LMFDB - Embedded newform 576.2.bb.e.529.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, degree $4$, not 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			529.16
Character	$\chi$	$=$	576.529
Dual form			576.2.bb.e.49.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64464 - 0.543291i) q^{3} +(-1.60558 - 0.430214i) q^{5} +(-3.62762 - 2.09441i) q^{7} +(2.40967 - 1.78703i) q^{9} +O(q^{10})$	\(q+(1.64464 - 0.543291i) q^{3} +(-1.60558 - 0.430214i) q^{5} +(-3.62762 - 2.09441i) q^{7} +(2.40967 - 1.78703i) q^{9} +(-1.24125 - 4.63241i) q^{11} +(-0.879738 + 3.28323i) q^{13} +(-2.87433 + 0.164751i) q^{15} -2.14142 q^{17} +(-1.03156 - 1.03156i) q^{19} +(-7.10399 - 1.47369i) q^{21} +(0.405884 - 0.234337i) q^{23} +(-1.93733 - 1.11852i) q^{25} +(2.99216 - 4.24818i) q^{27} +(6.55186 - 1.75557i) q^{29} +(-3.18054 - 5.50886i) q^{31} +(-4.55816 - 6.94428i) q^{33} +(4.92339 + 4.92339i) q^{35} +(-0.728237 + 0.728237i) q^{37} +(0.336896 + 5.87767i) q^{39} +(2.52351 - 1.45695i) q^{41} +(2.84802 + 10.6289i) q^{43} +(-4.63772 + 1.83255i) q^{45} +(4.61716 - 7.99715i) q^{47} +(5.27308 + 9.13324i) q^{49} +(-3.52186 + 1.16341i) q^{51} +(1.17892 - 1.17892i) q^{53} +7.97171i q^{55} +(-2.25698 - 1.13611i) q^{57} +(1.48185 + 0.397061i) q^{59} +(7.53224 - 2.01826i) q^{61} +(-12.4841 + 1.43585i) q^{63} +(2.82498 - 4.89300i) q^{65} +(-2.63252 + 9.82470i) q^{67} +(0.540220 - 0.605914i) q^{69} -8.27863i q^{71} -8.16641i q^{73} +(-3.79388 - 0.787022i) q^{75} +(-5.19937 + 19.4043i) q^{77} +(-3.63065 + 6.28847i) q^{79} +(2.61302 - 8.61232i) q^{81} +(7.59149 - 2.03413i) q^{83} +(3.43821 + 0.921267i) q^{85} +(9.82166 - 6.44684i) q^{87} -11.1968i q^{89} +(10.0678 - 10.0678i) q^{91} +(-8.22376 - 7.33213i) q^{93} +(1.21246 + 2.10004i) q^{95} +(-5.67759 + 9.83387i) q^{97} +(-11.2693 - 8.94443i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.64464	−	0.543291i	0.949532	−	0.313669i
$3$	1.64464	−	0.543291i	0.949532	−	0.313669i
$4$		0			0
$5$	−1.60558	−	0.430214i	−0.718037	−	0.192397i	−0.118741	−	0.992925i	$-0.537886\pi$
$5$	−1.60558	−	0.430214i	−0.718037	−	0.192397i	−0.599296	+	0.800528i	$0.704553\pi$
$6$		0			0
$7$	−3.62762	−	2.09441i	−1.37111	−	0.791611i	−0.380043	−	0.924969i	$-0.624091\pi$
$7$	−3.62762	−	2.09441i	−1.37111	−	0.791611i	−0.991068	+	0.133358i	$0.957424\pi$
$8$		0			0
$9$	2.40967	−	1.78703i	0.803223	−	0.595678i
$10$		0			0
$11$	−1.24125	−	4.63241i	−0.374251	−	1.39673i	−0.854436	−	0.519557i	$-0.826097\pi$
$11$	−1.24125	−	4.63241i	−0.374251	−	1.39673i	0.480184	−	0.877168i	$-0.340570\pi$
$12$		0			0
$13$	−0.879738	+	3.28323i	−0.243995	+	0.910603i	0.729890	+	0.683564i	$0.239571\pi$
$13$	−0.879738	+	3.28323i	−0.243995	+	0.910603i	−0.973886	+	0.227039i	$0.927096\pi$
$14$		0			0
$15$	−2.87433	+	0.164751i	−0.742148	+	0.0425384i
$16$		0			0
$17$	−2.14142			−0.519370			−0.259685	−	0.965693i	$-0.583619\pi$
$17$	−2.14142			−0.519370			−0.259685	+	0.965693i	$0.583619\pi$
$18$		0			0
$19$	−1.03156	−	1.03156i	−0.236656	−	0.236656i	0.578808	−	0.815464i	$-0.303518\pi$
$19$	−1.03156	−	1.03156i	−0.236656	−	0.236656i	−0.815464	+	0.578808i	$0.803518\pi$
$20$		0			0
$21$	−7.10399	−	1.47369i	−1.55022	−	0.321585i
$22$		0			0
$23$	0.405884	−	0.234337i	0.0846327	−	0.0488627i	−0.457086	−	0.889422i	$-0.651107\pi$
$23$	0.405884	−	0.234337i	0.0846327	−	0.0488627i	0.541719	+	0.840560i	$0.317774\pi$
$24$		0			0
$25$	−1.93733	−	1.11852i	−0.387465	−	0.223703i
$26$		0			0
$27$	2.99216	−	4.24818i	0.575841	−	0.817562i
$28$		0			0
$29$	6.55186	−	1.75557i	1.21665	−	0.326000i	0.407282	−	0.913302i	$-0.366477\pi$
$29$	6.55186	−	1.75557i	1.21665	−	0.326000i	0.809368	+	0.587302i	$0.199810\pi$
$30$		0			0
$31$	−3.18054	−	5.50886i	−0.571242	−	0.989421i	−0.996439	−	0.0843198i	$-0.973128\pi$
$31$	−3.18054	−	5.50886i	−0.571242	−	0.989421i	0.425196	−	0.905101i	$-0.360205\pi$
$32$		0			0
$33$	−4.55816	−	6.94428i	−0.793473	−	1.20884i
$34$		0			0
$35$	4.92339	+	4.92339i	0.832204	+	0.832204i
$36$		0			0
$37$	−0.728237	+	0.728237i	−0.119721	+	0.119721i	−0.764429	−	0.644708i	$-0.776979\pi$
$37$	−0.728237	+	0.728237i	−0.119721	+	0.119721i	0.644708	+	0.764429i	$0.276979\pi$
$38$		0			0
$39$	0.336896	+	5.87767i	0.0539466	+	0.941181i
$40$		0			0
$41$	2.52351	−	1.45695i	0.394105	−	0.227537i	−0.289832	−	0.957078i	$-0.593599\pi$
$41$	2.52351	−	1.45695i	0.394105	−	0.227537i	0.683937	+	0.729541i	$0.260266\pi$
$42$		0			0
$43$	2.84802	+	10.6289i	0.434318	+	1.62090i	0.742692	+	0.669633i	$0.233549\pi$
$43$	2.84802	+	10.6289i	0.434318	+	1.62090i	−0.308374	+	0.951265i	$0.599785\pi$
$44$		0			0
$45$	−4.63772	+	1.83255i	−0.691351	+	0.273181i
$46$		0			0
$47$	4.61716	−	7.99715i	0.673482	−	1.16650i	−0.303429	−	0.952854i	$-0.598131\pi$
$47$	4.61716	−	7.99715i	0.673482	−	1.16650i	0.976910	−	0.213650i	$-0.0685352\pi$
$48$		0			0
$49$	5.27308	+	9.13324i	0.753297	+	1.30475i
$50$		0			0
$51$	−3.52186	+	1.16341i	−0.493159	+	0.162910i
$52$		0			0
$53$	1.17892	−	1.17892i	0.161937	−	0.161937i	−0.621487	−	0.783424i	$-0.713471\pi$
$53$	1.17892	−	1.17892i	0.161937	−	0.161937i	0.783424	+	0.621487i	$0.213471\pi$
$54$		0			0
$55$			7.97171i			1.07491i
$56$		0			0
$57$	−2.25698	−	1.13611i	−0.298944	−	0.150481i
$58$		0			0
$59$	1.48185	+	0.397061i	0.192921	+	0.0516930i	0.353986	−	0.935251i	$-0.384826\pi$
$59$	1.48185	+	0.397061i	0.192921	+	0.0516930i	−0.161065	+	0.986944i	$0.551493\pi$
$60$		0			0
$61$	7.53224	−	2.01826i	0.964404	−	0.258411i	0.257941	−	0.966161i	$-0.416956\pi$
$61$	7.53224	−	2.01826i	0.964404	−	0.258411i	0.706464	+	0.707749i	$0.250289\pi$
$62$		0			0
$63$	−12.4841	+	1.43585i	−1.57285	+	0.180900i
$64$		0			0
$65$	2.82498	−	4.89300i	0.350395	−	0.606902i
$66$		0			0
$67$	−2.63252	+	9.82470i	−0.321614	+	1.20028i	0.596059	+	0.802941i	$0.296732\pi$
$67$	−2.63252	+	9.82470i	−0.321614	+	1.20028i	−0.917673	+	0.397338i	$0.869934\pi$
$68$		0			0
$69$	0.540220	−	0.605914i	0.0650348	−	0.0729434i
$70$		0			0
$71$		−	8.27863i		−	0.982493i	−0.871021	−	0.491246i	$-0.836542\pi$
$71$		−	8.27863i		−	0.982493i	0.871021	−	0.491246i	$-0.163458\pi$
$72$		0			0
$73$		−	8.16641i		−	0.955806i	−0.878413	−	0.477903i	$-0.841397\pi$
$73$		−	8.16641i		−	0.955806i	0.878413	−	0.477903i	$-0.158603\pi$
$74$		0			0
$75$	−3.79388	−	0.787022i	−0.438079	−	0.0908775i
$76$		0			0
$77$	−5.19937	+	19.4043i	−0.592523	+	2.21133i
$78$		0			0
$79$	−3.63065	+	6.28847i	−0.408480	+	0.707508i	−0.994720	−	0.102630i	$-0.967274\pi$
$79$	−3.63065	+	6.28847i	−0.408480	+	0.707508i	0.586240	+	0.810138i	$0.300608\pi$
$80$		0			0
$81$	2.61302	−	8.61232i	0.290336	−	0.956925i
$82$		0			0
$83$	7.59149	−	2.03413i	0.833274	−	0.223275i	0.183133	−	0.983088i	$-0.441376\pi$
$83$	7.59149	−	2.03413i	0.833274	−	0.223275i	0.650142	+	0.759813i	$0.274710\pi$
$84$		0			0
$85$	3.43821	+	0.921267i	0.372927	+	0.0999254i
$86$		0			0
$87$	9.82166	−	6.44684i	1.05299	−	0.691174i
$88$		0			0
$89$		−	11.1968i		−	1.18686i	−0.804886	−	0.593429i	$-0.797774\pi$
$89$		−	11.1968i		−	1.18686i	0.804886	−	0.593429i	$-0.202226\pi$
$90$		0			0
$91$	10.0678	−	10.0678i	1.05539	−	1.05539i
$92$		0			0
$93$	−8.22376	−	7.33213i	−0.852764	−	0.760306i
$94$		0			0
$95$	1.21246	+	2.10004i	0.124396	+	0.215460i
$96$		0			0
$97$	−5.67759	+	9.83387i	−0.576472	+	0.998479i	0.419408	+	0.907798i	$0.362238\pi$
$97$	−5.67759	+	9.83387i	−0.576472	+	0.998479i	−0.995880	+	0.0906808i	$0.971096\pi$
$98$		0			0
$99$	−11.2693	−	8.94443i	−1.13261	−	0.898949i
$100$		0			0
$101$	0.777558	+	2.90189i	0.0773699	+	0.288749i	0.993760	−	0.111537i	$-0.0355775\pi$
$101$	0.777558	+	2.90189i	0.0773699	+	0.288749i	−0.916390	+	0.400286i	$0.868911\pi$
$102$		0			0
$103$	1.24824	−	0.720669i	0.122992	−	0.0710096i	−0.437242	−	0.899344i	$-0.644045\pi$
$103$	1.24824	−	0.720669i	0.122992	−	0.0710096i	0.560234	+	0.828334i	$0.310711\pi$
$104$		0			0
$105$	10.7720	+	5.42236i	1.05124	+	0.529168i
$106$		0			0
$107$	−5.85602	+	5.85602i	−0.566123	+	0.566123i	−0.931040	−	0.364917i	$-0.881097\pi$
$107$	−5.85602	+	5.85602i	−0.566123	+	0.566123i	0.364917	+	0.931040i	$0.381097\pi$
$108$		0			0
$109$	−2.05249	−	2.05249i	−0.196593	−	0.196593i	0.601945	−	0.798538i	$-0.294393\pi$
$109$	−2.05249	−	2.05249i	−0.196593	−	0.196593i	−0.798538	+	0.601945i	$0.794393\pi$
$110$		0			0
$111$	−0.802042	+	1.59333i	−0.0761265	+	0.151232i
$112$		0			0
$113$	−4.12726	−	7.14862i	−0.388260	−	0.672486i	0.603956	−	0.797018i	$-0.293590\pi$
$113$	−4.12726	−	7.14862i	−0.388260	−	0.672486i	−0.992216	+	0.124532i	$0.960257\pi$
$114$		0			0
$115$	−0.752495	+	0.201630i	−0.0701705	+	0.0188021i
$116$		0			0
$117$	3.74736	+	9.48361i	0.346443	+	0.876760i
$118$		0			0
$119$	7.76824	+	4.48500i	0.712114	+	0.411139i
$120$		0			0
$121$	−10.3923	+	5.99998i	−0.944752	+	0.545453i
$122$		0			0
$123$	3.35871	−	3.76715i	0.302845	−	0.339672i
$124$		0			0
$125$	8.50616	+	8.50616i	0.760814	+	0.760814i
$126$		0			0
$127$	1.68483			0.149504			0.0747521	−	0.997202i	$-0.476183\pi$
$127$	1.68483			0.149504			0.0747521	+	0.997202i	$0.476183\pi$
$128$		0			0
$129$	10.4586	+	15.9335i	0.920825	+	1.40286i
$130$		0			0
$131$	−1.97334	+	7.36461i	−0.172412	+	0.643449i	0.824566	+	0.565765i	$0.191419\pi$
$131$	−1.97334	+	7.36461i	−0.172412	+	0.643449i	−0.996978	+	0.0776838i	$0.975248\pi$
$132$		0			0
$133$	1.58160	+	5.90261i	0.137142	+	0.511821i
$134$		0			0
$135$	−6.63177	+	5.53352i	−0.570772	+	0.476249i
$136$		0			0
$137$	8.26806	+	4.77357i	0.706388	+	0.407833i	0.809722	−	0.586813i	$-0.199618\pi$
$137$	8.26806	+	4.77357i	0.706388	+	0.407833i	−0.103334	+	0.994647i	$0.532951\pi$
$138$		0			0
$139$	13.9684	+	3.74281i	1.18478	+	0.317461i	0.796821	−	0.604215i	$-0.206513\pi$
$139$	13.9684	+	3.74281i	1.18478	+	0.317461i	0.387960	+	0.921676i	$0.373180\pi$
$140$		0			0
$141$	3.24877	−	15.6609i	0.273596	−	1.31888i
$142$		0			0
$143$	16.3012			1.36318
$144$		0			0
$145$	−11.2748			−0.936321
$146$		0			0
$147$	13.6343	+	12.1561i	1.12454	+	1.00261i
$148$		0			0
$149$	−1.66249	−	0.445462i	−0.136196	−	0.0364937i	0.190077	−	0.981769i	$-0.439126\pi$
$149$	−1.66249	−	0.445462i	−0.136196	−	0.0364937i	−0.326273	+	0.945276i	$0.605793\pi$
$150$		0			0
$151$	−18.5071	−	10.6851i	−1.50609	−	0.869542i	−0.999975	−	0.00707596i	$-0.997748\pi$
$151$	−18.5071	−	10.6851i	−1.50609	−	0.869542i	−0.506115	−	0.862466i	$-0.668919\pi$
$152$		0			0
$153$	−5.16011	+	3.82678i	−0.417170	+	0.309377i
$154$		0			0
$155$	2.73663	+	10.2132i	0.219811	+	0.820346i
$156$		0			0
$157$	2.74550	−	10.2463i	0.219114	−	0.817746i	−0.765563	−	0.643361i	$-0.777539\pi$
$157$	2.74550	−	10.2463i	0.219114	−	0.817746i	0.984677	−	0.174385i	$-0.0557938\pi$
$158$		0			0
$159$	1.29840	−	2.57939i	0.102970	−	0.204559i
$160$		0			0
$161$	−1.96319			−0.154721
$162$		0			0
$163$	3.47621	+	3.47621i	0.272278	+	0.272278i	0.830017	−	0.557739i	$-0.188331\pi$
$163$	3.47621	+	3.47621i	0.272278	+	0.272278i	−0.557739	+	0.830017i	$0.688331\pi$
$164$		0			0
$165$	4.33096	+	13.1106i	0.337165	+	1.02066i
$166$		0			0
$167$	−0.277442	+	0.160181i	−0.0214691	+	0.0123952i	−0.510696	−	0.859761i	$-0.670612\pi$
$167$	−0.277442	+	0.160181i	−0.0214691	+	0.0123952i	0.489227	+	0.872156i	$0.337279\pi$
$168$		0			0
$169$	1.25270	+	0.723245i	0.0963613	+	0.0556342i
$170$		0			0
$171$	−4.32915	−	0.642287i	−0.331059	−	0.0491169i
$172$		0			0
$173$	11.6901	−	3.13236i	0.888784	−	0.238149i	0.214591	−	0.976704i	$-0.431158\pi$
$173$	11.6901	−	3.13236i	0.888784	−	0.238149i	0.674193	+	0.738555i	$0.264491\pi$
$174$		0			0
$175$	4.68525	+	8.11510i	0.354172	+	0.613444i
$176$		0			0
$177$	2.65283	−	0.152055i	0.199399	−	0.0114291i
$178$		0			0
$179$	−18.6780	−	18.6780i	−1.39606	−	1.39606i	−0.810958	−	0.585104i	$-0.801054\pi$
$179$	−18.6780	−	18.6780i	−1.39606	−	1.39606i	−0.585104	−	0.810958i	$-0.698946\pi$
$180$		0			0
$181$	4.10527	−	4.10527i	0.305143	−	0.305143i	−0.537879	−	0.843022i	$-0.680774\pi$
$181$	4.10527	−	4.10527i	0.305143	−	0.305143i	0.843022	+	0.537879i	$0.180774\pi$
$182$		0			0
$183$	11.2913	−	7.41150i	0.834677	−	0.547874i
$184$		0			0
$185$	1.48254	−	0.855945i	0.108998	−	0.0629303i
$186$		0			0
$187$	2.65804	+	9.91993i	0.194375	+	0.725417i
$188$		0			0
$189$	−19.7518	+	9.14397i	−1.43673	+	0.665126i
$190$		0			0
$191$	−8.60099	+	14.8974i	−0.622346	+	1.07793i	0.366702	+	0.930338i	$0.380487\pi$
$191$	−8.60099	+	14.8974i	−0.622346	+	1.07793i	−0.989048	+	0.147596i	$0.952846\pi$
$192$		0			0
$193$	9.17459	+	15.8909i	0.660402	+	1.14385i	0.980510	+	0.196468i	$0.0629473\pi$
$193$	9.17459	+	15.8909i	0.660402	+	1.14385i	−0.320108	+	0.947381i	$0.603719\pi$
$194$		0			0
$195$	1.98774	−	9.58201i	0.142345	−	0.686182i
$196$		0			0
$197$	8.80431	−	8.80431i	0.627281	−	0.627281i	−0.320102	−	0.947383i	$-0.603717\pi$
$197$	8.80431	−	8.80431i	0.627281	−	0.627281i	0.947383	+	0.320102i	$0.103717\pi$
$198$		0			0
$199$			10.0277i			0.710847i	0.934705	+	0.355423i	$0.115663\pi$
$199$			10.0277i			0.710847i	−0.934705	+	0.355423i	$0.884337\pi$
$200$		0			0
$201$	1.00813	+	17.5883i	0.0711077	+	1.24058i
$202$		0			0
$203$	−27.4445	−	7.35374i	−1.92623	−	0.516131i
$204$		0			0
$205$	−4.67849	+	1.25360i	−0.326760	+	0.0875550i
$206$		0			0
$207$	0.559278	−	1.29001i	0.0388725	−	0.0896616i
$208$		0			0
$209$	−3.49819	+	6.05904i	−0.241975	+	0.419112i
$210$		0			0
$211$	5.14678	−	19.2080i	0.354319	−	1.32234i	−0.527021	−	0.849852i	$-0.676691\pi$
$211$	5.14678	−	19.2080i	0.354319	−	1.32234i	0.881340	−	0.472483i	$-0.156642\pi$
$212$		0			0
$213$	−4.49770	−	13.6154i	−0.308178	−	0.932908i
$214$		0			0
$215$		−	18.2909i		−	1.24743i
$216$		0			0
$217$			26.6454i			1.80881i
$218$		0			0
$219$	−4.43674	−	13.4308i	−0.299807	−	0.907569i
$220$		0			0
$221$	1.88389	−	7.03076i	0.126724	−	0.472940i
$222$		0			0
$223$	6.96587	−	12.0652i	0.466469	−	0.807948i	−0.532797	−	0.846243i	$-0.678859\pi$
$223$	6.96587	−	12.0652i	0.466469	−	0.807948i	0.999266	+	0.0382947i	$0.0121926\pi$
$224$		0			0
$225$	−6.66714	+	0.766813i	−0.444476	+	0.0511209i
$226$		0			0
$227$	7.32092	−	1.96164i	0.485907	−	0.130198i	−0.00754492	−	0.999972i	$-0.502402\pi$
$227$	7.32092	−	1.96164i	0.485907	−	0.130198i	0.493452	+	0.869773i	$0.335735\pi$
$228$		0			0
$229$	−18.4637	−	4.94734i	−1.22012	−	0.326930i	−0.409394	−	0.912358i	$-0.634260\pi$
$229$	−18.4637	−	4.94734i	−1.22012	−	0.326930i	−0.810724	+	0.585428i	$0.800926\pi$
$230$		0			0
$231$	1.99110	+	34.7378i	0.131005	+	2.28558i
$232$		0			0
$233$		−	10.7647i		−	0.705216i	−0.935771	−	0.352608i	$-0.885295\pi$
$233$		−	10.7647i		−	0.705216i	0.935771	−	0.352608i	$-0.114705\pi$
$234$		0			0
$235$	−10.8537	+	10.8537i	−0.708017	+	0.708017i
$236$		0			0
$237$	−2.55464	+	12.3147i	−0.165941	+	0.799929i
$238$		0			0
$239$	11.1429	+	19.3001i	0.720774	+	1.24842i	0.960690	+	0.277624i	$0.0895469\pi$
$239$	11.1429	+	19.3001i	0.720774	+	1.24842i	−0.239916	+	0.970794i	$0.577120\pi$
$240$		0			0
$241$	13.7285	−	23.7785i	0.884332	−	1.53171i	0.0378540	−	0.999283i	$-0.487948\pi$
$241$	13.7285	−	23.7785i	0.884332	−	1.53171i	0.846478	−	0.532424i	$-0.178719\pi$
$242$		0			0
$243$	−0.381525	−	15.5838i	−0.0244748	−	0.999700i
$244$		0			0
$245$	−4.53710	−	16.9327i	−0.289865	−	1.08179i
$246$		0			0
$247$	4.29435	−	2.47934i	0.273243	−	0.157757i
$248$		0			0
$249$	11.3801	−	7.46980i	0.721186	−	0.473379i
$250$		0			0
$251$	−11.4125	+	11.4125i	−0.720350	+	0.720350i	−0.968676	−	0.248326i	$-0.920119\pi$
$251$	−11.4125	+	11.4125i	−0.720350	+	0.720350i	0.248326	+	0.968676i	$0.420119\pi$
$252$		0			0
$253$	−1.58935	−	1.58935i	−0.0999217	−	0.0999217i
$254$		0			0
$255$	6.15514	−	0.352800i	0.385450	−	0.0220932i
$256$		0			0
$257$	−0.930384	−	1.61147i	−0.0580357	−	0.100521i	0.835548	−	0.549418i	$-0.185150\pi$
$257$	−0.930384	−	1.61147i	−0.0580357	−	0.100521i	−0.893584	+	0.448897i	$0.851817\pi$
$258$		0			0
$259$	4.16699	−	1.11654i	0.258924	−	0.0693785i
$260$		0			0
$261$	12.6506	−	15.9387i	0.783051	−	0.986583i
$262$		0			0
$263$	−0.0414842	−	0.0239509i	−0.00255802	−	0.00147687i	0.498720	−	0.866763i	$-0.333803\pi$
$263$	−0.0414842	−	0.0239509i	−0.00255802	−	0.00147687i	−0.501278	+	0.865286i	$0.667137\pi$
$264$		0			0
$265$	−2.40003	+	1.38566i	−0.147433	+	0.0851203i
$266$		0			0
$267$	−6.08312	−	18.4147i	−0.372281	−	1.12696i
$268$		0			0
$269$	−14.5681	−	14.5681i	−0.888235	−	0.888235i	0.106118	−	0.994354i	$-0.466158\pi$
$269$	−14.5681	−	14.5681i	−0.888235	−	0.888235i	−0.994354	+	0.106118i	$0.966158\pi$
$270$		0			0
$271$	15.7807			0.958607			0.479304	−	0.877649i	$-0.340889\pi$
$271$	15.7807			0.958607			0.479304	+	0.877649i	$0.340889\pi$
$272$		0			0
$273$	11.0881	−	22.0275i	0.671083	−	1.33317i
$274$		0			0
$275$	−2.77672	+	10.3629i	−0.167442	+	0.624904i
$276$		0			0
$277$	−1.93294	−	7.21383i	−0.116139	−	0.433437i	0.883231	−	0.468939i	$-0.155364\pi$
$277$	−1.93294	−	7.21383i	−0.116139	−	0.433437i	−0.999370	+	0.0355022i	$0.988697\pi$
$278$		0			0
$279$	−17.5086	−	7.59080i	−1.04821	−	0.454449i
$280$		0			0
$281$	−5.84440	−	3.37427i	−0.348648	−	0.201292i	0.315442	−	0.948945i	$-0.397847\pi$
$281$	−5.84440	−	3.37427i	−0.348648	−	0.201292i	−0.664089	+	0.747653i	$0.731181\pi$
$282$		0			0
$283$	−12.4414	−	3.33366i	−0.739563	−	0.198165i	−0.130679	−	0.991425i	$-0.541716\pi$
$283$	−12.4414	−	3.33366i	−0.739563	−	0.198165i	−0.608884	+	0.793259i	$0.708383\pi$
$284$		0			0
$285$	3.13499	+	2.79509i	0.185701	+	0.165567i
$286$		0			0
$287$	−12.2058			−0.720483
$288$		0			0
$289$	−12.4143			−0.730255
$290$		0			0
$291$	−3.99493	+	19.2577i	−0.234187	+	1.12891i
$292$		0			0
$293$	13.8785	+	3.71874i	0.810792	+	0.217251i	0.640317	−	0.768111i	$-0.278803\pi$
$293$	13.8785	+	3.71874i	0.810792	+	0.217251i	0.170475	+	0.985362i	$0.445470\pi$
$294$		0			0
$295$	−2.20841	−	1.27503i	−0.128579	−	0.0742349i
$296$		0			0
$297$	−23.3933	−	8.58785i	−1.35742	−	0.498318i
$298$		0			0
$299$	0.412311	+	1.53877i	0.0238446	+	0.0889891i
$300$		0			0
$301$	11.9298	−	44.5226i	0.687622	−	2.56624i
$302$		0			0
$303$	2.85537	+	4.35011i	0.164037	+	0.249907i
$304$		0			0
$305$	−12.9619			−0.742196
$306$		0			0
$307$	−12.2394	−	12.2394i	−0.698539	−	0.698539i	0.265556	−	0.964095i	$-0.414444\pi$
$307$	−12.2394	−	12.2394i	−0.698539	−	0.698539i	−0.964095	+	0.265556i	$0.914444\pi$
$308$		0			0
$309$	1.66136	−	1.86339i	0.0945116	−	0.106005i
$310$		0			0
$311$	0.742777	−	0.428842i	0.0421190	−	0.0243174i	−0.478793	−	0.877928i	$-0.658925\pi$
$311$	0.742777	−	0.428842i	0.0421190	−	0.0243174i	0.520912	+	0.853611i	$0.325592\pi$
$312$		0			0
$313$	−15.8984	−	9.17895i	−0.898631	−	0.518825i	−0.0218755	−	0.999761i	$-0.506964\pi$
$313$	−15.8984	−	9.17895i	−0.898631	−	0.518825i	−0.876756	+	0.480936i	$0.840297\pi$
$314$		0			0
$315$	20.6620	+	3.06548i	1.16417	+	0.172720i
$316$		0			0
$317$	−4.02641	+	1.07887i	−0.226146	+	0.0605956i	−0.370112	−	0.928987i	$-0.620681\pi$
$317$	−4.02641	+	1.07887i	−0.226146	+	0.0605956i	0.143967	+	0.989583i	$0.454014\pi$
$318$		0			0
$319$	−16.2650	−	28.1718i	−0.910666	−	1.57732i
$320$		0			0
$321$	−6.44952	+	12.8126i	−0.359977	+	0.715128i
$322$		0			0
$323$	2.20900	+	2.20900i	0.122912	+	0.122912i
$324$		0			0
$325$	5.37668	−	5.37668i	0.298244	−	0.298244i
$326$		0			0
$327$	−4.49070	−	2.26050i	−0.248336	−	0.125006i
$328$		0			0
$329$	−33.4986	+	19.3404i	−1.84684	+	1.06627i
$330$		0			0
$331$	−1.33734	−	4.99103i	−0.0735070	−	0.274332i	0.919384	−	0.393362i	$-0.128688\pi$
$331$	−1.33734	−	4.99103i	−0.0735070	−	0.274332i	−0.992891	+	0.119030i	$0.962021\pi$
$332$		0			0
$333$	−0.453427	+	3.05620i	−0.0248476	+	0.167478i
$334$		0			0
$335$	8.45344	−	14.6418i	0.461861	−	0.799966i
$336$		0			0
$337$	1.94762	+	3.37338i	0.106094	+	0.183760i	0.914185	−	0.405298i	$-0.132832\pi$
$337$	1.94762	+	3.37338i	0.106094	+	0.183760i	−0.808091	+	0.589058i	$0.799499\pi$
$338$		0			0
$339$	−10.6716	−	9.51459i	−0.579603	−	0.516762i
$340$		0			0
$341$	−21.5715	+	21.5715i	−1.16816	+	1.16816i
$342$		0			0
$343$		−	14.8542i		−	0.802049i
$344$		0			0
$345$	−1.12804	+	0.740433i	−0.0607315	+	0.0398635i
$346$		0			0
$347$	3.04812	+	0.816741i	0.163632	+	0.0438449i	0.339705	−	0.940532i	$-0.389673\pi$
$347$	3.04812	+	0.816741i	0.163632	+	0.0438449i	−0.176073	+	0.984377i	$0.556340\pi$
$348$		0			0
$349$	1.39893	−	0.374843i	0.0748831	−	0.0200649i	−0.221183	−	0.975232i	$-0.570992\pi$
$349$	1.39893	−	0.374843i	0.0748831	−	0.0200649i	0.296066	+	0.955167i	$0.404325\pi$
$350$		0			0
$351$	11.3154	+	13.5612i	0.603972	+	0.723844i
$352$		0			0
$353$	7.73892	−	13.4042i	0.411901	−	0.713434i	−0.583196	−	0.812331i	$-0.698198\pi$
$353$	7.73892	−	13.4042i	0.411901	−	0.713434i	0.995098	+	0.0988971i	$0.0315315\pi$
$354$		0			0
$355$	−3.56158	+	13.2920i	−0.189029	+	0.705466i
$356$		0			0
$357$	15.2126	+	3.15578i	0.805137	+	0.167022i
$358$		0			0
$359$			4.78775i			0.252688i	0.991987	+	0.126344i	$0.0403242\pi$
$359$			4.78775i			0.252688i	−0.991987	+	0.126344i	$0.959676\pi$
$360$		0			0
$361$		−	16.8718i		−	0.887988i
$362$		0			0
$363$	−13.8318	+	15.5138i	−0.725981	+	0.814264i
$364$		0			0
$365$	−3.51330	+	13.1118i	−0.183895	+	0.686304i
$366$		0			0
$367$	9.93807	−	17.2133i	0.518763	−	0.898524i	−0.480999	−	0.876721i	$-0.659726\pi$
$367$	9.93807	−	17.2133i	0.518763	−	0.898524i	0.999762	−	0.0218032i	$-0.00694073\pi$
$368$		0			0
$369$	3.47720	−	8.02035i	0.181016	−	0.417523i
$370$		0			0
$371$	−6.74579	+	1.80753i	−0.350224	+	0.0938422i
$372$		0			0
$373$	−0.427591	−	0.114573i	−0.0221398	−	0.00593235i	0.247732	−	0.968829i	$-0.420315\pi$
$373$	−0.427591	−	0.114573i	−0.0221398	−	0.00593235i	−0.269872	+	0.962896i	$0.586981\pi$
$374$		0			0
$375$	18.6109	+	9.36823i	0.961061	+	0.483774i
$376$		0			0
$377$			23.0557i			1.18743i
$378$		0			0
$379$	6.18132	−	6.18132i	0.317513	−	0.317513i	−0.530298	−	0.847811i	$-0.677920\pi$
$379$	6.18132	−	6.18132i	0.317513	−	0.317513i	0.847811	+	0.530298i	$0.177920\pi$
$380$		0			0
$381$	2.77093	−	0.915351i	0.141959	−	0.0468949i
$382$		0			0
$383$	−6.46708	−	11.2013i	−0.330452	−	0.572360i	0.652148	−	0.758091i	$-0.273868\pi$
$383$	−6.46708	−	11.2013i	−0.330452	−	0.572360i	−0.982601	+	0.185731i	$0.940535\pi$
$384$		0			0
$385$	16.6960	−	28.9183i	0.850907	−	1.47381i
$386$		0			0
$387$	25.8571	+	20.5227i	1.31439	+	1.04323i
$388$		0			0
$389$	7.08096	+	26.4265i	0.359019	+	1.33988i	0.875351	+	0.483489i	$0.160631\pi$
$389$	7.08096	+	26.4265i	0.359019	+	1.33988i	−0.516331	+	0.856389i	$0.672703\pi$
$390$		0			0
$391$	−0.869168	+	0.501814i	−0.0439557	+	0.0253778i
$392$		0			0
$393$	0.755693	+	13.1842i	0.0381197	+	0.665056i
$394$		0			0
$395$	8.53468	−	8.53468i	0.429426	−	0.429426i
$396$		0			0
$397$	21.9741	+	21.9741i	1.10285	+	1.10285i	0.994066	+	0.108781i	$0.0346948\pi$
$397$	21.9741	+	21.9741i	1.10285	+	1.10285i	0.108781	+	0.994066i	$0.465305\pi$
$398$		0			0
$399$	5.80799	+	8.84839i	0.290763	+	0.442974i
$400$		0			0
$401$	13.4970	+	23.3775i	0.674009	+	1.16742i	0.976758	+	0.214347i	$0.0687624\pi$
$401$	13.4970	+	23.3775i	0.674009	+	1.16742i	−0.302749	+	0.953070i	$0.597904\pi$
$402$		0			0
$403$	20.8849	−	5.59609i	1.04035	−	0.278761i
$404$		0			0
$405$	−7.90055	+	12.7036i	−0.392581	+	0.631248i
$406$		0			0
$407$	4.27742	+	2.46957i	0.212024	+	0.122412i
$408$		0			0
$409$	11.1537	−	6.43957i	0.551513	−	0.318416i	−0.198219	−	0.980158i	$-0.563516\pi$
$409$	11.1537	−	6.43957i	0.551513	−	0.318416i	0.749732	+	0.661741i	$0.230182\pi$
$410$		0			0
$411$	16.1914	+	3.35883i	0.798663	+	0.165679i
$412$		0			0
$413$	−4.54399	−	4.54399i	−0.223595	−	0.223595i
$414$		0			0
$415$	−13.0638			−0.641279
$416$		0			0
$417$	25.0063	−	1.43331i	1.22457	−	0.0701896i
$418$		0			0
$419$	0.0545100	−	0.203434i	0.00266299	−	0.00993841i	−0.964582	−	0.263785i	$-0.915029\pi$
$419$	0.0545100	−	0.203434i	0.00266299	−	0.00993841i	0.967245	+	0.253846i	$0.0816958\pi$
$420$		0			0
$421$	9.17194	+	34.2301i	0.447013	+	1.66827i	0.710567	+	0.703630i	$0.248439\pi$
$421$	9.17194	+	34.2301i	0.447013	+	1.66827i	−0.263554	+	0.964645i	$0.584895\pi$
$422$		0			0
$423$	−3.16535	−	27.5215i	−0.153905	−	1.33814i
$424$		0			0
$425$	4.14862	+	2.39521i	0.201238	+	0.116185i
$426$		0			0
$427$	−31.5511	−	8.45410i	−1.52687	−	0.409123i
$428$		0			0
$429$	26.8096	−	8.85631i	1.29438	−	0.427587i
$430$		0			0
$431$	−33.5339			−1.61527			−0.807635	−	0.589683i	$-0.799253\pi$
$431$	−33.5339			−1.61527			−0.807635	+	0.589683i	$0.799253\pi$
$432$		0			0
$433$	−28.9691			−1.39217			−0.696083	−	0.717962i	$-0.745075\pi$
$433$	−28.9691			−1.39217			−0.696083	+	0.717962i	$0.745075\pi$
$434$		0			0
$435$	−18.5430	+	6.12550i	−0.889067	+	0.293695i
$436$		0			0
$437$	−0.660427	−	0.176961i	−0.0315925	−	0.00846519i
$438$		0			0
$439$	14.6656	+	8.46718i	0.699950	+	0.404116i	0.807329	−	0.590102i	$-0.200912\pi$
$439$	14.6656	+	8.46718i	0.699950	+	0.404116i	−0.107379	+	0.994218i	$0.534246\pi$
$440$		0			0
$441$	29.0278	+	12.5849i	1.38227	+	0.599282i
$442$		0			0
$443$	−0.826654	−	3.08511i	−0.0392755	−	0.146578i	0.943504	−	0.331362i	$-0.107508\pi$
$443$	−0.826654	−	3.08511i	−0.0392755	−	0.146578i	−0.982779	+	0.184784i	$0.940841\pi$
$444$		0			0
$445$	−4.81702	+	17.9773i	−0.228348	+	0.852208i
$446$		0			0
$447$	−2.97621	+	0.170590i	−0.140770	+	0.00806863i
$448$		0			0
$449$	−41.9192			−1.97829			−0.989145	−	0.146944i	$-0.953056\pi$
$449$	−41.9192			−1.97829			−0.989145	+	0.146944i	$0.953056\pi$
$450$		0			0
$451$	−9.88149	−	9.88149i	−0.465301	−	0.465301i
$452$		0			0
$453$	−36.2427	−	7.51837i	−1.70283	−	0.353244i
$454$		0			0
$455$	−20.4959	+	11.8333i	−0.960862	+	0.554754i
$456$		0			0
$457$	4.93980	+	2.85199i	0.231074	+	0.133411i	0.611067	−	0.791579i	$-0.290740\pi$
$457$	4.93980	+	2.85199i	0.231074	+	0.133411i	−0.379993	+	0.924989i	$0.624074\pi$
$458$		0			0
$459$	−6.40745	+	9.09712i	−0.299074	+	0.424617i
$460$		0			0
$461$	−38.3338	+	10.2715i	−1.78538	+	0.478392i	−0.991548	−	0.129743i	$-0.958585\pi$
$461$	−38.3338	+	10.2715i	−1.78538	+	0.478392i	−0.793834	+	0.608135i	$0.791918\pi$
$462$		0			0
$463$	6.28293	+	10.8824i	0.291992	+	0.505746i	0.974281	−	0.225337i	$-0.0723485\pi$
$463$	6.28293	+	10.8824i	0.291992	+	0.505746i	−0.682288	+	0.731083i	$0.739015\pi$
$464$		0			0
$465$	10.0495	+	15.3103i	0.466035	+	0.709997i
$466$		0			0
$467$	−12.1784	−	12.1784i	−0.563550	−	0.563550i	0.366764	−	0.930314i	$-0.380466\pi$
$467$	−12.1784	−	12.1784i	−0.563550	−	0.563550i	−0.930314	+	0.366764i	$0.880466\pi$
$468$		0			0
$469$	30.1267	−	30.1267i	1.39112	−	1.39112i
$470$		0			0
$471$	−1.05139	−	18.3431i	−0.0484455	−	0.845206i
$472$		0			0
$473$	45.7025	−	26.3864i	2.10140	−	1.21325i
$474$		0			0
$475$	0.844652	+	3.15228i	0.0387553	+	0.144637i
$476$		0			0
$477$	0.734036	−	4.94756i	0.0336092	−	0.226533i
$478$		0			0
$479$	10.6864	−	18.5094i	0.488275	−	0.845717i	−0.511634	−	0.859204i	$-0.670960\pi$
$479$	10.6864	−	18.5094i	0.488275	−	0.845717i	0.999909	+	0.0134862i	$0.00429292\pi$
$480$		0			0
$481$	−1.75031	−	3.03162i	−0.0798072	−	0.138230i
$482$		0			0
$483$	−3.22874	+	1.06658i	−0.146913	+	0.0485313i
$484$		0			0
$485$	13.3465	−	13.3465i	0.606033	−	0.606033i
$486$		0			0
$487$			39.3716i			1.78410i	0.451939	+	0.892049i	$0.350732\pi$
$487$			39.3716i			1.78410i	−0.451939	+	0.892049i	$0.649268\pi$
$488$		0			0
$489$	7.60570	+	3.82851i	0.343942	+	0.173131i
$490$		0			0
$491$	33.8903	+	9.08087i	1.52945	+	0.409814i	0.922839	−	0.385187i	$-0.125863\pi$
$491$	33.8903	+	9.08087i	1.52945	+	0.409814i	0.606608	+	0.795001i	$0.292530\pi$
$492$		0			0
$493$	−14.0303	+	3.75940i	−0.631891	+	0.169315i
$494$		0			0
$495$	14.2457	+	19.2092i	0.640297	+	0.863389i
$496$		0			0
$497$	−17.3388	+	30.0317i	−0.777752	+	1.34711i
$498$		0			0
$499$	−3.38889	+	12.6475i	−0.151708	+	0.566181i	0.847657	+	0.530544i	$0.178012\pi$
$499$	−3.38889	+	12.6475i	−0.151708	+	0.566181i	−0.999365	+	0.0356364i	$0.988654\pi$
$500$		0			0
$501$	−0.369267	+	0.414172i	−0.0164976	+	0.0185039i
$502$		0			0
$503$		−	2.93881i		−	0.131035i	−0.997851	−	0.0655175i	$-0.979130\pi$
$503$		−	2.93881i		−	0.131035i	0.997851	−	0.0655175i	$-0.0208698\pi$
$504$		0			0
$505$		−	4.99373i		−	0.222218i
$506$		0			0
$507$	2.45317	+	0.508897i	0.108949	+	0.0226009i
$508$		0			0
$509$	4.11461	−	15.3559i	0.182377	−	0.680640i	−0.812800	−	0.582543i	$-0.802058\pi$
$509$	4.11461	−	15.3559i	0.182377	−	0.680640i	0.995177	−	0.0980972i	$-0.0312756\pi$
$510$		0			0
$511$	−17.1038	+	29.6246i	−0.756627	+	1.31052i
$512$		0			0
$513$	−7.46884	+	1.29566i	−0.329757	+	0.0572048i
$514$		0			0
$515$	−2.31418	+	0.620083i	−0.101975	+	0.0273241i
$516$		0			0
$517$	−42.7772	−	11.4621i	−1.88134	−	0.504103i
$518$		0			0
$519$	17.5243	−	11.5027i	0.769230	−	0.504914i
$520$		0			0
$521$		−	19.2119i		−	0.841689i	−0.907133	−	0.420844i	$-0.861734\pi$
$521$		−	19.2119i		−	0.841689i	0.907133	−	0.420844i	$-0.138266\pi$
$522$		0			0
$523$	10.0495	−	10.0495i	0.439436	−	0.439436i	−0.452386	−	0.891822i	$-0.649427\pi$
$523$	10.0495	−	10.0495i	0.439436	−	0.439436i	0.891822	+	0.452386i	$0.149427\pi$
$524$		0			0
$525$	12.1144	+	10.8009i	0.528716	+	0.471392i
$526$		0			0
$527$	6.81087	+	11.7968i	0.296686	+	0.513875i
$528$		0			0
$529$	−11.3902	+	19.7284i	−0.495225	+	0.857755i
$530$		0			0
$531$	4.28034	−	1.69133i	0.185751	−	0.0733976i
$532$		0			0
$533$	2.56346	+	9.56697i	0.111036	+	0.414392i
$534$		0			0
$535$	11.9217	−	6.88297i	0.515418	−	0.297577i
$536$		0			0
$537$	−40.8662	−	20.5710i	−1.76351	−	0.887705i
$538$		0			0
$539$	35.7637	−	35.7637i	1.54045	−	1.54045i
$540$		0			0
$541$	15.3802	+	15.3802i	0.661246	+	0.661246i	0.955674	−	0.294428i	$-0.0951290\pi$
$541$	15.3802	+	15.3802i	0.661246	+	0.661246i	−0.294428	+	0.955674i	$0.595129\pi$
$542$		0			0
$543$	4.52133	−	8.98205i	0.194029	−	0.385457i
$544$		0			0
$545$	2.41243	+	4.17844i	0.103337	+	0.178985i
$546$		0			0
$547$	23.1362	−	6.19933i	0.989233	−	0.265064i	0.272304	−	0.962211i	$-0.412214\pi$
$547$	23.1362	−	6.19933i	0.989233	−	0.265064i	0.716928	+	0.697147i	$0.245548\pi$
$548$		0			0
$549$	14.5435	−	18.3237i	0.620702	−	0.782036i
$550$		0			0
$551$	−8.56961	−	4.94767i	−0.365078	−	0.210778i
$552$		0			0
$553$	26.3412	−	15.2081i	1.12014	−	0.646714i
$554$		0			0
$555$	1.97321	−	2.21317i	0.0837583	−	0.0939438i
$556$		0			0
$557$	0.932077	+	0.932077i	0.0394934	+	0.0394934i	0.726578	−	0.687084i	$-0.241110\pi$
$557$	0.932077	+	0.932077i	0.0394934	+	0.0394934i	−0.687084	+	0.726578i	$0.741110\pi$
$558$		0			0
$559$	−37.4027			−1.58197
$560$		0			0
$561$	9.76092	+	14.8706i	0.412106	+	0.627838i
$562$		0			0
$563$	1.71390	−	6.39635i	0.0722321	−	0.269574i	−0.920359	−	0.391074i	$-0.872104\pi$
$563$	1.71390	−	6.39635i	0.0722321	−	0.269574i	0.992591	+	0.121500i	$0.0387704\pi$
$564$		0			0
$565$	3.55121	+	13.2533i	0.149400	+	0.557570i
$566$		0			0
$567$	−27.5167	+	25.7695i	−1.15559	+	1.08222i
$568$		0			0
$569$	7.84553	+	4.52962i	0.328902	+	0.189892i	0.655353	−	0.755322i	$-0.272520\pi$
$569$	7.84553	+	4.52962i	0.328902	+	0.189892i	−0.326452	+	0.945214i	$0.605853\pi$
$570$		0			0
$571$	17.9078	+	4.79838i	0.749417	+	0.200806i	0.613260	−	0.789881i	$-0.289858\pi$
$571$	17.9078	+	4.79838i	0.749417	+	0.200806i	0.136158	+	0.990687i	$0.456525\pi$
$572$		0			0
$573$	−6.05192	+	29.1736i	−0.252823	+	1.21874i
$574$		0			0
$575$	−1.04844			−0.0437230
$576$		0			0
$577$	43.3455			1.80450			0.902248	−	0.431217i	$-0.141916\pi$
$577$	43.3455			1.80450			0.902248	+	0.431217i	$0.141916\pi$
$578$		0			0
$579$	23.7223	+	21.1502i	0.985863	+	0.878974i
$580$		0			0
$581$	−31.7993	−	8.52060i	−1.31926	−	0.353494i
$582$		0			0
$583$	−6.92456	−	3.99790i	−0.286786	−	0.165576i
$584$		0			0
$585$	−1.93670	−	16.8389i	−0.0800727	−	0.696201i
$586$		0			0
$587$	6.81553	+	25.4359i	0.281307	+	1.04985i	0.951496	+	0.307662i	$0.0995465\pi$
$587$	6.81553	+	25.4359i	0.281307	+	1.04985i	−0.670189	+	0.742191i	$0.733787\pi$
$588$		0			0
$589$	−2.40180	+	8.96364i	−0.0989645	+	0.369341i
$590$		0			0
$591$	9.69660	−	19.2632i	0.398865	−	0.792382i
$592$		0			0
$593$	41.9274			1.72175			0.860876	−	0.508814i	$-0.169916\pi$
$593$	41.9274			1.72175			0.860876	+	0.508814i	$0.169916\pi$
$594$		0			0
$595$	−10.5430	−	10.5430i	−0.432222	−	0.432222i
$596$		0			0
$597$	5.44797	+	16.4920i	0.222971	+	0.674972i
$598$		0			0
$599$	21.1742	−	12.2249i	0.865154	−	0.499497i	−0.000580933	−	1.00000i	$-0.500185\pi$
$599$	21.1742	−	12.2249i	0.865154	−	0.499497i	0.865735	+	0.500503i	$0.166852\pi$
$600$		0			0
$601$	24.7521	+	14.2906i	1.00966	+	0.582928i	0.911092	−	0.412203i	$-0.135240\pi$
$601$	24.7521	+	14.2906i	1.00966	+	0.582928i	0.0985682	+	0.995130i	$0.468574\pi$
$602$		0			0
$603$	11.2136	+	28.3787i	0.456652	+	1.15567i
$604$		0			0
$605$	19.2669	−	5.16255i	0.783310	−	0.209887i
$606$		0			0
$607$	9.32245	+	16.1470i	0.378387	+	0.655385i	0.990828	−	0.135131i	$-0.0431456\pi$
$607$	9.32245	+	16.1470i	0.378387	+	0.655385i	−0.612441	+	0.790516i	$0.709812\pi$
$608$		0			0
$609$	−49.1315	+	2.81612i	−1.99091	+	0.114115i
$610$		0			0
$611$	22.1946	+	22.1946i	0.897896	+	0.897896i
$612$		0			0
$613$	−13.3177	+	13.3177i	−0.537896	+	0.537896i	−0.922911	−	0.385014i	$-0.874196\pi$
$613$	−13.3177	+	13.3177i	−0.537896	+	0.537896i	0.385014	+	0.922911i	$0.374196\pi$
$614$		0			0
$615$	−7.01335	+	4.60349i	−0.282806	+	0.185631i
$616$		0			0
$617$	−15.1035	+	8.72003i	−0.608045	+	0.351055i	−0.772200	−	0.635379i	$-0.780844\pi$
$617$	−15.1035	+	8.72003i	−0.608045	+	0.351055i	0.164155	+	0.986435i	$0.447510\pi$
$618$		0			0
$619$	−5.84959	−	21.8310i	−0.235115	−	0.877461i	−0.978097	−	0.208150i	$-0.933256\pi$
$619$	−5.84959	−	21.8310i	−0.235115	−	0.877461i	0.742982	−	0.669311i	$-0.233411\pi$
$620$		0			0
$621$	0.218963	−	2.42544i	0.00878667	−	0.0973297i
$622$		0			0
$623$	−23.4506	+	40.6177i	−0.939530	+	1.62731i
$624$		0			0
$625$	−4.40527	−	7.63015i	−0.176211	−	0.305206i
$626$		0			0
$627$	−2.46143	+	11.8655i	−0.0983001	+	0.473861i
$628$		0			0
$629$	1.55946	−	1.55946i	0.0621797	−	0.0621797i
$630$		0			0
$631$		−	19.8510i		−	0.790254i	−0.918627	−	0.395127i	$-0.870701\pi$
$631$		−	19.8510i		−	0.790254i	0.918627	−	0.395127i	$-0.129299\pi$
$632$		0			0
$633$	−1.97096	−	34.3865i	−0.0783387	−	1.36674i
$634$		0			0
$635$	−2.70512	−	0.724836i	−0.107350	−	0.0287642i
$636$		0			0
$637$	−34.6254	+	9.27785i	−1.37191	+	0.367602i
$638$		0			0
$639$	−14.7942	−	19.9488i	−0.585249	−	0.789161i
$640$		0			0
$641$	20.5842	−	35.6529i	0.813026	−	1.40820i	−0.0977099	−	0.995215i	$-0.531152\pi$
$641$	20.5842	−	35.6529i	0.813026	−	1.40820i	0.910736	−	0.412988i	$-0.135515\pi$
$642$		0			0
$643$	−6.73128	+	25.1215i	−0.265456	+	0.990694i	0.696515	+	0.717542i	$0.254733\pi$
$643$	−6.73128	+	25.1215i	−0.265456	+	0.990694i	−0.961971	+	0.273152i	$0.911934\pi$
$644$		0			0
$645$	−9.93726	−	30.0818i	−0.391279	−	1.18447i
$646$		0			0
$647$			40.3426i			1.58603i	0.609201	+	0.793016i	$0.291490\pi$
$647$			40.3426i			1.58603i	−0.609201	+	0.793016i	$0.708510\pi$
$648$		0			0
$649$		−	7.35741i		−	0.288803i
$650$		0			0
$651$	14.4762	+	43.8220i	0.567367	+	1.71752i
$652$		0			0
$653$	1.68547	−	6.29024i	0.0659574	−	0.246156i	−0.925074	−	0.379787i	$-0.875997\pi$
$653$	1.68547	−	6.29024i	0.0659574	−	0.246156i	0.991031	+	0.133631i	$0.0426638\pi$
$654$		0			0
$655$	6.33671	−	10.9755i	0.247596	−	0.428849i
$656$		0			0
$657$	−14.5937	−	19.6784i	−0.569353	−	0.767726i
$658$		0			0
$659$	−0.0887093	+	0.0237696i	−0.00345562	+	0.000925932i	−0.260546	−	0.965461i	$-0.583903\pi$
$659$	−0.0887093	+	0.0237696i	−0.00345562	+	0.000925932i	0.257091	+	0.966387i	$0.417236\pi$
$660$		0			0
$661$	27.0157	+	7.23883i	1.05079	+	0.281558i	0.742578	−	0.669760i	$-0.233603\pi$
$661$	27.0157	+	7.23883i	1.05079	+	0.281558i	0.308211	+	0.951318i	$0.400270\pi$
$662$		0			0
$663$	−0.721435	−	12.5865i	−0.0280182	−	0.488821i
$664$		0			0
$665$		−	10.1575i		−	0.393892i
$666$		0			0
$667$	2.24790	−	2.24790i	0.0870392	−	0.0870392i
$668$		0			0
$669$	4.90140	−	23.6274i	0.189499	−	0.913490i
$670$		0			0
$671$	−18.6988	−	32.3873i	−0.721859	−	1.25030i
$672$		0			0
$673$	2.48158	−	4.29822i	0.0956578	−	0.165684i	−0.814225	−	0.580549i	$-0.802838\pi$
$673$	2.48158	−	4.29822i	0.0956578	−	0.165684i	0.909883	+	0.414865i	$0.136171\pi$
$674$		0			0
$675$	−10.5484	+	4.88333i	−0.406009	+	0.187959i
$676$		0			0
$677$	1.77876	+	6.63841i	0.0683632	+	0.255135i	0.991647	−	0.128985i	$-0.0411718\pi$
$677$	1.77876	+	6.63841i	0.0683632	+	0.255135i	−0.923283	+	0.384119i	$0.874505\pi$
$678$		0			0
$679$	41.1923	−	23.7824i	1.58081	−	0.912683i
$680$		0			0
$681$	10.9745	−	7.20357i	0.420545	−	0.276041i
$682$		0			0
$683$	−20.7192	+	20.7192i	−0.792797	+	0.792797i	−0.981948	−	0.189151i	$-0.939426\pi$
$683$	−20.7192	+	20.7192i	−0.792797	+	0.792797i	0.189151	+	0.981948i	$0.439426\pi$
$684$		0			0
$685$	−11.2214	−	11.2214i	−0.428747	−	0.428747i
$686$		0			0
$687$	−33.0540	+	1.89459i	−1.26109	+	0.0722831i
$688$		0			0
$689$	2.83351	+	4.90779i	0.107948	+	0.186972i
$690$		0			0
$691$	5.31450	−	1.42402i	0.202173	−	0.0541721i	−0.156311	−	0.987708i	$-0.549960\pi$
$691$	5.31450	−	1.42402i	0.202173	−	0.0541721i	0.358484	+	0.933536i	$0.383294\pi$
$692$		0			0
$693$	22.1474	+	56.0494i	0.841310	+	2.12914i
$694$		0			0
$695$	−20.8171	−	12.0188i	−0.789638	−	0.455898i
$696$		0			0
$697$	−5.40388	+	3.11993i	−0.204687	+	0.118176i
$698$		0			0
$699$	−5.84834	−	17.7040i	−0.221205	−	0.669626i
$700$		0			0
$701$	−1.06232	−	1.06232i	−0.0401233	−	0.0401233i	0.686760	−	0.726884i	$-0.259032\pi$
$701$	−1.06232	−	1.06232i	−0.0401233	−	0.0401233i	−0.726884	+	0.686760i	$0.759032\pi$
$702$		0			0
$703$	1.50244			0.0566656
$704$		0			0
$705$	−11.9537	+	23.7471i	−0.450202	+	0.894368i
$706$		0			0
$707$	3.25705	−	12.1555i	0.122494	−	0.457153i
$708$		0			0
$709$	−9.50159	−	35.4604i	−0.356840	−	1.33174i	−0.878153	−	0.478379i	$-0.841224\pi$
$709$	−9.50159	−	35.4604i	−0.356840	−	1.33174i	0.521314	−	0.853365i	$-0.325442\pi$
$710$		0			0
$711$	2.48904	+	21.6412i	0.0933463	+	0.811609i
$712$		0			0
$713$	−2.58187	−	1.49064i	−0.0966916	−	0.0558249i
$714$		0			0
$715$	−26.1729	−	7.01301i	−0.978812	−	0.262272i
$716$		0			0
$717$	28.8116	+	25.6878i	1.07599	+	0.959328i
$718$		0			0
$719$	7.37513			0.275046			0.137523	−	0.990499i	$-0.456086\pi$
$719$	7.37513			0.275046			0.137523	+	0.990499i	$0.456086\pi$
$720$		0			0
$721$	−6.03749			−0.224848
$722$		0			0
$723$	9.65981	−	46.5656i	0.359252	−	1.73179i
$724$		0			0
$725$	−14.6567	−	3.92726i	−0.544337	−	0.145855i
$726$		0			0
$727$	−5.80127	−	3.34936i	−0.215157	−	0.124221i	0.388549	−	0.921428i	$-0.372977\pi$
$727$	−5.80127	−	3.34936i	−0.215157	−	0.124221i	−0.603706	+	0.797207i	$0.706310\pi$
$728$		0			0
$729$	−9.09400	−	25.4224i	−0.336815	−	0.941571i
$730$		0			0
$731$	−6.09879	−	22.7610i	−0.225572	−	0.841846i
$732$		0			0
$733$	−9.28281	+	34.6439i	−0.342868	+	1.27960i	0.552214	+	0.833702i	$0.313783\pi$
$733$	−9.28281	+	34.6439i	−0.342868	+	1.27960i	−0.895083	+	0.445900i	$0.852884\pi$
$734$		0			0
$735$	−16.6613	−	25.3832i	−0.614560	−	0.936272i
$736$		0			0
$737$	48.7797			1.79682
$738$		0			0
$739$	−4.01107	−	4.01107i	−0.147549	−	0.147549i	0.629473	−	0.777022i	$-0.283271\pi$
$739$	−4.01107	−	4.01107i	−0.147549	−	0.147549i	−0.777022	+	0.629473i	$0.783271\pi$
$740$		0			0
$741$	5.71564	−	6.41070i	0.209969	−	0.235503i
$742$		0			0
$743$	−19.1551	+	11.0592i	−0.702734	+	0.405724i	−0.808365	−	0.588682i	$-0.799647\pi$
$743$	−19.1551	+	11.0592i	−0.702734	+	0.405724i	0.105631	+	0.994405i	$0.466314\pi$
$744$		0			0
$745$	2.47761	+	1.43045i	0.0907726	+	0.0524076i
$746$		0			0
$747$	14.6579	−	18.4678i	0.536305	−	0.675703i
$748$		0			0
$749$	33.5083	−	8.97853i	1.22437	−	0.328068i
$750$		0			0
$751$	6.05672	+	10.4905i	0.221013	+	0.382805i	0.955116	−	0.296233i	$-0.0957304\pi$
$751$	6.05672	+	10.4905i	0.221013	+	0.382805i	−0.734103	+	0.679038i	$0.762397\pi$
$752$		0			0
$753$	−12.5691	+	24.9697i	−0.458044	+	0.909947i
$754$		0			0
$755$	25.1178	+	25.1178i	0.914131	+	0.914131i
$756$		0			0
$757$	−19.9365	+	19.9365i	−0.724604	+	0.724604i	−0.969539	−	0.244935i	$-0.921233\pi$
$757$	−19.9365	+	19.9365i	−0.724604	+	0.724604i	0.244935	+	0.969539i	$0.421233\pi$
$758$		0			0
$759$	−3.47739	−	1.75043i	−0.126221	−	0.0635366i
$760$		0			0
$761$	−37.1681	+	21.4590i	−1.34734	+	0.777889i	−0.987873	−	0.155267i	$-0.950376\pi$
$761$	−37.1681	+	21.4590i	−1.34734	+	0.777889i	−0.359471	+	0.933156i	$0.617043\pi$
$762$		0			0
$763$	3.14690	+	11.7444i	0.113925	+	0.425176i
$764$		0			0
$765$	9.93130	−	3.92426i	0.359067	−	0.141882i
$766$		0			0
$767$	−2.60728	+	4.51595i	−0.0941435	+	0.163061i
$768$		0			0
$769$	−13.7618	−	23.8361i	−0.496263	−	0.859553i	0.503728	−	0.863863i	$-0.331962\pi$
$769$	−13.7618	−	23.8361i	−0.496263	−	0.859553i	−0.999991	+	0.00430961i	$0.998628\pi$
$770$		0			0
$771$	−2.40564	−	2.14482i	−0.0866371	−	0.0772438i
$772$		0			0
$773$	−11.4688	+	11.4688i	−0.412504	+	0.412504i	−0.882610	−	0.470106i	$-0.844216\pi$
$773$	−11.4688	+	11.4688i	−0.412504	+	0.412504i	0.470106	+	0.882610i	$0.344216\pi$
$774$		0			0
$775$			14.2300i			0.511155i
$776$		0			0
$777$	6.24658	−	4.10019i	0.224095	−	0.147094i
$778$		0			0
$779$	−4.10608	−	1.10022i	−0.147115	−	0.0394195i
$780$		0			0
$781$	−38.3500	+	10.2759i	−1.37227	+	0.367699i
$782$		0			0
$783$	12.1462	−	33.0864i	0.434071	−	1.18241i
$784$		0			0
$785$	−8.81622	+	15.2701i	−0.314664	+	0.545015i
$786$		0			0
$787$	−11.4753	+	42.8263i	−0.409049	+	1.52659i	0.387414	+	0.921906i	$0.373368\pi$
$787$	−11.4753	+	42.8263i	−0.409049	+	1.52659i	−0.796463	+	0.604687i	$0.793298\pi$
$788$		0			0
$789$	−0.0812387	−	0.0168526i	−0.00289217	−	0.000599968i
$790$		0			0
$791$			34.5766i			1.22940i
$792$		0			0
$793$			26.5056i			0.941241i
$794$		0			0
$795$	−3.19437	+	3.58282i	−0.113292	+	0.127070i
$796$		0			0
$797$	7.68647	−	28.6863i	0.272269	−	1.01612i	−0.685381	−	0.728185i	$-0.740364\pi$
$797$	7.68647	−	28.6863i	0.272269	−	1.01612i	0.957650	−	0.287936i	$-0.0929690\pi$
$798$		0			0
$799$	−9.88726	+	17.1252i	−0.349786	+	0.605847i
$800$		0			0
$801$	−20.0091	−	26.9806i	−0.706985	−	0.953312i
$802$		0			0
$803$	−37.8302	+	10.1366i	−1.33500	+	0.357712i
$804$		0			0
$805$	3.15206	+	0.844592i	0.111096	+	0.0297679i
$806$		0			0
$807$	−31.8741	−	16.0446i	−1.12202	−	0.564796i
$808$		0			0
$809$			16.7474i			0.588806i	0.955681	+	0.294403i	$0.0951209\pi$
$809$			16.7474i			0.588806i	−0.955681	+	0.294403i	$0.904879\pi$
$810$		0			0
$811$	7.60619	−	7.60619i	0.267090	−	0.267090i	−0.560837	−	0.827926i	$-0.689520\pi$
$811$	7.60619	−	7.60619i	0.267090	−	0.267090i	0.827926	+	0.560837i	$0.189520\pi$
$812$		0			0
$813$	25.9535	−	8.57349i	0.910229	−	0.300685i
$814$		0			0
$815$	−4.08582	−	7.07684i	−0.143120	−	0.247891i
$816$		0			0
$817$	8.02649	−	13.9023i	0.280811	−	0.486379i
$818$		0			0
$819$	6.26855	−	42.2514i	0.219041	−	1.47638i
$820$		0			0
$821$	−9.99074	−	37.2860i	−0.348679	−	1.30129i	−0.888255	−	0.459351i	$-0.848082\pi$
$821$	−9.99074	−	37.2860i	−0.348679	−	1.30129i	0.539575	−	0.841937i	$-0.318585\pi$
$822$		0			0
$823$	23.9783	−	13.8439i	0.835831	−	0.482567i	−0.0200141	−	0.999800i	$-0.506371\pi$
$823$	23.9783	−	13.8439i	0.835831	−	0.482567i	0.855845	+	0.517233i	$0.173038\pi$
$824$		0			0
$825$	1.06335	+	18.5517i	0.0370210	+	0.645888i
$826$		0			0
$827$	27.6025	−	27.6025i	0.959833	−	0.959833i	−0.0393907	−	0.999224i	$-0.512542\pi$
$827$	27.6025	−	27.6025i	0.959833	−	0.959833i	0.999224	+	0.0393907i	$0.0125417\pi$
$828$		0			0
$829$	14.8542	+	14.8542i	0.515908	+	0.515908i	0.916330	−	0.400423i	$-0.131137\pi$
$829$	14.8542	+	14.8542i	0.515908	+	0.515908i	−0.400423	+	0.916330i	$0.631137\pi$
$830$		0			0
$831$	−7.09819	−	10.8140i	−0.246234	−	0.375133i
$832$		0			0
$833$	−11.2919	−	19.5581i	−0.391240	−	0.677647i
$834$		0			0
$835$	0.514368	−	0.137824i	0.0178004	−	0.00476961i
$836$		0			0
$837$	−32.9193	−	2.97187i	−1.13786	−	0.102723i
$838$		0			0
$839$	44.0413	+	25.4272i	1.52047	+	0.877846i	0.999708	+	0.0241463i	$0.00768676\pi$
$839$	44.0413	+	25.4272i	1.52047	+	0.877846i	0.520766	+	0.853700i	$0.325647\pi$
$840$		0			0
$841$	14.7301	−	8.50445i	0.507936	−	0.293257i
$842$		0			0
$843$	−11.4451	−	2.37424i	−0.394191	−	0.0817731i
$844$		0			0
$845$	−1.70015	−	1.70015i	−0.0584871	−	0.0584871i
$846$		0			0
$847$	50.2656			1.72715
$848$		0			0
$849$	−22.2727	+	1.27663i	−0.764398	+	0.0438137i
$850$		0			0
$851$	−0.124927	+	0.466233i	−0.00428244	+	0.0159823i
$852$		0			0
$853$	3.65390	+	13.6365i	0.125107	+	0.466906i	0.999843	−	0.0176931i	$-0.00563219\pi$
$853$	3.65390	+	13.6365i	0.125107	+	0.466906i	−0.874736	+	0.484599i	$0.838966\pi$
$854$		0			0
$855$	6.67448	+	2.89370i	0.228262	+	0.0989625i
$856$		0			0
$857$	14.7618	+	8.52275i	0.504255	+	0.291132i	0.730469	−	0.682946i	$-0.239302\pi$
$857$	14.7618	+	8.52275i	0.504255	+	0.291132i	−0.226214	+	0.974078i	$0.572635\pi$
$858$		0			0
$859$	−24.9255	−	6.67877i	−0.850448	−	0.227877i	−0.192833	−	0.981232i	$-0.561768\pi$
$859$	−24.9255	−	6.67877i	−0.850448	−	0.227877i	−0.657614	+	0.753355i	$0.728434\pi$
$860$		0			0
$861$	−20.0741	+	6.63128i	−0.684122	+	0.225993i
$862$		0			0
$863$	18.8217			0.640698			0.320349	−	0.947300i	$-0.396200\pi$
$863$	18.8217			0.640698			0.320349	+	0.947300i	$0.396200\pi$
$864$		0			0
$865$	−20.1170			−0.683999
$866$		0			0
$867$	−20.4171	+	6.74459i	−0.693401	+	0.229058i
$868$		0			0
$869$	33.6373	+	9.01309i	1.14107	+	0.305748i
$870$		0			0
$871$	−29.9408	−	17.2863i	−1.01450	−	0.585725i
$872$		0			0
$873$	3.89235	+	33.8424i	0.131736	+	1.14539i
$874$		0			0
$875$	−13.0417	−	48.6724i	−0.440891	−	1.64543i
$876$		0			0
$877$	2.80014	−	10.4503i	0.0945540	−	0.352880i	−0.902397	−	0.430905i	$-0.858195\pi$
$877$	2.80014	−	10.4503i	0.0945540	−	0.352880i	0.996951	+	0.0780244i	$0.0248612\pi$
$878$		0			0
$879$	24.8455	−	1.42409i	0.838018	−	0.0480335i
$880$		0			0
$881$	40.1658			1.35322			0.676610	−	0.736342i	$-0.263448\pi$
$881$	40.1658			1.35322			0.676610	+	0.736342i	$0.263448\pi$
$882$		0			0
$883$	16.5617	+	16.5617i	0.557346	+	0.557346i	0.928551	−	0.371205i	$-0.121055\pi$
$883$	16.5617	+	16.5617i	0.557346	+	0.557346i	−0.371205	+	0.928551i	$0.621055\pi$
$884$		0			0
$885$	−4.32475	−	0.897148i	−0.145375	−	0.0301573i
$886$		0			0
$887$	13.1259	−	7.57822i	0.440723	−	0.254452i	−0.263181	−	0.964746i	$-0.584772\pi$
$887$	13.1259	−	7.57822i	0.440723	−	0.254452i	0.703904	+	0.710295i	$0.251438\pi$
$888$		0			0
$889$	−6.11191	−	3.52871i	−0.204987	−	0.118349i
$890$		0			0
$891$	−43.1393	−	1.41453i	−1.44522	−	0.0473885i
$892$		0			0
$893$	−13.0124	+	3.48667i	−0.435444	+	0.116677i
$894$		0			0
$895$	21.9535	+	38.0246i	0.733826	+	1.27102i
$896$		0			0
$897$	1.51410	+	2.30671i	0.0505543	+	0.0770187i
$898$		0			0
$899$	−30.5097	−	30.5097i	−1.01755	−	1.01755i
$900$		0			0
$901$	−2.52455	+	2.52455i	−0.0841050	+	0.0841050i
$902$		0			0
$903$	−4.56853	−	79.7050i	−0.152031	−	2.65242i
$904$		0			0
$905$	−8.35749	+	4.82520i	−0.277812	+	0.160395i
$906$		0			0
$907$	2.61434	+	9.75684i	0.0868077	+	0.323971i	0.995650	−	0.0931683i	$-0.0296995\pi$
$907$	2.61434	+	9.75684i	0.0868077	+	0.323971i	−0.908843	+	0.417139i	$0.863033\pi$
$908$		0			0
$909$	7.05943	+	5.60307i	0.234146	+	0.185842i
$910$		0			0
$911$	25.2358	−	43.7097i	0.836099	−	1.44817i	−0.0570332	−	0.998372i	$-0.518164\pi$
$911$	25.2358	−	43.7097i	0.836099	−	1.44817i	0.893132	−	0.449794i	$-0.148503\pi$
$912$		0			0
$913$	−18.8459	−	32.6420i	−0.623708	−	1.08029i
$914$		0			0
$915$	−21.3176	+	7.04208i	−0.704739	+	0.232804i
$916$		0			0
$917$	22.5830	−	22.5830i	0.745757	−	0.745757i
$918$		0			0
$919$			16.7422i			0.552274i	0.961118	+	0.276137i	$0.0890544\pi$
$919$			16.7422i			0.552274i	−0.961118	+	0.276137i	$0.910946\pi$
$920$		0			0
$921$	−26.7789	−	13.4798i	−0.882396	−	0.444175i
$922$		0			0
$923$	27.1806	+	7.28302i	0.894661	+	0.239724i
$924$		0			0
$925$	2.22538	−	0.596288i	0.0731699	−	0.0196058i
$926$		0			0
$927$	1.71998	−	3.96721i	0.0564914	−	0.130300i
$928$		0			0
$929$	9.92665	−	17.1935i	0.325683	−	0.564099i	−0.655967	−	0.754789i	$-0.727739\pi$
$929$	9.92665	−	17.1935i	0.325683	−	0.564099i	0.981650	+	0.190690i	$0.0610725\pi$
$930$		0			0
$931$	3.98199	−	14.8610i	0.130504	−	0.487049i
$932$		0			0
$933$	0.988613	−	1.10883i	0.0323657	−	0.0363016i
$934$		0			0
$935$		−	17.0708i		−	0.558273i
$936$		0			0
$937$		−	3.05876i		−	0.0999253i	−0.998751	−	0.0499626i	$-0.984090\pi$
$937$		−	3.05876i		−	0.0999253i	0.998751	−	0.0499626i	$-0.0159102\pi$
$938$		0			0
$939$	−31.1340	−	6.45859i	−1.01602	−	0.210768i
$940$		0			0
$941$	3.07424	−	11.4732i	0.100217	−	0.374016i	−0.897541	−	0.440930i	$-0.854649\pi$
$941$	3.07424	−	11.4732i	0.100217	−	0.374016i	0.997759	+	0.0669140i	$0.0213153\pi$
$942$		0			0
$943$	0.682835	−	1.18270i	0.0222362	−	0.0385141i
$944$		0			0
$945$	35.6470	−	6.18387i	1.15960	−	0.201161i
$946$		0			0
$947$	55.6732	−	14.9176i	1.80914	−	0.484757i	0.813794	−	0.581153i	$-0.197398\pi$
$947$	55.6732	−	14.9176i	1.80914	−	0.484757i	0.995343	+	0.0963965i	$0.0307317\pi$
$948$		0			0
$949$	26.8122	+	7.18430i	0.870360	+	0.233212i
$950$		0			0
$951$	−6.03585	+	3.96187i	−0.195726	+	0.128472i
$952$		0			0
$953$			44.2546i			1.43355i	0.697306	+	0.716774i	$0.254382\pi$
$953$			44.2546i			1.43355i	−0.697306	+	0.716774i	$0.745618\pi$
$954$		0			0
$955$	20.2186	−	20.2186i	0.654259	−	0.654259i
$956$		0			0
$957$	−42.0556	−	37.4958i	−1.35946	−	1.21207i
$958$		0			0
$959$	−19.9956	−	34.6334i	−0.645691	−	1.11837i
$960$		0			0
$961$	−4.73171	+	8.19557i	−0.152636	+	0.264373i
$962$		0			0
$963$	−3.64617	+	24.5760i	−0.117496	+	0.791951i
$964$		0			0
$965$	−7.89407	−	29.4611i	−0.254119	−	0.948386i
$966$		0			0
$967$	−36.7930	+	21.2424i	−1.18318	+	0.683110i	−0.956748	−	0.290916i	$-0.906040\pi$
$967$	−36.7930	+	21.2424i	−1.18318	+	0.683110i	−0.226433	+	0.974027i	$0.572706\pi$
$968$		0			0
$969$	4.83314	+	2.43288i	0.155263	+	0.0781552i
$970$		0			0
$971$	−11.1469	+	11.1469i	−0.357720	+	0.357720i	−0.862972	−	0.505252i	$-0.831400\pi$
$971$	−11.1469	+	11.1469i	−0.357720	+	0.357720i	0.505252	+	0.862972i	$0.331400\pi$
$972$		0			0
$973$	−42.8329	−	42.8329i	−1.37316	−	1.37316i
$974$		0			0
$975$	5.92159	−	11.7638i	0.189643	−	0.376743i
$976$		0			0
$977$	−2.47430	−	4.28561i	−0.0791598	−	0.137109i	0.823728	−	0.566985i	$-0.191890\pi$
$977$	−2.47430	−	4.28561i	−0.0791598	−	0.137109i	−0.902888	+	0.429877i	$0.858557\pi$
$978$		0			0
$979$	−51.8682	+	13.8980i	−1.65771	+	0.444183i
$980$		0			0
$981$	−8.61369	−	1.27795i	−0.275014	−	0.0408019i
$982$		0			0
$983$	−41.6831	−	24.0658i	−1.32948	−	0.767578i	−0.344265	−	0.938873i	$-0.611872\pi$
$983$	−41.6831	−	24.0658i	−1.32948	−	0.767578i	−0.985220	+	0.171294i	$0.945205\pi$
$984$		0			0
$985$	−17.9237	+	10.3483i	−0.571098	+	0.329724i
$986$		0			0
$987$	−44.5856	+	50.0074i	−1.41917	+	1.59175i
$988$		0			0
$989$	3.64672	+	3.64672i	0.115959	+	0.115959i
$990$		0			0
$991$	8.90020			0.282724			0.141362	−	0.989958i	$-0.454852\pi$
$991$	8.90020			0.282724			0.141362	+	0.989958i	$0.454852\pi$
$992$		0			0
$993$	−4.91103	−	7.48188i	−0.155847	−	0.237430i
$994$		0			0
$995$	4.31407	−	16.1003i	0.136765	−	0.510414i
$996$		0			0
$997$	6.66586	+	24.8773i	0.211110	+	0.787873i	0.987500	+	0.157620i	$0.0503822\pi$
$997$	6.66586	+	24.8773i	0.211110	+	0.787873i	−0.776390	+	0.630253i	$0.782951\pi$
$998$		0			0
$999$	0.914680	+	5.27268i	0.0289392	+	0.166820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.529.16		72
3.2	odd	2		1728.2.bc.e.721.13		72
4.3	odd	2		144.2.x.e.61.7	yes	72
9.4	even	3	inner	576.2.bb.e.337.8		72
9.5	odd	6		1728.2.bc.e.145.6		72
12.11	even	2		432.2.y.e.397.12		72
16.5	even	4	inner	576.2.bb.e.241.8		72
16.11	odd	4		144.2.x.e.133.18	yes	72
36.23	even	6		432.2.y.e.253.1		72
36.31	odd	6		144.2.x.e.13.18	✓	72
48.5	odd	4		1728.2.bc.e.1585.6		72
48.11	even	4		432.2.y.e.181.1		72
144.5	odd	12		1728.2.bc.e.1009.13		72
144.59	even	12		432.2.y.e.37.12		72
144.85	even	12	inner	576.2.bb.e.49.16		72
144.139	odd	12		144.2.x.e.85.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.18	✓	72	36.31	odd	6
144.2.x.e.61.7	yes	72	4.3	odd	2
144.2.x.e.85.7	yes	72	144.139	odd	12
144.2.x.e.133.18	yes	72	16.11	odd	4
432.2.y.e.37.12		72	144.59	even	12
432.2.y.e.181.1		72	48.11	even	4
432.2.y.e.253.1		72	36.23	even	6
432.2.y.e.397.12		72	12.11	even	2
576.2.bb.e.49.16		72	144.85	even	12	inner
576.2.bb.e.241.8		72	16.5	even	4	inner
576.2.bb.e.337.8		72	9.4	even	3	inner
576.2.bb.e.529.16		72	1.1	even	1	trivial
1728.2.bc.e.145.6		72	9.5	odd	6
1728.2.bc.e.721.13		72	3.2	odd	2
1728.2.bc.e.1009.13		72	144.5	odd	12
1728.2.bc.e.1585.6		72	48.5	odd	4

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.64464 - 0.543291i) q^{3} +(-1.60558 - 0.430214i) q^{5} +(-3.62762 - 2.09441i) q^{7} +(2.40967 - 1.78703i) q^{9} +O(q^{10})\)	\(q+(1.64464 - 0.543291i) q^{3} +(-1.60558 - 0.430214i) q^{5} +(-3.62762 - 2.09441i) q^{7} +(2.40967 - 1.78703i) q^{9} +(-1.24125 - 4.63241i) q^{11} +(-0.879738 + 3.28323i) q^{13} +(-2.87433 + 0.164751i) q^{15} -2.14142 q^{17} +(-1.03156 - 1.03156i) q^{19} +(-7.10399 - 1.47369i) q^{21} +(0.405884 - 0.234337i) q^{23} +(-1.93733 - 1.11852i) q^{25} +(2.99216 - 4.24818i) q^{27} +(6.55186 - 1.75557i) q^{29} +(-3.18054 - 5.50886i) q^{31} +(-4.55816 - 6.94428i) q^{33} +(4.92339 + 4.92339i) q^{35} +(-0.728237 + 0.728237i) q^{37} +(0.336896 + 5.87767i) q^{39} +(2.52351 - 1.45695i) q^{41} +(2.84802 + 10.6289i) q^{43} +(-4.63772 + 1.83255i) q^{45} +(4.61716 - 7.99715i) q^{47} +(5.27308 + 9.13324i) q^{49} +(-3.52186 + 1.16341i) q^{51} +(1.17892 - 1.17892i) q^{53} +7.97171i q^{55} +(-2.25698 - 1.13611i) q^{57} +(1.48185 + 0.397061i) q^{59} +(7.53224 - 2.01826i) q^{61} +(-12.4841 + 1.43585i) q^{63} +(2.82498 - 4.89300i) q^{65} +(-2.63252 + 9.82470i) q^{67} +(0.540220 - 0.605914i) q^{69} -8.27863i q^{71} -8.16641i q^{73} +(-3.79388 - 0.787022i) q^{75} +(-5.19937 + 19.4043i) q^{77} +(-3.63065 + 6.28847i) q^{79} +(2.61302 - 8.61232i) q^{81} +(7.59149 - 2.03413i) q^{83} +(3.43821 + 0.921267i) q^{85} +(9.82166 - 6.44684i) q^{87} -11.1968i q^{89} +(10.0678 - 10.0678i) q^{91} +(-8.22376 - 7.33213i) q^{93} +(1.21246 + 2.10004i) q^{95} +(-5.67759 + 9.83387i) q^{97} +(-11.2693 - 8.94443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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