LMFDB - Embedded newform 280.2.b.d.141.11

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			141.11
Root			$-0.128739 + 1.40834i$ of defining polynomial
Character	$\chi$	$=$	280.141
Dual form			280.2.b.d.141.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40834 - 0.128739i) q^{2} -2.83397i q^{3} +(1.96685 - 0.362616i) q^{4} +1.00000i q^{5} +(-0.364842 - 3.99120i) q^{6} +1.00000 q^{7} +(2.72332 - 0.763897i) q^{8} -5.03141 q^{9} +O(q^{10})$	\(q+(1.40834 - 0.128739i) q^{2} -2.83397i q^{3} +(1.96685 - 0.362616i) q^{4} +1.00000i q^{5} +(-0.364842 - 3.99120i) q^{6} +1.00000 q^{7} +(2.72332 - 0.763897i) q^{8} -5.03141 q^{9} +(0.128739 + 1.40834i) q^{10} +4.54637i q^{11} +(-1.02764 - 5.57401i) q^{12} -4.44664i q^{13} +(1.40834 - 0.128739i) q^{14} +2.83397 q^{15} +(3.73702 - 1.42642i) q^{16} -8.18643 q^{17} +(-7.08595 + 0.647737i) q^{18} +5.76768i q^{19} +(0.362616 + 1.96685i) q^{20} -2.83397i q^{21} +(0.585293 + 6.40284i) q^{22} -0.380641 q^{23} +(-2.16486 - 7.71781i) q^{24} -1.00000 q^{25} +(-0.572454 - 6.26238i) q^{26} +5.75697i q^{27} +(1.96685 - 0.362616i) q^{28} +0.968288i q^{29} +(3.99120 - 0.364842i) q^{30} +7.25273 q^{31} +(5.07936 - 2.48999i) q^{32} +12.8843 q^{33} +(-11.5293 + 1.05391i) q^{34} +1.00000i q^{35} +(-9.89605 + 1.82447i) q^{36} +3.61936i q^{37} +(0.742523 + 8.12286i) q^{38} -12.6017 q^{39} +(0.763897 + 2.72332i) q^{40} -1.35073 q^{41} +(-0.364842 - 3.99120i) q^{42} -1.16422i q^{43} +(1.64858 + 8.94203i) q^{44} -5.03141i q^{45} +(-0.536072 + 0.0490032i) q^{46} +9.57395 q^{47} +(-4.04245 - 10.5906i) q^{48} +1.00000 q^{49} +(-1.40834 + 0.128739i) q^{50} +23.2001i q^{51} +(-1.61242 - 8.74588i) q^{52} +7.22532i q^{53} +(0.741144 + 8.10778i) q^{54} -4.54637 q^{55} +(2.72332 - 0.763897i) q^{56} +16.3455 q^{57} +(0.124656 + 1.36368i) q^{58} -5.89309i q^{59} +(5.57401 - 1.02764i) q^{60} -3.58478i q^{61} +(10.2143 - 0.933706i) q^{62} -5.03141 q^{63} +(6.83292 - 4.16067i) q^{64} +4.44664 q^{65} +(18.1455 - 1.65870i) q^{66} -9.25445i q^{67} +(-16.1015 + 2.96853i) q^{68} +1.07873i q^{69} +(0.128739 + 1.40834i) q^{70} -9.16190 q^{71} +(-13.7021 + 3.84348i) q^{72} -7.16190 q^{73} +(0.465951 + 5.09729i) q^{74} +2.83397i q^{75} +(2.09145 + 11.3442i) q^{76} +4.54637i q^{77} +(-17.7474 + 1.62232i) q^{78} -3.96361 q^{79} +(1.42642 + 3.73702i) q^{80} +1.22088 q^{81} +(-1.90229 + 0.173891i) q^{82} +3.45046i q^{83} +(-1.02764 - 5.57401i) q^{84} -8.18643i q^{85} +(-0.149880 - 1.63962i) q^{86} +2.74410 q^{87} +(3.47295 + 12.3812i) q^{88} -14.6907 q^{89} +(-0.647737 - 7.08595i) q^{90} -4.44664i q^{91} +(-0.748664 + 0.138026i) q^{92} -20.5540i q^{93} +(13.4834 - 1.23254i) q^{94} -5.76768 q^{95} +(-7.05657 - 14.3948i) q^{96} -1.74381 q^{97} +(1.40834 - 0.128739i) q^{98} -22.8746i 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 $

$2$	1.40834	−	0.128739i	0.995848	−	0.0910319i
$2$	1.40834	−	0.128739i	0.995848	−	0.0910319i
$3$		−	2.83397i		−	1.63620i	−0.575079	−	0.818098i	$-0.695029\pi$
$3$		−	2.83397i		−	1.63620i	0.575079	−	0.818098i	$-0.304971\pi$
$4$	1.96685	−	0.362616i	0.983426	−	0.181308i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.364842	−	3.99120i	−0.148946	−	1.62940i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.72332	−	0.763897i	0.962838	−	0.270078i
$9$	−5.03141			−1.67714
$10$	0.128739	+	1.40834i	0.0407107	+	0.445357i
$11$			4.54637i			1.37078i	0.728176	+	0.685391i	$0.240369\pi$
$11$			4.54637i			1.37078i	−0.728176	+	0.685391i	$0.759631\pi$
$12$	−1.02764	−	5.57401i	−0.296655	−	1.60908i
$13$		−	4.44664i		−	1.23328i	−0.787247	−	0.616638i	$-0.788494\pi$
$13$		−	4.44664i		−	1.23328i	0.787247	−	0.616638i	$-0.211506\pi$
$14$	1.40834	−	0.128739i	0.376395	−	0.0344068i
$15$	2.83397			0.731729
$16$	3.73702	−	1.42642i	0.934255	−	0.356606i
$17$	−8.18643			−1.98550			−0.992751	−	0.120192i	$-0.961649\pi$
$17$	−8.18643			−1.98550			−0.992751	+	0.120192i	$0.961649\pi$
$18$	−7.08595	+	0.647737i	−1.67017	+	0.152673i
$19$			5.76768i			1.32320i	0.749858	+	0.661598i	$0.230122\pi$
$19$			5.76768i			1.32320i	−0.749858	+	0.661598i	$0.769878\pi$
$20$	0.362616	+	1.96685i	0.0810834	+	0.439802i
$21$		−	2.83397i		−	0.618424i
$22$	0.585293	+	6.40284i	0.124785	+	1.36509i
$23$	−0.380641			−0.0793691			−0.0396846	−	0.999212i	$-0.512635\pi$
$23$	−0.380641			−0.0793691			−0.0396846	+	0.999212i	$0.512635\pi$
$24$	−2.16486	−	7.71781i	−0.441901	−	1.57539i
$25$	−1.00000			−0.200000
$26$	−0.572454	−	6.26238i	−0.112267	−	1.22815i
$27$			5.75697i			1.10793i
$28$	1.96685	−	0.362616i	0.371700	−	0.0685279i
$29$			0.968288i			0.179807i	0.995950	+	0.0899033i	$0.0286558\pi$
$29$			0.968288i			0.179807i	−0.995950	+	0.0899033i	$0.971344\pi$
$30$	3.99120	−	0.364842i	0.728691	−	0.0666107i
$31$	7.25273			1.30263			0.651314	−	0.758808i	$-0.274218\pi$
$31$	7.25273			1.30263			0.651314	+	0.758808i	$0.274218\pi$
$32$	5.07936	−	2.48999i	0.897913	−	0.440172i
$33$	12.8843			2.24287
$34$	−11.5293	+	1.05391i	−1.97726	+	0.180744i
$35$			1.00000i			0.169031i
$36$	−9.89605	+	1.82447i	−1.64934	+	0.304078i
$37$			3.61936i			0.595019i	0.954719	+	0.297509i	$0.0961560\pi$
$37$			3.61936i			0.595019i	−0.954719	+	0.297509i	$0.903844\pi$
$38$	0.742523	+	8.12286i	0.120453	+	1.31770i
$39$	−12.6017			−2.01788
$40$	0.763897	+	2.72332i	0.120783	+	0.430594i
$41$	−1.35073			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$41$	−1.35073			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$42$	−0.364842	−	3.99120i	−0.0562963	−	0.615856i
$43$		−	1.16422i		−	0.177542i	−0.996052	−	0.0887711i	$-0.971706\pi$
$43$		−	1.16422i		−	0.177542i	0.996052	−	0.0887711i	$-0.0282940\pi$
$44$	1.64858	+	8.94203i	0.248533	+	1.34806i
$45$		−	5.03141i		−	0.750039i
$46$	−0.536072	+	0.0490032i	−0.0790396	+	0.00722512i
$47$	9.57395			1.39650			0.698252	−	0.715852i	$-0.253961\pi$
$47$	9.57395			1.39650			0.698252	+	0.715852i	$0.253961\pi$
$48$	−4.04245	−	10.5906i	−0.583477	−	1.52862i
$49$	1.00000			0.142857
$50$	−1.40834	+	0.128739i	−0.199170	+	0.0182064i
$51$			23.2001i			3.24867i
$52$	−1.61242	−	8.74588i	−0.223602	−	1.21284i
$53$			7.22532i			0.992474i	0.868187	+	0.496237i	$0.165285\pi$
$53$			7.22532i			0.992474i	−0.868187	+	0.496237i	$0.834715\pi$
$54$	0.741144	+	8.10778i	0.100857	+	1.10333i
$55$	−4.54637			−0.613032
$56$	2.72332	−	0.763897i	0.363919	−	0.102080i
$57$	16.3455			2.16501
$58$	0.124656	+	1.36368i	0.0163681	+	0.179060i
$59$		−	5.89309i		−	0.767215i	−0.923496	−	0.383607i	$-0.874682\pi$
$59$		−	5.89309i		−	0.767215i	0.923496	−	0.383607i	$-0.125318\pi$
$60$	5.57401	−	1.02764i	0.719602	−	0.132668i
$61$		−	3.58478i		−	0.458984i	−0.973311	−	0.229492i	$-0.926294\pi$
$61$		−	3.58478i		−	0.458984i	0.973311	−	0.229492i	$-0.0737064\pi$
$62$	10.2143	−	0.933706i	1.29722	−	0.118581i
$63$	−5.03141			−0.633898
$64$	6.83292	−	4.16067i	0.854115	−	0.520083i
$65$	4.44664			0.551537
$66$	18.1455	−	1.65870i	2.23355	−	0.204172i
$67$		−	9.25445i		−	1.13061i	−0.824882	−	0.565306i	$-0.808758\pi$
$67$		−	9.25445i		−	1.13061i	0.824882	−	0.565306i	$-0.191242\pi$
$68$	−16.1015	+	2.96853i	−1.95259	+	0.359987i
$69$			1.07873i			0.129863i
$70$	0.128739	+	1.40834i	0.0153872	+	0.168329i
$71$	−9.16190			−1.08732			−0.543659	−	0.839306i	$-0.682961\pi$
$71$	−9.16190			−1.08732			−0.543659	+	0.839306i	$0.682961\pi$
$72$	−13.7021	+	3.84348i	−1.61481	+	0.452958i
$73$	−7.16190			−0.838237			−0.419118	−	0.907932i	$-0.637661\pi$
$73$	−7.16190			−0.838237			−0.419118	+	0.907932i	$0.637661\pi$
$74$	0.465951	+	5.09729i	0.0541657	+	0.592548i
$75$			2.83397i			0.327239i
$76$	2.09145	+	11.3442i	0.239906	+	1.30127i
$77$			4.54637i			0.518107i
$78$	−17.7474	+	1.62232i	−2.00950	+	0.183691i
$79$	−3.96361			−0.445941			−0.222971	−	0.974825i	$-0.571575\pi$
$79$	−3.96361			−0.445941			−0.222971	+	0.974825i	$0.571575\pi$
$80$	1.42642	+	3.73702i	0.159479	+	0.417811i
$81$	1.22088			0.135653
$82$	−1.90229	+	0.173891i	−0.210073	+	0.0192031i
$83$			3.45046i			0.378738i	0.981906	+	0.189369i	$0.0606442\pi$
$83$			3.45046i			0.378738i	−0.981906	+	0.189369i	$0.939356\pi$
$84$	−1.02764	−	5.57401i	−0.112125	−	0.608174i
$85$		−	8.18643i		−	0.887943i
$86$	−0.149880	−	1.63962i	−0.0161620	−	0.176805i
$87$	2.74410			0.294199
$88$	3.47295	+	12.3812i	0.370218	+	1.31984i
$89$	−14.6907			−1.55721			−0.778604	−	0.627515i	$-0.784072\pi$
$89$	−14.6907			−1.55721			−0.778604	+	0.627515i	$0.784072\pi$
$90$	−0.647737	−	7.08595i	−0.0682775	−	0.746925i
$91$		−	4.44664i		−	0.466134i
$92$	−0.748664	+	0.138026i	−0.0780537	+	0.0143902i
$93$		−	20.5540i		−	2.13135i
$94$	13.4834	−	1.23254i	1.39071	−	0.127126i
$95$	−5.76768			−0.591752
$96$	−7.05657	−	14.3948i	−0.720208	−	1.46916i
$97$	−1.74381			−0.177057			−0.0885283	−	0.996074i	$-0.528216\pi$
$97$	−1.74381			−0.177057			−0.0885283	+	0.996074i	$0.528216\pi$
$98$	1.40834	−	0.128739i	0.142264	−	0.0130046i
$99$		−	22.8746i		−	2.29899i
$100$	−1.96685	+	0.362616i	−0.196685	+	0.0362616i
$101$		−	5.77658i		−	0.574792i	−0.957812	−	0.287396i	$-0.907210\pi$
$101$		−	5.77658i		−	0.574792i	0.957812	−	0.287396i	$-0.0927895\pi$
$102$	2.98675	+	32.6737i	0.295733	+	3.23518i
$103$	−9.88054			−0.973559			−0.486779	−	0.873525i	$-0.661828\pi$
$103$	−9.88054			−0.973559			−0.486779	+	0.873525i	$0.661828\pi$
$104$	−3.39677	−	12.1096i	−0.333081	−	1.18744i
$105$	2.83397			0.276568
$106$	0.930178	+	10.1757i	0.0903468	+	0.988354i
$107$		−	3.38704i		−	0.327437i	−0.986507	−	0.163719i	$-0.947651\pi$
$107$		−	3.38704i		−	0.327437i	0.986507	−	0.163719i	$-0.0523490\pi$
$108$	2.08757	+	11.3231i	0.200876	+	1.08957i
$109$		−	11.3417i		−	1.08634i	−0.839622	−	0.543171i	$-0.817223\pi$
$109$		−	11.3417i		−	1.08634i	0.839622	−	0.543171i	$-0.182777\pi$
$110$	−6.40284	+	0.585293i	−0.610487	+	0.0558055i
$111$	10.2572			0.973568
$112$	3.73702	−	1.42642i	0.353115	−	0.134784i
$113$	5.95824			0.560504			0.280252	−	0.959926i	$-0.409582\pi$
$113$	5.95824			0.560504			0.280252	+	0.959926i	$0.409582\pi$
$114$	23.0200	−	2.10429i	2.15602	−	0.197085i
$115$		−	0.380641i		−	0.0354949i
$116$	0.351117	+	1.90448i	0.0326004	+	0.176827i
$117$			22.3729i			2.06837i
$118$	−0.758668	−	8.29948i	−0.0698410	−	0.764029i
$119$	−8.18643			−0.750449
$120$	7.71781	−	2.16486i	0.704537	−	0.197624i
$121$	−9.66945			−0.879041
$122$	−0.461499	−	5.04859i	−0.0417822	−	0.457078i
$123$			3.82794i			0.345154i
$124$	14.2650	−	2.62995i	1.28104	−	0.236177i
$125$		−	1.00000i		−	0.0894427i
$126$	−7.08595	+	0.647737i	−0.631266	+	0.0577050i
$127$	−0.523858			−0.0464849			−0.0232425	−	0.999730i	$-0.507399\pi$
$127$	−0.523858			−0.0464849			−0.0232425	+	0.999730i	$0.507399\pi$
$128$	9.08745	−	6.73930i	0.803225	−	0.595676i
$129$	−3.29938			−0.290494
$130$	6.26238	−	0.572454i	0.549247	−	0.0502075i
$131$			9.26163i			0.809192i	0.914495	+	0.404596i	$0.132588\pi$
$131$			9.26163i			0.809192i	−0.914495	+	0.404596i	$0.867412\pi$
$132$	25.3415	−	4.67205i	2.20569	−	0.406649i
$133$			5.76768i			0.500121i
$134$	−1.19140	−	13.0334i	−0.102922	−	1.12592i
$135$	−5.75697			−0.495481
$136$	−22.2943	+	6.25359i	−1.91172	+	0.536241i
$137$	6.66544			0.569467			0.284734	−	0.958607i	$-0.408095\pi$
$137$	6.66544			0.569467			0.284734	+	0.958607i	$0.408095\pi$
$138$	0.138874	+	1.51922i	0.0118217	+	0.129324i
$139$			10.4798i			0.888883i	0.895808	+	0.444441i	$0.146598\pi$
$139$			10.4798i			0.888883i	−0.895808	+	0.444441i	$0.853402\pi$
$140$	0.362616	+	1.96685i	0.0306466	+	0.166229i
$141$		−	27.1323i		−	2.28496i
$142$	−12.9031	+	1.17949i	−1.08280	+	0.0989806i
$143$	20.2160			1.69055
$144$	−18.8025	+	7.17693i	−1.56687	+	0.598077i
$145$	−0.968288			−0.0804120
$146$	−10.0864	+	0.922013i	−0.834757	+	0.0763063i
$147$		−	2.83397i		−	0.233742i
$148$	1.31244	+	7.11875i	0.107882	+	0.585157i
$149$			1.60512i			0.131497i	0.997836	+	0.0657484i	$0.0209435\pi$
$149$			1.60512i			0.131497i	−0.997836	+	0.0657484i	$0.979057\pi$
$150$	0.364842	+	3.99120i	0.0297892	+	0.325881i
$151$	15.7578			1.28235			0.641176	−	0.767394i	$-0.278447\pi$
$151$	15.7578			1.28235			0.641176	+	0.767394i	$0.278447\pi$
$152$	4.40591	+	15.7072i	0.357367	+	1.27402i
$153$	41.1893			3.32996
$154$	0.585293	+	6.40284i	0.0471642	+	0.515955i
$155$			7.25273i			0.582553i
$156$	−24.7856	+	4.56956i	−1.98444	+	0.365858i
$157$		−	10.7233i		−	0.855814i	−0.903823	−	0.427907i	$-0.859251\pi$
$157$		−	10.7233i		−	0.855814i	0.903823	−	0.427907i	$-0.140749\pi$
$158$	−5.58212	+	0.510270i	−0.444090	+	0.0405949i
$159$	20.4764			1.62388
$160$	2.48999	+	5.07936i	0.196851	+	0.401559i
$161$	−0.380641			−0.0299987
$162$	1.71941	−	0.157174i	0.135090	−	0.0123487i
$163$		−	1.45680i		−	0.114106i	−0.998371	−	0.0570528i	$-0.981830\pi$
$163$		−	1.45680i		−	0.114106i	0.998371	−	0.0570528i	$-0.0181703\pi$
$164$	−2.65669	+	0.489797i	−0.207453	+	0.0382467i
$165$			12.8843i			1.00304i
$166$	0.444208	+	4.85943i	0.0344772	+	0.377165i
$167$	−4.98727			−0.385926			−0.192963	−	0.981206i	$-0.561810\pi$
$167$	−4.98727			−0.385926			−0.192963	+	0.981206i	$0.561810\pi$
$168$	−2.16486	−	7.71781i	−0.167023	−	0.595442i
$169$	−6.77257			−0.520967
$170$	−1.05391	−	11.5293i	−0.0808312	−	0.884256i
$171$		−	29.0196i		−	2.21918i
$172$	−0.422165	−	2.28985i	−0.0321898	−	0.174600i
$173$			23.9542i			1.82121i	0.413281	+	0.910604i	$0.364383\pi$
$173$			23.9542i			1.82121i	−0.413281	+	0.910604i	$0.635617\pi$
$174$	3.86464	−	0.353272i	0.292977	−	0.0267815i
$175$	−1.00000			−0.0755929
$176$	6.48505	+	16.9899i	0.488829	+	1.28066i
$177$	−16.7009			−1.25531
$178$	−20.6895	+	1.89126i	−1.55074	+	0.141756i
$179$		−	9.74711i		−	0.728533i	−0.931295	−	0.364266i	$-0.881320\pi$
$179$		−	9.74711i		−	0.728533i	0.931295	−	0.364266i	$-0.118680\pi$
$180$	−1.82447	−	9.89605i	−0.135988	−	0.737608i
$181$		−	2.31806i		−	0.172300i	−0.996282	−	0.0861499i	$-0.972544\pi$
$181$		−	2.31806i		−	0.172300i	0.996282	−	0.0861499i	$-0.0274564\pi$
$182$	−0.572454	−	6.26238i	−0.0424331	−	0.464199i
$183$	−10.1592			−0.750987
$184$	−1.03661	+	0.290770i	−0.0764196	+	0.0214359i
$185$	−3.61936			−0.266101
$186$	−2.64610	−	28.9471i	−0.194021	−	2.12251i
$187$		−	37.2185i		−	2.72169i
$188$	18.8306	−	3.47167i	1.37336	−	0.253197i
$189$			5.75697i			0.418758i
$190$	−8.12286	+	0.742523i	−0.589295	+	0.0538683i
$191$	16.3365			1.18207			0.591033	−	0.806647i	$-0.298720\pi$
$191$	16.3365			1.18207			0.591033	+	0.806647i	$0.298720\pi$
$192$	−11.7912	−	19.3643i	−0.850959	−	1.39750i
$193$	−1.45853			−0.104987			−0.0524935	−	0.998621i	$-0.516717\pi$
$193$	−1.45853			−0.104987			−0.0524935	+	0.998621i	$0.516717\pi$
$194$	−2.45587	+	0.224495i	−0.176321	+	0.0161178i
$195$		−	12.6017i		−	0.902423i
$196$	1.96685	−	0.362616i	0.140489	−	0.0259011i
$197$		−	19.9922i		−	1.42439i	−0.701983	−	0.712193i	$-0.747702\pi$
$197$		−	19.9922i		−	1.42439i	0.701983	−	0.712193i	$-0.252298\pi$
$198$	−2.94485	−	32.2153i	−0.209281	−	2.28944i
$199$	13.9302			0.987488			0.493744	−	0.869607i	$-0.335628\pi$
$199$	13.9302			0.987488			0.493744	+	0.869607i	$0.335628\pi$
$200$	−2.72332	+	0.763897i	−0.192568	+	0.0540157i
$201$	−26.2269			−1.84990
$202$	−0.743669	−	8.13540i	−0.0523244	−	0.572405i
$203$			0.968288i			0.0679605i
$204$	8.41274	+	45.6313i	0.589009	+	3.19483i
$205$		−	1.35073i		−	0.0943392i
$206$	−13.9152	+	1.27201i	−0.969516	+	0.0886249i
$207$	1.91516			0.133113
$208$	−6.34279	−	16.6172i	−0.439793	−	1.15219i
$209$	−26.2220			−1.81381
$210$	3.99120	−	0.364842i	0.275419	−	0.0251765i
$211$		−	8.55342i		−	0.588842i	−0.955676	−	0.294421i	$-0.904873\pi$
$211$		−	8.55342i		−	0.588842i	0.955676	−	0.294421i	$-0.0951268\pi$
$212$	2.62002	+	14.2111i	0.179943	+	0.976026i
$213$			25.9646i			1.77906i
$214$	−0.436043	−	4.77011i	−0.0298073	−	0.326078i
$215$	1.16422			0.0793993
$216$	4.39773	+	15.6781i	0.299228	+	1.06676i
$217$	7.25273			0.492347
$218$	−1.46012	−	15.9731i	−0.0988918	−	1.08183i
$219$			20.2966i			1.37152i
$220$	−8.94203	+	1.64858i	−0.602872	+	0.111148i
$221$			36.4021i			2.44867i
$222$	14.4456	−	1.32049i	0.969525	−	0.0886257i
$223$	−5.22814			−0.350102			−0.175051	−	0.984559i	$-0.556009\pi$
$223$	−5.22814			−0.350102			−0.175051	+	0.984559i	$0.556009\pi$
$224$	5.07936	−	2.48999i	0.339379	−	0.166369i
$225$	5.03141			0.335428
$226$	8.39123	−	0.767055i	0.558177	−	0.0510237i
$227$			10.9066i			0.723896i	0.932198	+	0.361948i	$0.117888\pi$
$227$			10.9066i			0.723896i	−0.932198	+	0.361948i	$0.882112\pi$
$228$	32.1491	−	5.92712i	2.12913	−	0.392533i
$229$		−	5.58418i		−	0.369013i	−0.982831	−	0.184506i	$-0.940931\pi$
$229$		−	5.58418i		−	0.369013i	0.982831	−	0.184506i	$-0.0590687\pi$
$230$	−0.0490032	−	0.536072i	−0.00323117	−	0.0353476i
$231$	12.8843			0.847724
$232$	0.739672	+	2.63696i	0.0485619	+	0.173125i
$233$	−4.44263			−0.291046			−0.145523	−	0.989355i	$-0.546486\pi$
$233$	−4.44263			−0.291046			−0.145523	+	0.989355i	$0.546486\pi$
$234$	2.88025	+	31.5086i	0.188288	+	2.05978i
$235$			9.57395i			0.624536i
$236$	−2.13693	−	11.5908i	−0.139102	−	0.754499i
$237$			11.2328i			0.729648i
$238$	−11.5293	+	1.05391i	−0.747333	+	0.0683148i
$239$	−6.98851			−0.452049			−0.226025	−	0.974122i	$-0.572573\pi$
$239$	−6.98851			−0.452049			−0.226025	+	0.974122i	$0.572573\pi$
$240$	10.5906	−	4.04245i	0.683622	−	0.260939i
$241$	13.5241			0.871166			0.435583	−	0.900149i	$-0.356542\pi$
$241$	13.5241			0.871166			0.435583	+	0.900149i	$0.356542\pi$
$242$	−13.6179	+	1.24483i	−0.875391	+	0.0800208i
$243$			13.8110i			0.885975i
$244$	−1.29990	−	7.05073i	−0.0832173	−	0.451377i
$245$			1.00000i			0.0638877i
$246$	0.492804	+	5.39105i	0.0314200	+	0.343721i
$247$	25.6468			1.63187
$248$	19.7515	−	5.54033i	1.25422	−	0.351812i
$249$	9.77853			0.619689
$250$	−0.128739	−	1.40834i	−0.00814214	−	0.0890714i
$251$		−	16.7858i		−	1.05951i	−0.848151	−	0.529754i	$-0.822284\pi$
$251$		−	16.7858i		−	1.05951i	0.848151	−	0.529754i	$-0.177716\pi$
$252$	−9.89605	+	1.82447i	−0.623392	+	0.114931i
$253$		−	1.73053i		−	0.108798i
$254$	−0.737772	+	0.0674408i	−0.0462919	+	0.00423161i
$255$	−23.2001			−1.45285
$256$	11.9306	−	10.6611i	0.745664	−	0.666322i
$257$	−16.0535			−1.00139			−0.500694	−	0.865624i	$-0.666922\pi$
$257$	−16.0535			−1.00139			−0.500694	+	0.865624i	$0.666922\pi$
$258$	−4.64665	+	0.424757i	−0.289288	+	0.0264442i
$259$			3.61936i			0.224896i
$260$	8.74588	−	1.61242i	0.542396	−	0.0999981i
$261$		−	4.87186i		−	0.301560i
$262$	1.19233	+	13.0435i	0.0736623	+	0.805833i
$263$	−7.73843			−0.477172			−0.238586	−	0.971121i	$-0.576684\pi$
$263$	−7.73843			−0.477172			−0.238586	+	0.971121i	$0.576684\pi$
$264$	35.0880	−	9.84227i	2.15952	−	0.605750i
$265$	−7.22532			−0.443848
$266$	0.742523	+	8.12286i	0.0455270	+	0.498045i
$267$			41.6330i			2.54790i
$268$	−3.35581	−	18.2021i	−0.204989	−	1.11187i
$269$			30.5329i			1.86162i	0.365501	+	0.930811i	$0.380898\pi$
$269$			30.5329i			1.86162i	−0.365501	+	0.930811i	$0.619102\pi$
$270$	−8.10778	+	0.741144i	−0.493424	+	0.0451046i
$271$	−27.0981			−1.64609			−0.823047	−	0.567973i	$-0.807728\pi$
$271$	−27.0981			−1.64609			−0.823047	+	0.567973i	$0.807728\pi$
$272$	−30.5929	+	11.6773i	−1.85496	+	0.708042i
$273$	−12.6017			−0.762687
$274$	9.38722	−	0.858100i	0.567103	−	0.0518397i
$275$		−	4.54637i		−	0.274156i
$276$	0.391163	+	2.12170i	0.0235453	+	0.127711i
$277$		−	24.2326i		−	1.45600i	−0.685579	−	0.727999i	$-0.740451\pi$
$277$		−	24.2326i		−	1.45600i	0.685579	−	0.727999i	$-0.259549\pi$
$278$	1.34915	+	14.7591i	0.0809167	+	0.885192i
$279$	−36.4915			−2.18469
$280$	0.763897	+	2.72332i	0.0456516	+	0.162749i
$281$	−6.21748			−0.370904			−0.185452	−	0.982653i	$-0.559375\pi$
$281$	−6.21748			−0.370904			−0.185452	+	0.982653i	$0.559375\pi$
$282$	−3.49298	−	38.2116i	−0.208004	−	2.27547i
$283$		−	1.29632i		−	0.0770583i	−0.999257	−	0.0385292i	$-0.987733\pi$
$283$		−	1.29632i		−	0.0770583i	0.999257	−	0.0385292i	$-0.0122672\pi$
$284$	−18.0201	+	3.32225i	−1.06930	+	0.197139i
$285$			16.3455i			0.968222i
$286$	28.4711	−	2.60258i	1.68353	−	0.153894i
$287$	−1.35073			−0.0797312
$288$	−25.5564	+	12.5282i	−1.50592	+	0.738230i
$289$	50.0177			2.94222
$290$	−1.36368	+	0.124656i	−0.0800781	+	0.00732005i
$291$			4.94190i			0.289699i
$292$	−14.0864	+	2.59702i	−0.824344	+	0.151979i
$293$			15.0125i			0.877040i	0.898721	+	0.438520i	$0.144497\pi$
$293$			15.0125i			0.877040i	−0.898721	+	0.438520i	$0.855503\pi$
$294$	−0.364842	−	3.99120i	−0.0212780	−	0.232772i
$295$	5.89309			0.343109
$296$	2.76482	+	9.85667i	0.160702	+	0.572907i
$297$	−26.1733			−1.51873
$298$	0.206641	+	2.26056i	0.0119704	+	0.130951i
$299$			1.69257i			0.0978839i
$300$	1.02764	+	5.57401i	0.0593311	+	0.321816i
$301$		−	1.16422i		−	0.0671046i
$302$	22.1924	−	2.02864i	1.27703	−	0.116735i
$303$	−16.3707			−0.940472
$304$	8.22716	+	21.5539i	0.471860	+	1.23620i
$305$	3.58478			0.205264
$306$	58.0086	−	5.30265i	3.31613	−	0.303133i
$307$			27.1934i			1.55201i	0.630726	+	0.776006i	$0.282757\pi$
$307$			27.1934i			1.55201i	−0.630726	+	0.776006i	$0.717243\pi$
$308$	1.64858	+	8.94203i	0.0939368	+	0.509520i
$309$			28.0012i			1.59293i
$310$	0.933706	+	10.2143i	0.0530309	+	0.580134i
$311$	11.2491			0.637879			0.318940	−	0.947775i	$-0.396673\pi$
$311$	11.2491			0.637879			0.318940	+	0.947775i	$0.396673\pi$
$312$	−34.3183	+	9.62636i	−1.94289	+	0.544985i
$313$	25.2020			1.42450			0.712250	−	0.701926i	$-0.247676\pi$
$313$	25.2020			1.42450			0.712250	+	0.701926i	$0.247676\pi$
$314$	−1.38050	−	15.1021i	−0.0779064	−	0.852261i
$315$		−	5.03141i		−	0.283488i
$316$	−7.79585	+	1.43727i	−0.438551	+	0.0808527i
$317$			0.0762209i			0.00428099i	0.999998	+	0.00214050i	$0.000681341\pi$
$317$			0.0762209i			0.00428099i	−0.999998	+	0.00214050i	$0.999319\pi$
$318$	28.8377	−	2.63610i	1.61714	−	0.147825i
$319$	−4.40219			−0.246476
$320$	4.16067	+	6.83292i	0.232588	+	0.381972i
$321$	−9.59878			−0.535752
$322$	−0.536072	+	0.0490032i	−0.0298741	+	0.00273084i
$323$		−	47.2167i		−	2.62721i
$324$	2.40128	−	0.442709i	0.133405	−	0.0245950i
$325$			4.44664i			0.246655i
$326$	−0.187547	−	2.05168i	−0.0103873	−	0.113632i
$327$	−32.1422			−1.77747
$328$	−3.67847	+	1.03182i	−0.203110	+	0.0569727i
$329$	9.57395			0.527829
$330$	1.65870	+	18.1455i	0.0913087	+	0.998876i
$331$			10.5218i			0.578329i	0.957279	+	0.289165i	$0.0933775\pi$
$331$			10.5218i			0.578329i	−0.957279	+	0.289165i	$0.906622\pi$
$332$	1.25119	+	6.78655i	0.0686681	+	0.372460i
$333$		−	18.2105i		−	0.997929i
$334$	−7.02378	+	0.642054i	−0.384324	+	0.0351316i
$335$	9.25445			0.505625
$336$	−4.04245	−	10.5906i	−0.220534	−	0.577766i
$337$	−29.1778			−1.58942			−0.794709	−	0.606990i	$-0.792377\pi$
$337$	−29.1778			−1.58942			−0.794709	+	0.606990i	$0.792377\pi$
$338$	−9.53810	+	0.871892i	−0.518804	+	0.0474246i
$339$		−	16.8855i		−	0.917094i
$340$	−2.96853	−	16.1015i	−0.160991	−	0.873227i
$341$			32.9736i			1.78562i
$342$	−3.73594	−	40.8695i	−0.202016	−	2.20997i
$343$	1.00000			0.0539949
$344$	−0.889345	−	3.17055i	−0.0479503	−	0.170944i
$345$	−1.07873			−0.0580767
$346$	3.08383	+	33.7358i	0.165788	+	1.81365i
$347$		−	27.5540i		−	1.47918i	−0.673060	−	0.739588i	$-0.735020\pi$
$347$		−	27.5540i		−	1.47918i	0.673060	−	0.739588i	$-0.264980\pi$
$348$	5.39725	−	0.995055i	0.289323	−	0.0533406i
$349$		−	34.9835i		−	1.87262i	−0.351169	−	0.936312i	$-0.614216\pi$
$349$		−	34.9835i		−	1.87262i	0.351169	−	0.936312i	$-0.385784\pi$
$350$	−1.40834	+	0.128739i	−0.0752790	+	0.00688137i
$351$	25.5992			1.36638
$352$	11.3204	+	23.0927i	0.603380	+	1.23084i
$353$	24.8542			1.32285			0.661427	−	0.750009i	$-0.269951\pi$
$353$	24.8542			1.32285			0.661427	+	0.750009i	$0.269951\pi$
$354$	−23.5205	+	2.15005i	−1.25010	+	0.114274i
$355$		−	9.16190i		−	0.486263i
$356$	−28.8944	+	5.32707i	−1.53140	+	0.282334i
$357$			23.2001i			1.22788i
$358$	−1.25483	−	13.7273i	−0.0663197	−	0.725508i
$359$	20.7352			1.09436			0.547182	−	0.837014i	$-0.315701\pi$
$359$	20.7352			1.09436			0.547182	+	0.837014i	$0.315701\pi$
$360$	−3.84348	−	13.7021i	−0.202569	−	0.722166i
$361$	−14.2661			−0.750849
$362$	−0.298423	−	3.26462i	−0.0156848	−	0.171584i
$363$			27.4030i			1.43828i
$364$	−1.61242	−	8.74588i	−0.0845138	−	0.458409i
$365$		−	7.16190i		−	0.374871i
$366$	−14.3076	+	1.30788i	−0.747869	+	0.0683638i
$367$	10.2447			0.534767			0.267383	−	0.963590i	$-0.413841\pi$
$367$	10.2447			0.534767			0.267383	+	0.963590i	$0.413841\pi$
$368$	−1.42246	+	0.542955i	−0.0741510	+	0.0283035i
$369$	6.79609			0.353790
$370$	−5.09729	+	0.465951i	−0.264996	+	0.0242236i
$371$			7.22532i			0.375120i
$372$	−7.45322	−	40.4268i	−0.386431	−	2.09603i
$373$		−	1.45557i		−	0.0753664i	−0.999290	−	0.0376832i	$-0.988002\pi$
$373$		−	1.45557i		−	0.0753664i	0.999290	−	0.0376832i	$-0.0119978\pi$
$374$	−4.79146	−	52.4164i	−0.247760	−	2.71039i
$375$	−2.83397			−0.146346
$376$	26.0729	−	7.31351i	1.34461	−	0.377166i
$377$	4.30563			0.221751
$378$	0.741144	+	8.10778i	0.0381204	+	0.417019i
$379$			8.98237i			0.461394i	0.973026	+	0.230697i	$0.0741005\pi$
$379$			8.98237i			0.461394i	−0.973026	+	0.230697i	$0.925899\pi$
$380$	−11.3442	+	2.09145i	−0.581944	+	0.107289i
$381$			1.48460i			0.0760585i
$382$	23.0073	−	2.10313i	1.17716	−	0.107606i
$383$	−8.70087			−0.444594			−0.222297	−	0.974979i	$-0.571355\pi$
$383$	−8.70087			−0.444594			−0.222297	+	0.974979i	$0.571355\pi$
$384$	−19.0990	−	25.7536i	−0.974642	−	1.31423i
$385$	−4.54637			−0.231704
$386$	−2.05410	+	0.187769i	−0.104551	+	0.00955717i
$387$			5.85768i			0.297763i
$388$	−3.42981	+	0.632331i	−0.174122	+	0.0321018i
$389$			12.1578i			0.616427i	0.951317	+	0.308213i	$0.0997311\pi$
$389$			12.1578i			0.616427i	−0.951317	+	0.308213i	$0.900269\pi$
$390$	−1.62232	−	17.7474i	−0.0821493	−	0.898676i
$391$	3.11609			0.157587
$392$	2.72332	−	0.763897i	0.137548	−	0.0385826i
$393$	26.2472			1.32400
$394$	−2.57377	−	28.1559i	−0.129665	−	1.41847i
$395$		−	3.96361i		−	0.199431i
$396$	−8.29471	−	44.9911i	−0.416825	−	2.26089i
$397$		−	25.5180i		−	1.28071i	−0.768079	−	0.640355i	$-0.778787\pi$
$397$		−	25.5180i		−	1.28071i	0.768079	−	0.640355i	$-0.221213\pi$
$398$	19.6185	−	1.79336i	0.983388	−	0.0898929i
$399$	16.3455			0.818297
$400$	−3.73702	+	1.42642i	−0.186851	+	0.0713212i
$401$	24.2089			1.20893			0.604466	−	0.796631i	$-0.293386\pi$
$401$	24.2089			1.20893			0.604466	+	0.796631i	$0.293386\pi$
$402$	−36.9364	+	3.37641i	−1.84222	+	0.168400i
$403$		−	32.2502i		−	1.60650i
$404$	−2.09468	−	11.3617i	−0.104214	−	0.565265i
$405$			1.22088i			0.0606659i
$406$	0.124656	+	1.36368i	0.00618657	+	0.0676783i
$407$	−16.4549			−0.815641
$408$	17.7225	+	63.1814i	0.877395	+	3.12794i
$409$	−4.16694			−0.206042			−0.103021	−	0.994679i	$-0.532851\pi$
$409$	−4.16694			−0.206042			−0.103021	+	0.994679i	$0.532851\pi$
$410$	−0.173891	−	1.90229i	−0.00858788	−	0.0939475i
$411$		−	18.8897i		−	0.931760i
$412$	−19.4336	+	3.58284i	−0.957423	+	0.176514i
$413$		−	5.89309i		−	0.289980i
$414$	2.69720	−	0.246555i	0.132560	−	0.0121175i
$415$	−3.45046			−0.169377
$416$	−11.0721	−	22.5861i	−0.542853	−	1.10737i
$417$	29.6994			1.45439
$418$	−36.9295	+	3.37578i	−1.80628	+	0.165115i
$419$			31.8087i			1.55396i	0.629526	+	0.776979i	$0.283249\pi$
$419$			31.8087i			1.55396i	−0.629526	+	0.776979i	$0.716751\pi$
$420$	5.57401	−	1.02764i	0.271984	−	0.0501439i
$421$			34.3036i			1.67185i	0.548840	+	0.835927i	$0.315070\pi$
$421$			34.3036i			1.67185i	−0.548840	+	0.835927i	$0.684930\pi$
$422$	−1.10116	−	12.0461i	−0.0536034	−	0.586397i
$423$	−48.1705			−2.34213
$424$	5.51940	+	19.6769i	0.268046	+	0.955592i
$425$	8.18643			0.397100
$426$	3.34264	+	36.5670i	0.161952	+	1.77168i
$427$		−	3.58478i		−	0.173479i
$428$	−1.22819	−	6.66181i	−0.0593670	−	0.322011i
$429$		−	57.2917i		−	2.76607i
$430$	1.63962	−	0.149880i	0.0790696	−	0.00722787i
$431$	28.9872			1.39626			0.698132	−	0.715969i	$-0.254015\pi$
$431$	28.9872			1.39626			0.698132	+	0.715969i	$0.254015\pi$
$432$	8.21188	+	21.5139i	0.395094	+	1.03509i
$433$	−25.4121			−1.22123			−0.610614	−	0.791928i	$-0.709077\pi$
$433$	−25.4121			−1.22123			−0.610614	+	0.791928i	$0.709077\pi$
$434$	10.2143	−	0.933706i	0.490303	−	0.0448193i
$435$			2.74410i			0.131570i
$436$	−4.11270	−	22.3076i	−0.196962	−	1.06834i
$437$		−	2.19541i		−	0.105021i
$438$	2.61296	+	28.5846i	0.124852	+	1.36583i
$439$	13.1999			0.629995			0.314997	−	0.949093i	$-0.397996\pi$
$439$	13.1999			0.629995			0.314997	+	0.949093i	$0.397996\pi$
$440$	−12.3812	+	3.47295i	−0.590251	+	0.165567i
$441$	−5.03141			−0.239591
$442$	4.68635	+	51.2666i	0.222907	+	2.43850i
$443$			41.3116i			1.96277i	0.192047	+	0.981386i	$0.438488\pi$
$443$			41.3116i			1.96277i	−0.192047	+	0.981386i	$0.561512\pi$
$444$	20.1743	−	3.71941i	0.957432	−	0.176516i
$445$		−	14.6907i		−	0.696405i
$446$	−7.36301	+	0.673063i	−0.348649	+	0.0318705i
$447$	4.54888			0.215155
$448$	6.83292	−	4.16067i	0.322825	−	0.196573i
$449$	2.16460			0.102154			0.0510769	−	0.998695i	$-0.483735\pi$
$449$	2.16460			0.102154			0.0510769	+	0.998695i	$0.483735\pi$
$450$	7.08595	−	0.647737i	0.334035	−	0.0305346i
$451$		−	6.14093i		−	0.289165i
$452$	11.7190	−	2.16055i	0.551214	−	0.101624i
$453$		−	44.6572i		−	2.09818i
$454$	1.40410	+	15.3602i	0.0658976	+	0.720890i
$455$	4.44664			0.208462
$456$	44.5139	−	12.4862i	2.08455	−	0.584722i
$457$	−2.38342			−0.111492			−0.0557459	−	0.998445i	$-0.517754\pi$
$457$	−2.38342			−0.111492			−0.0557459	+	0.998445i	$0.517754\pi$
$458$	−0.718899	−	7.86443i	−0.0335920	−	0.367481i
$459$		−	47.1291i		−	2.19980i
$460$	−0.138026	−	0.748664i	−0.00643551	−	0.0349067i
$461$		−	6.43328i		−	0.299628i	−0.988714	−	0.149814i	$-0.952133\pi$
$461$		−	6.43328i		−	0.299628i	0.988714	−	0.149814i	$-0.0478674\pi$
$462$	18.1455	−	1.65870i	0.844204	−	0.0771699i
$463$	−10.1009			−0.469429			−0.234715	−	0.972064i	$-0.575416\pi$
$463$	−10.1009			−0.469429			−0.234715	+	0.972064i	$0.575416\pi$
$464$	1.38119	+	3.61851i	0.0641201	+	0.167985i
$465$	20.5540			0.953171
$466$	−6.25674	+	0.571937i	−0.289838	+	0.0264945i
$467$		−	11.8646i		−	0.549028i	−0.961583	−	0.274514i	$-0.911483\pi$
$467$		−	11.8646i		−	0.549028i	0.961583	−	0.274514i	$-0.0885170\pi$
$468$	8.11275	+	44.0041i	0.375012	+	2.03409i
$469$		−	9.25445i		−	0.427331i
$470$	1.23254	+	13.4834i	0.0568527	+	0.621943i
$471$	−30.3896			−1.40028
$472$	−4.50171	−	16.0488i	−0.207208	−	0.738704i
$473$	5.29298			0.243371
$474$	1.44609	+	15.8196i	0.0664212	+	0.726618i
$475$		−	5.76768i		−	0.264639i
$476$	−16.1015	+	2.96853i	−0.738011	+	0.136062i
$477$		−	36.3536i		−	1.66452i
$478$	−9.84221	+	0.899691i	−0.450172	+	0.0411509i
$479$	−11.3847			−0.520181			−0.260090	−	0.965584i	$-0.583752\pi$
$479$	−11.3847			−0.520181			−0.260090	+	0.965584i	$0.583752\pi$
$480$	14.3948	−	7.05657i	0.657029	−	0.322087i
$481$	16.0940			0.733822
$482$	19.0466	−	1.74108i	0.867549	−	0.0793039i
$483$			1.07873i			0.0490838i
$484$	−19.0184	+	3.50630i	−0.864472	+	0.159377i
$485$		−	1.74381i		−	0.0791821i
$486$	1.77801	+	19.4506i	0.0806520	+	0.882296i
$487$	36.8743			1.67093			0.835466	−	0.549542i	$-0.185198\pi$
$487$	36.8743			1.67093			0.835466	+	0.549542i	$0.185198\pi$
$488$	−2.73840	−	9.76249i	−0.123962	−	0.441927i
$489$	−4.12854			−0.186699
$490$	0.128739	+	1.40834i	0.00581582	+	0.0636224i
$491$		−	24.3208i		−	1.09758i	−0.835959	−	0.548792i	$-0.815088\pi$
$491$		−	24.3208i		−	1.09758i	0.835959	−	0.548792i	$-0.184912\pi$
$492$	1.38807	+	7.52900i	0.0625791	+	0.339433i
$493$		−	7.92682i		−	0.357006i
$494$	36.1194	−	3.30173i	1.62509	−	0.148552i
$495$	22.8746			1.02814
$496$	27.1036	−	10.3455i	1.21699	−	0.464525i
$497$	−9.16190			−0.410967
$498$	13.7715	−	1.25887i	0.617116	−	0.0564115i
$499$			42.8874i			1.91990i	0.280163	+	0.959952i	$0.409612\pi$
$499$			42.8874i			1.91990i	−0.280163	+	0.959952i	$0.590388\pi$
$500$	−0.362616	−	1.96685i	−0.0162167	−	0.0879603i
$501$			14.1338i			0.631451i
$502$	−2.16098	−	23.6401i	−0.0964490	−	1.05511i
$503$	37.2863			1.66251			0.831257	−	0.555888i	$-0.187622\pi$
$503$	37.2863			1.66251			0.831257	+	0.555888i	$0.187622\pi$
$504$	−13.7021	+	3.84348i	−0.610342	+	0.171202i
$505$	5.77658			0.257055
$506$	−0.222786	−	2.43718i	−0.00990406	−	0.108346i
$507$			19.1933i			0.852405i
$508$	−1.03035	+	0.189959i	−0.0457145	+	0.00842808i
$509$		−	28.5647i		−	1.26611i	−0.774108	−	0.633053i	$-0.781801\pi$
$509$		−	28.5647i		−	1.26611i	0.774108	−	0.633053i	$-0.218199\pi$
$510$	−32.6737	+	2.98675i	−1.44682	+	0.132256i
$511$	−7.16190			−0.316824
$512$	15.4299	−	16.5505i	0.681912	−	0.731434i
$513$	−33.2044			−1.46601
$514$	−22.6088	+	2.06670i	−0.997231	+	0.0911583i
$515$		−	9.88054i		−	0.435389i
$516$	−6.48939	+	1.19641i	−0.285679	+	0.0526688i
$517$			43.5267i			1.91430i
$518$	0.465951	+	5.09729i	0.0204727	+	0.223962i
$519$	67.8857			2.97985
$520$	12.1096	−	3.39677i	0.531041	−	0.148958i
$521$	23.3899			1.02473			0.512364	−	0.858768i	$-0.328770\pi$
$521$	23.3899			1.02473			0.512364	+	0.858768i	$0.328770\pi$
$522$	−0.627196	−	6.86124i	−0.0274516	−	0.300308i
$523$		−	6.51217i		−	0.284757i	−0.989812	−	0.142379i	$-0.954525\pi$
$523$		−	6.51217i		−	0.284757i	0.989812	−	0.142379i	$-0.0454751\pi$
$524$	3.35841	+	18.2163i	0.146713	+	0.795781i
$525$			2.83397i			0.123685i
$526$	−10.8984	+	0.996234i	−0.475191	+	0.0434379i
$527$	−59.3739			−2.58637
$528$	48.1488	−	18.3785i	2.09541	−	0.799820i
$529$	−22.8551			−0.993701
$530$	−10.1757	+	0.930178i	−0.442005	+	0.0404043i
$531$			29.6506i			1.28672i
$532$	2.09145	+	11.3442i	0.0906759	+	0.491832i
$533$			6.00622i			0.260158i
$534$	5.35977	+	58.6335i	0.231940	+	2.53732i
$535$	3.38704			0.146434
$536$	−7.06944	−	25.2028i	−0.305353	−	1.08860i
$537$	−27.6231			−1.19202
$538$	3.93076	+	43.0007i	0.169467	+	1.85389i
$539$			4.54637i			0.195826i
$540$	−11.3231	+	2.08757i	−0.487269	+	0.0898347i
$541$		−	12.4310i		−	0.534452i	−0.963634	−	0.267226i	$-0.913893\pi$
$541$		−	12.4310i		−	0.534452i	0.963634	−	0.267226i	$-0.0861070\pi$
$542$	−38.1634	+	3.48857i	−1.63926	+	0.149847i
$543$	−6.56932			−0.281916
$544$	−41.5819	+	20.3841i	−1.78281	+	0.873963i
$545$	11.3417			0.485827
$546$	−17.7474	+	1.62232i	−0.759520	+	0.0694288i
$547$			37.7733i			1.61507i	0.589820	+	0.807535i	$0.299199\pi$
$547$			37.7733i			1.61507i	−0.589820	+	0.807535i	$0.700801\pi$
$548$	13.1099	−	2.41700i	0.560029	−	0.103249i
$549$			18.0365i			0.769779i
$550$	−0.585293	−	6.40284i	−0.0249570	−	0.273018i
$551$	−5.58478			−0.237919
$552$	0.824036	+	2.93772i	0.0350733	+	0.125037i
$553$	−3.96361			−0.168550
$554$	−3.11967	−	34.1278i	−0.132542	−	1.44995i
$555$			10.2572i			0.435393i
$556$	3.80013	+	20.6122i	0.161161	+	0.874151i
$557$		−	30.9689i		−	1.31219i	−0.754676	−	0.656097i	$-0.772206\pi$
$557$		−	30.9689i		−	1.31219i	0.754676	−	0.656097i	$-0.227794\pi$
$558$	−51.3924	+	4.69786i	−2.17562	+	0.198876i
$559$	−5.17687			−0.218958
$560$	1.42642	+	3.73702i	0.0602774	+	0.157918i
$561$	−105.476			−4.45322
$562$	−8.75634	+	0.800429i	−0.369364	+	0.0337641i
$563$		−	26.5165i		−	1.11754i	−0.829323	−	0.558769i	$-0.811274\pi$
$563$		−	26.5165i		−	1.11754i	0.829323	−	0.558769i	$-0.188726\pi$
$564$	−9.83862	−	53.3653i	−0.414280	−	2.24709i
$565$			5.95824i			0.250665i
$566$	−0.166887	−	1.82566i	−0.00701477	−	0.0767384i
$567$	1.22088			0.0512720
$568$	−24.9508	+	6.99875i	−1.04691	+	0.293661i
$569$	−26.0083			−1.09032			−0.545162	−	0.838331i	$-0.683532\pi$
$569$	−26.0083			−1.09032			−0.545162	+	0.838331i	$0.683532\pi$
$570$	2.10429	+	23.0200i	0.0881391	+	0.964201i
$571$			26.9170i			1.12644i	0.826306	+	0.563221i	$0.190438\pi$
$571$			26.9170i			1.12644i	−0.826306	+	0.563221i	$0.809562\pi$
$572$	39.7620	−	7.33066i	1.66253	−	0.306510i
$573$		−	46.2972i		−	1.93409i
$574$	−1.90229	+	0.173891i	−0.0794002	+	0.00725808i
$575$	0.380641			0.0158738
$576$	−34.3793	+	20.9340i	−1.43247	+	0.872252i
$577$	22.7789			0.948296			0.474148	−	0.880445i	$-0.342756\pi$
$577$	22.7789			0.948296			0.474148	+	0.880445i	$0.342756\pi$
$578$	70.4420	−	6.43920i	2.93000	−	0.267835i
$579$			4.13343i			0.171779i
$580$	−1.90448	+	0.351117i	−0.0790792	+	0.0145793i
$581$			3.45046i			0.143149i
$582$	0.636213	+	6.95988i	0.0263719	+	0.288496i
$583$	−32.8490			−1.36047
$584$	−19.5041	+	5.47095i	−0.807087	+	0.226390i
$585$	−22.3729			−0.925004
$586$	1.93269	+	21.1427i	0.0798386	+	0.873398i
$587$		−	34.7755i		−	1.43534i	−0.696385	−	0.717668i	$-0.745209\pi$
$587$		−	34.7755i		−	1.43534i	0.696385	−	0.717668i	$-0.254791\pi$
$588$	−1.02764	−	5.57401i	−0.0423793	−	0.229868i
$589$			41.8314i			1.72363i
$590$	8.29948	−	0.758668i	0.341684	−	0.0312339i
$591$	−56.6575			−2.33058
$592$	5.16274	+	13.5256i	0.212187	+	0.555899i
$593$	0.606770			0.0249171			0.0124585	−	0.999922i	$-0.496034\pi$
$593$	0.606770			0.0249171			0.0124585	+	0.999922i	$0.496034\pi$
$594$	−36.8610	+	3.36951i	−1.51242	+	0.138253i
$595$		−	8.18643i		−	0.335611i
$596$	0.582043	+	3.15704i	0.0238414	+	0.129317i
$597$		−	39.4779i		−	1.61572i
$598$	0.217899	+	2.38372i	0.00891056	+	0.0974775i
$599$	−8.61328			−0.351929			−0.175965	−	0.984396i	$-0.556304\pi$
$599$	−8.61328			−0.351929			−0.175965	+	0.984396i	$0.556304\pi$
$600$	2.16486	+	7.71781i	0.0883802	+	0.315078i
$601$	5.72601			0.233569			0.116784	−	0.993157i	$-0.462741\pi$
$601$	5.72601			0.233569			0.116784	+	0.993157i	$0.462741\pi$
$602$	−0.149880	−	1.63962i	−0.00610866	−	0.0668260i
$603$			46.5630i			1.89619i
$604$	30.9933	−	5.71403i	1.26110	−	0.232501i
$605$		−	9.66945i		−	0.393119i
$606$	−23.0555	+	2.10754i	−0.936567	+	0.0856129i
$607$	22.9112			0.929936			0.464968	−	0.885328i	$-0.346066\pi$
$607$	22.9112			0.929936			0.464968	+	0.885328i	$0.346066\pi$
$608$	14.3615	+	29.2962i	0.582434	+	1.18812i
$609$	2.74410			0.111197
$610$	5.04859	−	0.461499i	0.204411	−	0.0186855i
$611$		−	42.5719i		−	1.72227i
$612$	81.0133	−	14.9359i	3.27477	−	0.603748i
$613$			5.31995i			0.214871i	0.994212	+	0.107435i	$0.0342639\pi$
$613$			5.31995i			0.214871i	−0.994212	+	0.107435i	$0.965736\pi$
$614$	3.50084	+	38.2977i	0.141283	+	1.54557i
$615$	−3.82794			−0.154357
$616$	3.47295	+	12.3812i	0.139929	+	0.498853i
$617$	25.6883			1.03417			0.517086	−	0.855933i	$-0.327017\pi$
$617$	25.6883			1.03417			0.517086	+	0.855933i	$0.327017\pi$
$618$	3.60483	+	39.4353i	0.145008	+	1.58632i
$619$		−	1.92228i		−	0.0772631i	−0.999254	−	0.0386315i	$-0.987700\pi$
$619$		−	1.92228i		−	0.0772631i	0.999254	−	0.0386315i	$-0.0122999\pi$
$620$	2.62995	+	14.2650i	0.105621	+	0.572898i
$621$		−	2.19134i		−	0.0879354i
$622$	15.8426	−	1.44820i	0.635231	−	0.0580673i
$623$	−14.6907			−0.588570
$624$	−47.0926	+	17.9753i	−1.88521	+	0.719588i
$625$	1.00000			0.0400000
$626$	35.4930	−	3.24447i	1.41859	−	0.129675i
$627$			74.3125i			2.96775i
$628$	−3.88845	−	21.0912i	−0.155166	−	0.841630i
$629$		−	29.6296i		−	1.18141i
$630$	−0.647737	−	7.08595i	−0.0258065	−	0.282311i
$631$	19.0406			0.757994			0.378997	−	0.925398i	$-0.376269\pi$
$631$	19.0406			0.757994			0.378997	+	0.925398i	$0.376269\pi$
$632$	−10.7942	+	3.02779i	−0.429370	+	0.120439i
$633$	−24.2402			−0.963461
$634$	0.00981257	+	0.107345i	0.000389707	+	0.00426322i
$635$		−	0.523858i		−	0.0207887i
$636$	40.2740	−	7.42506i	1.59697	−	0.294423i
$637$		−	4.44664i		−	0.176182i
$638$	−6.19979	+	0.566732i	−0.245452	+	0.0224371i
$639$	46.0973			1.82358
$640$	6.73930	+	9.08745i	0.266394	+	0.359213i
$641$	−40.9835			−1.61875			−0.809376	−	0.587291i	$-0.800194\pi$
$641$	−40.9835			−1.61875			−0.809376	+	0.587291i	$0.800194\pi$
$642$	−13.5184	+	1.23573i	−0.533527	+	0.0487705i
$643$		−	1.79701i		−	0.0708672i	−0.999372	−	0.0354336i	$-0.988719\pi$
$643$		−	1.79701i		−	0.0708672i	0.999372	−	0.0354336i	$-0.0112812\pi$
$644$	−0.748664	+	0.138026i	−0.0295015	+	0.00543900i
$645$		−	3.29938i		−	0.129913i
$646$	−6.07861	−	66.4973i	−0.239160	−	2.61630i
$647$	14.5992			0.573953			0.286977	−	0.957938i	$-0.407350\pi$
$647$	14.5992			0.573953			0.286977	+	0.957938i	$0.407350\pi$
$648$	3.32484	−	0.932624i	0.130612	−	0.0366369i
$649$	26.7921			1.05168
$650$	0.572454	+	6.26238i	0.0224535	+	0.245631i
$651$		−	20.5540i		−	0.805576i
$652$	−0.528260	−	2.86532i	−0.0206882	−	0.112214i
$653$			7.02884i			0.275060i	0.990498	+	0.137530i	$0.0439163\pi$
$653$			7.02884i			0.275060i	−0.990498	+	0.137530i	$0.956084\pi$
$654$	−45.2672	+	4.13794i	−1.77009	+	0.161806i
$655$	−9.26163			−0.361882
$656$	−5.04771	+	1.92672i	−0.197080	+	0.0752256i
$657$	36.0345			1.40584
$658$	13.4834	−	1.23254i	0.525638	−	0.0480493i
$659$		−	3.33841i		−	0.130046i	−0.997884	−	0.0650230i	$-0.979288\pi$
$659$		−	3.33841i		−	0.130046i	0.997884	−	0.0650230i	$-0.0207121\pi$
$660$	4.67205	+	25.3415i	0.181859	+	0.986417i
$661$			32.2890i			1.25590i	0.778255	+	0.627948i	$0.216105\pi$
$661$			32.2890i			1.25590i	−0.778255	+	0.627948i	$0.783895\pi$
$662$	1.35456	+	14.8183i	0.0526464	+	0.575928i
$663$	103.163			4.00650
$664$	2.63580	+	9.39671i	0.102289	+	0.364663i
$665$	−5.76768			−0.223661
$666$	−2.34439	−	25.6466i	−0.0908434	−	0.993785i
$667$		−	0.368570i		−	0.0142711i
$668$	−9.80922	+	1.80846i	−0.379530	+	0.0699715i
$669$			14.8164i			0.572836i
$670$	13.0334	−	1.19140i	0.503525	−	0.0460280i
$671$	16.2977			0.629166
$672$	−7.05657	−	14.3948i	−0.272213	−	0.555291i
$673$	−14.5415			−0.560533			−0.280266	−	0.959922i	$-0.590423\pi$
$673$	−14.5415			−0.560533			−0.280266	+	0.959922i	$0.590423\pi$
$674$	−41.0924	+	3.75631i	−1.58282	+	0.144688i
$675$		−	5.75697i		−	0.221586i
$676$	−13.3207	+	2.45584i	−0.512333	+	0.0944555i
$677$			46.2035i			1.77575i	0.460089	+	0.887873i	$0.347817\pi$
$677$			46.2035i			1.77575i	−0.460089	+	0.887873i	$0.652183\pi$
$678$	−2.17381	−	23.7805i	−0.0834848	−	0.913286i
$679$	−1.74381			−0.0669211
$680$	−6.25359	−	22.2943i	−0.239814	−	0.854946i
$681$	30.9090			1.18444
$682$	4.24497	+	46.4380i	0.162548	+	1.77820i
$683$		−	11.2797i		−	0.431606i	−0.976437	−	0.215803i	$-0.930763\pi$
$683$		−	11.2797i		−	0.431606i	0.976437	−	0.215803i	$-0.0692370\pi$
$684$	−10.5230	−	57.0772i	−0.402355	−	2.18240i
$685$			6.66544i			0.254674i
$686$	1.40834	−	0.128739i	0.0537707	−	0.00491526i
$687$	−15.8254			−0.603777
$688$	−1.66067	−	4.35072i	−0.0633126	−	0.165870i
$689$	32.1284			1.22399
$690$	−1.51922	+	0.138874i	−0.0578355	+	0.00528683i
$691$			22.1420i			0.842321i	0.906986	+	0.421161i	$0.138377\pi$
$691$			22.1420i			0.842321i	−0.906986	+	0.421161i	$0.861623\pi$
$692$	8.68619	+	47.1145i	0.330199	+	1.79102i
$693$		−	22.8746i		−	0.868936i
$694$	−3.54726	−	38.8054i	−0.134652	−	1.47303i
$695$	−10.4798			−0.397520
$696$	7.47307	−	2.09621i	0.283266	−	0.0794567i
$697$	11.0577			0.418839
$698$	−4.50373	−	49.2687i	−0.170469	−	1.86485i
$699$			12.5903i			0.476209i
$700$	−1.96685	+	0.362616i	−0.0743400	+	0.0137056i
$701$		−	37.2946i		−	1.40860i	−0.709903	−	0.704300i	$-0.751261\pi$
$701$		−	37.2946i		−	1.40860i	0.709903	−	0.704300i	$-0.248739\pi$
$702$	36.0524	−	3.29560i	1.36071	−	0.124384i
$703$	−20.8753			−0.787327
$704$	18.9159	+	31.0650i	0.712921	+	1.17081i
$705$	27.1323			1.02186
$706$	35.0032	−	3.19969i	1.31736	−	0.120422i
$707$		−	5.77658i		−	0.217251i
$708$	−32.8481	+	6.05600i	−1.23451	+	0.227598i
$709$			13.8733i			0.521021i	0.965471	+	0.260511i	$0.0838909\pi$
$709$			13.8733i			0.521021i	−0.965471	+	0.260511i	$0.916109\pi$
$710$	−1.17949	−	12.9031i	−0.0442655	−	0.484244i
$711$	19.9426			0.747905
$712$	−40.0074	+	11.2222i	−1.49934	+	0.420568i
$713$	−2.76068			−0.103388
$714$	2.98675	+	32.6737i	0.111776	+	1.22278i
$715$			20.2160i			0.756037i
$716$	−3.53445	−	19.1711i	−0.132089	−	0.716458i
$717$			19.8053i			0.739641i
$718$	29.2023	−	2.66942i	1.08982	−	0.0996220i
$719$	−41.2404			−1.53801			−0.769004	−	0.639244i	$-0.779248\pi$
$719$	−41.2404			−1.53801			−0.769004	+	0.639244i	$0.779248\pi$
$720$	−7.17693	−	18.8025i	−0.267468	−	0.700727i
$721$	−9.88054			−0.367971
$722$	−20.0916	+	1.83660i	−0.747732	+	0.0683512i
$723$		−	38.3271i		−	1.42540i
$724$	−0.840564	−	4.55928i	−0.0312393	−	0.169444i
$725$		−	0.968288i		−	0.0359613i
$726$	3.52782	+	38.5928i	0.130930	+	1.43231i
$727$	19.1957			0.711927			0.355964	−	0.934500i	$-0.384153\pi$
$727$	19.1957			0.711927			0.355964	+	0.934500i	$0.384153\pi$
$728$	−3.39677	−	12.1096i	−0.125893	−	0.448812i
$729$	42.8026			1.58528
$730$	−0.922013	−	10.0864i	−0.0341252	−	0.373314i
$731$			9.53082i			0.352510i
$732$	−19.9816	+	3.68387i	−0.738541	+	0.136160i
$733$			1.23639i			0.0456671i	0.999739	+	0.0228335i	$0.00726877\pi$
$733$			1.23639i			0.0456671i	−0.999739	+	0.0228335i	$0.992731\pi$
$734$	14.4280	−	1.31888i	0.532546	−	0.0486808i
$735$	2.83397			0.104533
$736$	−1.93341	+	0.947792i	−0.0712666	+	0.0349361i
$737$	42.0741			1.54982
$738$	9.57122	−	0.874919i	0.352321	−	0.0322062i
$739$			18.2637i			0.671843i	0.941890	+	0.335921i	$0.109048\pi$
$739$			18.2637i			0.671843i	−0.941890	+	0.335921i	$0.890952\pi$
$740$	−7.11875	+	1.31244i	−0.261690	+	0.0482461i
$741$		−	72.6823i		−	2.67005i
$742$	0.930178	+	10.1757i	0.0341479	+	0.373563i
$743$	−4.06988			−0.149309			−0.0746547	−	0.997209i	$-0.523785\pi$
$743$	−4.06988			−0.149309			−0.0746547	+	0.997209i	$0.523785\pi$
$744$	−15.7012	−	55.9752i	−0.575633	−	2.05215i
$745$	−1.60512			−0.0588072
$746$	−0.187388	−	2.04994i	−0.00686075	−	0.0750535i
$747$		−	17.3607i		−	0.635195i
$748$	−13.4960	−	73.2034i	−0.493463	−	2.67658i
$749$		−	3.38704i		−	0.123760i
$750$	−3.99120	+	0.364842i	−0.145738	+	0.0133221i
$751$	−26.1941			−0.955836			−0.477918	−	0.878404i	$-0.658608\pi$
$751$	−26.1941			−0.955836			−0.477918	+	0.878404i	$0.658608\pi$
$752$	35.7781	−	13.6565i	1.30469	−	0.498002i
$753$	−47.5704			−1.73356
$754$	6.06379	−	0.554300i	0.220830	−	0.0201864i
$755$			15.7578i			0.573486i
$756$	2.08757	+	11.3231i	0.0759242	+	0.411818i
$757$		−	37.9339i		−	1.37873i	−0.724414	−	0.689365i	$-0.757890\pi$
$757$		−	37.9339i		−	1.37873i	0.724414	−	0.689365i	$-0.242110\pi$
$758$	1.15638	+	12.6503i	0.0420015	+	0.459478i
$759$	−4.90429			−0.178014
$760$	−15.7072	+	4.40591i	−0.569761	+	0.159819i
$761$	−0.753386			−0.0273102			−0.0136551	−	0.999907i	$-0.504347\pi$
$761$	−0.753386			−0.0273102			−0.0136551	+	0.999907i	$0.504347\pi$
$762$	0.191125	+	2.09083i	0.00692375	+	0.0757427i
$763$		−	11.3417i		−	0.410599i
$764$	32.1314	−	5.92386i	1.16247	−	0.214318i
$765$			41.1893i			1.48920i
$766$	−12.2538	+	1.12014i	−0.442748	+	0.0404722i
$767$	−26.2044			−0.946187
$768$	−30.2134	−	33.8111i	−1.09023	−	1.22005i
$769$	7.17360			0.258687			0.129343	−	0.991600i	$-0.458713\pi$
$769$	7.17360			0.258687			0.129343	+	0.991600i	$0.458713\pi$
$770$	−6.40284	+	0.585293i	−0.230742	+	0.0210925i
$771$			45.4951i			1.63847i
$772$	−2.86871	+	0.528885i	−0.103247	+	0.0190350i
$773$		−	10.8724i		−	0.391054i	−0.980698	−	0.195527i	$-0.937358\pi$
$773$		−	10.8724i		−	0.391054i	0.980698	−	0.195527i	$-0.0626417\pi$
$774$	0.754109	+	8.24962i	0.0271059	+	0.296526i
$775$	−7.25273			−0.260526
$776$	−4.74894	+	1.33209i	−0.170477	+	0.0478191i
$777$	10.2572			0.367974
$778$	1.56518	+	17.1224i	0.0561145	+	0.613867i
$779$		−	7.79059i		−	0.279127i
$780$	−4.56956	−	24.7856i	−0.163616	−	0.887467i
$781$		−	41.6534i		−	1.49047i
$782$	4.38852	−	0.401161i	0.156933	−	0.0143455i
$783$	−5.57441			−0.199213
$784$	3.73702	−	1.42642i	0.133465	−	0.0509437i
$785$	10.7233			0.382732
$786$	36.9651	−	3.37903i	1.31850	−	0.120526i
$787$			20.5623i			0.732968i	0.930424	+	0.366484i	$0.119439\pi$
$787$			20.5623i			0.732968i	−0.930424	+	0.366484i	$0.880561\pi$
$788$	−7.24950	−	39.3218i	−0.258253	−	1.40078i
$789$			21.9305i			0.780747i
$790$	−0.510270	−	5.58212i	−0.0181546	−	0.198603i
$791$	5.95824			0.211851
$792$	−17.4739	−	62.2949i	−0.620907	−	2.21355i
$793$	−15.9402			−0.566053
$794$	−3.28514	−	35.9380i	−0.116585	−	1.27539i
$795$			20.4764i			0.726222i
$796$	27.3987	−	5.05132i	0.971122	−	0.179039i
$797$			23.6674i			0.838342i	0.907907	+	0.419171i	$0.137679\pi$
$797$			23.6674i			0.838342i	−0.907907	+	0.419171i	$0.862321\pi$
$798$	23.0200	−	2.10429i	0.814899	−	0.0744911i
$799$	−78.3765			−2.77276
$800$	−5.07936	+	2.48999i	−0.179583	+	0.0880345i
$801$	73.9149			2.61165
$802$	34.0943	−	3.11661i	1.20391	−	0.110051i
$803$		−	32.5606i		−	1.14904i
$804$	−51.5844	+	9.51028i	−1.81924	+	0.335402i
$805$		−	0.380641i		−	0.0134158i
$806$	−4.15185	−	45.4194i	−0.146243	−	1.59983i
$807$	86.5294			3.04598
$808$	−4.41271	−	15.7315i	−0.155239	−	0.553431i
$809$	−19.0543			−0.669912			−0.334956	−	0.942234i	$-0.608722\pi$
$809$	−19.0543			−0.669912			−0.334956	+	0.942234i	$0.608722\pi$
$810$	0.157174	+	1.71941i	0.00552253	+	0.0604140i
$811$		−	7.69760i		−	0.270299i	−0.990825	−	0.135150i	$-0.956848\pi$
$811$		−	7.69760i		−	0.270299i	0.990825	−	0.135150i	$-0.0431515\pi$
$812$	0.351117	+	1.90448i	0.0123218	+	0.0668342i
$813$			76.7954i			2.69333i
$814$	−23.1742	+	2.11838i	−0.812254	+	0.0742493i
$815$	1.45680			0.0510296
$816$	33.0932	+	86.6994i	1.15849	+	3.03509i
$817$	6.71486			0.234923
$818$	−5.86848	+	0.536446i	−0.205187	+	0.0187564i
$819$			22.3729i			0.781771i
$820$	−0.489797	−	2.65669i	−0.0171044	−	0.0927757i
$821$			3.40384i			0.118795i	0.998234	+	0.0593975i	$0.0189179\pi$
$821$			3.40384i			0.118795i	−0.998234	+	0.0593975i	$0.981082\pi$
$822$	−2.43183	−	26.6032i	−0.0848199	−	0.927891i
$823$	−39.2339			−1.36761			−0.683804	−	0.729665i	$-0.739676\pi$
$823$	−39.2339			−1.36761			−0.683804	+	0.729665i	$0.739676\pi$
$824$	−26.9079	+	7.54771i	−0.937380	+	0.262937i
$825$	−12.8843			−0.448573
$826$	−0.758668	−	8.29948i	−0.0263974	−	0.288776i
$827$			21.9059i			0.761742i	0.924628	+	0.380871i	$0.124376\pi$
$827$			21.9059i			0.761742i	−0.924628	+	0.380871i	$0.875624\pi$
$828$	3.76684	−	0.694468i	0.130907	−	0.0241344i
$829$		−	2.55583i		−	0.0887677i	−0.999015	−	0.0443839i	$-0.985868\pi$
$829$		−	2.55583i		−	0.0887677i	0.999015	−	0.0443839i	$-0.0141325\pi$
$830$	−4.85943	+	0.444208i	−0.168673	+	0.0154187i
$831$	−68.6746			−2.38230
$832$	−18.5010	−	30.3835i	−0.641406	−	1.05336i
$833$	−8.18643			−0.283643
$834$	41.8269	−	3.82346i	1.44835	−	0.132396i
$835$		−	4.98727i		−	0.172592i
$836$	−51.5748	+	9.50851i	−1.78375	+	0.328859i
$837$			41.7537i			1.44322i
$838$	4.09501	+	44.7976i	0.141460	+	1.54751i
$839$	6.48166			0.223772			0.111886	−	0.993721i	$-0.464311\pi$
$839$	6.48166			0.223772			0.111886	+	0.993721i	$0.464311\pi$
$840$	7.71781	−	2.16486i	0.266290	−	0.0746949i
$841$	28.0624			0.967670
$842$	4.41619	+	48.3112i	0.152192	+	1.66491i
$843$			17.6202i			0.606871i
$844$	−3.10161	−	16.8233i	−0.106762	−	0.579083i
$845$		−	6.77257i		−	0.232984i
$846$	−67.8405	+	6.20140i	−2.33241	+	0.213209i
$847$	−9.66945			−0.332246
$848$	10.3064	+	27.0012i	0.353922	+	0.927224i
$849$	−3.67374			−0.126083
$850$	11.5293	−	1.05391i	0.395451	−	0.0361488i
$851$		−	1.37768i		−	0.0472261i
$852$	9.41517	+	51.0685i	0.322558	+	1.74958i
$853$			44.0723i			1.50901i	0.656297	+	0.754503i	$0.272122\pi$
$853$			44.0723i			1.50901i	−0.656297	+	0.754503i	$0.727878\pi$
$854$	−0.461499	−	5.04859i	−0.0157922	−	0.172759i
$855$	29.0196			0.992449
$856$	−2.58735	−	9.22399i	−0.0884337	−	0.315269i
$857$	−34.7369			−1.18659			−0.593295	−	0.804985i	$-0.702173\pi$
$857$	−34.7369			−1.18659			−0.593295	+	0.804985i	$0.702173\pi$
$858$	−7.37566	−	80.6864i	−0.251801	−	2.75459i
$859$		−	3.81731i		−	0.130245i	−0.997877	−	0.0651224i	$-0.979256\pi$
$859$		−	3.81731i		−	0.130245i	0.997877	−	0.0651224i	$-0.0207438\pi$
$860$	2.28985	−	0.422165i	0.0780833	−	0.0143957i
$861$			3.82794i			0.130456i
$862$	40.8239	−	3.73177i	1.39047	−	0.127105i
$863$	−36.5512			−1.24422			−0.622108	−	0.782931i	$-0.713724\pi$
$863$	−36.5512			−1.24422			−0.622108	+	0.782931i	$0.713724\pi$
$864$	14.3348	+	29.2418i	0.487680	+	0.994825i
$865$	−23.9542			−0.814469
$866$	−35.7889	+	3.27152i	−1.21616	+	0.111171i
$867$		−	141.749i		−	4.81404i
$868$	14.2650	−	2.62995i	0.484187	−	0.0892664i
$869$		−	18.0200i		−	0.611288i
$870$	0.353272	+	3.86464i	0.0119770	+	0.131023i
$871$	−41.1512			−1.39435
$872$	−8.66393	−	30.8872i	−0.293398	−	1.04597i
$873$	8.77380			0.296948
$874$	−0.282635	−	3.09189i	−0.00956026	−	0.104585i
$875$		−	1.00000i		−	0.0338062i
$876$	7.35988	+	39.9205i	0.248667	+	1.34879i
$877$			13.4804i			0.455202i	0.973755	+	0.227601i	$0.0730882\pi$
$877$			13.4804i			0.455202i	−0.973755	+	0.227601i	$0.926912\pi$
$878$	18.5899	−	1.69933i	0.627379	−	0.0573496i
$879$	42.5451			1.43501
$880$	−16.9899	+	6.48505i	−0.572728	+	0.218611i
$881$	−23.5825			−0.794515			−0.397258	−	0.917707i	$-0.630038\pi$
$881$	−23.5825			−0.794515			−0.397258	+	0.917707i	$0.630038\pi$
$882$	−7.08595	+	0.647737i	−0.238596	+	0.0218104i
$883$			39.8484i			1.34101i	0.741907	+	0.670503i	$0.233922\pi$
$883$			39.8484i			1.34101i	−0.741907	+	0.670503i	$0.766078\pi$
$884$	13.2000	+	71.5975i	0.443963	+	2.40809i
$885$		−	16.7009i		−	0.561393i
$886$	5.31839	+	58.1808i	0.178675	+	1.95462i
$887$	−14.7202			−0.494257			−0.247128	−	0.968983i	$-0.579487\pi$
$887$	−14.7202			−0.494257			−0.247128	+	0.968983i	$0.579487\pi$
$888$	27.9335	−	7.83542i	0.937388	−	0.262939i
$889$	−0.523858			−0.0175696
$890$	−1.89126	−	20.6895i	−0.0633951	−	0.693513i
$891$			5.55055i			0.185951i
$892$	−10.2830	+	1.89581i	−0.344300	+	0.0634763i
$893$			55.2195i			1.84785i
$894$	6.40638	−	0.585616i	0.214261	−	0.0195859i
$895$	9.74711			0.325810
$896$	9.08745	−	6.73930i	0.303590	−	0.225144i
$897$	4.79670			0.160157
$898$	3.04850	−	0.278667i	0.101730	−	0.00929925i
$899$			7.02273i			0.234221i
$900$	9.89605	−	1.82447i	0.329868	−	0.0608157i
$901$		−	59.1496i		−	1.97056i
$902$	−0.790574	−	8.64852i	−0.0263232	−	0.287964i
$903$	−3.29938			−0.109796
$904$	16.2262	−	4.55148i	0.539675	−	0.151380i
$905$	2.31806			0.0770548
$906$	−5.74911	−	62.8927i	−0.191001	−	2.08947i
$907$		−	17.8794i		−	0.593677i	−0.954928	−	0.296839i	$-0.904068\pi$
$907$		−	17.8794i		−	0.593677i	0.954928	−	0.296839i	$-0.0959324\pi$
$908$	3.95490	+	21.4517i	0.131248	+	0.711898i
$909$			29.0644i			0.964005i
$910$	6.26238	−	0.572454i	0.207596	−	0.0189767i
$911$	9.00408			0.298318			0.149159	−	0.988813i	$-0.452343\pi$
$911$	9.00408			0.298318			0.149159	+	0.988813i	$0.452343\pi$
$912$	61.0833	−	23.3156i	2.02267	−	0.772055i
$913$	−15.6871			−0.519166
$914$	−3.35667	+	0.306838i	−0.111029	+	0.0101493i
$915$		−	10.1592i		−	0.335852i
$916$	−2.02491	−	10.9833i	−0.0669050	−	0.362897i
$917$			9.26163i			0.305846i
$918$	−6.06733	−	66.3738i	−0.200252	−	2.19066i
$919$	−55.8645			−1.84280			−0.921399	−	0.388617i	$-0.872953\pi$
$919$	−55.8645			−1.84280			−0.921399	+	0.388617i	$0.872953\pi$
$920$	−0.290770	−	1.03661i	−0.00958641	−	0.0341759i
$921$	77.0655			2.53940
$922$	−0.828211	−	9.06025i	−0.0272757	−	0.298384i
$923$			40.7396i			1.34096i
$924$	25.3415	−	4.67205i	0.833674	−	0.153699i
$925$		−	3.61936i		−	0.119004i
$926$	−14.2255	+	1.30038i	−0.467480	+	0.0427330i
$927$	49.7131			1.63279
$928$	2.41103	+	4.91829i	0.0791459	+	0.161451i
$929$	52.9144			1.73606			0.868032	−	0.496508i	$-0.165385\pi$
$929$	52.9144			1.73606			0.868032	+	0.496508i	$0.165385\pi$
$930$	28.9471	−	2.64610i	0.949213	−	0.0867690i
$931$			5.76768i			0.189028i
$932$	−8.73799	+	1.61097i	−0.286222	+	0.0527690i
$933$		−	31.8797i		−	1.04370i
$934$	−1.52743	−	16.7094i	−0.0499791	−	0.546749i
$935$	37.2185			1.21718
$936$	17.0906	+	60.9284i	0.558622	+	1.99151i
$937$	−41.4226			−1.35322			−0.676609	−	0.736342i	$-0.736551\pi$
$937$	−41.4226			−1.35322			−0.676609	+	0.736342i	$0.736551\pi$
$938$	−1.19140	−	13.0334i	−0.0389007	−	0.425557i
$939$		−	71.4218i		−	2.33076i
$940$	3.47167	+	18.8306i	0.113233	+	0.614185i
$941$		−	9.09637i		−	0.296533i	−0.988947	−	0.148267i	$-0.952631\pi$
$941$		−	9.09637i		−	0.296533i	0.988947	−	0.148267i	$-0.0473694\pi$
$942$	−42.7990	+	3.91232i	−1.39447	+	0.127470i
$943$	0.514144			0.0167428
$944$	−8.40604	−	22.0226i	−0.273593	−	0.716774i
$945$	−5.75697			−0.187274
$946$	7.45432	−	0.681411i	0.242361	−	0.0221546i
$947$		−	43.9590i		−	1.42848i	−0.699903	−	0.714238i	$-0.746773\pi$
$947$		−	43.9590i		−	1.42848i	0.699903	−	0.714238i	$-0.253227\pi$
$948$	4.07318	+	22.0932i	0.132291	+	0.717555i
$949$			31.8464i			1.03378i
$950$	−0.742523	−	8.12286i	−0.0240906	−	0.263541i
$951$	0.216008			0.00700454
$952$	−22.2943	+	6.25359i	−0.722561	+	0.202680i
$953$	−38.6275			−1.25127			−0.625634	−	0.780117i	$-0.715160\pi$
$953$	−38.6275			−1.25127			−0.625634	+	0.780117i	$0.715160\pi$
$954$	−4.68011	−	51.1983i	−0.151524	−	1.65761i
$955$			16.3365i			0.528636i
$956$	−13.7454	+	2.53414i	−0.444557	+	0.0819601i
$957$			12.4757i			0.403282i
$958$	−16.0336	+	1.46565i	−0.518021	+	0.0473531i
$959$	6.66544			0.215238
$960$	19.3643	−	11.7912i	0.624981	−	0.380560i
$961$	21.6020			0.696840
$962$	22.6658	−	2.07192i	0.730775	−	0.0668012i
$963$			17.0416i			0.549158i
$964$	26.6000	−	4.90406i	0.856728	−	0.157949i
$965$		−	1.45853i		−	0.0469517i
$966$	0.138874	+	1.51922i	0.00446819	+	0.0488800i
$967$	−54.9862			−1.76824			−0.884118	−	0.467264i	$-0.845240\pi$
$967$	−54.9862			−1.76824			−0.884118	+	0.467264i	$0.845240\pi$
$968$	−26.3330	+	7.38646i	−0.846375	+	0.237410i
$969$	−133.811			−4.29863
$970$	−0.224495	−	2.45587i	−0.00720810	−	0.0788533i
$971$		−	29.5963i		−	0.949791i	−0.880042	−	0.474895i	$-0.842486\pi$
$971$		−	29.5963i		−	0.949791i	0.880042	−	0.474895i	$-0.157514\pi$
$972$	5.00808	+	27.1642i	0.160634	+	0.871291i
$973$			10.4798i			0.335966i
$974$	51.9316	−	4.74714i	1.66399	−	0.152108i
$975$	12.6017			0.403576
$976$	−5.11341	−	13.3964i	−0.163676	−	0.428808i
$977$	−42.3769			−1.35576			−0.677879	−	0.735173i	$-0.737101\pi$
$977$	−42.3769			−1.35576			−0.677879	+	0.735173i	$0.737101\pi$
$978$	−5.81440	+	0.531503i	−0.185924	+	0.0169956i
$979$		−	66.7892i		−	2.13459i
$980$	0.362616	+	1.96685i	0.0115833	+	0.0628288i
$981$			57.0650i			1.82195i
$982$	−3.13103	−	34.2521i	−0.0999152	−	1.09303i
$983$	16.7929			0.535611			0.267806	−	0.963473i	$-0.413701\pi$
$983$	16.7929			0.535611			0.267806	+	0.963473i	$0.413701\pi$
$984$	2.92415	+	10.4247i	0.0932186	+	0.332327i
$985$	19.9922			0.637005
$986$	−1.02049	−	11.1637i	−0.0324990	−	0.355524i
$987$		−	27.1323i		−	0.863632i
$988$	50.4434	−	9.29993i	1.60482	−	0.295870i
$989$			0.443150i			0.0140914i
$990$	32.2153	−	2.94485i	1.02387	−	0.0935935i
$991$	2.51251			0.0798124			0.0399062	−	0.999203i	$-0.487294\pi$
$991$	2.51251			0.0798124			0.0399062	+	0.999203i	$0.487294\pi$
$992$	36.8392	−	18.0592i	1.16965	−	0.573381i
$993$	29.8185			0.946260
$994$	−12.9031	+	1.17949i	−0.409261	+	0.0374111i
$995$			13.9302i			0.441618i
$996$	19.2329	−	3.54585i	0.609418	−	0.112354i
$997$			24.9159i			0.789094i	0.918876	+	0.394547i	$0.129098\pi$
$997$			24.9159i			0.789094i	−0.918876	+	0.394547i	$0.870902\pi$
$998$	5.52127	+	60.4002i	0.174773	+	1.91193i
$999$	−20.8366			−0.659239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.b.d.141.11	✓	12
4.3	odd	2		1120.2.b.d.561.11		12
8.3	odd	2		1120.2.b.d.561.2		12
8.5	even	2	inner	280.2.b.d.141.12	yes	12
16.3	odd	4		8960.2.a.cg.1.1		6
16.5	even	4		8960.2.a.ca.1.1		6
16.11	odd	4		8960.2.a.cd.1.6		6
16.13	even	4		8960.2.a.cf.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.b.d.141.11	✓	12	1.1	even	1	trivial
280.2.b.d.141.12	yes	12	8.5	even	2	inner
1120.2.b.d.561.2		12	8.3	odd	2
1120.2.b.d.561.11		12	4.3	odd	2
8960.2.a.ca.1.1		6	16.5	even	4
8960.2.a.cd.1.6		6	16.11	odd	4
8960.2.a.cf.1.6		6	16.13	even	4
8960.2.a.cg.1.1		6	16.3	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)

\(f(q)\)	\(=\)	\(q+(1.40834 - 0.128739i) q^{2} -2.83397i q^{3} +(1.96685 - 0.362616i) q^{4} +1.00000i q^{5} +(-0.364842 - 3.99120i) q^{6} +1.00000 q^{7} +(2.72332 - 0.763897i) q^{8} -5.03141 q^{9} +O(q^{10})\)	\(q+(1.40834 - 0.128739i) q^{2} -2.83397i q^{3} +(1.96685 - 0.362616i) q^{4} +1.00000i q^{5} +(-0.364842 - 3.99120i) q^{6} +1.00000 q^{7} +(2.72332 - 0.763897i) q^{8} -5.03141 q^{9} +(0.128739 + 1.40834i) q^{10} +4.54637i q^{11} +(-1.02764 - 5.57401i) q^{12} -4.44664i q^{13} +(1.40834 - 0.128739i) q^{14} +2.83397 q^{15} +(3.73702 - 1.42642i) q^{16} -8.18643 q^{17} +(-7.08595 + 0.647737i) q^{18} +5.76768i q^{19} +(0.362616 + 1.96685i) q^{20} -2.83397i q^{21} +(0.585293 + 6.40284i) q^{22} -0.380641 q^{23} +(-2.16486 - 7.71781i) q^{24} -1.00000 q^{25} +(-0.572454 - 6.26238i) q^{26} +5.75697i q^{27} +(1.96685 - 0.362616i) q^{28} +0.968288i q^{29} +(3.99120 - 0.364842i) q^{30} +7.25273 q^{31} +(5.07936 - 2.48999i) q^{32} +12.8843 q^{33} +(-11.5293 + 1.05391i) q^{34} +1.00000i q^{35} +(-9.89605 + 1.82447i) q^{36} +3.61936i q^{37} +(0.742523 + 8.12286i) q^{38} -12.6017 q^{39} +(0.763897 + 2.72332i) q^{40} -1.35073 q^{41} +(-0.364842 - 3.99120i) q^{42} -1.16422i q^{43} +(1.64858 + 8.94203i) q^{44} -5.03141i q^{45} +(-0.536072 + 0.0490032i) q^{46} +9.57395 q^{47} +(-4.04245 - 10.5906i) q^{48} +1.00000 q^{49} +(-1.40834 + 0.128739i) q^{50} +23.2001i q^{51} +(-1.61242 - 8.74588i) q^{52} +7.22532i q^{53} +(0.741144 + 8.10778i) q^{54} -4.54637 q^{55} +(2.72332 - 0.763897i) q^{56} +16.3455 q^{57} +(0.124656 + 1.36368i) q^{58} -5.89309i q^{59} +(5.57401 - 1.02764i) q^{60} -3.58478i q^{61} +(10.2143 - 0.933706i) q^{62} -5.03141 q^{63} +(6.83292 - 4.16067i) q^{64} +4.44664 q^{65} +(18.1455 - 1.65870i) q^{66} -9.25445i q^{67} +(-16.1015 + 2.96853i) q^{68} +1.07873i q^{69} +(0.128739 + 1.40834i) q^{70} -9.16190 q^{71} +(-13.7021 + 3.84348i) q^{72} -7.16190 q^{73} +(0.465951 + 5.09729i) q^{74} +2.83397i q^{75} +(2.09145 + 11.3442i) q^{76} +4.54637i q^{77} +(-17.7474 + 1.62232i) q^{78} -3.96361 q^{79} +(1.42642 + 3.73702i) q^{80} +1.22088 q^{81} +(-1.90229 + 0.173891i) q^{82} +3.45046i q^{83} +(-1.02764 - 5.57401i) q^{84} -8.18643i q^{85} +(-0.149880 - 1.63962i) q^{86} +2.74410 q^{87} +(3.47295 + 12.3812i) q^{88} -14.6907 q^{89} +(-0.647737 - 7.08595i) q^{90} -4.44664i q^{91} +(-0.748664 + 0.138026i) q^{92} -20.5540i q^{93} +(13.4834 - 1.23254i) q^{94} -5.76768 q^{95} +(-7.05657 - 14.3948i) q^{96} -1.74381 q^{97} +(1.40834 - 0.128739i) q^{98} -22.8746i 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

L-functions

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