LMFDB - Embedded newform 1638.2.y.b.1331.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(827,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("1638.827");

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.y (of order $4$, 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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 4 x^{10} + 12 x^{9} - 40 x^{8} + 12 x^{7} + 230 x^{6} - 144 x^{5} + 129 x^{4} + \cdots + 2 $ x^12 - 4x^11 + 4x^10 + 12x^9 - 40x^8 + 12x^7 + 230x^6 - 144x^5 + 129x^4 - 56x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1331.3
Root			$0.981045 - 2.36845i$ of defining polynomial
Character	$\chi$	$=$	1638.1331
Dual form			1638.2.y.b.827.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.13273 + 2.13273i) q^{5} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.13273 + 2.13273i) q^{5} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.01614i q^{10} +(-1.84550 + 1.84550i) q^{11} +(-2.89707 + 2.14639i) q^{13} -1.00000i q^{14} -1.00000 q^{16} +1.26064 q^{17} +(-3.56626 + 3.56626i) q^{19} +(-2.13273 + 2.13273i) q^{20} +2.60992 q^{22} +2.60992 q^{23} +4.09707i q^{25} +(3.56626 + 0.530808i) q^{26} +(-0.707107 + 0.707107i) q^{28} +0.609925i q^{29} +(-2.67486 + 2.67486i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.891409 - 0.891409i) q^{34} +3.01614i q^{35} +(-4.46674 - 4.46674i) q^{37} +5.04346 q^{38} +3.01614 q^{40} +(-5.01614 - 5.01614i) q^{41} +12.4564i q^{43} +(-1.84550 - 1.84550i) q^{44} +(-1.84550 - 1.84550i) q^{46} +(3.00813 - 3.00813i) q^{47} +1.00000i q^{49} +(2.89707 - 2.89707i) q^{50} +(-2.14639 - 2.89707i) q^{52} +0.828427i q^{53} -7.87189 q^{55} +1.00000 q^{56} +(0.431282 - 0.431282i) q^{58} +(7.73927 - 7.73927i) q^{59} -11.3685 q^{61} +3.78282 q^{62} -1.00000i q^{64} +(-10.7563 - 1.60099i) q^{65} +(3.58260 - 3.58260i) q^{67} +1.26064i q^{68} +(2.13273 - 2.13273i) q^{70} +(1.76681 + 1.76681i) q^{71} +(-9.04689 - 9.04689i) q^{73} +6.31692i q^{74} +(-3.56626 - 3.56626i) q^{76} -2.60992 q^{77} -8.06641 q^{79} +(-2.13273 - 2.13273i) q^{80} +7.09389i q^{82} +(5.76681 + 5.76681i) q^{83} +(2.68861 + 2.68861i) q^{85} +(8.80802 - 8.80802i) q^{86} +2.60992i q^{88} +(-6.44167 + 6.44167i) q^{89} +(-3.56626 - 0.530808i) q^{91} +2.60992i q^{92} -4.25414 q^{94} -15.2118 q^{95} +(-1.40271 + 1.40271i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5}+O(q^{10}) $ 12 * q + 4 * q^5	$ 12 q + 4 q^{5} + 8 q^{11} - 16 q^{13} - 12 q^{16} + 8 q^{17} - 4 q^{20} + 8 q^{22} + 8 q^{23} - 8 q^{31} + 8 q^{34} + 16 q^{38} - 24 q^{41} + 8 q^{44} + 8 q^{46} + 4 q^{47} + 16 q^{50} - 16 q^{55} + 12 q^{56} - 8 q^{58} - 48 q^{59} + 32 q^{61} + 8 q^{62} + 8 q^{65} + 28 q^{67} + 4 q^{70} - 8 q^{71} + 16 q^{73} - 8 q^{77} - 32 q^{79} - 4 q^{80} + 40 q^{83} + 8 q^{85} + 40 q^{86} - 24 q^{89} - 8 q^{94} + 8 q^{95} + 8 q^{97}+O(q^{100}) $ 12 * q + 4 * q^5 + 8 * q^11 - 16 * q^13 - 12 * q^16 + 8 * q^17 - 4 * q^20 + 8 * q^22 + 8 * q^23 - 8 * q^31 + 8 * q^34 + 16 * q^38 - 24 * q^41 + 8 * q^44 + 8 * q^46 + 4 * q^47 + 16 * q^50 - 16 * q^55 + 12 * q^56 - 8 * q^58 - 48 * q^59 + 32 * q^61 + 8 * q^62 + 8 * q^65 + 28 * q^67 + 4 * q^70 - 8 * q^71 + 16 * q^73 - 8 * q^77 - 32 * q^79 - 4 * q^80 + 40 * q^83 + 8 * q^85 + 40 * q^86 - 24 * q^89 - 8 * q^94 + 8 * q^95 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	2.13273	+	2.13273i	0.953786	+	0.953786i	0.998978	−	0.0451925i	$-0.0143901\pi$
$5$	2.13273	+	2.13273i	0.953786	+	0.953786i	−0.0451925	+	0.998978i	$0.514390\pi$
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$		−	3.01614i		−	0.953786i
$11$	−1.84550	+	1.84550i	−0.556438	+	0.556438i	−0.928291	−	0.371854i	$-0.878722\pi$
$11$	−1.84550	+	1.84550i	−0.556438	+	0.556438i	0.371854	+	0.928291i	$0.378722\pi$
$12$		0			0
$13$	−2.89707	+	2.14639i	−0.803502	+	0.595302i
$13$	−2.89707	+	2.14639i	−0.803502	+	0.595302i
$14$		−	1.00000i		−	0.267261i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.26064			0.305751			0.152875	−	0.988245i	$-0.451147\pi$
$17$	1.26064			0.305751			0.152875	+	0.988245i	$0.451147\pi$
$18$		0			0
$19$	−3.56626	+	3.56626i	−0.818157	+	0.818157i	−0.985841	−	0.167684i	$-0.946371\pi$
$19$	−3.56626	+	3.56626i	−0.818157	+	0.818157i	0.167684	+	0.985841i	$0.446371\pi$
$20$	−2.13273	+	2.13273i	−0.476893	+	0.476893i
$21$		0			0
$22$	2.60992			0.556438
$23$	2.60992			0.544207			0.272103	−	0.962268i	$-0.412281\pi$
$23$	2.60992			0.544207			0.272103	+	0.962268i	$0.412281\pi$
$24$		0			0
$25$			4.09707i			0.819415i
$26$	3.56626	+	0.530808i	0.699402	+	0.104100i
$27$		0			0
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$			0.609925i			0.113260i	0.998395	+	0.0566301i	$0.0180356\pi$
$29$			0.609925i			0.113260i	−0.998395	+	0.0566301i	$0.981964\pi$
$30$		0			0
$31$	−2.67486	+	2.67486i	−0.480418	+	0.480418i	−0.905265	−	0.424847i	$-0.860328\pi$
$31$	−2.67486	+	2.67486i	−0.480418	+	0.480418i	0.424847	+	0.905265i	$0.360328\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−0.891409	−	0.891409i	−0.152875	−	0.152875i
$35$			3.01614i			0.509820i
$36$		0			0
$37$	−4.46674	−	4.46674i	−0.734327	−	0.734327i	0.237147	−	0.971474i	$-0.423788\pi$
$37$	−4.46674	−	4.46674i	−0.734327	−	0.734327i	−0.971474	+	0.237147i	$0.923788\pi$
$38$	5.04346			0.818157
$39$		0			0
$40$	3.01614			0.476893
$41$	−5.01614	−	5.01614i	−0.783389	−	0.783389i	0.197012	−	0.980401i	$-0.436876\pi$
$41$	−5.01614	−	5.01614i	−0.783389	−	0.783389i	−0.980401	+	0.197012i	$0.936876\pi$
$42$		0			0
$43$			12.4564i			1.89959i	0.312879	+	0.949793i	$0.398707\pi$
$43$			12.4564i			1.89959i	−0.312879	+	0.949793i	$0.601293\pi$
$44$	−1.84550	−	1.84550i	−0.278219	−	0.278219i
$45$		0			0
$46$	−1.84550	−	1.84550i	−0.272103	−	0.272103i
$47$	3.00813	−	3.00813i	0.438781	−	0.438781i	−0.452821	−	0.891602i	$-0.649582\pi$
$47$	3.00813	−	3.00813i	0.438781	−	0.438781i	0.891602	+	0.452821i	$0.149582\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	2.89707	−	2.89707i	0.409707	−	0.409707i
$51$		0			0
$52$	−2.14639	−	2.89707i	−0.297651	−	0.401751i
$53$			0.828427i			0.113793i	0.998380	+	0.0568966i	$0.0181205\pi$
$53$			0.828427i			0.113793i	−0.998380	+	0.0568966i	$0.981879\pi$
$54$		0			0
$55$	−7.87189			−1.06145
$56$	1.00000			0.133631
$57$		0			0
$58$	0.431282	−	0.431282i	0.0566301	−	0.0566301i
$59$	7.73927	−	7.73927i	1.00757	−	1.00757i	0.00759574	−	0.999971i	$-0.497582\pi$
$59$	7.73927	−	7.73927i	1.00757	−	1.00757i	0.999971	−	0.00759574i	$-0.00241782\pi$
$60$		0			0
$61$	−11.3685			−1.45559			−0.727795	−	0.685795i	$-0.759455\pi$
$61$	−11.3685			−1.45559			−0.727795	+	0.685795i	$0.759455\pi$
$62$	3.78282			0.480418
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−10.7563	−	1.60099i	−1.33416	−	0.198578i
$66$		0			0
$67$	3.58260	−	3.58260i	0.437684	−	0.437684i	−0.453548	−	0.891232i	$-0.649842\pi$
$67$	3.58260	−	3.58260i	0.437684	−	0.437684i	0.891232	+	0.453548i	$0.149842\pi$
$68$			1.26064i			0.152875i
$69$		0			0
$70$	2.13273	−	2.13273i	0.254910	−	0.254910i
$71$	1.76681	+	1.76681i	0.209682	+	0.209682i	0.804132	−	0.594450i	$-0.202630\pi$
$71$	1.76681	+	1.76681i	0.209682	+	0.209682i	−0.594450	+	0.804132i	$0.702630\pi$
$72$		0			0
$73$	−9.04689	−	9.04689i	−1.05886	−	1.05886i	−0.998156	−	0.0607020i	$-0.980666\pi$
$73$	−9.04689	−	9.04689i	−1.05886	−	1.05886i	−0.0607020	−	0.998156i	$-0.519334\pi$
$74$			6.31692i			0.734327i
$75$		0			0
$76$	−3.56626	−	3.56626i	−0.409079	−	0.409079i
$77$	−2.60992			−0.297429
$78$		0			0
$79$	−8.06641			−0.907542			−0.453771	−	0.891118i	$-0.649922\pi$
$79$	−8.06641			−0.907542			−0.453771	+	0.891118i	$0.649922\pi$
$80$	−2.13273	−	2.13273i	−0.238446	−	0.238446i
$81$		0			0
$82$			7.09389i			0.783389i
$83$	5.76681	+	5.76681i	0.632990	+	0.632990i	0.948817	−	0.315827i	$-0.102282\pi$
$83$	5.76681	+	5.76681i	0.632990	+	0.632990i	−0.315827	+	0.948817i	$0.602282\pi$
$84$		0			0
$85$	2.68861	+	2.68861i	0.291621	+	0.291621i
$86$	8.80802	−	8.80802i	0.949793	−	0.949793i
$87$		0			0
$88$			2.60992i			0.278219i
$89$	−6.44167	+	6.44167i	−0.682815	+	0.682815i	−0.960634	−	0.277818i	$-0.910389\pi$
$89$	−6.44167	+	6.44167i	−0.682815	+	0.682815i	0.277818	+	0.960634i	$0.410389\pi$
$90$		0			0
$91$	−3.56626	−	0.530808i	−0.373846	−	0.0556438i
$92$			2.60992i			0.272103i
$93$		0			0
$94$	−4.25414			−0.438781
$95$	−15.2118			−1.56069
$96$		0			0
$97$	−1.40271	+	1.40271i	−0.142424	+	0.142424i	−0.774724	−	0.632300i	$-0.782111\pi$
$97$	−1.40271	+	1.40271i	−0.142424	+	0.142424i	0.632300	+	0.774724i	$0.282111\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$		0			0
$100$	−4.09707			−0.409707
$101$	12.0709			1.20110			0.600550	−	0.799587i	$-0.294948\pi$
$101$	12.0709			1.20110			0.600550	+	0.799587i	$0.294948\pi$
$102$		0			0
$103$			10.1164i			0.996798i	0.866948	+	0.498399i	$0.166079\pi$
$103$			10.1164i			0.996798i	−0.866948	+	0.498399i	$0.833921\pi$
$104$	−0.530808	+	3.56626i	−0.0520500	+	0.349701i
$105$		0			0
$106$	0.585786	−	0.585786i	0.0568966	−	0.0568966i
$107$			8.63857i			0.835122i	0.908649	+	0.417561i	$0.137115\pi$
$107$			8.63857i			0.835122i	−0.908649	+	0.417561i	$0.862885\pi$
$108$		0			0
$109$	−2.93125	+	2.93125i	−0.280763	+	0.280763i	−0.833413	−	0.552650i	$-0.813616\pi$
$109$	−2.93125	+	2.93125i	−0.280763	+	0.280763i	0.552650	+	0.833413i	$0.313616\pi$
$110$	5.56626	+	5.56626i	0.530723	+	0.530723i
$111$		0			0
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$			1.25234i			0.117810i	0.998264	+	0.0589051i	$0.0187609\pi$
$113$			1.25234i			0.117810i	−0.998264	+	0.0589051i	$0.981239\pi$
$114$		0			0
$115$	5.56626	+	5.56626i	0.519057	+	0.519057i
$116$	−0.609925			−0.0566301
$117$		0			0
$118$	−10.9450			−1.00757
$119$	0.891409	+	0.891409i	0.0817153	+	0.0817153i
$120$		0			0
$121$			4.18829i			0.380754i
$122$	8.03875	+	8.03875i	0.727795	+	0.727795i
$123$		0			0
$124$	−2.67486	−	2.67486i	−0.240209	−	0.240209i
$125$	1.92570	−	1.92570i	0.172240	−	0.172240i
$126$		0			0
$127$		−	7.64085i		−	0.678016i	−0.940784	−	0.339008i	$-0.889909\pi$
$127$		−	7.64085i		−	0.678016i	0.940784	−	0.339008i	$-0.110091\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	6.47381	+	8.73795i	0.567791	+	0.766369i
$131$		−	8.42584i		−	0.736169i	−0.929792	−	0.368085i	$-0.880014\pi$
$131$		−	8.42584i		−	0.736169i	0.929792	−	0.368085i	$-0.119986\pi$
$132$		0			0
$133$	−5.04346			−0.437323
$134$	−5.06656			−0.437684
$135$		0			0
$136$	0.891409	−	0.891409i	0.0764377	−	0.0764377i
$137$	−14.1383	+	14.1383i	−1.20791	+	1.20791i	−0.236214	+	0.971701i	$0.575906\pi$
$137$	−14.1383	+	14.1383i	−1.20791	+	1.20791i	−0.971701	+	0.236214i	$0.924094\pi$
$138$		0			0
$139$	19.0228			1.61349			0.806746	−	0.590898i	$-0.201226\pi$
$139$	19.0228			1.61349			0.806746	+	0.590898i	$0.201226\pi$
$140$	−3.01614			−0.254910
$141$		0			0
$142$		−	2.49865i		−	0.209682i
$143$	1.38537	−	9.30768i	0.115850	−	0.778348i
$144$		0			0
$145$	−1.30081	+	1.30081i	−0.108026	+	0.108026i
$146$			12.7942i			1.05886i
$147$		0			0
$148$	4.46674	−	4.46674i	0.367164	−	0.367164i
$149$	5.33521	+	5.33521i	0.437077	+	0.437077i	0.891027	−	0.453950i	$-0.149986\pi$
$149$	5.33521	+	5.33521i	0.437077	+	0.437077i	−0.453950	+	0.891027i	$0.649986\pi$
$150$		0			0
$151$	13.9679	+	13.9679i	1.13669	+	1.13669i	0.989040	+	0.147650i	$0.0471708\pi$
$151$	13.9679	+	13.9679i	1.13669	+	1.13669i	0.147650	+	0.989040i	$0.452829\pi$
$152$			5.04346i			0.409079i
$153$		0			0
$154$	1.84550	+	1.84550i	0.148714	+	0.148714i
$155$	−11.4095			−0.916432
$156$		0			0
$157$	13.7895			1.10052			0.550261	−	0.834992i	$-0.314528\pi$
$157$	13.7895			1.10052			0.550261	+	0.834992i	$0.314528\pi$
$158$	5.70381	+	5.70381i	0.453771	+	0.453771i
$159$		0			0
$160$			3.01614i			0.238446i
$161$	1.84550	+	1.84550i	0.145445	+	0.145445i
$162$		0			0
$163$	5.75942	+	5.75942i	0.451113	+	0.451113i	0.895724	−	0.444611i	$-0.146658\pi$
$163$	5.75942	+	5.75942i	0.451113	+	0.451113i	−0.444611	+	0.895724i	$0.646658\pi$
$164$	5.01614	−	5.01614i	0.391694	−	0.391694i
$165$		0			0
$166$		−	8.15550i		−	0.632990i
$167$	−7.67104	+	7.67104i	−0.593603	+	0.593603i	−0.938603	−	0.345000i	$-0.887879\pi$
$167$	−7.67104	+	7.67104i	−0.593603	+	0.593603i	0.345000	+	0.938603i	$0.387879\pi$
$168$		0			0
$169$	3.78600	−	12.4365i	0.291231	−	0.956653i
$170$		−	3.80227i		−	0.291621i
$171$		0			0
$172$	−12.4564			−0.949793
$173$	−1.38198			−0.105070			−0.0525351	−	0.998619i	$-0.516730\pi$
$173$	−1.38198			−0.105070			−0.0525351	+	0.998619i	$0.516730\pi$
$174$		0			0
$175$	−2.89707	+	2.89707i	−0.218998	+	0.218998i
$176$	1.84550	−	1.84550i	0.139109	−	0.139109i
$177$		0			0
$178$	9.10989			0.682815
$179$	7.73498			0.578140			0.289070	−	0.957308i	$-0.406654\pi$
$179$	7.73498			0.578140			0.289070	+	0.957308i	$0.406654\pi$
$180$		0			0
$181$			7.37370i			0.548083i	0.961718	+	0.274042i	$0.0883606\pi$
$181$			7.37370i			0.548083i	−0.961718	+	0.274042i	$0.911639\pi$
$182$	2.14639	+	2.89707i	0.159101	+	0.214745i
$183$		0			0
$184$	1.84550	−	1.84550i	0.136052	−	0.136052i
$185$		−	19.0527i		−	1.40078i
$186$		0			0
$187$	−2.32651	+	2.32651i	−0.170131	+	0.170131i
$188$	3.00813	+	3.00813i	0.219391	+	0.219391i
$189$		0			0
$190$	10.7563	+	10.7563i	0.780347	+	0.780347i
$191$			24.2087i			1.75168i	0.482602	+	0.875840i	$0.339692\pi$
$191$			24.2087i			1.75168i	−0.482602	+	0.875840i	$0.660308\pi$
$192$		0			0
$193$	15.0111	+	15.0111i	1.08052	+	1.08052i	0.996461	+	0.0840621i	$0.0267894\pi$
$193$	15.0111	+	15.0111i	1.08052	+	1.08052i	0.0840621	+	0.996461i	$0.473211\pi$
$194$	1.98374			0.142424
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	−3.61327	−	3.61327i	−0.257435	−	0.257435i	0.566575	−	0.824010i	$-0.308268\pi$
$197$	−3.61327	−	3.61327i	−0.257435	−	0.257435i	−0.824010	+	0.566575i	$0.808268\pi$
$198$		0			0
$199$			18.1583i			1.28721i	0.765359	+	0.643604i	$0.222562\pi$
$199$			18.1583i			1.28721i	−0.765359	+	0.643604i	$0.777438\pi$
$200$	2.89707	+	2.89707i	0.204854	+	0.204854i
$201$		0			0
$202$	−8.53542	−	8.53542i	−0.600550	−	0.600550i
$203$	−0.431282	+	0.431282i	−0.0302701	+	0.0302701i
$204$		0			0
$205$		−	21.3961i		−	1.49437i
$206$	7.15337	−	7.15337i	0.498399	−	0.498399i
$207$		0			0
$208$	2.89707	−	2.14639i	0.200876	−	0.148826i
$209$		−	13.1631i		−	0.910507i
$210$		0			0
$211$	10.3716			0.714008			0.357004	−	0.934103i	$-0.383798\pi$
$211$	10.3716			0.714008			0.357004	+	0.934103i	$0.383798\pi$
$212$	−0.828427			−0.0568966
$213$		0			0
$214$	6.10839	−	6.10839i	0.417561	−	0.417561i
$215$	−26.5662	+	26.5662i	−1.81180	+	1.81180i
$216$		0			0
$217$	−3.78282			−0.256794
$218$	4.14541			0.280763
$219$		0			0
$220$		−	7.87189i		−	0.530723i
$221$	−3.65217	+	2.70583i	−0.245671	+	0.182014i
$222$		0			0
$223$	11.6199	−	11.6199i	0.778123	−	0.778123i	−0.201388	−	0.979512i	$-0.564545\pi$
$223$	11.6199	−	11.6199i	0.778123	−	0.778123i	0.979512	+	0.201388i	$0.0645453\pi$
$224$			1.00000i			0.0668153i
$225$		0			0
$226$	0.885538	−	0.885538i	0.0589051	−	0.0589051i
$227$	4.05766	+	4.05766i	0.269317	+	0.269317i	0.828825	−	0.559508i	$-0.189010\pi$
$227$	4.05766	+	4.05766i	0.269317	+	0.269317i	−0.559508	+	0.828825i	$0.689010\pi$
$228$		0			0
$229$	−11.4095	−	11.4095i	−0.753960	−	0.753960i	0.221256	−	0.975216i	$-0.428985\pi$
$229$	−11.4095	−	11.4095i	−0.753960	−	0.753960i	−0.975216	+	0.221256i	$0.928985\pi$
$230$		−	7.87189i		−	0.519057i
$231$		0			0
$232$	0.431282	+	0.431282i	0.0283151	+	0.0283151i
$233$	1.18529			0.0776508			0.0388254	−	0.999246i	$-0.487638\pi$
$233$	1.18529			0.0776508			0.0388254	+	0.999246i	$0.487638\pi$
$234$		0			0
$235$	12.8311			0.837006
$236$	7.73927	+	7.73927i	0.503783	+	0.503783i
$237$		0			0
$238$		−	1.26064i		−	0.0817153i
$239$	−7.96282	−	7.96282i	−0.515072	−	0.515072i	0.401004	−	0.916076i	$-0.368661\pi$
$239$	−7.96282	−	7.96282i	−0.515072	−	0.515072i	−0.916076	+	0.401004i	$0.868661\pi$
$240$		0			0
$241$	−9.06656	−	9.06656i	−0.584029	−	0.584029i	0.351979	−	0.936008i	$-0.385509\pi$
$241$	−9.06656	−	9.06656i	−0.584029	−	0.584029i	−0.936008	+	0.351979i	$0.885509\pi$
$242$	2.96157	−	2.96157i	0.190377	−	0.190377i
$243$		0			0
$244$		−	11.3685i		−	0.727795i
$245$	−2.13273	+	2.13273i	−0.136255	+	0.136255i
$246$		0			0
$247$	2.67711	−	17.9863i	0.170340	−	1.14444i
$248$			3.78282i			0.240209i
$249$		0			0
$250$	−2.72335			−0.172240
$251$	18.7819			1.18550			0.592750	−	0.805386i	$-0.298042\pi$
$251$	18.7819			1.18550			0.592750	+	0.805386i	$0.298042\pi$
$252$		0			0
$253$	−4.81660	+	4.81660i	−0.302817	+	0.302817i
$254$	−5.40290	+	5.40290i	−0.339008	+	0.339008i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.83076			−0.426091			−0.213045	−	0.977042i	$-0.568338\pi$
$257$	−6.83076			−0.426091			−0.213045	+	0.977042i	$0.568338\pi$
$258$		0			0
$259$		−	6.31692i		−	0.392514i
$260$	1.60099	−	10.7563i	0.0992891	−	0.667080i
$261$		0			0
$262$	−5.95797	+	5.95797i	−0.368085	+	0.368085i
$263$		−	21.0781i		−	1.29973i	−0.760049	−	0.649866i	$-0.774825\pi$
$263$		−	21.0781i		−	1.29973i	0.760049	−	0.649866i	$-0.225175\pi$
$264$		0			0
$265$	−1.76681	+	1.76681i	−0.108534	+	0.108534i
$266$	3.56626	+	3.56626i	0.218662	+	0.218662i
$267$		0			0
$268$	3.58260	+	3.58260i	0.218842	+	0.218842i
$269$		−	5.67619i		−	0.346084i	−0.984914	−	0.173042i	$-0.944640\pi$
$269$		−	5.67619i		−	0.346084i	0.984914	−	0.173042i	$-0.0553596\pi$
$270$		0			0
$271$	−7.89471	−	7.89471i	−0.479569	−	0.479569i	0.425425	−	0.904994i	$-0.360125\pi$
$271$	−7.89471	−	7.89471i	−0.479569	−	0.479569i	−0.904994	+	0.425425i	$0.860125\pi$
$272$	−1.26064			−0.0764377
$273$		0			0
$274$	19.9945			1.20791
$275$	−7.56113	−	7.56113i	−0.455953	−	0.455953i
$276$		0			0
$277$			23.6398i			1.42038i	0.704011	+	0.710189i	$0.251391\pi$
$277$			23.6398i			1.42038i	−0.704011	+	0.710189i	$0.748609\pi$
$278$	−13.4511	−	13.4511i	−0.806746	−	0.806746i
$279$		0			0
$280$	2.13273	+	2.13273i	0.127455	+	0.127455i
$281$	21.1599	−	21.1599i	1.26229	−	1.26229i	0.312315	−	0.949979i	$-0.398896\pi$
$281$	21.1599	−	21.1599i	1.26229	−	1.26229i	0.949979	−	0.312315i	$-0.101104\pi$
$282$		0			0
$283$			8.06150i			0.479206i	0.970871	+	0.239603i	$0.0770174\pi$
$283$			8.06150i			0.479206i	−0.970871	+	0.239603i	$0.922983\pi$
$284$	−1.76681	+	1.76681i	−0.104841	+	0.104841i
$285$		0			0
$286$	−7.56113	+	5.60192i	−0.447099	+	0.331249i
$287$		−	7.09389i		−	0.418739i
$288$		0			0
$289$	−15.4108			−0.906517
$290$	1.83962			0.108026
$291$		0			0
$292$	9.04689	−	9.04689i	0.529429	−	0.529429i
$293$	−11.0611	+	11.0611i	−0.646198	+	0.646198i	−0.952072	−	0.305874i	$-0.901051\pi$
$293$	−11.0611	+	11.0611i	−0.646198	+	0.646198i	0.305874	+	0.952072i	$0.401051\pi$
$294$		0			0
$295$	33.0115			1.92201
$296$	−6.31692			−0.367164
$297$		0			0
$298$		−	7.54512i		−	0.437077i
$299$	−7.56113	+	5.60192i	−0.437271	+	0.323968i
$300$		0			0
$301$	−8.80802	+	8.80802i	−0.507686	+	0.507686i
$302$		−	19.7536i		−	1.13669i
$303$		0			0
$304$	3.56626	−	3.56626i	0.204539	−	0.204539i
$305$	−24.2460	−	24.2460i	−1.38832	−	1.38832i
$306$		0			0
$307$	−22.8993	−	22.8993i	−1.30693	−	1.30693i	−0.923618	−	0.383314i	$-0.874783\pi$
$307$	−22.8993	−	22.8993i	−1.30693	−	1.30693i	−0.383314	−	0.923618i	$-0.625217\pi$
$308$		−	2.60992i		−	0.148714i
$309$		0			0
$310$	8.06773	+	8.06773i	0.458216	+	0.458216i
$311$	−10.4144			−0.590545			−0.295272	−	0.955413i	$-0.595410\pi$
$311$	−10.4144			−0.590545			−0.295272	+	0.955413i	$0.595410\pi$
$312$		0			0
$313$	−6.10029			−0.344809			−0.172404	−	0.985026i	$-0.555154\pi$
$313$	−6.10029			−0.344809			−0.172404	+	0.985026i	$0.555154\pi$
$314$	−9.75066	−	9.75066i	−0.550261	−	0.550261i
$315$		0			0
$316$		−	8.06641i		−	0.453771i
$317$	14.0334	+	14.0334i	0.788193	+	0.788193i	0.981198	−	0.193005i	$-0.0618234\pi$
$317$	14.0334	+	14.0334i	0.788193	+	0.788193i	−0.193005	+	0.981198i	$0.561823\pi$
$318$		0			0
$319$	−1.12561	−	1.12561i	−0.0630223	−	0.0630223i
$320$	2.13273	−	2.13273i	0.119223	−	0.119223i
$321$		0			0
$322$		−	2.60992i		−	0.145445i
$323$	−4.49578	+	4.49578i	−0.250152	+	0.250152i
$324$		0			0
$325$	−8.79392	−	11.8695i	−0.487799	−	0.658401i
$326$		−	8.14505i		−	0.451113i
$327$		0			0
$328$	−7.09389			−0.391694
$329$	4.25414			0.234538
$330$		0			0
$331$	−6.86358	+	6.86358i	−0.377257	+	0.377257i	−0.870112	−	0.492855i	$-0.835953\pi$
$331$	−6.86358	+	6.86358i	−0.377257	+	0.377257i	0.492855	+	0.870112i	$0.335953\pi$
$332$	−5.76681	+	5.76681i	−0.316495	+	0.316495i
$333$		0			0
$334$	10.8485			0.593603
$335$	15.2814			0.834914
$336$		0			0
$337$			16.7706i			0.913550i	0.889582	+	0.456775i	$0.150996\pi$
$337$			16.7706i			0.913550i	−0.889582	+	0.456775i	$0.849004\pi$
$338$	−11.4710	+	6.11681i	−0.623942	+	0.332711i
$339$		0			0
$340$	−2.68861	+	2.68861i	−0.145810	+	0.145810i
$341$		−	9.87287i		−	0.534646i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	8.80802	+	8.80802i	0.474897	+	0.474897i
$345$		0			0
$346$	0.977209	+	0.977209i	0.0525351	+	0.0525351i
$347$			5.66158i			0.303929i	0.988386	+	0.151965i	$0.0485600\pi$
$347$			5.66158i			0.303929i	−0.988386	+	0.151965i	$0.951440\pi$
$348$		0			0
$349$	5.79458	+	5.79458i	0.310177	+	0.310177i	0.844978	−	0.534801i	$-0.179614\pi$
$349$	5.79458	+	5.79458i	0.310177	+	0.310177i	−0.534801	+	0.844978i	$0.679614\pi$
$350$	4.09707			0.218998
$351$		0			0
$352$	−2.60992			−0.139109
$353$	−24.9514	−	24.9514i	−1.32803	−	1.32803i	−0.907087	−	0.420942i	$-0.861699\pi$
$353$	−24.9514	−	24.9514i	−1.32803	−	1.32803i	−0.420942	−	0.907087i	$-0.638301\pi$
$354$		0			0
$355$			7.53626i			0.399983i
$356$	−6.44167	−	6.44167i	−0.341408	−	0.341408i
$357$		0			0
$358$	−5.46946	−	5.46946i	−0.289070	−	0.289070i
$359$	−10.0917	+	10.0917i	−0.532619	+	0.532619i	−0.921351	−	0.388732i	$-0.872913\pi$
$359$	−10.0917	+	10.0917i	−0.532619	+	0.532619i	0.388732	+	0.921351i	$0.372913\pi$
$360$		0			0
$361$		−	6.43649i		−	0.338762i
$362$	5.21400	−	5.21400i	0.274042	−	0.274042i
$363$		0			0
$364$	0.530808	−	3.56626i	0.0278219	−	0.186923i
$365$		−	38.5891i		−	2.01985i
$366$		0			0
$367$	28.8170			1.50424			0.752118	−	0.659028i	$-0.229032\pi$
$367$	28.8170			1.50424			0.752118	+	0.659028i	$0.229032\pi$
$368$	−2.60992			−0.136052
$369$		0			0
$370$	−13.4723	+	13.4723i	−0.700391	+	0.700391i
$371$	−0.585786	+	0.585786i	−0.0304125	+	0.0304125i
$372$		0			0
$373$	1.80186			0.0932970			0.0466485	−	0.998911i	$-0.485146\pi$
$373$	1.80186			0.0932970			0.0466485	+	0.998911i	$0.485146\pi$
$374$	3.29018			0.170131
$375$		0			0
$376$		−	4.25414i		−	0.219391i
$377$	−1.30914	−	1.76699i	−0.0674240	−	0.0910048i
$378$		0			0
$379$	15.1190	−	15.1190i	0.776611	−	0.776611i	−0.202642	−	0.979253i	$-0.564953\pi$
$379$	15.1190	−	15.1190i	0.776611	−	0.776611i	0.979253	+	0.202642i	$0.0649527\pi$
$380$		−	15.2118i		−	0.780347i
$381$		0			0
$382$	17.1181	−	17.1181i	0.875840	−	0.875840i
$383$	15.1602	+	15.1602i	0.774653	+	0.774653i	0.978916	−	0.204263i	$-0.0654799\pi$
$383$	15.1602	+	15.1602i	0.774653	+	0.774653i	−0.204263	+	0.978916i	$0.565480\pi$
$384$		0			0
$385$	−5.56626	−	5.56626i	−0.283683	−	0.283683i
$386$		−	21.2289i		−	1.08052i
$387$		0			0
$388$	−1.40271	−	1.40271i	−0.0712120	−	0.0712120i
$389$	28.4235			1.44113			0.720565	−	0.693388i	$-0.243883\pi$
$389$	28.4235			1.44113			0.720565	+	0.693388i	$0.243883\pi$
$390$		0			0
$391$	3.29018			0.166392
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$		0			0
$394$			5.10993i			0.257435i
$395$	−17.2035	−	17.2035i	−0.865600	−	0.865600i
$396$		0			0
$397$	−9.81873	−	9.81873i	−0.492788	−	0.492788i	0.416396	−	0.909184i	$-0.363293\pi$
$397$	−9.81873	−	9.81873i	−0.492788	−	0.492788i	−0.909184	+	0.416396i	$0.863293\pi$
$398$	12.8399	−	12.8399i	0.643604	−	0.643604i
$399$		0			0
$400$		−	4.09707i		−	0.204854i
$401$	12.7573	−	12.7573i	0.637069	−	0.637069i	−0.312762	−	0.949831i	$-0.601254\pi$
$401$	12.7573	−	12.7573i	0.637069	−	0.637069i	0.949831	+	0.312762i	$0.101254\pi$
$402$		0			0
$403$	2.00795	−	13.4905i	0.100023	−	0.672011i
$404$			12.0709i			0.600550i
$405$		0			0
$406$	0.609925			0.0302701
$407$	16.4867			0.817215
$408$		0			0
$409$	7.87267	−	7.87267i	0.389279	−	0.389279i	−0.485151	−	0.874430i	$-0.661236\pi$
$409$	7.87267	−	7.87267i	0.389279	−	0.389279i	0.874430	+	0.485151i	$0.161236\pi$
$410$	−15.1293	+	15.1293i	−0.747185	+	0.747185i
$411$		0			0
$412$	−10.1164			−0.498399
$413$	10.9450			0.538567
$414$		0			0
$415$			24.5981i			1.20747i
$416$	−3.56626	−	0.530808i	−0.174851	−	0.0260250i
$417$		0			0
$418$	−9.30768	+	9.30768i	−0.455254	+	0.455254i
$419$		−	7.49257i		−	0.366036i	−0.983110	−	0.183018i	$-0.941413\pi$
$419$		−	7.49257i		−	0.366036i	0.983110	−	0.183018i	$-0.0585867\pi$
$420$		0			0
$421$	14.9523	−	14.9523i	0.728733	−	0.728733i	−0.241635	−	0.970367i	$-0.577684\pi$
$421$	14.9523	−	14.9523i	0.728733	−	0.728733i	0.970367	+	0.241635i	$0.0776836\pi$
$422$	−7.33381	−	7.33381i	−0.357004	−	0.357004i
$423$		0			0
$424$	0.585786	+	0.585786i	0.0284483	+	0.0284483i
$425$			5.16494i			0.250537i
$426$		0			0
$427$	−8.03875	−	8.03875i	−0.389023	−	0.389023i
$428$	−8.63857			−0.417561
$429$		0			0
$430$	37.5702			1.81180
$431$	10.5198	+	10.5198i	0.506720	+	0.506720i	0.913518	−	0.406798i	$-0.133355\pi$
$431$	10.5198	+	10.5198i	0.506720	+	0.506720i	−0.406798	+	0.913518i	$0.633355\pi$
$432$		0			0
$433$		−	24.8246i		−	1.19299i	−0.802615	−	0.596497i	$-0.796559\pi$
$433$		−	24.8246i		−	1.19299i	0.802615	−	0.596497i	$-0.203441\pi$
$434$	2.67486	+	2.67486i	0.128397	+	0.128397i
$435$		0			0
$436$	−2.93125	−	2.93125i	−0.140381	−	0.140381i
$437$	−9.30768	+	9.30768i	−0.445247	+	0.445247i
$438$		0			0
$439$			5.40822i			0.258120i	0.991637	+	0.129060i	$0.0411960\pi$
$439$			5.40822i			0.258120i	−0.991637	+	0.129060i	$0.958804\pi$
$440$	−5.56626	+	5.56626i	−0.265361	+	0.265361i
$441$		0			0
$442$	4.49578	+	0.669159i	0.213843	+	0.0318286i
$443$			19.8582i			0.943493i	0.881734	+	0.471747i	$0.156376\pi$
$443$			19.8582i			0.943493i	−0.881734	+	0.471747i	$0.843624\pi$
$444$		0			0
$445$	−27.4767			−1.30252
$446$	−16.4330			−0.778123
$447$		0			0
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	20.1381	−	20.1381i	0.950376	−	0.950376i	−0.0484499	−	0.998826i	$-0.515428\pi$
$449$	20.1381	−	20.1381i	0.950376	−	0.950376i	0.998826	+	0.0484499i	$0.0154281\pi$
$450$		0			0
$451$	18.5145			0.871814
$452$	−1.25234			−0.0589051
$453$		0			0
$454$		−	5.73840i		−	0.269317i
$455$	−6.47381	−	8.73795i	−0.303497	−	0.409641i
$456$		0			0
$457$	11.6194	−	11.6194i	0.543533	−	0.543533i	−0.381030	−	0.924563i	$-0.624430\pi$
$457$	11.6194	−	11.6194i	0.543533	−	0.543533i	0.924563	+	0.381030i	$0.124430\pi$
$458$			16.1355i			0.753960i
$459$		0			0
$460$	−5.56626	+	5.56626i	−0.259528	+	0.259528i
$461$	18.2100	+	18.2100i	0.848123	+	0.848123i	0.989899	−	0.141776i	$-0.0452811\pi$
$461$	18.2100	+	18.2100i	0.848123	+	0.848123i	−0.141776	+	0.989899i	$0.545281\pi$
$462$		0			0
$463$	−21.5269	−	21.5269i	−1.00044	−	1.00044i	−1.00000		0.000441341i	$-0.999860\pi$
$463$	−21.5269	−	21.5269i	−1.00044	−	1.00044i	−0.000441341	−	1.00000i	$-0.500140\pi$
$464$		−	0.609925i		−	0.0283151i
$465$		0			0
$466$	−0.838126	−	0.838126i	−0.0388254	−	0.0388254i
$467$	−8.68127			−0.401721			−0.200861	−	0.979620i	$-0.564374\pi$
$467$	−8.68127			−0.401721			−0.200861	+	0.979620i	$0.564374\pi$
$468$		0			0
$469$	5.06656			0.233952
$470$	−9.07293	−	9.07293i	−0.418503	−	0.418503i
$471$		0			0
$472$		−	10.9450i		−	0.503783i
$473$	−22.9883	−	22.9883i	−1.05700	−	1.05700i
$474$		0			0
$475$	−14.6112	−	14.6112i	−0.670410	−	0.670410i
$476$	−0.891409	+	0.891409i	−0.0408577	+	0.0408577i
$477$		0			0
$478$			11.2611i			0.515072i
$479$	−14.3935	+	14.3935i	−0.657654	+	0.657654i	−0.954824	−	0.297170i	$-0.903957\pi$
$479$	−14.3935	+	14.3935i	−0.657654	+	0.657654i	0.297170	+	0.954824i	$0.403957\pi$
$480$		0			0
$481$	22.5278	+	3.35307i	1.02718	+	0.152887i
$482$			12.8221i			0.584029i
$483$		0			0
$484$	−4.18829			−0.190377
$485$	−5.98321			−0.271684
$486$		0			0
$487$	18.5815	−	18.5815i	0.842009	−	0.842009i	−0.147111	−	0.989120i	$-0.546997\pi$
$487$	18.5815	−	18.5815i	0.842009	−	0.842009i	0.989120	+	0.147111i	$0.0469974\pi$
$488$	−8.03875	+	8.03875i	−0.363897	+	0.363897i
$489$		0			0
$490$	3.01614			0.136255
$491$	5.72291			0.258271			0.129136	−	0.991627i	$-0.458780\pi$
$491$	5.72291			0.258271			0.129136	+	0.991627i	$0.458780\pi$
$492$		0			0
$493$			0.768897i			0.0346294i
$494$	−14.6112	+	10.8252i	−0.657391	+	0.487051i
$495$		0			0
$496$	2.67486	−	2.67486i	0.120105	−	0.120105i
$497$			2.49865i			0.112080i
$498$		0			0
$499$	−7.84938	+	7.84938i	−0.351386	+	0.351386i	−0.860625	−	0.509239i	$-0.829927\pi$
$499$	−7.84938	+	7.84938i	−0.351386	+	0.351386i	0.509239	+	0.860625i	$0.329927\pi$
$500$	1.92570	+	1.92570i	0.0861199	+	0.0861199i
$501$		0			0
$502$	−13.2808	−	13.2808i	−0.592750	−	0.592750i
$503$			17.2168i			0.767660i	0.923404	+	0.383830i	$0.125395\pi$
$503$			17.2168i			0.767660i	−0.923404	+	0.383830i	$0.874605\pi$
$504$		0			0
$505$	25.7440	+	25.7440i	1.14559	+	1.14559i
$506$	6.81171			0.302817
$507$		0			0
$508$	7.64085			0.339008
$509$	6.20791	+	6.20791i	0.275161	+	0.275161i	0.831174	−	0.556013i	$-0.187670\pi$
$509$	6.20791	+	6.20791i	0.275161	+	0.275161i	−0.556013	+	0.831174i	$0.687670\pi$
$510$		0			0
$511$		−	12.7942i		−	0.565983i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	4.83007	+	4.83007i	0.213045	+	0.213045i
$515$	−21.5755	+	21.5755i	−0.950732	+	0.950732i
$516$		0			0
$517$			11.1030i			0.488309i
$518$	−4.46674	+	4.46674i	−0.196257	+	0.196257i
$519$		0			0
$520$	−8.73795	+	6.47381i	−0.383184	+	0.283895i
$521$		−	15.7357i		−	0.689394i	−0.938714	−	0.344697i	$-0.887982\pi$
$521$		−	15.7357i		−	0.689394i	0.938714	−	0.344697i	$-0.112018\pi$
$522$		0			0
$523$	−11.8537			−0.518325			−0.259163	−	0.965834i	$-0.583447\pi$
$523$	−11.8537			−0.518325			−0.259163	+	0.965834i	$0.583447\pi$
$524$	8.42584			0.368085
$525$		0			0
$526$	−14.9045	+	14.9045i	−0.649866	+	0.649866i
$527$	−3.37204	+	3.37204i	−0.146888	+	0.146888i
$528$		0			0
$529$	−16.1883			−0.703839
$530$	2.49865			0.108534
$531$		0			0
$532$		−	5.04346i		−	0.218662i
$533$	25.2987	+	3.76549i	1.09581	+	0.163102i
$534$		0			0
$535$	−18.4237	+	18.4237i	−0.796527	+	0.796527i
$536$		−	5.06656i		−	0.218842i
$537$		0			0
$538$	−4.01367	+	4.01367i	−0.173042	+	0.173042i
$539$	−1.84550	−	1.84550i	−0.0794911	−	0.0794911i
$540$		0			0
$541$	21.7511	+	21.7511i	0.935154	+	0.935154i	0.998022	−	0.0628678i	$-0.0200246\pi$
$541$	21.7511	+	21.7511i	0.935154	+	0.935154i	−0.0628678	+	0.998022i	$0.520025\pi$
$542$			11.1648i			0.479569i
$543$		0			0
$544$	0.891409	+	0.891409i	0.0382188	+	0.0382188i
$545$	−12.5031			−0.535575
$546$		0			0
$547$	33.6938			1.44064			0.720322	−	0.693640i	$-0.243994\pi$
$547$	33.6938			1.44064			0.720322	+	0.693640i	$0.243994\pi$
$548$	−14.1383	−	14.1383i	−0.603957	−	0.603957i
$549$		0			0
$550$			10.6931i			0.455953i
$551$	−2.17515	−	2.17515i	−0.0926647	−	0.0926647i
$552$		0			0
$553$	−5.70381	−	5.70381i	−0.242551	−	0.242551i
$554$	16.7159	−	16.7159i	0.710189	−	0.710189i
$555$		0			0
$556$			19.0228i			0.806746i
$557$	26.7991	−	26.7991i	1.13552	−	1.13552i	0.146272	−	0.989244i	$-0.453273\pi$
$557$	26.7991	−	26.7991i	1.13552	−	1.13552i	0.989244	−	0.146272i	$-0.0467275\pi$
$558$		0			0
$559$	−26.7364	−	36.0871i	−1.13083	−	1.52632i
$560$		−	3.01614i		−	0.127455i
$561$		0			0
$562$	−29.9246			−1.26229
$563$	17.5847			0.741106			0.370553	−	0.928811i	$-0.379168\pi$
$563$	17.5847			0.741106			0.370553	+	0.928811i	$0.379168\pi$
$564$		0			0
$565$	−2.67090	+	2.67090i	−0.112366	+	0.112366i
$566$	5.70034	−	5.70034i	0.239603	−	0.239603i
$567$		0			0
$568$	2.49865			0.104841
$569$	−5.21538			−0.218640			−0.109320	−	0.994007i	$-0.534867\pi$
$569$	−5.21538			−0.218640			−0.109320	+	0.994007i	$0.534867\pi$
$570$		0			0
$571$		−	1.36248i		−	0.0570180i	−0.999594	−	0.0285090i	$-0.990924\pi$
$571$		−	1.36248i		−	0.0570180i	0.999594	−	0.0285090i	$-0.00907592\pi$
$572$	9.30768	+	1.38537i	0.389174	+	0.0579252i
$573$		0			0
$574$	−5.01614	+	5.01614i	−0.209369	+	0.209369i
$575$			10.6931i			0.445931i
$576$		0			0
$577$	13.6575	−	13.6575i	0.568569	−	0.568569i	−0.363158	−	0.931727i	$-0.618302\pi$
$577$	13.6575	−	13.6575i	0.568569	−	0.568569i	0.931727	+	0.363158i	$0.118302\pi$
$578$	10.8971	+	10.8971i	0.453258	+	0.453258i
$579$		0			0
$580$	−1.30081	−	1.30081i	−0.0540130	−	0.0540130i
$581$			8.15550i			0.338347i
$582$		0			0
$583$	−1.52886	−	1.52886i	−0.0633189	−	0.0633189i
$584$	−12.7942			−0.529429
$585$		0			0
$586$	15.6428			0.646198
$587$	0.356637	+	0.356637i	0.0147200	+	0.0147200i	0.714428	−	0.699708i	$-0.246687\pi$
$587$	0.356637	+	0.356637i	0.0147200	+	0.0147200i	−0.699708	+	0.714428i	$0.746687\pi$
$588$		0			0
$589$		−	19.0785i		−	0.786115i
$590$	−23.3427	−	23.3427i	−0.961003	−	0.961003i
$591$		0			0
$592$	4.46674	+	4.46674i	0.183582	+	0.183582i
$593$	−19.6437	+	19.6437i	−0.806669	+	0.806669i	−0.984128	−	0.177459i	$-0.943212\pi$
$593$	−19.6437	+	19.6437i	−0.806669	+	0.806669i	0.177459	+	0.984128i	$0.443212\pi$
$594$		0			0
$595$			3.80227i			0.155878i
$596$	−5.33521	+	5.33521i	−0.218539	+	0.218539i
$597$		0			0
$598$	9.30768	+	1.38537i	0.380619	+	0.0566519i
$599$		−	29.7856i		−	1.21701i	−0.793551	−	0.608504i	$-0.791770\pi$
$599$		−	29.7856i		−	1.21701i	0.793551	−	0.608504i	$-0.208230\pi$
$600$		0			0
$601$	18.1371			0.739827			0.369913	−	0.929066i	$-0.379387\pi$
$601$	18.1371			0.739827			0.369913	+	0.929066i	$0.379387\pi$
$602$	12.4564			0.507686
$603$		0			0
$604$	−13.9679	+	13.9679i	−0.568345	+	0.568345i
$605$	−8.93249	+	8.93249i	−0.363158	+	0.363158i
$606$		0			0
$607$	−17.0733			−0.692985			−0.346493	−	0.938053i	$-0.612627\pi$
$607$	−17.0733			−0.692985			−0.346493	+	0.938053i	$0.612627\pi$
$608$	−5.04346			−0.204539
$609$		0			0
$610$			34.2890i			1.38832i
$611$	−2.25813	+	15.1714i	−0.0913542	+	0.613769i
$612$		0			0
$613$	9.57480	−	9.57480i	0.386723	−	0.386723i	−0.486794	−	0.873517i	$-0.661834\pi$
$613$	9.57480	−	9.57480i	0.386723	−	0.386723i	0.873517	+	0.486794i	$0.161834\pi$
$614$			32.3845i			1.30693i
$615$		0			0
$616$	−1.84550	+	1.84550i	−0.0743571	+	0.0743571i
$617$	−28.0815	−	28.0815i	−1.13052	−	1.13052i	−0.990091	−	0.140430i	$-0.955152\pi$
$617$	−28.0815	−	28.0815i	−1.13052	−	1.13052i	−0.140430	−	0.990091i	$-0.544848\pi$
$618$		0			0
$619$	9.68919	+	9.68919i	0.389441	+	0.389441i	0.874488	−	0.485047i	$-0.161197\pi$
$619$	9.68919	+	9.68919i	0.389441	+	0.389441i	−0.485047	+	0.874488i	$0.661197\pi$
$620$		−	11.4095i		−	0.458216i
$621$		0			0
$622$	7.36407	+	7.36407i	0.295272	+	0.295272i
$623$	−9.10989			−0.364980
$624$		0			0
$625$	28.6994			1.14797
$626$	4.31355	+	4.31355i	0.172404	+	0.172404i
$627$		0			0
$628$			13.7895i			0.550261i
$629$	−5.63096	−	5.63096i	−0.224521	−	0.224521i
$630$		0			0
$631$	13.9972	+	13.9972i	0.557222	+	0.557222i	0.928515	−	0.371294i	$-0.121086\pi$
$631$	13.9972	+	13.9972i	0.557222	+	0.557222i	−0.371294	+	0.928515i	$0.621086\pi$
$632$	−5.70381	+	5.70381i	−0.226885	+	0.226885i
$633$		0			0
$634$		−	19.8462i		−	0.788193i
$635$	16.2959	−	16.2959i	0.646682	−	0.646682i
$636$		0			0
$637$	−2.14639	−	2.89707i	−0.0850431	−	0.114786i
$638$			1.59186i			0.0630223i
$639$		0			0
$640$	−3.01614			−0.119223
$641$	49.5706			1.95792			0.978961	−	0.204046i	$-0.0654091\pi$
$641$	49.5706			1.95792			0.978961	+	0.204046i	$0.0654091\pi$
$642$		0			0
$643$	−27.7503	+	27.7503i	−1.09437	+	1.09437i	−0.0993085	+	0.995057i	$0.531663\pi$
$643$	−27.7503	+	27.7503i	−1.09437	+	1.09437i	−0.995057	+	0.0993085i	$0.968337\pi$
$644$	−1.84550	+	1.84550i	−0.0727227	+	0.0727227i
$645$		0			0
$646$	6.35800			0.250152
$647$	38.1315			1.49910			0.749552	−	0.661945i	$-0.230269\pi$
$647$	38.1315			1.49910			0.749552	+	0.661945i	$0.230269\pi$
$648$		0			0
$649$			28.5656i			1.12130i
$650$	−2.17476	+	14.6112i	−0.0853011	+	0.573100i
$651$		0			0
$652$	−5.75942	+	5.75942i	−0.225556	+	0.225556i
$653$		−	7.25470i		−	0.283898i	−0.989874	−	0.141949i	$-0.954663\pi$
$653$		−	7.25470i		−	0.283898i	0.989874	−	0.141949i	$-0.0453370\pi$
$654$		0			0
$655$	17.9700	−	17.9700i	0.702148	−	0.702148i
$656$	5.01614	+	5.01614i	0.195847	+	0.195847i
$657$		0			0
$658$	−3.00813	−	3.00813i	−0.117269	−	0.117269i
$659$		−	4.39203i		−	0.171089i	−0.996334	−	0.0855446i	$-0.972737\pi$
$659$		−	4.39203i		−	0.171089i	0.996334	−	0.0855446i	$-0.0272630\pi$
$660$		0			0
$661$	13.1583	+	13.1583i	0.511797	+	0.511797i	0.915077	−	0.403279i	$-0.132130\pi$
$661$	13.1583	+	13.1583i	0.511797	+	0.511797i	−0.403279	+	0.915077i	$0.632130\pi$
$662$	9.70657			0.377257
$663$		0			0
$664$	8.15550			0.316495
$665$	−10.7563	−	10.7563i	−0.417113	−	0.417113i
$666$		0			0
$667$			1.59186i			0.0616370i
$668$	−7.67104	−	7.67104i	−0.296801	−	0.296801i
$669$		0			0
$670$	−10.8056	−	10.8056i	−0.417457	−	0.417457i
$671$	20.9805	−	20.9805i	0.809945	−	0.809945i
$672$		0			0
$673$			23.8772i			0.920397i	0.887816	+	0.460198i	$0.152222\pi$
$673$			23.8772i			0.920397i	−0.887816	+	0.460198i	$0.847778\pi$
$674$	11.8586	−	11.8586i	0.456775	−	0.456775i
$675$		0			0
$676$	12.4365	+	3.78600i	0.478326	+	0.145616i
$677$		−	26.4212i		−	1.01545i	−0.861519	−	0.507725i	$-0.830487\pi$
$677$		−	26.4212i		−	1.01545i	0.861519	−	0.507725i	$-0.169513\pi$
$678$		0			0
$679$	−1.98374			−0.0761288
$680$	3.80227			0.145810
$681$		0			0
$682$	−6.98117	+	6.98117i	−0.267323	+	0.267323i
$683$	−13.7035	+	13.7035i	−0.524348	+	0.524348i	−0.918882	−	0.394534i	$-0.870906\pi$
$683$	−13.7035	+	13.7035i	−0.524348	+	0.524348i	0.394534	+	0.918882i	$0.370906\pi$
$684$		0			0
$685$	−60.3063			−2.30418
$686$	1.00000			0.0381802
$687$		0			0
$688$		−	12.4564i		−	0.474897i
$689$	−1.77813	−	2.40001i	−0.0677413	−	0.0914331i
$690$		0			0
$691$	5.96522	−	5.96522i	0.226928	−	0.226928i	−0.584480	−	0.811408i	$-0.698702\pi$
$691$	5.96522	−	5.96522i	0.226928	−	0.226928i	0.811408	+	0.584480i	$0.198702\pi$
$692$		−	1.38198i		−	0.0525351i
$693$		0			0
$694$	4.00334	−	4.00334i	0.151965	−	0.151965i
$695$	40.5705	+	40.5705i	1.53893	+	1.53893i
$696$		0			0
$697$	−6.32355	−	6.32355i	−0.239522	−	0.239522i
$698$		−	8.19477i		−	0.310177i
$699$		0			0
$700$	−2.89707	−	2.89707i	−0.109499	−	0.109499i
$701$	44.7097			1.68866			0.844332	−	0.535821i	$-0.179998\pi$
$701$	44.7097			1.68866			0.844332	+	0.535821i	$0.179998\pi$
$702$		0			0
$703$	31.8591			1.20159
$704$	1.84550	+	1.84550i	0.0695547	+	0.0695547i
$705$		0			0
$706$			35.2866i			1.32803i
$707$	8.53542	+	8.53542i	0.321008	+	0.321008i
$708$		0			0
$709$	−29.2283	−	29.2283i	−1.09769	−	1.09769i	−0.994680	−	0.103010i	$-0.967153\pi$
$709$	−29.2283	−	29.2283i	−1.09769	−	1.09769i	−0.103010	−	0.994680i	$-0.532847\pi$
$710$	5.32894	−	5.32894i	0.199992	−	0.199992i
$711$		0			0
$712$			9.10989i			0.341408i
$713$	−6.98117	+	6.98117i	−0.261447	+	0.261447i
$714$		0			0
$715$	22.8054	−	16.8962i	0.852873	−	0.631880i
$716$			7.73498i			0.289070i
$717$		0			0
$718$	14.2718			0.532619
$719$	−3.29230			−0.122782			−0.0613910	−	0.998114i	$-0.519554\pi$
$719$	−3.29230			−0.122782			−0.0613910	+	0.998114i	$0.519554\pi$
$720$		0			0
$721$	−7.15337	+	7.15337i	−0.266405	+	0.266405i
$722$	−4.55128	+	4.55128i	−0.169381	+	0.169381i
$723$		0			0
$724$	−7.37370			−0.274042
$725$	−2.49891			−0.0928071
$726$		0			0
$727$			13.3071i			0.493534i	0.969075	+	0.246767i	$0.0793682\pi$
$727$			13.3071i			0.493534i	−0.969075	+	0.246767i	$0.920632\pi$
$728$	−2.89707	+	2.14639i	−0.107372	+	0.0795506i
$729$		0			0
$730$	−27.2866	+	27.2866i	−1.00992	+	1.00992i
$731$			15.7031i			0.580800i
$732$		0			0
$733$	−35.2472	+	35.2472i	−1.30189	+	1.30189i	−0.374766	+	0.927119i	$0.622277\pi$
$733$	−35.2472	+	35.2472i	−1.30189	+	1.30189i	−0.927119	+	0.374766i	$0.877723\pi$
$734$	−20.3767	−	20.3767i	−0.752118	−	0.752118i
$735$		0			0
$736$	1.84550	+	1.84550i	0.0680259	+	0.0680259i
$737$			13.2233i			0.487088i
$738$		0			0
$739$	−18.7527	−	18.7527i	−0.689828	−	0.689828i	0.272366	−	0.962194i	$-0.412194\pi$
$739$	−18.7527	−	18.7527i	−0.689828	−	0.689828i	−0.962194	+	0.272366i	$0.912194\pi$
$740$	19.0527			0.700391
$741$		0			0
$742$	0.828427			0.0304125
$743$	−17.9745	−	17.9745i	−0.659422	−	0.659422i	0.295821	−	0.955243i	$-0.404407\pi$
$743$	−17.9745	−	17.9745i	−0.659422	−	0.659422i	−0.955243	+	0.295821i	$0.904407\pi$
$744$		0			0
$745$			22.7571i			0.833756i
$746$	−1.27411	−	1.27411i	−0.0466485	−	0.0466485i
$747$		0			0
$748$	−2.32651	−	2.32651i	−0.0850656	−	0.0850656i
$749$	−6.10839	+	6.10839i	−0.223196	+	0.223196i
$750$		0			0
$751$		−	31.9573i		−	1.16614i	−0.812422	−	0.583070i	$-0.801852\pi$
$751$		−	31.9573i		−	1.16614i	0.812422	−	0.583070i	$-0.198148\pi$
$752$	−3.00813	+	3.00813i	−0.109695	+	0.109695i
$753$		0			0
$754$	−0.323753	+	2.17515i	−0.0117904	+	0.0792144i
$755$			59.5794i			2.16832i
$756$		0			0
$757$	−19.7785			−0.718863			−0.359431	−	0.933171i	$-0.617029\pi$
$757$	−19.7785			−0.718863			−0.359431	+	0.933171i	$0.617029\pi$
$758$	−21.3815			−0.776611
$759$		0			0
$760$	−10.7563	+	10.7563i	−0.390173	+	0.390173i
$761$	−36.1688	+	36.1688i	−1.31112	+	1.31112i	−0.390526	+	0.920592i	$0.627707\pi$
$761$	−36.1688	+	36.1688i	−1.31112	+	1.31112i	−0.920592	+	0.390526i	$0.872293\pi$
$762$		0			0
$763$	−4.14541			−0.150074
$764$	−24.2087			−0.875840
$765$		0			0
$766$		−	21.4398i		−	0.774653i
$767$	−5.80968	+	39.0327i	−0.209775	+	1.40939i
$768$		0			0
$769$	−14.0374	+	14.0374i	−0.506202	+	0.506202i	−0.913358	−	0.407156i	$-0.866520\pi$
$769$	−14.0374	+	14.0374i	−0.506202	+	0.506202i	0.407156	+	0.913358i	$0.366520\pi$
$770$			7.87189i			0.283683i
$771$		0			0
$772$	−15.0111	+	15.0111i	−0.540261	+	0.540261i
$773$	−25.5243	−	25.5243i	−0.918047	−	0.918047i	0.0788403	−	0.996887i	$-0.474878\pi$
$773$	−25.5243	−	25.5243i	−0.918047	−	0.918047i	−0.996887	+	0.0788403i	$0.974878\pi$
$774$		0			0
$775$	−10.9591	−	10.9591i	−0.393662	−	0.393662i
$776$			1.98374i			0.0712120i
$777$		0			0
$778$	−20.0985	−	20.0985i	−0.720565	−	0.720565i
$779$	35.7777			1.28187
$780$		0			0
$781$	−6.52128			−0.233350
$782$	−2.32651	−	2.32651i	−0.0831958	−	0.0831958i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$	29.4093	+	29.4093i	1.04966	+	1.04966i
$786$		0			0
$787$	−17.7150	−	17.7150i	−0.631473	−	0.631473i	0.316965	−	0.948437i	$-0.397336\pi$
$787$	−17.7150	−	17.7150i	−0.631473	−	0.631473i	−0.948437	+	0.316965i	$0.897336\pi$
$788$	3.61327	−	3.61327i	0.128717	−	0.128717i
$789$		0			0
$790$			24.3294i			0.865600i
$791$	−0.885538	+	0.885538i	−0.0314861	+	0.0314861i
$792$		0			0
$793$	32.9354	−	24.4013i	1.16957	−	0.866515i
$794$			13.8858i			0.492788i
$795$		0			0
$796$	−18.1583			−0.643604
$797$	46.7606			1.65635			0.828173	−	0.560472i	$-0.189380\pi$
$797$	46.7606			1.65635			0.828173	+	0.560472i	$0.189380\pi$
$798$		0			0
$799$	3.79218	−	3.79218i	0.134158	−	0.134158i
$800$	−2.89707	+	2.89707i	−0.102427	+	0.102427i
$801$		0			0
$802$	−18.0415			−0.637069
$803$	33.3920			1.17838
$804$		0			0
$805$			7.87189i			0.277448i
$806$	−10.9591	+	8.11941i	−0.386017	+	0.285994i
$807$		0			0
$808$	8.53542	−	8.53542i	0.300275	−	0.300275i
$809$		−	39.5051i		−	1.38893i	−0.719528	−	0.694463i	$-0.755642\pi$
$809$		−	39.5051i		−	1.38893i	0.719528	−	0.694463i	$-0.244358\pi$
$810$		0			0
$811$	16.3036	−	16.3036i	0.572498	−	0.572498i	−0.360328	−	0.932826i	$-0.617335\pi$
$811$	16.3036	−	16.3036i	0.572498	−	0.572498i	0.932826	+	0.360328i	$0.117335\pi$
$812$	−0.431282	−	0.431282i	−0.0151350	−	0.0151350i
$813$		0			0
$814$	−11.6579	−	11.6579i	−0.408608	−	0.408608i
$815$			24.5666i			0.860529i
$816$		0			0
$817$	−44.4229	−	44.4229i	−1.55416	−	1.55416i
$818$	−11.1336			−0.389279
$819$		0			0
$820$	21.3961			0.747185
$821$	32.8163	+	32.8163i	1.14530	+	1.14530i	0.987466	+	0.157829i	$0.0504496\pi$
$821$	32.8163	+	32.8163i	1.14530	+	1.14530i	0.157829	+	0.987466i	$0.449550\pi$
$822$		0			0
$823$			39.2017i			1.36649i	0.730191	+	0.683243i	$0.239431\pi$
$823$			39.2017i			1.36649i	−0.730191	+	0.683243i	$0.760569\pi$
$824$	7.15337	+	7.15337i	0.249199	+	0.249199i
$825$		0			0
$826$	−7.73927	−	7.73927i	−0.269284	−	0.269284i
$827$	−23.0814	+	23.0814i	−0.802619	+	0.802619i	−0.983504	−	0.180886i	$-0.942104\pi$
$827$	−23.0814	+	23.0814i	−0.802619	+	0.802619i	0.180886	+	0.983504i	$0.442104\pi$
$828$		0			0
$829$		−	45.4366i		−	1.57808i	−0.614343	−	0.789039i	$-0.710579\pi$
$829$		−	45.4366i		−	1.57808i	0.614343	−	0.789039i	$-0.289421\pi$
$830$	17.3935	−	17.3935i	0.603737	−	0.603737i
$831$		0			0
$832$	2.14639	+	2.89707i	0.0744128	+	0.100438i
$833$			1.26064i			0.0436787i
$834$		0			0
$835$	−32.7205			−1.13234
$836$	13.1631			0.455254
$837$		0			0
$838$	−5.29805	+	5.29805i	−0.183018	+	0.183018i
$839$	−21.7742	+	21.7742i	−0.751730	+	0.751730i	−0.974802	−	0.223072i	$-0.928391\pi$
$839$	−21.7742	+	21.7742i	−0.751730	+	0.751730i	0.223072	+	0.974802i	$0.428391\pi$
$840$		0			0
$841$	28.6280			0.987172
$842$	−21.1458			−0.728733
$843$		0			0
$844$			10.3716i			0.357004i
$845$	34.5982	−	18.4491i	1.19021	−	0.634670i
$846$		0			0
$847$	−2.96157	+	2.96157i	−0.101761	+	0.101761i
$848$		−	0.828427i		−	0.0284483i
$849$		0			0
$850$	3.65217	−	3.65217i	0.125268	−	0.125268i
$851$	−11.6579	−	11.6579i	−0.399626	−	0.399626i
$852$		0			0
$853$	28.2430	+	28.2430i	0.967023	+	0.967023i	0.999473	−	0.0324499i	$-0.0103309\pi$
$853$	28.2430	+	28.2430i	0.967023	+	0.967023i	−0.0324499	+	0.999473i	$0.510331\pi$
$854$			11.3685i			0.389023i
$855$		0			0
$856$	6.10839	+	6.10839i	0.208780	+	0.208780i
$857$	−23.2331			−0.793627			−0.396814	−	0.917899i	$-0.629884\pi$
$857$	−23.2331			−0.793627			−0.396814	+	0.917899i	$0.629884\pi$
$858$		0			0
$859$	11.6255			0.396656			0.198328	−	0.980136i	$-0.436449\pi$
$859$	11.6255			0.396656			0.198328	+	0.980136i	$0.436449\pi$
$860$	−26.5662	−	26.5662i	−0.905899	−	0.905899i
$861$		0			0
$862$		−	14.8772i		−	0.506720i
$863$	−8.69219	−	8.69219i	−0.295886	−	0.295886i	0.543514	−	0.839400i	$-0.317093\pi$
$863$	−8.69219	−	8.69219i	−0.295886	−	0.295886i	−0.839400	+	0.543514i	$0.817093\pi$
$864$		0			0
$865$	−2.94740	−	2.94740i	−0.100214	−	0.100214i
$866$	−17.5536	+	17.5536i	−0.596497	+	0.596497i
$867$		0			0
$868$		−	3.78282i		−	0.128397i
$869$	14.8865	−	14.8865i	0.504991	−	0.504991i
$870$		0			0
$871$	−2.68937	+	18.0687i	−0.0911259	+	0.612235i
$872$			4.14541i			0.140381i
$873$		0			0
$874$	13.1631			0.445247
$875$	2.72335			0.0920661
$876$		0			0
$877$	−37.0893	+	37.0893i	−1.25242	+	1.25242i	−0.297785	+	0.954633i	$0.596248\pi$
$877$	−37.0893	+	37.0893i	−1.25242	+	1.25242i	−0.954633	+	0.297785i	$0.903752\pi$
$878$	3.82419	−	3.82419i	0.129060	−	0.129060i
$879$		0			0
$880$	7.87189			0.265361
$881$	43.7138			1.47275			0.736377	−	0.676571i	$-0.236535\pi$
$881$	43.7138			1.47275			0.736377	+	0.676571i	$0.236535\pi$
$882$		0			0
$883$			19.9670i			0.671944i	0.941872	+	0.335972i	$0.109065\pi$
$883$			19.9670i			0.671944i	−0.941872	+	0.335972i	$0.890935\pi$
$884$	−2.70583	−	3.65217i	−0.0910070	−	0.122836i
$885$		0			0
$886$	14.0419	−	14.0419i	0.471747	−	0.471747i
$887$			45.6512i			1.53282i	0.642354	+	0.766408i	$0.277958\pi$
$887$			45.6512i			1.53282i	−0.642354	+	0.766408i	$0.722042\pi$
$888$		0			0
$889$	5.40290	−	5.40290i	0.181207	−	0.181207i
$890$	19.4289	+	19.4289i	0.651260	+	0.651260i
$891$		0			0
$892$	11.6199	+	11.6199i	0.389062	+	0.389062i
$893$			21.4556i			0.717984i
$894$		0			0
$895$	16.4966	+	16.4966i	0.551421	+	0.551421i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−28.4796			−0.950376
$899$	−1.63146	−	1.63146i	−0.0544123	−	0.0544123i
$900$		0			0
$901$			1.04435i			0.0347924i
$902$	−13.0917	−	13.0917i	−0.435907	−	0.435907i
$903$		0			0
$904$	0.885538	+	0.885538i	0.0294525	+	0.0294525i
$905$	−15.7261	+	15.7261i	−0.522754	+	0.522754i
$906$		0			0
$907$			36.3639i			1.20744i	0.797195	+	0.603722i	$0.206316\pi$
$907$			36.3639i			1.20744i	−0.797195	+	0.603722i	$0.793684\pi$
$908$	−4.05766	+	4.05766i	−0.134658	+	0.134658i
$909$		0			0
$910$	−1.60099	+	10.7563i	−0.0530723	+	0.356569i
$911$		−	19.0726i		−	0.631905i	−0.948775	−	0.315952i	$-0.897676\pi$
$911$		−	19.0726i		−	0.631905i	0.948775	−	0.315952i	$-0.102324\pi$
$912$		0			0
$913$	−21.2852			−0.704439
$914$	−16.4323			−0.543533
$915$		0			0
$916$	11.4095	−	11.4095i	0.376980	−	0.376980i
$917$	5.95797	−	5.95797i	0.196750	−	0.196750i
$918$		0			0
$919$	40.7022			1.34264			0.671321	−	0.741167i	$-0.265727\pi$
$919$	40.7022			1.34264			0.671321	+	0.741167i	$0.265727\pi$
$920$	7.87189			0.259528
$921$		0			0
$922$		−	25.7528i		−	0.848123i
$923$	−8.91084	−	1.32630i	−0.293304	−	0.0436558i
$924$		0			0
$925$	18.3006	−	18.3006i	0.601718	−	0.601718i
$926$			30.4437i			1.00044i
$927$		0			0
$928$	−0.431282	+	0.431282i	−0.0141575	+	0.0141575i
$929$	−16.5156	−	16.5156i	−0.541858	−	0.541858i	0.382215	−	0.924073i	$-0.375161\pi$
$929$	−16.5156	−	16.5156i	−0.541858	−	0.541858i	−0.924073	+	0.382215i	$0.875161\pi$
$930$		0			0
$931$	−3.56626	−	3.56626i	−0.116880	−	0.116880i
$932$			1.18529i			0.0388254i
$933$		0			0
$934$	6.13858	+	6.13858i	0.200861	+	0.200861i
$935$	−9.92363			−0.324538
$936$		0			0
$937$	−20.9676			−0.684981			−0.342490	−	0.939521i	$-0.611270\pi$
$937$	−20.9676			−0.684981			−0.342490	+	0.939521i	$0.611270\pi$
$938$	−3.58260	−	3.58260i	−0.116976	−	0.116976i
$939$		0			0
$940$			12.8311i			0.418503i
$941$	−23.5986	−	23.5986i	−0.769292	−	0.769292i	0.208690	−	0.977982i	$-0.433080\pi$
$941$	−23.5986	−	23.5986i	−0.769292	−	0.769292i	−0.977982	+	0.208690i	$0.933080\pi$
$942$		0			0
$943$	−13.0917	−	13.0917i	−0.426326	−	0.426326i
$944$	−7.73927	+	7.73927i	−0.251892	+	0.251892i
$945$		0			0
$946$			32.5103i			1.05700i
$947$	2.41559	−	2.41559i	0.0784960	−	0.0784960i	−0.666769	−	0.745265i	$-0.732323\pi$
$947$	2.41559	−	2.41559i	0.0784960	−	0.0784960i	0.745265	+	0.666769i	$0.232323\pi$
$948$		0			0
$949$	45.6276	+	6.79128i	1.48113	+	0.220454i
$950$			20.6634i			0.670410i
$951$		0			0
$952$	1.26064			0.0408577
$953$	47.2860			1.53174			0.765871	−	0.642994i	$-0.222308\pi$
$953$	47.2860			1.53174			0.765871	+	0.642994i	$0.222308\pi$
$954$		0			0
$955$	−51.6306	+	51.6306i	−1.67073	+	1.67073i
$956$	7.96282	−	7.96282i	0.257536	−	0.257536i
$957$		0			0
$958$	20.3554			0.657654
$959$	−19.9945			−0.645658
$960$		0			0
$961$			16.6903i			0.538397i
$962$	−13.5586	−	18.3006i	−0.437147	−	0.590033i
$963$		0			0
$964$	9.06656	−	9.06656i	0.292014	−	0.292014i
$965$			64.0292i			2.06117i
$966$		0			0
$967$	3.99871	−	3.99871i	0.128590	−	0.128590i	−0.639883	−	0.768473i	$-0.721017\pi$
$967$	3.99871	−	3.99871i	0.128590	−	0.128590i	0.768473	+	0.639883i	$0.221017\pi$
$968$	2.96157	+	2.96157i	0.0951885	+	0.0951885i
$969$		0			0
$970$	4.23077	+	4.23077i	0.135842	+	0.135842i
$971$		−	56.4619i		−	1.81195i	−0.423332	−	0.905975i	$-0.639140\pi$
$971$		−	56.4619i		−	1.81195i	0.423332	−	0.905975i	$-0.360860\pi$
$972$		0			0
$973$	13.4511	+	13.4511i	0.431224	+	0.431224i
$974$	−26.2782			−0.842009
$975$		0			0
$976$	11.3685			0.363897
$977$	35.2647	+	35.2647i	1.12822	+	1.12822i	0.990467	+	0.137749i	$0.0439868\pi$
$977$	35.2647	+	35.2647i	1.12822	+	1.12822i	0.137749	+	0.990467i	$0.456013\pi$
$978$		0			0
$979$		−	23.7761i		−	0.759889i
$980$	−2.13273	−	2.13273i	−0.0681276	−	0.0681276i
$981$		0			0
$982$	−4.04671	−	4.04671i	−0.129136	−	0.129136i
$983$	−12.9055	+	12.9055i	−0.411620	+	0.411620i	−0.882303	−	0.470682i	$-0.844008\pi$
$983$	−12.9055	+	12.9055i	−0.411620	+	0.411620i	0.470682	+	0.882303i	$0.344008\pi$
$984$		0			0
$985$		−	15.4122i		−	0.491075i
$986$	0.543692	−	0.543692i	0.0173147	−	0.0173147i
$987$		0			0
$988$	17.9863	+	2.67711i	0.572221	+	0.0851702i
$989$			32.5103i			1.03377i
$990$		0			0
$991$	−33.5996			−1.06733			−0.533663	−	0.845697i	$-0.679185\pi$
$991$	−33.5996			−1.06733			−0.533663	+	0.845697i	$0.679185\pi$
$992$	−3.78282			−0.120105
$993$		0			0
$994$	1.76681	−	1.76681i	0.0560398	−	0.0560398i
$995$	−38.7267	+	38.7267i	−1.22772	+	1.22772i
$996$		0			0
$997$	−38.3328			−1.21401			−0.607006	−	0.794698i	$-0.707629\pi$
$997$	−38.3328			−1.21401			−0.607006	+	0.794698i	$0.707629\pi$
$998$	11.1007			0.351386
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.y.b.1331.3	yes	12
3.2	odd	2		1638.2.y.a.1331.4	yes	12
13.8	odd	4		1638.2.y.a.827.4	✓	12
39.8	even	4	inner	1638.2.y.b.827.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.y.a.827.4	✓	12	13.8	odd	4
1638.2.y.a.1331.4	yes	12	3.2	odd	2
1638.2.y.b.827.3	yes	12	39.8	even	4	inner
1638.2.y.b.1331.3	yes	12	1.1	even	1	trivial

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.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.13273 + 2.13273i) q^{5} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.13273 + 2.13273i) q^{5} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.01614i q^{10} +(-1.84550 + 1.84550i) q^{11} +(-2.89707 + 2.14639i) q^{13} -1.00000i q^{14} -1.00000 q^{16} +1.26064 q^{17} +(-3.56626 + 3.56626i) q^{19} +(-2.13273 + 2.13273i) q^{20} +2.60992 q^{22} +2.60992 q^{23} +4.09707i q^{25} +(3.56626 + 0.530808i) q^{26} +(-0.707107 + 0.707107i) q^{28} +0.609925i q^{29} +(-2.67486 + 2.67486i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.891409 - 0.891409i) q^{34} +3.01614i q^{35} +(-4.46674 - 4.46674i) q^{37} +5.04346 q^{38} +3.01614 q^{40} +(-5.01614 - 5.01614i) q^{41} +12.4564i q^{43} +(-1.84550 - 1.84550i) q^{44} +(-1.84550 - 1.84550i) q^{46} +(3.00813 - 3.00813i) q^{47} +1.00000i q^{49} +(2.89707 - 2.89707i) q^{50} +(-2.14639 - 2.89707i) q^{52} +0.828427i q^{53} -7.87189 q^{55} +1.00000 q^{56} +(0.431282 - 0.431282i) q^{58} +(7.73927 - 7.73927i) q^{59} -11.3685 q^{61} +3.78282 q^{62} -1.00000i q^{64} +(-10.7563 - 1.60099i) q^{65} +(3.58260 - 3.58260i) q^{67} +1.26064i q^{68} +(2.13273 - 2.13273i) q^{70} +(1.76681 + 1.76681i) q^{71} +(-9.04689 - 9.04689i) q^{73} +6.31692i q^{74} +(-3.56626 - 3.56626i) q^{76} -2.60992 q^{77} -8.06641 q^{79} +(-2.13273 - 2.13273i) q^{80} +7.09389i q^{82} +(5.76681 + 5.76681i) q^{83} +(2.68861 + 2.68861i) q^{85} +(8.80802 - 8.80802i) q^{86} +2.60992i q^{88} +(-6.44167 + 6.44167i) q^{89} +(-3.56626 - 0.530808i) q^{91} +2.60992i q^{92} -4.25414 q^{94} -15.2118 q^{95} +(-1.40271 + 1.40271i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5}+O(q^{10}) \) 12 * q + 4 * q^5	\( 12 q + 4 q^{5} + 8 q^{11} - 16 q^{13} - 12 q^{16} + 8 q^{17} - 4 q^{20} + 8 q^{22} + 8 q^{23} - 8 q^{31} + 8 q^{34} + 16 q^{38} - 24 q^{41} + 8 q^{44} + 8 q^{46} + 4 q^{47} + 16 q^{50} - 16 q^{55} + 12 q^{56} - 8 q^{58} - 48 q^{59} + 32 q^{61} + 8 q^{62} + 8 q^{65} + 28 q^{67} + 4 q^{70} - 8 q^{71} + 16 q^{73} - 8 q^{77} - 32 q^{79} - 4 q^{80} + 40 q^{83} + 8 q^{85} + 40 q^{86} - 24 q^{89} - 8 q^{94} + 8 q^{95} + 8 q^{97}+O(q^{100}) \) 12 * q + 4 * q^5 + 8 * q^11 - 16 * q^13 - 12 * q^16 + 8 * q^17 - 4 * q^20 + 8 * q^22 + 8 * q^23 - 8 * q^31 + 8 * q^34 + 16 * q^38 - 24 * q^41 + 8 * q^44 + 8 * q^46 + 4 * q^47 + 16 * q^50 - 16 * q^55 + 12 * q^56 - 8 * q^58 - 48 * q^59 + 32 * q^61 + 8 * q^62 + 8 * q^65 + 28 * q^67 + 4 * q^70 - 8 * q^71 + 16 * q^73 - 8 * q^77 - 32 * q^79 - 4 * q^80 + 40 * q^83 + 8 * q^85 + 40 * q^86 - 24 * q^89 - 8 * q^94 + 8 * q^95 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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