LMFDB - Embedded newform 414.2.i.h.73.2

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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 8 x^{18} + 53 x^{16} + 358 x^{14} + 1753 x^{12} + 7149 x^{10} + 23268 x^{8} + 37292 x^{6} + \cdots + 58081 $ x^20 + 8x^18 + 53x^16 + 358x^14 + 1753x^12 + 7149x^10 + 23268x^8 + 37292x^6 + 19057x^4 - 81217*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			73.2
Root			$1.95451 + 1.25609i$ of defining polynomial
Character	$\chi$	$=$	414.73
Dual form			414.2.i.h.397.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(-0.654861 + 0.755750i) q^{4} +(1.89092 + 1.21522i) q^{5} +(-0.521048 - 3.62397i) q^{7} +(0.959493 + 0.281733i) q^{8} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.654861 + 0.755750i) q^{4} +(1.89092 + 1.21522i) q^{5} +(-0.521048 - 3.62397i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.319886 - 2.22486i) q^{10} +(-0.0714536 + 0.156461i) q^{11} +(0.115327 - 0.802118i) q^{13} +(-3.08003 + 1.97941i) q^{14} +(-0.142315 - 0.989821i) q^{16} +(3.89530 + 4.49542i) q^{17} +(4.75093 - 5.48286i) q^{19} +(-2.15669 + 0.633260i) q^{20} +0.172005 q^{22} +(3.10271 - 3.65693i) q^{23} +(0.0217315 + 0.0475853i) q^{25} +(-0.777541 + 0.228307i) q^{26} +(3.08003 + 1.97941i) q^{28} +(-0.544162 - 0.627997i) q^{29} +(3.65181 + 1.07227i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(2.47101 - 5.41076i) q^{34} +(3.41865 - 7.48581i) q^{35} +(1.24724 - 0.801551i) q^{37} +(-6.96100 - 2.04393i) q^{38} +(1.47195 + 1.69872i) q^{40} +(-8.02508 - 5.15741i) q^{41} +(-10.6887 + 3.13849i) q^{43} +(-0.0714536 - 0.156461i) q^{44} +(-4.61538 - 1.30318i) q^{46} +2.95117 q^{47} +(-6.14522 + 1.80440i) q^{49} +(0.0342575 - 0.0395353i) q^{50} +(0.530677 + 0.612434i) q^{52} +(1.58519 + 11.0252i) q^{53} +(-0.325247 + 0.209024i) q^{55} +(0.521048 - 3.62397i) q^{56} +(-0.345193 + 0.755867i) q^{58} +(0.772001 - 5.36938i) q^{59} +(1.16323 + 0.341555i) q^{61} +(-0.541647 - 3.76724i) q^{62} +(0.841254 + 0.540641i) q^{64} +(1.19282 - 1.37659i) q^{65} +(3.43987 + 7.53227i) q^{67} -5.94829 q^{68} -8.22949 q^{70} +(4.73522 + 10.3687i) q^{71} +(-0.899010 + 1.03751i) q^{73} +(-1.24724 - 0.801551i) q^{74} +(1.03248 + 7.18103i) q^{76} +(0.604243 + 0.177422i) q^{77} +(0.923393 - 6.42234i) q^{79} +(0.933743 - 2.04461i) q^{80} +(-1.35760 + 9.44233i) q^{82} +(-5.16421 + 3.31884i) q^{83} +(1.90278 + 13.2341i) q^{85} +(7.29513 + 8.41902i) q^{86} +(-0.112639 + 0.129993i) q^{88} +(0.247460 - 0.0726609i) q^{89} -2.96694 q^{91} +(0.731881 + 4.73966i) q^{92} +(-1.22596 - 2.68448i) q^{94} +(15.6465 - 4.59422i) q^{95} +(11.7956 + 7.58058i) q^{97} +(4.19416 + 4.84031i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$3$		0			0
$3$		0			0
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	1.89092	+	1.21522i	0.845643	+	0.543462i	0.890213	−	0.455545i	$-0.150555\pi$
$5$	1.89092	+	1.21522i	0.845643	+	0.543462i	−0.0445701	+	0.999006i	$0.514192\pi$
$6$		0			0
$7$	−0.521048	−	3.62397i	−0.196938	−	1.36973i	−0.813105	−	0.582117i	$-0.802225\pi$
$7$	−0.521048	−	3.62397i	−0.196938	−	1.36973i	0.616167	−	0.787615i	$-0.288684\pi$
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$		0			0
$10$	0.319886	−	2.22486i	0.101157	−	0.703561i
$11$	−0.0714536	+	0.156461i	−0.0215441	+	0.0471749i	−0.920098	−	0.391688i	$-0.871891\pi$
$11$	−0.0714536	+	0.156461i	−0.0215441	+	0.0471749i	0.898554	+	0.438863i	$0.144619\pi$
$12$		0			0
$13$	0.115327	−	0.802118i	0.0319860	−	0.222468i	−0.967558	−	0.252647i	$-0.918699\pi$
$13$	0.115327	−	0.802118i	0.0319860	−	0.222468i	0.999544	+	0.0301796i	$0.00960791\pi$
$14$	−3.08003	+	1.97941i	−0.823172	+	0.529021i
$15$		0			0
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	3.89530	+	4.49542i	0.944750	+	1.09030i	0.995796	+	0.0916033i	$0.0291992\pi$
$17$	3.89530	+	4.49542i	0.944750	+	1.09030i	−0.0510456	+	0.998696i	$0.516255\pi$
$18$		0			0
$19$	4.75093	−	5.48286i	1.08994	−	1.25786i	0.125914	−	0.992041i	$-0.459814\pi$
$19$	4.75093	−	5.48286i	1.08994	−	1.25786i	0.964024	−	0.265814i	$-0.0856407\pi$
$20$	−2.15669	+	0.633260i	−0.482250	+	0.141601i
$21$		0			0
$22$	0.172005			0.0366716
$23$	3.10271	−	3.65693i	0.646961	−	0.762523i
$23$	3.10271	−	3.65693i	0.646961	−	0.762523i
$24$		0			0
$25$	0.0217315	+	0.0475853i	0.00434630	+	0.00951706i
$26$	−0.777541	+	0.228307i	−0.152488	+	0.0447746i
$27$		0			0
$28$	3.08003	+	1.97941i	0.582071	+	0.374074i
$29$	−0.544162	−	0.627997i	−0.101048	−	0.116616i	0.702973	−	0.711217i	$-0.251856\pi$
$29$	−0.544162	−	0.627997i	−0.101048	−	0.116616i	−0.804021	+	0.594601i	$0.797310\pi$
$30$		0			0
$31$	3.65181	+	1.07227i	0.655884	+	0.192585i	0.592708	−	0.805417i	$-0.298059\pi$
$31$	3.65181	+	1.07227i	0.655884	+	0.192585i	0.0631761	+	0.998002i	$0.479877\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$		0			0
$34$	2.47101	−	5.41076i	0.423775	−	0.927937i
$35$	3.41865	−	7.48581i	0.577858	−	1.26533i
$36$		0			0
$37$	1.24724	−	0.801551i	0.205045	−	0.131774i	−0.434089	−	0.900870i	$-0.642930\pi$
$37$	1.24724	−	0.801551i	0.205045	−	0.131774i	0.639133	+	0.769096i	$0.279293\pi$
$38$	−6.96100	−	2.04393i	−1.12922	−	0.331570i
$39$		0			0
$40$	1.47195	+	1.69872i	0.232736	+	0.268592i
$41$	−8.02508	−	5.15741i	−1.25331	−	0.805451i	−0.265953	−	0.963986i	$-0.585687\pi$
$41$	−8.02508	−	5.15741i	−1.25331	−	0.805451i	−0.987353	+	0.158535i	$0.949323\pi$
$42$		0			0
$43$	−10.6887	+	3.13849i	−1.63001	+	0.478615i	−0.963685	−	0.267042i	$-0.913954\pi$
$43$	−10.6887	+	3.13849i	−1.63001	+	0.478615i	−0.666329	+	0.745658i	$0.732135\pi$
$44$	−0.0714536	−	0.156461i	−0.0107720	−	0.0235875i
$45$		0			0
$46$	−4.61538	−	1.30318i	−0.680500	−	0.192144i
$47$	2.95117			0.430473			0.215236	−	0.976562i	$-0.430948\pi$
$47$	2.95117			0.430473			0.215236	+	0.976562i	$0.430948\pi$
$48$		0			0
$49$	−6.14522	+	1.80440i	−0.877889	+	0.257771i
$50$	0.0342575	−	0.0395353i	0.00484475	−	0.00559114i
$51$		0			0
$52$	0.530677	+	0.612434i	0.0735917	+	0.0849293i
$53$	1.58519	+	11.0252i	0.217742	+	1.51443i	0.746344	+	0.665561i	$0.231807\pi$
$53$	1.58519	+	11.0252i	0.217742	+	1.51443i	−0.528602	+	0.848870i	$0.677283\pi$
$54$		0			0
$55$	−0.325247	+	0.209024i	−0.0438563	+	0.0281848i
$56$	0.521048	−	3.62397i	0.0696280	−	0.484273i
$57$		0			0
$58$	−0.345193	+	0.755867i	−0.0453260	+	0.0992502i
$59$	0.772001	−	5.36938i	0.100506	−	0.699034i	−0.875805	−	0.482664i	$-0.839669\pi$
$59$	0.772001	−	5.36938i	0.100506	−	0.699034i	0.976311	−	0.216370i	$-0.0694218\pi$
$60$		0			0
$61$	1.16323	+	0.341555i	0.148936	+	0.0437317i	0.355351	−	0.934733i	$-0.384361\pi$
$61$	1.16323	+	0.341555i	0.148936	+	0.0437317i	−0.206415	+	0.978465i	$0.566180\pi$
$62$	−0.541647	−	3.76724i	−0.0687892	−	0.478440i
$63$		0			0
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	1.19282	−	1.37659i	0.147951	−	0.170745i
$66$		0			0
$67$	3.43987	+	7.53227i	0.420247	+	0.920214i	0.994810	+	0.101753i	$0.0324451\pi$
$67$	3.43987	+	7.53227i	0.420247	+	0.920214i	−0.574562	+	0.818461i	$0.694828\pi$
$68$	−5.94829			−0.721337
$69$		0			0
$70$	−8.22949			−0.983612
$71$	4.73522	+	10.3687i	0.561967	+	1.23054i	0.950965	+	0.309297i	$0.100094\pi$
$71$	4.73522	+	10.3687i	0.561967	+	1.23054i	−0.388999	+	0.921238i	$0.627179\pi$
$72$		0			0
$73$	−0.899010	+	1.03751i	−0.105221	+	0.121432i	−0.805917	−	0.592028i	$-0.798327\pi$
$73$	−0.899010	+	1.03751i	−0.105221	+	0.121432i	0.700696	+	0.713460i	$0.252873\pi$
$74$	−1.24724	−	0.801551i	−0.144988	−	0.0931784i
$75$		0			0
$76$	1.03248	+	7.18103i	0.118433	+	0.823720i
$77$	0.604243	+	0.177422i	0.0688598	+	0.0202191i
$78$		0			0
$79$	0.923393	−	6.42234i	0.103890	−	0.722570i	−0.869586	−	0.493781i	$-0.835614\pi$
$79$	0.923393	−	6.42234i	0.103890	−	0.722570i	0.973476	−	0.228789i	$-0.0734765\pi$
$80$	0.933743	−	2.04461i	0.104396	−	0.228595i
$81$		0			0
$82$	−1.35760	+	9.44233i	−0.149922	+	1.04273i
$83$	−5.16421	+	3.31884i	−0.566846	+	0.364290i	−0.792457	−	0.609928i	$-0.791198\pi$
$83$	−5.16421	+	3.31884i	−0.566846	+	0.364290i	0.225611	+	0.974217i	$0.427562\pi$
$84$		0			0
$85$	1.90278	+	13.2341i	0.206385	+	1.43544i
$86$	7.29513	+	8.41902i	0.786654	+	0.907847i
$87$		0			0
$88$	−0.112639	+	0.129993i	−0.0120074	+	0.0138573i
$89$	0.247460	−	0.0726609i	0.0262307	−	0.00770204i	−0.268591	−	0.963254i	$-0.586558\pi$
$89$	0.247460	−	0.0726609i	0.0262307	−	0.00770204i	0.294822	+	0.955552i	$0.404740\pi$
$90$		0			0
$91$	−2.96694			−0.311020
$92$	0.731881	+	4.73966i	0.0763039	+	0.494143i
$93$		0			0
$94$	−1.22596	−	2.68448i	−0.126448	−	0.276883i
$95$	15.6465	−	4.59422i	1.60529	−	0.471357i
$96$		0			0
$97$	11.7956	+	7.58058i	1.19766	+	0.769692i	0.978550	−	0.206008i	$-0.0660473\pi$
$97$	11.7956	+	7.58058i	1.19766	+	0.769692i	0.219113	+	0.975699i	$0.429684\pi$
$98$	4.19416	+	4.84031i	0.423674	+	0.488946i
$99$		0			0
$100$	−0.0501937	−	0.0147382i	−0.00501937	−	0.00147382i
$101$	−13.3691	+	8.59178i	−1.33027	+	0.854914i	−0.996154	−	0.0876174i	$-0.972075\pi$
$101$	−13.3691	+	8.59178i	−1.33027	+	0.854914i	−0.334118	+	0.942531i	$0.608438\pi$
$102$		0			0
$103$	−6.31668	+	13.8316i	−0.622401	+	1.36287i	0.291359	+	0.956614i	$0.405893\pi$
$103$	−6.31668	+	13.8316i	−0.622401	+	1.36287i	−0.913760	+	0.406255i	$0.866835\pi$
$104$	0.336638	−	0.737135i	0.0330101	−	0.0722821i
$105$		0			0
$106$	9.37038	−	6.02198i	0.910132	−	0.584906i
$107$	−8.79163	−	2.58145i	−0.849919	−	0.249559i	−0.172366	−	0.985033i	$-0.555141\pi$
$107$	−8.79163	−	2.58145i	−0.849919	−	0.249559i	−0.677553	+	0.735474i	$0.736959\pi$
$108$		0			0
$109$	−11.7808	−	13.5958i	−1.12840	−	1.30224i	−0.947865	−	0.318673i	$-0.896763\pi$
$109$	−11.7808	−	13.5958i	−1.12840	−	1.30224i	−0.180534	−	0.983569i	$-0.557783\pi$
$110$	0.325247	+	0.209024i	0.0310111	+	0.0199296i
$111$		0			0
$112$	−3.51293	+	1.03149i	−0.331941	+	0.0974666i
$113$	1.60456	+	3.51350i	0.150944	+	0.330522i	0.969966	−	0.243241i	$-0.0782105\pi$
$113$	1.60456	+	3.51350i	0.150944	+	0.330522i	−0.819022	+	0.573763i	$0.805483\pi$
$114$		0			0
$115$	10.3109	−	3.14448i	0.961500	−	0.293224i
$116$	0.830959			0.0771526
$117$		0			0
$118$	−5.20486	+	1.52829i	−0.479147	+	0.140690i
$119$	14.2616	−	16.4588i	1.30736	−	1.50878i
$120$		0			0
$121$	7.18409	+	8.29089i	0.653099	+	0.753717i
$122$	−0.172534	−	1.20000i	−0.0156205	−	0.108643i
$123$		0			0
$124$	−3.20179	+	2.05767i	−0.287529	+	0.184784i
$125$	1.58270	−	11.0079i	0.141561	−	0.984576i
$126$		0			0
$127$	−4.64692	+	10.1753i	−0.412348	+	0.902915i	0.583520	+	0.812099i	$0.301675\pi$
$127$	−4.64692	+	10.1753i	−0.412348	+	0.902915i	−0.995868	+	0.0908166i	$0.971052\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$		0			0
$130$	−1.74771	−	0.513173i	−0.153284	−	0.0450082i
$131$	1.05119	+	7.31121i	0.0918432	+	0.638784i	0.982797	+	0.184690i	$0.0591280\pi$
$131$	1.05119	+	7.31121i	0.0918432	+	0.638784i	−0.890954	+	0.454094i	$0.849963\pi$
$132$		0			0
$133$	−22.3452	−	14.3604i	−1.93757	−	1.24520i
$134$	5.42262	−	6.25804i	0.468443	−	0.540612i
$135$		0			0
$136$	2.47101	+	5.41076i	0.211887	+	0.463969i
$137$	−19.3270			−1.65122			−0.825608	−	0.564244i	$-0.809168\pi$
$137$	−19.3270			−1.65122			−0.825608	+	0.564244i	$0.809168\pi$
$138$		0			0
$139$	−7.09508			−0.601797			−0.300899	−	0.953656i	$-0.597287\pi$
$139$	−7.09508			−0.601797			−0.300899	+	0.953656i	$0.597287\pi$
$140$	3.41865	+	7.48581i	0.288929	+	0.632666i
$141$		0			0
$142$	7.46460	−	8.61461i	0.626415	−	0.722922i
$143$	0.117260	+	0.0753585i	0.00980578	+	0.00630179i
$144$		0			0
$145$	−0.265812	−	1.84876i	−0.0220745	−	0.153531i
$146$	1.31722	+	0.386770i	0.109014	+	0.0320093i
$147$		0			0
$148$	−0.210995	+	1.46750i	−0.0173437	+	0.120628i
$149$	−7.03151	+	15.3969i	−0.576044	+	1.26136i	0.367473	+	0.930034i	$0.380223\pi$
$149$	−7.03151	+	15.3969i	−0.576044	+	1.26136i	−0.943516	+	0.331326i	$0.892504\pi$
$150$		0			0
$151$	0.475127	−	3.30458i	0.0386653	−	0.268923i	−0.961313	−	0.275457i	$-0.911171\pi$
$151$	0.475127	−	3.30458i	0.0386653	−	0.268923i	0.999979	+	0.00653398i	$0.00207985\pi$
$152$	6.10318	−	3.92228i	0.495034	−	0.318139i
$153$		0			0
$154$	−0.0896231	−	0.623342i	−0.00722203	−	0.0502303i
$155$	5.60222	+	6.46531i	0.449981	+	0.519306i
$156$		0			0
$157$	6.70439	−	7.73727i	0.535068	−	0.617502i	−0.422270	−	0.906470i	$-0.638767\pi$
$157$	6.70439	−	7.73727i	0.535068	−	0.617502i	0.957339	+	0.288968i	$0.0933122\pi$
$158$	−6.22556	+	1.82799i	−0.495279	+	0.145427i
$159$		0			0
$160$	−2.24774			−0.177699
$161$	−14.8693	−	9.33870i	−1.17186	−	0.735993i
$162$		0			0
$163$	2.04389	+	4.47549i	0.160090	+	0.350547i	0.972631	−	0.232357i	$-0.0746437\pi$
$163$	2.04389	+	4.47549i	0.160090	+	0.350547i	−0.812541	+	0.582904i	$0.801916\pi$
$164$	9.15302	−	2.68757i	0.714730	−	0.209864i
$165$		0			0
$166$	5.16421	+	3.31884i	0.400820	+	0.257592i
$167$	−3.40628	−	3.93105i	−0.263586	−	0.304194i	0.608494	−	0.793559i	$-0.291774\pi$
$167$	−3.40628	−	3.93105i	−0.263586	−	0.304194i	−0.872079	+	0.489365i	$0.837229\pi$
$168$		0			0
$169$	11.8433	+	3.47751i	0.911024	+	0.267501i
$170$	11.2477	−	7.22847i	0.862661	−	0.554398i
$171$		0			0
$172$	4.62771	−	10.1333i	0.352859	−	0.772654i
$173$	−3.11907	+	6.82982i	−0.237139	+	0.519262i	−0.990362	−	0.138504i	$-0.955771\pi$
$173$	−3.11907	+	6.82982i	−0.237139	+	0.519262i	0.753223	+	0.657765i	$0.228498\pi$
$174$		0			0
$175$	0.161125	−	0.103549i	0.0121799	−	0.00782753i
$176$	0.165038	+	0.0484595i	0.0124402	+	0.00365277i
$177$		0			0
$178$	−0.168893	−	0.194913i	−0.0126591	−	0.0146094i
$179$	−9.54271	−	6.13273i	−0.713256	−	0.458382i	0.133029	−	0.991112i	$-0.457530\pi$
$179$	−9.54271	−	6.13273i	−0.713256	−	0.458382i	−0.846285	+	0.532731i	$0.821166\pi$
$180$		0			0
$181$	2.12362	−	0.623552i	0.157848	−	0.0463482i	−0.201854	−	0.979416i	$-0.564697\pi$
$181$	2.12362	−	0.623552i	0.157848	−	0.0463482i	0.359702	+	0.933067i	$0.382878\pi$
$182$	1.23251	+	2.69883i	0.0913599	+	0.200050i
$183$		0			0
$184$	4.00731	−	2.63467i	0.295423	−	0.194230i
$185$	3.33248			0.245009
$186$		0			0
$187$	−0.981694	+	0.288251i	−0.0717885	+	0.0210790i
$188$	−1.93261	+	2.23035i	−0.140950	+	0.162665i
$189$		0			0
$190$	−10.6788	−	12.3240i	−0.774724	−	0.894079i
$191$	−1.71248	−	11.9105i	−0.123911	−	0.861817i	−0.953058	−	0.302787i	$-0.902083\pi$
$191$	−1.71248	−	11.9105i	−0.123911	−	0.861817i	0.829148	−	0.559030i	$-0.188826\pi$
$192$		0			0
$193$	1.65077	−	1.06088i	0.118825	−	0.0763640i	−0.479878	−	0.877335i	$-0.659319\pi$
$193$	1.65077	−	1.06088i	0.118825	−	0.0763640i	0.598703	+	0.800971i	$0.295683\pi$
$194$	1.99546	−	13.8788i	0.143266	−	0.996437i
$195$		0			0
$196$	2.66059	−	5.82588i	0.190042	−	0.416134i
$197$	−3.70037	+	25.7366i	−0.263640	+	1.83366i	0.241237	+	0.970466i	$0.422447\pi$
$197$	−3.70037	+	25.7366i	−0.263640	+	1.83366i	−0.504877	+	0.863191i	$0.668462\pi$
$198$		0			0
$199$	9.40641	+	2.76197i	0.666803	+	0.195791i	0.597579	−	0.801810i	$-0.296130\pi$
$199$	9.40641	+	2.76197i	0.666803	+	0.195791i	0.0692239	+	0.997601i	$0.477948\pi$
$200$	0.00744487	+	0.0517802i	0.000526432	+	0.00366142i
$201$		0			0
$202$	13.3691	+	8.59178i	0.940644	+	0.604515i
$203$	−1.99231	+	2.29924i	−0.139833	+	0.161375i
$204$		0			0
$205$	−8.90737	−	19.5044i	−0.622118	−	1.36225i
$206$	15.2057			1.05943
$207$		0			0
$208$	−0.810367			−0.0561888
$209$	0.518386	+	1.13511i	0.0358575	+	0.0785170i
$210$		0			0
$211$	9.22914	−	10.6510i	0.635360	−	0.733245i	−0.343187	−	0.939267i	$-0.611506\pi$
$211$	9.22914	−	10.6510i	0.635360	−	0.733245i	0.978547	+	0.206022i	$0.0660519\pi$
$212$	−9.37038	−	6.02198i	−0.643561	−	0.413591i
$213$		0			0
$214$	1.30400	+	9.06952i	0.0891396	+	0.619980i
$215$	−24.0254	−	7.05450i	−1.63852	−	0.481113i
$216$		0			0
$217$	1.98310	−	13.7927i	0.134621	−	0.936313i
$218$	−7.47324	+	16.3641i	−0.506152	+	1.10832i
$219$		0			0
$220$	0.0550221	−	0.382687i	0.00370959	−	0.0258008i
$221$	4.05509	−	2.60605i	0.272775	−	0.175302i
$222$		0			0
$223$	−2.44895	−	17.0328i	−0.163994	−	1.14060i	−0.891011	−	0.453982i	$-0.850003\pi$
$223$	−2.44895	−	17.0328i	−0.163994	−	1.14060i	0.727017	−	0.686619i	$-0.240906\pi$
$224$	2.39760	+	2.76698i	0.160196	+	0.184876i
$225$		0			0
$226$	2.52943	−	2.91912i	0.168255	−	0.194177i
$227$	9.93021	−	2.91577i	0.659091	−	0.193527i	0.0649512	−	0.997888i	$-0.479311\pi$
$227$	9.93021	−	2.91577i	0.659091	−	0.193527i	0.594140	+	0.804362i	$0.297493\pi$
$228$		0			0
$229$	11.3156			0.747754			0.373877	−	0.927478i	$-0.378028\pi$
$229$	11.3156			0.747754			0.373877	+	0.927478i	$0.378028\pi$
$230$	−7.14364	−	8.07289i	−0.471038	−	0.532311i
$231$		0			0
$232$	−0.345193	−	0.755867i	−0.0226630	−	0.0496251i
$233$	−7.50313	+	2.20312i	−0.491546	+	0.144331i	−0.518106	−	0.855316i	$-0.673363\pi$
$233$	−7.50313	+	2.20312i	−0.491546	+	0.144331i	0.0265601	+	0.999647i	$0.491545\pi$
$234$		0			0
$235$	5.58042	+	3.58632i	0.364026	+	0.233946i
$236$	3.55236	+	4.09964i	0.231239	+	0.266864i
$237$		0			0
$238$	−20.8959	−	6.13560i	−1.35448	−	0.397712i
$239$	10.6554	−	6.84783i	0.689242	−	0.442949i	−0.148574	−	0.988901i	$-0.547468\pi$
$239$	10.6554	−	6.84783i	0.689242	−	0.442949i	0.837816	+	0.545952i	$0.183832\pi$
$240$		0			0
$241$	10.3533	−	22.6706i	0.666916	−	1.46034i	−0.209018	−	0.977912i	$-0.567027\pi$
$241$	10.3533	−	22.6706i	0.666916	−	1.46034i	0.875934	−	0.482431i	$-0.160246\pi$
$242$	4.55727	−	9.97904i	0.292953	−	0.641477i
$243$		0			0
$244$	−1.01988	+	0.655440i	−0.0652914	+	0.0419602i
$245$	−13.8128	−	4.05581i	−0.882469	−	0.259116i
$246$		0			0
$247$	−3.84999	−	4.44313i	−0.244969	−	0.282710i
$248$	3.20179	+	2.05767i	0.203314	+	0.130662i
$249$		0			0
$250$	−10.6706	+	3.13317i	−0.674868	+	0.198159i
$251$	−11.4987	−	25.1787i	−0.725793	−	1.58926i	−0.805604	−	0.592454i	$-0.798159\pi$
$251$	−11.4987	−	25.1787i	−0.725793	−	1.58926i	0.0798118	−	0.996810i	$-0.474568\pi$
$252$		0			0
$253$	0.350469	+	0.746756i	0.0220338	+	0.0469482i
$254$	11.1862			0.701886
$255$		0			0
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	19.2436	−	22.2083i	1.20039	−	1.38532i	0.297900	−	0.954597i	$-0.403714\pi$
$257$	19.2436	−	22.2083i	1.20039	−	1.38532i	0.902485	−	0.430721i	$-0.141741\pi$
$258$		0			0
$259$	−3.55467	−	4.10231i	−0.220876	−	0.254905i
$260$	0.259225	+	1.80295i	0.0160765	+	0.111814i
$261$		0			0
$262$	6.21383	−	3.99339i	0.383892	−	0.246712i
$263$	3.60919	−	25.1025i	0.222552	−	1.54788i	−0.505782	−	0.862661i	$-0.668796\pi$
$263$	3.60919	−	25.1025i	0.222552	−	1.54788i	0.728334	−	0.685222i	$-0.240295\pi$
$264$		0			0
$265$	−10.4006	+	22.7741i	−0.638903	+	1.39900i
$266$	−3.78014	+	26.2914i	−0.231775	+	1.61203i
$267$		0			0
$268$	−7.94515	−	2.33291i	−0.485327	−	0.142505i
$269$	3.00358	+	20.8904i	0.183132	+	1.27371i	0.849301	+	0.527909i	$0.177024\pi$
$269$	3.00358	+	20.8904i	0.183132	+	1.27371i	−0.666169	+	0.745801i	$0.732067\pi$
$270$		0			0
$271$	2.55617	+	1.64275i	0.155276	+	0.0997899i	0.615972	−	0.787768i	$-0.288764\pi$
$271$	2.55617	+	1.64275i	0.155276	+	0.0997899i	−0.460695	+	0.887558i	$0.652400\pi$
$272$	3.89530	−	4.49542i	0.236187	−	0.272575i
$273$		0			0
$274$	8.02872	+	17.5804i	0.485033	+	1.06207i
$275$	−0.00899806			−0.000542604
$276$		0			0
$277$	9.08699			0.545984			0.272992	−	0.962016i	$-0.411987\pi$
$277$	9.08699			0.545984			0.272992	+	0.962016i	$0.411987\pi$
$278$	2.94740	+	6.45392i	0.176774	+	0.387080i
$279$		0			0
$280$	5.38917	−	6.21943i	0.322064	−	0.371682i
$281$	9.58495	+	6.15987i	0.571790	+	0.367467i	0.794358	−	0.607450i	$-0.207808\pi$
$281$	9.58495	+	6.15987i	0.571790	+	0.367467i	−0.222568	+	0.974917i	$0.571444\pi$
$282$		0			0
$283$	−2.64841	−	18.4201i	−0.157432	−	1.09496i	−0.903344	−	0.428918i	$-0.858895\pi$
$283$	−2.64841	−	18.4201i	−0.157432	−	1.09496i	0.745912	−	0.666045i	$-0.232014\pi$
$284$	−10.9370	−	3.21140i	−0.648993	−	0.190562i
$285$		0			0
$286$	0.0198369	−	0.137969i	0.00117298	−	0.00815825i
$287$	−14.5088	+	31.7699i	−0.856429	+	1.87532i
$288$		0			0
$289$	−2.61606	+	18.1951i	−0.153886	+	1.07030i
$290$	−1.57127	+	1.00980i	−0.0922683	+	0.0592972i
$291$		0			0
$292$	−0.195374	−	1.35885i	−0.0114334	−	0.0795208i
$293$	12.3223	+	14.2207i	0.719876	+	0.830781i	0.991292	−	0.131681i	$-0.0420375\pi$
$293$	12.3223	+	14.2207i	0.719876	+	0.830781i	−0.271416	+	0.962462i	$0.587492\pi$
$294$		0			0
$295$	7.98476	−	9.21490i	0.464891	−	0.536512i
$296$	1.42254	−	0.417695i	0.0826834	−	0.0242780i
$297$		0			0
$298$	16.9265			0.980524
$299$	−2.57547	−	2.91049i	−0.148943	−	0.168318i
$300$		0			0
$301$	16.9431	+	37.1003i	0.976586	+	2.13843i
$302$	−3.20333	+	0.940583i	−0.184331	+	0.0541245i
$303$		0			0
$304$	−6.10318	−	3.92228i	−0.350042	−	0.224958i
$305$	1.78451	+	2.05943i	0.102181	+	0.117923i
$306$		0			0
$307$	−5.99711	−	1.76091i	−0.342273	−	0.100501i	0.106078	−	0.994358i	$-0.466171\pi$
$307$	−5.99711	−	1.76091i	−0.342273	−	0.100501i	−0.448352	+	0.893857i	$0.647989\pi$
$308$	−0.529781	+	0.340470i	−0.0301871	+	0.0194001i
$309$		0			0
$310$	3.55380	−	7.78174i	0.201842	−	0.441973i
$311$	−12.1745	+	26.6585i	−0.690355	+	1.51167i	0.160932	+	0.986965i	$0.448550\pi$
$311$	−12.1745	+	26.6585i	−0.690355	+	1.51167i	−0.851287	+	0.524700i	$0.824177\pi$
$312$		0			0
$313$	−17.3201	+	11.1310i	−0.978992	+	0.629160i	−0.929191	−	0.369599i	$-0.879495\pi$
$313$	−17.3201	+	11.1310i	−0.978992	+	0.629160i	−0.0498006	+	0.998759i	$0.515859\pi$
$314$	−9.82318	−	2.88434i	−0.554354	−	0.162773i
$315$		0			0
$316$	4.24899	+	4.90359i	0.239024	+	0.275849i
$317$	22.5901	+	14.5177i	1.26878	+	0.815398i	0.989461	−	0.144799i	$-0.0462537\pi$
$317$	22.5901	+	14.5177i	1.26878	+	0.815398i	0.279323	+	0.960197i	$0.409890\pi$
$318$		0			0
$319$	0.137140	−	0.0402678i	0.00767835	−	0.00225457i
$320$	0.933743	+	2.04461i	0.0521978	+	0.114297i
$321$		0			0
$322$	−2.31786	+	17.4050i	−0.129169	+	0.969944i
$323$	43.1541			2.40116
$324$		0			0
$325$	0.0406753	−	0.0119433i	0.00225626	−	0.000662497i
$326$	3.22199	−	3.71837i	0.178449	−	0.205941i
$327$		0			0
$328$	−6.24700	−	7.20942i	−0.344933	−	0.398074i
$329$	−1.53770	−	10.6950i	−0.0847764	−	0.589633i
$330$		0			0
$331$	−4.31546	+	2.77338i	−0.237199	+	0.152439i	−0.653841	−	0.756632i	$-0.726843\pi$
$331$	−4.31546	+	2.77338i	−0.237199	+	0.152439i	0.416642	+	0.909071i	$0.363207\pi$
$332$	0.873629	−	6.07623i	0.0479466	−	0.333476i
$333$		0			0
$334$	−2.16079	+	4.73148i	−0.118233	+	0.258895i
$335$	−2.64884	+	18.4231i	−0.144722	+	1.00656i
$336$		0			0
$337$	−16.9294	−	4.97091i	−0.922202	−	0.270783i	−0.214033	−	0.976826i	$-0.568660\pi$
$337$	−16.9294	−	4.97091i	−0.922202	−	0.270783i	−0.708169	+	0.706043i	$0.750478\pi$
$338$	−1.75664	−	12.2177i	−0.0955484	−	0.664554i
$339$		0			0
$340$	−11.2477	−	7.22847i	−0.609993	−	0.392019i
$341$	−0.428703	+	0.494750i	−0.0232156	+	0.0267922i
$342$		0			0
$343$	−0.905481	−	1.98273i	−0.0488914	−	0.107057i
$344$	−11.1400			−0.600627
$345$		0			0
$346$	7.50833			0.403650
$347$	3.08407	+	6.75318i	0.165562	+	0.362530i	0.974169	−	0.225819i	$-0.0725057\pi$
$347$	3.08407	+	6.75318i	0.165562	+	0.362530i	−0.808608	+	0.588348i	$0.799778\pi$
$348$		0			0
$349$	−22.7497	+	26.2546i	−1.21777	+	1.40538i	−0.330697	+	0.943737i	$0.607284\pi$
$349$	−22.7497	+	26.2546i	−1.21777	+	1.40538i	−0.887068	+	0.461639i	$0.847262\pi$
$350$	−0.161125	−	0.103549i	−0.00861247	−	0.00553490i
$351$		0			0
$352$	−0.0244789	−	0.170255i	−0.00130473	−	0.00907460i
$353$	−29.1384	−	8.55579i	−1.55088	−	0.455379i	−0.609515	−	0.792775i	$-0.708636\pi$
$353$	−29.1384	−	8.55579i	−1.55088	−	0.455379i	−0.941363	+	0.337396i	$0.890454\pi$
$354$		0			0
$355$	−3.64630	+	25.3606i	−0.193526	+	1.34600i
$356$	−0.107139	+	0.234601i	−0.00567833	+	0.0124338i
$357$		0			0
$358$	−1.61434	+	11.2280i	−0.0853205	+	0.593417i
$359$	−0.304549	+	0.195721i	−0.0160735	+	0.0103298i	−0.548653	−	0.836050i	$-0.684859\pi$
$359$	−0.304549	+	0.195721i	−0.0160735	+	0.0103298i	0.532579	+	0.846380i	$0.321223\pi$
$360$		0			0
$361$	−4.78649	−	33.2908i	−0.251921	−	1.75215i
$362$	−1.44939	−	1.67268i	−0.0761781	−	0.0879142i
$363$		0			0
$364$	1.94294	−	2.24227i	0.101837	−	0.117527i
$365$	−2.96075	+	0.869356i	−0.154973	+	0.0455042i
$366$		0			0
$367$	−14.3131			−0.747140			−0.373570	−	0.927602i	$-0.621866\pi$
$367$	−14.3131			−0.747140			−0.373570	+	0.927602i	$0.621866\pi$
$368$	−4.06127	−	2.55070i	−0.211709	−	0.132964i
$369$		0			0
$370$	−1.38436	−	3.03133i	−0.0719696	−	0.157591i
$371$	39.1291	−	11.4893i	2.03148	−	0.596497i
$372$		0			0
$373$	−11.8049	−	7.58653i	−0.611233	−	0.392815i	0.198086	−	0.980185i	$-0.436527\pi$
$373$	−11.8049	−	7.58653i	−0.611233	−	0.392815i	−0.809319	+	0.587369i	$0.800164\pi$
$374$	0.670013	+	0.773236i	0.0346455	+	0.0399831i
$375$		0			0
$376$	2.83163	+	0.831442i	0.146030	+	0.0428783i
$377$	−0.566484	+	0.364057i	−0.0291754	+	0.0187499i
$378$		0			0
$379$	−11.3797	+	24.9181i	−0.584538	+	1.27996i	0.354149	+	0.935189i	$0.384770\pi$
$379$	−11.3797	+	24.9181i	−0.584538	+	1.27996i	−0.938687	+	0.344770i	$0.887957\pi$
$380$	−6.77418	+	14.8334i	−0.347508	+	0.760937i
$381$		0			0
$382$	−10.1228	+	6.50554i	−0.517929	+	0.332853i
$383$	−1.31449	−	0.385968i	−0.0671671	−	0.0197221i	0.247976	−	0.968766i	$-0.420234\pi$
$383$	−1.31449	−	0.385968i	−0.0671671	−	0.0197221i	−0.315143	+	0.949044i	$0.602053\pi$
$384$		0			0
$385$	0.926966	+	1.06978i	0.0472425	+	0.0545208i
$386$	−1.65077	−	1.06088i	−0.0840218	−	0.0539975i
$387$		0			0
$388$	−13.4535	+	3.95031i	−0.682998	+	0.200546i
$389$	4.24544	+	9.29621i	0.215252	+	0.471337i	0.986199	−	0.165563i	$-0.0529440\pi$
$389$	4.24544	+	9.29621i	0.215252	+	0.471337i	−0.770947	+	0.636899i	$0.780217\pi$
$390$		0			0
$391$	28.5255	−	0.296866i	1.44259	−	0.0150132i
$392$	−6.40465			−0.323484
$393$		0			0
$394$	24.9480	−	7.32540i	1.25686	−	0.369049i
$395$	9.55060	−	11.0220i	0.480543	−	0.554576i
$396$		0			0
$397$	20.2955	+	23.4222i	1.01860	+	1.17553i	0.984370	+	0.176114i	$0.0563527\pi$
$397$	20.2955	+	23.4222i	1.01860	+	1.17553i	0.0342308	+	0.999414i	$0.489102\pi$
$398$	−1.39519	−	9.70373i	−0.0699344	−	0.486404i
$399$		0			0
$400$	0.0440082	−	0.0282824i	0.00220041	−	0.00141412i
$401$	5.22378	−	36.3322i	0.260863	−	1.81434i	−0.265532	−	0.964102i	$-0.585547\pi$
$401$	5.22378	−	36.3322i	0.260863	−	1.81434i	0.526395	−	0.850240i	$-0.323543\pi$
$402$		0			0
$403$	1.28124	−	2.80552i	0.0638230	−	0.139753i
$404$	2.26164	−	15.7301i	0.112521	−	0.782601i
$405$		0			0
$406$	2.91910	+	0.857125i	0.144873	+	0.0425384i
$407$	0.0362923	+	0.252418i	0.00179894	+	0.0125119i
$408$		0			0
$409$	5.98220	+	3.84453i	0.295801	+	0.190100i	0.680120	−	0.733100i	$-0.261927\pi$
$409$	5.98220	+	3.84453i	0.295801	+	0.190100i	−0.384319	+	0.923200i	$0.625564\pi$
$410$	−14.0416	+	16.2049i	−0.693465	+	0.800301i
$411$		0			0
$412$	−6.31668	−	13.8316i	−0.311201	−	0.681434i
$413$	−19.8607			−0.977283
$414$		0			0
$415$	−13.7982			−0.677327
$416$	0.336638	+	0.737135i	0.0165051	+	0.0361410i
$417$		0			0
$418$	0.817185	−	0.943082i	0.0399698	−	0.0461276i
$419$	−15.6146	−	10.0349i	−0.762824	−	0.490237i	0.100469	−	0.994940i	$-0.467966\pi$
$419$	−15.6146	−	10.0349i	−0.762824	−	0.490237i	−0.863293	+	0.504703i	$0.831602\pi$
$420$		0			0
$421$	0.959724	+	6.67503i	0.0467741	+	0.325321i	0.999752	+	0.0222805i	$0.00709267\pi$
$421$	0.959724	+	6.67503i	0.0467741	+	0.325321i	−0.952978	+	0.303041i	$0.901998\pi$
$422$	−13.5224	−	3.97054i	−0.658261	−	0.193283i
$423$		0			0
$424$	−1.58519	+	11.0252i	−0.0769835	+	0.535432i
$425$	−0.129265	+	0.283051i	−0.00627029	+	0.0137300i
$426$		0			0
$427$	0.631687	−	4.39348i	0.0305695	−	0.212615i
$428$	7.70823	−	4.95378i	0.372591	−	0.239450i
$429$		0			0
$430$	3.56352	+	24.7848i	0.171848	+	1.19523i
$431$	−6.60168	−	7.61875i	−0.317992	−	0.366982i	0.574140	−	0.818757i	$-0.305336\pi$
$431$	−6.60168	−	7.61875i	−0.317992	−	0.366982i	−0.892132	+	0.451775i	$0.850791\pi$
$432$		0			0
$433$	−18.6027	+	21.4687i	−0.893989	+	1.03172i	0.105315	+	0.994439i	$0.466415\pi$
$433$	−18.6027	+	21.4687i	−0.893989	+	1.03172i	−0.999305	+	0.0372799i	$0.988131\pi$
$434$	−13.3701	+	3.92583i	−0.641787	+	0.188446i
$435$		0			0
$436$	17.9898			0.861557
$437$	−5.30970	−	34.3856i	−0.253997	−	1.64489i
$438$		0			0
$439$	13.2770	+	29.0726i	0.633678	+	1.38756i	0.905141	+	0.425112i	$0.139765\pi$
$439$	13.2770	+	29.0726i	0.633678	+	1.38756i	−0.271463	+	0.962449i	$0.587507\pi$
$440$	−0.370961	+	0.108924i	−0.0176849	+	0.00519275i
$441$		0			0
$442$	−4.05509	−	2.60605i	−0.192881	−	0.123957i
$443$	21.7557	+	25.1074i	1.03365	+	1.19289i	0.980946	+	0.194280i	$0.0622370\pi$
$443$	21.7557	+	25.1074i	1.03365	+	1.19289i	0.0526993	+	0.998610i	$0.483218\pi$
$444$		0			0
$445$	0.556225	+	0.163322i	0.0263676	+	0.00774223i
$446$	−14.4763	+	9.30333i	−0.685471	+	0.440525i
$447$		0			0
$448$	1.52093	−	3.33038i	0.0718573	−	0.157346i
$449$	9.53323	−	20.8749i	0.449901	−	0.985146i	−0.539773	−	0.841810i	$-0.681490\pi$
$449$	9.53323	−	20.8749i	0.449901	−	0.985146i	0.989674	−	0.143335i	$-0.0457827\pi$
$450$		0			0
$451$	1.38036	−	0.887101i	0.0649984	−	0.0417719i
$452$	−3.70609	−	1.08821i	−0.174320	−	0.0511849i
$453$		0			0
$454$	−6.77744	−	7.82158i	−0.318081	−	0.367085i
$455$	−5.61024	−	3.60548i	−0.263012	−	0.169028i
$456$		0			0
$457$	30.8454	−	9.05701i	1.44288	−	0.423669i	0.535703	−	0.844407i	$-0.320047\pi$
$457$	30.8454	−	9.05701i	1.44288	−	0.423669i	0.907182	+	0.420738i	$0.138229\pi$
$458$	−4.70066	−	10.2930i	−0.219647	−	0.480960i
$459$		0			0
$460$	−4.37579	+	9.85168i	−0.204022	+	0.459337i
$461$	13.4524			0.626541			0.313271	−	0.949664i	$-0.398575\pi$
$461$	13.4524			0.626541			0.313271	+	0.949664i	$0.398575\pi$
$462$		0			0
$463$	−34.0446	+	9.99639i	−1.58219	+	0.464572i	−0.950518	−	0.310668i	$-0.899447\pi$
$463$	−34.0446	+	9.99639i	−1.58219	+	0.464572i	−0.631667	+	0.775240i	$0.717629\pi$
$464$	−0.544162	+	0.627997i	−0.0252621	+	0.0291540i
$465$		0			0
$466$	5.12094	+	5.90988i	0.237223	+	0.273770i
$467$	4.07403	+	28.3355i	0.188524	+	1.31121i	0.835833	+	0.548984i	$0.184985\pi$
$467$	4.07403	+	28.3355i	0.188524	+	1.31121i	−0.647309	+	0.762227i	$0.724106\pi$
$468$		0			0
$469$	25.5044	−	16.3907i	1.17768	−	0.756851i
$470$	0.944039	−	6.56594i	0.0435453	−	0.302864i
$471$		0			0
$472$	2.25346	−	4.93439i	0.103724	−	0.227124i
$473$	0.272694	−	1.89663i	0.0125385	−	0.0872071i
$474$		0			0
$475$	0.364149	+	0.106924i	0.0167083	+	0.00490599i
$476$	3.09935	+	21.5564i	0.142058	+	0.988038i
$477$		0			0
$478$	−10.6554	−	6.84783i	−0.487368	−	0.313212i
$479$	11.6572	−	13.4531i	0.532630	−	0.614688i	−0.424118	−	0.905607i	$-0.639416\pi$
$479$	11.6572	−	13.4531i	0.532630	−	0.614688i	0.956748	+	0.290919i	$0.0939611\pi$
$480$		0			0
$481$	−0.499098	−	1.09287i	−0.0227569	−	0.0498307i
$482$	−24.9228			−1.13520
$483$		0			0
$484$	−10.9704			−0.498655
$485$	13.0925	+	28.6685i	0.594498	+	1.30177i
$486$		0			0
$487$	16.1521	−	18.6405i	0.731922	−	0.844683i	−0.260764	−	0.965402i	$-0.583975\pi$
$487$	16.1521	−	18.6405i	0.731922	−	0.844683i	0.992687	+	0.120719i	$0.0385200\pi$
$488$	1.01988	+	0.655440i	0.0461680	+	0.0296704i
$489$		0			0
$490$	2.04876	+	14.2494i	0.0925535	+	0.643724i
$491$	−2.13665	−	0.627376i	−0.0964255	−	0.0283131i	0.233164	−	0.972437i	$-0.425092\pi$
$491$	−2.13665	−	0.627376i	−0.0964255	−	0.0283131i	−0.329589	+	0.944124i	$0.606910\pi$
$492$		0			0
$493$	0.703432	−	4.89248i	0.0316810	−	0.220346i
$494$	−2.44227	+	5.34782i	−0.109883	+	0.240610i
$495$		0			0
$496$	0.541647	−	3.76724i	0.0243207	−	0.169154i
$497$	35.1085	−	22.5629i	1.57483	−	1.01208i
$498$		0			0
$499$	−3.43819	−	23.9131i	−0.153914	−	1.07050i	−0.909577	−	0.415536i	$-0.863594\pi$
$499$	−3.43819	−	23.9131i	−0.153914	−	1.07050i	0.755662	−	0.654962i	$-0.227315\pi$
$500$	7.28277	+	8.40476i	0.325695	+	0.375872i
$501$		0			0
$502$	−18.1266	+	20.9192i	−0.809029	+	0.933670i
$503$	−38.2451	+	11.2298i	−1.70526	+	0.500711i	−0.981843	−	0.189696i	$-0.939250\pi$
$503$	−38.2451	+	11.2298i	−1.70526	+	0.500711i	−0.723421	+	0.690407i	$0.757431\pi$
$504$		0			0
$505$	−35.7206			−1.58955
$506$	0.533683	−	0.629012i	0.0237251	−	0.0279630i
$507$		0			0
$508$	−4.64692	−	10.1753i	−0.206174	−	0.451458i
$509$	27.4647	−	8.06437i	1.21735	−	0.357447i	0.390889	−	0.920438i	$-0.372168\pi$
$509$	27.4647	−	8.06437i	1.21735	−	0.357447i	0.826463	+	0.562991i	$0.190349\pi$
$510$		0			0
$511$	4.22834	+	2.71739i	0.187051	+	0.120210i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$		0			0
$514$	−28.1955	−	8.27895i	−1.24365	−	0.365169i
$515$	−28.7527	+	18.4782i	−1.26700	+	0.814249i
$516$		0			0
$517$	−0.210872	+	0.461745i	−0.00927414	+	0.0203075i
$518$	−2.25493	+	4.93760i	−0.0990758	+	0.216946i
$519$		0			0
$520$	1.53233	−	0.984772i	0.0671973	−	0.0431851i
$521$	−25.9230	−	7.61167i	−1.13571	−	0.333473i	−0.340758	−	0.940151i	$-0.610684\pi$
$521$	−25.9230	−	7.61167i	−1.13571	−	0.333473i	−0.794948	+	0.606678i	$0.792502\pi$
$522$		0			0
$523$	−8.53544	−	9.85043i	−0.373229	−	0.430729i	0.537799	−	0.843073i	$-0.319256\pi$
$523$	−8.53544	−	9.85043i	−0.373229	−	0.430729i	−0.911028	+	0.412344i	$0.864710\pi$
$524$	−6.21383	−	3.99339i	−0.271453	−	0.174452i
$525$		0			0
$526$	−24.3333	+	7.14490i	−1.06098	+	0.311533i
$527$	9.40461	+	20.5932i	0.409671	+	0.897055i
$528$		0			0
$529$	−3.74633	−	22.6928i	−0.162884	−	0.986645i
$530$	25.0366			1.08752
$531$		0			0
$532$	25.4859	−	7.48332i	1.10495	−	0.324443i
$533$	−5.06236	+	5.84227i	−0.219275	+	0.253057i
$534$		0			0
$535$	−13.4872	−	15.5650i	−0.583102	−	0.672936i
$536$	1.17845	+	8.19629i	0.0509012	+	0.354026i
$537$		0			0
$538$	17.7548	−	11.4103i	0.765465	−	0.491935i
$539$	0.156779	−	1.09042i	0.00675294	−	0.0469678i
$540$		0			0
$541$	3.45592	−	7.56740i	0.148582	−	0.325348i	−0.820677	−	0.571392i	$-0.806404\pi$
$541$	3.45592	−	7.56740i	0.148582	−	0.325348i	0.969259	+	0.246044i	$0.0791308\pi$
$542$	0.432427	−	3.00759i	0.0185743	−	0.129187i
$543$		0			0
$544$	−5.70735	−	1.67583i	−0.244700	−	0.0718505i
$545$	−5.75470	−	40.0248i	−0.246504	−	1.71447i
$546$		0			0
$547$	31.3934	+	20.1753i	1.34228	+	0.862633i	0.997115	−	0.0759079i	$-0.0241855\pi$
$547$	31.3934	+	20.1753i	1.34228	+	0.862633i	0.345168	+	0.938541i	$0.387822\pi$
$548$	12.6565	−	14.6064i	0.540658	−	0.623953i
$549$		0			0
$550$	0.00373793	+	0.00818492i	0.000159386	+	0.000349006i
$551$	−6.02850			−0.256823
$552$		0			0
$553$	−23.7555			−1.01019
$554$	−3.77487	−	8.26581i	−0.160379	−	0.351181i
$555$		0			0
$556$	4.64629	−	5.36211i	0.197047	−	0.227404i
$557$	4.55083	+	2.92464i	0.192825	+	0.123921i	0.633491	−	0.773750i	$-0.281621\pi$
$557$	4.55083	+	2.92464i	0.192825	+	0.123921i	−0.440666	+	0.897671i	$0.645258\pi$
$558$		0			0
$559$	1.28474	+	8.93557i	0.0543387	+	0.377934i
$560$	−7.89614	−	2.31852i	−0.333673	−	0.0979751i
$561$		0			0
$562$	1.62149	−	11.2777i	0.0683982	−	0.475720i
$563$	−8.85831	+	19.3970i	−0.373333	+	0.817486i	0.625958	+	0.779856i	$0.284708\pi$
$563$	−8.85831	+	19.3970i	−0.373333	+	0.817486i	−0.999292	+	0.0376295i	$0.988019\pi$
$564$		0			0
$565$	−1.23558	+	8.59362i	−0.0519811	+	0.361536i
$566$	−15.6553	+	10.0611i	−0.658043	+	0.422899i
$567$		0			0
$568$	1.62221	+	11.2827i	0.0680665	+	0.473413i
$569$	20.8748	+	24.0908i	0.875117	+	1.00994i	0.999843	+	0.0177474i	$0.00564947\pi$
$569$	20.8748	+	24.0908i	0.875117	+	1.00994i	−0.124726	+	0.992191i	$0.539805\pi$
$570$		0			0
$571$	11.2363	−	12.9674i	0.470225	−	0.542669i	−0.470249	−	0.882534i	$-0.655836\pi$
$571$	11.2363	−	12.9674i	0.470225	−	0.542669i	0.940474	+	0.339865i	$0.110381\pi$
$572$	−0.133741	+	0.0392699i	−0.00559200	+	0.00164196i
$573$		0			0
$574$	34.9261			1.45779
$575$	0.241443	+	0.0681730i	0.0100689	+	0.00284301i
$576$		0			0
$577$	−8.17218	−	17.8946i	−0.340212	−	0.744961i	0.659766	−	0.751471i	$-0.270655\pi$
$577$	−8.17218	−	17.8946i	−0.340212	−	0.744961i	−0.999979	+	0.00650954i	$0.997928\pi$
$578$	17.6376	−	5.17886i	0.733627	−	0.215412i
$579$		0			0
$580$	1.57127	+	1.00980i	0.0652435	+	0.0419295i
$581$	14.7182	+	16.9857i	0.610613	+	0.704684i
$582$		0			0
$583$	−1.83829	−	0.539771i	−0.0761342	−	0.0223550i
$584$	−1.15489	+	0.742206i	−0.0477899	+	0.0307127i
$585$		0			0
$586$	7.81672	−	17.1162i	0.322906	−	0.707065i
$587$	8.07980	−	17.6923i	0.333489	−	0.730239i	−0.666393	−	0.745601i	$-0.732163\pi$
$587$	8.07980	−	17.6923i	0.333489	−	0.730239i	0.999882	+	0.0153618i	$0.00489001\pi$
$588$		0			0
$589$	23.2286	−	14.9281i	0.957117	−	0.615102i
$590$	−11.6992	−	3.43518i	−0.481647	−	0.141424i
$591$		0			0
$592$	−0.970893	−	1.12047i	−0.0399035	−	0.0460511i
$593$	0.515015	+	0.330980i	0.0211491	+	0.0135917i	0.551173	−	0.834391i	$-0.314181\pi$
$593$	0.515015	+	0.330980i	0.0211491	+	0.0135917i	−0.530024	+	0.847983i	$0.677817\pi$
$594$		0			0
$595$	46.9685	−	13.7912i	1.92552	−	0.565384i
$596$	−7.03151	−	15.3969i	−0.288022	−	0.630680i
$597$		0			0
$598$	−1.57759	+	3.55179i	−0.0645123	+	0.145243i
$599$	31.3057			1.27911			0.639557	−	0.768744i	$-0.279118\pi$
$599$	31.3057			1.27911			0.639557	+	0.768744i	$0.279118\pi$
$600$		0			0
$601$	30.2101	−	8.87050i	1.23230	−	0.361835i	0.400181	−	0.916436i	$-0.368947\pi$
$601$	30.2101	−	8.87050i	1.23230	−	0.361835i	0.832116	+	0.554601i	$0.187129\pi$
$602$	26.7092	−	30.8240i	1.08858	−	1.25629i
$603$		0			0
$604$	2.18630	+	2.52312i	0.0889591	+	0.102664i
$605$	3.50928	+	24.4076i	0.142673	+	0.992310i
$606$		0			0
$607$	−11.5553	+	7.42616i	−0.469016	+	0.301418i	−0.753718	−	0.657198i	$-0.771742\pi$
$607$	−11.5553	+	7.42616i	−0.469016	+	0.301418i	0.284702	+	0.958616i	$0.408105\pi$
$608$	−1.03248	+	7.18103i	−0.0418724	+	0.291229i
$609$		0			0
$610$	1.13201	−	2.47876i	0.0458339	−	0.100362i
$611$	0.340351	−	2.36719i	0.0137691	−	0.0957663i
$612$		0			0
$613$	5.19366	+	1.52500i	0.209770	+	0.0615941i	0.384929	−	0.922946i	$-0.374226\pi$
$613$	5.19366	+	1.52500i	0.209770	+	0.0615941i	−0.175159	+	0.984540i	$0.556044\pi$
$614$	0.889510	+	6.18668i	0.0358977	+	0.249674i
$615$		0			0
$616$	0.529781	+	0.340470i	0.0213455	+	0.0137179i
$617$	−1.22788	+	1.41705i	−0.0494326	+	0.0570482i	−0.779927	−	0.625870i	$-0.784744\pi$
$617$	−1.22788	+	1.41705i	−0.0494326	+	0.0570482i	0.730495	+	0.682918i	$0.239289\pi$
$618$		0			0
$619$	−7.38515	−	16.1712i	−0.296834	−	0.649976i	0.701179	−	0.712986i	$-0.252658\pi$
$619$	−7.38515	−	16.1712i	−0.296834	−	0.649976i	−0.998013	+	0.0630092i	$0.979930\pi$
$620$	−8.55483			−0.343570
$621$		0			0
$622$	29.3069			1.17510
$623$	−0.392260	−	0.858929i	−0.0157156	−	0.0344123i
$624$		0			0
$625$	16.5410	−	19.0893i	0.661641	−	0.763574i
$626$	17.3201	+	11.1310i	0.692252	+	0.444883i
$627$		0			0
$628$	1.45700	+	10.1337i	0.0581407	+	0.404378i
$629$	8.46168	+	2.48457i	0.337389	+	0.0990664i
$630$		0			0
$631$	−3.91809	+	27.2509i	−0.155977	+	1.08484i	0.749976	+	0.661465i	$0.230065\pi$
$631$	−3.91809	+	27.2509i	−0.155977	+	1.08484i	−0.905953	+	0.423378i	$0.860844\pi$
$632$	2.69537	−	5.90204i	0.107216	−	0.234771i
$633$		0			0
$634$	3.82156	−	26.5795i	0.151773	−	1.05561i
$635$	−21.1522	+	13.5937i	−0.839399	+	0.539449i
$636$		0			0
$637$	0.738631	+	5.13729i	0.0292656	+	0.203547i
$638$	−0.0935988	−	0.108019i	−0.00370561	−	0.00427650i
$639$		0			0
$640$	1.47195	−	1.69872i	0.0581841	−	0.0671480i
$641$	−2.58734	+	0.759713i	−0.102194	+	0.0300068i	−0.332430	−	0.943128i	$-0.607868\pi$
$641$	−2.58734	+	0.759713i	−0.102194	+	0.0300068i	0.230236	+	0.973135i	$0.426050\pi$
$642$		0			0
$643$	−31.0307			−1.22373			−0.611865	−	0.790962i	$-0.709580\pi$
$643$	−31.0307			−1.22373			−0.611865	+	0.790962i	$0.709580\pi$
$644$	16.7950	−	5.12191i	0.661817	−	0.201831i
$645$		0			0
$646$	−17.9269	−	39.2543i	−0.705323	−	1.54444i
$647$	−33.0478	+	9.70371i	−1.29924	+	0.381492i	−0.856960	−	0.515383i	$-0.827650\pi$
$647$	−33.0478	+	9.70371i	−1.29924	+	0.381492i	−0.442283	+	0.896875i	$0.645831\pi$
$648$		0			0
$649$	0.784940	+	0.504450i	0.0308116	+	0.0198014i
$650$	−0.0277612	−	0.0320381i	−0.00108888	−	0.00125664i
$651$		0			0
$652$	−4.72081	−	1.38615i	−0.184881	−	0.0542860i
$653$	3.17768	−	2.04217i	0.124352	−	0.0799164i	−0.476986	−	0.878911i	$-0.658271\pi$
$653$	3.17768	−	2.04217i	0.124352	−	0.0799164i	0.601338	+	0.798994i	$0.294634\pi$
$654$		0			0
$655$	−6.89700	+	15.1023i	−0.269488	+	0.590096i
$656$	−3.96282	+	8.67737i	−0.154722	+	0.338794i
$657$		0			0
$658$	−9.08970	+	5.84160i	−0.354353	+	0.227729i
$659$	−31.5721	−	9.27039i	−1.22987	−	0.361123i	−0.398671	−	0.917094i	$-0.630528\pi$
$659$	−31.5721	−	9.27039i	−1.22987	−	0.361123i	−0.831202	+	0.555971i	$0.812347\pi$
$660$		0			0
$661$	7.52324	+	8.68228i	0.292620	+	0.337702i	0.882956	−	0.469456i	$-0.155550\pi$
$661$	7.52324	+	8.68228i	0.292620	+	0.337702i	−0.590336	+	0.807158i	$0.701005\pi$
$662$	4.31546	+	2.77338i	0.167725	+	0.107790i
$663$		0			0
$664$	−5.89005	+	1.72947i	−0.228578	+	0.0671166i
$665$	−24.8019	−	54.3086i	−0.961776	−	2.10600i
$666$		0			0
$667$	−3.98492	+	0.0414714i	−0.154297	+	0.00160578i
$668$	5.20153			0.201253
$669$		0			0
$670$	17.8586	−	5.24376i	0.689938	−	0.202584i
$671$	−0.136557	+	0.157595i	−0.00527173	+	0.00608390i
$672$		0			0
$673$	1.94268	+	2.24198i	0.0748849	+	0.0864218i	0.791956	−	0.610579i	$-0.209063\pi$
$673$	1.94268	+	2.24198i	0.0748849	+	0.0864218i	−0.717071	+	0.697000i	$0.754518\pi$
$674$	2.51102	+	17.4645i	0.0967207	+	0.672707i
$675$		0			0
$676$	−10.3838	+	6.67330i	−0.399379	+	0.256665i
$677$	−2.02768	+	14.1028i	−0.0779301	+	0.542016i	0.913033	+	0.407885i	$0.133733\pi$
$677$	−2.02768	+	14.1028i	−0.0779301	+	0.542016i	−0.990964	+	0.134131i	$0.957176\pi$
$678$		0			0
$679$	21.3257	−	46.6968i	0.818406	−	1.79206i
$680$	−1.90278	+	13.2341i	−0.0729681	+	0.507505i
$681$		0			0
$682$	0.628130	+	0.184436i	0.0240523	+	0.00706241i
$683$	2.14155	+	14.8948i	0.0819440	+	0.569933i	0.988886	+	0.148677i	$0.0475015\pi$
$683$	2.14155	+	14.8948i	0.0819440	+	0.569933i	−0.906942	+	0.421256i	$0.861589\pi$
$684$		0			0
$685$	−36.5457	−	23.4865i	−1.39634	−	0.897373i
$686$	−1.42740	+	1.64731i	−0.0544985	+	0.0628946i
$687$		0			0
$688$	4.62771	+	10.1333i	0.176430	+	0.386327i
$689$	9.02635			0.343876
$690$		0			0
$691$	8.92778			0.339629			0.169814	−	0.985476i	$-0.445683\pi$
$691$	8.92778			0.339629			0.169814	+	0.985476i	$0.445683\pi$
$692$	−3.11907	−	6.82982i	−0.118569	−	0.259631i
$693$		0			0
$694$	4.86174	−	5.61075i	0.184549	−	0.212981i
$695$	−13.4162	−	8.62207i	−0.508906	−	0.327054i
$696$		0			0
$697$	−8.07542	−	56.1658i	−0.305878	−	2.12743i
$698$	33.3326	+	9.78733i	1.26166	+	0.370456i
$699$		0			0
$700$	−0.0272574	+	0.189580i	−0.00103023	+	0.00716544i
$701$	9.09827	−	19.9224i	0.343637	−	0.752460i	−0.656361	−	0.754447i	$-0.727905\pi$
$701$	9.09827	−	19.9224i	0.343637	−	0.752460i	0.999998	+	0.00198703i	$0.000632493\pi$
$702$		0			0
$703$	1.53074	−	10.6466i	0.0577331	−	0.401542i
$704$	−0.144700	+	0.0929931i	−0.00545359	+	0.00350481i
$705$		0			0
$706$	4.32189	+	30.0594i	0.162656	+	1.13130i
$707$	38.1023	+	43.9724i	1.43298	+	1.65375i
$708$		0			0
$709$	−16.3923	+	18.9178i	−0.615627	+	0.710472i	−0.974871	−	0.222772i	$-0.928489\pi$
$709$	−16.3923	+	18.9178i	−0.615627	+	0.710472i	0.359243	+	0.933244i	$0.383035\pi$
$710$	24.5835	−	7.21838i	0.922604	−	0.270901i
$711$		0			0
$712$	0.257907			0.00966549
$713$	15.2517	−	10.0275i	0.571182	−	0.375532i
$714$		0			0
$715$	0.130152	+	0.284993i	0.00486741	+	0.0106581i
$716$	10.8840	−	3.19582i	0.406752	−	0.119433i
$717$		0			0
$718$	0.304549	+	0.195721i	0.0113656	+	0.00730426i
$719$	1.52209	+	1.75659i	0.0567645	+	0.0655097i	0.783422	−	0.621491i	$-0.213473\pi$
$719$	1.52209	+	1.75659i	0.0567645	+	0.0655097i	−0.726657	+	0.687000i	$0.758927\pi$
$720$		0			0
$721$	53.4166	+	15.6845i	1.98934	+	0.584123i
$722$	−28.2940	+	18.1834i	−1.05299	+	0.676718i
$723$		0			0
$724$	−0.919428	+	2.01327i	−0.0341703	+	0.0748225i
$725$	0.0180580	−	0.0395414i	0.000670656	−	0.00146853i
$726$		0			0
$727$	−9.49184	+	6.10004i	−0.352033	+	0.226238i	−0.704691	−	0.709514i	$-0.748914\pi$
$727$	−9.49184	+	6.10004i	−0.352033	+	0.226238i	0.352658	+	0.935752i	$0.385278\pi$
$728$	−2.84676	−	0.835885i	−0.105508	−	0.0309799i
$729$		0			0
$730$	2.02074	+	2.33205i	0.0747908	+	0.0863132i
$731$	−55.7446	−	35.8249i	−2.06179	−	1.32503i
$732$		0			0
$733$	24.4342	−	7.17452i	0.902496	−	0.264997i	0.202617	−	0.979258i	$-0.435055\pi$
$733$	24.4342	−	7.17452i	0.902496	−	0.264997i	0.699879	+	0.714261i	$0.253237\pi$
$734$	5.94590	+	13.0197i	0.219467	+	0.480566i
$735$		0			0
$736$	−0.633081	+	4.75386i	−0.0233357	+	0.175230i
$737$	−1.42430			−0.0524648
$738$		0			0
$739$	−24.5968	+	7.22226i	−0.904806	+	0.265675i	−0.700853	−	0.713306i	$-0.747197\pi$
$739$	−24.5968	+	7.22226i	−0.904806	+	0.265675i	−0.203953	+	0.978981i	$0.565379\pi$
$740$	−2.18231	+	2.51852i	−0.0802233	+	0.0925827i
$741$		0			0
$742$	−26.7059	−	30.8203i	−0.980404	−	1.13145i
$743$	−3.44509	−	23.9611i	−0.126388	−	0.879048i	−0.950079	−	0.312009i	$-0.898998\pi$
$743$	−3.44509	−	23.9611i	−0.126388	−	0.879048i	0.823691	−	0.567039i	$-0.191911\pi$
$744$		0			0
$745$	−32.0065	+	20.5693i	−1.17263	+	0.753602i
$746$	−1.99703	+	13.8896i	−0.0731164	+	0.508536i
$747$		0			0
$748$	0.425027	−	0.930679i	0.0155405	−	0.0340290i
$749$	−4.77425	+	33.2057i	−0.174447	+	1.21331i
$750$		0			0
$751$	−0.241949	−	0.0710425i	−0.00882883	−	0.00259238i	0.277315	−	0.960779i	$-0.410555\pi$
$751$	−0.241949	−	0.0710425i	−0.00882883	−	0.00259238i	−0.286144	+	0.958187i	$0.592374\pi$
$752$	−0.419996	−	2.92114i	−0.0153157	−	0.106523i
$753$		0			0
$754$	0.566484	+	0.364057i	0.0206301	+	0.0132582i
$755$	4.91421	−	5.67130i	0.178847	−	0.206400i
$756$		0			0
$757$	1.10736	+	2.42477i	0.0402475	+	0.0881298i	0.928688	−	0.370862i	$-0.120938\pi$
$757$	1.10736	+	2.42477i	0.0402475	+	0.0881298i	−0.888440	+	0.458992i	$0.848211\pi$
$758$	27.3937			0.994982
$759$		0			0
$760$	16.3070			0.591518
$761$	−1.06193	−	2.32530i	−0.0384949	−	0.0842920i	0.889408	−	0.457115i	$-0.151117\pi$
$761$	−1.06193	−	2.32530i	−0.0384949	−	0.0842920i	−0.927903	+	0.372823i	$0.878390\pi$
$762$		0			0
$763$	−43.1324	+	49.7775i	−1.56150	+	1.80207i
$764$	10.1228	+	6.50554i	0.366231	+	0.235362i
$765$		0			0
$766$	0.194969	+	1.35604i	0.00704450	+	0.0489956i
$767$	−4.21785	−	1.23847i	−0.152298	−	0.0447186i
$768$		0			0
$769$	1.81591	−	12.6300i	0.0654835	−	0.455448i	−0.930528	−	0.366221i	$-0.880651\pi$
$769$	1.81591	−	12.6300i	0.0654835	−	0.455448i	0.996011	−	0.0892267i	$-0.0284396\pi$
$770$	0.588026	−	1.28760i	0.0211910	−	0.0464018i
$771$		0			0
$772$	−0.279260	+	1.94230i	−0.0100508	+	0.0699048i
$773$	−14.5146	+	9.32799i	−0.522055	+	0.335505i	−0.774984	−	0.631980i	$-0.782242\pi$
$773$	−14.5146	+	9.32799i	−0.522055	+	0.335505i	0.252929	+	0.967485i	$0.418606\pi$
$774$		0			0
$775$	0.0283350	+	0.197074i	0.00101782	+	0.00707912i
$776$	9.18211	+	10.5967i	0.329619	+	0.380400i
$777$		0			0
$778$	6.69252	−	7.72357i	0.239938	−	0.276904i
$779$	−66.4039	+	19.4980i	−2.37917	+	0.698587i
$780$		0			0
$781$	−1.96065			−0.0701575
$782$	−12.1199	−	25.8244i	−0.433408	−	0.923477i
$783$		0			0
$784$	2.66059	+	5.82588i	0.0950210	+	0.208067i
$785$	22.0799	−	6.48324i	0.788065	−	0.231397i
$786$		0			0
$787$	2.36245	+	1.51826i	0.0842124	+	0.0541200i	0.582069	−	0.813139i	$-0.302243\pi$
$787$	2.36245	+	1.51826i	0.0842124	+	0.0541200i	−0.497857	+	0.867259i	$0.665880\pi$
$788$	−17.0272	−	19.6504i	−0.606569	−	0.700018i
$789$		0			0
$790$	−13.9934	−	4.10883i	−0.497863	−	0.146186i
$791$	11.8968	−	7.64558i	0.423000	−	0.271846i
$792$		0			0
$793$	0.408120	−	0.893658i	0.0144928	−	0.0317347i
$794$	12.8746	−	28.1914i	0.456901	−	1.00047i
$795$		0			0
$796$	−8.24725	+	5.30018i	−0.292316	+	0.187860i
$797$	−21.3951	−	6.28217i	−0.757854	−	0.222526i	−0.120095	−	0.992762i	$-0.538320\pi$
$797$	−21.3951	−	6.28217i	−0.757854	−	0.222526i	−0.637758	+	0.770236i	$0.720138\pi$
$798$		0			0
$799$	11.4957	+	13.2668i	0.406689	+	0.469345i
$800$	−0.0440082	−	0.0282824i	−0.00155593	−	0.000999933i
$801$		0			0
$802$	−35.2190	+	10.3412i	−1.24362	+	0.365161i
$803$	−0.0980933	−	0.214794i	−0.00346164	−	0.00757993i
$804$		0			0
$805$	−16.7680	−	35.7281i	−0.590994	−	1.25925i
$806$	−3.08424			−0.108638
$807$		0			0
$808$	−15.2481	+	4.47725i	−0.536427	+	0.157509i
$809$	15.0765	−	17.3992i	0.530061	−	0.611723i	−0.426060	−	0.904695i	$-0.640099\pi$
$809$	15.0765	−	17.3992i	0.530061	−	0.611723i	0.956121	+	0.292972i	$0.0946442\pi$
$810$		0			0
$811$	23.7763	+	27.4393i	0.834900	+	0.963526i	0.999740	−	0.0227944i	$-0.00725631\pi$
$811$	23.7763	+	27.4393i	0.834900	+	0.963526i	−0.164840	+	0.986320i	$0.552711\pi$
$812$	−0.432970	−	3.01137i	−0.0151943	−	0.105678i
$813$		0			0
$814$	0.214532	−	0.137871i	0.00751933	−	0.00483238i
$815$	−1.57387	+	10.9465i	−0.0551304	+	0.383440i
$816$		0			0
$817$	−33.5734	+	73.5155i	−1.17459	+	2.57198i
$818$	1.01201	−	7.03868i	0.0353841	−	0.246102i
$819$		0			0
$820$	20.5736	+	6.04094i	0.718460	+	0.210959i
$821$	−6.31711	−	43.9365i	−0.220469	−	1.53339i	−0.736271	−	0.676686i	$-0.763415\pi$
$821$	−6.31711	−	43.9365i	−0.220469	−	1.53339i	0.515803	−	0.856707i	$-0.327494\pi$
$822$		0			0
$823$	39.9533	+	25.6764i	1.39268	+	0.895024i	0.999699	−	0.0245205i	$-0.00780589\pi$
$823$	39.9533	+	25.6764i	1.39268	+	0.895024i	0.392986	+	0.919545i	$0.371442\pi$
$824$	−9.95762	+	11.4917i	−0.346890	+	0.400333i
$825$		0			0
$826$	8.25045	+	18.0660i	0.287070	+	0.628595i
$827$	−18.0251			−0.626794			−0.313397	−	0.949622i	$-0.601467\pi$
$827$	−18.0251			−0.626794			−0.313397	+	0.949622i	$0.601467\pi$
$828$		0			0
$829$	26.3986			0.916860			0.458430	−	0.888730i	$-0.348412\pi$
$829$	26.3986			0.916860			0.458430	+	0.888730i	$0.348412\pi$
$830$	5.73198	+	12.5513i	0.198960	+	0.435661i
$831$		0			0
$832$	0.530677	−	0.612434i	0.0183979	−	0.0212323i
$833$	−32.0490	−	20.5967i	−1.11043	−	0.713632i
$834$		0			0
$835$	−1.66390	−	11.5727i	−0.0575815	−	0.400488i
$836$	−1.19733	−	0.351567i	−0.0414105	−	0.0121592i
$837$		0			0
$838$	−2.64153	+	18.3722i	−0.0912500	+	0.634658i
$839$	−18.5156	+	40.5435i	−0.639229	+	1.39972i	0.261444	+	0.965219i	$0.415801\pi$
$839$	−18.5156	+	40.5435i	−0.639229	+	1.39972i	−0.900673	+	0.434498i	$0.856926\pi$
$840$		0			0
$841$	4.02886	−	28.0214i	0.138926	−	0.966254i
$842$	5.67314	−	3.64590i	0.195509	−	0.125646i
$843$		0			0
$844$	2.00568	+	13.9498i	0.0690385	+	0.480173i
$845$	18.1688	+	20.9679i	0.625025	+	0.721317i
$846$		0			0
$847$	26.3027	−	30.3549i	0.903770	−	1.04301i
$848$	10.6874	−	3.13811i	0.367007	−	0.107763i
$849$		0			0
$850$	0.311171			0.0106731
$851$	0.938603	−	7.04805i	0.0321749	−	0.241604i
$852$		0			0
$853$	5.55837	+	12.1711i	0.190315	+	0.416732i	0.980603	−	0.196003i	$-0.0627964\pi$
$853$	5.55837	+	12.1711i	0.190315	+	0.416732i	−0.790288	+	0.612735i	$0.790069\pi$
$854$	−4.25886	+	1.25051i	−0.145735	+	0.0427917i
$855$		0			0
$856$	−7.70823	−	4.95378i	−0.263462	−	0.169317i
$857$	−9.08103	−	10.4801i	−0.310202	−	0.357992i	0.579145	−	0.815224i	$-0.303386\pi$
$857$	−9.08103	−	10.4801i	−0.310202	−	0.357992i	−0.889347	+	0.457232i	$0.848841\pi$
$858$		0			0
$859$	9.59712	+	2.81797i	0.327449	+	0.0961478i	0.441325	−	0.897347i	$-0.354508\pi$
$859$	9.59712	+	2.81797i	0.327449	+	0.0961478i	−0.113876	+	0.993495i	$0.536327\pi$
$860$	21.0647	−	13.5375i	0.718301	−	0.461624i
$861$		0			0
$862$	−4.18782	+	9.17004i	−0.142638	+	0.312333i
$863$	3.88661	−	8.51050i	0.132302	−	0.289701i	−0.831874	−	0.554965i	$-0.812732\pi$
$863$	3.88661	−	8.51050i	0.132302	−	0.289701i	0.964176	+	0.265264i	$0.0854591\pi$
$864$		0			0
$865$	−14.1976	+	9.12426i	−0.482734	+	0.310234i
$866$	27.2564	+	8.00321i	0.926212	+	0.271960i
$867$		0			0
$868$	9.12521	+	10.5311i	0.309730	+	0.357447i
$869$	0.938869	+	0.603375i	0.0318490	+	0.0204681i
$870$		0			0
$871$	6.43848	−	1.89051i	0.218160	−	0.0640575i
$872$	−7.47324	−	16.3641i	−0.253076	−	0.554159i
$873$		0			0
$874$	−29.0725	+	19.1142i	−0.983392	+	0.646546i
$875$	−40.7169			−1.37648
$876$		0			0
$877$	−33.2112	+	9.75170i	−1.12146	+	0.329291i	−0.789347	−	0.613947i	$-0.789581\pi$
$877$	−33.2112	+	9.75170i	−1.12146	+	0.329291i	−0.332116	+	0.943238i	$0.607763\pi$
$878$	20.9299	−	24.1544i	0.706350	−	0.815172i
$879$		0			0
$880$	0.253184	+	0.292190i	0.00853482	+	0.00984971i
$881$	1.18287	+	8.22701i	0.0398517	+	0.277175i	0.999997	−	0.00232551i	$-0.000740234\pi$
$881$	1.18287	+	8.22701i	0.0398517	+	0.277175i	−0.960146	+	0.279500i	$0.909831\pi$
$882$		0			0
$883$	−25.8766	+	16.6299i	−0.870817	+	0.559640i	−0.898002	−	0.439991i	$-0.854982\pi$
$883$	−25.8766	+	16.6299i	−0.870817	+	0.559640i	0.0271859	+	0.999630i	$0.491345\pi$
$884$	−0.686000	+	4.77123i	−0.0230727	+	0.160474i
$885$		0			0
$886$	13.8009	−	30.2197i	0.463650	−	1.01525i
$887$	1.33071	−	9.25532i	0.0446810	−	0.310763i	−0.955209	−	0.295932i	$-0.904370\pi$
$887$	1.33071	−	9.25532i	0.0446810	−	0.310763i	0.999890	−	0.0148312i	$-0.00472109\pi$
$888$		0			0
$889$	39.2964	+	11.5385i	1.31796	+	0.386988i
$890$	−0.0825010	−	0.573807i	−0.00276544	−	0.0192341i
$891$		0			0
$892$	14.4763	+	9.30333i	0.484701	+	0.311498i
$893$	14.0208	−	16.1809i	0.469189	−	0.541473i
$894$		0			0
$895$	−10.5919	−	23.1929i	−0.354047	−	0.775254i
$896$	−3.66124			−0.122313
$897$		0			0
$898$	−22.9487			−0.765808
$899$	−1.31380	−	2.87681i	−0.0438175	−	0.0959470i
$900$		0			0
$901$	−43.3882	+	50.0727i	−1.44547	+	1.66816i
$902$	−1.38036	−	0.887101i	−0.0459608	−	0.0295372i
$903$		0			0
$904$	0.549698	+	3.82323i	0.0182827	+	0.127159i
$905$	4.77334	+	1.40158i	0.158671	+	0.0465901i
$906$		0			0
$907$	5.95935	−	41.4482i	0.197877	−	1.37626i	−0.612554	−	0.790429i	$-0.709858\pi$
$907$	5.95935	−	41.4482i	0.197877	−	1.37626i	0.810430	−	0.585835i	$-0.199233\pi$
$908$	−4.29931	+	9.41417i	−0.142678	+	0.312420i
$909$		0			0
$910$	−0.949084	+	6.60102i	−0.0314618	+	0.218822i
$911$	9.65986	−	6.20802i	0.320046	−	0.205681i	−0.370747	−	0.928734i	$-0.620898\pi$
$911$	9.65986	−	6.20802i	0.320046	−	0.205681i	0.690792	+	0.723053i	$0.257262\pi$
$912$		0			0
$913$	−0.150269	−	1.04514i	−0.00497317	−	0.0345892i
$914$	−21.0522	−	24.2955i	−0.696344	−	0.803624i
$915$		0			0
$916$	−7.41012	+	8.55173i	−0.244837	+	0.282557i
$917$	25.9479	−	7.61899i	0.856875	−	0.251601i
$918$		0			0
$919$	−15.2399			−0.502717			−0.251359	−	0.967894i	$-0.580877\pi$
$919$	−15.2399			−0.502717			−0.251359	+	0.967894i	$0.580877\pi$
$920$	10.7792	−	0.112180i	0.355379	−	0.00369845i
$921$		0			0
$922$	−5.58833	−	12.2367i	−0.184042	−	0.402996i
$923$	8.86300	−	2.60241i	0.291729	−	0.0856595i
$924$		0			0
$925$	0.0652464	+	0.0419313i	0.00214529	+	0.00137869i
$926$	23.2357	+	26.8154i	0.763571	+	0.881208i
$927$		0			0
$928$	0.797299	+	0.234108i	0.0261726	+	0.00768498i
$929$	−12.5350	+	8.05574i	−0.411259	+	0.264300i	−0.729871	−	0.683585i	$-0.760420\pi$
$929$	−12.5350	+	8.05574i	−0.411259	+	0.264300i	0.318612	+	0.947885i	$0.396783\pi$
$930$		0			0
$931$	−19.3022	+	42.2660i	−0.632605	+	1.38521i
$932$	3.24850	−	7.11322i	0.106408	−	0.233001i
$933$		0			0
$934$	24.0825	−	15.4769i	0.788003	−	0.506419i
$935$	−2.20659	−	0.647912i	−0.0721631	−	0.0211890i
$936$		0			0
$937$	26.8736	+	31.0138i	0.877923	+	1.01318i	0.999787	+	0.0206299i	$0.00656717\pi$
$937$	26.8736	+	31.0138i	0.877923	+	1.01318i	−0.121865	+	0.992547i	$0.538887\pi$
$938$	−25.5044	−	16.3907i	−0.832748	−	0.535175i
$939$		0			0
$940$	−6.36476	+	1.86886i	−0.207595	+	0.0609555i
$941$	6.95372	+	15.2265i	0.226685	+	0.496371i	0.988462	−	0.151468i	$-0.0484002\pi$
$941$	6.95372	+	15.2265i	0.226685	+	0.496371i	−0.761777	+	0.647839i	$0.775673\pi$
$942$		0			0
$943$	−43.7598	+	13.3452i	−1.42502	+	0.434581i
$944$	−5.42460			−0.176556
$945$		0			0
$946$	−1.83852	+	0.539837i	−0.0597753	+	0.0175516i
$947$	−27.7796	+	32.0594i	−0.902717	+	1.04179i	0.0962048	+	0.995362i	$0.469330\pi$
$947$	−27.7796	+	32.0594i	−0.902717	+	1.04179i	−0.998922	+	0.0464292i	$0.985216\pi$
$948$		0			0
$949$	0.728528	+	0.840766i	0.0236490	+	0.0272924i
$950$	−0.0540116	−	0.375659i	−0.00175237	−	0.0121880i
$951$		0			0
$952$	18.3209	−	11.7741i	0.593784	−	0.381602i
$953$	3.15431	−	21.9387i	0.102178	−	0.710665i	−0.872754	−	0.488161i	$-0.837668\pi$
$953$	3.15431	−	21.9387i	0.102178	−	0.710665i	0.974932	−	0.222504i	$-0.0714230\pi$
$954$		0			0
$955$	11.2357	−	24.6029i	0.363580	−	0.796130i
$956$	−1.80258	+	12.5372i	−0.0582995	+	0.405482i
$957$		0			0
$958$	−17.0799	−	5.01512i	−0.551828	−	0.162031i
$959$	10.0703	+	70.0404i	0.325187	+	2.26172i
$960$		0			0
$961$	−13.8929	−	8.92844i	−0.448159	−	0.288014i
$962$	−0.786779	+	0.907992i	−0.0253668	+	0.0292748i
$963$		0			0
$964$	10.3533	+	22.6706i	0.333458	+	0.730171i
$965$	4.41066			0.141984
$966$		0			0
$967$	10.8591			0.349204			0.174602	−	0.984639i	$-0.444136\pi$
$967$	10.8591			0.349204			0.174602	+	0.984639i	$0.444136\pi$
$968$	4.55727	+	9.97904i	0.146476	+	0.320738i
$969$		0			0
$970$	20.6390	−	23.8186i	0.662677	−	0.764770i
$971$	17.7012	+	11.3759i	0.568060	+	0.365070i	0.792924	−	0.609320i	$-0.208558\pi$
$971$	17.7012	+	11.3759i	0.568060	+	0.365070i	−0.224865	+	0.974390i	$0.572194\pi$
$972$		0			0
$973$	3.69688	+	25.7124i	0.118517	+	0.824301i
$974$	−23.6659	−	6.94892i	−0.758303	−	0.222658i
$975$		0			0
$976$	0.172534	−	1.20000i	0.00552267	−	0.0384110i
$977$	16.8507	−	36.8979i	0.539101	−	1.18047i	−0.422587	−	0.906322i	$-0.638878\pi$
$977$	16.8507	−	36.8979i	0.539101	−	1.18047i	0.961688	−	0.274145i	$-0.0883947\pi$
$978$		0			0
$979$	−0.00631329	+	0.0439099i	−0.000201774	+	0.00140337i
$980$	12.1107	−	7.78305i	0.386861	−	0.248620i
$981$		0			0
$982$	0.316914	+	2.20418i	0.0101131	+	0.0703383i
$983$	−19.7366	−	22.7773i	−0.629500	−	0.726482i	0.347982	−	0.937501i	$-0.386867\pi$
$983$	−19.7366	−	22.7773i	−0.629500	−	0.726482i	−0.977482	+	0.211020i	$0.932322\pi$
$984$		0			0
$985$	−38.2727	+	44.1690i	−1.21947	+	1.40734i
$986$	−4.74257	+	1.39254i	−0.151034	+	0.0443476i
$987$		0			0
$988$	5.87910			0.187039
$989$	−21.6868	+	48.8258i	−0.689599	+	1.55257i
$990$		0			0
$991$	−17.8960	−	39.1868i	−0.568486	−	1.24481i	−0.947599	−	0.319461i	$-0.896498\pi$
$991$	−17.8960	−	39.1868i	−0.568486	−	1.24481i	0.379113	−	0.925350i	$-0.376229\pi$
$992$	−3.65181	+	1.07227i	−0.115945	+	0.0340445i
$993$		0			0
$994$	−35.1085	−	22.5629i	−1.11357	−	0.715651i
$995$	14.4303	+	16.6535i	0.457472	+	0.527951i
$996$		0			0
$997$	24.6142	+	7.22739i	0.779541	+	0.228894i	0.647210	−	0.762312i	$-0.275936\pi$
$997$	24.6142	+	7.22739i	0.779541	+	0.228894i	0.132331	+	0.991206i	$0.457754\pi$
$998$	−20.3239	+	13.0614i	−0.643341	+	0.413450i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.h.73.2	yes	20
3.2	odd	2		414.2.i.g.73.1	✓	20
23.6	even	11	inner	414.2.i.h.397.2	yes	20
23.11	odd	22		9522.2.a.ch.1.1		10
23.12	even	11		9522.2.a.cg.1.10		10
69.11	even	22		9522.2.a.ci.1.10		10
69.29	odd	22		414.2.i.g.397.1	yes	20
69.35	odd	22		9522.2.a.cj.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.i.g.73.1	✓	20	3.2	odd	2
414.2.i.g.397.1	yes	20	69.29	odd	22
414.2.i.h.73.2	yes	20	1.1	even	1	trivial
414.2.i.h.397.2	yes	20	23.6	even	11	inner
9522.2.a.cg.1.10		10	23.12	even	11
9522.2.a.ch.1.1		10	23.11	odd	22
9522.2.a.ci.1.10		10	69.11	even	22
9522.2.a.cj.1.1		10	69.35	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)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.654861 + 0.755750i) q^{4} +(1.89092 + 1.21522i) q^{5} +(-0.521048 - 3.62397i) q^{7} +(0.959493 + 0.281733i) q^{8} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.654861 + 0.755750i) q^{4} +(1.89092 + 1.21522i) q^{5} +(-0.521048 - 3.62397i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.319886 - 2.22486i) q^{10} +(-0.0714536 + 0.156461i) q^{11} +(0.115327 - 0.802118i) q^{13} +(-3.08003 + 1.97941i) q^{14} +(-0.142315 - 0.989821i) q^{16} +(3.89530 + 4.49542i) q^{17} +(4.75093 - 5.48286i) q^{19} +(-2.15669 + 0.633260i) q^{20} +0.172005 q^{22} +(3.10271 - 3.65693i) q^{23} +(0.0217315 + 0.0475853i) q^{25} +(-0.777541 + 0.228307i) q^{26} +(3.08003 + 1.97941i) q^{28} +(-0.544162 - 0.627997i) q^{29} +(3.65181 + 1.07227i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(2.47101 - 5.41076i) q^{34} +(3.41865 - 7.48581i) q^{35} +(1.24724 - 0.801551i) q^{37} +(-6.96100 - 2.04393i) q^{38} +(1.47195 + 1.69872i) q^{40} +(-8.02508 - 5.15741i) q^{41} +(-10.6887 + 3.13849i) q^{43} +(-0.0714536 - 0.156461i) q^{44} +(-4.61538 - 1.30318i) q^{46} +2.95117 q^{47} +(-6.14522 + 1.80440i) q^{49} +(0.0342575 - 0.0395353i) q^{50} +(0.530677 + 0.612434i) q^{52} +(1.58519 + 11.0252i) q^{53} +(-0.325247 + 0.209024i) q^{55} +(0.521048 - 3.62397i) q^{56} +(-0.345193 + 0.755867i) q^{58} +(0.772001 - 5.36938i) q^{59} +(1.16323 + 0.341555i) q^{61} +(-0.541647 - 3.76724i) q^{62} +(0.841254 + 0.540641i) q^{64} +(1.19282 - 1.37659i) q^{65} +(3.43987 + 7.53227i) q^{67} -5.94829 q^{68} -8.22949 q^{70} +(4.73522 + 10.3687i) q^{71} +(-0.899010 + 1.03751i) q^{73} +(-1.24724 - 0.801551i) q^{74} +(1.03248 + 7.18103i) q^{76} +(0.604243 + 0.177422i) q^{77} +(0.923393 - 6.42234i) q^{79} +(0.933743 - 2.04461i) q^{80} +(-1.35760 + 9.44233i) q^{82} +(-5.16421 + 3.31884i) q^{83} +(1.90278 + 13.2341i) q^{85} +(7.29513 + 8.41902i) q^{86} +(-0.112639 + 0.129993i) q^{88} +(0.247460 - 0.0726609i) q^{89} -2.96694 q^{91} +(0.731881 + 4.73966i) q^{92} +(-1.22596 - 2.68448i) q^{94} +(15.6465 - 4.59422i) q^{95} +(11.7956 + 7.58058i) q^{97} +(4.19416 + 4.84031i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

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