LMFDB - Embedded newform 441.2.bb.e.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	441.37
Dual form			441.2.bb.e.298.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190250 + 0.129710i) q^{2} +(-0.711312 + 1.81239i) q^{4} +(-1.13743 - 0.350851i) q^{5} +(-2.33995 + 1.23477i) q^{7} +(-0.202234 - 0.886046i) q^{8} +O(q^{10})$	\(q+(-0.190250 + 0.129710i) q^{2} +(-0.711312 + 1.81239i) q^{4} +(-1.13743 - 0.350851i) q^{5} +(-2.33995 + 1.23477i) q^{7} +(-0.202234 - 0.886046i) q^{8} +(0.261905 - 0.0807869i) q^{10} +(-0.276984 - 3.69610i) q^{11} +(1.00902 + 0.485919i) q^{13} +(0.285013 - 0.538429i) q^{14} +(-2.70107 - 2.50623i) q^{16} +(-6.63269 - 0.999717i) q^{17} +(2.49731 - 4.32547i) q^{19} +(1.44495 - 1.81191i) q^{20} +(0.532118 + 0.667255i) q^{22} +(1.09199 - 0.164591i) q^{23} +(-2.96054 - 2.01846i) q^{25} +(-0.254995 + 0.0384343i) q^{26} +(-0.573448 - 5.11921i) q^{28} +(-4.32808 + 5.42724i) q^{29} +(-1.42347 - 2.46552i) q^{31} +(2.63632 + 0.397362i) q^{32} +(1.39154 - 0.670131i) q^{34} +(3.09474 - 0.583487i) q^{35} +(0.893462 + 2.27650i) q^{37} +(0.0859442 + 1.14685i) q^{38} +(-0.0808426 + 1.07877i) q^{40} +(-0.970126 - 4.25040i) q^{41} +(-2.16553 + 9.48782i) q^{43} +(6.89580 + 2.12707i) q^{44} +(-0.186401 + 0.172955i) q^{46} +(-6.47433 + 4.41412i) q^{47} +(3.95071 - 5.77857i) q^{49} +0.825059 q^{50} +(-1.59841 + 1.48310i) q^{52} +(1.47372 - 3.75499i) q^{53} +(-0.981728 + 4.30123i) q^{55} +(1.56728 + 1.82359i) q^{56} +(0.119448 - 1.59393i) q^{58} +(-13.6406 + 4.20757i) q^{59} +(-2.75362 - 7.01611i) q^{61} +(0.590618 + 0.284426i) q^{62} +(6.08648 - 2.93110i) q^{64} +(-0.977206 - 0.906715i) q^{65} +(1.69953 + 2.94368i) q^{67} +(6.52979 - 11.3099i) q^{68} +(-0.513091 + 0.512428i) q^{70} +(3.49266 + 4.37965i) q^{71} +(1.17183 + 0.798940i) q^{73} +(-0.465267 - 0.317213i) q^{74} +(6.06308 + 7.60286i) q^{76} +(5.21194 + 8.30666i) q^{77} +(-8.37241 + 14.5014i) q^{79} +(2.19297 + 3.79833i) q^{80} +(0.735886 + 0.682803i) q^{82} +(12.1399 - 5.84627i) q^{83} +(7.19347 + 3.46419i) q^{85} +(-0.818675 - 2.08595i) q^{86} +(-3.21890 + 0.992898i) q^{88} +(0.460090 - 6.13948i) q^{89} +(-2.96105 + 0.108880i) q^{91} +(-0.478441 + 2.09619i) q^{92} +(0.659183 - 1.67957i) q^{94} +(-4.35811 + 4.04373i) q^{95} -2.94332 q^{97} +(-0.00208186 + 1.61182i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.190250	+	0.129710i	−0.134527	+	0.0917190i	−0.628714	−	0.777637i	$-0.716418\pi$
$2$	−0.190250	+	0.129710i	−0.134527	+	0.0917190i	0.494187	+	0.869356i	$0.335466\pi$
$3$		0			0
$3$		0			0
$4$	−0.711312	+	1.81239i	−0.355656	+	0.906196i
$5$	−1.13743	−	0.350851i	−0.508674	−	0.156905i	0.0297859	−	0.999556i	$-0.490517\pi$
$5$	−1.13743	−	0.350851i	−0.508674	−	0.156905i	−0.538460	+	0.842651i	$0.680994\pi$
$6$		0			0
$7$	−2.33995	+	1.23477i	−0.884417	+	0.466698i
$7$	−2.33995	+	1.23477i	−0.884417	+	0.466698i
$8$	−0.202234	−	0.886046i	−0.0715006	−	0.313265i
$9$		0			0
$10$	0.261905	−	0.0807869i	0.0828216	−	0.0255471i
$11$	−0.276984	−	3.69610i	−0.0835139	−	1.11442i	−0.868761	−	0.495232i	$-0.835083\pi$
$11$	−0.276984	−	3.69610i	−0.0835139	−	1.11442i	0.785247	−	0.619183i	$-0.212536\pi$
$12$		0			0
$13$	1.00902	+	0.485919i	0.279852	+	0.134770i	0.568545	−	0.822652i	$-0.307506\pi$
$13$	1.00902	+	0.485919i	0.279852	+	0.134770i	−0.288693	+	0.957422i	$0.593221\pi$
$14$	0.285013	−	0.538429i	0.0761730	−	0.143901i
$15$		0			0
$16$	−2.70107	−	2.50623i	−0.675268	−	0.626557i
$17$	−6.63269	−	0.999717i	−1.60866	−	0.242467i	−0.717637	−	0.696418i	$-0.754776\pi$
$17$	−6.63269	−	0.999717i	−1.60866	−	0.242467i	−0.891027	+	0.453950i	$0.850014\pi$
$18$		0			0
$19$	2.49731	−	4.32547i	0.572922	−	0.992330i	−0.423342	−	0.905970i	$-0.639143\pi$
$19$	2.49731	−	4.32547i	0.572922	−	0.992330i	0.996264	−	0.0863600i	$-0.0275235\pi$
$20$	1.44495	−	1.81191i	0.323100	−	0.405154i
$21$		0			0
$22$	0.532118	+	0.667255i	0.113448	+	0.142259i
$23$	1.09199	−	0.164591i	0.227695	−	0.0343195i	−0.0342036	−	0.999415i	$-0.510889\pi$
$23$	1.09199	−	0.164591i	0.227695	−	0.0343195i	0.261899	+	0.965095i	$0.415651\pi$
$24$		0			0
$25$	−2.96054	−	2.01846i	−0.592109	−	0.403693i
$26$	−0.254995	+	0.0384343i	−0.0500086	+	0.00753759i
$27$		0			0
$28$	−0.573448	−	5.11921i	−0.108372	−	0.967439i
$29$	−4.32808	+	5.42724i	−0.803704	+	1.00781i	0.195926	+	0.980619i	$0.437229\pi$
$29$	−4.32808	+	5.42724i	−0.803704	+	1.00781i	−0.999630	+	0.0271942i	$0.991343\pi$
$30$		0			0
$31$	−1.42347	−	2.46552i	−0.255662	−	0.442820i	0.709413	−	0.704793i	$-0.248960\pi$
$31$	−1.42347	−	2.46552i	−0.255662	−	0.442820i	−0.965075	+	0.261973i	$0.915627\pi$
$32$	2.63632	+	0.397362i	0.466041	+	0.0702444i
$33$		0			0
$34$	1.39154	−	0.670131i	0.238648	−	0.114927i
$35$	3.09474	−	0.583487i	0.523107	−	0.0986273i
$36$		0			0
$37$	0.893462	+	2.27650i	0.146884	+	0.374255i	0.985313	−	0.170756i	$-0.0546209\pi$
$37$	0.893462	+	2.27650i	0.146884	+	0.374255i	−0.838429	+	0.545011i	$0.816526\pi$
$38$	0.0859442	+	1.14685i	0.0139420	+	0.186043i
$39$		0			0
$40$	−0.0808426	+	1.07877i	−0.0127823	+	0.170568i
$41$	−0.970126	−	4.25040i	−0.151508	−	0.663801i	−0.992447	−	0.122671i	$-0.960854\pi$
$41$	−0.970126	−	4.25040i	−0.151508	−	0.663801i	0.840939	−	0.541130i	$-0.182003\pi$
$42$		0			0
$43$	−2.16553	+	9.48782i	−0.330241	+	1.44688i	0.488423	+	0.872607i	$0.337572\pi$
$43$	−2.16553	+	9.48782i	−0.330241	+	1.44688i	−0.818664	+	0.574273i	$0.805285\pi$
$44$	6.89580	+	2.12707i	1.03958	+	0.320668i
$45$		0			0
$46$	−0.186401	+	0.172955i	−0.0274834	+	0.0255009i
$47$	−6.47433	+	4.41412i	−0.944377	+	0.643866i	−0.934454	−	0.356085i	$-0.884111\pi$
$47$	−6.47433	+	4.41412i	−0.944377	+	0.643866i	−0.00992387	+	0.999951i	$0.503159\pi$
$48$		0			0
$49$	3.95071	−	5.77857i	0.564387	−	0.825510i
$50$	0.825059			0.116681
$51$		0			0
$52$	−1.59841	+	1.48310i	−0.221659	+	0.205669i
$53$	1.47372	−	3.75499i	0.202431	−	0.515787i	−0.793221	−	0.608934i	$-0.791597\pi$
$53$	1.47372	−	3.75499i	0.202431	−	0.515787i	0.995652	+	0.0931471i	$0.0296927\pi$
$54$		0			0
$55$	−0.981728	+	4.30123i	−0.132376	+	0.579978i
$56$	1.56728	+	1.82359i	0.209436	+	0.243687i
$57$		0			0
$58$	0.119448	−	1.59393i	0.0156843	−	0.209293i
$59$	−13.6406	+	4.20757i	−1.77585	+	0.547779i	−0.996855	−	0.0792458i	$-0.974749\pi$
$59$	−13.6406	+	4.20757i	−1.77585	+	0.547779i	−0.779000	+	0.627024i	$0.784273\pi$
$60$		0			0
$61$	−2.75362	−	7.01611i	−0.352565	−	0.898321i	−0.991623	−	0.129163i	$-0.958771\pi$
$61$	−2.75362	−	7.01611i	−0.352565	−	0.898321i	0.639059	−	0.769158i	$-0.279324\pi$
$62$	0.590618	+	0.284426i	0.0750085	+	0.0361222i
$63$		0			0
$64$	6.08648	−	2.93110i	0.760810	−	0.366387i
$65$	−0.977206	−	0.906715i	−0.121208	−	0.112464i
$66$		0			0
$67$	1.69953	+	2.94368i	0.207631	+	0.359628i	0.950968	−	0.309290i	$-0.100091\pi$
$67$	1.69953	+	2.94368i	0.207631	+	0.359628i	−0.743337	+	0.668917i	$0.766758\pi$
$68$	6.52979	−	11.3099i	0.791853	−	1.37153i
$69$		0			0
$70$	−0.513091	+	0.512428i	−0.0613260	+	0.0612469i
$71$	3.49266	+	4.37965i	0.414502	+	0.519769i	0.944625	−	0.328151i	$-0.106426\pi$
$71$	3.49266	+	4.37965i	0.414502	+	0.519769i	−0.530123	+	0.847921i	$0.677854\pi$
$72$		0			0
$73$	1.17183	+	0.798940i	0.137152	+	0.0935088i	0.629953	−	0.776634i	$-0.283074\pi$
$73$	1.17183	+	0.798940i	0.137152	+	0.0935088i	−0.492800	+	0.870142i	$0.664027\pi$
$74$	−0.465267	−	0.317213i	−0.0540862	−	0.0368753i
$75$		0			0
$76$	6.06308	+	7.60286i	0.695483	+	0.872108i
$77$	5.21194	+	8.30666i	0.593956	+	0.946632i
$78$		0			0
$79$	−8.37241	+	14.5014i	−0.941970	+	1.63154i	−0.180263	+	0.983618i	$0.557695\pi$
$79$	−8.37241	+	14.5014i	−0.941970	+	1.63154i	−0.761707	+	0.647922i	$0.775638\pi$
$80$	2.19297	+	3.79833i	0.245181	+	0.424666i
$81$		0			0
$82$	0.735886	+	0.682803i	0.0812650	+	0.0754029i
$83$	12.1399	−	5.84627i	1.33253	−	0.641711i	0.374190	−	0.927352i	$-0.377921\pi$
$83$	12.1399	−	5.84627i	1.33253	−	0.641711i	0.958337	+	0.285641i	$0.0922064\pi$
$84$		0			0
$85$	7.19347	+	3.46419i	0.780241	+	0.375744i
$86$	−0.818675	−	2.08595i	−0.0882800	−	0.224934i
$87$		0			0
$88$	−3.21890	+	0.992898i	−0.343136	+	0.105843i
$89$	0.460090	−	6.13948i	0.0487695	−	0.650783i	−0.918237	−	0.396031i	$-0.870387\pi$
$89$	0.460090	−	6.13948i	0.0487695	−	0.650783i	0.967006	−	0.254752i	$-0.0819938\pi$
$90$		0			0
$91$	−2.96105	+	0.108880i	−0.310403	+	0.0114137i
$92$	−0.478441	+	2.09619i	−0.0498809	+	0.218542i
$93$		0			0
$94$	0.659183	−	1.67957i	0.0679896	−	0.173235i
$95$	−4.35811	+	4.04373i	−0.447132	+	0.414878i
$96$		0			0
$97$	−2.94332			−0.298849			−0.149424	−	0.988773i	$-0.547742\pi$
$97$	−2.94332			−0.298849			−0.149424	+	0.988773i	$0.547742\pi$
$98$	−0.00208186	+	1.61182i	−0.000210300	+	0.162818i
$99$		0			0
$100$	5.76412	−	3.92991i	0.576412	−	0.392991i
$101$	−0.438721	+	0.407073i	−0.0436543	+	0.0405053i	−0.701698	−	0.712474i	$-0.747575\pi$
$101$	−0.438721	+	0.407073i	−0.0436543	+	0.0405053i	0.658044	+	0.752979i	$0.271384\pi$
$102$		0			0
$103$	−3.03228	−	0.935334i	−0.298779	−	0.0921612i	0.141741	−	0.989904i	$-0.454730\pi$
$103$	−3.03228	−	0.935334i	−0.298779	−	0.0921612i	−0.440520	+	0.897743i	$0.645206\pi$
$104$	0.226488	−	0.992309i	0.0222090	−	0.0973040i
$105$		0			0
$106$	0.206684	+	0.905543i	0.0200749	+	0.0879541i
$107$	−1.30777	+	17.4510i	−0.126427	+	1.68705i	0.468653	+	0.883383i	$0.344740\pi$
$107$	−1.30777	+	17.4510i	−0.126427	+	1.68705i	−0.595079	+	0.803667i	$0.702879\pi$
$108$		0			0
$109$	−0.535242	−	7.14230i	−0.0512668	−	0.684109i	−0.962337	−	0.271858i	$-0.912362\pi$
$109$	−0.535242	−	7.14230i	−0.0512668	−	0.684109i	0.911071	−	0.412251i	$-0.135257\pi$
$110$	−0.371140	−	0.945649i	−0.0353868	−	0.0901641i
$111$		0			0
$112$	9.41497	+	2.52925i	0.889631	+	0.238992i
$113$	7.62512	−	3.67206i	0.717311	−	0.345439i	−0.0393687	−	0.999225i	$-0.512535\pi$
$113$	7.62512	−	3.67206i	0.717311	−	0.345439i	0.756679	+	0.653786i	$0.226820\pi$
$114$		0			0
$115$	−1.29981	−	0.195914i	−0.121207	−	0.0182691i
$116$	−6.75767	−	11.7046i	−0.627434	−	1.08675i
$117$		0			0
$118$	2.04936	−	2.56981i	0.188659	−	0.236571i
$119$	16.7546	−	5.85053i	1.53589	−	0.536317i
$120$		0			0
$121$	−2.70728	+	0.408056i	−0.246116	+	0.0370960i
$122$	1.43394	+	0.977642i	0.129823	+	0.0885115i
$123$		0			0
$124$	5.48102	−	0.826130i	0.492210	−	0.0741887i
$125$	6.36997	+	7.98769i	0.569747	+	0.714440i
$126$		0			0
$127$	4.69902	−	5.89238i	0.416970	−	0.522864i	−0.528342	−	0.849032i	$-0.677186\pi$
$127$	4.69902	−	5.89238i	0.416970	−	0.522864i	0.945312	+	0.326168i	$0.105757\pi$
$128$	−3.44386	+	5.96495i	−0.304397	+	0.527232i
$129$		0			0
$130$	0.303524	+	0.0457488i	0.0266208	+	0.00401244i
$131$	8.07194	+	7.48967i	0.705249	+	0.654375i	0.948932	−	0.315479i	$-0.102165\pi$
$131$	8.07194	+	7.48967i	0.705249	+	0.654375i	−0.243684	+	0.969855i	$0.578356\pi$
$132$		0			0
$133$	−0.502635	+	13.2050i	−0.0435839	+	1.14501i
$134$	−0.705161	−	0.339588i	−0.0609167	−	0.0293359i
$135$		0			0
$136$	0.455562	+	6.07905i	0.0390641	+	0.521274i
$137$	−5.92527	+	1.82770i	−0.506230	+	0.156151i	−0.537342	−	0.843365i	$-0.680571\pi$
$137$	−5.92527	+	1.82770i	−0.506230	+	0.156151i	0.0311117	+	0.999516i	$0.490095\pi$
$138$		0			0
$139$	−4.36141	−	19.1086i	−0.369930	−	1.62077i	−0.726961	−	0.686678i	$-0.759068\pi$
$139$	−4.36141	−	19.1086i	−0.369930	−	1.62077i	0.357031	−	0.934093i	$-0.383789\pi$
$140$	−1.14382	+	6.02393i	−0.0966704	+	0.509115i
$141$		0			0
$142$	−1.23256	−	0.380196i	−0.103434	−	0.0319053i
$143$	1.51652	−	3.86403i	0.126818	−	0.323127i
$144$		0			0
$145$	6.82703	−	4.65459i	0.566954	−	0.386543i
$146$	−0.326571			−0.0270272
$147$		0			0
$148$	−4.76145			−0.391389
$149$	−16.6449	+	11.3483i	−1.36361	+	0.929691i	−0.999998	−	0.00186111i	$-0.999408\pi$
$149$	−16.6449	+	11.3483i	−1.36361	+	0.929691i	−0.363608	+	0.931552i	$0.618455\pi$
$150$		0			0
$151$	−0.779366	+	1.98579i	−0.0634239	+	0.161601i	−0.959072	−	0.283161i	$-0.908617\pi$
$151$	−0.779366	+	1.98579i	−0.0634239	+	0.161601i	0.895648	+	0.444763i	$0.146712\pi$
$152$	−4.33760	−	1.33797i	−0.351826	−	0.108524i
$153$		0			0
$154$	−2.06903	−	0.904300i	−0.166727	−	0.0728706i
$155$	0.754066	+	3.30378i	0.0605680	+	0.265366i
$156$		0			0
$157$	−6.18985	+	1.90932i	−0.494004	+	0.152380i	−0.531740	−	0.846908i	$-0.678462\pi$
$157$	−6.18985	+	1.90932i	−0.494004	+	0.152380i	0.0377358	+	0.999288i	$0.487985\pi$
$158$	−0.288134	−	3.84489i	−0.0229227	−	0.305883i
$159$		0			0
$160$	−2.85922	−	1.37693i	−0.226041	−	0.108856i
$161$	−2.35196	+	1.73348i	−0.185361	+	0.136618i
$162$		0			0
$163$	2.49089	+	2.31121i	0.195101	+	0.181028i	0.771674	−	0.636018i	$-0.219420\pi$
$163$	2.49089	+	2.31121i	0.195101	+	0.181028i	−0.576573	+	0.817046i	$0.695610\pi$
$164$	8.39345	+	1.26511i	0.655419	+	0.0987884i
$165$		0			0
$166$	−1.55129	+	2.68692i	−0.120404	+	0.208546i
$167$	1.44643	−	1.81377i	0.111928	−	0.140354i	−0.722711	−	0.691150i	$-0.757104\pi$
$167$	1.44643	−	1.81377i	0.111928	−	0.140354i	0.834640	+	0.550796i	$0.185676\pi$
$168$		0			0
$169$	−7.32336	−	9.18320i	−0.563335	−	0.706400i
$170$	−1.81790	+	0.274004i	−0.139426	+	0.0210151i
$171$		0			0
$172$	−15.6553	−	10.6736i	−1.19370	−	0.813854i
$173$	1.84311	−	0.277804i	0.140129	−	0.0211211i	−0.0786031	−	0.996906i	$-0.525046\pi$
$173$	1.84311	−	0.277804i	0.140129	−	0.0211211i	0.218732	+	0.975785i	$0.429808\pi$
$174$		0			0
$175$	9.41985	+	1.06752i	0.712074	+	0.0806972i
$176$	−8.51511	+	10.6776i	−0.641850	+	0.804855i
$177$		0			0
$178$	0.708821	+	1.22771i	0.0531284	+	0.0920210i
$179$	−14.3861	−	2.16835i	−1.07526	−	0.162070i	−0.412545	−	0.910937i	$-0.635360\pi$
$179$	−14.3861	−	2.16835i	−1.07526	−	0.162070i	−0.662720	+	0.748867i	$0.730598\pi$
$180$		0			0
$181$	8.09337	−	3.89756i	0.601576	−	0.289704i	−0.108202	−	0.994129i	$-0.534509\pi$
$181$	8.09337	−	3.89756i	0.601576	−	0.289704i	0.709778	+	0.704425i	$0.248795\pi$
$182$	0.549218	−	0.404793i	0.0407107	−	0.0300053i
$183$		0			0
$184$	−0.366672	−	0.934265i	−0.0270314	−	0.0688750i
$185$	−0.217537	−	2.90283i	−0.0159937	−	0.213421i
$186$		0			0
$187$	−1.85790	+	24.7920i	−0.135863	+	1.81297i
$188$	−3.39486	−	14.8738i	−0.247595	−	1.08479i
$189$		0			0
$190$	0.304616	−	1.33461i	0.0220992	−	0.0968228i
$191$	−13.5189	−	4.17002i	−0.978191	−	0.301732i	−0.235876	−	0.971783i	$-0.575796\pi$
$191$	−13.5189	−	4.17002i	−0.978191	−	0.301732i	−0.742315	+	0.670051i	$0.766272\pi$
$192$		0			0
$193$	12.2377	−	11.3549i	0.880890	−	0.817347i	−0.103265	−	0.994654i	$-0.532929\pi$
$193$	12.2377	−	11.3549i	0.880890	−	0.817347i	0.984156	+	0.177307i	$0.0567386\pi$
$194$	0.559966	−	0.381779i	0.0402032	−	0.0274101i
$195$		0			0
$196$	7.66286	+	11.2706i	0.547347	+	0.805043i
$197$	26.2060			1.86710			0.933549	−	0.358450i	$-0.116695\pi$
$197$	26.2060			1.86710			0.933549	+	0.358450i	$0.116695\pi$
$198$		0			0
$199$	−3.17203	+	2.94321i	−0.224859	+	0.208639i	−0.784555	−	0.620059i	$-0.787108\pi$
$199$	−3.17203	+	2.94321i	−0.224859	+	0.208639i	0.559696	+	0.828698i	$0.310918\pi$
$200$	−1.18973	+	3.03138i	−0.0841266	+	0.214351i
$201$		0			0
$202$	0.0306650	−	0.134352i	0.00215758	−	0.00945299i
$203$	3.42611	−	18.0436i	0.240466	−	1.26641i
$204$		0			0
$205$	−0.387805	+	5.17490i	−0.0270855	+	0.361431i
$206$	0.698213	−	0.215370i	0.0486468	−	0.0150056i
$207$		0			0
$208$	−1.50762	−	3.84134i	−0.104534	−	0.266349i
$209$	−16.6791	−	8.03221i	−1.15371	−	0.555600i
$210$		0			0
$211$	−23.4337	+	11.2851i	−1.61325	+	0.776898i	−0.999916	−	0.0129291i	$-0.995884\pi$
$211$	−23.4337	+	11.2851i	−1.61325	+	0.776898i	−0.613329	+	0.789827i	$0.710170\pi$
$212$	5.75723	+	5.34193i	0.395408	+	0.366885i
$213$		0			0
$214$	−2.01477	−	3.48968i	−0.137727	−	0.238549i
$215$	5.79195	−	10.0320i	0.395008	−	0.684173i
$216$		0			0
$217$	6.37518	+	4.01153i	0.432775	+	0.272321i
$218$	1.02826	+	1.28940i	0.0696425	+	0.0873289i
$219$		0			0
$220$	−7.09720	−	4.83879i	−0.478493	−	0.326231i
$221$	−6.20675	−	4.23169i	−0.417511	−	0.284654i
$222$		0			0
$223$	−4.40502	−	5.52372i	−0.294982	−	0.369896i	0.612150	−	0.790741i	$-0.290305\pi$
$223$	−4.40502	−	5.52372i	−0.294982	−	0.369896i	−0.907132	+	0.420846i	$0.861733\pi$
$224$	−6.65951	+	2.32544i	−0.444957	+	0.155375i
$225$		0			0
$226$	−0.974374	+	1.68767i	−0.0648144	+	0.112262i
$227$	−8.67496	−	15.0255i	−0.575777	−	0.997275i	−0.995957	−	0.0898344i	$-0.971366\pi$
$227$	−8.67496	−	15.0255i	−0.575777	−	0.997275i	0.420180	−	0.907441i	$-0.361967\pi$
$228$		0			0
$229$	−21.4800	−	19.9306i	−1.41944	−	1.31705i	−0.879958	−	0.475052i	$-0.842429\pi$
$229$	−21.4800	−	19.9306i	−1.41944	−	1.31705i	−0.539483	−	0.841996i	$-0.681380\pi$
$230$	0.272700	−	0.131325i	0.0179813	−	0.00865934i
$231$		0			0
$232$	5.68407	+	2.73730i	0.373177	+	0.179713i
$233$	−10.2180	−	26.0349i	−0.669400	−	1.70560i	−0.707869	−	0.706344i	$-0.750343\pi$
$233$	−10.2180	−	26.0349i	−0.669400	−	1.70560i	0.0384684	−	0.999260i	$-0.487752\pi$
$234$		0			0
$235$	8.91279	−	2.74923i	0.581406	−	0.179340i
$236$	2.07695	−	27.7150i	0.135198	−	1.80409i
$237$		0			0
$238$	−2.42868	+	3.28630i	−0.157428	+	0.213019i
$239$	0.681307	−	2.98500i	0.0440701	−	0.193084i	−0.948101	−	0.317969i	$-0.896999\pi$
$239$	0.681307	−	2.98500i	0.0440701	−	0.193084i	0.992171	+	0.124885i	$0.0398563\pi$
$240$		0			0
$241$	−0.574566	+	1.46397i	−0.0370110	+	0.0943025i	−0.948184	−	0.317721i	$-0.897083\pi$
$241$	−0.574566	+	1.46397i	−0.0370110	+	0.0943025i	0.911173	+	0.412023i	$0.135178\pi$
$242$	0.462130	−	0.428794i	0.0297068	−	0.0275639i
$243$		0			0
$244$	14.6746			0.939447
$245$	−6.52107	+	5.18661i	−0.416616	+	0.331361i
$246$		0			0
$247$	4.62167	−	3.15100i	0.294070	−	0.200493i
$248$	−1.89669	+	1.75987i	−0.120440	+	0.111752i
$249$		0			0
$250$	−2.24797	−	0.693407i	−0.142174	−	0.0438549i
$251$	−2.42089	+	10.6066i	−0.152805	+	0.669484i	0.839257	+	0.543735i	$0.182990\pi$
$251$	−2.42089	+	10.6066i	−0.152805	+	0.669484i	−0.992062	+	0.125749i	$0.959867\pi$
$252$		0			0
$253$	−0.910806	−	3.99050i	−0.0572619	−	0.250881i
$254$	−0.129686	+	1.73054i	−0.00813720	+	0.108583i
$255$		0			0
$256$	0.891157	+	11.8917i	0.0556973	+	0.743229i
$257$	−5.36648	−	13.6736i	−0.334752	−	0.852934i	−0.994813	−	0.101722i	$-0.967565\pi$
$257$	−5.36648	−	13.6736i	−0.334752	−	0.852934i	0.660061	−	0.751212i	$-0.270530\pi$
$258$		0			0
$259$	−4.90160	−	4.22368i	−0.304571	−	0.262447i
$260$	2.33842	−	1.12612i	0.145023	−	0.0698393i
$261$		0			0
$262$	−2.50717	−	0.377895i	−0.154894	−	0.0233465i
$263$	5.71663	+	9.90149i	0.352502	+	0.610552i	0.986687	−	0.162630i	$-0.0519975\pi$
$263$	5.71663	+	9.90149i	0.352502	+	0.610552i	−0.634185	+	0.773181i	$0.718664\pi$
$264$		0			0
$265$	−2.99370	+	3.75397i	−0.183901	+	0.230605i
$266$	−1.61719	−	2.57744i	−0.0991563	−	0.158033i
$267$		0			0
$268$	−6.54400	+	0.986349i	−0.399738	+	0.0602509i
$269$	−12.0801	−	8.23610i	−0.736539	−	0.502164i	0.135999	−	0.990709i	$-0.456575\pi$
$269$	−12.0801	−	8.23610i	−0.736539	−	0.502164i	−0.872539	+	0.488545i	$0.837528\pi$
$270$		0			0
$271$	24.7952	−	3.73728i	1.50620	−	0.227024i	0.656516	−	0.754312i	$-0.272029\pi$
$271$	24.7952	−	3.73728i	1.50620	−	0.227024i	0.849686	+	0.527288i	$0.176791\pi$
$272$	15.4098	+	19.3233i	0.934359	+	1.17165i
$273$		0			0
$274$	0.890210	−	1.11629i	0.0537796	−	0.0674375i
$275$	−6.64042	+	11.5015i	−0.400432	+	0.693569i
$276$		0			0
$277$	−7.39918	−	1.11525i	−0.444574	−	0.0670087i	−0.0770592	−	0.997027i	$-0.524553\pi$
$277$	−7.39918	−	1.11525i	−0.444574	−	0.0670087i	−0.367514	+	0.930018i	$0.619791\pi$
$278$	3.30834	+	3.06969i	0.198421	+	0.184108i
$279$		0			0
$280$	−1.14286	−	2.62408i	−0.0682989	−	0.156819i
$281$	−0.115260	−	0.0555061i	−0.00687581	−	0.00331121i	0.430443	−	0.902618i	$-0.358357\pi$
$281$	−0.115260	−	0.0555061i	−0.00687581	−	0.00331121i	−0.437318	+	0.899307i	$0.644072\pi$
$282$		0			0
$283$	−0.866464	−	11.5622i	−0.0515059	−	0.687299i	−0.961873	−	0.273497i	$-0.911820\pi$
$283$	−0.866464	−	11.5622i	−0.0515059	−	0.687299i	0.910367	−	0.413802i	$-0.135799\pi$
$284$	−10.4220	+	3.21477i	−0.618433	+	0.190761i
$285$		0			0
$286$	0.212687	+	0.931841i	0.0125764	+	0.0551009i
$287$	7.51829	+	8.74783i	0.443791	+	0.516368i
$288$		0			0
$289$	26.7484	+	8.25079i	1.57344	+	0.485341i
$290$	−0.695095	+	1.77107i	−0.0408174	+	0.104001i
$291$		0			0
$292$	−2.28153	+	1.55552i	−0.133516	+	0.0910299i
$293$	13.0790			0.764085			0.382042	−	0.924145i	$-0.375221\pi$
$293$	13.0790			0.764085			0.382042	+	0.924145i	$0.375221\pi$
$294$		0			0
$295$	16.9914			0.989280
$296$	1.83640	−	1.25204i	0.106739	−	0.0727731i
$297$		0			0
$298$	1.69470	−	4.31804i	0.0981716	−	0.250137i
$299$	1.18182	+	0.364542i	0.0683462	+	0.0210820i
$300$		0			0
$301$	−6.64800	−	24.8749i	−0.383185	−	1.43377i
$302$	−0.109303	−	0.478888i	−0.00628969	−	0.0275569i
$303$		0			0
$304$	−17.5860	+	5.42457i	−1.00863	+	0.311120i
$305$	0.670443	+	8.94644i	0.0383895	+	0.512272i
$306$		0			0
$307$	−6.35216	−	3.05904i	−0.362537	−	0.174588i	0.243743	−	0.969840i	$-0.421625\pi$
$307$	−6.35216	−	3.05904i	−0.362537	−	0.174588i	−0.606280	+	0.795251i	$0.707339\pi$
$308$	−18.7623	+	3.53746i	−1.06908	+	0.201566i
$309$		0			0
$310$	−0.571995	−	0.530734i	−0.0324871	−	0.0301436i
$311$	24.3600	+	3.67167i	1.38133	+	0.208202i	0.797325	−	0.603550i	$-0.206248\pi$
$311$	24.3600	+	3.67167i	1.38133	+	0.208202i	0.584002	+	0.811752i	$0.301486\pi$
$312$		0			0
$313$	−13.2094	+	22.8793i	−0.746638	+	1.29321i	0.202788	+	0.979223i	$0.435000\pi$
$313$	−13.2094	+	22.8793i	−0.746638	+	1.29321i	−0.949426	+	0.313992i	$0.898333\pi$
$314$	0.929961	−	1.16613i	0.0524808	−	0.0658088i
$315$		0			0
$316$	−20.3269	−	25.4892i	−1.14348	−	1.43388i
$317$	16.8687	−	2.54255i	0.947443	−	0.142804i	0.342896	−	0.939373i	$-0.388592\pi$
$317$	16.8687	−	2.54255i	0.947443	−	0.142804i	0.604547	+	0.796569i	$0.293354\pi$
$318$		0			0
$319$	21.2584	+	14.4937i	1.19024	+	0.811494i
$320$	−7.95132	+	1.19847i	−0.444493	+	0.0669965i
$321$		0			0
$322$	0.222610	−	0.634868i	0.0124056	−	0.0353798i
$323$	−20.8881	+	26.1929i	−1.16225	+	1.45741i
$324$		0			0
$325$	−2.00644	−	3.47526i	−0.111297	−	0.192773i
$326$	−0.773678	−	0.116613i	−0.0428501	−	0.00645861i
$327$		0			0
$328$	−3.56986	+	1.71915i	−0.197112	+	0.0949243i
$329$	9.69918	−	18.3231i	0.534733	−	1.01018i
$330$		0			0
$331$	−4.35015	−	11.0840i	−0.239106	−	0.609232i	0.760069	−	0.649842i	$-0.225165\pi$
$331$	−4.35015	−	11.0840i	−0.239106	−	0.609232i	−0.999175	+	0.0406102i	$0.987070\pi$
$332$	1.96048	+	26.1608i	0.107595	+	1.43576i
$333$		0			0
$334$	−0.0399193	+	0.532686i	−0.00218429	+	0.0291473i
$335$	−0.900309	−	3.94451i	−0.0491891	−	0.215512i
$336$		0			0
$337$	−6.35533	+	27.8445i	−0.346197	+	1.51679i	0.439538	+	0.898224i	$0.355142\pi$
$337$	−6.35533	+	27.8445i	−0.346197	+	1.51679i	−0.785735	+	0.618563i	$0.787715\pi$
$338$	2.58442	+	0.797189i	0.140574	+	0.0433614i
$339$		0			0
$340$	−11.3953	+	10.5733i	−0.617995	+	0.573416i
$341$	−8.71852	+	5.94419i	−0.472134	+	0.321896i
$342$		0			0
$343$	−2.10926	+	18.3998i	−0.113890	+	0.993493i
$344$	8.84459			0.476869
$345$		0			0
$346$	−0.314617	+	0.291922i	−0.0169139	+	0.0156938i
$347$	−3.45745	+	8.80945i	−0.185606	+	0.472916i	−0.993144	−	0.116900i	$-0.962704\pi$
$347$	−3.45745	+	8.80945i	−0.185606	+	0.472916i	0.807538	+	0.589816i	$0.200800\pi$
$348$		0			0
$349$	3.65715	−	16.0230i	0.195763	−	0.857692i	−0.777662	−	0.628683i	$-0.783594\pi$
$349$	3.65715	−	16.0230i	0.195763	−	0.857692i	0.973424	−	0.229009i	$-0.0735486\pi$
$350$	−1.93059	+	1.01875i	−0.103195	+	0.0544547i
$351$		0			0
$352$	0.738468	−	9.85418i	0.0393605	−	0.525229i
$353$	−16.0177	+	4.94082i	−0.852538	+	0.262973i	−0.690072	−	0.723741i	$-0.742421\pi$
$353$	−16.0177	+	4.94082i	−0.852538	+	0.262973i	−0.162466	+	0.986714i	$0.551945\pi$
$354$		0			0
$355$	−2.43605	−	6.20695i	−0.129292	−	0.329431i
$356$	10.7999	+	5.20095i	0.572392	+	0.275650i
$357$		0			0
$358$	3.01820	−	1.45349i	0.159517	−	0.0768193i
$359$	17.2997	+	16.0518i	0.913045	+	0.847182i	0.988693	−	0.149952i	$-0.0479121\pi$
$359$	17.2997	+	16.0518i	0.913045	+	0.847182i	−0.0756480	+	0.997135i	$0.524103\pi$
$360$		0			0
$361$	−2.97310	−	5.14956i	−0.156479	−	0.271030i
$362$	−1.03421	+	1.79130i	−0.0543569	+	0.0941488i
$363$		0			0
$364$	1.90890	−	5.44404i	0.100054	−	0.285345i
$365$	−1.05256	−	1.31987i	−0.0550938	−	0.0690854i
$366$		0			0
$367$	20.6308	+	14.0659i	1.07692	+	0.734232i	0.965725	−	0.259566i	$-0.0835796\pi$
$367$	20.6308	+	14.0659i	1.07692	+	0.734232i	0.111196	+	0.993799i	$0.464532\pi$
$368$	−3.36204	−	2.29220i	−0.175258	−	0.119489i
$369$		0			0
$370$	0.417914	+	0.524047i	0.0217263	+	0.0272439i
$371$	1.18809	+	10.6062i	0.0616827	+	0.550645i
$372$		0			0
$373$	3.91904	−	6.78798i	0.202920	−	0.351468i	−0.746548	−	0.665332i	$-0.768290\pi$
$373$	3.91904	−	6.78798i	0.202920	−	0.351468i	0.949468	+	0.313864i	$0.101623\pi$
$374$	−2.86231	−	4.95766i	−0.148006	−	0.256354i
$375$		0			0
$376$	5.22044	+	4.84386i	0.269224	+	0.249803i
$377$	−7.00433	+	3.37311i	−0.360741	+	0.173724i
$378$		0			0
$379$	21.6880	+	10.4444i	1.11404	+	0.536492i	0.898045	−	0.439903i	$-0.144987\pi$
$379$	21.6880	+	10.4444i	1.11404	+	0.536492i	0.215992	+	0.976395i	$0.430702\pi$
$380$	−4.22886	−	10.7750i	−0.216936	−	0.552743i
$381$		0			0
$382$	3.11286	−	0.960189i	0.159268	−	0.0491275i
$383$	−2.22748	+	29.7236i	−0.113819	+	1.51880i	0.589406	+	0.807837i	$0.299362\pi$
$383$	−2.22748	+	29.7236i	−0.113819	+	1.51880i	−0.703225	+	0.710968i	$0.748257\pi$
$384$		0			0
$385$	−3.01382	−	11.2769i	−0.153599	−	0.574722i
$386$	−0.855373	+	3.74763i	−0.0435373	+	0.190750i
$387$		0			0
$388$	2.09362	−	5.33445i	0.106287	−	0.270816i
$389$	22.0653	−	20.4736i	1.11876	−	1.03805i	0.119781	−	0.992800i	$-0.461781\pi$
$389$	22.0653	−	20.4736i	1.11876	−	1.03805i	0.998976	−	0.0452536i	$-0.0144096\pi$
$390$		0			0
$391$	−7.40736			−0.374606
$392$	−5.91905	−	2.33188i	−0.298957	−	0.117778i
$393$		0			0
$394$	−4.98568	+	3.39918i	−0.251175	+	0.171248i
$395$	14.6109	−	13.5569i	0.735153	−	0.682122i
$396$		0			0
$397$	5.79883	+	1.78870i	0.291035	+	0.0897724i	0.436835	−	0.899542i	$-0.356099\pi$
$397$	5.79883	+	1.78870i	0.291035	+	0.0897724i	−0.145800	+	0.989314i	$0.546576\pi$
$398$	0.221714	−	0.971390i	0.0111135	−	0.0486914i
$399$		0			0
$400$	2.93791	+	12.8718i	0.146895	+	0.643591i
$401$	1.90623	−	25.4368i	0.0951924	−	1.27025i	−0.721188	−	0.692739i	$-0.756404\pi$
$401$	1.90623	−	25.4368i	0.0951924	−	1.27025i	0.816380	−	0.577515i	$-0.195977\pi$
$402$		0			0
$403$	−0.238267	−	3.17945i	−0.0118689	−	0.158380i
$404$	−0.425709	−	1.08469i	−0.0211798	−	0.0539653i
$405$		0			0
$406$	1.68862	+	3.87720i	0.0838050	+	0.192422i
$407$	8.16670	−	3.93288i	0.404808	−	0.194945i
$408$		0			0
$409$	4.23974	+	0.639038i	0.209641	+	0.0315984i	0.253023	−	0.967460i	$-0.418575\pi$
$409$	4.23974	+	0.639038i	0.209641	+	0.0315984i	−0.0433818	+	0.999059i	$0.513813\pi$
$410$	−0.597457	−	1.03483i	−0.0295063	−	0.0511064i
$411$		0			0
$412$	3.85209	−	4.83036i	0.189779	−	0.237975i
$413$	26.7229	−	26.6884i	1.31495	−	1.31325i
$414$		0			0
$415$	−15.8594	+	2.39043i	−0.778510	+	0.117341i
$416$	2.46702	+	1.68199i	0.120956	+	0.0824663i
$417$		0			0
$418$	4.21505	−	0.635316i	0.206165	−	0.0310743i
$419$	−4.11418	−	5.15902i	−0.200991	−	0.252035i	0.671113	−	0.741355i	$-0.265816\pi$
$419$	−4.11418	−	5.15902i	−0.200991	−	0.252035i	−0.872104	+	0.489320i	$0.837245\pi$
$420$		0			0
$421$	1.74087	−	2.18298i	0.0848448	−	0.106392i	−0.737597	−	0.675241i	$-0.764040\pi$
$421$	1.74087	−	2.18298i	0.0848448	−	0.106392i	0.822442	+	0.568849i	$0.192611\pi$
$422$	2.99448	−	5.18659i	0.145769	−	0.252479i
$423$		0			0
$424$	−3.62513	−	0.546400i	−0.176052	−	0.0265355i
$425$	17.6185	+	16.3476i	0.854622	+	0.792973i
$426$		0			0
$427$	15.1066	+	13.0173i	0.731059	+	0.629949i
$428$	−30.6978	−	14.7833i	−1.48383	−	0.714577i
$429$		0			0
$430$	0.199328	+	2.65985i	0.00961247	+	0.128269i
$431$	25.5749	−	7.88882i	1.23190	−	0.379991i	0.390601	−	0.920560i	$-0.372267\pi$
$431$	25.5749	−	7.88882i	1.23190	−	0.379991i	0.841300	+	0.540569i	$0.181791\pi$
$432$		0			0
$433$	4.70415	+	20.6102i	0.226067	+	0.990464i	0.952813	+	0.303558i	$0.0981745\pi$
$433$	4.70415	+	20.6102i	0.226067	+	0.990464i	−0.726746	+	0.686906i	$0.758968\pi$
$434$	−1.73321	+	0.0637314i	−0.0831969	+	0.00305921i
$435$		0			0
$436$	13.3254	+	4.11034i	0.638170	+	0.196849i
$437$	2.01510	−	5.13439i	0.0963952	−	0.245611i
$438$		0			0
$439$	12.4528	−	8.49015i	0.594338	−	0.405213i	−0.228455	−	0.973555i	$-0.573367\pi$
$439$	12.4528	−	8.49015i	0.594338	−	0.405213i	0.822792	+	0.568342i	$0.192415\pi$
$440$	4.00963			0.191152
$441$		0			0
$442$	1.72973			0.0822747
$443$	−6.25764	+	4.26638i	−0.297309	+	0.202702i	−0.702782	−	0.711405i	$-0.748059\pi$
$443$	−6.25764	+	4.26638i	−0.297309	+	0.202702i	0.405473	+	0.914107i	$0.367107\pi$
$444$		0			0
$445$	−2.67736	+	6.82180i	−0.126919	+	0.323384i
$446$	1.55454	+	0.479511i	0.0736095	+	0.0227055i
$447$		0			0
$448$	−10.6228	+	14.3740i	−0.501882	+	0.679107i
$449$	−3.06450	−	13.4265i	−0.144623	−	0.633634i	−0.994326	−	0.106373i	$-0.966076\pi$
$449$	−3.06450	−	13.4265i	−0.144623	−	0.633634i	0.849703	−	0.527261i	$-0.176781\pi$
$450$		0			0
$451$	−15.4412	+	4.76297i	−0.727097	+	0.224280i
$452$	1.23138	+	16.4317i	0.0579195	+	0.772882i
$453$		0			0
$454$	3.59937	+	1.73336i	0.168927	+	0.0813508i
$455$	3.40619	+	0.915044i	0.159685	+	0.0428979i
$456$		0			0
$457$	−6.97792	−	6.47456i	−0.326413	−	0.302867i	0.499894	−	0.866086i	$-0.333372\pi$
$457$	−6.97792	−	6.47456i	−0.326413	−	0.302867i	−0.826308	+	0.563219i	$0.809563\pi$
$458$	6.67177	+	1.00561i	0.311751	+	0.0469890i
$459$		0			0
$460$	1.27964	−	2.21640i	0.0596635	−	0.103340i
$461$	−3.84992	+	4.82765i	−0.179309	+	0.224846i	−0.863361	−	0.504587i	$-0.831645\pi$
$461$	−3.84992	+	4.82765i	−0.179309	+	0.224846i	0.684052	+	0.729433i	$0.260216\pi$
$462$		0			0
$463$	5.91446	+	7.41650i	0.274868	+	0.344674i	0.900035	−	0.435817i	$-0.143541\pi$
$463$	5.91446	+	7.41650i	0.274868	+	0.344674i	−0.625167	+	0.780491i	$0.714969\pi$
$464$	25.2923	−	3.81221i	1.17417	−	0.176977i
$465$		0			0
$466$	5.32096	+	3.62777i	0.246489	+	0.168053i
$467$	−30.6778	+	4.62394i	−1.41960	+	0.213970i	−0.813568	−	0.581470i	$-0.802478\pi$
$467$	−30.6778	+	4.62394i	−1.41960	+	0.213970i	−0.606032	+	0.795440i	$0.707240\pi$
$468$		0			0
$469$	−7.61157	−	4.78953i	−0.351470	−	0.221160i
$470$	−1.33905	+	1.67912i	−0.0617659	+	0.0774520i
$471$		0			0
$472$	6.48670	+	11.2353i	0.298574	+	0.517146i
$473$	35.6677	+	5.37605i	1.64000	+	0.247191i
$474$		0			0
$475$	−16.1242	+	7.76500i	−0.739829	+	0.356283i
$476$	−1.31425	+	34.5274i	−0.0602387	+	1.58256i
$477$		0			0
$478$	0.257567	+	0.656269i	0.0117808	+	0.0300170i
$479$	1.80930	+	24.1434i	0.0826688	+	1.10314i	0.872109	+	0.489311i	$0.162752\pi$
$479$	1.80930	+	24.1434i	0.0826688	+	1.10314i	−0.789440	+	0.613827i	$0.789629\pi$
$480$		0			0
$481$	−0.204675	+	2.73119i	−0.00933236	+	0.124532i
$482$	−0.0805807	−	0.353047i	−0.00367035	−	0.0160809i
$483$		0			0
$484$	1.18616	−	5.19690i	0.0539163	−	0.236223i
$485$	3.34782	+	1.03267i	0.152017	+	0.0468909i
$486$		0			0
$487$	−7.60487	+	7.05629i	−0.344610	+	0.319751i	−0.833421	−	0.552638i	$-0.813621\pi$
$487$	−7.60487	+	7.05629i	−0.344610	+	0.319751i	0.488811	+	0.872389i	$0.337431\pi$
$488$	−5.65972	+	3.85873i	−0.256204	+	0.174677i
$489$		0			0
$490$	0.567876	−	1.83260i	0.0256540	−	0.0827885i
$491$	18.0610			0.815083			0.407541	−	0.913187i	$-0.366386\pi$
$491$	18.0610			0.815083			0.407541	+	0.913187i	$0.366386\pi$
$492$		0			0
$493$	34.1325	−	31.6703i	1.53725	−	1.42636i
$494$	−0.470555	+	1.19895i	−0.0211713	+	0.0539435i
$495$		0			0
$496$	−2.33426	+	10.2271i	−0.104812	+	0.459209i
$497$	−13.5805	−	5.93555i	−0.609168	−	0.266246i
$498$		0			0
$499$	1.33757	−	17.8487i	0.0598780	−	0.799016i	−0.883740	−	0.467979i	$-0.844982\pi$
$499$	1.33757	−	17.8487i	0.0598780	−	0.799016i	0.943618	−	0.331037i	$-0.107399\pi$
$500$	−19.0079	+	5.86315i	−0.850057	+	0.262208i
$501$		0			0
$502$	−0.915212	−	2.33192i	−0.0408479	−	0.104079i
$503$	−24.1448	−	11.6275i	−1.07656	−	0.518445i	−0.190346	−	0.981717i	$-0.560961\pi$
$503$	−24.1448	−	11.6275i	−1.07656	−	0.518445i	−0.886216	+	0.463273i	$0.846675\pi$
$504$		0			0
$505$	0.641836	−	0.309092i	0.0285613	−	0.0137544i
$506$	0.690890	+	0.641052i	0.0307138	+	0.0284982i
$507$		0			0
$508$	7.33684	+	12.7078i	0.325520	+	0.563817i
$509$	3.91971	−	6.78913i	0.173738	−	0.300923i	−0.765986	−	0.642857i	$-0.777749\pi$
$509$	3.91971	−	6.78913i	0.173738	−	0.300923i	0.939724	+	0.341934i	$0.111082\pi$
$510$		0			0
$511$	−3.72852	−	0.422542i	−0.164940	−	0.0186922i
$512$	−10.3009	−	12.9169i	−0.455238	−	0.570851i
$513$		0			0
$514$	2.79458	+	1.90531i	0.123263	+	0.0840396i
$515$	3.12084	+	2.12775i	0.137521	+	0.0937600i
$516$		0			0
$517$	18.1083	+	22.7071i	0.796402	+	0.998657i
$518$	1.48038	+	0.167767i	0.0650443	+	0.00737128i
$519$		0			0
$520$	−0.605767	+	1.04922i	−0.0265646	+	0.0460113i
$521$	−13.6714	−	23.6795i	−0.598953	−	1.03742i	−0.992976	−	0.118316i	$-0.962250\pi$
$521$	−13.6714	−	23.6795i	−0.598953	−	1.03742i	0.394023	−	0.919100i	$-0.371083\pi$
$522$		0			0
$523$	−22.1090	−	20.5142i	−0.966760	−	0.897023i	0.0279637	−	0.999609i	$-0.491098\pi$
$523$	−22.1090	−	20.5142i	−0.966760	−	0.897023i	−0.994724	+	0.102586i	$0.967288\pi$
$524$	−19.3159	+	9.30204i	−0.843818	+	0.406362i
$525$		0			0
$526$	−2.37191	−	1.14225i	−0.103420	−	0.0498046i
$527$	6.97660	+	17.7761i	0.303905	+	0.774339i
$528$		0			0
$529$	−20.8128	+	6.41991i	−0.904906	+	0.279126i
$530$	0.0826214	−	1.10251i	0.00358885	−	0.0478898i
$531$		0			0
$532$	−23.5750	−	10.3038i	−1.02211	−	0.446727i
$533$	1.08647	−	4.76015i	0.0470603	−	0.206185i
$534$		0			0
$535$	7.61018	−	19.3904i	0.329017	−	0.838321i
$536$	2.26453	−	2.10118i	0.0978129	−	0.0907571i
$537$		0			0
$538$	3.36655			0.145142
$539$	−22.4525	−	13.0016i	−0.967096	−	0.560020i
$540$		0			0
$541$	−16.2272	+	11.0635i	−0.697664	+	0.475659i	−0.859485	−	0.511161i	$-0.829216\pi$
$541$	−16.2272	+	11.0635i	−0.697664	+	0.475659i	0.161821	+	0.986820i	$0.448263\pi$
$542$	−4.23253	+	3.92721i	−0.181803	+	0.168688i
$543$		0			0
$544$	−17.0887	−	5.27116i	−0.732671	−	0.225999i
$545$	−1.89708	+	8.31166i	−0.0812620	+	0.356032i
$546$		0			0
$547$	−8.66645	−	37.9702i	−0.370551	−	1.62349i	−0.725234	−	0.688503i	$-0.758268\pi$
$547$	−8.66645	−	37.9702i	−0.370551	−	1.62349i	0.354683	−	0.934987i	$-0.384589\pi$
$548$	0.902197	−	12.0390i	0.0385400	−	0.514280i
$549$		0			0
$550$	−0.228528	−	3.04950i	−0.00974448	−	0.130031i
$551$	12.6668	+	32.2744i	0.539623	+	1.37494i
$552$		0			0
$553$	1.68512	−	44.2706i	0.0716586	−	1.88258i
$554$	1.55235	−	0.747573i	0.0659531	−	0.0317613i
$555$		0			0
$556$	37.7346	+	5.68758i	1.60030	+	0.241207i
$557$	15.7975	+	27.3620i	0.669360	+	1.15937i	0.978083	+	0.208214i	$0.0667651\pi$
$557$	15.7975	+	27.3620i	0.669360	+	1.15937i	−0.308723	+	0.951152i	$0.599902\pi$
$558$		0			0
$559$	−6.79539	+	8.52115i	−0.287414	+	0.360406i
$560$	−9.82147	−	6.18009i	−0.415033	−	0.261157i
$561$		0			0
$562$	0.0291278	−	0.00439031i	0.00122868	−	0.000185194i
$563$	10.1391	+	6.91273i	0.427313	+	0.291337i	0.757817	−	0.652468i	$-0.226266\pi$
$563$	10.1391	+	6.91273i	0.427313	+	0.291337i	−0.330504	+	0.943805i	$0.607219\pi$
$564$		0			0
$565$	−9.96138	+	1.50144i	−0.419078	+	0.0631659i
$566$	1.66457	+	2.08731i	0.0699672	+	0.0877362i
$567$		0			0
$568$	3.17424	−	3.98037i	0.133188	−	0.167013i
$569$	15.6049	−	27.0285i	0.654191	−	1.13309i	−0.327905	−	0.944711i	$-0.606343\pi$
$569$	15.6049	−	27.0285i	0.654191	−	1.13309i	0.982096	−	0.188381i	$-0.0603240\pi$
$570$		0			0
$571$	28.8905	+	4.35454i	1.20903	+	0.182232i	0.722461	−	0.691412i	$-0.243011\pi$
$571$	28.8905	+	4.35454i	1.20903	+	0.182232i	0.486567	+	0.873643i	$0.338249\pi$
$572$	5.92443	+	5.49707i	0.247713	+	0.229844i
$573$		0			0
$574$	−2.56504	−	0.689075i	−0.107063	−	0.0287614i
$575$	−3.56510	−	1.71686i	−0.148675	−	0.0715980i
$576$		0			0
$577$	2.03753	+	27.1890i	0.0848236	+	1.13189i	0.863460	+	0.504417i	$0.168293\pi$
$577$	2.03753	+	27.1890i	0.0848236	+	1.13189i	−0.778637	+	0.627475i	$0.784088\pi$
$578$	−6.15909	+	1.89983i	−0.256185	+	0.0790225i
$579$		0			0
$580$	3.57980	+	15.6841i	0.148643	+	0.651248i
$581$	−21.1880	+	28.6699i	−0.879025	+	1.18943i
$582$		0			0
$583$	−14.2870	−	4.40695i	−0.591707	−	0.182517i
$584$	0.470913	−	1.19987i	0.0194865	−	0.0496509i
$585$		0			0
$586$	−2.48828	+	1.69648i	−0.102790	+	0.0700811i
$587$	−5.13774			−0.212057			−0.106029	−	0.994363i	$-0.533813\pi$
$587$	−5.13774			−0.212057			−0.106029	+	0.994363i	$0.533813\pi$
$588$		0			0
$589$	−14.2194			−0.585898
$590$	−3.23262	+	2.20396i	−0.133085	+	0.0907358i
$591$		0			0
$592$	3.29213	−	8.38822i	0.135306	−	0.344754i
$593$	7.13101	+	2.19963i	0.292836	+	0.0903278i	0.437692	−	0.899125i	$-0.355796\pi$
$593$	7.13101	+	2.19963i	0.292836	+	0.0903278i	−0.144857	+	0.989453i	$0.546272\pi$
$594$		0			0
$595$	−21.1098	+	0.776221i	−0.865417	+	0.0318220i
$596$	−8.72788	−	38.2394i	−0.357508	−	1.56635i
$597$		0			0
$598$	−0.272125	+	0.0839396i	−0.0111280	+	0.00343254i
$599$	−1.83455	−	24.4803i	−0.0749576	−	1.00024i	−0.900204	−	0.435467i	$-0.856583\pi$
$599$	−1.83455	−	24.4803i	−0.0749576	−	1.00024i	0.825247	−	0.564772i	$-0.191036\pi$
$600$		0			0
$601$	0.240286	+	0.115716i	0.00980149	+	0.00472015i	0.438778	−	0.898595i	$-0.355411\pi$
$601$	0.240286	+	0.115716i	0.00980149	+	0.00472015i	−0.428977	+	0.903316i	$0.641126\pi$
$602$	4.49131	+	3.87014i	0.183052	+	0.157735i
$603$		0			0
$604$	−3.04466	−	2.82503i	−0.123886	−	0.114949i
$605$	3.22250	+	0.485714i	0.131013	+	0.0197471i
$606$		0			0
$607$	13.1877	−	22.8417i	0.535271	−	0.927117i	−0.463879	−	0.885899i	$-0.653543\pi$
$607$	13.1877	−	22.8417i	0.535271	−	0.927117i	0.999150	−	0.0412183i	$-0.0131239\pi$
$608$	8.30249	−	10.4110i	0.336711	−	0.422222i
$609$		0			0
$610$	−1.28800	−	1.61510i	−0.0521494	−	0.0653933i
$611$	−8.67764	+	1.30794i	−0.351060	+	0.0529138i
$612$		0			0
$613$	−15.7701	−	10.7519i	−0.636950	−	0.434265i	0.201317	−	0.979526i	$-0.435478\pi$
$613$	−15.7701	−	10.7519i	−0.636950	−	0.434265i	−0.838266	+	0.545261i	$0.816430\pi$
$614$	1.60529	−	0.241958i	0.0647841	−	0.00976462i
$615$		0			0
$616$	6.30605	−	6.29791i	0.254078	−	0.253750i
$617$	−21.6921	+	27.2011i	−0.873293	+	1.09507i	0.121443	+	0.992598i	$0.461248\pi$
$617$	−21.6921	+	27.2011i	−0.873293	+	1.09507i	−0.994735	+	0.102476i	$0.967323\pi$
$618$		0			0
$619$	−2.80634	−	4.86072i	−0.112796	−	0.195369i	0.804100	−	0.594494i	$-0.202647\pi$
$619$	−2.80634	−	4.86072i	−0.112796	−	0.195369i	−0.916897	+	0.399125i	$0.869314\pi$
$620$	−6.52412	−	0.983353i	−0.262015	−	0.0394924i
$621$		0			0
$622$	−5.11074	+	2.46120i	−0.204922	+	0.0986852i
$623$	6.50423	+	14.9342i	0.260587	+	0.598325i
$624$		0			0
$625$	2.10247	+	5.35700i	0.0840987	+	0.214280i
$626$	−0.454597	−	6.06618i	−0.0181694	−	0.242453i
$627$		0			0
$628$	0.942484	−	12.5766i	0.0376092	−	0.501860i
$629$	−3.65020	−	15.9926i	−0.145543	−	0.637665i
$630$		0			0
$631$	−0.166820	+	0.730886i	−0.00664100	+	0.0290961i	−0.978140	−	0.207948i	$-0.933321\pi$
$631$	−0.166820	+	0.730886i	−0.00664100	+	0.0290961i	0.971499	+	0.237044i	$0.0761786\pi$
$632$	14.5421	+	4.48566i	0.578455	+	0.178430i
$633$		0			0
$634$	−2.87948	+	2.67177i	−0.114359	+	0.106110i
$635$	−7.41215	+	5.05352i	−0.294142	+	0.200543i
$636$		0			0
$637$	6.79427	−	3.91098i	0.269199	−	0.154959i
$638$	−5.92440			−0.234549
$639$		0			0
$640$	6.00996	−	5.57642i	0.237564	−	0.220428i
$641$	8.65988	−	22.0650i	0.342045	−	0.871516i	−0.651560	−	0.758597i	$-0.725885\pi$
$641$	8.65988	−	22.0650i	0.342045	−	0.871516i	0.993604	−	0.112918i	$-0.0360198\pi$
$642$		0			0
$643$	−6.65591	+	29.1614i	−0.262483	+	1.15001i	0.656065	+	0.754705i	$0.272220\pi$
$643$	−6.65591	+	29.1614i	−0.262483	+	1.15001i	−0.918548	+	0.395310i	$0.870637\pi$
$644$	−1.46877	−	5.49573i	−0.0578777	−	0.216562i
$645$		0			0
$646$	0.576480	−	7.69259i	0.0226813	−	0.302661i
$647$	17.6525	−	5.44507i	0.693991	−	0.214068i	0.0723605	−	0.997379i	$-0.476947\pi$
$647$	17.6525	−	5.44507i	0.693991	−	0.214068i	0.621630	+	0.783311i	$0.286471\pi$
$648$		0			0
$649$	19.3298	+	49.2516i	0.758761	+	1.93329i
$650$	0.832502	+	0.400912i	0.0326534	+	0.0157251i
$651$		0			0
$652$	−5.96061	+	2.87048i	−0.233436	+	0.112417i
$653$	−21.9331	−	20.3509i	−0.858307	−	0.796392i	0.122276	−	0.992496i	$-0.460981\pi$
$653$	−21.9331	−	20.3509i	−0.858307	−	0.796392i	−0.980583	+	0.196104i	$0.937171\pi$
$654$		0			0
$655$	−6.55351	−	11.3510i	−0.256067	−	0.443521i
$656$	−8.03209	+	13.9120i	−0.313600	+	0.543172i
$657$		0			0
$658$	0.531423	+	4.74405i	0.0207170	+	0.184942i
$659$	−23.7799	−	29.8190i	−0.926333	−	1.16159i	−0.986560	−	0.163400i	$-0.947754\pi$
$659$	−23.7799	−	29.8190i	−0.926333	−	1.16159i	0.0602266	−	0.998185i	$-0.480818\pi$
$660$		0			0
$661$	−40.2243	−	27.4244i	−1.56454	−	1.06669i	−0.963584	−	0.267406i	$-0.913833\pi$
$661$	−40.2243	−	27.4244i	−1.56454	−	1.06669i	−0.600958	−	0.799280i	$-0.705214\pi$
$662$	2.26532	+	1.54447i	0.0880443	+	0.0600276i
$663$		0			0
$664$	−7.63517	−	9.57420i	−0.296302	−	0.371551i
$665$	5.20468	−	14.8434i	0.201829	−	0.575601i
$666$		0			0
$667$	−3.83293	+	6.63884i	−0.148412	+	0.257057i
$668$	2.25840	+	3.91166i	0.0873799	+	0.151346i
$669$		0			0
$670$	0.682927	+	0.633663i	0.0263838	+	0.0244806i
$671$	−25.1695	+	12.1210i	−0.971658	+	0.467926i
$672$		0			0
$673$	9.84987	+	4.74345i	0.379684	+	0.182846i	0.613985	−	0.789318i	$-0.289566\pi$
$673$	9.84987	+	4.74345i	0.379684	+	0.182846i	−0.234300	+	0.972164i	$0.575280\pi$
$674$	−2.40262	−	6.12177i	−0.0925453	−	0.235802i
$675$		0			0
$676$	21.8528	−	6.74068i	0.840491	−	0.259257i
$677$	−0.480262	+	6.40865i	−0.0184580	+	0.246304i	0.980341	+	0.197310i	$0.0632206\pi$
$677$	−0.480262	+	6.40865i	−0.0184580	+	0.246304i	−0.998799	+	0.0489941i	$0.984398\pi$
$678$		0			0
$679$	6.88721	−	3.63431i	0.264307	−	0.139472i
$680$	1.61467	−	7.07432i	0.0619197	−	0.271288i
$681$		0			0
$682$	0.887676	−	2.26176i	0.0339909	−	0.0866073i
$683$	−24.0087	+	22.2769i	−0.918669	+	0.852400i	−0.989418	−	0.145094i	$-0.953652\pi$
$683$	−24.0087	+	22.2769i	−0.918669	+	0.852400i	0.0707487	+	0.997494i	$0.477461\pi$
$684$		0			0
$685$	7.38083			0.282007
$686$	−1.98535	−	3.77414i	−0.0758010	−	0.144098i
$687$		0			0
$688$	29.6279	−	20.2000i	1.12955	−	0.770116i
$689$	3.31164	−	3.07275i	0.126163	−	0.117063i
$690$		0			0
$691$	30.4917	+	9.40545i	1.15996	+	0.357800i	0.814235	−	0.580536i	$-0.197157\pi$
$691$	30.4917	+	9.40545i	1.15996	+	0.357800i	0.345725	+	0.938336i	$0.387633\pi$
$692$	−0.807535	+	3.53804i	−0.0306979	+	0.134496i
$693$		0			0
$694$	−0.484895	−	2.12446i	−0.0184064	−	0.0806435i
$695$	−1.74346	+	23.2649i	−0.0661333	+	0.882488i
$696$		0			0
$697$	2.18535	+	29.1614i	0.0827759	+	1.10457i
$698$	1.38258	+	3.52275i	0.0523313	+	0.133338i
$699$		0			0
$700$	−8.63522	+	16.3131i	−0.326381	+	0.616578i
$701$	7.81264	−	3.76237i	0.295079	−	0.142103i	−0.280487	−	0.959858i	$-0.590496\pi$
$701$	7.81264	−	3.76237i	0.295079	−	0.142103i	0.575566	+	0.817755i	$0.304782\pi$
$702$		0			0
$703$	12.0782	+	1.82049i	0.455537	+	0.0686612i
$704$	−12.5195	−	21.6844i	−0.471846	−	0.817260i
$705$		0			0
$706$	2.40650	−	3.01765i	0.0905698	−	0.113571i
$707$	0.523943	−	1.49425i	0.0197049	−	0.0561969i
$708$		0			0
$709$	−11.0565	+	1.66651i	−0.415237	+	0.0625869i	−0.353339	−	0.935496i	$-0.614954\pi$
$709$	−11.0565	+	1.66651i	−0.415237	+	0.0625869i	−0.0618986	+	0.998082i	$0.519716\pi$
$710$	1.26856	+	0.864891i	0.0476083	+	0.0324588i
$711$		0			0
$712$	−5.53291	+	0.833952i	−0.207354	+	0.0312537i
$713$	−1.96021	−	2.45803i	−0.0734105	−	0.0920538i
$714$		0			0
$715$	−3.08064	+	3.86300i	−0.115209	+	0.144468i
$716$	14.1629	−	24.5308i	0.529291	−	0.916760i
$717$		0			0
$718$	−5.37336	−	0.809903i	−0.200532	−	0.0302253i
$719$	1.28925	+	1.19625i	0.0480811	+	0.0446127i	0.703847	−	0.710351i	$-0.251464\pi$
$719$	1.28925	+	1.19625i	0.0480811	+	0.0446127i	−0.655766	+	0.754964i	$0.727654\pi$
$720$		0			0
$721$	8.25029	−	1.55552i	0.307257	−	0.0579306i
$722$	1.23358	+	0.594063i	0.0459092	+	0.0221087i
$723$		0			0
$724$	1.30700	+	17.4408i	0.0485744	+	0.648180i
$725$	23.7682	−	7.33150i	0.882727	−	0.272285i
$726$		0			0
$727$	−10.6997	−	46.8784i	−0.396830	−	1.73862i	−0.639754	−	0.768580i	$-0.720964\pi$
$727$	−10.6997	−	46.8784i	−0.396830	−	1.73862i	0.242924	−	0.970045i	$-0.421893\pi$
$728$	0.695299	+	2.60161i	0.0257695	+	0.0964221i
$729$		0			0
$730$	0.371452	+	0.114578i	0.0137480	+	0.00424071i
$731$	23.8485	−	60.7649i	0.882067	−	2.24747i
$732$		0			0
$733$	−24.5597	+	16.7445i	−0.907135	+	0.618474i	−0.924420	−	0.381377i	$-0.875450\pi$
$733$	−24.5597	+	16.7445i	−0.907135	+	0.618474i	0.0172850	+	0.999851i	$0.494498\pi$
$734$	−5.74950			−0.212218
$735$		0			0
$736$	2.94424			0.108526
$737$	10.4094	−	7.09699i	0.383434	−	0.261421i
$738$		0			0
$739$	−8.03459	+	20.4718i	−0.295557	+	0.753067i	0.703543	+	0.710653i	$0.251600\pi$
$739$	−8.03459	+	20.4718i	−0.295557	+	0.753067i	−0.999100	+	0.0424145i	$0.986495\pi$
$740$	5.41581	+	1.67056i	0.199089	+	0.0614109i
$741$		0			0
$742$	−1.60176	−	1.86372i	−0.0588026	−	0.0684191i
$743$	−11.3345	−	49.6595i	−0.415821	−	1.82183i	−0.555356	−	0.831613i	$-0.687418\pi$
$743$	−11.3345	−	49.6595i	−0.415821	−	1.82183i	0.139535	−	0.990217i	$-0.455439\pi$
$744$		0			0
$745$	22.9140	−	7.06804i	0.839504	−	0.258953i
$746$	0.134873	+	1.79975i	0.00493804	+	0.0658936i
$747$		0			0
$748$	−43.6112	−	21.0021i	−1.59459	−	0.767912i
$749$	−18.4878	−	42.4492i	−0.675528	−	1.55106i
$750$		0			0
$751$	−14.9242	−	13.8476i	−0.544592	−	0.505308i	0.359211	−	0.933256i	$-0.383046\pi$
$751$	−14.9242	−	13.8476i	−0.544592	−	0.505308i	−0.903803	+	0.427949i	$0.859236\pi$
$752$	28.5504	+	4.30328i	1.04113	+	0.156924i
$753$		0			0
$754$	0.895046	−	1.55027i	0.0325957	−	0.0564573i
$755$	1.58319	−	1.98526i	0.0576182	−	0.0722509i
$756$		0			0
$757$	−7.20271	−	9.03191i	−0.261787	−	0.328270i	0.633515	−	0.773731i	$-0.281612\pi$
$757$	−7.20271	−	9.03191i	−0.261787	−	0.328270i	−0.895302	+	0.445460i	$0.853040\pi$
$758$	−5.48088	+	0.826110i	−0.199075	+	0.0300057i
$759$		0			0
$760$	4.46429	+	3.04370i	0.161937	+	0.110407i
$761$	−25.3941	+	3.82754i	−0.920535	+	0.138748i	−0.592180	−	0.805806i	$-0.701732\pi$
$761$	−25.3941	+	3.82754i	−0.920535	+	0.138748i	−0.328355	+	0.944554i	$0.606494\pi$
$762$		0			0
$763$	10.0715	+	16.0517i	0.364613	+	0.581111i
$764$	17.1738	−	21.5353i	0.621328	−	0.779120i
$765$		0			0
$766$	−3.43168	−	5.94384i	−0.123991	−	0.214760i
$767$	−15.8082	−	2.38270i	−0.570801	−	0.0860344i
$768$		0			0
$769$	−33.0825	+	15.9317i	−1.19299	+	0.574512i	−0.921668	−	0.387978i	$-0.873174\pi$
$769$	−33.0825	+	15.9317i	−1.19299	+	0.574512i	−0.271317	+	0.962490i	$0.587459\pi$
$770$	2.03610	+	1.75450i	0.0733760	+	0.0632277i
$771$		0			0
$772$	11.8748	+	30.2565i	0.427383	+	1.08895i
$773$	3.15843	+	42.1463i	0.113601	+	1.51590i	0.704819	+	0.709387i	$0.251028\pi$
$773$	3.15843	+	42.1463i	0.113601	+	1.51590i	−0.591219	+	0.806511i	$0.701353\pi$
$774$		0			0
$775$	−0.762323	+	10.1725i	−0.0273835	+	0.365407i
$776$	0.595240	+	2.60792i	0.0213679	+	0.0936188i
$777$		0			0
$778$	−1.54229	+	6.75720i	−0.0552937	+	0.242257i
$779$	−20.8077	−	6.41831i	−0.745512	−	0.229960i
$780$		0			0
$781$	15.2202	−	14.1223i	0.544622	−	0.505336i
$782$	1.40925	−	0.960810i	0.0503947	−	0.0343585i
$783$		0			0
$784$	−25.1536	+	5.70696i	−0.898341	+	0.203820i
$785$	7.71041			0.275196
$786$		0			0
$787$	−31.4022	+	29.1370i	−1.11937	+	1.03862i	−0.120422	+	0.992723i	$0.538425\pi$
$787$	−31.4022	+	29.1370i	−1.11937	+	1.03862i	−0.998946	+	0.0458987i	$0.985385\pi$
$788$	−18.6406	+	47.4955i	−0.664044	+	1.69196i
$789$		0			0
$790$	−1.02125	+	4.47438i	−0.0363344	+	0.159191i
$791$	−13.3082	+	18.0077i	−0.473186	+	0.640279i
$792$		0			0
$793$	0.630800	−	8.41744i	0.0224004	−	0.298912i
$794$	−1.33524	+	0.411867i	−0.0473859	+	0.0146166i
$795$		0			0
$796$	−3.07796	−	7.84250i	−0.109095	−	0.277970i
$797$	−43.8793	−	21.1312i	−1.55429	−	0.748504i	−0.557620	−	0.830097i	$-0.688285\pi$
$797$	−43.8793	−	21.1312i	−1.55429	−	0.748504i	−0.996666	+	0.0815923i	$0.973999\pi$
$798$		0			0
$799$	47.3551	−	22.8050i	1.67530	−	0.806783i
$800$	−7.00289	−	6.49774i	−0.247590	−	0.229730i
$801$		0			0
$802$	2.93675	+	5.08661i	0.103700	+	0.179614i
$803$	2.62838	−	4.55249i	0.0927535	−	0.160654i
$804$		0			0
$805$	3.28338	−	1.14653i	0.115724	−	0.0404097i
$806$	0.457738	+	0.573985i	0.0161231	+	0.0202178i
$807$		0			0
$808$	0.449410	+	0.306403i	0.0158102	+	0.0107792i
$809$	14.1052	+	9.61676i	0.495912	+	0.338107i	0.785311	−	0.619101i	$-0.212503\pi$
$809$	14.1052	+	9.61676i	0.495912	+	0.338107i	−0.289399	+	0.957209i	$0.593455\pi$
$810$		0			0
$811$	−0.102516	−	0.128551i	−0.00359983	−	0.00451405i	0.780028	−	0.625744i	$-0.215205\pi$
$811$	−0.102516	−	0.128551i	−0.00359983	−	0.00451405i	−0.783628	+	0.621230i	$0.786633\pi$
$812$	30.2651	+	19.0441i	1.06210	+	0.668316i
$813$		0			0
$814$	−1.04358	+	1.80753i	−0.0365775	+	0.0633540i
$815$	−2.02232	−	3.50276i	−0.0708388	−	0.122696i
$816$		0			0
$817$	35.6312	+	33.0610i	1.24658	+	1.15666i
$818$	−0.889499	+	0.428360i	−0.0311006	+	0.0149773i
$819$		0			0
$820$	−9.10310	−	4.38382i	−0.317894	−	0.153090i
$821$	6.70480	+	17.0836i	0.233999	+	0.596220i	0.998848	−	0.0479898i	$-0.0152815\pi$
$821$	6.70480	+	17.0836i	0.233999	+	0.596220i	−0.764849	+	0.644210i	$0.777186\pi$
$822$		0			0
$823$	−7.00189	+	2.15980i	−0.244070	+	0.0752858i	−0.414377	−	0.910105i	$-0.636000\pi$
$823$	−7.00189	+	2.15980i	−0.244070	+	0.0752858i	0.170306	+	0.985391i	$0.445524\pi$
$824$	−0.215519	+	2.87589i	−0.00750794	+	0.100187i
$825$		0			0
$826$	−1.62227	+	8.54371i	−0.0564461	+	0.297274i
$827$	−3.21753	+	14.0969i	−0.111885	+	0.490198i	0.887674	+	0.460473i	$0.152320\pi$
$827$	−3.21753	+	14.0969i	−0.111885	+	0.490198i	−0.999558	+	0.0297249i	$0.990537\pi$
$828$		0			0
$829$	0.0303865	−	0.0774234i	0.00105537	−	0.00268903i	−0.930345	−	0.366685i	$-0.880493\pi$
$829$	0.0303865	−	0.0774234i	0.00105537	−	0.00268903i	0.931400	+	0.363996i	$0.118588\pi$
$830$	2.70720	−	2.51191i	0.0939681	−	0.0871897i
$831$		0			0
$832$	7.56567			0.262292
$833$	−31.9808	+	34.3779i	−1.10807	+	1.19112i
$834$		0			0
$835$	−2.28157	+	1.55555i	−0.0789572	+	0.0538321i
$836$	26.4215	−	24.5156i	0.913808	−	0.847890i
$837$		0			0
$838$	1.45190	+	0.447852i	0.0501551	+	0.0154708i
$839$	−9.68047	+	42.4129i	−0.334207	+	1.46426i	0.476692	+	0.879070i	$0.341836\pi$
$839$	−9.68047	+	42.4129i	−0.334207	+	1.46426i	−0.810899	+	0.585186i	$0.801021\pi$
$840$		0			0
$841$	−4.26955	−	18.7061i	−0.147226	−	0.645038i
$842$	−0.0480454	+	0.641121i	−0.00165575	+	0.0220945i
$843$		0			0
$844$	−3.78433	−	50.4984i	−0.130262	−	1.73823i
$845$	5.10787	+	13.0147i	0.175716	+	0.447718i
$846$		0			0
$847$	5.83103	−	4.29768i	0.200357	−	0.147670i
$848$	−13.3915	+	6.44900i	−0.459865	+	0.221459i
$849$		0			0
$850$	−5.47236	−	0.824825i	−0.187700	−	0.0282913i
$851$	1.35034	+	2.33886i	0.0462891	+	0.0801750i
$852$		0			0
$853$	15.0264	−	18.8425i	0.514493	−	0.645154i	−0.454936	−	0.890524i	$-0.650338\pi$
$853$	15.0264	−	18.8425i	0.514493	−	0.645154i	0.969430	+	0.245370i	$0.0789094\pi$
$854$	−4.56250	−	0.517054i	−0.156125	−	0.0176932i
$855$		0			0
$856$	15.7268	−	2.37044i	0.537533	−	0.0810200i
$857$	26.9888	+	18.4006i	0.921918	+	0.628553i	0.928463	−	0.371425i	$-0.121131\pi$
$857$	26.9888	+	18.4006i	0.921918	+	0.628553i	−0.00654460	+	0.999979i	$0.502083\pi$
$858$		0			0
$859$	−1.16051	+	0.174919i	−0.0395961	+	0.00596816i	−0.168810	−	0.985649i	$-0.553993\pi$
$859$	−1.16051	+	0.174919i	−0.0395961	+	0.00596816i	0.129214	+	0.991617i	$0.458754\pi$
$860$	14.0620	+	17.6331i	0.479509	+	0.601285i
$861$		0			0
$862$	−3.84237	+	4.81818i	−0.130872	+	0.164108i
$863$	−7.72452	+	13.3793i	−0.262946	+	0.455435i	−0.967023	−	0.254688i	$-0.918027\pi$
$863$	−7.72452	+	13.3793i	−0.262946	+	0.455435i	0.704078	+	0.710123i	$0.251361\pi$
$864$		0			0
$865$	−2.19388	−	0.330673i	−0.0745940	−	0.0112432i
$866$	−3.56832	−	3.31092i	−0.121256	−	0.112510i
$867$		0			0
$868$	−11.8052	+	8.70087i	−0.400695	+	0.295327i
$869$	55.9178	+	26.9286i	1.89688	+	0.913490i
$870$		0			0
$871$	0.284476	+	3.79607i	0.00963911	+	0.128625i
$872$	−6.22017	+	1.91867i	−0.210641	+	0.0649743i
$873$		0			0
$874$	0.282610	+	1.23820i	0.00955943	+	0.0418826i
$875$	−24.7683	−	10.8253i	−0.837322	−	0.365964i
$876$		0			0
$877$	−8.31700	−	2.56546i	−0.280845	−	0.0866293i	0.151133	−	0.988513i	$-0.451708\pi$
$877$	−8.31700	−	2.56546i	−0.280845	−	0.0866293i	−0.431978	+	0.901884i	$0.642184\pi$
$878$	−1.26788	+	3.23050i	−0.0427888	+	0.109024i
$879$		0			0
$880$	13.4316	−	9.15749i	0.452778	−	0.308699i
$881$	11.8364			0.398778			0.199389	−	0.979920i	$-0.436104\pi$
$881$	11.8364			0.398778			0.199389	+	0.979920i	$0.436104\pi$
$882$		0			0
$883$	9.93404			0.334307			0.167153	−	0.985931i	$-0.446542\pi$
$883$	9.93404			0.334307			0.167153	+	0.985931i	$0.446542\pi$
$884$	12.0844	−	8.23901i	0.406443	−	0.277108i
$885$		0			0
$886$	0.637121	−	1.62336i	0.0214045	−	0.0545378i
$887$	38.9760	+	12.0225i	1.30868	+	0.403676i	0.869149	−	0.494550i	$-0.164667\pi$
$887$	38.9760	+	12.0225i	1.30868	+	0.403676i	0.439535	+	0.898225i	$0.355143\pi$
$888$		0			0
$889$	−3.71974	+	19.5900i	−0.124756	+	0.657029i
$890$	−0.375490	−	1.64513i	−0.0125864	−	0.0551448i
$891$		0			0
$892$	13.1445	−	4.05454i	0.440110	−	0.135756i
$893$	2.92474	+	39.0279i	0.0978726	+	1.30602i
$894$		0			0
$895$	15.6024	+	7.51370i	0.521529	+	0.251155i
$896$	0.693148	−	18.2100i	0.0231564	−	0.608354i
$897$		0			0
$898$	2.32457	+	2.15689i	0.0775720	+	0.0719763i
$899$	19.5418	+	2.94546i	0.651757	+	0.0982365i
$900$		0			0
$901$	−13.5287	+	23.4323i	−0.450705	+	0.780645i
$902$	2.31988	−	2.90903i	0.0772434	−	0.0968602i
$903$		0			0
$904$	−4.79568	−	6.01359i	−0.159502	−	0.200009i
$905$	−10.5731	+	1.59364i	−0.351462	+	0.0529744i
$906$		0			0
$907$	19.4586	+	13.2666i	0.646112	+	0.440512i	0.841532	−	0.540208i	$-0.181654\pi$
$907$	19.4586	+	13.2666i	0.646112	+	0.440512i	−0.195419	+	0.980720i	$0.562607\pi$
$908$	33.4027	−	5.03464i	1.10851	−	0.167080i
$909$		0			0
$910$	−0.766718	+	0.267731i	−0.0254165	+	0.00887519i
$911$	−24.8640	+	31.1785i	−0.823781	+	1.03299i	0.175045	+	0.984560i	$0.443993\pi$
$911$	−24.8640	+	31.1785i	−0.823781	+	1.03299i	−0.998827	+	0.0484288i	$0.984579\pi$
$912$		0			0
$913$	−24.9709	−	43.2509i	−0.826417	−	1.43140i
$914$	2.16737	+	0.326678i	0.0716901	+	0.0108055i
$915$		0			0
$916$	51.4010	−	24.7534i	1.69834	−	0.817876i
$917$	−28.1359	−	7.55847i	−0.929129	−	0.249603i
$918$		0			0
$919$	4.98770	+	12.7085i	0.164529	+	0.419213i	0.989233	−	0.146352i	$-0.0467532\pi$
$919$	4.98770	+	12.7085i	0.164529	+	0.419213i	−0.824703	+	0.565565i	$0.808658\pi$
$920$	0.0892762	+	1.19131i	0.00294335	+	0.0392763i
$921$		0			0
$922$	0.106252	−	1.41783i	0.00349922	−	0.0466938i
$923$	1.39601	+	6.11632i	0.0459502	+	0.201321i
$924$		0			0
$925$	1.94991	−	8.54311i	0.0641126	−	0.280896i
$926$	−2.08722	−	0.643823i	−0.0685904	−	0.0211573i
$927$		0			0
$928$	−13.5668	+	12.5882i	−0.445352	+	0.413226i
$929$	−0.681947	+	0.464944i	−0.0223740	+	0.0152543i	−0.574455	−	0.818536i	$-0.694786\pi$
$929$	−0.681947	+	0.464944i	−0.0223740	+	0.0152543i	0.552081	+	0.833790i	$0.313834\pi$
$930$		0			0
$931$	−15.1289	−	31.5195i	−0.495829	−	1.03301i
$932$	54.4536			1.78369
$933$		0			0
$934$	5.23668	−	4.85893i	0.171349	−	0.158989i
$935$	10.8115	−	27.5473i	0.353574	−	0.900892i
$936$		0			0
$937$	4.41379	−	19.3381i	0.144192	−	0.631748i	−0.850242	−	0.526392i	$-0.823545\pi$
$937$	4.41379	−	19.3381i	0.144192	−	0.631748i	0.994435	−	0.105356i	$-0.0335983\pi$
$938$	2.06935	−	0.0760914i	0.0675667	−	0.00248447i
$939$		0			0
$940$	−1.35708	+	18.1090i	−0.0442632	+	0.590651i
$941$	−28.1377	+	8.67935i	−0.917264	+	0.282939i	−0.717219	−	0.696848i	$-0.754585\pi$
$941$	−28.1377	+	8.67935i	−0.917264	+	0.282939i	−0.200046	+	0.979787i	$0.564109\pi$
$942$		0			0
$943$	−1.75894	−	4.48171i	−0.0572790	−	0.145944i
$944$	47.3893	+	22.8215i	1.54239	+	0.742777i
$945$		0			0
$946$	−7.48311	+	3.60368i	−0.243297	+	0.117166i
$947$	−1.46127	−	1.35586i	−0.0474849	−	0.0440595i	0.656073	−	0.754697i	$-0.272216\pi$
$947$	−1.46127	−	1.35586i	−0.0474849	−	0.0440595i	−0.703558	+	0.710638i	$0.748407\pi$
$948$		0			0
$949$	0.794181	+	1.37556i	0.0257802	+	0.0446526i
$950$	2.06043	−	3.56876i	0.0668491	−	0.115786i
$951$		0			0
$952$	−8.57219	−	13.6621i	−0.277826	−	0.442792i
$953$	−9.00489	−	11.2918i	−0.291697	−	0.365777i	0.614291	−	0.789079i	$-0.289442\pi$
$953$	−9.00489	−	11.2918i	−0.291697	−	0.365777i	−0.905988	+	0.423303i	$0.860871\pi$
$954$		0			0
$955$	13.9137	+	9.48620i	0.450237	+	0.306966i
$956$	4.92537	+	3.35806i	0.159298	+	0.108608i
$957$		0			0
$958$	−3.47586	−	4.35859i	−0.112300	−	0.140820i
$959$	11.6080	−	11.5931i	0.374843	−	0.374359i
$960$		0			0
$961$	11.4475	−	19.8276i	0.369274	−	0.639600i
$962$	−0.315324	−	0.546157i	−0.0101665	−	0.0176088i
$963$		0			0
$964$	−2.24459	−	2.08268i	−0.0722934	−	0.0670785i
$965$	−17.9034	+	8.62184i	−0.576332	+	0.277547i
$966$		0			0
$967$	−28.9134	−	13.9240i	−0.929793	−	0.447765i	−0.0932360	−	0.995644i	$-0.529721\pi$
$967$	−28.9134	−	13.9240i	−0.929793	−	0.447765i	−0.836558	+	0.547879i	$0.815435\pi$
$968$	0.909060	+	2.31625i	0.0292183	+	0.0744470i
$969$		0			0
$970$	−0.770870	+	0.237782i	−0.0247511	+	0.00763471i
$971$	0.364565	−	4.86478i	0.0116994	−	0.156118i	−0.988294	−	0.152560i	$-0.951248\pi$
$971$	0.364565	−	4.86478i	0.0116994	−	0.156118i	0.999994	−	0.00355830i	$-0.00113264\pi$
$972$		0			0
$973$	33.8001	+	39.3278i	1.08358	+	1.26079i
$974$	0.531554	−	2.32889i	0.0170321	−	0.0746224i
$975$		0			0
$976$	−10.1462	+	25.8522i	−0.324773	+	0.827509i
$977$	−13.4991	+	12.5253i	−0.431875	+	0.400721i	−0.865930	−	0.500165i	$-0.833273\pi$
$977$	−13.4991	+	12.5253i	−0.431875	+	0.400721i	0.434055	+	0.900886i	$0.357082\pi$
$978$		0			0
$979$	−22.8195			−0.729316
$980$	−4.76167	−	15.5080i	−0.152106	−	0.495386i
$981$		0			0
$982$	−3.43611	+	2.34270i	−0.109651	+	0.0747585i
$983$	24.0688	−	22.3325i	0.767674	−	0.712297i	−0.195639	−	0.980676i	$-0.562678\pi$
$983$	24.0688	−	22.3325i	0.767674	−	0.712297i	0.963314	+	0.268378i	$0.0864878\pi$
$984$		0			0
$985$	−29.8074	−	9.19438i	−0.949744	−	0.292957i
$986$	−2.38574	+	10.4526i	−0.0759775	+	0.332879i
$987$		0			0
$988$	2.42340	+	10.6176i	0.0770987	+	0.337791i
$989$	−0.803129	+	10.7170i	−0.0255380	+	0.340781i
$990$		0			0
$991$	2.77132	+	36.9807i	0.0880339	+	1.17473i	0.849881	+	0.526974i	$0.176673\pi$
$991$	2.77132	+	36.9807i	0.0880339	+	1.17473i	−0.761848	+	0.647756i	$0.775707\pi$
$992$	−2.77302	−	7.06554i	−0.0880435	−	0.224331i
$993$		0			0
$994$	3.35359	−	0.632290i	0.106369	−	0.0200550i
$995$	4.64059	−	2.23479i	0.147117	−	0.0708476i
$996$		0			0
$997$	34.7619	+	5.23952i	1.10092	+	0.165937i	0.674274	−	0.738481i	$-0.264457\pi$
$997$	34.7619	+	5.23952i	1.10092	+	0.165937i	0.426647	+	0.904418i	$0.359695\pi$
$998$	2.06068	+	3.56921i	0.0652297	+	0.112981i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.37.3		60
3.2	odd	2		147.2.m.b.37.3	yes	60
49.4	even	21	inner	441.2.bb.e.298.3		60
147.2	odd	42		7203.2.a.n.1.16		30
147.47	even	42		7203.2.a.m.1.16		30
147.53	odd	42		147.2.m.b.4.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.4.3	✓	60	147.53	odd	42
147.2.m.b.37.3	yes	60	3.2	odd	2
441.2.bb.e.37.3		60	1.1	even	1	trivial
441.2.bb.e.298.3		60	49.4	even	21	inner
7203.2.a.m.1.16		30	147.47	even	42
7203.2.a.n.1.16		30	147.2	odd	42

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.190250 + 0.129710i) q^{2} +(-0.711312 + 1.81239i) q^{4} +(-1.13743 - 0.350851i) q^{5} +(-2.33995 + 1.23477i) q^{7} +(-0.202234 - 0.886046i) q^{8} +O(q^{10})\)	\(q+(-0.190250 + 0.129710i) q^{2} +(-0.711312 + 1.81239i) q^{4} +(-1.13743 - 0.350851i) q^{5} +(-2.33995 + 1.23477i) q^{7} +(-0.202234 - 0.886046i) q^{8} +(0.261905 - 0.0807869i) q^{10} +(-0.276984 - 3.69610i) q^{11} +(1.00902 + 0.485919i) q^{13} +(0.285013 - 0.538429i) q^{14} +(-2.70107 - 2.50623i) q^{16} +(-6.63269 - 0.999717i) q^{17} +(2.49731 - 4.32547i) q^{19} +(1.44495 - 1.81191i) q^{20} +(0.532118 + 0.667255i) q^{22} +(1.09199 - 0.164591i) q^{23} +(-2.96054 - 2.01846i) q^{25} +(-0.254995 + 0.0384343i) q^{26} +(-0.573448 - 5.11921i) q^{28} +(-4.32808 + 5.42724i) q^{29} +(-1.42347 - 2.46552i) q^{31} +(2.63632 + 0.397362i) q^{32} +(1.39154 - 0.670131i) q^{34} +(3.09474 - 0.583487i) q^{35} +(0.893462 + 2.27650i) q^{37} +(0.0859442 + 1.14685i) q^{38} +(-0.0808426 + 1.07877i) q^{40} +(-0.970126 - 4.25040i) q^{41} +(-2.16553 + 9.48782i) q^{43} +(6.89580 + 2.12707i) q^{44} +(-0.186401 + 0.172955i) q^{46} +(-6.47433 + 4.41412i) q^{47} +(3.95071 - 5.77857i) q^{49} +0.825059 q^{50} +(-1.59841 + 1.48310i) q^{52} +(1.47372 - 3.75499i) q^{53} +(-0.981728 + 4.30123i) q^{55} +(1.56728 + 1.82359i) q^{56} +(0.119448 - 1.59393i) q^{58} +(-13.6406 + 4.20757i) q^{59} +(-2.75362 - 7.01611i) q^{61} +(0.590618 + 0.284426i) q^{62} +(6.08648 - 2.93110i) q^{64} +(-0.977206 - 0.906715i) q^{65} +(1.69953 + 2.94368i) q^{67} +(6.52979 - 11.3099i) q^{68} +(-0.513091 + 0.512428i) q^{70} +(3.49266 + 4.37965i) q^{71} +(1.17183 + 0.798940i) q^{73} +(-0.465267 - 0.317213i) q^{74} +(6.06308 + 7.60286i) q^{76} +(5.21194 + 8.30666i) q^{77} +(-8.37241 + 14.5014i) q^{79} +(2.19297 + 3.79833i) q^{80} +(0.735886 + 0.682803i) q^{82} +(12.1399 - 5.84627i) q^{83} +(7.19347 + 3.46419i) q^{85} +(-0.818675 - 2.08595i) q^{86} +(-3.21890 + 0.992898i) q^{88} +(0.460090 - 6.13948i) q^{89} +(-2.96105 + 0.108880i) q^{91} +(-0.478441 + 2.09619i) q^{92} +(0.659183 - 1.67957i) q^{94} +(-4.35811 + 4.04373i) q^{95} -2.94332 q^{97} +(-0.00208186 + 1.61182i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Introduction

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