LMFDB - Embedded newform 414.2.i.a.271.1

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			271.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	414.271
Dual form			414.2.i.a.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(0.0651865 - 0.453382i) q^{5} +(-0.134858 - 0.295298i) q^{7} +(-0.654861 - 0.755750i) q^{8} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(0.0651865 - 0.453382i) q^{5} +(-0.134858 - 0.295298i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.190279 + 0.416652i) q^{10} +(2.38745 - 0.701020i) q^{11} +(0.564582 - 1.23626i) q^{13} +(0.0462003 + 0.321330i) q^{14} +(0.415415 + 0.909632i) q^{16} +(2.26811 - 1.45762i) q^{17} +(-2.43450 - 1.56456i) q^{19} +(0.299955 - 0.346167i) q^{20} -2.48825 q^{22} +(4.35491 - 2.00868i) q^{23} +(4.59616 + 1.34955i) q^{25} +(-0.890008 + 1.02712i) q^{26} +(0.0462003 - 0.321330i) q^{28} +(1.83493 - 1.17924i) q^{29} +(-1.61291 - 1.86139i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-2.58689 + 0.759581i) q^{34} +(-0.142674 + 0.0418928i) q^{35} +(-0.0683786 - 0.475583i) q^{37} +(1.89510 + 2.18706i) q^{38} +(-0.385331 + 0.247638i) q^{40} +(0.120602 - 0.838807i) q^{41} +(5.76770 - 6.65628i) q^{43} +(2.38745 + 0.701020i) q^{44} +(-4.74441 + 0.700397i) q^{46} +2.71406 q^{47} +(4.51501 - 5.21060i) q^{49} +(-4.02977 - 2.58978i) q^{50} +(1.14333 - 0.734774i) q^{52} +(-3.62496 - 7.93756i) q^{53} +(-0.162200 - 1.12813i) q^{55} +(-0.134858 + 0.295298i) q^{56} +(-2.09283 + 0.614511i) q^{58} +(-4.52108 + 9.89978i) q^{59} +(7.89921 + 9.11618i) q^{61} +(1.02316 + 2.24040i) q^{62} +(-0.142315 + 0.989821i) q^{64} +(-0.523697 - 0.336559i) q^{65} +(-10.1378 - 2.97673i) q^{67} +2.69611 q^{68} +0.148697 q^{70} +(-15.7422 - 4.62233i) q^{71} +(9.89520 + 6.35926i) q^{73} +(-0.0683786 + 0.475583i) q^{74} +(-1.20217 - 2.63238i) q^{76} +(-0.528978 - 0.610473i) q^{77} +(-4.45637 + 9.75808i) q^{79} +(0.439490 - 0.129046i) q^{80} +(-0.352036 + 0.770851i) q^{82} +(1.15039 + 8.00114i) q^{83} +(-0.513011 - 1.12334i) q^{85} +(-7.40935 + 4.76170i) q^{86} +(-2.09325 - 1.34525i) q^{88} +(-6.74394 + 7.78292i) q^{89} -0.441205 q^{91} +(4.74955 + 0.664630i) q^{92} +(-2.60412 - 0.764638i) q^{94} +(-0.868039 + 1.00177i) q^{95} +(0.0319166 - 0.221985i) q^{97} +(-5.80012 + 3.72751i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8	$ 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8} - 13 q^{10} + 5 q^{11} + 13 q^{13} - 9 q^{14} - q^{16} + 9 q^{20} - 6 q^{22} + 32 q^{23} + q^{25} + 13 q^{26} - 9 q^{28} - 27 q^{29} - 8 q^{31} - q^{32} - 11 q^{34} + 26 q^{35} - 11 q^{37} - 11 q^{38} + 9 q^{40} + 10 q^{41} + 34 q^{43} + 5 q^{44} - q^{46} - 8 q^{47} + 25 q^{49} - 21 q^{50} + 2 q^{52} - 9 q^{53} - 23 q^{55} + 2 q^{56} - 5 q^{58} + 21 q^{59} - 4 q^{61} - 8 q^{62} - q^{64} - 29 q^{65} - 32 q^{67} - 22 q^{68} - 18 q^{70} - 22 q^{71} + 43 q^{73} - 11 q^{74} - 10 q^{77} - 16 q^{79} - 2 q^{80} + 32 q^{82} + 3 q^{83} + 33 q^{85} - 32 q^{86} - 6 q^{88} + 11 q^{89} - 70 q^{91} + 21 q^{92} + 3 q^{94} + 39 q^{97} + 14 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8 - 13 * q^10 + 5 * q^11 + 13 * q^13 - 9 * q^14 - q^16 + 9 * q^20 - 6 * q^22 + 32 * q^23 + q^25 + 13 * q^26 - 9 * q^28 - 27 * q^29 - 8 * q^31 - q^32 - 11 * q^34 + 26 * q^35 - 11 * q^37 - 11 * q^38 + 9 * q^40 + 10 * q^41 + 34 * q^43 + 5 * q^44 - q^46 - 8 * q^47 + 25 * q^49 - 21 * q^50 + 2 * q^52 - 9 * q^53 - 23 * q^55 + 2 * q^56 - 5 * q^58 + 21 * q^59 - 4 * q^61 - 8 * q^62 - q^64 - 29 * q^65 - 32 * q^67 - 22 * q^68 - 18 * q^70 - 22 * q^71 + 43 * q^73 - 11 * q^74 - 10 * q^77 - 16 * q^79 - 2 * q^80 + 32 * q^82 + 3 * q^83 + 33 * q^85 - 32 * q^86 - 6 * q^88 + 11 * q^89 - 70 * q^91 + 21 * q^92 + 3 * q^94 + 39 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$		0			0
$3$		0			0
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.0651865	−	0.453382i	0.0291523	−	0.202759i	−0.970040	−	0.242946i	$-0.921886\pi$
$5$	0.0651865	−	0.453382i	0.0291523	−	0.202759i	0.999192	+	0.0401871i	$0.0127954\pi$
$6$		0			0
$7$	−0.134858	−	0.295298i	−0.0509716	−	0.111612i	0.882433	−	0.470439i	$-0.155904\pi$
$7$	−0.134858	−	0.295298i	−0.0509716	−	0.111612i	−0.933404	+	0.358826i	$0.883177\pi$
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$		0			0
$10$	−0.190279	+	0.416652i	−0.0601714	+	0.131757i
$11$	2.38745	−	0.701020i	0.719844	−	0.211365i	0.0987625	−	0.995111i	$-0.468512\pi$
$11$	2.38745	−	0.701020i	0.719844	−	0.211365i	0.621082	+	0.783746i	$0.286693\pi$
$12$		0			0
$13$	0.564582	−	1.23626i	0.156587	−	0.342878i	−0.815037	−	0.579409i	$-0.803283\pi$
$13$	0.564582	−	1.23626i	0.156587	−	0.342878i	0.971624	+	0.236531i	$0.0760106\pi$
$14$	0.0462003	+	0.321330i	0.0123476	+	0.0858792i
$15$		0			0
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	2.26811	−	1.45762i	0.550097	−	0.353526i	−0.235879	−	0.971782i	$-0.575797\pi$
$17$	2.26811	−	1.45762i	0.550097	−	0.353526i	0.785976	+	0.618256i	$0.212161\pi$
$18$		0			0
$19$	−2.43450	−	1.56456i	−0.558512	−	0.358934i	0.230728	−	0.973018i	$-0.425889\pi$
$19$	−2.43450	−	1.56456i	−0.558512	−	0.358934i	−0.789241	+	0.614084i	$0.789526\pi$
$20$	0.299955	−	0.346167i	0.0670720	−	0.0774053i
$21$		0			0
$22$	−2.48825			−0.530496
$23$	4.35491	−	2.00868i	0.908061	−	0.418839i
$23$	4.35491	−	2.00868i	0.908061	−	0.418839i
$24$		0			0
$25$	4.59616	+	1.34955i	0.919232	+	0.269911i
$26$	−0.890008	+	1.02712i	−0.174545	+	0.201436i
$27$		0			0
$28$	0.0462003	−	0.321330i	0.00873105	−	0.0607258i
$29$	1.83493	−	1.17924i	0.340738	−	0.218979i	−0.359069	−	0.933311i	$-0.616906\pi$
$29$	1.83493	−	1.17924i	0.340738	−	0.218979i	0.699807	+	0.714332i	$0.253269\pi$
$30$		0			0
$31$	−1.61291	−	1.86139i	−0.289686	−	0.334316i	0.592188	−	0.805799i	$-0.298264\pi$
$31$	−1.61291	−	1.86139i	−0.289686	−	0.334316i	−0.881875	+	0.471484i	$0.843719\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$		0			0
$34$	−2.58689	+	0.759581i	−0.443649	+	0.130267i
$35$	−0.142674	+	0.0418928i	−0.0241163	+	0.00708118i
$36$		0			0
$37$	−0.0683786	−	0.475583i	−0.0112414	−	0.0781854i	0.983428	−	0.181297i	$-0.0580294\pi$
$37$	−0.0683786	−	0.475583i	−0.0112414	−	0.0781854i	−0.994670	+	0.103111i	$0.967120\pi$
$38$	1.89510	+	2.18706i	0.307425	+	0.354788i
$39$		0			0
$40$	−0.385331	+	0.247638i	−0.0609263	+	0.0391549i
$41$	0.120602	−	0.838807i	0.0188349	−	0.131000i	−0.978234	−	0.207503i	$-0.933466\pi$
$41$	0.120602	−	0.838807i	0.0188349	−	0.131000i	0.997069	+	0.0765031i	$0.0243755\pi$
$42$		0			0
$43$	5.76770	−	6.65628i	0.879565	−	1.01507i	−0.120185	−	0.992751i	$-0.538349\pi$
$43$	5.76770	−	6.65628i	0.879565	−	1.01507i	0.999751	−	0.0223211i	$-0.00710563\pi$
$44$	2.38745	+	0.701020i	0.359922	+	0.105683i
$45$		0			0
$46$	−4.74441	+	0.700397i	−0.699525	+	0.103268i
$47$	2.71406			0.395886			0.197943	−	0.980214i	$-0.436574\pi$
$47$	2.71406			0.395886			0.197943	+	0.980214i	$0.436574\pi$
$48$		0			0
$49$	4.51501	−	5.21060i	0.645002	−	0.744371i
$50$	−4.02977	−	2.58978i	−0.569895	−	0.366250i
$51$		0			0
$52$	1.14333	−	0.734774i	0.158552	−	0.101895i
$53$	−3.62496	−	7.93756i	−0.497927	−	1.09031i	−0.977138	−	0.212608i	$-0.931804\pi$
$53$	−3.62496	−	7.93756i	−0.497927	−	1.09031i	0.479210	−	0.877700i	$-0.340923\pi$
$54$		0			0
$55$	−0.162200	−	1.12813i	−0.0218711	−	0.152116i
$56$	−0.134858	+	0.295298i	−0.0180212	+	0.0394609i
$57$		0			0
$58$	−2.09283	+	0.614511i	−0.274802	+	0.0806893i
$59$	−4.52108	+	9.89978i	−0.588594	+	1.28884i	0.347694	+	0.937608i	$0.386965\pi$
$59$	−4.52108	+	9.89978i	−0.588594	+	1.28884i	−0.936288	+	0.351233i	$0.885762\pi$
$60$		0			0
$61$	7.89921	+	9.11618i	1.01139	+	1.16721i	0.985866	+	0.167533i	$0.0535801\pi$
$61$	7.89921	+	9.11618i	1.01139	+	1.16721i	0.0255243	+	0.999674i	$0.491874\pi$
$62$	1.02316	+	2.24040i	0.129941	+	0.284531i
$63$		0			0
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−0.523697	−	0.336559i	−0.0649566	−	0.0417450i
$66$		0			0
$67$	−10.1378	−	2.97673i	−1.23853	−	0.363665i	−0.404067	−	0.914730i	$-0.632404\pi$
$67$	−10.1378	−	2.97673i	−1.23853	−	0.363665i	−0.834463	+	0.551065i	$0.814222\pi$
$68$	2.69611			0.326951
$69$		0			0
$70$	0.148697			0.0177727
$71$	−15.7422	−	4.62233i	−1.86826	−	0.548570i	−0.998480	−	0.0551238i	$-0.982445\pi$
$71$	−15.7422	−	4.62233i	−1.86826	−	0.548570i	−0.869777	−	0.493446i	$-0.835737\pi$
$72$		0			0
$73$	9.89520	+	6.35926i	1.15814	+	0.744295i	0.971245	−	0.238084i	$-0.0765194\pi$
$73$	9.89520	+	6.35926i	1.15814	+	0.744295i	0.186900	+	0.982379i	$0.440156\pi$
$74$	−0.0683786	+	0.475583i	−0.00794885	+	0.0552854i
$75$		0			0
$76$	−1.20217	−	2.63238i	−0.137898	−	0.301955i
$77$	−0.528978	−	0.610473i	−0.0602826	−	0.0695698i
$78$		0			0
$79$	−4.45637	+	9.75808i	−0.501380	+	1.09787i	0.474638	+	0.880181i	$0.342579\pi$
$79$	−4.45637	+	9.75808i	−0.501380	+	1.09787i	−0.976018	+	0.217689i	$0.930148\pi$
$80$	0.439490	−	0.129046i	0.0491365	−	0.0144278i
$81$		0			0
$82$	−0.352036	+	0.770851i	−0.0388759	+	0.0851263i
$83$	1.15039	+	8.00114i	0.126272	+	0.878240i	0.950221	+	0.311576i	$0.100857\pi$
$83$	1.15039	+	8.00114i	0.126272	+	0.878240i	−0.823949	+	0.566663i	$0.808234\pi$
$84$		0			0
$85$	−0.513011	−	1.12334i	−0.0556439	−	0.121843i
$86$	−7.40935	+	4.76170i	−0.798971	+	0.513468i
$87$		0			0
$88$	−2.09325	−	1.34525i	−0.223141	−	0.143404i
$89$	−6.74394	+	7.78292i	−0.714856	+	0.824988i	−0.990679	−	0.136220i	$-0.956504\pi$
$89$	−6.74394	+	7.78292i	−0.714856	+	0.824988i	0.275822	+	0.961209i	$0.411050\pi$
$90$		0			0
$91$	−0.441205			−0.0462508
$92$	4.74955	+	0.664630i	0.495175	+	0.0692924i
$93$		0			0
$94$	−2.60412	−	0.764638i	−0.268594	−	0.0788664i
$95$	−0.868039	+	1.00177i	−0.0890589	+	0.102779i
$96$		0			0
$97$	0.0319166	−	0.221985i	0.00324064	−	0.0225392i	−0.988137	−	0.153575i	$-0.950921\pi$
$97$	0.0319166	−	0.221985i	0.00324064	−	0.0225392i	0.991378	+	0.131036i	$0.0418304\pi$
$98$	−5.80012	+	3.72751i	−0.585900	+	0.376535i
$99$		0			0
$100$	3.13691	+	3.62019i	0.313691	+	0.362019i
$101$	1.52215	+	10.5868i	0.151460	+	1.05342i	0.913775	+	0.406220i	$0.133153\pi$
$101$	1.52215	+	10.5868i	0.151460	+	1.05342i	−0.762316	+	0.647205i	$0.775938\pi$
$102$		0			0
$103$	−1.94475	+	0.571031i	−0.191622	+	0.0562653i	−0.376135	−	0.926565i	$-0.622747\pi$
$103$	−1.94475	+	0.571031i	−0.191622	+	0.0562653i	0.184513	+	0.982830i	$0.440929\pi$
$104$	−1.30403	+	0.382897i	−0.127870	+	0.0375462i
$105$		0			0
$106$	1.24186	+	8.63731i	0.120620	+	0.838930i
$107$	1.41996	+	1.63873i	0.137273	+	0.158422i	0.820224	−	0.572043i	$-0.193849\pi$
$107$	1.41996	+	1.63873i	0.137273	+	0.158422i	−0.682950	+	0.730465i	$0.739304\pi$
$108$		0			0
$109$	−7.08241	+	4.55159i	−0.678372	+	0.435963i	−0.833935	−	0.551863i	$-0.813917\pi$
$109$	−7.08241	+	4.55159i	−0.678372	+	0.435963i	0.155563	+	0.987826i	$0.450281\pi$
$110$	−0.162200	+	1.12813i	−0.0154652	+	0.107563i
$111$		0			0
$112$	0.212591	−	0.245343i	0.0200879	−	0.0231827i
$113$	0.186034	+	0.0546244i	0.0175006	+	0.00513863i	0.290471	−	0.956884i	$-0.406188\pi$
$113$	0.186034	+	0.0546244i	0.0175006	+	0.00513863i	−0.272971	+	0.962022i	$0.588006\pi$
$114$		0			0
$115$	−0.626819	−	2.10538i	−0.0584512	−	0.196327i
$116$	2.18119			0.202518
$117$		0			0
$118$	7.12703	−	8.22504i	0.656097	−	0.757176i
$119$	−0.736307	−	0.473196i	−0.0674971	−	0.0433778i
$120$		0			0
$121$	−4.04528	+	2.59974i	−0.367753	+	0.236340i
$122$	−5.01092	−	10.9724i	−0.453667	−	0.993392i
$123$		0			0
$124$	−0.350518	−	2.43790i	−0.0314774	−	0.218930i
$125$	1.86286	−	4.07910i	0.166620	−	0.364846i
$126$		0			0
$127$	−12.4055	+	3.64259i	−1.10081	+	0.323228i	−0.781175	−	0.624312i	$-0.785379\pi$
$127$	−12.4055	+	3.64259i	−1.10081	+	0.323228i	−0.319638	+	0.947540i	$0.603561\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$		0			0
$130$	0.407663	+	0.470469i	0.0357544	+	0.0412628i
$131$	2.44775	+	5.35982i	0.213861	+	0.468289i	0.985911	−	0.167272i	$-0.0534959\pi$
$131$	2.44775	+	5.35982i	0.213861	+	0.468289i	−0.772050	+	0.635562i	$0.780769\pi$
$132$		0			0
$133$	−0.133699	+	0.929896i	−0.0115932	+	0.0806322i
$134$	8.88851	+	5.71230i	0.767850	+	0.493467i
$135$		0			0
$136$	−2.58689	−	0.759581i	−0.221824	−	0.0651335i
$137$	16.2119			1.38508			0.692538	−	0.721381i	$-0.256492\pi$
$137$	16.2119			1.38508			0.692538	+	0.721381i	$0.256492\pi$
$138$		0			0
$139$	−19.6328			−1.66524			−0.832618	−	0.553848i	$-0.813159\pi$
$139$	−19.6328			−1.66524			−0.832618	+	0.553848i	$0.813159\pi$
$140$	−0.142674	−	0.0418928i	−0.0120581	−	0.00354059i
$141$		0			0
$142$	13.8023	+	8.87018i	1.15826	+	0.744369i
$143$	0.481270	−	3.34730i	0.0402458	−	0.279916i
$144$		0			0
$145$	−0.415033	−	0.908795i	−0.0344666	−	0.0754713i
$146$	−7.70276	−	8.88946i	−0.637485	−	0.735697i
$147$		0			0
$148$	0.199596	−	0.437054i	0.0164067	−	0.0359256i
$149$	3.05112	−	0.895889i	0.249957	−	0.0733941i	−0.154354	−	0.988016i	$-0.549330\pi$
$149$	3.05112	−	0.895889i	0.249957	−	0.0733941i	0.404311	+	0.914622i	$0.367511\pi$
$150$		0			0
$151$	−0.529537	+	1.15953i	−0.0430931	+	0.0943608i	−0.929954	−	0.367675i	$-0.880154\pi$
$151$	−0.529537	+	1.15953i	−0.0430931	+	0.0943608i	0.886861	+	0.462036i	$0.152881\pi$
$152$	0.411844	+	2.86444i	0.0334050	+	0.232337i
$153$		0			0
$154$	0.335560	+	0.734774i	0.0270402	+	0.0592098i
$155$	−0.949062	+	0.609925i	−0.0762305	+	0.0489903i
$156$		0			0
$157$	−14.5837	−	9.37238i	−1.16391	−	0.747998i	−0.191547	−	0.981483i	$-0.561350\pi$
$157$	−14.5837	−	9.37238i	−1.16391	−	0.747998i	−0.972360	+	0.233486i	$0.924987\pi$
$158$	7.02502	−	8.10731i	0.558881	−	0.644983i
$159$		0			0
$160$	−0.458044			−0.0362116
$161$	−1.18045	−	1.01511i	−0.0930328	−	0.0800018i
$162$		0			0
$163$	5.05886	+	1.48542i	0.396241	+	0.116347i	0.473782	−	0.880642i	$-0.342889\pi$
$163$	5.05886	+	1.48542i	0.396241	+	0.116347i	−0.0775408	+	0.996989i	$0.524707\pi$
$164$	0.554950	−	0.640447i	0.0433343	−	0.0500105i
$165$		0			0
$166$	1.15039	−	8.00114i	0.0892876	−	0.621009i
$167$	2.48840	−	1.59920i	0.192558	−	0.123749i	−0.440810	−	0.897601i	$-0.645309\pi$
$167$	2.48840	−	1.59920i	0.192558	−	0.123749i	0.633367	+	0.773851i	$0.281672\pi$
$168$		0			0
$169$	7.30360	+	8.42880i	0.561815	+	0.648369i
$170$	0.175750	+	1.22237i	0.0134794	+	0.0937512i
$171$		0			0
$172$	8.45075	−	2.48136i	0.644364	−	0.189202i
$173$	3.96538	−	1.16434i	0.301482	−	0.0885232i	−0.127493	−	0.991840i	$-0.540693\pi$
$173$	3.96538	−	1.16434i	0.301482	−	0.0885232i	0.428975	+	0.903316i	$0.358875\pi$
$174$		0			0
$175$	−0.221309	−	1.53924i	−0.0167294	−	0.116355i
$176$	1.62945	+	1.88049i	0.122825	+	0.141747i
$177$		0			0
$178$	8.66347	−	5.56767i	0.649354	−	0.417315i
$179$	1.44265	−	10.0338i	0.107829	−	0.749965i	−0.862129	−	0.506689i	$-0.830869\pi$
$179$	1.44265	−	10.0338i	0.107829	−	0.749965i	0.969957	−	0.243275i	$-0.0782218\pi$
$180$		0			0
$181$	17.4442	−	20.1316i	1.29661	−	1.49637i	0.541655	−	0.840601i	$-0.317798\pi$
$181$	17.4442	−	20.1316i	1.29661	−	1.49637i	0.754959	−	0.655772i	$-0.227657\pi$
$182$	0.423333	+	0.124302i	0.0313795	+	0.00921386i
$183$		0			0
$184$	−4.36992	−	1.97581i	−0.322155	−	0.145659i
$185$	−0.220078			−0.0161805
$186$		0			0
$187$	4.39318	−	5.07000i	0.321261	−	0.370755i
$188$	2.28321	+	1.46733i	0.166520	+	0.107016i
$189$		0			0
$190$	1.11511	−	0.716637i	0.0808985	−	0.0519903i
$191$	−9.71754	−	21.2784i	−0.703136	−	1.53965i	−0.836127	−	0.548536i	$-0.815185\pi$
$191$	−9.71754	−	21.2784i	−0.703136	−	1.53965i	0.132991	−	0.991117i	$-0.457542\pi$
$192$		0			0
$193$	−0.856252	−	5.95536i	−0.0616344	−	0.428676i	−0.997153	−	0.0754000i	$-0.975977\pi$
$193$	−0.856252	−	5.95536i	−0.0616344	−	0.428676i	0.935519	−	0.353276i	$-0.114932\pi$
$194$	−0.0931641	+	0.204001i	−0.00668880	+	0.0146464i
$195$		0			0
$196$	6.61533	−	1.94244i	0.472524	−	0.138745i
$197$	−6.42396	+	14.0665i	−0.457688	+	1.00220i	0.530320	+	0.847797i	$0.322072\pi$
$197$	−6.42396	+	14.0665i	−0.457688	+	1.00220i	−0.988008	+	0.154400i	$0.950656\pi$
$198$		0			0
$199$	7.66908	+	8.85059i	0.543647	+	0.627402i	0.959391	−	0.282080i	$-0.0910243\pi$
$199$	7.66908	+	8.85059i	0.543647	+	0.627402i	−0.415744	+	0.909482i	$0.636479\pi$
$200$	−1.98992	−	4.35731i	−0.140709	−	0.308109i
$201$		0			0
$202$	1.52215	−	10.5868i	0.107098	−	0.744884i
$203$	−0.595682	−	0.382822i	−0.0418087	−	0.0268688i
$204$		0			0
$205$	−0.372438	−	0.109358i	−0.0260122	−	0.00763788i
$206$	2.02685			0.141218
$207$		0			0
$208$	1.35908			0.0942353
$209$	−6.90904	−	2.02868i	−0.477908	−	0.140327i
$210$		0			0
$211$	8.98039	+	5.77135i	0.618236	+	0.397316i	0.811937	−	0.583745i	$-0.198413\pi$
$211$	8.98039	+	5.77135i	0.618236	+	0.397316i	−0.193702	+	0.981060i	$0.562049\pi$
$212$	1.24186	−	8.63731i	0.0852911	−	0.593213i
$213$		0			0
$214$	−0.900763	−	1.97240i	−0.0615749	−	0.134830i
$215$	−2.64186	−	3.04887i	−0.180173	−	0.207931i
$216$		0			0
$217$	−0.332152	+	0.727312i	−0.0225480	+	0.0493731i
$218$	8.07785	−	2.37187i	0.547101	−	0.160643i
$219$		0			0
$220$	0.473460	−	1.03673i	0.0319206	−	0.0698965i
$221$	−0.521474	−	3.62693i	−0.0350781	−	0.243974i
$222$		0			0
$223$	3.14540	+	6.88747i	0.210632	+	0.461219i	0.985230	−	0.171234i	$-0.0547754\pi$
$223$	3.14540	+	6.88747i	0.210632	+	0.461219i	−0.774599	+	0.632453i	$0.782048\pi$
$224$	−0.273100	+	0.175511i	−0.0182473	+	0.0117268i
$225$		0			0
$226$	−0.163109	−	0.104824i	−0.0108498	−	0.00697276i
$227$	−8.28049	+	9.55620i	−0.549596	+	0.634267i	−0.960789	−	0.277281i	$-0.910567\pi$
$227$	−8.28049	+	9.55620i	−0.549596	+	0.634267i	0.411193	+	0.911548i	$0.365112\pi$
$228$		0			0
$229$	−8.39479			−0.554743			−0.277372	−	0.960763i	$-0.589463\pi$
$229$	−8.39479			−0.554743			−0.277372	+	0.960763i	$0.589463\pi$
$230$	0.00827561	+	2.19669i	0.000545678	+	0.144845i
$231$		0			0
$232$	−2.09283	−	0.614511i	−0.137401	−	0.0403446i
$233$	17.2108	−	19.8623i	1.12752	−	1.30122i	0.179231	−	0.983807i	$-0.442639\pi$
$233$	17.2108	−	19.8623i	1.12752	−	1.30122i	0.948286	−	0.317417i	$-0.102816\pi$
$234$		0			0
$235$	0.176920	−	1.23050i	0.0115410	−	0.0802693i
$236$	−9.15560	+	5.88395i	−0.595979	+	0.383012i
$237$		0			0
$238$	0.573167	+	0.661470i	0.0371529	+	0.0428767i
$239$	1.11770	+	7.77380i	0.0722983	+	0.502846i	0.993506	+	0.113776i	$0.0362945\pi$
$239$	1.11770	+	7.77380i	0.0722983	+	0.502846i	−0.921208	+	0.389070i	$0.872796\pi$
$240$		0			0
$241$	25.4306	−	7.46711i	1.63813	−	0.480999i	0.672324	−	0.740257i	$-0.265296\pi$
$241$	25.4306	−	7.46711i	1.63813	−	0.480999i	0.965808	+	0.259258i	$0.0834781\pi$
$242$	4.61385	−	1.35475i	0.296590	−	0.0870866i
$243$		0			0
$244$	1.71666	+	11.9397i	0.109898	+	0.764358i
$245$	−2.06808	−	2.38669i	−0.132125	−	0.152480i
$246$		0			0
$247$	−3.30868	+	2.12636i	−0.210526	+	0.135297i
$248$	−0.350518	+	2.43790i	−0.0222579	+	0.154807i
$249$		0			0
$250$	−2.93662	+	3.38904i	−0.185728	+	0.214342i
$251$	−17.3220	−	5.08620i	−1.09336	−	0.321038i	−0.315147	−	0.949043i	$-0.602054\pi$
$251$	−17.3220	−	5.08620i	−1.09336	−	0.321038i	−0.778210	+	0.628005i	$0.783872\pi$
$252$		0			0
$253$	8.98901	−	7.84851i	0.565134	−	0.493431i
$254$	12.9293			0.811253
$255$		0			0
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	19.2275	+	12.3568i	1.19938	+	0.770794i	0.978849	−	0.204586i	$-0.0655848\pi$
$257$	19.2275	+	12.3568i	1.19938	+	0.770794i	0.220531	+	0.975380i	$0.429221\pi$
$258$		0			0
$259$	−0.131217	+	0.0843284i	−0.00815346	+	0.00523991i
$260$	−0.258604	−	0.566263i	−0.0160379	−	0.0351182i
$261$		0			0
$262$	−0.838560	−	5.83232i	−0.0518064	−	0.360322i
$263$	7.73481	−	16.9369i	0.476949	−	1.04437i	−0.506343	−	0.862332i	$-0.669003\pi$
$263$	7.73481	−	16.9369i	0.476949	−	1.04437i	0.983291	−	0.182039i	$-0.0582698\pi$
$264$		0			0
$265$	−3.83505	+	1.12607i	−0.235585	+	0.0691741i
$266$	0.390265	−	0.854562i	0.0239287	−	0.0523965i
$267$		0			0
$268$	−6.91912	−	7.98509i	−0.422653	−	0.487767i
$269$	−0.327653	−	0.717460i	−0.0199774	−	0.0437443i	0.899380	−	0.437167i	$-0.144018\pi$
$269$	−0.327653	−	0.717460i	−0.0199774	−	0.0437443i	−0.919358	+	0.393423i	$0.871291\pi$
$270$		0			0
$271$	−4.17271	+	29.0218i	−0.253474	+	1.76295i	0.323540	+	0.946215i	$0.395127\pi$
$271$	−4.17271	+	29.0218i	−0.253474	+	1.76295i	−0.577013	+	0.816735i	$0.695782\pi$
$272$	2.26811	+	1.45762i	0.137524	+	0.0883815i
$273$		0			0
$274$	−15.5552	−	4.56742i	−0.939725	−	0.275928i
$275$	11.9192			0.718754
$276$		0			0
$277$	−25.4356			−1.52828			−0.764138	−	0.645053i	$-0.776835\pi$
$277$	−25.4356			−1.52828			−0.764138	+	0.645053i	$0.776835\pi$
$278$	18.8376	+	5.53121i	1.12980	+	0.331740i
$279$		0			0
$280$	0.125092	+	0.0803918i	0.00747568	+	0.00480433i
$281$	−3.35608	+	23.3420i	−0.200207	+	1.39247i	0.603462	+	0.797391i	$0.293787\pi$
$281$	−3.35608	+	23.3420i	−0.200207	+	1.39247i	−0.803669	+	0.595077i	$0.797122\pi$
$282$		0			0
$283$	−11.0626	−	24.2237i	−0.657602	−	1.43995i	−0.884740	−	0.466085i	$-0.845664\pi$
$283$	−11.0626	−	24.2237i	−0.657602	−	1.43995i	0.227138	−	0.973863i	$-0.427063\pi$
$284$	−10.7442	−	12.3994i	−0.637549	−	0.735771i
$285$		0			0
$286$	−1.40482	+	3.07613i	−0.0830687	+	0.181895i
$287$	−0.263962	+	0.0775063i	−0.0155812	+	0.00457505i
$288$		0			0
$289$	−4.04241	+	8.85164i	−0.237789	+	0.520685i
$290$	0.142184	+	0.988911i	0.00834933	+	0.0580709i
$291$		0			0
$292$	4.88629	+	10.6995i	0.285949	+	0.626140i
$293$	5.54585	−	3.56410i	0.323992	−	0.208217i	−0.368526	−	0.929617i	$-0.620138\pi$
$293$	5.54585	−	3.56410i	0.323992	−	0.208217i	0.692518	+	0.721400i	$0.256501\pi$
$294$		0			0
$295$	4.19367	+	2.69511i	0.244165	+	0.156915i
$296$	−0.314643	+	0.363118i	−0.0182883	+	0.0211058i
$297$		0			0
$298$	−3.17993			−0.184208
$299$	−0.0245549	−	6.51787i	−0.00142005	−	0.376938i
$300$		0			0
$301$	−2.74341	−	0.805537i	−0.158127	−	0.0464304i
$302$	0.834763	−	0.963368i	0.0480352	−	0.0554356i
$303$		0			0
$304$	0.411844	−	2.86444i	0.0236209	−	0.164287i
$305$	4.64804	−	2.98711i	0.266146	−	0.171041i
$306$		0			0
$307$	−14.6003	−	16.8497i	−0.833285	−	0.961662i	0.166417	−	0.986055i	$-0.446780\pi$
$307$	−14.6003	−	16.8497i	−0.833285	−	0.961662i	−0.999702	+	0.0243932i	$0.992235\pi$
$308$	−0.114958	−	0.799549i	−0.00655033	−	0.0455585i
$309$		0			0
$310$	1.08245	−	0.317837i	0.0614792	−	0.0180519i
$311$	−12.3837	+	3.63618i	−0.702214	+	0.206189i	−0.613299	−	0.789851i	$-0.710158\pi$
$311$	−12.3837	+	3.63618i	−0.702214	+	0.206189i	−0.0889146	+	0.996039i	$0.528340\pi$
$312$		0			0
$313$	2.73568	+	19.0271i	0.154630	+	1.07547i	0.908330	+	0.418255i	$0.137358\pi$
$313$	2.73568	+	19.0271i	0.154630	+	1.07547i	−0.753700	+	0.657219i	$0.771733\pi$
$314$	11.3525	+	13.1014i	0.640657	+	0.739357i
$315$		0			0
$316$	−9.02455	+	5.79973i	−0.507671	+	0.326260i
$317$	−1.52863	+	10.6319i	−0.0858564	+	0.597144i	0.900788	+	0.434258i	$0.142989\pi$
$317$	−1.52863	+	10.6319i	−0.0858564	+	0.597144i	−0.986645	+	0.162886i	$0.947920\pi$
$318$		0			0
$319$	3.55414	−	4.10170i	0.198994	−	0.229651i
$320$	0.439490	+	0.129046i	0.0245683	+	0.00721389i
$321$		0			0
$322$	0.846649	+	1.30656i	0.0471819	+	0.0728119i
$323$	−7.80224			−0.434128
$324$		0			0
$325$	4.26331	−	4.92013i	0.236486	−	0.272920i
$326$	−4.43545	−	2.85049i	−0.245657	−	0.157874i
$327$		0			0
$328$	−0.712905	+	0.458156i	−0.0393636	+	0.0252975i
$329$	−0.366013	−	0.801456i	−0.0201789	−	0.0441857i
$330$		0			0
$331$	2.49561	+	17.3573i	0.137171	+	0.954045i	0.935878	+	0.352324i	$0.114609\pi$
$331$	2.49561	+	17.3573i	0.137171	+	0.954045i	−0.798707	+	0.601720i	$0.794482\pi$
$332$	−3.35797	+	7.35294i	−0.184293	+	0.403545i
$333$		0			0
$334$	−2.83814	+	0.833354i	−0.155296	+	0.0455991i
$335$	−2.01044	+	4.40226i	−0.109842	+	0.240521i
$336$		0			0
$337$	8.65628	+	9.98988i	0.471538	+	0.544184i	0.940839	−	0.338855i	$-0.110040\pi$
$337$	8.65628	+	9.98988i	0.471538	+	0.544184i	−0.469301	+	0.883038i	$0.655494\pi$
$338$	−4.63308	−	10.1450i	−0.252006	−	0.551817i
$339$		0			0
$340$	0.175750	−	1.22237i	0.00953137	−	0.0662921i
$341$	−5.15561	−	3.31331i	−0.279192	−	0.179426i
$342$		0			0
$343$	−4.32796	−	1.27080i	−0.233688	−	0.0686170i
$344$	−8.80752			−0.474869
$345$		0			0
$346$	−4.13279			−0.222180
$347$	−15.3250	−	4.49983i	−0.822690	−	0.241564i	−0.156816	−	0.987628i	$-0.550123\pi$
$347$	−15.3250	−	4.49983i	−0.822690	−	0.241564i	−0.665874	+	0.746064i	$0.731941\pi$
$348$		0			0
$349$	2.41073	+	1.54928i	0.129043	+	0.0829311i	0.603570	−	0.797310i	$-0.293744\pi$
$349$	2.41073	+	1.54928i	0.129043	+	0.0829311i	−0.474527	+	0.880241i	$0.657381\pi$
$350$	−0.221309	+	1.53924i	−0.0118294	+	0.0822756i
$351$		0			0
$352$	−1.03365	−	2.26339i	−0.0550940	−	0.120639i
$353$	5.27311	+	6.08549i	0.280659	+	0.323898i	0.878523	−	0.477700i	$-0.158529\pi$
$353$	5.27311	+	6.08549i	0.280659	+	0.323898i	−0.597864	+	0.801597i	$0.703984\pi$
$354$		0			0
$355$	−3.12186	+	6.83592i	−0.165691	+	0.362813i
$356$	−9.88113	+	2.90136i	−0.523699	+	0.153772i
$357$		0			0
$358$	−4.21107	+	9.22096i	−0.222562	+	0.487343i
$359$	1.11880	+	7.78141i	0.0590479	+	0.410687i	0.997811	+	0.0661249i	$0.0210636\pi$
$359$	1.11880	+	7.78141i	0.0590479	+	0.410687i	−0.938763	+	0.344562i	$0.888027\pi$
$360$		0			0
$361$	−4.41394	−	9.66518i	−0.232313	−	0.508694i
$362$	−22.4093	+	14.4016i	−1.17781	+	0.756930i
$363$		0			0
$364$	−0.371165	−	0.238533i	−0.0194543	−	0.0125025i
$365$	3.52821	−	4.07177i	0.184675	−	0.213126i
$366$		0			0
$367$	13.9011			0.725631			0.362816	−	0.931861i	$-0.381816\pi$
$367$	13.9011			0.725631			0.362816	+	0.931861i	$0.381816\pi$
$368$	3.63625	+	3.12693i	0.189553	+	0.163002i
$369$		0			0
$370$	0.211164	+	0.0620032i	0.0109779	+	0.00322339i
$371$	−1.85509	+	2.14089i	−0.0963116	+	0.111150i
$372$		0			0
$373$	1.37506	−	9.56372i	0.0711977	−	0.495191i	−0.922755	−	0.385386i	$-0.874068\pi$
$373$	1.37506	−	9.56372i	0.0711977	−	0.495191i	0.993953	−	0.109805i	$-0.0350226\pi$
$374$	−5.64361	+	3.62693i	−0.291824	+	0.187544i
$375$		0			0
$376$	−1.77733	−	2.05115i	−0.0916587	−	0.105780i
$377$	−0.421879	−	2.93423i	−0.0217279	−	0.151121i
$378$		0			0
$379$	19.1257	−	5.61580i	0.982419	−	0.288464i	0.249197	−	0.968453i	$-0.419833\pi$
$379$	19.1257	−	5.61580i	0.982419	−	0.288464i	0.733223	+	0.679989i	$0.238015\pi$
$380$	−1.27184	+	0.373446i	−0.0652440	+	0.0191574i
$381$		0			0
$382$	3.32908	+	23.1543i	0.170331	+	1.18467i
$383$	18.3187	+	21.1409i	0.936043	+	1.08025i	0.996625	+	0.0820878i	$0.0261588\pi$
$383$	18.3187	+	21.1409i	0.936043	+	1.08025i	−0.0605823	+	0.998163i	$0.519296\pi$
$384$		0			0
$385$	−0.311260	+	0.200034i	−0.0158633	+	0.0101947i
$386$	−0.856252	+	5.95536i	−0.0435821	+	0.303120i
$387$		0			0
$388$	0.146864	−	0.169490i	0.00745589	−	0.00860456i
$389$	−25.4067	−	7.46007i	−1.28817	−	0.378240i	−0.435262	−	0.900304i	$-0.643344\pi$
$389$	−25.4067	−	7.46007i	−1.28817	−	0.378240i	−0.852907	+	0.522064i	$0.825162\pi$
$390$		0			0
$391$	6.94949	−	10.9037i	0.351451	−	0.551425i
$392$	−6.89461			−0.348231
$393$		0			0
$394$	10.1267	−	11.6869i	0.510178	−	0.588777i
$395$	4.13365	+	2.65653i	0.207986	+	0.133665i
$396$		0			0
$397$	−13.8368	+	8.89236i	−0.694448	+	0.446295i	−0.839665	−	0.543105i	$-0.817248\pi$
$397$	−13.8368	+	8.89236i	−0.694448	+	0.446295i	0.145216	+	0.989400i	$0.453612\pi$
$398$	−4.86493	−	10.6527i	−0.243857	−	0.533972i
$399$		0			0
$400$	0.681716	+	4.74144i	0.0340858	+	0.237072i
$401$	−8.40890	+	18.4129i	−0.419920	+	0.919497i	0.574936	+	0.818198i	$0.305027\pi$
$401$	−8.40890	+	18.4129i	−0.419920	+	0.919497i	−0.994856	+	0.101298i	$0.967700\pi$
$402$		0			0
$403$	−3.21179	+	0.943066i	−0.159991	+	0.0469775i
$404$	−4.44314	+	9.72911i	−0.221054	+	0.484041i
$405$		0			0
$406$	0.463700	+	0.535138i	0.0230130	+	0.0265584i
$407$	−0.496644	−	1.08750i	−0.0246177	−	0.0539053i
$408$		0			0
$409$	−2.48089	+	17.2550i	−0.122672	+	0.853204i	0.831836	+	0.555021i	$0.187290\pi$
$409$	−2.48089	+	17.2550i	−0.122672	+	0.853204i	−0.954509	+	0.298183i	$0.903619\pi$
$410$	0.326542	+	0.209856i	0.0161268	+	0.0103641i
$411$		0			0
$412$	−1.94475	−	0.571031i	−0.0958110	−	0.0281327i
$413$	3.53309			0.173852
$414$		0			0
$415$	3.70257			0.181752
$416$	−1.30403	−	0.382897i	−0.0639352	−	0.0187731i
$417$		0			0
$418$	6.05763	+	3.89300i	0.296288	+	0.190413i
$419$	−2.34268	+	16.2937i	−0.114447	+	0.795998i	0.849056	+	0.528303i	$0.177171\pi$
$419$	−2.34268	+	16.2937i	−0.114447	+	0.795998i	−0.963503	+	0.267696i	$0.913738\pi$
$420$		0			0
$421$	−12.8684	−	28.1779i	−0.627169	−	1.37331i	−0.910189	−	0.414194i	$-0.864064\pi$
$421$	−12.8684	−	28.1779i	−0.627169	−	1.37331i	0.283020	−	0.959114i	$-0.408664\pi$
$422$	−6.99065	−	8.06764i	−0.340299	−	0.392726i
$423$		0			0
$424$	−3.62496	+	7.93756i	−0.176044	+	0.385482i
$425$	12.3917	−	3.63854i	0.601087	−	0.176495i
$426$		0			0
$427$	1.62672	−	3.56202i	0.0787224	−	0.172378i
$428$	0.308588	+	2.14627i	0.0149162	+	0.103744i
$429$		0			0
$430$	1.67588	+	3.66967i	0.0808182	+	0.176967i
$431$	15.4083	−	9.90232i	0.742192	−	0.476978i	−0.114100	−	0.993469i	$-0.536399\pi$
$431$	15.4083	−	9.90232i	0.742192	−	0.476978i	0.856292	+	0.516491i	$0.172762\pi$
$432$		0			0
$433$	12.7448	+	8.19061i	0.612478	+	0.393616i	0.809785	−	0.586726i	$-0.199583\pi$
$433$	12.7448	+	8.19061i	0.612478	+	0.393616i	−0.197308	+	0.980342i	$0.563220\pi$
$434$	0.523605	−	0.604273i	0.0251339	−	0.0290060i
$435$		0			0
$436$	−8.41887			−0.403191
$437$	−13.7447	−	1.92337i	−0.657499	−	0.0920072i
$438$		0			0
$439$	−5.59553	−	1.64300i	−0.267060	−	0.0784159i	0.145461	−	0.989364i	$-0.453533\pi$
$439$	−5.59553	−	1.64300i	−0.267060	−	0.0784159i	−0.412521	+	0.910948i	$0.635352\pi$
$440$	−0.746362	+	0.861348i	−0.0355814	+	0.0410632i
$441$		0			0
$442$	−0.521474	+	3.62693i	−0.0248040	+	0.172515i
$443$	14.5928	−	9.37820i	0.693323	−	0.445572i	−0.145943	−	0.989293i	$-0.546622\pi$
$443$	14.5928	−	9.37820i	0.693323	−	0.445572i	0.839266	+	0.543721i	$0.182985\pi$
$444$		0			0
$445$	3.08902	+	3.56492i	0.146434	+	0.168994i
$446$	−1.07757	−	7.49464i	−0.0510242	−	0.354881i
$447$		0			0
$448$	0.311485	−	0.0914602i	0.0147163	−	0.00432109i
$449$	−17.7555	+	5.21348i	−0.837932	+	0.246039i	−0.672421	−	0.740169i	$-0.734746\pi$
$449$	−17.7555	+	5.21348i	−0.837932	+	0.246039i	−0.165511	+	0.986208i	$0.552927\pi$
$450$		0			0
$451$	−0.300088	−	2.08716i	−0.0141306	−	0.0982804i
$452$	0.126969	+	0.146530i	0.00597214	+	0.00689221i
$453$		0			0
$454$	10.6374	−	6.83622i	0.499236	−	0.320840i
$455$	−0.0287606	+	0.200034i	−0.00134832	+	0.00937776i
$456$		0			0
$457$	3.77320	−	4.35450i	0.176503	−	0.203695i	−0.660604	−	0.750734i	$-0.729700\pi$
$457$	3.77320	−	4.35450i	0.176503	−	0.203695i	0.837107	+	0.547039i	$0.184245\pi$
$458$	8.05474	+	2.36508i	0.376373	+	0.110513i
$459$		0			0
$460$	0.610938	−	2.11004i	0.0284851	−	0.0983811i
$461$	−22.5329			−1.04946			−0.524730	−	0.851269i	$-0.675834\pi$
$461$	−22.5329			−1.04946			−0.524730	+	0.851269i	$0.675834\pi$
$462$		0			0
$463$	19.6456	−	22.6722i	0.913009	−	1.05367i	−0.0853472	−	0.996351i	$-0.527200\pi$
$463$	19.6456	−	22.6722i	0.913009	−	1.05367i	0.998356	−	0.0573171i	$-0.0182546\pi$
$464$	1.83493	+	1.17924i	0.0851845	+	0.0547448i
$465$		0			0
$466$	−22.1095	+	14.2089i	−1.02420	+	0.658215i
$467$	4.83680	+	10.5911i	0.223821	+	0.490099i	0.987913	−	0.155008i	$-0.0495403\pi$
$467$	4.83680	+	10.5911i	0.223821	+	0.490099i	−0.764093	+	0.645107i	$0.776813\pi$
$468$		0			0
$469$	0.488143	+	3.39511i	0.0225404	+	0.156772i
$470$	−0.516427	+	1.13082i	−0.0238210	+	0.0521607i
$471$		0			0
$472$	10.4424	−	3.06617i	0.480652	−	0.141132i
$473$	9.10393	−	19.9348i	0.418599	−	0.916604i
$474$		0			0
$475$	−9.07789	−	10.4764i	−0.416522	−	0.480692i
$476$	−0.363592	−	0.796155i	−0.0166652	−	0.0364917i
$477$		0			0
$478$	1.11770	−	7.77380i	0.0511226	−	0.355565i
$479$	−11.2218	−	7.21182i	−0.512738	−	0.329517i	0.258556	−	0.965996i	$-0.416754\pi$
$479$	−11.2218	−	7.21182i	−0.512738	−	0.329517i	−0.771293	+	0.636480i	$0.780390\pi$
$480$		0			0
$481$	−0.626551	−	0.183972i	−0.0285683	−	0.00838841i
$482$	−26.5043			−1.20724
$483$		0			0
$484$	−4.80864			−0.218574
$485$	−0.0985635	−	0.0289408i	−0.00447554	−	0.00131414i
$486$		0			0
$487$	−11.3740	−	7.30962i	−0.515405	−	0.331231i	0.256947	−	0.966425i	$-0.417283\pi$
$487$	−11.3740	−	7.30962i	−0.515405	−	0.331231i	−0.772352	+	0.635195i	$0.780920\pi$
$488$	1.71666	−	11.9397i	0.0777097	−	0.540483i
$489$		0			0
$490$	1.31190	+	2.87265i	0.0592655	+	0.129773i
$491$	26.8145	+	30.9455i	1.21012	+	1.39655i	0.894140	+	0.447787i	$0.147788\pi$
$491$	26.8145	+	30.9455i	1.21012	+	1.39655i	0.315979	+	0.948766i	$0.397667\pi$
$492$		0			0
$493$	2.44293	−	5.34928i	0.110024	−	0.240919i
$494$	3.77372	−	1.10806i	0.169788	−	0.0498542i
$495$		0			0
$496$	1.02316	−	2.24040i	0.0459411	−	0.100597i
$497$	0.758000	+	5.27200i	0.0340009	+	0.236482i
$498$		0			0
$499$	8.88711	+	19.4601i	0.397842	+	0.871152i	0.997485	+	0.0708840i	$0.0225820\pi$
$499$	8.88711	+	19.4601i	0.397842	+	0.871152i	−0.599643	+	0.800268i	$0.704691\pi$
$500$	3.77247	−	2.42442i	0.168710	−	0.108423i
$501$		0			0
$502$	15.1874	+	9.76036i	0.677847	+	0.435626i
$503$	14.2265	−	16.4183i	0.634330	−	0.732055i	−0.344032	−	0.938958i	$-0.611793\pi$
$503$	14.2265	−	16.4183i	0.634330	−	0.732055i	0.978362	+	0.206903i	$0.0663383\pi$
$504$		0			0
$505$	4.89909			0.218006
$506$	−10.8361	+	4.99809i	−0.481722	+	0.222192i
$507$		0			0
$508$	−12.4055	−	3.64259i	−0.550406	−	0.161614i
$509$	20.5288	−	23.6915i	0.909924	−	1.05011i	−0.0886141	−	0.996066i	$-0.528244\pi$
$509$	20.5288	−	23.6915i	0.909924	−	1.05011i	0.998539	−	0.0540428i	$-0.0172107\pi$
$510$		0			0
$511$	0.543429	−	3.77963i	0.0240399	−	0.167201i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$		0			0
$514$	−14.9674	−	17.2732i	−0.660182	−	0.761890i
$515$	0.132124	+	0.918939i	0.00582206	+	0.0404933i
$516$		0			0
$517$	6.47968	−	1.90261i	0.284976	−	0.0836765i
$518$	0.149660	−	0.0439442i	0.00657570	−	0.00193080i
$519$		0			0
$520$	0.0885937	+	0.616183i	0.00388509	+	0.0270214i
$521$	−5.97938	−	6.90057i	−0.261961	−	0.302319i	0.609498	−	0.792788i	$-0.291371\pi$
$521$	−5.97938	−	6.90057i	−0.261961	−	0.302319i	−0.871459	+	0.490468i	$0.836826\pi$
$522$		0			0
$523$	14.5013	−	9.31942i	0.634098	−	0.407510i	−0.183727	−	0.982977i	$-0.558816\pi$
$523$	14.5013	−	9.31942i	0.634098	−	0.407510i	0.817825	+	0.575468i	$0.195180\pi$
$524$	−0.838560	+	5.83232i	−0.0366327	+	0.254786i
$525$		0			0
$526$	−12.1932	+	14.0717i	−0.531647	+	0.613553i
$527$	−6.37145	−	1.87083i	−0.277545	−	0.0814945i
$528$		0			0
$529$	14.9304	−	17.4952i	0.649148	−	0.760662i
$530$	3.99695			0.173617
$531$		0			0
$532$	−0.615215	+	0.709996i	−0.0266729	+	0.0307822i
$533$	−0.968896	−	0.622672i	−0.0419675	−	0.0269709i
$534$		0			0
$535$	0.835532	−	0.536964i	0.0361232	−	0.0232150i
$536$	4.38919	+	9.61098i	0.189584	+	0.415131i
$537$		0			0
$538$	0.112249	+	0.780708i	0.00483939	+	0.0336587i
$539$	7.12665	−	15.6052i	0.306966	−	0.672163i
$540$		0			0
$541$	−41.0532	+	12.0543i	−1.76501	+	0.518255i	−0.993079	−	0.117446i	$-0.962529\pi$
$541$	−41.0532	+	12.0543i	−1.76501	+	0.518255i	−0.771935	+	0.635701i	$0.780711\pi$
$542$	12.1801	−	26.6706i	0.523179	−	1.14560i
$543$		0			0
$544$	−1.76557	−	2.03758i	−0.0756984	−	0.0873606i
$545$	1.60193	+	3.50774i	0.0686192	+	0.150255i
$546$		0			0
$547$	−2.55493	+	17.7699i	−0.109241	+	0.759786i	0.859397	+	0.511309i	$0.170839\pi$
$547$	−2.55493	+	17.7699i	−0.109241	+	0.759786i	−0.968638	+	0.248477i	$0.920070\pi$
$548$	13.6383	+	8.76482i	0.582600	+	0.374414i
$549$		0			0
$550$	−11.4364	−	3.35802i	−0.487648	−	0.143187i
$551$	−6.31212			−0.268905
$552$		0			0
$553$	3.48252			0.148092
$554$	24.4053	+	7.16603i	1.03688	+	0.304455i
$555$		0			0
$556$	−16.5162	−	10.6143i	−0.700443	−	0.450147i
$557$	2.00861	−	13.9702i	0.0851075	−	0.591936i	−0.901983	−	0.431772i	$-0.857889\pi$
$557$	2.00861	−	13.9702i	0.0851075	−	0.591936i	0.987090	−	0.160164i	$-0.0512023\pi$
$558$		0			0
$559$	−4.97257	−	10.8884i	−0.210317	−	0.460531i
$560$	−0.0973759	−	0.112378i	−0.00411488	−	0.00474883i
$561$		0			0
$562$	9.79634	−	21.4510i	0.413234	−	0.904855i
$563$	21.3328	−	6.26389i	0.899072	−	0.263991i	0.200638	−	0.979665i	$-0.435699\pi$
$563$	21.3328	−	6.26389i	0.899072	−	0.263991i	0.698434	+	0.715674i	$0.253880\pi$
$564$		0			0
$565$	0.0368926	−	0.0807836i	0.00155209	−	0.00339859i
$566$	3.78987	+	26.3591i	0.159300	+	1.10796i
$567$		0			0
$568$	6.81563	+	14.9241i	0.285977	+	0.626203i
$569$	11.0733	−	7.11640i	0.464218	−	0.298335i	−0.287546	−	0.957767i	$-0.592839\pi$
$569$	11.0733	−	7.11640i	0.464218	−	0.298335i	0.751764	+	0.659432i	$0.229203\pi$
$570$		0			0
$571$	17.6085	+	11.3163i	0.736893	+	0.473573i	0.854476	−	0.519490i	$-0.173878\pi$
$571$	17.6085	+	11.3163i	0.736893	+	0.473573i	−0.117583	+	0.993063i	$0.537515\pi$
$572$	2.21456	−	2.55574i	0.0925954	−	0.106861i
$573$		0			0
$574$	0.275106			0.0114827
$575$	22.7267	−	3.35504i	0.947767	−	0.139915i
$576$		0			0
$577$	0.990929	+	0.290963i	0.0412529	+	0.0121129i	0.302294	−	0.953215i	$-0.402248\pi$
$577$	0.990929	+	0.290963i	0.0412529	+	0.0121129i	−0.261041	+	0.965328i	$0.584066\pi$
$578$	6.37246	−	7.35421i	0.265059	−	0.305895i
$579$		0			0
$580$	0.142184	−	0.988911i	0.00590387	−	0.0410623i
$581$	2.20758	−	1.41873i	0.0915860	−	0.0588588i
$582$		0			0
$583$	−14.2188	−	16.4094i	−0.588884	−	0.679608i
$584$	−1.67397	−	11.6427i	−0.0692694	−	0.481779i
$585$		0			0
$586$	−6.32533	+	1.85728i	−0.261297	+	0.0767237i
$587$	−4.49531	+	1.31994i	−0.185541	+	0.0544798i	−0.373183	−	0.927758i	$-0.621734\pi$
$587$	−4.49531	+	1.31994i	−0.185541	+	0.0544798i	0.187642	+	0.982237i	$0.439916\pi$
$588$		0			0
$589$	1.01436	+	7.05504i	0.0417960	+	0.290698i
$590$	−3.26450	−	3.76743i	−0.134397	−	0.155103i
$591$		0			0
$592$	0.404200	−	0.259764i	0.0166125	−	0.0106762i
$593$	−4.46279	+	31.0394i	−0.183265	+	1.27463i	0.665714	+	0.746207i	$0.268127\pi$
$593$	−4.46279	+	31.0394i	−0.183265	+	1.27463i	−0.848979	+	0.528427i	$0.822782\pi$
$594$		0			0
$595$	−0.262536	+	0.302982i	−0.0107629	+	0.0124211i
$596$	3.05112	+	0.895889i	0.124979	+	0.0366970i
$597$		0			0
$598$	−1.81274	+	6.26077i	−0.0741283	+	0.256022i
$599$	−27.2585			−1.11375			−0.556875	−	0.830596i	$-0.688000\pi$
$599$	−27.2585			−1.11375			−0.556875	+	0.830596i	$0.688000\pi$
$600$		0			0
$601$	−11.3031	+	13.0444i	−0.461062	+	0.532094i	−0.937904	−	0.346895i	$-0.887236\pi$
$601$	−11.3031	+	13.0444i	−0.461062	+	0.532094i	0.476842	+	0.878989i	$0.341781\pi$
$602$	2.40533	+	1.54581i	0.0980341	+	0.0630027i
$603$		0			0
$604$	−1.07236	+	0.689165i	−0.0436338	+	0.0280417i
$605$	0.914980	+	2.00353i	0.0371992	+	0.0814550i
$606$		0			0
$607$	6.49805	+	45.1949i	0.263748	+	1.83441i	0.504011	+	0.863697i	$0.331857\pi$
$607$	6.49805	+	45.1949i	0.263748	+	1.83441i	−0.240263	+	0.970708i	$0.577234\pi$
$608$	−1.20217	+	2.63238i	−0.0487543	+	0.106757i
$609$		0			0
$610$	−5.30132	+	1.55661i	−0.214644	+	0.0630253i
$611$	1.53231	−	3.35529i	0.0619906	−	0.135740i
$612$		0			0
$613$	1.32116	+	1.52470i	0.0533611	+	0.0615820i	0.781803	−	0.623526i	$-0.214300\pi$
$613$	1.32116	+	1.52470i	0.0533611	+	0.0615820i	−0.728441	+	0.685108i	$0.759755\pi$
$614$	9.26181	+	20.2805i	0.373776	+	0.818456i
$615$		0			0
$616$	−0.114958	+	0.799549i	−0.00463178	+	0.0322148i
$617$	−31.5453	−	20.2730i	−1.26997	−	0.816159i	−0.280352	−	0.959897i	$-0.590451\pi$
$617$	−31.5453	−	20.2730i	−1.26997	−	0.816159i	−0.989616	+	0.143739i	$0.954087\pi$
$618$		0			0
$619$	−25.2336	−	7.40924i	−1.01422	−	0.297803i	−0.267943	−	0.963435i	$-0.586344\pi$
$619$	−25.2336	−	7.40924i	−1.01422	−	0.297803i	−0.746280	+	0.665632i	$0.768162\pi$
$620$	−1.12815			−0.0453077
$621$		0			0
$622$	12.9065			0.517503
$623$	3.20776	+	0.941883i	0.128516	+	0.0377357i
$624$		0			0
$625$	18.4209	+	11.8384i	0.736835	+	0.473535i
$626$	2.73568	−	19.0271i	0.109340	−	0.760474i
$627$		0			0
$628$	−7.20151	−	15.7691i	−0.287371	−	0.629256i
$629$	−0.848312	−	0.979004i	−0.0338244	−	0.0390355i
$630$		0			0
$631$	8.49601	−	18.6037i	0.338221	−	0.740600i	−0.661737	−	0.749736i	$-0.730181\pi$
$631$	8.49601	−	18.6037i	0.338221	−	0.740600i	0.999958	+	0.00913542i	$0.00290794\pi$
$632$	10.2930	−	3.02229i	0.409432	−	0.120220i
$633$		0			0
$634$	4.46205	−	9.77052i	0.177211	−	0.388037i
$635$	0.842813	+	5.86189i	0.0334460	+	0.232622i
$636$		0			0
$637$	−3.89258	−	8.52355i	−0.154230	−	0.337716i
$638$	−4.56576	+	2.93423i	−0.180760	+	0.116167i
$639$		0			0
$640$	−0.385331	−	0.247638i	−0.0152316	−	0.00978873i
$641$	18.6345	−	21.5053i	0.736018	−	0.849410i	−0.257117	−	0.966380i	$-0.582773\pi$
$641$	18.6345	−	21.5053i	0.736018	−	0.849410i	0.993135	+	0.116970i	$0.0373181\pi$
$642$		0			0
$643$	35.1379			1.38570			0.692851	−	0.721080i	$-0.256354\pi$
$643$	35.1379			1.38570			0.692851	+	0.721080i	$0.256354\pi$
$644$	−0.444252	−	1.49217i	−0.0175060	−	0.0587996i
$645$		0			0
$646$	7.48620	+	2.19815i	0.294541	+	0.0864849i
$647$	−8.02115	+	9.25690i	−0.315344	+	0.363926i	−0.891189	−	0.453633i	$-0.850128\pi$
$647$	−8.02115	+	9.25690i	−0.315344	+	0.363926i	0.575845	+	0.817559i	$0.304673\pi$
$648$		0			0
$649$	−3.85392	+	26.8046i	−0.151280	+	1.05217i
$650$	−5.47678	+	3.51971i	−0.214817	+	0.138054i
$651$		0			0
$652$	3.45271	+	3.98464i	0.135219	+	0.156051i
$653$	−3.40835	−	23.7056i	−0.133379	−	0.927671i	−0.941105	−	0.338113i	$-0.890211\pi$
$653$	−3.40835	−	23.7056i	−0.133379	−	0.927671i	0.807726	−	0.589558i	$-0.200698\pi$
$654$		0			0
$655$	2.58961	−	0.760377i	0.101184	−	0.0297104i
$656$	0.813105	−	0.238749i	0.0317464	−	0.00932159i
$657$		0			0
$658$	0.125390	+	0.872109i	0.00488822	+	0.0339983i
$659$	−6.13650	−	7.08190i	−0.239044	−	0.275872i	0.623533	−	0.781797i	$-0.285697\pi$
$659$	−6.13650	−	7.08190i	−0.239044	−	0.275872i	−0.862577	+	0.505925i	$0.831151\pi$
$660$		0			0
$661$	17.3162	−	11.1284i	0.673520	−	0.432845i	−0.158673	−	0.987331i	$-0.550721\pi$
$661$	17.3162	−	11.1284i	0.673520	−	0.432845i	0.832193	+	0.554486i	$0.187085\pi$
$662$	2.49561	−	17.3573i	0.0969945	−	0.674611i
$663$		0			0
$664$	5.29352	−	6.10904i	0.205428	−	0.237077i
$665$	0.412883	+	0.121233i	0.0160109	+	0.00470123i
$666$		0			0
$667$	5.62224	−	8.82126i	0.217694	−	0.341561i
$668$	2.95796			0.114447
$669$		0			0
$670$	3.16926	−	3.65753i	0.122439	−	0.141303i
$671$	25.2496	+	16.2270i	0.974751	+	0.626435i
$672$		0			0
$673$	−4.24556	+	2.72845i	−0.163654	+	0.105174i	−0.619904	−	0.784677i	$-0.712829\pi$
$673$	−4.24556	+	2.72845i	−0.163654	+	0.105174i	0.456250	+	0.889852i	$0.349192\pi$
$674$	−5.49117	−	12.0240i	−0.211512	−	0.463146i
$675$		0			0
$676$	1.58722	+	11.0394i	0.0610470	+	0.424592i
$677$	−14.9029	+	32.6328i	−0.572765	+	1.25418i	0.372547	+	0.928013i	$0.378485\pi$
$677$	−14.9029	+	32.6328i	−0.572765	+	1.25418i	−0.945312	+	0.326168i	$0.894243\pi$
$678$		0			0
$679$	−0.0698560	+	0.0205116i	−0.00268083	+	0.000787161i
$680$	−0.513011	+	1.12334i	−0.0196731	+	0.0430780i
$681$		0			0
$682$	4.01330	+	4.63160i	0.153677	+	0.177353i
$683$	−9.19582	−	20.1360i	−0.351868	−	0.770484i	−0.999960	−	0.00892206i	$-0.997160\pi$
$683$	−9.19582	−	20.1360i	−0.351868	−	0.770484i	0.648092	−	0.761562i	$-0.275567\pi$
$684$		0			0
$685$	1.05680	−	7.35019i	0.0403782	−	0.280836i
$686$	3.79462	+	2.43865i	0.144879	+	0.0931083i
$687$		0			0
$688$	8.45075	+	2.48136i	0.322182	+	0.0946011i
$689$	−11.8595			−0.451811
$690$		0			0
$691$	19.2304			0.731560			0.365780	−	0.930701i	$-0.380802\pi$
$691$	19.2304			0.731560			0.365780	+	0.930701i	$0.380802\pi$
$692$	3.96538	+	1.16434i	0.150741	+	0.0442616i
$693$		0			0
$694$	13.4365	+	8.63512i	0.510043	+	0.327784i
$695$	−1.27980	+	8.90118i	−0.0485455	+	0.337641i
$696$		0			0
$697$	−0.949126	−	2.07830i	−0.0359507	−	0.0787211i
$698$	−1.87659	−	2.16570i	−0.0710301	−	0.0819731i
$699$		0			0
$700$	0.645997	−	1.41454i	0.0244164	−	0.0534644i
$701$	−22.7658	+	6.68465i	−0.859853	+	0.252476i	−0.681794	−	0.731544i	$-0.738800\pi$
$701$	−22.7658	+	6.68465i	−0.859853	+	0.252476i	−0.178059	+	0.984020i	$0.556982\pi$
$702$		0			0
$703$	−0.577610	+	1.26479i	−0.0217850	+	0.0477024i
$704$	0.354114	+	2.46292i	0.0133462	+	0.0928247i
$705$		0			0
$706$	−3.34503	−	7.32459i	−0.125892	−	0.275665i
$707$	2.92099	−	1.87720i	0.109855	−	0.0705995i
$708$		0			0
$709$	−17.6711	−	11.3565i	−0.663653	−	0.426504i	0.164980	−	0.986297i	$-0.447244\pi$
$709$	−17.6711	−	11.3565i	−0.663653	−	0.426504i	−0.828632	+	0.559793i	$0.810881\pi$
$710$	4.92131	−	5.67949i	0.184693	−	0.213147i
$711$		0			0
$712$	10.2983			0.385945
$713$	−10.7630	−	4.86637i	−0.403077	−	0.182247i
$714$		0			0
$715$	−1.48624	−	0.436398i	−0.0555821	−	0.0163204i
$716$	6.63834	−	7.66105i	0.248086	−	0.286307i
$717$		0			0
$718$	1.11880	−	7.78141i	0.0417532	−	0.290400i
$719$	−10.3821	+	6.67218i	−0.387187	+	0.248830i	−0.719724	−	0.694260i	$-0.755732\pi$
$719$	−10.3821	+	6.67218i	−0.387187	+	0.248830i	0.332537	+	0.943090i	$0.392095\pi$
$720$		0			0
$721$	0.430890	+	0.497274i	0.0160472	+	0.0185194i
$722$	1.51215	+	10.5172i	0.0562763	+	0.391411i
$723$		0			0
$724$	25.5589	−	7.50478i	0.949891	−	0.278913i
$725$	10.0251	−	2.94363i	0.372322	−	0.109324i
$726$		0			0
$727$	−1.68354	−	11.7093i	−0.0624390	−	0.434273i	−0.996931	−	0.0782882i	$-0.975055\pi$
$727$	−1.68354	−	11.7093i	−0.0624390	−	0.434273i	0.934492	−	0.355985i	$-0.115855\pi$
$728$	0.288928	+	0.333440i	0.0107084	+	0.0123581i
$729$		0			0
$730$	−4.53244	+	2.91282i	−0.167753	+	0.107808i
$731$	3.37941	−	23.5043i	0.124992	−	0.869338i
$732$		0			0
$733$	−29.9830	+	34.6022i	−1.10745	+	1.27806i	−0.150242	+	0.988649i	$0.548005\pi$
$733$	−29.9830	+	34.6022i	−1.10745	+	1.27806i	−0.957204	+	0.289413i	$0.906540\pi$
$734$	−13.3380	−	3.91639i	−0.492315	−	0.144557i
$735$		0			0
$736$	−2.60800	−	4.02471i	−0.0961323	−	0.148353i
$737$	−26.2903			−0.968415
$738$		0			0
$739$	5.80020	−	6.69379i	0.213364	−	0.246235i	−0.638972	−	0.769230i	$-0.720640\pi$
$739$	5.80020	−	6.69379i	0.213364	−	0.246235i	0.852336	+	0.522995i	$0.175185\pi$
$740$	−0.185142	−	0.118983i	−0.00680594	−	0.00437391i
$741$		0			0
$742$	2.38311	−	1.53153i	0.0874866	−	0.0562242i
$743$	14.6652	+	32.1123i	0.538014	+	1.17809i	0.962158	+	0.272492i	$0.0878479\pi$
$743$	14.6652	+	32.1123i	0.538014	+	1.17809i	−0.424144	+	0.905595i	$0.639425\pi$
$744$		0			0
$745$	−0.207288	−	1.44172i	−0.00759446	−	0.0528206i
$746$	−4.01377	+	8.78893i	−0.146954	+	0.321785i
$747$		0			0
$748$	6.43683	−	1.89002i	0.235354	−	0.0691061i
$749$	0.292419	−	0.640308i	0.0106848	−	0.0233964i
$750$		0			0
$751$	−11.6294	−	13.4211i	−0.424364	−	0.489742i	0.502798	−	0.864404i	$-0.332304\pi$
$751$	−11.6294	−	13.4211i	−0.424364	−	0.489742i	−0.927161	+	0.374662i	$0.877759\pi$
$752$	1.12746	+	2.46879i	0.0411142	+	0.0900276i
$753$		0			0
$754$	−0.421879	+	2.93423i	−0.0153639	+	0.106859i
$755$	0.491189	+	0.315668i	0.0178762	+	0.0114883i
$756$		0			0
$757$	−7.70494	−	2.26237i	−0.280041	−	0.0822274i	0.138696	−	0.990335i	$-0.455709\pi$
$757$	−7.70494	−	2.26237i	−0.280041	−	0.0822274i	−0.418737	+	0.908108i	$0.637527\pi$
$758$	−19.9331			−0.724002
$759$		0			0
$760$	1.32553			0.0480821
$761$	19.9673	+	5.86292i	0.723813	+	0.212531i	0.622830	−	0.782358i	$-0.285983\pi$
$761$	19.9673	+	5.86292i	0.723813	+	0.212531i	0.100983	+	0.994888i	$0.467801\pi$
$762$		0			0
$763$	2.29920	+	1.47760i	0.0832365	+	0.0534928i
$764$	3.32908	−	23.1543i	0.120442	−	0.837692i
$765$		0			0
$766$	−11.6206	−	25.4456i	−0.419869	−	0.919385i
$767$	9.68621	+	11.1785i	0.349749	+	0.403632i
$768$		0			0
$769$	12.1816	−	26.6740i	0.439279	−	0.961888i	−0.552450	−	0.833546i	$-0.686307\pi$
$769$	12.1816	−	26.6740i	0.439279	−	0.961888i	0.991730	−	0.128342i	$-0.0409656\pi$
$770$	0.355008	−	0.104240i	0.0127936	−	0.00375654i
$771$		0			0
$772$	2.49939	−	5.47289i	0.0899549	−	0.196974i
$773$	−5.93473	−	41.2770i	−0.213457	−	1.48463i	−0.761493	−	0.648174i	$-0.775533\pi$
$773$	−5.93473	−	41.2770i	−0.213457	−	1.48463i	0.548035	−	0.836455i	$-0.315376\pi$
$774$		0			0
$775$	−4.90112	−	10.7320i	−0.176053	−	0.385503i
$776$	−0.188666	+	0.121248i	−0.00677271	+	0.00435256i
$777$		0			0
$778$	22.2758	+	14.3158i	0.798625	+	0.513245i
$779$	−1.60597	+	1.85338i	−0.0575397	+	0.0664044i
$780$		0			0
$781$	−40.8241			−1.46080
$782$	−9.73993	+	8.50415i	−0.348299	+	0.304108i
$783$		0			0
$784$	6.61533	+	1.94244i	0.236262	+	0.0693727i
$785$	−5.19993	+	6.00104i	−0.185594	+	0.214186i
$786$		0			0
$787$	−6.28618	+	43.7214i	−0.224078	+	1.55850i	0.498303	+	0.867003i	$0.333957\pi$
$787$	−6.28618	+	43.7214i	−0.224078	+	1.55850i	−0.722381	+	0.691495i	$0.756952\pi$
$788$	−13.0091	+	8.36045i	−0.463430	+	0.297829i
$789$		0			0
$790$	−3.21777	−	3.71351i	−0.114483	−	0.132121i
$791$	−0.00895767	−	0.0623020i	−0.000318498	−	0.00221520i
$792$		0			0
$793$	15.7298	−	4.61867i	0.558580	−	0.164014i
$794$	15.7816	−	4.63388i	0.560067	−	0.164450i
$795$		0			0
$796$	1.66665	+	11.5918i	0.0590729	+	0.410861i
$797$	−20.2917	−	23.4179i	−0.718769	−	0.829504i	0.272389	−	0.962187i	$-0.412186\pi$
$797$	−20.2917	−	23.4179i	−0.718769	−	0.829504i	−0.991158	+	0.132683i	$0.957641\pi$
$798$		0			0
$799$	6.15577	−	3.95607i	0.217776	−	0.139956i
$800$	0.681716	−	4.74144i	0.0241023	−	0.167635i
$801$		0			0
$802$	13.2558	−	15.2980i	0.468078	−	0.540191i
$803$	28.0823	+	8.24570i	0.991002	+	0.290985i
$804$		0			0
$805$	−0.537182	+	0.469026i	−0.0189332	+	0.0165310i
$806$	3.34738			0.117906
$807$		0			0
$808$	7.00416	−	8.08324i	0.246406	−	0.284367i
$809$	21.4348	+	13.7753i	0.753609	+	0.484315i	0.860180	−	0.509990i	$-0.170351\pi$
$809$	21.4348	+	13.7753i	0.753609	+	0.484315i	−0.106571	+	0.994305i	$0.533987\pi$
$810$		0			0
$811$	−18.1906	+	11.6904i	−0.638758	+	0.410505i	−0.819543	−	0.573018i	$-0.805772\pi$
$811$	−18.1906	+	11.6904i	−0.638758	+	0.410505i	0.180785	+	0.983523i	$0.442136\pi$
$812$	−0.294151	−	0.644100i	−0.0103227	−	0.0226035i
$813$		0			0
$814$	0.170143	+	1.18337i	0.00596350	+	0.0414770i
$815$	1.00323	−	2.19677i	0.0351417	−	0.0769495i
$816$		0			0
$817$	−24.4556	+	7.18080i	−0.855592	+	0.251225i
$818$	7.24169	−	15.8571i	0.253200	−	0.554430i
$819$		0			0
$820$	−0.254192	−	0.293353i	−0.00887676	−	0.0102443i
$821$	19.8677	+	43.5042i	0.693387	+	1.51831i	0.847809	+	0.530301i	$0.177921\pi$
$821$	19.8677	+	43.5042i	0.693387	+	1.51831i	−0.154422	+	0.988005i	$0.549351\pi$
$822$		0			0
$823$	3.03301	−	21.0951i	0.105724	−	0.735327i	−0.866143	−	0.499797i	$-0.833408\pi$
$823$	3.03301	−	21.0951i	0.105724	−	0.735327i	0.971867	−	0.235531i	$-0.0756829\pi$
$824$	1.70510	+	1.09580i	0.0593999	+	0.0381740i
$825$		0			0
$826$	−3.38998	−	0.995387i	−0.117952	−	0.0346339i
$827$	−8.52696			−0.296512			−0.148256	−	0.988949i	$-0.547366\pi$
$827$	−8.52696			−0.296512			−0.148256	+	0.988949i	$0.547366\pi$
$828$		0			0
$829$	−28.0337			−0.973651			−0.486826	−	0.873499i	$-0.661845\pi$
$829$	−28.0337			−0.973651			−0.486826	+	0.873499i	$0.661845\pi$
$830$	−3.55259	−	1.04313i	−0.123312	−	0.0362077i
$831$		0			0
$832$	1.14333	+	0.734774i	0.0396379	+	0.0254737i
$833$	2.64543	−	18.3994i	0.0916589	−	0.637501i
$834$		0			0
$835$	−0.562837	−	1.23244i	−0.0194778	−	0.0426504i
$836$	−4.71547	−	5.44194i	−0.163088	−	0.188213i
$837$		0			0
$838$	6.83824	−	14.9737i	0.236223	−	0.517257i
$839$	37.8397	−	11.1107i	1.30637	−	0.383585i	0.446815	−	0.894626i	$-0.352558\pi$
$839$	37.8397	−	11.1107i	1.30637	−	0.383585i	0.859556	+	0.511041i	$0.170740\pi$
$840$		0			0
$841$	−10.0707	+	22.0517i	−0.347264	+	0.760403i
$842$	4.40853	+	30.6620i	0.151928	+	1.05668i
$843$		0			0
$844$	4.43456	+	9.71033i	0.152644	+	0.334243i
$845$	4.29756	−	2.76188i	0.147841	−	0.0950114i
$846$		0			0
$847$	1.31324	+	0.843968i	0.0451234	+	0.0289991i
$848$	5.71440	−	6.59477i	0.196233	−	0.226465i
$849$		0			0
$850$	−12.9149			−0.442976
$851$	−1.25308	−	1.93377i	−0.0429549	−	0.0662888i
$852$		0			0
$853$	−44.2335	−	12.9881i	−1.51453	−	0.444705i	−0.584252	−	0.811572i	$-0.698612\pi$
$853$	−44.2335	−	12.9881i	−1.51453	−	0.444705i	−0.930273	+	0.366867i	$0.880430\pi$
$854$	−2.56436	+	2.95943i	−0.0877506	+	0.101270i
$855$		0			0
$856$	0.308588	−	2.14627i	0.0105473	−	0.0733582i
$857$	10.5582	−	6.78534i	0.360661	−	0.231783i	−0.347743	−	0.937590i	$-0.613052\pi$
$857$	10.5582	−	6.78534i	0.360661	−	0.231783i	0.708404	+	0.705807i	$0.249416\pi$
$858$		0			0
$859$	3.21092	+	3.70559i	0.109555	+	0.126433i	0.807878	−	0.589349i	$-0.200616\pi$
$859$	3.21092	+	3.70559i	0.109555	+	0.126433i	−0.698323	+	0.715782i	$0.746070\pi$
$860$	−0.574131	−	3.99317i	−0.0195777	−	0.136166i
$861$		0			0
$862$	−17.5740	+	5.16018i	−0.598572	+	0.175757i
$863$	−38.1184	+	11.1926i	−1.29757	+	0.381000i	−0.856348	−	0.516400i	$-0.827272\pi$
$863$	−38.1184	+	11.1926i	−1.29757	+	0.381000i	−0.441219	+	0.897400i	$0.645454\pi$
$864$		0			0
$865$	−0.269402	−	1.87373i	−0.00915995	−	0.0637088i
$866$	−9.92102	−	11.4495i	−0.337130	−	0.389069i
$867$		0			0
$868$	−0.672639	+	0.432279i	−0.0228308	+	0.0146725i
$869$	−3.79876	+	26.4210i	−0.128864	+	0.896270i
$870$		0			0
$871$	−9.40364	+	10.8524i	−0.318630	+	0.367719i
$872$	8.07785	+	2.37187i	0.273551	+	0.0803217i
$873$		0			0
$874$	12.6461	+	5.71779i	0.427760	+	0.193407i
$875$	−1.45577			−0.0492142
$876$		0			0
$877$	−1.42882	+	1.64894i	−0.0482478	+	0.0556809i	−0.779360	−	0.626576i	$-0.784456\pi$
$877$	−1.42882	+	1.64894i	−0.0482478	+	0.0556809i	0.731113	+	0.682257i	$0.239001\pi$
$878$	4.90599	+	3.15289i	0.165569	+	0.106405i
$879$		0			0
$880$	0.958799	−	0.616183i	0.0323211	−	0.0207715i
$881$	21.0662	+	46.1285i	0.709738	+	1.55411i	0.827751	+	0.561096i	$0.189620\pi$
$881$	21.0662	+	46.1285i	0.709738	+	1.55411i	−0.118013	+	0.993012i	$0.537652\pi$
$882$		0			0
$883$	5.44954	+	37.9024i	0.183392	+	1.27552i	0.848670	+	0.528922i	$0.177404\pi$
$883$	5.44954	+	37.9024i	0.183392	+	1.27552i	−0.665279	+	0.746595i	$0.731687\pi$
$884$	1.52217	−	3.33310i	0.0511962	−	0.112104i
$885$		0			0
$886$	−16.6438	+	4.88706i	−0.559159	+	0.164184i
$887$	−8.95322	+	19.6048i	−0.300620	+	0.658266i	−0.998309	−	0.0581352i	$-0.981485\pi$
$887$	−8.95322	+	19.6048i	−0.300620	+	0.658266i	0.697689	+	0.716401i	$0.254212\pi$
$888$		0			0
$889$	2.74864	+	3.17210i	0.0921863	+	0.106389i
$890$	−1.95954	−	4.29080i	−0.0656840	−	0.143828i
$891$		0			0
$892$	−1.07757	+	7.49464i	−0.0360796	+	0.250939i
$893$	−6.60736	−	4.24630i	−0.221107	−	0.142097i
$894$		0			0
$895$	−4.45513	−	1.30814i	−0.148918	−	0.0437264i
$896$	−0.324635			−0.0108453
$897$		0			0
$898$	18.5051			0.617522
$899$	−5.15459	−	1.51353i	−0.171915	−	0.0504789i
$900$		0			0
$901$	−19.7918	−	12.7194i	−0.659361	−	0.423745i
$902$	−0.300088	+	2.08716i	−0.00999183	+	0.0694947i
$903$		0			0
$904$	−0.0805438	−	0.176366i	−0.00267885	−	0.00586586i
$905$	−7.99020	−	9.22118i	−0.265603	−	0.306523i
$906$		0			0
$907$	11.9325	−	26.1286i	0.396214	−	0.867587i	−0.601426	−	0.798928i	$-0.705401\pi$
$907$	11.9325	−	26.1286i	0.396214	−	0.867587i	0.997640	−	0.0686589i	$-0.0218720\pi$
$908$	−12.1325	+	3.56241i	−0.402630	+	0.118223i
$909$		0			0
$910$	0.0839518	−	0.183829i	0.00278298	−	0.00609387i
$911$	−0.517595	−	3.59995i	−0.0171487	−	0.119272i	0.979449	−	0.201692i	$-0.0646441\pi$
$911$	−0.517595	−	3.59995i	−0.0171487	−	0.119272i	−0.996598	+	0.0824204i	$0.973735\pi$
$912$		0			0
$913$	8.35546	+	18.2959i	0.276526	+	0.605506i
$914$	−4.84716	+	3.11508i	−0.160330	+	0.103038i
$915$		0			0
$916$	−7.06214	−	4.53856i	−0.233340	−	0.149958i
$917$	1.25265	−	1.44563i	0.0413660	−	0.0477389i
$918$		0			0
$919$	14.2577			0.470318			0.235159	−	0.971957i	$-0.424439\pi$
$919$	14.2577			0.470318			0.235159	+	0.971957i	$0.424439\pi$
$920$	−1.18066	+	1.85245i	−0.0389251	+	0.0610733i
$921$		0			0
$922$	21.6201	+	6.34824i	0.712021	+	0.209068i
$923$	−14.6022	+	16.8518i	−0.480637	+	0.554684i
$924$		0			0
$925$	0.327547	−	2.27814i	0.0107697	−	0.0749047i
$926$	−25.2373	+	16.2190i	−0.829350	+	0.532991i
$927$		0			0
$928$	−1.42837	−	1.64843i	−0.0468886	−	0.0541124i
$929$	7.42433	+	51.6373i	0.243584	+	1.69417i	0.633844	+	0.773461i	$0.281476\pi$
$929$	7.42433	+	51.6373i	0.243584	+	1.69417i	−0.390260	+	0.920705i	$0.627615\pi$
$930$		0			0
$931$	−19.1441	+	5.62121i	−0.627422	+	0.184228i
$932$	25.2170	−	7.40439i	0.826011	−	0.242539i
$933$		0			0
$934$	−1.65702	−	11.5248i	−0.0542192	−	0.377103i
$935$	−2.01227	−	2.32229i	−0.0658083	−	0.0759469i
$936$		0			0
$937$	−30.9751	+	19.9065i	−1.01191	+	0.650317i	−0.937888	−	0.346939i	$-0.887221\pi$
$937$	−30.9751	+	19.9065i	−1.01191	+	0.650317i	−0.0740256	+	0.997256i	$0.523585\pi$
$938$	0.488143	−	3.39511i	0.0159384	−	0.110854i
$939$		0			0
$940$	0.814095	−	0.939516i	0.0265529	−	0.0306436i
$941$	−15.8211	−	4.64550i	−0.515754	−	0.151439i	0.0134897	−	0.999909i	$-0.495706\pi$
$941$	−15.8211	−	4.64550i	−0.515754	−	0.151439i	−0.529243	+	0.848470i	$0.677524\pi$
$942$		0			0
$943$	−1.15968	−	3.89517i	−0.0377645	−	0.126844i
$944$	−10.8833			−0.354221
$945$		0			0
$946$	−14.3514	+	16.5624i	−0.466606	+	0.538492i
$947$	−40.8392	−	26.2458i	−1.32710	−	0.852874i	−0.331217	−	0.943555i	$-0.607459\pi$
$947$	−40.8392	−	26.2458i	−1.32710	−	0.852874i	−0.995880	+	0.0906811i	$0.971096\pi$
$948$		0			0
$949$	13.4484	−	8.64274i	0.436552	−	0.280555i
$950$	5.75862	+	12.6096i	0.186834	+	0.409110i
$951$		0			0
$952$	0.124561	+	0.866341i	0.00403705	+	0.0280783i
$953$	−23.5811	+	51.6354i	−0.763867	+	1.67264i	−0.0241587	+	0.999708i	$0.507691\pi$
$953$	−23.5811	+	51.6354i	−0.763867	+	1.67264i	−0.739708	+	0.672928i	$0.765037\pi$
$954$		0			0
$955$	−10.2807	+	3.01869i	−0.332676	+	0.0976825i
$956$	−3.26256	+	7.14402i	−0.105519	+	0.231054i
$957$		0			0
$958$	8.73545	+	10.0812i	0.282230	+	0.325710i
$959$	−2.18631	−	4.78735i	−0.0705996	−	0.154591i
$960$		0			0
$961$	3.54844	−	24.6800i	0.114466	−	0.796128i
$962$	0.549341	+	0.353040i	0.0177115	+	0.0113825i
$963$		0			0
$964$	25.4306	+	7.46711i	0.819066	+	0.240499i
$965$	−2.75587			−0.0887146
$966$		0			0
$967$	26.3683			0.847948			0.423974	−	0.905674i	$-0.360635\pi$
$967$	26.3683			0.847948			0.423974	+	0.905674i	$0.360635\pi$
$968$	4.61385	+	1.35475i	0.148295	+	0.0435433i
$969$		0			0
$970$	0.0864174	+	0.0555371i	0.00277469	+	0.00178319i
$971$	0.832978	−	5.79349i	0.0267315	−	0.185922i	−0.972081	−	0.234647i	$-0.924607\pi$
$971$	0.832978	−	5.79349i	0.0267315	−	0.185922i	0.998812	+	0.0487249i	$0.0155157\pi$
$972$		0			0
$973$	2.64765	+	5.79754i	0.0848797	+	0.185861i
$974$	8.85391	+	10.2180i	0.283697	+	0.327404i
$975$		0			0
$976$	−5.01092	+	10.9724i	−0.160396	+	0.351217i
$977$	−30.4209	+	8.93237i	−0.973249	+	0.285772i	−0.729435	−	0.684050i	$-0.760217\pi$
$977$	−30.4209	+	8.93237i	−0.973249	+	0.285772i	−0.243814	+	0.969822i	$0.578399\pi$
$978$		0			0
$979$	−10.6449	+	23.3090i	−0.340211	+	0.744959i
$980$	−0.449436	−	3.12589i	−0.0143567	−	0.0998530i
$981$		0			0
$982$	−17.0099	−	37.2465i	−0.542808	−	1.18858i
$983$	−21.8073	+	14.0147i	−0.695543	+	0.446999i	−0.840053	−	0.542505i	$-0.817476\pi$
$983$	−21.8073	+	14.0147i	−0.695543	+	0.446999i	0.144509	+	0.989503i	$0.453840\pi$
$984$		0			0
$985$	5.95875	+	3.82946i	0.189862	+	0.122017i
$986$	−3.85105	+	4.44434i	−0.122642	+	0.141537i
$987$		0			0
$988$	−3.93303			−0.125127
$989$	11.7474	−	40.5729i	0.373547	−	1.29014i
$990$		0			0
$991$	37.8199	+	11.1049i	1.20139	+	0.352760i	0.820384	−	0.571813i	$-0.193760\pi$
$991$	37.8199	+	11.1049i	1.20139	+	0.352760i	0.381006	+	0.924573i	$0.375578\pi$
$992$	−1.61291	+	1.86139i	−0.0512098	+	0.0590992i
$993$		0			0
$994$	0.758000	−	5.27200i	0.0240423	−	0.167218i
$995$	4.51262	−	2.90009i	0.143060	−	0.0919389i
$996$		0			0
$997$	19.4890	+	22.4915i	0.617223	+	0.712314i	0.975177	−	0.221426i	$-0.0710710\pi$
$997$	19.4890	+	22.4915i	0.617223	+	0.712314i	−0.357954	+	0.933739i	$0.616526\pi$
$998$	−3.04459	−	21.1756i	−0.0963747	−	0.670301i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.a.271.1		10
3.2	odd	2		138.2.e.d.133.1	yes	10
23.3	even	11		9522.2.a.bx.1.3		5
23.9	even	11	inner	414.2.i.a.55.1		10
23.20	odd	22		9522.2.a.by.1.3		5
69.20	even	22		3174.2.a.w.1.3		5
69.26	odd	22		3174.2.a.x.1.3		5
69.32	odd	22		138.2.e.d.55.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.d.55.1	✓	10	69.32	odd	22
138.2.e.d.133.1	yes	10	3.2	odd	2
414.2.i.a.55.1		10	23.9	even	11	inner
414.2.i.a.271.1		10	1.1	even	1	trivial
3174.2.a.w.1.3		5	69.20	even	22
3174.2.a.x.1.3		5	69.26	odd	22
9522.2.a.bx.1.3		5	23.3	even	11
9522.2.a.by.1.3		5	23.20	odd	22

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)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(0.0651865 - 0.453382i) q^{5} +(-0.134858 - 0.295298i) q^{7} +(-0.654861 - 0.755750i) q^{8} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(0.0651865 - 0.453382i) q^{5} +(-0.134858 - 0.295298i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.190279 + 0.416652i) q^{10} +(2.38745 - 0.701020i) q^{11} +(0.564582 - 1.23626i) q^{13} +(0.0462003 + 0.321330i) q^{14} +(0.415415 + 0.909632i) q^{16} +(2.26811 - 1.45762i) q^{17} +(-2.43450 - 1.56456i) q^{19} +(0.299955 - 0.346167i) q^{20} -2.48825 q^{22} +(4.35491 - 2.00868i) q^{23} +(4.59616 + 1.34955i) q^{25} +(-0.890008 + 1.02712i) q^{26} +(0.0462003 - 0.321330i) q^{28} +(1.83493 - 1.17924i) q^{29} +(-1.61291 - 1.86139i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-2.58689 + 0.759581i) q^{34} +(-0.142674 + 0.0418928i) q^{35} +(-0.0683786 - 0.475583i) q^{37} +(1.89510 + 2.18706i) q^{38} +(-0.385331 + 0.247638i) q^{40} +(0.120602 - 0.838807i) q^{41} +(5.76770 - 6.65628i) q^{43} +(2.38745 + 0.701020i) q^{44} +(-4.74441 + 0.700397i) q^{46} +2.71406 q^{47} +(4.51501 - 5.21060i) q^{49} +(-4.02977 - 2.58978i) q^{50} +(1.14333 - 0.734774i) q^{52} +(-3.62496 - 7.93756i) q^{53} +(-0.162200 - 1.12813i) q^{55} +(-0.134858 + 0.295298i) q^{56} +(-2.09283 + 0.614511i) q^{58} +(-4.52108 + 9.89978i) q^{59} +(7.89921 + 9.11618i) q^{61} +(1.02316 + 2.24040i) q^{62} +(-0.142315 + 0.989821i) q^{64} +(-0.523697 - 0.336559i) q^{65} +(-10.1378 - 2.97673i) q^{67} +2.69611 q^{68} +0.148697 q^{70} +(-15.7422 - 4.62233i) q^{71} +(9.89520 + 6.35926i) q^{73} +(-0.0683786 + 0.475583i) q^{74} +(-1.20217 - 2.63238i) q^{76} +(-0.528978 - 0.610473i) q^{77} +(-4.45637 + 9.75808i) q^{79} +(0.439490 - 0.129046i) q^{80} +(-0.352036 + 0.770851i) q^{82} +(1.15039 + 8.00114i) q^{83} +(-0.513011 - 1.12334i) q^{85} +(-7.40935 + 4.76170i) q^{86} +(-2.09325 - 1.34525i) q^{88} +(-6.74394 + 7.78292i) q^{89} -0.441205 q^{91} +(4.74955 + 0.664630i) q^{92} +(-2.60412 - 0.764638i) q^{94} +(-0.868039 + 1.00177i) q^{95} +(0.0319166 - 0.221985i) q^{97} +(-5.80012 + 3.72751i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8	\( 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8} - 13 q^{10} + 5 q^{11} + 13 q^{13} - 9 q^{14} - q^{16} + 9 q^{20} - 6 q^{22} + 32 q^{23} + q^{25} + 13 q^{26} - 9 q^{28} - 27 q^{29} - 8 q^{31} - q^{32} - 11 q^{34} + 26 q^{35} - 11 q^{37} - 11 q^{38} + 9 q^{40} + 10 q^{41} + 34 q^{43} + 5 q^{44} - q^{46} - 8 q^{47} + 25 q^{49} - 21 q^{50} + 2 q^{52} - 9 q^{53} - 23 q^{55} + 2 q^{56} - 5 q^{58} + 21 q^{59} - 4 q^{61} - 8 q^{62} - q^{64} - 29 q^{65} - 32 q^{67} - 22 q^{68} - 18 q^{70} - 22 q^{71} + 43 q^{73} - 11 q^{74} - 10 q^{77} - 16 q^{79} - 2 q^{80} + 32 q^{82} + 3 q^{83} + 33 q^{85} - 32 q^{86} - 6 q^{88} + 11 q^{89} - 70 q^{91} + 21 q^{92} + 3 q^{94} + 39 q^{97} + 14 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8 - 13 * q^10 + 5 * q^11 + 13 * q^13 - 9 * q^14 - q^16 + 9 * q^20 - 6 * q^22 + 32 * q^23 + q^25 + 13 * q^26 - 9 * q^28 - 27 * q^29 - 8 * q^31 - q^32 - 11 * q^34 + 26 * q^35 - 11 * q^37 - 11 * q^38 + 9 * q^40 + 10 * q^41 + 34 * q^43 + 5 * q^44 - q^46 - 8 * q^47 + 25 * q^49 - 21 * q^50 + 2 * q^52 - 9 * q^53 - 23 * q^55 + 2 * q^56 - 5 * q^58 + 21 * q^59 - 4 * q^61 - 8 * q^62 - q^64 - 29 * q^65 - 32 * q^67 - 22 * q^68 - 18 * q^70 - 22 * q^71 + 43 * q^73 - 11 * q^74 - 10 * q^77 - 16 * q^79 - 2 * q^80 + 32 * q^82 + 3 * q^83 + 33 * q^85 - 32 * q^86 - 6 * q^88 + 11 * q^89 - 70 * q^91 + 21 * q^92 + 3 * q^94 + 39 * q^97 + 14 * q^98

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