LMFDB - Embedded newform 1950.2.bc.f.751.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, degree $2$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.f.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(2.53906 + 1.46593i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(2.53906 + 1.46593i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.992694 + 0.573132i) q^{11} +1.00000 q^{12} +(1.86250 + 3.08725i) q^{13} -2.93185 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.276457 - 0.478838i) q^{17} -1.00000i q^{18} +(0.723543 + 0.417738i) q^{19} +2.93185i q^{21} +(0.573132 - 0.992694i) q^{22} +(0.496476 + 0.859921i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-3.15660 - 1.74238i) q^{26} -1.00000 q^{27} +(2.53906 - 1.46593i) q^{28} +(1.03786 + 1.79762i) q^{29} +4.36673i q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.992694 - 0.573132i) q^{33} +0.552914i q^{34} +(0.500000 + 0.866025i) q^{36} +(7.00449 - 4.04404i) q^{37} -0.835475 q^{38} +(-1.74238 + 3.15660i) q^{39} +(-9.67739 + 5.58725i) q^{41} +(-1.46593 - 2.53906i) q^{42} +(-3.94036 + 6.82490i) q^{43} +1.14626i q^{44} +(-0.859921 - 0.496476i) q^{46} -10.9489i q^{47} +(0.500000 - 0.866025i) q^{48} +(0.797877 + 1.38196i) q^{49} +0.552914 q^{51} +(3.60488 - 0.0693504i) q^{52} +3.56753 q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.46593 + 2.53906i) q^{56} +0.835475i q^{57} +(-1.79762 - 1.03786i) q^{58} +(-4.75442 - 2.74496i) q^{59} +(-1.43368 + 2.48320i) q^{61} +(-2.18336 - 3.78170i) q^{62} +(-2.53906 + 1.46593i) q^{63} -1.00000 q^{64} +1.14626 q^{66} +(8.88828 - 5.13165i) q^{67} +(-0.276457 - 0.478838i) q^{68} +(-0.496476 + 0.859921i) q^{69} +(9.85992 + 5.69263i) q^{71} +(-0.866025 - 0.500000i) q^{72} +8.19151i q^{73} +(-4.04404 + 7.00449i) q^{74} +(0.723543 - 0.417738i) q^{76} -3.36068 q^{77} +(-0.0693504 - 3.60488i) q^{78} +1.68973 q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.58725 - 9.67739i) q^{82} +8.77729i q^{83} +(2.53906 + 1.46593i) q^{84} -7.88072i q^{86} +(-1.03786 + 1.79762i) q^{87} +(-0.573132 - 0.992694i) q^{88} +(-3.93073 + 2.26941i) q^{89} +(0.203325 + 10.5690i) q^{91} +0.992952 q^{92} +(-3.78170 + 2.18336i) q^{93} +(5.47443 + 9.48200i) q^{94} +1.00000i q^{96} +(9.19453 + 5.30847i) q^{97} +(-1.38196 - 0.797877i) q^{98} -1.14626i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} - 12 q^{11} + 8 q^{12} - 8 q^{14} - 4 q^{16} - 4 q^{17} + 12 q^{19} - 8 q^{22} - 4 q^{23} - 8 q^{27} + 4 q^{29} - 12 q^{33} + 4 q^{36} + 24 q^{37} - 4 q^{42} + 4 q^{43} + 12 q^{46} + 4 q^{48} - 16 q^{49} - 8 q^{51} + 8 q^{53} - 4 q^{56} - 12 q^{58} - 12 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 16 q^{66} - 24 q^{67} + 4 q^{68} + 4 q^{69} + 60 q^{71} + 16 q^{74} + 12 q^{76} + 8 q^{77} - 8 q^{79} - 4 q^{81} + 20 q^{82} - 4 q^{87} + 8 q^{88} + 24 q^{89} + 8 q^{91} - 8 q^{92} + 24 q^{93} + 16 q^{94} - 12 q^{97} - 12 q^{98}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 - 12 * q^11 + 8 * q^12 - 8 * q^14 - 4 * q^16 - 4 * q^17 + 12 * q^19 - 8 * q^22 - 4 * q^23 - 8 * q^27 + 4 * q^29 - 12 * q^33 + 4 * q^36 + 24 * q^37 - 4 * q^42 + 4 * q^43 + 12 * q^46 + 4 * q^48 - 16 * q^49 - 8 * q^51 + 8 * q^53 - 4 * q^56 - 12 * q^58 - 12 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 - 16 * q^66 - 24 * q^67 + 4 * q^68 + 4 * q^69 + 60 * q^71 + 16 * q^74 + 12 * q^76 + 8 * q^77 - 8 * q^79 - 4 * q^81 + 20 * q^82 - 4 * q^87 + 8 * q^88 + 24 * q^89 + 8 * q^91 - 8 * q^92 + 24 * q^93 + 16 * q^94 - 12 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	2.53906	+	1.46593i	0.959674	+	0.554068i	0.896073	−	0.443908i	$-0.146408\pi$
$7$	2.53906	+	1.46593i	0.959674	+	0.554068i	0.0636011	+	0.997975i	$0.479741\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.992694	+	0.573132i	−0.299309	+	0.172806i	−0.642132	−	0.766594i	$-0.721950\pi$
$11$	−0.992694	+	0.573132i	−0.299309	+	0.172806i	0.342824	+	0.939400i	$0.388617\pi$
$12$	1.00000			0.288675
$13$	1.86250	+	3.08725i	0.516565	+	0.856248i
$13$	1.86250	+	3.08725i	0.516565	+	0.856248i
$14$	−2.93185			−0.783570
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.276457	−	0.478838i	0.0670507	−	0.116135i	−0.830551	−	0.556942i	$-0.811974\pi$
$17$	0.276457	−	0.478838i	0.0670507	−	0.116135i	0.897602	+	0.440807i	$0.145308\pi$
$18$		−	1.00000i		−	0.235702i
$19$	0.723543	+	0.417738i	0.165992	+	0.0958356i	0.580695	−	0.814121i	$-0.302781\pi$
$19$	0.723543	+	0.417738i	0.165992	+	0.0958356i	−0.414703	+	0.909957i	$0.636114\pi$
$20$		0			0
$21$			2.93185i			0.639782i
$22$	0.573132	−	0.992694i	0.122192	−	0.211643i
$23$	0.496476	+	0.859921i	0.103522	+	0.179306i	0.913134	−	0.407661i	$-0.133655\pi$
$23$	0.496476	+	0.859921i	0.103522	+	0.179306i	−0.809611	+	0.586967i	$0.800322\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	−3.15660	−	1.74238i	−0.619060	−	0.341709i
$27$	−1.00000			−0.192450
$28$	2.53906	−	1.46593i	0.479837	−	0.277034i
$29$	1.03786	+	1.79762i	0.192725	+	0.333810i	0.946152	−	0.323722i	$-0.104934\pi$
$29$	1.03786	+	1.79762i	0.192725	+	0.333810i	−0.753427	+	0.657531i	$0.771601\pi$
$30$		0			0
$31$			4.36673i			0.784288i	0.919904	+	0.392144i	$0.128266\pi$
$31$			4.36673i			0.784288i	−0.919904	+	0.392144i	$0.871734\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.992694	−	0.573132i	−0.172806	−	0.0997695i
$34$			0.552914i			0.0948240i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	7.00449	−	4.04404i	1.15153	−	0.664836i	0.202271	−	0.979330i	$-0.435168\pi$
$37$	7.00449	−	4.04404i	1.15153	−	0.664836i	0.949260	+	0.314493i	$0.101835\pi$
$38$	−0.835475			−0.135532
$39$	−1.74238	+	3.15660i	−0.279005	+	0.505460i
$40$		0			0
$41$	−9.67739	+	5.58725i	−1.51136	+	0.872581i	−0.511443	+	0.859317i	$0.670889\pi$
$41$	−9.67739	+	5.58725i	−1.51136	+	0.872581i	−0.999912	+	0.0132641i	$0.995778\pi$
$42$	−1.46593	−	2.53906i	−0.226197	−	0.391785i
$43$	−3.94036	+	6.82490i	−0.600899	+	1.04079i	0.391786	+	0.920056i	$0.371857\pi$
$43$	−3.94036	+	6.82490i	−0.600899	+	1.04079i	−0.992685	+	0.120732i	$0.961476\pi$
$44$			1.14626i			0.172806i
$45$		0			0
$46$	−0.859921	−	0.496476i	−0.126789	−	0.0732014i
$47$		−	10.9489i		−	1.59706i	−0.601957	−	0.798528i	$-0.705612\pi$
$47$		−	10.9489i		−	1.59706i	0.601957	−	0.798528i	$-0.294388\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	0.797877	+	1.38196i	0.113982	+	0.197423i
$50$		0			0
$51$	0.552914			0.0774235
$52$	3.60488	−	0.0693504i	0.499908	−	0.00961716i
$53$	3.56753			0.490037			0.245019	−	0.969518i	$-0.421206\pi$
$53$	3.56753			0.490037			0.245019	+	0.969518i	$0.421206\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	−1.46593	+	2.53906i	−0.195893	+	0.339296i
$57$			0.835475i			0.110661i
$58$	−1.79762	−	1.03786i	−0.236039	−	0.136277i
$59$	−4.75442	−	2.74496i	−0.618972	−	0.357364i	0.157497	−	0.987520i	$-0.449658\pi$
$59$	−4.75442	−	2.74496i	−0.618972	−	0.357364i	−0.776469	+	0.630156i	$0.782991\pi$
$60$		0			0
$61$	−1.43368	+	2.48320i	−0.183563	+	0.317941i	−0.943091	−	0.332533i	$-0.892097\pi$
$61$	−1.43368	+	2.48320i	−0.183563	+	0.317941i	0.759528	+	0.650474i	$0.225430\pi$
$62$	−2.18336	−	3.78170i	−0.277288	−	0.480276i
$63$	−2.53906	+	1.46593i	−0.319891	+	0.184689i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.14626			0.141095
$67$	8.88828	−	5.13165i	1.08588	−	0.626931i	0.153401	−	0.988164i	$-0.450977\pi$
$67$	8.88828	−	5.13165i	1.08588	−	0.626931i	0.932476	+	0.361233i	$0.117644\pi$
$68$	−0.276457	−	0.478838i	−0.0335254	−	0.0580676i
$69$	−0.496476	+	0.859921i	−0.0597687	+	0.103522i
$70$		0			0
$71$	9.85992	+	5.69263i	1.17016	+	0.675591i	0.953717	−	0.300705i	$-0.0972220\pi$
$71$	9.85992	+	5.69263i	1.17016	+	0.675591i	0.216440	+	0.976296i	$0.430555\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			8.19151i			0.958744i	0.877612	+	0.479372i	$0.159135\pi$
$73$			8.19151i			0.958744i	−0.877612	+	0.479372i	$0.840865\pi$
$74$	−4.04404	+	7.00449i	−0.470110	+	0.814255i
$75$		0			0
$76$	0.723543	−	0.417738i	0.0829961	−	0.0479178i
$77$	−3.36068			−0.382985
$78$	−0.0693504	−	3.60488i	−0.00785238	−	0.408173i
$79$	1.68973			0.190109			0.0950545	−	0.995472i	$-0.469697\pi$
$79$	1.68973			0.190109			0.0950545	+	0.995472i	$0.469697\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.58725	−	9.67739i	0.617008	−	1.06869i
$83$			8.77729i			0.963433i	0.876327	+	0.481717i	$0.159987\pi$
$83$			8.77729i			0.963433i	−0.876327	+	0.481717i	$0.840013\pi$
$84$	2.53906	+	1.46593i	0.277034	+	0.159946i
$85$		0			0
$86$		−	7.88072i		−	0.849800i
$87$	−1.03786	+	1.79762i	−0.111270	+	0.192725i
$88$	−0.573132	−	0.992694i	−0.0610961	−	0.105822i
$89$	−3.93073	+	2.26941i	−0.416657	+	0.240557i	−0.693646	−	0.720316i	$-0.743997\pi$
$89$	−3.93073	+	2.26941i	−0.416657	+	0.240557i	0.276989	+	0.960873i	$0.410663\pi$
$90$		0			0
$91$	0.203325	+	10.5690i	0.0213142	+	1.10793i
$92$	0.992952			0.103522
$93$	−3.78170	+	2.18336i	−0.392144	+	0.226404i
$94$	5.47443	+	9.48200i	0.564645	+	0.977993i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	9.19453	+	5.30847i	0.933564	+	0.538993i	0.887937	−	0.459965i	$-0.152138\pi$
$97$	9.19453	+	5.30847i	0.933564	+	0.538993i	0.0456267	+	0.998959i	$0.485472\pi$
$98$	−1.38196	−	0.797877i	−0.139599	−	0.0805978i
$99$		−	1.14626i		−	0.115204i
$100$		0			0
$101$	−7.07313	−	12.2510i	−0.703803	−	1.21902i	−0.967122	−	0.254314i	$-0.918150\pi$
$101$	−7.07313	−	12.2510i	−0.703803	−	1.21902i	0.263319	−	0.964709i	$-0.415183\pi$
$102$	−0.478838	+	0.276457i	−0.0474120	+	0.0273733i
$103$	−6.72500			−0.662634			−0.331317	−	0.943519i	$-0.607493\pi$
$103$	−6.72500			−0.662634			−0.331317	+	0.943519i	$0.607493\pi$
$104$	−3.08725	+	1.86250i	−0.302729	+	0.182633i
$105$		0			0
$106$	−3.08957	+	1.78376i	−0.300085	+	0.173254i
$107$	0.123385	+	0.213709i	0.0119281	+	0.0206600i	0.871928	−	0.489634i	$-0.162870\pi$
$107$	0.123385	+	0.213709i	0.0119281	+	0.0206600i	−0.860000	+	0.510294i	$0.829536\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$			4.13797i			0.396346i	0.980167	+	0.198173i	$0.0635008\pi$
$109$			4.13797i			0.396346i	−0.980167	+	0.198173i	$0.936499\pi$
$110$		0			0
$111$	7.00449	+	4.04404i	0.664836	+	0.383843i
$112$		−	2.93185i		−	0.277034i
$113$	−0.828427	+	1.43488i	−0.0779319	+	0.134982i	−0.902357	−	0.430988i	$-0.858165\pi$
$113$	−0.828427	+	1.43488i	−0.0779319	+	0.134982i	0.824426	+	0.565970i	$0.191498\pi$
$114$	−0.417738	−	0.723543i	−0.0391247	−	0.0677660i
$115$		0			0
$116$	2.07571			0.192725
$117$	−3.60488	+	0.0693504i	−0.333272	+	0.00641144i
$118$	5.48993			0.505389
$119$	1.40388	−	0.810531i	0.128694	−	0.0743013i
$120$		0			0
$121$	−4.84304	+	8.38839i	−0.440276	+	0.762581i
$122$		−	2.86735i		−	0.259598i
$123$	−9.67739	−	5.58725i	−0.872581	−	0.503785i
$124$	3.78170	+	2.18336i	0.339607	+	0.196072i
$125$		0			0
$126$	1.46593	−	2.53906i	0.130595	−	0.226197i
$127$	3.80260	+	6.58630i	0.337426	+	0.584440i	0.983948	−	0.178456i	$-0.0571102\pi$
$127$	3.80260	+	6.58630i	0.337426	+	0.584440i	−0.646521	+	0.762896i	$0.723777\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−7.88072			−0.693859
$130$		0			0
$131$	5.45340			0.476466			0.238233	−	0.971208i	$-0.423432\pi$
$131$	5.45340			0.476466			0.238233	+	0.971208i	$0.423432\pi$
$132$	−0.992694	+	0.573132i	−0.0864029	+	0.0498848i
$133$	1.22474	+	2.12132i	0.106199	+	0.183942i
$134$	−5.13165	+	8.88828i	−0.443307	+	0.767831i
$135$		0			0
$136$	0.478838	+	0.276457i	0.0410600	+	0.0237060i
$137$	0.276333	+	0.159541i	0.0236087	+	0.0136305i	0.511758	−	0.859130i	$-0.328994\pi$
$137$	0.276333	+	0.159541i	0.0236087	+	0.0136305i	−0.488149	+	0.872760i	$0.662328\pi$
$138$		−	0.992952i		−	0.0845257i
$139$	−5.84046	+	10.1160i	−0.495381	+	0.858026i	−0.999986	−	0.00532505i	$-0.998305\pi$
$139$	−5.84046	+	10.1160i	−0.495381	+	0.858026i	0.504605	+	0.863351i	$0.331638\pi$
$140$		0			0
$141$	9.48200	−	5.47443i	0.798528	−	0.461030i
$142$	−11.3853			−0.955430
$143$	−3.61829	−	1.99723i	−0.302577	−	0.167017i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−4.09575	−	7.09405i	−0.338967	−	0.587108i
$147$	−0.797877	+	1.38196i	−0.0658078	+	0.113982i
$148$		−	8.08808i		−	0.664836i
$149$	4.33221	+	2.50120i	0.354908	+	0.204906i	0.666845	−	0.745196i	$-0.267644\pi$
$149$	4.33221	+	2.50120i	0.354908	+	0.204906i	−0.311937	+	0.950103i	$0.600978\pi$
$150$		0			0
$151$		−	12.9005i		−	1.04983i	−0.851156	−	0.524914i	$-0.824098\pi$
$151$		−	12.9005i		−	1.04983i	0.851156	−	0.524914i	$-0.175902\pi$
$152$	−0.417738	+	0.723543i	−0.0338830	+	0.0586871i
$153$	0.276457	+	0.478838i	0.0223502	+	0.0387117i
$154$	2.91043	−	1.68034i	0.234529	−	0.135406i
$155$		0			0
$156$	1.86250	+	3.08725i	0.149119	+	0.247178i
$157$	8.66531			0.691567			0.345784	−	0.938314i	$-0.387613\pi$
$157$	8.66531			0.691567			0.345784	+	0.938314i	$0.387613\pi$
$158$	−1.46335	+	0.844863i	−0.116418	+	0.0672137i
$159$	1.78376	+	3.08957i	0.141462	+	0.245019i
$160$		0			0
$161$			2.91119i			0.229434i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	1.59928	+	0.923344i	0.125265	+	0.0723219i	0.561323	−	0.827597i	$-0.310292\pi$
$163$	1.59928	+	0.923344i	0.125265	+	0.0723219i	−0.436058	+	0.899919i	$0.643626\pi$
$164$			11.1745i			0.872581i
$165$		0			0
$166$	−4.38865	−	7.60136i	−0.340625	−	0.589980i
$167$	−18.8898	+	10.9060i	−1.46174	+	0.843935i	−0.999092	−	0.0426077i	$-0.986433\pi$
$167$	−18.8898	+	10.9060i	−1.46174	+	0.843935i	−0.462647	+	0.886543i	$0.653100\pi$
$168$	−2.93185			−0.226197
$169$	−6.06218	+	11.5000i	−0.466321	+	0.884615i
$170$		0			0
$171$	−0.723543	+	0.417738i	−0.0553307	+	0.0319452i
$172$	3.94036	+	6.82490i	0.300450	+	0.520394i
$173$	−5.93942	+	10.2874i	−0.451565	+	0.782134i	−0.998483	−	0.0550519i	$-0.982468\pi$
$173$	−5.93942	+	10.2874i	−0.451565	+	0.782134i	0.546918	+	0.837186i	$0.315801\pi$
$174$		−	2.07571i		−	0.157359i
$175$		0			0
$176$	0.992694	+	0.573132i	0.0748271	+	0.0432015i
$177$		−	5.48993i		−	0.412648i
$178$	2.26941	−	3.93073i	0.170099	−	0.294621i
$179$	−4.47746	−	7.75519i	−0.334661	−	0.579650i	0.648759	−	0.760994i	$-0.275288\pi$
$179$	−4.47746	−	7.75519i	−0.334661	−	0.579650i	−0.983420	+	0.181344i	$0.941955\pi$
$180$		0			0
$181$	−21.2297			−1.57799			−0.788996	−	0.614399i	$-0.789399\pi$
$181$	−21.2297			−1.57799			−0.788996	+	0.614399i	$0.789399\pi$
$182$	−5.46058	−	9.05135i	−0.404765	−	0.670931i
$183$	−2.86735			−0.211961
$184$	−0.859921	+	0.496476i	−0.0633943	+	0.0366007i
$185$		0			0
$186$	2.18336	−	3.78170i	0.160092	−	0.277288i
$187$			0.633786i			0.0463470i
$188$	−9.48200	−	5.47443i	−0.691546	−	0.399264i
$189$	−2.53906	−	1.46593i	−0.184689	−	0.106630i
$190$		0			0
$191$	−2.25347	+	3.90313i	−0.163055	+	0.282420i	−0.935963	−	0.352098i	$-0.885468\pi$
$191$	−2.25347	+	3.90313i	−0.163055	+	0.282420i	0.772908	+	0.634519i	$0.218802\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−2.30090	+	1.32843i	−0.165623	+	0.0956223i	−0.580520	−	0.814246i	$-0.697151\pi$
$193$	−2.30090	+	1.32843i	−0.165623	+	0.0956223i	0.414898	+	0.909868i	$0.363817\pi$
$194$	−10.6169			−0.762251
$195$		0			0
$196$	1.59575			0.113982
$197$	−1.68375	+	0.972112i	−0.119962	+	0.0692601i	−0.558780	−	0.829316i	$-0.688731\pi$
$197$	−1.68375	+	0.972112i	−0.119962	+	0.0692601i	0.438818	+	0.898576i	$0.355397\pi$
$198$	0.573132	+	0.992694i	0.0407307	+	0.0705477i
$199$	7.50877	−	13.0056i	0.532282	−	0.921940i	−0.467007	−	0.884253i	$-0.654668\pi$
$199$	7.50877	−	13.0056i	0.532282	−	0.921940i	0.999290	−	0.0376865i	$-0.0119988\pi$
$200$		0			0
$201$	8.88828	+	5.13165i	0.626931	+	0.361959i
$202$	12.2510	+	7.07313i	0.861979	+	0.497664i
$203$			6.08568i			0.427131i
$204$	0.276457	−	0.478838i	0.0193559	−	0.0335254i
$205$		0			0
$206$	5.82402	−	3.36250i	0.405779	−	0.234277i
$207$	−0.992952			−0.0690149
$208$	1.74238	−	3.15660i	0.120813	−	0.218871i
$209$	−0.957676			−0.0662438
$210$		0			0
$211$	−0.379882	−	0.657974i	−0.0261521	−	0.0452968i	0.852653	−	0.522477i	$-0.174992\pi$
$211$	−0.379882	−	0.657974i	−0.0261521	−	0.0452968i	−0.878805	+	0.477181i	$0.841659\pi$
$212$	1.78376	−	3.08957i	0.122509	−	0.212192i
$213$			11.3853i			0.780105i
$214$	−0.213709	−	0.123385i	−0.0146088	−	0.00843441i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−6.40130	+	11.0874i	−0.434549	+	0.752660i
$218$	−2.06899	−	3.58359i	−0.140129	−	0.242711i
$219$	−7.09405	+	4.09575i	−0.479372	+	0.276765i
$220$		0			0
$221$	1.99319	−	0.0383448i	0.134077	−	0.00257935i
$222$	−8.08808			−0.542837
$223$	18.5939	−	10.7352i	1.24514	−	0.718883i	0.275005	−	0.961443i	$-0.411320\pi$
$223$	18.5939	−	10.7352i	1.24514	−	0.718883i	0.970136	+	0.242560i	$0.0779871\pi$
$224$	1.46593	+	2.53906i	0.0979463	+	0.169648i
$225$		0			0
$226$		−	1.65685i		−	0.110212i
$227$	−19.1406	−	11.0508i	−1.27041	−	0.733471i	−0.295344	−	0.955391i	$-0.595434\pi$
$227$	−19.1406	−	11.0508i	−1.27041	−	0.733471i	−0.975065	+	0.221920i	$0.928767\pi$
$228$	0.723543	+	0.417738i	0.0479178	+	0.0276654i
$229$		−	21.6368i		−	1.42980i	−0.699226	−	0.714901i	$-0.746472\pi$
$229$		−	21.6368i		−	1.42980i	0.699226	−	0.714901i	$-0.253528\pi$
$230$		0			0
$231$	−1.68034	−	2.91043i	−0.110558	−	0.191492i
$232$	−1.79762	+	1.03786i	−0.118019	+	0.0681386i
$233$	5.95668			0.390235			0.195118	−	0.980780i	$-0.437491\pi$
$233$	5.95668			0.390235			0.195118	+	0.980780i	$0.437491\pi$
$234$	3.08725	−	1.86250i	0.201820	−	0.121756i
$235$		0			0
$236$	−4.75442	+	2.74496i	−0.309486	+	0.178682i
$237$	0.844863	+	1.46335i	0.0548798	+	0.0950545i
$238$	−0.810531	+	1.40388i	−0.0525389	+	0.0910001i
$239$		−	28.8408i		−	1.86556i	−0.360451	−	0.932778i	$-0.617377\pi$
$239$		−	28.8408i		−	1.86556i	0.360451	−	0.932778i	$-0.382623\pi$
$240$		0			0
$241$	4.95886	+	2.86300i	0.319428	+	0.184422i	0.651138	−	0.758960i	$-0.274292\pi$
$241$	4.95886	+	2.86300i	0.319428	+	0.184422i	−0.331709	+	0.943382i	$0.607625\pi$
$242$		−	9.68608i		−	0.622645i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.43368	+	2.48320i	0.0917817	+	0.158971i
$245$		0			0
$246$	11.1745			0.712460
$247$	0.0579405	+	3.01179i	0.00368667	+	0.191636i
$248$	−4.36673			−0.277288
$249$	−7.60136	+	4.38865i	−0.481717	+	0.278119i
$250$		0			0
$251$	3.33171	−	5.77069i	0.210296	−	0.364243i	−0.741511	−	0.670940i	$-0.765891\pi$
$251$	3.33171	−	5.77069i	0.210296	−	0.364243i	0.951807	+	0.306697i	$0.0992240\pi$
$252$			2.93185i			0.184689i
$253$	−0.985697	−	0.569093i	−0.0619703	−	0.0357785i
$254$	−6.58630	−	3.80260i	−0.413261	−	0.238597i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.01607	+	8.68809i	0.312894	+	0.541948i	0.978988	−	0.203920i	$-0.0653682\pi$
$257$	5.01607	+	8.68809i	0.312894	+	0.541948i	−0.666094	+	0.745868i	$0.732035\pi$
$258$	6.82490	−	3.94036i	0.424900	−	0.245316i
$259$	23.7131			1.47346
$260$		0			0
$261$	−2.07571			−0.128483
$262$	−4.72279	+	2.72670i	−0.291775	+	0.168456i
$263$	12.5202	+	21.6856i	0.772027	+	1.33719i	0.936450	+	0.350800i	$0.114090\pi$
$263$	12.5202	+	21.6856i	0.772027	+	1.33719i	−0.164423	+	0.986390i	$0.552576\pi$
$264$	0.573132	−	0.992694i	0.0352738	−	0.0610961i
$265$		0			0
$266$	−2.12132	−	1.22474i	−0.130066	−	0.0750939i
$267$	−3.93073	−	2.26941i	−0.240557	−	0.138886i
$268$		−	10.2633i		−	0.626931i
$269$	−11.6268	+	20.1382i	−0.708899	+	1.22785i	0.256367	+	0.966579i	$0.417474\pi$
$269$	−11.6268	+	20.1382i	−0.708899	+	1.22785i	−0.965266	+	0.261269i	$0.915859\pi$
$270$		0			0
$271$	−5.32698	+	3.07554i	−0.323591	+	0.186826i	−0.652992	−	0.757365i	$-0.726487\pi$
$271$	−5.32698	+	3.07554i	−0.323591	+	0.186826i	0.329401	+	0.944190i	$0.393153\pi$
$272$	−0.552914			−0.0335254
$273$	−9.05135	+	5.46058i	−0.547812	+	0.330489i
$274$	−0.319082			−0.0192764
$275$		0			0
$276$	0.496476	+	0.859921i	0.0298843	+	0.0517612i
$277$	3.44464	−	5.96629i	0.206968	−	0.358480i	−0.743790	−	0.668414i	$-0.766974\pi$
$277$	3.44464	−	5.96629i	0.206968	−	0.358480i	0.950758	+	0.309934i	$0.100307\pi$
$278$		−	11.6809i		−	0.700575i
$279$	−3.78170	−	2.18336i	−0.226404	−	0.130715i
$280$		0			0
$281$		−	0.545617i		−	0.0325488i	−0.999868	−	0.0162744i	$-0.994819\pi$
$281$		−	0.545617i		−	0.0325488i	0.999868	−	0.0162744i	$-0.00518053\pi$
$282$	−5.47443	+	9.48200i	−0.325998	+	0.564645i
$283$	4.21329	+	7.29764i	0.250454	+	0.433799i	0.963651	−	0.267164i	$-0.0860867\pi$
$283$	4.21329	+	7.29764i	0.250454	+	0.433799i	−0.713197	+	0.700964i	$0.752753\pi$
$284$	9.85992	−	5.69263i	0.585079	−	0.337795i
$285$		0			0
$286$	4.13215	−	0.0794938i	0.244339	−	0.00470057i
$287$	−32.7620			−1.93388
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	8.34714	+	14.4577i	0.491008	+	0.850452i
$290$		0			0
$291$			10.6169i			0.622376i
$292$	7.09405	+	4.09575i	0.415148	+	0.239686i
$293$	−5.87017	−	3.38915i	−0.342939	−	0.197996i	0.318632	−	0.947879i	$-0.396777\pi$
$293$	−5.87017	−	3.38915i	−0.342939	−	0.197996i	−0.661571	+	0.749883i	$0.730110\pi$
$294$		−	1.59575i		−	0.0930663i
$295$		0			0
$296$	4.04404	+	7.00449i	0.235055	+	0.407127i
$297$	0.992694	−	0.573132i	0.0576020	−	0.0332565i
$298$	−5.00240			−0.289781
$299$	−1.73010	+	3.13435i	−0.100054	+	0.181264i
$300$		0			0
$301$	−20.0096	+	11.5525i	−1.15333	+	0.665878i
$302$	6.45025	+	11.1722i	0.371170	+	0.642885i
$303$	7.07313	−	12.2510i	0.406341	−	0.703803i
$304$		−	0.835475i		−	0.0479178i
$305$		0			0
$306$	−0.478838	−	0.276457i	−0.0273733	−	0.0158040i
$307$		−	34.6432i		−	1.97719i	−0.150601	−	0.988595i	$-0.548121\pi$
$307$		−	34.6432i		−	1.97719i	0.150601	−	0.988595i	$-0.451879\pi$
$308$	−1.68034	+	2.91043i	−0.0957462	+	0.165837i
$309$	−3.36250	−	5.82402i	−0.191286	−	0.331317i
$310$		0			0
$311$	20.2203			1.14659			0.573293	−	0.819351i	$-0.305666\pi$
$311$	20.2203			1.14659			0.573293	+	0.819351i	$0.305666\pi$
$312$	−3.15660	−	1.74238i	−0.178707	−	0.0986430i
$313$	22.3326			1.26231			0.631157	−	0.775655i	$-0.282580\pi$
$313$	22.3326			1.26231			0.631157	+	0.775655i	$0.282580\pi$
$314$	−7.50438	+	4.33266i	−0.423497	+	0.244506i
$315$		0			0
$316$	0.844863	−	1.46335i	0.0475273	−	0.0823196i
$317$			11.4292i			0.641930i	0.947091	+	0.320965i	$0.104007\pi$
$317$			11.4292i			0.641930i	−0.947091	+	0.320965i	$0.895993\pi$
$318$	−3.08957	−	1.78376i	−0.173254	−	0.100028i
$319$	−2.06055	−	1.18966i	−0.115368	−	0.0666080i
$320$		0			0
$321$	−0.123385	+	0.213709i	−0.00688666	+	0.0119281i
$322$	−1.45559	−	2.52116i	−0.0811171	−	0.140499i
$323$	0.400057	−	0.230973i	0.0222598	−	0.0128517i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−1.84669			−0.102279
$327$	−3.58359	+	2.06899i	−0.198173	+	0.114415i
$328$	−5.58725	−	9.67739i	−0.308504	−	0.534345i
$329$	16.0502	−	27.7998i	0.884878	−	1.53265i
$330$		0			0
$331$	1.53602	+	0.886823i	0.0844274	+	0.0487442i	0.541619	−	0.840624i	$-0.317811\pi$
$331$	1.53602	+	0.886823i	0.0844274	+	0.0487442i	−0.457192	+	0.889368i	$0.651145\pi$
$332$	7.60136	+	4.38865i	0.417179	+	0.240858i
$333$			8.08808i			0.443224i
$334$	10.9060	−	18.8898i	0.596752	−	1.03361i
$335$		0			0
$336$	2.53906	−	1.46593i	0.138517	−	0.0799728i
$337$	12.0024			0.653815			0.326907	−	0.945056i	$-0.393994\pi$
$337$	12.0024			0.653815			0.326907	+	0.945056i	$0.393994\pi$
$338$	−0.500000	−	12.9904i	−0.0271964	−	0.706584i
$339$	−1.65685			−0.0899880
$340$		0			0
$341$	−2.50271	−	4.33483i	−0.135530	−	0.234744i
$342$	0.417738	−	0.723543i	0.0225887	−	0.0391247i
$343$		−	15.8444i		−	0.855520i
$344$	−6.82490	−	3.94036i	−0.367974	−	0.212450i
$345$		0			0
$346$		−	11.8788i		−	0.638610i
$347$	−13.7793	+	23.8664i	−0.739709	+	1.28121i	0.212917	+	0.977070i	$0.431704\pi$
$347$	−13.7793	+	23.8664i	−0.739709	+	1.28121i	−0.952626	+	0.304143i	$0.901630\pi$
$348$	1.03786	+	1.79762i	0.0556349	+	0.0963625i
$349$	12.2674	−	7.08260i	0.656660	−	0.379123i	−0.134343	−	0.990935i	$-0.542892\pi$
$349$	12.2674	−	7.08260i	0.656660	−	0.379123i	0.791003	+	0.611812i	$0.209559\pi$
$350$		0			0
$351$	−1.86250	−	3.08725i	−0.0994130	−	0.164785i
$352$	−1.14626			−0.0610961
$353$	27.3612	−	15.7970i	1.45629	−	0.840790i	0.457465	−	0.889228i	$-0.348757\pi$
$353$	27.3612	−	15.7970i	1.45629	−	0.840790i	0.998826	+	0.0484373i	$0.0154241\pi$
$354$	2.74496	+	4.75442i	0.145893	+	0.252694i
$355$		0			0
$356$			4.53882i			0.240557i
$357$	1.40388	+	0.810531i	0.0743013	+	0.0428979i
$358$	7.75519	+	4.47746i	0.409874	+	0.236641i
$359$		−	12.1714i		−	0.642380i	−0.947015	−	0.321190i	$-0.895917\pi$
$359$		−	12.1714i		−	0.642380i	0.947015	−	0.321190i	$-0.104083\pi$
$360$		0			0
$361$	−9.15099	−	15.8500i	−0.481631	−	0.834209i
$362$	18.3855	−	10.6149i	0.966318	−	0.557904i
$363$	−9.68608			−0.508387
$364$	9.25467	+	5.10841i	0.485077	+	0.267753i
$365$		0			0
$366$	2.48320	−	1.43368i	0.129799	−	0.0749394i
$367$	14.9977	+	25.9768i	0.782873	+	1.35598i	0.930262	+	0.366897i	$0.119580\pi$
$367$	14.9977	+	25.9768i	0.782873	+	1.35598i	−0.147389	+	0.989079i	$0.547087\pi$
$368$	0.496476	−	0.859921i	0.0258806	−	0.0448265i
$369$		−	11.1745i		−	0.581721i
$370$		0			0
$371$	9.05816	+	5.22973i	0.470276	+	0.271514i
$372$			4.36673i			0.226404i
$373$	−18.3785	+	31.8325i	−0.951604	+	1.64823i	−0.209650	+	0.977777i	$0.567232\pi$
$373$	−18.3785	+	31.8325i	−0.951604	+	1.64823i	−0.741954	+	0.670450i	$0.766101\pi$
$374$	−0.316893	−	0.548875i	−0.0163861	−	0.0283816i
$375$		0			0
$376$	10.9489			0.564645
$377$	−3.61669	+	6.55219i	−0.186269	+	0.337455i
$378$	2.93185			0.150798
$379$	4.47699	−	2.58479i	0.229967	−	0.132772i	−0.380590	−	0.924744i	$-0.624279\pi$
$379$	4.47699	−	2.58479i	0.229967	−	0.132772i	0.610557	+	0.791972i	$0.290946\pi$
$380$		0			0
$381$	−3.80260	+	6.58630i	−0.194813	+	0.337426i
$382$		−	4.50694i		−	0.230595i
$383$	−2.42657	−	1.40098i	−0.123992	−	0.0715867i	0.436721	−	0.899597i	$-0.356140\pi$
$383$	−2.42657	−	1.40098i	−0.123992	−	0.0715867i	−0.560713	+	0.828010i	$0.689473\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	1.32843	−	2.30090i	0.0676152	−	0.117113i
$387$	−3.94036	−	6.82490i	−0.200300	−	0.346929i
$388$	9.19453	−	5.30847i	0.466782	−	0.269497i
$389$	11.8936			0.603030			0.301515	−	0.953461i	$-0.402508\pi$
$389$	11.8936			0.603030			0.301515	+	0.953461i	$0.402508\pi$
$390$		0			0
$391$	0.549017			0.0277650
$392$	−1.38196	+	0.797877i	−0.0697997	+	0.0402989i
$393$	2.72670	+	4.72279i	0.137544	+	0.238233i
$394$	0.972112	−	1.68375i	0.0489743	−	0.0848259i
$395$		0			0
$396$	−0.992694	−	0.573132i	−0.0498848	−	0.0288010i
$397$	33.7790	+	19.5023i	1.69532	+	0.978792i	0.950087	+	0.311986i	$0.100994\pi$
$397$	33.7790	+	19.5023i	1.69532	+	0.978792i	0.745231	+	0.666806i	$0.232339\pi$
$398$			15.0175i			0.752761i
$399$	−1.22474	+	2.12132i	−0.0613139	+	0.106199i
$400$		0			0
$401$	23.4558	−	13.5422i	1.17133	−	0.676266i	0.217335	−	0.976097i	$-0.430264\pi$
$401$	23.4558	−	13.5422i	1.17133	−	0.676266i	0.953992	+	0.299831i	$0.0969303\pi$
$402$	−10.2633			−0.511887
$403$	−13.4812	+	8.13304i	−0.671545	+	0.405136i
$404$	−14.1463			−0.703803
$405$		0			0
$406$	−3.04284	−	5.27035i	−0.151014	−	0.261563i
$407$	−4.63554	+	8.02899i	−0.229775	+	0.397982i
$408$			0.552914i			0.0273733i
$409$	−13.8087	−	7.97248i	−0.682798	−	0.394214i	0.118110	−	0.993000i	$-0.462316\pi$
$409$	−13.8087	−	7.97248i	−0.682798	−	0.394214i	−0.800908	+	0.598787i	$0.795650\pi$
$410$		0			0
$411$			0.319082i			0.0157391i
$412$	−3.36250	+	5.82402i	−0.165659	+	0.286929i
$413$	−8.04782	−	13.9392i	−0.396008	−	0.685905i
$414$	0.859921	−	0.496476i	0.0422628	−	0.0244005i
$415$		0			0
$416$	0.0693504	+	3.60488i	0.00340018	+	0.176744i
$417$	−11.6809			−0.572017
$418$	0.829371	−	0.478838i	0.0405659	−	0.0234207i
$419$	−9.71670	−	16.8298i	−0.474692	−	0.822190i	0.524888	−	0.851171i	$-0.324107\pi$
$419$	−9.71670	−	16.8298i	−0.474692	−	0.822190i	−0.999580	+	0.0289808i	$0.990774\pi$
$420$		0			0
$421$		−	21.5769i		−	1.05160i	−0.850610	−	0.525798i	$-0.823767\pi$
$421$		−	21.5769i		−	1.05160i	0.850610	−	0.525798i	$-0.176233\pi$
$422$	0.657974	+	0.379882i	0.0320297	+	0.0184924i
$423$	9.48200	+	5.47443i	0.461030	+	0.266176i
$424$			3.56753i			0.173254i
$425$		0			0
$426$	−5.69263	−	9.85992i	−0.275809	−	0.477715i
$427$	−7.28037	+	4.20332i	−0.352322	+	0.203413i
$428$	0.246769			0.0119281
$429$	−0.0794938	−	4.13215i	−0.00383800	−	0.199502i
$430$		0			0
$431$	0.550541	−	0.317855i	0.0265186	−	0.0153105i	−0.486682	−	0.873579i	$-0.661793\pi$
$431$	0.550541	−	0.317855i	0.0265186	−	0.0153105i	0.513201	+	0.858269i	$0.328460\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	5.30090	−	9.18143i	0.254745	−	0.441232i	−0.710081	−	0.704120i	$-0.751342\pi$
$433$	5.30090	−	9.18143i	0.254745	−	0.441232i	0.964826	+	0.262888i	$0.0846751\pi$
$434$		−	12.8026i		−	0.614545i
$435$		0			0
$436$	3.58359	+	2.06899i	0.171623	+	0.0990865i
$437$			0.829587i			0.0396845i
$438$	4.09575	−	7.09405i	0.195703	−	0.338967i
$439$	−7.65685	−	13.2621i	−0.365442	−	0.632964i	0.623405	−	0.781899i	$-0.285749\pi$
$439$	−7.65685	−	13.2621i	−0.365442	−	0.632964i	−0.988847	+	0.148935i	$0.952415\pi$
$440$		0			0
$441$	−1.59575			−0.0759883
$442$	−1.70698	+	1.02980i	−0.0811929	+	0.0489828i
$443$	18.4800			0.878009			0.439005	−	0.898485i	$-0.355331\pi$
$443$	18.4800			0.878009			0.439005	+	0.898485i	$0.355331\pi$
$444$	7.00449	−	4.04404i	0.332418	−	0.191922i
$445$		0			0
$446$	−10.7352	+	18.5939i	−0.508327	+	0.880448i
$447$			5.00240i			0.236606i
$448$	−2.53906	−	1.46593i	−0.119959	−	0.0692585i
$449$	22.5084	+	12.9952i	1.06224	+	0.613283i	0.926050	−	0.377400i	$-0.123182\pi$
$449$	22.5084	+	12.9952i	1.06224	+	0.613283i	0.136187	+	0.990683i	$0.456515\pi$
$450$		0			0
$451$	6.40446	−	11.0929i	0.301574	−	0.522342i
$452$	0.828427	+	1.43488i	0.0389659	+	0.0674910i
$453$	11.1722	−	6.45025i	0.524914	−	0.303059i
$454$	22.1017			1.03728
$455$		0			0
$456$	−0.835475			−0.0391247
$457$	35.9475	−	20.7543i	1.68155	−	0.970846i	0.720924	−	0.693014i	$-0.243718\pi$
$457$	35.9475	−	20.7543i	1.68155	−	0.970846i	0.960630	−	0.277832i	$-0.0896157\pi$
$458$	10.8184	+	18.7380i	0.505511	+	0.875571i
$459$	−0.276457	+	0.478838i	−0.0129039	+	0.0223502i
$460$		0			0
$461$	13.8532	+	7.99818i	0.645210	+	0.372512i	0.786619	−	0.617439i	$-0.211830\pi$
$461$	13.8532	+	7.99818i	0.645210	+	0.372512i	−0.141409	+	0.989951i	$0.545163\pi$
$462$	2.91043	+	1.68034i	0.135406	+	0.0781764i
$463$		−	18.8328i		−	0.875232i	−0.899162	−	0.437616i	$-0.855823\pi$
$463$		−	18.8328i		−	0.875232i	0.899162	−	0.437616i	$-0.144177\pi$
$464$	1.03786	−	1.79762i	0.0481813	−	0.0834524i
$465$		0			0
$466$	−5.15864	+	2.97834i	−0.238969	+	0.137969i
$467$	3.43738			0.159063			0.0795316	−	0.996832i	$-0.474658\pi$
$467$	3.43738			0.159063			0.0795316	+	0.996832i	$0.474658\pi$
$468$	−1.74238	+	3.15660i	−0.0805417	+	0.145914i
$469$	30.0905			1.38945
$470$		0			0
$471$	4.33266	+	7.50438i	0.199638	+	0.345784i
$472$	2.74496	−	4.75442i	0.126347	−	0.218840i
$473$		−	9.03339i		−	0.415356i
$474$	−1.46335	−	0.844863i	−0.0672137	−	0.0388059i
$475$		0			0
$476$		−	1.62106i		−	0.0743013i
$477$	−1.78376	+	3.08957i	−0.0816729	+	0.141462i
$478$	14.4204	+	24.9769i	0.659574	+	1.14242i
$479$	22.4648	−	12.9700i	1.02644	−	0.592617i	0.110479	−	0.993878i	$-0.464762\pi$
$479$	22.4648	−	12.9700i	1.02644	−	0.592617i	0.915963	+	0.401262i	$0.131428\pi$
$480$		0			0
$481$	25.5308	+	14.0925i	1.16411	+	0.642564i
$482$	−5.72600			−0.260812
$483$	−2.52116	+	1.45559i	−0.114717	+	0.0662318i
$484$	4.84304	+	8.38839i	0.220138	+	0.381290i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−15.6047	−	9.00939i	−0.707117	−	0.408254i	0.102875	−	0.994694i	$-0.467196\pi$
$487$	−15.6047	−	9.00939i	−0.707117	−	0.408254i	−0.809993	+	0.586440i	$0.800529\pi$
$488$	−2.48320	−	1.43368i	−0.112409	−	0.0648995i
$489$			1.84669i			0.0835101i
$490$		0			0
$491$	−15.7564	−	27.2908i	−0.711075	−	1.23162i	−0.964454	−	0.264251i	$-0.914875\pi$
$491$	−15.7564	−	27.2908i	−0.711075	−	1.23162i	0.253379	−	0.967367i	$-0.418458\pi$
$492$	−9.67739	+	5.58725i	−0.436291	+	0.251893i
$493$	1.14769			0.0516894
$494$	−1.55607	−	2.57932i	−0.0700111	−	0.116049i
$495$		0			0
$496$	3.78170	−	2.18336i	0.169803	−	0.0980360i
$497$	16.6899	+	28.9078i	0.748646	+	1.29669i
$498$	4.38865	−	7.60136i	0.196660	−	0.340625i
$499$			5.57925i			0.249762i	0.992172	+	0.124881i	$0.0398549\pi$
$499$			5.57925i			0.249762i	−0.992172	+	0.124881i	$0.960145\pi$
$500$		0			0
$501$	−18.8898	−	10.9060i	−0.843935	−	0.487246i
$502$			6.66342i			0.297403i
$503$	18.8126	−	32.5844i	0.838812	−	1.45286i	−0.0520768	−	0.998643i	$-0.516584\pi$
$503$	18.8126	−	32.5844i	0.838812	−	1.45286i	0.890889	−	0.454222i	$-0.150083\pi$
$504$	−1.46593	−	2.53906i	−0.0652975	−	0.113099i
$505$		0			0
$506$	1.13819			0.0505985
$507$	−12.9904	+	0.500000i	−0.576923	+	0.0222058i
$508$	7.60521			0.337426
$509$	25.5466	−	14.7493i	1.13233	−	0.653753i	0.187813	−	0.982205i	$-0.439860\pi$
$509$	25.5466	−	14.7493i	1.13233	−	0.653753i	0.944521	+	0.328452i	$0.106527\pi$
$510$		0			0
$511$	−12.0081	+	20.7987i	−0.531209	+	0.920081i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.723543	−	0.417738i	−0.0319452	−	0.0184436i
$514$	−8.68809	−	5.01607i	−0.383215	−	0.221249i
$515$		0			0
$516$	−3.94036	+	6.82490i	−0.173465	+	0.300450i
$517$	6.27515	+	10.8689i	0.275981	+	0.478013i
$518$	−20.5361	+	11.8565i	−0.902305	+	0.520946i
$519$	−11.8788			−0.521423
$520$		0			0
$521$	−3.16676			−0.138738			−0.0693692	−	0.997591i	$-0.522099\pi$
$521$	−3.16676			−0.138738			−0.0693692	+	0.997591i	$0.522099\pi$
$522$	1.79762	−	1.03786i	0.0786797	−	0.0454257i
$523$	−15.7956	−	27.3587i	−0.690691	−	1.19631i	−0.971612	−	0.236581i	$-0.923973\pi$
$523$	−15.7956	−	27.3587i	−0.690691	−	1.19631i	0.280920	−	0.959731i	$-0.409360\pi$
$524$	2.72670	−	4.72279i	0.119117	−	0.206316i
$525$		0			0
$526$	−21.6856	−	12.5202i	−0.945536	−	0.545906i
$527$	2.09096	+	1.20721i	0.0910834	+	0.0525870i
$528$			1.14626i			0.0498848i
$529$	11.0070	−	19.0647i	0.478566	−	0.828901i
$530$		0			0
$531$	4.75442	−	2.74496i	0.206324	−	0.119121i
$532$	2.44949			0.106199
$533$	−35.2734	−	19.4702i	−1.52786	−	0.843350i
$534$	4.53882			0.196414
$535$		0			0
$536$	5.13165	+	8.88828i	0.221654	+	0.383915i
$537$	4.47746	−	7.75519i	0.193217	−	0.334661i
$538$		−	23.2536i		−	1.00253i
$539$	−1.58410	−	0.914578i	−0.0682318	−	0.0393937i
$540$		0			0
$541$		−	10.1369i		−	0.435821i	−0.975969	−	0.217911i	$-0.930076\pi$
$541$		−	10.1369i		−	0.435821i	0.975969	−	0.217911i	$-0.0699241\pi$
$542$	3.07554	−	5.32698i	0.132106	−	0.228814i
$543$	−10.6149	−	18.3855i	−0.455527	−	0.788996i
$544$	0.478838	−	0.276457i	0.0205300	−	0.0118530i
$545$		0			0
$546$	5.10841	−	9.25467i	0.218620	−	0.396063i
$547$	−32.1457			−1.37445			−0.687225	−	0.726445i	$-0.741171\pi$
$547$	−32.1457			−1.37445			−0.687225	+	0.726445i	$0.741171\pi$
$548$	0.276333	−	0.159541i	0.0118044	−	0.00681525i
$549$	−1.43368	−	2.48320i	−0.0611878	−	0.105980i
$550$		0			0
$551$			1.73421i			0.0738797i
$552$	−0.859921	−	0.496476i	−0.0366007	−	0.0211314i
$553$	4.29031	+	2.47701i	0.182443	+	0.105333i
$554$			6.88928i			0.292697i
$555$		0			0
$556$	5.84046	+	10.1160i	0.247691	+	0.429013i
$557$	−4.50313	+	2.59988i	−0.190804	+	0.110161i	−0.592359	−	0.805674i	$-0.701803\pi$
$557$	−4.50313	+	2.59988i	−0.190804	+	0.110161i	0.401555	+	0.915835i	$0.368470\pi$
$558$	4.36673			0.184858
$559$	−28.4091	+	0.546531i	−1.20158	+	0.0231158i
$560$		0			0
$561$	−0.548875	+	0.316893i	−0.0231735	+	0.0133792i
$562$	0.272809	+	0.472519i	0.0115077	+	0.0199320i
$563$	8.18180	−	14.1713i	0.344822	−	0.597249i	−0.640500	−	0.767958i	$-0.721273\pi$
$563$	8.18180	−	14.1713i	0.344822	−	0.597249i	0.985321	+	0.170710i	$0.0546060\pi$
$564$		−	10.9489i		−	0.461030i
$565$		0			0
$566$	−7.29764	−	4.21329i	−0.306743	−	0.177098i
$567$		−	2.93185i		−	0.123126i
$568$	−5.69263	+	9.85992i	−0.238857	+	0.413713i
$569$	7.90761	+	13.6964i	0.331504	+	0.574182i	0.982807	−	0.184636i	$-0.0591105\pi$
$569$	7.90761	+	13.6964i	0.331504	+	0.574182i	−0.651303	+	0.758818i	$0.725777\pi$
$570$		0			0
$571$	−18.8170			−0.787467			−0.393734	−	0.919225i	$-0.628817\pi$
$571$	−18.8170			−0.787467			−0.393734	+	0.919225i	$0.628817\pi$
$572$	−3.53880	+	2.13492i	−0.147965	+	0.0892654i
$573$	−4.50694			−0.188280
$574$	28.3727	−	16.3810i	1.18425	−	0.683729i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	22.3581i		−	0.930778i	−0.885106	−	0.465389i	$-0.845914\pi$
$577$		−	22.3581i		−	0.930778i	0.885106	−	0.465389i	$-0.154086\pi$
$578$	−14.4577	−	8.34714i	−0.601360	−	0.347195i
$579$	−2.30090	−	1.32843i	−0.0956223	−	0.0552075i
$580$		0			0
$581$	−12.8669	+	22.2861i	−0.533807	+	0.924582i
$582$	−5.30847	−	9.19453i	−0.220043	−	0.381126i
$583$	−3.54146	+	2.04466i	−0.146672	+	0.0846813i
$584$	−8.19151			−0.338967
$585$		0			0
$586$	6.77829			0.280009
$587$	37.1967	−	21.4755i	1.53527	−	0.886389i	0.536165	−	0.844113i	$-0.319872\pi$
$587$	37.1967	−	21.4755i	1.53527	−	0.886389i	0.999106	−	0.0422761i	$-0.0134609\pi$
$588$	0.797877	+	1.38196i	0.0329039	+	0.0569912i
$589$	−1.82415	+	3.15952i	−0.0751627	+	0.130186i
$590$		0			0
$591$	−1.68375	−	0.972112i	−0.0692601	−	0.0399873i
$592$	−7.00449	−	4.04404i	−0.287883	−	0.166209i
$593$		−	30.8372i		−	1.26633i	−0.774016	−	0.633166i	$-0.781755\pi$
$593$		−	30.8372i		−	1.26633i	0.774016	−	0.633166i	$-0.218245\pi$
$594$	−0.573132	+	0.992694i	−0.0235159	+	0.0407307i
$595$		0			0
$596$	4.33221	−	2.50120i	0.177454	−	0.102453i
$597$	15.0175			0.614627
$598$	−0.0688616	−	3.57948i	−0.00281596	−	0.146376i
$599$	9.63447			0.393654			0.196827	−	0.980438i	$-0.436936\pi$
$599$	9.63447			0.393654			0.196827	+	0.980438i	$0.436936\pi$
$600$		0			0
$601$	−17.1757	−	29.7491i	−0.700609	−	1.21349i	−0.968253	−	0.249973i	$-0.919578\pi$
$601$	−17.1757	−	29.7491i	−0.700609	−	1.21349i	0.267643	−	0.963518i	$-0.413755\pi$
$602$	11.5525	−	20.0096i	0.470847	−	0.815531i
$603$			10.2633i			0.417954i
$604$	−11.1722	−	6.45025i	−0.454588	−	0.262457i
$605$		0			0
$606$			14.1463i			0.574653i
$607$	14.7047	−	25.4692i	0.596844	−	1.03376i	−0.396439	−	0.918061i	$-0.629754\pi$
$607$	14.7047	−	25.4692i	0.596844	−	1.03376i	0.993284	−	0.115704i	$-0.0369124\pi$
$608$	0.417738	+	0.723543i	0.0169415	+	0.0293435i
$609$	−5.27035	+	3.04284i	−0.213565	+	0.123302i
$610$		0			0
$611$	33.8018	−	20.3923i	1.36748	−	0.824983i
$612$	0.552914			0.0223502
$613$	33.2034	−	19.1700i	1.34107	−	0.774268i	0.354106	−	0.935205i	$-0.384785\pi$
$613$	33.2034	−	19.1700i	1.34107	−	0.774268i	0.986965	+	0.160938i	$0.0514518\pi$
$614$	17.3216	+	30.0019i	0.699042	+	1.21078i
$615$		0			0
$616$		−	3.36068i		−	0.135406i
$617$	0.526095	+	0.303741i	0.0211798	+	0.0122281i	0.510553	−	0.859847i	$-0.329441\pi$
$617$	0.526095	+	0.303741i	0.0211798	+	0.0122281i	−0.489373	+	0.872075i	$0.662774\pi$
$618$	5.82402	+	3.36250i	0.234277	+	0.135260i
$619$		−	28.6848i		−	1.15294i	−0.817118	−	0.576470i	$-0.804430\pi$
$619$		−	28.6848i		−	1.15294i	0.817118	−	0.576470i	$-0.195570\pi$
$620$		0			0
$621$	−0.496476	−	0.859921i	−0.0199229	−	0.0345075i
$622$	−17.5113	+	10.1101i	−0.702137	+	0.405379i
$623$	−13.3071			−0.533139
$624$	3.60488	−	0.0693504i	0.144311	−	0.00277624i
$625$		0			0
$626$	−19.3406	+	11.1663i	−0.773006	+	0.446295i
$627$	−0.478838	−	0.829371i	−0.0191229	−	0.0331219i
$628$	4.33266	−	7.50438i	0.172892	−	0.299457i
$629$		−	4.47202i		−	0.178311i
$630$		0			0
$631$	3.94547	+	2.27792i	0.157067	+	0.0906824i	0.576473	−	0.817116i	$-0.304429\pi$
$631$	3.94547	+	2.27792i	0.157067	+	0.0906824i	−0.419407	+	0.907798i	$0.637762\pi$
$632$			1.68973i			0.0672137i
$633$	0.379882	−	0.657974i	0.0150989	−	0.0261521i
$634$	−5.71462	−	9.89801i	−0.226957	−	0.393100i
$635$		0			0
$636$	3.56753			0.141462
$637$	−2.78041	+	5.03715i	−0.110164	+	0.199579i
$638$	2.37931			0.0941980
$639$	−9.85992	+	5.69263i	−0.390052	+	0.225197i
$640$		0			0
$641$	−11.8057	+	20.4481i	−0.466297	+	0.807650i	−0.999259	−	0.0384890i	$-0.987746\pi$
$641$	−11.8057	+	20.4481i	−0.466297	+	0.807650i	0.532962	+	0.846139i	$0.321079\pi$
$642$		−	0.246769i		−	0.00973921i
$643$	9.66855	+	5.58214i	0.381290	+	0.220138i	0.678379	−	0.734712i	$-0.262683\pi$
$643$	9.66855	+	5.58214i	0.381290	+	0.220138i	−0.297089	+	0.954850i	$0.596016\pi$
$644$	2.52116	+	1.45559i	0.0993477	+	0.0573584i
$645$		0			0
$646$	−0.230973	+	0.400057i	−0.00908752	+	0.0157400i
$647$	−5.68594	−	9.84834i	−0.223538	−	0.387178i	0.732342	−	0.680937i	$-0.238427\pi$
$647$	−5.68594	−	9.84834i	−0.223538	−	0.387178i	−0.955880	+	0.293758i	$0.905094\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	6.29291			0.247018
$650$		0			0
$651$	−12.8026			−0.501774
$652$	1.59928	−	0.923344i	0.0626326	−	0.0361609i
$653$	4.51599	+	7.82192i	0.176724	+	0.306096i	0.940757	−	0.339082i	$-0.110117\pi$
$653$	4.51599	+	7.82192i	0.176724	+	0.306096i	−0.764032	+	0.645178i	$0.776783\pi$
$654$	2.06899	−	3.58359i	0.0809037	−	0.140129i
$655$		0			0
$656$	9.67739	+	5.58725i	0.377839	+	0.218145i
$657$	−7.09405	−	4.09575i	−0.276765	−	0.159791i
$658$			32.1005i			1.25141i
$659$	−9.57118	+	16.5778i	−0.372840	+	0.645778i	−0.990001	−	0.141059i	$-0.954949\pi$
$659$	−9.57118	+	16.5778i	−0.372840	+	0.645778i	0.617161	+	0.786837i	$0.288283\pi$
$660$		0			0
$661$	15.6116	−	9.01337i	0.607221	−	0.350579i	−0.164656	−	0.986351i	$-0.552651\pi$
$661$	15.6116	−	9.01337i	0.607221	−	0.350579i	0.771877	+	0.635772i	$0.219318\pi$
$662$	−1.77365			−0.0689347
$663$	1.02980	+	1.70698i	0.0399943	+	0.0662937i
$664$	−8.77729			−0.340625
$665$		0			0
$666$	−4.04404	−	7.00449i	−0.156703	−	0.271418i
$667$	−1.03054	+	1.78495i	−0.0399027	+	0.0691135i
$668$			21.8121i			0.843935i
$669$	18.5939	+	10.7352i	0.718883	+	0.415047i
$670$		0			0
$671$		−	3.28674i		−	0.126883i
$672$	−1.46593	+	2.53906i	−0.0565493	+	0.0979463i
$673$	−3.91832	−	6.78672i	−0.151040	−	0.261609i	0.780570	−	0.625068i	$-0.214929\pi$
$673$	−3.91832	−	6.78672i	−0.151040	−	0.261609i	−0.931610	+	0.363459i	$0.881596\pi$
$674$	−10.3944	+	6.00122i	−0.400378	+	0.231158i
$675$		0			0
$676$	6.92820	+	11.0000i	0.266469	+	0.423077i
$677$	−23.4860			−0.902641			−0.451321	−	0.892362i	$-0.649047\pi$
$677$	−23.4860			−0.902641			−0.451321	+	0.892362i	$0.649047\pi$
$678$	1.43488	−	0.828427i	0.0551062	−	0.0318156i
$679$	15.5636	+	26.9570i	0.597278	+	1.03452i
$680$		0			0
$681$		−	22.1017i		−	0.846939i
$682$	4.33483	+	2.50271i	0.165989	+	0.0958338i
$683$	−15.4729	−	8.93327i	−0.592053	−	0.341822i	0.173856	−	0.984771i	$-0.444377\pi$
$683$	−15.4729	−	8.93327i	−0.592053	−	0.341822i	−0.765909	+	0.642949i	$0.777711\pi$
$684$			0.835475i			0.0319452i
$685$		0			0
$686$	7.92222	+	13.7217i	0.302472	+	0.523897i
$687$	18.7380	−	10.8184i	0.714901	−	0.412748i
$688$	7.88072			0.300450
$689$	6.64452	+	11.0138i	0.253136	+	0.419594i
$690$		0			0
$691$	−18.7634	+	10.8331i	−0.713795	+	0.412109i	−0.812464	−	0.583011i	$-0.801875\pi$
$691$	−18.7634	+	10.8331i	−0.713795	+	0.412109i	0.0986699	+	0.995120i	$0.468541\pi$
$692$	5.93942	+	10.2874i	0.225783	+	0.391067i
$693$	1.68034	−	2.91043i	0.0638308	−	0.110558i
$694$		−	27.5585i		−	1.04611i
$695$		0			0
$696$	−1.79762	−	1.03786i	−0.0681386	−	0.0393398i
$697$			6.17854i			0.234029i
$698$	−7.08260	+	12.2674i	−0.268080	+	0.464329i
$699$	2.97834	+	5.15864i	0.112651	+	0.195118i
$700$		0			0
$701$	42.8171			1.61718			0.808590	−	0.588372i	$-0.200231\pi$
$701$	42.8171			1.61718			0.808590	+	0.588372i	$0.200231\pi$
$702$	3.15660	+	1.74238i	0.119138	+	0.0657620i
$703$	6.75739			0.254860
$704$	0.992694	−	0.573132i	0.0374136	−	0.0216007i
$705$		0			0
$706$	−15.7970	+	27.3612i	−0.594528	+	1.02975i
$707$		−	41.4747i		−	1.55982i
$708$	−4.75442	−	2.74496i	−0.178682	−	0.103162i
$709$	10.7389	+	6.20012i	0.403309	+	0.232851i	0.687911	−	0.725795i	$-0.258528\pi$
$709$	10.7389	+	6.20012i	0.403309	+	0.232851i	−0.284602	+	0.958646i	$0.591861\pi$
$710$		0			0
$711$	−0.844863	+	1.46335i	−0.0316848	+	0.0548798i
$712$	−2.26941	−	3.93073i	−0.0850497	−	0.147310i
$713$	−3.75504	+	2.16798i	−0.140628	+	0.0811913i
$714$	−1.62106			−0.0606667
$715$		0			0
$716$	−8.95492			−0.334661
$717$	24.9769	−	14.4204i	0.932778	−	0.538540i
$718$	6.08568	+	10.5407i	0.227116	+	0.393376i
$719$	0.822357	−	1.42436i	0.0306687	−	0.0531198i	−0.850284	−	0.526325i	$-0.823570\pi$
$719$	0.822357	−	1.42436i	0.0306687	−	0.0531198i	0.880952	+	0.473205i	$0.156903\pi$
$720$		0			0
$721$	−17.0752	−	9.85835i	−0.635913	−	0.367144i
$722$	15.8500	+	9.15099i	0.589875	+	0.340565i
$723$			5.72600i			0.212952i
$724$	−10.6149	+	18.3855i	−0.394498	+	0.683290i
$725$		0			0
$726$	8.38839	−	4.84304i	0.311322	−	0.179742i
$727$	−48.0577			−1.78236			−0.891180	−	0.453650i	$-0.850122\pi$
$727$	−48.0577			−1.78236			−0.891180	+	0.453650i	$0.850122\pi$
$728$	−10.5690	+	0.203325i	−0.391713	+	0.00753572i
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.17868	+	3.77359i	0.0805814	+	0.139571i
$732$	−1.43368	+	2.48320i	−0.0529902	+	0.0917817i
$733$			5.56731i			0.205633i	0.994700	+	0.102817i	$0.0327855\pi$
$733$			5.56731i			0.205633i	−0.994700	+	0.102817i	$0.967214\pi$
$734$	−25.9768	−	14.9977i	−0.958820	−	0.553575i
$735$		0			0
$736$			0.992952i			0.0366007i
$737$	−5.88223	+	10.1883i	−0.216675	+	0.375292i
$738$	5.58725	+	9.67739i	0.205669	+	0.356230i
$739$	−44.1546	+	25.4927i	−1.62425	+	0.937763i	−0.638489	+	0.769631i	$0.720440\pi$
$739$	−44.1546	+	25.4927i	−1.62425	+	0.937763i	−0.985765	+	0.168132i	$0.946227\pi$
$740$		0			0
$741$	−2.57932	+	1.55607i	−0.0947536	+	0.0571638i
$742$	−10.4595			−0.383979
$743$	−35.1316	+	20.2832i	−1.28885	+	0.744120i	−0.978450	−	0.206485i	$-0.933798\pi$
$743$	−35.1316	+	20.2832i	−1.28885	+	0.744120i	−0.310404	+	0.950605i	$0.600464\pi$
$744$	−2.18336	−	3.78170i	−0.0800460	−	0.138644i
$745$		0			0
$746$		−	36.7571i		−	1.34577i
$747$	−7.60136	−	4.38865i	−0.278119	−	0.160572i
$748$	0.548875	+	0.316893i	0.0200688	+	0.0115868i
$749$			0.723491i			0.0264358i
$750$		0			0
$751$	12.1132	+	20.9807i	0.442018	+	0.765597i	0.997839	−	0.0657048i	$-0.0209296\pi$
$751$	12.1132	+	20.9807i	0.442018	+	0.765597i	−0.555822	+	0.831302i	$0.687596\pi$
$752$	−9.48200	+	5.47443i	−0.345773	+	0.199632i
$753$	6.66342			0.242829
$754$	−0.143951	−	7.48270i	−0.00524240	−	0.272504i
$755$		0			0
$756$	−2.53906	+	1.46593i	−0.0923446	+	0.0533152i
$757$	21.0629	+	36.4820i	0.765544	+	1.32596i	0.939959	+	0.341288i	$0.110863\pi$
$757$	21.0629	+	36.4820i	0.765544	+	1.32596i	−0.174415	+	0.984672i	$0.555803\pi$
$758$	−2.58479	+	4.47699i	−0.0938838	+	0.162612i
$759$		−	1.13819i		−	0.0413135i
$760$		0			0
$761$	−7.41955	−	4.28368i	−0.268959	−	0.155283i	0.359456	−	0.933162i	$-0.382962\pi$
$761$	−7.41955	−	4.28368i	−0.268959	−	0.155283i	−0.628414	+	0.777879i	$0.716296\pi$
$762$		−	7.60521i		−	0.275508i
$763$	−6.06596	+	10.5066i	−0.219602	+	0.380363i
$764$	2.25347	+	3.90313i	0.0815277	+	0.141210i
$765$		0			0
$766$	2.80196			0.101239
$767$	−0.380728	−	19.7905i	−0.0137473	−	0.714595i
$768$	−1.00000			−0.0360844
$769$	−42.1226	+	24.3195i	−1.51898	+	0.876983i	−0.519229	+	0.854635i	$0.673781\pi$
$769$	−42.1226	+	24.3195i	−1.51898	+	0.876983i	−0.999750	+	0.0223481i	$0.992886\pi$
$770$		0			0
$771$	−5.01607	+	8.68809i	−0.180649	+	0.312894i
$772$			2.65685i			0.0956223i
$773$	42.1294	+	24.3234i	1.51529	+	0.874853i	0.999839	+	0.0179335i	$0.00570872\pi$
$773$	42.1294	+	24.3234i	1.51529	+	0.874853i	0.515450	+	0.856919i	$0.327625\pi$
$774$	6.82490	+	3.94036i	0.245316	+	0.141633i
$775$		0			0
$776$	−5.30847	+	9.19453i	−0.190563	+	0.330065i
$777$	11.8565	+	20.5361i	0.425351	+	0.736729i
$778$	−10.3002	+	5.94680i	−0.369279	+	0.213203i
$779$	−9.33601			−0.334497
$780$		0			0
$781$	−13.0505			−0.466984
$782$	−0.475463	+	0.274509i	−0.0170025	+	0.00981641i
$783$	−1.03786	−	1.79762i	−0.0370899	−	0.0642417i
$784$	0.797877	−	1.38196i	0.0284956	−	0.0493558i
$785$		0			0
$786$	−4.72279	−	2.72670i	−0.168456	−	0.0972583i
$787$	15.2172	+	8.78564i	0.542434	+	0.313174i	0.746065	−	0.665874i	$-0.231941\pi$
$787$	15.2172	+	8.78564i	0.542434	+	0.313174i	−0.203631	+	0.979048i	$0.565274\pi$
$788$			1.94422i			0.0692601i
$789$	−12.5202	+	21.6856i	−0.445730	+	0.772027i
$790$		0			0
$791$	−4.20685	+	2.42883i	−0.149578	+	0.0863591i
$792$	1.14626			0.0407307
$793$	−10.3365	+	0.198852i	−0.367059	+	0.00706144i
$794$	−39.0046			−1.38422
$795$		0			0
$796$	−7.50877	−	13.0056i	−0.266141	−	0.460970i
$797$	−17.3430	+	30.0390i	−0.614321	+	1.06403i	0.376183	+	0.926546i	$0.377237\pi$
$797$	−17.3430	+	30.0390i	−0.614321	+	1.06403i	−0.990503	+	0.137489i	$0.956097\pi$
$798$		−	2.44949i		−	0.0867110i
$799$	−5.24273	−	3.02689i	−0.185475	−	0.107084i
$800$		0			0
$801$		−	4.53882i		−	0.160371i
$802$	−13.5422	+	23.4558i	−0.478192	+	0.828253i
$803$	−4.69482	−	8.13166i	−0.165676	−	0.286960i
$804$	8.88828	−	5.13165i	0.313466	−	0.180979i
$805$		0			0
$806$	7.60852	−	13.7840i	0.267999	−	0.485521i
$807$	−23.2536			−0.818566
$808$	12.2510	−	7.07313i	0.430990	−	0.248832i
$809$	23.2482	+	40.2670i	0.817362	+	1.41571i	0.907619	+	0.419795i	$0.137898\pi$
$809$	23.2482	+	40.2670i	0.817362	+	1.41571i	−0.0902566	+	0.995919i	$0.528769\pi$
$810$		0			0
$811$			11.0542i			0.388165i	0.980985	+	0.194082i	$0.0621729\pi$
$811$			11.0542i			0.388165i	−0.980985	+	0.194082i	$0.937827\pi$
$812$	5.27035	+	3.04284i	0.184953	+	0.106783i
$813$	−5.32698	−	3.07554i	−0.186826	−	0.107864i
$814$		−	9.27108i		−	0.324951i
$815$		0			0
$816$	−0.276457	−	0.478838i	−0.00967794	−	0.0167627i
$817$	−5.70204	+	3.29207i	−0.199489	+	0.115175i
$818$	15.9450			0.557502
$819$	−9.25467	−	5.10841i	−0.323384	−	0.178502i
$820$		0			0
$821$	−15.7133	+	9.07206i	−0.548397	+	0.316617i	−0.748475	−	0.663163i	$-0.769214\pi$
$821$	−15.7133	+	9.07206i	−0.548397	+	0.316617i	0.200078	+	0.979780i	$0.435880\pi$
$822$	−0.159541	−	0.276333i	−0.00556463	−	0.00963821i
$823$	0.275929	−	0.477923i	0.00961827	−	0.0166593i	−0.861176	−	0.508307i	$-0.830272\pi$
$823$	0.275929	−	0.477923i	0.00961827	−	0.0166593i	0.870794	+	0.491647i	$0.163605\pi$
$824$		−	6.72500i		−	0.234277i
$825$		0			0
$826$	13.9392	+	8.04782i	0.485008	+	0.280020i
$827$		−	34.0321i		−	1.18341i	−0.806154	−	0.591705i	$-0.798455\pi$
$827$		−	34.0321i		−	1.18341i	0.806154	−	0.591705i	$-0.201545\pi$
$828$	−0.496476	+	0.859921i	−0.0172537	+	0.0298843i
$829$	13.0638	+	22.6271i	0.453724	+	0.785872i	0.998614	−	0.0526352i	$-0.0167620\pi$
$829$	13.0638	+	22.6271i	0.453724	+	0.785872i	−0.544890	+	0.838507i	$0.683429\pi$
$830$		0			0
$831$	6.88928			0.238986
$832$	−1.86250	−	3.08725i	−0.0645706	−	0.107031i
$833$	0.882315			0.0305704
$834$	10.1160	−	5.84046i	0.350287	−	0.202239i
$835$		0			0
$836$	−0.478838	+	0.829371i	−0.0165610	+	0.0286844i
$837$		−	4.36673i		−	0.150936i
$838$	16.8298	+	9.71670i	0.581376	+	0.335658i
$839$	35.9524	+	20.7571i	1.24121	+	0.716616i	0.969342	−	0.245717i	$-0.0790235\pi$
$839$	35.9524	+	20.7571i	1.24121	+	0.716616i	0.271873	+	0.962333i	$0.412357\pi$
$840$		0			0
$841$	12.3457	−	21.3834i	0.425714	−	0.737359i
$842$	10.7885	+	18.6862i	0.371795	+	0.643968i
$843$	0.472519	−	0.272809i	0.0162744	−	0.00939603i
$844$	−0.759763			−0.0261521
$845$		0			0
$846$	−10.9489			−0.376430
$847$	−24.5935	+	14.1991i	−0.845043	+	0.487886i
$848$	−1.78376	−	3.08957i	−0.0612547	−	0.106096i
$849$	−4.21329	+	7.29764i	−0.144600	+	0.250454i
$850$		0			0
$851$	6.95512	+	4.01554i	0.238418	+	0.137651i
$852$	9.85992	+	5.69263i	0.337795	+	0.195026i
$853$			18.1928i			0.622908i	0.950261	+	0.311454i	$0.100816\pi$
$853$			18.1928i			0.622908i	−0.950261	+	0.311454i	$0.899184\pi$
$854$	4.20332	−	7.28037i	0.143835	−	0.249129i
$855$		0			0
$856$	−0.213709	+	0.123385i	−0.00730441	+	0.00421720i
$857$	52.4732			1.79245			0.896224	−	0.443601i	$-0.146299\pi$
$857$	52.4732			1.79245			0.896224	+	0.443601i	$0.146299\pi$
$858$	2.13492	+	3.53880i	0.0728849	+	0.120813i
$859$	−53.9248			−1.83989			−0.919945	−	0.392047i	$-0.871767\pi$
$859$	−53.9248			−1.83989			−0.919945	+	0.392047i	$0.871767\pi$
$860$		0			0
$861$	−16.3810	−	28.3727i	−0.558262	−	0.966938i
$862$	−0.317855	+	0.550541i	−0.0108262	+	0.0187515i
$863$		−	9.53847i		−	0.324693i	−0.986734	−	0.162347i	$-0.948094\pi$
$863$		−	9.53847i		−	0.324693i	0.986734	−	0.162347i	$-0.0519063\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$			10.6018i			0.360264i
$867$	−8.34714	+	14.4577i	−0.283484	+	0.491008i
$868$	6.40130	+	11.0874i	0.217274	+	0.376330i
$869$	−1.67738	+	0.968437i	−0.0569013	+	0.0328520i
$870$		0			0
$871$	32.3971	+	17.8826i	1.09773	+	0.605929i
$872$	−4.13797			−0.140129
$873$	−9.19453	+	5.30847i	−0.311188	+	0.179664i
$874$	−0.414793	−	0.718443i	−0.0140306	−	0.0243017i
$875$		0			0
$876$			8.19151i			0.276765i
$877$	−39.6842	−	22.9117i	−1.34004	−	0.773672i	−0.353226	−	0.935538i	$-0.614915\pi$
$877$	−39.6842	−	22.9117i	−1.34004	−	0.773672i	−0.986813	+	0.161866i	$0.948249\pi$
$878$	13.2621	+	7.65685i	0.447573	+	0.258406i
$879$		−	6.77829i		−	0.228626i
$880$		0			0
$881$	−15.1002	−	26.1544i	−0.508740	−	0.881164i	−0.999949	−	0.0101217i	$-0.996778\pi$
$881$	−15.1002	−	26.1544i	−0.508740	−	0.881164i	0.491209	−	0.871042i	$-0.336555\pi$
$882$	1.38196	−	0.797877i	0.0465331	−	0.0268659i
$883$	−22.0417			−0.741761			−0.370880	−	0.928681i	$-0.620944\pi$
$883$	−22.0417			−0.741761			−0.370880	+	0.928681i	$0.620944\pi$
$884$	0.963388	−	1.74533i	0.0324023	−	0.0587017i
$885$		0			0
$886$	−16.0041	+	9.23998i	−0.537669	+	0.310423i
$887$	13.3918	+	23.1953i	0.449652	+	0.778821i	0.998363	−	0.0571915i	$-0.0182146\pi$
$887$	13.3918	+	23.1953i	0.449652	+	0.778821i	−0.548711	+	0.836012i	$0.684881\pi$
$888$	−4.04404	+	7.00449i	−0.135709	+	0.235055i
$889$			22.2973i			0.747829i
$890$		0			0
$891$	0.992694	+	0.573132i	0.0332565	+	0.0192007i
$892$		−	21.4704i		−	0.718883i
$893$	4.57375	−	7.92197i	0.153055	−	0.265099i
$894$	−2.50120	−	4.33221i	−0.0836527	−	0.144891i
$895$		0			0
$896$	2.93185			0.0979463
$897$	−3.57948	+	0.0688616i	−0.119515	+	0.00229922i
$898$	−25.9905			−0.867313
$899$	−7.84972	+	4.53204i	−0.261803	+	0.151152i
$900$		0			0
$901$	0.986268	−	1.70827i	0.0328574	−	0.0569106i
$902$			12.8089i			0.426490i
$903$	−20.0096	−	11.5525i	−0.665878	−	0.384445i
$904$	−1.43488	−	0.828427i	−0.0477233	−	0.0275531i
$905$		0			0
$906$	−6.45025	+	11.1722i	−0.214295	+	0.371170i
$907$	−11.6972	−	20.2602i	−0.388400	−	0.672729i	0.603834	−	0.797110i	$-0.293639\pi$
$907$	−11.6972	−	20.2602i	−0.388400	−	0.672729i	−0.992235	+	0.124381i	$0.960306\pi$
$908$	−19.1406	+	11.0508i	−0.635204	+	0.366735i
$909$	14.1463			0.469202
$910$		0			0
$911$	29.1351			0.965289			0.482644	−	0.875816i	$-0.339676\pi$
$911$	29.1351			0.965289			0.482644	+	0.875816i	$0.339676\pi$
$912$	0.723543	−	0.417738i	0.0239589	−	0.0138327i
$913$	−5.03055	−	8.71317i	−0.166487	−	0.288364i
$914$	−20.7543	+	35.9475i	−0.686492	+	1.18904i
$915$		0			0
$916$	−18.7380	−	10.8184i	−0.619123	−	0.357451i
$917$	13.8465	+	7.99429i	0.457252	+	0.263995i
$918$		−	0.552914i		−	0.0182489i
$919$	−22.1754	+	38.4089i	−0.731499	+	1.26699i	0.224743	+	0.974418i	$0.427846\pi$
$919$	−22.1754	+	38.4089i	−0.731499	+	1.26699i	−0.956242	+	0.292576i	$0.905488\pi$
$920$		0			0
$921$	30.0019	−	17.3216i	0.988595	−	0.570765i
$922$	−15.9964			−0.526812
$923$	0.789572	+	41.0425i	0.0259891	+	1.35093i
$924$	−3.36068			−0.110558
$925$		0			0
$926$	9.41638	+	16.3096i	0.309441	+	0.535968i
$927$	3.36250	−	5.82402i	0.110439	−	0.191286i
$928$			2.07571i			0.0681386i
$929$	−10.9917	−	6.34607i	−0.360626	−	0.208208i	0.308729	−	0.951150i	$-0.400096\pi$
$929$	−10.9917	−	6.34607i	−0.360626	−	0.208208i	−0.669355	+	0.742942i	$0.733430\pi$
$930$		0			0
$931$			1.33321i			0.0436943i
$932$	2.97834	−	5.15864i	0.0975588	−	0.168977i
$933$	10.1101	+	17.5113i	0.330991	+	0.573293i
$934$	−2.97686	+	1.71869i	−0.0974059	+	0.0562373i
$935$		0			0
$936$	−0.0693504	−	3.60488i	−0.00226679	−	0.117829i
$937$	−47.6859			−1.55783			−0.778915	−	0.627130i	$-0.784229\pi$
$937$	−47.6859			−1.55783			−0.778915	+	0.627130i	$0.784229\pi$
$938$	−26.0591	+	15.0452i	−0.850861	+	0.491245i
$939$	11.1663	+	19.3406i	0.364399	+	0.631157i
$940$		0			0
$941$			53.8451i			1.75530i	0.479301	+	0.877650i	$0.340890\pi$
$941$			53.8451i			1.75530i	−0.479301	+	0.877650i	$0.659110\pi$
$942$	−7.50438	−	4.33266i	−0.244506	−	0.141166i
$943$	−9.60919	−	5.54787i	−0.312918	−	0.180663i
$944$			5.48993i			0.178682i
$945$		0			0
$946$	4.51669	+	7.82314i	0.146850	+	0.254352i
$947$	−24.1725	+	13.9560i	−0.785500	+	0.453509i	−0.838376	−	0.545093i	$-0.816495\pi$
$947$	−24.1725	+	13.9560i	−0.785500	+	0.453509i	0.0528760	+	0.998601i	$0.483161\pi$
$948$	1.68973			0.0548798
$949$	−25.2892	+	15.2567i	−0.820922	+	0.495253i
$950$		0			0
$951$	−9.89801	+	5.71462i	−0.320965	+	0.185309i
$952$	0.810531	+	1.40388i	0.0262695	+	0.0455001i
$953$	26.6171	−	46.1023i	0.862214	−	1.49340i	−0.00757307	−	0.999971i	$-0.502411\pi$
$953$	26.6171	−	46.1023i	0.862214	−	1.49340i	0.869787	−	0.493427i	$-0.164256\pi$
$954$		−	3.56753i		−	0.115503i
$955$		0			0
$956$	−24.9769	−	14.4204i	−0.807810	−	0.466389i
$957$		−	2.37931i		−	0.0769123i
$958$	−12.9700	+	22.4648i	−0.419043	+	0.725804i
$959$	0.467750	+	0.810167i	0.0151044	+	0.0261617i
$960$		0			0
$961$	11.9317			0.384893
$962$	−29.1566	+	0.560911i	−0.940047	+	0.0180845i
$963$	−0.246769			−0.00795203
$964$	4.95886	−	2.86300i	0.159714	−	0.0922110i
$965$		0			0
$966$	1.45559	−	2.52116i	0.0468330	−	0.0811171i
$967$		−	18.2209i		−	0.585946i	−0.956121	−	0.292973i	$-0.905355\pi$
$967$		−	18.2209i		−	0.585946i	0.956121	−	0.292973i	$-0.0946446\pi$
$968$	−8.38839	−	4.84304i	−0.269613	−	0.155661i
$969$	0.400057	+	0.230973i	0.0128517	+	0.00741993i
$970$		0			0
$971$	26.5276	−	45.9471i	0.851311	−	1.47451i	−0.0287154	−	0.999588i	$-0.509142\pi$
$971$	26.5276	−	45.9471i	0.851311	−	1.47451i	0.880026	−	0.474926i	$-0.157525\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−29.6585	+	17.1234i	−0.950809	+	0.548950i
$974$	18.0188			0.577359
$975$		0			0
$976$	2.86735			0.0917817
$977$	49.6962	−	28.6921i	1.58992	−	0.917943i	0.596605	−	0.802535i	$-0.296516\pi$
$977$	49.6962	−	28.6921i	1.58992	−	0.917943i	0.993318	−	0.115408i	$-0.0368174\pi$
$978$	−0.923344	−	1.59928i	−0.0295253	−	0.0511393i
$979$	2.60134	−	4.50566i	0.0831393	−	0.144001i
$980$		0			0
$981$	−3.58359	−	2.06899i	−0.114415	−	0.0660576i
$982$	27.2908	+	15.7564i	0.870886	+	0.502806i
$983$		−	6.53308i		−	0.208373i	−0.994558	−	0.104186i	$-0.966776\pi$
$983$		−	6.53308i		−	0.208373i	0.994558	−	0.104186i	$-0.0332239\pi$
$984$	5.58725	−	9.67739i	0.178115	−	0.308504i
$985$		0			0
$986$	−0.993929	+	0.573845i	−0.0316532	+	0.0182750i
$987$	32.1005			1.02177
$988$	2.63726	+	1.45572i	0.0839024	+	0.0463126i
$989$	−7.82517			−0.248826
$990$		0			0
$991$	12.9156	+	22.3704i	0.410277	+	0.710620i	0.994920	−	0.100670i	$-0.0320987\pi$
$991$	12.9156	+	22.3704i	0.410277	+	0.710620i	−0.584643	+	0.811291i	$0.698765\pi$
$992$	−2.18336	+	3.78170i	−0.0693219	+	0.120069i
$993$			1.77365i			0.0562850i
$994$	−28.9078	−	16.6899i	−0.916901	−	0.529373i
$995$		0			0
$996$			8.77729i			0.278119i
$997$	11.7814	−	20.4060i	0.373121	−	0.646265i	−0.616923	−	0.787024i	$-0.711621\pi$
$997$	11.7814	−	20.4060i	0.373121	−	0.646265i	0.990044	+	0.140759i	$0.0449542\pi$
$998$	−2.78963	−	4.83178i	−0.0883041	−	0.152947i
$999$	−7.00449	+	4.04404i	−0.221612	+	0.127948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.f.751.2	yes	8
5.2	odd	4		1950.2.y.i.49.3		8
5.3	odd	4		1950.2.y.l.49.2		8
5.4	even	2		1950.2.bc.e.751.3	✓	8
13.4	even	6	inner	1950.2.bc.f.901.2	yes	8
65.4	even	6		1950.2.bc.e.901.3	yes	8
65.17	odd	12		1950.2.y.l.199.2		8
65.43	odd	12		1950.2.y.i.199.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.i.49.3		8	5.2	odd	4
1950.2.y.i.199.3		8	65.43	odd	12
1950.2.y.l.49.2		8	5.3	odd	4
1950.2.y.l.199.2		8	65.17	odd	12
1950.2.bc.e.751.3	✓	8	5.4	even	2
1950.2.bc.e.901.3	yes	8	65.4	even	6
1950.2.bc.f.751.2	yes	8	1.1	even	1	trivial
1950.2.bc.f.901.2	yes	8	13.4	even	6	inner

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(2.53906 + 1.46593i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(2.53906 + 1.46593i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.992694 + 0.573132i) q^{11} +1.00000 q^{12} +(1.86250 + 3.08725i) q^{13} -2.93185 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.276457 - 0.478838i) q^{17} -1.00000i q^{18} +(0.723543 + 0.417738i) q^{19} +2.93185i q^{21} +(0.573132 - 0.992694i) q^{22} +(0.496476 + 0.859921i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-3.15660 - 1.74238i) q^{26} -1.00000 q^{27} +(2.53906 - 1.46593i) q^{28} +(1.03786 + 1.79762i) q^{29} +4.36673i q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.992694 - 0.573132i) q^{33} +0.552914i q^{34} +(0.500000 + 0.866025i) q^{36} +(7.00449 - 4.04404i) q^{37} -0.835475 q^{38} +(-1.74238 + 3.15660i) q^{39} +(-9.67739 + 5.58725i) q^{41} +(-1.46593 - 2.53906i) q^{42} +(-3.94036 + 6.82490i) q^{43} +1.14626i q^{44} +(-0.859921 - 0.496476i) q^{46} -10.9489i q^{47} +(0.500000 - 0.866025i) q^{48} +(0.797877 + 1.38196i) q^{49} +0.552914 q^{51} +(3.60488 - 0.0693504i) q^{52} +3.56753 q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.46593 + 2.53906i) q^{56} +0.835475i q^{57} +(-1.79762 - 1.03786i) q^{58} +(-4.75442 - 2.74496i) q^{59} +(-1.43368 + 2.48320i) q^{61} +(-2.18336 - 3.78170i) q^{62} +(-2.53906 + 1.46593i) q^{63} -1.00000 q^{64} +1.14626 q^{66} +(8.88828 - 5.13165i) q^{67} +(-0.276457 - 0.478838i) q^{68} +(-0.496476 + 0.859921i) q^{69} +(9.85992 + 5.69263i) q^{71} +(-0.866025 - 0.500000i) q^{72} +8.19151i q^{73} +(-4.04404 + 7.00449i) q^{74} +(0.723543 - 0.417738i) q^{76} -3.36068 q^{77} +(-0.0693504 - 3.60488i) q^{78} +1.68973 q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.58725 - 9.67739i) q^{82} +8.77729i q^{83} +(2.53906 + 1.46593i) q^{84} -7.88072i q^{86} +(-1.03786 + 1.79762i) q^{87} +(-0.573132 - 0.992694i) q^{88} +(-3.93073 + 2.26941i) q^{89} +(0.203325 + 10.5690i) q^{91} +0.992952 q^{92} +(-3.78170 + 2.18336i) q^{93} +(5.47443 + 9.48200i) q^{94} +1.00000i q^{96} +(9.19453 + 5.30847i) q^{97} +(-1.38196 - 0.797877i) q^{98} -1.14626i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} - 12 q^{11} + 8 q^{12} - 8 q^{14} - 4 q^{16} - 4 q^{17} + 12 q^{19} - 8 q^{22} - 4 q^{23} - 8 q^{27} + 4 q^{29} - 12 q^{33} + 4 q^{36} + 24 q^{37} - 4 q^{42} + 4 q^{43} + 12 q^{46} + 4 q^{48} - 16 q^{49} - 8 q^{51} + 8 q^{53} - 4 q^{56} - 12 q^{58} - 12 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 16 q^{66} - 24 q^{67} + 4 q^{68} + 4 q^{69} + 60 q^{71} + 16 q^{74} + 12 q^{76} + 8 q^{77} - 8 q^{79} - 4 q^{81} + 20 q^{82} - 4 q^{87} + 8 q^{88} + 24 q^{89} + 8 q^{91} - 8 q^{92} + 24 q^{93} + 16 q^{94} - 12 q^{97} - 12 q^{98}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 - 12 * q^11 + 8 * q^12 - 8 * q^14 - 4 * q^16 - 4 * q^17 + 12 * q^19 - 8 * q^22 - 4 * q^23 - 8 * q^27 + 4 * q^29 - 12 * q^33 + 4 * q^36 + 24 * q^37 - 4 * q^42 + 4 * q^43 + 12 * q^46 + 4 * q^48 - 16 * q^49 - 8 * q^51 + 8 * q^53 - 4 * q^56 - 12 * q^58 - 12 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 - 16 * q^66 - 24 * q^67 + 4 * q^68 + 4 * q^69 + 60 * q^71 + 16 * q^74 + 12 * q^76 + 8 * q^77 - 8 * q^79 - 4 * q^81 + 20 * q^82 - 4 * q^87 + 8 * q^88 + 24 * q^89 + 8 * q^91 - 8 * q^92 + 24 * q^93 + 16 * q^94 - 12 * q^97 - 12 * q^98

Introduction

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