LMFDB - Embedded newform 3288.1.cj.b.755.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3288,1,Mod(35,3288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3288, base_ring=CyclotomicField(136))

chi = DirichletCharacter(H, H._module([68, 68, 68, 117]))

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

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

chi := DirichletCharacter("3288.35");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3288 = 2^{3} \cdot 3 \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3288.cj (of order $136$, degree $64$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.64092576154$
Analytic rank:	$0$
Dimension:	$64$
Coefficient field:	$\Q(\zeta_{136})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{64} - x^{60} + x^{56} - x^{52} + x^{48} - x^{44} + x^{40} - x^{36} + x^{32} - x^{28} + x^{24} + \cdots + 1 $ x^64 - x^60 + x^56 - x^52 + x^48 - x^44 + x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{136}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{136} - \cdots)$

Embedding invariants

Embedding label			755.1
Root			$0.873622 + 0.486604i$ of defining polynomial
Character	$\chi$	$=$	3288.755
Dual form			3288.1.cj.b.2147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.873622 + 0.486604i) q^{2} +(-0.990410 - 0.138156i) q^{3} +(0.526432 - 0.850217i) q^{4} +(0.932472 - 0.361242i) q^{6} +(-0.0461835 + 0.998933i) q^{8} +(0.961826 + 0.273663i) q^{9} +O(q^{10})$	\(q+(-0.873622 + 0.486604i) q^{2} +(-0.990410 - 0.138156i) q^{3} +(0.526432 - 0.850217i) q^{4} +(0.932472 - 0.361242i) q^{6} +(-0.0461835 + 0.998933i) q^{8} +(0.961826 + 0.273663i) q^{9} +(0.409896 + 1.74277i) q^{11} +(-0.638847 + 0.769334i) q^{12} +(-0.445738 - 0.895163i) q^{16} +(-0.634905 + 0.0293534i) q^{17} +(-0.973438 + 0.228951i) q^{18} +(-1.97871 + 0.276018i) q^{19} +(-1.20614 - 1.32307i) q^{22} +(0.183750 - 0.982973i) q^{24} +(-0.973438 - 0.228951i) q^{25} +(-0.914794 - 0.403921i) q^{27} +(0.824997 + 0.565136i) q^{32} +(-0.165190 - 1.78269i) q^{33} +(0.540383 - 0.334591i) q^{34} +(0.739009 - 0.673696i) q^{36} +(1.59433 - 1.20398i) q^{38} +(0.157976 - 0.381387i) q^{41} +(0.330027 - 1.27074i) q^{43} +(1.69752 + 0.568950i) q^{44} +(0.317791 + 0.948161i) q^{48} +(0.183750 + 0.982973i) q^{49} +(0.961826 - 0.273663i) q^{50} +(0.632872 + 0.0586442i) q^{51} +(0.995734 - 0.0922684i) q^{54} +1.99787 q^{57} +(-0.694903 + 1.79375i) q^{59} +(-0.995734 - 0.0922684i) q^{64} +(1.01178 + 1.47701i) q^{66} +(-0.811852 - 0.251402i) q^{67} +(-0.309277 + 0.555259i) q^{68} +(-0.317791 + 0.948161i) q^{72} +(0.152242 - 1.64296i) q^{73} +(0.932472 + 0.361242i) q^{75} +(-0.806980 + 1.82764i) q^{76} +(0.850217 + 0.526432i) q^{81} +(0.0475735 + 0.410060i) q^{82} +(-1.60157 - 0.751834i) q^{83} +(0.330027 + 1.27074i) q^{86} +(-1.75984 + 0.328972i) q^{88} +(-1.20194 - 1.51743i) q^{89} +(-0.739009 - 0.673696i) q^{96} +(0.317791 - 1.94816i) q^{97} +(-0.638847 - 0.769334i) q^{98} +(-0.0826835 + 1.78842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{6}+O(q^{10}) $ 64 * q - 4 * q^6	$ 64 q - 4 q^{6} + 4 q^{16} - 4 q^{17} - 4 q^{19} - 4 q^{36} + 4 q^{41} - 4 q^{68} - 4 q^{75} + 4 q^{76} + 4 q^{81} - 4 q^{83} + 4 q^{96}+O(q^{100}) $ 64 * q - 4 * q^6 + 4 * q^16 - 4 * q^17 - 4 * q^19 - 4 * q^36 + 4 * q^41 - 4 * q^68 - 4 * q^75 + 4 * q^76 + 4 * q^81 - 4 * q^83 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3288\mathbb{Z}\right)^\times$.

$n$	$823$	$1097$	$1645$	$1921$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{127}{136}\right)$

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 $

$2$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$2$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$3$	−0.990410	−	0.138156i	−0.990410	−	0.138156i
$3$	−0.990410	−	0.138156i	−0.990410	−	0.138156i
$4$	0.526432	−	0.850217i	0.526432	−	0.850217i
$5$		0			0		0.115243	−	0.993337i	$-0.463235\pi$
$5$		0			0		−0.115243	+	0.993337i	$0.536765\pi$
$6$	0.932472	−	0.361242i	0.932472	−	0.361242i
$7$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$7$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$8$	−0.0461835	+	0.998933i	−0.0461835	+	0.998933i
$9$	0.961826	+	0.273663i	0.961826	+	0.273663i
$10$		0			0
$11$	0.409896	+	1.74277i	0.409896	+	1.74277i	0.638847	+	0.769334i	$0.279412\pi$
$11$	0.409896	+	1.74277i	0.409896	+	1.74277i	−0.228951	+	0.973438i	$0.573529\pi$
$12$	−0.638847	+	0.769334i	−0.638847	+	0.769334i
$13$		0			0		−0.466296	−	0.884629i	$-0.654412\pi$
$13$		0			0		0.466296	+	0.884629i	$0.345588\pi$
$14$		0			0
$15$		0			0
$16$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$17$	−0.634905	+	0.0293534i	−0.634905	+	0.0293534i	−0.361242	−	0.932472i	$-0.617647\pi$
$17$	−0.634905	+	0.0293534i	−0.634905	+	0.0293534i	−0.273663	+	0.961826i	$0.588235\pi$
$18$	−0.973438	+	0.228951i	−0.973438	+	0.228951i
$19$	−1.97871	+	0.276018i	−1.97871	+	0.276018i	−0.982973	+	0.183750i	$0.941176\pi$
$19$	−1.97871	+	0.276018i	−1.97871	+	0.276018i	−0.995734	+	0.0922684i	$0.970588\pi$
$20$		0			0
$21$		0			0
$22$	−1.20614	−	1.32307i	−1.20614	−	1.32307i
$23$		0			0		−0.754373	−	0.656446i	$-0.772059\pi$
$23$		0			0		0.754373	+	0.656446i	$0.227941\pi$
$24$	0.183750	−	0.982973i	0.183750	−	0.982973i
$25$	−0.973438	−	0.228951i	−0.973438	−	0.228951i
$26$		0			0
$27$	−0.914794	−	0.403921i	−0.914794	−	0.403921i
$28$		0			0
$29$		0			0		−0.0692444	−	0.997600i	$-0.522059\pi$
$29$		0			0		0.0692444	+	0.997600i	$0.477941\pi$
$30$		0			0
$31$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$31$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$32$	0.824997	+	0.565136i	0.824997	+	0.565136i
$33$	−0.165190	−	1.78269i	−0.165190	−	1.78269i
$34$	0.540383	−	0.334591i	0.540383	−	0.334591i
$35$		0			0
$36$	0.739009	−	0.673696i	0.739009	−	0.673696i
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$	1.59433	−	1.20398i	1.59433	−	1.20398i
$39$		0			0
$40$		0			0
$41$	0.157976	−	0.381387i	0.157976	−	0.381387i	−0.824997	−	0.565136i	$-0.808824\pi$
$41$	0.157976	−	0.381387i	0.157976	−	0.381387i	0.982973	+	0.183750i	$0.0588235\pi$
$42$		0			0
$43$	0.330027	−	1.27074i	0.330027	−	1.27074i	−0.565136	−	0.824997i	$-0.691176\pi$
$43$	0.330027	−	1.27074i	0.330027	−	1.27074i	0.895163	−	0.445738i	$-0.147059\pi$
$44$	1.69752	+	0.568950i	1.69752	+	0.568950i
$45$		0			0
$46$		0			0
$47$		0			0		−0.723251	−	0.690585i	$-0.757353\pi$
$47$		0			0		0.723251	+	0.690585i	$0.242647\pi$
$48$	0.317791	+	0.948161i	0.317791	+	0.948161i
$49$	0.183750	+	0.982973i	0.183750	+	0.982973i
$50$	0.961826	−	0.273663i	0.961826	−	0.273663i
$51$	0.632872	+	0.0586442i	0.632872	+	0.0586442i
$52$		0			0
$53$		0			0		0.862150	−	0.506653i	$-0.169118\pi$
$53$		0			0		−0.862150	+	0.506653i	$0.830882\pi$
$54$	0.995734	−	0.0922684i	0.995734	−	0.0922684i
$55$		0			0
$56$		0			0
$57$	1.99787			1.99787
$58$		0			0
$59$	−0.694903	+	1.79375i	−0.694903	+	1.79375i	−0.0922684	+	0.995734i	$0.529412\pi$
$59$	−0.694903	+	1.79375i	−0.694903	+	1.79375i	−0.602635	+	0.798017i	$0.705882\pi$
$60$		0			0
$61$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$61$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$62$		0			0
$63$		0			0
$64$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$65$		0			0
$66$	1.01178	+	1.47701i	1.01178	+	1.47701i
$67$	−0.811852	−	0.251402i	−0.811852	−	0.251402i	−0.138156	−	0.990410i	$-0.544118\pi$
$67$	−0.811852	−	0.251402i	−0.811852	−	0.251402i	−0.673696	+	0.739009i	$0.735294\pi$
$68$	−0.309277	+	0.555259i	−0.309277	+	0.555259i
$69$		0			0
$70$		0			0
$71$		0			0		−0.811724	−	0.584041i	$-0.801471\pi$
$71$		0			0		0.811724	+	0.584041i	$0.198529\pi$
$72$	−0.317791	+	0.948161i	−0.317791	+	0.948161i
$73$	0.152242	−	1.64296i	0.152242	−	1.64296i	−0.486604	−	0.873622i	$-0.661765\pi$
$73$	0.152242	−	1.64296i	0.152242	−	1.64296i	0.638847	−	0.769334i	$-0.279412\pi$
$74$		0			0
$75$	0.932472	+	0.361242i	0.932472	+	0.361242i
$76$	−0.806980	+	1.82764i	−0.806980	+	1.82764i
$77$		0			0
$78$		0			0
$79$		0			0		0.837831	−	0.545930i	$-0.183824\pi$
$79$		0			0		−0.837831	+	0.545930i	$0.816176\pi$
$80$		0			0
$81$	0.850217	+	0.526432i	0.850217	+	0.526432i
$82$	0.0475735	+	0.410060i	0.0475735	+	0.410060i
$83$	−1.60157	−	0.751834i	−1.60157	−	0.751834i	−0.602635	−	0.798017i	$-0.705882\pi$
$83$	−1.60157	−	0.751834i	−1.60157	−	0.751834i	−0.998933	+	0.0461835i	$0.985294\pi$
$84$		0			0
$85$		0			0
$86$	0.330027	+	1.27074i	0.330027	+	1.27074i
$87$		0			0
$88$	−1.75984	+	0.328972i	−1.75984	+	0.328972i
$89$	−1.20194	−	1.51743i	−1.20194	−	1.51743i	−0.798017	−	0.602635i	$-0.794118\pi$
$89$	−1.20194	−	1.51743i	−1.20194	−	1.51743i	−0.403921	−	0.914794i	$-0.632353\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$97$	0.317791	−	1.94816i	0.317791	−	1.94816i		−	1.00000i	$-0.5\pi$
$97$	0.317791	−	1.94816i	0.317791	−	1.94816i	0.317791	−	0.948161i	$-0.397059\pi$
$98$	−0.638847	−	0.769334i	−0.638847	−	0.769334i
$99$	−0.0826835	+	1.78842i	−0.0826835	+	1.78842i
$100$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$101$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$101$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$102$	−0.581427	+	0.256725i	−0.581427	+	0.256725i
$103$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$103$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.104288	+	0.152242i	0.104288	+	0.152242i	0.873622	−	0.486604i	$-0.161765\pi$
$107$	0.104288	+	0.152242i	0.104288	+	0.152242i	−0.769334	+	0.638847i	$0.779412\pi$
$108$	−0.824997	+	0.565136i	−0.824997	+	0.565136i
$109$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$109$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.07762	+	0.175785i	−1.07762	+	0.175785i	−0.673696	−	0.739009i	$-0.735294\pi$
$113$	−1.07762	+	0.175785i	−1.07762	+	0.175785i	−0.403921	+	0.914794i	$0.632353\pi$
$114$	−1.74538	+	0.972171i	−1.74538	+	0.972171i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.265765	−	1.90520i	−0.265765	−	1.90520i
$119$		0			0
$120$		0			0
$121$	−1.97408	+	0.982973i	−1.97408	+	0.982973i
$122$		0			0
$123$	−0.209152	+	0.355904i	−0.209152	+	0.355904i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$127$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$128$	0.914794	−	0.403921i	0.914794	−	0.403921i
$129$	−0.502422	+	1.21295i	−0.502422	+	1.21295i
$130$		0			0
$131$	0.0909104	+	0.104472i	0.0909104	+	0.104472i	0.798017	−	0.602635i	$-0.205882\pi$
$131$	0.0909104	+	0.104472i	0.0909104	+	0.104472i	−0.707107	+	0.707107i	$0.750000\pi$
$132$	−1.60263	−	0.798017i	−1.60263	−	0.798017i
$133$		0			0
$134$	0.831585	−	0.175421i	0.831585	−	0.175421i
$135$		0			0
$136$		−	0.635583i		−	0.635583i
$137$	−0.138156	+	0.990410i	−0.138156	+	0.990410i
$137$	−0.138156	+	0.990410i	−0.138156	+	0.990410i
$138$		0			0
$139$	0.655647	+	1.17711i	0.655647	+	1.17711i	0.973438	+	0.228951i	$0.0735294\pi$
$139$	0.655647	+	1.17711i	0.655647	+	1.17711i	−0.317791	+	0.948161i	$0.602941\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$145$		0			0
$146$	0.666468	+	1.50941i	0.666468	+	1.50941i
$147$	−0.0461835	−	0.998933i	−0.0461835	−	0.998933i
$148$		0			0
$149$		0			0		−0.940567	−	0.339607i	$-0.889706\pi$
$149$		0			0		0.940567	+	0.339607i	$0.110294\pi$
$150$	−0.990410	+	0.138156i	−0.990410	+	0.138156i
$151$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$151$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$152$	−0.184340	−	1.98934i	−0.184340	−	1.98934i
$153$	−0.618701	−	0.145517i	−0.618701	−	0.145517i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.620906	−	0.783885i	$-0.286765\pi$
$157$		0			0		−0.620906	+	0.783885i	$0.713235\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.998933	−	0.0461835i	−0.998933	−	0.0461835i
$163$	−0.886289	+	1.36017i	−0.886289	+	1.36017i	0.0461835	+	0.998933i	$0.485294\pi$
$163$	−0.886289	+	1.36017i	−0.886289	+	1.36017i	−0.932472	+	0.361242i	$0.882353\pi$
$164$	−0.241098	−	0.335088i	−0.241098	−	0.335088i
$165$		0			0
$166$	1.76501	−	0.122511i	1.76501	−	0.122511i
$167$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$167$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$168$		0			0
$169$	−0.565136	+	0.824997i	−0.565136	+	0.824997i
$170$		0			0
$171$	−1.97871	−	0.276018i	−1.97871	−	0.276018i
$172$	−0.906665	−	0.949551i	−0.906665	−	0.949551i
$173$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$173$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$174$		0			0
$175$		0			0
$176$	1.37736	−	1.14374i	1.37736	−	1.14374i
$177$	0.936057	−	1.68054i	0.936057	−	1.68054i
$178$	1.78843	+	0.740791i	1.78843	+	0.740791i
$179$	−1.67521	+	0.0387043i	−1.67521	+	0.0387043i	−0.850217	−	0.526432i	$-0.823529\pi$
$179$	−1.67521	+	0.0387043i	−1.67521	+	0.0387043i	−0.824997	+	0.565136i	$0.808824\pi$
$180$		0			0
$181$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$181$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.311401	−	1.09446i	−0.311401	−	1.09446i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.424943	−	0.905220i	$-0.360294\pi$
$191$		0			0		−0.424943	+	0.905220i	$0.639706\pi$
$192$	0.973438	+	0.228951i	0.973438	+	0.228951i
$193$	1.43876	+	1.31160i	1.43876	+	1.31160i	0.873622	+	0.486604i	$0.161765\pi$
$193$	1.43876	+	1.31160i	1.43876	+	1.31160i	0.565136	+	0.824997i	$0.308824\pi$
$194$	0.670354	+	1.85660i	0.670354	+	1.85660i
$195$		0			0
$196$	0.932472	+	0.361242i	0.932472	+	0.361242i
$197$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$197$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$198$	−0.798017	−	1.60263i	−0.798017	−	1.60263i
$199$		0			0		0.0230979	−	0.999733i	$-0.492647\pi$
$199$		0			0		−0.0230979	+	0.999733i	$0.507353\pi$
$200$	0.273663	−	0.961826i	0.273663	−	0.961826i
$201$	0.769334	+	0.361153i	0.769334	+	0.361153i
$202$		0			0
$203$		0			0
$204$	0.383024	−	0.507206i	0.383024	−	0.507206i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.29210	−	3.33530i	−1.29210	−	3.33530i
$210$		0			0
$211$	0.266331	−	0.936057i	0.266331	−	0.936057i	−0.707107	−	0.707107i	$-0.750000\pi$
$211$	0.266331	−	0.936057i	0.266331	−	0.936057i	0.973438	−	0.228951i	$-0.0735294\pi$
$212$		0			0
$213$		0			0
$214$	−0.165190	−	0.0822551i	−0.165190	−	0.0822551i
$215$		0			0
$216$	0.445738	−	0.895163i	0.445738	−	0.895163i
$217$		0			0
$218$		0			0
$219$	−0.377767	+	1.60617i	−0.377767	+	1.60617i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.967890	−	0.251374i	$-0.0808824\pi$
$223$		0			0		−0.967890	+	0.251374i	$0.919118\pi$
$224$		0			0
$225$	−0.873622	−	0.486604i	−0.873622	−	0.486604i
$226$	0.855892	−	0.677943i	0.855892	−	0.677943i
$227$	−0.644034	+	0.674498i	−0.644034	+	0.674498i	−0.961826	−	0.273663i	$-0.911765\pi$
$227$	−0.644034	+	0.674498i	−0.644034	+	0.674498i	0.317791	+	0.948161i	$0.397059\pi$
$228$	1.05174	−	1.69862i	1.05174	−	1.69862i
$229$		0			0		−0.295806	−	0.955248i	$-0.595588\pi$
$229$		0			0		0.295806	+	0.955248i	$0.404412\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.07917	−	0.447006i	−1.07917	−	0.447006i	−0.228951	−	0.973438i	$-0.573529\pi$
$233$	−1.07917	−	0.447006i	−1.07917	−	0.447006i	−0.850217	+	0.526432i	$0.823529\pi$
$234$		0			0
$235$		0			0
$236$	1.15926	+	1.53511i	1.15926	+	1.53511i
$237$		0			0
$238$		0			0
$239$		0			0		−0.690585	−	0.723251i	$-0.742647\pi$
$239$		0			0		0.690585	+	0.723251i	$0.257353\pi$
$240$		0			0
$241$	−0.136828	−	0.291473i	−0.136828	−	0.291473i	0.824997	−	0.565136i	$-0.191176\pi$
$241$	−0.136828	−	0.291473i	−0.136828	−	0.291473i	−0.961826	+	0.273663i	$0.911765\pi$
$242$	1.24628	−	1.81934i	1.24628	−	1.81934i
$243$	−0.769334	−	0.638847i	−0.769334	−	0.638847i
$244$		0			0
$245$		0			0
$246$	0.00953505	−	0.412700i	0.00953505	−	0.412700i
$247$		0			0
$248$		0			0
$249$	1.48234	+	0.965891i	1.48234	+	0.965891i
$250$		0			0
$251$	1.30974	−	1.50512i	1.30974	−	1.50512i	0.602635	−	0.798017i	$-0.294118\pi$
$251$	1.30974	−	1.50512i	1.30974	−	1.50512i	0.707107	−	0.707107i	$-0.250000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$257$	0.0169724	+	0.367107i	0.0169724	+	0.367107i	0.990410	+	0.138156i	$0.0441176\pi$
$257$	0.0169724	+	0.367107i	0.0169724	+	0.367107i	−0.973438	+	0.228951i	$0.926471\pi$
$258$	−0.151302	−	1.30415i	−0.151302	−	1.30415i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.130258	−	0.0470318i	−0.130258	−	0.0470318i
$263$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$263$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$264$	1.78842	−	0.0826835i	1.78842	−	0.0826835i
$265$		0			0
$266$		0			0
$267$	0.980770	+	1.66893i	0.980770	+	1.66893i
$268$	−0.641131	+	0.557905i	−0.641131	+	0.557905i
$269$		0			0		−0.993337	−	0.115243i	$-0.963235\pi$
$269$		0			0		0.993337	+	0.115243i	$0.0367647\pi$
$270$		0			0
$271$		0			0		−0.206405	−	0.978467i	$-0.566176\pi$
$271$		0			0		0.206405	+	0.978467i	$0.433824\pi$
$272$	0.309277	+	0.555259i	0.309277	+	0.555259i
$273$		0			0
$274$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$275$		−	1.79033i		−	1.79033i
$276$		0			0
$277$		0			0		0.978467	−	0.206405i	$-0.0661765\pi$
$277$		0			0		−0.978467	+	0.206405i	$0.933824\pi$
$278$	−1.14558	−	0.709310i	−1.14558	−	0.709310i
$279$		0			0
$280$		0			0
$281$	−0.944227	+	1.13709i	−0.944227	+	1.13709i	0.0461835	+	0.998933i	$0.485294\pi$
$281$	−0.944227	+	1.13709i	−0.944227	+	1.13709i	−0.990410	+	0.138156i	$0.955882\pi$
$282$		0			0
$283$	−0.739009	+	0.326304i	−0.739009	+	0.326304i	−0.739009	−	0.673696i	$-0.764706\pi$
$283$	−0.739009	+	0.326304i	−0.739009	+	0.326304i			1.00000i	$0.5\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.638847	+	0.769334i	0.638847	+	0.769334i
$289$	−0.593492	+	0.0549951i	−0.593492	+	0.0549951i
$290$		0			0
$291$	−0.583895	+	1.88557i	−0.583895	+	1.88557i
$292$	−1.31672	−	0.994344i	−1.31672	−	0.994344i
$293$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$293$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$294$	0.526432	+	0.850217i	0.526432	+	0.850217i
$295$		0			0
$296$		0			0
$297$	0.328972	−	1.75984i	0.328972	−	1.75984i
$298$		0			0
$299$		0			0
$300$	0.798017	−	0.602635i	0.798017	−	0.602635i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.12907	+	1.64823i	1.12907	+	1.64823i
$305$		0			0
$306$	0.611320	−	0.173936i	0.611320	−	0.173936i
$307$	−1.63885	+	0.769334i	−1.63885	+	0.769334i	−0.638847	+	0.769334i	$0.720588\pi$
$307$	−1.63885	+	0.769334i	−1.63885	+	0.769334i	−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$311$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$312$		0			0
$313$	1.26544	+	1.52391i	1.26544	+	1.52391i	0.739009	+	0.673696i	$0.235294\pi$
$313$	1.26544	+	1.52391i	1.26544	+	1.52391i	0.526432	+	0.850217i	$0.323529\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.967890	−	0.251374i	$-0.919118\pi$
$317$		0			0		0.967890	+	0.251374i	$0.0808824\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.0822551	−	0.165190i	−0.0822551	−	0.165190i
$322$		0			0
$323$	1.24819	−	0.233327i	1.24819	−	0.233327i
$324$	0.895163	−	0.445738i	0.895163	−	0.445738i
$325$		0			0
$326$	0.112415	−	1.61955i	0.112415	−	1.61955i
$327$		0			0
$328$	0.373684	+	0.175421i	0.373684	+	0.175421i
$329$		0			0
$330$		0			0
$331$	0.719879	−	0.259924i	0.719879	−	0.259924i	0.0461835	−	0.998933i	$-0.485294\pi$
$331$	0.719879	−	0.259924i	0.719879	−	0.259924i	0.673696	+	0.739009i	$0.264706\pi$
$332$	−1.48234	+	0.965891i	−1.48234	+	0.965891i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.08713	−	0.309314i	−1.08713	−	0.309314i	−0.317791	−	0.948161i	$-0.602941\pi$
$337$	−1.08713	−	0.309314i	−1.08713	−	0.309314i	−0.769334	+	0.638847i	$0.779412\pi$
$338$	0.0922684	−	0.995734i	0.0922684	−	0.995734i
$339$	1.09157	−	0.0252197i	1.09157	−	0.0252197i
$340$		0			0
$341$		0			0
$342$	1.86295	−	0.721712i	1.86295	−	0.721712i
$343$		0			0
$344$	1.25414	+	0.388362i	1.25414	+	0.388362i
$345$		0			0
$346$		0			0
$347$	−1.85699	−	0.172075i	−1.85699	−	0.172075i	−0.895163	−	0.445738i	$-0.852941\pi$
$347$	−1.85699	−	0.172075i	−1.85699	−	0.172075i	−0.961826	+	0.273663i	$0.911765\pi$
$348$		0			0
$349$		0			0		−0.999733	−	0.0230979i	$-0.992647\pi$
$349$		0			0		0.999733	+	0.0230979i	$0.00735294\pi$
$350$		0			0
$351$		0			0
$352$	−0.646741	+	1.66943i	−0.646741	+	1.66943i
$353$	1.04300	+	1.60067i	1.04300	+	1.60067i	0.769334	+	0.638847i	$0.220588\pi$
$353$	1.04300	+	1.60067i	1.04300	+	1.60067i	0.273663	+	0.961826i	$0.411765\pi$
$354$			1.92365i			1.92365i
$355$		0			0
$356$	−1.92288	+	0.223085i	−1.92288	+	0.223085i
$357$		0			0
$358$	1.44467	−	0.848980i	1.44467	−	0.848980i
$359$		0			0		−0.997600	−	0.0692444i	$-0.977941\pi$
$359$		0			0		0.997600	+	0.0692444i	$0.0220588\pi$
$360$		0			0
$361$	2.87727	−	0.818654i	2.87727	−	0.818654i
$362$		0			0
$363$	2.09095	−	0.700816i	2.09095	−	0.700816i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$367$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$368$		0			0
$369$	0.256316	−	0.323596i	0.256316	−	0.323596i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$373$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$374$	0.804617	+	0.804617i	0.804617	+	0.804617i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.868610	+	0.595012i	0.868610	+	0.595012i	0.914794	−	0.403921i	$-0.132353\pi$
$379$	0.868610	+	0.595012i	0.868610	+	0.595012i	−0.0461835	+	0.998933i	$0.514706\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$383$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$384$	−0.961826	+	0.273663i	−0.961826	+	0.273663i
$385$		0			0
$386$	−1.89516	−	0.445738i	−1.89516	−	0.445738i
$387$	0.665182	−	1.13191i	0.665182	−	1.13191i
$388$	−1.48906	−	1.29577i	−1.48906	−	1.29577i
$389$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$389$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$390$		0			0
$391$		0			0
$392$	−0.990410	+	0.138156i	−0.990410	+	0.138156i
$393$	−0.0756052	−	0.116030i	−0.0756052	−	0.116030i
$394$		0			0
$395$		0			0
$396$	1.47701	+	1.01178i	1.47701	+	1.01178i
$397$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$397$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$398$		0			0
$399$		0			0
$400$	0.228951	+	0.973438i	0.228951	+	0.973438i
$401$	0.765163	+	1.84727i	0.765163	+	1.84727i	0.403921	+	0.914794i	$0.367647\pi$
$401$	0.765163	+	1.84727i	0.765163	+	1.84727i	0.361242	+	0.932472i	$0.382353\pi$
$402$	−0.847846	+	0.0588498i	−0.847846	+	0.0588498i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.0878098	+	0.629488i	−0.0878098	+	0.629488i
$409$	−1.48554	+	0.827439i	−1.48554	+	0.827439i	−0.998933	−	0.0461835i	$-0.985294\pi$
$409$	−1.48554	+	0.827439i	−1.48554	+	0.827439i	−0.486604	+	0.873622i	$0.661765\pi$
$410$		0			0
$411$	0.273663	−	0.961826i	0.273663	−	0.961826i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.486734	−	1.25640i	−0.486734	−	1.25640i
$418$	2.75178	+	2.28505i	2.75178	+	2.28505i
$419$	0.0785319	−	1.69862i	0.0785319	−	1.69862i	−0.486604	−	0.873622i	$-0.661765\pi$
$419$	0.0785319	−	1.69862i	0.0785319	−	1.69862i	0.565136	−	0.824997i	$-0.308824\pi$
$420$		0			0
$421$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$421$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$422$	0.222817	+	0.947359i	0.222817	+	0.947359i
$423$		0			0
$424$		0			0
$425$	0.624761	+	0.116788i	0.624761	+	0.116788i
$426$		0			0
$427$		0			0
$428$	0.184340	−	0.00852254i	0.184340	−	0.00852254i
$429$		0			0
$430$		0			0
$431$		0			0		−0.783885	−	0.620906i	$-0.786765\pi$
$431$		0			0		0.783885	+	0.620906i	$0.213235\pi$
$432$	0.0461835	+	0.998933i	0.0461835	+	0.998933i
$433$	−0.308486	−	0.338393i	−0.308486	−	0.338393i	0.565136	−	0.824997i	$-0.308824\pi$
$433$	−0.308486	−	0.338393i	−0.308486	−	0.338393i	−0.873622	+	0.486604i	$0.838235\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.451543	−	1.58701i	−0.451543	−	1.58701i
$439$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$439$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$440$		0			0
$441$	−0.0922684	+	0.995734i	−0.0922684	+	0.995734i
$442$		0			0
$443$	0.377767	+	0.258777i	0.377767	+	0.258777i	0.739009	−	0.673696i	$-0.235294\pi$
$443$	0.377767	+	0.258777i	0.377767	+	0.258777i	−0.361242	+	0.932472i	$0.617647\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.840204	+	0.634493i	−0.840204	+	0.634493i	−0.932472	−	0.361242i	$-0.882353\pi$
$449$	−0.840204	+	0.634493i	−0.840204	+	0.634493i	0.0922684	+	0.995734i	$0.470588\pi$
$450$	1.00000			1.00000
$451$	0.729424	+	0.118986i	0.729424	+	0.118986i
$452$	−0.417837	+	1.00875i	−0.417837	+	1.00875i
$453$		0			0
$454$	0.234429	−	0.902646i	0.234429	−	0.902646i
$455$		0			0
$456$	−0.0922684	+	1.99573i	−0.0922684	+	1.99573i
$457$	1.47626	+	0.311413i	1.47626	+	0.311413i	0.873622	−	0.486604i	$-0.161765\pi$
$457$	1.47626	+	0.311413i	1.47626	+	0.311413i	0.602635	+	0.798017i	$0.294118\pi$
$458$		0			0
$459$	0.592663	+	0.229599i	0.592663	+	0.229599i
$460$		0			0
$461$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$461$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$462$		0			0
$463$		0			0		−0.997600	−	0.0692444i	$-0.977941\pi$
$463$		0			0		0.997600	+	0.0692444i	$0.0220588\pi$
$464$		0			0
$465$		0			0
$466$	1.16030	−	0.134613i	1.16030	−	0.134613i
$467$	−1.32445	+	1.45285i	−1.32445	+	1.45285i	−0.526432	+	0.850217i	$0.676471\pi$
$467$	−1.32445	+	1.45285i	−1.32445	+	1.45285i	−0.798017	+	0.602635i	$0.794118\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.75974	−	0.777003i	−1.75974	−	0.777003i
$473$	2.34988	+	0.0542917i	2.34988	+	0.0542917i
$474$		0			0
$475$	1.98934	+	0.184340i	1.98934	+	0.184340i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.486604	−	0.873622i	$-0.338235\pi$
$479$		0			0		−0.486604	+	0.873622i	$0.661765\pi$
$480$		0			0
$481$		0			0
$482$	0.261368	+	0.188057i	0.261368	+	0.188057i
$483$		0			0
$484$	−0.203477	+	2.19586i	−0.203477	+	2.19586i
$485$		0			0
$486$	0.982973	+	0.183750i	0.982973	+	0.183750i
$487$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$487$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$488$		0			0
$489$	1.06571	−	1.22468i	1.06571	−	1.22468i
$490$		0			0
$491$	1.47459	−	0.532426i	1.47459	−	0.532426i	0.526432	−	0.850217i	$-0.323529\pi$
$491$	1.47459	−	0.532426i	1.47459	−	0.532426i	0.948161	+	0.317791i	$0.102941\pi$
$492$	0.192492	+	0.365184i	0.192492	+	0.365184i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.76501	−	0.122511i	−1.76501	−	0.122511i
$499$	1.83319	−	0.342683i	1.83319	−	0.342683i	0.850217	−	0.526432i	$-0.176471\pi$
$499$	1.83319	−	0.342683i	1.83319	−	0.342683i	0.982973	+	0.183750i	$0.0588235\pi$
$500$		0			0
$501$		0			0
$502$	−0.411819	+	1.95224i	−0.411819	+	1.95224i
$503$		0			0		0.955248	−	0.295806i	$-0.0955882\pi$
$503$		0			0		−0.955248	+	0.295806i	$0.904412\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.673696	−	0.739009i	0.673696	−	0.739009i
$508$		0			0
$509$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$509$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$510$		0			0
$511$		0			0
$512$	0.138156	−	0.990410i	0.138156	−	0.990410i
$513$	1.92160	+	0.546742i	1.92160	+	0.546742i
$514$	−0.193463	−	0.312454i	−0.193463	−	0.312454i
$515$		0			0
$516$	0.766784	+	1.06571i	0.766784	+	1.06571i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.58849	+	1.14293i	−1.58849	+	1.14293i	−0.673696	+	0.739009i	$0.735294\pi$
$521$	−1.58849	+	1.14293i	−1.58849	+	1.14293i	−0.914794	+	0.403921i	$0.867647\pi$
$522$		0			0
$523$	−0.165413	+	0.703293i	−0.165413	+	0.703293i	0.824997	+	0.565136i	$0.191176\pi$
$523$	−0.165413	+	0.703293i	−0.165413	+	0.703293i	−0.990410	+	0.138156i	$0.955882\pi$
$524$	0.136682	−	0.0222961i	0.136682	−	0.0222961i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.52217	+	0.942485i	−1.52217	+	0.942485i
$529$	0.138156	+	0.990410i	0.138156	+	0.990410i
$530$		0			0
$531$	−1.15926	+	1.53511i	−1.15926	+	1.53511i
$532$		0			0
$533$		0			0
$534$	−1.66893	−	0.980770i	−1.66893	−	0.980770i
$535$		0			0
$536$	0.288627	−	0.799375i	0.288627	−	0.799375i
$537$	1.66450	+	0.193108i	1.66450	+	0.193108i
$538$		0			0
$539$	−1.63778	+	0.723151i	−1.63778	+	0.723151i
$540$		0			0
$541$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$541$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$542$		0			0
$543$		0			0
$544$	−0.540383	−	0.334591i	−0.540383	−	0.334591i
$545$		0			0
$546$		0			0
$547$		−	1.96595i		−	1.96595i	−0.183750	−	0.982973i	$-0.558824\pi$
$547$		−	1.96595i		−	1.96595i	0.183750	−	0.982973i	$-0.441176\pi$
$548$	0.769334	+	0.638847i	0.769334	+	0.638847i
$549$		0			0
$550$	0.871181	+	1.56407i	0.871181	+	1.56407i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.34595	+	0.0622272i	1.34595	+	0.0622272i
$557$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$557$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.157208	+	1.12699i	0.157208	+	1.12699i
$562$	0.271585	−	1.45285i	0.271585	−	1.45285i
$563$	−0.183750	−	1.98297i	−0.183750	−	1.98297i	−0.183750	−	0.982973i	$-0.558824\pi$
$563$	−0.183750	−	1.98297i	−0.183750	−	1.98297i		−	1.00000i	$-0.5\pi$
$564$		0			0
$565$		0			0
$566$	0.486834	−	0.644672i	0.486834	−	0.644672i
$567$		0			0
$568$		0			0
$569$	0.674498	−	1.27962i	0.674498	−	1.27962i	−0.273663	−	0.961826i	$-0.588235\pi$
$569$	0.674498	−	1.27962i	0.674498	−	1.27962i	0.948161	−	0.317791i	$-0.102941\pi$
$570$		0			0
$571$	0.388362	−	0.446296i	0.388362	−	0.446296i	−0.526432	−	0.850217i	$-0.676471\pi$
$571$	0.388362	−	0.446296i	0.388362	−	0.446296i	0.914794	+	0.403921i	$0.132353\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.932472	−	0.361242i	−0.932472	−	0.361242i
$577$	0.0460849	−	0.00319880i	0.0460849	−	0.00319880i	−0.0461835	−	0.998933i	$-0.514706\pi$
$577$	0.0460849	−	0.00319880i	0.0460849	−	0.00319880i	0.0922684	+	0.995734i	$0.470588\pi$
$578$	0.491727	−	0.336841i	0.491727	−	0.336841i
$579$	−1.24376	−	1.49780i	−1.24376	−	1.49780i
$580$		0			0
$581$		0			0
$582$	−0.407425	−	1.93141i	−0.407425	−	1.93141i
$583$		0			0
$584$	1.63417	+	0.227957i	1.63417	+	0.227957i
$585$		0			0
$586$		0			0
$587$	1.22788	−	1.01962i	1.22788	−	1.01962i	0.228951	−	0.973438i	$-0.426471\pi$
$587$	1.22788	−	1.01962i	1.22788	−	1.01962i	0.998933	−	0.0461835i	$-0.0147059\pi$
$588$	−0.873622	−	0.486604i	−0.873622	−	0.486604i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.0681792	−	0.220171i	−0.0681792	−	0.220171i	0.914794	−	0.403921i	$-0.132353\pi$
$593$	−0.0681792	−	0.220171i	−0.0681792	−	0.220171i	−0.982973	+	0.183750i	$0.941176\pi$
$594$	0.568950	+	1.69752i	0.568950	+	1.69752i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.967890	−	0.251374i	$-0.0808824\pi$
$599$		0			0		−0.967890	+	0.251374i	$0.919118\pi$
$600$	−0.403921	+	0.914794i	−0.403921	+	0.914794i
$601$	−0.299742	−	0.510058i	−0.299742	−	0.510058i	0.673696	−	0.739009i	$-0.264706\pi$
$601$	−0.299742	−	0.510058i	−0.299742	−	0.510058i	−0.973438	+	0.228951i	$0.926471\pi$
$602$		0			0
$603$	−0.712061	−	0.463978i	−0.712061	−	0.463978i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$607$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$608$	−1.78842	−	0.890525i	−1.78842	−	0.890525i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.449425	+	0.449425i	−0.449425	+	0.449425i
$613$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$613$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$614$	1.05737	−	1.46958i	1.05737	−	1.46958i
$615$		0			0
$616$		0			0
$617$	1.73049	+	0.963876i	1.73049	+	0.963876i	0.932472	+	0.361242i	$0.117647\pi$
$617$	1.73049	+	0.963876i	1.73049	+	0.963876i	0.798017	+	0.602635i	$0.205882\pi$
$618$		0			0
$619$	−0.0269802	+	0.0374982i	−0.0269802	+	0.0374982i	−0.824997	−	0.565136i	$-0.808824\pi$
$619$	−0.0269802	+	0.0374982i	−0.0269802	+	0.0374982i	0.798017	+	0.602635i	$0.205882\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.895163	+	0.445738i	0.895163	+	0.445738i
$626$	−1.84706	−	0.715555i	−1.84706	−	0.715555i
$627$	0.818918	+	3.48182i	0.818918	+	3.48182i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.424943	−	0.905220i	$-0.360294\pi$
$631$		0			0		−0.424943	+	0.905220i	$0.639706\pi$
$632$		0			0
$633$	−0.393100	+	0.890286i	−0.393100	+	0.890286i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.256725	−	0.765964i	0.256725	−	0.765964i	−0.739009	−	0.673696i	$-0.764706\pi$
$641$	0.256725	−	0.765964i	0.256725	−	0.765964i	0.995734	−	0.0922684i	$-0.0294118\pi$
$642$	0.152242	+	0.104288i	0.152242	+	0.104288i
$643$	1.38080	−	0.0319021i	1.38080	−	0.0319021i	0.673696	−	0.739009i	$-0.264706\pi$
$643$	1.38080	−	0.0319021i	1.38080	−	0.0319021i	0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$	−0.976907	+	0.811214i	−0.976907	+	0.811214i
$647$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$647$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$648$	−0.565136	+	0.824997i	−0.565136	+	0.824997i
$649$	−3.41094	−	0.475806i	−3.41094	−	0.475806i
$650$		0			0
$651$		0			0
$652$	0.689873	+	1.46958i	0.689873	+	1.46958i
$653$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$653$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$654$		0			0
$655$		0			0
$656$	−0.411819	+	0.0285848i	−0.411819	+	0.0285848i
$657$	0.596047	−	1.53857i	0.596047	−	1.53857i
$658$		0			0
$659$	0.322979	−	0.495671i	0.322979	−	0.495671i	−0.638847	−	0.769334i	$-0.720588\pi$
$659$	0.322979	−	0.495671i	0.322979	−	0.495671i	0.961826	+	0.273663i	$0.0882353\pi$
$660$		0			0
$661$		0			0		−0.160996	−	0.986955i	$-0.551471\pi$
$661$		0			0		0.160996	+	0.986955i	$0.448529\pi$
$662$	−0.502422	+	0.577372i	−0.502422	+	0.577372i
$663$		0			0
$664$	0.824997	−	1.56514i	0.824997	−	1.56514i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.87662	−	0.677584i	−1.87662	−	0.677584i	−0.961826	−	0.273663i	$-0.911765\pi$
$673$	−1.87662	−	0.677584i	−1.87662	−	0.677584i	−0.914794	−	0.403921i	$-0.867647\pi$
$674$	1.10025	−	0.258777i	1.10025	−	0.258777i
$675$	0.798017	+	0.602635i	0.798017	+	0.602635i
$676$	0.403921	+	0.914794i	0.403921	+	0.914794i
$677$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$677$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$678$	−0.941347	+	0.553195i	−0.941347	+	0.553195i
$679$		0			0
$680$		0			0
$681$	0.731044	−	0.579052i	0.731044	−	0.579052i
$682$		0			0
$683$	0.549996	+	0.987432i	0.549996	+	0.987432i	0.995734	+	0.0922684i	$0.0294118\pi$
$683$	0.549996	+	0.987432i	0.549996	+	0.987432i	−0.445738	+	0.895163i	$0.647059\pi$
$684$	−1.27633	+	1.53703i	−1.27633	+	1.53703i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.28462	+	0.270988i	−1.28462	+	0.270988i
$689$		0			0
$690$		0			0
$691$	1.21295	+	1.39390i	1.21295	+	1.39390i	0.895163	+	0.445738i	$0.147059\pi$
$691$	1.21295	+	1.39390i	1.21295	+	1.39390i	0.317791	+	0.948161i	$0.397059\pi$
$692$		0			0
$693$		0			0
$694$	1.70604	−	0.753290i	1.70604	−	0.753290i
$695$		0			0
$696$		0			0
$697$	−0.0891045	+	0.246781i	−0.0891045	+	0.246781i
$698$		0			0
$699$	1.00706	+	0.591813i	1.00706	+	0.591813i
$700$		0			0
$701$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$701$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$702$		0			0
$703$		0			0
$704$	−0.247345	−	1.77316i	−0.247345	−	1.77316i
$705$		0			0
$706$	−1.69008	−	0.890856i	−1.69008	−	0.890856i
$707$		0			0
$708$	−0.936057	−	1.68054i	−0.936057	−	1.68054i
$709$		0			0		0.986955	−	0.160996i	$-0.0514706\pi$
$709$		0			0		−0.986955	+	0.160996i	$0.948529\pi$
$710$		0			0
$711$		0			0
$712$	1.57132	−	1.13058i	1.57132	−	1.13058i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.848980	+	1.44467i	−0.848980	+	1.44467i
$717$		0			0
$718$		0			0
$719$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$719$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$720$		0			0
$721$		0			0
$722$	−2.11529	+	2.11529i	−2.11529	+	2.11529i
$723$	0.0952471	+	0.307582i	0.0952471	+	0.307582i
$724$		0			0
$725$		0			0
$726$	−1.48568	+	1.62971i	−1.48568	+	1.62971i
$727$		0			0		−0.0230979	−	0.999733i	$-0.507353\pi$
$727$		0			0		0.0230979	+	0.999733i	$0.492647\pi$
$728$		0			0
$729$	0.673696	+	0.739009i	0.673696	+	0.739009i
$730$		0			0
$731$	−0.172235	+	0.816484i	−0.172235	+	0.816484i
$732$		0			0
$733$		0			0		−0.620906	−	0.783885i	$-0.713235\pi$
$733$		0			0		0.620906	+	0.783885i	$0.286765\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.105360	−	1.51792i	0.105360	−	1.51792i
$738$	−0.0664607	+	0.407425i	−0.0664607	+	0.407425i
$739$	1.79838	+	0.844224i	1.79838	+	0.844224i	0.948161	+	0.317791i	$0.102941\pi$
$739$	1.79838	+	0.844224i	1.79838	+	0.844224i	0.850217	+	0.526432i	$0.176471\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.837831	−	0.545930i	$-0.183824\pi$
$743$		0			0		−0.837831	+	0.545930i	$0.816176\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.33468	−	1.16142i	−1.33468	−	1.16142i
$748$	−1.09446	−	0.311401i	−1.09446	−	0.311401i
$749$		0			0
$750$		0			0
$751$		0			0		−0.811724	−	0.584041i	$-0.801471\pi$
$751$		0			0		0.811724	+	0.584041i	$0.198529\pi$
$752$		0			0
$753$	−1.50512	+	1.30974i	−1.50512	+	1.30974i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$757$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$758$	−1.04837	−	0.0971461i	−1.04837	−	0.0971461i
$759$		0			0
$760$		0			0
$761$	1.82178	+	0.804396i	1.82178	+	0.804396i	0.948161	+	0.317791i	$0.102941\pi$
$761$	1.82178	+	0.804396i	1.82178	+	0.804396i	0.873622	+	0.486604i	$0.161765\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.707107	−	0.707107i	0.707107	−	0.707107i
$769$	−1.35165	+	0.794316i	−1.35165	+	0.794316i	−0.990410	−	0.138156i	$-0.955882\pi$
$769$	−1.35165	+	0.794316i	−1.35165	+	0.794316i	−0.361242	+	0.932472i	$0.617647\pi$
$770$		0			0
$771$	0.0339085	−	0.365931i	0.0339085	−	0.365931i
$772$	1.87256	−	0.532788i	1.87256	−	0.532788i
$773$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$773$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$774$	−0.0303251	+	1.31254i	−0.0303251	+	1.31254i
$775$		0			0
$776$	1.93141	+	0.407425i	1.93141	+	0.407425i
$777$		0			0
$778$		0			0
$779$	−0.207318	+	0.798257i	−0.207318	+	0.798257i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.798017	−	0.602635i	0.798017	−	0.602635i
$785$		0			0
$786$	0.122511	+	0.0645767i	0.122511	+	0.0645767i
$787$	−0.844817	+	0.806661i	−0.844817	+	0.806661i	−0.982973	−	0.183750i	$-0.941176\pi$
$787$	−0.844817	+	0.806661i	−0.844817	+	0.806661i	0.138156	+	0.990410i	$0.455882\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−1.78269	−	0.165190i	−1.78269	−	0.165190i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$797$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$798$		0			0
$799$		0			0
$800$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$801$	−0.740791	−	1.78843i	−0.740791	−	1.78843i
$802$	−1.56735	−	1.24148i	−1.56735	−	1.24148i
$803$	2.92570	−	0.408118i	2.92570	−	0.408118i
$804$	0.712061	−	0.463978i	0.712061	−	0.463978i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.579052	−	1.09854i	−0.579052	−	1.09854i	−0.982973	−	0.183750i	$-0.941176\pi$
$809$	−0.579052	−	1.09854i	−0.579052	−	1.09854i	0.403921	−	0.914794i	$-0.367647\pi$
$810$		0			0
$811$	−0.400033	−	1.70083i	−0.400033	−	1.70083i	−0.673696	−	0.739009i	$-0.735294\pi$
$811$	−0.400033	−	1.70083i	−0.400033	−	1.70083i	0.273663	−	0.961826i	$-0.411765\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.229599	−	0.592663i	−0.229599	−	0.592663i
$817$	−0.302281	+	2.60551i	−0.302281	+	2.60551i
$818$	0.895163	−	1.44574i	0.895163	−	1.44574i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	0.228951	+	0.973438i	0.228951	+	0.973438i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	−0.247345	+	1.77316i	−0.247345	+	1.77316i
$826$		0			0
$827$	−0.225523	+	1.94389i	−0.225523	+	1.94389i	0.0922684	+	0.995734i	$0.470588\pi$
$827$	−0.225523	+	1.94389i	−0.225523	+	1.94389i	−0.317791	+	0.948161i	$0.602941\pi$
$828$		0			0
$829$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$829$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.145517	−	0.618701i	−0.145517	−	0.618701i
$834$	1.03659	+	0.860777i	1.03659	+	0.860777i
$835$		0			0
$836$	−3.51593	−	0.657241i	−3.51593	−	0.657241i
$837$		0			0
$838$	0.757949	+	1.52217i	0.757949	+	1.52217i
$839$		0			0		0.998933	−	0.0461835i	$-0.0147059\pi$
$839$		0			0		−0.998933	+	0.0461835i	$0.985294\pi$
$840$		0			0
$841$	−0.990410	+	0.138156i	−0.990410	+	0.138156i
$842$		0			0
$843$	1.09227	−	0.995734i	1.09227	−	0.995734i
$844$	−0.655647	−	0.719210i	−0.655647	−	0.719210i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.777003	−	0.221076i	0.777003	−	0.221076i
$850$	−0.602635	+	0.201983i	−0.602635	+	0.201983i
$851$		0			0
$852$		0			0
$853$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$853$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$854$		0			0
$855$		0			0
$856$	−0.156896	+	0.0971461i	−0.156896	+	0.0971461i
$857$	−1.30940	+	1.25026i	−1.30940	+	1.25026i	−0.361242	+	0.932472i	$0.617647\pi$
$857$	−1.30940	+	1.25026i	−1.30940	+	1.25026i	−0.948161	+	0.317791i	$0.897059\pi$
$858$		0			0
$859$	−0.259861	−	0.259861i	−0.259861	−	0.259861i	0.565136	−	0.824997i	$-0.308824\pi$
$859$	−0.259861	−	0.259861i	−0.259861	−	0.259861i	−0.824997	+	0.565136i	$0.808824\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$863$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$864$	−0.526432	−	0.850217i	−0.526432	−	0.850217i
$865$		0			0
$866$	0.434164	+	0.145517i	0.434164	+	0.145517i
$867$	0.595398	+	0.0275269i	0.595398	+	0.0275269i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.838799	−	1.78682i	0.838799	−	1.78682i
$874$		0			0
$875$		0			0
$876$	1.16672	+	1.16672i	1.16672	+	1.16672i
$877$		0			0		0.993337	−	0.115243i	$-0.0367647\pi$
$877$		0			0		−0.993337	+	0.115243i	$0.963235\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.165413	+	0.426980i	−0.165413	+	0.426980i	−0.990410	−	0.138156i	$-0.955882\pi$
$881$	−0.165413	+	0.426980i	−0.165413	+	0.426980i	0.824997	+	0.565136i	$0.191176\pi$
$882$	−0.403921	−	0.914794i	−0.403921	−	0.914794i
$883$	−1.35208	−	0.597002i	−1.35208	−	0.597002i	−0.403921	−	0.914794i	$-0.632353\pi$
$883$	−1.35208	−	0.597002i	−1.35208	−	0.597002i	−0.948161	+	0.317791i	$0.897059\pi$
$884$		0			0
$885$		0			0
$886$	−0.455948	−	0.0422498i	−0.455948	−	0.0422498i
$887$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$887$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.568950	+	1.69752i	−0.568950	+	1.69752i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.425274	−	0.963154i	0.425274	−	0.963154i
$899$		0			0
$900$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$901$		0			0
$902$	−0.695141	+	0.250992i	−0.695141	+	0.250992i
$903$		0			0
$904$	−0.125829	−	1.08459i	−0.125829	−	1.08459i
$905$		0			0
$906$		0			0
$907$	0.132291	−	1.90591i	0.132291	−	1.90591i	−0.228951	−	0.973438i	$-0.573529\pi$
$907$	0.132291	−	1.90591i	0.132291	−	1.90591i	0.361242	−	0.932472i	$-0.382353\pi$
$908$	0.234429	+	0.902646i	0.234429	+	0.902646i
$909$		0			0
$910$		0			0
$911$		0			0		−0.620906	−	0.783885i	$-0.713235\pi$
$911$		0			0		0.620906	+	0.783885i	$0.286765\pi$
$912$	−0.890525	−	1.78842i	−0.890525	−	1.78842i
$913$	0.653798	−	3.09934i	0.653798	−	3.09934i
$914$	−1.44123	+	0.446296i	−1.44123	+	0.446296i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.629488	+	0.0878098i	−0.629488	+	0.0878098i
$919$		0			0		0.160996	−	0.986955i	$-0.448529\pi$
$919$		0			0		−0.160996	+	0.986955i	$0.551471\pi$
$920$		0			0
$921$	1.72942	−	0.535539i	1.72942	−	0.535539i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.156154	−	0.227957i	−0.156154	−	0.227957i	0.739009	−	0.673696i	$-0.235294\pi$
$929$	−0.156154	−	0.227957i	−0.156154	−	0.227957i	−0.895163	+	0.445738i	$0.852941\pi$
$930$		0			0
$931$	−0.634905	−	1.89430i	−0.634905	−	1.89430i
$932$	−0.948161	+	0.682209i	−0.948161	+	0.682209i
$933$		0			0
$934$	0.450104	−	1.91373i	0.450104	−	1.91373i
$935$		0			0
$936$		0			0
$937$	1.35208	−	1.23259i	1.35208	−	1.23259i	0.403921	−	0.914794i	$-0.367647\pi$
$937$	1.35208	−	1.23259i	1.35208	−	1.23259i	0.948161	−	0.317791i	$-0.102941\pi$
$938$		0			0
$939$	−1.04277	−	1.68413i	−1.04277	−	1.68413i
$940$		0			0
$941$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$941$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$942$		0			0
$943$		0			0
$944$	1.91545	−	0.177492i	1.91545	−	0.177492i
$945$		0			0
$946$	−2.07933	+	1.09603i	−2.07933	+	1.09603i
$947$	−0.0782748	+	0.216788i	−0.0782748	+	0.216788i	−0.973438	−	0.228951i	$-0.926471\pi$
$947$	−0.0782748	+	0.216788i	−0.0782748	+	0.216788i	0.895163	+	0.445738i	$0.147059\pi$
$948$		0			0
$949$		0			0
$950$	−1.82764	+	0.806980i	−1.82764	+	0.806980i
$951$		0			0
$952$		0			0
$953$	0.665182	+	0.764411i	0.665182	+	0.764411i	0.982973	−	0.183750i	$-0.0588235\pi$
$953$	0.665182	+	0.764411i	0.665182	+	0.764411i	−0.317791	+	0.948161i	$0.602941\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.486604	+	0.873622i	0.486604	+	0.873622i
$962$		0			0
$963$	0.0586442	+	0.174970i	0.0586442	+	0.174970i
$964$	−0.319846	−	0.0371073i	−0.319846	−	0.0371073i
$965$		0			0
$966$		0			0
$967$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$967$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$968$	−0.890755	−	2.01737i	−0.890755	−	2.01737i
$969$	−1.26845	+	0.0586442i	−1.26845	+	0.0586442i
$970$		0			0
$971$	−1.88063	−	0.679033i	−1.88063	−	0.679033i	−0.948161	−	0.317791i	$-0.897059\pi$
$971$	−1.88063	−	0.679033i	−1.88063	−	0.679033i	−0.932472	−	0.361242i	$-0.882353\pi$
$972$	−0.948161	+	0.317791i	−0.948161	+	0.317791i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.852254	−	1.12857i	0.852254	−	1.12857i	−0.138156	−	0.990410i	$-0.544118\pi$
$977$	0.852254	−	1.12857i	0.852254	−	1.12857i	0.990410	−	0.138156i	$-0.0441176\pi$
$978$	−0.335088	+	1.58849i	−0.335088	+	1.58849i
$979$	2.15186	−	2.71669i	2.15186	−	2.71669i
$980$		0			0
$981$		0			0
$982$	−1.02916	+	1.18268i	−1.02916	+	1.18268i
$983$		0			0		−0.160996	−	0.986955i	$-0.551471\pi$
$983$		0			0		0.160996	+	0.986955i	$0.448529\pi$
$984$	−0.345865	−	0.225365i	−0.345865	−	0.225365i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$991$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$992$		0			0
$993$	−0.748886	+	0.157976i	−0.748886	+	0.157976i
$994$		0			0
$995$		0			0
$996$	1.60157	−	0.751834i	1.60157	−	0.751834i
$997$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$997$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$998$	−1.43477	+	1.19141i	−1.43477	+	1.19141i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3288.1.cj.b.755.1	yes	64
3.2	odd	2		3288.1.cj.a.755.1	✓	64
8.3	odd	2	CM	3288.1.cj.b.755.1	yes	64
24.11	even	2		3288.1.cj.a.755.1	✓	64
137.92	odd	136		3288.1.cj.a.2147.1	yes	64
411.92	even	136	inner	3288.1.cj.b.2147.1	yes	64
1096.1051	even	136		3288.1.cj.a.2147.1	yes	64
3288.2147	odd	136	inner	3288.1.cj.b.2147.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3288.1.cj.a.755.1	✓	64	3.2	odd	2
3288.1.cj.a.755.1	✓	64	24.11	even	2
3288.1.cj.a.2147.1	yes	64	137.92	odd	136
3288.1.cj.a.2147.1	yes	64	1096.1051	even	136
3288.1.cj.b.755.1	yes	64	1.1	even	1	trivial
3288.1.cj.b.755.1	yes	64	8.3	odd	2	CM
3288.1.cj.b.2147.1	yes	64	411.92	even	136	inner
3288.1.cj.b.2147.1	yes	64	3288.2147	odd	136	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3288 = 2^{3} \cdot 3 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3288.cj (of order \(136\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.873622 + 0.486604i) q^{2} +(-0.990410 - 0.138156i) q^{3} +(0.526432 - 0.850217i) q^{4} +(0.932472 - 0.361242i) q^{6} +(-0.0461835 + 0.998933i) q^{8} +(0.961826 + 0.273663i) q^{9} +O(q^{10})\)	\(q+(-0.873622 + 0.486604i) q^{2} +(-0.990410 - 0.138156i) q^{3} +(0.526432 - 0.850217i) q^{4} +(0.932472 - 0.361242i) q^{6} +(-0.0461835 + 0.998933i) q^{8} +(0.961826 + 0.273663i) q^{9} +(0.409896 + 1.74277i) q^{11} +(-0.638847 + 0.769334i) q^{12} +(-0.445738 - 0.895163i) q^{16} +(-0.634905 + 0.0293534i) q^{17} +(-0.973438 + 0.228951i) q^{18} +(-1.97871 + 0.276018i) q^{19} +(-1.20614 - 1.32307i) q^{22} +(0.183750 - 0.982973i) q^{24} +(-0.973438 - 0.228951i) q^{25} +(-0.914794 - 0.403921i) q^{27} +(0.824997 + 0.565136i) q^{32} +(-0.165190 - 1.78269i) q^{33} +(0.540383 - 0.334591i) q^{34} +(0.739009 - 0.673696i) q^{36} +(1.59433 - 1.20398i) q^{38} +(0.157976 - 0.381387i) q^{41} +(0.330027 - 1.27074i) q^{43} +(1.69752 + 0.568950i) q^{44} +(0.317791 + 0.948161i) q^{48} +(0.183750 + 0.982973i) q^{49} +(0.961826 - 0.273663i) q^{50} +(0.632872 + 0.0586442i) q^{51} +(0.995734 - 0.0922684i) q^{54} +1.99787 q^{57} +(-0.694903 + 1.79375i) q^{59} +(-0.995734 - 0.0922684i) q^{64} +(1.01178 + 1.47701i) q^{66} +(-0.811852 - 0.251402i) q^{67} +(-0.309277 + 0.555259i) q^{68} +(-0.317791 + 0.948161i) q^{72} +(0.152242 - 1.64296i) q^{73} +(0.932472 + 0.361242i) q^{75} +(-0.806980 + 1.82764i) q^{76} +(0.850217 + 0.526432i) q^{81} +(0.0475735 + 0.410060i) q^{82} +(-1.60157 - 0.751834i) q^{83} +(0.330027 + 1.27074i) q^{86} +(-1.75984 + 0.328972i) q^{88} +(-1.20194 - 1.51743i) q^{89} +(-0.739009 - 0.673696i) q^{96} +(0.317791 - 1.94816i) q^{97} +(-0.638847 - 0.769334i) q^{98} +(-0.0826835 + 1.78842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{6}+O(q^{10}) \) 64 * q - 4 * q^6	\( 64 q - 4 q^{6} + 4 q^{16} - 4 q^{17} - 4 q^{19} - 4 q^{36} + 4 q^{41} - 4 q^{68} - 4 q^{75} + 4 q^{76} + 4 q^{81} - 4 q^{83} + 4 q^{96}+O(q^{100}) \) 64 * q - 4 * q^6 + 4 * q^16 - 4 * q^17 - 4 * q^19 - 4 * q^36 + 4 * q^41 - 4 * q^68 - 4 * q^75 + 4 * q^76 + 4 * q^81 - 4 * q^83 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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