LMFDB - Embedded newform 1638.2.p.h.991.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(919,1638)]

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, 4]))

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

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

chi := DirichletCharacter("1638.919");

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.p (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			991.4
Root			$1.19003 + 0.764088i$ of defining polynomial
Character	$\chi$	$=$	1638.991
Dual form			1638.2.p.h.919.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.924396 + 1.60110i) q^{5} +(-1.65876 - 2.06119i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.924396 + 1.60110i) q^{5} +(-1.65876 - 2.06119i) q^{7} -1.00000 q^{8} +1.84879 q^{10} -0.715381 q^{11} +(-2.81454 + 2.25352i) q^{13} +(-2.61442 + 0.405935i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.15578 + 3.73392i) q^{17} -6.87573 q^{19} +(0.924396 - 1.60110i) q^{20} +(-0.357690 + 0.619538i) q^{22} +(-3.58017 + 6.20104i) q^{23} +(0.790985 - 1.37003i) q^{25} +(0.544337 + 3.56422i) q^{26} +(-0.955663 + 2.46713i) q^{28} +(4.63798 + 8.03322i) q^{29} +(1.11104 - 1.92438i) q^{31} +(0.500000 + 0.866025i) q^{32} +4.31156 q^{34} +(1.76682 - 4.56120i) q^{35} +(-1.06671 + 1.84759i) q^{37} +(-3.43786 + 5.95456i) q^{38} +(-0.924396 - 1.60110i) q^{40} +(-2.23138 - 3.86487i) q^{41} +(-0.0979721 + 0.169693i) q^{43} +(0.357690 + 0.619538i) q^{44} +(3.58017 + 6.20104i) q^{46} +(-4.60553 - 7.97700i) q^{47} +(-1.49702 + 6.83805i) q^{49} +(-0.790985 - 1.37003i) q^{50} +(3.35888 + 1.31070i) q^{52} +(-3.80147 + 6.58434i) q^{53} +(-0.661295 - 1.14540i) q^{55} +(1.65876 + 2.06119i) q^{56} +9.27596 q^{58} +(-1.24028 - 2.14823i) q^{59} +8.62311 q^{61} +(-1.11104 - 1.92438i) q^{62} +1.00000 q^{64} +(-6.20986 - 2.42321i) q^{65} -13.9264 q^{67} +(2.15578 - 3.73392i) q^{68} +(-3.06671 - 3.81071i) q^{70} +(-7.50874 + 13.0055i) q^{71} +(-0.989914 + 1.71458i) q^{73} +(1.06671 + 1.84759i) q^{74} +(3.43786 + 5.95456i) q^{76} +(1.18665 + 1.47454i) q^{77} +(7.37533 + 12.7744i) q^{79} -1.84879 q^{80} -4.46276 q^{82} +9.71538 q^{83} +(-3.98558 + 6.90323i) q^{85} +(0.0979721 + 0.169693i) q^{86} +0.715381 q^{88} +(-2.23476 + 3.87073i) q^{89} +(9.31359 + 2.06325i) q^{91} +7.16035 q^{92} -9.21105 q^{94} +(-6.35589 - 11.0087i) q^{95} +(1.39194 - 2.41091i) q^{97} +(5.17342 + 4.71548i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} - 4 q^{10} + 8 q^{11} + 3 q^{13} - 3 q^{14} - 4 q^{16} + 2 q^{17} + 8 q^{19} - 2 q^{20} + 4 q^{22} - 4 q^{23} + 2 q^{25} + 12 q^{26} - 2 q^{29} + 14 q^{31} + 4 q^{32} + 4 q^{34} + 4 q^{35} - 6 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} + 4 q^{46} - 7 q^{47} - 7 q^{49} - 2 q^{50} + 9 q^{52} + q^{53} - 25 q^{55} + 3 q^{56} - 4 q^{58} - 16 q^{59} + 8 q^{61} - 14 q^{62} + 8 q^{64} - q^{65} - 38 q^{67} + 2 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} + 6 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} + 4 q^{80} - 24 q^{82} + 64 q^{83} + 15 q^{85} - 8 q^{88} + 11 q^{89} - 20 q^{91} + 8 q^{92} - 14 q^{94} - 28 q^{95} + 11 q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8 - 4 * q^10 + 8 * q^11 + 3 * q^13 - 3 * q^14 - 4 * q^16 + 2 * q^17 + 8 * q^19 - 2 * q^20 + 4 * q^22 - 4 * q^23 + 2 * q^25 + 12 * q^26 - 2 * q^29 + 14 * q^31 + 4 * q^32 + 4 * q^34 + 4 * q^35 - 6 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 + 4 * q^46 - 7 * q^47 - 7 * q^49 - 2 * q^50 + 9 * q^52 + q^53 - 25 * q^55 + 3 * q^56 - 4 * q^58 - 16 * q^59 + 8 * q^61 - 14 * q^62 + 8 * q^64 - q^65 - 38 * q^67 + 2 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 + 6 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 + 4 * q^80 - 24 * q^82 + 64 * q^83 + 15 * q^85 - 8 * q^88 + 11 * q^89 - 20 * q^91 + 8 * q^92 - 14 * q^94 - 28 * q^95 + 11 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.924396	+	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
$7$	−1.65876	−	2.06119i	−0.626953	−	0.779057i
$7$	−1.65876	−	2.06119i	−0.626953	−	0.779057i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.84879			0.584639
$11$	−0.715381			−0.215695			−0.107848	−	0.994167i	$-0.534396\pi$
$11$	−0.715381			−0.215695			−0.107848	+	0.994167i	$0.534396\pi$
$12$		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
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.15578	+	3.73392i	0.522853	+	0.905608i	0.999646	+	0.0265925i	$0.00846567\pi$
$17$	2.15578	+	3.73392i	0.522853	+	0.905608i	−0.476793	+	0.879015i	$0.658201\pi$
$18$		0			0
$19$	−6.87573			−1.57740			−0.788700	−	0.614778i	$-0.789246\pi$
$19$	−6.87573			−1.57740			−0.788700	+	0.614778i	$0.789246\pi$
$20$	0.924396	−	1.60110i	0.206701	−	0.358017i
$21$		0			0
$22$	−0.357690	+	0.619538i	−0.0762599	+	0.132086i
$23$	−3.58017	+	6.20104i	−0.746518	+	1.29301i	0.202964	+	0.979186i	$0.434942\pi$
$23$	−3.58017	+	6.20104i	−0.746518	+	1.29301i	−0.949482	+	0.313821i	$0.898391\pi$
$24$		0			0
$25$	0.790985	−	1.37003i	0.158197	−	0.274005i
$26$	0.544337	+	3.56422i	0.106753	+	0.699002i
$27$		0			0
$28$	−0.955663	+	2.46713i	−0.180603	+	0.466243i
$29$	4.63798	+	8.03322i	0.861251	+	1.49173i	0.870722	+	0.491776i	$0.163652\pi$
$29$	4.63798	+	8.03322i	0.861251	+	1.49173i	−0.00947068	+	0.999955i	$0.503015\pi$
$30$		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	$0.102719\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	4.31156			0.739426
$35$	1.76682	−	4.56120i	0.298647	−	0.770984i
$36$		0			0
$37$	−1.06671	+	1.84759i	−0.175365	+	0.303742i	−0.940288	−	0.340381i	$-0.889444\pi$
$37$	−1.06671	+	1.84759i	−0.175365	+	0.303742i	0.764922	+	0.644122i	$0.222777\pi$
$38$	−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	0.637497	−	0.770453i	$-0.279970\pi$
$41$	−2.23138	−	3.86487i	−0.348483	−	0.603591i	−0.985980	+	0.166862i	$0.946637\pi$
$42$		0			0
$43$	−0.0979721	+	0.169693i	−0.0149406	+	0.0258779i	−0.873399	−	0.487005i	$-0.838089\pi$
$43$	−0.0979721	+	0.169693i	−0.0149406	+	0.0258779i	0.858458	+	0.512883i	$0.171423\pi$
$44$	0.357690	+	0.619538i	0.0539239	+	0.0933989i
$45$		0			0
$46$	3.58017	+	6.20104i	0.527868	+	0.914294i
$47$	−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
$49$	−1.49702	+	6.83805i	−0.213859	+	0.976864i
$50$	−0.790985	−	1.37003i	−0.111862	−	0.193751i
$51$		0			0
$52$	3.35888	+	1.31070i	0.465793	+	0.181762i
$53$	−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
$56$	1.65876	+	2.06119i	0.221661	+	0.275438i
$57$		0			0
$58$	9.27596			1.21799
$59$	−1.24028	−	2.14823i	−0.161471	−	0.279676i	0.773926	−	0.633277i	$-0.218290\pi$
$59$	−1.24028	−	2.14823i	−0.161471	−	0.279676i	−0.935396	+	0.353601i	$0.884957\pi$
$60$		0			0
$61$	8.62311			1.10408			0.552038	−	0.833819i	$-0.313850\pi$
$61$	8.62311			1.10408			0.552038	+	0.833819i	$0.313850\pi$
$62$	−1.11104	−	1.92438i	−0.141103	−	0.244397i
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.20986	−	2.42321i	−0.770239	−	0.300563i
$66$		0			0
$67$	−13.9264			−1.70138			−0.850692	−	0.525664i	$-0.823817\pi$
$67$	−13.9264			−1.70138			−0.850692	+	0.525664i	$0.823817\pi$
$68$	2.15578	−	3.73392i	0.261426	−	0.452804i
$69$		0			0
$70$	−3.06671	−	3.81071i	−0.366541	−	0.455467i
$71$	−7.50874	+	13.0055i	−0.891124	+	1.54347i	−0.0525935	+	0.998616i	$0.516749\pi$
$71$	−7.50874	+	13.0055i	−0.891124	+	1.54347i	−0.838530	+	0.544855i	$0.816585\pi$
$72$		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	$0.203629\pi$
$74$	1.06671	+	1.84759i	0.124002	+	0.214778i
$75$		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	$0.521794\pi$
$80$	−1.84879			−0.206701
$81$		0			0
$82$	−4.46276			−0.492830
$83$	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
$88$	0.715381			0.0762599
$89$	−2.23476	+	3.87073i	−0.236885	+	0.410296i	−0.959819	−	0.280621i	$-0.909460\pi$
$89$	−2.23476	+	3.87073i	−0.236885	+	0.410296i	0.722934	+	0.690917i	$0.242793\pi$
$90$		0			0
$91$	9.31359	+	2.06325i	0.976330	+	0.216287i
$92$	7.16035			0.746518
$93$		0			0
$94$	−9.21105			−0.950047
$95$	−6.35589	−	11.0087i	−0.652101	−	1.12947i
$96$		0			0
$97$	1.39194	−	2.41091i	0.141330	−	0.244791i	−0.786668	−	0.617377i	$-0.788195\pi$
$97$	1.39194	−	2.41091i	0.141330	−	0.244791i	0.927998	+	0.372586i	$0.121529\pi$
$98$	5.17342	+	4.71548i	0.522594	+	0.476335i
$99$		0			0
$100$	−1.58197			−0.158197
$101$	−5.35550			−0.532892			−0.266446	−	0.963850i	$-0.585849\pi$
$101$	−5.35550			−0.532892			−0.266446	+	0.963850i	$0.585849\pi$
$102$		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
$107$	−2.30997	+	4.00099i	−0.223313	+	0.386790i	−0.955812	−	0.293978i	$-0.905021\pi$
$107$	−2.30997	+	4.00099i	−0.223313	+	0.386790i	0.732499	+	0.680768i	$0.238354\pi$
$108$		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	$0.00939913\pi$
$110$	−1.32259			−0.126104
$111$		0			0
$112$	2.61442	−	0.405935i	0.247040	−	0.0383572i
$113$	−1.50417	+	2.60530i	−0.141501	+	0.245086i	−0.928062	−	0.372426i	$-0.878526\pi$
$113$	−1.50417	+	2.60530i	−0.141501	+	0.245086i	0.786561	+	0.617512i	$0.211859\pi$
$114$		0			0
$115$	−13.2380			−1.23445
$116$	4.63798	−	8.03322i	0.430626	−	0.745865i
$117$		0			0
$118$	−2.48056			−0.228354
$119$	4.12039	−	10.6372i	0.377716	−	0.975106i
$120$		0			0
$121$	−10.4882			−0.953475
$122$	4.31156	−	7.46783i	0.390350	−	0.676106i
$123$		0			0
$124$	−2.22209			−0.199549
$125$	12.1687			1.08840
$126$		0			0
$127$	−7.58356	−	13.1351i	−0.672932	−	1.16555i	−0.977069	−	0.212924i	$-0.931701\pi$
$127$	−7.58356	−	13.1351i	−0.672932	−	1.16555i	0.304137	−	0.952628i	$-0.401632\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−5.20350	+	4.16629i	−0.456377	+	0.365408i
$131$	−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
$133$	11.4052	+	14.1722i	0.988956	+	1.22888i
$134$	−6.96322	+	12.0606i	−0.601530	+	1.04188i
$135$		0			0
$136$	−2.15578	−	3.73392i	−0.184856	−	0.320181i
$137$	−2.37414	−	4.11214i	−0.202837	−	0.351324i	0.746605	−	0.665268i	$-0.231683\pi$
$137$	−2.37414	−	4.11214i	−0.202837	−	0.351324i	−0.949441	+	0.313945i	$0.898349\pi$
$138$		0			0
$139$	−7.69027	+	13.3199i	−0.652280	+	1.12978i	0.330288	+	0.943880i	$0.392854\pi$
$139$	−7.69027	+	13.3199i	−0.652280	+	1.12978i	−0.982568	+	0.185902i	$0.940479\pi$
$140$	−4.83353	+	0.750489i	−0.408507	+	0.0634279i
$141$		0			0
$142$	7.50874	+	13.0055i	0.630120	+	1.09140i
$143$	2.01347	−	1.61213i	0.168375	−	0.134813i
$144$		0			0
$145$	−8.57466	+	14.8517i	−0.712086	+	1.23337i
$146$	0.989914	+	1.71458i	0.0819258	+	0.141900i
$147$		0			0
$148$	2.13341			0.175365
$149$	11.6477			0.954215			0.477107	−	0.878845i	$-0.341685\pi$
$149$	11.6477			0.954215			0.477107	+	0.878845i	$0.341685\pi$
$150$		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	$0.274823\pi$
$152$	6.87573			0.557695
$153$		0			0
$154$	1.87031	−	0.290398i	0.150714	−	0.0234009i
$155$	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	$-0.199292\pi$
$158$	14.7507			1.17350
$159$		0			0
$160$	−0.924396	+	1.60110i	−0.0730799	+	0.126578i
$161$	18.7202	−	2.90663i	1.47536	−	0.229075i
$162$		0			0
$163$	18.0385			1.41288			0.706440	−	0.707773i	$-0.250300\pi$
$163$	18.0385			1.41288			0.706440	+	0.707773i	$0.250300\pi$
$164$	−2.23138	+	3.86487i	−0.174242	+	0.301795i
$165$		0			0
$166$	4.85769	−	8.41377i	0.377030	−	0.653035i
$167$	−3.86936	−	6.70193i	−0.299420	−	0.518611i	0.676583	−	0.736366i	$-0.263460\pi$
$167$	−3.86936	−	6.70193i	−0.299420	−	0.518611i	−0.976003	+	0.217755i	$0.930127\pi$
$168$		0			0
$169$	2.84327	−	12.6853i	0.218713	−	0.975789i
$170$	3.98558	+	6.90323i	0.305680	+	0.529454i
$171$		0			0
$172$	0.195944			0.0149406
$173$	−12.0242			−0.914186			−0.457093	−	0.889419i	$-0.651109\pi$
$173$	−12.0242			−0.914186			−0.457093	+	0.889419i	$0.651109\pi$
$174$		0			0
$175$	−4.13594	+	0.642177i	−0.312648	+	0.0485440i
$176$	0.357690	−	0.619538i	0.0269619	−	0.0466994i
$177$		0			0
$178$	2.23476	+	3.87073i	0.167503	+	0.290123i
$179$	−11.3148			−0.845710			−0.422855	−	0.906197i	$-0.638972\pi$
$179$	−11.3148			−0.845710			−0.422855	+	0.906197i	$0.638972\pi$
$180$		0			0
$181$	−2.49725			−0.185619			−0.0928095	−	0.995684i	$-0.529585\pi$
$181$	−2.49725			−0.185619			−0.0928095	+	0.995684i	$0.529585\pi$
$182$	6.44362	−	7.03418i	0.477633	−	0.521408i
$183$		0			0
$184$	3.58017	−	6.20104i	0.263934	−	0.457147i
$185$	−3.94423			−0.289986
$186$		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
$191$	5.32698			0.385447			0.192723	−	0.981253i	$-0.438268\pi$
$191$	5.32698			0.385447			0.192723	+	0.981253i	$0.438268\pi$
$192$		0			0
$193$	9.72372			0.699929			0.349964	−	0.936763i	$-0.386194\pi$
$193$	9.72372			0.699929			0.349964	+	0.936763i	$0.386194\pi$
$194$	−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	0.954766	−	0.297358i	$-0.0961055\pi$
$197$	3.08593	+	5.34499i	0.219863	+	0.380815i	−0.734903	+	0.678173i	$0.762772\pi$
$198$		0			0
$199$	−2.70727	−	4.68913i	−0.191913	−	0.332404i	0.753971	−	0.656908i	$-0.228136\pi$
$199$	−2.70727	−	4.68913i	−0.191913	−	0.332404i	−0.945884	+	0.324504i	$0.894803\pi$
$200$	−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
$205$	4.12536	−	7.14533i	0.288128	−	0.499052i
$206$	6.52858			0.454867
$207$		0			0
$208$	−0.544337	−	3.56422i	−0.0377430	−	0.247135i
$209$	4.91877			0.340238
$210$		0			0
$211$	13.6366	+	23.6193i	0.938785	+	1.62602i	0.767742	+	0.640759i	$0.221380\pi$
$211$	13.6366	+	23.6193i	0.938785	+	1.62602i	0.171043	+	0.985264i	$0.445286\pi$
$212$	7.60294			0.522172
$213$		0			0
$214$	2.30997	+	4.00099i	0.157906	+	0.273502i
$215$	−0.362260			−0.0247059
$216$		0			0
$217$	−5.80947	+	0.902022i	−0.394373	+	0.0612332i
$218$	−4.95093	−	8.57527i	−0.335320	−	0.580791i
$219$		0			0
$220$	−0.661295	+	1.14540i	−0.0445845	+	0.0772226i
$221$	−14.4820	−	5.65117i	−0.974164	−	0.380139i
$222$		0			0
$223$	−2.88502	−	4.99700i	−0.193195	−	0.334624i	0.753112	−	0.657892i	$-0.228552\pi$
$223$	−2.88502	−	4.99700i	−0.193195	−	0.334624i	−0.946307	+	0.323268i	$0.895218\pi$
$224$	0.955663	−	2.46713i	0.0638529	−	0.164842i
$225$		0			0
$226$	1.50417	+	2.60530i	0.100056	+	0.173302i
$227$	8.49229	+	14.7091i	0.563653	+	0.976276i	0.997174	+	0.0751319i	$0.0239378\pi$
$227$	8.49229	+	14.7091i	0.563653	+	0.976276i	−0.433521	+	0.901144i	$0.642729\pi$
$228$		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
$236$	−1.24028	+	2.14823i	−0.0807355	+	0.139838i
$237$		0			0
$238$	−7.15185	−	8.88694i	−0.463585	−	0.576055i
$239$	−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
$241$	−5.37945	−	9.31748i	−0.346521	−	0.600192i	0.639108	−	0.769117i	$-0.279304\pi$
$241$	−5.37945	−	9.31748i	−0.346521	−	0.600192i	−0.985629	+	0.168925i	$0.945970\pi$
$242$	−5.24412	+	9.08307i	−0.337104	+	0.583882i
$243$		0			0
$244$	−4.31156	−	7.46783i	−0.276019	−	0.478079i
$245$	−12.3322	+	3.92419i	−0.787878	+	0.250707i
$246$		0			0
$247$	19.3520	−	15.4946i	1.23134	−	0.985898i
$248$	−1.11104	+	1.92438i	−0.0705513	+	0.122198i
$249$		0			0
$250$	6.08435	−	10.5384i	0.384808	−	0.666507i
$251$	11.8267	−	20.4844i	0.746492	−	1.29296i	−0.203002	−	0.979178i	$-0.565070\pi$
$251$	11.8267	−	20.4844i	0.746492	−	1.29296i	0.949494	−	0.313784i	$-0.101597\pi$
$252$		0			0
$253$	2.56119	−	4.43611i	0.161021	−	0.278896i
$254$	−15.1671			−0.951669
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.59702	+	16.6225i	−0.598646	+	1.03689i	0.394375	+	0.918949i	$0.370961\pi$
$257$	−9.59702	+	16.6225i	−0.598646	+	1.03689i	−0.993021	+	0.117936i	$0.962372\pi$
$258$		0			0
$259$	5.57764	−	0.866025i	0.346578	−	0.0538122i
$260$	1.00637	+	6.58951i	0.0624122	+	0.408664i
$261$		0			0
$262$	−19.3889			−1.19785
$263$	−10.9913			−0.677755			−0.338878	−	0.940830i	$-0.610047\pi$
$263$	−10.9913			−0.677755			−0.338878	+	0.940830i	$0.610047\pi$
$264$		0			0
$265$	−14.0562			−0.863469
$266$	17.9761	−	2.79110i	1.10218	−	0.171133i
$267$		0			0
$268$	6.96322	+	12.0606i	0.425346	+	0.736721i
$269$	8.25877	+	14.3046i	0.503546	+	0.872168i	0.999992	+	0.00409959i	$0.00130494\pi$
$269$	8.25877	+	14.3046i	0.503546	+	0.872168i	−0.496445	+	0.868068i	$0.665362\pi$
$270$		0			0
$271$	9.09528	−	15.7535i	0.552499	−	0.956956i	−0.445594	−	0.895235i	$-0.647008\pi$
$271$	9.09528	−	15.7535i	0.552499	−	0.956956i	0.998093	−	0.0617213i	$-0.0196590\pi$
$272$	−4.31156			−0.261426
$273$		0			0
$274$	−4.74829			−0.286854
$275$	−0.565856	+	0.980091i	−0.0341224	+	0.0591017i
$276$		0			0
$277$	−8.24469	−	14.2802i	−0.495376	−	0.858016i	0.504610	−	0.863347i	$-0.331636\pi$
$277$	−8.24469	−	14.2802i	−0.495376	−	0.858016i	−0.999986	+	0.00533162i	$0.998303\pi$
$278$	7.69027	+	13.3199i	0.461232	+	0.798877i
$279$		0			0
$280$	−1.76682	+	4.56120i	−0.105588	+	0.272584i
$281$	−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
$283$	−9.15675			−0.544313			−0.272156	−	0.962253i	$-0.587737\pi$
$283$	−9.15675			−0.544313			−0.272156	+	0.962253i	$0.587737\pi$
$284$	15.0175			0.891124
$285$		0			0
$286$	−0.389409	−	2.54978i	−0.0230262	−	0.150772i
$287$	−4.26490	+	11.0102i	−0.251749	+	0.649912i
$288$		0			0
$289$	−0.794759	+	1.37656i	−0.0467505	+	0.0809742i
$290$	8.57466	+	14.8517i	0.503521	+	0.872124i
$291$		0			0
$292$	1.97983			0.115861
$293$	−5.93488	+	10.2795i	−0.346719	+	0.600536i	−0.985665	−	0.168717i	$-0.946038\pi$
$293$	−5.93488	+	10.2795i	−0.346719	+	0.600536i	0.638945	+	0.769252i	$0.279371\pi$
$294$		0			0
$295$	2.29302	−	3.97163i	0.133505	−	0.231237i
$296$	1.06671	−	1.84759i	0.0620010	−	0.107389i
$297$		0			0
$298$	5.82384	−	10.0872i	0.337366	−	0.584335i
$299$	−3.89765	−	25.5211i	−0.225407	−	1.47592i
$300$		0			0
$301$	0.512281	−	0.0795406i	0.0295274	−	0.00458464i
$302$	4.09544	+	7.09351i	0.235666	+	0.408186i
$303$		0			0
$304$	3.43786	−	5.95456i	0.197175	−	0.341517i
$305$	7.97117	+	13.8065i	0.456428	+	0.790556i
$306$		0			0
$307$	−28.0679			−1.60192			−0.800959	−	0.598719i	$-0.795677\pi$
$307$	−28.0679			−1.60192			−0.800959	+	0.598719i	$0.795677\pi$
$308$	0.683663	−	1.76493i	0.0389553	−	0.100566i
$309$		0			0
$310$	2.05409	−	3.55778i	0.116664	−	0.202068i
$311$	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
$319$	−3.31792	−	5.74681i	−0.185768	−	0.321760i
$320$	0.924396	+	1.60110i	0.0516753	+	0.0895042i
$321$		0			0
$322$	6.84288	−	17.6655i	0.381339	−	0.984459i
$323$	−14.8225	−	25.6734i	−0.824748	−	1.42851i
$324$		0			0
$325$	0.861126	+	5.63850i	0.0477667	+	0.312768i
$326$	9.01923	−	15.6218i	0.499529	−	0.865209i
$327$		0			0
$328$	2.23138	+	3.86487i	0.123207	+	0.213402i
$329$	−8.80266	+	22.7248i	−0.485306	+	1.25286i
$330$		0			0
$331$	24.0394			1.32132			0.660661	−	0.750684i	$-0.270276\pi$
$331$	24.0394			1.32132			0.660661	+	0.750684i	$0.270276\pi$
$332$	−4.85769	−	8.41377i	−0.266600	−	0.461765i
$333$		0			0
$334$	−7.73872			−0.423444
$335$	−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	$0.519253\pi$
$338$	−9.56412	−	8.80498i	−0.520220	−	0.478928i
$339$		0			0
$340$	7.97117			0.432297
$341$	−0.794819	+	1.37667i	−0.0430418	+	0.0745507i
$342$		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
$347$	−1.00948	−	1.74847i	−0.0541916	−	0.0938625i	0.837657	−	0.546197i	$-0.183925\pi$
$347$	−1.00948	−	1.74847i	−0.0541916	−	0.0938625i	−0.891849	+	0.452334i	$0.850591\pi$
$348$		0			0
$349$	−16.8191	−	29.1316i	−0.900306	−	1.55938i	−0.827097	−	0.562060i	$-0.810009\pi$
$349$	−16.8191	−	29.1316i	−0.900306	−	1.55938i	−0.0732096	−	0.997317i	$-0.523324\pi$
$350$	−1.51183	+	3.90292i	−0.0808107	+	0.208620i
$351$		0			0
$352$	−0.357690	−	0.619538i	−0.0190650	−	0.0330215i
$353$	−23.2777			−1.23894			−0.619472	−	0.785018i	$-0.712653\pi$
$353$	−23.2777			−1.23894			−0.619472	+	0.785018i	$0.712653\pi$
$354$		0			0
$355$	−27.7642			−1.47357
$356$	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
$361$	28.2756			1.48819
$362$	−1.24862	+	2.16268i	−0.0656262	+	0.113668i
$363$		0			0
$364$	−2.86997	−	9.09743i	−0.150427	−	0.476835i
$365$	−3.66029			−0.191588
$366$		0			0
$367$	4.88788			0.255145			0.127573	−	0.991829i	$-0.459281\pi$
$367$	4.88788			0.255145			0.127573	+	0.991829i	$0.459281\pi$
$368$	−3.58017	−	6.20104i	−0.186629	−	0.323252i
$369$		0			0
$370$	−1.97212	+	3.41580i	−0.102525	+	0.177579i
$371$	19.8773	−	3.08630i	1.03198	−	0.160233i
$372$		0			0
$373$	−15.3673			−0.795690			−0.397845	−	0.917453i	$-0.630242\pi$
$373$	−15.3673			−0.795690			−0.397845	+	0.917453i	$0.630242\pi$
$374$	−3.08441			−0.159491
$375$		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	0.998063	−	0.0622101i	$-0.0198149\pi$
$379$	8.66626	+	15.0104i	0.445156	+	0.771033i	−0.552907	+	0.833243i	$0.686482\pi$
$380$	−6.35589	+	11.0087i	−0.326050	+	0.564736i
$381$		0			0
$382$	2.66349	−	4.61330i	0.136276	−	0.236037i
$383$	11.9926			0.612791			0.306396	−	0.951904i	$-0.400877\pi$
$383$	11.9926			0.612791			0.306396	+	0.951904i	$0.400877\pi$
$384$		0			0
$385$	−1.26395	+	3.26300i	−0.0644169	+	0.166298i
$386$	4.86186	−	8.42099i	0.247462	−	0.428617i
$387$		0			0
$388$	−2.78388			−0.141330
$389$	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
$392$	1.49702	−	6.83805i	0.0756107	−	0.345374i
$393$		0			0
$394$	6.17186			0.310934
$395$	−13.6354	+	23.6173i	−0.686074	+	1.18831i
$396$		0			0
$397$	14.0590			0.705603			0.352802	−	0.935698i	$-0.385229\pi$
$397$	14.0590			0.705603			0.352802	+	0.935698i	$0.385229\pi$
$398$	−5.41454			−0.271406
$399$		0			0
$400$	0.790985	+	1.37003i	0.0395493	+	0.0685013i
$401$	2.06536	−	3.57731i	0.103139	−	0.178642i	−0.809837	−	0.586655i	$-0.800445\pi$
$401$	2.06536	−	3.57731i	0.103139	−	0.178642i	0.912976	+	0.408012i	$0.133778\pi$
$402$		0			0
$403$	1.20956	+	7.92001i	0.0602527	+	0.394524i
$404$	2.67775	+	4.63800i	0.133223	+	0.230749i
$405$		0			0
$406$	−15.3866	−	19.1195i	−0.763625	−	0.948886i
$407$	0.763101	−	1.32173i	0.0378255	−	0.0655157i
$408$		0			0
$409$	2.60745	+	4.51623i	0.128930	+	0.223313i	0.923262	−	0.384170i	$-0.125512\pi$
$409$	2.60745	+	4.51623i	0.128930	+	0.223313i	−0.794332	+	0.607484i	$0.792179\pi$
$410$	−4.12536	−	7.14533i	−0.203737	−	0.352883i
$411$		0			0
$412$	3.26429	−	5.65391i	0.160820	−	0.278548i
$413$	−2.37058	+	6.11986i	−0.116649	+	0.301139i
$414$		0			0
$415$	8.98086	+	15.5553i	0.440853	+	0.763580i
$416$	−3.35888	−	1.31070i	−0.164683	−	0.0642625i
$417$		0			0
$418$	2.45938	−	4.25978i	0.120292	−	0.208352i
$419$	−3.69624	−	6.40207i	−0.180573	−	0.312762i	0.761503	−	0.648162i	$-0.224462\pi$
$419$	−3.69624	−	6.40207i	−0.180573	−	0.312762i	−0.942076	+	0.335400i	$0.891129\pi$
$420$		0			0
$421$	4.67144			0.227672			0.113836	−	0.993500i	$-0.463686\pi$
$421$	4.67144			0.227672			0.113836	+	0.993500i	$0.463686\pi$
$422$	27.2733			1.32764
$423$		0			0
$424$	3.80147	−	6.58434i	0.184616	−	0.319764i
$425$	6.82076			0.330855
$426$		0			0
$427$	−14.3037	−	17.7739i	−0.692204	−	0.860138i
$428$	4.61994			0.223313
$429$		0			0
$430$	−0.181130	+	0.313726i	−0.00873486	+	0.0151292i
$431$	22.0178			1.06056			0.530280	−	0.847823i	$-0.322087\pi$
$431$	22.0178			1.06056			0.530280	+	0.847823i	$0.322087\pi$
$432$		0			0
$433$	−12.5366	+	21.7141i	−0.602472	+	1.04351i	0.389973	+	0.920826i	$0.372484\pi$
$433$	−12.5366	+	21.7141i	−0.602472	+	1.04351i	−0.992446	+	0.122686i	$0.960849\pi$
$434$	−2.12356	+	5.48216i	−0.101934	+	0.263152i
$435$		0			0
$436$	−9.90187			−0.474214
$437$	24.6163	−	42.6367i	1.17756	−	2.03959i
$438$		0			0
$439$	6.97465	−	12.0804i	0.332882	−	0.576568i	−0.650194	−	0.759768i	$-0.725312\pi$
$439$	6.97465	−	12.0804i	0.332882	−	0.576568i	0.983076	+	0.183200i	$0.0586457\pi$
$440$	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
$445$	−8.26323			−0.391715
$446$	−5.77004			−0.273219
$447$		0			0
$448$	−1.65876	−	2.06119i	−0.0783691	−	0.0973821i
$449$	−7.51094	+	13.0093i	−0.354463	+	0.613948i	−0.987026	−	0.160561i	$-0.948670\pi$
$449$	−7.51094	+	13.0093i	−0.354463	+	0.613948i	0.632563	+	0.774509i	$0.282003\pi$
$450$		0			0
$451$	1.59629	+	2.76485i	0.0751663	+	0.130192i
$452$	3.00834			0.141501
$453$		0			0
$454$	16.9846			0.797126
$455$	5.30598	+	16.8193i	0.248748	+	0.788499i
$456$		0			0
$457$	5.98236	−	10.3618i	0.279843	−	0.484702i	−0.691503	−	0.722374i	$-0.743051\pi$
$457$	5.98236	−	10.3618i	0.279843	−	0.484702i	0.971346	+	0.237672i	$0.0763843\pi$
$458$	0.920781			0.0430253
$459$		0			0
$460$	6.61899	+	11.4644i	0.308612	+	0.534532i
$461$	−5.35595	+	9.27677i	−0.249451	+	0.432062i	−0.963374	−	0.268163i	$-0.913584\pi$
$461$	−5.35595	+	9.27677i	−0.249451	+	0.432062i	0.713922	+	0.700225i	$0.246917\pi$
$462$		0			0
$463$	−13.5305			−0.628814			−0.314407	−	0.949288i	$-0.601806\pi$
$463$	−13.5305			−0.628814			−0.314407	+	0.949288i	$0.601806\pi$
$464$	−9.27596			−0.430626
$465$		0			0
$466$	5.00565			0.231882
$467$	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
$472$	1.24028	+	2.14823i	0.0570886	+	0.0988803i
$473$	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
$478$	−6.91196	+	11.9719i	−0.316146	+	0.547580i
$479$	11.5852			0.529343			0.264672	−	0.964339i	$-0.414736\pi$
$479$	11.5852			0.529343			0.264672	+	0.964339i	$0.414736\pi$
$480$		0			0
$481$	−1.16130	−	7.60395i	−0.0529505	−	0.346710i
$482$	−10.7589			−0.490054
$483$		0			0
$484$	5.24412	+	9.08307i	0.238369	+	0.412867i
$485$	5.14682			0.233705
$486$		0			0
$487$	4.24168	+	7.34681i	0.192209	+	0.332916i	0.945982	−	0.324219i	$-0.105102\pi$
$487$	4.24168	+	7.34681i	0.192209	+	0.332916i	−0.753773	+	0.657135i	$0.771768\pi$
$488$	−8.62311			−0.390350
$489$		0			0
$490$	−2.76767	+	12.6421i	−0.125031	+	0.571113i
$491$	14.8606	+	25.7394i	0.670650	+	1.16160i	0.977720	+	0.209914i	$0.0673183\pi$
$491$	14.8606	+	25.7394i	0.670650	+	1.16160i	−0.307069	+	0.951687i	$0.599348\pi$
$492$		0			0
$493$	−19.9969	+	34.6357i	−0.900616	+	1.55991i
$494$	−3.74272	−	24.5066i	−0.168393	−	1.10261i
$495$		0			0
$496$	1.11104	+	1.92438i	0.0498873	+	0.0864073i
$497$	39.2621	−	6.09612i	1.76114	−	0.273448i
$498$		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	$0.539970\pi$
$500$	−6.08435	−	10.5384i	−0.272100	−	0.471291i
$501$		0			0
$502$	−11.8267	−	20.4844i	−0.527850	−	0.914263i
$503$	−13.5658	+	23.4966i	−0.604867	+	1.04766i	0.387205	+	0.921994i	$0.373440\pi$
$503$	−13.5658	+	23.4966i	−0.604867	+	1.04766i	−0.992072	+	0.125667i	$0.959893\pi$
$504$		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
$509$	3.60835	−	6.24985i	0.159937	−	0.277020i	−0.774909	−	0.632073i	$-0.782204\pi$
$509$	3.60835	−	6.24985i	0.159937	−	0.277020i	0.934846	+	0.355054i	$0.115537\pi$
$510$		0			0
$511$	5.17611	−	0.803681i	0.228978	−	0.0355527i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	9.59702	+	16.6225i	0.423307	+	0.733189i
$515$	−6.03499	+	10.4529i	−0.265933	+	0.460610i
$516$		0			0
$517$	3.29471	+	5.70660i	0.144901	+	0.250976i
$518$	2.03882	−	5.26339i	0.0895806	−	0.231260i
$519$		0			0
$520$	6.20986	+	2.42321i	0.272321	+	0.106265i
$521$	−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
$523$	19.8613	−	34.4008i	0.868475	−	1.50424i	0.00491926	−	0.999988i	$-0.498434\pi$
$523$	19.8613	−	34.4008i	0.868475	−	1.50424i	0.863555	−	0.504254i	$-0.168233\pi$
$524$	−9.69444	+	16.7913i	−0.423504	+	0.733530i
$525$		0			0
$526$	−5.49567	+	9.51878i	−0.239623	+	0.415039i
$527$	9.58065			0.417339
$528$		0			0
$529$	−14.1353	−	24.4830i	−0.614578	−	1.06448i
$530$	−7.02812	+	12.1731i	−0.305282	+	0.528764i
$531$		0			0
$532$	6.57088	−	16.9633i	0.284884	−	0.735452i
$533$	14.9899	+	5.84936i	0.649284	+	0.253364i
$534$		0			0
$535$	−8.54131			−0.369273
$536$	13.9264			0.601530
$537$		0			0
$538$	16.5175			0.712122
$539$	1.07094	−	4.89181i	0.0461285	−	0.210705i
$540$		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	$0.559476\pi$
$542$	−9.09528	−	15.7535i	−0.390676	−	0.676670i
$543$		0			0
$544$	−2.15578	+	3.73392i	−0.0924282	+	0.160090i
$545$	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	$0.794773\pi$
$548$	−2.37414	+	4.11214i	−0.101418	+	0.175662i
$549$		0			0
$550$	0.565856	+	0.980091i	0.0241282	+	0.0417912i
$551$	−31.8895	−	55.2342i	−1.35854	−	2.35306i
$552$		0			0
$553$	14.0967	−	36.3917i	0.599451	−	1.54753i
$554$	−16.4894			−0.700567
$555$		0			0
$556$	15.3805			0.652280
$557$	−33.2700			−1.40969			−0.704847	−	0.709359i	$-0.748985\pi$
$557$	−33.2700			−1.40969			−0.704847	+	0.709359i	$0.748985\pi$
$558$		0			0
$559$	−0.106660	−	0.698389i	−0.00451123	−	0.0295387i
$560$	3.06671	+	3.81071i	0.129592	+	0.161032i
$561$		0			0
$562$	−7.63838	+	13.2301i	−0.322206	+	0.558076i
$563$	7.32051	+	12.6795i	0.308523	+	0.534377i	0.978039	−	0.208420i	$-0.0668321\pi$
$563$	7.32051	+	12.6795i	0.308523	+	0.534377i	−0.669517	+	0.742797i	$0.733499\pi$
$564$		0			0
$565$	−5.56180			−0.233987
$566$	−4.57838	+	7.92998i	−0.192444	+	0.333322i
$567$		0			0
$568$	7.50874	−	13.0055i	0.315060	−	0.545700i
$569$	17.4098	−	30.1547i	0.729858	−	1.26415i	−0.227085	−	0.973875i	$-0.572920\pi$
$569$	17.4098	−	30.1547i	0.729858	−	1.26415i	0.956943	−	0.290276i	$-0.0937470\pi$
$570$		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	$-0.0924199\pi$
$572$	−2.40288	−	0.937651i	−0.100469	−	0.0392052i
$573$		0			0
$574$	7.40267	+	9.19861i	0.308981	+	0.383943i
$575$	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	$0.321077\pi$
$578$	0.794759	+	1.37656i	0.0330576	+	0.0572574i
$579$		0			0
$580$	17.1493			0.712086
$581$	−16.1155	−	20.0253i	−0.668584	−	0.830788i
$582$		0			0
$583$	2.71950	−	4.71031i	0.112630	−	0.195081i
$584$	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	0.978936	−	0.204165i	$-0.0654480\pi$
$587$	7.57505	+	13.1204i	0.312656	+	0.541536i	−0.666280	+	0.745701i	$0.732115\pi$
$588$		0			0
$589$	−7.63923	+	13.2315i	−0.314769	+	0.545196i
$590$	−2.29302	−	3.97163i	−0.0944022	−	0.163509i
$591$		0			0
$592$	−1.06671	−	1.84759i	−0.0438413	−	0.0759354i
$593$	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
$595$	20.8400	−	3.23577i	0.854357	−	0.132654i
$596$	−5.82384	−	10.0872i	−0.238554	−	0.413187i
$597$		0			0
$598$	−24.0507	−	9.38508i	−0.983508	−	0.383785i
$599$	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	0.946848	−	0.321681i	$-0.104248\pi$
$601$	4.77657	+	8.27326i	0.194840	+	0.337473i	−0.752008	+	0.659154i	$0.770914\pi$
$602$	0.187257	−	0.483419i	0.00763201	−	0.0197027i
$603$		0			0
$604$	8.19088			0.333282
$605$	−9.69527	−	16.7927i	−0.394169	−	0.682721i
$606$		0			0
$607$	21.5238			0.873625			0.436813	−	0.899553i	$-0.356107\pi$
$607$	21.5238			0.873625			0.436813	+	0.899553i	$0.356107\pi$
$608$	−3.43786	−	5.95456i	−0.139424	−	0.241489i
$609$		0			0
$610$	15.9423			0.645486
$611$	30.9388	+	12.0729i	1.25165	+	0.488419i
$612$		0			0
$613$	−36.9890			−1.49397			−0.746985	−	0.664841i	$-0.768499\pi$
$613$	−36.9890			−1.49397			−0.746985	+	0.664841i	$0.768499\pi$
$614$	−14.0339	+	24.3075i	−0.566363	+	0.980970i
$615$		0			0
$616$	−1.18665	−	1.47454i	−0.0478114	−	0.0594108i
$617$	−1.88766	+	3.26953i	−0.0759945	+	0.131626i	−0.901518	−	0.432741i	$-0.857546\pi$
$617$	−1.88766	+	3.26953i	−0.0759945	+	0.131626i	0.825524	+	0.564367i	$0.190880\pi$
$618$		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	$0.976246\pi$
$620$	−2.05409	−	3.55778i	−0.0824941	−	0.142884i
$621$		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
$626$	−17.6441			−0.705199
$627$		0			0
$628$	−22.8707			−0.912639
$629$	−9.19832			−0.366761
$630$		0			0
$631$	6.85038	−	11.8652i	0.272709	−	0.472346i	−0.696845	−	0.717221i	$-0.745414\pi$
$631$	6.85038	−	11.8652i	0.272709	−	0.472346i	0.969555	+	0.244875i	$0.0787470\pi$
$632$	−7.37533	−	12.7744i	−0.293375	−	0.508140i
$633$		0			0
$634$	29.7420			1.18121
$635$	14.0204	−	24.2841i	0.556383	−	0.963684i
$636$		0			0
$637$	−11.1963	−	22.6195i	−0.443613	−	0.896218i
$638$	−6.63585			−0.262716
$639$		0			0
$640$	1.84879			0.0730799
$641$	−3.20167	−	5.54546i	−0.126458	−	0.219032i	0.795844	−	0.605502i	$-0.207028\pi$
$641$	−3.20167	−	5.54546i	−0.126458	−	0.219032i	−0.922302	+	0.386470i	$0.873694\pi$
$642$		0			0
$643$	9.93369	−	17.2057i	0.391747	−	0.678525i	−0.600933	−	0.799299i	$-0.705204\pi$
$643$	9.93369	−	17.2057i	0.391747	−	0.678525i	0.992680	+	0.120774i	$0.0385377\pi$
$644$	−11.8773	−	14.7588i	−0.468032	−	0.581580i
$645$		0			0
$646$	−29.6451			−1.16637
$647$	−30.5184			−1.19980			−0.599902	−	0.800074i	$-0.704794\pi$
$647$	−30.5184			−1.19980			−0.599902	+	0.800074i	$0.704794\pi$
$648$		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
$653$	1.82706	−	3.16456i	0.0714984	−	0.123839i	−0.828060	−	0.560640i	$-0.810555\pi$
$653$	1.82706	−	3.16456i	0.0714984	−	0.123839i	0.899558	+	0.436801i	$0.143889\pi$
$654$		0			0
$655$	17.9230	−	31.0435i	0.700309	−	1.21297i
$656$	4.46276			0.174242
$657$		0			0
$658$	15.2789	+	18.9857i	0.595635	+	0.740141i
$659$	−4.12332	+	7.14181i	−0.160622	+	0.278205i	−0.935092	−	0.354405i	$-0.884683\pi$
$659$	−4.12332	+	7.14181i	−0.160622	+	0.278205i	0.774470	+	0.632611i	$0.218017\pi$
$660$		0			0
$661$	46.1131			1.79359			0.896796	−	0.442445i	$-0.145889\pi$
$661$	46.1131			1.79359			0.896796	+	0.442445i	$0.145889\pi$
$662$	12.0197	−	20.8187i	0.467158	−	0.809141i
$663$		0			0
$664$	−9.71538			−0.377030
$665$	−12.1482	+	31.3616i	−0.471086	+	1.21615i
$666$		0			0
$667$	−66.4191			−2.57176
$668$	−3.86936	+	6.70193i	−0.149710	+	0.259306i
$669$		0			0
$670$	−25.7471			−0.994696
$671$	−6.16881			−0.238144
$672$		0			0
$673$	−3.98669	−	6.90515i	−0.153676	−	0.266174i	0.778900	−	0.627148i	$-0.215778\pi$
$673$	−3.98669	−	6.90515i	−0.153676	−	0.266174i	−0.932576	+	0.360974i	$0.882444\pi$
$674$	−1.10970	+	1.92205i	−0.0427439	+	0.0740347i
$675$		0			0
$676$	−12.4074	+	3.88028i	−0.477207	+	0.149242i
$677$	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
$679$	−7.27825	+	1.13007i	−0.279314	+	0.0433683i
$680$	3.98558	−	6.90323i	0.152840	−	0.264727i
$681$		0			0
$682$	0.794819	+	1.37667i	0.0304352	+	0.0527153i
$683$	17.6333	+	30.5417i	0.674718	+	1.16865i	0.976551	+	0.215285i	$0.0690680\pi$
$683$	17.6333	+	30.5417i	0.674718	+	1.16865i	−0.301833	+	0.953361i	$0.597599\pi$
$684$		0			0
$685$	4.38930	−	7.60248i	0.167706	−	0.290476i
$686$	1.13803	−	18.4853i	0.0434503	−	0.705771i
$687$		0			0
$688$	−0.0979721	−	0.169693i	−0.00373515	−	0.00646947i
$689$	−4.13856	−	27.0986i	−0.157667	−	1.03237i
$690$		0			0
$691$	−20.3538	+	35.2537i	−0.774293	+	1.34112i	0.160897	+	0.986971i	$0.448561\pi$
$691$	−20.3538	+	35.2537i	−0.774293	+	1.34112i	−0.935191	+	0.354144i	$0.884772\pi$
$692$	6.01212	+	10.4133i	0.228547	+	0.395854i
$693$		0			0
$694$	−2.01895			−0.0766384
$695$	−28.4354			−1.07862
$696$		0			0
$697$	9.62073	−	16.6636i	0.364411	−	0.631179i
$698$	−33.6382			−1.27323
$699$		0			0
$700$	2.62411	+	3.26074i	0.0991822	+	0.123245i
$701$	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
$704$	−0.715381			−0.0269619
$705$		0			0
$706$	−11.6388	+	20.1590i	−0.438033	+	0.758696i
$707$	8.88349	+	11.0387i	0.334098	+	0.415153i
$708$		0			0
$709$	−3.35360			−0.125947			−0.0629736	−	0.998015i	$-0.520058\pi$
$709$	−3.35360			−0.125947			−0.0629736	+	0.998015i	$0.520058\pi$
$710$	−13.8821	+	24.0445i	−0.520986	+	0.902374i
$711$		0			0
$712$	2.23476	−	3.87073i	0.0837513	−	0.145062i
$713$	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
$718$	−10.8979			−0.406707
$719$	39.1082			1.45849			0.729245	−	0.684253i	$-0.239871\pi$
$719$	39.1082			1.45849			0.729245	+	0.684253i	$0.239871\pi$
$720$		0			0
$721$	6.23912	−	16.1068i	0.232357	−	0.599849i
$722$	14.1378	−	24.4874i	0.526155	−	0.911328i
$723$		0			0
$724$	1.24862	+	2.16268i	0.0464048	+	0.0803754i
$725$	14.6743			0.544990
$726$		0			0
$727$	−3.65073			−0.135398			−0.0676990	−	0.997706i	$-0.521566\pi$
$727$	−3.65073			−0.135398			−0.0676990	+	0.997706i	$0.521566\pi$
$728$	−9.31359	−	2.06325i	−0.345185	−	0.0764690i
$729$		0			0
$730$	−1.83014	+	3.16990i	−0.0677367	+	0.117323i
$731$	−0.844824			−0.0312470
$732$		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
$737$	9.96270			0.366981
$738$		0			0
$739$	10.2301			0.376321			0.188160	−	0.982138i	$-0.439748\pi$
$739$	10.2301			0.376321			0.188160	+	0.982138i	$0.439748\pi$
$740$	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	−0.987915	−	0.154994i	$-0.950464\pi$
$743$	−17.1231	−	29.6581i	−0.628186	−	1.08805i	0.359729	−	0.933057i	$-0.382869\pi$
$744$		0			0
$745$	10.7671	+	18.6491i	0.394475	+	0.683250i
$746$	−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
$751$	−5.89627	+	10.2126i	−0.215158	+	0.372665i	−0.953321	−	0.301957i	$-0.902360\pi$
$751$	−5.89627	+	10.2126i	−0.215158	+	0.372665i	0.738163	+	0.674622i	$0.235693\pi$
$752$	9.21105			0.335892
$753$		0			0
$754$	−26.1076	+	20.9036i	−0.950781	+	0.761264i
$755$	−15.1432			−0.551118
$756$		0			0
$757$	24.1278	+	41.7906i	0.876940	+	1.51890i	0.854682	+	0.519152i	$0.173752\pi$
$757$	24.1278	+	41.7906i	0.876940	+	1.51890i	0.0222575	+	0.999752i	$0.492915\pi$
$758$	17.3325			0.629546
$759$		0			0
$760$	6.35589	+	11.0087i	0.230552	+	0.399329i
$761$	−12.2380			−0.443627			−0.221813	−	0.975089i	$-0.571198\pi$
$761$	−12.2380			−0.443627			−0.221813	+	0.975089i	$0.571198\pi$
$762$		0			0
$763$	−25.8877	+	4.01951i	−0.937197	+	0.145516i
$764$	−2.66349	−	4.61330i	−0.0963617	−	0.166903i
$765$		0			0
$766$	5.99628	−	10.3859i	0.216654	−	0.375256i
$767$	8.33191	+	3.25128i	0.300848	+	0.117397i
$768$		0			0
$769$	0.357690	+	0.619538i	0.0128986	+	0.0223411i	0.872403	−	0.488788i	$-0.162561\pi$
$769$	0.357690	+	0.619538i	0.0128986	+	0.0223411i	−0.859504	+	0.511129i	$0.829227\pi$
$770$	2.19386	+	2.72611i	0.0790613	+	0.0982422i
$771$		0			0
$772$	−4.86186	−	8.42099i	−0.174982	−	0.303078i
$773$	2.71533	+	4.70309i	0.0976636	+	0.169158i	0.910717	−	0.413031i	$-0.135530\pi$
$773$	2.71533	+	4.70309i	0.0976636	+	0.169158i	−0.813054	+	0.582189i	$0.802196\pi$
$774$		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
$782$	−15.4361	+	26.7361i	−0.551995	+	0.956083i
$783$		0			0
$784$	−5.17342	−	4.71548i	−0.184765	−	0.168410i
$785$	42.2831			1.50915
$786$		0			0
$787$	2.58513	+	4.47758i	0.0921501	+	0.159609i	0.908416	−	0.418068i	$-0.137293\pi$
$787$	2.58513	+	4.47758i	0.0921501	+	0.159609i	−0.816266	+	0.577677i	$0.803959\pi$
$788$	3.08593	−	5.34499i	0.109932	−	0.190407i
$789$		0			0
$790$	13.6354	+	23.6173i	0.485127	+	0.840265i
$791$	7.86509	−	1.22119i	0.279650	−	0.0434205i
$792$		0			0
$793$	−24.2701	+	19.4324i	−0.861856	+	0.690064i
$794$	7.02952	−	12.1755i	0.249468	−	0.432092i
$795$		0			0
$796$	−2.70727	+	4.68913i	−0.0959567	+	0.166202i
$797$	−3.24073	+	5.61311i	−0.114793	+	0.198827i	−0.917697	−	0.397281i	$-0.869954\pi$
$797$	−3.24073	+	5.61311i	−0.114793	+	0.198827i	0.802904	+	0.596108i	$0.203287\pi$
$798$		0			0
$799$	19.8570	−	34.3933i	0.702490	−	1.21675i
$800$	1.58197			0.0559311
$801$		0			0
$802$	−2.06536	−	3.57731i	−0.0729304	−	0.126319i
$803$	0.708165	−	1.22658i	0.0249906	−	0.0432850i
$804$		0			0
$805$	21.9587	+	27.2860i	0.773942	+	0.961706i
$806$	7.46371	+	2.91249i	0.262898	+	0.102588i
$807$		0			0
$808$	5.35550			0.188406
$809$	−46.5817			−1.63773			−0.818863	−	0.573989i	$-0.805395\pi$
$809$	−46.5817			−1.63773			−0.818863	+	0.573989i	$0.805395\pi$
$810$		0			0
$811$	44.2321			1.55320			0.776600	−	0.629994i	$-0.216943\pi$
$811$	44.2321			1.55320			0.776600	+	0.629994i	$0.216943\pi$
$812$	−24.2513	+	3.76543i	−0.851054	+	0.132141i
$813$		0			0
$814$	−0.763101	−	1.32173i	−0.0267467	−	0.0463266i
$815$	16.6747	+	28.8814i	0.584088	+	1.01167i
$816$		0			0
$817$	0.673630	−	1.16676i	0.0235673	−	0.0408198i
$818$	5.21490			0.182335
$819$		0			0
$820$	−8.25072			−0.288128
$821$	−4.13283	+	7.15828i	−0.144237	+	0.249826i	−0.929088	−	0.369859i	$-0.879406\pi$
$821$	−4.13283	+	7.15828i	−0.144237	+	0.249826i	0.784851	+	0.619684i	$0.212739\pi$
$822$		0			0
$823$	25.6181	+	44.3718i	0.892989	+	1.54670i	0.836274	+	0.548312i	$0.184729\pi$
$823$	25.6181	+	44.3718i	0.892989	+	1.54670i	0.0567156	+	0.998390i	$0.481937\pi$
$824$	−3.26429	−	5.65391i	−0.113717	−	0.196963i
$825$		0			0
$826$	4.11466	+	5.11291i	0.143167	+	0.177901i
$827$	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
$829$	1.99519			0.0692957			0.0346479	−	0.999400i	$-0.488969\pi$
$829$	1.99519			0.0692957			0.0346479	+	0.999400i	$0.488969\pi$
$830$	17.9617			0.623460
$831$		0			0
$832$	−2.81454	+	2.25352i	−0.0975766	+	0.0781268i
$833$	−28.7600	+	9.15159i	−0.996473	+	0.317084i
$834$		0			0
$835$	7.15364	−	12.3905i	0.247562	−	0.428790i
$836$	−2.45938	−	4.25978i	−0.0850595	−	0.147327i
$837$		0			0
$838$	−7.39247			−0.255369
$839$	−11.0996	+	19.2251i	−0.383201	+	0.663724i	−0.991518	−	0.129971i	$-0.958512\pi$
$839$	−11.0996	+	19.2251i	−0.383201	+	0.663724i	0.608317	+	0.793694i	$0.291845\pi$
$840$		0			0
$841$	−28.5217	+	49.4011i	−0.983507	+	1.70348i
$842$	2.33572	−	4.04559i	0.0804943	−	0.139420i
$843$		0			0
$844$	13.6366	−	23.6193i	0.469392	−	0.813011i
$845$	22.9387	−	7.17383i	0.789115	−	0.246787i
$846$		0			0
$847$	17.3975	+	21.6182i	0.597784	+	0.742812i
$848$	−3.80147	−	6.58434i	−0.130543	−	0.226107i
$849$		0			0
$850$	3.41038	−	5.90695i	0.116975	−	0.202607i
$851$	−7.63798	−	13.2294i	−0.261827	−	0.453497i
$852$		0			0
$853$	−20.8901			−0.715262			−0.357631	−	0.933863i	$-0.616415\pi$
$853$	−20.8901			−0.715262			−0.357631	+	0.933863i	$0.616415\pi$
$854$	−22.5445	+	3.50042i	−0.771456	+	0.119782i
$855$		0			0
$856$	2.30997	−	4.00099i	0.0789532	−	0.136751i
$857$	−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
$865$	−11.1152	−	19.2520i	−0.377927	−	0.654588i
$866$	12.5366	+	21.7141i	0.426012	+	0.737875i
$867$		0			0
$868$	3.68591	+	4.58014i	0.125108	+	0.155460i
$869$	−5.27617	−	9.13860i	−0.178982	−	0.310006i
$870$		0			0
$871$	39.1965	−	31.3835i	1.32812	−	1.06339i
$872$	−4.95093	+	8.57527i	−0.167660	+	0.290395i
$873$		0			0
$874$	−24.6163	−	42.6367i	−0.832659	−	1.44221i
$875$	−20.1850	−	25.0820i	−0.682376	−	0.847926i
$876$		0			0
$877$	−31.2349			−1.05473			−0.527363	−	0.849640i	$-0.676819\pi$
$877$	−31.2349			−1.05473			−0.527363	+	0.849640i	$0.676819\pi$
$878$	−6.97465	−	12.0804i	−0.235383	−	0.407695i
$879$		0			0
$880$	1.32259			0.0445845
$881$	19.0177	+	32.9396i	0.640722	+	1.10976i	0.985272	+	0.170994i	$0.0546980\pi$
$881$	19.0177	+	32.9396i	0.640722	+	1.10976i	−0.344550	+	0.938768i	$0.611969\pi$
$882$		0			0
$883$	22.5813			0.759921			0.379961	−	0.925003i	$-0.375938\pi$
$883$	22.5813			0.759921			0.379961	+	0.925003i	$0.375938\pi$
$884$	2.34694	+	15.3674i	0.0789362	+	0.516860i
$885$		0			0
$886$	−3.38275			−0.113646
$887$	3.86823	−	6.69997i	0.129882	−	0.224963i	−0.793748	−	0.608246i	$-0.791873\pi$
$887$	3.86823	−	6.69997i	0.129882	−	0.224963i	0.923631	+	0.383283i	$0.125207\pi$
$888$		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
$893$	31.6663	+	54.8477i	1.05967	+	1.83541i
$894$		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
$899$	20.6120			0.687448
$900$		0			0
$901$	−32.7805			−1.09208
$902$	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
$907$	−40.6410			−1.34946			−0.674731	−	0.738064i	$-0.735740\pi$
$907$	−40.6410			−1.34946			−0.674731	+	0.738064i	$0.735740\pi$
$908$	8.49229	−	14.7091i	0.281826	−	0.488138i
$909$		0			0
$910$	17.2189	+	3.81451i	0.570801	+	0.126450i
$911$	−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
$913$	−6.95020			−0.230018
$914$	−5.98236	−	10.3618i	−0.197879	−	0.342736i
$915$		0			0
$916$	0.460390	−	0.797420i	0.0152117	−	0.0263475i
$917$	−18.5292	+	47.8348i	−0.611889	+	1.57964i
$918$		0			0
$919$	13.2539			0.437206			0.218603	−	0.975814i	$-0.429850\pi$
$919$	13.2539			0.437206			0.218603	+	0.975814i	$0.429850\pi$
$920$	13.2380			0.436444
$921$		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
$926$	−6.76524	+	11.7177i	−0.222319	+	0.385069i
$927$		0			0
$928$	−4.63798	+	8.03322i	−0.152249	+	0.263703i
$929$	24.6516			0.808794			0.404397	−	0.914584i	$-0.367481\pi$
$929$	24.6516			0.808794			0.404397	+	0.914584i	$0.367481\pi$
$930$		0			0
$931$	10.2931	−	47.0166i	0.337342	−	1.54091i
$932$	2.50283	−	4.33502i	0.0819828	−	0.141998i
$933$		0			0
$934$	27.9566			0.914769
$935$	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	$0.643544\pi$
$938$	36.4096	−	5.65322i	1.18882	−	0.184584i
$939$		0			0
$940$	−17.0293			−0.555435
$941$	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
$943$	31.9549			1.04060
$944$	2.48056			0.0807355
$945$		0			0
$946$	−0.0700874	−	0.121395i	−0.00227874	−	0.00394689i
$947$	2.75927	−	4.77919i	0.0896641	−	0.155303i	−0.817705	−	0.575637i	$-0.804754\pi$
$947$	2.75927	−	4.77919i	0.0896641	−	0.155303i	0.907369	+	0.420335i	$0.138087\pi$
$948$		0			0
$949$	−1.07769	−	7.05655i	−0.0349834	−	0.229065i
$950$	5.43860	+	9.41993i	0.176451	+	0.305623i
$951$		0			0
$952$	−4.12039	+	10.6372i	−0.133543	+	0.344752i
$953$	2.92091	−	5.05916i	0.0946175	−	0.163882i	−0.814831	−	0.579698i	$-0.803171\pi$
$953$	2.92091	−	5.05916i	0.0946175	−	0.163882i	0.909449	+	0.415816i	$0.136504\pi$
$954$		0			0
$955$	4.92424	+	8.52903i	0.159345	+	0.275993i
$956$	6.91196	+	11.9719i	0.223549	+	0.387198i
$957$		0			0
$958$	5.79262	−	10.0331i	0.187151	−	0.324155i
$959$	−4.53776	+	11.7146i	−0.146532	+	0.378285i
$960$		0			0
$961$	13.0312	+	22.5706i	0.420360	+	0.728085i
$962$	−7.16586	−	2.79627i	−0.231037	−	0.0901552i
$963$		0			0
$964$	−5.37945	+	9.31748i	−0.173260	+	0.300096i
$965$	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	$0.474457\pi$
$968$	10.4882			0.337104
$969$		0			0
$970$	2.57341	−	4.45728i	0.0826272	−	0.143115i
$971$	2.74480			0.0880848			0.0440424	−	0.999030i	$-0.485976\pi$
$971$	2.74480			0.0880848			0.0440424	+	0.999030i	$0.485976\pi$
$972$		0			0
$973$	40.2113	−	6.24349i	1.28911	−	0.200157i
$974$	8.48336			0.271824
$975$		0			0
$976$	−4.31156	+	7.46783i	−0.138010	+	0.239040i
$977$	16.3946			0.524509			0.262255	−	0.964999i	$-0.415534\pi$
$977$	16.3946			0.524509			0.262255	+	0.964999i	$0.415534\pi$
$978$		0			0
$979$	1.59871	−	2.76904i	0.0510949	−	0.0884990i
$980$	9.56457	+	8.71794i	0.305529	+	0.278484i
$981$		0			0
$982$	29.7212			0.948443
$983$	−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
$985$	−5.70524	+	9.88177i	−0.181784	+	0.314859i
$986$	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
$991$	20.0545			0.637051			0.318525	−	0.947914i	$-0.396812\pi$
$991$	20.0545			0.637051			0.318525	+	0.947914i	$0.396812\pi$
$992$	2.22209			0.0705513
$993$		0			0
$994$	14.3516	−	37.0500i	0.455207	−	1.17516i
$995$	5.00518	−	8.66922i	0.158675	−	0.274833i
$996$		0			0
$997$	21.7439	+	37.6615i	0.688635	+	1.19275i	0.972279	+	0.233822i	$0.0751232\pi$
$997$	21.7439	+	37.6615i	0.688635	+	1.19275i	−0.283644	+	0.958930i	$0.591543\pi$
$998$	35.5888			1.12654
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.1	✓	8	21.2	odd	6
546.2.j.c.529.1	yes	8	39.35	odd	6
546.2.k.c.373.1	yes	8	273.191	odd	6
546.2.k.c.445.1	yes	8	3.2	odd	2
1638.2.m.h.289.4		8	7.2	even	3
1638.2.m.h.1621.4		8	13.9	even	3
1638.2.p.h.919.4		8	91.9	even	3	inner
1638.2.p.h.991.4		8	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.p (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.924396 + 1.60110i) q^{5} +(-1.65876 - 2.06119i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.924396 + 1.60110i) q^{5} +(-1.65876 - 2.06119i) q^{7} -1.00000 q^{8} +1.84879 q^{10} -0.715381 q^{11} +(-2.81454 + 2.25352i) q^{13} +(-2.61442 + 0.405935i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.15578 + 3.73392i) q^{17} -6.87573 q^{19} +(0.924396 - 1.60110i) q^{20} +(-0.357690 + 0.619538i) q^{22} +(-3.58017 + 6.20104i) q^{23} +(0.790985 - 1.37003i) q^{25} +(0.544337 + 3.56422i) q^{26} +(-0.955663 + 2.46713i) q^{28} +(4.63798 + 8.03322i) q^{29} +(1.11104 - 1.92438i) q^{31} +(0.500000 + 0.866025i) q^{32} +4.31156 q^{34} +(1.76682 - 4.56120i) q^{35} +(-1.06671 + 1.84759i) q^{37} +(-3.43786 + 5.95456i) q^{38} +(-0.924396 - 1.60110i) q^{40} +(-2.23138 - 3.86487i) q^{41} +(-0.0979721 + 0.169693i) q^{43} +(0.357690 + 0.619538i) q^{44} +(3.58017 + 6.20104i) q^{46} +(-4.60553 - 7.97700i) q^{47} +(-1.49702 + 6.83805i) q^{49} +(-0.790985 - 1.37003i) q^{50} +(3.35888 + 1.31070i) q^{52} +(-3.80147 + 6.58434i) q^{53} +(-0.661295 - 1.14540i) q^{55} +(1.65876 + 2.06119i) q^{56} +9.27596 q^{58} +(-1.24028 - 2.14823i) q^{59} +8.62311 q^{61} +(-1.11104 - 1.92438i) q^{62} +1.00000 q^{64} +(-6.20986 - 2.42321i) q^{65} -13.9264 q^{67} +(2.15578 - 3.73392i) q^{68} +(-3.06671 - 3.81071i) q^{70} +(-7.50874 + 13.0055i) q^{71} +(-0.989914 + 1.71458i) q^{73} +(1.06671 + 1.84759i) q^{74} +(3.43786 + 5.95456i) q^{76} +(1.18665 + 1.47454i) q^{77} +(7.37533 + 12.7744i) q^{79} -1.84879 q^{80} -4.46276 q^{82} +9.71538 q^{83} +(-3.98558 + 6.90323i) q^{85} +(0.0979721 + 0.169693i) q^{86} +0.715381 q^{88} +(-2.23476 + 3.87073i) q^{89} +(9.31359 + 2.06325i) q^{91} +7.16035 q^{92} -9.21105 q^{94} +(-6.35589 - 11.0087i) q^{95} +(1.39194 - 2.41091i) q^{97} +(5.17342 + 4.71548i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} - 4 q^{10} + 8 q^{11} + 3 q^{13} - 3 q^{14} - 4 q^{16} + 2 q^{17} + 8 q^{19} - 2 q^{20} + 4 q^{22} - 4 q^{23} + 2 q^{25} + 12 q^{26} - 2 q^{29} + 14 q^{31} + 4 q^{32} + 4 q^{34} + 4 q^{35} - 6 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} + 4 q^{46} - 7 q^{47} - 7 q^{49} - 2 q^{50} + 9 q^{52} + q^{53} - 25 q^{55} + 3 q^{56} - 4 q^{58} - 16 q^{59} + 8 q^{61} - 14 q^{62} + 8 q^{64} - q^{65} - 38 q^{67} + 2 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} + 6 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} + 4 q^{80} - 24 q^{82} + 64 q^{83} + 15 q^{85} - 8 q^{88} + 11 q^{89} - 20 q^{91} + 8 q^{92} - 14 q^{94} - 28 q^{95} + 11 q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8 - 4 * q^10 + 8 * q^11 + 3 * q^13 - 3 * q^14 - 4 * q^16 + 2 * q^17 + 8 * q^19 - 2 * q^20 + 4 * q^22 - 4 * q^23 + 2 * q^25 + 12 * q^26 - 2 * q^29 + 14 * q^31 + 4 * q^32 + 4 * q^34 + 4 * q^35 - 6 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 + 4 * q^46 - 7 * q^47 - 7 * q^49 - 2 * q^50 + 9 * q^52 + q^53 - 25 * q^55 + 3 * q^56 - 4 * q^58 - 16 * q^59 + 8 * q^61 - 14 * q^62 + 8 * q^64 - q^65 - 38 * q^67 + 2 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 + 6 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 + 4 * q^80 - 24 * q^82 + 64 * q^83 + 15 * q^85 - 8 * q^88 + 11 * q^89 - 20 * q^91 + 8 * q^92 - 14 * q^94 - 28 * q^95 + 11 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more