LMFDB - Embedded newform 495.2.bj.c.442.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(28,495)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 18]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("495.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			442.11
Character	$\chi$	$=$	495.442
Dual form			495.2.bj.c.28.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.986271 + 1.93567i) q^{2} +(-1.59850 + 2.20015i) q^{4} +(0.401727 - 2.19969i) q^{5} +(3.95619 - 0.626599i) q^{7} +(-1.54390 - 0.244529i) q^{8} +O(q^{10})$	\(q+(0.986271 + 1.93567i) q^{2} +(-1.59850 + 2.20015i) q^{4} +(0.401727 - 2.19969i) q^{5} +(3.95619 - 0.626599i) q^{7} +(-1.54390 - 0.244529i) q^{8} +(4.65407 - 1.39188i) q^{10} +(-2.42559 - 2.26197i) q^{11} +(4.53814 - 2.31230i) q^{13} +(5.11476 + 7.03987i) q^{14} +(0.631388 + 1.94321i) q^{16} +(1.11142 + 0.566297i) q^{17} +(-4.58879 + 3.33395i) q^{19} +(4.19747 + 4.40006i) q^{20} +(1.98614 - 6.92604i) q^{22} +(-2.70988 + 2.70988i) q^{23} +(-4.67723 - 1.76735i) q^{25} +(8.95168 + 6.50377i) q^{26} +(-4.94536 + 9.70582i) q^{28} +(-3.13702 - 2.27918i) q^{29} +(0.236665 - 0.728379i) q^{31} +(-5.34931 + 5.34931i) q^{32} +2.70986i q^{34} +(0.210988 - 8.95410i) q^{35} +(1.34128 + 8.46850i) q^{37} +(-10.9792 - 5.59418i) q^{38} +(-1.15811 + 3.29786i) q^{40} +(2.45935 + 3.38501i) q^{41} +(-5.05226 - 5.05226i) q^{43} +(8.85398 - 1.72088i) q^{44} +(-7.91810 - 2.57275i) q^{46} +(4.13303 + 0.654608i) q^{47} +(8.60143 - 2.79477i) q^{49} +(-1.19203 - 10.7966i) q^{50} +(-2.16682 + 13.6808i) q^{52} +(1.51295 + 2.96933i) q^{53} +(-5.95006 + 4.42683i) q^{55} -6.26118 q^{56} +(1.31778 - 8.32012i) q^{58} +(0.431206 - 0.593505i) q^{59} +(-4.43475 + 1.44094i) q^{61} +(1.64331 - 0.260275i) q^{62} +(-11.7439 - 3.81583i) q^{64} +(-3.26324 - 10.9114i) q^{65} +(-9.74376 - 9.74376i) q^{67} +(-3.02254 + 1.54006i) q^{68} +(17.5402 - 8.42276i) q^{70} +(3.59115 + 11.0524i) q^{71} +(0.361793 + 2.28427i) q^{73} +(-15.0693 + 10.9485i) q^{74} -15.4253i q^{76} +(-11.0134 - 7.42893i) q^{77} +(3.35829 - 10.3357i) q^{79} +(4.52810 - 0.608214i) q^{80} +(-4.12666 + 8.09902i) q^{82} +(-0.0222139 + 0.0435972i) q^{83} +(1.69216 - 2.21728i) q^{85} +(4.79659 - 14.7624i) q^{86} +(3.19174 + 4.08538i) q^{88} -4.99151i q^{89} +(16.5049 - 11.9915i) q^{91} +(-1.63039 - 10.2939i) q^{92} +(2.80919 + 8.64578i) q^{94} +(5.49020 + 11.4332i) q^{95} +(5.14342 - 2.62070i) q^{97} +(13.8931 + 13.8931i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{5} - 20 q^{7}+O(q^{10}) $ 96 * q + 8 * q^5 - 20 * q^7	$ 96 q + 8 q^{5} - 20 q^{7} - 8 q^{11} + 8 q^{16} + 20 q^{17} + 60 q^{20} - 32 q^{22} - 32 q^{23} - 32 q^{25} - 60 q^{28} + 16 q^{31} + 8 q^{37} - 56 q^{38} + 120 q^{41} - 200 q^{46} - 60 q^{47} - 80 q^{50} + 40 q^{52} - 36 q^{53} + 80 q^{55} + 80 q^{56} + 44 q^{58} + 40 q^{61} - 80 q^{62} - 48 q^{67} - 80 q^{68} - 92 q^{70} - 32 q^{71} - 60 q^{73} + 24 q^{77} + 80 q^{80} + 32 q^{82} + 200 q^{83} - 80 q^{85} + 80 q^{86} - 144 q^{88} + 56 q^{91} - 20 q^{92} - 60 q^{95} + 32 q^{97}+O(q^{100}) $ 96 * q + 8 * q^5 - 20 * q^7 - 8 * q^11 + 8 * q^16 + 20 * q^17 + 60 * q^20 - 32 * q^22 - 32 * q^23 - 32 * q^25 - 60 * q^28 + 16 * q^31 + 8 * q^37 - 56 * q^38 + 120 * q^41 - 200 * q^46 - 60 * q^47 - 80 * q^50 + 40 * q^52 - 36 * q^53 + 80 * q^55 + 80 * q^56 + 44 * q^58 + 40 * q^61 - 80 * q^62 - 48 * q^67 - 80 * q^68 - 92 * q^70 - 32 * q^71 - 60 * q^73 + 24 * q^77 + 80 * q^80 + 32 * q^82 + 200 * q^83 - 80 * q^85 + 80 * q^86 - 144 * q^88 + 56 * q^91 - 20 * q^92 - 60 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.986271	+	1.93567i	0.697399	+	1.36872i	0.919263	+	0.393645i	$0.128786\pi$
$2$	0.986271	+	1.93567i	0.697399	+	1.36872i	−0.221864	+	0.975078i	$0.571214\pi$
$3$		0			0
$3$		0			0
$4$	−1.59850	+	2.20015i	−0.799250	+	1.10007i
$5$	0.401727	−	2.19969i	0.179658	−	0.983729i
$5$	0.401727	−	2.19969i	0.179658	−	0.983729i
$6$		0			0
$7$	3.95619	−	0.626599i	1.49530	−	0.236832i	0.645428	−	0.763821i	$-0.276679\pi$
$7$	3.95619	−	0.626599i	1.49530	−	0.236832i	0.849872	+	0.526989i	$0.176679\pi$
$8$	−1.54390	−	0.244529i	−0.545850	−	0.0864542i
$9$		0			0
$10$	4.65407	−	1.39188i	1.47175	−	0.440150i
$11$	−2.42559	−	2.26197i	−0.731342	−	0.682011i
$11$	−2.42559	−	2.26197i	−0.731342	−	0.682011i
$12$		0			0
$13$	4.53814	−	2.31230i	1.25865	−	0.641316i	0.307946	−	0.951404i	$-0.400358\pi$
$13$	4.53814	−	2.31230i	1.25865	−	0.641316i	0.950708	+	0.310087i	$0.100358\pi$
$14$	5.11476	+	7.03987i	1.36698	+	1.88148i
$15$		0			0
$16$	0.631388	+	1.94321i	0.157847	+	0.485803i
$17$	1.11142	+	0.566297i	0.269559	+	0.137347i	0.583546	−	0.812080i	$-0.301665\pi$
$17$	1.11142	+	0.566297i	0.269559	+	0.137347i	−0.313987	+	0.949427i	$0.601665\pi$
$18$		0			0
$19$	−4.58879	+	3.33395i	−1.05274	+	0.764860i	−0.972732	−	0.231934i	$-0.925495\pi$
$19$	−4.58879	+	3.33395i	−1.05274	+	0.764860i	−0.0800083	+	0.996794i	$0.525495\pi$
$20$	4.19747	+	4.40006i	0.938583	+	0.983882i
$21$		0			0
$22$	1.98614	−	6.92604i	0.423446	−	1.47664i
$23$	−2.70988	+	2.70988i	−0.565049	+	0.565049i	−0.930737	−	0.365688i	$-0.880834\pi$
$23$	−2.70988	+	2.70988i	−0.565049	+	0.565049i	0.365688	+	0.930737i	$0.380834\pi$
$24$		0			0
$25$	−4.67723	−	1.76735i	−0.935446	−	0.353469i
$26$	8.95168	+	6.50377i	1.75557	+	1.27549i
$27$		0			0
$28$	−4.94536	+	9.70582i	−0.934586	+	1.83423i
$29$	−3.13702	−	2.27918i	−0.582531	−	0.423233i	0.257105	−	0.966383i	$-0.417231\pi$
$29$	−3.13702	−	2.27918i	−0.582531	−	0.423233i	−0.839636	+	0.543150i	$0.817231\pi$
$30$		0			0
$31$	0.236665	−	0.728379i	0.0425063	−	0.130821i	−0.927551	−	0.373696i	$-0.878090\pi$
$31$	0.236665	−	0.728379i	0.0425063	−	0.130821i	0.970058	+	0.242875i	$0.0780904\pi$
$32$	−5.34931	+	5.34931i	−0.945633	+	0.945633i
$33$		0			0
$34$			2.70986i			0.464737i
$35$	0.210988	−	8.95410i	0.0356635	−	1.51352i
$36$		0			0
$37$	1.34128	+	8.46850i	0.220505	+	1.39221i	0.810941	+	0.585129i	$0.198956\pi$
$37$	1.34128	+	8.46850i	0.220505	+	1.39221i	−0.590436	+	0.807085i	$0.701044\pi$
$38$	−10.9792	−	5.59418i	−1.78106	−	0.907496i
$39$		0			0
$40$	−1.15811	+	3.29786i	−0.183114	+	0.521437i
$41$	2.45935	+	3.38501i	0.384086	+	0.528650i	0.956661	−	0.291203i	$-0.0940554\pi$
$41$	2.45935	+	3.38501i	0.384086	+	0.528650i	−0.572575	+	0.819852i	$0.694055\pi$
$42$		0			0
$43$	−5.05226	−	5.05226i	−0.770463	−	0.770463i	0.207725	−	0.978187i	$-0.433394\pi$
$43$	−5.05226	−	5.05226i	−0.770463	−	0.770463i	−0.978187	+	0.207725i	$0.933394\pi$
$44$	8.85398	−	1.72088i	1.33479	−	0.259433i
$45$		0			0
$46$	−7.91810	−	2.57275i	−1.16746	−	0.379331i
$47$	4.13303	+	0.654608i	0.602864	+	0.0954843i	0.450403	−	0.892825i	$-0.351280\pi$
$47$	4.13303	+	0.654608i	0.602864	+	0.0954843i	0.152461	+	0.988309i	$0.451280\pi$
$48$		0			0
$49$	8.60143	−	2.79477i	1.22878	−	0.399253i
$50$	−1.19203	−	10.7966i	−0.168578	−	1.52687i
$51$		0			0
$52$	−2.16682	+	13.6808i	−0.300484	+	1.89718i
$53$	1.51295	+	2.96933i	0.207820	+	0.407869i	0.971264	−	0.238005i	$-0.0764933\pi$
$53$	1.51295	+	2.96933i	0.207820	+	0.407869i	−0.763444	+	0.645873i	$0.776493\pi$
$54$		0			0
$55$	−5.95006	+	4.42683i	−0.802305	+	0.596914i
$56$	−6.26118			−0.836685
$57$		0			0
$58$	1.31778	−	8.32012i	0.173033	−	1.09248i
$59$	0.431206	−	0.593505i	0.0561383	−	0.0772677i	−0.780025	−	0.625749i	$-0.784794\pi$
$59$	0.431206	−	0.593505i	0.0561383	−	0.0772677i	0.836163	+	0.548481i	$0.184794\pi$
$60$		0			0
$61$	−4.43475	+	1.44094i	−0.567812	+	0.184493i	−0.578833	−	0.815446i	$-0.696492\pi$
$61$	−4.43475	+	1.44094i	−0.567812	+	0.184493i	0.0110211	+	0.999939i	$0.496492\pi$
$62$	1.64331	−	0.260275i	0.208701	−	0.0330550i
$63$		0			0
$64$	−11.7439	−	3.81583i	−1.46799	−	0.476978i
$65$	−3.26324	−	10.9114i	−0.404755	−	1.35339i
$66$		0			0
$67$	−9.74376	−	9.74376i	−1.19039	−	1.19039i	−0.976958	−	0.213431i	$-0.931536\pi$
$67$	−9.74376	−	9.74376i	−1.19039	−	1.19039i	−0.213431	−	0.976958i	$-0.568464\pi$
$68$	−3.02254	+	1.54006i	−0.366537	+	0.186760i
$69$		0			0
$70$	17.5402	−	8.42276i	2.09646	−	1.00671i
$71$	3.59115	+	11.0524i	0.426192	+	1.31168i	0.901849	+	0.432052i	$0.142210\pi$
$71$	3.59115	+	11.0524i	0.426192	+	1.31168i	−0.475657	+	0.879631i	$0.657790\pi$
$72$		0			0
$73$	0.361793	+	2.28427i	0.0423447	+	0.267354i	0.999773	−	0.0213181i	$-0.00678626\pi$
$73$	0.361793	+	2.28427i	0.0423447	+	0.267354i	−0.957428	+	0.288672i	$0.906786\pi$
$74$	−15.0693	+	10.9485i	−1.75177	+	1.27274i
$75$		0			0
$76$		−	15.4253i		−	1.76941i
$77$	−11.0134	−	7.42893i	−1.25510	−	0.846605i
$78$		0			0
$79$	3.35829	−	10.3357i	0.377837	−	1.16286i	−0.563708	−	0.825974i	$-0.690626\pi$
$79$	3.35829	−	10.3357i	0.377837	−	1.16286i	0.941545	−	0.336888i	$-0.109374\pi$
$80$	4.52810	−	0.608214i	0.506257	−	0.0680004i
$81$		0			0
$82$	−4.12666	+	8.09902i	−0.455713	+	0.894387i
$83$	−0.0222139	+	0.0435972i	−0.00243829	+	0.00478542i	−0.892222	−	0.451596i	$-0.850855\pi$
$83$	−0.0222139	+	0.0435972i	−0.00243829	+	0.00478542i	0.889784	+	0.456382i	$0.150855\pi$
$84$		0			0
$85$	1.69216	−	2.21728i	0.183541	−	0.240498i
$86$	4.79659	−	14.7624i	0.517230	−	1.59187i
$87$		0			0
$88$	3.19174	+	4.08538i	0.340241	+	0.435503i
$89$		−	4.99151i		−	0.529099i	−0.964372	−	0.264550i	$-0.914777\pi$
$89$		−	4.99151i		−	0.529099i	0.964372	−	0.264550i	$-0.0852233\pi$
$90$		0			0
$91$	16.5049	−	11.9915i	1.73018	−	1.25705i
$92$	−1.63039	−	10.2939i	−0.169980	−	1.07321i
$93$		0			0
$94$	2.80919	+	8.64578i	0.289745	+	0.891744i
$95$	5.49020	+	11.4332i	0.563282	+	1.17302i
$96$		0			0
$97$	5.14342	−	2.62070i	0.522235	−	0.266092i	−0.172940	−	0.984932i	$-0.555327\pi$
$97$	5.14342	−	2.62070i	0.522235	−	0.266092i	0.695175	+	0.718840i	$0.255327\pi$
$98$	13.8931	+	13.8931i	1.40341	+	1.40341i
$99$		0			0
$100$	11.3650	−	7.46549i	1.13650	−	0.746549i
$101$	−3.17814	−	1.03264i	−0.316237	−	0.102752i	0.146598	−	0.989196i	$-0.453168\pi$
$101$	−3.17814	−	1.03264i	−0.316237	−	0.102752i	−0.462835	+	0.886445i	$0.653168\pi$
$102$		0			0
$103$	−16.1724	+	2.56145i	−1.59351	+	0.252388i	−0.889206	−	0.457508i	$-0.848742\pi$
$103$	−16.1724	+	2.56145i	−1.59351	+	0.252388i	−0.704307	+	0.709895i	$0.748742\pi$
$104$	−7.57185	+	2.46024i	−0.742481	+	0.241247i
$105$		0			0
$106$	−4.25545	+	5.85713i	−0.413326	+	0.568894i
$107$	−1.86160	+	11.7537i	−0.179967	+	1.13627i	0.717946	+	0.696098i	$0.245082\pi$
$107$	−1.86160	+	11.7537i	−0.179967	+	1.13627i	−0.897914	+	0.440171i	$0.854918\pi$
$108$		0			0
$109$	7.37791			0.706676			0.353338	−	0.935496i	$-0.385047\pi$
$109$	7.37791			0.706676			0.353338	+	0.935496i	$0.385047\pi$
$110$	−14.4372	−	7.15126i	−1.37654	−	0.681846i
$111$		0			0
$112$	3.71551	+	7.29209i	0.351082	+	0.689038i
$113$	0.736136	−	4.64778i	0.0692499	−	0.437227i	−0.928566	−	0.371168i	$-0.878958\pi$
$113$	0.736136	−	4.64778i	0.0692499	−	0.437227i	0.997816	−	0.0660588i	$-0.0210425\pi$
$114$		0			0
$115$	4.87225	+	7.04952i	0.454340	+	0.657371i
$116$	10.0291	−	3.25864i	0.931175	−	0.302557i
$117$		0			0
$118$	1.57411	+	0.249315i	0.144909	+	0.0229513i
$119$	4.75183	+	1.54396i	0.435600	+	0.141535i
$120$		0			0
$121$	0.766946	+	10.9732i	0.0697224	+	0.997566i
$122$	−7.16305	−	7.16305i	−0.648512	−	0.648512i
$123$		0			0
$124$	1.22423	+	1.68501i	0.109939	+	0.151319i
$125$	−5.76658	+	9.57844i	−0.515778	+	0.856722i
$126$		0			0
$127$	−3.54861	−	1.80811i	−0.314888	−	0.160444i	0.289402	−	0.957208i	$-0.406543\pi$
$127$	−3.54861	−	1.80811i	−0.314888	−	0.160444i	−0.604291	+	0.796764i	$0.706543\pi$
$128$	−1.82964	−	11.5519i	−0.161719	−	1.02105i
$129$		0			0
$130$	17.9024	−	17.0781i	1.57014	−	1.49785i
$131$		−	6.08791i		−	0.531903i	−0.963986	−	0.265952i	$-0.914314\pi$
$131$		−	6.08791i		−	0.531903i	0.963986	−	0.265952i	$-0.0856862\pi$
$132$		0			0
$133$	−16.0651	+	16.0651i	−1.39302	+	1.39302i
$134$	9.25067	−	28.4706i	0.799136	−	2.45949i
$135$		0			0
$136$	−1.57744	−	1.14608i	−0.135265	−	0.0982756i
$137$	2.96228	−	5.81380i	0.253085	−	0.496707i	−0.729152	−	0.684352i	$-0.760085\pi$
$137$	2.96228	−	5.81380i	0.253085	−	0.496707i	0.982237	+	0.187645i	$0.0600854\pi$
$138$		0			0
$139$	8.08385	+	5.87326i	0.685664	+	0.498164i	0.875232	−	0.483704i	$-0.160709\pi$
$139$	8.08385	+	5.87326i	0.685664	+	0.498164i	−0.189568	+	0.981868i	$0.560709\pi$
$140$	19.3631	+	14.7773i	1.63648	+	1.24891i
$141$		0			0
$142$	−17.8520	+	17.8520i	−1.49810	+	1.49810i
$143$	−16.2380	−	4.65648i	−1.35789	−	0.389394i
$144$		0			0
$145$	−6.27371	+	5.98485i	−0.521003	+	0.497015i
$146$	−4.06476	+	2.95322i	−0.336402	+	0.244411i
$147$		0			0
$148$	−20.7760	−	10.5859i	−1.70778	−	0.870155i
$149$	1.31084	+	4.03436i	0.107389	+	0.330508i	0.990284	−	0.139062i	$-0.0444089\pi$
$149$	1.31084	+	4.03436i	0.107389	+	0.330508i	−0.882895	+	0.469570i	$0.844409\pi$
$150$		0			0
$151$	1.16711	+	1.60638i	0.0949777	+	0.130726i	0.853861	−	0.520501i	$-0.174255\pi$
$151$	1.16711	+	1.60638i	0.0949777	+	0.130726i	−0.758883	+	0.651227i	$0.774255\pi$
$152$	7.89987	−	4.02518i	0.640764	−	0.326486i
$153$		0			0
$154$	3.51769	−	28.6453i	0.283464	−	2.30830i
$155$	−1.50713	−	0.813198i	−0.121056	−	0.0653176i
$156$		0			0
$157$	3.65256	+	0.578509i	0.291506	+	0.0461701i	0.300475	−	0.953790i	$-0.402855\pi$
$157$	3.65256	+	0.578509i	0.291506	+	0.0461701i	−0.00896859	+	0.999960i	$0.502855\pi$
$158$	23.3187	−	3.69332i	1.85514	−	0.293825i
$159$		0			0
$160$	9.61783	+	13.9158i	0.760356	+	1.10014i
$161$	−9.02280	+	12.4188i	−0.711096	+	0.978740i
$162$		0			0
$163$	−1.68568	−	3.30833i	−0.132033	−	0.259129i	0.815520	−	0.578729i	$-0.196451\pi$
$163$	−1.68568	−	3.30833i	−0.132033	−	0.259129i	−0.947552	+	0.319601i	$0.896451\pi$
$164$	−11.3788			−0.888534
$165$		0			0
$166$	−0.106299			−0.00825037
$167$	3.67785	+	7.21819i	0.284601	+	0.558560i	0.988406	−	0.151832i	$-0.0485174\pi$
$167$	3.67785	+	7.21819i	0.284601	+	0.558560i	−0.703806	+	0.710393i	$0.748517\pi$
$168$		0			0
$169$	7.60680	−	10.4699i	0.585139	−	0.805374i
$170$	5.96084	+	1.08862i	0.457176	+	0.0834937i
$171$		0			0
$172$	19.1918	−	3.03968i	1.46336	−	0.231773i
$173$	−19.6406	−	3.11076i	−1.49325	−	0.236507i	−0.644212	−	0.764847i	$-0.722815\pi$
$173$	−19.6406	−	3.11076i	−1.49325	−	0.236507i	−0.849033	+	0.528340i	$0.822815\pi$
$174$		0			0
$175$	−19.6114	−	4.06121i	−1.48249	−	0.306999i
$176$	2.86401	−	6.14161i	0.215883	−	0.462942i
$177$		0			0
$178$	9.66189	−	4.92298i	0.724190	−	0.368993i
$179$	−12.5391	−	17.2586i	−0.937215	−	1.28997i	−0.956978	−	0.290161i	$-0.906291\pi$
$179$	−12.5391	−	17.2586i	−0.937215	−	1.28997i	0.0197634	−	0.999805i	$-0.493709\pi$
$180$		0			0
$181$	−2.65677	−	8.17671i	−0.197477	−	0.607770i	−0.999939	−	0.0110673i	$-0.996477\pi$
$181$	−2.65677	−	8.17671i	−0.197477	−	0.607770i	0.802462	−	0.596703i	$-0.203523\pi$
$182$	39.4898	+	20.1211i	2.92718	+	1.49147i
$183$		0			0
$184$	4.84643	−	3.52113i	0.357283	−	0.259582i
$185$	19.1669	+	0.451635i	1.40918	+	0.0332049i
$186$		0			0
$187$	−1.41490	−	3.88761i	−0.103468	−	0.284290i
$188$	−8.04688	+	8.04688i	−0.586879	+	0.586879i
$189$		0			0
$190$	−16.7161	+	21.9034i	−1.21271	+	1.58904i
$191$	−0.708879	−	0.515031i	−0.0512927	−	0.0372663i	0.561844	−	0.827244i	$-0.310092\pi$
$191$	−0.708879	−	0.515031i	−0.0512927	−	0.0372663i	−0.613136	+	0.789977i	$0.710092\pi$
$192$		0			0
$193$	10.9523	−	21.4951i	0.788363	−	1.54725i	−0.0478565	−	0.998854i	$-0.515239\pi$
$193$	10.9523	−	21.4951i	0.788363	−	1.54725i	0.836219	−	0.548395i	$-0.184761\pi$
$194$	10.1456	+	7.37122i	0.728413	+	0.529223i
$195$		0			0
$196$	−7.60047	+	23.3918i	−0.542891	+	1.67085i
$197$	1.54634	−	1.54634i	0.110173	−	0.110173i	−0.649872	−	0.760044i	$-0.725177\pi$
$197$	1.54634	−	1.54634i	0.110173	−	0.110173i	0.760044	+	0.649872i	$0.225177\pi$
$198$		0			0
$199$			2.84042i			0.201352i	0.994919	+	0.100676i	$0.0321006\pi$
$199$			2.84042i			0.201352i	−0.994919	+	0.100676i	$0.967899\pi$
$200$	6.78900	+	3.87232i	0.480055	+	0.273815i
$201$		0			0
$202$	−1.13566	−	7.17028i	−0.0799048	−	0.504499i
$203$	−13.8388	−	7.05122i	−0.971293	−	0.494899i
$204$		0			0
$205$	8.43394	−	4.04995i	0.589052	−	0.282861i
$206$	−20.9085	−	28.7780i	−1.45676	−	2.00506i
$207$		0			0
$208$	7.35862	+	7.35862i	0.510228	+	0.510228i
$209$	18.6718	+	2.29293i	1.29156	+	0.158606i
$210$		0			0
$211$	−18.1842	−	5.90839i	−1.25185	−	0.406750i	−0.393266	−	0.919425i	$-0.628655\pi$
$211$	−18.1842	−	5.90839i	−1.25185	−	0.406750i	−0.858583	+	0.512674i	$0.828655\pi$
$212$	−8.95141	−	1.41776i	−0.614785	−	0.0973724i
$213$		0			0
$214$	−24.5872	+	7.98887i	−1.68075	+	0.546108i
$215$	−13.1430	+	9.08376i	−0.896346	+	0.619507i
$216$		0			0
$217$	0.479889	−	3.02990i	0.0325770	−	0.205683i
$218$	7.27662	+	14.2812i	0.492835	+	0.967243i
$219$		0			0
$220$	−0.228516	−	20.1673i	−0.0154065	−	1.35968i
$221$	6.35323			0.427365
$222$		0			0
$223$	−1.52789	+	9.64672i	−0.102315	+	0.645992i	0.882224	+	0.470829i	$0.156045\pi$
$223$	−1.52789	+	9.64672i	−0.102315	+	0.645992i	−0.984539	+	0.175163i	$0.943955\pi$
$224$	−17.8110	+	24.5148i	−1.19005	+	1.63796i
$225$		0			0
$226$	9.72258	−	3.15906i	0.646736	−	0.210137i
$227$	−22.9413	+	3.63355i	−1.52267	+	0.241167i	−0.860991	−	0.508621i	$-0.830156\pi$
$227$	−22.9413	+	3.63355i	−1.52267	+	0.241167i	−0.661679	+	0.749788i	$0.730156\pi$
$228$		0			0
$229$	0.687116	+	0.223257i	0.0454059	+	0.0147533i	0.331632	−	0.943409i	$-0.392401\pi$
$229$	0.687116	+	0.223257i	0.0454059	+	0.0147533i	−0.286226	+	0.958162i	$0.592401\pi$
$230$	−8.84015	+	16.3838i	−0.582902	+	1.08031i
$231$		0			0
$232$	4.28592	+	4.28592i	0.281384	+	0.281384i
$233$	13.4026	−	6.82897i	0.878034	−	0.447380i	0.0439598	−	0.999033i	$-0.486003\pi$
$233$	13.4026	−	6.82897i	0.878034	−	0.447380i	0.834074	+	0.551653i	$0.186003\pi$
$234$		0			0
$235$	3.10028	−	8.82839i	0.202240	−	0.575901i
$236$	0.616514	+	1.89743i	0.0401316	+	0.123512i
$237$		0			0
$238$	1.69800	+	10.7207i	0.110065	+	0.694922i
$239$	3.25568	−	2.36539i	0.210593	−	0.153004i	−0.477489	−	0.878638i	$-0.658453\pi$
$239$	3.25568	−	2.36539i	0.210593	−	0.153004i	0.688082	+	0.725633i	$0.258453\pi$
$240$		0			0
$241$			25.0056i			1.61075i	0.592766	+	0.805375i	$0.298036\pi$
$241$			25.0056i			1.61075i	−0.592766	+	0.805375i	$0.701964\pi$
$242$	−20.4841	+	12.3071i	−1.31677	+	0.791132i
$243$		0			0
$244$	3.91868	−	12.0605i	0.250868	−	0.772091i
$245$	−2.69220	−	20.0432i	−0.171998	−	1.28051i
$246$		0			0
$247$	−13.1155	+	25.7406i	−0.834518	+	1.63783i
$248$	−0.543497	+	1.06667i	−0.0345121	+	0.0677337i
$249$		0			0
$250$	−24.2281	−	1.71522i	−1.53232	−	0.108480i
$251$	−1.74476	+	5.36983i	−0.110128	+	0.338941i	−0.990900	−	0.134601i	$-0.957025\pi$
$251$	−1.74476	+	5.36983i	−0.110128	+	0.338941i	0.880771	+	0.473542i	$0.157025\pi$
$252$		0			0
$253$	12.7027	−	0.443372i	0.798614	−	0.0278745i
$254$		−	8.65220i		−	0.542887i
$255$		0			0
$256$	0.576106	−	0.418566i	0.0360066	−	0.0261604i
$257$	1.21694	+	7.68343i	0.0759104	+	0.479279i	0.996131	+	0.0878795i	$0.0280090\pi$
$257$	1.21694	+	7.68343i	0.0759104	+	0.479279i	−0.920221	+	0.391400i	$0.871991\pi$
$258$		0			0
$259$	10.6127	+	32.6626i	0.659442	+	2.02955i
$260$	29.2230	+	10.2623i	1.81233	+	0.636439i
$261$		0			0
$262$	11.7842	−	6.00433i	0.728028	−	0.370949i
$263$	22.4683	+	22.4683i	1.38546	+	1.38546i	0.834602	+	0.550853i	$0.185697\pi$
$263$	22.4683	+	22.4683i	1.38546	+	1.38546i	0.550853	+	0.834602i	$0.314303\pi$
$264$		0			0
$265$	7.13938	−	2.13515i	0.438569	−	0.131161i
$266$	−46.9411	−	15.2521i	−2.87814	−	0.935166i
$267$		0			0
$268$	37.0131	−	5.86230i	2.26093	−	0.358097i
$269$	25.7878	−	8.37895i	1.57231	−	0.510873i	0.612247	−	0.790667i	$-0.290266\pi$
$269$	25.7878	−	8.37895i	1.57231	−	0.510873i	0.960060	+	0.279793i	$0.0902660\pi$
$270$		0			0
$271$	−12.8302	+	17.6592i	−0.779378	+	1.07272i	0.215972	+	0.976399i	$0.430708\pi$
$271$	−12.8302	+	17.6592i	−0.779378	+	1.07272i	−0.995350	+	0.0963220i	$0.969292\pi$
$272$	−0.398698	+	2.51728i	−0.0241746	+	0.152632i
$273$		0			0
$274$	14.1752			0.856355
$275$	7.34734	+	14.8666i	0.443061	+	0.896491i
$276$		0			0
$277$	−1.74955	−	3.43369i	−0.105120	−	0.206310i	0.832455	−	0.554093i	$-0.186935\pi$
$277$	−1.74955	−	3.43369i	−0.105120	−	0.206310i	−0.937575	+	0.347782i	$0.886935\pi$
$278$	−3.39580	+	21.4403i	−0.203667	+	1.28590i
$279$		0			0
$280$	−2.51528	+	13.7726i	−0.150317	+	0.823072i
$281$	−26.3633	+	8.56595i	−1.57270	+	0.511002i	−0.960163	−	0.279439i	$-0.909851\pi$
$281$	−26.3633	+	8.56595i	−1.57270	+	0.511002i	−0.612538	+	0.790441i	$0.709851\pi$
$282$		0			0
$283$	−23.5731	−	3.73361i	−1.40127	−	0.221940i	−0.590376	−	0.807128i	$-0.701021\pi$
$283$	−23.5731	−	3.73361i	−1.40127	−	0.221940i	−0.810898	+	0.585188i	$0.801021\pi$
$284$	−30.0574	−	9.76625i	−1.78358	−	0.579520i
$285$		0			0
$286$	−7.00170	−	36.0239i	−0.414019	−	2.13014i
$287$	11.8507	+	11.8507i	0.699526	+	0.699526i
$288$		0			0
$289$	−9.07779	−	12.4945i	−0.533987	−	0.734971i
$290$	−17.7723	−	6.24111i	−1.04362	−	0.366491i
$291$		0			0
$292$	−5.60406	−	2.85541i	−0.327953	−	0.167100i
$293$	−2.03085	−	12.8223i	−0.118644	−	0.749087i	−0.973239	−	0.229793i	$-0.926195\pi$
$293$	−2.03085	−	12.8223i	−0.118644	−	0.749087i	0.854596	−	0.519294i	$-0.173805\pi$
$294$		0			0
$295$	−1.13230	−	1.18695i	−0.0659248	−	0.0691066i
$296$		−	13.4025i		−	0.779004i
$297$		0			0
$298$	−6.51633	+	6.51633i	−0.377481	+	0.377481i
$299$	−6.03177	+	18.5639i	−0.348826	+	1.07358i
$300$		0			0
$301$	−23.1535	−	16.8220i	−1.33454	−	0.969602i
$302$	−1.95834	+	3.84346i	−0.112690	+	0.221166i
$303$		0			0
$304$	−9.37588	−	6.81197i	−0.537743	−	0.390693i
$305$	1.38805	+	10.3339i	0.0794796	+	0.591719i
$306$		0			0
$307$	−0.378913	+	0.378913i	−0.0216257	+	0.0216257i	−0.717837	−	0.696211i	$-0.754868\pi$
$307$	−0.378913	+	0.378913i	−0.0216257	+	0.0216257i	0.696211	+	0.717837i	$0.254868\pi$
$308$	33.9497	−	12.3560i	1.93446	−	0.704050i
$309$		0			0
$310$	0.0876398	−	3.71933i	0.00497761	−	0.211244i
$311$	16.4773	−	11.9714i	0.934340	−	0.678838i	−0.0127116	−	0.999919i	$-0.504046\pi$
$311$	16.4773	−	11.9714i	0.934340	−	0.678838i	0.947052	+	0.321082i	$0.104046\pi$
$312$		0			0
$313$	4.57744	+	2.33232i	0.258732	+	0.131831i	0.578546	−	0.815650i	$-0.303620\pi$
$313$	4.57744	+	2.33232i	0.258732	+	0.131831i	−0.319814	+	0.947480i	$0.603620\pi$
$314$	2.48262	+	7.64071i	0.140102	+	0.431190i
$315$		0			0
$316$	17.3719	+	23.9104i	0.977248	+	1.34507i
$317$	23.9090	−	12.1823i	1.34287	−	0.684224i	0.372992	−	0.927835i	$-0.378332\pi$
$317$	23.9090	−	12.1823i	1.34287	−	0.684224i	0.969873	+	0.243610i	$0.0783318\pi$
$318$		0			0
$319$	2.45367	+	12.6242i	0.137379	+	0.706820i
$320$	−13.1115	+	24.3000i	−0.732953	+	1.35841i
$321$		0			0
$322$	−32.9376	−	5.21680i	−1.83554	−	0.290721i
$323$	−6.98808	+	1.10680i	−0.388827	+	0.0615842i
$324$		0			0
$325$	−25.3126	+	2.79469i	−1.40409	+	0.155021i
$326$	4.74129	−	6.52582i	0.262596	−	0.361432i
$327$		0			0
$328$	−2.96926	−	5.82749i	−0.163950	−	0.321769i
$329$	16.7612			0.924077
$330$		0			0
$331$	33.1897			1.82427			0.912135	−	0.409890i	$-0.134433\pi$
$331$	33.1897			1.82427			0.912135	+	0.409890i	$0.134433\pi$
$332$	−0.0604114	−	0.118564i	−0.00331550	−	0.00650704i
$333$		0			0
$334$	−10.3446	+	14.2382i	−0.566034	+	0.779079i
$335$	−25.3475	+	17.5189i	−1.38488	+	0.957158i
$336$		0			0
$337$	29.1418	−	4.61561i	1.58745	−	0.251428i	0.700626	−	0.713528i	$-0.252904\pi$
$337$	29.1418	−	4.61561i	1.58745	−	0.251428i	0.886828	+	0.462100i	$0.152904\pi$
$338$	27.7685	+	4.39810i	1.51041	+	0.239225i
$339$		0			0
$340$	2.17342	+	7.26733i	0.117870	+	0.394126i
$341$	−2.22163	+	1.23142i	−0.120308	+	0.0666850i
$342$		0			0
$343$	7.29516	−	3.71707i	0.393902	−	0.200703i
$344$	6.56475	+	9.03561i	0.353948	+	0.487167i
$345$		0			0
$346$	−13.3495	−	41.0856i	−0.717675	−	2.20878i
$347$	11.0730	+	5.64195i	0.594428	+	0.302876i	0.725202	−	0.688536i	$-0.241746\pi$
$347$	11.0730	+	5.64195i	0.594428	+	0.302876i	−0.130774	+	0.991412i	$0.541746\pi$
$348$		0			0
$349$	9.84617	−	7.15366i	0.527053	−	0.382927i	−0.292201	−	0.956357i	$-0.594388\pi$
$349$	9.84617	−	7.15366i	0.527053	−	0.382927i	0.819254	+	0.573430i	$0.194388\pi$
$350$	−11.4810	−	41.9666i	−0.613688	−	2.24321i
$351$		0			0
$352$	25.0752	−	0.875216i	1.33651	−	0.0466492i
$353$	21.2693	−	21.2693i	1.13205	−	1.13205i	0.142216	−	0.989836i	$-0.454577\pi$
$353$	21.2693	−	21.2693i	1.13205	−	1.13205i	0.989836	−	0.142216i	$-0.0454227\pi$
$354$		0			0
$355$	25.7545	−	3.45935i	1.36691	−	0.183603i
$356$	10.9821	+	7.97893i	0.582048	+	0.422882i
$357$		0			0
$358$	21.0399	−	41.2931i	1.11199	−	2.18241i
$359$	17.1501	+	12.4603i	0.905149	+	0.657629i	0.939783	−	0.341771i	$-0.111027\pi$
$359$	17.1501	+	12.4603i	0.905149	+	0.657629i	−0.0346345	+	0.999400i	$0.511027\pi$
$360$		0			0
$361$	4.07043	−	12.5275i	0.214233	−	0.659341i
$362$	13.2071	−	13.2071i	0.694149	−	0.694149i
$363$		0			0
$364$			55.4815i			2.90802i
$365$	5.17003	+	0.121823i	0.270612	+	0.00637650i
$366$		0			0
$367$	2.16192	+	13.6498i	0.112851	+	0.712514i	0.977625	+	0.210353i	$0.0674614\pi$
$367$	2.16192	+	13.6498i	0.112851	+	0.712514i	−0.864774	+	0.502161i	$0.832539\pi$
$368$	−6.97686	−	3.55489i	−0.363694	−	0.185311i
$369$		0			0
$370$	18.0295	+	37.5461i	0.937310	+	1.95193i
$371$	7.84610	+	10.7992i	0.407349	+	0.560668i
$372$		0			0
$373$	12.0946	+	12.0946i	0.626236	+	0.626236i	0.947119	−	0.320883i	$-0.103980\pi$
$373$	12.0946	+	12.0946i	0.626236	+	0.626236i	−0.320883	+	0.947119i	$0.603980\pi$
$374$	6.12964	−	6.57300i	0.316956	−	0.339882i
$375$		0			0
$376$	−6.22091	−	2.02129i	−0.320819	−	0.104240i
$377$	−19.5064	−	3.08951i	−1.00463	−	0.159118i
$378$		0			0
$379$	−0.349194	+	0.113460i	−0.0179369	+	0.00582804i	−0.317972	−	0.948100i	$-0.603002\pi$
$379$	−0.349194	+	0.113460i	−0.0179369	+	0.00582804i	0.300035	+	0.953928i	$0.403002\pi$
$380$	−33.9309	−	6.19677i	−1.74062	−	0.317888i
$381$		0			0
$382$	0.297780	−	1.88011i	0.0152358	−	0.0961949i
$383$	−14.2865	−	28.0388i	−0.730005	−	1.43272i	−0.894836	−	0.446394i	$-0.852708\pi$
$383$	−14.2865	−	28.0388i	−0.730005	−	1.43272i	0.164831	−	0.986322i	$-0.447292\pi$
$384$		0			0
$385$	−20.7657	+	21.2417i	−1.05832	+	1.08258i
$386$	52.4092			2.66756
$387$		0			0
$388$	−2.45583	+	15.5055i	−0.124676	+	0.787171i
$389$	20.5153	−	28.2368i	1.04016	−	1.43166i	0.143130	−	0.989704i	$-0.454283\pi$
$389$	20.5153	−	28.2368i	1.04016	−	1.43166i	0.897035	−	0.441960i	$-0.145717\pi$
$390$		0			0
$391$	−4.54642	+	1.47722i	−0.229922	+	0.0747062i
$392$	−13.9631	+	2.21154i	−0.705245	+	0.111700i
$393$		0			0
$394$	4.51832	+	1.46809i	0.227630	+	0.0739614i
$395$	−21.3863	−	11.5393i	−1.07606	−	0.580607i
$396$		0			0
$397$	8.10434	+	8.10434i	0.406745	+	0.406745i	0.880602	−	0.473857i	$-0.157139\pi$
$397$	8.10434	+	8.10434i	0.406745	+	0.406745i	−0.473857	+	0.880602i	$0.657139\pi$
$398$	−5.49811	+	2.80143i	−0.275595	+	0.140423i
$399$		0			0
$400$	0.481182	−	10.2047i	0.0240591	−	0.510237i
$401$	7.45244	+	22.9363i	0.372157	+	1.14538i	0.945377	+	0.325980i	$0.105694\pi$
$401$	7.45244	+	22.9363i	0.372157	+	1.14538i	−0.573220	+	0.819402i	$0.694306\pi$
$402$		0			0
$403$	−0.610212	−	3.85273i	−0.0303968	−	0.191918i
$404$	7.35221	−	5.34170i	0.365786	−	0.265759i
$405$		0			0
$406$		−	33.7417i		−	1.67457i
$407$	15.9021	−	23.5750i	0.788240	−	1.16857i
$408$		0			0
$409$	4.96063	−	15.2673i	0.245288	−	0.754918i	−0.750301	−	0.661096i	$-0.770092\pi$
$409$	4.96063	−	15.2673i	0.245288	−	0.754918i	0.995589	−	0.0938217i	$-0.0299084\pi$
$410$	16.1575	+	12.3309i	0.797962	+	0.608982i
$411$		0			0
$412$	20.2160	−	39.6761i	0.995970	−	1.95470i
$413$	1.33405	−	2.61821i	0.0656441	−	0.128834i
$414$		0			0
$415$	0.0869762	+	0.0663777i	0.00426950	+	0.00325836i
$416$	−11.9067	+	36.6451i	−0.583775	+	1.79667i
$417$		0			0
$418$	13.9771	+	38.4038i	0.683643	+	1.87839i
$419$			1.01897i			0.0497800i	0.999690	+	0.0248900i	$0.00792355\pi$
$419$			1.01897i			0.0497800i	−0.999690	+	0.0248900i	$0.992076\pi$
$420$		0			0
$421$	2.48285	−	1.80389i	0.121007	−	0.0879164i	−0.525636	−	0.850710i	$-0.676173\pi$
$421$	2.48285	−	1.80389i	0.121007	−	0.0879164i	0.646642	+	0.762793i	$0.276173\pi$
$422$	−6.49784	−	41.0257i	−0.316310	−	1.99710i
$423$		0			0
$424$	−1.60975	−	4.95430i	−0.0781764	−	0.240602i
$425$	−4.19753	−	4.61297i	−0.203610	−	0.223762i
$426$		0			0
$427$	−16.6418	+	8.47944i	−0.805355	+	0.410349i
$428$	−22.8840	−	22.8840i	−1.10614	−	1.10614i
$429$		0			0
$430$	−30.5457	−	16.4814i	−1.47304	−	0.794806i
$431$	−3.18922	−	1.03624i	−0.153620	−	0.0499140i	0.231198	−	0.972907i	$-0.425736\pi$
$431$	−3.18922	−	1.03624i	−0.153620	−	0.0499140i	−0.384817	+	0.922993i	$0.625736\pi$
$432$		0			0
$433$	1.27152	−	0.201389i	0.0611054	−	0.00967815i	−0.125807	−	0.992055i	$-0.540152\pi$
$433$	1.27152	−	0.201389i	0.0611054	−	0.00967815i	0.186912	+	0.982377i	$0.440152\pi$
$434$	6.33818	−	2.05940i	0.304242	−	0.0988543i
$435$		0			0
$436$	−11.7936	+	16.2325i	−0.564811	+	0.777395i
$437$	3.40046	−	21.4697i	0.162666	−	1.02703i
$438$		0			0
$439$	29.7921			1.42190			0.710950	−	0.703243i	$-0.248265\pi$
$439$	29.7921			1.42190			0.710950	+	0.703243i	$0.248265\pi$
$440$	10.2688	−	5.37961i	0.489544	−	0.256463i
$441$		0			0
$442$	6.26601	+	12.2977i	0.298044	+	0.584944i
$443$	0.526532	−	3.32439i	0.0250163	−	0.157947i	−0.972018	−	0.234907i	$-0.924521\pi$
$443$	0.526532	−	3.32439i	0.0250163	−	0.157947i	0.997034	+	0.0769603i	$0.0245215\pi$
$444$		0			0
$445$	−10.9798	−	2.00522i	−0.520490	−	0.0950568i
$446$	−20.1797	+	6.55680i	−0.955539	+	0.310473i
$447$		0			0
$448$	−48.8521	−	7.73742i	−2.30805	−	0.365559i
$449$	−39.2062	−	12.7389i	−1.85026	−	0.601185i	−0.996792	−	0.0800330i	$-0.974497\pi$
$449$	−39.2062	−	12.7389i	−1.85026	−	0.601185i	−0.853464	−	0.521152i	$-0.825503\pi$
$450$		0			0
$451$	1.69143	−	13.7736i	0.0796462	−	0.648575i
$452$	9.04909	+	9.04909i	0.425633	+	0.425633i
$453$		0			0
$454$	−29.6597	−	40.8231i	−1.39200	−	1.91592i
$455$	−19.7471	−	41.1228i	−0.925756	−	1.92787i
$456$		0			0
$457$	−6.13680	−	3.12685i	−0.287067	−	0.146268i	0.304528	−	0.952504i	$-0.401501\pi$
$457$	−6.13680	−	3.12685i	−0.287067	−	0.146268i	−0.591595	+	0.806235i	$0.701501\pi$
$458$	0.245530	+	1.55022i	0.0114729	+	0.0724369i
$459$		0			0
$460$	−23.2983	−	0.548984i	−1.08629	−	0.0255965i
$461$		−	0.943983i		−	0.0439657i	−0.999758	−	0.0219828i	$-0.993002\pi$
$461$		−	0.943983i		−	0.0439657i	0.999758	−	0.0219828i	$-0.00699792\pi$
$462$		0			0
$463$	16.3776	−	16.3776i	0.761130	−	0.761130i	−0.215397	−	0.976527i	$-0.569105\pi$
$463$	16.3776	−	16.3776i	0.761130	−	0.761130i	0.976527	+	0.215397i	$0.0691045\pi$
$464$	2.44825	−	7.53495i	0.113657	−	0.349801i
$465$		0			0
$466$	26.4372	+	19.2077i	1.22468	+	0.889782i
$467$	−9.33204	+	18.3152i	−0.431835	+	0.847525i	0.567867	+	0.823120i	$0.307769\pi$
$467$	−9.33204	+	18.3152i	−0.431835	+	0.847525i	−0.999702	+	0.0244042i	$0.992231\pi$
$468$		0			0
$469$	−44.6536	−	32.4427i	−2.06191	−	1.49807i
$470$	20.1465	−	2.70608i	0.929290	−	0.124822i
$471$		0			0
$472$	−0.810868	+	0.810868i	−0.0373232	+	0.0373232i
$473$	0.826616	+	23.6828i	0.0380078	+	1.08894i
$474$		0			0
$475$	27.3551	−	7.48367i	1.25514	−	0.343374i
$476$	−10.9928	+	7.98670i	−0.503852	+	0.366070i
$477$		0			0
$478$	7.78959	+	3.96900i	0.356288	+	0.181538i
$479$	3.19706	+	9.83953i	0.146077	+	0.449580i	0.997148	−	0.0754715i	$-0.0240462\pi$
$479$	3.19706	+	9.83953i	0.146077	+	0.449580i	−0.851071	+	0.525051i	$0.824046\pi$
$480$		0			0
$481$	25.6686	+	35.3298i	1.17039	+	1.61090i
$482$	−48.4024	+	24.6623i	−2.20467	+	1.12333i
$483$		0			0
$484$	−25.3687	−	15.8533i	−1.15312	−	0.720605i
$485$	−3.69847	−	12.3667i	−0.167939	−	0.561544i
$486$		0			0
$487$	−9.68467	−	1.53390i	−0.438854	−	0.0695077i	−0.0669020	−	0.997760i	$-0.521311\pi$
$487$	−9.68467	−	1.53390i	−0.438854	−	0.0695077i	−0.371952	+	0.928252i	$0.621311\pi$
$488$	7.19916	−	1.14024i	0.325891	−	0.0516160i
$489$		0			0
$490$	36.1416	−	24.9792i	1.63271	−	1.12844i
$491$	6.32001	−	8.69875i	0.285218	−	0.392569i	−0.642235	−	0.766507i	$-0.721993\pi$
$491$	6.32001	−	8.69875i	0.285218	−	0.392569i	0.927454	+	0.373938i	$0.121993\pi$
$492$		0			0
$493$	−2.19586	−	4.30962i	−0.0988965	−	0.194095i
$494$	−62.7606			−2.82373
$495$		0			0
$496$	1.56482			0.0702626
$497$	21.1327	+	41.4753i	0.947933	+	1.86042i
$498$		0			0
$499$	0.911997	−	1.25526i	0.0408266	−	0.0561930i	−0.788116	−	0.615527i	$-0.788943\pi$
$499$	0.911997	−	1.25526i	0.0408266	−	0.0561930i	0.828942	+	0.559334i	$0.188943\pi$
$500$	−11.8561	−	27.9985i	−0.530221	−	1.25213i
$501$		0			0
$502$	−12.1150	+	1.91883i	−0.540719	+	0.0856415i
$503$	−26.7879	−	4.24279i	−1.19441	−	0.189177i	−0.472608	−	0.881273i	$-0.656687\pi$
$503$	−26.7879	−	4.24279i	−1.19441	−	0.189177i	−0.721805	+	0.692096i	$0.756687\pi$
$504$		0			0
$505$	−3.54823	+	6.57607i	−0.157894	+	0.292631i
$506$	13.3866	+	24.1510i	0.595105	+	1.07364i
$507$		0			0
$508$	9.65055	−	4.91720i	0.428174	−	0.218166i
$509$	10.6136	+	14.6084i	0.470442	+	0.647507i	0.976633	−	0.214914i	$-0.0689471\pi$
$509$	10.6136	+	14.6084i	0.470442	+	0.647507i	−0.506191	+	0.862421i	$0.668947\pi$
$510$		0			0
$511$	2.86265	+	8.81032i	0.126636	+	0.389746i
$512$	−19.4638	−	9.91729i	−0.860186	−	0.438287i
$513$		0			0
$514$	−13.6723	+	9.93353i	−0.603060	+	0.438149i
$515$	−0.862492	+	36.6032i	−0.0380059	+	1.61293i
$516$		0			0
$517$	−8.54432	−	10.9366i	−0.375779	−	0.480992i
$518$	−52.7568	+	52.7568i	−2.31800	+	2.31800i
$519$		0			0
$520$	2.36995	+	17.6440i	0.103929	+	0.773743i
$521$	10.1987	+	7.40977i	0.446812	+	0.324628i	0.788336	−	0.615245i	$-0.210943\pi$
$521$	10.1987	+	7.40977i	0.446812	+	0.324628i	−0.341524	+	0.939873i	$0.610943\pi$
$522$		0			0
$523$	−7.40503	+	14.5332i	−0.323800	+	0.635492i	−0.994324	−	0.106395i	$-0.966069\pi$
$523$	−7.40503	+	14.5332i	−0.323800	+	0.635492i	0.670524	+	0.741888i	$0.266069\pi$
$524$	13.3943	+	9.73153i	0.585133	+	0.425124i
$525$		0			0
$526$	−21.3313	+	65.6510i	−0.930088	+	2.86252i
$527$	0.675513	−	0.675513i	0.0294258	−	0.0294258i
$528$		0			0
$529$			8.31309i			0.361438i
$530$	11.1743	+	11.7136i	0.485381	+	0.508807i
$531$		0			0
$532$	−9.66549	−	61.0255i	−0.419052	−	2.64579i
$533$	18.9880	+	9.67489i	0.822464	+	0.419066i
$534$		0			0
$535$	25.1065	+	8.81669i	1.08545	+	0.381179i
$536$	12.6607	+	17.4260i	0.546860	+	0.752689i
$537$		0			0
$538$	41.6525	+	41.6525i	1.79577	+	1.79577i
$539$	−27.1852	−	12.6772i	−1.17095	−	0.546047i
$540$		0			0
$541$	15.3752	+	4.99571i	0.661033	+	0.214783i	0.620272	−	0.784386i	$-0.287022\pi$
$541$	15.3752	+	4.99571i	0.661033	+	0.214783i	0.0407602	+	0.999169i	$0.487022\pi$
$542$	−46.8364	−	7.41815i	−2.01179	−	0.318637i
$543$		0			0
$544$	−8.97463	+	2.91603i	−0.384784	+	0.125024i
$545$	2.96391	−	16.2291i	0.126960	−	0.695178i
$546$		0			0
$547$	3.09956	−	19.5699i	0.132528	−	0.836747i	−0.828438	−	0.560080i	$-0.810770\pi$
$547$	3.09956	−	19.5699i	0.132528	−	0.836747i	0.960966	−	0.276666i	$-0.0892297\pi$
$548$	8.05601	+	15.8108i	0.344136	+	0.675405i
$549$		0			0
$550$	−21.5303	+	28.8845i	−0.918057	+	1.23164i
$551$	21.9938			0.936967
$552$		0			0
$553$	6.80966	−	42.9945i	0.289576	−	1.82831i
$554$	4.92094	−	6.77310i	0.209071	−	0.287761i
$555$		0			0
$556$	−25.8441	+	8.39725i	−1.09603	+	0.356123i
$557$	4.41885	−	0.699877i	0.187233	−	0.0296547i	−0.0621139	−	0.998069i	$-0.519784\pi$
$557$	4.41885	−	0.699877i	0.187233	−	0.0296547i	0.249346	+	0.968414i	$0.419784\pi$
$558$		0			0
$559$	−34.6102	−	11.2455i	−1.46386	−	0.475636i
$560$	17.5329	−	5.24351i	0.740901	−	0.221579i
$561$		0			0
$562$	−42.5821	−	42.5821i	−1.79622	−	1.79622i
$563$	13.7225	−	6.99197i	0.578335	−	0.294676i	−0.140249	−	0.990116i	$-0.544790\pi$
$563$	13.7225	−	6.99197i	0.578335	−	0.294676i	0.718584	+	0.695440i	$0.244790\pi$
$564$		0			0
$565$	−9.92793	−	3.48641i	−0.417671	−	0.146674i
$566$	−16.0224	−	49.3119i	−0.673473	−	2.07274i
$567$		0			0
$568$	−2.84173	−	17.9420i	−0.119236	−	0.752829i
$569$	−1.28307	+	0.932205i	−0.0537891	+	0.0390801i	−0.614355	−	0.789030i	$-0.710584\pi$
$569$	−1.28307	+	0.932205i	−0.0537891	+	0.0390801i	0.560566	+	0.828110i	$0.310584\pi$
$570$		0			0
$571$		−	13.0509i		−	0.546163i	−0.961991	−	0.273081i	$-0.911957\pi$
$571$		−	13.0509i		−	0.546163i	0.961991	−	0.273081i	$-0.0880428\pi$
$572$	36.2014	−	28.2826i	1.51366	−	1.18256i
$573$		0			0
$574$	−11.2510	+	34.6270i	−0.469608	+	1.44530i
$575$	17.4640	−	7.88544i	0.728301	−	0.328846i
$576$		0			0
$577$	8.20279	−	16.0989i	0.341486	−	0.670205i	−0.654847	−	0.755762i	$-0.727267\pi$
$577$	8.20279	−	16.0989i	0.341486	−	0.670205i	0.996333	+	0.0855567i	$0.0272669\pi$
$578$	15.2320	−	29.8945i	0.633568	−	1.24345i
$579$		0			0
$580$	−3.13904	−	23.3699i	−0.130341	−	0.970381i
$581$	−0.0605644	+	0.186398i	−0.00251264	+	0.00773310i
$582$		0			0
$583$	3.04676	−	10.6246i	0.126184	−	0.440027i
$584$		−	3.61516i		−	0.149596i
$585$		0			0
$586$	22.8167	−	16.5773i	0.942550	−	0.684803i
$587$	1.85227	+	11.6948i	0.0764514	+	0.482695i	0.995973	+	0.0896552i	$0.0285765\pi$
$587$	1.85227	+	11.6948i	0.0764514	+	0.482695i	−0.919522	+	0.393040i	$0.871423\pi$
$588$		0			0
$589$	1.34238	+	4.13141i	0.0553116	+	0.170232i
$590$	1.18078	−	3.36240i	0.0486119	−	0.138428i
$591$		0			0
$592$	−15.6092	+	7.95330i	−0.641535	+	0.326879i
$593$	8.80231	+	8.80231i	0.361467	+	0.361467i	0.864353	−	0.502886i	$-0.167728\pi$
$593$	8.80231	+	8.80231i	0.361467	+	0.361467i	−0.502886	+	0.864353i	$0.667728\pi$
$594$		0			0
$595$	5.30518	−	9.83229i	0.217491	−	0.403084i
$596$	−10.9716	−	3.56488i	−0.449413	−	0.146023i
$597$		0			0
$598$	−41.8824	+	6.63353i	−1.71270	+	0.271265i
$599$	7.01059	−	2.27788i	0.286445	−	0.0930716i	−0.162270	−	0.986746i	$-0.551882\pi$
$599$	7.01059	−	2.27788i	0.286445	−	0.0930716i	0.448715	+	0.893675i	$0.351882\pi$
$600$		0			0
$601$	3.77835	−	5.20046i	0.154122	−	0.212131i	−0.724973	−	0.688777i	$-0.758148\pi$
$601$	3.77835	−	5.20046i	0.154122	−	0.212131i	0.879095	+	0.476646i	$0.158148\pi$
$602$	9.72613	−	61.4084i	0.396407	−	2.50282i
$603$		0			0
$604$	−5.39990			−0.219719
$605$	24.4458	+	2.72120i	0.993861	+	0.110633i
$606$		0			0
$607$	−13.0738	−	25.6589i	−0.530651	−	1.04146i	−0.988328	−	0.152342i	$-0.951318\pi$
$607$	−13.0738	−	25.6589i	−0.530651	−	1.04146i	0.457677	−	0.889119i	$-0.348682\pi$
$608$	6.71251	−	42.3811i	0.272228	−	1.71878i
$609$		0			0
$610$	−18.6340	+	12.8789i	−0.754470	+	0.521450i
$611$	20.2699	−	6.58610i	0.820033	−	0.266445i
$612$		0			0
$613$	−33.5860	−	5.31950i	−1.35653	−	0.214853i	−0.564547	−	0.825401i	$-0.690949\pi$
$613$	−33.5860	−	5.31950i	−1.35653	−	0.214853i	−0.791979	+	0.610549i	$0.790949\pi$
$614$	−1.10716	−	0.359738i	−0.0446814	−	0.0145179i
$615$		0			0
$616$	15.1870	+	14.1626i	0.611903	+	0.570628i
$617$	−31.1826	−	31.1826i	−1.25536	−	1.25536i	−0.953282	−	0.302082i	$-0.902318\pi$
$617$	−31.1826	−	31.1826i	−1.25536	−	1.25536i	−0.302082	−	0.953282i	$-0.597682\pi$
$618$		0			0
$619$	21.3297	+	29.3578i	0.857311	+	1.17999i	0.982204	+	0.187818i	$0.0601414\pi$
$619$	21.3297	+	29.3578i	0.857311	+	1.17999i	−0.124892	+	0.992170i	$0.539859\pi$
$620$	4.19830	−	2.01601i	0.168608	−	0.0809650i
$621$		0			0
$622$	39.4237	+	20.0874i	1.58075	+	0.805431i
$623$	−3.12768	−	19.7474i	−0.125308	−	0.791162i
$624$		0			0
$625$	18.7530	+	16.5326i	0.750119	+	0.661303i
$626$			11.1607i			0.446071i
$627$		0			0
$628$	−7.11143	+	7.11143i	−0.283777	+	0.283777i
$629$	−3.30496	+	10.1716i	−0.131778	+	0.405569i
$630$		0			0
$631$	38.7679	+	28.1666i	1.54333	+	1.12129i	0.948206	+	0.317657i	$0.102896\pi$
$631$	38.7679	+	28.1666i	1.54333	+	1.12129i	0.595122	+	0.803636i	$0.297104\pi$
$632$	−7.71225	+	15.1361i	−0.306777	+	0.602083i
$633$		0			0
$634$	47.1616	+	34.2649i	1.87303	+	1.36083i
$635$	−5.40284	+	7.07946i	−0.214405	+	0.280940i
$636$		0			0
$637$	32.5721	−	32.5721i	1.29056	−	1.29056i
$638$	−22.0163	+	17.2004i	−0.871632	+	0.680970i
$639$		0			0
$640$	−26.1455	−	0.616074i	−1.03349	−	0.0243525i
$641$	19.0504	−	13.8409i	0.752446	−	0.546684i	−0.144138	−	0.989558i	$-0.546041\pi$
$641$	19.0504	−	13.8409i	0.752446	−	0.546684i	0.896584	+	0.442874i	$0.146041\pi$
$642$		0			0
$643$	21.7694	+	11.0921i	0.858501	+	0.437428i	0.827084	−	0.562078i	$-0.189998\pi$
$643$	21.7694	+	11.0921i	0.858501	+	0.437428i	0.0314167	+	0.999506i	$0.489998\pi$
$644$	−12.9003	−	39.7030i	−0.508342	−	1.56452i
$645$		0			0
$646$	−9.03454	−	12.4350i	−0.355459	−	0.489247i
$647$	1.41419	−	0.720564i	0.0555974	−	0.0283283i	−0.425971	−	0.904737i	$-0.640067\pi$
$647$	1.41419	−	0.720564i	0.0555974	−	0.0283283i	0.481568	+	0.876409i	$0.340067\pi$
$648$		0			0
$649$	−2.38842	+	0.464220i	−0.0937537	+	0.0182222i
$650$	−30.3746	−	46.2404i	−1.19139	−	1.81370i
$651$		0			0
$652$	9.97338	+	1.57963i	0.390588	+	0.0618630i
$653$	−21.8933	+	3.46756i	−0.856750	+	0.135696i	−0.569330	−	0.822109i	$-0.692797\pi$
$653$	−21.8933	+	3.46756i	−0.856750	+	0.135696i	−0.287420	+	0.957805i	$0.592797\pi$
$654$		0			0
$655$	−13.3915	−	2.44568i	−0.523249	−	0.0955606i
$656$	−5.02499	+	6.91630i	−0.196193	+	0.270036i
$657$		0			0
$658$	16.5311	+	32.4441i	0.644450	+	1.26480i
$659$	13.1372			0.511752			0.255876	−	0.966710i	$-0.417636\pi$
$659$	13.1372			0.511752			0.255876	+	0.966710i	$0.417636\pi$
$660$		0			0
$661$	30.1682			1.17341			0.586703	−	0.809802i	$-0.300426\pi$
$661$	30.1682			1.17341			0.586703	+	0.809802i	$0.300426\pi$
$662$	32.7340	+	64.2441i	1.27224	+	2.49692i
$663$		0			0
$664$	0.0449568	−	0.0618777i	0.00174466	−	0.00240132i
$665$	28.8843	+	41.7919i	1.12009	+	1.62062i
$666$		0			0
$667$	14.6773	−	2.32465i	0.568306	−	0.0900109i
$668$	−21.7601	−	3.44647i	−0.841924	−	0.133348i
$669$		0			0
$670$	−58.9102	−	31.7860i	−2.27590	−	1.22800i
$671$	14.0163	+	6.53618i	0.541091	+	0.252326i
$672$		0			0
$673$	−40.0641	+	20.4137i	−1.54436	+	0.786889i	−0.998693	−	0.0511145i	$-0.983723\pi$
$673$	−40.0641	+	20.4137i	−1.54436	+	0.786889i	−0.545664	+	0.838004i	$0.683723\pi$
$674$	37.6760	+	51.8565i	1.45122	+	1.99744i
$675$		0			0
$676$	10.8758	+	33.4722i	0.418299	+	1.28739i
$677$	−30.4100	−	15.4947i	−1.16875	−	0.595508i	−0.241666	−	0.970360i	$-0.577694\pi$
$677$	−30.4100	−	15.4947i	−1.16875	−	0.595508i	−0.927085	+	0.374852i	$0.877694\pi$
$678$		0			0
$679$	18.7062	−	13.5909i	0.717879	−	0.521570i
$680$	−3.15472	+	3.00947i	−0.120978	+	0.115408i
$681$		0			0
$682$	−4.57474	−	3.08581i	−0.175176	−	0.118162i
$683$	−11.7243	+	11.7243i	−0.448619	+	0.448619i	−0.894895	−	0.446276i	$-0.852750\pi$
$683$	−11.7243	+	11.7243i	−0.448619	+	0.448619i	0.446276	+	0.894895i	$0.352750\pi$
$684$		0			0
$685$	−11.5985	−	8.85165i	−0.443156	−	0.338204i
$686$	14.3900	+	10.4550i	0.549413	+	0.399172i
$687$		0			0
$688$	6.62768	−	13.0076i	0.252678	−	0.495908i
$689$	13.7320	+	9.97685i	0.523146	+	0.380088i
$690$		0			0
$691$	−1.81718	+	5.59270i	−0.0691287	+	0.212756i	−0.979653	−	0.200700i	$-0.935678\pi$
$691$	−1.81718	+	5.59270i	−0.0691287	+	0.212756i	0.910524	+	0.413456i	$0.135678\pi$
$692$	38.2396	−	38.2396i	1.45365	−	1.45365i
$693$		0			0
$694$			26.9980i			1.02483i
$695$	16.1668	−	15.4225i	0.613243	−	0.585008i
$696$		0			0
$697$	0.816455	+	5.15489i	0.0309254	+	0.195256i
$698$	23.5581	+	12.0034i	0.891687	+	0.454337i
$699$		0			0
$700$	40.2841	−	36.6562i	1.52260	−	1.38547i
$701$	−15.7245	−	21.6429i	−0.593905	−	0.817440i	0.401228	−	0.915978i	$-0.368583\pi$
$701$	−15.7245	−	21.6429i	−0.593905	−	0.817440i	−0.995133	+	0.0985379i	$0.968583\pi$
$702$		0			0
$703$	−34.3884	−	34.3884i	−1.29698	−	1.29698i
$704$	19.8546	+	35.8200i	0.748297	+	1.35002i
$705$		0			0
$706$	62.1476	+	20.1930i	2.33896	+	0.759973i
$707$	−13.2204	−	2.09390i	−0.497203	−	0.0787493i
$708$		0			0
$709$	9.52249	−	3.09405i	0.357625	−	0.116199i	−0.124694	−	0.992195i	$-0.539795\pi$
$709$	9.52249	−	3.09405i	0.357625	−	0.116199i	0.482318	+	0.875996i	$0.339795\pi$
$710$	32.0971	+	46.4403i	1.20458	+	1.74287i
$711$		0			0
$712$	−1.22057	+	7.70638i	−0.0457428	+	0.288809i
$713$	1.33249	+	2.61516i	0.0499021	+	0.0979383i
$714$		0			0
$715$	−16.7660	+	33.8479i	−0.627014	+	1.26584i
$716$	58.0151			2.16813
$717$		0			0
$718$	−7.20429	+	45.4861i	−0.268862	+	1.69753i
$719$	−15.3603	+	21.1417i	−0.572843	+	0.788451i	−0.992888	−	0.119053i	$-0.962014\pi$
$719$	−15.3603	+	21.1417i	−0.572843	+	0.788451i	0.420045	+	0.907503i	$0.362014\pi$
$720$		0			0
$721$	−62.3761	+	20.2672i	−2.32301	+	0.754790i
$722$	28.2636	−	4.47651i	1.05186	−	0.166598i
$723$		0			0
$724$	22.2368	+	7.22518i	0.826425	+	0.268522i
$725$	10.6445	+	16.2045i	0.395326	+	0.601819i
$726$		0			0
$727$	−19.2017	−	19.2017i	−0.712150	−	0.712150i	0.254835	−	0.966985i	$-0.417979\pi$
$727$	−19.2017	−	19.2017i	−0.712150	−	0.712150i	−0.966985	+	0.254835i	$0.917979\pi$
$728$	−28.4141	+	14.4777i	−1.05310	+	0.536580i
$729$		0			0
$730$	4.86324	+	10.1276i	0.179996	+	0.374839i
$731$	−2.75411	−	8.47627i	−0.101864	−	0.313506i
$732$		0			0
$733$	−0.423100	−	2.67135i	−0.0156276	−	0.0986686i	0.978642	−	0.205573i	$-0.0659060\pi$
$733$	−0.423100	−	2.67135i	−0.0156276	−	0.0986686i	−0.994269	+	0.106905i	$0.965906\pi$
$734$	−24.2892	+	17.6471i	−0.896531	+	0.651368i
$735$		0			0
$736$		−	28.9920i		−	1.06866i
$737$	1.59421	+	45.6745i	0.0587233	+	1.68244i
$738$		0			0
$739$	2.74727	−	8.45522i	0.101060	−	0.311030i	−0.887726	−	0.460373i	$-0.847716\pi$
$739$	2.74727	−	8.45522i	0.101060	−	0.311030i	0.988786	+	0.149343i	$0.0477157\pi$
$740$	−31.6319	+	41.4480i	−1.16281	+	1.52366i
$741$		0			0
$742$	−13.1653	+	25.8384i	−0.483314	+	0.948557i
$743$	−20.1098	+	39.4677i	−0.737758	+	1.44793i	0.150512	+	0.988608i	$0.451908\pi$
$743$	−20.1098	+	39.4677i	−0.737758	+	1.44793i	−0.888269	+	0.459323i	$0.848092\pi$
$744$		0			0
$745$	9.40093	−	1.26273i	0.344423	−	0.0462629i
$746$	−11.4826	+	35.3397i	−0.420407	+	1.29388i
$747$		0			0
$748$	10.8150	+	3.10136i	0.395436	+	0.113397i
$749$			47.6662i			1.74169i
$750$		0			0
$751$	−36.3237	+	26.3907i	−1.32547	+	0.963011i	−0.325624	+	0.945499i	$0.605574\pi$
$751$	−36.3237	+	26.3907i	−1.32547	+	0.963011i	−0.999847	+	0.0175112i	$0.994426\pi$
$752$	1.33750	+	8.44467i	0.0487737	+	0.307945i
$753$		0			0
$754$	−13.2583	−	40.8050i	−0.482840	−	1.48603i
$755$	4.00240	−	1.92194i	0.145662	−	0.0699465i
$756$		0			0
$757$	35.4916	−	18.0839i	1.28997	−	0.657270i	0.331764	−	0.943363i	$-0.392356\pi$
$757$	35.4916	−	18.0839i	1.28997	−	0.657270i	0.958202	+	0.286092i	$0.0923564\pi$
$758$	−0.564020	−	0.564020i	−0.0204861	−	0.0204861i
$759$		0			0
$760$	−5.68055	−	18.9942i	−0.206055	−	0.688994i
$761$	21.3924	+	6.95080i	0.775472	+	0.251966i	0.669906	−	0.742446i	$-0.266334\pi$
$761$	21.3924	+	6.95080i	0.775472	+	0.251966i	0.105566	+	0.994412i	$0.466334\pi$
$762$		0			0
$763$	29.1884	−	4.62299i	1.05669	−	0.167364i
$764$	2.26629	−	0.736361i	0.0819913	−	0.0266406i
$765$		0			0
$766$	40.1834	−	55.3077i	1.45189	−	1.99835i
$767$	0.584516	−	3.69049i	0.0211056	−	0.133256i
$768$		0			0
$769$	−30.3985			−1.09620			−0.548098	−	0.836414i	$-0.684648\pi$
$769$	−30.3985			−1.09620			−0.548098	+	0.836414i	$0.684648\pi$
$770$	−61.5974	−	19.2454i	−2.21982	−	0.693556i
$771$		0			0
$772$	29.7851	+	58.4565i	1.07199	+	2.10390i
$773$	−2.64872	+	16.7233i	−0.0952677	+	0.601497i	0.893152	+	0.449754i	$0.148488\pi$
$773$	−2.64872	+	16.7233i	−0.0952677	+	0.601497i	−0.988420	+	0.151743i	$0.951512\pi$
$774$		0			0
$775$	−2.39423	+	2.98853i	−0.0860034	+	0.107351i
$776$	−8.58176	+	2.78838i	−0.308067	+	0.100097i
$777$		0			0
$778$	74.8906	+	11.8615i	2.68496	+	0.425256i
$779$	−22.5709	−	7.33373i	−0.808686	−	0.262758i
$780$		0			0
$781$	16.2897	−	34.9317i	0.582890	−	1.24996i
$782$	−7.34340	−	7.34340i	−0.262600	−	0.262600i
$783$		0			0
$784$	10.8617	+	14.9498i	0.387917	+	0.533922i
$785$	2.73987	−	7.80209i	0.0977902	−	0.278468i
$786$		0			0
$787$	−10.5077	−	5.35395i	−0.374560	−	0.190848i	0.256569	−	0.966526i	$-0.417408\pi$
$787$	−10.5077	−	5.35395i	−0.374560	−	0.190848i	−0.631129	+	0.775678i	$0.717408\pi$
$788$	0.930353	+	5.87402i	0.0331425	+	0.209253i
$789$		0			0
$790$	1.24361	−	52.7776i	0.0442458	−	1.87774i
$791$		−	18.8488i		−	0.670185i
$792$		0			0
$793$	−16.7937	+	16.7937i	−0.596361	+	0.596361i
$794$	−7.69422	+	23.6804i	−0.273058	+	0.840385i
$795$		0			0
$796$	−6.24935	−	4.54042i	−0.221502	−	0.160931i
$797$	16.6985	−	32.7726i	0.591490	−	1.16086i	−0.380267	−	0.924877i	$-0.624168\pi$
$797$	16.6985	−	32.7726i	0.591490	−	1.16086i	0.971756	−	0.235987i	$-0.0758322\pi$
$798$		0			0
$799$	4.22283	+	3.06807i	0.149393	+	0.108540i
$800$	34.4740	−	15.5659i	1.21884	−	0.550337i
$801$		0			0
$802$	−37.0468	+	37.0468i	−1.30817	+	1.30817i
$803$	4.28941	−	6.35907i	0.151370	−	0.224407i
$804$		0			0
$805$	23.6928	+	24.8363i	0.835061	+	0.875364i
$806$	6.85576	−	4.98100i	0.241484	−	0.175448i
$807$		0			0
$808$	4.65421	+	2.37144i	0.163735	+	0.0834269i
$809$	−4.62822	−	14.2442i	−0.162719	−	0.500799i	0.836142	−	0.548514i	$-0.184806\pi$
$809$	−4.62822	−	14.2442i	−0.162719	−	0.500799i	−0.998861	+	0.0477147i	$0.984806\pi$
$810$		0			0
$811$	−4.13735	−	5.69458i	−0.145282	−	0.199964i	0.730174	−	0.683261i	$-0.239439\pi$
$811$	−4.13735	−	5.69458i	−0.145282	−	0.199964i	−0.875456	+	0.483298i	$0.839439\pi$
$812$	37.6350	−	19.1760i	1.32073	−	0.672946i
$813$		0			0
$814$	61.3172	+	7.52987i	2.14917	+	0.263922i
$815$	−7.95447	+	2.37892i	−0.278633	+	0.0833299i
$816$		0			0
$817$	40.0277	+	6.33977i	1.40039	+	0.221801i
$818$	34.4448	−	5.45553i	1.20434	−	0.190748i
$819$		0			0
$820$	−4.57117	+	25.0298i	−0.159632	+	0.874077i
$821$	−1.28819	+	1.77304i	−0.0449580	+	0.0618794i	−0.830904	−	0.556416i	$-0.812176\pi$
$821$	−1.28819	+	1.77304i	−0.0449580	+	0.0618794i	0.785946	+	0.618295i	$0.212176\pi$
$822$		0			0
$823$	−13.0870	−	25.6846i	−0.456183	−	0.895309i	−0.998480	−	0.0551219i	$-0.982445\pi$
$823$	−13.0870	−	25.6846i	−0.456183	−	0.895309i	0.542297	−	0.840187i	$-0.317555\pi$
$824$	25.5949			0.891640
$825$		0			0
$826$	6.38371			0.222118
$827$	−20.5507	−	40.3331i	−0.714619	−	1.40252i	−0.906971	−	0.421192i	$-0.861612\pi$
$827$	−20.5507	−	40.3331i	−0.714619	−	1.40252i	0.192353	−	0.981326i	$-0.438388\pi$
$828$		0			0
$829$	3.77021	−	5.18925i	0.130945	−	0.180230i	−0.738510	−	0.674242i	$-0.764470\pi$
$829$	3.77021	−	5.18925i	0.130945	−	0.180230i	0.869455	+	0.494012i	$0.164470\pi$
$830$	−0.0427030	+	0.233823i	−0.00148224	+	0.00811613i
$831$		0			0
$832$	−62.1189	+	9.83866i	−2.15358	+	0.341094i
$833$	11.1425	+	1.76479i	0.386064	+	0.0611465i
$834$		0			0
$835$	17.3552	−	5.19037i	0.600603	−	0.179620i
$836$	−34.8917	+	37.4155i	−1.20675	+	1.29404i
$837$		0			0
$838$	−1.97239	+	1.00498i	−0.0681349	+	0.0347165i
$839$	−23.1815	−	31.9066i	−0.800314	−	1.10154i	−0.992746	−	0.120227i	$-0.961638\pi$
$839$	−23.1815	−	31.9066i	−0.800314	−	1.10154i	0.192433	−	0.981310i	$-0.438362\pi$
$840$		0			0
$841$	−4.31524	−	13.2810i	−0.148802	−	0.457964i
$842$	5.94049	+	3.02683i	0.204723	+	0.104312i
$843$		0			0
$844$	42.0667	−	30.5633i	1.44800	−	1.05203i
$845$	−19.9746	−	20.9386i	−0.687145	−	0.720310i
$846$		0			0
$847$	9.91000	+	42.9316i	0.340512	+	1.47515i
$848$	−4.81478	+	4.81478i	−0.165340	+	0.165340i
$849$		0			0
$850$	4.78926	−	12.6746i	0.164270	−	0.434737i
$851$	−26.5833	−	19.3139i	−0.911265	−	0.662073i
$852$		0			0
$853$	−19.7855	+	38.8312i	−0.677442	+	1.32955i	0.254545	+	0.967061i	$0.418074\pi$
$853$	−19.7855	+	38.8312i	−0.677442	+	1.32955i	−0.931986	+	0.362493i	$0.881926\pi$
$854$	−32.8267	−	23.8500i	−1.12331	−	0.816131i
$855$		0			0
$856$	5.74823	−	17.6912i	0.196471	−	0.604674i
$857$	−10.6030	+	10.6030i	−0.362190	+	0.362190i	−0.864619	−	0.502428i	$-0.832440\pi$
$857$	−10.6030	+	10.6030i	−0.362190	+	0.362190i	0.502428	+	0.864619i	$0.332440\pi$
$858$		0			0
$859$			45.6295i			1.55686i	0.627733	+	0.778429i	$0.283983\pi$
$859$			45.6295i			1.55686i	−0.627733	+	0.778429i	$0.716017\pi$
$860$	1.02352	−	43.4370i	0.0349017	−	1.48119i
$861$		0			0
$862$	−1.13962	−	7.19529i	−0.0388157	−	0.245072i
$863$	−2.39724	−	1.22146i	−0.0816030	−	0.0415788i	0.412713	−	0.910861i	$-0.364581\pi$
$863$	−2.39724	−	1.22146i	−0.0816030	−	0.0415788i	−0.494316	+	0.869282i	$0.664581\pi$
$864$		0			0
$865$	−14.7328	+	41.9534i	−0.500932	+	1.42646i
$866$	1.64389	+	2.26262i	0.0558615	+	0.0768868i
$867$		0			0
$868$	5.89913	+	5.89913i	0.200229	+	0.200229i
$869$	−31.5250	+	17.4739i	−1.06941	+	0.592761i
$870$		0			0
$871$	−66.7490	−	21.6881i	−2.26170	−	0.734872i
$872$	−11.3907	−	1.80412i	−0.385739	−	0.0610951i
$873$		0			0
$874$	44.9119	−	14.5928i	1.51917	−	0.493607i
$875$	−16.8118	+	41.5075i	−0.568344	+	1.40321i
$876$		0			0
$877$	−3.81279	+	24.0730i	−0.128749	+	0.812887i	0.835810	+	0.549019i	$0.184998\pi$
$877$	−3.81279	+	24.0730i	−0.128749	+	0.812887i	−0.964559	+	0.263868i	$0.915002\pi$
$878$	29.3831	+	57.6676i	0.991631	+	1.94619i
$879$		0			0
$880$	−12.3591	−	8.76717i	−0.416624	−	0.295541i
$881$	−12.4368			−0.419006			−0.209503	−	0.977808i	$-0.567185\pi$
$881$	−12.4368			−0.419006			−0.209503	+	0.977808i	$0.567185\pi$
$882$		0			0
$883$	5.87975	−	37.1233i	0.197869	−	1.24930i	−0.666141	−	0.745825i	$-0.732055\pi$
$883$	5.87975	−	37.1233i	0.197869	−	1.24930i	0.864011	−	0.503473i	$-0.167945\pi$
$884$	−10.1556	+	13.9780i	−0.341571	+	0.470133i
$885$		0			0
$886$	6.95421	−	2.25956i	0.233631	−	0.0759114i
$887$	50.1114	−	7.93686i	1.68258	−	0.266494i	0.759330	−	0.650705i	$-0.225527\pi$
$887$	50.1114	−	7.93686i	1.68258	−	0.266494i	0.923245	+	0.384211i	$0.125527\pi$
$888$		0			0
$889$	−15.1719	−	4.92966i	−0.508850	−	0.165335i
$890$	−6.94756	−	23.2308i	−0.232883	−	0.778699i
$891$		0			0
$892$	−18.7819	−	18.7819i	−0.628864	−	0.628864i
$893$	−21.1480	+	10.7755i	−0.707692	+	0.360587i
$894$		0			0
$895$	−43.0007	+	20.6488i	−1.43735	+	0.690213i
$896$	−14.4768	−	44.5550i	−0.483635	−	1.48848i
$897$		0			0
$898$	−14.0098	−	88.4541i	−0.467512	−	2.95175i
$899$	−2.40253	+	1.74554i	−0.0801289	+	0.0582171i
$900$		0			0
$901$			4.15695i			0.138488i
$902$	28.3293	−	10.3105i	0.943264	−	0.343302i
$903$		0			0
$904$	−2.27304	+	6.99569i	−0.0756001	+	0.232673i
$905$	−19.0535	+	2.55926i	−0.633359	+	0.0850727i
$906$		0			0
$907$	−21.9176	+	43.0157i	−0.727761	+	1.42831i	0.168918	+	0.985630i	$0.445973\pi$
$907$	−21.9176	+	43.0157i	−0.727761	+	1.42831i	−0.896679	+	0.442681i	$0.854027\pi$
$908$	28.6774	−	56.2825i	0.951692	−	1.86780i
$909$		0			0
$910$	60.1241	−	78.7820i	1.99309	−	2.61160i
$911$	9.96214	−	30.6603i	0.330060	−	1.01582i	−0.639044	−	0.769170i	$-0.720670\pi$
$911$	9.96214	−	30.6603i	0.330060	−	1.01582i	0.969104	−	0.246651i	$-0.0793302\pi$
$912$		0			0
$913$	0.152497	−	0.0555016i	0.00504693	−	0.00183683i
$914$		−	14.9627i		−	0.494922i
$915$		0			0
$916$	−1.58955	+	1.15488i	−0.0525203	+	0.0381582i
$917$	−3.81468	−	24.0849i	−0.125972	−	0.795355i
$918$		0			0
$919$	−6.16632	−	18.9780i	−0.203408	−	0.626026i	−0.999775	−	0.0212122i	$-0.993247\pi$
$919$	−6.16632	−	18.9780i	−0.203408	−	0.626026i	0.796367	−	0.604814i	$-0.206753\pi$
$920$	−5.79845	−	12.0751i	−0.191169	−	0.398106i
$921$		0			0
$922$	1.82724	−	0.931023i	0.0601768	−	0.0306616i
$923$	41.8537	+	41.8537i	1.37763	+	1.37763i
$924$		0			0
$925$	8.69330	−	41.9796i	0.285834	−	1.38028i
$926$	47.8542	+	15.5488i	1.57259	+	0.510964i
$927$		0			0
$928$	28.9729	−	4.58886i	0.951083	−	0.150637i
$929$	−2.36893	+	0.769713i	−0.0777222	+	0.0252535i	−0.347620	−	0.937635i	$-0.613010\pi$
$929$	−2.36893	+	0.769713i	−0.0777222	+	0.0252535i	0.269898	+	0.962889i	$0.413010\pi$
$930$		0			0
$931$	−30.1525	+	41.5013i	−0.988208	+	1.36015i
$932$	−6.39933	+	40.4038i	−0.209617	+	1.32347i
$933$		0			0
$934$	−44.6559			−1.46119
$935$	−9.11992	+	1.55057i	−0.298253	+	0.0507092i
$936$		0			0
$937$	7.04703	+	13.8306i	0.230216	+	0.451825i	0.976999	−	0.213243i	$-0.0684025\pi$
$937$	7.04703	+	13.8306i	0.230216	+	0.451825i	−0.746783	+	0.665068i	$0.768403\pi$
$938$	18.7577	−	118.432i	0.612462	−	3.86693i
$939$		0			0
$940$	14.4680	+	20.9333i	0.471893	+	0.682767i
$941$	−8.61830	+	2.80026i	−0.280949	+	0.0912858i	−0.446102	−	0.894982i	$-0.647188\pi$
$941$	−8.61830	+	2.80026i	−0.280949	+	0.0912858i	0.165153	+	0.986268i	$0.447188\pi$
$942$		0			0
$943$	−15.8375	−	2.50842i	−0.515741	−	0.0816853i
$944$	1.42556	+	0.463194i	0.0463982	+	0.0150757i
$945$		0			0
$946$	−45.0267	+	24.9577i	−1.46394	+	0.811445i
$947$	−0.626498	−	0.626498i	−0.0203585	−	0.0203585i	0.696854	−	0.717213i	$-0.254582\pi$
$947$	−0.626498	−	0.626498i	−0.0203585	−	0.0203585i	−0.717213	+	0.696854i	$0.754582\pi$
$948$		0			0
$949$	6.92379	+	9.52979i	0.224756	+	0.309350i
$950$	41.4654	+	45.5693i	1.34531	+	1.47846i
$951$		0			0
$952$	−6.95880	−	3.54569i	−0.225536	−	0.114916i
$953$	6.28614	+	39.6892i	0.203628	+	1.28566i	0.851680	+	0.524062i	$0.175584\pi$
$953$	6.28614	+	39.6892i	0.203628	+	1.28566i	−0.648052	+	0.761596i	$0.724416\pi$
$954$		0			0
$955$	−1.41768	+	1.35241i	−0.0458751	+	0.0437629i
$956$			10.9441i			0.353956i
$957$		0			0
$958$	−15.8929	+	15.8929i	−0.513475	+	0.513475i
$959$	8.07643	−	24.8567i	0.260801	−	0.802664i
$960$		0			0
$961$	24.6050	+	17.8766i	0.793710	+	0.576664i
$962$	−43.0705	+	84.5307i	−1.38865	+	2.72538i
$963$		0			0
$964$	−55.0159	−	39.9714i	−1.77194	−	1.28739i
$965$	−42.8826	−	32.7267i	−1.38044	−	1.05351i
$966$		0			0
$967$	12.8842	−	12.8842i	0.414326	−	0.414326i	−0.468916	−	0.883243i	$-0.655355\pi$
$967$	12.8842	−	12.8842i	0.414326	−	0.414326i	0.883243	+	0.468916i	$0.155355\pi$
$968$	1.49919	−	17.1291i	0.0481858	−	0.550550i
$969$		0			0
$970$	20.2901	−	19.3559i	0.651477	−	0.621482i
$971$	−19.2161	+	13.9613i	−0.616673	+	0.448039i	−0.851758	−	0.523936i	$-0.824463\pi$
$971$	−19.2161	+	13.9613i	−0.616673	+	0.448039i	0.235085	+	0.971975i	$0.424463\pi$
$972$		0			0
$973$	35.6615	+	18.1704i	1.14325	+	0.582517i
$974$	−6.58259	−	20.2591i	−0.210920	−	0.649144i
$975$		0			0
$976$	−5.60010	−	7.70788i	−0.179255	−	0.246723i
$977$	44.2200	−	22.5312i	1.41472	−	0.720838i	0.431309	−	0.902204i	$-0.358052\pi$
$977$	44.2200	−	22.5312i	1.41472	−	0.720838i	0.983416	+	0.181366i	$0.0580519\pi$
$978$		0			0
$979$	−11.2907	+	12.1073i	−0.360851	+	0.386952i
$980$	48.4014	+	26.1158i	1.54613	+	0.834238i
$981$		0			0
$982$	23.0711	+	3.65410i	0.736229	+	0.116607i
$983$	−29.4377	+	4.66247i	−0.938916	+	0.148710i	−0.607092	−	0.794632i	$-0.707664\pi$
$983$	−29.4377	+	4.66247i	−0.938916	+	0.148710i	−0.331824	+	0.943341i	$0.607664\pi$
$984$		0			0
$985$	−2.78026	−	4.02268i	−0.0885866	−	0.128173i
$986$	6.17626	−	8.50090i	0.196692	−	0.270724i
$987$		0			0
$988$	−35.6680	−	70.0023i	−1.13475	−	2.22707i
$989$	27.3821			0.870699
$990$		0			0
$991$	30.9346			0.982669			0.491335	−	0.870971i	$-0.336509\pi$
$991$	30.9346			0.982669			0.491335	+	0.870971i	$0.336509\pi$
$992$	2.63033	+	5.16232i	0.0835131	+	0.163904i
$993$		0			0
$994$	−59.4398	+	81.8118i	−1.88531	+	2.59491i
$995$	6.24804	+	1.14108i	0.198076	+	0.0361745i
$996$		0			0
$997$	−20.1863	+	3.19720i	−0.639307	+	0.101256i	−0.467669	−	0.883904i	$-0.654906\pi$
$997$	−20.1863	+	3.19720i	−0.639307	+	0.101256i	−0.171638	+	0.985160i	$0.554906\pi$
$998$	3.32923	+	0.527299i	0.105385	+	0.0166913i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.c.442.11		96
3.2	odd	2		165.2.w.a.112.2	yes	96
5.3	odd	4	inner	495.2.bj.c.343.11		96
11.6	odd	10	inner	495.2.bj.c.127.11		96
15.2	even	4		825.2.cw.b.343.11		96
15.8	even	4		165.2.w.a.13.2	✓	96
15.14	odd	2		825.2.cw.b.607.11		96
33.17	even	10		165.2.w.a.127.2	yes	96
55.28	even	20	inner	495.2.bj.c.28.11		96
165.17	odd	20		825.2.cw.b.193.11		96
165.83	odd	20		165.2.w.a.28.2	yes	96
165.149	even	10		825.2.cw.b.457.11		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.w.a.13.2	✓	96	15.8	even	4
165.2.w.a.28.2	yes	96	165.83	odd	20
165.2.w.a.112.2	yes	96	3.2	odd	2
165.2.w.a.127.2	yes	96	33.17	even	10
495.2.bj.c.28.11		96	55.28	even	20	inner
495.2.bj.c.127.11		96	11.6	odd	10	inner
495.2.bj.c.343.11		96	5.3	odd	4	inner
495.2.bj.c.442.11		96	1.1	even	1	trivial
825.2.cw.b.193.11		96	165.17	odd	20
825.2.cw.b.343.11		96	15.2	even	4
825.2.cw.b.457.11		96	165.149	even	10
825.2.cw.b.607.11		96	15.14	odd	2

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.986271 + 1.93567i) q^{2} +(-1.59850 + 2.20015i) q^{4} +(0.401727 - 2.19969i) q^{5} +(3.95619 - 0.626599i) q^{7} +(-1.54390 - 0.244529i) q^{8} +O(q^{10})\)	\(q+(0.986271 + 1.93567i) q^{2} +(-1.59850 + 2.20015i) q^{4} +(0.401727 - 2.19969i) q^{5} +(3.95619 - 0.626599i) q^{7} +(-1.54390 - 0.244529i) q^{8} +(4.65407 - 1.39188i) q^{10} +(-2.42559 - 2.26197i) q^{11} +(4.53814 - 2.31230i) q^{13} +(5.11476 + 7.03987i) q^{14} +(0.631388 + 1.94321i) q^{16} +(1.11142 + 0.566297i) q^{17} +(-4.58879 + 3.33395i) q^{19} +(4.19747 + 4.40006i) q^{20} +(1.98614 - 6.92604i) q^{22} +(-2.70988 + 2.70988i) q^{23} +(-4.67723 - 1.76735i) q^{25} +(8.95168 + 6.50377i) q^{26} +(-4.94536 + 9.70582i) q^{28} +(-3.13702 - 2.27918i) q^{29} +(0.236665 - 0.728379i) q^{31} +(-5.34931 + 5.34931i) q^{32} +2.70986i q^{34} +(0.210988 - 8.95410i) q^{35} +(1.34128 + 8.46850i) q^{37} +(-10.9792 - 5.59418i) q^{38} +(-1.15811 + 3.29786i) q^{40} +(2.45935 + 3.38501i) q^{41} +(-5.05226 - 5.05226i) q^{43} +(8.85398 - 1.72088i) q^{44} +(-7.91810 - 2.57275i) q^{46} +(4.13303 + 0.654608i) q^{47} +(8.60143 - 2.79477i) q^{49} +(-1.19203 - 10.7966i) q^{50} +(-2.16682 + 13.6808i) q^{52} +(1.51295 + 2.96933i) q^{53} +(-5.95006 + 4.42683i) q^{55} -6.26118 q^{56} +(1.31778 - 8.32012i) q^{58} +(0.431206 - 0.593505i) q^{59} +(-4.43475 + 1.44094i) q^{61} +(1.64331 - 0.260275i) q^{62} +(-11.7439 - 3.81583i) q^{64} +(-3.26324 - 10.9114i) q^{65} +(-9.74376 - 9.74376i) q^{67} +(-3.02254 + 1.54006i) q^{68} +(17.5402 - 8.42276i) q^{70} +(3.59115 + 11.0524i) q^{71} +(0.361793 + 2.28427i) q^{73} +(-15.0693 + 10.9485i) q^{74} -15.4253i q^{76} +(-11.0134 - 7.42893i) q^{77} +(3.35829 - 10.3357i) q^{79} +(4.52810 - 0.608214i) q^{80} +(-4.12666 + 8.09902i) q^{82} +(-0.0222139 + 0.0435972i) q^{83} +(1.69216 - 2.21728i) q^{85} +(4.79659 - 14.7624i) q^{86} +(3.19174 + 4.08538i) q^{88} -4.99151i q^{89} +(16.5049 - 11.9915i) q^{91} +(-1.63039 - 10.2939i) q^{92} +(2.80919 + 8.64578i) q^{94} +(5.49020 + 11.4332i) q^{95} +(5.14342 - 2.62070i) q^{97} +(13.8931 + 13.8931i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{5} - 20 q^{7}+O(q^{10}) \) 96 * q + 8 * q^5 - 20 * q^7	\( 96 q + 8 q^{5} - 20 q^{7} - 8 q^{11} + 8 q^{16} + 20 q^{17} + 60 q^{20} - 32 q^{22} - 32 q^{23} - 32 q^{25} - 60 q^{28} + 16 q^{31} + 8 q^{37} - 56 q^{38} + 120 q^{41} - 200 q^{46} - 60 q^{47} - 80 q^{50} + 40 q^{52} - 36 q^{53} + 80 q^{55} + 80 q^{56} + 44 q^{58} + 40 q^{61} - 80 q^{62} - 48 q^{67} - 80 q^{68} - 92 q^{70} - 32 q^{71} - 60 q^{73} + 24 q^{77} + 80 q^{80} + 32 q^{82} + 200 q^{83} - 80 q^{85} + 80 q^{86} - 144 q^{88} + 56 q^{91} - 20 q^{92} - 60 q^{95} + 32 q^{97}+O(q^{100}) \) 96 * q + 8 * q^5 - 20 * q^7 - 8 * q^11 + 8 * q^16 + 20 * q^17 + 60 * q^20 - 32 * q^22 - 32 * q^23 - 32 * q^25 - 60 * q^28 + 16 * q^31 + 8 * q^37 - 56 * q^38 + 120 * q^41 - 200 * q^46 - 60 * q^47 - 80 * q^50 + 40 * q^52 - 36 * q^53 + 80 * q^55 + 80 * q^56 + 44 * q^58 + 40 * q^61 - 80 * q^62 - 48 * q^67 - 80 * q^68 - 92 * q^70 - 32 * q^71 - 60 * q^73 + 24 * q^77 + 80 * q^80 + 32 * q^82 + 200 * q^83 - 80 * q^85 + 80 * q^86 - 144 * q^88 + 56 * q^91 - 20 * q^92 - 60 * q^95 + 32 * q^97

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