LMFDB - Embedded newform 207.2.i.a.118.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			118.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	207.118
Dual form			207.2.i.a.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.357685 - 2.48775i) q^{2} +(-4.14200 + 1.21620i) q^{4} +(-2.65565 + 3.06479i) q^{5} +(-1.15843 + 0.744479i) q^{7} +(2.41899 + 5.29684i) q^{8} +O(q^{10})$	\(q+(-0.357685 - 2.48775i) q^{2} +(-4.14200 + 1.21620i) q^{4} +(-2.65565 + 3.06479i) q^{5} +(-1.15843 + 0.744479i) q^{7} +(2.41899 + 5.29684i) q^{8} +(8.57432 + 5.51038i) q^{10} +(0.00388573 - 0.0270259i) q^{11} +(-0.527646 - 0.339098i) q^{13} +(2.26643 + 2.61561i) q^{14} +(5.04885 - 3.24470i) q^{16} +(-4.13515 - 1.21419i) q^{17} +(-4.79898 + 1.40911i) q^{19} +(7.27232 - 15.9241i) q^{20} -0.0686236 q^{22} +(-1.11722 + 4.66388i) q^{23} +(-1.62885 - 11.3289i) q^{25} +(-0.654861 + 1.43394i) q^{26} +(3.89279 - 4.49252i) q^{28} +(3.54487 + 1.04087i) q^{29} +(-0.200359 - 0.438726i) q^{31} +(-2.25133 - 2.59818i) q^{32} +(-1.54152 + 10.7215i) q^{34} +(0.794723 - 5.52742i) q^{35} +(1.44203 + 1.66419i) q^{37} +(5.22204 + 11.4347i) q^{38} +(-22.6577 - 6.65289i) q^{40} +(6.56243 - 7.57345i) q^{41} +(-1.36272 + 2.98394i) q^{43} +(0.0167742 + 0.116667i) q^{44} +(12.0022 + 1.11118i) q^{46} -8.98345 q^{47} +(-2.12019 + 4.64257i) q^{49} +(-27.6009 + 8.10436i) q^{50} +(2.59792 + 0.762819i) q^{52} +(-1.54567 + 0.993342i) q^{53} +(0.0725093 + 0.0836802i) q^{55} +(-6.74562 - 4.33514i) q^{56} +(1.32148 - 9.19107i) q^{58} +(3.51609 + 2.25965i) q^{59} +(1.92053 + 4.20538i) q^{61} +(-1.01978 + 0.655371i) q^{62} +(2.20204 - 2.54129i) q^{64} +(2.44051 - 0.716597i) q^{65} +(-0.630353 - 4.38420i) q^{67} +18.6045 q^{68} -14.0351 q^{70} +(-1.02832 - 7.15212i) q^{71} +(-5.72936 + 1.68229i) q^{73} +(3.62430 - 4.18266i) q^{74} +(18.1636 - 11.6731i) q^{76} +(0.0156188 + 0.0342005i) q^{77} +(1.26938 + 0.815780i) q^{79} +(-3.46368 + 24.0904i) q^{80} +(-21.1882 - 13.6168i) q^{82} +(-5.61081 - 6.47522i) q^{83} +(14.7027 - 9.44888i) q^{85} +(7.91074 + 2.32280i) q^{86} +(0.152551 - 0.0447931i) q^{88} +(-5.53741 + 12.1252i) q^{89} +0.863693 q^{91} +(-1.04468 - 20.6766i) q^{92} +(3.21325 + 22.3486i) q^{94} +(8.42581 - 18.4500i) q^{95} +(-1.41765 + 1.63606i) q^{97} +(12.3079 + 3.61394i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 14 q^{4} + 3 q^{5} + 6 q^{7} + 7 q^{8}+O(q^{10}) $ 10 * q - 4 * q^2 - 14 * q^4 + 3 * q^5 + 6 * q^7 + 7 * q^8	$ 10 q - 4 q^{2} - 14 q^{4} + 3 q^{5} + 6 q^{7} + 7 q^{8} + 12 q^{10} + 15 q^{11} + 8 q^{13} - 9 q^{14} + 12 q^{16} - q^{17} - 9 q^{19} + 9 q^{20} - 28 q^{22} - 21 q^{23} - 4 q^{25} - q^{26} + 29 q^{28} + 8 q^{29} - 23 q^{31} + q^{32} - 15 q^{34} - 18 q^{35} + 3 q^{37} - 3 q^{38} - 32 q^{40} + 15 q^{41} + 22 q^{43} + q^{44} + 26 q^{46} - 4 q^{47} - 29 q^{49} - 49 q^{50} + 2 q^{52} - 29 q^{53} + 43 q^{55} + 2 q^{56} + 21 q^{58} + 54 q^{59} - 30 q^{61} + 7 q^{62} - 31 q^{64} + 9 q^{65} + q^{67} + 30 q^{68} - 94 q^{70} + 3 q^{71} - 47 q^{73} + 12 q^{74} + 50 q^{76} - 13 q^{77} + 18 q^{79} - 3 q^{80} - 28 q^{82} - 18 q^{83} + 58 q^{85} + 16 q^{88} - 25 q^{89} + 18 q^{91} + 3 q^{92} + 39 q^{94} + 16 q^{95} + 21 q^{97} + 27 q^{98}+O(q^{100}) $ 10 * q - 4 * q^2 - 14 * q^4 + 3 * q^5 + 6 * q^7 + 7 * q^8 + 12 * q^10 + 15 * q^11 + 8 * q^13 - 9 * q^14 + 12 * q^16 - q^17 - 9 * q^19 + 9 * q^20 - 28 * q^22 - 21 * q^23 - 4 * q^25 - q^26 + 29 * q^28 + 8 * q^29 - 23 * q^31 + q^32 - 15 * q^34 - 18 * q^35 + 3 * q^37 - 3 * q^38 - 32 * q^40 + 15 * q^41 + 22 * q^43 + q^44 + 26 * q^46 - 4 * q^47 - 29 * q^49 - 49 * q^50 + 2 * q^52 - 29 * q^53 + 43 * q^55 + 2 * q^56 + 21 * q^58 + 54 * q^59 - 30 * q^61 + 7 * q^62 - 31 * q^64 + 9 * q^65 + q^67 + 30 * q^68 - 94 * q^70 + 3 * q^71 - 47 * q^73 + 12 * q^74 + 50 * q^76 - 13 * q^77 + 18 * q^79 - 3 * q^80 - 28 * q^82 - 18 * q^83 + 58 * q^85 + 16 * q^88 - 25 * q^89 + 18 * q^91 + 3 * q^92 + 39 * q^94 + 16 * q^95 + 21 * q^97 + 27 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$

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 $

$2$	−0.357685	−	2.48775i	−0.252922	−	1.75911i	−0.580477	−	0.814276i	$-0.697134\pi$
$2$	−0.357685	−	2.48775i	−0.252922	−	1.75911i	0.327556	−	0.944832i	$-0.393775\pi$
$3$		0			0
$3$		0			0
$4$	−4.14200	+	1.21620i	−2.07100	+	0.608100i
$5$	−2.65565	+	3.06479i	−1.18764	+	1.37061i	−0.275213	+	0.961383i	$0.588748\pi$
$5$	−2.65565	+	3.06479i	−1.18764	+	1.37061i	−0.912431	+	0.409230i	$0.865797\pi$
$6$		0			0
$7$	−1.15843	+	0.744479i	−0.437846	+	0.281387i	−0.740936	−	0.671575i	$-0.765618\pi$
$7$	−1.15843	+	0.744479i	−0.437846	+	0.281387i	0.303090	+	0.952962i	$0.401982\pi$
$8$	2.41899	+	5.29684i	0.855241	+	1.87272i
$9$		0			0
$10$	8.57432	+	5.51038i	2.71144	+	1.74254i
$11$	0.00388573	−	0.0270259i	0.00117159	−	0.00814861i	−0.989227	−	0.146388i	$-0.953235\pi$
$11$	0.00388573	−	0.0270259i	0.00117159	−	0.00814861i	0.990399	+	0.138239i	$0.0441443\pi$
$12$		0			0
$13$	−0.527646	−	0.339098i	−0.146343	−	0.0940488i	0.465420	−	0.885090i	$-0.345903\pi$
$13$	−0.527646	−	0.339098i	−0.146343	−	0.0940488i	−0.611763	+	0.791041i	$0.709539\pi$
$14$	2.26643	+	2.61561i	0.605730	+	0.699050i
$15$		0			0
$16$	5.04885	−	3.24470i	1.26221	−	0.811175i
$17$	−4.13515	−	1.21419i	−1.00292	−	0.294484i	−0.261267	−	0.965267i	$-0.584140\pi$
$17$	−4.13515	−	1.21419i	−1.00292	−	0.294484i	−0.741654	+	0.670783i	$0.765958\pi$
$18$		0			0
$19$	−4.79898	+	1.40911i	−1.10096	+	0.323272i	−0.781234	−	0.624238i	$-0.785410\pi$
$19$	−4.79898	+	1.40911i	−1.10096	+	0.323272i	−0.319728	+	0.947509i	$0.603591\pi$
$20$	7.27232	−	15.9241i	1.62614	−	3.56075i
$21$		0			0
$22$	−0.0686236			−0.0146306
$23$	−1.11722	+	4.66388i	−0.232957	+	0.972487i
$23$	−1.11722	+	4.66388i	−0.232957	+	0.972487i
$24$		0			0
$25$	−1.62885	−	11.3289i	−0.325770	−	2.26578i
$26$	−0.654861	+	1.43394i	−0.128429	+	0.281220i
$27$		0			0
$28$	3.89279	−	4.49252i	0.735668	−	0.849006i
$29$	3.54487	+	1.04087i	0.658266	+	0.193284i	0.593771	−	0.804634i	$-0.297638\pi$
$29$	3.54487	+	1.04087i	0.658266	+	0.193284i	0.0644943	+	0.997918i	$0.479457\pi$
$30$		0			0
$31$	−0.200359	−	0.438726i	−0.0359856	−	0.0787975i	0.890786	−	0.454424i	$-0.150155\pi$
$31$	−0.200359	−	0.438726i	−0.0359856	−	0.0787975i	−0.926771	+	0.375626i	$0.877428\pi$
$32$	−2.25133	−	2.59818i	−0.397983	−	0.459297i
$33$		0			0
$34$	−1.54152	+	10.7215i	−0.264369	+	1.83873i
$35$	0.794723	−	5.52742i	0.134333	−	0.934305i
$36$		0			0
$37$	1.44203	+	1.66419i	0.237067	+	0.273590i	0.861800	−	0.507249i	$-0.169337\pi$
$37$	1.44203	+	1.66419i	0.237067	+	0.273590i	−0.624732	+	0.780839i	$0.714792\pi$
$38$	5.22204	+	11.4347i	0.847127	+	1.85495i
$39$		0			0
$40$	−22.6577	−	6.65289i	−3.58249	−	1.05191i
$41$	6.56243	−	7.57345i	1.02488	−	1.18277i	0.0418888	−	0.999122i	$-0.486662\pi$
$41$	6.56243	−	7.57345i	1.02488	−	1.18277i	0.982991	−	0.183652i	$-0.0587921\pi$
$42$		0			0
$43$	−1.36272	+	2.98394i	−0.207813	+	0.455047i	−0.984624	−	0.174687i	$-0.944109\pi$
$43$	−1.36272	+	2.98394i	−0.207813	+	0.455047i	0.776811	+	0.629734i	$0.216836\pi$
$44$	0.0167742	+	0.116667i	0.00252880	+	0.0175882i
$45$		0			0
$46$	12.0022	+	1.11118i	1.76963	+	0.163834i
$47$	−8.98345			−1.31037			−0.655186	−	0.755468i	$-0.727410\pi$
$47$	−8.98345			−1.31037			−0.655186	+	0.755468i	$0.727410\pi$
$48$		0			0
$49$	−2.12019	+	4.64257i	−0.302884	+	0.663224i
$50$	−27.6009	+	8.10436i	−3.90336	+	1.14613i
$51$		0			0
$52$	2.59792	+	0.762819i	0.360267	+	0.105784i
$53$	−1.54567	+	0.993342i	−0.212314	+	0.136446i	−0.642476	−	0.766306i	$-0.722093\pi$
$53$	−1.54567	+	0.993342i	−0.212314	+	0.136446i	0.430162	+	0.902752i	$0.358456\pi$
$54$		0			0
$55$	0.0725093	+	0.0836802i	0.00977716	+	0.0112834i
$56$	−6.74562	−	4.33514i	−0.901421	−	0.579308i
$57$		0			0
$58$	1.32148	−	9.19107i	0.173518	−	1.20685i
$59$	3.51609	+	2.25965i	0.457756	+	0.294182i	0.749125	−	0.662429i	$-0.230474\pi$
$59$	3.51609	+	2.25965i	0.457756	+	0.294182i	−0.291369	+	0.956611i	$0.594111\pi$
$60$		0			0
$61$	1.92053	+	4.20538i	0.245899	+	0.538444i	0.991828	−	0.127582i	$-0.0407215\pi$
$61$	1.92053	+	4.20538i	0.245899	+	0.538444i	−0.745929	+	0.666025i	$0.767994\pi$
$62$	−1.01978	+	0.655371i	−0.129512	+	0.0832322i
$63$		0			0
$64$	2.20204	−	2.54129i	0.275255	−	0.317661i
$65$	2.44051	−	0.716597i	0.302708	−	0.0888830i
$66$		0			0
$67$	−0.630353	−	4.38420i	−0.0770099	−	0.535616i	−0.991409	−	0.130801i	$-0.958245\pi$
$67$	−0.630353	−	4.38420i	−0.0770099	−	0.535616i	0.914399	−	0.404815i	$-0.132664\pi$
$68$	18.6045			2.25612
$69$		0			0
$70$	−14.0351			−1.67752
$71$	−1.02832	−	7.15212i	−0.122039	−	0.848801i	−0.955240	−	0.295831i	$-0.904403\pi$
$71$	−1.02832	−	7.15212i	−0.122039	−	0.848801i	0.833201	−	0.552970i	$-0.186506\pi$
$72$		0			0
$73$	−5.72936	+	1.68229i	−0.670571	+	0.196898i	−0.599257	−	0.800556i	$-0.704537\pi$
$73$	−5.72936	+	1.68229i	−0.670571	+	0.196898i	−0.0713140	+	0.997454i	$0.522719\pi$
$74$	3.62430	−	4.18266i	0.421316	−	0.486224i
$75$		0			0
$76$	18.1636	−	11.6731i	2.08351	−	1.33899i
$77$	0.0156188	+	0.0342005i	0.00177993	+	0.00389751i
$78$		0			0
$79$	1.26938	+	0.815780i	0.142816	+	0.0917824i	0.610098	−	0.792326i	$-0.291130\pi$
$79$	1.26938	+	0.815780i	0.142816	+	0.0917824i	−0.467281	+	0.884109i	$0.654767\pi$
$80$	−3.46368	+	24.0904i	−0.387252	+	2.69339i
$81$		0			0
$82$	−21.1882	−	13.6168i	−2.33984	−	1.50373i
$83$	−5.61081	−	6.47522i	−0.615866	−	0.710748i	0.359050	−	0.933318i	$-0.383101\pi$
$83$	−5.61081	−	6.47522i	−0.615866	−	0.710748i	−0.974917	+	0.222570i	$0.928555\pi$
$84$		0			0
$85$	14.7027	−	9.44888i	1.59474	−	1.02487i
$86$	7.91074	+	2.32280i	0.853037	+	0.250474i
$87$		0			0
$88$	0.152551	−	0.0447931i	0.0162620	−	0.00477496i
$89$	−5.53741	+	12.1252i	−0.586965	+	1.28527i	0.350295	+	0.936640i	$0.386081\pi$
$89$	−5.53741	+	12.1252i	−0.586965	+	1.28527i	−0.937259	+	0.348634i	$0.886646\pi$
$90$		0			0
$91$	0.863693			0.0905397
$92$	−1.04468	−	20.6766i	−0.108916	−	2.15568i
$93$		0			0
$94$	3.21325	+	22.3486i	0.331421	+	2.30509i
$95$	8.42581	−	18.4500i	0.864470	−	1.89293i
$96$		0			0
$97$	−1.41765	+	1.63606i	−0.143941	+	0.166117i	−0.823142	−	0.567835i	$-0.807781\pi$
$97$	−1.41765	+	1.63606i	−0.143941	+	0.166117i	0.679201	+	0.733952i	$0.262326\pi$
$98$	12.3079	+	3.61394i	1.24329	+	0.365063i
$99$		0			0
$100$	20.5249	+	44.9433i	2.05249	+	4.49433i
$101$	8.74204	+	10.0889i	0.869866	+	1.00388i	0.999923	+	0.0123724i	$0.00393834\pi$
$101$	8.74204	+	10.0889i	0.869866	+	1.00388i	−0.130058	+	0.991506i	$0.541516\pi$
$102$		0			0
$103$	−1.34518	+	9.35596i	−0.132545	+	0.921870i	0.809676	+	0.586877i	$0.199643\pi$
$103$	−1.34518	+	9.35596i	−0.132545	+	0.921870i	−0.942221	+	0.334993i	$0.891266\pi$
$104$	0.519777	−	3.61513i	0.0509684	−	0.354493i
$105$		0			0
$106$	3.02406	+	3.48995i	0.293722	+	0.338974i
$107$	5.72839	+	12.5434i	0.553785	+	1.21262i	0.954992	+	0.296632i	$0.0958634\pi$
$107$	5.72839	+	12.5434i	0.553785	+	1.21262i	−0.401207	+	0.915987i	$0.631409\pi$
$108$		0			0
$109$	7.83275	+	2.29990i	0.750242	+	0.220291i	0.634430	−	0.772980i	$-0.281235\pi$
$109$	7.83275	+	2.29990i	0.750242	+	0.220291i	0.115812	+	0.993271i	$0.463053\pi$
$110$	0.182240	−	0.210317i	0.0173759	−	0.0200529i
$111$		0			0
$112$	−3.43314	+	7.51753i	−0.324401	+	0.710340i
$113$	−2.08128	−	14.4756i	−0.195790	−	1.36175i	−0.816335	−	0.577578i	$-0.803998\pi$
$113$	−2.08128	−	14.4756i	−0.195790	−	1.36175i	0.620545	−	0.784171i	$-0.286911\pi$
$114$		0			0
$115$	−11.3268	−	15.8097i	−1.05623	−	1.47426i
$116$	−15.9488			−1.48080
$117$		0			0
$118$	4.36381	−	9.55541i	0.401721	−	0.879647i
$119$	5.69422	−	1.67197i	0.521989	−	0.153270i
$120$		0			0
$121$	10.5537	+	3.09885i	0.959428	+	0.281713i
$122$	9.77501	−	6.28201i	0.884987	−	0.568747i
$123$		0			0
$124$	1.36347	+	1.57353i	0.122443	+	0.141307i
$125$	21.9887	+	14.1313i	1.96673	+	1.26394i
$126$		0			0
$127$	−0.258432	+	1.79743i	−0.0229321	+	0.159496i	−0.998070	−	0.0621040i	$-0.980219\pi$
$127$	−0.258432	+	1.79743i	−0.0229321	+	0.159496i	0.975138	+	0.221600i	$0.0711281\pi$
$128$	−12.8940	−	8.28647i	−1.13968	−	0.732428i
$129$		0			0
$130$	−2.65565	−	5.81507i	−0.232916	−	0.510015i
$131$	−4.99336	+	3.20904i	−0.436272	+	0.280375i	−0.740285	−	0.672293i	$-0.765310\pi$
$131$	−4.99336	+	3.20904i	−0.436272	+	0.280375i	0.304013	+	0.952668i	$0.401673\pi$
$132$		0			0
$133$	4.51024	−	5.20510i	0.391088	−	0.451339i
$134$	−10.6814	+	3.13633i	−0.922728	+	0.270938i
$135$		0			0
$136$	−3.57150	−	24.8403i	−0.306254	−	2.13004i
$137$	−8.05383			−0.688085			−0.344043	−	0.938954i	$-0.611796\pi$
$137$	−8.05383			−0.688085			−0.344043	+	0.938954i	$0.611796\pi$
$138$		0			0
$139$	−7.68012			−0.651419			−0.325709	−	0.945470i	$-0.605603\pi$
$139$	−7.68012			−0.651419			−0.325709	+	0.945470i	$0.605603\pi$
$140$	3.43071	+	23.8611i	0.289948	+	2.01663i
$141$		0			0
$142$	−17.4249	+	5.11642i	−1.46227	+	0.429360i
$143$	−0.0112147	+	0.0129425i	−0.000937821	+	0.00108230i
$144$		0			0
$145$	−12.6040	+	8.10008i	−1.04670	+	0.672675i
$146$	6.23444	+	13.6515i	0.515966	+	1.12981i
$147$		0			0
$148$	−7.99685	−	5.13926i	−0.657337	−	0.422445i
$149$	−0.411897	+	2.86481i	−0.0337439	+	0.234694i	−0.999713	−	0.0239640i	$-0.992371\pi$
$149$	−0.411897	+	2.86481i	−0.0337439	+	0.234694i	0.965969	+	0.258658i	$0.0832804\pi$
$150$		0			0
$151$	1.73780	+	1.11682i	0.141420	+	0.0908852i	0.609438	−	0.792834i	$-0.291395\pi$
$151$	1.73780	+	1.11682i	0.141420	+	0.0908852i	−0.468018	+	0.883719i	$0.655032\pi$
$152$	−19.0725	−	22.0108i	−1.54698	−	1.78531i
$153$		0			0
$154$	0.0794958	−	0.0510888i	0.00640595	−	0.00411685i
$155$	1.87669	+	0.551045i	0.150739	+	0.0442610i
$156$		0			0
$157$	18.5997	−	5.46138i	1.48442	−	0.435865i	0.563665	−	0.826003i	$-0.309391\pi$
$157$	18.5997	−	5.46138i	1.48442	−	0.435865i	0.920756	+	0.390138i	$0.127573\pi$
$158$	1.57542	−	3.44970i	0.125334	−	0.274443i
$159$		0			0
$160$	13.9416			1.10218
$161$	−2.17794	−	6.23454i	−0.171645	−	0.491351i
$162$		0			0
$163$	−3.33835	−	23.2187i	−0.261480	−	1.81863i	−0.521753	−	0.853097i	$-0.674722\pi$
$163$	−3.33835	−	23.2187i	−0.261480	−	1.81863i	0.260273	−	0.965535i	$-0.416188\pi$
$164$	−17.9708	+	39.3505i	−1.40328	+	3.07276i
$165$		0			0
$166$	−14.1019	+	16.2744i	−1.09452	+	1.26314i
$167$	−19.9215	−	5.84948i	−1.54157	−	0.452647i	−0.603004	−	0.797738i	$-0.706030\pi$
$167$	−19.9215	−	5.84948i	−1.54157	−	0.452647i	−0.938569	+	0.345092i	$0.887848\pi$
$168$		0			0
$169$	−5.23697	−	11.4674i	−0.402844	−	0.882105i
$170$	−28.7654	−	33.1971i	−2.20621	−	2.54610i
$171$		0			0
$172$	2.01532	−	14.0168i	0.153666	−	1.06877i
$173$	−0.510183	+	3.54840i	−0.0387885	+	0.269780i	−0.999981	−	0.00609715i	$-0.998059\pi$
$173$	−0.510183	+	3.54840i	−0.0387885	+	0.269780i	0.961193	+	0.275877i	$0.0889683\pi$
$174$		0			0
$175$	10.3210	+	11.9111i	0.780197	+	0.900396i
$176$	−0.0680724	−	0.149058i	−0.00513115	−	0.0112356i
$177$		0			0
$178$	32.1453	+	9.43871i	2.40939	+	0.707461i
$179$	−13.5335	+	15.6184i	−1.01154	+	1.16738i	−0.0257010	+	0.999670i	$0.508182\pi$
$179$	−13.5335	+	15.6184i	−1.01154	+	1.16738i	−0.985837	+	0.167707i	$0.946364\pi$
$180$		0			0
$181$	−10.7612	+	23.5637i	−0.799873	+	1.75148i	−0.153943	+	0.988080i	$0.549197\pi$
$181$	−10.7612	+	23.5637i	−0.799873	+	1.75148i	−0.645929	+	0.763397i	$0.723530\pi$
$182$	−0.308930	−	2.14866i	−0.0228994	−	0.159269i
$183$		0			0
$184$	−27.4064	+	5.36412i	−2.02043	+	0.395448i
$185$	−8.92989			−0.656539
$186$		0			0
$187$	−0.0488826	+	0.107038i	−0.00357465	+	0.00782739i
$188$	37.2095	−	10.9257i	2.71378	−	0.796837i
$189$		0			0
$190$	−48.9128	−	14.3621i	−3.54850	−	1.04193i
$191$	6.97368	−	4.48171i	0.504598	−	0.324285i	−0.263455	−	0.964672i	$-0.584862\pi$
$191$	6.97368	−	4.48171i	0.504598	−	0.324285i	0.768053	+	0.640386i	$0.221226\pi$
$192$		0			0
$193$	11.1106	+	12.8223i	0.799756	+	0.922967i	0.998368	−	0.0571110i	$-0.0181889\pi$
$193$	11.1106	+	12.8223i	0.799756	+	0.922967i	−0.198612	+	0.980078i	$0.563643\pi$
$194$	4.57719	+	2.94158i	0.328623	+	0.211193i
$195$		0			0
$196$	3.13553	−	21.8081i	0.223966	−	1.55772i
$197$	11.4221	+	7.34055i	0.813792	+	0.522992i	0.880090	−	0.474808i	$-0.157482\pi$
$197$	11.4221	+	7.34055i	0.813792	+	0.522992i	−0.0662977	+	0.997800i	$0.521119\pi$
$198$		0			0
$199$	−5.33322	−	11.6781i	−0.378062	−	0.827840i	−0.999031	−	0.0440054i	$-0.985988\pi$
$199$	−5.33322	−	11.6781i	−0.378062	−	0.827840i	0.620969	−	0.783835i	$-0.286739\pi$
$200$	56.0672	−	36.0322i	3.96455	−	2.54786i
$201$		0			0
$202$	21.9717	−	25.3567i	1.54592	−	1.78409i
$203$	−4.88139	+	1.43331i	−0.342607	+	0.100598i
$204$		0			0
$205$	5.78347	+	40.2249i	0.403935	+	2.80943i
$206$	23.7565			1.65519
$207$		0			0
$208$	−3.76428			−0.261006
$209$	0.0194348	+	0.135172i	0.00134433	+	0.00935005i
$210$		0			0
$211$	1.29335	−	0.379761i	0.0890377	−	0.0261438i	−0.236910	−	0.971532i	$-0.576135\pi$
$211$	1.29335	−	0.379761i	0.0890377	−	0.0261438i	0.325948	+	0.945388i	$0.394317\pi$
$212$	5.19406	−	5.99427i	0.356730	−	0.411688i
$213$		0			0
$214$	29.1560	−	18.7374i	1.99306	−	1.28086i
$215$	−5.52623	−	12.1008i	−0.376886	−	0.825265i
$216$		0			0
$217$	0.558725	+	0.359071i	0.0379287	+	0.0243753i
$218$	2.91994	−	20.3086i	0.197763	−	1.37547i
$219$		0			0
$220$	−0.402106	−	0.258418i	−0.0271100	−	0.0174225i
$221$	1.77017	+	2.04288i	0.119074	+	0.137419i
$222$		0			0
$223$	−19.6245	+	12.6119i	−1.31415	+	0.844555i	−0.994677	−	0.103039i	$-0.967143\pi$
$223$	−19.6245	+	12.6119i	−1.31415	+	0.844555i	−0.319476	+	0.947594i	$0.603507\pi$
$224$	4.54231	+	1.33374i	0.303496	+	0.0891143i
$225$		0			0
$226$	−35.2673	+	10.3554i	−2.34594	+	0.688831i
$227$	−2.54103	+	5.56408i	−0.168654	+	0.369301i	−0.975020	−	0.222116i	$-0.928704\pi$
$227$	−2.54103	+	5.56408i	−0.168654	+	0.369301i	0.806366	+	0.591416i	$0.201431\pi$
$228$		0			0
$229$	13.7597			0.909269			0.454635	−	0.890678i	$-0.349770\pi$
$229$	13.7597			0.909269			0.454635	+	0.890678i	$0.349770\pi$
$230$	−35.2792	+	33.8333i	−2.32624	+	2.23090i
$231$		0			0
$232$	3.06168	+	21.2944i	0.201009	+	1.39805i
$233$	−5.88397	+	12.8841i	−0.385472	+	0.844065i	0.613067	+	0.790031i	$0.289935\pi$
$233$	−5.88397	+	12.8841i	−0.385472	+	0.844065i	−0.998539	+	0.0540345i	$0.982792\pi$
$234$		0			0
$235$	23.8569	−	27.5324i	1.55625	−	1.79601i
$236$	−17.3118	−	5.08321i	−1.12690	−	0.330889i
$237$		0			0
$238$	−6.19620	−	13.5678i	−0.401640	−	0.879469i
$239$	13.3179	+	15.3697i	0.861465	+	0.994183i	0.999993	+	0.00382482i	$0.00121748\pi$
$239$	13.3179	+	15.3697i	0.861465	+	0.994183i	−0.138528	+	0.990359i	$0.544237\pi$
$240$		0			0
$241$	−1.11118	+	7.72840i	−0.0715772	+	0.497830i	0.922224	+	0.386657i	$0.126370\pi$
$241$	−1.11118	+	7.72840i	−0.0715772	+	0.497830i	−0.993801	+	0.111174i	$0.964539\pi$
$242$	3.93427	−	27.3634i	0.252904	−	1.75899i
$243$		0			0
$244$	−13.0694	−	15.0829i	−0.836684	−	0.965585i
$245$	−8.59799	−	18.8270i	−0.549305	−	1.20281i
$246$		0			0
$247$	3.00999	+	0.883813i	0.191521	+	0.0562357i
$248$	1.83920	−	2.12254i	0.116789	−	0.134782i
$249$		0			0
$250$	27.2901	−	59.7570i	1.72598	−	3.77936i
$251$	2.12432	+	14.7750i	0.134086	+	0.932587i	0.940151	+	0.340759i	$0.110684\pi$
$251$	2.12432	+	14.7750i	0.134086	+	0.932587i	−0.806065	+	0.591827i	$0.798407\pi$
$252$		0			0
$253$	0.121704	+	0.0483165i	0.00765148	+	0.00303763i
$254$	4.56401			0.286372
$255$		0			0
$256$	−13.2090	+	28.9236i	−0.825560	+	1.80772i
$257$	13.0843	−	3.84190i	0.816177	−	0.239651i	0.153108	−	0.988209i	$-0.451072\pi$
$257$	13.0843	−	3.84190i	0.816177	−	0.239651i	0.663069	+	0.748558i	$0.269254\pi$
$258$		0			0
$259$	−2.90944	−	0.854288i	−0.180784	−	0.0530829i
$260$	−9.23705	+	5.93629i	−0.572858	+	0.368153i
$261$		0			0
$262$	9.76935	+	11.2744i	0.603553	+	0.696537i
$263$	−5.98538	−	3.84657i	−0.369075	−	0.237190i	0.342936	−	0.939359i	$-0.388579\pi$
$263$	−5.98538	−	3.84657i	−0.369075	−	0.237190i	−0.712010	+	0.702169i	$0.752215\pi$
$264$		0			0
$265$	1.06038	−	7.37512i	0.0651388	−	0.453050i
$266$	−14.5623	−	9.35859i	−0.892869	−	0.573812i
$267$		0			0
$268$	7.94299	+	17.3927i	0.485196	+	1.06243i
$269$	11.9712	−	7.69340i	0.729894	−	0.469075i	−0.122172	−	0.992509i	$-0.538986\pi$
$269$	11.9712	−	7.69340i	0.729894	−	0.469075i	0.852066	+	0.523434i	$0.175349\pi$
$270$		0			0
$271$	−5.31964	+	6.13920i	−0.323145	+	0.372930i	−0.893958	−	0.448151i	$-0.852083\pi$
$271$	−5.31964	+	6.13920i	−0.323145	+	0.372930i	0.570813	+	0.821080i	$0.306628\pi$
$272$	−24.8174	+	7.28705i	−1.50478	+	0.441843i
$273$		0			0
$274$	2.88074	+	20.0360i	0.174032	+	1.21042i
$275$	−0.312503			−0.0188446
$276$		0			0
$277$	−3.71245			−0.223060			−0.111530	−	0.993761i	$-0.535575\pi$
$277$	−3.71245			−0.223060			−0.111530	+	0.993761i	$0.535575\pi$
$278$	2.74706	+	19.1062i	0.164758	+	1.14592i
$279$		0			0
$280$	31.2003	−	9.16123i	1.86457	−	0.547488i
$281$	8.20261	−	9.46632i	0.489327	−	0.564713i	−0.456359	−	0.889796i	$-0.650847\pi$
$281$	8.20261	−	9.46632i	0.489327	−	0.564713i	0.945686	+	0.325083i	$0.105392\pi$
$282$		0			0
$283$	−20.5721	+	13.2209i	−1.22289	+	0.785901i	−0.982768	−	0.184842i	$-0.940823\pi$
$283$	−20.5721	+	13.2209i	−1.22289	+	0.785901i	−0.240118	+	0.970744i	$0.577186\pi$
$284$	12.9577	+	28.3735i	0.768899	+	1.68365i
$285$		0			0
$286$	0.0362090	+	0.0232701i	0.00214108	+	0.00137599i
$287$	−1.96386	+	13.6589i	−0.115923	+	0.806261i
$288$		0			0
$289$	1.32388	+	0.850806i	0.0778753	+	0.0500474i
$290$	24.6593	+	28.4583i	1.44804	+	1.67113i
$291$		0			0
$292$	21.6850	−	13.9361i	1.26902	−	0.815550i
$293$	−16.3811	−	4.80992i	−0.956993	−	0.280999i	−0.234297	−	0.972165i	$-0.575279\pi$
$293$	−16.3811	−	4.80992i	−0.956993	−	0.280999i	−0.722696	+	0.691166i	$0.757097\pi$
$294$		0			0
$295$	−16.2629	+	4.77521i	−0.946860	+	0.278023i
$296$	−5.32669	+	11.6638i	−0.309607	+	0.677946i
$297$		0			0
$298$	7.27427			0.421387
$299$	2.17101	−	2.08203i	0.125553	−	0.120407i
$300$		0			0
$301$	−0.642863	−	4.47121i	−0.0370540	−	0.257716i
$302$	2.15678	−	4.72269i	0.124109	−	0.271760i
$303$		0			0
$304$	−19.6572	+	22.6856i	−1.12742	+	1.30111i
$305$	−17.9888	−	5.28200i	−1.03004	−	0.302447i
$306$		0			0
$307$	9.16309	+	20.0644i	0.522965	+	1.14513i	0.968305	+	0.249772i	$0.0803556\pi$
$307$	9.16309	+	20.0644i	0.522965	+	1.14513i	−0.445340	+	0.895362i	$0.646917\pi$
$308$	−0.106288	−	0.122663i	−0.00605631	−	0.00698936i
$309$		0			0
$310$	0.699602	−	4.86584i	0.0397347	−	0.276361i
$311$	−0.775655	+	5.39480i	−0.0439833	+	0.305911i	0.955940	+	0.293561i	$0.0948403\pi$
$311$	−0.775655	+	5.39480i	−0.0439833	+	0.305911i	−0.999924	+	0.0123500i	$0.996069\pi$
$312$		0			0
$313$	−20.0600	−	23.1505i	−1.13386	−	1.30854i	−0.945198	−	0.326498i	$-0.894131\pi$
$313$	−20.0600	−	23.1505i	−1.13386	−	1.30854i	−0.188659	−	0.982043i	$-0.560414\pi$
$314$	−20.2394	−	44.3182i	−1.14218	−	2.50102i
$315$		0			0
$316$	−6.24992	−	1.83514i	−0.351585	−	0.103235i
$317$	0.468539	−	0.540723i	0.0263158	−	0.0303700i	−0.742439	−	0.669914i	$-0.766331\pi$
$317$	0.468539	−	0.540723i	0.0263158	−	0.0303700i	0.768755	+	0.639544i	$0.220877\pi$
$318$		0			0
$319$	0.0419048	−	0.0917586i	0.00234622	−	0.00513750i
$320$	1.94066	+	13.4976i	0.108486	+	0.754536i
$321$		0			0
$322$	−14.7310	+	7.64817i	−0.820926	+	0.426216i
$323$	21.5554			1.19938
$324$		0			0
$325$	−2.98215	+	6.52999i	−0.165420	+	0.362219i
$326$	−56.5685	+	16.6100i	−3.13304	+	0.919943i
$327$		0			0
$328$	55.9898	+	16.4401i	3.09152	+	0.907752i
$329$	10.4067	−	6.68799i	0.573741	−	0.368721i
$330$		0			0
$331$	−18.3506	−	21.1777i	−1.00864	−	1.16403i	−0.986414	−	0.164281i	$-0.947470\pi$
$331$	−18.3506	−	21.1777i	−1.00864	−	1.16403i	−0.0222271	−	0.999753i	$-0.507076\pi$
$332$	31.1151	+	19.9965i	1.70767	+	1.09745i
$333$		0			0
$334$	−7.42645	+	51.6521i	−0.406357	+	2.82628i
$335$	15.1106	+	9.71102i	0.825582	+	0.530570i
$336$		0			0
$337$	−7.81892	−	17.1210i	−0.425924	−	0.932643i	−0.993971	−	0.109647i	$-0.965028\pi$
$337$	−7.81892	−	17.1210i	−0.425924	−	0.932643i	0.568047	−	0.822996i	$-0.307699\pi$
$338$	−26.6548	+	17.1300i	−1.44983	+	0.931750i
$339$		0			0
$340$	−49.4070	+	57.0187i	−2.67947	+	3.09228i
$341$	−0.0126355	+	0.00371012i	−0.000684251	+	0.000200914i
$342$		0			0
$343$	−2.37200	−	16.4976i	−0.128076	−	0.890789i
$344$	−19.1019			−1.02990
$345$		0			0
$346$	9.01004			0.484383
$347$	2.03201	+	14.1329i	0.109084	+	0.758696i	0.968786	+	0.247900i	$0.0797403\pi$
$347$	2.03201	+	14.1329i	0.109084	+	0.758696i	−0.859702	+	0.510796i	$0.829351\pi$
$348$		0			0
$349$	4.50865	−	1.32386i	0.241343	−	0.0708646i	−0.158824	−	0.987307i	$-0.550770\pi$
$349$	4.50865	−	1.32386i	0.241343	−	0.0708646i	0.400167	+	0.916442i	$0.368952\pi$
$350$	25.9402	−	29.9366i	1.38656	−	1.60018i
$351$		0			0
$352$	−0.0789661	+	0.0507484i	−0.00420891	+	0.00270490i
$353$	−7.42472	−	16.2579i	−0.395178	−	0.865320i	−0.997737	−	0.0672447i	$-0.978579\pi$
$353$	−7.42472	−	16.2579i	−0.395178	−	0.865320i	0.602558	−	0.798075i	$-0.294148\pi$
$354$		0			0
$355$	24.6506	+	15.8420i	1.30832	+	0.840805i
$356$	8.18923	−	56.9574i	0.434028	−	3.01873i
$357$		0			0
$358$	43.6956	+	28.0814i	2.30938	+	1.48415i
$359$	−22.9288	−	26.4612i	−1.21013	−	1.39657i	−0.894127	−	0.447814i	$-0.852203\pi$
$359$	−22.9288	−	26.4612i	−1.21013	−	1.39657i	−0.316008	−	0.948757i	$-0.602343\pi$
$360$		0			0
$361$	5.06084	−	3.25240i	0.266360	−	0.171179i
$362$	62.4699	+	18.3428i	3.28334	+	0.964076i
$363$		0			0
$364$	−3.57742	+	1.05042i	−0.187508	+	0.0550572i
$365$	10.0593	−	22.0269i	0.526529	−	1.15294i
$366$		0			0
$367$	14.8756			0.776498			0.388249	−	0.921554i	$-0.373080\pi$
$367$	14.8756			0.776498			0.388249	+	0.921554i	$0.373080\pi$
$368$	9.49221	+	27.1723i	0.494816	+	1.41645i
$369$		0			0
$370$	3.19409	+	22.2154i	0.166053	+	1.15492i
$371$	1.05103	−	2.30144i	0.0545668	−	0.119485i
$372$		0			0
$373$	11.4264	−	13.1868i	0.591636	−	0.682785i	−0.378429	−	0.925630i	$-0.623535\pi$
$373$	11.4264	−	13.1868i	0.591636	−	0.682785i	0.970065	+	0.242846i	$0.0780809\pi$
$374$	0.283769	+	0.0833220i	0.0146733	+	0.00430848i
$375$		0			0
$376$	−21.7308	−	47.5839i	−1.12068	−	2.45395i
$377$	−1.51748	−	1.75127i	−0.0781543	−	0.0901948i
$378$		0			0
$379$	1.67590	−	11.6561i	0.0860852	−	0.598736i	−0.900422	−	0.435018i	$-0.856742\pi$
$379$	1.67590	−	11.6561i	0.0860852	−	0.598736i	0.986507	−	0.163718i	$-0.0523487\pi$
$380$	−12.4609	+	86.6672i	−0.639229	+	4.44593i
$381$		0			0
$382$	−13.6438	−	15.7458i	−0.698077	−	0.805624i
$383$	−1.19882	−	2.62505i	−0.0612568	−	0.134134i	0.876528	−	0.481351i	$-0.159854\pi$
$383$	−1.19882	−	2.62505i	−0.0612568	−	0.134134i	−0.937785	+	0.347217i	$0.887127\pi$
$384$		0			0
$385$	−0.146295	−	0.0429562i	−0.00745590	−	0.00218925i
$386$	27.9246	−	32.2267i	1.42132	−	1.64030i
$387$		0			0
$388$	3.88215	−	8.50072i	0.197086	−	0.431559i
$389$	−0.649215	−	4.51539i	−0.0329165	−	0.228939i	0.966722	−	0.255830i	$-0.0823486\pi$
$389$	−0.649215	−	4.51539i	−0.0329165	−	0.228939i	−0.999638	+	0.0268904i	$0.991439\pi$
$390$		0			0
$391$	10.2827	−	17.9293i	0.520019	−	0.906725i
$392$	−29.7197			−1.50107
$393$		0			0
$394$	14.1760	−	31.0410i	0.714175	−	1.56382i
$395$	−5.87122	+	1.72395i	−0.295413	+	0.0867411i
$396$		0			0
$397$	−4.25519	−	1.24944i	−0.213562	−	0.0627074i	0.173202	−	0.984886i	$-0.444589\pi$
$397$	−4.25519	−	1.24944i	−0.213562	−	0.0627074i	−0.386763	+	0.922179i	$0.626407\pi$
$398$	−27.1447	+	17.4448i	−1.36064	+	0.874431i
$399$		0			0
$400$	−44.9827	−	51.9128i	−2.24914	−	2.59564i
$401$	−4.63189	−	2.97674i	−0.231306	−	0.148651i	0.419855	−	0.907591i	$-0.362081\pi$
$401$	−4.63189	−	2.97674i	−0.231306	−	0.148651i	−0.651160	+	0.758940i	$0.725717\pi$
$402$		0			0
$403$	−0.0430521	+	0.299434i	−0.00214458	+	0.0149159i
$404$	−48.4796	−	31.1560i	−2.41195	−	1.55007i
$405$		0			0
$406$	5.31172	+	11.6310i	0.263616	+	0.577239i
$407$	0.0505794	−	0.0325054i	0.00250713	−	0.00161123i
$408$		0			0
$409$	−20.4190	+	23.5648i	−1.00966	+	1.16521i	−0.0234433	+	0.999725i	$0.507463\pi$
$409$	−20.4190	+	23.5648i	−1.00966	+	1.16521i	−0.986213	+	0.165480i	$0.947083\pi$
$410$	98.0011	−	28.7757i	4.83993	−	1.42113i
$411$		0			0
$412$	−5.80697	−	40.3884i	−0.286089	−	1.98979i
$413$	−5.75541			−0.283205
$414$		0			0
$415$	34.7455			1.70559
$416$	0.306872	+	2.13434i	0.0150456	+	0.104645i
$417$		0			0
$418$	0.329324	−	0.0966981i	0.0161077	−	0.00472966i
$419$	25.3369	−	29.2403i	1.23779	−	1.42848i	0.371880	−	0.928281i	$-0.378713\pi$
$419$	25.3369	−	29.2403i	1.23779	−	1.42848i	0.865908	−	0.500203i	$-0.166741\pi$
$420$		0			0
$421$	5.63619	−	3.62216i	0.274691	−	0.176533i	−0.396041	−	0.918233i	$-0.629616\pi$
$421$	5.63619	−	3.62216i	0.274691	−	0.176533i	0.670732	+	0.741699i	$0.265980\pi$
$422$	−1.40736	−	3.08170i	−0.0685094	−	0.150015i
$423$		0			0
$424$	−9.00053	−	5.78429i	−0.437104	−	0.280910i
$425$	−7.01989	+	48.8244i	−0.340515	+	2.36833i
$426$		0			0
$427$	−5.35562	−	3.44185i	−0.259177	−	0.166563i
$428$	−38.9823	−	44.9880i	−1.88428	−	2.17458i
$429$		0			0
$430$	−28.1271	+	18.0762i	−1.35641	+	0.871711i
$431$	4.72227	+	1.38658i	0.227464	+	0.0667894i	0.393478	−	0.919334i	$-0.371272\pi$
$431$	4.72227	+	1.38658i	0.227464	+	0.0667894i	−0.166015	+	0.986123i	$0.553090\pi$
$432$		0			0
$433$	24.8366	−	7.29268i	1.19357	−	0.350464i	0.376179	−	0.926547i	$-0.377238\pi$
$433$	24.8366	−	7.29268i	1.19357	−	0.350464i	0.817391	+	0.576083i	$0.195420\pi$
$434$	0.693432	−	1.51841i	0.0332858	−	0.0728858i
$435$		0			0
$436$	−35.2404			−1.68771
$437$	−1.21038	−	23.9562i	−0.0579005	−	1.14598i
$438$		0			0
$439$	−0.315656	−	2.19544i	−0.0150655	−	0.104783i	0.980901	−	0.194507i	$-0.0623106\pi$
$439$	−0.315656	−	2.19544i	−0.0150655	−	0.104783i	−0.995967	+	0.0897241i	$0.971401\pi$
$440$	−0.267842	+	0.586492i	−0.0127689	+	0.0279599i
$441$		0			0
$442$	4.44903	−	5.13445i	0.211619	−	0.244221i
$443$	7.47429	+	2.19465i	0.355114	+	0.104271i	0.454424	−	0.890786i	$-0.349845\pi$
$443$	7.47429	+	2.19465i	0.355114	+	0.104271i	−0.0993095	+	0.995057i	$0.531663\pi$
$444$		0			0
$445$	−22.4558	−	49.1714i	−1.06451	−	2.33095i
$446$	38.3947	+	44.3098i	1.81804	+	2.09813i
$447$		0			0
$448$	−0.658976	+	4.58328i	−0.0311337	+	0.216540i
$449$	−1.01858	+	7.08436i	−0.0480697	+	0.334332i	0.951569	+	0.307437i	$0.0994712\pi$
$449$	−1.01858	+	7.08436i	−0.0480697	+	0.334332i	−0.999638	+	0.0268953i	$0.991438\pi$
$450$		0			0
$451$	−0.179179	−	0.206784i	−0.00843722	−	0.00973707i
$452$	26.2259	+	57.4266i	1.23356	+	2.70112i
$453$		0			0
$454$	14.7510	+	4.33127i	0.692297	+	0.203277i
$455$	−2.29367	+	2.64703i	−0.107529	+	0.124095i
$456$		0			0
$457$	−1.85262	+	4.05667i	−0.0866618	+	0.189763i	−0.948001	−	0.318268i	$-0.896899\pi$
$457$	−1.85262	+	4.05667i	−0.0866618	+	0.189763i	0.861339	+	0.508030i	$0.169626\pi$
$458$	−4.92165	−	34.2309i	−0.229974	−	1.59950i
$459$		0			0
$460$	66.1436	+	51.7081i	3.08396	+	2.41090i
$461$	24.0540			1.12031			0.560153	−	0.828389i	$-0.310742\pi$
$461$	24.0540			1.12031			0.560153	+	0.828389i	$0.310742\pi$
$462$		0			0
$463$	−1.36569	+	2.99043i	−0.0634688	+	0.138977i	−0.938708	−	0.344712i	$-0.887976\pi$
$463$	−1.36569	+	2.99043i	−0.0634688	+	0.138977i	0.875240	+	0.483690i	$0.160704\pi$
$464$	21.2748	−	6.24685i	0.987659	−	0.290003i
$465$		0			0
$466$	34.1571	+	10.0294i	1.58230	+	0.464604i
$467$	−11.5767	+	7.43992i	−0.535708	+	0.344278i	−0.780358	−	0.625333i	$-0.784963\pi$
$467$	−11.5767	+	7.43992i	−0.535708	+	0.344278i	0.244650	+	0.969611i	$0.421327\pi$
$468$		0			0
$469$	3.99417	+	4.60951i	0.184434	+	0.212848i
$470$	−77.0270	−	49.5023i	−3.55299	−	2.28337i
$471$		0			0
$472$	−3.46365	+	24.0902i	−0.159428	+	1.10884i
$473$	0.0753485	+	0.0484235i	0.00346453	+	0.00222652i
$474$		0			0
$475$	23.7805	+	52.0720i	1.09112	+	2.38923i
$476$	−21.5520	+	13.8506i	−0.987835	+	0.634843i
$477$		0			0
$478$	33.4724	−	38.6292i	1.53099	−	1.76686i
$479$	−22.1960	+	6.51733i	−1.01416	+	0.297784i	−0.746255	−	0.665661i	$-0.768150\pi$
$479$	−22.1960	+	6.51733i	−1.01416	+	0.297784i	−0.267906	+	0.963445i	$0.586332\pi$
$480$		0			0
$481$	−0.196558	−	1.36709i	−0.00896226	−	0.0623339i
$482$	19.6238			0.893841
$483$		0			0
$484$	−47.4823			−2.15829
$485$	−1.24938	−	8.68962i	−0.0567313	−	0.394575i
$486$		0			0
$487$	−11.1600	+	3.27689i	−0.505710	+	0.148490i	−0.524629	−	0.851331i	$-0.675796\pi$
$487$	−11.1600	+	3.27689i	−0.505710	+	0.148490i	0.0189187	+	0.999821i	$0.493978\pi$
$488$	−17.6295	+	20.3455i	−0.798049	+	0.920998i
$489$		0			0
$490$	−43.7615	+	28.1238i	−1.97694	+	1.27050i
$491$	12.6159	+	27.6249i	0.569346	+	1.24669i	0.947145	+	0.320806i	$0.103954\pi$
$491$	12.6159	+	27.6249i	0.569346	+	1.24669i	−0.377799	+	0.925888i	$0.623319\pi$
$492$		0			0
$493$	−13.3947	−	8.60828i	−0.603269	−	0.387697i
$494$	1.12208	−	7.80425i	0.0504848	−	0.351130i
$495$		0			0
$496$	−2.43512	−	1.56496i	−0.109340	−	0.0702686i
$497$	6.51584	+	7.51968i	0.292276	+	0.337304i
$498$		0			0
$499$	−29.3390	+	18.8551i	−1.31340	+	0.844068i	−0.994603	−	0.103756i	$-0.966914\pi$
$499$	−29.3390	+	18.8551i	−1.31340	+	0.844068i	−0.318793	+	0.947824i	$0.603277\pi$
$500$	−108.264	−	31.7890i	−4.84169	−	1.42165i
$501$		0			0
$502$	35.9966	−	10.5696i	1.60661	−	0.471743i
$503$	−4.66816	+	10.2218i	−0.208143	+	0.455770i	−0.984696	−	0.174283i	$-0.944239\pi$
$503$	−4.66816	+	10.2218i	−0.208143	+	0.455770i	0.776553	+	0.630052i	$0.216967\pi$
$504$		0			0
$505$	−54.1360			−2.40902
$506$	0.0766679	−	0.320053i	0.00340830	−	0.0142281i
$507$		0			0
$508$	−1.11562	−	7.75927i	−0.0494974	−	0.344262i
$509$	−1.81739	+	3.97954i	−0.0805546	+	0.176390i	−0.945624	−	0.325263i	$-0.894547\pi$
$509$	−1.81739	+	3.97954i	−0.0805546	+	0.176390i	0.865069	+	0.501653i	$0.167274\pi$
$510$		0			0
$511$	5.38465	−	6.21421i	0.238203	−	0.274901i
$512$	47.2669	+	13.8788i	2.08892	+	0.613363i
$513$		0			0
$514$	−14.2378	−	31.1764i	−0.628001	−	1.37513i
$515$	−25.1017	−	28.9689i	−1.10611	−	1.27652i
$516$		0			0
$517$	−0.0349073	+	0.242786i	−0.00153522	+	0.0106777i
$518$	−1.08460	+	7.54354i	−0.0476544	+	0.331444i
$519$		0			0
$520$	9.69925	+	11.1935i	0.425340	+	0.490869i
$521$	1.29520	+	2.83608i	0.0567436	+	0.124251i	0.935880	−	0.352319i	$-0.114607\pi$
$521$	1.29520	+	2.83608i	0.0567436	+	0.124251i	−0.879136	+	0.476571i	$0.841880\pi$
$522$		0			0
$523$	−12.4643	−	3.65986i	−0.545027	−	0.160034i	−0.00238288	−	0.999997i	$-0.500758\pi$
$523$	−12.4643	−	3.65986i	−0.545027	−	0.160034i	−0.542644	+	0.839963i	$0.682577\pi$
$524$	16.7797	−	19.3648i	0.733023	−	0.845954i
$525$		0			0
$526$	−7.42845	+	16.2660i	−0.323896	+	0.709233i
$527$	0.295820	+	2.05747i	0.0128861	+	0.0896249i
$528$		0			0
$529$	−20.5036	−	10.4212i	−0.891462	−	0.453096i
$530$	−18.7268			−0.813439
$531$		0			0
$532$	−12.3510	+	27.0449i	−0.535483	+	1.17254i
$533$	−6.03079	+	1.77080i	−0.261222	+	0.0767018i
$534$		0			0
$535$	−53.6555	−	15.7547i	−2.31973	−	0.681135i
$536$	21.6976	−	13.9442i	0.937194	−	0.602298i
$537$		0			0
$538$	−23.4212	−	27.0295i	−1.00976	−	1.16532i
$539$	0.117231	+	0.0753398i	0.00504949	+	0.00324511i
$540$		0			0
$541$	4.61797	−	32.1187i	0.198542	−	1.38089i	−0.609976	−	0.792420i	$-0.708821\pi$
$541$	4.61797	−	32.1187i	0.198542	−	1.38089i	0.808518	−	0.588471i	$-0.200270\pi$
$542$	17.1756	+	11.0381i	0.737754	+	0.474126i
$543$		0			0
$544$	6.15492	+	13.4774i	0.263890	+	0.577839i
$545$	−27.8498	+	17.8980i	−1.19295	+	0.766665i
$546$		0			0
$547$	5.89308	−	6.80097i	0.251970	−	0.290789i	−0.615647	−	0.788022i	$-0.711105\pi$
$547$	5.89308	−	6.80097i	0.251970	−	0.290789i	0.867617	+	0.497233i	$0.165651\pi$
$548$	33.3590	−	9.79507i	1.42502	−	0.418425i
$549$		0			0
$550$	0.111778	+	0.777430i	0.00476621	+	0.0331497i
$551$	−18.4785			−0.787209
$552$		0			0
$553$	−2.07782			−0.0883579
$554$	1.32789	+	9.23567i	0.0564166	+	0.392386i
$555$		0			0
$556$	31.8110	−	9.34056i	1.34909	−	0.396128i
$557$	−20.6639	+	23.8474i	−0.875556	+	1.01045i	0.124279	+	0.992247i	$0.460338\pi$
$557$	−20.6639	+	23.8474i	−0.875556	+	1.01045i	−0.999834	+	0.0181980i	$0.994207\pi$
$558$		0			0
$559$	1.73088	−	1.11237i	0.0732086	−	0.0470483i
$560$	−13.9224	−	30.4858i	−0.588328	−	1.28826i
$561$		0			0
$562$	−26.4838	−	17.0201i	−1.11715	−	0.717951i
$563$	5.12498	−	35.6450i	0.215992	−	1.50226i	−0.536636	−	0.843814i	$-0.680305\pi$
$563$	5.12498	−	35.6450i	0.215992	−	1.50226i	0.752628	−	0.658446i	$-0.228786\pi$
$564$		0			0
$565$	49.8917	+	32.0635i	2.09896	+	1.34892i
$566$	40.2487	+	46.4495i	1.69178	+	1.95242i
$567$		0			0
$568$	35.3962	−	22.7477i	1.48519	−	0.954474i
$569$	31.2963	+	9.18942i	1.31201	+	0.385241i	0.861603	−	0.507583i	$-0.169461\pi$
$569$	31.2963	+	9.18942i	1.31201	+	0.385241i	0.450406	+	0.892824i	$0.351279\pi$
$570$		0			0
$571$	32.7363	−	9.61224i	1.36997	−	0.402260i	0.487704	−	0.873009i	$-0.337835\pi$
$571$	32.7363	−	9.61224i	1.36997	−	0.402260i	0.882267	+	0.470749i	$0.156016\pi$
$572$	0.0307107	−	0.0672470i	0.00128408	−	0.00281174i
$573$		0			0
$574$	34.6825			1.44762
$575$	54.6565	+	5.06014i	2.27933	+	0.211022i
$576$		0			0
$577$	5.54883	+	38.5929i	0.231001	+	1.60664i	0.693791	+	0.720177i	$0.255939\pi$
$577$	5.54883	+	38.5929i	0.231001	+	1.60664i	−0.462790	+	0.886468i	$0.653152\pi$
$578$	1.64306	−	3.59781i	0.0683425	−	0.149649i
$579$		0			0
$580$	42.3543	−	48.8795i	1.75867	−	2.02961i
$581$	11.3204	+	3.32397i	0.469650	+	0.137902i
$582$		0			0
$583$	0.0208399	+	0.0456330i	0.000863099	+	0.00188992i
$584$	−22.7701	−	26.2781i	−0.942233	−	1.08739i
$585$		0			0
$586$	−6.10663	+	42.4726i	−0.252263	+	1.75453i
$587$	4.67494	−	32.5149i	0.192955	−	1.34203i	−0.631177	−	0.775638i	$-0.717428\pi$
$587$	4.67494	−	32.5149i	0.192955	−	1.34203i	0.824133	−	0.566396i	$-0.191663\pi$
$588$		0			0
$589$	1.57973	+	1.82311i	0.0650918	+	0.0751200i
$590$	17.6965	+	38.7500i	0.728555	+	1.59531i
$591$		0			0
$592$	12.6804	+	3.72329i	0.521159	+	0.153026i
$593$	−0.143737	+	0.165882i	−0.00590259	+	0.00681195i	−0.758693	−	0.651448i	$-0.774162\pi$
$593$	−0.143737	+	0.165882i	−0.00590259	+	0.00681195i	0.752791	+	0.658260i	$0.228707\pi$
$594$		0			0
$595$	−9.99763	+	21.8918i	−0.409863	+	0.897475i
$596$	−1.77810	−	12.3670i	−0.0728340	−	0.506572i
$597$		0			0
$598$	−5.95613	−	4.65623i	−0.243564	−	0.190407i
$599$	3.53619			0.144485			0.0722425	−	0.997387i	$-0.476984\pi$
$599$	3.53619			0.144485			0.0722425	+	0.997387i	$0.476984\pi$
$600$		0			0
$601$	15.0669	−	32.9918i	0.614590	−	1.34577i	−0.304799	−	0.952417i	$-0.598589\pi$
$601$	15.0669	−	32.9918i	0.614590	−	1.34577i	0.919389	−	0.393348i	$-0.128683\pi$
$602$	−10.8933	+	3.19857i	−0.443979	+	0.130364i
$603$		0			0
$604$	−8.55624	−	2.51234i	−0.348148	−	0.102226i
$605$	−37.5243	+	24.1154i	−1.52558	+	0.980430i
$606$		0			0
$607$	29.3523	+	33.8743i	1.19137	+	1.37492i	0.909626	+	0.415428i	$0.136368\pi$
$607$	29.3523	+	33.8743i	1.19137	+	1.37492i	0.281746	+	0.959489i	$0.409086\pi$
$608$	14.4652	+	9.29624i	0.586643	+	0.377012i
$609$		0			0
$610$	−6.70598	+	46.6411i	−0.271517	+	1.88844i
$611$	4.74009	+	3.04627i	0.191763	+	0.123239i
$612$		0			0
$613$	0.674111	+	1.47610i	0.0272271	+	0.0596190i	0.922757	−	0.385382i	$-0.125930\pi$
$613$	0.674111	+	1.47610i	0.0272271	+	0.0596190i	−0.895530	+	0.445001i	$0.853203\pi$
$614$	46.6377	−	29.9722i	1.88214	−	1.20958i
$615$		0			0
$616$	−0.143373	+	0.165461i	−0.00577665	+	0.00666661i
$617$	−18.6179	+	5.46671i	−0.749529	+	0.220082i	−0.634118	−	0.773236i	$-0.718637\pi$
$617$	−18.6179	+	5.46671i	−0.749529	+	0.220082i	−0.115411	+	0.993318i	$0.536818\pi$
$618$		0			0
$619$	1.55013	+	10.7814i	0.0623051	+	0.433341i	0.996968	+	0.0778073i	$0.0247919\pi$
$619$	1.55013	+	10.7814i	0.0623051	+	0.433341i	−0.934663	+	0.355534i	$0.884299\pi$
$620$	−8.44342			−0.339096
$621$		0			0
$622$	13.6984			0.549255
$623$	−2.61227	−	18.1688i	−0.104658	−	0.727916i
$624$		0			0
$625$	−46.7946	+	13.7401i	−1.87178	+	0.549606i
$626$	−50.4175	+	58.1849i	−2.01509	+	2.32554i
$627$		0			0
$628$	−70.3980	+	45.2421i	−2.80919	+	1.80535i
$629$	−3.94235	−	8.63254i	−0.157192	−	0.344202i
$630$		0			0
$631$	36.6812	+	23.5736i	1.46026	+	0.938449i	0.998681	+	0.0513479i	$0.0163517\pi$
$631$	36.6812	+	23.5736i	1.46026	+	0.938449i	0.461575	+	0.887101i	$0.347285\pi$
$632$	−1.25045	+	8.69706i	−0.0497401	+	0.345950i
$633$		0			0
$634$	−1.51278	−	0.972203i	−0.0600800	−	0.0386111i
$635$	−4.82244	−	5.56540i	−0.191373	−	0.220856i
$636$		0			0
$637$	2.69299	−	1.73068i	0.106700	−	0.0685721i
$638$	−0.243262	−	0.0714281i	−0.00963082	−	0.00282786i
$639$		0			0
$640$	59.6382	−	17.5114i	2.35741	−	0.692198i
$641$	2.92279	−	6.40002i	0.115443	−	0.252786i	−0.843086	−	0.537778i	$-0.819264\pi$
$641$	2.92279	−	6.40002i	0.115443	−	0.252786i	0.958530	+	0.284993i	$0.0919911\pi$
$642$		0			0
$643$	−9.53363			−0.375970			−0.187985	−	0.982172i	$-0.560196\pi$
$643$	−9.53363			−0.375970			−0.187985	+	0.982172i	$0.560196\pi$
$644$	16.6035	+	23.1747i	0.654268	+	0.913209i
$645$		0			0
$646$	−7.71006	−	53.6246i	−0.303348	−	2.10983i
$647$	7.37566	−	16.1504i	0.289967	−	0.634939i	−0.707450	−	0.706763i	$-0.750155\pi$
$647$	7.37566	−	16.1504i	0.289967	−	0.634939i	0.997417	+	0.0718238i	$0.0228819\pi$
$648$		0			0
$649$	0.0747317	−	0.0862450i	0.00293347	−	0.00338541i
$650$	17.3117	+	5.08317i	0.679020	+	0.199378i
$651$		0			0
$652$	42.0661	+	92.1119i	1.64744	+	3.60738i
$653$	−16.0888	−	18.5675i	−0.629604	−	0.726602i	0.347897	−	0.937533i	$-0.386896\pi$
$653$	−16.0888	−	18.5675i	−0.629604	−	0.726602i	−0.977501	+	0.210931i	$0.932350\pi$
$654$		0			0
$655$	3.42562	−	23.8257i	0.133850	−	0.930946i
$656$	8.55918	−	59.5304i	0.334180	−	2.32427i
$657$		0			0
$658$	−20.3604	−	23.4972i	−0.793731	−	0.916015i
$659$	0.693556	+	1.51868i	0.0270171	+	0.0591592i	0.922659	−	0.385616i	$-0.126011\pi$
$659$	0.693556	+	1.51868i	0.0270171	+	0.0591592i	−0.895642	+	0.444775i	$0.853284\pi$
$660$		0			0
$661$	−12.6102	−	3.70269i	−0.490480	−	0.144018i	0.0271347	−	0.999632i	$-0.491362\pi$
$661$	−12.6102	−	3.70269i	−0.490480	−	0.144018i	−0.517615	+	0.855614i	$0.673180\pi$
$662$	−46.1213	+	53.2268i	−1.79255	+	2.06872i
$663$		0			0
$664$	20.7257	−	45.3830i	0.804315	−	1.76120i
$665$	3.97487	+	27.6459i	0.154139	+	1.07206i
$666$		0			0
$667$	−8.81489	+	15.3700i	−0.341314	+	0.595128i
$668$	89.6290			3.46785
$669$		0			0
$670$	18.7538	−	41.0651i	0.724522	−	1.58648i
$671$	0.121117	−	0.0355631i	0.00467566	−	0.00137290i
$672$		0			0
$673$	22.3895	+	6.57416i	0.863053	+	0.253415i	0.683158	−	0.730271i	$-0.260606\pi$
$673$	22.3895	+	6.57416i	0.863053	+	0.253415i	0.179895	+	0.983686i	$0.442424\pi$
$674$	−39.7963	+	25.5755i	−1.53289	+	0.985131i
$675$		0			0
$676$	35.6382	+	41.1286i	1.37070	+	1.58187i
$677$	20.2228	+	12.9964i	0.777224	+	0.499491i	0.868111	−	0.496370i	$-0.165334\pi$
$677$	20.2228	+	12.9964i	0.777224	+	0.499491i	−0.0908875	+	0.995861i	$0.528970\pi$
$678$		0			0
$679$	0.424244	−	2.95068i	0.0162810	−	0.113237i
$680$	85.6149	+	55.0214i	3.28318	+	2.10997i
$681$		0			0
$682$	0.0137494	+	0.0301070i	0.000526491	+	0.00115286i
$683$	5.04023	−	3.23916i	0.192859	−	0.123943i	−0.440648	−	0.897680i	$-0.645251\pi$
$683$	5.04023	−	3.23916i	0.192859	−	0.123943i	0.633507	+	0.773737i	$0.281615\pi$
$684$		0			0
$685$	21.3882	−	24.6833i	0.817200	−	0.943099i
$686$	−40.1936	+	11.8019i	−1.53460	+	0.450599i
$687$		0			0
$688$	2.80182	+	19.4871i	0.106819	+	0.742939i
$689$	1.15241			0.0439032
$690$		0			0
$691$	27.1419			1.03253			0.516264	−	0.856430i	$-0.327322\pi$
$691$	27.1419			1.03253			0.516264	+	0.856430i	$0.327322\pi$
$692$	−2.20239	−	15.3180i	−0.0837223	−	0.582302i
$693$		0			0
$694$	34.4325	−	10.1103i	1.30704	−	0.383781i
$695$	20.3957	−	23.5379i	0.773654	−	0.892844i
$696$		0			0
$697$	−36.3322	+	23.3493i	−1.37618	+	0.884418i
$698$	−4.90612	−	10.7429i	−0.185699	−	0.406625i
$699$		0			0
$700$	−57.2360	−	36.7834i	−2.16332	−	1.39028i
$701$	−7.12129	+	49.5297i	−0.268967	+	1.87071i	0.189334	+	0.981913i	$0.439367\pi$
$701$	−7.12129	+	49.5297i	−0.268967	+	1.87071i	−0.458301	+	0.888797i	$0.651542\pi$
$702$		0			0
$703$	−9.26527	−	5.95443i	−0.349446	−	0.224576i
$704$	−0.0601240	−	0.0693868i	−0.00226601	−	0.00261511i
$705$		0			0
$706$	−37.7899	+	24.2861i	−1.42224	+	0.914019i
$707$	−17.6380	−	5.17898i	−0.663345	−	0.194776i
$708$		0			0
$709$	−29.6798	+	8.71476i	−1.11465	+	0.327290i	−0.786656	−	0.617391i	$-0.788190\pi$
$709$	−29.6798	+	8.71476i	−1.11465	+	0.327290i	−0.327990	+	0.944681i	$0.606371\pi$
$710$	30.5938	−	66.9911i	1.14816	−	2.51413i
$711$		0			0
$712$	−77.6204			−2.90895
$713$	2.27001	−	0.444298i	0.0850127	−	0.0166391i
$714$		0			0
$715$	−0.00988351	−	0.0687413i	−0.000369622	−	0.00257078i
$716$	37.0604	−	81.1510i	1.38501	−	3.03275i
$717$		0			0
$718$	−57.6278	+	66.5060i	−2.15065	+	2.48198i
$719$	−18.1350	−	5.32490i	−0.676320	−	0.198585i	−0.0745044	−	0.997221i	$-0.523737\pi$
$719$	−18.1350	−	5.32490i	−0.676320	−	0.198585i	−0.601815	+	0.798635i	$0.705556\pi$
$720$		0			0
$721$	−5.40701	−	11.8397i	−0.201368	−	0.440933i
$722$	−9.90136	−	11.4268i	−0.368491	−	0.425261i
$723$		0			0
$724$	15.9146	−	110.689i	0.591462	−	4.11371i
$725$	6.01782	−	41.8549i	0.223496	−	1.55445i
$726$		0			0
$727$	−1.32855	−	1.53323i	−0.0492731	−	0.0568642i	0.730578	−	0.682829i	$-0.239251\pi$
$727$	−1.32855	−	1.53323i	−0.0492731	−	0.0568642i	−0.779851	+	0.625965i	$0.784705\pi$
$728$	2.08926	+	4.57485i	0.0774332	+	0.169555i
$729$		0			0
$730$	−58.3955	−	17.1465i	−2.16131	−	0.634619i
$731$	9.25812	−	10.6844i	0.342424	−	0.395178i
$732$		0			0
$733$	16.5986	−	36.3460i	0.613085	−	1.34247i	−0.307359	−	0.951594i	$-0.599445\pi$
$733$	16.5986	−	36.3460i	0.613085	−	1.34247i	0.920444	−	0.390875i	$-0.127828\pi$
$734$	−5.32077	−	37.0068i	−0.196393	−	1.36594i
$735$		0			0
$736$	14.6328	−	7.59722i	0.539374	−	0.280037i
$737$	−0.120936			−0.00445474
$738$		0			0
$739$	0.869793	−	1.90458i	0.0319958	−	0.0700611i	−0.892959	−	0.450137i	$-0.851375\pi$
$739$	0.869793	−	1.90458i	0.0319958	−	0.0700611i	0.924955	+	0.380076i	$0.124102\pi$
$740$	36.9876	−	10.8605i	1.35969	−	0.399241i
$741$		0			0
$742$	−6.10135	−	1.79152i	−0.223988	−	0.0657687i
$743$	−42.2305	+	27.1399i	−1.54929	+	0.995666i	−0.563801	+	0.825911i	$0.690662\pi$
$743$	−42.2305	+	27.1399i	−1.54929	+	0.995666i	−0.985486	+	0.169756i	$0.945702\pi$
$744$		0			0
$745$	−7.68617	−	8.87031i	−0.281599	−	0.324983i
$746$	−36.8925	−	23.7094i	−1.35073	−	0.868061i
$747$		0			0
$748$	0.0722920	−	0.502802i	0.00264326	−	0.0183843i
$749$	−15.9743	−	10.2660i	−0.583687	−	0.375113i
$750$		0			0
$751$	6.50791	+	14.2503i	0.237477	+	0.520002i	0.990421	−	0.138083i	$-0.0440941\pi$
$751$	6.50791	+	14.2503i	0.237477	+	0.520002i	−0.752944	+	0.658085i	$0.771367\pi$
$752$	−45.3561	+	29.1486i	−1.65397	+	1.06294i
$753$		0			0
$754$	−3.81394	+	4.40152i	−0.138896	+	0.160294i
$755$	−8.03779	+	2.36011i	−0.292525	+	0.0858932i
$756$		0			0
$757$	4.29183	+	29.8503i	0.155989	+	1.08493i	0.905931	+	0.423425i	$0.139172\pi$
$757$	4.29183	+	29.8503i	0.155989	+	1.08493i	−0.749942	+	0.661503i	$0.769919\pi$
$758$	−29.5971			−1.07501
$759$		0			0
$760$	118.108			4.28424
$761$	−3.59171	−	24.9809i	−0.130199	−	0.905555i	−0.945292	−	0.326225i	$-0.894223\pi$
$761$	−3.59171	−	24.9809i	−0.130199	−	0.905555i	0.815093	−	0.579330i	$-0.196686\pi$
$762$		0			0
$763$	−10.7859	+	3.16704i	−0.390477	+	0.114654i
$764$	−23.4343	+	27.0447i	−0.847824	+	0.978441i
$765$		0			0
$766$	−6.10168	+	3.92131i	−0.220463	+	0.141683i
$767$	−1.08901	−	2.38460i	−0.0393218	−	0.0861028i
$768$		0			0
$769$	21.5111	+	13.8243i	0.775708	+	0.498517i	0.867607	−	0.497251i	$-0.165657\pi$
$769$	21.5111	+	13.8243i	0.775708	+	0.498517i	−0.0918985	+	0.995768i	$0.529294\pi$
$770$	−0.0545368	+	0.379312i	−0.00196537	+	0.0136694i
$771$		0			0
$772$	−61.6144	−	39.5972i	−2.21755	−	1.42513i
$773$	−17.3482	−	20.0209i	−0.623971	−	0.720101i	0.352485	−	0.935818i	$-0.385337\pi$
$773$	−17.3482	−	20.0209i	−0.623971	−	0.720101i	−0.976456	+	0.215716i	$0.930791\pi$
$774$		0			0
$775$	−4.64393	+	2.98447i	−0.166815	+	0.107205i
$776$	−12.0952	−	3.55148i	−0.434194	−	0.127491i
$777$		0			0
$778$	−11.0010	+	3.23017i	−0.394404	+	0.115807i
$779$	−20.8212	+	45.5921i	−0.745997	+	1.63350i
$780$		0			0
$781$	−0.197288			−0.00705952
$782$	−48.2817	−	19.1678i	−1.72655	−	0.685440i
$783$		0			0
$784$	4.35922	+	30.3190i	0.155686	+	1.08282i
$785$	−32.6565	+	71.5078i	−1.16556	+	2.55222i
$786$		0			0
$787$	11.2996	−	13.0404i	0.402786	−	0.464839i	−0.517731	−	0.855544i	$-0.673223\pi$
$787$	11.2996	−	13.0404i	0.402786	−	0.464839i	0.920516	+	0.390704i	$0.127768\pi$
$788$	−56.2380	−	16.5130i	−2.00340	−	0.588250i
$789$		0			0
$790$	6.38880	+	13.9895i	0.227303	+	0.497725i
$791$	13.1878	+	15.2195i	0.468904	+	0.541144i
$792$		0			0
$793$	0.412673	−	2.87020i	0.0146544	−	0.101924i
$794$	−1.58627	+	11.0328i	−0.0562947	+	0.391538i
$795$		0			0
$796$	36.2931	+	41.8845i	1.28638	+	1.48456i
$797$	13.3136	+	29.1526i	0.471590	+	1.03264i	0.984691	+	0.174310i	$0.0557695\pi$
$797$	13.3136	+	29.1526i	0.471590	+	1.03264i	−0.513101	+	0.858328i	$0.671503\pi$
$798$		0			0
$799$	37.1479	+	10.9076i	1.31420	+	0.385883i
$800$	−25.7674	+	29.7372i	−0.911016	+	1.05137i
$801$		0			0
$802$	−5.74863	+	12.5877i	−0.202991	+	0.444489i
$803$	0.0232027	+	0.161378i	0.000818804	+	0.00569491i
$804$		0			0
$805$	24.8914	+	9.88186i	0.877305	+	0.348290i
$806$	0.760317			0.0267810
$807$		0			0
$808$	−32.2922	+	70.7100i	−1.13604	+	2.48757i
$809$	12.0192	−	3.52914i	0.422571	−	0.124078i	−0.0635315	−	0.997980i	$-0.520236\pi$
$809$	12.0192	−	3.52914i	0.422571	−	0.124078i	0.486102	+	0.873902i	$0.338418\pi$
$810$		0			0
$811$	−7.39961	−	2.17272i	−0.259836	−	0.0762946i	0.149220	−	0.988804i	$-0.452324\pi$
$811$	−7.39961	−	2.17272i	−0.259836	−	0.0762946i	−0.409056	+	0.912509i	$0.634142\pi$
$812$	18.4755	−	11.8735i	0.648364	−	0.416678i
$813$		0			0
$814$	−0.0989570	−	0.114202i	−0.00346844	−	0.00400279i
$815$	80.0260	+	51.4296i	2.80319	+	1.80150i
$816$		0			0
$817$	2.33498	−	16.2401i	0.0816905	−	0.568170i
$818$	65.9271	+	42.3688i	2.30509	+	1.48139i
$819$		0			0
$820$	−72.8767	−	159.578i	−2.54496	−	5.57270i
$821$	27.6782	−	17.7877i	0.965977	−	0.620796i	0.0403314	−	0.999186i	$-0.487159\pi$
$821$	27.6782	−	17.7877i	0.965977	−	0.620796i	0.925646	+	0.378390i	$0.123522\pi$
$822$		0			0
$823$	−18.7991	+	21.6953i	−0.655295	+	0.756251i	−0.982001	−	0.188875i	$-0.939516\pi$
$823$	−18.7991	+	21.6953i	−0.655295	+	0.756251i	0.326706	+	0.945126i	$0.394061\pi$
$824$	−52.8110	+	15.5067i	−1.83976	+	0.540202i
$825$		0			0
$826$	2.05863	+	14.3181i	0.0716288	+	0.498189i
$827$	10.6363			0.369861			0.184931	−	0.982752i	$-0.440794\pi$
$827$	10.6363			0.369861			0.184931	+	0.982752i	$0.440794\pi$
$828$		0			0
$829$	−22.6856			−0.787903			−0.393952	−	0.919131i	$-0.628892\pi$
$829$	−22.6856			−0.787903			−0.393952	+	0.919131i	$0.628892\pi$
$830$	−12.4280	−	86.4383i	−0.431381	−	3.00032i
$831$		0			0
$832$	−2.02364	+	0.594195i	−0.0701572	+	0.0206000i
$833$	14.4043	−	16.6234i	0.499078	−	0.575966i
$834$		0			0
$835$	70.8320	−	45.5210i	2.45124	−	1.57532i
$836$	−0.244895	−	0.536246i	−0.00846989	−	0.0185465i
$837$		0			0
$838$	−81.8054	−	52.5731i	−2.82592	−	1.81611i
$839$	1.65201	−	11.4900i	0.0570337	−	0.396678i	−0.941230	−	0.337767i	$-0.890328\pi$
$839$	1.65201	−	11.4900i	0.0570337	−	0.396678i	0.998263	−	0.0589104i	$-0.0187626\pi$
$840$		0			0
$841$	−12.9137	−	8.29911i	−0.445299	−	0.286176i
$842$	−11.0270	−	12.7259i	−0.380016	−	0.438562i
$843$		0			0
$844$	−4.89518	+	3.14594i	−0.168499	+	0.108288i
$845$	49.0526	+	14.4031i	1.68746	+	0.495483i
$846$		0			0
$847$	−14.5328	+	4.26721i	−0.499352	+	0.146623i
$848$	−4.58077	+	10.0305i	−0.157304	+	0.344448i
$849$		0			0
$850$	123.974			4.25228
$851$	−9.37263	+	4.86617i	−0.321290	+	0.166810i
$852$		0			0
$853$	2.17228	+	15.1086i	0.0743776	+	0.517307i	0.992618	+	0.121284i	$0.0387011\pi$
$853$	2.17228	+	15.1086i	0.0743776	+	0.517307i	−0.918240	+	0.396024i	$0.870390\pi$
$854$	−6.64685	+	14.5546i	−0.227450	+	0.498047i
$855$		0			0
$856$	−52.5836	+	60.6848i	−1.79727	+	2.07416i
$857$	26.1726	+	7.68498i	0.894040	+	0.262514i	0.696309	−	0.717742i	$-0.254824\pi$
$857$	26.1726	+	7.68498i	0.894040	+	0.262514i	0.197731	+	0.980256i	$0.436643\pi$
$858$		0			0
$859$	5.19844	+	11.3830i	0.177368	+	0.388383i	0.977346	−	0.211647i	$-0.0678827\pi$
$859$	5.19844	+	11.3830i	0.177368	+	0.388383i	−0.799978	+	0.600030i	$0.795155\pi$
$860$	37.6066	+	43.4003i	1.28237	+	1.47994i
$861$		0			0
$862$	1.76039	−	12.2438i	0.0599593	−	0.417026i
$863$	−2.92036	+	20.3116i	−0.0994102	+	0.691413i	0.877783	+	0.479059i	$0.159022\pi$
$863$	−2.92036	+	20.3116i	−0.0994102	+	0.691413i	−0.977193	+	0.212354i	$0.931887\pi$
$864$		0			0
$865$	−9.52022	−	10.9869i	−0.323697	−	0.373567i
$866$	−27.0261	−	59.1789i	−0.918384	−	2.01098i
$867$		0			0
$868$	−2.75094	−	0.807749i	−0.0933730	−	0.0274168i
$869$	0.0269796	−	0.0311362i	0.000915221	−	0.00105622i
$870$		0			0
$871$	−1.15407	+	2.52706i	−0.0391042	+	0.0856262i
$872$	6.76510	+	47.0523i	0.229095	+	1.59339i
$873$		0			0
$874$	−59.1642	+	11.5799i	−2.00126	+	0.391696i
$875$	−35.9928			−1.21678
$876$		0			0
$877$	−19.8073	+	43.3720i	−0.668846	+	1.46457i	0.205197	+	0.978721i	$0.434217\pi$
$877$	−19.8073	+	43.3720i	−0.668846	+	1.46457i	−0.874043	+	0.485849i	$0.838511\pi$
$878$	−5.34880	+	1.57055i	−0.180513	+	0.0530035i
$879$		0			0
$880$	0.637606	+	0.187218i	0.0214937	+	0.00631112i
$881$	44.2013	−	28.4064i	1.48918	−	0.957038i	0.492970	−	0.870046i	$-0.335911\pi$
$881$	44.2013	−	28.4064i	1.48918	−	0.957038i	0.996209	−	0.0869915i	$-0.0277253\pi$
$882$		0			0
$883$	10.7972	+	12.4607i	0.363356	+	0.419336i	0.907761	−	0.419487i	$-0.137790\pi$
$883$	10.7972	+	12.4607i	0.363356	+	0.419336i	−0.544405	+	0.838822i	$0.683245\pi$
$884$	−9.81658	−	6.30874i	−0.330167	−	0.212186i
$885$		0			0
$886$	2.78631	−	19.3792i	0.0936078	−	0.651057i
$887$	22.1023	+	14.2043i	0.742121	+	0.476933i	0.856268	−	0.516531i	$-0.172777\pi$
$887$	22.1023	+	14.2043i	0.742121	+	0.476933i	−0.114147	+	0.993464i	$0.536413\pi$
$888$		0			0
$889$	−1.03878	−	2.27460i	−0.0348394	−	0.0762877i
$890$	−114.294	+	73.4525i	−3.83115	+	2.46213i
$891$		0			0
$892$	65.9461	−	76.1058i	2.20804	−	2.54821i
$893$	43.1114	−	12.6587i	1.44267	−	0.423606i
$894$		0			0
$895$	−11.9270	−	82.9543i	−0.398676	−	2.77286i
$896$	21.1059			0.705099
$897$		0			0
$898$	17.9885			0.600284
$899$	−0.253592	−	1.76377i	−0.00845778	−	0.0588252i
$900$		0			0
$901$	7.59768	−	2.23088i	0.253115	−	0.0743214i
$902$	−0.450338	+	0.519718i	−0.0149946	+	0.0173047i
$903$		0			0
$904$	71.6403	−	46.0404i	2.38272	−	1.53128i
$905$	−43.6398	−	95.5577i	−1.45063	−	3.17645i
$906$		0			0
$907$	32.9483	+	21.1746i	1.09403	+	0.703091i	0.957757	−	0.287580i	$-0.0928508\pi$
$907$	32.9483	+	21.1746i	1.09403	+	0.703091i	0.136274	+	0.990671i	$0.456487\pi$
$908$	3.75791	−	26.1368i	0.124711	−	0.867381i
$909$		0			0
$910$	7.40559	+	4.75928i	0.245493	+	0.157769i
$911$	17.4784	+	20.1712i	0.579086	+	0.668301i	0.967408	−	0.253223i	$-0.0814907\pi$
$911$	17.4784	+	20.1712i	0.579086	+	0.668301i	−0.388322	+	0.921524i	$0.626945\pi$
$912$		0			0
$913$	−0.196801	+	0.126476i	−0.00651315	+	0.00418575i
$914$	10.7546	+	3.15785i	0.355732	+	0.104452i
$915$		0			0
$916$	−56.9928	+	16.7346i	−1.88310	+	0.552927i
$917$	3.39541	−	7.43490i	0.112126	−	0.245522i
$918$		0			0
$919$	25.3453			0.836064			0.418032	−	0.908432i	$-0.362720\pi$
$919$	25.3453			0.836064			0.418032	+	0.908432i	$0.362720\pi$
$920$	56.3420	−	98.2400i	1.85754	−	3.23888i
$921$		0			0
$922$	−8.60376	−	59.8404i	−0.283350	−	1.97074i
$923$	−1.88268	+	4.12249i	−0.0619691	+	0.135694i
$924$		0			0
$925$	16.5046	−	19.0473i	0.542666	−	0.626270i
$926$	7.92795	+	2.32786i	0.260529	+	0.0764981i
$927$		0			0
$928$	−5.27633	−	11.5535i	−0.173204	−	0.379264i
$929$	−5.35859	−	6.18415i	−0.175810	−	0.202895i	0.661005	−	0.750382i	$-0.270130\pi$
$929$	−5.35859	−	6.18415i	−0.175810	−	0.202895i	−0.836815	+	0.547486i	$0.815585\pi$
$930$		0			0
$931$	3.63287	−	25.2672i	0.119063	−	0.828099i
$932$	8.70175	−	60.5220i	0.285035	−	1.98246i
$933$		0			0
$934$	22.6495	+	26.1389i	0.741115	+	0.855292i
$935$	−0.198233	−	0.434070i	−0.00648292	−	0.0141956i
$936$		0			0
$937$	−26.8166	−	7.87408i	−0.876061	−	0.257235i	−0.187370	−	0.982289i	$-0.559996\pi$
$937$	−26.8166	−	7.87408i	−0.876061	−	0.257235i	−0.688691	+	0.725055i	$0.741815\pi$
$938$	10.0387	−	11.5853i	0.327775	−	0.378272i
$939$		0			0
$940$	−65.3305	+	143.054i	−2.13085	+	4.66590i
$941$	−4.68100	−	32.5571i	−0.152596	−	1.06133i	−0.911846	−	0.410532i	$-0.865343\pi$
$941$	−4.68100	−	32.5571i	−0.152596	−	1.06133i	0.759250	−	0.650799i	$-0.225566\pi$
$942$		0			0
$943$	27.9900	+	39.0677i	0.911480	+	1.27222i
$944$	25.0841			0.816418
$945$		0			0
$946$	0.0935148	−	0.204769i	0.00304043	−	0.00665761i
$947$	19.2462	−	5.65120i	0.625418	−	0.183639i	0.0463589	−	0.998925i	$-0.485238\pi$
$947$	19.2462	−	5.65120i	0.625418	−	0.183639i	0.579059	+	0.815286i	$0.303420\pi$
$948$		0			0
$949$	3.59354	+	1.05516i	0.116651	+	0.0342519i
$950$	121.036	−	77.7854i	3.92694	−	2.52369i
$951$		0			0
$952$	22.6304	+	26.1169i	0.733456	+	0.846454i
$953$	−24.5517	−	15.7784i	−0.795308	−	0.511113i	0.0787738	−	0.996893i	$-0.474900\pi$
$953$	−24.5517	−	15.7784i	−0.795308	−	0.511113i	−0.874082	+	0.485779i	$0.838536\pi$
$954$		0			0
$955$	−4.78418	+	33.2747i	−0.154812	+	1.07674i
$956$	−73.8555	−	47.4640i	−2.38866	−	1.53510i
$957$		0			0
$958$	24.1527	+	52.8870i	0.780338	+	1.70870i
$959$	9.32981	−	5.99591i	0.301275	−	0.193618i
$960$		0			0
$961$	20.1483	−	23.2524i	0.649947	−	0.750078i
$962$	−3.33068	+	0.977975i	−0.107385	+	0.0315312i
$963$		0			0
$964$	−4.79680	−	33.3625i	−0.154494	−	1.07453i
$965$	−68.8033			−2.21486
$966$		0			0
$967$	−48.3376			−1.55443			−0.777216	−	0.629233i	$-0.783369\pi$
$967$	−48.3376			−1.55443			−0.777216	+	0.629233i	$0.783369\pi$
$968$	9.11517	+	63.3974i	0.292973	+	2.03767i
$969$		0			0
$970$	−21.1708	+	6.21629i	−0.679752	+	0.199593i
$971$	−23.1379	+	26.7026i	−0.742532	+	0.856927i	−0.993822	−	0.110985i	$-0.964600\pi$
$971$	−23.1379	+	26.7026i	−0.742532	+	0.856927i	0.251291	+	0.967912i	$0.419145\pi$
$972$		0			0
$973$	8.89689	−	5.71768i	0.285221	−	0.183301i
$974$	12.1439	+	26.5914i	0.389115	+	0.852042i
$975$		0			0
$976$	23.3417	+	15.0008i	0.747149	+	0.480163i
$977$	−1.79485	+	12.4835i	−0.0574224	+	0.399382i	0.940758	+	0.339079i	$0.110116\pi$
$977$	−1.79485	+	12.4835i	−0.0574224	+	0.399382i	−0.998180	+	0.0603022i	$0.980794\pi$
$978$		0			0
$979$	0.306178	+	0.196769i	0.00978550	+	0.00628876i
$980$	58.5103	+	67.5244i	1.86904	+	2.15699i
$981$		0			0
$982$	64.2114	−	41.2662i	2.04907	−	1.31686i
$983$	11.0543	+	3.24584i	0.352577	+	0.103526i	0.453225	−	0.891396i	$-0.350273\pi$
$983$	11.0543	+	3.24584i	0.352577	+	0.103526i	−0.100648	+	0.994922i	$0.532092\pi$
$984$		0			0
$985$	−52.8304	+	15.5124i	−1.68332	+	0.494266i
$986$	−16.6242	+	36.4019i	−0.529422	+	1.15927i
$987$		0			0
$988$	−13.5423			−0.430837
$989$	−12.3943	−	9.68930i	−0.394116	−	0.308102i
$990$		0			0
$991$	−3.57914	−	24.8934i	−0.113695	−	0.790766i	−0.964272	−	0.264915i	$-0.914656\pi$
$991$	−3.57914	−	24.8934i	−0.113695	−	0.790766i	0.850577	−	0.525851i	$-0.176253\pi$
$992$	−0.688812	+	1.50829i	−0.0218698	+	0.0478882i
$993$		0			0
$994$	16.3765	−	18.8995i	0.519431	−	0.599456i
$995$	49.9541	+	14.6679i	1.58365	+	0.465002i
$996$		0			0
$997$	−5.65570	−	12.3843i	−0.179118	−	0.392214i	0.798682	−	0.601753i	$-0.205531\pi$
$997$	−5.65570	−	12.3843i	−0.179118	−	0.392214i	−0.977800	+	0.209539i	$0.932804\pi$
$998$	57.4009	+	66.2442i	1.81699	+	2.09692i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.a.118.1		10
3.2	odd	2		69.2.e.b.49.1	yes	10
23.8	even	11	inner	207.2.i.a.100.1		10
23.10	odd	22		4761.2.a.bm.1.5		5
23.13	even	11		4761.2.a.bp.1.5		5
69.8	odd	22		69.2.e.b.31.1	✓	10
69.56	even	22		1587.2.a.r.1.1		5
69.59	odd	22		1587.2.a.q.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.b.31.1	✓	10	69.8	odd	22
69.2.e.b.49.1	yes	10	3.2	odd	2
207.2.i.a.100.1		10	23.8	even	11	inner
207.2.i.a.118.1		10	1.1	even	1	trivial
1587.2.a.q.1.1		5	69.59	odd	22
1587.2.a.r.1.1		5	69.56	even	22
4761.2.a.bm.1.5		5	23.10	odd	22
4761.2.a.bp.1.5		5	23.13	even	11

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.357685 - 2.48775i) q^{2} +(-4.14200 + 1.21620i) q^{4} +(-2.65565 + 3.06479i) q^{5} +(-1.15843 + 0.744479i) q^{7} +(2.41899 + 5.29684i) q^{8} +O(q^{10})\)	\(q+(-0.357685 - 2.48775i) q^{2} +(-4.14200 + 1.21620i) q^{4} +(-2.65565 + 3.06479i) q^{5} +(-1.15843 + 0.744479i) q^{7} +(2.41899 + 5.29684i) q^{8} +(8.57432 + 5.51038i) q^{10} +(0.00388573 - 0.0270259i) q^{11} +(-0.527646 - 0.339098i) q^{13} +(2.26643 + 2.61561i) q^{14} +(5.04885 - 3.24470i) q^{16} +(-4.13515 - 1.21419i) q^{17} +(-4.79898 + 1.40911i) q^{19} +(7.27232 - 15.9241i) q^{20} -0.0686236 q^{22} +(-1.11722 + 4.66388i) q^{23} +(-1.62885 - 11.3289i) q^{25} +(-0.654861 + 1.43394i) q^{26} +(3.89279 - 4.49252i) q^{28} +(3.54487 + 1.04087i) q^{29} +(-0.200359 - 0.438726i) q^{31} +(-2.25133 - 2.59818i) q^{32} +(-1.54152 + 10.7215i) q^{34} +(0.794723 - 5.52742i) q^{35} +(1.44203 + 1.66419i) q^{37} +(5.22204 + 11.4347i) q^{38} +(-22.6577 - 6.65289i) q^{40} +(6.56243 - 7.57345i) q^{41} +(-1.36272 + 2.98394i) q^{43} +(0.0167742 + 0.116667i) q^{44} +(12.0022 + 1.11118i) q^{46} -8.98345 q^{47} +(-2.12019 + 4.64257i) q^{49} +(-27.6009 + 8.10436i) q^{50} +(2.59792 + 0.762819i) q^{52} +(-1.54567 + 0.993342i) q^{53} +(0.0725093 + 0.0836802i) q^{55} +(-6.74562 - 4.33514i) q^{56} +(1.32148 - 9.19107i) q^{58} +(3.51609 + 2.25965i) q^{59} +(1.92053 + 4.20538i) q^{61} +(-1.01978 + 0.655371i) q^{62} +(2.20204 - 2.54129i) q^{64} +(2.44051 - 0.716597i) q^{65} +(-0.630353 - 4.38420i) q^{67} +18.6045 q^{68} -14.0351 q^{70} +(-1.02832 - 7.15212i) q^{71} +(-5.72936 + 1.68229i) q^{73} +(3.62430 - 4.18266i) q^{74} +(18.1636 - 11.6731i) q^{76} +(0.0156188 + 0.0342005i) q^{77} +(1.26938 + 0.815780i) q^{79} +(-3.46368 + 24.0904i) q^{80} +(-21.1882 - 13.6168i) q^{82} +(-5.61081 - 6.47522i) q^{83} +(14.7027 - 9.44888i) q^{85} +(7.91074 + 2.32280i) q^{86} +(0.152551 - 0.0447931i) q^{88} +(-5.53741 + 12.1252i) q^{89} +0.863693 q^{91} +(-1.04468 - 20.6766i) q^{92} +(3.21325 + 22.3486i) q^{94} +(8.42581 - 18.4500i) q^{95} +(-1.41765 + 1.63606i) q^{97} +(12.3079 + 3.61394i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 14 q^{4} + 3 q^{5} + 6 q^{7} + 7 q^{8}+O(q^{10}) \) 10 * q - 4 * q^2 - 14 * q^4 + 3 * q^5 + 6 * q^7 + 7 * q^8	\( 10 q - 4 q^{2} - 14 q^{4} + 3 q^{5} + 6 q^{7} + 7 q^{8} + 12 q^{10} + 15 q^{11} + 8 q^{13} - 9 q^{14} + 12 q^{16} - q^{17} - 9 q^{19} + 9 q^{20} - 28 q^{22} - 21 q^{23} - 4 q^{25} - q^{26} + 29 q^{28} + 8 q^{29} - 23 q^{31} + q^{32} - 15 q^{34} - 18 q^{35} + 3 q^{37} - 3 q^{38} - 32 q^{40} + 15 q^{41} + 22 q^{43} + q^{44} + 26 q^{46} - 4 q^{47} - 29 q^{49} - 49 q^{50} + 2 q^{52} - 29 q^{53} + 43 q^{55} + 2 q^{56} + 21 q^{58} + 54 q^{59} - 30 q^{61} + 7 q^{62} - 31 q^{64} + 9 q^{65} + q^{67} + 30 q^{68} - 94 q^{70} + 3 q^{71} - 47 q^{73} + 12 q^{74} + 50 q^{76} - 13 q^{77} + 18 q^{79} - 3 q^{80} - 28 q^{82} - 18 q^{83} + 58 q^{85} + 16 q^{88} - 25 q^{89} + 18 q^{91} + 3 q^{92} + 39 q^{94} + 16 q^{95} + 21 q^{97} + 27 q^{98}+O(q^{100}) \) 10 * q - 4 * q^2 - 14 * q^4 + 3 * q^5 + 6 * q^7 + 7 * q^8 + 12 * q^10 + 15 * q^11 + 8 * q^13 - 9 * q^14 + 12 * q^16 - q^17 - 9 * q^19 + 9 * q^20 - 28 * q^22 - 21 * q^23 - 4 * q^25 - q^26 + 29 * q^28 + 8 * q^29 - 23 * q^31 + q^32 - 15 * q^34 - 18 * q^35 + 3 * q^37 - 3 * q^38 - 32 * q^40 + 15 * q^41 + 22 * q^43 + q^44 + 26 * q^46 - 4 * q^47 - 29 * q^49 - 49 * q^50 + 2 * q^52 - 29 * q^53 + 43 * q^55 + 2 * q^56 + 21 * q^58 + 54 * q^59 - 30 * q^61 + 7 * q^62 - 31 * q^64 + 9 * q^65 + q^67 + 30 * q^68 - 94 * q^70 + 3 * q^71 - 47 * q^73 + 12 * q^74 + 50 * q^76 - 13 * q^77 + 18 * q^79 - 3 * q^80 - 28 * q^82 - 18 * q^83 + 58 * q^85 + 16 * q^88 - 25 * q^89 + 18 * q^91 + 3 * q^92 + 39 * q^94 + 16 * q^95 + 21 * q^97 + 27 * q^98

Introduction

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