LMFDB - Embedded newform 3620.1.dy.a.1939.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3620,1,Mod(219,3620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3620, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([45, 45, 68]))

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

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

chi := DirichletCharacter("3620.219");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3620 = 2^{2} \cdot 5 \cdot 181 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3620.dy (of order $90$, degree $24$, 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:	$1.80661534573$
Analytic rank:	$0$
Dimension:	$24$
Coefficient field:	$\Q(\zeta_{45})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 $ x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{45}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{45} - \cdots)$

Embedding invariants

Embedding label			1939.1
Root			$-0.615661 - 0.788011i$ of defining polynomial
Character	$\chi$	$=$	3620.1939
Dual form			3620.1.dy.a.2259.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.241922 + 0.970296i) q^{2} +(0.0916445 - 0.187899i) q^{3} +(-0.882948 + 0.469472i) q^{4} +(0.913545 - 0.406737i) q^{5} +(0.204489 + 0.0434654i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(-0.669131 - 0.743145i) q^{8} +(0.588754 + 0.753571i) q^{9} +O(q^{10})$	\(q+(0.241922 + 0.970296i) q^{2} +(0.0916445 - 0.187899i) q^{3} +(-0.882948 + 0.469472i) q^{4} +(0.913545 - 0.406737i) q^{5} +(0.204489 + 0.0434654i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(-0.669131 - 0.743145i) q^{8} +(0.588754 + 0.753571i) q^{9} +(0.615661 + 0.788011i) q^{10} +(0.00729598 + 0.208930i) q^{12} +(1.35192 - 1.30553i) q^{14} +(0.00729598 - 0.208930i) q^{15} +(0.559193 - 0.829038i) q^{16} +(-0.588754 + 0.753571i) q^{18} +(-0.615661 + 0.788011i) q^{20} +(-0.391941 + 0.0274072i) q^{21} +(0.328433 + 0.812901i) q^{23} +(-0.200958 + 0.0576239i) q^{24} +(0.669131 - 0.743145i) q^{25} +(0.400040 - 0.0850311i) q^{27} +(1.59381 + 0.995922i) q^{28} +(-1.33500 - 1.48267i) q^{29} +(0.204489 - 0.0434654i) q^{30} +(0.939693 + 0.342020i) q^{32} +(-1.52045 - 1.10467i) q^{35} +(-0.873619 - 0.388960i) q^{36} +(-0.913545 - 0.406737i) q^{40} +(1.51718 + 0.213226i) q^{41} +(-0.121412 - 0.373669i) q^{42} +(-0.333843 - 1.89332i) q^{43} +(0.844359 + 0.448953i) q^{45} +(-0.709299 + 0.515336i) q^{46} +(-0.0467046 - 1.33745i) q^{47} +(-0.104528 - 0.181049i) q^{48} +(-1.26604 + 2.19285i) q^{49} +(0.882948 + 0.469472i) q^{50} +(0.179284 + 0.367586i) q^{54} +(-0.580762 + 1.78740i) q^{56} +(1.11566 - 1.65404i) q^{58} +(0.0916445 + 0.187899i) q^{60} +(1.51718 - 1.27306i) q^{61} +(0.673261 - 1.66638i) q^{63} +(-0.104528 + 0.994522i) q^{64} +(1.78716 + 0.379874i) q^{67} +(0.182843 + 0.0127856i) q^{69} +(0.704030 - 1.74254i) q^{70} +(0.166059 - 0.941767i) q^{72} +(-0.0783141 - 0.193834i) q^{75} +(0.173648 - 0.984808i) q^{80} +(-0.210665 + 0.844929i) q^{81} +(0.160147 + 1.52370i) q^{82} +(-0.594092 - 0.170353i) q^{83} +(0.333197 - 0.208204i) q^{84} +(1.75631 - 0.781961i) q^{86} +(-0.400938 + 0.114967i) q^{87} +(-1.35275 - 1.13510i) q^{89} +(-0.231349 + 0.927889i) q^{90} +(-0.671624 - 0.563559i) q^{92} +(1.28642 - 0.368875i) q^{94} +(0.150383 - 0.145223i) q^{96} +(-2.43400 - 0.697938i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8}+O(q^{10}) $ 24 * q + 3 * q^5 - 3 * q^6 - 3 * q^8	$ 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{14} - 18 q^{21} - 3 q^{23} + 3 q^{25} + 12 q^{27} - 3 q^{28} - 3 q^{30} - 3 q^{40} + 3 q^{41} - 3 q^{43} + 3 q^{48} - 12 q^{49} + 12 q^{58} + 3 q^{61} + 15 q^{63} + 3 q^{64} + 3 q^{67} - 3 q^{69} + 3 q^{70} - 3 q^{84} + 3 q^{87} + 3 q^{89} - 3 q^{92} - 3 q^{98}+O(q^{100}) $ 24 * q + 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^14 - 18 * q^21 - 3 * q^23 + 3 * q^25 + 12 * q^27 - 3 * q^28 - 3 * q^30 - 3 * q^40 + 3 * q^41 - 3 * q^43 + 3 * q^48 - 12 * q^49 + 12 * q^58 + 3 * q^61 + 15 * q^63 + 3 * q^64 + 3 * q^67 - 3 * q^69 + 3 * q^70 - 3 * q^84 + 3 * q^87 + 3 * q^89 - 3 * q^92 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3620\mathbb{Z}\right)^\times$.

$n$	$1811$	$2897$	$3441$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{19}{45}\right)$

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 $

$2$	0.241922	+	0.970296i	0.241922	+	0.970296i
$2$	0.241922	+	0.970296i	0.241922	+	0.970296i
$3$	0.0916445	−	0.187899i	0.0916445	−	0.187899i	−0.848048	−	0.529919i	$-0.822222\pi$
$3$	0.0916445	−	0.187899i	0.0916445	−	0.187899i	0.939693	+	0.342020i	$0.111111\pi$
$4$	−0.882948	+	0.469472i	−0.882948	+	0.469472i
$5$	0.913545	−	0.406737i	0.913545	−	0.406737i
$5$	0.913545	−	0.406737i	0.913545	−	0.406737i
$6$	0.204489	+	0.0434654i	0.204489	+	0.0434654i
$7$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$7$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$8$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$9$	0.588754	+	0.753571i	0.588754	+	0.753571i
$10$	0.615661	+	0.788011i	0.615661	+	0.788011i
$11$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$11$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$12$	0.00729598	+	0.208930i	0.00729598	+	0.208930i
$13$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$13$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$14$	1.35192	−	1.30553i	1.35192	−	1.30553i
$15$	0.00729598	−	0.208930i	0.00729598	−	0.208930i
$16$	0.559193	−	0.829038i	0.559193	−	0.829038i
$17$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$17$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$18$	−0.588754	+	0.753571i	−0.588754	+	0.753571i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−0.615661	+	0.788011i	−0.615661	+	0.788011i
$21$	−0.391941	+	0.0274072i	−0.391941	+	0.0274072i
$22$		0			0
$23$	0.328433	+	0.812901i	0.328433	+	0.812901i	0.997564	+	0.0697565i	$0.0222222\pi$
$23$	0.328433	+	0.812901i	0.328433	+	0.812901i	−0.669131	+	0.743145i	$0.733333\pi$
$24$	−0.200958	+	0.0576239i	−0.200958	+	0.0576239i
$25$	0.669131	−	0.743145i	0.669131	−	0.743145i
$26$		0			0
$27$	0.400040	−	0.0850311i	0.400040	−	0.0850311i
$28$	1.59381	+	0.995922i	1.59381	+	0.995922i
$29$	−1.33500	−	1.48267i	−1.33500	−	1.48267i	−0.719340	−	0.694658i	$-0.755556\pi$
$29$	−1.33500	−	1.48267i	−1.33500	−	1.48267i	−0.615661	−	0.788011i	$-0.711111\pi$
$30$	0.204489	−	0.0434654i	0.204489	−	0.0434654i
$31$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$31$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$32$	0.939693	+	0.342020i	0.939693	+	0.342020i
$33$		0			0
$34$		0			0
$35$	−1.52045	−	1.10467i	−1.52045	−	1.10467i
$36$	−0.873619	−	0.388960i	−0.873619	−	0.388960i
$37$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$37$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$38$		0			0
$39$		0			0
$40$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$41$	1.51718	+	0.213226i	1.51718	+	0.213226i	0.848048	−	0.529919i	$-0.177778\pi$
$41$	1.51718	+	0.213226i	1.51718	+	0.213226i	0.669131	+	0.743145i	$0.266667\pi$
$42$	−0.121412	−	0.373669i	−0.121412	−	0.373669i
$43$	−0.333843	−	1.89332i	−0.333843	−	1.89332i	−0.438371	−	0.898794i	$-0.644444\pi$
$43$	−0.333843	−	1.89332i	−0.333843	−	1.89332i	0.104528	−	0.994522i	$-0.466667\pi$
$44$		0			0
$45$	0.844359	+	0.448953i	0.844359	+	0.448953i
$46$	−0.709299	+	0.515336i	−0.709299	+	0.515336i
$47$	−0.0467046	−	1.33745i	−0.0467046	−	1.33745i	−0.766044	−	0.642788i	$-0.777778\pi$
$47$	−0.0467046	−	1.33745i	−0.0467046	−	1.33745i	0.719340	−	0.694658i	$-0.244444\pi$
$48$	−0.104528	−	0.181049i	−0.104528	−	0.181049i
$49$	−1.26604	+	2.19285i	−1.26604	+	2.19285i
$50$	0.882948	+	0.469472i	0.882948	+	0.469472i
$51$		0			0
$52$		0			0
$53$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$53$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$54$	0.179284	+	0.367586i	0.179284	+	0.367586i
$55$		0			0
$56$	−0.580762	+	1.78740i	−0.580762	+	1.78740i
$57$		0			0
$58$	1.11566	−	1.65404i	1.11566	−	1.65404i
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$	0.0916445	+	0.187899i	0.0916445	+	0.187899i
$61$	1.51718	−	1.27306i	1.51718	−	1.27306i	0.669131	−	0.743145i	$-0.266667\pi$
$61$	1.51718	−	1.27306i	1.51718	−	1.27306i	0.848048	−	0.529919i	$-0.177778\pi$
$62$		0			0
$63$	0.673261	−	1.66638i	0.673261	−	1.66638i
$64$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$65$		0			0
$66$		0			0
$67$	1.78716	+	0.379874i	1.78716	+	0.379874i	0.978148	−	0.207912i	$-0.0666667\pi$
$67$	1.78716	+	0.379874i	1.78716	+	0.379874i	0.809017	+	0.587785i	$0.200000\pi$
$68$		0			0
$69$	0.182843	+	0.0127856i	0.182843	+	0.0127856i
$70$	0.704030	−	1.74254i	0.704030	−	1.74254i
$71$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$71$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$72$	0.166059	−	0.941767i	0.166059	−	0.941767i
$73$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$73$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$74$		0			0
$75$	−0.0783141	−	0.193834i	−0.0783141	−	0.193834i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$79$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$80$	0.173648	−	0.984808i	0.173648	−	0.984808i
$81$	−0.210665	+	0.844929i	−0.210665	+	0.844929i
$82$	0.160147	+	1.52370i	0.160147	+	1.52370i
$83$	−0.594092	−	0.170353i	−0.594092	−	0.170353i	−0.0348995	−	0.999391i	$-0.511111\pi$
$83$	−0.594092	−	0.170353i	−0.594092	−	0.170353i	−0.559193	+	0.829038i	$0.688889\pi$
$84$	0.333197	−	0.208204i	0.333197	−	0.208204i
$85$		0			0
$86$	1.75631	−	0.781961i	1.75631	−	0.781961i
$87$	−0.400938	+	0.114967i	−0.400938	+	0.114967i
$88$		0			0
$89$	−1.35275	−	1.13510i	−1.35275	−	1.13510i	−0.978148	−	0.207912i	$-0.933333\pi$
$89$	−1.35275	−	1.13510i	−1.35275	−	1.13510i	−0.374607	−	0.927184i	$-0.622222\pi$
$90$	−0.231349	+	0.927889i	−0.231349	+	0.927889i
$91$		0			0
$92$	−0.671624	−	0.563559i	−0.671624	−	0.563559i
$93$		0			0
$94$	1.28642	−	0.368875i	1.28642	−	0.368875i
$95$		0			0
$96$	0.150383	−	0.145223i	0.150383	−	0.145223i
$97$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$97$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$98$	−2.43400	−	0.697938i	−2.43400	−	0.697938i
$99$		0			0
$100$	−0.241922	+	0.970296i	−0.241922	+	0.970296i
$101$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	−0.978148	−	0.207912i	$-0.933333\pi$
$101$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	0.990268	+	0.139173i	$0.0444444\pi$
$102$		0			0
$103$	0.116903	+	0.173316i	0.116903	+	0.173316i	0.882948	−	0.469472i	$-0.155556\pi$
$103$	0.116903	+	0.173316i	0.116903	+	0.173316i	−0.766044	+	0.642788i	$0.777778\pi$
$104$		0			0
$105$	−0.346909	+	0.184455i	−0.346909	+	0.184455i
$106$		0			0
$107$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$107$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$108$	−0.313295	+	0.262885i	−0.313295	+	0.262885i
$109$	−0.130100	+	0.737831i	−0.130100	+	0.737831i	0.848048	+	0.529919i	$0.177778\pi$
$109$	−0.130100	+	0.737831i	−0.130100	+	0.737831i	−0.978148	+	0.207912i	$0.933333\pi$
$110$		0			0
$111$		0			0
$112$	−1.87481	−	0.131099i	−1.87481	−	0.131099i
$113$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$113$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$114$		0			0
$115$	0.630676	+	0.609036i	0.630676	+	0.609036i
$116$	1.87481	+	0.682374i	1.87481	+	0.682374i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.160147	+	0.134379i	−0.160147	+	0.134379i
$121$	0.438371	+	0.898794i	0.438371	+	0.898794i
$122$	1.60229	+	1.16413i	1.60229	+	1.16413i
$123$	0.179106	−	0.265536i	0.179106	−	0.265536i
$124$		0			0
$125$	0.309017	−	0.951057i	0.309017	−	0.951057i
$126$	1.77976	+	0.250128i	1.77976	+	0.250128i
$127$	−0.152245	−	0.312148i	−0.152245	−	0.312148i	0.809017	−	0.587785i	$-0.200000\pi$
$127$	−0.152245	−	0.312148i	−0.152245	−	0.312148i	−0.961262	+	0.275637i	$0.911111\pi$
$128$	−0.990268	+	0.139173i	−0.990268	+	0.139173i
$129$	−0.386347	−	0.110783i	−0.386347	−	0.110783i
$130$		0			0
$131$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$131$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$132$		0			0
$133$		0			0
$134$	0.0637646	+	1.82598i	0.0637646	+	1.82598i
$135$	0.330869	−	0.240391i	0.330869	−	0.240391i
$136$		0			0
$137$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$137$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$138$	0.0318278	+	0.180504i	0.0318278	+	0.180504i
$139$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$139$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$140$	1.86110	+	0.261560i	1.86110	+	0.261560i
$141$	−0.255585	−	0.113794i	−0.255585	−	0.113794i
$142$		0			0
$143$		0			0
$144$	0.953966	−	0.0667078i	0.953966	−	0.0667078i
$145$	−1.82264	−	0.811492i	−1.82264	−	0.811492i
$146$		0			0
$147$	0.296009	+	0.438852i	0.296009	+	0.438852i
$148$		0			0
$149$	−1.05094	−	0.382510i	−1.05094	−	0.382510i	−0.241922	−	0.970296i	$-0.577778\pi$
$149$	−1.05094	−	0.382510i	−1.05094	−	0.382510i	−0.809017	+	0.587785i	$0.800000\pi$
$150$	0.169131	−	0.122881i	0.169131	−	0.122881i
$151$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$151$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.961262	−	0.275637i	$-0.0888889\pi$
$157$		0			0		−0.961262	+	0.275637i	$0.911111\pi$
$158$		0			0
$159$		0			0
$160$	0.997564	−	0.0697565i	0.997564	−	0.0697565i
$161$	1.01445	−	1.29843i	1.01445	−	1.29843i
$162$	−0.870796			−0.870796
$163$	−0.758078	+	0.970296i	−0.758078	+	0.970296i	0.241922	+	0.970296i	$0.422222\pi$
$163$	−0.758078	+	0.970296i	−0.758078	+	0.970296i	−1.00000			$\pi$
$164$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$165$		0			0
$166$	0.0215691	−	0.617657i	0.0215691	−	0.617657i
$167$	−0.538939	+	0.520447i	−0.538939	+	0.520447i	−0.913545	−	0.406737i	$-0.866667\pi$
$167$	−0.538939	+	0.520447i	−0.538939	+	0.520447i	0.374607	+	0.927184i	$0.377778\pi$
$168$	0.282628	+	0.272930i	0.282628	+	0.272930i
$169$	0.0348995	+	0.999391i	0.0348995	+	0.999391i
$170$		0			0
$171$		0			0
$172$	1.18362	+	1.51497i	1.18362	+	1.51497i
$173$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$173$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$174$	−0.208548	−	0.361215i	−0.208548	−	0.361215i
$175$	−1.83832	−	0.390746i	−1.83832	−	0.390746i
$176$		0			0
$177$		0			0
$178$	0.774117	−	1.58718i	0.774117	−	1.58718i
$179$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$179$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$180$	−0.956295			−0.956295
$181$	−0.882948	+	0.469472i	−0.882948	+	0.469472i
$181$	−0.882948	+	0.469472i	−0.882948	+	0.469472i
$182$		0			0
$183$	−0.100167	−	0.401746i	−0.100167	−	0.401746i
$184$	0.384339	−	0.788011i	0.384339	−	0.788011i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.669131	+	1.15897i	0.669131	+	1.15897i
$189$	−0.514311	−	0.571200i	−0.514311	−	0.571200i
$190$		0			0
$191$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$191$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$192$	0.177290	+	0.110783i	0.177290	+	0.110783i
$193$		0			0		−0.0348995	−	0.999391i	$-0.511111\pi$
$193$		0			0		0.0348995	+	0.999391i	$0.488889\pi$
$194$		0			0
$195$		0			0
$196$	0.0883686	−	2.53055i	0.0883686	−	2.53055i
$197$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$197$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$198$		0			0
$199$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$199$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$200$	−1.00000			−1.00000
$201$	0.235162	−	0.300993i	0.235162	−	0.300993i
$202$	0.0696290	−	0.00486893i	0.0696290	−	0.00486893i
$203$	−1.15869	+	3.56610i	−1.15869	+	3.56610i
$204$		0			0
$205$	1.47274	−	0.422301i	1.47274	−	0.422301i
$206$	−0.139886	+	0.155360i	−0.139886	+	0.155360i
$207$	−0.419212	+	0.726097i	−0.419212	+	0.726097i
$208$		0			0
$209$		0			0
$210$	−0.262900	−	0.291980i	−0.262900	−	0.291980i
$211$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$211$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$212$		0			0
$213$		0			0
$214$	−1.37217	+	0.857427i	−1.37217	+	0.857427i
$215$	−1.07506	−	1.59384i	−1.07506	−	1.59384i
$216$	−0.330869	−	0.240391i	−0.330869	−	0.240391i
$217$		0			0
$218$	−0.747388	+	0.0522625i	−0.747388	+	0.0522625i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.444576	+	1.36827i	0.444576	+	1.36827i	0.882948	+	0.469472i	$0.155556\pi$
$223$	0.444576	+	1.36827i	0.444576	+	1.36827i	−0.438371	+	0.898794i	$0.644444\pi$
$224$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$225$	0.953966	+	0.0667078i	0.953966	+	0.0667078i
$226$		0			0
$227$	−0.996161	+	0.723753i	−0.996161	+	0.723753i	−0.961262	−	0.275637i	$-0.911111\pi$
$227$	−0.996161	+	0.723753i	−0.996161	+	0.723753i	−0.0348995	+	0.999391i	$0.511111\pi$
$228$		0			0
$229$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$229$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$230$	−0.438371	+	0.759281i	−0.438371	+	0.759281i
$231$		0			0
$232$	−0.208548	+	1.98420i	−0.208548	+	1.98420i
$233$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$233$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$234$		0			0
$235$	−0.586655	−	1.20282i	−0.586655	−	1.20282i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$239$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$240$	−0.169131	−	0.122881i	−0.169131	−	0.122881i
$241$	−0.438371	−	0.898794i	−0.438371	−	0.898794i	−0.997564	−	0.0697565i	$-0.977778\pi$
$241$	−0.438371	−	0.898794i	−0.438371	−	0.898794i	0.559193	−	0.829038i	$-0.311111\pi$
$242$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$243$	0.452750	+	0.379902i	0.452750	+	0.379902i
$244$	−0.741922	+	1.83632i	−0.741922	+	1.83632i
$245$	−0.264675	+	2.51822i	−0.264675	+	2.51822i
$246$	0.300978	+	0.109547i	0.300978	+	0.109547i
$247$		0			0
$248$		0			0
$249$	−0.0864545	+	0.0960175i	−0.0864545	+	0.0960175i
$250$	0.997564	+	0.0697565i	0.997564	+	0.0697565i
$251$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$251$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$252$	0.187863	+	1.78740i	0.187863	+	1.78740i
$253$		0			0
$254$	0.266044	−	0.223238i	0.266044	−	0.223238i
$255$		0			0
$256$	−0.374607	−	0.927184i	−0.374607	−	0.927184i
$257$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$257$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$258$	0.0140267	−	0.401672i	0.0140267	−	0.401672i
$259$		0			0
$260$		0			0
$261$	0.331309	−	1.87895i	0.331309	−	1.87895i
$262$		0			0
$263$	0.139886	+	1.33093i	0.139886	+	1.33093i	0.809017	+	0.587785i	$0.200000\pi$
$263$	0.139886	+	1.33093i	0.139886	+	1.33093i	−0.669131	+	0.743145i	$0.733333\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.337256	+	0.150156i	−0.337256	+	0.150156i
$268$	−1.75631	+	0.503615i	−1.75631	+	0.503615i
$269$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$269$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$270$	0.313295	+	0.262885i	0.313295	+	0.262885i
$271$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$271$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.167443	+	0.0745504i	−0.167443	+	0.0745504i
$277$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$277$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$278$		0			0
$279$		0			0
$280$	0.196449	+	1.86909i	0.196449	+	1.86909i
$281$	−0.410323	+	1.64571i	−0.410323	+	1.64571i	0.309017	+	0.951057i	$0.400000\pi$
$281$	−0.410323	+	1.64571i	−0.410323	+	1.64571i	−0.719340	+	0.694658i	$0.755556\pi$
$282$	0.0485820	−	0.275522i	0.0485820	−	0.275522i
$283$	1.60229	−	0.225187i	1.60229	−	0.225187i	0.719340	−	0.694658i	$-0.244444\pi$
$283$	1.60229	−	0.225187i	1.60229	−	0.225187i	0.882948	+	0.469472i	$0.155556\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.07864	−	2.66972i	−1.07864	−	2.66972i
$288$	0.295511	+	0.909491i	0.295511	+	0.909491i
$289$	0.766044	−	0.642788i	0.766044	−	0.642788i
$290$	0.346450	−	1.96482i	0.346450	−	1.96482i
$291$		0			0
$292$		0			0
$293$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$293$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$294$	−0.354205	+	0.393384i	−0.354205	+	0.393384i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.116903	−	1.11226i	0.116903	−	1.11226i
$299$		0			0
$300$	0.160147	+	0.134379i	0.160147	+	0.134379i
$301$	−2.76784	+	2.32250i	−2.76784	+	2.32250i
$302$		0			0
$303$	−0.0118051	−	0.00857694i	−0.0118051	−	0.00857694i
$304$		0			0
$305$	0.868210	−	1.78009i	0.868210	−	1.78009i
$306$		0			0
$307$	1.93726	+	0.272264i	1.93726	+	0.272264i	0.997564	−	0.0697565i	$-0.0222222\pi$
$307$	1.93726	+	0.272264i	1.93726	+	0.272264i	0.939693	+	0.342020i	$0.111111\pi$
$308$		0			0
$309$	0.0432795	−	0.00608253i	0.0432795	−	0.00608253i
$310$		0			0
$311$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$311$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$	−0.0627230	−	1.79615i	−0.0627230	−	1.79615i
$316$		0			0
$317$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$317$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$318$		0			0
$319$		0			0
$320$	0.309017	+	0.951057i	0.309017	+	0.951057i
$321$	0.334969	+	0.0470769i	0.334969	+	0.0470769i
$322$	1.50528	+	0.670195i	1.50528	+	0.670195i
$323$		0			0
$324$	−0.210665	−	0.844929i	−0.210665	−	0.844929i
$325$		0			0
$326$	−1.12487	−	0.500824i	−1.12487	−	0.500824i
$327$	0.126715	+	0.0920637i	0.126715	+	0.0920637i
$328$	−0.856733	−	1.27016i	−0.856733	−	1.27016i
$329$	−2.13293	+	1.33280i	−2.13293	+	1.33280i
$330$		0			0
$331$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$331$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$332$	0.604528	−	0.128496i	0.604528	−	0.128496i
$333$		0			0
$334$	−0.635369	−	0.397023i	−0.635369	−	0.397023i
$335$	1.78716	−	0.379874i	1.78716	−	0.379874i
$336$	−0.196449	+	0.340260i	−0.196449	+	0.340260i
$337$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$337$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$338$	−0.961262	+	0.275637i	−0.961262	+	0.275637i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	2.87939			2.87939
$344$	−1.18362	+	1.51497i	−1.18362	+	1.51497i
$345$	0.172235	−	0.0626885i	0.172235	−	0.0626885i
$346$		0			0
$347$	−0.0591929	+	1.69506i	−0.0591929	+	1.69506i	0.500000	+	0.866025i	$0.333333\pi$
$347$	−0.0591929	+	1.69506i	−0.0591929	+	1.69506i	−0.559193	+	0.829038i	$0.688889\pi$
$348$	0.300033	−	0.289739i	0.300033	−	0.289739i
$349$	−0.962665	−	0.929634i	−0.962665	−	0.929634i	0.0348995	−	0.999391i	$-0.488889\pi$
$349$	−0.962665	−	0.929634i	−0.962665	−	0.929634i	−0.997564	+	0.0697565i	$0.977778\pi$
$350$	−0.0655896	−	1.87824i	−0.0655896	−	1.87824i
$351$		0			0
$352$		0			0
$353$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$353$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$354$		0			0
$355$		0			0
$356$	1.72731	+	0.367150i	1.72731	+	0.367150i
$357$		0			0
$358$		0			0
$359$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$359$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$360$	−0.231349	−	0.927889i	−0.231349	−	0.927889i
$361$	1.00000			1.00000
$362$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$363$	0.209057			0.209057
$364$		0			0
$365$		0			0
$366$	0.365580	−	0.194382i	0.365580	−	0.194382i
$367$	−1.82709	+	0.813473i	−1.82709	+	0.813473i	−0.913545	+	0.406737i	$0.866667\pi$
$367$	−1.82709	+	0.813473i	−1.82709	+	0.813473i	−0.913545	+	0.406737i	$0.866667\pi$
$368$	0.857583	+	0.182285i	0.857583	+	0.182285i
$369$	0.732565	+	1.26884i	0.732565	+	1.26884i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$373$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$374$		0			0
$375$	−0.150383	−	0.145223i	−0.150383	−	0.145223i
$376$	−0.962665	+	0.929634i	−0.962665	+	0.929634i
$377$		0			0
$378$	0.429810	−	0.637219i	0.429810	−	0.637219i
$379$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$379$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$380$		0			0
$381$	−0.0726047			−0.0726047
$382$		0			0
$383$	−1.76159	+	0.123183i	−1.76159	+	0.123183i	−0.913545	−	0.406737i	$-0.866667\pi$
$383$	−1.76159	+	0.123183i	−1.76159	+	0.123183i	−0.848048	+	0.529919i	$0.822222\pi$
$384$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$385$		0			0
$386$		0			0
$387$	1.23020	−	1.36627i	1.23020	−	1.36627i
$388$		0			0
$389$	1.72731	−	0.367150i	1.72731	−	0.367150i	0.766044	−	0.642788i	$-0.222222\pi$
$389$	1.72731	−	0.367150i	1.72731	−	0.367150i	0.961262	+	0.275637i	$0.0888889\pi$
$390$		0			0
$391$		0			0
$392$	2.47676	−	0.526451i	2.47676	−	0.526451i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$397$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$398$		0			0
$399$		0			0
$400$	−0.241922	−	0.970296i	−0.241922	−	0.970296i
$401$	0.454664	−	0.165484i	0.454664	−	0.165484i	−0.104528	−	0.994522i	$-0.533333\pi$
$401$	0.454664	−	0.165484i	0.454664	−	0.165484i	0.559193	+	0.829038i	$0.311111\pi$
$402$	0.348943	+	0.155360i	0.348943	+	0.155360i
$403$		0			0
$404$	0.0215691	+	0.0663828i	0.0215691	+	0.0663828i
$405$	0.151212	+	0.857566i	0.151212	+	0.857566i
$406$	−3.74048	−	0.261560i	−3.74048	−	0.261560i
$407$		0			0
$408$		0			0
$409$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i	−0.882948	−	0.469472i	$-0.844444\pi$
$409$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i	0.848048	−	0.529919i	$-0.177778\pi$
$410$	0.766044	+	1.32683i	0.766044	+	1.32683i
$411$		0			0
$412$	−0.184586	−	0.0981463i	−0.184586	−	0.0981463i
$413$		0			0
$414$	−0.805945	−	0.231101i	−0.805945	−	0.231101i
$415$	−0.612019	+	0.0860137i	−0.612019	+	0.0860137i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$419$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$420$	0.219706	−	0.325728i	0.219706	−	0.325728i
$421$	−0.904793	−	0.657371i	−0.904793	−	0.657371i	0.0348995	−	0.999391i	$-0.488889\pi$
$421$	−0.904793	−	0.657371i	−0.904793	−	0.657371i	−0.939693	+	0.342020i	$0.888889\pi$
$422$		0			0
$423$	0.980363	−	0.822622i	0.980363	−	0.822622i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.49771	−	1.27306i	−3.49771	−	1.27306i
$428$	−1.16392	−	1.12398i	−1.16392	−	1.12398i
$429$		0			0
$430$	1.28642	−	1.42871i	1.28642	−	1.42871i
$431$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$431$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$432$	0.153206	−	0.379197i	0.153206	−	0.379197i
$433$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$433$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$434$		0			0
$435$	−0.319514	+	0.268104i	−0.319514	+	0.268104i
$436$	−0.231520	−	0.712544i	−0.231520	−	0.712544i
$437$		0			0
$438$		0			0
$439$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$439$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$440$		0			0
$441$	−2.39786	+	0.336997i	−2.39786	+	0.336997i
$442$		0			0
$443$	0.0840186	−	0.336980i	0.0840186	−	0.336980i	−0.913545	−	0.406737i	$-0.866667\pi$
$443$	0.0840186	−	0.336980i	0.0840186	−	0.336980i	0.997564	+	0.0697565i	$0.0222222\pi$
$444$		0			0
$445$	−1.69749	−	0.486747i	−1.69749	−	0.486747i
$446$	−1.22007	+	0.762384i	−1.22007	+	0.762384i
$447$	−0.168186	+	0.162416i	−0.168186	+	0.162416i
$448$	1.71690	−	0.764415i	1.71690	−	0.764415i
$449$	−0.465101	+	0.133365i	−0.465101	+	0.133365i	−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−0.465101	+	0.133365i	−0.465101	+	0.133365i	0.0348995	+	0.999391i	$0.488889\pi$
$450$	0.166059	+	0.941767i	0.166059	+	0.941767i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.943248	−	0.791479i	−0.943248	−	0.791479i
$455$		0			0
$456$		0			0
$457$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$457$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$458$	−1.16392	+	1.12398i	−1.16392	+	1.12398i
$459$		0			0
$460$	−0.842779	−	0.241663i	−0.842779	−	0.241663i
$461$	−0.116903	−	1.11226i	−0.116903	−	1.11226i	−0.882948	−	0.469472i	$-0.844444\pi$
$461$	−0.116903	−	1.11226i	−0.116903	−	1.11226i	0.766044	−	0.642788i	$-0.222222\pi$
$462$		0			0
$463$	0.346450	−	1.96482i	0.346450	−	1.96482i	0.104528	−	0.994522i	$-0.466667\pi$
$463$	0.346450	−	1.96482i	0.346450	−	1.96482i	0.241922	−	0.970296i	$-0.422222\pi$
$464$	−1.97571	+	0.277668i	−1.97571	+	0.277668i
$465$		0			0
$466$		0			0
$467$	1.35275	−	0.719272i	1.35275	−	0.719272i	0.374607	−	0.927184i	$-0.377778\pi$
$467$	1.35275	−	0.719272i	1.35275	−	0.719272i	0.978148	+	0.207912i	$0.0666667\pi$
$468$		0			0
$469$	−1.06110	−	3.26575i	−1.06110	−	3.26575i
$470$	1.02517	−	0.860218i	1.02517	−	0.860218i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$479$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$480$	0.0783141	−	0.193834i	0.0783141	−	0.193834i
$481$		0			0
$482$	0.766044	−	0.642788i	0.766044	−	0.642788i
$483$	−0.151006	−	0.309608i	−0.151006	−	0.309608i
$484$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$485$		0			0
$486$	−0.259087	+	0.531208i	−0.259087	+	0.531208i
$487$	−0.524123	+	1.61308i	−0.524123	+	1.61308i	0.241922	+	0.970296i	$0.422222\pi$
$487$	−0.524123	+	1.61308i	−0.524123	+	1.61308i	−0.766044	+	0.642788i	$0.777778\pi$
$488$	−1.96126	−	0.275637i	−1.96126	−	0.275637i
$489$	0.112844	+	0.231364i	0.112844	+	0.231364i
$490$	−2.50745	+	0.352399i	−2.50745	+	0.352399i
$491$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$491$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$492$	−0.0334798	+	0.318539i	−0.0334798	+	0.318539i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.114081	−	0.0606577i	−0.114081	−	0.0606577i
$499$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$499$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$500$	0.173648	+	0.984808i	0.173648	+	0.984808i
$501$	0.0484008	+	0.148962i	0.0484008	+	0.148962i
$502$		0			0
$503$	1.61323	+	0.718254i	1.61323	+	0.718254i	0.997564	−	0.0697565i	$-0.0222222\pi$
$503$	1.61323	+	0.718254i	1.61323	+	0.718254i	0.615661	+	0.788011i	$0.288889\pi$
$504$	−1.68886	+	0.614695i	−1.68886	+	0.614695i
$505$	−0.0168859	−	0.0677257i	−0.0168859	−	0.0677257i
$506$		0			0
$507$	0.190983	+	0.0850311i	0.190983	+	0.0850311i
$508$	0.280969	+	0.204136i	0.280969	+	0.204136i
$509$	1.07506	+	1.59384i	1.07506	+	1.59384i	0.766044	+	0.642788i	$0.222222\pi$
$509$	1.07506	+	1.59384i	1.07506	+	1.59384i	0.309017	+	0.951057i	$0.400000\pi$
$510$		0			0
$511$		0			0
$512$	0.809017	−	0.587785i	0.809017	−	0.587785i
$513$		0			0
$514$		0			0
$515$	0.177290	+	0.110783i	0.177290	+	0.110783i
$516$	0.393134	−	0.0835632i	0.393134	−	0.0835632i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$521$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$522$	1.90328	−	0.133091i	1.90328	−	0.133091i
$523$	0.943248	−	1.20730i	0.943248	−	1.20730i	−0.0348995	−	0.999391i	$-0.511111\pi$
$523$	0.943248	−	1.20730i	0.943248	−	1.20730i	0.978148	−	0.207912i	$-0.0666667\pi$
$524$		0			0
$525$	−0.241892	+	0.309608i	−0.241892	+	0.309608i
$526$	−1.25755	+	0.457712i	−1.25755	+	0.457712i
$527$		0			0
$528$		0			0
$529$	0.166400	−	0.160690i	0.166400	−	0.160690i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.227285	−	0.290912i	−0.227285	−	0.290912i
$535$	1.08268	+	1.20243i	1.08268	+	1.20243i
$536$	−0.913545	−	1.58231i	−0.913545	−	1.58231i
$537$		0			0
$538$	−0.317271	+	0.141258i	−0.317271	+	0.141258i
$539$		0			0
$540$	−0.179284	+	0.367586i	−0.179284	+	0.367586i
$541$	−0.483844	−	1.94059i	−0.483844	−	1.94059i	−0.241922	−	0.970296i	$-0.577778\pi$
$541$	−0.483844	−	1.94059i	−0.483844	−	1.94059i	−0.241922	−	0.970296i	$-0.577778\pi$
$542$		0			0
$543$	0.00729598	+	0.208930i	0.00729598	+	0.208930i
$544$		0			0
$545$	0.181251	+	0.726958i	0.181251	+	0.726958i
$546$		0			0
$547$	−1.76159	+	0.936656i	−1.76159	+	0.936656i	−0.848048	+	0.529919i	$0.822222\pi$
$547$	−1.76159	+	0.936656i	−1.76159	+	0.936656i	−0.913545	+	0.406737i	$0.866667\pi$
$548$		0			0
$549$	1.85259	+	0.393780i	1.85259	+	0.393780i
$550$		0			0
$551$		0			0
$552$	−0.112844	−	0.144434i	−0.112844	−	0.144434i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$557$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$558$		0			0
$559$		0			0
$560$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$561$		0			0
$562$	−1.69610			−1.69610
$563$	0.688547	−	0.881300i	0.688547	−	0.881300i	−0.309017	−	0.951057i	$-0.600000\pi$
$563$	0.688547	−	0.881300i	0.688547	−	0.881300i	0.997564	+	0.0697565i	$0.0222222\pi$
$564$	0.279091	−	0.0195160i	0.279091	−	0.0195160i
$565$		0			0
$566$	0.606126	+	1.50021i	0.606126	+	1.50021i
$567$	1.57316	−	0.451097i	1.57316	−	0.451097i
$568$		0			0
$569$	−0.559193	+	0.968551i	−0.559193	+	0.968551i	0.438371	+	0.898794i	$0.355556\pi$
$569$	−0.559193	+	0.968551i	−0.559193	+	0.968551i	−0.997564	+	0.0697565i	$0.977778\pi$
$570$		0			0
$571$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$571$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$572$		0			0
$573$		0			0
$574$	2.32947	−	1.69246i	2.32947	−	1.69246i
$575$	0.823868	+	0.299864i	0.823868	+	0.299864i
$576$	−0.810984	+	0.506759i	−0.810984	+	0.506759i
$577$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$577$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$578$	0.809017	+	0.587785i	0.809017	+	0.587785i
$579$		0			0
$580$	1.99027	−	0.139173i	1.99027	−	0.139173i
$581$	0.280998	+	1.12702i	0.280998	+	1.12702i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.22832	−	0.0858927i	−1.22832	−	0.0858927i	−0.559193	−	0.829038i	$-0.688889\pi$
$587$	−1.22832	−	0.0858927i	−1.22832	−	0.0858927i	−0.669131	+	0.743145i	$0.733333\pi$
$588$	−0.467389	−	0.248515i	−0.467389	−	0.248515i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$593$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$594$		0			0
$595$		0			0
$596$	1.10750	−	0.155649i	1.10750	−	0.155649i
$597$		0			0
$598$		0			0
$599$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$599$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$600$	−0.0916445	+	0.187899i	−0.0916445	+	0.187899i
$601$	−1.09395	+	1.62184i	−1.09395	+	1.62184i	−0.374607	+	0.927184i	$0.622222\pi$
$601$	−1.09395	+	1.62184i	−1.09395	+	1.62184i	−0.719340	+	0.694658i	$0.755556\pi$
$602$	−2.92311	−	2.12376i	−2.92311	−	2.12376i
$603$	0.765939	+	1.57041i	0.765939	+	1.57041i
$604$		0			0
$605$	0.766044	+	0.642788i	0.766044	+	0.642788i
$606$	0.00546625	−	0.0135294i	0.00546625	−	0.0135294i
$607$	−0.196449	+	1.86909i	−0.196449	+	1.86909i	0.241922	+	0.970296i	$0.422222\pi$
$607$	−0.196449	+	1.86909i	−0.196449	+	1.86909i	−0.438371	+	0.898794i	$0.644444\pi$
$608$		0			0
$609$	0.563878	+	0.544531i	0.563878	+	0.544531i
$610$	1.93726	+	0.411777i	1.93726	+	0.411777i
$611$		0			0
$612$		0			0
$613$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$613$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$614$	0.204489	+	1.94558i	0.204489	+	1.94558i
$615$	0.0556184	−	0.315428i	0.0556184	−	0.315428i
$616$		0			0
$617$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$617$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$618$	0.0163721	+	0.0405224i	0.0163721	+	0.0405224i
$619$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$619$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$620$		0			0
$621$	0.200508	+	0.297266i	0.200508	+	0.297266i
$622$		0			0
$623$	−0.576303	+	3.26838i	−0.576303	+	3.26838i
$624$		0			0
$625$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	1.72762	−	0.495388i	1.72762	−	0.495388i
$631$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$631$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.848048	+	0.529919i	−0.848048	+	0.529919i
$641$	−1.38295	−	0.396554i	−1.38295	−	0.396554i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	−1.38295	−	0.396554i	−1.38295	−	0.396554i	−0.882948	+	0.469472i	$0.844444\pi$
$642$	0.0353579	+	0.336408i	0.0353579	+	0.336408i
$643$	−0.241922	+	0.970296i	−0.241922	+	0.970296i	0.719340	+	0.694658i	$0.244444\pi$
$643$	−0.241922	+	0.970296i	−0.241922	+	0.970296i	−0.961262	+	0.275637i	$0.911111\pi$
$644$	−0.286126	+	1.62270i	−0.286126	+	1.62270i
$645$	−0.398005	+	0.0559360i	−0.398005	+	0.0559360i
$646$		0			0
$647$	−0.0591929	+	1.69506i	−0.0591929	+	1.69506i	0.500000	+	0.866025i	$0.333333\pi$
$647$	−0.0591929	+	1.69506i	−0.0591929	+	1.69506i	−0.559193	+	0.829038i	$0.688889\pi$
$648$	0.768867	−	0.408814i	0.768867	−	0.408814i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.213817	−	1.21262i	0.213817	−	1.21262i
$653$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$653$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$654$	−0.0586740	+	0.145223i	−0.0586740	+	0.145223i
$655$		0			0
$656$	1.02517	−	1.13856i	1.02517	−	1.13856i
$657$		0			0
$658$	−1.80922	−	1.74714i	−1.80922	−	1.74714i
$659$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$659$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$660$		0			0
$661$	0.732841	−	1.81385i	0.732841	−	1.81385i	0.173648	−	0.984808i	$-0.444444\pi$
$661$	0.732841	−	1.81385i	0.732841	−	1.81385i	0.559193	−	0.829038i	$-0.311111\pi$
$662$		0			0
$663$		0			0
$664$	0.270928	+	0.555485i	0.270928	+	0.555485i
$665$		0			0
$666$		0			0
$667$	0.766805	−	1.57218i	0.766805	−	1.57218i
$668$	0.231520	−	0.712544i	0.231520	−	0.712544i
$669$	0.297839	+	0.0418585i	0.297839	+	0.0418585i
$670$	0.800944	+	1.64218i	0.800944	+	1.64218i
$671$		0			0
$672$	−0.377678	−	0.108298i	−0.377678	−	0.108298i
$673$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$673$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$674$		0			0
$675$	0.204489	−	0.354185i	0.204489	−	0.354185i
$676$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$677$		0			0		−0.0348995	−	0.999391i	$-0.511111\pi$
$677$		0			0		0.0348995	+	0.999391i	$0.488889\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.0446999	+	0.253506i	0.0446999	+	0.253506i
$682$		0			0
$683$	−1.90381	−	0.267564i	−1.90381	−	0.267564i	−0.913545	−	0.406737i	$-0.866667\pi$
$683$	−1.90381	−	0.267564i	−1.90381	−	0.267564i	−0.990268	+	0.139173i	$0.955556\pi$
$684$		0			0
$685$		0			0
$686$	0.696586	+	2.79386i	0.696586	+	2.79386i
$687$	0.337437	−	0.0235959i	0.337437	−	0.0235959i
$688$	−1.75631	−	0.781961i	−1.75631	−	0.781961i
$689$		0			0
$690$	0.102494	+	0.151954i	0.102494	+	0.151954i
$691$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$691$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$692$		0			0
$693$		0			0
$694$	−1.65903	+	0.352638i	−1.65903	+	0.352638i
$695$		0			0
$696$	0.353717	+	0.221027i	0.353717	+	0.221027i
$697$		0			0
$698$	0.669131	−	1.15897i	0.669131	−	1.15897i
$699$		0			0
$700$	1.80658	−	0.518029i	1.80658	−	0.518029i
$701$	0.461262	+	1.14166i	0.461262	+	1.14166i	0.961262	+	0.275637i	$0.0888889\pi$
$701$	0.461262	+	1.14166i	0.461262	+	1.14166i	−0.500000	+	0.866025i	$0.666667\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.279773			−0.279773
$706$		0			0
$707$	−0.123268	+	0.0448659i	−0.123268	+	0.0448659i
$708$		0			0
$709$	0.0390311	−	1.11770i	0.0390311	−	1.11770i	−0.809017	−	0.587785i	$-0.800000\pi$
$709$	0.0390311	−	1.11770i	0.0390311	−	1.11770i	0.848048	−	0.529919i	$-0.177778\pi$
$710$		0			0
$711$		0			0
$712$	0.0616289	+	1.76482i	0.0616289	+	1.76482i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$719$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$720$	0.844359	−	0.448953i	0.844359	−	0.448953i
$721$	0.172235	−	0.353135i	0.172235	−	0.353135i
$722$	0.241922	+	0.970296i	0.241922	+	0.970296i
$723$	−0.209057			−0.209057
$724$	0.559193	−	0.829038i	0.559193	−	0.829038i
$725$	−1.99513			−1.99513
$726$	0.0505754	+	0.202847i	0.0505754	+	0.202847i
$727$	0.709299	−	1.45428i	0.709299	−	1.45428i	−0.173648	−	0.984808i	$-0.555556\pi$
$727$	0.709299	−	1.45428i	0.709299	−	1.45428i	0.882948	−	0.469472i	$-0.155556\pi$
$728$		0			0
$729$	−0.682636	+	0.303929i	−0.682636	+	0.303929i
$730$		0			0
$731$		0			0
$732$	0.277050	+	0.307695i	0.277050	+	0.307695i
$733$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$733$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$734$	−1.23132	−	1.57602i	−1.23132	−	1.57602i
$735$	0.448915	+	0.280513i	0.448915	+	0.280513i
$736$	0.0305979	+	0.876208i	0.0305979	+	0.876208i
$737$		0			0
$738$	−1.05393	+	1.01776i	−1.05393	+	1.01776i
$739$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$739$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.749213			0.749213			0.374607	−	0.927184i	$-0.377778\pi$
$743$	0.749213			0.749213			0.374607	+	0.927184i	$0.377778\pi$
$744$		0			0
$745$	−1.11566	+	0.0780147i	−1.11566	+	0.0780147i
$746$		0			0
$747$	−0.221401	−	0.547987i	−0.221401	−	0.547987i
$748$		0			0
$749$	2.03477	−	2.25984i	2.03477	−	2.25984i
$750$	0.104528	−	0.181049i	0.104528	−	0.181049i
$751$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$751$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$752$	−1.13491	−	0.709170i	−1.13491	−	0.709170i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.722272	+	0.262885i	0.722272	+	0.262885i
$757$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$757$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.82264	+	0.127451i	−1.82264	+	0.127451i	−0.939693	−	0.342020i	$-0.888889\pi$
$761$	−1.82264	+	0.127451i	−1.82264	+	0.127451i	−0.882948	+	0.469472i	$0.844444\pi$
$762$	−0.0175647	−	0.0704480i	−0.0175647	−	0.0704480i
$763$	1.32314	−	0.481585i	1.32314	−	0.481585i
$764$		0			0
$765$		0			0
$766$	−0.545692	−	1.67947i	−0.545692	−	1.67947i
$767$		0			0
$768$	−0.208548	−	0.0145831i	−0.208548	−	0.0145831i
$769$	0.427209	+	0.227151i	0.427209	+	0.227151i	0.669131	−	0.743145i	$-0.266667\pi$
$769$	0.427209	+	0.227151i	0.427209	+	0.227151i	−0.241922	+	0.970296i	$0.577778\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$773$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$774$	1.62330	+	0.863123i	1.62330	+	0.863123i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.774117	+	1.58718i	0.774117	+	1.58718i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.660127	−	0.479610i	−0.660127	−	0.479610i
$784$	1.10999	+	2.27583i	1.10999	+	2.27583i
$785$		0			0
$786$		0			0
$787$	0.741922	−	1.83632i	0.741922	−	1.83632i	0.241922	−	0.970296i	$-0.422222\pi$
$787$	0.741922	−	1.83632i	0.741922	−	1.83632i	0.500000	−	0.866025i	$-0.333333\pi$
$788$		0			0
$789$	0.262900	+	0.0956879i	0.262900	+	0.0956879i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$797$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$798$		0			0
$799$		0			0
$800$	0.882948	−	0.469472i	0.882948	−	0.469472i
$801$	0.0589354	−	1.68769i	0.0589354	−	1.68769i
$802$	0.270562	+	0.401125i	0.270562	+	0.401125i
$803$		0			0
$804$	−0.0663277	+	0.376163i	−0.0663277	+	0.376163i
$805$	0.398624	−	1.59879i	0.398624	−	1.59879i
$806$		0			0
$807$	0.0697921	+	0.0200126i	0.0697921	+	0.0200126i
$808$	−0.0591929	+	0.0369878i	−0.0591929	+	0.0369878i
$809$	−1.31430	+	1.26920i	−1.31430	+	1.26920i	−0.374607	+	0.927184i	$0.622222\pi$
$809$	−1.31430	+	1.26920i	−1.31430	+	1.26920i	−0.939693	+	0.342020i	$0.888889\pi$
$810$	−0.795511	+	0.354185i	−0.795511	+	0.354185i
$811$		0			0		0.961262	−	0.275637i	$-0.0888889\pi$
$811$		0			0		−0.961262	+	0.275637i	$0.911111\pi$
$812$	−0.651114	−	3.69265i	−0.651114	−	3.69265i
$813$		0			0
$814$		0			0
$815$	−0.297884	+	1.19475i	−0.297884	+	1.19475i
$816$		0			0
$817$		0			0
$818$	0.961262	−	0.275637i	0.961262	−	0.275637i
$819$		0			0
$820$	−1.10209	+	1.06428i	−1.10209	+	1.06428i
$821$	1.63039	−	1.01878i	1.63039	−	1.01878i	0.669131	−	0.743145i	$-0.266667\pi$
$821$	1.63039	−	1.01878i	1.63039	−	1.01878i	0.961262	−	0.275637i	$-0.0888889\pi$
$822$		0			0
$823$	0.0916445	+	0.871939i	0.0916445	+	0.871939i	0.939693	+	0.342020i	$0.111111\pi$
$823$	0.0916445	+	0.871939i	0.0916445	+	0.871939i	−0.848048	+	0.529919i	$0.822222\pi$
$824$	0.0505754	−	0.202847i	0.0505754	−	0.202847i
$825$		0			0
$826$		0			0
$827$	−0.0390311	−	0.0578660i	−0.0390311	−	0.0578660i	0.809017	−	0.587785i	$-0.200000\pi$
$827$	−0.0390311	−	0.0578660i	−0.0390311	−	0.0578660i	−0.848048	+	0.529919i	$0.822222\pi$
$828$	0.0292606	−	0.837914i	0.0292606	−	0.837914i
$829$	−0.545692	+	0.290149i	−0.545692	+	0.290149i	−0.719340	−	0.694658i	$-0.755556\pi$
$829$	−0.545692	+	0.290149i	−0.545692	+	0.290149i	0.173648	+	0.984808i	$0.444444\pi$
$830$	−0.231520	−	0.573031i	−0.231520	−	0.573031i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.280660	+	0.694658i	−0.280660	+	0.694658i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$839$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$840$	0.369204	+	0.134379i	0.369204	+	0.134379i
$841$	−0.311551	+	2.96421i	−0.311551	+	2.96421i
$842$	0.418955	−	1.03695i	0.418955	−	1.03695i
$843$	0.271625	+	0.227920i	0.271625	+	0.227920i
$844$		0			0
$845$	0.438371	+	0.898794i	0.438371	+	0.898794i
$846$	1.03536	+	0.752232i	1.03536	+	0.752232i
$847$	1.05094	−	1.55808i	1.05094	−	1.55808i
$848$		0			0
$849$	0.104528	−	0.321706i	0.104528	−	0.321706i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$853$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$854$	0.389075	−	3.70180i	0.389075	−	3.70180i
$855$		0			0
$856$	0.809017	−	1.40126i	0.809017	−	1.40126i
$857$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$857$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$858$		0			0
$859$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$859$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$860$	1.69749	+	0.902570i	1.69749	+	0.902570i
$861$	−0.600489	−	0.0419903i	−0.600489	−	0.0419903i
$862$		0			0
$863$	−0.0215691	−	0.0663828i	−0.0215691	−	0.0663828i	0.939693	−	0.342020i	$-0.111111\pi$
$863$	−0.0215691	−	0.0663828i	−0.0215691	−	0.0663828i	−0.961262	+	0.275637i	$0.911111\pi$
$864$	0.404997	+	0.0569186i	0.404997	+	0.0569186i
$865$		0			0
$866$		0			0
$867$	−0.0505754	−	0.202847i	−0.0505754	−	0.202847i
$868$		0			0
$869$		0			0
$870$	−0.337437	−	0.245162i	−0.337437	−	0.245162i
$871$		0			0
$872$	0.635369	−	0.397023i	0.635369	−	0.397023i
$873$		0			0
$874$		0			0
$875$	−1.83832	+	0.390746i	−1.83832	+	0.390746i
$876$		0			0
$877$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$877$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.18362	+	0.339399i	−1.18362	+	0.339399i	−0.809017	−	0.587785i	$-0.800000\pi$
$881$	−1.18362	+	0.339399i	−1.18362	+	0.339399i	−0.374607	+	0.927184i	$0.622222\pi$
$882$	−0.907082	−	2.24511i	−0.907082	−	2.24511i
$883$	−0.107320	+	0.330298i	−0.107320	+	0.330298i	−0.990268	−	0.139173i	$-0.955556\pi$
$883$	−0.107320	+	0.330298i	−0.107320	+	0.330298i	0.882948	+	0.469472i	$0.155556\pi$
$884$		0			0
$885$		0			0
$886$	0.347296			0.347296
$887$	1.21934	−	1.56068i	1.21934	−	1.56068i	0.500000	−	0.866025i	$-0.333333\pi$
$887$	1.21934	−	1.56068i	1.21934	−	1.56068i	0.719340	−	0.694658i	$-0.244444\pi$
$888$		0			0
$889$	−0.364987	+	0.541116i	−0.364987	+	0.541116i
$890$	0.0616289	−	1.76482i	0.0616289	−	1.76482i
$891$		0			0
$892$	−1.03490	−	0.999391i	−1.03490	−	0.999391i
$893$		0			0
$894$	−0.198279	−	0.123898i	−0.198279	−	0.123898i
$895$		0			0
$896$	1.15707	+	1.48098i	1.15707	+	1.48098i
$897$		0			0
$898$	−0.241922	−	0.419021i	−0.241922	−	0.419021i
$899$		0			0
$900$	−0.873619	+	0.388960i	−0.873619	+	0.388960i
$901$		0			0
$902$		0			0
$903$	0.182737	+	0.732919i	0.182737	+	0.732919i
$904$		0			0
$905$	−0.615661	+	0.788011i	−0.615661	+	0.788011i
$906$		0			0
$907$	−0.482665	−	1.93586i	−0.482665	−	1.93586i	−0.309017	−	0.951057i	$-0.600000\pi$
$907$	−0.482665	−	1.93586i	−0.482665	−	1.93586i	−0.173648	−	0.984808i	$-0.555556\pi$
$908$	0.539776	−	1.10671i	0.539776	−	1.10671i
$909$	0.0589354	−	0.0313365i	0.0589354	−	0.0313365i
$910$		0			0
$911$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$911$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.254911	−	0.326272i	−0.254911	−	0.326272i
$916$	−1.37217	−	0.857427i	−1.37217	−	0.857427i
$917$		0			0
$918$		0			0
$919$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$919$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$920$	0.0305979	−	0.876208i	0.0305979	−	0.876208i
$921$	0.228697	−	0.339057i	0.228697	−	0.339057i
$922$	1.05094	−	0.382510i	1.05094	−	0.382510i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	1.99027	−	0.139173i	1.99027	−	0.139173i
$927$	−0.0617787	+	0.190135i	−0.0617787	+	0.190135i
$928$	−0.747388	−	1.84985i	−0.747388	−	1.84985i
$929$	0.594092	−	0.170353i	0.594092	−	0.170353i	0.0348995	−	0.999391i	$-0.488889\pi$
$929$	0.594092	−	0.170353i	0.594092	−	0.170353i	0.559193	+	0.829038i	$0.311111\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	1.02517	+	1.13856i	1.02517	+	1.13856i
$935$		0			0
$936$		0			0
$937$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$937$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$938$	2.91203	−	1.81964i	2.91203	−	1.81964i
$939$		0			0
$940$	1.08268	+	0.786610i	1.08268	+	0.786610i
$941$	1.80931	+	0.805557i	1.80931	+	0.805557i	0.961262	+	0.275637i	$0.0888889\pi$
$941$	1.80931	+	0.805557i	1.80931	+	0.805557i	0.848048	+	0.529919i	$0.177778\pi$
$942$		0			0
$943$	0.324961	+	1.30335i	0.324961	+	1.30335i
$944$		0			0
$945$	−0.702174	−	0.312628i	−0.702174	−	0.312628i
$946$		0			0
$947$	0.545692	+	1.67947i	0.545692	+	1.67947i	0.719340	+	0.694658i	$0.244444\pi$
$947$	0.545692	+	1.67947i	0.545692	+	1.67947i	−0.173648	+	0.984808i	$0.555556\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$953$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.207022	+	0.0290951i	0.207022	+	0.0290951i
$961$	0.309017	−	0.951057i	0.309017	−	0.951057i
$962$		0			0
$963$	−0.865249	+	1.28278i	−0.865249	+	1.28278i
$964$	0.809017	+	0.587785i	0.809017	+	0.587785i
$965$		0			0
$966$	0.263880	−	0.221422i	0.263880	−	0.221422i
$967$	−1.47274	−	1.23577i	−1.47274	−	1.23577i	−0.913545	−	0.406737i	$-0.866667\pi$
$967$	−1.47274	−	1.23577i	−1.47274	−	1.23577i	−0.559193	−	0.829038i	$-0.688889\pi$
$968$	0.374607	−	0.927184i	0.374607	−	0.927184i
$969$		0			0
$970$		0			0
$971$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$971$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$972$	−0.578108	−	0.122881i	−0.578108	−	0.122881i
$973$		0			0
$974$	−1.69196	−	0.118314i	−1.69196	−	0.118314i
$975$		0			0
$976$	−0.207022	−	1.96969i	−0.207022	−	1.96969i
$977$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$977$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$978$	−0.197193	+	0.165464i	−0.197193	+	0.165464i
$979$		0			0
$980$	−0.948537	−	2.34771i	−0.948537	−	2.34771i
$981$	−0.632605	+	0.336362i	−0.632605	+	0.336362i
$982$		0			0
$983$	0.559193	+	0.829038i	0.559193	+	0.829038i	0.997564	−	0.0697565i	$-0.0222222\pi$
$983$	0.559193	+	0.829038i	0.559193	+	0.829038i	−0.438371	+	0.898794i	$0.644444\pi$
$984$	−0.317177	+	0.0445763i	−0.317177	+	0.0445763i
$985$		0			0
$986$		0			0
$987$	0.0549612	+	0.522920i	0.0549612	+	0.522920i
$988$		0			0
$989$	1.42943	−	0.893209i	1.42943	−	0.893209i
$990$		0			0
$991$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$991$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.0312573	−	0.125366i	0.0312573	−	0.125366i
$997$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$997$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3620.1.dy.a.1939.1	✓	24
4.3	odd	2		3620.1.dy.b.1939.1	yes	24
5.4	even	2		3620.1.dy.b.1939.1	yes	24
20.19	odd	2	CM	3620.1.dy.a.1939.1	✓	24
181.87	even	45	inner	3620.1.dy.a.2259.1	yes	24
724.87	odd	90		3620.1.dy.b.2259.1	yes	24
905.449	even	90		3620.1.dy.b.2259.1	yes	24
3620.2259	odd	90	inner	3620.1.dy.a.2259.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3620.1.dy.a.1939.1	✓	24	1.1	even	1	trivial
3620.1.dy.a.1939.1	✓	24	20.19	odd	2	CM
3620.1.dy.a.2259.1	yes	24	181.87	even	45	inner
3620.1.dy.a.2259.1	yes	24	3620.2259	odd	90	inner
3620.1.dy.b.1939.1	yes	24	4.3	odd	2
3620.1.dy.b.1939.1	yes	24	5.4	even	2
3620.1.dy.b.2259.1	yes	24	724.87	odd	90
3620.1.dy.b.2259.1	yes	24	905.449	even	90

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:	\( N \)	\(=\)	\( 3620 = 2^{2} \cdot 5 \cdot 181 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3620.dy (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.241922 + 0.970296i) q^{2} +(0.0916445 - 0.187899i) q^{3} +(-0.882948 + 0.469472i) q^{4} +(0.913545 - 0.406737i) q^{5} +(0.204489 + 0.0434654i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(-0.669131 - 0.743145i) q^{8} +(0.588754 + 0.753571i) q^{9} +O(q^{10})\)	\(q+(0.241922 + 0.970296i) q^{2} +(0.0916445 - 0.187899i) q^{3} +(-0.882948 + 0.469472i) q^{4} +(0.913545 - 0.406737i) q^{5} +(0.204489 + 0.0434654i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(-0.669131 - 0.743145i) q^{8} +(0.588754 + 0.753571i) q^{9} +(0.615661 + 0.788011i) q^{10} +(0.00729598 + 0.208930i) q^{12} +(1.35192 - 1.30553i) q^{14} +(0.00729598 - 0.208930i) q^{15} +(0.559193 - 0.829038i) q^{16} +(-0.588754 + 0.753571i) q^{18} +(-0.615661 + 0.788011i) q^{20} +(-0.391941 + 0.0274072i) q^{21} +(0.328433 + 0.812901i) q^{23} +(-0.200958 + 0.0576239i) q^{24} +(0.669131 - 0.743145i) q^{25} +(0.400040 - 0.0850311i) q^{27} +(1.59381 + 0.995922i) q^{28} +(-1.33500 - 1.48267i) q^{29} +(0.204489 - 0.0434654i) q^{30} +(0.939693 + 0.342020i) q^{32} +(-1.52045 - 1.10467i) q^{35} +(-0.873619 - 0.388960i) q^{36} +(-0.913545 - 0.406737i) q^{40} +(1.51718 + 0.213226i) q^{41} +(-0.121412 - 0.373669i) q^{42} +(-0.333843 - 1.89332i) q^{43} +(0.844359 + 0.448953i) q^{45} +(-0.709299 + 0.515336i) q^{46} +(-0.0467046 - 1.33745i) q^{47} +(-0.104528 - 0.181049i) q^{48} +(-1.26604 + 2.19285i) q^{49} +(0.882948 + 0.469472i) q^{50} +(0.179284 + 0.367586i) q^{54} +(-0.580762 + 1.78740i) q^{56} +(1.11566 - 1.65404i) q^{58} +(0.0916445 + 0.187899i) q^{60} +(1.51718 - 1.27306i) q^{61} +(0.673261 - 1.66638i) q^{63} +(-0.104528 + 0.994522i) q^{64} +(1.78716 + 0.379874i) q^{67} +(0.182843 + 0.0127856i) q^{69} +(0.704030 - 1.74254i) q^{70} +(0.166059 - 0.941767i) q^{72} +(-0.0783141 - 0.193834i) q^{75} +(0.173648 - 0.984808i) q^{80} +(-0.210665 + 0.844929i) q^{81} +(0.160147 + 1.52370i) q^{82} +(-0.594092 - 0.170353i) q^{83} +(0.333197 - 0.208204i) q^{84} +(1.75631 - 0.781961i) q^{86} +(-0.400938 + 0.114967i) q^{87} +(-1.35275 - 1.13510i) q^{89} +(-0.231349 + 0.927889i) q^{90} +(-0.671624 - 0.563559i) q^{92} +(1.28642 - 0.368875i) q^{94} +(0.150383 - 0.145223i) q^{96} +(-2.43400 - 0.697938i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8}+O(q^{10}) \) 24 * q + 3 * q^5 - 3 * q^6 - 3 * q^8	\( 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{14} - 18 q^{21} - 3 q^{23} + 3 q^{25} + 12 q^{27} - 3 q^{28} - 3 q^{30} - 3 q^{40} + 3 q^{41} - 3 q^{43} + 3 q^{48} - 12 q^{49} + 12 q^{58} + 3 q^{61} + 15 q^{63} + 3 q^{64} + 3 q^{67} - 3 q^{69} + 3 q^{70} - 3 q^{84} + 3 q^{87} + 3 q^{89} - 3 q^{92} - 3 q^{98}+O(q^{100}) \) 24 * q + 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^14 - 18 * q^21 - 3 * q^23 + 3 * q^25 + 12 * q^27 - 3 * q^28 - 3 * q^30 - 3 * q^40 + 3 * q^41 - 3 * q^43 + 3 * q^48 - 12 * q^49 + 12 * q^58 + 3 * q^61 + 15 * q^63 + 3 * q^64 + 3 * q^67 - 3 * q^69 + 3 * q^70 - 3 * q^84 + 3 * q^87 + 3 * q^89 - 3 * q^92 - 3 * q^98

Introduction

L-functions

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Database

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