LMFDB - Embedded newform 414.2.i.d.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			163.1
Root			$0.142315 - 0.989821i$ of defining polynomial
Character	$\chi$	$=$	414.163
Dual form			414.2.i.d.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(-1.18639 - 0.348356i) q^{5} +(0.968468 - 1.11767i) q^{7} +(0.142315 - 0.989821i) q^{8} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(-1.18639 - 0.348356i) q^{5} +(0.968468 - 1.11767i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.809721 + 0.934468i) q^{10} +(0.745983 - 0.479414i) q^{11} +(-0.0440780 - 0.0508687i) q^{13} +(-1.41899 + 0.416652i) q^{14} +(-0.654861 + 0.755750i) q^{16} +(1.78287 - 3.90393i) q^{17} +(-1.93899 - 4.24579i) q^{19} +(-0.175969 - 1.22389i) q^{20} -0.886752 q^{22} +(4.72041 + 0.847210i) q^{23} +(-2.92009 - 1.87663i) q^{25} +(0.00957906 + 0.0666238i) q^{26} +(1.41899 + 0.416652i) q^{28} +(3.18962 - 6.98430i) q^{29} +(0.226488 - 1.57526i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-3.61047 + 2.32031i) q^{34} +(-1.53833 + 0.988626i) q^{35} +(5.01691 - 1.47310i) q^{37} +(-0.664268 + 4.62008i) q^{38} +(-0.513652 + 1.12474i) q^{40} +(-0.130426 - 0.0382966i) q^{41} +(-0.936145 - 6.51103i) q^{43} +(0.745983 + 0.479414i) q^{44} +(-3.51302 - 3.26476i) q^{46} -8.31271 q^{47} +(0.684944 + 4.76389i) q^{49} +(1.44196 + 3.15744i) q^{50} +(0.0279611 - 0.0612263i) q^{52} +(-1.96169 + 2.26391i) q^{53} +(-1.05204 + 0.308906i) q^{55} +(-0.968468 - 1.11767i) q^{56} +(-6.45928 + 4.15112i) q^{58} +(-4.47647 - 5.16612i) q^{59} +(0.654669 - 4.55332i) q^{61} +(-1.04218 + 1.20274i) q^{62} +(-0.959493 - 0.281733i) q^{64} +(0.0345733 + 0.0757051i) q^{65} +(10.4358 + 6.70671i) q^{67} +4.29177 q^{68} +1.82862 q^{70} +(6.15647 + 3.95652i) q^{71} +(5.48256 + 12.0051i) q^{73} +(-5.01691 - 1.47310i) q^{74} +(3.05662 - 3.52753i) q^{76} +(0.186633 - 1.29806i) q^{77} +(-5.16977 - 5.96624i) q^{79} +(1.04019 - 0.668491i) q^{80} +(0.0890169 + 0.102731i) q^{82} +(-8.06797 + 2.36897i) q^{83} +(-3.47514 + 4.01052i) q^{85} +(-2.73259 + 5.98354i) q^{86} +(-0.368370 - 0.806618i) q^{88} +(1.66842 + 11.6041i) q^{89} -0.0995426 q^{91} +(1.19028 + 4.64578i) q^{92} +(6.99309 + 4.49419i) q^{94} +(0.821353 + 5.71264i) q^{95} +(16.4711 + 4.83636i) q^{97} +(1.99934 - 4.37795i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8}+O(q^{10}) $ 10 * q + q^2 - q^4 - 8 * q^5 + 8 * q^7 + q^8	$ 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8} - 3 q^{10} - 7 q^{11} + 3 q^{13} + 3 q^{14} - q^{16} - 4 q^{17} + 3 q^{20} - 26 q^{22} + 12 q^{23} - 15 q^{25} - 3 q^{26} - 3 q^{28} + 25 q^{29} + 6 q^{31} + q^{32} - 7 q^{34} - 2 q^{35} + 9 q^{37} - 11 q^{38} - 3 q^{40} - 24 q^{41} - 30 q^{43} - 7 q^{44} + 21 q^{46} + 48 q^{47} + 9 q^{49} - 7 q^{50} + 14 q^{52} - 15 q^{53} - 23 q^{55} - 8 q^{56} - 3 q^{58} - 5 q^{59} + 12 q^{61} - 28 q^{62} - q^{64} + 13 q^{65} + 18 q^{67} + 18 q^{68} + 2 q^{70} - 28 q^{71} + 19 q^{73} - 9 q^{74} + 22 q^{76} + 12 q^{77} - 52 q^{79} - 8 q^{80} - 20 q^{82} - 7 q^{83} + 23 q^{85} - 14 q^{86} - 4 q^{88} - 3 q^{89} + 42 q^{91} + 23 q^{92} + 29 q^{94} - 22 q^{95} + 51 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + q^2 - q^4 - 8 * q^5 + 8 * q^7 + q^8 - 3 * q^10 - 7 * q^11 + 3 * q^13 + 3 * q^14 - q^16 - 4 * q^17 + 3 * q^20 - 26 * q^22 + 12 * q^23 - 15 * q^25 - 3 * q^26 - 3 * q^28 + 25 * q^29 + 6 * q^31 + q^32 - 7 * q^34 - 2 * q^35 + 9 * q^37 - 11 * q^38 - 3 * q^40 - 24 * q^41 - 30 * q^43 - 7 * q^44 + 21 * q^46 + 48 * q^47 + 9 * q^49 - 7 * q^50 + 14 * q^52 - 15 * q^53 - 23 * q^55 - 8 * q^56 - 3 * q^58 - 5 * q^59 + 12 * q^61 - 28 * q^62 - q^64 + 13 * q^65 + 18 * q^67 + 18 * q^68 + 2 * q^70 - 28 * q^71 + 19 * q^73 - 9 * q^74 + 22 * q^76 + 12 * q^77 - 52 * q^79 - 8 * q^80 - 20 * q^82 - 7 * q^83 + 23 * q^85 - 14 * q^86 - 4 * q^88 - 3 * q^89 + 42 * q^91 + 23 * q^92 + 29 * q^94 - 22 * q^95 + 51 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$3$		0			0
$3$		0			0
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	−1.18639	−	0.348356i	−0.530571	−	0.155790i	0.00546462	−	0.999985i	$-0.498261\pi$
$5$	−1.18639	−	0.348356i	−0.530571	−	0.155790i	−0.536036	+	0.844195i	$0.680079\pi$
$6$		0			0
$7$	0.968468	−	1.11767i	0.366046	−	0.422440i	−0.542610	−	0.839985i	$-0.682564\pi$
$7$	0.968468	−	1.11767i	0.366046	−	0.422440i	0.908656	+	0.417545i	$0.137109\pi$
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$		0			0
$10$	0.809721	+	0.934468i	0.256056	+	0.295505i
$11$	0.745983	−	0.479414i	0.224922	−	0.144549i	−0.423327	−	0.905977i	$-0.639138\pi$
$11$	0.745983	−	0.479414i	0.224922	−	0.144549i	0.648249	+	0.761428i	$0.275501\pi$
$12$		0			0
$13$	−0.0440780	−	0.0508687i	−0.0122250	−	0.0141084i	0.749604	−	0.661886i	$-0.230244\pi$
$13$	−0.0440780	−	0.0508687i	−0.0122250	−	0.0141084i	−0.761829	+	0.647778i	$0.775698\pi$
$14$	−1.41899	+	0.416652i	−0.379240	+	0.111355i
$15$		0			0
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	1.78287	−	3.90393i	0.432409	−	0.946843i	−0.560521	−	0.828140i	$-0.689399\pi$
$17$	1.78287	−	3.90393i	0.432409	−	0.946843i	0.992930	−	0.118703i	$-0.0378735\pi$
$18$		0			0
$19$	−1.93899	−	4.24579i	−0.444834	−	0.974052i	−0.990686	−	0.136169i	$-0.956521\pi$
$19$	−1.93899	−	4.24579i	−0.444834	−	0.974052i	0.545851	−	0.837882i	$-0.316206\pi$
$20$	−0.175969	−	1.22389i	−0.0393479	−	0.273671i
$21$		0			0
$22$	−0.886752			−0.189056
$23$	4.72041	+	0.847210i	0.984273	+	0.176655i
$23$	4.72041	+	0.847210i	0.984273	+	0.176655i
$24$		0			0
$25$	−2.92009	−	1.87663i	−0.584018	−	0.375326i
$26$	0.00957906	+	0.0666238i	0.00187861	+	0.0130660i
$27$		0			0
$28$	1.41899	+	0.416652i	0.268163	+	0.0787398i
$29$	3.18962	−	6.98430i	0.592298	−	1.29695i	−0.341746	−	0.939792i	$-0.611018\pi$
$29$	3.18962	−	6.98430i	0.592298	−	1.29695i	0.934044	−	0.357159i	$-0.116255\pi$
$30$		0			0
$31$	0.226488	−	1.57526i	0.0406784	−	0.282924i	−0.959321	−	0.282316i	$-0.908897\pi$
$31$	0.226488	−	1.57526i	0.0406784	−	0.282924i	1.00000		0.000608171i	$-0.000193587\pi$
$32$	0.959493	−	0.281733i	0.169616	−	0.0498038i
$33$		0			0
$34$	−3.61047	+	2.32031i	−0.619190	+	0.397929i
$35$	−1.53833	+	0.988626i	−0.260025	+	0.167108i
$36$		0			0
$37$	5.01691	−	1.47310i	0.824775	−	0.242176i	0.158004	−	0.987439i	$-0.449494\pi$
$37$	5.01691	−	1.47310i	0.824775	−	0.242176i	0.666771	+	0.745263i	$0.267676\pi$
$38$	−0.664268	+	4.62008i	−0.107758	+	0.749477i
$39$		0			0
$40$	−0.513652	+	1.12474i	−0.0812155	+	0.177837i
$41$	−0.130426	−	0.0382966i	−0.0203692	−	0.00598093i	0.271532	−	0.962429i	$-0.412470\pi$
$41$	−0.130426	−	0.0382966i	−0.0203692	−	0.00598093i	−0.291901	+	0.956448i	$0.594288\pi$
$42$		0			0
$43$	−0.936145	−	6.51103i	−0.142761	−	0.992923i	−0.927694	−	0.373342i	$-0.878212\pi$
$43$	−0.936145	−	6.51103i	−0.142761	−	0.992923i	0.784933	−	0.619581i	$-0.212697\pi$
$44$	0.745983	+	0.479414i	0.112461	+	0.0722745i
$45$		0			0
$46$	−3.51302	−	3.26476i	−0.517967	−	0.481363i
$47$	−8.31271			−1.21253			−0.606266	−	0.795262i	$-0.707334\pi$
$47$	−8.31271			−1.21253			−0.606266	+	0.795262i	$0.707334\pi$
$48$		0			0
$49$	0.684944	+	4.76389i	0.0978492	+	0.680556i
$50$	1.44196	+	3.15744i	0.203923	+	0.446530i
$51$		0			0
$52$	0.0279611	−	0.0612263i	0.00387751	−	0.00849057i
$53$	−1.96169	+	2.26391i	−0.269458	+	0.310971i	−0.874311	−	0.485366i	$-0.838686\pi$
$53$	−1.96169	+	2.26391i	−0.269458	+	0.310971i	0.604853	+	0.796337i	$0.293232\pi$
$54$		0			0
$55$	−1.05204	+	0.308906i	−0.141857	+	0.0416528i
$56$	−0.968468	−	1.11767i	−0.129417	−	0.149355i
$57$		0			0
$58$	−6.45928	+	4.15112i	−0.848144	+	0.545069i
$59$	−4.47647	−	5.16612i	−0.582787	−	0.672572i	0.385415	−	0.922743i	$-0.374058\pi$
$59$	−4.47647	−	5.16612i	−0.582787	−	0.672572i	−0.968202	+	0.250172i	$0.919513\pi$
$60$		0			0
$61$	0.654669	−	4.55332i	0.0838218	−	0.582993i	−0.904015	−	0.427500i	$-0.859394\pi$
$61$	0.654669	−	4.55332i	0.0838218	−	0.582993i	0.987837	−	0.155493i	$-0.0496966\pi$
$62$	−1.04218	+	1.20274i	−0.132357	+	0.152748i
$63$		0			0
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	0.0345733	+	0.0757051i	0.00428830	+	0.00939006i
$66$		0			0
$67$	10.4358	+	6.70671i	1.27494	+	0.819355i	0.990255	−	0.139266i	$-0.0444743\pi$
$67$	10.4358	+	6.70671i	1.27494	+	0.819355i	0.284686	+	0.958621i	$0.408111\pi$
$68$	4.29177			0.520454
$69$		0			0
$70$	1.82862			0.218562
$71$	6.15647	+	3.95652i	0.730639	+	0.469553i	0.852323	−	0.523016i	$-0.175193\pi$
$71$	6.15647	+	3.95652i	0.730639	+	0.469553i	−0.121684	+	0.992569i	$0.538830\pi$
$72$		0			0
$73$	5.48256	+	12.0051i	0.641686	+	1.40510i	0.898646	+	0.438674i	$0.144552\pi$
$73$	5.48256	+	12.0051i	0.641686	+	1.40510i	−0.256961	+	0.966422i	$0.582721\pi$
$74$	−5.01691	−	1.47310i	−0.583204	−	0.171244i
$75$		0			0
$76$	3.05662	−	3.52753i	0.350619	−	0.404636i
$77$	0.186633	−	1.29806i	0.0212688	−	0.147928i
$78$		0			0
$79$	−5.16977	−	5.96624i	−0.581645	−	0.671254i	0.386313	−	0.922368i	$-0.373749\pi$
$79$	−5.16977	−	5.96624i	−0.581645	−	0.671254i	−0.967958	+	0.251114i	$0.919203\pi$
$80$	1.04019	−	0.668491i	0.116297	−	0.0747396i
$81$		0			0
$82$	0.0890169	+	0.102731i	0.00983027	+	0.0113447i
$83$	−8.06797	+	2.36897i	−0.885575	+	0.260028i	−0.692727	−	0.721200i	$-0.743591\pi$
$83$	−8.06797	+	2.36897i	−0.885575	+	0.260028i	−0.192848	+	0.981229i	$0.561773\pi$
$84$		0			0
$85$	−3.47514	+	4.01052i	−0.376932	+	0.435002i
$86$	−2.73259	+	5.98354i	−0.294663	+	0.645222i
$87$		0			0
$88$	−0.368370	−	0.806618i	−0.0392684	−	0.0859858i
$89$	1.66842	+	11.6041i	0.176852	+	1.23004i	0.863990	+	0.503509i	$0.167958\pi$
$89$	1.66842	+	11.6041i	0.176852	+	1.23004i	−0.687138	+	0.726527i	$0.741133\pi$
$90$		0			0
$91$	−0.0995426			−0.0104349
$92$	1.19028	+	4.64578i	0.124095	+	0.484356i
$93$		0			0
$94$	6.99309	+	4.49419i	0.721283	+	0.463540i
$95$	0.821353	+	5.71264i	0.0842691	+	0.586104i
$96$		0			0
$97$	16.4711	+	4.83636i	1.67239	+	0.491058i	0.974357	−	0.225008i	$-0.0722409\pi$
$97$	16.4711	+	4.83636i	1.67239	+	0.491058i	0.698033	+	0.716066i	$0.254059\pi$
$98$	1.99934	−	4.37795i	0.201964	−	0.442240i
$99$		0			0
$100$	0.493992	−	3.43579i	0.0493992	−	0.343579i
$101$	5.74460	−	1.68677i	0.571609	−	0.167840i	0.0168608	−	0.999858i	$-0.494633\pi$
$101$	5.74460	−	1.68677i	0.571609	−	0.167840i	0.554748	+	0.832018i	$0.312815\pi$
$102$		0			0
$103$	−13.1585	+	8.45644i	−1.29654	+	0.833238i	−0.992831	−	0.119526i	$-0.961862\pi$
$103$	−13.1585	+	8.45644i	−1.29654	+	0.833238i	−0.303712	+	0.952764i	$0.598226\pi$
$104$	−0.0566239	+	0.0363899i	−0.00555243	+	0.00356833i
$105$		0			0
$106$	2.87423	−	0.843951i	0.279170	−	0.0819718i
$107$	−1.96658	+	13.6779i	−0.190117	+	1.32229i	0.641578	+	0.767057i	$0.278280\pi$
$107$	−1.96658	+	13.6779i	−0.190117	+	1.32229i	−0.831695	+	0.555233i	$0.812629\pi$
$108$		0			0
$109$	4.48089	−	9.81177i	0.429191	−	0.939797i	−0.564266	−	0.825593i	$-0.690841\pi$
$109$	4.48089	−	9.81177i	0.429191	−	0.939797i	0.993457	−	0.114204i	$-0.0364319\pi$
$110$	1.05204	+	0.308906i	0.100308	+	0.0294530i
$111$		0			0
$112$	0.210468	+	1.46384i	0.0198874	+	0.138320i
$113$	3.84480	+	2.47090i	0.361688	+	0.232443i	0.708845	−	0.705364i	$-0.249217\pi$
$113$	3.84480	+	2.47090i	0.361688	+	0.232443i	−0.347157	+	0.937807i	$0.612853\pi$
$114$		0			0
$115$	−5.30513	−	2.64951i	−0.494705	−	0.247068i
$116$	7.67816			0.712899
$117$		0			0
$118$	0.972830	+	6.76618i	0.0895563	+	0.622878i
$119$	−2.63667	−	5.77349i	−0.241703	−	0.529255i
$120$		0			0
$121$	−4.24291	+	9.29068i	−0.385719	+	0.844607i
$122$	−3.01245	+	3.47656i	−0.272735	+	0.314753i
$123$		0			0
$124$	1.52699	−	0.448364i	0.137128	−	0.0402643i
$125$	6.85925	+	7.91599i	0.613510	+	0.708028i
$126$		0			0
$127$	−12.1204	+	7.78931i	−1.07551	+	0.691190i	−0.953516	−	0.301341i	$-0.902566\pi$
$127$	−12.1204	+	7.78931i	−1.07551	+	0.691190i	−0.121996	+	0.992531i	$0.538929\pi$
$128$	0.654861	+	0.755750i	0.0578821	+	0.0667995i
$129$		0			0
$130$	0.0118443	−	0.0823789i	0.00103881	−	0.00722511i
$131$	−2.99925	+	3.46132i	−0.262045	+	0.302417i	−0.871491	−	0.490411i	$-0.836847\pi$
$131$	−2.99925	+	3.46132i	−0.262045	+	0.302417i	0.609446	+	0.792828i	$0.291392\pi$
$132$		0			0
$133$	−6.62325	−	1.94476i	−0.574309	−	0.168632i
$134$	−5.15327	−	11.2841i	−0.445175	−	0.974796i
$135$		0			0
$136$	−3.61047	−	2.32031i	−0.309595	−	0.198965i
$137$	9.22788			0.788391			0.394196	−	0.919027i	$-0.371023\pi$
$137$	9.22788			0.788391			0.394196	+	0.919027i	$0.371023\pi$
$138$		0			0
$139$	7.82143			0.663405			0.331702	−	0.943384i	$-0.392377\pi$
$139$	7.82143			0.663405			0.331702	+	0.943384i	$0.392377\pi$
$140$	−1.53833	−	0.988626i	−0.130013	−	0.0835541i
$141$		0			0
$142$	−3.04009	−	6.65688i	−0.255119	−	0.558633i
$143$	−0.0572686	−	0.0168156i	−0.00478904	−	0.00140619i
$144$		0			0
$145$	−6.21717	+	7.17499i	−0.516308	+	0.595851i
$146$	1.87824	−	13.0635i	0.155444	−	1.08114i
$147$		0			0
$148$	3.42408	+	3.95159i	0.281457	+	0.324819i
$149$	4.16624	−	2.67748i	0.341312	−	0.219348i	−0.358744	−	0.933436i	$-0.616795\pi$
$149$	4.16624	−	2.67748i	0.341312	−	0.219348i	0.700056	+	0.714088i	$0.253159\pi$
$150$		0			0
$151$	−10.0611	−	11.6111i	−0.818757	−	0.944896i	0.180495	−	0.983576i	$-0.442230\pi$
$151$	−10.0611	−	11.6111i	−0.818757	−	0.944896i	−0.999252	+	0.0386804i	$0.987685\pi$
$152$	−4.47852	+	1.31501i	−0.363256	+	0.106662i
$153$		0			0
$154$	−0.858791	+	0.991098i	−0.0692034	+	0.0798649i
$155$	−0.817453	+	1.78997i	−0.0656594	+	0.143774i
$156$		0			0
$157$	5.19570	+	11.3770i	0.414662	+	0.907983i	0.995571	+	0.0940146i	$0.0299701\pi$
$157$	5.19570	+	11.3770i	0.414662	+	0.907983i	−0.580909	+	0.813969i	$0.697303\pi$
$158$	1.12350	+	7.81411i	0.0893808	+	0.621657i
$159$		0			0
$160$	−1.23648			−0.0977522
$161$	5.51846	−	4.45537i	0.434916	−	0.351132i
$162$		0			0
$163$	−8.77430	−	5.63890i	−0.687257	−	0.441673i	0.149853	−	0.988708i	$-0.452120\pi$
$163$	−8.77430	−	5.63890i	−0.687257	−	0.441673i	−0.837110	+	0.547035i	$0.815756\pi$
$164$	−0.0193452	−	0.134549i	−0.00151061	−	0.0105065i
$165$		0			0
$166$	8.06797	+	2.36897i	0.626196	+	0.183868i
$167$	10.5384	−	23.0759i	0.815486	−	1.78567i	0.233732	−	0.972301i	$-0.424906\pi$
$167$	10.5384	−	23.0759i	0.815486	−	1.78567i	0.581755	−	0.813364i	$-0.302366\pi$
$168$		0			0
$169$	1.84945	−	12.8632i	0.142265	−	0.989476i
$170$	5.09173	−	1.49507i	0.390518	−	0.114666i
$171$		0			0
$172$	5.53375	−	3.55633i	0.421945	−	0.271167i
$173$	−14.4651	+	9.29615i	−1.09976	+	0.706773i	−0.959039	−	0.283276i	$-0.908579\pi$
$173$	−14.4651	+	9.29615i	−1.09976	+	0.706773i	−0.140722	+	0.990049i	$0.544942\pi$
$174$		0			0
$175$	−4.92547	+	1.44625i	−0.372331	+	0.109326i
$176$	−0.126198	+	0.877726i	−0.00951253	+	0.0661611i
$177$		0			0
$178$	4.87010	−	10.6640i	0.365030	−	0.799304i
$179$	−5.86058	−	1.72082i	−0.438040	−	0.128620i	0.0552742	−	0.998471i	$-0.482397\pi$
$179$	−5.86058	−	1.72082i	−0.438040	−	0.128620i	−0.493315	+	0.869851i	$0.664215\pi$
$180$		0			0
$181$	−3.05836	−	21.2713i	−0.227326	−	1.58109i	−0.709304	−	0.704903i	$-0.750991\pi$
$181$	−3.05836	−	21.2713i	−0.227326	−	1.58109i	0.481978	−	0.876183i	$-0.339919\pi$
$182$	0.0837405	+	0.0538168i	0.00620726	+	0.00398916i
$183$		0			0
$184$	1.51037	−	4.55179i	0.111346	−	0.335562i
$185$	−6.46519			−0.475330
$186$		0			0
$187$	−0.541613	−	3.76700i	−0.0396067	−	0.275470i
$188$	−3.45322	−	7.56150i	−0.251852	−	0.551479i
$189$		0			0
$190$	2.39752	−	5.24983i	0.173934	−	0.380863i
$191$	−1.85635	+	2.14235i	−0.134321	+	0.155015i	−0.818925	−	0.573900i	$-0.805430\pi$
$191$	−1.85635	+	2.14235i	−0.134321	+	0.155015i	0.684604	+	0.728915i	$0.259975\pi$
$192$		0			0
$193$	23.1120	−	6.78629i	1.66364	−	0.488488i	0.691398	−	0.722474i	$-0.256995\pi$
$193$	23.1120	−	6.78629i	1.66364	−	0.488488i	0.972240	+	0.233986i	$0.0751770\pi$
$194$	−11.2417	−	12.9736i	−0.807104	−	0.931448i
$195$		0			0
$196$	−4.04885	+	2.60204i	−0.289204	+	0.185860i
$197$	−16.1131	−	18.5955i	−1.14801	−	1.32488i	−0.937781	−	0.347226i	$-0.887124\pi$
$197$	−16.1131	−	18.5955i	−1.14801	−	1.32488i	−0.210232	−	0.977652i	$-0.567422\pi$
$198$		0			0
$199$	−0.893429	+	6.21393i	−0.0633335	+	0.440494i	0.933340	+	0.358994i	$0.116880\pi$
$199$	−0.893429	+	6.21393i	−0.0633335	+	0.440494i	−0.996673	+	0.0815000i	$0.974029\pi$
$200$	−2.27310	+	2.62330i	−0.160732	+	0.185495i
$201$		0			0
$202$	−5.74460	−	1.68677i	−0.404189	−	0.118680i
$203$	−4.71710	−	10.3290i	−0.331076	−	0.724955i
$204$		0			0
$205$	0.141396	+	0.0908697i	0.00987552	+	0.00634661i
$206$	15.6415			1.08980
$207$		0			0
$208$	0.0673089			0.00466703
$209$	−3.48195	−	2.23771i	−0.240851	−	0.154786i
$210$		0			0
$211$	8.05469	+	17.6373i	0.554508	+	1.21420i	0.954645	+	0.297748i	$0.0962354\pi$
$211$	8.05469	+	17.6373i	0.554508	+	1.21420i	−0.400137	+	0.916455i	$0.631037\pi$
$212$	−2.87423	−	0.843951i	−0.197403	−	0.0579628i
$213$		0			0
$214$	9.04921	−	10.4433i	0.618591	−	0.713892i
$215$	−1.15752	+	8.05075i	−0.0789424	+	0.549057i
$216$		0			0
$217$	−1.54127	−	1.77872i	−0.104628	−	0.120748i
$218$	−9.07421	+	5.83164i	−0.614583	+	0.394968i
$219$		0			0
$220$	−0.718022	−	0.828642i	−0.0484091	−	0.0558670i
$221$	−0.277173	+	0.0813853i	−0.0186447	+	0.00547457i
$222$		0			0
$223$	−13.4728	+	15.5484i	−0.902204	+	1.04120i	0.0967422	+	0.995309i	$0.469158\pi$
$223$	−13.4728	+	15.5484i	−0.902204	+	1.04120i	−0.998947	+	0.0458898i	$0.985388\pi$
$224$	0.614354	−	1.34525i	0.0410482	−	0.0898831i
$225$		0			0
$226$	−1.89858	−	4.15731i	−0.126292	−	0.276540i
$227$	−3.27655	−	22.7889i	−0.217472	−	1.51255i	−0.747323	−	0.664461i	$-0.768661\pi$
$227$	−3.27655	−	22.7889i	−0.217472	−	1.51255i	0.529851	−	0.848091i	$-0.322248\pi$
$228$		0			0
$229$	7.50367			0.495857			0.247928	−	0.968778i	$-0.420250\pi$
$229$	7.50367			0.495857			0.247928	+	0.968778i	$0.420250\pi$
$230$	3.03052	+	5.09707i	0.199827	+	0.336091i
$231$		0			0
$232$	−6.45928	−	4.15112i	−0.424072	−	0.272535i
$233$	3.46796	+	24.1202i	0.227194	+	1.58017i	0.709848	+	0.704355i	$0.248764\pi$
$233$	3.46796	+	24.1202i	0.227194	+	1.58017i	−0.482654	+	0.875811i	$0.660327\pi$
$234$		0			0
$235$	9.86214	+	2.89578i	0.643335	+	0.188900i
$236$	2.83968	−	6.21803i	0.184847	−	0.404759i
$237$		0			0
$238$	−0.903281	+	6.28246i	−0.0585510	+	0.407231i
$239$	8.34418	−	2.45007i	0.539740	−	0.158482i	−0.000489053	−	1.00000i	$-0.500156\pi$
$239$	8.34418	−	2.45007i	0.539740	−	0.158482i	0.540229	+	0.841518i	$0.318337\pi$
$240$		0			0
$241$	−4.77592	+	3.06930i	−0.307644	+	0.197711i	−0.685348	−	0.728216i	$-0.740350\pi$
$241$	−4.77592	+	3.06930i	−0.307644	+	0.197711i	0.377704	+	0.925926i	$0.376714\pi$
$242$	8.59229	−	5.52193i	0.552333	−	0.354963i
$243$		0			0
$244$	4.41381	−	1.29601i	0.282565	−	0.0829686i
$245$	0.846919	−	5.89045i	0.0541077	−	0.376327i
$246$		0			0
$247$	−0.130511	+	0.285780i	−0.00830423	+	0.0181837i
$248$	−1.52699	−	0.448364i	−0.0969639	−	0.0284712i
$249$		0			0
$250$	−1.49066	−	10.3677i	−0.0942774	−	0.655714i
$251$	−5.03416	−	3.23526i	−0.317753	−	0.204208i	0.372035	−	0.928219i	$-0.378660\pi$
$251$	−5.03416	−	3.23526i	−0.317753	−	0.204208i	−0.689788	+	0.724011i	$0.742296\pi$
$252$		0			0
$253$	3.92751	−	1.63103i	0.246920	−	0.102542i
$254$	14.4076			0.904010
$255$		0			0
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−6.46313	−	14.1523i	−0.403159	−	0.882794i	−0.996940	−	0.0781681i	$-0.975093\pi$
$257$	−6.46313	−	14.1523i	−0.403159	−	0.882794i	0.593781	−	0.804626i	$-0.297634\pi$
$258$		0			0
$259$	3.21228	−	7.03390i	0.199601	−	0.437065i
$260$	−0.0545015	+	0.0628980i	−0.00338004	+	0.00390077i
$261$		0			0
$262$	4.39446	−	1.29033i	0.271490	−	0.0797168i
$263$	6.72323	+	7.75903i	0.414572	+	0.478442i	0.924176	−	0.381967i	$-0.124753\pi$
$263$	6.72323	+	7.75903i	0.414572	+	0.478442i	−0.509603	+	0.860409i	$0.670208\pi$
$264$		0			0
$265$	3.11597	−	2.00252i	0.191413	−	0.123014i
$266$	4.52041	+	5.21684i	0.277164	+	0.319865i
$267$		0			0
$268$	−1.76543	+	12.2788i	−0.107841	+	0.750050i
$269$	−2.12380	+	2.45100i	−0.129491	+	0.149440i	−0.816792	−	0.576932i	$-0.804250\pi$
$269$	−2.12380	+	2.45100i	−0.129491	+	0.149440i	0.687301	+	0.726372i	$0.258795\pi$
$270$		0			0
$271$	−14.8782	−	4.36865i	−0.903789	−	0.265376i	−0.203365	−	0.979103i	$-0.565188\pi$
$271$	−14.8782	−	4.36865i	−0.903789	−	0.265376i	−0.700424	+	0.713727i	$0.747006\pi$
$272$	1.78287	+	3.90393i	0.108102	+	0.236711i
$273$		0			0
$274$	−7.76299	−	4.98897i	−0.468979	−	0.301395i
$275$	−3.07802			−0.185612
$276$		0			0
$277$	2.16313			0.129970			0.0649849	−	0.997886i	$-0.479300\pi$
$277$	2.16313			0.129970			0.0649849	+	0.997886i	$0.479300\pi$
$278$	−6.57980	−	4.22858i	−0.394630	−	0.253613i
$279$		0			0
$280$	0.759635	+	1.66337i	0.0453969	+	0.0994053i
$281$	19.7234	+	5.79132i	1.17660	+	0.345481i	0.810863	−	0.585237i	$-0.198998\pi$
$281$	19.7234	+	5.79132i	1.17660	+	0.345481i	0.365738	+	0.930718i	$0.380817\pi$
$282$		0			0
$283$	−11.0909	+	12.7996i	−0.659288	+	0.760859i	−0.982661	−	0.185412i	$-0.940638\pi$
$283$	−11.0909	+	12.7996i	−0.659288	+	0.760859i	0.323372	+	0.946272i	$0.395183\pi$
$284$	−1.04149	+	7.24372i	−0.0618011	+	0.429836i
$285$		0			0
$286$	0.0390862	+	0.0451079i	0.00231122	+	0.00266729i
$287$	−0.169117	+	0.108685i	−0.00998264	+	0.00641546i
$288$		0			0
$289$	−0.929446	−	1.07264i	−0.0546733	−	0.0630963i
$290$	9.10931	−	2.67473i	0.534917	−	0.157066i
$291$		0			0
$292$	−8.64272	+	9.97423i	−0.505777	+	0.583698i
$293$	−0.856727	+	1.87597i	−0.0500505	+	0.109595i	−0.933005	−	0.359863i	$-0.882823\pi$
$293$	−0.856727	+	1.87597i	−0.0500505	+	0.109595i	0.882955	+	0.469458i	$0.155551\pi$
$294$		0			0
$295$	3.51120	+	7.68846i	0.204430	+	0.447639i
$296$	−0.744123	−	5.17549i	−0.0432513	−	0.300819i
$297$		0			0
$298$	−4.95242			−0.286886
$299$	−0.164969	−	0.277464i	−0.00954043	−	0.0160462i
$300$		0			0
$301$	−8.18382	−	5.25942i	−0.471707	−	0.303148i
$302$	2.18648	+	15.2073i	0.125818	+	0.875080i
$303$		0			0
$304$	4.47852	+	1.31501i	0.256861	+	0.0754212i
$305$	−2.36287	+	5.17397i	−0.135298	+	0.296261i
$306$		0			0
$307$	0.581067	−	4.04141i	0.0331633	−	0.230656i	−0.966498	−	0.256673i	$-0.917374\pi$
$307$	0.581067	−	4.04141i	0.0331633	−	0.230656i	0.999661	+	0.0260178i	$0.00828265\pi$
$308$	1.25829	−	0.369467i	0.0716977	−	0.0210523i
$309$		0			0
$310$	1.65542	−	1.06387i	0.0940214	−	0.0604239i
$311$	10.7254	−	6.89278i	0.608180	−	0.390854i	−0.199994	−	0.979797i	$-0.564092\pi$
$311$	10.7254	−	6.89278i	0.608180	−	0.390854i	0.808174	+	0.588944i	$0.200456\pi$
$312$		0			0
$313$	7.46705	−	2.19252i	0.422062	−	0.123929i	−0.0638026	−	0.997963i	$-0.520323\pi$
$313$	7.46705	−	2.19252i	0.422062	−	0.123929i	0.485865	+	0.874034i	$0.338505\pi$
$314$	1.77997	−	12.3799i	0.100449	−	0.698641i
$315$		0			0
$316$	3.27948	−	7.18106i	0.184485	−	0.403966i
$317$	18.9507	+	5.56442i	1.06438	+	0.312529i	0.766612	−	0.642111i	$-0.221941\pi$
$317$	18.9507	+	5.56442i	1.06438	+	0.312529i	0.297764	+	0.954640i	$0.403759\pi$
$318$		0			0
$319$	−0.968968	−	6.73932i	−0.0542518	−	0.377329i
$320$	1.04019	+	0.668491i	0.0581485	+	0.0373698i
$321$		0			0
$322$	−7.05118	+	0.764587i	−0.392947	+	0.0426088i
$323$	−20.0322			−1.11462
$324$		0			0
$325$	0.0332501	+	0.231259i	0.00184438	+	0.0128280i
$326$	4.33279	+	9.48749i	0.239971	+	0.525464i
$327$		0			0
$328$	−0.0564684	+	0.123649i	−0.00311795	+	0.00682735i
$329$	−8.05059	+	9.29088i	−0.443843	+	0.512223i
$330$		0			0
$331$	4.11794	−	1.20914i	0.226342	−	0.0664601i	−0.166595	−	0.986025i	$-0.553277\pi$
$331$	4.11794	−	1.20914i	0.226342	−	0.0664601i	0.392937	+	0.919565i	$0.371459\pi$
$332$	−5.50645	−	6.35478i	−0.302206	−	0.348764i
$333$		0			0
$334$	−21.3412	+	13.7152i	−1.16774	+	0.750461i
$335$	−10.0447	−	11.5922i	−0.548800	−	0.633349i
$336$		0			0
$337$	−4.12123	+	28.6637i	−0.224497	+	1.56141i	0.496227	+	0.868193i	$0.334718\pi$
$337$	−4.12123	+	28.6637i	−0.224497	+	1.56141i	−0.720725	+	0.693221i	$0.756191\pi$
$338$	−8.51022	+	9.82132i	−0.462895	+	0.534209i
$339$		0			0
$340$	−5.09173	−	1.49507i	−0.276138	−	0.0810813i
$341$	−0.586244	−	1.28370i	−0.0317469	−	0.0695160i
$342$		0			0
$343$	14.6967	+	9.44498i	0.793546	+	0.509981i
$344$	−6.57798			−0.354661
$345$		0			0
$346$	17.1947			0.924392
$347$	15.8066	+	10.1583i	0.848542	+	0.545325i	0.891120	−	0.453768i	$-0.149921\pi$
$347$	15.8066	+	10.1583i	0.848542	+	0.545325i	−0.0425775	+	0.999093i	$0.513557\pi$
$348$		0			0
$349$	−6.47312	−	14.1742i	−0.346498	−	0.758726i	−0.999998	−	0.00179906i	$-0.999427\pi$
$349$	−6.47312	−	14.1742i	−0.346498	−	0.758726i	0.653500	−	0.756926i	$-0.273300\pi$
$350$	4.92547	+	1.44625i	0.263277	+	0.0773052i
$351$		0			0
$352$	0.580699	−	0.670163i	0.0309514	−	0.0357198i
$353$	−3.30751	+	23.0043i	−0.176041	+	1.22439i	0.689772	+	0.724026i	$0.257711\pi$
$353$	−3.30751	+	23.0043i	−0.176041	+	1.22439i	−0.865813	+	0.500367i	$0.833198\pi$
$354$		0			0
$355$	−5.92571	−	6.83864i	−0.314504	−	0.362957i
$356$	−9.86241	+	6.33818i	−0.522706	+	0.335923i
$357$		0			0
$358$	3.99989	+	4.61612i	0.211401	+	0.243969i
$359$	13.8642	−	4.07088i	0.731722	−	0.214853i	0.105414	−	0.994428i	$-0.466383\pi$
$359$	13.8642	−	4.07088i	0.731722	−	0.214853i	0.626308	+	0.779575i	$0.284565\pi$
$360$		0			0
$361$	−1.82472	+	2.10584i	−0.0960381	+	0.110834i
$362$	−8.92730	+	19.5481i	−0.469209	+	1.02742i
$363$		0			0
$364$	−0.0413515	−	0.0905471i	−0.00216741	−	0.00474596i
$365$	−2.32241	−	16.1527i	−0.121560	−	0.845471i
$366$		0			0
$367$	26.6056			1.38880			0.694400	−	0.719589i	$-0.255670\pi$
$367$	26.6056			1.38880			0.694400	+	0.719589i	$0.255670\pi$
$368$	−3.73149	+	3.01264i	−0.194517	+	0.157045i
$369$		0			0
$370$	5.43886	+	3.49534i	0.282753	+	0.181714i
$371$	0.630473	+	4.38504i	0.0327326	+	0.227660i
$372$		0			0
$373$	4.68285	+	1.37501i	0.242469	+	0.0711952i	0.400709	−	0.916205i	$-0.368764\pi$
$373$	4.68285	+	1.37501i	0.242469	+	0.0711952i	−0.158240	+	0.987401i	$0.550582\pi$
$374$	−1.58096	+	3.46182i	−0.0817495	+	0.179007i
$375$		0			0
$376$	−1.18302	+	8.22810i	−0.0610097	+	0.424332i
$377$	−0.495874	+	0.145602i	−0.0255388	+	0.00749887i
$378$		0			0
$379$	2.86938	−	1.84404i	0.147390	−	0.0947219i	−0.464867	−	0.885380i	$-0.653898\pi$
$379$	2.86938	−	1.84404i	0.147390	−	0.0947219i	0.612257	+	0.790658i	$0.290262\pi$
$380$	−4.85519	+	3.12024i	−0.249066	+	0.160065i
$381$		0			0
$382$	2.71990	−	0.798636i	0.139162	−	0.0408618i
$383$	−4.03782	+	28.0837i	−0.206323	+	1.43501i	0.578699	+	0.815541i	$0.303561\pi$
$383$	−4.03782	+	28.0837i	−0.206323	+	1.43501i	−0.785022	+	0.619468i	$0.787348\pi$
$384$		0			0
$385$	−0.673608	+	1.47500i	−0.0343303	+	0.0751728i
$386$	−23.1120	−	6.78629i	−1.17637	−	0.345413i
$387$		0			0
$388$	2.44305	+	16.9918i	0.124027	+	0.862626i
$389$	8.96250	+	5.75985i	0.454417	+	0.292036i	0.747757	−	0.663972i	$-0.231131\pi$
$389$	8.96250	+	5.75985i	0.454417	+	0.292036i	−0.293341	+	0.956008i	$0.594767\pi$
$390$		0			0
$391$	11.7233	−	16.9177i	0.592873	−	0.855564i
$392$	4.81288			0.243087
$393$		0			0
$394$	3.50172	+	24.3550i	0.176414	+	1.22699i
$395$	4.05501	+	8.87922i	0.204029	+	0.446762i
$396$		0			0
$397$	8.68866	−	19.0255i	0.436071	−	0.954863i	−0.556231	−	0.831028i	$-0.687753\pi$
$397$	8.68866	−	19.0255i	0.436071	−	0.954863i	0.992303	−	0.123836i	$-0.0395196\pi$
$398$	4.11111	−	4.74447i	0.206071	−	0.237819i
$399$		0			0
$400$	3.33052	−	0.977928i	0.166526	−	0.0488964i
$401$	2.65293	+	3.06164i	0.132481	+	0.152891i	0.818114	−	0.575056i	$-0.195020\pi$
$401$	2.65293	+	3.06164i	0.132481	+	0.152891i	−0.685633	+	0.727948i	$0.740474\pi$
$402$		0			0
$403$	−0.0901143	+	0.0579129i	−0.00448891	+	0.00288485i
$404$	3.92073	+	4.52476i	0.195064	+	0.225115i
$405$		0			0
$406$	−1.61601	+	11.2396i	−0.0802011	+	0.557811i
$407$	3.03631	−	3.50408i	0.150504	−	0.173691i
$408$		0			0
$409$	−23.3930	−	6.86879i	−1.15671	−	0.339640i	−0.353555	−	0.935414i	$-0.615027\pi$
$409$	−23.3930	−	6.86879i	−1.15671	−	0.339640i	−0.803152	+	0.595774i	$0.796845\pi$
$410$	−0.0698220	−	0.152889i	−0.00344826	−	0.00755064i
$411$		0			0
$412$	−13.1585	−	8.45644i	−0.648272	−	0.416619i
$413$	−10.1093			−0.497448
$414$		0			0
$415$	10.3970			0.510370
$416$	−0.0566239	−	0.0363899i	−0.00277621	−	0.00178416i
$417$		0			0
$418$	1.71940	+	3.76497i	0.0840987	+	0.184151i
$419$	13.5462	+	3.97753i	0.661777	+	0.194315i	0.595338	−	0.803475i	$-0.297018\pi$
$419$	13.5462	+	3.97753i	0.661777	+	0.194315i	0.0664387	+	0.997791i	$0.478836\pi$
$420$		0			0
$421$	−14.6127	+	16.8639i	−0.712179	+	0.821898i	−0.990343	−	0.138635i	$-0.955728\pi$
$421$	−14.6127	+	16.8639i	−0.712179	+	0.821898i	0.278165	+	0.960533i	$0.410274\pi$
$422$	2.75941	−	19.1922i	0.134326	−	0.934259i
$423$		0			0
$424$	1.96169	+	2.26391i	0.0952679	+	0.109945i
$425$	−12.5324	+	8.05406i	−0.607909	+	0.390679i
$426$		0			0
$427$	−4.45509	−	5.14145i	−0.215597	−	0.248812i
$428$	−13.2588	+	3.89313i	−0.640887	+	0.188182i
$429$		0			0
$430$	5.32633	−	6.14692i	0.256859	−	0.296431i
$431$	7.48448	−	16.3887i	0.360515	−	0.789417i	−0.639276	−	0.768977i	$-0.720766\pi$
$431$	7.48448	−	16.3887i	0.360515	−	0.789417i	0.999791	−	0.0204400i	$-0.00650671\pi$
$432$		0			0
$433$	8.60579	+	18.8441i	0.413568	+	0.905588i	0.995712	+	0.0925023i	$0.0294865\pi$
$433$	8.60579	+	18.8441i	0.413568	+	0.905588i	−0.582144	+	0.813085i	$0.697786\pi$
$434$	0.334950	+	2.32963i	0.0160781	+	0.111826i
$435$		0			0
$436$	10.7865			0.516581
$437$	−5.55574	−	21.6846i	−0.265767	−	1.03731i
$438$		0			0
$439$	−11.4339	−	7.34811i	−0.545709	−	0.350706i	0.238559	−	0.971128i	$-0.423325\pi$
$439$	−11.4339	−	7.34811i	−0.545709	−	0.350706i	−0.784268	+	0.620422i	$0.786961\pi$
$440$	0.156041	+	1.08529i	0.00743897	+	0.0517392i
$441$		0			0
$442$	0.277173	+	0.0813853i	0.0131838	+	0.00387111i
$443$	−4.32136	+	9.46245i	−0.205314	+	0.449575i	−0.984077	−	0.177744i	$-0.943120\pi$
$443$	−4.32136	+	9.46245i	−0.205314	+	0.449575i	0.778763	+	0.627318i	$0.215847\pi$
$444$		0			0
$445$	2.06297	−	14.3483i	0.0977941	−	0.680173i
$446$	19.7401	−	5.79623i	0.934723	−	0.274459i
$447$		0			0
$448$	−1.24412	+	0.799549i	−0.0587793	+	0.0377751i
$449$	−9.02816	+	5.80205i	−0.426065	+	0.273816i	−0.736052	−	0.676925i	$-0.763312\pi$
$449$	−9.02816	+	5.80205i	−0.426065	+	0.273816i	0.309986	+	0.950741i	$0.399676\pi$
$450$		0			0
$451$	−0.115656	+	0.0339596i	−0.00544602	+	0.00159910i
$452$	−0.650424	+	4.52380i	−0.0305934	+	0.212782i
$453$		0			0
$454$	−9.56420	+	20.9427i	−0.448870	+	0.982888i
$455$	0.118097	+	0.0346763i	0.00553645	+	0.00162565i
$456$		0			0
$457$	−0.120293	−	0.836659i	−0.00562709	−	0.0391373i	0.986814	−	0.161856i	$-0.0517479\pi$
$457$	−0.120293	−	0.836659i	−0.00562709	−	0.0391373i	−0.992442	+	0.122718i	$0.960839\pi$
$458$	−6.31249	−	4.05679i	−0.294963	−	0.189561i
$459$		0			0
$460$	0.206248	−	5.92636i	0.00961635	−	0.276318i
$461$	17.2385			0.802875			0.401437	−	0.915886i	$-0.368511\pi$
$461$	17.2385			0.802875			0.401437	+	0.915886i	$0.368511\pi$
$462$		0			0
$463$	0.257950	+	1.79408i	0.0119879	+	0.0833780i	0.994937	−	0.100500i	$-0.0320441\pi$
$463$	0.257950	+	1.79408i	0.0119879	+	0.0833780i	−0.982949	+	0.183878i	$0.941135\pi$
$464$	3.18962	+	6.98430i	0.148074	+	0.324238i
$465$		0			0
$466$	10.1229	−	22.1661i	0.468936	−	1.02683i
$467$	−21.4942	+	24.8056i	−0.994632	+	1.14787i	−0.00562656	+	0.999984i	$0.501791\pi$
$467$	−21.4942	+	24.8056i	−0.994632	+	1.14787i	−0.989005	+	0.147882i	$0.952754\pi$
$468$		0			0
$469$	17.6027	−	5.16861i	0.812816	−	0.238664i
$470$	−6.73098	−	7.76796i	−0.310477	−	0.358309i
$471$		0			0
$472$	−5.75061	+	3.69569i	−0.264693	+	0.170108i
$473$	−3.81983	−	4.40832i	−0.175636	−	0.202695i
$474$		0			0
$475$	−2.30575	+	16.0369i	−0.105795	+	0.735822i
$476$	4.15644	−	4.79679i	0.190510	−	0.219861i
$477$		0			0
$478$	−8.34418	−	2.45007i	−0.381654	−	0.112064i
$479$	8.40139	+	18.3965i	0.383869	+	0.840556i	0.998654	+	0.0518616i	$0.0165155\pi$
$479$	8.40139	+	18.3965i	0.383869	+	0.840556i	−0.614785	+	0.788695i	$0.710757\pi$
$480$		0			0
$481$	−0.296070	−	0.190272i	−0.0134996	−	0.00867567i
$482$	5.67714			0.258587
$483$		0			0
$484$	−10.2137			−0.464258
$485$	−17.8564	−	11.4756i	−0.810820	−	0.521082i
$486$		0			0
$487$	−16.4337	−	35.9848i	−0.744683	−	1.63063i	−0.775694	−	0.631109i	$-0.782600\pi$
$487$	−16.4337	−	35.9848i	−0.744683	−	1.63063i	0.0310108	−	0.999519i	$-0.490127\pi$
$488$	−4.41381	−	1.29601i	−0.199804	−	0.0586676i
$489$		0			0
$490$	−3.89709	+	4.49748i	−0.176053	+	0.203176i
$491$	3.46222	−	24.0803i	0.156248	−	1.08673i	−0.749223	−	0.662318i	$-0.769573\pi$
$491$	3.46222	−	24.0803i	0.156248	−	1.08673i	0.905471	−	0.424409i	$-0.139518\pi$
$492$		0			0
$493$	−21.5796	−	24.9041i	−0.971894	−	1.12163i
$494$	0.264297	−	0.169853i	0.0118913	−	0.00764207i
$495$		0			0
$496$	1.04218	+	1.20274i	0.0467953	+	0.0540047i
$497$	10.3844	−	3.04915i	0.465806	−	0.136773i
$498$		0			0
$499$	10.3963	−	11.9980i	0.465402	−	0.537103i	−0.473725	−	0.880673i	$-0.657091\pi$
$499$	10.3963	−	11.9980i	0.465402	−	0.537103i	0.939127	+	0.343570i	$0.111636\pi$
$500$	−4.35121	+	9.52781i	−0.194592	+	0.426097i
$501$		0			0
$502$	2.48589	+	5.44334i	0.110951	+	0.242948i
$503$	0.931282	+	6.47721i	0.0415238	+	0.288804i	0.999993	+	0.00360998i	$0.00114909\pi$
$503$	0.931282	+	6.47721i	0.0415238	+	0.288804i	−0.958470	+	0.285194i	$0.907942\pi$
$504$		0			0
$505$	−7.40295			−0.329427
$506$	−4.18583	−	0.751265i	−0.186083	−	0.0333978i
$507$		0			0
$508$	−12.1204	−	7.78931i	−0.537756	−	0.345595i
$509$	−2.54211	−	17.6808i	−0.112677	−	0.783686i	−0.965297	−	0.261155i	$-0.915897\pi$
$509$	−2.54211	−	17.6808i	−0.112677	−	0.783686i	0.852620	−	0.522532i	$-0.175012\pi$
$510$		0			0
$511$	18.7275	+	5.49889i	0.828456	+	0.243256i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$		0			0
$514$	−2.21417	+	15.3999i	−0.0976628	+	0.679259i
$515$	18.5570	−	5.44882i	0.817718	−	0.240104i
$516$		0			0
$517$	−6.20114	+	3.98523i	−0.272726	+	0.175270i
$518$	−6.50515	+	4.18061i	−0.285820	+	0.183685i
$519$		0			0
$520$	0.0798548	−	0.0234475i	0.00350186	−	0.00102824i
$521$	1.68411	−	11.7133i	0.0737824	−	0.513168i	−0.919096	−	0.394034i	$-0.871079\pi$
$521$	1.68411	−	11.7133i	0.0737824	−	0.513168i	0.992878	−	0.119134i	$-0.0380117\pi$
$522$		0			0
$523$	−6.65182	+	14.5655i	−0.290864	+	0.636903i	−0.997499	−	0.0706745i	$-0.977485\pi$
$523$	−6.65182	+	14.5655i	−0.290864	+	0.636903i	0.706635	+	0.707578i	$0.250212\pi$
$524$	−4.39446	−	1.29033i	−0.191973	−	0.0563683i
$525$		0			0
$526$	−1.46110	−	10.1622i	−0.0637069	−	0.443091i
$527$	−5.74589	−	3.69266i	−0.250295	−	0.160855i
$528$		0			0
$529$	21.5645	+	7.99835i	0.937586	+	0.347754i
$530$	−3.70397			−0.160890
$531$		0			0
$532$	−0.982380	−	6.83260i	−0.0425916	−	0.296231i
$533$	0.00380083	+	0.00832265i	0.000164632	+	0.000360494i
$534$		0			0
$535$	7.09791	−	15.5423i	0.306870	−	0.671951i
$536$	8.12362	−	9.37515i	0.350887	−	0.404945i
$537$		0			0
$538$	3.11177	−	0.913697i	0.134158	−	0.0393923i
$539$	2.79484	+	3.22541i	0.120382	+	0.138928i
$540$		0			0
$541$	−16.4485	+	10.5708i	−0.707176	+	0.454474i	−0.844155	−	0.536100i	$-0.819897\pi$
$541$	−16.4485	+	10.5708i	−0.707176	+	0.454474i	0.136979	+	0.990574i	$0.456261\pi$
$542$	10.1545	+	11.7189i	0.436173	+	0.503371i
$543$		0			0
$544$	0.610783	−	4.24809i	0.0261871	−	0.182135i
$545$	−8.73408	+	10.0797i	−0.374127	+	0.431766i
$546$		0			0
$547$	1.08922	+	0.319825i	0.0465718	+	0.0136747i	0.304936	−	0.952373i	$-0.401365\pi$
$547$	1.08922	+	0.319825i	0.0465718	+	0.0136747i	−0.258364	+	0.966048i	$0.583183\pi$
$548$	3.83340	+	8.39398i	0.163755	+	0.358573i
$549$		0			0
$550$	2.58940	+	1.66411i	0.110412	+	0.0709577i
$551$	−35.8385			−1.52677
$552$		0			0
$553$	−11.6751			−0.496474
$554$	−1.81974	−	1.16948i	−0.0773134	−	0.0496863i
$555$		0			0
$556$	3.24914	+	7.11462i	0.137794	+	0.301727i
$557$	39.5797	+	11.6216i	1.67704	+	0.492425i	0.975463	−	0.220165i	$-0.0706595\pi$
$557$	39.5797	+	11.6216i	1.67704	+	0.492425i	0.701581	+	0.712589i	$0.252478\pi$
$558$		0			0
$559$	−0.289944	+	0.334613i	−0.0122633	+	0.0141526i
$560$	0.260239	−	1.81001i	0.0109971	−	0.0764867i
$561$		0			0
$562$	−13.4614	−	15.5353i	−0.567834	−	0.655315i
$563$	23.7576	−	15.2681i	1.00126	−	0.643472i	0.0661443	−	0.997810i	$-0.478930\pi$
$563$	23.7576	−	15.2681i	1.00126	−	0.643472i	0.935117	+	0.354338i	$0.115294\pi$
$564$		0			0
$565$	−3.70069	−	4.27082i	−0.155689	−	0.179675i
$566$	16.2503	−	4.77152i	0.683051	−	0.200562i
$567$		0			0
$568$	4.79241	−	5.53073i	0.201085	−	0.232064i
$569$	17.2528	−	37.7784i	0.723276	−	1.58375i	−0.0859792	−	0.996297i	$-0.527402\pi$
$569$	17.2528	−	37.7784i	0.723276	−	1.58375i	0.809255	−	0.587457i	$-0.199871\pi$
$570$		0			0
$571$	−13.0934	−	28.6706i	−0.547943	−	1.19983i	−0.957736	−	0.287649i	$-0.907126\pi$
$571$	−13.0934	−	28.6706i	−0.547943	−	1.19983i	0.409793	−	0.912178i	$-0.365601\pi$
$572$	−0.00849425	−	0.0590788i	−0.000355162	−	0.00247021i
$573$		0			0
$574$	0.201029			0.00839081
$575$	−12.1941	−	11.3324i	−0.508530	−	0.472593i
$576$		0			0
$577$	17.3206	+	11.1313i	0.721065	+	0.463400i	0.849007	−	0.528381i	$-0.177201\pi$
$577$	17.3206	+	11.1313i	0.721065	+	0.463400i	−0.127942	+	0.991782i	$0.540837\pi$
$578$	0.201988	+	1.40486i	0.00840159	+	0.0584343i
$579$		0			0
$580$	−9.10931	−	2.67473i	−0.378243	−	0.111062i
$581$	−5.16584	+	11.3116i	−0.214315	+	0.469285i
$582$		0			0
$583$	−0.378036	+	2.62930i	−0.0156566	+	0.108894i
$584$	12.6632	−	3.71825i	0.524007	−	0.153862i
$585$		0			0
$586$	1.73495	−	1.11498i	0.0716701	−	0.0460596i
$587$	−7.15977	+	4.60131i	−0.295515	+	0.189916i	−0.679994	−	0.733218i	$-0.738018\pi$
$587$	−7.15977	+	4.60131i	−0.295515	+	0.189916i	0.384479	+	0.923134i	$0.374381\pi$
$588$		0			0
$589$	−7.12736	+	2.09278i	−0.293678	+	0.0862316i
$590$	1.20288	−	8.36624i	0.0495219	−	0.344433i
$591$		0			0
$592$	−2.17208	+	4.75620i	−0.0892721	+	0.195479i
$593$	−9.09061	−	2.66924i	−0.373306	−	0.109613i	0.0896971	−	0.995969i	$-0.471410\pi$
$593$	−9.09061	−	2.66924i	−0.373306	−	0.109613i	−0.463004	+	0.886356i	$0.653228\pi$
$594$		0			0
$595$	1.11689	+	7.76813i	0.0457880	+	0.318462i
$596$	4.16624	+	2.67748i	0.170656	+	0.109674i
$597$		0			0
$598$	−0.0112273	+	0.322607i	−0.000459118	+	0.0131924i
$599$	2.52422			0.103137			0.0515684	−	0.998669i	$-0.483578\pi$
$599$	2.52422			0.103137			0.0515684	+	0.998669i	$0.483578\pi$
$600$		0			0
$601$	2.68152	+	18.6504i	0.109381	+	0.760765i	0.968505	+	0.248996i	$0.0801006\pi$
$601$	2.68152	+	18.6504i	0.109381	+	0.760765i	−0.859123	+	0.511769i	$0.828990\pi$
$602$	4.04121	+	8.84901i	0.164707	+	0.360659i
$603$		0			0
$604$	6.38229	−	13.9753i	0.259692	−	0.568646i
$605$	8.27023	−	9.54435i	0.336233	−	0.388033i
$606$		0			0
$607$	−3.12161	+	0.916586i	−0.126702	+	0.0372031i	−0.344469	−	0.938798i	$-0.611941\pi$
$607$	−3.12161	+	0.916586i	−0.126702	+	0.0372031i	0.217767	+	0.976001i	$0.430123\pi$
$608$	−3.05662	−	3.52753i	−0.123962	−	0.143060i
$609$		0			0
$610$	4.78504	−	3.07516i	0.193740	−	0.124509i
$611$	0.366407	+	0.422856i	0.0148232	+	0.0171069i
$612$		0			0
$613$	−2.29523	+	15.9637i	−0.0927036	+	0.644767i	0.889498	+	0.456939i	$0.151054\pi$
$613$	−2.29523	+	15.9637i	−0.0927036	+	0.644767i	−0.982202	+	0.187829i	$0.939855\pi$
$614$	−2.67378	+	3.08570i	−0.107905	+	0.124529i
$615$		0			0
$616$	−1.25829	−	0.369467i	−0.0506979	−	0.0148862i
$617$	−0.963458	−	2.10968i	−0.0387874	−	0.0849325i	0.889247	−	0.457428i	$-0.151229\pi$
$617$	−0.963458	−	2.10968i	−0.0387874	−	0.0849325i	−0.928034	+	0.372496i	$0.878502\pi$
$618$		0			0
$619$	27.7569	+	17.8383i	1.11565	+	0.716982i	0.962516	−	0.271224i	$-0.0874285\pi$
$619$	27.7569	+	17.8383i	1.11565	+	0.716982i	0.153130	+	0.988206i	$0.451065\pi$
$620$	−1.96780			−0.0790287
$621$		0			0
$622$	−12.7493			−0.511199
$623$	14.5854	+	9.37349i	0.584353	+	0.375541i
$624$		0			0
$625$	1.82960	+	4.00627i	0.0731841	+	0.160251i
$626$	−7.46705	−	2.19252i	−0.298443	−	0.0876308i
$627$		0			0
$628$	−8.19051	+	9.45235i	−0.326837	+	0.377190i
$629$	3.19360	−	22.2120i	0.127337	−	0.885651i
$630$		0			0
$631$	19.9373	+	23.0089i	0.793693	+	0.915971i	0.998018	−	0.0629326i	$-0.0200453\pi$
$631$	19.9373	+	23.0089i	0.793693	+	0.915971i	−0.204325	+	0.978903i	$0.565500\pi$
$632$	−6.64125	+	4.26807i	−0.264175	+	0.169775i
$633$		0			0
$634$	−12.9340	−	14.9266i	−0.513674	−	0.592811i
$635$	17.0930	−	5.01896i	0.678316	−	0.199171i
$636$		0			0
$637$	0.212142	−	0.244825i	0.00840537	−	0.00970031i
$638$	−2.82840	+	6.19334i	−0.111978	+	0.245197i
$639$		0			0
$640$	−0.513652	−	1.12474i	−0.0203039	−	0.0444593i
$641$	−6.36692	−	44.2829i	−0.251478	−	1.74907i	−0.589349	−	0.807878i	$-0.700616\pi$
$641$	−6.36692	−	44.2829i	−0.251478	−	1.74907i	0.337871	−	0.941192i	$-0.390293\pi$
$642$		0			0
$643$	26.8514			1.05892			0.529459	−	0.848336i	$-0.322395\pi$
$643$	26.8514			1.05892			0.529459	+	0.848336i	$0.322395\pi$
$644$	6.34520	+	3.16894i	0.250036	+	0.124874i
$645$		0			0
$646$	16.8522	+	10.8302i	0.663041	+	0.426110i
$647$	−3.26100	−	22.6807i	−0.128203	−	0.891672i	−0.947831	−	0.318775i	$-0.896729\pi$
$647$	−3.26100	−	22.6807i	−0.128203	−	0.891672i	0.819627	−	0.572897i	$-0.194180\pi$
$648$		0			0
$649$	−5.81609	−	1.70776i	−0.228301	−	0.0670353i
$650$	0.0970564	−	0.212524i	0.00380687	−	0.00833588i
$651$		0			0
$652$	1.48435	−	10.3239i	0.0581316	−	0.404314i
$653$	−44.1721	+	12.9701i	−1.72859	+	0.507559i	−0.986643	−	0.162900i	$-0.947915\pi$
$653$	−44.1721	+	12.9701i	−1.72859	+	0.507559i	−0.741946	+	0.670460i	$0.766097\pi$
$654$		0			0
$655$	4.76406	−	3.06167i	0.186147	−	0.119629i
$656$	0.114354	−	0.0734907i	0.00446476	−	0.00286933i
$657$		0			0
$658$	11.7956	−	3.46350i	0.459841	−	0.135021i
$659$	−3.93338	+	27.3572i	−0.153223	+	1.06569i	0.757550	+	0.652777i	$0.226396\pi$
$659$	−3.93338	+	27.3572i	−0.153223	+	1.06569i	−0.910772	+	0.412909i	$0.864513\pi$
$660$		0			0
$661$	2.19760	−	4.81208i	0.0854769	−	0.187168i	−0.862067	−	0.506795i	$-0.830830\pi$
$661$	2.19760	−	4.81208i	0.0854769	−	0.187168i	0.947544	+	0.319627i	$0.103557\pi$
$662$	−4.11794	−	1.20914i	−0.160048	−	0.0469944i
$663$		0			0
$664$	1.19667	+	8.32299i	0.0464396	+	0.322995i
$665$	7.18031	+	4.61450i	0.278440	+	0.178943i
$666$		0			0
$667$	20.9735	−	30.2664i	0.812096	−	1.17192i
$668$	25.3684			0.981532
$669$		0			0
$670$	2.18292	+	15.1825i	0.0843335	+	0.586552i
$671$	−1.69456	−	3.71056i	−0.0654176	−	0.143245i
$672$		0			0
$673$	−16.8850	+	36.9729i	−0.650867	+	1.42520i	0.239925	+	0.970791i	$0.422877\pi$
$673$	−16.8850	+	36.9729i	−0.650867	+	1.42520i	−0.890793	+	0.454410i	$0.849850\pi$
$674$	18.9638	−	21.8854i	0.730458	−	0.842993i
$675$		0			0
$676$	12.4691	−	3.66125i	0.479579	−	0.140817i
$677$	−10.1058	−	11.6627i	−0.388398	−	0.448235i	0.527555	−	0.849521i	$-0.323109\pi$
$677$	−10.1058	−	11.6627i	−0.388398	−	0.448235i	−0.915953	+	0.401286i	$0.868563\pi$
$678$		0			0
$679$	21.3572	−	13.7255i	0.819615	−	0.526734i
$680$	3.47514	+	4.01052i	0.133266	+	0.153797i
$681$		0			0
$682$	−0.200838	+	1.39686i	−0.00769050	+	0.0534886i
$683$	0.212035	−	0.244701i	0.00811329	−	0.00936324i	−0.751678	−	0.659530i	$-0.770755\pi$
$683$	0.212035	−	0.244701i	0.00811329	−	0.00936324i	0.759792	+	0.650167i	$0.225301\pi$
$684$		0			0
$685$	−10.9479	−	3.21459i	−0.418298	−	0.122823i
$686$	−7.25729	−	15.8912i	−0.277084	−	0.606730i
$687$		0			0
$688$	5.53375	+	3.55633i	0.210972	+	0.135584i
$689$	0.201629			0.00768145
$690$		0			0
$691$	−11.8762			−0.451791			−0.225896	−	0.974152i	$-0.572531\pi$
$691$	−11.8762			−0.451791			−0.225896	+	0.974152i	$0.572531\pi$
$692$	−14.4651	−	9.29615i	−0.549880	−	0.353387i
$693$		0			0
$694$	−7.80537	−	17.0914i	−0.296288	−	0.648780i
$695$	−9.27928	−	2.72464i	−0.351983	−	0.103352i
$696$		0			0
$697$	−0.382040	+	0.440898i	−0.0144708	+	0.0167002i
$698$	−2.21759	+	15.4237i	−0.0839371	+	0.583796i
$699$		0			0
$700$	−3.36167	−	3.87957i	−0.127059	−	0.146634i
$701$	−24.5131	+	15.7536i	−0.925847	+	0.595006i	−0.914349	−	0.404928i	$-0.867297\pi$
$701$	−24.5131	+	15.7536i	−0.925847	+	0.595006i	−0.0114986	+	0.999934i	$0.503660\pi$
$702$		0			0
$703$	−15.9822	−	18.4444i	−0.602780	−	0.695645i
$704$	−0.850833	+	0.249827i	−0.0320670	+	0.00941571i
$705$		0			0
$706$	15.2195	−	17.5642i	0.572793	−	0.661039i
$707$	3.67821	−	8.05415i	0.138333	−	0.302908i
$708$		0			0
$709$	−5.53351	−	12.1167i	−0.207815	−	0.455052i	0.776809	−	0.629736i	$-0.216837\pi$
$709$	−5.53351	−	12.1167i	−0.207815	−	0.455052i	−0.984625	+	0.174684i	$0.944110\pi$
$710$	1.28778	+	8.95671i	0.0483295	+	0.336139i
$711$		0			0
$712$	11.7235			0.439355
$713$	2.40368	−	7.24396i	0.0900187	−	0.271289i
$714$		0			0
$715$	0.0620853	+	0.0398998i	0.00232186	+	0.00149217i
$716$	−0.869259	−	6.04583i	−0.0324857	−	0.225943i
$717$		0			0
$718$	−13.8642	−	4.07088i	−0.517406	−	0.151924i
$719$	−16.9387	+	37.0905i	−0.631705	+	1.38324i	0.274987	+	0.961448i	$0.411327\pi$
$719$	−16.9387	+	37.0905i	−0.631705	+	1.38324i	−0.906692	+	0.421793i	$0.861401\pi$
$720$		0			0
$721$	−3.29204	+	22.8966i	−0.122602	+	0.852716i
$722$	2.67356	−	0.785028i	0.0994996	−	0.0292157i
$723$		0			0
$724$	18.0786	−	11.6184i	0.671886	−	0.431795i
$725$	−22.4209	+	14.4091i	−0.832692	+	0.535139i
$726$		0			0
$727$	31.5364	−	9.25993i	1.16962	−	0.343432i	0.361457	−	0.932389i	$-0.382279\pi$
$727$	31.5364	−	9.25993i	1.16962	−	0.343432i	0.808164	+	0.588957i	$0.200461\pi$
$728$	−0.0141664	+	0.0985294i	−0.000525041	+	0.00365174i
$729$		0			0
$730$	−6.77908	+	14.8441i	−0.250905	+	0.549405i
$731$	−27.0876	−	7.95365i	−1.00187	−	0.294176i
$732$		0			0
$733$	−6.98884	−	48.6085i	−0.258139	−	1.79539i	−0.546066	−	0.837742i	$-0.683875\pi$
$733$	−6.98884	−	48.6085i	−0.258139	−	1.79539i	0.287927	−	0.957652i	$-0.407034\pi$
$734$	−22.3820	−	14.3841i	−0.826136	−	0.530925i
$735$		0			0
$736$	4.76788	−	0.517000i	0.175747	−	0.0190569i
$737$	11.0003			0.405200
$738$		0			0
$739$	6.02772	+	41.9237i	0.221733	+	1.54219i	0.731480	+	0.681863i	$0.238830\pi$
$739$	6.02772	+	41.9237i	0.221733	+	1.54219i	−0.509746	+	0.860325i	$0.670261\pi$
$740$	−2.68574	−	5.88094i	−0.0987296	−	0.216188i
$741$		0			0
$742$	1.84034	−	4.02979i	0.0675611	−	0.147938i
$743$	−1.74263	+	2.01110i	−0.0639308	+	0.0737800i	−0.786814	−	0.617190i	$-0.788271\pi$
$743$	−1.74263	+	2.01110i	−0.0639308	+	0.0737800i	0.722883	+	0.690970i	$0.242816\pi$
$744$		0			0
$745$	−5.87551	+	1.72521i	−0.215262	+	0.0632067i
$746$	−3.19608	−	3.68847i	−0.117017	−	0.135044i
$747$		0			0
$748$	3.20159	−	2.05754i	0.117062	−	0.0752310i
$749$	13.3828	+	15.4446i	0.488997	+	0.564333i
$750$		0			0
$751$	−5.28345	+	36.7472i	−0.192796	+	1.34093i	0.631768	+	0.775157i	$0.282329\pi$
$751$	−5.28345	+	36.7472i	−0.192796	+	1.34093i	−0.824564	+	0.565768i	$0.808580\pi$
$752$	5.44367	−	6.28232i	0.198510	−	0.229093i
$753$		0			0
$754$	0.495874	+	0.145602i	0.0180587	+	0.00530250i
$755$	7.89157	+	17.2801i	0.287204	+	0.628888i
$756$		0			0
$757$	−19.5572	−	12.5686i	−0.710817	−	0.456814i	0.134615	−	0.990898i	$-0.457020\pi$
$757$	−19.5572	−	12.5686i	−0.710817	−	0.456814i	−0.845432	+	0.534084i	$0.820657\pi$
$758$	−3.41084			−0.123887
$759$		0			0
$760$	5.77138			0.209350
$761$	−14.8440	−	9.53963i	−0.538093	−	0.345811i	0.243200	−	0.969976i	$-0.421803\pi$
$761$	−14.8440	−	9.53963i	−0.538093	−	0.345811i	−0.781293	+	0.624165i	$0.785439\pi$
$762$		0			0
$763$	−6.62674	−	14.5105i	−0.239904	−	0.525317i
$764$	−2.71990	−	0.798636i	−0.0984027	−	0.0288936i
$765$		0			0
$766$	18.5800	−	21.4425i	0.671324	−	0.774749i
$767$	−0.0654801	+	0.455424i	−0.00236435	+	0.0164444i
$768$		0			0
$769$	−23.9460	−	27.6351i	−0.863513	−	0.996548i	−0.999983	−	0.00590334i	$-0.998121\pi$
$769$	−23.9460	−	27.6351i	−0.863513	−	0.996548i	0.136469	−	0.990644i	$-0.456425\pi$
$770$	1.36412	−	0.876666i	0.0491594	−	0.0315928i
$771$		0			0
$772$	15.7741	+	18.2043i	0.567722	+	0.655186i
$773$	9.45937	−	2.77752i	0.340230	−	0.0999005i	−0.107154	−	0.994242i	$-0.534174\pi$
$773$	9.45937	−	2.77752i	0.340230	−	0.0999005i	0.447384	+	0.894342i	$0.352356\pi$
$774$		0			0
$775$	−3.61753	+	4.17486i	−0.129946	+	0.149965i
$776$	7.13122	−	15.6152i	0.255996	−	0.560553i
$777$		0			0
$778$	−4.42572	−	9.69098i	−0.158670	−	0.347439i
$779$	0.0902956	+	0.628020i	0.00323518	+	0.0225011i
$780$		0			0
$781$	6.48944			0.232210
$782$	−19.0087	+	7.89397i	−0.679748	+	0.282288i
$783$		0			0
$784$	−4.04885	−	2.60204i	−0.144602	−	0.0929300i
$785$	−2.20089	−	15.3075i	−0.0785532	−	0.546350i
$786$		0			0
$787$	−37.3444	−	10.9653i	−1.33119	−	0.390871i	−0.462669	−	0.886531i	$-0.653108\pi$
$787$	−37.3444	−	10.9653i	−1.33119	−	0.390871i	−0.868517	+	0.495660i	$0.834926\pi$
$788$	10.2215	−	22.3819i	0.364125	−	0.797322i
$789$		0			0
$790$	1.38918	−	9.66198i	0.0494249	−	0.343758i
$791$	6.48522	−	1.90423i	0.230588	−	0.0677067i
$792$		0			0
$793$	−0.260478	+	0.167399i	−0.00924984	+	0.00594451i
$794$	−17.5953	+	11.3078i	−0.624435	+	0.401300i
$795$		0			0
$796$	−6.02354	+	1.76867i	−0.213499	+	0.0626888i
$797$	0.194869	−	1.35534i	0.00690262	−	0.0480088i	−0.986079	−	0.166277i	$-0.946825\pi$
$797$	0.194869	−	1.35534i	0.00690262	−	0.0480088i	0.992982	+	0.118269i	$0.0377344\pi$
$798$		0			0
$799$	−14.8204	+	32.4522i	−0.524310	+	1.14808i
$800$	−3.33052	−	0.977928i	−0.117751	−	0.0345750i
$801$		0			0
$802$	−0.576537	−	4.00990i	−0.0203582	−	0.141595i
$803$	9.84534	+	6.32722i	0.347435	+	0.223283i
$804$		0			0
$805$	−8.09912	+	3.36342i	−0.285457	+	0.118545i
$806$	0.107119			0.00377311
$807$		0			0
$808$	−0.852056	−	5.92618i	−0.0299752	−	0.208482i
$809$	17.9872	+	39.3865i	0.632397	+	1.38476i	0.906150	+	0.422956i	$0.139008\pi$
$809$	17.9872	+	39.3865i	0.632397	+	1.38476i	−0.273753	+	0.961800i	$0.588265\pi$
$810$		0			0
$811$	3.97959	−	8.71409i	0.139742	−	0.305993i	−0.826802	−	0.562493i	$-0.809842\pi$
$811$	3.97959	−	8.71409i	0.139742	−	0.305993i	0.966544	+	0.256500i	$0.0825694\pi$
$812$	7.43605	−	8.58166i	0.260954	−	0.301157i
$813$		0			0
$814$	−4.44875	+	1.30627i	−0.155929	+	0.0457848i
$815$	8.44542	+	9.74654i	0.295830	+	0.341406i
$816$		0			0
$817$	−25.8293	+	16.5995i	−0.903653	+	0.580743i
$818$	15.9659	+	18.4256i	0.558233	+	0.644235i
$819$		0			0
$820$	−0.0239199	+	0.166367i	−0.000835321	+	0.00580978i
$821$	15.3589	−	17.7252i	0.536030	−	0.618612i	−0.421541	−	0.906810i	$-0.638510\pi$
$821$	15.3589	−	17.7252i	0.536030	−	0.618612i	0.957571	+	0.288197i	$0.0930559\pi$
$822$		0			0
$823$	8.95845	+	2.63044i	0.312272	+	0.0916913i	0.434113	−	0.900858i	$-0.357062\pi$
$823$	8.95845	+	2.63044i	0.312272	+	0.0916913i	−0.121841	+	0.992550i	$0.538880\pi$
$824$	6.49772	+	14.2280i	0.226359	+	0.495657i
$825$		0			0
$826$	8.50452	+	5.46553i	0.295910	+	0.190170i
$827$	54.7053			1.90229			0.951145	−	0.308745i	$-0.0999089\pi$
$827$	54.7053			1.90229			0.951145	+	0.308745i	$0.0999089\pi$
$828$		0			0
$829$	−55.3720			−1.92315			−0.961574	−	0.274545i	$-0.911473\pi$
$829$	−55.3720			−1.92315			−0.961574	+	0.274545i	$0.911473\pi$
$830$	−8.74654	−	5.62106i	−0.303597	−	0.195110i
$831$		0			0
$832$	0.0279611	+	0.0612263i	0.000969378	+	0.00212264i
$833$	19.8191	+	5.81941i	0.686690	+	0.201630i
$834$		0			0
$835$	−20.5413	+	23.7059i	−0.710862	+	0.820378i
$836$	0.589041	−	4.09687i	0.0203724	−	0.141693i
$837$		0			0
$838$	−9.24540	−	10.6698i	−0.319377	−	0.368581i
$839$	−9.81379	+	6.30694i	−0.338810	+	0.217740i	−0.698970	−	0.715151i	$-0.746358\pi$
$839$	−9.81379	+	6.30694i	−0.338810	+	0.217740i	0.360161	+	0.932890i	$0.382722\pi$
$840$		0			0
$841$	−19.6157	−	22.6378i	−0.676405	−	0.780613i
$842$	21.4103	−	6.28663i	0.737848	−	0.216652i
$843$		0			0
$844$	−12.6974	+	14.6536i	−0.437064	+	0.504398i
$845$	−6.67515	+	14.6165i	−0.229632	+	0.502824i
$846$		0			0
$847$	6.27481	+	13.7399i	0.215605	+	0.472109i
$848$	−0.426315	−	2.96509i	−0.0146397	−	0.101821i
$849$		0			0
$850$	14.8973			0.510972
$851$	24.9299	−	2.70324i	0.854585	−	0.0926660i
$852$		0			0
$853$	32.8461	+	21.1089i	1.12463	+	0.722756i	0.964433	−	0.264329i	$-0.0851504\pi$
$853$	32.8461	+	21.1089i	1.12463	+	0.722756i	0.160198	+	0.987085i	$0.448787\pi$
$854$	0.968184	+	6.73387i	0.0331306	+	0.230428i
$855$		0			0
$856$	13.2588	+	3.89313i	0.453176	+	0.133064i
$857$	−15.2899	+	33.4803i	−0.522294	+	1.14366i	0.446270	+	0.894898i	$0.352752\pi$
$857$	−15.2899	+	33.4803i	−0.522294	+	1.14366i	−0.968564	+	0.248765i	$0.919975\pi$
$858$		0			0
$859$	0.433930	−	3.01805i	0.0148055	−	0.102975i	−0.981079	−	0.193609i	$-0.937981\pi$
$859$	0.433930	−	3.01805i	0.0148055	−	0.102975i	0.995884	+	0.0906349i	$0.0288896\pi$
$860$	−7.80407	+	2.29148i	−0.266117	+	0.0781389i
$861$		0			0
$862$	−15.1568	+	9.74066i	−0.516241	+	0.331768i
$863$	11.5401	−	7.41637i	0.392830	−	0.252456i	−0.329284	−	0.944231i	$-0.606807\pi$
$863$	11.5401	−	7.41637i	0.392830	−	0.252456i	0.722113	+	0.691775i	$0.243171\pi$
$864$		0			0
$865$	20.3997	−	5.98988i	0.693609	−	0.203662i
$866$	2.94821	−	20.5053i	0.100184	−	0.696798i
$867$		0			0
$868$	0.977716	−	2.14090i	0.0331858	−	0.0726668i
$869$	−6.71687	−	1.97225i	−0.227854	−	0.0669040i
$870$		0			0
$871$	−0.118829	−	0.826475i	−0.00402637	−	0.0280041i
$872$	−9.07421	−	5.83164i	−0.307291	−	0.197484i
$873$		0			0
$874$	−7.04979	+	21.2459i	−0.238463	+	0.718653i
$875$	15.4904			0.523673
$876$		0			0
$877$	−3.00085	−	20.8714i	−0.101332	−	0.704776i	−0.975636	−	0.219397i	$-0.929591\pi$
$877$	−3.00085	−	20.8714i	−0.101332	−	0.704776i	0.874304	−	0.485379i	$-0.161318\pi$
$878$	5.64610	+	12.3632i	0.190547	+	0.417239i
$879$		0			0
$880$	0.455482	−	0.997366i	0.0153543	−	0.0336212i
$881$	−6.08185	+	7.01883i	−0.204903	+	0.236471i	−0.848895	−	0.528562i	$-0.822732\pi$
$881$	−6.08185	+	7.01883i	−0.204903	+	0.236471i	0.643992	+	0.765032i	$0.277277\pi$
$882$		0			0
$883$	−43.6009	+	12.8024i	−1.46729	+	0.430835i	−0.915216	−	0.402962i	$-0.867981\pi$
$883$	−43.6009	+	12.8024i	−1.46729	+	0.430835i	−0.552071	+	0.833797i	$0.686162\pi$
$884$	−0.189173	−	0.218317i	−0.00636256	−	0.00734279i
$885$		0			0
$886$	8.75114	−	5.62402i	0.294000	−	0.188943i
$887$	3.74676	+	4.32399i	0.125804	+	0.145186i	0.815157	−	0.579240i	$-0.196651\pi$
$887$	3.74676	+	4.32399i	0.125804	+	0.145186i	−0.689353	+	0.724426i	$0.742105\pi$
$888$		0			0
$889$	−3.03233	+	21.0903i	−0.101701	+	0.707347i
$890$	−9.49274	+	10.9552i	−0.318197	+	0.367219i
$891$		0			0
$892$	−19.7401	−	5.79623i	−0.660949	−	0.194072i
$893$	16.1182	+	35.2940i	0.539376	+	1.18107i
$894$		0			0
$895$	6.35349	+	4.08314i	0.212374	+	0.136484i
$896$	1.47889			0.0494063
$897$		0			0
$898$	10.7318			0.358125
$899$	−10.2796	−	6.60632i	−0.342845	−	0.220333i
$900$		0			0
$901$	5.34071	+	11.6945i	0.177925	+	0.389601i
$902$	0.115656	+	0.0339596i	0.00385092	+	0.00113073i
$903$		0			0
$904$	2.99292	−	3.45402i	0.0995431	−	0.114879i
$905$	−3.78159	+	26.3016i	−0.125704	+	0.874294i
$906$		0			0
$907$	17.2174	+	19.8700i	0.571695	+	0.659772i	0.965798	−	0.259295i	$-0.0834901\pi$
$907$	17.2174	+	19.8700i	0.571695	+	0.659772i	−0.394103	+	0.919066i	$0.628945\pi$
$908$	19.3684	−	12.4473i	0.642762	−	0.413078i
$909$		0			0
$910$	−0.0806018	−	0.0930194i	−0.00267192	−	0.00308356i
$911$	−47.3923	+	13.9156i	−1.57018	+	0.461046i	−0.947053	−	0.321077i	$-0.895955\pi$
$911$	−47.3923	+	13.9156i	−1.57018	+	0.461046i	−0.623124	+	0.782123i	$0.714137\pi$
$912$		0			0
$913$	−4.88286	+	5.63512i	−0.161599	+	0.186495i
$914$	−0.351135	+	0.768878i	−0.0116145	+	0.0254322i
$915$		0			0
$916$	3.11714	+	6.82558i	0.102993	+	0.225524i
$917$	0.963939	+	6.70435i	0.0318321	+	0.221397i
$918$		0			0
$919$	28.9737			0.955753			0.477876	−	0.878427i	$-0.341407\pi$
$919$	28.9737			0.955753			0.477876	+	0.878427i	$0.341407\pi$
$920$	−3.37754	+	4.87406i	−0.111354	+	0.160693i
$921$		0			0
$922$	−14.5019	−	9.31981i	−0.477595	−	0.306932i
$923$	−0.0701016	−	0.487567i	−0.00230742	−	0.0160485i
$924$		0			0
$925$	−17.4143	−	5.11330i	−0.572578	−	0.168124i
$926$	0.752952	−	1.64873i	0.0247435	−	0.0541808i
$927$		0			0
$928$	1.09272	−	7.60000i	0.0358701	−	0.249482i
$929$	−46.9634	+	13.7897i	−1.54082	+	0.452425i	−0.938341	−	0.345711i	$-0.887638\pi$
$929$	−46.9634	+	13.7897i	−1.54082	+	0.452425i	−0.602477	+	0.798136i	$0.705820\pi$
$930$		0			0
$931$	18.8984	−	12.1453i	0.619370	−	0.398045i
$932$	−20.4999	+	13.1745i	−0.671495	+	0.431544i
$933$		0			0
$934$	31.4930	−	9.24717i	1.03048	−	0.302577i
$935$	−0.669693	+	4.65782i	−0.0219013	+	0.152327i
$936$		0			0
$937$	19.0744	−	41.7671i	0.623134	−	1.36447i	−0.290084	−	0.957001i	$-0.593683\pi$
$937$	19.0744	−	41.7671i	0.623134	−	1.36447i	0.913218	−	0.407472i	$-0.133589\pi$
$938$	−17.6027	−	5.16861i	−0.574748	−	0.168761i
$939$		0			0
$940$	1.46278	+	10.1739i	0.0477107	+	0.331835i
$941$	31.6678	+	20.3516i	1.03234	+	0.663445i	0.943081	−	0.332564i	$-0.107914\pi$
$941$	31.6678	+	20.3516i	1.03234	+	0.663445i	0.0892594	+	0.996008i	$0.471550\pi$
$942$		0			0
$943$	−0.583220	−	0.291274i	−0.0189923	−	0.00948519i
$944$	6.83576			0.222485
$945$		0			0
$946$	0.830128	+	5.77367i	0.0269898	+	0.187718i
$947$	3.56072	+	7.79688i	0.115708	+	0.253365i	0.958621	−	0.284684i	$-0.0918888\pi$
$947$	3.56072	+	7.79688i	0.115708	+	0.253365i	−0.842914	+	0.538049i	$0.819162\pi$
$948$		0			0
$949$	0.369025	−	0.808053i	0.0119791	−	0.0262305i
$950$	10.6099	−	12.2445i	0.344231	−	0.397264i
$951$		0			0
$952$	−6.08996	+	1.78817i	−0.197377	+	0.0579551i
$953$	25.4412	+	29.3607i	0.824122	+	0.951087i	0.999441	−	0.0334245i	$-0.0106413\pi$
$953$	25.4412	+	29.3607i	0.824122	+	0.951087i	−0.175320	+	0.984512i	$0.556096\pi$
$954$		0			0
$955$	2.94867	−	1.89499i	0.0954166	−	0.0613205i
$956$	5.69496	+	6.57234i	0.184188	+	0.212565i
$957$		0			0
$958$	2.87819	−	20.0182i	0.0929900	−	0.646760i
$959$	8.93691	−	10.3137i	0.288588	−	0.333048i
$960$		0			0
$961$	27.3141	+	8.02016i	0.881102	+	0.258715i
$962$	0.146201	+	0.320135i	0.00471370	+	0.0103216i
$963$		0			0
$964$	−4.77592	−	3.06930i	−0.153822	−	0.0988553i
$965$	−29.7840			−0.958779
$966$		0			0
$967$	17.0473			0.548205			0.274103	−	0.961700i	$-0.411619\pi$
$967$	17.0473			0.548205			0.274103	+	0.961700i	$0.411619\pi$
$968$	8.59229	+	5.52193i	0.276167	+	0.177481i
$969$		0			0
$970$	8.81760	+	19.3079i	0.283116	+	0.619938i
$971$	−44.6690	−	13.1160i	−1.43350	−	0.420913i	−0.529449	−	0.848342i	$-0.677601\pi$
$971$	−44.6690	−	13.1160i	−1.43350	−	0.420913i	−0.904049	+	0.427429i	$0.859419\pi$
$972$		0			0
$973$	7.57480	−	8.74178i	0.242837	−	0.280249i
$974$	−5.62994	+	39.1571i	−0.180395	+	1.25467i
$975$		0			0
$976$	3.01245	+	3.47656i	0.0964263	+	0.111282i
$977$	4.03085	−	2.59047i	0.128958	−	0.0828765i	−0.474571	−	0.880217i	$-0.657397\pi$
$977$	4.03085	−	2.59047i	0.128958	−	0.0828765i	0.603530	+	0.797341i	$0.293761\pi$
$978$		0			0
$979$	6.80781	+	7.85663i	0.217578	+	0.251099i
$980$	5.70997	−	1.67660i	0.182398	−	0.0535569i
$981$		0			0
$982$	−15.9314	+	18.3858i	−0.508391	+	0.586714i
$983$	10.7234	−	23.4810i	0.342024	−	0.748929i	−0.657967	−	0.753047i	$-0.728583\pi$
$983$	10.7234	−	23.4810i	0.342024	−	0.748929i	0.999992	+	0.00411763i	$0.00131069\pi$
$984$		0			0
$985$	12.6386	+	27.6747i	0.402700	+	0.881790i
$986$	4.68969	+	32.6175i	0.149350	+	1.03875i
$987$		0			0
$988$	−0.314171			−0.00999510
$989$	1.09722	−	31.5278i	0.0348897	−	1.00253i
$990$		0			0
$991$	15.2984	+	9.83170i	0.485971	+	0.312314i	0.760583	−	0.649241i	$-0.224913\pi$
$991$	15.2984	+	9.83170i	0.485971	+	0.312314i	−0.274613	+	0.961555i	$0.588550\pi$
$992$	−0.226488	−	1.57526i	−0.00719099	−	0.0500144i
$993$		0			0
$994$	−10.3844	−	3.04915i	−0.329374	−	0.0967130i
$995$	3.22462	−	7.06093i	0.102227	−	0.223847i
$996$		0			0
$997$	−0.613793	+	4.26902i	−0.0194390	+	0.135201i	−0.997230	−	0.0743819i	$-0.976302\pi$
$997$	−0.613793	+	4.26902i	−0.0194390	+	0.135201i	0.977791	+	0.209583i	$0.0672107\pi$
$998$	−15.2325	+	4.47267i	−0.482177	+	0.141580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.d.163.1		10
3.2	odd	2		138.2.e.a.25.1	✓	10
23.9	even	11		9522.2.a.bt.1.2		5
23.12	even	11	inner	414.2.i.d.127.1		10
23.14	odd	22		9522.2.a.bq.1.4		5
69.14	even	22		3174.2.a.bd.1.2		5
69.32	odd	22		3174.2.a.bc.1.4		5
69.35	odd	22		138.2.e.a.127.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.a.25.1	✓	10	3.2	odd	2
138.2.e.a.127.1	yes	10	69.35	odd	22
414.2.i.d.127.1		10	23.12	even	11	inner
414.2.i.d.163.1		10	1.1	even	1	trivial
3174.2.a.bc.1.4		5	69.32	odd	22
3174.2.a.bd.1.2		5	69.14	even	22
9522.2.a.bq.1.4		5	23.14	odd	22
9522.2.a.bt.1.2		5	23.9	even	11

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(-1.18639 - 0.348356i) q^{5} +(0.968468 - 1.11767i) q^{7} +(0.142315 - 0.989821i) q^{8} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(-1.18639 - 0.348356i) q^{5} +(0.968468 - 1.11767i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.809721 + 0.934468i) q^{10} +(0.745983 - 0.479414i) q^{11} +(-0.0440780 - 0.0508687i) q^{13} +(-1.41899 + 0.416652i) q^{14} +(-0.654861 + 0.755750i) q^{16} +(1.78287 - 3.90393i) q^{17} +(-1.93899 - 4.24579i) q^{19} +(-0.175969 - 1.22389i) q^{20} -0.886752 q^{22} +(4.72041 + 0.847210i) q^{23} +(-2.92009 - 1.87663i) q^{25} +(0.00957906 + 0.0666238i) q^{26} +(1.41899 + 0.416652i) q^{28} +(3.18962 - 6.98430i) q^{29} +(0.226488 - 1.57526i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-3.61047 + 2.32031i) q^{34} +(-1.53833 + 0.988626i) q^{35} +(5.01691 - 1.47310i) q^{37} +(-0.664268 + 4.62008i) q^{38} +(-0.513652 + 1.12474i) q^{40} +(-0.130426 - 0.0382966i) q^{41} +(-0.936145 - 6.51103i) q^{43} +(0.745983 + 0.479414i) q^{44} +(-3.51302 - 3.26476i) q^{46} -8.31271 q^{47} +(0.684944 + 4.76389i) q^{49} +(1.44196 + 3.15744i) q^{50} +(0.0279611 - 0.0612263i) q^{52} +(-1.96169 + 2.26391i) q^{53} +(-1.05204 + 0.308906i) q^{55} +(-0.968468 - 1.11767i) q^{56} +(-6.45928 + 4.15112i) q^{58} +(-4.47647 - 5.16612i) q^{59} +(0.654669 - 4.55332i) q^{61} +(-1.04218 + 1.20274i) q^{62} +(-0.959493 - 0.281733i) q^{64} +(0.0345733 + 0.0757051i) q^{65} +(10.4358 + 6.70671i) q^{67} +4.29177 q^{68} +1.82862 q^{70} +(6.15647 + 3.95652i) q^{71} +(5.48256 + 12.0051i) q^{73} +(-5.01691 - 1.47310i) q^{74} +(3.05662 - 3.52753i) q^{76} +(0.186633 - 1.29806i) q^{77} +(-5.16977 - 5.96624i) q^{79} +(1.04019 - 0.668491i) q^{80} +(0.0890169 + 0.102731i) q^{82} +(-8.06797 + 2.36897i) q^{83} +(-3.47514 + 4.01052i) q^{85} +(-2.73259 + 5.98354i) q^{86} +(-0.368370 - 0.806618i) q^{88} +(1.66842 + 11.6041i) q^{89} -0.0995426 q^{91} +(1.19028 + 4.64578i) q^{92} +(6.99309 + 4.49419i) q^{94} +(0.821353 + 5.71264i) q^{95} +(16.4711 + 4.83636i) q^{97} +(1.99934 - 4.37795i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8}+O(q^{10}) \) 10 * q + q^2 - q^4 - 8 * q^5 + 8 * q^7 + q^8	\( 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8} - 3 q^{10} - 7 q^{11} + 3 q^{13} + 3 q^{14} - q^{16} - 4 q^{17} + 3 q^{20} - 26 q^{22} + 12 q^{23} - 15 q^{25} - 3 q^{26} - 3 q^{28} + 25 q^{29} + 6 q^{31} + q^{32} - 7 q^{34} - 2 q^{35} + 9 q^{37} - 11 q^{38} - 3 q^{40} - 24 q^{41} - 30 q^{43} - 7 q^{44} + 21 q^{46} + 48 q^{47} + 9 q^{49} - 7 q^{50} + 14 q^{52} - 15 q^{53} - 23 q^{55} - 8 q^{56} - 3 q^{58} - 5 q^{59} + 12 q^{61} - 28 q^{62} - q^{64} + 13 q^{65} + 18 q^{67} + 18 q^{68} + 2 q^{70} - 28 q^{71} + 19 q^{73} - 9 q^{74} + 22 q^{76} + 12 q^{77} - 52 q^{79} - 8 q^{80} - 20 q^{82} - 7 q^{83} + 23 q^{85} - 14 q^{86} - 4 q^{88} - 3 q^{89} + 42 q^{91} + 23 q^{92} + 29 q^{94} - 22 q^{95} + 51 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + q^2 - q^4 - 8 * q^5 + 8 * q^7 + q^8 - 3 * q^10 - 7 * q^11 + 3 * q^13 + 3 * q^14 - q^16 - 4 * q^17 + 3 * q^20 - 26 * q^22 + 12 * q^23 - 15 * q^25 - 3 * q^26 - 3 * q^28 + 25 * q^29 + 6 * q^31 + q^32 - 7 * q^34 - 2 * q^35 + 9 * q^37 - 11 * q^38 - 3 * q^40 - 24 * q^41 - 30 * q^43 - 7 * q^44 + 21 * q^46 + 48 * q^47 + 9 * q^49 - 7 * q^50 + 14 * q^52 - 15 * q^53 - 23 * q^55 - 8 * q^56 - 3 * q^58 - 5 * q^59 + 12 * q^61 - 28 * q^62 - q^64 + 13 * q^65 + 18 * q^67 + 18 * q^68 + 2 * q^70 - 28 * q^71 + 19 * q^73 - 9 * q^74 + 22 * q^76 + 12 * q^77 - 52 * q^79 - 8 * q^80 - 20 * q^82 - 7 * q^83 + 23 * q^85 - 14 * q^86 - 4 * q^88 - 3 * q^89 + 42 * q^91 + 23 * q^92 + 29 * q^94 - 22 * q^95 + 51 * q^97 + 2 * q^98

Introduction

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