LMFDB - Embedded newform 968.1.z.a.267.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,1,Mod(59,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([55, 55, 32]))

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

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

chi := DirichletCharacter("968.59");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	968.z (of order $110$, degree $40$, 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:	$0.483094932229$
Analytic rank:	$0$
Dimension:	$40$
Coefficient field:	$\Q(\zeta_{55})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{39} + x^{35} - x^{34} + x^{30} - x^{28} + x^{25} - x^{23} + x^{20} - x^{17} + x^{15} + \cdots + 1 $ x^40 - x^39 + x^35 - x^34 + x^30 - x^28 + x^25 - x^23 + x^20 - x^17 + x^15 - x^12 + x^10 - x^6 + x^5 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{55}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{55} + \cdots)$

Embedding invariants

Embedding label			267.1
Root			$0.941844 + 0.336049i$ of defining polynomial
Character	$\chi$	$=$	968.267
Dual form			968.1.z.a.939.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.466667 - 0.884433i) q^{2} +(0.582092 + 1.79149i) q^{3} +(-0.564443 + 0.825472i) q^{4} +(1.31281 - 1.35085i) q^{6} +(0.993482 + 0.113991i) q^{8} +(-2.06160 + 1.49784i) q^{9} +(-0.736741 + 0.676175i) q^{11} +(-1.80739 - 0.530696i) q^{12} +(-0.362808 - 0.931864i) q^{16} +(1.93533 - 0.450041i) q^{17} +(2.28683 + 1.12436i) q^{18} +(-0.760903 + 1.26182i) q^{19} +(0.941844 + 0.336049i) q^{22} +(0.374083 + 1.84617i) q^{24} +(-0.921124 - 0.389270i) q^{25} +(-2.35948 - 1.71427i) q^{27} +(-0.654861 + 0.755750i) q^{32} +(-1.64021 - 0.926272i) q^{33} +(-1.30118 - 1.50165i) q^{34} +(-0.0727689 - 2.54724i) q^{36} +(1.47108 + 0.0841194i) q^{38} +(0.714988 - 0.123734i) q^{41} +(0.0710983 - 0.155684i) q^{43} +(-0.142315 - 0.989821i) q^{44} +(1.45824 - 1.19240i) q^{48} +(-0.870746 + 0.491733i) q^{49} +(0.0855750 + 0.996332i) q^{50} +(1.93278 + 3.20516i) q^{51} +(-0.415059 + 2.88680i) q^{54} +(-2.70345 - 0.628660i) q^{57} +(1.11235 + 0.192500i) q^{59} +(0.974012 + 0.226497i) q^{64} +(-0.0537907 + 1.88292i) q^{66} +(-0.0879554 + 0.611743i) q^{67} +(-0.720886 + 1.85158i) q^{68} +(-2.21891 + 1.25307i) q^{72} +(0.945456 - 0.773095i) q^{73} +(0.161197 - 1.87678i) q^{75} +(-0.612107 - 1.34033i) q^{76} +(0.910198 - 2.80130i) q^{81} +(-0.443096 - 0.574616i) q^{82} +(1.61540 + 0.0923716i) q^{83} +(-0.170871 + 0.00977075i) q^{86} +(-0.809017 + 0.587785i) q^{88} +(1.30759 - 1.50903i) q^{89} +(-1.73511 - 0.733264i) q^{96} +(0.276810 + 1.36611i) q^{97} +(0.841254 + 0.540641i) q^{98} +(0.506065 - 2.49753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{2} + 2 q^{3} + q^{4} - 3 q^{6} + q^{8} - 8 q^{9} + q^{11} - 9 q^{12} + q^{16} + 2 q^{17} - 2 q^{18} - 3 q^{19} + q^{22} - 3 q^{24} + q^{25} - q^{27} - 4 q^{32} - 3 q^{33} + 2 q^{34} - 2 q^{36}+ \cdots + 3 q^{99}+O(q^{100}) $ 40 * q + q^2 + 2 * q^3 + q^4 - 3 * q^6 + q^8 - 8 * q^9 + q^11 - 9 * q^12 + q^16 + 2 * q^17 - 2 * q^18 - 3 * q^19 + q^22 - 3 * q^24 + q^25 - q^27 - 4 * q^32 - 3 * q^33 + 2 * q^34 - 2 * q^36 + 2 * q^38 + 2 * q^41 + 2 * q^43 - 4 * q^44 + 2 * q^48 + q^49 + q^50 - 12 * q^51 + 4 * q^54 - 12 * q^57 - 3 * q^59 + q^64 - 9 * q^66 + 2 * q^67 + 2 * q^68 + 3 * q^72 + 2 * q^73 - 3 * q^75 - 9 * q^76 - 11 * q^81 - 3 * q^82 - 3 * q^83 - 3 * q^86 - 10 * q^88 + 2 * q^89 + 2 * q^96 - 3 * q^97 - 4 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{19}{55}\right)$

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 $

$2$	−0.466667	−	0.884433i	−0.466667	−	0.884433i
$2$	−0.466667	−	0.884433i	−0.466667	−	0.884433i
$3$	0.582092	+	1.79149i	0.582092	+	1.79149i	0.610648	+	0.791902i	$0.290909\pi$
$3$	0.582092	+	1.79149i	0.582092	+	1.79149i	−0.0285561	+	0.999592i	$0.509091\pi$
$4$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$5$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$5$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$6$	1.31281	−	1.35085i	1.31281	−	1.35085i
$7$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$7$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$8$	0.993482	+	0.113991i	0.993482	+	0.113991i
$9$	−2.06160	+	1.49784i	−2.06160	+	1.49784i
$10$		0			0
$11$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$11$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$12$	−1.80739	−	0.530696i	−1.80739	−	0.530696i
$13$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$13$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$14$		0			0
$15$		0			0
$16$	−0.362808	−	0.931864i	−0.362808	−	0.931864i
$17$	1.93533	−	0.450041i	1.93533	−	0.450041i	0.941844	−	0.336049i	$-0.109091\pi$
$17$	1.93533	−	0.450041i	1.93533	−	0.450041i	0.993482	−	0.113991i	$-0.0363636\pi$
$18$	2.28683	+	1.12436i	2.28683	+	1.12436i
$19$	−0.760903	+	1.26182i	−0.760903	+	1.26182i	0.198590	+	0.980083i	$0.436364\pi$
$19$	−0.760903	+	1.26182i	−0.760903	+	1.26182i	−0.959493	+	0.281733i	$0.909091\pi$
$20$		0			0
$21$		0			0
$22$	0.941844	+	0.336049i	0.941844	+	0.336049i
$23$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$23$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$24$	0.374083	+	1.84617i	0.374083	+	1.84617i
$25$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$26$		0			0
$27$	−2.35948	−	1.71427i	−2.35948	−	1.71427i
$28$		0			0
$29$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$29$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$30$		0			0
$31$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$31$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$32$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$33$	−1.64021	−	0.926272i	−1.64021	−	0.926272i
$34$	−1.30118	−	1.50165i	−1.30118	−	1.50165i
$35$		0			0
$36$	−0.0727689	−	2.54724i	−0.0727689	−	2.54724i
$37$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$37$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$38$	1.47108	+	0.0841194i	1.47108	+	0.0841194i
$39$		0			0
$40$		0			0
$41$	0.714988	−	0.123734i	0.714988	−	0.123734i	0.198590	−	0.980083i	$-0.436364\pi$
$41$	0.714988	−	0.123734i	0.714988	−	0.123734i	0.516397	+	0.856349i	$0.327273\pi$
$42$		0			0
$43$	0.0710983	−	0.155684i	0.0710983	−	0.155684i	−0.870746	−	0.491733i	$-0.836364\pi$
$43$	0.0710983	−	0.155684i	0.0710983	−	0.155684i	0.941844	+	0.336049i	$0.109091\pi$
$44$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$45$		0			0
$46$		0			0
$47$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$47$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$48$	1.45824	−	1.19240i	1.45824	−	1.19240i
$49$	−0.870746	+	0.491733i	−0.870746	+	0.491733i
$50$	0.0855750	+	0.996332i	0.0855750	+	0.996332i
$51$	1.93278	+	3.20516i	1.93278	+	3.20516i
$52$		0			0
$53$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$53$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$54$	−0.415059	+	2.88680i	−0.415059	+	2.88680i
$55$		0			0
$56$		0			0
$57$	−2.70345	−	0.628660i	−2.70345	−	0.628660i
$58$		0			0
$59$	1.11235	+	0.192500i	1.11235	+	0.192500i	0.696938	−	0.717132i	$-0.254545\pi$
$59$	1.11235	+	0.192500i	1.11235	+	0.192500i	0.415415	+	0.909632i	$0.363636\pi$
$60$		0			0
$61$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$61$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$62$		0			0
$63$		0			0
$64$	0.974012	+	0.226497i	0.974012	+	0.226497i
$65$		0			0
$66$	−0.0537907	+	1.88292i	−0.0537907	+	1.88292i
$67$	−0.0879554	+	0.611743i	−0.0879554	+	0.611743i	0.897398	+	0.441221i	$0.145455\pi$
$67$	−0.0879554	+	0.611743i	−0.0879554	+	0.611743i	−0.985354	+	0.170522i	$0.945455\pi$
$68$	−0.720886	+	1.85158i	−0.720886	+	1.85158i
$69$		0			0
$70$		0			0
$71$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$71$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$72$	−2.21891	+	1.25307i	−2.21891	+	1.25307i
$73$	0.945456	−	0.773095i	0.945456	−	0.773095i	−0.0285561	−	0.999592i	$-0.509091\pi$
$73$	0.945456	−	0.773095i	0.945456	−	0.773095i	0.974012	+	0.226497i	$0.0727273\pi$
$74$		0			0
$75$	0.161197	−	1.87678i	0.161197	−	1.87678i
$76$	−0.612107	−	1.34033i	−0.612107	−	1.34033i
$77$		0			0
$78$		0			0
$79$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$79$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$80$		0			0
$81$	0.910198	−	2.80130i	0.910198	−	2.80130i
$82$	−0.443096	−	0.574616i	−0.443096	−	0.574616i
$83$	1.61540	+	0.0923716i	1.61540	+	0.0923716i	0.841254	−	0.540641i	$-0.181818\pi$
$83$	1.61540	+	0.0923716i	1.61540	+	0.0923716i	0.774142	+	0.633012i	$0.218182\pi$
$84$		0			0
$85$		0			0
$86$	−0.170871	+	0.00977075i	−0.170871	+	0.00977075i
$87$		0			0
$88$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$89$	1.30759	−	1.50903i	1.30759	−	1.50903i	0.610648	−	0.791902i	$-0.290909\pi$
$89$	1.30759	−	1.50903i	1.30759	−	1.50903i	0.696938	−	0.717132i	$-0.254545\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.73511	−	0.733264i	−1.73511	−	0.733264i
$97$	0.276810	+	1.36611i	0.276810	+	1.36611i	0.841254	+	0.540641i	$0.181818\pi$
$97$	0.276810	+	1.36611i	0.276810	+	1.36611i	−0.564443	+	0.825472i	$0.690909\pi$
$98$	0.841254	+	0.540641i	0.841254	+	0.540641i
$99$	0.506065	−	2.49753i	0.506065	−	2.49753i
$100$	0.841254	−	0.540641i	0.841254	−	0.540641i
$101$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$101$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$102$	1.93278	−	3.20516i	1.93278	−	3.20516i
$103$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$103$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.28303	−	1.17755i	1.28303	−	1.17755i	0.309017	−	0.951057i	$-0.400000\pi$
$107$	1.28303	−	1.17755i	1.28303	−	1.17755i	0.974012	−	0.226497i	$-0.0727273\pi$
$108$	2.74687	−	0.980083i	2.74687	−	0.980083i
$109$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$109$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.95786	−	0.224644i	−1.95786	−	0.224644i	−0.959493	−	0.281733i	$-0.909091\pi$
$113$	−1.95786	−	0.224644i	−1.95786	−	0.224644i	−0.998369	+	0.0570888i	$0.981818\pi$
$114$	0.705604	+	2.68440i	0.705604	+	2.68440i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.348845	−	1.07363i	−0.348845	−	1.07363i
$119$		0			0
$120$		0			0
$121$	0.0855750	−	0.996332i	0.0855750	−	0.996332i
$122$		0			0
$123$	0.637857	+	1.20887i	0.637857	+	1.20887i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$127$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$128$	−0.254218	−	0.967147i	−0.254218	−	0.967147i
$129$	0.320292	+	0.0367501i	0.320292	+	0.0367501i
$130$		0			0
$131$	1.89088	−	0.555213i	1.89088	−	0.555213i	0.897398	−	0.441221i	$-0.145455\pi$
$131$	1.89088	−	0.555213i	1.89088	−	0.555213i	0.993482	−	0.113991i	$-0.0363636\pi$
$132$	1.69042	−	0.831123i	1.69042	−	0.831123i
$133$		0			0
$134$	0.582092	−	0.207690i	0.582092	−	0.207690i
$135$		0			0
$136$	1.97401	−	0.226497i	1.97401	−	0.226497i
$137$	0.631827	+	1.62283i	0.631827	+	1.62283i	0.774142	+	0.633012i	$0.218182\pi$
$137$	0.631827	+	1.62283i	0.631827	+	1.62283i	−0.142315	+	0.989821i	$0.545455\pi$
$138$		0			0
$139$	−1.72209	−	0.846697i	−1.72209	−	0.846697i	−0.985354	−	0.170522i	$-0.945455\pi$
$139$	−1.72209	−	0.846697i	−1.72209	−	0.846697i	−0.736741	−	0.676175i	$-0.763636\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	2.14375	+	1.37771i	2.14375	+	1.37771i
$145$		0			0
$146$	−1.12496	−	0.475414i	−1.12496	−	0.475414i
$147$	−1.38779	−	1.27370i	−1.38779	−	1.27370i
$148$		0			0
$149$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$149$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$150$	−1.73511	+	0.733264i	−1.73511	+	0.733264i
$151$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$151$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$152$	−0.899779	+	1.16685i	−0.899779	+	1.16685i
$153$	−3.31579	+	3.82662i	−3.31579	+	3.82662i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$157$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−2.90232	+	0.502267i	−2.90232	+	0.502267i
$163$	0.0497301	+	0.0280839i	0.0497301	+	0.0280839i	0.516397	−	0.856349i	$-0.327273\pi$
$163$	0.0497301	+	0.0280839i	0.0497301	+	0.0280839i	−0.466667	+	0.884433i	$0.654545\pi$
$164$	−0.301432	+	0.660043i	−0.301432	+	0.660043i
$165$		0			0
$166$	−0.672156	−	1.47182i	−0.672156	−	1.47182i
$167$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$167$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$168$		0			0
$169$	0.774142	−	0.633012i	0.774142	−	0.633012i
$170$		0			0
$171$	−0.321321	−	3.74108i	−0.321321	−	3.74108i
$172$	0.0883814	+	0.146564i	0.0883814	+	0.146564i
$173$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$173$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$174$		0			0
$175$		0			0
$176$	0.897398	+	0.441221i	0.897398	+	0.441221i
$177$	0.302628	+	2.10483i	0.302628	+	2.10483i
$178$	−1.94485	−	0.452255i	−1.94485	−	0.452255i
$179$	−0.393602	−	0.321847i	−0.393602	−	0.321847i	0.415415	−	0.909632i	$-0.363636\pi$
$179$	−0.393602	−	0.321847i	−0.393602	−	0.321847i	−0.809017	+	0.587785i	$0.800000\pi$
$180$		0			0
$181$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$181$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.12153	+	1.64018i	−1.12153	+	1.64018i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$191$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$192$	0.161197	+	1.87678i	0.161197	+	1.87678i
$193$	0.247840	−	0.139962i	0.247840	−	0.139962i	−0.362808	−	0.931864i	$-0.618182\pi$
$193$	0.247840	−	0.139962i	0.247840	−	0.139962i	0.610648	+	0.791902i	$0.290909\pi$
$194$	1.07906	−	0.882340i	1.07906	−	0.882340i
$195$		0			0
$196$	0.0855750	−	0.996332i	0.0855750	−	0.996332i
$197$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$197$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$198$	−2.44506	+	0.717934i	−2.44506	+	0.717934i
$199$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$199$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$200$	−0.870746	−	0.491733i	−0.870746	−	0.491733i
$201$	−1.14713	+	0.198519i	−1.14713	+	0.198519i
$202$		0			0
$203$		0			0
$204$	−3.73672	−	0.213673i	−3.73672	−	0.213673i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.292620	−	1.44413i	−0.292620	−	1.44413i
$210$		0			0
$211$	0.242538	−	0.314528i	0.242538	−	0.314528i	−0.654861	−	0.755750i	$-0.727273\pi$
$211$	0.242538	−	0.314528i	0.242538	−	0.314528i	0.897398	+	0.441221i	$0.145455\pi$
$212$		0			0
$213$		0			0
$214$	−1.64021	−	0.585227i	−1.64021	−	0.585227i
$215$		0			0
$216$	−2.14869	−	1.97205i	−2.14869	−	1.97205i
$217$		0			0
$218$		0			0
$219$	1.93534	+	1.24377i	1.93534	+	1.24377i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$223$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$224$		0			0
$225$	2.48206	−	0.577178i	2.48206	−	0.577178i
$226$	0.714988	+	1.83643i	0.714988	+	1.83643i
$227$	−0.505123	+	0.0579574i	−0.505123	+	0.0579574i	−0.362808	−	0.931864i	$-0.618182\pi$
$227$	−0.505123	+	0.0579574i	−0.505123	+	0.0579574i	−0.142315	+	0.989821i	$0.545455\pi$
$228$	2.04489	−	1.87678i	2.04489	−	1.87678i
$229$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$229$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.321326	+	0.233457i	−0.321326	+	0.233457i	−0.736741	−	0.676175i	$-0.763636\pi$
$233$	−0.321326	+	0.233457i	−0.321326	+	0.233457i	0.415415	+	0.909632i	$0.363636\pi$
$234$		0			0
$235$		0			0
$236$	−0.786763	+	0.809560i	−0.786763	+	0.809560i
$237$		0			0
$238$		0			0
$239$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$239$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$240$		0			0
$241$	−0.0571121			−0.0571121			−0.0285561	−	0.999592i	$-0.509091\pi$
$241$	−0.0571121			−0.0571121			−0.0285561	+	0.999592i	$0.509091\pi$
$242$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$243$	2.63185			2.63185
$244$		0			0
$245$		0			0
$246$	0.771500	−	1.12828i	0.771500	−	1.12828i
$247$		0			0
$248$		0			0
$249$	0.774825	+	2.94774i	0.774825	+	2.94774i
$250$		0			0
$251$	−1.36118	+	0.988953i	−1.36118	+	0.988953i	−0.362808	+	0.931864i	$0.618182\pi$
$251$	−1.36118	+	0.988953i	−1.36118	+	0.988953i	−0.998369	+	0.0570888i	$0.981818\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$257$	−0.927251	+	0.106392i	−0.927251	+	0.106392i	−0.564443	−	0.825472i	$-0.690909\pi$
$257$	−0.927251	+	0.106392i	−0.927251	+	0.106392i	−0.362808	+	0.931864i	$0.618182\pi$
$258$	−0.116967	−	0.300427i	−0.116967	−	0.300427i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.37346	−	1.41326i	−1.37346	−	1.41326i
$263$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$263$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$264$	−1.52394	−	1.10720i	−1.52394	−	1.10720i
$265$		0			0
$266$		0			0
$267$	3.46456	+	1.46414i	3.46456	+	1.46414i
$268$	−0.455331	−	0.417899i	−0.455331	−	0.417899i
$269$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$269$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$270$		0			0
$271$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$271$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$272$	−1.12153	−	1.64018i	−1.12153	−	1.64018i
$273$		0			0
$274$	1.14043	−	1.31613i	1.14043	−	1.31613i
$275$	0.941844	−	0.336049i	0.941844	−	0.336049i
$276$		0			0
$277$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$277$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$278$	0.0547987	+	1.91820i	0.0547987	+	1.91820i
$279$		0			0
$280$		0			0
$281$	−1.21930	−	1.58122i	−1.21930	−	1.58122i	−0.654861	−	0.755750i	$-0.727273\pi$
$281$	−1.21930	−	1.58122i	−1.21930	−	1.58122i	−0.564443	−	0.825472i	$-0.690909\pi$
$282$		0			0
$283$	−0.818662	+	0.141675i	−0.818662	+	0.141675i	−0.564443	−	0.825472i	$-0.690909\pi$
$283$	−0.818662	+	0.141675i	−0.818662	+	0.141675i	−0.254218	+	0.967147i	$0.581818\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.218069	−	2.53894i	0.218069	−	2.53894i
$289$	2.64555	−	1.30073i	2.64555	−	1.30073i
$290$		0			0
$291$	−2.28625	+	1.29111i	−2.28625	+	1.29111i
$292$	0.104512	+	1.21682i	0.104512	+	1.21682i
$293$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$293$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$294$	−0.478868	+	1.82180i	−0.478868	+	1.82180i
$295$		0			0
$296$		0			0
$297$	2.89747	−	0.332454i	2.89747	−	0.332454i
$298$		0			0
$299$		0			0
$300$	1.45824	+	1.19240i	1.45824	+	1.19240i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.45190	+	0.251261i	1.45190	+	0.251261i
$305$		0			0
$306$	4.93176	+	1.14683i	4.93176	+	1.14683i
$307$	−0.198369	−	1.37969i	−0.198369	−	1.37969i	−0.809017	−	0.587785i	$-0.800000\pi$
$307$	−0.198369	−	1.37969i	−0.198369	−	1.37969i	0.610648	−	0.791902i	$-0.290909\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$311$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$312$		0			0
$313$	−0.157650	−	1.83549i	−0.157650	−	1.83549i	−0.466667	−	0.884433i	$-0.654545\pi$
$313$	−0.157650	−	1.83549i	−0.157650	−	1.83549i	0.309017	−	0.951057i	$-0.400000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$317$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	2.85642	+	1.61310i	2.85642	+	1.61310i
$322$		0			0
$323$	−0.904726	+	2.78446i	−0.904726	+	2.78446i
$324$	1.79864	+	2.33252i	1.79864	+	2.33252i
$325$		0			0
$326$	0.00163090	−	0.0570888i	0.00163090	−	0.0570888i
$327$		0			0
$328$	0.724432	−	0.0414245i	0.724432	−	0.0414245i
$329$		0			0
$330$		0			0
$331$	−0.799779	+	0.922994i	−0.799779	+	0.922994i	−0.998369	−	0.0570888i	$-0.981818\pi$
$331$	−0.799779	+	0.922994i	−0.799779	+	0.922994i	0.198590	+	0.980083i	$0.436364\pi$
$332$	−0.988049	+	1.28132i	−0.988049	+	1.28132i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.455331	−	0.417899i	−0.455331	−	0.417899i	0.415415	−	0.909632i	$-0.363636\pi$
$337$	−0.455331	−	0.417899i	−0.455331	−	0.417899i	−0.870746	+	0.491733i	$0.836364\pi$
$338$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$339$	−0.737207	−	3.63826i	−0.737207	−	3.63826i
$340$		0			0
$341$		0			0
$342$	−3.15878	+	2.03003i	−3.15878	+	2.03003i
$343$		0			0
$344$	0.0883814	−	0.146564i	0.0883814	−	0.146564i
$345$		0			0
$346$		0			0
$347$	0.409569	+	1.05197i	0.409569	+	1.05197i	0.974012	+	0.226497i	$0.0727273\pi$
$347$	0.409569	+	1.05197i	0.409569	+	1.05197i	−0.564443	+	0.825472i	$0.690909\pi$
$348$		0			0
$349$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$349$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$350$		0			0
$351$		0			0
$352$	−0.0285561	−	0.999592i	−0.0285561	−	0.999592i
$353$	−1.72209	+	0.505653i	−1.72209	+	0.505653i	−0.985354	−	0.170522i	$-0.945455\pi$
$353$	−1.72209	+	0.505653i	−1.72209	+	0.505653i	−0.736741	+	0.676175i	$0.763636\pi$
$354$	1.72035	−	1.24991i	1.72035	−	1.24991i
$355$		0			0
$356$	0.507607	+	1.93114i	0.507607	+	1.93114i
$357$		0			0
$358$	−0.100971	+	0.498310i	−0.100971	+	0.498310i
$359$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$359$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$360$		0			0
$361$	−0.546537	−	1.03580i	−0.546537	−	1.03580i
$362$		0			0
$363$	1.83474	−	0.426649i	1.83474	−	0.426649i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$367$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$368$		0			0
$369$	−1.28869	+	1.32603i	−1.28869	+	1.32603i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$373$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$374$	1.97401	+	0.226497i	1.97401	+	0.226497i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.338621	+	0.869741i	0.338621	+	0.869741i	0.993482	+	0.113991i	$0.0363636\pi$
$379$	0.338621	+	0.869741i	0.338621	+	0.869741i	−0.654861	+	0.755750i	$0.727273\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$383$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$384$	1.58466	−	1.01840i	1.58466	−	1.01840i
$385$		0			0
$386$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$387$	0.0866130	+	0.427452i	0.0866130	+	0.427452i
$388$	−1.28393	−	0.542594i	−1.28393	−	0.542594i
$389$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$389$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$390$		0			0
$391$		0			0
$392$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$393$	2.09533	+	3.06432i	2.09533	+	3.06432i
$394$		0			0
$395$		0			0
$396$	1.77599	+	1.82745i	1.77599	+	1.82745i
$397$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$397$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$398$		0			0
$399$		0			0
$400$	−0.0285561	+	0.999592i	−0.0285561	+	0.999592i
$401$	0.724432	+	0.0414245i	0.724432	+	0.0414245i	0.415415	−	0.909632i	$-0.363636\pi$
$401$	0.724432	+	0.0414245i	0.724432	+	0.0414245i	0.309017	+	0.951057i	$0.400000\pi$
$402$	0.710906	+	0.921920i	0.710906	+	0.921920i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.55482	+	3.40459i	1.55482	+	3.40459i
$409$	−0.112079	+	1.30492i	−0.112079	+	1.30492i	0.696938	+	0.717132i	$0.254545\pi$
$409$	−0.112079	+	1.30492i	−0.112079	+	1.30492i	−0.809017	+	0.587785i	$0.800000\pi$
$410$		0			0
$411$	−2.53952	+	2.07655i	−2.53952	+	2.07655i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.514436	−	3.57798i	0.514436	−	3.57798i
$418$	−1.14068	+	0.932733i	−1.14068	+	0.932733i
$419$	−0.277233	−	1.92820i	−0.277233	−	1.92820i	−0.362808	−	0.931864i	$-0.618182\pi$
$419$	−0.277233	−	1.92820i	−0.277233	−	1.92820i	0.0855750	−	0.996332i	$-0.472727\pi$
$420$		0			0
$421$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$421$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$422$	−0.391364	−	0.0677282i	−0.391364	−	0.0677282i
$423$		0			0
$424$		0			0
$425$	−1.95786	−	0.338821i	−1.95786	−	0.338821i
$426$		0			0
$427$		0			0
$428$	0.247840	+	1.72377i	0.247840	+	1.72377i
$429$		0			0
$430$		0			0
$431$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$431$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$432$	−0.741424	+	2.82067i	−0.741424	+	2.82067i
$433$	0.926829	+	1.53697i	0.926829	+	1.53697i	0.841254	+	0.540641i	$0.181818\pi$
$433$	0.926829	+	1.53697i	0.926829	+	1.53697i	0.0855750	+	0.996332i	$0.472727\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.196869	−	2.29210i	0.196869	−	2.29210i
$439$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$439$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$440$		0			0
$441$	1.05860	−	2.31800i	1.05860	−	2.31800i
$442$		0			0
$443$	−1.37346	+	0.237687i	−1.37346	+	0.237687i	−0.809017	−	0.587785i	$-0.800000\pi$
$443$	−1.37346	+	0.237687i	−1.37346	+	0.237687i	−0.564443	+	0.825472i	$0.690909\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.83924	−	0.105172i	1.83924	−	0.105172i	0.897398	−	0.441221i	$-0.145455\pi$
$449$	1.83924	−	0.105172i	1.83924	−	0.105172i	0.941844	+	0.336049i	$0.109091\pi$
$450$	−1.66877	−	1.92586i	−1.66877	−	1.92586i
$451$	−0.443096	+	0.574616i	−0.443096	+	0.574616i
$452$	1.29054	−	1.48936i	1.29054	−	1.48936i
$453$		0			0
$454$	0.286984	+	0.419700i	0.286984	+	0.419700i
$455$		0			0
$456$	−2.61417	−	0.932733i	−2.61417	−	0.932733i
$457$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$457$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$458$		0			0
$459$	−5.33786	−	2.25580i	−5.33786	−	2.25580i
$460$		0			0
$461$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$461$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$462$		0			0
$463$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$463$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$464$		0			0
$465$		0			0
$466$	0.356430	+	0.175245i	0.356430	+	0.175245i
$467$	0.809238	−	0.188180i	0.809238	−	0.188180i	0.198590	−	0.980083i	$-0.436364\pi$
$467$	0.809238	−	0.188180i	0.809238	−	0.188180i	0.610648	+	0.791902i	$0.290909\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.08316	+	0.318044i	1.08316	+	0.318044i
$473$	0.0528883	+	0.162773i	0.0528883	+	0.162773i
$474$		0			0
$475$	1.19207	−	0.866091i	1.19207	−	0.866091i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$479$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$480$		0			0
$481$		0			0
$482$	0.0266524	+	0.0505118i	0.0266524	+	0.0505118i
$483$		0			0
$484$	0.774142	+	0.633012i	0.774142	+	0.633012i
$485$		0			0
$486$	−1.22820	−	2.32770i	−1.22820	−	2.32770i
$487$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$487$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$488$		0			0
$489$	−0.0213646	+	0.105439i	−0.0213646	+	0.105439i
$490$		0			0
$491$	−0.310476	−	1.18117i	−0.310476	−	1.18117i	−0.921124	−	0.389270i	$-0.872727\pi$
$491$	−0.310476	−	1.18117i	−0.310476	−	1.18117i	0.610648	−	0.791902i	$-0.290909\pi$
$492$	−1.35792	−	0.155807i	−1.35792	−	0.155807i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.24549	−	2.06089i	2.24549	−	2.06089i
$499$	−1.98372	+	0.227611i	−1.98372	+	0.227611i	−0.985354	+	0.170522i	$0.945455\pi$
$499$	−1.98372	+	0.227611i	−1.98372	+	0.227611i	−0.998369	+	0.0570888i	$0.981818\pi$
$500$		0			0
$501$		0			0
$502$	1.50988	+	0.742358i	1.50988	+	0.742358i
$503$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$503$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.58466	+	1.01840i	1.58466	+	1.01840i
$508$		0			0
$509$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$509$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$510$		0			0
$511$		0			0
$512$	0.941844	+	0.336049i	0.941844	+	0.336049i
$513$	3.95842	−	1.67284i	3.95842	−	1.67284i
$514$	0.526814	+	0.770442i	0.526814	+	0.770442i
$515$		0			0
$516$	−0.211123	+	0.243649i	−0.211123	+	0.243649i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.0176486	+	0.617782i	−0.0176486	+	0.617782i	0.941844	+	0.336049i	$0.109091\pi$
$521$	−0.0176486	+	0.617782i	−0.0176486	+	0.617782i	−0.959493	+	0.281733i	$0.909091\pi$
$522$		0			0
$523$	−1.12496	−	1.45888i	−1.12496	−	1.45888i	−0.870746	−	0.491733i	$-0.836364\pi$
$523$	−1.12496	−	1.45888i	−1.12496	−	1.45888i	−0.254218	−	0.967147i	$-0.581818\pi$
$524$	−0.608982	+	1.87425i	−0.608982	+	1.87425i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.268077	+	1.86452i	−0.268077	+	1.86452i
$529$	0.415415	+	0.909632i	0.415415	+	0.909632i
$530$		0			0
$531$	−2.58157	+	1.26927i	−2.58157	+	1.26927i
$532$		0			0
$533$		0			0
$534$	−0.321868	−	3.74744i	−0.321868	−	3.74744i
$535$		0			0
$536$	−0.157116	+	0.597730i	−0.157116	+	0.597730i
$537$	0.347474	−	0.892480i	0.347474	−	0.892480i
$538$		0			0
$539$	0.309017	−	0.951057i	0.309017	−	0.951057i
$540$		0			0
$541$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$541$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$542$		0			0
$543$		0			0
$544$	−0.927251	+	1.75734i	−0.927251	+	1.75734i
$545$		0			0
$546$		0			0
$547$	0.799530	+	0.653772i	0.799530	+	0.653772i	0.941844	−	0.336049i	$-0.109091\pi$
$547$	0.799530	+	0.653772i	0.799530	+	0.653772i	−0.142315	+	0.989821i	$0.545455\pi$
$548$	−1.69623	−	0.394442i	−1.69623	−	0.394442i
$549$		0			0
$550$	−0.736741	−	0.676175i	−0.736741	−	0.676175i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.67095	−	0.943629i	1.67095	−	0.943629i
$557$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$557$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−3.59121	−	1.05447i	−3.59121	−	1.05447i
$562$	−0.829475	+	1.81630i	−0.829475	+	1.81630i
$563$	0.812697	+	0.458951i	0.812697	+	0.458951i	0.841254	−	0.540641i	$-0.181818\pi$
$563$	0.812697	+	0.458951i	0.812697	+	0.458951i	−0.0285561	+	0.999592i	$0.509091\pi$
$564$		0			0
$565$		0			0
$566$	0.507345	+	0.657936i	0.507345	+	0.657936i
$567$		0			0
$568$		0			0
$569$	−0.0294925	−	1.03237i	−0.0294925	−	1.03237i	−0.870746	−	0.491733i	$-0.836364\pi$
$569$	−0.0294925	−	1.03237i	−0.0294925	−	1.03237i	0.841254	−	0.540641i	$-0.181818\pi$
$570$		0			0
$571$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$571$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−2.34728	+	0.991970i	−2.34728	+	0.991970i
$577$	−1.06324	−	0.379362i	−1.06324	−	0.379362i	−0.254218	−	0.967147i	$-0.581818\pi$
$577$	−1.06324	−	0.379362i	−1.06324	−	0.379362i	−0.809017	+	0.587785i	$0.800000\pi$
$578$	−2.38500	−	1.73280i	−2.38500	−	1.73280i
$579$	0.395006	+	0.362534i	0.395006	+	0.362534i
$580$		0			0
$581$		0			0
$582$	2.20882	+	1.41952i	2.20882	+	1.41952i
$583$		0			0
$584$	1.02742	−	0.660282i	1.02742	−	0.660282i
$585$		0			0
$586$		0			0
$587$	−1.65323	−	0.812838i	−1.65323	−	0.812838i	−0.998369	−	0.0570888i	$-0.981818\pi$
$587$	−1.65323	−	0.812838i	−1.65323	−	0.812838i	−0.654861	−	0.755750i	$-0.727273\pi$
$588$	1.83474	−	0.426649i	1.83474	−	0.426649i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.72209	−	0.505653i	−1.72209	−	0.505653i	−0.736741	−	0.676175i	$-0.763636\pi$
$593$	−1.72209	−	0.505653i	−1.72209	−	0.505653i	−0.985354	+	0.170522i	$0.945455\pi$
$594$	−1.64619	−	2.40748i	−1.64619	−	2.40748i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$599$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$600$	0.374083	−	1.84617i	0.374083	−	1.84617i
$601$	−1.09955	+	1.60804i	−1.09955	+	1.60804i	−0.362808	+	0.931864i	$0.618182\pi$
$601$	−1.09955	+	1.60804i	−1.09955	+	1.60804i	−0.736741	+	0.676175i	$0.763636\pi$
$602$		0			0
$603$	−0.734966	−	1.39292i	−0.734966	−	1.39292i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$607$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$608$	−0.455331	−	1.40136i	−0.455331	−	1.40136i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.28720	−	4.89700i	−1.28720	−	4.89700i
$613$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$613$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$614$	−1.12767	+	0.819299i	−1.12767	+	0.819299i
$615$		0			0
$616$		0			0
$617$	0.0547987	+	0.0160903i	0.0547987	+	0.0160903i	0.309017	−	0.951057i	$-0.400000\pi$
$617$	0.0547987	+	0.0160903i	0.0547987	+	0.0160903i	−0.254218	+	0.967147i	$0.581818\pi$
$618$		0			0
$619$	−1.32230	+	1.21360i	−1.32230	+	1.21360i	−0.362808	+	0.931864i	$0.618182\pi$
$619$	−1.32230	+	1.21360i	−1.32230	+	1.21360i	−0.959493	+	0.281733i	$0.909091\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.696938	+	0.717132i	0.696938	+	0.717132i
$626$	−1.54980	+	0.995994i	−1.54980	+	0.995994i
$627$	2.41683	−	1.36485i	2.41683	−	1.36485i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$631$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$632$		0			0
$633$	0.704655	+	0.251420i	0.704655	+	0.251420i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.0556279	−	1.94723i	−0.0556279	−	1.94723i	−0.254218	−	0.967147i	$-0.581818\pi$
$641$	−0.0556279	−	1.94723i	−0.0556279	−	1.94723i	0.198590	−	0.980083i	$-0.436364\pi$
$642$	0.0936761	−	3.27909i	0.0936761	−	3.27909i
$643$	−0.396533	−	0.0226746i	−0.396533	−	0.0226746i	−0.142315	−	0.989821i	$-0.545455\pi$
$643$	−0.396533	−	0.0226746i	−0.396533	−	0.0226746i	−0.254218	+	0.967147i	$0.581818\pi$
$644$		0			0
$645$		0			0
$646$	2.88488	−	0.499247i	2.88488	−	0.499247i
$647$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$647$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$648$	1.22359	−	2.67929i	1.22359	−	2.67929i
$649$	−0.949680	+	0.610322i	−0.949680	+	0.610322i
$650$		0			0
$651$		0			0
$652$	−0.0512523	+	0.0251991i	−0.0512523	+	0.0251991i
$653$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$653$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$654$		0			0
$655$		0			0
$656$	−0.374706	−	0.621380i	−0.374706	−	0.621380i
$657$	−0.791180	+	3.00996i	−0.791180	+	3.00996i
$658$		0			0
$659$	0.262179	−	1.82350i	0.262179	−	1.82350i	−0.254218	−	0.967147i	$-0.581818\pi$
$659$	0.262179	−	1.82350i	0.262179	−	1.82350i	0.516397	−	0.856349i	$-0.327273\pi$
$660$		0			0
$661$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$661$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$662$	1.18956	+	0.276620i	1.18956	+	0.276620i
$663$		0			0
$664$	1.59434	+	0.275911i	1.59434	+	0.275911i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.651166	+	1.67251i	−0.651166	+	1.67251i	0.0855750	+	0.996332i	$0.472727\pi$
$673$	−0.651166	+	1.67251i	−0.651166	+	1.67251i	−0.736741	+	0.676175i	$0.763636\pi$
$674$	−0.157116	+	0.597730i	−0.157116	+	0.597730i
$675$	1.50606	+	2.49753i	1.50606	+	2.49753i
$676$	0.0855750	+	0.996332i	0.0855750	+	0.996332i
$677$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$677$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$678$	−2.87377	+	2.34987i	−2.87377	+	2.34987i
$679$		0			0
$680$		0			0
$681$	−0.397858	−	0.871188i	−0.397858	−	0.871188i
$682$		0			0
$683$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$683$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$684$	3.26952	+	1.84638i	3.26952	+	1.84638i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.170871	−	0.00977075i	−0.170871	−	0.00977075i
$689$		0			0
$690$		0			0
$691$	0.507607	−	0.0290260i	0.507607	−	0.0290260i	0.198590	−	0.980083i	$-0.436364\pi$
$691$	0.507607	−	0.0290260i	0.507607	−	0.0290260i	0.309017	+	0.951057i	$0.400000\pi$
$692$		0			0
$693$		0			0
$694$	0.739263	−	0.853155i	0.739263	−	0.853155i
$695$		0			0
$696$		0			0
$697$	1.32805	−	0.561238i	1.32805	−	0.561238i
$698$		0			0
$699$	−0.605278	−	0.439760i	−0.605278	−	0.439760i
$700$		0			0
$701$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$701$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$702$		0			0
$703$		0			0
$704$	−0.870746	+	0.491733i	−0.870746	+	0.491733i
$705$		0			0
$706$	1.25086	+	1.28711i	1.25086	+	1.28711i
$707$		0			0
$708$	−1.90829	−	0.938244i	−1.90829	−	0.938244i
$709$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$709$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$710$		0			0
$711$		0			0
$712$	1.47108	−	1.35014i	1.47108	−	1.35014i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.487841	−	0.143243i	0.487841	−	0.143243i
$717$		0			0
$718$		0			0
$719$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$719$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$720$		0			0
$721$		0			0
$722$	−0.661048	+	0.966751i	−0.661048	+	0.966751i
$723$	−0.0332445	−	0.102316i	−0.0332445	−	0.102316i
$724$		0			0
$725$		0			0
$726$	−1.23355	−	1.42360i	−1.23355	−	1.42360i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	0.621782	+	1.91365i	0.621782	+	1.91365i
$730$		0			0
$731$	0.0675344	−	0.333296i	0.0675344	−	0.333296i
$732$		0			0
$733$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$733$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.348845	−	0.510170i	−0.348845	−	0.510170i
$738$	1.77417	+	0.520944i	1.77417	+	0.520944i
$739$	−0.478868	+	0.170860i	−0.478868	+	0.170860i	−0.564443	−	0.825472i	$-0.690909\pi$
$739$	−0.478868	+	0.170860i	−0.478868	+	0.170860i	0.0855750	+	0.996332i	$0.472727\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$743$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.46866	+	2.22918i	−3.46866	+	2.22918i
$748$	−0.720886	−	1.85158i	−0.720886	−	1.85158i
$749$		0			0
$750$		0			0
$751$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$751$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$752$		0			0
$753$	−2.56403	−	1.86288i	−2.56403	−	1.86288i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$757$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$758$	0.611204	−	0.705367i	0.611204	−	0.705367i
$759$		0			0
$760$		0			0
$761$	1.12705	−	0.0644468i	1.12705	−	0.0644468i	0.516397	−	0.856349i	$-0.327273\pi$
$761$	1.12705	−	0.0644468i	1.12705	−	0.0644468i	0.610648	+	0.791902i	$0.290909\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.64021	−	0.926272i	−1.64021	−	0.926272i
$769$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$769$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$770$		0			0
$771$	−0.730346	−	1.59923i	−0.730346	−	1.59923i
$772$	−0.0243572	+	0.283586i	−0.0243572	+	0.283586i
$773$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$773$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$774$	0.337633	−	0.276081i	0.337633	−	0.276081i
$775$		0			0
$776$	0.119281	+	1.38876i	0.119281	+	1.38876i
$777$		0			0
$778$		0			0
$779$	−0.387907	+	0.996332i	−0.387907	+	0.996332i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.774142	+	0.633012i	0.774142	+	0.633012i
$785$		0			0
$786$	1.73236	−	3.28319i	1.73236	−	3.28319i
$787$	−0.288416	+	0.546610i	−0.288416	+	0.546610i	−0.985354	−	0.170522i	$-0.945455\pi$
$787$	−0.288416	+	0.546610i	−0.288416	+	0.546610i	0.696938	+	0.717132i	$0.254545\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.787463	−	2.42356i	0.787463	−	2.42356i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$797$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$798$		0			0
$799$		0			0
$800$	0.897398	−	0.441221i	0.897398	−	0.441221i
$801$	−0.435427	+	5.06959i	−0.435427	+	5.06959i
$802$	−0.301432	−	0.660043i	−0.301432	−	0.660043i
$803$	−0.173809	+	1.20886i	−0.173809	+	1.20886i
$804$	0.483619	−	1.05898i	0.483619	−	1.05898i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0570190	+	0.00326046i	0.0570190	+	0.00326046i	0.0855750	−	0.996332i	$-0.472727\pi$
$809$	0.0570190	+	0.00326046i	0.0570190	+	0.00326046i	−0.0285561	+	0.999592i	$0.509091\pi$
$810$		0			0
$811$	0.0207207	+	0.725319i	0.0207207	+	0.725319i	0.941844	+	0.336049i	$0.109091\pi$
$811$	0.0207207	+	0.725319i	0.0207207	+	0.725319i	−0.921124	+	0.389270i	$0.872727\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	2.28555	−	2.96395i	2.28555	−	2.96395i
$817$	0.142345	+	0.208173i	0.142345	+	0.208173i
$818$	1.20642	−	0.509835i	1.20642	−	0.509835i
$819$		0			0
$820$		0			0
$821$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$821$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$822$	3.02168	+	1.27697i	3.02168	+	1.27697i
$823$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$823$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$824$		0			0
$825$	1.15027	+	1.49170i	1.15027	+	1.49170i
$826$		0			0
$827$	0.719794	+	0.740650i	0.719794	+	0.740650i	0.974012	−	0.226497i	$-0.0727273\pi$
$827$	0.719794	+	0.740650i	0.719794	+	0.740650i	−0.254218	+	0.967147i	$0.581818\pi$
$828$		0			0
$829$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$829$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.46388	+	1.34353i	−1.46388	+	1.34353i
$834$	−3.40455	+	1.21474i	−3.40455	+	1.21474i
$835$		0			0
$836$	1.35726	+	0.573583i	1.35726	+	0.573583i
$837$		0			0
$838$	−1.57598	+	1.14502i	−1.57598	+	1.14502i
$839$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$839$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$840$		0			0
$841$	0.696938	−	0.717132i	0.696938	−	0.717132i
$842$		0			0
$843$	2.12300	−	3.10479i	2.12300	−	3.10479i
$844$	0.122736	+	0.377742i	0.122736	+	0.377742i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.730346	−	1.38416i	−0.730346	−	1.38416i
$850$	0.614005	+	1.88971i	0.614005	+	1.88971i
$851$		0			0
$852$		0			0
$853$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$853$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$854$		0			0
$855$		0			0
$856$	1.40890	−	1.02362i	1.40890	−	1.02362i
$857$	−0.164217	+	0.0482185i	−0.164217	+	0.0482185i	−0.362808	−	0.931864i	$-0.618182\pi$
$857$	−0.164217	+	0.0482185i	−0.164217	+	0.0482185i	0.198590	+	0.980083i	$0.436364\pi$
$858$		0			0
$859$	1.76762	+	0.519021i	1.76762	+	0.519021i	0.993482	−	0.113991i	$-0.0363636\pi$
$859$	1.76762	+	0.519021i	1.76762	+	0.519021i	0.774142	+	0.633012i	$0.218182\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$863$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$864$	2.84069	−	0.660574i	2.84069	−	0.660574i
$865$		0			0
$866$	0.926829	−	1.53697i	0.926829	−	1.53697i
$867$	3.87021	+	3.98235i	3.87021	+	3.98235i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−2.61690	−	2.40177i	−2.61690	−	2.40177i
$874$		0			0
$875$		0			0
$876$	−2.11908	+	0.895532i	−2.11908	+	0.895532i
$877$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$877$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.05959	+	1.22283i	1.05959	+	1.22283i	0.974012	+	0.226497i	$0.0727273\pi$
$881$	1.05959	+	1.22283i	1.05959	+	1.22283i	0.0855750	+	0.996332i	$0.472727\pi$
$882$	−2.54413	+	0.145478i	−2.54413	+	0.145478i
$883$	−0.00488737	−	0.171080i	−0.00488737	−	0.171080i	−0.998369	−	0.0570888i	$-0.981818\pi$
$883$	−0.00488737	−	0.171080i	−0.00488737	−	0.171080i	0.993482	−	0.113991i	$-0.0363636\pi$
$884$		0			0
$885$		0			0
$886$	0.851167	+	1.10381i	0.851167	+	1.10381i
$887$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$887$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.22359	+	2.67929i	1.22359	+	2.67929i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.951332	−	1.57761i	−0.951332	−	1.57761i
$899$		0			0
$900$	−0.924537	+	2.37465i	−0.924537	+	2.37465i
$901$		0			0
$902$	0.714988	+	0.123734i	0.714988	+	0.123734i
$903$		0			0
$904$	−1.91949	−	0.446359i	−1.91949	−	0.446359i
$905$		0			0
$906$		0			0
$907$	0.687626	−	1.30320i	0.687626	−	1.30320i	−0.254218	−	0.967147i	$-0.581818\pi$
$907$	0.687626	−	1.30320i	0.687626	−	1.30320i	0.941844	−	0.336049i	$-0.109091\pi$
$908$	0.237271	−	0.449678i	0.237271	−	0.449678i
$909$		0			0
$910$		0			0
$911$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$911$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$912$	0.395006	+	2.74733i	0.395006	+	2.74733i
$913$	−1.25259	+	1.02424i	−1.25259	+	1.02424i
$914$	0.230270	−	1.60156i	0.230270	−	1.60156i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.495903	+	5.77369i	0.495903	+	5.77369i
$919$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$919$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$920$		0			0
$921$	2.35623	−	1.15848i	2.35623	−	1.15848i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.21334	+	1.57348i	1.21334	+	1.57348i	0.696938	+	0.717132i	$0.254545\pi$
$929$	1.21334	+	1.57348i	1.21334	+	1.57348i	0.516397	+	0.856349i	$0.327273\pi$
$930$		0			0
$931$	0.0420768	−	1.47288i	0.0420768	−	1.47288i
$932$	−0.0113419	−	0.397019i	−0.0113419	−	0.397019i
$933$		0			0
$934$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$935$		0			0
$936$		0			0
$937$	0.630674	−	0.817873i	0.630674	−	0.817873i	−0.362808	−	0.931864i	$-0.618182\pi$
$937$	0.630674	−	0.817873i	0.630674	−	0.817873i	0.993482	+	0.113991i	$0.0363636\pi$
$938$		0			0
$939$	3.19650	−	1.35085i	3.19650	−	1.35085i
$940$		0			0
$941$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$941$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$942$		0			0
$943$		0			0
$944$	−0.224186	−	1.10640i	−0.224186	−	1.10640i
$945$		0			0
$946$	0.119281	−	0.122737i	0.119281	−	0.122737i
$947$	1.67154	−	1.07423i	1.67154	−	1.07423i	0.774142	−	0.633012i	$-0.218182\pi$
$947$	1.67154	−	1.07423i	1.67154	−	1.07423i	0.897398	−	0.441221i	$-0.145455\pi$
$948$		0			0
$949$		0			0
$950$	−1.32230	−	0.650131i	−1.32230	−	0.650131i
$951$		0			0
$952$		0			0
$953$	1.93533	−	0.222058i	1.93533	−	0.222058i	0.941844	−	0.336049i	$-0.109091\pi$
$953$	1.93533	−	0.222058i	1.93533	−	0.222058i	0.993482	+	0.113991i	$0.0363636\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.254218	−	0.967147i	−0.254218	−	0.967147i
$962$		0			0
$963$	−0.881308	+	4.34943i	−0.881308	+	4.34943i
$964$	0.0322365	−	0.0471444i	0.0322365	−	0.0471444i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.198590	−	0.980083i	0.198590	−	0.980083i
$969$	−5.51498			−5.51498
$970$		0			0
$971$	−0.592999	−	1.82506i	−0.592999	−	1.82506i	−0.564443	−	0.825472i	$-0.690909\pi$
$971$	−0.592999	−	1.82506i	−0.592999	−	1.82506i	−0.0285561	−	0.999592i	$-0.509091\pi$
$972$	−1.48553	+	2.17252i	−1.48553	+	2.17252i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.672156	+	0.488350i	−0.672156	+	0.488350i	−0.870746	−	0.491733i	$-0.836364\pi$
$977$	−0.672156	+	0.488350i	−0.672156	+	0.488350i	0.198590	+	0.980083i	$0.436364\pi$
$978$	0.103224	−	0.0303092i	0.103224	−	0.0303092i
$979$	0.0570190	+	1.99592i	0.0570190	+	1.99592i
$980$		0			0
$981$		0			0
$982$	−0.899779	+	0.825810i	−0.899779	+	0.825810i
$983$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$983$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$984$	0.495898	+	1.27370i	0.495898	+	1.27370i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$991$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$992$		0			0
$993$	−2.11908	−	0.895532i	−2.11908	−	0.895532i
$994$		0			0
$995$		0			0
$996$	−2.87062	−	1.02424i	−2.87062	−	1.02424i
$997$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$997$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$998$	1.12705	+	1.64825i	1.12705	+	1.64825i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.1.z.a.267.1	✓	40
4.3	odd	2		3872.1.bx.a.751.1		40
8.3	odd	2	CM	968.1.z.a.267.1	✓	40
8.5	even	2		3872.1.bx.a.751.1		40
121.92	even	55	inner	968.1.z.a.939.1	yes	40
484.455	odd	110		3872.1.bx.a.1423.1		40
968.213	even	110		3872.1.bx.a.1423.1		40
968.939	odd	110	inner	968.1.z.a.939.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.1.z.a.267.1	✓	40	1.1	even	1	trivial
968.1.z.a.267.1	✓	40	8.3	odd	2	CM
968.1.z.a.939.1	yes	40	121.92	even	55	inner
968.1.z.a.939.1	yes	40	968.939	odd	110	inner
3872.1.bx.a.751.1		40	4.3	odd	2
3872.1.bx.a.751.1		40	8.5	even	2
3872.1.bx.a.1423.1		40	484.455	odd	110
3872.1.bx.a.1423.1		40	968.213	even	110

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	968.z (of order \(110\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.466667 - 0.884433i) q^{2} +(0.582092 + 1.79149i) q^{3} +(-0.564443 + 0.825472i) q^{4} +(1.31281 - 1.35085i) q^{6} +(0.993482 + 0.113991i) q^{8} +(-2.06160 + 1.49784i) q^{9} +(-0.736741 + 0.676175i) q^{11} +(-1.80739 - 0.530696i) q^{12} +(-0.362808 - 0.931864i) q^{16} +(1.93533 - 0.450041i) q^{17} +(2.28683 + 1.12436i) q^{18} +(-0.760903 + 1.26182i) q^{19} +(0.941844 + 0.336049i) q^{22} +(0.374083 + 1.84617i) q^{24} +(-0.921124 - 0.389270i) q^{25} +(-2.35948 - 1.71427i) q^{27} +(-0.654861 + 0.755750i) q^{32} +(-1.64021 - 0.926272i) q^{33} +(-1.30118 - 1.50165i) q^{34} +(-0.0727689 - 2.54724i) q^{36} +(1.47108 + 0.0841194i) q^{38} +(0.714988 - 0.123734i) q^{41} +(0.0710983 - 0.155684i) q^{43} +(-0.142315 - 0.989821i) q^{44} +(1.45824 - 1.19240i) q^{48} +(-0.870746 + 0.491733i) q^{49} +(0.0855750 + 0.996332i) q^{50} +(1.93278 + 3.20516i) q^{51} +(-0.415059 + 2.88680i) q^{54} +(-2.70345 - 0.628660i) q^{57} +(1.11235 + 0.192500i) q^{59} +(0.974012 + 0.226497i) q^{64} +(-0.0537907 + 1.88292i) q^{66} +(-0.0879554 + 0.611743i) q^{67} +(-0.720886 + 1.85158i) q^{68} +(-2.21891 + 1.25307i) q^{72} +(0.945456 - 0.773095i) q^{73} +(0.161197 - 1.87678i) q^{75} +(-0.612107 - 1.34033i) q^{76} +(0.910198 - 2.80130i) q^{81} +(-0.443096 - 0.574616i) q^{82} +(1.61540 + 0.0923716i) q^{83} +(-0.170871 + 0.00977075i) q^{86} +(-0.809017 + 0.587785i) q^{88} +(1.30759 - 1.50903i) q^{89} +(-1.73511 - 0.733264i) q^{96} +(0.276810 + 1.36611i) q^{97} +(0.841254 + 0.540641i) q^{98} +(0.506065 - 2.49753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{2} + 2 q^{3} + q^{4} - 3 q^{6} + q^{8} - 8 q^{9} + q^{11} - 9 q^{12} + q^{16} + 2 q^{17} - 2 q^{18} - 3 q^{19} + q^{22} - 3 q^{24} + q^{25} - q^{27} - 4 q^{32} - 3 q^{33} + 2 q^{34} - 2 q^{36}+ \cdots + 3 q^{99}+O(q^{100}) \) 40 * q + q^2 + 2 * q^3 + q^4 - 3 * q^6 + q^8 - 8 * q^9 + q^11 - 9 * q^12 + q^16 + 2 * q^17 - 2 * q^18 - 3 * q^19 + q^22 - 3 * q^24 + q^25 - q^27 - 4 * q^32 - 3 * q^33 + 2 * q^34 - 2 * q^36 + 2 * q^38 + 2 * q^41 + 2 * q^43 - 4 * q^44 + 2 * q^48 + q^49 + q^50 - 12 * q^51 + 4 * q^54 - 12 * q^57 - 3 * q^59 + q^64 - 9 * q^66 + 2 * q^67 + 2 * q^68 + 3 * q^72 + 2 * q^73 - 3 * q^75 - 9 * q^76 - 11 * q^81 - 3 * q^82 - 3 * q^83 - 3 * q^86 - 10 * q^88 + 2 * q^89 + 2 * q^96 - 3 * q^97 - 4 * q^98 + 3 * q^99

Introduction

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