LMFDB - Embedded newform 201.2.p.a.2.1

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			2.1
Root			$0.723734 - 0.690079i$ of defining polynomial
Character	$\chi$	$=$	201.2
Dual form			201.2.p.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.487975 - 1.66189i) q^{3} +(1.99094 + 0.190112i) q^{4} +(2.32668 + 4.51312i) q^{7} +(-2.52376 - 1.62192i) q^{9} +O(q^{10})$	$q+(0.487975 - 1.66189i) q^{3} +(1.99094 + 0.190112i) q^{4} +(2.32668 + 4.51312i) q^{7} +(-2.52376 - 1.62192i) q^{9} +(1.28748 - 3.21596i) q^{12} +(-3.24013 - 4.12016i) q^{13} +(3.92771 + 0.757005i) q^{16} +(-7.69011 - 3.96453i) q^{19} +(8.63568 - 1.66439i) q^{21} +(0.711574 + 4.94911i) q^{25} +(-3.92699 + 3.40276i) q^{27} +(3.77428 + 9.42770i) q^{28} +(-0.235527 + 0.299497i) q^{31} +(-4.71632 - 3.70895i) q^{36} +(-2.71727 - 4.70645i) q^{37} +(-8.42836 + 3.37421i) q^{39} +(6.07141 + 2.77272i) q^{43} +(3.17469 - 6.15803i) q^{48} +(-10.8945 + 15.2991i) q^{49} +(-5.66762 - 8.81899i) q^{52} +(-10.3412 + 10.8455i) q^{57} +(-4.39135 - 1.51986i) q^{61} +(1.44796 - 15.1637i) q^{63} +(7.67594 + 2.25386i) q^{64} +(8.07068 + 1.36532i) q^{67} +(-4.06926 + 11.7573i) q^{73} +(8.57211 + 1.23248i) q^{75} +(-14.5569 - 9.35513i) q^{76} +(5.97911 - 14.9351i) q^{79} +(3.73874 + 8.18669i) q^{81} +(17.5096 - 1.67196i) q^{84} +(11.0561 - 24.2094i) q^{91} +(0.382799 + 0.537567i) q^{93} +(8.95348 - 5.16930i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

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

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		−0.998867	−	0.0475819i	$-0.984848\pi$
$2$		0			0		0.998867	+	0.0475819i	$0.0151515\pi$
$3$	0.487975	−	1.66189i	0.281733	−	0.959493i
$3$	0.487975	−	1.66189i	0.281733	−	0.959493i
$4$	1.99094	+	0.190112i	0.995472	+	0.0950560i
$5$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$5$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$6$		0			0
$7$	2.32668	+	4.51312i	0.879401	+	1.70580i	0.689881	+	0.723923i	$0.257663\pi$
$7$	2.32668	+	4.51312i	0.879401	+	1.70580i	0.189520	+	0.981877i	$0.439307\pi$
$8$		0			0
$9$	−2.52376	−	1.62192i	−0.841254	−	0.540641i
$10$		0			0
$11$		0			0		0.945001	−	0.327068i	$-0.106061\pi$
$11$		0			0		−0.945001	+	0.327068i	$0.893939\pi$
$12$	1.28748	−	3.21596i	0.371662	−	0.928368i
$13$	−3.24013	−	4.12016i	−0.898650	−	1.14273i	−0.989162	−	0.146831i	$-0.953093\pi$
$13$	−3.24013	−	4.12016i	−0.898650	−	1.14273i	0.0905113	−	0.995895i	$-0.471150\pi$
$14$		0			0
$15$		0			0
$16$	3.92771	+	0.757005i	0.981929	+	0.189251i
$17$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$17$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$18$		0			0
$19$	−7.69011	−	3.96453i	−1.76423	−	0.909525i	−0.938353	−	0.345677i	$-0.887649\pi$
$19$	−7.69011	−	3.96453i	−1.76423	−	0.909525i	−0.825879	−	0.563848i	$-0.809320\pi$
$20$		0			0
$21$	8.63568	−	1.66439i	1.88446	−	0.363200i
$22$		0			0
$23$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$23$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$24$		0			0
$25$	0.711574	+	4.94911i	0.142315	+	0.989821i
$26$		0			0
$27$	−3.92699	+	3.40276i	−0.755750	+	0.654861i
$28$	3.77428	+	9.42770i	0.713272	+	1.78167i
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$		0			0
$31$	−0.235527	+	0.299497i	−0.0423019	+	0.0537912i	−0.806744	−	0.590901i	$-0.798772\pi$
$31$	−0.235527	+	0.299497i	−0.0423019	+	0.0537912i	0.764442	+	0.644693i	$0.223015\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−4.71632	−	3.70895i	−0.786053	−	0.618159i
$37$	−2.71727	−	4.70645i	−0.446716	−	0.773735i	0.551454	−	0.834205i	$-0.314073\pi$
$37$	−2.71727	−	4.70645i	−0.446716	−	0.773735i	−0.998170	+	0.0604704i	$0.980740\pi$
$38$		0			0
$39$	−8.42836	+	3.37421i	−1.34962	+	0.540305i
$40$		0			0
$41$		0			0		0.814576	−	0.580057i	$-0.196970\pi$
$41$		0			0		−0.814576	+	0.580057i	$0.803030\pi$
$42$		0			0
$43$	6.07141	+	2.77272i	0.925882	+	0.422836i	0.820533	−	0.571599i	$-0.193677\pi$
$43$	6.07141	+	2.77272i	0.925882	+	0.422836i	0.105349	+	0.994435i	$0.466404\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$47$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$48$	3.17469	−	6.15803i	0.458227	−	0.888835i
$49$	−10.8945	+	15.2991i	−1.55635	+	2.18559i
$50$		0			0
$51$		0			0
$52$	−5.66762	−	8.81899i	−0.785958	−	1.22297i
$53$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$53$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−10.3412	+	10.8455i	−1.36972	+	1.43653i
$58$		0			0
$59$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$59$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$60$		0			0
$61$	−4.39135	−	1.51986i	−0.562255	−	0.194598i	0.0311325	−	0.999515i	$-0.490089\pi$
$61$	−4.39135	−	1.51986i	−0.562255	−	0.194598i	−0.593388	+	0.804917i	$0.702210\pi$
$62$		0			0
$63$	1.44796	−	15.1637i	0.182426	−	1.91045i
$64$	7.67594	+	2.25386i	0.959493	+	0.281733i
$65$		0			0
$66$		0			0
$67$	8.07068	+	1.36532i	0.985991	+	0.166800i
$67$	8.07068	+	1.36532i	0.985991	+	0.166800i
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$71$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$72$		0			0
$73$	−4.06926	+	11.7573i	−0.476271	+	1.37609i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−4.06926	+	11.7573i	−0.476271	+	1.37609i	−0.885915	+	0.463848i	$0.846468\pi$
$74$		0			0
$75$	8.57211	+	1.23248i	0.989821	+	0.142315i
$76$	−14.5569	−	9.35513i	−1.66979	−	1.07311i
$77$		0			0
$78$		0			0
$79$	5.97911	−	14.9351i	0.672702	−	1.68033i	−0.0586047	−	0.998281i	$-0.518665\pi$
$79$	5.97911	−	14.9351i	0.672702	−	1.68033i	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		−0.981929	−	0.189251i	$-0.939394\pi$
$83$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$84$	17.5096	−	1.67196i	1.91045	−	0.182426i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$89$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$90$		0			0
$91$	11.0561	−	24.2094i	1.15899	−	2.53783i
$92$		0			0
$93$	0.382799	+	0.537567i	0.0396945	+	0.0557431i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	8.95348	−	5.16930i	0.909088	−	0.524862i	0.0289506	−	0.999581i	$-0.490783\pi$
$97$	8.95348	−	5.16930i	0.909088	−	0.524862i	0.880138	+	0.474718i	$0.157450\pi$
$98$		0			0
$99$		0			0
$100$	0.475819	+	9.98867i	0.0475819	+	0.998867i
$101$		0			0		0.998867	−	0.0475819i	$-0.0151515\pi$
$101$		0			0		−0.998867	+	0.0475819i	$0.984848\pi$
$102$		0			0
$103$	14.6975	+	11.5583i	1.44819	+	1.13887i	0.964645	+	0.263553i	$0.0848943\pi$
$103$	14.6975	+	11.5583i	1.44819	+	1.13887i	0.483547	+	0.875318i	$0.339348\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$107$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$108$	−8.46532	+	6.02813i	−0.814576	+	0.580057i
$109$	−20.5759	+	2.95837i	−1.97082	+	0.283361i	−0.971983	+	0.235050i	$0.924475\pi$
$109$	−20.5759	+	2.95837i	−1.97082	+	0.283361i	−0.998832	+	0.0483110i	$0.984616\pi$
$110$		0			0
$111$	−9.14756	+	2.21917i	−0.868248	+	0.210635i
$112$	5.72206	+	19.4876i	0.540684	+	1.84140i
$113$		0			0		−0.189251	−	0.981929i	$-0.560606\pi$
$113$		0			0		0.189251	+	0.981929i	$0.439394\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.49473	+	15.6535i	0.138188	+	1.44717i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	8.64658	−	6.79975i	0.786053	−	0.618159i
$122$		0			0
$123$		0			0
$124$	−0.525859	+	0.551505i	−0.0472235	+	0.0495266i
$125$		0			0
$126$		0			0
$127$	19.9364	−	10.2779i	1.76907	−	0.912018i	0.839510	−	0.543345i	$-0.182842\pi$
$127$	19.9364	−	10.2779i	1.76907	−	0.912018i	0.929559	−	0.368674i	$-0.120188\pi$
$128$		0			0
$129$	7.57066	−	8.73701i	0.666559	−	0.769251i
$130$		0			0
$131$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$131$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$132$		0			0
$133$		−	43.9306i		−	3.80926i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$137$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$138$		0			0
$139$	−14.8372	−	12.8565i	−1.25848	−	1.09048i	−0.991948	−	0.126649i	$-0.959578\pi$
$139$	−14.8372	−	12.8565i	−1.25848	−	1.09048i	−0.266529	−	0.963827i	$-0.585877\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−8.68481	−	8.28095i	−0.723734	−	0.690079i
$145$		0			0
$146$		0			0
$147$	20.1092	+	25.5710i	1.65858	+	2.10906i
$148$	−4.51518	−	9.88686i	−0.371145	−	0.812694i
$149$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$149$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$150$		0			0
$151$	−24.1136	+	2.30257i	−1.96234	+	0.187381i	−0.997225	−	0.0744455i	$-0.976281\pi$
$151$	−24.1136	+	2.30257i	−1.96234	+	0.187381i	−0.965115	+	0.261826i	$0.915675\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−17.4219	+	5.11552i	−1.39487	+	0.409569i
$157$	0.127437	+	0.525304i	0.0101706	+	0.0419238i	0.976671	−	0.214742i	$-0.0688911\pi$
$157$	0.127437	+	0.525304i	0.0101706	+	0.0419238i	−0.966500	+	0.256666i	$0.917376\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	5.13438	−	8.89301i	0.402156	−	0.696554i	−0.591830	−	0.806063i	$-0.701594\pi$
$163$	5.13438	−	8.89301i	0.402156	−	0.696554i	0.993986	+	0.109509i	$0.0349277\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$167$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$168$		0			0
$169$	−3.41241	+	14.0662i	−0.262493	+	1.08201i
$170$		0			0
$171$	12.9778	+	22.4783i	0.992440	+	1.71896i
$172$	11.5607	+	6.67458i	0.881496	+	0.508932i
$173$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$173$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$174$		0			0
$175$	−20.6803	+	14.7264i	−1.56329	+	1.11321i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$179$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$180$		0			0
$181$	−0.436539	+	0.416239i	−0.0324477	+	0.0309388i	−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−0.436539	+	0.416239i	−0.0324477	+	0.0309388i	0.673682	+	0.739022i	$0.264712\pi$
$182$		0			0
$183$	−4.66871	+	6.55629i	−0.345121	+	0.484655i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−24.4939	−	9.80587i	−1.78167	−	0.713272i
$190$		0			0
$191$		0			0		0.690079	−	0.723734i	$-0.257576\pi$
$191$		0			0		−0.690079	+	0.723734i	$0.742424\pi$
$192$	7.49134	−	11.6568i	0.540641	−	0.841254i
$193$	−3.95302	+	27.4939i	−0.284545	+	1.97905i	−0.118080	+	0.993004i	$0.537674\pi$
$193$	−3.95302	+	27.4939i	−0.284545	+	1.97905i	−0.166465	+	0.986047i	$0.553235\pi$
$194$		0			0
$195$		0			0
$196$	−24.5988	+	28.3885i	−1.75706	+	2.02775i
$197$		0			0		0.0950560	−	0.995472i	$-0.469697\pi$
$197$		0			0		−0.0950560	+	0.995472i	$0.530303\pi$
$198$		0			0
$199$	0.907072	−	19.0418i	0.0643006	−	1.34984i	−0.704207	−	0.709995i	$-0.748697\pi$
$199$	0.907072	−	19.0418i	0.0643006	−	1.34984i	0.768507	−	0.639841i	$-0.221000\pi$
$200$		0			0
$201$	6.20730	−	12.7463i	0.437829	−	0.899058i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−9.60732	−	18.6356i	−0.666148	−	1.29215i
$209$		0			0
$210$		0			0
$211$	8.04920	+	7.67489i	0.554130	+	0.528361i	0.914574	−	0.404419i	$-0.132526\pi$
$211$	8.04920	+	7.67489i	0.554130	+	0.528361i	−0.360444	+	0.932781i	$0.617375\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−1.89966	−	0.366129i	−0.128957	−	0.0248545i
$218$		0			0
$219$	17.5537	+	12.5000i	1.18617	+	0.844669i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	16.0241	−	4.70511i	1.07305	−	0.315077i	0.302957	−	0.953004i	$-0.402026\pi$
$223$	16.0241	−	4.70511i	1.07305	−	0.315077i	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		−0.580057	−	0.814576i	$-0.696970\pi$
$227$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$228$	−22.6506	+	19.6269i	−1.50007	+	1.29982i
$229$	1.01773	+	2.54216i	0.0672533	+	0.167991i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	1.01773	+	2.54216i	0.0672533	+	0.167991i	−0.890934	+	0.454133i	$0.849949\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.971812	−	0.235759i	$-0.924242\pi$
$233$		0			0		0.971812	+	0.235759i	$0.0757576\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−21.9028	−	17.2246i	−1.42274	−	1.11886i
$238$		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
$241$	−4.01180	−	4.62986i	−0.258422	−	0.298235i	0.611681	−	0.791104i	$-0.290494\pi$
$241$	−4.01180	−	4.62986i	−0.258422	−	0.298235i	−0.870103	+	0.492869i	$0.835948\pi$
$242$		0			0
$243$	15.4298	−	2.21847i	0.989821	−	0.142315i
$244$	−8.45399	−	3.86081i	−0.541211	−	0.247163i
$245$		0			0
$246$		0			0
$247$	8.58247	+	44.5301i	0.546089	+	2.83338i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.0950560	−	0.995472i	$-0.530303\pi$
$251$		0			0		0.0950560	+	0.995472i	$0.469697\pi$
$252$	5.76562	−	29.9149i	0.363200	−	1.88446i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	14.8539	+	5.94660i	0.928368	+	0.371662i
$257$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$257$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$258$		0			0
$259$	14.9186	−	23.2137i	0.926994	−	1.44243i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$263$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	15.8087	+	4.25261i	0.965671	+	0.259769i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$	7.64739	−	26.0446i	0.464546	−	1.58210i	−0.310745	−	0.950493i	$-0.600579\pi$
$271$	7.64739	−	26.0446i	0.464546	−	1.58210i	0.775291	−	0.631604i	$-0.217603\pi$
$272$		0			0
$273$	−34.8383	−	30.1875i	−2.10851	−	1.82703i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	23.4356	+	15.0612i	1.40811	+	0.904937i	0.999968	−	0.00798138i	$-0.00254058\pi$
$277$	23.4356	+	15.0612i	1.40811	+	0.904937i	0.408142	+	0.912919i	$0.366177\pi$
$278$		0			0
$279$	1.08017	−	0.373852i	0.0646683	−	0.0223819i
$280$		0			0
$281$		0			0		−0.618159	−	0.786053i	$-0.712121\pi$
$281$		0			0		0.618159	+	0.786053i	$0.287879\pi$
$282$		0			0
$283$	−11.0217	+	7.08324i	−0.655174	+	0.421055i	−0.825554	−	0.564324i	$-0.809137\pi$
$283$	−11.0217	+	7.08324i	−0.655174	+	0.421055i	0.170379	+	0.985379i	$0.445501\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	16.6928	−	3.21727i	0.981929	−	0.189251i
$290$		0			0
$291$	−4.22173	−	17.4022i	−0.247482	−	1.02013i
$292$	−10.3369	+	22.6346i	−0.604920	+	1.32459i
$293$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$293$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	16.8323	+	4.08346i	0.971812	+	0.235759i
$301$	1.61258	+	33.8523i	0.0929477	+	1.95121i
$302$		0			0
$303$		0			0
$304$	−27.2034	−	21.3930i	−1.56022	−	1.22697i
$305$		0			0
$306$		0			0
$307$	14.9607	−	5.98936i	0.853852	−	0.341831i	0.0968945	−	0.995295i	$-0.469109\pi$
$307$	14.9607	−	5.98936i	0.853852	−	0.341831i	0.756958	+	0.653464i	$0.226685\pi$
$308$		0			0
$309$	26.3806	−	18.7856i	1.50074	−	1.06867i
$310$		0			0
$311$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$311$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$312$		0			0
$313$	−3.21722	−	10.9568i	−0.181848	−	0.619317i	−0.999075	−	0.0430013i	$-0.986308\pi$
$313$	−3.21722	−	10.9568i	−0.181848	−	0.619317i	0.817227	−	0.576316i	$-0.195510\pi$
$314$		0			0
$315$		0			0
$316$	14.7434	−	28.5982i	0.829382	−	1.60878i
$317$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$317$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	5.88722	+	17.0100i	0.327068	+	0.945001i
$325$	18.0855	−	18.9675i	1.00320	−	1.05213i
$326$		0			0
$327$	−5.12405	+	35.6385i	−0.283361	+	1.97082i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3.29065	+	34.4612i	−0.180870	+	1.89416i	0.216166	+	0.976357i	$0.430645\pi$
$331$	−3.29065	+	34.4612i	−0.180870	+	1.89416i	−0.397036	+	0.917803i	$0.629961\pi$
$332$		0			0
$333$	−0.775757	+	16.2851i	−0.0425112	+	0.892420i
$334$		0			0
$335$		0			0
$336$	35.1784			1.91914
$337$	−25.4715	−	1.21336i	−1.38752	−	0.0660957i	−0.659527	−	0.751681i	$-0.729244\pi$
$337$	−25.4715	−	1.21336i	−1.38752	−	0.0660957i	−0.727993	+	0.685585i	$0.759547\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−59.2134	−	8.51361i	−3.19723	−	0.459692i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		0.371662	−	0.928368i	$-0.378788\pi$
$347$		0			0		−0.371662	+	0.928368i	$0.621212\pi$
$348$		0			0
$349$	11.7634	+	25.7582i	0.629678	+	1.37880i	0.908266	+	0.418392i	$0.137406\pi$
$349$	11.7634	+	25.7582i	0.629678	+	1.37880i	−0.278588	+	0.960411i	$0.589866\pi$
$350$		0			0
$351$	26.7439	+	5.15446i	1.42748	+	0.275124i
$352$		0			0
$353$		0			0		−0.814576	−	0.580057i	$-0.803030\pi$
$353$		0			0		0.814576	+	0.580057i	$0.196970\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$359$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$360$		0			0
$361$	32.3992	+	45.4984i	1.70522	+	2.39465i
$362$		0			0
$363$	−7.08112	−	17.6878i	−0.371662	−	0.928368i
$364$	26.6145	−	46.0976i	1.39498	−	2.41617i
$365$		0			0
$366$		0			0
$367$	21.3124	+	5.17032i	1.11250	+	0.269889i	0.749567	−	0.661928i	$-0.230262\pi$
$367$	21.3124	+	5.17032i	1.11250	+	0.269889i	0.362929	+	0.931817i	$0.381777\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.659934	+	1.14304i	0.0342160	+	0.0592639i
$373$	−32.5862	−	18.8137i	−1.68725	−	0.974134i	−0.956610	−	0.291370i	$-0.905889\pi$
$373$	−32.5862	−	18.8137i	−1.68725	−	0.974134i	−0.730639	−	0.682764i	$-0.760778\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−6.00368	+	1.45648i	−0.308388	+	0.0748142i	−0.386967	−	0.922094i	$-0.626477\pi$
$379$	−6.00368	+	1.45648i	−0.308388	+	0.0748142i	0.0785782	+	0.996908i	$0.474962\pi$
$380$		0			0
$381$	−7.35232	−	38.1475i	−0.376671	−	1.95435i
$382$		0			0
$383$		0			0		0.458227	−	0.888835i	$-0.348485\pi$
$383$		0			0		−0.458227	+	0.888835i	$0.651515\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−10.8257	−	16.8450i	−0.550299	−	0.856282i
$388$	18.8086	−	8.58961i	0.954863	−	0.436071i
$389$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$389$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−24.0023	+	27.7002i	−1.20464	+	1.39023i	−0.305722	+	0.952121i	$0.598898\pi$
$397$	−24.0023	+	27.7002i	−1.20464	+	1.39023i	−0.898921	+	0.438111i	$0.855648\pi$
$398$		0			0
$399$	−73.0078	−	21.4370i	−3.65496	−	1.07319i
$400$	−0.951638	+	19.9773i	−0.0475819	+	0.998867i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$	1.99711			0.0994832
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−9.00162	−	17.4607i	−0.445101	−	0.863376i	−0.999515	−	0.0311349i	$-0.990088\pi$
$409$	−9.00162	−	17.4607i	−0.445101	−	0.863376i	0.554414	−	0.832241i	$-0.312942\pi$
$410$		0			0
$411$		0			0
$412$	27.0646	+	25.8061i	1.33338	+	1.27137i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−28.6063	+	18.3842i	−1.40086	+	0.900277i
$418$		0			0
$419$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$419$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$420$		0			0
$421$	−29.5972	−	15.2584i	−1.44248	−	0.743650i	−0.453438	−	0.891288i	$-0.649803\pi$
$421$	−29.5972	−	15.2584i	−1.44248	−	0.743650i	−0.989041	+	0.147638i	$0.952833\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.35793	−	23.3549i	−0.162502	−	1.13022i
$428$		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
$433$	−2.43324	+	3.09412i	−0.116934	+	0.148694i	−0.840996	−	0.541041i	$-0.818030\pi$
$433$	−2.43324	+	3.09412i	−0.116934	+	0.148694i	0.724062	+	0.689735i	$0.242273\pi$
$434$		0			0
$435$		0			0
$436$	−41.5279	+	1.97822i	−1.98883	+	0.0947395i
$437$		0			0
$438$		0			0
$439$	12.4548	+	21.5724i	0.594437	+	1.02959i	0.993626	+	0.112726i	$0.0359582\pi$
$439$	12.4548	+	21.5724i	0.594437	+	1.02959i	−0.399190	+	0.916868i	$0.630708\pi$
$440$		0			0
$441$	52.3090	−	20.9414i	2.49090	−	0.997207i
$442$		0			0
$443$		0			0		0.814576	−	0.580057i	$-0.196970\pi$
$443$		0			0		−0.814576	+	0.580057i	$0.803030\pi$
$444$	−18.6342	+	2.67919i	−0.884338	+	0.127149i
$445$		0			0
$446$		0			0
$447$		0			0
$448$	7.68749	+	39.8865i	0.363200	+	1.88446i
$449$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$449$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−7.94023	+	41.1978i	−0.373065	+	1.93564i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.43200	−	3.77600i	−0.441210	−	0.176634i	0.140412	−	0.990093i	$-0.455157\pi$
$457$	−9.43200	−	3.77600i	−0.441210	−	0.176634i	−0.581622	+	0.813459i	$0.697582\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$461$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$462$		0			0
$463$	−40.5111	−	14.0210i	−1.88271	−	0.651613i	−0.970055	−	0.242887i	$-0.921906\pi$
$463$	−40.5111	−	14.0210i	−1.88271	−	0.651613i	−0.912657	−	0.408726i	$-0.865973\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$467$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$468$			31.4495i			1.45375i
$469$	12.6160	+	39.6006i	0.582553	+	1.82859i
$470$		0			0
$471$	0.935184	+	0.0445483i	0.0430910	+	0.00205268i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	14.1488	−	40.8802i	0.649191	−	1.87571i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$479$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$480$		0			0
$481$	−10.5870	+	26.4451i	−0.482726	+	1.20579i
$482$		0			0
$483$		0			0
$484$	18.5076	−	11.8941i	0.841254	−	0.540641i
$485$		0			0
$486$		0			0
$487$	−6.21593	−	4.42635i	−0.281671	−	0.200577i	0.430486	−	0.902597i	$-0.358342\pi$
$487$	−6.21593	−	4.42635i	−0.281671	−	0.200577i	−0.712157	+	0.702020i	$0.752282\pi$
$488$		0			0
$489$	−12.2738	−	12.8723i	−0.555038	−	0.582108i
$490$		0			0
$491$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$491$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−1.15180	+	0.998043i	−0.0517175	+	0.0448134i
$497$		0			0
$498$		0			0
$499$	31.2732	−	18.0556i	1.39998	−	0.808280i	0.405592	−	0.914054i	$-0.367065\pi$
$499$	31.2732	−	18.0556i	1.39998	−	0.808280i	0.994390	+	0.105774i	$0.0337320\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.998867	−	0.0475819i	$-0.0151515\pi$
$503$		0			0		−0.998867	+	0.0475819i	$0.984848\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	21.7112	+	12.5350i	0.964230	+	0.556698i
$508$	41.6462	−	16.6726i	1.84775	−	0.739728i
$509$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$509$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$510$		0			0
$511$	−62.5302	+	8.99049i	−2.76617	+	0.397716i
$512$		0			0
$513$	43.6893	−	10.5989i	1.92893	−	0.467953i
$514$		0			0
$515$		0			0
$516$	16.7338	−	15.9556i	0.736663	−	0.702407i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$521$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$522$		0			0
$523$	−13.8478	+	10.8900i	−0.605520	+	0.476186i	−0.873227	−	0.487314i	$-0.837977\pi$
$523$	−13.8478	+	10.8900i	−0.605520	+	0.476186i	0.267707	+	0.963501i	$0.413734\pi$
$524$		0			0
$525$	14.3822	+	41.5545i	0.627689	+	1.81359i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−20.4432	+	10.5392i	−0.888835	+	0.458227i
$530$		0			0
$531$		0			0
$532$	8.35173	−	87.4633i	0.362094	−	3.79202i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.90770	−	1.65303i	−0.0820186	−	0.0710695i	0.612887	−	0.790171i	$-0.290008\pi$
$541$	−1.90770	−	1.65303i	−0.0820186	−	0.0710695i	−0.694905	+	0.719101i	$0.744554\pi$
$542$		0			0
$543$	0.478723	+	0.928594i	0.0205440	+	0.0398498i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	26.4044	−	9.13866i	1.12897	−	0.390741i	0.302181	−	0.953251i	$-0.402285\pi$
$547$	26.4044	−	9.13866i	1.12897	−	0.390741i	0.826791	+	0.562510i	$0.190164\pi$
$548$		0			0
$549$	8.61762	+	10.9582i	0.367791	+	0.467685i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	81.3154	−	7.76468i	3.45788	−	0.330188i
$554$		0			0
$555$		0			0
$556$	−27.0959	−	28.4173i	−1.14912	−	1.20516i
$557$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$557$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$558$		0			0
$559$	−8.24811	−	33.9992i	−0.348858	−	1.43801i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$563$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−28.2487	+	35.9211i	−1.18633	+	1.50855i
$568$		0			0
$569$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$569$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$570$		0			0
$571$	−10.0566	+	41.4539i	−0.420856	+	1.73479i	0.227799	+	0.973708i	$0.426847\pi$
$571$	−10.0566	+	41.4539i	−0.420856	+	1.73479i	−0.648655	+	0.761083i	$0.724668\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−15.7167	−	18.1380i	−0.654861	−	0.755750i
$577$	18.1745	−	12.9420i	0.756613	−	0.538781i	−0.135400	−	0.990791i	$-0.543232\pi$
$577$	18.1745	−	12.9420i	0.756613	−	0.538781i	0.892013	+	0.452009i	$0.149293\pi$
$578$		0			0
$579$	43.7628	+	19.9858i	1.81872	+	0.830582i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.189251	−	0.981929i	$-0.439394\pi$
$587$		0			0		−0.189251	+	0.981929i	$0.560606\pi$
$588$	35.1750	+	54.7334i	1.45059	+	2.25717i
$589$	2.99859	−	1.36941i	0.123555	−	0.0564256i
$590$		0			0
$591$		0			0
$592$	−7.10985	−	20.5426i	−0.292213	−	0.844294i
$593$		0			0		0.690079	−	0.723734i	$-0.257576\pi$
$593$		0			0		−0.690079	+	0.723734i	$0.742424\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−31.2027	−	10.7994i	−1.27704	−	0.441989i
$598$		0			0
$599$		0			0		0.0950560	−	0.995472i	$-0.469697\pi$
$599$		0			0		−0.0950560	+	0.995472i	$0.530303\pi$
$600$		0			0
$601$	2.27378	−	47.7326i	0.0927496	−	1.94705i	−0.177192	−	0.984176i	$-0.556701\pi$
$601$	2.27378	−	47.7326i	0.0927496	−	1.94705i	0.269942	−	0.962877i	$-0.412995\pi$
$602$		0			0
$603$	−18.1540	−	16.5358i	−0.739289	−	0.673388i
$604$	−48.4466			−1.97127
$605$		0			0
$606$		0			0
$607$	−45.7260	−	4.36630i	−1.85596	−	0.177223i	−0.893575	−	0.448914i	$-0.851811\pi$
$607$	−45.7260	−	4.36630i	−1.85596	−	0.177223i	−0.962384	+	0.271691i	$0.912417\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	24.3929	+	23.2586i	0.985221	+	0.939406i	0.998168	−	0.0605099i	$-0.0192727\pi$
$613$	24.3929	+	23.2586i	0.985221	+	0.939406i	−0.0129467	+	0.999916i	$0.504121\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$617$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$618$		0			0
$619$	25.0816	+	4.83408i	1.00811	+	0.194298i	0.666471	−	0.745531i	$-0.267804\pi$
$619$	25.0816	+	4.83408i	1.00811	+	0.194298i	0.341644	+	0.939829i	$0.389016\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−35.6585	+	6.87261i	−1.42748	+	0.275124i
$625$	−23.9873	+	7.04331i	−0.959493	+	0.281733i
$626$		0			0
$627$		0			0
$628$	0.153854	+	1.07008i	0.00613944	+	0.0427008i
$629$		0			0
$630$		0			0
$631$	−13.2545	−	33.1081i	−0.527653	−	1.31801i	−0.917720	−	0.397227i	$-0.869973\pi$
$631$	−13.2545	−	33.1081i	−0.527653	−	1.31801i	0.390068	−	0.920786i	$-0.372452\pi$
$632$		0			0
$633$	16.6826	−	9.63173i	0.663075	−	0.382827i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	98.3342	−	4.68424i	3.89614	−	0.185596i
$638$		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
$643$	7.68998	+	8.87471i	0.303263	+	0.349984i	0.886843	−	0.462072i	$-0.152894\pi$
$643$	7.68998	+	8.87471i	0.303263	+	0.349984i	−0.583579	+	0.812056i	$0.698348\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.971812	−	0.235759i	$-0.0757576\pi$
$647$		0			0		−0.971812	+	0.235759i	$0.924242\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−1.53545	+	2.97836i	−0.0601792	+	0.116731i
$652$	11.9129	−	16.7294i	0.466546	−	0.655173i
$653$		0			0		−0.0950560	−	0.995472i	$-0.530303\pi$
$653$		0			0		0.0950560	+	0.995472i	$0.469697\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	29.3393	−	23.0727i	1.14464	−	0.900152i
$658$		0			0
$659$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$659$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$660$		0			0
$661$	20.5964	−	32.0486i	0.801107	−	1.24655i	−0.164457	−	0.986384i	$-0.552587\pi$
$661$	20.5964	−	32.0486i	0.801107	−	1.24655i	0.965565	−	0.260163i	$-0.0837764\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		−	28.9263i		−	1.11836i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	12.0351	−	40.9877i	0.463918	−	1.57996i	−0.312614	−	0.949880i	$-0.601205\pi$
$673$	12.0351	−	40.9877i	0.463918	−	1.57996i	0.776532	−	0.630078i	$-0.216977\pi$
$674$		0			0
$675$	−19.6349	−	17.0138i	−0.755750	−	0.654861i
$676$	−9.46807	+	27.3562i	−0.364156	+	1.05216i
$677$		0			0		−0.458227	−	0.888835i	$-0.651515\pi$
$677$		0			0		0.458227	+	0.888835i	$0.348485\pi$
$678$		0			0
$679$	44.1615	+	28.3809i	1.69476	+	1.08916i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.618159	−	0.786053i	$-0.712121\pi$
$683$		0			0		0.618159	+	0.786053i	$0.287879\pi$
$684$	21.5648	+	47.2202i	0.824549	+	1.80551i
$685$		0			0
$686$		0			0
$687$	4.72141	−	0.450840i	0.180133	−	0.0172006i
$688$	21.7478	+	15.4866i	0.829128	+	0.590419i
$689$		0			0
$690$		0			0
$691$	−49.3852	+	9.51822i	−1.87870	+	0.362090i	−0.994476	−	0.104967i	$-0.966526\pi$
$691$	−49.3852	+	9.51822i	−1.87870	+	0.362090i	−0.884227	+	0.467057i	$0.845314\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−43.9730	+	25.3878i	−1.66202	+	0.959570i
$701$		0			0		0.618159	−	0.786053i	$-0.287879\pi$
$701$		0			0		−0.618159	+	0.786053i	$0.712121\pi$
$702$		0			0
$703$	2.23726	+	46.9658i	0.0843797	+	1.77135i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−6.91220	+	2.76723i	−0.259593	+	0.103925i	−0.497809	−	0.867287i	$-0.665862\pi$
$709$	−6.91220	+	2.76723i	−0.259593	+	0.103925i	0.238215	+	0.971212i	$0.423438\pi$
$710$		0			0
$711$	−39.3134	+	27.9950i	−1.47437	+	1.04989i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$719$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$720$		0			0
$721$	−17.9675	+	93.2242i	−0.669144	+	3.47185i
$722$		0			0
$723$	−9.65197	+	4.40791i	−0.358961	+	0.163932i
$724$	−0.948256	+	0.745717i	−0.0352417	+	0.0277144i
$725$		0			0
$726$		0			0
$727$	12.2537	−	12.8513i	0.454465	−	0.476629i	−0.456140	−	0.889908i	$-0.650768\pi$
$727$	12.2537	−	12.8513i	0.454465	−	0.476629i	0.910604	+	0.413279i	$0.135617\pi$
$728$		0			0
$729$	3.84250	−	26.7252i	0.142315	−	0.989821i
$730$		0			0
$731$		0			0
$732$	−10.5416	+	12.1656i	−0.389628	+	0.449655i
$733$	0.907492	−	9.50369i	0.0335190	−	0.351027i	−0.963118	−	0.269080i	$-0.913280\pi$
$733$	0.907492	−	9.50369i	0.0335190	−	0.351027i	0.996637	−	0.0819464i	$-0.0261136\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	43.1250	+	2.05429i	1.58638	+	0.0755685i	0.822109	−	0.569330i	$-0.192797\pi$
$739$	43.1250	+	2.05429i	1.58638	+	0.0755685i	0.764268	+	0.644899i	$0.223100\pi$
$740$		0			0
$741$	78.1921	+	7.46644i	2.87246	+	0.274287i
$742$		0			0
$743$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$743$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−2.42864	−	5.31797i	−0.0886222	−	0.194056i	0.860131	−	0.510073i	$-0.170382\pi$
$751$	−2.42864	−	5.31797i	−0.0886222	−	0.194056i	−0.948753	+	0.316017i	$0.897654\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−46.9017	−	24.1795i	−1.70580	−	0.879401i
$757$	−27.9013	−	29.2620i	−1.01409	−	1.06355i	−0.997971	−	0.0636752i	$-0.979718\pi$
$757$	−27.9013	−	29.2620i	−1.01409	−	1.06355i	−0.0161178	−	0.999870i	$-0.505131\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$761$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$762$		0			0
$763$	−61.2250	−	85.9785i	−2.21649	−	3.11263i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	17.1309	−	21.7837i	0.618159	−	0.786053i
$769$	−50.7273	−	12.3063i	−1.82927	−	0.443777i	−0.834964	−	0.550305i	$-0.814511\pi$
$769$	−50.7273	−	12.3063i	−1.82927	−	0.443777i	−0.994310	+	0.106528i	$0.966026\pi$
$770$		0			0
$771$		0			0
$772$	−13.0972	+	53.9872i	−0.471377	+	1.94304i
$773$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$773$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$774$		0			0
$775$	−1.64984	−	0.952533i	−0.0592639	−	0.0342160i
$776$		0			0
$777$	−31.2988	−	36.1207i	−1.12284	−	1.29582i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−54.3718	+	51.8434i	−1.94185	+	1.85155i
$785$		0			0
$786$		0			0
$787$	5.22209	+	54.6882i	0.186148	+	1.94943i	0.295310	+	0.955402i	$0.404577\pi$
$787$	5.22209	+	54.6882i	0.186148	+	1.94943i	−0.109162	+	0.994024i	$0.534817\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	7.96648	+	23.0176i	0.282898	+	0.817380i
$794$		0			0
$795$		0			0
$796$	5.42600	−	37.7387i	0.192319	−	1.33761i
$797$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$797$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$	14.7816	−	24.1972i	0.521308	−	0.853369i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$809$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$810$		0			0
$811$	19.6056	+	38.0295i	0.688445	+	1.33540i	0.930914	+	0.365239i	$0.119013\pi$
$811$	19.6056	+	38.0295i	0.688445	+	1.33540i	−0.242469	+	0.970159i	$0.577957\pi$
$812$		0			0
$813$	−39.5516	−	25.4182i	−1.38713	−	0.891457i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−35.6973	−	45.3928i	−1.24889	−	1.58809i
$818$		0			0
$819$	−67.1686	+	43.1666i	−2.34706	+	1.50836i
$820$		0			0
$821$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$821$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$822$		0			0
$823$	−23.7279	−	12.2326i	−0.827103	−	0.426401i	−0.00794450	−	0.999968i	$-0.502529\pi$
$823$	−23.7279	−	12.2326i	−0.827103	−	0.426401i	−0.819159	+	0.573567i	$0.805559\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$827$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$828$		0			0
$829$	6.04822	+	42.0663i	0.210063	+	1.46102i	0.772939	+	0.634481i	$0.218786\pi$
$829$	6.04822	+	42.0663i	0.210063	+	1.46102i	−0.562875	+	0.826542i	$0.690305\pi$
$830$		0			0
$831$	36.4660	−	31.5980i	1.26499	−	1.09612i
$832$	−15.5848	−	38.9289i	−0.540305	−	1.34962i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.0942028	−	1.97756i	−0.00325613	−	0.0683545i
$838$		0			0
$839$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$839$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$840$		0			0
$841$	−14.5000	−	25.1147i	−0.500000	−	0.866025i
$842$		0			0
$843$		0			0
$844$	14.5664	+	16.8105i	0.501396	+	0.578642i
$845$		0			0
$846$		0			0
$847$	50.8059	+	23.2023i	1.74571	+	0.797240i
$848$		0			0
$849$	6.39324	+	21.7734i	0.219415	+	0.747260i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−32.7270	+	45.9586i	−1.12055	+	1.57359i	−0.349360	+	0.936989i	$0.613601\pi$
$853$	−32.7270	+	45.9586i	−1.12055	+	1.57359i	−0.771191	+	0.636604i	$0.780338\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$857$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$858$		0			0
$859$	42.2883	+	16.9297i	1.44286	+	0.577633i	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	42.2883	+	16.9297i	1.44286	+	0.577633i	0.487510	+	0.873117i	$0.337905\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$863$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	2.79891	−	29.3115i	0.0950560	−	0.995472i
$868$	−3.71251	−	1.09009i	−0.126011	−	0.0370001i
$869$		0			0
$870$		0			0
$871$	−20.5247	−	37.6763i	−0.695454	−	1.27661i
$872$		0			0
$873$	−30.9806	−	1.47579i	−1.04854	−	0.0499479i
$874$		0			0
$875$		0			0
$876$	32.5721	+	28.2239i	1.10051	+	0.953597i
$877$	2.61576	−	7.55774i	0.0883279	−	0.255207i	−0.892182	−	0.451676i	$-0.850826\pi$
$877$	2.61576	−	7.55774i	0.0883279	−	0.255207i	0.980510	+	0.196469i	$0.0629476\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$881$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$882$		0			0
$883$	−20.1628	+	50.3643i	−0.678534	+	1.69490i	0.0398103	+	0.999207i	$0.487325\pi$
$883$	−20.1628	+	50.3643i	−0.678534	+	1.69490i	−0.718344	+	0.695688i	$0.755100\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$887$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$888$		0			0
$889$	92.7711	+	66.0620i	3.11144	+	2.21565i
$890$		0			0
$891$		0			0
$892$	32.7976	−	6.32122i	1.09815	−	0.211650i
$893$		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
$903$	57.0457	+	13.8391i	1.89836	+	0.460537i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−47.3427	−	37.2307i	−1.57199	−	1.23622i	−0.793582	−	0.608463i	$-0.791787\pi$
$907$	−47.3427	−	37.2307i	−1.57199	−	1.23622i	−0.778405	−	0.627762i	$-0.783971\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$911$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$912$	−48.8274	+	34.7698i	−1.61684	+	1.15134i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	1.54294	+	5.25478i	0.0509802	+	0.173623i
$917$		0			0
$918$		0			0
$919$	8.65244	−	16.7834i	0.285417	−	0.553633i	−0.701922	−	0.712254i	$-0.747675\pi$
$919$	8.65244	−	16.7834i	0.285417	−	0.553633i	0.987340	+	0.158621i	$0.0507048\pi$
$920$		0			0
$921$	−2.65321	−	27.7857i	−0.0874263	−	0.915570i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	21.3592	−	16.7970i	0.702285	−	0.552283i
$926$		0			0
$927$	−18.3465	−	53.0086i	−0.602577	−	1.74103i
$928$		0			0
$929$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$929$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$930$		0			0
$931$	144.433	−	74.4605i	4.73361	−	2.44035i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$			53.3290i			1.74218i	0.491121	+	0.871091i	$0.336587\pi$
$937$			53.3290i			1.74218i	−0.491121	+	0.871091i	$0.663413\pi$
$938$		0			0
$939$	−19.7790			−0.645463
$940$		0			0
$941$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$941$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$947$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$948$	−40.3327	−	38.4572i	−1.30995	−	1.24903i
$949$	61.6271	−	21.3293i	2.00050	−	0.692380i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$953$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	7.27430	+	29.9851i	0.234655	+	0.967261i
$962$		0			0
$963$		0			0
$964$	−7.10707	−	9.98048i	−0.228903	−	0.321450i
$965$		0			0
$966$		0			0
$967$	−26.2573	+	45.4789i	−0.844377	+	1.46250i	0.0417844	+	0.999127i	$0.486696\pi$
$967$	−26.2573	+	45.4789i	−0.844377	+	1.46250i	−0.886161	+	0.463377i	$0.846638\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$971$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$972$	31.1416	−	1.48346i	0.998867	−	0.0475819i
$973$	23.5017	−	96.8751i	0.753428	−	3.10567i
$974$		0			0
$975$	−22.6967	−	39.3118i	−0.726876	−	1.25899i
$976$	−16.0974	−	9.29386i	−0.515266	−	0.297489i
$977$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$977$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	56.7269	+	25.9063i	1.81115	+	0.827125i
$982$		0			0
$983$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$983$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	8.62151	+	90.2885i	0.274287	+	2.87246i
$989$		0			0
$990$		0			0
$991$	−57.0735	+	26.0646i	−1.81300	+	0.827970i	−0.872058	+	0.489402i	$0.837215\pi$
$991$	−57.0735	+	26.0646i	−1.81300	+	0.827970i	−0.940942	+	0.338567i	$0.890058\pi$
$992$		0			0
$993$	55.6650	+	22.2849i	1.76648	+	0.707190i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	3.86556	−	26.8856i	0.122424	−	0.851474i	−0.832373	−	0.554215i	$-0.813018\pi$
$997$	3.86556	−	26.8856i	0.122424	−	0.851474i	0.954797	−	0.297259i	$-0.0960725\pi$
$998$		0			0
$999$	26.6856	+	9.23597i	0.844294	+	0.292213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.p.a.2.1	✓	20
3.2	odd	2	CM	201.2.p.a.2.1	✓	20
67.34	odd	66	inner	201.2.p.a.101.1	yes	20
201.101	even	66	inner	201.2.p.a.101.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.p.a.2.1	✓	20	1.1	even	1	trivial
201.2.p.a.2.1	✓	20	3.2	odd	2	CM
201.2.p.a.101.1	yes	20	67.34	odd	66	inner
201.2.p.a.101.1	yes	20	201.101	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)

\(f(q)\)	\(=\)	\(q+(0.487975 - 1.66189i) q^{3} +(1.99094 + 0.190112i) q^{4} +(2.32668 + 4.51312i) q^{7} +(-2.52376 - 1.62192i) q^{9} +O(q^{10})\)	\(q+(0.487975 - 1.66189i) q^{3} +(1.99094 + 0.190112i) q^{4} +(2.32668 + 4.51312i) q^{7} +(-2.52376 - 1.62192i) q^{9} +(1.28748 - 3.21596i) q^{12} +(-3.24013 - 4.12016i) q^{13} +(3.92771 + 0.757005i) q^{16} +(-7.69011 - 3.96453i) q^{19} +(8.63568 - 1.66439i) q^{21} +(0.711574 + 4.94911i) q^{25} +(-3.92699 + 3.40276i) q^{27} +(3.77428 + 9.42770i) q^{28} +(-0.235527 + 0.299497i) q^{31} +(-4.71632 - 3.70895i) q^{36} +(-2.71727 - 4.70645i) q^{37} +(-8.42836 + 3.37421i) q^{39} +(6.07141 + 2.77272i) q^{43} +(3.17469 - 6.15803i) q^{48} +(-10.8945 + 15.2991i) q^{49} +(-5.66762 - 8.81899i) q^{52} +(-10.3412 + 10.8455i) q^{57} +(-4.39135 - 1.51986i) q^{61} +(1.44796 - 15.1637i) q^{63} +(7.67594 + 2.25386i) q^{64} +(8.07068 + 1.36532i) q^{67} +(-4.06926 + 11.7573i) q^{73} +(8.57211 + 1.23248i) q^{75} +(-14.5569 - 9.35513i) q^{76} +(5.97911 - 14.9351i) q^{79} +(3.73874 + 8.18669i) q^{81} +(17.5096 - 1.67196i) q^{84} +(11.0561 - 24.2094i) q^{91} +(0.382799 + 0.537567i) q^{93} +(8.95348 - 5.16930i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 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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