LMFDB - Embedded newform 201.2.p.a.95.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(2,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 1]))

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

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

chi := DirichletCharacter("201.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.p (of order $66$, degree $20$, 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:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 $ x^20 - x^19 + x^17 - x^16 + x^14 - x^13 + x^11 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{66}]$

Embedding invariants

Embedding label			95.1
Root			$0.981929 - 0.189251i$ of defining polynomial
Character	$\chi$	$=$	201.95
Dual form			201.2.p.a.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30900 - 1.13425i) q^{3} +(-1.44747 + 1.38016i) q^{4} +(2.75125 - 3.49850i) q^{7} +(0.426945 - 2.96946i) q^{9} +O(q^{10})$	$q+(1.30900 - 1.13425i) q^{3} +(-1.44747 + 1.38016i) q^{4} +(2.75125 - 3.49850i) q^{7} +(0.426945 - 2.96946i) q^{9} +(-0.329284 + 3.44842i) q^{12} +(5.44320 + 3.87609i) q^{13} +(0.190328 - 3.99547i) q^{16} +(-6.17592 + 4.85680i) q^{19} +(-0.366802 - 7.70013i) q^{21} +(-2.07708 - 4.54816i) q^{25} +(-2.80925 - 4.37128i) q^{27} +(0.846134 + 8.86112i) q^{28} +(-9.01732 + 6.42120i) q^{31} +(3.48034 + 4.88746i) q^{36} +(1.07398 + 1.86019i) q^{37} +(11.5216 - 1.10018i) q^{39} +(2.70035 + 9.19655i) q^{43} +(-4.28273 - 5.44594i) q^{48} +(-3.01980 - 12.4478i) q^{49} +(-13.2285 + 1.90197i) q^{52} +(-2.57543 + 13.3626i) q^{57} +(-1.90324 + 3.69176i) q^{61} +(-9.21403 - 9.66339i) q^{63} +(5.23889 + 6.04600i) q^{64} +(-8.12842 + 0.963760i) q^{67} +(11.8792 + 6.12415i) q^{73} +(-7.87764 - 3.59760i) q^{75} +(2.23630 - 15.5538i) q^{76} +(1.26474 - 13.2449i) q^{79} +(-8.63544 - 2.53559i) q^{81} +(11.1583 + 10.6394i) q^{84} +(28.5361 - 8.37895i) q^{91} +(-4.52038 + 18.6332i) q^{93} +(15.3823 - 8.88100i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9}+O(q^{10}) $ 20 * q - 2 * q^4 - 6 * q^7 + 6 * q^9	$ 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9} - 6 q^{12} - 3 q^{13} + 4 q^{16} - 8 q^{19} + 6 q^{21} + 10 q^{25} - 12 q^{28} + 15 q^{31} + 6 q^{36} + 10 q^{37} - 3 q^{39} - 12 q^{48} - 5 q^{49} - 154 q^{52} - 75 q^{57} + 15 q^{61} - 15 q^{63} + 16 q^{64} + 5 q^{67} + 60 q^{73} - 32 q^{76} + 134 q^{79} - 18 q^{81} + 186 q^{84} - 12 q^{91} - 15 q^{93} + 9 q^{97}+O(q^{100}) $ 20 * q - 2 * q^4 - 6 * q^7 + 6 * q^9 - 6 * q^12 - 3 * q^13 + 4 * q^16 - 8 * q^19 + 6 * q^21 + 10 * q^25 - 12 * q^28 + 15 * q^31 + 6 * q^36 + 10 * q^37 - 3 * q^39 - 12 * q^48 - 5 * q^49 - 154 * q^52 - 75 * q^57 + 15 * q^61 - 15 * q^63 + 16 * q^64 + 5 * q^67 + 60 * q^73 - 32 * q^76 + 134 * q^79 - 18 * q^81 + 186 * q^84 - 12 * q^91 - 15 * q^93 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$e\left(\frac{25}{66}\right)$

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			0		−0.371662	−	0.928368i	$-0.621212\pi$
$2$		0			0		0.371662	+	0.928368i	$0.378788\pi$
$3$	1.30900	−	1.13425i	0.755750	−	0.654861i
$3$	1.30900	−	1.13425i	0.755750	−	0.654861i
$4$	−1.44747	+	1.38016i	−0.723734	+	0.690079i
$5$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$5$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$6$		0			0
$7$	2.75125	−	3.49850i	1.03987	−	1.32231i	0.0947833	−	0.995498i	$-0.469784\pi$
$7$	2.75125	−	3.49850i	1.03987	−	1.32231i	0.945090	−	0.326809i	$-0.105973\pi$
$8$		0			0
$9$	0.426945	−	2.96946i	0.142315	−	0.989821i
$10$		0			0
$11$		0			0		−0.458227	−	0.888835i	$-0.651515\pi$
$11$		0			0		0.458227	+	0.888835i	$0.348485\pi$
$12$	−0.329284	+	3.44842i	−0.0950560	+	0.995472i
$13$	5.44320	+	3.87609i	1.50967	+	1.07503i	0.972878	+	0.231321i	$0.0743047\pi$
$13$	5.44320	+	3.87609i	1.50967	+	1.07503i	0.536795	+	0.843712i	$0.319635\pi$
$14$		0			0
$15$		0			0
$16$	0.190328	−	3.99547i	0.0475819	−	0.998867i
$17$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$17$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$18$		0			0
$19$	−6.17592	+	4.85680i	−1.41685	+	1.11423i	−0.440574	+	0.897716i	$0.645225\pi$
$19$	−6.17592	+	4.85680i	−1.41685	+	1.11423i	−0.976280	+	0.216510i	$0.930533\pi$
$20$		0			0
$21$	−0.366802	−	7.70013i	−0.0800428	−	1.68031i
$22$		0			0
$23$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$23$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$24$		0			0
$25$	−2.07708	−	4.54816i	−0.415415	−	0.909632i
$26$		0			0
$27$	−2.80925	−	4.37128i	−0.540641	−	0.841254i
$28$	0.846134	+	8.86112i	0.159904	+	1.67459i
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$		0			0
$31$	−9.01732	+	6.42120i	−1.61956	+	1.15328i	−0.746922	+	0.664912i	$0.768469\pi$
$31$	−9.01732	+	6.42120i	−1.61956	+	1.15328i	−0.872636	+	0.488371i	$0.837591\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	3.48034	+	4.88746i	0.580057	+	0.814576i
$37$	1.07398	+	1.86019i	0.176562	+	0.305814i	0.940701	−	0.339238i	$-0.110169\pi$
$37$	1.07398	+	1.86019i	0.176562	+	0.305814i	−0.764139	+	0.645052i	$0.776836\pi$
$38$		0			0
$39$	11.5216	−	1.10018i	1.84493	−	0.176170i
$40$		0			0
$41$		0			0		−0.971812	−	0.235759i	$-0.924242\pi$
$41$		0			0		0.971812	+	0.235759i	$0.0757576\pi$
$42$		0			0
$43$	2.70035	+	9.19655i	0.411800	+	1.40246i	0.860807	+	0.508932i	$0.169960\pi$
$43$	2.70035	+	9.19655i	0.411800	+	1.40246i	−0.449007	+	0.893528i	$0.648222\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$47$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$48$	−4.28273	−	5.44594i	−0.618159	−	0.786053i
$49$	−3.01980	−	12.4478i	−0.431400	−	1.77825i
$50$		0			0
$51$		0			0
$52$	−13.2285	+	1.90197i	−1.83446	+	0.263755i
$53$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$53$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.57543	+	13.3626i	−0.341124	+	1.76992i
$58$		0			0
$59$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$59$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$60$		0			0
$61$	−1.90324	+	3.69176i	−0.243684	+	0.472682i	−0.978680	−	0.205390i	$-0.934154\pi$
$61$	−1.90324	+	3.69176i	−0.243684	+	0.472682i	0.734996	+	0.678072i	$0.237184\pi$
$62$		0			0
$63$	−9.21403	−	9.66339i	−1.16086	−	1.21747i
$64$	5.23889	+	6.04600i	0.654861	+	0.755750i
$65$		0			0
$66$		0			0
$67$	−8.12842	+	0.963760i	−0.993044	+	0.117742i
$67$	−8.12842	+	0.963760i	−0.993044	+	0.117742i
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$71$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$72$		0			0
$73$	11.8792	+	6.12415i	1.39035	+	0.716777i	0.980710	−	0.195468i	$-0.0626226\pi$
$73$	11.8792	+	6.12415i	1.39035	+	0.716777i	0.409644	+	0.912245i	$0.365653\pi$
$74$		0			0
$75$	−7.87764	−	3.59760i	−0.909632	−	0.415415i
$76$	2.23630	−	15.5538i	0.256521	−	1.78414i
$77$		0			0
$78$		0			0
$79$	1.26474	−	13.2449i	0.142294	−	1.49017i	−0.589013	−	0.808124i	$-0.700483\pi$
$79$	1.26474	−	13.2449i	0.142294	−	1.49017i	0.731307	−	0.682048i	$-0.238911\pi$
$80$		0			0
$81$	−8.63544	−	2.53559i	−0.959493	−	0.281733i
$82$		0			0
$83$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$83$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$84$	11.1583	+	10.6394i	1.21747	+	1.16086i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$89$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$90$		0			0
$91$	28.5361	−	8.37895i	2.99139	−	0.878352i
$92$		0			0
$93$	−4.52038	+	18.6332i	−0.468741	+	1.93218i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	15.3823	−	8.88100i	1.56184	−	0.901729i	0.564769	−	0.825249i	$-0.308965\pi$
$97$	15.3823	−	8.88100i	1.56184	−	0.901729i	0.997071	−	0.0764798i	$-0.0243681\pi$
$98$		0			0
$99$		0			0
$100$	9.28368	+	3.71662i	0.928368	+	0.371662i
$101$		0			0		0.371662	−	0.928368i	$-0.378788\pi$
$101$		0			0		−0.371662	+	0.928368i	$0.621212\pi$
$102$		0			0
$103$	−0.337909	−	0.474527i	−0.0332952	−	0.0467566i	0.797593	−	0.603196i	$-0.206106\pi$
$103$	−0.337909	−	0.474527i	−0.0332952	−	0.0467566i	−0.830888	+	0.556440i	$0.812167\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$107$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$108$	10.0994	+	2.45008i	0.971812	+	0.235759i
$109$	−0.917603	+	0.419055i	−0.0878904	+	0.0401382i	−0.458875	−	0.888501i	$-0.651747\pi$
$109$	−0.917603	+	0.419055i	−0.0878904	+	0.0401382i	0.370985	+	0.928639i	$0.379020\pi$
$110$		0			0
$111$	3.51577	+	1.21682i	0.333702	+	0.115495i
$112$	−13.4545	−	11.6584i	−1.27133	−	1.10161i
$113$		0			0		0.998867	−	0.0475819i	$-0.0151515\pi$
$113$		0			0		−0.998867	+	0.0475819i	$0.984848\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	13.8338	−	14.5085i	1.27894	−	1.34131i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−6.38063	+	8.96034i	−0.580057	+	0.814576i
$122$		0			0
$123$		0			0
$124$	4.19001	−	21.7398i	0.376274	−	1.95229i
$125$		0			0
$126$		0			0
$127$	−16.4264	−	12.9178i	−1.45761	−	1.14627i	−0.960394	−	0.278644i	$-0.910115\pi$
$127$	−16.4264	−	12.9178i	−1.45761	−	1.14627i	−0.497211	−	0.867630i	$-0.665643\pi$
$128$		0			0
$129$	13.9660	+	8.97537i	1.22963	+	0.790237i
$130$		0			0
$131$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$131$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$132$		0			0
$133$			34.9687i			3.03217i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$137$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$138$		0			0
$139$	−5.11178	+	7.95408i	−0.433575	+	0.674656i	−0.987448	−	0.157945i	$-0.949513\pi$
$139$	−5.11178	+	7.95408i	−0.433575	+	0.674656i	0.553873	+	0.832601i	$0.313149\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−11.7831	−	2.27101i	−0.981929	−	0.189251i
$145$		0			0
$146$		0			0
$147$	−18.0718	−	12.8689i	−1.49054	−	1.06141i
$148$	−4.12192	−	1.21030i	−0.338819	−	0.0994863i
$149$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$149$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$150$		0			0
$151$	−5.46858	−	5.21428i	−0.445027	−	0.424332i	0.434141	−	0.900845i	$-0.357052\pi$
$151$	−5.46858	−	5.21428i	−0.445027	−	0.424332i	−0.879167	+	0.476513i	$0.841901\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−15.1587	+	17.4941i	−1.21367	+	1.40065i
$157$	7.38044	−	21.3244i	0.589023	−	1.70187i	−0.116506	−	0.993190i	$-0.537169\pi$
$157$	7.38044	−	21.3244i	0.589023	−	1.70187i	0.705529	−	0.708681i	$-0.250709\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	5.47183	−	9.47748i	0.428587	−	0.742334i	−0.568161	−	0.822917i	$-0.692345\pi$
$163$	5.47183	−	9.47748i	0.428587	−	0.742334i	0.996748	+	0.0805835i	$0.0256784\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$167$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$168$		0			0
$169$	10.3525	+	29.9117i	0.796348	+	2.30090i
$170$		0			0
$171$	11.7853	+	20.4128i	0.901246	+	1.56100i
$172$	−16.6014	−	9.58480i	−1.26584	−	0.730834i
$173$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$173$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$174$		0			0
$175$	−21.6263	−	5.24647i	−1.63479	−	0.396596i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$179$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$180$		0			0
$181$	−14.7789	+	2.84841i	−1.09851	+	0.211720i	−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−14.7789	+	2.84841i	−1.09851	+	0.211720i	−0.392380	+	0.919803i	$0.628348\pi$
$182$		0			0
$183$	1.69606	+	6.99126i	0.125376	+	0.516809i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−23.0219	−	2.19832i	−1.67459	−	0.159904i
$190$		0			0
$191$		0			0		0.189251	−	0.981929i	$-0.439394\pi$
$191$		0			0		−0.189251	+	0.981929i	$0.560606\pi$
$192$	13.7154	+	1.97197i	0.989821	+	0.142315i
$193$	5.05001	−	11.0580i	0.363508	−	0.795971i	−0.636193	−	0.771530i	$-0.719492\pi$
$193$	5.05001	−	11.0580i	0.363508	−	0.795971i	0.999701	−	0.0244416i	$-0.00778076\pi$
$194$		0			0
$195$		0			0
$196$	21.5510	+	13.8500i	1.53935	+	0.989282i
$197$		0			0		−0.690079	−	0.723734i	$-0.742424\pi$
$197$		0			0		0.690079	+	0.723734i	$0.257576\pi$
$198$		0			0
$199$	3.00308	−	1.20225i	0.212883	−	0.0852254i	−0.262770	−	0.964858i	$-0.584636\pi$
$199$	3.00308	−	1.20225i	0.212883	−	0.0852254i	0.475653	+	0.879633i	$0.342212\pi$
$200$		0			0
$201$	−9.54692	+	10.4812i	−0.673388	+	0.739289i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	16.5228	−	21.0104i	1.14565	−	1.45681i
$209$		0			0
$210$		0			0
$211$	24.5311	+	4.72798i	1.68879	+	0.325488i	0.940989	−	0.338436i	$-0.109898\pi$
$211$	24.5311	+	4.72798i	1.68879	+	0.325488i	0.747800	+	0.663924i	$0.231110\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.34432	+	49.2134i	−0.159143	+	3.34082i
$218$		0			0
$219$	22.4961	−	5.45751i	1.52015	−	0.368784i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.434064	−	0.500936i	0.0290671	−	0.0335452i	−0.741030	−	0.671472i	$-0.765662\pi$
$223$	0.434064	−	0.500936i	0.0290671	−	0.0335452i	0.770097	+	0.637927i	$0.220208\pi$
$224$		0			0
$225$	−14.3924	+	4.22599i	−0.959493	+	0.281733i
$226$		0			0
$227$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$227$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$228$	−14.7146	−	22.8964i	−0.974501	−	1.51635i
$229$	−0.557448	−	5.83786i	−0.0368372	−	0.385777i	−0.995024	−	0.0996338i	$-0.968233\pi$
$229$	−0.557448	−	5.83786i	−0.0368372	−	0.385777i	0.958187	−	0.286143i	$-0.0923732\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.945001	−	0.327068i	$-0.106061\pi$
$233$		0			0		−0.945001	+	0.327068i	$0.893939\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−13.3676	−	18.7721i	−0.868316	−	1.21938i
$238$		0			0
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	−12.1590	+	7.81409i	−0.783228	+	0.503350i	−0.870103	−	0.492869i	$-0.835948\pi$
$241$	−12.1590	+	7.81409i	−0.783228	+	0.503350i	0.0868754	+	0.996219i	$0.472312\pi$
$242$		0			0
$243$	−14.1798	+	6.47568i	−0.909632	+	0.415415i
$244$	−2.34034	−	7.97048i	−0.149825	−	0.510258i
$245$		0			0
$246$		0			0
$247$	−52.4422	+	2.49813i	−3.33682	+	0.158952i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.690079	−	0.723734i	$-0.257576\pi$
$251$		0			0		−0.690079	+	0.723734i	$0.742424\pi$
$252$	26.6740	+	1.27064i	1.68031	+	0.0800428i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−15.9276	−	1.52090i	−0.995472	−	0.0950560i
$257$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$257$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$258$		0			0
$259$	9.46267	+	1.36053i	0.587981	+	0.0845390i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$263$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	10.4355	−	12.6135i	0.637449	−	0.770493i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$	−4.28756	+	3.71519i	−0.260451	+	0.225682i	−0.775291	−	0.631604i	$-0.782397\pi$
$271$	−4.28756	+	3.71519i	−0.260451	+	0.225682i	0.514840	+	0.857286i	$0.327851\pi$
$272$		0			0
$273$	27.8498	−	43.3351i	1.68555	−	2.62276i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.636725	−	4.42852i	0.0382571	−	0.266084i	−0.961711	−	0.274066i	$-0.911631\pi$
$277$	0.636725	−	4.42852i	0.0382571	−	0.266084i	0.999968	+	0.00798138i	$0.00254058\pi$
$278$		0			0
$279$	15.2176	+	29.5181i	0.911056	+	1.76720i
$280$		0			0
$281$		0			0		−0.814576	−	0.580057i	$-0.803030\pi$
$281$		0			0		0.814576	+	0.580057i	$0.196970\pi$
$282$		0			0
$283$	−4.63073	−	32.2074i	−0.275268	−	1.91453i	−0.389404	−	0.921067i	$-0.627319\pi$
$283$	−4.63073	−	32.2074i	−0.275268	−	1.91453i	0.114135	−	0.993465i	$-0.463590\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.808893	+	16.9807i	0.0475819	+	0.998867i
$290$		0			0
$291$	10.0621	−	29.0727i	0.589853	−	1.70427i
$292$	−25.6470	+	7.53065i	−1.50088	+	0.440698i
$293$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$293$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	16.3679	−	5.66498i	0.945001	−	0.327068i
$301$	39.6034	+	15.8548i	2.28270	+	0.913856i
$302$		0			0
$303$		0			0
$304$	18.2297	+	25.6001i	1.04555	+	1.46827i
$305$		0			0
$306$		0			0
$307$	33.9160	−	3.23858i	1.93569	−	0.184836i	0.945603	−	0.325322i	$-0.105473\pi$
$307$	33.9160	−	3.23858i	1.93569	−	0.184836i	0.990083	+	0.140486i	$0.0448666\pi$
$308$		0			0
$309$	−0.980556	−	0.237880i	−0.0557819	−	0.0135325i
$310$		0			0
$311$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$311$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$312$		0			0
$313$	19.4379	+	16.8430i	1.09869	+	0.952024i	0.999075	−	0.0430013i	$-0.0136920\pi$
$313$	19.4379	+	16.8430i	1.09869	+	0.952024i	0.0996196	+	0.995026i	$0.468237\pi$
$314$		0			0
$315$		0			0
$316$	16.4494	+	20.9172i	0.925353	+	1.17668i
$317$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$317$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	15.9990	−	8.24808i	0.888835	−	0.458227i
$325$	6.32312	−	32.8075i	0.350744	−	1.81983i
$326$		0			0
$327$	−0.725825	+	1.58934i	−0.0401382	+	0.0878904i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−15.9157	−	16.6919i	−0.874804	−	0.917468i	0.122378	−	0.992484i	$-0.460948\pi$
$331$	−15.9157	−	16.6919i	−0.874804	−	0.917468i	−0.997182	+	0.0750153i	$0.976099\pi$
$332$		0			0
$333$	5.98231	−	2.39495i	0.327828	−	0.131243i
$334$		0			0
$335$		0			0
$336$	−30.8354			−1.68221
$337$	6.32776	+	15.8060i	0.344695	+	0.861007i	0.994864	+	0.101218i	$0.0322738\pi$
$337$	6.32776	+	15.8060i	0.344695	+	0.861007i	−0.650169	+	0.759790i	$0.725302\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−23.5171	−	10.7399i	−1.26980	−	0.579900i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		0.0950560	−	0.995472i	$-0.469697\pi$
$347$		0			0		−0.0950560	+	0.995472i	$0.530303\pi$
$348$		0			0
$349$	9.98728	+	2.93253i	0.534607	+	0.156975i	0.537882	−	0.843020i	$-0.319224\pi$
$349$	9.98728	+	2.93253i	0.534607	+	0.156975i	−0.00327558	+	0.999995i	$0.501043\pi$
$350$		0			0
$351$	1.65214	−	34.6827i	0.0881847	−	1.85122i
$352$		0			0
$353$		0			0		0.971812	−	0.235759i	$-0.0757576\pi$
$353$		0			0		−0.971812	+	0.235759i	$0.924242\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$359$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$360$		0			0
$361$	10.0741	−	41.5260i	0.530216	−	2.18558i
$362$		0			0
$363$	1.81106	+	18.9663i	0.0950560	+	0.995472i
$364$	−29.7408	+	51.5125i	−1.55884	+	2.69999i
$365$		0			0
$366$		0			0
$367$	−32.3366	+	11.1918i	−1.68796	+	0.584208i	−0.991114	−	0.133014i	$-0.957534\pi$
$367$	−32.3366	+	11.1918i	−1.68796	+	0.584208i	−0.696844	+	0.717222i	$0.745413\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−19.1737	−	33.2099i	−0.994111	−	1.72185i
$373$	−6.66082	−	3.84563i	−0.344884	−	0.199119i	0.317546	−	0.948243i	$-0.397141\pi$
$373$	−6.66082	−	3.84563i	−0.344884	−	0.199119i	−0.662430	+	0.749124i	$0.730475\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	30.6202	+	10.5977i	1.57285	+	0.544370i	0.967779	−	0.251800i	$-0.0810226\pi$
$379$	30.6202	+	10.5977i	1.57285	+	0.544370i	0.605073	+	0.796170i	$0.293144\pi$
$380$		0			0
$381$	−36.1542	+	1.72224i	−1.85223	+	0.0882328i
$382$		0			0
$383$		0			0		−0.618159	−	0.786053i	$-0.712121\pi$
$383$		0			0		0.618159	+	0.786053i	$0.287879\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	28.4617	−	4.09218i	1.44679	−	0.208017i
$388$	−10.0083	+	34.0850i	−0.508093	+	1.73040i
$389$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$389$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−10.2489	−	6.58658i	−0.514379	−	0.330571i	0.257566	−	0.966261i	$-0.417080\pi$
$397$	−10.2489	−	6.58658i	−0.514379	−	0.330571i	−0.771945	+	0.635690i	$0.780716\pi$
$398$		0			0
$399$	39.6633	+	45.7739i	1.98565	+	2.29156i
$400$	−18.5674	+	7.43325i	−0.928368	+	0.371662i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$	−73.9722			−3.68482
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	19.9054	−	25.3118i	0.984259	−	1.25159i	0.0164592	−	0.999865i	$-0.494761\pi$
$409$	19.9054	−	25.3118i	0.984259	−	1.25159i	0.967800	−	0.251722i	$-0.0809969\pi$
$410$		0			0
$411$		0			0
$412$	1.14404	+	0.220495i	0.0563626	+	0.0108630i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.33063	+	16.2099i	0.114132	+	0.793802i
$418$		0			0
$419$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$419$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$420$		0			0
$421$	19.8032	−	15.5734i	0.965149	−	0.759002i	−0.00537983	−	0.999986i	$-0.501712\pi$
$421$	19.8032	−	15.5734i	0.965149	−	0.759002i	0.970529	+	0.240984i	$0.0774700\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	7.67934	+	16.8154i	0.371630	+	0.813755i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	−18.0000	+	10.3923i	−0.866025	+	0.500000i
$433$	−12.5846	+	8.96142i	−0.604775	+	0.430659i	−0.840996	−	0.541041i	$-0.818030\pi$
$433$	−12.5846	+	8.96142i	−0.604775	+	0.430659i	0.236221	+	0.971699i	$0.424091\pi$
$434$		0			0
$435$		0			0
$436$	0.749839	−	1.87301i	0.0359108	−	0.0897008i
$437$		0			0
$438$		0			0
$439$	−20.8895	−	36.1818i	−0.997004	−	1.72686i	−0.565494	−	0.824752i	$-0.691315\pi$
$439$	−20.8895	−	36.1818i	−0.997004	−	1.72686i	−0.431509	−	0.902108i	$-0.642019\pi$
$440$		0			0
$441$	−38.2525	+	3.65267i	−1.82155	+	0.173937i
$442$		0			0
$443$		0			0		−0.971812	−	0.235759i	$-0.924242\pi$
$443$		0			0		0.971812	+	0.235759i	$0.0757576\pi$
$444$	−6.76836	+	3.09101i	−0.321212	+	0.146693i
$445$		0			0
$446$		0			0
$447$		0			0
$448$	35.5654	−	1.69419i	1.68031	−	0.0800428i
$449$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$449$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−13.0727	−	0.622727i	−0.614207	−	0.0292583i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−33.4050	−	3.18979i	−1.56262	−	0.149212i	−0.722406	−	0.691469i	$-0.756964\pi$
$457$	−33.4050	−	3.18979i	−1.56262	−	0.149212i	−0.840213	+	0.542257i	$0.817570\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$461$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$462$		0			0
$463$	6.58632	−	12.7757i	0.306092	−	0.593736i	−0.684747	−	0.728781i	$-0.740087\pi$
$463$	6.58632	−	12.7757i	0.306092	−	0.593736i	0.990840	+	0.135044i	$0.0431177\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$467$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$468$			40.0935i			1.85332i
$469$	−18.9916	+	31.0888i	−0.876950	+	1.43555i
$470$		0			0
$471$	−14.5262	−	36.2848i	−0.669334	−	1.67192i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	34.9174	+	18.0012i	1.60212	+	0.825950i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$479$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$480$		0			0
$481$	−1.36436	+	14.2883i	−0.0622096	+	0.651488i
$482$		0			0
$483$		0			0
$484$	−3.13093	−	21.7761i	−0.142315	−	0.989821i
$485$		0			0
$486$		0			0
$487$	27.0712	−	6.56739i	1.22671	−	0.297597i	0.430486	−	0.902597i	$-0.358342\pi$
$487$	27.0712	−	6.56739i	1.22671	−	0.297597i	0.796225	+	0.605000i	$0.206827\pi$
$488$		0			0
$489$	−3.58725	−	18.6124i	−0.162221	−	0.841683i
$490$		0			0
$491$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$491$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	23.9395	+	37.2506i	1.07491	+	1.67260i
$497$		0			0
$498$		0			0
$499$	−36.4247	+	21.0298i	−1.63059	+	0.941423i	−0.646682	+	0.762760i	$0.723844\pi$
$499$	−36.4247	+	21.0298i	−1.63059	+	0.941423i	−0.983910	+	0.178663i	$0.942823\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.371662	−	0.928368i	$-0.378788\pi$
$503$		0			0		−0.371662	+	0.928368i	$0.621212\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	47.4788	+	27.4119i	2.10861	+	1.21740i
$508$	41.6053	−	3.97283i	1.84594	−	0.176266i
$509$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$509$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$510$		0			0
$511$	54.1079	−	24.7102i	2.39359	−	1.09312i
$512$		0			0
$513$	38.5802	+	13.3527i	1.70336	+	0.589537i
$514$		0			0
$515$		0			0
$516$	−32.6027	+	6.28366i	−1.43525	+	0.276623i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$521$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$522$		0			0
$523$	26.5164	−	37.2371i	1.15948	−	1.62826i	0.552855	−	0.833278i	$-0.313538\pi$
$523$	26.5164	−	37.2371i	1.15948	−	1.62826i	0.606627	−	0.794987i	$-0.292522\pi$
$524$		0			0
$525$	−34.2595	+	17.6620i	−1.49521	+	0.770834i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−18.0792	−	14.2177i	−0.786053	−	0.618159i
$530$		0			0
$531$		0			0
$532$	−48.2623	−	50.6161i	−2.09244	−	2.19449i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	19.8728	−	30.9226i	0.854397	−	1.32947i	−0.0883944	−	0.996086i	$-0.528174\pi$
$541$	19.8728	−	30.9226i	0.854397	−	1.32947i	0.942792	−	0.333383i	$-0.108190\pi$
$542$		0			0
$543$	−16.1148	+	20.4916i	−0.691551	+	0.879378i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.60680	−	8.93595i	−0.196973	−	0.382073i	0.769577	−	0.638554i	$-0.220467\pi$
$547$	−4.60680	−	8.93595i	−0.196973	−	0.382073i	−0.966549	+	0.256481i	$0.917437\pi$
$548$		0			0
$549$	10.1500	+	7.22777i	0.433191	+	0.308474i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−42.8577	−	40.8648i	−1.82250	−	1.73775i
$554$		0			0
$555$		0			0
$556$	−3.57875	−	18.5683i	−0.151773	−	0.787473i
$557$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$557$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$558$		0			0
$559$	−20.9481	+	60.5255i	−0.886009	+	2.55995i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$563$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−32.6290	+	23.2350i	−1.37029	+	0.975778i
$568$		0			0
$569$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$569$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$570$		0			0
$571$	7.92599	+	22.9007i	0.331692	+	0.958362i	0.980347	+	0.197280i	$0.0632107\pi$
$571$	7.92599	+	22.9007i	0.331692	+	0.958362i	−0.648655	+	0.761083i	$0.724668\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	20.1901	−	12.9754i	0.841254	−	0.540641i
$577$	44.0120	+	10.6772i	1.83224	+	0.444497i	0.994784	−	0.102004i	$-0.0325255\pi$
$577$	44.0120	+	10.6772i	1.83224	+	0.444497i	0.837458	+	0.546501i	$0.184041\pi$
$578$		0			0
$579$	−5.93209	−	20.2029i	−0.246529	−	0.839602i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.998867	−	0.0475819i	$-0.984848\pi$
$587$		0			0		0.998867	+	0.0475819i	$0.0151515\pi$
$588$	43.9195	−	6.31467i	1.81121	−	0.260412i
$589$	24.5038	−	83.4522i	1.00966	−	3.43859i
$590$		0			0
$591$		0			0
$592$	7.63675	−	3.93702i	0.313869	−	0.161810i
$593$		0			0		0.189251	−	0.981929i	$-0.439394\pi$
$593$		0			0		−0.189251	+	0.981929i	$0.560606\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.56737	−	4.98000i	0.105075	−	0.203818i
$598$		0			0
$599$		0			0		−0.690079	−	0.723734i	$-0.742424\pi$
$599$		0			0		0.690079	+	0.723734i	$0.257576\pi$
$600$		0			0
$601$	3.77066	−	1.50955i	0.153809	−	0.0615756i	−0.293481	−	0.955965i	$-0.594814\pi$
$601$	3.77066	−	1.50955i	0.153809	−	0.0615756i	0.447289	+	0.894389i	$0.352389\pi$
$602$		0			0
$603$	−0.608533	+	24.5485i	−0.0247814	+	0.999693i
$604$	15.1121			0.614904
$605$		0			0
$606$		0			0
$607$	25.5511	−	24.3629i	1.03709	−	0.988861i	0.0371420	−	0.999310i	$-0.488175\pi$
$607$	25.5511	−	24.3629i	1.03709	−	0.988861i	0.999945	+	0.0104491i	$0.00332612\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−48.5936	−	9.36566i	−1.96268	−	0.378275i	−0.987896	−	0.155118i	$-0.950424\pi$
$613$	−48.5936	−	9.36566i	−1.96268	−	0.378275i	−0.974782	−	0.223157i	$-0.928364\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$617$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$618$		0			0
$619$	−2.18418	+	45.8515i	−0.0877895	+	1.84293i	0.341644	+	0.939829i	$0.389016\pi$
$619$	−2.18418	+	45.8515i	−0.0877895	+	1.84293i	−0.429433	+	0.903099i	$0.641287\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−2.20285	−	46.2436i	−0.0881847	−	1.85122i
$625$	−16.3715	+	18.8937i	−0.654861	+	0.755750i
$626$		0			0
$627$		0			0
$628$	18.7481	+	41.0525i	0.748129	+	1.63817i
$629$		0			0
$630$		0			0
$631$	4.67034	+	48.9100i	0.185923	+	1.94708i	0.300775	+	0.953695i	$0.402755\pi$
$631$	4.67034	+	48.9100i	0.185923	+	1.94708i	−0.114852	+	0.993383i	$0.536639\pi$
$632$		0			0
$633$	37.4738	−	21.6355i	1.48945	−	0.859935i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	31.8113	−	79.4607i	1.26041	−	3.14835i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$	−24.8979	+	16.0009i	−0.981877	+	0.631014i	−0.929969	−	0.367638i	$-0.880167\pi$
$643$	−24.8979	+	16.0009i	−0.981877	+	0.631014i	−0.0519076	+	0.998652i	$0.516530\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.945001	−	0.327068i	$-0.893939\pi$
$647$		0			0		0.945001	+	0.327068i	$0.106061\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	52.7517	+	67.0792i	2.06750	+	2.62904i
$652$	5.16013	+	21.2703i	0.202086	+	0.833011i
$653$		0			0		0.690079	−	0.723734i	$-0.257576\pi$
$653$		0			0		−0.690079	+	0.723734i	$0.742424\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	23.2572	−	32.6602i	0.907350	−	1.27419i
$658$		0			0
$659$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$659$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$660$		0			0
$661$	1.14039	+	0.163964i	0.0443561	+	0.00637745i	0.164457	−	0.986384i	$-0.447413\pi$
$661$	1.14039	+	0.163964i	0.0443561	+	0.00637745i	−0.120101	+	0.992762i	$0.538322\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		−	1.14806i		−	0.0443866i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−26.6231	+	23.0690i	−1.02624	+	0.889246i	−0.993906	−	0.110231i	$-0.964841\pi$
$673$	−26.6231	+	23.0690i	−1.02624	+	0.889246i	−0.0323386	+	0.999477i	$0.510295\pi$
$674$		0			0
$675$	−14.0463	+	21.8564i	−0.540641	+	0.841254i
$676$	−56.2678	−	29.0080i	−2.16414	−	1.11569i
$677$		0			0		0.618159	−	0.786053i	$-0.287879\pi$
$677$		0			0		−0.618159	+	0.786053i	$0.712121\pi$
$678$		0			0
$679$	11.2505	−	78.2489i	0.431754	−	3.00292i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.814576	−	0.580057i	$-0.803030\pi$
$683$		0			0		0.814576	+	0.580057i	$0.196970\pi$
$684$	−45.2317	−	13.2812i	−1.72948	−	0.507821i
$685$		0			0
$686$		0			0
$687$	−7.35130	−	7.00945i	−0.280470	−	0.267427i
$688$	37.2585	−	9.03881i	1.42047	−	0.344601i
$689$		0			0
$690$		0			0
$691$	2.09087	+	43.8928i	0.0795405	+	1.66976i	0.588142	+	0.808758i	$0.299860\pi$
$691$	2.09087	+	43.8928i	0.0795405	+	1.66976i	−0.508601	+	0.861002i	$0.669837\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	38.5443	−	22.2536i	1.45684	−	0.841105i
$701$		0			0		0.814576	−	0.580057i	$-0.196970\pi$
$701$		0			0		−0.814576	+	0.580057i	$0.803030\pi$
$702$		0			0
$703$	−15.6674	−	6.27229i	−0.590908	−	0.236564i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−22.1442	+	2.11452i	−0.831645	+	0.0794124i	−0.502188	−	0.864758i	$-0.667472\pi$
$709$	−22.1442	+	2.11452i	−0.831645	+	0.0794124i	−0.329456	+	0.944171i	$0.606865\pi$
$710$		0			0
$711$	−38.7904	−	9.41045i	−1.45475	−	0.352919i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$719$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$720$		0			0
$721$	−2.58980	−	0.123368i	−0.0964494	−	0.00459445i
$722$		0			0
$723$	−7.05290	+	24.0200i	−0.262300	+	0.893312i
$724$	17.4608	−	24.5202i	0.648925	−	0.911288i
$725$		0			0
$726$		0			0
$727$	−9.48337	+	49.2044i	−0.351719	+	1.82489i	0.186947	+	0.982370i	$0.440141\pi$
$727$	−9.48337	+	49.2044i	−0.351719	+	1.82489i	−0.538665	+	0.842520i	$0.681071\pi$
$728$		0			0
$729$	−11.2162	+	24.5601i	−0.415415	+	0.909632i
$730$		0			0
$731$		0			0
$732$	−12.1040	−	7.77879i	−0.447378	−	0.287512i
$733$	36.1940	+	37.9591i	1.33685	+	1.40205i	0.848296	+	0.529522i	$0.177629\pi$
$733$	36.1940	+	37.9591i	1.33685	+	1.40205i	0.488559	+	0.872531i	$0.337523\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−1.22596	−	3.06231i	−0.0450978	−	0.112649i	0.904109	−	0.427302i	$-0.140536\pi$
$739$	−1.22596	−	3.06231i	−0.0450978	−	0.112649i	−0.949207	+	0.314653i	$0.898112\pi$
$740$		0			0
$741$	−65.8131	+	62.7527i	−2.41771	+	2.30528i
$742$		0			0
$743$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$743$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−43.1905	−	12.6819i	−1.57604	−	0.462768i	−0.627290	−	0.778785i	$-0.715836\pi$
$751$	−43.1905	−	12.6819i	−1.57604	−	0.462768i	−0.948753	+	0.316017i	$0.897654\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	36.3574	−	28.5918i	1.32231	−	1.03987i
$757$	−5.90319	−	30.6287i	−0.214555	−	1.11322i	−0.916209	−	0.400700i	$-0.868767\pi$
$757$	−5.90319	−	30.6287i	−0.214555	−	1.11322i	0.701654	−	0.712517i	$-0.252445\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$761$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$762$		0			0
$763$	−1.05849	+	4.36316i	−0.0383199	+	0.157957i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−22.5742	+	16.0750i	−0.814576	+	0.580057i
$769$	52.3197	−	18.1080i	1.88670	−	0.652993i	0.924021	−	0.382343i	$-0.124883\pi$
$769$	52.3197	−	18.1080i	1.88670	−	0.652993i	0.962678	−	0.270650i	$-0.0872386\pi$
$770$		0			0
$771$		0			0
$772$	7.95203	+	22.9759i	0.286200	+	0.826921i
$773$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$773$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$774$		0			0
$775$	47.9343	+	27.6749i	1.72185	+	0.994111i
$776$		0			0
$777$	13.9298	−	8.95212i	0.499728	−	0.321156i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−50.3094	+	9.69635i	−1.79677	+	0.346298i
$785$		0			0
$786$		0			0
$787$	−34.1592	+	35.8251i	−1.21764	+	1.27703i	−0.268099	+	0.963391i	$0.586395\pi$
$787$	−34.1592	+	35.8251i	−1.21764	+	1.27703i	−0.949544	+	0.313635i	$0.898453\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−24.6693	+	12.7179i	−0.876033	+	0.451626i
$794$		0			0
$795$		0			0
$796$	−2.68757	+	5.88495i	−0.0952582	+	0.208586i
$797$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$797$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−0.646888	−	28.3475i	−0.0228140	−	0.999740i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$809$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$810$		0			0
$811$	31.9244	−	40.5952i	1.12102	−	1.42549i	0.229038	−	0.973417i	$-0.426442\pi$
$811$	31.9244	−	40.5952i	1.12102	−	1.42549i	0.891981	−	0.452074i	$-0.149316\pi$
$812$		0			0
$813$	−1.39844	+	9.72635i	−0.0490454	+	0.341118i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−61.3430	−	43.6821i	−2.14612	−	1.52824i
$818$		0			0
$819$	−12.6977	−	88.3142i	−0.443692	−	3.08595i
$820$		0			0
$821$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$821$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$822$		0			0
$823$	−45.0310	+	35.4128i	−1.56968	+	1.23441i	−0.750523	+	0.660844i	$0.770198\pi$
$823$	−45.0310	+	35.4128i	−1.56968	+	1.23441i	−0.819159	+	0.573567i	$0.805559\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$827$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$828$		0			0
$829$	23.7604	+	52.0280i	0.825233	+	1.80701i	0.518022	+	0.855367i	$0.326668\pi$
$829$	23.7604	+	52.0280i	0.825233	+	1.80701i	0.307211	+	0.951641i	$0.400604\pi$
$830$		0			0
$831$	−4.18959	−	6.51913i	−0.145335	−	0.226146i
$832$	5.08151	+	53.2160i	0.176170	+	1.84493i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	53.4008	+	21.3785i	1.84580	+	0.738948i
$838$		0			0
$839$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$839$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$840$		0			0
$841$	−14.5000	−	25.1147i	−0.500000	−	0.866025i
$842$		0			0
$843$		0			0
$844$	−42.0333	+	27.0132i	−1.44685	+	0.929832i
$845$		0			0
$846$		0			0
$847$	13.7930	+	46.9747i	0.473934	+	1.61407i
$848$		0			0
$849$	−42.5929	−	36.9070i	−1.46179	−	1.26664i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	13.7674	+	56.7498i	0.471386	+	1.94308i	0.258712	+	0.965955i	$0.416702\pi$
$853$	13.7674	+	56.7498i	0.471386	+	1.94308i	0.212674	+	0.977123i	$0.431783\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$857$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$858$		0			0
$859$	53.8550	+	5.14253i	1.83751	+	0.175461i	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	53.8550	+	5.14253i	1.83751	+	0.175461i	0.882163	+	0.470945i	$0.156087\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$863$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	20.3193	+	21.3103i	0.690079	+	0.723734i
$868$	−64.5289	−	74.4703i	−2.19025	−	2.52769i
$869$		0			0
$870$		0			0
$871$	−47.9802	−	26.2605i	−1.62575	−	0.889804i
$872$		0			0
$873$	−19.8044	−	49.4690i	−0.670278	−	1.67427i
$874$		0			0
$875$		0			0
$876$	−25.0302	+	38.9478i	−0.845693	+	1.31592i
$877$	50.4013	+	25.9837i	1.70193	+	0.877407i	0.983294	+	0.182023i	$0.0582646\pi$
$877$	50.4013	+	25.9837i	1.70193	+	0.877407i	0.718638	+	0.695384i	$0.244766\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$881$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$882$		0			0
$883$	3.09109	−	32.3713i	0.104023	−	1.08938i	−0.781221	−	0.624255i	$-0.785403\pi$
$883$	3.09109	−	32.3713i	0.104023	−	1.08938i	0.885244	−	0.465127i	$-0.153991\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$887$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$888$		0			0
$889$	−90.3861	+	21.9274i	−3.03145	+	0.735422i
$890$		0			0
$891$		0			0
$892$	0.0630778	+	1.32417i	0.00211200	+	0.0443363i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	15.0000	−	25.9808i	0.500000	−	0.866025i
$901$		0			0
$902$		0			0
$903$	69.8241	−	24.1664i	2.32360	−	0.804206i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−5.39644	−	7.57824i	−0.179186	−	0.251631i	0.715208	−	0.698912i	$-0.246332\pi$
$907$	−5.39644	−	7.57824i	−0.179186	−	0.251631i	−0.894394	+	0.447280i	$0.852393\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$911$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$912$	52.8996	+	12.8333i	1.75168	+	0.424954i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	8.86406	+	7.68075i	0.292877	+	0.253779i
$917$		0			0
$918$		0			0
$919$	−33.5914	−	42.7149i	−1.10808	−	1.40904i	−0.902657	−	0.430362i	$-0.858386\pi$
$919$	−33.5914	−	42.7149i	−1.10808	−	1.40904i	−0.205421	−	0.978674i	$-0.565856\pi$
$920$		0			0
$921$	40.7225	−	42.7085i	1.34185	−	1.40729i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	6.22971	−	8.74840i	0.204832	−	0.287646i
$926$		0			0
$927$	−1.55336	+	0.800813i	−0.0510191	+	0.0263022i
$928$		0			0
$929$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$929$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$930$		0			0
$931$	79.1064	+	62.2099i	2.59261	+	2.03885i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	12.2000i		−	0.398557i	−0.979943	−	0.199279i	$-0.936140\pi$
$937$		−	12.2000i		−	0.398557i	0.979943	−	0.199279i	$-0.0638599\pi$
$938$		0			0
$939$	44.5484			1.45378
$940$		0			0
$941$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$941$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$947$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$948$	45.2576	+	8.72269i	1.46990	+	0.283300i
$949$	40.9231	+	79.3798i	1.32842	+	2.57678i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$953$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	29.9411	−	86.5091i	0.965841	−	2.79061i
$962$		0			0
$963$		0			0
$964$	6.81503	−	28.0920i	0.219497	−	0.904781i
$965$		0			0
$966$		0			0
$967$	−31.0961	+	53.8600i	−0.999983	+	1.73202i	−0.494966	+	0.868912i	$0.664819\pi$
$967$	−31.0961	+	53.8600i	−0.999983	+	1.73202i	−0.505017	+	0.863109i	$0.668514\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$971$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$972$	11.5873	−	28.9436i	0.371662	−	0.928368i
$973$	13.7635	+	39.7672i	0.441239	+	1.27488i
$974$		0			0
$975$	−28.9350	−	50.1169i	−0.926662	−	1.60503i
$976$	14.3881	+	8.30697i	0.460552	+	0.265900i
$977$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$977$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.852604	+	2.90370i	0.0272216	+	0.0927081i
$982$		0			0
$983$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$983$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	72.4606	−	75.9945i	2.30528	−	2.41771i
$989$		0			0
$990$		0			0
$991$	−3.97137	+	13.5252i	−0.126155	+	0.429644i	−0.998213	−	0.0597587i	$-0.980967\pi$
$991$	−3.97137	+	13.5252i	−0.126155	+	0.429644i	0.872058	+	0.489402i	$0.162785\pi$
$992$		0			0
$993$	−39.7663	−	3.79723i	−1.26195	−	0.120501i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−22.2964	+	48.8222i	−0.706133	+	1.54621i	0.126241	+	0.992000i	$0.459709\pi$
$997$	−22.2964	+	48.8222i	−0.706133	+	1.54621i	−0.832373	+	0.554215i	$0.813018\pi$
$998$		0			0
$999$	5.11434	−	9.92043i	0.161810	−	0.313869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.p.a.95.1	✓	20
3.2	odd	2	CM	201.2.p.a.95.1	✓	20
67.12	odd	66	inner	201.2.p.a.146.1	yes	20
201.146	even	66	inner	201.2.p.a.146.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.p.a.95.1	✓	20	1.1	even	1	trivial
201.2.p.a.95.1	✓	20	3.2	odd	2	CM
201.2.p.a.146.1	yes	20	67.12	odd	66	inner
201.2.p.a.146.1	yes	20	201.146	even	66	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30900 - 1.13425i) q^{3} +(-1.44747 + 1.38016i) q^{4} +(2.75125 - 3.49850i) q^{7} +(0.426945 - 2.96946i) q^{9} +O(q^{10})\)	\(q+(1.30900 - 1.13425i) q^{3} +(-1.44747 + 1.38016i) q^{4} +(2.75125 - 3.49850i) q^{7} +(0.426945 - 2.96946i) q^{9} +(-0.329284 + 3.44842i) q^{12} +(5.44320 + 3.87609i) q^{13} +(0.190328 - 3.99547i) q^{16} +(-6.17592 + 4.85680i) q^{19} +(-0.366802 - 7.70013i) q^{21} +(-2.07708 - 4.54816i) q^{25} +(-2.80925 - 4.37128i) q^{27} +(0.846134 + 8.86112i) q^{28} +(-9.01732 + 6.42120i) q^{31} +(3.48034 + 4.88746i) q^{36} +(1.07398 + 1.86019i) q^{37} +(11.5216 - 1.10018i) q^{39} +(2.70035 + 9.19655i) q^{43} +(-4.28273 - 5.44594i) q^{48} +(-3.01980 - 12.4478i) q^{49} +(-13.2285 + 1.90197i) q^{52} +(-2.57543 + 13.3626i) q^{57} +(-1.90324 + 3.69176i) q^{61} +(-9.21403 - 9.66339i) q^{63} +(5.23889 + 6.04600i) q^{64} +(-8.12842 + 0.963760i) q^{67} +(11.8792 + 6.12415i) q^{73} +(-7.87764 - 3.59760i) q^{75} +(2.23630 - 15.5538i) q^{76} +(1.26474 - 13.2449i) q^{79} +(-8.63544 - 2.53559i) q^{81} +(11.1583 + 10.6394i) q^{84} +(28.5361 - 8.37895i) q^{91} +(-4.52038 + 18.6332i) q^{93} +(15.3823 - 8.88100i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 20 * q - 2 * q^4 - 6 * q^7 + 6 * q^9	\( 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9} - 6 q^{12} - 3 q^{13} + 4 q^{16} - 8 q^{19} + 6 q^{21} + 10 q^{25} - 12 q^{28} + 15 q^{31} + 6 q^{36} + 10 q^{37} - 3 q^{39} - 12 q^{48} - 5 q^{49} - 154 q^{52} - 75 q^{57} + 15 q^{61} - 15 q^{63} + 16 q^{64} + 5 q^{67} + 60 q^{73} - 32 q^{76} + 134 q^{79} - 18 q^{81} + 186 q^{84} - 12 q^{91} - 15 q^{93} + 9 q^{97}+O(q^{100}) \) 20 * q - 2 * q^4 - 6 * q^7 + 6 * q^9 - 6 * q^12 - 3 * q^13 + 4 * q^16 - 8 * q^19 + 6 * q^21 + 10 * q^25 - 12 * q^28 + 15 * q^31 + 6 * q^36 + 10 * q^37 - 3 * q^39 - 12 * q^48 - 5 * q^49 - 154 * q^52 - 75 * q^57 + 15 * q^61 - 15 * q^63 + 16 * q^64 + 5 * q^67 + 60 * q^73 - 32 * q^76 + 134 * q^79 - 18 * q^81 + 186 * q^84 - 12 * q^91 - 15 * q^93 + 9 * q^97

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