LMFDB - Embedded newform 525.2.j.c.407.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(218,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("525.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			407.1
Character	$\chi$	$=$	525.407
Dual form			525.2.j.c.218.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90099 + 1.90099i) q^{2} +(0.394708 + 1.68648i) q^{3} -5.22756i q^{4} +(-3.95632 - 2.45565i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(6.13557 + 6.13557i) q^{8} +(-2.68841 + 1.33133i) q^{9} +O(q^{10})$	\(q+(-1.90099 + 1.90099i) q^{2} +(0.394708 + 1.68648i) q^{3} -5.22756i q^{4} +(-3.95632 - 2.45565i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(6.13557 + 6.13557i) q^{8} +(-2.68841 + 1.33133i) q^{9} +3.76571i q^{11} +(8.81616 - 2.06336i) q^{12} +(-3.48012 + 3.48012i) q^{13} +2.68841 q^{14} -12.8723 q^{16} +(0.131909 - 0.131909i) q^{17} +(2.57980 - 7.64151i) q^{18} -3.89623i q^{19} +(0.913419 - 1.47162i) q^{21} +(-7.15860 - 7.15860i) q^{22} +(-3.35232 - 3.35232i) q^{23} +(-7.92574 + 12.7693i) q^{24} -13.2314i q^{26} +(-3.30640 - 4.00846i) q^{27} +(-3.69644 + 3.69644i) q^{28} -4.27537 q^{29} +3.35375 q^{31} +(12.1989 - 12.1989i) q^{32} +(-6.35079 + 1.48636i) q^{33} +0.501515i q^{34} +(6.95961 + 14.0538i) q^{36} +(-4.98611 - 4.98611i) q^{37} +(7.40671 + 7.40671i) q^{38} +(-7.24276 - 4.49551i) q^{39} -1.16173i q^{41} +(1.06114 + 4.53395i) q^{42} +(2.05955 - 2.05955i) q^{43} +19.6855 q^{44} +12.7455 q^{46} +(-7.97686 + 7.97686i) q^{47} +(-5.08077 - 21.7088i) q^{48} +1.00000i q^{49} +(0.274526 + 0.170396i) q^{51} +(18.1925 + 18.1925i) q^{52} +(3.80199 + 3.80199i) q^{53} +(13.9055 + 1.33462i) q^{54} -8.67701i q^{56} +(6.57090 - 1.53787i) q^{57} +(8.12745 - 8.12745i) q^{58} -7.06590 q^{59} -4.11035 q^{61} +(-6.37546 + 6.37546i) q^{62} +(2.84239 + 0.959601i) q^{63} +20.6357i q^{64} +(9.24726 - 14.8984i) q^{66} +(0.153550 + 0.153550i) q^{67} +(-0.689561 - 0.689561i) q^{68} +(4.33043 - 6.97680i) q^{69} +2.12077i q^{71} +(-24.6634 - 8.32647i) q^{72} +(9.79331 - 9.79331i) q^{73} +18.9571 q^{74} -20.3678 q^{76} +(2.66276 - 2.66276i) q^{77} +(22.3144 - 5.22252i) q^{78} -0.147763i q^{79} +(5.45512 - 7.15833i) q^{81} +(2.20845 + 2.20845i) q^{82} +(-2.58598 - 2.58598i) q^{83} +(-7.69298 - 4.77495i) q^{84} +7.83038i q^{86} +(-1.68752 - 7.21031i) q^{87} +(-23.1048 + 23.1048i) q^{88} +1.17942 q^{89} +4.92163 q^{91} +(-17.5245 + 17.5245i) q^{92} +(1.32375 + 5.65603i) q^{93} -30.3279i q^{94} +(25.3882 + 15.7582i) q^{96} +(-1.52395 - 1.52395i) q^{97} +(-1.90099 - 1.90099i) q^{98} +(-5.01341 - 10.1238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{6}+O(q^{10}) $ 32 * q - 16 * q^6	$ 32 q - 16 q^{6} - 16 q^{16} - 8 q^{21} + 16 q^{31} + 48 q^{36} + 144 q^{46} - 64 q^{51} - 112 q^{61} - 192 q^{76} - 64 q^{81} + 64 q^{91} + 360 q^{96}+O(q^{100}) $ 32 * q - 16 * q^6 - 16 * q^16 - 8 * q^21 + 16 * q^31 + 48 * q^36 + 144 * q^46 - 64 * q^51 - 112 * q^61 - 192 * q^76 - 64 * q^81 + 64 * q^91 + 360 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.90099	+	1.90099i	−1.34421	+	1.34421i	−0.452381	+	0.891825i	$0.649425\pi$
$2$	−1.90099	+	1.90099i	−1.34421	+	1.34421i	−0.891825	+	0.452381i	$0.850575\pi$
$3$	0.394708	+	1.68648i	0.227885	+	0.973688i
$3$	0.394708	+	1.68648i	0.227885	+	0.973688i
$4$		−	5.22756i		−	2.61378i
$5$		0			0
$5$		0			0
$6$	−3.95632	−	2.45565i	−1.61516	−	1.00251i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	6.13557	+	6.13557i	2.16925	+	2.16925i
$9$	−2.68841	+	1.33133i	−0.896137	+	0.443777i
$10$		0			0
$11$			3.76571i			1.13541i	0.823234	+	0.567703i	$0.192168\pi$
$11$			3.76571i			1.13541i	−0.823234	+	0.567703i	$0.807832\pi$
$12$	8.81616	−	2.06336i	2.54501	−	0.595640i
$13$	−3.48012	+	3.48012i	−0.965210	+	0.965210i	−0.999415	−	0.0342046i	$-0.989110\pi$
$13$	−3.48012	+	3.48012i	−0.965210	+	0.965210i	0.0342046	+	0.999415i	$0.489110\pi$
$14$	2.68841			0.718508
$15$		0			0
$16$	−12.8723			−3.21806
$17$	0.131909	−	0.131909i	0.0319926	−	0.0319926i	−0.690930	−	0.722922i	$-0.742799\pi$
$17$	0.131909	−	0.131909i	0.0319926	−	0.0319926i	0.722922	+	0.690930i	$0.242799\pi$
$18$	2.57980	−	7.64151i	0.608066	−	1.80112i
$19$		−	3.89623i		−	0.893856i	−0.894570	−	0.446928i	$-0.852518\pi$
$19$		−	3.89623i		−	0.893856i	0.894570	−	0.446928i	$-0.147482\pi$
$20$		0			0
$21$	0.913419	−	1.47162i	0.199324	−	0.321134i
$22$	−7.15860	−	7.15860i	−1.52622	−	1.52622i
$23$	−3.35232	−	3.35232i	−0.699007	−	0.699007i	0.265189	−	0.964196i	$-0.414566\pi$
$23$	−3.35232	−	3.35232i	−0.699007	−	0.699007i	−0.964196	+	0.265189i	$0.914566\pi$
$24$	−7.92574	+	12.7693i	−1.61784	+	2.60651i
$25$		0			0
$26$		−	13.2314i		−	2.59488i
$27$	−3.30640	−	4.00846i	−0.636316	−	0.771428i
$28$	−3.69644	+	3.69644i	−0.698562	+	0.698562i
$29$	−4.27537			−0.793916			−0.396958	−	0.917837i	$-0.629934\pi$
$29$	−4.27537			−0.793916			−0.396958	+	0.917837i	$0.629934\pi$
$30$		0			0
$31$	3.35375			0.602352			0.301176	−	0.953569i	$-0.402621\pi$
$31$	3.35375			0.602352			0.301176	+	0.953569i	$0.402621\pi$
$32$	12.1989	−	12.1989i	2.15649	−	2.15649i
$33$	−6.35079	+	1.48636i	−1.10553	+	0.258741i
$34$			0.501515i			0.0860092i
$35$		0			0
$36$	6.95961	+	14.0538i	1.15993	+	2.34231i
$37$	−4.98611	−	4.98611i	−0.819711	−	0.819711i	0.166355	−	0.986066i	$-0.446800\pi$
$37$	−4.98611	−	4.98611i	−0.819711	−	0.819711i	−0.986066	+	0.166355i	$0.946800\pi$
$38$	7.40671	+	7.40671i	1.20153	+	1.20153i
$39$	−7.24276	−	4.49551i	−1.15977	−	0.719857i
$40$		0			0
$41$		−	1.16173i		−	0.181432i	−0.995877	−	0.0907161i	$-0.971084\pi$
$41$		−	1.16173i		−	0.181432i	0.995877	−	0.0907161i	$-0.0289156\pi$
$42$	1.06114	+	4.53395i	0.163737	+	0.699603i
$43$	2.05955	−	2.05955i	0.314078	−	0.314078i	−0.532409	−	0.846487i	$-0.678713\pi$
$43$	2.05955	−	2.05955i	0.314078	−	0.314078i	0.846487	+	0.532409i	$0.178713\pi$
$44$	19.6855			2.96770
$45$		0			0
$46$	12.7455			1.87922
$47$	−7.97686	+	7.97686i	−1.16354	+	1.16354i	−0.179851	+	0.983694i	$0.557562\pi$
$47$	−7.97686	+	7.97686i	−1.16354	+	1.16354i	−0.983694	+	0.179851i	$0.942438\pi$
$48$	−5.08077	−	21.7088i	−0.733347	−	3.13339i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	0.274526	+	0.170396i	0.0384414	+	0.0238602i
$52$	18.1925	+	18.1925i	2.52285	+	2.52285i
$53$	3.80199	+	3.80199i	0.522243	+	0.522243i	0.918248	−	0.396005i	$-0.129604\pi$
$53$	3.80199	+	3.80199i	0.522243	+	0.522243i	−0.396005	+	0.918248i	$0.629604\pi$
$54$	13.9055	+	1.33462i	1.89230	+	0.181619i
$55$		0			0
$56$		−	8.67701i		−	1.15951i
$57$	6.57090	−	1.53787i	0.870337	−	0.203696i
$58$	8.12745	−	8.12745i	1.06719	−	1.06719i
$59$	−7.06590			−0.919901			−0.459951	−	0.887945i	$-0.652133\pi$
$59$	−7.06590			−0.919901			−0.459951	+	0.887945i	$0.652133\pi$
$60$		0			0
$61$	−4.11035			−0.526276			−0.263138	−	0.964758i	$-0.584758\pi$
$61$	−4.11035			−0.526276			−0.263138	+	0.964758i	$0.584758\pi$
$62$	−6.37546	+	6.37546i	−0.809685	+	0.809685i
$63$	2.84239	+	0.959601i	0.358107	+	0.120898i
$64$			20.6357i			2.57946i
$65$		0			0
$66$	9.24726	−	14.8984i	1.13826	−	1.83386i
$67$	0.153550	+	0.153550i	0.0187591	+	0.0187591i	0.716424	−	0.697665i	$-0.245778\pi$
$67$	0.153550	+	0.153550i	0.0187591	+	0.0187591i	−0.697665	+	0.716424i	$0.745778\pi$
$68$	−0.689561	−	0.689561i	−0.0836215	−	0.0836215i
$69$	4.33043	−	6.97680i	0.521322	−	0.839908i
$70$		0			0
$71$			2.12077i			0.251689i	0.992050	+	0.125844i	$0.0401640\pi$
$71$			2.12077i			0.251689i	−0.992050	+	0.125844i	$0.959836\pi$
$72$	−24.6634	−	8.32647i	−2.90661	−	0.981283i
$73$	9.79331	−	9.79331i	1.14622	−	1.14622i	0.158930	−	0.987290i	$-0.449196\pi$
$73$	9.79331	−	9.79331i	1.14622	−	1.14622i	0.987290	−	0.158930i	$-0.0508045\pi$
$74$	18.9571			2.20372
$75$		0			0
$76$	−20.3678			−2.33634
$77$	2.66276	−	2.66276i	0.303450	−	0.303450i
$78$	22.3144	−	5.22252i	2.52661	−	0.591334i
$79$		−	0.147763i		−	0.0166247i	−0.999965	−	0.00831234i	$-0.997354\pi$
$79$		−	0.147763i		−	0.0166247i	0.999965	−	0.00831234i	$-0.00264593\pi$
$80$		0			0
$81$	5.45512	−	7.15833i	0.606124	−	0.795370i
$82$	2.20845	+	2.20845i	0.243882	+	0.243882i
$83$	−2.58598	−	2.58598i	−0.283848	−	0.283848i	0.550794	−	0.834642i	$-0.314325\pi$
$83$	−2.58598	−	2.58598i	−0.283848	−	0.283848i	−0.834642	+	0.550794i	$0.814325\pi$
$84$	−7.69298	−	4.77495i	−0.839373	−	0.520990i
$85$		0			0
$86$			7.83038i			0.844372i
$87$	−1.68752	−	7.21031i	−0.180921	−	0.773027i
$88$	−23.1048	+	23.1048i	−2.46298	+	2.46298i
$89$	1.17942			0.125018			0.0625089	−	0.998044i	$-0.480090\pi$
$89$	1.17942			0.125018			0.0625089	+	0.998044i	$0.480090\pi$
$90$		0			0
$91$	4.92163			0.515927
$92$	−17.5245	+	17.5245i	−1.82705	+	1.82705i
$93$	1.32375	+	5.65603i	0.137267	+	0.586503i
$94$		−	30.3279i		−	3.12809i
$95$		0			0
$96$	25.3882	+	15.7582i	2.59118	+	1.60832i
$97$	−1.52395	−	1.52395i	−0.154734	−	0.154734i	0.625495	−	0.780228i	$-0.284897\pi$
$97$	−1.52395	−	1.52395i	−0.154734	−	0.154734i	−0.780228	+	0.625495i	$0.784897\pi$
$98$	−1.90099	−	1.90099i	−0.192029	−	0.192029i
$99$	−5.01341	−	10.1238i	−0.503867	−	1.01748i
$100$		0			0
$101$			11.2192i			1.11635i	0.829723	+	0.558175i	$0.188498\pi$
$101$			11.2192i			1.11635i	−0.829723	+	0.558175i	$0.811502\pi$
$102$	−0.845794	+	0.197952i	−0.0837461	+	0.0196002i
$103$	−13.7215	+	13.7215i	−1.35202	+	1.35202i	−0.468625	+	0.883397i	$0.655251\pi$
$103$	−13.7215	+	13.7215i	−1.35202	+	1.35202i	−0.883397	+	0.468625i	$0.844749\pi$
$104$	−42.7050			−4.18757
$105$		0			0
$106$	−14.4551			−1.40401
$107$	−7.86779	+	7.86779i	−0.760608	+	0.760608i	−0.976432	−	0.215824i	$-0.930756\pi$
$107$	−7.86779	+	7.86779i	−0.760608	+	0.760608i	0.215824	+	0.976432i	$0.430756\pi$
$108$	−20.9545	+	17.2844i	−2.01634	+	1.66319i
$109$			17.0460i			1.63271i	0.577551	+	0.816354i	$0.304008\pi$
$109$			17.0460i			1.63271i	−0.577551	+	0.816354i	$0.695992\pi$
$110$		0			0
$111$	6.44090	−	10.3770i	0.611343	−	0.984942i
$112$	9.10206	+	9.10206i	0.860063	+	0.860063i
$113$	−12.4798	−	12.4798i	−1.17400	−	1.17400i	−0.981246	−	0.192757i	$-0.938257\pi$
$113$	−12.4798	−	12.4798i	−1.17400	−	1.17400i	−0.192757	−	0.981246i	$-0.561743\pi$
$114$	−9.56776	+	15.4147i	−0.896103	+	1.44372i
$115$		0			0
$116$			22.3497i			2.07512i
$117$	4.72280	−	13.9892i	0.436623	−	1.29330i
$118$	13.4322	−	13.4322i	1.23654	−	1.23654i
$119$	−0.186547			−0.0171007
$120$		0			0
$121$	−3.18059			−0.289145
$122$	7.81375	−	7.81375i	0.707424	−	0.707424i
$123$	1.95924	−	0.458545i	0.176658	−	0.0413456i
$124$		−	17.5319i		−	1.57441i
$125$		0			0
$126$	−7.22756	+	3.57917i	−0.643882	+	0.318857i
$127$	8.66204	+	8.66204i	0.768632	+	0.768632i	0.977866	−	0.209234i	$-0.0670969\pi$
$127$	8.66204	+	8.66204i	0.768632	+	0.768632i	−0.209234	+	0.977866i	$0.567097\pi$
$128$	−14.8305	−	14.8305i	−1.31084	−	1.31084i
$129$	4.28630	+	2.66046i	0.377388	+	0.234241i
$130$		0			0
$131$		−	3.23990i		−	0.283072i	−0.989933	−	0.141536i	$-0.954796\pi$
$131$		−	3.23990i		−	0.283072i	0.989933	−	0.141536i	$-0.0452041\pi$
$132$	7.77001	+	33.1991i	0.676292	+	2.88961i
$133$	−2.75505	+	2.75505i	−0.238893	+	0.238893i
$134$	−0.583796			−0.0504323
$135$		0			0
$136$	1.61867			0.138800
$137$	5.54149	−	5.54149i	0.473442	−	0.473442i	−0.429585	−	0.903026i	$-0.641340\pi$
$137$	5.54149	−	5.54149i	0.473442	−	0.473442i	0.903026	+	0.429585i	$0.141340\pi$
$138$	5.03074	+	21.4950i	0.428245	+	1.82977i
$139$			18.9037i			1.60339i	0.597735	+	0.801694i	$0.296067\pi$
$139$			18.9037i			1.60339i	−0.597735	+	0.801694i	$0.703933\pi$
$140$		0			0
$141$	−16.6013	−	10.3043i	−1.39808	−	0.867776i
$142$	−4.03157	−	4.03157i	−0.338322	−	0.338322i
$143$	−13.1051	−	13.1051i	−1.09590	−	1.09590i
$144$	34.6059	−	17.1372i	2.88383	−	1.42810i
$145$		0			0
$146$			37.2340i			3.08151i
$147$	−1.68648	+	0.394708i	−0.139098	+	0.0325549i
$148$	−26.0652	+	26.0652i	−2.14254	+	2.14254i
$149$	4.47960			0.366983			0.183491	−	0.983021i	$-0.441260\pi$
$149$	4.47960			0.366983			0.183491	+	0.983021i	$0.441260\pi$
$150$		0			0
$151$	2.07180			0.168600			0.0843002	−	0.996440i	$-0.473135\pi$
$151$	2.07180			0.168600			0.0843002	+	0.996440i	$0.473135\pi$
$152$	23.9056	−	23.9056i	1.93900	−	1.93900i
$153$	−0.179011	+	0.530239i	−0.0144722	+	0.0428673i
$154$			10.1238i			0.815798i
$155$		0			0
$156$	−23.5005	+	37.8620i	−1.88155	+	3.03138i
$157$	5.17869	+	5.17869i	0.413304	+	0.413304i	0.882888	−	0.469584i	$-0.155596\pi$
$157$	5.17869	+	5.17869i	0.413304	+	0.413304i	−0.469584	+	0.882888i	$0.655596\pi$
$158$	0.280897	+	0.280897i	0.0223470	+	0.0223470i
$159$	−4.91129	+	7.91264i	−0.389491	+	0.627513i
$160$		0			0
$161$			4.74090i			0.373635i
$162$	3.23780	+	23.9781i	0.254386	+	1.88390i
$163$	1.14611	−	1.14611i	0.0897706	−	0.0897706i	−0.660795	−	0.750566i	$-0.729781\pi$
$163$	1.14611	−	1.14611i	0.0897706	−	0.0897706i	0.750566	+	0.660795i	$0.229781\pi$
$164$	−6.07303			−0.474224
$165$		0			0
$166$	9.83186			0.763100
$167$	−1.04994	+	1.04994i	−0.0812469	+	0.0812469i	−0.746562	−	0.665315i	$-0.768297\pi$
$167$	−1.04994	+	1.04994i	−0.0812469	+	0.0812469i	0.665315	+	0.746562i	$0.268297\pi$
$168$	14.6336	−	3.42488i	1.12900	−	0.264235i
$169$		−	11.2224i		−	0.863262i
$170$		0			0
$171$	5.18717	+	10.4747i	0.396673	+	0.801018i
$172$	−10.7664	−	10.7664i	−0.820931	−	0.820931i
$173$	3.39494	+	3.39494i	0.258113	+	0.258113i	0.824286	−	0.566173i	$-0.191577\pi$
$173$	3.39494	+	3.39494i	0.258113	+	0.258113i	−0.566173	+	0.824286i	$0.691577\pi$
$174$	16.9147	+	10.4988i	1.28230	+	0.795912i
$175$		0			0
$176$		−	48.4732i		−	3.65380i
$177$	−2.78896	−	11.9165i	−0.209631	−	0.895697i
$178$	−2.24206	+	2.24206i	−0.168050	+	0.168050i
$179$	−15.7574			−1.17776			−0.588881	−	0.808220i	$-0.700431\pi$
$179$	−15.7574			−1.17776			−0.588881	+	0.808220i	$0.700431\pi$
$180$		0			0
$181$	−5.06040			−0.376137			−0.188068	−	0.982156i	$-0.560223\pi$
$181$	−5.06040			−0.376137			−0.188068	+	0.982156i	$0.560223\pi$
$182$	−9.35598	+	9.35598i	−0.693512	+	0.693512i
$183$	−1.62239	−	6.93201i	−0.119930	−	0.512429i
$184$		−	41.1368i		−	3.03265i
$185$		0			0
$186$	−13.2685	−	8.23563i	−0.972895	−	0.603866i
$187$	0.496730	+	0.496730i	0.0363245	+	0.0363245i
$188$	41.6995	+	41.6995i	3.04125	+	3.04125i
$189$	−0.496434	+	5.17238i	−0.0361103	+	0.376236i
$190$		0			0
$191$			0.726830i			0.0525916i	0.999654	+	0.0262958i	$0.00837117\pi$
$191$			0.726830i			0.0525916i	−0.999654	+	0.0262958i	$0.991629\pi$
$192$	−34.8017	+	8.14507i	−2.51159	+	0.587820i
$193$	11.8926	−	11.8926i	0.856050	−	0.856050i	−0.134820	−	0.990870i	$-0.543046\pi$
$193$	11.8926	−	11.8926i	0.856050	−	0.856050i	0.990870	+	0.134820i	$0.0430458\pi$
$194$	5.79404			0.415988
$195$		0			0
$196$	5.22756			0.373397
$197$	12.6242	−	12.6242i	0.899440	−	0.899440i	−0.0959464	−	0.995387i	$-0.530588\pi$
$197$	12.6242	−	12.6242i	0.899440	−	0.899440i	0.995387	+	0.0959464i	$0.0305877\pi$
$198$	28.7757	+	9.71480i	2.04500	+	0.690401i
$199$		−	1.56130i		−	0.110677i	−0.998468	−	0.0553387i	$-0.982376\pi$
$199$		−	1.56130i		−	0.110677i	0.998468	−	0.0553387i	$-0.0176239\pi$
$200$		0			0
$201$	−0.198351	+	0.319566i	−0.0139906	+	0.0225405i
$202$	−21.3276	−	21.3276i	−1.50060	−	1.50060i
$203$	3.02314	+	3.02314i	0.212183	+	0.212183i
$204$	0.890753	−	1.43510i	0.0623652	−	0.100477i
$205$		0			0
$206$		−	52.1691i		−	3.63479i
$207$	13.4755	+	4.54937i	0.936610	+	0.316203i
$208$	44.7969	−	44.7969i	3.10611	−	3.10611i
$209$	14.6721			1.01489
$210$		0			0
$211$	−4.06281			−0.279696			−0.139848	−	0.990173i	$-0.544661\pi$
$211$	−4.06281			−0.279696			−0.139848	+	0.990173i	$0.544661\pi$
$212$	19.8751	−	19.8751i	1.36503	−	1.36503i
$213$	−3.57663	+	0.837083i	−0.245066	+	0.0573560i
$214$		−	29.9133i		−	2.04483i
$215$		0			0
$216$	4.30756	−	44.8808i	0.293092	−	3.05375i
$217$	−2.37146	−	2.37146i	−0.160985	−	0.160985i
$218$	−32.4043	−	32.4043i	−2.19470	−	2.19470i
$219$	20.3817	+	12.6507i	1.37727	+	0.854855i
$220$		0			0
$221$			0.918115i			0.0617591i
$222$	7.48252	+	31.9708i	0.502194	+	2.14574i
$223$	−19.2652	+	19.2652i	−1.29010	+	1.29010i	−0.355370	+	0.934726i	$0.615645\pi$
$223$	−19.2652	+	19.2652i	−1.29010	+	1.29010i	−0.934726	+	0.355370i	$0.884355\pi$
$224$	−17.2519			−1.15269
$225$		0			0
$226$	47.4482			3.15621
$227$	−15.5808	+	15.5808i	−1.03414	+	1.03414i	−0.0347402	+	0.999396i	$0.511060\pi$
$227$	−15.5808	+	15.5808i	−1.03414	+	1.03414i	−0.999396	+	0.0347402i	$0.988940\pi$
$228$	−8.03931	−	34.3498i	−0.532416	−	2.27487i
$229$			25.2714i			1.66998i	0.550264	+	0.834991i	$0.314527\pi$
$229$			25.2714i			1.66998i	−0.550264	+	0.834991i	$0.685473\pi$
$230$		0			0
$231$	5.54170	+	3.43967i	0.364617	+	0.226314i
$232$	−26.2318	−	26.2318i	−1.72220	−	1.72220i
$233$	−8.15021	−	8.15021i	−0.533938	−	0.533938i	0.387804	−	0.921742i	$-0.373234\pi$
$233$	−8.15021	−	8.15021i	−0.533938	−	0.533938i	−0.921742	+	0.387804i	$0.873234\pi$
$234$	17.6153	+	35.5713i	1.15155	+	2.32537i
$235$		0			0
$236$			36.9374i			2.40442i
$237$	0.249200	−	0.0583233i	0.0161872	−	0.00378851i
$238$	0.354625	−	0.354625i	0.0229869	−	0.0229869i
$239$	20.4397			1.32213			0.661066	−	0.750328i	$-0.270104\pi$
$239$	20.4397			1.32213			0.661066	+	0.750328i	$0.270104\pi$
$240$		0			0
$241$	−13.2544			−0.853790			−0.426895	−	0.904301i	$-0.640393\pi$
$241$	−13.2544			−0.853790			−0.426895	+	0.904301i	$0.640393\pi$
$242$	6.04628	−	6.04628i	0.388670	−	0.388670i
$243$	14.2255	+	6.37448i	0.912569	+	0.408923i
$244$			21.4871i			1.37557i
$245$		0			0
$246$	−2.85281	+	4.59619i	−0.181888	+	0.293042i
$247$	13.5593	+	13.5593i	0.862759	+	0.862759i
$248$	20.5772	+	20.5772i	1.30665	+	1.30665i
$249$	3.34049	−	5.38190i	0.211695	−	0.341064i
$250$		0			0
$251$			17.9297i			1.13171i	0.824505	+	0.565855i	$0.191454\pi$
$251$			17.9297i			1.13171i	−0.824505	+	0.565855i	$0.808546\pi$
$252$	5.01637	−	14.8587i	0.316002	−	0.936013i
$253$	12.6239	−	12.6239i	0.793656	−	0.793656i
$254$	−32.9330			−2.06640
$255$		0			0
$256$	15.1139			0.944622
$257$	1.92762	−	1.92762i	0.120242	−	0.120242i	−0.644425	−	0.764667i	$-0.722903\pi$
$257$	1.92762	−	1.92762i	0.120242	−	0.120242i	0.764667	+	0.644425i	$0.222903\pi$
$258$	−13.2058	+	3.09071i	−0.822155	+	0.192419i
$259$			7.05142i			0.438154i
$260$		0			0
$261$	11.4940	−	5.69193i	0.711458	−	0.352322i
$262$	6.15904	+	6.15904i	0.380507	+	0.380507i
$263$	−11.8215	−	11.8215i	−0.728943	−	0.728943i	0.241466	−	0.970409i	$-0.422372\pi$
$263$	−11.8215	−	11.8215i	−0.728943	−	0.728943i	−0.970409	+	0.241466i	$0.922372\pi$
$264$	−48.0853	−	29.8461i	−2.95945	−	1.83690i
$265$		0			0
$266$		−	10.4747i		−	0.642243i
$267$	0.465524	+	1.98906i	0.0284896	+	0.121728i
$268$	0.802692	−	0.802692i	0.0490322	−	0.0490322i
$269$	−14.6150			−0.891092			−0.445546	−	0.895259i	$-0.646991\pi$
$269$	−14.6150			−0.891092			−0.445546	+	0.895259i	$0.646991\pi$
$270$		0			0
$271$	−3.12917			−0.190084			−0.0950418	−	0.995473i	$-0.530298\pi$
$271$	−3.12917			−0.190084			−0.0950418	+	0.995473i	$0.530298\pi$
$272$	−1.69796	+	1.69796i	−0.102954	+	0.102954i
$273$	1.94260	+	8.30021i	0.117572	+	0.502352i
$274$			21.0687i			1.27281i
$275$		0			0
$276$	−36.4716	−	22.6376i	−2.19533	−	1.36262i
$277$	9.61019	+	9.61019i	0.577421	+	0.577421i	0.934192	−	0.356771i	$-0.116122\pi$
$277$	9.61019	+	9.61019i	0.577421	+	0.577421i	−0.356771	+	0.934192i	$0.616122\pi$
$278$	−35.9357	−	35.9357i	−2.15528	−	2.15528i
$279$	−9.01627	+	4.46495i	−0.539790	+	0.267310i
$280$		0			0
$281$		−	8.72113i		−	0.520259i	−0.965574	−	0.260130i	$-0.916235\pi$
$281$		−	8.72113i		−	0.520259i	0.965574	−	0.260130i	$-0.0837653\pi$
$282$	51.1474	−	11.9707i	3.04578	−	0.712843i
$283$	11.6672	−	11.6672i	0.693545	−	0.693545i	−0.269465	−	0.963010i	$-0.586847\pi$
$283$	11.6672	−	11.6672i	0.693545	−	0.693545i	0.963010	+	0.269465i	$0.0868469\pi$
$284$	11.0864			0.657859
$285$		0			0
$286$	49.8255			2.94624
$287$	−0.821469	+	0.821469i	−0.0484898	+	0.0484898i
$288$	−16.5549	+	49.0366i	−0.975509	+	2.88951i
$289$			16.9652i			0.997953i
$290$		0			0
$291$	1.96859	−	3.17162i	0.115401	−	0.185924i
$292$	−51.1951	−	51.1951i	−2.99597	−	2.99597i
$293$	14.4218	+	14.4218i	0.842532	+	0.842532i	0.989188	−	0.146655i	$-0.0468508\pi$
$293$	14.4218	+	14.4218i	0.842532	+	0.842532i	−0.146655	+	0.989188i	$0.546851\pi$
$294$	2.45565	−	3.95632i	0.143216	−	0.230737i
$295$		0			0
$296$		−	61.1852i		−	3.55632i
$297$	15.0947	−	12.4509i	0.875884	−	0.722477i
$298$	−8.51569	+	8.51569i	−0.493301	+	0.493301i
$299$	23.3329			1.34938
$300$		0			0
$301$	−2.91264			−0.167882
$302$	−3.93847	+	3.93847i	−0.226634	+	0.226634i
$303$	−18.9209	+	4.42829i	−1.08698	+	0.254399i
$304$			50.1532i			2.87648i
$305$		0			0
$306$	−0.667683	−	1.34828i	−0.0381689	−	0.0770760i
$307$	6.03004	+	6.03004i	0.344153	+	0.344153i	0.857926	−	0.513773i	$-0.171753\pi$
$307$	6.03004	+	6.03004i	0.344153	+	0.344153i	−0.513773	+	0.857926i	$0.671753\pi$
$308$	−13.9197	−	13.9197i	−0.793151	−	0.793151i
$309$	−28.5570	−	17.7251i	−1.62455	−	1.00834i
$310$		0			0
$311$			20.3414i			1.15345i	0.816937	+	0.576727i	$0.195670\pi$
$311$			20.3414i			1.15345i	−0.816937	+	0.576727i	$0.804330\pi$
$312$	−16.8560	−	72.0210i	−0.954282	−	4.07739i
$313$	13.6095	−	13.6095i	0.769254	−	0.769254i	−0.208721	−	0.977975i	$-0.566930\pi$
$313$	13.6095	−	13.6095i	0.769254	−	0.769254i	0.977975	+	0.208721i	$0.0669302\pi$
$314$	−19.6893			−1.11113
$315$		0			0
$316$	−0.772442			−0.0434532
$317$	−13.3563	+	13.3563i	−0.750166	+	0.750166i	−0.974510	−	0.224344i	$-0.927976\pi$
$317$	−13.3563	+	13.3563i	−0.750166	+	0.750166i	0.224344	+	0.974510i	$0.427976\pi$
$318$	−5.70554	−	24.3782i	−0.319951	−	1.36706i
$319$		−	16.0998i		−	0.901416i
$320$		0			0
$321$	−16.3743	−	10.1634i	−0.913926	−	0.567265i
$322$	−9.01242	−	9.01242i	−0.502243	−	0.502243i
$323$	−0.513946	−	0.513946i	−0.0285967	−	0.0285967i
$324$	−37.4206	−	28.5169i	−2.07892	−	1.58427i
$325$		0			0
$326$			4.35751i			0.241340i
$327$	−28.7477	+	6.72818i	−1.58975	+	0.372069i
$328$	7.12789	−	7.12789i	0.393572	−	0.393572i
$329$	11.2810			0.621941
$330$		0			0
$331$	−28.5981			−1.57189			−0.785946	−	0.618295i	$-0.787824\pi$
$331$	−28.5981			−1.57189			−0.785946	+	0.618295i	$0.787824\pi$
$332$	−13.5184	+	13.5184i	−0.741916	+	0.741916i
$333$	20.0429	+	6.76655i	1.09834	+	0.370805i
$334$		−	3.99187i		−	0.218425i
$335$		0			0
$336$	−11.7578	+	18.9431i	−0.641438	+	1.03343i
$337$	17.2226	+	17.2226i	0.938172	+	0.938172i	0.998197	−	0.0600247i	$-0.0191180\pi$
$337$	17.2226	+	17.2226i	0.938172	+	0.938172i	−0.0600247	+	0.998197i	$0.519118\pi$
$338$	21.3337	+	21.3337i	1.16040	+	1.16040i
$339$	16.1211	−	25.9728i	0.875576	−	1.41065i
$340$		0			0
$341$			12.6293i			0.683913i
$342$	−29.7731	−	10.0515i	−1.60994	−	0.543523i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	25.2730			1.36263
$345$		0			0
$346$	−12.9075			−0.693914
$347$	−0.679325	+	0.679325i	−0.0364681	+	0.0364681i	−0.725106	−	0.688638i	$-0.758209\pi$
$347$	−0.679325	+	0.679325i	−0.0364681	+	0.0364681i	0.688638	+	0.725106i	$0.258209\pi$
$348$	−37.6923	+	8.82161i	−2.02052	+	0.472888i
$349$		−	6.95006i		−	0.372028i	−0.982547	−	0.186014i	$-0.940443\pi$
$349$		−	6.95006i		−	0.372028i	0.982547	−	0.186014i	$-0.0595570\pi$
$350$		0			0
$351$	25.4565	+	2.44326i	1.35877	+	0.130412i
$352$	45.9377	+	45.9377i	2.44849	+	2.44849i
$353$	21.2979	+	21.2979i	1.13358	+	1.13358i	0.989578	+	0.143997i	$0.0459956\pi$
$353$	21.2979	+	21.2979i	1.13358	+	1.13358i	0.143997	+	0.989578i	$0.454004\pi$
$354$	27.9549	+	17.3513i	1.48579	+	0.922214i
$355$		0			0
$356$		−	6.16546i		−	0.326769i
$357$	−0.0736316	−	0.314607i	−0.00389699	−	0.0166508i
$358$	29.9547	−	29.9547i	1.58315	−	1.58315i
$359$	−5.03756			−0.265872			−0.132936	−	0.991125i	$-0.542441\pi$
$359$	−5.03756			−0.265872			−0.132936	+	0.991125i	$0.542441\pi$
$360$		0			0
$361$	3.81941			0.201022
$362$	9.61980	−	9.61980i	0.505605	−	0.505605i
$363$	−1.25540	−	5.36399i	−0.0658916	−	0.281537i
$364$		−	25.7281i		−	1.34852i
$365$		0			0
$366$	16.2619	+	10.0936i	0.850021	+	0.527599i
$367$	0.135150	+	0.135150i	0.00705477	+	0.00705477i	0.710625	−	0.703571i	$-0.248412\pi$
$367$	0.135150	+	0.135150i	0.00705477	+	0.00705477i	−0.703571	+	0.710625i	$0.748412\pi$
$368$	43.1519	+	43.1519i	2.24945	+	2.24945i
$369$	1.54665	+	3.12322i	0.0805154	+	0.162588i
$370$		0			0
$371$		−	5.37682i		−	0.279151i
$372$	29.5672	−	6.91999i	1.53299	−	0.358785i
$373$	−14.5624	+	14.5624i	−0.754012	+	0.754012i	−0.975225	−	0.221213i	$-0.928998\pi$
$373$	−14.5624	+	14.5624i	−0.754012	+	0.754012i	0.221213	+	0.975225i	$0.428998\pi$
$374$	−1.88856			−0.0976553
$375$		0			0
$376$	−97.8852			−5.04804
$377$	14.8788	−	14.8788i	0.766296	−	0.766296i
$378$	−8.88895	−	10.7764i	−0.457198	−	0.554278i
$379$		−	33.5148i		−	1.72154i	−0.508994	−	0.860770i	$-0.669982\pi$
$379$		−	33.5148i		−	1.72154i	0.508994	−	0.860770i	$-0.330018\pi$
$380$		0			0
$381$	−11.1894	+	18.0273i	−0.573249	+	0.923567i
$382$	−1.38170	−	1.38170i	−0.0706939	−	0.0706939i
$383$	24.3438	+	24.3438i	1.24391	+	1.24391i	0.958365	+	0.285546i	$0.0921751\pi$
$383$	24.3438	+	24.3438i	1.24391	+	1.24391i	0.285546	+	0.958365i	$0.407825\pi$
$384$	19.1576	−	30.8650i	0.977631	−	1.57507i
$385$		0			0
$386$			45.2156i			2.30141i
$387$	−2.79497	+	8.27885i	−0.142077	+	0.420838i
$388$	−7.96654	+	7.96654i	−0.404440	+	0.404440i
$389$	9.70050			0.491835			0.245917	−	0.969291i	$-0.420911\pi$
$389$	9.70050			0.491835			0.245917	+	0.969291i	$0.420911\pi$
$390$		0			0
$391$	−0.884401			−0.0447261
$392$	−6.13557	+	6.13557i	−0.309893	+	0.309893i
$393$	5.46403	−	1.27881i	0.275624	−	0.0645077i
$394$			47.9972i			2.41807i
$395$		0			0
$396$	−52.9227	+	26.2079i	−2.65946	+	1.31700i
$397$	3.59901	+	3.59901i	0.180629	+	0.180629i	0.791630	−	0.611001i	$-0.209233\pi$
$397$	3.59901	+	3.59901i	0.180629	+	0.180629i	−0.611001	+	0.791630i	$0.709233\pi$
$398$	2.96802	+	2.96802i	0.148773	+	0.148773i
$399$	−5.73377	−	3.55889i	−0.287047	−	0.178167i
$400$		0			0
$401$		−	38.9834i		−	1.94674i	−0.229244	−	0.973369i	$-0.573625\pi$
$401$		−	38.9834i		−	1.94674i	0.229244	−	0.973369i	$-0.426375\pi$
$402$	−0.230429	−	0.984558i	−0.0114927	−	0.0491053i
$403$	−11.6714	+	11.6714i	−0.581396	+	0.581396i
$404$	58.6489			2.91789
$405$		0			0
$406$	−11.4940			−0.570435
$407$	18.7762	−	18.7762i	0.930704	−	0.930704i
$408$	0.638901	+	2.72985i	0.0316303	+	0.135148i
$409$		−	1.53194i		−	0.0757493i	−0.999282	−	0.0378747i	$-0.987941\pi$
$409$		−	1.53194i		−	0.0757493i	0.999282	−	0.0378747i	$-0.0120588\pi$
$410$		0			0
$411$	11.5329	+	7.15833i	0.568874	+	0.353094i
$412$	71.7301	+	71.7301i	3.53389	+	3.53389i
$413$	4.99634	+	4.99634i	0.245854	+	0.245854i
$414$	−34.2651	+	16.9685i	−1.68404	+	0.833954i
$415$		0			0
$416$			84.9074i			4.16293i
$417$	−31.8806	+	7.46142i	−1.56120	+	0.365387i
$418$	−27.8915	+	27.8915i	−1.36422	+	1.36422i
$419$	25.9795			1.26918			0.634591	−	0.772848i	$-0.281169\pi$
$419$	25.9795			1.26918			0.634591	+	0.772848i	$0.281169\pi$
$420$		0			0
$421$	−3.34632			−0.163090			−0.0815449	−	0.996670i	$-0.525985\pi$
$421$	−3.34632			−0.163090			−0.0815449	+	0.996670i	$0.525985\pi$
$422$	7.72338	−	7.72338i	0.375968	−	0.375968i
$423$	10.8252	−	32.0649i	0.526342	−	1.55905i
$424$			46.6547i			2.26575i
$425$		0			0
$426$	5.20786	−	8.39044i	0.252321	−	0.406518i
$427$	2.90646	+	2.90646i	0.140653	+	0.140653i
$428$	41.1294	+	41.1294i	1.98806	+	1.98806i
$429$	16.9288	−	27.2742i	0.817330	−	1.31681i
$430$		0			0
$431$			21.5955i			1.04022i	0.854099	+	0.520110i	$0.174109\pi$
$431$			21.5955i			1.04022i	−0.854099	+	0.520110i	$0.825891\pi$
$432$	42.5608	+	51.5979i	2.04771	+	2.48250i
$433$	−10.0406	+	10.0406i	−0.482523	+	0.482523i	−0.905936	−	0.423414i	$-0.860832\pi$
$433$	−10.0406	+	10.0406i	−0.482523	+	0.482523i	0.423414	+	0.905936i	$0.360832\pi$
$434$	9.01627			0.432795
$435$		0			0
$436$	89.1089			4.26754
$437$	−13.0614	+	13.0614i	−0.624812	+	0.624812i
$438$	−62.7944	+	14.6966i	−3.00043	+	0.702229i
$439$			24.0394i			1.14734i	0.819087	+	0.573669i	$0.194480\pi$
$439$			24.0394i			1.14734i	−0.819087	+	0.573669i	$0.805520\pi$
$440$		0			0
$441$	−1.33133	−	2.68841i	−0.0633967	−	0.128020i
$442$	−1.74533	−	1.74533i	−0.0830170	−	0.0830170i
$443$	−4.25893	−	4.25893i	−0.202348	−	0.202348i	0.598657	−	0.801005i	$-0.295701\pi$
$443$	−4.25893	−	4.25893i	−0.202348	−	0.202348i	−0.801005	+	0.598657i	$0.795701\pi$
$444$	−54.2464	−	33.6702i	−2.57442	−	1.59792i
$445$		0			0
$446$		−	73.2462i		−	3.46831i
$447$	1.76813	+	7.55474i	0.0836297	+	0.357327i
$448$	14.5916	−	14.5916i	0.689391	−	0.689391i
$449$	−30.2607			−1.42809			−0.714046	−	0.700099i	$-0.753139\pi$
$449$	−30.2607			−1.42809			−0.714046	+	0.700099i	$0.753139\pi$
$450$		0			0
$451$	4.37475			0.205999
$452$	−65.2390	+	65.2390i	−3.06859	+	3.06859i
$453$	0.817754	+	3.49404i	0.0384214	+	0.164164i
$454$		−	59.2382i		−	2.78019i
$455$		0			0
$456$	49.7519	+	30.8805i	2.32985	+	1.44611i
$457$	−10.5131	−	10.5131i	−0.491783	−	0.491783i	0.417085	−	0.908868i	$-0.363052\pi$
$457$	−10.5131	−	10.5131i	−0.491783	−	0.491783i	−0.908868	+	0.417085i	$0.863052\pi$
$458$	−48.0408	−	48.0408i	−2.24480	−	2.24480i
$459$	−0.964893	−	0.0926083i	−0.0450374	−	0.00432259i
$460$		0			0
$461$		−	39.7882i		−	1.85312i	−0.376146	−	0.926560i	$-0.622751\pi$
$461$		−	39.7882i		−	1.85312i	0.376146	−	0.926560i	$-0.377249\pi$
$462$	−17.0735	+	3.99593i	−0.794333	+	0.185908i
$463$	24.1384	−	24.1384i	1.12181	−	1.12181i	0.130335	−	0.991470i	$-0.458395\pi$
$463$	24.1384	−	24.1384i	1.12181	−	1.12181i	0.991470	−	0.130335i	$-0.0416053\pi$
$464$	55.0336			2.55487
$465$		0			0
$466$	30.9870			1.43544
$467$	−13.5195	+	13.5195i	−0.625610	+	0.625610i	−0.946960	−	0.321351i	$-0.895863\pi$
$467$	−13.5195	+	13.5195i	−0.625610	+	0.625610i	0.321351	+	0.946960i	$0.395863\pi$
$468$	−73.1292	−	24.6887i	−3.38040	−	1.14124i
$469$		−	0.217153i		−	0.0100272i
$470$		0			0
$471$	−6.68967	+	10.7778i	−0.308244	+	0.496615i
$472$	−43.3533	−	43.3533i	−1.99550	−	1.99550i
$473$	7.75567	+	7.75567i	0.356606	+	0.356606i
$474$	−0.362855	+	0.584599i	−0.0166665	+	0.0268515i
$475$		0			0
$476$			0.975186i			0.0446976i
$477$	−15.2830	−	5.15961i	−0.699761	−	0.236242i
$478$	−38.8557	+	38.8557i	−1.77722	+	1.77722i
$479$	−37.0916			−1.69476			−0.847380	−	0.530987i	$-0.821821\pi$
$479$	−37.0916			−1.69476			−0.847380	+	0.530987i	$0.821821\pi$
$480$		0			0
$481$	34.7045			1.58239
$482$	25.1965	−	25.1965i	1.14767	−	1.14767i
$483$	−7.99542	+	1.87127i	−0.363804	+	0.0851457i
$484$			16.6267i			0.755760i
$485$		0			0
$486$	−39.1605	+	14.9248i	−1.77636	+	0.677003i
$487$	−12.3041	−	12.3041i	−0.557551	−	0.557551i	0.371059	−	0.928609i	$-0.378995\pi$
$487$	−12.3041	−	12.3041i	−0.557551	−	0.557551i	−0.928609	+	0.371059i	$0.878995\pi$
$488$	−25.2193	−	25.2193i	−1.14163	−	1.14163i
$489$	2.38527	+	1.48052i	0.107866	+	0.0669512i
$490$		0			0
$491$			15.1173i			0.682233i	0.940021	+	0.341116i	$0.110805\pi$
$491$			15.1173i			0.682233i	−0.940021	+	0.341116i	$0.889195\pi$
$492$	−2.39707	−	10.2420i	−0.108068	−	0.461746i
$493$	−0.563958	+	0.563958i	−0.0253994	+	0.0253994i
$494$	−51.5524			−2.31945
$495$		0			0
$496$	−43.1703			−1.93841
$497$	1.49961	−	1.49961i	0.0672667	−	0.0672667i
$498$	3.88071	+	16.5812i	0.173899	+	0.743022i
$499$		−	23.2266i		−	1.03976i	−0.854238	−	0.519882i	$-0.825976\pi$
$499$		−	23.2266i		−	1.03976i	0.854238	−	0.519882i	$-0.174024\pi$
$500$		0			0
$501$	−2.18512	−	1.35628i	−0.0976241	−	0.0605943i
$502$	−34.0842	−	34.0842i	−1.52125	−	1.52125i
$503$	−1.88391	−	1.88391i	−0.0839996	−	0.0839996i	0.663859	−	0.747858i	$-0.268918\pi$
$503$	−1.88391	−	1.88391i	−0.0839996	−	0.0839996i	−0.747858	+	0.663859i	$0.768918\pi$
$504$	11.5520	+	23.3274i	0.514565	+	1.03908i
$505$		0			0
$506$			47.9958i			2.13368i
$507$	18.9263	−	4.42957i	0.840548	−	0.196724i
$508$	45.2813	−	45.2813i	2.00903	−	2.00903i
$509$	−34.4950			−1.52897			−0.764483	−	0.644644i	$-0.777006\pi$
$509$	−34.4950			−1.52897			−0.764483	+	0.644644i	$0.777006\pi$
$510$		0			0
$511$	−13.8498			−0.612680
$512$	0.929454	−	0.929454i	0.0410764	−	0.0410764i
$513$	−15.6179	+	12.8825i	−0.689546	+	0.568775i
$514$			7.32879i			0.323259i
$515$		0			0
$516$	13.9077	−	22.4069i	0.612253	−	0.986408i
$517$	−30.0386	−	30.0386i	−1.32109	−	1.32109i
$518$	−13.4047	−	13.4047i	−0.588969	−	0.588969i
$519$	−4.38549	+	7.06551i	−0.192501	+	0.310141i
$520$		0			0
$521$		−	40.9966i		−	1.79609i	−0.439902	−	0.898046i	$-0.644987\pi$
$521$		−	40.9966i		−	1.79609i	0.439902	−	0.898046i	$-0.355013\pi$
$522$	−11.0296	+	32.6703i	−0.482753	+	1.42994i
$523$	−8.92643	+	8.92643i	−0.390326	+	0.390326i	−0.874803	−	0.484478i	$-0.839010\pi$
$523$	−8.92643	+	8.92643i	−0.390326	+	0.390326i	0.484478	+	0.874803i	$0.339010\pi$
$524$	−16.9368			−0.739887
$525$		0			0
$526$	44.9451			1.95970
$527$	0.442389	−	0.442389i	0.0192708	−	0.0192708i
$528$	81.7489	−	19.1327i	3.55767	−	0.832645i
$529$		−	0.523883i		−	0.0227775i
$530$		0			0
$531$	18.9960	−	9.40704i	0.824358	−	0.408231i
$532$	14.4022	+	14.4022i	0.624414	+	0.624414i
$533$	4.04296	+	4.04296i	0.175120	+	0.175120i
$534$	−4.66615	−	2.89623i	−0.201924	−	0.125332i
$535$		0			0
$536$			1.88424i			0.0813866i
$537$	−6.21956	−	26.5745i	−0.268394	−	1.14677i
$538$	27.7830	−	27.7830i	1.19781	−	1.19781i
$539$	−3.76571			−0.162201
$540$		0			0
$541$	−5.75064			−0.247239			−0.123620	−	0.992330i	$-0.539450\pi$
$541$	−5.75064			−0.247239			−0.123620	+	0.992330i	$0.539450\pi$
$542$	5.94854	−	5.94854i	0.255511	−	0.255511i
$543$	−1.99738	−	8.53426i	−0.0857158	−	0.366240i
$544$		−	3.21829i		−	0.137983i
$545$		0			0
$546$	−19.4715	−	12.0858i	−0.833305	−	0.517223i
$547$	6.93451	+	6.93451i	0.296498	+	0.296498i	0.839641	−	0.543142i	$-0.182766\pi$
$547$	6.93451	+	6.93451i	0.296498	+	0.296498i	−0.543142	+	0.839641i	$0.682766\pi$
$548$	−28.9685	−	28.9685i	−1.23747	−	1.23747i
$549$	11.0503	−	5.47223i	0.471616	−	0.233549i
$550$		0			0
$551$			16.6578i			0.709647i
$552$	69.3763	−	16.2370i	2.95285	−	0.691093i
$553$	−0.104484	+	0.104484i	−0.00444313	+	0.00444313i
$554$	−36.5378			−1.55234
$555$		0			0
$556$	98.8200			4.19090
$557$	23.5163	−	23.5163i	0.996416	−	0.996416i	−0.00357756	−	0.999994i	$-0.501139\pi$
$557$	23.5163	−	23.5163i	0.996416	−	0.996416i	0.999994	+	0.00357756i	$0.00113878\pi$
$558$	8.65202	−	25.6277i	0.366269	−	1.08491i
$559$			14.3349i			0.606303i
$560$		0			0
$561$	−0.641661	+	1.03379i	−0.0270910	+	0.0436465i
$562$	16.5788	+	16.5788i	0.699335	+	0.699335i
$563$	16.6973	+	16.6973i	0.703708	+	0.703708i	0.965205	−	0.261496i	$-0.0842158\pi$
$563$	16.6973	+	16.6973i	0.703708	+	0.703708i	−0.261496	+	0.965205i	$0.584216\pi$
$564$	−53.8662	+	86.7844i	−2.26817	+	3.65428i
$565$		0			0
$566$			44.3587i			1.86453i
$567$	−8.91905	+	1.20435i	−0.374565	+	0.0505781i
$568$	−13.0121	+	13.0121i	−0.545976	+	0.545976i
$569$	32.5519			1.36465			0.682323	−	0.731051i	$-0.260970\pi$
$569$	32.5519			1.36465			0.682323	+	0.731051i	$0.260970\pi$
$570$		0			0
$571$	−20.4341			−0.855141			−0.427571	−	0.903982i	$-0.640630\pi$
$571$	−20.4341			−0.855141			−0.427571	+	0.903982i	$0.640630\pi$
$572$	−68.5077	+	68.5077i	−2.86445	+	2.86445i
$573$	−1.22578	+	0.286885i	−0.0512078	+	0.0119848i
$574$		−	3.12322i		−	0.130361i
$575$		0			0
$576$	−27.4730	−	55.4773i	−1.14471	−	2.31155i
$577$	−30.6497	−	30.6497i	−1.27596	−	1.27596i	−0.942907	−	0.333056i	$-0.891920\pi$
$577$	−30.6497	−	30.6497i	−1.27596	−	1.27596i	−0.333056	−	0.942907i	$-0.608080\pi$
$578$	−32.2507	−	32.2507i	−1.34145	−	1.34145i
$579$	24.7507	+	15.3625i	1.02861	+	0.638445i
$580$		0			0
$581$			3.65713i			0.151723i
$582$	2.28695	+	9.77152i	0.0947973	+	0.405043i
$583$	−14.3172	+	14.3172i	−0.592958	+	0.592958i
$584$	120.175			4.97288
$585$		0			0
$586$	−54.8316			−2.26507
$587$	−33.7010	+	33.7010i	−1.39099	+	1.39099i	−0.567872	+	0.823117i	$0.692233\pi$
$587$	−33.7010	+	33.7010i	−1.39099	+	1.39099i	−0.823117	+	0.567872i	$0.807767\pi$
$588$	2.06336	+	8.81616i	0.0850914	+	0.363572i
$589$		−	13.0670i		−	0.538416i
$590$		0			0
$591$	26.2734	+	16.3076i	1.08074	+	0.670806i
$592$	64.1824	+	64.1824i	2.63788	+	2.63788i
$593$	−8.74429	−	8.74429i	−0.359085	−	0.359085i	0.504391	−	0.863476i	$-0.331717\pi$
$593$	−8.74429	−	8.74429i	−0.359085	−	0.359085i	−0.863476	+	0.504391i	$0.831717\pi$
$594$	−5.02579	+	52.3641i	−0.206211	+	2.14853i
$595$		0			0
$596$		−	23.4174i		−	0.959212i
$597$	2.63309	−	0.616256i	0.107765	−	0.0252217i
$598$	−44.3558	+	44.3558i	−1.81384	+	1.81384i
$599$	21.6454			0.884407			0.442203	−	0.896915i	$-0.354197\pi$
$599$	21.6454			0.884407			0.442203	+	0.896915i	$0.354197\pi$
$600$		0			0
$601$	32.8086			1.33829			0.669146	−	0.743131i	$-0.266660\pi$
$601$	32.8086			1.33829			0.669146	+	0.743131i	$0.266660\pi$
$602$	5.53691	−	5.53691i	0.225668	−	0.225668i
$603$	−0.617232	−	0.208380i	−0.0251356	−	0.00848589i
$604$		−	10.8304i		−	0.440684i
$605$		0			0
$606$	27.5503	−	44.3867i	1.11916	−	1.80308i
$607$	0.943000	+	0.943000i	0.0382752	+	0.0382752i	0.725985	−	0.687710i	$-0.241384\pi$
$607$	0.943000	+	0.943000i	0.0382752	+	0.0382752i	−0.687710	+	0.725985i	$0.741384\pi$
$608$	−47.5298	−	47.5298i	−1.92759	−	1.92759i
$609$	−3.90520	+	6.29172i	−0.158247	+	0.254953i
$610$		0			0
$611$		−	55.5208i		−	2.24613i
$612$	2.77186	+	0.935790i	0.112046	+	0.0378271i
$613$	10.2906	−	10.2906i	0.415635	−	0.415635i	−0.468061	−	0.883696i	$-0.655047\pi$
$613$	10.2906	−	10.2906i	0.415635	−	0.415635i	0.883696	+	0.468061i	$0.155047\pi$
$614$	−22.9261			−0.925224
$615$		0			0
$616$	32.6751			1.31652
$617$	−18.2623	+	18.2623i	−0.735212	+	0.735212i	−0.971647	−	0.236435i	$-0.924021\pi$
$617$	−18.2623	+	18.2623i	−0.735212	+	0.735212i	0.236435	+	0.971647i	$0.424021\pi$
$618$	87.9820	−	20.5915i	3.53916	−	0.828313i
$619$		−	1.95142i		−	0.0784343i	−0.999231	−	0.0392171i	$-0.987514\pi$
$619$		−	1.95142i		−	0.0784343i	0.999231	−	0.0392171i	$-0.0124864\pi$
$620$		0			0
$621$	−2.35354	+	24.5217i	−0.0944445	+	0.984024i
$622$	−38.6688	−	38.6688i	−1.55048	−	1.55048i
$623$	−0.833973	−	0.833973i	−0.0334124	−	0.0334124i
$624$	93.2307	+	57.8673i	3.73221	+	2.31655i
$625$		0			0
$626$			51.7431i			2.06807i
$627$	5.79118	+	24.7441i	0.231277	+	0.988185i
$628$	27.0719	−	27.0719i	1.08029	−	1.08029i
$629$	−1.31542			−0.0524493
$630$		0			0
$631$	−4.02214			−0.160119			−0.0800594	−	0.996790i	$-0.525511\pi$
$631$	−4.02214			−0.160119			−0.0800594	+	0.996790i	$0.525511\pi$
$632$	0.906612	−	0.906612i	0.0360631	−	0.0360631i
$633$	−1.60362	−	6.85184i	−0.0637383	−	0.272336i
$634$		−	50.7806i		−	2.01675i
$635$		0			0
$636$	41.3638	+	25.6741i	1.64018	+	1.01804i
$637$	−3.48012	−	3.48012i	−0.137887	−	0.137887i
$638$	30.6056	+	30.6056i	1.21169	+	1.21169i
$639$	−2.82344	−	5.70150i	−0.111694	−	0.225548i
$640$		0			0
$641$		−	20.9832i		−	0.828785i	−0.910098	−	0.414393i	$-0.863994\pi$
$641$		−	20.9832i		−	0.828785i	0.910098	−	0.414393i	$-0.136006\pi$
$642$	50.4480	−	11.8070i	1.99103	−	0.465985i
$643$	10.7521	−	10.7521i	0.424021	−	0.424021i	−0.462564	−	0.886586i	$-0.653071\pi$
$643$	10.7521	−	10.7521i	0.424021	−	0.424021i	0.886586	+	0.462564i	$0.153071\pi$
$644$	24.7833			0.976600
$645$		0			0
$646$	1.95402			0.0768798
$647$	11.3490	−	11.3490i	0.446174	−	0.446174i	−0.447907	−	0.894080i	$-0.647830\pi$
$647$	11.3490	−	11.3490i	0.446174	−	0.446174i	0.894080	+	0.447907i	$0.147830\pi$
$648$	77.3907	−	10.4502i	3.04019	−	0.410522i
$649$		−	26.6081i		−	1.04446i
$650$		0			0
$651$	3.06338	−	4.93545i	0.120063	−	0.193435i
$652$	−5.99138	−	5.99138i	−0.234640	−	0.234640i
$653$	9.15252	+	9.15252i	0.358166	+	0.358166i	0.863136	−	0.504971i	$-0.168497\pi$
$653$	9.15252	+	9.15252i	0.358166	+	0.358166i	−0.504971	+	0.863136i	$0.668497\pi$
$654$	41.8589	−	67.4394i	1.63681	−	2.63709i
$655$		0			0
$656$			14.9541i			0.583860i
$657$	−13.2903	+	39.3666i	−0.518505	+	1.53584i
$658$	−21.4451	+	21.4451i	−0.836017	+	0.836017i
$659$	35.5908			1.38642			0.693210	−	0.720736i	$-0.256196\pi$
$659$	35.5908			1.38642			0.693210	+	0.720736i	$0.256196\pi$
$660$		0			0
$661$	1.77542			0.0690558			0.0345279	−	0.999404i	$-0.489007\pi$
$661$	1.77542			0.0690558			0.0345279	+	0.999404i	$0.489007\pi$
$662$	54.3648	−	54.3648i	2.11295	−	2.11295i
$663$	−1.54838	+	0.362387i	−0.0601341	+	0.0140739i
$664$		−	31.7329i		−	1.23148i
$665$		0			0
$666$	−50.9645	+	25.2382i	−1.97484	+	0.977960i
$667$	14.3324	+	14.3324i	0.554953	+	0.554953i
$668$	5.48863	+	5.48863i	0.212362	+	0.212362i
$669$	−40.0945	−	24.8863i	−1.55014	−	0.962158i
$670$		0			0
$671$		−	15.4784i		−	0.597537i
$672$	−6.80945	−	29.0949i	−0.262680	−	1.12236i
$673$	18.9037	−	18.9037i	0.728683	−	0.728683i	−0.241675	−	0.970357i	$-0.577697\pi$
$673$	18.9037	−	18.9037i	0.728683	−	0.728683i	0.970357	+	0.241675i	$0.0776967\pi$
$674$	−65.4799			−2.52219
$675$		0			0
$676$	−58.6658			−2.25638
$677$	9.88243	−	9.88243i	0.379813	−	0.379813i	−0.491222	−	0.871035i	$-0.663450\pi$
$677$	9.88243	−	9.88243i	0.379813	−	0.379813i	0.871035	+	0.491222i	$0.163450\pi$
$678$	18.7282	+	80.0203i	0.719250	+	3.07316i
$679$			2.15519i			0.0827087i
$680$		0			0
$681$	−32.4266	−	20.1269i	−1.24259	−	0.771263i
$682$	−24.0082	−	24.0082i	−0.919320	−	0.919320i
$683$	4.96110	+	4.96110i	0.189831	+	0.189831i	0.795623	−	0.605792i	$-0.207144\pi$
$683$	4.96110	+	4.96110i	0.189831	+	0.189831i	−0.605792	+	0.795623i	$0.707144\pi$
$684$	54.7569	−	27.1162i	2.09368	−	1.03681i
$685$		0			0
$686$			2.68841i			0.102644i
$687$	−42.6197	+	9.97482i	−1.62604	+	0.380563i
$688$	−26.5110	+	26.5110i	−1.01072	+	1.01072i
$689$	−26.4627			−1.00815
$690$		0			0
$691$	42.8476			1.63000			0.814999	−	0.579462i	$-0.196737\pi$
$691$	42.8476			1.63000			0.814999	+	0.579462i	$0.196737\pi$
$692$	17.7473	−	17.7473i	0.674650	−	0.674650i
$693$	−3.61358	+	10.7036i	−0.137269	+	0.406597i
$694$		−	2.58279i		−	0.0980412i
$695$		0			0
$696$	33.8855	−	54.5933i	1.28443	−	2.06935i
$697$	−0.153243	−	0.153243i	−0.00580448	−	0.00580448i
$698$	13.2120	+	13.2120i	0.500082	+	0.500082i
$699$	10.5282	−	16.9621i	0.398213	−	0.641565i
$700$		0			0
$701$		−	6.14360i		−	0.232040i	−0.993247	−	0.116020i	$-0.962986\pi$
$701$		−	6.14360i		−	0.232040i	0.993247	−	0.116020i	$-0.0370137\pi$
$702$	−53.0374	+	43.7481i	−2.00177	+	1.65117i
$703$	−19.4270	+	19.4270i	−0.732703	+	0.732703i
$704$	−77.7081			−2.92874
$705$		0			0
$706$	−80.9745			−3.04752
$707$	7.93316	−	7.93316i	0.298357	−	0.298357i
$708$	−62.2941	+	14.5795i	−2.34115	+	0.547930i
$709$		−	18.2416i		−	0.685078i	−0.939504	−	0.342539i	$-0.888713\pi$
$709$		−	18.2416i		−	0.685078i	0.939504	−	0.342539i	$-0.111287\pi$
$710$		0			0
$711$	0.196722	+	0.397249i	0.00737765	+	0.0148980i
$712$	7.23639	+	7.23639i	0.271195	+	0.271195i
$713$	−11.2429	−	11.2429i	−0.421048	−	0.421048i
$714$	0.738040	+	0.458094i	0.0276205	+	0.0171437i
$715$		0			0
$716$			82.3726i			3.07841i
$717$	8.06769	+	34.4710i	0.301294	+	1.28734i
$718$	9.57638	−	9.57638i	0.357387	−	0.357387i
$719$	−34.6302			−1.29149			−0.645744	−	0.763554i	$-0.723453\pi$
$719$	−34.6302			−1.29149			−0.645744	+	0.763554i	$0.723453\pi$
$720$		0			0
$721$	19.4052			0.722686
$722$	−7.26068	+	7.26068i	−0.270214	+	0.270214i
$723$	−5.23160	−	22.3532i	−0.194565	−	0.831325i
$724$			26.4536i			0.983139i
$725$		0			0
$726$	12.5834	+	7.81041i	0.467015	+	0.289871i
$727$	13.6940	+	13.6940i	0.507883	+	0.507883i	0.913876	−	0.405993i	$-0.133074\pi$
$727$	13.6940	+	13.6940i	0.507883	+	0.507883i	−0.405993	+	0.913876i	$0.633074\pi$
$728$	30.1970	+	30.1970i	1.11917	+	1.11917i
$729$	−5.13550	+	26.5071i	−0.190204	+	0.981745i
$730$		0			0
$731$		−	0.543345i		−	0.0200963i
$732$	−36.2375	+	8.48112i	−1.33938	+	0.313471i
$733$	27.6570	−	27.6570i	1.02154	−	1.02154i	0.0217732	−	0.999763i	$-0.493069\pi$
$733$	27.6570	−	27.6570i	1.02154	−	1.02154i	0.999763	−	0.0217732i	$-0.00693118\pi$
$734$	−0.513839			−0.0189661
$735$		0			0
$736$	−81.7895			−3.01480
$737$	−0.578226	+	0.578226i	−0.0212992	+	0.0212992i
$738$	−8.87739	−	2.99704i	−0.326781	−	0.110323i
$739$		−	34.9352i		−	1.28511i	−0.766238	−	0.642556i	$-0.777874\pi$
$739$		−	34.9352i		−	1.28511i	0.766238	−	0.642556i	$-0.222126\pi$
$740$		0			0
$741$	−17.5155	+	28.2195i	−0.643449	+	1.03667i
$742$	10.2213	+	10.2213i	0.375236	+	0.375236i
$743$	−30.9489	−	30.9489i	−1.13541	−	1.13541i	−0.989263	−	0.146143i	$-0.953314\pi$
$743$	−30.9489	−	30.9489i	−1.13541	−	1.13541i	−0.146143	−	0.989263i	$-0.546686\pi$
$744$	−26.5810	+	42.8249i	−0.974506	+	1.57004i
$745$		0			0
$746$		−	55.3660i		−	2.02709i
$747$	10.3950	+	3.50938i	0.380332	+	0.128402i
$748$	2.59669	−	2.59669i	0.0949443	−	0.0949443i
$749$	11.1267			0.406562
$750$		0			0
$751$	2.98931			0.109082			0.0545408	−	0.998512i	$-0.482631\pi$
$751$	2.98931			0.109082			0.0545408	+	0.998512i	$0.482631\pi$
$752$	102.680	−	102.680i	3.74436	−	3.74436i
$753$	−30.2380	+	7.07697i	−1.10193	+	0.257899i
$754$			56.5689i			2.06012i
$755$		0			0
$756$	27.0389	+	2.59514i	0.983397	+	0.0943843i
$757$	19.4775	+	19.4775i	0.707921	+	0.707921i	0.966098	−	0.258177i	$-0.0831217\pi$
$757$	19.4775	+	19.4775i	0.707921	+	0.707921i	−0.258177	+	0.966098i	$0.583122\pi$
$758$	63.7115	+	63.7115i	2.31411	+	2.31411i
$759$	26.2726	+	16.3071i	0.953636	+	0.591912i
$760$		0			0
$761$		−	17.8797i		−	0.648138i	−0.946033	−	0.324069i	$-0.894949\pi$
$761$		−	17.8797i		−	0.648138i	0.946033	−	0.324069i	$-0.105051\pi$
$762$	−12.9989	−	55.5407i	−0.470900	−	2.01203i
$763$	12.0533	−	12.0533i	0.436360	−	0.436360i
$764$	3.79955			0.137463
$765$		0			0
$766$	−92.5549			−3.34415
$767$	24.5901	−	24.5901i	0.887898	−	0.887898i
$768$	5.96559	+	25.4893i	0.215265	+	0.919767i
$769$			29.7657i			1.07338i	0.843780	+	0.536690i	$0.180325\pi$
$769$			29.7657i			1.07338i	−0.843780	+	0.536690i	$0.819675\pi$
$770$		0			0
$771$	4.01173	+	2.49004i	0.144479	+	0.0896766i
$772$	−62.1694	−	62.1694i	−2.23752	−	2.23752i
$773$	−4.25392	−	4.25392i	−0.153003	−	0.153003i	0.626455	−	0.779458i	$-0.284505\pi$
$773$	−4.25392	−	4.25392i	−0.153003	−	0.153003i	−0.779458	+	0.626455i	$0.784505\pi$
$774$	−10.4248	−	21.0513i	−0.374713	−	0.756673i
$775$		0			0
$776$		−	18.7006i		−	0.671313i
$777$	−11.8921	+	2.78325i	−0.426625	+	0.0998485i
$778$	−18.4406	+	18.4406i	−0.661127	+	0.661127i
$779$	−4.52638			−0.162174
$780$		0			0
$781$	−7.98620			−0.285769
$782$	1.68124	−	1.68124i	0.0601211	−	0.0601211i
$783$	14.1361	+	17.1376i	0.505182	+	0.612449i
$784$		−	12.8723i		−	0.459723i
$785$		0			0
$786$	−7.95606	+	12.8181i	−0.283783	+	0.457207i
$787$	25.4846	+	25.4846i	0.908427	+	0.908427i	0.996145	−	0.0877179i	$-0.0279574\pi$
$787$	25.4846	+	25.4846i	0.908427	+	0.908427i	−0.0877179	+	0.996145i	$0.527957\pi$
$788$	−65.9940	−	65.9940i	−2.35094	−	2.35094i
$789$	15.2706	−	24.6027i	0.543649	−	0.875878i
$790$		0			0
$791$			17.6491i			0.627531i
$792$	31.3551	−	92.8753i	1.11415	−	3.30018i
$793$	14.3045	−	14.3045i	0.507967	−	0.507967i
$794$	−13.6834			−0.485605
$795$		0			0
$796$	−8.16177			−0.289286
$797$	33.4559	−	33.4559i	1.18507	−	1.18507i	0.206654	−	0.978414i	$-0.433743\pi$
$797$	33.4559	−	33.4559i	1.18507	−	1.18507i	0.978414	−	0.206654i	$-0.0662574\pi$
$798$	17.6653	−	4.13443i	0.625344	−	0.146357i
$799$			2.10444i			0.0744496i
$800$		0			0
$801$	−3.17075	+	1.57019i	−0.112033	+	0.0554800i
$802$	74.1072	+	74.1072i	2.61682	+	2.61682i
$803$	36.8788	+	36.8788i	1.30142	+	1.30142i
$804$	1.67055	+	1.03689i	0.0589158	+	0.0365684i
$805$		0			0
$806$		−	44.3747i		−	1.56303i
$807$	−5.76865	−	24.6479i	−0.203066	−	0.867646i
$808$	−68.8360	+	68.8360i	−2.42164	+	2.42164i
$809$	17.3685			0.610644			0.305322	−	0.952249i	$-0.401236\pi$
$809$	17.3685			0.610644			0.305322	+	0.952249i	$0.401236\pi$
$810$		0			0
$811$	−32.6279			−1.14572			−0.572860	−	0.819654i	$-0.694166\pi$
$811$	−32.6279			−1.14572			−0.572860	+	0.819654i	$0.694166\pi$
$812$	15.8037	−	15.8037i	0.554599	−	0.554599i
$813$	−1.23511	−	5.27728i	−0.0433171	−	0.185082i
$814$			71.3871i			2.50212i
$815$		0			0
$816$	−3.53377	−	2.19338i	−0.123707	−	0.0767835i
$817$	−8.02447	−	8.02447i	−0.280741	−	0.280741i
$818$	2.91220	+	2.91220i	0.101823	+	0.101823i
$819$	−13.2314	+	6.55231i	−0.462341	+	0.228956i
$820$		0			0
$821$			20.4956i			0.715302i	0.933855	+	0.357651i	$0.116422\pi$
$821$			20.4956i			0.715302i	−0.933855	+	0.357651i	$0.883578\pi$
$822$	−35.5319	+	8.31597i	−1.23932	+	0.290053i
$823$	−7.29225	+	7.29225i	−0.254192	+	0.254192i	−0.822687	−	0.568495i	$-0.807526\pi$
$823$	−7.29225	+	7.29225i	−0.254192	+	0.254192i	0.568495	+	0.822687i	$0.307526\pi$
$824$	−168.379			−5.86575
$825$		0			0
$826$	−18.9960			−0.660957
$827$	34.4662	−	34.4662i	1.19851	−	1.19851i	0.223891	−	0.974614i	$-0.428124\pi$
$827$	34.4662	−	34.4662i	1.19851	−	1.19851i	0.974614	−	0.223891i	$-0.0718761\pi$
$828$	23.7821	−	70.4438i	0.826485	−	2.44809i
$829$			31.3135i			1.08756i	0.839227	+	0.543782i	$0.183008\pi$
$829$			31.3135i			1.08756i	−0.839227	+	0.543782i	$0.816992\pi$
$830$		0			0
$831$	−12.4142	+	20.0006i	−0.430642	+	0.693813i
$832$	−71.8146	−	71.8146i	−2.48972	−	2.48972i
$833$	0.131909	+	0.131909i	0.00457037	+	0.00457037i
$834$	46.4207	−	74.7889i	1.60742	−	2.58973i
$835$		0			0
$836$		−	76.6991i		−	2.65269i
$837$	−11.0888	−	13.4434i	−0.383286	−	0.464671i
$838$	−49.3869	+	49.3869i	−1.70604	+	1.70604i
$839$	−0.518418			−0.0178978			−0.00894889	−	0.999960i	$-0.502849\pi$
$839$	−0.518418			−0.0178978			−0.00894889	+	0.999960i	$0.502849\pi$
$840$		0			0
$841$	−10.7212			−0.369697
$842$	6.36134	−	6.36134i	0.219226	−	0.219226i
$843$	14.7080	−	3.44230i	0.506570	−	0.118559i
$844$			21.2386i			0.731062i
$845$		0			0
$846$	40.3765	+	81.5340i	1.38817	+	2.80320i
$847$	2.24902	+	2.24902i	0.0772771	+	0.0772771i
$848$	−48.9401	−	48.9401i	−1.68061	−	1.68061i
$849$	24.2817	+	15.0714i	0.833345	+	0.517248i
$850$		0			0
$851$			33.4301i			1.14597i
$852$	4.37590	+	18.6970i	0.149916	+	0.640549i
$853$	−13.6122	+	13.6122i	−0.466071	+	0.466071i	−0.900639	−	0.434568i	$-0.856901\pi$
$853$	−13.6122	+	13.6122i	−0.466071	+	0.466071i	0.434568	+	0.900639i	$0.356901\pi$
$854$	−11.0503			−0.378134
$855$		0			0
$856$	−96.5468			−3.29990
$857$	−14.6366	+	14.6366i	−0.499977	+	0.499977i	−0.911431	−	0.411454i	$-0.865021\pi$
$857$	−14.6366	+	14.6366i	−0.499977	+	0.499977i	0.411454	+	0.911431i	$0.365021\pi$
$858$	19.6665	+	84.0296i	0.671403	+	2.86872i
$859$			18.2644i			0.623173i	0.950218	+	0.311587i	$0.100860\pi$
$859$			18.2644i			0.623173i	−0.950218	+	0.311587i	$0.899140\pi$
$860$		0			0
$861$	−1.70963	−	1.06115i	−0.0582640	−	0.0361639i
$862$	−41.0530	−	41.0530i	−1.39827	−	1.39827i
$863$	−31.7103	−	31.7103i	−1.07943	−	1.07943i	−0.996560	−	0.0828701i	$-0.973591\pi$
$863$	−31.7103	−	31.7103i	−1.07943	−	1.07943i	−0.0828701	−	0.996560i	$-0.526409\pi$
$864$	−89.2334	−	8.56443i	−3.03578	−	0.291368i
$865$		0			0
$866$		−	38.1744i		−	1.29722i
$867$	−28.6114	+	6.69629i	−0.971695	+	0.227418i
$868$	−12.3970	+	12.3970i	−0.420780	+	0.420780i
$869$	0.556434			0.0188757
$870$		0			0
$871$	−1.06874			−0.0362130
$872$	−104.587	+	104.587i	−3.54176	+	3.54176i
$873$	6.12589	+	2.06813i	0.207330	+	0.0699954i
$874$		−	49.6593i		−	1.67975i
$875$		0			0
$876$	66.1323	−	106.546i	2.23440	−	3.59987i
$877$	−10.9530	−	10.9530i	−0.369855	−	0.369855i	0.497569	−	0.867424i	$-0.334226\pi$
$877$	−10.9530	−	10.9530i	−0.369855	−	0.369855i	−0.867424	+	0.497569i	$0.834226\pi$
$878$	−45.6988	−	45.6988i	−1.54226	−	1.54226i
$879$	−18.6297	+	30.0145i	−0.628364	+	1.01236i
$880$		0			0
$881$			45.9978i			1.54970i	0.632142	+	0.774852i	$0.282176\pi$
$881$			45.9978i			1.54970i	−0.632142	+	0.774852i	$0.717824\pi$
$882$	7.64151	+	2.57980i	0.257303	+	0.0868665i
$883$	−41.0408	+	41.0408i	−1.38113	+	1.38113i	−0.538521	+	0.842612i	$0.681017\pi$
$883$	−41.0408	+	41.0408i	−1.38113	+	1.38113i	−0.842612	+	0.538521i	$0.818983\pi$
$884$	4.79950			0.161425
$885$		0			0
$886$	16.1924			0.543995
$887$	3.68081	−	3.68081i	0.123590	−	0.123590i	−0.642607	−	0.766196i	$-0.722147\pi$
$887$	3.68081	−	3.68081i	0.123590	−	0.123590i	0.766196	+	0.642607i	$0.222147\pi$
$888$	103.187	−	24.1503i	3.46275	−	0.810430i
$889$		−	12.2500i		−	0.410851i
$890$		0			0
$891$	26.9562	+	20.5424i	0.903067	+	0.688196i
$892$	100.710	+	100.710i	3.37203	+	3.37203i
$893$	31.0797	+	31.0797i	1.04004	+	1.04004i
$894$	−17.7227	−	11.0003i	−0.592737	−	0.367905i
$895$		0			0
$896$			20.9735i			0.700675i
$897$	9.20968	+	39.3505i	0.307502	+	1.31387i
$898$	57.5255	−	57.5255i	1.91965	−	1.91965i
$899$	−14.3385			−0.478217
$900$		0			0
$901$	1.00303			0.0334158
$902$	−8.31638	+	8.31638i	−0.276905	+	0.276905i
$903$	−1.14964	−	4.91210i	−0.0382577	−	0.163465i
$904$		−	153.142i		−	5.09342i
$905$		0			0
$906$	−8.19669	−	5.08760i	−0.272317	−	0.169024i
$907$	2.57083	+	2.57083i	0.0853631	+	0.0853631i	0.748499	−	0.663136i	$-0.230775\pi$
$907$	2.57083	+	2.57083i	0.0853631	+	0.0853631i	−0.663136	+	0.748499i	$0.730775\pi$
$908$	81.4497	+	81.4497i	2.70300	+	2.70300i
$909$	−14.9364	−	30.1618i	−0.495410	−	1.00040i
$910$		0			0
$911$			4.65152i			0.154112i	0.997027	+	0.0770559i	$0.0245520\pi$
$911$			4.65152i			0.154112i	−0.997027	+	0.0770559i	$0.975448\pi$
$912$	−84.5823	+	19.7959i	−2.80080	+	0.655506i
$913$	9.73805	−	9.73805i	0.322282	−	0.322282i
$914$	39.9708			1.32212
$915$		0			0
$916$	132.108			4.36496
$917$	−2.29096	+	2.29096i	−0.0756541	+	0.0756541i
$918$	2.01030	−	1.65821i	0.0663499	−	0.0547290i
$919$			0.422209i			0.0139274i	0.999976	+	0.00696370i	$0.00221663\pi$
$919$			0.422209i			0.0139274i	−0.999976	+	0.00696370i	$0.997783\pi$
$920$		0			0
$921$	−7.78942	+	12.5496i	−0.256670	+	0.413524i
$922$	75.6371	+	75.6371i	2.49098	+	2.49098i
$923$	−7.38051	−	7.38051i	−0.242933	−	0.242933i
$924$	17.9811	−	28.9695i	0.591535	−	0.953028i
$925$		0			0
$926$			91.7738i			3.01587i
$927$	18.6212	−	55.1570i	0.611601	−	1.81159i
$928$	−52.1549	+	52.1549i	−1.71207	+	1.71207i
$929$	−2.97387			−0.0975694			−0.0487847	−	0.998809i	$-0.515535\pi$
$929$	−2.97387			−0.0975694			−0.0487847	+	0.998809i	$0.515535\pi$
$930$		0			0
$931$	3.89623			0.127694
$932$	−42.6057	+	42.6057i	−1.39560	+	1.39560i
$933$	−34.3053	+	8.02890i	−1.12310	+	0.262854i
$934$		−	51.4011i		−	1.68190i
$935$		0			0
$936$	114.809	−	56.8545i	3.75264	−	1.85835i
$937$	0.345323	+	0.345323i	0.0112812	+	0.0112812i	0.712725	−	0.701444i	$-0.247461\pi$
$937$	0.345323	+	0.345323i	0.0112812	+	0.0112812i	−0.701444	+	0.712725i	$0.747461\pi$
$938$	0.412806	+	0.412806i	0.0134786	+	0.0134786i
$939$	28.3239	+	17.5803i	0.924314	+	0.573712i
$940$		0			0
$941$		−	35.5643i		−	1.15936i	−0.814843	−	0.579682i	$-0.803177\pi$
$941$		−	35.5643i		−	1.15936i	0.814843	−	0.579682i	$-0.196823\pi$
$942$	−7.77152	−	33.2056i	−0.253210	−	1.08190i
$943$	−3.89450	+	3.89450i	−0.126822	+	0.126822i
$944$	90.9540			2.96030
$945$		0			0
$946$	−29.4870			−0.958704
$947$	−1.40196	+	1.40196i	−0.0455577	+	0.0455577i	−0.729519	−	0.683961i	$-0.760256\pi$
$947$	−1.40196	+	1.40196i	−0.0455577	+	0.0455577i	0.683961	+	0.729519i	$0.260256\pi$
$948$	−0.304889	−	1.30271i	−0.00990232	−	0.0423099i
$949$			68.1637i			2.21269i
$950$		0			0
$951$	−27.7970	−	17.2533i	−0.901379	−	0.559476i
$952$	−1.14457	−	1.14457i	−0.0370958	−	0.0370958i
$953$	−14.2215	−	14.2215i	−0.460680	−	0.460680i	0.438199	−	0.898878i	$-0.355617\pi$
$953$	−14.2215	−	14.2215i	−0.460680	−	0.460680i	−0.898878	+	0.438199i	$0.855617\pi$
$954$	38.8613	−	19.2445i	1.25818	−	0.623065i
$955$		0			0
$956$		−	106.850i		−	3.45576i
$957$	27.1520	−	6.35472i	0.877698	−	0.205419i
$958$	70.5110	−	70.5110i	2.27811	−	2.27811i
$959$	−7.83685			−0.253065
$960$		0			0
$961$	−19.7523			−0.637172
$962$	−65.9730	+	65.9730i	−2.12705	+	2.12705i
$963$	10.6772	−	31.6265i	0.344069	−	1.01915i
$964$			69.2880i			2.23162i
$965$		0			0
$966$	11.6420	−	18.7565i	0.374574	−	0.603481i
$967$	−20.8267	−	20.8267i	−0.669740	−	0.669740i	0.287916	−	0.957656i	$-0.407038\pi$
$967$	−20.8267	−	20.8267i	−0.669740	−	0.669740i	−0.957656	+	0.287916i	$0.907038\pi$
$968$	−19.5147	−	19.5147i	−0.627227	−	0.627227i
$969$	0.663900	−	1.06962i	0.0213276	−	0.0343611i
$970$		0			0
$971$		−	21.8627i		−	0.701608i	−0.936449	−	0.350804i	$-0.885908\pi$
$971$		−	21.8627i		−	0.701608i	0.936449	−	0.350804i	$-0.114092\pi$
$972$	33.3230	−	74.3648i	1.06884	−	2.38525i
$973$	13.3669	−	13.3669i	0.428523	−	0.428523i
$974$	46.7799			1.49893
$975$		0			0
$976$	52.9094			1.69359
$977$	−20.2336	+	20.2336i	−0.647331	+	0.647331i	−0.952347	−	0.305016i	$-0.901338\pi$
$977$	−20.2336	+	20.2336i	−0.647331	+	0.647331i	0.305016	+	0.952347i	$0.401338\pi$
$978$	−7.34884	+	1.71994i	−0.234990	+	0.0549977i
$979$			4.44134i			0.141946i
$980$		0			0
$981$	−22.6938	−	45.8266i	−0.724559	−	1.46313i
$982$	−28.7378	−	28.7378i	−0.917061	−	0.917061i
$983$	5.04301	+	5.04301i	0.160847	+	0.160847i	0.782942	−	0.622095i	$-0.213718\pi$
$983$	5.04301	+	5.04301i	0.160847	+	0.160847i	−0.622095	+	0.782942i	$0.713718\pi$
$984$	14.8345	+	9.20760i	0.472906	+	0.293528i
$985$		0			0
$986$		−	2.14416i		−	0.0682841i
$987$	4.45269	+	19.0251i	0.141731	+	0.605576i
$988$	70.8821	−	70.8821i	2.25506	−	2.25506i
$989$	−13.8085			−0.439086
$990$		0			0
$991$	21.6595			0.688038			0.344019	−	0.938963i	$-0.388211\pi$
$991$	21.6595			0.688038			0.344019	+	0.938963i	$0.388211\pi$
$992$	40.9122	−	40.9122i	1.29896	−	1.29896i
$993$	−11.2879	−	48.2300i	−0.358210	−	1.53053i
$994$			5.70150i			0.180840i
$995$		0			0
$996$	−28.1342	−	17.4626i	−0.891466	−	0.553324i
$997$	22.8411	+	22.8411i	0.723386	+	0.723386i	0.969293	−	0.245907i	$-0.0790858\pi$
$997$	22.8411	+	22.8411i	0.723386	+	0.723386i	−0.245907	+	0.969293i	$0.579086\pi$
$998$	44.1536	+	44.1536i	1.39766	+	1.39766i
$999$	−3.50057	+	36.4726i	−0.110753	+	1.15394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.c.407.1	yes	32
3.2	odd	2	inner	525.2.j.c.407.15	yes	32
5.2	odd	4	inner	525.2.j.c.218.2	yes	32
5.3	odd	4	inner	525.2.j.c.218.15	yes	32
5.4	even	2	inner	525.2.j.c.407.16	yes	32
15.2	even	4	inner	525.2.j.c.218.16	yes	32
15.8	even	4	inner	525.2.j.c.218.1	✓	32
15.14	odd	2	inner	525.2.j.c.407.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.j.c.218.1	✓	32	15.8	even	4	inner
525.2.j.c.218.2	yes	32	5.2	odd	4	inner
525.2.j.c.218.15	yes	32	5.3	odd	4	inner
525.2.j.c.218.16	yes	32	15.2	even	4	inner
525.2.j.c.407.1	yes	32	1.1	even	1	trivial
525.2.j.c.407.2	yes	32	15.14	odd	2	inner
525.2.j.c.407.15	yes	32	3.2	odd	2	inner
525.2.j.c.407.16	yes	32	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.90099 + 1.90099i) q^{2} +(0.394708 + 1.68648i) q^{3} -5.22756i q^{4} +(-3.95632 - 2.45565i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(6.13557 + 6.13557i) q^{8} +(-2.68841 + 1.33133i) q^{9} +O(q^{10})\)	\(q+(-1.90099 + 1.90099i) q^{2} +(0.394708 + 1.68648i) q^{3} -5.22756i q^{4} +(-3.95632 - 2.45565i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(6.13557 + 6.13557i) q^{8} +(-2.68841 + 1.33133i) q^{9} +3.76571i q^{11} +(8.81616 - 2.06336i) q^{12} +(-3.48012 + 3.48012i) q^{13} +2.68841 q^{14} -12.8723 q^{16} +(0.131909 - 0.131909i) q^{17} +(2.57980 - 7.64151i) q^{18} -3.89623i q^{19} +(0.913419 - 1.47162i) q^{21} +(-7.15860 - 7.15860i) q^{22} +(-3.35232 - 3.35232i) q^{23} +(-7.92574 + 12.7693i) q^{24} -13.2314i q^{26} +(-3.30640 - 4.00846i) q^{27} +(-3.69644 + 3.69644i) q^{28} -4.27537 q^{29} +3.35375 q^{31} +(12.1989 - 12.1989i) q^{32} +(-6.35079 + 1.48636i) q^{33} +0.501515i q^{34} +(6.95961 + 14.0538i) q^{36} +(-4.98611 - 4.98611i) q^{37} +(7.40671 + 7.40671i) q^{38} +(-7.24276 - 4.49551i) q^{39} -1.16173i q^{41} +(1.06114 + 4.53395i) q^{42} +(2.05955 - 2.05955i) q^{43} +19.6855 q^{44} +12.7455 q^{46} +(-7.97686 + 7.97686i) q^{47} +(-5.08077 - 21.7088i) q^{48} +1.00000i q^{49} +(0.274526 + 0.170396i) q^{51} +(18.1925 + 18.1925i) q^{52} +(3.80199 + 3.80199i) q^{53} +(13.9055 + 1.33462i) q^{54} -8.67701i q^{56} +(6.57090 - 1.53787i) q^{57} +(8.12745 - 8.12745i) q^{58} -7.06590 q^{59} -4.11035 q^{61} +(-6.37546 + 6.37546i) q^{62} +(2.84239 + 0.959601i) q^{63} +20.6357i q^{64} +(9.24726 - 14.8984i) q^{66} +(0.153550 + 0.153550i) q^{67} +(-0.689561 - 0.689561i) q^{68} +(4.33043 - 6.97680i) q^{69} +2.12077i q^{71} +(-24.6634 - 8.32647i) q^{72} +(9.79331 - 9.79331i) q^{73} +18.9571 q^{74} -20.3678 q^{76} +(2.66276 - 2.66276i) q^{77} +(22.3144 - 5.22252i) q^{78} -0.147763i q^{79} +(5.45512 - 7.15833i) q^{81} +(2.20845 + 2.20845i) q^{82} +(-2.58598 - 2.58598i) q^{83} +(-7.69298 - 4.77495i) q^{84} +7.83038i q^{86} +(-1.68752 - 7.21031i) q^{87} +(-23.1048 + 23.1048i) q^{88} +1.17942 q^{89} +4.92163 q^{91} +(-17.5245 + 17.5245i) q^{92} +(1.32375 + 5.65603i) q^{93} -30.3279i q^{94} +(25.3882 + 15.7582i) q^{96} +(-1.52395 - 1.52395i) q^{97} +(-1.90099 - 1.90099i) q^{98} +(-5.01341 - 10.1238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{6}+O(q^{10}) \) 32 * q - 16 * q^6	\( 32 q - 16 q^{6} - 16 q^{16} - 8 q^{21} + 16 q^{31} + 48 q^{36} + 144 q^{46} - 64 q^{51} - 112 q^{61} - 192 q^{76} - 64 q^{81} + 64 q^{91} + 360 q^{96}+O(q^{100}) \) 32 * q - 16 * q^6 - 16 * q^16 - 8 * q^21 + 16 * q^31 + 48 * q^36 + 144 * q^46 - 64 * q^51 - 112 * q^61 - 192 * q^76 - 64 * q^81 + 64 * q^91 + 360 * q^96

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