LMFDB - Embedded newform 693.2.m.i.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.1
Root			$-1.38112 + 1.00344i$ of defining polynomial
Character	$\chi$	$=$	693.190
Dual form			693.2.m.i.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38112 + 1.00344i) q^{2} +(0.282562 - 0.869638i) q^{4} +(3.28976 + 2.39015i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.572703 - 1.76260i) q^{8} +O(q^{10})$	\(q+(-1.38112 + 1.00344i) q^{2} +(0.282562 - 0.869638i) q^{4} +(3.28976 + 2.39015i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.572703 - 1.76260i) q^{8} -6.94194 q^{10} +(0.582050 + 3.26515i) q^{11} +(-2.65189 + 1.92671i) q^{13} +(0.527541 + 1.62360i) q^{14} +(4.03916 + 2.93462i) q^{16} +(-1.06862 - 0.776394i) q^{17} +(0.668017 + 2.05594i) q^{19} +(3.00813 - 2.18553i) q^{20} +(-4.08027 - 3.92552i) q^{22} +1.86611 q^{23} +(3.56462 + 10.9708i) q^{25} +(1.72924 - 5.32205i) q^{26} +(-0.739758 - 0.537466i) q^{28} +(0.0754316 - 0.232155i) q^{29} +(5.55785 - 4.03801i) q^{31} -4.81667 q^{32} +2.25495 q^{34} +(3.28976 - 2.39015i) q^{35} +(0.0789907 - 0.243108i) q^{37} +(-2.98563 - 2.16919i) q^{38} +(2.32882 - 7.16738i) q^{40} +(1.77139 + 5.45177i) q^{41} -8.01781 q^{43} +(3.00397 + 0.416437i) q^{44} +(-2.57733 + 1.87254i) q^{46} +(1.25698 + 3.86859i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-15.9317 - 11.5751i) q^{50} +(0.926218 + 2.85060i) q^{52} +(-4.04982 + 2.94237i) q^{53} +(-5.88941 + 12.1328i) q^{55} -1.85331 q^{56} +(0.128774 + 0.396325i) q^{58} +(0.303947 - 0.935452i) q^{59} +(-1.49402 - 1.08547i) q^{61} +(-3.62414 + 11.1540i) q^{62} +(-1.42591 + 1.03598i) q^{64} -13.3292 q^{65} -3.00700 q^{67} +(-0.977133 + 0.709928i) q^{68} +(-2.14518 + 6.60218i) q^{70} +(5.23953 + 3.80674i) q^{71} +(-2.98252 + 9.17926i) q^{73} +(0.134850 + 0.415025i) q^{74} +1.97668 q^{76} +(3.28521 + 0.455425i) q^{77} +(4.47750 - 3.25310i) q^{79} +(6.27368 + 19.3084i) q^{80} +(-7.91704 - 5.75206i) q^{82} +(1.67485 + 1.21685i) q^{83} +(-1.65979 - 5.10831i) q^{85} +(11.0736 - 8.04542i) q^{86} +(5.42181 - 2.89588i) q^{88} -16.6306 q^{89} +(1.01293 + 3.11749i) q^{91} +(0.527294 - 1.62284i) q^{92} +(-5.61795 - 4.08168i) q^{94} +(-2.71640 + 8.36023i) q^{95} +(2.09179 - 1.51977i) q^{97} +1.70716 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.38112	+	1.00344i	−0.976600	+	0.709541i	−0.956946	−	0.290266i	$-0.906256\pi$
$2$	−1.38112	+	1.00344i	−0.976600	+	0.709541i	−0.0196536	+	0.999807i	$0.506256\pi$
$3$		0			0
$3$		0			0
$4$	0.282562	−	0.869638i	0.141281	−	0.434819i
$5$	3.28976	+	2.39015i	1.47123	+	1.06891i	0.980256	+	0.197732i	$0.0633577\pi$
$5$	3.28976	+	2.39015i	1.47123	+	1.06891i	0.490971	+	0.871176i	$0.336642\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−0.572703	−	1.76260i	−0.202481	−	0.623173i
$9$		0			0
$10$	−6.94194			−2.19523
$11$	0.582050	+	3.26515i	0.175495	+	0.984480i
$11$	0.582050	+	3.26515i	0.175495	+	0.984480i
$12$		0			0
$13$	−2.65189	+	1.92671i	−0.735503	+	0.534374i	−0.891300	−	0.453415i	$-0.850206\pi$
$13$	−2.65189	+	1.92671i	−0.735503	+	0.534374i	0.155796	+	0.987789i	$0.450206\pi$
$14$	0.527541	+	1.62360i	0.140991	+	0.433927i
$15$		0			0
$16$	4.03916	+	2.93462i	1.00979	+	0.733655i
$17$	−1.06862	−	0.776394i	−0.259177	−	0.188303i	0.450607	−	0.892722i	$-0.351208\pi$
$17$	−1.06862	−	0.776394i	−0.259177	−	0.188303i	−0.709784	+	0.704419i	$0.751208\pi$
$18$		0			0
$19$	0.668017	+	2.05594i	0.153254	+	0.471666i	0.997980	−	0.0635328i	$-0.0202368\pi$
$19$	0.668017	+	2.05594i	0.153254	+	0.471666i	−0.844726	+	0.535199i	$0.820237\pi$
$20$	3.00813	−	2.18553i	0.672638	−	0.488700i
$21$		0			0
$22$	−4.08027	−	3.92552i	−0.869917	−	0.836923i
$23$	1.86611			0.389112			0.194556	−	0.980891i	$-0.437673\pi$
$23$	1.86611			0.389112			0.194556	+	0.980891i	$0.437673\pi$
$24$		0			0
$25$	3.56462	+	10.9708i	0.712925	+	2.19416i
$26$	1.72924	−	5.32205i	0.339132	−	1.04374i
$27$		0			0
$28$	−0.739758	−	0.537466i	−0.139801	−	0.101571i
$29$	0.0754316	−	0.232155i	0.0140073	−	0.0431100i	−0.943809	−	0.330493i	$-0.892785\pi$
$29$	0.0754316	−	0.232155i	0.0140073	−	0.0431100i	0.957816	+	0.287383i	$0.0927851\pi$
$30$		0			0
$31$	5.55785	−	4.03801i	0.998219	−	0.725249i	0.0365136	−	0.999333i	$-0.488375\pi$
$31$	5.55785	−	4.03801i	0.998219	−	0.725249i	0.961706	+	0.274084i	$0.0883748\pi$
$32$	−4.81667			−0.851475
$33$		0			0
$34$	2.25495			0.386721
$35$	3.28976	−	2.39015i	0.556071	−	0.404009i
$36$		0			0
$37$	0.0789907	−	0.243108i	0.0129860	−	0.0399668i	−0.944354	−	0.328932i	$-0.893311\pi$
$37$	0.0789907	−	0.243108i	0.0129860	−	0.0399668i	0.957340	+	0.288965i	$0.0933112\pi$
$38$	−2.98563	−	2.16919i	−0.484334	−	0.351889i
$39$		0			0
$40$	2.32882	−	7.16738i	0.368219	−	1.13326i
$41$	1.77139	+	5.45177i	0.276644	+	0.851423i	0.988780	+	0.149381i	$0.0477282\pi$
$41$	1.77139	+	5.45177i	0.276644	+	0.851423i	−0.712136	+	0.702042i	$0.752272\pi$
$42$		0			0
$43$	−8.01781			−1.22270			−0.611352	−	0.791358i	$-0.709374\pi$
$43$	−8.01781			−1.22270			−0.611352	+	0.791358i	$0.709374\pi$
$44$	3.00397	+	0.416437i	0.452865	+	0.0627803i
$45$		0			0
$46$	−2.57733	+	1.87254i	−0.380006	+	0.276091i
$47$	1.25698	+	3.86859i	0.183350	+	0.564292i	0.999916	−	0.0129595i	$-0.00412525\pi$
$47$	1.25698	+	3.86859i	0.183350	+	0.564292i	−0.816566	+	0.577251i	$0.804125\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−15.9317	−	11.5751i	−2.25309	−	1.63696i
$51$		0			0
$52$	0.926218	+	2.85060i	0.128443	+	0.395308i
$53$	−4.04982	+	2.94237i	−0.556285	+	0.404165i	−0.830098	−	0.557618i	$-0.811715\pi$
$53$	−4.04982	+	2.94237i	−0.556285	+	0.404165i	0.273812	+	0.961783i	$0.411715\pi$
$54$		0			0
$55$	−5.88941	+	12.1328i	−0.794127	+	1.63598i
$56$	−1.85331			−0.247658
$57$		0			0
$58$	0.128774	+	0.396325i	0.0169088	+	0.0520400i
$59$	0.303947	−	0.935452i	0.0395705	−	0.121785i	−0.929320	−	0.369276i	$-0.879606\pi$
$59$	0.303947	−	0.935452i	0.0395705	−	0.121785i	0.968890	+	0.247490i	$0.0796058\pi$
$60$		0			0
$61$	−1.49402	−	1.08547i	−0.191290	−	0.138980i	0.488018	−	0.872833i	$-0.337720\pi$
$61$	−1.49402	−	1.08547i	−0.191290	−	0.138980i	−0.679308	+	0.733853i	$0.737720\pi$
$62$	−3.62414	+	11.1540i	−0.460267	+	1.41656i
$63$		0			0
$64$	−1.42591	+	1.03598i	−0.178239	+	0.129498i
$65$	−13.3292			−1.65329
$66$		0			0
$67$	−3.00700			−0.367364			−0.183682	−	0.982986i	$-0.558802\pi$
$67$	−3.00700			−0.367364			−0.183682	+	0.982986i	$0.558802\pi$
$68$	−0.977133	+	0.709928i	−0.118495	+	0.0860915i
$69$		0			0
$70$	−2.14518	+	6.60218i	−0.256398	+	0.789111i
$71$	5.23953	+	3.80674i	0.621818	+	0.451777i	0.853556	−	0.521001i	$-0.174441\pi$
$71$	5.23953	+	3.80674i	0.621818	+	0.451777i	−0.231738	+	0.972778i	$0.574441\pi$
$72$		0			0
$73$	−2.98252	+	9.17926i	−0.349078	+	1.07435i	0.610287	+	0.792181i	$0.291054\pi$
$73$	−2.98252	+	9.17926i	−0.349078	+	1.07435i	−0.959364	+	0.282170i	$0.908946\pi$
$74$	0.134850	+	0.415025i	0.0156760	+	0.0482456i
$75$		0			0
$76$	1.97668			0.226741
$77$	3.28521	+	0.455425i	0.374384	+	0.0519005i
$78$		0			0
$79$	4.47750	−	3.25310i	0.503759	−	0.366002i	−0.306692	−	0.951809i	$-0.599222\pi$
$79$	4.47750	−	3.25310i	0.503759	−	0.366002i	0.810451	+	0.585807i	$0.199222\pi$
$80$	6.27368	+	19.3084i	0.701419	+	2.15874i
$81$		0			0
$82$	−7.91704	−	5.75206i	−0.874290	−	0.635209i
$83$	1.67485	+	1.21685i	0.183839	+	0.133567i	0.675898	−	0.736995i	$-0.263756\pi$
$83$	1.67485	+	1.21685i	0.183839	+	0.133567i	−0.492060	+	0.870561i	$0.663756\pi$
$84$		0			0
$85$	−1.65979	−	5.10831i	−0.180029	−	0.554074i
$86$	11.0736	−	8.04542i	1.19409	−	0.867559i
$87$		0			0
$88$	5.42181	−	2.89588i	0.577967	−	0.308702i
$89$	−16.6306			−1.76284			−0.881421	−	0.472331i	$-0.843413\pi$
$89$	−16.6306			−1.76284			−0.881421	+	0.472331i	$0.843413\pi$
$90$		0			0
$91$	1.01293	+	3.11749i	0.106184	+	0.326802i
$92$	0.527294	−	1.62284i	0.0549742	−	0.169193i
$93$		0			0
$94$	−5.61795	−	4.08168i	−0.579448	−	0.420993i
$95$	−2.71640	+	8.36023i	−0.278697	+	0.857741i
$96$		0			0
$97$	2.09179	−	1.51977i	0.212389	−	0.154310i	−0.476505	−	0.879172i	$-0.658097\pi$
$97$	2.09179	−	1.51977i	0.212389	−	0.154310i	0.688894	+	0.724862i	$0.258097\pi$
$98$	1.70716			0.172449
$99$		0			0
$100$	10.5478			1.05478
$101$	8.55018	−	6.21207i	0.850775	−	0.618124i	−0.0745850	−	0.997215i	$-0.523763\pi$
$101$	8.55018	−	6.21207i	0.850775	−	0.618124i	0.925359	+	0.379091i	$0.123763\pi$
$102$		0			0
$103$	4.27954	−	13.1711i	0.421676	−	1.29778i	−0.484466	−	0.874810i	$-0.660986\pi$
$103$	4.27954	−	13.1711i	0.421676	−	1.29778i	0.906142	−	0.422974i	$-0.139014\pi$
$104$	4.91477	+	3.57079i	0.481933	+	0.350145i
$105$		0			0
$106$	2.64079	−	8.12752i	0.256496	−	0.789415i
$107$	−3.84066	−	11.8203i	−0.371291	−	1.14272i	−0.945947	−	0.324321i	$-0.894864\pi$
$107$	−3.84066	−	11.8203i	−0.371291	−	1.14272i	0.574656	−	0.818395i	$-0.305136\pi$
$108$		0			0
$109$	−7.36748			−0.705676			−0.352838	−	0.935684i	$-0.614783\pi$
$109$	−7.36748			−0.705676			−0.352838	+	0.935684i	$0.614783\pi$
$110$	−4.04055	−	22.6665i	−0.385252	−	2.16116i
$111$		0			0
$112$	4.03916	−	2.93462i	0.381664	−	0.277295i
$113$	−3.52535	−	10.8499i	−0.331637	−	1.02067i	−0.968355	−	0.249577i	$-0.919708\pi$
$113$	−3.52535	−	10.8499i	−0.331637	−	1.02067i	0.636718	−	0.771097i	$-0.280292\pi$
$114$		0			0
$115$	6.13907	+	4.46030i	0.572471	+	0.415925i
$116$	−0.180576	−	0.131196i	−0.0167661	−	0.0121813i
$117$		0			0
$118$	0.518885	+	1.59696i	0.0477673	+	0.147013i
$119$	−1.06862	+	0.776394i	−0.0979598	+	0.0711720i
$120$		0			0
$121$	−10.3224	+	3.80096i	−0.938403	+	0.345542i
$122$	3.15263			0.285425
$123$		0			0
$124$	−1.94117	−	5.97431i	−0.174322	−	0.536509i
$125$	−8.21219	+	25.2745i	−0.734521	+	2.26062i
$126$		0			0
$127$	7.07765	+	5.14221i	0.628040	+	0.456297i	0.855720	−	0.517438i	$-0.173114\pi$
$127$	7.07765	+	5.14221i	0.628040	+	0.456297i	−0.227681	+	0.973736i	$0.573114\pi$
$128$	3.90667	−	12.0235i	0.345304	−	1.06274i
$129$		0			0
$130$	18.4093	−	13.3751i	1.61460	−	1.17308i
$131$	12.5516			1.09664			0.548319	−	0.836269i	$-0.315268\pi$
$131$	12.5516			1.09664			0.548319	+	0.836269i	$0.315268\pi$
$132$		0			0
$133$	2.16175			0.187447
$134$	4.15303	−	3.01735i	0.358767	−	0.260660i
$135$		0			0
$136$	−0.756473	+	2.32818i	−0.0648670	+	0.199640i
$137$	−5.11961	−	3.71962i	−0.437398	−	0.317788i	0.347202	−	0.937790i	$-0.387132\pi$
$137$	−5.11961	−	3.71962i	−0.437398	−	0.317788i	−0.784600	+	0.620002i	$0.787132\pi$
$138$		0			0
$139$	4.46311	−	13.7361i	0.378556	−	1.16508i	−0.562491	−	0.826803i	$-0.690157\pi$
$139$	4.46311	−	13.7361i	0.378556	−	1.16508i	0.941048	−	0.338274i	$-0.109843\pi$
$140$	−1.14900	−	3.53627i	−0.0971085	−	0.298869i
$141$		0			0
$142$	−11.0563			−0.927822
$143$	−7.83455	−	7.53740i	−0.655158	−	0.630309i
$144$		0			0
$145$	0.803037	−	0.583440i	0.0666886	−	0.0484521i
$146$	−5.09164	−	15.6704i	−0.421387	−	1.29690i
$147$		0			0
$148$	−0.189096	−	0.137387i	−0.0155436	−	0.0112931i
$149$	19.4643	+	14.1417i	1.59458	+	1.15853i	0.897009	+	0.442012i	$0.145735\pi$
$149$	19.4643	+	14.1417i	1.59458	+	1.15853i	0.697570	+	0.716517i	$0.254265\pi$
$150$		0			0
$151$	−0.409195	−	1.25937i	−0.0332998	−	0.102486i	0.933025	−	0.359811i	$-0.117159\pi$
$151$	−0.409195	−	1.25937i	−0.0332998	−	0.102486i	−0.966325	+	0.257325i	$0.917159\pi$
$152$	3.24123	−	2.35489i	0.262898	−	0.191007i
$153$		0			0
$154$	−4.99426	+	2.66752i	−0.402449	+	0.214955i
$155$	27.9355			2.24383
$156$		0			0
$157$	4.51600	+	13.8988i	0.360416	+	1.10925i	0.952802	+	0.303592i	$0.0981859\pi$
$157$	4.51600	+	13.8988i	0.360416	+	1.10925i	−0.592386	+	0.805654i	$0.701814\pi$
$158$	−2.91968	+	8.98584i	−0.232277	+	0.714875i
$159$		0			0
$160$	−15.8457	−	11.5126i	−1.25271	−	0.910149i
$161$	0.576661	−	1.77478i	0.0454472	−	0.139872i
$162$		0			0
$163$	16.9258	−	12.2973i	1.32573	−	0.963202i	0.325892	−	0.945407i	$-0.394335\pi$
$163$	16.9258	−	12.2973i	1.32573	−	0.963202i	0.999842	−	0.0177952i	$-0.00566470\pi$
$164$	5.24159			0.409300
$165$		0			0
$166$	−3.53421			−0.274308
$167$	3.97498	−	2.88799i	0.307593	−	0.223480i	−0.423270	−	0.906004i	$-0.639118\pi$
$167$	3.97498	−	2.88799i	0.307593	−	0.223480i	0.730863	+	0.682524i	$0.239118\pi$
$168$		0			0
$169$	−0.696904	+	2.14485i	−0.0536080	+	0.164989i
$170$	7.41826	+	5.38968i	0.568955	+	0.413370i
$171$		0			0
$172$	−2.26553	+	6.97259i	−0.172745	+	0.531655i
$173$	−6.07460	−	18.6957i	−0.461844	−	1.42141i	−0.862909	−	0.505359i	$-0.831360\pi$
$173$	−6.07460	−	18.6957i	−0.461844	−	1.42141i	0.401066	−	0.916049i	$-0.368640\pi$
$174$		0			0
$175$	11.5354			0.871992
$176$	−7.23099	+	14.8966i	−0.545056	+	1.12287i
$177$		0			0
$178$	22.9689	−	16.6879i	1.72159	−	1.25081i
$179$	7.83631	+	24.1177i	0.585714	+	1.80264i	0.596386	+	0.802698i	$0.296603\pi$
$179$	7.83631	+	24.1177i	0.585714	+	1.80264i	−0.0106719	+	0.999943i	$0.503397\pi$
$180$		0			0
$181$	1.59836	+	1.16128i	0.118805	+	0.0863172i	0.645601	−	0.763675i	$-0.276607\pi$
$181$	1.59836	+	1.16128i	0.118805	+	0.0863172i	−0.526796	+	0.849992i	$0.676607\pi$
$182$	−4.52720	−	3.28921i	−0.335579	−	0.243812i
$183$		0			0
$184$	−1.06873	−	3.28921i	−0.0787878	−	0.242484i
$185$	0.840927	−	0.610969i	0.0618262	−	0.0449194i
$186$		0			0
$187$	1.91306	−	3.94109i	0.139897	−	0.288201i
$188$	3.71945			0.271269
$189$		0			0
$190$	−4.63733	−	14.2722i	−0.336427	−	1.03542i
$191$	−0.300672	+	0.925373i	−0.0217559	+	0.0669577i	−0.961345	−	0.275347i	$-0.911207\pi$
$191$	−0.300672	+	0.925373i	−0.0217559	+	0.0669577i	0.939589	+	0.342304i	$0.111207\pi$
$192$		0			0
$193$	18.7147	+	13.5970i	1.34711	+	0.978735i	0.999150	+	0.0412267i	$0.0131266\pi$
$193$	18.7147	+	13.5970i	1.34711	+	0.978735i	0.347963	+	0.937508i	$0.386873\pi$
$194$	−1.36401	+	4.19798i	−0.0979299	+	0.301397i
$195$		0			0
$196$	−0.739758	+	0.537466i	−0.0528399	+	0.0383904i
$197$	9.91237			0.706227			0.353114	−	0.935580i	$-0.385123\pi$
$197$	9.91237			0.706227			0.353114	+	0.935580i	$0.385123\pi$
$198$		0			0
$199$	10.3847			0.736154			0.368077	−	0.929795i	$-0.380016\pi$
$199$	10.3847			0.736154			0.368077	+	0.929795i	$0.380016\pi$
$200$	17.2956	−	12.5660i	1.22299	−	0.888551i
$201$		0			0
$202$	−5.57537	+	17.1592i	−0.392282	+	1.20732i
$203$	−0.197482	−	0.143479i	−0.0138606	−	0.0100703i
$204$		0			0
$205$	−7.20312	+	22.1689i	−0.503087	+	1.54834i
$206$	7.30586	+	22.4851i	0.509023	+	1.56661i
$207$		0			0
$208$	−16.3656			−1.13475
$209$	−6.32415	+	3.37784i	−0.437451	+	0.233650i
$210$		0			0
$211$	10.5104	−	7.63627i	0.723567	−	0.525702i	−0.163955	−	0.986468i	$-0.552425\pi$
$211$	10.5104	−	7.63627i	0.723567	−	0.525702i	0.887522	+	0.460766i	$0.152425\pi$
$212$	1.41447	+	4.35328i	0.0971459	+	0.298984i
$213$		0			0
$214$	17.1655	+	12.4714i	1.17341	+	0.852530i
$215$	−26.3767	−	19.1638i	−1.79888	−	1.30696i
$216$		0			0
$217$	−2.12291	−	6.53364i	−0.144112	−	0.443533i
$218$	10.1754	−	7.39284i	0.689163	−	0.500706i
$219$		0			0
$220$	8.88698	+	8.54991i	0.599160	+	0.576435i
$221$	4.32975			0.291250
$222$		0			0
$223$	−4.43522	−	13.6502i	−0.297004	−	0.914086i	−0.982541	−	0.186047i	$-0.940432\pi$
$223$	−4.43522	−	13.6502i	−0.297004	−	0.914086i	0.685536	−	0.728038i	$-0.259568\pi$
$224$	−1.48843	+	4.58093i	−0.0994501	+	0.306076i
$225$		0			0
$226$	15.7562	+	11.4476i	1.04809	+	0.761480i
$227$	−1.96992	+	6.06279i	−0.130748	+	0.402401i	−0.994904	−	0.100822i	$-0.967853\pi$
$227$	−1.96992	+	6.06279i	−0.130748	+	0.402401i	0.864156	+	0.503223i	$0.167853\pi$
$228$		0			0
$229$	6.47405	−	4.70368i	0.427817	−	0.310828i	−0.352958	−	0.935639i	$-0.614824\pi$
$229$	6.47405	−	4.70368i	0.427817	−	0.310828i	0.780776	+	0.624812i	$0.214824\pi$
$230$	−12.9545			−0.854191
$231$		0			0
$232$	−0.452395			−0.0297012
$233$	−8.73915	+	6.34937i	−0.572521	+	0.415961i	−0.836020	−	0.548699i	$-0.815123\pi$
$233$	−8.73915	+	6.34937i	−0.572521	+	0.415961i	0.263499	+	0.964660i	$0.415123\pi$
$234$		0			0
$235$	−5.11135	+	15.7311i	−0.333428	+	1.02619i
$236$	−0.727620	−	0.528647i	−0.0473641	−	0.0344120i
$237$		0			0
$238$	0.696819	−	2.14459i	0.0451681	−	0.139013i
$239$	−7.77433	−	23.9269i	−0.502880	−	1.54770i	−0.804306	−	0.594215i	$-0.797463\pi$
$239$	−7.77433	−	23.9269i	−0.502880	−	1.54770i	0.301427	−	0.953489i	$-0.402537\pi$
$240$		0			0
$241$	−18.2462			−1.17534			−0.587669	−	0.809101i	$-0.699954\pi$
$241$	−18.2462			−1.17534			−0.587669	+	0.809101i	$0.699954\pi$
$242$	10.4425	−	15.6076i	0.671268	−	1.00329i
$243$		0			0
$244$	−1.36612	+	0.992543i	−0.0874568	+	0.0635411i
$245$	−1.25658	−	3.86735i	−0.0802798	−	0.247076i
$246$		0			0
$247$	−5.73273	−	4.16507i	−0.364765	−	0.265017i
$248$	−10.3004	−	7.48368i	−0.654076	−	0.475214i
$249$		0			0
$250$	−14.0195	−	43.1476i	−0.886672	−	2.72890i
$251$	12.4009	−	9.00981i	0.782740	−	0.568694i	−0.123060	−	0.992399i	$-0.539271\pi$
$251$	12.4009	−	9.00981i	0.782740	−	0.568694i	0.905800	+	0.423705i	$0.139271\pi$
$252$		0			0
$253$	1.08617	+	6.09315i	0.0682870	+	0.383073i
$254$	−14.9350			−0.937105
$255$		0			0
$256$	5.58000	+	17.1735i	0.348750	+	1.07334i
$257$	−0.828102	+	2.54864i	−0.0516556	+	0.158980i	−0.973557	−	0.228446i	$-0.926636\pi$
$257$	−0.828102	+	2.54864i	−0.0516556	+	0.158980i	0.921901	+	0.387426i	$0.126636\pi$
$258$		0			0
$259$	−0.206800	−	0.150249i	−0.0128500	−	0.00933604i
$260$	−3.76634	+	11.5916i	−0.233579	+	0.718881i
$261$		0			0
$262$	−17.3353	+	12.5948i	−1.07098	+	0.778110i
$263$	9.97733			0.615229			0.307614	−	0.951511i	$-0.400469\pi$
$263$	9.97733			0.615229			0.307614	+	0.951511i	$0.400469\pi$
$264$		0			0
$265$	−20.3556			−1.25044
$266$	−2.98563	+	2.16919i	−0.183061	+	0.133002i
$267$		0			0
$268$	−0.849665	+	2.61500i	−0.0519016	+	0.159737i
$269$	−17.4565	−	12.6829i	−1.06434	−	0.773288i	−0.0894538	−	0.995991i	$-0.528512\pi$
$269$	−17.4565	−	12.6829i	−1.06434	−	0.773288i	−0.974886	+	0.222703i	$0.928512\pi$
$270$		0			0
$271$	−4.63100	+	14.2528i	−0.281313	+	0.865793i	0.706166	+	0.708046i	$0.250423\pi$
$271$	−4.63100	+	14.2528i	−0.281313	+	0.865793i	−0.987480	+	0.157747i	$0.949577\pi$
$272$	−2.03788	−	6.27196i	−0.123565	−	0.380293i
$273$		0			0
$274$	10.8032			0.652647
$275$	−33.7465	+	18.0246i	−2.03499	+	1.08692i
$276$		0			0
$277$	−4.21207	+	3.06025i	−0.253079	+	0.183872i	−0.707090	−	0.707123i	$-0.749992\pi$
$277$	−4.21207	+	3.06025i	−0.253079	+	0.183872i	0.454012	+	0.890996i	$0.349992\pi$
$278$	7.61924	+	23.4496i	0.456972	+	1.40641i
$279$		0			0
$280$	−6.09694	−	4.42968i	−0.364362	−	0.264724i
$281$	12.2647	+	8.91086i	0.731654	+	0.531577i	0.890086	−	0.455792i	$-0.150644\pi$
$281$	12.2647	+	8.91086i	0.731654	+	0.531577i	−0.158433	+	0.987370i	$0.550644\pi$
$282$		0			0
$283$	−1.75076	−	5.38829i	−0.104072	−	0.320301i	0.885439	−	0.464755i	$-0.153857\pi$
$283$	−1.75076	−	5.38829i	−0.104072	−	0.320301i	−0.989512	+	0.144454i	$0.953857\pi$
$284$	4.79098	−	3.48085i	0.284292	−	0.206551i
$285$		0			0
$286$	18.3838	+	2.54853i	1.08706	+	0.150698i
$287$	5.73233			0.338369
$288$		0			0
$289$	−4.71414	−	14.5086i	−0.277302	−	0.853449i
$290$	−0.523642	+	1.61160i	−0.0307493	+	0.0946366i
$291$		0			0
$292$	7.13988	+	5.18743i	0.417830	+	0.303571i
$293$	8.32502	−	25.6218i	0.486353	−	1.49684i	−0.343659	−	0.939095i	$-0.611666\pi$
$293$	8.32502	−	25.6218i	0.486353	−	1.49684i	0.830012	−	0.557746i	$-0.188334\pi$
$294$		0			0
$295$	3.23579	−	2.35094i	0.188395	−	0.136877i
$296$	−0.473741			−0.0275356
$297$		0			0
$298$	−41.0729			−2.37929
$299$	−4.94874	+	3.59547i	−0.286193	+	0.207931i
$300$		0			0
$301$	−2.47764	+	7.62539i	−0.142809	+	0.439520i
$302$	1.82885	+	1.32874i	0.105239	+	0.0764604i
$303$		0			0
$304$	−3.33519	+	10.2647i	−0.191286	+	0.588718i
$305$	−2.32053	−	7.14187i	−0.132873	−	0.408942i
$306$		0			0
$307$	24.6157			1.40489			0.702447	−	0.711736i	$-0.252091\pi$
$307$	24.6157			1.40489			0.702447	+	0.711736i	$0.252091\pi$
$308$	1.32433	−	2.72825i	0.0754608	−	0.155457i
$309$		0			0
$310$	−38.5823	+	28.0316i	−2.19132	+	1.59209i
$311$	3.15602	+	9.71323i	0.178962	+	0.550787i	0.999792	−	0.0203847i	$-0.00648910\pi$
$311$	3.15602	+	9.71323i	0.178962	+	0.550787i	−0.820831	+	0.571172i	$0.806489\pi$
$312$		0			0
$313$	−18.1222	−	13.1665i	−1.02433	−	0.744217i	−0.0571612	−	0.998365i	$-0.518205\pi$
$313$	−18.1222	−	13.1665i	−1.02433	−	0.744217i	−0.967165	+	0.254148i	$0.918205\pi$
$314$	−20.1838	−	14.6644i	−1.13904	−	0.827559i
$315$		0			0
$316$	−1.56384	−	4.81301i	−0.0879730	−	0.270753i
$317$	18.8982	−	13.7304i	1.06143	−	0.771174i	0.0870776	−	0.996202i	$-0.472247\pi$
$317$	18.8982	−	13.7304i	1.06143	−	0.771174i	0.974352	+	0.225028i	$0.0722472\pi$
$318$		0			0
$319$	0.801925	+	0.111170i	0.0448992	+	0.00622433i
$320$	−7.16707			−0.400651
$321$		0			0
$322$	0.984452	+	3.02983i	0.0548614	+	0.168846i
$323$	0.882371	−	2.71566i	0.0490964	−	0.151103i
$324$		0			0
$325$	−30.5906	−	22.2254i	−1.69686	−	1.23284i
$326$	−11.0369	+	33.9682i	−0.611280	+	1.88133i
$327$		0			0
$328$	8.59480	−	6.24449i	0.474569	−	0.344794i
$329$	4.06768			0.224258
$330$		0			0
$331$	15.6444			0.859892			0.429946	−	0.902855i	$-0.358533\pi$
$331$	15.6444			0.859892			0.429946	+	0.902855i	$0.358533\pi$
$332$	1.53147	−	1.11268i	0.0840502	−	0.0610660i
$333$		0			0
$334$	−2.59199	+	7.97734i	−0.141828	+	0.436500i
$335$	−9.89232	−	7.18719i	−0.540475	−	0.392678i
$336$		0			0
$337$	10.0712	−	30.9959i	0.548611	−	1.68845i	−0.163634	−	0.986521i	$-0.552322\pi$
$337$	10.0712	−	30.9959i	0.548611	−	1.68845i	0.712245	−	0.701931i	$-0.247678\pi$
$338$	−1.18973	−	3.66160i	−0.0647126	−	0.199165i
$339$		0			0
$340$	−4.91137			−0.266356
$341$	16.4197	+	15.7969i	0.889175	+	0.855450i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	4.59183	+	14.1322i	0.247575	+	0.761957i
$345$		0			0
$346$	27.1498	+	19.7255i	1.45958	+	1.06045i
$347$	4.65414	+	3.38143i	0.249848	+	0.181525i	0.705659	−	0.708551i	$-0.250651\pi$
$347$	4.65414	+	3.38143i	0.249848	+	0.181525i	−0.455812	+	0.890076i	$0.650651\pi$
$348$		0			0
$349$	−0.0568404	−	0.174937i	−0.00304260	−	0.00936415i	0.949524	−	0.313695i	$-0.101567\pi$
$349$	−0.0568404	−	0.174937i	−0.00304260	−	0.00936415i	−0.952566	+	0.304331i	$0.901567\pi$
$350$	−15.9317	+	11.5751i	−0.851587	+	0.618714i
$351$		0			0
$352$	−2.80354	−	15.7272i	−0.149429	−	0.838260i
$353$	−19.0211			−1.01239			−0.506195	−	0.862419i	$-0.668948\pi$
$353$	−19.0211			−1.01239			−0.506195	+	0.862419i	$0.668948\pi$
$354$		0			0
$355$	8.13812	+	25.0466i	0.431927	+	1.32933i
$356$	−4.69919	+	14.4626i	−0.249057	+	0.766517i
$357$		0			0
$358$	−35.0236	−	25.4462i	−1.85106	−	1.34487i
$359$	0.222161	−	0.683741i	0.0117252	−	0.0360865i	−0.945023	−	0.327005i	$-0.893961\pi$
$359$	0.222161	−	0.683741i	0.0117252	−	0.0360865i	0.956748	+	0.290918i	$0.0939607\pi$
$360$		0			0
$361$	11.5907	−	8.42111i	0.610035	−	0.443216i
$362$	−3.37281			−0.177271
$363$		0			0
$364$	2.99730			0.157101
$365$	−31.7516	+	23.0689i	−1.66196	+	1.20748i
$366$		0			0
$367$	−2.43906	+	7.50664i	−0.127318	+	0.391843i	−0.994316	−	0.106467i	$-0.966046\pi$
$367$	−2.43906	+	7.50664i	−0.127318	+	0.391843i	0.866999	+	0.498311i	$0.166046\pi$
$368$	7.53753	+	5.47633i	0.392921	+	0.285474i
$369$		0			0
$370$	−0.548349	+	1.68764i	−0.0285073	+	0.0877364i
$371$	1.54689	+	4.76085i	0.0803107	+	0.247171i
$372$		0			0
$373$	15.6686			0.811292			0.405646	−	0.914030i	$-0.367047\pi$
$373$	15.6686			0.811292			0.405646	+	0.914030i	$0.367047\pi$
$374$	1.31250	+	7.36277i	0.0678675	+	0.380720i
$375$		0			0
$376$	6.09890	−	4.43111i	0.314527	−	0.228517i
$377$	0.247259	+	0.760984i	0.0127345	+	0.0391927i
$378$		0			0
$379$	10.7716	+	7.82600i	0.553298	+	0.401995i	0.829000	−	0.559248i	$-0.188910\pi$
$379$	10.7716	+	7.82600i	0.553298	+	0.401995i	−0.275702	+	0.961243i	$0.588910\pi$
$380$	6.50282	+	4.72457i	0.333587	+	0.242365i
$381$		0			0
$382$	−0.513295	−	1.57976i	−0.0262625	−	0.0808275i
$383$	9.58558	−	6.96433i	0.489800	−	0.355861i	−0.315307	−	0.948990i	$-0.602108\pi$
$383$	9.58558	−	6.96433i	0.489800	−	0.355861i	0.805107	+	0.593129i	$0.202108\pi$
$384$		0			0
$385$	9.71902	+	9.35039i	0.495327	+	0.476540i
$386$	−39.4911			−2.01004
$387$		0			0
$388$	−0.730591	−	2.24853i	−0.0370901	−	0.114152i
$389$	1.86947	−	5.75362i	0.0947857	−	0.291720i	−0.892412	−	0.451221i	$-0.850989\pi$
$389$	1.86947	−	5.75362i	0.0947857	−	0.291720i	0.987198	+	0.159501i	$0.0509885\pi$
$390$		0			0
$391$	−1.99416	−	1.44884i	−0.100849	−	0.0732710i
$392$	−0.572703	+	1.76260i	−0.0289259	+	0.0890247i
$393$		0			0
$394$	−13.6902	+	9.94650i	−0.689701	+	0.501097i
$395$	22.5053			1.13237
$396$		0			0
$397$	−11.5763			−0.580996			−0.290498	−	0.956876i	$-0.593821\pi$
$397$	−11.5763			−0.580996			−0.290498	+	0.956876i	$0.593821\pi$
$398$	−14.3426	+	10.4205i	−0.718927	+	0.522331i
$399$		0			0
$400$	−17.7970	+	54.7735i	−0.889850	+	2.73868i
$401$	27.3386	+	19.8627i	1.36522	+	0.991894i	0.998093	+	0.0617249i	$0.0196601\pi$
$401$	27.3386	+	19.8627i	1.36522	+	0.991894i	0.367132	+	0.930169i	$0.380340\pi$
$402$		0			0
$403$	−6.95873	+	21.4168i	−0.346639	+	1.06685i
$404$	−2.98629	−	9.19086i	−0.148573	−	0.457262i
$405$		0			0
$406$	0.416720			0.0206815
$407$	0.839763	+	0.116416i	0.0416255	+	0.00577051i
$408$		0			0
$409$	−14.6044	+	10.6107i	−0.722139	+	0.524665i	−0.887067	−	0.461641i	$-0.847261\pi$
$409$	−14.6044	+	10.6107i	−0.722139	+	0.524665i	0.164928	+	0.986306i	$0.447261\pi$
$410$	−12.2969	−	37.8458i	−0.607299	−	1.86907i
$411$		0			0
$412$	−10.2448	−	7.44330i	−0.504726	−	0.366705i
$413$	−0.795743	−	0.578141i	−0.0391559	−	0.0284485i
$414$		0			0
$415$	2.60140	+	8.00629i	0.127698	+	0.393013i
$416$	12.7733	−	9.28034i	0.626262	−	0.455006i
$417$		0			0
$418$	5.34495	−	11.0111i	0.261430	−	0.538572i
$419$	−2.58559			−0.126314			−0.0631571	−	0.998004i	$-0.520117\pi$
$419$	−2.58559			−0.126314			−0.0631571	+	0.998004i	$0.520117\pi$
$420$		0			0
$421$	4.32462	+	13.3098i	0.210769	+	0.648681i	0.999427	+	0.0338486i	$0.0107764\pi$
$421$	4.32462	+	13.3098i	0.210769	+	0.648681i	−0.788658	+	0.614833i	$0.789224\pi$
$422$	−6.85360	+	21.0932i	−0.333628	+	1.02680i
$423$		0			0
$424$	7.50556	+	5.45311i	0.364502	+	0.264826i
$425$	4.70845	−	14.4911i	0.228393	−	0.702922i
$426$		0			0
$427$	−1.49402	+	1.08547i	−0.0723007	+	0.0525295i
$428$	−11.3646			−0.549331
$429$		0			0
$430$	55.6592			2.68412
$431$	−27.2381	+	19.7897i	−1.31201	+	0.953234i	−0.312019	+	0.950076i	$0.601005\pi$
$431$	−27.2381	+	19.7897i	−1.31201	+	0.953234i	−0.999995	+	0.00315862i	$0.998995\pi$
$432$		0			0
$433$	2.32471	−	7.15472i	0.111718	−	0.343834i	−0.879530	−	0.475843i	$-0.842143\pi$
$433$	2.32471	−	7.15472i	0.111718	−	0.343834i	0.991248	+	0.132009i	$0.0421429\pi$
$434$	9.48813	+	6.89353i	0.455445	+	0.330900i
$435$		0			0
$436$	−2.08177	+	6.40704i	−0.0996988	+	0.306841i
$437$	1.24660	+	3.83663i	0.0596327	+	0.183531i
$438$		0			0
$439$	−22.0123			−1.05059			−0.525294	−	0.850921i	$-0.676045\pi$
$439$	−22.0123			−1.05059			−0.525294	+	0.850921i	$0.676045\pi$
$440$	24.7581	+	3.43219i	1.18030	+	0.163623i
$441$		0			0
$442$	−5.97990	+	4.34465i	−0.284435	+	0.206654i
$443$	−7.32039	−	22.5299i	−0.347802	−	1.07043i	−0.960066	−	0.279772i	$-0.909741\pi$
$443$	−7.32039	−	22.5299i	−0.347802	−	1.07043i	0.612264	−	0.790653i	$-0.290259\pi$
$444$		0			0
$445$	−54.7108	−	39.7497i	−2.59354	−	1.88432i
$446$	19.8228	+	14.4021i	0.938636	+	0.681959i
$447$		0			0
$448$	0.544649	+	1.67626i	0.0257323	+	0.0791958i
$449$	1.84062	−	1.33729i	0.0868643	−	0.0631106i	−0.543505	−	0.839406i	$-0.682903\pi$
$449$	1.84062	−	1.33729i	0.0868643	−	0.0631106i	0.630370	+	0.776295i	$0.282903\pi$
$450$		0			0
$451$	−16.7698	+	8.95705i	−0.789660	+	0.421771i
$452$	−10.4316			−0.490663
$453$		0			0
$454$	−3.36297	−	10.3501i	−0.157832	−	0.485756i
$455$	−4.11896	+	12.6769i	−0.193100	+	0.594300i
$456$		0			0
$457$	22.0970	+	16.0544i	1.03365	+	0.750993i	0.969037	−	0.246917i	$-0.0794174\pi$
$457$	22.0970	+	16.0544i	1.03365	+	0.750993i	0.0646170	+	0.997910i	$0.479417\pi$
$458$	−4.22158	+	12.9927i	−0.197261	+	0.607108i
$459$		0			0
$460$	5.61351	−	4.07846i	0.261731	−	0.190159i
$461$	8.21908			0.382801			0.191400	−	0.981512i	$-0.438697\pi$
$461$	8.21908			0.382801			0.191400	+	0.981512i	$0.438697\pi$
$462$		0			0
$463$	−27.9839			−1.30052			−0.650261	−	0.759711i	$-0.725340\pi$
$463$	−27.9839			−1.30052			−0.650261	+	0.759711i	$0.725340\pi$
$464$	0.985965	−	0.716345i	0.0457723	−	0.0332555i
$465$		0			0
$466$	5.69860	−	17.5385i	0.263982	−	0.812454i
$467$	21.5801	+	15.6789i	0.998610	+	0.725533i	0.961790	−	0.273789i	$-0.0882770\pi$
$467$	21.5801	+	15.6789i	0.998610	+	0.725533i	0.0368204	+	0.999322i	$0.488277\pi$
$468$		0			0
$469$	−0.929214	+	2.85983i	−0.0429071	+	0.132055i
$470$	−8.72589	−	26.8555i	−0.402495	−	1.23875i
$471$		0			0
$472$	−1.82290			−0.0839057
$473$	−4.66676	−	26.1794i	−0.214578	−	1.20373i
$474$		0			0
$475$	−20.1741	+	14.6573i	−0.925651	+	0.672525i
$476$	0.373231	+	1.14869i	0.0171070	+	0.0526500i
$477$		0			0
$478$	34.7466	+	25.2449i	1.58927	+	1.15467i
$479$	−18.7886	−	13.6507i	−0.858473	−	0.623717i	0.0689958	−	0.997617i	$-0.478020\pi$
$479$	−18.7886	−	13.6507i	−0.858473	−	0.623717i	−0.927469	+	0.373900i	$0.878020\pi$
$480$		0			0
$481$	0.258925	+	0.796890i	0.0118060	+	0.0363351i
$482$	25.2001	−	18.3090i	1.14783	−	0.833951i
$483$		0			0
$484$	0.388726	+	10.0508i	0.0176694	+	0.456854i
$485$	10.5140			0.477415
$486$		0			0
$487$	−5.80706	−	17.8723i	−0.263143	−	0.809870i	−0.992115	−	0.125327i	$-0.960002\pi$
$487$	−5.80706	−	17.8723i	−0.263143	−	0.809870i	0.728973	−	0.684543i	$-0.239998\pi$
$488$	−1.05762	+	3.25501i	−0.0478761	+	0.147347i
$489$		0			0
$490$	5.61615	+	4.08037i	0.253712	+	0.184332i
$491$	−2.28850	+	7.04327i	−0.103278	+	0.317858i	−0.989323	−	0.145743i	$-0.953443\pi$
$491$	−2.28850	+	7.04327i	−0.103278	+	0.317858i	0.886044	+	0.463601i	$0.153443\pi$
$492$		0			0
$493$	−0.260851	+	0.189519i	−0.0117481	+	0.00853552i
$494$	12.0970			0.544269
$495$		0			0
$496$	34.2991			1.54007
$497$	5.23953	−	3.80674i	0.235025	−	0.170756i
$498$		0			0
$499$	7.31454	−	22.5118i	0.327444	−	1.00777i	−0.642882	−	0.765965i	$-0.722261\pi$
$499$	7.31454	−	22.5118i	0.327444	−	1.00777i	0.970325	−	0.241803i	$-0.0777386\pi$
$500$	19.6592	+	14.2833i	0.879188	+	0.638767i
$501$		0			0
$502$	−8.08636	+	24.8873i	−0.360912	+	1.11077i
$503$	2.59491	+	7.98632i	0.115701	+	0.356092i	0.992093	−	0.125507i	$-0.0400559\pi$
$503$	2.59491	+	7.98632i	0.115701	+	0.356092i	−0.876391	+	0.481600i	$0.840056\pi$
$504$		0			0
$505$	42.9758			1.91240
$506$	−7.61426	−	7.32546i	−0.338495	−	0.325656i
$507$		0			0
$508$	6.47174	−	4.70199i	0.287137	−	0.208617i
$509$	−4.42094	−	13.6062i	−0.195955	−	0.603086i	−0.999964	−	0.00846991i	$-0.997304\pi$
$509$	−4.42094	−	13.6062i	−0.195955	−	0.603086i	0.804009	−	0.594616i	$-0.202696\pi$
$510$		0			0
$511$	7.80834	+	5.67309i	0.345421	+	0.250963i
$512$	−4.48369	−	3.25759i	−0.198153	−	0.143967i
$513$		0			0
$514$	−1.41370	−	4.35093i	−0.0623557	−	0.191911i
$515$	45.5595	−	33.1009i	2.00759	−	1.45860i
$516$		0			0
$517$	−11.8999	+	6.35595i	−0.523358	+	0.279534i
$518$	0.436383			0.0191736
$519$		0			0
$520$	7.63370	+	23.4941i	0.334760	+	1.03028i
$521$	10.3114	−	31.7352i	0.451750	−	1.39034i	−0.423158	−	0.906056i	$-0.639079\pi$
$521$	10.3114	−	31.7352i	0.451750	−	1.39034i	0.874909	−	0.484288i	$-0.160921\pi$
$522$		0			0
$523$	−10.8261	−	7.86559i	−0.473390	−	0.343938i	0.325371	−	0.945587i	$-0.394511\pi$
$523$	−10.8261	−	7.86559i	−0.473390	−	0.343938i	−0.798761	+	0.601648i	$0.794511\pi$
$524$	3.54661	−	10.9153i	0.154934	−	0.476839i
$525$		0			0
$526$	−13.7799	+	10.0117i	−0.600832	+	0.436530i
$527$	−9.07430			−0.395283
$528$		0			0
$529$	−19.5176			−0.848592
$530$	28.1136	−	20.4257i	1.22118	−	0.887237i
$531$		0			0
$532$	0.610829	−	1.87994i	0.0264828	−	0.0815056i
$533$	−15.2015	−	11.0446i	−0.658451	−	0.478393i
$534$		0			0
$535$	15.6176	−	48.0659i	0.675206	−	2.07807i
$536$	1.72212	+	5.30014i	0.0743842	+	0.228931i
$537$		0			0
$538$	36.8360			1.58811
$539$	1.44832	−	2.98368i	0.0623836	−	0.128516i
$540$		0			0
$541$	27.5583	−	20.0223i	1.18482	−	0.860825i	0.192117	−	0.981372i	$-0.438465\pi$
$541$	27.5583	−	20.0223i	1.18482	−	0.860825i	0.992708	+	0.120547i	$0.0384648\pi$
$542$	−7.90586	−	24.3317i	−0.339586	−	1.04514i
$543$		0			0
$544$	5.14717	+	3.73964i	0.220683	+	0.160336i
$545$	−24.2373	−	17.6094i	−1.03821	−	0.754304i
$546$		0			0
$547$	−4.87054	−	14.9900i	−0.208249	−	0.640925i	−0.999564	−	0.0295167i	$-0.990603\pi$
$547$	−4.87054	−	14.9900i	−0.208249	−	0.640925i	0.791315	−	0.611409i	$-0.209397\pi$
$548$	−4.68133	+	3.40118i	−0.199976	+	0.145291i
$549$		0			0
$550$	28.5213	−	58.7568i	1.21615	−	2.50540i
$551$	0.527686			0.0224802
$552$		0			0
$553$	−1.71025	−	5.26362i	−0.0727274	−	0.223832i
$554$	2.74659	−	8.45314i	0.116691	−	0.359139i
$555$		0			0
$556$	−10.6843	−	7.76258i	−0.453114	−	0.329207i
$557$	−4.97593	+	15.3143i	−0.210837	+	0.648889i	0.788586	+	0.614924i	$0.210813\pi$
$557$	−4.97593	+	15.3143i	−0.210837	+	0.648889i	−0.999423	+	0.0339647i	$0.989187\pi$
$558$		0			0
$559$	21.2624	−	15.4480i	0.899303	−	0.653382i
$560$	20.3020			0.857918
$561$		0			0
$562$	−25.8806			−1.09171
$563$	−13.9397	+	10.1278i	−0.587490	+	0.426836i	−0.841416	−	0.540387i	$-0.818278\pi$
$563$	−13.9397	+	10.1278i	−0.587490	+	0.426836i	0.253927	+	0.967223i	$0.418278\pi$
$564$		0			0
$565$	14.3354	−	44.1198i	0.603094	−	1.85613i
$566$	7.82486	+	5.68509i	0.328903	+	0.238962i
$567$		0			0
$568$	3.70907	−	11.4153i	0.155629	−	0.478977i
$569$	11.0054	+	33.8712i	0.461371	+	1.41995i	0.863490	+	0.504366i	$0.168274\pi$
$569$	11.0054	+	33.8712i	0.461371	+	1.41995i	−0.402119	+	0.915587i	$0.631726\pi$
$570$		0			0
$571$	26.6026			1.11329			0.556643	−	0.830752i	$-0.312089\pi$
$571$	26.6026			1.11329			0.556643	+	0.830752i	$0.312089\pi$
$572$	−8.76855	+	4.68343i	−0.366632	+	0.195824i
$573$		0			0
$574$	−7.91704	+	5.75206i	−0.330451	+	0.240087i
$575$	6.65200	+	20.4727i	0.277407	+	0.853772i
$576$		0			0
$577$	−23.3584	−	16.9708i	−0.972421	−	0.706505i	−0.0164191	−	0.999865i	$-0.505227\pi$
$577$	−23.3584	−	16.9708i	−0.972421	−	0.706505i	−0.956002	+	0.293360i	$0.905227\pi$
$578$	21.0694	+	15.3078i	0.876370	+	0.636720i
$579$		0			0
$580$	−0.280474	−	0.863209i	−0.0116460	−	0.0358428i
$581$	1.67485	−	1.21685i	0.0694844	−	0.0504834i
$582$		0			0
$583$	−11.9645	−	11.5107i	−0.495518	−	0.476723i
$584$	17.8874			0.740188
$585$		0			0
$586$	14.2121	+	43.7404i	0.587098	+	1.80690i
$587$	−0.752191	+	2.31500i	−0.0310462	+	0.0955505i	−0.965379	−	0.260852i	$-0.915997\pi$
$587$	−0.752191	+	2.31500i	−0.0310462	+	0.0955505i	0.934333	+	0.356402i	$0.115997\pi$
$588$		0			0
$589$	12.0147	+	8.72917i	0.495056	+	0.359679i
$590$	−2.10998	+	6.49385i	−0.0868665	+	0.267348i
$591$		0			0
$592$	1.03249	−	0.750145i	0.0424349	−	0.0308308i
$593$	−15.6870			−0.644187			−0.322093	−	0.946708i	$-0.604387\pi$
$593$	−15.6870			−0.644187			−0.322093	+	0.946708i	$0.604387\pi$
$594$		0			0
$595$	−5.37119			−0.220197
$596$	17.7980	−	12.9310i	0.729034	−	0.529675i
$597$		0			0
$598$	3.22696	−	9.93155i	0.131960	−	0.406131i
$599$	−10.6967	−	7.77160i	−0.437055	−	0.317539i	0.347409	−	0.937714i	$-0.387062\pi$
$599$	−10.6967	−	7.77160i	−0.437055	−	0.317539i	−0.784464	+	0.620175i	$0.787062\pi$
$600$		0			0
$601$	−3.47035	+	10.6806i	−0.141559	+	0.435673i	−0.996552	−	0.0829656i	$-0.973561\pi$
$601$	−3.47035	+	10.6806i	−0.141559	+	0.435673i	0.854994	+	0.518638i	$0.173561\pi$
$602$	−4.22973	−	13.0178i	−0.172391	−	0.530564i
$603$		0			0
$604$	−1.21082			−0.0492676
$605$	−43.0432	−	12.1679i	−1.74996	−	0.494697i
$606$		0			0
$607$	−15.6526	+	11.3723i	−0.635319	+	0.461587i	−0.858239	−	0.513250i	$-0.828441\pi$
$607$	−15.6526	+	11.3723i	−0.635319	+	0.461587i	0.222920	+	0.974837i	$0.428441\pi$
$608$	−3.21762	−	9.90280i	−0.130492	−	0.401612i
$609$		0			0
$610$	10.3714	+	7.53526i	0.419925	+	0.305094i
$611$	−10.7870	−	7.83725i	−0.436397	−	0.317061i
$612$		0			0
$613$	6.50631	+	20.0244i	0.262787	+	0.808776i	0.992195	+	0.124697i	$0.0397958\pi$
$613$	6.50631	+	20.0244i	0.262787	+	0.808776i	−0.729408	+	0.684079i	$0.760204\pi$
$614$	−33.9973	+	24.7005i	−1.37202	+	0.996830i
$615$		0			0
$616$	−1.07872	−	6.05133i	−0.0434627	−	0.243815i
$617$	24.1496			0.972228			0.486114	−	0.873895i	$-0.338414\pi$
$617$	24.1496			0.972228			0.486114	+	0.873895i	$0.338414\pi$
$618$		0			0
$619$	0.811091	+	2.49628i	0.0326005	+	0.100334i	0.966033	−	0.258420i	$-0.0832018\pi$
$619$	0.811091	+	2.49628i	0.0326005	+	0.100334i	−0.933432	+	0.358754i	$0.883202\pi$
$620$	7.89352	−	24.2937i	0.317011	−	0.975660i
$621$		0			0
$622$	−14.1055	−	10.2483i	−0.565580	−	0.410918i
$623$	−5.13915	+	15.8167i	−0.205896	+	0.633681i
$624$		0			0
$625$	−40.7646	+	29.6172i	−1.63058	+	1.18469i
$626$	38.2408			1.52841
$627$		0			0
$628$	13.3630			0.533241
$629$	−0.273159	+	0.198461i	−0.0108916	+	0.00791318i
$630$		0			0
$631$	−7.76175	+	23.8882i	−0.308991	+	0.950975i	0.669167	+	0.743112i	$0.266651\pi$
$631$	−7.76175	+	23.8882i	−0.308991	+	0.950975i	−0.978158	+	0.207863i	$0.933349\pi$
$632$	−8.29819	−	6.02899i	−0.330084	−	0.239820i
$633$		0			0
$634$	−12.3231	+	37.9266i	−0.489412	+	1.50626i
$635$	10.9931	+	33.8333i	0.436248	+	1.34263i
$636$		0			0
$637$	3.27792			0.129876
$638$	−1.21911	+	0.651146i	−0.0482649	+	0.0257791i
$639$		0			0
$640$	41.5900	−	30.2169i	1.64399	−	1.19443i
$641$	−6.38380	−	19.6473i	−0.252145	−	0.776022i	−0.994379	−	0.105881i	$-0.966234\pi$
$641$	−6.38380	−	19.6473i	−0.252145	−	0.776022i	0.742234	−	0.670141i	$-0.233766\pi$
$642$		0			0
$643$	−13.3190	−	9.67683i	−0.525251	−	0.381617i	0.293328	−	0.956012i	$-0.405237\pi$
$643$	−13.3190	−	9.67683i	−0.525251	−	0.381617i	−0.818578	+	0.574395i	$0.805237\pi$
$644$	−1.38047	−	1.00297i	−0.0543983	−	0.0395226i
$645$		0			0
$646$	1.50635	+	4.63606i	0.0592664	+	0.182403i
$647$	−28.2819	+	20.5480i	−1.11188	+	0.807825i	−0.982958	−	0.183830i	$-0.941150\pi$
$647$	−28.2819	+	20.5480i	−1.11188	+	0.807825i	−0.128918	+	0.991655i	$0.541150\pi$
$648$		0			0
$649$	3.23130	+	0.447953i	0.126840	+	0.0175837i
$650$	64.5511			2.53190
$651$		0			0
$652$	−5.91163	−	18.1941i	−0.231517	−	0.712537i
$653$	−0.746736	+	2.29822i	−0.0292221	+	0.0899362i	−0.964604	−	0.263703i	$-0.915056\pi$
$653$	−0.746736	+	2.29822i	−0.0292221	+	0.0899362i	0.935382	+	0.353639i	$0.115056\pi$
$654$		0			0
$655$	41.2918	+	30.0002i	1.61340	+	1.17221i
$656$	−8.84395	+	27.2189i	−0.345298	+	1.06272i
$657$		0			0
$658$	−5.61795	+	4.08168i	−0.219011	+	0.159121i
$659$	−16.9733			−0.661186			−0.330593	−	0.943773i	$-0.607249\pi$
$659$	−16.9733			−0.661186			−0.330593	+	0.943773i	$0.607249\pi$
$660$		0			0
$661$	7.96946			0.309976			0.154988	−	0.987916i	$-0.450466\pi$
$661$	7.96946			0.309976			0.154988	+	0.987916i	$0.450466\pi$
$662$	−21.6068	+	15.6982i	−0.839770	+	0.610129i
$663$		0			0
$664$	1.18563	−	3.64898i	0.0460112	−	0.141608i
$665$	7.11164	+	5.16691i	0.275777	+	0.200364i
$666$		0			0
$667$	0.140764	−	0.433227i	0.00545040	−	0.0167746i
$668$	−1.38833	−	4.27283i	−0.0537160	−	0.165321i
$669$		0			0
$670$	20.8744			0.806449
$671$	2.67463	−	5.51000i	0.103253	−	0.212711i
$672$		0			0
$673$	−12.9645	+	9.41925i	−0.499744	+	0.363085i	−0.808919	−	0.587920i	$-0.799947\pi$
$673$	−12.9645	+	9.41925i	−0.499744	+	0.363085i	0.309175	+	0.951005i	$0.399947\pi$
$674$	17.1931	+	52.9148i	0.662253	+	2.03820i
$675$		0			0
$676$	1.66832	+	1.21211i	0.0641663	+	0.0466196i
$677$	12.3266	+	8.95583i	0.473751	+	0.344200i	0.798901	−	0.601462i	$-0.205415\pi$
$677$	12.3266	+	8.95583i	0.473751	+	0.344200i	−0.325150	+	0.945662i	$0.605415\pi$
$678$		0			0
$679$	−0.798992	−	2.45904i	−0.0306625	−	0.0943694i
$680$	−8.05333	+	5.85109i	−0.308831	+	0.224379i
$681$		0			0
$682$	−38.5288	−	5.34122i	−1.47535	−	0.204526i
$683$	−14.3742			−0.550013			−0.275007	−	0.961442i	$-0.588680\pi$
$683$	−14.3742			−0.550013			−0.275007	+	0.961442i	$0.588680\pi$
$684$		0			0
$685$	−7.95186	−	24.4733i	−0.303825	−	0.935077i
$686$	0.527541	−	1.62360i	0.0201416	−	0.0619895i
$687$		0			0
$688$	−32.3852	−	23.5292i	−1.23467	−	0.897043i
$689$	5.07059	−	15.6057i	0.193174	−	0.594529i
$690$		0			0
$691$	36.2422	−	26.3315i	1.37872	−	1.00170i	0.381720	−	0.924278i	$-0.375332\pi$
$691$	36.2422	−	26.3315i	1.37872	−	1.00170i	0.996999	−	0.0774200i	$-0.0246682\pi$
$692$	−17.9750			−0.683305
$693$		0			0
$694$	−9.82101			−0.372800
$695$	47.5138	−	34.5208i	1.80230	−	1.30945i
$696$		0			0
$697$	2.33979	−	7.20114i	0.0886259	−	0.272763i
$698$	0.254043	+	0.184573i	0.00961565	+	0.00698618i
$699$		0			0
$700$	3.25946	−	10.0316i	0.123196	−	0.379158i
$701$	0.0742660	+	0.228567i	0.00280499	+	0.00863287i	0.952449	−	0.304697i	$-0.0985553\pi$
$701$	0.0742660	+	0.228567i	0.00280499	+	0.00863287i	−0.949644	+	0.313330i	$0.898555\pi$
$702$		0			0
$703$	0.552584			0.0208411
$704$	−4.21260	−	4.05282i	−0.158768	−	0.152746i
$705$		0			0
$706$	26.2704	−	19.0866i	0.988699	−	0.718332i
$707$	−3.26588	−	10.0513i	−0.122826	−	0.378019i
$708$		0			0
$709$	−8.69968	−	6.32068i	−0.326723	−	0.237378i	0.412316	−	0.911041i	$-0.364720\pi$
$709$	−8.69968	−	6.32068i	−0.326723	−	0.237378i	−0.739039	+	0.673663i	$0.764720\pi$
$710$	−36.3725	−	26.4262i	−1.36504	−	0.991757i
$711$		0			0
$712$	9.52441	+	29.3131i	0.356942	+	1.09856i
$713$	10.3716	−	7.53539i	0.388419	−	0.282203i
$714$		0			0
$715$	−7.75828	−	43.5220i	−0.290143	−	1.62763i
$716$	23.1879			0.866573
$717$		0			0
$718$	0.379264	+	1.16725i	0.0141540	+	0.0435615i
$719$	7.96486	−	24.5133i	0.297039	−	0.914193i	−0.685489	−	0.728083i	$-0.740412\pi$
$719$	7.96486	−	24.5133i	0.297039	−	0.914193i	0.982529	−	0.186111i	$-0.0595883\pi$
$720$		0			0
$721$	−11.2040	−	8.14017i	−0.417258	−	0.303156i
$722$	−7.55800	+	23.2611i	−0.281280	+	0.865690i
$723$		0			0
$724$	1.46153	−	1.06186i	0.0543174	−	0.0394639i
$725$	2.81580			0.104576
$726$		0			0
$727$	−5.47160			−0.202930			−0.101465	−	0.994839i	$-0.532353\pi$
$727$	−5.47160			−0.202930			−0.101465	+	0.994839i	$0.532353\pi$
$728$	4.91477	−	3.57079i	0.182154	−	0.132342i
$729$		0			0
$730$	20.7045	−	63.7218i	0.766307	−	2.35845i
$731$	8.56796	+	6.22498i	0.316897	+	0.230239i
$732$		0			0
$733$	−6.13595	+	18.8845i	−0.226636	+	0.697515i	0.771485	+	0.636248i	$0.219514\pi$
$733$	−6.13595	+	18.8845i	−0.226636	+	0.697515i	−0.998121	+	0.0612676i	$0.980486\pi$
$734$	−4.16386	−	12.8150i	−0.153691	−	0.473011i
$735$		0			0
$736$	−8.98845			−0.331319
$737$	−1.75022	−	9.81831i	−0.0644703	−	0.361662i
$738$		0			0
$739$	−1.45685	+	1.05847i	−0.0535912	+	0.0389363i	−0.614258	−	0.789105i	$-0.710545\pi$
$739$	−1.45685	+	1.05847i	−0.0535912	+	0.0389363i	0.560667	+	0.828041i	$0.310545\pi$
$740$	−0.293708	−	0.903939i	−0.0107969	−	0.0332295i
$741$		0			0
$742$	−6.91368	−	5.02309i	−0.253809	−	0.184403i
$743$	38.8797	+	28.2477i	1.42636	+	1.03631i	0.990681	+	0.136205i	$0.0434906\pi$
$743$	38.8797	+	28.2477i	1.42636	+	1.03631i	0.435676	+	0.900104i	$0.356509\pi$
$744$		0			0
$745$	30.2323	+	93.0454i	1.10762	+	3.40892i
$746$	−21.6403	+	15.7226i	−0.792307	+	0.575645i
$747$		0			0
$748$	−2.88676	−	2.77727i	−0.105551	−	0.101547i
$749$	−12.4286			−0.454133
$750$		0			0
$751$	−7.73980	−	23.8207i	−0.282429	−	0.869228i	−0.987157	−	0.159751i	$-0.948931\pi$
$751$	−7.73980	−	23.8207i	−0.282429	−	0.869228i	0.704728	−	0.709478i	$-0.251069\pi$
$752$	−6.27569	+	19.3146i	−0.228851	+	0.704331i
$753$		0			0
$754$	−1.10510	−	0.802901i	−0.0402453	−	0.0292399i
$755$	1.66394	−	5.12107i	0.0605569	−	0.186375i
$756$		0			0
$757$	−8.61495	+	6.25913i	−0.313116	+	0.227492i	−0.733232	−	0.679978i	$-0.761989\pi$
$757$	−8.61495	+	6.25913i	−0.313116	+	0.227492i	0.420116	+	0.907470i	$0.361989\pi$
$758$	−22.7298			−0.825583
$759$		0			0
$760$	16.2914			0.590952
$761$	−24.1216	+	17.5254i	−0.874408	+	0.635295i	−0.931766	−	0.363059i	$-0.881732\pi$
$761$	−24.1216	+	17.5254i	−0.874408	+	0.635295i	0.0573579	+	0.998354i	$0.481732\pi$
$762$		0			0
$763$	−2.27668	+	7.00689i	−0.0824212	+	0.253666i
$764$	0.719781	+	0.522952i	0.0260408	+	0.0189197i
$765$		0			0
$766$	−6.25053	+	19.2372i	−0.225841	+	0.695067i
$767$	0.996314	+	3.06634i	0.0359748	+	0.110719i
$768$		0			0
$769$	−28.3115			−1.02094			−0.510470	−	0.859896i	$-0.670529\pi$
$769$	−28.3115			−1.02094			−0.510470	+	0.859896i	$0.670529\pi$
$770$	−22.8057	−	3.16154i	−0.821861	−	0.113934i
$771$		0			0
$772$	17.1126	−	12.4330i	0.615894	−	0.447473i
$773$	−4.09645	−	12.6076i	−0.147339	−	0.453463i	0.849965	−	0.526839i	$-0.176623\pi$
$773$	−4.09645	−	12.6076i	−0.147339	−	0.453463i	−0.997304	+	0.0733754i	$0.976623\pi$
$774$		0			0
$775$	64.1118	+	46.5800i	2.30296	+	1.67320i
$776$	−3.87672	−	2.81660i	−0.139166	−	0.101110i
$777$		0			0
$778$	3.19147	+	9.82235i	0.114420	+	0.352148i
$779$	−10.0252	+	7.28374i	−0.359191	+	0.260967i
$780$		0			0
$781$	−9.37993	+	19.3236i	−0.335640	+	0.691452i
$782$	4.20800			0.150478
$783$		0			0
$784$	−1.54282	−	4.74831i	−0.0551007	−	0.169583i
$785$	−18.3637	+	56.5177i	−0.655429	+	2.01720i
$786$		0			0
$787$	−42.6167	−	30.9628i	−1.51912	−	1.10370i	−0.961922	−	0.273325i	$-0.911876\pi$
$787$	−42.6167	−	30.9628i	−1.51912	−	1.10370i	−0.557198	−	0.830380i	$-0.688124\pi$
$788$	2.80086	−	8.62017i	0.0997767	−	0.307081i
$789$		0			0
$790$	−31.0826	+	22.5828i	−1.10587	+	0.803460i
$791$	−11.4083			−0.405632
$792$		0			0
$793$	6.05337			0.214961
$794$	15.9882	−	11.6161i	0.567401	−	0.412241i
$795$		0			0
$796$	2.93433	−	9.03095i	0.104005	−	0.320094i
$797$	−5.93398	−	4.31129i	−0.210192	−	0.152714i	0.477708	−	0.878518i	$-0.341468\pi$
$797$	−5.93398	−	4.31129i	−0.210192	−	0.152714i	−0.687901	+	0.725805i	$0.741468\pi$
$798$		0			0
$799$	1.66032	−	5.10995i	0.0587380	−	0.180777i
$800$	−17.1696	−	52.8426i	−0.607038	−	1.86827i
$801$		0			0
$802$	−57.6890			−2.03707
$803$	−31.7076	−	4.39560i	−1.11894	−	0.155117i
$804$		0			0
$805$	6.13907	−	4.46030i	0.216374	−	0.157205i
$806$	−11.8797	−	36.5618i	−0.418443	−	1.28784i
$807$		0			0
$808$	−15.8461	−	11.5129i	−0.557464	−	0.405021i
$809$	7.01263	+	5.09497i	0.246551	+	0.179130i	0.704197	−	0.710005i	$-0.251307\pi$
$809$	7.01263	+	5.09497i	0.246551	+	0.179130i	−0.457646	+	0.889135i	$0.651307\pi$
$810$		0			0
$811$	6.16449	+	18.9723i	0.216464	+	0.666209i	0.999046	+	0.0436614i	$0.0139023\pi$
$811$	6.16449	+	18.9723i	0.216464	+	0.666209i	−0.782582	+	0.622548i	$0.786098\pi$
$812$	−0.180576	+	0.131196i	−0.00633698	+	0.00460409i
$813$		0			0
$814$	−1.27663	+	0.681870i	−0.0447459	+	0.0238995i
$815$	85.0745			2.98003
$816$		0			0
$817$	−5.35603	−	16.4842i	−0.187384	−	0.576708i
$818$	9.52316	−	29.3093i	0.332969	−	1.02477i
$819$		0			0
$820$	17.2436	+	12.5282i	0.602172	+	0.437504i
$821$	−16.5524	+	50.9432i	−0.577684	+	1.77793i	0.0491669	+	0.998791i	$0.484343\pi$
$821$	−16.5524	+	50.9432i	−0.577684	+	1.77793i	−0.626851	+	0.779139i	$0.715657\pi$
$822$		0			0
$823$	6.83491	−	4.96585i	0.238250	−	0.173099i	−0.462253	−	0.886748i	$-0.652959\pi$
$823$	6.83491	−	4.96585i	0.238250	−	0.173099i	0.700503	+	0.713649i	$0.252959\pi$
$824$	−25.6662			−0.894125
$825$		0			0
$826$	1.67915			0.0584250
$827$	−2.57477	+	1.87068i	−0.0895337	+	0.0650500i	−0.631652	−	0.775252i	$-0.717623\pi$
$827$	−2.57477	+	1.87068i	−0.0895337	+	0.0650500i	0.542118	+	0.840302i	$0.317623\pi$
$828$		0			0
$829$	17.7712	−	54.6943i	0.617221	−	1.89961i	0.259837	−	0.965652i	$-0.416331\pi$
$829$	17.7712	−	54.6943i	0.617221	−	1.89961i	0.357384	−	0.933958i	$-0.383669\pi$
$830$	−11.6267	−	8.44729i	−0.403569	−	0.293210i
$831$		0			0
$832$	1.78532	−	5.49464i	0.0618948	−	0.190492i
$833$	0.408175	+	1.25623i	0.0141424	+	0.0435259i
$834$		0			0
$835$	19.9795			0.691419
$836$	1.15053	+	6.45417i	0.0397918	+	0.223222i
$837$		0			0
$838$	3.57101	−	2.59449i	0.123358	−	0.0896251i
$839$	−3.88108	−	11.9447i	−0.133990	−	0.412378i	0.861442	−	0.507856i	$-0.169562\pi$
$839$	−3.88108	−	11.9447i	−0.133990	−	0.412378i	−0.995432	+	0.0954784i	$0.969562\pi$
$840$		0			0
$841$	23.4133	+	17.0107i	0.807355	+	0.586578i
$842$	−19.3285	−	14.0430i	−0.666103	−	0.483952i
$843$		0			0
$844$	−3.67094	−	11.2980i	−0.126359	−	0.388892i
$845$	−7.41917	+	5.39034i	−0.255227	+	0.185433i
$846$		0			0
$847$	0.425120	+	10.9918i	0.0146073	+	0.377682i
$848$	−24.9926			−0.858248
$849$		0			0
$850$	8.03806	+	24.7386i	0.275703	+	0.848528i
$851$	0.147406	−	0.453668i	0.00505300	−	0.0155515i
$852$		0			0
$853$	−26.9658	−	19.5918i	−0.923290	−	0.670810i	0.0210505	−	0.999778i	$-0.493299\pi$
$853$	−26.9658	−	19.5918i	−0.923290	−	0.670810i	−0.944341	+	0.328969i	$0.893299\pi$
$854$	0.974215	−	2.99833i	0.0333370	−	0.102601i
$855$		0			0
$856$	−18.6350	+	13.5391i	−0.636930	+	0.462757i
$857$	−54.0291			−1.84560			−0.922800	−	0.385279i	$-0.874105\pi$
$857$	−54.0291			−1.84560			−0.922800	+	0.385279i	$0.874105\pi$
$858$		0			0
$859$	−12.8624			−0.438860			−0.219430	−	0.975628i	$-0.570420\pi$
$859$	−12.8624			−0.438860			−0.219430	+	0.975628i	$0.570420\pi$
$860$	−24.1186	+	17.5232i	−0.822438	+	0.597536i
$861$		0			0
$862$	17.7613	−	54.6638i	0.604954	−	1.86186i
$863$	−26.8813	−	19.5304i	−0.915049	−	0.664822i	0.0272379	−	0.999629i	$-0.491329\pi$
$863$	−26.8813	−	19.5304i	−0.915049	−	0.664822i	−0.942287	+	0.334807i	$0.891329\pi$
$864$		0			0
$865$	24.7016	−	76.0237i	0.839879	−	2.58488i
$866$	3.96865	+	12.2143i	0.134860	+	0.415057i
$867$		0			0
$868$	−6.28176			−0.213217
$869$	13.2280	+	12.7263i	0.448729	+	0.431709i
$870$		0			0
$871$	7.97425	−	5.79363i	0.270197	−	0.196310i
$872$	4.21938	+	12.9859i	0.142886	+	0.439758i
$873$		0			0
$874$	−5.57153	−	4.04796i	−0.188460	−	0.136924i
$875$	21.4998	+	15.6205i	0.726826	+	0.528070i
$876$		0			0
$877$	8.55077	+	26.3166i	0.288739	+	0.888647i	0.985253	+	0.171104i	$0.0547333\pi$
$877$	8.55077	+	26.3166i	0.288739	+	0.888647i	−0.696514	+	0.717543i	$0.745267\pi$
$878$	30.4016	−	22.0880i	1.02600	−	0.745435i
$879$		0			0
$880$	−59.3933	+	31.7230i	−2.00215	+	1.06938i
$881$	−48.9636			−1.64963			−0.824813	−	0.565406i	$-0.808720\pi$
$881$	−48.9636			−1.64963			−0.824813	+	0.565406i	$0.808720\pi$
$882$		0			0
$883$	6.58897	+	20.2788i	0.221736	+	0.682435i	0.998607	+	0.0527736i	$0.0168062\pi$
$883$	6.58897	+	20.2788i	0.221736	+	0.682435i	−0.776870	+	0.629661i	$0.783194\pi$
$884$	1.22342	−	3.76531i	0.0411482	−	0.126641i
$885$		0			0
$886$	32.7178	+	23.7708i	1.09917	+	0.798597i
$887$	13.9825	−	43.0337i	0.469487	−	1.44493i	−0.383765	−	0.923431i	$-0.625373\pi$
$887$	13.9825	−	43.0337i	0.469487	−	1.44493i	0.853251	−	0.521500i	$-0.174627\pi$
$888$		0			0
$889$	7.07765	−	5.14221i	0.237377	−	0.172464i
$890$	115.449			3.86985
$891$		0			0
$892$	−13.1240			−0.439423
$893$	−7.11392	+	5.16857i	−0.238058	+	0.172959i
$894$		0			0
$895$	−31.8654	+	98.0715i	−1.06514	+	3.27817i
$896$	−10.2278	−	7.43092i	−0.341687	−	0.248250i
$897$		0			0
$898$	−1.20023	+	3.69392i	−0.0400521	+	0.123268i
$899$	−0.518206	−	1.59487i	−0.0172831	−	0.0531920i
$900$		0			0
$901$	6.61213			0.220282
$902$	14.1733	−	29.1983i	0.471918	−	0.972198i
$903$		0			0
$904$	−17.1051	+	12.4276i	−0.568906	+	0.413335i
$905$	2.48260	+	7.64067i	0.0825245	+	0.253984i
$906$		0			0
$907$	36.4596	+	26.4894i	1.21062	+	0.879568i	0.995287	−	0.0969727i	$-0.0309160\pi$
$907$	36.4596	+	26.4894i	1.21062	+	0.879568i	0.215334	+	0.976540i	$0.430916\pi$
$908$	4.71581	+	3.42623i	0.156499	+	0.113704i
$909$		0			0
$910$	−7.03172	−	21.6414i	−0.233099	−	0.717406i
$911$	−7.45484	+	5.41626i	−0.246990	+	0.179449i	−0.704392	−	0.709812i	$-0.748780\pi$
$911$	−7.45484	+	5.41626i	−0.246990	+	0.179449i	0.457402	+	0.889260i	$0.348780\pi$
$912$		0			0
$913$	−2.99835	+	6.17690i	−0.0992310	+	0.204426i
$914$	−46.6283			−1.54233
$915$		0			0
$916$	−2.26117	−	6.95916i	−0.0747111	−	0.229937i
$917$	3.87866	−	11.9373i	0.128085	−	0.394204i
$918$		0			0
$919$	−40.2198	−	29.2214i	−1.32673	−	0.963924i	−0.999822	−	0.0188673i	$-0.993994\pi$
$919$	−40.2198	−	29.2214i	−1.32673	−	0.963924i	−0.326906	−	0.945057i	$-0.606006\pi$
$920$	4.34585	−	13.3751i	0.143278	−	0.440966i
$921$		0			0
$922$	−11.3515	+	8.24738i	−0.373843	+	0.271613i
$923$	−21.2292			−0.698767
$924$		0			0
$925$	2.94866			0.0969514
$926$	38.6491	−	28.0802i	1.27009	−	0.922773i
$927$		0			0
$928$	−0.363329	+	1.11821i	−0.0119269	+	0.0367071i
$929$	40.0548	+	29.1015i	1.31416	+	0.954790i	0.999985	+	0.00542290i	$0.00172617\pi$
$929$	40.0548	+	29.1015i	1.31416	+	0.954790i	0.314170	+	0.949367i	$0.398274\pi$
$930$		0			0
$931$	0.668017	−	2.05594i	0.0218934	−	0.0673808i
$932$	3.05229	+	9.39399i	0.0999812	+	0.307710i
$933$		0			0
$934$	−45.5377			−1.49004
$935$	15.7133	−	8.39275i	0.513881	−	0.274472i
$936$		0			0
$937$	−5.65333	+	4.10739i	−0.184686	+	0.134182i	−0.676287	−	0.736638i	$-0.736412\pi$
$937$	−5.65333	+	4.10739i	−0.184686	+	0.134182i	0.491601	+	0.870821i	$0.336412\pi$
$938$	−1.58632	−	4.88218i	−0.0517951	−	0.159409i
$939$		0			0
$940$	12.2361	+	8.89005i	0.399098	+	0.289961i
$941$	37.8815	+	27.5225i	1.23490	+	0.897208i	0.997248	−	0.0741421i	$-0.0236219\pi$
$941$	37.8815	+	27.5225i	1.23490	+	0.897208i	0.237653	+	0.971350i	$0.423622\pi$
$942$		0			0
$943$	3.30561	+	10.1736i	0.107645	+	0.331299i
$944$	3.97288	−	2.88647i	0.129306	−	0.0939465i
$945$		0			0
$946$	32.7149	+	31.4740i	1.06365	+	1.02331i
$947$	−15.1286			−0.491614			−0.245807	−	0.969319i	$-0.579053\pi$
$947$	−15.1286			−0.491614			−0.245807	+	0.969319i	$0.579053\pi$
$948$		0			0
$949$	−9.77647	−	30.0889i	−0.317358	−	0.976726i
$950$	13.1551	−	40.4871i	0.426806	−	1.31357i
$951$		0			0
$952$	1.98047	+	1.43890i	0.0641875	+	0.0466349i
$953$	17.3752	−	53.4753i	0.562838	−	1.73224i	−0.111453	−	0.993770i	$-0.535550\pi$
$953$	17.3752	−	53.4753i	0.562838	−	1.73224i	0.674291	−	0.738466i	$-0.264450\pi$
$954$		0			0
$955$	−3.20092	+	2.32561i	−0.103579	+	0.0752549i
$956$	−23.0045			−0.744019
$957$		0			0
$958$	39.6470			1.28094
$959$	−5.11961	+	3.71962i	−0.165321	+	0.120113i
$960$		0			0
$961$	5.00461	−	15.4026i	0.161439	−	0.496858i
$962$	−1.15724	−	0.840785i	−0.0373110	−	0.0271080i
$963$		0			0
$964$	−5.15568	+	15.8675i	−0.166053	+	0.511059i
$965$	29.0679	+	89.4619i	0.935730	+	2.87988i
$966$		0			0
$967$	46.3761			1.49136			0.745678	−	0.666307i	$-0.232126\pi$
$967$	46.3761			1.49136			0.745678	+	0.666307i	$0.232126\pi$
$968$	12.6113	+	16.0175i	0.405341	+	0.514822i
$969$		0			0
$970$	−14.5211	+	10.5502i	−0.466243	+	0.338746i
$971$	−4.80211	−	14.7794i	−0.154107	−	0.474293i	0.843962	−	0.536403i	$-0.180217\pi$
$971$	−4.80211	−	14.7794i	−0.154107	−	0.474293i	−0.998069	+	0.0621097i	$0.980217\pi$
$972$		0			0
$973$	−11.6846	−	8.48935i	−0.374591	−	0.272156i
$974$	25.9541	+	18.8567i	0.831622	+	0.604208i
$975$		0			0
$976$	−2.84914	−	8.76876i	−0.0911988	−	0.280681i
$977$	26.5590	−	19.2962i	0.849697	−	0.617341i	−0.0753657	−	0.997156i	$-0.524012\pi$
$977$	26.5590	−	19.2962i	0.849697	−	0.617341i	0.925062	+	0.379815i	$0.124012\pi$
$978$		0			0
$979$	−9.67985	−	54.3015i	−0.309369	−	1.73548i
$980$	−3.71825			−0.118775
$981$		0			0
$982$	−3.90683	−	12.0240i	−0.124672	−	0.383701i
$983$	−7.51478	+	23.1281i	−0.239684	+	0.737673i	0.756781	+	0.653668i	$0.226771\pi$
$983$	−7.51478	+	23.1281i	−0.239684	+	0.737673i	−0.996465	+	0.0840042i	$0.973229\pi$
$984$		0			0
$985$	32.6093	+	23.6921i	1.03902	+	0.754892i
$986$	0.170095	−	0.523498i	0.00541692	−	0.0166716i
$987$		0			0
$988$	−5.24195	+	3.80850i	−0.166769	+	0.121165i
$989$	−14.9622			−0.475769
$990$		0			0
$991$	−47.7104			−1.51557			−0.757786	−	0.652503i	$-0.773719\pi$
$991$	−47.7104			−1.51557			−0.757786	+	0.652503i	$0.773719\pi$
$992$	−26.7703	+	19.4498i	−0.849959	+	0.617531i
$993$		0			0
$994$	−3.41658	+	10.5151i	−0.108367	+	0.333520i
$995$	34.1633	+	24.8211i	1.08305	+	0.786881i
$996$		0			0
$997$	6.13241	−	18.8736i	0.194215	−	0.597733i	−0.805770	−	0.592229i	$-0.798248\pi$
$997$	6.13241	−	18.8736i	0.194215	−	0.597733i	0.999985	−	0.00550400i	$-0.00175199\pi$
$998$	12.4871	+	38.4313i	0.395272	+	1.21652i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.i.190.1		16
3.2	odd	2		77.2.f.b.36.4	yes	16
11.2	odd	10		7623.2.a.cw.1.2		8
11.4	even	5	inner	693.2.m.i.631.1		16
11.9	even	5		7623.2.a.ct.1.7		8
21.2	odd	6		539.2.q.g.410.1		32
21.5	even	6		539.2.q.f.410.1		32
21.11	odd	6		539.2.q.g.520.4		32
21.17	even	6		539.2.q.f.520.4		32
21.20	even	2		539.2.f.e.344.4		16
33.2	even	10		847.2.a.o.1.7		8
33.5	odd	10		847.2.f.w.372.1		16
33.8	even	10		847.2.f.v.148.4		16
33.14	odd	10		847.2.f.w.148.1		16
33.17	even	10		847.2.f.v.372.4		16
33.20	odd	10		847.2.a.p.1.2		8
33.26	odd	10		77.2.f.b.15.4	✓	16
33.29	even	10		847.2.f.x.323.1		16
33.32	even	2		847.2.f.x.729.1		16
231.20	even	10		5929.2.a.bt.1.2		8
231.26	even	30		539.2.q.f.312.4		32
231.59	even	30		539.2.q.f.422.1		32
231.125	even	10		539.2.f.e.246.4		16
231.158	odd	30		539.2.q.g.422.1		32
231.167	odd	10		5929.2.a.bs.1.7		8
231.191	odd	30		539.2.q.g.312.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.4	✓	16	33.26	odd	10
77.2.f.b.36.4	yes	16	3.2	odd	2
539.2.f.e.246.4		16	231.125	even	10
539.2.f.e.344.4		16	21.20	even	2
539.2.q.f.312.4		32	231.26	even	30
539.2.q.f.410.1		32	21.5	even	6
539.2.q.f.422.1		32	231.59	even	30
539.2.q.f.520.4		32	21.17	even	6
539.2.q.g.312.4		32	231.191	odd	30
539.2.q.g.410.1		32	21.2	odd	6
539.2.q.g.422.1		32	231.158	odd	30
539.2.q.g.520.4		32	21.11	odd	6
693.2.m.i.190.1		16	1.1	even	1	trivial
693.2.m.i.631.1		16	11.4	even	5	inner
847.2.a.o.1.7		8	33.2	even	10
847.2.a.p.1.2		8	33.20	odd	10
847.2.f.v.148.4		16	33.8	even	10
847.2.f.v.372.4		16	33.17	even	10
847.2.f.w.148.1		16	33.14	odd	10
847.2.f.w.372.1		16	33.5	odd	10
847.2.f.x.323.1		16	33.29	even	10
847.2.f.x.729.1		16	33.32	even	2
5929.2.a.bs.1.7		8	231.167	odd	10
5929.2.a.bt.1.2		8	231.20	even	10
7623.2.a.ct.1.7		8	11.9	even	5
7623.2.a.cw.1.2		8	11.2	odd	10

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.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38112 + 1.00344i) q^{2} +(0.282562 - 0.869638i) q^{4} +(3.28976 + 2.39015i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.572703 - 1.76260i) q^{8} +O(q^{10})\)	\(q+(-1.38112 + 1.00344i) q^{2} +(0.282562 - 0.869638i) q^{4} +(3.28976 + 2.39015i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.572703 - 1.76260i) q^{8} -6.94194 q^{10} +(0.582050 + 3.26515i) q^{11} +(-2.65189 + 1.92671i) q^{13} +(0.527541 + 1.62360i) q^{14} +(4.03916 + 2.93462i) q^{16} +(-1.06862 - 0.776394i) q^{17} +(0.668017 + 2.05594i) q^{19} +(3.00813 - 2.18553i) q^{20} +(-4.08027 - 3.92552i) q^{22} +1.86611 q^{23} +(3.56462 + 10.9708i) q^{25} +(1.72924 - 5.32205i) q^{26} +(-0.739758 - 0.537466i) q^{28} +(0.0754316 - 0.232155i) q^{29} +(5.55785 - 4.03801i) q^{31} -4.81667 q^{32} +2.25495 q^{34} +(3.28976 - 2.39015i) q^{35} +(0.0789907 - 0.243108i) q^{37} +(-2.98563 - 2.16919i) q^{38} +(2.32882 - 7.16738i) q^{40} +(1.77139 + 5.45177i) q^{41} -8.01781 q^{43} +(3.00397 + 0.416437i) q^{44} +(-2.57733 + 1.87254i) q^{46} +(1.25698 + 3.86859i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-15.9317 - 11.5751i) q^{50} +(0.926218 + 2.85060i) q^{52} +(-4.04982 + 2.94237i) q^{53} +(-5.88941 + 12.1328i) q^{55} -1.85331 q^{56} +(0.128774 + 0.396325i) q^{58} +(0.303947 - 0.935452i) q^{59} +(-1.49402 - 1.08547i) q^{61} +(-3.62414 + 11.1540i) q^{62} +(-1.42591 + 1.03598i) q^{64} -13.3292 q^{65} -3.00700 q^{67} +(-0.977133 + 0.709928i) q^{68} +(-2.14518 + 6.60218i) q^{70} +(5.23953 + 3.80674i) q^{71} +(-2.98252 + 9.17926i) q^{73} +(0.134850 + 0.415025i) q^{74} +1.97668 q^{76} +(3.28521 + 0.455425i) q^{77} +(4.47750 - 3.25310i) q^{79} +(6.27368 + 19.3084i) q^{80} +(-7.91704 - 5.75206i) q^{82} +(1.67485 + 1.21685i) q^{83} +(-1.65979 - 5.10831i) q^{85} +(11.0736 - 8.04542i) q^{86} +(5.42181 - 2.89588i) q^{88} -16.6306 q^{89} +(1.01293 + 3.11749i) q^{91} +(0.527294 - 1.62284i) q^{92} +(-5.61795 - 4.08168i) q^{94} +(-2.71640 + 8.36023i) q^{95} +(2.09179 - 1.51977i) q^{97} +1.70716 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

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