LMFDB - Embedded newform 804.2.ba.b.353.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(41,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 33, 53]))

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

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

chi := DirichletCharacter("804.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.ba (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			353.8
Character	$\chi$	$=$	804.353
Dual form			804.2.ba.b.41.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05930 - 1.37036i) q^{3} +(-0.533599 - 3.71127i) q^{5} +(0.465124 - 4.87100i) q^{7} +(-0.755762 + 2.90324i) q^{9} +O(q^{10})$	\(q+(-1.05930 - 1.37036i) q^{3} +(-0.533599 - 3.71127i) q^{5} +(0.465124 - 4.87100i) q^{7} +(-0.755762 + 2.90324i) q^{9} +(-4.53378 - 1.81505i) q^{11} +(3.30733 - 3.46863i) q^{13} +(-4.52052 + 4.66257i) q^{15} +(5.33974 + 1.84810i) q^{17} +(-0.797858 + 0.0761862i) q^{19} +(-7.16773 + 4.52247i) q^{21} +(2.77501 + 0.132190i) q^{23} +(-8.69130 + 2.55200i) q^{25} +(4.77906 - 2.03974i) q^{27} +(0.708402 + 0.408996i) q^{29} +(5.31235 + 5.57143i) q^{31} +(2.31537 + 8.13559i) q^{33} +(-18.3258 + 0.872965i) q^{35} +(2.23579 + 3.87250i) q^{37} +(-8.25673 - 0.857906i) q^{39} +(7.67348 - 1.47894i) q^{41} +(0.934610 - 0.809844i) q^{43} +(11.1780 + 1.25566i) q^{45} +(0.757376 + 1.46910i) q^{47} +(-16.6368 - 3.20649i) q^{49} +(-3.12383 - 9.27505i) q^{51} +(-1.96721 + 2.27028i) q^{53} +(-4.31692 + 17.7946i) q^{55} +(0.949574 + 1.01265i) q^{57} +(2.87219 - 9.78178i) q^{59} +(-1.09942 - 2.74622i) q^{61} +(13.7902 + 5.03169i) q^{63} +(-14.6378 - 10.4235i) q^{65} +(-8.18444 + 0.122098i) q^{67} +(-2.75843 - 3.94279i) q^{69} +(-0.732584 + 0.253550i) q^{71} +(7.12244 - 2.85140i) q^{73} +(12.7039 + 9.20686i) q^{75} +(-10.9499 + 21.2398i) q^{77} +(-8.83315 - 2.14290i) q^{79} +(-7.85765 - 4.38832i) q^{81} +(-1.89921 - 2.41505i) q^{83} +(4.00952 - 20.8033i) q^{85} +(-0.189940 - 1.40401i) q^{87} +(2.68891 + 4.18402i) q^{89} +(-15.3574 - 17.7234i) q^{91} +(2.00748 - 13.1816i) q^{93} +(0.708484 + 2.92041i) q^{95} +(-3.01975 + 1.74345i) q^{97} +(8.69600 - 11.7909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) $ 440 * q - 12 * q^7 + 4 * q^9	$ 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) $ 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{13}{66}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.05930	−	1.37036i	−0.611588	−	0.791177i
$3$	−1.05930	−	1.37036i	−0.611588	−	0.791177i
$4$		0			0
$5$	−0.533599	−	3.71127i	−0.238633	−	1.65973i	−0.658827	−	0.752294i	$-0.728947\pi$
$5$	−0.533599	−	3.71127i	−0.238633	−	1.65973i	0.420194	−	0.907434i	$-0.361962\pi$
$6$		0			0
$7$	0.465124	−	4.87100i	0.175801	−	1.84107i	−0.291023	−	0.956716i	$-0.593996\pi$
$7$	0.465124	−	4.87100i	0.175801	−	1.84107i	0.466824	−	0.884350i	$-0.345398\pi$
$8$		0			0
$9$	−0.755762	+	2.90324i	−0.251921	+	0.967748i
$10$		0			0
$11$	−4.53378	−	1.81505i	−1.36699	−	0.547259i	−0.431978	−	0.901884i	$-0.642184\pi$
$11$	−4.53378	−	1.81505i	−1.36699	−	0.547259i	−0.935009	+	0.354625i	$0.884608\pi$
$12$		0			0
$13$	3.30733	−	3.46863i	0.917289	−	0.962026i	−0.0821118	−	0.996623i	$-0.526166\pi$
$13$	3.30733	−	3.46863i	0.917289	−	0.962026i	0.999401	+	0.0345976i	$0.0110150\pi$
$14$		0			0
$15$	−4.52052	+	4.66257i	−1.16719	+	1.20387i
$16$		0			0
$17$	5.33974	+	1.84810i	1.29508	+	0.448231i	0.885752	−	0.464158i	$-0.153643\pi$
$17$	5.33974	+	1.84810i	1.29508	+	0.448231i	0.409325	+	0.912389i	$0.365764\pi$
$18$		0			0
$19$	−0.797858	+	0.0761862i	−0.183041	+	0.0174783i	−0.186174	−	0.982517i	$-0.559609\pi$
$19$	−0.797858	+	0.0761862i	−0.183041	+	0.0174783i	0.00313289	+	0.999995i	$0.499003\pi$
$20$		0			0
$21$	−7.16773	+	4.52247i	−1.56413	+	0.986885i
$22$		0			0
$23$	2.77501	+	0.132190i	0.578630	+	0.0275635i	0.334857	−	0.942269i	$-0.391312\pi$
$23$	2.77501	+	0.132190i	0.578630	+	0.0275635i	0.243773	+	0.969832i	$0.421615\pi$
$24$		0			0
$25$	−8.69130	+	2.55200i	−1.73826	+	0.510399i
$26$		0			0
$27$	4.77906	−	2.03974i	0.919731	−	0.392549i
$28$		0			0
$29$	0.708402	+	0.408996i	0.131547	+	0.0759486i	0.564329	−	0.825550i	$-0.309135\pi$
$29$	0.708402	+	0.408996i	0.131547	+	0.0759486i	−0.432782	+	0.901498i	$0.642468\pi$
$30$		0			0
$31$	5.31235	+	5.57143i	0.954126	+	1.00066i	0.999999	+	0.00171155i	$0.000544804\pi$
$31$	5.31235	+	5.57143i	0.954126	+	1.00066i	−0.0458722	+	0.998947i	$0.514607\pi$
$32$		0			0
$33$	2.31537	+	8.13559i	0.403054	+	1.41622i
$34$		0			0
$35$	−18.3258	+	0.872965i	−3.09762	+	0.147558i
$36$		0			0
$37$	2.23579	+	3.87250i	0.367561	+	0.636635i	0.989184	−	0.146682i	$-0.0468594\pi$
$37$	2.23579	+	3.87250i	0.367561	+	0.636635i	−0.621622	+	0.783317i	$0.713526\pi$
$38$		0			0
$39$	−8.25673	−	0.857906i	−1.32214	−	0.137375i
$40$		0			0
$41$	7.67348	−	1.47894i	1.19840	−	0.230972i	0.449268	−	0.893397i	$-0.351685\pi$
$41$	7.67348	−	1.47894i	1.19840	−	0.230972i	0.749128	+	0.662425i	$0.230473\pi$
$42$		0			0
$43$	0.934610	−	0.809844i	0.142527	−	0.123500i	−0.580680	−	0.814132i	$-0.697213\pi$
$43$	0.934610	−	0.809844i	0.142527	−	0.123500i	0.723206	+	0.690632i	$0.242668\pi$
$44$		0			0
$45$	11.1780	+	1.25566i	1.66632	+	0.187183i
$46$		0			0
$47$	0.757376	+	1.46910i	0.110475	+	0.214291i	0.937591	−	0.347740i	$-0.113051\pi$
$47$	0.757376	+	1.46910i	0.110475	+	0.214291i	−0.827117	+	0.562030i	$0.810020\pi$
$48$		0			0
$49$	−16.6368	−	3.20649i	−2.37669	−	0.458070i
$50$		0			0
$51$	−3.12383	−	9.27505i	−0.437424	−	1.29877i
$52$		0			0
$53$	−1.96721	+	2.27028i	−0.270217	+	0.311846i	−0.874598	−	0.484848i	$-0.838875\pi$
$53$	−1.96721	+	2.27028i	−0.270217	+	0.311846i	0.604382	+	0.796695i	$0.293420\pi$
$54$		0			0
$55$	−4.31692	+	17.7946i	−0.582093	+	2.39942i
$56$		0			0
$57$	0.949574	+	1.01265i	0.125774	+	0.134128i
$58$		0			0
$59$	2.87219	−	9.78178i	0.373927	−	1.27348i	−0.530804	−	0.847495i	$-0.678110\pi$
$59$	2.87219	−	9.78178i	0.373927	−	1.27348i	0.904731	−	0.425984i	$-0.140072\pi$
$60$		0			0
$61$	−1.09942	−	2.74622i	−0.140766	−	0.351617i	0.841186	−	0.540746i	$-0.181858\pi$
$61$	−1.09942	−	2.74622i	−0.140766	−	0.351617i	−0.981952	+	0.189129i	$0.939434\pi$
$62$		0			0
$63$	13.7902	+	5.03169i	1.73740	+	0.633933i
$64$		0			0
$65$	−14.6378	−	10.4235i	−1.81560	−	1.29288i
$66$		0			0
$67$	−8.18444	+	0.122098i	−0.999889	+	0.0149167i
$67$	−8.18444	+	0.122098i	−0.999889	+	0.0149167i
$68$		0			0
$69$	−2.75843	−	3.94279i	−0.332075	−	0.474656i
$70$		0			0
$71$	−0.732584	+	0.253550i	−0.0869417	+	0.0300908i	−0.370193	−	0.928955i	$-0.620708\pi$
$71$	−0.732584	+	0.253550i	−0.0869417	+	0.0300908i	0.283251	+	0.959046i	$0.408587\pi$
$72$		0			0
$73$	7.12244	−	2.85140i	0.833619	−	0.333731i	0.0847116	−	0.996406i	$-0.473003\pi$
$73$	7.12244	−	2.85140i	0.833619	−	0.333731i	0.748907	+	0.662675i	$0.230579\pi$
$74$		0			0
$75$	12.7039	+	9.20686i	1.46691	+	1.06312i
$76$		0			0
$77$	−10.9499	+	21.2398i	−1.24786	+	2.42050i
$78$		0			0
$79$	−8.83315	−	2.14290i	−0.993807	−	0.241095i	−0.294294	−	0.955715i	$-0.595085\pi$
$79$	−8.83315	−	2.14290i	−0.993807	−	0.241095i	−0.699513	+	0.714620i	$0.746600\pi$
$80$		0			0
$81$	−7.85765	−	4.38832i	−0.873072	−	0.487591i
$82$		0			0
$83$	−1.89921	−	2.41505i	−0.208466	−	0.265086i	0.670565	−	0.741851i	$-0.266052\pi$
$83$	−1.89921	−	2.41505i	−0.208466	−	0.265086i	−0.879031	+	0.476765i	$0.841809\pi$
$84$		0			0
$85$	4.00952	−	20.8033i	0.434893	−	2.25644i
$86$		0			0
$87$	−0.189940	−	1.40401i	−0.0203637	−	0.150526i
$88$		0			0
$89$	2.68891	+	4.18402i	0.285024	+	0.443506i	0.954012	−	0.299767i	$-0.0969089\pi$
$89$	2.68891	+	4.18402i	0.285024	+	0.443506i	−0.668989	+	0.743273i	$0.733273\pi$
$90$		0			0
$91$	−15.3574	−	17.7234i	−1.60989	−	1.85792i
$92$		0			0
$93$	2.00748	−	13.1816i	0.208166	−	1.36687i
$94$		0			0
$95$	0.708484	+	2.92041i	0.0726889	+	0.299628i
$96$		0			0
$97$	−3.01975	+	1.74345i	−0.306609	+	0.177021i	−0.645408	−	0.763838i	$-0.723313\pi$
$97$	−3.01975	+	1.74345i	−0.306609	+	0.177021i	0.338799	+	0.940859i	$0.389979\pi$
$98$		0			0
$99$	8.69600	−	11.7909i	0.873981	−	1.18503i
$100$		0			0
$101$	3.43000	+	4.81676i	0.341298	+	0.479286i	0.949177	−	0.314744i	$-0.101919\pi$
$101$	3.43000	+	4.81676i	0.341298	+	0.479286i	−0.607879	+	0.794030i	$0.707979\pi$
$102$		0			0
$103$	8.46000	−	8.06659i	0.833589	−	0.794825i	−0.147362	−	0.989083i	$-0.547078\pi$
$103$	8.46000	−	8.06659i	0.833589	−	0.794825i	0.980951	+	0.194257i	$0.0622297\pi$
$104$		0			0
$105$	20.6088	+	24.1881i	2.01121	+	2.36052i
$106$		0			0
$107$	6.07296	+	0.873160i	0.587095	+	0.0844115i	0.429460	−	0.903086i	$-0.358704\pi$
$107$	6.07296	+	0.873160i	0.587095	+	0.0844115i	0.157635	+	0.987497i	$0.449613\pi$
$108$		0			0
$109$	3.94134	+	13.4230i	0.377512	+	1.28569i	0.901061	+	0.433692i	$0.142789\pi$
$109$	3.94134	+	13.4230i	0.377512	+	1.28569i	−0.523549	+	0.851995i	$0.675392\pi$
$110$		0			0
$111$	2.93834	−	7.16597i	0.278895	−	0.680164i
$112$		0			0
$113$	11.7712	+	9.25700i	1.10734	+	0.870825i	0.992462	−	0.122554i	$-0.0391084\pi$
$113$	11.7712	+	9.25700i	1.10734	+	0.870825i	0.114882	+	0.993379i	$0.463351\pi$
$114$		0			0
$115$	−0.990152	−	10.3693i	−0.0923322	−	0.966946i
$116$		0			0
$117$	7.57073	+	12.2235i	0.699914	+	1.13006i
$118$		0			0
$119$	11.4858	−	25.1503i	1.05290	−	2.30552i
$120$		0			0
$121$	9.29969	+	8.86723i	0.845426	+	0.806112i
$122$		0			0
$123$	−10.1552	−	8.94877i	−0.915664	−	0.806883i
$124$		0			0
$125$	6.32096	+	13.8410i	0.565364	+	1.23798i
$126$		0			0
$127$	7.86576	+	0.751089i	0.697974	+	0.0666484i	0.438010	−	0.898970i	$-0.355683\pi$
$127$	7.86576	+	0.751089i	0.697974	+	0.0666484i	0.259963	+	0.965618i	$0.416289\pi$
$128$		0			0
$129$	−2.09981	−	0.422881i	−0.184878	−	0.0372326i
$130$		0			0
$131$	−10.9782	+	17.0825i	−0.959173	+	1.49250i	−0.0912354	+	0.995829i	$0.529082\pi$
$131$	−10.9782	+	17.0825i	−0.959173	+	1.49250i	−0.867938	+	0.496673i	$0.834555\pi$
$132$		0			0
$133$			3.92180i			0.340064i
$134$		0			0
$135$	−10.1201	−	16.6480i	−0.871003	−	1.43283i
$136$		0			0
$137$	0.698213	+	0.448714i	0.0596523	+	0.0383362i	0.570127	−	0.821557i	$-0.306894\pi$
$137$	0.698213	+	0.448714i	0.0596523	+	0.0383362i	−0.510475	+	0.859893i	$0.670530\pi$
$138$		0			0
$139$	−14.4038	+	2.07095i	−1.22171	+	0.175656i	−0.722837	−	0.691019i	$-0.757162\pi$
$139$	−14.4038	+	2.07095i	−1.22171	+	0.175656i	−0.498874	+	0.866674i	$0.666253\pi$
$140$		0			0
$141$	1.21091	−	2.59410i	0.101977	−	0.218463i
$142$		0			0
$143$	−21.2905	+	9.72304i	−1.78040	+	0.813081i
$144$		0			0
$145$	1.13989	−	2.84731i	0.0946627	−	0.236456i
$146$		0			0
$147$	13.2294	+	26.1951i	1.09114	+	2.16053i
$148$		0			0
$149$	15.8294	+	7.22903i	1.29679	+	0.592225i	0.939750	−	0.341863i	$-0.111058\pi$
$149$	15.8294	+	7.22903i	1.29679	+	0.592225i	0.357042	+	0.934088i	$0.383785\pi$
$150$		0			0
$151$	−1.33081	+	3.84513i	−0.108300	+	0.312912i	−0.986109	−	0.166098i	$-0.946883\pi$
$151$	−1.33081	+	3.84513i	−0.108300	+	0.312912i	0.877809	+	0.479010i	$0.159004\pi$
$152$		0			0
$153$	−9.40106	+	14.1058i	−0.760031	+	1.14039i
$154$		0			0
$155$	17.8424	−	22.6885i	1.43314	−	1.82238i
$156$		0			0
$157$	0.486177	−	10.2061i	0.0388012	−	0.814536i	−0.892668	−	0.450715i	$-0.851169\pi$
$157$	0.486177	−	10.2061i	0.0388012	−	0.814536i	0.931469	−	0.363821i	$-0.118528\pi$
$158$		0			0
$159$	5.19496	+	0.290870i	0.411987	+	0.0230675i
$160$		0			0
$161$	1.93462	−	13.4556i	0.152470	−	1.06045i
$162$		0			0
$163$	9.53176	−	16.5095i	0.746585	−	1.29312i	−0.202866	−	0.979207i	$-0.565026\pi$
$163$	9.53176	−	16.5095i	0.746585	−	1.29312i	0.949451	−	0.313916i	$-0.101641\pi$
$164$		0			0
$165$	28.9579	−	12.9341i	2.25437	−	1.00692i
$166$		0			0
$167$	13.0007	−	9.25777i	1.00603	−	0.716387i	0.0467636	−	0.998906i	$-0.485109\pi$
$167$	13.0007	−	9.25777i	1.00603	−	0.716387i	0.959262	+	0.282519i	$0.0911699\pi$
$168$		0			0
$169$	−0.474386	−	9.95858i	−0.0364912	−	0.766045i
$170$		0			0
$171$	0.381804	−	2.37395i	0.0291973	−	0.181541i
$172$		0			0
$173$	−13.9426	+	3.38243i	−1.06003	+	0.257161i	−0.727626	−	0.685974i	$-0.759376\pi$
$173$	−13.9426	+	3.38243i	−1.06003	+	0.257161i	−0.332408	+	0.943136i	$0.607861\pi$
$174$		0			0
$175$	8.38825	+	43.5224i	0.634092	+	3.28998i
$176$		0			0
$177$	−16.4470	+	6.42592i	−1.23624	+	0.483002i
$178$		0			0
$179$	4.92153	−	3.16288i	0.367853	−	0.236404i	−0.343635	−	0.939103i	$-0.611658\pi$
$179$	4.92153	−	3.16288i	0.367853	−	0.236404i	0.711487	+	0.702699i	$0.248022\pi$
$180$		0			0
$181$	18.2823	−	9.42518i	1.35891	−	0.700568i	0.384036	−	0.923318i	$-0.374534\pi$
$181$	18.2823	−	9.42518i	1.35891	−	0.700568i	0.974876	+	0.222750i	$0.0715034\pi$
$182$		0			0
$183$	−2.59868	+	4.41567i	−0.192100	+	0.326416i
$184$		0			0
$185$	13.1789	−	10.3640i	0.968929	−	0.761974i
$186$		0			0
$187$	−20.8548	−	18.0708i	−1.52505	−	1.32147i
$188$		0			0
$189$	−7.71275	−	24.2276i	−0.561020	−	1.76230i
$190$		0			0
$191$	−5.09319	−	2.62572i	−0.368530	−	0.189991i	0.264006	−	0.964521i	$-0.414956\pi$
$191$	−5.09319	−	2.62572i	−0.368530	−	0.189991i	−0.632537	+	0.774530i	$0.717986\pi$
$192$		0			0
$193$	−22.9411	−	6.73612i	−1.65134	−	0.484877i	−0.682153	−	0.731210i	$-0.738956\pi$
$193$	−22.9411	−	6.73612i	−1.65134	−	0.484877i	−0.969185	+	0.246333i	$0.920774\pi$
$194$		0			0
$195$	1.22187	+	31.1007i	0.0875000	+	2.22717i
$196$		0			0
$197$	−3.54775	−	10.2505i	−0.252767	−	0.730321i	−0.997982	−	0.0634974i	$-0.979775\pi$
$197$	−3.54775	−	10.2505i	−0.252767	−	0.730321i	0.745215	−	0.666824i	$-0.232347\pi$
$198$		0			0
$199$	−8.11414	+	11.3947i	−0.575196	+	0.807750i	−0.995001	−	0.0998647i	$-0.968159\pi$
$199$	−8.11414	+	11.3947i	−0.575196	+	0.807750i	0.419805	+	0.907614i	$0.362098\pi$
$200$		0			0
$201$	8.83711	+	11.0863i	0.623321	+	0.781966i
$202$		0			0
$203$	2.32172	−	3.26039i	0.162952	−	0.228835i
$204$		0			0
$205$	−9.58331	−	27.6892i	−0.669328	−	1.93390i
$206$		0			0
$207$	−2.48103	+	7.95663i	−0.172443	+	0.553024i
$208$		0			0
$209$	3.75560	+	1.10274i	0.259780	+	0.0762783i
$210$		0			0
$211$	5.45382	+	2.81164i	0.375456	+	0.193561i	0.635618	−	0.772004i	$-0.280745\pi$
$211$	5.45382	+	2.81164i	0.375456	+	0.193561i	−0.260161	+	0.965565i	$0.583776\pi$
$212$		0			0
$213$	1.12348	+	0.735317i	0.0769796	+	0.0503831i
$214$		0			0
$215$	−3.50425	−	3.03645i	−0.238988	−	0.207084i
$216$		0			0
$217$	29.6094	−	23.2851i	2.01002	−	1.58069i
$218$		0			0
$219$	−11.4522	−	6.73981i	−0.773871	−	0.455434i
$220$		0			0
$221$	24.0707	−	12.4093i	1.61917	−	0.834740i
$222$		0			0
$223$	−2.10672	+	1.35391i	−0.141077	+	0.0906645i	−0.609275	−	0.792959i	$-0.708540\pi$
$223$	−2.10672	+	1.35391i	−0.141077	+	0.0906645i	0.468199	+	0.883623i	$0.344903\pi$
$224$		0			0
$225$	−0.840511	−	27.1617i	−0.0560341	−	1.81078i
$226$		0			0
$227$	0.199328	+	1.03421i	0.0132298	+	0.0686430i	0.987944	−	0.154814i	$-0.0494779\pi$
$227$	0.199328	+	1.03421i	0.0132298	+	0.0686430i	−0.974714	+	0.223457i	$0.928266\pi$
$228$		0			0
$229$	−15.4322	+	3.74380i	−1.01979	+	0.247397i	−0.710594	−	0.703602i	$-0.751574\pi$
$229$	−15.4322	+	3.74380i	−1.01979	+	0.247397i	−0.309192	+	0.951000i	$0.600059\pi$
$230$		0			0
$231$	40.7054	−	7.49411i	2.67822	−	0.493076i
$232$		0			0
$233$	0.834864	+	17.5260i	0.0546938	+	1.14816i	0.844761	+	0.535144i	$0.179743\pi$
$233$	0.834864	+	17.5260i	0.0546938	+	1.14816i	−0.790067	+	0.613020i	$0.789954\pi$
$234$		0			0
$235$	5.04810	−	3.59474i	0.329302	−	0.234495i
$236$		0			0
$237$	6.42043	+	14.3746i	0.417052	+	0.933728i
$238$		0			0
$239$	−9.54110	+	16.5257i	−0.617162	+	1.06896i	0.372839	+	0.927896i	$0.378385\pi$
$239$	−9.54110	+	16.5257i	−0.617162	+	1.06896i	−0.990001	+	0.141060i	$0.954949\pi$
$240$		0			0
$241$	0.0434228	−	0.302012i	0.00279711	−	0.0194543i	−0.988375	−	0.152035i	$-0.951417\pi$
$241$	0.0434228	−	0.302012i	0.00279711	−	0.0194543i	0.991172	+	0.132581i	$0.0423264\pi$
$242$		0			0
$243$	2.31004	+	15.4163i	0.148189	+	0.988959i
$244$		0			0
$245$	−3.02272	+	63.4547i	−0.193115	+	4.05397i
$246$		0			0
$247$	−2.37452	+	3.01945i	−0.151087	+	0.192123i
$248$		0			0
$249$	−1.29764	+	5.16086i	−0.0822345	+	0.327056i
$250$		0			0
$251$	4.47101	−	12.9181i	0.282207	−	0.815385i	−0.711430	−	0.702757i	$-0.751952\pi$
$251$	4.47101	−	12.9181i	0.282207	−	0.815385i	0.993637	−	0.112628i	$-0.0359267\pi$
$252$		0			0
$253$	−12.3414	−	5.63611i	−0.775895	−	0.354339i
$254$		0			0
$255$	−32.7553	+	16.5425i	−2.05122	+	1.03593i
$256$		0			0
$257$	−0.845843	+	2.11281i	−0.0527622	+	0.131794i	−0.952407	−	0.304828i	$-0.901401\pi$
$257$	−0.845843	+	2.11281i	−0.0527622	+	0.131794i	0.899645	+	0.436622i	$0.143825\pi$
$258$		0			0
$259$	19.9029	−	9.08934i	1.23670	−	0.564784i
$260$		0			0
$261$	−1.72280	+	1.74756i	−0.106638	+	0.108171i
$262$		0			0
$263$	−19.7695	+	2.84242i	−1.21904	+	0.175271i	−0.721651	−	0.692257i	$-0.756617\pi$
$263$	−19.7695	+	2.84242i	−1.21904	+	0.175271i	−0.497388	+	0.867528i	$0.665707\pi$
$264$		0			0
$265$	9.47530	+	6.08941i	0.582063	+	0.374069i
$266$		0			0
$267$	2.88525	−	8.11691i	0.176574	−	0.496747i
$268$		0			0
$269$		−	9.12100i		−	0.556117i	−0.960564	−	0.278059i	$-0.910309\pi$
$269$		−	9.12100i		−	0.556117i	0.960564	−	0.278059i	$-0.0896910\pi$
$270$		0			0
$271$	10.8934	−	16.9505i	0.661728	−	1.02967i	−0.334458	−	0.942411i	$-0.608553\pi$
$271$	10.8934	−	16.9505i	0.661728	−	1.02967i	0.996186	−	0.0872580i	$-0.0278105\pi$
$272$		0			0
$273$	−8.01927	+	39.8195i	−0.485348	+	2.40999i
$274$		0			0
$275$	44.0365	+	4.20497i	2.65550	+	0.253569i
$276$		0			0
$277$	9.75628	+	21.3633i	0.586198	+	1.28359i	0.937713	+	0.347412i	$0.112939\pi$
$277$	9.75628	+	21.3633i	0.586198	+	1.28359i	−0.351515	+	0.936182i	$0.614333\pi$
$278$		0			0
$279$	−20.1901	+	11.2124i	−1.20875	+	0.671267i
$280$		0			0
$281$	−0.823515	−	0.785220i	−0.0491268	−	0.0468423i	0.665118	−	0.746738i	$-0.268381\pi$
$281$	−0.823515	−	0.785220i	−0.0491268	−	0.0468423i	−0.714245	+	0.699896i	$0.753230\pi$
$282$		0			0
$283$	−13.7602	+	30.1306i	−0.817957	+	1.79108i	−0.249471	+	0.968382i	$0.580257\pi$
$283$	−13.7602	+	30.1306i	−0.817957	+	1.79108i	−0.568486	+	0.822693i	$0.692471\pi$
$284$		0			0
$285$	3.25151	−	4.06447i	0.192603	−	0.240758i
$286$		0			0
$287$	−3.63481	−	38.0654i	−0.214556	−	2.24693i
$288$		0			0
$289$	11.7344	+	9.22806i	0.690261	+	0.542827i
$290$		0			0
$291$	5.58797	+	2.29129i	0.327573	+	0.134318i
$292$		0			0
$293$	−9.21663	−	31.3890i	−0.538441	−	1.83376i	−0.551984	−	0.833855i	$-0.686129\pi$
$293$	−9.21663	−	31.3890i	−0.538441	−	1.83376i	0.0135425	−	0.999908i	$-0.495689\pi$
$294$		0			0
$295$	−37.8354	−	5.43990i	−2.20286	−	0.316724i
$296$		0			0
$297$	−25.3695	+	0.573508i	−1.47209	+	0.0332783i
$298$		0			0
$299$	9.63641	−	9.18830i	0.557288	−	0.531373i
$300$		0			0
$301$	−3.51004	−	4.92916i	−0.202315	−	0.284112i
$302$		0			0
$303$	2.96729	−	9.80273i	0.170466	−	0.563152i
$304$		0			0
$305$	−9.60529	+	5.54562i	−0.549997	+	0.317541i
$306$		0			0
$307$	4.87404	+	20.0911i	0.278176	+	1.14666i	0.923761	+	0.382969i	$0.125098\pi$
$307$	4.87404	+	20.0911i	0.278176	+	1.14666i	−0.645585	+	0.763688i	$0.723386\pi$
$308$		0			0
$309$	−20.0158	−	3.04828i	−1.13866	−	0.173410i
$310$		0			0
$311$	8.21488	+	9.48048i	0.465823	+	0.537589i	0.939245	−	0.343247i	$-0.111527\pi$
$311$	8.21488	+	9.48048i	0.465823	+	0.537589i	−0.473422	+	0.880836i	$0.656981\pi$
$312$		0			0
$313$	−3.46146	−	5.38613i	−0.195653	−	0.304442i	0.729540	−	0.683938i	$-0.239734\pi$
$313$	−3.46146	−	5.38613i	−0.195653	−	0.304442i	−0.925194	+	0.379495i	$0.876098\pi$
$314$		0			0
$315$	11.3155	−	53.8640i	0.637556	−	3.03489i
$316$		0			0
$317$	−2.26860	+	11.7706i	−0.127417	+	0.661102i	0.860910	+	0.508757i	$0.169895\pi$
$317$	−2.26860	+	11.7706i	−0.127417	+	0.661102i	−0.988327	+	0.152345i	$0.951317\pi$
$318$		0			0
$319$	−2.46939	−	3.14008i	−0.138259	−	0.175811i
$320$		0			0
$321$	−5.23655	−	9.24707i	−0.292276	−	0.516121i
$322$		0			0
$323$	−4.40115	−	1.06771i	−0.244887	−	0.0594089i
$324$		0			0
$325$	−19.8931	+	38.5872i	−1.10347	+	2.14043i
$326$		0			0
$327$	14.2192	−	19.6200i	0.786324	−	1.08499i
$328$		0			0
$329$	7.50828	−	3.00586i	0.413945	−	0.165719i
$330$		0			0
$331$	10.7107	−	3.70701i	0.588714	−	0.203756i	−0.0164396	−	0.999865i	$-0.505233\pi$
$331$	10.7107	−	3.70701i	0.588714	−	0.203756i	0.605153	+	0.796109i	$0.293112\pi$
$332$		0			0
$333$	−12.9325	+	3.56435i	−0.708699	+	0.195325i
$334$		0			0
$335$	4.82035	+	30.3095i	0.263364	+	1.65598i
$336$		0			0
$337$	−8.64439	−	6.15564i	−0.470890	−	0.335319i	0.319854	−	0.947467i	$-0.396366\pi$
$337$	−8.64439	−	6.15564i	−0.470890	−	0.335319i	−0.790743	+	0.612148i	$0.790306\pi$
$338$		0			0
$339$	0.216123	−	25.9368i	0.0117382	−	1.40869i
$340$		0			0
$341$	−13.9726	−	34.9019i	−0.756658	−	1.89004i
$342$		0			0
$343$	−13.7071	+	46.6820i	−0.740112	+	2.52059i
$344$		0			0
$345$	−13.1608	+	12.3411i	−0.708556	+	0.664424i
$346$		0			0
$347$	−1.36470	+	5.62536i	−0.0732608	+	0.301985i	−0.996640	−	0.0819032i	$-0.973900\pi$
$347$	−1.36470	+	5.62536i	−0.0732608	+	0.301985i	0.923379	+	0.383889i	$0.125415\pi$
$348$		0			0
$349$	5.43189	−	6.26874i	0.290762	−	0.335558i	−0.591509	−	0.806298i	$-0.701468\pi$
$349$	5.43189	−	6.26874i	0.290762	−	0.335558i	0.882272	+	0.470740i	$0.156013\pi$
$350$		0			0
$351$	8.73083	−	23.3229i	0.466017	−	1.24489i
$352$		0			0
$353$	6.86685	+	1.32348i	0.365485	+	0.0704415i	0.368688	−	0.929553i	$-0.379807\pi$
$353$	6.86685	+	1.32348i	0.365485	+	0.0704415i	−0.00320227	+	0.999995i	$0.501019\pi$
$354$		0			0
$355$	1.33190	+	2.58352i	0.0706897	+	0.137119i
$356$		0			0
$357$	−46.6318	+	10.9021i	−2.46802	+	0.577002i
$358$		0			0
$359$	12.2268	−	10.5946i	0.645305	−	0.559160i	−0.269528	−	0.962993i	$-0.586868\pi$
$359$	12.2268	−	10.5946i	0.645305	−	0.559160i	0.914833	+	0.403832i	$0.132322\pi$
$360$		0			0
$361$	−18.0259	+	3.47420i	−0.948730	+	0.182853i
$362$		0			0
$363$	2.30012	−	22.1370i	0.120725	−	1.16189i
$364$		0			0
$365$	−14.3828	−	24.9118i	−0.752831	−	1.30394i
$366$		0			0
$367$	−9.72493	+	0.463255i	−0.507637	+	0.0241817i	−0.299839	−	0.953990i	$-0.596933\pi$
$367$	−9.72493	+	0.463255i	−0.507637	+	0.0241817i	−0.207798	+	0.978172i	$0.566630\pi$
$368$		0			0
$369$	−1.50560	+	23.3957i	−0.0783782	+	1.21793i
$370$		0			0
$371$	10.1435	+	10.6382i	0.526626	+	0.552309i
$372$		0			0
$373$	−25.0267	−	14.4491i	−1.29583	−	0.748148i	−0.316150	−	0.948709i	$-0.602390\pi$
$373$	−25.0267	−	14.4491i	−1.29583	−	0.748148i	−0.979681	+	0.200561i	$0.935724\pi$
$374$		0			0
$375$	12.2713	−	23.3238i	0.633687	−	1.20443i
$376$		0			0
$377$	3.76158	−	1.10450i	0.193731	−	0.0568846i
$378$		0			0
$379$	18.3552	+	0.874365i	0.942843	+	0.0449131i	0.513371	−	0.858167i	$-0.328397\pi$
$379$	18.3552	+	0.874365i	0.942843	+	0.0449131i	0.429472	+	0.903080i	$0.358700\pi$
$380$		0			0
$381$	−7.30295	−	11.5745i	−0.374141	−	0.592982i
$382$		0			0
$383$	−22.0786	+	2.10825i	−1.12816	+	0.107727i	−0.642405	−	0.766366i	$-0.722063\pi$
$383$	−22.0786	+	2.10825i	−1.12816	+	0.107727i	−0.485760	+	0.874092i	$0.661457\pi$
$384$		0			0
$385$	84.6696	+	29.3044i	4.31516	+	1.49349i
$386$		0			0
$387$	1.64483	+	3.32545i	0.0836115	+	0.169042i
$388$		0			0
$389$	−15.4709	+	16.2254i	−0.784404	+	0.822660i	−0.987684	−	0.156461i	$-0.949991\pi$
$389$	−15.4709	+	16.2254i	−0.784404	+	0.822660i	0.203280	+	0.979121i	$0.434840\pi$
$390$		0			0
$391$	14.5735	+	5.83436i	0.737015	+	0.295056i
$392$		0			0
$393$	35.0384	−	3.05137i	1.76745	−	0.153921i
$394$		0			0
$395$	−3.23950	+	33.9256i	−0.162997	+	1.70698i
$396$		0			0
$397$	−1.76566	−	12.2804i	−0.0886159	−	0.616337i	−0.984935	−	0.172927i	$-0.944678\pi$
$397$	−1.76566	−	12.2804i	−0.0886159	−	0.616337i	0.896319	−	0.443410i	$-0.146232\pi$
$398$		0			0
$399$	5.37428	−	4.15437i	0.269050	−	0.207979i
$400$		0			0
$401$	−2.10669			−0.105203			−0.0526014	−	0.998616i	$-0.516751\pi$
$401$	−2.10669			−0.105203			−0.0526014	+	0.998616i	$0.516751\pi$
$402$		0			0
$403$	36.8950			1.83787
$404$		0			0
$405$	−12.0934	+	31.5034i	−0.600926	+	1.56542i
$406$		0			0
$407$	−3.10779	−	21.6151i	−0.154047	−	1.07142i
$408$		0			0
$409$	−1.28849	+	13.4937i	−0.0637118	+	0.667220i	0.906051	+	0.423169i	$0.139082\pi$
$409$	−1.28849	+	13.4937i	−0.0637118	+	0.667220i	−0.969762	+	0.244051i	$0.921524\pi$
$410$		0			0
$411$	−0.124719	−	1.43212i	−0.00615192	−	0.0706415i
$412$		0			0
$413$	−46.3111	−	18.5402i	−2.27882	−	0.912303i
$414$		0			0
$415$	−7.94946	+	8.33715i	−0.390224	+	0.409255i
$416$		0			0
$417$	18.0959	+	17.5446i	0.886158	+	0.859160i
$418$		0			0
$419$	−17.8513	−	6.17839i	−0.872092	−	0.301834i	−0.145878	−	0.989303i	$-0.546601\pi$
$419$	−17.8513	−	6.17839i	−0.872092	−	0.301834i	−0.726214	+	0.687468i	$0.758722\pi$
$420$		0			0
$421$	23.2635	−	2.22139i	1.13379	−	0.108264i	0.488760	−	0.872419i	$-0.337450\pi$
$421$	23.2635	−	2.22139i	1.13379	−	0.108264i	0.645033	+	0.764154i	$0.276843\pi$
$422$		0			0
$423$	−4.83756	+	1.08855i	−0.235210	+	0.0529273i
$424$		0			0
$425$	−51.1256	−	2.43541i	−2.47996	−	0.118135i
$426$		0			0
$427$	−13.8882	+	4.07794i	−0.672097	+	0.197345i
$428$		0			0
$429$	35.8771	+	18.8760i	1.73216	+	0.911340i
$430$		0			0
$431$	6.01884	+	3.47498i	0.289918	+	0.167384i	0.637905	−	0.770115i	$-0.279801\pi$
$431$	6.01884	+	3.47498i	0.289918	+	0.167384i	−0.347987	+	0.937499i	$0.613135\pi$
$432$		0			0
$433$	−0.695343	−	0.729255i	−0.0334161	−	0.0350458i	0.706814	−	0.707400i	$-0.250132\pi$
$433$	−0.695343	−	0.729255i	−0.0334161	−	0.0350458i	−0.740230	+	0.672354i	$0.765283\pi$
$434$		0			0
$435$	−5.10932	+	1.45410i	−0.244973	+	0.0697187i
$436$		0			0
$437$	−2.22414	+	0.105949i	−0.106395	+	0.00506821i
$438$		0			0
$439$	−5.84219	−	10.1190i	−0.278832	−	0.482952i	0.692262	−	0.721646i	$-0.256614\pi$
$439$	−5.84219	−	10.1190i	−0.278832	−	0.482952i	−0.971095	+	0.238694i	$0.923281\pi$
$440$		0			0
$441$	21.8827	−	45.8774i	1.04203	−	2.18464i
$442$		0			0
$443$	9.84616	−	1.89769i	0.467805	−	0.0901620i	0.0500990	−	0.998744i	$-0.484046\pi$
$443$	9.84616	−	1.89769i	0.467805	−	0.0901620i	0.417706	+	0.908582i	$0.362834\pi$
$444$		0			0
$445$	14.0932	−	12.2119i	0.668083	−	0.578897i
$446$		0			0
$447$	−6.86171	−	29.3496i	−0.324548	−	1.38819i
$448$		0			0
$449$	−9.45743	−	18.3448i	−0.446323	−	0.865747i	−0.999467	−	0.0326605i	$-0.989602\pi$
$449$	−9.45743	−	18.3448i	−0.446323	−	0.865747i	0.553143	−	0.833086i	$-0.313428\pi$
$450$		0			0
$451$	−37.4742	−	7.22257i	−1.76459	−	0.340097i
$452$		0			0
$453$	6.67893	−	2.24946i	0.313804	−	0.105689i
$454$		0			0
$455$	−57.5815	+	66.4526i	−2.69946	+	3.11535i
$456$		0			0
$457$	9.84714	−	40.5905i	0.460630	−	1.89874i	0.0226813	−	0.999743i	$-0.492780\pi$
$457$	9.84714	−	40.5905i	0.460630	−	1.89874i	0.437949	−	0.899000i	$-0.355705\pi$
$458$		0			0
$459$	29.2886	−	2.05951i	1.36708	−	0.0961298i
$460$		0			0
$461$	−2.29028	+	7.79999i	−0.106669	+	0.363282i	−0.995478	−	0.0949973i	$-0.969716\pi$
$461$	−2.29028	+	7.79999i	−0.106669	+	0.363282i	0.888808	+	0.458279i	$0.151534\pi$
$462$		0			0
$463$	15.3993	+	38.4657i	0.715668	+	1.78765i	0.608715	+	0.793389i	$0.291685\pi$
$463$	15.3993	+	38.4657i	0.715668	+	1.78765i	0.106953	+	0.994264i	$0.465890\pi$
$464$		0			0
$465$	−49.9918	−	0.416566i	−2.31831	−	0.0193178i
$466$		0			0
$467$	−9.76188	−	6.95140i	−0.451726	−	0.321673i	0.331450	−	0.943473i	$-0.392462\pi$
$467$	−9.76188	−	6.95140i	−0.451726	−	0.321673i	−0.783176	+	0.621800i	$0.786402\pi$
$468$		0			0
$469$	−3.21204	+	39.9232i	−0.148318	+	1.84348i
$470$		0			0
$471$	−14.5010	+	10.1451i	−0.668172	+	0.467462i
$472$		0			0
$473$	−5.70722	+	1.97529i	−0.262418	+	0.0908239i
$474$		0			0
$475$	6.74000	−	2.69829i	0.309252	−	0.123806i
$476$		0			0
$477$	−5.10443	−	7.42707i	−0.233716	−	0.340062i
$478$		0			0
$479$	−4.33542	+	8.40954i	−0.198090	+	0.384242i	−0.966869	−	0.255273i	$-0.917835\pi$
$479$	−4.33542	+	8.40954i	−0.198090	+	0.384242i	0.768779	+	0.639515i	$0.220865\pi$
$480$		0			0
$481$	20.8268	+	5.05252i	0.949619	+	0.230375i
$482$		0			0
$483$	−20.4883	+	11.6024i	−0.932252	+	0.527928i
$484$		0			0
$485$	8.08175	+	10.2768i	0.366973	+	0.466645i
$486$		0			0
$487$	2.76782	−	14.3608i	0.125422	−	0.650750i	−0.863742	−	0.503934i	$-0.831885\pi$
$487$	2.76782	−	14.3608i	0.125422	−	0.650750i	0.989164	−	0.146816i	$-0.0469024\pi$
$488$		0			0
$489$	−32.7209	+	4.42660i	−1.47969	+	0.200178i
$490$		0			0
$491$	−15.2253	−	23.6910i	−0.687107	−	1.06916i	−0.993116	−	0.117131i	$-0.962630\pi$
$491$	−15.2253	−	23.6910i	−0.687107	−	1.06916i	0.306010	−	0.952028i	$-0.401006\pi$
$492$		0			0
$493$	3.02681	+	3.49313i	0.136321	+	0.157323i
$494$		0			0
$495$	−48.3994	−	25.9815i	−2.17539	−	1.16778i
$496$		0			0
$497$	0.894299	+	3.68635i	0.0401148	+	0.165355i
$498$		0			0
$499$	11.0192	−	6.36192i	0.493285	−	0.284798i	−0.232651	−	0.972560i	$-0.574740\pi$
$499$	11.0192	−	6.36192i	0.493285	−	0.284798i	0.725936	+	0.687762i	$0.241407\pi$
$500$		0			0
$501$	−26.4581	−	8.00887i	−1.18206	−	0.357810i
$502$		0			0
$503$	5.49284	+	7.71361i	0.244914	+	0.343933i	0.918674	−	0.395017i	$-0.129261\pi$
$503$	5.49284	+	7.71361i	0.244914	+	0.343933i	−0.673760	+	0.738950i	$0.735322\pi$
$504$		0			0
$505$	16.0460	−	15.2999i	0.714039	−	0.680835i
$506$		0			0
$507$	−13.1443	+	11.1992i	−0.583759	+	0.497374i
$508$		0			0
$509$	−8.35315	−	1.20100i	−0.370247	−	0.0532335i	−0.0453199	−	0.998973i	$-0.514431\pi$
$509$	−8.35315	−	1.20100i	−0.370247	−	0.0532335i	−0.324927	+	0.945739i	$0.605340\pi$
$510$		0			0
$511$	−10.5763	−	36.0197i	−0.467870	−	1.59342i
$512$		0			0
$513$	−3.65761	+	1.99152i	−0.161488	+	0.0879280i
$514$		0			0
$515$	−34.4515	−	27.0930i	−1.51812	−	1.19386i
$516$		0			0
$517$	−0.767276	−	8.03527i	−0.0337447	−	0.353391i
$518$		0			0
$519$	19.4045	+	15.5233i	0.851764	+	0.681397i
$520$		0			0
$521$	8.77518	−	19.2150i	0.384447	−	0.841822i	−0.614166	−	0.789177i	$-0.710507\pi$
$521$	8.77518	−	19.2150i	0.384447	−	0.841822i	0.998613	−	0.0526454i	$-0.0167653\pi$
$522$		0			0
$523$	27.3032	+	26.0335i	1.19388	+	1.13837i	0.987121	+	0.159975i	$0.0511414\pi$
$523$	27.3032	+	26.0335i	1.19388	+	1.13837i	0.206763	+	0.978391i	$0.433707\pi$
$524$		0			0
$525$	50.7555	−	57.5982i	2.21515	−	2.51379i
$526$		0			0
$527$	18.0700	+	39.5678i	0.787141	+	1.72360i
$528$		0			0
$529$	−15.2126	−	1.45263i	−0.661419	−	0.0631579i
$530$		0			0
$531$	26.2282	+	15.7314i	1.13821	+	0.682683i
$532$		0			0
$533$	20.2489	−	31.5078i	0.877075	−	1.36476i
$534$		0			0
$535$		−	23.0043i		−	0.994562i
$536$		0			0
$537$	−9.54766	−	3.39382i	−0.412012	−	0.146454i
$538$		0			0
$539$	69.6078	+	44.7342i	2.99822	+	1.92684i
$540$		0			0
$541$	23.0816	−	3.31863i	0.992356	−	0.142679i	0.373035	−	0.927817i	$-0.378317\pi$
$541$	23.0816	−	3.31863i	0.992356	−	0.142679i	0.619321	+	0.785138i	$0.287408\pi$
$542$		0			0
$543$	−32.2823	−	15.0692i	−1.38537	−	0.646681i
$544$		0			0
$545$	47.7131	−	21.7899i	2.04381	−	0.933375i
$546$		0			0
$547$	6.94641	−	17.3513i	0.297007	−	0.741888i	−0.702535	−	0.711649i	$-0.747949\pi$
$547$	6.94641	−	17.3513i	0.297007	−	0.741888i	0.999543	−	0.0302394i	$-0.00962697\pi$
$548$		0			0
$549$	8.80383	−	1.11640i	0.375738	−	0.0476466i
$550$		0			0
$551$	−0.596364	−	0.272350i	−0.0254059	−	0.0116025i
$552$		0			0
$553$	−14.5466	+	42.0296i	−0.618584	+	1.78728i
$554$		0			0
$555$	−28.1627	−	7.08119i	−1.19544	−	0.300580i
$556$		0			0
$557$	−17.6149	+	22.3992i	−0.746367	+	0.949083i	−0.999833	−	0.0182614i	$-0.994187\pi$
$557$	−17.6149	+	22.3992i	−0.746367	+	0.949083i	0.253466	+	0.967344i	$0.418429\pi$
$558$		0			0
$559$	0.282016	−	5.92024i	0.0119280	−	0.250400i
$560$		0			0
$561$	−2.67194	+	47.7210i	−0.112809	+	2.01478i
$562$		0			0
$563$	0.0111183	−	0.0773297i	0.000468582	−	0.00325906i	−0.989586	−	0.143944i	$-0.954021\pi$
$563$	0.0111183	−	0.0773297i	0.000468582	−	0.00325906i	0.990054	+	0.140685i	$0.0449305\pi$
$564$		0			0
$565$	28.0741	−	48.6257i	1.18108	−	2.04570i
$566$		0			0
$567$	−25.0303	+	36.2335i	−1.05117	+	1.52166i
$568$		0			0
$569$	−9.88026	+	7.03570i	−0.414202	+	0.294952i	−0.768097	−	0.640333i	$-0.778796\pi$
$569$	−9.88026	+	7.03570i	−0.414202	+	0.294952i	0.353895	+	0.935285i	$0.384857\pi$
$570$		0			0
$571$	1.63747	+	34.3747i	0.0685258	+	1.43853i	0.727365	+	0.686251i	$0.240745\pi$
$571$	1.63747	+	34.3747i	0.0685258	+	1.43853i	−0.658839	+	0.752284i	$0.728952\pi$
$572$		0			0
$573$	1.79704	+	9.76093i	0.0750726	+	0.407769i
$574$		0			0
$575$	−24.4558	+	5.93292i	−1.01988	+	0.247420i
$576$		0			0
$577$	3.04334	+	15.7903i	0.126696	+	0.657361i	0.988633	+	0.150346i	$0.0480389\pi$
$577$	3.04334	+	15.7903i	0.126696	+	0.657361i	−0.861937	+	0.507015i	$0.830749\pi$
$578$		0			0
$579$	15.0707	+	38.5731i	0.626315	+	1.60304i
$580$		0			0
$581$	−12.6471	+	8.12778i	−0.524689	+	0.337197i
$582$		0			0
$583$	13.0396	−	6.72236i	0.540043	−	0.278412i
$584$		0			0
$585$	41.3248	−	34.6194i	1.70857	−	1.43134i
$586$		0			0
$587$	35.7420	−	28.1078i	1.47523	−	1.16013i	0.523975	−	0.851734i	$-0.324449\pi$
$587$	35.7420	−	28.1078i	1.47523	−	1.16013i	0.951257	−	0.308401i	$-0.0997938\pi$
$588$		0			0
$589$	−4.66297	−	4.04048i	−0.192134	−	0.166485i
$590$		0			0
$591$	−10.2888	+	15.7201i	−0.423224	+	0.646639i
$592$		0			0
$593$	−33.7065	−	17.3769i	−1.38416	−	0.713583i	−0.404553	−	0.914515i	$-0.632573\pi$
$593$	−33.7065	−	17.3769i	−1.38416	−	0.713583i	−0.979605	+	0.200931i	$0.935603\pi$
$594$		0			0
$595$	−99.4682	−	29.2065i	−4.07780	−	1.19735i
$596$		0			0
$597$	24.2101	−	0.951158i	0.990855	−	0.0389283i
$598$		0			0
$599$	3.15041	+	9.10251i	0.128722	+	0.371919i	0.990885	−	0.134714i	$-0.0430114\pi$
$599$	3.15041	+	9.10251i	0.128722	+	0.371919i	−0.862162	+	0.506632i	$0.830890\pi$
$600$		0			0
$601$	−10.8131	+	15.1848i	−0.441075	+	0.619403i	−0.973942	−	0.226796i	$-0.927175\pi$
$601$	−10.8131	+	15.1848i	−0.441075	+	0.619403i	0.532868	+	0.846199i	$0.321114\pi$
$602$		0			0
$603$	5.83101	−	23.8537i	0.237457	−	0.971398i
$604$		0			0
$605$	27.9464	−	39.2452i	1.13618	−	1.59554i
$606$		0			0
$607$	3.93230	+	11.3616i	0.159607	+	0.461154i	0.996243	−	0.0866057i	$-0.0276020\pi$
$607$	3.93230	+	11.3616i	0.159607	+	0.461154i	−0.836636	+	0.547760i	$0.815481\pi$
$608$		0			0
$609$	−6.92730	+	0.272157i	−0.280708	+	0.0110284i
$610$		0			0
$611$	7.60068	+	2.23176i	0.307490	+	0.0902873i
$612$		0			0
$613$	−17.1672	−	8.85032i	−0.693378	−	0.357461i	0.0752434	−	0.997165i	$-0.476027\pi$
$613$	−17.1672	−	8.85032i	−0.693378	−	0.357461i	−0.768621	+	0.639704i	$0.779057\pi$
$614$		0			0
$615$	−27.7925	+	42.4637i	−1.12070	+	1.71230i
$616$		0			0
$617$	24.4072	+	21.1489i	0.982596	+	0.851424i	0.988904	−	0.148556i	$-0.0474625\pi$
$617$	24.4072	+	21.1489i	0.982596	+	0.851424i	−0.00630820	+	0.999980i	$0.502008\pi$
$618$		0			0
$619$	−26.6396	+	20.9496i	−1.07074	+	0.842037i	−0.987988	−	0.154533i	$-0.950613\pi$
$619$	−26.6396	+	20.9496i	−1.07074	+	0.842037i	−0.0827500	+	0.996570i	$0.526370\pi$
$620$		0			0
$621$	13.5316	−	5.02857i	0.543004	−	0.201790i
$622$		0			0
$623$	21.6311	−	11.1516i	0.866631	−	0.446779i
$624$		0			0
$625$	9.89339	−	6.35810i	0.395736	−	0.254324i
$626$		0			0
$627$	−2.46715	−	6.31465i	−0.0985287	−	0.252183i
$628$		0			0
$629$	4.78176	+	24.8101i	0.190661	+	0.989244i
$630$		0			0
$631$	38.0721	−	9.23620i	1.51563	−	0.367687i	0.610221	−	0.792232i	$-0.291081\pi$
$631$	38.0721	−	9.23620i	1.51563	−	0.367687i	0.905407	+	0.424544i	$0.139566\pi$
$632$		0			0
$633$	−1.92428	−	10.4521i	−0.0764835	−	0.415432i
$634$		0			0
$635$	−1.40967	−	29.5927i	−0.0559412	−	1.17435i
$636$		0			0
$637$	−66.1457	+	47.1021i	−2.62079	+	1.86625i
$638$		0			0
$639$	−0.182458	−	2.31849i	−0.00721791	−	0.0917182i
$640$		0			0
$641$	16.4876	−	28.5574i	0.651223	−	1.12795i	−0.331604	−	0.943419i	$-0.607590\pi$
$641$	16.4876	−	28.5574i	0.651223	−	1.12795i	0.982826	−	0.184532i	$-0.0590770\pi$
$642$		0			0
$643$	−3.51556	+	24.4512i	−0.138640	+	0.964263i	0.795143	+	0.606422i	$0.207396\pi$
$643$	−3.51556	+	24.4512i	−0.138640	+	0.964263i	−0.933783	+	0.357841i	$0.883513\pi$
$644$		0			0
$645$	−0.448968	+	8.01860i	−0.0176781	+	0.315732i
$646$		0			0
$647$	0.690949	−	14.5048i	0.0271640	−	0.570243i	−0.943728	−	0.330724i	$-0.892707\pi$
$647$	0.690949	−	14.5048i	0.0271640	−	0.570243i	0.970892	−	0.239519i	$-0.0769898\pi$
$648$		0			0
$649$	−30.7763	+	39.1353i	−1.20808	+	1.53619i
$650$		0			0
$651$	−63.2741	−	15.9095i	−2.47991	−	0.623544i
$652$		0			0
$653$	−2.80684	+	8.10983i	−0.109840	+	0.317362i	−0.986503	−	0.163743i	$-0.947643\pi$
$653$	−2.80684	+	8.10983i	−0.109840	+	0.317362i	0.876663	+	0.481105i	$0.159764\pi$
$654$		0			0
$655$	69.2556	+	31.6280i	2.70604	+	1.23581i
$656$		0			0
$657$	2.89543	+	22.8332i	0.112961	+	0.890807i
$658$		0			0
$659$	−16.5295	+	41.2886i	−0.643896	+	1.60837i	0.141894	+	0.989882i	$0.454681\pi$
$659$	−16.5295	+	41.2886i	−0.643896	+	1.60837i	−0.785790	+	0.618493i	$0.787744\pi$
$660$		0			0
$661$	4.92817	−	2.25062i	0.191684	−	0.0875390i	−0.317261	−	0.948338i	$-0.602763\pi$
$661$	4.92817	−	2.25062i	0.191684	−	0.0875390i	0.508945	+	0.860799i	$0.330036\pi$
$662$		0			0
$663$	−42.5033	−	19.8403i	−1.65069	−	0.770532i
$664$		0			0
$665$	14.5549	−	2.09267i	0.564413	−	0.0811504i
$666$		0			0
$667$	1.91176	+	1.22861i	0.0740235	+	0.0475720i
$668$		0			0
$669$	4.08700	+	1.45277i	0.158012	+	0.0561673i
$670$		0			0
$671$			14.4462i			0.557691i
$672$		0			0
$673$	−0.328051	+	0.510457i	−0.0126454	+	0.0196767i	−0.847519	−	0.530766i	$-0.821904\pi$
$673$	−0.328051	+	0.510457i	−0.0126454	+	0.0196767i	0.834873	+	0.550442i	$0.185541\pi$
$674$		0			0
$675$	−36.3309	+	29.9242i	−1.39838	+	1.15178i
$676$		0			0
$677$	39.1751	+	3.74077i	1.50562	+	0.143769i	0.815006	−	0.579452i	$-0.196733\pi$
$677$	39.1751	+	3.74077i	1.50562	+	0.143769i	0.690616	+	0.723222i	$0.257340\pi$
$678$		0			0
$679$	7.08780	+	15.5201i	0.272005	+	0.595608i
$680$		0			0
$681$	1.20609	−	1.36869i	0.0462175	−	0.0524483i
$682$		0			0
$683$	3.94309	+	3.75973i	0.150878	+	0.143862i	0.761759	−	0.647861i	$-0.224336\pi$
$683$	3.94309	+	3.75973i	0.150878	+	0.143862i	−0.610881	+	0.791723i	$0.709185\pi$
$684$		0			0
$685$	1.29273	−	2.83069i	0.0493927	−	0.108155i
$686$		0			0
$687$	21.4777	+	17.1818i	0.819424	+	0.655525i
$688$		0			0
$689$	1.36855	+	14.3321i	0.0521375	+	0.546009i
$690$		0			0
$691$	24.3141	+	19.1208i	0.924950	+	0.727389i	0.962322	−	0.271913i	$-0.0876561\pi$
$691$	24.3141	+	19.1208i	0.924950	+	0.727389i	−0.0373717	+	0.999301i	$0.511899\pi$
$692$		0			0
$693$	−53.3889	−	47.8425i	−2.02808	−	1.81739i
$694$		0			0
$695$	15.3717	+	52.3511i	0.583081	+	1.98579i
$696$		0			0
$697$	43.7076	+	6.28421i	1.65554	+	0.238031i
$698$		0			0
$699$	23.1325	−	19.7093i	0.874950	−	0.745476i
$700$		0			0
$701$	22.5112	−	21.4644i	0.850236	−	0.810698i	−0.133363	−	0.991067i	$-0.542578\pi$
$701$	22.5112	−	21.4644i	0.850236	−	0.810698i	0.983599	+	0.180369i	$0.0577292\pi$
$702$		0			0
$703$	−2.07887	−	2.91937i	−0.0784062	−	0.110106i
$704$		0			0
$705$	−10.2735	−	3.10980i	−0.386924	−	0.117122i
$706$		0			0
$707$	25.0578	−	14.4672i	0.942397	−	0.544093i
$708$		0			0
$709$	−3.87992	−	15.9933i	−0.145714	−	0.600640i	−0.997100	−	0.0761008i	$-0.975753\pi$
$709$	−3.87992	−	15.9933i	−0.145714	−	0.600640i	0.851387	−	0.524539i	$-0.175762\pi$
$710$		0			0
$711$	12.8971	−	24.0253i	0.483680	−	0.901018i
$712$		0			0
$713$	14.0053	+	16.1630i	0.524504	+	0.605310i
$714$		0			0
$715$	47.4454	+	73.8264i	1.77436	+	2.76095i
$716$		0			0
$717$	32.7530	−	4.43094i	1.22318	−	0.165476i
$718$		0			0
$719$	−6.50917	+	33.7728i	−0.242751	+	1.25951i	0.632011	+	0.774959i	$0.282230\pi$
$719$	−6.50917	+	33.7728i	−0.242751	+	1.25951i	−0.874762	+	0.484552i	$0.838983\pi$
$720$		0			0
$721$	−35.3575	−	44.9607i	−1.31678	−	1.67442i
$722$		0			0
$723$	−0.459862	+	0.260417i	−0.0171025	+	0.00968501i
$724$		0			0
$725$	−7.20069	−	1.74687i	−0.267427	−	0.0648770i
$726$		0			0
$727$	6.11610	−	11.8636i	0.226834	−	0.439996i	−0.747762	−	0.663967i	$-0.768872\pi$
$727$	6.11610	−	11.8636i	0.226834	−	0.439996i	0.974596	+	0.223971i	$0.0719020\pi$
$728$		0			0
$729$	18.6789	−	19.4961i	0.691810	−	0.722079i
$730$		0			0
$731$	6.48725	−	2.59710i	0.239939	−	0.0960573i
$732$		0			0
$733$	16.9333	−	5.86068i	0.625446	−	0.216469i	0.00408290	−	0.999992i	$-0.498700\pi$
$733$	16.9333	−	5.86068i	0.625446	−	0.216469i	0.621363	+	0.783523i	$0.286579\pi$
$734$		0			0
$735$	90.1576	−	63.0754i	3.32551	−	2.32657i
$736$		0			0
$737$	37.3281	+	14.3016i	1.37500	+	0.526807i
$738$		0			0
$739$	−5.44897	−	3.88019i	−0.200443	−	0.142735i	0.475428	−	0.879755i	$-0.342293\pi$
$739$	−5.44897	−	3.88019i	−0.200443	−	0.142735i	−0.675872	+	0.737019i	$0.736233\pi$
$740$		0			0
$741$	6.65306	+	0.0554379i	0.244406	+	0.00203656i
$742$		0			0
$743$	−4.78178	−	11.9443i	−0.175427	−	0.438194i	0.814430	−	0.580261i	$-0.197050\pi$
$743$	−4.78178	−	11.9443i	−0.175427	−	0.438194i	−0.989857	+	0.142067i	$0.954625\pi$
$744$		0			0
$745$	18.3823	−	62.6044i	0.673476	−	2.29365i
$746$		0			0
$747$	8.44682	−	3.68868i	0.309053	−	0.134962i
$748$		0			0
$749$	7.07785	−	29.1753i	0.258619	−	1.06604i
$750$		0			0
$751$	2.13402	−	2.46280i	0.0778716	−	0.0898687i	−0.715477	−	0.698637i	$-0.753790\pi$
$751$	2.13402	−	2.46280i	0.0778716	−	0.0898687i	0.793348	+	0.608768i	$0.208336\pi$
$752$		0			0
$753$	−22.4386	+	7.55730i	−0.817708	+	0.275403i
$754$		0			0
$755$	14.9804	+	2.88724i	0.545193	+	0.105077i
$756$		0			0
$757$	−3.03669	−	5.89035i	−0.110370	−	0.214088i	0.827181	−	0.561936i	$-0.189943\pi$
$757$	−3.03669	−	5.89035i	−0.110370	−	0.214088i	−0.937551	+	0.347847i	$0.886913\pi$
$758$		0			0
$759$	5.34973	+	22.8824i	0.194183	+	0.830579i
$760$		0			0
$761$	1.35085	−	1.17052i	0.0489682	−	0.0424312i	−0.630033	−	0.776568i	$-0.716959\pi$
$761$	1.35085	−	1.17052i	0.0489682	−	0.0424312i	0.679001	+	0.734137i	$0.262413\pi$
$762$		0			0
$763$	67.2166	−	12.9549i	2.43340	−	0.469000i
$764$		0			0
$765$	57.3669	+	27.3630i	2.07411	+	0.989310i
$766$		0			0
$767$	−24.4301	−	42.3142i	−0.882120	−	1.52788i
$768$		0			0
$769$	40.5918	−	1.93363i	1.46378	−	0.0697283i	0.699508	−	0.714625i	$-0.253403\pi$
$769$	40.5918	−	1.93363i	1.46378	−	0.0697283i	0.764270	+	0.644897i	$0.223100\pi$
$770$		0			0
$771$	3.79131	−	1.07900i	0.136541	−	0.0388592i
$772$		0			0
$773$	20.8125	+	21.8276i	0.748575	+	0.785083i	0.982319	−	0.187215i	$-0.0599462\pi$
$773$	20.8125	+	21.8276i	0.748575	+	0.785083i	−0.233744	+	0.972298i	$0.575098\pi$
$774$		0			0
$775$	−60.3895	−	34.8659i	−2.16926	−	1.25242i
$776$		0			0
$777$	−33.5388	−	17.6457i	−1.20320	−	0.633037i
$778$		0			0
$779$	−6.00967	+	1.76460i	−0.215319	+	0.0632233i
$780$		0			0
$781$	3.78158	+	0.180139i	0.135316	+	0.00644588i
$782$		0			0
$783$	4.21974	+	0.509658i	0.150801	+	0.0182137i
$784$		0			0
$785$	−38.1370	+	3.64164i	−1.36117	+	0.129976i
$786$		0			0
$787$	−36.5990	−	12.6670i	−1.30461	−	0.451531i	−0.415656	−	0.909522i	$-0.636448\pi$
$787$	−36.5990	−	12.6670i	−1.30461	−	0.451531i	−0.888957	+	0.457991i	$0.848569\pi$
$788$		0			0
$789$	24.8370	+	24.0803i	0.884220	+	0.857281i
$790$		0			0
$791$	50.5660	−	53.0321i	1.79792	−	1.88560i
$792$		0			0
$793$	−13.1618	−	5.26917i	−0.467388	−	0.187114i
$794$		0			0
$795$	−1.69253	−	19.4351i	−0.0600279	−	0.689291i
$796$		0			0
$797$	3.87073	−	40.5361i	0.137108	−	1.43586i	−0.621040	−	0.783779i	$-0.713290\pi$
$797$	3.87073	−	40.5361i	0.137108	−	1.43586i	0.758148	−	0.652082i	$-0.226104\pi$
$798$		0			0
$799$	1.32914	+	9.24434i	0.0470214	+	0.327041i
$800$		0			0
$801$	−14.1794	+	4.64443i	−0.501005	+	0.164103i
$802$		0			0
$803$	−37.4670			−1.32218
$804$		0			0
$805$	−50.9696			−1.79644
$806$		0			0
$807$	−12.4990	+	9.66189i	−0.439987	+	0.340115i
$808$		0			0
$809$	−6.82473	−	47.4670i	−0.239945	−	1.66885i	−0.652401	−	0.757874i	$-0.726238\pi$
$809$	−6.82473	−	47.4670i	−0.239945	−	1.66885i	0.412456	−	0.910978i	$-0.364671\pi$
$810$		0			0
$811$	−3.05288	+	31.9712i	−0.107201	+	1.12266i	0.768514	+	0.639833i	$0.220997\pi$
$811$	−3.05288	+	31.9712i	−0.107201	+	1.12266i	−0.875715	+	0.482828i	$0.839610\pi$
$812$		0			0
$813$	−34.7676	+	3.02779i	−1.21935	+	0.106189i
$814$		0			0
$815$	−66.3572	−	26.5654i	−2.32439	−	0.930547i
$816$		0			0
$817$	−0.683987	+	0.717345i	−0.0239297	+	0.0250967i
$818$		0			0
$819$	63.0618	−	31.1916i	2.20356	−	1.08992i
$820$		0			0
$821$	45.2105	+	15.6475i	1.57786	+	0.546102i	0.968975	−	0.247159i	$-0.0794970\pi$
$821$	45.2105	+	15.6475i	1.57786	+	0.546102i	0.608882	+	0.793261i	$0.291618\pi$
$822$		0			0
$823$	1.47099	−	0.140462i	0.0512753	−	0.00489620i	−0.0693868	−	0.997590i	$-0.522104\pi$
$823$	1.47099	−	0.140462i	0.0512753	−	0.00489620i	0.120662	+	0.992694i	$0.461498\pi$
$824$		0			0
$825$	−40.8856	−	64.8001i	−1.42345	−	2.25605i
$826$		0			0
$827$	29.6580	+	1.41279i	1.03131	+	0.0491274i	0.556407	−	0.830910i	$-0.312180\pi$
$827$	29.6580	+	1.41279i	1.03131	+	0.0491274i	0.474904	+	0.880038i	$0.342483\pi$
$828$		0			0
$829$	−26.2591	+	7.71037i	−0.912017	+	0.267792i	−0.703890	−	0.710309i	$-0.748555\pi$
$829$	−26.2591	+	7.71037i	−0.912017	+	0.267792i	−0.208127	+	0.978102i	$0.566737\pi$
$830$		0			0
$831$	18.9405	−	35.9997i	0.657038	−	1.24882i
$832$		0			0
$833$	−82.9105	−	47.8684i	−2.87268	−	1.65854i
$834$		0			0
$835$	−41.2952	−	43.3092i	−1.42908	−	1.49878i
$836$		0			0
$837$	36.7524	+	15.7904i	1.27035	+	0.545796i
$838$		0			0
$839$	27.0786	−	1.28991i	0.934857	−	0.0445327i	0.425378	−	0.905016i	$-0.360141\pi$
$839$	27.0786	−	1.28991i	0.934857	−	0.0445327i	0.509479	+	0.860483i	$0.329838\pi$
$840$		0			0
$841$	−14.1654	−	24.5353i	−0.488464	−	0.846044i
$842$		0			0
$843$	−0.203682	+	1.96029i	−0.00701518	+	0.0675161i
$844$		0			0
$845$	−36.7058	+	7.07446i	−1.26272	+	0.243369i
$846$		0			0
$847$	47.5178	−	41.1744i	1.63273	−	1.41477i
$848$		0			0
$849$	55.8658	−	13.0610i	1.91731	−	0.448252i
$850$		0			0
$851$	5.69243	+	11.0418i	0.195134	+	0.378507i
$852$		0			0
$853$	−2.15764	−	0.415851i	−0.0738762	−	0.0142385i	0.152179	−	0.988353i	$-0.451371\pi$
$853$	−2.15764	−	0.415851i	−0.0738762	−	0.0142385i	−0.226055	+	0.974114i	$0.572583\pi$
$854$		0			0
$855$	−9.01411	−	0.150234i	−0.308276	−	0.00513789i
$856$		0			0
$857$	0.777566	−	0.897359i	0.0265611	−	0.0306532i	−0.742314	−	0.670053i	$-0.766272\pi$
$857$	0.777566	−	0.897359i	0.0265611	−	0.0306532i	0.768875	+	0.639399i	$0.220817\pi$
$858$		0			0
$859$	1.41042	−	5.81385i	0.0481231	−	0.198366i	−0.942675	−	0.333711i	$-0.891699\pi$
$859$	1.41042	−	5.81385i	0.0481231	−	0.198366i	0.990799	+	0.135345i	$0.0432142\pi$
$860$		0			0
$861$	−48.3129	+	45.3038i	−1.64650	+	1.54395i
$862$		0			0
$863$	−12.6540	+	43.0956i	−0.430748	+	1.46699i	0.403181	+	0.915120i	$0.367904\pi$
$863$	−12.6540	+	43.0956i	−0.430748	+	1.46699i	−0.833929	+	0.551872i	$0.813914\pi$
$864$		0			0
$865$	19.9928	+	49.9397i	0.679777	+	1.69800i
$866$		0			0
$867$	0.215447	−	25.8557i	0.00731698	−	0.878105i
$868$		0			0
$869$	36.1581	+	25.7481i	1.22658	+	0.873443i
$870$		0			0
$871$	−26.6452	+	28.7926i	−0.902837	+	0.975601i
$872$		0			0
$873$	−2.77946	−	10.0847i	−0.0940703	−	0.341315i
$874$		0			0
$875$	70.3595	−	24.3517i	2.37859	−	0.823237i
$876$		0			0
$877$	−11.8424	+	4.74097i	−0.399888	+	0.160091i	−0.562884	−	0.826536i	$-0.690308\pi$
$877$	−11.8424	+	4.74097i	−0.399888	+	0.160091i	0.162996	+	0.986627i	$0.447884\pi$
$878$		0			0
$879$	−33.2509	+	45.8805i	−1.12153	+	1.54751i
$880$		0			0
$881$	18.2120	−	35.3264i	0.613580	−	1.19018i	−0.353435	−	0.935459i	$-0.614987\pi$
$881$	18.2120	−	35.3264i	0.613580	−	1.19018i	0.967015	−	0.254719i	$-0.0819831\pi$
$882$		0			0
$883$	20.0460	+	4.86310i	0.674600	+	0.163656i	0.558403	−	0.829570i	$-0.311414\pi$
$883$	20.0460	+	4.86310i	0.674600	+	0.163656i	0.116197	+	0.993226i	$0.462930\pi$
$884$		0			0
$885$	32.6244	+	57.6105i	1.09666	+	1.93656i
$886$		0			0
$887$	−4.30726	−	5.47713i	−0.144624	−	0.183904i	0.708345	−	0.705867i	$-0.249442\pi$
$887$	−4.30726	−	5.47713i	−0.144624	−	0.183904i	−0.852968	+	0.521963i	$0.825200\pi$
$888$		0			0
$889$	7.31712	−	37.9648i	0.245408	−	1.27330i
$890$		0			0
$891$	27.6598	+	34.1577i	0.926639	+	1.14433i
$892$		0			0
$893$	−0.716204	−	1.11443i	−0.0239668	−	0.0372931i
$894$		0			0
$895$	−14.3644	−	16.5774i	−0.480149	−	0.554121i
$896$		0			0
$897$	−22.7991	−	3.47216i	−0.761240	−	0.115932i
$898$		0			0
$899$	1.48458	+	6.11954i	0.0495137	+	0.204098i
$900$		0			0
$901$	−14.7001	+	8.48709i	−0.489730	+	0.282746i
$902$		0			0
$903$	−3.03653	+	10.0315i	−0.101049	+	0.333827i
$904$		0			0
$905$	−44.7348	−	62.8212i	−1.48703	−	2.08825i
$906$		0			0
$907$	36.1736	−	34.4915i	1.20113	−	1.14527i	0.215469	−	0.976511i	$-0.430872\pi$
$907$	36.1736	−	34.4915i	1.20113	−	1.14527i	0.985657	−	0.168761i	$-0.0539765\pi$
$908$		0			0
$909$	−16.5765	+	6.31780i	−0.549808	+	0.209548i
$910$		0			0
$911$	−26.7249	−	3.84246i	−0.885435	−	0.127306i	−0.315431	−	0.948948i	$-0.602149\pi$
$911$	−26.7249	−	3.84246i	−0.885435	−	0.127306i	−0.570004	+	0.821642i	$0.693058\pi$
$912$		0			0
$913$	4.22718	+	14.3965i	0.139899	+	0.476453i
$914$		0			0
$915$	17.7744	+	7.28821i	0.587603	+	0.240941i
$916$		0			0
$917$	78.1025	+	61.4205i	2.57917	+	2.02828i
$918$		0			0
$919$	−1.39067	−	14.5637i	−0.0458738	−	0.480413i	−0.988993	−	0.147959i	$-0.952730\pi$
$919$	−1.39067	−	14.5637i	−0.0458738	−	0.480413i	0.943120	−	0.332454i	$-0.107876\pi$
$920$		0			0
$921$	22.3689	−	27.9617i	0.737079	−	0.921368i
$922$		0			0
$923$	−1.54343	+	3.37964i	−0.0508026	+	0.111242i
$924$		0			0
$925$	−29.3145	−	27.9513i	−0.963856	−	0.919034i
$926$		0			0
$927$	17.0255	+	30.6579i	0.559192	+	1.00694i
$928$		0			0
$929$	−16.7379	−	36.6510i	−0.549154	−	1.20248i	−0.957176	−	0.289507i	$-0.906509\pi$
$929$	−16.7379	−	36.6510i	−0.549154	−	1.20248i	0.408022	−	0.912972i	$-0.366219\pi$
$930$		0			0
$931$	13.5181	+	1.29082i	0.443039	+	0.0423050i
$932$		0			0
$933$	4.28962	−	21.3000i	0.140436	−	0.697331i
$934$		0			0
$935$	−55.9374	+	87.0403i	−1.82935	+	2.84652i
$936$		0			0
$937$		−	10.7529i		−	0.351282i	−0.984454	−	0.175641i	$-0.943800\pi$
$937$		−	10.7529i		−	0.351282i	0.984454	−	0.175641i	$-0.0561997\pi$
$938$		0			0
$939$	−3.71420	+	10.4490i	−0.121208	+	0.340989i
$940$		0			0
$941$	20.6942	+	13.2993i	0.674611	+	0.433546i	0.832585	−	0.553897i	$-0.186860\pi$
$941$	20.6942	+	13.2993i	0.674611	+	0.433546i	−0.157974	+	0.987443i	$0.550496\pi$
$942$		0			0
$943$	21.4895	−	3.08972i	0.699794	−	0.100615i
$944$		0			0
$945$	−85.7994	+	41.5519i	−2.79106	+	1.35168i
$946$		0			0
$947$	−10.4012	+	4.75008i	−0.337995	+	0.154357i	−0.577180	−	0.816617i	$-0.695847\pi$
$947$	−10.4012	+	4.75008i	−0.337995	+	0.154357i	0.239185	+	0.970974i	$0.423120\pi$
$948$		0			0
$949$	13.6659	−	34.1357i	0.443612	−	1.10809i
$950$		0			0
$951$	18.5331	−	9.35981i	0.600975	−	0.303513i
$952$		0			0
$953$	42.7154	+	19.5075i	1.38369	+	0.631908i	0.961552	−	0.274625i	$-0.0885536\pi$
$953$	42.7154	+	19.5075i	1.38369	+	0.631908i	0.422135	+	0.906533i	$0.361281\pi$
$954$		0			0
$955$	−7.02703	+	20.3033i	−0.227389	+	0.656998i
$956$		0			0
$957$	−1.68721	+	6.71024i	−0.0545398	+	0.216911i
$958$		0			0
$959$	2.51044	−	3.19229i	0.0810665	−	0.103084i
$960$		0			0
$961$	−1.34476	+	28.2299i	−0.0433793	+	0.910643i
$962$		0			0
$963$	−7.12471	+	16.9714i	−0.229590	+	0.546895i
$964$		0			0
$965$	−12.7582	+	88.7350i	−0.410700	+	2.85648i
$966$		0			0
$967$	−9.39655	+	16.2753i	−0.302173	+	0.523378i	−0.976628	−	0.214938i	$-0.931045\pi$
$967$	−9.39655	+	16.2753i	−0.302173	+	0.523378i	0.674455	+	0.738316i	$0.264379\pi$
$968$		0			0
$969$	3.19900	+	7.16218i	0.102767	+	0.230082i
$970$		0			0
$971$	5.66381	−	4.03318i	0.181760	−	0.129431i	−0.485555	−	0.874206i	$-0.661383\pi$
$971$	5.66381	−	4.03318i	0.181760	−	0.129431i	0.667316	+	0.744775i	$0.267443\pi$
$972$		0			0
$973$	3.38805	+	71.1240i	0.108616	+	2.28013i
$974$		0			0
$975$	73.9511	−	13.6148i	2.36833	−	0.436024i
$976$		0			0
$977$	−52.4640	+	12.7276i	−1.67847	+	0.407193i	−0.958109	−	0.286403i	$-0.907540\pi$
$977$	−52.4640	+	12.7276i	−1.67847	+	0.407193i	−0.720364	+	0.693596i	$0.756025\pi$
$978$		0			0
$979$	−4.59670	−	23.8500i	−0.146911	−	0.762248i
$980$		0			0
$981$	−41.9489	+	1.29810i	−1.33932	+	0.0414451i
$982$		0			0
$983$	−37.4416	+	24.0622i	−1.19420	+	0.767466i	−0.977943	−	0.208870i	$-0.933021\pi$
$983$	−37.4416	+	24.0622i	−1.19420	+	0.767466i	−0.216258	+	0.976336i	$0.569385\pi$
$984$		0			0
$985$	−36.1494	+	18.6363i	−1.15182	+	0.593803i
$986$		0			0
$987$	−12.0726	−	7.10492i	−0.384276	−	0.226152i
$988$		0			0
$989$	2.70061	−	2.12378i	0.0858743	−	0.0675323i
$990$		0			0
$991$	22.4691	+	19.4696i	0.713754	+	0.618471i	0.934126	−	0.356945i	$-0.116182\pi$
$991$	22.4691	+	19.4696i	0.713754	+	0.618471i	−0.220372	+	0.975416i	$0.570727\pi$
$992$		0			0
$993$	−16.4258	−	10.7507i	−0.521257	−	0.341162i
$994$		0			0
$995$	46.6185	+	24.0335i	1.47791	+	0.761913i
$996$		0			0
$997$	54.5206	+	16.0087i	1.72668	+	0.507000i	0.986268	−	0.165150i	$-0.0528108\pi$
$997$	54.5206	+	16.0087i	1.72668	+	0.507000i	0.740415	+	0.672150i	$0.234629\pi$
$998$		0			0
$999$	18.5839	+	13.9465i	0.587968	+	0.441247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.353.8	yes	440
3.2	odd	2	inner	804.2.ba.b.353.22	yes	440
67.41	odd	66	inner	804.2.ba.b.41.22	yes	440
201.41	even	66	inner	804.2.ba.b.41.8	✓	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.8	✓	440	201.41	even	66	inner
804.2.ba.b.41.22	yes	440	67.41	odd	66	inner
804.2.ba.b.353.8	yes	440	1.1	even	1	trivial
804.2.ba.b.353.22	yes	440	3.2	odd	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05930 - 1.37036i) q^{3} +(-0.533599 - 3.71127i) q^{5} +(0.465124 - 4.87100i) q^{7} +(-0.755762 + 2.90324i) q^{9} +O(q^{10})\)	\(q+(-1.05930 - 1.37036i) q^{3} +(-0.533599 - 3.71127i) q^{5} +(0.465124 - 4.87100i) q^{7} +(-0.755762 + 2.90324i) q^{9} +(-4.53378 - 1.81505i) q^{11} +(3.30733 - 3.46863i) q^{13} +(-4.52052 + 4.66257i) q^{15} +(5.33974 + 1.84810i) q^{17} +(-0.797858 + 0.0761862i) q^{19} +(-7.16773 + 4.52247i) q^{21} +(2.77501 + 0.132190i) q^{23} +(-8.69130 + 2.55200i) q^{25} +(4.77906 - 2.03974i) q^{27} +(0.708402 + 0.408996i) q^{29} +(5.31235 + 5.57143i) q^{31} +(2.31537 + 8.13559i) q^{33} +(-18.3258 + 0.872965i) q^{35} +(2.23579 + 3.87250i) q^{37} +(-8.25673 - 0.857906i) q^{39} +(7.67348 - 1.47894i) q^{41} +(0.934610 - 0.809844i) q^{43} +(11.1780 + 1.25566i) q^{45} +(0.757376 + 1.46910i) q^{47} +(-16.6368 - 3.20649i) q^{49} +(-3.12383 - 9.27505i) q^{51} +(-1.96721 + 2.27028i) q^{53} +(-4.31692 + 17.7946i) q^{55} +(0.949574 + 1.01265i) q^{57} +(2.87219 - 9.78178i) q^{59} +(-1.09942 - 2.74622i) q^{61} +(13.7902 + 5.03169i) q^{63} +(-14.6378 - 10.4235i) q^{65} +(-8.18444 + 0.122098i) q^{67} +(-2.75843 - 3.94279i) q^{69} +(-0.732584 + 0.253550i) q^{71} +(7.12244 - 2.85140i) q^{73} +(12.7039 + 9.20686i) q^{75} +(-10.9499 + 21.2398i) q^{77} +(-8.83315 - 2.14290i) q^{79} +(-7.85765 - 4.38832i) q^{81} +(-1.89921 - 2.41505i) q^{83} +(4.00952 - 20.8033i) q^{85} +(-0.189940 - 1.40401i) q^{87} +(2.68891 + 4.18402i) q^{89} +(-15.3574 - 17.7234i) q^{91} +(2.00748 - 13.1816i) q^{93} +(0.708484 + 2.92041i) q^{95} +(-3.01975 + 1.74345i) q^{97} +(8.69600 - 11.7909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 440 * q - 12 * q^7 + 4 * q^9	\( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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