LMFDB - Embedded newform 1096.1.z.a.299.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1096,1,Mod(11,1096)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1096, base_ring=CyclotomicField(68))

chi = DirichletCharacter(H, H._module([34, 34, 61]))

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

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

chi := DirichletCharacter("1096.11");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1096 = 2^{3} \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1096.z (of order $68$, degree $32$, 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:	$0.546975253846$
Analytic rank:	$0$
Dimension:	$32$
Coefficient field:	$\Q(\zeta_{68})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} + \cdots + 1 $ x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{68}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{68} - \cdots)$

Embedding invariants

Embedding label			299.1
Root			$0.361242 - 0.932472i$ of defining polynomial
Character	$\chi$	$=$	1096.299
Dual form			1096.1.z.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.995734 + 0.0922684i) q^{2} +(-1.65667 - 0.555259i) q^{3} +(0.982973 + 0.183750i) q^{4} +(-1.59837 - 0.705749i) q^{6} +(0.961826 + 0.273663i) q^{8} +(1.63822 + 1.23713i) q^{9} +O(q^{10})$	\(q+(0.995734 + 0.0922684i) q^{2} +(-1.65667 - 0.555259i) q^{3} +(0.982973 + 0.183750i) q^{4} +(-1.59837 - 0.705749i) q^{6} +(0.961826 + 0.273663i) q^{8} +(1.63822 + 1.23713i) q^{9} +(-0.342683 + 1.83319i) q^{11} +(-1.52643 - 0.850217i) q^{12} +(0.932472 + 0.361242i) q^{16} +(0.694903 - 0.197717i) q^{17} +(1.51709 + 1.38301i) q^{18} +(1.29596 - 1.42160i) q^{19} +(-0.510366 + 1.79375i) q^{22} +(-1.44147 - 0.987432i) q^{24} +(-0.183750 - 0.982973i) q^{25} +(-1.03963 - 1.51768i) q^{27} +(0.895163 + 0.445738i) q^{32} +(1.58561 - 2.84671i) q^{33} +(0.710182 - 0.132756i) q^{34} +(1.38301 + 1.51709i) q^{36} +(1.42160 - 1.29596i) q^{38} +(1.34090 + 1.34090i) q^{41} +(-1.82764 + 0.0844967i) q^{43} +(-0.673696 + 1.73901i) q^{44} +(-1.34421 - 1.11622i) q^{48} +(-0.445738 + 0.895163i) q^{49} +(-0.0922684 - 0.995734i) q^{50} +(-1.26101 - 0.0582999i) q^{51} +(-0.895163 - 1.60713i) q^{54} +(-2.93632 + 1.63552i) q^{57} +(-0.111208 + 0.147263i) q^{59} +(0.850217 + 0.526432i) q^{64} +(1.84151 - 2.68827i) q^{66} +(0.947359 + 0.222817i) q^{67} +(0.719401 - 0.0666624i) q^{68} +(1.23713 + 1.63822i) q^{72} +(-1.52217 - 0.942485i) q^{73} +(-0.241393 + 1.73049i) q^{75} +(1.53511 - 1.15926i) q^{76} +(0.317829 + 1.11705i) q^{81} +(1.21146 + 1.45890i) q^{82} +(-0.222817 - 0.400033i) q^{83} +(-1.82764 - 0.0844967i) q^{86} +(-0.831277 + 1.66943i) q^{88} +(-1.53703 - 1.27633i) q^{89} +(-1.23549 - 1.23549i) q^{96} +(-1.36124 + 0.932472i) q^{97} +(-0.526432 + 0.850217i) q^{98} +(-2.82928 + 2.57923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6}+O(q^{10}) $ 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6	$ 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6} - 32 q^{12} - 2 q^{16} - 2 q^{18} - 4 q^{22} + 2 q^{24} + 4 q^{33} - 2 q^{41} + 2 q^{43} - 2 q^{48} + 2 q^{49} + 2 q^{50} - 4 q^{59} + 2 q^{64} - 4 q^{66} + 2 q^{67} + 2 q^{72} - 2 q^{75} - 2 q^{81} + 2 q^{82} - 2 q^{83} + 2 q^{86} + 4 q^{88} + 2 q^{89} - 2 q^{96} - 32 q^{97} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6 - 32 * q^12 - 2 * q^16 - 2 * q^18 - 4 * q^22 + 2 * q^24 + 4 * q^33 - 2 * q^41 + 2 * q^43 - 2 * q^48 + 2 * q^49 + 2 * q^50 - 4 * q^59 + 2 * q^64 - 4 * q^66 + 2 * q^67 + 2 * q^72 - 2 * q^75 - 2 * q^81 + 2 * q^82 - 2 * q^83 + 2 * q^86 + 4 * q^88 + 2 * q^89 - 2 * q^96 - 32 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1096\mathbb{Z}\right)^\times$.

$n$	$549$	$823$	$825$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{68}\right)$

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 $

$2$	0.995734	+	0.0922684i	0.995734	+	0.0922684i
$2$	0.995734	+	0.0922684i	0.995734	+	0.0922684i
$3$	−1.65667	−	0.555259i	−1.65667	−	0.555259i	−0.673696	−	0.739009i	$-0.735294\pi$
$3$	−1.65667	−	0.555259i	−1.65667	−	0.555259i	−0.982973	+	0.183750i	$0.941176\pi$
$4$	0.982973	+	0.183750i	0.982973	+	0.183750i
$5$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$5$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$6$	−1.59837	−	0.705749i	−1.59837	−	0.705749i
$7$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$7$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$8$	0.961826	+	0.273663i	0.961826	+	0.273663i
$9$	1.63822	+	1.23713i	1.63822	+	1.23713i
$10$		0			0
$11$	−0.342683	+	1.83319i	−0.342683	+	1.83319i	0.183750	+	0.982973i	$0.441176\pi$
$11$	−0.342683	+	1.83319i	−0.342683	+	1.83319i	−0.526432	+	0.850217i	$0.676471\pi$
$12$	−1.52643	−	0.850217i	−1.52643	−	0.850217i
$13$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$13$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$14$		0			0
$15$		0			0
$16$	0.932472	+	0.361242i	0.932472	+	0.361242i
$17$	0.694903	−	0.197717i	0.694903	−	0.197717i	0.0922684	−	0.995734i	$-0.470588\pi$
$17$	0.694903	−	0.197717i	0.694903	−	0.197717i	0.602635	+	0.798017i	$0.294118\pi$
$18$	1.51709	+	1.38301i	1.51709	+	1.38301i
$19$	1.29596	−	1.42160i	1.29596	−	1.42160i	0.445738	−	0.895163i	$-0.352941\pi$
$19$	1.29596	−	1.42160i	1.29596	−	1.42160i	0.850217	−	0.526432i	$-0.176471\pi$
$20$		0			0
$21$		0			0
$22$	−0.510366	+	1.79375i	−0.510366	+	1.79375i
$23$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$23$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$24$	−1.44147	−	0.987432i	−1.44147	−	0.987432i
$25$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$26$		0			0
$27$	−1.03963	−	1.51768i	−1.03963	−	1.51768i
$28$		0			0
$29$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$29$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$30$		0			0
$31$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$31$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$32$	0.895163	+	0.445738i	0.895163	+	0.445738i
$33$	1.58561	−	2.84671i	1.58561	−	2.84671i
$34$	0.710182	−	0.132756i	0.710182	−	0.132756i
$35$		0			0
$36$	1.38301	+	1.51709i	1.38301	+	1.51709i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	1.42160	−	1.29596i	1.42160	−	1.29596i
$39$		0			0
$40$		0			0
$41$	1.34090	+	1.34090i	1.34090	+	1.34090i	0.895163	+	0.445738i	$0.147059\pi$
$41$	1.34090	+	1.34090i	1.34090	+	1.34090i	0.445738	+	0.895163i	$0.352941\pi$
$42$		0			0
$43$	−1.82764	+	0.0844967i	−1.82764	+	0.0844967i	−0.932472	−	0.361242i	$-0.882353\pi$
$43$	−1.82764	+	0.0844967i	−1.82764	+	0.0844967i	−0.895163	+	0.445738i	$0.852941\pi$
$44$	−0.673696	+	1.73901i	−0.673696	+	1.73901i
$45$		0			0
$46$		0			0
$47$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$47$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$48$	−1.34421	−	1.11622i	−1.34421	−	1.11622i
$49$	−0.445738	+	0.895163i	−0.445738	+	0.895163i
$50$	−0.0922684	−	0.995734i	−0.0922684	−	0.995734i
$51$	−1.26101	−	0.0582999i	−1.26101	−	0.0582999i
$52$		0			0
$53$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$53$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$54$	−0.895163	−	1.60713i	−0.895163	−	1.60713i
$55$		0			0
$56$		0			0
$57$	−2.93632	+	1.63552i	−2.93632	+	1.63552i
$58$		0			0
$59$	−0.111208	+	0.147263i	−0.111208	+	0.147263i	−0.850217	−	0.526432i	$-0.823529\pi$
$59$	−0.111208	+	0.147263i	−0.111208	+	0.147263i	0.739009	+	0.673696i	$0.235294\pi$
$60$		0			0
$61$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$61$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$62$		0			0
$63$		0			0
$64$	0.850217	+	0.526432i	0.850217	+	0.526432i
$65$		0			0
$66$	1.84151	−	2.68827i	1.84151	−	2.68827i
$67$	0.947359	+	0.222817i	0.947359	+	0.222817i	0.673696	−	0.739009i	$-0.264706\pi$
$67$	0.947359	+	0.222817i	0.947359	+	0.222817i	0.273663	+	0.961826i	$0.411765\pi$
$68$	0.719401	−	0.0666624i	0.719401	−	0.0666624i
$69$		0			0
$70$		0			0
$71$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$71$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$72$	1.23713	+	1.63822i	1.23713	+	1.63822i
$73$	−1.52217	−	0.942485i	−1.52217	−	0.942485i	−0.995734	−	0.0922684i	$-0.970588\pi$
$73$	−1.52217	−	0.942485i	−1.52217	−	0.942485i	−0.526432	−	0.850217i	$-0.676471\pi$
$74$		0			0
$75$	−0.241393	+	1.73049i	−0.241393	+	1.73049i
$76$	1.53511	−	1.15926i	1.53511	−	1.15926i
$77$		0			0
$78$		0			0
$79$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$79$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$80$		0			0
$81$	0.317829	+	1.11705i	0.317829	+	1.11705i
$82$	1.21146	+	1.45890i	1.21146	+	1.45890i
$83$	−0.222817	−	0.400033i	−0.222817	−	0.400033i	0.739009	−	0.673696i	$-0.235294\pi$
$83$	−0.222817	−	0.400033i	−0.222817	−	0.400033i	−0.961826	+	0.273663i	$0.911765\pi$
$84$		0			0
$85$		0			0
$86$	−1.82764	−	0.0844967i	−1.82764	−	0.0844967i
$87$		0			0
$88$	−0.831277	+	1.66943i	−0.831277	+	1.66943i
$89$	−1.53703	−	1.27633i	−1.53703	−	1.27633i	−0.798017	−	0.602635i	$-0.794118\pi$
$89$	−1.53703	−	1.27633i	−1.53703	−	1.27633i	−0.739009	−	0.673696i	$-0.764706\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.23549	−	1.23549i	−1.23549	−	1.23549i
$97$	−1.36124	+	0.932472i	−1.36124	+	0.932472i	−0.361242	+	0.932472i	$0.617647\pi$
$97$	−1.36124	+	0.932472i	−1.36124	+	0.932472i	−1.00000			$\pi$
$98$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$99$	−2.82928	+	2.57923i	−2.82928	+	2.57923i
$100$		−	1.00000i		−	1.00000i
$101$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$101$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$102$	−1.25025	−	0.174402i	−1.25025	−	0.174402i
$103$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$103$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.52217	−	0.757949i	1.52217	−	0.757949i	0.526432	−	0.850217i	$-0.323529\pi$
$107$	1.52217	−	0.757949i	1.52217	−	0.757949i	0.995734	+	0.0922684i	$0.0294118\pi$
$108$	−0.743058	−	1.68287i	−0.743058	−	1.68287i
$109$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$109$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.524354	−	0.359191i	−0.524354	−	0.359191i	0.273663	−	0.961826i	$-0.411765\pi$
$113$	−0.524354	−	0.359191i	−0.524354	−	0.359191i	−0.798017	+	0.602635i	$0.794118\pi$
$114$	−3.07470	+	1.35761i	−3.07470	+	1.35761i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.124322	+	0.136374i	−0.124322	+	0.136374i
$119$		0			0
$120$		0			0
$121$	−2.31068	−	0.895163i	−2.31068	−	0.895163i
$122$		0			0
$123$	−1.47688	−	2.96598i	−1.47688	−	2.96598i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	0.798017	+	0.602635i	0.798017	+	0.602635i
$129$	3.07470	+	0.874829i	3.07470	+	0.874829i
$130$		0			0
$131$	−0.739009	−	0.326304i	−0.739009	−	0.326304i		−	1.00000i	$-0.5\pi$
$131$	−0.739009	−	0.326304i	−0.739009	−	0.326304i	−0.739009	+	0.673696i	$0.764706\pi$
$132$	2.08169	−	2.50689i	2.08169	−	2.50689i
$133$		0			0
$134$	0.922758	+	0.309277i	0.922758	+	0.309277i
$135$		0			0
$136$	0.722483			0.722483
$137$	0.673696	+	0.739009i	0.673696	+	0.739009i
$137$	0.673696	+	0.739009i	0.673696	+	0.739009i
$138$		0			0
$139$	−0.544991	−	0.0505009i	−0.544991	−	0.0505009i	−0.183750	−	0.982973i	$-0.558824\pi$
$139$	−0.544991	−	0.0505009i	−0.544991	−	0.0505009i	−0.361242	+	0.932472i	$0.617647\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.08069	+	1.74538i	1.08069	+	1.74538i
$145$		0			0
$146$	−1.42871	−	1.07891i	−1.42871	−	1.07891i
$147$	1.23549	−	1.23549i	1.23549	−	1.23549i
$148$		0			0
$149$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$149$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$150$	−0.400033	+	1.70083i	−0.400033	+	1.70083i
$151$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$151$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$152$	1.63552	−	1.01267i	1.63552	−	1.01267i
$153$	1.38301	+	0.535779i	1.38301	+	0.535779i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$157$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.213404	+	1.14161i	0.213404	+	1.14161i
$163$	0.359191	−	1.07168i	0.359191	−	1.07168i	−0.602635	−	0.798017i	$-0.705882\pi$
$163$	0.359191	−	1.07168i	0.359191	−	1.07168i	0.961826	−	0.273663i	$-0.0882353\pi$
$164$	1.07168	+	1.56446i	1.07168	+	1.56446i
$165$		0			0
$166$	−0.184956	−	0.418885i	−0.184956	−	0.418885i
$167$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$167$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$168$		0			0
$169$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$170$		0			0
$171$	3.88176	−	0.725626i	3.88176	−	0.725626i
$172$	−1.81204	−	0.252769i	−1.81204	−	0.252769i
$173$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$173$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$174$		0			0
$175$		0			0
$176$	−0.981767	+	1.58561i	−0.981767	+	1.58561i
$177$	0.266005	−	0.182217i	0.266005	−	0.182217i
$178$	−1.41270	−	1.41270i	−1.41270	−	1.41270i
$179$	−0.0878098	−	0.629488i	−0.0878098	−	0.629488i	−0.982973	−	0.183750i	$-0.941176\pi$
$179$	−0.0878098	−	0.629488i	−0.0878098	−	0.629488i	0.895163	−	0.445738i	$-0.147059\pi$
$180$		0			0
$181$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$181$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.124322	+	1.34164i	0.124322	+	1.34164i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$191$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$192$	−1.11622	−	1.34421i	−1.11622	−	1.34421i
$193$	0.100571	+	0.353470i	0.100571	+	0.353470i	0.995734	−	0.0922684i	$-0.0294118\pi$
$193$	0.100571	+	0.353470i	0.100571	+	0.353470i	−0.895163	+	0.445738i	$0.852941\pi$
$194$	−1.44147	+	0.802895i	−1.44147	+	0.802895i
$195$		0			0
$196$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$197$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$197$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$198$	−3.05519	+	2.30717i	−3.05519	+	2.30717i
$199$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$199$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$200$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$201$	−1.44574	−	0.895163i	−1.44574	−	0.895163i
$202$		0			0
$203$		0			0
$204$	−1.22882	−	0.289017i	−1.22882	−	0.289017i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.16195	+	2.86289i	2.16195	+	2.86289i
$210$		0			0
$211$	−0.183750	+	1.98297i	−0.183750	+	1.98297i			1.00000i	$0.5\pi$
$211$	−0.183750	+	1.98297i	−0.183750	+	1.98297i	−0.183750	+	0.982973i	$0.558824\pi$
$212$		0			0
$213$		0			0
$214$	1.58561	−	0.614268i	1.58561	−	0.614268i
$215$		0			0
$216$	−0.584613	−	1.74425i	−0.584613	−	1.74425i
$217$		0			0
$218$		0			0
$219$	1.99840	+	2.40658i	1.99840	+	2.40658i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$223$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$224$		0			0
$225$	0.915040	−	1.83765i	0.915040	−	1.83765i
$226$	−0.488975	−	0.406040i	−0.488975	−	0.406040i
$227$	−0.453510	+	0.0632619i	−0.453510	+	0.0632619i	−0.361242	−	0.932472i	$-0.617647\pi$
$227$	−0.453510	+	0.0632619i	−0.453510	+	0.0632619i	−0.0922684	+	0.995734i	$0.529412\pi$
$228$	−3.18685	+	1.06813i	−3.18685	+	1.06813i
$229$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$229$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.799224	−	0.799224i	−0.799224	−	0.799224i	0.183750	−	0.982973i	$-0.441176\pi$
$233$	−0.799224	−	0.799224i	−0.799224	−	0.799224i	−0.982973	+	0.183750i	$0.941176\pi$
$234$		0			0
$235$		0			0
$236$	−0.136374	+	0.124322i	−0.136374	+	0.124322i
$237$		0			0
$238$		0			0
$239$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$239$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$240$		0			0
$241$	0.802895	−	1.44147i	0.802895	−	1.44147i	−0.0922684	−	0.995734i	$-0.529412\pi$
$241$	0.802895	−	1.44147i	0.802895	−	1.44147i	0.895163	−	0.445738i	$-0.147059\pi$
$242$	−2.21823	−	1.10455i	−2.21823	−	1.10455i
$243$	0.00875716	−	0.189414i	0.00875716	−	0.189414i
$244$		0			0
$245$		0			0
$246$	−1.19692	−	3.08960i	−1.19692	−	3.08960i
$247$		0			0
$248$		0			0
$249$	0.147012	+	0.786443i	0.147012	+	0.786443i
$250$		0			0
$251$	0.739009	−	0.326304i	0.739009	−	0.326304i		−	1.00000i	$-0.5\pi$
$251$	0.739009	−	0.326304i	0.739009	−	0.326304i	0.739009	+	0.673696i	$0.235294\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.739009	+	0.673696i	0.739009	+	0.673696i
$257$	−0.857445	+	0.243964i	−0.857445	+	0.243964i	−0.673696	−	0.739009i	$-0.735294\pi$
$257$	−0.857445	+	0.243964i	−0.857445	+	0.243964i	−0.183750	+	0.982973i	$0.558824\pi$
$258$	2.98087	+	1.15479i	2.98087	+	1.15479i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.705749	−	0.393100i	−0.705749	−	0.393100i
$263$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$263$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$264$	2.30412	−	2.30412i	2.30412	−	2.30412i
$265$		0			0
$266$		0			0
$267$	1.83765	+	2.96790i	1.83765	+	2.96790i
$268$	0.890286	+	0.393100i	0.890286	+	0.393100i
$269$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$269$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$270$		0			0
$271$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$271$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$272$	0.719401	+	0.0666624i	0.719401	+	0.0666624i
$273$		0			0
$274$	0.602635	+	0.798017i	0.602635	+	0.798017i
$275$	1.86494			1.86494
$276$		0			0
$277$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$277$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$278$	−0.538007	−	0.100571i	−0.538007	−	0.100571i
$279$		0			0
$280$		0			0
$281$	0.288130	+	0.465346i	0.288130	+	0.465346i	0.961826	−	0.273663i	$-0.0882353\pi$
$281$	0.288130	+	0.465346i	0.288130	+	0.465346i	−0.673696	+	0.739009i	$0.735294\pi$
$282$		0			0
$283$	−1.27366	−	0.961826i	−1.27366	−	0.961826i	−0.273663	−	0.961826i	$-0.588235\pi$
$283$	−1.27366	−	0.961826i	−1.27366	−	0.961826i	−1.00000			$\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.915040	+	1.83765i	0.915040	+	1.83765i
$289$	−0.406419	+	0.251644i	−0.406419	+	0.251644i
$290$		0			0
$291$	2.77289	−	0.788955i	2.77289	−	0.788955i
$292$	−1.32307	−	1.20614i	−1.32307	−	1.20614i
$293$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$293$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$294$	1.34421	−	1.11622i	1.34421	−	1.11622i
$295$		0			0
$296$		0			0
$297$	3.13845	−	1.38576i	3.13845	−	1.38576i
$298$		0			0
$299$		0			0
$300$	−0.555259	+	1.65667i	−0.555259	+	1.65667i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.72198	−	0.857445i	1.72198	−	0.857445i
$305$		0			0
$306$	1.32767	+	0.661101i	1.32767	+	0.661101i
$307$	0.473568	−	0.850217i	0.473568	−	0.850217i	−0.526432	−	0.850217i	$-0.676471\pi$
$307$	0.473568	−	0.850217i	0.473568	−	0.850217i	1.00000			$0$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	0.709310	−	1.14558i	0.709310	−	1.14558i	−0.273663	−	0.961826i	$-0.588235\pi$
$313$	0.709310	−	1.14558i	0.709310	−	1.14558i	0.982973	−	0.183750i	$-0.0588235\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.998933	−	0.0461835i	$-0.0147059\pi$
$317$		0			0		−0.998933	+	0.0461835i	$0.985294\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−2.94258	+	0.410473i	−2.94258	+	0.410473i
$322$		0			0
$323$	0.619490	−	1.24410i	0.619490	−	1.24410i
$324$	0.107159	+	1.15643i	0.107159	+	1.15643i
$325$		0			0
$326$	0.456541	−	1.03397i	0.456541	−	1.03397i
$327$		0			0
$328$	0.922758	+	1.65667i	0.922758	+	1.65667i
$329$		0			0
$330$		0			0
$331$	1.23549	−	0.688163i	1.23549	−	0.688163i	0.273663	−	0.961826i	$-0.411765\pi$
$331$	1.23549	−	0.688163i	1.23549	−	0.688163i	0.961826	+	0.273663i	$0.0882353\pi$
$332$	−0.145517	−	0.434164i	−0.145517	−	0.434164i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.165190	−	1.78269i	0.165190	−	1.78269i	−0.361242	−	0.932472i	$-0.617647\pi$
$337$	0.165190	−	1.78269i	0.165190	−	1.78269i	0.526432	−	0.850217i	$-0.323529\pi$
$338$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$339$	0.669237	+	0.886213i	0.669237	+	0.886213i
$340$		0			0
$341$		0			0
$342$	3.93215	−	0.364367i	3.93215	−	0.364367i
$343$		0			0
$344$	−1.78099	−	0.418885i	−1.78099	−	0.418885i
$345$		0			0
$346$		0			0
$347$	−1.02474	−	0.634493i	−1.02474	−	0.634493i	−0.0922684	−	0.995734i	$-0.529412\pi$
$347$	−1.02474	−	0.634493i	−1.02474	−	0.634493i	−0.932472	+	0.361242i	$0.882353\pi$
$348$		0			0
$349$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$349$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$350$		0			0
$351$		0			0
$352$	−1.12388	+	1.48826i	−1.12388	+	1.48826i
$353$	0.618701	+	1.84595i	0.618701	+	1.84595i	0.526432	+	0.850217i	$0.323529\pi$
$353$	0.618701	+	1.84595i	0.618701	+	1.84595i	0.0922684	+	0.995734i	$0.470588\pi$
$354$	0.281683	−	0.156896i	0.281683	−	0.156896i
$355$		0			0
$356$	−1.27633	−	1.53703i	−1.27633	−	1.53703i
$357$		0			0
$358$	−0.0293534	−	0.634905i	−0.0293534	−	0.634905i
$359$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$359$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$360$		0			0
$361$	−0.249165	−	2.68891i	−0.249165	−	2.68891i
$362$		0			0
$363$	3.33099	+	2.76602i	3.33099	+	2.76602i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$367$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$368$		0			0
$369$	0.537828	+	3.85556i	0.537828	+	3.85556i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$373$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$374$			1.34739i			1.34739i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.75984	+	0.876298i	1.75984	+	0.876298i	0.961826	+	0.273663i	$0.0882353\pi$
$379$	1.75984	+	0.876298i	1.75984	+	0.876298i	0.798017	+	0.602635i	$0.205882\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$383$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$384$	−0.987432	−	1.44147i	−0.987432	−	1.44147i
$385$		0			0
$386$	0.0675278	+	0.361242i	0.0675278	+	0.361242i
$387$	−3.09860	−	2.12259i	−3.09860	−	2.12259i
$388$	−1.50941	+	0.666468i	−1.50941	+	0.666468i
$389$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$389$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$390$		0			0
$391$		0			0
$392$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$393$	1.04311	+	0.950920i	1.04311	+	0.950920i
$394$		0			0
$395$		0			0
$396$	−3.25504	+	2.01543i	−3.25504	+	2.01543i
$397$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$397$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$398$		0			0
$399$		0			0
$400$	0.183750	−	0.982973i	0.183750	−	0.982973i
$401$	−0.195383	+	0.195383i	−0.195383	+	0.195383i	−0.798017	−	0.602635i	$-0.794118\pi$
$401$	−0.195383	+	0.195383i	−0.195383	+	0.195383i	0.602635	+	0.798017i	$0.294118\pi$
$402$	−1.35698	−	1.02474i	−1.35698	−	1.02474i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.19692	−	0.401166i	−1.19692	−	0.401166i
$409$	−1.95756	−	0.181395i	−1.95756	−	0.181395i	−0.961826	−	0.273663i	$-0.911765\pi$
$409$	−1.95756	−	0.181395i	−1.95756	−	0.181395i	−0.995734	+	0.0922684i	$0.970588\pi$
$410$		0			0
$411$	−0.705749	−	1.59837i	−0.705749	−	1.59837i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.874829	+	0.386275i	0.874829	+	0.386275i
$418$	1.88858	+	3.05016i	1.88858	+	3.05016i
$419$	−1.89090	−	0.538007i	−1.89090	−	0.538007i	−0.995734	−	0.0922684i	$-0.970588\pi$
$419$	−1.89090	−	0.538007i	−1.89090	−	0.538007i	−0.895163	−	0.445738i	$-0.852941\pi$
$420$		0			0
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$	−0.365931	+	1.95756i	−0.365931	+	1.95756i
$423$		0			0
$424$		0			0
$425$	−0.322039	−	0.646741i	−0.322039	−	0.646741i
$426$		0			0
$427$		0			0
$428$	1.63552	−	0.465346i	1.63552	−	0.465346i
$429$		0			0
$430$		0			0
$431$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$431$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$432$	−0.421180	−	1.79075i	−0.421180	−	1.79075i
$433$	0.100571	−	0.353470i	0.100571	−	0.353470i	−0.895163	−	0.445738i	$-0.852941\pi$
$433$	0.100571	−	0.353470i	0.100571	−	0.353470i	0.995734	+	0.0922684i	$0.0294118\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.76783	+	2.58071i	1.76783	+	2.58071i
$439$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$439$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$440$		0			0
$441$	−1.83765	+	0.915040i	−1.83765	+	0.915040i
$442$		0			0
$443$	0.328972	+	0.163808i	0.328972	+	0.163808i	0.602635	−	0.798017i	$-0.294118\pi$
$443$	0.328972	+	0.163808i	0.328972	+	0.163808i	−0.273663	+	0.961826i	$0.588235\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.602635	+	0.798017i	$0.705882\pi$
$449$	−1.45285	+	1.32445i	−1.45285	+	1.32445i	−0.850217	+	0.526432i	$0.823529\pi$
$450$	1.08069	−	1.74538i	1.08069	−	1.74538i
$451$	−2.91763	+	1.99862i	−2.91763	+	1.99862i
$452$	−0.449425	−	0.449425i	−0.449425	−	0.449425i
$453$		0			0
$454$	−0.457413	+	0.0211475i	−0.457413	+	0.0211475i
$455$		0			0
$456$	−3.27181	+	0.769523i	−3.27181	+	0.769523i
$457$	1.73474	−	0.581427i	1.73474	−	0.581427i	0.739009	−	0.673696i	$-0.235294\pi$
$457$	1.73474	−	0.581427i	1.73474	−	0.581427i	0.995734	+	0.0922684i	$0.0294118\pi$
$458$		0			0
$459$	−1.02251	−	0.849084i	−1.02251	−	0.849084i
$460$		0			0
$461$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$461$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$462$		0			0
$463$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$463$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$464$		0			0
$465$		0			0
$466$	−0.722071	−	0.869557i	−0.722071	−	0.869557i
$467$	0.243964	+	0.857445i	0.243964	+	0.857445i	0.982973	+	0.183750i	$0.0588235\pi$
$467$	0.243964	+	0.857445i	0.243964	+	0.857445i	−0.739009	+	0.673696i	$0.764706\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.147263	+	0.111208i	−0.147263	+	0.111208i
$473$	0.471400	−	3.37936i	0.471400	−	3.37936i
$474$		0			0
$475$	−1.63552	−	1.01267i	−1.63552	−	1.01267i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$479$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$480$		0			0
$481$		0			0
$482$	0.932472	−	1.36124i	0.932472	−	1.36124i
$483$		0			0
$484$	−2.10685	−	1.30451i	−2.10685	−	1.30451i
$485$		0			0
$486$	0.0261968	−	0.187798i	0.0261968	−	0.187798i
$487$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$487$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$488$		0			0
$489$	−1.19012	+	1.57597i	−1.19012	+	1.57597i
$490$		0			0
$491$	1.34421	−	0.748723i	1.34421	−	0.748723i	0.361242	−	0.932472i	$-0.382353\pi$
$491$	1.34421	−	0.748723i	1.34421	−	0.748723i	0.982973	+	0.183750i	$0.0588235\pi$
$492$	−0.906738	−	3.18685i	−0.906738	−	3.18685i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0738207	+	0.796652i	0.0738207	+	0.796652i
$499$	−0.537235	+	1.07891i	−0.537235	+	1.07891i	0.445738	+	0.895163i	$0.352941\pi$
$499$	−0.537235	+	1.07891i	−0.537235	+	1.07891i	−0.982973	+	0.183750i	$0.941176\pi$
$500$		0			0
$501$		0			0
$502$	0.765964	−	0.256725i	0.765964	−	0.256725i
$503$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$503$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.23549	+	1.23549i	1.23549	+	1.23549i
$508$		0			0
$509$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$509$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$510$		0			0
$511$		0			0
$512$	0.673696	+	0.739009i	0.673696	+	0.739009i
$513$	−3.50484	−	0.488904i	−3.50484	−	0.488904i
$514$	−0.876298	+	0.163808i	−0.876298	+	0.163808i
$515$		0			0
$516$	2.86160	+	1.42491i	2.86160	+	1.42491i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.07168	+	1.56446i	1.07168	+	1.56446i	0.798017	+	0.602635i	$0.205882\pi$
$521$	1.07168	+	1.56446i	1.07168	+	1.56446i	0.273663	+	0.961826i	$0.411765\pi$
$522$		0			0
$523$	0.221468	+	1.18475i	0.221468	+	1.18475i	0.895163	+	0.445738i	$0.147059\pi$
$523$	0.221468	+	1.18475i	0.221468	+	1.18475i	−0.673696	+	0.739009i	$0.735294\pi$
$524$	−0.666468	−	0.456541i	−0.666468	−	0.456541i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	2.50689	−	2.08169i	2.50689	−	2.08169i
$529$	0.673696	−	0.739009i	0.673696	−	0.739009i
$530$		0			0
$531$	−0.364367	+	0.103671i	−0.364367	+	0.103671i
$532$		0			0
$533$		0			0
$534$	1.55597	+	3.12480i	1.55597	+	3.12480i
$535$		0			0
$536$	0.850217	+	0.473568i	0.850217	+	0.473568i
$537$	−0.204057	+	1.09161i	−0.204057	+	1.09161i
$538$		0			0
$539$	−1.48826	−	1.12388i	−1.48826	−	1.12388i
$540$		0			0
$541$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$541$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$542$		0			0
$543$		0			0
$544$	0.710182	+	0.132756i	0.710182	+	0.132756i
$545$		0			0
$546$		0			0
$547$	−0.891477			−0.891477			−0.445738	−	0.895163i	$-0.647059\pi$
$547$	−0.891477			−0.891477			−0.445738	+	0.895163i	$0.647059\pi$
$548$	0.526432	+	0.850217i	0.526432	+	0.850217i
$549$		0			0
$550$	1.85699	+	0.172075i	1.85699	+	0.172075i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.526432	−	0.149783i	−0.526432	−	0.149783i
$557$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$557$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.539001	−	2.29169i	0.539001	−	2.29169i
$562$	0.243964	+	0.489946i	0.243964	+	0.489946i
$563$	−1.44574	+	0.895163i	−1.44574	+	0.895163i	−0.445738	+	0.895163i	$0.647059\pi$
$563$	−1.44574	+	0.895163i	−1.44574	+	0.895163i	−1.00000			$1.00000\pi$
$564$		0			0
$565$		0			0
$566$	−1.17948	−	1.07524i	−1.17948	−	1.07524i
$567$		0			0
$568$		0			0
$569$	0.453510	+	1.92821i	0.453510	+	1.92821i	0.361242	+	0.932472i	$0.382353\pi$
$569$	0.453510	+	1.92821i	0.453510	+	1.92821i	0.0922684	+	0.995734i	$0.470588\pi$
$570$		0			0
$571$	1.78099	−	0.786384i	1.78099	−	0.786384i	0.798017	−	0.602635i	$-0.205882\pi$
$571$	1.78099	−	0.786384i	1.78099	−	0.786384i	0.982973	−	0.183750i	$-0.0588235\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.741580	+	1.91424i	0.741580	+	1.91424i
$577$	0.111609	+	0.252769i	0.111609	+	0.252769i	0.961826	−	0.273663i	$-0.0882353\pi$
$577$	0.111609	+	0.252769i	0.111609	+	0.252769i	−0.850217	+	0.526432i	$0.823529\pi$
$578$	−0.427904	+	0.213071i	−0.427904	+	0.213071i
$579$	0.0296549	−	0.641426i	0.0296549	−	0.641426i
$580$		0			0
$581$		0			0
$582$	2.83386	−	0.529740i	2.83386	−	0.529740i
$583$		0			0
$584$	−1.20614	−	1.32307i	−1.20614	−	1.32307i
$585$		0			0
$586$		0			0
$587$	−0.778076	+	1.25664i	−0.778076	+	1.25664i	0.183750	+	0.982973i	$0.441176\pi$
$587$	−0.778076	+	1.25664i	−0.778076	+	1.25664i	−0.961826	+	0.273663i	$0.911765\pi$
$588$	1.44147	−	0.987432i	1.44147	−	0.987432i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.24376	−	0.292529i	1.24376	−	0.292529i	0.445738	−	0.895163i	$-0.352941\pi$
$593$	1.24376	−	0.292529i	1.24376	−	0.292529i	0.798017	+	0.602635i	$0.205882\pi$
$594$	3.25292	−	1.09027i	3.25292	−	1.09027i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$599$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$600$	−0.705749	+	1.59837i	−0.705749	+	1.59837i
$601$	0.0899135	+	1.94480i	0.0899135	+	1.94480i	0.273663	+	0.961826i	$0.411765\pi$
$601$	0.0899135	+	1.94480i	0.0899135	+	1.94480i	−0.183750	+	0.982973i	$0.558824\pi$
$602$		0			0
$603$	1.27633	+	1.53703i	1.27633	+	1.53703i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$607$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$608$	1.79375	−	0.694903i	1.79375	−	0.694903i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.26101	+	0.780783i	1.26101	+	0.780783i
$613$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$613$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$614$	0.549996	−	0.802895i	0.549996	−	0.802895i
$615$		0			0
$616$		0			0
$617$	−1.34164	+	0.124322i	−1.34164	+	0.124322i	−0.739009	−	0.673696i	$-0.764706\pi$
$617$	−1.34164	+	0.124322i	−1.34164	+	0.124322i	−0.602635	+	0.798017i	$0.705882\pi$
$618$		0			0
$619$	0.156154	−	0.227957i	0.156154	−	0.227957i	−0.739009	−	0.673696i	$-0.764706\pi$
$619$	0.156154	−	0.227957i	0.156154	−	0.227957i	0.895163	+	0.445738i	$0.147059\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.932472	+	0.361242i	−0.932472	+	0.361242i
$626$	0.811985	−	1.07524i	0.811985	−	1.07524i
$627$	−1.99199	−	5.94330i	−1.99199	−	5.94330i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$631$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$632$		0			0
$633$	1.40548	−	3.18310i	1.40548	−	3.18310i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.576554	−	1.48826i	0.576554	−	1.48826i	−0.273663	−	0.961826i	$-0.588235\pi$
$641$	0.576554	−	1.48826i	0.576554	−	1.48826i	0.850217	−	0.526432i	$-0.176471\pi$
$642$	−2.96790	+	0.137215i	−2.96790	+	0.137215i
$643$	0.273663	+	1.96183i	0.273663	+	1.96183i	0.273663	+	0.961826i	$0.411765\pi$
$643$	0.273663	+	1.96183i	0.273663	+	1.96183i			1.00000i	$0.5\pi$
$644$		0			0
$645$		0			0
$646$	0.731639	−	1.18164i	0.731639	−	1.18164i
$647$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$647$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$648$			1.16139i			1.16139i
$649$	−0.231853	−	0.254330i	−0.231853	−	0.254330i
$650$		0			0
$651$		0			0
$652$	0.549996	−	0.987432i	0.549996	−	0.987432i
$653$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$653$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$654$		0			0
$655$		0			0
$656$	0.765964	+	1.73474i	0.765964	+	1.73474i
$657$	−1.32767	−	3.42711i	−1.32767	−	3.42711i
$658$		0			0
$659$	−0.618701	+	1.84595i	−0.618701	+	1.84595i	−0.0922684	+	0.995734i	$0.529412\pi$
$659$	−0.618701	+	1.84595i	−0.618701	+	1.84595i	−0.526432	+	0.850217i	$0.676471\pi$
$660$		0			0
$661$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$661$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$662$	1.29371	−	0.571231i	1.29371	−	0.571231i
$663$		0			0
$664$	−0.104837	−	0.445738i	−0.104837	−	0.445738i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.705749	+	0.393100i	0.705749	+	0.393100i	0.798017	−	0.602635i	$-0.205882\pi$
$673$	0.705749	+	0.393100i	0.705749	+	0.393100i	−0.0922684	+	0.995734i	$0.529412\pi$
$674$	0.328972	−	1.75984i	0.328972	−	1.75984i
$675$	−1.30080	+	1.30080i	−1.30080	+	1.30080i
$676$	−0.798017	−	0.602635i	−0.798017	−	0.602635i
$677$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$677$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$678$	0.584613	+	0.944182i	0.584613	+	0.944182i
$679$		0			0
$680$		0			0
$681$	0.786443	+	0.147012i	0.786443	+	0.147012i
$682$		0			0
$683$	1.78269	+	0.165190i	1.78269	+	0.165190i	0.932472	−	0.361242i	$-0.117647\pi$
$683$	1.78269	+	0.165190i	1.78269	+	0.165190i	0.850217	+	0.526432i	$0.176471\pi$
$684$	3.94900			3.94900
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.73474	−	0.581427i	−1.73474	−	0.581427i
$689$		0			0
$690$		0			0
$691$	−1.29371	−	0.571231i	−1.29371	−	0.571231i	−0.361242	−	0.932472i	$-0.617647\pi$
$691$	−1.29371	−	0.571231i	−1.29371	−	0.571231i	−0.932472	+	0.361242i	$0.882353\pi$
$692$		0			0
$693$		0			0
$694$	−0.961826	−	0.726337i	−0.961826	−	0.726337i
$695$		0			0
$696$		0			0
$697$	1.19692	+	0.666678i	1.19692	+	0.666678i
$698$		0			0
$699$	0.880272	+	1.76783i	0.880272	+	1.76783i
$700$		0			0
$701$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$701$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$702$		0			0
$703$		0			0
$704$	−1.25640	+	1.37821i	−1.25640	+	1.37821i
$705$		0			0
$706$	0.445738	+	1.89516i	0.445738	+	1.89516i
$707$		0			0
$708$	0.294958	−	0.130237i	0.294958	−	0.130237i
$709$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$709$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$710$		0			0
$711$		0			0
$712$	−1.12907	−	1.64823i	−1.12907	−	1.64823i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.0293534	−	0.634905i	0.0293534	−	0.634905i
$717$		0			0
$718$		0			0
$719$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$719$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$720$		0			0
$721$		0			0
$722$		−	2.70043i		−	2.70043i
$723$	−2.13052	+	1.94223i	−2.13052	+	1.94223i
$724$		0			0
$725$		0			0
$726$	3.06156	+	3.06156i	3.06156	+	3.06156i
$727$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$727$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$728$		0			0
$729$	0.299860	−	0.774027i	0.299860	−	0.774027i
$730$		0			0
$731$	−1.25332	+	0.420072i	−1.25332	+	0.420072i
$732$		0			0
$733$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$733$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.733109	+	1.66033i	−0.733109	+	1.66033i
$738$	0.179787	+	3.88874i	0.179787	+	3.88874i
$739$	−0.621731	−	1.11622i	−0.621731	−	1.11622i	−0.982973	−	0.183750i	$-0.941176\pi$
$739$	−0.621731	−	1.11622i	−0.621731	−	1.11622i	0.361242	−	0.932472i	$-0.382353\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$743$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.129868	−	0.930995i	0.129868	−	0.930995i
$748$	−0.124322	+	1.34164i	−0.124322	+	1.34164i
$749$		0			0
$750$		0			0
$751$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$751$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$752$		0			0
$753$	−1.40548	+	0.130237i	−1.40548	+	0.130237i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$757$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$758$	1.67148	+	1.03494i	1.67148	+	1.03494i
$759$		0			0
$760$		0			0
$761$	1.35698	−	1.02474i	1.35698	−	1.02474i	0.361242	−	0.932472i	$-0.382353\pi$
$761$	1.35698	−	1.02474i	1.35698	−	1.02474i	0.995734	−	0.0922684i	$-0.0294118\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.850217	−	1.52643i	−0.850217	−	1.52643i
$769$	−0.0710610	−	1.53703i	−0.0710610	−	1.53703i	−0.673696	−	0.739009i	$-0.735294\pi$
$769$	−0.0710610	−	1.53703i	−0.0710610	−	1.53703i	0.602635	−	0.798017i	$-0.294118\pi$
$770$		0			0
$771$	1.55597	+	0.0719366i	1.55597	+	0.0719366i
$772$	0.0339085	+	0.365931i	0.0339085	+	0.365931i
$773$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$773$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$774$	−2.88954	−	2.39944i	−2.88954	−	2.39944i
$775$		0			0
$776$	−1.56446	+	0.524354i	−1.56446	+	0.524354i
$777$		0			0
$778$		0			0
$779$	3.64397	−	0.168471i	3.64397	−	0.168471i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$785$		0			0
$786$	0.950920	+	1.04311i	0.950920	+	1.04311i
$787$	1.11943	+	0.156154i	1.11943	+	0.156154i	0.673696	−	0.739009i	$-0.264706\pi$
$787$	1.11943	+	0.156154i	1.11943	+	0.156154i	0.445738	+	0.895163i	$0.352941\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−3.42711	+	1.70650i	−3.42711	+	1.70650i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$797$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$798$		0			0
$799$		0			0
$800$	0.273663	−	0.961826i	0.273663	−	0.961826i
$801$	−0.939006	−	3.99241i	−0.939006	−	3.99241i
$802$	−0.212577	+	0.176521i	−0.212577	+	0.176521i
$803$	2.24938	−	2.46745i	2.24938	−	2.46745i
$804$	−1.25664	−	1.14558i	−1.25664	−	1.14558i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.352279	+	1.49780i	−0.352279	+	1.49780i	0.445738	+	0.895163i	$0.352941\pi$
$809$	−0.352279	+	1.49780i	−0.352279	+	1.49780i	−0.798017	+	0.602635i	$0.794118\pi$
$810$		0			0
$811$	0.365931	−	1.95756i	0.365931	−	1.95756i	0.0922684	−	0.995734i	$-0.470588\pi$
$811$	0.365931	−	1.95756i	0.365931	−	1.95756i	0.273663	−	0.961826i	$-0.411765\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.15479	−	0.509892i	−1.15479	−	0.509892i
$817$	−2.24841	+	2.70766i	−2.24841	+	2.70766i
$818$	−1.93247	−	0.361242i	−1.93247	−	0.361242i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	−0.555259	−	1.65667i	−0.555259	−	1.65667i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	−3.08960	−	1.03553i	−3.08960	−	1.03553i
$826$		0			0
$827$	−1.21146	+	1.45890i	−1.21146	+	1.45890i	−0.361242	+	0.932472i	$0.617647\pi$
$827$	−1.21146	+	1.45890i	−1.21146	+	1.45890i	−0.850217	+	0.526432i	$0.823529\pi$
$828$		0			0
$829$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$829$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.132756	+	0.710182i	−0.132756	+	0.710182i
$834$	0.835456	+	0.465346i	0.835456	+	0.465346i
$835$		0			0
$836$	1.59909	+	3.21140i	1.59909	+	3.21140i
$837$		0			0
$838$	−1.83319	−	0.710182i	−1.83319	−	0.710182i
$839$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$839$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$840$		0			0
$841$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$842$		0			0
$843$	−0.218948	−	0.930911i	−0.218948	−	0.930911i
$844$	−0.544991	+	1.91545i	−0.544991	+	1.91545i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.57597	+	2.30064i	1.57597	+	2.30064i
$850$	−0.260991	−	0.673696i	−0.260991	−	0.673696i
$851$		0			0
$852$		0			0
$853$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$853$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$854$		0			0
$855$		0			0
$856$	1.67148	−	0.312454i	1.67148	−	0.312454i
$857$	0.963876	+	0.134455i	0.963876	+	0.134455i	0.602635	−	0.798017i	$-0.294118\pi$
$857$	0.963876	+	0.134455i	0.963876	+	0.134455i	0.361242	+	0.932472i	$0.382353\pi$
$858$		0			0
$859$		−	0.891477i		−	0.891477i	−0.895163	−	0.445738i	$-0.852941\pi$
$859$		−	0.891477i		−	0.891477i	0.895163	−	0.445738i	$-0.147059\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$863$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$864$	−0.254154	−	1.82197i	−0.254154	−	1.82197i
$865$		0			0
$866$	0.132756	−	0.342683i	0.132756	−	0.342683i
$867$	0.813029	−	0.191223i	0.813029	−	0.191223i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−3.38360	−	0.156433i	−3.38360	−	0.156433i
$874$		0			0
$875$		0			0
$876$	1.52217	+	2.73281i	1.52217	+	2.73281i
$877$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$877$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.221468	−	0.293271i	0.221468	−	0.293271i	−0.673696	−	0.739009i	$-0.735294\pi$
$881$	0.221468	−	0.293271i	0.221468	−	0.293271i	0.895163	+	0.445738i	$0.147059\pi$
$882$	−1.91424	+	0.741580i	−1.91424	+	0.741580i
$883$	−0.436776	+	0.329838i	−0.436776	+	0.329838i	−0.798017	−	0.602635i	$-0.794118\pi$
$883$	−0.436776	+	0.329838i	−0.436776	+	0.329838i	0.361242	+	0.932472i	$0.382353\pi$
$884$		0			0
$885$		0			0
$886$	0.312454	+	0.193463i	0.312454	+	0.193463i
$887$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$887$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.15668	+	0.199846i	−2.15668	+	0.199846i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.56886	+	1.18475i	−1.56886	+	1.18475i
$899$		0			0
$900$	1.23713	−	1.63822i	1.23713	−	1.63822i
$901$		0			0
$902$	−3.08960	+	1.72089i	−3.08960	+	1.72089i
$903$		0			0
$904$	−0.406040	−	0.488975i	−0.406040	−	0.488975i
$905$		0			0
$906$		0			0
$907$	0.786384	−	1.78099i	0.786384	−	1.78099i	0.183750	−	0.982973i	$-0.441176\pi$
$907$	0.786384	−	1.78099i	0.786384	−	1.78099i	0.602635	−	0.798017i	$-0.294118\pi$
$908$	−0.457413	−	0.0211475i	−0.457413	−	0.0211475i
$909$		0			0
$910$		0			0
$911$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$911$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$912$	−3.32886	+	0.464356i	−3.32886	+	0.464356i
$913$	0.809691	−	0.271381i	0.809691	−	0.271381i
$914$	1.78099	−	0.418885i	1.78099	−	0.418885i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.939808	−	0.939808i	−0.939808	−	0.939808i
$919$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$919$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$920$		0			0
$921$	−1.25664	+	1.14558i	−1.25664	+	1.14558i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.20614	+	0.600584i	−1.20614	+	0.600584i	−0.932472	−	0.361242i	$-0.882353\pi$
$929$	−1.20614	+	0.600584i	−1.20614	+	0.600584i	−0.273663	+	0.961826i	$0.588235\pi$
$930$		0			0
$931$	0.694903	+	1.79375i	0.694903	+	1.79375i
$932$	−0.638758	−	0.932472i	−0.638758	−	0.932472i
$933$		0			0
$934$	0.163808	+	0.876298i	0.163808	+	0.876298i
$935$		0			0
$936$		0			0
$937$	−0.436776	+	1.53511i	−0.436776	+	1.53511i	0.361242	+	0.932472i	$0.382353\pi$
$937$	−0.436776	+	1.53511i	−0.436776	+	1.53511i	−0.798017	+	0.602635i	$0.794118\pi$
$938$		0			0
$939$	−1.81118	+	1.50399i	−1.81118	+	1.50399i
$940$		0			0
$941$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$941$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$942$		0			0
$943$		0			0
$944$	−0.156896	+	0.0971461i	−0.156896	+	0.0971461i
$945$		0			0
$946$	0.781197	−	3.32145i	0.781197	−	3.32145i
$947$	−1.11622	−	0.621731i	−1.11622	−	0.621731i	−0.183750	−	0.982973i	$-0.558824\pi$
$947$	−1.11622	−	0.621731i	−1.11622	−	0.621731i	−0.932472	+	0.361242i	$0.882353\pi$
$948$		0			0
$949$		0			0
$950$	−1.53511	−	1.15926i	−1.53511	−	1.15926i
$951$		0			0
$952$		0			0
$953$	0.0844967	+	0.0373089i	0.0844967	+	0.0373089i	0.445738	−	0.895163i	$-0.352941\pi$
$953$	0.0844967	+	0.0373089i	0.0844967	+	0.0373089i	−0.361242	+	0.932472i	$0.617647\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$962$		0			0
$963$	3.43132	+	0.641426i	3.43132	+	0.641426i
$964$	1.05409	−	1.26940i	1.05409	−	1.26940i
$965$		0			0
$966$		0			0
$967$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$967$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$968$	−1.97750	−	1.49334i	−1.97750	−	1.49334i
$969$	−1.71709	+	1.71709i	−1.71709	+	1.71709i
$970$		0			0
$971$	−0.241393	−	0.134455i	−0.241393	−	0.134455i	0.361242	−	0.932472i	$-0.382353\pi$
$971$	−0.241393	−	0.134455i	−0.241393	−	0.134455i	−0.602635	+	0.798017i	$0.705882\pi$
$972$	0.0434129	−	0.184580i	0.0434129	−	0.184580i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$977$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$978$	−1.33046	+	1.45944i	−1.33046	+	1.45944i
$979$	2.86647	−	2.38029i	2.86647	−	2.38029i
$980$		0			0
$981$		0			0
$982$	1.40756	−	0.621500i	1.40756	−	0.621500i
$983$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$983$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$984$	−0.608824	−	3.25692i	−0.608824	−	3.25692i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$991$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$992$		0			0
$993$	−2.42890	+	0.454041i	−2.42890	+	0.454041i
$994$		0			0
$995$		0			0
$996$			0.800065i			0.800065i
$997$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$997$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$998$	−0.634493	+	1.02474i	−0.634493	+	1.02474i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1096.1.z.a.299.1	yes	32
8.3	odd	2	CM	1096.1.z.a.299.1	yes	32
137.11	even	68	inner	1096.1.z.a.11.1	✓	32
1096.11	odd	68	inner	1096.1.z.a.11.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1096.1.z.a.11.1	✓	32	137.11	even	68	inner
1096.1.z.a.11.1	✓	32	1096.11	odd	68	inner
1096.1.z.a.299.1	yes	32	1.1	even	1	trivial
1096.1.z.a.299.1	yes	32	8.3	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1096 = 2^{3} \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1096.z (of order \(68\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.995734 + 0.0922684i) q^{2} +(-1.65667 - 0.555259i) q^{3} +(0.982973 + 0.183750i) q^{4} +(-1.59837 - 0.705749i) q^{6} +(0.961826 + 0.273663i) q^{8} +(1.63822 + 1.23713i) q^{9} +O(q^{10})\)	\(q+(0.995734 + 0.0922684i) q^{2} +(-1.65667 - 0.555259i) q^{3} +(0.982973 + 0.183750i) q^{4} +(-1.59837 - 0.705749i) q^{6} +(0.961826 + 0.273663i) q^{8} +(1.63822 + 1.23713i) q^{9} +(-0.342683 + 1.83319i) q^{11} +(-1.52643 - 0.850217i) q^{12} +(0.932472 + 0.361242i) q^{16} +(0.694903 - 0.197717i) q^{17} +(1.51709 + 1.38301i) q^{18} +(1.29596 - 1.42160i) q^{19} +(-0.510366 + 1.79375i) q^{22} +(-1.44147 - 0.987432i) q^{24} +(-0.183750 - 0.982973i) q^{25} +(-1.03963 - 1.51768i) q^{27} +(0.895163 + 0.445738i) q^{32} +(1.58561 - 2.84671i) q^{33} +(0.710182 - 0.132756i) q^{34} +(1.38301 + 1.51709i) q^{36} +(1.42160 - 1.29596i) q^{38} +(1.34090 + 1.34090i) q^{41} +(-1.82764 + 0.0844967i) q^{43} +(-0.673696 + 1.73901i) q^{44} +(-1.34421 - 1.11622i) q^{48} +(-0.445738 + 0.895163i) q^{49} +(-0.0922684 - 0.995734i) q^{50} +(-1.26101 - 0.0582999i) q^{51} +(-0.895163 - 1.60713i) q^{54} +(-2.93632 + 1.63552i) q^{57} +(-0.111208 + 0.147263i) q^{59} +(0.850217 + 0.526432i) q^{64} +(1.84151 - 2.68827i) q^{66} +(0.947359 + 0.222817i) q^{67} +(0.719401 - 0.0666624i) q^{68} +(1.23713 + 1.63822i) q^{72} +(-1.52217 - 0.942485i) q^{73} +(-0.241393 + 1.73049i) q^{75} +(1.53511 - 1.15926i) q^{76} +(0.317829 + 1.11705i) q^{81} +(1.21146 + 1.45890i) q^{82} +(-0.222817 - 0.400033i) q^{83} +(-1.82764 - 0.0844967i) q^{86} +(-0.831277 + 1.66943i) q^{88} +(-1.53703 - 1.27633i) q^{89} +(-1.23549 - 1.23549i) q^{96} +(-1.36124 + 0.932472i) q^{97} +(-0.526432 + 0.850217i) q^{98} +(-2.82928 + 2.57923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6}+O(q^{10}) \) 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6	\( 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6} - 32 q^{12} - 2 q^{16} - 2 q^{18} - 4 q^{22} + 2 q^{24} + 4 q^{33} - 2 q^{41} + 2 q^{43} - 2 q^{48} + 2 q^{49} + 2 q^{50} - 4 q^{59} + 2 q^{64} - 4 q^{66} + 2 q^{67} + 2 q^{72} - 2 q^{75} - 2 q^{81} + 2 q^{82} - 2 q^{83} + 2 q^{86} + 4 q^{88} + 2 q^{89} - 2 q^{96} - 32 q^{97} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6 - 32 * q^12 - 2 * q^16 - 2 * q^18 - 4 * q^22 + 2 * q^24 + 4 * q^33 - 2 * q^41 + 2 * q^43 - 2 * q^48 + 2 * q^49 + 2 * q^50 - 4 * q^59 + 2 * q^64 - 4 * q^66 + 2 * q^67 + 2 * q^72 - 2 * q^75 - 2 * q^81 + 2 * q^82 - 2 * q^83 + 2 * q^86 + 4 * q^88 + 2 * q^89 - 2 * q^96 - 32 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

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Database

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