LMFDB - Embedded newform 1386.2.bu.a.701.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.7
Character	$\chi$	$=$	1386.701
Dual form			1386.2.bu.a.953.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.741879 - 1.02111i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.741879 - 1.02111i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +1.26216i q^{10} +(3.31562 + 0.0815558i) q^{11} +(1.32934 + 1.82967i) q^{13} +(0.951057 - 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(3.80312 + 2.76313i) q^{17} +(-5.66000 + 1.83905i) q^{19} +(-0.741879 - 1.02111i) q^{20} +(-2.73033 + 1.88289i) q^{22} -4.32750i q^{23} +(1.05281 + 3.24020i) q^{25} +(-2.15091 - 0.698874i) q^{26} +(-0.587785 + 0.809017i) q^{28} +(1.09670 - 3.37529i) q^{29} +(1.65845 - 1.20493i) q^{31} +1.00000 q^{32} -4.70091 q^{34} +(-1.02111 + 0.741879i) q^{35} +(-0.883434 + 2.71893i) q^{37} +(3.49807 - 4.81469i) q^{38} +(1.20039 + 0.390029i) q^{40} +(2.43080 + 7.48122i) q^{41} -5.70787i q^{43} +(1.10215 - 3.12814i) q^{44} +(2.54364 + 3.50102i) q^{46} +(12.2074 - 3.96643i) q^{47} +(0.809017 + 0.587785i) q^{49} +(-2.75628 - 2.00256i) q^{50} +(2.15091 - 0.698874i) q^{52} +(-1.30959 - 1.80249i) q^{53} +(2.54307 - 3.32511i) q^{55} -1.00000i q^{56} +(1.09670 + 3.37529i) q^{58} +(8.76233 + 2.84705i) q^{59} +(-0.606496 + 0.834770i) q^{61} +(-0.633471 + 1.94962i) q^{62} +(-0.809017 + 0.587785i) q^{64} +2.85450 q^{65} -1.83635 q^{67} +(3.80312 - 2.76313i) q^{68} +(0.390029 - 1.20039i) q^{70} +(6.53316 - 8.99213i) q^{71} +(1.28656 + 0.418028i) q^{73} +(-0.883434 - 2.71893i) q^{74} +5.95128i q^{76} +(-3.12814 - 1.10215i) q^{77} +(8.05887 + 11.0921i) q^{79} +(-1.20039 + 0.390029i) q^{80} +(-6.36391 - 4.62365i) q^{82} +(-2.78744 - 2.02520i) q^{83} +(5.64291 - 1.83349i) q^{85} +(3.35500 + 4.61776i) q^{86} +(0.947019 + 3.17855i) q^{88} -6.74959i q^{89} +(-0.698874 - 2.15091i) q^{91} +(-4.11570 - 1.33727i) q^{92} +(-7.54459 + 10.3842i) q^{94} +(-2.32117 + 7.14383i) q^{95} +(2.44544 - 1.77672i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.741879	−	1.02111i	0.331778	−	0.456654i	−0.610239	−	0.792217i	$-0.708927\pi$
$5$	0.741879	−	1.02111i	0.331778	−	0.456654i	0.942018	+	0.335563i	$0.108927\pi$
$6$		0			0
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$			1.26216i			0.399130i
$11$	3.31562	+	0.0815558i	0.999698	+	0.0245900i
$11$	3.31562	+	0.0815558i	0.999698	+	0.0245900i
$12$		0			0
$13$	1.32934	+	1.82967i	0.368692	+	0.507460i	0.952545	−	0.304399i	$-0.0984556\pi$
$13$	1.32934	+	1.82967i	0.368692	+	0.507460i	−0.583853	+	0.811859i	$0.698456\pi$
$14$	0.951057	−	0.309017i	0.254181	−	0.0825883i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.80312	+	2.76313i	0.922392	+	0.670157i	0.944118	−	0.329607i	$-0.106916\pi$
$17$	3.80312	+	2.76313i	0.922392	+	0.670157i	−0.0217262	+	0.999764i	$0.506916\pi$
$18$		0			0
$19$	−5.66000	+	1.83905i	−1.29849	+	0.421906i	−0.875057	−	0.484020i	$-0.839176\pi$
$19$	−5.66000	+	1.83905i	−1.29849	+	0.421906i	−0.423437	+	0.905926i	$0.639176\pi$
$20$	−0.741879	−	1.02111i	−0.165889	−	0.228327i
$21$		0			0
$22$	−2.73033	+	1.88289i	−0.582109	+	0.401434i
$23$		−	4.32750i		−	0.902346i	−0.892437	−	0.451173i	$-0.851006\pi$
$23$		−	4.32750i		−	0.902346i	0.892437	−	0.451173i	$-0.148994\pi$
$24$		0			0
$25$	1.05281	+	3.24020i	0.210561	+	0.648041i
$26$	−2.15091	−	0.698874i	−0.421828	−	0.137060i
$27$		0			0
$28$	−0.587785	+	0.809017i	−0.111081	+	0.152890i
$29$	1.09670	−	3.37529i	0.203652	−	0.626775i	−0.796114	−	0.605146i	$-0.793115\pi$
$29$	1.09670	−	3.37529i	0.203652	−	0.626775i	0.999766	−	0.0216292i	$-0.00688531\pi$
$30$		0			0
$31$	1.65845	−	1.20493i	0.297866	−	0.216412i	−0.428806	−	0.903396i	$-0.641066\pi$
$31$	1.65845	−	1.20493i	0.297866	−	0.216412i	0.726673	+	0.686984i	$0.241066\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−4.70091			−0.806200
$35$	−1.02111	+	0.741879i	−0.172599	+	0.125400i
$36$		0			0
$37$	−0.883434	+	2.71893i	−0.145236	+	0.446989i	−0.997041	−	0.0768687i	$-0.975508\pi$
$37$	−0.883434	+	2.71893i	−0.145236	+	0.446989i	0.851806	+	0.523858i	$0.175508\pi$
$38$	3.49807	−	4.81469i	0.567463	−	0.781045i
$39$		0			0
$40$	1.20039	+	0.390029i	0.189798	+	0.0616690i
$41$	2.43080	+	7.48122i	0.379627	+	1.16837i	0.940304	+	0.340336i	$0.110541\pi$
$41$	2.43080	+	7.48122i	0.379627	+	1.16837i	−0.560677	+	0.828034i	$0.689459\pi$
$42$		0			0
$43$		−	5.70787i		−	0.870441i	−0.900324	−	0.435221i	$-0.856670\pi$
$43$		−	5.70787i		−	0.870441i	0.900324	−	0.435221i	$-0.143330\pi$
$44$	1.10215	−	3.12814i	0.166155	−	0.471585i
$45$		0			0
$46$	2.54364	+	3.50102i	0.375039	+	0.516197i
$47$	12.2074	−	3.96643i	1.78063	−	0.578563i	0.781653	−	0.623713i	$-0.214377\pi$
$47$	12.2074	−	3.96643i	1.78063	−	0.578563i	0.998980	+	0.0451506i	$0.0143768\pi$
$48$		0			0
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−2.75628	−	2.00256i	−0.389797	−	0.283204i
$51$		0			0
$52$	2.15091	−	0.698874i	0.298278	−	0.0969163i
$53$	−1.30959	−	1.80249i	−0.179886	−	0.247591i	0.709547	−	0.704659i	$-0.248900\pi$
$53$	−1.30959	−	1.80249i	−0.179886	−	0.247591i	−0.889432	+	0.457067i	$0.848900\pi$
$54$		0			0
$55$	2.54307	−	3.32511i	0.342907	−	0.448357i
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	1.09670	+	3.37529i	0.144003	+	0.443197i
$59$	8.76233	+	2.84705i	1.14076	+	0.370655i	0.817655	−	0.575709i	$-0.195274\pi$
$59$	8.76233	+	2.84705i	1.14076	+	0.370655i	0.323104	+	0.946364i	$0.395274\pi$
$60$		0			0
$61$	−0.606496	+	0.834770i	−0.0776538	+	0.106881i	−0.846077	−	0.533061i	$-0.821042\pi$
$61$	−0.606496	+	0.834770i	−0.0776538	+	0.106881i	0.768423	+	0.639942i	$0.221042\pi$
$62$	−0.633471	+	1.94962i	−0.0804509	+	0.247602i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	2.85450			0.354058
$66$		0			0
$67$	−1.83635			−0.224346			−0.112173	−	0.993689i	$-0.535781\pi$
$67$	−1.83635			−0.224346			−0.112173	+	0.993689i	$0.535781\pi$
$68$	3.80312	−	2.76313i	0.461196	−	0.335079i
$69$		0			0
$70$	0.390029	−	1.20039i	0.0466174	−	0.143473i
$71$	6.53316	−	8.99213i	0.775344	−	1.06717i	−0.220437	−	0.975401i	$-0.570748\pi$
$71$	6.53316	−	8.99213i	0.775344	−	1.06717i	0.995780	−	0.0917678i	$-0.0292518\pi$
$72$		0			0
$73$	1.28656	+	0.418028i	0.150580	+	0.0489265i	0.383337	−	0.923608i	$-0.374775\pi$
$73$	1.28656	+	0.418028i	0.150580	+	0.0489265i	−0.232757	+	0.972535i	$0.574775\pi$
$74$	−0.883434	−	2.71893i	−0.102697	−	0.316069i
$75$		0			0
$76$			5.95128i			0.682659i
$77$	−3.12814	−	1.10215i	−0.356485	−	0.125601i
$78$		0			0
$79$	8.05887	+	11.0921i	0.906694	+	1.24796i	0.968283	+	0.249855i	$0.0803831\pi$
$79$	8.05887	+	11.0921i	0.906694	+	1.24796i	−0.0615893	+	0.998102i	$0.519617\pi$
$80$	−1.20039	+	0.390029i	−0.134207	+	0.0436065i
$81$		0			0
$82$	−6.36391	−	4.62365i	−0.702776	−	0.510597i
$83$	−2.78744	−	2.02520i	−0.305962	−	0.222294i	0.424200	−	0.905568i	$-0.360555\pi$
$83$	−2.78744	−	2.02520i	−0.305962	−	0.222294i	−0.730162	+	0.683274i	$0.760555\pi$
$84$		0			0
$85$	5.64291	−	1.83349i	0.612059	−	0.198870i
$86$	3.35500	+	4.61776i	0.361779	+	0.497946i
$87$		0			0
$88$	0.947019	+	3.17855i	0.100953	+	0.338834i
$89$		−	6.74959i		−	0.715455i	−0.933826	−	0.357728i	$-0.883552\pi$
$89$		−	6.74959i		−	0.715455i	0.933826	−	0.357728i	$-0.116448\pi$
$90$		0			0
$91$	−0.698874	−	2.15091i	−0.0732619	−	0.225477i
$92$	−4.11570	−	1.33727i	−0.429091	−	0.139420i
$93$		0			0
$94$	−7.54459	+	10.3842i	−0.778165	+	1.07105i
$95$	−2.32117	+	7.14383i	−0.238147	+	0.732941i
$96$		0			0
$97$	2.44544	−	1.77672i	0.248297	−	0.180398i	−0.456675	−	0.889634i	$-0.650960\pi$
$97$	2.44544	−	1.77672i	0.248297	−	0.180398i	0.704972	+	0.709235i	$0.250960\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	3.40695			0.340695
$101$	3.89617	−	2.83073i	0.387683	−	0.281668i	−0.376822	−	0.926286i	$-0.622983\pi$
$101$	3.89617	−	2.83073i	0.387683	−	0.281668i	0.764505	+	0.644617i	$0.222983\pi$
$102$		0			0
$103$	3.83810	−	11.8125i	0.378179	−	1.16392i	−0.563130	−	0.826369i	$-0.690403\pi$
$103$	3.83810	−	11.8125i	0.378179	−	1.16392i	0.941309	−	0.337547i	$-0.109597\pi$
$104$	−1.32934	+	1.82967i	−0.130352	+	0.179414i
$105$		0			0
$106$	2.11896	+	0.688490i	0.205811	+	0.0668721i
$107$	3.03598	+	9.34379i	0.293499	+	0.903298i	0.983721	+	0.179700i	$0.0575128\pi$
$107$	3.03598	+	9.34379i	0.293499	+	0.903298i	−0.690222	+	0.723598i	$0.742487\pi$
$108$		0			0
$109$		−	11.2613i		−	1.07864i	−0.842101	−	0.539320i	$-0.818681\pi$
$109$		−	11.2613i		−	1.07864i	0.842101	−	0.539320i	$-0.181319\pi$
$110$	−0.102936	+	4.18484i	−0.00981460	+	0.399009i
$111$		0			0
$112$	0.587785	+	0.809017i	0.0555405	+	0.0764449i
$113$	−11.8113	+	3.83773i	−1.11112	+	0.361023i	−0.806371	−	0.591410i	$-0.798571\pi$
$113$	−11.8113	+	3.83773i	−1.11112	+	0.361023i	−0.304745	+	0.952434i	$0.598571\pi$
$114$		0			0
$115$	−4.41885	−	3.21048i	−0.412060	−	0.299379i
$116$	−2.87119	−	2.08604i	−0.266583	−	0.193684i
$117$		0			0
$118$	−8.76233	+	2.84705i	−0.806638	+	0.262093i
$119$	−2.76313	−	3.80312i	−0.253296	−	0.348631i
$120$		0			0
$121$	10.9867	+	0.540816i	0.998791	+	0.0491651i
$122$		−	1.03183i		−	0.0934177i
$123$		0			0
$124$	−0.633471	−	1.94962i	−0.0568874	−	0.175081i
$125$	10.0916	+	3.27895i	0.902618	+	0.293279i
$126$		0			0
$127$	−7.75786	+	10.6778i	−0.688399	+	0.947500i	−0.999996	−	0.00271414i	$-0.999136\pi$
$127$	−7.75786	+	10.6778i	−0.688399	+	0.947500i	0.311597	+	0.950214i	$0.399136\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	−2.30934	+	1.67783i	−0.202543	+	0.147156i
$131$	9.19985			0.803794			0.401897	−	0.915685i	$-0.368351\pi$
$131$	9.19985			0.803794			0.401897	+	0.915685i	$0.368351\pi$
$132$		0			0
$133$	5.95128			0.516041
$134$	1.48564	−	1.07938i	0.128340	−	0.0932442i
$135$		0			0
$136$	−1.45266	+	4.47084i	−0.124565	+	0.383371i
$137$	−10.1296	+	13.9423i	−0.865434	+	1.19117i	0.114813	+	0.993387i	$0.463373\pi$
$137$	−10.1296	+	13.9423i	−0.865434	+	1.19117i	−0.980246	+	0.197780i	$0.936627\pi$
$138$		0			0
$139$	9.94422	+	3.23107i	0.843458	+	0.274056i	0.698703	−	0.715411i	$-0.253761\pi$
$139$	9.94422	+	3.23107i	0.843458	+	0.274056i	0.144755	+	0.989468i	$0.453761\pi$
$140$	0.390029	+	1.20039i	0.0329634	+	0.101451i
$141$		0			0
$142$			11.1149i			0.932740i
$143$	4.25836	+	6.17492i	0.356102	+	0.516373i
$144$		0			0
$145$	−2.63292	−	3.62390i	−0.218652	−	0.300949i
$146$	−1.28656	+	0.418028i	−0.106476	+	0.0345963i
$147$		0			0
$148$	2.31286	+	1.68039i	0.190116	+	0.138127i
$149$	10.6311	+	7.72395i	0.870934	+	0.632770i	0.930837	−	0.365434i	$-0.119079\pi$
$149$	10.6311	+	7.72395i	0.870934	+	0.632770i	−0.0599035	+	0.998204i	$0.519079\pi$
$150$		0			0
$151$	14.2486	−	4.62966i	1.15954	−	0.376757i	0.334809	−	0.942286i	$-0.391328\pi$
$151$	14.2486	−	4.62966i	1.15954	−	0.376757i	0.824728	+	0.565529i	$0.191328\pi$
$152$	−3.49807	−	4.81469i	−0.283731	−	0.390523i
$153$		0			0
$154$	3.17855	−	0.947019i	0.256135	−	0.0763130i
$155$		−	2.58737i		−	0.207823i
$156$		0			0
$157$	7.28531	+	22.4219i	0.581431	+	1.78946i	0.613153	+	0.789964i	$0.289901\pi$
$157$	7.28531	+	22.4219i	0.581431	+	1.78946i	−0.0317225	+	0.999497i	$0.510099\pi$
$158$	−13.0395	−	4.23680i	−1.03737	−	0.337062i
$159$		0			0
$160$	0.741879	−	1.02111i	0.0586507	−	0.0807257i
$161$	−1.33727	+	4.11570i	−0.105392	+	0.324362i
$162$		0			0
$163$	−6.38359	+	4.63795i	−0.500002	+	0.363272i	−0.809018	−	0.587784i	$-0.800000\pi$
$163$	−6.38359	+	4.63795i	−0.500002	+	0.363272i	0.309016	+	0.951057i	$0.400000\pi$
$164$	7.86622			0.614249
$165$		0			0
$166$	3.44547			0.267420
$167$	2.65123	−	1.92623i	0.205158	−	0.149056i	−0.480462	−	0.877016i	$-0.659531\pi$
$167$	2.65123	−	1.92623i	0.205158	−	0.149056i	0.685620	+	0.727959i	$0.259531\pi$
$168$		0			0
$169$	2.43665	−	7.49923i	0.187434	−	0.576864i
$170$	−3.48751	+	4.80014i	−0.267480	+	0.368154i
$171$		0			0
$172$	−5.42850	−	1.76383i	−0.413920	−	0.134491i
$173$	1.63176	+	5.02204i	0.124061	+	0.381819i	0.993729	−	0.111818i	$-0.0356673\pi$
$173$	1.63176	+	5.02204i	0.124061	+	0.381819i	−0.869668	+	0.493637i	$0.835667\pi$
$174$		0			0
$175$		−	3.40695i		−	0.257541i
$176$	−2.63446	−	2.01485i	−0.198580	−	0.151875i
$177$		0			0
$178$	3.96731	+	5.46054i	0.297363	+	0.409284i
$179$	4.16533	−	1.35340i	0.311332	−	0.101158i	−0.149184	−	0.988809i	$-0.547665\pi$
$179$	4.16533	−	1.35340i	0.311332	−	0.101158i	0.460515	+	0.887652i	$0.347665\pi$
$180$		0			0
$181$	−12.8971	−	9.37028i	−0.958633	−	0.696488i	−0.00580017	−	0.999983i	$-0.501846\pi$
$181$	−12.8971	−	9.37028i	−0.958633	−	0.696488i	−0.952833	+	0.303496i	$0.901846\pi$
$182$	1.82967	+	1.32934i	0.135625	+	0.0985370i
$183$		0			0
$184$	4.11570	−	1.33727i	0.303413	−	0.0985849i
$185$	2.12092	+	2.91920i	0.155933	+	0.214624i
$186$		0			0
$187$	12.3844	+	9.47166i	0.905634	+	0.692636i
$188$		−	12.8356i		−	0.936134i
$189$		0			0
$190$	−2.32117	−	7.14383i	−0.168395	−	0.518268i
$191$	−20.6792	−	6.71908i	−1.49629	−	0.486176i	−0.557360	−	0.830271i	$-0.688186\pi$
$191$	−20.6792	−	6.71908i	−1.49629	−	0.486176i	−0.938935	+	0.344095i	$0.888186\pi$
$192$		0			0
$193$	−6.29264	+	8.66107i	−0.452954	+	0.623438i	−0.973029	−	0.230683i	$-0.925904\pi$
$193$	−6.29264	+	8.66107i	−0.452954	+	0.623438i	0.520075	+	0.854121i	$0.325904\pi$
$194$	−0.934076	+	2.87479i	−0.0670628	+	0.206398i
$195$		0			0
$196$	0.809017	−	0.587785i	0.0577869	−	0.0419847i
$197$	−11.5842			−0.825341			−0.412670	−	0.910880i	$-0.635404\pi$
$197$	−11.5842			−0.825341			−0.412670	+	0.910880i	$0.635404\pi$
$198$		0			0
$199$	13.4295			0.951993			0.475996	−	0.879447i	$-0.342088\pi$
$199$	13.4295			0.951993			0.475996	+	0.879447i	$0.342088\pi$
$200$	−2.75628	+	2.00256i	−0.194899	+	0.141602i
$201$		0			0
$202$	−1.48820	+	4.58022i	−0.104710	+	0.322263i
$203$	−2.08604	+	2.87119i	−0.146411	+	0.201518i
$204$		0			0
$205$	9.44250	+	3.06805i	0.659493	+	0.214282i
$206$	3.83810	+	11.8125i	0.267413	+	0.823012i
$207$		0			0
$208$		−	2.26160i		−	0.156814i
$209$	−18.9164	+	5.63598i	−1.30848	+	0.389849i
$210$		0			0
$211$	−11.6882	−	16.0874i	−0.804649	−	1.10750i	−0.992127	−	0.125236i	$-0.960031\pi$
$211$	−11.6882	−	16.0874i	−0.804649	−	1.10750i	0.187478	−	0.982269i	$-0.439969\pi$
$212$	−2.11896	+	0.688490i	−0.145530	+	0.0472857i
$213$		0			0
$214$	−7.94830	−	5.77478i	−0.543335	−	0.394756i
$215$	−5.82835	−	4.23455i	−0.397490	−	0.288794i
$216$		0			0
$217$	−1.94962	+	0.633471i	−0.132349	+	0.0430028i
$218$	6.61924	+	9.11060i	0.448312	+	0.617048i
$219$		0			0
$220$	−2.37651	−	3.44611i	−0.160224	−	0.232337i
$221$			10.6316i			0.715159i
$222$		0			0
$223$	−6.74245	−	20.7511i	−0.451508	−	1.38960i	−0.875187	−	0.483785i	$-0.839262\pi$
$223$	−6.74245	−	20.7511i	−0.451508	−	1.38960i	0.423679	−	0.905812i	$-0.360738\pi$
$224$	−0.951057	−	0.309017i	−0.0635451	−	0.0206471i
$225$		0			0
$226$	7.29980	−	10.0473i	0.485575	−	0.668337i
$227$	2.39943	−	7.38469i	0.159256	−	0.490139i	−0.839311	−	0.543651i	$-0.817042\pi$
$227$	2.39943	−	7.38469i	0.159256	−	0.490139i	0.998567	+	0.0535119i	$0.0170415\pi$
$228$		0			0
$229$	−12.2756	+	8.91872i	−0.811192	+	0.589366i	−0.914176	−	0.405317i	$-0.867161\pi$
$229$	−12.2756	+	8.91872i	−0.811192	+	0.589366i	0.102984	+	0.994683i	$0.467161\pi$
$230$	5.46199			0.360153
$231$		0			0
$232$	3.54899			0.233002
$233$	5.14339	−	3.73689i	0.336954	−	0.244812i	−0.406421	−	0.913686i	$-0.633223\pi$
$233$	5.14339	−	3.73689i	0.336954	−	0.244812i	0.743376	+	0.668874i	$0.233223\pi$
$234$		0			0
$235$	5.00626	−	15.4077i	0.326573	−	1.00509i
$236$	5.41542	−	7.45368i	0.352514	−	0.485194i
$237$		0			0
$238$	4.47084	+	1.45266i	0.289801	+	0.0941621i
$239$	7.60227	+	23.3974i	0.491750	+	1.51345i	0.821961	+	0.569543i	$0.192880\pi$
$239$	7.60227	+	23.3974i	0.491750	+	1.51345i	−0.330212	+	0.943907i	$0.607120\pi$
$240$		0			0
$241$		−	3.32191i		−	0.213983i	−0.994260	−	0.106991i	$-0.965878\pi$
$241$		−	3.32191i		−	0.213983i	0.994260	−	0.106991i	$-0.0341217\pi$
$242$	−9.20631	+	6.02029i	−0.591804	+	0.386999i
$243$		0			0
$244$	0.606496	+	0.834770i	0.0388269	+	0.0534407i
$245$	1.20039	−	0.390029i	0.0766898	−	0.0249180i
$246$		0			0
$247$	−10.8889	−	7.91125i	−0.692844	−	0.503381i
$248$	1.65845	+	1.20493i	0.105312	+	0.0765133i
$249$		0			0
$250$	−10.0916	+	3.27895i	−0.638248	+	0.207379i
$251$	−11.7449	−	16.1655i	−0.741332	−	1.02036i	−0.998541	−	0.0540006i	$-0.982803\pi$
$251$	−11.7449	−	16.1655i	−0.741332	−	1.02036i	0.257209	−	0.966356i	$-0.417197\pi$
$252$		0			0
$253$	0.352933	−	14.3484i	0.0221887	−	0.902073i
$254$		−	13.1985i		−	0.828146i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.45562	+	0.797880i	0.153178	+	0.0497704i	0.384602	−	0.923082i	$-0.374339\pi$
$257$	2.45562	+	0.797880i	0.153178	+	0.0497704i	−0.231425	+	0.972853i	$0.574339\pi$
$258$		0			0
$259$	1.68039	−	2.31286i	0.104414	−	0.143714i
$260$	0.882090	−	2.71479i	0.0547049	−	0.168364i
$261$		0			0
$262$	−7.44283	+	5.40753i	−0.459820	+	0.334079i
$263$	−0.660800			−0.0407467			−0.0203733	−	0.999792i	$-0.506485\pi$
$263$	−0.660800			−0.0407467			−0.0203733	+	0.999792i	$0.506485\pi$
$264$		0			0
$265$	−2.81209			−0.172746
$266$	−4.81469	+	3.49807i	−0.295207	+	0.214481i
$267$		0			0
$268$	−0.567464	+	1.74647i	−0.0346634	+	0.106683i
$269$	5.07675	−	6.98754i	0.309535	−	0.426038i	−0.625701	−	0.780063i	$-0.715187\pi$
$269$	5.07675	−	6.98754i	0.309535	−	0.426038i	0.935236	+	0.354025i	$0.115187\pi$
$270$		0			0
$271$	−24.9802	−	8.11656i	−1.51744	−	0.493046i	−0.572392	−	0.819980i	$-0.693985\pi$
$271$	−24.9802	−	8.11656i	−1.51744	−	0.493046i	−0.945047	+	0.326934i	$0.893985\pi$
$272$	−1.45266	−	4.47084i	−0.0880806	−	0.271084i
$273$		0			0
$274$		−	17.2336i		−	1.04112i
$275$	3.22645	+	10.8292i	0.194562	+	0.653023i
$276$		0			0
$277$	11.3659	+	15.6438i	0.682910	+	0.939945i	0.999964	−	0.00846238i	$-0.00269369\pi$
$277$	11.3659	+	15.6438i	0.682910	+	0.939945i	−0.317054	+	0.948407i	$0.602694\pi$
$278$	−9.94422	+	3.23107i	−0.596415	+	0.193787i
$279$		0			0
$280$	−1.02111	−	0.741879i	−0.0610229	−	0.0443357i
$281$	−24.8924	−	18.0854i	−1.48495	−	1.07888i	−0.975918	−	0.218138i	$-0.930002\pi$
$281$	−24.8924	−	18.0854i	−1.48495	−	1.07888i	−0.509036	−	0.860745i	$-0.669998\pi$
$282$		0			0
$283$	−10.4708	+	3.40217i	−0.622425	+	0.202238i	−0.603217	−	0.797577i	$-0.706115\pi$
$283$	−10.4708	+	3.40217i	−0.622425	+	0.202238i	−0.0192086	+	0.999815i	$0.506115\pi$
$284$	−6.53316	−	8.99213i	−0.387672	−	0.533585i
$285$		0			0
$286$	−7.07461	−	2.49262i	−0.418331	−	0.147392i
$287$		−	7.86622i		−	0.464328i
$288$		0			0
$289$	1.57555	+	4.84906i	0.0926796	+	0.285239i
$290$	4.26015	+	1.38421i	0.250165	+	0.0812835i
$291$		0			0
$292$	0.795137	−	1.09441i	0.0465319	−	0.0640456i
$293$	−5.75403	+	17.7091i	−0.336154	+	1.03458i	0.629997	+	0.776598i	$0.283056\pi$
$293$	−5.75403	+	17.7091i	−0.336154	+	1.03458i	−0.966151	+	0.257978i	$0.916944\pi$
$294$		0			0
$295$	9.40774	−	6.83512i	0.547740	−	0.397956i
$296$	−2.85885			−0.166167
$297$		0			0
$298$	−13.1408			−0.761224
$299$	7.91792	−	5.75270i	0.457905	−	0.332687i
$300$		0			0
$301$	−1.76383	+	5.42850i	−0.101665	+	0.312894i
$302$	−8.80614	+	12.1206i	−0.506736	+	0.697463i
$303$		0			0
$304$	5.66000	+	1.83905i	0.324623	+	0.105477i
$305$	0.402444	+	1.23860i	0.0230439	+	0.0709218i
$306$		0			0
$307$		−	18.9134i		−	1.07944i	−0.841844	−	0.539721i	$-0.818530\pi$
$307$		−	18.9134i		−	1.07944i	0.841844	−	0.539721i	$-0.181470\pi$
$308$	−2.01485	+	2.63446i	−0.114807	+	0.150112i
$309$		0			0
$310$	1.52082	+	2.09323i	0.0863767	+	0.118887i
$311$	20.7892	−	6.75481i	1.17885	−	0.383030i	0.346908	−	0.937899i	$-0.387232\pi$
$311$	20.7892	−	6.75481i	1.17885	−	0.383030i	0.831938	+	0.554869i	$0.187232\pi$
$312$		0			0
$313$	−4.50307	−	3.27167i	−0.254528	−	0.184926i	0.453203	−	0.891407i	$-0.350281\pi$
$313$	−4.50307	−	3.27167i	−0.254528	−	0.184926i	−0.707731	+	0.706482i	$0.750281\pi$
$314$	−19.0732	−	13.8575i	−1.07636	−	0.782023i
$315$		0			0
$316$	13.0395	−	4.23680i	0.733531	−	0.238339i
$317$	−4.53807	−	6.24612i	−0.254883	−	0.350817i	0.662331	−	0.749212i	$-0.269567\pi$
$317$	−4.53807	−	6.24612i	−0.254883	−	0.350817i	−0.917214	+	0.398395i	$0.869567\pi$
$318$		0			0
$319$	3.91151	−	11.1017i	0.219002	−	0.621578i
$320$			1.26216i			0.0705569i
$321$		0			0
$322$	−1.33727	−	4.11570i	−0.0745232	−	0.229359i
$323$	−26.6072	−	8.64520i	−1.48046	−	0.481032i
$324$		0			0
$325$	−4.52899	+	6.23362i	−0.251223	+	0.345779i
$326$	2.43832	−	7.50436i	0.135046	−	0.415628i
$327$		0			0
$328$	−6.36391	+	4.62365i	−0.351388	+	0.255298i
$329$	−12.8356			−0.707651
$330$		0			0
$331$	−16.8302			−0.925070			−0.462535	−	0.886601i	$-0.653060\pi$
$331$	−16.8302			−0.925070			−0.462535	+	0.886601i	$0.653060\pi$
$332$	−2.78744	+	2.02520i	−0.152981	+	0.111147i
$333$		0			0
$334$	−1.01268	+	3.11671i	−0.0554114	+	0.170539i
$335$	−1.36235	+	1.87511i	−0.0744331	+	0.102448i
$336$		0			0
$337$	−6.53461	−	2.12322i	−0.355963	−	0.115659i	0.125576	−	0.992084i	$-0.459922\pi$
$337$	−6.53461	−	2.12322i	−0.355963	−	0.115659i	−0.481539	+	0.876425i	$0.659922\pi$
$338$	2.43665	+	7.49923i	0.132536	+	0.407904i
$339$		0			0
$340$		−	5.93330i		−	0.321779i
$341$	5.59706	−	3.85985i	0.303098	−	0.209022i
$342$		0			0
$343$	−0.587785	−	0.809017i	−0.0317374	−	0.0436828i
$344$	5.42850	−	1.76383i	0.292685	−	0.0950992i
$345$		0			0
$346$	−4.27201	−	3.10379i	−0.229664	−	0.166861i
$347$	−7.72783	−	5.61460i	−0.414852	−	0.301407i	0.360711	−	0.932677i	$-0.382534\pi$
$347$	−7.72783	−	5.61460i	−0.414852	−	0.301407i	−0.775563	+	0.631270i	$0.782534\pi$
$348$		0			0
$349$	18.8527	−	6.12560i	1.00916	−	0.327896i	0.242640	−	0.970116i	$-0.421987\pi$
$349$	18.8527	−	6.12560i	1.00916	−	0.327896i	0.766520	+	0.642220i	$0.221987\pi$
$350$	2.00256	+	2.75628i	0.107041	+	0.147330i
$351$		0			0
$352$	3.31562	+	0.0815558i	0.176723	+	0.00434694i
$353$			22.7576i			1.21127i	0.795744	+	0.605633i	$0.207080\pi$
$353$			22.7576i			1.21127i	−0.795744	+	0.605633i	$0.792920\pi$
$354$		0			0
$355$	−4.33512	−	13.3421i	−0.230084	−	0.708127i
$356$	−6.41924	−	2.08574i	−0.340219	−	0.110544i
$357$		0			0
$358$	−2.57432	+	3.54324i	−0.136057	+	0.187266i
$359$	−5.02591	+	15.4682i	−0.265258	+	0.816379i	0.726376	+	0.687297i	$0.241203\pi$
$359$	−5.02591	+	15.4682i	−0.265258	+	0.816379i	−0.991634	+	0.129082i	$0.958797\pi$
$360$		0			0
$361$	13.2822	−	9.65009i	0.699064	−	0.507900i
$362$	15.9417			0.837876
$363$		0			0
$364$	−2.26160			−0.118540
$365$	1.38132	−	1.00359i	0.0723017	−	0.0525303i
$366$		0			0
$367$	−8.37309	+	25.7697i	−0.437072	+	1.34517i	0.453877	+	0.891064i	$0.350041\pi$
$367$	−8.37309	+	25.7697i	−0.437072	+	1.34517i	−0.890949	+	0.454104i	$0.849959\pi$
$368$	−2.54364	+	3.50102i	−0.132596	+	0.182503i
$369$		0			0
$370$	−3.43172	−	1.11503i	−0.178407	−	0.0579679i
$371$	0.688490	+	2.11896i	0.0357446	+	0.110011i
$372$		0			0
$373$			0.966539i			0.0500455i	0.999687	+	0.0250227i	$0.00796582\pi$
$373$			0.966539i			0.0500455i	−0.999687	+	0.0250227i	$0.992034\pi$
$374$	−15.5865	−	0.383387i	−0.805956	−	0.0198245i
$375$		0			0
$376$	7.54459	+	10.3842i	0.389083	+	0.535526i
$377$	7.63356	−	2.48029i	0.393148	−	0.127742i
$378$		0			0
$379$	−30.0985	−	21.8679i	−1.54606	−	1.12328i	−0.946390	−	0.323026i	$-0.895300\pi$
$379$	−30.0985	−	21.8679i	−1.54606	−	1.12328i	−0.599667	−	0.800250i	$-0.704700\pi$
$380$	6.07690	+	4.41513i	0.311739	+	0.226491i
$381$		0			0
$382$	20.6792	−	6.71908i	1.05804	−	0.343778i
$383$	−14.4905	−	19.9445i	−0.740430	−	1.01911i	−0.998594	−	0.0530135i	$-0.983117\pi$
$383$	−14.4905	−	19.9445i	−0.740430	−	1.01911i	0.258164	−	0.966101i	$-0.416883\pi$
$384$		0			0
$385$	−3.44611	+	2.37651i	−0.175630	+	0.121118i
$386$		−	10.7057i		−	0.544905i
$387$		0			0
$388$	−0.934076	−	2.87479i	−0.0474205	−	0.145945i
$389$	−29.9322	−	9.72556i	−1.51762	−	0.493106i	−0.572523	−	0.819888i	$-0.694035\pi$
$389$	−29.9322	−	9.72556i	−1.51762	−	0.493106i	−0.945099	+	0.326783i	$0.894035\pi$
$390$		0			0
$391$	11.9574	−	16.4580i	0.604714	−	0.832317i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$		0			0
$394$	9.37182	−	6.80903i	0.472146	−	0.343034i
$395$	17.3049			0.870705
$396$		0			0
$397$	−4.05765			−0.203647			−0.101824	−	0.994802i	$-0.532468\pi$
$397$	−4.05765			−0.203647			−0.101824	+	0.994802i	$0.532468\pi$
$398$	−10.8647	+	7.89367i	−0.544598	+	0.395674i
$399$		0			0
$400$	1.05281	−	3.24020i	0.0526403	−	0.162010i
$401$	22.4447	−	30.8925i	1.12084	−	1.54270i	0.316434	−	0.948614i	$-0.397514\pi$
$401$	22.4447	−	30.8925i	1.12084	−	1.54270i	0.804402	−	0.594085i	$-0.202486\pi$
$402$		0			0
$403$	4.40927	+	1.43266i	0.219641	+	0.0713658i
$404$	−1.48820	−	4.58022i	−0.0740409	−	0.227875i
$405$		0			0
$406$		−	3.54899i		−	0.176133i
$407$	−3.15088	+	8.94289i	−0.156183	+	0.443283i
$408$		0			0
$409$	14.6728	+	20.1954i	0.725522	+	0.998596i	0.999322	+	0.0368092i	$0.0117194\pi$
$409$	14.6728	+	20.1954i	0.725522	+	0.998596i	−0.273800	+	0.961787i	$0.588281\pi$
$410$	−9.44250	+	3.06805i	−0.466332	+	0.151520i
$411$		0			0
$412$	−10.0483	−	7.30050i	−0.495043	−	0.359670i
$413$	−7.45368	−	5.41542i	−0.366772	−	0.266475i
$414$		0			0
$415$	−4.13589	+	1.34383i	−0.203023	+	0.0659661i
$416$	1.32934	+	1.82967i	0.0651761	+	0.0897072i
$417$		0			0
$418$	11.9910	−	15.6784i	0.586497	−	0.766855i
$419$			12.0131i			0.586876i	0.955978	+	0.293438i	$0.0947994\pi$
$419$			12.0131i			0.586876i	−0.955978	+	0.293438i	$0.905201\pi$
$420$		0			0
$421$	7.09545	+	21.8375i	0.345811	+	1.06430i	0.961148	+	0.276033i	$0.0890198\pi$
$421$	7.09545	+	21.8375i	0.345811	+	1.06430i	−0.615337	+	0.788264i	$0.710980\pi$
$422$	18.9119	+	6.14485i	0.920617	+	0.299127i
$423$		0			0
$424$	1.30959	−	1.80249i	0.0635991	−	0.0875367i
$425$	−4.94915	+	15.2319i	−0.240069	+	0.738857i
$426$		0			0
$427$	0.834770	−	0.606496i	0.0403973	−	0.0293504i
$428$	9.82464			0.474892
$429$		0			0
$430$	7.20424			0.347419
$431$	−17.4674	+	12.6908i	−0.841376	+	0.611296i	−0.922755	−	0.385388i	$-0.874068\pi$
$431$	−17.4674	+	12.6908i	−0.841376	+	0.611296i	0.0813785	+	0.996683i	$0.474068\pi$
$432$		0			0
$433$	−3.19036	+	9.81890i	−0.153319	+	0.471866i	−0.997987	−	0.0634242i	$-0.979798\pi$
$433$	−3.19036	+	9.81890i	−0.153319	+	0.471866i	0.844668	+	0.535291i	$0.179798\pi$
$434$	1.20493	−	1.65845i	0.0578387	−	0.0796081i
$435$		0			0
$436$	−10.7102	−	3.47994i	−0.512923	−	0.166659i
$437$	7.95847	+	24.4937i	0.380705	+	1.17169i
$438$		0			0
$439$		−	10.6518i		−	0.508382i	−0.967154	−	0.254191i	$-0.918191\pi$
$439$		−	10.6518i		−	0.508382i	0.967154	−	0.254191i	$-0.0818092\pi$
$440$	3.94821	+	1.39109i	0.188224	+	0.0663174i
$441$		0			0
$442$	−6.24910	−	8.60114i	−0.297239	−	0.409115i
$443$	20.8361	−	6.77007i	0.989955	−	0.321656i	0.231110	−	0.972928i	$-0.425764\pi$
$443$	20.8361	−	6.77007i	0.989955	−	0.321656i	0.758845	+	0.651272i	$0.225764\pi$
$444$		0			0
$445$	−6.89207	−	5.00738i	−0.326715	−	0.237373i
$446$	17.6520	+	12.8249i	0.835844	+	0.607276i
$447$		0			0
$448$	0.951057	−	0.309017i	0.0449332	−	0.0145997i
$449$	−17.5311	−	24.1295i	−0.827344	−	1.13874i	−0.988412	−	0.151798i	$-0.951494\pi$
$449$	−17.5311	−	24.1295i	−0.827344	−	1.13874i	0.161067	−	0.986943i	$-0.448506\pi$
$450$		0			0
$451$	7.44947	+	25.0032i	0.350782	+	1.17735i
$452$			12.4192i			0.584148i
$453$		0			0
$454$	2.39943	+	7.38469i	0.112611	+	0.346581i
$455$	−2.71479	−	0.882090i	−0.127271	−	0.0413530i
$456$		0			0
$457$	−23.4611	+	32.2914i	−1.09746	+	1.51053i	−0.258755	+	0.965943i	$0.583312\pi$
$457$	−23.4611	+	32.2914i	−1.09746	+	1.51053i	−0.838706	+	0.544584i	$0.816688\pi$
$458$	4.68885	−	14.4308i	0.219095	−	0.674307i
$459$		0			0
$460$	−4.41885	+	3.21048i	−0.206030	+	0.149689i
$461$	3.70574			0.172593			0.0862967	−	0.996269i	$-0.472497\pi$
$461$	3.70574			0.172593			0.0862967	+	0.996269i	$0.472497\pi$
$462$		0			0
$463$	−8.33299			−0.387267			−0.193633	−	0.981074i	$-0.562027\pi$
$463$	−8.33299			−0.387267			−0.193633	+	0.981074i	$0.562027\pi$
$464$	−2.87119	+	2.08604i	−0.133292	+	0.0968421i
$465$		0			0
$466$	−1.96460	+	6.04641i	−0.0910083	+	0.280095i
$467$	3.71253	−	5.10986i	0.171796	−	0.236456i	−0.714434	−	0.699703i	$-0.753316\pi$
$467$	3.71253	−	5.10986i	0.171796	−	0.236456i	0.886229	+	0.463247i	$0.153316\pi$
$468$		0			0
$469$	1.74647	+	0.567464i	0.0806447	+	0.0262030i
$470$	5.00626	+	15.4077i	0.230922	+	0.710704i
$471$		0			0
$472$			9.21326i			0.424075i
$473$	0.465510	−	18.9251i	0.0214042	−	0.870178i
$474$		0			0
$475$	−11.9178	−	16.4034i	−0.546825	−	0.752640i
$476$	−4.47084	+	1.45266i	−0.204920	+	0.0665827i
$477$		0			0
$478$	−19.9030	−	14.4604i	−0.910342	−	0.661402i
$479$	−8.78231	−	6.38072i	−0.401274	−	0.291543i	0.368786	−	0.929514i	$-0.379774\pi$
$479$	−8.78231	−	6.38072i	−0.401274	−	0.291543i	−0.770060	+	0.637972i	$0.779774\pi$
$480$		0			0
$481$	−6.14914	+	1.99798i	−0.280377	+	0.0910999i
$482$	1.95257	+	2.68748i	0.0889370	+	0.122411i
$483$		0			0
$484$	3.90942	−	10.2818i	0.177701	−	0.467357i
$485$		−	3.81517i		−	0.173238i
$486$		0			0
$487$	0.566271	+	1.74280i	0.0256602	+	0.0789739i	0.963067	−	0.269264i	$-0.0867803\pi$
$487$	0.566271	+	1.74280i	0.0256602	+	0.0789739i	−0.937406	+	0.348237i	$0.886780\pi$
$488$	−0.981331	−	0.318854i	−0.0444228	−	0.0144338i
$489$		0			0
$490$	−0.741879	+	1.02111i	−0.0335147	+	0.0461290i
$491$	4.66453	−	14.3560i	0.210507	−	0.647875i	−0.788935	−	0.614477i	$-0.789367\pi$
$491$	4.66453	−	14.3560i	0.210507	−	0.647875i	0.999442	−	0.0333981i	$-0.0106329\pi$
$492$		0			0
$493$	13.4972	−	9.80631i	0.607884	−	0.441654i
$494$	13.4594			0.605568
$495$		0			0
$496$	−2.04996			−0.0920457
$497$	−8.99213	+	6.53316i	−0.403352	+	0.293052i
$498$		0			0
$499$	−10.2855	+	31.6557i	−0.460444	+	1.41710i	0.404178	+	0.914680i	$0.367558\pi$
$499$	−10.2855	+	31.6557i	−0.460444	+	1.41710i	−0.864623	+	0.502422i	$0.832442\pi$
$500$	6.23694	−	8.58441i	0.278924	−	0.383907i
$501$		0			0
$502$	19.0037	+	6.17467i	0.848175	+	0.275589i
$503$	0.193083	+	0.594250i	0.00860917	+	0.0264963i	0.955269	−	0.295739i	$-0.0955658\pi$
$503$	0.193083	+	0.594250i	0.00860917	+	0.0264963i	−0.946660	+	0.322235i	$0.895566\pi$
$504$		0			0
$505$		−	6.07847i		−	0.270488i
$506$	8.14822	+	11.8155i	0.362233	+	0.525263i
$507$		0			0
$508$	7.75786	+	10.6778i	0.344200	+	0.473750i
$509$	−15.1033	+	4.90737i	−0.669444	+	0.217516i	−0.623968	−	0.781450i	$-0.714480\pi$
$509$	−15.1033	+	4.90737i	−0.669444	+	0.217516i	−0.0454760	+	0.998965i	$0.514480\pi$
$510$		0			0
$511$	−1.09441	−	0.795137i	−0.0484139	−	0.0351748i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	−2.45562	+	0.797880i	−0.108313	+	0.0351930i
$515$	−9.21439	−	12.6825i	−0.406035	−	0.558859i
$516$		0			0
$517$	40.7986	−	12.1556i	1.79432	−	0.534602i
$518$			2.85885i			0.125611i
$519$		0			0
$520$	0.882090	+	2.71479i	0.0386822	+	0.119052i
$521$	5.70147	+	1.85252i	0.249786	+	0.0811604i	0.431234	−	0.902240i	$-0.358078\pi$
$521$	5.70147	+	1.85252i	0.249786	+	0.0811604i	−0.181448	+	0.983401i	$0.558078\pi$
$522$		0			0
$523$	−18.9478	+	26.0794i	−0.828530	+	1.14037i	0.159665	+	0.987171i	$0.448959\pi$
$523$	−18.9478	+	26.0794i	−0.828530	+	1.14037i	−0.988195	+	0.153203i	$0.951041\pi$
$524$	2.84291	−	8.74957i	0.124193	−	0.382227i
$525$		0			0
$526$	0.534598	−	0.388408i	0.0233096	−	0.0169354i
$527$	9.63666			0.419780
$528$		0			0
$529$	4.27275			0.185772
$530$	2.27503	−	1.65291i	0.0988211	−	0.0717977i
$531$		0			0
$532$	1.83905	−	5.66000i	0.0797328	−	0.245392i
$533$	−10.4569	+	14.3926i	−0.452937	+	0.623414i
$534$		0			0
$535$	11.7934	+	3.83189i	0.509871	+	0.165667i
$536$	−0.567464	−	1.74647i	−0.0245107	−	0.0754362i
$537$		0			0
$538$			8.63708i			0.372371i
$539$	2.63446	+	2.01485i	0.113474	+	0.0867859i
$540$		0			0
$541$	−6.78381	−	9.33711i	−0.291659	−	0.401434i	0.637893	−	0.770125i	$-0.279806\pi$
$541$	−6.78381	−	9.33711i	−0.291659	−	0.401434i	−0.929552	+	0.368691i	$0.879806\pi$
$542$	24.9802	−	8.11656i	1.07299	−	0.348636i
$543$		0			0
$544$	3.80312	+	2.76313i	0.163057	+	0.118468i
$545$	−11.4990	−	8.35454i	−0.492565	−	0.357869i
$546$		0			0
$547$	−39.9851	+	12.9919i	−1.70964	+	0.555496i	−0.990273	−	0.139136i	$-0.955568\pi$
$547$	−39.9851	+	12.9919i	−1.70964	+	0.555496i	−0.719366	+	0.694631i	$0.755568\pi$
$548$	10.1296	+	13.9423i	0.432717	+	0.595584i
$549$		0			0
$550$	−8.97547	−	6.86451i	−0.382715	−	0.292704i
$551$			21.1210i			0.899786i
$552$		0			0
$553$	−4.23680	−	13.0395i	−0.180167	−	0.554497i
$554$	−18.3904	−	5.97540i	−0.781333	−	0.253870i
$555$		0			0
$556$	6.14587	−	8.45906i	0.260643	−	0.358744i
$557$	−8.70871	+	26.8026i	−0.369000	+	1.13566i	0.578439	+	0.815726i	$0.303662\pi$
$557$	−8.70871	+	26.8026i	−0.369000	+	1.13566i	−0.947438	+	0.319938i	$0.896338\pi$
$558$		0			0
$559$	10.4435	−	7.58767i	0.441715	−	0.320924i
$560$	1.26216			0.0533360
$561$		0			0
$562$	30.7687			1.29790
$563$	17.1548	−	12.4637i	0.722987	−	0.525281i	−0.164350	−	0.986402i	$-0.552553\pi$
$563$	17.1548	−	12.4637i	0.722987	−	0.525281i	0.887337	+	0.461121i	$0.152553\pi$
$564$		0			0
$565$	−4.84383	+	14.9078i	−0.203781	+	0.627175i
$566$	6.47132	−	8.90701i	0.272010	−	0.374390i
$567$		0			0
$568$	10.5709	+	3.43469i	0.443544	+	0.144116i
$569$	−2.47020	−	7.60250i	−0.103556	−	0.318713i	0.885833	−	0.464005i	$-0.153588\pi$
$569$	−2.47020	−	7.60250i	−0.103556	−	0.318713i	−0.989389	+	0.145292i	$0.953588\pi$
$570$		0			0
$571$		−	11.2855i		−	0.472284i	−0.971719	−	0.236142i	$-0.924117\pi$
$571$		−	11.2855i		−	0.472284i	0.971719	−	0.236142i	$-0.0758830\pi$
$572$	7.18861	−	2.14178i	0.300571	−	0.0895524i
$573$		0			0
$574$	4.62365	+	6.36391i	0.192987	+	0.265624i
$575$	14.0220	−	4.55602i	0.584757	−	0.189999i
$576$		0			0
$577$	−35.5443	−	25.8244i	−1.47973	−	1.07509i	−0.977644	−	0.210267i	$-0.932567\pi$
$577$	−35.5443	−	25.8244i	−1.47973	−	1.07509i	−0.502085	−	0.864818i	$-0.667433\pi$
$578$	−4.12485	−	2.99688i	−0.171571	−	0.124654i
$579$		0			0
$580$	−4.26015	+	1.38421i	−0.176893	+	0.0574761i
$581$	2.02520	+	2.78744i	0.0840193	+	0.115643i
$582$		0			0
$583$	−4.19509	−	6.08318i	−0.173743	−	0.251940i
$584$			1.35277i			0.0559779i
$585$		0			0
$586$	−5.75403	−	17.7091i	−0.237697	−	0.731555i
$587$	15.0479	+	4.88936i	0.621093	+	0.201805i	0.602626	−	0.798024i	$-0.294121\pi$
$587$	15.0479	+	4.88936i	0.621093	+	0.201805i	0.0184676	+	0.999829i	$0.494121\pi$
$588$		0			0
$589$	−7.17090	+	9.86989i	−0.295472	+	0.406682i
$590$	−3.59344	+	11.0595i	−0.147939	+	0.455311i
$591$		0			0
$592$	2.31286	−	1.68039i	0.0950580	−	0.0690636i
$593$	16.3163			0.670032			0.335016	−	0.942212i	$-0.391258\pi$
$593$	16.3163			0.670032			0.335016	+	0.942212i	$0.391258\pi$
$594$		0			0
$595$	−5.93330			−0.243242
$596$	10.6311	−	7.72395i	0.435467	−	0.316385i
$597$		0			0
$598$	−3.02437	+	9.30807i	−0.123676	+	0.380635i
$599$	11.0918	−	15.2666i	0.453199	−	0.623774i	−0.519882	−	0.854238i	$-0.674024\pi$
$599$	11.0918	−	15.2666i	0.453199	−	0.623774i	0.973081	+	0.230463i	$0.0740242\pi$
$600$		0			0
$601$	32.2356	+	10.4740i	1.31492	+	0.427243i	0.880747	−	0.473587i	$-0.157041\pi$
$601$	32.2356	+	10.4740i	1.31492	+	0.427243i	0.434172	+	0.900830i	$0.357041\pi$
$602$	−1.76383	−	5.42850i	−0.0718883	−	0.221249i
$603$		0			0
$604$		−	14.9819i		−	0.609605i
$605$	8.70303	−	10.8174i	0.353828	−	0.439789i
$606$		0			0
$607$	13.3345	+	18.3534i	0.541231	+	0.744941i	0.988790	−	0.149314i	$-0.0477064\pi$
$607$	13.3345	+	18.3534i	0.541231	+	0.744941i	−0.447558	+	0.894255i	$0.647706\pi$
$608$	−5.66000	+	1.83905i	−0.229543	+	0.0745832i
$609$		0			0
$610$	−1.05361	−	0.765494i	−0.0426595	−	0.0309940i
$611$	23.4850	+	17.0629i	0.950102	+	0.690290i
$612$		0			0
$613$	−4.72196	+	1.53426i	−0.190718	+	0.0619681i	−0.402819	−	0.915280i	$-0.631970\pi$
$613$	−4.72196	+	1.53426i	−0.190718	+	0.0619681i	0.212101	+	0.977248i	$0.431970\pi$
$614$	11.1170	+	15.3012i	0.448645	+	0.617508i
$615$		0			0
$616$	0.0815558	−	3.31562i	0.00328598	−	0.133590i
$617$			9.70050i			0.390527i	0.980751	+	0.195264i	$0.0625563\pi$
$617$			9.70050i			0.390527i	−0.980751	+	0.195264i	$0.937444\pi$
$618$		0			0
$619$	13.0812	+	40.2597i	0.525776	+	1.61817i	0.762776	+	0.646663i	$0.223836\pi$
$619$	13.0812	+	40.2597i	0.525776	+	1.61817i	−0.237000	+	0.971510i	$0.576164\pi$
$620$	−2.46074	−	0.799542i	−0.0988255	−	0.0321104i
$621$		0			0
$622$	−12.8484	+	17.6843i	−0.515174	+	0.709077i
$623$	−2.08574	+	6.41924i	−0.0835634	+	0.257182i
$624$		0			0
$625$	−2.94652	+	2.14077i	−0.117861	+	0.0856308i
$626$	5.56610			0.222466
$627$		0			0
$628$	23.5758			0.940775
$629$	−10.8726	+	7.89937i	−0.433517	+	0.314969i
$630$		0			0
$631$	6.85685	−	21.1032i	0.272967	−	0.840105i	−0.716783	−	0.697296i	$-0.754386\pi$
$631$	6.85685	−	21.1032i	0.272967	−	0.840105i	0.989750	−	0.142809i	$-0.0456136\pi$
$632$	−8.05887	+	11.0921i	−0.320565	+	0.441219i
$633$		0			0
$634$	7.34275	+	2.38580i	0.291618	+	0.0947524i
$635$	5.14778	+	15.8432i	0.204284	+	0.628720i
$636$		0			0
$637$			2.26160i			0.0896079i
$638$	3.36096	+	11.2806i	0.133062	+	0.446604i
$639$		0			0
$640$	−0.741879	−	1.02111i	−0.0293253	−	0.0403629i
$641$	6.30284	−	2.04792i	0.248947	−	0.0808879i	−0.181885	−	0.983320i	$-0.558220\pi$
$641$	6.30284	−	2.04792i	0.248947	−	0.0808879i	0.430833	+	0.902432i	$0.358220\pi$
$642$		0			0
$643$	15.8308	+	11.5017i	0.624304	+	0.453583i	0.854422	−	0.519579i	$-0.173911\pi$
$643$	15.8308	+	11.5017i	0.624304	+	0.453583i	−0.230118	+	0.973163i	$0.573911\pi$
$644$	3.50102	+	2.54364i	0.137960	+	0.100233i
$645$		0			0
$646$	26.6072	−	8.64520i	1.04685	−	0.340141i
$647$	16.5477	+	22.7759i	0.650556	+	0.895413i	0.999123	−	0.0418707i	$-0.0133317\pi$
$647$	16.5477	+	22.7759i	0.650556	+	0.895413i	−0.348567	+	0.937284i	$0.613332\pi$
$648$		0			0
$649$	28.8204	+	10.1544i	1.13130	+	0.398594i
$650$		−	7.70517i		−	0.302222i
$651$		0			0
$652$	2.43832	+	7.50436i	0.0954918	+	0.293894i
$653$	−7.49022	−	2.43372i	−0.293115	−	0.0952389i	0.158768	−	0.987316i	$-0.449248\pi$
$653$	−7.49022	−	2.43372i	−0.293115	−	0.0952389i	−0.451883	+	0.892077i	$0.649248\pi$
$654$		0			0
$655$	6.82517	−	9.39404i	0.266681	−	0.367056i
$656$	2.43080	−	7.48122i	0.0949067	−	0.292093i
$657$		0			0
$658$	10.3842	−	7.54459i	0.404820	−	0.294119i
$659$	−24.5444			−0.956116			−0.478058	−	0.878328i	$-0.658659\pi$
$659$	−24.5444			−0.956116			−0.478058	+	0.878328i	$0.658659\pi$
$660$		0			0
$661$	4.35261			0.169297			0.0846484	−	0.996411i	$-0.473023\pi$
$661$	4.35261			0.169297			0.0846484	+	0.996411i	$0.473023\pi$
$662$	13.6159	−	9.89252i	0.529197	−	0.384484i
$663$		0			0
$664$	1.06471	−	3.27684i	0.0413187	−	0.127166i
$665$	4.41513	−	6.07690i	0.171211	−	0.235652i
$666$		0			0
$667$	−14.6066	−	4.74596i	−0.565568	−	0.183764i
$668$	−1.01268	−	3.11671i	−0.0391818	−	0.120589i
$669$		0			0
$670$		−	2.31777i		−	0.0895432i
$671$	−2.07899	+	2.71832i	−0.0802586	+	0.104939i
$672$		0			0
$673$	29.3355	+	40.3768i	1.13080	+	1.55641i	0.786543	+	0.617536i	$0.211869\pi$
$673$	29.3355	+	40.3768i	1.13080	+	1.55641i	0.344257	+	0.938876i	$0.388131\pi$
$674$	6.53461	−	2.12322i	0.251704	−	0.0817835i
$675$		0			0
$676$	−6.37922	−	4.63478i	−0.245355	−	0.178261i
$677$	−24.3249	−	17.6731i	−0.934883	−	0.679232i	0.0123006	−	0.999924i	$-0.496084\pi$
$677$	−24.3249	−	17.6731i	−0.934883	−	0.679232i	−0.947183	+	0.320692i	$0.896084\pi$
$678$		0			0
$679$	−2.87479	+	0.934076i	−0.110324	+	0.0358466i
$680$	3.48751	+	4.80014i	0.133740	+	0.184077i
$681$		0			0
$682$	−2.25935	+	6.41255i	−0.0865151	+	0.245549i
$683$		−	15.7616i		−	0.603100i	−0.953450	−	0.301550i	$-0.902496\pi$
$683$		−	15.7616i		−	0.603100i	0.953450	−	0.301550i	$-0.0975039\pi$
$684$		0			0
$685$	6.72159	+	20.6869i	0.256819	+	0.790407i
$686$	0.951057	+	0.309017i	0.0363115	+	0.0117983i
$687$		0			0
$688$	−3.35500	+	4.61776i	−0.127908	+	0.176050i
$689$	1.55709	−	4.79223i	0.0593205	−	0.182570i
$690$		0			0
$691$	−35.5140	+	25.8024i	−1.35102	+	0.981571i	−0.352057	+	0.935979i	$0.614518\pi$
$691$	−35.5140	+	25.8024i	−1.35102	+	0.981571i	−0.998960	+	0.0455924i	$0.985482\pi$
$692$	5.28049			0.200734
$693$		0			0
$694$	9.55212			0.362594
$695$	10.6767	−	7.75707i	0.404990	−	0.294242i
$696$		0			0
$697$	−11.4270	+	35.1686i	−0.432827	+	1.33211i
$698$	−11.6516	+	16.0370i	−0.441019	+	0.607011i
$699$		0			0
$700$	−3.24020	−	1.05281i	−0.122468	−	0.0397923i
$701$	−6.52300	−	20.0757i	−0.246370	−	0.758249i	−0.995408	−	0.0957222i	$-0.969484\pi$
$701$	−6.52300	−	20.0757i	−0.246370	−	0.758249i	0.749038	−	0.662527i	$-0.230516\pi$
$702$		0			0
$703$		−	17.0138i		−	0.641689i
$704$	−2.73033	+	1.88289i	−0.102903	+	0.0709642i
$705$		0			0
$706$	−13.3766	−	18.4113i	−0.503434	−	0.692918i
$707$	−4.58022	+	1.48820i	−0.172257	+	0.0559697i
$708$		0			0
$709$	25.6530	+	18.6380i	0.963418	+	0.699964i	0.953942	−	0.299991i	$-0.0969836\pi$
$709$	25.6530	+	18.6380i	0.963418	+	0.699964i	0.00947612	+	0.999955i	$0.496984\pi$
$710$	11.3495	+	8.24589i	0.425939	+	0.309463i
$711$		0			0
$712$	6.41924	−	2.08574i	0.240571	−	0.0781664i
$713$	−5.21435	−	7.17693i	−0.195279	−	0.268778i
$714$		0			0
$715$	9.46445	+	0.232801i	0.353950	+	0.00870627i
$716$		−	4.37969i		−	0.163677i
$717$		0			0
$718$	−5.02591	−	15.4682i	−0.187565	−	0.577267i
$719$	13.2477	+	4.30442i	0.494054	+	0.160528i	0.545438	−	0.838151i	$-0.316363\pi$
$719$	13.2477	+	4.30442i	0.494054	+	0.160528i	−0.0513841	+	0.998679i	$0.516363\pi$
$720$		0			0
$721$	−7.30050	+	10.0483i	−0.271885	+	0.374217i
$722$	−5.07335	+	15.6142i	−0.188811	+	0.581100i
$723$		0			0
$724$	−12.8971	+	9.37028i	−0.479317	+	0.348244i
$725$	12.0912			0.449057
$726$		0			0
$727$	−30.2218			−1.12086			−0.560432	−	0.828201i	$-0.689365\pi$
$727$	−30.2218			−1.12086			−0.560432	+	0.828201i	$0.689365\pi$
$728$	1.82967	−	1.32934i	0.0678123	−	0.0492685i
$729$		0			0
$730$	−0.527618	+	1.62384i	−0.0195280	+	0.0601011i
$731$	15.7716	−	21.7077i	0.583332	−	0.802888i
$732$		0			0
$733$	9.26370	+	3.00996i	0.342163	+	0.111175i	0.475057	−	0.879955i	$-0.342427\pi$
$733$	9.26370	+	3.00996i	0.342163	+	0.111175i	−0.132895	+	0.991130i	$0.542427\pi$
$734$	−8.37309	−	25.7697i	−0.309056	−	0.951178i
$735$		0			0
$736$		−	4.32750i		−	0.159514i
$737$	−6.08865	−	0.149765i	−0.224278	−	0.00551667i
$738$		0			0
$739$	−16.5420	−	22.7681i	−0.608506	−	0.837537i	0.387947	−	0.921682i	$-0.373184\pi$
$739$	−16.5420	−	22.7681i	−0.608506	−	0.837537i	−0.996454	+	0.0841444i	$0.973184\pi$
$740$	3.43172	−	1.11503i	0.126153	−	0.0409895i
$741$		0			0
$742$	−1.80249	−	1.30959i	−0.0661715	−	0.0480764i
$743$	−23.8486	−	17.3270i	−0.874920	−	0.635666i	0.0569829	−	0.998375i	$-0.481852\pi$
$743$	−23.8486	−	17.3270i	−0.874920	−	0.635666i	−0.931902	+	0.362709i	$0.881852\pi$
$744$		0			0
$745$	15.7740	−	5.12528i	0.577914	−	0.187776i
$746$	−0.568117	−	0.781946i	−0.0208003	−	0.0286291i
$747$		0			0
$748$	12.8351	−	8.85132i	0.469296	−	0.323636i
$749$		−	9.82464i		−	0.358984i
$750$		0			0
$751$	−1.28104	−	3.94264i	−0.0467458	−	0.143869i	0.924959	−	0.380066i	$-0.124099\pi$
$751$	−1.28104	−	3.94264i	−0.0467458	−	0.143869i	−0.971705	+	0.236197i	$0.924099\pi$
$752$	−12.2074	−	3.96643i	−0.445158	−	0.144641i
$753$		0			0
$754$	−4.71780	+	6.49349i	−0.171812	+	0.236479i
$755$	5.84337	−	17.9840i	0.212662	−	0.654507i
$756$		0			0
$757$	−27.3652	+	19.8820i	−0.994605	+	0.722623i	−0.960925	−	0.276809i	$-0.910723\pi$
$757$	−27.3652	+	19.8820i	−0.994605	+	0.722623i	−0.0336806	+	0.999433i	$0.510723\pi$
$758$	37.2038			1.35130
$759$		0			0
$760$	−7.51146			−0.272469
$761$	15.2458	−	11.0767i	0.552661	−	0.401532i	−0.276105	−	0.961128i	$-0.589044\pi$
$761$	15.2458	−	11.0767i	0.552661	−	0.401532i	0.828766	+	0.559596i	$0.189044\pi$
$762$		0			0
$763$	−3.47994	+	10.7102i	−0.125982	+	0.387734i
$764$	−12.7805	+	17.5908i	−0.462380	+	0.636412i
$765$		0			0
$766$	23.4461	+	7.61811i	0.847143	+	0.275253i
$767$	6.43890	+	19.8169i	0.232495	+	0.715547i
$768$		0			0
$769$			7.84807i			0.283009i	0.989938	+	0.141504i	$0.0451939\pi$
$769$			7.84807i			0.283009i	−0.989938	+	0.141504i	$0.954806\pi$
$770$	1.39109	−	3.94821i	0.0501313	−	0.142284i
$771$		0			0
$772$	6.29264	+	8.66107i	0.226477	+	0.311719i
$773$	33.2516	−	10.8041i	1.19598	−	0.388596i	0.357697	−	0.933838i	$-0.383562\pi$
$773$	33.2516	−	10.8041i	1.19598	−	0.388596i	0.838279	+	0.545241i	$0.183562\pi$
$774$		0			0
$775$	5.65026	+	4.10515i	0.202963	+	0.147461i
$776$	2.44544	+	1.77672i	0.0877863	+	0.0637805i
$777$		0			0
$778$	29.9322	−	9.72556i	1.07312	−	0.348678i
$779$	−27.5166	−	37.8734i	−0.985886	−	1.35696i
$780$		0			0
$781$	22.3949	−	29.2817i	0.801351	−	1.04778i
$782$			20.3432i			0.727472i
$783$		0			0
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	28.3000	+	9.19522i	1.01007	+	0.328192i
$786$		0			0
$787$	−0.809524	+	1.11421i	−0.0288564	+	0.0397175i	−0.823201	−	0.567749i	$-0.807814\pi$
$787$	−0.809524	+	1.11421i	−0.0288564	+	0.0397175i	0.794345	+	0.607467i	$0.207814\pi$
$788$	−3.57972	+	11.0172i	−0.127522	+	0.392473i
$789$		0			0
$790$	−14.0000	+	10.1716i	−0.498097	+	0.361889i
$791$	12.4192			0.441575
$792$		0			0
$793$	−2.33359			−0.0828684
$794$	3.28271	−	2.38503i	0.116499	−	0.0846414i
$795$		0			0
$796$	4.14995	−	12.7722i	0.147091	−	0.452699i
$797$	10.4576	−	14.3937i	0.370429	−	0.509851i	−0.582589	−	0.812767i	$-0.697960\pi$
$797$	10.4576	−	14.3937i	0.370429	−	0.509851i	0.953017	+	0.302916i	$0.0979601\pi$
$798$		0			0
$799$	57.3860	+	18.6458i	2.03017	+	0.659642i
$800$	1.05281	+	3.24020i	0.0372223	+	0.114559i
$801$		0			0
$802$			38.1853i			1.34837i
$803$	4.23165	+	1.49095i	0.149332	+	0.0526145i
$804$		0			0
$805$	3.21048	+	4.41885i	0.113155	+	0.155744i
$806$	−4.40927	+	1.43266i	−0.155310	+	0.0504633i
$807$		0			0
$808$	3.89617	+	2.83073i	0.137067	+	0.0995848i
$809$	−18.4081	−	13.3743i	−0.647194	−	0.470214i	0.215120	−	0.976588i	$-0.430986\pi$
$809$	−18.4081	−	13.3743i	−0.647194	−	0.470214i	−0.862314	+	0.506374i	$0.830986\pi$
$810$		0			0
$811$	15.0252	−	4.88198i	0.527605	−	0.171429i	−0.0330886	−	0.999452i	$-0.510534\pi$
$811$	15.0252	−	4.88198i	0.527605	−	0.171429i	0.560694	+	0.828023i	$0.310534\pi$
$812$	2.08604	+	2.87119i	0.0732057	+	0.100759i
$813$		0			0
$814$	−2.70739	−	9.08699i	−0.0948939	−	0.318499i
$815$			9.95914i			0.348853i
$816$		0			0
$817$	10.4970	+	32.3065i	0.367245	+	1.13026i
$818$	−23.7411	−	7.71394i	−0.830087	−	0.269712i
$819$		0			0
$820$	5.83578	−	8.03227i	0.203794	−	0.280499i
$821$	−1.52931	+	4.70672i	−0.0533732	+	0.164266i	−0.974190	−	0.225730i	$-0.927523\pi$
$821$	−1.52931	+	4.70672i	−0.0533732	+	0.164266i	0.920817	+	0.389995i	$0.127523\pi$
$822$		0			0
$823$	−0.260325	+	0.189137i	−0.00907435	+	0.00659290i	−0.592313	−	0.805708i	$-0.701785\pi$
$823$	−0.260325	+	0.189137i	−0.00907435	+	0.00659290i	0.583239	+	0.812301i	$0.301785\pi$
$824$	12.4203			0.432683
$825$		0			0
$826$	9.21326			0.320570
$827$	2.86886	−	2.08435i	0.0997600	−	0.0724799i	−0.536787	−	0.843718i	$-0.680362\pi$
$827$	2.86886	−	2.08435i	0.0997600	−	0.0724799i	0.636547	+	0.771238i	$0.280362\pi$
$828$		0			0
$829$	−8.33908	+	25.6650i	−0.289628	+	0.891384i	0.695345	+	0.718676i	$0.255252\pi$
$829$	−8.33908	+	25.6650i	−0.289628	+	0.891384i	−0.984973	+	0.172708i	$0.944748\pi$
$830$	2.55612	−	3.51820i	0.0887243	−	0.122118i
$831$		0			0
$832$	−2.15091	−	0.698874i	−0.0745694	−	0.0242291i
$833$	1.45266	+	4.47084i	0.0503318	+	0.154905i
$834$		0			0
$835$		−	4.13622i		−	0.143140i
$836$	−0.485361	+	19.7322i	−0.0167866	+	0.682452i
$837$		0			0
$838$	−7.06110	−	9.71876i	−0.243921	−	0.335729i
$839$	7.28432	−	2.36682i	0.251483	−	0.0817116i	−0.180563	−	0.983563i	$-0.557792\pi$
$839$	7.28432	−	2.36682i	0.251483	−	0.0817116i	0.432046	+	0.901852i	$0.357792\pi$
$840$		0			0
$841$	13.2717	+	9.64243i	0.457644	+	0.332498i
$842$	−18.5761	−	13.4963i	−0.640175	−	0.465115i
$843$		0			0
$844$	−18.9119	+	6.14485i	−0.650975	+	0.211515i
$845$	−5.84983	−	8.05160i	−0.201240	−	0.276983i
$846$		0			0
$847$	−10.2818	−	3.90942i	−0.353289	−	0.134329i
$848$			2.22800i			0.0765099i
$849$		0			0
$850$	−4.94915	−	15.2319i	−0.169755	−	0.522451i
$851$	11.7662	+	3.82306i	0.403339	+	0.131053i
$852$		0			0
$853$	−18.0789	+	24.8835i	−0.619011	+	0.851996i	−0.997280	−	0.0736996i	$-0.976519\pi$
$853$	−18.0789	+	24.8835i	−0.619011	+	0.851996i	0.378269	+	0.925696i	$0.376519\pi$
$854$	−0.318854	+	0.981331i	−0.0109109	+	0.0335804i
$855$		0			0
$856$	−7.94830	+	5.77478i	−0.271667	+	0.197378i
$857$	57.4958			1.96402			0.982010	−	0.188827i	$-0.0604686\pi$
$857$	57.4958			1.96402			0.982010	+	0.188827i	$0.0604686\pi$
$858$		0			0
$859$	26.6675			0.909885			0.454942	−	0.890521i	$-0.349660\pi$
$859$	26.6675			0.909885			0.454942	+	0.890521i	$0.349660\pi$
$860$	−5.82835	+	4.23455i	−0.198745	+	0.144397i
$861$		0			0
$862$	6.67196	−	20.5342i	0.227248	−	0.699397i
$863$	6.91612	−	9.51922i	0.235427	−	0.324038i	−0.674914	−	0.737897i	$-0.735819\pi$
$863$	6.91612	−	9.51922i	0.235427	−	0.324038i	0.910341	+	0.413859i	$0.135819\pi$
$864$		0			0
$865$	6.33862	+	2.05954i	0.215520	+	0.0700266i
$866$	−3.19036	−	9.81890i	−0.108413	−	0.333660i
$867$		0			0
$868$			2.04996i			0.0695800i
$869$	25.8155	+	37.4344i	0.875732	+	1.26988i
$870$		0			0
$871$	−2.44113	−	3.35992i	−0.0827145	−	0.113847i
$872$	10.7102	−	3.47994i	0.362692	−	0.117846i
$873$		0			0
$874$	−20.8355	−	15.1379i	−0.704773	−	0.512048i
$875$	−8.58441	−	6.23694i	−0.290206	−	0.210847i
$876$		0			0
$877$	−19.6619	+	6.38854i	−0.663935	+	0.215726i	−0.621548	−	0.783376i	$-0.713496\pi$
$877$	−19.6619	+	6.38854i	−0.663935	+	0.215726i	−0.0423865	+	0.999101i	$0.513496\pi$
$878$	6.26097	+	8.61748i	0.211297	+	0.290826i
$879$		0			0
$880$	−4.01183	+	1.19529i	−0.135239	+	0.0402932i
$881$			45.4428i			1.53101i	0.643431	+	0.765504i	$0.277510\pi$
$881$			45.4428i			1.53101i	−0.643431	+	0.765504i	$0.722490\pi$
$882$		0			0
$883$	−9.04496	−	27.8375i	−0.304387	−	0.936807i	−0.979905	−	0.199464i	$-0.936080\pi$
$883$	−9.04496	−	27.8375i	−0.304387	−	0.936807i	0.675518	−	0.737343i	$-0.263920\pi$
$884$	10.1113	+	3.28534i	0.340078	+	0.110498i
$885$		0			0
$886$	−12.8774	+	17.7243i	−0.432626	+	0.595459i
$887$	4.34287	−	13.3660i	0.145819	−	0.448785i	−0.851296	−	0.524685i	$-0.824183\pi$
$887$	4.34287	−	13.3660i	0.145819	−	0.448785i	0.997115	+	0.0759000i	$0.0241830\pi$
$888$		0			0
$889$	10.6778	−	7.75786i	0.358121	−	0.260190i
$890$	8.51906			0.285560
$891$		0			0
$892$	−21.8190			−0.730555
$893$	−61.7995	+	44.9000i	−2.06804	+	1.50252i
$894$		0			0
$895$	1.70821	−	5.25732i	0.0570990	−	0.175733i
$896$	−0.587785	+	0.809017i	−0.0196365	+	0.0270274i
$897$		0			0
$898$	28.3659	+	9.21665i	0.946583	+	0.307564i
$899$	−2.24818	−	6.91919i	−0.0749810	−	0.230768i
$900$		0			0
$901$		−	10.4736i		−	0.348928i
$902$	−20.7232	−	15.8493i	−0.690008	−	0.527724i
$903$		0			0
$904$	−7.29980	−	10.0473i	−0.242788	−	0.334169i
$905$	−19.1362	+	6.21771i	−0.636107	+	0.206684i
$906$		0			0
$907$	−36.4198	−	26.4605i	−1.20930	−	0.878607i	−0.214131	−	0.976805i	$-0.568692\pi$
$907$	−36.4198	−	26.4605i	−1.20930	−	0.878607i	−0.995167	+	0.0981984i	$0.968692\pi$
$908$	−6.28179	−	4.56399i	−0.208469	−	0.151461i
$909$		0			0
$910$	2.71479	−	0.882090i	0.0899945	−	0.0292410i
$911$	10.2893	+	14.1620i	0.340900	+	0.469209i	0.944704	−	0.327924i	$-0.106349\pi$
$911$	10.2893	+	14.1620i	0.340900	+	0.469209i	−0.603804	+	0.797133i	$0.706349\pi$
$912$		0			0
$913$	−9.07694	−	6.94212i	−0.300403	−	0.229751i
$914$		−	39.9143i		−	1.32025i
$915$		0			0
$916$	4.68885	+	14.4308i	0.154924	+	0.476807i
$917$	−8.74957	−	2.84291i	−0.288936	−	0.0938811i
$918$		0			0
$919$	11.6663	−	16.0573i	0.384836	−	0.529681i	−0.572022	−	0.820238i	$-0.693841\pi$
$919$	11.6663	−	16.0573i	0.384836	−	0.529681i	0.956858	+	0.290557i	$0.0938407\pi$
$920$	1.68785	−	5.19467i	0.0556467	−	0.171263i
$921$		0			0
$922$	−2.99800	+	2.17818i	−0.0987340	+	0.0717345i
$923$	25.1374			0.827409
$924$		0			0
$925$	−9.73997			−0.320248
$926$	6.74153	−	4.89801i	0.221540	−	0.160959i
$927$		0			0
$928$	1.09670	−	3.37529i	0.0360009	−	0.110799i
$929$	2.62915	−	3.61871i	0.0862595	−	0.118726i	−0.763706	−	0.645564i	$-0.776622\pi$
$929$	2.62915	−	3.61871i	0.0862595	−	0.118726i	0.849966	+	0.526838i	$0.176622\pi$
$930$		0			0
$931$	−5.66000	−	1.83905i	−0.185499	−	0.0602723i
$932$	−1.96460	−	6.04641i	−0.0643526	−	0.198057i
$933$		0			0
$934$			6.31614i			0.206670i
$935$	18.8593	−	5.61895i	0.616764	−	0.183759i
$936$		0			0
$937$	−10.5308	−	14.4945i	−0.344027	−	0.473513i	0.601585	−	0.798809i	$-0.294536\pi$
$937$	−10.5308	−	14.4945i	−0.344027	−	0.473513i	−0.945612	+	0.325296i	$0.894536\pi$
$938$	−1.74647	+	0.567464i	−0.0570244	+	0.0185283i
$939$		0			0
$940$	−13.1066	−	9.52248i	−0.427489	−	0.310589i
$941$	18.0214	+	13.0933i	0.587482	+	0.426831i	0.841414	−	0.540392i	$-0.181724\pi$
$941$	18.0214	+	13.0933i	0.587482	+	0.426831i	−0.253932	+	0.967222i	$0.581724\pi$
$942$		0			0
$943$	32.3750	−	10.5193i	1.05427	−	0.342555i
$944$	−5.41542	−	7.45368i	−0.176257	−	0.242597i
$945$		0			0
$946$	10.7473	+	15.5844i	0.349425	+	0.506692i
$947$		−	6.54279i		−	0.212612i	−0.994333	−	0.106306i	$-0.966098\pi$
$947$		−	6.54279i		−	0.212612i	0.994333	−	0.106306i	$-0.0339023\pi$
$948$		0			0
$949$	0.945414	+	2.90968i	0.0306894	+	0.0944523i
$950$	19.2834	+	6.26554i	0.625635	+	0.203281i
$951$		0			0
$952$	2.76313	−	3.80312i	0.0895535	−	0.123260i
$953$	−4.22309	+	12.9973i	−0.136799	+	0.421025i	−0.995866	−	0.0908396i	$-0.971045\pi$
$953$	−4.22309	+	12.9973i	−0.136799	+	0.421025i	0.859066	+	0.511864i	$0.171045\pi$
$954$		0			0
$955$	−22.2024	+	16.1310i	−0.718452	+	0.521986i
$956$	24.6015			0.795668
$957$		0			0
$958$	10.8555			0.350726
$959$	13.9423	−	10.1296i	0.450219	−	0.327103i
$960$		0			0
$961$	−8.28094	+	25.4861i	−0.267127	+	0.822133i
$962$	3.80038	−	5.23077i	0.122529	−	0.168647i
$963$		0			0
$964$	−3.15932	−	1.02653i	−0.101755	−	0.0330622i
$965$	4.17552	+	12.8509i	0.134415	+	0.413686i
$966$		0			0
$967$		−	54.3113i		−	1.74653i	−0.487241	−	0.873267i	$-0.661997\pi$
$967$		−	54.3113i		−	1.74653i	0.487241	−	0.873267i	$-0.338003\pi$
$968$	2.88073	+	10.6161i	0.0925901	+	0.341214i
$969$		0			0
$970$	2.24250	+	3.08654i	0.0720024	+	0.0991028i
$971$	−32.7802	+	10.6509i	−1.05197	+	0.341804i	−0.783439	−	0.621468i	$-0.786536\pi$
$971$	−32.7802	+	10.6509i	−1.05197	+	0.341804i	−0.268526	+	0.963272i	$0.586536\pi$
$972$		0			0
$973$	−8.45906	−	6.14587i	−0.271185	−	0.197028i
$974$	−1.48252	−	1.07711i	−0.0475029	−	0.0345129i
$975$		0			0
$976$	0.981331	−	0.318854i	0.0314116	−	0.0102063i
$977$	13.9113	+	19.1473i	0.445063	+	0.612577i	0.971328	−	0.237744i	$-0.0764079\pi$
$977$	13.9113	+	19.1473i	0.445063	+	0.612577i	−0.526265	+	0.850321i	$0.676408\pi$
$978$		0			0
$979$	0.550468	−	22.3791i	0.0175930	−	0.715239i
$980$		−	1.26216i		−	0.0403182i
$981$		0			0
$982$	4.66453	+	14.3560i	0.148851	+	0.458117i
$983$	−53.9618	−	17.5332i	−1.72111	−	0.559223i	−0.728994	−	0.684521i	$-0.760012\pi$
$983$	−53.9618	−	17.5332i	−1.72111	−	0.559223i	−0.992119	+	0.125297i	$0.960012\pi$
$984$		0			0
$985$	−8.59408	+	11.8287i	−0.273830	+	0.376895i
$986$	−5.15548	+	15.8669i	−0.164184	+	0.505306i
$987$		0			0
$988$	−10.8889	+	7.91125i	−0.346422	+	0.251690i
$989$	−24.7008			−0.785439
$990$		0			0
$991$	−9.09545			−0.288926			−0.144463	−	0.989510i	$-0.546146\pi$
$991$	−9.09545			−0.288926			−0.144463	+	0.989510i	$0.546146\pi$
$992$	1.65845	−	1.20493i	0.0526558	−	0.0382567i
$993$		0			0
$994$	3.43469	−	10.5709i	0.108942	−	0.335288i
$995$	9.96307	−	13.7130i	0.315851	−	0.434731i
$996$		0			0
$997$	−33.0102	−	10.7257i	−1.04544	−	0.339685i	−0.264565	−	0.964368i	$-0.585228\pi$
$997$	−33.0102	−	10.7257i	−1.04544	−	0.339685i	−0.780879	+	0.624683i	$0.785228\pi$
$998$	−10.2855	−	31.6557i	−0.325583	−	1.00204i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.a.701.7	✓	48
3.2	odd	2		1386.2.bu.b.701.6	yes	48
11.7	odd	10		1386.2.bu.b.953.6	yes	48
33.29	even	10	inner	1386.2.bu.a.953.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.701.7	✓	48	1.1	even	1	trivial
1386.2.bu.a.953.7	yes	48	33.29	even	10	inner
1386.2.bu.b.701.6	yes	48	3.2	odd	2
1386.2.bu.b.953.6	yes	48	11.7	odd	10

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.741879 - 1.02111i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.741879 - 1.02111i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +1.26216i q^{10} +(3.31562 + 0.0815558i) q^{11} +(1.32934 + 1.82967i) q^{13} +(0.951057 - 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(3.80312 + 2.76313i) q^{17} +(-5.66000 + 1.83905i) q^{19} +(-0.741879 - 1.02111i) q^{20} +(-2.73033 + 1.88289i) q^{22} -4.32750i q^{23} +(1.05281 + 3.24020i) q^{25} +(-2.15091 - 0.698874i) q^{26} +(-0.587785 + 0.809017i) q^{28} +(1.09670 - 3.37529i) q^{29} +(1.65845 - 1.20493i) q^{31} +1.00000 q^{32} -4.70091 q^{34} +(-1.02111 + 0.741879i) q^{35} +(-0.883434 + 2.71893i) q^{37} +(3.49807 - 4.81469i) q^{38} +(1.20039 + 0.390029i) q^{40} +(2.43080 + 7.48122i) q^{41} -5.70787i q^{43} +(1.10215 - 3.12814i) q^{44} +(2.54364 + 3.50102i) q^{46} +(12.2074 - 3.96643i) q^{47} +(0.809017 + 0.587785i) q^{49} +(-2.75628 - 2.00256i) q^{50} +(2.15091 - 0.698874i) q^{52} +(-1.30959 - 1.80249i) q^{53} +(2.54307 - 3.32511i) q^{55} -1.00000i q^{56} +(1.09670 + 3.37529i) q^{58} +(8.76233 + 2.84705i) q^{59} +(-0.606496 + 0.834770i) q^{61} +(-0.633471 + 1.94962i) q^{62} +(-0.809017 + 0.587785i) q^{64} +2.85450 q^{65} -1.83635 q^{67} +(3.80312 - 2.76313i) q^{68} +(0.390029 - 1.20039i) q^{70} +(6.53316 - 8.99213i) q^{71} +(1.28656 + 0.418028i) q^{73} +(-0.883434 - 2.71893i) q^{74} +5.95128i q^{76} +(-3.12814 - 1.10215i) q^{77} +(8.05887 + 11.0921i) q^{79} +(-1.20039 + 0.390029i) q^{80} +(-6.36391 - 4.62365i) q^{82} +(-2.78744 - 2.02520i) q^{83} +(5.64291 - 1.83349i) q^{85} +(3.35500 + 4.61776i) q^{86} +(0.947019 + 3.17855i) q^{88} -6.74959i q^{89} +(-0.698874 - 2.15091i) q^{91} +(-4.11570 - 1.33727i) q^{92} +(-7.54459 + 10.3842i) q^{94} +(-2.32117 + 7.14383i) q^{95} +(2.44544 - 1.77672i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

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