LMFDB - Embedded newform 1638.2.j.n.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(235,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1638.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.j (of order $3$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1638.235
Dual form			1638.2.j.n.1171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000 q^{8} +(0.707107 - 1.22474i) q^{10} +(0.207107 - 0.358719i) q^{11} +1.00000 q^{13} +(1.62132 + 2.09077i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.62132 - 4.54026i) q^{17} +(-1.50000 - 2.59808i) q^{19} +1.41421 q^{20} +0.414214 q^{22} +(-4.53553 - 7.85578i) q^{23} +(1.50000 - 2.59808i) q^{25} +(0.500000 + 0.866025i) q^{26} +(-1.00000 + 2.44949i) q^{28} -5.00000 q^{29} +(-3.41421 + 5.91359i) q^{31} +(0.500000 - 0.866025i) q^{32} +5.24264 q^{34} +(-2.29289 - 2.95680i) q^{35} +(2.53553 + 4.39167i) q^{37} +(1.50000 - 2.59808i) q^{38} +(0.707107 + 1.22474i) q^{40} -4.58579 q^{41} +4.82843 q^{43} +(0.207107 + 0.358719i) q^{44} +(4.53553 - 7.85578i) q^{46} +(4.50000 + 7.79423i) q^{47} +(6.74264 - 1.88064i) q^{49} +3.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(6.15685 - 10.6640i) q^{53} -0.585786 q^{55} +(-2.62132 + 0.358719i) q^{56} +(-2.50000 - 4.33013i) q^{58} +(3.79289 - 6.56948i) q^{59} +(2.62132 + 4.54026i) q^{61} -6.82843 q^{62} +1.00000 q^{64} +(-0.707107 - 1.22474i) q^{65} +(7.32843 - 12.6932i) q^{67} +(2.62132 + 4.54026i) q^{68} +(1.41421 - 3.46410i) q^{70} +1.00000 q^{71} +(0.535534 - 0.927572i) q^{73} +(-2.53553 + 4.39167i) q^{74} +3.00000 q^{76} +(0.414214 - 1.01461i) q^{77} +(-6.65685 - 11.5300i) q^{79} +(-0.707107 + 1.22474i) q^{80} +(-2.29289 - 3.97141i) q^{82} +7.65685 q^{83} -7.41421 q^{85} +(2.41421 + 4.18154i) q^{86} +(-0.207107 + 0.358719i) q^{88} +(-3.12132 - 5.40629i) q^{89} +(2.62132 - 0.358719i) q^{91} +9.07107 q^{92} +(-4.50000 + 7.79423i) q^{94} +(-2.12132 + 3.67423i) q^{95} +7.89949 q^{97} +(5.00000 + 4.89898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{7} - 4 q^{8} - 2 q^{11} + 4 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} - 6 q^{19} - 4 q^{22} - 4 q^{23} + 6 q^{25} + 2 q^{26} - 4 q^{28} - 20 q^{29} - 8 q^{31} + 2 q^{32} + 4 q^{34} - 12 q^{35} - 4 q^{37} + 6 q^{38} - 24 q^{41} + 8 q^{43} - 2 q^{44} + 4 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 2 q^{52} + 2 q^{53} - 8 q^{55} - 2 q^{56} - 10 q^{58} + 18 q^{59} + 2 q^{61} - 16 q^{62} + 4 q^{64} + 18 q^{67} + 2 q^{68} + 4 q^{71} - 12 q^{73} + 4 q^{74} + 12 q^{76} - 4 q^{77} - 4 q^{79} - 12 q^{82} + 8 q^{83} - 24 q^{85} + 4 q^{86} + 2 q^{88} - 4 q^{89} + 2 q^{91} + 8 q^{92} - 18 q^{94} - 8 q^{97} + 20 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 - 4 * q^8 - 2 * q^11 + 4 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^17 - 6 * q^19 - 4 * q^22 - 4 * q^23 + 6 * q^25 + 2 * q^26 - 4 * q^28 - 20 * q^29 - 8 * q^31 + 2 * q^32 + 4 * q^34 - 12 * q^35 - 4 * q^37 + 6 * q^38 - 24 * q^41 + 8 * q^43 - 2 * q^44 + 4 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 2 * q^52 + 2 * q^53 - 8 * q^55 - 2 * q^56 - 10 * q^58 + 18 * q^59 + 2 * q^61 - 16 * q^62 + 4 * q^64 + 18 * q^67 + 2 * q^68 + 4 * q^71 - 12 * q^73 + 4 * q^74 + 12 * q^76 - 4 * q^77 - 4 * q^79 - 12 * q^82 + 8 * q^83 - 24 * q^85 + 4 * q^86 + 2 * q^88 - 4 * q^89 + 2 * q^91 + 8 * q^92 - 18 * q^94 - 8 * q^97 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.707107	−	1.22474i	−0.316228	−	0.547723i	0.663470	−	0.748203i	$-0.269083\pi$
$5$	−0.707107	−	1.22474i	−0.316228	−	0.547723i	−0.979698	+	0.200480i	$0.935750\pi$
$6$		0			0
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.707107	−	1.22474i	0.223607	−	0.387298i
$11$	0.207107	−	0.358719i	0.0624450	−	0.108158i	−0.833113	−	0.553103i	$-0.813444\pi$
$11$	0.207107	−	0.358719i	0.0624450	−	0.108158i	0.895558	+	0.444945i	$0.146777\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	1.62132	+	2.09077i	0.433316	+	0.558782i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.62132	−	4.54026i	0.635764	−	1.10117i	−0.350589	−	0.936529i	$-0.614019\pi$
$17$	2.62132	−	4.54026i	0.635764	−	1.10117i	0.986353	−	0.164645i	$-0.0526480\pi$
$18$		0			0
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	0.641071	−	0.767482i	$-0.278491\pi$
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	−0.985194	+	0.171442i	$0.945157\pi$
$20$	1.41421			0.316228
$21$		0			0
$22$	0.414214			0.0883106
$23$	−4.53553	−	7.85578i	−0.945724	−	1.63804i	−0.754295	−	0.656536i	$-0.772021\pi$
$23$	−4.53553	−	7.85578i	−0.945724	−	1.63804i	−0.191429	−	0.981506i	$-0.561312\pi$
$24$		0			0
$25$	1.50000	−	2.59808i	0.300000	−	0.519615i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$		0			0
$28$	−1.00000	+	2.44949i	−0.188982	+	0.462910i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	−3.41421	+	5.91359i	−0.613211	+	1.06211i	0.377485	+	0.926016i	$0.376789\pi$
$31$	−3.41421	+	5.91359i	−0.613211	+	1.06211i	−0.990696	+	0.136097i	$0.956544\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	5.24264			0.899105
$35$	−2.29289	−	2.95680i	−0.387570	−	0.499790i
$36$		0			0
$37$	2.53553	+	4.39167i	0.416839	+	0.721987i	0.995620	−	0.0934968i	$-0.0298045\pi$
$37$	2.53553	+	4.39167i	0.416839	+	0.721987i	−0.578780	+	0.815483i	$0.696471\pi$
$38$	1.50000	−	2.59808i	0.243332	−	0.421464i
$39$		0			0
$40$	0.707107	+	1.22474i	0.111803	+	0.193649i
$41$	−4.58579			−0.716180			−0.358090	−	0.933687i	$-0.616572\pi$
$41$	−4.58579			−0.716180			−0.358090	+	0.933687i	$0.616572\pi$
$42$		0			0
$43$	4.82843			0.736328			0.368164	−	0.929761i	$-0.379986\pi$
$43$	4.82843			0.736328			0.368164	+	0.929761i	$0.379986\pi$
$44$	0.207107	+	0.358719i	0.0312225	+	0.0540790i
$45$		0			0
$46$	4.53553	−	7.85578i	0.668728	−	1.15827i
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	3.00000			0.424264
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	6.15685	−	10.6640i	0.845709	−	1.46481i	−0.0392951	−	0.999228i	$-0.512511\pi$
$53$	6.15685	−	10.6640i	0.845709	−	1.46481i	0.885004	−	0.465583i	$-0.154155\pi$
$54$		0			0
$55$	−0.585786			−0.0789874
$56$	−2.62132	+	0.358719i	−0.350289	+	0.0479359i
$57$		0			0
$58$	−2.50000	−	4.33013i	−0.328266	−	0.568574i
$59$	3.79289	−	6.56948i	0.493793	−	0.855274i	−0.506182	−	0.862427i	$-0.668944\pi$
$59$	3.79289	−	6.56948i	0.493793	−	0.855274i	0.999974	+	0.00715287i	$0.00227685\pi$
$60$		0			0
$61$	2.62132	+	4.54026i	0.335626	+	0.581321i	0.983605	−	0.180337i	$-0.0577189\pi$
$61$	2.62132	+	4.54026i	0.335626	+	0.581321i	−0.647979	+	0.761658i	$0.724386\pi$
$62$	−6.82843			−0.867211
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.707107	−	1.22474i	−0.0877058	−	0.151911i
$66$		0			0
$67$	7.32843	−	12.6932i	0.895310	−	1.55072i	0.0618892	−	0.998083i	$-0.480287\pi$
$67$	7.32843	−	12.6932i	0.895310	−	1.55072i	0.833421	−	0.552639i	$-0.186379\pi$
$68$	2.62132	+	4.54026i	0.317882	+	0.550587i
$69$		0			0
$70$	1.41421	−	3.46410i	0.169031	−	0.414039i
$71$	1.00000			0.118678			0.0593391	−	0.998238i	$-0.481101\pi$
$71$	1.00000			0.118678			0.0593391	+	0.998238i	$0.481101\pi$
$72$		0			0
$73$	0.535534	−	0.927572i	0.0626795	−	0.108564i	−0.832983	−	0.553299i	$-0.813369\pi$
$73$	0.535534	−	0.927572i	0.0626795	−	0.108564i	0.895662	+	0.444735i	$0.146702\pi$
$74$	−2.53553	+	4.39167i	−0.294750	+	0.510522i
$75$		0			0
$76$	3.00000			0.344124
$77$	0.414214	−	1.01461i	0.0472040	−	0.115626i
$78$		0			0
$79$	−6.65685	−	11.5300i	−0.748955	−	1.29723i	−0.948324	−	0.317303i	$-0.897223\pi$
$79$	−6.65685	−	11.5300i	−0.748955	−	1.29723i	0.199370	−	0.979924i	$-0.436111\pi$
$80$	−0.707107	+	1.22474i	−0.0790569	+	0.136931i
$81$		0			0
$82$	−2.29289	−	3.97141i	−0.253208	−	0.438569i
$83$	7.65685			0.840449			0.420224	−	0.907420i	$-0.361951\pi$
$83$	7.65685			0.840449			0.420224	+	0.907420i	$0.361951\pi$
$84$		0			0
$85$	−7.41421			−0.804184
$86$	2.41421	+	4.18154i	0.260331	+	0.450907i
$87$		0			0
$88$	−0.207107	+	0.358719i	−0.0220777	+	0.0382396i
$89$	−3.12132	−	5.40629i	−0.330859	−	0.573065i	0.651821	−	0.758373i	$-0.274005\pi$
$89$	−3.12132	−	5.40629i	−0.330859	−	0.573065i	−0.982681	+	0.185307i	$0.940672\pi$
$90$		0			0
$91$	2.62132	−	0.358719i	0.274789	−	0.0376040i
$92$	9.07107			0.945724
$93$		0			0
$94$	−4.50000	+	7.79423i	−0.464140	+	0.803913i
$95$	−2.12132	+	3.67423i	−0.217643	+	0.376969i
$96$		0			0
$97$	7.89949			0.802072			0.401036	−	0.916062i	$-0.368650\pi$
$97$	7.89949			0.802072			0.401036	+	0.916062i	$0.368650\pi$
$98$	5.00000	+	4.89898i	0.505076	+	0.494872i
$99$		0			0
$100$	1.50000	+	2.59808i	0.150000	+	0.259808i
$101$	−0.585786	+	1.01461i	−0.0582879	+	0.100958i	−0.893697	−	0.448671i	$-0.851897\pi$
$101$	−0.585786	+	1.01461i	−0.0582879	+	0.100958i	0.835409	+	0.549629i	$0.185231\pi$
$102$		0			0
$103$	−3.24264	−	5.61642i	−0.319507	−	0.553402i	0.660878	−	0.750493i	$-0.270184\pi$
$103$	−3.24264	−	5.61642i	−0.319507	−	0.553402i	−0.980385	+	0.197091i	$0.936851\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	12.3137			1.19601
$107$	6.82843	+	11.8272i	0.660129	+	1.14338i	0.980581	+	0.196112i	$0.0628317\pi$
$107$	6.82843	+	11.8272i	0.660129	+	1.14338i	−0.320452	+	0.947265i	$0.603835\pi$
$108$		0			0
$109$	−0.828427	+	1.43488i	−0.0793489	+	0.137436i	−0.902969	−	0.429705i	$-0.858617\pi$
$109$	−0.828427	+	1.43488i	−0.0793489	+	0.137436i	0.823620	+	0.567142i	$0.191951\pi$
$110$	−0.292893	−	0.507306i	−0.0279263	−	0.0483697i
$111$		0			0
$112$	−1.62132	−	2.09077i	−0.153200	−	0.197559i
$113$	6.07107			0.571118			0.285559	−	0.958361i	$-0.407821\pi$
$113$	6.07107			0.571118			0.285559	+	0.958361i	$0.407821\pi$
$114$		0			0
$115$	−6.41421	+	11.1097i	−0.598128	+	1.03599i
$116$	2.50000	−	4.33013i	0.232119	−	0.402042i
$117$		0			0
$118$	7.58579			0.698328
$119$	5.24264	−	12.8418i	0.480592	−	1.17721i
$120$		0			0
$121$	5.41421	+	9.37769i	0.492201	+	0.852518i
$122$	−2.62132	+	4.54026i	−0.237323	+	0.411056i
$123$		0			0
$124$	−3.41421	−	5.91359i	−0.306605	−	0.531056i
$125$	−11.3137			−1.01193
$126$		0			0
$127$	9.89949			0.878438			0.439219	−	0.898380i	$-0.355255\pi$
$127$	9.89949			0.878438			0.439219	+	0.898380i	$0.355255\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	0.707107	−	1.22474i	0.0620174	−	0.107417i
$131$	4.94975	+	8.57321i	0.432461	+	0.749045i	0.997085	−	0.0763036i	$-0.0243118\pi$
$131$	4.94975	+	8.57321i	0.432461	+	0.749045i	−0.564623	+	0.825349i	$0.690978\pi$
$132$		0			0
$133$	−4.86396	−	6.27231i	−0.421759	−	0.543878i
$134$	14.6569			1.26616
$135$		0			0
$136$	−2.62132	+	4.54026i	−0.224776	+	0.389324i
$137$	−6.53553	+	11.3199i	−0.558368	+	0.967122i	0.439265	+	0.898358i	$0.355239\pi$
$137$	−6.53553	+	11.3199i	−0.558368	+	0.967122i	−0.997633	+	0.0687646i	$0.978094\pi$
$138$		0			0
$139$	−21.2132			−1.79928			−0.899640	−	0.436632i	$-0.856171\pi$
$139$	−21.2132			−1.79928			−0.899640	+	0.436632i	$0.856171\pi$
$140$	3.70711	−	0.507306i	0.313308	−	0.0428752i
$141$		0			0
$142$	0.500000	+	0.866025i	0.0419591	+	0.0726752i
$143$	0.207107	−	0.358719i	0.0173191	−	0.0299976i
$144$		0			0
$145$	3.53553	+	6.12372i	0.293610	+	0.508548i
$146$	1.07107			0.0886422
$147$		0			0
$148$	−5.07107			−0.416839
$149$	7.94975	+	13.7694i	0.651269	+	1.12803i	0.982815	+	0.184592i	$0.0590962\pi$
$149$	7.94975	+	13.7694i	0.651269	+	1.12803i	−0.331547	+	0.943439i	$0.607570\pi$
$150$		0			0
$151$	3.79289	−	6.56948i	0.308661	−	0.534617i	−0.669408	−	0.742895i	$-0.733452\pi$
$151$	3.79289	−	6.56948i	0.308661	−	0.534617i	0.978070	+	0.208278i	$0.0667857\pi$
$152$	1.50000	+	2.59808i	0.121666	+	0.210732i
$153$		0			0
$154$	1.08579	−	0.148586i	0.0874952	−	0.0119734i
$155$	9.65685			0.775657
$156$		0			0
$157$	−3.96447	+	6.86666i	−0.316399	+	0.548019i	−0.979734	−	0.200304i	$-0.935807\pi$
$157$	−3.96447	+	6.86666i	−0.316399	+	0.548019i	0.663335	+	0.748323i	$0.269140\pi$
$158$	6.65685	−	11.5300i	0.529591	−	0.917278i
$159$		0			0
$160$	−1.41421			−0.111803
$161$	−14.7071	−	18.9655i	−1.15908	−	1.49469i
$162$		0			0
$163$	−8.57107	−	14.8455i	−0.671338	−	1.16279i	−0.977525	−	0.210820i	$-0.932387\pi$
$163$	−8.57107	−	14.8455i	−0.671338	−	1.16279i	0.306187	−	0.951971i	$-0.400947\pi$
$164$	2.29289	−	3.97141i	0.179045	−	0.310115i
$165$		0			0
$166$	3.82843	+	6.63103i	0.297144	+	0.514668i
$167$	−12.3137			−0.952863			−0.476432	−	0.879211i	$-0.658070\pi$
$167$	−12.3137			−0.952863			−0.476432	+	0.879211i	$0.658070\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−3.70711	−	6.42090i	−0.284322	−	0.492460i
$171$		0			0
$172$	−2.41421	+	4.18154i	−0.184082	+	0.318839i
$173$	10.1569	+	17.5922i	0.772211	+	1.33751i	0.936349	+	0.351072i	$0.114183\pi$
$173$	10.1569	+	17.5922i	0.772211	+	1.33751i	−0.164137	+	0.986438i	$0.552484\pi$
$174$		0			0
$175$	3.00000	−	7.34847i	0.226779	−	0.555492i
$176$	−0.414214			−0.0312225
$177$		0			0
$178$	3.12132	−	5.40629i	0.233953	−	0.405218i
$179$	−6.17157	+	10.6895i	−0.461285	+	0.798969i	−0.999025	−	0.0441415i	$-0.985945\pi$
$179$	−6.17157	+	10.6895i	−0.461285	+	0.798969i	0.537740	+	0.843111i	$0.319278\pi$
$180$		0			0
$181$	−11.5858			−0.861165			−0.430582	−	0.902551i	$-0.641692\pi$
$181$	−11.5858			−0.861165			−0.430582	+	0.902551i	$0.641692\pi$
$182$	1.62132	+	2.09077i	0.120180	+	0.154978i
$183$		0			0
$184$	4.53553	+	7.85578i	0.334364	+	0.579135i
$185$	3.58579	−	6.21076i	0.263632	−	0.456624i
$186$		0			0
$187$	−1.08579	−	1.88064i	−0.0794006	−	0.137526i
$188$	−9.00000			−0.656392
$189$		0			0
$190$	−4.24264			−0.307794
$191$	1.17157	+	2.02922i	0.0847720	+	0.146829i	0.905294	−	0.424785i	$-0.139650\pi$
$191$	1.17157	+	2.02922i	0.0847720	+	0.146829i	−0.820522	+	0.571615i	$0.806317\pi$
$192$		0			0
$193$	7.87868	−	13.6463i	0.567120	−	0.982280i	−0.429729	−	0.902958i	$-0.641391\pi$
$193$	7.87868	−	13.6463i	0.567120	−	0.982280i	0.996849	−	0.0793225i	$-0.0252757\pi$
$194$	3.94975	+	6.84116i	0.283575	+	0.491167i
$195$		0			0
$196$	−1.74264	+	6.77962i	−0.124474	+	0.484258i
$197$	−9.55635			−0.680862			−0.340431	−	0.940270i	$-0.610573\pi$
$197$	−9.55635			−0.680862			−0.340431	+	0.940270i	$0.610573\pi$
$198$		0			0
$199$	−5.29289	+	9.16756i	−0.375203	+	0.649871i	−0.990357	−	0.138536i	$-0.955760\pi$
$199$	−5.29289	+	9.16756i	−0.375203	+	0.649871i	0.615154	+	0.788407i	$0.289094\pi$
$200$	−1.50000	+	2.59808i	−0.106066	+	0.183712i
$201$		0			0
$202$	−1.17157			−0.0824316
$203$	−13.1066	+	1.79360i	−0.919903	+	0.125886i
$204$		0			0
$205$	3.24264	+	5.61642i	0.226476	+	0.392268i
$206$	3.24264	−	5.61642i	0.225925	−	0.391314i
$207$		0			0
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	−1.24264			−0.0859553
$210$		0			0
$211$	−28.3848			−1.95409			−0.977044	−	0.213036i	$-0.931665\pi$
$211$	−28.3848			−1.95409			−0.977044	+	0.213036i	$0.931665\pi$
$212$	6.15685	+	10.6640i	0.422854	+	0.732405i
$213$		0			0
$214$	−6.82843	+	11.8272i	−0.466782	+	0.808490i
$215$	−3.41421	−	5.91359i	−0.232847	−	0.403304i
$216$		0			0
$217$	−6.82843	+	16.7262i	−0.463544	+	1.13545i
$218$	−1.65685			−0.112216
$219$		0			0
$220$	0.292893	−	0.507306i	0.0197469	−	0.0342026i
$221$	2.62132	−	4.54026i	0.176329	−	0.305411i
$222$		0			0
$223$	21.3848			1.43203			0.716015	−	0.698085i	$-0.245964\pi$
$223$	21.3848			1.43203			0.716015	+	0.698085i	$0.245964\pi$
$224$	1.00000	−	2.44949i	0.0668153	−	0.163663i
$225$		0			0
$226$	3.03553	+	5.25770i	0.201921	+	0.349737i
$227$	−13.0711	+	22.6398i	−0.867557	+	1.50265i	−0.00307185	+	0.999995i	$0.500978\pi$
$227$	−13.0711	+	22.6398i	−0.867557	+	1.50265i	−0.864485	+	0.502658i	$0.832356\pi$
$228$		0			0
$229$	3.58579	+	6.21076i	0.236955	+	0.410419i	0.959839	−	0.280551i	$-0.0905171\pi$
$229$	3.58579	+	6.21076i	0.236955	+	0.410419i	−0.722884	+	0.690970i	$0.757184\pi$
$230$	−12.8284			−0.845881
$231$		0			0
$232$	5.00000			0.328266
$233$	−1.86396	−	3.22848i	−0.122112	−	0.211504i	0.798488	−	0.602010i	$-0.205633\pi$
$233$	−1.86396	−	3.22848i	−0.122112	−	0.211504i	−0.920600	+	0.390506i	$0.872300\pi$
$234$		0			0
$235$	6.36396	−	11.0227i	0.415139	−	0.719042i
$236$	3.79289	+	6.56948i	0.246896	+	0.427637i
$237$		0			0
$238$	13.7426	−	1.88064i	0.890803	−	0.121904i
$239$	2.51472			0.162664			0.0813318	−	0.996687i	$-0.474083\pi$
$239$	2.51472			0.162664			0.0813318	+	0.996687i	$0.474083\pi$
$240$		0			0
$241$	8.24264	−	14.2767i	0.530955	−	0.919641i	−0.468392	−	0.883521i	$-0.655167\pi$
$241$	8.24264	−	14.2767i	0.530955	−	0.919641i	0.999347	−	0.0361207i	$-0.0115001\pi$
$242$	−5.41421	+	9.37769i	−0.348039	+	0.602821i
$243$		0			0
$244$	−5.24264			−0.335626
$245$	−7.07107	−	6.92820i	−0.451754	−	0.442627i
$246$		0			0
$247$	−1.50000	−	2.59808i	−0.0954427	−	0.165312i
$248$	3.41421	−	5.91359i	0.216803	−	0.375513i
$249$		0			0
$250$	−5.65685	−	9.79796i	−0.357771	−	0.619677i
$251$	−12.8284			−0.809723			−0.404862	−	0.914378i	$-0.632680\pi$
$251$	−12.8284			−0.809723			−0.404862	+	0.914378i	$0.632680\pi$
$252$		0			0
$253$	−3.75736			−0.236223
$254$	4.94975	+	8.57321i	0.310575	+	0.537931i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.8995	−	18.8785i	−0.679892	−	1.17761i	−0.975013	−	0.222147i	$-0.928693\pi$
$257$	−10.8995	−	18.8785i	−0.679892	−	1.17761i	0.295121	−	0.955460i	$-0.404640\pi$
$258$		0			0
$259$	8.22183	+	10.6024i	0.510879	+	0.658803i
$260$	1.41421			0.0877058
$261$		0			0
$262$	−4.94975	+	8.57321i	−0.305796	+	0.529655i
$263$	−3.77817	+	6.54399i	−0.232972	+	0.403520i	−0.958681	−	0.284482i	$-0.908178\pi$
$263$	−3.77817	+	6.54399i	−0.232972	+	0.403520i	0.725709	+	0.688002i	$0.241512\pi$
$264$		0			0
$265$	−17.4142			−1.06975
$266$	3.00000	−	7.34847i	0.183942	−	0.450564i
$267$		0			0
$268$	7.32843	+	12.6932i	0.447655	+	0.775361i
$269$	−1.84315	+	3.19242i	−0.112379	+	0.194645i	−0.916729	−	0.399510i	$-0.869180\pi$
$269$	−1.84315	+	3.19242i	−0.112379	+	0.194645i	0.804350	+	0.594155i	$0.202514\pi$
$270$		0			0
$271$	7.69239	+	13.3236i	0.467279	+	0.809351i	0.999301	−	0.0373791i	$-0.0119009\pi$
$271$	7.69239	+	13.3236i	0.467279	+	0.809351i	−0.532022	+	0.846731i	$0.678568\pi$
$272$	−5.24264			−0.317882
$273$		0			0
$274$	−13.0711			−0.789652
$275$	−0.621320	−	1.07616i	−0.0374670	−	0.0648948i
$276$		0			0
$277$	8.20711	−	14.2151i	0.493117	−	0.854104i	−0.506851	−	0.862033i	$-0.669191\pi$
$277$	8.20711	−	14.2151i	0.493117	−	0.854104i	0.999969	+	0.00792936i	$0.00252402\pi$
$278$	−10.6066	−	18.3712i	−0.636142	−	1.10183i
$279$		0			0
$280$	2.29289	+	2.95680i	0.137027	+	0.176702i
$281$	−7.31371			−0.436299			−0.218150	−	0.975915i	$-0.570002\pi$
$281$	−7.31371			−0.436299			−0.218150	+	0.975915i	$0.570002\pi$
$282$		0			0
$283$	−8.53553	+	14.7840i	−0.507385	+	0.878816i	0.492579	+	0.870268i	$0.336054\pi$
$283$	−8.53553	+	14.7840i	−0.507385	+	0.878816i	−0.999963	+	0.00854836i	$0.997279\pi$
$284$	−0.500000	+	0.866025i	−0.0296695	+	0.0513892i
$285$		0			0
$286$	0.414214			0.0244930
$287$	−12.0208	+	1.64501i	−0.709566	+	0.0971019i
$288$		0			0
$289$	−5.24264	−	9.08052i	−0.308391	−	0.534148i
$290$	−3.53553	+	6.12372i	−0.207614	+	0.359597i
$291$		0			0
$292$	0.535534	+	0.927572i	0.0313398	+	0.0542820i
$293$	18.7279			1.09410			0.547048	−	0.837101i	$-0.315751\pi$
$293$	18.7279			1.09410			0.547048	+	0.837101i	$0.315751\pi$
$294$		0			0
$295$	−10.7279			−0.624604
$296$	−2.53553	−	4.39167i	−0.147375	−	0.255261i
$297$		0			0
$298$	−7.94975	+	13.7694i	−0.460517	+	0.797638i
$299$	−4.53553	−	7.85578i	−0.262297	−	0.454311i
$300$		0			0
$301$	12.6569	−	1.73205i	0.729529	−	0.0998337i
$302$	7.58579			0.436513
$303$		0			0
$304$	−1.50000	+	2.59808i	−0.0860309	+	0.149010i
$305$	3.70711	−	6.42090i	0.212268	−	0.367660i
$306$		0			0
$307$	−19.6274			−1.12020			−0.560098	−	0.828426i	$-0.689237\pi$
$307$	−19.6274			−1.12020			−0.560098	+	0.828426i	$0.689237\pi$
$308$	0.671573	+	0.866025i	0.0382664	+	0.0493464i
$309$		0			0
$310$	4.82843	+	8.36308i	0.274236	+	0.474991i
$311$	−3.29289	+	5.70346i	−0.186723	+	0.323413i	−0.944156	−	0.329500i	$-0.893120\pi$
$311$	−3.29289	+	5.70346i	−0.186723	+	0.323413i	0.757433	+	0.652913i	$0.226453\pi$
$312$		0			0
$313$	−9.07107	−	15.7116i	−0.512727	−	0.888069i	−0.999891	−	0.0147588i	$-0.995302\pi$
$313$	−9.07107	−	15.7116i	−0.512727	−	0.888069i	0.487164	−	0.873310i	$-0.338031\pi$
$314$	−7.92893			−0.447456
$315$		0			0
$316$	13.3137			0.748955
$317$	0.414214	+	0.717439i	0.0232646	+	0.0402954i	0.877423	−	0.479717i	$-0.159261\pi$
$317$	0.414214	+	0.717439i	0.0232646	+	0.0402954i	−0.854159	+	0.520012i	$0.825927\pi$
$318$		0			0
$319$	−1.03553	+	1.79360i	−0.0579788	+	0.100422i
$320$	−0.707107	−	1.22474i	−0.0395285	−	0.0684653i
$321$		0			0
$322$	9.07107	−	22.2195i	0.505511	−	1.23824i
$323$	−15.7279			−0.875125
$324$		0			0
$325$	1.50000	−	2.59808i	0.0832050	−	0.144115i
$326$	8.57107	−	14.8455i	0.474708	−	0.822218i
$327$		0			0
$328$	4.58579			0.253208
$329$	14.5919	+	18.8169i	0.804477	+	1.03741i
$330$		0			0
$331$	11.2426	+	19.4728i	0.617951	+	1.07032i	0.989859	+	0.142053i	$0.0453705\pi$
$331$	11.2426	+	19.4728i	0.617951	+	1.07032i	−0.371908	+	0.928270i	$0.621296\pi$
$332$	−3.82843	+	6.63103i	−0.210112	+	0.363925i
$333$		0			0
$334$	−6.15685	−	10.6640i	−0.336888	−	0.583507i
$335$	−20.7279			−1.13249
$336$		0			0
$337$	28.6569			1.56104			0.780519	−	0.625132i	$-0.214955\pi$
$337$	28.6569			1.56104			0.780519	+	0.625132i	$0.214955\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$		0			0
$340$	3.70711	−	6.42090i	0.201046	−	0.348222i
$341$	1.41421	+	2.44949i	0.0765840	+	0.132647i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$	−4.82843			−0.260331
$345$		0			0
$346$	−10.1569	+	17.5922i	−0.546036	+	0.945762i
$347$	2.87868	−	4.98602i	0.154536	−	0.267664i	−0.778354	−	0.627825i	$-0.783945\pi$
$347$	2.87868	−	4.98602i	0.154536	−	0.267664i	0.932890	+	0.360162i	$0.117279\pi$
$348$		0			0
$349$	5.41421			0.289816			0.144908	−	0.989445i	$-0.453711\pi$
$349$	5.41421			0.289816			0.144908	+	0.989445i	$0.453711\pi$
$350$	7.86396	−	1.07616i	0.420346	−	0.0575231i
$351$		0			0
$352$	−0.207107	−	0.358719i	−0.0110388	−	0.0191198i
$353$	6.31371	−	10.9357i	0.336045	−	0.582047i	−0.647640	−	0.761946i	$-0.724244\pi$
$353$	6.31371	−	10.9357i	0.336045	−	0.582047i	0.983685	+	0.179900i	$0.0575773\pi$
$354$		0			0
$355$	−0.707107	−	1.22474i	−0.0375293	−	0.0650027i
$356$	6.24264			0.330859
$357$		0			0
$358$	−12.3431			−0.652356
$359$	−7.72792	−	13.3852i	−0.407864	−	0.706441i	0.586786	−	0.809742i	$-0.300393\pi$
$359$	−7.72792	−	13.3852i	−0.407864	−	0.706441i	−0.994650	+	0.103301i	$0.967060\pi$
$360$		0			0
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	−5.79289	−	10.0336i	−0.304468	−	0.527354i
$363$		0			0
$364$	−1.00000	+	2.44949i	−0.0524142	+	0.128388i
$365$	−1.51472			−0.0792840
$366$		0			0
$367$	−7.00000	+	12.1244i	−0.365397	+	0.632886i	−0.988840	−	0.148983i	$-0.952400\pi$
$367$	−7.00000	+	12.1244i	−0.365397	+	0.632886i	0.623443	+	0.781869i	$0.285733\pi$
$368$	−4.53553	+	7.85578i	−0.236431	+	0.409511i
$369$		0			0
$370$	7.17157			0.372832
$371$	12.3137	−	30.1623i	0.639296	−	1.56595i
$372$		0			0
$373$	5.55025	+	9.61332i	0.287381	+	0.497759i	0.973184	−	0.230029i	$-0.0738820\pi$
$373$	5.55025	+	9.61332i	0.287381	+	0.497759i	−0.685803	+	0.727788i	$0.740549\pi$
$374$	1.08579	−	1.88064i	0.0561447	−	0.0972454i
$375$		0			0
$376$	−4.50000	−	7.79423i	−0.232070	−	0.401957i
$377$	−5.00000			−0.257513
$378$		0			0
$379$	−33.6569			−1.72884			−0.864418	−	0.502773i	$-0.832313\pi$
$379$	−33.6569			−1.72884			−0.864418	+	0.502773i	$0.832313\pi$
$380$	−2.12132	−	3.67423i	−0.108821	−	0.188484i
$381$		0			0
$382$	−1.17157	+	2.02922i	−0.0599429	+	0.103824i
$383$	3.24264	+	5.61642i	0.165691	+	0.286986i	0.936901	−	0.349596i	$-0.113681\pi$
$383$	3.24264	+	5.61642i	0.165691	+	0.286986i	−0.771209	+	0.636582i	$0.780348\pi$
$384$		0			0
$385$	−1.53553	+	0.210133i	−0.0782581	+	0.0107094i
$386$	15.7574			0.802028
$387$		0			0
$388$	−3.94975	+	6.84116i	−0.200518	+	0.347307i
$389$	11.5000	−	19.9186i	0.583073	−	1.00991i	−0.412039	−	0.911166i	$-0.635183\pi$
$389$	11.5000	−	19.9186i	0.583073	−	1.00991i	0.995113	−	0.0987463i	$-0.0314832\pi$
$390$		0			0
$391$	−47.5563			−2.40503
$392$	−6.74264	+	1.88064i	−0.340555	+	0.0949865i
$393$		0			0
$394$	−4.77817	−	8.27604i	−0.240721	−	0.416941i
$395$	−9.41421	+	16.3059i	−0.473680	+	0.820439i
$396$		0			0
$397$	9.87868	+	17.1104i	0.495797	+	0.858745i	0.999988	−	0.00484675i	$-0.00154277\pi$
$397$	9.87868	+	17.1104i	0.495797	+	0.858745i	−0.504192	+	0.863592i	$0.668209\pi$
$398$	−10.5858			−0.530618
$399$		0			0
$400$	−3.00000			−0.150000
$401$	9.53553	+	16.5160i	0.476182	+	0.824771i	0.999628	−	0.0272878i	$-0.00868707\pi$
$401$	9.53553	+	16.5160i	0.476182	+	0.824771i	−0.523446	+	0.852059i	$0.675354\pi$
$402$		0			0
$403$	−3.41421	+	5.91359i	−0.170074	+	0.294577i
$404$	−0.585786	−	1.01461i	−0.0291440	−	0.0504788i
$405$		0			0
$406$	−8.10660	−	10.4539i	−0.402324	−	0.518816i
$407$	2.10051			0.104118
$408$		0			0
$409$	1.29289	−	2.23936i	0.0639295	−	0.110729i	−0.832289	−	0.554342i	$-0.812970\pi$
$409$	1.29289	−	2.23936i	0.0639295	−	0.110729i	0.896219	+	0.443613i	$0.146303\pi$
$410$	−3.24264	+	5.61642i	−0.160143	+	0.277375i
$411$		0			0
$412$	6.48528			0.319507
$413$	7.58579	−	18.5813i	0.373272	−	0.914326i
$414$		0			0
$415$	−5.41421	−	9.37769i	−0.265773	−	0.460333i
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$		0			0
$418$	−0.621320	−	1.07616i	−0.0303898	−	0.0526366i
$419$	27.4558			1.34131			0.670653	−	0.741771i	$-0.266014\pi$
$419$	27.4558			1.34131			0.670653	+	0.741771i	$0.266014\pi$
$420$		0			0
$421$	10.5858			0.515920			0.257960	−	0.966156i	$-0.416950\pi$
$421$	10.5858			0.515920			0.257960	+	0.966156i	$0.416950\pi$
$422$	−14.1924	−	24.5819i	−0.690875	−	1.19663i
$423$		0			0
$424$	−6.15685	+	10.6640i	−0.299003	+	0.517889i
$425$	−7.86396	−	13.6208i	−0.381458	−	0.660705i
$426$		0			0
$427$	8.50000	+	10.9612i	0.411344	+	0.530448i
$428$	−13.6569			−0.660129
$429$		0			0
$430$	3.41421	−	5.91359i	0.164648	−	0.285179i
$431$	7.24264	−	12.5446i	0.348866	−	0.604253i	−0.637183	−	0.770713i	$-0.719900\pi$
$431$	7.24264	−	12.5446i	0.348866	−	0.604253i	0.986048	+	0.166460i	$0.0532336\pi$
$432$		0			0
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	−17.8995	+	2.44949i	−0.859203	+	0.117579i
$435$		0			0
$436$	−0.828427	−	1.43488i	−0.0396745	−	0.0687182i
$437$	−13.6066	+	23.5673i	−0.650892	+	1.12738i
$438$		0			0
$439$	5.29289	+	9.16756i	0.252616	+	0.437544i	0.964245	−	0.265011i	$-0.0853757\pi$
$439$	5.29289	+	9.16756i	0.252616	+	0.437544i	−0.711629	+	0.702555i	$0.752042\pi$
$440$	0.585786			0.0279263
$441$		0			0
$442$	5.24264			0.249367
$443$	11.3640	+	19.6830i	0.539918	+	0.935166i	0.998908	+	0.0467240i	$0.0148781\pi$
$443$	11.3640	+	19.6830i	0.539918	+	0.935166i	−0.458990	+	0.888442i	$0.651789\pi$
$444$		0			0
$445$	−4.41421	+	7.64564i	−0.209254	+	0.362438i
$446$	10.6924	+	18.5198i	0.506299	+	0.876936i
$447$		0			0
$448$	2.62132	−	0.358719i	0.123846	−	0.0169479i
$449$	33.9411			1.60178			0.800890	−	0.598811i	$-0.204360\pi$
$449$	33.9411			1.60178			0.800890	+	0.598811i	$0.204360\pi$
$450$		0			0
$451$	−0.949747	+	1.64501i	−0.0447219	+	0.0774605i
$452$	−3.03553	+	5.25770i	−0.142780	+	0.247301i
$453$		0			0
$454$	−26.1421			−1.22691
$455$	−2.29289	−	2.95680i	−0.107492	−	0.138617i
$456$		0			0
$457$	7.60660	+	13.1750i	0.355822	+	0.616301i	0.987258	−	0.159126i	$-0.0508677\pi$
$457$	7.60660	+	13.1750i	0.355822	+	0.616301i	−0.631436	+	0.775428i	$0.717534\pi$
$458$	−3.58579	+	6.21076i	−0.167553	+	0.290210i
$459$		0			0
$460$	−6.41421	−	11.1097i	−0.299064	−	0.517994i
$461$	33.4558			1.55819			0.779097	−	0.626903i	$-0.215678\pi$
$461$	33.4558			1.55819			0.779097	+	0.626903i	$0.215678\pi$
$462$		0			0
$463$	−37.9411			−1.76327			−0.881637	−	0.471929i	$-0.843558\pi$
$463$	−37.9411			−1.76327			−0.881637	+	0.471929i	$0.843558\pi$
$464$	2.50000	+	4.33013i	0.116060	+	0.201021i
$465$		0			0
$466$	1.86396	−	3.22848i	0.0863463	−	0.149556i
$467$	−0.121320	−	0.210133i	−0.00561404	−	0.00972380i	0.863205	−	0.504854i	$-0.168454\pi$
$467$	−0.121320	−	0.210133i	−0.00561404	−	0.00972380i	−0.868819	+	0.495130i	$0.835120\pi$
$468$		0			0
$469$	14.6569	−	35.9018i	0.676791	−	1.65779i
$470$	12.7279			0.587095
$471$		0			0
$472$	−3.79289	+	6.56948i	−0.174582	+	0.302385i
$473$	1.00000	−	1.73205i	0.0459800	−	0.0796398i
$474$		0			0
$475$	−9.00000			−0.412948
$476$	8.50000	+	10.9612i	0.389597	+	0.502404i
$477$		0			0
$478$	1.25736	+	2.17781i	0.0575103	+	0.0996107i
$479$	−15.5711	+	26.9699i	−0.711460	+	1.23229i	0.252849	+	0.967506i	$0.418632\pi$
$479$	−15.5711	+	26.9699i	−0.711460	+	1.23229i	−0.964309	+	0.264779i	$0.914701\pi$
$480$		0			0
$481$	2.53553	+	4.39167i	0.115610	+	0.200243i
$482$	16.4853			0.750884
$483$		0			0
$484$	−10.8284			−0.492201
$485$	−5.58579	−	9.67487i	−0.253637	−	0.439313i
$486$		0			0
$487$	11.8640	−	20.5490i	0.537607	−	0.931163i	−0.461425	−	0.887179i	$-0.652662\pi$
$487$	11.8640	−	20.5490i	0.537607	−	0.931163i	0.999032	−	0.0439840i	$-0.0140051\pi$
$488$	−2.62132	−	4.54026i	−0.118662	−	0.205528i
$489$		0			0
$490$	2.46447	−	9.58783i	0.111333	−	0.433134i
$491$	26.2843			1.18619			0.593096	−	0.805132i	$-0.297905\pi$
$491$	26.2843			1.18619			0.593096	+	0.805132i	$0.297905\pi$
$492$		0			0
$493$	−13.1066	+	22.7013i	−0.590292	+	1.02242i
$494$	1.50000	−	2.59808i	0.0674882	−	0.116893i
$495$		0			0
$496$	6.82843			0.306605
$497$	2.62132	−	0.358719i	0.117582	−	0.0160908i
$498$		0			0
$499$	15.0000	+	25.9808i	0.671492	+	1.16306i	0.977481	+	0.211024i	$0.0676797\pi$
$499$	15.0000	+	25.9808i	0.671492	+	1.16306i	−0.305989	+	0.952035i	$0.598987\pi$
$500$	5.65685	−	9.79796i	0.252982	−	0.438178i
$501$		0			0
$502$	−6.41421	−	11.1097i	−0.286280	−	0.495852i
$503$	−35.7990			−1.59620			−0.798099	−	0.602526i	$-0.794161\pi$
$503$	−35.7990			−1.59620			−0.798099	+	0.602526i	$0.794161\pi$
$504$		0			0
$505$	1.65685			0.0737290
$506$	−1.87868	−	3.25397i	−0.0835175	−	0.144657i
$507$		0			0
$508$	−4.94975	+	8.57321i	−0.219610	+	0.380375i
$509$	6.48528	+	11.2328i	0.287455	+	0.497887i	0.973202	−	0.229954i	$-0.0738575\pi$
$509$	6.48528	+	11.2328i	0.287455	+	0.497887i	−0.685747	+	0.727840i	$0.740524\pi$
$510$		0			0
$511$	1.07107	−	2.62357i	0.0473813	−	0.116060i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	10.8995	−	18.8785i	0.480756	−	0.832694i
$515$	−4.58579	+	7.94282i	−0.202074	+	0.350002i
$516$		0			0
$517$	3.72792			0.163954
$518$	−5.07107	+	12.4215i	−0.222810	+	0.545771i
$519$		0			0
$520$	0.707107	+	1.22474i	0.0310087	+	0.0537086i
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	−0.977633	−	0.210318i	$-0.932550\pi$
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	0.670957	+	0.741496i	$0.265883\pi$
$522$		0			0
$523$	1.92893	+	3.34101i	0.0843463	+	0.146092i	0.905112	−	0.425172i	$-0.139786\pi$
$523$	1.92893	+	3.34101i	0.0843463	+	0.146092i	−0.820766	+	0.571264i	$0.806453\pi$
$524$	−9.89949			−0.432461
$525$		0			0
$526$	−7.55635			−0.329472
$527$	17.8995	+	31.0028i	0.779714	+	1.35050i
$528$		0			0
$529$	−29.6421	+	51.3417i	−1.28879	+	2.23225i
$530$	−8.70711	−	15.0812i	−0.378213	−	0.655083i
$531$		0			0
$532$	7.86396	−	1.07616i	0.340946	−	0.0466574i
$533$	−4.58579			−0.198632
$534$		0			0
$535$	9.65685	−	16.7262i	0.417502	−	0.723135i
$536$	−7.32843	+	12.6932i	−0.316540	+	0.548263i
$537$		0			0
$538$	−3.68629			−0.158927
$539$	0.721825	−	2.80821i	0.0310912	−	0.120958i
$540$		0			0
$541$	−6.43503	−	11.1458i	−0.276663	−	0.479195i	0.693890	−	0.720081i	$-0.255895\pi$
$541$	−6.43503	−	11.1458i	−0.276663	−	0.479195i	−0.970553	+	0.240886i	$0.922562\pi$
$542$	−7.69239	+	13.3236i	−0.330416	+	0.572298i
$543$		0			0
$544$	−2.62132	−	4.54026i	−0.112388	−	0.194662i
$545$	2.34315			0.100369
$546$		0			0
$547$	−5.75736			−0.246167			−0.123083	−	0.992396i	$-0.539278\pi$
$547$	−5.75736			−0.246167			−0.123083	+	0.992396i	$0.539278\pi$
$548$	−6.53553	−	11.3199i	−0.279184	−	0.483561i
$549$		0			0
$550$	0.621320	−	1.07616i	0.0264932	−	0.0458875i
$551$	7.50000	+	12.9904i	0.319511	+	0.553409i
$552$		0			0
$553$	−21.5858	−	27.8359i	−0.917921	−	1.18370i
$554$	16.4142			0.697373
$555$		0			0
$556$	10.6066	−	18.3712i	0.449820	−	0.779111i
$557$	−5.48528	+	9.50079i	−0.232419	+	0.402561i	−0.958519	−	0.285027i	$-0.907997\pi$
$557$	−5.48528	+	9.50079i	−0.232419	+	0.402561i	0.726101	+	0.687589i	$0.241331\pi$
$558$		0			0
$559$	4.82843			0.204221
$560$	−1.41421	+	3.46410i	−0.0597614	+	0.146385i
$561$		0			0
$562$	−3.65685	−	6.33386i	−0.154255	−	0.267178i
$563$	−0.242641	+	0.420266i	−0.0102261	+	0.0177121i	−0.871093	−	0.491118i	$-0.836588\pi$
$563$	−0.242641	+	0.420266i	−0.0102261	+	0.0177121i	0.860867	+	0.508830i	$0.169922\pi$
$564$		0			0
$565$	−4.29289	−	7.43551i	−0.180603	−	0.312814i
$566$	−17.0711			−0.717551
$567$		0			0
$568$	−1.00000			−0.0419591
$569$	−12.7929	−	22.1579i	−0.536306	−	0.928909i	−0.999099	−	0.0424428i	$-0.986486\pi$
$569$	−12.7929	−	22.1579i	−0.536306	−	0.928909i	0.462793	−	0.886466i	$-0.346847\pi$
$570$		0			0
$571$	0.828427	−	1.43488i	0.0346686	−	0.0600478i	−0.848171	−	0.529723i	$-0.822296\pi$
$571$	0.828427	−	1.43488i	0.0346686	−	0.0600478i	0.882839	+	0.469676i	$0.155629\pi$
$572$	0.207107	+	0.358719i	0.00865957	+	0.0149988i
$573$		0			0
$574$	−7.43503	−	9.58783i	−0.310332	−	0.400188i
$575$	−27.2132			−1.13487
$576$		0			0
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	−0.615603	−	0.788056i	$-0.711088\pi$
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	0.990278	+	0.139100i	$0.0444210\pi$
$578$	5.24264	−	9.08052i	0.218065	−	0.377700i
$579$		0			0
$580$	−7.07107			−0.293610
$581$	20.0711	−	2.74666i	0.832688	−	0.113951i
$582$		0			0
$583$	−2.55025	−	4.41717i	−0.105621	−	0.182940i
$584$	−0.535534	+	0.927572i	−0.0221606	+	0.0383832i
$585$		0			0
$586$	9.36396	+	16.2189i	0.386822	+	0.669995i
$587$	−11.2426			−0.464033			−0.232017	−	0.972712i	$-0.574532\pi$
$587$	−11.2426			−0.464033			−0.232017	+	0.972712i	$0.574532\pi$
$588$		0			0
$589$	20.4853			0.844081
$590$	−5.36396	−	9.29065i	−0.220831	−	0.382490i
$591$		0			0
$592$	2.53553	−	4.39167i	0.104210	−	0.180497i
$593$	−14.2929	−	24.7560i	−0.586939	−	1.01661i	−0.994631	−	0.103488i	$-0.967000\pi$
$593$	−14.2929	−	24.7560i	−0.586939	−	1.01661i	0.407692	−	0.913120i	$-0.366334\pi$
$594$		0			0
$595$	−19.4350	+	2.65962i	−0.796759	+	0.109034i
$596$	−15.8995			−0.651269
$597$		0			0
$598$	4.53553	−	7.85578i	0.185472	−	0.321247i
$599$	−7.43503	+	12.8778i	−0.303787	+	0.526175i	−0.976991	−	0.213283i	$-0.931584\pi$
$599$	−7.43503	+	12.8778i	−0.303787	+	0.526175i	0.673203	+	0.739457i	$0.264918\pi$
$600$		0			0
$601$	−17.8284			−0.727237			−0.363618	−	0.931548i	$-0.618459\pi$
$601$	−17.8284			−0.727237			−0.363618	+	0.931548i	$0.618459\pi$
$602$	7.82843	+	10.0951i	0.319063	+	0.411447i
$603$		0			0
$604$	3.79289	+	6.56948i	0.154331	+	0.267309i
$605$	7.65685	−	13.2621i	0.311295	−	0.539179i
$606$		0			0
$607$	−13.5355	−	23.4442i	−0.549390	−	0.951572i	−0.998316	−	0.0580031i	$-0.981527\pi$
$607$	−13.5355	−	23.4442i	−0.549390	−	0.951572i	0.448926	−	0.893569i	$-0.351807\pi$
$608$	−3.00000			−0.121666
$609$		0			0
$610$	7.41421			0.300193
$611$	4.50000	+	7.79423i	0.182051	+	0.315321i
$612$		0			0
$613$	17.8995	−	31.0028i	0.722954	−	1.25219i	−0.236857	−	0.971545i	$-0.576117\pi$
$613$	17.8995	−	31.0028i	0.722954	−	1.25219i	0.959811	−	0.280648i	$-0.0905494\pi$
$614$	−9.81371	−	16.9978i	−0.396049	−	0.685977i
$615$		0			0
$616$	−0.414214	+	1.01461i	−0.0166891	+	0.0408799i
$617$	6.48528			0.261088			0.130544	−	0.991443i	$-0.458328\pi$
$617$	6.48528			0.261088			0.130544	+	0.991443i	$0.458328\pi$
$618$		0			0
$619$	−21.7279	+	37.6339i	−0.873319	+	1.51263i	−0.0147761	+	0.999891i	$0.504704\pi$
$619$	−21.7279	+	37.6339i	−0.873319	+	1.51263i	−0.858543	+	0.512742i	$0.828630\pi$
$620$	−4.82843	+	8.36308i	−0.193914	+	0.335869i
$621$		0			0
$622$	−6.58579			−0.264066
$623$	−10.1213	−	13.0519i	−0.405502	−	0.522914i
$624$		0			0
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	9.07107	−	15.7116i	0.362553	−	0.627960i
$627$		0			0
$628$	−3.96447	−	6.86666i	−0.158199	−	0.274009i
$629$	26.5858			1.06004
$630$		0			0
$631$	36.6274			1.45811			0.729057	−	0.684453i	$-0.239959\pi$
$631$	36.6274			1.45811			0.729057	+	0.684453i	$0.239959\pi$
$632$	6.65685	+	11.5300i	0.264795	+	0.458639i
$633$		0			0
$634$	−0.414214	+	0.717439i	−0.0164505	+	0.0284931i
$635$	−7.00000	−	12.1244i	−0.277787	−	0.481140i
$636$		0			0
$637$	6.74264	−	1.88064i	0.267153	−	0.0745136i
$638$	−2.07107			−0.0819944
$639$		0			0
$640$	0.707107	−	1.22474i	0.0279508	−	0.0484123i
$641$	16.5858	−	28.7274i	0.655099	−	1.13467i	−0.326770	−	0.945104i	$-0.605960\pi$
$641$	16.5858	−	28.7274i	0.655099	−	1.13467i	0.981869	−	0.189561i	$-0.0607065\pi$
$642$		0			0
$643$	36.3137			1.43207			0.716036	−	0.698063i	$-0.245954\pi$
$643$	36.3137			1.43207			0.716036	+	0.698063i	$0.245954\pi$
$644$	23.7782	−	3.25397i	0.936991	−	0.128224i
$645$		0			0
$646$	−7.86396	−	13.6208i	−0.309403	−	0.535902i
$647$	14.3137	−	24.7921i	0.562730	−	0.974677i	−0.434527	−	0.900659i	$-0.643084\pi$
$647$	14.3137	−	24.7921i	0.562730	−	0.974677i	0.997257	−	0.0740180i	$-0.0235822\pi$
$648$		0			0
$649$	−1.57107	−	2.72117i	−0.0616698	−	0.106815i
$650$	3.00000			0.117670
$651$		0			0
$652$	17.1421			0.671338
$653$	7.55635	+	13.0880i	0.295703	+	0.512172i	0.975148	−	0.221554i	$-0.0711129\pi$
$653$	7.55635	+	13.0880i	0.295703	+	0.512172i	−0.679445	+	0.733726i	$0.737780\pi$
$654$		0			0
$655$	7.00000	−	12.1244i	0.273513	−	0.473738i
$656$	2.29289	+	3.97141i	0.0895224	+	0.155057i
$657$		0			0
$658$	−9.00000	+	22.0454i	−0.350857	+	0.859419i
$659$	−30.7279			−1.19699			−0.598495	−	0.801127i	$-0.704234\pi$
$659$	−30.7279			−1.19699			−0.598495	+	0.801127i	$0.704234\pi$
$660$		0			0
$661$	6.77817	−	11.7401i	0.263640	−	0.456639i	−0.703566	−	0.710630i	$-0.748410\pi$
$661$	6.77817	−	11.7401i	0.263640	−	0.456639i	0.967207	+	0.253991i	$0.0817434\pi$
$662$	−11.2426	+	19.4728i	−0.436958	+	0.756833i
$663$		0			0
$664$	−7.65685			−0.297144
$665$	−4.24264	+	10.3923i	−0.164523	+	0.402996i
$666$		0			0
$667$	22.6777	+	39.2789i	0.878083	+	1.52088i
$668$	6.15685	−	10.6640i	0.238216	−	0.412602i
$669$		0			0
$670$	−10.3640	−	17.9509i	−0.400395	−	0.693504i
$671$	2.17157			0.0838326
$672$		0			0
$673$	−1.17157			−0.0451608			−0.0225804	−	0.999745i	$-0.507188\pi$
$673$	−1.17157			−0.0451608			−0.0225804	+	0.999745i	$0.507188\pi$
$674$	14.3284	+	24.8176i	0.551910	+	0.955937i
$675$		0			0
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	14.0858	+	24.3973i	0.541361	+	0.937664i	0.998826	+	0.0484369i	$0.0154240\pi$
$677$	14.0858	+	24.3973i	0.541361	+	0.937664i	−0.457465	+	0.889227i	$0.651243\pi$
$678$		0			0
$679$	20.7071	−	2.83370i	0.794666	−	0.108748i
$680$	7.41421			0.284322
$681$		0			0
$682$	−1.41421	+	2.44949i	−0.0541530	+	0.0937958i
$683$	2.72792	−	4.72490i	0.104381	−	0.180793i	−0.809104	−	0.587665i	$-0.800047\pi$
$683$	2.72792	−	4.72490i	0.104381	−	0.180793i	0.913485	+	0.406872i	$0.133381\pi$
$684$		0			0
$685$	18.4853			0.706286
$686$	14.8640	+	11.0482i	0.567509	+	0.421822i
$687$		0			0
$688$	−2.41421	−	4.18154i	−0.0920410	−	0.159420i
$689$	6.15685	−	10.6640i	0.234557	−	0.406265i
$690$		0			0
$691$	−5.57107	−	9.64937i	−0.211933	−	0.367079i	0.740386	−	0.672182i	$-0.234643\pi$
$691$	−5.57107	−	9.64937i	−0.211933	−	0.367079i	−0.952320	+	0.305102i	$0.901309\pi$
$692$	−20.3137			−0.772211
$693$		0			0
$694$	5.75736			0.218546
$695$	15.0000	+	25.9808i	0.568982	+	0.985506i
$696$		0			0
$697$	−12.0208	+	20.8207i	−0.455321	+	0.788639i
$698$	2.70711	+	4.68885i	0.102466	+	0.177475i
$699$		0			0
$700$	4.86396	+	6.27231i	0.183840	+	0.237071i
$701$	−48.4853			−1.83126			−0.915632	−	0.402018i	$-0.868309\pi$
$701$	−48.4853			−1.83126			−0.915632	+	0.402018i	$0.868309\pi$
$702$		0			0
$703$	7.60660	−	13.1750i	0.286888	−	0.496905i
$704$	0.207107	−	0.358719i	0.00780563	−	0.0135197i
$705$		0			0
$706$	12.6274			0.475239
$707$	−1.17157	+	2.86976i	−0.0440615	+	0.107928i
$708$		0			0
$709$	16.0208	+	27.7489i	0.601674	+	1.04213i	0.992568	+	0.121695i	$0.0388328\pi$
$709$	16.0208	+	27.7489i	0.601674	+	1.04213i	−0.390893	+	0.920436i	$0.627834\pi$
$710$	0.707107	−	1.22474i	0.0265372	−	0.0459639i
$711$		0			0
$712$	3.12132	+	5.40629i	0.116976	+	0.202609i
$713$	61.9411			2.31971
$714$		0			0
$715$	−0.585786			−0.0219072
$716$	−6.17157	−	10.6895i	−0.230643	−	0.399485i
$717$		0			0
$718$	7.72792	−	13.3852i	0.288403	−	0.499529i
$719$	−11.1421	−	19.2987i	−0.415532	−	0.719722i	0.579953	−	0.814650i	$-0.303071\pi$
$719$	−11.1421	−	19.2987i	−0.415532	−	0.719722i	−0.995484	+	0.0949285i	$0.969738\pi$
$720$		0			0
$721$	−10.5147	−	13.5592i	−0.391589	−	0.504972i
$722$	10.0000			0.372161
$723$		0			0
$724$	5.79289	−	10.0336i	0.215291	−	0.372895i
$725$	−7.50000	+	12.9904i	−0.278543	+	0.482451i
$726$		0			0
$727$	−38.8284			−1.44007			−0.720033	−	0.693939i	$-0.755874\pi$
$727$	−38.8284			−1.44007			−0.720033	+	0.693939i	$0.755874\pi$
$728$	−2.62132	+	0.358719i	−0.0971526	+	0.0132950i
$729$		0			0
$730$	−0.757359	−	1.31178i	−0.0280311	−	0.0485513i
$731$	12.6569	−	21.9223i	0.468131	−	0.810826i
$732$		0			0
$733$	14.5061	+	25.1253i	0.535795	+	0.928024i	0.999124	+	0.0418379i	$0.0133213\pi$
$733$	14.5061	+	25.1253i	0.535795	+	0.928024i	−0.463330	+	0.886186i	$0.653345\pi$
$734$	−14.0000			−0.516749
$735$		0			0
$736$	−9.07107			−0.334364
$737$	−3.03553	−	5.25770i	−0.111815	−	0.193670i
$738$		0			0
$739$	−3.48528	+	6.03668i	−0.128208	+	0.222063i	−0.922982	−	0.384842i	$-0.874256\pi$
$739$	−3.48528	+	6.03668i	−0.128208	+	0.222063i	0.794774	+	0.606905i	$0.207589\pi$
$740$	3.58579	+	6.21076i	0.131816	+	0.228312i
$741$		0			0
$742$	32.2782	−	4.41717i	1.18497	−	0.162159i
$743$	−11.4853			−0.421354			−0.210677	−	0.977556i	$-0.567567\pi$
$743$	−11.4853			−0.421354			−0.210677	+	0.977556i	$0.567567\pi$
$744$		0			0
$745$	11.2426	−	19.4728i	0.411898	−	0.713429i
$746$	−5.55025	+	9.61332i	−0.203209	+	0.351969i
$747$		0			0
$748$	2.17157			0.0794006
$749$	22.1421	+	28.5533i	0.809056	+	1.04332i
$750$		0			0
$751$	17.1716	+	29.7420i	0.626600	+	1.08530i	0.988229	+	0.152980i	$0.0488872\pi$
$751$	17.1716	+	29.7420i	0.626600	+	1.08530i	−0.361630	+	0.932322i	$0.617780\pi$
$752$	4.50000	−	7.79423i	0.164098	−	0.284226i
$753$		0			0
$754$	−2.50000	−	4.33013i	−0.0910446	−	0.157694i
$755$	−10.7279			−0.390429
$756$		0			0
$757$	23.4437			0.852074			0.426037	−	0.904706i	$-0.359909\pi$
$757$	23.4437			0.852074			0.426037	+	0.904706i	$0.359909\pi$
$758$	−16.8284	−	29.1477i	−0.611236	−	1.05869i
$759$		0			0
$760$	2.12132	−	3.67423i	0.0769484	−	0.133278i
$761$	−8.92893	−	15.4654i	−0.323674	−	0.560619i	0.657569	−	0.753394i	$-0.271585\pi$
$761$	−8.92893	−	15.4654i	−0.323674	−	0.560619i	−0.981243	+	0.192775i	$0.938251\pi$
$762$		0			0
$763$	−1.65685	+	4.05845i	−0.0599822	+	0.146926i
$764$	−2.34315			−0.0847720
$765$		0			0
$766$	−3.24264	+	5.61642i	−0.117161	+	0.202929i
$767$	3.79289	−	6.56948i	0.136953	−	0.237210i
$768$		0			0
$769$	−6.92893			−0.249864			−0.124932	−	0.992165i	$-0.539871\pi$
$769$	−6.92893			−0.249864			−0.124932	+	0.992165i	$0.539871\pi$
$770$	−0.949747	−	1.22474i	−0.0342265	−	0.0441367i
$771$		0			0
$772$	7.87868	+	13.6463i	0.283560	+	0.491140i
$773$	−14.7990	+	25.6326i	−0.532283	+	0.921941i	0.467007	+	0.884254i	$0.345332\pi$
$773$	−14.7990	+	25.6326i	−0.532283	+	0.921941i	−0.999290	+	0.0376870i	$0.988001\pi$
$774$		0			0
$775$	10.2426	+	17.7408i	0.367927	+	0.637267i
$776$	−7.89949			−0.283575
$777$		0			0
$778$	23.0000			0.824590
$779$	6.87868	+	11.9142i	0.246454	+	0.426871i
$780$		0			0
$781$	0.207107	−	0.358719i	0.00741086	−	0.0128360i
$782$	−23.7782	−	41.1850i	−0.850306	−	1.47277i
$783$		0			0
$784$	−5.00000	−	4.89898i	−0.178571	−	0.174964i
$785$	11.2132			0.400216
$786$		0			0
$787$	4.08579	−	7.07679i	0.145643	−	0.252260i	−0.783970	−	0.620799i	$-0.786808\pi$
$787$	4.08579	−	7.07679i	0.145643	−	0.252260i	0.929612	+	0.368538i	$0.120142\pi$
$788$	4.77817	−	8.27604i	0.170215	−	0.294822i
$789$		0			0
$790$	−18.8284			−0.669885
$791$	15.9142	−	2.17781i	0.565844	−	0.0774340i
$792$		0			0
$793$	2.62132	+	4.54026i	0.0930858	+	0.161229i
$794$	−9.87868	+	17.1104i	−0.350581	+	0.607224i
$795$		0			0
$796$	−5.29289	−	9.16756i	−0.187602	−	0.324936i
$797$	36.9706			1.30956			0.654782	−	0.755818i	$-0.272760\pi$
$797$	36.9706			1.30956			0.654782	+	0.755818i	$0.272760\pi$
$798$		0			0
$799$	47.1838			1.66924
$800$	−1.50000	−	2.59808i	−0.0530330	−	0.0918559i
$801$		0			0
$802$	−9.53553	+	16.5160i	−0.336711	+	0.583201i
$803$	−0.221825	−	0.384213i	−0.00782805	−	0.0135586i
$804$		0			0
$805$	−12.8284	+	31.4231i	−0.452143	+	1.10752i
$806$	−6.82843			−0.240521
$807$		0			0
$808$	0.585786	−	1.01461i	0.0206079	−	0.0356939i
$809$	17.5208	−	30.3469i	0.615999	−	1.06694i	−0.374209	−	0.927344i	$-0.622086\pi$
$809$	17.5208	−	30.3469i	0.615999	−	1.06694i	0.990208	−	0.139597i	$-0.0445808\pi$
$810$		0			0
$811$	26.7696			0.940006			0.470003	−	0.882665i	$-0.344253\pi$
$811$	26.7696			0.940006			0.470003	+	0.882665i	$0.344253\pi$
$812$	5.00000	−	12.2474i	0.175466	−	0.429801i
$813$		0			0
$814$	1.05025	+	1.81909i	0.0368113	+	0.0637591i
$815$	−12.1213	+	20.9947i	−0.424591	+	0.735414i
$816$		0			0
$817$	−7.24264	−	12.5446i	−0.253388	−	0.438881i
$818$	2.58579			0.0904099
$819$		0			0
$820$	−6.48528			−0.226476
$821$	−4.80761	−	8.32703i	−0.167787	−	0.290615i	0.769855	−	0.638219i	$-0.220329\pi$
$821$	−4.80761	−	8.32703i	−0.167787	−	0.290615i	−0.937641	+	0.347604i	$0.886995\pi$
$822$		0			0
$823$	4.05025	−	7.01524i	0.141183	−	0.244536i	−0.786759	−	0.617260i	$-0.788243\pi$
$823$	4.05025	−	7.01524i	0.141183	−	0.244536i	0.927942	+	0.372724i	$0.121576\pi$
$824$	3.24264	+	5.61642i	0.112963	+	0.195657i
$825$		0			0
$826$	19.8848	−	2.72117i	0.691880	−	0.0946816i
$827$	−13.5269			−0.470377			−0.235188	−	0.971950i	$-0.575571\pi$
$827$	−13.5269			−0.470377			−0.235188	+	0.971950i	$0.575571\pi$
$828$		0			0
$829$	−9.34924	+	16.1934i	−0.324713	+	0.562419i	−0.981454	−	0.191697i	$-0.938601\pi$
$829$	−9.34924	+	16.1934i	−0.324713	+	0.562419i	0.656742	+	0.754116i	$0.271934\pi$
$830$	5.41421	−	9.37769i	0.187930	−	0.325504i
$831$		0			0
$832$	1.00000			0.0346688
$833$	9.13604	−	35.5431i	0.316545	−	1.23150i
$834$		0			0
$835$	8.70711	+	15.0812i	0.301322	+	0.521905i
$836$	0.621320	−	1.07616i	0.0214888	−	0.0372197i
$837$		0			0
$838$	13.7279	+	23.7775i	0.474223	+	0.821379i
$839$	−2.51472			−0.0868177			−0.0434089	−	0.999057i	$-0.513822\pi$
$839$	−2.51472			−0.0868177			−0.0434089	+	0.999057i	$0.513822\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	5.29289	+	9.16756i	0.182405	+	0.315935i
$843$		0			0
$844$	14.1924	−	24.5819i	0.488522	−	0.846145i
$845$	−0.707107	−	1.22474i	−0.0243252	−	0.0421325i
$846$		0			0
$847$	17.5563	+	22.6398i	0.603243	+	0.777911i
$848$	−12.3137			−0.422854
$849$		0			0
$850$	7.86396	−	13.6208i	0.269732	−	0.467189i
$851$	23.0000	−	39.8372i	0.788430	−	1.36560i
$852$		0			0
$853$	−17.6985			−0.605985			−0.302992	−	0.952993i	$-0.597986\pi$
$853$	−17.6985			−0.605985			−0.302992	+	0.952993i	$0.597986\pi$
$854$	−5.24264	+	12.8418i	−0.179399	+	0.439437i
$855$		0			0
$856$	−6.82843	−	11.8272i	−0.233391	−	0.404245i
$857$	−25.6924	+	44.5005i	−0.877635	+	1.52011i	−0.0237065	+	0.999719i	$0.507547\pi$
$857$	−25.6924	+	44.5005i	−0.877635	+	1.52011i	−0.853929	+	0.520390i	$0.825787\pi$
$858$		0			0
$859$	−0.100505	−	0.174080i	−0.00342919	−	0.00593953i	0.864306	−	0.502967i	$-0.167758\pi$
$859$	−0.100505	−	0.174080i	−0.00342919	−	0.00593953i	−0.867735	+	0.497027i	$0.834425\pi$
$860$	6.82843			0.232847
$861$		0			0
$862$	14.4853			0.493371
$863$	2.00000	+	3.46410i	0.0680808	+	0.117919i	0.898056	−	0.439880i	$-0.144979\pi$
$863$	2.00000	+	3.46410i	0.0680808	+	0.117919i	−0.829976	+	0.557800i	$0.811646\pi$
$864$		0			0
$865$	14.3640	−	24.8791i	0.488389	−	0.845915i
$866$	−9.50000	−	16.4545i	−0.322823	−	0.559146i
$867$		0			0
$868$	−11.0711	−	14.2767i	−0.375777	−	0.484582i
$869$	−5.51472			−0.187074
$870$		0			0
$871$	7.32843	−	12.6932i	0.248314	−	0.430093i
$872$	0.828427	−	1.43488i	0.0280541	−	0.0485911i
$873$		0			0
$874$	−27.2132			−0.920500
$875$	−29.6569	+	4.05845i	−1.00258	+	0.137201i
$876$		0			0
$877$	−11.7071	−	20.2773i	−0.395321	−	0.684716i	0.597821	−	0.801629i	$-0.296033\pi$
$877$	−11.7071	−	20.2773i	−0.395321	−	0.684716i	−0.993142	+	0.116914i	$0.962700\pi$
$878$	−5.29289	+	9.16756i	−0.178626	+	0.309390i
$879$		0			0
$880$	0.292893	+	0.507306i	0.00987343	+	0.0171013i
$881$	41.1127			1.38512			0.692561	−	0.721359i	$-0.256482\pi$
$881$	41.1127			1.38512			0.692561	+	0.721359i	$0.256482\pi$
$882$		0			0
$883$	−0.928932			−0.0312611			−0.0156305	−	0.999878i	$-0.504976\pi$
$883$	−0.928932			−0.0312611			−0.0156305	+	0.999878i	$0.504976\pi$
$884$	2.62132	+	4.54026i	0.0881645	+	0.152705i
$885$		0			0
$886$	−11.3640	+	19.6830i	−0.381780	+	0.661262i
$887$	20.6569	+	35.7787i	0.693589	+	1.20133i	0.970654	+	0.240481i	$0.0773050\pi$
$887$	20.6569	+	35.7787i	0.693589	+	1.20133i	−0.277065	+	0.960851i	$0.589362\pi$
$888$		0			0
$889$	25.9497	−	3.55114i	0.870327	−	0.119101i
$890$	−8.82843			−0.295930
$891$		0			0
$892$	−10.6924	+	18.5198i	−0.358008	+	0.620087i
$893$	13.5000	−	23.3827i	0.451760	−	0.782472i
$894$		0			0
$895$	17.4558			0.583485
$896$	1.62132	+	2.09077i	0.0541645	+	0.0698477i
$897$		0			0
$898$	16.9706	+	29.3939i	0.566315	+	0.980886i
$899$	17.0711	−	29.5680i	0.569352	−	0.986147i
$900$		0			0
$901$	−32.2782	−	55.9074i	−1.07534	−	1.86255i
$902$	−1.89949			−0.0632463
$903$		0			0
$904$	−6.07107			−0.201921
$905$	8.19239	+	14.1896i	0.272324	+	0.471679i
$906$		0			0
$907$	16.0503	−	27.7999i	0.532940	−	0.923079i	−0.466320	−	0.884616i	$-0.654421\pi$
$907$	16.0503	−	27.7999i	0.532940	−	0.923079i	0.999260	−	0.0384629i	$-0.0122462\pi$
$908$	−13.0711	−	22.6398i	−0.433779	−	0.751327i
$909$		0			0
$910$	1.41421	−	3.46410i	0.0468807	−	0.114834i
$911$	−54.0000			−1.78910			−0.894550	−	0.446968i	$-0.852504\pi$
$911$	−54.0000			−1.78910			−0.894550	+	0.446968i	$0.852504\pi$
$912$		0			0
$913$	1.58579	−	2.74666i	0.0524819	−	0.0909013i
$914$	−7.60660	+	13.1750i	−0.251604	+	0.435791i
$915$		0			0
$916$	−7.17157			−0.236955
$917$	16.0503	+	20.6976i	0.530026	+	0.683494i
$918$		0			0
$919$	12.8995	+	22.3426i	0.425515	+	0.737014i	0.996468	−	0.0839688i	$-0.0267596\pi$
$919$	12.8995	+	22.3426i	0.425515	+	0.737014i	−0.570953	+	0.820983i	$0.693426\pi$
$920$	6.41421	−	11.1097i	0.211470	−	0.366277i
$921$		0			0
$922$	16.7279	+	28.9736i	0.550905	+	0.954195i
$923$	1.00000			0.0329154
$924$		0			0
$925$	15.2132			0.500207
$926$	−18.9706	−	32.8580i	−0.623411	−	1.07978i
$927$		0			0
$928$	−2.50000	+	4.33013i	−0.0820665	+	0.142143i
$929$	9.14214	+	15.8346i	0.299944	+	0.519518i	0.976123	−	0.217220i	$-0.0696988\pi$
$929$	9.14214	+	15.8346i	0.299944	+	0.519518i	−0.676179	+	0.736737i	$0.736365\pi$
$930$		0			0
$931$	−15.0000	−	14.6969i	−0.491605	−	0.481673i
$932$	3.72792			0.122112
$933$		0			0
$934$	0.121320	−	0.210133i	0.00396972	−	0.00687576i
$935$	−1.53553	+	2.65962i	−0.0502173	+	0.0869790i
$936$		0			0
$937$	40.5980			1.32628			0.663139	−	0.748496i	$-0.269224\pi$
$937$	40.5980			1.32628			0.663139	+	0.748496i	$0.269224\pi$
$938$	38.4203	−	5.25770i	1.25447	−	0.171670i
$939$		0			0
$940$	6.36396	+	11.0227i	0.207570	+	0.359521i
$941$	−10.4853	+	18.1610i	−0.341810	+	0.592033i	−0.984769	−	0.173868i	$-0.944373\pi$
$941$	−10.4853	+	18.1610i	−0.341810	+	0.592033i	0.642959	+	0.765901i	$0.277707\pi$
$942$		0			0
$943$	20.7990	+	36.0249i	0.677308	+	1.17313i
$944$	−7.58579			−0.246896
$945$		0			0
$946$	2.00000			0.0650256
$947$	8.62132	+	14.9326i	0.280155	+	0.485243i	0.971423	−	0.237356i	$-0.0762807\pi$
$947$	8.62132	+	14.9326i	0.280155	+	0.485243i	−0.691268	+	0.722599i	$0.742947\pi$
$948$		0			0
$949$	0.535534	−	0.927572i	0.0173842	−	0.0301103i
$950$	−4.50000	−	7.79423i	−0.145999	−	0.252878i
$951$		0			0
$952$	−5.24264	+	12.8418i	−0.169915	+	0.416205i
$953$	10.2132			0.330838			0.165419	−	0.986223i	$-0.447102\pi$
$953$	10.2132			0.330838			0.165419	+	0.986223i	$0.447102\pi$
$954$		0			0
$955$	1.65685	−	2.86976i	0.0536145	−	0.0928631i
$956$	−1.25736	+	2.17781i	−0.0406659	+	0.0704354i
$957$		0			0
$958$	−31.1421			−1.00616
$959$	−13.0711	+	32.0174i	−0.422087	+	1.03390i
$960$		0			0
$961$	−7.81371	−	13.5337i	−0.252055	−	0.436572i
$962$	−2.53553	+	4.39167i	−0.0817489	+	0.141593i
$963$		0			0
$964$	8.24264	+	14.2767i	0.265478	+	0.459821i
$965$	−22.2843			−0.717356
$966$		0			0
$967$	9.38478			0.301794			0.150897	−	0.988549i	$-0.451784\pi$
$967$	9.38478			0.301794			0.150897	+	0.988549i	$0.451784\pi$
$968$	−5.41421	−	9.37769i	−0.174019	−	0.301410i
$969$		0			0
$970$	5.58579	−	9.67487i	0.179349	−	0.310641i
$971$	28.7782	+	49.8453i	0.923536	+	1.59961i	0.793900	+	0.608049i	$0.208048\pi$
$971$	28.7782	+	49.8453i	0.923536	+	1.59961i	0.129636	+	0.991562i	$0.458619\pi$
$972$		0			0
$973$	−55.6066	+	7.60959i	−1.78267	+	0.243952i
$974$	23.7279			0.760292
$975$		0			0
$976$	2.62132	−	4.54026i	0.0839064	−	0.145330i
$977$	1.24264	−	2.15232i	0.0397556	−	0.0688587i	−0.845463	−	0.534034i	$-0.820675\pi$
$977$	1.24264	−	2.15232i	0.0397556	−	0.0688587i	0.885219	+	0.465175i	$0.154009\pi$
$978$		0			0
$979$	−2.58579			−0.0826421
$980$	9.53553	−	2.65962i	0.304601	−	0.0849585i
$981$		0			0
$982$	13.1421	+	22.7628i	0.419382	+	0.726392i
$983$	−11.0858	+	19.2011i	−0.353582	+	0.612421i	−0.986874	−	0.161491i	$-0.948370\pi$
$983$	−11.0858	+	19.2011i	−0.353582	+	0.612421i	0.633292	+	0.773913i	$0.281703\pi$
$984$		0			0
$985$	6.75736	+	11.7041i	0.215307	+	0.372923i
$986$	−26.2132			−0.834798
$987$		0			0
$988$	3.00000			0.0954427
$989$	−21.8995	−	37.9310i	−0.696363	−	1.20614i
$990$		0			0
$991$	3.65685	−	6.33386i	0.116164	−	0.201202i	−0.802081	−	0.597216i	$-0.796274\pi$
$991$	3.65685	−	6.33386i	0.116164	−	0.201202i	0.918244	+	0.396014i	$0.129607\pi$
$992$	3.41421	+	5.91359i	0.108401	+	0.187757i
$993$		0			0
$994$	1.62132	+	2.09077i	0.0514252	+	0.0663152i
$995$	14.9706			0.474599
$996$		0			0
$997$	−3.34924	+	5.80106i	−0.106072	+	0.183721i	−0.914176	−	0.405319i	$-0.867161\pi$
$997$	−3.34924	+	5.80106i	−0.106072	+	0.183721i	0.808104	+	0.589040i	$0.200494\pi$
$998$	−15.0000	+	25.9808i	−0.474817	+	0.822407i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.j.n.235.1		4
3.2	odd	2		546.2.i.h.235.2	yes	4
7.2	even	3	inner	1638.2.j.n.1171.1		4
21.2	odd	6		546.2.i.h.79.2	✓	4
21.11	odd	6		3822.2.a.bs.1.1		2
21.17	even	6		3822.2.a.bp.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.h.79.2	✓	4	21.2	odd	6
546.2.i.h.235.2	yes	4	3.2	odd	2
1638.2.j.n.235.1		4	1.1	even	1	trivial
1638.2.j.n.1171.1		4	7.2	even	3	inner
3822.2.a.bp.1.2		2	21.17	even	6
3822.2.a.bs.1.1		2	21.11	odd	6

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000 q^{8} +(0.707107 - 1.22474i) q^{10} +(0.207107 - 0.358719i) q^{11} +1.00000 q^{13} +(1.62132 + 2.09077i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.62132 - 4.54026i) q^{17} +(-1.50000 - 2.59808i) q^{19} +1.41421 q^{20} +0.414214 q^{22} +(-4.53553 - 7.85578i) q^{23} +(1.50000 - 2.59808i) q^{25} +(0.500000 + 0.866025i) q^{26} +(-1.00000 + 2.44949i) q^{28} -5.00000 q^{29} +(-3.41421 + 5.91359i) q^{31} +(0.500000 - 0.866025i) q^{32} +5.24264 q^{34} +(-2.29289 - 2.95680i) q^{35} +(2.53553 + 4.39167i) q^{37} +(1.50000 - 2.59808i) q^{38} +(0.707107 + 1.22474i) q^{40} -4.58579 q^{41} +4.82843 q^{43} +(0.207107 + 0.358719i) q^{44} +(4.53553 - 7.85578i) q^{46} +(4.50000 + 7.79423i) q^{47} +(6.74264 - 1.88064i) q^{49} +3.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(6.15685 - 10.6640i) q^{53} -0.585786 q^{55} +(-2.62132 + 0.358719i) q^{56} +(-2.50000 - 4.33013i) q^{58} +(3.79289 - 6.56948i) q^{59} +(2.62132 + 4.54026i) q^{61} -6.82843 q^{62} +1.00000 q^{64} +(-0.707107 - 1.22474i) q^{65} +(7.32843 - 12.6932i) q^{67} +(2.62132 + 4.54026i) q^{68} +(1.41421 - 3.46410i) q^{70} +1.00000 q^{71} +(0.535534 - 0.927572i) q^{73} +(-2.53553 + 4.39167i) q^{74} +3.00000 q^{76} +(0.414214 - 1.01461i) q^{77} +(-6.65685 - 11.5300i) q^{79} +(-0.707107 + 1.22474i) q^{80} +(-2.29289 - 3.97141i) q^{82} +7.65685 q^{83} -7.41421 q^{85} +(2.41421 + 4.18154i) q^{86} +(-0.207107 + 0.358719i) q^{88} +(-3.12132 - 5.40629i) q^{89} +(2.62132 - 0.358719i) q^{91} +9.07107 q^{92} +(-4.50000 + 7.79423i) q^{94} +(-2.12132 + 3.67423i) q^{95} +7.89949 q^{97} +(5.00000 + 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{7} - 4 q^{8} - 2 q^{11} + 4 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} - 6 q^{19} - 4 q^{22} - 4 q^{23} + 6 q^{25} + 2 q^{26} - 4 q^{28} - 20 q^{29} - 8 q^{31} + 2 q^{32} + 4 q^{34} - 12 q^{35} - 4 q^{37} + 6 q^{38} - 24 q^{41} + 8 q^{43} - 2 q^{44} + 4 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 2 q^{52} + 2 q^{53} - 8 q^{55} - 2 q^{56} - 10 q^{58} + 18 q^{59} + 2 q^{61} - 16 q^{62} + 4 q^{64} + 18 q^{67} + 2 q^{68} + 4 q^{71} - 12 q^{73} + 4 q^{74} + 12 q^{76} - 4 q^{77} - 4 q^{79} - 12 q^{82} + 8 q^{83} - 24 q^{85} + 4 q^{86} + 2 q^{88} - 4 q^{89} + 2 q^{91} + 8 q^{92} - 18 q^{94} - 8 q^{97} + 20 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 - 4 * q^8 - 2 * q^11 + 4 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^17 - 6 * q^19 - 4 * q^22 - 4 * q^23 + 6 * q^25 + 2 * q^26 - 4 * q^28 - 20 * q^29 - 8 * q^31 + 2 * q^32 + 4 * q^34 - 12 * q^35 - 4 * q^37 + 6 * q^38 - 24 * q^41 + 8 * q^43 - 2 * q^44 + 4 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 2 * q^52 + 2 * q^53 - 8 * q^55 - 2 * q^56 - 10 * q^58 + 18 * q^59 + 2 * q^61 - 16 * q^62 + 4 * q^64 + 18 * q^67 + 2 * q^68 + 4 * q^71 - 12 * q^73 + 4 * q^74 + 12 * q^76 - 4 * q^77 - 4 * q^79 - 12 * q^82 + 8 * q^83 - 24 * q^85 + 4 * q^86 + 2 * q^88 - 4 * q^89 + 2 * q^91 + 8 * q^92 - 18 * q^94 - 8 * q^97 + 20 * q^98

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