LMFDB - Embedded newform 280.2.b.d.141.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(141,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("280.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.8272021826830336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 4x^{9} + 4x^{8} - 12x^{7} + 10x^{6} - 24x^{5} + 16x^{4} - 32x^{3} + 48x^{2} + 64 $ x^12 + 3x^10 - 4x^9 + 4x^8 - 12x^7 + 10x^6 - 24x^5 + 16x^4 - 32x^3 + 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			141.3
Root			$0.832593 + 1.14315i$ of defining polynomial
Character	$\chi$	$=$	280.141
Dual form			280.2.b.d.141.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14315 - 0.832593i) q^{2} -3.42822i q^{3} +(0.613577 + 1.90356i) q^{4} -1.00000i q^{5} +(-2.85431 + 3.91897i) q^{6} +1.00000 q^{7} +(0.883477 - 2.68691i) q^{8} -8.75270 q^{9} +O(q^{10})$	\(q+(-1.14315 - 0.832593i) q^{2} -3.42822i q^{3} +(0.613577 + 1.90356i) q^{4} -1.00000i q^{5} +(-2.85431 + 3.91897i) q^{6} +1.00000 q^{7} +(0.883477 - 2.68691i) q^{8} -8.75270 q^{9} +(-0.832593 + 1.14315i) q^{10} -4.42233i q^{11} +(6.52581 - 2.10348i) q^{12} +0.766954i q^{13} +(-1.14315 - 0.832593i) q^{14} -3.42822 q^{15} +(-3.24705 + 2.33596i) q^{16} -0.356460 q^{17} +(10.0056 + 7.28744i) q^{18} +3.20107i q^{19} +(1.90356 - 0.613577i) q^{20} -3.42822i q^{21} +(-3.68200 + 5.05538i) q^{22} +4.70190 q^{23} +(-9.21131 - 3.02875i) q^{24} -1.00000 q^{25} +(0.638561 - 0.876742i) q^{26} +19.7215i q^{27} +(0.613577 + 1.90356i) q^{28} +4.05669i q^{29} +(3.91897 + 2.85431i) q^{30} +2.12931 q^{31} +(5.65676 + 0.0331222i) q^{32} -15.1607 q^{33} +(0.407487 + 0.296786i) q^{34} -1.00000i q^{35} +(-5.37046 - 16.6613i) q^{36} -8.70190i q^{37} +(2.66519 - 3.65929i) q^{38} +2.62929 q^{39} +(-2.68691 - 0.883477i) q^{40} -3.95885 q^{41} +(-2.85431 + 3.91897i) q^{42} -5.28922i q^{43} +(8.41815 - 2.71344i) q^{44} +8.75270i q^{45} +(-5.37497 - 3.91477i) q^{46} +3.32777 q^{47} +(8.00818 + 11.1316i) q^{48} +1.00000 q^{49} +(1.14315 + 0.832593i) q^{50} +1.22203i q^{51} +(-1.45994 + 0.470586i) q^{52} -12.3904i q^{53} +(16.4200 - 22.5446i) q^{54} -4.42233 q^{55} +(0.883477 - 2.68691i) q^{56} +10.9740 q^{57} +(3.37758 - 4.63740i) q^{58} -5.63257i q^{59} +(-2.10348 - 6.52581i) q^{60} +10.9857i q^{61} +(-2.43411 - 1.77285i) q^{62} -8.75270 q^{63} +(-6.43894 - 4.74764i) q^{64} +0.766954 q^{65} +(17.3310 + 12.6227i) q^{66} -0.0448574i q^{67} +(-0.218716 - 0.678542i) q^{68} -16.1192i q^{69} +(-0.832593 + 1.14315i) q^{70} -4.27696 q^{71} +(-7.73281 + 23.5177i) q^{72} -2.27696 q^{73} +(-7.24514 + 9.94756i) q^{74} +3.42822i q^{75} +(-6.09341 + 1.96410i) q^{76} -4.42233i q^{77} +(-3.00567 - 2.18913i) q^{78} +6.43359 q^{79} +(2.33596 + 3.24705i) q^{80} +41.3517 q^{81} +(4.52555 + 3.29611i) q^{82} -9.61422i q^{83} +(6.52581 - 2.10348i) q^{84} +0.356460i q^{85} +(-4.40377 + 6.04636i) q^{86} +13.9072 q^{87} +(-11.8824 - 3.90703i) q^{88} +13.4944 q^{89} +(7.28744 - 10.0056i) q^{90} +0.766954i q^{91} +(2.88498 + 8.95033i) q^{92} -7.29973i q^{93} +(-3.80413 - 2.77067i) q^{94} +3.20107 q^{95} +(0.113550 - 19.3926i) q^{96} -11.6033 q^{97} +(-1.14315 - 0.832593i) q^{98} +38.7073i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9	$ 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9} + 16 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{20} + 12 q^{22} + 8 q^{23} - 24 q^{24} - 12 q^{25} + 6 q^{28} + 12 q^{30} + 24 q^{31} - 2 q^{32} - 24 q^{33} - 20 q^{34} - 18 q^{36} + 12 q^{38} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 16 q^{44} - 48 q^{46} - 16 q^{47} + 20 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{52} + 44 q^{54} - 8 q^{55} + 10 q^{56} + 40 q^{57} + 4 q^{58} - 8 q^{60} + 8 q^{62} - 20 q^{63} - 6 q^{64} + 8 q^{65} + 64 q^{66} - 56 q^{68} - 32 q^{71} - 46 q^{72} - 8 q^{73} - 32 q^{74} - 12 q^{76} - 24 q^{78} + 8 q^{80} + 60 q^{81} - 28 q^{82} + 16 q^{84} - 76 q^{86} + 48 q^{87} - 40 q^{88} - 48 q^{89} + 24 q^{90} + 12 q^{94} + 28 q^{96} + 32 q^{97} - 2 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9 + 16 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^20 + 12 * q^22 + 8 * q^23 - 24 * q^24 - 12 * q^25 + 6 * q^28 + 12 * q^30 + 24 * q^31 - 2 * q^32 - 24 * q^33 - 20 * q^34 - 18 * q^36 + 12 * q^38 - 48 * q^39 + 12 * q^40 - 16 * q^41 + 16 * q^44 - 48 * q^46 - 16 * q^47 + 20 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^52 + 44 * q^54 - 8 * q^55 + 10 * q^56 + 40 * q^57 + 4 * q^58 - 8 * q^60 + 8 * q^62 - 20 * q^63 - 6 * q^64 + 8 * q^65 + 64 * q^66 - 56 * q^68 - 32 * q^71 - 46 * q^72 - 8 * q^73 - 32 * q^74 - 12 * q^76 - 24 * q^78 + 8 * q^80 + 60 * q^81 - 28 * q^82 + 16 * q^84 - 76 * q^86 + 48 * q^87 - 40 * q^88 - 48 * q^89 + 24 * q^90 + 12 * q^94 + 28 * q^96 + 32 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.14315	−	0.832593i	−0.808328	−	0.588732i
$2$	−1.14315	−	0.832593i	−0.808328	−	0.588732i
$3$		−	3.42822i		−	1.97928i	−0.143555	−	0.989642i	$-0.545853\pi$
$3$		−	3.42822i		−	1.97928i	0.143555	−	0.989642i	$-0.454147\pi$
$4$	0.613577	+	1.90356i	0.306789	+	0.951778i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−2.85431	+	3.91897i	−1.16527	+	1.59991i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	0.883477	−	2.68691i	0.312356	−	0.949965i
$9$	−8.75270			−2.91757
$10$	−0.832593	+	1.14315i	−0.263289	+	0.361495i
$11$		−	4.42233i		−	1.33338i	−0.745334	−	0.666691i	$-0.767710\pi$
$11$		−	4.42233i		−	1.33338i	0.745334	−	0.666691i	$-0.232290\pi$
$12$	6.52581	−	2.10348i	1.88384	−	0.607222i
$13$			0.766954i			0.212715i	0.994328	+	0.106357i	$0.0339188\pi$
$13$			0.766954i			0.212715i	−0.994328	+	0.106357i	$0.966081\pi$
$14$	−1.14315	−	0.832593i	−0.305519	−	0.222520i
$15$	−3.42822			−0.885163
$16$	−3.24705	+	2.33596i	−0.811761	+	0.583989i
$17$	−0.356460			−0.0864543			−0.0432272	−	0.999065i	$-0.513764\pi$
$17$	−0.356460			−0.0864543			−0.0432272	+	0.999065i	$0.513764\pi$
$18$	10.0056	+	7.28744i	2.35835	+	1.71767i
$19$			3.20107i			0.734375i	0.930147	+	0.367188i	$0.119679\pi$
$19$			3.20107i			0.734375i	−0.930147	+	0.367188i	$0.880321\pi$
$20$	1.90356	−	0.613577i	0.425648	−	0.137200i
$21$		−	3.42822i		−	0.748099i
$22$	−3.68200	+	5.05538i	−0.785005	+	1.07781i
$23$	4.70190			0.980414			0.490207	−	0.871606i	$-0.336921\pi$
$23$	4.70190			0.980414			0.490207	+	0.871606i	$0.336921\pi$
$24$	−9.21131	−	3.02875i	−1.88025	−	0.618242i
$25$	−1.00000			−0.200000
$26$	0.638561	−	0.876742i	0.125232	−	0.171943i
$27$			19.7215i			3.79541i
$28$	0.613577	+	1.90356i	0.115955	+	0.359738i
$29$			4.05669i			0.753309i	0.926354	+	0.376655i	$0.122926\pi$
$29$			4.05669i			0.753309i	−0.926354	+	0.376655i	$0.877074\pi$
$30$	3.91897	+	2.85431i	0.715502	+	0.521124i
$31$	2.12931			0.382435			0.191217	−	0.981548i	$-0.438756\pi$
$31$	2.12931			0.382435			0.191217	+	0.981548i	$0.438756\pi$
$32$	5.65676	+	0.0331222i	0.999983	+	0.00585524i
$33$	−15.1607			−2.63914
$34$	0.407487	+	0.296786i	0.0698835	+	0.0508985i
$35$		−	1.00000i		−	0.169031i
$36$	−5.37046	−	16.6613i	−0.895077	−	2.77688i
$37$		−	8.70190i		−	1.43058i	−0.698826	−	0.715292i	$-0.746294\pi$
$37$		−	8.70190i		−	1.43058i	0.698826	−	0.715292i	$-0.253706\pi$
$38$	2.66519	−	3.65929i	0.432350	−	0.593616i
$39$	2.62929			0.421023
$40$	−2.68691	−	0.883477i	−0.424837	−	0.139690i
$41$	−3.95885			−0.618268			−0.309134	−	0.951019i	$-0.600039\pi$
$41$	−3.95885			−0.618268			−0.309134	+	0.951019i	$0.600039\pi$
$42$	−2.85431	+	3.91897i	−0.440430	+	0.604710i
$43$		−	5.28922i		−	0.806598i	−0.915068	−	0.403299i	$-0.867863\pi$
$43$		−	5.28922i		−	0.806598i	0.915068	−	0.403299i	$-0.132137\pi$
$44$	8.41815	−	2.71344i	1.26908	−	0.409067i
$45$			8.75270i			1.30478i
$46$	−5.37497	−	3.91477i	−0.792496	−	0.577201i
$47$	3.32777			0.485405			0.242702	−	0.970101i	$-0.421966\pi$
$47$	3.32777			0.485405			0.242702	+	0.970101i	$0.421966\pi$
$48$	8.00818	+	11.1316i	1.15588	+	1.60671i
$49$	1.00000			0.142857
$50$	1.14315	+	0.832593i	0.161666	+	0.117746i
$51$			1.22203i			0.171118i
$52$	−1.45994	+	0.470586i	−0.202457	+	0.0652585i
$53$		−	12.3904i		−	1.70195i	−0.525210	−	0.850973i	$-0.676013\pi$
$53$		−	12.3904i		−	1.70195i	0.525210	−	0.850973i	$-0.323987\pi$
$54$	16.4200	−	22.5446i	2.23448	−	3.06794i
$55$	−4.42233			−0.596307
$56$	0.883477	−	2.68691i	0.118060	−	0.359053i
$57$	10.9740			1.45354
$58$	3.37758	−	4.63740i	0.443497	−	0.608921i
$59$		−	5.63257i		−	0.733299i	−0.930359	−	0.366649i	$-0.880505\pi$
$59$		−	5.63257i		−	0.733299i	0.930359	−	0.366649i	$-0.119495\pi$
$60$	−2.10348	−	6.52581i	−0.271558	−	0.842478i
$61$			10.9857i			1.40658i	0.710903	+	0.703290i	$0.248287\pi$
$61$			10.9857i			1.40658i	−0.710903	+	0.703290i	$0.751713\pi$
$62$	−2.43411	−	1.77285i	−0.309133	−	0.225152i
$63$	−8.75270			−1.10274
$64$	−6.43894	−	4.74764i	−0.804867	−	0.593455i
$65$	0.766954			0.0951289
$66$	17.3310	+	12.6227i	2.13329	+	1.55375i
$67$		−	0.0448574i		−	0.00548021i	−0.999996	−	0.00274010i	$-0.999128\pi$
$67$		−	0.0448574i		−	0.00548021i	0.999996	−	0.00274010i	$-0.000872203\pi$
$68$	−0.218716	−	0.678542i	−0.0265232	−	0.0822853i
$69$		−	16.1192i		−	1.94052i
$70$	−0.832593	+	1.14315i	−0.0995139	+	0.136632i
$71$	−4.27696			−0.507582			−0.253791	−	0.967259i	$-0.581678\pi$
$71$	−4.27696			−0.507582			−0.253791	+	0.967259i	$0.581678\pi$
$72$	−7.73281	+	23.5177i	−0.911321	+	2.77159i
$73$	−2.27696			−0.266498			−0.133249	−	0.991083i	$-0.542541\pi$
$73$	−2.27696			−0.266498			−0.133249	+	0.991083i	$0.542541\pi$
$74$	−7.24514	+	9.94756i	−0.842231	+	1.15638i
$75$			3.42822i			0.395857i
$76$	−6.09341	+	1.96410i	−0.698962	+	0.225298i
$77$		−	4.42233i		−	0.503971i
$78$	−3.00567	−	2.18913i	−0.340325	−	0.247870i
$79$	6.43359			0.723835			0.361918	−	0.932210i	$-0.382122\pi$
$79$	6.43359			0.723835			0.361918	+	0.932210i	$0.382122\pi$
$80$	2.33596	+	3.24705i	0.261168	+	0.363031i
$81$	41.3517			4.59463
$82$	4.52555	+	3.29611i	0.499763	+	0.363994i
$83$		−	9.61422i		−	1.05530i	−0.849463	−	0.527649i	$-0.823074\pi$
$83$		−	9.61422i		−	1.05530i	0.849463	−	0.527649i	$-0.176926\pi$
$84$	6.52581	−	2.10348i	0.712024	−	0.229508i
$85$			0.356460i			0.0386636i
$86$	−4.40377	+	6.04636i	−0.474870	+	0.651996i
$87$	13.9072			1.49101
$88$	−11.8824	−	3.90703i	−1.26667	−	0.416490i
$89$	13.4944			1.43040			0.715201	−	0.698919i	$-0.246335\pi$
$89$	13.4944			1.43040			0.715201	+	0.698919i	$0.246335\pi$
$90$	7.28744	−	10.0056i	0.768164	−	1.05469i
$91$			0.766954i			0.0803986i
$92$	2.88498	+	8.95033i	0.300780	+	0.933136i
$93$		−	7.29973i		−	0.756947i
$94$	−3.80413	−	2.77067i	−0.392366	−	0.285773i
$95$	3.20107			0.328423
$96$	0.113550	−	19.3926i	0.0115892	−	1.97925i
$97$	−11.6033			−1.17813			−0.589066	−	0.808085i	$-0.700504\pi$
$97$	−11.6033			−1.17813			−0.589066	+	0.808085i	$0.700504\pi$
$98$	−1.14315	−	0.832593i	−0.115475	−	0.0841046i
$99$			38.7073i			3.89023i
$100$	−0.613577	−	1.90356i	−0.0613577	−	0.190356i
$101$			0.601967i			0.0598979i	0.999551	+	0.0299490i	$0.00953448\pi$
$101$			0.601967i			0.0598979i	−0.999551	+	0.0299490i	$0.990466\pi$
$102$	1.01745	−	1.39696i	0.100743	−	0.138319i
$103$	11.1164			1.09533			0.547665	−	0.836697i	$-0.315517\pi$
$103$	11.1164			1.09533			0.547665	+	0.836697i	$0.315517\pi$
$104$	2.06073	+	0.677586i	0.202072	+	0.0664428i
$105$	−3.42822			−0.334560
$106$	−10.3161	+	14.1640i	−1.00199	+	1.37573i
$107$		−	0.499167i		−	0.0482563i	−0.999709	−	0.0241281i	$-0.992319\pi$
$107$		−	0.499167i		−	0.0482563i	0.999709	−	0.0241281i	$-0.00768097\pi$
$108$	−37.5410	+	12.1007i	−3.61239	+	1.16439i
$109$		−	6.73579i		−	0.645172i	−0.946540	−	0.322586i	$-0.895448\pi$
$109$		−	6.73579i		−	0.645172i	0.946540	−	0.322586i	$-0.104552\pi$
$110$	5.05538	+	3.68200i	0.482012	+	0.351065i
$111$	−29.8320			−2.83153
$112$	−3.24705	+	2.33596i	−0.306817	+	0.220727i
$113$	0.306652			0.0288474			0.0144237	−	0.999896i	$-0.495409\pi$
$113$	0.306652			0.0288474			0.0144237	+	0.999896i	$0.495409\pi$
$114$	−12.5449	−	9.13685i	−1.17494	−	0.855744i
$115$		−	4.70190i		−	0.438454i
$116$	−7.72214	+	2.48910i	−0.716983	+	0.231107i
$117$		−	6.71292i		−	0.620610i
$118$	−4.68964	+	6.43887i	−0.431716	+	0.592746i
$119$	−0.356460			−0.0326767
$120$	−3.02875	+	9.21131i	−0.276486	+	0.840874i
$121$	−8.55700			−0.777910
$122$	9.14666	−	12.5583i	0.828100	−	1.13698i
$123$			13.5718i			1.22373i
$124$	1.30649	+	4.05325i	0.117327	+	0.363993i
$125$			1.00000i			0.0894427i
$126$	10.0056	+	7.28744i	0.891373	+	0.649217i
$127$	−0.472661			−0.0419419			−0.0209709	−	0.999780i	$-0.506676\pi$
$127$	−0.472661			−0.0419419			−0.0209709	+	0.999780i	$0.506676\pi$
$128$	3.40781	+	10.7883i	0.301211	+	0.953558i
$129$	−18.1326			−1.59649
$130$	−0.876742	−	0.638561i	−0.0768954	−	0.0560055i
$131$		−	7.93234i		−	0.693052i	−0.938040	−	0.346526i	$-0.887361\pi$
$131$		−	7.93234i		−	0.693052i	0.938040	−	0.346526i	$-0.112639\pi$
$132$	−9.30228	−	28.8593i	−0.809659	−	2.51188i
$133$			3.20107i			0.277568i
$134$	−0.0373480	+	0.0512787i	−0.00322638	+	0.00442981i
$135$	19.7215			1.69736
$136$	−0.314925	+	0.957776i	−0.0270046	+	0.0821286i
$137$	−8.45674			−0.722508			−0.361254	−	0.932467i	$-0.617651\pi$
$137$	−8.45674			−0.722508			−0.361254	+	0.932467i	$0.617651\pi$
$138$	−13.4207	+	18.4266i	−1.14245	+	1.56858i
$139$		−	6.34549i		−	0.538218i	−0.963110	−	0.269109i	$-0.913271\pi$
$139$		−	6.34549i		−	0.538218i	0.963110	−	0.269109i	$-0.0867291\pi$
$140$	1.90356	−	0.613577i	0.160880	−	0.0518568i
$141$		−	11.4083i		−	0.960754i
$142$	4.88920	+	3.56097i	0.410293	+	0.298830i
$143$	3.39172			0.283630
$144$	28.4204	−	20.4459i	2.36837	−	1.70383i
$145$	4.05669			0.336890
$146$	2.60291	+	1.89578i	0.215418	+	0.156896i
$147$		−	3.42822i		−	0.282755i
$148$	16.5645	−	5.33929i	1.36160	−	0.438887i
$149$			18.3618i			1.50426i	0.659014	+	0.752131i	$0.270974\pi$
$149$			18.3618i			1.50426i	−0.659014	+	0.752131i	$0.729026\pi$
$150$	2.85431	−	3.91897i	0.233054	−	0.319982i
$151$	10.3288			0.840543			0.420271	−	0.907399i	$-0.361935\pi$
$151$	10.3288			0.840543			0.420271	+	0.907399i	$0.361935\pi$
$152$	8.60097	+	2.82807i	0.697631	+	0.229387i
$153$	3.11999			0.252236
$154$	−3.68200	+	5.05538i	−0.296704	+	0.407374i
$155$		−	2.12931i		−	0.171030i
$156$	1.61327	+	5.00500i	0.129165	+	0.400720i
$157$			17.7834i			1.41927i	0.704569	+	0.709635i	$0.251140\pi$
$157$			17.7834i			1.41927i	−0.704569	+	0.709635i	$0.748860\pi$
$158$	−7.35455	−	5.35656i	−0.585097	−	0.426145i
$159$	−42.4769			−3.36863
$160$	0.0331222	−	5.65676i	0.00261854	−	0.447206i
$161$	4.70190			0.370562
$162$	−47.2711	−	34.4291i	−3.71397	−	2.70501i
$163$		−	4.45888i		−	0.349247i	−0.984635	−	0.174623i	$-0.944129\pi$
$163$		−	4.45888i		−	0.349247i	0.984635	−	0.174623i	$-0.0558708\pi$
$164$	−2.42906	−	7.53588i	−0.189678	−	0.588453i
$165$			15.1607i			1.18026i
$166$	−8.00473	+	10.9905i	−0.621288	+	0.853027i
$167$	8.65030			0.669380			0.334690	−	0.942328i	$-0.391368\pi$
$167$	8.65030			0.669380			0.334690	+	0.942328i	$0.391368\pi$
$168$	−9.21131	−	3.02875i	−0.710668	−	0.233674i
$169$	12.4118			0.954752
$170$	0.296786	−	0.407487i	0.0227625	−	0.0312528i
$171$		−	28.0180i		−	2.14259i
$172$	10.0683	−	3.24534i	0.767702	−	0.247455i
$173$			18.6030i			1.41436i	0.707033	+	0.707181i	$0.250033\pi$
$173$			18.6030i			1.41436i	−0.707033	+	0.707181i	$0.749967\pi$
$174$	−15.8980	−	11.5791i	−1.20523	−	0.877808i
$175$	−1.00000			−0.0755929
$176$	10.3304	+	14.3595i	0.778681	+	1.08239i
$177$	−19.3097			−1.45141
$178$	−15.4261	−	11.2353i	−1.15623	−	0.842124i
$179$		−	12.1917i		−	0.911251i	−0.890171	−	0.455626i	$-0.849416\pi$
$179$		−	12.1917i		−	0.911251i	0.890171	−	0.455626i	$-0.150584\pi$
$180$	−16.6613	+	5.37046i	−1.24186	+	0.400290i
$181$			7.23501i			0.537774i	0.963172	+	0.268887i	$0.0866558\pi$
$181$			7.23501i			0.537774i	−0.963172	+	0.268887i	$0.913344\pi$
$182$	0.638561	−	0.876742i	0.0473333	−	0.0649885i
$183$	37.6616			2.78402
$184$	4.15402	−	12.6336i	0.306238	−	0.931359i
$185$	−8.70190			−0.639776
$186$	−6.07771	+	8.34468i	−0.445639	+	0.611861i
$187$			1.57639i			0.115277i
$188$	2.04184	+	6.33459i	0.148917	+	0.461997i
$189$			19.7215i			1.43453i
$190$	−3.65929	−	2.66519i	−0.265473	−	0.193353i
$191$	−9.72067			−0.703363			−0.351681	−	0.936120i	$-0.614390\pi$
$191$	−9.72067			−0.703363			−0.351681	+	0.936120i	$0.614390\pi$
$192$	−16.2760	+	22.0741i	−1.17462	+	1.59306i
$193$	8.63304			0.621420			0.310710	−	0.950505i	$-0.399433\pi$
$193$	8.63304			0.621420			0.310710	+	0.950505i	$0.399433\pi$
$194$	13.2642	+	9.66079i	0.952317	+	0.693604i
$195$		−	2.62929i		−	0.188287i
$196$	0.613577	+	1.90356i	0.0438270	+	0.135968i
$197$			9.41482i			0.670778i	0.942080	+	0.335389i	$0.108868\pi$
$197$			9.41482i			0.670778i	−0.942080	+	0.335389i	$0.891132\pi$
$198$	32.2275	−	44.2482i	2.29031	−	3.14459i
$199$	15.9597			1.13135			0.565677	−	0.824627i	$-0.308615\pi$
$199$	15.9597			1.13135			0.565677	+	0.824627i	$0.308615\pi$
$200$	−0.883477	+	2.68691i	−0.0624713	+	0.189993i
$201$	−0.153781			−0.0108469
$202$	0.501193	−	0.688137i	0.0352638	−	0.0484172i
$203$			4.05669i			0.284724i
$204$	−2.32619	+	0.749807i	−0.162866	+	0.0524970i
$205$			3.95885i			0.276498i
$206$	−12.7077	−	9.25543i	−0.885387	−	0.644857i
$207$	−41.1543			−2.86042
$208$	−1.79157	−	2.49033i	−0.124223	−	0.172674i
$209$	14.1562			0.979203
$210$	3.91897	+	2.85431i	0.270434	+	0.196966i
$211$			25.5089i			1.75610i	0.478565	+	0.878052i	$0.341157\pi$
$211$			25.5089i			1.75610i	−0.478565	+	0.878052i	$0.658843\pi$
$212$	23.5857	−	7.60244i	1.61987	−	0.522138i
$213$			14.6624i			1.00465i
$214$	−0.415603	+	0.570622i	−0.0284100	+	0.0390069i
$215$	−5.28922			−0.360722
$216$	52.9899	+	17.4235i	3.60551	+	1.18552i
$217$	2.12931			0.144547
$218$	−5.60817	+	7.70001i	−0.379833	+	0.521510i
$219$			7.80593i			0.527476i
$220$	−2.71344	−	8.41815i	−0.182940	−	0.567552i
$221$		−	0.273389i		−	0.0183901i
$222$	34.1025	+	24.8380i	2.28881	+	1.66701i
$223$	26.8751			1.79969			0.899845	−	0.436211i	$-0.143680\pi$
$223$	26.8751			1.79969			0.899845	+	0.436211i	$0.143680\pi$
$224$	5.65676	+	0.0331222i	0.377958	+	0.00221307i
$225$	8.75270			0.583514
$226$	−0.350549	−	0.255316i	−0.0233182	−	0.0169834i
$227$			8.34425i			0.553827i	0.960895	+	0.276914i	$0.0893116\pi$
$227$			8.34425i			0.553827i	−0.960895	+	0.276914i	$0.910688\pi$
$228$	6.73338	+	20.8896i	0.445929	+	1.38344i
$229$			10.3778i			0.685782i	0.939375	+	0.342891i	$0.111406\pi$
$229$			10.3778i			0.685782i	−0.939375	+	0.342891i	$0.888594\pi$
$230$	−3.91477	+	5.37497i	−0.258132	+	0.354415i
$231$	−15.1607			−0.997503
$232$	10.9000	+	3.58400i	0.715617	+	0.235301i
$233$	13.2468			0.867826			0.433913	−	0.900955i	$-0.357132\pi$
$233$	13.2468			0.867826			0.433913	+	0.900955i	$0.357132\pi$
$234$	−5.58913	+	7.67387i	−0.365373	+	0.501656i
$235$		−	3.32777i		−	0.217080i
$236$	10.7219	−	3.45602i	0.697937	−	0.224968i
$237$		−	22.0558i		−	1.43268i
$238$	0.407487	+	0.296786i	0.0264135	+	0.0192378i
$239$	16.2949			1.05403			0.527016	−	0.849855i	$-0.323311\pi$
$239$	16.2949			1.05403			0.527016	+	0.849855i	$0.323311\pi$
$240$	11.1316	−	8.00818i	0.718541	−	0.516926i
$241$	−6.63899			−0.427655			−0.213827	−	0.976871i	$-0.568593\pi$
$241$	−6.63899			−0.427655			−0.213827	+	0.976871i	$0.568593\pi$
$242$	9.78193	+	7.12450i	0.628806	+	0.457980i
$243$		−	82.5982i		−	5.29867i
$244$	−20.9120	+	6.74061i	−1.33875	+	0.431523i
$245$		−	1.00000i		−	0.0638877i
$246$	11.2998	−	15.5146i	0.720448	−	0.989174i
$247$	−2.45507			−0.156212
$248$	1.88119	−	5.72125i	0.119456	−	0.363299i
$249$	−32.9597			−2.08873
$250$	0.832593	−	1.14315i	0.0526578	−	0.0722991i
$251$		−	4.70665i		−	0.297081i	−0.988906	−	0.148540i	$-0.952542\pi$
$251$		−	4.70665i		−	0.297081i	0.988906	−	0.148540i	$-0.0474575\pi$
$252$	−5.37046	−	16.6613i	−0.338307	−	1.04956i
$253$		−	20.7934i		−	1.30727i
$254$	0.540322	+	0.393534i	0.0339028	+	0.0246925i
$255$	1.22203			0.0765262
$256$	5.08661	−	15.1699i	0.317913	−	0.948120i
$257$	−12.7516			−0.795424			−0.397712	−	0.917510i	$-0.630196\pi$
$257$	−12.7516			−0.795424			−0.397712	+	0.917510i	$0.630196\pi$
$258$	20.7283	+	15.0971i	1.29049	+	0.939904i
$259$		−	8.70190i		−	0.540710i
$260$	0.470586	+	1.45994i	0.0291845	+	0.0905416i
$261$		−	35.5070i		−	2.19783i
$262$	−6.60441	+	9.06784i	−0.408022	+	0.560213i
$263$	−22.3435			−1.37776			−0.688880	−	0.724876i	$-0.741897\pi$
$263$	−22.3435			−1.37776			−0.688880	+	0.724876i	$0.741897\pi$
$264$	−13.3942	+	40.7355i	−0.824353	+	2.50709i
$265$	−12.3904			−0.761133
$266$	2.66519	−	3.65929i	0.163413	−	0.224366i
$267$		−	46.2617i		−	2.83117i
$268$	0.0853886	−	0.0275235i	0.00521594	−	0.00168127i
$269$			12.8984i			0.786427i	0.919447	+	0.393213i	$0.128637\pi$
$269$			12.8984i			0.786427i	−0.919447	+	0.393213i	$0.871363\pi$
$270$	−22.5446	−	16.4200i	−1.37202	−	0.999290i
$271$	19.0653			1.15814			0.579068	−	0.815280i	$-0.303417\pi$
$271$	19.0653			1.15814			0.579068	+	0.815280i	$0.303417\pi$
$272$	1.15744	−	0.832676i	0.0701803	−	0.0504884i
$273$	2.62929			0.159132
$274$	9.66731	+	7.04103i	0.584024	+	0.425364i
$275$			4.42233i			0.266677i
$276$	30.6837	−	9.89035i	1.84694	−	0.595329i
$277$		−	16.5273i		−	0.993029i	−0.868028	−	0.496515i	$-0.834613\pi$
$277$		−	16.5273i		−	0.993029i	0.868028	−	0.496515i	$-0.165387\pi$
$278$	−5.28321	+	7.25384i	−0.316866	+	0.435057i
$279$	−18.6372			−1.11578
$280$	−2.68691	−	0.883477i	−0.160573	−	0.0527979i
$281$	−12.0500			−0.718843			−0.359422	−	0.933175i	$-0.617026\pi$
$281$	−12.0500			−0.718843			−0.359422	+	0.933175i	$0.617026\pi$
$282$	−9.49849	+	13.0414i	−0.565627	+	0.776604i
$283$			19.3067i			1.14766i	0.818974	+	0.573831i	$0.194543\pi$
$283$			19.3067i			1.14766i	−0.818974	+	0.573831i	$0.805457\pi$
$284$	−2.62425	−	8.14144i	−0.155720	−	0.483105i
$285$		−	10.9740i		−	0.650042i
$286$	−3.87724	−	2.82393i	−0.229266	−	0.166982i
$287$	−3.95885			−0.233683
$288$	−49.5119	−	0.289909i	−2.91752	−	0.0170830i
$289$	−16.8729			−0.992526
$290$	−4.63740	−	3.37758i	−0.272318	−	0.198338i
$291$			39.7785i			2.33186i
$292$	−1.39709	−	4.33433i	−0.0817587	−	0.253647i
$293$			11.6879i			0.682817i	0.939915	+	0.341408i	$0.110904\pi$
$293$			11.6879i			0.682817i	−0.939915	+	0.341408i	$0.889096\pi$
$294$	−2.85431	+	3.91897i	−0.166467	+	0.228559i
$295$	−5.63257			−0.327941
$296$	−23.3812	−	7.68793i	−1.35900	−	0.446852i
$297$	87.2152			5.06074
$298$	15.2879	−	20.9903i	0.885607	−	1.21594i
$299$			3.60614i			0.208549i
$300$	−6.52581	+	2.10348i	−0.376768	+	0.121444i
$301$		−	5.28922i		−	0.304865i
$302$	−11.8073	−	8.59965i	−0.679434	−	0.494855i
$303$	2.06368			0.118555
$304$	−7.47755	−	10.3940i	−0.428867	−	0.596137i
$305$	10.9857			0.629042
$306$	−3.56661	−	2.59768i	−0.203890	−	0.148500i
$307$		−	0.271250i		−	0.0154811i	−0.999970	−	0.00774054i	$-0.997536\pi$
$307$		−	0.271250i		−	0.0154811i	0.999970	−	0.00774054i	$-0.00246391\pi$
$308$	8.41815	−	2.71344i	0.479669	−	0.154613i
$309$		−	38.1095i		−	2.16797i
$310$	−1.77285	+	2.43411i	−0.100691	+	0.138248i
$311$	−19.3056			−1.09472			−0.547359	−	0.836898i	$-0.684367\pi$
$311$	−19.3056			−1.09472			−0.547359	+	0.836898i	$0.684367\pi$
$312$	2.32292	−	7.06465i	0.131509	−	0.399957i
$313$	−6.25868			−0.353761			−0.176881	−	0.984232i	$-0.556601\pi$
$313$	−6.25868			−0.353761			−0.176881	+	0.984232i	$0.556601\pi$
$314$	14.8063	−	20.3291i	0.835571	−	1.14724i
$315$			8.75270i			0.493159i
$316$	3.94751	+	12.2467i	0.222065	+	0.688930i
$317$		−	12.5189i		−	0.703129i	−0.936164	−	0.351564i	$-0.885650\pi$
$317$		−	12.5189i		−	0.703129i	0.936164	−	0.351564i	$-0.114350\pi$
$318$	48.5574	+	35.3659i	2.72296	+	1.98322i
$319$	17.9400			1.00445
$320$	−4.74764	+	6.43894i	−0.265401	+	0.359948i
$321$	−1.71125			−0.0955129
$322$	−5.37497	−	3.91477i	−0.299535	−	0.218162i
$323$		−	1.14105i		−	0.0634899i
$324$	25.3725	+	78.7152i	1.40958	+	4.37307i
$325$		−	0.766954i		−	0.0425430i
$326$	−3.71243	+	5.09716i	−0.205613	+	0.282306i
$327$	−23.0918			−1.27698
$328$	−3.49755	+	10.6370i	−0.193120	+	0.587333i
$329$	3.32777			0.183466
$330$	12.6227	−	17.3310i	0.694858	−	0.954038i
$331$			16.5821i			0.911433i	0.890125	+	0.455716i	$0.150617\pi$
$331$			16.5821i			0.911433i	−0.890125	+	0.455716i	$0.849383\pi$
$332$	18.3012	−	5.89907i	1.00441	−	0.323753i
$333$			76.1651i			4.17382i
$334$	−9.88858	−	7.20218i	−0.541079	−	0.394086i
$335$	−0.0448574			−0.00245082
$336$	8.00818	+	11.1316i	0.436882	+	0.607278i
$337$	28.5592			1.55572			0.777859	−	0.628439i	$-0.216306\pi$
$337$	28.5592			1.55572			0.777859	+	0.628439i	$0.216306\pi$
$338$	−14.1885	−	10.3340i	−0.771753	−	0.562094i
$339$		−	1.05127i		−	0.0570972i
$340$	−0.678542	+	0.218716i	−0.0367991	+	0.0118615i
$341$		−	9.41649i		−	0.509932i
$342$	−23.3276	+	32.0287i	−1.26141	+	1.73191i
$343$	1.00000			0.0539949
$344$	−14.2116	−	4.67290i	−0.766240	−	0.251946i
$345$	−16.1192			−0.867826
$346$	15.4887	−	21.2660i	0.832680	−	1.14327i
$347$		−	36.4715i		−	1.95789i	−0.204119	−	0.978946i	$-0.565433\pi$
$347$		−	36.4715i		−	1.95789i	0.204119	−	0.978946i	$-0.434567\pi$
$348$	8.53317	+	26.4732i	0.457426	+	1.41911i
$349$			24.7783i			1.32635i	0.748464	+	0.663175i	$0.230792\pi$
$349$			24.7783i			1.32635i	−0.748464	+	0.663175i	$0.769208\pi$
$350$	1.14315	+	0.832593i	0.0611039	+	0.0445040i
$351$	−15.1255			−0.807340
$352$	0.146477	−	25.0160i	0.00780727	−	1.33336i
$353$	−27.3290			−1.45457			−0.727287	−	0.686333i	$-0.759219\pi$
$353$	−27.3290			−1.45457			−0.727287	+	0.686333i	$0.759219\pi$
$354$	22.0739	+	16.0771i	1.17321	+	0.854490i
$355$			4.27696i			0.226998i
$356$	8.27985	+	25.6873i	0.438831	+	1.36142i
$357$			1.22203i			0.0646764i
$358$	−10.1507	+	13.9369i	−0.536483	+	0.736590i
$359$	−19.3124			−1.01927			−0.509634	−	0.860391i	$-0.670219\pi$
$359$	−19.3124			−1.01927			−0.509634	+	0.860391i	$0.670219\pi$
$360$	23.5177	+	7.73281i	1.23949	+	0.407555i
$361$	8.75317			0.460693
$362$	6.02382	−	8.27069i	0.316605	−	0.434698i
$363$			29.3353i			1.53970i
$364$	−1.45994	+	0.470586i	−0.0765216	+	0.0246654i
$365$			2.27696i			0.119182i
$366$	−43.0528	−	31.3568i	−2.25040	−	1.63904i
$367$	−34.5493			−1.80346			−0.901729	−	0.432302i	$-0.857701\pi$
$367$	−34.5493			−1.80346			−0.901729	+	0.432302i	$0.857701\pi$
$368$	−15.2673	+	10.9834i	−0.795862	+	0.572551i
$369$	34.6506			1.80384
$370$	9.94756	+	7.24514i	0.517149	+	0.376657i
$371$		−	12.3904i		−	0.643275i
$372$	13.8954	−	4.47895i	0.720445	−	0.232223i
$373$		−	11.4633i		−	0.593548i	−0.954948	−	0.296774i	$-0.904089\pi$
$373$		−	11.4633i		−	0.593548i	0.954948	−	0.296774i	$-0.0959107\pi$
$374$	1.31249	−	1.80204i	0.0678671	−	0.0931814i
$375$	3.42822			0.177033
$376$	2.94000	−	8.94140i	0.151619	−	0.461117i
$377$	−3.11130			−0.160240
$378$	16.4200	−	22.5446i	0.844555	−	1.15957i
$379$		−	5.56041i		−	0.285619i	−0.989750	−	0.142810i	$-0.954386\pi$
$379$		−	5.56041i		−	0.285619i	0.989750	−	0.142810i	$-0.0456137\pi$
$380$	1.96410	+	6.09341i	0.100756	+	0.312585i
$381$			1.62039i			0.0830149i
$382$	11.1122	+	8.09336i	0.568548	+	0.414092i
$383$	−11.3097			−0.577899			−0.288950	−	0.957344i	$-0.593306\pi$
$383$	−11.3097			−0.577899			−0.288950	+	0.957344i	$0.593306\pi$
$384$	36.9846	−	11.6827i	1.88736	−	0.596181i
$385$	−4.42233			−0.225383
$386$	−9.86885	−	7.18781i	−0.502311	−	0.365850i
$387$			46.2949i			2.35330i
$388$	−7.11949	−	22.0874i	−0.361438	−	1.12132i
$389$			36.6617i			1.85882i	0.369048	+	0.929411i	$0.379684\pi$
$389$			36.6617i			1.85882i	−0.369048	+	0.929411i	$0.620316\pi$
$390$	−2.18913	+	3.00567i	−0.110851	+	0.152198i
$391$	−1.67604			−0.0847610
$392$	0.883477	−	2.68691i	0.0446223	−	0.135709i
$393$	−27.1938			−1.37175
$394$	7.83872	−	10.7625i	0.394909	−	0.542209i
$395$		−	6.43359i		−	0.323709i
$396$	−73.6816	+	23.7499i	−3.70264	+	1.19348i
$397$		−	11.4293i		−	0.573622i	−0.957987	−	0.286811i	$-0.907405\pi$
$397$		−	11.4293i		−	0.573622i	0.957987	−	0.286811i	$-0.0925951\pi$
$398$	−18.2443	−	13.2879i	−0.914505	−	0.666065i
$399$	10.9740			0.549385
$400$	3.24705	−	2.33596i	0.162352	−	0.116798i
$401$	−0.585473			−0.0292371			−0.0146186	−	0.999893i	$-0.504653\pi$
$401$	−0.585473			−0.0292371			−0.0146186	+	0.999893i	$0.504653\pi$
$402$	0.175795	+	0.128037i	0.00876785	+	0.00638592i
$403$			1.63308i			0.0813495i
$404$	−1.14588	+	0.369353i	−0.0570095	+	0.0183760i
$405$		−	41.3517i		−	2.05478i
$406$	3.37758	−	4.63740i	0.167626	−	0.230150i
$407$	−38.4827			−1.90752
$408$	3.28347	+	1.07963i	0.162556	+	0.0534497i
$409$	33.0764			1.63552			0.817761	−	0.575557i	$-0.195215\pi$
$409$	33.0764			1.63552			0.817761	+	0.575557i	$0.195215\pi$
$410$	3.29611	−	4.52555i	0.162783	−	0.223501i
$411$			28.9916i			1.43005i
$412$	6.82077	+	21.1607i	0.336035	+	1.04251i
$413$		−	5.63257i		−	0.277161i
$414$	47.0455	+	34.2648i	2.31216	+	1.68402i
$415$	−9.61422			−0.471944
$416$	−0.0254032	+	4.33847i	−0.00124550	+	0.212711i
$417$	−21.7538			−1.06529
$418$	−16.1826	−	11.7863i	−0.791517	−	0.576488i
$419$		−	12.0977i		−	0.591013i	−0.955341	−	0.295506i	$-0.904512\pi$
$419$		−	12.0977i		−	0.591013i	0.955341	−	0.295506i	$-0.0954883\pi$
$420$	−2.10348	−	6.52581i	−0.102639	−	0.318427i
$421$		−	1.62244i		−	0.0790728i	−0.999218	−	0.0395364i	$-0.987412\pi$
$421$		−	1.62244i		−	0.0790728i	0.999218	−	0.0395364i	$-0.0125881\pi$
$422$	21.2385	−	29.1604i	1.03387	−	1.41951i
$423$	−29.1269			−1.41620
$424$	−33.2917	−	10.9466i	−1.61679	−	0.531613i
$425$	0.356460			0.0172909
$426$	12.2078	−	16.7613i	0.591470	−	0.812086i
$427$			10.9857i			0.531638i
$428$	0.950192	−	0.306277i	0.0459292	−	0.0148045i
$429$		−	11.6276i		−	0.561385i
$430$	6.04636	+	4.40377i	0.291581	+	0.212368i
$431$	22.9788			1.10685			0.553424	−	0.832900i	$-0.313321\pi$
$431$	22.9788			1.10685			0.553424	+	0.832900i	$0.313321\pi$
$432$	−46.0687	−	64.0367i	−2.21648	−	3.08097i
$433$	−12.8060			−0.615416			−0.307708	−	0.951481i	$-0.599562\pi$
$433$	−12.8060			−0.615416			−0.307708	+	0.951481i	$0.599562\pi$
$434$	−2.43411	−	1.77285i	−0.116841	−	0.0850993i
$435$		−	13.9072i		−	0.666801i
$436$	12.8220	−	4.13293i	0.614060	−	0.197931i
$437$			15.0511i			0.719992i
$438$	6.49917	−	8.92334i	0.310542	−	0.426374i
$439$	−8.91025			−0.425263			−0.212632	−	0.977132i	$-0.568203\pi$
$439$	−8.91025			−0.425263			−0.212632	+	0.977132i	$0.568203\pi$
$440$	−3.90703	+	11.8824i	−0.186260	+	0.566471i
$441$	−8.75270			−0.416795
$442$	−0.227622	+	0.312524i	−0.0108269	+	0.0148652i
$443$			17.7956i			0.845496i	0.906247	+	0.422748i	$0.138934\pi$
$443$			17.7956i			0.845496i	−0.906247	+	0.422748i	$0.861066\pi$
$444$	−18.3043	−	56.7869i	−0.868682	−	2.69499i
$445$		−	13.4944i		−	0.639695i
$446$	−30.7222	−	22.3760i	−1.45474	−	1.05953i
$447$	62.9485			2.97736
$448$	−6.43894	−	4.74764i	−0.304211	−	0.224305i
$449$	13.9064			0.656282			0.328141	−	0.944629i	$-0.393578\pi$
$449$	13.9064			0.656282			0.328141	+	0.944629i	$0.393578\pi$
$450$	−10.0056	−	7.28744i	−0.471670	−	0.343533i
$451$			17.5073i			0.824388i
$452$	0.188155	+	0.583729i	0.00885005	+	0.0274563i
$453$		−	35.4093i		−	1.66367i
$454$	6.94736	−	9.53871i	0.326056	−	0.447674i
$455$	0.766954			0.0359554
$456$	9.69525	−	29.4860i	0.454022	−	1.38081i
$457$	20.2132			0.945536			0.472768	−	0.881187i	$-0.343255\pi$
$457$	20.2132			0.945536			0.472768	+	0.881187i	$0.343255\pi$
$458$	8.64046	−	11.8633i	0.403742	−	0.554337i
$459$		−	7.02995i		−	0.328130i
$460$	8.95033	−	2.88498i	0.417311	−	0.134513i
$461$		−	22.0006i		−	1.02467i	−0.858786	−	0.512335i	$-0.828781\pi$
$461$		−	22.0006i		−	1.02467i	0.858786	−	0.512335i	$-0.171219\pi$
$462$	17.3310	+	12.6227i	0.806309	+	0.587262i
$463$	8.79116			0.408560			0.204280	−	0.978912i	$-0.434515\pi$
$463$	8.79116			0.408560			0.204280	+	0.978912i	$0.434515\pi$
$464$	−9.47626	−	13.1723i	−0.439924	−	0.611507i
$465$	−7.29973			−0.338517
$466$	−15.1431	−	11.0292i	−0.701488	−	0.510917i
$467$			27.0707i			1.25268i	0.779549	+	0.626341i	$0.215448\pi$
$467$			27.0707i			1.25268i	−0.779549	+	0.626341i	$0.784552\pi$
$468$	12.7784	−	4.11890i	0.590682	−	0.190396i
$469$		−	0.0448574i		−	0.00207132i
$470$	−2.77067	+	3.80413i	−0.127802	+	0.175471i
$471$	60.9655			2.80914
$472$	−15.1342	−	4.97625i	−0.696608	−	0.229050i
$473$	−23.3907			−1.07550
$474$	−18.3635	+	25.2130i	−0.843463	+	1.15807i
$475$		−	3.20107i		−	0.146875i
$476$	−0.218716	−	0.678542i	−0.0100248	−	0.0311009i
$477$			108.449i			4.96554i
$478$	−18.6275	−	13.5671i	−0.852004	−	0.620543i
$479$	−9.06701			−0.414282			−0.207141	−	0.978311i	$-0.566416\pi$
$479$	−9.06701			−0.414282			−0.207141	+	0.978311i	$0.566416\pi$
$480$	−19.3926	−	0.113550i	−0.885148	−	0.00518284i
$481$	6.67396			0.304306
$482$	7.58935	+	5.52757i	0.345685	+	0.251774i
$483$		−	16.1192i		−	0.733447i
$484$	−5.25038	−	16.2887i	−0.238654	−	0.740397i
$485$			11.6033i			0.526877i
$486$	−68.7707	+	94.4220i	−3.11950	+	4.28307i
$487$	16.7119			0.757287			0.378644	−	0.925543i	$-0.376391\pi$
$487$	16.7119			0.757287			0.378644	+	0.925543i	$0.376391\pi$
$488$	29.5177	+	9.70566i	1.33620	+	0.439354i
$489$	−15.2860			−0.691258
$490$	−0.832593	+	1.14315i	−0.0376127	+	0.0516422i
$491$		−	12.7970i		−	0.577521i	−0.957401	−	0.288760i	$-0.906757\pi$
$491$		−	12.7970i		−	0.577521i	0.957401	−	0.288760i	$-0.0932431\pi$
$492$	−25.8347	+	8.32735i	−1.16472	+	0.375426i
$493$		−	1.44605i		−	0.0651269i
$494$	2.80651	+	2.04408i	0.126271	+	0.0919673i
$495$	38.7073			1.73977
$496$	−6.91395	+	4.97397i	−0.310446	+	0.223338i
$497$	−4.27696			−0.191848
$498$	37.6778	+	27.4420i	1.68838	+	1.22971i
$499$		−	11.9078i		−	0.533064i	−0.963826	−	0.266532i	$-0.914122\pi$
$499$		−	11.9078i		−	0.533064i	0.963826	−	0.266532i	$-0.0858778\pi$
$500$	−1.90356	+	0.613577i	−0.0851296	+	0.0274400i
$501$		−	29.6551i		−	1.32489i
$502$	−3.91872	+	5.38040i	−0.174901	+	0.240139i
$503$	15.7627			0.702823			0.351412	−	0.936221i	$-0.385702\pi$
$503$	15.7627			0.702823			0.351412	+	0.936221i	$0.385702\pi$
$504$	−7.73281	+	23.5177i	−0.344447	+	1.04756i
$505$	0.601967			0.0267872
$506$	−17.3124	+	23.7699i	−0.769630	+	1.05670i
$507$		−	42.5503i		−	1.88973i
$508$	−0.290014	−	0.899736i	−0.0128673	−	0.0399193i
$509$			0.329139i			0.0145888i	0.999973	+	0.00729441i	$0.00232190\pi$
$509$			0.329139i			0.0145888i	−0.999973	+	0.00729441i	$0.997678\pi$
$510$	−1.39696	−	1.01745i	−0.0618583	−	0.0450534i
$511$	−2.27696			−0.100727
$512$	−18.4451	+	13.1064i	−0.815167	+	0.579226i
$513$	−63.1300			−2.78726
$514$	14.5770	+	10.6169i	0.642963	+	0.468292i
$515$		−	11.1164i		−	0.489847i
$516$	−11.1258	−	34.5164i	−0.489784	−	1.51950i
$517$		−	14.7165i		−	0.647230i
$518$	−7.24514	+	9.94756i	−0.318333	+	0.437071i
$519$	63.7753			2.79942
$520$	0.677586	−	2.06073i	0.0297141	−	0.0903692i
$521$	6.75606			0.295989			0.147994	−	0.988988i	$-0.452718\pi$
$521$	6.75606			0.295989			0.147994	+	0.988988i	$0.452718\pi$
$522$	−29.5629	+	40.5898i	−1.29393	+	1.77657i
$523$			20.1810i			0.882452i	0.897396	+	0.441226i	$0.145456\pi$
$523$			20.1810i			0.882452i	−0.897396	+	0.441226i	$0.854544\pi$
$524$	15.0996	−	4.86710i	0.659631	−	0.212620i
$525$			3.42822i			0.149620i
$526$	25.5419	+	18.6030i	1.11368	+	0.811131i
$527$	−0.759013			−0.0330631
$528$	49.2276	−	35.4148i	2.14236	−	1.54123i
$529$	−0.892136			−0.0387885
$530$	14.1640	+	10.3161i	0.615245	+	0.448104i
$531$			49.3002i			2.13945i
$532$	−6.09341	+	1.96410i	−0.264183	+	0.0851546i
$533$		−	3.03625i		−	0.131515i
$534$	−38.5172	+	52.8840i	−1.66680	+	2.28852i
$535$	−0.499167			−0.0215809
$536$	−0.120528	−	0.0396305i	−0.00520601	−	0.00171178i
$537$	−41.7959			−1.80363
$538$	10.7391	−	14.7447i	0.462995	−	0.635691i
$539$		−	4.42233i		−	0.190483i
$540$	12.1007	+	37.5410i	0.520731	+	1.61551i
$541$			2.45720i			0.105643i	0.998604	+	0.0528216i	$0.0168215\pi$
$541$			2.45720i			0.105643i	−0.998604	+	0.0528216i	$0.983179\pi$
$542$	−21.7945	−	15.8736i	−0.936153	−	0.681832i
$543$	24.8032			1.06441
$544$	−2.01641	−	0.0118068i	−0.0864529	−	0.000506211i
$545$	−6.73579			−0.288530
$546$	−3.00567	−	2.18913i	−0.128631	−	0.0936860i
$547$		−	0.331277i		−	0.0141644i	−0.999975	−	0.00708219i	$-0.997746\pi$
$547$		−	0.331277i		−	0.0141644i	0.999975	−	0.00708219i	$-0.00225435\pi$
$548$	−5.18887	−	16.0979i	−0.221657	−	0.687667i
$549$		−	96.1550i		−	4.10380i
$550$	3.68200	−	5.05538i	0.157001	−	0.215562i
$551$	−12.9857			−0.553211
$552$	−43.3107	−	14.2409i	−1.84342	−	0.606133i
$553$	6.43359			0.273584
$554$	−13.7605	+	18.8932i	−0.584628	+	0.802694i
$555$			29.8320i			1.26630i
$556$	12.0790	−	3.89345i	0.512264	−	0.165119i
$557$			33.4448i			1.41710i	0.705660	+	0.708550i	$0.250651\pi$
$557$			33.4448i			1.41710i	−0.705660	+	0.708550i	$0.749349\pi$
$558$	21.3051	+	15.5172i	0.901915	+	0.656895i
$559$	4.05659			0.171575
$560$	2.33596	+	3.24705i	0.0987122	+	0.137213i
$561$	5.40420			0.228165
$562$	13.7749	+	10.0328i	0.581061	+	0.423206i
$563$		−	0.0576848i		−	0.00243112i	−0.999999	−	0.00121556i	$-0.999613\pi$
$563$		−	0.0576848i		−	0.00243112i	0.999999	−	0.00121556i	$-0.000386925\pi$
$564$	21.7164	−	6.99989i	0.914424	−	0.294748i
$565$		−	0.306652i		−	0.0129009i
$566$	16.0746	−	22.0704i	0.675666	−	0.927688i
$567$	41.3517			1.73661
$568$	−3.77860	+	11.4918i	−0.158546	+	0.482185i
$569$	46.5307			1.95067			0.975334	−	0.220736i	$-0.0708458\pi$
$569$	46.5307			1.95067			0.975334	+	0.220736i	$0.0708458\pi$
$570$	−9.13685	+	12.5449i	−0.382700	+	0.525447i
$571$		−	28.1127i		−	1.17648i	−0.808686	−	0.588241i	$-0.799821\pi$
$571$		−	28.1127i		−	1.17648i	0.808686	−	0.588241i	$-0.200179\pi$
$572$	2.08109	+	6.45633i	0.0870145	+	0.269953i
$573$			33.3246i			1.39216i
$574$	4.52555	+	3.29611i	0.188893	+	0.137577i
$575$	−4.70190			−0.196083
$576$	56.3581	+	41.5547i	2.34825	+	1.73145i
$577$	7.65344			0.318617			0.159308	−	0.987229i	$-0.449074\pi$
$577$	7.65344			0.318617			0.159308	+	0.987229i	$0.449074\pi$
$578$	19.2883	+	14.0483i	0.802286	+	0.584332i
$579$		−	29.5960i		−	1.22997i
$580$	2.48910	+	7.72214i	0.103354	+	0.320644i
$581$		−	9.61422i		−	0.398865i
$582$	33.1193	−	45.4728i	1.37284	−	1.88491i
$583$	−54.7942			−2.26934
$584$	−2.01164	+	6.11799i	−0.0832424	+	0.253164i
$585$	−6.71292			−0.277545
$586$	9.73130	−	13.3611i	0.401996	−	0.551940i
$587$		−	8.40138i		−	0.346762i	−0.984855	−	0.173381i	$-0.944531\pi$
$587$		−	8.40138i		−	0.346762i	0.984855	−	0.173381i	$-0.0554692\pi$
$588$	6.52581	−	2.10348i	0.269120	−	0.0867460i
$589$			6.81605i			0.280850i
$590$	6.43887	+	4.68964i	0.265084	+	0.193069i
$591$	32.2761			1.32766
$592$	20.3273	+	28.2555i	0.835445	+	1.16129i
$593$	40.0189			1.64338			0.821690	−	0.569935i	$-0.193032\pi$
$593$	40.0189			1.64338			0.821690	+	0.569935i	$0.193032\pi$
$594$	−99.6999	−	72.6147i	−4.09074	−	2.97942i
$595$			0.356460i			0.0146135i
$596$	−34.9528	+	11.2664i	−1.43172	+	0.461490i
$597$		−	54.7134i		−	2.23927i
$598$	3.00245	−	4.12236i	0.122779	−	0.168576i
$599$	−46.8331			−1.91355			−0.956774	−	0.290832i	$-0.906068\pi$
$599$	−46.8331			−1.91355			−0.956774	+	0.290832i	$0.906068\pi$
$600$	9.21131	+	3.02875i	0.376050	+	0.123648i
$601$	−22.7703			−0.928822			−0.464411	−	0.885620i	$-0.653734\pi$
$601$	−22.7703			−0.928822			−0.464411	+	0.885620i	$0.653734\pi$
$602$	−4.40377	+	6.04636i	−0.179484	+	0.246431i
$603$			0.392624i			0.0159889i
$604$	6.33749	+	19.6614i	0.257869	+	0.800010i
$605$			8.55700i			0.347892i
$606$	−2.35909	−	1.71820i	−0.0958314	−	0.0697972i
$607$	23.3825			0.949067			0.474534	−	0.880237i	$-0.342617\pi$
$607$	23.3825			0.949067			0.474534	+	0.880237i	$0.342617\pi$
$608$	−0.106026	+	18.1077i	−0.00429994	+	0.734363i
$609$	13.9072			0.563550
$610$	−12.5583	−	9.14666i	−0.508472	−	0.370337i
$611$			2.55224i			0.103253i
$612$	1.91436	+	5.93908i	0.0773833	+	0.240073i
$613$		−	33.1233i		−	1.33784i	−0.743336	−	0.668918i	$-0.766758\pi$
$613$		−	33.1233i		−	1.33784i	0.743336	−	0.668918i	$-0.233242\pi$
$614$	−0.225841	+	0.310079i	−0.00911421	+	0.0125138i
$615$	13.5718			0.547268
$616$	−11.8824	−	3.90703i	−0.478755	−	0.157419i
$617$	−37.1000			−1.49359			−0.746794	−	0.665055i	$-0.768408\pi$
$617$	−37.1000			−1.49359			−0.746794	+	0.665055i	$0.768408\pi$
$618$	−31.7297	+	43.5648i	−1.27635	+	1.75243i
$619$			33.9936i			1.36632i	0.730271	+	0.683158i	$0.239394\pi$
$619$			33.9936i			1.36632i	−0.730271	+	0.683158i	$0.760606\pi$
$620$	4.05325	−	1.30649i	0.162782	−	0.0524701i
$621$			92.7287i			3.72107i
$622$	22.0691	+	16.0737i	0.884892	+	0.644496i
$623$	13.4944			0.540641
$624$	−8.53742	+	6.14190i	−0.341770	+	0.245873i
$625$	1.00000			0.0400000
$626$	7.15460	+	5.21093i	0.285955	+	0.208271i
$627$		−	48.5305i		−	1.93812i
$628$	−33.8517	+	10.9115i	−1.35083	+	0.435416i
$629$			3.10188i			0.123680i
$630$	7.28744	−	10.0056i	0.290339	−	0.398634i
$631$	0.197223			0.00785133			0.00392567	−	0.999992i	$-0.498750\pi$
$631$	0.197223			0.00785133			0.00392567	+	0.999992i	$0.498750\pi$
$632$	5.68393	−	17.2865i	0.226095	−	0.687618i
$633$	87.4501			3.47583
$634$	−10.4231	+	14.3109i	−0.413955	+	0.568359i
$635$			0.472661i			0.0187570i
$636$	−26.0628	−	80.8571i	−1.03346	−	3.20619i
$637$			0.766954i			0.0303878i
$638$	−20.5081	−	14.9368i	−0.811925	−	0.591352i
$639$	37.4350			1.48091
$640$	10.7883	−	3.40781i	0.426444	−	0.134705i
$641$	−7.88234			−0.311334			−0.155667	−	0.987810i	$-0.549753\pi$
$641$	−7.88234			−0.311334			−0.155667	+	0.987810i	$0.549753\pi$
$642$	1.95622	+	1.42478i	0.0772058	+	0.0562315i
$643$		−	13.8540i		−	0.546350i	−0.961964	−	0.273175i	$-0.911926\pi$
$643$		−	13.8540i		−	0.546350i	0.961964	−	0.273175i	$-0.0880737\pi$
$644$	2.88498	+	8.95033i	0.113684	+	0.352692i
$645$			18.1326i			0.713971i
$646$	−0.950033	+	1.30439i	−0.0373786	+	0.0513207i
$647$	−22.5097			−0.884950			−0.442475	−	0.896781i	$-0.645899\pi$
$647$	−22.5097			−0.884950			−0.442475	+	0.896781i	$0.645899\pi$
$648$	36.5333	−	111.108i	1.43516	−	4.36474i
$649$	−24.9091			−0.977768
$650$	−0.638561	+	0.876742i	−0.0250464	+	0.0343887i
$651$		−	7.29973i		−	0.286099i
$652$	8.48773	−	2.73587i	0.332405	−	0.107145i
$653$			14.9861i			0.586450i	0.956043	+	0.293225i	$0.0947285\pi$
$653$			14.9861i			0.586450i	−0.956043	+	0.293225i	$0.905271\pi$
$654$	26.3973	+	19.2261i	1.03222	+	0.751798i
$655$	−7.93234			−0.309942
$656$	12.8546	−	9.24769i	0.501886	−	0.361062i
$657$	19.9296			0.777527
$658$	−3.80413	−	2.77067i	−0.148300	−	0.108012i
$659$			36.8133i			1.43404i	0.697052	+	0.717021i	$0.254495\pi$
$659$			36.8133i			1.43404i	−0.697052	+	0.717021i	$0.745505\pi$
$660$	−28.8593	+	9.30228i	−1.12335	+	0.362091i
$661$			15.5005i			0.602898i	0.953482	+	0.301449i	$0.0974704\pi$
$661$			15.5005i			0.602898i	−0.953482	+	0.301449i	$0.902530\pi$
$662$	13.8061	−	18.9558i	0.536590	−	0.736737i
$663$	−0.937237			−0.0363993
$664$	−25.8325	−	8.49394i	−1.00250	−	0.329629i
$665$	3.20107			0.124132
$666$	63.4146	−	87.0681i	2.45726	−	3.37382i
$667$			19.0742i			0.738555i
$668$	5.30763	+	16.4663i	0.205358	+	0.637101i
$669$		−	92.1338i		−	3.56210i
$670$	0.0512787	+	0.0373480i	0.00198107	+	0.00144288i
$671$	48.5826			1.87551
$672$	0.113550	−	19.3926i	0.00438030	−	0.748086i
$673$	−24.6330			−0.949534			−0.474767	−	0.880111i	$-0.657468\pi$
$673$	−24.6330			−0.949534			−0.474767	+	0.880111i	$0.657468\pi$
$674$	−32.6474	−	23.7782i	−1.25753	−	0.915901i
$675$		−	19.7215i		−	0.759082i
$676$	7.61559	+	23.6265i	0.292907	+	0.908712i
$677$			27.5087i			1.05724i	0.848857	+	0.528622i	$0.177291\pi$
$677$			27.5087i			1.05724i	−0.848857	+	0.528622i	$0.822709\pi$
$678$	−0.875281	+	1.20176i	−0.0336150	+	0.0461533i
$679$	−11.6033			−0.445292
$680$	0.957776	+	0.314925i	0.0367290	+	0.0120768i
$681$	28.6059			1.09618
$682$	−7.84011	+	10.7645i	−0.300213	+	0.412192i
$683$			31.8101i			1.21718i	0.793486	+	0.608589i	$0.208264\pi$
$683$			31.8101i			1.21718i	−0.793486	+	0.608589i	$0.791736\pi$
$684$	53.3338	−	17.1912i	2.03927	−	0.657322i
$685$			8.45674i			0.323116i
$686$	−1.14315	−	0.832593i	−0.0436456	−	0.0317886i
$687$	35.5773			1.35736
$688$	12.3554	+	17.1743i	0.471045	+	0.654765i
$689$	9.50283			0.362029
$690$	18.4266	+	13.4207i	0.701488	+	0.510917i
$691$			28.8712i			1.09831i	0.835720	+	0.549156i	$0.185051\pi$
$691$			28.8712i			1.09831i	−0.835720	+	0.549156i	$0.814949\pi$
$692$	−35.4119	+	11.4144i	−1.34616	+	0.433910i
$693$			38.7073i			1.47037i
$694$	−30.3659	+	41.6923i	−1.15267	+	1.58262i
$695$	−6.34549			−0.240698
$696$	12.2867	−	37.3675i	0.465727	−	1.41641i
$697$	1.41117			0.0534519
$698$	20.6302	−	28.3252i	0.780865	−	1.07213i
$699$		−	45.4129i		−	1.71768i
$700$	−0.613577	−	1.90356i	−0.0231910	−	0.0719476i
$701$		−	35.3524i		−	1.33524i	−0.744502	−	0.667620i	$-0.767313\pi$
$701$		−	35.3524i		−	1.33524i	0.744502	−	0.667620i	$-0.232687\pi$
$702$	17.2907	+	12.5934i	0.652596	+	0.475307i
$703$	27.8554			1.05058
$704$	−20.9956	+	28.4751i	−0.791303	+	1.07320i
$705$	−11.4083			−0.429662
$706$	31.2411	+	22.7539i	1.17577	+	0.856355i
$707$			0.601967i			0.0226393i
$708$	−11.8480	−	36.7571i	−0.445275	−	1.38142i
$709$		−	15.4314i		−	0.579539i	−0.957097	−	0.289769i	$-0.906421\pi$
$709$		−	15.4314i		−	0.579539i	0.957097	−	0.289769i	$-0.0935786\pi$
$710$	3.56097	−	4.88920i	0.133641	−	0.183489i
$711$	−56.3113			−2.11184
$712$	11.9220	−	36.2582i	0.446795	−	1.35883i
$713$	10.0118			0.374944
$714$	1.01745	−	1.39696i	0.0380771	−	0.0522798i
$715$		−	3.39172i		−	0.126843i
$716$	23.2076	−	7.48056i	0.867309	−	0.279562i
$717$		−	55.8627i		−	2.08623i
$718$	22.0769	+	16.0794i	0.823904	+	0.600076i
$719$	−19.5671			−0.729731			−0.364865	−	0.931060i	$-0.618885\pi$
$719$	−19.5671			−0.729731			−0.364865	+	0.931060i	$0.618885\pi$
$720$	−20.4459	−	28.4204i	−0.761975	−	1.05917i
$721$	11.1164			0.413996
$722$	−10.0062	−	7.28783i	−0.372391	−	0.271225i
$723$			22.7599i			0.846450i
$724$	−13.7722	+	4.43924i	−0.511841	+	0.164983i
$725$		−	4.05669i		−	0.150662i
$726$	24.4244	−	33.5346i	0.906474	−	1.24459i
$727$	−30.9531			−1.14799			−0.573994	−	0.818860i	$-0.694607\pi$
$727$	−30.9531			−1.14799			−0.573994	+	0.818860i	$0.694607\pi$
$728$	2.06073	+	0.677586i	0.0763759	+	0.0251130i
$729$	−159.110			−5.89295
$730$	1.89578	−	2.60291i	0.0701661	−	0.0963379i
$731$			1.88540i			0.0697339i
$732$	23.1083	+	71.6909i	0.854107	+	2.64977i
$733$		−	37.4907i		−	1.38475i	−0.721538	−	0.692374i	$-0.756565\pi$
$733$		−	37.4907i		−	1.38475i	0.721538	−	0.692374i	$-0.243435\pi$
$734$	39.4950	+	28.7655i	1.45779	+	1.06175i
$735$	−3.42822			−0.126452
$736$	26.5975	+	0.155737i	0.980397	+	0.00574056i
$737$	−0.198374			−0.00730722
$738$	−39.6108	−	28.8498i	−1.45809	−	1.06198i
$739$		−	8.05784i		−	0.296413i	−0.988956	−	0.148206i	$-0.952650\pi$
$739$		−	8.05784i		−	0.296413i	0.988956	−	0.148206i	$-0.0473500\pi$
$740$	−5.33929	−	16.5645i	−0.196276	−	0.608925i
$741$			8.41653i			0.309189i
$742$	−10.3161	+	14.1640i	−0.378717	+	0.519977i
$743$	−28.5920			−1.04894			−0.524469	−	0.851430i	$-0.675736\pi$
$743$	−28.5920			−1.04894			−0.524469	+	0.851430i	$0.675736\pi$
$744$	−19.6137	−	6.44915i	−0.719073	−	0.236437i
$745$	18.3618			0.672726
$746$	−9.54427	+	13.1043i	−0.349441	+	0.479781i
$747$			84.1504i			3.07890i
$748$	−3.00074	+	0.967234i	−0.109718	+	0.0353656i
$749$		−	0.499167i		−	0.0182392i
$750$	−3.91897	−	2.85431i	−0.143100	−	0.104225i
$751$	−15.1551			−0.553016			−0.276508	−	0.961012i	$-0.589177\pi$
$751$	−15.1551			−0.553016			−0.276508	+	0.961012i	$0.589177\pi$
$752$	−10.8054	+	7.77352i	−0.394033	+	0.283471i
$753$	−16.1354			−0.588008
$754$	3.55668	+	2.59045i	0.129526	+	0.0943385i
$755$		−	10.3288i		−	0.375902i
$756$	−37.5410	+	12.1007i	−1.36535	+	0.440098i
$757$		−	29.4386i		−	1.06996i	−0.844863	−	0.534982i	$-0.820318\pi$
$757$		−	29.4386i		−	1.06996i	0.844863	−	0.534982i	$-0.179682\pi$
$758$	−4.62956	+	6.35638i	−0.168153	+	0.230874i
$759$	−71.2842			−2.58745
$760$	2.82807	−	8.60097i	0.102585	−	0.311990i
$761$	46.5407			1.68710			0.843549	−	0.537053i	$-0.180462\pi$
$761$	46.5407			1.68710			0.843549	+	0.537053i	$0.180462\pi$
$762$	1.34912	−	1.85234i	0.0488736	−	0.0671033i
$763$		−	6.73579i		−	0.243852i
$764$	−5.96438	−	18.5038i	−0.215784	−	0.669445i
$765$		−	3.11999i		−	0.112804i
$766$	12.9287	+	9.41638i	0.467132	+	0.340228i
$767$	4.31992			0.155983
$768$	−52.0058	−	17.4380i	−1.87660	−	0.629241i
$769$	16.2312			0.585310			0.292655	−	0.956218i	$-0.405461\pi$
$769$	16.2312			0.585310			0.292655	+	0.956218i	$0.405461\pi$
$770$	5.05538	+	3.68200i	0.182183	+	0.132690i
$771$			43.7154i			1.57437i
$772$	5.29704	+	16.4335i	0.190645	+	0.591454i
$773$		−	7.14496i		−	0.256986i	−0.991710	−	0.128493i	$-0.958986\pi$
$773$		−	7.14496i		−	0.256986i	0.991710	−	0.128493i	$-0.0410141\pi$
$774$	38.5449	−	52.9220i	1.38547	−	1.90224i
$775$	−2.12931			−0.0764869
$776$	−10.2512	+	31.1769i	−0.367997	+	1.11918i
$777$	−29.8320			−1.07022
$778$	30.5243	−	41.9097i	1.09435	−	1.50254i
$779$		−	12.6725i		−	0.454040i
$780$	5.00500	−	1.61327i	0.179208	−	0.0577644i
$781$			18.9141i			0.676801i
$782$	1.91596	+	1.39546i	0.0685147	+	0.0499016i
$783$	−80.0043			−2.85912
$784$	−3.24705	+	2.33596i	−0.115966	+	0.0834270i
$785$	17.7834			0.634717
$786$	31.0866	+	22.6414i	1.10882	+	0.807591i
$787$			10.9982i			0.392042i	0.980600	+	0.196021i	$0.0628022\pi$
$787$			10.9982i			0.392042i	−0.980600	+	0.196021i	$0.937198\pi$
$788$	−17.9216	+	5.77672i	−0.638432	+	0.205787i
$789$			76.5985i			2.72698i
$790$	−5.35656	+	7.35455i	−0.190578	+	0.261663i
$791$	0.306652			0.0109033
$792$	104.003	+	34.1970i	3.69559	+	1.21514i
$793$	−8.42556			−0.299201
$794$	−9.51598	+	13.0654i	−0.337710	+	0.463675i
$795$			42.4769i			1.50650i
$796$	9.79252	+	30.3802i	0.347087	+	1.07680i
$797$			11.2185i			0.397380i	0.980062	+	0.198690i	$0.0636687\pi$
$797$			11.2185i			0.397380i	−0.980062	+	0.198690i	$0.936331\pi$
$798$	−12.5449	−	9.13685i	−0.444084	−	0.323441i
$799$	−1.18622			−0.0419653
$800$	−5.65676	−	0.0331222i	−0.199997	−	0.00117105i
$801$	−118.112			−4.17329
$802$	0.669282	+	0.487460i	0.0236332	+	0.0172128i
$803$			10.0695i			0.355344i
$804$	−0.0943567	−	0.292731i	−0.00332770	−	0.0103238i
$805$		−	4.70190i		−	0.165720i
$806$	1.35969	−	1.86685i	0.0478931	−	0.0657571i
$807$	44.2184			1.55656
$808$	1.61743	+	0.531824i	0.0569009	+	0.0187095i
$809$	1.99459			0.0701262			0.0350631	−	0.999385i	$-0.488837\pi$
$809$	1.99459			0.0701262			0.0350631	+	0.999385i	$0.488837\pi$
$810$	−34.4291	+	47.2711i	−1.20972	+	1.66094i
$811$			22.8245i			0.801477i	0.916192	+	0.400739i	$0.131246\pi$
$811$			22.8245i			0.801477i	−0.916192	+	0.400739i	$0.868754\pi$
$812$	−7.72214	+	2.48910i	−0.270994	+	0.0873501i
$813$		−	65.3601i		−	2.29228i
$814$	43.9914	+	32.0404i	1.54190	+	1.12302i
$815$	−4.45888			−0.156188
$816$	−2.85460	−	3.96797i	−0.0999309	−	0.138907i
$817$	16.9311			0.592346
$818$	−37.8112	−	27.5392i	−1.32204	−	0.962885i
$819$		−	6.71292i		−	0.234568i
$820$	−7.53588	+	2.42906i	−0.263164	+	0.0848264i
$821$		−	12.6513i		−	0.441533i	−0.975327	−	0.220767i	$-0.929144\pi$
$821$		−	12.6513i		−	0.441533i	0.975327	−	0.220767i	$-0.0708559\pi$
$822$	24.1382	−	33.1417i	0.841916	−	1.15595i
$823$	50.2062			1.75008			0.875039	−	0.484053i	$-0.160836\pi$
$823$	50.2062			1.75008			0.875039	+	0.484053i	$0.160836\pi$
$824$	9.82108	−	29.8687i	0.342133	−	1.04053i
$825$	15.1607			0.527829
$826$	−4.68964	+	6.43887i	−0.163173	+	0.224037i
$827$		−	12.7729i		−	0.444157i	−0.975029	−	0.222079i	$-0.928716\pi$
$827$		−	12.7729i		−	0.444157i	0.975029	−	0.222079i	$-0.0712841\pi$
$828$	−25.2514	−	78.3396i	−0.877546	−	2.72249i
$829$			28.5874i			0.992883i	0.868070	+	0.496441i	$0.165360\pi$
$829$			28.5874i			0.992883i	−0.868070	+	0.496441i	$0.834640\pi$
$830$	10.9905	+	8.00473i	0.381485	+	0.277848i
$831$	−56.6593			−1.96549
$832$	3.64122	−	4.93837i	0.126237	−	0.171207i
$833$	−0.356460			−0.0123506
$834$	24.8678	+	18.1120i	0.861101	+	0.627168i
$835$		−	8.65030i		−	0.299356i
$836$	8.68591	+	26.9471i	0.300408	+	0.931984i
$837$			41.9932i			1.45150i
$838$	−10.0725	+	13.8295i	−0.347948	+	0.477732i
$839$	31.9545			1.10319			0.551597	−	0.834111i	$-0.314019\pi$
$839$	31.9545			1.10319			0.551597	+	0.834111i	$0.314019\pi$
$840$	−3.02875	+	9.21131i	−0.104502	+	0.317820i
$841$	12.5432			0.432525
$842$	−1.35083	+	1.85469i	−0.0465527	+	0.0639167i
$843$			41.3101i			1.42280i
$844$	−48.5576	+	15.6517i	−1.67142	+	0.538753i
$845$		−	12.4118i		−	0.426978i
$846$	33.2964	+	24.2509i	1.14475	+	0.833763i
$847$	−8.55700			−0.294022
$848$	28.9433	+	40.2320i	0.993918	+	1.38157i
$849$	66.1875			2.27155
$850$	−0.407487	−	0.296786i	−0.0139767	−	0.0101797i
$851$		−	40.9155i		−	1.40256i
$852$	−27.9106	+	8.99650i	−0.956203	+	0.308215i
$853$			23.0408i			0.788903i	0.918917	+	0.394452i	$0.129065\pi$
$853$			23.0408i			0.788903i	−0.918917	+	0.394452i	$0.870935\pi$
$854$	9.14666	−	12.5583i	0.312992	−	0.429738i
$855$	−28.0180			−0.958195
$856$	−1.34121	−	0.441002i	−0.0458418	−	0.0150732i
$857$	−34.7882			−1.18834			−0.594171	−	0.804338i	$-0.702520\pi$
$857$	−34.7882			−1.18834			−0.594171	+	0.804338i	$0.702520\pi$
$858$	−9.68104	+	13.2921i	−0.330505	+	0.453783i
$859$		−	51.3266i		−	1.75124i	−0.482998	−	0.875621i	$-0.660452\pi$
$859$		−	51.3266i		−	1.75124i	0.482998	−	0.875621i	$-0.339548\pi$
$860$	−3.24534	−	10.0683i	−0.110665	−	0.343327i
$861$			13.5718i			0.462526i
$862$	−26.2681	−	19.1320i	−0.894697	−	0.651637i
$863$	36.6163			1.24643			0.623217	−	0.782049i	$-0.285825\pi$
$863$	36.6163			1.24643			0.623217	+	0.782049i	$0.285825\pi$
$864$	−0.653221	+	111.560i	−0.0222230	+	3.79535i
$865$	18.6030			0.632522
$866$	14.6391	+	10.6622i	0.497458	+	0.362315i
$867$			57.8442i			1.96449i
$868$	1.30649	+	4.05325i	0.0443453	+	0.137576i
$869$		−	28.4515i		−	0.965150i
$870$	−11.5791	+	15.8980i	−0.392567	+	0.538994i
$871$	0.0344036			0.00116572
$872$	−18.0984	−	5.95092i	−0.612891	−	0.201523i
$873$	101.560			3.43728
$874$	12.5314	−	17.2056i	0.423882	−	0.581989i
$875$			1.00000i			0.0338062i
$876$	−14.8590	+	4.78954i	−0.502040	+	0.161824i
$877$		−	25.2293i		−	0.851933i	−0.904739	−	0.425967i	$-0.859934\pi$
$877$		−	25.2293i		−	0.851933i	0.904739	−	0.425967i	$-0.140066\pi$
$878$	10.1857	+	7.41861i	0.343752	+	0.250366i
$879$	40.0689			1.35149
$880$	14.3595	−	10.3304i	0.484059	−	0.348237i
$881$	34.6188			1.16634			0.583168	−	0.812352i	$-0.301813\pi$
$881$	34.6188			1.16634			0.583168	+	0.812352i	$0.301813\pi$
$882$	10.0056	+	7.28744i	0.336907	+	0.245381i
$883$		−	26.3989i		−	0.888392i	−0.895930	−	0.444196i	$-0.853489\pi$
$883$		−	26.3989i		−	0.888392i	0.895930	−	0.444196i	$-0.146511\pi$
$884$	0.520411	−	0.167745i	0.0175033	−	0.00564188i
$885$			19.3097i			0.649089i
$886$	14.8165	−	20.3431i	0.497771	−	0.683438i
$887$	−50.9584			−1.71102			−0.855508	−	0.517789i	$-0.826755\pi$
$887$	−50.9584			−1.71102			−0.855508	+	0.517789i	$0.826755\pi$
$888$	−26.3559	+	80.1559i	−0.884447	+	2.68986i
$889$	−0.472661			−0.0158525
$890$	−11.2353	+	15.4261i	−0.376609	+	0.517084i
$891$		−	182.871i		−	6.12640i
$892$	16.4899	+	51.1582i	0.552124	+	1.71290i
$893$			10.6524i			0.356469i
$894$	−71.9595	−	52.4105i	−2.40668	−	1.75287i
$895$	−12.1917			−0.407524
$896$	3.40781	+	10.7883i	0.113847	+	0.360411i
$897$	12.3627			0.412777
$898$	−15.8971	−	11.5784i	−0.530492	−	0.386375i
$899$			8.63794i			0.288091i
$900$	5.37046	+	16.6613i	0.179015	+	0.555375i
$901$			4.41667i			0.147141i
$902$	14.5765	−	20.0135i	0.485344	−	0.666376i
$903$	−18.1326			−0.603415
$904$	0.270920	−	0.823945i	0.00901067	−	0.0274040i
$905$	7.23501			0.240500
$906$	−29.4815	+	40.4781i	−0.979458	+	1.34479i
$907$			29.9749i			0.995300i	0.867378	+	0.497650i	$0.165804\pi$
$907$			29.9749i			0.995300i	−0.867378	+	0.497650i	$0.834196\pi$
$908$	−15.8837	+	5.11984i	−0.527120	+	0.169908i
$909$		−	5.26884i		−	0.174756i
$910$	−0.876742	−	0.638561i	−0.0290637	−	0.0211681i
$911$	−34.2943			−1.13622			−0.568111	−	0.822952i	$-0.692325\pi$
$911$	−34.2943			−1.13622			−0.568111	+	0.822952i	$0.692325\pi$
$912$	−35.6330	+	25.6347i	−1.17993	+	0.848850i
$913$	−42.5173			−1.40712
$914$	−23.1067	−	16.8294i	−0.764303	−	0.556667i
$915$		−	37.6616i		−	1.24505i
$916$	−19.7547	+	6.36756i	−0.652712	+	0.210390i
$917$		−	7.93234i		−	0.261949i
$918$	−5.85309	+	8.03627i	−0.193181	+	0.265237i
$919$	−52.5175			−1.73239			−0.866197	−	0.499703i	$-0.833443\pi$
$919$	−52.5175			−1.73239			−0.866197	+	0.499703i	$0.833443\pi$
$920$	−12.6336	−	4.15402i	−0.416516	−	0.136954i
$921$	−0.929906			−0.0306415
$922$	−18.3175	+	25.1499i	−0.603256	+	0.828269i
$923$		−	3.28023i		−	0.107970i
$924$	−9.30228	−	28.8593i	−0.306023	−	0.949401i
$925$			8.70190i			0.286117i
$926$	−10.0496	−	7.31946i	−0.330251	−	0.240532i
$927$	−97.2985			−3.19570
$928$	−0.134367	+	22.9477i	−0.00441080	+	0.753296i
$929$	−24.5913			−0.806814			−0.403407	−	0.915021i	$-0.632174\pi$
$929$	−24.5913			−0.806814			−0.403407	+	0.915021i	$0.632174\pi$
$930$	8.34468	+	6.07771i	0.273633	+	0.199296i
$931$			3.20107i			0.104911i
$932$	8.12793	+	25.2160i	0.266239	+	0.825978i
$933$			66.1838i			2.16676i
$934$	22.5389	−	30.9458i	0.737494	−	1.01258i
$935$	1.57639			0.0515533
$936$	−18.0370	−	5.93071i	−0.589558	−	0.193851i
$937$	−55.8180			−1.82349			−0.911747	−	0.410752i	$-0.865266\pi$
$937$	−55.8180			−1.82349			−0.911747	+	0.410752i	$0.865266\pi$
$938$	−0.0373480	+	0.0512787i	−0.00121946	+	0.00167431i
$939$			21.4561i			0.700194i
$940$	6.33459	−	2.04184i	0.206611	−	0.0665975i
$941$		−	37.6577i		−	1.22761i	−0.789459	−	0.613803i	$-0.789639\pi$
$941$		−	37.6577i		−	1.22761i	0.789459	−	0.613803i	$-0.210361\pi$
$942$	−69.6926	−	50.7594i	−2.27071	−	1.65383i
$943$	−18.6141			−0.606158
$944$	13.1574	+	18.2892i	0.428238	+	0.595263i
$945$	19.7215			0.641542
$946$	26.7390	+	19.4749i	0.869360	+	0.633184i
$947$			0.295619i			0.00960632i	0.999988	+	0.00480316i	$0.00152890\pi$
$947$			0.295619i			0.00960632i	−0.999988	+	0.00480316i	$0.998471\pi$
$948$	41.9844	−	13.5329i	1.36359	−	0.439529i
$949$		−	1.74633i		−	0.0566881i
$950$	−2.66519	+	3.65929i	−0.0864701	+	0.118723i
$951$	−42.9174			−1.39169
$952$	−0.314925	+	0.957776i	−0.0102068	+	0.0310417i
$953$	5.06138			0.163954			0.0819771	−	0.996634i	$-0.473877\pi$
$953$	5.06138			0.163954			0.0819771	+	0.996634i	$0.473877\pi$
$954$	90.2939	−	123.973i	2.92337	−	4.01379i
$955$			9.72067i			0.314553i
$956$	9.99820	+	31.0183i	0.323365	+	1.00320i
$957$		−	61.5024i		−	1.98809i
$958$	10.3649	+	7.54913i	0.334876	+	0.243901i
$959$	−8.45674			−0.273082
$960$	22.0741	+	16.2760i	0.712439	+	0.525305i
$961$	−26.4661			−0.853744
$962$	−7.62932	−	5.55669i	−0.245979	−	0.179155i
$963$			4.36906i			0.140791i
$964$	−4.07353	−	12.6377i	−0.131200	−	0.407032i
$965$		−	8.63304i		−	0.277908i
$966$	−13.4207	+	18.4266i	−0.431804	+	0.592866i
$967$	−36.3763			−1.16978			−0.584891	−	0.811112i	$-0.698863\pi$
$967$	−36.3763			−1.16978			−0.584891	+	0.811112i	$0.698863\pi$
$968$	−7.55992	+	22.9919i	−0.242985	+	0.738987i
$969$	−3.91178			−0.125665
$970$	9.66079	−	13.2642i	0.310189	−	0.425889i
$971$		−	56.5690i		−	1.81539i	−0.419636	−	0.907693i	$-0.637842\pi$
$971$		−	56.5690i		−	1.81539i	0.419636	−	0.907693i	$-0.362158\pi$
$972$	157.230	−	50.6804i	5.04316	−	1.62557i
$973$		−	6.34549i		−	0.203427i
$974$	−19.1042	−	13.9142i	−0.612137	−	0.445840i
$975$	−2.62929			−0.0842046
$976$	−25.6622	−	35.6712i	−0.821428	−	1.14181i
$977$	50.9647			1.63050			0.815252	−	0.579106i	$-0.196598\pi$
$977$	50.9647			1.63050			0.815252	+	0.579106i	$0.196598\pi$
$978$	17.4742	+	12.7270i	0.558764	+	0.406966i
$979$		−	59.6766i		−	1.90727i
$980$	1.90356	−	0.613577i	0.0608068	−	0.0196000i
$981$			58.9564i			1.88233i
$982$	−10.6547	+	14.6289i	−0.340005	+	0.466826i
$983$	27.7912			0.886402			0.443201	−	0.896422i	$-0.353843\pi$
$983$	27.7912			0.886402			0.443201	+	0.896422i	$0.353843\pi$
$984$	36.4662	+	11.9904i	1.16250	+	0.382239i
$985$	9.41482			0.299981
$986$	−1.20397	+	1.65305i	−0.0383423	+	0.0526439i
$987$		−	11.4083i		−	0.363131i
$988$	−1.50638	−	4.67336i	−0.0479242	−	0.148680i
$989$		−	24.8694i		−	0.790800i
$990$	−44.2482	−	32.2275i	−1.40630	−	1.02426i
$991$	9.34516			0.296859			0.148429	−	0.988923i	$-0.452578\pi$
$991$	9.34516			0.296859			0.148429	+	0.988923i	$0.452578\pi$
$992$	12.0450	+	0.0705273i	0.382428	+	0.00223925i
$993$	56.8470			1.80398
$994$	4.88920	+	3.56097i	0.155076	+	0.112947i
$995$		−	15.9597i		−	0.505957i
$996$	−20.2233	−	62.7406i	−0.640800	−	1.98801i
$997$			6.79455i			0.215186i	0.994195	+	0.107593i	$0.0343143\pi$
$997$			6.79455i			0.215186i	−0.994195	+	0.107593i	$0.965686\pi$
$998$	−9.91431	+	13.6123i	−0.313832	+	0.430891i
$999$	171.615			5.42965

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.b.d.141.3	✓	12
4.3	odd	2		1120.2.b.d.561.12		12
8.3	odd	2		1120.2.b.d.561.1		12
8.5	even	2	inner	280.2.b.d.141.4	yes	12
16.3	odd	4		8960.2.a.cd.1.1		6
16.5	even	4		8960.2.a.cf.1.1		6
16.11	odd	4		8960.2.a.cg.1.6		6
16.13	even	4		8960.2.a.ca.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.b.d.141.3	✓	12	1.1	even	1	trivial
280.2.b.d.141.4	yes	12	8.5	even	2	inner
1120.2.b.d.561.1		12	8.3	odd	2
1120.2.b.d.561.12		12	4.3	odd	2
8960.2.a.ca.1.6		6	16.13	even	4
8960.2.a.cd.1.1		6	16.3	odd	4
8960.2.a.cf.1.1		6	16.5	even	4
8960.2.a.cg.1.6		6	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14315 - 0.832593i) q^{2} -3.42822i q^{3} +(0.613577 + 1.90356i) q^{4} -1.00000i q^{5} +(-2.85431 + 3.91897i) q^{6} +1.00000 q^{7} +(0.883477 - 2.68691i) q^{8} -8.75270 q^{9} +O(q^{10})\)	\(q+(-1.14315 - 0.832593i) q^{2} -3.42822i q^{3} +(0.613577 + 1.90356i) q^{4} -1.00000i q^{5} +(-2.85431 + 3.91897i) q^{6} +1.00000 q^{7} +(0.883477 - 2.68691i) q^{8} -8.75270 q^{9} +(-0.832593 + 1.14315i) q^{10} -4.42233i q^{11} +(6.52581 - 2.10348i) q^{12} +0.766954i q^{13} +(-1.14315 - 0.832593i) q^{14} -3.42822 q^{15} +(-3.24705 + 2.33596i) q^{16} -0.356460 q^{17} +(10.0056 + 7.28744i) q^{18} +3.20107i q^{19} +(1.90356 - 0.613577i) q^{20} -3.42822i q^{21} +(-3.68200 + 5.05538i) q^{22} +4.70190 q^{23} +(-9.21131 - 3.02875i) q^{24} -1.00000 q^{25} +(0.638561 - 0.876742i) q^{26} +19.7215i q^{27} +(0.613577 + 1.90356i) q^{28} +4.05669i q^{29} +(3.91897 + 2.85431i) q^{30} +2.12931 q^{31} +(5.65676 + 0.0331222i) q^{32} -15.1607 q^{33} +(0.407487 + 0.296786i) q^{34} -1.00000i q^{35} +(-5.37046 - 16.6613i) q^{36} -8.70190i q^{37} +(2.66519 - 3.65929i) q^{38} +2.62929 q^{39} +(-2.68691 - 0.883477i) q^{40} -3.95885 q^{41} +(-2.85431 + 3.91897i) q^{42} -5.28922i q^{43} +(8.41815 - 2.71344i) q^{44} +8.75270i q^{45} +(-5.37497 - 3.91477i) q^{46} +3.32777 q^{47} +(8.00818 + 11.1316i) q^{48} +1.00000 q^{49} +(1.14315 + 0.832593i) q^{50} +1.22203i q^{51} +(-1.45994 + 0.470586i) q^{52} -12.3904i q^{53} +(16.4200 - 22.5446i) q^{54} -4.42233 q^{55} +(0.883477 - 2.68691i) q^{56} +10.9740 q^{57} +(3.37758 - 4.63740i) q^{58} -5.63257i q^{59} +(-2.10348 - 6.52581i) q^{60} +10.9857i q^{61} +(-2.43411 - 1.77285i) q^{62} -8.75270 q^{63} +(-6.43894 - 4.74764i) q^{64} +0.766954 q^{65} +(17.3310 + 12.6227i) q^{66} -0.0448574i q^{67} +(-0.218716 - 0.678542i) q^{68} -16.1192i q^{69} +(-0.832593 + 1.14315i) q^{70} -4.27696 q^{71} +(-7.73281 + 23.5177i) q^{72} -2.27696 q^{73} +(-7.24514 + 9.94756i) q^{74} +3.42822i q^{75} +(-6.09341 + 1.96410i) q^{76} -4.42233i q^{77} +(-3.00567 - 2.18913i) q^{78} +6.43359 q^{79} +(2.33596 + 3.24705i) q^{80} +41.3517 q^{81} +(4.52555 + 3.29611i) q^{82} -9.61422i q^{83} +(6.52581 - 2.10348i) q^{84} +0.356460i q^{85} +(-4.40377 + 6.04636i) q^{86} +13.9072 q^{87} +(-11.8824 - 3.90703i) q^{88} +13.4944 q^{89} +(7.28744 - 10.0056i) q^{90} +0.766954i q^{91} +(2.88498 + 8.95033i) q^{92} -7.29973i q^{93} +(-3.80413 - 2.77067i) q^{94} +3.20107 q^{95} +(0.113550 - 19.3926i) q^{96} -11.6033 q^{97} +(-1.14315 - 0.832593i) q^{98} +38.7073i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9	\( 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9} + 16 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{20} + 12 q^{22} + 8 q^{23} - 24 q^{24} - 12 q^{25} + 6 q^{28} + 12 q^{30} + 24 q^{31} - 2 q^{32} - 24 q^{33} - 20 q^{34} - 18 q^{36} + 12 q^{38} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 16 q^{44} - 48 q^{46} - 16 q^{47} + 20 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{52} + 44 q^{54} - 8 q^{55} + 10 q^{56} + 40 q^{57} + 4 q^{58} - 8 q^{60} + 8 q^{62} - 20 q^{63} - 6 q^{64} + 8 q^{65} + 64 q^{66} - 56 q^{68} - 32 q^{71} - 46 q^{72} - 8 q^{73} - 32 q^{74} - 12 q^{76} - 24 q^{78} + 8 q^{80} + 60 q^{81} - 28 q^{82} + 16 q^{84} - 76 q^{86} + 48 q^{87} - 40 q^{88} - 48 q^{89} + 24 q^{90} + 12 q^{94} + 28 q^{96} + 32 q^{97} - 2 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9 + 16 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^20 + 12 * q^22 + 8 * q^23 - 24 * q^24 - 12 * q^25 + 6 * q^28 + 12 * q^30 + 24 * q^31 - 2 * q^32 - 24 * q^33 - 20 * q^34 - 18 * q^36 + 12 * q^38 - 48 * q^39 + 12 * q^40 - 16 * q^41 + 16 * q^44 - 48 * q^46 - 16 * q^47 + 20 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^52 + 44 * q^54 - 8 * q^55 + 10 * q^56 + 40 * q^57 + 4 * q^58 - 8 * q^60 + 8 * q^62 - 20 * q^63 - 6 * q^64 + 8 * q^65 + 64 * q^66 - 56 * q^68 - 32 * q^71 - 46 * q^72 - 8 * q^73 - 32 * q^74 - 12 * q^76 - 24 * q^78 + 8 * q^80 + 60 * q^81 - 28 * q^82 + 16 * q^84 - 76 * q^86 + 48 * q^87 - 40 * q^88 - 48 * q^89 + 24 * q^90 + 12 * q^94 + 28 * q^96 + 32 * q^97 - 2 * q^98

Introduction

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