LMFDB - Embedded newform 441.2.bg.a.395.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			395.4
Character	$\chi$	$=$	441.395
Dual form			441.2.bg.a.278.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72508 - 0.677046i) q^{2} +(1.05142 + 0.975576i) q^{4} +(-0.820216 - 0.559214i) q^{5} +(0.202012 + 2.63803i) q^{7} +(0.454856 + 0.944519i) q^{8} +O(q^{10})$	\(q+(-1.72508 - 0.677046i) q^{2} +(1.05142 + 0.975576i) q^{4} +(-0.820216 - 0.559214i) q^{5} +(0.202012 + 2.63803i) q^{7} +(0.454856 + 0.944519i) q^{8} +(1.03633 + 1.52001i) q^{10} +(-0.669436 - 4.44142i) q^{11} +(0.491128 - 0.391661i) q^{13} +(1.43758 - 4.68759i) q^{14} +(-0.359555 - 4.79792i) q^{16} +(-7.67525 - 2.36750i) q^{17} +(0.358138 - 0.206771i) q^{19} +(-0.316837 - 1.38815i) q^{20} +(-1.85221 + 8.11506i) q^{22} +(2.22443 + 7.21144i) q^{23} +(-1.46667 - 3.73702i) q^{25} +(-1.11241 + 0.343133i) q^{26} +(-2.36120 + 2.97076i) q^{28} +(0.523301 - 0.119440i) q^{29} +(-7.47171 - 4.31379i) q^{31} +(-2.01015 + 6.51673i) q^{32} +(11.6376 + 9.28064i) q^{34} +(1.30953 - 2.27672i) q^{35} +(-5.17164 + 4.79859i) q^{37} +(-0.757811 + 0.114222i) q^{38} +(0.155108 - 1.02907i) q^{40} +(-4.20951 + 2.02719i) q^{41} +(-6.50862 - 3.13439i) q^{43} +(3.62908 - 5.32289i) q^{44} +(1.04514 - 13.9464i) q^{46} +(2.32547 - 5.92521i) q^{47} +(-6.91838 + 1.06583i) q^{49} +7.43967i q^{50} +(0.898477 + 0.0673315i) q^{52} +(-1.40866 + 1.51817i) q^{53} +(-1.93462 + 4.01728i) q^{55} +(-2.39978 + 1.39073i) q^{56} +(-0.983605 - 0.148255i) q^{58} +(-10.2496 + 6.98805i) q^{59} +(3.28105 + 3.53613i) q^{61} +(9.96870 + 12.5003i) q^{62} +(1.88011 - 2.35758i) q^{64} +(-0.621853 + 0.0466015i) q^{65} +(1.75271 - 3.03578i) q^{67} +(-5.76024 - 9.97704i) q^{68} +(-3.80049 + 3.04093i) q^{70} +(2.14164 + 0.488815i) q^{71} +(2.40700 - 0.944676i) q^{73} +(12.1704 - 4.77652i) q^{74} +(0.578274 + 0.131987i) q^{76} +(11.5814 - 2.66321i) q^{77} +(-6.85221 - 11.8684i) q^{79} +(-2.38815 + 4.13640i) q^{80} +(8.63426 - 0.647049i) q^{82} +(6.36642 - 7.98324i) q^{83} +(4.97143 + 6.23397i) q^{85} +(9.10580 + 9.81371i) q^{86} +(3.89051 - 2.65250i) q^{88} +(-6.09136 - 0.918124i) q^{89} +(1.13243 + 1.21649i) q^{91} +(-4.69649 + 9.75236i) q^{92} +(-8.02328 + 8.64704i) q^{94} +(-0.409380 - 0.0306788i) q^{95} -12.9594i q^{97} +(12.6564 + 2.84542i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

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 $

$2$	−1.72508	−	0.677046i	−1.21982	−	0.478744i	−0.333911	−	0.942605i	$-0.608368\pi$
$2$	−1.72508	−	0.677046i	−1.21982	−	0.478744i	−0.885908	+	0.463861i	$0.846464\pi$
$3$		0			0
$3$		0			0
$4$	1.05142	+	0.975576i	0.525710	+	0.487788i
$5$	−0.820216	−	0.559214i	−0.366812	−	0.250088i	0.365860	−	0.930670i	$-0.380775\pi$
$5$	−0.820216	−	0.559214i	−0.366812	−	0.250088i	−0.732672	+	0.680582i	$0.761727\pi$
$6$		0			0
$7$	0.202012	+	2.63803i	0.0763535	+	0.997081i
$7$	0.202012	+	2.63803i	0.0763535	+	0.997081i
$8$	0.454856	+	0.944519i	0.160816	+	0.333938i
$9$		0			0
$10$	1.03633	+	1.52001i	0.327716	+	0.480671i
$11$	−0.669436	−	4.44142i	−0.201843	−	1.33914i	−0.828564	−	0.559895i	$-0.810842\pi$
$11$	−0.669436	−	4.44142i	−0.201843	−	1.33914i	0.626721	−	0.779244i	$-0.284397\pi$
$12$		0			0
$13$	0.491128	−	0.391661i	0.136214	−	0.108627i	−0.553012	−	0.833173i	$-0.686522\pi$
$13$	0.491128	−	0.391661i	0.136214	−	0.108627i	0.689227	+	0.724546i	$0.257950\pi$
$14$	1.43758	−	4.68759i	0.384209	−	1.25281i
$15$		0			0
$16$	−0.359555	−	4.79792i	−0.0898887	−	1.19948i
$17$	−7.67525	−	2.36750i	−1.86152	−	0.574204i	−0.997493	−	0.0707625i	$-0.977457\pi$
$17$	−7.67525	−	2.36750i	−1.86152	−	0.574204i	−0.864029	−	0.503441i	$-0.832067\pi$
$18$		0			0
$19$	0.358138	−	0.206771i	0.0821624	−	0.0474365i	−0.458356	−	0.888769i	$-0.651561\pi$
$19$	0.358138	−	0.206771i	0.0821624	−	0.0474365i	0.540518	+	0.841332i	$0.318228\pi$
$20$	−0.316837	−	1.38815i	−0.0708468	−	0.310400i
$21$		0			0
$22$	−1.85221	+	8.11506i	−0.394892	+	1.73014i
$23$	2.22443	+	7.21144i	0.463827	+	1.50369i	0.821701	+	0.569919i	$0.193025\pi$
$23$	2.22443	+	7.21144i	0.463827	+	1.50369i	−0.357874	+	0.933770i	$0.616498\pi$
$24$		0			0
$25$	−1.46667	−	3.73702i	−0.293334	−	0.747403i
$26$	−1.11241	+	0.343133i	−0.218161	+	0.0672939i
$27$		0			0
$28$	−2.36120	+	2.97076i	−0.446224	+	0.561420i
$29$	0.523301	−	0.119440i	0.0971746	−	0.0221795i	−0.173657	−	0.984806i	$-0.555558\pi$
$29$	0.523301	−	0.119440i	0.0971746	−	0.0221795i	0.270832	+	0.962627i	$0.412701\pi$
$30$		0			0
$31$	−7.47171	−	4.31379i	−1.34196	−	0.774780i	−0.354864	−	0.934918i	$-0.615473\pi$
$31$	−7.47171	−	4.31379i	−1.34196	−	0.774780i	−0.987095	+	0.160137i	$0.948806\pi$
$32$	−2.01015	+	6.51673i	−0.355347	+	1.15201i
$33$		0			0
$34$	11.6376	+	9.28064i	1.99582	+	1.59162i
$35$	1.30953	−	2.27672i	0.221351	−	0.384836i
$36$		0			0
$37$	−5.17164	+	4.79859i	−0.850213	+	0.788883i	−0.979228	−	0.202760i	$-0.935009\pi$
$37$	−5.17164	+	4.79859i	−0.850213	+	0.788883i	0.129015	+	0.991643i	$0.458818\pi$
$38$	−0.757811	+	0.114222i	−0.122933	+	0.0185292i
$39$		0			0
$40$	0.155108	−	1.02907i	0.0245247	−	0.162711i
$41$	−4.20951	+	2.02719i	−0.657415	+	0.316594i	−0.732684	−	0.680569i	$-0.761733\pi$
$41$	−4.20951	+	2.02719i	−0.657415	+	0.316594i	0.0752690	+	0.997163i	$0.476018\pi$
$42$		0			0
$43$	−6.50862	−	3.13439i	−0.992555	−	0.477989i	−0.134150	−	0.990961i	$-0.542830\pi$
$43$	−6.50862	−	3.13439i	−0.992555	−	0.477989i	−0.858406	+	0.512972i	$0.828545\pi$
$44$	3.62908	−	5.32289i	0.547105	−	0.802455i
$45$		0			0
$46$	1.04514	−	13.9464i	0.154097	−	2.05628i
$47$	2.32547	−	5.92521i	0.339205	−	0.864281i	−0.654885	−	0.755728i	$-0.727283\pi$
$47$	2.32547	−	5.92521i	0.339205	−	0.864281i	0.994091	−	0.108553i	$-0.0346216\pi$
$48$		0			0
$49$	−6.91838	+	1.06583i	−0.988340	+	0.152261i
$50$			7.43967i			1.05213i
$51$		0			0
$52$	0.898477	+	0.0673315i	0.124596	+	0.00933720i
$53$	−1.40866	+	1.51817i	−0.193494	+	0.208537i	−0.822346	−	0.568988i	$-0.807335\pi$
$53$	−1.40866	+	1.51817i	−0.193494	+	0.208537i	0.628851	+	0.777525i	$0.283525\pi$
$54$		0			0
$55$	−1.93462	+	4.01728i	−0.260864	+	0.541690i
$56$	−2.39978	+	1.39073i	−0.320684	+	0.185844i
$57$		0			0
$58$	−0.983605	−	0.148255i	−0.129154	−	0.0194668i
$59$	−10.2496	+	6.98805i	−1.33438	+	0.909767i	−0.999472	−	0.0324825i	$-0.989659\pi$
$59$	−10.2496	+	6.98805i	−1.33438	+	0.909767i	−0.334911	+	0.942250i	$0.608706\pi$
$60$		0			0
$61$	3.28105	+	3.53613i	0.420096	+	0.452756i	0.907270	−	0.420549i	$-0.138163\pi$
$61$	3.28105	+	3.53613i	0.420096	+	0.452756i	−0.487174	+	0.873305i	$0.661972\pi$
$62$	9.96870	+	12.5003i	1.26603	+	1.58755i
$63$		0			0
$64$	1.88011	−	2.35758i	0.235013	−	0.294697i
$65$	−0.621853	+	0.0466015i	−0.0771314	+	0.00578020i
$66$		0			0
$67$	1.75271	−	3.03578i	0.214127	−	0.370879i	−0.738875	−	0.673843i	$-0.764643\pi$
$67$	1.75271	−	3.03578i	0.214127	−	0.370879i	0.953002	+	0.302963i	$0.0979759\pi$
$68$	−5.76024	−	9.97704i	−0.698532	−	1.20989i
$69$		0			0
$70$	−3.80049	+	3.04093i	−0.454245	+	0.363460i
$71$	2.14164	+	0.488815i	0.254166	+	0.0580117i	0.347705	−	0.937604i	$-0.386961\pi$
$71$	2.14164	+	0.488815i	0.254166	+	0.0580117i	−0.0935395	+	0.995616i	$0.529818\pi$
$72$		0			0
$73$	2.40700	−	0.944676i	0.281718	−	0.110566i	−0.220275	−	0.975438i	$-0.570696\pi$
$73$	2.40700	−	0.944676i	0.281718	−	0.110566i	0.501993	+	0.864872i	$0.332600\pi$
$74$	12.1704	−	4.77652i	1.41478	−	0.555260i
$75$		0			0
$76$	0.578274	+	0.131987i	0.0663326	+	0.0151400i
$77$	11.5814	−	2.66321i	1.31982	−	0.303501i
$78$		0			0
$79$	−6.85221	−	11.8684i	−0.770934	−	1.33530i	−0.937052	−	0.349191i	$-0.886457\pi$
$79$	−6.85221	−	11.8684i	−0.770934	−	1.33530i	0.166118	−	0.986106i	$-0.446877\pi$
$80$	−2.38815	+	4.13640i	−0.267004	+	0.462464i
$81$		0			0
$82$	8.63426	−	0.647049i	0.953495	−	0.0714546i
$83$	6.36642	−	7.98324i	0.698806	−	0.876275i	−0.298128	−	0.954526i	$-0.596362\pi$
$83$	6.36642	−	7.98324i	0.698806	−	0.876275i	0.996934	+	0.0782513i	$0.0249336\pi$
$84$		0			0
$85$	4.97143	+	6.23397i	0.539227	+	0.676169i
$86$	9.10580	+	9.81371i	0.981903	+	1.05824i
$87$		0			0
$88$	3.89051	−	2.65250i	0.414730	−	0.282758i
$89$	−6.09136	−	0.918124i	−0.645683	−	0.0973210i	−0.181966	−	0.983305i	$-0.558246\pi$
$89$	−6.09136	−	0.918124i	−0.645683	−	0.0973210i	−0.463716	+	0.885984i	$0.653484\pi$
$90$		0			0
$91$	1.13243	+	1.21649i	0.118711	+	0.127523i
$92$	−4.69649	+	9.75236i	−0.489643	+	1.01675i
$93$		0			0
$94$	−8.02328	+	8.64704i	−0.827538	+	0.891874i
$95$	−0.409380	−	0.0306788i	−0.0420015	−	0.00314757i
$96$		0			0
$97$		−	12.9594i		−	1.31582i	−0.753095	−	0.657912i	$-0.771440\pi$
$97$		−	12.9594i		−	1.31582i	0.753095	−	0.657912i	$-0.228560\pi$
$98$	12.6564	+	2.84542i	1.27849	+	0.287430i
$99$		0			0
$100$	2.10365	−	5.36003i	0.210365	−	0.536003i
$101$	0.00754295	−	0.100654i	0.000750552	−	0.0100154i	−0.996816	−	0.0797369i	$-0.974592\pi$
$101$	0.00754295	−	0.100654i	0.000750552	−	0.0100154i	0.997566	+	0.0697214i	$0.0222110\pi$
$102$		0			0
$103$	0.269415	−	0.395159i	0.0265462	−	0.0389362i	−0.812736	−	0.582632i	$-0.802023\pi$
$103$	0.269415	−	0.395159i	0.0265462	−	0.0389362i	0.839283	+	0.543696i	$0.182975\pi$
$104$	0.593324	+	0.285730i	0.0581802	+	0.0280181i
$105$		0			0
$106$	3.45793	−	1.66525i	0.335863	−	0.161743i
$107$	−0.0362310	+	0.240377i	−0.00350259	+	0.0232381i	−0.990514	−	0.137413i	$-0.956121\pi$
$107$	−0.0362310	+	0.240377i	−0.00350259	+	0.0232381i	0.987011	+	0.160651i	$0.0513594\pi$
$108$		0			0
$109$	12.8218	−	1.93257i	1.22810	−	0.185107i	0.497230	−	0.867619i	$-0.334351\pi$
$109$	12.8218	−	1.93257i	1.22810	−	0.185107i	0.730875	+	0.682512i	$0.239112\pi$
$110$	6.05727	−	5.62032i	0.577538	−	0.535877i
$111$		0			0
$112$	12.5844	−	1.91776i	1.18912	−	0.181211i
$113$	0.781027	+	0.622848i	0.0734728	+	0.0585926i	0.659538	−	0.751672i	$-0.270752\pi$
$113$	0.781027	+	0.622848i	0.0734728	+	0.0585926i	−0.586065	+	0.810264i	$0.699324\pi$
$114$		0			0
$115$	2.20822	−	7.15887i	0.205918	−	0.667568i
$116$	0.666733	+	0.384938i	0.0619046	+	0.0357406i
$117$		0			0
$118$	22.4126	−	5.11554i	2.06325	−	0.470924i
$119$	4.69504	−	20.7258i	0.430394	−	1.89993i
$120$		0			0
$121$	−8.76676	+	2.70419i	−0.796978	+	0.245835i
$122$	−3.26597	−	8.32155i	−0.295687	−	0.753398i
$123$		0			0
$124$	−3.64748	−	11.8248i	−0.327553	−	1.06190i
$125$	−1.99130	+	8.72445i	−0.178107	+	0.780339i
$126$		0			0
$127$	3.34854	+	14.6709i	0.297135	+	1.30183i	0.874372	+	0.485256i	$0.161274\pi$
$127$	3.34854	+	14.6709i	0.297135	+	1.30183i	−0.577237	+	0.816577i	$0.695869\pi$
$128$	6.97256	−	4.02561i	0.616293	−	0.355817i
$129$		0			0
$130$	1.10430	+	0.340632i	0.0968535	+	0.0298754i
$131$	−1.56593	−	20.8959i	−0.136816	−	1.82568i	−0.469823	−	0.882760i	$-0.655682\pi$
$131$	−1.56593	−	20.8959i	−0.136816	−	1.82568i	0.333007	−	0.942924i	$-0.391937\pi$
$132$		0			0
$133$	0.617816	+	0.903007i	0.0535714	+	0.0783006i
$134$	−5.07893	+	4.05031i	−0.438753	+	0.349893i
$135$		0			0
$136$	−1.25499	−	8.32630i	−0.107614	−	0.713974i
$137$	1.62029	+	2.37653i	0.138431	+	0.203040i	0.889193	−	0.457531i	$-0.151266\pi$
$137$	1.62029	+	2.37653i	0.138431	+	0.203040i	−0.750763	+	0.660572i	$0.770314\pi$
$138$		0			0
$139$	7.02750	+	14.5927i	0.596064	+	1.23774i	0.952818	+	0.303542i	$0.0981693\pi$
$139$	7.02750	+	14.5927i	0.596064	+	1.23774i	−0.356754	+	0.934198i	$0.616116\pi$
$140$	3.59798	−	1.11625i	0.304085	−	0.0943402i
$141$		0			0
$142$	−3.36356	−	2.29323i	−0.282263	−	0.192444i
$143$	−2.06831	−	1.91911i	−0.172961	−	0.160484i
$144$		0			0
$145$	−0.496013	−	0.194671i	−0.0411916	−	0.0161665i
$146$	−4.79186			−0.396577
$147$		0			0
$148$	−10.1190			−0.831773
$149$	10.5563	+	4.14306i	0.864809	+	0.339412i	0.755938	−	0.654643i	$-0.227181\pi$
$149$	10.5563	+	4.14306i	0.864809	+	0.339412i	0.108871	+	0.994056i	$0.465276\pi$
$150$		0			0
$151$	5.26545	+	4.88563i	0.428497	+	0.397587i	0.864722	−	0.502251i	$-0.167495\pi$
$151$	5.26545	+	4.88563i	0.428497	+	0.397587i	−0.436225	+	0.899837i	$0.643685\pi$
$152$	0.358200	+	0.244217i	0.0290539	+	0.0198086i
$153$		0			0
$154$	−21.7819	−	3.24684i	−1.75524	−	0.261638i
$155$	3.71608	+	7.71653i	0.298483	+	0.619807i
$156$		0			0
$157$	8.37154	+	12.2788i	0.668121	+	0.979954i	0.999337	+	0.0363992i	$0.0115888\pi$
$157$	8.37154	+	12.2788i	0.668121	+	0.979954i	−0.331216	+	0.943555i	$0.607459\pi$
$158$	3.78521	+	25.1132i	0.301135	+	1.99790i
$159$		0			0
$160$	5.29300	−	4.22103i	0.418449	−	0.333702i
$161$	−18.5746	+	7.32492i	−1.46388	+	0.577285i
$162$		0			0
$163$	−0.909893	−	12.1417i	−0.0712684	−	0.951010i	−0.912167	−	0.409818i	$-0.865592\pi$
$163$	−0.909893	−	12.1417i	−0.0712684	−	0.951010i	0.840899	−	0.541192i	$-0.182027\pi$
$164$	−6.40365	−	1.97526i	−0.500041	−	0.154242i
$165$		0			0
$166$	−16.3876	+	9.46141i	−1.27193	+	0.734347i
$167$	−0.136107	−	0.596325i	−0.0105323	−	0.0461450i	0.969389	−	0.245531i	$-0.0789624\pi$
$167$	−0.136107	−	0.596325i	−0.0105323	−	0.0461450i	−0.979921	+	0.199386i	$0.936105\pi$
$168$		0			0
$169$	−2.80496	+	12.2894i	−0.215766	+	0.945335i
$170$	−4.35545	−	14.1200i	−0.334048	−	1.08296i
$171$		0			0
$172$	−3.78547	−	9.64521i	−0.288639	−	0.735441i
$173$	−13.2392	+	4.08374i	−1.00655	+	0.310481i	−0.753839	−	0.657060i	$-0.771800\pi$
$173$	−13.2392	+	4.08374i	−1.00655	+	0.310481i	−0.252716	+	0.967541i	$0.581324\pi$
$174$		0			0
$175$	9.56207	−	4.62404i	0.722824	−	0.349545i
$176$	−21.0689	+	4.80884i	−1.58813	+	0.362480i
$177$		0			0
$178$	9.88649	+	5.70797i	0.741024	+	0.427830i
$179$	1.47460	−	4.78053i	0.110217	−	0.357313i	−0.883615	−	0.468214i	$-0.844897\pi$
$179$	1.47460	−	4.78053i	0.110217	−	0.357313i	0.993831	+	0.110901i	$0.0353737\pi$
$180$		0			0
$181$	−14.6220	−	11.6606i	−1.08684	−	0.866727i	−0.0951625	−	0.995462i	$-0.530337\pi$
$181$	−14.6220	−	11.6606i	−1.08684	−	0.866727i	−0.991679	+	0.128735i	$0.958908\pi$
$182$	−1.12991	−	2.86525i	−0.0837548	−	0.212386i
$183$		0			0
$184$	−5.79954	+	5.38119i	−0.427548	+	0.396707i
$185$	6.92530	−	1.04382i	0.509158	−	0.0767433i
$186$		0			0
$187$	−5.37698	+	35.6739i	−0.393204	+	2.60874i
$188$	8.22555	−	3.96121i	0.599910	−	0.288901i
$189$		0			0
$190$	0.685443	+	0.330092i	0.0497273	+	0.0239474i
$191$	5.70823	−	8.37244i	0.413033	−	0.605809i	−0.562196	−	0.827004i	$-0.690043\pi$
$191$	5.70823	−	8.37244i	0.413033	−	0.605809i	0.975230	+	0.221195i	$0.0709958\pi$
$192$		0			0
$193$	−0.696044	+	9.28806i	−0.0501023	+	0.668569i	0.914454	+	0.404691i	$0.132621\pi$
$193$	−0.696044	+	9.28806i	−0.0501023	+	0.668569i	−0.964556	+	0.263878i	$0.914998\pi$
$194$	−8.77408	+	22.3560i	−0.629942	+	1.60507i
$195$		0			0
$196$	−8.31393	−	5.62877i	−0.593852	−	0.402055i
$197$			8.73158i			0.622099i	0.950394	+	0.311050i	$0.100681\pi$
$197$			8.73158i			0.622099i	−0.950394	+	0.311050i	$0.899319\pi$
$198$		0			0
$199$	−11.0033	−	0.824586i	−0.780006	−	0.0584533i	−0.321225	−	0.947003i	$-0.604095\pi$
$199$	−11.0033	−	0.824586i	−0.780006	−	0.0584533i	−0.458781	+	0.888550i	$0.651714\pi$
$200$	2.86256	−	3.08510i	0.202413	−	0.218150i
$201$		0			0
$202$	−0.0811594	+	0.168529i	−0.00571036	+	0.0118577i
$203$	0.420800	+	1.35635i	0.0295343	+	0.0951974i
$204$		0			0
$205$	4.58634	+	0.691280i	0.320324	+	0.0482811i
$206$	−0.732304	+	0.499276i	−0.0510220	+	0.0347862i
$207$		0			0
$208$	−2.05575	−	2.21557i	−0.142540	−	0.153622i
$209$	−1.15811	−	1.45222i	−0.0801079	−	0.100452i
$210$		0			0
$211$	1.58614	−	1.98896i	0.109195	−	0.136926i	−0.724231	−	0.689558i	$-0.757805\pi$
$211$	1.58614	−	1.98896i	0.109195	−	0.136926i	0.833426	+	0.552632i	$0.186376\pi$
$212$	−2.96219	+	0.221985i	−0.203444	+	0.0152460i
$213$		0			0
$214$	0.225248	−	0.390141i	0.0153976	−	0.0266695i
$215$	3.58568	+	6.21059i	0.244542	+	0.423558i
$216$		0			0
$217$	9.87053	−	20.5820i	0.670055	−	1.39720i
$218$	−23.4271	−	5.34708i	−1.58668	−	0.362150i
$219$		0			0
$220$	−5.95327	+	2.33648i	−0.401369	+	0.157526i
$221$	−4.69679	+	1.84335i	−0.315940	+	0.123997i
$222$		0			0
$223$	−20.1361	−	4.59593i	−1.34841	−	0.307766i	−0.513471	−	0.858107i	$-0.671640\pi$
$223$	−20.1361	−	4.59593i	−1.34841	−	0.307766i	−0.834940	+	0.550341i	$0.814498\pi$
$224$	−17.5974	−	3.98636i	−1.17578	−	0.266350i
$225$		0			0
$226$	−0.925640	−	1.60326i	−0.0615727	−	0.106647i
$227$	−2.55915	+	4.43258i	−0.169857	+	0.294201i	−0.938369	−	0.345634i	$-0.887664\pi$
$227$	−2.55915	+	4.43258i	−0.169857	+	0.294201i	0.768512	+	0.639835i	$0.220997\pi$
$228$		0			0
$229$	−17.1475	+	1.28503i	−1.13314	+	0.0849172i	−0.628068	−	0.778159i	$-0.716154\pi$
$229$	−17.1475	+	1.28503i	−1.13314	+	0.0849172i	−0.505074	+	0.863076i	$0.668535\pi$
$230$	−8.65625	+	10.8546i	−0.570776	+	0.715731i
$231$		0			0
$232$	0.350840	+	0.439940i	0.0230338	+	0.0288835i
$233$	2.12482	+	2.29001i	0.139202	+	0.150024i	0.798805	−	0.601591i	$-0.205466\pi$
$233$	2.12482	+	2.29001i	0.139202	+	0.150024i	−0.659603	+	0.751614i	$0.729276\pi$
$234$		0			0
$235$	−5.22085	+	3.55952i	−0.340571	+	0.232197i
$236$	−17.5940	−	2.65187i	−1.14527	−	0.172622i
$237$		0			0
$238$	−22.1317	+	32.5750i	−1.43458	+	2.11152i
$239$	10.2085	−	21.1981i	0.660332	−	1.37119i	−0.254387	−	0.967103i	$-0.581874\pi$
$239$	10.2085	−	21.1981i	0.660332	−	1.37119i	0.914719	−	0.404091i	$-0.132412\pi$
$240$		0			0
$241$	3.01254	−	3.24675i	0.194055	−	0.209142i	−0.628527	−	0.777787i	$-0.716342\pi$
$241$	3.01254	−	3.24675i	0.194055	−	0.209142i	0.822582	+	0.568646i	$0.192533\pi$
$242$	16.9543	+	1.27055i	1.08986	+	0.0816738i
$243$		0			0
$244$			6.91888i			0.442936i
$245$	6.27060	+	2.99465i	0.400614	+	0.191321i
$246$		0			0
$247$	0.0949072	−	0.241820i	0.00603880	−	0.0153866i
$248$	0.675905	−	9.01933i	0.0429200	−	0.572728i
$249$		0			0
$250$	9.34201	−	13.7022i	0.590841	−	0.866604i
$251$	12.7904	+	6.15955i	0.807325	+	0.388787i	0.791562	−	0.611089i	$-0.209268\pi$
$251$	12.7904	+	6.15955i	0.807325	+	0.388787i	0.0157627	+	0.999876i	$0.494982\pi$
$252$		0			0
$253$	30.5399	−	14.7072i	1.92003	−	0.924637i
$254$	4.15636	−	27.5757i	0.260793	−	1.73025i
$255$		0			0
$256$	−20.7173	+	3.12263i	−1.29483	+	0.195165i
$257$	21.1023	−	19.5801i	1.31633	−	1.22137i	0.358669	−	0.933465i	$-0.383231\pi$
$257$	21.1023	−	19.5801i	1.31633	−	1.22137i	0.957658	−	0.287908i	$-0.0929598\pi$
$258$		0			0
$259$	−13.7035	−	12.6736i	−0.851496	−	0.787497i
$260$	−0.699293	−	0.557667i	−0.0433683	−	0.0345851i
$261$		0			0
$262$	−11.4461	+	37.1074i	−0.707144	+	2.29250i
$263$	−9.22658	−	5.32697i	−0.568935	−	0.328475i	0.187789	−	0.982209i	$-0.439868\pi$
$263$	−9.22658	−	5.32697i	−0.568935	−	0.328475i	−0.756724	+	0.653734i	$0.773201\pi$
$264$		0			0
$265$	2.00439	−	0.457488i	0.123129	−	0.0281033i
$266$	−0.454407	−	1.97605i	−0.0278615	−	0.121160i
$267$		0			0
$268$	4.80447	−	1.48198i	0.293479	−	0.0905264i
$269$	6.03987	+	15.3893i	0.368257	+	0.938304i	0.988132	+	0.153604i	$0.0490880\pi$
$269$	6.03987	+	15.3893i	0.368257	+	0.938304i	−0.619875	+	0.784700i	$0.712817\pi$
$270$		0			0
$271$	−5.23438	−	16.9695i	−0.317966	−	1.03082i	−0.963639	−	0.267207i	$-0.913899\pi$
$271$	−5.23438	−	16.9695i	−0.317966	−	1.03082i	0.645673	−	0.763614i	$-0.276577\pi$
$272$	−8.59942	+	37.6765i	−0.521417	+	2.28448i
$273$		0			0
$274$	−1.18612	−	5.19672i	−0.0716559	−	0.313945i
$275$	−15.6158	+	9.01579i	−0.941669	+	0.543673i
$276$		0			0
$277$	30.7732	+	9.49229i	1.84899	+	0.570336i	0.999056	+	0.0434394i	$0.0138316\pi$
$277$	30.7732	+	9.49229i	1.84899	+	0.570336i	0.849929	+	0.526897i	$0.176645\pi$
$278$	−2.24307	−	29.9316i	−0.134530	−	1.79518i
$279$		0			0
$280$	2.74605	+	0.201293i	0.164108	+	0.0120296i
$281$	5.50516	−	4.39022i	0.328410	−	0.261899i	−0.445378	−	0.895343i	$-0.646931\pi$
$281$	5.50516	−	4.39022i	0.328410	−	0.261899i	0.773789	+	0.633444i	$0.218359\pi$
$282$		0			0
$283$	1.92498	+	12.7714i	0.114428	+	0.759180i	0.970285	+	0.241967i	$0.0777925\pi$
$283$	1.92498	+	12.7714i	0.114428	+	0.759180i	−0.855856	+	0.517213i	$0.826969\pi$
$284$	1.77489	+	2.60328i	0.105320	+	0.154476i
$285$		0			0
$286$	2.26868	+	4.71097i	0.134150	+	0.278565i
$287$	−6.19817	−	10.6953i	−0.365866	−	0.631323i
$288$		0			0
$289$	39.2584	+	26.7659i	2.30932	+	1.57447i
$290$	0.723863	+	0.671646i	0.0425067	+	0.0394404i
$291$		0			0
$292$	3.45237	+	1.35496i	0.202035	+	0.0792928i
$293$	−12.8563			−0.751072			−0.375536	−	0.926808i	$-0.622541\pi$
$293$	−12.8563			−0.751072			−0.375536	+	0.926808i	$0.622541\pi$
$294$		0			0
$295$	12.3147			0.716990
$296$	−6.88471	−	2.70205i	−0.400166	−	0.157053i
$297$		0			0
$298$	−15.4055	−	14.2942i	−0.892418	−	0.828043i
$299$	3.91692	+	2.67051i	0.226521	+	0.154440i
$300$		0			0
$301$	6.95378	−	17.8031i	0.400809	−	1.02615i
$302$	−5.77556	−	11.9931i	−0.332346	−	0.690124i
$303$		0			0
$304$	−1.12084	−	1.64397i	−0.0642847	−	0.0942883i
$305$	−0.713717	−	4.73520i	−0.0408673	−	0.271137i
$306$		0			0
$307$	−3.22712	+	2.57354i	−0.184182	+	0.146880i	−0.711240	−	0.702949i	$-0.751866\pi$
$307$	−3.22712	+	2.57354i	−0.184182	+	0.146880i	0.527059	+	0.849829i	$0.323295\pi$
$308$	14.7750	+	8.49833i	0.841886	+	0.484237i
$309$		0			0
$310$	−1.18612	−	15.8276i	−0.0673669	−	0.898948i
$311$	−22.1482	−	6.83180i	−1.25591	−	0.387396i	−0.405778	−	0.913972i	$-0.633000\pi$
$311$	−22.1482	−	6.83180i	−1.25591	−	0.387396i	−0.850128	+	0.526576i	$0.823476\pi$
$312$		0			0
$313$	−21.1197	+	12.1935i	−1.19375	+	0.689215i	−0.959156	−	0.282878i	$-0.908711\pi$
$313$	−21.1197	+	12.1935i	−1.19375	+	0.689215i	−0.234599	+	0.972092i	$0.575378\pi$
$314$	−6.12831	−	26.8499i	−0.345840	−	1.51523i
$315$		0			0
$316$	4.37395	−	19.1635i	0.246054	−	1.07803i
$317$	5.67594	+	18.4010i	0.318793	+	1.03350i	0.963193	+	0.268812i	$0.0866310\pi$
$317$	5.67594	+	18.4010i	0.318793	+	1.03350i	−0.644400	+	0.764689i	$0.722893\pi$
$318$		0			0
$319$	−0.880800	−	2.24424i	−0.0493153	−	0.125653i
$320$	−2.86049	+	0.882343i	−0.159906	+	0.0493245i
$321$		0			0
$322$	37.0021	−	0.0602417i	2.06205	−	0.00335714i
$323$	−3.23833	+	0.739128i	−0.180185	+	0.0411262i
$324$		0			0
$325$	−2.18397	−	1.26091i	−0.121145	−	0.0699429i
$326$	−6.65083	+	21.5615i	−0.368356	+	1.19418i
$327$		0			0
$328$	−3.82945	−	3.05388i	−0.211446	−	0.168622i
$329$	16.1006	+	4.93770i	0.887657	+	0.272224i
$330$		0			0
$331$	−6.09235	+	5.65287i	−0.334866	+	0.310710i	−0.829626	−	0.558319i	$-0.811446\pi$
$331$	−6.09235	+	5.65287i	−0.334866	+	0.310710i	0.494760	+	0.869030i	$0.335256\pi$
$332$	14.4820	−	2.18282i	0.794806	−	0.119798i
$333$		0			0
$334$	−0.168943	+	1.12086i	−0.00924414	+	0.0613309i
$335$	−3.13525	+	1.50986i	−0.171297	+	0.0824922i
$336$		0			0
$337$	25.4191	+	12.2412i	1.38467	+	0.666820i	0.969989	−	0.243149i	$-0.0781806\pi$
$337$	25.4191	+	12.2412i	1.38467	+	0.666820i	0.414676	+	0.909969i	$0.363895\pi$
$338$	13.1593	−	19.3011i	0.715769	−	1.04984i
$339$		0			0
$340$	−0.854652	+	11.4045i	−0.0463500	+	0.618498i
$341$	−14.1575	+	36.0728i	−0.766674	+	1.95345i
$342$		0			0
$343$	−4.20928	−	18.0356i	−0.227280	−	0.973829i
$344$		−	7.57321i		−	0.408320i
$345$		0			0
$346$	25.6035	+	1.91872i	1.37645	+	0.103151i
$347$	1.79422	−	1.93371i	0.0963188	−	0.103807i	−0.683053	−	0.730369i	$-0.739348\pi$
$347$	1.79422	−	1.93371i	0.0963188	−	0.103807i	0.779371	+	0.626562i	$0.215539\pi$
$348$		0			0
$349$	−8.44042	+	17.5267i	−0.451805	+	0.938184i	0.543316	+	0.839528i	$0.317168\pi$
$349$	−8.44042	+	17.5267i	−0.451805	+	0.938184i	−0.995122	+	0.0986556i	$0.968546\pi$
$350$	−19.6261	+	1.50291i	−1.04906	+	0.0803337i
$351$		0			0
$352$	30.2892	+	4.56536i	1.61442	+	0.243335i
$353$	−14.3780	+	9.80275i	−0.765263	+	0.521748i	−0.881905	−	0.471426i	$-0.843739\pi$
$353$	−14.3780	+	9.80275i	−0.765263	+	0.521748i	0.116642	+	0.993174i	$0.462787\pi$
$354$		0			0
$355$	−1.48325	−	1.59857i	−0.0787230	−	0.0848432i
$356$	−5.50888	−	6.90792i	−0.291970	−	0.366119i
$357$		0			0
$358$	−5.78044	+	7.24844i	−0.305506	+	0.383092i
$359$	6.62300	−	0.496326i	0.349549	−	0.0261951i	0.101201	−	0.994866i	$-0.467731\pi$
$359$	6.62300	−	0.496326i	0.349549	−	0.0261951i	0.248348	+	0.968671i	$0.420112\pi$
$360$		0			0
$361$	−9.41449	+	16.3064i	−0.495500	+	0.858230i
$362$	17.3293	+	30.0153i	0.910810	+	1.57757i
$363$		0			0
$364$	0.00388099	+	2.38381i	0.000203419	+	0.124946i
$365$	−2.50253	−	0.571187i	−0.130989	−	0.0298973i
$366$		0			0
$367$	20.6789	−	8.11586i	1.07943	−	0.423645i	0.242048	−	0.970264i	$-0.422181\pi$
$367$	20.6789	−	8.11586i	1.07943	−	0.423645i	0.837381	+	0.546620i	$0.184086\pi$
$368$	33.8001	−	13.2656i	1.76195	−	0.691516i
$369$		0			0
$370$	−12.6534	−	2.88807i	−0.657821	−	0.150143i
$371$	−4.28955	−	3.40939i	−0.222702	−	0.177007i
$372$		0			0
$373$	2.15951	+	3.74039i	0.111815	+	0.193670i	0.916502	−	0.400030i	$-0.131000\pi$
$373$	2.15951	+	3.74039i	0.111815	+	0.193670i	−0.804687	+	0.593699i	$0.797667\pi$
$374$	33.4286	−	57.9001i	1.72855	−	2.99394i
$375$		0			0
$376$	6.65423	−	0.498666i	0.343166	−	0.0257167i
$377$	0.210228	−	0.263617i	0.0108273	−	0.0135770i
$378$		0			0
$379$	−17.9466	−	22.5043i	−0.921853	−	1.15597i	−0.987420	−	0.158119i	$-0.949457\pi$
$379$	−17.9466	−	22.5043i	−0.921853	−	1.15597i	0.0655670	−	0.997848i	$-0.479114\pi$
$380$	−0.400501	−	0.431637i	−0.0205453	−	0.0221425i
$381$		0			0
$382$	−15.5157	+	10.5784i	−0.793853	+	0.541240i
$383$	27.5261	+	4.14889i	1.40652	+	0.211998i	0.808033	−	0.589137i	$-0.200532\pi$
$383$	27.5261	+	4.14889i	1.40652	+	0.211998i	0.598483	+	0.801135i	$0.295770\pi$
$384$		0			0
$385$	−10.9885	−	4.29204i	−0.560027	−	0.218743i
$386$	7.48917	−	15.5514i	0.381189	−	0.791547i
$387$		0			0
$388$	12.6428	−	13.6257i	0.641843	−	0.691743i
$389$	25.2049	+	1.88884i	1.27794	+	0.0957681i	0.696342	−	0.717710i	$-0.254810\pi$
$389$	25.2049	+	1.88884i	1.27794	+	0.0957681i	0.581595	+	0.813478i	$0.302429\pi$
$390$		0			0
$391$		−	60.6160i		−	3.06548i
$392$	−4.15357	−	6.04974i	−0.209787	−	0.305558i
$393$		0			0
$394$	5.91168	−	15.0627i	0.297826	−	0.758849i
$395$	−1.01667	+	13.5665i	−0.0511541	+	0.682604i
$396$		0			0
$397$	−2.72275	+	3.99355i	−0.136651	+	0.200430i	−0.888464	−	0.458946i	$-0.848227\pi$
$397$	−2.72275	+	3.99355i	−0.136651	+	0.200430i	0.751813	+	0.659376i	$0.229180\pi$
$398$	18.4234	+	8.87224i	0.923481	+	0.444725i
$399$		0			0
$400$	−17.4026	+	8.38064i	−0.870129	+	0.419032i
$401$	0.602095	−	3.99464i	0.0300672	−	0.199483i	−0.968754	−	0.248024i	$-0.920219\pi$
$401$	0.602095	−	3.99464i	0.0300672	−	0.199483i	0.998821	+	0.0485407i	$0.0154571\pi$
$402$		0			0
$403$	−5.35911	+	0.807756i	−0.266956	+	0.0402372i
$404$	0.106126	−	0.0984707i	0.00527997	−	0.00489910i
$405$		0			0
$406$	0.192399	−	2.62473i	0.00954862	−	0.130263i
$407$	24.7746	+	19.7571i	1.22803	+	0.979323i
$408$		0			0
$409$	2.49502	−	8.08867i	0.123371	−	0.399959i	−0.872727	−	0.488208i	$-0.837651\pi$
$409$	2.49502	−	8.08867i	0.123371	−	0.399959i	0.996098	+	0.0882487i	$0.0281270\pi$
$410$	−7.44380	−	4.29768i	−0.367623	−	0.212247i
$411$		0			0
$412$	0.668776	−	0.152644i	0.0329482	−	0.00752022i
$413$	−20.5052	−	25.6270i	−1.00900	−	1.26102i
$414$		0			0
$415$	−9.68618	+	2.98779i	−0.475476	+	0.146665i
$416$	1.56511	+	3.98784i	0.0767360	+	0.195520i
$417$		0			0
$418$	1.01461	+	3.28929i	0.0496263	+	0.160885i
$419$	−6.41958	+	28.1260i	−0.313617	+	1.37405i	0.534917	+	0.844904i	$0.320343\pi$
$419$	−6.41958	+	28.1260i	−0.313617	+	1.37405i	−0.848534	+	0.529141i	$0.822514\pi$
$420$		0			0
$421$	−7.12201	−	31.2035i	−0.347105	−	1.52077i	−0.783717	−	0.621118i	$-0.786679\pi$
$421$	−7.12201	−	31.2035i	−0.347105	−	1.52077i	0.436612	−	0.899650i	$-0.356178\pi$
$422$	−4.08285	+	2.35724i	−0.198750	+	0.114748i
$423$		0			0
$424$	−2.07468	−	0.639954i	−0.100755	−	0.0310789i
$425$	2.40968	+	32.1549i	0.116886	+	1.55974i
$426$		0			0
$427$	−8.66561	+	9.36985i	−0.419358	+	0.453439i
$428$	−0.272600	+	0.217392i	−0.0131766	+	0.0105080i
$429$		0			0
$430$	−1.98076	−	13.1415i	−0.0955205	−	0.633737i
$431$	−14.8179	−	21.7338i	−0.713751	−	1.04688i	−0.996157	−	0.0875856i	$-0.972085\pi$
$431$	−14.8179	−	21.7338i	−0.713751	−	1.04688i	0.282406	−	0.959295i	$-0.408868\pi$
$432$		0			0
$433$	6.84177	+	14.2071i	0.328794	+	0.682748i	0.998189	−	0.0601587i	$-0.0191607\pi$
$433$	6.84177	+	14.2071i	0.328794	+	0.682748i	−0.669394	+	0.742907i	$0.733446\pi$
$434$	−30.9625	+	28.8229i	−1.48625	+	1.38354i
$435$		0			0
$436$	15.3665	+	10.4767i	0.735920	+	0.501742i
$437$	2.28777	+	2.12274i	0.109439	+	0.101544i
$438$		0			0
$439$	−10.8305	−	4.25068i	−0.516914	−	0.202874i	0.0925199	−	0.995711i	$-0.470508\pi$
$439$	−10.8305	−	4.25068i	−0.516914	−	0.202874i	−0.609434	+	0.792837i	$0.708603\pi$
$440$	−4.67437			−0.222842
$441$		0			0
$442$	9.35039			0.444753
$443$	1.42415	+	0.558937i	0.0676633	+	0.0265559i	0.398931	−	0.916981i	$-0.369381\pi$
$443$	1.42415	+	0.558937i	0.0676633	+	0.0265559i	−0.331268	+	0.943537i	$0.607476\pi$
$444$		0			0
$445$	4.48280	+	4.15943i	0.212505	+	0.197176i
$446$	31.6248	+	21.5614i	1.49748	+	1.02096i
$447$		0			0
$448$	6.59917	+	4.48351i	0.311781	+	0.211826i
$449$	8.49715	+	17.6445i	0.401005	+	0.832696i	0.999502	+	0.0315705i	$0.0100509\pi$
$449$	8.49715	+	17.6445i	0.401005	+	0.832696i	−0.598496	+	0.801126i	$0.704235\pi$
$450$		0			0
$451$	11.8216	+	17.3391i	0.556658	+	0.816468i
$452$	0.213552	+	1.41683i	0.0100446	+	0.0666419i
$453$		0			0
$454$	7.41582	−	5.91392i	0.348042	−	0.277554i
$455$	−0.248558	−	1.63105i	−0.0116526	−	0.0764649i
$456$		0			0
$457$	−2.42706	−	32.3868i	−0.113533	−	1.51499i	−0.705315	−	0.708894i	$-0.749194\pi$
$457$	−2.42706	−	32.3868i	−0.113533	−	1.51499i	0.591782	−	0.806098i	$-0.298425\pi$
$458$	30.4510	+	9.39289i	1.42288	+	0.438901i
$459$		0			0
$460$	9.30579	−	5.37270i	0.433885	−	0.250504i
$461$	−2.97254	−	13.0235i	−0.138445	−	0.606567i	−0.995777	−	0.0918033i	$-0.970737\pi$
$461$	−2.97254	−	13.0235i	−0.138445	−	0.606567i	0.857332	−	0.514763i	$-0.172120\pi$
$462$		0			0
$463$	2.86102	−	12.5350i	0.132963	−	0.582549i	−0.863918	−	0.503632i	$-0.831997\pi$
$463$	2.86102	−	12.5350i	0.132963	−	0.582549i	0.996881	−	0.0789168i	$-0.0251461\pi$
$464$	−0.761220	−	2.46781i	−0.0353387	−	0.114565i
$465$		0			0
$466$	−2.11505	−	5.38906i	−0.0979778	−	0.249643i
$467$	−4.18418	+	1.29065i	−0.193621	+	0.0597241i	−0.390049	−	0.920794i	$-0.627542\pi$
$467$	−4.18418	+	1.29065i	−0.193621	+	0.0597241i	0.196428	+	0.980518i	$0.437066\pi$
$468$		0			0
$469$	8.36254	+	4.01043i	0.386146	+	0.185184i
$470$	11.4164	−	2.60571i	0.526598	−	0.120192i
$471$		0			0
$472$	−11.2624	−	6.50238i	−0.518396	−	0.299296i
$473$	−9.56402	+	31.0058i	−0.439754	+	1.42565i
$474$		0			0
$475$	−1.29798	−	1.03510i	−0.0595552	−	0.0474937i
$476$	25.1561	−	17.2112i	1.15303	−	0.788873i
$477$		0			0
$478$	−31.9626	+	29.6570i	−1.46194	+	1.35648i
$479$	20.9513	−	3.15790i	0.957290	−	0.144288i	0.348227	−	0.937410i	$-0.386784\pi$
$479$	20.9513	−	3.15790i	0.957290	−	0.144288i	0.609063	+	0.793122i	$0.291546\pi$
$480$		0			0
$481$	−0.660518	+	4.38225i	−0.0301170	+	0.199813i
$482$	−7.39509	+	3.56129i	−0.336837	+	0.162212i
$483$		0			0
$484$	−11.8557	−	5.70940i	−0.538895	−	0.259518i
$485$	−7.24706	+	10.6295i	−0.329072	+	0.482660i
$486$		0			0
$487$	0.730807	−	9.75194i	0.0331160	−	0.441902i	−0.955860	−	0.293824i	$-0.905072\pi$
$487$	0.730807	−	9.75194i	0.0331160	−	0.441902i	0.988976	−	0.148079i	$-0.0473089\pi$
$488$	−1.84754	+	4.70745i	−0.0836341	+	0.213096i
$489$		0			0
$490$	−8.78979	−	9.41150i	−0.397082	−	0.425168i
$491$		−	23.7594i		−	1.07224i	−0.844140	−	0.536122i	$-0.819889\pi$
$491$		−	23.7594i		−	1.07224i	0.844140	−	0.536122i	$-0.180111\pi$
$492$		0			0
$493$	−4.29924	−	0.322184i	−0.193628	−	0.0145104i
$494$	−0.327446	+	0.352903i	−0.0147325	+	0.0158778i
$495$		0			0
$496$	−18.0108	+	37.3998i	−0.808708	+	1.67930i
$497$	−0.856870	+	5.74845i	−0.0384359	+	0.257853i
$498$		0			0
$499$	21.3120	+	3.21226i	0.954055	+	0.143801i	0.607580	−	0.794259i	$-0.292141\pi$
$499$	21.3120	+	3.21226i	0.954055	+	0.143801i	0.346475	+	0.938059i	$0.387379\pi$
$500$	−10.6051	+	7.23041i	−0.474273	+	0.323354i
$501$		0			0
$502$	−17.8943	−	19.2854i	−0.798661	−	0.860751i
$503$	−10.7609	−	13.4938i	−0.479807	−	0.601659i	0.481735	−	0.876317i	$-0.340007\pi$
$503$	−10.7609	−	13.4938i	−0.479807	−	0.601659i	−0.961542	+	0.274658i	$0.911435\pi$
$504$		0			0
$505$	−0.0624738	+	0.0783397i	−0.00278005	+	0.00348607i
$506$	−62.6414	+	4.69432i	−2.78475	+	0.208688i
$507$		0			0
$508$	−10.7919	+	18.6921i	−0.478812	+	0.829326i
$509$	−16.3177	−	28.2630i	−0.723268	−	1.25274i	−0.959683	−	0.281085i	$-0.909306\pi$
$509$	−16.3177	−	28.2630i	−0.723268	−	1.25274i	0.236415	−	0.971652i	$-0.424028\pi$
$510$		0			0
$511$	2.97833	+	6.15889i	0.131753	+	0.272453i
$512$	22.1546	+	5.05664i	0.979104	+	0.223474i
$513$		0			0
$514$	−49.6599	+	19.4901i	−2.19040	+	0.859671i
$515$	−0.441957	+	0.173455i	−0.0194749	+	0.00764335i
$516$		0			0
$517$	−27.8731	−	6.36185i	−1.22586	−	0.279794i
$518$	15.0592	+	31.1409i	0.661662	+	1.36825i
$519$		0			0
$520$	−0.326870	−	0.566155i	−0.0143342	−	0.0248275i
$521$	−7.83292	+	13.5670i	−0.343166	+	0.594382i	−0.985019	−	0.172446i	$-0.944833\pi$
$521$	−7.83292	+	13.5670i	−0.343166	+	0.594382i	0.641852	+	0.766828i	$0.278166\pi$
$522$		0			0
$523$	25.4385	−	1.90635i	1.11235	−	0.0833589i	0.494146	−	0.869379i	$-0.335481\pi$
$523$	25.4385	−	1.90635i	1.11235	−	0.0833589i	0.618201	+	0.786020i	$0.287862\pi$
$524$	18.7391	−	23.4981i	0.818621	−	1.02652i
$525$		0			0
$526$	12.3100	+	15.4363i	0.536743	+	0.673054i
$527$	47.1344	+	50.7988i	2.05321	+	2.21283i
$528$		0			0
$529$	−28.0533	+	19.1264i	−1.21971	+	0.831582i
$530$	−3.76748	−	0.567856i	−0.163649	−	0.0246661i
$531$		0			0
$532$	−0.231368	+	1.55217i	−0.0100311	+	0.0672950i
$533$	−1.27343	+	2.64431i	−0.0551585	+	0.114538i
$534$		0			0
$535$	0.164140	−	0.176900i	0.00709637	−	0.00764807i
$536$	3.66458	+	0.274622i	0.158286	+	0.0118619i
$537$		0			0
$538$		−	30.6372i		−	1.32086i
$539$	9.36521	+	30.0139i	0.403388	+	1.29279i
$540$		0			0
$541$	−1.49182	+	3.80109i	−0.0641383	+	0.163422i	−0.959350	−	0.282220i	$-0.908929\pi$
$541$	−1.49182	+	3.80109i	−0.0641383	+	0.163422i	0.895211	+	0.445642i	$0.147024\pi$
$542$	−2.45934	+	32.8176i	−0.105638	+	1.40964i
$543$		0			0
$544$	30.8568	−	45.2586i	1.32297	−	1.94044i
$545$	−11.5974	−	5.58499i	−0.496776	−	0.239235i
$546$		0			0
$547$	−19.6664	+	9.47084i	−0.840875	+	0.404944i	−0.804182	−	0.594383i	$-0.797396\pi$
$547$	−19.6664	+	9.47084i	−0.840875	+	0.404944i	−0.0366923	+	0.999327i	$0.511682\pi$
$548$	−0.614877	+	4.07944i	−0.0262662	+	0.174265i
$549$		0			0
$550$	33.0427	−	4.98039i	1.40895	−	0.212364i
$551$	0.162717	−	0.150979i	0.00693198	−	0.00643194i
$552$		0			0
$553$	29.9249	−	20.4739i	1.27253	−	0.870638i
$554$	−46.6597	−	37.2099i	−1.98238	−	1.58090i
$555$		0			0
$556$	−6.84748	+	22.1990i	−0.290398	+	0.941446i
$557$	−16.2512	−	9.38264i	−0.688586	−	0.397555i	0.114496	−	0.993424i	$-0.463475\pi$
$557$	−16.2512	−	9.38264i	−0.688586	−	0.397555i	−0.803082	+	0.595868i	$0.796808\pi$
$558$		0			0
$559$	−4.42418	+	1.00979i	−0.187123	+	0.0427096i
$560$	−11.3944	−	5.46441i	−0.481501	−	0.230914i
$561$		0			0
$562$	−12.4692	+	3.84625i	−0.525984	+	0.162244i
$563$	−14.0988	−	35.9232i	−0.594194	−	1.51398i	−0.838845	−	0.544370i	$-0.816769\pi$
$563$	−14.0988	−	35.9232i	−0.594194	−	1.51398i	0.244651	−	0.969611i	$-0.421326\pi$
$564$		0			0
$565$	−0.292305	−	0.947631i	−0.0122974	−	0.0398671i
$566$	5.32607	−	23.3350i	0.223871	−	0.980844i
$567$		0			0
$568$	0.512443	+	2.24516i	0.0215016	+	0.0942048i
$569$	−5.55960	+	3.20984i	−0.233071	+	0.134563i	−0.611988	−	0.790867i	$-0.709630\pi$
$569$	−5.55960	+	3.20984i	−0.233071	+	0.134563i	0.378917	+	0.925431i	$0.376297\pi$
$570$		0			0
$571$	6.14518	+	1.89554i	0.257168	+	0.0793258i	0.420658	−	0.907219i	$-0.361799\pi$
$571$	6.14518	+	1.89554i	0.257168	+	0.0793258i	−0.163491	+	0.986545i	$0.552275\pi$
$572$	−0.302425	−	4.03559i	−0.0126450	−	0.168736i
$573$		0			0
$574$	3.45116	+	22.6467i	0.144049	+	0.945256i
$575$	23.6868	−	18.8896i	0.987806	−	0.787749i
$576$		0			0
$577$	−6.23729	−	41.3817i	−0.259662	−	1.72274i	−0.615449	−	0.788177i	$-0.711025\pi$
$577$	−6.23729	−	41.3817i	−0.259662	−	1.72274i	0.355787	−	0.934567i	$-0.384213\pi$
$578$	−49.6023	−	72.7532i	−2.06318	−	3.02613i
$579$		0			0
$580$	−0.331602	−	0.688579i	−0.0137690	−	0.0285917i
$581$	22.3461	+	15.1821i	0.927073	+	0.629859i
$582$		0			0
$583$	7.68585	+	5.24012i	0.318315	+	0.217024i
$584$	1.98710	+	1.84376i	0.0822269	+	0.0762954i
$585$		0			0
$586$	22.1782	+	8.70429i	0.916172	+	0.359571i
$587$	−21.8194			−0.900582			−0.450291	−	0.892882i	$-0.648680\pi$
$587$	−21.8194			−0.900582			−0.450291	+	0.892882i	$0.648680\pi$
$588$		0			0
$589$	−3.56787			−0.147011
$590$	−21.2439	−	8.33761i	−0.874597	−	0.343254i
$591$		0			0
$592$	24.8827	+	23.0878i	1.02267	+	0.948903i
$593$	−6.97370	−	4.75459i	−0.286375	−	0.195247i	0.411609	−	0.911361i	$-0.364967\pi$
$593$	−6.97370	−	4.75459i	−0.286375	−	0.195247i	−0.697984	+	0.716113i	$0.745919\pi$
$594$		0			0
$595$	−15.4411	+	14.3741i	−0.633024	+	0.589281i
$596$	7.05729	+	14.6546i	0.289078	+	0.600276i
$597$		0			0
$598$	−4.94896	−	7.25879i	−0.202378	−	0.296834i
$599$	−0.490638	−	3.25517i	−0.0200469	−	0.133003i	0.976569	−	0.215206i	$-0.0690424\pi$
$599$	−0.490638	−	3.25517i	−0.0200469	−	0.133003i	−0.996616	+	0.0822034i	$0.973804\pi$
$600$		0			0
$601$	−7.11733	+	5.67588i	−0.290322	+	0.231524i	−0.757810	−	0.652475i	$-0.773731\pi$
$601$	−7.11733	+	5.67588i	−0.290322	+	0.231524i	0.467488	+	0.883999i	$0.345159\pi$
$602$	−24.0494	+	26.0038i	−0.980179	+	1.05984i
$603$		0			0
$604$	0.769908	+	10.2737i	0.0313271	+	0.418031i
$605$	8.70286	+	2.68448i	0.353822	+	0.109140i
$606$		0			0
$607$	−21.0241	+	12.1383i	−0.853343	+	0.492678i	−0.861777	−	0.507287i	$-0.830649\pi$
$607$	−21.0241	+	12.1383i	−0.853343	+	0.492678i	0.00843430	+	0.999964i	$0.497315\pi$
$608$	0.627562	+	2.74953i	0.0254510	+	0.111508i
$609$		0			0
$610$	−1.97473	+	8.65185i	−0.0799544	+	0.350303i
$611$	−1.17857	−	3.82083i	−0.0476799	−	0.154574i
$612$		0			0
$613$	−6.08264	−	15.4983i	−0.245675	−	0.625971i	0.753841	−	0.657057i	$-0.228199\pi$
$613$	−6.08264	−	15.4983i	−0.245675	−	0.625971i	−0.999517	+	0.0310857i	$0.990104\pi$
$614$	7.30947	−	2.25467i	0.294986	−	0.0909911i
$615$		0			0
$616$	7.78331	+	9.72743i	0.313598	+	0.391929i
$617$	−12.8385	+	2.93030i	−0.516857	+	0.117969i	−0.472989	−	0.881068i	$-0.656825\pi$
$617$	−12.8385	+	2.93030i	−0.516857	+	0.117969i	−0.0438676	+	0.999037i	$0.513968\pi$
$618$		0			0
$619$	17.8653	+	10.3145i	0.718066	+	0.414575i	0.814040	−	0.580808i	$-0.197263\pi$
$619$	17.8653	+	10.3145i	0.718066	+	0.414575i	−0.0959747	+	0.995384i	$0.530597\pi$
$620$	−3.62089	+	11.7386i	−0.145419	+	0.471435i
$621$		0			0
$622$	33.5820	+	26.7807i	1.34652	+	1.07381i
$623$	1.19151	−	16.2546i	0.0477368	−	0.651229i
$624$		0			0
$625$	−8.20215	+	7.61048i	−0.328086	+	0.304419i
$626$	44.6887	−	6.73574i	1.78612	−	0.269214i
$627$		0			0
$628$	−3.17688	+	21.0772i	−0.126771	+	0.841074i
$629$	51.0544	−	24.5865i	2.03567	−	0.980327i
$630$		0			0
$631$	−9.60985	−	4.62786i	−0.382562	−	0.184232i	0.232712	−	0.972546i	$-0.425240\pi$
$631$	−9.60985	−	4.62786i	−0.382562	−	0.184232i	−0.615274	+	0.788314i	$0.710954\pi$
$632$	8.09313	−	11.8704i	0.321928	−	0.472181i
$633$		0			0
$634$	2.66681	−	35.5861i	0.105912	−	1.41330i
$635$	5.45765	−	13.9059i	0.216580	−	0.551838i
$636$		0			0
$637$	−2.98036	+	3.23312i	−0.118086	+	0.128101i
$638$			4.46785i			0.176884i
$639$		0			0
$640$	−7.97018	−	0.597283i	−0.315049	−	0.0236097i
$641$	−16.3629	+	17.6350i	−0.646295	+	0.696540i	−0.968185	−	0.250237i	$-0.919492\pi$
$641$	−16.3629	+	17.6350i	−0.646295	+	0.696540i	0.321890	+	0.946777i	$0.395682\pi$
$642$		0			0
$643$	−14.0765	+	29.2301i	−0.555122	+	1.15272i	0.414937	+	0.909850i	$0.363804\pi$
$643$	−14.0765	+	29.2301i	−0.555122	+	1.15272i	−0.970058	+	0.242872i	$0.921911\pi$
$644$	−26.6758	−	10.4194i	−1.05117	−	0.410581i
$645$		0			0
$646$	6.08681	+	0.917440i	0.239482	+	0.0360962i
$647$	−5.94010	+	4.04989i	−0.233529	+	0.159218i	−0.674431	−	0.738338i	$-0.735611\pi$
$647$	−5.94010	+	4.04989i	−0.233529	+	0.159218i	0.440902	+	0.897555i	$0.354659\pi$
$648$		0			0
$649$	37.8983	+	40.8447i	1.48764	+	1.60329i
$650$	2.91383	+	3.65383i	0.114290	+	0.143315i
$651$		0			0
$652$	10.8885	−	13.6537i	0.426425	−	0.534720i
$653$	−43.3656	+	3.24980i	−1.69703	+	0.127174i	−0.887772	−	0.460284i	$-0.847747\pi$
$653$	−43.3656	+	3.24980i	−1.69703	+	0.127174i	−0.809254	+	0.587459i	$0.800128\pi$
$654$		0			0
$655$	−10.4009	+	18.0149i	−0.406396	+	0.703899i
$656$	11.2399	+	19.4680i	0.438843	+	0.760099i
$657$		0			0
$658$	−24.4319	−	19.4188i	−0.952456	−	0.757024i
$659$	−2.19881	−	0.501864i	−0.0856535	−	0.0195498i	0.179479	−	0.983762i	$-0.442559\pi$
$659$	−2.19881	−	0.501864i	−0.0856535	−	0.0195498i	−0.265133	+	0.964212i	$0.585416\pi$
$660$		0			0
$661$	12.9098	−	5.06672i	0.502133	−	0.197073i	−0.100736	−	0.994913i	$-0.532120\pi$
$661$	12.9098	−	5.06672i	0.502133	−	0.197073i	0.602868	+	0.797841i	$0.294024\pi$
$662$	14.3371	−	5.62688i	0.557226	−	0.218695i
$663$		0			0
$664$	10.4361	+	2.38198i	0.405000	+	0.0924387i
$665$	−0.00176832	−	1.08615i	−6.85727e−5	−	0.0421192i
$666$		0			0
$667$	2.02538	+	3.50807i	0.0784232	+	0.135833i
$668$	0.438655	−	0.759772i	0.0169721	−	0.0293965i
$669$		0			0
$670$	6.43081	−	0.481922i	0.248444	−	0.0186183i
$671$	13.5090	−	16.9397i	0.521509	−	0.653952i
$672$		0			0
$673$	−4.69254	−	5.88425i	−0.180884	−	0.226821i	0.683120	−	0.730306i	$-0.260622\pi$
$673$	−4.69254	−	5.88425i	−0.180884	−	0.226821i	−0.864004	+	0.503485i	$0.832051\pi$
$674$	−35.5622	−	38.3269i	−1.36980	−	1.47630i
$675$		0			0
$676$	−14.9384	+	10.1848i	−0.574554	+	0.391724i
$677$	−42.8122	−	6.45290i	−1.64541	−	0.248005i	−0.740017	−	0.672588i	$-0.765182\pi$
$677$	−42.8122	−	6.45290i	−1.64541	−	0.248005i	−0.905389	+	0.424584i	$0.860421\pi$
$678$		0			0
$679$	34.1872	−	2.61795i	1.31198	−	0.100468i
$680$	−3.62682	+	7.53117i	−0.139082	+	0.288807i
$681$		0			0
$682$	48.8459	−	52.6433i	1.87041	−	2.01582i
$683$	−42.8746	−	3.21301i	−1.64055	−	0.122942i	−0.777780	−	0.628537i	$-0.783654\pi$
$683$	−42.8746	−	3.21301i	−1.64055	−	0.122942i	−0.862771	+	0.505595i	$0.831273\pi$
$684$		0			0
$685$		−	2.85535i		−	0.109097i
$686$	−4.94954	+	33.9628i	−0.188974	+	1.29670i
$687$		0			0
$688$	−12.6983	+	32.3549i	−0.484120	+	1.23352i
$689$	−0.0972217	+	1.29733i	−0.00370385	+	0.0494245i
$690$		0			0
$691$	26.8099	−	39.3229i	1.01990	−	1.49591i	0.158907	−	0.987294i	$-0.449203\pi$
$691$	26.8099	−	39.3229i	1.01990	−	1.49591i	0.860991	−	0.508621i	$-0.169845\pi$
$692$	−17.9039	−	8.62208i	−0.680605	−	0.327762i
$693$		0			0
$694$	−4.40439	+	2.12104i	−0.167188	+	0.0805137i
$695$	2.39640	−	15.8991i	0.0909007	−	0.603086i
$696$		0			0
$697$	37.1085	−	5.59320i	1.40558	−	0.211858i
$698$	26.4268	−	24.5205i	1.00027	−	0.928115i
$699$		0			0
$700$	14.5649	+	4.46671i	0.550500	+	0.168826i
$701$	23.0987	+	18.4206i	0.872425	+	0.695736i	0.953636	−	0.300961i	$-0.0973074\pi$
$701$	23.0987	+	18.4206i	0.872425	+	0.695736i	−0.0812112	+	0.996697i	$0.525879\pi$
$702$		0			0
$703$	−0.859953	+	2.78790i	−0.0324338	+	0.105148i
$704$	−11.7296	−	6.77210i	−0.442076	−	0.255233i
$705$		0			0
$706$	31.4402	−	7.17601i	1.18327	−	0.270073i
$707$	0.267051		0.000434776i	0.0100435		1.63514e-5i
$708$		0			0
$709$	−44.0766	+	13.5958i	−1.65533	+	0.510602i	−0.974982	−	0.222285i	$-0.928648\pi$
$709$	−44.0766	+	13.5958i	−1.65533	+	0.510602i	−0.680350	+	0.732887i	$0.738172\pi$
$710$	1.47644	+	3.76190i	0.0554096	+	0.141181i
$711$		0			0
$712$	−1.90351	−	6.17102i	−0.0713369	−	0.231269i
$713$	14.4883	−	63.4775i	0.542592	−	2.37725i
$714$		0			0
$715$	0.623268	+	2.73071i	0.0233089	+	0.102123i
$716$	6.21419	−	3.58776i	0.232235	−	0.134081i
$717$		0			0
$718$	−11.7613	−	3.62787i	−0.438927	−	0.135391i
$719$	−2.85860	−	38.1454i	−0.106608	−	1.42258i	−0.752218	−	0.658914i	$-0.771016\pi$
$719$	−2.85860	−	38.1454i	−0.106608	−	1.42258i	0.645610	−	0.763667i	$-0.276603\pi$
$720$		0			0
$721$	1.09687	+	0.630897i	0.0408494	+	0.0234958i
$722$	27.2810	−	21.7558i	1.01529	−	0.809668i
$723$		0			0
$724$	−3.99801	−	26.5251i	−0.148585	−	0.985796i
$725$	−1.21386	−	1.78041i	−0.0450816	−	0.0661226i
$726$		0			0
$727$	−2.68945	−	5.58469i	−0.0997460	−	0.207125i	0.845124	−	0.534570i	$-0.179526\pi$
$727$	−2.68945	−	5.58469i	−0.0997460	−	0.207125i	−0.944870	+	0.327446i	$0.893812\pi$
$728$	−0.633904	+	1.62293i	−0.0234941	+	0.0601496i
$729$		0			0
$730$	3.93036	+	2.67968i	0.145469	+	0.0991792i
$731$	42.5347	+	39.4664i	1.57320	+	1.45972i
$732$		0			0
$733$	14.3982	+	5.65086i	0.531808	+	0.208719i	0.616023	−	0.787728i	$-0.288743\pi$
$733$	14.3982	+	5.65086i	0.531808	+	0.208719i	−0.0842147	+	0.996448i	$0.526838\pi$
$734$	−41.1676			−1.51952
$735$		0			0
$736$	−51.4665			−1.89708
$737$	−14.6565	−	5.75225i	−0.539879	−	0.211887i
$738$		0			0
$739$	−19.7284	−	18.3053i	−0.725720	−	0.673370i	0.228138	−	0.973629i	$-0.426736\pi$
$739$	−19.7284	−	18.3053i	−0.725720	−	0.673370i	−0.953858	+	0.300259i	$0.902927\pi$
$740$	8.29973	+	5.65866i	0.305104	+	0.208017i
$741$		0			0
$742$	5.09152	+	8.78570i	0.186916	+	0.322533i
$743$	−2.69592	−	5.59814i	−0.0989037	−	0.205376i	0.845646	−	0.533744i	$-0.179216\pi$
$743$	−2.69592	−	5.59814i	−0.0989037	−	0.205376i	−0.944550	+	0.328369i	$0.893501\pi$
$744$		0			0
$745$	−6.34162	−	9.30145i	−0.232339	−	0.340779i
$746$	−1.19293	−	7.91457i	−0.0436762	−	0.289773i
$747$		0			0
$748$	−40.4561	+	32.2627i	−1.47922	+	1.17964i
$749$	−0.641441	−	0.0470193i	−0.0234377	−	0.00171805i
$750$		0			0
$751$	0.320811	+	4.28092i	0.0117065	+	0.156213i	0.999993	+	0.00360597i	$0.00114782\pi$
$751$	0.320811	+	4.28092i	0.0117065	+	0.156213i	−0.988287	+	0.152607i	$0.951233\pi$
$752$	−29.2649	−	9.02701i	−1.06718	−	0.329181i
$753$		0			0
$754$	−0.541141	+	0.312428i	−0.0197072	+	0.0113780i
$755$	−1.58670	−	6.95179i	−0.0577459	−	0.253001i
$756$		0			0
$757$	−3.16549	+	13.8689i	−0.115052	+	0.504074i	0.884261	+	0.466994i	$0.154663\pi$
$757$	−3.16549	+	13.8689i	−0.115052	+	0.504074i	−0.999312	+	0.0370804i	$0.988194\pi$
$758$	15.7229	+	50.9724i	0.571082	+	1.85140i
$759$		0			0
$760$	−0.157232	−	0.400621i	−0.00570341	−	0.0145321i
$761$	21.2922	−	6.56776i	0.771840	−	0.238081i	0.116272	−	0.993217i	$-0.462905\pi$
$761$	21.2922	−	6.56776i	0.771840	−	0.238081i	0.655568	+	0.755136i	$0.272429\pi$
$762$		0			0
$763$	7.68834	+	33.4338i	0.278337	+	1.21039i
$764$	14.1697	−	3.23414i	0.512642	−	0.117007i
$765$		0			0
$766$	−44.6758	−	25.7936i	−1.61420	−	0.931960i
$767$	−2.29691	+	7.44639i	−0.0829366	+	0.268874i
$768$		0			0
$769$	15.8299	+	12.6239i	0.570841	+	0.455230i	0.865878	−	0.500255i	$-0.166761\pi$
$769$	15.8299	+	12.6239i	0.570841	+	0.455230i	−0.295037	+	0.955486i	$0.595332\pi$
$770$	16.0502	+	14.8439i	0.578410	+	0.534936i
$771$		0			0
$772$	−9.79304	+	9.08662i	−0.352459	+	0.327034i
$773$	−34.2387	+	5.16066i	−1.23148	+	0.185616i	−0.732361	−	0.680917i	$-0.761582\pi$
$773$	−34.2387	+	5.16066i	−1.23148	+	0.185616i	−0.499120	+	0.866533i	$0.666343\pi$
$774$		0			0
$775$	−5.16218	+	34.2488i	−0.185431	+	1.23025i
$776$	12.2404	−	5.89465i	0.439404	−	0.211606i
$777$		0			0
$778$	−42.2017	−	20.3233i	−1.51300	−	0.728624i
$779$	−1.08842	+	1.59642i	−0.0389967	+	0.0571976i
$780$		0			0
$781$	0.737342	−	9.83915i	0.0263842	−	0.352072i
$782$	−41.0398	+	104.568i	−1.46758	+	3.73933i
$783$		0			0
$784$	7.60130	+	32.8107i	0.271475	+	1.17181i
$785$		−	14.7527i		−	0.526548i
$786$		0			0
$787$	20.7770	+	1.55702i	0.740621	+	0.0555019i	0.439697	−	0.898146i	$-0.355086\pi$
$787$	20.7770	+	1.55702i	0.740621	+	0.0555019i	0.300924	+	0.953648i	$0.402705\pi$
$788$	−8.51832	+	9.18057i	−0.303453	+	0.327044i
$789$		0			0
$790$	10.9390	−	22.7150i	0.389191	−	0.808163i
$791$	−1.48531	+	2.18619i	−0.0528117	+	0.0777321i
$792$		0			0
$793$	2.99638	+	0.451632i	0.106405	+	0.0160379i
$794$	7.40080	−	5.04578i	0.262644	−	0.179068i
$795$		0			0
$796$	−10.7647	−	11.6016i	−0.381544	−	0.411207i
$797$	−2.48670	−	3.11822i	−0.0880834	−	0.110453i	0.735837	−	0.677159i	$-0.236789\pi$
$797$	−2.48670	−	3.11822i	−0.0880834	−	0.110453i	−0.823920	+	0.566706i	$0.808218\pi$
$798$		0			0
$799$	−31.8766	+	39.9719i	−1.12771	+	1.41411i
$800$	27.3014	−	2.04595i	0.965249	−	0.0723354i
$801$		0			0
$802$	−3.74322	+	6.48344i	−0.132178	+	0.228938i
$803$	−5.80704	−	10.0581i	−0.204926	−	0.354942i
$804$		0			0
$805$	19.3314	+	4.37916i	0.681342	+	0.154345i
$806$	9.79180	+	2.23491i	0.344902	+	0.0787215i
$807$		0			0
$808$	0.0985003	−	0.0386585i	0.00346523	−	0.00136000i
$809$	−7.80390	+	3.06281i	−0.274371	+	0.107683i	−0.498537	−	0.866868i	$-0.666129\pi$
$809$	−7.80390	+	3.06281i	−0.274371	+	0.107683i	0.224167	+	0.974551i	$0.428034\pi$
$810$		0			0
$811$	−12.6949	−	2.89753i	−0.445779	−	0.101746i	−0.00626183	−	0.999980i	$-0.501993\pi$
$811$	−12.6949	−	2.89753i	−0.445779	−	0.101746i	−0.439517	+	0.898234i	$0.644850\pi$
$812$	−0.880790	+	1.83662i	−0.0309097	+	0.0644528i
$813$		0			0
$814$	−29.3618	−	50.8562i	−1.02913	−	1.78251i
$815$	−6.04349	+	10.4676i	−0.211694	+	0.366665i
$816$		0			0
$817$	−2.97908	+	0.223251i	−0.104225	+	0.00781058i
$818$	−9.78053	+	12.2644i	−0.341968	+	0.428814i
$819$		0			0
$820$	4.14778	+	5.20115i	0.144847	+	0.181632i
$821$	1.00421	+	1.08228i	0.0350473	+	0.0377720i	0.750332	−	0.661061i	$-0.229894\pi$
$821$	1.00421	+	1.08228i	0.0350473	+	0.0377720i	−0.715285	+	0.698833i	$0.753703\pi$
$822$		0			0
$823$	6.68392	−	4.55702i	0.232987	−	0.158848i	−0.441200	−	0.897409i	$-0.645447\pi$
$823$	6.68392	−	4.55702i	0.232987	−	0.158848i	0.674186	+	0.738561i	$0.264495\pi$
$824$	0.495780	+	0.0747269i	0.0172713	+	0.00260323i
$825$		0			0
$826$	18.0226	+	58.0918i	0.627085	+	2.02127i
$827$	−4.18745	+	8.69534i	−0.145612	+	0.302367i	−0.961000	−	0.276548i	$-0.910809\pi$
$827$	−4.18745	+	8.69534i	−0.145612	+	0.302367i	0.815388	+	0.578915i	$0.196524\pi$
$828$		0			0
$829$	−23.6459	+	25.4843i	−0.821257	+	0.885105i	−0.995019	−	0.0996828i	$-0.968217\pi$
$829$	−23.6459	+	25.4843i	−0.821257	+	0.885105i	0.173762	+	0.984788i	$0.444408\pi$
$830$	18.7324	+	1.40380i	0.650209	+	0.0487265i
$831$		0			0
$832$		−	1.89424i		−	0.0656709i
$833$	55.6237	+	8.19878i	1.92725	+	0.284071i
$834$		0			0
$835$	−0.221836	+	0.565229i	−0.00767695	+	0.0195606i
$836$	0.199093	−	2.65672i	0.00688579	−	0.0918844i
$837$		0			0
$838$	30.1169	−	44.1734i	1.04037	−	1.52594i
$839$	17.9886	+	8.66283i	0.621034	+	0.299074i	0.717817	−	0.696231i	$-0.245141\pi$
$839$	17.9886	+	8.66283i	0.621034	+	0.299074i	−0.0967837	+	0.995305i	$0.530856\pi$
$840$		0			0
$841$	−25.8685	+	12.4576i	−0.892018	+	0.429573i
$842$	−8.84017	+	58.6507i	−0.304652	+	2.02124i
$843$		0			0
$844$	3.60809	−	0.543832i	0.124196	−	0.0187195i
$845$	9.17305	−	8.51135i	0.315563	−	0.292799i
$846$		0			0
$847$	−8.90472	−	22.5807i	−0.305970	−	0.775882i
$848$	7.79057	+	6.21277i	0.267529	+	0.213347i
$849$		0			0
$850$	17.6134	−	57.1014i	0.604136	−	1.95856i
$851$	−46.1087	−	26.6209i	−1.58059	−	0.912551i
$852$		0			0
$853$	12.1711	−	2.77797i	0.416730	−	0.0951160i	−0.00901424	−	0.999959i	$-0.502869\pi$
$853$	12.1711	−	2.77797i	0.416730	−	0.0951160i	0.425745	+	0.904843i	$0.360012\pi$
$854$	21.2927	−	10.2968i	0.728622	−	0.352348i
$855$		0			0
$856$	−0.243521	+	0.0751162i	−0.00832337	+	0.00256742i
$857$	−10.6036	−	27.0176i	−0.362213	−	0.922905i	−0.989554	−	0.144160i	$-0.953952\pi$
$857$	−10.6036	−	27.0176i	−0.362213	−	0.922905i	0.627341	−	0.778745i	$-0.284143\pi$
$858$		0			0
$859$	−13.2901	−	43.0854i	−0.453452	−	1.47005i	−0.837344	−	0.546676i	$-0.815893\pi$
$859$	−13.2901	−	43.0854i	−0.453452	−	1.47005i	0.383892	−	0.923378i	$-0.374583\pi$
$860$	−2.28884	+	10.0280i	−0.0780487	+	0.341954i
$861$		0			0
$862$	10.8473	+	47.5250i	0.369460	+	1.61871i
$863$	−31.4136	+	18.1366i	−1.06933	+	0.617378i	−0.927998	−	0.372584i	$-0.878472\pi$
$863$	−31.4136	+	18.1366i	−1.06933	+	0.617378i	−0.141332	+	0.989962i	$0.545138\pi$
$864$		0			0
$865$	13.1427	+	4.05397i	0.446864	+	0.137839i
$866$	−2.18379	−	29.1406i	−0.0742080	−	0.990238i
$867$		0			0
$868$	30.4574	−	12.0109i	1.03379	−	0.407677i
$869$	−48.1253	+	38.3787i	−1.63254	+	1.30191i
$870$		0			0
$871$	−0.328194	−	2.17742i	−0.0111204	−	0.0737791i
$872$	7.65743	+	11.2314i	0.259313	+	0.380343i
$873$		0			0
$874$	−2.50940	−	5.21083i	−0.0848818	−	0.176259i
$875$	−23.4176	−	3.49066i	−0.791660	−	0.118006i
$876$		0			0
$877$	−37.7445	−	25.7338i	−1.27454	−	0.868968i	−0.278728	−	0.960370i	$-0.589913\pi$
$877$	−37.7445	−	25.7338i	−1.27454	−	0.868968i	−0.995814	+	0.0914022i	$0.970865\pi$
$878$	15.8057	+	14.6655i	0.533416	+	0.494938i
$879$		0			0
$880$	19.9702	+	7.83773i	0.673196	+	0.264210i
$881$	23.9043			0.805355			0.402677	−	0.915342i	$-0.368080\pi$
$881$	23.9043			0.805355			0.402677	+	0.915342i	$0.368080\pi$
$882$		0			0
$883$	41.9735			1.41252			0.706261	−	0.707952i	$-0.250381\pi$
$883$	41.9735			1.41252			0.706261	+	0.707952i	$0.250381\pi$
$884$	−6.73663	−	2.64393i	−0.226577	−	0.0889251i
$885$		0			0
$886$	−2.07835	−	1.92843i	−0.0698235	−	0.0647867i
$887$	24.2880	+	16.5592i	0.815510	+	0.556005i	0.897698	−	0.440612i	$-0.145238\pi$
$887$	24.2880	+	16.5592i	0.815510	+	0.556005i	−0.0821881	+	0.996617i	$0.526191\pi$
$888$		0			0
$889$	−38.0258	+	11.7972i	−1.27535	+	0.395667i
$890$	−4.91709	−	10.2104i	−0.164821	−	0.342254i
$891$		0			0
$892$	−16.6878	−	24.4765i	−0.558749	−	0.819534i
$893$	−0.392321	−	2.60288i	−0.0131285	−	0.0871021i
$894$		0			0
$895$	−3.88283	+	3.09645i	−0.129789	+	0.103503i
$896$	12.0282	+	17.5806i	0.401834	+	0.587326i
$897$		0			0
$898$	−2.71216	−	36.1912i	−0.0905059	−	1.20772i
$899$	−4.42519	−	1.36499i	−0.147589	−	0.0455250i
$900$		0			0
$901$	14.4061	−	8.31736i	0.479936	−	0.277091i
$902$	−8.65390	−	37.9152i	−0.288143	−	1.26244i
$903$		0			0
$904$	−0.233037	+	1.02100i	−0.00775069	+	0.0339580i
$905$	5.47238	+	17.7410i	0.181908	+	0.589732i
$906$		0			0
$907$	9.77804	+	24.9140i	0.324675	+	0.827257i	0.996266	+	0.0863356i	$0.0275157\pi$
$907$	9.77804	+	24.9140i	0.324675	+	0.827257i	−0.671592	+	0.740922i	$0.734389\pi$
$908$	−7.01507	+	2.16386i	−0.232803	+	0.0718103i
$909$		0			0
$910$	−0.675513	+	2.98199i	−0.0223930	+	0.0988519i
$911$	43.4725	−	9.92232i	1.44031	−	0.328741i	0.570161	−	0.821533i	$-0.306881\pi$
$911$	43.4725	−	9.92232i	1.44031	−	0.328741i	0.870147	+	0.492792i	$0.164023\pi$
$912$		0			0
$913$	−39.7188	−	22.9317i	−1.31450	−	0.758928i
$914$	−17.7405	+	57.5133i	−0.586803	+	1.90237i
$915$		0			0
$916$	−19.2829	−	15.3776i	−0.637126	−	0.508091i
$917$	54.8077	−	8.35221i	1.80991	−	0.275814i
$918$		0			0
$919$	2.19981	−	2.04113i	0.0725652	−	0.0673306i	−0.643057	−	0.765819i	$-0.722334\pi$
$919$	2.19981	−	2.04113i	0.0725652	−	0.0673306i	0.715622	+	0.698488i	$0.246143\pi$
$920$	7.76612	−	1.17055i	0.256041	−	0.0385920i
$921$		0			0
$922$	−3.68965	+	24.4792i	−0.121512	+	0.806181i
$923$	1.24327	−	0.598726i	0.0409227	−	0.0197073i
$924$		0			0
$925$	25.5175	+	12.2886i	0.839010	+	0.404046i
$926$	−13.4222	+	19.6868i	−0.441082	+	0.646949i
$927$		0			0
$928$	−0.273553	+	3.65031i	−0.00897981	+	0.119827i
$929$	−0.149790	+	0.381659i	−0.00491446	+	0.0125218i	−0.933310	−	0.359072i	$-0.883093\pi$
$929$	−0.149790	+	0.381659i	−0.00491446	+	0.0125218i	0.928395	+	0.371594i	$0.121189\pi$
$930$		0			0
$931$	−2.25735	+	1.81223i	−0.0739817	+	0.0593936i
$932$			4.48069i			0.146770i
$933$		0			0
$934$	8.09189	+	0.606403i	0.264775	+	0.0198421i
$935$	24.3596	−	26.2534i	0.796645	−	0.858579i
$936$		0			0
$937$	9.13163	−	18.9620i	0.298317	−	0.619462i	−0.696898	−	0.717170i	$-0.745437\pi$
$937$	9.13163	−	18.9620i	0.298317	−	0.619462i	0.995215	+	0.0977083i	$0.0311512\pi$
$938$	−11.7108	−	12.5801i	−0.382372	−	0.410756i
$939$		0			0
$940$	−8.96189	−	1.35079i	−0.292305	−	0.0440578i
$941$	36.2793	−	24.7348i	1.18267	−	0.806332i	0.197906	−	0.980221i	$-0.436586\pi$
$941$	36.2793	−	24.7348i	1.18267	−	0.806332i	0.984765	+	0.173889i	$0.0556335\pi$
$942$		0			0
$943$	−23.9828	−	25.8473i	−0.780986	−	0.841703i
$944$	37.2134	+	46.6642i	1.21119	+	1.51879i
$945$		0			0
$946$	37.4911	−	47.0123i	1.21894	−	1.52850i
$947$	−6.23216	+	0.467036i	−0.202518	+	0.0151766i	−0.175603	−	0.984461i	$-0.556187\pi$
$947$	−6.23216	+	0.467036i	−0.202518	+	0.0151766i	−0.0269152	+	0.999638i	$0.508568\pi$
$948$		0			0
$949$	0.812149	−	1.40668i	0.0263635	−	0.0456629i
$950$	1.53831	+	2.66443i	0.0499093	+	0.0864454i
$951$		0			0
$952$	21.7115	−	4.99271i	0.703673	−	0.161815i
$953$	52.5111	+	11.9853i	1.70100	+	0.388243i	0.959278	−	0.282463i	$-0.0911515\pi$
$953$	52.5111	+	11.9853i	1.70100	+	0.388243i	0.741724	+	0.670706i	$0.234009\pi$
$954$		0			0
$955$	−9.36397	+	3.67509i	−0.303011	+	0.118923i
$956$	31.4138	−	12.3290i	1.01600	−	0.398749i
$957$		0			0
$958$	−38.2808	−	8.73735i	−1.23680	−	0.282291i
$959$	−5.94202	+	4.75445i	−0.191878	+	0.153529i
$960$		0			0
$961$	21.7176	+	37.6161i	0.700569	+	1.21342i
$962$	4.10643	−	7.11255i	0.132397	−	0.229318i
$963$		0			0
$964$	6.33490	−	0.474735i	0.204033	−	0.0152902i
$965$	5.76492	−	7.22898i	0.185579	−	0.232709i
$966$		0			0
$967$	−20.1564	−	25.2754i	−0.648187	−	0.812801i	0.343813	−	0.939038i	$-0.388281\pi$
$967$	−20.1564	−	25.2754i	−0.648187	−	0.812801i	−0.992000	+	0.126237i	$0.959710\pi$
$968$	−6.54178	−	7.05036i	−0.210261	−	0.226607i
$969$		0			0
$970$	19.6984	−	13.4302i	0.632479	−	0.431217i
$971$	−33.4042	−	5.03488i	−1.07199	−	0.161577i	−0.410750	−	0.911748i	$-0.634733\pi$
$971$	−33.4042	−	5.03488i	−1.07199	−	0.161577i	−0.661244	+	0.750171i	$0.729971\pi$
$972$		0			0
$973$	−37.0764	+	21.4866i	−1.18862	+	0.688830i
$974$	−7.86321	+	16.3281i	−0.251953	+	0.523187i
$975$		0			0
$976$	15.7864	−	17.0137i	0.505310	−	0.544595i
$977$	−12.6219	−	0.945882i	−0.403811	−	0.0302615i	−0.128723	−	0.991681i	$-0.541088\pi$
$977$	−12.6219	−	0.945882i	−0.403811	−	0.0302615i	−0.275088	+	0.961419i	$0.588707\pi$
$978$		0			0
$979$			27.6689i			0.884302i
$980$	3.67153	+	9.26607i	0.117283	+	0.295994i
$981$		0			0
$982$	−16.0862	+	40.9869i	−0.513330	+	1.30794i
$983$	−2.51842	+	33.6060i	−0.0803252	+	1.07186i	0.800784	+	0.598953i	$0.204416\pi$
$983$	−2.51842	+	33.6060i	−0.0803252	+	1.07186i	−0.881110	+	0.472912i	$0.843203\pi$
$984$		0			0
$985$	4.88282	−	7.16178i	0.155580	−	0.228193i
$986$	7.19842	+	3.46658i	0.229245	+	0.110398i
$987$		0			0
$988$	0.335701	−	0.161665i	0.0106801	−	0.00514325i
$989$	8.12544	−	53.9088i	0.258374	−	1.71420i
$990$		0			0
$991$	−53.5331	+	8.06882i	−1.70053	+	0.256314i	−0.926355	−	0.376652i	$-0.877075\pi$
$991$	−53.5331	+	8.06882i	−1.70053	+	0.256314i	−0.774180	+	0.632966i	$0.781837\pi$
$992$	43.1311	−	40.0198i	1.36941	−	1.27063i
$993$		0			0
$994$	5.37014	−	9.33642i	0.170330	−	0.296133i
$995$	8.56399	+	6.82956i	0.271497	+	0.216511i
$996$		0			0
$997$	4.61763	−	14.9700i	0.146242	−	0.474104i	−0.852582	−	0.522594i	$-0.824964\pi$
$997$	4.61763	−	14.9700i	0.146242	−	0.474104i	0.998824	+	0.0484893i	$0.0154407\pi$
$998$	−34.5901	−	19.9706i	−1.09493	−	0.632158i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.395.4	yes	216
3.2	odd	2	inner	441.2.bg.a.395.15	yes	216
49.33	odd	42	inner	441.2.bg.a.278.15	yes	216
147.131	even	42	inner	441.2.bg.a.278.4	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.278.4	✓	216	147.131	even	42	inner
441.2.bg.a.278.15	yes	216	49.33	odd	42	inner
441.2.bg.a.395.4	yes	216	1.1	even	1	trivial
441.2.bg.a.395.15	yes	216	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72508 - 0.677046i) q^{2} +(1.05142 + 0.975576i) q^{4} +(-0.820216 - 0.559214i) q^{5} +(0.202012 + 2.63803i) q^{7} +(0.454856 + 0.944519i) q^{8} +O(q^{10})\)	\(q+(-1.72508 - 0.677046i) q^{2} +(1.05142 + 0.975576i) q^{4} +(-0.820216 - 0.559214i) q^{5} +(0.202012 + 2.63803i) q^{7} +(0.454856 + 0.944519i) q^{8} +(1.03633 + 1.52001i) q^{10} +(-0.669436 - 4.44142i) q^{11} +(0.491128 - 0.391661i) q^{13} +(1.43758 - 4.68759i) q^{14} +(-0.359555 - 4.79792i) q^{16} +(-7.67525 - 2.36750i) q^{17} +(0.358138 - 0.206771i) q^{19} +(-0.316837 - 1.38815i) q^{20} +(-1.85221 + 8.11506i) q^{22} +(2.22443 + 7.21144i) q^{23} +(-1.46667 - 3.73702i) q^{25} +(-1.11241 + 0.343133i) q^{26} +(-2.36120 + 2.97076i) q^{28} +(0.523301 - 0.119440i) q^{29} +(-7.47171 - 4.31379i) q^{31} +(-2.01015 + 6.51673i) q^{32} +(11.6376 + 9.28064i) q^{34} +(1.30953 - 2.27672i) q^{35} +(-5.17164 + 4.79859i) q^{37} +(-0.757811 + 0.114222i) q^{38} +(0.155108 - 1.02907i) q^{40} +(-4.20951 + 2.02719i) q^{41} +(-6.50862 - 3.13439i) q^{43} +(3.62908 - 5.32289i) q^{44} +(1.04514 - 13.9464i) q^{46} +(2.32547 - 5.92521i) q^{47} +(-6.91838 + 1.06583i) q^{49} +7.43967i q^{50} +(0.898477 + 0.0673315i) q^{52} +(-1.40866 + 1.51817i) q^{53} +(-1.93462 + 4.01728i) q^{55} +(-2.39978 + 1.39073i) q^{56} +(-0.983605 - 0.148255i) q^{58} +(-10.2496 + 6.98805i) q^{59} +(3.28105 + 3.53613i) q^{61} +(9.96870 + 12.5003i) q^{62} +(1.88011 - 2.35758i) q^{64} +(-0.621853 + 0.0466015i) q^{65} +(1.75271 - 3.03578i) q^{67} +(-5.76024 - 9.97704i) q^{68} +(-3.80049 + 3.04093i) q^{70} +(2.14164 + 0.488815i) q^{71} +(2.40700 - 0.944676i) q^{73} +(12.1704 - 4.77652i) q^{74} +(0.578274 + 0.131987i) q^{76} +(11.5814 - 2.66321i) q^{77} +(-6.85221 - 11.8684i) q^{79} +(-2.38815 + 4.13640i) q^{80} +(8.63426 - 0.647049i) q^{82} +(6.36642 - 7.98324i) q^{83} +(4.97143 + 6.23397i) q^{85} +(9.10580 + 9.81371i) q^{86} +(3.89051 - 2.65250i) q^{88} +(-6.09136 - 0.918124i) q^{89} +(1.13243 + 1.21649i) q^{91} +(-4.69649 + 9.75236i) q^{92} +(-8.02328 + 8.64704i) q^{94} +(-0.409380 - 0.0306788i) q^{95} -12.9594i q^{97} +(12.6564 + 2.84542i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more