LMFDB - Embedded newform 3288.1.cj.b.659.1

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			659.1
Root			$0.973438 - 0.228951i$ of defining polynomial
Character	$\chi$	$=$	3288.659
Dual form			3288.1.cj.b.2819.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.973438 - 0.228951i) q^{2} +(-0.873622 - 0.486604i) q^{3} +(0.895163 + 0.445738i) q^{4} +(0.739009 + 0.673696i) q^{6} +(-0.769334 - 0.638847i) q^{8} +(0.526432 + 0.850217i) q^{9} +O(q^{10})$	\(q+(-0.973438 - 0.228951i) q^{2} +(-0.873622 - 0.486604i) q^{3} +(0.895163 + 0.445738i) q^{4} +(0.739009 + 0.673696i) q^{6} +(-0.769334 - 0.638847i) q^{8} +(0.526432 + 0.850217i) q^{9} +(1.51330 - 0.507206i) q^{11} +(-0.565136 - 0.824997i) q^{12} +(0.602635 + 0.798017i) q^{16} +(-0.176521 - 0.212577i) q^{17} +(-0.317791 - 0.948161i) q^{18} +(1.11622 - 0.621731i) q^{19} +(-1.58923 + 0.147263i) q^{22} +(0.361242 + 0.932472i) q^{24} +(-0.317791 + 0.948161i) q^{25} +(-0.0461835 - 0.998933i) q^{27} +(-0.403921 - 0.914794i) q^{32} +(-1.56886 - 0.293271i) q^{33} +(0.123163 + 0.247345i) q^{34} +(0.0922684 + 0.995734i) q^{36} +(-1.22892 + 0.349657i) q^{38} +(-0.528551 + 1.27604i) q^{41} +(0.116777 + 1.00656i) q^{43} +(1.58073 + 0.220502i) q^{44} +(-0.138156 - 0.990410i) q^{48} +(0.361242 - 0.932472i) q^{49} +(0.526432 - 0.850217i) q^{50} +(0.0507723 + 0.271608i) q^{51} +(-0.183750 + 0.982973i) q^{54} -1.27769 q^{57} +(0.709310 + 0.778076i) q^{59} +(0.183750 + 0.982973i) q^{64} +(1.46004 + 0.644672i) q^{66} +(0.509130 - 0.781354i) q^{67} +(-0.0632619 - 0.268973i) q^{68} +(0.138156 - 0.990410i) q^{72} +(0.794087 - 0.148441i) q^{73} +(0.739009 - 0.673696i) q^{75} +(1.27633 - 0.0590083i) q^{76} +(-0.445738 + 0.895163i) q^{81} +(0.806661 - 1.12113i) q^{82} +(0.365184 - 0.192492i) q^{83} +(0.116777 - 1.00656i) q^{86} +(-1.48826 - 0.576554i) q^{88} +(-1.96076 - 0.319846i) q^{89} +(-0.0922684 + 0.995734i) q^{96} +(-0.138156 - 0.00958957i) q^{97} +(-0.565136 + 0.824997i) q^{98} +(1.22788 + 1.01962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3288\mathbb{Z}\right)^\times$.

$n$	$823$	$1097$	$1645$	$1921$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{103}{136}\right)$

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 $

$2$	−0.973438	−	0.228951i	−0.973438	−	0.228951i
$2$	−0.973438	−	0.228951i	−0.973438	−	0.228951i
$3$	−0.873622	−	0.486604i	−0.873622	−	0.486604i
$3$	−0.873622	−	0.486604i	−0.873622	−	0.486604i
$4$	0.895163	+	0.445738i	0.895163	+	0.445738i
$5$		0			0		−0.584041	−	0.811724i	$-0.698529\pi$
$5$		0			0		0.584041	+	0.811724i	$0.301471\pi$
$6$	0.739009	+	0.673696i	0.739009	+	0.673696i
$7$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$7$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$8$	−0.769334	−	0.638847i	−0.769334	−	0.638847i
$9$	0.526432	+	0.850217i	0.526432	+	0.850217i
$10$		0			0
$11$	1.51330	−	0.507206i	1.51330	−	0.507206i	0.565136	−	0.824997i	$-0.308824\pi$
$11$	1.51330	−	0.507206i	1.51330	−	0.507206i	0.948161	+	0.317791i	$0.102941\pi$
$12$	−0.565136	−	0.824997i	−0.565136	−	0.824997i
$13$		0			0		0.978467	−	0.206405i	$-0.0661765\pi$
$13$		0			0		−0.978467	+	0.206405i	$0.933824\pi$
$14$		0			0
$15$		0			0
$16$	0.602635	+	0.798017i	0.602635	+	0.798017i
$17$	−0.176521	−	0.212577i	−0.176521	−	0.212577i	0.673696	−	0.739009i	$-0.264706\pi$
$17$	−0.176521	−	0.212577i	−0.176521	−	0.212577i	−0.850217	+	0.526432i	$0.823529\pi$
$18$	−0.317791	−	0.948161i	−0.317791	−	0.948161i
$19$	1.11622	−	0.621731i	1.11622	−	0.621731i	0.183750	−	0.982973i	$-0.441176\pi$
$19$	1.11622	−	0.621731i	1.11622	−	0.621731i	0.932472	+	0.361242i	$0.117647\pi$
$20$		0			0
$21$		0			0
$22$	−1.58923	+	0.147263i	−1.58923	+	0.147263i
$23$		0			0		−0.862150	−	0.506653i	$-0.830882\pi$
$23$		0			0		0.862150	+	0.506653i	$0.169118\pi$
$24$	0.361242	+	0.932472i	0.361242	+	0.932472i
$25$	−0.317791	+	0.948161i	−0.317791	+	0.948161i
$26$		0			0
$27$	−0.0461835	−	0.998933i	−0.0461835	−	0.998933i
$28$		0			0
$29$		0			0		−0.251374	−	0.967890i	$-0.580882\pi$
$29$		0			0		0.251374	+	0.967890i	$0.419118\pi$
$30$		0			0
$31$		0			0		−0.620906	−	0.783885i	$-0.713235\pi$
$31$		0			0		0.620906	+	0.783885i	$0.286765\pi$
$32$	−0.403921	−	0.914794i	−0.403921	−	0.914794i
$33$	−1.56886	−	0.293271i	−1.56886	−	0.293271i
$34$	0.123163	+	0.247345i	0.123163	+	0.247345i
$35$		0			0
$36$	0.0922684	+	0.995734i	0.0922684	+	0.995734i
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$	−1.22892	+	0.349657i	−1.22892	+	0.349657i
$39$		0			0
$40$		0			0
$41$	−0.528551	+	1.27604i	−0.528551	+	1.27604i	0.403921	+	0.914794i	$0.367647\pi$
$41$	−0.528551	+	1.27604i	−0.528551	+	1.27604i	−0.932472	+	0.361242i	$0.882353\pi$
$42$		0			0
$43$	0.116777	+	1.00656i	0.116777	+	1.00656i	0.914794	+	0.403921i	$0.132353\pi$
$43$	0.116777	+	1.00656i	0.116777	+	1.00656i	−0.798017	+	0.602635i	$0.794118\pi$
$44$	1.58073	+	0.220502i	1.58073	+	0.220502i
$45$		0			0
$46$		0			0
$47$		0			0		0.940567	−	0.339607i	$-0.110294\pi$
$47$		0			0		−0.940567	+	0.339607i	$0.889706\pi$
$48$	−0.138156	−	0.990410i	−0.138156	−	0.990410i
$49$	0.361242	−	0.932472i	0.361242	−	0.932472i
$50$	0.526432	−	0.850217i	0.526432	−	0.850217i
$51$	0.0507723	+	0.271608i	0.0507723	+	0.271608i
$52$		0			0
$53$		0			0		0.620906	−	0.783885i	$-0.286765\pi$
$53$		0			0		−0.620906	+	0.783885i	$0.713235\pi$
$54$	−0.183750	+	0.982973i	−0.183750	+	0.982973i
$55$		0			0
$56$		0			0
$57$	−1.27769			−1.27769
$58$		0			0
$59$	0.709310	+	0.778076i	0.709310	+	0.778076i	0.982973	−	0.183750i	$-0.0588235\pi$
$59$	0.709310	+	0.778076i	0.709310	+	0.778076i	−0.273663	+	0.961826i	$0.588235\pi$
$60$		0			0
$61$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$61$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$62$		0			0
$63$		0			0
$64$	0.183750	+	0.982973i	0.183750	+	0.982973i
$65$		0			0
$66$	1.46004	+	0.644672i	1.46004	+	0.644672i
$67$	0.509130	−	0.781354i	0.509130	−	0.781354i	−0.486604	−	0.873622i	$-0.661765\pi$
$67$	0.509130	−	0.781354i	0.509130	−	0.781354i	0.995734	+	0.0922684i	$0.0294118\pi$
$68$	−0.0632619	−	0.268973i	−0.0632619	−	0.268973i
$69$		0			0
$70$		0			0
$71$		0			0		0.656446	−	0.754373i	$-0.272059\pi$
$71$		0			0		−0.656446	+	0.754373i	$0.727941\pi$
$72$	0.138156	−	0.990410i	0.138156	−	0.990410i
$73$	0.794087	−	0.148441i	0.794087	−	0.148441i	0.228951	−	0.973438i	$-0.426471\pi$
$73$	0.794087	−	0.148441i	0.794087	−	0.148441i	0.565136	+	0.824997i	$0.308824\pi$
$74$		0			0
$75$	0.739009	−	0.673696i	0.739009	−	0.673696i
$76$	1.27633	−	0.0590083i	1.27633	−	0.0590083i
$77$		0			0
$78$		0			0
$79$		0			0		0.999733	−	0.0230979i	$-0.00735294\pi$
$79$		0			0		−0.999733	+	0.0230979i	$0.992647\pi$
$80$		0			0
$81$	−0.445738	+	0.895163i	−0.445738	+	0.895163i
$82$	0.806661	−	1.12113i	0.806661	−	1.12113i
$83$	0.365184	−	0.192492i	0.365184	−	0.192492i	−0.273663	−	0.961826i	$-0.588235\pi$
$83$	0.365184	−	0.192492i	0.365184	−	0.192492i	0.638847	+	0.769334i	$0.279412\pi$
$84$		0			0
$85$		0			0
$86$	0.116777	−	1.00656i	0.116777	−	1.00656i
$87$		0			0
$88$	−1.48826	−	0.576554i	−1.48826	−	0.576554i
$89$	−1.96076	−	0.319846i	−1.96076	−	0.319846i	−0.998933	−	0.0461835i	$-0.985294\pi$
$89$	−1.96076	−	0.319846i	−1.96076	−	0.319846i	−0.961826	−	0.273663i	$-0.911765\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.0922684	+	0.995734i	−0.0922684	+	0.995734i
$97$	−0.138156	−	0.00958957i	−0.138156	−	0.00958957i		−	1.00000i	$-0.5\pi$
$97$	−0.138156	−	0.00958957i	−0.138156	−	0.00958957i	−0.138156	+	0.990410i	$0.544118\pi$
$98$	−0.565136	+	0.824997i	−0.565136	+	0.824997i
$99$	1.22788	+	1.01962i	1.22788	+	1.01962i
$100$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$101$		0			0		0.486604	−	0.873622i	$-0.338235\pi$
$101$		0			0		−0.486604	+	0.873622i	$0.661765\pi$
$102$	0.0127611	−	0.276018i	0.0127611	−	0.276018i
$103$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$103$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.79844	+	0.794087i	1.79844	+	0.794087i	0.973438	+	0.228951i	$0.0735294\pi$
$107$	1.79844	+	0.794087i	1.79844	+	0.794087i	0.824997	+	0.565136i	$0.191176\pi$
$108$	0.403921	−	0.914794i	0.403921	−	0.914794i
$109$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$109$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.00319880	−	0.0460849i	−0.00319880	−	0.0460849i	0.995734	−	0.0922684i	$-0.0294118\pi$
$113$	−0.00319880	−	0.0460849i	−0.00319880	−	0.0460849i	−0.998933	+	0.0461835i	$0.985294\pi$
$114$	1.24376	+	0.292529i	1.24376	+	0.292529i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.512328	−	0.919806i	−0.512328	−	0.919806i
$119$		0			0
$120$		0			0
$121$	1.23479	−	0.932472i	1.23479	−	0.932472i
$122$		0			0
$123$	1.08268	−	0.857578i	1.08268	−	0.857578i
$124$		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	$0.875000\pi$
$128$	0.0461835	−	0.998933i	0.0461835	−	0.998933i
$129$	0.387776	−	0.936174i	0.387776	−	0.936174i
$130$		0			0
$131$	0.254719	+	0.433444i	0.254719	+	0.433444i	0.961826	−	0.273663i	$-0.0882353\pi$
$131$	0.254719	+	0.433444i	0.254719	+	0.433444i	−0.707107	+	0.707107i	$0.750000\pi$
$132$	−1.27366	−	0.961826i	−1.27366	−	0.961826i
$133$		0			0
$134$	−0.674498	+	0.644034i	−0.674498	+	0.644034i
$135$		0			0
$136$			0.276313i			0.276313i
$137$	−0.486604	+	0.873622i	−0.486604	+	0.873622i
$137$	−0.486604	+	0.873622i	−0.486604	+	0.873622i
$138$		0			0
$139$	0.455948	−	1.93857i	0.455948	−	1.93857i	0.138156	−	0.990410i	$-0.455882\pi$
$139$	0.455948	−	1.93857i	0.455948	−	1.93857i	0.317791	−	0.948161i	$-0.397059\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.361242	+	0.932472i	−0.361242	+	0.932472i
$145$		0			0
$146$	−0.806980	−	0.0373089i	−0.806980	−	0.0373089i
$147$	−0.769334	+	0.638847i	−0.769334	+	0.638847i
$148$		0			0
$149$		0			0		−0.295806	−	0.955248i	$-0.595588\pi$
$149$		0			0		0.295806	+	0.955248i	$0.404412\pi$
$150$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$151$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$151$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$152$	−1.25594	−	0.234776i	−1.25594	−	0.234776i
$153$	0.0878098	−	0.261989i	0.0878098	−	0.261989i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.986955	−	0.160996i	$-0.0514706\pi$
$157$		0			0		−0.986955	+	0.160996i	$0.948529\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.638847	−	0.769334i	0.638847	−	0.769334i
$163$	0.0303251	−	1.31254i	0.0303251	−	1.31254i	−0.739009	−	0.673696i	$-0.764706\pi$
$163$	0.0303251	−	1.31254i	0.0303251	−	1.31254i	0.769334	−	0.638847i	$-0.220588\pi$
$164$	−1.04192	+	0.906665i	−1.04192	+	0.906665i
$165$		0			0
$166$	−0.399555	+	0.103770i	−0.399555	+	0.103770i
$167$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$167$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$168$		0			0
$169$	0.914794	−	0.403921i	0.914794	−	0.403921i
$170$		0			0
$171$	1.11622	+	0.621731i	1.11622	+	0.621731i
$172$	−0.344126	+	0.953083i	−0.344126	+	0.953083i
$173$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$173$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$174$		0			0
$175$		0			0
$176$	1.31672	+	0.901977i	1.31672	+	0.901977i
$177$	−0.241054	−	1.02490i	−0.241054	−	1.02490i
$178$	1.83545	+	0.760267i	1.83545	+	0.760267i
$179$	0.849659	−	1.80996i	0.849659	−	1.80996i	0.403921	−	0.914794i	$-0.367647\pi$
$179$	0.849659	−	1.80996i	0.849659	−	1.80996i	0.445738	−	0.895163i	$-0.352941\pi$
$180$		0			0
$181$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$181$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.374950	−	0.232159i	−0.374950	−	0.232159i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.466296	−	0.884629i	$-0.654412\pi$
$191$		0			0		0.466296	+	0.884629i	$0.345588\pi$
$192$	0.317791	−	0.948161i	0.317791	−	0.948161i
$193$	0.0586442	−	0.632872i	0.0586442	−	0.632872i	−0.914794	−	0.403921i	$-0.867647\pi$
$193$	0.0586442	−	0.632872i	0.0586442	−	0.632872i	0.973438	−	0.228951i	$-0.0735294\pi$
$194$	0.132291	+	0.0409658i	0.132291	+	0.0409658i
$195$		0			0
$196$	0.739009	−	0.673696i	0.739009	−	0.673696i
$197$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$197$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$198$	−0.961826	−	1.27366i	−0.961826	−	1.27366i
$199$		0			0		0.905220	−	0.424943i	$-0.139706\pi$
$199$		0			0		−0.905220	+	0.424943i	$0.860294\pi$
$200$	0.850217	−	0.526432i	0.850217	−	0.526432i
$201$	−0.824997	+	0.434864i	−0.824997	+	0.434864i
$202$		0			0
$203$		0			0
$204$	−0.0756166	+	0.265765i	−0.0756166	+	0.265765i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.37383	−	1.50702i	1.37383	−	1.50702i
$210$		0			0
$211$	−0.389315	+	0.241054i	−0.389315	+	0.241054i	−0.707107	−	0.707107i	$-0.750000\pi$
$211$	−0.389315	+	0.241054i	−0.389315	+	0.241054i	0.317791	+	0.948161i	$0.397059\pi$
$212$		0			0
$213$		0			0
$214$	−1.56886	−	1.18475i	−1.56886	−	1.18475i
$215$		0			0
$216$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$217$		0			0
$218$		0			0
$219$	−0.765964	−	0.256725i	−0.765964	−	0.256725i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.993337	−	0.115243i	$-0.963235\pi$
$223$		0			0		0.993337	+	0.115243i	$0.0367647\pi$
$224$		0			0
$225$	−0.973438	+	0.228951i	−0.973438	+	0.228951i
$226$	−0.00743733	+	0.0455932i	−0.00743733	+	0.0455932i
$227$	−0.664589	−	1.84063i	−0.664589	−	1.84063i	−0.526432	−	0.850217i	$-0.676471\pi$
$227$	−0.664589	−	1.84063i	−0.664589	−	1.84063i	−0.138156	−	0.990410i	$-0.544118\pi$
$228$	−1.14374	−	0.569517i	−1.14374	−	0.569517i
$229$		0			0		0.837831	−	0.545930i	$-0.183824\pi$
$229$		0			0		−0.837831	+	0.545930i	$0.816176\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.39390	+	0.577372i	1.39390	+	0.577372i	0.948161	−	0.317791i	$-0.102941\pi$
$233$	1.39390	+	0.577372i	1.39390	+	0.577372i	0.445738	+	0.895163i	$0.352941\pi$
$234$		0			0
$235$		0			0
$236$	0.288130	+	1.01267i	0.288130	+	1.01267i
$237$		0			0
$238$		0			0
$239$		0			0		0.339607	−	0.940567i	$-0.389706\pi$
$239$		0			0		−0.339607	+	0.940567i	$0.610294\pi$
$240$		0			0
$241$	−0.930353	+	1.76501i	−0.930353	+	1.76501i	−0.403921	+	0.914794i	$0.632353\pi$
$241$	−0.930353	+	1.76501i	−0.930353	+	1.76501i	−0.526432	+	0.850217i	$0.676471\pi$
$242$	−1.41548	+	0.624997i	−1.41548	+	0.624997i
$243$	0.824997	−	0.565136i	0.824997	−	0.565136i
$244$		0			0
$245$		0			0
$246$	−1.25026	+	0.586919i	−1.25026	+	0.586919i
$247$		0			0
$248$		0			0
$249$	−0.412700	−	0.00953505i	−0.412700	−	0.00953505i
$250$		0			0
$251$	0.980770	−	1.66893i	0.980770	−	1.66893i	0.273663	−	0.961826i	$-0.411765\pi$
$251$	0.980770	−	1.66893i	0.980770	−	1.66893i	0.707107	−	0.707107i	$-0.250000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$257$	0.555831	−	0.461556i	0.555831	−	0.461556i	−0.317791	−	0.948161i	$-0.602941\pi$
$257$	0.555831	−	0.461556i	0.555831	−	0.461556i	0.873622	+	0.486604i	$0.161765\pi$
$258$	−0.591813	+	0.822526i	−0.591813	+	0.822526i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.148716	−	0.480249i	−0.148716	−	0.480249i
$263$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$263$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$264$	1.01962	+	1.22788i	1.01962	+	1.22788i
$265$		0			0
$266$		0			0
$267$	1.55732	+	1.23354i	1.55732	+	1.23354i
$268$	0.804034	−	0.472501i	0.804034	−	0.472501i
$269$		0			0		0.811724	−	0.584041i	$-0.198529\pi$
$269$		0			0		−0.811724	+	0.584041i	$0.801471\pi$
$270$		0			0
$271$		0			0		−0.690585	−	0.723251i	$-0.742647\pi$
$271$		0			0		0.690585	+	0.723251i	$0.257353\pi$
$272$	0.0632619	−	0.268973i	0.0632619	−	0.268973i
$273$		0			0
$274$	0.673696	−	0.739009i	0.673696	−	0.739009i
$275$			1.59603i			1.59603i
$276$		0			0
$277$		0			0		0.723251	−	0.690585i	$-0.242647\pi$
$277$		0			0		−0.723251	+	0.690585i	$0.757353\pi$
$278$	−0.887674	+	1.78269i	−0.887674	+	1.78269i
$279$		0			0
$280$		0			0
$281$	−0.104288	−	0.152242i	−0.104288	−	0.152242i	0.769334	−	0.638847i	$-0.220588\pi$
$281$	−0.104288	−	0.152242i	−0.104288	−	0.152242i	−0.873622	+	0.486604i	$0.838235\pi$
$282$		0			0
$283$	−0.0922684	+	1.99573i	−0.0922684	+	1.99573i			1.00000i	$0.5\pi$
$283$	−0.0922684	+	1.99573i	−0.0922684	+	1.99573i	−0.0922684	+	0.995734i	$0.529412\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.565136	−	0.824997i	0.565136	−	0.824997i
$289$	0.169720	−	0.907924i	0.169720	−	0.907924i
$290$		0			0
$291$	0.116030	+	0.0756052i	0.116030	+	0.0756052i
$292$	0.777003	+	0.221076i	0.777003	+	0.221076i
$293$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$293$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$294$	0.895163	−	0.445738i	0.895163	−	0.445738i
$295$		0			0
$296$		0			0
$297$	−0.576554	−	1.48826i	−0.576554	−	1.48826i
$298$		0			0
$299$		0			0
$300$	0.961826	−	0.273663i	0.961826	−	0.273663i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.16883	+	0.516087i	1.16883	+	0.516087i
$305$		0			0
$306$	−0.145460	+	0.234926i	−0.145460	+	0.234926i
$307$	−1.56514	−	0.824997i	−1.56514	−	0.824997i	−0.565136	−	0.824997i	$-0.691176\pi$
$307$	−1.56514	−	0.824997i	−1.56514	−	0.824997i	−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
$313$	0.987432	−	1.44147i	0.987432	−	1.44147i	0.0922684	−	0.995734i	$-0.470588\pi$
$313$	0.987432	−	1.44147i	0.987432	−	1.44147i	0.895163	−	0.445738i	$-0.147059\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.993337	−	0.115243i	$-0.0367647\pi$
$317$		0			0		−0.993337	+	0.115243i	$0.963235\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.18475	−	1.56886i	−1.18475	−	1.56886i
$322$		0			0
$323$	−0.329203	−	0.127534i	−0.329203	−	0.127534i
$324$	−0.798017	+	0.602635i	−0.798017	+	0.602635i
$325$		0			0
$326$	−0.330027	+	1.27074i	−0.330027	+	1.27074i
$327$		0			0
$328$	1.22182	−	0.644034i	1.22182	−	0.644034i
$329$		0			0
$330$		0			0
$331$	−0.226400	+	0.731115i	−0.226400	+	0.731115i	0.769334	+	0.638847i	$0.220588\pi$
$331$	−0.226400	+	0.731115i	−0.226400	+	0.731115i	−0.995734	+	0.0922684i	$0.970588\pi$
$332$	0.412700	−	0.00953505i	0.412700	−	0.00953505i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.963154	+	1.55555i	0.963154	+	1.55555i	0.824997	+	0.565136i	$0.191176\pi$
$337$	0.963154	+	1.55555i	0.963154	+	1.55555i	0.138156	+	0.990410i	$0.455882\pi$
$338$	−0.982973	+	0.183750i	−0.982973	+	0.183750i
$339$	−0.0196306	+	0.0418174i	−0.0196306	+	0.0418174i
$340$		0			0
$341$		0			0
$342$	−0.944227	−	0.860777i	−0.944227	−	0.860777i
$343$		0			0
$344$	0.553195	−	0.848980i	0.553195	−	0.848980i
$345$		0			0
$346$		0			0
$347$	0.271585	+	1.45285i	0.271585	+	1.45285i	0.798017	+	0.602635i	$0.205882\pi$
$347$	0.271585	+	1.45285i	0.271585	+	1.45285i	−0.526432	+	0.850217i	$0.676471\pi$
$348$		0			0
$349$		0			0		−0.424943	−	0.905220i	$-0.639706\pi$
$349$		0			0		0.424943	+	0.905220i	$0.360294\pi$
$350$		0			0
$351$		0			0
$352$	−1.07524	−	1.17948i	−1.07524	−	1.17948i
$353$	0.0252197	+	1.09157i	0.0252197	+	1.09157i	0.850217	+	0.526432i	$0.176471\pi$
$353$	0.0252197	+	1.09157i	0.0252197	+	1.09157i	−0.824997	+	0.565136i	$0.808824\pi$
$354$			1.05286i			1.05286i
$355$		0			0
$356$	−1.61263	−	1.16030i	−1.61263	−	1.16030i
$357$		0			0
$358$	−1.24148	+	1.56735i	−1.24148	+	1.56735i
$359$		0			0		−0.967890	−	0.251374i	$-0.919118\pi$
$359$		0			0		0.967890	+	0.251374i	$0.0808824\pi$
$360$		0			0
$361$	0.332969	−	0.537763i	0.332969	−	0.537763i
$362$		0			0
$363$	−1.53249	+	0.213773i	−1.53249	+	0.213773i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.990410	−	0.138156i	$-0.955882\pi$
$367$		0			0		0.990410	+	0.138156i	$0.0441176\pi$
$368$		0			0
$369$	−1.36315	+	0.222363i	−1.36315	+	0.222363i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$373$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$374$	0.311837	+	0.311837i	0.311837	+	0.311837i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.723151	−	1.63778i	−0.723151	−	1.63778i	−0.769334	−	0.638847i	$-0.779412\pi$
$379$	−0.723151	−	1.63778i	−0.723151	−	1.63778i	0.0461835	−	0.998933i	$-0.485294\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$383$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$384$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$385$		0			0
$386$	−0.201983	+	0.602635i	−0.201983	+	0.602635i
$387$	−0.794316	+	0.629169i	−0.794316	+	0.629169i
$388$	−0.119398	−	0.0701658i	−0.119398	−	0.0701658i
$389$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$389$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$390$		0			0
$391$		0			0
$392$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$393$	−0.0116124	−	0.502614i	−0.0116124	−	0.502614i
$394$		0			0
$395$		0			0
$396$	0.644672	+	1.46004i	0.644672	+	1.46004i
$397$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$397$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$398$		0			0
$399$		0			0
$400$	−0.948161	+	0.317791i	−0.948161	+	0.317791i
$401$	0.325237	+	0.785192i	0.325237	+	0.785192i	0.998933	+	0.0461835i	$0.0147059\pi$
$401$	0.325237	+	0.785192i	0.325237	+	0.785192i	−0.673696	+	0.739009i	$0.735294\pi$
$402$	0.902646	−	0.234429i	0.902646	−	0.234429i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.134455	−	0.241393i	0.134455	−	0.241393i
$409$	0.867797	+	0.204104i	0.867797	+	0.204104i	0.638847	−	0.769334i	$-0.279412\pi$
$409$	0.867797	+	0.204104i	0.867797	+	0.204104i	0.228951	+	0.973438i	$0.426471\pi$
$410$		0			0
$411$	0.850217	−	0.526432i	0.850217	−	0.526432i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.34164	+	1.47171i	−1.34164	+	1.47171i
$418$	−1.68237	+	1.15245i	−1.68237	+	1.15245i
$419$	−0.685843	−	0.569517i	−0.685843	−	0.569517i	0.228951	−	0.973438i	$-0.426471\pi$
$419$	−0.685843	−	0.569517i	−0.685843	−	0.569517i	−0.914794	+	0.403921i	$0.867647\pi$
$420$		0			0
$421$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$421$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$422$	0.434164	−	0.145517i	0.434164	−	0.145517i
$423$		0			0
$424$		0			0
$425$	0.257654	−	0.0998157i	0.257654	−	0.0998157i
$426$		0			0
$427$		0			0
$428$	1.25594	+	1.51247i	1.25594	+	1.51247i
$429$		0			0
$430$		0			0
$431$		0			0		−0.160996	−	0.986955i	$-0.551471\pi$
$431$		0			0		0.160996	+	0.986955i	$0.448529\pi$
$432$	0.769334	−	0.638847i	0.769334	−	0.638847i
$433$	−1.88823	+	0.174970i	−1.88823	+	0.174970i	−0.973438	−	0.228951i	$-0.926471\pi$
$433$	−1.88823	+	0.174970i	−1.88823	+	0.174970i	−0.914794	+	0.403921i	$0.867647\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.686841	+	0.425274i	0.686841	+	0.425274i
$439$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$439$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$440$		0			0
$441$	0.982973	−	0.183750i	0.982973	−	0.183750i
$442$		0			0
$443$	0.765964	+	1.73474i	0.765964	+	1.73474i	0.673696	+	0.739009i	$0.264706\pi$
$443$	0.765964	+	1.73474i	0.765964	+	1.73474i	0.0922684	+	0.995734i	$0.470588\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.72198	+	0.489946i	−1.72198	+	0.489946i	−0.982973	−	0.183750i	$-0.941176\pi$
$449$	−1.72198	+	0.489946i	−1.72198	+	0.489946i	−0.739009	+	0.673696i	$0.764706\pi$
$450$	1.00000			1.00000
$451$	−0.152642	+	2.19911i	−0.152642	+	2.19911i
$452$	0.0176784	−	0.0426793i	0.0176784	−	0.0426793i
$453$		0			0
$454$	0.225523	+	1.94389i	0.225523	+	1.94389i
$455$		0			0
$456$	0.982973	+	0.816250i	0.982973	+	0.816250i
$457$	1.24710	+	1.19078i	1.24710	+	1.19078i	0.973438	+	0.228951i	$0.0735294\pi$
$457$	1.24710	+	1.19078i	1.24710	+	1.19078i	0.273663	+	0.961826i	$0.411765\pi$
$458$		0			0
$459$	−0.204198	+	0.186151i	−0.204198	+	0.186151i
$460$		0			0
$461$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$461$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$462$		0			0
$463$		0			0		−0.967890	−	0.251374i	$-0.919118\pi$
$463$		0			0		0.967890	+	0.251374i	$0.0808824\pi$
$464$		0			0
$465$		0			0
$466$	−1.22468	−	0.881170i	−1.22468	−	0.881170i
$467$	−1.85699	−	0.172075i	−1.85699	−	0.172075i	−0.895163	−	0.445738i	$-0.852941\pi$
$467$	−1.85699	−	0.172075i	−1.85699	−	0.172075i	−0.961826	+	0.273663i	$0.911765\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.0486249	−	1.05174i	−0.0486249	−	1.05174i
$473$	0.687249	+	1.46399i	0.687249	+	1.46399i
$474$		0			0
$475$	0.234776	+	1.25594i	0.234776	+	1.25594i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$479$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$480$		0			0
$481$		0			0
$482$	1.30974	−	1.50512i	1.30974	−	1.50512i
$483$		0			0
$484$	1.52098	−	0.284320i	1.52098	−	0.284320i
$485$		0			0
$486$	−0.932472	+	0.361242i	−0.932472	+	0.361242i
$487$		0			0		0.998933	−	0.0461835i	$-0.0147059\pi$
$487$		0			0		−0.998933	+	0.0461835i	$0.985294\pi$
$488$		0			0
$489$	−0.665182	+	1.13191i	−0.665182	+	1.13191i
$490$		0			0
$491$	−0.0952471	+	0.307582i	−0.0952471	+	0.307582i	−0.990410	−	0.138156i	$-0.955882\pi$
$491$	−0.0952471	+	0.307582i	−0.0952471	+	0.307582i	0.895163	+	0.445738i	$0.147059\pi$
$492$	1.35143	−	0.285081i	1.35143	−	0.285081i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.399555	+	0.103770i	0.399555	+	0.103770i
$499$	−1.37821	−	0.533922i	−1.37821	−	0.533922i	−0.445738	−	0.895163i	$-0.647059\pi$
$499$	−1.37821	−	0.533922i	−1.37821	−	0.533922i	−0.932472	+	0.361242i	$0.882353\pi$
$500$		0			0
$501$		0			0
$502$	−1.33682	+	1.40005i	−1.33682	+	1.40005i
$503$		0			0		−0.545930	−	0.837831i	$-0.683824\pi$
$503$		0			0		0.545930	+	0.837831i	$0.316176\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$508$		0			0
$509$		0			0		0.565136	−	0.824997i	$-0.308824\pi$
$509$		0			0		−0.565136	+	0.824997i	$0.691176\pi$
$510$		0			0
$511$		0			0
$512$	0.486604	−	0.873622i	0.486604	−	0.873622i
$513$	−0.672619	−	1.08632i	−0.672619	−	1.08632i
$514$	−0.646741	+	0.322039i	−0.646741	+	0.322039i
$515$		0			0
$516$	0.764411	−	0.665182i	0.764411	−	0.665182i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.949551	+	1.09120i	0.949551	+	1.09120i	0.995734	+	0.0922684i	$0.0294118\pi$
$521$	0.949551	+	1.09120i	0.949551	+	1.09120i	−0.0461835	+	0.998933i	$0.514706\pi$
$522$		0			0
$523$	−1.27754	−	0.428189i	−1.27754	−	0.428189i	−0.403921	−	0.914794i	$-0.632353\pi$
$523$	−1.27754	−	0.428189i	−1.27754	−	0.428189i	−0.873622	+	0.486604i	$0.838235\pi$
$524$	0.0348125	+	0.501541i	0.0348125	+	0.501541i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.711414	−	1.42871i	−0.711414	−	1.42871i
$529$	0.486604	+	0.873622i	0.486604	+	0.873622i
$530$		0			0
$531$	−0.288130	+	1.01267i	−0.288130	+	1.01267i
$532$		0			0
$533$		0			0
$534$	−1.23354	−	1.55732i	−1.23354	−	1.55732i
$535$		0			0
$536$	−0.890856	+	0.275866i	−0.890856	+	0.275866i
$537$	−1.62301	+	1.16777i	−1.62301	+	1.16777i
$538$		0			0
$539$	0.0737104	−	1.59433i	0.0737104	−	1.59433i
$540$		0			0
$541$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$541$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$542$		0			0
$543$		0			0
$544$	−0.123163	+	0.247345i	−0.123163	+	0.247345i
$545$		0			0
$546$		0			0
$547$			1.86494i			1.86494i	0.361242	+	0.932472i	$0.382353\pi$
$547$			1.86494i			1.86494i	−0.361242	+	0.932472i	$0.617647\pi$
$548$	−0.824997	+	0.565136i	−0.824997	+	0.565136i
$549$		0			0
$550$	0.365413	−	1.55364i	0.365413	−	1.55364i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.27224	−	1.53210i	1.27224	−	1.53210i
$557$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$557$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.214595	+	0.385271i	0.214595	+	0.385271i
$562$	0.0666624	+	0.172075i	0.0666624	+	0.172075i
$563$	−0.361242	−	0.0675278i	−0.361242	−	0.0675278i		−	1.00000i	$-0.5\pi$
$563$	−0.361242	−	0.0675278i	−0.361242	−	0.0675278i	−0.361242	+	0.932472i	$0.617647\pi$
$564$		0			0
$565$		0			0
$566$	0.546742	−	1.92160i	0.546742	−	1.92160i
$567$		0			0
$568$		0			0
$569$	−1.84063	−	0.388276i	−1.84063	−	0.388276i	−0.850217	−	0.526432i	$-0.823529\pi$
$569$	−1.84063	−	0.388276i	−1.84063	−	0.388276i	−0.990410	+	0.138156i	$0.955882\pi$
$570$		0			0
$571$	−0.848980	+	1.44467i	−0.848980	+	1.44467i	0.0461835	+	0.998933i	$0.485294\pi$
$571$	−0.848980	+	1.44467i	−0.848980	+	1.44467i	−0.895163	+	0.445738i	$0.852941\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$577$	−1.75231	+	0.455097i	−1.75231	+	0.455097i	−0.982973	−	0.183750i	$-0.941176\pi$
$577$	−1.75231	+	0.455097i	−1.75231	+	0.455097i	−0.769334	+	0.638847i	$0.779412\pi$
$578$	−0.373082	+	0.844951i	−0.373082	+	0.844951i
$579$	−0.359191	+	0.524354i	−0.359191	+	0.524354i
$580$		0			0
$581$		0			0
$582$	−0.0956383	−	0.100162i	−0.0956383	−	0.100162i
$583$		0			0
$584$	−0.705749	−	0.393100i	−0.705749	−	0.393100i
$585$		0			0
$586$		0			0
$587$	−1.58701	−	1.08713i	−1.58701	−	1.08713i	−0.948161	−	0.317791i	$-0.897059\pi$
$587$	−1.58701	−	1.08713i	−1.58701	−	1.08713i	−0.638847	−	0.769334i	$-0.720588\pi$
$588$	−0.973438	+	0.228951i	−0.973438	+	0.228951i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.978656	−	0.637691i	0.978656	−	0.637691i	0.0461835	−	0.998933i	$-0.485294\pi$
$593$	0.978656	−	0.637691i	0.978656	−	0.637691i	0.932472	+	0.361242i	$0.117647\pi$
$594$	0.220502	+	1.58073i	0.220502	+	1.58073i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.993337	−	0.115243i	$-0.963235\pi$
$599$		0			0		0.993337	+	0.115243i	$0.0367647\pi$
$600$	−0.998933	+	0.0461835i	−0.998933	+	0.0461835i
$601$	−1.31353	−	1.04043i	−1.31353	−	1.04043i	−0.995734	−	0.0922684i	$-0.970588\pi$
$601$	−1.31353	−	1.04043i	−1.31353	−	1.04043i	−0.317791	−	0.948161i	$-0.602941\pi$
$602$		0			0
$603$	0.932343	+	0.0215409i	0.932343	+	0.0215409i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$607$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$608$	−1.01962	−	0.769982i	−1.01962	−	0.769982i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.195383	−	0.195383i	0.195383	−	0.195383i
$613$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$613$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$614$	1.33468	+	1.16142i	1.33468	+	1.16142i
$615$		0			0
$616$		0			0
$617$	1.70083	−	0.400033i	1.70083	−	0.400033i	0.739009	−	0.673696i	$-0.235294\pi$
$617$	1.70083	−	0.400033i	1.70083	−	0.400033i	0.961826	+	0.273663i	$0.0882353\pi$
$618$		0			0
$619$	1.36575	+	1.18846i	1.36575	+	1.18846i	0.961826	+	0.273663i	$0.0882353\pi$
$619$	1.36575	+	1.18846i	1.36575	+	1.18846i	0.403921	+	0.914794i	$0.367647\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.798017	−	0.602635i	−0.798017	−	0.602635i
$626$	−1.29123	+	1.17711i	−1.29123	+	1.17711i
$627$	−1.93353	+	0.648054i	−1.93353	+	0.648054i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.466296	−	0.884629i	$-0.654412\pi$
$631$		0			0		0.466296	+	0.884629i	$0.345588\pi$
$632$		0			0
$633$	0.457413	−	0.0211475i	0.457413	−	0.0211475i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.276018	+	1.97871i	−0.276018	+	1.97871i	−0.0922684	+	0.995734i	$0.529412\pi$
$641$	−0.276018	+	1.97871i	−0.276018	+	1.97871i	−0.183750	+	0.982973i	$0.558824\pi$
$642$	0.794087	+	1.79844i	0.794087	+	1.79844i
$643$	−0.288627	+	0.614838i	−0.288627	+	0.614838i	−0.995734	−	0.0922684i	$-0.970588\pi$
$643$	−0.288627	+	0.614838i	−0.288627	+	0.614838i	0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$	0.291260	+	0.199517i	0.291260	+	0.199517i
$647$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$647$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$648$	0.914794	−	0.403921i	0.914794	−	0.403921i
$649$	1.46804	+	0.817694i	1.46804	+	0.817694i
$650$		0			0
$651$		0			0
$652$	0.612196	−	1.16142i	0.612196	−	1.16142i
$653$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$653$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$654$		0			0
$655$		0			0
$656$	−1.33682	+	0.347190i	−1.33682	+	0.347190i
$657$	0.544240	+	0.597002i	0.544240	+	0.597002i
$658$		0			0
$659$	−0.0387043	+	1.67521i	−0.0387043	+	1.67521i	0.526432	+	0.850217i	$0.323529\pi$
$659$	−0.0387043	+	1.67521i	−0.0387043	+	1.67521i	−0.565136	+	0.824997i	$0.691176\pi$
$660$		0			0
$661$		0			0		0.997600	−	0.0692444i	$-0.0220588\pi$
$661$		0			0		−0.997600	+	0.0692444i	$0.977941\pi$
$662$	0.387776	−	0.659861i	0.387776	−	0.659861i
$663$		0			0
$664$	−0.403921	−	0.0852061i	−0.403921	−	0.0852061i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.572616	−	1.84915i	−0.572616	−	1.84915i	−0.526432	−	0.850217i	$-0.676471\pi$
$673$	−0.572616	−	1.84915i	−0.572616	−	1.84915i	−0.0461835	−	0.998933i	$-0.514706\pi$
$674$	−0.581427	−	1.73474i	−0.581427	−	1.73474i
$675$	0.961826	+	0.273663i	0.961826	+	0.273663i
$676$	0.998933	+	0.0461835i	0.998933	+	0.0461835i
$677$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$677$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$678$	0.0286833	−	0.0362122i	0.0286833	−	0.0362122i
$679$		0			0
$680$		0			0
$681$	−0.315058	+	1.93141i	−0.315058	+	1.93141i
$682$		0			0
$683$	0.418885	−	1.78099i	0.418885	−	1.78099i	−0.183750	−	0.982973i	$-0.558824\pi$
$683$	0.418885	−	1.78099i	0.418885	−	1.78099i	0.602635	−	0.798017i	$-0.294118\pi$
$684$	0.722071	+	1.05409i	0.722071	+	1.05409i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.732875	+	0.699775i	−0.732875	+	0.699775i
$689$		0			0
$690$		0			0
$691$	−0.936174	−	1.59305i	−0.936174	−	1.59305i	−0.798017	−	0.602635i	$-0.794118\pi$
$691$	−0.936174	−	1.59305i	−0.936174	−	1.59305i	−0.138156	−	0.990410i	$-0.544118\pi$
$692$		0			0
$693$		0			0
$694$	0.0682600	−	1.47644i	0.0682600	−	1.47644i
$695$		0			0
$696$		0			0
$697$	0.364556	−	0.112890i	0.364556	−	0.112890i
$698$		0			0
$699$	−0.936790	−	1.18268i	−0.936790	−	1.18268i
$700$		0			0
$701$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$701$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$702$		0			0
$703$		0			0
$704$	0.776638	+	1.39433i	0.776638	+	1.39433i
$705$		0			0
$706$	0.225365	−	1.06835i	0.225365	−	1.06835i
$707$		0			0
$708$	0.241054	−	1.02490i	0.241054	−	1.02490i
$709$		0			0		−0.0692444	−	0.997600i	$-0.522059\pi$
$709$		0			0		0.0692444	+	0.997600i	$0.477941\pi$
$710$		0			0
$711$		0			0
$712$	1.30415	+	1.49869i	1.30415	+	1.49869i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.56735	−	1.24148i	1.56735	−	1.24148i
$717$		0			0
$718$		0			0
$719$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$719$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$720$		0			0
$721$		0			0
$722$	−0.447246	+	0.447246i	−0.447246	+	0.447246i
$723$	1.67164	−	1.08924i	1.67164	−	1.08924i
$724$		0			0
$725$		0			0
$726$	1.54073	+	0.142769i	1.54073	+	0.142769i
$727$		0			0		−0.905220	−	0.424943i	$-0.860294\pi$
$727$		0			0		0.905220	+	0.424943i	$0.139706\pi$
$728$		0			0
$729$	−0.995734	+	0.0922684i	−0.995734	+	0.0922684i
$730$		0			0
$731$	0.193357	−	0.202503i	0.193357	−	0.202503i
$732$		0			0
$733$		0			0		−0.986955	−	0.160996i	$-0.948529\pi$
$733$		0			0		0.986955	+	0.160996i	$0.0514706\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.374157	−	1.44065i	0.374157	−	1.44065i
$738$	1.37786	+	0.0956383i	1.37786	+	0.0956383i
$739$	−1.43615	+	0.757007i	−1.43615	+	0.757007i	−0.990410	−	0.138156i	$-0.955882\pi$
$739$	−1.43615	+	0.757007i	−1.43615	+	0.757007i	−0.445738	+	0.895163i	$0.647059\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.999733	−	0.0230979i	$-0.00735294\pi$
$743$		0			0		−0.999733	+	0.0230979i	$0.992647\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.355904	+	0.209152i	0.355904	+	0.209152i
$748$	−0.232159	−	0.374950i	−0.232159	−	0.374950i
$749$		0			0
$750$		0			0
$751$		0			0		0.656446	−	0.754373i	$-0.272059\pi$
$751$		0			0		−0.656446	+	0.754373i	$0.727941\pi$
$752$		0			0
$753$	−1.66893	+	0.980770i	−1.66893	+	0.980770i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$757$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$758$	0.328972	+	1.75984i	0.328972	+	1.75984i
$759$		0			0
$760$		0			0
$761$	−0.0169724	−	0.367107i	−0.0169724	−	0.367107i	−0.990410	−	0.138156i	$-0.955882\pi$
$761$	−0.0169724	−	0.367107i	−0.0169724	−	0.367107i	0.973438	−	0.228951i	$-0.0735294\pi$
$762$		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
$769$	−0.199927	+	0.252404i	−0.199927	+	0.252404i	−0.873622	−	0.486604i	$-0.838235\pi$
$769$	−0.199927	+	0.252404i	−0.199927	+	0.252404i	0.673696	+	0.739009i	$0.264706\pi$
$770$		0			0
$771$	−0.710182	+	0.132756i	−0.710182	+	0.132756i
$772$	0.334591	−	0.540383i	0.334591	−	0.540383i
$773$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$773$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$774$	0.917266	−	0.430598i	0.917266	−	0.430598i
$775$		0			0
$776$	0.100162	+	0.0956383i	0.100162	+	0.0956383i
$777$		0			0
$778$		0			0
$779$	0.203371	+	1.75296i	0.203371	+	1.75296i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.961826	−	0.273663i	0.961826	−	0.273663i
$785$		0			0
$786$	−0.103770	+	0.491922i	−0.103770	+	0.491922i
$787$	1.41908	+	0.512381i	1.41908	+	0.512381i	0.932472	−	0.361242i	$-0.117647\pi$
$787$	1.41908	+	0.512381i	1.41908	+	0.512381i	0.486604	+	0.873622i	$0.338235\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.293271	−	1.56886i	−0.293271	−	1.56886i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$797$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$798$		0			0
$799$		0			0
$800$	0.995734	−	0.0922684i	0.995734	−	0.0922684i
$801$	−0.760267	−	1.83545i	−0.760267	−	1.83545i
$802$	−0.136828	−	0.838799i	−0.136828	−	0.838799i
$803$	1.12640	−	0.627400i	1.12640	−	0.627400i
$804$	−0.932343	+	0.0215409i	−0.932343	+	0.0215409i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.93141	−	0.407425i	1.93141	−	0.407425i	0.932472	−	0.361242i	$-0.117647\pi$
$809$	1.93141	−	0.407425i	1.93141	−	0.407425i	0.998933	−	0.0461835i	$-0.0147059\pi$
$810$		0			0
$811$	1.84595	−	0.618701i	1.84595	−	0.618701i	0.850217	−	0.526432i	$-0.176471\pi$
$811$	1.84595	−	0.618701i	1.84595	−	0.618701i	0.995734	−	0.0922684i	$-0.0294118\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.186151	+	0.204198i	−0.186151	+	0.204198i
$817$	0.756156	+	1.05094i	0.756156	+	1.05094i
$818$	−0.798017	−	0.397365i	−0.798017	−	0.397365i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	−0.948161	+	0.317791i	−0.948161	+	0.317791i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	0.776638	−	1.39433i	0.776638	−	1.39433i
$826$		0			0
$827$	−0.844817	−	1.17416i	−0.844817	−	1.17416i	−0.982973	−	0.183750i	$-0.941176\pi$
$827$	−0.844817	−	1.17416i	−0.844817	−	1.17416i	0.138156	−	0.990410i	$-0.455882\pi$
$828$		0			0
$829$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$829$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.261989	+	0.0878098i	−0.261989	+	0.0878098i
$834$	1.64296	−	1.12545i	1.64296	−	1.12545i
$835$		0			0
$836$	1.90154	−	0.736660i	1.90154	−	0.736660i
$837$		0			0
$838$	0.537235	+	0.711414i	0.537235	+	0.711414i
$839$		0			0		−0.638847	−	0.769334i	$-0.720588\pi$
$839$		0			0		0.638847	+	0.769334i	$0.279412\pi$
$840$		0			0
$841$	−0.873622	+	0.486604i	−0.873622	+	0.486604i
$842$		0			0
$843$	0.0170269	+	0.183750i	0.0170269	+	0.183750i
$844$	−0.455948	+	0.0422498i	−0.455948	+	0.0422498i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.05174	−	1.69862i	1.05174	−	1.69862i
$850$	−0.273663	+	0.0381744i	−0.273663	+	0.0381744i
$851$		0			0
$852$		0			0
$853$		0			0		−0.620906	−	0.783885i	$-0.713235\pi$
$853$		0			0		0.620906	+	0.783885i	$0.286765\pi$
$854$		0			0
$855$		0			0
$856$	−0.876298	−	1.75984i	−0.876298	−	1.75984i
$857$	1.66411	+	0.600853i	1.66411	+	0.600853i	0.990410	−	0.138156i	$-0.0441176\pi$
$857$	1.66411	+	0.600853i	1.66411	+	0.600853i	0.673696	+	0.739009i	$0.264706\pi$
$858$		0			0
$859$	−0.510873	−	0.510873i	−0.510873	−	0.510873i	0.403921	−	0.914794i	$-0.367647\pi$
$859$	−0.510873	−	0.510873i	−0.510873	−	0.510873i	−0.914794	+	0.403921i	$0.867647\pi$
$860$		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	$0.625000\pi$
$864$	−0.895163	+	0.445738i	−0.895163	+	0.445738i
$865$		0			0
$866$	1.87814	+	0.261989i	1.87814	+	0.261989i
$867$	−0.590072	+	0.710596i	−0.590072	+	0.710596i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.0645767	−	0.122511i	−0.0645767	−	0.122511i
$874$		0			0
$875$		0			0
$876$	−0.571231	−	0.571231i	−0.571231	−	0.571231i
$877$		0			0		−0.811724	−	0.584041i	$-0.801471\pi$
$877$		0			0		0.811724	+	0.584041i	$0.198529\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.27754	−	1.40140i	−1.27754	−	1.40140i	−0.873622	−	0.486604i	$-0.838235\pi$
$881$	−1.27754	−	1.40140i	−1.27754	−	1.40140i	−0.403921	−	0.914794i	$-0.632353\pi$
$882$	−0.998933	−	0.0461835i	−0.998933	−	0.0461835i
$883$	−0.00852254	−	0.184340i	−0.00852254	−	0.184340i	−0.998933	−	0.0461835i	$-0.985294\pi$
$883$	−0.00852254	−	0.184340i	−0.00852254	−	0.184340i	0.990410	−	0.138156i	$-0.0441176\pi$
$884$		0			0
$885$		0			0
$886$	−0.348448	−	1.86403i	−0.348448	−	1.86403i
$887$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$887$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.220502	+	1.58073i	−0.220502	+	1.58073i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.78842	−	0.0826835i	1.78842	−	0.0826835i
$899$		0			0
$900$	−0.973438	−	0.228951i	−0.973438	−	0.228951i
$901$		0			0
$902$	0.652074	−	2.10575i	0.652074	−	2.10575i
$903$		0			0
$904$	−0.0269802	+	0.0374982i	−0.0269802	+	0.0374982i
$905$		0			0
$906$		0			0
$907$	0.274465	−	1.05680i	0.274465	−	1.05680i	−0.673696	−	0.739009i	$-0.735294\pi$
$907$	0.274465	−	1.05680i	0.274465	−	1.05680i	0.948161	−	0.317791i	$-0.102941\pi$
$908$	0.225523	−	1.94389i	0.225523	−	1.94389i
$909$		0			0
$910$		0			0
$911$		0			0		−0.986955	−	0.160996i	$-0.948529\pi$
$911$		0			0		0.986955	+	0.160996i	$0.0514706\pi$
$912$	−0.769982	−	1.01962i	−0.769982	−	1.01962i
$913$	0.454999	−	0.476521i	0.454999	−	0.476521i
$914$	−0.941347	−	1.44467i	−0.941347	−	1.44467i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.241393	−	0.134455i	0.241393	−	0.134455i
$919$		0			0		−0.997600	−	0.0692444i	$-0.977941\pi$
$919$		0			0		0.997600	+	0.0692444i	$0.0220588\pi$
$920$		0			0
$921$	0.965891	+	1.48234i	0.965891	+	1.48234i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.890286	+	0.393100i	0.890286	+	0.393100i	0.798017	−	0.602635i	$-0.205882\pi$
$929$	0.890286	+	0.393100i	0.890286	+	0.393100i	0.0922684	+	0.995734i	$0.470588\pi$
$930$		0			0
$931$	−0.176521	−	1.26544i	−0.176521	−	1.26544i
$932$	0.990410	+	1.13816i	0.990410	+	1.13816i
$933$		0			0
$934$	1.76827	+	0.592663i	1.76827	+	0.592663i
$935$		0			0
$936$		0			0
$937$	0.00852254	+	0.0919729i	0.00852254	+	0.0919729i	0.998933	−	0.0461835i	$-0.0147059\pi$
$937$	0.00852254	+	0.0919729i	0.00852254	+	0.0919729i	−0.990410	+	0.138156i	$0.955882\pi$
$938$		0			0
$939$	−1.56407	+	0.778814i	−1.56407	+	0.778814i
$940$		0			0
$941$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$941$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$942$		0			0
$943$		0			0
$944$	−0.193463	+	1.03494i	−0.193463	+	1.03494i
$945$		0			0
$946$	−0.333813	−	1.58245i	−0.333813	−	1.58245i
$947$	−1.11581	+	0.345526i	−1.11581	+	0.345526i	−0.798017	−	0.602635i	$-0.794118\pi$
$947$	−1.11581	+	0.345526i	−1.11581	+	0.345526i	−0.317791	+	0.948161i	$0.602941\pi$
$948$		0			0
$949$		0			0
$950$	0.0590083	−	1.27633i	0.0590083	−	1.27633i
$951$		0			0
$952$		0			0
$953$	−0.794316	−	1.35165i	−0.794316	−	1.35165i	−0.932472	−	0.361242i	$-0.882353\pi$
$953$	−0.794316	−	1.35165i	−0.794316	−	1.35165i	0.138156	−	0.990410i	$-0.455882\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.228951	+	0.973438i	−0.228951	+	0.973438i
$962$		0			0
$963$	0.271608	+	1.94709i	0.271608	+	1.94709i
$964$	−1.61955	+	1.16528i	−1.61955	+	1.16528i
$965$		0			0
$966$		0			0
$967$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$967$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$968$	−1.54567	−	0.0714609i	−1.54567	−	0.0714609i
$969$	0.225540	+	0.271608i	0.225540	+	0.271608i
$970$		0			0
$971$	0.251402	+	0.811852i	0.251402	+	0.811852i	0.990410	+	0.138156i	$0.0441176\pi$
$971$	0.251402	+	0.811852i	0.251402	+	0.811852i	−0.739009	+	0.673696i	$0.764706\pi$
$972$	0.990410	−	0.138156i	0.990410	−	0.138156i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.387018	−	1.36023i	0.387018	−	1.36023i	−0.486604	−	0.873622i	$-0.661765\pi$
$977$	0.387018	−	1.36023i	0.387018	−	1.36023i	0.873622	−	0.486604i	$-0.161765\pi$
$978$	0.906665	−	0.949551i	0.906665	−	0.949551i
$979$	−3.12944	+	0.510486i	−3.12944	+	0.510486i
$980$		0			0
$981$		0			0
$982$	0.163138	−	0.277605i	0.163138	−	0.277605i
$983$		0			0		0.997600	−	0.0692444i	$-0.0220588\pi$
$983$		0			0		−0.997600	+	0.0692444i	$0.977941\pi$
$984$	−1.38080	−	0.0319021i	−1.38080	−	0.0319021i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$991$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$992$		0			0
$993$	0.553552	−	0.528551i	0.553552	−	0.528551i
$994$		0			0
$995$		0			0
$996$	−0.365184	−	0.192492i	−0.365184	−	0.192492i
$997$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$997$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$998$	1.21936	+	0.835282i	1.21936	+	0.835282i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3288.1.cj.b.659.1	yes	64
3.2	odd	2		3288.1.cj.a.659.1	✓	64
8.3	odd	2	CM	3288.1.cj.b.659.1	yes	64
24.11	even	2		3288.1.cj.a.659.1	✓	64
137.79	odd	136		3288.1.cj.a.2819.1	yes	64
411.353	even	136	inner	3288.1.cj.b.2819.1	yes	64
1096.627	even	136		3288.1.cj.a.2819.1	yes	64
3288.2819	odd	136	inner	3288.1.cj.b.2819.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3288.1.cj.a.659.1	✓	64	3.2	odd	2
3288.1.cj.a.659.1	✓	64	24.11	even	2
3288.1.cj.a.2819.1	yes	64	137.79	odd	136
3288.1.cj.a.2819.1	yes	64	1096.627	even	136
3288.1.cj.b.659.1	yes	64	1.1	even	1	trivial
3288.1.cj.b.659.1	yes	64	8.3	odd	2	CM
3288.1.cj.b.2819.1	yes	64	411.353	even	136	inner
3288.1.cj.b.2819.1	yes	64	3288.2819	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)

\(f(q)\)	\(=\)	\(q+(-0.973438 - 0.228951i) q^{2} +(-0.873622 - 0.486604i) q^{3} +(0.895163 + 0.445738i) q^{4} +(0.739009 + 0.673696i) q^{6} +(-0.769334 - 0.638847i) q^{8} +(0.526432 + 0.850217i) q^{9} +O(q^{10})\)	\(q+(-0.973438 - 0.228951i) q^{2} +(-0.873622 - 0.486604i) q^{3} +(0.895163 + 0.445738i) q^{4} +(0.739009 + 0.673696i) q^{6} +(-0.769334 - 0.638847i) q^{8} +(0.526432 + 0.850217i) q^{9} +(1.51330 - 0.507206i) q^{11} +(-0.565136 - 0.824997i) q^{12} +(0.602635 + 0.798017i) q^{16} +(-0.176521 - 0.212577i) q^{17} +(-0.317791 - 0.948161i) q^{18} +(1.11622 - 0.621731i) q^{19} +(-1.58923 + 0.147263i) q^{22} +(0.361242 + 0.932472i) q^{24} +(-0.317791 + 0.948161i) q^{25} +(-0.0461835 - 0.998933i) q^{27} +(-0.403921 - 0.914794i) q^{32} +(-1.56886 - 0.293271i) q^{33} +(0.123163 + 0.247345i) q^{34} +(0.0922684 + 0.995734i) q^{36} +(-1.22892 + 0.349657i) q^{38} +(-0.528551 + 1.27604i) q^{41} +(0.116777 + 1.00656i) q^{43} +(1.58073 + 0.220502i) q^{44} +(-0.138156 - 0.990410i) q^{48} +(0.361242 - 0.932472i) q^{49} +(0.526432 - 0.850217i) q^{50} +(0.0507723 + 0.271608i) q^{51} +(-0.183750 + 0.982973i) q^{54} -1.27769 q^{57} +(0.709310 + 0.778076i) q^{59} +(0.183750 + 0.982973i) q^{64} +(1.46004 + 0.644672i) q^{66} +(0.509130 - 0.781354i) q^{67} +(-0.0632619 - 0.268973i) q^{68} +(0.138156 - 0.990410i) q^{72} +(0.794087 - 0.148441i) q^{73} +(0.739009 - 0.673696i) q^{75} +(1.27633 - 0.0590083i) q^{76} +(-0.445738 + 0.895163i) q^{81} +(0.806661 - 1.12113i) q^{82} +(0.365184 - 0.192492i) q^{83} +(0.116777 - 1.00656i) q^{86} +(-1.48826 - 0.576554i) q^{88} +(-1.96076 - 0.319846i) q^{89} +(-0.0922684 + 0.995734i) q^{96} +(-0.138156 - 0.00958957i) q^{97} +(-0.565136 + 0.824997i) q^{98} +(1.22788 + 1.01962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{6}+O(q^{10}) \) 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

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