LMFDB - Embedded newform 414.2.i.d.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.d.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.455922 + 3.17101i) q^{5} +(0.628663 + 1.37658i) q^{7} +(0.654861 + 0.755750i) q^{8} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.455922 + 3.17101i) q^{5} +(0.628663 + 1.37658i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-1.33083 + 2.91411i) q^{10} +(-6.27358 + 1.84209i) q^{11} +(1.19894 - 2.62531i) q^{13} +(0.215370 + 1.49793i) q^{14} +(0.415415 + 0.909632i) q^{16} +(1.00654 - 0.646863i) q^{17} +(0.467362 + 0.300355i) q^{19} +(-2.09792 + 2.42113i) q^{20} -6.53843 q^{22} +(4.66752 + 1.10192i) q^{23} +(-5.04996 - 1.48280i) q^{25} +(1.89001 - 2.18119i) q^{26} +(-0.215370 + 1.49793i) q^{28} +(7.29298 - 4.68691i) q^{29} +(4.41087 + 5.09042i) q^{31} +(0.142315 + 0.989821i) q^{32} +(1.14801 - 0.337086i) q^{34} +(-4.65177 + 1.36588i) q^{35} +(0.206897 + 1.43900i) q^{37} +(0.363811 + 0.419860i) q^{38} +(-2.69505 + 1.73201i) q^{40} +(-0.262991 + 1.82915i) q^{41} +(-1.42353 + 1.64284i) q^{43} +(-6.27358 - 1.84209i) q^{44} +(4.16801 + 2.37227i) q^{46} +11.4135 q^{47} +(3.08427 - 3.55944i) q^{49} +(-4.42765 - 2.84548i) q^{50} +(2.42796 - 1.56036i) q^{52} +(-5.01045 - 10.9714i) q^{53} +(-2.98101 - 20.7334i) q^{55} +(-0.628663 + 1.37658i) q^{56} +(8.31801 - 2.44239i) q^{58} +(-1.64562 + 3.60341i) q^{59} +(-5.91634 - 6.82782i) q^{61} +(2.79806 + 6.12691i) q^{62} +(-0.142315 + 0.989821i) q^{64} +(7.77825 + 4.99878i) q^{65} +(7.35733 + 2.16031i) q^{67} +1.19647 q^{68} -4.84815 q^{70} +(-9.07303 - 2.66408i) q^{71} +(-0.527969 - 0.339305i) q^{73} +(-0.206897 + 1.43900i) q^{74} +(0.230786 + 0.505350i) q^{76} +(-6.47975 - 7.47803i) q^{77} +(-5.72115 + 12.5276i) q^{79} +(-3.07385 + 0.902563i) q^{80} +(-0.767668 + 1.68096i) q^{82} +(-2.21852 - 15.4302i) q^{83} +(1.59230 + 3.48666i) q^{85} +(-1.82871 + 1.17524i) q^{86} +(-5.50048 - 3.53494i) q^{88} +(-3.67930 + 4.24613i) q^{89} +4.36768 q^{91} +(3.33083 + 3.45045i) q^{92} +(10.9512 + 3.21556i) q^{94} +(-1.16551 + 1.34507i) q^{95} +(1.03139 - 7.17350i) q^{97} +(3.96215 - 2.54632i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

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

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
$5$	−0.455922	+	3.17101i	−0.203895	+	1.41812i	0.588692	+	0.808358i	$0.299643\pi$
$5$	−0.455922	+	3.17101i	−0.203895	+	1.41812i	−0.792586	+	0.609760i	$0.791266\pi$
$6$		0			0
$7$	0.628663	+	1.37658i	0.237612	+	0.520298i	0.990444	−	0.137915i	$-0.0440399\pi$
$7$	0.628663	+	1.37658i	0.237612	+	0.520298i	−0.752832	+	0.658213i	$0.771313\pi$
$8$	0.654861	+	0.755750i	0.231528	+	0.267198i
$9$		0			0
$10$	−1.33083	+	2.91411i	−0.420845	+	0.921523i
$11$	−6.27358	+	1.84209i	−1.89155	+	0.555411i	−0.898311	+	0.439360i	$0.855205\pi$
$11$	−6.27358	+	1.84209i	−1.89155	+	0.555411i	−0.993243	+	0.116051i	$0.962976\pi$
$12$		0			0
$13$	1.19894	−	2.62531i	0.332526	−	0.728130i	−0.667336	−	0.744757i	$-0.732565\pi$
$13$	1.19894	−	2.62531i	0.332526	−	0.728130i	0.999862	+	0.0166269i	$0.00529276\pi$
$14$	0.215370	+	1.49793i	0.0575601	+	0.400340i
$15$		0			0
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	1.00654	−	0.646863i	0.244121	−	0.156887i	−0.412859	−	0.910795i	$-0.635470\pi$
$17$	1.00654	−	0.646863i	0.244121	−	0.156887i	0.656980	+	0.753908i	$0.271833\pi$
$18$		0			0
$19$	0.467362	+	0.300355i	0.107220	+	0.0689062i	0.593152	−	0.805090i	$-0.297883\pi$
$19$	0.467362	+	0.300355i	0.107220	+	0.0689062i	−0.485932	+	0.873997i	$0.661520\pi$
$20$	−2.09792	+	2.42113i	−0.469110	+	0.541381i
$21$		0			0
$22$	−6.53843			−1.39400
$23$	4.66752	+	1.10192i	0.973246	+	0.229765i
$23$	4.66752	+	1.10192i	0.973246	+	0.229765i
$24$		0			0
$25$	−5.04996	−	1.48280i	−1.00999	−	0.296560i
$26$	1.89001	−	2.18119i	0.370661	−	0.427766i
$27$		0			0
$28$	−0.215370	+	1.49793i	−0.0407012	+	0.283083i
$29$	7.29298	−	4.68691i	1.35427	−	0.870337i	0.356323	−	0.934363i	$-0.384030\pi$
$29$	7.29298	−	4.68691i	1.35427	−	0.870337i	0.997948	+	0.0640253i	$0.0203938\pi$
$30$		0			0
$31$	4.41087	+	5.09042i	0.792216	+	0.914266i	0.997928	−	0.0643467i	$-0.0204963\pi$
$31$	4.41087	+	5.09042i	0.792216	+	0.914266i	−0.205712	+	0.978613i	$0.565951\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$		0			0
$34$	1.14801	−	0.337086i	0.196882	−	0.0578097i
$35$	−4.65177	+	1.36588i	−0.786292	+	0.230876i
$36$		0			0
$37$	0.206897	+	1.43900i	0.0340137	+	0.236570i	0.999735	−	0.0230098i	$-0.00732488\pi$
$37$	0.206897	+	1.43900i	0.0340137	+	0.236570i	−0.965722	+	0.259580i	$0.916416\pi$
$38$	0.363811	+	0.419860i	0.0590179	+	0.0681103i
$39$		0			0
$40$	−2.69505	+	1.73201i	−0.426125	+	0.273854i
$41$	−0.262991	+	1.82915i	−0.0410724	+	0.285665i	0.958926	+	0.283658i	$0.0915479\pi$
$41$	−0.262991	+	1.82915i	−0.0410724	+	0.285665i	−0.999998	+	0.00200695i	$0.999361\pi$
$42$		0			0
$43$	−1.42353	+	1.64284i	−0.217086	+	0.250531i	−0.853839	−	0.520537i	$-0.825732\pi$
$43$	−1.42353	+	1.64284i	−0.217086	+	0.250531i	0.636753	+	0.771068i	$0.280277\pi$
$44$	−6.27358	−	1.84209i	−0.945777	−	0.277705i
$45$		0			0
$46$	4.16801	+	2.37227i	0.614540	+	0.349773i
$47$	11.4135			1.66483			0.832416	−	0.554152i	$-0.186957\pi$
$47$	11.4135			1.66483			0.832416	+	0.554152i	$0.186957\pi$
$48$		0			0
$49$	3.08427	−	3.55944i	0.440610	−	0.508491i
$50$	−4.42765	−	2.84548i	−0.626164	−	0.402411i
$51$		0			0
$52$	2.42796	−	1.56036i	0.336698	−	0.216382i
$53$	−5.01045	−	10.9714i	−0.688238	−	1.50703i	−0.853672	−	0.520811i	$-0.825630\pi$
$53$	−5.01045	−	10.9714i	−0.688238	−	1.50703i	0.165434	−	0.986221i	$-0.447098\pi$
$54$		0			0
$55$	−2.98101	−	20.7334i	−0.401960	−	2.79569i
$56$	−0.628663	+	1.37658i	−0.0840086	+	0.183953i
$57$		0			0
$58$	8.31801	−	2.44239i	1.09221	−	0.320701i
$59$	−1.64562	+	3.60341i	−0.214242	+	0.469125i	−0.985990	−	0.166804i	$-0.946655\pi$
$59$	−1.64562	+	3.60341i	−0.214242	+	0.469125i	0.771748	+	0.635928i	$0.219383\pi$
$60$		0			0
$61$	−5.91634	−	6.82782i	−0.757510	−	0.874213i	0.237764	−	0.971323i	$-0.423586\pi$
$61$	−5.91634	−	6.82782i	−0.757510	−	0.874213i	−0.995274	+	0.0971102i	$0.969040\pi$
$62$	2.79806	+	6.12691i	0.355355	+	0.778118i
$63$		0			0
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	7.77825	+	4.99878i	0.964774	+	0.620022i
$66$		0			0
$67$	7.35733	+	2.16031i	0.898841	+	0.263924i	0.698337	−	0.715769i	$-0.253924\pi$
$67$	7.35733	+	2.16031i	0.898841	+	0.263924i	0.200504	+	0.979693i	$0.435742\pi$
$68$	1.19647			0.145094
$69$		0			0
$70$	−4.84815			−0.579465
$71$	−9.07303	−	2.66408i	−1.07677	−	0.316168i	−0.305184	−	0.952293i	$-0.598718\pi$
$71$	−9.07303	−	2.66408i	−1.07677	−	0.316168i	−0.771586	+	0.636125i	$0.780536\pi$
$72$		0			0
$73$	−0.527969	−	0.339305i	−0.0617941	−	0.0397127i	0.509379	−	0.860542i	$-0.329875\pi$
$73$	−0.527969	−	0.339305i	−0.0617941	−	0.0397127i	−0.571173	+	0.820830i	$0.693512\pi$
$74$	−0.206897	+	1.43900i	−0.0240513	+	0.167281i
$75$		0			0
$76$	0.230786	+	0.505350i	0.0264729	+	0.0579676i
$77$	−6.47975	−	7.47803i	−0.738436	−	0.852200i
$78$		0			0
$79$	−5.72115	+	12.5276i	−0.643680	+	1.40946i	0.253298	+	0.967388i	$0.418485\pi$
$79$	−5.72115	+	12.5276i	−0.643680	+	1.40946i	−0.896978	+	0.442074i	$0.854243\pi$
$80$	−3.07385	+	0.902563i	−0.343667	+	0.100910i
$81$		0			0
$82$	−0.767668	+	1.68096i	−0.0847748	+	0.185631i
$83$	−2.21852	−	15.4302i	−0.243515	−	1.69368i	−0.634209	−	0.773161i	$-0.718674\pi$
$83$	−2.21852	−	15.4302i	−0.243515	−	1.69368i	0.390695	−	0.920520i	$-0.372235\pi$
$84$		0			0
$85$	1.59230	+	3.48666i	0.172710	+	0.378181i
$86$	−1.82871	+	1.17524i	−0.197195	+	0.126729i
$87$		0			0
$88$	−5.50048	−	3.53494i	−0.586353	−	0.376826i
$89$	−3.67930	+	4.24613i	−0.390005	+	0.450089i	−0.916468	−	0.400109i	$-0.868972\pi$
$89$	−3.67930	+	4.24613i	−0.390005	+	0.450089i	0.526463	+	0.850198i	$0.323518\pi$
$90$		0			0
$91$	4.36768			0.457857
$92$	3.33083	+	3.45045i	0.347263	+	0.359734i
$93$		0			0
$94$	10.9512	+	3.21556i	1.12953	+	0.331659i
$95$	−1.16551	+	1.34507i	−0.119579	+	0.138001i
$96$		0			0
$97$	1.03139	−	7.17350i	0.104722	−	0.728359i	−0.868030	−	0.496512i	$-0.834614\pi$
$97$	1.03139	−	7.17350i	0.104722	−	0.728359i	0.972752	−	0.231847i	$-0.0744769\pi$
$98$	3.96215	−	2.54632i	0.400237	−	0.257217i
$99$		0			0
$100$	−3.44663	−	3.97763i	−0.344663	−	0.397763i
$101$	−0.145699	−	1.01336i	−0.0144976	−	0.100833i	0.981288	−	0.192546i	$-0.0616746\pi$
$101$	−0.145699	−	1.01336i	−0.0144976	−	0.100833i	−0.995785	+	0.0917137i	$0.970766\pi$
$102$		0			0
$103$	−4.36497	+	1.28167i	−0.430093	+	0.126287i	−0.489612	−	0.871940i	$-0.662862\pi$
$103$	−4.36497	+	1.28167i	−0.430093	+	0.126287i	0.0595187	+	0.998227i	$0.481043\pi$
$104$	2.76921	−	0.813115i	0.271544	−	0.0797325i
$105$		0			0
$106$	−1.71650	−	11.9385i	−0.166722	−	1.15957i
$107$	−0.394872	−	0.455707i	−0.0381738	−	0.0440549i	0.736342	−	0.676610i	$-0.236552\pi$
$107$	−0.394872	−	0.455707i	−0.0381738	−	0.0440549i	−0.774515	+	0.632555i	$0.782006\pi$
$108$		0			0
$109$	−4.94301	+	3.17668i	−0.473454	+	0.304271i	−0.755521	−	0.655124i	$-0.772616\pi$
$109$	−4.94301	+	3.17668i	−0.473454	+	0.304271i	0.282067	+	0.959395i	$0.408980\pi$
$110$	2.98101	−	20.7334i	0.284229	−	1.97685i
$111$		0			0
$112$	−0.991025	+	1.14370i	−0.0936431	+	0.108070i
$113$	11.8091	+	3.46746i	1.11091	+	0.326191i	0.785177	−	0.619272i	$-0.212572\pi$
$113$	11.8091	+	3.46746i	1.11091	+	0.326191i	0.325729	+	0.945463i	$0.394390\pi$
$114$		0			0
$115$	−5.62221	+	14.2984i	−0.524274	+	1.33333i
$116$	8.66918			0.804913
$117$		0			0
$118$	−2.59416	+	2.99382i	−0.238812	+	0.275604i
$119$	1.52323	+	0.978921i	0.139634	+	0.0897375i
$120$		0			0
$121$	26.7107	−	17.1659i	2.42824	−	1.56054i
$122$	−3.75307	−	8.21807i	−0.339787	−	0.744029i
$123$		0			0
$124$	0.958574	+	6.66703i	0.0860825	+	0.598717i
$125$	0.350212	−	0.766857i	0.0313239	−	0.0685898i
$126$		0			0
$127$	−8.51054	+	2.49892i	−0.755188	+	0.221743i	−0.636594	−	0.771199i	$-0.719657\pi$
$127$	−8.51054	+	2.49892i	−0.755188	+	0.221743i	−0.118595	+	0.992943i	$0.537839\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$		0			0
$130$	6.05486	+	6.98768i	0.531046	+	0.612860i
$131$	−5.20867	−	11.4054i	−0.455083	−	0.996493i	−0.988581	−	0.150692i	$-0.951850\pi$
$131$	−5.20867	−	11.4054i	−0.455083	−	0.996493i	0.533498	−	0.845802i	$-0.320877\pi$
$132$		0			0
$133$	−0.119650	+	0.832183i	−0.0103750	+	0.0721594i
$134$	6.45068	+	4.14560i	0.557254	+	0.358125i
$135$		0			0
$136$	1.14801	+	0.337086i	0.0984409	+	0.0289049i
$137$	13.6483			1.16606			0.583028	−	0.812452i	$-0.301868\pi$
$137$	13.6483			1.16606			0.583028	+	0.812452i	$0.301868\pi$
$138$		0			0
$139$	−11.6537			−0.988455			−0.494227	−	0.869333i	$-0.664549\pi$
$139$	−11.6537			−0.988455			−0.494227	+	0.869333i	$0.664549\pi$
$140$	−4.65177	−	1.36588i	−0.393146	−	0.115438i
$141$		0			0
$142$	−7.95495	−	5.11234i	−0.667565	−	0.429018i
$143$	−2.68558	+	18.6786i	−0.224580	+	1.56199i
$144$		0			0
$145$	11.5372	+	25.2629i	0.958112	+	2.09797i
$146$	−0.410989	−	0.474307i	−0.0340137	−	0.0392539i
$147$		0			0
$148$	−0.603930	+	1.32242i	−0.0496428	+	0.108702i
$149$	16.6025	−	4.87494i	1.36013	−	0.399371i	0.481322	−	0.876544i	$-0.340157\pi$
$149$	16.6025	−	4.87494i	1.36013	−	0.399371i	0.878809	+	0.477173i	$0.158339\pi$
$150$		0			0
$151$	−2.00749	+	4.39579i	−0.163367	+	0.357724i	−0.973557	−	0.228443i	$-0.926637\pi$
$151$	−2.00749	+	4.39579i	−0.163367	+	0.357724i	0.810190	+	0.586167i	$0.199364\pi$
$152$	0.0790636	+	0.549899i	0.00641291	+	0.0446027i
$153$		0			0
$154$	−4.11047	−	9.00067i	−0.331231	−	0.725295i
$155$	−18.1528	+	11.6661i	−1.45807	+	0.937042i
$156$		0			0
$157$	−4.24859	−	2.73040i	−0.339075	−	0.217910i	0.360011	−	0.932948i	$-0.382773\pi$
$157$	−4.24859	−	2.73040i	−0.339075	−	0.217910i	−0.699086	+	0.715038i	$0.746409\pi$
$158$	−9.01883	+	10.4083i	−0.717500	+	0.828039i
$159$		0			0
$160$	−3.20362			−0.253268
$161$	1.41742	+	7.11795i	0.111709	+	0.560973i
$162$		0			0
$163$	−3.42292	−	1.00506i	−0.268104	−	0.0787225i	0.144917	−	0.989444i	$-0.453708\pi$
$163$	−3.42292	−	1.00506i	−0.268104	−	0.0787225i	−0.413021	+	0.910721i	$0.635527\pi$
$164$	−1.21015	+	1.39659i	−0.0944971	+	0.109055i
$165$		0			0
$166$	2.21852	−	15.4302i	0.172191	−	1.19761i
$167$	−3.83643	+	2.46553i	−0.296872	+	0.190788i	−0.680594	−	0.732660i	$-0.738278\pi$
$167$	−3.83643	+	2.46553i	−0.296872	+	0.190788i	0.383722	+	0.923449i	$0.374642\pi$
$168$		0			0
$169$	3.05839	+	3.52957i	0.235261	+	0.271506i
$170$	0.545499	+	3.79403i	0.0418378	+	0.290989i
$171$		0			0
$172$	−2.08574	+	0.612427i	−0.159036	+	0.0466971i
$173$	−14.9808	+	4.39875i	−1.13897	+	0.334431i	−0.796226	−	0.605000i	$-0.793173\pi$
$173$	−14.9808	+	4.39875i	−1.13897	+	0.334431i	−0.342740	+	0.939430i	$0.611355\pi$
$174$		0			0
$175$	−1.13353	−	7.88385i	−0.0856866	−	0.595963i
$176$	−4.28176	−	4.94141i	−0.322750	−	0.372473i
$177$		0			0
$178$	−4.72653	+	3.03756i	−0.354269	+	0.227675i
$179$	0.911557	−	6.34002i	0.0681330	−	0.473875i	−0.926978	−	0.375115i	$-0.877603\pi$
$179$	0.911557	−	6.34002i	0.0681330	−	0.473875i	0.995111	−	0.0987602i	$-0.0314877\pi$
$180$		0			0
$181$	14.4962	−	16.7295i	1.07750	−	1.24350i	0.109112	−	0.994029i	$-0.465199\pi$
$181$	14.4962	−	16.7295i	1.07750	−	1.24350i	0.968383	−	0.249467i	$-0.0802554\pi$
$182$	4.19075	+	1.23052i	0.310639	+	0.0912120i
$183$		0			0
$184$	2.22381	+	4.24908i	0.163941	+	0.313246i
$185$	−4.65742			−0.342420
$186$		0			0
$187$	−5.12301	+	5.91227i	−0.374632	+	0.432348i
$188$	9.60165	+	6.17061i	0.700273	+	0.450038i
$189$		0			0
$190$	−1.49725	+	0.962223i	−0.108622	+	0.0698070i
$191$	0.892788	+	1.95493i	0.0645999	+	0.141454i	0.939178	−	0.343430i	$-0.111589\pi$
$191$	0.892788	+	1.95493i	0.0645999	+	0.141454i	−0.874578	+	0.484884i	$0.838862\pi$
$192$		0			0
$193$	1.60048	+	11.1316i	0.115205	+	0.801267i	0.962721	+	0.270497i	$0.0871880\pi$
$193$	1.60048	+	11.1316i	0.115205	+	0.801267i	−0.847516	+	0.530770i	$0.821903\pi$
$194$	3.01062	−	6.59235i	0.216150	−	0.473303i
$195$		0			0
$196$	4.51903	−	1.32691i	0.322788	−	0.0947791i
$197$	−4.32551	+	9.47155i	−0.308180	+	0.674820i	−0.998830	−	0.0483697i	$-0.984597\pi$
$197$	−4.32551	+	9.47155i	−0.308180	+	0.674820i	0.690650	+	0.723190i	$0.257325\pi$
$198$		0			0
$199$	−9.88825	−	11.4117i	−0.700960	−	0.808950i	0.287922	−	0.957654i	$-0.407036\pi$
$199$	−9.88825	−	11.4117i	−0.700960	−	0.808950i	−0.988882	+	0.148703i	$0.952490\pi$
$200$	−2.18639	−	4.78753i	−0.154601	−	0.338530i
$201$		0			0
$202$	0.145699	−	1.01336i	0.0102513	−	0.0712995i
$203$	11.0367	+	7.09288i	0.774627	+	0.497822i
$204$		0			0
$205$	−5.68033	−	1.66790i	−0.396732	−	0.116491i
$206$	−4.54925			−0.316961
$207$		0			0
$208$	2.88612			0.200117
$209$	−3.48531	−	1.02338i	−0.241084	−	0.0707887i
$210$		0			0
$211$	9.65999	+	6.20810i	0.665021	+	0.427383i	0.829127	−	0.559060i	$-0.188838\pi$
$211$	9.65999	+	6.20810i	0.665021	+	0.427383i	−0.164107	+	0.986443i	$0.552474\pi$
$212$	1.71650	−	11.9385i	0.117890	−	0.819943i
$213$		0			0
$214$	−0.250490	−	0.548496i	−0.0171231	−	0.0374944i
$215$	−4.56044	−	5.26303i	−0.311019	−	0.358936i
$216$		0			0
$217$	−4.23441	+	9.27207i	−0.287451	+	0.629429i
$218$	−5.63776	+	1.65539i	−0.381837	+	0.112117i
$219$		0			0
$220$	8.70154	−	19.0537i	0.586658	−	1.28460i
$221$	−0.491437	−	3.41802i	−0.0330577	−	0.229921i
$222$		0			0
$223$	−6.56619	−	14.3779i	−0.439704	−	0.962818i	−0.991652	−	0.128940i	$-0.958843\pi$
$223$	−6.56619	−	14.3779i	−0.439704	−	0.962818i	0.551948	−	0.833879i	$-0.313885\pi$
$224$	−1.27310	+	0.818172i	−0.0850626	+	0.0546664i
$225$		0			0
$226$	10.3538	+	6.65401i	0.688727	+	0.442618i
$227$	−1.69916	+	1.96094i	−0.112777	+	0.130152i	−0.809331	−	0.587352i	$-0.800170\pi$
$227$	−1.69916	+	1.96094i	−0.112777	+	0.130152i	0.696554	+	0.717504i	$0.254716\pi$
$228$		0			0
$229$	9.99374			0.660405			0.330202	−	0.943910i	$-0.392883\pi$
$229$	9.99374			0.660405			0.330202	+	0.943910i	$0.392883\pi$
$230$	−9.42279	+	12.1352i	−0.621320	+	0.800173i
$231$		0			0
$232$	8.31801	+	2.44239i	0.546104	+	0.160351i
$233$	−17.8743	+	20.6280i	−1.17098	+	1.35139i	−0.246971	+	0.969023i	$0.579435\pi$
$233$	−17.8743	+	20.6280i	−1.17098	+	1.35139i	−0.924012	+	0.382363i	$0.875110\pi$
$234$		0			0
$235$	−5.20367	+	36.1923i	−0.339450	+	2.36093i
$236$	−3.33254	+	2.14169i	−0.216930	+	0.139412i
$237$		0			0
$238$	1.18574	+	1.36841i	0.0768598	+	0.0887010i
$239$	2.03776	+	14.1729i	0.131812	+	0.916771i	0.943191	+	0.332251i	$0.107808\pi$
$239$	2.03776	+	14.1729i	0.131812	+	0.916771i	−0.811379	+	0.584520i	$0.801283\pi$
$240$		0			0
$241$	−13.6207	+	3.99940i	−0.877387	+	0.257624i	−0.689254	−	0.724520i	$-0.742062\pi$
$241$	−13.6207	+	3.99940i	−0.877387	+	0.257624i	−0.188133	+	0.982144i	$0.560244\pi$
$242$	30.4649	−	8.94531i	1.95836	−	0.575026i
$243$		0			0
$244$	−1.28574	−	8.94254i	−0.0823113	−	0.572488i
$245$	9.88082	+	11.4031i	0.631262	+	0.728515i
$246$		0			0
$247$	1.34886	−	0.866862i	0.0858262	−	0.0551571i
$248$	−0.958574	+	6.66703i	−0.0608695	+	0.423357i
$249$		0			0
$250$	0.552075	−	0.637128i	0.0349163	−	0.0402955i
$251$	11.4799	+	3.37080i	0.724604	+	0.212763i	0.623178	−	0.782080i	$-0.285841\pi$
$251$	11.4799	+	3.37080i	0.724604	+	0.212763i	0.101426	+	0.994843i	$0.467659\pi$
$252$		0			0
$253$	−31.3119	+	1.68503i	−1.96856	+	0.105937i
$254$	−8.86983			−0.556543
$255$		0			0
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−21.8698	−	14.0549i	−1.36420	−	0.876720i	−0.365663	−	0.930747i	$-0.619158\pi$
$257$	−21.8698	−	14.0549i	−1.36420	−	0.876720i	−0.998539	+	0.0540274i	$0.982794\pi$
$258$		0			0
$259$	−1.85083	+	1.18946i	−0.115005	+	0.0739093i
$260$	3.84094	+	8.41048i	0.238205	+	0.521596i
$261$		0			0
$262$	−1.78441	−	12.4108i	−0.110241	−	0.766744i
$263$	−2.38558	+	5.22370i	−0.147101	+	0.322107i	−0.968812	−	0.247798i	$-0.920293\pi$
$263$	−2.38558	+	5.22370i	−0.147101	+	0.322107i	0.821710	+	0.569906i	$0.193020\pi$
$264$		0			0
$265$	37.0746	−	10.8861i	2.27748	−	0.668727i
$266$	−0.349256	+	0.764765i	−0.0214143	+	0.0468907i
$267$		0			0
$268$	5.02143	+	5.79504i	0.306733	+	0.353988i
$269$	−3.39779	−	7.44012i	−0.207167	−	0.453632i	0.777317	−	0.629110i	$-0.216580\pi$
$269$	−3.39779	−	7.44012i	−0.207167	−	0.453632i	−0.984483	+	0.175477i	$0.943853\pi$
$270$		0			0
$271$	1.92200	−	13.3678i	0.116753	−	0.812036i	−0.844339	−	0.535809i	$-0.820007\pi$
$271$	1.92200	−	13.3678i	0.116753	−	0.812036i	0.961092	−	0.276227i	$-0.0890841\pi$
$272$	1.00654	+	0.646863i	0.0610303	+	0.0392218i
$273$		0			0
$274$	13.0955	+	3.84518i	0.791127	+	0.232296i
$275$	34.4128			2.07517
$276$		0			0
$277$	14.9697			0.899440			0.449720	−	0.893169i	$-0.351524\pi$
$277$	14.9697			0.899440			0.449720	+	0.893169i	$0.351524\pi$
$278$	−11.1817	−	3.28323i	−0.670631	−	0.196915i
$279$		0			0
$280$	−4.07852	−	2.62111i	−0.243738	−	0.156641i
$281$	3.83880	−	26.6994i	0.229003	−	1.59275i	−0.473317	−	0.880892i	$-0.656944\pi$
$281$	3.83880	−	26.6994i	0.229003	−	1.59275i	0.702320	−	0.711861i	$-0.252147\pi$
$282$		0			0
$283$	5.69920	+	12.4795i	0.338783	+	0.741830i	0.999965	−	0.00839502i	$-0.00267225\pi$
$283$	5.69920	+	12.4795i	0.338783	+	0.741830i	−0.661182	+	0.750225i	$0.729945\pi$
$284$	−6.19241	−	7.14642i	−0.367452	−	0.424062i
$285$		0			0
$286$	−7.83918	+	17.1654i	−0.463540	+	1.01501i
$287$	−2.68330	+	0.787887i	−0.158390	+	0.0465075i
$288$		0			0
$289$	−6.46737	+	14.1616i	−0.380433	+	0.833033i
$290$	3.95247	+	27.4900i	0.232097	+	1.61427i
$291$		0			0
$292$	−0.260714	−	0.570883i	−0.0152571	−	0.0334084i
$293$	−7.74373	+	4.97659i	−0.452393	+	0.290736i	−0.746928	−	0.664905i	$-0.768472\pi$
$293$	−7.74373	+	4.97659i	−0.452393	+	0.290736i	0.294534	+	0.955641i	$0.404835\pi$
$294$		0			0
$295$	−10.6762	−	6.86116i	−0.621591	−	0.399472i
$296$	−0.952036	+	1.09871i	−0.0553360	+	0.0638611i
$297$		0			0
$298$	17.3034			1.00236
$299$	8.48895	−	10.9326i	0.490928	−	0.632247i
$300$		0			0
$301$	−3.15642	−	0.926809i	−0.181933	−	0.0534204i
$302$	−3.16461	+	3.65215i	−0.182103	+	0.210158i
$303$		0			0
$304$	−0.0790636	+	0.549899i	−0.00453461	+	0.0315389i
$305$	24.3485	−	15.6478i	1.39419	−	0.895991i
$306$		0			0
$307$	−1.15044	−	1.32767i	−0.0656588	−	0.0757743i	0.721970	−	0.691924i	$-0.243237\pi$
$307$	−1.15044	−	1.32767i	−0.0656588	−	0.0757743i	−0.787629	+	0.616150i	$0.788691\pi$
$308$	−1.40818	−	9.79413i	−0.0802387	−	0.558072i
$309$		0			0
$310$	−20.7042	+	6.07929i	−1.17592	+	0.345281i
$311$	29.1330	−	8.55421i	1.65198	−	0.485065i	0.682632	−	0.730762i	$-0.260835\pi$
$311$	29.1330	−	8.55421i	1.65198	−	0.485065i	0.969347	+	0.245697i	$0.0790168\pi$
$312$		0			0
$313$	−1.56820	−	10.9071i	−0.0886398	−	0.616503i	−0.984919	−	0.173014i	$-0.944649\pi$
$313$	−1.56820	−	10.9071i	−0.0886398	−	0.616503i	0.896280	−	0.443489i	$-0.146260\pi$
$314$	−3.30725	−	3.81677i	−0.186639	−	0.215393i
$315$		0			0
$316$	−11.5859	+	7.44578i	−0.651756	+	0.418858i
$317$	−1.44409	+	10.0439i	−0.0811081	+	0.564119i	0.908229	+	0.418474i	$0.137435\pi$
$317$	−1.44409	+	10.0439i	−0.0811081	+	0.564119i	−0.989337	+	0.145645i	$0.953474\pi$
$318$		0			0
$319$	−37.1193	+	42.8380i	−2.07828	+	2.39847i
$320$	−3.07385	−	0.902563i	−0.171833	−	0.0504548i
$321$		0			0
$322$	−0.645351	+	7.22896i	−0.0359640	+	0.402854i
$323$	0.664706			0.0369852
$324$		0			0
$325$	−9.94740	+	11.4799i	−0.551783	+	0.636791i
$326$	−3.00111	−	1.92870i	−0.166216	−	0.106821i
$327$		0			0
$328$	−1.55460	+	0.999080i	−0.0858384	+	0.0551650i
$329$	7.17525	+	15.7116i	0.395584	+	0.866209i
$330$		0			0
$331$	−4.23799	−	29.4759i	−0.232941	−	1.62014i	−0.685270	−	0.728289i	$-0.740316\pi$
$331$	−4.23799	−	29.4759i	−0.232941	−	1.62014i	0.452329	−	0.891851i	$-0.350593\pi$
$332$	6.47584	−	14.1801i	0.355408	−	0.778235i
$333$		0			0
$334$	−4.37565	+	1.28481i	−0.239425	+	0.0703015i
$335$	−10.2047	+	22.3452i	−0.557544	+	1.22085i
$336$		0			0
$337$	12.4809	+	14.4037i	0.679876	+	0.784619i	0.985888	−	0.167409i	$-0.0535400\pi$
$337$	12.4809	+	14.4037i	0.679876	+	0.784619i	−0.306011	+	0.952028i	$0.598995\pi$
$338$	1.94011	+	4.24825i	0.105528	+	0.231074i
$339$		0			0
$340$	−0.545499	+	3.79403i	−0.0295838	+	0.205760i
$341$	−37.0489	−	23.8099i	−2.00631	−	1.28938i
$342$		0			0
$343$	17.0031	+	4.99255i	0.918080	+	0.269572i
$344$	−2.17379			−0.117203
$345$		0			0
$346$	−15.6132			−0.839371
$347$	−11.6990	−	3.43514i	−0.628036	−	0.184408i	−0.0478007	−	0.998857i	$-0.515221\pi$
$347$	−11.6990	−	3.43514i	−0.628036	−	0.184408i	−0.580235	+	0.814449i	$0.697039\pi$
$348$		0			0
$349$	−12.9571	−	8.32704i	−0.693579	−	0.445736i	0.145778	−	0.989317i	$-0.453432\pi$
$349$	−12.9571	−	8.32704i	−0.693579	−	0.445736i	−0.839357	+	0.543581i	$0.817068\pi$
$350$	1.13353	−	7.88385i	0.0605896	−	0.421410i
$351$		0			0
$352$	−2.71616	−	5.94756i	−0.144772	−	0.317006i
$353$	12.1351	+	14.0046i	0.645886	+	0.745392i	0.980404	−	0.196997i	$-0.0631191\pi$
$353$	12.1351	+	14.0046i	0.645886	+	0.745392i	−0.334518	+	0.942389i	$0.608574\pi$
$354$		0			0
$355$	12.5844	−	27.5560i	0.667912	−	1.46252i
$356$	−5.39085	+	1.58290i	−0.285715	+	0.0838934i
$357$		0			0
$358$	2.66082	−	5.82639i	0.140629	−	0.307934i
$359$	−1.67363	−	11.6404i	−0.0883310	−	0.614356i	−0.985116	−	0.171890i	$-0.945013\pi$
$359$	−1.67363	−	11.6404i	−0.0883310	−	0.614356i	0.896785	−	0.442466i	$-0.145896\pi$
$360$		0			0
$361$	−7.76467	−	17.0023i	−0.408667	−	0.894856i
$362$	18.6223	−	11.9678i	0.978765	−	0.629014i
$363$		0			0
$364$	3.67432	+	2.36134i	0.192587	+	0.123768i
$365$	1.31665	−	1.51950i	0.0689167	−	0.0795341i
$366$		0			0
$367$	−7.81907			−0.408152			−0.204076	−	0.978955i	$-0.565419\pi$
$367$	−7.81907			−0.408152			−0.204076	+	0.978955i	$0.565419\pi$
$368$	0.936621	+	4.70348i	0.0488247	+	0.245186i
$369$		0			0
$370$	−4.46876	−	1.31215i	−0.232320	−	0.0682152i
$371$	11.9531	−	13.7946i	0.620572	−	0.716179i
$372$		0			0
$373$	−0.304293	+	2.11640i	−0.0157557	+	0.109583i	−0.996182	−	0.0873051i	$-0.972175\pi$
$373$	−0.304293	+	2.11640i	−0.0157557	+	0.109583i	0.980426	+	0.196888i	$0.0630836\pi$
$374$	−6.58118	+	4.22946i	−0.340304	+	0.218700i
$375$		0			0
$376$	7.47426	+	8.62575i	0.385455	+	0.444839i
$377$	−3.56076	−	24.7656i	−0.183389	−	1.27550i
$378$		0			0
$379$	20.7946	−	6.10585i	1.06815	−	0.313636i	0.300019	−	0.953933i	$-0.403007\pi$
$379$	20.7946	−	6.10585i	1.06815	−	0.313636i	0.768128	+	0.640297i	$0.221189\pi$
$380$	−1.70769	+	0.501423i	−0.0876026	+	0.0257224i
$381$		0			0
$382$	0.305856	+	2.12727i	0.0156489	+	0.108841i
$383$	3.28069	+	3.78612i	0.167635	+	0.193462i	0.833351	−	0.552744i	$-0.186419\pi$
$383$	3.28069	+	3.78612i	0.167635	+	0.193462i	−0.665716	+	0.746205i	$0.731874\pi$
$384$		0			0
$385$	26.6671	−	17.1379i	1.35908	−	0.873430i
$386$	−1.60048	+	11.1316i	−0.0814620	+	0.566581i
$387$		0			0
$388$	4.74595	−	5.47712i	0.240939	−	0.278059i
$389$	−5.77784	−	1.69653i	−0.292948	−	0.0860174i	0.131956	−	0.991256i	$-0.457874\pi$
$389$	−5.77784	−	1.69653i	−0.292948	−	0.0860174i	−0.424905	+	0.905238i	$0.639692\pi$
$390$		0			0
$391$	5.41083	−	1.91013i	0.273637	−	0.0965992i
$392$	4.70981			0.237881
$393$		0			0
$394$	−6.81874	+	7.86925i	−0.343523	+	0.396447i
$395$	−37.1166	−	23.8534i	−1.86754	−	1.20020i
$396$		0			0
$397$	20.1916	−	12.9763i	1.01339	−	0.651263i	0.0751183	−	0.997175i	$-0.476067\pi$
$397$	20.1916	−	12.9763i	1.01339	−	0.651263i	0.938267	+	0.345911i	$0.112430\pi$
$398$	−6.27267	−	13.7352i	−0.314421	−	0.688485i
$399$		0			0
$400$	−0.749025	−	5.20958i	−0.0374512	−	0.260479i
$401$	6.01379	−	13.1684i	0.300314	−	0.657596i	−0.697972	−	0.716125i	$-0.745914\pi$
$401$	6.01379	−	13.1684i	0.300314	−	0.657596i	0.998286	+	0.0585293i	$0.0186411\pi$
$402$		0			0
$403$	18.6523	−	5.47681i	0.929137	−	0.272819i
$404$	0.425292	−	0.931260i	0.0211591	−	0.0463319i
$405$		0			0
$406$	8.59137	+	9.91497i	0.426383	+	0.492072i
$407$	−3.94875	−	8.64657i	−0.195733	−	0.428594i
$408$		0			0
$409$	4.64566	−	32.3112i	0.229713	−	1.59769i	−0.469604	−	0.882877i	$-0.655603\pi$
$409$	4.64566	−	32.3112i	0.229713	−	1.59769i	0.699317	−	0.714811i	$-0.253487\pi$
$410$	−4.98034	−	3.20067i	−0.245961	−	0.158070i
$411$		0			0
$412$	−4.36497	−	1.28167i	−0.215047	−	0.0631434i
$413$	−5.99493			−0.294991
$414$		0			0
$415$	49.9407			2.45149
$416$	2.76921	+	0.813115i	0.135772	+	0.0398662i
$417$		0			0
$418$	−3.05581	−	1.96385i	−0.149465	−	0.0960551i
$419$	−5.15788	+	35.8738i	−0.251979	+	1.75255i	0.334324	+	0.942458i	$0.391492\pi$
$419$	−5.15788	+	35.8738i	−0.251979	+	1.75255i	−0.586302	+	0.810092i	$0.699417\pi$
$420$		0			0
$421$	2.90196	+	6.35441i	0.141433	+	0.309695i	0.967072	−	0.254504i	$-0.0819123\pi$
$421$	2.90196	+	6.35441i	0.141433	+	0.309695i	−0.825639	+	0.564199i	$0.809185\pi$
$422$	7.51967	+	8.67816i	0.366052	+	0.422446i
$423$		0			0
$424$	5.01045	−	10.9714i	0.243329	−	0.532816i
$425$	−6.04214	+	1.77413i	−0.293087	+	0.0860581i
$426$		0			0
$427$	5.67966	−	12.4367i	0.274858	−	0.601855i
$428$	−0.0858140	−	0.596849i	−0.00414798	−	0.0288498i
$429$		0			0
$430$	−2.89294	−	6.33466i	−0.139510	−	0.305485i
$431$	28.0183	−	18.0063i	1.34959	−	0.867331i	0.351955	−	0.936017i	$-0.385517\pi$
$431$	28.0183	−	18.0063i	1.34959	−	0.867331i	0.997638	+	0.0686858i	$0.0218806\pi$
$432$		0			0
$433$	−18.1413	−	11.6587i	−0.871816	−	0.560282i	0.0264914	−	0.999649i	$-0.491567\pi$
$433$	−18.1413	−	11.6587i	−0.871816	−	0.560282i	−0.898308	+	0.439367i	$0.855203\pi$
$434$	−6.67514	+	7.70352i	−0.320417	+	0.369781i
$435$		0			0
$436$	−5.87577			−0.281398
$437$	1.85046	+	1.91691i	0.0885193	+	0.0916982i
$438$		0			0
$439$	−16.5410	−	4.85686i	−0.789457	−	0.231805i	−0.137941	−	0.990440i	$-0.544048\pi$
$439$	−16.5410	−	4.85686i	−0.789457	−	0.231805i	−0.651516	+	0.758635i	$0.725867\pi$
$440$	13.7171	−	15.8304i	0.653938	−	0.754684i
$441$		0			0
$442$	0.491437	−	3.41802i	0.0233753	−	0.162579i
$443$	−15.9136	+	10.2271i	−0.756080	+	0.485903i	−0.861017	−	0.508576i	$-0.830172\pi$
$443$	−15.9136	+	10.2271i	−0.756080	+	0.485903i	0.104937	+	0.994479i	$0.466536\pi$
$444$		0			0
$445$	−11.7870	−	13.6030i	−0.558760	−	0.644843i
$446$	−2.24948	−	15.6454i	−0.106516	−	0.740833i
$447$		0			0
$448$	−1.45204	+	0.426356i	−0.0686023	+	0.0201434i
$449$	22.1174	−	6.49424i	1.04378	−	0.306482i	0.285480	−	0.958385i	$-0.407847\pi$
$449$	22.1174	−	6.49424i	1.04378	−	0.306482i	0.758303	+	0.651902i	$0.226029\pi$
$450$		0			0
$451$	−1.71955	−	11.9597i	−0.0809705	−	0.563162i
$452$	8.05979	+	9.30149i	0.379101	+	0.437505i
$453$		0			0
$454$	−2.18279	+	1.40280i	−0.102444	+	0.0658365i
$455$	−1.99132	+	13.8499i	−0.0933545	+	0.649295i
$456$		0			0
$457$	−9.94760	+	11.4801i	−0.465329	+	0.537019i	−0.939107	−	0.343626i	$-0.888345\pi$
$457$	−9.94760	+	11.4801i	−0.465329	+	0.537019i	0.473777	+	0.880645i	$0.342890\pi$
$458$	9.58892	+	2.81556i	0.448061	+	0.131563i
$459$		0			0
$460$	−12.4600	+	8.98895i	−0.580950	+	0.419112i
$461$	−19.2440			−0.896281			−0.448141	−	0.893963i	$-0.647914\pi$
$461$	−19.2440			−0.896281			−0.448141	+	0.893963i	$0.647914\pi$
$462$		0			0
$463$	1.98580	−	2.29173i	0.0922878	−	0.106506i	−0.707727	−	0.706486i	$-0.750279\pi$
$463$	1.98580	−	2.29173i	0.0922878	−	0.106506i	0.800015	+	0.599980i	$0.204825\pi$
$464$	7.29298	+	4.68691i	0.338568	+	0.217584i
$465$		0			0
$466$	−22.9618	+	14.7567i	−1.06369	+	0.683590i
$467$	−1.18398	−	2.59256i	−0.0547882	−	0.119969i	0.880258	−	0.474495i	$-0.157369\pi$
$467$	−1.18398	−	2.59256i	−0.0547882	−	0.119969i	−0.935046	+	0.354526i	$0.884642\pi$
$468$		0			0
$469$	1.65145	+	11.4861i	0.0762567	+	0.530377i
$470$	−15.1894	+	33.2602i	−0.700637	+	1.53418i
$471$		0			0
$472$	−3.80093	+	1.11605i	−0.174952	+	0.0513706i
$473$	5.90436	−	12.9287i	0.271483	−	0.594465i
$474$		0			0
$475$	−1.91479	−	2.20979i	−0.0878566	−	0.101392i
$476$	0.752179	+	1.64704i	0.0344761	+	0.0754920i
$477$		0			0
$478$	−2.03776	+	14.1729i	−0.0932050	+	0.648255i
$479$	−31.3457	−	20.1447i	−1.43222	−	0.920433i	−0.999824	−	0.0187506i	$-0.994031\pi$
$479$	−31.3457	−	20.1447i	−1.43222	−	0.920433i	−0.432398	−	0.901683i	$-0.642332\pi$
$480$		0			0
$481$	4.02588	+	1.18211i	0.183564	+	0.0538994i
$482$	−14.1957			−0.646598
$483$		0			0
$484$	31.7511			1.44323
$485$	22.2770	+	6.54111i	1.01155	+	0.297017i
$486$		0			0
$487$	−25.8648	−	16.6223i	−1.17204	−	0.753227i	−0.198137	−	0.980174i	$-0.563489\pi$
$487$	−25.8648	−	16.6223i	−1.17204	−	0.753227i	−0.973907	+	0.226947i	$0.927126\pi$
$488$	1.28574	−	8.94254i	0.0582029	−	0.404810i
$489$		0			0
$490$	6.26796	+	13.7249i	0.283157	+	0.620028i
$491$	5.11770	+	5.90614i	0.230959	+	0.266540i	0.859386	−	0.511328i	$-0.170846\pi$
$491$	5.11770	+	5.90614i	0.230959	+	0.266540i	−0.628427	+	0.777869i	$0.716301\pi$
$492$		0			0
$493$	4.30887	−	9.43510i	0.194062	−	0.424936i
$494$	1.53845	−	0.451729i	0.0692181	−	0.0203243i
$495$		0			0
$496$	−2.79806	+	6.12691i	−0.125637	+	0.275106i
$497$	−2.03656	−	14.1646i	−0.0913520	−	0.635367i
$498$		0			0
$499$	5.38364	+	11.7885i	0.241005	+	0.527727i	0.991023	−	0.133690i	$-0.0426827\pi$
$499$	5.38364	+	11.7885i	0.241005	+	0.527727i	−0.750018	+	0.661417i	$0.769955\pi$
$500$	0.709211	−	0.455783i	0.0317169	−	0.0203832i
$501$		0			0
$502$	10.0652	+	6.46851i	0.449232	+	0.288704i
$503$	12.8552	−	14.8357i	0.573184	−	0.661489i	−0.392941	−	0.919564i	$-0.628542\pi$
$503$	12.8552	−	14.8357i	0.573184	−	0.661489i	0.966125	+	0.258074i	$0.0830879\pi$
$504$		0			0
$505$	3.27979			0.145949
$506$	−30.5183	−	7.20480i	−1.35670	−	0.320293i
$507$		0			0
$508$	−8.51054	−	2.49892i	−0.377594	−	0.110872i
$509$	4.09448	−	4.72528i	0.181484	−	0.209444i	−0.657717	−	0.753265i	$-0.728478\pi$
$509$	4.09448	−	4.72528i	0.181484	−	0.209444i	0.839201	+	0.543821i	$0.183023\pi$
$510$		0			0
$511$	0.135166	−	0.940100i	0.00597939	−	0.0415876i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$		0			0
$514$	−17.0242	−	19.6470i	−0.750907	−	0.866592i
$515$	−2.07410	−	14.4257i	−0.0913958	−	0.635672i
$516$		0			0
$517$	−71.6035	+	21.0247i	−3.14912	+	0.924665i
$518$	−2.11097	+	0.619837i	−0.0927507	+	0.0272341i
$519$		0			0
$520$	1.31585	+	9.15192i	0.0577037	+	0.401338i
$521$	15.7103	+	18.1307i	0.688283	+	0.794321i	0.987120	−	0.159984i	$-0.0511441\pi$
$521$	15.7103	+	18.1307i	0.688283	+	0.794321i	−0.298837	+	0.954304i	$0.596599\pi$
$522$		0			0
$523$	−6.24846	+	4.01564i	−0.273226	+	0.175592i	−0.670077	−	0.742291i	$-0.733739\pi$
$523$	−6.24846	+	4.01564i	−0.273226	+	0.175592i	0.396852	+	0.917883i	$0.370103\pi$
$524$	1.78441	−	12.4108i	0.0779523	−	0.542170i
$525$		0			0
$526$	−3.76064	+	4.34001i	−0.163972	+	0.189233i
$527$	7.73251	+	2.27047i	0.336833	+	0.0989032i
$528$		0			0
$529$	20.5716	+	10.2864i	0.894416	+	0.447237i
$530$	38.6398			1.67841
$531$		0			0
$532$	−0.550568	+	0.635389i	−0.0238702	+	0.0275476i
$533$	4.48676	+	2.88347i	0.194343	+	0.124897i
$534$		0			0
$535$	1.62508	−	1.04438i	0.0702584	−	0.0451523i
$536$	3.18538	+	6.97500i	0.137587	+	0.301274i
$537$		0			0
$538$	−1.16403	−	8.09601i	−0.0501849	−	0.349044i
$539$	−12.7926	+	28.0119i	−0.551017	+	1.20656i
$540$		0			0
$541$	−19.6113	+	5.75840i	−0.843157	+	0.247573i	−0.674660	−	0.738129i	$-0.735710\pi$
$541$	−19.6113	+	5.75840i	−0.843157	+	0.247573i	−0.168497	+	0.985702i	$0.553891\pi$
$542$	5.61029	−	12.2848i	0.240982	−	0.527678i
$543$		0			0
$544$	0.783524	+	0.904235i	0.0335933	+	0.0387687i
$545$	−7.81964	−	17.1226i	−0.334957	−	0.733453i
$546$		0			0
$547$	1.32499	−	9.21550i	0.0566524	−	0.394026i	−0.941690	−	0.336481i	$-0.890763\pi$
$547$	1.32499	−	9.21550i	0.0566524	−	0.394026i	0.998343	−	0.0575459i	$-0.0183275\pi$
$548$	11.4817	+	7.37884i	0.490474	+	0.315209i
$549$		0			0
$550$	33.0188	+	9.69519i	1.40793	+	0.413404i
$551$	4.81620			0.205177
$552$		0			0
$553$	−20.8419			−0.886287
$554$	14.3633	+	4.21744i	0.610238	+	0.179182i
$555$		0			0
$556$	−9.80372	−	6.30047i	−0.415771	−	0.267199i
$557$	−4.54281	+	31.5960i	−0.192485	+	1.33876i	0.632917	+	0.774219i	$0.281857\pi$
$557$	−4.54281	+	31.5960i	−0.192485	+	1.33876i	−0.825402	+	0.564545i	$0.809052\pi$
$558$		0			0
$559$	2.60624	+	5.70687i	0.110232	+	0.241375i
$560$	−3.17486	−	3.66399i	−0.134162	−	0.154832i
$561$		0			0
$562$	11.2054	−	24.5364i	0.472671	−	1.03500i
$563$	−16.1686	+	4.74754i	−0.681427	+	0.200085i	−0.604085	−	0.796920i	$-0.706461\pi$
$563$	−16.1686	+	4.74754i	−0.681427	+	0.200085i	−0.0773416	+	0.997005i	$0.524643\pi$
$564$		0			0
$565$	−16.3794	+	35.8658i	−0.689085	+	1.50889i
$566$	1.95246	+	13.5797i	0.0820680	+	0.570796i
$567$		0			0
$568$	−3.92819	−	8.60154i	−0.164823	−	0.360913i
$569$	1.83549	−	1.17960i	0.0769478	−	0.0494513i	−0.501601	−	0.865099i	$-0.667256\pi$
$569$	1.83549	−	1.17960i	0.0769478	−	0.0494513i	0.578549	+	0.815648i	$0.303619\pi$
$570$		0			0
$571$	−7.55227	−	4.85355i	−0.316053	−	0.203115i	0.372990	−	0.927835i	$-0.378332\pi$
$571$	−7.55227	−	4.85355i	−0.316053	−	0.203115i	−0.689043	+	0.724721i	$0.741969\pi$
$572$	−12.3577	+	14.2615i	−0.516701	+	0.596305i
$573$		0			0
$574$	−2.79658			−0.116727
$575$	−21.9369	−	12.4856i	−0.914831	−	0.520687i
$576$		0			0
$577$	39.5160	+	11.6029i	1.64507	+	0.483037i	0.967595	−	0.252508i	$-0.0812553\pi$
$577$	39.5160	+	11.6029i	1.64507	+	0.483037i	0.677477	+	0.735544i	$0.263073\pi$
$578$	−10.1952	+	11.7658i	−0.424063	+	0.489395i
$579$		0			0
$580$	−3.95247	+	27.4900i	−0.164117	+	1.14146i
$581$	19.8462	−	12.7544i	0.823358	−	0.529140i
$582$		0			0
$583$	51.6437	+	59.6000i	2.13886	+	2.46838i
$584$	−0.0893165	−	0.621210i	−0.00369594	−	0.0257059i
$585$		0			0
$586$	−8.83212	+	2.59334i	−0.364851	+	0.107130i
$587$	9.22184	−	2.70778i	0.380626	−	0.111762i	−0.0858220	−	0.996310i	$-0.527352\pi$
$587$	9.22184	−	2.70778i	0.380626	−	0.111762i	0.466448	+	0.884549i	$0.345533\pi$
$588$		0			0
$589$	0.532540	+	3.70390i	0.0219429	+	0.152616i
$590$	−8.31070	−	9.59106i	−0.342146	−	0.394858i
$591$		0			0
$592$	−1.22301	+	0.785983i	−0.0502656	+	0.0323037i
$593$	−5.18844	+	36.0864i	−0.213064	+	1.48189i	0.549781	+	0.835309i	$0.314711\pi$
$593$	−5.18844	+	36.0864i	−0.213064	+	1.48189i	−0.762845	+	0.646581i	$0.776198\pi$
$594$		0			0
$595$	−3.79864	+	4.38386i	−0.155729	+	0.179721i
$596$	16.6025	+	4.87494i	0.680066	+	0.199685i
$597$		0			0
$598$	11.2251	−	8.09811i	0.459030	−	0.331156i
$599$	6.93439			0.283331			0.141666	−	0.989915i	$-0.454754\pi$
$599$	6.93439			0.283331			0.141666	+	0.989915i	$0.454754\pi$
$600$		0			0
$601$	−10.9824	+	12.6744i	−0.447983	+	0.517000i	−0.934157	−	0.356862i	$-0.883847\pi$
$601$	−10.9824	+	12.6744i	−0.447983	+	0.517000i	0.486174	+	0.873862i	$0.338392\pi$
$602$	−2.76745	−	1.77853i	−0.112793	−	0.0724876i
$603$		0			0
$604$	−4.06535	+	2.61264i	−0.165417	+	0.106307i
$605$	42.2553	+	92.5261i	1.71792	+	3.76172i
$606$		0			0
$607$	1.54717	+	10.7608i	0.0627977	+	0.436768i	0.996829	+	0.0795759i	$0.0253566\pi$
$607$	1.54717	+	10.7608i	0.0627977	+	0.436768i	−0.934031	+	0.357192i	$0.883734\pi$
$608$	−0.230786	+	0.505350i	−0.00935959	+	0.0204946i
$609$		0			0
$610$	27.7707	−	8.15420i	1.12440	−	0.330154i
$611$	13.6841	−	29.9640i	0.553599	−	1.21221i
$612$		0			0
$613$	−13.5856	−	15.6786i	−0.548717	−	0.633253i	0.411867	−	0.911244i	$-0.364877\pi$
$613$	−13.5856	−	15.6786i	−0.548717	−	0.633253i	−0.960584	+	0.277991i	$0.910331\pi$
$614$	−0.729786	−	1.59801i	−0.0294518	−	0.0644903i
$615$		0			0
$616$	1.40818	−	9.79413i	0.0567373	−	0.394617i
$617$	−2.60245	−	1.67249i	−0.104771	−	0.0673321i	0.487206	−	0.873287i	$-0.338016\pi$
$617$	−2.60245	−	1.67249i	−0.104771	−	0.0673321i	−0.591977	+	0.805955i	$0.701652\pi$
$618$		0			0
$619$	12.4859	+	3.66620i	0.501851	+	0.147357i	0.522853	−	0.852423i	$-0.324868\pi$
$619$	12.4859	+	3.66620i	0.501851	+	0.147357i	−0.0210022	+	0.999779i	$0.506686\pi$
$620$	−21.5782			−0.866603
$621$		0			0
$622$	30.3629			1.21744
$623$	−8.15818	−	2.39546i	−0.326850	−	0.0959720i
$624$		0			0
$625$	−19.8662	−	12.7672i	−0.794648	−	0.510689i
$626$	1.56820	−	10.9071i	0.0626778	−	0.435934i
$627$		0			0
$628$	−2.09798	−	4.59393i	−0.0837183	−	0.183318i
$629$	1.13909	+	1.31458i	0.0454184	+	0.0524156i
$630$		0			0
$631$	4.08060	−	8.93527i	0.162446	−	0.355707i	−0.810852	−	0.585251i	$-0.800996\pi$
$631$	4.08060	−	8.93527i	0.162446	−	0.355707i	0.973298	+	0.229544i	$0.0737233\pi$
$632$	−13.2143	+	3.88006i	−0.525635	+	0.154340i
$633$		0			0
$634$	−4.21527	+	9.23016i	−0.167410	+	0.366577i
$635$	−4.04395	−	28.1263i	−0.160479	−	1.11616i
$636$		0			0
$637$	−5.64677	−	12.3647i	−0.223733	−	0.489908i
$638$	−47.6846	+	30.6450i	−1.88785	+	1.21325i
$639$		0			0
$640$	−2.69505	−	1.73201i	−0.106531	−	0.0684635i
$641$	8.92969	−	10.3054i	0.352702	−	0.407039i	−0.551480	−	0.834188i	$-0.685937\pi$
$641$	8.92969	−	10.3054i	0.352702	−	0.407039i	0.904181	+	0.427149i	$0.140482\pi$
$642$		0			0
$643$	3.57857			0.141125			0.0705626	−	0.997507i	$-0.477521\pi$
$643$	3.57857			0.141125			0.0705626	+	0.997507i	$0.477521\pi$
$644$	−2.65584	+	6.75432i	−0.104655	+	0.266158i
$645$		0			0
$646$	0.637781	+	0.187269i	0.0250931	+	0.00736801i
$647$	−17.1896	+	19.8379i	−0.675793	+	0.779906i	−0.985271	−	0.171000i	$-0.945300\pi$
$647$	−17.1896	+	19.8379i	−0.675793	+	0.779906i	0.309478	+	0.950907i	$0.399846\pi$
$648$		0			0
$649$	3.68614	−	25.6377i	0.144694	−	1.00637i
$650$	−12.7787	+	8.21239i	−0.501223	+	0.322116i
$651$		0			0
$652$	−2.33617	−	2.69608i	−0.0914915	−	0.105587i
$653$	3.66305	+	25.4771i	0.143346	+	0.996994i	0.926803	+	0.375548i	$0.122546\pi$
$653$	3.66305	+	25.4771i	0.143346	+	0.996994i	−0.783457	+	0.621446i	$0.786545\pi$
$654$		0			0
$655$	38.5413	−	11.3167i	1.50593	−	0.442182i
$656$	−1.77310	+	0.520629i	−0.0692279	+	0.0203272i
$657$		0			0
$658$	2.45813	+	17.0967i	0.0958279	+	0.666498i
$659$	−6.67928	−	7.70831i	−0.260188	−	0.300273i	0.610592	−	0.791945i	$-0.290931\pi$
$659$	−6.67928	−	7.70831i	−0.260188	−	0.300273i	−0.870780	+	0.491672i	$0.836386\pi$
$660$		0			0
$661$	−25.1993	+	16.1946i	−0.980140	+	0.629897i	−0.929501	−	0.368820i	$-0.879762\pi$
$661$	−25.1993	+	16.1946i	−0.980140	+	0.629897i	−0.0506386	+	0.998717i	$0.516126\pi$
$662$	4.23799	−	29.4759i	0.164714	−	1.14561i
$663$		0			0
$664$	10.2085	−	11.7813i	0.396168	−	0.457202i
$665$	−2.58431	−	0.758821i	−0.100215	−	0.0294258i
$666$		0			0
$667$	39.2047	−	13.8400i	1.51801	−	0.535888i
$668$	−4.56038			−0.176446
$669$		0			0
$670$	−16.0867	+	18.5651i	−0.621485	+	0.717232i
$671$	49.6941	+	31.9364i	1.91842	+	1.23289i
$672$		0			0
$673$	−1.70536	+	1.09597i	−0.0657367	+	0.0422464i	−0.573096	−	0.819488i	$-0.694258\pi$
$673$	−1.70536	+	1.09597i	−0.0657367	+	0.0422464i	0.507360	+	0.861734i	$0.330622\pi$
$674$	7.91732	+	17.3365i	0.304964	+	0.667777i
$675$		0			0
$676$	0.664652	+	4.62276i	0.0255636	+	0.177798i
$677$	−1.02323	+	2.24056i	−0.0393259	+	0.0861116i	−0.928275	−	0.371894i	$-0.878709\pi$
$677$	−1.02323	+	2.24056i	−0.0393259	+	0.0861116i	0.888950	+	0.458005i	$0.151436\pi$
$678$		0			0
$679$	10.5233	−	3.08992i	0.403847	−	0.118580i
$680$	−1.59230	+	3.48666i	−0.0610620	+	0.133707i
$681$		0			0
$682$	−28.8402	−	33.2833i	−1.10435	−	1.27448i
$683$	12.5872	+	27.5621i	0.481635	+	1.05463i	0.982011	+	0.188825i	$0.0604678\pi$
$683$	12.5872	+	27.5621i	0.481635	+	1.05463i	−0.500376	+	0.865808i	$0.666805\pi$
$684$		0			0
$685$	−6.22257	+	43.2790i	−0.237752	+	1.65360i
$686$	14.9078	+	9.58064i	0.569181	+	0.365790i
$687$		0			0
$688$	−2.08574	−	0.612427i	−0.0795179	−	0.0233486i
$689$	−34.8104			−1.32617
$690$		0			0
$691$	−1.71993			−0.0654294			−0.0327147	−	0.999465i	$-0.510415\pi$
$691$	−1.71993			−0.0654294			−0.0327147	+	0.999465i	$0.510415\pi$
$692$	−14.9808	−	4.39875i	−0.569483	−	0.167215i
$693$		0			0
$694$	−10.2573	−	6.59199i	−0.389363	−	0.250228i
$695$	5.31318	−	36.9540i	0.201541	−	1.40175i
$696$		0			0
$697$	0.918495	+	2.01122i	0.0347905	+	0.0761805i
$698$	−10.0863	−	11.6402i	−0.381771	−	0.440587i
$699$		0			0
$700$	3.30875	−	7.24515i	0.125059	−	0.273841i
$701$	−0.709124	+	0.208218i	−0.0267833	+	0.00786427i	−0.295097	−	0.955467i	$-0.595352\pi$
$701$	−0.709124	+	0.208218i	−0.0267833	+	0.00786427i	0.268313	+	0.963332i	$0.413534\pi$
$702$		0			0
$703$	−0.335516	+	0.734677i	−0.0126542	+	0.0277089i
$704$	−0.930515	−	6.47188i	−0.0350701	−	0.243918i
$705$		0			0
$706$	7.69797	+	16.8562i	0.289717	+	0.634392i
$707$	1.30337	−	0.837626i	0.0490183	−	0.0315022i
$708$		0			0
$709$	18.9971	+	12.2087i	0.713451	+	0.458507i	0.846353	−	0.532622i	$-0.178793\pi$
$709$	18.9971	+	12.2087i	0.713451	+	0.458507i	−0.132902	+	0.991129i	$0.542430\pi$
$710$	19.8381	−	22.8944i	0.744510	−	0.859211i
$711$		0			0
$712$	−5.61844			−0.210560
$713$	14.9786	+	28.6201i	0.560954	+	1.07183i
$714$		0			0
$715$	−58.0057	−	17.0320i	−2.16929	−	0.636961i
$716$	4.19452	−	4.84074i	0.156757	−	0.180907i
$717$		0			0
$718$	1.67363	−	11.6404i	0.0624595	−	0.434415i
$719$	−9.21249	+	5.92051i	−0.343568	+	0.220798i	−0.701033	−	0.713129i	$-0.747277\pi$
$719$	−9.21249	+	5.92051i	−0.343568	+	0.220798i	0.357465	+	0.933926i	$0.383641\pi$
$720$		0			0
$721$	−4.50842	−	5.20299i	−0.167902	−	0.193769i
$722$	−2.66006	−	18.5011i	−0.0989971	−	0.688540i
$723$		0			0
$724$	21.2397	−	6.23653i	0.789366	−	0.231779i
$725$	−43.7790	+	12.8547i	−1.62591	+	0.477410i
$726$		0			0
$727$	−5.30540	−	36.8999i	−0.196766	−	1.36854i	−0.813590	−	0.581439i	$-0.802490\pi$
$727$	−5.30540	−	36.8999i	−0.196766	−	1.36854i	0.616824	−	0.787101i	$-0.288419\pi$
$728$	2.86022	+	3.30087i	0.106007	+	0.122338i
$729$		0			0
$730$	1.69141	−	1.08700i	0.0626019	−	0.0402318i
$731$	−0.370144	+	2.57441i	−0.0136903	+	0.0952179i
$732$		0			0
$733$	−21.0216	+	24.2602i	−0.776449	+	0.896070i	−0.996848	−	0.0793401i	$-0.974719\pi$
$733$	−21.0216	+	24.2602i	−0.776449	+	0.896070i	0.220399	+	0.975410i	$0.429264\pi$
$734$	−7.50235	−	2.20289i	−0.276917	−	0.0813101i
$735$		0			0
$736$	−0.426443	+	4.77683i	−0.0157189	+	0.176076i
$737$	−50.1363			−1.84679
$738$		0			0
$739$	−24.5623	+	28.3464i	−0.903537	+	1.04274i	0.0953439	+	0.995444i	$0.469605\pi$
$739$	−24.5623	+	28.3464i	−0.903537	+	1.04274i	−0.998881	+	0.0472931i	$0.984941\pi$
$740$	−3.91807	−	2.51799i	−0.144031	−	0.0925631i
$741$		0			0
$742$	15.3553	−	9.86823i	0.563709	−	0.362274i
$743$	−13.2431	−	28.9983i	−0.485841	−	1.06384i	−0.980816	−	0.194936i	$-0.937550\pi$
$743$	−13.2431	−	28.9983i	−0.485841	−	1.06384i	0.494975	−	0.868907i	$-0.335177\pi$
$744$		0			0
$745$	7.88901	+	54.8693i	0.289031	+	2.01026i
$746$	−0.888226	+	1.94494i	−0.0325203	+	0.0712094i
$747$		0			0
$748$	−7.50617	+	2.20401i	−0.274453	+	0.0805866i
$749$	0.379076	−	0.830060i	0.0138511	−	0.0303297i
$750$		0			0
$751$	11.7544	+	13.5652i	0.428923	+	0.495003i	0.928534	−	0.371246i	$-0.121069\pi$
$751$	11.7544	+	13.5652i	0.428923	+	0.495003i	−0.499612	+	0.866249i	$0.666524\pi$
$752$	4.74134	+	10.3821i	0.172899	+	0.378596i
$753$		0			0
$754$	3.56076	−	24.7656i	0.129675	−	0.901911i
$755$	−13.0238	−	8.36990i	−0.473985	−	0.304612i
$756$		0			0
$757$	10.5177	+	3.08827i	0.382271	+	0.112245i	0.467222	−	0.884140i	$-0.345255\pi$
$757$	10.5177	+	3.08827i	0.382271	+	0.112245i	−0.0849504	+	0.996385i	$0.527073\pi$
$758$	21.6725			0.787180
$759$		0			0
$760$	−1.77978			−0.0645595
$761$	−0.351035	−	0.103073i	−0.0127250	−	0.00373640i	0.275364	−	0.961340i	$-0.411202\pi$
$761$	−0.351035	−	0.103073i	−0.0127250	−	0.00373640i	−0.288089	+	0.957604i	$0.593020\pi$
$762$		0			0
$763$	−7.48044	−	4.80739i	−0.270810	−	0.174039i
$764$	−0.305856	+	2.12727i	−0.0110655	+	0.0769620i
$765$		0			0
$766$	2.08113	+	4.55703i	0.0751942	+	0.164652i
$767$	7.48708	+	8.64055i	0.270343	+	0.311992i
$768$		0			0
$769$	0.127106	−	0.278324i	0.00458358	−	0.0100366i	−0.907326	−	0.420427i	$-0.861880\pi$
$769$	0.127106	−	0.278324i	0.00458358	−	0.0100366i	0.911910	+	0.410390i	$0.134608\pi$
$770$	30.4152	−	8.93072i	1.09609	−	0.321841i
$771$		0			0
$772$	−4.67176	+	10.2297i	−0.168140	+	0.368176i
$773$	−0.502419	−	3.49440i	−0.0180708	−	0.125685i	0.978789	−	0.204870i	$-0.0656772\pi$
$773$	−0.502419	−	3.49440i	−0.0180708	−	0.125685i	−0.996860	+	0.0791853i	$0.974768\pi$
$774$		0			0
$775$	−14.7266	−	32.2468i	−0.528997	−	1.15834i
$776$	6.09679	−	3.91817i	0.218862	−	0.140654i
$777$		0			0
$778$	−5.06583	−	3.25561i	−0.181619	−	0.116719i
$779$	−0.672306	+	0.775882i	−0.0240879	+	0.0277989i
$780$		0			0
$781$	61.8278			2.21237
$782$	5.72980	−	0.308346i	0.204897	−	0.0110264i
$783$		0			0
$784$	4.51903	+	1.32691i	0.161394	+	0.0473895i
$785$	10.5952	−	12.2275i	0.378157	−	0.436417i
$786$		0			0
$787$	0.320128	−	2.22654i	0.0114113	−	0.0793675i	−0.983320	−	0.181884i	$-0.941780\pi$
$787$	0.320128	−	2.22654i	0.0114113	−	0.0793675i	0.994731	+	0.102517i	$0.0326895\pi$
$788$	−8.75956	+	5.62943i	−0.312046	+	0.200540i
$789$		0			0
$790$	−28.8929	−	33.3442i	−1.02796	−	1.18633i
$791$	2.65070	+	18.4360i	0.0942480	+	0.655510i
$792$		0			0
$793$	−25.0185	+	7.34609i	−0.888432	+	0.260867i
$794$	23.0295	−	6.76208i	0.817287	−	0.239977i
$795$		0			0
$796$	−2.14892	−	14.9461i	−0.0761665	−	0.529750i
$797$	−25.9779	−	29.9801i	−0.920185	−	1.06195i	−0.997887	−	0.0649735i	$-0.979304\pi$
$797$	−25.9779	−	29.9801i	−0.920185	−	1.06195i	0.0777020	−	0.996977i	$-0.475242\pi$
$798$		0			0
$799$	11.4881	−	7.38297i	0.406421	−	0.261191i
$800$	0.749025	−	5.20958i	0.0264820	−	0.184187i
$801$		0			0
$802$	9.48014	−	10.9407i	0.334755	−	0.386328i
$803$	3.93728	+	1.15609i	0.138944	+	0.0407976i
$804$		0			0
$805$	−23.2173	+	1.24943i	−0.818303	+	0.0440366i
$806$	19.4397			0.684735
$807$		0			0
$808$	0.670431	−	0.773719i	0.0235857	−	0.0272193i
$809$	32.3796	+	20.8091i	1.13841	+	0.731610i	0.967298	−	0.253642i	$-0.0816284\pi$
$809$	32.3796	+	20.8091i	1.13841	+	0.731610i	0.171110	+	0.985252i	$0.445265\pi$
$810$		0			0
$811$	−12.1468	+	7.80630i	−0.426533	+	0.274116i	−0.736246	−	0.676714i	$-0.763403\pi$
$811$	−12.1468	+	7.80630i	−0.426533	+	0.274116i	0.309713	+	0.950830i	$0.399767\pi$
$812$	5.44999	+	11.9338i	0.191257	+	0.418795i
$813$		0			0
$814$	−1.35278	−	9.40881i	−0.0474150	−	0.329779i
$815$	4.74764	−	10.3959i	0.166303	−	0.364152i
$816$		0			0
$817$	−1.15874	+	0.340236i	−0.0405391	+	0.0119034i
$818$	13.5606	−	29.6936i	0.474135	−	1.03821i
$819$		0			0
$820$	−3.87687	−	4.47414i	−0.135386	−	0.156244i
$821$	−12.1602	−	26.6271i	−0.424393	−	0.929291i	−0.994203	−	0.107515i	$-0.965711\pi$
$821$	−12.1602	−	26.6271i	−0.424393	−	0.929291i	0.569810	−	0.821776i	$-0.307017\pi$
$822$		0			0
$823$	2.37652	−	16.5290i	0.0828401	−	0.576166i	−0.905551	−	0.424237i	$-0.860542\pi$
$823$	2.37652	−	16.5290i	0.0828401	−	0.576166i	0.988391	−	0.151929i	$-0.0485485\pi$
$824$	−3.82707	−	2.45951i	−0.133322	−	0.0856810i
$825$		0			0
$826$	−5.75209	−	1.68897i	−0.200141	−	0.0587667i
$827$	20.3196			0.706582			0.353291	−	0.935514i	$-0.385063\pi$
$827$	20.3196			0.706582			0.353291	+	0.935514i	$0.385063\pi$
$828$		0			0
$829$	0.285271			0.00990788			0.00495394	−	0.999988i	$-0.498423\pi$
$829$	0.285271			0.00990788			0.00495394	+	0.999988i	$0.498423\pi$
$830$	47.9177	+	14.0699i	1.66325	+	0.488374i
$831$		0			0
$832$	2.42796	+	1.56036i	0.0841744	+	0.0540956i
$833$	0.801968	−	5.57781i	0.0277865	−	0.193260i
$834$		0			0
$835$	−6.06909	−	13.2894i	−0.210029	−	0.459900i
$836$	−2.37875	−	2.74522i	−0.0822708	−	0.0949456i
$837$		0			0
$838$	−15.0558	+	32.9675i	−0.520093	+	1.13884i
$839$	−23.4619	+	6.88905i	−0.809996	+	0.237836i	−0.660403	−	0.750911i	$-0.729615\pi$
$839$	−23.4619	+	6.88905i	−0.809996	+	0.237836i	−0.149593	+	0.988748i	$0.547796\pi$
$840$		0			0
$841$	19.1733	−	41.9837i	0.661149	−	1.44771i
$842$	0.994168	+	6.91459i	0.0342613	+	0.238293i
$843$		0			0
$844$	4.77015	+	10.4452i	0.164195	+	0.359537i
$845$	−12.5867	+	8.08898i	−0.432995	+	0.278269i
$846$		0			0
$847$	40.4223	+	25.9778i	1.38893	+	0.892608i
$848$	7.89848	−	9.11533i	0.271235	−	0.313022i
$849$		0			0
$850$	−6.29722			−0.215993
$851$	−0.619962	+	6.94456i	−0.0212520	+	0.238056i
$852$		0			0
$853$	−27.7862	−	8.15876i	−0.951381	−	0.279351i	−0.231019	−	0.972949i	$-0.574206\pi$
$853$	−27.7862	−	8.15876i	−0.951381	−	0.279351i	−0.720362	+	0.693599i	$0.756024\pi$
$854$	8.95342	−	10.3328i	0.306380	−	0.353581i
$855$		0			0
$856$	0.0858140	−	0.596849i	0.00293306	−	0.0203999i
$857$	25.6181	−	16.4638i	0.875099	−	0.562392i	−0.0242097	−	0.999707i	$-0.507707\pi$
$857$	25.6181	−	16.4638i	0.875099	−	0.562392i	0.899308	+	0.437315i	$0.144071\pi$
$858$		0			0
$859$	−27.7481	−	32.0230i	−0.946753	−	1.09261i	−0.995591	−	0.0938044i	$-0.970097\pi$
$859$	−27.7481	−	32.0230i	−0.946753	−	1.09261i	0.0488378	−	0.998807i	$-0.484448\pi$
$860$	−0.991078	−	6.89310i	−0.0337955	−	0.235053i
$861$		0			0
$862$	31.9563	−	9.38322i	1.08844	−	0.319594i
$863$	−47.6728	+	13.9980i	−1.62280	+	0.476497i	−0.961769	−	0.273861i	$-0.911699\pi$
$863$	−47.6728	+	13.9980i	−1.62280	+	0.476497i	−0.661031	+	0.750358i	$0.729881\pi$
$864$		0			0
$865$	−7.11840	−	49.5096i	−0.242033	−	1.68338i
$866$	−14.1218	−	16.2975i	−0.479879	−	0.553810i
$867$		0			0
$868$	−8.57508	+	5.51087i	−0.291057	+	0.187051i
$869$	12.8152	−	89.1316i	0.434725	−	3.02358i
$870$		0			0
$871$	14.4925	−	16.7252i	0.491059	−	0.566712i
$872$	−5.63776	−	1.65539i	−0.190918	−	0.0560587i
$873$		0			0
$874$	1.23544	+	2.36059i	0.0417895	+	0.0798483i
$875$	1.27581			0.0431301
$876$		0			0
$877$	−3.26487	+	3.76787i	−0.110247	+	0.127232i	−0.808191	−	0.588921i	$-0.799553\pi$
$877$	−3.26487	+	3.76787i	−0.110247	+	0.127232i	0.697944	+	0.716152i	$0.254098\pi$
$878$	−14.5026	−	9.32025i	−0.489439	−	0.314543i
$879$		0			0
$880$	17.6214	−	11.3246i	0.594018	−	0.381752i
$881$	−20.4593	−	44.7996i	−0.689291	−	1.50934i	−0.852490	−	0.522744i	$-0.824908\pi$
$881$	−20.4593	−	44.7996i	−0.689291	−	1.50934i	0.163198	−	0.986593i	$-0.447819\pi$
$882$		0			0
$883$	4.15048	+	28.8672i	0.139675	+	0.971459i	0.932284	+	0.361728i	$0.117813\pi$
$883$	4.15048	+	28.8672i	0.139675	+	0.971459i	−0.792609	+	0.609730i	$0.791278\pi$
$884$	1.43450	−	3.14111i	0.0482474	−	0.105647i
$885$		0			0
$886$	−18.1503	+	5.32942i	−0.609772	+	0.179045i
$887$	−2.53121	+	5.54257i	−0.0849897	+	0.186101i	−0.947355	−	0.320185i	$-0.896255\pi$
$887$	−2.53121	+	5.54257i	−0.0849897	+	0.186101i	0.862365	+	0.506287i	$0.168982\pi$
$888$		0			0
$889$	−8.79022	−	10.1445i	−0.294815	−	0.340234i
$890$	−7.47719	−	16.3728i	−0.250636	−	0.548816i
$891$		0			0
$892$	2.24948	−	15.6454i	0.0753180	−	0.523848i
$893$	5.33424	+	3.42811i	0.178504	+	0.114717i
$894$		0			0
$895$	19.6886	+	5.78111i	0.658119	+	0.193241i
$896$	−1.51334			−0.0505570
$897$		0			0
$898$	23.0511			0.769225
$899$	56.0267	+	16.4509i	1.86860	+	0.548669i
$900$		0			0
$901$	−12.1402	−	7.80201i	−0.404448	−	0.259923i
$902$	1.71955	−	11.9597i	0.0572548	−	0.398216i
$903$		0			0
$904$	5.11278	+	11.1954i	0.170048	+	0.372354i
$905$	46.4403	+	53.5950i	1.54373	+	1.78156i
$906$		0			0
$907$	−1.02214	+	2.23817i	−0.0339396	+	0.0743173i	−0.925842	−	0.377910i	$-0.876643\pi$
$907$	−1.02214	+	2.23817i	−0.0339396	+	0.0743173i	0.891903	+	0.452227i	$0.149370\pi$
$908$	−2.48959	+	0.731009i	−0.0826199	+	0.0242594i
$909$		0			0
$910$	−5.81264	+	12.7279i	−0.192687	+	0.421926i
$911$	−7.45933	−	51.8808i	−0.247139	−	1.71889i	−0.614593	−	0.788845i	$-0.710680\pi$
$911$	−7.45933	−	51.8808i	−0.247139	−	1.71889i	0.367454	−	0.930042i	$-0.380229\pi$
$912$		0			0
$913$	42.3418	+	92.7157i	1.40131	+	3.06844i
$914$	−12.7790	+	8.21256i	−0.422691	+	0.271647i
$915$		0			0
$916$	8.40727	+	5.40302i	0.277784	+	0.178521i
$917$	12.4259	−	14.3403i	0.410340	−	0.473558i
$918$		0			0
$919$	−12.0132			−0.396280			−0.198140	−	0.980174i	$-0.563490\pi$
$919$	−12.0132			−0.396280			−0.198140	+	0.980174i	$0.563490\pi$
$920$	−14.4877	+	5.11445i	−0.477647	+	0.168619i
$921$		0			0
$922$	−18.4645	−	5.42165i	−0.608095	−	0.178553i
$923$	−17.8720	+	20.6254i	−0.588266	+	0.678895i
$924$		0			0
$925$	1.08893	−	7.57369i	0.0358039	−	0.249021i
$926$	2.55101	−	1.63944i	0.0838315	−	0.0538752i
$927$		0			0
$928$	5.67710	+	6.55173i	0.186360	+	0.215071i
$929$	−2.45403	−	17.0682i	−0.0805142	−	0.559989i	−0.989651	−	0.143492i	$-0.954167\pi$
$929$	−2.45403	−	17.0682i	−0.0805142	−	0.559989i	0.909137	−	0.416497i	$-0.136742\pi$
$930$		0			0
$931$	2.51057	−	0.737169i	0.0822805	−	0.0241597i
$932$	−26.1891	+	7.68983i	−0.857854	+	0.251889i
$933$		0			0
$934$	−0.405614	−	2.82111i	−0.0132721	−	0.0923095i
$935$	−16.4122	−	18.9407i	−0.536735	−	0.619426i
$936$		0			0
$937$	16.7304	−	10.7520i	0.546559	−	0.351252i	−0.238040	−	0.971255i	$-0.576505\pi$
$937$	16.7304	−	10.7520i	0.546559	−	0.351252i	0.784599	+	0.620003i	$0.212869\pi$
$938$	−1.65145	+	11.4861i	−0.0539216	+	0.375033i
$939$		0			0
$940$	−23.9447	+	27.6336i	−0.780988	+	0.901309i
$941$	−14.1949	−	4.16801i	−0.462742	−	0.135873i	0.0420478	−	0.999116i	$-0.486612\pi$
$941$	−14.1949	−	4.16801i	−0.462742	−	0.135873i	−0.504790	+	0.863242i	$0.668430\pi$
$942$		0			0
$943$	−3.24308	+	8.24779i	−0.105609	+	0.268585i
$944$	−3.96140			−0.128933
$945$		0			0
$946$	9.30764	−	10.7416i	0.302618	−	0.349239i
$947$	15.2688	+	9.81269i	0.496171	+	0.318869i	0.764683	−	0.644407i	$-0.222896\pi$
$947$	15.2688	+	9.81269i	0.496171	+	0.318869i	−0.268512	+	0.963276i	$0.586532\pi$
$948$		0			0
$949$	−1.52378	+	0.979276i	−0.0494641	+	0.0317886i
$950$	−1.21466	−	2.65973i	−0.0394088	−	0.0862932i
$951$		0			0
$952$	0.257685	+	1.79224i	0.00835162	+	0.0580868i
$953$	10.8698	−	23.8016i	0.352108	−	0.771008i	−0.647850	−	0.761768i	$-0.724332\pi$
$953$	10.8698	−	23.8016i	0.352108	−	0.771008i	0.999957	−	0.00923998i	$-0.00294122\pi$
$954$		0			0
$955$	−6.60615	+	1.93974i	−0.213770	+	0.0627685i
$956$	−5.94819	+	13.0247i	−0.192378	+	0.421250i
$957$		0			0
$958$	−24.4006	−	28.1598i	−0.788347	−	0.909801i
$959$	8.58020	+	18.7880i	0.277069	+	0.606697i
$960$		0			0
$961$	−2.04480	+	14.2219i	−0.0659613	+	0.458771i
$962$	3.52977	+	2.26844i	0.113804	+	0.0731376i
$963$		0			0
$964$	−13.6207	−	3.99940i	−0.438694	−	0.128812i
$965$	−36.0279			−1.15978
$966$		0			0
$967$	−22.8164			−0.733726			−0.366863	−	0.930275i	$-0.619568\pi$
$967$	−22.8164			−0.733726			−0.366863	+	0.930275i	$0.619568\pi$
$968$	30.4649	+	8.94531i	0.979179	+	0.287513i
$969$		0			0
$970$	19.5318	+	12.5523i	0.627127	+	0.403030i
$971$	−0.323393	+	2.24925i	−0.0103782	+	0.0721818i	−0.994352	−	0.106129i	$-0.966154\pi$
$971$	−0.323393	+	2.24925i	−0.0103782	+	0.0721818i	0.983974	+	0.178311i	$0.0570633\pi$
$972$		0			0
$973$	−7.32626	−	16.0423i	−0.234869	−	0.514291i
$974$	−20.1340	−	23.2359i	−0.645136	−	0.744526i
$975$		0			0
$976$	3.75307	−	8.21807i	0.120133	−	0.263054i
$977$	−36.2549	+	10.6454i	−1.15990	+	0.340577i	−0.804393	−	0.594098i	$-0.797509\pi$
$977$	−36.2549	+	10.6454i	−1.15990	+	0.340577i	−0.355505	+	0.934674i	$0.615691\pi$
$978$		0			0
$979$	15.2606	−	33.4160i	0.487731	−	1.06798i
$980$	2.14731	+	14.9348i	0.0685932	+	0.477076i
$981$		0			0
$982$	3.24644	+	7.10872i	0.103598	+	0.226848i
$983$	44.8441	−	28.8196i	1.43031	−	0.919202i	0.430444	−	0.902617i	$-0.358357\pi$
$983$	44.8441	−	28.8196i	1.43031	−	0.919202i	0.999862	−	0.0165844i	$-0.00527921\pi$
$984$		0			0
$985$	−28.0623	−	18.0345i	−0.894138	−	0.574627i
$986$	6.79250	−	7.83897i	0.216317	−	0.249644i
$987$		0			0
$988$	1.60340			0.0510109
$989$	−8.45463	+	6.09939i	−0.268842	+	0.193949i
$990$		0			0
$991$	−16.4716	−	4.83651i	−0.523238	−	0.153637i	0.00943830	−	0.999955i	$-0.496996\pi$
$991$	−16.4716	−	4.83651i	−0.523238	−	0.153637i	−0.532677	+	0.846319i	$0.678814\pi$
$992$	−4.41087	+	5.09042i	−0.140045	+	0.161621i
$993$		0			0
$994$	2.03656	−	14.1646i	0.0645956	−	0.449273i
$995$	40.6947	−	26.1529i	1.29011	−	0.829103i
$996$		0			0
$997$	18.9102	+	21.8236i	0.598893	+	0.691160i	0.971557	−	0.236807i	$-0.0761009\pi$
$997$	18.9102	+	21.8236i	0.598893	+	0.691160i	−0.372664	+	0.927967i	$0.621555\pi$
$998$	1.84435	+	12.8278i	0.0583820	+	0.406055i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.d.271.1		10
3.2	odd	2		138.2.e.a.133.1	yes	10
23.3	even	11		9522.2.a.bt.1.5		5
23.9	even	11	inner	414.2.i.d.55.1		10
23.20	odd	22		9522.2.a.bq.1.1		5
69.20	even	22		3174.2.a.bd.1.5		5
69.26	odd	22		3174.2.a.bc.1.1		5
69.32	odd	22		138.2.e.a.55.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.a.55.1	✓	10	69.32	odd	22
138.2.e.a.133.1	yes	10	3.2	odd	2
414.2.i.d.55.1		10	23.9	even	11	inner
414.2.i.d.271.1		10	1.1	even	1	trivial
3174.2.a.bc.1.1		5	69.26	odd	22
3174.2.a.bd.1.5		5	69.20	even	22
9522.2.a.bq.1.1		5	23.20	odd	22
9522.2.a.bt.1.5		5	23.3	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)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.455922 + 3.17101i) q^{5} +(0.628663 + 1.37658i) q^{7} +(0.654861 + 0.755750i) q^{8} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.455922 + 3.17101i) q^{5} +(0.628663 + 1.37658i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-1.33083 + 2.91411i) q^{10} +(-6.27358 + 1.84209i) q^{11} +(1.19894 - 2.62531i) q^{13} +(0.215370 + 1.49793i) q^{14} +(0.415415 + 0.909632i) q^{16} +(1.00654 - 0.646863i) q^{17} +(0.467362 + 0.300355i) q^{19} +(-2.09792 + 2.42113i) q^{20} -6.53843 q^{22} +(4.66752 + 1.10192i) q^{23} +(-5.04996 - 1.48280i) q^{25} +(1.89001 - 2.18119i) q^{26} +(-0.215370 + 1.49793i) q^{28} +(7.29298 - 4.68691i) q^{29} +(4.41087 + 5.09042i) q^{31} +(0.142315 + 0.989821i) q^{32} +(1.14801 - 0.337086i) q^{34} +(-4.65177 + 1.36588i) q^{35} +(0.206897 + 1.43900i) q^{37} +(0.363811 + 0.419860i) q^{38} +(-2.69505 + 1.73201i) q^{40} +(-0.262991 + 1.82915i) q^{41} +(-1.42353 + 1.64284i) q^{43} +(-6.27358 - 1.84209i) q^{44} +(4.16801 + 2.37227i) q^{46} +11.4135 q^{47} +(3.08427 - 3.55944i) q^{49} +(-4.42765 - 2.84548i) q^{50} +(2.42796 - 1.56036i) q^{52} +(-5.01045 - 10.9714i) q^{53} +(-2.98101 - 20.7334i) q^{55} +(-0.628663 + 1.37658i) q^{56} +(8.31801 - 2.44239i) q^{58} +(-1.64562 + 3.60341i) q^{59} +(-5.91634 - 6.82782i) q^{61} +(2.79806 + 6.12691i) q^{62} +(-0.142315 + 0.989821i) q^{64} +(7.77825 + 4.99878i) q^{65} +(7.35733 + 2.16031i) q^{67} +1.19647 q^{68} -4.84815 q^{70} +(-9.07303 - 2.66408i) q^{71} +(-0.527969 - 0.339305i) q^{73} +(-0.206897 + 1.43900i) q^{74} +(0.230786 + 0.505350i) q^{76} +(-6.47975 - 7.47803i) q^{77} +(-5.72115 + 12.5276i) q^{79} +(-3.07385 + 0.902563i) q^{80} +(-0.767668 + 1.68096i) q^{82} +(-2.21852 - 15.4302i) q^{83} +(1.59230 + 3.48666i) q^{85} +(-1.82871 + 1.17524i) q^{86} +(-5.50048 - 3.53494i) q^{88} +(-3.67930 + 4.24613i) q^{89} +4.36768 q^{91} +(3.33083 + 3.45045i) q^{92} +(10.9512 + 3.21556i) q^{94} +(-1.16551 + 1.34507i) q^{95} +(1.03139 - 7.17350i) q^{97} +(3.96215 - 2.54632i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8}+O(q^{10}) \) 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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