	+	0.0104507i
$222$		0			0
$223$	−16.8020			−1.12515			−0.562573	−	0.826748i	$-0.690188\pi$
$223$	−16.8020			−1.12515			−0.562573	+	0.826748i	$0.690188\pi$
$224$	0.0184044	−	4.45402i	0.00122970	−	0.297597i
$225$		0			0
$226$	8.66927	−	15.0156i	0.576671	−	0.998823i
$227$	2.71008	+	4.69399i	0.179874	+	0.311551i	0.941837	−	0.336069i	$-0.109098\pi$
$227$	2.71008	+	4.69399i	0.179874	+	0.311551i	−0.761963	+	0.647620i	$0.775764\pi$
$228$		0			0
$229$	−14.1161	+	24.4499i	−0.932820	+	1.61569i	−0.154345	+	0.988017i	$0.549327\pi$
$229$	−14.1161	+	24.4499i	−0.932820	+	1.61569i	−0.778476	+	0.627675i	$0.784007\pi$
$230$	−25.1585			−1.65890
$231$		0			0
$232$	13.0327			0.855637
$233$	2.80566	−	4.85955i	0.183805	−	0.318360i	−0.759368	−	0.650661i	$-0.774492\pi$
$233$	2.80566	−	4.85955i	0.183805	−	0.318360i	0.943173	+	0.332302i	$0.107825\pi$
$234$		0			0
$235$	2.68317	+	4.64738i	0.175031	+	0.303162i
$236$	0.743476	−	1.28774i	0.0483962	−	0.0838246i
$237$		0			0
$238$	−0.404235	−	0.235618i	−0.0262027	−	0.0152728i
$239$	−12.0153			−0.777205			−0.388603	−	0.921405i	$-0.627042\pi$
$239$	−12.0153			−0.777205			−0.388603	+	0.921405i	$0.627042\pi$
$240$		0			0
$241$	10.3663	+	17.9550i	0.667754	+	1.15658i	0.978531	+	0.206101i	$0.0660776\pi$
$241$	10.3663	+	17.9550i	0.667754	+	1.15658i	−0.310776	+	0.950483i	$0.600589\pi$
$242$	−0.758290	−	1.31340i	−0.0487447	−	0.0844283i
$243$		0			0
$244$	−1.37155			−0.0878043
$245$	−16.3317	−	0.134970i	−1.04339	−	0.00862291i
$246$		0			0
$247$	−2.77791	+	4.81148i	−0.176754	+	0.306147i
$248$	−5.64219	−	9.77256i	−0.358279	−	0.620558i
$249$		0			0
$250$	8.06111	−	13.9622i	0.509829	−	0.883050i
$251$	27.2885			1.72243			0.861217	−	0.508237i	$-0.169703\pi$
$251$	27.2885			1.72243			0.861217	+	0.508237i	$0.169703\pi$
$252$		0			0
$253$	−7.11005			−0.447005
$254$	−0.178121	+	0.308514i	−0.0111763	+	0.0193579i
$255$		0			0
$256$	−3.52321	−	6.10238i	−0.220201	−	0.381399i
$257$	4.45099	−	7.70933i	0.277645	−	0.480895i	−0.693154	−	0.720789i	$-0.743779\pi$
$257$	4.45099	−	7.70933i	0.277645	−	0.480895i	0.970799	+	0.239894i	$0.0771128\pi$
$258$		0			0
$259$	−0.689053	+	0.394038i	−0.0428157	+	0.0244843i
$260$	−1.07689			−0.0667858
$261$		0			0
$262$	−4.36664	−	7.56325i	−0.269772	−	0.467259i
$263$	−1.12790	−	1.95359i	−0.0695495	−	0.120463i	0.829154	−	0.559021i	$-0.188823\pi$
$263$	−1.12790	−	1.95359i	−0.0695495	−	0.120463i	−0.898703	+	0.438558i	$0.855490\pi$
$264$		0			0
$265$	27.7343			1.70370
$266$	0.0598751	−	14.4903i	0.00367118	−	0.888456i
$267$		0			0
$268$	−1.84350	+	3.19304i	−0.112610	+	0.195046i
$269$	4.18444	+	7.24767i	0.255130	+	0.441898i	0.964931	−	0.262504i	$-0.0845484\pi$
$269$	4.18444	+	7.24767i	0.255130	+	0.441898i	−0.709801	+	0.704402i	$0.751215\pi$
$270$		0			0
$271$	−4.44734	+	7.70302i	−0.270157	+	0.467925i	−0.968902	−	0.247445i	$-0.920409\pi$
$271$	−4.44734	+	7.70302i	−0.270157	+	0.467925i	0.698745	+	0.715371i	$0.253742\pi$
$272$	−0.525907			−0.0318878
$273$		0			0
$274$	−24.3965			−1.47384
$275$	−0.221850	+	0.384256i	−0.0133781	+	0.0231715i
$276$		0			0
$277$	2.69999	+	4.67651i	0.162226	+	0.280984i	0.935667	−	0.352885i	$-0.114799\pi$
$277$	2.69999	+	4.67651i	0.162226	+	0.280984i	−0.773440	+	0.633869i	$0.781466\pi$
$278$	10.8382	−	18.7723i	0.650033	−	1.12589i
$279$		0			0
$280$	−13.8156	+	7.90048i	−0.825638	+	0.472144i
$281$	19.7416			1.17768			0.588841	−	0.808249i	$-0.299584\pi$
$281$	19.7416			1.17768			0.588841	+	0.808249i	$0.299584\pi$
$282$		0			0
$283$	5.05259	+	8.75133i	0.300345	+	0.520213i	0.976214	−	0.216809i	$-0.0695649\pi$
$283$	5.05259	+	8.75133i	0.300345	+	0.520213i	−0.675869	+	0.737022i	$0.736232\pi$
$284$	0.638473	+	1.10587i	0.0378864	+	0.0656212i
$285$		0			0
$286$	−2.33317			−0.137963
$287$	18.7545	+	10.9315i	1.10705	+	0.645267i
$288$		0			0
$289$	8.49320	−	14.7107i	0.499600	−	0.865333i
$290$	8.94346	+	15.4905i	0.525178	+	0.909635i
$291$		0			0
$292$	−1.56578	+	2.71200i	−0.0916301	+	0.158708i
$293$	16.1108			0.941201			0.470601	−	0.882346i	$-0.344037\pi$
$293$	16.1108			0.941201			0.470601	+	0.882346i	$0.344037\pi$
$294$		0			0
$295$	−11.5638			−0.673273
$296$	−0.386743	+	0.669859i	−0.0224790	+	0.0389347i
$297$		0			0
$298$	−0.510259	−	0.883795i	−0.0295585	−	0.0511969i
$299$	−5.46921	+	9.47295i	−0.316292	+	0.547835i
$300$		0			0
$301$	9.56135	+	5.57305i	0.551107	+	0.321225i
$302$	36.0527			2.07460
$303$		0			0
$304$	−8.14357	−	14.1051i	−0.467066	−	0.808982i
$305$	5.33317	+	9.23733i	0.305377	+	0.528928i
$306$		0			0
$307$	27.8168			1.58759			0.793795	−	0.608185i	$-0.208102\pi$
$307$	27.8168			1.58759			0.793795	+	0.608185i	$0.208102\pi$
$308$	0.689053	−	0.394038i	0.0392625	−	0.0224524i
$309$		0			0
$310$	7.74372	−	13.4125i	0.439813	−	0.761779i
$311$	4.52139	+	7.83127i	0.256384	+	0.444071i	0.965271	−	0.261252i	$-0.0841354\pi$
$311$	4.52139	+	7.83127i	0.256384	+	0.444071i	−0.708886	+	0.705323i	$0.750802\pi$
$312$		0			0
$313$	8.08842	−	14.0096i	0.457185	−	0.791867i	−0.541626	−	0.840619i	$-0.682191\pi$
$313$	8.08842	−	14.0096i	0.457185	−	0.791867i	0.998811	+	0.0487523i	$0.0155245\pi$
$314$	−23.1366			−1.30568
$315$		0			0
$316$	4.29466			0.241593
$317$	−2.61685	+	4.53251i	−0.146977	+	0.254571i	−0.930109	−	0.367284i	$-0.880288\pi$
$317$	−2.61685	+	4.53251i	−0.146977	+	0.254571i	0.783132	+	0.621856i	$0.213621\pi$
$318$		0			0
$319$	2.52751	+	4.37778i	0.141514	+	0.245109i
$320$	−7.54422	+	13.0670i	−0.421734	+	0.730466i
$321$		0			0
$322$	0.117883	−	28.5288i	0.00656938	−	1.58985i
$323$	−0.421111			−0.0234312
$324$		0			0
$325$	0.341305	+	0.591157i	0.0189322	+	0.0327915i
$326$	−0.318962	−	0.552458i	−0.0176657	−	0.0305978i
$327$		0			0
$328$	21.1533			1.16800
$329$	−5.28252	+	3.02083i	−0.291235	+	0.166544i
$330$		0			0
$331$	9.76510	−	16.9137i	0.536739	−	0.929658i	−0.462338	−	0.886704i	$-0.652989\pi$
$331$	9.76510	−	16.9137i	0.536739	−	0.929658i	0.999077	−	0.0429549i	$-0.0136772\pi$
$332$	−1.67812	−	2.90659i	−0.0920988	−	0.159520i
$333$		0			0
$334$	12.4611	−	21.5832i	0.681840	−	1.18098i
$335$	28.6734			1.56660
$336$		0			0
$337$	−0.243643			−0.0132721			−0.00663605	−	0.999978i	$-0.502112\pi$
$337$	−0.243643			−0.0132721			−0.00663605	+	0.999978i	$0.502112\pi$
$338$	8.06304	−	13.9656i	0.438572	−	0.759628i
$339$		0			0
$340$	−0.0408121	−	0.0706887i	−0.00221335	−	0.00383363i
$341$	2.18845	−	3.79051i	0.118511	−	0.205268i
$342$		0			0
$343$	0.229575	−	18.5188i	0.0123959	−	0.999923i
$344$	10.7843			0.581449
$345$		0			0
$346$	2.92816	+	5.07172i	0.157419	+	0.272657i
$347$	11.0805	+	19.1920i	0.594834	+	1.03028i	0.993570	+	0.113217i	$0.0361156\pi$
$347$	11.0805	+	19.1920i	0.594834	+	1.03028i	−0.398736	+	0.917066i	$0.630551\pi$
$348$		0			0
$349$	−16.1822			−0.866213			−0.433107	−	0.901343i	$-0.642583\pi$
$349$	−16.1822			−0.866213			−0.433107	+	0.901343i	$0.642583\pi$
$350$	−1.53813	−	0.896537i	−0.0822167	−	0.0479219i
$351$		0			0
$352$	0.841739	−	1.45793i	0.0448648	−	0.0777082i
$353$	−3.88844	−	6.73497i	−0.206961	−	0.358466i	0.743795	−	0.668408i	$-0.233024\pi$
$353$	−3.88844	−	6.73497i	−0.206961	−	0.358466i	−0.950756	+	0.309941i	$0.899691\pi$
$354$		0			0
$355$	4.96533	−	8.60020i	0.263532	−	0.456451i
$356$	−4.18002			−0.221540
$357$		0			0
$358$	19.2751			1.01872
$359$	5.40642	−	9.36420i	0.285340	−	0.494223i	−0.687352	−	0.726325i	$-0.741227\pi$
$359$	5.40642	−	9.36420i	0.285340	−	0.494223i	0.972692	+	0.232102i	$0.0745602\pi$
$360$		0			0
$361$	2.97917	+	5.16008i	0.156798	+	0.271583i
$362$	−12.5267	+	21.6968i	−0.658387	+	1.14036i
$363$		0			0
$364$	0.00504590	−	1.22115i	0.000264477	−	0.0640057i
$365$	24.3537			1.27473
$366$		0			0
$367$	0.878346	+	1.52134i	0.0458493	+	0.0794133i	0.888039	−	0.459768i	$-0.152067\pi$
$367$	0.878346	+	1.52134i	0.0458493	+	0.0794133i	−0.842190	+	0.539181i	$0.818734\pi$
$368$	−16.0332	−	27.7704i	−0.835790	−	1.44763i
$369$		0			0
$370$	−1.06158			−0.0551891
$371$	−0.129952	+	31.4496i	−0.00674679	+	1.63278i
$372$		0			0
$373$	4.63683	−	8.03123i	0.240086	−	0.415841i	−0.720653	−	0.693296i	$-0.756158\pi$
$373$	4.63683	−	8.03123i	0.240086	−	0.415841i	0.960739	+	0.277455i	$0.0894910\pi$
$374$	−0.0884231	−	0.153153i	−0.00457225	−	0.00791936i
$375$		0			0
$376$	−2.96491	+	5.13537i	−0.152903	+	0.264836i
$377$	7.77687			0.400529
$378$		0			0
$379$	−11.5130			−0.591386			−0.295693	−	0.955283i	$-0.595550\pi$
$379$	−11.5130			−0.591386			−0.295693	+	0.955283i	$0.595550\pi$
$380$	1.26394	−	2.18920i	0.0648386	−	0.112304i
$381$		0			0
$382$	−12.4432	−	21.5523i	−0.636651	−	1.10271i
$383$	−11.2392	+	19.4669i	−0.574298	+	0.994713i	0.421820	+	0.906680i	$0.361391\pi$
$383$	−11.2392	+	19.4669i	−0.574298	+	0.994713i	−0.996118	+	0.0880331i	$0.971942\pi$
$384$		0			0
$385$	−5.33317	−	3.10856i	−0.271804	−	0.158427i
$386$	31.3223			1.59426
$387$		0			0
$388$	2.46163	+	4.26366i	0.124970	+	0.216455i
$389$	−17.1663	−	29.7329i	−0.870365	−	1.50752i	−0.861620	−	0.507554i	$-0.830550\pi$
$389$	−17.1663	−	29.7329i	−0.870365	−	1.50752i	−0.00874493	−	0.999962i	$-0.502784\pi$
$390$		0			0
$391$	−0.829092			−0.0419290
$392$	−8.89410	−	15.7033i	−0.449220	−	0.793138i
$393$		0			0
$394$	19.9530	−	34.5596i	1.00522	−	1.74109i
$395$	−16.6995	−	28.9244i	−0.840243	−	1.45534i
$396$		0			0
$397$	4.89980	−	8.48671i	0.245914	−	0.425936i	−0.716474	−	0.697614i	$-0.754245\pi$
$397$	4.89980	−	8.48671i	0.245914	−	0.425936i	0.962388	+	0.271678i	$0.0875785\pi$
$398$	−16.6984			−0.837016
$399$		0			0
$400$	−2.00110			−0.100055
$401$	1.73819	−	3.01064i	0.0868011	−	0.150344i	−0.819356	−	0.573285i	$-0.805669\pi$
$401$	1.73819	−	3.01064i	0.0868011	−	0.150344i	0.906157	+	0.422941i	$0.139002\pi$
$402$		0			0
$403$	−3.36681	−	5.83149i	−0.167713	−	0.290487i
$404$	1.44833	−	2.50858i	0.0720570	−	0.124806i
$405$		0			0
$406$	−17.6076	+	10.0690i	−0.873849	+	0.499714i
$407$	−0.300014			−0.0148712
$408$		0			0
$409$	−17.5609	−	30.4164i	−0.868332	−	1.50399i	−0.863700	−	0.504006i	$-0.831859\pi$
$409$	−17.5609	−	30.4164i	−0.868332	−	1.50399i	−0.00463138	−	0.999989i	$-0.501474\pi$
$410$	14.5161	+	25.1426i	0.716899	+	1.24171i
$411$		0			0
$412$	2.64616			0.130367
$413$	0.0541838	−	13.1129i	0.00266621	−	0.645246i
$414$		0			0
$415$	−13.0505	+	22.6042i	−0.640626	+	1.10960i
$416$	−1.29497	−	2.24295i	−0.0634911	−	0.109970i
$417$		0			0
$418$	2.73843	−	4.74310i	0.133941	−	0.231993i
$419$	−13.8100			−0.674664			−0.337332	−	0.941386i	$-0.609525\pi$
$419$	−13.8100			−0.674664			−0.337332	+	0.941386i	$0.609525\pi$
$420$		0			0
$421$	9.72050			0.473748			0.236874	−	0.971540i	$-0.423877\pi$
$421$	9.72050			0.473748			0.236874	+	0.971540i	$0.423877\pi$
$422$	−16.8701	+	29.2199i	−0.821224	+	1.42240i
$423$		0			0
$424$	15.3232	+	26.5406i	0.744161	+	1.28893i
$425$	−0.0258696	+	0.0448075i	−0.00125486	+	0.00217348i
$426$		0			0
$427$	−10.4998	+	6.00433i	−0.508119	+	0.290570i
$428$	−3.14539			−0.152038
$429$		0			0
$430$	7.40053	+	12.8181i	0.356885	+	0.618143i
$431$	−5.09584	−	8.82625i	−0.245458	−	0.425145i	0.716802	−	0.697276i	$-0.245605\pi$
$431$	−5.09584	−	8.82625i	−0.245458	−	0.425145i	−0.962260	+	0.272131i	$0.912272\pi$
$432$		0			0
$433$	−21.0101			−1.00968			−0.504840	−	0.863213i	$-0.668449\pi$
$433$	−21.0101			−1.00968			−0.504840	+	0.863213i	$0.668449\pi$
$434$	15.1730	+	8.84392i	0.728326	+	0.424522i
$435$		0			0
$436$	−1.57926	+	2.73535i	−0.0756327	+	0.131000i
$437$	−12.8383	−	22.2367i	−0.614141	−	1.06372i
$438$		0			0
$439$	−4.92336	+	8.52751i	−0.234979	+	0.406996i	−0.959267	−	0.282502i	$-0.908836\pi$
$439$	−4.92336	+	8.52751i	−0.234979	+	0.406996i	0.724287	+	0.689498i	$0.242169\pi$
$440$	−6.01531			−0.286768
$441$		0			0
$442$	−0.272068			−0.0129410
$443$	7.77560	−	13.4677i	0.369430	−	0.639871i	−0.620047	−	0.784565i	$-0.712886\pi$
$443$	7.77560	−	13.4677i	0.369430	−	0.639871i	0.989477	+	0.144694i	$0.0462197\pi$
$444$		0			0
$445$	16.2537	+	28.1523i	0.770501	+	1.33455i
$446$	12.7408	−	22.0677i	0.603294	−	1.04494i
$447$		0			0
$448$	−14.7821	−	8.61607i	−0.698388	−	0.407071i
$449$	−2.62021			−0.123655			−0.0618277	−	0.998087i	$-0.519693\pi$
$449$	−2.62021			−0.123655			−0.0618277	+	0.998087i	$0.519693\pi$
$450$		0			0
$451$	4.10240	+	7.10556i	0.193174	+	0.334588i
$452$	1.71498	+	2.97043i	0.0806659	+	0.139717i
$453$		0			0
$454$	−8.22010			−0.385788
$455$	−8.24403	+	4.71438i	−0.386486	+	0.221014i
$456$		0			0
$457$	−3.81295	+	6.60423i	−0.178362	+	0.308933i	−0.941320	−	0.337516i	$-0.890413\pi$
$457$	−3.81295	+	6.60423i	−0.178362	+	0.308933i	0.762957	+	0.646449i	$0.223747\pi$
$458$	−21.4082	−	37.0802i	−1.00034	−	1.73264i
$459$		0			0
$460$	2.48847	−	4.31015i	0.116025	−	0.200962i
$461$	12.7392			0.593325			0.296662	−	0.954982i	$-0.404126\pi$
$461$	12.7392			0.593325			0.296662	+	0.954982i	$0.404126\pi$
$462$		0			0
$463$	−8.76838			−0.407501			−0.203751	−	0.979023i	$-0.565313\pi$
$463$	−8.76838			−0.407501			−0.203751	+	0.979023i	$0.565313\pi$
$464$	−11.3991	+	19.7439i	−0.529191	+	0.916586i
$465$		0			0
$466$	4.25501	+	7.36989i	0.197110	+	0.341404i
$467$	−9.68413	+	16.7734i	−0.448128	+	0.776181i	−0.998264	−	0.0588943i	$-0.981243\pi$
$467$	−9.68413	+	16.7734i	−0.448128	+	0.776181i	0.550136	+	0.835075i	$0.314576\pi$
$468$		0			0
$469$	−0.134353	+	32.5145i	−0.00620384	+	1.50138i
$470$	−8.13847			−0.375400
$471$		0			0
$472$	−6.38904	−	11.0661i	−0.294079	−	0.509360i
$473$	2.09146	+	3.62252i	0.0961656	+	0.166564i
$474$		0			0
$475$	−1.60235			−0.0735207
$476$	0.0803495	−	0.0459482i	0.00368281	−	0.00210603i
$477$		0			0
$478$	9.11108	−	15.7809i	0.416731	−	0.721800i
$479$	12.0995	+	20.9569i	0.552839	+	0.957546i	0.998068	+	0.0621289i	$0.0197890\pi$
$479$	12.0995	+	20.9569i	0.552839	+	0.957546i	−0.445229	+	0.895417i	$0.646878\pi$
$480$		0			0
$481$	−0.230778	+	0.399719i	−0.0105226	+	0.0182256i
$482$	−31.4427			−1.43218
$483$		0			0
$484$	0.300014			0.0136370
$485$	19.1438	−	33.1580i	0.869274	−	1.50563i
$486$		0			0
$487$	10.6093	+	18.3759i	0.480755	+	0.832692i	0.999756	−	0.0220818i	$-0.00702942\pi$
$487$	10.6093	+	18.3759i	0.480755	+	0.832692i	−0.519001	+	0.854773i	$0.673696\pi$
$488$	−5.89317	+	10.2073i	−0.266771	+	0.462062i
$489$		0			0
$490$	12.5614	−	21.3476i	0.567466	−	0.964386i
$491$	28.2038			1.27282			0.636411	−	0.771350i	$-0.280418\pi$
$491$	28.2038			1.27282			0.636411	+	0.771350i	$0.280418\pi$
$492$		0			0
$493$	0.294729	+	0.510486i	0.0132739	+	0.0229911i
$494$	−4.21292	−	7.29700i	−0.189548	−	0.328307i
$495$		0			0
$496$	19.7399			0.886349
$497$	9.72902	+	5.67078i	0.436406	+	0.254369i
$498$		0			0
$499$	17.7490	−	30.7422i	0.794555	−	1.37621i	−0.128567	−	0.991701i	$-0.541038\pi$
$499$	17.7490	−	30.7422i	0.794555	−	1.37621i	0.923122	−	0.384508i	$-0.125629\pi$
$500$	1.59467	+	2.76205i	0.0713159	+	0.123523i
$501$		0			0
$502$	−20.6926	+	35.8406i	−0.923555	+	1.59964i
$503$	−16.0477			−0.715529			−0.357765	−	0.933812i	$-0.616461\pi$
$503$	−16.0477			−0.715529			−0.357765	+	0.933812i	$0.616461\pi$
$504$		0			0
$505$	−22.5269			−1.00243
$506$	5.39148	−	9.33831i	0.239680	−	0.415139i
$507$		0			0
$508$	−0.0352364	−	0.0610313i	−0.00156336	−	0.00270782i
$509$	4.10652	−	7.11270i	0.182018	−	0.315265i	−0.760550	−	0.649280i	$-0.775070\pi$
$509$	4.10652	−	7.11270i	0.182018	−	0.315265i	0.942568	+	0.334015i	$0.108404\pi$
$510$		0			0
$511$	−0.114112	+	27.6161i	−0.00504803	+	1.22167i
$512$	−15.6626			−0.692197
$513$		0			0
$514$	6.75027	+	11.6918i	0.297742	+	0.515704i
$515$	−10.2894	−	17.8218i	−0.453407	−	0.785324i
$516$		0			0
$517$	−2.30001			−0.101155
$518$	0.00497418	−	1.20380i	0.000218553	−	0.0528917i
$519$		0			0
$520$	−4.62711	+	8.01438i	−0.202912	+	0.351454i
$521$	−4.27767	−	7.40914i	−0.187408	−	0.324601i	0.756977	−	0.653441i	$-0.226675\pi$
$521$	−4.27767	−	7.40914i	−0.187408	−	0.324601i	−0.944385	+	0.328841i	$0.893342\pi$
$522$		0			0
$523$	−15.0185	+	26.0128i	−0.656712	+	1.13746i	0.324750	+	0.945800i	$0.394720\pi$
$523$	−15.0185	+	26.0128i	−0.656712	+	1.13746i	−0.981462	+	0.191658i	$0.938613\pi$
$524$	1.72765			0.0754725
$525$		0			0
$526$	3.42111			0.149168
$527$	0.255192	−	0.442006i	0.0111163	−	0.0192541i
$528$		0			0
$529$	−13.7764	−	23.8614i	−0.598974	−	1.03745i
$530$	−21.0306	+	36.4261i	−0.913511	+	1.58225i
$531$		0			0
$532$	2.47655	+	1.44351i	0.107372	+	0.0625843i
$533$	12.6226			0.546746
$534$		0			0
$535$	12.2307	+	21.1841i	0.528778	+	0.915870i
$536$	15.8421	+	27.4393i	0.684275	+	1.18520i
$537$		0			0
$538$	−12.6921			−0.547194
$539$	3.54998	−	6.03305i	0.152908	−	0.259862i
$540$		0			0
$541$	−9.50845	+	16.4691i	−0.408800	+	0.708063i	−0.994756	−	0.102281i	$-0.967386\pi$
$541$	−9.50845	+	16.4691i	−0.408800	+	0.708063i	0.585955	+	0.810343i	$0.300719\pi$
$542$	−6.74475	−	11.6823i	−0.289712	−	0.501796i
$543$		0			0
$544$	0.0981539	−	0.170008i	0.00420831	−	0.00728901i
$545$	24.5634			1.05218
$546$		0			0
$547$	34.4968			1.47498			0.737489	−	0.675360i	$-0.236012\pi$
$547$	34.4968			1.47498			0.737489	+	0.675360i	$0.236012\pi$
$548$	2.41309	−	4.17960i	0.103082	−	0.178543i
$549$		0			0
$550$	−0.336454	−	0.582755i	−0.0143464	−	0.0248488i
$551$	−9.12766	+	15.8096i	−0.388852	+	0.673511i
$552$		0			0
$553$	32.8774	−	18.8011i	1.39809	−	0.799503i
$554$	−8.18949			−0.347938
$555$		0			0
$556$	2.14405	+	3.71360i	0.0909279	+	0.157492i
$557$	2.71456	+	4.70176i	0.115020	+	0.199220i	0.917788	−	0.397072i	$-0.129974\pi$
$557$	2.71456	+	4.70176i	0.115020	+	0.199220i	−0.802768	+	0.596292i	$0.796640\pi$
$558$		0			0
$559$	6.43520			0.272180
$560$	0.115038	−	27.8401i	0.00486123	−	1.17646i
$561$		0			0
$562$	−14.9698	+	25.9285i	−0.631464	+	1.09373i
$563$	−17.0841	−	29.5905i	−0.720007	−	1.24709i	−0.960996	−	0.276562i	$-0.910805\pi$
$563$	−17.0841	−	29.5905i	−0.720007	−	1.24709i	0.240989	−	0.970528i	$-0.422528\pi$
$564$		0			0
$565$	13.3372	−	23.1007i	0.561100	−	0.971853i
$566$	−15.3253			−0.644170
$567$		0			0
$568$	10.9734			0.460434
$569$	−8.29626	+	14.3695i	−0.347797	+	0.602402i	−0.985858	−	0.167584i	$-0.946404\pi$
$569$	−8.29626	+	14.3695i	−0.347797	+	0.602402i	0.638061	+	0.769986i	$0.279737\pi$
$570$		0			0
$571$	−6.96720	−	12.0675i	−0.291568	−	0.505011i	0.682612	−	0.730781i	$-0.260844\pi$
$571$	−6.96720	−	12.0675i	−0.291568	−	0.505011i	−0.974181	+	0.225769i	$0.927510\pi$
$572$	0.230778	−	0.399719i	0.00964930	−	0.0167131i
$573$		0			0
$574$	−28.5788	+	16.3429i	−1.19286	+	0.682139i
$575$	−3.15473			−0.131562
$576$		0			0
$577$	−22.8387	−	39.5578i	−0.950788	−	1.64681i	−0.743726	−	0.668485i	$-0.766943\pi$
$577$	−22.8387	−	39.5578i	−0.950788	−	1.64681i	−0.207062	−	0.978328i	$-0.566390\pi$
$578$	12.8806	+	22.3099i	0.535763	+	0.927969i
$579$		0			0
$580$	−3.53844			−0.146926
$581$	−25.5711	−	14.9047i	−1.06087	−	0.618352i
$582$		0			0
$583$	−5.94346	+	10.2944i	−0.246153	+	0.426350i
$584$	13.4554	+	23.3055i	0.556790	+	0.964389i
$585$		0			0
$586$	−12.2166	+	21.1598i	−0.504665	+	0.874105i
$587$	−29.3966			−1.21333			−0.606664	−	0.794958i	$-0.707493\pi$
$587$	−29.3966			−1.21333			−0.606664	+	0.794958i	$0.707493\pi$
$588$		0			0
$589$	15.8064			0.651292
$590$	8.76874	−	15.1879i	0.361003	−	0.625276i
$591$		0			0
$592$	−0.676535	−	1.17179i	−0.0278054	−	0.0481604i
$593$	−0.912178	+	1.57994i	−0.0374587	+	0.0648803i	−0.884147	−	0.467209i	$-0.845260\pi$
$593$	−0.912178	+	1.57994i	−0.0374587	+	0.0648803i	0.846688	+	0.532089i	$0.178593\pi$
$594$		0			0
$595$	−0.621893	−	0.362485i	−0.0254951	−	0.0148604i
$596$	0.201882			0.00826941
$597$		0			0
$598$	−8.29449	−	14.3665i	−0.339187	−	0.587489i
$599$	−11.2497	−	19.4851i	−0.459651	−	0.796139i	0.539291	−	0.842119i	$-0.318692\pi$
$599$	−11.2497	−	19.4851i	−0.459651	−	0.796139i	−0.998942	+	0.0459800i	$0.985359\pi$
$600$		0			0
$601$	−10.3352			−0.421583			−0.210792	−	0.977531i	$-0.567604\pi$
$601$	−10.3352			−0.421583			−0.210792	+	0.977531i	$0.567604\pi$
$602$	−14.5699	+	8.33185i	−0.593825	+	0.339581i
$603$		0			0
$604$	−3.56603	+	6.17654i	−0.145100	+	0.251320i
$605$	−1.16659	−	2.02059i	−0.0474285	−	0.0821486i
$606$		0			0
$607$	16.3137	−	28.2562i	0.662155	−	1.14689i	−0.317894	−	0.948126i	$-0.602976\pi$
$607$	16.3137	−	28.2562i	0.662155	−	1.14689i	0.980048	−	0.198759i	$-0.0636911\pi$
$608$	6.07958			0.246560
$609$		0			0
$610$	−16.1764			−0.654962
$611$	−1.76922	+	3.06438i	−0.0715751	+	0.123972i
$612$		0			0
$613$	3.19350	+	5.53130i	0.128984	+	0.223407i	0.923283	−	0.384120i	$-0.125495\pi$
$613$	3.19350	+	5.53130i	0.128984	+	0.223407i	−0.794299	+	0.607527i	$0.792162\pi$
$614$	−21.0932	+	36.5345i	−0.851253	+	1.47441i
$615$		0			0
$616$	0.0281855	−	6.82112i	0.00113562	−	0.274831i
$617$	−4.14609			−0.166915			−0.0834577	−	0.996511i	$-0.526596\pi$
$617$	−4.14609			−0.166915			−0.0834577	+	0.996511i	$0.526596\pi$
$618$		0			0
$619$	19.2980	+	33.4252i	0.775653	+	1.34347i	0.934427	+	0.356155i	$0.115913\pi$
$619$	19.2980	+	33.4252i	0.775653	+	1.34347i	−0.158774	+	0.987315i	$0.550754\pi$
$620$	1.53188	+	2.65330i	0.0615220	+	0.106559i
$621$		0			0
$622$	−13.7141			−0.549885
$623$	−31.9998	+	18.2992i	−1.28204	+	0.733142i
$624$		0			0
$625$	13.5108	−	23.4014i	0.540433	−	0.936057i
$626$	12.2667	+	21.2466i	0.490278	+	0.849186i
$627$		0			0
$628$	2.28848	−	3.96376i	0.0913203	−	0.158171i
$629$	−0.0349842			−0.00139491
$630$		0			0
$631$	−8.89990			−0.354299			−0.177150	−	0.984184i	$-0.556688\pi$
$631$	−8.89990			−0.354299			−0.177150	+	0.984184i	$0.556688\pi$
$632$	18.4530	−	31.9615i	0.734021	−	1.27136i
$633$		0			0
$634$	−3.96866	−	6.87392i	−0.157616	−	0.272998i
$635$	−0.274029	+	0.474632i	−0.0108745	+	0.0188352i
$636$		0			0
$637$	−5.30730	−	9.37050i	−0.210283	−	0.371273i
$638$	−7.66635			−0.303514
$639$		0			0
$640$	−15.3693	−	26.6203i	−0.607523	−	1.05226i
$641$	18.6648	+	32.3284i	0.737217	+	1.27690i	0.953744	+	0.300620i	$0.0971936\pi$
$641$	18.6648	+	32.3284i	0.737217	+	1.27690i	−0.216527	+	0.976277i	$0.569473\pi$
$642$		0			0
$643$	15.9206			0.627846			0.313923	−	0.949449i	$-0.398357\pi$
$643$	15.9206			0.627846			0.313923	+	0.949449i	$0.398357\pi$
$644$	4.87588	+	2.84202i	0.192137	+	0.111991i
$645$		0			0
$646$	0.319324	−	0.553086i	0.0125636	−	0.0217609i
$647$	8.77640	+	15.2012i	0.345036	+	0.597619i	0.985360	−	0.170485i	$-0.0545335\pi$
$647$	8.77640	+	15.2012i	0.345036	+	0.597619i	−0.640325	+	0.768105i	$0.721200\pi$
$648$		0			0
$649$	2.47814	−	4.29226i	0.0972753	−	0.168486i
$650$	−1.03523			−0.0406051
$651$		0			0
$652$	0.126196			0.00494221
$653$	−11.9829	+	20.7549i	−0.468926	+	0.812204i	−0.999369	−	0.0355170i	$-0.988692\pi$
$653$	−11.9829	+	20.7549i	−0.468926	+	0.812204i	0.530443	+	0.847721i	$0.322026\pi$
$654$		0			0
$655$	−6.71784	−	11.6356i	−0.262488	−	0.454642i
$656$	−18.5019	+	32.0462i	−0.722377	+	1.25119i
$657$		0			0
$658$	0.0381338	−	9.22871i	0.00148661	−	0.359773i
$659$	38.6166			1.50429			0.752144	−	0.658999i	$-0.229020\pi$
$659$	38.6166			1.50429			0.752144	+	0.658999i	$0.229020\pi$
$660$		0			0
$661$	−5.18942	−	8.98833i	−0.201845	−	0.349606i	0.747278	−	0.664512i	$-0.231360\pi$
$661$	−5.18942	−	8.98833i	−0.201845	−	0.349606i	−0.949123	+	0.314906i	$0.898027\pi$
$662$	14.8096	+	25.6509i	0.575590	+	0.996951i
$663$		0			0
$664$	−28.8418			−1.11928
$665$	0.0921145	−	22.2925i	0.00357205	−	0.864466i
$666$		0			0
$667$	−17.9707	+	31.1262i	−0.695830	+	1.20521i
$668$	2.46509	+	4.26966i	0.0953771	+	0.165198i
$669$		0			0
$670$	−21.7428	+	37.6596i	−0.839996	+	1.45492i
$671$	−4.57160			−0.176485
$672$		0			0
$673$	−11.8103			−0.455253			−0.227627	−	0.973748i	$-0.573097\pi$
$673$	−11.8103			−0.455253			−0.227627	+	0.973748i	$0.573097\pi$
$674$	0.184752	−	0.320000i	0.00711640	−	0.0123260i
$675$		0			0
$676$	1.59505	+	2.76272i	0.0613483	+	0.106258i
$677$	20.9845	−	36.3462i	0.806499	−	1.39690i	−0.108776	−	0.994066i	$-0.534693\pi$
$677$	20.9845	−	36.3462i	0.806499	−	1.39690i	0.915275	−	0.402830i	$-0.131974\pi$
$678$		0			0
$679$	37.5102	+	21.8637i	1.43951	+	0.839050i
$680$	−0.701436			−0.0268988
$681$		0			0
$682$	3.31896	+	5.74861i	0.127090	+	0.220126i
$683$	12.0767	+	20.9174i	0.462100	+	0.800381i	0.999065	−	0.0432234i	$-0.0137627\pi$
$683$	12.0767	+	20.9174i	0.462100	+	0.800381i	−0.536965	+	0.843604i	$0.680429\pi$
$684$		0			0
$685$	−37.5326			−1.43405
$686$	24.1485	+	14.3442i	0.921994	+	0.547663i
$687$		0			0
$688$	−9.43254	+	16.3376i	−0.359612	+	0.622867i
$689$	9.14369	+	15.8373i	0.348347	+	0.603354i
$690$		0			0
$691$	2.63720	−	4.56776i	0.100324	−	0.173766i	−0.811494	−	0.584360i	$-0.801345\pi$
$691$	2.63720	−	4.56776i	0.100324	−	0.173766i	0.911818	+	0.410595i	$0.134679\pi$
$692$	−1.15851			−0.0440401
$693$		0			0
$694$	−33.6090			−1.27578
$695$	16.6740	−	28.8802i	0.632481	−	1.09549i
$696$		0			0
$697$	0.478374	+	0.828569i	0.0181197	+	0.0313843i
$698$	12.2708	−	21.2537i	0.464457	−	0.804463i
$699$		0			0
$700$	0.305733	−	0.174835i	0.0115556	−	0.00660814i
$701$	−26.9166			−1.01662			−0.508312	−	0.861173i	$-0.669730\pi$
$701$	−26.9166			−1.01662			−0.508312	+	0.861173i	$0.669730\pi$
$702$		0			0
$703$	−0.541724	−	0.938294i	−0.0204315	−	0.0353884i
$704$	−3.23346	−	5.60051i	−0.121865	−	0.211077i
$705$		0			0
$706$	11.7943			0.443883
$707$	0.105553	−	25.5447i	0.00396972	−	0.960705i
$708$		0			0
$709$	−5.87138	+	10.1695i	−0.220504	+	0.381925i	−0.954961	−	0.296731i	$-0.904104\pi$
$709$	−5.87138	+	10.1695i	−0.220504	+	0.381925i	0.734457	+	0.678655i	$0.237437\pi$
$710$	7.53031	+	13.0429i	0.282608	+	0.489491i
$711$		0			0
$712$	−17.9604	+	31.1084i	−0.673095	+	1.16584i
$713$	31.1200			1.16545
$714$		0			0
$715$	−3.58946			−0.134238
$716$	−1.90653	+	3.30221i	−0.0712504	+	0.123409i
$717$		0			0
$718$	8.19927	+	14.2015i	0.305994	+	0.529997i
$719$	14.0839	−	24.3941i	0.525242	−	0.909746i	−0.474326	−	0.880349i	$-0.657308\pi$
$719$	14.0839	−	24.3941i	0.525242	−	0.909746i	0.999568	−	0.0293966i	$-0.00935859\pi$
$720$		0			0
$721$	20.2575	−	11.5843i	0.754428	−	0.431423i
$722$	−9.03630			−0.336296
$723$		0			0
$724$	−2.47806	−	4.29213i	−0.0920965	−	0.159516i
$725$	1.12146	+	1.94242i	0.0416499	+	0.0721398i
$726$		0			0
$727$	32.9885			1.22347			0.611737	−	0.791061i	$-0.290471\pi$
$727$	32.9885			1.22347			0.611737	+	0.791061i	$0.290471\pi$
$728$	−9.06632	−	5.28451i	−0.336020	−	0.195857i
$729$		0			0
$730$	−18.4672	+	31.9861i	−0.683500	+	1.18386i
$731$	0.243882	+	0.422417i	0.00902032	+	0.0156237i
$732$		0			0
$733$	−0.953106	+	1.65083i	−0.0352038	+	0.0609747i	−0.883090	−	0.469203i	$-0.844541\pi$
$733$	−0.953106	+	1.65083i	−0.0352038	+	0.0609747i	0.847887	+	0.530177i	$0.177875\pi$
$734$	−2.66416			−0.0983360
$735$		0			0
$736$	11.9696			0.441206
$737$	−6.14472	+	10.6430i	−0.226344	+	0.392039i
$738$		0			0
$739$	18.9136	+	32.7594i	0.695749	+	1.20507i	0.969927	+	0.243394i	$0.0782609\pi$
$739$	18.9136	+	32.7594i	0.695749	+	1.20507i	−0.274178	+	0.961679i	$0.588406\pi$
$740$	0.105003	−	0.181870i	0.00385998	−	0.00668569i
$741$		0			0
$742$	−41.2072	−	24.0186i	−1.51276	−	0.881750i
$743$	−46.4995			−1.70590			−0.852950	−	0.521993i	$-0.825189\pi$
$743$	−46.4995			−1.70590			−0.852950	+	0.521993i	$0.825189\pi$
$744$		0			0
$745$	−0.785005	−	1.35967i	−0.0287604	−	0.0498144i
$746$	7.03212	+	12.1800i	0.257464	+	0.445941i
$747$		0			0
$748$	0.0349842			0.00127915
$749$	−24.0793	+	13.7698i	−0.879838	+	0.503139i
$750$		0			0
$751$	−2.07408	+	3.59242i	−0.0756843	+	0.131089i	−0.901384	−	0.433021i	$-0.857447\pi$
$751$	−2.07408	+	3.59242i	−0.0756843	+	0.131089i	0.825699	+	0.564110i	$0.190781\pi$
$752$	−5.18656	−	8.98338i	−0.189134	−	0.327590i
$753$		0			0
$754$	−5.89713	+	10.2141i	−0.214761	+	0.371976i
$755$	55.4651			2.01858
$756$		0			0
$757$	4.56418			0.165888			0.0829439	−	0.996554i	$-0.473568\pi$
$757$	4.56418			0.165888			0.0829439	+	0.996554i	$0.473568\pi$
$758$	8.73023	−	15.1212i	0.317096	−	0.549227i
$759$		0			0
$760$	−10.8616	−	18.8129i	−0.393992	−	0.682414i
$761$	−6.52544	+	11.3024i	−0.236547	+	0.409711i	−0.959721	−	0.280954i	$-0.909349\pi$
$761$	−6.52544	+	11.3024i	−0.236547	+	0.409711i	0.723174	+	0.690666i	$0.242682\pi$
$762$		0			0
$763$	−0.115095	+	27.8539i	−0.00416671	+	1.00838i
$764$	4.92311			0.178112
$765$		0			0
$766$	−17.0452	−	29.5231i	−0.615868	−	1.06671i
$767$	−3.81247	−	6.60340i	−0.137660	−	0.238435i
$768$		0			0
$769$	−4.40156			−0.158724			−0.0793622	−	0.996846i	$-0.525288\pi$
$769$	−4.40156			−0.158724			−0.0793622	+	0.996846i	$0.525288\pi$
$770$	8.12687	−	4.64738i	0.292872	−	0.167480i
$771$		0			0
$772$	−3.09813	+	5.36612i	−0.111504	+	0.193131i
$773$	11.2048	+	19.4073i	0.403008	+	0.698031i	0.994087	−	0.108583i	$-0.0346312\pi$
$773$	11.2048	+	19.4073i	0.403008	+	0.698031i	−0.591079	+	0.806614i	$0.701298\pi$
$774$		0			0
$775$	0.971018	−	1.68185i	0.0348800	−	0.0604139i
$776$	42.3078			1.51876
$777$		0			0
$778$	52.0681			1.86673
$779$	−14.8151	+	25.6605i	−0.530805	+	0.919382i
$780$		0			0
$781$	2.12814	+	3.68605i	0.0761509	+	0.131897i
$782$	0.628692	−	1.08893i

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.758290 + 1.31340i) q^{2} +(-0.150007 - 0.259820i) q^{4} +(-1.16659 + 2.02059i) q^{5} +(-2.28580 - 1.33233i) q^{7} -2.57816 q^{8} +O(q^{10})\)	\(q+(-0.758290 + 1.31340i) q^{2} +(-0.150007 - 0.259820i) q^{4} +(-1.16659 + 2.02059i) q^{5} +(-2.28580 - 1.33233i) q^{7} -2.57816 q^{8} +(-1.76922 - 3.06438i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.53844 q^{13} +(3.48318 - 1.99187i) q^{14} +(2.25501 - 3.90579i) q^{16} +(-0.0583043 - 0.100986i) q^{17} +(1.80566 - 3.12750i) q^{19} +0.699986 q^{20} +1.51658 q^{22} +(3.55502 - 6.15748i) q^{23} +(-0.221850 - 0.384256i) q^{25} +(1.16659 - 2.02059i) q^{26} +(-0.00327987 + 0.793757i) q^{28} -5.05502 q^{29} +(2.18845 + 3.79051i) q^{31} +(0.841739 + 1.45793i) q^{32} +0.176846 q^{34} +(5.35868 - 3.06438i) q^{35} +(0.150007 - 0.259820i) q^{37} +(2.73843 + 4.74310i) q^{38} +(3.00765 - 5.20941i) q^{40} -8.20479 q^{41} -4.18293 q^{43} +(-0.150007 + 0.259820i) q^{44} +(5.39148 + 9.33831i) q^{46} +(1.15001 - 1.99187i) q^{47} +(3.44978 + 6.09089i) q^{49} +0.672908 q^{50} +(0.230778 + 0.399719i) q^{52} +(-5.94346 - 10.2944i) q^{53} +2.33317 q^{55} +(5.89317 + 3.43497i) q^{56} +(3.83317 - 6.63925i) q^{58} +(2.47814 + 4.29226i) q^{59} +(2.28580 - 3.95913i) q^{61} -6.63792 q^{62} +6.46691 q^{64} +(1.79473 - 3.10856i) q^{65} +(-6.14472 - 10.6430i) q^{67} +(-0.0174921 + 0.0302972i) q^{68} +(-0.0386836 + 9.36176i) q^{70} -4.25628 q^{71} +(-5.21900 - 9.03958i) q^{73} +(0.227498 + 0.394038i) q^{74} -1.08345 q^{76} +(-0.0109324 + 2.64573i) q^{77} +(-7.15742 + 12.3970i) q^{79} +(5.26133 + 9.11289i) q^{80} +(6.22161 - 10.7761i) q^{82} +11.1869 q^{83} +0.272068 q^{85} +(3.17187 - 5.49384i) q^{86} +(1.28908 + 2.23276i) q^{88} +(6.96636 - 12.0661i) q^{89} +(3.51658 + 2.04972i) q^{91} -2.13312 q^{92} +(1.74408 + 3.02083i) q^{94} +(4.21292 + 7.29700i) q^{95} -16.4101 q^{97} +(-10.6157 - 0.0877314i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8	\( 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8} - 10 q^{10} - 4 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{17} - 4 q^{22} + 4 q^{23} - 4 q^{25} - 4 q^{26} - 22 q^{28} - 16 q^{29} + 12 q^{31} + 26 q^{32} - 32 q^{34} + 2 q^{35} + 4 q^{37} + 8 q^{38} + 6 q^{40} - 4 q^{41} + 36 q^{43} - 4 q^{44} + 14 q^{46} + 12 q^{47} - 4 q^{49} - 4 q^{50} + 6 q^{52} - 12 q^{53} - 8 q^{55} - 48 q^{56} + 4 q^{58} + 12 q^{59} - 2 q^{61} + 52 q^{62} + 112 q^{64} - 4 q^{65} - 28 q^{67} - 48 q^{68} - 32 q^{70} - 24 q^{71} - 6 q^{73} - 16 q^{74} - 36 q^{76} - 4 q^{77} - 2 q^{79} + 16 q^{80} + 12 q^{82} + 24 q^{83} + 36 q^{85} + 36 q^{86} + 12 q^{88} + 8 q^{89} + 12 q^{91} + 32 q^{92} - 20 q^{94} + 34 q^{95} - 88 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8 - 10 * q^10 - 4 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^17 - 4 * q^22 + 4 * q^23 - 4 * q^25 - 4 * q^26 - 22 * q^28 - 16 * q^29 + 12 * q^31 + 26 * q^32 - 32 * q^34 + 2 * q^35 + 4 * q^37 + 8 * q^38 + 6 * q^40 - 4 * q^41 + 36 * q^43 - 4 * q^44 + 14 * q^46 + 12 * q^47 - 4 * q^49 - 4 * q^50 + 6 * q^52 - 12 * q^53 - 8 * q^55 - 48 * q^56 + 4 * q^58 + 12 * q^59 - 2 * q^61 + 52 * q^62 + 112 * q^64 - 4 * q^65 - 28 * q^67 - 48 * q^68 - 32 * q^70 - 24 * q^71 - 6 * q^73 - 16 * q^74 - 36 * q^76 - 4 * q^77 - 2 * q^79 + 16 * q^80 + 12 * q^82 + 24 * q^83 + 36 * q^85 + 36 * q^86 + 12 * q^88 + 8 * q^89 + 12 * q^91 + 32 * q^92 - 20 * q^94 + 34 * q^95 - 88 * q^97 - 16 * q^98

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