LMFDB - Embedded newform 552.2.f.d.277.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, 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("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 2x^17 + x^16 - 4x^15 + 16x^14 - 24x^13 + 32x^12 - 16x^11 - 16x^10 - 32x^9 + 128x^8 - 192x^7 + 256x^6 - 128x^5 + 64x^4 - 256x^3 + 512x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.10
Root			$0.459619 - 1.33744i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.d.277.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.459619 + 1.33744i) q^{2} +1.00000i q^{3} +(-1.57750 - 1.22943i) q^{4} +2.04946i q^{5} +(-1.33744 - 0.459619i) q^{6} -4.47395 q^{7} +(2.36933 - 1.54475i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.459619 + 1.33744i) q^{2} +1.00000i q^{3} +(-1.57750 - 1.22943i) q^{4} +2.04946i q^{5} +(-1.33744 - 0.459619i) q^{6} -4.47395 q^{7} +(2.36933 - 1.54475i) q^{8} -1.00000 q^{9} +(-2.74104 - 0.941972i) q^{10} -3.86022i q^{11} +(1.22943 - 1.57750i) q^{12} -5.65791i q^{13} +(2.05631 - 5.98365i) q^{14} -2.04946 q^{15} +(0.977023 + 3.87884i) q^{16} -0.763773 q^{17} +(0.459619 - 1.33744i) q^{18} +5.88237i q^{19} +(2.51966 - 3.23303i) q^{20} -4.47395i q^{21} +(5.16282 + 1.77423i) q^{22} +1.00000 q^{23} +(1.54475 + 2.36933i) q^{24} +0.799698 q^{25} +(7.56712 + 2.60048i) q^{26} -1.00000i q^{27} +(7.05766 + 5.50039i) q^{28} -3.85821i q^{29} +(0.941972 - 2.74104i) q^{30} -9.20798 q^{31} +(-5.63679 - 0.476077i) q^{32} +3.86022 q^{33} +(0.351044 - 1.02150i) q^{34} -9.16920i q^{35} +(1.57750 + 1.22943i) q^{36} -3.75374i q^{37} +(-7.86733 - 2.70365i) q^{38} +5.65791 q^{39} +(3.16591 + 4.85587i) q^{40} -3.32369 q^{41} +(5.98365 + 2.05631i) q^{42} -1.84754i q^{43} +(-4.74585 + 6.08950i) q^{44} -2.04946i q^{45} +(-0.459619 + 1.33744i) q^{46} -6.55588 q^{47} +(-3.87884 + 0.977023i) q^{48} +13.0162 q^{49} +(-0.367556 + 1.06955i) q^{50} -0.763773i q^{51} +(-6.95598 + 8.92536i) q^{52} -2.26808i q^{53} +(1.33744 + 0.459619i) q^{54} +7.91138 q^{55} +(-10.6003 + 6.91113i) q^{56} -5.88237 q^{57} +(5.16013 + 1.77330i) q^{58} -10.6144i q^{59} +(3.23303 + 2.51966i) q^{60} +9.32173i q^{61} +(4.23216 - 12.3151i) q^{62} +4.47395 q^{63} +(3.22750 - 7.32006i) q^{64} +11.5957 q^{65} +(-1.77423 + 5.16282i) q^{66} -3.64203i q^{67} +(1.20485 + 0.939003i) q^{68} +1.00000i q^{69} +(12.2633 + 4.21433i) q^{70} -6.14881 q^{71} +(-2.36933 + 1.54475i) q^{72} -2.21431 q^{73} +(5.02041 + 1.72529i) q^{74} +0.799698i q^{75} +(7.23194 - 9.27945i) q^{76} +17.2704i q^{77} +(-2.60048 + 7.56712i) q^{78} -5.59406 q^{79} +(-7.94955 + 2.00237i) q^{80} +1.00000 q^{81} +(1.52763 - 4.44524i) q^{82} -3.14859i q^{83} +(-5.50039 + 7.05766i) q^{84} -1.56533i q^{85} +(2.47098 + 0.849164i) q^{86} +3.85821 q^{87} +(-5.96307 - 9.14615i) q^{88} -0.345205 q^{89} +(2.74104 + 0.941972i) q^{90} +25.3132i q^{91} +(-1.57750 - 1.22943i) q^{92} -9.20798i q^{93} +(3.01320 - 8.76810i) q^{94} -12.0557 q^{95} +(0.476077 - 5.63679i) q^{96} -19.4812 q^{97} +(-5.98250 + 17.4085i) q^{98} +3.86022i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	−0.459619	+	1.33744i	−0.324999	+	0.945714i
$2$	−0.459619	+	1.33744i	−0.324999	+	0.945714i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.57750	−	1.22943i	−0.788751	−	0.614713i
$5$			2.04946i			0.916548i	0.888811	+	0.458274i	$0.151532\pi$
$5$			2.04946i			0.916548i	−0.888811	+	0.458274i	$0.848468\pi$
$6$	−1.33744	−	0.459619i	−0.546008	−	0.187638i
$7$	−4.47395			−1.69099			−0.845497	−	0.533980i	$-0.820696\pi$
$7$	−4.47395			−1.69099			−0.845497	+	0.533980i	$0.820696\pi$
$8$	2.36933	−	1.54475i	0.837686	−	0.546152i
$9$	−1.00000			−0.333333
$10$	−2.74104	−	0.941972i	−0.866793	−	0.297878i
$11$		−	3.86022i		−	1.16390i	−0.813225	−	0.581950i	$-0.802290\pi$
$11$		−	3.86022i		−	1.16390i	0.813225	−	0.581950i	$-0.197710\pi$
$12$	1.22943	−	1.57750i	0.354905	−	0.455385i
$13$		−	5.65791i		−	1.56922i	−0.619989	−	0.784611i	$-0.712863\pi$
$13$		−	5.65791i		−	1.56922i	0.619989	−	0.784611i	$-0.287137\pi$
$14$	2.05631	−	5.98365i	0.549572	−	1.59920i
$15$	−2.04946			−0.529169
$16$	0.977023	+	3.87884i	0.244256	+	0.969711i
$17$	−0.763773			−0.185242			−0.0926211	−	0.995701i	$-0.529525\pi$
$17$	−0.763773			−0.185242			−0.0926211	+	0.995701i	$0.529525\pi$
$18$	0.459619	−	1.33744i	0.108333	−	0.315238i
$19$			5.88237i			1.34951i	0.738043	+	0.674754i	$0.235750\pi$
$19$			5.88237i			1.34951i	−0.738043	+	0.674754i	$0.764250\pi$
$20$	2.51966	−	3.23303i	0.563414	−	0.722928i
$21$		−	4.47395i		−	0.976296i
$22$	5.16282	+	1.77423i	1.10072	+	0.378267i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	1.54475	+	2.36933i	0.315321	+	0.483638i
$25$	0.799698			0.159940
$26$	7.56712	+	2.60048i	1.48403	+	0.509996i
$27$		−	1.00000i		−	0.192450i
$28$	7.05766	+	5.50039i	1.33377	+	1.03948i
$29$		−	3.85821i		−	0.716451i	−0.933635	−	0.358226i	$-0.883382\pi$
$29$		−	3.85821i		−	0.716451i	0.933635	−	0.358226i	$-0.116618\pi$
$30$	0.941972	−	2.74104i	0.171980	−	0.500443i
$31$	−9.20798			−1.65380			−0.826901	−	0.562348i	$-0.809898\pi$
$31$	−9.20798			−1.65380			−0.826901	+	0.562348i	$0.809898\pi$
$32$	−5.63679	−	0.476077i	−0.996452	−	0.0841593i
$33$	3.86022			0.671978
$34$	0.351044	−	1.02150i	0.0602036	−	0.175186i
$35$		−	9.16920i		−	1.54988i
$36$	1.57750	+	1.22943i	0.262917	+	0.204904i
$37$		−	3.75374i		−	0.617111i	−0.951206	−	0.308556i	$-0.900154\pi$
$37$		−	3.75374i		−	0.617111i	0.951206	−	0.308556i	$-0.0998456\pi$
$38$	−7.86733	−	2.70365i	−1.27625	−	0.438589i
$39$	5.65791			0.905990
$40$	3.16591	+	4.85587i	0.500574	+	0.767780i
$41$	−3.32369			−0.519073			−0.259536	−	0.965733i	$-0.583570\pi$
$41$	−3.32369			−0.519073			−0.259536	+	0.965733i	$0.583570\pi$
$42$	5.98365	+	2.05631i	0.923297	+	0.317296i
$43$		−	1.84754i		−	0.281747i	−0.990028	−	0.140874i	$-0.955009\pi$
$43$		−	1.84754i		−	0.281747i	0.990028	−	0.140874i	$-0.0449912\pi$
$44$	−4.74585	+	6.08950i	−0.715464	+	0.918027i
$45$		−	2.04946i		−	0.305516i
$46$	−0.459619	+	1.33744i	−0.0677671	+	0.197195i
$47$	−6.55588			−0.956273			−0.478136	−	0.878286i	$-0.658688\pi$
$47$	−6.55588			−0.956273			−0.478136	+	0.878286i	$0.658688\pi$
$48$	−3.87884	+	0.977023i	−0.559863	+	0.141021i
$49$	13.0162			1.85946
$50$	−0.367556	+	1.06955i	−0.0519803	+	0.151257i
$51$		−	0.763773i		−	0.106950i
$52$	−6.95598	+	8.92536i	−0.964621	+	1.23772i
$53$		−	2.26808i		−	0.311545i	−0.987793	−	0.155773i	$-0.950213\pi$
$53$		−	2.26808i		−	0.311545i	0.987793	−	0.155773i	$-0.0497867\pi$
$54$	1.33744	+	0.459619i	0.182003	+	0.0625462i
$55$	7.91138			1.06677
$56$	−10.6003	+	6.91113i	−1.41652	+	0.923539i
$57$	−5.88237			−0.779139
$58$	5.16013	+	1.77330i	0.677558	+	0.232846i
$59$		−	10.6144i		−	1.38188i	−0.722913	−	0.690939i	$-0.757197\pi$
$59$		−	10.6144i		−	1.38188i	0.722913	−	0.690939i	$-0.242803\pi$
$60$	3.23303	+	2.51966i	0.417383	+	0.325287i
$61$			9.32173i			1.19353i	0.802418	+	0.596763i	$0.203547\pi$
$61$			9.32173i			1.19353i	−0.802418	+	0.596763i	$0.796453\pi$
$62$	4.23216	−	12.3151i	0.537484	−	1.56402i
$63$	4.47395			0.563665
$64$	3.22750	−	7.32006i	0.403437	−	0.915007i
$65$	11.5957			1.43827
$66$	−1.77423	+	5.16282i	−0.218392	+	0.635499i
$67$		−	3.64203i		−	0.444945i	−0.974939	−	0.222472i	$-0.928587\pi$
$67$		−	3.64203i		−	0.444945i	0.974939	−	0.222472i	$-0.0714127\pi$
$68$	1.20485	+	0.939003i	0.146110	+	0.113871i
$69$			1.00000i			0.120386i
$70$	12.2633	+	4.21433i	1.46574	+	0.503709i
$71$	−6.14881			−0.729729			−0.364865	−	0.931061i	$-0.618885\pi$
$71$	−6.14881			−0.729729			−0.364865	+	0.931061i	$0.618885\pi$
$72$	−2.36933	+	1.54475i	−0.279229	+	0.182051i
$73$	−2.21431			−0.259166			−0.129583	−	0.991569i	$-0.541364\pi$
$73$	−2.21431			−0.259166			−0.129583	+	0.991569i	$0.541364\pi$
$74$	5.02041	+	1.72529i	0.583611	+	0.200561i
$75$			0.799698i			0.0923412i
$76$	7.23194	−	9.27945i	0.829560	−	1.06443i
$77$			17.2704i			1.96815i
$78$	−2.60048	+	7.56712i	−0.294446	+	0.856808i
$79$	−5.59406			−0.629381			−0.314691	−	0.949194i	$-0.601901\pi$
$79$	−5.59406			−0.629381			−0.314691	+	0.949194i	$0.601901\pi$
$80$	−7.94955	+	2.00237i	−0.888787	+	0.223872i
$81$	1.00000			0.111111
$82$	1.52763	−	4.44524i	0.168698	−	0.490894i
$83$		−	3.14859i		−	0.345603i	−0.984957	−	0.172801i	$-0.944718\pi$
$83$		−	3.14859i		−	0.345603i	0.984957	−	0.172801i	$-0.0552818\pi$
$84$	−5.50039	+	7.05766i	−0.600142	+	0.770054i
$85$		−	1.56533i		−	0.169783i
$86$	2.47098	+	0.849164i	0.266453	+	0.0915678i
$87$	3.85821			0.413643
$88$	−5.96307	−	9.14615i	−0.635665	−	0.974983i
$89$	−0.345205			−0.0365917			−0.0182958	−	0.999833i	$-0.505824\pi$
$89$	−0.345205			−0.0365917			−0.0182958	+	0.999833i	$0.505824\pi$
$90$	2.74104	+	0.941972i	0.288931	+	0.0992925i
$91$			25.3132i			2.65354i
$92$	−1.57750	−	1.22943i	−0.164466	−	0.128177i
$93$		−	9.20798i		−	0.954823i
$94$	3.01320	−	8.76810i	0.310788	−	0.904361i
$95$	−12.0557			−1.23689
$96$	0.476077	−	5.63679i	0.0485894	−	0.575302i
$97$	−19.4812			−1.97802			−0.989009	−	0.147857i	$-0.952763\pi$
$97$	−19.4812			−1.97802			−0.989009	+	0.147857i	$0.952763\pi$
$98$	−5.98250	+	17.4085i	−0.604324	+	1.75852i
$99$			3.86022i			0.387966i
$100$	−1.26153	−	0.983170i	−0.126153	−	0.0983170i
$101$		−	15.8617i		−	1.57830i	−0.614202	−	0.789149i	$-0.710522\pi$
$101$		−	15.8617i		−	1.57830i	0.614202	−	0.789149i	$-0.289478\pi$
$102$	1.02150	+	0.351044i	0.101144	+	0.0347586i
$103$	−12.3123			−1.21316			−0.606582	−	0.795021i	$-0.707460\pi$
$103$	−12.3123			−1.21316			−0.606582	+	0.795021i	$0.707460\pi$
$104$	−8.74005	−	13.4055i	−0.857032	−	1.31452i
$105$	9.16920			0.894822
$106$	3.03343	+	1.04245i	0.294633	+	0.101252i
$107$		−	1.24916i		−	0.120761i	−0.998175	−	0.0603805i	$-0.980769\pi$
$107$		−	1.24916i		−	0.120761i	0.998175	−	0.0603805i	$-0.0192314\pi$
$108$	−1.22943	+	1.57750i	−0.118302	+	0.151795i
$109$			11.2279i			1.07544i	0.843125	+	0.537718i	$0.180714\pi$
$109$			11.2279i			1.07544i	−0.843125	+	0.537718i	$0.819286\pi$
$110$	−3.63621	+	10.5810i	−0.346699	+	1.00886i
$111$	3.75374			0.356289
$112$	−4.37115	−	17.3538i	−0.413035	−	1.63978i
$113$	13.4161			1.26208			0.631040	−	0.775751i	$-0.282629\pi$
$113$	13.4161			1.26208			0.631040	+	0.775751i	$0.282629\pi$
$114$	2.70365	−	7.86733i	0.253220	−	0.736843i
$115$			2.04946i			0.191113i
$116$	−4.74338	+	6.08633i	−0.440412	+	0.565102i
$117$			5.65791i			0.523074i
$118$	14.1962	+	4.87858i	1.30686	+	0.449110i
$119$	3.41708			0.313244
$120$	−4.85587	+	3.16591i	−0.443278	+	0.289007i
$121$	−3.90128			−0.354662
$122$	−12.4673	−	4.28444i	−1.12873	−	0.387895i
$123$		−	3.32369i		−	0.299687i
$124$	14.5256	+	11.3205i	1.30444	+	1.01661i
$125$			11.8863i			1.06314i
$126$	−2.05631	+	5.98365i	−0.183191	+	0.533066i
$127$	−12.9809			−1.15186			−0.575932	−	0.817497i	$-0.695361\pi$
$127$	−12.9809			−1.15186			−0.575932	+	0.817497i	$0.695361\pi$
$128$	8.30674	+	7.68102i	0.734219	+	0.678913i
$129$	1.84754			0.162667
$130$	−5.32959	+	15.5085i	−0.467436	+	1.36019i
$131$			12.7610i			1.11494i	0.830199	+	0.557468i	$0.188227\pi$
$131$			12.7610i			1.11494i	−0.830199	+	0.557468i	$0.811773\pi$
$132$	−6.08950	−	4.74585i	−0.530023	−	0.413073i
$133$		−	26.3174i		−	2.28201i
$134$	4.87100	+	1.67394i	0.420791	+	0.144607i
$135$	2.04946			0.176390
$136$	−1.80963	+	1.17984i	−0.155175	+	0.101170i
$137$	−4.90524			−0.419083			−0.209541	−	0.977800i	$-0.567197\pi$
$137$	−4.90524			−0.419083			−0.209541	+	0.977800i	$0.567197\pi$
$138$	−1.33744	−	0.459619i	−0.113851	−	0.0391253i
$139$		−	7.62325i		−	0.646595i	−0.946297	−	0.323298i	$-0.895208\pi$
$139$		−	7.62325i		−	0.646595i	0.946297	−	0.323298i	$-0.104792\pi$
$140$	−11.2729	+	14.4644i	−0.952730	+	1.22247i
$141$		−	6.55588i		−	0.552104i
$142$	2.82611	−	8.22368i	0.237162	−	0.690116i
$143$	−21.8408			−1.82642
$144$	−0.977023	−	3.87884i	−0.0814186	−	0.323237i
$145$	7.90726			0.656662
$146$	1.01774	−	2.96152i	0.0842287	−	0.245097i
$147$			13.0162i			1.07356i
$148$	−4.61495	+	5.92153i	−0.379346	+	0.486747i
$149$		−	13.5441i		−	1.10958i	−0.831991	−	0.554789i	$-0.812799\pi$
$149$		−	13.5441i		−	1.10958i	0.831991	−	0.554789i	$-0.187201\pi$
$150$	−1.06955	−	0.367556i	−0.0873284	−	0.0300108i
$151$	5.53587			0.450502			0.225251	−	0.974301i	$-0.427680\pi$
$151$	5.53587			0.450502			0.225251	+	0.974301i	$0.427680\pi$
$152$	9.08679	+	13.9373i	0.737036	+	1.13046i
$153$	0.763773			0.0617474
$154$	−23.0982	−	7.93781i	−1.86131	−	0.639647i
$155$		−	18.8714i		−	1.51579i
$156$	−8.92536	−	6.95598i	−0.714601	−	0.556924i
$157$			12.3678i			0.987057i	0.869730	+	0.493529i	$0.164293\pi$
$157$			12.3678i			0.987057i	−0.869730	+	0.493529i	$0.835707\pi$
$158$	2.57114	−	7.48173i	0.204549	−	0.595215i
$159$	2.26808			0.179871
$160$	0.975703	−	11.5524i	0.0771361	−	0.913296i
$161$	−4.47395			−0.352597
$162$	−0.459619	+	1.33744i	−0.0361110	+	0.105079i
$163$			7.18190i			0.562530i	0.959630	+	0.281265i	$0.0907540\pi$
$163$			7.18190i			0.562530i	−0.959630	+	0.281265i	$0.909246\pi$
$164$	5.24312	+	4.08623i	0.409419	+	0.319081i
$165$			7.91138i			0.615900i
$166$	4.21106	+	1.44715i	0.326841	+	0.112321i
$167$	−15.2632			−1.18110			−0.590551	−	0.807001i	$-0.701089\pi$
$167$	−15.2632			−1.18110			−0.590551	+	0.807001i	$0.701089\pi$
$168$	−6.91113	−	10.6003i	−0.533206	−	0.817830i
$169$	−19.0119			−1.46245
$170$	2.09353	+	0.719453i	0.160567	+	0.0551795i
$171$		−	5.88237i		−	0.449836i
$172$	−2.27142	+	2.91450i	−0.173194	+	0.222229i
$173$		−	11.3689i		−	0.864360i	−0.901787	−	0.432180i	$-0.857745\pi$
$173$		−	11.3689i		−	0.864360i	0.901787	−	0.432180i	$-0.142255\pi$
$174$	−1.77330	+	5.16013i	−0.134434	+	0.391188i
$175$	−3.57781			−0.270457
$176$	14.9732	−	3.77152i	1.12865	−	0.284289i
$177$	10.6144			0.797828
$178$	0.158663	−	0.461692i	0.0118923	−	0.0346053i
$179$			17.7371i			1.32573i	0.748738	+	0.662867i	$0.230660\pi$
$179$			17.7371i			1.32573i	−0.748738	+	0.662867i	$0.769340\pi$
$180$	−2.51966	+	3.23303i	−0.187805	+	0.240976i
$181$			17.8184i			1.32443i	0.749313	+	0.662216i	$0.230384\pi$
$181$			17.8184i			1.32443i	−0.749313	+	0.662216i	$0.769616\pi$
$182$	−33.8549	−	11.6344i	−2.50949	−	0.862400i
$183$	−9.32173			−0.689082
$184$	2.36933	−	1.54475i	0.174670	−	0.113880i
$185$	7.69316			0.565612
$186$	12.3151	+	4.23216i	0.902989	+	0.310317i
$187$			2.94833i			0.215603i
$188$	10.3419	+	8.05997i	0.754261	+	0.587833i
$189$			4.47395i			0.325432i
$190$	5.54103	−	16.1238i	0.401988	−	1.16974i
$191$	25.6997			1.85957			0.929783	−	0.368107i	$-0.119994\pi$
$191$	25.6997			1.85957			0.929783	+	0.368107i	$0.119994\pi$
$192$	7.32006	+	3.22750i	0.528280	+	0.232924i
$193$	−1.77067			−0.127456			−0.0637278	−	0.997967i	$-0.520299\pi$
$193$	−1.77067			−0.127456			−0.0637278	+	0.997967i	$0.520299\pi$
$194$	8.95393	−	26.0550i	0.642854	−	1.87064i
$195$			11.5957i			0.830384i
$196$	−20.5331	−	16.0025i	−1.46665	−	1.14304i
$197$			1.85673i			0.132287i	0.997810	+	0.0661433i	$0.0210694\pi$
$197$			1.85673i			0.132287i	−0.997810	+	0.0661433i	$0.978931\pi$
$198$	−5.16282	−	1.77423i	−0.366905	−	0.126089i
$199$	16.0802			1.13989			0.569946	−	0.821682i	$-0.306964\pi$
$199$	16.0802			1.13989			0.569946	+	0.821682i	$0.306964\pi$
$200$	1.89475	−	1.23533i	0.133979	−	0.0873513i
$201$	3.64203			0.256889
$202$	21.2141	+	7.29033i	1.49262	+	0.512946i
$203$			17.2614i			1.21152i
$204$	−0.939003	+	1.20485i	−0.0657433	+	0.0843566i
$205$		−	6.81178i		−	0.475755i
$206$	5.65895	−	16.4670i	0.394278	−	1.14731i
$207$	−1.00000			−0.0695048
$208$	21.9461	−	5.52790i	1.52169	−	0.383291i
$209$	22.7072			1.57069
$210$	−4.21433	+	12.2633i	−0.290817	+	0.846246i
$211$			27.8897i			1.92001i	0.279988	+	0.960003i	$0.409669\pi$
$211$			27.8897i			1.92001i	−0.279988	+	0.960003i	$0.590331\pi$
$212$	−2.78844	+	3.57790i	−0.191511	+	0.245731i
$213$		−	6.14881i		−	0.421310i
$214$	1.67068	+	0.574137i	0.114205	+	0.0392472i
$215$	3.78647			0.258235
$216$	−1.54475	−	2.36933i	−0.105107	−	0.161213i
$217$	41.1960			2.79657
$218$	−15.0166	−	5.16054i	−1.01706	−	0.349516i
$219$		−	2.21431i		−	0.149629i
$220$	−12.4802	−	9.72645i	−0.841415	−	0.655757i
$221$			4.32136i			0.290686i
$222$	−1.72529	+	5.02041i	−0.115794	+	0.336948i
$223$	−25.8723			−1.73254			−0.866270	−	0.499576i	$-0.833489\pi$
$223$	−25.8723			−1.73254			−0.866270	+	0.499576i	$0.833489\pi$
$224$	25.2187	+	2.12995i	1.68500	+	0.142313i
$225$	−0.799698			−0.0533132
$226$	−6.16628	+	17.9432i	−0.410175	+	1.19357i
$227$		−	22.2054i		−	1.47382i	−0.675990	−	0.736910i	$-0.736284\pi$
$227$		−	22.2054i		−	1.47382i	0.675990	−	0.736910i	$-0.263716\pi$
$228$	9.27945	+	7.23194i	0.614547	+	0.478947i
$229$		−	0.213220i		−	0.0140900i	−0.999975	−	0.00704498i	$-0.997757\pi$
$229$		−	0.213220i		−	0.0140900i	0.999975	−	0.00704498i	$-0.00224251\pi$
$230$	−2.74104	−	0.941972i	−0.180739	−	0.0621118i
$231$	−17.2704			−1.13631
$232$	−5.95997	−	9.14139i	−0.391291	−	0.600162i
$233$	−0.228333			−0.0149586			−0.00747928	−	0.999972i	$-0.502381\pi$
$233$	−0.228333			−0.0149586			−0.00747928	+	0.999972i	$0.502381\pi$
$234$	−7.56712	−	2.60048i	−0.494678	−	0.169999i
$235$		−	13.4360i		−	0.876470i
$236$	−13.0496	+	16.7442i	−0.849459	+	1.08996i
$237$		−	5.59406i		−	0.363373i
$238$	−1.57055	+	4.57015i	−0.101804	+	0.296239i
$239$	27.9596			1.80856			0.904279	−	0.426943i	$-0.140409\pi$
$239$	27.9596			1.80856			0.904279	+	0.426943i	$0.140409\pi$
$240$	−2.00237	−	7.94955i	−0.129253	−	0.513141i
$241$	3.82994			0.246708			0.123354	−	0.992363i	$-0.460635\pi$
$241$	3.82994			0.246708			0.123354	+	0.992363i	$0.460635\pi$
$242$	1.79310	−	5.21773i	0.115265	−	0.335409i
$243$			1.00000i			0.0641500i
$244$	11.4604	−	14.7050i	0.733676	−	0.941394i
$245$			26.6763i			1.70429i
$246$	4.44524	+	1.52763i	0.283418	+	0.0973980i
$247$	33.2819			2.11768
$248$	−21.8168	+	14.2240i	−1.38537	+	0.903226i
$249$	3.14859			0.199534
$250$	−15.8972	−	5.46315i	−1.00543	−	0.345520i
$251$			17.0981i			1.07922i	0.841915	+	0.539610i	$0.181428\pi$
$251$			17.0981i			1.07922i	−0.841915	+	0.539610i	$0.818572\pi$
$252$	−7.05766	−	5.50039i	−0.444591	−	0.346492i
$253$		−	3.86022i		−	0.242690i
$254$	5.96624	−	17.3611i	0.374355	−	1.08933i
$255$	1.56533			0.0980245
$256$	−14.0909	+	7.57944i	−0.880678	+	0.473715i
$257$	−21.8093			−1.36043			−0.680215	−	0.733013i	$-0.738113\pi$
$257$	−21.8093			−1.36043			−0.680215	+	0.733013i	$0.738113\pi$
$258$	−0.849164	+	2.47098i	−0.0528667	+	0.153836i
$259$			16.7941i			1.04353i
$260$	−18.2922	−	14.2560i	−1.13443	−	0.884121i
$261$			3.85821i			0.238817i
$262$	−17.0671	−	5.86520i	−1.05441	−	0.362353i
$263$	17.8688			1.10184			0.550918	−	0.834560i	$-0.314278\pi$
$263$	17.8688			1.10184			0.550918	+	0.834560i	$0.314278\pi$
$264$	9.14615	−	5.96307i	0.562907	−	0.367002i
$265$	4.64835			0.285546
$266$	35.1980	+	12.0960i	2.15813	+	0.741652i
$267$		−	0.345205i		−	0.0211262i
$268$	−4.47761	+	5.74531i	−0.273513	+	0.350951i
$269$			12.7899i			0.779811i	0.920855	+	0.389906i	$0.127492\pi$
$269$			12.7899i			0.779811i	−0.920855	+	0.389906i	$0.872508\pi$
$270$	−0.941972	+	2.74104i	−0.0573266	+	0.166814i
$271$	15.1428			0.919858			0.459929	−	0.887956i	$-0.347875\pi$
$271$	15.1428			0.919858			0.459929	+	0.887956i	$0.347875\pi$
$272$	−0.746224	−	2.96256i	−0.0452465	−	0.179631i
$273$	−25.3132			−1.53202
$274$	2.25454	−	6.56047i	0.136202	−	0.396333i
$275$		−	3.08701i		−	0.186154i
$276$	1.22943	−	1.57750i	0.0740028	−	0.0949544i
$277$		−	18.6751i		−	1.12208i	−0.827789	−	0.561039i	$-0.810402\pi$
$277$		−	18.6751i		−	1.12208i	0.827789	−	0.561039i	$-0.189598\pi$
$278$	10.1957	+	3.50379i	0.611495	+	0.210143i
$279$	9.20798			0.551267
$280$	−14.1641	−	21.7249i	−0.846468	−	1.29831i
$281$	11.8997			0.709875			0.354938	−	0.934890i	$-0.384502\pi$
$281$	11.8997			0.709875			0.354938	+	0.934890i	$0.384502\pi$
$282$	8.76810	+	3.01320i	0.522133	+	0.179434i
$283$		−	11.3565i		−	0.675074i	−0.941312	−	0.337537i	$-0.890406\pi$
$283$		−	11.3565i		−	0.675074i	0.941312	−	0.337537i	$-0.109594\pi$
$284$	9.69976	+	7.55951i	0.575575	+	0.448574i
$285$		−	12.0557i		−	0.714118i
$286$	10.0384	−	29.2107i	0.593584	−	1.72727i
$287$	14.8700			0.877749
$288$	5.63679	+	0.476077i	0.332151	+	0.0280531i
$289$	−16.4167			−0.965685
$290$	−3.63432	+	10.5755i	−0.213415	+	0.621015i
$291$		−	19.4812i		−	1.14201i
$292$	3.49308	+	2.72234i	0.204417	+	0.159313i
$293$		−	1.87110i		−	0.109311i	−0.998505	−	0.0546553i	$-0.982594\pi$
$293$		−	1.87110i		−	0.109311i	0.998505	−	0.0546553i	$-0.0174060\pi$
$294$	−17.4085	−	5.98250i	−1.01528	−	0.348907i
$295$	21.7538			1.26656
$296$	−5.79859	−	8.89387i	−0.337036	−	0.516946i
$297$	−3.86022			−0.223993
$298$	18.1145	+	6.22513i	1.04934	+	0.360612i
$299$		−	5.65791i		−	0.327205i
$300$	0.983170	−	1.26153i	0.0567633	−	0.0728342i
$301$			8.26581i			0.476433i
$302$	−2.54439	+	7.40390i	−0.146413	+	0.426046i
$303$	15.8617			0.911231
$304$	−22.8168	+	5.74721i	−1.30863	+	0.329625i
$305$	−19.1046			−1.09392
$306$	−0.351044	+	1.02150i	−0.0200679	+	0.0583954i
$307$		−	25.5322i		−	1.45720i	−0.684941	−	0.728598i	$-0.740172\pi$
$307$		−	25.5322i		−	1.45720i	0.684941	−	0.728598i	$-0.259828\pi$
$308$	21.2327	−	27.2441i	1.20985	−	1.55238i
$309$		−	12.3123i		−	0.700421i
$310$	25.2394	+	8.67365i	1.43350	+	0.492630i
$311$	−13.4590			−0.763187			−0.381594	−	0.924330i	$-0.624625\pi$
$311$	−13.4590			−0.763187			−0.381594	+	0.924330i	$0.624625\pi$
$312$	13.4055	−	8.74005i	0.758936	−	0.494808i
$313$	−29.8742			−1.68859			−0.844294	−	0.535881i	$-0.819980\pi$
$313$	−29.8742			−1.68859			−0.844294	+	0.535881i	$0.819980\pi$
$314$	−16.5412	−	5.68447i	−0.933474	−	0.320793i
$315$			9.16920i			0.516626i
$316$	8.82464	+	6.87749i	0.496425	+	0.386889i
$317$		−	1.94005i		−	0.108964i	−0.998515	−	0.0544820i	$-0.982649\pi$
$317$		−	1.94005i		−	0.108964i	0.998515	−	0.0544820i	$-0.0173507\pi$
$318$	−1.04245	+	3.03343i	−0.0584579	+	0.170106i
$319$	−14.8935			−0.833877
$320$	15.0022	+	6.61464i	0.838648	+	0.369769i
$321$	1.24916			0.0697213
$322$	2.05631	−	5.98365i	0.114594	−	0.333456i
$323$		−	4.49280i		−	0.249986i
$324$	−1.57750	−	1.22943i	−0.0876390	−	0.0683015i
$325$		−	4.52462i		−	0.250981i
$326$	−9.60537	−	3.30093i	−0.531993	−	0.182822i
$327$	−11.2279			−0.620904
$328$	−7.87493	+	5.13426i	−0.434820	+	0.283492i
$329$	29.3307			1.61705
$330$	−10.5810	−	3.63621i	−0.582465	−	0.200167i
$331$		−	20.1078i		−	1.10522i	−0.833439	−	0.552612i	$-0.813631\pi$
$331$		−	20.1078i		−	1.10522i	0.833439	−	0.552612i	$-0.186369\pi$
$332$	−3.87096	+	4.96690i	−0.212446	+	0.272594i
$333$			3.75374i			0.205704i
$334$	7.01525	−	20.4136i	0.383857	−	1.11698i
$335$	7.46421			0.407813
$336$	17.3538	−	4.37115i	0.946725	−	0.238466i
$337$	5.22684			0.284724			0.142362	−	0.989815i	$-0.454530\pi$
$337$	5.22684			0.284724			0.142362	+	0.989815i	$0.454530\pi$
$338$	8.73823	−	25.4273i	0.475297	−	1.38306i
$339$			13.4161i			0.728662i
$340$	−1.92445	+	2.46930i	−0.104368	+	0.133917i
$341$			35.5448i			1.92486i
$342$	7.86733	+	2.70365i	0.425416	+	0.146196i
$343$	−26.9164			−1.45335
$344$	−2.85399	−	4.37745i	−0.153877	−	0.236016i
$345$	−2.04946			−0.110339
$346$	15.2052	+	5.22535i	0.817437	+	0.280916i
$347$		−	24.3781i		−	1.30868i	−0.756199	−	0.654342i	$-0.772946\pi$
$347$		−	24.3781i		−	1.30868i	0.756199	−	0.654342i	$-0.227054\pi$
$348$	−6.08633	−	4.74338i	−0.326262	−	0.254272i
$349$		−	28.7527i		−	1.53910i	−0.638588	−	0.769549i	$-0.720481\pi$
$349$		−	28.7527i		−	1.53910i	0.638588	−	0.769549i	$-0.279519\pi$
$350$	1.64443	−	4.78511i	0.0878984	−	0.255775i
$351$	−5.65791			−0.301997
$352$	−1.83776	+	21.7592i	−0.0979530	+	1.15977i
$353$	31.8467			1.69503			0.847514	−	0.530772i	$-0.178098\pi$
$353$	31.8467			1.69503			0.847514	+	0.530772i	$0.178098\pi$
$354$	−4.87858	+	14.1962i	−0.259294	+	0.754517i
$355$		−	12.6018i		−	0.668832i
$356$	0.544562	+	0.424404i	0.0288617	+	0.0224934i
$357$			3.41708i			0.180851i
$358$	−23.7223	−	8.15230i	−1.25376	−	0.430862i
$359$	20.9020			1.10317			0.551583	−	0.834120i	$-0.314024\pi$
$359$	20.9020			1.10317			0.551583	+	0.834120i	$0.314024\pi$
$360$	−3.16591	−	4.85587i	−0.166858	−	0.255927i
$361$	−15.6023			−0.821173
$362$	−23.8311	−	8.18967i	−1.25253	−	0.430440i
$363$		−	3.90128i		−	0.204764i
$364$	31.1207	−	39.9316i	1.63117	−	2.09299i
$365$		−	4.53816i		−	0.237538i
$366$	4.28444	−	12.4673i	0.223951	−	0.651675i
$367$	22.6066			1.18005			0.590027	−	0.807384i	$-0.299117\pi$
$367$	22.6066			1.18005			0.590027	+	0.807384i	$0.299117\pi$
$368$	0.977023	+	3.87884i	0.0509308	+	0.202199i
$369$	3.32369			0.173024
$370$	−3.53592	+	10.2891i	−0.183824	+	0.534907i
$371$			10.1473i			0.526821i
$372$	−11.3205	+	14.5256i	−0.586942	+	0.753117i
$373$			2.55027i			0.132048i	0.997818	+	0.0660241i	$0.0210314\pi$
$373$			2.55027i			0.132048i	−0.997818	+	0.0660241i	$0.978969\pi$
$374$	−3.94322	−	1.35511i	−0.203899	−	0.0700709i
$375$	−11.8863			−0.613804
$376$	−15.5331	+	10.1272i	−0.801057	+	0.522270i
$377$	−21.8294			−1.12427
$378$	−5.98365	−	2.05631i	−0.307766	−	0.105765i
$379$			12.2107i			0.627222i	0.949552	+	0.313611i	$0.101539\pi$
$379$			12.2107i			0.627222i	−0.949552	+	0.313611i	$0.898461\pi$
$380$	19.0179	+	14.8216i	0.975597	+	0.760332i
$381$		−	12.9809i		−	0.665029i
$382$	−11.8121	+	34.3719i	−0.604358	+	1.75862i
$383$	−16.6355			−0.850034			−0.425017	−	0.905185i	$-0.639732\pi$
$383$	−16.6355			−0.850034			−0.425017	+	0.905185i	$0.639732\pi$
$384$	−7.68102	+	8.30674i	−0.391971	+	0.423901i
$385$	−35.3951			−1.80390
$386$	0.813832	−	2.36817i	0.0414230	−	0.120537i
$387$			1.84754i			0.0939158i
$388$	30.7316	+	23.9507i	1.56016	+	1.21591i
$389$			20.3819i			1.03340i	0.856165	+	0.516702i	$0.172841\pi$
$389$			20.3819i			1.03340i	−0.856165	+	0.516702i	$0.827159\pi$
$390$	−15.5085	−	5.32959i	−0.785306	−	0.269874i
$391$	−0.763773			−0.0386257
$392$	30.8398	−	20.1068i	1.55765	−	1.01555i
$393$	−12.7610			−0.643708
$394$	−2.48327	−	0.853387i	−0.125105	−	0.0429930i
$395$		−	11.4648i		−	0.576858i
$396$	4.74585	−	6.08950i	0.238488	−	0.306009i
$397$			28.9234i			1.45163i	0.687892	+	0.725813i	$0.258536\pi$
$397$			28.9234i			1.45163i	−0.687892	+	0.725813i	$0.741464\pi$
$398$	−7.39074	+	21.5063i	−0.370464	+	1.07801i
$399$	26.3174			1.31752
$400$	0.781323	+	3.10190i	0.0390662	+	0.155095i
$401$	−0.638188			−0.0318696			−0.0159348	−	0.999873i	$-0.505072\pi$
$401$	−0.638188			−0.0318696			−0.0159348	+	0.999873i	$0.505072\pi$
$402$	−1.67394	+	4.87100i	−0.0834888	+	0.242944i
$403$			52.0979i			2.59518i
$404$	−19.5008	+	25.0219i	−0.970200	+	1.24488i
$405$			2.04946i			0.101839i
$406$	−23.0862	−	7.93368i	−1.14575	−	0.393742i
$407$	−14.4903			−0.718255
$408$	−1.17984	−	1.80963i	−0.0584107	−	0.0895903i
$409$	−15.9037			−0.786387			−0.393194	−	0.919456i	$-0.628630\pi$
$409$	−15.9037			−0.786387			−0.393194	+	0.919456i	$0.628630\pi$
$410$	9.11035	+	3.13082i	0.449928	+	0.154620i
$411$		−	4.90524i		−	0.241958i
$412$	19.4226	+	15.1370i	0.956884	+	0.745748i
$413$			47.4883i			2.33675i
$414$	0.459619	−	1.33744i	0.0225890	−	0.0657317i
$415$	6.45292			0.316761
$416$	−2.69360	+	31.8924i	−0.132065	+	1.56365i
$417$	7.62325			0.373312
$418$	−10.4367	+	30.3696i	−0.510474	+	1.48543i
$419$		−	40.1052i		−	1.95927i	−0.200791	−	0.979634i	$-0.564351\pi$
$419$		−	40.1052i		−	1.95927i	0.200791	−	0.979634i	$-0.435649\pi$
$420$	−14.4644	−	11.2729i	−0.705792	−	0.550059i
$421$			8.56735i			0.417547i	0.977964	+	0.208773i	$0.0669471\pi$
$421$			8.56735i			0.417547i	−0.977964	+	0.208773i	$0.933053\pi$
$422$	−37.3009	−	12.8186i	−1.81578	−	0.624001i
$423$	6.55588			0.318758
$424$	−3.50362	−	5.37385i	−0.170151	−	0.260977i
$425$	−0.610788			−0.0296276
$426$	8.22368	+	2.82611i	0.398438	+	0.136925i
$427$		−	41.7050i		−	2.01825i
$428$	−1.53575	+	1.97055i	−0.0742333	+	0.0952503i
$429$		−	21.8408i		−	1.05448i
$430$	−1.74033	+	5.06418i	−0.0839262	+	0.244217i
$431$	32.6773			1.57401			0.787006	−	0.616945i	$-0.211630\pi$
$431$	32.6773			1.57401			0.787006	+	0.616945i	$0.211630\pi$
$432$	3.87884	−	0.977023i	0.186621	−	0.0470070i
$433$	9.73944			0.468048			0.234024	−	0.972231i	$-0.424811\pi$
$433$	9.73944			0.468048			0.234024	+	0.972231i	$0.424811\pi$
$434$	−18.9345	+	55.0973i	−0.908883	+	2.64476i
$435$			7.90726i			0.379124i
$436$	13.8039	−	17.7120i	0.661085	−	0.848251i
$437$			5.88237i			0.281392i
$438$	2.96152	+	1.01774i	0.141507	+	0.0486295i
$439$	8.12707			0.387884			0.193942	−	0.981013i	$-0.437873\pi$
$439$	8.12707			0.387884			0.193942	+	0.981013i	$0.437873\pi$
$440$	18.7447	−	12.2211i	0.893618	−	0.582618i
$441$	−13.0162			−0.619821
$442$	−5.77956	−	1.98618i	−0.274906	−	0.0944728i
$443$			9.89346i			0.470052i	0.971989	+	0.235026i	$0.0755176\pi$
$443$			9.89346i			0.470052i	−0.971989	+	0.235026i	$0.924482\pi$
$444$	−5.92153	−	4.61495i	−0.281024	−	0.219016i
$445$		−	0.707485i		−	0.0335380i
$446$	11.8914	−	34.6027i	0.563074	−	1.63849i
$447$	13.5441			0.640615
$448$	−14.4397	+	32.7496i	−0.682210	+	1.54727i
$449$	27.8834			1.31590			0.657950	−	0.753062i	$-0.271424\pi$
$449$	27.8834			1.31590			0.657950	+	0.753062i	$0.271424\pi$
$450$	0.367556	−	1.06955i	0.0173268	−	0.0504191i
$451$			12.8302i			0.604148i
$452$	−21.1639	−	16.4941i	−0.995466	−	0.775817i
$453$			5.53587i			0.260098i
$454$	29.6984	+	10.2060i	1.39381	+	0.478991i
$455$	−51.8785			−2.43210
$456$	−13.9373	+	9.08679i	−0.652674	+	0.425528i
$457$	2.41513			0.112975			0.0564874	−	0.998403i	$-0.482010\pi$
$457$	2.41513			0.112975			0.0564874	+	0.998403i	$0.482010\pi$
$458$	0.285169	+	0.0979998i	0.0133251	+	0.00457923i
$459$			0.763773i			0.0356499i
$460$	2.51966	−	3.23303i	0.117480	−	0.150741i
$461$		−	9.11797i		−	0.424666i	−0.977197	−	0.212333i	$-0.931894\pi$
$461$		−	9.11797i		−	0.424666i	0.977197	−	0.212333i	$-0.0681062\pi$
$462$	7.93781	−	23.0982i	0.369300	−	1.07462i
$463$	−30.3895			−1.41232			−0.706159	−	0.708053i	$-0.749574\pi$
$463$	−30.3895			−1.41232			−0.706159	+	0.708053i	$0.749574\pi$
$464$	14.9654	−	3.76956i	0.694751	−	0.174997i
$465$	18.8714			0.875141
$466$	0.104946	−	0.305382i	0.00486153	−	0.0141465i
$467$		−	11.1150i		−	0.514342i	−0.966366	−	0.257171i	$-0.917210\pi$
$467$		−	11.1150i		−	0.514342i	0.966366	−	0.257171i	$-0.0827903\pi$
$468$	6.95598	−	8.92536i	0.321540	−	0.412575i
$469$			16.2943i			0.752399i
$470$	17.9699	+	6.17545i	0.828890	+	0.284852i
$471$	−12.3678			−0.569878
$472$	−16.3966	−	25.1491i	−0.754715	−	1.15758i
$473$	−7.13191			−0.327926
$474$	7.48173	+	2.57114i	0.343647	+	0.118096i
$475$			4.70412i			0.215840i
$476$	−5.39046	−	4.20105i	−0.247071	−	0.192555i
$477$			2.26808i			0.103848i
$478$	−12.8508	+	37.3944i	−0.587780	+	1.71038i
$479$	−40.5092			−1.85091			−0.925456	−	0.378855i	$-0.876318\pi$
$479$	−40.5092			−1.85091			−0.925456	+	0.378855i	$0.876318\pi$
$480$	11.5524	+	0.975703i	0.527292	+	0.0445345i
$481$	−21.2383			−0.968384
$482$	−1.76031	+	5.12233i	−0.0801800	+	0.233316i
$483$		−	4.47395i		−	0.203572i
$484$	6.15427	+	4.79633i	0.279740	+	0.218015i
$485$		−	39.9260i		−	1.81295i
$486$	−1.33744	−	0.459619i	−0.0606676	−	0.0208487i
$487$	16.6686			0.755328			0.377664	−	0.925943i	$-0.376727\pi$
$487$	16.6686			0.755328			0.377664	+	0.925943i	$0.376727\pi$
$488$	14.3997	+	22.0863i	0.651846	+	0.999800i
$489$	−7.18190			−0.324777
$490$	−35.6780	−	12.2609i	−1.61177	−	0.553892i
$491$			0.559301i			0.0252409i	0.999920	+	0.0126204i	$0.00401732\pi$
$491$			0.559301i			0.0252409i	−0.999920	+	0.0126204i	$0.995983\pi$
$492$	−4.08623	+	5.24312i	−0.184221	+	0.236378i
$493$			2.94680i			0.132717i
$494$	−15.2970	+	44.5126i	−0.688244	+	2.00272i
$495$	−7.91138			−0.355590
$496$	−8.99640	−	35.7163i	−0.403950	−	1.60371i
$497$	27.5095			1.23397
$498$	−1.44715	+	4.21106i	−0.0648483	+	0.188702i
$499$			26.2401i			1.17467i	0.809345	+	0.587334i	$0.199823\pi$
$499$			26.2401i			1.17467i	−0.809345	+	0.587334i	$0.800177\pi$
$500$	14.6133	−	18.7506i	0.653526	−	0.838553i
$501$		−	15.2632i		−	0.681909i
$502$	−22.8677	−	7.85859i	−1.02063	−	0.350746i
$503$	8.22830			0.366882			0.183441	−	0.983031i	$-0.441276\pi$
$503$	8.22830			0.366882			0.183441	+	0.983031i	$0.441276\pi$
$504$	10.6003	−	6.91113i	0.472174	−	0.307846i
$505$	32.5080			1.44659
$506$	5.16282	+	1.77423i	0.229515	+	0.0788740i
$507$		−	19.0119i		−	0.844349i
$508$	20.4773	+	15.9590i	0.908534	+	0.708066i
$509$		−	5.03601i		−	0.223217i	−0.993752	−	0.111609i	$-0.964400\pi$
$509$		−	5.03601i		−	0.223217i	0.993752	−	0.111609i	$-0.0356003\pi$
$510$	−0.719453	+	2.09353i	−0.0318579	+	0.0927031i
$511$	9.90673			0.438248
$512$	−3.66064	−	22.3293i	−0.161779	−	0.986827i
$513$	5.88237			0.259713
$514$	10.0240	−	29.1687i	0.442139	−	1.28658i
$515$		−	25.2336i		−	1.11192i
$516$	−2.91450	−	2.27142i	−0.128304	−	0.0999935i
$517$			25.3071i			1.11301i
$518$	−22.4611	−	7.71886i	−0.986883	−	0.339147i
$519$	11.3689			0.499038
$520$	27.4740	−	17.9124i	1.20482	−	0.785511i
$521$	−41.3800			−1.81289			−0.906446	−	0.422322i	$-0.861215\pi$
$521$	−41.3800			−1.81289			−0.906446	+	0.422322i	$0.861215\pi$
$522$	−5.16013	−	1.77330i	−0.225853	−	0.0776154i
$523$		−	1.78626i		−	0.0781077i	−0.999237	−	0.0390538i	$-0.987566\pi$
$523$		−	1.78626i		−	0.0781077i	0.999237	−	0.0390538i	$-0.0124344\pi$
$524$	15.6887	−	20.1305i	0.685366	−	0.879406i
$525$		−	3.57781i		−	0.156148i
$526$	−8.21281	+	23.8984i	−0.358096	+	1.04202i
$527$	7.03281			0.306354
$528$	3.77152	+	14.9732i	0.164134	+	0.651624i
$529$	1.00000			0.0434783
$530$	−2.13647	+	6.21690i	−0.0928023	+	0.270045i
$531$			10.6144i			0.460626i
$532$	−32.3553	+	41.5158i	−1.40278	+	1.79994i
$533$			18.8051i			0.814540i
$534$	0.461692	+	0.158663i	0.0199794	+	0.00686600i
$535$	2.56011			0.110683
$536$	−5.62603	−	8.62919i	−0.243007	−	0.372724i
$537$	−17.7371			−0.765412
$538$	−17.1057	−	5.87845i	−0.737479	−	0.253438i
$539$		−	50.2455i		−	2.16423i
$540$	−3.23303	−	2.51966i	−0.139128	−	0.108429i
$541$		−	33.3527i		−	1.43394i	−0.697102	−	0.716972i	$-0.745528\pi$
$541$		−	33.3527i		−	1.43394i	0.697102	−	0.716972i	$-0.254472\pi$
$542$	−6.95990	+	20.2526i	−0.298953	+	0.869922i
$543$	−17.8184			−0.764661
$544$	4.30523	+	0.363615i	0.184585	+	0.0155899i
$545$	−23.0111			−0.985689
$546$	11.6344	−	33.8549i	0.497907	−	1.44886i
$547$		−	16.9036i		−	0.722744i	−0.932422	−	0.361372i	$-0.882308\pi$
$547$		−	16.9036i		−	0.722744i	0.932422	−	0.361372i	$-0.117692\pi$
$548$	7.73802	+	6.03063i	0.330552	+	0.257616i
$549$		−	9.32173i		−	0.397842i
$550$	4.12870	+	1.41885i	0.176048	+	0.0604998i
$551$	22.6954			0.966857
$552$	1.54475	+	2.36933i	0.0657489	+	0.100846i
$553$	25.0276			1.06428
$554$	24.9769	+	8.58343i	1.06117	+	0.364675i
$555$			7.69316i			0.326556i
$556$	−9.37222	+	12.0257i	−0.397471	+	0.510003i
$557$			14.2233i			0.602660i	0.953520	+	0.301330i	$0.0974306\pi$
$557$			14.2233i			0.602660i	−0.953520	+	0.301330i	$0.902569\pi$
$558$	−4.23216	+	12.3151i	−0.179161	+	0.521341i
$559$	−10.4532			−0.442124
$560$	35.5659	−	8.95852i	1.50293	−	0.378566i
$561$	−2.94833			−0.124479
$562$	−5.46931	+	15.9151i	−0.230709	+	0.671339i
$563$		−	5.79487i		−	0.244225i	−0.992516	−	0.122112i	$-0.961033\pi$
$563$		−	5.79487i		−	0.244225i	0.992516	−	0.122112i	$-0.0389668\pi$
$564$	−8.05997	+	10.3419i	−0.339386	+	0.435473i
$565$			27.4958i			1.15676i
$566$	15.1887	+	5.21966i	0.638427	+	0.219399i
$567$	−4.47395			−0.187888
$568$	−14.5686	+	9.49837i	−0.611284	+	0.398543i
$569$	−40.3221			−1.69039			−0.845195	−	0.534458i	$-0.820516\pi$
$569$	−40.3221			−1.69039			−0.845195	+	0.534458i	$0.820516\pi$
$570$	16.1238	+	5.54103i	0.675352	+	0.232088i
$571$		−	1.27604i		−	0.0534007i	−0.999643	−	0.0267003i	$-0.991500\pi$
$571$		−	1.27604i		−	0.0534007i	0.999643	−	0.0267003i	$-0.00849999\pi$
$572$	34.4538	+	26.8516i	1.44059	+	1.12272i
$573$			25.6997i			1.07362i
$574$	−6.83453	+	19.8878i	−0.285268	+	0.830100i
$575$	0.799698			0.0333497
$576$	−3.22750	+	7.32006i	−0.134479	+	0.305002i
$577$	−37.0698			−1.54323			−0.771617	−	0.636087i	$-0.780552\pi$
$577$	−37.0698			−1.54323			−0.771617	+	0.636087i	$0.780552\pi$
$578$	7.54540	−	21.9563i	0.313847	−	0.913262i
$579$		−	1.77067i		−	0.0735865i
$580$	−12.4737	−	9.72139i	−0.517943	−	0.403659i
$581$			14.0866i			0.584412i
$582$	26.0550	+	8.95393i	1.08001	+	0.371152i
$583$	−8.75529			−0.362607
$584$	−5.24645	+	3.42056i	−0.217100	+	0.141544i
$585$	−11.5957			−0.479422
$586$	2.50248	+	0.859991i	0.103377	+	0.0355259i
$587$			18.0620i			0.745498i	0.927932	+	0.372749i	$0.121585\pi$
$587$			18.0620i			0.745498i	−0.927932	+	0.372749i	$0.878415\pi$
$588$	16.0025	−	20.5331i	0.659932	−	0.846772i
$589$		−	54.1647i		−	2.23182i
$590$	−9.99847	+	29.0945i	−0.411631	+	1.19780i
$591$	−1.85673			−0.0763756
$592$	14.5602	−	3.66749i	0.598419	−	0.150733i
$593$	−13.3673			−0.548928			−0.274464	−	0.961597i	$-0.588500\pi$
$593$	−13.3673			−0.548928			−0.274464	+	0.961597i	$0.588500\pi$
$594$	1.77423	−	5.16282i	0.0727974	−	0.211833i
$595$			7.00319i			0.287103i
$596$	−16.6515	+	21.3659i	−0.682072	+	0.875180i
$597$			16.0802i			0.658117i
$598$	7.56712	+	2.60048i	0.309443	+	0.106341i
$599$	−30.4425			−1.24385			−0.621923	−	0.783078i	$-0.713648\pi$
$599$	−30.4425			−1.24385			−0.621923	+	0.783078i	$0.713648\pi$
$600$	1.23533	+	1.89475i	0.0504323	+	0.0773530i
$601$	8.85784			0.361319			0.180659	−	0.983546i	$-0.442177\pi$
$601$	8.85784			0.361319			0.180659	+	0.983546i	$0.442177\pi$
$602$	−11.0550	−	3.79912i	−0.450570	−	0.154841i
$603$			3.64203i			0.148315i
$604$	−8.73284	−	6.80594i	−0.355334	−	0.276930i
$605$		−	7.99553i		−	0.325065i
$606$	−7.29033	+	21.2141i	−0.296149	+	0.861764i
$607$	46.9548			1.90584			0.952918	−	0.303228i	$-0.0980643\pi$
$607$	46.9548			1.90584			0.952918	+	0.303228i	$0.0980643\pi$
$608$	2.80046	−	33.1577i	0.113574	−	1.34472i
$609$	−17.2614			−0.699469
$610$	8.78081	−	25.5512i	0.355524	−	1.03454i
$611$			37.0925i			1.50060i
$612$	−1.20485	−	0.939003i	−0.0487033	−	0.0379569i
$613$		−	7.81557i		−	0.315668i	−0.987466	−	0.157834i	$-0.949549\pi$
$613$		−	7.81557i		−	0.315668i	0.987466	−	0.157834i	$-0.0504511\pi$
$614$	34.1478	+	11.7351i	1.37809	+	0.473588i
$615$	6.81178			0.274677
$616$	26.6785	+	40.9194i	1.07491	+	1.64869i
$617$	−18.1672			−0.731385			−0.365692	−	0.930736i	$-0.619168\pi$
$617$	−18.1672			−0.731385			−0.365692	+	0.930736i	$0.619168\pi$
$618$	16.4670	+	5.65895i	0.662398	+	0.227636i
$619$			25.9300i			1.04222i	0.853491	+	0.521108i	$0.174481\pi$
$619$			25.9300i			1.04222i	−0.853491	+	0.521108i	$0.825519\pi$
$620$	−23.2010	+	29.7697i	−0.931775	+	1.19558i
$621$		−	1.00000i		−	0.0401286i
$622$	6.18598	−	18.0006i	0.248035	−	0.721757i
$623$	1.54443			0.0618763
$624$	5.52790	+	21.9461i	0.221293	+	0.878549i
$625$	−20.3620			−0.814480
$626$	13.7307	−	39.9549i	0.548790	−	1.59692i
$627$			22.7072i			0.906839i
$628$	15.2053	−	19.5102i	0.606757	−	0.778542i
$629$			2.86701i			0.114315i
$630$	−12.2633	−	4.21433i	−0.488580	−	0.167903i
$631$	−15.9334			−0.634298			−0.317149	−	0.948376i	$-0.602726\pi$
$631$	−15.9334			−0.634298			−0.317149	+	0.948376i	$0.602726\pi$
$632$	−13.2542	+	8.64143i	−0.527224	+	0.343738i
$633$	−27.8897			−1.10852
$634$	2.59470	+	0.891682i	0.103049	+	0.0354132i
$635$		−	26.6038i		−	1.05574i
$636$	−3.57790	−	2.78844i	−0.141873	−	0.110569i
$637$		−	73.6447i		−	2.91791i
$638$	6.84534	−	19.9192i	0.271010	−	0.788610i
$639$	6.14881			0.243243
$640$	−15.7420	+	17.0244i	−0.622256	+	0.672947i
$641$	−26.6807			−1.05383			−0.526913	−	0.849919i	$-0.676651\pi$
$641$	−26.6807			−1.05383			−0.526913	+	0.849919i	$0.676651\pi$
$642$	−0.574137	+	1.67068i	−0.0226594	+	0.0659365i
$643$		−	10.5858i		−	0.417464i	−0.977973	−	0.208732i	$-0.933066\pi$
$643$		−	10.5858i		−	0.417464i	0.977973	−	0.208732i	$-0.0669336\pi$
$644$	7.05766	+	5.50039i	0.278111	+	0.216746i
$645$			3.78647i			0.149092i
$646$	6.00885	+	2.06497i	0.236415	+	0.0812453i
$647$	−1.96369			−0.0772005			−0.0386003	−	0.999255i	$-0.512290\pi$
$647$	−1.96369			−0.0772005			−0.0386003	+	0.999255i	$0.512290\pi$
$648$	2.36933	−	1.54475i	0.0930763	−	0.0606835i
$649$	−40.9739			−1.60837
$650$	6.05141	+	2.07960i	0.237356	+	0.0815686i
$651$			41.1960i			1.61460i
$652$	8.82962	−	11.3295i	0.345794	−	0.443696i
$653$		−	15.2529i		−	0.596893i	−0.954426	−	0.298447i	$-0.903531\pi$
$653$		−	15.2529i		−	0.596893i	0.954426	−	0.298447i	$-0.0964685\pi$
$654$	5.16054	−	15.0166i	0.201793	−	0.587197i
$655$	−26.1533			−1.02189
$656$	−3.24732	−	12.8921i	−0.126786	−	0.503350i
$657$	2.21431			0.0863886
$658$	−13.4809	+	39.2281i	−0.525541	+	1.52927i
$659$			31.3355i			1.22066i	0.792149	+	0.610328i	$0.208962\pi$
$659$			31.3355i			1.22066i	−0.792149	+	0.610328i	$0.791038\pi$
$660$	9.72645	−	12.4802i	0.378602	−	0.485791i
$661$			11.5349i			0.448657i	0.974514	+	0.224329i	$0.0720189\pi$
$661$			11.5349i			0.448657i	−0.974514	+	0.224329i	$0.927981\pi$
$662$	26.8930	+	9.24191i	1.04523	+	0.359197i
$663$	−4.32136			−0.167828
$664$	−4.86378	−	7.46006i	−0.188751	−	0.289507i
$665$	53.9366			2.09157
$666$	−5.02041	−	1.72529i	−0.194537	−	0.0668536i
$667$		−	3.85821i		−	0.149390i
$668$	24.0777	+	18.7650i	0.931594	+	0.726038i
$669$		−	25.8723i		−	1.00028i
$670$	−3.43069	+	9.98295i	−0.132539	+	0.385675i
$671$	35.9839			1.38914
$672$	−2.12995	+	25.2187i	−0.0821644	+	0.972833i
$673$	−8.43821			−0.325269			−0.162635	−	0.986686i	$-0.551999\pi$
$673$	−8.43821			−0.325269			−0.162635	+	0.986686i	$0.551999\pi$
$674$	−2.40235	+	6.99059i	−0.0925351	+	0.269268i
$675$		−	0.799698i		−	0.0307804i
$676$	29.9913	+	23.3737i	1.15351	+	0.898990i
$677$		−	21.4224i		−	0.823329i	−0.911336	−	0.411664i	$-0.864948\pi$
$677$		−	21.4224i		−	0.823329i	0.911336	−	0.411664i	$-0.135052\pi$
$678$	−17.9432	−	6.16628i	−0.689106	−	0.236815i
$679$	87.1580			3.34482
$680$	−2.41804	−	3.70878i	−0.0927275	−	0.142225i
$681$	22.2054			0.850911
$682$	−47.5391	−	16.3370i	−1.82037	−	0.625578i
$683$		−	19.2709i		−	0.737382i	−0.929552	−	0.368691i	$-0.879806\pi$
$683$		−	19.2709i		−	0.737382i	0.929552	−	0.368691i	$-0.120194\pi$
$684$	−7.23194	+	9.27945i	−0.276520	+	0.354809i
$685$		−	10.0531i		−	0.384110i
$686$	12.3713	−	35.9991i	0.472337	−	1.37445i
$687$	0.213220			0.00813485
$688$	7.16633	−	1.80509i	0.273214	−	0.0688184i
$689$	−12.8326			−0.488883
$690$	0.941972	−	2.74104i	0.0358602	−	0.104350i
$691$			1.72817i			0.0657428i	0.999460	+	0.0328714i	$0.0104652\pi$
$691$			1.72817i			0.0657428i	−0.999460	+	0.0328714i	$0.989535\pi$
$692$	−13.9772	+	17.9344i	−0.531333	+	0.681764i
$693$		−	17.2704i		−	0.656049i
$694$	32.6043	+	11.2046i	1.23764	+	0.425321i
$695$	15.6236			0.592636
$696$	9.14139	−	5.95997i	0.346503	−	0.225912i
$697$	2.53854			0.0961542
$698$	38.4551	+	13.2153i	1.45555	+	0.500206i
$699$		−	0.228333i		−	0.00863633i
$700$	5.64400	+	4.39865i	0.213323	+	0.166253i
$701$			17.3189i			0.654126i	0.945002	+	0.327063i	$0.106059\pi$
$701$			17.3189i			0.654126i	−0.945002	+	0.327063i	$0.893941\pi$
$702$	2.60048	−	7.56712i	0.0981487	−	0.285603i
$703$	22.0809			0.832797
$704$	−28.2570	−	12.4588i	−1.06498	−	0.469560i
$705$	13.4360			0.506030
$706$	−14.6373	+	42.5931i	−0.550883	+	1.60301i
$707$			70.9645i			2.66889i
$708$	−16.7442	−	13.0496i	−0.629287	−	0.490435i
$709$		−	32.7526i		−	1.23005i	−0.788507	−	0.615025i	$-0.789146\pi$
$709$		−	32.7526i		−	1.23005i	0.788507	−	0.615025i	$-0.210854\pi$
$710$	16.8541	+	5.79200i	0.632524	+	0.217370i
$711$	5.59406			0.209794
$712$	−0.817906	+	0.533255i	−0.0306523	+	0.0199846i
$713$	−9.20798			−0.344841
$714$	−4.57015	−	1.57055i	−0.171034	−	0.0587765i
$715$		−	44.7618i		−	1.67400i
$716$	21.8065	−	27.9803i	0.814946	−	1.04567i
$717$			27.9596i			1.04417i
$718$	−9.60695	+	27.9552i	−0.358528	+	1.04328i
$719$	33.6230			1.25393			0.626963	−	0.779049i	$-0.284298\pi$
$719$	33.6230			1.25393			0.626963	+	0.779049i	$0.284298\pi$
$720$	7.94955	−	2.00237i	0.296262	−	0.0746240i
$721$	55.0845			2.05145
$722$	7.17110	−	20.8671i	0.266881	−	0.776595i
$723$			3.82994i			0.142437i
$724$	21.9064	−	28.1086i	0.814146	−	1.04465i
$725$		−	3.08540i		−	0.114589i
$726$	5.21773	+	1.79310i	0.193648	+	0.0665482i
$727$	11.4940			0.426291			0.213145	−	0.977021i	$-0.431629\pi$
$727$	11.4940			0.426291			0.213145	+	0.977021i	$0.431629\pi$
$728$	39.1026	+	59.9754i	1.44924	+	2.22284i
$729$	−1.00000			−0.0370370
$730$	6.06952	+	2.08582i	0.224643	+	0.0771997i
$731$			1.41110i			0.0521915i
$732$	14.7050	+	11.4604i	0.543514	+	0.423588i
$733$		−	1.18924i		−	0.0439256i	−0.999759	−	0.0219628i	$-0.993008\pi$
$733$		−	1.18924i		−	0.0439256i	0.999759	−	0.0219628i	$-0.00699154\pi$
$734$	−10.3904	+	30.2350i	−0.383517	+	1.11599i
$735$	−26.6763			−0.983970
$736$	−5.63679	−	0.476077i	−0.207775	−	0.0175484i
$737$	−14.0590			−0.517871
$738$	−1.52763	+	4.44524i	−0.0562328	+	0.163631i
$739$		−	43.3003i		−	1.59283i	−0.604751	−	0.796415i	$-0.706727\pi$
$739$		−	43.3003i		−	1.59283i	0.604751	−	0.796415i	$-0.293273\pi$
$740$	−12.1360	−	9.45817i	−0.446127	−	0.347689i
$741$			33.2819i			1.22264i
$742$	−13.5714	−	4.66388i	−0.498222	−	0.171217i
$743$	26.6989			0.979489			0.489744	−	0.871866i	$-0.337090\pi$
$743$	26.6989			0.979489			0.489744	+	0.871866i	$0.337090\pi$
$744$	−14.2240	−	21.8168i	−0.521478	−	0.799842i
$745$	27.7582			1.01698
$746$	−3.41084	−	1.17215i	−0.124880	−	0.0429156i
$747$			3.14859i			0.115201i
$748$	3.62475	−	4.65100i	0.132534	−	0.170057i
$749$			5.58868i			0.204206i
$750$	5.46315	−	15.8972i	0.199486	−	0.580484i
$751$	3.00670			0.109716			0.0548580	−	0.998494i	$-0.482529\pi$
$751$	3.00670			0.109716			0.0548580	+	0.998494i	$0.482529\pi$
$752$	−6.40524	−	25.4292i	−0.233575	−	0.927308i
$753$	−17.0981			−0.623088
$754$	10.0332	−	29.1955i	0.365387	−	1.06324i
$755$			11.3456i			0.412907i
$756$	5.50039	−	7.05766i	0.200047	−	0.256685i
$757$			3.75871i			0.136613i	0.997664	+	0.0683064i	$0.0217595\pi$
$757$			3.75871i			0.136613i	−0.997664	+	0.0683064i	$0.978240\pi$
$758$	−16.3311	−	5.61227i	−0.593173	−	0.203847i
$759$	3.86022			0.140117
$760$	−28.5640	+	18.6230i	−1.03613	+	0.675529i
$761$	−29.6377			−1.07437			−0.537183	−	0.843466i	$-0.680512\pi$
$761$	−29.6377			−1.07437			−0.537183	+	0.843466i	$0.680512\pi$
$762$	17.3611	+	5.96624i	0.628928	+	0.216134i
$763$		−	50.2330i		−	1.81856i
$764$	−40.5414	−	31.5959i	−1.46673	−	1.14310i
$765$			1.56533i			0.0565945i
$766$	7.64598	−	22.2490i	0.276261	−	0.803890i
$767$	−60.0553			−2.16847
$768$	−7.57944	−	14.0909i	−0.273499	−	0.508460i
$769$	26.1210			0.941947			0.470974	−	0.882147i	$-0.343903\pi$
$769$	26.1210			0.941947			0.470974	+	0.882147i	$0.343903\pi$
$770$	16.2682	−	47.3389i	0.586267	−	1.70598i
$771$		−	21.8093i		−	0.785444i
$772$	2.79323	+	2.17691i	0.100531	+	0.0783486i
$773$		−	29.8661i		−	1.07421i	−0.843515	−	0.537105i	$-0.819518\pi$
$773$		−	29.8661i		−	1.07421i	0.843515	−	0.537105i	$-0.180482\pi$
$774$	−2.47098	−	0.849164i	−0.0888175	−	0.0305226i
$775$	−7.36360			−0.264508
$776$	−46.1575	+	30.0936i	−1.65696	+	1.08030i
$777$	−16.7941			−0.602483
$778$	−27.2596	−	9.36791i	−0.977305	−	0.335856i
$779$		−	19.5512i		−	0.700493i
$780$	14.2560	−	18.2922i	0.510448	−	0.654966i
$781$			23.7357i			0.849332i
$782$	0.351044	−	1.02150i	0.0125533	−	0.0365288i
$783$	−3.85821			−0.137881
$784$	12.7172	+	50.4879i	0.454184	+	1.80314i
$785$	−25.3473			−0.904685
$786$	5.86520	−	17.0671i	0.209205	−	0.608764i
$787$			49.4864i			1.76400i	0.471249	+	0.882000i	$0.343803\pi$
$787$			49.4864i			1.76400i	−0.471249	+	0.882000i	$0.656197\pi$
$788$	2.28271	−	2.92899i	0.0813182	−	0.104341i
$789$			17.8688i			0.636145i
$790$	15.3335	+	5.26945i	0.545543	+	0.187479i
$791$	−60.0229			−2.13417
$792$	5.96307	+	9.14615i	0.211888	+	0.324994i
$793$	52.7415			1.87291
$794$	−38.6834	−	13.2938i	−1.37282	−	0.471778i
$795$			4.64835i			0.164860i
$796$	−25.3665	−	19.7694i	−0.899091	−	0.700706i
$797$			37.7309i			1.33650i	0.743938	+	0.668248i	$0.232956\pi$
$797$			37.7309i			1.33650i	−0.743938	+	0.668248i	$0.767044\pi$
$798$	−12.0960	+	35.1980i	−0.428193	+	1.24600i
$799$	5.00720			0.177142
$800$	−4.50773	−	0.380718i	−0.159372	−	0.0134604i
$801$	0.345205			0.0121972
$802$	0.293323	−	0.853540i	0.0103576	−	0.0301395i
$803$			8.54773i			0.301643i
$804$	−5.74531	−	4.47761i	−0.202621	−	0.157913i
$805$		−	9.16920i		−	0.323172i
$806$	−69.6779	−	23.9451i	−2.45430	−	0.843432i
$807$	−12.7899			−0.450224
$808$	−24.5024	−	37.5817i	−0.861990	−	1.32212i
$809$	11.4041			0.400948			0.200474	−	0.979699i	$-0.435752\pi$
$809$	11.4041			0.400948			0.200474	+	0.979699i	$0.435752\pi$
$810$	−2.74104	−	0.941972i	−0.0963103	−	0.0330975i
$811$		−	31.2220i		−	1.09635i	−0.836363	−	0.548177i	$-0.815322\pi$
$811$		−	31.2220i		−	1.09635i	0.836363	−	0.548177i	$-0.184678\pi$
$812$	21.2217	−	27.2299i	0.744734	−	0.955584i
$813$			15.1428i			0.531080i
$814$	6.65999	−	19.3799i	0.233433	−	0.679264i
$815$	−14.7190			−0.515586
$816$	2.96256	−	0.746224i	0.103710	−	0.0261231i
$817$	10.8679			0.380221
$818$	7.30963	−	21.2703i	0.255575	−	0.743698i
$819$		−	25.3132i		−	0.884515i
$820$	−8.37458	+	10.7456i	−0.292453	+	0.375252i
$821$		−	21.0012i		−	0.732945i	−0.930429	−	0.366473i	$-0.880565\pi$
$821$		−	21.0012i		−	0.732945i	0.930429	−	0.366473i	$-0.119435\pi$
$822$	6.56047	+	2.25454i	0.228823	+	0.0786361i
$823$	−34.3851			−1.19859			−0.599295	−	0.800528i	$-0.704553\pi$
$823$	−34.3851			−1.19859			−0.599295	+	0.800528i	$0.704553\pi$
$824$	−29.1719	+	19.0194i	−1.01625	+	0.662572i
$825$	3.08701			0.107476
$826$	−63.5129	−	21.8265i	−2.20990	−	0.759442i
$827$			12.3383i			0.429045i	0.976719	+	0.214523i	$0.0688195\pi$
$827$			12.3383i			0.429045i	−0.976719	+	0.214523i	$0.931180\pi$
$828$	1.57750	+	1.22943i	0.0548220	+	0.0427255i
$829$		−	3.18747i		−	0.110706i	−0.998467	−	0.0553528i	$-0.982372\pi$
$829$		−	3.18747i		−	0.110706i	0.998467	−	0.0553528i	$-0.0176283\pi$
$830$	−2.96588	+	8.63041i	−0.102947	+	0.299566i
$831$	18.6751			0.647833
$832$	−41.4162	−	18.2609i	−1.43585	−	0.633082i
$833$	−9.94145			−0.344451
$834$	−3.50379	+	10.1957i	−0.121326	+	0.353047i
$835$		−	31.2814i		−	1.08254i
$836$	−35.8207	−	27.9169i	−1.23888	−	0.965525i
$837$			9.20798i			0.318274i
$838$	53.6384	+	18.4331i	1.85291	+	0.636761i
$839$	18.5211			0.639419			0.319710	−	0.947516i	$-0.396415\pi$
$839$	18.5211			0.639419			0.319710	+	0.947516i	$0.396415\pi$
$840$	21.7249	−	14.1641i	0.749581	−	0.488709i
$841$	14.1142			0.486697
$842$	−11.4583	−	3.93771i	−0.394880	−	0.135702i
$843$			11.8997i			0.409847i
$844$	34.2883	−	43.9961i	1.18025	−	1.51441i
$845$		−	38.9642i		−	1.34041i
$846$	−3.01320	+	8.76810i	−0.103596	+	0.301454i
$847$	17.4541			0.599731
$848$	8.79754	−	2.21597i	0.302109	−	0.0760967i
$849$	11.3565			0.389754
$850$	0.280730	−	0.816894i	0.00962894	−	0.0280192i
$851$		−	3.75374i		−	0.128677i
$852$	−7.55951	+	9.69976i	−0.258984	+	0.332308i
$853$			7.00562i			0.239868i	0.992782	+	0.119934i	$0.0382683\pi$
$853$			7.00562i			0.239868i	−0.992782	+	0.119934i	$0.961732\pi$
$854$	55.7780	+	19.1684i	1.90868	+	0.655928i
$855$	12.0557			0.412296
$856$	−1.92964	−	2.95968i	−0.0659538	−	0.101160i
$857$	−23.2176			−0.793098			−0.396549	−	0.918014i	$-0.629792\pi$
$857$	−23.2176			−0.793098			−0.396549	+	0.918014i	$0.629792\pi$
$858$	29.2107	+	10.0384i	0.997238	+	0.342706i
$859$		−	2.51057i		−	0.0856596i	−0.999082	−	0.0428298i	$-0.986363\pi$
$859$		−	2.51057i		−	0.0856596i	0.999082	−	0.0428298i	$-0.0136373\pi$
$860$	−5.97316	−	4.65519i	−0.203683	−	0.158740i
$861$			14.8700i			0.506769i
$862$	−15.0191	+	43.7040i	−0.511553	+	1.48857i
$863$	11.9257			0.405957			0.202978	−	0.979183i	$-0.434938\pi$
$863$	11.9257			0.405957			0.202978	+	0.979183i	$0.434938\pi$
$864$	−0.476077	+	5.63679i	−0.0161965	+	0.191767i
$865$	23.3001			0.792227
$866$	−4.47643	+	13.0259i	−0.152115	+	0.442639i
$867$		−	16.4167i		−	0.557539i
$868$	−64.9868	−	50.6475i	−2.20580	−	1.71909i
$869$			21.5943i			0.732537i
$870$	−10.5755	−	3.63432i	−0.358543	−	0.123215i
$871$	−20.6063			−0.698217
$872$	17.3443	+	26.6026i	0.587351	+	0.900879i
$873$	19.4812			0.659339
$874$	−7.86733	−	2.70365i	−0.266116	−	0.0914522i
$875$		−	53.1786i		−	1.79776i
$876$	−2.72234	+	3.49308i	−0.0919792	+	0.118020i
$877$		−	21.3278i		−	0.720187i	−0.932916	−	0.360094i	$-0.882745\pi$
$877$		−	21.3278i		−	0.720187i	0.932916	−	0.360094i	$-0.117255\pi$
$878$	−3.73535	+	10.8695i	−0.126062	+	0.366827i
$879$	1.87110			0.0631105
$880$	7.72959	+	30.6870i	0.260565	+	1.03446i
$881$	21.8892			0.737466			0.368733	−	0.929535i	$-0.379792\pi$
$881$	21.8892			0.737466			0.368733	+	0.929535i	$0.379792\pi$
$882$	5.98250	−	17.4085i	0.201441	−	0.586173i
$883$		−	36.3987i		−	1.22491i	−0.790504	−	0.612457i	$-0.790181\pi$
$883$		−	36.3987i		−	1.22491i	0.790504	−	0.612457i	$-0.209819\pi$
$884$	5.31279	−	6.81695i	0.178688	−	0.229279i
$885$			21.7538i			0.731248i
$886$	−13.2319	−	4.54722i	−0.444535	−	0.152767i
$887$	47.0347			1.57927			0.789635	−	0.613577i	$-0.210270\pi$
$887$	47.0347			1.57927			0.789635	+	0.613577i	$0.210270\pi$
$888$	8.89387	−	5.79859i	0.298459	−	0.194588i
$889$	58.0757			1.94780
$890$	0.946220	+	0.325173i	0.0317174	+	0.0108998i
$891$		−	3.86022i		−	0.129322i
$892$	40.8137	+	31.8081i	1.36654	+	1.06501i
$893$		−	38.5641i		−	1.29050i
$894$	−6.22513	+	18.1145i	−0.208199	+	0.605839i
$895$	−36.3515			−1.21510
$896$	−37.1639	−	34.3645i	−1.24156	−	1.14804i
$897$	5.65791			0.188912
$898$	−12.8157	+	37.2924i	−0.427667	+	1.24447i
$899$			35.5263i			1.18487i
$900$	1.26153	+	0.983170i	0.0420508	+	0.0327723i
$901$			1.73230i			0.0577113i
$902$	−17.1596	−	5.89698i	−0.571352	−	0.196348i
$903$	−8.26581			−0.275069
$904$	31.7872	−	20.7245i	1.05723	−	0.689287i
$905$	−36.5182			−1.21391
$906$	−7.40390	−	2.54439i	−0.245978	−	0.0845316i
$907$		−	5.64255i		−	0.187358i	−0.995602	−	0.0936788i	$-0.970137\pi$
$907$		−	5.64255i		−	0.187358i	0.995602	−	0.0936788i	$-0.0298627\pi$
$908$	−27.2998	+	35.0290i	−0.905977	+	1.16248i
$909$			15.8617i			0.526099i
$910$	23.8443	−	69.3845i	0.790431	−	2.30007i
$911$	−51.1763			−1.69555			−0.847773	−	0.530359i	$-0.822057\pi$
$911$	−51.1763			−1.69555			−0.847773	+	0.530359i	$0.822057\pi$
$912$	−5.74721	−	22.8168i	−0.190309	−	0.755540i
$913$	−12.1542			−0.402247
$914$	−1.11004	+	3.23009i	−0.0367168	+	0.106842i
$915$		−	19.1046i		−	0.631577i
$916$	−0.262138	+	0.336355i	−0.00866129	+	0.0111135i
$917$		−	57.0922i		−	1.88535i
$918$	−1.02150	−	0.351044i	−0.0337146	−	0.0115862i
$919$	−15.4063			−0.508207			−0.254103	−	0.967177i	$-0.581780\pi$
$919$	−15.4063			−0.508207			−0.254103	+	0.967177i	$0.581780\pi$
$920$	3.16591	+	4.85587i	0.104377	+	0.160093i
$921$	25.5322			0.841313
$922$	12.1947	+	4.19079i	0.401613	+	0.138016i
$923$			34.7894i			1.14511i
$924$	27.2441	+	21.2327i	0.896266	+	0.698505i
$925$		−	3.00186i		−	0.0987006i
$926$	13.9676	−	40.6442i	0.459003	−	1.33565i
$927$	12.3123			0.404388
$928$	−1.83680	+	21.7479i	−0.0602961	+	0.713910i
$929$	47.2943			1.55168			0.775838	−	0.630932i	$-0.217327\pi$
$929$	47.2943			1.55168			0.775838	+	0.630932i	$0.217327\pi$
$930$	−8.67365	+	25.2394i	−0.284420	+	0.827633i
$931$			76.5663i			2.50936i
$932$	0.360195	+	0.280718i	0.0117986	+	0.00919523i
$933$		−	13.4590i		−	0.440626i
$934$	14.8657	+	5.10867i	0.486420	+	0.167161i
$935$	−6.04250			−0.197611
$936$	8.74005	+	13.4055i	0.285677	+	0.438172i
$937$	35.5164			1.16027			0.580134	−	0.814521i	$-0.303000\pi$
$937$	35.5164			1.16027			0.580134	+	0.814521i	$0.303000\pi$
$938$	−21.7926	−	7.48915i	−0.711555	−	0.244529i
$939$		−	29.8742i		−	0.974906i
$940$	−16.5186	+	21.1954i	−0.538778	+	0.691317i
$941$		−	21.4937i		−	0.700675i	−0.936623	−	0.350338i	$-0.886067\pi$
$941$		−	21.4937i		−	0.700675i	0.936623	−	0.350338i	$-0.113933\pi$
$942$	5.68447	−	16.5412i	0.185210	−	0.538941i
$943$	−3.32369			−0.108234
$944$	41.1716	−	10.3705i	1.34002	−	0.337532i
$945$	−9.16920			−0.298274
$946$	3.27796	−	9.53852i	0.106576	−	0.310124i
$947$		−	11.0365i		−	0.358638i	−0.983791	−	0.179319i	$-0.942611\pi$
$947$		−	11.0365i		−	0.358638i	0.983791	−	0.179319i	$-0.0573895\pi$
$948$	−6.87749	+	8.82464i	−0.223370	+	0.286611i
$949$			12.5284i			0.406688i
$950$	−6.29149	−	2.16210i	−0.204123	−	0.0701478i
$951$	1.94005			0.0629104
$952$	8.09622	−	5.27854i	0.262400	−	0.171078i
$953$	−30.8466			−0.999220			−0.499610	−	0.866251i	$-0.666523\pi$
$953$	−30.8466			−0.999220			−0.499610	+	0.866251i	$0.666523\pi$
$954$	−3.03343	−	1.04245i	−0.0982109	−	0.0337507i
$955$			52.6707i			1.70438i
$956$	−44.1063	−	34.3743i	−1.42650	−	1.11174i
$957$		−	14.8935i		−	0.481439i
$958$	18.6188	−	54.1787i	0.601545	−	1.75043i
$959$	21.9458			0.708667
$960$	−6.61464	+	15.0022i	−0.213486	+	0.484194i
$961$	53.7868			1.73506
$962$	9.76152	−	28.4050i	0.314724	−	0.915815i
$963$			1.24916i			0.0402536i
$964$	−6.04174	−	4.70863i	−0.194591	−	0.151655i
$965$		−	3.62892i		−	0.116819i
$966$	5.98365	+	2.05631i	0.192521	+	0.0661607i
$967$	−23.7758			−0.764577			−0.382289	−	0.924043i	$-0.624864\pi$
$967$	−23.7758			−0.764577			−0.382289	+	0.924043i	$0.624864\pi$
$968$	−9.24344	+	6.02650i	−0.297095	+	0.193699i
$969$	4.49280			0.144329
$970$	53.3988	+	18.3507i	1.71453	+	0.589207i
$971$		−	41.9725i		−	1.34696i	−0.739204	−	0.673481i	$-0.764798\pi$
$971$		−	41.9725i		−	1.34696i	0.739204	−	0.673481i	$-0.235202\pi$
$972$	1.22943	−	1.57750i	0.0394339	−	0.0505984i
$973$			34.1060i			1.09339i
$974$	−7.66121	+	22.2933i	−0.245481	+	0.714324i
$975$	4.52462			0.144904
$976$	−36.1575	+	9.10755i	−1.15737	+	0.291525i
$977$	−12.5499			−0.401506			−0.200753	−	0.979642i	$-0.564339\pi$
$977$	−12.5499			−0.401506			−0.200753	+	0.979642i	$0.564339\pi$
$978$	3.30093	−	9.60537i	0.105552	−	0.307146i
$979$			1.33257i			0.0425890i
$980$	32.7965	−	42.0819i	1.04765	−	1.34426i
$981$		−	11.2279i		−	0.358479i
$982$	−0.748032	−	0.257065i	−0.0238707	−	0.00820328i
$983$	−2.78114			−0.0887047			−0.0443523	−	0.999016i	$-0.514122\pi$
$983$	−2.78114			−0.0887047			−0.0443523	+	0.999016i	$0.514122\pi$
$984$	−5.13426	−	7.87493i	−0.163674	−	0.251044i
$985$	−3.80530			−0.121247
$986$	−3.94117	−	1.35440i	−0.125512	−	0.0431330i
$987$			29.3307i			0.933606i
$988$	−52.5023	−	40.9176i	−1.67032	−	1.30176i
$989$		−	1.84754i		−	0.0587484i
$990$	3.63621	−	10.5810i	0.115566	−	0.336286i
$991$	0.0891600			0.00283226			0.00141613	−	0.999999i	$-0.499549\pi$
$991$	0.0891600			0.00283226			0.00141613	+	0.999999i	$0.499549\pi$
$992$	51.9034	+	4.38371i	1.64793	+	0.139183i
$993$	20.1078			0.638101
$994$	−12.6439	+	36.7923i	−0.401039	+	1.16698i
$995$			32.9557i			1.04477i
$996$	−4.96690	−	3.87096i	−0.157382	−	0.122656i
$997$			60.6262i			1.92005i	0.279910	+	0.960026i	$0.409695\pi$
$997$			60.6262i			1.92005i	−0.279910	+	0.960026i	$0.590305\pi$
$998$	−35.0946	−	12.0604i	−1.11090	−	0.381766i
$999$	−3.75374			−0.118763

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.d.277.10	yes	20
4.3	odd	2		2208.2.f.d.1105.8		20
8.3	odd	2		2208.2.f.d.1105.13		20
8.5	even	2	inner	552.2.f.d.277.9	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.d.277.9	✓	20	8.5	even	2	inner
552.2.f.d.277.10	yes	20	1.1	even	1	trivial
2208.2.f.d.1105.8		20	4.3	odd	2
2208.2.f.d.1105.13		20	8.3	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.459619 + 1.33744i) q^{2} +1.00000i q^{3} +(-1.57750 - 1.22943i) q^{4} +2.04946i q^{5} +(-1.33744 - 0.459619i) q^{6} -4.47395 q^{7} +(2.36933 - 1.54475i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.459619 + 1.33744i) q^{2} +1.00000i q^{3} +(-1.57750 - 1.22943i) q^{4} +2.04946i q^{5} +(-1.33744 - 0.459619i) q^{6} -4.47395 q^{7} +(2.36933 - 1.54475i) q^{8} -1.00000 q^{9} +(-2.74104 - 0.941972i) q^{10} -3.86022i q^{11} +(1.22943 - 1.57750i) q^{12} -5.65791i q^{13} +(2.05631 - 5.98365i) q^{14} -2.04946 q^{15} +(0.977023 + 3.87884i) q^{16} -0.763773 q^{17} +(0.459619 - 1.33744i) q^{18} +5.88237i q^{19} +(2.51966 - 3.23303i) q^{20} -4.47395i q^{21} +(5.16282 + 1.77423i) q^{22} +1.00000 q^{23} +(1.54475 + 2.36933i) q^{24} +0.799698 q^{25} +(7.56712 + 2.60048i) q^{26} -1.00000i q^{27} +(7.05766 + 5.50039i) q^{28} -3.85821i q^{29} +(0.941972 - 2.74104i) q^{30} -9.20798 q^{31} +(-5.63679 - 0.476077i) q^{32} +3.86022 q^{33} +(0.351044 - 1.02150i) q^{34} -9.16920i q^{35} +(1.57750 + 1.22943i) q^{36} -3.75374i q^{37} +(-7.86733 - 2.70365i) q^{38} +5.65791 q^{39} +(3.16591 + 4.85587i) q^{40} -3.32369 q^{41} +(5.98365 + 2.05631i) q^{42} -1.84754i q^{43} +(-4.74585 + 6.08950i) q^{44} -2.04946i q^{45} +(-0.459619 + 1.33744i) q^{46} -6.55588 q^{47} +(-3.87884 + 0.977023i) q^{48} +13.0162 q^{49} +(-0.367556 + 1.06955i) q^{50} -0.763773i q^{51} +(-6.95598 + 8.92536i) q^{52} -2.26808i q^{53} +(1.33744 + 0.459619i) q^{54} +7.91138 q^{55} +(-10.6003 + 6.91113i) q^{56} -5.88237 q^{57} +(5.16013 + 1.77330i) q^{58} -10.6144i q^{59} +(3.23303 + 2.51966i) q^{60} +9.32173i q^{61} +(4.23216 - 12.3151i) q^{62} +4.47395 q^{63} +(3.22750 - 7.32006i) q^{64} +11.5957 q^{65} +(-1.77423 + 5.16282i) q^{66} -3.64203i q^{67} +(1.20485 + 0.939003i) q^{68} +1.00000i q^{69} +(12.2633 + 4.21433i) q^{70} -6.14881 q^{71} +(-2.36933 + 1.54475i) q^{72} -2.21431 q^{73} +(5.02041 + 1.72529i) q^{74} +0.799698i q^{75} +(7.23194 - 9.27945i) q^{76} +17.2704i q^{77} +(-2.60048 + 7.56712i) q^{78} -5.59406 q^{79} +(-7.94955 + 2.00237i) q^{80} +1.00000 q^{81} +(1.52763 - 4.44524i) q^{82} -3.14859i q^{83} +(-5.50039 + 7.05766i) q^{84} -1.56533i q^{85} +(2.47098 + 0.849164i) q^{86} +3.85821 q^{87} +(-5.96307 - 9.14615i) q^{88} -0.345205 q^{89} +(2.74104 + 0.941972i) q^{90} +25.3132i q^{91} +(-1.57750 - 1.22943i) q^{92} -9.20798i q^{93} +(3.01320 - 8.76810i) q^{94} -12.0557 q^{95} +(0.476077 - 5.63679i) q^{96} -19.4812 q^{97} +(-5.98250 + 17.4085i) q^{98} +3.86022i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Introduction

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