LMFDB - Embedded newform 441.2.u.c.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

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("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.1
Character	$\chi$	$=$	441.190
Dual form			441.2.u.c.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18466 + 1.48552i) q^{2} +(-0.358304 - 1.56983i) q^{4} +(0.295313 + 0.142215i) q^{5} +(-2.01260 - 1.71740i) q^{7} +(-0.667291 - 0.321350i) q^{8} +O(q^{10})$	\(q+(-1.18466 + 1.48552i) q^{2} +(-0.358304 - 1.56983i) q^{4} +(0.295313 + 0.142215i) q^{5} +(-2.01260 - 1.71740i) q^{7} +(-0.667291 - 0.321350i) q^{8} +(-0.561110 + 0.270216i) q^{10} +(0.320589 - 0.402005i) q^{11} +(-0.333248 + 0.417880i) q^{13} +(4.93548 - 0.955219i) q^{14} +(4.16937 - 2.00786i) q^{16} +(1.75860 - 7.70492i) q^{17} -5.08389 q^{19} +(0.117442 - 0.514547i) q^{20} +(0.217398 + 0.952482i) q^{22} +(0.0438964 + 0.192322i) q^{23} +(-3.05046 - 3.82516i) q^{25} +(-0.225983 - 0.990094i) q^{26} +(-1.97490 + 3.77479i) q^{28} +(0.477947 - 2.09402i) q^{29} +2.48475 q^{31} +(-1.62696 + 7.12820i) q^{32} +(9.36247 + 11.7402i) q^{34} +(-0.350106 - 0.793391i) q^{35} +(1.18663 - 5.19896i) q^{37} +(6.02270 - 7.55223i) q^{38} +(-0.151359 - 0.189798i) q^{40} +(1.92273 + 0.925936i) q^{41} +(9.46803 - 4.55956i) q^{43} +(-0.745949 - 0.359230i) q^{44} +(-0.337702 - 0.162629i) q^{46} +(-5.00777 + 6.27955i) q^{47} +(1.10110 + 6.91286i) q^{49} +9.29613 q^{50} +(0.775405 + 0.373415i) q^{52} +(-1.18664 - 5.19903i) q^{53} +(0.151845 - 0.0731247i) q^{55} +(0.791102 + 1.79275i) q^{56} +(2.54451 + 3.19071i) q^{58} +(0.263805 - 0.127042i) q^{59} +(0.889807 - 3.89850i) q^{61} +(-2.94359 + 3.69115i) q^{62} +(-2.89110 - 3.62532i) q^{64} +(-0.157841 + 0.0760123i) q^{65} -10.4502 q^{67} -12.7255 q^{68} +(1.59336 + 0.419812i) q^{70} +(2.09042 + 9.15871i) q^{71} +(-6.25159 - 7.83924i) q^{73} +(6.31741 + 7.92178i) q^{74} +(1.82158 + 7.98085i) q^{76} +(-1.33562 + 0.258497i) q^{77} +3.83303 q^{79} +1.51682 q^{80} +(-3.65328 + 1.75933i) q^{82} +(5.28762 + 6.63047i) q^{83} +(1.61509 - 2.02526i) q^{85} +(-4.44310 + 19.4665i) q^{86} +(-0.343110 + 0.165233i) q^{88} +(-8.30354 - 10.4123i) q^{89} +(1.38836 - 0.268705i) q^{91} +(0.286186 - 0.137820i) q^{92} +(-3.39588 - 14.8783i) q^{94} +(-1.50134 - 0.723006i) q^{95} -9.62539 q^{97} +(-11.5736 - 6.55371i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$

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 $

$2$	−1.18466	+	1.48552i	−0.837684	+	1.05042i	0.160307	+	0.987067i	$0.448751\pi$
$2$	−1.18466	+	1.48552i	−0.837684	+	1.05042i	−0.997991	+	0.0633551i	$0.979820\pi$
$3$		0			0
$3$		0			0
$4$	−0.358304	−	1.56983i	−0.179152	−	0.784915i
$5$	0.295313	+	0.142215i	0.132068	+	0.0636005i	0.498751	−	0.866745i	$-0.333792\pi$
$5$	0.295313	+	0.142215i	0.132068	+	0.0636005i	−0.366683	+	0.930346i	$0.619507\pi$
$6$		0			0
$7$	−2.01260	−	1.71740i	−0.760690	−	0.649115i
$7$	−2.01260	−	1.71740i	−0.760690	−	0.649115i
$8$	−0.667291	−	0.321350i	−0.235923	−	0.113614i
$9$		0			0
$10$	−0.561110	+	0.270216i	−0.177438	+	0.0854499i
$11$	0.320589	−	0.402005i	0.0966611	−	0.121209i	−0.731148	−	0.682218i	$-0.761015\pi$
$11$	0.320589	−	0.402005i	0.0966611	−	0.121209i	0.827810	+	0.561009i	$0.189587\pi$
$12$		0			0
$13$	−0.333248	+	0.417880i	−0.0924264	+	0.115899i	−0.825894	−	0.563825i	$-0.809329\pi$
$13$	−0.333248	+	0.417880i	−0.0924264	+	0.115899i	0.733468	+	0.679724i	$0.237901\pi$
$14$	4.93548	−	0.955219i	1.31906	−	0.255293i
$15$		0			0
$16$	4.16937	−	2.00786i	1.04234	−	0.501966i
$17$	1.75860	−	7.70492i	0.426522	−	1.86872i	−0.0650535	−	0.997882i	$-0.520722\pi$
$17$	1.75860	−	7.70492i	0.426522	−	1.86872i	0.491576	−	0.870835i	$-0.336421\pi$
$18$		0			0
$19$	−5.08389			−1.16632			−0.583162	−	0.812356i	$-0.698185\pi$
$19$	−5.08389			−1.16632			−0.583162	+	0.812356i	$0.698185\pi$
$20$	0.117442	−	0.514547i	0.0262608	−	0.115056i
$21$		0			0
$22$	0.217398	+	0.952482i	0.0463494	+	0.203070i
$23$	0.0438964	+	0.192322i	0.00915302	+	0.0401020i	0.979298	−	0.202423i	$-0.0648815\pi$
$23$	0.0438964	+	0.192322i	0.00915302	+	0.0401020i	−0.970145	+	0.242525i	$0.922024\pi$
$24$		0			0
$25$	−3.05046	−	3.82516i	−0.610093	−	0.765032i
$26$	−0.225983	−	0.990094i	−0.0443188	−	0.194173i
$27$		0			0
$28$	−1.97490	+	3.77479i	−0.373221	+	0.713368i
$29$	0.477947	−	2.09402i	0.0887525	−	0.388850i	−0.910968	−	0.412476i	$-0.864664\pi$
$29$	0.477947	−	2.09402i	0.0887525	−	0.388850i	0.999721	+	0.0236262i	$0.00752115\pi$
$30$		0			0
$31$	2.48475			0.446274			0.223137	−	0.974787i	$-0.428370\pi$
$31$	2.48475			0.446274			0.223137	+	0.974787i	$0.428370\pi$
$32$	−1.62696	+	7.12820i	−0.287609	+	1.26010i
$33$		0			0
$34$	9.36247	+	11.7402i	1.60565	+	2.01342i
$35$	−0.350106	−	0.793391i	−0.0591787	−	0.134107i
$36$		0			0
$37$	1.18663	−	5.19896i	0.195081	−	0.854704i	−0.778733	−	0.627356i	$-0.784137\pi$
$37$	1.18663	−	5.19896i	0.195081	−	0.854704i	0.973813	−	0.227348i	$-0.0730056\pi$
$38$	6.02270	−	7.55223i	0.977011	−	1.22513i
$39$		0			0
$40$	−0.151359	−	0.189798i	−0.0239319	−	0.0300096i
$41$	1.92273	+	0.925936i	0.300279	+	0.144607i	0.577957	−	0.816067i	$-0.303850\pi$
$41$	1.92273	+	0.925936i	0.300279	+	0.144607i	−0.277677	+	0.960674i	$0.589565\pi$
$42$		0			0
$43$	9.46803	−	4.55956i	1.44386	−	0.695327i	0.462343	−	0.886701i	$-0.347009\pi$
$43$	9.46803	−	4.55956i	1.44386	−	0.695327i	0.981517	+	0.191374i	$0.0612945\pi$
$44$	−0.745949	−	0.359230i	−0.112456	−	0.0541559i
$45$		0			0
$46$	−0.337702	−	0.162629i	−0.0497914	−	0.0239783i
$47$	−5.00777	+	6.27955i	−0.730459	+	0.915966i	−0.998879	−	0.0473355i	$-0.984927\pi$
$47$	−5.00777	+	6.27955i	−0.730459	+	0.915966i	0.268420	+	0.963302i	$0.413498\pi$
$48$		0			0
$49$	1.10110	+	6.91286i	0.157299	+	0.987551i
$50$	9.29613			1.31467
$51$		0			0
$52$	0.775405	+	0.373415i	0.107529	+	0.0517834i
$53$	−1.18664	−	5.19903i	−0.162998	−	0.714141i	−0.988684	−	0.150011i	$-0.952069\pi$
$53$	−1.18664	−	5.19903i	−0.162998	−	0.714141i	0.825686	−	0.564130i	$-0.190788\pi$
$54$		0			0
$55$	0.151845	−	0.0731247i	0.0204748	−	0.00986014i
$56$	0.791102	+	1.79275i	0.105715	+	0.239567i
$57$		0			0
$58$	2.54451	+	3.19071i	0.334110	+	0.418961i
$59$	0.263805	−	0.127042i	0.0343444	−	0.0165394i	−0.416633	−	0.909075i	$-0.636790\pi$
$59$	0.263805	−	0.127042i	0.0343444	−	0.0165394i	0.450977	+	0.892535i	$0.351076\pi$
$60$		0			0
$61$	0.889807	−	3.89850i	0.113928	−	0.499151i	−0.885478	−	0.464682i	$-0.846169\pi$
$61$	0.889807	−	3.89850i	0.113928	−	0.499151i	0.999406	−	0.0344695i	$-0.0109742\pi$
$62$	−2.94359	+	3.69115i	−0.373836	+	0.468776i
$63$		0			0
$64$	−2.89110	−	3.62532i	−0.361387	−	0.453165i
$65$	−0.157841	+	0.0760123i	−0.0195778	+	0.00942816i
$66$		0			0
$67$	−10.4502			−1.27670			−0.638350	−	0.769746i	$-0.720383\pi$
$67$	−10.4502			−1.27670			−0.638350	+	0.769746i	$0.720383\pi$
$68$	−12.7255			−1.54320
$69$		0			0
$70$	1.59336	+	0.419812i	0.190443	+	0.0501771i
$71$	2.09042	+	9.15871i	0.248087	+	1.08694i	0.933441	+	0.358730i	$0.116790\pi$
$71$	2.09042	+	9.15871i	0.248087	+	1.08694i	−0.685355	+	0.728209i	$0.740353\pi$
$72$		0			0
$73$	−6.25159	−	7.83924i	−0.731693	−	0.917514i	0.267243	−	0.963629i	$-0.413887\pi$
$73$	−6.25159	−	7.83924i	−0.731693	−	0.917514i	−0.998936	+	0.0461151i	$0.985316\pi$
$74$	6.31741	+	7.92178i	0.734384	+	0.920889i
$75$		0			0
$76$	1.82158	+	7.98085i	0.208949	+	0.915466i
$77$	−1.33562	+	0.258497i	−0.152208	+	0.0294585i
$78$		0			0
$79$	3.83303			0.431249			0.215625	−	0.976476i	$-0.430821\pi$
$79$	3.83303			0.431249			0.215625	+	0.976476i	$0.430821\pi$
$80$	1.51682			0.169585
$81$		0			0
$82$	−3.65328	+	1.75933i	−0.403438	+	0.194285i
$83$	5.28762	+	6.63047i	0.580392	+	0.727789i	0.982180	−	0.187944i	$-0.0601824\pi$
$83$	5.28762	+	6.63047i	0.580392	+	0.727789i	−0.401788	+	0.915733i	$0.631611\pi$
$84$		0			0
$85$	1.61509	−	2.02526i	0.175181	−	0.219670i
$86$	−4.44310	+	19.4665i	−0.479112	+	2.09913i
$87$		0			0
$88$	−0.343110	+	0.165233i	−0.0365757	+	0.0176139i
$89$	−8.30354	−	10.4123i	−0.880173	−	1.10370i	−0.993910	−	0.110191i	$-0.964854\pi$
$89$	−8.30354	−	10.4123i	−0.880173	−	1.10370i	0.113737	−	0.993511i	$-0.463718\pi$
$90$		0			0
$91$	1.38836	−	0.268705i	0.145540	−	0.0281679i
$92$	0.286186	−	0.137820i	0.0298369	−	0.0143687i
$93$		0			0
$94$	−3.39588	−	14.8783i	−0.350258	−	1.53458i
$95$	−1.50134	−	0.723006i	−0.154034	−	0.0741788i
$96$		0			0
$97$	−9.62539			−0.977310			−0.488655	−	0.872477i	$-0.662512\pi$
$97$	−9.62539			−0.977310			−0.488655	+	0.872477i	$0.662512\pi$
$98$	−11.5736	−	6.55371i	−1.16911	−	0.662025i
$99$		0			0
$100$	−4.91186	+	6.15928i	−0.491186	+	0.615928i
$101$	−15.8484	−	7.63217i	−1.57697	−	0.759430i	−0.578553	−	0.815644i	$-0.696383\pi$
$101$	−15.8484	−	7.63217i	−1.57697	−	0.759430i	−0.998419	+	0.0562147i	$0.982097\pi$
$102$		0			0
$103$	0.531663	+	0.256036i	0.0523863	+	0.0252279i	0.459894	−	0.887974i	$-0.347888\pi$
$103$	0.531663	+	0.256036i	0.0523863	+	0.0252279i	−0.407507	+	0.913202i	$0.633602\pi$
$104$	0.356659	−	0.171758i	0.0349733	−	0.0168423i
$105$		0			0
$106$	9.12904	+	4.39631i	0.886690	+	0.427008i
$107$	−12.5074	−	15.6837i	−1.20913	−	1.51620i	−0.795724	−	0.605660i	$-0.792909\pi$
$107$	−12.5074	−	15.6837i	−1.20913	−	1.51620i	−0.413409	−	0.910545i	$-0.635662\pi$
$108$		0			0
$109$	−6.37438	+	7.99322i	−0.610555	+	0.765611i	−0.986981	−	0.160835i	$-0.948581\pi$
$109$	−6.37438	+	7.99322i	−0.610555	+	0.765611i	0.376427	+	0.926446i	$0.377153\pi$
$110$	−0.0712570	+	0.312197i	−0.00679409	+	0.0297668i
$111$		0			0
$112$	−11.8396	−	3.11944i	−1.11873	−	0.294760i
$113$	5.97655	+	7.49436i	0.562226	+	0.705010i	0.978968	−	0.204016i	$-0.0653993\pi$
$113$	5.97655	+	7.49436i	0.562226	+	0.705010i	−0.416741	+	0.909025i	$0.636828\pi$
$114$		0			0
$115$	−0.0143880	+	0.0630380i	−0.00134169	+	0.00587832i
$116$	−3.45851			−0.321115
$117$		0			0
$118$	−0.123797	+	0.542389i	−0.0113964	+	0.0499310i
$119$	−16.7717	+	12.4867i	−1.53746	+	1.14465i
$120$		0			0
$121$	2.38890	+	10.4665i	0.217173	+	0.951495i
$122$	4.73718	+	5.94024i	0.428884	+	0.537804i
$123$		0			0
$124$	−0.890294	−	3.90063i	−0.0799508	−	0.350287i
$125$	−0.721526	−	3.16121i	−0.0645353	−	0.282747i
$126$		0			0
$127$	2.55336	−	11.1870i	0.226574	−	0.992686i	−0.725836	−	0.687868i	$-0.758547\pi$
$127$	2.55336	−	11.1870i	0.226574	−	0.992686i	0.952410	−	0.304819i	$-0.0985959\pi$
$128$	−5.81256			−0.513763
$129$		0			0
$130$	0.0740708	−	0.324525i	0.00649644	−	0.0284628i
$131$	3.18909	−	1.53578i	0.278632	−	0.134182i	−0.289349	−	0.957224i	$-0.593439\pi$
$131$	3.18909	−	1.53578i	0.278632	−	0.134182i	0.567981	+	0.823041i	$0.307725\pi$
$132$		0			0
$133$	10.2318	+	8.73106i	0.887211	+	0.757079i
$134$	12.3800	−	15.5241i	1.06947	−	1.34107i
$135$		0			0
$136$	−3.64947	+	4.57629i	−0.312940	+	0.392414i
$137$	8.70890	−	4.19399i	0.744052	−	0.358316i	−0.0231417	−	0.999732i	$-0.507367\pi$
$137$	8.70890	−	4.19399i	0.744052	−	0.358316i	0.767193	+	0.641416i	$0.221653\pi$
$138$		0			0
$139$	−17.7360	−	8.54120i	−1.50435	−	0.724455i	−0.513330	−	0.858191i	$-0.671588\pi$
$139$	−17.7360	−	8.54120i	−1.50435	−	0.724455i	−0.991017	+	0.133736i	$0.957302\pi$
$140$	−1.12005	+	0.833882i	−0.0946611	+	0.0704759i
$141$		0			0
$142$	−16.0819	−	7.74464i	−1.34956	−	0.649915i
$143$	0.0611544	+	0.267935i	0.00511399	+	0.0224058i
$144$		0			0
$145$	0.438945	−	0.550420i	0.0364524	−	0.0457099i
$146$	19.0514			1.57670
$147$		0			0
$148$	−8.58666			−0.705819
$149$	11.7308	−	14.7100i	0.961027	−	1.20509i	−0.0176835	−	0.999844i	$-0.505629\pi$
$149$	11.7308	−	14.7100i	0.961027	−	1.20509i	0.978710	−	0.205246i	$-0.0657995\pi$
$150$		0			0
$151$	5.15178	+	22.5714i	0.419246	+	1.83684i	0.536719	+	0.843761i	$0.319663\pi$
$151$	5.15178	+	22.5714i	0.419246	+	1.83684i	−0.117473	+	0.993076i	$0.537479\pi$
$152$	3.39243	+	1.63371i	0.275163	+	0.132511i
$153$		0			0
$154$	1.19826	−	2.29032i	0.0965582	−	0.184559i
$155$	0.733777	+	0.353368i	0.0589384	+	0.0283832i
$156$		0			0
$157$	9.88772	−	4.76168i	0.789126	−	0.380023i	0.00449801	−	0.999990i	$-0.498568\pi$
$157$	9.88772	−	4.76168i	0.789126	−	0.380023i	0.784628	+	0.619967i	$0.212854\pi$
$158$	−4.54085	+	5.69405i	−0.361251	+	0.452994i
$159$		0			0
$160$	−1.49420	+	1.87367i	−0.118127	+	0.148126i
$161$	0.241948	−	0.462455i	0.0190682	−	0.0364466i
$162$		0			0
$163$	10.5307	−	5.07133i	0.824830	−	0.397217i	0.0266563	−	0.999645i	$-0.491514\pi$
$163$	10.5307	−	5.07133i	0.824830	−	0.397217i	0.798174	+	0.602428i	$0.205800\pi$
$164$	0.764643	−	3.35012i	0.0597086	−	0.261601i
$165$		0			0
$166$	−16.1138			−1.25067
$167$	−2.28991	+	10.0328i	−0.177199	+	0.776358i	0.805717	+	0.592301i	$0.201780\pi$
$167$	−2.28991	+	10.0328i	−0.177199	+	0.776358i	−0.982916	+	0.184057i	$0.941077\pi$
$168$		0			0
$169$	2.82920	+	12.3955i	0.217631	+	0.953504i
$170$	1.09523	+	4.79850i	0.0840001	+	0.368028i
$171$		0			0
$172$	−10.5502	−	13.2295i	−0.804443	−	1.00874i
$173$	−2.56254	−	11.2272i	−0.194826	−	0.853589i	−0.973958	−	0.226729i	$-0.927197\pi$
$173$	−2.56254	−	11.2272i	−0.194826	−	0.853589i	0.779132	−	0.626860i	$-0.215660\pi$
$174$		0			0
$175$	−0.429964	+	12.9374i	−0.0325022	+	0.977973i
$176$	0.529481	−	2.31981i	0.0399111	−	0.174862i
$177$		0			0
$178$	25.3046			1.89666
$179$	−4.43478	+	19.4300i	−0.331471	+	1.45227i	0.484813	+	0.874618i	$0.338888\pi$
$179$	−4.43478	+	19.4300i	−0.331471	+	1.45227i	−0.816284	+	0.577651i	$0.803970\pi$
$180$		0			0
$181$	9.18299	+	11.5151i	0.682566	+	0.855911i	0.995588	−	0.0938352i	$-0.0299127\pi$
$181$	9.18299	+	11.5151i	0.682566	+	0.855911i	−0.313022	+	0.949746i	$0.601341\pi$
$182$	−1.24557	+	2.38076i	−0.0923280	+	0.176474i
$183$		0			0
$184$	0.0325113	−	0.142441i	0.00239676	−	0.0105009i
$185$	1.08980	−	1.36656i	0.0801235	−	0.100472i
$186$		0			0
$187$	−2.53363	−	3.17707i	−0.185277	−	0.232331i
$188$	11.6521	+	5.61137i	0.849819	+	0.409251i
$189$		0			0
$190$	2.85262	−	1.37375i	0.206951	−	0.0996622i
$191$	9.92319	+	4.77876i	0.718017	+	0.345779i	0.756959	−	0.653463i	$-0.226684\pi$
$191$	9.92319	+	4.77876i	0.718017	+	0.345779i	−0.0389417	+	0.999241i	$0.512399\pi$
$192$		0			0
$193$	10.4067	+	5.01160i	0.749090	+	0.360743i	0.769160	−	0.639056i	$-0.220675\pi$
$193$	10.4067	+	5.01160i	0.749090	+	0.360743i	−0.0200702	+	0.999799i	$0.506389\pi$
$194$	11.4029	−	14.2987i	0.818677	−	1.02659i
$195$		0			0
$196$	10.4575	−	4.20544i	0.746964	−	0.300388i
$197$	−0.252349			−0.0179791			−0.00898956	−	0.999960i	$-0.502862\pi$
$197$	−0.252349			−0.0179791			−0.00898956	+	0.999960i	$0.502862\pi$
$198$		0			0
$199$	−15.8123	−	7.61481i	−1.12090	−	0.539799i	−0.220733	−	0.975334i	$-0.570845\pi$
$199$	−15.8123	−	7.61481i	−1.12090	−	0.539799i	−0.900172	+	0.435535i	$0.856559\pi$
$200$	0.806330	+	3.53276i	0.0570161	+	0.249804i
$201$		0			0
$202$	30.1128	−	14.5015i	2.11873	−	1.02032i
$203$	−4.55818	+	3.39360i	−0.319921	+	0.238184i
$204$		0			0
$205$	0.436123	+	0.546881i	0.0304602	+	0.0381958i
$206$	−1.01019	+	0.486481i	−0.0703832	+	0.0338947i
$207$		0			0
$208$	−0.550389	+	2.41141i	−0.0381626	+	0.167201i
$209$	−1.62984	+	2.04375i	−0.112738	+	0.141369i
$210$		0			0
$211$	10.1869	+	12.7740i	0.701295	+	0.879396i	0.997120	−	0.0758464i	$-0.0241659\pi$
$211$	10.1869	+	12.7740i	0.701295	+	0.879396i	−0.295825	+	0.955242i	$0.595594\pi$
$212$	−7.73641	+	3.72566i	−0.531339	+	0.255879i
$213$		0			0
$214$	38.1156			2.60553
$215$	3.44447			0.234911
$216$		0			0
$217$	−5.00080	−	4.26730i	−0.339476	−	0.289683i
$218$	−4.32260	−	18.9385i	−0.292763	−	1.28268i
$219$		0			0
$220$	−0.169200	−	0.212170i	−0.0114075	−	0.0143045i
$221$	2.63368	+	3.30253i	0.177160	+	0.222152i
$222$		0			0
$223$	−4.90788	−	21.5028i	−0.328656	−	1.43994i	−0.821694	−	0.569928i	$-0.806971\pi$
$223$	−4.90788	−	21.5028i	−0.328656	−	1.43994i	0.493038	−	0.870008i	$-0.335886\pi$
$224$	15.5164	−	11.5521i	1.03673	−	0.771854i
$225$		0			0
$226$	−18.2132			−1.21153
$227$	−4.74850			−0.315169			−0.157585	−	0.987505i	$-0.550371\pi$
$227$	−4.74850			−0.315169			−0.157585	+	0.987505i	$0.550371\pi$
$228$		0			0
$229$	21.3927	−	10.3022i	1.41367	−	0.680786i	0.437785	−	0.899080i	$-0.355763\pi$
$229$	21.3927	−	10.3022i	1.41367	−	0.680786i	0.975883	+	0.218293i	$0.0700490\pi$
$230$	−0.0765993	−	0.0960525i	−0.00505081	−	0.00633351i
$231$		0			0
$232$	−0.991844	+	1.24373i	−0.0651177	+	0.0816550i
$233$	−1.13282	+	4.96319i	−0.0742132	+	0.325149i	−0.998384	−	0.0568307i	$-0.981900\pi$
$233$	−1.13282	+	4.96319i	−0.0742132	+	0.325149i	0.924171	+	0.381980i	$0.124758\pi$
$234$		0			0
$235$	−2.37191	+	1.14225i	−0.154726	+	0.0745121i
$236$	−0.293956	−	0.368609i	−0.0191349	−	0.0239944i
$237$		0			0
$238$	1.31964	−	39.7073i	0.0855397	−	2.57384i
$239$	13.3073	−	6.40844i	0.860775	−	0.414527i	0.0492093	−	0.998788i	$-0.484330\pi$
$239$	13.3073	−	6.40844i	0.860775	−	0.414527i	0.811566	+	0.584261i	$0.198616\pi$
$240$		0			0
$241$	0.526528	+	2.30687i	0.0339166	+	0.148598i	0.989051	−	0.147575i	$-0.0471466\pi$
$241$	0.526528	+	2.30687i	0.0339166	+	0.148598i	−0.955134	+	0.296173i	$0.904290\pi$
$242$	−18.3782	−	8.85046i	−1.18139	−	0.568929i
$243$		0			0
$244$	−6.43880			−0.412202
$245$	−0.657945	+	2.19805i	−0.0420346	+	0.140428i
$246$		0			0
$247$	1.69420	−	2.12445i	0.107799	−	0.135176i
$248$	−1.65805	−	0.798474i	−0.105286	−	0.0507032i
$249$		0			0
$250$	5.55081	+	2.67313i	0.351064	+	0.169064i
$251$	−8.31054	+	4.00214i	−0.524556	+	0.252613i	−0.677371	−	0.735642i	$-0.736881\pi$
$251$	−8.31054	+	4.00214i	−0.524556	+	0.252613i	0.152814	+	0.988255i	$0.451166\pi$
$252$		0			0
$253$	0.0913873	+	0.0440098i	0.00574547	+	0.00276687i
$254$	13.5937	+	17.0459i	0.852942	+	1.06956i
$255$		0			0
$256$	12.6681	−	15.8853i	0.791758	−	0.992833i
$257$	1.05484	−	4.62156i	0.0657992	−	0.288285i	−0.931314	−	0.364218i	$-0.881336\pi$
$257$	1.05484	−	4.62156i	0.0657992	−	0.288285i	0.997113	+	0.0759328i	$0.0241935\pi$
$258$		0			0
$259$	−11.3169	+	8.42550i	−0.703197	+	0.523535i
$260$	0.175882	+	0.220548i	0.0109077	+	0.0136778i
$261$		0			0
$262$	−1.49656	+	6.55685i	−0.0924577	+	0.405084i
$263$	9.30500			0.573771			0.286886	−	0.957965i	$-0.407380\pi$
$263$	9.30500			0.573771			0.286886	+	0.957965i	$0.407380\pi$
$264$		0			0
$265$	0.388949	−	1.70410i	0.0238929	−	0.104682i
$266$	−25.0914	+	4.85623i	−1.53845	+	0.297754i
$267$		0			0
$268$	3.74436	+	16.4051i	0.228723	+	1.00210i
$269$	17.5997	+	22.0694i	1.07307	+	1.34559i	0.934790	+	0.355201i	$0.115587\pi$
$269$	17.5997	+	22.0694i	1.07307	+	1.34559i	0.138285	+	0.990393i	$0.455841\pi$
$270$		0			0
$271$	2.83323	+	12.4132i	0.172107	+	0.754048i	0.985129	+	0.171816i	$0.0549634\pi$
$271$	2.83323	+	12.4132i	0.172107	+	0.754048i	−0.813023	+	0.582232i	$0.802179\pi$
$272$	−8.13818	−	35.6557i	−0.493449	−	2.16194i
$273$		0			0
$274$	−4.08686	+	17.9057i	−0.246897	+	1.08172i
$275$	−2.51568			−0.151701
$276$		0			0
$277$	2.42279	−	10.6149i	0.145571	−	0.637789i	−0.848513	−	0.529175i	$-0.822502\pi$
$277$	2.42279	−	10.6149i	0.145571	−	0.637789i	0.994084	−	0.108614i	$-0.0346412\pi$
$278$	33.6993	−	16.2287i	2.02115	−	0.973335i
$279$		0			0
$280$	−0.0213340	+	0.641929i	−0.00127495	+	0.0383626i
$281$	15.1508	−	18.9985i	0.903819	−	1.13335i	−0.0867354	−	0.996231i	$-0.527643\pi$
$281$	15.1508	−	18.9985i	0.903819	−	1.13335i	0.990554	−	0.137122i	$-0.0437851\pi$
$282$		0			0
$283$	−4.25543	+	5.33615i	−0.252959	+	0.317201i	−0.892055	−	0.451926i	$-0.850737\pi$
$283$	−4.25543	+	5.33615i	−0.252959	+	0.317201i	0.639096	+	0.769127i	$0.279309\pi$
$284$	13.6286	−	6.56320i	0.808710	−	0.389454i
$285$		0			0
$286$	−0.470471	−	0.226567i	−0.0278195	−	0.0133972i
$287$	−2.27947	−	5.16562i	−0.134553	−	0.304917i
$288$		0			0
$289$	−40.9566	−	19.7237i	−2.40921	−	1.16021i
$290$	0.297658	+	1.30412i	0.0174791	+	0.0765808i
$291$		0			0
$292$	−10.0663	+	12.6228i	−0.589087	+	0.738692i
$293$	11.8677			0.693319			0.346660	−	0.937991i	$-0.387316\pi$
$293$	11.8677			0.693319			0.346660	+	0.937991i	$0.387316\pi$
$294$		0			0
$295$	0.0959721			0.00558771
$296$	−2.46251	+	3.08790i	−0.143131	+	0.179480i
$297$		0			0
$298$	7.95492	+	34.8528i	0.460816	+	2.01897i
$299$	−0.0949961	−	0.0457477i	−0.00549376	−	0.00264566i
$300$		0			0
$301$	−26.8859	−	7.08380i	−1.54968	−	0.408303i
$302$	−39.6335	−	19.0865i	−2.28065	−	1.09830i
$303$		0			0
$304$	−21.1966	+	10.2078i	−1.21571	+	0.585455i
$305$	0.817196	−	1.02473i	0.0467925	−	0.0586760i
$306$		0			0
$307$	5.29108	−	6.63480i	0.301978	−	0.378668i	−0.607571	−	0.794265i	$-0.707856\pi$
$307$	5.29108	−	6.63480i	0.301978	−	0.378668i	0.909549	+	0.415597i	$0.136427\pi$
$308$	0.884354	+	2.00407i	0.0503907	+	0.114193i
$309$		0			0
$310$	−1.39422	+	0.671419i	−0.0791861	+	0.0381340i
$311$	3.95571	−	17.3311i	0.224308	−	0.982756i	−0.729887	−	0.683568i	$-0.760427\pi$
$311$	3.95571	−	17.3311i	0.224308	−	0.982756i	0.954194	−	0.299188i	$-0.0967157\pi$
$312$		0			0
$313$	3.25433			0.183946			0.0919729	−	0.995762i	$-0.470683\pi$
$313$	3.25433			0.183946			0.0919729	+	0.995762i	$0.470683\pi$
$314$	−4.64005	+	20.3294i	−0.261853	+	1.14725i
$315$		0			0
$316$	−1.37339	−	6.01721i	−0.0772591	−	0.338494i
$317$	6.42965	+	28.1701i	0.361125	+	1.58219i	0.750344	+	0.661048i	$0.229888\pi$
$317$	6.42965	+	28.1701i	0.361125	+	1.58219i	−0.389219	+	0.921145i	$0.627255\pi$
$318$		0			0
$319$	−0.688584	−	0.863456i	−0.0385533	−	0.0483443i
$320$	−0.338202	−	1.48176i	−0.0189061	−	0.0828329i
$321$		0			0
$322$	0.400360	+	0.907273i	0.0223112	+	0.0505604i
$323$	−8.94051	+	39.1709i	−0.497463	+	2.17953i
$324$		0			0
$325$	2.61502			0.145055
$326$	−4.94180	+	21.6514i	−0.273701	+	1.19916i
$327$		0			0
$328$	−0.985468	−	1.23574i	−0.0544133	−	0.0682322i
$329$	20.8631	−	4.03787i	1.15022	−	0.222615i
$330$		0			0
$331$	−5.09581	+	22.3262i	−0.280091	+	1.22716i	0.617585	+	0.786504i	$0.288111\pi$
$331$	−5.09581	+	22.3262i	−0.280091	+	1.22716i	−0.897676	+	0.440656i	$0.854746\pi$
$332$	8.51414	−	10.6764i	0.467274	−	0.585943i
$333$		0			0
$334$	−12.1911	−	15.2872i	−0.667067	−	0.836476i
$335$	−3.08609	−	1.48618i	−0.168611	−	0.0811987i
$336$		0			0
$337$	−19.3276	+	9.30767i	−1.05284	+	0.507021i	−0.878539	−	0.477671i	$-0.841481\pi$
$337$	−19.3276	+	9.30767i	−1.05284	+	0.507021i	−0.174301	+	0.984692i	$0.555767\pi$
$338$	−21.7655	−	10.4817i	−1.18389	−	0.570130i
$339$		0			0
$340$	−3.75801	−	1.80976i	−0.203807	−	0.0981481i
$341$	0.796582	−	0.998882i	0.0431373	−	0.0540925i
$342$		0			0
$343$	9.65606	−	15.8038i	0.521378	−	0.853326i
$344$	−7.78314			−0.419639
$345$		0			0
$346$	19.7140	+	9.49377i	1.05983	+	0.510388i
$347$	−3.51346	−	15.3935i	−0.188612	−	0.826365i	−0.977349	−	0.211634i	$-0.932122\pi$
$347$	−3.51346	−	15.3935i	−0.188612	−	0.826365i	0.788737	−	0.614731i	$-0.210736\pi$
$348$		0			0
$349$	7.67393	−	3.69557i	0.410776	−	0.197819i	−0.217071	−	0.976156i	$-0.569650\pi$
$349$	7.67393	−	3.69557i	0.410776	−	0.197819i	0.627848	+	0.778336i	$0.283936\pi$
$350$	−18.7094	−	15.9652i	−1.00006	−	0.853373i
$351$		0			0
$352$	2.34399	+	2.93927i	0.124935	+	0.156664i
$353$	−16.2883	+	7.84405i	−0.866941	+	0.417497i	−0.813838	−	0.581092i	$-0.802625\pi$
$353$	−16.2883	+	7.84405i	−0.866941	+	0.417497i	−0.0531031	+	0.998589i	$0.516911\pi$
$354$		0			0
$355$	−0.685181	+	3.00197i	−0.0363656	+	0.159328i
$356$	−13.3704	+	16.7659i	−0.708628	+	0.888592i
$357$		0			0
$358$	−23.6100	−	29.6060i	−1.24783	−	1.56473i
$359$	20.8538	−	10.0426i	1.10062	−	0.530030i	0.206766	−	0.978390i	$-0.433706\pi$
$359$	20.8538	−	10.0426i	1.10062	−	0.530030i	0.893853	+	0.448360i	$0.147992\pi$
$360$		0			0
$361$	6.84593			0.360312
$362$	−27.9847			−1.47084
$363$		0			0
$364$	−0.919275	−	2.08321i	−0.0481831	−	0.109190i
$365$	−0.731314	−	3.20410i	−0.0382787	−	0.167710i
$366$		0			0
$367$	11.1961	+	14.0395i	0.584433	+	0.732856i	0.982862	−	0.184343i	$-0.0590158\pi$
$367$	11.1961	+	14.0395i	0.584433	+	0.732856i	−0.398429	+	0.917199i	$0.630444\pi$
$368$	0.569178	+	0.713726i	0.0296704	+	0.0372055i
$369$		0			0
$370$	0.739015	+	3.23783i	0.0384195	+	0.168327i
$371$	−6.54055	+	12.5015i	−0.339569	+	0.649045i
$372$		0			0
$373$	14.3809			0.744617			0.372309	−	0.928109i	$-0.378566\pi$
$373$	14.3809			0.744617			0.372309	+	0.928109i	$0.378566\pi$
$374$	7.72111			0.399249
$375$		0			0
$376$	5.35958	−	2.58104i	0.276399	−	0.133107i
$377$	0.715774	+	0.897553i	0.0368643	+	0.0462263i
$378$		0			0
$379$	−3.78120	+	4.74147i	−0.194227	+	0.243553i	−0.869403	−	0.494104i	$-0.835496\pi$
$379$	−3.78120	+	4.74147i	−0.194227	+	0.243553i	0.675176	+	0.737657i	$0.264068\pi$
$380$	−0.597062	+	2.61590i	−0.0306286	+	0.134193i
$381$		0			0
$382$	−18.8546	+	9.07989i	−0.964685	+	0.464568i
$383$	8.67188	+	10.8742i	0.443112	+	0.555645i	0.952360	−	0.304975i	$-0.0986480\pi$
$383$	8.67188	+	10.8742i	0.443112	+	0.555645i	−0.509248	+	0.860620i	$0.670077\pi$
$384$		0			0
$385$	−0.431187	−	0.113608i	−0.0219753	−	0.00578998i
$386$	−19.7733	+	9.52231i	−1.00643	+	0.484673i
$387$		0			0
$388$	3.44881	+	15.1102i	0.175087	+	0.767106i
$389$	−12.0895	−	5.82199i	−0.612962	−	0.295187i	0.101528	−	0.994833i	$-0.467627\pi$
$389$	−12.0895	−	5.82199i	−0.612962	−	0.295187i	−0.714490	+	0.699646i	$0.753341\pi$
$390$		0			0
$391$	1.55902			0.0788433
$392$	1.48670	−	4.96672i	0.0750895	−	0.250857i
$393$		0			0
$394$	0.298949	−	0.374870i	0.0150608	−	0.0188857i
$395$	1.13194	+	0.545114i	0.0569542	+	0.0274277i
$396$		0			0
$397$	15.8469	+	7.63147i	0.795333	+	0.383012i	0.787000	−	0.616953i	$-0.211633\pi$
$397$	15.8469	+	7.63147i	0.795333	+	0.383012i	0.00833333	+	0.999965i	$0.497347\pi$
$398$	30.0442	−	14.4685i	1.50598	−	0.725242i
$399$		0			0
$400$	−20.3989	−	9.82360i	−1.01995	−	0.491180i
$401$	−4.23137	−	5.30597i	−0.211305	−	0.264968i	0.664873	−	0.746957i	$-0.268486\pi$
$401$	−4.23137	−	5.30597i	−0.211305	−	0.264968i	−0.876177	+	0.481989i	$0.839914\pi$
$402$		0			0
$403$	−0.828037	+	1.03833i	−0.0412475	+	0.0517227i
$404$	−6.30269	+	27.6139i	−0.313571	+	1.37384i
$405$		0			0
$406$	0.358649	−	10.7915i	0.0177994	−	0.535575i
$407$	−1.70959	−	2.14376i	−0.0847413	−	0.106262i
$408$		0			0
$409$	3.22689	−	14.1379i	0.159560	−	0.699077i	−0.830334	−	0.557266i	$-0.811850\pi$
$409$	3.22689	−	14.1379i	0.159560	−	0.699077i	0.989894	−	0.141811i	$-0.0452924\pi$
$410$	−1.32906			−0.0656378
$411$		0			0
$412$	0.211436	−	0.926360i	0.0104167	−	0.0456385i
$413$	−0.749113	−	0.197374i	−0.0368615	−	0.00971212i
$414$		0			0
$415$	0.618549	+	2.71004i	0.0303634	+	0.133031i
$416$	−2.43655	−	3.05533i	−0.119462	−	0.149800i
$417$		0			0
$418$	−1.10523	−	4.84232i	−0.0540584	−	0.236845i
$419$	−3.31218	−	14.5116i	−0.161811	−	0.708939i	−0.989110	−	0.147177i	$-0.952981\pi$
$419$	−3.31218	−	14.5116i	−0.161811	−	0.708939i	0.827300	−	0.561761i	$-0.189876\pi$
$420$		0			0
$421$	6.36984	−	27.9081i	0.310447	−	1.36016i	−0.543330	−	0.839519i	$-0.682837\pi$
$421$	6.36984	−	27.9081i	0.310447	−	1.36016i	0.853777	−	0.520639i	$-0.174306\pi$
$422$	−31.0440			−1.51120
$423$		0			0
$424$	−0.878872	+	3.85059i	−0.0426818	+	0.187001i
$425$	−34.8371	+	16.7767i	−1.68985	+	0.813787i
$426$		0			0
$427$	−8.48609	+	6.31795i	−0.410671	+	0.305747i
$428$	−20.1394	+	25.2540i	−0.973474	+	1.22070i
$429$		0			0
$430$	−4.08053	+	5.11683i	−0.196781	+	0.246755i
$431$	13.4527	−	6.47850i	0.647996	−	0.312058i	−0.0808602	−	0.996725i	$-0.525767\pi$
$431$	13.4527	−	6.47850i	0.647996	−	0.312058i	0.728856	+	0.684667i	$0.240052\pi$
$432$		0			0
$433$	−21.6689	−	10.4352i	−1.04134	−	0.501484i	−0.166576	−	0.986029i	$-0.553271\pi$
$433$	−21.6689	−	10.4352i	−1.04134	−	0.501484i	−0.874767	+	0.484544i	$0.838985\pi$
$434$	12.2634	−	2.37348i	0.588663	−	0.113931i
$435$		0			0
$436$	14.8320	+	7.14270i	0.710322	+	0.342073i
$437$	−0.223164	−	0.977746i	−0.0106754	−	0.0467719i
$438$		0			0
$439$	10.8638	−	13.6227i	0.518499	−	0.650177i	−0.451790	−	0.892124i	$-0.649215\pi$
$439$	10.8638	−	13.6227i	0.518499	−	0.650177i	0.970289	+	0.241947i	$0.0777860\pi$
$440$	−0.124823			−0.00595073
$441$		0			0
$442$	−8.02600			−0.381758
$443$	1.21877	−	1.52829i	0.0579055	−	0.0726112i	−0.752035	−	0.659123i	$-0.770928\pi$
$443$	1.21877	−	1.52829i	0.0579055	−	0.0726112i	0.809941	+	0.586512i	$0.199499\pi$
$444$		0			0
$445$	−0.971353	−	4.25577i	−0.0460465	−	0.201743i
$446$	37.7571	+	18.1829i	1.78785	+	0.860983i
$447$		0			0
$448$	−0.407501	+	12.2615i	−0.0192526	+	0.579300i
$449$	25.9202	+	12.4825i	1.22325	+	0.589086i	0.930215	−	0.367016i	$-0.119621\pi$
$449$	25.9202	+	12.4825i	1.22325	+	0.589086i	0.293035	+	0.956102i	$0.405335\pi$
$450$		0			0
$451$	0.988635	−	0.476102i	0.0465530	−	0.0224188i
$452$	9.62345	−	12.0674i	0.452649	−	0.567604i
$453$		0			0
$454$	5.62538	−	7.05400i	0.264012	−	0.331061i
$455$	0.448214	+	0.118094i	0.0210126	+	0.00553632i
$456$		0			0
$457$	16.6268	−	8.00702i	0.777767	−	0.374553i	−0.00250222	−	0.999997i	$-0.500796\pi$
$457$	16.6268	−	8.00702i	0.777767	−	0.374553i	0.780269	+	0.625444i	$0.215082\pi$
$458$	−10.0390	+	43.9839i	−0.469093	+	2.05523i
$459$		0			0
$460$	0.104114			0.00485435
$461$	4.30219	−	18.8491i	0.200373	−	0.877891i	−0.770337	−	0.637637i	$-0.779912\pi$
$461$	4.30219	−	18.8491i	0.200373	−	0.877891i	0.970710	−	0.240254i	$-0.0772308\pi$
$462$		0			0
$463$	5.84121	+	25.5920i	0.271464	+	1.18936i	0.908286	+	0.418350i	$0.137391\pi$
$463$	5.84121	+	25.5920i	0.271464	+	1.18936i	−0.636822	+	0.771011i	$0.719751\pi$
$464$	−2.21177	−	9.69040i	−0.102679	−	0.449866i
$465$		0			0
$466$	−6.03092	−	7.56253i	−0.279377	−	0.350327i
$467$	−0.974650	−	4.27022i	−0.0451014	−	0.197602i	0.947358	−	0.320176i	$-0.103742\pi$
$467$	−0.974650	−	4.27022i	−0.0451014	−	0.197602i	−0.992459	+	0.122574i	$0.960885\pi$
$468$		0			0
$469$	21.0321	+	17.9472i	0.971173	+	0.828725i
$470$	1.11307	−	4.87670i	0.0513423	−	0.224945i
$471$		0			0
$472$	−0.216859			−0.00998176
$473$	1.20237	−	5.26794i	0.0552852	−	0.242220i
$474$		0			0
$475$	15.5082	+	19.4467i	0.711566	+	0.892276i
$476$	25.6114	+	21.8548i	1.17389	+	1.00171i
$477$		0			0
$478$	−6.24476	+	27.3601i	−0.285628	+	1.25142i
$479$	−10.9526	+	13.7341i	−0.500436	+	0.627527i	−0.966328	−	0.257315i	$-0.917162\pi$
$479$	−10.9526	+	13.7341i	−0.500436	+	0.627527i	0.465891	+	0.884842i	$0.345734\pi$
$480$		0			0
$481$	1.77710	+	2.22841i	0.0810288	+	0.101607i
$482$	−4.05066	−	1.95069i	−0.184502	−	0.0888517i
$483$		0			0
$484$	15.5746	−	7.50034i	0.707937	−	0.340924i
$485$	−2.84250	−	1.36888i	−0.129071	−	0.0621574i
$486$		0			0
$487$	−11.4867	−	5.53169i	−0.520511	−	0.250665i	0.155132	−	0.987894i	$-0.450420\pi$
$487$	−11.4867	−	5.53169i	−0.520511	−	0.250665i	−0.675643	+	0.737229i	$0.736134\pi$
$488$	−1.84654	+	2.31549i	−0.0835891	+	0.104817i
$489$		0			0
$490$	−2.48580	−	3.58134i	−0.112297	−	0.161788i
$491$	−6.03979			−0.272572			−0.136286	−	0.990670i	$-0.543517\pi$
$491$	−6.03979			−0.272572			−0.136286	+	0.990670i	$0.543517\pi$
$492$		0			0
$493$	−15.2937	−	7.36508i	−0.688795	−	0.331706i
$494$	1.14887	+	5.03353i	0.0516901	+	0.226469i
$495$		0			0
$496$	10.3598	−	4.98903i	0.465170	−	0.224014i
$497$	11.5220	−	22.0229i	0.516831	−	0.987861i
$498$		0			0
$499$	1.19012	+	1.49236i	0.0532769	+	0.0668072i	0.807756	−	0.589517i	$-0.200682\pi$
$499$	1.19012	+	1.49236i	0.0532769	+	0.0668072i	−0.754479	+	0.656324i	$0.772110\pi$
$500$	−4.70404	+	2.26535i	−0.210371	+	0.101309i
$501$		0			0
$502$	3.89992	−	17.0867i	0.174062	−	0.762616i
$503$	−15.1640	+	19.0150i	−0.676127	+	0.847837i	−0.994991	−	0.0999637i	$-0.968127\pi$
$503$	−15.1640	+	19.0150i	−0.676127	+	0.847837i	0.318864	+	0.947801i	$0.396699\pi$
$504$		0			0
$505$	−3.59481	−	4.50776i	−0.159967	−	0.200592i
$506$	−0.173641	+	0.0836210i	−0.00771928	+	0.00371741i
$507$		0			0
$508$	−18.4766			−0.819766
$509$	−32.9072			−1.45858			−0.729292	−	0.684202i	$-0.760150\pi$
$509$	−32.9072			−1.45858			−0.729292	+	0.684202i	$0.760150\pi$
$510$		0			0
$511$	−0.881163	+	26.5137i	−0.0389803	+	1.17290i
$512$	6.00369	+	26.3039i	0.265328	+	1.16248i
$513$		0			0
$514$	5.61580	+	7.04199i	0.247702	+	0.310609i
$515$	0.120595	+	0.151221i	0.00531404	+	0.00666359i
$516$		0			0
$517$	0.918978	+	4.02630i	0.0404166	+	0.177077i
$518$	0.890441	−	26.7929i	0.0391237	−	1.17721i
$519$		0			0
$520$	0.129752			0.00569002
$521$	38.1074			1.66952			0.834759	−	0.550616i	$-0.185607\pi$
$521$	38.1074			1.66952			0.834759	+	0.550616i	$0.185607\pi$
$522$		0			0
$523$	32.6614	−	15.7289i	1.42818	−	0.687777i	0.449525	−	0.893268i	$-0.351593\pi$
$523$	32.6614	−	15.7289i	1.42818	−	0.687777i	0.978659	+	0.205491i	$0.0658790\pi$
$524$	−3.55358	−	4.45605i	−0.155239	−	0.194664i
$525$		0			0
$526$	−11.0233	+	13.8228i	−0.480639	+	0.602702i
$527$	4.36967	−	19.1448i	0.190346	−	0.833959i
$528$		0			0
$529$	20.6872	−	9.96244i	0.899444	−	0.433150i
$530$	2.07070	+	2.59657i	0.0899454	+	0.112788i
$531$		0			0
$532$	10.0402	−	19.1906i	0.435297	−	0.832018i
$533$	−1.02767	+	0.494902i	−0.0445135	+	0.0214366i
$534$		0			0
$535$	−1.46312	−	6.41034i	−0.0632562	−	0.277143i
$536$	6.97335	+	3.35819i	0.301203	+	0.145052i
$537$		0			0
$538$	−53.6343			−2.31234
$539$	3.13200	+	1.77354i	0.134905	+	0.0763916i
$540$		0			0
$541$	23.7907	−	29.8326i	1.02284	−	1.28260i	0.0642154	−	0.997936i	$-0.479546\pi$
$541$	23.7907	−	29.8326i	1.02284	−	1.28260i	0.958626	−	0.284667i	$-0.0918830\pi$
$542$	−21.7965	−	10.4966i	−0.936240	−	0.450869i
$543$		0			0
$544$	52.0610	+	25.0713i	2.23210	+	1.07492i
$545$	−3.01919	+	1.45397i	−0.129328	+	0.0622810i
$546$		0			0
$547$	−2.84460	−	1.36989i	−0.121626	−	0.0585721i	0.372081	−	0.928200i	$-0.378644\pi$
$547$	−2.84460	−	1.36989i	−0.121626	−	0.0585721i	−0.493707	+	0.869628i	$0.664359\pi$
$548$	−9.70428	−	12.1688i	−0.414546	−	0.519825i
$549$		0			0
$550$	2.98023	−	3.73710i	0.127078	−	0.159350i
$551$	−2.42983	+	10.6458i	−0.103514	+	0.453525i
$552$		0			0
$553$	−7.71434	−	6.58283i	−0.328047	−	0.279930i
$554$	12.8985	+	16.1742i	0.548005	+	0.687176i
$555$		0			0
$556$	−7.05337	+	30.9028i	−0.299130	+	1.31057i
$557$	−25.7487			−1.09101			−0.545505	−	0.838108i	$-0.683662\pi$
$557$	−25.7487			−1.09101			−0.545505	+	0.838108i	$0.683662\pi$
$558$		0			0
$559$	−1.24985	+	5.47596i	−0.0528631	+	0.231608i
$560$	−3.05274	−	2.60498i	−0.129002	−	0.110080i
$561$		0			0
$562$	10.2741	+	45.0136i	0.433385	+	1.89878i
$563$	−7.15266	−	8.96915i	−0.301449	−	0.378005i	0.607918	−	0.794000i	$-0.292005\pi$
$563$	−7.15266	−	8.96915i	−0.301449	−	0.378005i	−0.909367	+	0.415995i	$0.863433\pi$
$564$		0			0
$565$	0.699140	+	3.06313i	0.0294130	+	0.128867i
$566$	−2.88570	−	12.6431i	−0.121295	−	0.531428i
$567$		0			0
$568$	1.54824	−	6.78328i	0.0649627	−	0.284620i
$569$	31.2990			1.31212			0.656061	−	0.754708i	$-0.272221\pi$
$569$	31.2990			1.31212			0.656061	+	0.754708i	$0.272221\pi$
$570$		0			0
$571$	−1.87936	+	8.23403i	−0.0786489	+	0.344583i	−0.998908	−	0.0467269i	$-0.985121\pi$
$571$	−1.87936	+	8.23403i	−0.0786489	+	0.344583i	0.920259	+	0.391310i	$0.127978\pi$
$572$	0.398701	−	0.192004i	0.0166705	−	0.00802810i
$573$		0			0
$574$	10.3741	+	2.73332i	0.433005	+	0.114086i
$575$	0.601760	−	0.754584i	0.0250951	−	0.0314683i
$576$		0			0
$577$	14.6164	−	18.3284i	0.608488	−	0.763019i	−0.378186	−	0.925729i	$-0.623452\pi$
$577$	14.6164	−	18.3284i	0.608488	−	0.763019i	0.986674	+	0.162710i	$0.0520236\pi$
$578$	77.8197	−	37.4760i	3.23687	−	1.55880i
$579$		0			0
$580$	−1.02134	−	0.491852i	−0.0424089	−	0.0204230i
$581$	0.745292	−	22.4254i	0.0309199	−	0.930363i
$582$		0			0
$583$	−2.47046	−	1.18971i	−0.102316	−	0.0492728i
$584$	1.65248	+	7.24000i	0.0683803	+	0.299593i
$585$		0			0
$586$	−14.0592	+	17.6297i	−0.580782	+	0.728278i
$587$	−12.2705			−0.506457			−0.253229	−	0.967406i	$-0.581493\pi$
$587$	−12.2705			−0.506457			−0.253229	+	0.967406i	$0.581493\pi$
$588$		0			0
$589$	−12.6322			−0.520500
$590$	−0.113695	+	0.142569i	−0.00468073	+	0.00586946i
$591$		0			0
$592$	−5.49131	−	24.0590i	−0.225691	−	0.988819i
$593$	20.0451	+	9.65322i	0.823154	+	0.396410i	0.797543	−	0.603262i	$-0.206133\pi$
$593$	20.0451	+	9.65322i	0.823154	+	0.396410i	0.0256109	+	0.999672i	$0.491847\pi$
$594$		0			0
$595$	−6.72870	+	1.30228i	−0.275850	+	0.0533883i
$596$	−27.2954	−	13.1448i	−1.11806	−	0.538431i
$597$		0			0
$598$	0.180498	−	0.0869230i	0.00738109	−	0.00355455i
$599$	−9.92694	+	12.4480i	−0.405604	+	0.508611i	−0.942119	−	0.335280i	$-0.891169\pi$
$599$	−9.92694	+	12.4480i	−0.405604	+	0.508611i	0.536515	+	0.843891i	$0.319741\pi$
$600$		0			0
$601$	−14.2966	+	17.9273i	−0.583169	+	0.731271i	−0.982650	−	0.185471i	$-0.940619\pi$
$601$	−14.2966	+	17.9273i	−0.583169	+	0.731271i	0.399481	+	0.916742i	$0.369190\pi$
$602$	42.3739	−	31.5477i	1.72703	−	1.28579i
$603$		0			0
$604$	33.5874	−	16.1749i	1.36665	−	0.658145i
$605$	−0.783015	+	3.43061i	−0.0318341	+	0.139474i
$606$		0			0
$607$	−41.1112			−1.66865			−0.834325	−	0.551273i	$-0.814142\pi$
$607$	−41.1112			−1.66865			−0.834325	+	0.551273i	$0.814142\pi$
$608$	8.27131	−	36.2390i	0.335446	−	1.46968i
$609$		0			0
$610$	0.554158	+	2.42792i	0.0224372	+	0.0983038i
$611$	−0.955266	−	4.18529i	−0.0386459	−	0.169319i
$612$		0			0
$613$	−8.48740	−	10.6429i	−0.342803	−	0.429861i	0.580307	−	0.814398i	$-0.302933\pi$
$613$	−8.48740	−	10.6429i	−0.342803	−	0.429861i	−0.923110	+	0.384537i	$0.874361\pi$
$614$	3.58799	+	15.7200i	0.144799	+	0.634408i
$615$		0			0
$616$	0.974314	+	0.256709i	0.0392562	+	0.0103431i
$617$	1.73617	−	7.60665i	0.0698955	−	0.306232i	−0.927881	−	0.372876i	$-0.878372\pi$
$617$	1.73617	−	7.60665i	0.0698955	−	0.306232i	0.997777	+	0.0666434i	$0.0212290\pi$
$618$		0			0
$619$	−37.1189			−1.49193			−0.745967	−	0.665983i	$-0.768012\pi$
$619$	−37.1189			−1.49193			−0.745967	+	0.665983i	$0.768012\pi$
$620$	0.291814	−	1.27852i	0.0117195	−	0.0513466i
$621$		0			0
$622$	21.0595	+	26.4078i	0.844410	+	1.05886i
$623$	−1.17039	+	35.2163i	−0.0468905	+	1.41091i
$624$		0			0
$625$	−5.20699	+	22.8133i	−0.208280	+	0.912533i
$626$	−3.85529	+	4.83438i	−0.154088	+	0.193221i
$627$		0			0
$628$	−11.0178	−	13.8159i	−0.439659	−	0.551315i
$629$	−37.9708	−	18.2858i	−1.51399	−	0.729101i
$630$		0			0
$631$	13.1280	−	6.32213i	0.522619	−	0.251680i	−0.153925	−	0.988083i	$-0.549191\pi$
$631$	13.1280	−	6.32213i	0.522619	−	0.251680i	0.676544	+	0.736403i	$0.263477\pi$
$632$	−2.55774	−	1.23174i	−0.101742	−	0.0489962i
$633$		0			0
$634$	−49.4643	−	23.8208i	−1.96448	−	0.946043i
$635$	2.34500	−	2.94054i	0.0930585	−	0.116692i
$636$		0			0
$637$	−3.25568	−	1.84357i	−0.128995	−	0.0730449i
$638$	2.09842			0.0830774
$639$		0			0
$640$	−1.71652	−	0.826634i	−0.0678515	−	0.0326756i
$641$	3.72154	+	16.3051i	0.146992	+	0.644014i	0.993711	+	0.111974i	$0.0357173\pi$
$641$	3.72154	+	16.3051i	0.146992	+	0.644014i	−0.846719	+	0.532040i	$0.821426\pi$
$642$		0			0
$643$	3.18720	−	1.53487i	0.125691	−	0.0605295i	−0.369981	−	0.929039i	$-0.620636\pi$
$643$	3.18720	−	1.53487i	0.125691	−	0.0605295i	0.495672	+	0.868510i	$0.334922\pi$
$644$	−0.812667	−	0.214119i	−0.0320236	−	0.00843746i
$645$		0			0
$646$	−47.5978	−	59.6857i	−1.87271	−	2.34830i
$647$	6.03571	−	2.90664i	0.237288	−	0.114272i	−0.311461	−	0.950259i	$-0.600818\pi$
$647$	6.03571	−	2.90664i	0.237288	−	0.114272i	0.548749	+	0.835987i	$0.315104\pi$
$648$		0			0
$649$	0.0335013	−	0.146779i	0.00131504	−	0.00576158i
$650$	−3.09792	+	3.88467i	−0.121510	+	0.152369i
$651$		0			0
$652$	−11.7343	−	14.7144i	−0.459552	−	0.576260i
$653$	11.2811	−	5.43269i	0.441464	−	0.212598i	−0.199929	−	0.979810i	$-0.564071\pi$
$653$	11.2811	−	5.43269i	0.441464	−	0.212598i	0.641393	+	0.767213i	$0.278357\pi$
$654$		0			0
$655$	1.16019			0.0453324
$656$	9.87571			0.385582
$657$		0			0
$658$	−18.7174	+	35.7761i	−0.729681	+	1.39470i
$659$	−2.40074	−	10.5183i	−0.0935195	−	0.409736i	0.906400	−	0.422420i	$-0.138819\pi$
$659$	−2.40074	−	10.5183i	−0.0935195	−	0.409736i	−0.999920	+	0.0126846i	$0.995962\pi$
$660$		0			0
$661$	9.56257	+	11.9911i	0.371941	+	0.466399i	0.932213	−	0.361909i	$-0.117875\pi$
$661$	9.56257	+	11.9911i	0.371941	+	0.466399i	−0.560272	+	0.828308i	$0.689304\pi$
$662$	−27.1293	−	34.0190i	−1.05441	−	1.32219i
$663$		0			0
$664$	−1.39768	−	6.12363i	−0.0542405	−	0.237643i
$665$	1.77990	+	4.03351i	0.0690215	+	0.156413i
$666$		0			0
$667$	0.423707			0.0164060
$668$	16.5702			0.641121
$669$		0			0
$670$	5.86373	−	2.82382i	0.226536	−	0.109094i
$671$	−1.28196	−	1.60752i	−0.0494893	−	0.0620577i
$672$		0			0
$673$	7.28909	−	9.14023i	0.280974	−	0.352330i	−0.621239	−	0.783621i	$-0.713370\pi$
$673$	7.28909	−	9.14023i	0.280974	−	0.352330i	0.902213	+	0.431291i	$0.141942\pi$
$674$	9.06994	−	39.7380i	0.349361	−	1.53065i
$675$		0			0
$676$	18.4452	−	8.88274i	0.709431	−	0.341644i
$677$	4.93508	+	6.18839i	0.189670	+	0.237839i	0.867570	−	0.497316i	$-0.165681\pi$
$677$	4.93508	+	6.18839i	0.189670	+	0.237839i	−0.677899	+	0.735155i	$0.737109\pi$
$678$		0			0
$679$	19.3720	+	16.5306i	0.743430	+	0.634387i
$680$	−1.72855	+	0.832427i	−0.0662870	+	0.0319221i
$681$		0			0
$682$	0.540179	+	2.36668i	0.0206845	+	0.0906248i
$683$	−20.2309	−	9.74268i	−0.774113	−	0.372793i	0.00474857	−	0.999989i	$-0.498488\pi$
$683$	−20.2309	−	9.74268i	−0.774113	−	0.372793i	−0.778862	+	0.627195i	$0.784203\pi$
$684$		0			0
$685$	3.16830			0.121054
$686$	12.0377	+	33.0665i	0.459603	+	1.26248i
$687$		0			0
$688$	30.3207	−	38.0210i	1.15597	−	1.44954i
$689$	2.56801	+	1.23669i	0.0978335	+	0.0471142i
$690$		0			0
$691$	−30.2885	−	14.5862i	−1.15223	−	0.554884i	−0.242527	−	0.970145i	$-0.577976\pi$
$691$	−30.2885	−	14.5862i	−1.15223	−	0.554884i	−0.909703	+	0.415260i	$0.863691\pi$
$692$	−16.7067	+	8.04551i	−0.635092	+	0.305844i
$693$		0			0
$694$	27.0296	+	13.0168i	1.02603	+	0.494110i
$695$	−4.02297	−	5.04465i	−0.152600	−	0.191354i
$696$		0			0
$697$	10.5156	−	13.1861i	0.398305	−	0.499459i
$698$	−3.60118	+	15.7778i	−0.136307	+	0.597198i
$699$		0			0
$700$	20.4635	−	3.96054i	0.773449	−	0.149694i
$701$	0.340419	+	0.426872i	0.0128575	+	0.0161227i	0.788219	−	0.615395i	$-0.211004\pi$
$701$	0.340419	+	0.426872i	0.0128575	+	0.0161227i	−0.775361	+	0.631518i	$0.782432\pi$
$702$		0			0
$703$	−6.03269	+	26.4309i	−0.227527	+	0.996862i
$704$	−2.38425			−0.0898598
$705$		0			0
$706$	7.64370	−	33.4892i	0.287674	−	1.26038i
$707$	18.7889	+	42.5784i	0.706630	+	1.60133i
$708$		0			0
$709$	−10.2575	−	44.9409i	−0.385227	−	1.68779i	−0.680799	−	0.732470i	$-0.738367\pi$
$709$	−10.2575	−	44.9409i	−0.385227	−	1.68779i	0.295572	−	0.955321i	$-0.404490\pi$
$710$	−3.64779	−	4.57418i	−0.136899	−	0.171666i
$711$		0			0
$712$	2.19488	+	9.61638i	0.0822564	+	0.360389i
$713$	0.109071	+	0.477873i	0.00408475	+	0.0178965i
$714$		0			0
$715$	−0.0200447	+	0.0878217i	−0.000749630	+	0.00328434i
$716$	32.0909			1.19929
$717$		0			0
$718$	−9.78613	+	42.8758i	−0.365215	+	1.60011i
$719$	38.4386	−	18.5110i	1.43352	−	0.690345i	0.453869	−	0.891068i	$-0.350043\pi$
$719$	38.4386	−	18.5110i	1.43352	−	0.690345i	0.979648	+	0.200723i	$0.0643291\pi$
$720$		0			0
$721$	−0.630309	−	1.42837i	−0.0234739	−	0.0531954i
$722$	−8.11012	+	10.1698i	−0.301828	+	0.378480i
$723$		0			0
$724$	14.7865	−	18.5416i	0.549535	−	0.689095i
$725$	−9.46793	+	4.55951i	−0.351630	+	0.169336i
$726$		0			0
$727$	−11.4063	−	5.49300i	−0.423037	−	0.203724i	0.210239	−	0.977650i	$-0.432576\pi$
$727$	−11.4063	−	5.49300i	−0.423037	−	0.203724i	−0.633276	+	0.773926i	$0.718290\pi$
$728$	−1.01279	−	0.266846i	−0.0375364	−	0.00988995i
$729$		0			0
$730$	5.62612	+	2.70940i	0.208232	+	0.100279i
$731$	−18.4806	−	80.9688i	−0.683529	−	2.99474i
$732$		0			0
$733$	−10.6768	+	13.3883i	−0.394358	+	0.494509i	−0.938884	−	0.344235i	$-0.888138\pi$
$733$	−10.6768	+	13.3883i	−0.394358	+	0.494509i	0.544525	+	0.838744i	$0.316710\pi$
$734$	−34.1196			−1.25938
$735$		0			0
$736$	−1.44233			−0.0531650
$737$	−3.35023	+	4.20105i	−0.123407	+	0.154748i
$738$		0			0
$739$	−5.06165	−	22.1765i	−0.186196	−	0.815777i	−0.978599	−	0.205778i	$-0.934027\pi$
$739$	−5.06165	−	22.1765i	−0.186196	−	0.815777i	0.792403	−	0.609998i	$-0.208830\pi$
$740$	−2.53575	−	1.22115i	−0.0932160	−	0.0448905i
$741$		0			0
$742$	−10.8229	−	24.5262i	−0.397320	−	0.900385i
$743$	34.6362	+	16.6799i	1.27068	+	0.611927i	0.942978	−	0.332854i	$-0.108012\pi$
$743$	34.6362	+	16.6799i	1.27068	+	0.611927i	0.327701	+	0.944781i	$0.393726\pi$
$744$		0			0
$745$	5.55624	−	2.67575i	0.203565	−	0.0980318i
$746$	−17.0366	+	21.3632i	−0.623754	+	0.782162i
$747$		0			0
$748$	−4.07966	+	5.11573i	−0.149167	+	0.187050i
$749$	−1.76292	+	53.0452i	−0.0644156	+	1.93823i
$750$		0			0
$751$	37.9127	−	18.2578i	1.38346	−	0.666237i	0.413722	−	0.910403i	$-0.364228\pi$
$751$	37.9127	−	18.2578i	1.38346	−	0.666237i	0.969733	+	0.244166i	$0.0785142\pi$
$752$	−8.27079	+	36.2367i	−0.301605	+	1.32142i
$753$		0			0
$754$	−2.18129			−0.0794377
$755$	−1.68861	+	7.39829i	−0.0614549	+	0.269251i
$756$		0			0
$757$	−0.561069	−	2.45820i	−0.0203924	−	0.0893449i	0.963708	−	0.266960i	$-0.0860190\pi$
$757$	−0.561069	−	2.45820i	−0.0203924	−	0.0893449i	−0.984100	+	0.177615i	$0.943162\pi$
$758$	−2.56411	−	11.2341i	−0.0931326	−	0.408041i
$759$		0			0
$760$	0.769490	+	0.964910i	0.0279123	+	0.0350010i
$761$	−8.95304	−	39.2258i	−0.324548	−	1.42194i	−0.829364	−	0.558709i	$-0.811297\pi$
$761$	−8.95304	−	39.2258i	−0.324548	−	1.42194i	0.504816	−	0.863227i	$-0.331560\pi$
$762$		0			0
$763$	26.5566	−	5.13979i	0.961413	−	0.186073i
$764$	3.94633	−	17.2900i	0.142773	−	0.625530i
$765$		0			0
$766$	−26.4271			−0.954850
$767$	−0.0348242	+	0.152575i	−0.00125743	+	0.00550916i
$768$		0			0
$769$	21.8800	+	27.4366i	0.789012	+	0.989389i	0.999929	+	0.0118856i	$0.00378340\pi$
$769$	21.8800	+	27.4366i	0.789012	+	0.989389i	−0.210918	+	0.977504i	$0.567645\pi$
$770$	0.679578	−	0.505951i	0.0244903	−	0.0182332i
$771$		0			0
$772$	4.13861	−	18.1324i	0.148952	−	0.652600i
$773$	−7.01272	+	8.79367i	−0.252230	+	0.316286i	−0.891785	−	0.452459i	$-0.850547\pi$
$773$	−7.01272	+	8.79367i	−0.252230	+	0.316286i	0.639555	+	0.768745i	$0.279118\pi$
$774$		0			0
$775$	−7.57963	−	9.50456i	−0.272268	−	0.341414i
$776$	6.42293	+	3.09312i	0.230570	+	0.111037i
$777$		0			0
$778$	22.9707	−	11.0621i	0.823539	−	0.396595i
$779$	−9.77493	−	4.70736i	−0.350223	−	0.168659i
$780$		0			0
$781$	4.35202	+	2.09582i	0.155727	+	0.0749943i
$782$	−1.84692	+	2.31596i	−0.0660457	+	0.0828187i
$783$		0			0
$784$	18.4710	+	26.6114i	0.659677	+	0.950408i
$785$	3.59715			0.128388
$786$		0			0
$787$	−22.2589	−	10.7193i	−0.793443	−	0.382102i	−0.00716462	−	0.999974i	$-0.502281\pi$
$787$	−22.2589	−	10.7193i	−0.793443	−	0.382102i	−0.786278	+	0.617872i	$0.787995\pi$
$788$	0.0904175	+	0.396145i	0.00322099	+	0.0141121i
$789$		0			0
$790$	−2.15075	+	1.03575i	−0.0765202	+	0.0368502i
$791$	0.842396	−	25.3472i	0.0299522	−	0.901244i
$792$		0			0
$793$	1.33258	+	1.67100i	0.0473212	+	0.0593389i
$794$	−30.1100	+	14.5002i	−1.06856	+	0.514593i
$795$		0			0
$796$	−6.28835	+	27.5511i	−0.222885	+	0.976521i
$797$	−20.8274	+	26.1168i	−0.737746	+	0.925104i	−0.999195	−	0.0401132i	$-0.987228\pi$
$797$	−20.8274	+	26.1168i	−0.737746	+	0.925104i	0.261449	+	0.965217i	$0.415800\pi$
$798$		0			0
$799$	39.5767	+	49.6277i	1.40012	+	1.75570i
$800$	32.2295	−	15.5209i	1.13949	−	0.548747i
$801$		0			0
$802$	12.8949			0.455334
$803$	−5.15561			−0.181937
$804$		0			0
$805$	0.137218	−	0.102160i	0.00483632	−	0.00360067i
$806$	−0.561509	−	2.46013i	−0.0197783	−	0.0866545i
$807$		0			0
$808$	8.12287	+	10.1858i	0.285762	+	0.358334i
$809$	−26.4431	−	33.1586i	−0.929689	−	1.16579i	−0.985894	−	0.167374i	$-0.946471\pi$
$809$	−26.4431	−	33.1586i	−0.929689	−	1.16579i	0.0562047	−	0.998419i	$-0.482100\pi$
$810$		0			0
$811$	−1.04624	−	4.58390i	−0.0367386	−	0.160962i	0.953231	−	0.302243i	$-0.0977353\pi$
$811$	−1.04624	−	4.58390i	−0.0367386	−	0.160962i	−0.989970	+	0.141280i	$0.954878\pi$
$812$	6.96059	+	5.93963i	0.244269	+	0.208440i
$813$		0			0
$814$	5.20989			0.182607
$815$	3.83107			0.134197
$816$		0			0
$817$	−48.1344	+	23.1803i	−1.68401	+	0.810976i
$818$	17.1794	+	21.5423i	0.600665	+	0.753210i
$819$		0			0
$820$	0.702247	−	0.880589i	0.0245235	−	0.0307515i
$821$	−4.86304	+	21.3064i	−0.169721	+	0.743598i	0.816389	+	0.577503i	$0.195973\pi$
$821$	−4.86304	+	21.3064i	−0.169721	+	0.743598i	−0.986110	+	0.166095i	$0.946884\pi$
$822$		0			0
$823$	−21.6167	+	10.4100i	−0.753509	+	0.362871i	−0.770882	−	0.636978i	$-0.780184\pi$
$823$	−21.6167	+	10.4100i	−0.753509	+	0.362871i	0.0173727	+	0.999849i	$0.494470\pi$
$824$	−0.272497	−	0.341700i	−0.00949288	−	0.0119037i
$825$		0			0
$826$	1.18065	−	0.879003i	0.0410801	−	0.0305844i
$827$	−43.1281	+	20.7694i	−1.49971	+	0.722223i	−0.990383	−	0.138349i	$-0.955820\pi$
$827$	−43.1281	+	20.7694i	−1.49971	+	0.722223i	−0.509328	+	0.860572i	$0.670106\pi$
$828$		0			0
$829$	1.91724	+	8.39999i	0.0665886	+	0.291744i	0.997248	−	0.0741441i	$-0.0236225\pi$
$829$	1.91724	+	8.39999i	0.0665886	+	0.291744i	−0.930659	+	0.365888i	$0.880765\pi$
$830$	−4.75860	−	2.29162i	−0.165173	−	0.0795433i
$831$		0			0
$832$	2.47840			0.0859231
$833$	55.1994	+	3.67308i	1.91254	+	0.127265i
$834$		0			0
$835$	−2.10305	+	2.63714i	−0.0727790	+	0.0912620i
$836$	3.79232	+	1.82629i	0.131160	+	0.0631634i
$837$		0			0
$838$	25.4811	+	12.2711i	0.880231	+	0.423897i
$839$	−0.287710	+	0.138554i	−0.00993285	+	0.00478341i	−0.438844	−	0.898563i	$-0.644612\pi$
$839$	−0.287710	+	0.138554i	−0.00993285	+	0.00478341i	0.428911	+	0.903347i	$0.358897\pi$
$840$		0			0
$841$	21.9716	+	10.5810i	0.757642	+	0.364861i
$842$	33.9120	+	42.5243i	1.16868	+	1.46548i
$843$		0			0
$844$	16.4030	−	20.5687i	0.564613	−	0.708003i
$845$	−0.927334	+	4.06292i	−0.0319013	+	0.139769i
$846$		0			0
$847$	13.1672	−	25.1674i	0.452429	−	0.864763i
$848$	−15.3865	−	19.2940i	−0.528374	−	0.662560i
$849$		0			0
$850$	16.3482	−	71.6259i	0.560737	−	2.45675i
$851$	1.05197			0.0360609
$852$		0			0
$853$	−7.86772	+	34.4707i	−0.269385	+	1.18025i	0.641345	+	0.767253i	$0.278377\pi$
$853$	−7.86772	+	34.4707i	−0.269385	+	1.18025i	−0.910730	+	0.413002i	$0.864480\pi$
$854$	0.667707	−	20.0909i	0.0228484	−	0.687497i
$855$		0			0
$856$	3.30608	+	14.4849i	0.112999	+	0.495082i
$857$	4.14028	+	5.19175i	0.141429	+	0.177347i	0.847501	−	0.530793i	$-0.178106\pi$
$857$	4.14028	+	5.19175i	0.141429	+	0.177347i	−0.706072	+	0.708140i	$0.749535\pi$
$858$		0			0
$859$	8.00372	+	35.0666i	0.273083	+	1.19646i	0.906352	+	0.422524i	$0.138856\pi$
$859$	8.00372	+	35.0666i	0.273083	+	1.19646i	−0.633268	+	0.773932i	$0.718287\pi$
$860$	−1.23416	−	5.40723i	−0.0420847	−	0.184385i
$861$		0			0
$862$	−6.31303	+	27.6592i	−0.215023	+	0.942075i
$863$	6.01001			0.204583			0.102292	−	0.994754i	$-0.467383\pi$
$863$	6.01001			0.204583			0.102292	+	0.994754i	$0.467383\pi$
$864$		0			0
$865$	0.839929	−	3.67997i	0.0285584	−	0.125123i
$866$	41.1721	−	19.8275i	1.39909	−	0.673764i
$867$		0			0
$868$	−4.90713	+	9.37939i	−0.166559	+	0.318357i
$869$	1.22883	−	1.54090i	0.0416850	−	0.0522714i
$870$		0			0
$871$	3.48252	−	4.36694i	0.118001	−	0.147968i
$872$	6.82218	−	3.28539i	0.231028	−	0.111257i
$873$		0			0
$874$	1.71684	+	0.826785i	0.0580729	+	0.0279664i
$875$	−3.97691	+	7.60139i	−0.134444	+	0.256974i
$876$		0			0
$877$	10.2960	+	4.95831i	0.347673	+	0.167430i	0.599567	−	0.800324i	$-0.295339\pi$
$877$	10.2960	+	4.95831i	0.347673	+	0.167430i	−0.251895	+	0.967755i	$0.581054\pi$
$878$	7.36695	+	32.2767i	0.248622	+	1.08929i
$879$		0			0
$880$	0.486274	−	0.609768i	0.0163923	−	0.0205553i
$881$	−11.0685			−0.372907			−0.186453	−	0.982464i	$-0.559699\pi$
$881$	−11.0685			−0.372907			−0.186453	+	0.982464i	$0.559699\pi$
$882$		0			0
$883$	23.0593			0.776006			0.388003	−	0.921658i	$-0.373165\pi$
$883$	23.0593			0.776006			0.388003	+	0.921658i	$0.373165\pi$
$884$	4.24076	−	5.31774i	0.142632	−	0.178855i
$885$		0			0
$886$	0.826474	+	3.62102i	0.0277659	+	0.121650i
$887$	50.9661	+	24.5440i	1.71127	+	0.824106i	0.991532	+	0.129863i	$0.0414538\pi$
$887$	50.9661	+	24.5440i	1.71127	+	0.824106i	0.719741	+	0.694242i	$0.244260\pi$
$888$		0			0
$889$	−24.3514	+	18.1298i	−0.816720	+	0.608054i
$890$	7.47277	+	3.59870i	0.250488	+	0.120629i
$891$		0			0
$892$	−31.9973	+	15.4091i	−1.07135	+	0.515934i
$893$	25.4590	−	31.9245i	0.851952	−	1.06831i
$894$		0			0
$895$	−4.07289	+	5.10724i	−0.136142	+	0.170716i
$896$	11.6983	+	9.98247i	0.390814	+	0.333491i
$897$		0			0
$898$	−49.2497	+	23.7174i	−1.64348	+	0.791461i
$899$	1.18758	−	5.20311i	0.0396079	−	0.173534i
$900$		0			0
$901$	−42.1449			−1.40405
$902$	−0.463941	+	2.03266i	−0.0154476	+	0.0676802i
$903$		0			0
$904$	−1.57978	−	6.92148i	−0.0525428	−	0.230205i
$905$	1.07423	+	4.70651i	0.0357087	+	0.156450i
$906$		0			0
$907$	−7.95738	−	9.97824i	−0.264220	−	0.331322i	0.631969	−	0.774994i	$-0.282247\pi$
$907$	−7.95738	−	9.97824i	−0.264220	−	0.331322i	−0.896189	+	0.443672i	$0.853676\pi$
$908$	1.70141	+	7.45435i	0.0564632	+	0.247381i
$909$		0			0
$910$	−0.706414	+	0.525930i	−0.0234174	+	0.0174344i
$911$	6.31313	−	27.6596i	0.209163	−	0.916405i	−0.755962	−	0.654616i	$-0.772830\pi$
$911$	6.31313	−	27.6596i	0.209163	−	0.916405i	0.965125	−	0.261789i	$-0.0843124\pi$
$912$		0			0
$913$	4.36064			0.144316
$914$	−7.80251	+	34.1850i	−0.258084	+	1.13074i
$915$		0			0
$916$	−23.8377	−	29.8916i	−0.787621	−	0.987645i
$917$	−9.05590	−	2.38602i	−0.299052	−	0.0787932i
$918$		0			0
$919$	1.51006	−	6.61601i	0.0498123	−	0.218242i	−0.943896	−	0.330244i	$-0.892869\pi$
$919$	1.51006	−	6.61601i	0.0498123	−	0.218242i	0.993708	+	0.112002i	$0.0357262\pi$
$920$	0.0298583	−	0.0374411i	0.000984397	−	0.00123440i
$921$		0			0
$922$	22.9041	+	28.7209i	0.754307	+	0.945871i
$923$	−4.52387	−	2.17858i	−0.148905	−	0.0717088i
$924$		0			0
$925$	−23.5066	+	11.3202i	−0.772894	+	0.372206i
$926$	−44.9373	−	21.6407i	−1.47673	−	0.711157i
$927$		0			0
$928$	14.1490	+	6.81380i	0.464464	+	0.223674i
$929$	−28.4597	+	35.6873i	−0.933733	+	1.17086i	0.0513324	+	0.998682i	$0.483653\pi$
$929$	−28.4597	+	35.6873i	−0.933733	+	1.17086i	−0.985065	+	0.172182i	$0.944918\pi$
$930$		0			0
$931$	−5.59785	−	35.1442i	−0.183462	−	1.15180i
$932$	8.19726			0.268510
$933$		0			0
$934$	7.49814	+	3.61091i	0.245347	+	0.118153i
$935$	−0.296386	−	1.29855i	−0.00969285	−	0.0424671i
$936$		0			0
$937$	−21.6888	+	10.4448i	−0.708541	+	0.341216i	−0.753204	−	0.657787i	$-0.771493\pi$
$937$	−21.6888	+	10.4448i	−0.708541	+	0.341216i	0.0446629	+	0.999002i	$0.485779\pi$
$938$	−51.5769	+	9.98226i	−1.68405	+	0.325932i
$939$		0			0
$940$	2.64300	+	3.31422i	0.0862052	+	0.108098i
$941$	4.29691	−	2.06928i	0.140075	−	0.0674567i	−0.362533	−	0.931971i	$-0.618088\pi$
$941$	4.29691	−	2.06928i	0.140075	−	0.0674567i	0.502608	+	0.864514i	$0.332374\pi$
$942$		0			0
$943$	−0.0936777	+	0.410429i	−0.00305056	+	0.0133654i
$944$	0.844817	−	1.05937i	0.0274965	−	0.0344795i
$945$		0			0
$946$	6.40123	+	8.02689i	0.208122	+	0.260977i
$947$	28.3835	−	13.6688i	0.922340	−	0.444175i	0.0884337	−	0.996082i	$-0.471814\pi$
$947$	28.3835	−	13.6688i	0.922340	−	0.444175i	0.833906	+	0.551907i	$0.186100\pi$
$948$		0			0
$949$	5.35919			0.173967
$950$	−47.2605			−1.53333
$951$		0			0
$952$	15.2042	−	2.94264i	0.492772	−	0.0953716i
$953$	−5.03286	−	22.0504i	−0.163030	−	0.714283i	−0.988673	−	0.150089i	$-0.952044\pi$
$953$	−5.03286	−	22.0504i	−0.163030	−	0.714283i	0.825642	−	0.564194i	$-0.190813\pi$
$954$		0			0
$955$	2.25083	+	2.82246i	0.0728352	+	0.0913325i
$956$	−14.8282	−	18.5940i	−0.479578	−	0.601372i
$957$		0			0
$958$	−7.42718	−	32.5406i	−0.239961	−	1.05134i
$959$	−24.7303	−	6.51584i	−0.798582	−	0.210407i
$960$		0			0
$961$	−24.8260			−0.800840
$962$	−5.41562			−0.174607
$963$		0			0
$964$	3.43274	−	1.65312i	0.110561	−	0.0532434i
$965$	2.36050	+	2.95998i	0.0759873	+	0.0952850i
$966$		0			0
$967$	−25.1694	+	31.5614i	−0.809393	+	1.01495i	0.190056	+	0.981773i	$0.439133\pi$
$967$	−25.1694	+	31.5614i	−0.809393	+	1.01495i	−0.999450	+	0.0331737i	$0.989439\pi$
$968$	1.76931	−	7.75184i	0.0568677	−	0.249154i
$969$		0			0
$970$	5.40090	−	2.60094i	0.173412	−	0.0835110i
$971$	−23.0758	−	28.9361i	−0.740537	−	0.928604i	0.258766	−	0.965940i	$-0.416684\pi$
$971$	−23.0758	−	28.9361i	−0.740537	−	0.928604i	−0.999303	+	0.0373364i	$0.988113\pi$
$972$		0			0
$973$	21.0268	+	47.6497i	0.674087	+	1.52758i
$974$	21.8253	−	10.5105i	0.699328	−	0.336778i
$975$		0			0
$976$	−4.11772	−	18.0409i	−0.131805	−	0.577475i
$977$	−34.7378	−	16.7288i	−1.11136	−	0.535203i	−0.214148	−	0.976801i	$-0.568697\pi$
$977$	−34.7378	−	16.7288i	−1.11136	−	0.535203i	−0.897213	+	0.441598i	$0.854412\pi$
$978$		0			0
$979$	−6.84782			−0.218857
$980$	3.68631	+	0.245294i	0.117755	+	0.00783563i
$981$		0			0
$982$	7.15512	−	8.97224i	0.228329	−	0.286316i
$983$	4.12278	+	1.98543i	0.131496	+	0.0633252i	0.498475	−	0.866904i	$-0.333894\pi$
$983$	4.12278	+	1.98543i	0.131496	+	0.0633252i	−0.366979	+	0.930229i	$0.619608\pi$
$984$		0			0
$985$	−0.0745218	−	0.0358878i	−0.00237446	−	0.00114348i
$986$	29.0589	−	13.9940i	0.925425	−	0.445661i
$987$		0			0
$988$	−3.94207	−	1.89840i	−0.125414	−	0.0603962i
$989$	1.29252	+	1.62077i	0.0410997	+	0.0515374i
$990$		0			0
$991$	5.71436	−	7.16558i	0.181523	−	0.227622i	−0.682742	−	0.730659i	$-0.739213\pi$
$991$	5.71436	−	7.16558i	0.181523	−	0.227622i	0.864265	+	0.503037i	$0.167784\pi$
$992$	−4.04260	+	17.7118i	−0.128353	+	0.562349i
$993$		0			0
$994$	19.0658	+	43.2058i	0.604730	+	1.37041i
$995$	−3.58663	−	4.49750i	−0.113704	−	0.142580i
$996$		0			0
$997$	0.150867	−	0.660992i	0.00477801	−	0.0209338i	−0.972483	−	0.232975i	$-0.925154\pi$
$997$	0.150867	−	0.660992i	0.00477801	−	0.0209338i	0.977261	+	0.212041i	$0.0680111\pi$
$998$	−3.62682			−0.114805
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.c.190.1		24
3.2	odd	2		147.2.i.a.43.4	✓	24
49.8	even	7	inner	441.2.u.c.253.1		24
147.8	odd	14		147.2.i.a.106.4	yes	24
147.20	even	14		7203.2.a.b.1.11		12
147.29	odd	14		7203.2.a.a.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.a.43.4	✓	24	3.2	odd	2
147.2.i.a.106.4	yes	24	147.8	odd	14
441.2.u.c.190.1		24	1.1	even	1	trivial
441.2.u.c.253.1		24	49.8	even	7	inner
7203.2.a.a.1.11		12	147.29	odd	14
7203.2.a.b.1.11		12	147.20	even	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18466 + 1.48552i) q^{2} +(-0.358304 - 1.56983i) q^{4} +(0.295313 + 0.142215i) q^{5} +(-2.01260 - 1.71740i) q^{7} +(-0.667291 - 0.321350i) q^{8} +O(q^{10})\)	\(q+(-1.18466 + 1.48552i) q^{2} +(-0.358304 - 1.56983i) q^{4} +(0.295313 + 0.142215i) q^{5} +(-2.01260 - 1.71740i) q^{7} +(-0.667291 - 0.321350i) q^{8} +(-0.561110 + 0.270216i) q^{10} +(0.320589 - 0.402005i) q^{11} +(-0.333248 + 0.417880i) q^{13} +(4.93548 - 0.955219i) q^{14} +(4.16937 - 2.00786i) q^{16} +(1.75860 - 7.70492i) q^{17} -5.08389 q^{19} +(0.117442 - 0.514547i) q^{20} +(0.217398 + 0.952482i) q^{22} +(0.0438964 + 0.192322i) q^{23} +(-3.05046 - 3.82516i) q^{25} +(-0.225983 - 0.990094i) q^{26} +(-1.97490 + 3.77479i) q^{28} +(0.477947 - 2.09402i) q^{29} +2.48475 q^{31} +(-1.62696 + 7.12820i) q^{32} +(9.36247 + 11.7402i) q^{34} +(-0.350106 - 0.793391i) q^{35} +(1.18663 - 5.19896i) q^{37} +(6.02270 - 7.55223i) q^{38} +(-0.151359 - 0.189798i) q^{40} +(1.92273 + 0.925936i) q^{41} +(9.46803 - 4.55956i) q^{43} +(-0.745949 - 0.359230i) q^{44} +(-0.337702 - 0.162629i) q^{46} +(-5.00777 + 6.27955i) q^{47} +(1.10110 + 6.91286i) q^{49} +9.29613 q^{50} +(0.775405 + 0.373415i) q^{52} +(-1.18664 - 5.19903i) q^{53} +(0.151845 - 0.0731247i) q^{55} +(0.791102 + 1.79275i) q^{56} +(2.54451 + 3.19071i) q^{58} +(0.263805 - 0.127042i) q^{59} +(0.889807 - 3.89850i) q^{61} +(-2.94359 + 3.69115i) q^{62} +(-2.89110 - 3.62532i) q^{64} +(-0.157841 + 0.0760123i) q^{65} -10.4502 q^{67} -12.7255 q^{68} +(1.59336 + 0.419812i) q^{70} +(2.09042 + 9.15871i) q^{71} +(-6.25159 - 7.83924i) q^{73} +(6.31741 + 7.92178i) q^{74} +(1.82158 + 7.98085i) q^{76} +(-1.33562 + 0.258497i) q^{77} +3.83303 q^{79} +1.51682 q^{80} +(-3.65328 + 1.75933i) q^{82} +(5.28762 + 6.63047i) q^{83} +(1.61509 - 2.02526i) q^{85} +(-4.44310 + 19.4665i) q^{86} +(-0.343110 + 0.165233i) q^{88} +(-8.30354 - 10.4123i) q^{89} +(1.38836 - 0.268705i) q^{91} +(0.286186 - 0.137820i) q^{92} +(-3.39588 - 14.8783i) q^{94} +(-1.50134 - 0.723006i) q^{95} -9.62539 q^{97} +(-11.5736 - 6.55371i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

Introduction

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