LMFDB - Embedded newform 1638.2.m.h.1621.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(289,1638)]

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, 2, 2]))

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

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

chi := DirichletCharacter("1638.289");

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.m (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.4
Root			$1.19003 + 0.764088i$ of defining polynomial
Character	$\chi$	$=$	1638.1621
Dual form			1638.2.m.h.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(0.924396 + 1.60110i) q^{5} +(2.61442 - 0.405935i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.924396 + 1.60110i) q^{5} +(2.61442 - 0.405935i) q^{7} -1.00000 q^{8} +(-0.924396 - 1.60110i) q^{10} +(0.357690 + 0.619538i) q^{11} +(-2.81454 - 2.25352i) q^{13} +(-2.61442 + 0.405935i) q^{14} +1.00000 q^{16} -4.31156 q^{17} +(3.43786 - 5.95456i) q^{19} +(0.924396 + 1.60110i) q^{20} +(-0.357690 - 0.619538i) q^{22} +7.16035 q^{23} +(0.790985 - 1.37003i) q^{25} +(2.81454 + 2.25352i) q^{26} +(2.61442 - 0.405935i) q^{28} +(4.63798 - 8.03322i) q^{29} +(1.11104 - 1.92438i) q^{31} -1.00000 q^{32} +4.31156 q^{34} +(3.06671 + 3.81071i) q^{35} +2.13341 q^{37} +(-3.43786 + 5.95456i) q^{38} +(-0.924396 - 1.60110i) q^{40} +(-2.23138 + 3.86487i) q^{41} +(-0.0979721 - 0.169693i) q^{43} +(0.357690 + 0.619538i) q^{44} -7.16035 q^{46} +(-4.60553 - 7.97700i) q^{47} +(6.67043 - 2.12257i) q^{49} +(-0.790985 + 1.37003i) q^{50} +(-2.81454 - 2.25352i) q^{52} +(-3.80147 + 6.58434i) q^{53} +(-0.661295 + 1.14540i) q^{55} +(-2.61442 + 0.405935i) q^{56} +(-4.63798 + 8.03322i) q^{58} +2.48056 q^{59} +(-4.31156 + 7.46783i) q^{61} +(-1.11104 + 1.92438i) q^{62} +1.00000 q^{64} +(1.00637 - 6.58951i) q^{65} +(6.96322 + 12.0606i) q^{67} -4.31156 q^{68} +(-3.06671 - 3.81071i) q^{70} +(-7.50874 - 13.0055i) q^{71} +(-0.989914 + 1.71458i) q^{73} -2.13341 q^{74} +(3.43786 - 5.95456i) q^{76} +(1.18665 + 1.47454i) q^{77} +(7.37533 + 12.7744i) q^{79} +(0.924396 + 1.60110i) q^{80} +(2.23138 - 3.86487i) q^{82} +9.71538 q^{83} +(-3.98558 - 6.90323i) q^{85} +(0.0979721 + 0.169693i) q^{86} +(-0.357690 - 0.619538i) q^{88} +4.46953 q^{89} +(-8.27319 - 4.74914i) q^{91} +7.16035 q^{92} +(4.60553 + 7.97700i) q^{94} +12.7118 q^{95} +(1.39194 + 2.41091i) q^{97} +(-6.67043 + 2.12257i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} + 2 q^{10} - 4 q^{11} + 3 q^{13} - 3 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} + 2 q^{25} - 3 q^{26} + 3 q^{28} - 2 q^{29} + 14 q^{31} - 8 q^{32} + 4 q^{34} + 22 q^{35} + 12 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} - 8 q^{46} - 7 q^{47} + 5 q^{49} - 2 q^{50} + 3 q^{52} + q^{53} - 25 q^{55} - 3 q^{56} + 2 q^{58} + 32 q^{59} - 4 q^{61} - 14 q^{62} + 8 q^{64} - 10 q^{65} + 19 q^{67} - 4 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} - 12 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} - 2 q^{80} + 12 q^{82} + 64 q^{83} + 15 q^{85} + 4 q^{88} - 22 q^{89} - 38 q^{91} + 8 q^{92} + 7 q^{94} + 56 q^{95} + 11 q^{97} - 5 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 + 2 * q^10 - 4 * q^11 + 3 * q^13 - 3 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 + 2 * q^25 - 3 * q^26 + 3 * q^28 - 2 * q^29 + 14 * q^31 - 8 * q^32 + 4 * q^34 + 22 * q^35 + 12 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 - 8 * q^46 - 7 * q^47 + 5 * q^49 - 2 * q^50 + 3 * q^52 + q^53 - 25 * q^55 - 3 * q^56 + 2 * q^58 + 32 * q^59 - 4 * q^61 - 14 * q^62 + 8 * q^64 - 10 * q^65 + 19 * q^67 - 4 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 - 12 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 - 2 * q^80 + 12 * q^82 + 64 * q^83 + 15 * q^85 + 4 * q^88 - 22 * q^89 - 38 * q^91 + 8 * q^92 + 7 * q^94 + 56 * q^95 + 11 * q^97 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	0.924396	+	1.60110i	0.413402	+	0.716034i	0.995259	−	0.0972573i	$-0.0310070\pi$
$5$	0.924396	+	1.60110i	0.413402	+	0.716034i	−0.581857	+	0.813291i	$0.697674\pi$
$6$		0			0
$7$	2.61442	−	0.405935i	0.988160	−	0.153429i
$7$	2.61442	−	0.405935i	0.988160	−	0.153429i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.924396	−	1.60110i	−0.292320	−	0.506312i
$11$	0.357690	+	0.619538i	0.107848	+	0.186798i	0.914898	−	0.403685i	$-0.132271\pi$
$11$	0.357690	+	0.619538i	0.107848	+	0.186798i	−0.807050	+	0.590483i	$0.798937\pi$
$12$		0			0
$13$	−2.81454	−	2.25352i	−0.780613	−	0.625015i
$13$	−2.81454	−	2.25352i	−0.780613	−	0.625015i
$14$	−2.61442	+	0.405935i	−0.698734	+	0.108491i
$15$		0			0
$16$	1.00000			0.250000
$17$	−4.31156			−1.04571			−0.522853	−	0.852423i	$-0.675132\pi$
$17$	−4.31156			−1.04571			−0.522853	+	0.852423i	$0.675132\pi$
$18$		0			0
$19$	3.43786	−	5.95456i	0.788700	−	1.36607i	−0.138063	−	0.990423i	$-0.544088\pi$
$19$	3.43786	−	5.95456i	0.788700	−	1.36607i	0.926763	−	0.375645i	$-0.122579\pi$
$20$	0.924396	+	1.60110i	0.206701	+	0.358017i
$21$		0			0
$22$	−0.357690	−	0.619538i	−0.0762599	−	0.132086i
$23$	7.16035			1.49304			0.746518	−	0.665365i	$-0.231724\pi$
$23$	7.16035			1.49304			0.746518	+	0.665365i	$0.231724\pi$
$24$		0			0
$25$	0.790985	−	1.37003i	0.158197	−	0.274005i
$26$	2.81454	+	2.25352i	0.551977	+	0.441952i
$27$		0			0
$28$	2.61442	−	0.405935i	0.494080	−	0.0767145i
$29$	4.63798	−	8.03322i	0.861251	−	1.49173i	−0.00947068	−	0.999955i	$-0.503015\pi$
$29$	4.63798	−	8.03322i	0.861251	−	1.49173i	0.870722	−	0.491776i	$-0.163652\pi$
$30$		0			0
$31$	1.11104	−	1.92438i	0.199549	−	0.345629i	−0.748833	−	0.662759i	$-0.769386\pi$
$31$	1.11104	−	1.92438i	0.199549	−	0.345629i	0.948382	+	0.317129i	$0.102719\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	4.31156			0.739426
$35$	3.06671	+	3.81071i	0.518368	+	0.644128i
$36$		0			0
$37$	2.13341			0.350731			0.175365	−	0.984503i	$-0.443889\pi$
$37$	2.13341			0.350731			0.175365	+	0.984503i	$0.443889\pi$
$38$	−3.43786	+	5.95456i	−0.557695	+	0.965956i
$39$		0			0
$40$	−0.924396	−	1.60110i	−0.146160	−	0.253156i
$41$	−2.23138	+	3.86487i	−0.348483	+	0.603591i	−0.985980	−	0.166862i	$-0.946637\pi$
$41$	−2.23138	+	3.86487i	−0.348483	+	0.603591i	0.637497	+	0.770453i	$0.279970\pi$
$42$		0			0
$43$	−0.0979721	−	0.169693i	−0.0149406	−	0.0258779i	0.858458	−	0.512883i	$-0.171423\pi$
$43$	−0.0979721	−	0.169693i	−0.0149406	−	0.0258779i	−0.873399	+	0.487005i	$0.838089\pi$
$44$	0.357690	+	0.619538i	0.0539239	+	0.0933989i
$45$		0			0
$46$	−7.16035			−1.05574
$47$	−4.60553	−	7.97700i	−0.671785	−	1.16357i	−0.977398	−	0.211410i	$-0.932195\pi$
$47$	−4.60553	−	7.97700i	−0.671785	−	1.16357i	0.305613	−	0.952156i	$-0.401139\pi$
$48$		0			0
$49$	6.67043	−	2.12257i	0.952919	−	0.303225i
$50$	−0.790985	+	1.37003i	−0.111862	+	0.193751i
$51$		0			0
$52$	−2.81454	−	2.25352i	−0.390307	−	0.312507i
$53$	−3.80147	+	6.58434i	−0.522172	+	0.904429i	0.477495	+	0.878634i	$0.341545\pi$
$53$	−3.80147	+	6.58434i	−0.522172	+	0.904429i	−0.999667	+	0.0257942i	$0.991789\pi$
$54$		0			0
$55$	−0.661295	+	1.14540i	−0.0891690	+	0.154445i
$56$	−2.61442	+	0.405935i	−0.349367	+	0.0542453i
$57$		0			0
$58$	−4.63798	+	8.03322i	−0.608997	+	1.05481i
$59$	2.48056			0.322942			0.161471	−	0.986877i	$-0.448376\pi$
$59$	2.48056			0.322942			0.161471	+	0.986877i	$0.448376\pi$
$60$		0			0
$61$	−4.31156	+	7.46783i	−0.552038	+	0.956158i	0.446089	+	0.894989i	$0.352816\pi$
$61$	−4.31156	+	7.46783i	−0.552038	+	0.956158i	−0.998127	+	0.0611697i	$0.980517\pi$
$62$	−1.11104	+	1.92438i	−0.141103	+	0.244397i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00637	−	6.58951i	0.124824	−	0.817328i
$66$		0			0
$67$	6.96322	+	12.0606i	0.850692	+	1.47344i	0.880585	+	0.473889i	$0.157150\pi$
$67$	6.96322	+	12.0606i	0.850692	+	1.47344i	−0.0298923	+	0.999553i	$0.509516\pi$
$68$	−4.31156			−0.522853
$69$		0			0
$70$	−3.06671	−	3.81071i	−0.366541	−	0.455467i
$71$	−7.50874	−	13.0055i	−0.891124	−	1.54347i	−0.838530	−	0.544855i	$-0.816585\pi$
$71$	−7.50874	−	13.0055i	−0.891124	−	1.54347i	−0.0525935	−	0.998616i	$-0.516749\pi$
$72$		0			0
$73$	−0.989914	+	1.71458i	−0.115861	+	0.200676i	−0.918123	−	0.396294i	$-0.870296\pi$
$73$	−0.989914	+	1.71458i	−0.115861	+	0.200676i	0.802263	+	0.596971i	$0.203629\pi$
$74$	−2.13341			−0.248004
$75$		0			0
$76$	3.43786	−	5.95456i	0.394350	−	0.683034i
$77$	1.18665	+	1.47454i	0.135231	+	0.168039i
$78$		0			0
$79$	7.37533	+	12.7744i	0.829790	+	1.43724i	0.898203	+	0.439581i	$0.144873\pi$
$79$	7.37533	+	12.7744i	0.829790	+	1.43724i	−0.0684137	+	0.997657i	$0.521794\pi$
$80$	0.924396	+	1.60110i	0.103351	+	0.179008i
$81$		0			0
$82$	2.23138	−	3.86487i	0.246415	−	0.426803i
$83$	9.71538			1.06640			0.533201	−	0.845989i	$-0.320989\pi$
$83$	9.71538			1.06640			0.533201	+	0.845989i	$0.320989\pi$
$84$		0			0
$85$	−3.98558	−	6.90323i	−0.432297	−	0.748761i
$86$	0.0979721	+	0.169693i	0.0105646	+	0.0182984i
$87$		0			0
$88$	−0.357690	−	0.619538i	−0.0381299	−	0.0660430i
$89$	4.46953			0.473769			0.236885	−	0.971538i	$-0.423874\pi$
$89$	4.46953			0.473769			0.236885	+	0.971538i	$0.423874\pi$
$90$		0			0
$91$	−8.27319	−	4.74914i	−0.867266	−	0.497846i
$92$	7.16035			0.746518
$93$		0			0
$94$	4.60553	+	7.97700i	0.475024	+	0.822765i
$95$	12.7118			1.30420
$96$		0			0
$97$	1.39194	+	2.41091i	0.141330	+	0.244791i	0.927998	−	0.372586i	$-0.121529\pi$
$97$	1.39194	+	2.41091i	0.141330	+	0.244791i	−0.786668	+	0.617377i	$0.788195\pi$
$98$	−6.67043	+	2.12257i	−0.673816	+	0.214412i
$99$		0			0
$100$	0.790985	−	1.37003i	0.0790985	−	0.137003i
$101$	2.67775	+	4.63800i	0.266446	+	0.461498i	0.967941	−	0.251176i	$-0.0808173\pi$
$101$	2.67775	+	4.63800i	0.266446	+	0.461498i	−0.701496	+	0.712674i	$0.747484\pi$
$102$		0			0
$103$	3.26429	+	5.65391i	0.321640	+	0.557097i	0.980827	−	0.194883i	$-0.0624326\pi$
$103$	3.26429	+	5.65391i	0.321640	+	0.557097i	−0.659187	+	0.751979i	$0.729099\pi$
$104$	2.81454	+	2.25352i	0.275988	+	0.220976i
$105$		0			0
$106$	3.80147	−	6.58434i	0.369231	−	0.639528i
$107$	4.61994			0.446627			0.223313	−	0.974747i	$-0.428313\pi$
$107$	4.61994			0.446627			0.223313	+	0.974747i	$0.428313\pi$
$108$		0			0
$109$	4.95093	−	8.57527i	0.474214	−	0.821362i	−0.525351	−	0.850886i	$-0.676066\pi$
$109$	4.95093	−	8.57527i	0.474214	−	0.821362i	0.999564	+	0.0295240i	$0.00939913\pi$
$110$	0.661295	−	1.14540i	0.0630520	−	0.109209i
$111$		0			0
$112$	2.61442	−	0.405935i	0.247040	−	0.0383572i
$113$	−1.50417	−	2.60530i	−0.141501	−	0.245086i	0.786561	−	0.617512i	$-0.211859\pi$
$113$	−1.50417	−	2.60530i	−0.141501	−	0.245086i	−0.928062	+	0.372426i	$0.878526\pi$
$114$		0			0
$115$	6.61899	+	11.4644i	0.617224	+	1.06906i
$116$	4.63798	−	8.03322i	0.430626	−	0.745865i
$117$		0			0
$118$	−2.48056			−0.228354
$119$	−11.2722	+	1.75021i	−1.03332	+	0.160442i
$120$		0			0
$121$	5.24412	−	9.08307i	0.476738	−	0.825734i
$122$	4.31156	−	7.46783i	0.390350	−	0.676106i
$123$		0			0
$124$	1.11104	−	1.92438i	0.0997746	−	0.172815i
$125$	12.1687			1.08840
$126$		0			0
$127$	−7.58356	+	13.1351i	−0.672932	+	1.16555i	0.304137	+	0.952628i	$0.401632\pi$
$127$	−7.58356	+	13.1351i	−0.672932	+	1.16555i	−0.977069	+	0.212924i	$0.931701\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−1.00637	+	6.58951i	−0.0882642	+	0.577938i
$131$	−9.69444	−	16.7913i	−0.847007	−	1.46706i	−0.883867	−	0.467739i	$-0.845069\pi$
$131$	−9.69444	−	16.7913i	−0.847007	−	1.46706i	0.0368595	−	0.999320i	$-0.488265\pi$
$132$		0			0
$133$	6.57088	−	16.9633i	0.569767	−	1.47090i
$134$	−6.96322	−	12.0606i	−0.601530	−	1.04188i
$135$		0			0
$136$	4.31156			0.369713
$137$	4.74829			0.405673			0.202837	−	0.979213i	$-0.434984\pi$
$137$	4.74829			0.405673			0.202837	+	0.979213i	$0.434984\pi$
$138$		0			0
$139$	−7.69027	−	13.3199i	−0.652280	−	1.12978i	−0.982568	−	0.185902i	$-0.940479\pi$
$139$	−7.69027	−	13.3199i	−0.652280	−	1.12978i	0.330288	−	0.943880i	$-0.392854\pi$
$140$	3.06671	+	3.81071i	0.259184	+	0.322064i
$141$		0			0
$142$	7.50874	+	13.0055i	0.630120	+	1.09140i
$143$	0.389409	−	2.54978i	0.0325640	−	0.213223i
$144$		0			0
$145$	17.1493			1.42417
$146$	0.989914	−	1.71458i	0.0819258	−	0.141900i
$147$		0			0
$148$	2.13341			0.175365
$149$	−5.82384	+	10.0872i	−0.477107	+	0.826374i	−0.999656	−	0.0262354i	$-0.991648\pi$
$149$	−5.82384	+	10.0872i	−0.477107	+	0.826374i	0.522548	+	0.852610i	$0.324981\pi$
$150$		0			0
$151$	−4.09544	+	7.09351i	−0.333282	+	0.577262i	−0.983153	−	0.182783i	$-0.941489\pi$
$151$	−4.09544	+	7.09351i	−0.333282	+	0.577262i	0.649871	+	0.760044i	$0.274823\pi$
$152$	−3.43786	+	5.95456i	−0.278848	+	0.482978i
$153$		0			0
$154$	−1.18665	−	1.47454i	−0.0956227	−	0.118822i
$155$	4.10817			0.329976
$156$		0			0
$157$	11.4353	−	19.8066i	0.912639	−	1.58074i	0.102317	−	0.994752i	$-0.467374\pi$
$157$	11.4353	−	19.8066i	0.912639	−	1.58074i	0.810322	−	0.585985i	$-0.199292\pi$
$158$	−7.37533	−	12.7744i	−0.586750	−	1.01628i
$159$		0			0
$160$	−0.924396	−	1.60110i	−0.0730799	−	0.126578i
$161$	18.7202	−	2.90663i	1.47536	−	0.229075i
$162$		0			0
$163$	−9.01923	+	15.6218i	−0.706440	+	1.22359i	0.259729	+	0.965682i	$0.416367\pi$
$163$	−9.01923	+	15.6218i	−0.706440	+	1.22359i	−0.966169	+	0.257909i	$0.916967\pi$
$164$	−2.23138	+	3.86487i	−0.174242	+	0.301795i
$165$		0			0
$166$	−9.71538			−0.754060
$167$	−3.86936	+	6.70193i	−0.299420	+	0.518611i	−0.976003	−	0.217755i	$-0.930127\pi$
$167$	−3.86936	+	6.70193i	−0.299420	+	0.518611i	0.676583	+	0.736366i	$0.263460\pi$
$168$		0			0
$169$	2.84327	+	12.6853i	0.218713	+	0.975789i
$170$	3.98558	+	6.90323i	0.305680	+	0.529454i
$171$		0			0
$172$	−0.0979721	−	0.169693i	−0.00747030	−	0.0129389i
$173$	6.01212	−	10.4133i	0.457093	−	0.791709i	−0.541713	−	0.840564i	$-0.682224\pi$
$173$	6.01212	−	10.4133i	0.457093	−	0.791709i	0.998806	+	0.0488550i	$0.0155572\pi$
$174$		0			0
$175$	1.51183	−	3.90292i	0.114284	−	0.295033i
$176$	0.357690	+	0.619538i	0.0269619	+	0.0466994i
$177$		0			0
$178$	−4.46953			−0.335005
$179$	5.65742	+	9.79893i	0.422855	+	0.732407i	0.996217	−	0.0868953i	$-0.0276946\pi$
$179$	5.65742	+	9.79893i	0.422855	+	0.732407i	−0.573362	+	0.819302i	$0.694361\pi$
$180$		0			0
$181$	−2.49725			−0.185619			−0.0928095	−	0.995684i	$-0.529585\pi$
$181$	−2.49725			−0.185619			−0.0928095	+	0.995684i	$0.529585\pi$
$182$	8.27319	+	4.74914i	0.613249	+	0.352030i
$183$		0			0
$184$	−7.16035			−0.527868
$185$	1.97212	+	3.41580i	0.144993	+	0.251135i
$186$		0			0
$187$	−1.54220	−	2.67117i	−0.112777	−	0.195336i
$188$	−4.60553	−	7.97700i	−0.335892	−	0.581783i
$189$		0			0
$190$	−12.7118			−0.922210
$191$	−2.66349	+	4.61330i	−0.192723	+	0.333807i	−0.946152	−	0.323723i	$-0.895065\pi$
$191$	−2.66349	+	4.61330i	−0.192723	+	0.333807i	0.753428	+	0.657530i	$0.228399\pi$
$192$		0			0
$193$	−4.86186	−	8.42099i	−0.349964	−	0.606156i	0.636278	−	0.771460i	$-0.280473\pi$
$193$	−4.86186	−	8.42099i	−0.349964	−	0.606156i	−0.986243	+	0.165303i	$0.947140\pi$
$194$	−1.39194	−	2.41091i	−0.0999356	−	0.173093i
$195$		0			0
$196$	6.67043	−	2.12257i	0.476460	−	0.151612i
$197$	3.08593	−	5.34499i	0.219863	−	0.380815i	−0.734903	−	0.678173i	$-0.762772\pi$
$197$	3.08593	−	5.34499i	0.219863	−	0.380815i	0.954766	+	0.297358i	$0.0961055\pi$
$198$		0			0
$199$	5.41454			0.383827			0.191913	−	0.981412i	$-0.438531\pi$
$199$	5.41454			0.383827			0.191913	+	0.981412i	$0.438531\pi$
$200$	−0.790985	+	1.37003i	−0.0559311	+	0.0968755i
$201$		0			0
$202$	−2.67775	−	4.63800i	−0.188406	−	0.326328i
$203$	8.86469	−	22.8850i	0.622179	−	1.60621i
$204$		0			0
$205$	−8.25072			−0.576255
$206$	−3.26429	−	5.65391i	−0.227434	−	0.393927i
$207$		0			0
$208$	−2.81454	−	2.25352i	−0.195153	−	0.156254i
$209$	4.91877			0.340238
$210$		0			0
$211$	13.6366	−	23.6193i	0.938785	−	1.62602i	0.171043	−	0.985264i	$-0.445286\pi$
$211$	13.6366	−	23.6193i	0.938785	−	1.62602i	0.767742	−	0.640759i	$-0.221380\pi$
$212$	−3.80147	+	6.58434i	−0.261086	+	0.452214i
$213$		0			0
$214$	−4.61994			−0.315813
$215$	0.181130	−	0.313726i	0.0123530	−	0.0213960i
$216$		0			0
$217$	2.12356	−	5.48216i	0.144157	−	0.372153i
$218$	−4.95093	+	8.57527i	−0.335320	+	0.580791i
$219$		0			0
$220$	−0.661295	+	1.14540i	−0.0445845	+	0.0772226i
$221$	12.1350	+	9.71619i	0.816292	+	0.653582i
$222$		0			0
$223$	−2.88502	+	4.99700i	−0.193195	+	0.334624i	−0.946307	−	0.323268i	$-0.895218\pi$
$223$	−2.88502	+	4.99700i	−0.193195	+	0.334624i	0.753112	+	0.657892i	$0.228552\pi$
$224$	−2.61442	+	0.405935i	−0.174684	+	0.0271227i
$225$		0			0
$226$	1.50417	+	2.60530i	0.100056	+	0.173302i
$227$	−16.9846			−1.12731			−0.563653	−	0.826012i	$-0.690604\pi$
$227$	−16.9846			−1.12731			−0.563653	+	0.826012i	$0.690604\pi$
$228$		0			0
$229$	0.460390	+	0.797420i	0.0304235	+	0.0526950i	0.880836	−	0.473421i	$-0.156981\pi$
$229$	0.460390	+	0.797420i	0.0304235	+	0.0526950i	−0.850413	+	0.526116i	$0.823648\pi$
$230$	−6.61899	−	11.4644i	−0.436444	−	0.755942i
$231$		0			0
$232$	−4.63798	+	8.03322i	−0.304498	+	0.527407i
$233$	2.50283	+	4.33502i	0.163966	+	0.283997i	0.936287	−	0.351235i	$-0.114238\pi$
$233$	2.50283	+	4.33502i	0.163966	+	0.283997i	−0.772322	+	0.635231i	$0.780905\pi$
$234$		0			0
$235$	8.51466	−	14.7478i	0.555435	−	0.962041i
$236$	2.48056			0.161471
$237$		0			0
$238$	11.2722	−	1.75021i	0.730671	−	0.113449i
$239$	−13.8239			−0.894195			−0.447097	−	0.894485i	$-0.647542\pi$
$239$	−13.8239			−0.894195			−0.447097	+	0.894485i	$0.647542\pi$
$240$		0			0
$241$	10.7589			0.693041			0.346521	−	0.938042i	$-0.387363\pi$
$241$	10.7589			0.693041			0.346521	+	0.938042i	$0.387363\pi$
$242$	−5.24412	+	9.08307i	−0.337104	+	0.583882i
$243$		0			0
$244$	−4.31156	+	7.46783i	−0.276019	+	0.478079i
$245$	9.56457	+	8.71794i	0.611058	+	0.556969i
$246$		0			0
$247$	−23.0947	+	9.01203i	−1.46948	+	0.573422i
$248$	−1.11104	+	1.92438i	−0.0705513	+	0.122198i
$249$		0			0
$250$	−12.1687			−0.769616
$251$	11.8267	+	20.4844i	0.746492	+	1.29296i	0.949494	+	0.313784i	$0.101597\pi$
$251$	11.8267	+	20.4844i	0.746492	+	1.29296i	−0.203002	+	0.979178i	$0.565070\pi$
$252$		0			0
$253$	2.56119	+	4.43611i	0.161021	+	0.278896i
$254$	7.58356	−	13.1351i	0.475835	−	0.824170i
$255$		0			0
$256$	1.00000			0.0625000
$257$	19.1940			1.19729			0.598646	−	0.801014i	$-0.295706\pi$
$257$	19.1940			1.19729			0.598646	+	0.801014i	$0.295706\pi$
$258$		0			0
$259$	5.57764	−	0.866025i	0.346578	−	0.0538122i
$260$	1.00637	−	6.58951i	0.0624122	−	0.408664i
$261$		0			0
$262$	9.69444	+	16.7913i	0.598925	+	1.03737i
$263$	5.49567	+	9.51878i	0.338878	+	0.586953i	0.984222	−	0.176939i	$-0.0566194\pi$
$263$	5.49567	+	9.51878i	0.338878	+	0.586953i	−0.645344	+	0.763892i	$0.723286\pi$
$264$		0			0
$265$	−14.0562			−0.863469
$266$	−6.57088	+	16.9633i	−0.402886	+	1.04009i
$267$		0			0
$268$	6.96322	+	12.0606i	0.425346	+	0.736721i
$269$	−16.5175			−1.00709			−0.503546	−	0.863968i	$-0.667972\pi$
$269$	−16.5175			−1.00709			−0.503546	+	0.863968i	$0.667972\pi$
$270$		0			0
$271$	−18.1906			−1.10500			−0.552499	−	0.833514i	$-0.686326\pi$
$271$	−18.1906			−1.10500			−0.552499	+	0.833514i	$0.686326\pi$
$272$	−4.31156			−0.261426
$273$		0			0
$274$	−4.74829			−0.286854
$275$	1.13171			0.0682448
$276$		0			0
$277$	16.4894			0.990751			0.495376	−	0.868679i	$-0.335030\pi$
$277$	16.4894			0.990751			0.495376	+	0.868679i	$0.335030\pi$
$278$	7.69027	+	13.3199i	0.461232	+	0.798877i
$279$		0			0
$280$	−3.06671	−	3.81071i	−0.183271	−	0.227734i
$281$	−15.2768			−0.911335			−0.455667	−	0.890150i	$-0.650599\pi$
$281$	−15.2768			−0.911335			−0.455667	+	0.890150i	$0.650599\pi$
$282$		0			0
$283$	4.57838	+	7.92998i	0.272156	+	0.471388i	0.969414	−	0.245432i	$-0.0789299\pi$
$283$	4.57838	+	7.92998i	0.272156	+	0.471388i	−0.697257	+	0.716821i	$0.745597\pi$
$284$	−7.50874	−	13.0055i	−0.445562	−	0.771736i
$285$		0			0
$286$	−0.389409	+	2.54978i	−0.0230262	+	0.150772i
$287$	−4.26490	+	11.0102i	−0.251749	+	0.649912i
$288$		0			0
$289$	1.58952			0.0935010
$290$	−17.1493			−1.00704
$291$		0			0
$292$	−0.989914	+	1.71458i	−0.0579303	+	0.100338i
$293$	−5.93488	−	10.2795i	−0.346719	−	0.600536i	0.638945	−	0.769252i	$-0.279371\pi$
$293$	−5.93488	−	10.2795i	−0.346719	−	0.600536i	−0.985665	+	0.168717i	$0.946038\pi$
$294$		0			0
$295$	2.29302	+	3.97163i	0.133505	+	0.231237i
$296$	−2.13341			−0.124002
$297$		0			0
$298$	5.82384	−	10.0872i	0.337366	−	0.584335i
$299$	−20.1531	−	16.1360i	−1.16548	−	0.933169i
$300$		0			0
$301$	−0.325025	−	0.403878i	−0.0187341	−	0.0232792i
$302$	4.09544	−	7.09351i	0.235666	−	0.408186i
$303$		0			0
$304$	3.43786	−	5.95456i	0.197175	−	0.341517i
$305$	−15.9423			−0.912855
$306$		0			0
$307$	−28.0679			−1.60192			−0.800959	−	0.598719i	$-0.795677\pi$
$307$	−28.0679			−1.60192			−0.800959	+	0.598719i	$0.795677\pi$
$308$	1.18665	+	1.47454i	0.0676155	+	0.0840195i
$309$		0			0
$310$	−4.10817			−0.233328
$311$	12.7326	−	22.0536i	0.722001	−	1.25054i	−0.238195	−	0.971217i	$-0.576556\pi$
$311$	12.7326	−	22.0536i	0.722001	−	1.25054i	0.960196	−	0.279325i	$-0.0901108\pi$
$312$		0			0
$313$	−8.82204	−	15.2802i	−0.498651	−	0.863689i	0.501348	−	0.865246i	$-0.332838\pi$
$313$	−8.82204	−	15.2802i	−0.498651	−	0.863689i	−0.999999	+	0.00155673i	$0.999504\pi$
$314$	−11.4353	+	19.8066i	−0.645333	+	1.11775i
$315$		0			0
$316$	7.37533	+	12.7744i	0.414895	+	0.718619i
$317$	14.8710	+	25.7573i	0.835239	+	1.44668i	0.893836	+	0.448394i	$0.148004\pi$
$317$	14.8710	+	25.7573i	0.835239	+	1.44668i	−0.0585974	+	0.998282i	$0.518663\pi$
$318$		0			0
$319$	6.63585			0.371536
$320$	0.924396	+	1.60110i	0.0516753	+	0.0895042i
$321$		0			0
$322$	−18.7202	+	2.90663i	−1.04324	+	0.161980i
$323$	−14.8225	+	25.6734i	−0.824748	+	1.42851i
$324$		0			0
$325$	−5.31365	+	2.07349i	−0.294748	+	0.115017i
$326$	9.01923	−	15.6218i	0.499529	−	0.865209i
$327$		0			0
$328$	2.23138	−	3.86487i	0.123207	−	0.213402i
$329$	−15.2789	−	18.9857i	−0.842355	−	1.04672i
$330$		0			0
$331$	−12.0197	+	20.8187i	−0.660661	+	1.14430i	0.319781	+	0.947491i	$0.396391\pi$
$331$	−12.0197	+	20.8187i	−0.660661	+	1.14430i	−0.980442	+	0.196807i	$0.936943\pi$
$332$	9.71538			0.533201
$333$		0			0
$334$	3.86936	−	6.70193i	0.211722	−	0.366713i
$335$	−12.8735	+	22.2976i	−0.703356	+	1.21825i
$336$		0			0
$337$	−2.21939			−0.120898			−0.0604490	−	0.998171i	$-0.519253\pi$
$337$	−2.21939			−0.120898			−0.0604490	+	0.998171i	$0.519253\pi$
$338$	−2.84327	−	12.6853i	−0.154654	−	0.689987i
$339$		0			0
$340$	−3.98558	−	6.90323i	−0.216149	−	0.374380i
$341$	1.58964			0.0860837
$342$		0			0
$343$	16.5777	−	8.25707i	0.895113	−	0.445840i
$344$	0.0979721	+	0.169693i	0.00528230	+	0.00914921i
$345$		0			0
$346$	−6.01212	+	10.4133i	−0.323214	+	0.559823i
$347$	2.01895			0.108383			0.0541916	−	0.998531i	$-0.482742\pi$
$347$	2.01895			0.108383			0.0541916	+	0.998531i	$0.482742\pi$
$348$		0			0
$349$	−16.8191	+	29.1316i	−0.900306	+	1.55938i	−0.0732096	+	0.997317i	$0.523324\pi$
$349$	−16.8191	+	29.1316i	−0.900306	+	1.55938i	−0.827097	+	0.562060i	$0.810009\pi$
$350$	−1.51183	+	3.90292i	−0.0808107	+	0.208620i
$351$		0			0
$352$	−0.357690	−	0.619538i	−0.0190650	−	0.0330215i
$353$	11.6388	+	20.1590i	0.619472	+	1.07296i	0.989582	+	0.143970i	$0.0459867\pi$
$353$	11.6388	+	20.1590i	0.619472	+	1.07296i	−0.370110	+	0.928988i	$0.620680\pi$
$354$		0			0
$355$	13.8821	−	24.0445i	0.736785	−	1.27615i
$356$	4.46953			0.236885
$357$		0			0
$358$	−5.65742	−	9.79893i	−0.299004	−	0.517890i
$359$	−5.44896	−	9.43787i	−0.287585	−	0.498112i	0.685648	−	0.727933i	$-0.259519\pi$
$359$	−5.44896	−	9.43787i	−0.287585	−	0.498112i	−0.973233	+	0.229822i	$0.926186\pi$
$360$		0			0
$361$	−14.1378	−	24.4874i	−0.744096	−	1.28881i
$362$	2.49725			0.131252
$363$		0			0
$364$	−8.27319	−	4.74914i	−0.433633	−	0.248923i
$365$	−3.66029			−0.191588
$366$		0			0
$367$	−2.44394	−	4.23302i	−0.127573	−	0.220962i	0.795163	−	0.606396i	$-0.207385\pi$
$367$	−2.44394	−	4.23302i	−0.127573	−	0.220962i	−0.922736	+	0.385434i	$0.874052\pi$
$368$	7.16035			0.373259
$369$		0			0
$370$	−1.97212	−	3.41580i	−0.102525	−	0.177579i
$371$	−7.26584	+	18.7574i	−0.377224	+	0.973836i
$372$		0			0
$373$	7.68366	−	13.3085i	0.397845	−	0.689088i	−0.595615	−	0.803270i	$-0.703092\pi$
$373$	7.68366	−	13.3085i	0.397845	−	0.689088i	0.993460	+	0.114182i	$0.0364249\pi$
$374$	1.54220	+	2.67117i	0.0797454	+	0.138123i
$375$		0			0
$376$	4.60553	+	7.97700i	0.237512	+	0.411383i
$377$	−31.1568	+	12.1580i	−1.60466	+	0.626170i
$378$		0			0
$379$	8.66626	−	15.0104i	0.445156	−	0.771033i	−0.552907	−	0.833243i	$-0.686482\pi$
$379$	8.66626	−	15.0104i	0.445156	−	0.771033i	0.998063	+	0.0622101i	$0.0198149\pi$
$380$	12.7118			0.652101
$381$		0			0
$382$	2.66349	−	4.61330i	0.136276	−	0.236037i
$383$	−5.99628	+	10.3859i	−0.306396	+	0.530693i	−0.977571	−	0.210606i	$-0.932456\pi$
$383$	−5.99628	+	10.3859i	−0.306396	+	0.530693i	0.671175	+	0.741298i	$0.265790\pi$
$384$		0			0
$385$	−1.26395	+	3.26300i	−0.0644169	+	0.166298i
$386$	4.86186	+	8.42099i	0.247462	+	0.428617i
$387$		0			0
$388$	1.39194	+	2.41091i	0.0706651	+	0.122396i
$389$	8.89274	−	15.4027i	0.450880	−	0.780947i	−0.547561	−	0.836766i	$-0.684444\pi$
$389$	8.89274	−	15.4027i	0.450880	−	0.780947i	0.998441	+	0.0558191i	$0.0177770\pi$
$390$		0			0
$391$	−30.8722			−1.56128
$392$	−6.67043	+	2.12257i	−0.336908	+	0.107206i
$393$		0			0
$394$	−3.08593	+	5.34499i	−0.155467	+	0.269277i
$395$	−13.6354	+	23.6173i	−0.686074	+	1.18831i
$396$		0			0
$397$	−7.02952	+	12.1755i	−0.352802	+	0.611070i	−0.986739	−	0.162314i	$-0.948104\pi$
$397$	−7.02952	+	12.1755i	−0.352802	+	0.611070i	0.633938	+	0.773384i	$0.281438\pi$
$398$	−5.41454			−0.271406
$399$		0			0
$400$	0.790985	−	1.37003i	0.0395493	−	0.0685013i
$401$	−4.13072			−0.206278			−0.103139	−	0.994667i	$-0.532889\pi$
$401$	−4.13072			−0.206278			−0.103139	+	0.994667i	$0.532889\pi$
$402$		0			0
$403$	−7.46371	+	2.91249i	−0.371794	+	0.145082i
$404$	2.67775	+	4.63800i	0.133223	+	0.230749i
$405$		0			0
$406$	−8.86469	+	22.8850i	−0.439947	+	1.13576i
$407$	0.763101	+	1.32173i	0.0378255	+	0.0655157i
$408$		0			0
$409$	−5.21490			−0.257860			−0.128930	−	0.991654i	$-0.541154\pi$
$409$	−5.21490			−0.257860			−0.128930	+	0.991654i	$0.541154\pi$
$410$	8.25072			0.407474
$411$		0			0
$412$	3.26429	+	5.65391i	0.160820	+	0.278548i
$413$	6.48525	−	1.00695i	0.319118	−	0.0495486i
$414$		0			0
$415$	8.98086	+	15.5553i	0.440853	+	0.763580i
$416$	2.81454	+	2.25352i	0.137994	+	0.110488i
$417$		0			0
$418$	−4.91877			−0.240585
$419$	−3.69624	+	6.40207i	−0.180573	+	0.312762i	−0.942076	−	0.335400i	$-0.891129\pi$
$419$	−3.69624	+	6.40207i	−0.180573	+	0.312762i	0.761503	+	0.648162i	$0.224462\pi$
$420$		0			0
$421$	4.67144			0.227672			0.113836	−	0.993500i	$-0.463686\pi$
$421$	4.67144			0.227672			0.113836	+	0.993500i	$0.463686\pi$
$422$	−13.6366	+	23.6193i	−0.663821	+	1.14977i
$423$		0			0
$424$	3.80147	−	6.58434i	0.184616	−	0.319764i
$425$	−3.41038	+	5.90695i	−0.165428	+	0.286529i
$426$		0			0
$427$	−8.24079	+	21.2743i	−0.398800	+	1.02954i
$428$	4.61994			0.223313
$429$		0			0
$430$	−0.181130	+	0.313726i	−0.00873486	+	0.0151292i
$431$	−11.0089	−	19.0680i	−0.530280	−	0.918472i	−0.999376	−	0.0353247i	$-0.988753\pi$
$431$	−11.0089	−	19.0680i	−0.530280	−	0.918472i	0.469096	−	0.883147i	$-0.344580\pi$
$432$		0			0
$433$	−12.5366	−	21.7141i	−0.602472	−	1.04351i	−0.992446	−	0.122686i	$-0.960849\pi$
$433$	−12.5366	−	21.7141i	−0.602472	−	1.04351i	0.389973	−	0.920826i	$-0.372484\pi$
$434$	−2.12356	+	5.48216i	−0.101934	+	0.263152i
$435$		0			0
$436$	4.95093	−	8.57527i	0.237107	−	0.410681i
$437$	24.6163	−	42.6367i	1.17756	−	2.03959i
$438$		0			0
$439$	−13.9493			−0.665764			−0.332882	−	0.942969i	$-0.608021\pi$
$439$	−13.9493			−0.665764			−0.332882	+	0.942969i	$0.608021\pi$
$440$	0.661295	−	1.14540i	0.0315260	−	0.0546046i
$441$		0			0
$442$	−12.1350	−	9.71619i	−0.577205	−	0.462152i
$443$	−1.69137	−	2.92955i	−0.0803596	−	0.139187i	0.823045	−	0.567976i	$-0.192274\pi$
$443$	−1.69137	−	2.92955i	−0.0803596	−	0.139187i	−0.903404	+	0.428789i	$0.858940\pi$
$444$		0			0
$445$	4.13161	+	7.15616i	0.195857	+	0.339235i
$446$	2.88502	−	4.99700i	0.136610	−	0.236615i
$447$		0			0
$448$	2.61442	−	0.405935i	0.123520	−	0.0191786i
$449$	−7.51094	−	13.0093i	−0.354463	−	0.613948i	0.632563	−	0.774509i	$-0.282003\pi$
$449$	−7.51094	−	13.0093i	−0.354463	−	0.613948i	−0.987026	+	0.160561i	$0.948670\pi$
$450$		0			0
$451$	−3.19258			−0.150333
$452$	−1.50417	−	2.60530i	−0.0707503	−	0.122543i
$453$		0			0
$454$	16.9846			0.797126
$455$	−0.0438411	−	17.6363i	−0.00205530	−	0.826802i
$456$		0			0
$457$	−11.9647			−0.559686			−0.279843	−	0.960046i	$-0.590282\pi$
$457$	−11.9647			−0.559686			−0.279843	+	0.960046i	$0.590282\pi$
$458$	−0.460390	−	0.797420i	−0.0215126	−	0.0372610i
$459$		0			0
$460$	6.61899	+	11.4644i	0.308612	+	0.534532i
$461$	−5.35595	−	9.27677i	−0.249451	−	0.432062i	0.713922	−	0.700225i	$-0.246917\pi$
$461$	−5.35595	−	9.27677i	−0.249451	−	0.432062i	−0.963374	+	0.268163i	$0.913584\pi$
$462$		0			0
$463$	−13.5305			−0.628814			−0.314407	−	0.949288i	$-0.601806\pi$
$463$	−13.5305			−0.628814			−0.314407	+	0.949288i	$0.601806\pi$
$464$	4.63798	−	8.03322i	0.215313	−	0.372933i
$465$		0			0
$466$	−2.50283	−	4.33502i	−0.115941	−	0.200816i
$467$	13.9783	+	24.2112i	0.646840	+	1.12036i	0.983873	+	0.178867i	$0.0572430\pi$
$467$	13.9783	+	24.2112i	0.646840	+	1.12036i	−0.337034	+	0.941493i	$0.609424\pi$
$468$		0			0
$469$	23.1006	+	28.7050i	1.06669	+	1.32548i
$470$	−8.51466	+	14.7478i	−0.392752	+	0.680266i
$471$		0			0
$472$	−2.48056			−0.114177
$473$	0.0700874	−	0.121395i	0.00322262	−	0.00558174i
$474$		0			0
$475$	−5.43860	−	9.41993i	−0.249540	−	0.432216i
$476$	−11.2722	+	1.75021i	−0.516662	+	0.0802208i
$477$		0			0
$478$	13.8239			0.632291
$479$	−5.79262	−	10.0331i	−0.264672	−	0.458425i	0.702806	−	0.711382i	$-0.251930\pi$
$479$	−5.79262	−	10.0331i	−0.264672	−	0.458425i	−0.967478	+	0.252957i	$0.918597\pi$
$480$		0			0
$481$	−6.00457	−	4.80769i	−0.273785	−	0.219212i
$482$	−10.7589			−0.490054
$483$		0			0
$484$	5.24412	−	9.08307i	0.238369	−	0.412867i
$485$	−2.57341	+	4.45728i	−0.116853	+	0.202394i
$486$		0			0
$487$	−8.48336			−0.384418			−0.192209	−	0.981354i	$-0.561565\pi$
$487$	−8.48336			−0.384418			−0.192209	+	0.981354i	$0.561565\pi$
$488$	4.31156	−	7.46783i	0.195175	−	0.338053i
$489$		0			0
$490$	−9.56457	−	8.71794i	−0.432083	−	0.393836i
$491$	14.8606	−	25.7394i	0.670650	−	1.16160i	−0.307069	−	0.951687i	$-0.599348\pi$
$491$	14.8606	−	25.7394i	0.670650	−	1.16160i	0.977720	−	0.209914i	$-0.0673183\pi$
$492$		0			0
$493$	−19.9969	+	34.6357i	−0.900616	+	1.55991i
$494$	23.0947	−	9.01203i	1.03908	−	0.405471i
$495$		0			0
$496$	1.11104	−	1.92438i	0.0498873	−	0.0864073i
$497$	−24.9104	−	30.9539i	−1.11739	−	1.38847i
$498$		0			0
$499$	17.7944	+	30.8208i	0.796586	+	1.37973i	0.921827	+	0.387601i	$0.126696\pi$
$499$	17.7944	+	30.8208i	0.796586	+	1.37973i	−0.125241	+	0.992126i	$0.539970\pi$
$500$	12.1687			0.544200
$501$		0			0
$502$	−11.8267	−	20.4844i	−0.527850	−	0.914263i
$503$	−13.5658	−	23.4966i	−0.604867	−	1.04766i	−0.992072	−	0.125667i	$-0.959893\pi$
$503$	−13.5658	−	23.4966i	−0.604867	−	1.04766i	0.387205	−	0.921994i	$-0.373440\pi$
$504$		0			0
$505$	−4.95060	+	8.57469i	−0.220299	+	0.381568i
$506$	−2.56119	−	4.43611i	−0.113859	−	0.197209i
$507$		0			0
$508$	−7.58356	+	13.1351i	−0.336466	+	0.582776i
$509$	−7.21670			−0.319875			−0.159937	−	0.987127i	$-0.551129\pi$
$509$	−7.21670			−0.319875			−0.159937	+	0.987127i	$0.551129\pi$
$510$		0			0
$511$	−1.89205	+	4.88448i	−0.0836992	+	0.216077i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−19.1940			−0.846613
$515$	−6.03499	+	10.4529i	−0.265933	+	0.460610i
$516$		0			0
$517$	3.29471	−	5.70660i	0.144901	−	0.250976i
$518$	−5.57764	+	0.866025i	−0.245067	+	0.0380510i
$519$		0			0
$520$	−1.00637	+	6.58951i	−0.0441321	+	0.288969i
$521$	−11.6165	+	20.1203i	−0.508926	+	0.881486i	0.491020	+	0.871148i	$0.336624\pi$
$521$	−11.6165	+	20.1203i	−0.508926	+	0.881486i	−0.999947	+	0.0103382i	$0.996709\pi$
$522$		0			0
$523$	−39.7226			−1.73695			−0.868475	−	0.495734i	$-0.834899\pi$
$523$	−39.7226			−1.73695			−0.868475	+	0.495734i	$0.834899\pi$
$524$	−9.69444	−	16.7913i	−0.423504	−	0.733530i
$525$		0			0
$526$	−5.49567	−	9.51878i	−0.239623	−	0.415039i
$527$	−4.79032	+	8.29708i	−0.208670	+	0.361427i
$528$		0			0
$529$	28.2706			1.22916
$530$	14.0562			0.610564
$531$		0			0
$532$	6.57088	−	16.9633i	0.284884	−	0.735452i
$533$	14.9899	−	5.84936i	0.649284	−	0.253364i
$534$		0			0
$535$	4.27065	+	7.39699i	0.184636	+	0.319800i
$536$	−6.96322	−	12.0606i	−0.300765	−	0.520940i
$537$		0			0
$538$	16.5175			0.712122
$539$	3.70096	+	3.37336i	0.159412	+	0.145301i
$540$		0			0
$541$	17.6323	+	30.5400i	0.758070	+	1.31302i	0.943834	+	0.330421i	$0.107191\pi$
$541$	17.6323	+	30.5400i	0.758070	+	1.31302i	−0.185764	+	0.982594i	$0.559476\pi$
$542$	18.1906			0.781352
$543$		0			0
$544$	4.31156			0.184856
$545$	18.3065			0.784164
$546$		0			0
$547$	−37.3861			−1.59851			−0.799257	−	0.600990i	$-0.794773\pi$
$547$	−37.3861			−1.59851			−0.799257	+	0.600990i	$0.794773\pi$
$548$	4.74829			0.202837
$549$		0			0
$550$	−1.13171			−0.0482563
$551$	−31.8895	−	55.2342i	−1.35854	−	2.35306i
$552$		0			0
$553$	24.4678	+	30.4039i	1.04048	+	1.29291i
$554$	−16.4894			−0.700567
$555$		0			0
$556$	−7.69027	−	13.3199i	−0.326140	−	0.564891i
$557$	16.6350	+	28.8127i	0.704847	+	1.22083i	0.966747	+	0.255736i	$0.0823179\pi$
$557$	16.6350	+	28.8127i	0.704847	+	1.22083i	−0.261899	+	0.965095i	$0.584349\pi$
$558$		0			0
$559$	−0.106660	+	0.698389i	−0.00451123	+	0.0295387i
$560$	3.06671	+	3.81071i	0.129592	+	0.161032i
$561$		0			0
$562$	15.2768			0.644411
$563$	−14.6410			−0.617045			−0.308523	−	0.951217i	$-0.599835\pi$
$563$	−14.6410			−0.617045			−0.308523	+	0.951217i	$0.599835\pi$
$564$		0			0
$565$	2.78090	−	4.81666i	0.116993	−	0.202638i
$566$	−4.57838	−	7.92998i	−0.192444	−	0.333322i
$567$		0			0
$568$	7.50874	+	13.0055i	0.315060	+	0.545700i
$569$	−34.8196			−1.45972			−0.729858	−	0.683599i	$-0.760414\pi$
$569$	−34.8196			−1.45972			−0.729858	+	0.683599i	$0.760414\pi$
$570$		0			0
$571$	17.3721	−	30.0894i	0.727001	−	1.25920i	−0.231144	−	0.972920i	$-0.574247\pi$
$571$	17.3721	−	30.0894i	0.727001	−	1.25920i	0.958145	−	0.286283i	$-0.0924199\pi$
$572$	0.389409	−	2.54978i	0.0162820	−	0.106612i
$573$		0			0
$574$	4.26490	−	11.0102i	0.178013	−	0.459557i
$575$	5.66373	−	9.80987i	0.236194	−	0.409100i
$576$		0			0
$577$	−11.2007	+	19.4003i	−0.466293	+	0.807643i	−0.999259	−	0.0384934i	$-0.987744\pi$
$577$	−11.2007	+	19.4003i	−0.466293	+	0.807643i	0.532966	+	0.846137i	$0.321077\pi$
$578$	−1.58952			−0.0661152
$579$		0			0
$580$	17.1493			0.712086
$581$	25.4001	−	3.94381i	1.05378	−	0.163617i
$582$		0			0
$583$	−5.43900			−0.225260
$584$	0.989914	−	1.71458i	0.0409629	−	0.0709499i
$585$		0			0
$586$	5.93488	+	10.2795i	0.245168	+	0.424643i
$587$	7.57505	−	13.1204i	0.312656	−	0.541536i	−0.666280	−	0.745701i	$-0.732115\pi$
$587$	7.57505	−	13.1204i	0.312656	−	0.541536i	0.978936	+	0.204165i	$0.0654480\pi$
$588$		0			0
$589$	−7.63923	−	13.2315i	−0.314769	−	0.545196i
$590$	−2.29302	−	3.97163i	−0.0944022	−	0.163509i
$591$		0			0
$592$	2.13341			0.0876826
$593$	3.85455	+	6.67627i	0.158287	+	0.274162i	0.934251	−	0.356616i	$-0.116069\pi$
$593$	3.85455	+	6.67627i	0.158287	+	0.274162i	−0.775964	+	0.630777i	$0.782736\pi$
$594$		0			0
$595$	−13.2223	−	16.4301i	−0.542060	−	0.673568i
$596$	−5.82384	+	10.0872i	−0.238554	+	0.413187i
$597$		0			0
$598$	20.1531	+	16.1360i	0.824121	+	0.659850i
$599$	8.99448	−	15.5789i	0.367505	−	0.636537i	−0.621670	−	0.783279i	$-0.713546\pi$
$599$	8.99448	−	15.5789i	0.367505	−	0.636537i	0.989175	+	0.146743i	$0.0468789\pi$
$600$		0			0
$601$	4.77657	−	8.27326i	0.194840	−	0.337473i	−0.752008	−	0.659154i	$-0.770914\pi$
$601$	4.77657	−	8.27326i	0.194840	−	0.337473i	0.946848	+	0.321681i	$0.104248\pi$
$602$	0.325025	+	0.403878i	0.0132470	+	0.0164609i
$603$		0			0
$604$	−4.09544	+	7.09351i	−0.166641	+	0.288631i
$605$	19.3905			0.788338
$606$		0			0
$607$	−10.7619	+	18.6402i	−0.436813	+	0.756582i	−0.997442	−	0.0714855i	$-0.977226\pi$
$607$	−10.7619	+	18.6402i	−0.436813	+	0.756582i	0.560629	+	0.828067i	$0.310559\pi$
$608$	−3.43786	+	5.95456i	−0.139424	+	0.241489i
$609$		0			0
$610$	15.9423			0.645486
$611$	−5.01392	+	32.8303i	−0.202841	+	1.32817i
$612$		0			0
$613$	18.4945	+	32.0334i	0.746985	+	1.29382i	0.949262	+	0.314488i	$0.101833\pi$
$613$	18.4945	+	32.0334i	0.746985	+	1.29382i	−0.202276	+	0.979328i	$0.564834\pi$
$614$	28.0679			1.13273
$615$		0			0
$616$	−1.18665	−	1.47454i	−0.0478114	−	0.0594108i
$617$	−1.88766	−	3.26953i	−0.0759945	−	0.131626i	0.825524	−	0.564367i	$-0.190880\pi$
$617$	−1.88766	−	3.26953i	−0.0759945	−	0.131626i	−0.901518	+	0.432741i	$0.857546\pi$
$618$		0			0
$619$	−14.0117	+	24.2689i	−0.563177	+	0.975451i	0.434040	+	0.900894i	$0.357088\pi$
$619$	−14.0117	+	24.2689i	−0.563177	+	0.975451i	−0.997217	+	0.0745570i	$0.976246\pi$
$620$	4.10817			0.164988
$621$		0			0
$622$	−12.7326	+	22.0536i	−0.510532	+	0.884267i
$623$	11.6852	−	1.81434i	0.468160	−	0.0726899i
$624$		0			0
$625$	7.29376	+	12.6332i	0.291750	+	0.505326i
$626$	8.82204	+	15.2802i	0.352600	+	0.610721i
$627$		0			0
$628$	11.4353	−	19.8066i	0.456319	−	0.790368i
$629$	−9.19832			−0.366761
$630$		0			0
$631$	6.85038	+	11.8652i	0.272709	+	0.472346i	0.969555	−	0.244875i	$-0.0787470\pi$
$631$	6.85038	+	11.8652i	0.272709	+	0.472346i	−0.696845	+	0.717221i	$0.745414\pi$
$632$	−7.37533	−	12.7744i	−0.293375	−	0.508140i
$633$		0			0
$634$	−14.8710	−	25.7573i	−0.590603	−	1.02295i
$635$	−28.0408			−1.11277
$636$		0			0
$637$	−23.5575	−	9.05791i	−0.933381	−	0.358887i
$638$	−6.63585			−0.262716
$639$		0			0
$640$	−0.924396	−	1.60110i	−0.0365399	−	0.0632890i
$641$	6.40335			0.252917			0.126458	−	0.991972i	$-0.459639\pi$
$641$	6.40335			0.252917			0.126458	+	0.991972i	$0.459639\pi$
$642$		0			0
$643$	9.93369	+	17.2057i	0.391747	+	0.678525i	0.992680	−	0.120774i	$-0.0385377\pi$
$643$	9.93369	+	17.2057i	0.391747	+	0.678525i	−0.600933	+	0.799299i	$0.705204\pi$
$644$	18.7202	−	2.90663i	0.737679	−	0.114537i
$645$		0			0
$646$	14.8225	−	25.6734i	0.583185	−	1.01011i
$647$	15.2592	+	26.4297i	0.599902	+	1.03906i	0.992835	+	0.119494i	$0.0381271\pi$
$647$	15.2592	+	26.4297i	0.599902	+	1.03906i	−0.392933	+	0.919567i	$0.628540\pi$
$648$		0			0
$649$	0.887274	+	1.53680i	0.0348285	+	0.0603248i
$650$	5.31365	−	2.07349i	0.208418	−	0.0813291i
$651$		0			0
$652$	−9.01923	+	15.6218i	−0.353220	+	0.611795i
$653$	−3.65412			−0.142997			−0.0714984	−	0.997441i	$-0.522778\pi$
$653$	−3.65412			−0.142997			−0.0714984	+	0.997441i	$0.522778\pi$
$654$		0			0
$655$	17.9230	−	31.0435i	0.700309	−	1.21297i
$656$	−2.23138	+	3.86487i	−0.0871208	+	0.150898i
$657$		0			0
$658$	15.2789	+	18.9857i	0.595635	+	0.740141i
$659$	−4.12332	−	7.14181i	−0.160622	−	0.278205i	0.774470	−	0.632611i	$-0.218017\pi$
$659$	−4.12332	−	7.14181i	−0.160622	−	0.278205i	−0.935092	+	0.354405i	$0.884683\pi$
$660$		0			0
$661$	−23.0565	−	39.9351i	−0.896796	−	1.55330i	−0.831567	−	0.555425i	$-0.812556\pi$
$661$	−23.0565	−	39.9351i	−0.896796	−	1.55330i	−0.0652290	−	0.997870i	$-0.520778\pi$
$662$	12.0197	−	20.8187i	0.467158	−	0.809141i
$663$		0			0
$664$	−9.71538			−0.377030
$665$	33.2340	−	5.16016i	1.28876	−	0.200102i
$666$		0			0
$667$	33.2095	−	57.5206i	1.28588	−	2.22721i
$668$	−3.86936	+	6.70193i	−0.149710	+	0.259306i
$669$		0			0
$670$	12.8735	−	22.2976i	0.497348	−	0.861432i
$671$	−6.16881			−0.238144
$672$		0			0
$673$	−3.98669	+	6.90515i	−0.153676	+	0.266174i	−0.932576	−	0.360974i	$-0.882444\pi$
$673$	−3.98669	+	6.90515i	−0.153676	+	0.266174i	0.778900	+	0.627148i	$0.215778\pi$
$674$	2.21939			0.0854879
$675$		0			0
$676$	2.84327	+	12.6853i	0.109357	+	0.487895i
$677$	20.4979	+	35.5033i	0.787797	+	1.36450i	0.927314	+	0.374285i	$0.122112\pi$
$677$	20.4979	+	35.5033i	0.787797	+	1.36450i	−0.139517	+	0.990220i	$0.544555\pi$
$678$		0			0
$679$	4.61780	+	5.73811i	0.177215	+	0.220209i
$680$	3.98558	+	6.90323i	0.152840	+	0.264727i
$681$		0			0
$682$	−1.58964			−0.0608704
$683$	−35.2665			−1.34944			−0.674718	−	0.738076i	$-0.735735\pi$
$683$	−35.2665			−1.34944			−0.674718	+	0.738076i	$0.735735\pi$
$684$		0			0
$685$	4.38930	+	7.60248i	0.167706	+	0.290476i
$686$	−16.5777	+	8.25707i	−0.632940	+	0.315256i
$687$		0			0
$688$	−0.0979721	−	0.169693i	−0.00373515	−	0.00646947i
$689$	25.5373	−	9.96519i	0.972895	−	0.379644i
$690$		0			0
$691$	40.7075			1.54859			0.774293	−	0.632827i	$-0.218105\pi$
$691$	40.7075			1.54859			0.774293	+	0.632827i	$0.218105\pi$
$692$	6.01212	−	10.4133i	0.228547	−	0.395854i
$693$		0			0
$694$	−2.01895			−0.0766384
$695$	14.2177	−	24.6258i	0.539308	−	0.934109i
$696$		0			0
$697$	9.62073	−	16.6636i	0.364411	−	0.631179i
$698$	16.8191	−	29.1316i	0.636613	−	1.10265i
$699$		0			0
$700$	1.51183	−	3.90292i	0.0571418	−	0.147517i
$701$	33.7968			1.27649			0.638243	−	0.769835i	$-0.279661\pi$
$701$	33.7968			1.27649			0.638243	+	0.769835i	$0.279661\pi$
$702$		0			0
$703$	7.33438	−	12.7035i	0.276621	−	0.479122i
$704$	0.357690	+	0.619538i	0.0134810	+	0.0233497i
$705$		0			0
$706$	−11.6388	−	20.1590i	−0.438033	−	0.758696i
$707$	8.88349	+	11.0387i	0.334098	+	0.415153i
$708$		0			0
$709$	1.67680	−	2.90430i	0.0629736	−	0.109073i	−0.832820	−	0.553544i	$-0.813275\pi$
$709$	1.67680	−	2.90430i	0.0629736	−	0.109073i	0.895793	+	0.444471i	$0.146608\pi$
$710$	−13.8821	+	24.0445i	−0.520986	+	0.902374i
$711$		0			0
$712$	−4.46953			−0.167503
$713$	7.95545	−	13.7792i	0.297934	−	0.516037i
$714$		0			0
$715$	4.44242	−	1.73352i	0.166137	−	0.0648300i
$716$	5.65742	+	9.79893i	0.211428	+	0.366203i
$717$		0			0
$718$	5.44896	+	9.43787i	0.203353	+	0.352218i
$719$	−19.5541	+	33.8687i	−0.729245	+	1.26309i	0.227958	+	0.973671i	$0.426795\pi$
$719$	−19.5541	+	33.8687i	−0.729245	+	1.26309i	−0.957203	+	0.289419i	$0.906538\pi$
$720$		0			0
$721$	10.8294	+	13.4566i	0.403306	+	0.501151i
$722$	14.1378	+	24.4874i	0.526155	+	0.911328i
$723$		0			0
$724$	−2.49725			−0.0928095
$725$	−7.33715	−	12.7083i	−0.272495	−	0.471975i
$726$		0			0
$727$	−3.65073			−0.135398			−0.0676990	−	0.997706i	$-0.521566\pi$
$727$	−3.65073			−0.135398			−0.0676990	+	0.997706i	$0.521566\pi$
$728$	8.27319	+	4.74914i	0.306625	+	0.176015i
$729$		0			0
$730$	3.66029			0.135473
$731$	0.422412	+	0.731639i	0.0156235	+	0.0270607i
$732$		0			0
$733$	16.3999	+	28.4054i	0.605744	+	1.04918i	0.991933	+	0.126760i	$0.0404577\pi$
$733$	16.3999	+	28.4054i	0.605744	+	1.04918i	−0.386190	+	0.922419i	$0.626209\pi$
$734$	2.44394	+	4.23302i	0.0902074	+	0.156244i
$735$		0			0
$736$	−7.16035			−0.263934
$737$	−4.98135	+	8.62796i	−0.183490	+	0.317815i
$738$		0			0
$739$	−5.11506	−	8.85954i	−0.188160	−	0.325903i	0.756477	−	0.654021i	$-0.226919\pi$
$739$	−5.11506	−	8.85954i	−0.188160	−	0.325903i	−0.944637	+	0.328118i	$0.893586\pi$
$740$	1.97212	+	3.41580i	0.0724964	+	0.125567i
$741$		0			0
$742$	7.26584	−	18.7574i	0.266738	−	0.688606i
$743$	−17.1231	+	29.6581i	−0.628186	+	1.08805i	0.359729	+	0.933057i	$0.382869\pi$
$743$	−17.1231	+	29.6581i	−0.628186	+	1.08805i	−0.987915	+	0.154994i	$0.950464\pi$
$744$		0			0
$745$	−21.5341			−0.788949
$746$	−7.68366	+	13.3085i	−0.281319	+	0.487259i
$747$		0			0
$748$	−1.54220	−	2.67117i	−0.0563885	−	0.0976678i
$749$	12.0785	−	1.87539i	0.441338	−	0.0685254i
$750$		0			0
$751$	11.7925			0.430316			0.215158	−	0.976579i	$-0.430973\pi$
$751$	11.7925			0.430316			0.215158	+	0.976579i	$0.430973\pi$
$752$	−4.60553	−	7.97700i	−0.167946	−	0.290891i
$753$		0			0
$754$	31.1568	−	12.1580i	1.13466	−	0.442769i
$755$	−15.1432			−0.551118
$756$		0			0
$757$	24.1278	−	41.7906i	0.876940	−	1.51890i	0.0222575	−	0.999752i	$-0.492915\pi$
$757$	24.1278	−	41.7906i	0.876940	−	1.51890i	0.854682	−	0.519152i	$-0.173752\pi$
$758$	−8.66626	+	15.0104i	−0.314773	+	0.545203i
$759$		0			0
$760$	−12.7118			−0.461105
$761$	6.11899	−	10.5984i	0.221813	−	0.384192i	−0.733545	−	0.679641i	$-0.762136\pi$
$761$	6.11899	−	10.5984i	0.221813	−	0.384192i	0.955359	+	0.295449i	$0.0954691\pi$
$762$		0			0
$763$	9.46285	−	24.4292i	0.342578	−	0.884395i
$764$	−2.66349	+	4.61330i	−0.0963617	+	0.166903i
$765$		0			0
$766$	5.99628	−	10.3859i	0.216654	−	0.375256i
$767$	−6.98165	−	5.59000i	−0.252093	−	0.201843i
$768$		0			0
$769$	0.357690	−	0.619538i	0.0128986	−	0.0223411i	−0.859504	−	0.511129i	$-0.829227\pi$
$769$	0.357690	−	0.619538i	0.0128986	−	0.0223411i	0.872403	+	0.488788i	$0.162561\pi$
$770$	1.26395	−	3.26300i	0.0455496	−	0.117590i
$771$		0			0
$772$	−4.86186	−	8.42099i	−0.174982	−	0.303078i
$773$	−5.43066			−0.195327			−0.0976636	−	0.995219i	$-0.531137\pi$
$773$	−5.43066			−0.195327			−0.0976636	+	0.995219i	$0.531137\pi$
$774$		0			0
$775$	−1.75764	−	3.04432i	−0.0631362	−	0.109355i
$776$	−1.39194	−	2.41091i	−0.0499678	−	0.0865467i
$777$		0			0
$778$	−8.89274	+	15.4027i	−0.318820	+	0.552213i
$779$	15.3424	+	26.5738i	0.549698	+	0.952105i
$780$		0			0
$781$	5.37161	−	9.30390i	0.192211	−	0.332920i
$782$	30.8722			1.10399
$783$		0			0
$784$	6.67043	−	2.12257i	0.238230	−	0.0758061i
$785$	42.2831			1.50915
$786$		0			0
$787$	−5.17027			−0.184300			−0.0921501	−	0.995745i	$-0.529374\pi$
$787$	−5.17027			−0.184300			−0.0921501	+	0.995745i	$0.529374\pi$
$788$	3.08593	−	5.34499i	0.109932	−	0.190407i
$789$		0			0
$790$	13.6354	−	23.6173i	0.485127	−	0.840265i
$791$	−4.99013	−	6.20077i	−0.177428	−	0.220474i
$792$		0			0
$793$	28.9640	−	11.3023i	1.02854	−	0.401358i
$794$	7.02952	−	12.1755i	0.249468	−	0.432092i
$795$		0			0
$796$	5.41454			0.191913
$797$	−3.24073	−	5.61311i	−0.114793	−	0.198827i	0.802904	−	0.596108i	$-0.203287\pi$
$797$	−3.24073	−	5.61311i	−0.114793	−	0.198827i	−0.917697	+	0.397281i	$0.869954\pi$
$798$		0			0
$799$	19.8570	+	34.3933i	0.702490	+	1.21675i
$800$	−0.790985	+	1.37003i	−0.0279656	+	0.0484378i
$801$		0			0
$802$	4.13072			0.145861
$803$	−1.41633			−0.0499812
$804$		0			0
$805$	21.9587	+	27.2860i	0.773942	+	0.961706i
$806$	7.46371	−	2.91249i	0.262898	−	0.102588i
$807$		0			0
$808$	−2.67775	−	4.63800i	−0.0942028	−	0.163164i
$809$	23.2909	+	40.3409i	0.818863	+	1.41831i	0.906521	+	0.422161i	$0.138728\pi$
$809$	23.2909	+	40.3409i	0.818863	+	1.41831i	−0.0876578	+	0.996151i	$0.527938\pi$
$810$		0			0
$811$	44.2321			1.55320			0.776600	−	0.629994i	$-0.216943\pi$
$811$	44.2321			1.55320			0.776600	+	0.629994i	$0.216943\pi$
$812$	8.86469	−	22.8850i	0.311090	−	0.803105i
$813$		0			0
$814$	−0.763101	−	1.32173i	−0.0267467	−	0.0463266i
$815$	−33.3493			−1.16818
$816$		0			0
$817$	−1.34726			−0.0471346
$818$	5.21490			0.182335
$819$		0			0
$820$	−8.25072			−0.288128
$821$	8.26567			0.288474			0.144237	−	0.989543i	$-0.453927\pi$
$821$	8.26567			0.288474			0.144237	+	0.989543i	$0.453927\pi$
$822$		0			0
$823$	−51.2361			−1.78598			−0.892989	−	0.450078i	$-0.851396\pi$
$823$	−51.2361			−1.78598			−0.892989	+	0.450078i	$0.851396\pi$
$824$	−3.26429	−	5.65391i	−0.113717	−	0.196963i
$825$		0			0
$826$	−6.48525	+	1.00695i	−0.225651	+	0.0350362i
$827$	4.84895			0.168615			0.0843073	−	0.996440i	$-0.473132\pi$
$827$	4.84895			0.168615			0.0843073	+	0.996440i	$0.473132\pi$
$828$		0			0
$829$	−0.997594	−	1.72788i	−0.0346479	−	0.0600118i	0.848181	−	0.529706i	$-0.177698\pi$
$829$	−0.997594	−	1.72788i	−0.0346479	−	0.0600118i	−0.882829	+	0.469694i	$0.844364\pi$
$830$	−8.98086	−	15.5553i	−0.311730	−	0.539932i
$831$		0			0
$832$	−2.81454	−	2.25352i	−0.0975766	−	0.0781268i
$833$	−28.7600	+	9.15159i	−0.996473	+	0.317084i
$834$		0			0
$835$	−14.3073			−0.495124
$836$	4.91877			0.170119
$837$		0			0
$838$	3.69624	−	6.40207i	0.127684	−	0.221156i
$839$	−11.0996	−	19.2251i	−0.383201	−	0.663724i	0.608317	−	0.793694i	$-0.291845\pi$
$839$	−11.0996	−	19.2251i	−0.383201	−	0.663724i	−0.991518	+	0.129971i	$0.958512\pi$
$840$		0			0
$841$	−28.5217	−	49.4011i	−0.983507	−	1.70348i
$842$	−4.67144			−0.160989
$843$		0			0
$844$	13.6366	−	23.6193i	0.469392	−	0.813011i
$845$	−17.6821	+	16.2786i	−0.608281	+	0.560000i
$846$		0			0
$847$	10.0232	−	25.8758i	0.344402	−	0.889102i
$848$	−3.80147	+	6.58434i	−0.130543	+	0.226107i
$849$		0			0
$850$	3.41038	−	5.90695i	0.116975	−	0.202607i
$851$	15.2760			0.523653
$852$		0			0
$853$	−20.8901			−0.715262			−0.357631	−	0.933863i	$-0.616415\pi$
$853$	−20.8901			−0.715262			−0.357631	+	0.933863i	$0.616415\pi$
$854$	8.24079	−	21.2743i	0.281994	−	0.727992i
$855$		0			0
$856$	−4.61994			−0.157906
$857$	−6.25195	+	10.8287i	−0.213563	+	0.369901i	−0.952827	−	0.303514i	$-0.901840\pi$
$857$	−6.25195	+	10.8287i	−0.213563	+	0.369901i	0.739264	+	0.673415i	$0.235173\pi$
$858$		0			0
$859$	4.94030	+	8.55685i	0.168561	+	0.291956i	0.937914	−	0.346868i	$-0.112755\pi$
$859$	4.94030	+	8.55685i	0.168561	+	0.291956i	−0.769353	+	0.638824i	$0.779421\pi$
$860$	0.181130	−	0.313726i	0.00617648	−	0.0106980i
$861$		0			0
$862$	11.0089	+	19.0680i	0.374965	+	0.649458i
$863$	20.2808	+	35.1274i	0.690367	+	1.19575i	0.971718	+	0.236146i	$0.0758844\pi$
$863$	20.2808	+	35.1274i	0.690367	+	1.19575i	−0.281350	+	0.959605i	$0.590782\pi$
$864$		0			0
$865$	22.2303			0.755854
$866$	12.5366	+	21.7141i	0.426012	+	0.737875i
$867$		0			0
$868$	2.12356	−	5.48216i	0.0720784	−	0.186077i
$869$	−5.27617	+	9.13860i	−0.178982	+	0.310006i
$870$		0			0
$871$	7.58068	−	49.6369i	0.256861	−	1.68188i
$872$	−4.95093	+	8.57527i	−0.167660	+	0.290395i
$873$		0			0
$874$	−24.6163	+	42.6367i	−0.832659	+	1.44221i
$875$	31.8141	−	4.93969i	1.07551	−	0.166992i
$876$		0			0
$877$	15.6174	−	27.0502i	0.527363	−	0.913420i	−0.472128	−	0.881530i	$-0.656514\pi$
$877$	15.6174	−	27.0502i	0.527363	−	0.913420i	0.999491	−	0.0318902i	$-0.0101527\pi$
$878$	13.9493			0.470766
$879$		0			0
$880$	−0.661295	+	1.14540i	−0.0222923	+	0.0386113i
$881$	19.0177	−	32.9396i	0.640722	−	1.10976i	−0.344550	−	0.938768i	$-0.611969\pi$
$881$	19.0177	−	32.9396i	0.640722	−	1.10976i	0.985272	−	0.170994i	$-0.0546980\pi$
$882$		0			0
$883$	22.5813			0.759921			0.379961	−	0.925003i	$-0.375938\pi$
$883$	22.5813			0.759921			0.379961	+	0.925003i	$0.375938\pi$
$884$	12.1350	+	9.71619i	0.408146	+	0.326791i
$885$		0			0
$886$	1.69137	+	2.92955i	0.0568228	+	0.0984201i
$887$	−7.73646			−0.259765			−0.129882	−	0.991529i	$-0.541460\pi$
$887$	−7.73646			−0.259765			−0.129882	+	0.991529i	$0.541460\pi$
$888$		0			0
$889$	−14.4946	+	37.4192i	−0.486135	+	1.25500i
$890$	−4.13161	−	7.15616i	−0.138492	−	0.239875i
$891$		0			0
$892$	−2.88502	+	4.99700i	−0.0965976	+	0.167312i
$893$	−63.3327			−2.11935
$894$		0			0
$895$	−10.4594	+	18.1162i	−0.349619	+	0.605557i
$896$	−2.61442	+	0.405935i	−0.0873418	+	0.0135613i
$897$		0			0
$898$	7.51094	+	13.0093i	0.250643	+	0.434127i
$899$	−10.3060	−	17.8505i	−0.343724	−	0.595347i
$900$		0			0
$901$	16.3903	−	28.3887i	0.546038	−	0.945766i
$902$	3.19258			0.106301
$903$		0			0
$904$	1.50417	+	2.60530i	0.0500280	+	0.0866510i
$905$	−2.30845	−	3.99835i	−0.0767353	−	0.132909i
$906$		0			0
$907$	20.3205	+	35.1961i	0.674731	+	1.16867i	0.976548	+	0.215302i	$0.0690735\pi$
$907$	20.3205	+	35.1961i	0.674731	+	1.16867i	−0.301817	+	0.953366i	$0.597593\pi$
$908$	−16.9846			−0.563653
$909$		0			0
$910$	0.0438411	+	17.6363i	0.00145332	+	0.584637i
$911$	−2.41059			−0.0798664			−0.0399332	−	0.999202i	$-0.512715\pi$
$911$	−2.41059			−0.0798664			−0.0399332	+	0.999202i	$0.512715\pi$
$912$		0			0
$913$	3.47510	+	6.01905i	0.115009	+	0.199201i
$914$	11.9647			0.395758
$915$		0			0
$916$	0.460390	+	0.797420i	0.0152117	+	0.0263475i
$917$	−32.1615	−	39.9642i	−1.06207	−	1.31973i
$918$		0			0
$919$	−6.62695	+	11.4782i	−0.218603	+	0.378631i	−0.954381	−	0.298591i	$-0.903483\pi$
$919$	−6.62695	+	11.4782i	−0.218603	+	0.378631i	0.735778	+	0.677223i	$0.236817\pi$
$920$	−6.61899	−	11.4644i	−0.218222	−	0.377971i
$921$		0			0
$922$	5.35595	+	9.27677i	0.176389	+	0.305514i
$923$	−8.17458	+	53.5257i	−0.269069	+	1.76182i
$924$		0			0
$925$	1.68750	−	2.92283i	0.0554845	−	0.0961020i
$926$	13.5305			0.444639
$927$		0			0
$928$	−4.63798	+	8.03322i	−0.152249	+	0.263703i
$929$	−12.3258	+	21.3489i	−0.404397	+	0.700436i	−0.994251	−	0.107074i	$-0.965852\pi$
$929$	−12.3258	+	21.3489i	−0.404397	+	0.700436i	0.589854	+	0.807510i	$0.299185\pi$
$930$		0			0
$931$	10.2931	−	47.0166i	0.337342	−	1.54091i
$932$	2.50283	+	4.33502i	0.0819828	+	0.141998i
$933$		0			0
$934$	−13.9783	−	24.2112i	−0.457385	−	0.792214i
$935$	2.85121	−	4.93844i	0.0932446	−	0.161504i
$936$		0			0
$937$	−26.6818			−0.871656			−0.435828	−	0.900030i	$-0.643544\pi$
$937$	−26.6818			−0.871656			−0.435828	+	0.900030i	$0.643544\pi$
$938$	−23.1006	−	28.7050i	−0.754263	−	0.937253i
$939$		0			0
$940$	8.51466	−	14.7478i	0.277717	−	0.481021i
$941$	20.1805	−	34.9536i	0.657865	−	1.13946i	−0.323303	−	0.946296i	$-0.604793\pi$
$941$	20.1805	−	34.9536i	0.657865	−	1.13946i	0.981167	−	0.193159i	$-0.0618735\pi$
$942$		0			0
$943$	−15.9775	+	27.6738i	−0.520298	+	0.901183i
$944$	2.48056			0.0807355
$945$		0			0
$946$	−0.0700874	+	0.121395i	−0.00227874	+	0.00394689i
$947$	−5.51853			−0.179328			−0.0896641	−	0.995972i	$-0.528579\pi$
$947$	−5.51853			−0.179328			−0.0896641	+	0.995972i	$0.528579\pi$
$948$		0			0
$949$	6.65000	−	2.59496i	0.215868	−	0.0842361i
$950$	5.43860	+	9.41993i	0.176451	+	0.305623i
$951$		0			0
$952$	11.2722	−	1.75021i	0.365335	−	0.0567246i
$953$	2.92091	+	5.05916i	0.0946175	+	0.163882i	0.909449	−	0.415816i	$-0.136504\pi$
$953$	2.92091	+	5.05916i	0.0946175	+	0.163882i	−0.814831	+	0.579698i	$0.803171\pi$
$954$		0			0
$955$	−9.84847			−0.318689
$956$	−13.8239			−0.447097
$957$		0			0
$958$	5.79262	+	10.0331i	0.187151	+	0.324155i
$959$	12.4140	−	1.92749i	0.400870	−	0.0622420i
$960$		0			0
$961$	13.0312	+	22.5706i	0.420360	+	0.728085i
$962$	6.00457	+	4.80769i	0.193595	+	0.155006i
$963$		0			0
$964$	10.7589			0.346521
$965$	8.98857	−	15.5687i	0.289352	−	0.501173i
$966$		0			0
$967$	4.98537			0.160319			0.0801594	−	0.996782i	$-0.474457\pi$
$967$	4.98537			0.160319			0.0801594	+	0.996782i	$0.474457\pi$
$968$	−5.24412	+	9.08307i	−0.168552	+	0.291941i
$969$		0			0
$970$	2.57341	−	4.45728i	0.0826272	−	0.143115i
$971$	−1.37240	+	2.37707i	−0.0440424	+	0.0762837i	−0.887206	−	0.461373i	$-0.847357\pi$
$971$	−1.37240	+	2.37707i	−0.0440424	+	0.0762837i	0.843164	+	0.537657i	$0.180690\pi$
$972$		0			0
$973$	−25.5127	−	31.7022i	−0.817898	−	1.01633i
$974$	8.48336			0.271824
$975$		0			0
$976$	−4.31156	+	7.46783i	−0.138010	+	0.239040i
$977$	−8.19729	−	14.1981i	−0.262255	−	0.454238i	0.704586	−	0.709618i	$-0.251133\pi$
$977$	−8.19729	−	14.1981i	−0.262255	−	0.454238i	−0.966841	+	0.255380i	$0.917799\pi$
$978$		0			0
$979$	1.59871	+	2.76904i	0.0510949	+	0.0884990i
$980$	9.56457	+	8.71794i	0.305529	+	0.278484i
$981$		0			0
$982$	−14.8606	+	25.7394i	−0.474221	+	0.821376i
$983$	−15.1127	+	26.1760i	−0.482021	+	0.834884i	−0.999787	−	0.0206379i	$-0.993430\pi$
$983$	−15.1127	+	26.1760i	−0.482021	+	0.834884i	0.517766	+	0.855522i	$0.326764\pi$
$984$		0			0
$985$	11.4105			0.363568
$986$	19.9969	−	34.6357i	0.636831	−	1.10302i
$987$		0			0
$988$	−23.0947	+	9.01203i	−0.734741	+	0.286711i
$989$	−0.701514	−	1.21506i	−0.0223069	−	0.0386366i
$990$		0			0
$991$	−10.0272	−	17.3677i	−0.318525	−	0.551702i	0.661655	−	0.749808i	$-0.269854\pi$
$991$	−10.0272	−	17.3677i	−0.318525	−	0.551702i	−0.980181	+	0.198106i	$0.936521\pi$
$992$	−1.11104	+	1.92438i	−0.0352756	+	0.0610992i
$993$		0			0
$994$	24.9104	+	30.9539i	0.790111	+	0.981798i
$995$	5.00518	+	8.66922i	0.158675	+	0.274833i
$996$		0			0
$997$	−43.4877			−1.37727			−0.688635	−	0.725108i	$-0.741790\pi$
$997$	−43.4877			−1.37727			−0.688635	+	0.725108i	$0.741790\pi$
$998$	−17.7944	−	30.8208i	−0.563272	−	0.975615i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.m.h.1621.4		8
3.2	odd	2		546.2.j.c.529.1	yes	8
7.2	even	3		1638.2.p.h.919.4		8
13.3	even	3		1638.2.p.h.991.4		8
21.2	odd	6		546.2.k.c.373.1	yes	8
39.29	odd	6		546.2.k.c.445.1	yes	8
91.16	even	3	inner	1638.2.m.h.289.4		8
273.107	odd	6		546.2.j.c.289.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.1	✓	8	273.107	odd	6
546.2.j.c.529.1	yes	8	3.2	odd	2
546.2.k.c.373.1	yes	8	21.2	odd	6
546.2.k.c.445.1	yes	8	39.29	odd	6
1638.2.m.h.289.4		8	91.16	even	3	inner
1638.2.m.h.1621.4		8	1.1	even	1	trivial
1638.2.p.h.919.4		8	7.2	even	3
1638.2.p.h.991.4		8	13.3	even	3

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.m (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.924396 + 1.60110i) q^{5} +(2.61442 - 0.405935i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.924396 + 1.60110i) q^{5} +(2.61442 - 0.405935i) q^{7} -1.00000 q^{8} +(-0.924396 - 1.60110i) q^{10} +(0.357690 + 0.619538i) q^{11} +(-2.81454 - 2.25352i) q^{13} +(-2.61442 + 0.405935i) q^{14} +1.00000 q^{16} -4.31156 q^{17} +(3.43786 - 5.95456i) q^{19} +(0.924396 + 1.60110i) q^{20} +(-0.357690 - 0.619538i) q^{22} +7.16035 q^{23} +(0.790985 - 1.37003i) q^{25} +(2.81454 + 2.25352i) q^{26} +(2.61442 - 0.405935i) q^{28} +(4.63798 - 8.03322i) q^{29} +(1.11104 - 1.92438i) q^{31} -1.00000 q^{32} +4.31156 q^{34} +(3.06671 + 3.81071i) q^{35} +2.13341 q^{37} +(-3.43786 + 5.95456i) q^{38} +(-0.924396 - 1.60110i) q^{40} +(-2.23138 + 3.86487i) q^{41} +(-0.0979721 - 0.169693i) q^{43} +(0.357690 + 0.619538i) q^{44} -7.16035 q^{46} +(-4.60553 - 7.97700i) q^{47} +(6.67043 - 2.12257i) q^{49} +(-0.790985 + 1.37003i) q^{50} +(-2.81454 - 2.25352i) q^{52} +(-3.80147 + 6.58434i) q^{53} +(-0.661295 + 1.14540i) q^{55} +(-2.61442 + 0.405935i) q^{56} +(-4.63798 + 8.03322i) q^{58} +2.48056 q^{59} +(-4.31156 + 7.46783i) q^{61} +(-1.11104 + 1.92438i) q^{62} +1.00000 q^{64} +(1.00637 - 6.58951i) q^{65} +(6.96322 + 12.0606i) q^{67} -4.31156 q^{68} +(-3.06671 - 3.81071i) q^{70} +(-7.50874 - 13.0055i) q^{71} +(-0.989914 + 1.71458i) q^{73} -2.13341 q^{74} +(3.43786 - 5.95456i) q^{76} +(1.18665 + 1.47454i) q^{77} +(7.37533 + 12.7744i) q^{79} +(0.924396 + 1.60110i) q^{80} +(2.23138 - 3.86487i) q^{82} +9.71538 q^{83} +(-3.98558 - 6.90323i) q^{85} +(0.0979721 + 0.169693i) q^{86} +(-0.357690 - 0.619538i) q^{88} +4.46953 q^{89} +(-8.27319 - 4.74914i) q^{91} +7.16035 q^{92} +(4.60553 + 7.97700i) q^{94} +12.7118 q^{95} +(1.39194 + 2.41091i) q^{97} +(-6.67043 + 2.12257i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} + 2 q^{10} - 4 q^{11} + 3 q^{13} - 3 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} + 2 q^{25} - 3 q^{26} + 3 q^{28} - 2 q^{29} + 14 q^{31} - 8 q^{32} + 4 q^{34} + 22 q^{35} + 12 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} - 8 q^{46} - 7 q^{47} + 5 q^{49} - 2 q^{50} + 3 q^{52} + q^{53} - 25 q^{55} - 3 q^{56} + 2 q^{58} + 32 q^{59} - 4 q^{61} - 14 q^{62} + 8 q^{64} - 10 q^{65} + 19 q^{67} - 4 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} - 12 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} - 2 q^{80} + 12 q^{82} + 64 q^{83} + 15 q^{85} + 4 q^{88} - 22 q^{89} - 38 q^{91} + 8 q^{92} + 7 q^{94} + 56 q^{95} + 11 q^{97} - 5 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 + 2 * q^10 - 4 * q^11 + 3 * q^13 - 3 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 + 2 * q^25 - 3 * q^26 + 3 * q^28 - 2 * q^29 + 14 * q^31 - 8 * q^32 + 4 * q^34 + 22 * q^35 + 12 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 - 8 * q^46 - 7 * q^47 + 5 * q^49 - 2 * q^50 + 3 * q^52 + q^53 - 25 * q^55 - 3 * q^56 + 2 * q^58 + 32 * q^59 - 4 * q^61 - 14 * q^62 + 8 * q^64 - 10 * q^65 + 19 * q^67 - 4 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 - 12 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 - 2 * q^80 + 12 * q^82 + 64 * q^83 + 15 * q^85 + 4 * q^88 - 22 * q^89 - 38 * q^91 + 8 * q^92 + 7 * q^94 + 56 * q^95 + 11 * q^97 - 5 * q^98

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