LMFDB - Embedded newform 414.2.i.b.55.1

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			55.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	414.55
Dual form			414.2.i.b.271.1

$q$-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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$

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	0.494947	+	0.868923i	$0.335187\pi$
$5$	0.592229	+	4.11904i	0.264853	+	1.84209i	−0.230094	+	0.973168i	$0.573904\pi$
$6$		0			0
$7$	−1.22301	+	2.67803i	−0.462256	+	1.01220i	0.524712	+	0.851280i	$0.324173\pi$
$7$	−1.22301	+	2.67803i	−0.462256	+	1.01220i	−0.986968	+	0.160919i	$0.948554\pi$
$8$	−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	−0.230245	−	0.973133i	$-0.573953\pi$
$11$	−3.15098	−	0.925210i	−0.950055	−	0.278961i	−0.719810	+	0.694171i	$0.755771\pi$
$12$		0			0
$13$	−0.0583872	−	0.127850i	−0.0161937	−	0.0354592i	0.901362	−	0.433066i	$-0.142568\pi$
$13$	−0.0583872	−	0.127850i	−0.0161937	−	0.0354592i	−0.917556	+	0.397606i	$0.869841\pi$
$14$	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	−0.285453	−	0.958393i	$-0.592144\pi$
$17$	−5.26034	−	3.38061i	−1.27582	−	0.819919i	−0.990366	+	0.138474i	$0.955780\pi$
$18$		0			0
$19$	1.99782	−	1.28392i	0.458332	−	0.294552i	−0.291028	−	0.956714i	$-0.593997\pi$
$19$	1.99782	−	1.28392i	0.458332	−	0.294552i	0.749361	+	0.662162i	$0.230361\pi$
$20$	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	0.984647	+	0.174555i	$0.0558488\pi$
$29$	8.36028	+	5.37283i	1.55247	+	0.997709i	0.567818	+	0.823154i	$0.307788\pi$
$30$		0			0
$31$	−1.49745	+	1.72814i	−0.268949	+	0.310384i	−0.874118	−	0.485713i	$-0.838560\pi$
$31$	−1.49745	+	1.72814i	−0.268949	+	0.310384i	0.605169	+	0.796097i	$0.293105\pi$
$32$	−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	0.778632	+	0.627481i	$0.215914\pi$
$37$	−0.883471	+	6.14467i	−0.145242	+	1.01018i	−0.923874	+	0.382697i	$0.874995\pi$
$38$	−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	0.926724	+	0.375743i	$0.122613\pi$
$41$	0.918195	+	6.38618i	0.143398	+	0.997354i	−0.783326	+	0.621611i	$0.786478\pi$
$42$		0			0
$43$	0.839356	+	0.968669i	0.128001	+	0.147721i	0.816132	−	0.577866i	$-0.196114\pi$
$43$	0.839356	+	0.968669i	0.128001	+	0.147721i	−0.688131	+	0.725586i	$0.741569\pi$
$44$	−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	−0.992203	−	0.124629i	$-0.960226\pi$
$53$	−1.80736	+	3.95756i	−0.248260	+	0.543613i	0.743944	+	0.668242i	$0.232953\pi$
$54$		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	0.907641	−	0.419747i	$-0.137881\pi$
$59$	−0.0304261	−	0.0666238i	−0.00396114	−	0.00867368i	−0.911602	+	0.411073i	$0.865154\pi$
$60$		0			0
$61$	−1.25866	+	1.45257i	−0.161155	+	0.185982i	−0.830584	−	0.556893i	$-0.811993\pi$
$61$	−1.25866	+	1.45257i	−0.161155	+	0.185982i	0.669429	+	0.742876i	$0.266539\pi$
$62$	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	−0.525670	−	0.850688i	$-0.676186\pi$
$67$	−4.15796	+	1.22089i	−0.507976	+	0.149155i	0.0176947	+	0.999843i	$0.494367\pi$
$68$	−6.25297			−0.758285
$69$		0			0
$70$	12.2515			1.46433
$71$	9.39090	−	2.75742i	1.11449	−	0.327245i	0.327898	−	0.944713i	$-0.393660\pi$
$71$	9.39090	−	2.75742i	1.11449	−	0.327245i	0.786596	+	0.617468i	$0.211841\pi$
$72$		0			0
$73$	4.61462	−	2.96563i	0.540100	−	0.347101i	−0.241978	−	0.970282i	$-0.577796\pi$
$73$	4.61462	−	2.96563i	0.540100	−	0.347101i	0.782078	+	0.623181i	$0.214160\pi$
$74$	−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	0.989701	+	0.143149i	$0.0457227\pi$
$79$	3.99764	+	8.75360i	0.449769	+	0.984857i	−0.539932	+	0.841709i	$0.681550\pi$
$80$	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	0.702764	+	0.711423i	$0.251949\pi$
$83$	−1.56667	+	10.8964i	−0.171964	+	1.19604i	−0.874728	+	0.484614i	$0.838960\pi$
$84$		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	0.998557	+	0.0536996i	$0.0171014\pi$
$89$	8.58116	+	9.90318i	0.909601	+	1.04974i	−0.0889564	+	0.996036i	$0.528353\pi$
$90$		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	0.864930	+	0.501893i	$0.167363\pi$
$97$	1.73769	+	12.0859i	0.176435	+	1.22714i	−0.688494	+	0.725242i	$0.741728\pi$
$98$	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	−0.997360	−	0.0726159i	$-0.976865\pi$
$101$	−0.200413	+	1.39390i	−0.0199418	+	0.138698i	0.977418	+	0.211314i	$0.0677744\pi$
$102$		0			0
$103$	−7.71117	−	2.26420i	−0.759804	−	0.223099i	−0.121194	−	0.992629i	$-0.538672\pi$
$103$	−7.71117	−	2.26420i	−0.759804	−	0.223099i	−0.638610	+	0.769530i	$0.720490\pi$
$104$	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	0.342558	−	0.939497i	$-0.388707\pi$
$107$	12.6585	−	14.6087i	1.22374	−	1.41227i	0.881183	−	0.472776i	$-0.156748\pi$
$108$		0			0
$109$	5.45071	+	3.50296i	0.522084	+	0.335523i	0.774996	−	0.631966i	$-0.217752\pi$
$109$	5.45071	+	3.50296i	0.522084	+	0.335523i	−0.252912	+	0.967489i	$0.581388\pi$
$110$	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	−0.715999	−	0.698102i	$-0.754028\pi$
$113$	−10.0020	+	2.93686i	−0.940913	+	0.276277i	−0.224914	+	0.974379i	$0.572210\pi$
$114$		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	0.533474	−	0.845817i	$-0.320886\pi$
$127$	5.91619	+	1.73715i	0.524977	+	0.154147i	−0.00849658	+	0.999964i	$0.502705\pi$
$128$	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	−0.755857	−	0.654736i	$-0.772780\pi$
$131$	2.67757	−	5.86307i	0.233941	−	0.512259i	0.989798	+	0.142478i	$0.0455069\pi$
$132$		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	0.436856	−	0.899532i	$-0.356092\pi$
$149$	3.88215	+	1.13990i	0.318038	+	0.0933845i	−0.118817	+	0.992916i	$0.537910\pi$
$150$		0			0
$151$	−7.27336	−	15.9264i	−0.591898	−	1.29607i	−0.934289	−	0.356517i	$-0.883964\pi$
$151$	−7.27336	−	15.9264i	−0.591898	−	1.29607i	0.342391	−	0.939558i	$-0.388763\pi$
$152$	−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	−0.632581	−	0.774494i	$-0.718004\pi$
$157$	−2.39146	+	1.53690i	−0.190859	+	0.122658i	0.441721	+	0.897152i	$0.354368\pi$
$158$	−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	−0.205348	−	0.978689i	$-0.565833\pi$
$163$	1.92812	−	0.566146i	0.151022	−	0.0443440i	0.356370	+	0.934345i	$0.384014\pi$
$164$	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	0.805359	−	0.592787i	$-0.201973\pi$
$167$	7.76274	+	4.98881i	0.600699	+	0.386046i	−0.204660	+	0.978833i	$0.565609\pi$
$168$		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	0.605877	−	0.795559i	$-0.292822\pi$
$173$	9.01583	+	2.64729i	0.685461	+	0.201270i	0.0795845	+	0.996828i	$0.474641\pi$
$174$		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	−0.748027	−	0.663668i	$-0.768999\pi$
$179$	−2.90697	−	20.2184i	−0.217277	−	1.51120i	0.530750	−	0.847528i	$-0.321910\pi$
$180$		0			0
$181$	−9.77927	−	11.2859i	−0.726887	−	0.838873i	0.265230	−	0.964185i	$-0.414552\pi$
$181$	−9.77927	−	11.2859i	−0.726887	−	0.838873i	−0.992117	+	0.125312i	$0.960007\pi$
$182$	−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	0.115076	+	0.993357i	$0.463289\pi$
$191$	−9.82638	+	21.5168i	−0.711012	+	1.55690i	−0.826088	+	0.563542i	$0.809438\pi$
$192$		0			0
$193$	0.278201	−	1.93493i	0.0200254	−	0.139280i	−0.977356	−	0.211602i	$-0.932132\pi$
$193$	0.278201	−	1.93493i	0.0200254	−	0.139280i	0.997381	+	0.0723224i	$0.0230411\pi$
$194$	−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	0.879777	−	0.475387i	$-0.157692\pi$
$197$	−0.780774	−	1.70966i	−0.0556279	−	0.121808i	−0.935405	+	0.353579i	$0.884965\pi$
$198$		0			0
$199$	10.8077	−	12.4728i	0.766139	−	0.884172i	−0.229888	−	0.973217i	$-0.573836\pi$
$199$	10.8077	−	12.4728i	0.766139	−	0.884172i	0.996028	+	0.0890450i	$0.0283815\pi$
$200$	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	−0.355959	−	0.934502i	$-0.615846\pi$
$211$	5.02917	−	3.23205i	0.346223	−	0.222504i	0.702182	+	0.711998i	$0.252209\pi$
$212$	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	0.392428	+	0.919783i	$0.371635\pi$
$223$	−8.35785	+	18.3011i	−0.559683	+	1.22553i	−0.952111	+	0.305752i	$0.901092\pi$
$224$	−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	0.964844	−	0.262824i	$-0.0846539\pi$
$227$	8.54849	+	9.86548i	0.567383	+	0.654795i	−0.397461	+	0.917619i	$0.630108\pi$
$228$		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	0.925946	−	0.377655i	$-0.123270\pi$
$233$	6.41650	+	7.40504i	0.420359	+	0.485120i	−0.505587	+	0.862775i	$0.668724\pi$
$234$		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	−0.971377	−	0.237545i	$-0.923657\pi$
$239$	0.426324	−	2.96515i	0.0275766	−	0.191799i	0.998953	+	0.0457456i	$0.0145664\pi$
$240$		0			0
$241$	19.6038	+	5.75619i	1.26279	+	0.370789i	0.843533	−	0.537078i	$-0.180472\pi$
$241$	19.6038	+	5.75619i	1.26279	+	0.370789i	0.419258	+	0.907867i	$0.362290\pi$
$242$	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	−0.311706	−	0.950179i	$-0.600900\pi$
$251$	−0.954130	+	0.280158i	−0.0602241	+	0.0176834i	0.251482	+	0.967862i	$0.419082\pi$
$252$		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	−0.343310	−	0.939222i	$-0.611548\pi$
$257$	5.90622	−	3.79570i	0.368420	−	0.236769i	0.711730	+	0.702453i	$0.247912\pi$
$258$		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	0.990653	+	0.136408i	$0.0435558\pi$
$263$	7.21674	+	15.8025i	0.445003	+	0.974422i	−0.545649	+	0.838014i	$0.683717\pi$
$264$		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	−0.0440310	+	0.999030i	$0.514020\pi$
$269$	−12.6324	+	27.6612i	−0.770213	+	1.68653i	−0.726182	+	0.687502i	$0.758707\pi$
$270$		0			0
$271$	0.861807	+	5.99400i	0.0523510	+	0.364109i	0.999111	+	0.0421677i	$0.0134264\pi$
$271$	0.861807	+	5.99400i	0.0523510	+	0.364109i	−0.946760	+	0.321942i	$0.895665\pi$
$272$	−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	−0.943377	−	0.331723i	$-0.892370\pi$
$281$	−2.20720	−	15.3514i	−0.131670	−	0.915788i	0.811706	−	0.584066i	$-0.198539\pi$
$282$		0			0
$283$	−3.91431	+	8.57115i	−0.232682	+	0.509502i	−0.989572	−	0.144040i	$-0.953991\pi$
$283$	−3.91431	+	8.57115i	−0.232682	+	0.509502i	0.756890	+	0.653542i	$0.226718\pi$
$284$	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	0.680955	−	0.732325i	$-0.261565\pi$
$293$	5.09559	+	3.27474i	0.297688	+	0.191312i	−0.383267	+	0.923637i	$0.625201\pi$
$294$		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	−0.203985	−	0.978974i	$-0.565390\pi$
$307$	13.9130	−	16.0564i	0.794054	−	0.916387i	0.998040	+	0.0625866i	$0.0199350\pi$
$308$	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	0.514118	−	0.857719i	$-0.328119\pi$
$311$	8.51610	+	2.50055i	0.482904	+	0.141793i	−0.0312144	+	0.999513i	$0.509937\pi$
$312$		0			0
$313$	−1.54784	+	10.7655i	−0.0874891	+	0.608500i	0.898157	+	0.439675i	$0.144906\pi$
$313$	−1.54784	+	10.7655i	−0.0874891	+	0.608500i	−0.985646	+	0.168825i	$0.946003\pi$
$314$	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	−0.515400	−	0.856950i	$-0.672357\pi$
$317$	−4.67026	−	32.4824i	−0.262308	−	1.82439i	0.253092	−	0.967442i	$-0.418553\pi$
$318$		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	−0.797246	−	0.603655i	$-0.793711\pi$
$331$	2.50660	−	17.4338i	0.137775	−	0.958247i	0.935021	−	0.354592i	$-0.115380\pi$
$332$	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	−0.228982	−	0.973431i	$-0.573540\pi$
$337$	14.0826	−	16.2522i	0.767128	−	0.885313i	0.996110	+	0.0881177i	$0.0280852\pi$
$338$	−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	0.320702	−	0.947180i	$-0.396081\pi$
$347$	20.5387	−	6.03072i	1.10258	−	0.323746i	0.781876	+	0.623434i	$0.214263\pi$
$348$		0			0
$349$	24.8430	−	15.9656i	1.32981	−	0.854619i	0.333698	−	0.942680i	$-0.391703\pi$
$349$	24.8430	−	15.9656i	1.32981	−	0.854619i	0.996115	+	0.0880610i	$0.0280670\pi$
$350$	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	−0.889289	−	0.457346i	$-0.848800\pi$
$353$	−5.82510	+	6.72252i	−0.310039	+	0.357804i	0.579250	+	0.815150i	$0.303346\pi$
$354$		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	−0.711732	−	0.702451i	$-0.752089\pi$
$359$	3.20348	−	22.2807i	0.169073	−	1.17593i	0.880805	−	0.473479i	$-0.157002\pi$
$360$		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	−0.943693	−	0.330821i	$-0.892674\pi$
$373$	−2.53832	−	17.6544i	−0.131429	−	0.914111i	0.812264	−	0.583290i	$-0.198235\pi$
$374$	−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	0.756605	−	0.653872i	$-0.226856\pi$
$379$	20.2387	+	5.94262i	1.03959	+	0.305252i	0.282987	+	0.959124i	$0.408675\pi$
$380$	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	−0.774282	−	0.632840i	$-0.781889\pi$
$383$	−0.737643	+	0.851285i	−0.0376918	+	0.0434986i	0.736591	+	0.676339i	$0.236434\pi$
$384$		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	−0.204974	−	0.978767i	$-0.565711\pi$
$389$	2.99302	−	0.878831i	0.151752	−	0.0445585i	0.356726	+	0.934209i	$0.383893\pi$
$390$		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	0.0262310	−	0.999656i	$-0.491649\pi$
$397$	−17.3783	−	11.1683i	−0.872191	−	0.560523i	−0.898422	+	0.439133i	$0.855286\pi$
$398$	−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	0.985886	−	0.167417i	$-0.0535426\pi$
$401$	4.28020	+	9.37233i	0.213743	+	0.468032i	−0.772143	+	0.635448i	$0.780815\pi$
$402$		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	0.973211	−	0.229915i	$-0.0738449\pi$
$409$	−0.512727	−	3.56610i	−0.0253527	−	0.176332i	−0.998563	+	0.0535831i	$0.982936\pi$
$410$	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	0.981401	+	0.191971i	$0.0614880\pi$
$419$	1.92082	+	13.3596i	0.0938382	+	0.652659i	−0.887562	+	0.460687i	$0.847603\pi$
$420$		0			0
$421$	6.91556	−	15.1430i	0.337044	−	0.738023i	−0.662899	−	0.748709i	$-0.730674\pi$
$421$	6.91556	−	15.1430i	0.337044	−	0.738023i	0.999943	+	0.0106857i	$0.00340143\pi$
$422$	−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	0.892080	−	0.451878i	$-0.149246\pi$
$431$	17.6801	+	11.3623i	0.851621	+	0.547304i	−0.0404589	+	0.999181i	$0.512882\pi$
$432$		0			0
$433$	−1.74431	+	1.12100i	−0.0838263	+	0.0538719i	−0.581883	−	0.813273i	$-0.697684\pi$
$433$	−1.74431	+	1.12100i	−0.0838263	+	0.0538719i	0.498056	+	0.867145i	$0.334047\pi$
$434$	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	−0.333284	−	0.942826i	$-0.608157\pi$
$439$	−2.17757	+	0.639393i	−0.103930	+	0.0305166i	0.229354	+	0.973343i	$0.426339\pi$
$440$	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	−0.119215	−	0.992868i	$-0.538038\pi$
$443$	−22.5605	−	14.4988i	−1.07188	−	0.688858i	−0.952669	+	0.304011i	$0.901674\pi$
$444$		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	0.383544	−	0.923522i	$-0.374703\pi$
$449$	4.38432	+	1.28735i	0.206909	+	0.0607539i	−0.176636	+	0.984276i	$0.556521\pi$
$450$		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	0.999349	−	0.0360845i	$-0.0114885\pi$
$457$	17.5597	+	20.2650i	0.821409	+	0.947957i	−0.177939	+	0.984041i	$0.556943\pi$
$458$	−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	0.958677	+	0.284498i	$0.0918268\pi$
$463$	23.7519	+	27.4112i	1.10384	+	1.27390i	0.145168	+	0.989407i	$0.453628\pi$
$464$	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	−0.737261	−	0.675608i	$-0.763881\pi$
$467$	5.53507	−	12.1201i	0.256132	−	0.560852i	0.993394	+	0.114756i	$0.0366086\pi$
$468$		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	−0.940146	−	0.340771i	$-0.889312\pi$
$479$	−22.3396	+	14.3568i	−1.02072	+	0.655977i	−0.0805743	+	0.996749i	$0.525675\pi$
$480$		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	−0.765463	−	0.643480i	$-0.777490\pi$
$487$	−10.9925	+	7.06445i	−0.498118	+	0.320121i	0.267345	+	0.963601i	$0.413854\pi$
$488$	−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	−0.00392677	+	0.999992i	$0.501250\pi$
$491$	−22.0074	+	25.3979i	−0.993182	+	1.14619i	−0.989255	+	0.146201i	$0.953296\pi$
$492$		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	−0.539245	−	0.842149i	$-0.681290\pi$
$499$	10.0598	−	22.0279i	0.450339	−	0.986104i	0.989584	−	0.143956i	$-0.0459823\pi$
$500$	−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	−0.909422	−	0.415874i	$-0.863476\pi$
$503$	−26.7257	−	30.8431i	−1.19164	−	1.37522i	−0.282216	−	0.959351i	$-0.591070\pi$
$504$		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	0.653451	−	0.756969i	$-0.273321\pi$
$509$	−4.25973	−	4.91599i	−0.188809	−	0.217897i	−0.842260	+	0.539072i	$0.818775\pi$
$510$		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	0.217481	−	0.976065i	$-0.430216\pi$
$521$	26.3099	−	30.3633i	1.15266	−	1.33024i	0.935179	−	0.354176i	$-0.115239\pi$
$522$		0			0
$523$	−10.3505	−	6.65184i	−0.452594	−	0.290865i	0.294416	−	0.955677i	$-0.404875\pi$
$523$	−10.3505	−	6.65184i	−0.452594	−	0.290865i	−0.747010	+	0.664813i	$0.768511\pi$
$524$	−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	0.221311	−	0.975203i	$-0.428967\pi$
$541$	−2.78522	−	0.817814i	−0.119746	−	0.0351606i	−0.341056	+	0.940043i	$0.610785\pi$
$542$	−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	−0.893931	−	0.448204i	$-0.852064\pi$
$547$	−3.80018	−	26.4309i	−0.162484	−	1.13010i	0.731447	−	0.681898i	$-0.238845\pi$
$548$	−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	−0.915107	−	0.403211i	$-0.867894\pi$
$557$	−3.55584	−	24.7314i	−0.150666	−	1.04790i	0.764441	−	0.644693i	$-0.223015\pi$
$558$		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	0.842944	−	0.538001i	$-0.180820\pi$
$563$	29.9255	+	8.78692i	1.26121	+	0.370325i	0.418265	+	0.908325i	$0.362638\pi$
$564$		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	0.429242	−	0.903189i	$-0.358781\pi$
$569$	−5.10503	−	3.28080i	−0.214014	−	0.137538i	−0.643256	+	0.765651i	$0.722417\pi$
$570$		0			0
$571$	−29.8567	+	19.1877i	−1.24946	+	0.802982i	−0.986806	−	0.161907i	$-0.948236\pi$
$571$	−29.8567	+	19.1877i	−1.24946	+	0.802982i	−0.262658	+	0.964889i	$0.584599\pi$
$572$	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	−0.398949	−	0.916973i	$-0.630625\pi$
$577$	−5.73647	+	1.68438i	−0.238812	+	0.0701216i	0.160136	+	0.987095i	$0.448807\pi$
$578$	−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	0.124975	−	0.992160i	$-0.460115\pi$
$587$	−7.42084	−	2.17895i	−0.306291	−	0.0899351i	−0.431266	+	0.902225i	$0.641933\pi$
$588$		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	0.965081	+	0.261953i	$0.0843664\pi$
$593$	2.74913	+	19.1206i	0.112893	+	0.785189i	−0.852188	+	0.523236i	$0.824724\pi$
$594$		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	0.999877	−	0.0156953i	$-0.00499619\pi$
$601$	20.6430	+	23.8232i	0.842044	+	0.971771i	−0.157833	+	0.987466i	$0.550451\pi$
$602$	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	0.943579	+	0.331148i	$0.107436\pi$
$607$	−1.35687	+	9.43722i	−0.0550735	+	0.383045i	−0.998652	+	0.0518971i	$0.983473\pi$
$608$	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	−0.535128	−	0.844771i	$-0.679737\pi$
$613$	9.33907	−	10.7779i	0.377201	−	0.435314i	0.912329	+	0.409457i	$0.134282\pi$
$614$	−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	−0.487077	−	0.873359i	$-0.661937\pi$
$617$	2.60863	−	1.67647i	0.105020	−	0.0674921i	0.592096	+	0.805867i	$0.298300\pi$
$618$		0			0
$619$	−43.4217	+	12.7498i	−1.74526	+	0.512456i	−0.989767	−	0.142696i	$-0.954423\pi$
$619$	−43.4217	+	12.7498i	−1.74526	+	0.512456i	−0.755497	+	0.655152i	$0.772605\pi$
$620$	−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	0.998920	+	0.0464653i	$0.0147957\pi$
$631$	9.54254	+	20.8953i	0.379883	+	0.831827i	−0.619037	+	0.785362i	$0.712477\pi$
$632$	−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	0.441922	−	0.897053i	$-0.354297\pi$
$641$	−12.8841	−	14.8691i	−0.508893	−	0.587293i	−0.950815	+	0.309760i	$0.899751\pi$
$642$		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	0.993384	+	0.114841i	$0.0366358\pi$
$647$	24.5633	+	28.3475i	0.965683	+	1.11446i	−0.0277013	+	0.999616i	$0.508819\pi$
$648$		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	0.918217	+	0.396077i	$0.129629\pi$
$653$	−1.90104	+	13.2220i	−0.0743935	+	0.517418i	−0.992611	+	0.121341i	$0.961280\pi$
$654$		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	−0.906241	−	0.422762i	$-0.861061\pi$
$659$	−9.21102	+	10.6301i	−0.358810	+	0.414089i	0.547430	+	0.836851i	$0.315606\pi$
$660$		0			0
$661$	−6.47163	−	4.15906i	−0.251717	−	0.161769i	0.408697	−	0.912670i	$-0.365983\pi$
$661$	−6.47163	−	4.15906i	−0.251717	−	0.161769i	−0.660415	+	0.750901i	$0.729619\pi$
$662$	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	−0.968455	−	0.249190i	$-0.919836\pi$
$673$	−41.4411	−	26.6326i	−1.59744	−	1.02661i	−0.628982	−	0.777420i	$-0.716528\pi$
$674$	−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	0.986442	+	0.164109i	$0.0524749\pi$
$677$	12.0855	+	26.4637i	0.464485	+	1.01708i	−0.521957	+	0.852972i	$0.674798\pi$
$678$		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	−0.830505	−	0.557012i	$-0.811948\pi$
$683$	3.51040	−	7.68671i	0.134322	−	0.294124i	0.964826	+	0.262888i	$0.0846751\pi$
$684$		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	−0.254227	−	0.967145i	$-0.581821\pi$
$701$	−26.2374	−	7.70400i	−0.990973	−	0.290976i	−0.736747	+	0.676169i	$0.763639\pi$
$702$		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	−0.551831	−	0.833956i	$-0.686071\pi$
$709$	−0.598495	+	0.384630i	−0.0224770	+	0.0144451i	0.529354	+	0.848401i	$0.322434\pi$
$710$	−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	0.812824	−	0.582509i	$-0.197929\pi$
$719$	16.6413	+	10.6947i	0.620615	+	0.398845i	−0.192209	+	0.981354i	$0.561565\pi$
$720$		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	−0.669380	−	0.742920i	$-0.733440\pi$
$727$	4.91238	−	34.1664i	0.182190	−	1.26716i	0.851570	−	0.524241i	$-0.175651\pi$
$728$	−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	0.855368	−	0.518021i	$-0.173331\pi$
$733$	5.98030	+	6.90163i	0.220887	+	0.254918i	−0.634480	+	0.772939i	$0.718786\pi$
$734$	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	0.674814	−	0.737988i	$-0.264224\pi$
$739$	−4.12387	−	4.75920i	−0.151699	−	0.175070i	−0.826513	+	0.562918i	$0.809679\pi$
$740$	−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	0.640934	+	0.767596i	$0.278547\pi$
$743$	−9.78288	+	21.4215i	−0.358899	+	0.785879i	−0.999833	+	0.0182830i	$0.994180\pi$
$744$		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	−0.996201	−	0.0870877i	$-0.972244\pi$
$751$	−21.0527	+	24.2962i	−0.768225	+	0.886579i	0.227975	+	0.973667i	$0.426789\pi$
$752$	−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	−0.201607	−	0.979466i	$-0.564616\pi$
$757$	4.35621	−	1.27910i	0.158329	−	0.0464897i	0.359937	+	0.932977i	$0.382798\pi$
$758$	−21.0931			−0.766137
$759$		0			0
$760$	−9.88257			−0.358478
$761$	37.7141	−	11.0738i	1.36713	−	0.401427i	0.485861	−	0.874036i	$-0.338506\pi$
$761$	37.7141	−	11.0738i	1.36713	−	0.401427i	0.881272	+	0.472609i	$0.156688\pi$
$762$		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	0.877381	−	0.479795i	$-0.159289\pi$
$769$	−1.65793	−	3.63035i	−0.0597863	−	0.130914i	−0.937167	+	0.348881i	$0.886562\pi$
$770$	−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	−0.781093	−	0.624415i	$-0.785337\pi$
$773$	4.01135	−	27.8996i	0.144278	−	1.00348i	0.925371	−	0.379063i	$-0.123754\pi$
$774$		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	0.974461	+	0.224555i	$0.0720929\pi$
$787$	2.88214	+	20.0457i	0.102737	+	0.714552i	−0.871724	+	0.489997i	$0.836998\pi$
$788$	−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	−0.764098	−	0.645100i	$-0.776816\pi$
$797$	−0.474904	+	0.548068i	−0.0168220	+	0.0194136i	0.747276	+	0.664514i	$0.231361\pi$
$798$		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	0.349867	−	0.936799i	$-0.386227\pi$
$809$	38.3226	−	24.6284i	1.34735	−	0.865889i	0.997483	+	0.0709105i	$0.0225905\pi$
$810$		0			0
$811$	−11.0752	−	7.11758i	−0.388902	−	0.249932i	0.331549	−	0.943438i	$-0.392429\pi$
$811$	−11.0752	−	7.11758i	−0.388902	−	0.249932i	−0.720451	+	0.693506i	$0.756065\pi$
$812$	−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	−0.651637	−	0.758531i	$-0.725917\pi$
$821$	9.98143	−	21.8563i	0.348354	−	0.762790i	0.999991	−	0.00425830i	$-0.00135546\pi$
$822$		0			0
$823$	−0.701939	−	4.88209i	−0.0244680	−	0.170179i	0.973923	−	0.226878i	$-0.0728517\pi$
$823$	−0.701939	−	4.88209i	−0.0244680	−	0.170179i	−0.998391	+	0.0566985i	$0.981943\pi$
$824$	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	−0.483227	−	0.875495i	$-0.660536\pi$
$839$	−39.4821	−	11.5930i	−1.36307	−	0.400234i	−0.879845	+	0.475261i	$0.842354\pi$
$840$		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	−0.00692206	−	0.999976i	$-0.502203\pi$
$853$	15.4174	−	4.52696i	0.527883	−	0.155000i	0.534805	+	0.844976i	$0.320385\pi$
$854$	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	0.858227	−	0.513270i	$-0.171566\pi$
$857$	21.8933	+	14.0700i	0.747860	+	0.480620i	−0.110367	+	0.993891i	$0.535203\pi$
$858$		0			0
$859$	7.71658	−	8.90541i	0.263286	−	0.303849i	−0.608679	−	0.793417i	$-0.708300\pi$
$859$	7.71658	−	8.90541i	0.263286	−	0.303849i	0.871965	+	0.489568i	$0.162846\pi$
$860$	−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	−0.0199513	−	0.999801i	$-0.506351\pi$
$863$	−16.9583	−	4.97942i	−0.577269	−	0.169501i	−0.557317	+	0.830300i	$0.688169\pi$
$864$		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	0.990530	−	0.137300i	$-0.0438424\pi$
$877$	21.1345	+	24.3905i	0.713660	+	0.823608i	−0.276869	+	0.960908i	$0.589297\pi$
$878$	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	−0.823189	−	0.567767i	$-0.807808\pi$
$881$	4.30308	−	9.42243i	0.144974	−	0.317450i	0.968164	+	0.250317i	$0.0805348\pi$
$882$		0			0
$883$	−8.08407	+	56.2259i	−0.272051	+	1.89215i	0.154983	+	0.987917i	$0.450468\pi$
$883$	−8.08407	+	56.2259i	−0.272051	+	1.89215i	−0.427033	+	0.904236i	$0.640441\pi$
$884$	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	−0.938274	−	0.345893i	$-0.887576\pi$
$887$	−17.4300	−	38.1665i	−0.585244	−	1.28151i	0.353030	−	0.935612i	$-0.385151\pi$
$888$		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	0.708834	−	0.705376i	$-0.249222\pi$
$907$	−8.68682	−	19.0215i	−0.288441	−	0.631598i	−0.997275	+	0.0737778i	$0.976494\pi$
$908$	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	−0.994666	−	0.103148i	$-0.967108\pi$
$911$	−0.338973	+	2.35761i	−0.0112307	+	0.0781112i	0.983435	+	0.181260i	$0.0580174\pi$
$912$		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	−0.972809	−	0.231608i	$-0.925601\pi$
$929$	0.787770	−	5.47906i	0.0258459	−	0.179762i	0.998655	+	0.0518458i	$0.0165104\pi$
$930$		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	0.177052	−	0.984202i	$-0.443344\pi$
$937$	−19.7333	−	12.6818i	−0.644660	−	0.414298i	−0.821711	+	0.569904i	$0.806980\pi$
$938$	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	−0.0558410	−	0.998440i	$-0.517784\pi$
$941$	13.4047	−	3.93597i	0.436980	−	0.128309i	0.492821	+	0.870131i	$0.335966\pi$
$942$		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	−0.997257	−	0.0740197i	$-0.976417\pi$
$947$	−41.3656	+	26.5841i	−1.34420	+	0.863866i	−0.346945	+	0.937886i	$0.612781\pi$
$948$		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	0.958806	−	0.284061i	$-0.0916817\pi$
$953$	3.58850	+	7.85773i	0.116243	+	0.254537i	−0.842563	+	0.538597i	$0.818954\pi$
$954$		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	−0.979960	−	0.199194i	$-0.936167\pi$
$971$	−2.98567	−	20.7658i	−0.0958148	−	0.666407i	0.884145	−	0.467212i	$-0.154742\pi$
$972$		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	0.382856	−	0.923808i	$-0.374940\pi$
$977$	6.42291	+	1.88594i	0.205487	+	0.0603364i	−0.177369	+	0.984144i	$0.556759\pi$
$978$		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	0.472530	−	0.881314i	$-0.343341\pi$
$983$	−4.16508	−	2.67673i	−0.132845	−	0.0853745i	−0.605376	+	0.795940i	$0.706977\pi$
$984$		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	0.0508777	−	0.998705i	$-0.483798\pi$
$991$	19.9464	−	5.85680i	0.633619	−	0.186047i	0.582742	+	0.812657i	$0.301980\pi$
$992$	−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	−0.261640	−	0.965166i	$-0.584263\pi$
$997$	23.0796	−	26.6352i	0.730937	−	0.843546i	0.992577	+	0.121619i	$0.0388087\pi$
$998$	−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.55.1		10
3.2	odd	2		138.2.e.c.55.1	✓	10
23.8	even	11		9522.2.a.bv.1.2		5
23.15	odd	22		9522.2.a.ca.1.4		5
23.18	even	11	inner	414.2.i.b.271.1		10
69.8	odd	22		3174.2.a.z.1.4		5
69.38	even	22		3174.2.a.y.1.2		5
69.41	odd	22		138.2.e.c.133.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.c.55.1	✓	10	3.2	odd	2
138.2.e.c.133.1	yes	10	69.41	odd	22
414.2.i.b.55.1		10	1.1	even	1	trivial
414.2.i.b.271.1		10	23.18	even	11	inner
3174.2.a.y.1.2		5	69.38	even	22
3174.2.a.z.1.4		5	69.8	odd	22
9522.2.a.bv.1.2		5	23.8	even	11
9522.2.a.ca.1.4		5	23.15	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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