LMFDB - Embedded newform 3484.1.dz.b.155.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3484,1,Mod(103,3484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3484, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 14]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3484.103");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3484 = 2^{2} \cdot 13 \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3484.dz (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:	$1.73874250401$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{33}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{33} - \cdots)$

Embedding invariants

Embedding label			155.1
Root			$0.235759 - 0.971812i$ of defining polynomial
Character	$\chi$	$=$	3484.155
Dual form			3484.1.dz.b.2495.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.981929 - 0.189251i) q^{2} +(0.928368 - 0.371662i) q^{4} +(-0.0311250 + 0.0899299i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.981929 - 0.189251i) q^{2} +(0.928368 - 0.371662i) q^{4} +(-0.0311250 + 0.0899299i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-0.308779 - 1.27280i) q^{11} +(-0.888835 + 0.458227i) q^{13} +(-0.0135432 + 0.0941952i) q^{14} +(0.723734 - 0.690079i) q^{16} +(0.437742 + 0.175245i) q^{17} +(-0.786053 - 0.618159i) q^{18} +(-0.550294 - 1.58997i) q^{19} +(-0.544078 - 1.19136i) q^{22} +(0.841254 + 0.540641i) q^{25} +(-0.786053 + 0.618159i) q^{26} +(0.00452808 + 0.0950560i) q^{28} +(-0.928368 - 1.60798i) q^{29} +(0.888835 + 0.458227i) q^{31} +(0.580057 - 0.814576i) q^{32} +(0.462997 + 0.0892353i) q^{34} +(-0.888835 - 0.458227i) q^{36} +(-0.841254 - 1.45709i) q^{38} +(-0.759713 - 1.06687i) q^{44} +(1.98193 - 0.189251i) q^{47} +(0.778934 + 0.612561i) q^{49} +(0.928368 + 0.371662i) q^{50} +(-0.654861 + 0.755750i) q^{52} +(-0.279486 + 1.94387i) q^{53} +(0.0224357 + 0.0924813i) q^{56} +(-1.21590 - 1.40323i) q^{58} +(0.698939 - 0.449181i) q^{59} +(-0.370638 + 1.52779i) q^{61} +(0.959493 + 0.281733i) q^{62} +(0.0883470 - 0.0353688i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.786053 + 0.618159i) q^{67} +0.471518 q^{68} +(-1.65033 + 0.660694i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(-1.10181 - 1.27155i) q^{76} +(0.124074 + 0.0118476i) q^{77} +(-0.142315 + 0.989821i) q^{81} +(1.34378 - 1.28129i) q^{83} +(-0.947890 - 0.903811i) q^{88} +(-0.0135432 - 0.0941952i) q^{91} +(1.91030 - 0.560914i) q^{94} +(0.880786 + 0.454077i) q^{98} +(-0.759713 + 1.06687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + q^{4} - q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + q^2 + q^4 - q^7 - 2 * q^8 - 2 * q^9	$ 20 q + q^{2} + q^{4} - q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{11} + q^{13} + 2 q^{14} + q^{16} - q^{17} + q^{18} + 2 q^{19} - 4 q^{22} - 2 q^{25} + q^{26} + 21 q^{28} - q^{29} - q^{31} + q^{32} - q^{34} + q^{36} + 2 q^{38} + 2 q^{44} + 21 q^{47} + q^{50} - 2 q^{52} + 2 q^{53} - q^{56} + 2 q^{58} - 4 q^{59} - q^{61} + 2 q^{62} - q^{63} - 2 q^{64} + q^{67} + 2 q^{68} - q^{71} - 2 q^{72} - 4 q^{76} - 2 q^{77} - 2 q^{81} - q^{83} + 2 q^{88} + 2 q^{91} + 2 q^{94} + 2 q^{99}+O(q^{100}) $ 20 * q + q^2 + q^4 - q^7 - 2 * q^8 - 2 * q^9 + 2 * q^11 + q^13 + 2 * q^14 + q^16 - q^17 + q^18 + 2 * q^19 - 4 * q^22 - 2 * q^25 + q^26 + 21 * q^28 - q^29 - q^31 + q^32 - q^34 + q^36 + 2 * q^38 + 2 * q^44 + 21 * q^47 + q^50 - 2 * q^52 + 2 * q^53 - q^56 + 2 * q^58 - 4 * q^59 - q^61 + 2 * q^62 - q^63 - 2 * q^64 + q^67 + 2 * q^68 - q^71 - 2 * q^72 - 4 * q^76 - 2 * q^77 - 2 * q^81 - q^83 + 2 * q^88 + 2 * q^91 + 2 * q^94 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3484\mathbb{Z}\right)^\times$.

$n$	$1341$	$1743$	$3017$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{31}{33}\right)$

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 $

$2$	0.981929	−	0.189251i	0.981929	−	0.189251i
$2$	0.981929	−	0.189251i	0.981929	−	0.189251i
$3$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$3$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$4$	0.928368	−	0.371662i	0.928368	−	0.371662i
$5$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$5$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$6$		0			0
$7$	−0.0311250	+	0.0899299i	−0.0311250	+	0.0899299i	−0.959493	−	0.281733i	$-0.909091\pi$
$7$	−0.0311250	+	0.0899299i	−0.0311250	+	0.0899299i	0.928368	+	0.371662i	$0.121212\pi$
$8$	0.841254	−	0.540641i	0.841254	−	0.540641i
$9$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$10$		0			0
$11$	−0.308779	−	1.27280i	−0.308779	−	1.27280i	−0.888835	−	0.458227i	$-0.848485\pi$
$11$	−0.308779	−	1.27280i	−0.308779	−	1.27280i	0.580057	−	0.814576i	$-0.303030\pi$
$12$		0			0
$13$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$13$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$14$	−0.0135432	+	0.0941952i	−0.0135432	+	0.0941952i
$15$		0			0
$16$	0.723734	−	0.690079i	0.723734	−	0.690079i
$17$	0.437742	+	0.175245i	0.437742	+	0.175245i	0.580057	−	0.814576i	$-0.303030\pi$
$17$	0.437742	+	0.175245i	0.437742	+	0.175245i	−0.142315	+	0.989821i	$0.545455\pi$
$18$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$19$	−0.550294	−	1.58997i	−0.550294	−	1.58997i	−0.786053	−	0.618159i	$-0.787879\pi$
$19$	−0.550294	−	1.58997i	−0.550294	−	1.58997i	0.235759	−	0.971812i	$-0.424242\pi$
$20$		0			0
$21$		0			0
$22$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$23$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$23$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$24$		0			0
$25$	0.841254	+	0.540641i	0.841254	+	0.540641i
$26$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$27$		0			0
$28$	0.00452808	+	0.0950560i	0.00452808	+	0.0950560i
$29$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.786053	−	0.618159i	$-0.787879\pi$
$29$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.142315	−	0.989821i	$-0.545455\pi$
$30$		0			0
$31$	0.888835	+	0.458227i	0.888835	+	0.458227i	0.841254	−	0.540641i	$-0.181818\pi$
$31$	0.888835	+	0.458227i	0.888835	+	0.458227i	0.0475819	+	0.998867i	$0.484848\pi$
$32$	0.580057	−	0.814576i	0.580057	−	0.814576i
$33$		0			0
$34$	0.462997	+	0.0892353i	0.462997	+	0.0892353i
$35$		0			0
$36$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	−0.841254	−	1.45709i	−0.841254	−	1.45709i
$39$		0			0
$40$		0			0
$41$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$41$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$42$		0			0
$43$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$43$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$44$	−0.759713	−	1.06687i	−0.759713	−	1.06687i
$45$		0			0
$46$		0			0
$47$	1.98193	−	0.189251i	1.98193	−	0.189251i	0.981929	−	0.189251i	$-0.0606061\pi$
$47$	1.98193	−	0.189251i	1.98193	−	0.189251i	1.00000			$0$
$48$		0			0
$49$	0.778934	+	0.612561i	0.778934	+	0.612561i
$50$	0.928368	+	0.371662i	0.928368	+	0.371662i
$51$		0			0
$52$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$53$	−0.279486	+	1.94387i	−0.279486	+	1.94387i	0.0475819	+	0.998867i	$0.484848\pi$
$53$	−0.279486	+	1.94387i	−0.279486	+	1.94387i	−0.327068	+	0.945001i	$0.606061\pi$
$54$		0			0
$55$		0			0
$56$	0.0224357	+	0.0924813i	0.0224357	+	0.0924813i
$57$		0			0
$58$	−1.21590	−	1.40323i	−1.21590	−	1.40323i
$59$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$59$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$60$		0			0
$61$	−0.370638	+	1.52779i	−0.370638	+	1.52779i	0.415415	+	0.909632i	$0.363636\pi$
$61$	−0.370638	+	1.52779i	−0.370638	+	1.52779i	−0.786053	+	0.618159i	$0.787879\pi$
$62$	0.959493	+	0.281733i	0.959493	+	0.281733i
$63$	0.0883470	−	0.0353688i	0.0883470	−	0.0353688i
$64$	0.415415	−	0.909632i	0.415415	−	0.909632i
$65$		0			0
$66$		0			0
$67$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$67$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$68$	0.471518			0.471518
$69$		0			0
$70$		0			0
$71$	−1.65033	+	0.660694i	−1.65033	+	0.660694i	−0.995472	−	0.0950560i	$-0.969697\pi$
$71$	−1.65033	+	0.660694i	−1.65033	+	0.660694i	−0.654861	+	0.755750i	$0.727273\pi$
$72$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$73$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$73$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$74$		0			0
$75$		0			0
$76$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$77$	0.124074	+	0.0118476i	0.124074	+	0.0118476i
$78$		0			0
$79$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$79$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$82$		0			0
$83$	1.34378	−	1.28129i	1.34378	−	1.28129i	0.415415	−	0.909632i	$-0.363636\pi$
$83$	1.34378	−	1.28129i	1.34378	−	1.28129i	0.928368	−	0.371662i	$-0.121212\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.947890	−	0.903811i	−0.947890	−	0.903811i
$89$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$89$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$90$		0			0
$91$	−0.0135432	−	0.0941952i	−0.0135432	−	0.0941952i
$92$		0			0
$93$		0			0
$94$	1.91030	−	0.560914i	1.91030	−	0.560914i
$95$		0			0
$96$		0			0
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	0.880786	+	0.454077i	0.880786	+	0.454077i
$99$	−0.759713	+	1.06687i	−0.759713	+	1.06687i
$100$	0.981929	+	0.189251i	0.981929	+	0.189251i
$101$	−0.642315	−	0.123796i	−0.642315	−	0.123796i	−0.142315	−	0.989821i	$-0.545455\pi$
$101$	−0.642315	−	0.123796i	−0.642315	−	0.123796i	−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$103$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$104$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$105$		0			0
$106$	0.0934441	+	1.96163i	0.0934441	+	1.96163i
$107$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$107$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$108$		0			0
$109$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$109$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$110$		0			0
$111$		0			0
$112$	0.0395325	+	0.0865641i	0.0395325	+	0.0865641i
$113$	1.04758	+	0.998867i	1.04758	+	0.998867i	1.00000			$0$
$113$	1.04758	+	0.998867i	1.04758	+	0.998867i	0.0475819	+	0.998867i	$0.484848\pi$
$114$		0			0
$115$		0			0
$116$	−1.45949	−	1.14776i	−1.45949	−	1.14776i
$117$	0.928368	+	0.371662i	0.928368	+	0.371662i
$118$	0.601300	−	0.573338i	0.601300	−	0.573338i
$119$	−0.0293845	+	0.0339116i	−0.0293845	+	0.0339116i
$120$		0			0
$121$	−0.635847	+	0.327802i	−0.635847	+	0.327802i
$122$	−0.0748038	+	1.57033i	−0.0748038	+	1.57033i
$123$		0			0
$124$	0.995472	+	0.0950560i	0.995472	+	0.0950560i
$125$		0			0
$126$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i
$127$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$127$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$128$	0.235759	−	0.971812i	0.235759	−	0.971812i
$129$		0			0
$130$		0			0
$131$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$131$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$132$		0			0
$133$	0.160114			0.160114
$134$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$135$		0			0
$136$	0.462997	−	0.0892353i	0.462997	−	0.0892353i
$137$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$137$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$138$		0			0
$139$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$139$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$140$		0			0
$141$		0			0
$142$	−1.49547	+	0.961081i	−1.49547	+	0.961081i
$143$	0.857685	+	0.989821i	0.857685	+	0.989821i
$144$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$149$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$150$		0			0
$151$	−1.78153	−	0.713215i	−1.78153	−	0.713215i	−0.995472	−	0.0950560i	$-0.969697\pi$
$151$	−1.78153	−	0.713215i	−1.78153	−	0.713215i	−0.786053	−	0.618159i	$-0.787879\pi$
$152$	−1.32254	−	1.04006i	−1.32254	−	1.04006i
$153$	−0.154218	−	0.445585i	−0.154218	−	0.445585i
$154$	0.124074	−	0.0118476i	0.124074	−	0.0118476i
$155$		0			0
$156$		0			0
$157$	0.672932	+	0.945001i	0.672932	+	0.945001i	1.00000			$0$
$157$	0.672932	+	0.945001i	0.672932	+	0.945001i	−0.327068	+	0.945001i	$0.606061\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$163$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	0.723734	−	0.690079i	$-0.242424\pi$
$163$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	−0.959493	+	0.281733i	$0.909091\pi$
$164$		0			0
$165$		0			0
$166$	1.07701	−	1.51245i	1.07701	−	1.51245i
$167$	−0.279486	−	0.0538665i	−0.279486	−	0.0538665i	0.0475819	−	0.998867i	$-0.484848\pi$
$167$	−0.279486	−	0.0538665i	−0.279486	−	0.0538665i	−0.327068	+	0.945001i	$0.606061\pi$
$168$		0			0
$169$	0.580057	−	0.814576i	0.580057	−	0.814576i
$170$		0			0
$171$	−0.841254	+	1.45709i	−0.841254	+	1.45709i
$172$		0			0
$173$	0.0395325	+	0.829889i	0.0395325	+	0.829889i	0.928368	+	0.371662i	$0.121212\pi$
$173$	0.0395325	+	0.829889i	0.0395325	+	0.829889i	−0.888835	+	0.458227i	$0.848485\pi$
$174$		0			0
$175$	−0.0748038	+	0.0588264i	−0.0748038	+	0.0588264i
$176$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$177$		0			0
$178$		0			0
$179$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$179$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$180$		0			0
$181$	0.651174	−	0.0621796i	0.651174	−	0.0621796i	0.235759	−	0.971812i	$-0.424242\pi$
$181$	0.651174	−	0.0621796i	0.651174	−	0.0621796i	0.415415	+	0.909632i	$0.363636\pi$
$182$	−0.0311250	−	0.0899299i	−0.0311250	−	0.0899299i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.0878875	−	0.611271i	0.0878875	−	0.611271i
$188$	1.76962	−	0.912303i	1.76962	−	0.912303i
$189$		0			0
$190$		0			0
$191$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$191$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$192$		0			0
$193$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$193$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$194$		0			0
$195$		0			0
$196$	0.950804	+	0.279181i	0.950804	+	0.279181i
$197$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$197$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$198$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$199$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$199$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$200$	1.00000			1.00000
$201$		0			0
$202$	−0.654136			−0.654136
$203$	0.173501	−	0.0334396i	0.173501	−	0.0334396i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$209$	−1.85380	+	1.19136i	−1.85380	+	1.19136i
$210$		0			0
$211$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$211$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$212$	0.462997	+	1.90850i	0.462997	+	1.90850i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.0688733	+	0.0656706i	−0.0688733	+	0.0656706i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.469383	+	0.0448206i	−0.469383	+	0.0448206i
$222$		0			0
$223$	0.481929	+	1.05528i	0.481929	+	1.05528i	0.981929	+	0.189251i	$0.0606061\pi$
$223$	0.481929	+	1.05528i	0.481929	+	1.05528i	−0.500000	+	0.866025i	$0.666667\pi$
$224$	0.0552004	+	0.0775182i	0.0552004	+	0.0775182i
$225$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$226$	1.21769	+	0.782560i	1.21769	+	0.782560i
$227$	0.786053	−	0.618159i	0.786053	−	0.618159i	−0.142315	−	0.989821i	$-0.545455\pi$
$227$	0.786053	−	0.618159i	0.786053	−	0.618159i	0.928368	+	0.371662i	$0.121212\pi$
$228$		0			0
$229$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$229$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$230$		0			0
$231$		0			0
$232$	−1.65033	−	0.850806i	−1.65033	−	0.850806i
$233$	−0.759713	+	1.06687i	−0.759713	+	1.06687i	0.235759	+	0.971812i	$0.424242\pi$
$233$	−0.759713	+	1.06687i	−0.759713	+	1.06687i	−0.995472	+	0.0950560i	$0.969697\pi$
$234$	0.981929	+	0.189251i	0.981929	+	0.189251i
$235$		0			0
$236$	0.481929	−	0.676774i	0.481929	−	0.676774i
$237$		0			0
$238$	−0.0224357	+	0.0388598i	−0.0224357	+	0.0388598i
$239$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	−0.888835	−	0.458227i	$-0.848485\pi$
$239$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	0.0475819	−	0.998867i	$-0.484848\pi$
$240$		0			0
$241$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$241$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$242$	−0.562319	+	0.442213i	−0.562319	+	0.442213i
$243$		0			0
$244$	0.223734	+	1.55610i	0.223734	+	1.55610i
$245$		0			0
$246$		0			0
$247$	1.21769	+	1.16106i	1.21769	+	1.16106i
$248$	0.995472	−	0.0950560i	0.995472	−	0.0950560i
$249$		0			0
$250$		0			0
$251$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$251$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$252$	0.0688733	−	0.0656706i	0.0688733	−	0.0656706i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$257$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	−0.500000	−	0.866025i	$-0.666667\pi$
$257$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	0.0475819	−	0.998867i	$-0.484848\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.607279	+	1.75462i	−0.607279	+	1.75462i
$262$		0			0
$263$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$263$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$264$		0			0
$265$		0			0
$266$	0.157220	−	0.0303017i	0.157220	−	0.0303017i
$267$		0			0
$268$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$269$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$269$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$270$		0			0
$271$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$271$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$272$	0.437742	−	0.175245i	0.437742	−	0.175245i
$273$		0			0
$274$		0			0
$275$	0.428368	−	1.23769i	0.428368	−	1.23769i
$276$		0			0
$277$	−1.28605	−	1.48418i	−1.28605	−	1.48418i	−0.786053	−	0.618159i	$-0.787879\pi$
$277$	−1.28605	−	1.48418i	−1.28605	−	1.48418i	−0.500000	−	0.866025i	$-0.666667\pi$
$278$		0			0
$279$	−0.235759	−	0.971812i	−0.235759	−	0.971812i
$280$		0			0
$281$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$281$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$282$		0			0
$283$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$283$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$284$	−1.28656	+	1.22673i	−1.28656	+	1.22673i
$285$		0			0
$286$	1.02951	+	0.809616i	1.02951	+	0.809616i
$287$		0			0
$288$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$289$	−0.562827	−	0.536654i	−0.562827	−	0.536654i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$293$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−1.88431	−	0.363170i	−1.88431	−	0.363170i
$303$		0			0
$304$	−1.49547	−	0.770969i	−1.49547	−	0.770969i
$305$		0			0
$306$	−0.235759	−	0.408346i	−0.235759	−	0.408346i
$307$	0.0688733	+	1.44583i	0.0688733	+	1.44583i	0.723734	+	0.690079i	$0.242424\pi$
$307$	0.0688733	+	1.44583i	0.0688733	+	1.44583i	−0.654861	+	0.755750i	$0.727273\pi$
$308$	0.119589	−	0.0351146i	0.119589	−	0.0351146i
$309$		0			0
$310$		0			0
$311$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$311$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$312$		0			0
$313$	0.195876	+	0.428908i	0.195876	+	0.428908i	0.981929	−	0.189251i	$-0.0606061\pi$
$313$	0.195876	+	0.428908i	0.195876	+	0.428908i	−0.786053	+	0.618159i	$0.787879\pi$
$314$	0.839614	+	0.800570i	0.839614	+	0.800570i
$315$		0			0
$316$		0			0
$317$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$317$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$318$		0			0
$319$	−1.75998	+	1.67814i	−1.75998	+	1.67814i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.0377483	−	0.792434i	0.0377483	−	0.792434i
$324$	0.235759	+	0.971812i	0.235759	+	0.971812i
$325$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$326$	−0.308779	−	0.356349i	−0.308779	−	0.356349i
$327$		0			0
$328$		0			0
$329$	−0.0446683	+	0.184125i	−0.0446683	+	0.184125i
$330$		0			0
$331$	0.771316	−	0.308788i	0.771316	−	0.308788i	0.0475819	−	0.998867i	$-0.484848\pi$
$331$	0.771316	−	0.308788i	0.771316	−	0.308788i	0.723734	+	0.690079i	$0.242424\pi$
$332$	0.771316	−	1.68895i	0.771316	−	1.68895i
$333$		0			0
$334$	−0.284630			−0.284630
$335$		0			0
$336$		0			0
$337$	−1.28605	+	0.247866i	−1.28605	+	0.247866i	−0.786053	−	0.618159i	$-0.787879\pi$
$337$	−1.28605	+	0.247866i	−1.28605	+	0.247866i	−0.500000	+	0.866025i	$0.666667\pi$
$338$	0.415415	−	0.909632i	0.415415	−	0.909632i
$339$		0			0
$340$		0			0
$341$	0.308779	−	1.27280i	0.308779	−	1.27280i
$342$	−0.550294	+	1.58997i	−0.550294	+	1.58997i
$343$	−0.159389	+	0.102433i	−0.159389	+	0.102433i
$344$		0			0
$345$		0			0
$346$	0.195876	+	0.807410i	0.195876	+	0.807410i
$347$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$347$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$348$		0			0
$349$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$349$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$350$	−0.0623191	+	0.0719200i	−0.0623191	+	0.0719200i
$351$		0			0
$352$	−1.21590	−	0.486774i	−1.21590	−	0.486774i
$353$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$353$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.0930932	+	0.647478i	0.0930932	+	0.647478i	0.981929	+	0.189251i	$0.0606061\pi$
$359$	0.0930932	+	0.647478i	0.0930932	+	0.647478i	−0.888835	+	0.458227i	$0.848485\pi$
$360$		0			0
$361$	−1.43913	+	1.13174i	−1.43913	+	1.13174i
$362$	0.627639	−	0.184291i	0.627639	−	0.184291i
$363$		0			0
$364$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i
$365$		0			0
$366$		0			0
$367$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$367$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.166113	−	0.0856371i	−0.166113	−	0.0856371i
$372$		0			0
$373$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.723734	+	0.690079i	$0.242424\pi$
$373$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.235759	+	0.971812i	$0.424242\pi$
$374$	−0.0293845	−	0.616858i	−0.0293845	−	0.616858i
$375$		0			0
$376$	1.56499	−	1.23072i	1.56499	−	1.23072i
$377$	1.56199	+	1.00383i	1.56199	+	1.00383i
$378$		0			0
$379$	0.839614	+	1.17907i	0.839614	+	1.17907i	0.981929	+	0.189251i	$0.0606061\pi$
$379$	0.839614	+	1.17907i	0.839614	+	1.17907i	−0.142315	+	0.989821i	$0.545455\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.514186	+	1.48564i	0.514186	+	1.48564i	0.841254	+	0.540641i	$0.181818\pi$
$383$	0.514186	+	1.48564i	0.514186	+	1.48564i	−0.327068	+	0.945001i	$0.606061\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.70566	−	0.879330i	1.70566	−	0.879330i	0.723734	−	0.690079i	$-0.242424\pi$
$389$	1.70566	−	0.879330i	1.70566	−	0.879330i	0.981929	−	0.189251i	$-0.0606061\pi$
$390$		0			0
$391$		0			0
$392$	0.986457	+	0.0941952i	0.986457	+	0.0941952i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−0.308779	+	1.27280i	−0.308779	+	1.27280i
$397$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$397$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$398$		0			0
$399$		0			0
$400$	0.981929	−	0.189251i	0.981929	−	0.189251i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$	−1.00000			−1.00000
$404$	−0.642315	+	0.123796i	−0.642315	+	0.123796i
$405$		0			0
$406$	0.164037	−	0.0656706i	0.164037	−	0.0656706i
$407$		0			0
$408$		0			0
$409$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$409$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.0186403	+	0.0768363i	0.0186403	+	0.0768363i
$414$		0			0
$415$		0			0
$416$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$417$		0			0
$418$	−1.59483	+	1.52067i	−1.59483	+	1.52067i
$419$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$419$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$420$		0			0
$421$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$421$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$422$		0			0
$423$	−1.44091	−	1.37391i	−1.44091	−	1.37391i
$424$	0.815816	+	1.78639i	0.815816	+	1.78639i
$425$	0.273507	+	0.384087i	0.273507	+	0.384087i
$426$		0			0
$427$	−0.125858	−	0.0808840i	−0.125858	−	0.0808840i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.723734	+	0.690079i	$0.242424\pi$
$431$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.235759	+	0.971812i	$0.424242\pi$
$432$		0			0
$433$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i	0.415415	−	0.909632i	$-0.363636\pi$
$433$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i	−0.500000	+	0.866025i	$0.666667\pi$
$434$	−0.0552004	+	0.0775182i	−0.0552004	+	0.0775182i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	−0.0471510	−	0.989821i	−0.0471510	−	0.989821i
$442$	−0.452418	+	0.132842i	−0.452418	+	0.132842i
$443$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$443$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$444$		0			0
$445$		0			0
$446$	0.672932	+	0.945001i	0.672932	+	0.945001i
$447$		0			0
$448$	0.0688733	+	0.0656706i	0.0688733	+	0.0656706i
$449$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$449$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$450$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$451$		0			0
$452$	1.34378	+	0.537970i	1.34378	+	0.537970i
$453$		0			0
$454$	0.654861	−	0.755750i	0.654861	−	0.755750i
$455$		0			0
$456$		0			0
$457$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$457$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$461$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$462$		0			0
$463$	0.273507	−	1.12741i	0.273507	−	1.12741i	−0.654861	−	0.755750i	$-0.727273\pi$
$463$	0.273507	−	1.12741i	0.273507	−	1.12741i	0.928368	−	0.371662i	$-0.121212\pi$
$464$	−1.78153	−	0.523103i	−1.78153	−	0.523103i
$465$		0			0
$466$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$467$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$467$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$468$	1.00000			1.00000
$469$	−0.0311250	−	0.0899299i	−0.0311250	−	0.0899299i
$470$		0			0
$471$		0			0
$472$	0.345139	−	0.755750i	0.345139	−	0.755750i
$473$		0			0
$474$		0			0
$475$	0.396666	−	1.63508i	0.396666	−	1.63508i
$476$	−0.0146760	+	0.0424036i	−0.0146760	+	0.0424036i
$477$	1.65210	−	1.06174i	1.65210	−	1.06174i
$478$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$479$	1.56499	+	0.149438i	1.56499	+	0.149438i	0.841254	−	0.540641i	$-0.181818\pi$
$479$	1.56499	+	0.149438i	1.56499	+	0.149438i	0.723734	+	0.690079i	$0.242424\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.468468	+	0.540641i	−0.468468	+	0.540641i
$485$		0			0
$486$		0			0
$487$	1.23576	+	0.971812i	1.23576	+	0.971812i	1.00000			$0$
$487$	1.23576	+	0.971812i	1.23576	+	0.971812i	0.235759	+	0.971812i	$0.424242\pi$
$488$	0.514186	+	1.48564i	0.514186	+	1.48564i
$489$		0			0
$490$		0			0
$491$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$491$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$492$		0			0
$493$	−0.124594	−	0.866573i	−0.124594	−	0.866573i
$494$	1.41542	+	0.909632i	1.41542	+	0.909632i
$495$		0			0
$496$	0.959493	−	0.281733i	0.959493	−	0.281733i
$497$	−0.00804943	−	0.168978i	−0.00804943	−	0.168978i
$498$		0			0
$499$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.327068	+	0.945001i	$0.606061\pi$
$499$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.654861	+	0.755750i	$0.727273\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$503$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$504$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$509$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$510$		0			0
$511$		0			0
$512$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$513$		0			0
$514$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$515$		0			0
$516$		0			0
$517$	−0.852856	−	2.46417i	−0.852856	−	2.46417i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.16413	−	1.34347i	1.16413	−	1.34347i	0.235759	−	0.971812i	$-0.424242\pi$
$521$	1.16413	−	1.34347i	1.16413	−	1.34347i	0.928368	−	0.371662i	$-0.121212\pi$
$522$	−0.264241	+	1.83784i	−0.264241	+	1.83784i
$523$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$523$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.308779	+	0.356349i	0.308779	+	0.356349i
$528$		0			0
$529$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$530$		0			0
$531$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$532$	0.148645	−	0.0595083i	0.148645	−	0.0595083i
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$537$		0			0
$538$	1.65210	−	0.318417i	1.65210	−	0.318417i
$539$	0.539151	−	1.18058i	0.539151	−	1.18058i
$540$		0			0
$541$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$541$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$542$	−0.0671040	+	0.276606i	−0.0671040	+	0.276606i
$543$		0			0
$544$	0.396666	−	0.254922i	0.396666	−	0.254922i
$545$		0			0
$546$		0			0
$547$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$547$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$548$		0			0
$549$	1.39734	−	0.720381i	1.39734	−	0.720381i
$550$	0.186393	−	1.29639i	0.186393	−	1.29639i
$551$	−2.04577	+	2.36094i	−2.04577	+	2.36094i
$552$		0			0
$553$		0			0
$554$	−1.54370	−	1.21398i	−1.54370	−	1.21398i
$555$		0			0
$556$		0			0
$557$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$557$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$558$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$563$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i
$568$	−1.03115	+	1.44805i	−1.03115	+	1.44805i
$569$	1.13915	+	0.219553i	1.13915	+	0.219553i	0.723734	−	0.690079i	$-0.242424\pi$
$569$	1.13915	+	0.219553i	1.13915	+	0.219553i	0.415415	+	0.909632i	$0.363636\pi$
$570$		0			0
$571$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$571$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$572$	1.16413	+	0.600149i	1.16413	+	0.600149i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$577$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$577$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$578$	−0.654218	−	0.420441i	−0.654218	−	0.420441i
$579$		0			0
$580$		0			0
$581$	0.0734014	+	0.160727i	0.0734014	+	0.160727i
$582$		0			0
$583$	2.56046	−	0.244494i	2.56046	−	0.244494i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.13779	+	1.08488i	−1.13779	+	1.08488i	−0.142315	+	0.989821i	$0.545455\pi$
$587$	−1.13779	+	1.08488i	−1.13779	+	1.08488i	−0.995472	+	0.0950560i	$0.969697\pi$
$588$		0			0
$589$	0.239446	−	1.66538i	0.239446	−	1.66538i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$593$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$599$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$600$		0			0
$601$	−1.88431	+	0.363170i	−1.88431	+	0.363170i	−0.995472	−	0.0950560i	$-0.969697\pi$
$601$	−1.88431	+	0.363170i	−1.88431	+	0.363170i	−0.888835	+	0.458227i	$0.848485\pi$
$602$		0			0
$603$	0.981929	+	0.189251i	0.981929	+	0.189251i
$604$	−1.91899			−1.91899
$605$		0			0
$606$		0			0
$607$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$607$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$608$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$609$		0			0
$610$		0			0
$611$	−1.67489	+	1.07639i	−1.67489	+	1.07639i
$612$	−0.308779	−	0.356349i	−0.308779	−	0.356349i
$613$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$613$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$614$	0.341254	+	1.40667i	0.341254	+	1.40667i
$615$		0			0
$616$	0.110783	−	0.0571125i	0.110783	−	0.0571125i
$617$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$617$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$618$		0			0
$619$	−1.13779	+	1.08488i	−1.13779	+	1.08488i	−0.142315	+	0.989821i	$0.545455\pi$
$619$	−1.13779	+	1.08488i	−1.13779	+	1.08488i	−0.995472	+	0.0950560i	$0.969697\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.415415	+	0.909632i	0.415415	+	0.909632i
$626$	0.273507	+	0.384087i	0.273507	+	0.384087i
$627$		0			0
$628$	0.975950	+	0.627205i	0.975950	+	0.627205i
$629$		0			0
$630$		0			0
$631$	−0.0947329	−	1.98869i	−0.0947329	−	1.98869i	−0.142315	−	0.989821i	$-0.545455\pi$
$631$	−0.0947329	−	1.98869i	−0.0947329	−	1.98869i	0.0475819	−	0.998867i	$-0.484848\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.973036	−	0.187537i	−0.973036	−	0.187537i
$638$	−1.41059	+	1.98089i	−1.41059	+	1.98089i
$639$	1.58006	+	0.814576i	1.58006	+	0.814576i
$640$		0			0
$641$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$641$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$642$		0			0
$643$	−1.88431	+	0.553283i	−1.88431	+	0.553283i	−0.888835	+	0.458227i	$0.848485\pi$
$643$	−1.88431	+	0.553283i	−1.88431	+	0.553283i	−0.995472	+	0.0950560i	$0.969697\pi$
$644$		0			0
$645$		0			0
$646$	−0.112903	−	0.785257i	−0.112903	−	0.785257i
$647$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$647$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$648$	0.415415	+	0.909632i	0.415415	+	0.909632i
$649$	−0.787535	−	0.750914i	−0.787535	−	0.750914i
$650$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$651$		0			0
$652$	−0.370638	−	0.291473i	−0.370638	−	0.291473i
$653$	−1.84833	−	0.739959i	−1.84833	−	0.739959i	−0.959493	−	0.281733i	$-0.909091\pi$
$653$	−1.84833	−	0.739959i	−1.84833	−	0.739959i	−0.888835	−	0.458227i	$-0.848485\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−0.00901515	+	0.189251i	−0.00901515	+	0.189251i
$659$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$659$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$660$		0			0
$661$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$661$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$662$	0.698939	−	0.449181i	0.698939	−	0.449181i
$663$		0			0
$664$	0.437742	−	1.80440i	0.437742	−	1.80440i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.279486	+	0.0538665i	−0.279486	+	0.0538665i
$669$		0			0
$670$		0			0
$671$	2.05902			2.05902
$672$		0			0
$673$	0.771316	−	1.68895i	0.771316	−	1.68895i	0.0475819	−	0.998867i	$-0.484848\pi$
$673$	0.771316	−	1.68895i	0.771316	−	1.68895i	0.723734	−	0.690079i	$-0.242424\pi$
$674$	−1.21590	+	0.486774i	−1.21590	+	0.486774i
$675$		0			0
$676$	0.235759	−	0.971812i	0.235759	−	0.971812i
$677$	0.327068	−	0.945001i	0.327068	−	0.945001i	−0.654861	−	0.755750i	$-0.727273\pi$
$677$	0.327068	−	0.945001i	0.327068	−	0.945001i	0.981929	−	0.189251i	$-0.0606061\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	0.0623191	−	1.30824i	0.0623191	−	1.30824i
$683$	0.252989	−	0.130425i	0.252989	−	0.130425i	−0.327068	−	0.945001i	$-0.606061\pi$
$683$	0.252989	−	0.130425i	0.252989	−	0.130425i	0.580057	+	0.814576i	$0.303030\pi$
$684$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$685$		0			0
$686$	−0.137123	+	0.130746i	−0.137123	+	0.130746i
$687$		0			0
$688$		0			0
$689$	−0.642315	−	1.85585i	−0.642315	−	1.85585i
$690$		0			0
$691$	−0.473420	−	0.451405i	−0.473420	−	0.451405i	0.415415	−	0.909632i	$-0.363636\pi$
$691$	−0.473420	−	0.451405i	−0.473420	−	0.451405i	−0.888835	+	0.458227i	$0.848485\pi$
$692$	0.345139	+	0.755750i	0.345139	+	0.755750i
$693$	−0.0722972	−	0.101527i	−0.0722972	−	0.101527i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i
$701$	1.16413	+	0.600149i	1.16413	+	0.600149i	0.928368	−	0.371662i	$-0.121212\pi$
$701$	1.16413	+	0.600149i	1.16413	+	0.600149i	0.235759	+	0.971812i	$0.424242\pi$
$702$		0			0
$703$		0			0
$704$	−1.28605	−	0.247866i	−1.28605	−	0.247866i
$705$		0			0
$706$		0			0
$707$	0.0311250	−	0.0539102i	0.0311250	−	0.0539102i
$708$		0			0
$709$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$709$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	0.213947	+	0.618159i	0.213947	+	0.618159i
$719$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$719$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$720$		0			0
$721$		0			0
$722$	−1.19894	+	1.38365i	−1.19894	+	1.38365i
$723$		0			0
$724$	0.581419	−	0.299742i	0.581419	−	0.299742i
$725$	0.0883470	−	1.85463i	0.0883470	−	1.85463i
$726$		0			0
$727$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$727$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$728$	−0.0623191	−	0.0719200i	−0.0623191	−	0.0719200i
$729$	0.841254	−	0.540641i	0.841254	−	0.540641i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$733$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.02951	+	0.809616i	1.02951	+	0.809616i
$738$		0			0
$739$	−1.88431	+	0.363170i	−1.88431	+	0.363170i	−0.995472	−	0.0950560i	$-0.969697\pi$
$739$	−1.88431	+	0.363170i	−1.88431	+	0.363170i	−0.888835	+	0.458227i	$0.848485\pi$
$740$		0			0
$741$		0			0
$742$	−0.179318	−	0.0526525i	−0.179318	−	0.0526525i
$743$	0.341254	−	1.40667i	0.341254	−	1.40667i	−0.500000	−	0.866025i	$-0.666667\pi$
$743$	0.341254	−	1.40667i	0.341254	−	1.40667i	0.841254	−	0.540641i	$-0.181818\pi$
$744$		0			0
$745$		0			0
$746$	1.25667	+	1.45027i	1.25667	+	1.45027i
$747$	−1.84833	−	0.176494i	−1.84833	−	0.176494i
$748$	−0.145595	−	0.600149i	−0.145595	−	0.600149i
$749$		0			0
$750$		0			0
$751$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$751$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$752$	1.30379	−	1.50465i	1.30379	−	1.50465i
$753$		0			0
$754$	1.72373	+	0.690079i	1.72373	+	0.690079i
$755$		0			0
$756$		0			0
$757$	0.283341	−	0.0270558i	0.283341	−	0.0270558i	0.0475819	−	0.998867i	$-0.484848\pi$
$757$	0.283341	−	0.0270558i	0.283341	−	0.0270558i	0.235759	+	0.971812i	$0.424242\pi$
$758$	1.04758	+	0.998867i	1.04758	+	0.998867i
$759$		0			0
$760$		0			0
$761$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$761$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.786053	+	1.36148i	0.786053	+	1.36148i
$767$	−0.415415	+	0.719520i	−0.415415	+	0.719520i
$768$		0			0
$769$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$769$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$773$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$774$		0			0
$775$	0.500000	+	0.866025i	0.500000	+	0.866025i
$776$		0			0
$777$		0			0
$778$	1.50842	−	1.18624i	1.50842	−	1.18624i
$779$		0			0
$780$		0			0
$781$	1.35052	+	1.89654i	1.35052	+	1.89654i
$782$		0			0
$783$		0			0
$784$	0.986457	−	0.0941952i	0.986457	−	0.0941952i
$785$		0			0
$786$		0			0
$787$	−1.84833	−	0.739959i	−1.84833	−	0.739959i	−0.959493	−	0.281733i	$-0.909091\pi$
$787$	−1.84833	−	0.739959i	−1.84833	−	0.739959i	−0.888835	−	0.458227i	$-0.848485\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.122434	+	0.0631191i	−0.122434	+	0.0631191i
$792$	−0.0623191	+	1.30824i	−0.0623191	+	1.30824i
$793$	−0.370638	−	1.52779i	−0.370638	−	1.52779i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.271738	+	0.785135i	−0.271738	+	0.785135i	0.723734	+	0.690079i	$0.242424\pi$
$797$	−0.271738	+	0.785135i	−0.271738	+	0.785135i	−0.995472	+	0.0950560i	$0.969697\pi$
$798$		0			0
$799$	0.900739	+	0.264481i	0.900739	+	0.264481i
$800$	0.928368	−	0.371662i	0.928368	−	0.371662i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−0.981929	+	0.189251i	−0.981929	+	0.189251i
$807$		0			0
$808$	−0.607279	+	0.243118i	−0.607279	+	0.243118i
$809$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.981929	+	0.189251i	$0.0606061\pi$
$809$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.928368	+	0.371662i	$0.121212\pi$
$810$		0			0
$811$	0.213947	−	0.618159i	0.213947	−	0.618159i	−0.786053	−	0.618159i	$-0.787879\pi$
$811$	0.213947	−	0.618159i	0.213947	−	0.618159i	1.00000			$0$
$812$	0.148645	−	0.0955280i	0.148645	−	0.0955280i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−0.0623191	+	0.0719200i	−0.0623191	+	0.0719200i
$820$		0			0
$821$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$821$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$822$		0			0
$823$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$823$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$824$		0			0
$825$		0			0
$826$	0.0328448	+	0.0719200i	0.0328448	+	0.0719200i
$827$	0.0552004	+	0.0775182i	0.0552004	+	0.0775182i	0.841254	−	0.540641i	$-0.181818\pi$
$827$	0.0552004	+	0.0775182i	0.0552004	+	0.0775182i	−0.786053	+	0.618159i	$0.787879\pi$
$828$		0			0
$829$	1.21769	+	0.782560i	1.21769	+	0.782560i	0.981929	−	0.189251i	$-0.0606061\pi$
$829$	1.21769	+	0.782560i	1.21769	+	0.782560i	0.235759	+	0.971812i	$0.424242\pi$
$830$		0			0
$831$		0			0
$832$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$833$	0.233624	+	0.404648i	0.233624	+	0.404648i
$834$		0			0
$835$		0			0
$836$	−1.27822	+	1.79501i	−1.27822	+	1.79501i
$837$		0			0
$838$		0			0
$839$	0.273507	−	0.384087i	0.273507	−	0.384087i	−0.654861	−	0.755750i	$-0.727273\pi$
$839$	0.273507	−	0.384087i	0.273507	−	0.384087i	0.928368	+	0.371662i	$0.121212\pi$
$840$		0			0
$841$	−1.22373	+	2.11957i	−1.22373	+	2.11957i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$	−1.67489	−	1.07639i	−1.67489	−	1.07639i
$847$	−0.00968842	−	0.0673845i	−0.00968842	−	0.0673845i
$848$	1.13915	+	1.59971i	1.13915	+	1.59971i
$849$		0			0
$850$	0.341254	+	0.325385i	0.341254	+	0.325385i
$851$		0			0
$852$		0			0
$853$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$853$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$854$	−0.138891	−	0.0556035i	−0.138891	−	0.0556035i
$855$		0			0
$856$		0			0
$857$	0.283341	−	1.97068i	0.283341	−	1.97068i	0.0475819	−	0.998867i	$-0.484848\pi$
$857$	0.283341	−	1.97068i	0.283341	−	1.97068i	0.235759	−	0.971812i	$-0.424242\pi$
$858$		0			0
$859$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$859$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$860$		0			0
$861$		0			0
$862$	1.25667	+	1.45027i	1.25667	+	1.45027i
$863$	−1.49547	+	0.961081i	−1.49547	+	0.961081i	−0.500000	+	0.866025i	$0.666667\pi$
$863$	−1.49547	+	0.961081i	−1.49547	+	0.961081i	−0.995472	+	0.0950560i	$0.969697\pi$
$864$		0			0
$865$		0			0
$866$	−0.0913090	−	0.0268107i	−0.0913090	−	0.0268107i
$867$		0			0
$868$	−0.0395325	+	0.0865641i	−0.0395325	+	0.0865641i
$869$		0			0
$870$		0			0
$871$	0.415415	−	0.909632i	0.415415	−	0.909632i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$877$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.95496	−	0.186677i	−1.95496	−	0.186677i	−0.959493	−	0.281733i	$-0.909091\pi$
$881$	−1.95496	−	0.186677i	−1.95496	−	0.186677i	−0.995472	+	0.0950560i	$0.969697\pi$
$882$	−0.233624	−	0.963011i	−0.233624	−	0.963011i
$883$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$883$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$884$	−0.419102	+	0.216062i	−0.419102	+	0.216062i
$885$		0			0
$886$		0			0
$887$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$887$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.30379	−	0.124497i	1.30379	−	0.124497i
$892$	0.839614	+	0.800570i	0.839614	+	0.800570i
$893$	−1.39155	−	3.04706i	−1.39155	−	3.04706i
$894$		0			0
$895$		0			0
$896$	0.0800569	+	0.0514495i	0.0800569	+	0.0514495i
$897$		0			0
$898$		0			0
$899$	−0.0883470	−	1.85463i	−0.0883470	−	1.85463i
$900$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$901$	−0.462997	+	0.801934i	−0.462997	+	0.801934i
$902$		0			0
$903$		0			0
$904$	1.42131	+	0.273935i	1.42131	+	0.273935i
$905$		0			0
$906$		0			0
$907$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$907$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$908$	0.500000	−	0.866025i	0.500000	−	0.866025i
$909$	0.327068	+	0.566498i	0.327068	+	0.566498i
$910$		0			0
$911$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$911$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$912$		0			0
$913$	−2.04577	−	1.31473i	−2.04577	−	1.31473i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$919$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.16413	−	1.34347i	1.16413	−	1.34347i
$924$		0			0
$925$		0			0
$926$	0.0552004	−	1.15880i	0.0552004	−	1.15880i
$927$		0			0
$928$	−1.84833	−	0.176494i	−1.84833	−	0.176494i
$929$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$929$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$930$		0			0
$931$	0.545311	−	1.57557i	0.545311	−	1.57557i
$932$	−0.308779	+	1.27280i	−0.308779	+	1.27280i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.981929	−	0.189251i	0.981929	−	0.189251i
$937$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$937$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$938$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i
$939$		0			0
$940$		0			0
$941$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$941$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$942$		0			0
$943$		0			0
$944$	0.195876	−	0.807410i	0.195876	−	0.807410i
$945$		0			0
$946$		0			0
$947$	−1.28605	−	1.48418i	−1.28605	−	1.48418i	−0.786053	−	0.618159i	$-0.787879\pi$
$947$	−1.28605	−	1.48418i	−1.28605	−	1.48418i	−0.500000	−	0.866025i	$-0.666667\pi$
$948$		0			0
$949$		0			0
$950$	0.0800569	−	1.68060i	0.0800569	−	1.68060i
$951$		0			0
$952$	−0.00638587	+	0.0444147i	−0.00638587	+	0.0444147i
$953$	0.654861	−	0.755750i	0.654861	−	0.755750i	−0.327068	−	0.945001i	$-0.606061\pi$
$953$	0.654861	−	0.755750i	0.654861	−	0.755750i	0.981929	+	0.189251i	$0.0606061\pi$
$954$	1.42131	−	1.35522i	1.42131	−	1.35522i
$955$		0			0
$956$	−1.32254	−	1.04006i	−1.32254	−	1.04006i
$957$		0			0
$958$	1.56499	−	0.149438i	1.56499	−	0.149438i
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.786053	−	0.618159i	$-0.787879\pi$
$967$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.142315	−	0.989821i	$-0.545455\pi$
$968$	−0.357685	+	0.619529i	−0.357685	+	0.619529i
$969$		0			0
$970$		0			0
$971$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$971$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$972$		0			0
$973$		0			0
$974$	1.39734	+	0.720381i	1.39734	+	0.720381i
$975$		0			0
$976$	0.786053	+	1.36148i	0.786053	+	1.36148i
$977$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$977$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	0.601300	+	1.31666i	0.601300	+	1.31666i	0.928368	+	0.371662i	$0.121212\pi$
$983$	0.601300	+	1.31666i	0.601300	+	1.31666i	−0.327068	+	0.945001i	$0.606061\pi$
$984$		0			0
$985$		0			0
$986$	−0.286343	−	0.827333i	−0.286343	−	0.827333i
$987$		0			0
$988$	1.56199	+	0.625325i	1.56199	+	0.625325i
$989$		0			0
$990$		0			0
$991$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$991$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$992$	0.888835	−	0.458227i	0.888835	−	0.458227i
$993$		0			0
$994$	−0.0398833	−	0.164401i	−0.0398833	−	0.164401i
$995$		0			0
$996$		0			0
$997$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$997$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$998$	−0.642315	+	1.85585i	−0.642315	+	1.85585i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3484.1.dz.b.155.1	yes	20
4.3	odd	2		3484.1.dz.a.155.1	✓	20
13.12	even	2		3484.1.dz.a.155.1	✓	20
52.51	odd	2	CM	3484.1.dz.b.155.1	yes	20
67.16	even	33	inner	3484.1.dz.b.2495.1	yes	20
268.83	odd	66		3484.1.dz.a.2495.1	yes	20
871.753	even	66		3484.1.dz.a.2495.1	yes	20
3484.2495	odd	66	inner	3484.1.dz.b.2495.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3484.1.dz.a.155.1	✓	20	4.3	odd	2
3484.1.dz.a.155.1	✓	20	13.12	even	2
3484.1.dz.a.2495.1	yes	20	268.83	odd	66
3484.1.dz.a.2495.1	yes	20	871.753	even	66
3484.1.dz.b.155.1	yes	20	1.1	even	1	trivial
3484.1.dz.b.155.1	yes	20	52.51	odd	2	CM
3484.1.dz.b.2495.1	yes	20	67.16	even	33	inner
3484.1.dz.b.2495.1	yes	20	3484.2495	odd	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:	\( N \)	\(=\)	\( 3484 = 2^{2} \cdot 13 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3484.dz (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.981929 - 0.189251i) q^{2} +(0.928368 - 0.371662i) q^{4} +(-0.0311250 + 0.0899299i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.981929 - 0.189251i) q^{2} +(0.928368 - 0.371662i) q^{4} +(-0.0311250 + 0.0899299i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-0.308779 - 1.27280i) q^{11} +(-0.888835 + 0.458227i) q^{13} +(-0.0135432 + 0.0941952i) q^{14} +(0.723734 - 0.690079i) q^{16} +(0.437742 + 0.175245i) q^{17} +(-0.786053 - 0.618159i) q^{18} +(-0.550294 - 1.58997i) q^{19} +(-0.544078 - 1.19136i) q^{22} +(0.841254 + 0.540641i) q^{25} +(-0.786053 + 0.618159i) q^{26} +(0.00452808 + 0.0950560i) q^{28} +(-0.928368 - 1.60798i) q^{29} +(0.888835 + 0.458227i) q^{31} +(0.580057 - 0.814576i) q^{32} +(0.462997 + 0.0892353i) q^{34} +(-0.888835 - 0.458227i) q^{36} +(-0.841254 - 1.45709i) q^{38} +(-0.759713 - 1.06687i) q^{44} +(1.98193 - 0.189251i) q^{47} +(0.778934 + 0.612561i) q^{49} +(0.928368 + 0.371662i) q^{50} +(-0.654861 + 0.755750i) q^{52} +(-0.279486 + 1.94387i) q^{53} +(0.0224357 + 0.0924813i) q^{56} +(-1.21590 - 1.40323i) q^{58} +(0.698939 - 0.449181i) q^{59} +(-0.370638 + 1.52779i) q^{61} +(0.959493 + 0.281733i) q^{62} +(0.0883470 - 0.0353688i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.786053 + 0.618159i) q^{67} +0.471518 q^{68} +(-1.65033 + 0.660694i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(-1.10181 - 1.27155i) q^{76} +(0.124074 + 0.0118476i) q^{77} +(-0.142315 + 0.989821i) q^{81} +(1.34378 - 1.28129i) q^{83} +(-0.947890 - 0.903811i) q^{88} +(-0.0135432 - 0.0941952i) q^{91} +(1.91030 - 0.560914i) q^{94} +(0.880786 + 0.454077i) q^{98} +(-0.759713 + 1.06687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + q^{4} - q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + q^2 + q^4 - q^7 - 2 * q^8 - 2 * q^9	\( 20 q + q^{2} + q^{4} - q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{11} + q^{13} + 2 q^{14} + q^{16} - q^{17} + q^{18} + 2 q^{19} - 4 q^{22} - 2 q^{25} + q^{26} + 21 q^{28} - q^{29} - q^{31} + q^{32} - q^{34} + q^{36} + 2 q^{38} + 2 q^{44} + 21 q^{47} + q^{50} - 2 q^{52} + 2 q^{53} - q^{56} + 2 q^{58} - 4 q^{59} - q^{61} + 2 q^{62} - q^{63} - 2 q^{64} + q^{67} + 2 q^{68} - q^{71} - 2 q^{72} - 4 q^{76} - 2 q^{77} - 2 q^{81} - q^{83} + 2 q^{88} + 2 q^{91} + 2 q^{94} + 2 q^{99}+O(q^{100}) \) 20 * q + q^2 + q^4 - q^7 - 2 * q^8 - 2 * q^9 + 2 * q^11 + q^13 + 2 * q^14 + q^16 - q^17 + q^18 + 2 * q^19 - 4 * q^22 - 2 * q^25 + q^26 + 21 * q^28 - q^29 - q^31 + q^32 - q^34 + q^36 + 2 * q^38 + 2 * q^44 + 21 * q^47 + q^50 - 2 * q^52 + 2 * q^53 - q^56 + 2 * q^58 - 4 * q^59 - q^61 + 2 * q^62 - q^63 - 2 * q^64 + q^67 + 2 * q^68 - q^71 - 2 * q^72 - 4 * q^76 - 2 * q^77 - 2 * q^81 - q^83 + 2 * q^88 + 2 * q^91 + 2 * q^94 + 2 * q^99

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