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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(0.592229 - 4.11904i) q^{5} +(-1.22301 - 2.67803i) q^{7} +(-0.654861 - 0.755750i) q^{8} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(0.592229 - 4.11904i) q^{5} +(-1.22301 - 2.67803i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-1.72871 + 3.78534i) q^{10} +(-3.15098 + 0.925210i) q^{11} +(-0.0583872 + 0.127850i) q^{13} +(0.418986 + 2.91411i) q^{14} +(0.415415 + 0.909632i) q^{16} +(-5.26034 + 3.38061i) q^{17} +(1.99782 + 1.28392i) q^{19} +(2.72514 - 3.14498i) q^{20} +3.28400 q^{22} +(0.435919 + 4.77598i) q^{23} +(-11.8183 - 3.47017i) q^{25} +(0.0920417 - 0.106222i) q^{26} +(0.418986 - 2.91411i) q^{28} +(8.36028 - 5.37283i) q^{29} +(-1.49745 - 1.72814i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(5.99969 - 1.76167i) q^{34} +(-11.7552 + 3.45164i) q^{35} +(-0.883471 - 6.14467i) q^{37} +(-1.55518 - 1.79477i) q^{38} +(-3.50079 + 2.24982i) q^{40} +(0.918195 - 6.38618i) q^{41} +(0.839356 - 0.968669i) q^{43} +(-3.15098 - 0.925210i) q^{44} +(0.927287 - 4.70533i) q^{46} -2.84018 q^{47} +(-1.09204 + 1.26028i) q^{49} +(10.3619 + 6.65920i) q^{50} +(-0.118239 + 0.0759879i) q^{52} +(-1.80736 - 3.95756i) q^{53} +(1.94488 + 13.5269i) q^{55} +(-1.22301 + 2.67803i) q^{56} +(-9.53533 + 2.79983i) q^{58} +(-0.0304261 + 0.0666238i) q^{59} +(-1.25866 - 1.45257i) q^{61} +(0.949914 + 2.08002i) q^{62} +(-0.142315 + 0.989821i) q^{64} +(0.492041 + 0.316216i) q^{65} +(-4.15796 - 1.22089i) q^{67} -6.25297 q^{68} +12.2515 q^{70} +(9.39090 + 2.75742i) q^{71} +(4.61462 + 2.96563i) q^{73} +(-0.883471 + 6.14467i) q^{74} +(0.986535 + 2.16021i) q^{76} +(6.33142 + 7.30685i) q^{77} +(3.99764 - 8.75360i) q^{79} +(3.99283 - 1.17240i) q^{80} +(-2.68020 + 5.86881i) q^{82} +(-1.56667 - 10.8964i) q^{83} +(10.8096 + 23.6696i) q^{85} +(-1.07826 + 0.692957i) q^{86} +(2.76268 + 1.77546i) q^{88} +(8.58116 - 9.90318i) q^{89} +0.413795 q^{91} +(-2.21537 + 4.25348i) q^{92} +(2.72514 + 0.800172i) q^{94} +(6.47170 - 7.46874i) q^{95} +(1.73769 - 12.0859i) q^{97} +(1.40287 - 0.901569i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 - 2 * q^7 - q^8	$ 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8} + 11 q^{10} - 11 q^{11} - 13 q^{13} - 13 q^{14} - q^{16} - 2 q^{19} + 11 q^{20} - 22 q^{22} + 10 q^{23} + 5 q^{25} + 9 q^{26} - 13 q^{28} + 27 q^{29} - 18 q^{31} - q^{32} + 33 q^{34} - 44 q^{35} - q^{37} - 13 q^{38} - 11 q^{40} + 16 q^{41} + 20 q^{43} - 11 q^{44} - q^{46} - 19 q^{49} + 27 q^{50} - 2 q^{52} + q^{53} + 33 q^{55} - 2 q^{56} - 17 q^{58} + q^{59} - 34 q^{61} + 4 q^{62} - q^{64} - 11 q^{65} + 8 q^{67} - 22 q^{68} + 22 q^{70} + 22 q^{71} + 31 q^{73} - q^{74} - 2 q^{76} - 22 q^{77} + 32 q^{79} - 28 q^{82} - 33 q^{83} - 11 q^{85} + 20 q^{86} + 22 q^{88} + 23 q^{89} + 18 q^{91} - 23 q^{92} + 11 q^{94} + 22 q^{95} - q^{97} + 14 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 - 2 * q^7 - q^8 + 11 * q^10 - 11 * q^11 - 13 * q^13 - 13 * q^14 - q^16 - 2 * q^19 + 11 * q^20 - 22 * q^22 + 10 * q^23 + 5 * q^25 + 9 * q^26 - 13 * q^28 + 27 * q^29 - 18 * q^31 - q^32 + 33 * q^34 - 44 * q^35 - q^37 - 13 * q^38 - 11 * q^40 + 16 * q^41 + 20 * q^43 - 11 * q^44 - q^46 - 19 * q^49 + 27 * q^50 - 2 * q^52 + q^53 + 33 * q^55 - 2 * q^56 - 17 * q^58 + q^59 - 34 * q^61 + 4 * q^62 - q^64 - 11 * q^65 + 8 * q^67 - 22 * q^68 + 22 * q^70 + 22 * q^71 + 31 * q^73 - q^74 - 2 * q^76 - 22 * q^77 + 32 * q^79 - 28 * q^82 - 33 * q^83 - 11 * q^85 + 20 * q^86 + 22 * q^88 + 23 * q^89 + 18 * q^91 - 23 * q^92 + 11 * q^94 + 22 * q^95 - q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$		0			0
$3$		0			0
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.592229	−	4.11904i	0.264853	−	1.84209i	−0.230094	−	0.973168i	$-0.573904\pi$
$5$	0.592229	−	4.11904i	0.264853	−	1.84209i	0.494947	−	0.868923i	$-0.335187\pi$
$6$		0			0
$7$	−1.22301	−	2.67803i	−0.462256	−	1.01220i	−0.986968	−	0.160919i	$-0.948554\pi$
$7$	−1.22301	−	2.67803i	−0.462256	−	1.01220i	0.524712	−	0.851280i	$-0.324173\pi$
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$		0			0
$10$	−1.72871	+	3.78534i	−0.546665	+	1.19703i
$11$	−3.15098	+	0.925210i	−0.950055	+	0.278961i	−0.719810	−	0.694171i	$-0.755771\pi$
$11$	−3.15098	+	0.925210i	−0.950055	+	0.278961i	−0.230245	+	0.973133i	$0.573953\pi$
$12$		0			0
$13$	−0.0583872	+	0.127850i	−0.0161937	+	0.0354592i	−0.917556	−	0.397606i	$-0.869841\pi$
$13$	−0.0583872	+	0.127850i	−0.0161937	+	0.0354592i	0.901362	+	0.433066i	$0.142568\pi$
$14$	0.418986	+	2.91411i	0.111979	+	0.778829i
$15$		0			0
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−5.26034	+	3.38061i	−1.27582	+	0.819919i	−0.990366	−	0.138474i	$-0.955780\pi$
$17$	−5.26034	+	3.38061i	−1.27582	+	0.819919i	−0.285453	+	0.958393i	$0.592144\pi$
$18$		0			0
$19$	1.99782	+	1.28392i	0.458332	+	0.294552i	0.749361	−	0.662162i	$-0.230361\pi$
$19$	1.99782	+	1.28392i	0.458332	+	0.294552i	−0.291028	+	0.956714i	$0.593997\pi$
$20$	2.72514	−	3.14498i	0.609359	−	0.703238i
$21$		0			0
$22$	3.28400			0.700151
$23$	0.435919	+	4.77598i	0.0908955	+	0.995860i
$23$	0.435919	+	4.77598i	0.0908955	+	0.995860i
$24$		0			0
$25$	−11.8183	−	3.47017i	−2.36366	−	0.694033i
$26$	0.0920417	−	0.106222i	0.0180509	−	0.0208318i
$27$		0			0
$28$	0.418986	−	2.91411i	0.0791809	−	0.550715i
$29$	8.36028	−	5.37283i	1.55247	−	0.997709i	0.567818	−	0.823154i	$-0.307788\pi$
$29$	8.36028	−	5.37283i	1.55247	−	0.997709i	0.984647	−	0.174555i	$-0.0558488\pi$
$30$		0			0
$31$	−1.49745	−	1.72814i	−0.268949	−	0.310384i	0.605169	−	0.796097i	$-0.293105\pi$
$31$	−1.49745	−	1.72814i	−0.268949	−	0.310384i	−0.874118	+	0.485713i	$0.838560\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$		0			0
$34$	5.99969	−	1.76167i	1.02894	−	0.302123i
$35$	−11.7552	+	3.45164i	−1.98699	+	0.583434i
$36$		0			0
$37$	−0.883471	−	6.14467i	−0.145242	−	1.01018i	−0.923874	−	0.382697i	$-0.874995\pi$
$37$	−0.883471	−	6.14467i	−0.145242	−	1.01018i	0.778632	−	0.627481i	$-0.215914\pi$
$38$	−1.55518	−	1.79477i	−0.252283	−	0.291150i
$39$		0			0
$40$	−3.50079	+	2.24982i	−0.553524	+	0.355728i
$41$	0.918195	−	6.38618i	0.143398	−	0.997354i	−0.783326	−	0.621611i	$-0.786478\pi$
$41$	0.918195	−	6.38618i	0.143398	−	0.997354i	0.926724	−	0.375743i	$-0.122613\pi$
$42$		0			0
$43$	0.839356	−	0.968669i	0.128001	−	0.147721i	−0.688131	−	0.725586i	$-0.741569\pi$
$43$	0.839356	−	0.968669i	0.128001	−	0.147721i	0.816132	+	0.577866i	$0.196114\pi$
$44$	−3.15098	−	0.925210i	−0.475027	−	0.139481i
$45$		0			0
$46$	0.927287	−	4.70533i	0.136721	−	0.693763i
$47$	−2.84018			−0.414283			−0.207142	−	0.978311i	$-0.566416\pi$
$47$	−2.84018			−0.414283			−0.207142	+	0.978311i	$0.566416\pi$
$48$		0			0
$49$	−1.09204	+	1.26028i	−0.156006	+	0.180040i
$50$	10.3619	+	6.65920i	1.46540	+	0.941753i
$51$		0			0
$52$	−0.118239	+	0.0759879i	−0.0163969	+	0.0105376i
$53$	−1.80736	−	3.95756i	−0.248260	−	0.543613i	0.743944	−	0.668242i	$-0.232953\pi$
$53$	−1.80736	−	3.95756i	−0.248260	−	0.543613i	−0.992203	+	0.124629i	$0.960226\pi$
$54$		0			0
$55$	1.94488	+	13.5269i	0.262247	+	1.82397i
$56$	−1.22301	+	2.67803i	−0.163432	+	0.357866i
$57$		0			0
$58$	−9.53533	+	2.79983i	−1.25205	+	0.367635i
$59$	−0.0304261	+	0.0666238i	−0.00396114	+	0.00867368i	−0.911602	−	0.411073i	$-0.865154\pi$
$59$	−0.0304261	+	0.0666238i	−0.00396114	+	0.00867368i	0.907641	+	0.419747i	$0.137881\pi$
$60$		0			0
$61$	−1.25866	−	1.45257i	−0.161155	−	0.185982i	0.669429	−	0.742876i	$-0.266539\pi$
$61$	−1.25866	−	1.45257i	−0.161155	−	0.185982i	−0.830584	+	0.556893i	$0.811993\pi$
$62$	0.949914	+	2.08002i	0.120639	+	0.264163i
$63$		0			0
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	0.492041	+	0.316216i	0.0610302	+	0.0392217i
$66$		0			0
$67$	−4.15796	−	1.22089i	−0.507976	−	0.149155i	0.0176947	−	0.999843i	$-0.494367\pi$
$67$	−4.15796	−	1.22089i	−0.507976	−	0.149155i	−0.525670	+	0.850688i	$0.676186\pi$
$68$	−6.25297			−0.758285
$69$		0			0
$70$	12.2515			1.46433
$71$	9.39090	+	2.75742i	1.11449	+	0.327245i	0.786596	−	0.617468i	$-0.211841\pi$
$71$	9.39090	+	2.75742i	1.11449	+	0.327245i	0.327898	+	0.944713i	$0.393660\pi$
$72$		0			0
$73$	4.61462	+	2.96563i	0.540100	+	0.347101i	0.782078	−	0.623181i	$-0.214160\pi$
$73$	4.61462	+	2.96563i	0.540100	+	0.347101i	−0.241978	+	0.970282i	$0.577796\pi$
$74$	−0.883471	+	6.14467i	−0.102701	+	0.714304i
$75$		0			0
$76$	0.986535	+	2.16021i	0.113163	+	0.247793i
$77$	6.33142	+	7.30685i	0.721533	+	0.832693i
$78$		0			0
$79$	3.99764	−	8.75360i	0.449769	−	0.984857i	−0.539932	−	0.841709i	$-0.681550\pi$
$79$	3.99764	−	8.75360i	0.449769	−	0.984857i	0.989701	−	0.143149i	$-0.0457227\pi$
$80$	3.99283	−	1.17240i	0.446412	−	0.131078i
$81$		0			0
$82$	−2.68020	+	5.86881i	−0.295978	+	0.648102i
$83$	−1.56667	−	10.8964i	−0.171964	−	1.19604i	−0.874728	−	0.484614i	$-0.838960\pi$
$83$	−1.56667	−	10.8964i	−0.171964	−	1.19604i	0.702764	−	0.711423i	$-0.251949\pi$
$84$		0			0
$85$	10.8096	+	23.6696i	1.17246	+	2.56733i
$86$	−1.07826	+	0.692957i	−0.116272	+	0.0747235i
$87$		0			0
$88$	2.76268	+	1.77546i	0.294502	+	0.189265i
$89$	8.58116	−	9.90318i	0.909601	−	1.04974i	−0.0889564	−	0.996036i	$-0.528353\pi$
$89$	8.58116	−	9.90318i	0.909601	−	1.04974i	0.998557	−	0.0536996i	$-0.0171014\pi$
$90$		0			0
$91$	0.413795			0.0433775
$92$	−2.21537	+	4.25348i	−0.230968	+	0.443456i
$93$		0			0
$94$	2.72514	+	0.800172i	0.281076	+	0.0825315i
$95$	6.47170	−	7.46874i	0.663983	−	0.766277i
$96$		0			0
$97$	1.73769	−	12.0859i	0.176435	−	1.22714i	−0.688494	−	0.725242i	$-0.741728\pi$
$97$	1.73769	−	12.0859i	0.176435	−	1.22714i	0.864930	−	0.501893i	$-0.167363\pi$
$98$	1.40287	−	0.901569i	0.141711	−	0.0910722i
$99$		0			0
$100$	−8.06608	−	9.30875i	−0.806608	−	0.930875i
$101$	−0.200413	−	1.39390i	−0.0199418	−	0.138698i	0.977418	−	0.211314i	$-0.0677744\pi$
$101$	−0.200413	−	1.39390i	−0.0199418	−	0.138698i	−0.997360	+	0.0726159i	$0.976865\pi$
$102$		0			0
$103$	−7.71117	+	2.26420i	−0.759804	+	0.223099i	−0.638610	−	0.769530i	$-0.720490\pi$
$103$	−7.71117	+	2.26420i	−0.759804	+	0.223099i	−0.121194	+	0.992629i	$0.538672\pi$
$104$	0.134858	−	0.0395979i	0.0132239	−	0.00388290i
$105$		0			0
$106$	0.619173	+	4.30645i	0.0601394	+	0.418279i
$107$	12.6585	+	14.6087i	1.22374	+	1.41227i	0.881183	+	0.472776i	$0.156748\pi$
$107$	12.6585	+	14.6087i	1.22374	+	1.41227i	0.342558	+	0.939497i	$0.388707\pi$
$108$		0			0
$109$	5.45071	−	3.50296i	0.522084	−	0.335523i	−0.252912	−	0.967489i	$-0.581388\pi$
$109$	5.45071	−	3.50296i	0.522084	−	0.335523i	0.774996	+	0.631966i	$0.217752\pi$
$110$	1.94488	−	13.5269i	0.185437	−	1.28974i
$111$		0			0
$112$	1.92796	−	2.22499i	0.182175	−	0.210241i
$113$	−10.0020	−	2.93686i	−0.940913	−	0.276277i	−0.224914	−	0.974379i	$-0.572210\pi$
$113$	−10.0020	−	2.93686i	−0.940913	−	0.276277i	−0.715999	+	0.698102i	$0.754028\pi$
$114$		0			0
$115$	19.9306	+	1.03290i	1.85854	+	0.0963186i
$116$	9.93789			0.922710
$117$		0			0
$118$	0.0479637	−	0.0553531i	0.00441542	−	0.00509566i
$119$	15.4868	+	9.95279i	1.41968	+	0.912371i
$120$		0			0
$121$	−0.181158	+	0.116423i	−0.0164690	+	0.0105840i
$122$	0.798437	+	1.74833i	0.0722871	+	0.158287i
$123$		0			0
$124$	−0.325426	−	2.26339i	−0.0292241	−	0.203258i
$125$	−12.6494	+	27.6982i	−1.13139	+	2.47741i
$126$		0			0
$127$	5.91619	−	1.73715i	0.524977	−	0.154147i	−0.00849658	−	0.999964i	$-0.502705\pi$
$127$	5.91619	−	1.73715i	0.524977	−	0.154147i	0.533474	+	0.845817i	$0.320886\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$		0			0
$130$	−0.383022	−	0.442031i	−0.0335933	−	0.0387687i
$131$	2.67757	+	5.86307i	0.233941	+	0.512259i	0.989798	−	0.142478i	$-0.0455069\pi$
$131$	2.67757	+	5.86307i	0.233941	+	0.512259i	−0.755857	+	0.654736i	$0.772780\pi$
$132$		0			0
$133$	0.995016	−	6.92049i	0.0862788	−	0.600082i
$134$	3.64557	+	2.34287i	0.314929	+	0.202393i
$135$		0			0
$136$	5.99969	+	1.76167i	0.514469	+	0.151062i
$137$	−14.3939			−1.22975			−0.614877	−	0.788623i	$-0.710794\pi$
$137$	−14.3939			−1.22975			−0.614877	+	0.788623i	$0.710794\pi$
$138$		0			0
$139$	−10.9441			−0.928268			−0.464134	−	0.885765i	$-0.653634\pi$
$139$	−10.9441			−0.928268			−0.464134	+	0.885765i	$0.653634\pi$
$140$	−11.7552	−	3.45164i	−0.993497	−	0.291717i
$141$		0			0
$142$	−8.23365	−	5.29144i	−0.690952	−	0.444048i
$143$	0.0656884	−	0.456873i	0.00549314	−	0.0382056i
$144$		0			0
$145$	−17.1797	−	37.6183i	−1.42670	−	3.12403i
$146$	−3.59218	−	4.14559i	−0.297291	−	0.343092i
$147$		0			0
$148$	2.57884	−	5.64687i	0.211979	−	0.464170i
$149$	3.88215	−	1.13990i	0.318038	−	0.0933845i	−0.118817	−	0.992916i	$-0.537910\pi$
$149$	3.88215	−	1.13990i	0.318038	−	0.0933845i	0.436856	+	0.899532i	$0.356092\pi$
$150$		0			0
$151$	−7.27336	+	15.9264i	−0.591898	+	1.29607i	0.342391	+	0.939558i	$0.388763\pi$
$151$	−7.27336	+	15.9264i	−0.591898	+	1.29607i	−0.934289	+	0.356517i	$0.883964\pi$
$152$	−0.337972	−	2.35065i	−0.0274131	−	0.190663i
$153$		0			0
$154$	−4.01638	−	8.79464i	−0.323649	−	0.708692i
$155$	−8.00513	+	5.14458i	−0.642987	+	0.413223i
$156$		0			0
$157$	−2.39146	−	1.53690i	−0.190859	−	0.122658i	0.441721	−	0.897152i	$-0.354368\pi$
$157$	−2.39146	−	1.53690i	−0.190859	−	0.122658i	−0.632581	+	0.774494i	$0.718004\pi$
$158$	−6.30188	+	7.27276i	−0.501351	+	0.578590i
$159$		0			0
$160$	−4.16140			−0.328987
$161$	12.2571	−	7.00849i	0.965992	−	0.552347i
$162$		0			0
$163$	1.92812	+	0.566146i	0.151022	+	0.0443440i	0.356370	−	0.934345i	$-0.384014\pi$
$163$	1.92812	+	0.566146i	0.151022	+	0.0443440i	−0.205348	+	0.978689i	$0.565833\pi$
$164$	4.22507	−	4.87599i	0.329922	−	0.380751i
$165$		0			0
$166$	−1.56667	+	10.8964i	−0.121597	+	0.845726i
$167$	7.76274	−	4.98881i	0.600699	−	0.386046i	−0.204660	−	0.978833i	$-0.565609\pi$
$167$	7.76274	−	4.98881i	0.600699	−	0.386046i	0.805359	+	0.592787i	$0.201973\pi$
$168$		0			0
$169$	8.50025	+	9.80981i	0.653866	+	0.754601i
$170$	−3.70319	−	25.7563i	−0.284022	−	1.97542i
$171$		0			0
$172$	1.22981	−	0.361106i	0.0937724	−	0.0275341i
$173$	9.01583	−	2.64729i	0.685461	−	0.201270i	0.0795845	−	0.996828i	$-0.474641\pi$
$173$	9.01583	−	2.64729i	0.685461	−	0.201270i	0.605877	+	0.795559i	$0.292822\pi$
$174$		0			0
$175$	5.16075	+	35.8938i	0.390116	+	2.71332i
$176$	−2.15056	−	2.48188i	−0.162105	−	0.187079i
$177$		0			0
$178$	−11.0236	+	7.08444i	−0.826254	+	0.531001i
$179$	−2.90697	+	20.2184i	−0.217277	+	1.51120i	0.530750	+	0.847528i	$0.321910\pi$
$179$	−2.90697	+	20.2184i	−0.217277	+	1.51120i	−0.748027	+	0.663668i	$0.768999\pi$
$180$		0			0
$181$	−9.77927	+	11.2859i	−0.726887	+	0.838873i	−0.992117	−	0.125312i	$-0.960007\pi$
$181$	−9.77927	+	11.2859i	−0.726887	+	0.838873i	0.265230	+	0.964185i	$0.414552\pi$
$182$	−0.397033	−	0.116579i	−0.0294300	−	0.00864144i
$183$		0			0
$184$	3.32398	−	3.45705i	0.245047	−	0.254857i
$185$	−25.8334			−1.89931
$186$		0			0
$187$	13.4474	−	15.5191i	0.983372	−	1.13487i
$188$	−2.38931	−	1.53552i	−0.174259	−	0.111989i
$189$		0			0
$190$	−8.31374	+	5.34292i	−0.603142	+	0.387616i
$191$	−9.82638	−	21.5168i	−0.711012	−	1.55690i	−0.826088	−	0.563542i	$-0.809438\pi$
$191$	−9.82638	−	21.5168i	−0.711012	−	1.55690i	0.115076	−	0.993357i	$-0.463289\pi$
$192$		0			0
$193$	0.278201	+	1.93493i	0.0200254	+	0.139280i	0.997381	−	0.0723224i	$-0.0230411\pi$
$193$	0.278201	+	1.93493i	0.0200254	+	0.139280i	−0.977356	+	0.211602i	$0.932132\pi$
$194$	−5.07228	+	11.1068i	−0.364169	+	0.797418i
$195$		0			0
$196$	−1.60004	+	0.469815i	−0.114289	+	0.0335582i
$197$	−0.780774	+	1.70966i	−0.0556279	+	0.121808i	−0.935405	−	0.353579i	$-0.884965\pi$
$197$	−0.780774	+	1.70966i	−0.0556279	+	0.121808i	0.879777	+	0.475387i	$0.157692\pi$
$198$		0			0
$199$	10.8077	+	12.4728i	0.766139	+	0.884172i	0.996028	−	0.0890450i	$-0.0283815\pi$
$199$	10.8077	+	12.4728i	0.766139	+	0.884172i	−0.229888	+	0.973217i	$0.573836\pi$
$200$	5.11677	+	11.2042i	0.361810	+	0.792253i
$201$		0			0
$202$	−0.200413	+	1.39390i	−0.0141010	+	0.0980745i
$203$	−24.6133	−	15.8180i	−1.72752	−	1.11021i
$204$		0			0
$205$	−25.7612	−	7.56416i	−1.79924	−	0.528304i
$206$	8.03671			0.559944
$207$		0			0
$208$	−0.140551			−0.00974549
$209$	−7.48299	−	2.19721i	−0.517609	−	0.151984i
$210$		0			0
$211$	5.02917	+	3.23205i	0.346223	+	0.222504i	0.702182	−	0.711998i	$-0.252209\pi$
$211$	5.02917	+	3.23205i	0.346223	+	0.222504i	−0.355959	+	0.934502i	$0.615846\pi$
$212$	0.619173	−	4.30645i	0.0425250	−	0.295768i
$213$		0			0
$214$	−8.02998	−	17.5832i	−0.548918	−	1.20196i
$215$	−3.49290	−	4.03102i	−0.238214	−	0.274913i
$216$		0			0
$217$	−2.79662	+	6.12374i	−0.189847	+	0.415707i
$218$	−6.21682	+	1.82542i	−0.421056	+	0.123633i
$219$		0			0
$220$	−5.67708	+	12.4311i	−0.382748	+	0.838102i
$221$	−0.125076	−	0.869919i	−0.00841349	−	0.0585171i
$222$		0			0
$223$	−8.35785	−	18.3011i	−0.559683	−	1.22553i	−0.952111	−	0.305752i	$-0.901092\pi$
$223$	−8.35785	−	18.3011i	−0.559683	−	1.22553i	0.392428	−	0.919783i	$-0.371635\pi$
$224$	−2.47672	+	1.59169i	−0.165483	+	0.106349i
$225$		0			0
$226$	8.76948	+	5.63580i	0.583337	+	0.374888i
$227$	8.54849	−	9.86548i	0.567383	−	0.654795i	−0.397461	−	0.917619i	$-0.630108\pi$
$227$	8.54849	−	9.86548i	0.567383	−	0.654795i	0.964844	+	0.262824i	$0.0846539\pi$
$228$		0			0
$229$	17.7990			1.17619			0.588095	−	0.808792i	$-0.299878\pi$
$229$	17.7990			1.17619			0.588095	+	0.808792i	$0.299878\pi$
$230$	−18.8323	−	6.60617i	−1.24176	−	0.435598i
$231$		0			0
$232$	−9.53533	−	2.79983i	−0.626025	−	0.183818i
$233$	6.41650	−	7.40504i	0.420359	−	0.485120i	−0.505587	−	0.862775i	$-0.668724\pi$
$233$	6.41650	−	7.40504i	0.420359	−	0.485120i	0.925946	+	0.377655i	$0.123270\pi$
$234$		0			0
$235$	−1.68204	+	11.6988i	−0.109724	+	0.763148i
$236$	−0.0616156	+	0.0395979i	−0.00401083	+	0.00257761i
$237$		0			0
$238$	−12.0555	−	13.9128i	−0.781441	−	0.901831i
$239$	0.426324	+	2.96515i	0.0275766	+	0.191799i	0.998953	−	0.0457456i	$-0.0145664\pi$
$239$	0.426324	+	2.96515i	0.0275766	+	0.191799i	−0.971377	+	0.237545i	$0.923657\pi$
$240$		0			0
$241$	19.6038	−	5.75619i	1.26279	−	0.370789i	0.419258	−	0.907867i	$-0.362290\pi$
$241$	19.6038	−	5.75619i	1.26279	−	0.370789i	0.843533	+	0.537078i	$0.180472\pi$
$242$	0.206621	−	0.0606693i	0.0132821	−	0.00389997i
$243$		0			0
$244$	−0.273532	−	1.90246i	−0.0175111	−	0.121792i
$245$	4.54442	+	5.24454i	0.290332	+	0.335061i
$246$		0			0
$247$	−0.280797	+	0.180457i	−0.0178667	+	0.0114822i
$248$	−0.325426	+	2.26339i	−0.0206646	+	0.143725i
$249$		0			0
$250$	19.9405	−	23.0125i	1.26115	−	1.45544i
$251$	−0.954130	−	0.280158i	−0.0602241	−	0.0176834i	0.251482	−	0.967862i	$-0.419082\pi$
$251$	−0.954130	−	0.280158i	−0.0602241	−	0.0176834i	−0.311706	+	0.950179i	$0.600900\pi$
$252$		0			0
$253$	−5.79235	−	14.6457i	−0.364162	−	0.920766i
$254$	−6.16595			−0.386886
$255$		0			0
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	5.90622	+	3.79570i	0.368420	+	0.236769i	0.711730	−	0.702453i	$-0.247912\pi$
$257$	5.90622	+	3.79570i	0.368420	+	0.236769i	−0.343310	+	0.939222i	$0.611548\pi$
$258$		0			0
$259$	−15.3751	+	9.88098i	−0.955363	+	0.613974i
$260$	0.242972	+	0.532035i	0.0150685	+	0.0329954i
$261$		0			0
$262$	−0.917296	−	6.37993i	−0.0566707	−	0.394154i
$263$	7.21674	−	15.8025i	0.445003	−	0.974422i	−0.545649	−	0.838014i	$-0.683717\pi$
$263$	7.21674	−	15.8025i	0.445003	−	0.974422i	0.990653	−	0.136408i	$-0.0435558\pi$
$264$		0			0
$265$	−17.3717	+	5.10080i	−1.06714	+	0.313340i
$266$	−2.90444	+	6.35983i	−0.178082	+	0.389946i
$267$		0			0
$268$	−2.83784	−	3.27504i	−0.173349	−	0.200055i
$269$	−12.6324	−	27.6612i	−0.770213	−	1.68653i	−0.726182	−	0.687502i	$-0.758707\pi$
$269$	−12.6324	−	27.6612i	−0.770213	−	1.68653i	−0.0440310	−	0.999030i	$-0.514020\pi$
$270$		0			0
$271$	0.861807	−	5.99400i	0.0523510	−	0.364109i	−0.946760	−	0.321942i	$-0.895665\pi$
$271$	0.861807	−	5.99400i	0.0523510	−	0.364109i	0.999111	−	0.0421677i	$-0.0134264\pi$
$272$	−5.26034	−	3.38061i	−0.318955	−	0.204980i
$273$		0			0
$274$	13.8108	+	4.05523i	0.834344	+	0.244985i
$275$	40.4498			2.43922
$276$		0			0
$277$	7.58051			0.455469			0.227734	−	0.973723i	$-0.426868\pi$
$277$	7.58051			0.455469			0.227734	+	0.973723i	$0.426868\pi$
$278$	10.5008	+	3.08331i	0.629796	+	0.184925i
$279$		0			0
$280$	10.3066	+	6.62365i	0.615937	+	0.395839i
$281$	−2.20720	+	15.3514i	−0.131670	+	0.915788i	0.811706	+	0.584066i	$0.198539\pi$
$281$	−2.20720	+	15.3514i	−0.131670	+	0.915788i	−0.943377	+	0.331723i	$0.892370\pi$
$282$		0			0
$283$	−3.91431	−	8.57115i	−0.232682	−	0.509502i	0.756890	−	0.653542i	$-0.226718\pi$
$283$	−3.91431	−	8.57115i	−0.232682	−	0.509502i	−0.989572	+	0.144040i	$0.953991\pi$
$284$	6.40935	+	7.39679i	0.380325	+	0.438919i
$285$		0			0
$286$	−0.191744	+	0.419860i	−0.0113380	+	0.0248268i
$287$	−18.2253	+	5.35144i	−1.07581	+	0.315886i
$288$		0			0
$289$	9.18054	−	20.1026i	0.540032	−	1.18251i
$290$	5.88550	+	40.9346i	0.345609	+	2.40376i
$291$		0			0
$292$	2.27872	+	4.98970i	0.133352	+	0.292000i
$293$	5.09559	−	3.27474i	0.297688	−	0.191312i	−0.383267	−	0.923637i	$-0.625201\pi$
$293$	5.09559	−	3.27474i	0.297688	−	0.191312i	0.680955	+	0.732325i	$0.261565\pi$
$294$		0			0
$295$	0.256407	+	0.164783i	0.0149286	+	0.00959402i
$296$	−4.06528	+	4.69159i	−0.236290	+	0.272693i
$297$		0			0
$298$	−4.04605			−0.234381
$299$	−0.636062	−	0.223124i	−0.0367844	−	0.0129036i
$300$		0			0
$301$	−3.62067	−	1.06312i	−0.208692	−	0.0612774i
$302$	11.4657	−	13.2322i	0.659779	−	0.761425i
$303$		0			0
$304$	−0.337972	+	2.35065i	−0.0193840	+	0.134819i
$305$	−6.72860	+	4.32421i	−0.385278	+	0.247603i
$306$		0			0
$307$	13.9130	+	16.0564i	0.794054	+	0.916387i	0.998040	−	0.0625866i	$-0.0199350\pi$
$307$	13.9130	+	16.0564i	0.794054	+	0.916387i	−0.203985	+	0.978974i	$0.565390\pi$
$308$	1.37595	+	9.56994i	0.0784020	+	0.545298i
$309$		0			0
$310$	9.13026	−	2.68089i	0.518564	−	0.152264i
$311$	8.51610	−	2.50055i	0.482904	−	0.141793i	−0.0312144	−	0.999513i	$-0.509937\pi$
$311$	8.51610	−	2.50055i	0.482904	−	0.141793i	0.514118	+	0.857719i	$0.328119\pi$
$312$		0			0
$313$	−1.54784	−	10.7655i	−0.0874891	−	0.608500i	−0.985646	−	0.168825i	$-0.946003\pi$
$313$	−1.54784	−	10.7655i	−0.0874891	−	0.608500i	0.898157	−	0.439675i	$-0.144906\pi$
$314$	1.86160	+	2.14840i	0.105056	+	0.121241i
$315$		0			0
$316$	8.09558	−	5.20271i	0.455412	−	0.292676i
$317$	−4.67026	+	32.4824i	−0.262308	+	1.82439i	0.253092	+	0.967442i	$0.418553\pi$
$317$	−4.67026	+	32.4824i	−0.262308	+	1.82439i	−0.515400	+	0.856950i	$0.672357\pi$
$318$		0			0
$319$	−21.3721	+	24.6647i	−1.19661	+	1.38096i
$320$	3.99283	+	1.17240i	0.223206	+	0.0655392i
$321$		0			0
$322$	−13.7351	+	3.27139i	−0.765427	+	0.182307i
$323$	−14.8497			−0.826258
$324$		0			0
$325$	1.13370	−	1.30836i	0.0628863	−	0.0725747i
$326$	−1.69051	−	1.08643i	−0.0936288	−	0.0601716i
$327$		0			0
$328$	−5.42765	+	3.48814i	−0.299692	+	0.192600i
$329$	3.47358	+	7.60609i	0.191505	+	0.419337i
$330$		0			0
$331$	2.50660	+	17.4338i	0.137775	+	0.958247i	0.935021	+	0.354592i	$0.115380\pi$
$331$	2.50660	+	17.4338i	0.137775	+	0.958247i	−0.797246	+	0.603655i	$0.793711\pi$
$332$	4.57308	−	10.0137i	0.250981	−	0.549571i
$333$		0			0
$334$	−8.85381	+	2.59971i	−0.484459	+	0.142250i
$335$	−7.49135	+	16.4038i	−0.409296	+	0.896234i
$336$		0			0
$337$	14.0826	+	16.2522i	0.767128	+	0.885313i	0.996110	−	0.0881177i	$-0.0280852\pi$
$337$	14.0826	+	16.2522i	0.767128	+	0.885313i	−0.228982	+	0.973431i	$0.573540\pi$
$338$	−5.39219	−	11.8072i	−0.293296	−	0.642230i
$339$		0			0
$340$	−3.70319	+	25.7563i	−0.200834	+	1.39683i
$341$	6.31731	+	4.05989i	0.342101	+	0.219855i
$342$		0			0
$343$	−15.0631	−	4.42292i	−0.813331	−	0.238815i
$344$	−1.28173			−0.0691064
$345$		0			0
$346$	−9.39646			−0.505157
$347$	20.5387	+	6.03072i	1.10258	+	0.323746i	0.781876	−	0.623434i	$-0.214263\pi$
$347$	20.5387	+	6.03072i	1.10258	+	0.323746i	0.320702	+	0.947180i	$0.396081\pi$
$348$		0			0
$349$	24.8430	+	15.9656i	1.32981	+	0.854619i	0.996115	−	0.0880610i	$-0.0280670\pi$
$349$	24.8430	+	15.9656i	1.32981	+	0.854619i	0.333698	+	0.942680i	$0.391703\pi$
$350$	5.16075	−	35.8938i	0.275854	−	1.91860i
$351$		0			0
$352$	1.36422	+	2.98723i	0.0727133	+	0.159220i
$353$	−5.82510	−	6.72252i	−0.310039	−	0.357804i	0.579250	−	0.815150i	$-0.303346\pi$
$353$	−5.82510	−	6.72252i	−0.310039	−	0.357804i	−0.889289	+	0.457346i	$0.848800\pi$
$354$		0			0
$355$	16.9195	−	37.0485i	0.897992	−	1.96633i
$356$	12.5730	−	3.69176i	0.666367	−	0.195663i
$357$		0			0
$358$	8.48541	−	18.5805i	0.448468	−	0.982007i
$359$	3.20348	+	22.2807i	0.169073	+	1.17593i	0.880805	+	0.473479i	$0.157002\pi$
$359$	3.20348	+	22.2807i	0.169073	+	1.17593i	−0.711732	+	0.702451i	$0.752089\pi$
$360$		0			0
$361$	−5.55004	−	12.1529i	−0.292108	−	0.639626i
$362$	12.5627	−	8.07358i	0.660283	−	0.424338i
$363$		0			0
$364$	0.348106	+	0.223714i	0.0182457	+	0.0117258i
$365$	14.9485	−	17.2515i	0.782439	−	0.902983i
$366$		0			0
$367$	−7.06807			−0.368950			−0.184475	−	0.982837i	$-0.559058\pi$
$367$	−7.06807			−0.368950			−0.184475	+	0.982837i	$0.559058\pi$
$368$	−4.16330	+	2.38054i	−0.217027	+	0.124094i
$369$		0			0
$370$	24.7869	+	7.27810i	1.28861	+	0.378371i
$371$	−8.38804	+	9.68031i	−0.435485	+	0.502577i
$372$		0			0
$373$	−2.53832	+	17.6544i	−0.131429	+	0.914111i	0.812264	+	0.583290i	$0.198235\pi$
$373$	−2.53832	+	17.6544i	−0.131429	+	0.914111i	−0.943693	+	0.330821i	$0.892674\pi$
$374$	−17.2749	+	11.1019i	−0.893266	+	0.574067i
$375$		0			0
$376$	1.85992	+	2.14647i	0.0959183	+	0.110696i
$377$	0.198783	+	1.38257i	0.0102379	+	0.0712059i
$378$		0			0
$379$	20.2387	−	5.94262i	1.03959	−	0.305252i	0.282987	−	0.959124i	$-0.408675\pi$
$379$	20.2387	−	5.94262i	1.03959	−	0.305252i	0.756605	+	0.653872i	$0.226856\pi$
$380$	9.48225	−	2.78424i	0.486429	−	0.142829i
$381$		0			0
$382$	3.36637	+	23.4136i	0.172238	+	1.19794i
$383$	−0.737643	−	0.851285i	−0.0376918	−	0.0434986i	0.736591	−	0.676339i	$-0.236434\pi$
$383$	−0.737643	−	0.851285i	−0.0376918	−	0.0434986i	−0.774282	+	0.632840i	$0.781889\pi$
$384$		0			0
$385$	33.8469	−	21.7521i	1.72500	−	1.10859i
$386$	0.278201	−	1.93493i	0.0141601	−	0.0984855i
$387$		0			0
$388$	7.99595	−	9.22782i	0.405933	−	0.468472i
$389$	2.99302	+	0.878831i	0.151752	+	0.0445585i	0.356726	−	0.934209i	$-0.383893\pi$
$389$	2.99302	+	0.878831i	0.151752	+	0.0445585i	−0.204974	+	0.978767i	$0.565711\pi$
$390$		0			0
$391$	−18.4388	−	23.6496i	−0.932491	−	1.19601i
$392$	1.66759			0.0842262
$393$		0			0
$394$	1.23081	−	1.42043i	0.0620075	−	0.0715604i
$395$	−33.6889	−	21.6506i	−1.69507	−	1.08936i
$396$		0			0
$397$	−17.3783	+	11.1683i	−0.872191	+	0.560523i	−0.898422	−	0.439133i	$-0.855286\pi$
$397$	−17.3783	+	11.1683i	−0.872191	+	0.560523i	0.0262310	+	0.999656i	$0.491649\pi$
$398$	−6.85595	−	15.0124i	−0.343658	−	0.752505i
$399$		0			0
$400$	−1.75293	−	12.1919i	−0.0876463	−	0.609593i
$401$	4.28020	−	9.37233i	0.213743	−	0.468032i	−0.772143	−	0.635448i	$-0.780815\pi$
$401$	4.28020	−	9.37233i	0.213743	−	0.468032i	0.985886	+	0.167417i	$0.0535426\pi$
$402$		0			0
$403$	0.308375	−	0.0905471i	0.0153613	−	0.00451047i
$404$	0.585002	−	1.28098i	0.0291049	−	0.0637309i
$405$		0			0
$406$	19.1599	+	22.1117i	0.950888	+	1.09738i
$407$	8.46891	+	18.5443i	0.419788	+	0.919208i
$408$		0			0
$409$	−0.512727	+	3.56610i	−0.0253527	+	0.176332i	−0.998563	−	0.0535831i	$-0.982936\pi$
$409$	−0.512727	+	3.56610i	−0.0253527	+	0.176332i	0.973211	+	0.229915i	$0.0738449\pi$
$410$	22.5866	+	14.5155i	1.11547	+	0.716871i
$411$		0			0
$412$	−7.71117	−	2.26420i	−0.379902	−	0.111549i
$413$	0.215632			0.0106106
$414$		0			0
$415$	−45.8106			−2.24876
$416$	0.134858	+	0.0395979i	0.00661197	+	0.00194145i
$417$		0			0
$418$	6.56086	+	4.21641i	0.320902	+	0.206231i
$419$	1.92082	−	13.3596i	0.0938382	−	0.652659i	−0.887562	−	0.460687i	$-0.847603\pi$
$419$	1.92082	−	13.3596i	0.0938382	−	0.652659i	0.981401	−	0.191971i	$-0.0614880\pi$
$420$		0			0
$421$	6.91556	+	15.1430i	0.337044	+	0.738023i	0.999943	−	0.0106857i	$-0.00340143\pi$
$421$	6.91556	+	15.1430i	0.337044	+	0.738023i	−0.662899	+	0.748709i	$0.730674\pi$
$422$	−3.91488	−	4.51801i	−0.190573	−	0.219933i
$423$		0			0
$424$	−1.80736	+	3.95756i	−0.0877731	+	0.192196i
$425$	73.8995	−	21.6989i	3.58465	−	1.05255i
$426$		0			0
$427$	−2.35066	+	5.14723i	−0.113756	+	0.249092i
$428$	2.75095	+	19.1333i	0.132972	+	0.924842i
$429$		0			0
$430$	2.21574	+	4.85180i	0.106853	+	0.233974i
$431$	17.6801	−	11.3623i	0.851621	−	0.547304i	−0.0404589	−	0.999181i	$-0.512882\pi$
$431$	17.6801	−	11.3623i	0.851621	−	0.547304i	0.892080	+	0.451878i	$0.149246\pi$
$432$		0			0
$433$	−1.74431	−	1.12100i	−0.0838263	−	0.0538719i	0.498056	−	0.867145i	$-0.334047\pi$
$433$	−1.74431	−	1.12100i	−0.0838263	−	0.0538719i	−0.581883	+	0.813273i	$0.697684\pi$
$434$	4.40860	−	5.08779i	0.211619	−	0.244222i
$435$		0			0
$436$	6.47928			0.310301
$437$	−5.26110	+	10.1013i	−0.251673	+	0.483209i
$438$		0			0
$439$	−2.17757	−	0.639393i	−0.103930	−	0.0305166i	0.229354	−	0.973343i	$-0.426339\pi$
$439$	−2.17757	−	0.639393i	−0.103930	−	0.0305166i	−0.333284	+	0.942826i	$0.608157\pi$
$440$	8.94935	−	10.3281i	0.426643	−	0.492373i
$441$		0			0
$442$	−0.125076	+	0.869919i	−0.00594924	+	0.0413778i
$443$	−22.5605	+	14.4988i	−1.07188	+	0.688858i	−0.952669	−	0.304011i	$-0.901674\pi$
$443$	−22.5605	+	14.4988i	−1.07188	+	0.688858i	−0.119215	+	0.992868i	$0.538038\pi$
$444$		0			0
$445$	−35.7096	−	41.2111i	−1.69280	−	1.95359i
$446$	2.86327	+	19.9145i	0.135580	+	0.942978i
$447$		0			0
$448$	2.82482	−	0.829443i	0.133460	−	0.0391875i
$449$	4.38432	−	1.28735i	0.206909	−	0.0607539i	−0.176636	−	0.984276i	$-0.556521\pi$
$449$	4.38432	−	1.28735i	0.206909	−	0.0607539i	0.383544	+	0.923522i	$0.374703\pi$
$450$		0			0
$451$	3.01535	+	20.9722i	0.141987	+	0.987544i
$452$	−6.82646	−	7.87816i	−0.321090	−	0.370557i
$453$		0			0
$454$	−10.9816	+	7.05747i	−0.515394	+	0.331224i
$455$	0.245061	−	1.70444i	0.0114886	−	0.0799052i
$456$		0			0
$457$	17.5597	−	20.2650i	0.821409	−	0.947957i	−0.177939	−	0.984041i	$-0.556943\pi$
$457$	17.5597	−	20.2650i	0.821409	−	0.947957i	0.999349	+	0.0360845i	$0.0114885\pi$
$458$	−17.0780	−	5.01455i	−0.798002	−	0.234315i
$459$		0			0
$460$	16.2083	+	11.6442i	0.755715	+	0.542915i
$461$	1.33658			0.0622507			0.0311253	−	0.999515i	$-0.490091\pi$
$461$	1.33658			0.0622507			0.0311253	+	0.999515i	$0.490091\pi$
$462$		0			0
$463$	23.7519	−	27.4112i	1.10384	−	1.27390i	0.145168	−	0.989407i	$-0.453628\pi$
$463$	23.7519	−	27.4112i	1.10384	−	1.27390i	0.958677	−	0.284498i	$-0.0918268\pi$
$464$	8.36028	+	5.37283i	0.388116	+	0.249427i
$465$		0			0
$466$	−8.24283	+	5.29734i	−0.381842	+	0.245395i
$467$	5.53507	+	12.1201i	0.256132	+	0.560852i	0.993394	−	0.114756i	$-0.0366086\pi$
$467$	5.53507	+	12.1201i	0.256132	+	0.560852i	−0.737261	+	0.675608i	$0.763881\pi$
$468$		0			0
$469$	1.81567	+	12.6283i	0.0838401	+	0.583121i
$470$	4.90985	−	10.7511i	0.226474	−	0.495910i
$471$		0			0
$472$	0.0702757	−	0.0206348i	0.00323470	−	0.000949795i
$473$	−1.74857	+	3.82883i	−0.0803993	+	0.176050i
$474$		0			0
$475$	−19.1555	−	22.1066i	−0.878913	−	1.01432i
$476$	7.64748	+	16.7456i	0.350521	+	0.767535i
$477$		0			0
$478$	0.426324	−	2.96515i	0.0194996	−	0.135623i
$479$	−22.3396	−	14.3568i	−1.02072	−	0.655977i	−0.0805743	−	0.996749i	$-0.525675\pi$
$479$	−22.3396	−	14.3568i	−1.02072	−	0.655977i	−0.940146	+	0.340771i	$0.889312\pi$
$480$		0			0
$481$	0.837181	+	0.245818i	0.0381722	+	0.0112084i
$482$	−20.4314			−0.930625
$483$		0			0
$484$	−0.215343			−0.00978834
$485$	−48.7531	−	14.3152i	−2.21377	−	0.650020i
$486$		0			0
$487$	−10.9925	−	7.06445i	−0.498118	−	0.320121i	0.267345	−	0.963601i	$-0.413854\pi$
$487$	−10.9925	−	7.06445i	−0.498118	−	0.320121i	−0.765463	+	0.643480i	$0.777490\pi$
$488$	−0.273532	+	1.90246i	−0.0123822	+	0.0861203i
$489$		0			0
$490$	−2.88278	−	6.31241i	−0.130231	−	0.285166i
$491$	−22.0074	−	25.3979i	−0.993182	−	1.14619i	−0.989255	−	0.146201i	$-0.953296\pi$
$491$	−22.0074	−	25.3979i	−0.993182	−	1.14619i	−0.00392677	−	0.999992i	$-0.501250\pi$
$492$		0			0
$493$	−25.8145	+	56.5258i	−1.16262	+	2.54579i
$494$	0.320264	−	0.0940379i	0.0144093	−	0.00423096i
$495$		0			0
$496$	0.949914	−	2.08002i	0.0426524	−	0.0933957i
$497$	−4.10076	−	28.5214i	−0.183944	−	1.27936i
$498$		0			0
$499$	10.0598	+	22.0279i	0.450339	+	0.986104i	0.989584	+	0.143956i	$0.0459823\pi$
$499$	10.0598	+	22.0279i	0.450339	+	0.986104i	−0.539245	+	0.842149i	$0.681290\pi$
$500$	−25.6161	+	16.4625i	−1.14559	+	0.736225i
$501$		0			0
$502$	0.836551	+	0.537619i	0.0373371	+	0.0239951i
$503$	−26.7257	+	30.8431i	−1.19164	+	1.37522i	−0.282216	+	0.959351i	$0.591070\pi$
$503$	−26.7257	+	30.8431i	−1.19164	+	1.37522i	−0.909422	+	0.415874i	$0.863476\pi$
$504$		0			0
$505$	−5.86023			−0.260777
$506$	1.43156	+	15.6843i	0.0636406	+	0.697253i
$507$		0			0
$508$	5.91619	+	1.73715i	0.262488	+	0.0770736i
$509$	−4.25973	+	4.91599i	−0.188809	+	0.217897i	−0.842260	−	0.539072i	$-0.818775\pi$
$509$	−4.25973	+	4.91599i	−0.188809	+	0.217897i	0.653451	+	0.756969i	$0.273321\pi$
$510$		0			0
$511$	2.29831	−	15.9851i	0.101671	−	0.707138i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$		0			0
$514$	−4.59761	−	5.30592i	−0.202792	−	0.234034i
$515$	4.75957	+	33.1036i	0.209732	+	1.45872i
$516$		0			0
$517$	8.94935	−	2.62777i	0.393592	−	0.115569i
$518$	17.5361	−	5.14906i	0.770492	−	0.226237i
$519$		0			0
$520$	−0.0832386	−	0.578937i	−0.00365026	−	0.0253881i
$521$	26.3099	+	30.3633i	1.15266	+	1.33024i	0.935179	+	0.354176i	$0.115239\pi$
$521$	26.3099	+	30.3633i	1.15266	+	1.33024i	0.217481	+	0.976065i	$0.430216\pi$
$522$		0			0
$523$	−10.3505	+	6.65184i	−0.452594	+	0.290865i	−0.747010	−	0.664813i	$-0.768511\pi$
$523$	−10.3505	+	6.65184i	−0.452594	+	0.290865i	0.294416	+	0.955677i	$0.404875\pi$
$524$	−0.917296	+	6.37993i	−0.0400722	+	0.278709i
$525$		0			0
$526$	−11.3765	+	13.1292i	−0.496038	+	0.572459i
$527$	13.7193	+	4.02834i	0.597620	+	0.175477i
$528$		0			0
$529$	−22.6199	+	4.16388i	−0.983476	+	0.181038i
$530$	18.1051			0.786436
$531$		0			0
$532$	4.57856	−	5.28394i	0.198506	−	0.229088i
$533$	0.762864	+	0.490263i	0.0330433	+	0.0212356i
$534$		0			0
$535$	67.6704	−	43.4891i	2.92565	−	1.88020i
$536$	1.80020	+	3.94189i	0.0777568	+	0.170264i
$537$		0			0
$538$	4.32768	+	30.0997i	0.186580	+	1.29769i
$539$	2.27497	−	4.98149i	0.0979899	−	0.214568i
$540$		0			0
$541$	−2.78522	+	0.817814i	−0.119746	+	0.0351606i	−0.341056	−	0.940043i	$-0.610785\pi$
$541$	−2.78522	+	0.817814i	−0.119746	+	0.0351606i	0.221311	+	0.975203i	$0.428967\pi$
$542$	−2.51560	+	5.50840i	−0.108054	+	0.236606i
$543$		0			0
$544$	4.09483	+	4.72568i	0.175564	+	0.202612i
$545$	−11.2008	−	24.5263i	−0.479788	−	1.05059i
$546$		0			0
$547$	−3.80018	+	26.4309i	−0.162484	+	1.13010i	0.731447	+	0.681898i	$0.238845\pi$
$547$	−3.80018	+	26.4309i	−0.162484	+	1.13010i	−0.893931	+	0.448204i	$0.852064\pi$
$548$	−12.1089	−	7.78193i	−0.517267	−	0.332428i
$549$		0			0
$550$	−38.8113	−	11.3960i	−1.65492	−	0.485928i
$551$	23.6007			1.00542
$552$		0			0
$553$	−28.3316			−1.20478
$554$	−7.27345	−	2.13568i	−0.309019	−	0.0907362i
$555$		0			0
$556$	−9.20678	−	5.91684i	−0.390454	−	0.250930i
$557$	−3.55584	+	24.7314i	−0.150666	+	1.04790i	0.764441	+	0.644693i	$0.223015\pi$
$557$	−3.55584	+	24.7314i	−0.150666	+	1.04790i	−0.915107	+	0.403211i	$0.867894\pi$
$558$		0			0
$559$	0.0748368	+	0.163870i	0.00316526	+	0.00693095i
$560$	−8.02301	−	9.25905i	−0.339034	−	0.391266i
$561$		0			0
$562$	6.44278	−	14.1077i	0.271772	−	0.595099i
$563$	29.9255	−	8.78692i	1.26121	−	0.370325i	0.418265	−	0.908325i	$-0.362638\pi$
$563$	29.9255	−	8.78692i	1.26121	−	0.370325i	0.842944	+	0.538001i	$0.180820\pi$
$564$		0			0
$565$	−18.0206	+	39.4595i	−0.758131	+	1.66007i
$566$	1.34098	+	9.32675i	0.0563658	+	0.392033i
$567$		0			0
$568$	−4.06581	−	8.90289i	−0.170598	−	0.373557i
$569$	−5.10503	+	3.28080i	−0.214014	+	0.137538i	−0.643256	−	0.765651i	$-0.722417\pi$
$569$	−5.10503	+	3.28080i	−0.214014	+	0.137538i	0.429242	+	0.903189i	$0.358781\pi$
$570$		0			0
$571$	−29.8567	−	19.1877i	−1.24946	−	0.802982i	−0.262658	−	0.964889i	$-0.584599\pi$
$571$	−29.8567	−	19.1877i	−1.24946	−	0.802982i	−0.986806	+	0.161907i	$0.948236\pi$
$572$	0.302265	−	0.348832i	0.0126383	−	0.0145854i
$573$		0			0
$574$	18.9948			0.792826
$575$	11.4216	−	57.9567i	0.476314	−	2.41696i
$576$		0			0
$577$	−5.73647	−	1.68438i	−0.238812	−	0.0701216i	0.160136	−	0.987095i	$-0.448807\pi$
$577$	−5.73647	−	1.68438i	−0.238812	−	0.0701216i	−0.398949	+	0.916973i	$0.630625\pi$
$578$	−14.4722	+	16.7018i	−0.601965	+	0.694705i
$579$		0			0
$580$	5.88550	−	40.9346i	0.244382	−	1.69972i
$581$	−27.2648	+	17.5221i	−1.13114	+	0.726937i
$582$		0			0
$583$	9.35652	+	10.7980i	0.387507	+	0.447207i
$584$	−0.780654	−	5.42957i	−0.0323037	−	0.224677i
$585$		0			0
$586$	−5.81179	+	1.70649i	−0.240083	+	0.0704946i
$587$	−7.42084	+	2.17895i	−0.306291	+	0.0899351i	−0.431266	−	0.902225i	$-0.641933\pi$
$587$	−7.42084	+	2.17895i	−0.306291	+	0.0899351i	0.124975	+	0.992160i	$0.460115\pi$
$588$		0			0
$589$	−0.772828	−	5.37513i	−0.0318438	−	0.221479i
$590$	−0.199596	−	0.230346i	−0.00821724	−	0.00948320i
$591$		0			0
$592$	5.22238	−	3.35622i	0.214639	−	0.137940i
$593$	2.74913	−	19.1206i	0.112893	−	0.785189i	−0.852188	−	0.523236i	$-0.824724\pi$
$593$	2.74913	−	19.1206i	0.112893	−	0.785189i	0.965081	−	0.261953i	$-0.0843664\pi$
$594$		0			0
$595$	50.1677	−	57.8966i	2.05668	−	2.37353i
$596$	3.88215	+	1.13990i	0.159019	+	0.0466922i
$597$		0			0
$598$	0.547435	+	0.393285i	0.0223863	+	0.0160826i
$599$	−18.1025			−0.739648			−0.369824	−	0.929102i	$-0.620582\pi$
$599$	−18.1025			−0.739648			−0.369824	+	0.929102i	$0.620582\pi$
$600$		0			0
$601$	20.6430	−	23.8232i	0.842044	−	0.971771i	−0.157833	−	0.987466i	$-0.550451\pi$
$601$	20.6430	−	23.8232i	0.842044	−	0.971771i	0.999877	+	0.0156953i	$0.00499619\pi$
$602$	3.17449	+	2.04012i	0.129382	+	0.0831490i
$603$		0			0
$604$	−14.7292	+	9.46590i	−0.599323	+	0.385162i
$605$	0.372266	+	0.815149i	0.0151348	+	0.0331405i
$606$		0			0
$607$	−1.35687	−	9.43722i	−0.0550735	−	0.383045i	−0.998652	−	0.0518971i	$-0.983473\pi$
$607$	−1.35687	−	9.43722i	−0.0550735	−	0.383045i	0.943579	−	0.331148i	$-0.107436\pi$
$608$	0.986535	−	2.16021i	0.0400093	−	0.0876081i
$609$		0			0
$610$	7.67431	−	2.25338i	0.310724	−	0.0912368i
$611$	0.165830	−	0.363118i	0.00670878	−	0.0146902i
$612$		0			0
$613$	9.33907	+	10.7779i	0.377201	+	0.435314i	0.912329	−	0.409457i	$-0.134282\pi$
$613$	9.33907	+	10.7779i	0.377201	+	0.435314i	−0.535128	+	0.844771i	$0.679737\pi$
$614$	−8.82577	−	19.3257i	−0.356179	−	0.779923i
$615$		0			0
$616$	1.37595	−	9.56994i	0.0554386	−	0.385584i
$617$	2.60863	+	1.67647i	0.105020	+	0.0674921i	0.592096	−	0.805867i	$-0.298300\pi$
$617$	2.60863	+	1.67647i	0.105020	+	0.0674921i	−0.487077	+	0.873359i	$0.661937\pi$
$618$		0			0
$619$	−43.4217	−	12.7498i	−1.74526	−	0.512456i	−0.755497	−	0.655152i	$-0.772605\pi$
$619$	−43.4217	−	12.7498i	−1.74526	−	0.512456i	−0.989767	+	0.142696i	$0.954423\pi$
$620$	−9.51571			−0.382160
$621$		0			0
$622$	−8.87563			−0.355880
$623$	−37.0159	−	10.8688i	−1.48301	−	0.435451i
$624$		0			0
$625$	54.7893	+	35.2109i	2.19157	+	1.40844i
$626$	−1.54784	+	10.7655i	−0.0618642	+	0.430275i
$627$		0			0
$628$	−1.18092	−	2.58584i	−0.0471237	−	0.103186i
$629$	25.4201	+	29.3364i	1.01357	+	1.16972i
$630$		0			0
$631$	9.54254	−	20.8953i	0.379883	−	0.831827i	−0.619037	−	0.785362i	$-0.712477\pi$
$631$	9.54254	−	20.8953i	0.379883	−	0.831827i	0.998920	−	0.0464653i	$-0.0147957\pi$
$632$	−9.23343	+	2.71118i	−0.367286	+	0.107845i
$633$		0			0
$634$	13.6324	−	29.8508i	0.541413	−	1.18553i
$635$	−3.65166	−	25.3978i	−0.144912	−	1.00788i
$636$		0			0
$637$	−0.0973661	−	0.213202i	−0.00385779	−	0.00844737i
$638$	27.4552	−	17.6444i	1.08696	−	0.698547i
$639$		0			0
$640$	−3.50079	−	2.24982i	−0.138381	−	0.0889320i
$641$	−12.8841	+	14.8691i	−0.508893	+	0.587293i	−0.950815	−	0.309760i	$-0.899751\pi$
$641$	−12.8841	+	14.8691i	−0.508893	+	0.587293i	0.441922	+	0.897053i	$0.354297\pi$
$642$		0			0
$643$	−23.1768			−0.914005			−0.457003	−	0.889465i	$-0.651077\pi$
$643$	−23.1768			−0.914005			−0.457003	+	0.889465i	$0.651077\pi$
$644$	14.1004	+	0.730750i	0.555633	+	0.0287956i
$645$		0			0
$646$	14.2482	+	4.18364i	0.560586	+	0.164603i
$647$	24.5633	−	28.3475i	0.965683	−	1.11446i	−0.0277013	−	0.999616i	$-0.508819\pi$
$647$	24.5633	−	28.3475i	0.965683	−	1.11446i	0.993384	−	0.114841i	$-0.0366358\pi$
$648$		0			0
$649$	0.0342308	−	0.238080i	0.00134368	−	0.00934547i
$650$	−1.45638	+	0.935961i	−0.0571241	+	0.0367114i
$651$		0			0
$652$	1.31595	+	1.51869i	0.0515367	+	0.0594765i
$653$	−1.90104	−	13.2220i	−0.0743935	−	0.517418i	−0.992611	−	0.121341i	$-0.961280\pi$
$653$	−1.90104	−	13.2220i	−0.0743935	−	0.517418i	0.918217	−	0.396077i	$-0.129629\pi$
$654$		0			0
$655$	25.7360	−	7.55676i	1.00559	−	0.295267i
$656$	6.19051	−	1.81770i	0.241699	−	0.0709692i
$657$		0			0
$658$	−1.19000	−	8.27661i	−0.0463909	−	0.322656i
$659$	−9.21102	−	10.6301i	−0.358810	−	0.414089i	0.547430	−	0.836851i	$-0.315606\pi$
$659$	−9.21102	−	10.6301i	−0.358810	−	0.414089i	−0.906241	+	0.422762i	$0.861061\pi$
$660$		0			0
$661$	−6.47163	+	4.15906i	−0.251717	+	0.161769i	−0.660415	−	0.750901i	$-0.729619\pi$
$661$	−6.47163	+	4.15906i	−0.251717	+	0.161769i	0.408697	+	0.912670i	$0.365983\pi$
$662$	2.50660	−	17.4338i	0.0974217	−	0.677583i
$663$		0			0
$664$	−7.20901	+	8.31965i	−0.279764	+	0.322865i
$665$	−27.9165	−	8.19702i	−1.08255	−	0.317867i
$666$		0			0
$667$	29.3049	+	37.5864i	1.13469	+	1.45535i
$668$	9.22759			0.357026
$669$		0			0
$670$	11.8094	−	13.6287i	0.456236	−	0.526524i
$671$	5.30993	+	3.41248i	0.204987	+	0.131737i
$672$		0			0
$673$	−41.4411	+	26.6326i	−1.59744	+	1.02661i	−0.628982	+	0.777420i	$0.716528\pi$
$673$	−41.4411	+	26.6326i	−1.59744	+	1.02661i	−0.968455	+	0.249190i	$0.919836\pi$
$674$	−8.93338	−	19.5614i	−0.344101	−	0.753476i
$675$		0			0
$676$	1.84728	+	12.8481i	0.0710493	+	0.494159i
$677$	12.0855	−	26.4637i	0.464485	−	1.01708i	−0.521957	−	0.852972i	$-0.674798\pi$
$677$	12.0855	−	26.4637i	0.464485	−	1.01708i	0.986442	−	0.164109i	$-0.0524749\pi$
$678$		0			0
$679$	−34.4915	+	10.1276i	−1.32366	+	0.388663i
$680$	10.8096	−	23.6696i	0.414528	−	0.907689i
$681$		0			0
$682$	−4.91761	−	5.67523i	−0.188305	−	0.217316i
$683$	3.51040	+	7.68671i	0.134322	+	0.294124i	0.964826	−	0.262888i	$-0.0846751\pi$
$683$	3.51040	+	7.68671i	0.134322	+	0.294124i	−0.830505	+	0.557012i	$0.811948\pi$
$684$		0			0
$685$	−8.52448	+	59.2891i	−0.325704	+	2.26532i
$686$	13.2069	+	8.48753i	0.504240	+	0.324055i
$687$		0			0
$688$	1.22981	+	0.361106i	0.0468862	+	0.0137670i
$689$	0.611502			0.0232964
$690$		0			0
$691$	16.9073			0.643183			0.321592	−	0.946878i	$-0.395782\pi$
$691$	16.9073			0.643183			0.321592	+	0.946878i	$0.395782\pi$
$692$	9.01583	+	2.64729i	0.342731	+	0.100635i
$693$		0			0
$694$	−18.0077	−	11.5729i	−0.683564	−	0.439300i
$695$	−6.48142	+	45.0793i	−0.245854	+	1.70995i
$696$		0			0
$697$	16.7592	+	36.6975i	0.634800	+	1.39002i
$698$	−19.3386	−	22.3180i	−0.731977	−	0.844747i
$699$		0			0
$700$	−15.0642	+	32.9859i	−0.569372	+	1.24675i
$701$	−26.2374	+	7.70400i	−0.990973	+	0.290976i	−0.736747	−	0.676169i	$-0.763639\pi$
$701$	−26.2374	+	7.70400i	−0.990973	+	0.290976i	−0.254227	+	0.967145i	$0.581821\pi$
$702$		0			0
$703$	6.12427	−	13.4103i	0.230981	−	0.505779i
$704$	−0.467362	−	3.25057i	−0.0176144	−	0.122511i
$705$		0			0
$706$	3.69519	+	8.09134i	0.139070	+	0.304521i
$707$	−3.48780	+	2.24147i	−0.131172	+	0.0842992i
$708$		0			0
$709$	−0.598495	−	0.384630i	−0.0224770	−	0.0144451i	0.529354	−	0.848401i	$-0.322434\pi$
$709$	−0.598495	−	0.384630i	−0.0224770	−	0.0144451i	−0.551831	+	0.833956i	$0.686071\pi$
$710$	−26.6719	+	30.7810i	−1.00098	+	1.15519i
$711$		0			0
$712$	−13.1038			−0.491085
$713$	7.60081	−	7.90510i	0.284653	−	0.296048i
$714$		0			0
$715$	−1.84298	−	0.541147i	−0.0689234	−	0.0202377i
$716$	−13.3764	+	15.4372i	−0.499900	+	0.576915i
$717$		0			0
$718$	3.20348	−	22.2807i	0.119553	−	0.831508i
$719$	16.6413	−	10.6947i	0.620615	−	0.398845i	−0.192209	−	0.981354i	$-0.561565\pi$
$719$	16.6413	−	10.6947i	0.620615	−	0.398845i	0.812824	+	0.582509i	$0.197929\pi$
$720$		0			0
$721$	15.4945	+	17.8816i	0.577044	+	0.665944i
$722$	1.90136	+	13.2242i	0.0707613	+	0.492156i
$723$		0			0
$724$	−14.3285	+	4.20721i	−0.532513	+	0.156360i
$725$	−117.449	+	34.4861i	−4.36195	+	1.28078i
$726$		0			0
$727$	4.91238	+	34.1664i	0.182190	+	1.26716i	0.851570	+	0.524241i	$0.175651\pi$
$727$	4.91238	+	34.1664i	0.182190	+	1.26716i	−0.669380	+	0.742920i	$0.733440\pi$
$728$	−0.270978	−	0.312725i	−0.0100431	−	0.0115904i
$729$		0			0
$730$	−19.2033	+	12.3412i	−0.710744	+	0.456768i
$731$	−1.14060	+	7.93306i	−0.0421867	+	0.293415i
$732$		0			0
$733$	5.98030	−	6.90163i	0.220887	−	0.254918i	−0.634480	−	0.772939i	$-0.718786\pi$
$733$	5.98030	−	6.90163i	0.220887	−	0.254918i	0.855368	+	0.518021i	$0.173331\pi$
$734$	6.78176	+	1.99130i	0.250319	+	0.0735004i
$735$		0			0
$736$	4.66533	−	1.11118i	0.171966	−	0.0409585i
$737$	14.2312			0.524213
$738$		0			0
$739$	−4.12387	+	4.75920i	−0.151699	+	0.175070i	−0.826513	−	0.562918i	$-0.809679\pi$
$739$	−4.12387	+	4.75920i	−0.151699	+	0.175070i	0.674814	+	0.737988i	$0.264224\pi$
$740$	−21.7324	−	13.9666i	−0.798900	−	0.513422i
$741$		0			0
$742$	10.7755	−	6.92501i	0.395582	−	0.254225i
$743$	−9.78288	−	21.4215i	−0.358899	−	0.785879i	−0.999833	−	0.0182830i	$-0.994180\pi$
$743$	−9.78288	−	21.4215i	−0.358899	−	0.785879i	0.640934	−	0.767596i	$-0.278547\pi$
$744$		0			0
$745$	−2.39618	−	16.6658i	−0.0877894	−	0.610589i
$746$	7.40933	−	16.2242i	0.271275	−	0.594009i
$747$		0			0
$748$	19.7030	−	5.78531i	0.720412	−	0.211532i
$749$	23.6409	−	51.7663i	0.863820	−	1.89150i
$750$		0			0
$751$	−21.0527	−	24.2962i	−0.768225	−	0.886579i	0.227975	−	0.973667i	$-0.426789\pi$
$751$	−21.0527	−	24.2962i	−0.768225	−	0.886579i	−0.996201	+	0.0870877i	$0.972244\pi$
$752$	−1.17986	−	2.58352i	−0.0430249	−	0.0942114i
$753$		0			0
$754$	0.198783	−	1.38257i	0.00723926	−	0.0503502i
$755$	61.2942	+	39.3914i	2.23072	+	1.43360i
$756$		0			0
$757$	4.35621	+	1.27910i	0.158329	+	0.0464897i	0.359937	−	0.932977i	$-0.382798\pi$
$757$	4.35621	+	1.27910i	0.158329	+	0.0464897i	−0.201607	+	0.979466i	$0.564616\pi$
$758$	−21.0931			−0.766137
$759$		0			0
$760$	−9.88257			−0.358478
$761$	37.7141	+	11.0738i	1.36713	+	0.401427i	0.881272	−	0.472609i	$-0.156688\pi$
$761$	37.7141	+	11.0738i	1.36713	+	0.401427i	0.485861	+	0.874036i	$0.338506\pi$
$762$		0			0
$763$	−16.0473	−	10.3130i	−0.580952	−	0.373355i
$764$	3.36637	−	23.4136i	0.121791	−	0.847074i
$765$		0			0
$766$	0.467928	+	1.02462i	0.0169069	+	0.0370210i
$767$	−0.00674137	−	0.00777995i	−0.000243417	−	0.000280918i
$768$		0			0
$769$	−1.65793	+	3.63035i	−0.0597863	+	0.130914i	−0.937167	−	0.348881i	$-0.886562\pi$
$769$	−1.65793	+	3.63035i	−0.0597863	+	0.130914i	0.877381	+	0.479795i	$0.159289\pi$
$770$	−38.6041	+	11.3352i	−1.39120	+	0.408492i
$771$		0			0
$772$	−0.812066	+	1.77818i	−0.0292269	+	0.0639980i
$773$	4.01135	+	27.8996i	0.144278	+	1.00348i	0.925371	+	0.379063i	$0.123754\pi$
$773$	4.01135	+	27.8996i	0.144278	+	1.00348i	−0.781093	+	0.624415i	$0.785337\pi$
$774$		0			0
$775$	11.7003	+	25.6201i	0.420288	+	0.920302i
$776$	−10.2718	+	6.60131i	−0.368738	+	0.236973i
$777$		0			0
$778$	−2.62419	−	1.68646i	−0.0940818	−	0.0604627i
$779$	10.0338	−	11.5796i	0.359497	−	0.414882i
$780$		0			0
$781$	−32.1417			−1.15012
$782$	11.0291	+	27.8864i	0.394398	+	0.997217i
$783$		0			0
$784$	−1.60004	−	0.469815i	−0.0571444	−	0.0167791i
$785$	−7.74685	+	8.94034i	−0.276497	+	0.319094i
$786$		0			0
$787$	2.88214	−	20.0457i	0.102737	−	0.714552i	−0.871724	−	0.489997i	$-0.836998\pi$
$787$	2.88214	−	20.0457i	0.102737	−	0.714552i	0.974461	−	0.224555i	$-0.0720929\pi$
$788$	−1.58114	+	1.01614i	−0.0563258	+	0.0361984i
$789$		0			0
$790$	26.2246	+	30.2648i	0.933031	+	1.07677i
$791$	4.36763	+	30.3776i	0.155295	+	1.08010i
$792$		0			0
$793$	0.259200	−	0.0761081i	0.00920448	−	0.00270268i
$794$	19.8208	−	5.81992i	0.703415	−	0.206541i
$795$		0			0
$796$	2.34874	+	16.3359i	0.0832490	+	0.579010i
$797$	−0.474904	−	0.548068i	−0.0168220	−	0.0194136i	0.747276	−	0.664514i	$-0.231361\pi$
$797$	−0.474904	−	0.548068i	−0.0168220	−	0.0194136i	−0.764098	+	0.645100i	$0.776816\pi$
$798$		0			0
$799$	14.9403	−	9.60156i	0.528551	−	0.339679i
$800$	−1.75293	+	12.1919i	−0.0619753	+	0.431048i
$801$		0			0
$802$	−6.74731	+	7.78681i	−0.238256	+	0.274962i
$803$	−17.2844	−	5.07515i	−0.609952	−	0.179098i
$804$		0			0
$805$	−21.6093	−	54.6380i	−0.761627	−	1.92574i
$806$	−0.321394			−0.0113206
$807$		0			0
$808$	−0.922198	+	1.06427i	−0.0324428	+	0.0374410i
$809$	38.3226	+	24.6284i	1.34735	+	0.865889i	0.997483	−	0.0709105i	$-0.0225905\pi$
$809$	38.3226	+	24.6284i	1.34735	+	0.865889i	0.349867	+	0.936799i	$0.386227\pi$
$810$		0			0
$811$	−11.0752	+	7.11758i	−0.388902	+	0.249932i	−0.720451	−	0.693506i	$-0.756065\pi$
$811$	−11.0752	+	7.11758i	−0.388902	+	0.249932i	0.331549	+	0.943438i	$0.392429\pi$
$812$	−12.1542	−	26.6139i	−0.426528	−	0.933966i
$813$		0			0
$814$	−2.90132	−	20.1791i	−0.101691	−	0.707277i
$815$	3.47386	−	7.60670i	0.121684	−	0.266451i
$816$		0			0
$817$	2.92058	−	0.857561i	0.102178	−	0.0300023i
$818$	1.49664	−	3.27719i	0.0523289	−	0.114584i
$819$		0			0
$820$	−17.5822	−	20.2909i	−0.613997	−	0.708590i
$821$	9.98143	+	21.8563i	0.348354	+	0.762790i	0.999991	+	0.00425830i	$0.00135546\pi$
$821$	9.98143	+	21.8563i	0.348354	+	0.762790i	−0.651637	+	0.758531i	$0.725917\pi$
$822$		0			0
$823$	−0.701939	+	4.88209i	−0.0244680	+	0.170179i	−0.998391	−	0.0566985i	$-0.981943\pi$
$823$	−0.701939	+	4.88209i	−0.0244680	+	0.170179i	0.973923	+	0.226878i	$0.0728517\pi$
$824$	6.76091	+	4.34498i	0.235528	+	0.151364i
$825$		0			0
$826$	−0.206897	−	0.0607505i	−0.00719888	−	0.00211378i
$827$	−7.46011			−0.259413			−0.129707	−	0.991552i	$-0.541404\pi$
$827$	−7.46011			−0.259413			−0.129707	+	0.991552i	$0.541404\pi$
$828$		0			0
$829$	41.5609			1.44347			0.721735	−	0.692170i	$-0.243345\pi$
$829$	41.5609			1.44347			0.721735	+	0.692170i	$0.243345\pi$
$830$	43.9550	+	12.9063i	1.52570	+	0.447986i
$831$		0			0
$832$	−0.118239	−	0.0759879i	−0.00409922	−	0.00263441i
$833$	1.48398	−	10.3213i	0.0514167	−	0.357611i
$834$		0			0
$835$	−15.9518	−	34.9296i	−0.552035	−	1.20879i
$836$	−5.10720	−	5.89402i	−0.176636	−	0.203849i
$837$		0			0
$838$	−5.60684	+	12.2773i	−0.193685	+	0.424111i
$839$	−39.4821	+	11.5930i	−1.36307	+	0.400234i	−0.879845	−	0.475261i	$-0.842354\pi$
$839$	−39.4821	+	11.5930i	−1.36307	+	0.400234i	−0.483227	+	0.875495i	$0.660536\pi$
$840$		0			0
$841$	28.9800	−	63.4574i	0.999311	−	2.18819i
$842$	−2.36917	−	16.4779i	−0.0816468	−	0.567866i
$843$		0			0
$844$	2.48343	+	5.43795i	0.0854832	+	0.187182i
$845$	45.4411	−	29.2032i	1.56322	−	1.00462i
$846$		0			0
$847$	0.533345	+	0.342760i	0.0183259	+	0.0117774i
$848$	2.84912	−	3.28806i	0.0978393	−	0.112913i
$849$		0			0
$850$	−77.0194			−2.64174
$851$	28.9617	−	6.89802i	0.992795	−	0.236461i
$852$		0			0
$853$	15.4174	+	4.52696i	0.527883	+	0.155000i	0.534805	−	0.844976i	$-0.320385\pi$
$853$	15.4174	+	4.52696i	0.527883	+	0.155000i	−0.00692206	+	0.999976i	$0.502203\pi$
$854$	3.70558	−	4.27647i	0.126802	−	0.146338i
$855$		0			0
$856$	2.75095	−	19.1333i	0.0940255	−	0.653962i
$857$	21.8933	−	14.0700i	0.747860	−	0.480620i	−0.110367	−	0.993891i	$-0.535203\pi$
$857$	21.8933	−	14.0700i	0.747860	−	0.480620i	0.858227	+	0.513270i	$0.171566\pi$
$858$		0			0
$859$	7.71658	+	8.90541i	0.263286	+	0.303849i	0.871965	−	0.489568i	$-0.162846\pi$
$859$	7.71658	+	8.90541i	0.263286	+	0.303849i	−0.608679	+	0.793417i	$0.708300\pi$
$860$	−0.759079	−	5.27951i	−0.0258844	−	0.180030i
$861$		0			0
$862$	−20.1651	+	5.92100i	−0.686825	+	0.201670i
$863$	−16.9583	+	4.97942i	−0.577269	+	0.169501i	−0.557317	−	0.830300i	$-0.688169\pi$
$863$	−16.9583	+	4.97942i	−0.577269	+	0.169501i	−0.0199513	+	0.999801i	$0.506351\pi$
$864$		0			0
$865$	−5.56485	−	38.7044i	−0.189211	−	1.31599i
$866$	1.35783	+	1.56702i	0.0461410	+	0.0532496i
$867$		0			0
$868$	−5.66341	+	3.63965i	−0.192229	+	0.123538i
$869$	−4.49753	+	31.2810i	−0.152568	+	1.06114i
$870$		0			0
$871$	0.398862	−	0.460312i	0.0135149	−	0.0155971i
$872$	−6.21682	−	1.82542i	−0.210528	−	0.0618166i
$873$		0			0
$874$	7.89384	−	8.20986i	0.267013	−	0.277703i
$875$	89.6470			3.03062
$876$		0			0
$877$	21.1345	−	24.3905i	0.713660	−	0.823608i	−0.276869	−	0.960908i	$-0.589297\pi$
$877$	21.1345	−	24.3905i	0.713660	−	0.823608i	0.990530	+	0.137300i	$0.0438424\pi$
$878$	1.90923	+	1.22699i	0.0644333	+	0.0414088i
$879$		0			0
$880$	−11.4966	+	7.38842i	−0.387550	+	0.249063i
$881$	4.30308	+	9.42243i	0.144974	+	0.317450i	0.968164	−	0.250317i	$-0.0805348\pi$
$881$	4.30308	+	9.42243i	0.144974	+	0.317450i	−0.823189	+	0.567767i	$0.807808\pi$
$882$		0			0
$883$	−8.08407	−	56.2259i	−0.272051	−	1.89215i	−0.427033	−	0.904236i	$-0.640441\pi$
$883$	−8.08407	−	56.2259i	−0.272051	−	1.89215i	0.154983	−	0.987917i	$-0.450468\pi$
$884$	0.365094	−	0.799444i	0.0122794	−	0.0268882i
$885$		0			0
$886$	25.7315	−	7.55544i	0.864465	−	0.253830i
$887$	−17.4300	+	38.1665i	−0.585244	+	1.28151i	0.353030	+	0.935612i	$0.385151\pi$
$887$	−17.4300	+	38.1665i	−0.585244	+	1.28151i	−0.938274	+	0.345893i	$0.887576\pi$
$888$		0			0
$889$	−11.8877	−	13.7192i	−0.398701	−	0.460126i
$890$	22.6526	+	49.6023i	0.759317	+	1.66267i
$891$		0			0
$892$	2.86327	−	19.9145i	0.0958694	−	0.666786i
$893$	−5.67419	−	3.64658i	−0.189879	−	0.122028i
$894$		0			0
$895$	81.5590	+	23.9479i	2.72622	+	0.800489i
$896$	−2.94408			−0.0983547
$897$		0			0
$898$	−4.56941			−0.152483
$899$	−21.8041	−	6.40226i	−0.727207	−	0.213527i
$900$		0			0
$901$	22.8863	+	14.7081i	0.762453	+	0.489999i
$902$	3.01535	−	20.9722i	0.100400	−	0.698299i
$903$		0			0
$904$	4.33041	+	9.48227i	0.144027	+	0.315376i
$905$	40.6954	+	46.9650i	1.35276	+	1.56117i
$906$		0			0
$907$	−8.68682	+	19.0215i	−0.288441	+	0.631598i	−0.997275	−	0.0737778i	$-0.976494\pi$
$907$	−8.68682	+	19.0215i	−0.288441	+	0.631598i	0.708834	+	0.705376i	$0.249222\pi$
$908$	12.5251	−	3.67771i	0.415661	−	0.122049i
$909$		0			0
$910$	−0.715330	+	1.56635i	−0.0237129	+	0.0519241i
$911$	−0.338973	−	2.35761i	−0.0112307	−	0.0781112i	0.983435	−	0.181260i	$-0.0580174\pi$
$911$	−0.338973	−	2.35761i	−0.0112307	−	0.0781112i	−0.994666	+	0.103148i	$0.967108\pi$
$912$		0			0
$913$	15.0180	+	32.8848i	0.497023	+	1.08833i
$914$	−22.5577	+	14.4970i	−0.746144	+	0.479518i
$915$		0			0
$916$	14.9735	+	9.62285i	0.494737	+	0.317948i
$917$	12.4267	−	14.3412i	0.410367	−	0.473589i
$918$		0			0
$919$	33.7332			1.11275			0.556377	−	0.830930i	$-0.312191\pi$
$919$	33.7332			1.11275			0.556377	+	0.830930i	$0.312191\pi$
$920$	−12.2712	−	15.7390i	−0.404568	−	0.518898i
$921$		0			0
$922$	−1.28244	−	0.376558i	−0.0422348	−	0.0124013i
$923$	−0.900844	+	1.03963i	−0.0296516	+	0.0342198i
$924$		0			0
$925$	−10.8819	+	75.6854i	−0.357795	+	2.48852i
$926$	−30.5124	+	19.6091i	−1.00270	+	0.644396i
$927$		0			0
$928$	−6.50793	−	7.51056i	−0.213633	−	0.246546i
$929$	0.787770	+	5.47906i	0.0258459	+	0.179762i	0.998655	−	0.0518458i	$-0.0165104\pi$
$929$	0.787770	+	5.47906i	0.0258459	+	0.179762i	−0.972809	+	0.231608i	$0.925601\pi$
$930$		0			0
$931$	−3.79982	+	1.11573i	−0.124534	+	0.0365665i
$932$	9.40137	−	2.76049i	0.307952	−	0.0904229i
$933$		0			0
$934$	−1.89623	−	13.1886i	−0.0620465	−	0.431543i
$935$	−55.9600	−	64.5813i	−1.83009	−	2.11204i
$936$		0			0
$937$	−19.7333	+	12.6818i	−0.644660	+	0.414298i	−0.821711	−	0.569904i	$-0.806980\pi$
$937$	−19.7333	+	12.6818i	−0.644660	+	0.414298i	0.177052	+	0.984202i	$0.443344\pi$
$938$	1.81567	−	12.6283i	0.0592839	−	0.412329i
$939$		0			0
$940$	−7.73989	+	8.93231i	−0.252447	+	0.291340i
$941$	13.4047	+	3.93597i	0.436980	+	0.128309i	0.492821	−	0.870131i	$-0.335966\pi$
$941$	13.4047	+	3.93597i	0.436980	+	0.128309i	−0.0558410	+	0.998440i	$0.517784\pi$
$942$		0			0
$943$	30.9005	+	1.60142i	1.00626	+	0.0521493i
$944$	−0.0732426			−0.00238384
$945$		0			0
$946$	2.75645	−	3.18111i	0.0896198	−	0.103427i
$947$	−41.3656	−	26.5841i	−1.34420	−	0.863866i	−0.346945	−	0.937886i	$-0.612781\pi$
$947$	−41.3656	−	26.5841i	−1.34420	−	0.863866i	−0.997257	+	0.0740197i	$0.976417\pi$
$948$		0			0
$949$	−0.648591	+	0.416824i	−0.0210542	+	0.0135307i
$950$	12.1514	+	26.6078i	0.394243	+	0.863272i
$951$		0			0
$952$	−2.61991	−	18.2219i	−0.0849117	−	0.590574i
$953$	3.58850	−	7.85773i	0.116243	−	0.254537i	−0.842563	−	0.538597i	$-0.818954\pi$
$953$	3.58850	−	7.85773i	0.116243	−	0.254537i	0.958806	+	0.284061i	$0.0916817\pi$
$954$		0			0
$955$	−94.4479	+	27.7324i	−3.05626	+	0.897400i
$956$	−1.24443	+	2.72493i	−0.0402479	+	0.0881305i
$957$		0			0
$958$	17.3899	+	20.0690i	0.561842	+	0.648400i
$959$	17.6039	+	38.5473i	0.568461	+	1.24476i
$960$		0			0
$961$	3.66762	−	25.5089i	0.118310	−	0.822866i
$962$	−0.734014	−	0.471722i	−0.0236656	−	0.0152089i
$963$		0			0
$964$	19.6038	+	5.75619i	0.631396	+	0.185394i
$965$	8.13483			0.261869
$966$		0			0
$967$	−36.8290			−1.18434			−0.592170	−	0.805813i	$-0.701728\pi$
$967$	−36.8290			−1.18434			−0.592170	+	0.805813i	$0.701728\pi$
$968$	0.206621	+	0.0606693i	0.00664104	+	0.00194998i
$969$		0			0
$970$	42.7452	+	27.4707i	1.37247	+	0.882031i
$971$	−2.98567	+	20.7658i	−0.0958148	+	0.666407i	0.884145	+	0.467212i	$0.154742\pi$
$971$	−2.98567	+	20.7658i	−0.0958148	+	0.666407i	−0.979960	+	0.199194i	$0.936167\pi$
$972$		0			0
$973$	13.3848	+	29.3086i	0.429097	+	0.939592i
$974$	8.55694	+	9.87523i	0.274182	+	0.316423i
$975$		0			0
$976$	0.798437	−	1.74833i	0.0255573	−	0.0559628i
$977$	6.42291	−	1.88594i	0.205487	−	0.0603364i	−0.177369	−	0.984144i	$-0.556759\pi$
$977$	6.42291	−	1.88594i	0.205487	−	0.0603364i	0.382856	+	0.923808i	$0.374940\pi$
$978$		0			0
$979$	−17.8765	+	39.1440i	−0.571335	+	1.25105i
$980$	0.987597	+	6.86889i	0.0315476	+	0.219419i
$981$		0			0
$982$	13.9606	+	30.5694i	0.445499	+	0.975507i
$983$	−4.16508	+	2.67673i	−0.132845	+	0.0853745i	−0.605376	−	0.795940i	$-0.706977\pi$
$983$	−4.16508	+	2.67673i	−0.132845	+	0.0853745i	0.472530	+	0.881314i	$0.343341\pi$
$984$		0			0
$985$	6.57975	+	4.22855i	0.209648	+	0.134733i
$986$	40.6939	−	46.9633i	1.29596	−	1.49562i
$987$		0			0
$988$	−0.333784			−0.0106191
$989$	4.99223	+	3.58649i	0.158744	+	0.114044i
$990$		0			0
$991$	19.9464	+	5.85680i	0.633619	+	0.186047i	0.582742	−	0.812657i	$-0.301980\pi$
$991$	19.9464	+	5.85680i	0.633619	+	0.186047i	0.0508777	+	0.998705i	$0.483798\pi$
$992$	−1.49745	+	1.72814i	−0.0475439	+	0.0548686i
$993$		0			0
$994$	−4.10076	+	28.5214i	−0.130068	+	0.904645i
$995$	57.7766	−	37.1307i	1.83164	−	1.17712i
$996$		0			0
$997$	23.0796	+	26.6352i	0.730937	+	0.843546i	0.992577	−	0.121619i	$-0.0388087\pi$
$997$	23.0796	+	26.6352i	0.730937	+	0.843546i	−0.261640	+	0.965166i	$0.584263\pi$
$998$	−3.44634	−	23.9698i	−0.109092	−	0.758750i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.b.271.1		10
3.2	odd	2		138.2.e.c.133.1	yes	10
23.3	even	11		9522.2.a.bv.1.2		5
23.9	even	11	inner	414.2.i.b.55.1		10
23.20	odd	22		9522.2.a.ca.1.4		5
69.20	even	22		3174.2.a.y.1.2		5
69.26	odd	22		3174.2.a.z.1.4		5
69.32	odd	22		138.2.e.c.55.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.c.55.1	✓	10	69.32	odd	22
138.2.e.c.133.1	yes	10	3.2	odd	2
414.2.i.b.55.1		10	23.9	even	11	inner
414.2.i.b.271.1		10	1.1	even	1	trivial
3174.2.a.y.1.2		5	69.20	even	22
3174.2.a.z.1.4		5	69.26	odd	22
9522.2.a.bv.1.2		5	23.3	even	11
9522.2.a.ca.1.4		5	23.20	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(0.592229 - 4.11904i) q^{5} +(-1.22301 - 2.67803i) q^{7} +(-0.654861 - 0.755750i) q^{8} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(0.592229 - 4.11904i) q^{5} +(-1.22301 - 2.67803i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-1.72871 + 3.78534i) q^{10} +(-3.15098 + 0.925210i) q^{11} +(-0.0583872 + 0.127850i) q^{13} +(0.418986 + 2.91411i) q^{14} +(0.415415 + 0.909632i) q^{16} +(-5.26034 + 3.38061i) q^{17} +(1.99782 + 1.28392i) q^{19} +(2.72514 - 3.14498i) q^{20} +3.28400 q^{22} +(0.435919 + 4.77598i) q^{23} +(-11.8183 - 3.47017i) q^{25} +(0.0920417 - 0.106222i) q^{26} +(0.418986 - 2.91411i) q^{28} +(8.36028 - 5.37283i) q^{29} +(-1.49745 - 1.72814i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(5.99969 - 1.76167i) q^{34} +(-11.7552 + 3.45164i) q^{35} +(-0.883471 - 6.14467i) q^{37} +(-1.55518 - 1.79477i) q^{38} +(-3.50079 + 2.24982i) q^{40} +(0.918195 - 6.38618i) q^{41} +(0.839356 - 0.968669i) q^{43} +(-3.15098 - 0.925210i) q^{44} +(0.927287 - 4.70533i) q^{46} -2.84018 q^{47} +(-1.09204 + 1.26028i) q^{49} +(10.3619 + 6.65920i) q^{50} +(-0.118239 + 0.0759879i) q^{52} +(-1.80736 - 3.95756i) q^{53} +(1.94488 + 13.5269i) q^{55} +(-1.22301 + 2.67803i) q^{56} +(-9.53533 + 2.79983i) q^{58} +(-0.0304261 + 0.0666238i) q^{59} +(-1.25866 - 1.45257i) q^{61} +(0.949914 + 2.08002i) q^{62} +(-0.142315 + 0.989821i) q^{64} +(0.492041 + 0.316216i) q^{65} +(-4.15796 - 1.22089i) q^{67} -6.25297 q^{68} +12.2515 q^{70} +(9.39090 + 2.75742i) q^{71} +(4.61462 + 2.96563i) q^{73} +(-0.883471 + 6.14467i) q^{74} +(0.986535 + 2.16021i) q^{76} +(6.33142 + 7.30685i) q^{77} +(3.99764 - 8.75360i) q^{79} +(3.99283 - 1.17240i) q^{80} +(-2.68020 + 5.86881i) q^{82} +(-1.56667 - 10.8964i) q^{83} +(10.8096 + 23.6696i) q^{85} +(-1.07826 + 0.692957i) q^{86} +(2.76268 + 1.77546i) q^{88} +(8.58116 - 9.90318i) q^{89} +0.413795 q^{91} +(-2.21537 + 4.25348i) q^{92} +(2.72514 + 0.800172i) q^{94} +(6.47170 - 7.46874i) q^{95} +(1.73769 - 12.0859i) q^{97} +(1.40287 - 0.901569i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 - 2 * q^7 - q^8	\( 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8} + 11 q^{10} - 11 q^{11} - 13 q^{13} - 13 q^{14} - q^{16} - 2 q^{19} + 11 q^{20} - 22 q^{22} + 10 q^{23} + 5 q^{25} + 9 q^{26} - 13 q^{28} + 27 q^{29} - 18 q^{31} - q^{32} + 33 q^{34} - 44 q^{35} - q^{37} - 13 q^{38} - 11 q^{40} + 16 q^{41} + 20 q^{43} - 11 q^{44} - q^{46} - 19 q^{49} + 27 q^{50} - 2 q^{52} + q^{53} + 33 q^{55} - 2 q^{56} - 17 q^{58} + q^{59} - 34 q^{61} + 4 q^{62} - q^{64} - 11 q^{65} + 8 q^{67} - 22 q^{68} + 22 q^{70} + 22 q^{71} + 31 q^{73} - q^{74} - 2 q^{76} - 22 q^{77} + 32 q^{79} - 28 q^{82} - 33 q^{83} - 11 q^{85} + 20 q^{86} + 22 q^{88} + 23 q^{89} + 18 q^{91} - 23 q^{92} + 11 q^{94} + 22 q^{95} - q^{97} + 14 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 - 2 * q^7 - q^8 + 11 * q^10 - 11 * q^11 - 13 * q^13 - 13 * q^14 - q^16 - 2 * q^19 + 11 * q^20 - 22 * q^22 + 10 * q^23 + 5 * q^25 + 9 * q^26 - 13 * q^28 + 27 * q^29 - 18 * q^31 - q^32 + 33 * q^34 - 44 * q^35 - q^37 - 13 * q^38 - 11 * q^40 + 16 * q^41 + 20 * q^43 - 11 * q^44 - q^46 - 19 * q^49 + 27 * q^50 - 2 * q^52 + q^53 + 33 * q^55 - 2 * q^56 - 17 * q^58 + q^59 - 34 * q^61 + 4 * q^62 - q^64 - 11 * q^65 + 8 * q^67 - 22 * q^68 + 22 * q^70 + 22 * q^71 + 31 * q^73 - q^74 - 2 * q^76 - 22 * q^77 + 32 * q^79 - 28 * q^82 - 33 * q^83 - 11 * q^85 + 20 * q^86 + 22 * q^88 + 23 * q^89 + 18 * q^91 - 23 * q^92 + 11 * q^94 + 22 * q^95 - q^97 + 14 * q^98

Introduction

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