LMFDB - Embedded newform 201.2.p.a.182.1

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			182.1
Root			$0.235759 - 0.971812i$ of defining polynomial
Character	$\chi$	$=$	201.182
Dual form			201.2.p.a.74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.487975 - 1.66189i) q^{3} +(-1.16011 - 1.62915i) q^{4} +(-2.19700 + 0.104656i) q^{7} +(-2.52376 + 1.62192i) q^{9} +O(q^{10})$	$q+(-0.487975 - 1.66189i) q^{3} +(-1.16011 - 1.62915i) q^{4} +(-2.19700 + 0.104656i) q^{7} +(-2.52376 + 1.62192i) q^{9} +(-2.14137 + 2.72297i) q^{12} +(-0.865004 - 2.16068i) q^{13} +(-1.30827 + 3.78000i) q^{16} +(0.318799 - 6.69240i) q^{19} +(1.24601 + 3.60010i) q^{21} +(0.711574 - 4.94911i) q^{25} +(3.92699 + 3.40276i) q^{27} +(2.71927 + 3.45783i) q^{28} +(4.07398 - 10.1763i) q^{31} +(5.57021 + 2.22997i) q^{36} +(4.14042 + 7.17141i) q^{37} +(-3.16871 + 2.49190i) q^{39} +(2.93232 - 1.33914i) q^{43} +(6.92036 + 0.329657i) q^{48} +(-2.15246 + 0.205535i) q^{49} +(-2.51657 + 3.91585i) q^{52} +(-11.2776 + 2.73592i) q^{57} +(-2.26571 + 11.7556i) q^{61} +(5.37495 - 3.82748i) q^{63} +(7.67594 - 2.25386i) q^{64} +(-7.35911 - 3.58379i) q^{67} +(9.64611 + 1.85914i) q^{73} +(-8.57211 + 1.23248i) q^{75} +(-11.2728 + 7.24458i) q^{76} +(10.8589 - 13.8082i) q^{79} +(3.73874 - 8.18669i) q^{81} +(4.41960 - 6.20646i) q^{84} +(2.12654 + 4.65647i) q^{91} +(-18.8999 - 1.80472i) q^{93} +(-0.318045 + 0.183623i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$e\left(\frac{43}{66}\right)$

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		0.458227	−	0.888835i	$-0.348485\pi$
$2$		0			0		−0.458227	+	0.888835i	$0.651515\pi$
$3$	−0.487975	−	1.66189i	−0.281733	−	0.959493i
$3$	−0.487975	−	1.66189i	−0.281733	−	0.959493i
$4$	−1.16011	−	1.62915i	−0.580057	−	0.814576i
$5$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$5$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$6$		0			0
$7$	−2.19700	+	0.104656i	−0.830387	+	0.0395562i	−0.458470	−	0.888710i	$-0.651602\pi$
$7$	−2.19700	+	0.104656i	−0.830387	+	0.0395562i	−0.371917	+	0.928266i	$0.621299\pi$
$8$		0			0
$9$	−2.52376	+	1.62192i	−0.841254	+	0.540641i
$10$		0			0
$11$		0			0		−0.189251	−	0.981929i	$-0.560606\pi$
$11$		0			0		0.189251	+	0.981929i	$0.439394\pi$
$12$	−2.14137	+	2.72297i	−0.618159	+	0.786053i
$13$	−0.865004	−	2.16068i	−0.239909	−	0.599264i	0.758731	−	0.651404i	$-0.225820\pi$
$13$	−0.865004	−	2.16068i	−0.239909	−	0.599264i	−0.998640	+	0.0521407i	$0.983396\pi$
$14$		0			0
$15$		0			0
$16$	−1.30827	+	3.78000i	−0.327068	+	0.945001i
$17$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$17$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$18$		0			0
$19$	0.318799	−	6.69240i	0.0731374	−	1.53534i	−0.602506	−	0.798114i	$-0.705831\pi$
$19$	0.318799	−	6.69240i	0.0731374	−	1.53534i	0.675643	−	0.737229i	$-0.263866\pi$
$20$		0			0
$21$	1.24601	+	3.60010i	0.271901	+	0.785606i
$22$		0			0
$23$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$23$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$24$		0			0
$25$	0.711574	−	4.94911i	0.142315	−	0.989821i
$26$		0			0
$27$	3.92699	+	3.40276i	0.755750	+	0.654861i
$28$	2.71927	+	3.45783i	0.513893	+	0.653468i
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$		0			0
$31$	4.07398	−	10.1763i	0.731709	−	1.82772i	0.202369	−	0.979309i	$-0.435136\pi$
$31$	4.07398	−	10.1763i	0.731709	−	1.82772i	0.529339	−	0.848410i	$-0.322440\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	5.57021	+	2.22997i	0.928368	+	0.371662i
$37$	4.14042	+	7.17141i	0.680680	+	1.17897i	0.974774	+	0.223196i	$0.0716490\pi$
$37$	4.14042	+	7.17141i	0.680680	+	1.17897i	−0.294093	+	0.955777i	$0.595018\pi$
$38$		0			0
$39$	−3.16871	+	2.49190i	−0.507399	+	0.399023i
$40$		0			0
$41$		0			0		0.0950560	−	0.995472i	$-0.469697\pi$
$41$		0			0		−0.0950560	+	0.995472i	$0.530303\pi$
$42$		0			0
$43$	2.93232	−	1.33914i	0.447174	−	0.204218i	−0.179083	−	0.983834i	$-0.557313\pi$
$43$	2.93232	−	1.33914i	0.447174	−	0.204218i	0.626258	+	0.779616i	$0.284586\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$47$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$48$	6.92036	+	0.329657i	0.998867	+	0.0475819i
$49$	−2.15246	+	0.205535i	−0.307494	+	0.0293622i
$50$		0			0
$51$		0			0
$52$	−2.51657	+	3.91585i	−0.348985	+	0.543031i
$53$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$53$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−11.2776	+	2.73592i	−1.49376	+	0.362381i
$58$		0			0
$59$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$59$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$60$		0			0
$61$	−2.26571	+	11.7556i	−0.290095	+	1.50515i	0.485676	+	0.874139i	$0.338573\pi$
$61$	−2.26571	+	11.7556i	−0.290095	+	1.50515i	−0.775771	+	0.631015i	$0.782639\pi$
$62$		0			0
$63$	5.37495	−	3.82748i	0.677180	−	0.482218i
$64$	7.67594	−	2.25386i	0.959493	−	0.281733i
$65$		0			0
$66$		0			0
$67$	−7.35911	−	3.58379i	−0.899058	−	0.437829i
$67$	−7.35911	−	3.58379i	−0.899058	−	0.437829i
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$71$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$72$		0			0
$73$	9.64611	+	1.85914i	1.12899	+	0.217595i	0.719348	−	0.694650i	$-0.244441\pi$
$73$	9.64611	+	1.85914i	1.12899	+	0.217595i	0.409644	+	0.912245i	$0.365653\pi$
$74$		0			0
$75$	−8.57211	+	1.23248i	−0.989821	+	0.142315i
$76$	−11.2728	+	7.24458i	−1.29308	+	0.831010i
$77$		0			0
$78$		0			0
$79$	10.8589	−	13.8082i	1.22172	−	1.55354i	0.490410	−	0.871492i	$-0.336847\pi$
$79$	10.8589	−	13.8082i	1.22172	−	1.55354i	0.731307	−	0.682048i	$-0.238911\pi$
$80$		0			0
$81$	3.73874	−	8.18669i	0.415415	−	0.909632i
$82$		0			0
$83$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$83$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$84$	4.41960	−	6.20646i	0.482218	−	0.677180i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$89$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$90$		0			0
$91$	2.12654	+	4.65647i	0.222922	+	0.488131i
$92$		0			0
$93$	−18.8999	−	1.80472i	−1.95983	−	0.187141i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.318045	+	0.183623i	−0.0322926	+	0.0186441i	−0.516059	−	0.856553i	$-0.672602\pi$
$97$	−0.318045	+	0.183623i	−0.0322926	+	0.0186441i	0.483767	+	0.875197i	$0.339268\pi$
$98$		0			0
$99$		0			0
$100$	−8.88835	+	4.58227i	−0.888835	+	0.458227i
$101$		0			0		−0.458227	−	0.888835i	$-0.651515\pi$
$101$		0			0		0.458227	+	0.888835i	$0.348485\pi$
$102$		0			0
$103$	−13.8812	−	5.55718i	−1.36775	−	0.547566i	−0.432528	−	0.901620i	$-0.642378\pi$
$103$	−13.8812	−	5.55718i	−1.36775	−	0.547566i	−0.935225	+	0.354055i	$0.884803\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$107$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$108$	0.987851	−	10.3452i	0.0950560	−	0.995472i
$109$	−4.85802	−	0.698478i	−0.465314	−	0.0669021i	−0.0943294	−	0.995541i	$-0.530071\pi$
$109$	−4.85802	−	0.698478i	−0.465314	−	0.0669021i	−0.370985	+	0.928639i	$0.620980\pi$
$110$		0			0
$111$	9.89768	−	10.3804i	0.939446	−	0.985263i
$112$	2.47867	−	8.44157i	0.234212	−	0.797654i
$113$		0			0		0.945001	−	0.327068i	$-0.106061\pi$
$113$		0			0		−0.945001	+	0.327068i	$0.893939\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.68751	+	4.05006i	0.525811	+	0.374428i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.2120	+	4.08829i	−0.928368	+	0.371662i
$122$		0			0
$123$		0			0
$124$	−21.3050	+	5.16855i	−1.91325	+	0.464149i
$125$		0			0
$126$		0			0
$127$	1.05371	+	22.1201i	0.0935016	+	1.96284i	0.232631	+	0.972565i	$0.425267\pi$
$127$	1.05371	+	22.1201i	0.0935016	+	1.96284i	−0.139129	+	0.990274i	$0.544430\pi$
$128$		0			0
$129$	−3.65641	−	4.21972i	−0.321929	−	0.371526i
$130$		0			0
$131$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$131$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$132$		0			0
$133$			14.7366i			1.27782i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$137$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$138$		0			0
$139$	17.8181	−	15.4395i	1.51131	−	1.30956i	0.745302	−	0.666727i	$-0.232305\pi$
$139$	17.8181	−	15.4395i	1.51131	−	1.30956i	0.766008	−	0.642831i	$-0.222240\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−2.82911	−	11.6617i	−0.235759	−	0.971812i
$145$		0			0
$146$		0			0
$147$	1.39192	+	3.47686i	0.114804	+	0.286766i
$148$	6.87996	−	15.0650i	0.565530	−	1.23834i
$149$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$149$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$150$		0			0
$151$	0.383640	−	0.538748i	0.0312202	−	0.0438426i	−0.798671	−	0.601768i	$-0.794463\pi$
$151$	0.383640	−	0.538748i	0.0312202	−	0.0438426i	0.829891	+	0.557926i	$0.188403\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	7.73574	+	2.27142i	0.619355	+	0.181859i
$157$	16.6564	+	15.8819i	1.32933	+	1.26751i	0.937726	+	0.347375i	$0.112927\pi$
$157$	16.6564	+	15.8819i	1.32933	+	1.26751i	0.391601	+	0.920135i	$0.371921\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−12.1964	+	21.1248i	−0.955299	+	1.65463i	−0.221615	+	0.975134i	$0.571133\pi$
$163$	−12.1964	+	21.1248i	−0.955299	+	1.65463i	−0.733683	+	0.679492i	$0.762200\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$167$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$168$		0			0
$169$	5.48825	−	5.23304i	0.422173	−	0.402542i
$170$		0			0
$171$	10.0500	+	17.4071i	0.768542	+	1.33115i
$172$	−5.58349	−	3.22363i	−0.425737	−	0.245800i
$173$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$173$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$174$		0			0
$175$	−1.04537	+	10.9476i	−0.0790228	+	0.827564i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$179$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$180$		0			0
$181$	3.30913	−	13.6404i	0.245966	−	1.01388i	−0.706129	−	0.708083i	$-0.749560\pi$
$181$	3.30913	−	13.6404i	0.245966	−	1.01388i	0.952095	−	0.305802i	$-0.0989245\pi$
$182$		0			0
$183$	20.6422	−	1.97109i	1.52591	−	0.145707i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−8.98370	−	7.06486i	−0.653468	−	0.513893i
$190$		0			0
$191$		0			0		0.971812	−	0.235759i	$-0.0757576\pi$
$191$		0			0		−0.971812	+	0.235759i	$0.924242\pi$
$192$	−7.49134	−	11.6568i	−0.540641	−	0.841254i
$193$	−1.55423	−	10.8099i	−0.111876	−	0.778115i	−0.966092	−	0.258197i	$-0.916872\pi$
$193$	−1.55423	−	10.8099i	−0.111876	−	0.778115i	0.854216	−	0.519918i	$-0.174037\pi$
$194$		0			0
$195$		0			0
$196$	2.83195	+	3.26824i	0.202282	+	0.233446i
$197$		0			0		0.814576	−	0.580057i	$-0.196970\pi$
$197$		0			0		−0.814576	+	0.580057i	$0.803030\pi$
$198$		0			0
$199$	25.0674	+	12.9231i	1.77698	+	0.916097i	0.901269	+	0.433260i	$0.142637\pi$
$199$	25.0674	+	12.9231i	1.77698	+	0.916097i	0.875710	+	0.482837i	$0.160394\pi$
$200$		0			0
$201$	−2.36480	+	13.9788i	−0.166800	+	0.985991i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	9.29902	−	0.442967i	0.644771	−	0.0307142i
$209$		0			0
$210$		0			0
$211$	−6.63618	−	27.3547i	−0.456853	−	1.88317i	−0.468908	−	0.883247i	$-0.655352\pi$
$211$	−6.63618	−	27.3547i	−0.456853	−	1.88317i	0.0120548	−	0.999927i	$-0.496163\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−7.88551	+	22.7837i	−0.535303	+	1.54666i
$218$		0			0
$219$	−1.61738	−	16.9380i	−0.109293	−	1.14456i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	26.3247	+	7.72963i	1.76283	+	0.517614i	0.992736	−	0.120312i	$-0.0383896\pi$
$223$	26.3247	+	7.72963i	1.76283	+	0.517614i	0.770097	+	0.637927i	$0.220208\pi$
$224$		0			0
$225$	6.23123	+	13.6445i	0.415415	+	0.909632i
$226$		0			0
$227$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$227$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$228$	17.5405	+	15.1990i	1.16165	+	1.00658i
$229$	6.87343	+	8.74027i	0.454209	+	0.577574i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	6.87343	+	8.74027i	0.454209	+	0.577574i	−0.503978	+	0.863716i	$0.668131\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.690079	−	0.723734i	$-0.742424\pi$
$233$		0			0		0.690079	+	0.723734i	$0.257576\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−28.2465	−	11.3082i	−1.83481	−	0.734546i
$238$		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
$241$	−1.76638	+	2.03851i	−0.113783	+	0.131312i	−0.809784	−	0.586729i	$-0.800415\pi$
$241$	−1.76638	+	2.03851i	−0.113783	+	0.131312i	0.696001	+	0.718041i	$0.254961\pi$
$242$		0			0
$243$	−15.4298	−	2.21847i	−0.989821	−	0.142315i
$244$	21.7802	−	9.94668i	1.39433	−	0.636771i
$245$		0			0
$246$		0			0
$247$	−14.7359	+	5.10014i	−0.937622	+	0.324514i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.814576	−	0.580057i	$-0.803030\pi$
$251$		0			0		0.814576	+	0.580057i	$0.196970\pi$
$252$	−12.4711	−	4.31629i	−0.785606	−	0.271901i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−12.5768	−	9.89054i	−0.786053	−	0.618159i
$257$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$257$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$258$		0			0
$259$	−9.84701	−	15.3222i	−0.611864	−	0.952078i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$263$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	2.69887	+	16.1467i	0.164860	+	0.986317i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$	−7.95202	−	27.0821i	−0.483051	−	1.64512i	−0.735511	−	0.677513i	$-0.763058\pi$
$271$	−7.95202	−	27.0821i	−0.483051	−	1.64512i	0.252460	−	0.967607i	$-0.418760\pi$
$272$		0			0
$273$	6.70085	−	5.80632i	0.405554	−	0.351414i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−26.9303	+	17.3071i	−1.61809	+	1.03988i	−0.660872	+	0.750499i	$0.729813\pi$
$277$	−26.9303	+	17.3071i	−1.61809	+	1.03988i	−0.957214	+	0.289382i	$0.906550\pi$
$278$		0			0
$279$	6.22344	+	32.2903i	0.372587	+	1.93317i
$280$		0			0
$281$		0			0		−0.371662	−	0.928368i	$-0.621212\pi$
$281$		0			0		0.371662	+	0.928368i	$0.378788\pi$
$282$		0			0
$283$	−24.2361	−	15.5756i	−1.44069	−	0.925874i	−0.999596	−	0.0284112i	$-0.990955\pi$
$283$	−24.2361	−	15.5756i	−1.44069	−	0.925874i	−0.441091	−	0.897462i	$-0.645408\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−5.56016	−	16.0650i	−0.327068	−	0.945001i
$290$		0			0
$291$	0.460360	+	0.438952i	0.0269868	+	0.0257319i
$292$	−8.16177	−	17.8718i	−0.477632	−	1.04587i
$293$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$293$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	11.9525	+	12.5354i	0.690079	+	0.723734i
$301$	−6.30214	+	3.24898i	−0.363250	+	0.187268i
$302$		0			0
$303$		0			0
$304$	24.8802	+	9.96054i	1.42698	+	0.571276i
$305$		0			0
$306$		0			0
$307$	−10.1904	+	8.01381i	−0.581596	+	0.457372i	−0.865100	−	0.501599i	$-0.832745\pi$
$307$	−10.1904	+	8.01381i	−0.581596	+	0.457372i	0.283504	+	0.958971i	$0.408503\pi$
$308$		0			0
$309$	−2.46176	+	25.7808i	−0.140045	+	1.46662i
$310$		0			0
$311$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$311$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$312$		0			0
$313$	9.91913	−	33.7814i	0.560662	−	1.90944i	0.184747	−	0.982786i	$-0.440853\pi$
$313$	9.91913	−	33.7814i	0.560662	−	1.90944i	0.375915	−	0.926654i	$-0.377328\pi$
$314$		0			0
$315$		0			0
$316$	−35.0931	−	1.67169i	−1.97414	−	0.0940400i
$317$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$317$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−17.6747	+	3.40652i	−0.981929	+	0.189251i
$325$	−11.3089	+	2.74352i	−0.627307	+	0.152183i
$326$		0			0
$327$	1.20980	+	8.41434i	0.0669021	+	0.465314i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	28.6580	−	20.4072i	1.57518	−	1.12168i	0.639528	−	0.768768i	$-0.279130\pi$
$331$	28.6580	−	20.4072i	1.57518	−	1.12168i	0.935655	−	0.352915i	$-0.114810\pi$
$332$		0			0
$333$	−22.0809	−	11.3835i	−1.21003	−	0.623811i
$334$		0			0
$335$		0			0
$336$	−15.2385			−0.831328
$337$	14.6217	−	28.3621i	0.796493	−	1.54498i	−0.0413966	−	0.999143i	$-0.513181\pi$
$337$	14.6217	−	28.3621i	0.796493	−	1.54498i	0.837890	−	0.545839i	$-0.183789\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	19.9471	−	2.86797i	1.07704	−	0.154856i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		0.618159	−	0.786053i	$-0.287879\pi$
$347$		0			0		−0.618159	+	0.786053i	$0.712121\pi$
$348$		0			0
$349$	14.0974	−	30.8689i	0.754615	−	1.65238i	−0.00327558	−	0.999995i	$-0.501043\pi$
$349$	14.0974	−	30.8689i	0.754615	−	1.65238i	0.757891	−	0.652382i	$-0.226230\pi$
$350$		0			0
$351$	3.95539	−	11.4284i	0.211123	−	0.610000i
$352$		0			0
$353$		0			0		−0.0950560	−	0.995472i	$-0.530303\pi$
$353$		0			0		0.0950560	+	0.995472i	$0.469697\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$359$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$360$		0			0
$361$	−25.7727	−	2.46099i	−1.35646	−	0.129526i
$362$		0			0
$363$	11.7775	+	14.9763i	0.618159	+	0.786053i
$364$	5.11907	−	8.86649i	0.268312	−	0.464730i
$365$		0			0
$366$		0			0
$367$	19.3060	+	20.2476i	1.00777	+	1.05691i	0.998377	+	0.0569590i	$0.0181404\pi$
$367$	19.3060	+	20.2476i	1.00777	+	1.05691i	0.00938982	+	0.999956i	$0.497011\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	18.9859	+	32.8845i	0.984372	+	1.70498i
$373$	−20.4128	−	11.7853i	−1.05693	−	0.610221i	−0.132351	−	0.991203i	$-0.542253\pi$
$373$	−20.4128	−	11.7853i	−1.05693	−	0.610221i	−0.924582	+	0.380982i	$0.875586\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−25.9021	+	27.1654i	−1.33050	+	1.39539i	−0.472865	+	0.881135i	$0.656780\pi$
$379$	−25.9021	+	27.1654i	−1.33050	+	1.39539i	−0.857637	+	0.514255i	$0.828068\pi$
$380$		0			0
$381$	36.2470	−	12.5452i	1.85699	−	0.642710i
$382$		0			0
$383$		0			0		−0.998867	−	0.0475819i	$-0.984848\pi$
$383$		0			0		0.998867	+	0.0475819i	$0.0151515\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.22848	+	8.13567i	−0.265779	+	0.413560i
$388$	0.668119	+	0.305120i	0.0339186	+	0.0154901i
$389$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$389$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	23.4583	+	27.0723i	1.17734	+	1.35872i	0.919770	+	0.392458i	$0.128375\pi$
$397$	23.4583	+	27.0723i	1.17734	+	1.35872i	0.257566	+	0.966261i	$0.417080\pi$
$398$		0			0
$399$	24.4905	−	7.19107i	1.22606	−	0.360004i
$400$	17.7767	+	9.16453i	0.888835	+	0.458227i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$	−25.5117			−1.27083
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	37.7497	−	1.79824i	1.86660	−	0.0889172i	0.916346	−	0.400387i	$-0.131124\pi$
$409$	37.7497	−	1.79824i	1.86660	−	0.0889172i	0.950256	+	0.311470i	$0.100821\pi$
$410$		0			0
$411$		0			0
$412$	7.05025	+	29.0615i	0.347341	+	1.43176i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−34.3535	−	22.0776i	−1.68230	−	1.08115i
$418$		0			0
$419$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$419$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$420$		0			0
$421$	−1.84174	+	38.6630i	−0.0897612	+	1.88432i	0.286890	+	0.957963i	$0.407378\pi$
$421$	−1.84174	+	38.6630i	−0.0897612	+	1.88432i	−0.376652	+	0.926355i	$0.622925\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.74747	−	26.0642i	0.181353	−	1.26133i
$428$		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
$433$	2.93448	−	7.32998i	0.141022	−	0.352257i	−0.840996	−	0.541041i	$-0.818030\pi$
$433$	2.93448	−	7.32998i	0.141022	−	0.352257i	0.982019	+	0.188784i	$0.0604547\pi$
$434$		0			0
$435$		0			0
$436$	4.49793	+	8.72477i	0.215412	+	0.417841i
$437$		0			0
$438$		0			0
$439$	4.57719	+	7.92792i	0.218457	+	0.378379i	0.954336	−	0.298734i	$-0.0965643\pi$
$439$	4.57719	+	7.92792i	0.218457	+	0.378379i	−0.735879	+	0.677113i	$0.763231\pi$
$440$		0			0
$441$	5.09893	−	4.00985i	0.242806	−	0.190945i
$442$		0			0
$443$		0			0		0.0950560	−	0.995472i	$-0.469697\pi$
$443$		0			0		−0.0950560	+	0.995472i	$0.530303\pi$
$444$	−28.3937	−	4.08239i	−1.34750	−	0.193742i
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−16.6281	+	5.75506i	−0.785606	+	0.271901i
$449$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$449$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−1.08255	−	0.374673i	−0.0508625	−	0.0176037i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	33.0126	+	25.9614i	1.54427	+	1.21442i	0.887953	+	0.459935i	$0.152127\pi$
$457$	33.0126	+	25.9614i	1.54427	+	1.21442i	0.656312	+	0.754489i	$0.272115\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$461$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$462$		0			0
$463$	−4.02031	+	20.8594i	−0.186840	+	0.969416i	0.760537	+	0.649295i	$0.224936\pi$
$463$	−4.02031	+	20.8594i	−0.186840	+	0.969416i	−0.947376	+	0.320122i	$0.896276\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$467$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$468$		−	13.9644i		−	0.645502i
$469$	16.5430	+	7.10340i	0.763885	+	0.328004i
$470$		0			0
$471$	18.2660	−	35.4311i	0.841653	−	1.63258i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−32.8946	−	6.33991i	−1.50931	−	0.290895i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$479$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$480$		0			0
$481$	11.9136	−	15.1494i	0.543214	−	0.690753i
$482$		0			0
$483$		0			0
$484$	18.5076	+	11.8941i	0.841254	+	0.540641i
$485$		0			0
$486$		0			0
$487$	−3.59794	−	37.6793i	−0.163038	−	1.70741i	−0.593524	−	0.804816i	$-0.702264\pi$
$487$	−3.59794	−	37.6793i	−0.163038	−	1.70741i	0.430486	−	0.902597i	$-0.358342\pi$
$488$		0			0
$489$	41.0587	+	9.96074i	1.85674	+	0.450440i
$490$		0			0
$491$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$491$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	33.1366	+	28.7130i	1.48788	+	1.28925i
$497$		0			0
$498$		0			0
$499$	−23.5882	+	13.6187i	−1.05595	+	0.609656i	−0.924310	−	0.381641i	$-0.875359\pi$
$499$	−23.5882	+	13.6187i	−1.05595	+	0.609656i	−0.131644	+	0.991297i	$0.542026\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.458227	−	0.888835i	$-0.651515\pi$
$503$		0			0		0.458227	+	0.888835i	$0.348485\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−11.3749	−	6.56728i	−0.505176	−	0.291663i
$508$	34.8145	−	27.3785i	1.54465	−	1.21472i
$509$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$509$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$510$		0			0
$511$	−21.3870	−	3.07499i	−0.946107	−	0.136030i
$512$		0			0
$513$	24.0245	−	25.1962i	1.06071	−	1.11244i
$514$		0			0
$515$		0			0
$516$	−2.63272	+	10.8522i	−0.115899	+	0.477742i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$521$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$522$		0			0
$523$	−28.8508	+	11.5501i	−1.26156	+	0.505051i	−0.903476	−	0.428640i	$-0.858993\pi$
$523$	−28.8508	+	11.5501i	−1.26156	+	0.505051i	−0.358081	+	0.933691i	$0.616569\pi$
$524$		0			0
$525$	18.7039	−	3.60488i	0.816305	−	0.157330i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	1.09438	+	22.9739i	0.0475819	+	0.998867i
$530$		0			0
$531$		0			0
$532$	24.0081	−	17.0961i	1.04088	−	0.741209i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	25.2811	−	21.9062i	1.08692	−	0.941822i	0.0883944	−	0.996086i	$-0.471826\pi$
$541$	25.2811	−	21.9062i	1.08692	−	0.941822i	0.998527	+	0.0542631i	$0.0172810\pi$
$542$		0			0
$543$	−24.2837	+	1.15677i	−1.04211	+	0.0496419i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−8.82832	−	45.8057i	−0.377472	−	1.95851i	−0.261156	−	0.965297i	$-0.584104\pi$
$547$	−8.82832	−	45.8057i	−0.377472	−	1.95851i	−0.116316	−	0.993212i	$-0.537109\pi$
$548$		0			0
$549$	−13.3486	−	33.3432i	−0.569704	−	1.42305i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−22.4118	+	31.4729i	−0.953046	+	1.33837i
$554$		0			0
$555$		0			0
$556$	−45.8242	−	11.1168i	−1.94338	−	0.471459i
$557$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$557$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$558$		0			0
$559$	−5.42993	−	5.17742i	−0.229661	−	0.218982i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$563$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−7.35720	+	18.3774i	−0.308974	+	0.771779i
$568$		0			0
$569$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$569$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$570$		0			0
$571$	−34.4035	+	32.8036i	−1.43974	+	1.37279i	−0.648655	+	0.761083i	$0.724668\pi$
$571$	−34.4035	+	32.8036i	−1.43974	+	1.37279i	−0.791085	+	0.611706i	$0.790483\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−15.7167	+	18.1380i	−0.654861	+	0.755750i
$577$	−3.70130	+	38.7617i	−0.154087	+	1.61367i	0.506034	+	0.862513i	$0.331111\pi$
$577$	−3.70130	+	38.7617i	−0.154087	+	1.61367i	−0.660121	+	0.751159i	$0.729495\pi$
$578$		0			0
$579$	−17.2065	+	7.85793i	−0.715076	+	0.326564i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.945001	−	0.327068i	$-0.893939\pi$
$587$		0			0		0.945001	+	0.327068i	$0.106061\pi$
$588$	4.04954	−	6.30121i	0.167000	−	0.259857i
$589$	−66.8052	−	30.5089i	−2.75266	−	1.25710i
$590$		0			0
$591$		0			0
$592$	−32.5247	+	6.26863i	−1.33676	+	0.257639i
$593$		0			0		0.971812	−	0.235759i	$-0.0757576\pi$
$593$		0			0		−0.971812	+	0.235759i	$0.924242\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	9.24457	−	47.9654i	0.378355	−	1.96309i
$598$		0			0
$599$		0			0		0.814576	−	0.580057i	$-0.196970\pi$
$599$		0			0		−0.814576	+	0.580057i	$0.803030\pi$
$600$		0			0
$601$	15.6996	+	8.09371i	0.640400	+	0.330149i	0.747660	−	0.664082i	$-0.231177\pi$
$601$	15.6996	+	8.09371i	0.640400	+	0.330149i	−0.107260	+	0.994231i	$0.534208\pi$
$602$		0			0
$603$	24.3853	−	2.89128i	0.993044	−	0.117742i
$604$	−1.32277			−0.0538227
$605$		0			0
$606$		0			0
$607$	1.65824	+	2.32867i	0.0673059	+	0.0945179i	0.846857	−	0.531821i	$-0.178492\pi$
$607$	1.65824	+	2.32867i	0.0673059	+	0.0945179i	−0.779551	+	0.626339i	$0.784553\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.26007	+	5.19409i	0.0508938	+	0.209787i	0.991581	−	0.129488i	$-0.0413334\pi$
$613$	1.26007	+	5.19409i	0.0508938	+	0.209787i	−0.940687	+	0.339275i	$0.889818\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$617$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$618$		0			0
$619$	−12.6357	+	36.5084i	−0.507870	+	1.46740i	0.341644	+	0.939829i	$0.389016\pi$
$619$	−12.6357	+	36.5084i	−0.507870	+	1.46740i	−0.849514	+	0.527566i	$0.823105\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−5.27385	−	15.2378i	−0.211123	−	0.610000i
$625$	−23.9873	−	7.04331i	−0.959493	−	0.281733i
$626$		0			0
$627$		0			0
$628$	6.55063	−	45.5606i	0.261398	−	1.81807i
$629$		0			0
$630$		0			0
$631$	6.71953	+	8.54458i	0.267500	+	0.340154i	0.901183	−	0.433439i	$-0.142700\pi$
$631$	6.71953	+	8.54458i	0.267500	+	0.340154i	−0.633683	+	0.773593i	$0.718457\pi$
$632$		0			0
$633$	−42.2222	+	24.3770i	−1.67818	+	0.968899i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	2.30598	+	4.47298i	0.0913664	+	0.177226i
$638$		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
$643$	−29.4531	+	33.9907i	−1.16152	+	1.34046i	−0.231548	+	0.972824i	$0.574379\pi$
$643$	−29.4531	+	33.9907i	−1.16152	+	1.34046i	−0.929969	+	0.367638i	$0.880167\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.690079	−	0.723734i	$-0.257576\pi$
$647$		0			0		−0.690079	+	0.723734i	$0.742424\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	41.7119	+	1.98698i	1.63482	+	0.0778761i
$652$	48.5648	−	4.63738i	1.90195	−	0.181614i
$653$		0			0		−0.814576	−	0.580057i	$-0.803030\pi$
$653$		0			0		0.814576	+	0.580057i	$0.196970\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−27.3598	+	10.9532i	−1.06741	+	0.427326i
$658$		0			0
$659$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$659$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$660$		0			0
$661$	27.5984	+	42.9440i	1.07345	+	1.67033i	0.637763	+	0.770233i	$0.279860\pi$
$661$	27.5984	+	42.9440i	1.07345	+	1.67033i	0.435692	+	0.900096i	$0.356504\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		−	47.5207i		−	1.83725i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−6.49917	−	22.1341i	−0.250524	−	0.853208i	−0.984701	−	0.174250i	$-0.944250\pi$
$673$	−6.49917	−	22.1341i	−0.250524	−	0.853208i	0.734177	−	0.678958i	$-0.237568\pi$
$674$		0			0
$675$	19.6349	−	17.0138i	0.755750	−	0.654861i
$676$	−14.8924	−	2.87028i	−0.572785	−	0.110395i
$677$		0			0		0.998867	−	0.0475819i	$-0.0151515\pi$
$677$		0			0		−0.998867	+	0.0475819i	$0.984848\pi$
$678$		0			0
$679$	0.679527	−	0.436705i	0.0260778	−	0.0167592i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.371662	−	0.928368i	$-0.621212\pi$
$683$		0			0		0.371662	+	0.928368i	$0.378788\pi$
$684$	16.6997	−	36.5672i	0.638528	−	1.39818i
$685$		0			0
$686$		0			0
$687$	11.1713	−	15.6879i	0.426212	−	0.598532i
$688$	1.22570	+	12.8361i	0.0467295	+	0.489373i
$689$		0			0
$690$		0			0
$691$	−17.1943	−	49.6798i	−0.654103	−	1.88991i	−0.336465	−	0.941696i	$-0.609231\pi$
$691$	−17.1943	−	49.6798i	−0.654103	−	1.88991i	−0.317639	−	0.948212i	$-0.602890\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	19.0481	−	10.9974i	0.719952	−	0.415664i
$701$		0			0		0.371662	−	0.928368i	$-0.378788\pi$
$701$		0			0		−0.371662	+	0.928368i	$0.621212\pi$
$702$		0			0
$703$	49.3139	−	25.4231i	1.85991	−	0.958851i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	27.3328	−	21.4947i	1.02650	−	0.807251i	0.0450561	−	0.998984i	$-0.485653\pi$
$709$	27.3328	−	21.4947i	1.02650	−	0.807251i	0.981447	+	0.191733i	$0.0614109\pi$
$710$		0			0
$711$	−5.00939	+	52.4607i	−0.187867	+	1.96743i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$719$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$720$		0			0
$721$	31.0785	+	10.7564i	1.15742	+	0.400588i
$722$		0			0
$723$	4.24974	+	1.94079i	0.158049	+	0.0721787i
$724$	−26.0613	+	10.4334i	−0.968560	+	0.387753i
$725$		0			0
$726$		0			0
$727$	26.0963	−	6.33090i	0.967859	−	0.234800i	0.279480	−	0.960151i	$-0.409838\pi$
$727$	26.0963	−	6.33090i	0.967859	−	0.234800i	0.688379	+	0.725351i	$0.258323\pi$
$728$		0			0
$729$	3.84250	+	26.7252i	0.142315	+	0.989821i
$730$		0			0
$731$		0			0
$732$	−27.1585	−	31.3426i	−1.00381	−	1.15845i
$733$	36.2626	−	25.8225i	1.33939	−	0.953775i	0.339477	−	0.940614i	$-0.389750\pi$
$733$	36.2626	−	25.8225i	1.33939	−	0.953775i	0.999913	−	0.0131610i	$-0.00418940\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−24.3992	+	47.3279i	−0.897541	+	1.74099i	−0.269132	+	0.963103i	$0.586737\pi$
$739$	−24.3992	+	47.3279i	−0.897541	+	1.74099i	−0.628409	+	0.777883i	$0.716294\pi$
$740$		0			0
$741$	15.6666	+	22.0007i	0.575527	+	0.808215i
$742$		0			0
$743$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$743$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−15.5186	+	33.9810i	−0.566282	+	1.23998i	0.382472	+	0.923967i	$0.375073\pi$
$751$	−15.5186	+	33.9810i	−0.566282	+	1.23998i	−0.948753	+	0.316017i	$0.897654\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−1.08762	+	22.8319i	−0.0395562	+	0.830387i
$757$	41.4968	+	10.0670i	1.50823	+	0.365892i	0.902818	−	0.430022i	$-0.141494\pi$
$757$	41.4968	+	10.0670i	1.50823	+	0.365892i	0.605409	+	0.795914i	$0.293009\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$761$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$762$		0			0
$763$	10.7462	+	1.02613i	0.389037	+	0.0371485i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−10.2998	+	25.7277i	−0.371662	+	0.928368i
$769$	30.9182	+	32.4260i	1.11494	+	1.16931i	0.984046	+	0.177916i	$0.0569356\pi$
$769$	30.9182	+	32.4260i	1.11494	+	1.16931i	0.130892	+	0.991397i	$0.458216\pi$
$770$		0			0
$771$		0			0
$772$	−15.8079	+	15.0728i	−0.568939	+	0.542482i
$773$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$773$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$774$		0			0
$775$	−47.4647	−	27.4038i	−1.70498	−	0.984372i
$776$		0			0
$777$	−20.6588	+	23.8415i	−0.741131	+	0.855310i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	2.03908	−	8.40521i	0.0728243	−	0.300186i
$785$		0			0
$786$		0			0
$787$	45.5535	+	32.4385i	1.62381	+	1.15631i	0.858848	+	0.512230i	$0.171180\pi$
$787$	45.5535	+	32.4385i	1.62381	+	1.15631i	0.764959	+	0.644078i	$0.222759\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	27.3600	−	5.27320i	0.971580	−	0.187257i
$794$		0			0
$795$		0			0
$796$	−8.02727	−	55.8309i	−0.284519	−	1.97887i
$797$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$797$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$	25.5171	−	12.3644i	0.899918	−	0.436059i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$809$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$810$		0			0
$811$	−30.4265	+	1.44939i	−1.06842	+	0.0508950i	−0.574414	−	0.818565i	$-0.694770\pi$
$811$	−30.4265	+	1.44939i	−1.06842	+	0.0508950i	−0.494004	+	0.869460i	$0.664467\pi$
$812$		0			0
$813$	−41.1271	+	26.4308i	−1.44239	+	0.926968i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−8.02728	−	20.0512i	−0.280839	−	0.701502i
$818$		0			0
$819$	−12.9193	−	8.30274i	−0.451437	−	0.290121i
$820$		0			0
$821$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$821$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$822$		0			0
$823$	−1.67051	+	35.0683i	−0.0582302	+	1.22240i	0.760928	+	0.648836i	$0.224744\pi$
$823$	−1.67051	+	35.0683i	−0.0582302	+	1.22240i	−0.819159	+	0.573567i	$0.805559\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$827$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$828$		0			0
$829$	0.218470	−	1.51950i	0.00758779	−	0.0527743i	−0.985676	−	0.168651i	$-0.946059\pi$
$829$	0.218470	−	1.51950i	0.00758779	−	0.0527743i	0.993264	+	0.115877i	$0.0369679\pi$
$830$		0			0
$831$	41.9038	+	36.3098i	1.45363	+	1.25957i
$832$	−11.5096	−	14.6356i	−0.399023	−	0.507399i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	50.6260	−	26.0995i	1.74989	−	0.902131i
$838$		0			0
$839$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$839$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$840$		0			0
$841$	−14.5000	−	25.1147i	−0.500000	−	0.866025i
$842$		0			0
$843$		0			0
$844$	−36.8662	+	42.5459i	−1.26899	+	1.46449i
$845$		0			0
$846$		0			0
$847$	22.0080	−	10.0507i	0.756203	−	0.345346i
$848$		0			0
$849$	−14.0583	+	47.8783i	−0.482481	+	1.64318i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−49.6480	+	4.74081i	−1.69991	+	0.162322i	−0.899440	−	0.437045i	$-0.856025\pi$
$853$	−49.6480	+	4.74081i	−1.69991	+	0.162322i	−0.800475	+	0.599367i	$0.795419\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$857$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$858$		0			0
$859$	26.1851	+	20.5922i	0.893425	+	0.702597i	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	26.1851	+	20.5922i	0.893425	+	0.702597i	−0.0619231	+	0.998081i	$0.519723\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$863$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−23.9851	+	17.0797i	−0.814576	+	0.580057i
$868$	46.2662	−	13.5850i	1.57038	−	0.461104i
$869$		0			0
$870$		0			0
$871$	−1.37775	+	19.0006i	−0.0466831	+	0.643812i
$872$		0			0
$873$	0.504847	−	0.979266i	0.0170865	−	0.0331431i
$874$		0			0
$875$		0			0
$876$	−25.7182	+	22.2850i	−0.868938	+	0.752939i
$877$	49.1556	+	9.47397i	1.65987	+	0.319913i	0.931077	−	0.364823i	$-0.118871\pi$
$877$	49.1556	+	9.47397i	1.65987	+	0.319913i	0.728791	+	0.684737i	$0.240083\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$881$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$882$		0			0
$883$	36.3219	−	46.1870i	1.22233	−	1.55432i	0.493248	−	0.869889i	$-0.335809\pi$
$883$	36.3219	−	46.1870i	1.22233	−	1.55432i	0.729080	−	0.684428i	$-0.239948\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$887$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$888$		0			0
$889$	−4.62999	−	48.4875i	−0.155285	−	1.62622i
$890$		0			0
$891$		0			0
$892$	−17.9469	−	51.8542i	−0.600907	−	1.73621i
$893$		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
$903$	8.47474	+	8.88805i	0.282022	+	0.295776i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−7.27793	−	2.91364i	−0.241660	−	0.0967459i	0.247671	−	0.968844i	$-0.420335\pi$
$907$	−7.27793	−	2.91364i	−0.241660	−	0.0967459i	−0.489331	+	0.872098i	$0.662759\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$911$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$912$	4.41240	−	46.2087i	0.146109	−	1.53012i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	6.26528	−	21.3376i	0.207011	−	0.705013i
$917$		0			0
$918$		0			0
$919$	−59.6479	−	2.84138i	−1.96760	−	0.0937284i	−0.975568	−	0.219698i	$-0.929493\pi$
$919$	−59.6479	−	2.84138i	−1.96760	−	0.0937284i	−0.992034	+	0.125970i	$0.959796\pi$
$920$		0			0
$921$	18.2907	+	13.0248i	0.602700	+	0.429181i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	38.4383	−	15.3884i	1.26384	−	0.505967i
$926$		0			0
$927$	44.0461	−	8.48919i	1.44666	−	0.278822i
$928$		0			0
$929$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$929$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$930$		0			0
$931$	0.689323	+	14.4707i	0.0225916	+	0.474257i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	57.6461i		−	1.88322i	−0.336711	−	0.941608i	$-0.609314\pi$
$937$		−	57.6461i		−	1.88322i	0.336711	−	0.941608i	$-0.390686\pi$
$938$		0			0
$939$	−60.9814			−1.99005
$940$		0			0
$941$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$941$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$947$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$948$	14.3464	+	59.1367i	0.465949	+	1.92067i
$949$	−4.32694	−	22.4503i	−0.140458	−	0.728767i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$953$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−64.5242	−	61.5237i	−2.08143	−	1.98464i
$962$		0			0
$963$		0			0
$964$	5.37025	+	0.512797i	0.172964	+	0.0165161i
$965$		0			0
$966$		0			0
$967$	−13.0819	+	22.6586i	−0.420687	+	0.728651i	−0.996007	−	0.0892774i	$-0.971544\pi$
$967$	−13.0819	+	22.6586i	−0.420687	+	0.728651i	0.575320	+	0.817928i	$0.304878\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$971$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$972$	14.2861	+	27.7111i	0.458227	+	0.888835i
$973$	−37.5304	+	35.7852i	−1.20317	+	1.14722i
$974$		0			0
$975$	10.0779	+	17.4554i	0.322751	+	0.559021i
$976$	−41.4721	−	23.9440i	−1.32749	−	0.766427i
$977$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$977$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	13.3934	−	6.11654i	0.427617	−	0.195286i
$982$		0			0
$983$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$983$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	25.4042	+	18.0902i	0.808215	+	0.575527i
$989$		0			0
$990$		0			0
$991$	−3.42242	−	1.56297i	−0.108717	−	0.0496493i	0.360314	−	0.932831i	$-0.382669\pi$
$991$	−3.42242	−	1.56297i	−0.108717	−	0.0496493i	−0.469031	+	0.883182i	$0.655397\pi$
$992$		0			0
$993$	−47.8990	−	37.6682i	−1.52003	−	1.19536i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.13456	−	7.89103i	−0.0359318	−	0.249911i	0.963937	−	0.266132i	$-0.0857457\pi$
$997$	−1.13456	−	7.89103i	−0.0359318	−	0.249911i	−0.999868	+	0.0162206i	$0.994837\pi$
$998$		0			0
$999$	−8.14319	+	42.2509i	−0.257639	+	1.33676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.p.a.182.1	yes	20
3.2	odd	2	CM	201.2.p.a.182.1	yes	20
67.7	odd	66	inner	201.2.p.a.74.1	✓	20
201.74	even	66	inner	201.2.p.a.74.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.p.a.74.1	✓	20	67.7	odd	66	inner
201.2.p.a.74.1	✓	20	201.74	even	66	inner
201.2.p.a.182.1	yes	20	1.1	even	1	trivial
201.2.p.a.182.1	yes	20	3.2	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(-0.487975 - 1.66189i) q^{3} +(-1.16011 - 1.62915i) q^{4} +(-2.19700 + 0.104656i) q^{7} +(-2.52376 + 1.62192i) q^{9} +O(q^{10})\)	\(q+(-0.487975 - 1.66189i) q^{3} +(-1.16011 - 1.62915i) q^{4} +(-2.19700 + 0.104656i) q^{7} +(-2.52376 + 1.62192i) q^{9} +(-2.14137 + 2.72297i) q^{12} +(-0.865004 - 2.16068i) q^{13} +(-1.30827 + 3.78000i) q^{16} +(0.318799 - 6.69240i) q^{19} +(1.24601 + 3.60010i) q^{21} +(0.711574 - 4.94911i) q^{25} +(3.92699 + 3.40276i) q^{27} +(2.71927 + 3.45783i) q^{28} +(4.07398 - 10.1763i) q^{31} +(5.57021 + 2.22997i) q^{36} +(4.14042 + 7.17141i) q^{37} +(-3.16871 + 2.49190i) q^{39} +(2.93232 - 1.33914i) q^{43} +(6.92036 + 0.329657i) q^{48} +(-2.15246 + 0.205535i) q^{49} +(-2.51657 + 3.91585i) q^{52} +(-11.2776 + 2.73592i) q^{57} +(-2.26571 + 11.7556i) q^{61} +(5.37495 - 3.82748i) q^{63} +(7.67594 - 2.25386i) q^{64} +(-7.35911 - 3.58379i) q^{67} +(9.64611 + 1.85914i) q^{73} +(-8.57211 + 1.23248i) q^{75} +(-11.2728 + 7.24458i) q^{76} +(10.8589 - 13.8082i) q^{79} +(3.73874 - 8.18669i) q^{81} +(4.41960 - 6.20646i) q^{84} +(2.12654 + 4.65647i) q^{91} +(-18.8999 - 1.80472i) q^{93} +(-0.318045 + 0.183623i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 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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