LMFDB - Embedded newform 722.2.e.f.245.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			245.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	722.245
Dual form			722.2.e.f.389.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.347296 - 1.96962i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.347296 - 1.96962i) q^{9} +(3.00000 - 5.19615i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(3.83022 - 3.21394i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.520945 - 2.95442i) q^{17} +2.00000 q^{18} +(-0.173648 + 0.984808i) q^{21} +(4.59627 + 3.85673i) q^{22} +(-2.81908 - 1.02606i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-3.83022 + 3.21394i) q^{25} +(2.50000 + 4.33013i) q^{26} +(2.50000 - 4.33013i) q^{27} +(-0.173648 - 0.984808i) q^{28} +(1.56283 + 8.86327i) q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(5.63816 - 2.05212i) q^{33} +(2.81908 + 1.02606i) q^{34} +(-0.347296 + 1.96962i) q^{36} +2.00000 q^{37} +5.00000 q^{39} +(-0.939693 - 0.342020i) q^{42} +(-7.51754 + 2.73616i) q^{43} +(-4.59627 + 3.85673i) q^{44} +(1.50000 - 2.59808i) q^{46} +(0.173648 + 0.984808i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-2.50000 - 4.33013i) q^{50} +(2.29813 - 1.92836i) q^{51} +(-4.69846 + 1.71010i) q^{52} +(2.81908 + 1.02606i) q^{53} +(3.83022 + 3.21394i) q^{54} +1.00000 q^{56} -9.00000 q^{58} +(1.56283 - 8.86327i) q^{59} +(9.39693 + 3.42020i) q^{61} +(-3.75877 + 1.36808i) q^{62} +(1.53209 - 1.28558i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.04189 + 5.90885i) q^{66} +(0.868241 + 4.92404i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-1.50000 - 2.59808i) q^{69} +(5.63816 - 2.05212i) q^{71} +(-1.87939 - 0.684040i) q^{72} +(-5.36231 - 4.49951i) q^{73} +(-0.347296 + 1.96962i) q^{74} -5.00000 q^{75} +6.00000 q^{77} +(-0.868241 + 4.92404i) q^{78} +(-7.66044 - 6.42788i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(3.00000 + 5.19615i) q^{83} +(0.500000 - 0.866025i) q^{84} +(-1.38919 - 7.87846i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(-9.19253 + 7.71345i) q^{89} +(4.69846 + 1.71010i) q^{91} +(2.29813 + 1.92836i) q^{92} +(-0.694593 + 3.93923i) q^{93} -1.00000 q^{96} +(-1.73648 + 9.84808i) q^{97} +(4.59627 + 3.85673i) q^{98} +(-11.2763 - 4.10424i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^7 + 3 * q^8	$ 6 q + 3 q^{7} + 3 q^{8} + 18 q^{11} - 3 q^{12} + 12 q^{18} + 15 q^{26} + 15 q^{27} + 12 q^{31} + 12 q^{37} + 30 q^{39} + 9 q^{46} + 18 q^{49} - 15 q^{50} + 6 q^{56} - 54 q^{58} - 3 q^{64} - 9 q^{68} - 9 q^{69} - 30 q^{75} + 36 q^{77} + 18 q^{83} + 3 q^{84} - 27 q^{87} - 18 q^{88} - 6 q^{96}+O(q^{100}) $ 6 * q + 3 * q^7 + 3 * q^8 + 18 * q^11 - 3 * q^12 + 12 * q^18 + 15 * q^26 + 15 * q^27 + 12 * q^31 + 12 * q^37 + 30 * q^39 + 9 * q^46 + 18 * q^49 - 15 * q^50 + 6 * q^56 - 54 * q^58 - 3 * q^64 - 9 * q^68 - 9 * q^69 - 30 * q^75 + 36 * q^77 + 18 * q^83 + 3 * q^84 - 27 * q^87 - 18 * q^88 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i	0.836560	−	0.547875i	$-0.184563\pi$
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i	−0.394284	+	0.918989i	$0.629007\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$5$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.347296	−	1.96962i	−0.115765	−	0.656539i
$10$		0			0
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	3.83022	−	3.21394i	1.06231	−	0.891386i	0.0679785	−	0.997687i	$-0.478345\pi$
$13$	3.83022	−	3.21394i	1.06231	−	0.891386i	0.994334	+	0.106301i	$0.0339006\pi$
$14$	−0.939693	+	0.342020i	−0.251143	+	0.0914087i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.520945	−	2.95442i	0.126348	−	0.716553i	−0.854151	−	0.520026i	$-0.825922\pi$
$17$	0.520945	−	2.95442i	0.126348	−	0.716553i	0.980498	−	0.196527i	$-0.0629665\pi$
$18$	2.00000			0.471405
$19$		0			0
$19$		0			0
$20$		0			0
$21$	−0.173648	+	0.984808i	−0.0378931	+	0.214903i
$22$	4.59627	+	3.85673i	0.979927	+	0.822257i
$23$	−2.81908	−	1.02606i	−0.587818	−	0.213948i	0.0309512	−	0.999521i	$-0.490146\pi$
$23$	−2.81908	−	1.02606i	−0.587818	−	0.213948i	−0.618770	+	0.785573i	$0.712369\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	−3.83022	+	3.21394i	−0.766044	+	0.642788i
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$	2.50000	−	4.33013i	0.481125	−	0.833333i
$28$	−0.173648	−	0.984808i	−0.0328164	−	0.186111i
$29$	1.56283	+	8.86327i	0.290211	+	1.64587i	0.686055	+	0.727550i	$0.259341\pi$
$29$	1.56283	+	8.86327i	0.290211	+	1.64587i	−0.395844	+	0.918318i	$0.629548\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	5.63816	−	2.05212i	0.981477	−	0.357228i
$34$	2.81908	+	1.02606i	0.483468	+	0.175968i
$35$		0			0
$36$	−0.347296	+	1.96962i	−0.0578827	+	0.328269i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	5.00000			0.800641
$40$		0			0
$41$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$41$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$42$	−0.939693	−	0.342020i	−0.144998	−	0.0527749i
$43$	−7.51754	+	2.73616i	−1.14641	+	0.417261i	−0.844226	−	0.535988i	$-0.819939\pi$
$43$	−7.51754	+	2.73616i	−1.14641	+	0.417261i	−0.302188	+	0.953248i	$0.597717\pi$
$44$	−4.59627	+	3.85673i	−0.692913	+	0.581423i
$45$		0			0
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$47$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$48$	0.173648	+	0.984808i	0.0250640	+	0.142145i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−2.50000	−	4.33013i	−0.353553	−	0.612372i
$51$	2.29813	−	1.92836i	0.321803	−	0.270025i
$52$	−4.69846	+	1.71010i	−0.651560	+	0.237148i
$53$	2.81908	+	1.02606i	0.387230	+	0.140940i	0.528297	−	0.849060i	$-0.322831\pi$
$53$	2.81908	+	1.02606i	0.387230	+	0.140940i	−0.141066	+	0.990000i	$0.545053\pi$
$54$	3.83022	+	3.21394i	0.521227	+	0.437362i
$55$		0			0
$56$	1.00000			0.133631
$57$		0			0
$58$	−9.00000			−1.18176
$59$	1.56283	−	8.86327i	0.203464	−	1.15390i	−0.696376	−	0.717678i	$-0.745205\pi$
$59$	1.56283	−	8.86327i	0.203464	−	1.15390i	0.899839	−	0.436222i	$-0.143684\pi$
$60$		0			0
$61$	9.39693	+	3.42020i	1.20315	+	0.437912i	0.864324	−	0.502936i	$-0.167747\pi$
$61$	9.39693	+	3.42020i	1.20315	+	0.437912i	0.338829	+	0.940848i	$0.389969\pi$
$62$	−3.75877	+	1.36808i	−0.477364	+	0.173746i
$63$	1.53209	−	1.28558i	0.193025	−	0.161967i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	1.04189	+	5.90885i	0.128248	+	0.727329i
$67$	0.868241	+	4.92404i	0.106073	+	0.601567i	0.990787	+	0.135433i	$0.0432425\pi$
$67$	0.868241	+	4.92404i	0.106073	+	0.601567i	−0.884714	+	0.466134i	$0.845646\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	−1.50000	−	2.59808i	−0.180579	−	0.312772i
$70$		0			0
$71$	5.63816	−	2.05212i	0.669126	−	0.243542i	0.0149545	−	0.999888i	$-0.495240\pi$
$71$	5.63816	−	2.05212i	0.669126	−	0.243542i	0.654172	+	0.756346i	$0.273017\pi$
$72$	−1.87939	−	0.684040i	−0.221488	−	0.0806149i
$73$	−5.36231	−	4.49951i	−0.627611	−	0.526628i	0.272575	−	0.962135i	$-0.412125\pi$
$73$	−5.36231	−	4.49951i	−0.627611	−	0.526628i	−0.900186	+	0.435506i	$0.856569\pi$
$74$	−0.347296	+	1.96962i	−0.0403724	+	0.228963i
$75$	−5.00000			−0.577350
$76$		0			0
$77$	6.00000			0.683763
$78$	−0.868241	+	4.92404i	−0.0983089	+	0.557538i
$79$	−7.66044	−	6.42788i	−0.861867	−	0.723193i	0.100502	−	0.994937i	$-0.467955\pi$
$79$	−7.66044	−	6.42788i	−0.861867	−	0.723193i	−0.962369	+	0.271744i	$0.912400\pi$
$80$		0			0
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$		0			0
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$	0.500000	−	0.866025i	0.0545545	−	0.0944911i
$85$		0			0
$86$	−1.38919	−	7.87846i	−0.149800	−	0.849556i
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$	−9.19253	+	7.71345i	−0.974407	+	0.817624i	−0.983236	−	0.182337i	$-0.941634\pi$
$89$	−9.19253	+	7.71345i	−0.974407	+	0.817624i	0.00882955	+	0.999961i	$0.497189\pi$
$90$		0			0
$91$	4.69846	+	1.71010i	0.492533	+	0.179267i
$92$	2.29813	+	1.92836i	0.239597	+	0.201046i
$93$	−0.694593	+	3.93923i	−0.0720259	+	0.408479i
$94$		0			0
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−1.73648	+	9.84808i	−0.176313	+	0.999921i	0.760304	+	0.649567i	$0.225050\pi$
$97$	−1.73648	+	9.84808i	−0.176313	+	0.999921i	−0.936617	+	0.350354i	$0.886061\pi$
$98$	4.59627	+	3.85673i	0.464293	+	0.389588i
$99$	−11.2763	−	4.10424i	−1.13331	−	0.412492i
$100$	4.69846	−	1.71010i	0.469846	−	0.171010i
$101$	13.7888	−	11.5702i	1.37204	−	1.15128i	0.399982	−	0.916523i	$-0.369016\pi$
$101$	13.7888	−	11.5702i	1.37204	−	1.15128i	0.972055	−	0.234753i	$-0.0754280\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$	−0.868241	−	4.92404i	−0.0851380	−	0.482842i
$105$		0			0
$106$	−1.50000	+	2.59808i	−0.145693	+	0.252347i
$107$	4.50000	+	7.79423i	0.435031	+	0.753497i	0.997298	−	0.0734594i	$-0.0234039\pi$
$107$	4.50000	+	7.79423i	0.435031	+	0.753497i	−0.562267	+	0.826956i	$0.690071\pi$
$108$	−3.83022	+	3.21394i	−0.368563	+	0.309261i
$109$	−10.3366	+	3.76222i	−0.990069	+	0.360355i	−0.785747	−	0.618548i	$-0.787721\pi$
$109$	−10.3366	+	3.76222i	−0.990069	+	0.360355i	−0.204322	+	0.978904i	$0.565499\pi$
$110$		0			0
$111$	1.53209	+	1.28558i	0.145419	+	0.122021i
$112$	−0.173648	+	0.984808i	−0.0164082	+	0.0930556i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$		0			0
$116$	1.56283	−	8.86327i	0.145105	−	0.822934i
$117$	−7.66044	−	6.42788i	−0.708208	−	0.594257i
$118$	8.45723	+	3.07818i	0.778551	+	0.283370i
$119$	2.81908	−	1.02606i	0.258424	−	0.0940588i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	−5.00000	+	8.66025i	−0.452679	+	0.784063i
$123$		0			0
$124$	−0.694593	−	3.93923i	−0.0623763	−	0.353753i
$125$		0			0
$126$	1.00000	+	1.73205i	0.0890871	+	0.154303i
$127$	1.53209	−	1.28558i	0.135951	−	0.114076i	−0.572276	−	0.820061i	$-0.693940\pi$
$127$	1.53209	−	1.28558i	0.135951	−	0.114076i	0.708227	+	0.705984i	$0.249495\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−7.51754	−	2.73616i	−0.661883	−	0.240906i
$130$		0			0
$131$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$131$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$	−5.00000			−0.431934
$135$		0			0
$136$	−2.29813	−	1.92836i	−0.197063	−	0.165356i
$137$	8.45723	+	3.07818i	0.722550	+	0.262987i	0.677008	−	0.735976i	$-0.263276\pi$
$137$	8.45723	+	3.07818i	0.722550	+	0.262987i	0.0455422	+	0.998962i	$0.485498\pi$
$138$	2.81908	−	1.02606i	0.239976	−	0.0873441i
$139$	−3.06418	+	2.57115i	−0.259900	+	0.218082i	−0.763421	−	0.645901i	$-0.776482\pi$
$139$	−3.06418	+	2.57115i	−0.259900	+	0.218082i	0.503521	+	0.863983i	$0.332038\pi$
$140$		0			0
$141$		0			0
$142$	1.04189	+	5.90885i	0.0874334	+	0.495859i
$143$	−5.20945	−	29.5442i	−0.435636	−	2.47061i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$		0			0
$146$	5.36231	−	4.49951i	0.443788	−	0.372382i
$147$	5.63816	−	2.05212i	0.465027	−	0.169256i
$148$	−1.87939	−	0.684040i	−0.154485	−	0.0562278i
$149$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$149$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$150$	0.868241	−	4.92404i	0.0708916	−	0.402046i
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	−1.04189	+	5.90885i	−0.0839578	+	0.476148i
$155$		0			0
$156$	−4.69846	−	1.71010i	−0.376178	−	0.136918i
$157$	20.6732	−	7.52444i	1.64990	−	0.600516i	0.661175	−	0.750232i	$-0.270058\pi$
$157$	20.6732	−	7.52444i	1.64990	−	0.600516i	0.988729	+	0.149716i	$0.0478359\pi$
$158$	7.66044	−	6.42788i	0.609432	−	0.511374i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$		0			0
$161$	−0.520945	−	2.95442i	−0.0410562	−	0.232841i
$162$	−0.173648	−	0.984808i	−0.0136431	−	0.0773738i
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$		0			0
$165$		0			0
$166$	−5.63816	+	2.05212i	−0.437606	+	0.159275i
$167$	−11.2763	−	4.10424i	−0.872587	−	0.317596i	−0.133373	−	0.991066i	$-0.542581\pi$
$167$	−11.2763	−	4.10424i	−0.872587	−	0.317596i	−0.739214	+	0.673470i	$0.764803\pi$
$168$	0.766044	+	0.642788i	0.0591016	+	0.0495921i
$169$	2.08378	−	11.8177i	0.160291	−	0.909053i
$170$		0			0
$171$		0			0
$172$	8.00000			0.609994
$173$	1.04189	−	5.90885i	0.0792134	−	0.449241i	−0.919243	−	0.393692i	$-0.871198\pi$
$173$	1.04189	−	5.90885i	0.0792134	−	0.449241i	0.998456	−	0.0555496i	$-0.0176911\pi$
$174$	−6.89440	−	5.78509i	−0.522663	−	0.438566i
$175$	−4.69846	−	1.71010i	−0.355170	−	0.129271i
$176$	5.63816	−	2.05212i	0.424992	−	0.154684i
$177$	6.89440	−	5.78509i	0.518215	−	0.434834i
$178$	−6.00000	−	10.3923i	−0.449719	−	0.778936i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$		0			0
$181$	0.347296	+	1.96962i	0.0258143	+	0.146400i	0.994991	−	0.0999676i	$-0.0318739\pi$
$181$	0.347296	+	1.96962i	0.0258143	+	0.146400i	−0.969176	+	0.246368i	$0.920763\pi$
$182$	−2.50000	+	4.33013i	−0.185312	+	0.320970i
$183$	5.00000	+	8.66025i	0.369611	+	0.640184i
$184$	−2.29813	+	1.92836i	−0.169421	+	0.142161i
$185$		0			0
$186$	−3.75877	−	1.36808i	−0.275606	−	0.100313i
$187$	−13.7888	−	11.5702i	−1.00834	−	0.846095i
$188$		0			0
$189$	5.00000			0.363696
$190$		0			0
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	0.173648	−	0.984808i	0.0125320	−	0.0710724i
$193$	10.7246	+	8.99903i	0.771975	+	0.647764i	0.941214	−	0.337811i	$-0.109686\pi$
$193$	10.7246	+	8.99903i	0.771975	+	0.647764i	−0.169239	+	0.985575i	$0.554131\pi$
$194$	−9.39693	−	3.42020i	−0.674660	−	0.245556i
$195$		0			0
$196$	−4.59627	+	3.85673i	−0.328305	+	0.275480i
$197$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$197$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$198$	6.00000	−	10.3923i	0.426401	−	0.738549i
$199$	1.91013	+	10.8329i	0.135406	+	0.767923i	0.974576	+	0.224055i	$0.0719296\pi$
$199$	1.91013	+	10.8329i	0.135406	+	0.767923i	−0.839171	+	0.543868i	$0.816959\pi$
$200$	0.868241	+	4.92404i	0.0613939	+	0.348182i
$201$	−2.50000	+	4.33013i	−0.176336	+	0.305424i
$202$	9.00000	+	15.5885i	0.633238	+	1.09680i
$203$	−6.89440	+	5.78509i	−0.483892	+	0.406034i
$204$	−2.81908	+	1.02606i	−0.197375	+	0.0718386i
$205$		0			0
$206$	−10.7246	−	8.99903i	−0.747220	−	0.626992i
$207$	−1.04189	+	5.90885i	−0.0724163	+	0.410693i
$208$	5.00000			0.346688
$209$		0			0
$210$		0			0
$211$	0.868241	−	4.92404i	0.0597722	−	0.338985i	−0.940227	−	0.340549i	$-0.889387\pi$
$211$	0.868241	−	4.92404i	0.0597722	−	0.338985i	0.999999	+	0.00156464i	$0.000498040\pi$
$212$	−2.29813	−	1.92836i	−0.157836	−	0.132441i
$213$	5.63816	+	2.05212i	0.386320	+	0.140609i
$214$	−8.45723	+	3.07818i	−0.578125	+	0.210420i
$215$		0			0
$216$	−2.50000	−	4.33013i	−0.170103	−	0.294628i
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$	−1.91013	−	10.8329i	−0.129370	−	0.733696i
$219$	−1.21554	−	6.89365i	−0.0821384	−	0.465830i
$220$		0			0
$221$	−7.50000	−	12.9904i	−0.504505	−	0.873828i
$222$	−1.53209	+	1.28558i	−0.102827	+	0.0862822i
$223$	−24.4320	+	8.89252i	−1.63609	+	0.595487i	−0.986349	−	0.164670i	$-0.947344\pi$
$223$	−24.4320	+	8.89252i	−1.63609	+	0.595487i	−0.649739	+	0.760157i	$0.725122\pi$
$224$	−0.939693	−	0.342020i	−0.0627859	−	0.0228522i
$225$	7.66044	+	6.42788i	0.510696	+	0.428525i
$226$	−1.04189	+	5.90885i	−0.0693054	+	0.393051i
$227$	−15.0000			−0.995585			−0.497792	−	0.867296i	$-0.665856\pi$
$227$	−15.0000			−0.995585			−0.497792	+	0.867296i	$0.665856\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	4.59627	+	3.85673i	0.302412	+	0.253754i
$232$	8.45723	+	3.07818i	0.555245	+	0.202093i
$233$	5.63816	−	2.05212i	0.369368	−	0.134439i	−0.150666	−	0.988585i	$-0.548142\pi$
$233$	5.63816	−	2.05212i	0.369368	−	0.134439i	0.520033	+	0.854146i	$0.325919\pi$
$234$	7.66044	−	6.42788i	0.500779	−	0.420203i
$235$		0			0
$236$	−4.50000	+	7.79423i	−0.292925	+	0.507361i
$237$	−1.73648	−	9.84808i	−0.112797	−	0.639701i
$238$	0.520945	+	2.95442i	0.0337678	+	0.191507i
$239$	10.5000	−	18.1865i	0.679189	−	1.17639i	−0.296037	−	0.955176i	$-0.595665\pi$
$239$	10.5000	−	18.1865i	0.679189	−	1.17639i	0.975226	−	0.221213i	$-0.0710015\pi$
$240$		0			0
$241$	6.12836	−	5.14230i	0.394762	−	0.331245i	−0.423703	−	0.905801i	$-0.639270\pi$
$241$	6.12836	−	5.14230i	0.394762	−	0.331245i	0.818465	+	0.574557i	$0.194825\pi$
$242$	23.4923	−	8.55050i	1.51014	−	0.549647i
$243$	−15.0351	−	5.47232i	−0.964501	−	0.351050i
$244$	−7.66044	−	6.42788i	−0.490410	−	0.411503i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	4.00000			0.254000
$249$	−1.04189	+	5.90885i	−0.0660270	+	0.374458i
$250$		0			0
$251$	−5.63816	−	2.05212i	−0.355877	−	0.129529i	0.157894	−	0.987456i	$-0.449530\pi$
$251$	−5.63816	−	2.05212i	−0.355877	−	0.129529i	−0.513771	+	0.857927i	$0.671752\pi$
$252$	−1.87939	+	0.684040i	−0.118390	+	0.0430905i
$253$	−13.7888	+	11.5702i	−0.866894	+	0.727411i
$254$	1.00000	+	1.73205i	0.0627456	+	0.108679i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	2.08378	+	11.8177i	0.129983	+	0.737167i	0.978223	+	0.207556i	$0.0665510\pi$
$257$	2.08378	+	11.8177i	0.129983	+	0.737167i	−0.848241	+	0.529611i	$0.822338\pi$
$258$	4.00000	−	6.92820i	0.249029	−	0.431331i
$259$	1.00000	+	1.73205i	0.0621370	+	0.107624i
$260$		0			0
$261$	16.9145	−	6.15636i	1.04698	−	0.381069i
$262$		0			0
$263$	18.3851	+	15.4269i	1.13367	+	0.951264i	0.999213	−	0.0396557i	$-0.0126261\pi$
$263$	18.3851	+	15.4269i	1.13367	+	0.951264i	0.134458	+	0.990919i	$0.457071\pi$
$264$	1.04189	−	5.90885i	0.0641238	−	0.363664i
$265$		0			0
$266$		0			0
$267$	−12.0000			−0.734388
$268$	0.868241	−	4.92404i	0.0530363	−	0.300784i
$269$	−4.59627	−	3.85673i	−0.280239	−	0.235149i	0.491824	−	0.870695i	$-0.336331\pi$
$269$	−4.59627	−	3.85673i	−0.280239	−	0.235149i	−0.772063	+	0.635546i	$0.780775\pi$
$270$		0			0
$271$	−10.3366	+	3.76222i	−0.627905	+	0.228539i	−0.636319	−	0.771426i	$-0.719544\pi$
$271$	−10.3366	+	3.76222i	−0.627905	+	0.228539i	0.00841427	+	0.999965i	$0.497322\pi$
$272$	2.29813	−	1.92836i	0.139345	−	0.116924i
$273$	2.50000	+	4.33013i	0.151307	+	0.262071i
$274$	−4.50000	+	7.79423i	−0.271855	+	0.470867i
$275$	5.20945	+	29.5442i	0.314141	+	1.78158i
$276$	0.520945	+	2.95442i	0.0313572	+	0.177835i
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	−2.00000	−	3.46410i	−0.119952	−	0.207763i
$279$	6.12836	−	5.14230i	0.366895	−	0.307862i
$280$		0			0
$281$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$281$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$282$		0			0
$283$	−3.82026	+	21.6658i	−0.227091	+	1.28790i	0.631557	+	0.775330i	$0.282416\pi$
$283$	−3.82026	+	21.6658i	−0.227091	+	1.28790i	−0.858647	+	0.512567i	$0.828695\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	30.0000			1.77394
$287$		0			0
$288$	1.53209	+	1.28558i	0.0902792	+	0.0757532i
$289$	7.51754	+	2.73616i	0.442208	+	0.160951i
$290$		0			0
$291$	−7.66044	+	6.42788i	−0.449063	+	0.376809i
$292$	3.50000	+	6.06218i	0.204822	+	0.354762i
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	−0.377244	−	0.926114i	$-0.623128\pi$
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	0.990660	−	0.136355i	$-0.0435386\pi$
$294$	1.04189	+	5.90885i	0.0607642	+	0.344611i
$295$		0			0
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	−15.0000	−	25.9808i	−0.870388	−	1.50756i
$298$		0			0
$299$	−14.0954	+	5.13030i	−0.815157	+	0.296693i
$300$	4.69846	+	1.71010i	0.271266	+	0.0987327i
$301$	−6.12836	−	5.14230i	−0.353233	−	0.296397i
$302$	1.73648	−	9.84808i	0.0999233	−	0.566693i
$303$	18.0000			1.03407
$304$		0			0
$305$		0			0
$306$	1.04189	−	5.90885i	0.0595608	−	0.337786i
$307$	15.3209	+	12.8558i	0.874409	+	0.733717i	0.965022	−	0.262170i	$-0.0844380\pi$
$307$	15.3209	+	12.8558i	0.874409	+	0.733717i	−0.0906125	+	0.995886i	$0.528882\pi$
$308$	−5.63816	−	2.05212i	−0.321264	−	0.116930i
$309$	−13.1557	+	4.78828i	−0.748401	+	0.272396i
$310$		0			0
$311$	10.5000	+	18.1865i	0.595400	+	1.03126i	0.993490	+	0.113917i	$0.0363399\pi$
$311$	10.5000	+	18.1865i	0.595400	+	1.03126i	−0.398090	+	0.917346i	$0.630327\pi$
$312$	2.50000	−	4.33013i	0.141535	−	0.245145i
$313$	−3.29932	−	18.7113i	−0.186488	−	1.05763i	−0.924028	−	0.382324i	$-0.875124\pi$
$313$	−3.29932	−	18.7113i	−0.186488	−	1.05763i	0.737540	−	0.675304i	$-0.235987\pi$
$314$	3.82026	+	21.6658i	0.215590	+	1.22267i
$315$		0			0
$316$	5.00000	+	8.66025i	0.281272	+	0.487177i
$317$	−6.89440	+	5.78509i	−0.387228	+	0.324923i	−0.815532	−	0.578712i	$-0.803556\pi$
$317$	−6.89440	+	5.78509i	−0.387228	+	0.324923i	0.428304	+	0.903635i	$0.359111\pi$
$318$	−2.81908	+	1.02606i	−0.158086	+	0.0575386i
$319$	50.7434	+	18.4691i	2.84109	+	1.03407i
$320$		0			0
$321$	−1.56283	+	8.86327i	−0.0872289	+	0.494699i
$322$	3.00000			0.167183
$323$		0			0
$324$	1.00000			0.0555556
$325$	−4.34120	+	24.6202i	−0.240807	+	1.36568i
$326$	−15.3209	−	12.8558i	−0.848546	−	0.712014i
$327$	−10.3366	−	3.76222i	−0.571616	−	0.208051i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	0.879440	+	0.476011i	$0.157918\pi$
$332$	−1.04189	−	5.90885i	−0.0571811	−	0.324290i
$333$	−0.694593	−	3.93923i	−0.0380634	−	0.215869i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$		0			0
$336$	−0.766044	+	0.642788i	−0.0417912	+	0.0350669i
$337$	3.75877	−	1.36808i	0.204753	−	0.0745241i	−0.237608	−	0.971361i	$-0.576363\pi$
$337$	3.75877	−	1.36808i	0.204753	−	0.0745241i	0.442361	+	0.896837i	$0.354141\pi$
$338$	11.2763	+	4.10424i	0.613350	+	0.223241i
$339$	4.59627	+	3.85673i	0.249635	+	0.209469i
$340$		0			0
$341$	24.0000			1.29967
$342$		0			0
$343$	13.0000			0.701934
$344$	−1.38919	+	7.87846i	−0.0748999	+	0.424778i
$345$		0			0
$346$	5.63816	+	2.05212i	0.303109	+	0.110323i
$347$	−16.9145	+	6.15636i	−0.908016	+	0.330491i	−0.753460	−	0.657493i	$-0.771617\pi$
$347$	−16.9145	+	6.15636i	−0.908016	+	0.330491i	−0.154556	+	0.987984i	$0.549395\pi$
$348$	6.89440	−	5.78509i	0.369579	−	0.310113i
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$	2.50000	−	4.33013i	0.133631	−	0.231455i
$351$	−4.34120	−	24.6202i	−0.231716	−	1.31413i
$352$	1.04189	+	5.90885i	0.0555329	+	0.314943i
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	−0.594441	−	0.804139i	$-0.702627\pi$
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	0.993626	+	0.112731i	$0.0359599\pi$
$354$	4.50000	+	7.79423i	0.239172	+	0.414259i
$355$		0			0
$356$	11.2763	−	4.10424i	0.597643	−	0.217524i
$357$	2.81908	+	1.02606i	0.149201	+	0.0543049i
$358$		0			0
$359$	3.64661	−	20.6810i	0.192461	−	1.09150i	−0.723528	−	0.690295i	$-0.757481\pi$
$359$	3.64661	−	20.6810i	0.192461	−	1.09150i	0.915989	−	0.401204i	$-0.131408\pi$
$360$		0			0
$361$		0			0
$362$	−2.00000			−0.105118
$363$	4.34120	−	24.6202i	0.227854	−	1.29223i
$364$	−3.83022	−	3.21394i	−0.200758	−	0.168456i
$365$		0			0
$366$	−9.39693	+	3.42020i	−0.491185	+	0.178777i
$367$	−21.4492	+	17.9981i	−1.11964	+	0.939491i	−0.998586	−	0.0531551i	$-0.983072\pi$
$367$	−21.4492	+	17.9981i	−1.11964	+	0.939491i	−0.121055	+	0.992646i	$0.538628\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$		0			0
$370$		0			0
$371$	0.520945	+	2.95442i	0.0270461	+	0.153386i
$372$	2.00000	−	3.46410i	0.103695	−	0.179605i
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	−0.993484	−	0.113975i	$-0.963641\pi$
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	0.398036	−	0.917370i	$-0.369692\pi$
$374$	13.7888	−	11.5702i	0.713002	−	0.598280i
$375$		0			0
$376$		0			0
$377$	34.4720	+	28.9254i	1.77540	+	1.48974i
$378$	−0.868241	+	4.92404i	−0.0446575	+	0.253265i
$379$	−7.00000			−0.359566			−0.179783	−	0.983706i	$-0.557540\pi$
$379$	−7.00000			−0.359566			−0.179783	+	0.983706i	$0.557540\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	−0.520945	+	2.95442i	−0.0266538	+	0.151161i
$383$	13.7888	+	11.5702i	0.704575	+	0.591208i	0.923071	−	0.384629i	$-0.125671\pi$
$383$	13.7888	+	11.5702i	0.704575	+	0.591208i	−0.218496	+	0.975838i	$0.570115\pi$
$384$	0.939693	+	0.342020i	0.0479535	+	0.0174536i
$385$		0			0
$386$	−10.7246	+	8.99903i	−0.545869	+	0.458038i
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	5.00000	−	8.66025i	0.253837	−	0.439658i
$389$	3.12567	+	17.7265i	0.158478	+	0.898771i	0.955537	+	0.294871i	$0.0952765\pi$
$389$	3.12567	+	17.7265i	0.158478	+	0.898771i	−0.797060	+	0.603901i	$0.793612\pi$
$390$		0			0
$391$	−4.50000	+	7.79423i	−0.227575	+	0.394171i
$392$	−3.00000	−	5.19615i	−0.151523	−	0.262445i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	9.19253	+	7.71345i	0.461942	+	0.387616i
$397$	3.47296	−	19.6962i	0.174303	−	0.988522i	−0.764642	−	0.644455i	$-0.777084\pi$
$397$	3.47296	−	19.6962i	0.174303	−	0.988522i	0.938945	−	0.344067i	$-0.111805\pi$
$398$	−11.0000			−0.551380
$399$		0			0
$400$	−5.00000			−0.250000
$401$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$401$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$402$	−3.83022	−	3.21394i	−0.191034	−	0.160297i
$403$	18.7939	+	6.84040i	0.936188	+	0.340745i
$404$	−16.9145	+	6.15636i	−0.841526	+	0.306290i
$405$		0			0
$406$	−4.50000	−	7.79423i	−0.223331	−	0.386821i
$407$	6.00000	−	10.3923i	0.297409	−	0.515127i
$408$	−0.520945	−	2.95442i	−0.0257906	−	0.146266i
$409$	5.55674	+	31.5138i	0.274763	+	1.55826i	0.739713	+	0.672922i	$0.234961\pi$
$409$	5.55674	+	31.5138i	0.274763	+	1.55826i	−0.464950	+	0.885337i	$0.653928\pi$
$410$		0			0
$411$	4.50000	+	7.79423i	0.221969	+	0.384461i
$412$	10.7246	−	8.99903i	0.528364	−	0.443350i
$413$	8.45723	−	3.07818i	0.416153	−	0.151467i
$414$	−5.63816	−	2.05212i	−0.277100	−	0.100856i
$415$		0			0
$416$	−0.868241	+	4.92404i	−0.0425690	+	0.241421i
$417$	−4.00000			−0.195881
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	13.0228	+	10.9274i	0.634690	+	0.532568i	0.902382	−	0.430936i	$-0.141817\pi$
$421$	13.0228	+	10.9274i	0.634690	+	0.532568i	−0.267692	+	0.963504i	$0.586261\pi$
$422$	4.69846	+	1.71010i	0.228718	+	0.0832464i
$423$		0			0
$424$	2.29813	−	1.92836i	0.111607	−	0.0936496i
$425$	7.50000	+	12.9904i	0.363803	+	0.630126i
$426$	−3.00000	+	5.19615i	−0.145350	+	0.251754i
$427$	1.73648	+	9.84808i	0.0840342	+	0.476582i
$428$	−1.56283	−	8.86327i	−0.0755424	−	0.428422i
$429$	15.0000	−	25.9808i	0.724207	−	1.25436i
$430$		0			0
$431$	4.59627	−	3.85673i	0.221394	−	0.185772i	−0.525344	−	0.850890i	$-0.676063\pi$
$431$	4.59627	−	3.85673i	0.221394	−	0.185772i	0.746738	+	0.665118i	$0.231619\pi$
$432$	4.69846	−	1.71010i	0.226055	−	0.0822773i
$433$	−1.87939	−	0.684040i	−0.0903175	−	0.0328729i	0.296466	−	0.955043i	$-0.404192\pi$
$433$	−1.87939	−	0.684040i	−0.0903175	−	0.0328729i	−0.386784	+	0.922170i	$0.626414\pi$
$434$	−3.06418	−	2.57115i	−0.147085	−	0.123419i
$435$		0			0
$436$	11.0000			0.526804
$437$		0			0
$438$	7.00000			0.334473
$439$	−4.86215	+	27.5746i	−0.232058	+	1.31606i	0.616665	+	0.787226i	$0.288483\pi$
$439$	−4.86215	+	27.5746i	−0.232058	+	1.31606i	−0.848722	+	0.528839i	$0.822628\pi$
$440$		0			0
$441$	−11.2763	−	4.10424i	−0.536967	−	0.195440i
$442$	14.0954	−	5.13030i	0.670449	−	0.244024i
$443$	−13.7888	+	11.5702i	−0.655126	+	0.549716i	−0.908621	−	0.417621i	$-0.862864\pi$
$443$	−13.7888	+	11.5702i	−0.655126	+	0.549716i	0.253496	+	0.967336i	$0.418420\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$		0			0
$446$	−4.51485	−	25.6050i	−0.213784	−	1.21243i
$447$		0			0
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	9.00000	+	15.5885i	0.424736	+	0.735665i	0.996396	−	0.0848262i	$-0.0270335\pi$
$449$	9.00000	+	15.5885i	0.424736	+	0.735665i	−0.571660	+	0.820491i	$0.693700\pi$
$450$	−7.66044	+	6.42788i	−0.361117	+	0.303013i
$451$		0			0
$452$	−5.63816	−	2.05212i	−0.265197	−	0.0965236i
$453$	−7.66044	−	6.42788i	−0.359919	−	0.302008i
$454$	2.60472	−	14.7721i	0.122246	−	0.693290i
$455$		0			0
$456$		0			0
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$	3.82026	−	21.6658i	0.178509	−	1.01237i
$459$	−11.4907	−	9.64181i	−0.536338	−	0.450041i
$460$		0			0
$461$	11.2763	−	4.10424i	0.525190	−	0.191154i	−0.0657993	−	0.997833i	$-0.520960\pi$
$461$	11.2763	−	4.10424i	0.525190	−	0.191154i	0.590989	+	0.806679i	$0.298737\pi$
$462$	−4.59627	+	3.85673i	−0.213838	+	0.179431i
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	0.908750	−	0.417340i	$-0.137038\pi$
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	−0.815802	+	0.578331i	$0.803704\pi$
$464$	−4.50000	+	7.79423i	−0.208907	+	0.361838i
$465$		0			0
$466$	1.04189	+	5.90885i	0.0482646	+	0.273722i
$467$	−9.00000	+	15.5885i	−0.416470	+	0.721348i	−0.995582	−	0.0939008i	$-0.970066\pi$
$467$	−9.00000	+	15.5885i	−0.416470	+	0.721348i	0.579111	+	0.815249i	$0.303400\pi$
$468$	5.00000	+	8.66025i	0.231125	+	0.400320i
$469$	−3.83022	+	3.21394i	−0.176863	+	0.148406i
$470$		0			0
$471$	20.6732	+	7.52444i	0.952573	+	0.346708i
$472$	−6.89440	−	5.78509i	−0.317340	−	0.266280i
$473$	−8.33511	+	47.2708i	−0.383249	+	2.17351i
$474$	10.0000			0.459315
$475$		0			0
$476$	−3.00000			−0.137505
$477$	1.04189	−	5.90885i	0.0477048	−	0.270547i
$478$	16.0869	+	13.4985i	0.735799	+	0.617409i
$479$	−33.8289	−	12.3127i	−1.54568	−	0.562583i	−0.578283	−	0.815836i	$-0.696277\pi$
$479$	−33.8289	−	12.3127i	−1.54568	−	0.562583i	−0.967400	+	0.253253i	$0.918499\pi$
$480$		0			0
$481$	7.66044	−	6.42788i	0.349286	−	0.293086i
$482$	4.00000	+	6.92820i	0.182195	+	0.315571i
$483$	1.50000	−	2.59808i	0.0682524	−	0.118217i
$484$	4.34120	+	24.6202i	0.197327	+	1.11910i
$485$		0			0
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$	7.66044	−	6.42788i	0.346772	−	0.290976i
$489$	−18.7939	+	6.84040i	−0.849887	+	0.309334i
$490$		0			0
$491$	−27.5776	−	23.1404i	−1.24456	−	1.04431i	−0.997154	−	0.0753977i	$-0.975977\pi$
$491$	−27.5776	−	23.1404i	−1.24456	−	1.04431i	−0.247406	−	0.968912i	$-0.579578\pi$
$492$		0			0
$493$	27.0000			1.21602
$494$		0			0
$495$		0			0
$496$	−0.694593	+	3.93923i	−0.0311881	+	0.176877i
$497$	4.59627	+	3.85673i	0.206171	+	0.172998i
$498$	−5.63816	−	2.05212i	−0.252652	−	0.0919577i
$499$	3.75877	−	1.36808i	0.168266	−	0.0612437i	−0.256514	−	0.966541i	$-0.582574\pi$
$499$	3.75877	−	1.36808i	0.168266	−	0.0612437i	0.424779	+	0.905297i	$0.360352\pi$
$500$		0			0
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	3.00000	−	5.19615i	0.133897	−	0.231916i
$503$	−3.64661	−	20.6810i	−0.162594	−	0.922119i	−0.951510	−	0.307617i	$-0.900468\pi$
$503$	−3.64661	−	20.6810i	−0.162594	−	0.922119i	0.788916	−	0.614501i	$-0.210643\pi$
$504$	−0.347296	−	1.96962i	−0.0154698	−	0.0877336i
$505$		0			0
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$	9.19253	−	7.71345i	0.408255	−	0.342566i
$508$	−1.87939	+	0.684040i	−0.0833842	+	0.0303494i
$509$	−28.1908	−	10.2606i	−1.24953	−	0.454793i	−0.369290	−	0.929314i	$-0.620399\pi$
$509$	−28.1908	−	10.2606i	−1.24953	−	0.454793i	−0.880244	+	0.474521i	$0.842621\pi$
$510$		0			0
$511$	1.21554	−	6.89365i	0.0537722	−	0.304957i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−12.0000			−0.529297
$515$		0			0
$516$	6.12836	+	5.14230i	0.269786	+	0.226377i
$517$		0			0
$518$	−1.87939	+	0.684040i	−0.0825754	+	0.0300550i
$519$	4.59627	−	3.85673i	0.201754	−	0.169291i
$520$		0			0
$521$	18.0000	−	31.1769i	0.788594	−	1.36589i	−0.138234	−	0.990400i	$-0.544143\pi$
$521$	18.0000	−	31.1769i	0.788594	−	1.36589i	0.926828	−	0.375486i	$-0.122524\pi$
$522$	3.12567	+	17.7265i	0.136807	+	0.775870i
$523$	1.91013	+	10.8329i	0.0835242	+	0.473689i	0.997665	+	0.0682930i	$0.0217553\pi$
$523$	1.91013	+	10.8329i	0.0835242	+	0.473689i	−0.914141	+	0.405396i	$0.867134\pi$
$524$		0			0
$525$	−2.50000	−	4.33013i	−0.109109	−	0.188982i
$526$	−18.3851	+	15.4269i	−0.801627	+	0.672645i
$527$	11.2763	−	4.10424i	0.491204	−	0.178784i
$528$	5.63816	+	2.05212i	0.245369	+	0.0893071i
$529$	−10.7246	−	8.99903i	−0.466288	−	0.391262i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$		0			0
$534$	2.08378	−	11.8177i	0.0901739	−	0.511402i
$535$		0			0
$536$	4.69846	+	1.71010i	0.202943	+	0.0738651i
$537$		0			0
$538$	4.59627	−	3.85673i	0.198159	−	0.166275i
$539$	−18.0000	−	31.1769i	−0.775315	−	1.34288i
$540$		0			0
$541$	0.347296	+	1.96962i	0.0149314	+	0.0846804i	0.991363	−	0.131147i	$-0.0418661\pi$
$541$	0.347296	+	1.96962i	0.0149314	+	0.0846804i	−0.976431	+	0.215828i	$0.930755\pi$
$542$	−1.91013	−	10.8329i	−0.0820471	−	0.465312i
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$		0			0
$546$	−4.69846	+	1.71010i	−0.201076	+	0.0731856i
$547$	−41.3465	−	15.0489i	−1.76785	−	0.643444i	−0.999996	−	0.00281615i	$-0.999104\pi$
$547$	−41.3465	−	15.0489i	−1.76785	−	0.643444i	−0.767852	−	0.640628i	$-0.778674\pi$
$548$	−6.89440	−	5.78509i	−0.294514	−	0.247127i
$549$	3.47296	−	19.6962i	0.148222	−	0.840611i
$550$	−30.0000			−1.27920
$551$		0			0
$552$	−3.00000			−0.127688
$553$	1.73648	−	9.84808i	0.0738427	−	0.418783i
$554$	−6.12836	−	5.14230i	−0.260369	−	0.218475i
$555$		0			0
$556$	3.75877	−	1.36808i	0.159407	−	0.0580195i
$557$	18.3851	−	15.4269i	0.779000	−	0.653659i	−0.163996	−	0.986461i	$-0.552439\pi$
$557$	18.3851	−	15.4269i	0.779000	−	0.653659i	0.942997	+	0.332802i	$0.107994\pi$
$558$	4.00000	+	6.92820i	0.169334	+	0.293294i
$559$	−20.0000	+	34.6410i	−0.845910	+	1.46516i
$560$		0			0
$561$	−3.12567	−	17.7265i	−0.131966	−	0.748415i
$562$		0			0
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$		0			0
$566$	−20.6732	−	7.52444i	−0.868961	−	0.316276i
$567$	−0.766044	−	0.642788i	−0.0321708	−	0.0269945i
$568$	1.04189	−	5.90885i	0.0437167	−	0.247930i
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−5.20945	+	29.5442i	−0.217818	+	1.23531i
$573$	2.29813	+	1.92836i	0.0960059	+	0.0805585i
$574$		0			0
$575$	14.0954	−	5.13030i	0.587818	−	0.213948i
$576$	−1.53209	+	1.28558i	−0.0638370	+	0.0535656i
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	2.43107	+	13.7873i	0.101032	+	0.572981i
$580$		0			0
$581$	−3.00000	+	5.19615i	−0.124461	+	0.215573i
$582$	−5.00000	−	8.66025i	−0.207257	−	0.358979i
$583$	13.7888	−	11.5702i	0.571074	−	0.479188i
$584$	−6.57785	+	2.39414i	−0.272193	+	0.0990703i
$585$		0			0
$586$	16.0869	+	13.4985i	0.664545	+	0.557620i
$587$	−2.08378	+	11.8177i	−0.0860067	+	0.487768i	0.911128	+	0.412123i	$0.135213\pi$
$587$	−2.08378	+	11.8177i	−0.0860067	+	0.487768i	−0.997135	+	0.0756451i	$0.975898\pi$
$588$	−6.00000			−0.247436
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.53209	+	1.28558i	0.0629685	+	0.0528368i
$593$	28.1908	+	10.2606i	1.15766	+	0.421353i	0.848260	−	0.529580i	$-0.177651\pi$
$593$	28.1908	+	10.2606i	1.15766	+	0.421353i	0.309397	+	0.950933i	$0.399873\pi$
$594$	28.1908	−	10.2606i	1.15668	−	0.420998i
$595$		0			0
$596$		0			0
$597$	−5.50000	+	9.52628i	−0.225100	+	0.389885i
$598$	−2.60472	−	14.7721i	−0.106515	−	0.604077i
$599$	−4.16756	−	23.6354i	−0.170282	−	0.965716i	−0.943450	−	0.331515i	$-0.892440\pi$
$599$	−4.16756	−	23.6354i	−0.170282	−	0.965716i	0.773168	−	0.634201i	$-0.218671\pi$
$600$	−2.50000	+	4.33013i	−0.102062	+	0.176777i
$601$	14.0000	+	24.2487i	0.571072	+	0.989126i	0.996456	+	0.0841128i	$0.0268056\pi$
$601$	14.0000	+	24.2487i	0.571072	+	0.989126i	−0.425384	+	0.905013i	$0.639861\pi$
$602$	6.12836	−	5.14230i	0.249773	−	0.209585i
$603$	9.39693	−	3.42020i	0.382672	−	0.139281i
$604$	9.39693	+	3.42020i	0.382356	+	0.139166i
$605$		0			0
$606$	−3.12567	+	17.7265i	−0.126972	+	0.720091i
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$		0			0
$609$	−9.00000			−0.364698
$610$		0			0
$611$		0			0
$612$	5.63816	+	2.05212i	0.227909	+	0.0829521i
$613$	−1.87939	+	0.684040i	−0.0759077	+	0.0276281i	−0.379695	−	0.925112i	$-0.623971\pi$
$613$	−1.87939	+	0.684040i	−0.0759077	+	0.0276281i	0.303787	+	0.952740i	$0.401749\pi$
$614$	−15.3209	+	12.8558i	−0.618301	+	0.518816i
$615$		0			0
$616$	3.00000	−	5.19615i	0.120873	−	0.209359i
$617$	−1.04189	−	5.90885i	−0.0419449	−	0.237881i	0.956626	−	0.291318i	$-0.0940937\pi$
$617$	−1.04189	−	5.90885i	−0.0419449	−	0.237881i	−0.998571	+	0.0534364i	$0.982983\pi$
$618$	−2.43107	−	13.7873i	−0.0977922	−	0.554607i
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$		0			0
$621$	−11.4907	+	9.64181i	−0.461105	+	0.386913i
$622$	−19.7335	+	7.18242i	−0.791243	+	0.287989i
$623$	−11.2763	−	4.10424i	−0.451776	−	0.164433i
$624$	3.83022	+	3.21394i	0.153332	+	0.128660i
$625$	4.34120	−	24.6202i	0.173648	−	0.984808i
$626$	19.0000			0.759393
$627$		0			0
$628$	−22.0000			−0.877896
$629$	1.04189	−	5.90885i	0.0415428	−	0.235601i
$630$		0			0
$631$	15.0351	+	5.47232i	0.598537	+	0.217850i	0.623480	−	0.781839i	$-0.285718\pi$
$631$	15.0351	+	5.47232i	0.598537	+	0.217850i	−0.0249430	+	0.999689i	$0.507940\pi$
$632$	−9.39693	+	3.42020i	−0.373790	+	0.136048i
$633$	3.83022	−	3.21394i	0.152238	−	0.127743i
$634$	−4.50000	−	7.79423i	−0.178718	−	0.309548i
$635$		0			0
$636$	−0.520945	−	2.95442i	−0.0206568	−	0.117151i
$637$	−5.20945	−	29.5442i	−0.206406	−	1.17059i
$638$	−27.0000	+	46.7654i	−1.06894	+	1.85146i
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$		0			0
$641$	−5.63816	+	2.05212i	−0.222694	+	0.0810539i	−0.450957	−	0.892545i	$-0.648917\pi$
$641$	−5.63816	+	2.05212i	−0.222694	+	0.0810539i	0.228264	+	0.973599i	$0.426695\pi$
$642$	−8.45723	−	3.07818i	−0.333780	−	0.121486i
$643$	−16.8530	−	14.1413i	−0.664617	−	0.557680i	0.246850	−	0.969054i	$-0.420605\pi$
$643$	−16.8530	−	14.1413i	−0.664617	−	0.557680i	−0.911467	+	0.411374i	$0.865049\pi$
$644$	−0.520945	+	2.95442i	−0.0205281	+	0.116421i
$645$		0			0
$646$		0			0
$647$	27.0000			1.06148			0.530740	−	0.847535i	$-0.321914\pi$
$647$	27.0000			1.06148			0.530740	+	0.847535i	$0.321914\pi$
$648$	−0.173648	+	0.984808i	−0.00682154	+	0.0386869i
$649$	−41.3664	−	34.7105i	−1.62377	−	1.36251i
$650$	−23.4923	−	8.55050i	−0.921444	−	0.335378i
$651$	−3.75877	+	1.36808i	−0.147318	+	0.0536193i
$652$	15.3209	−	12.8558i	0.600012	−	0.503470i
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$	5.50000	−	9.52628i	0.215067	−	0.372507i
$655$		0			0
$656$		0			0
$657$	−7.00000	+	12.1244i	−0.273096	+	0.473016i
$658$		0			0
$659$	−34.4720	+	28.9254i	−1.34284	+	1.12678i	−0.361951	+	0.932197i	$0.617889\pi$
$659$	−34.4720	+	28.9254i	−1.34284	+	1.12678i	−0.980887	+	0.194578i	$0.937666\pi$
$660$		0			0
$661$	12.2160	+	4.44626i	0.475147	+	0.172940i	0.568483	−	0.822695i	$-0.307531\pi$
$661$	12.2160	+	4.44626i	0.475147	+	0.172940i	−0.0933352	+	0.995635i	$0.529753\pi$
$662$	0.766044	+	0.642788i	0.0297732	+	0.0249826i
$663$	2.60472	−	14.7721i	0.101159	−	0.573701i
$664$	6.00000			0.232845
$665$		0			0
$666$	4.00000			0.154997
$667$	4.68850	−	26.5898i	0.181539	−	1.02956i
$668$	9.19253	+	7.71345i	0.355670	+	0.298442i
$669$	−24.4320	−	8.89252i	−0.944596	−	0.343805i
$670$		0			0
$671$	45.9627	−	38.5673i	1.77437	−	1.48887i
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	−22.0000	+	38.1051i	−0.848038	+	1.46884i	0.0349191	+	0.999390i	$0.488883\pi$
$673$	−22.0000	+	38.1051i	−0.848038	+	1.46884i	−0.882957	+	0.469454i	$0.844451\pi$
$674$	0.694593	+	3.93923i	0.0267547	+	0.151734i
$675$	4.34120	+	24.6202i	0.167093	+	0.947632i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	0.986695	+	0.162581i	$0.0519817\pi$
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	−0.352549	+	0.935793i	$0.614685\pi$
$678$	−4.59627	+	3.85673i	−0.176519	+	0.148117i
$679$	−9.39693	+	3.42020i	−0.360621	+	0.131255i
$680$		0			0
$681$	−11.4907	−	9.64181i	−0.440323	−	0.369475i
$682$	−4.16756	+	23.6354i	−0.159584	+	0.905046i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$		0			0
$686$	−2.25743	+	12.8025i	−0.0861889	+	0.488802i
$687$	−16.8530	−	14.1413i	−0.642981	−	0.539525i
$688$	−7.51754	−	2.73616i	−0.286604	−	0.104315i
$689$	14.0954	−	5.13030i	0.536992	−	0.195449i
$690$		0			0
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	0.945319	−	0.326146i	$-0.105750\pi$
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	−0.755110	+	0.655598i	$0.772417\pi$
$692$	−3.00000	+	5.19615i	−0.114043	+	0.197528i
$693$	−2.08378	−	11.8177i	−0.0791562	−	0.448917i
$694$	−3.12567	−	17.7265i	−0.118649	−	0.672890i
$695$		0			0
$696$	4.50000	+	7.79423i	0.170572	+	0.295439i
$697$		0			0
$698$	−9.39693	+	3.42020i	−0.355679	+	0.129457i
$699$	5.63816	+	2.05212i	0.213255	+	0.0776183i
$700$	3.83022	+	3.21394i	0.144769	+	0.121475i
$701$	2.08378	−	11.8177i	0.0787032	−	0.446348i	−0.919835	−	0.392305i	$-0.871678\pi$
$701$	2.08378	−	11.8177i	0.0787032	−	0.446348i	0.998539	−	0.0540435i	$-0.0172110\pi$
$702$	25.0000			0.943564
$703$		0			0
$704$	−6.00000			−0.226134
$705$		0			0
$706$	11.4907	+	9.64181i	0.432457	+	0.362874i
$707$	16.9145	+	6.15636i	0.636134	+	0.231534i
$708$	−8.45723	+	3.07818i	−0.317842	+	0.115685i
$709$	−7.66044	+	6.42788i	−0.287694	+	0.241404i	−0.775200	−	0.631716i	$-0.782351\pi$
$709$	−7.66044	+	6.42788i	−0.287694	+	0.241404i	0.487506	+	0.873119i	$0.337907\pi$
$710$		0			0
$711$	−10.0000	+	17.3205i	−0.375029	+	0.649570i
$712$	2.08378	+	11.8177i	0.0780929	+	0.442887i
$713$	−2.08378	−	11.8177i	−0.0780381	−	0.442576i
$714$	−1.50000	+	2.59808i	−0.0561361	+	0.0972306i
$715$		0			0
$716$		0			0
$717$	19.7335	−	7.18242i	0.736963	−	0.268233i
$718$	19.7335	+	7.18242i	0.736449	+	0.268046i
$719$	29.8757	+	25.0687i	1.11418	+	0.934905i	0.998296	−	0.0583577i	$-0.0185864\pi$
$719$	29.8757	+	25.0687i	1.11418	+	0.934905i	0.115881	+	0.993263i	$0.463031\pi$
$720$		0			0
$721$	−14.0000			−0.521387
$722$		0			0
$723$	8.00000			0.297523
$724$	0.347296	−	1.96962i	0.0129072	−	0.0732002i
$725$	−34.4720	−	28.9254i	−1.28026	−	1.07426i
$726$	23.4923	+	8.55050i	0.871882	+	0.317339i
$727$	34.7686	−	12.6547i	1.28950	−	0.469339i	0.395935	−	0.918279i	$-0.370421\pi$
$727$	34.7686	−	12.6547i	1.28950	−	0.469339i	0.893562	+	0.448940i	$0.148198\pi$
$728$	3.83022	−	3.21394i	0.141957	−	0.119116i
$729$	−6.50000	−	11.2583i	−0.240741	−	0.416975i
$730$		0			0
$731$	4.16756	+	23.6354i	0.154143	+	0.874186i
$732$	−1.73648	−	9.84808i	−0.0641822	−	0.363995i
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	0.403128	+	0.915144i	$0.367923\pi$
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	−0.994102	+	0.108453i	$0.965410\pi$
$734$	−14.0000	−	24.2487i	−0.516749	−	0.895036i
$735$		0			0
$736$	2.81908	−	1.02606i	0.103913	−	0.0378211i
$737$	28.1908	+	10.2606i	1.03842	+	0.377954i
$738$		0			0
$739$	−2.77837	+	15.7569i	−0.102204	+	0.579628i	0.890096	+	0.455773i	$0.150637\pi$
$739$	−2.77837	+	15.7569i	−0.102204	+	0.579628i	−0.992300	+	0.123855i	$0.960474\pi$
$740$		0			0
$741$		0			0
$742$	−3.00000			−0.110133
$743$	−6.25133	+	35.4531i	−0.229339	+	1.30065i	0.624874	+	0.780725i	$0.285150\pi$
$743$	−6.25133	+	35.4531i	−0.229339	+	1.30065i	−0.854214	+	0.519922i	$0.825961\pi$
$744$	3.06418	+	2.57115i	0.112338	+	0.0942629i
$745$		0			0
$746$	21.6129	−	7.86646i	0.791306	−	0.288012i
$747$	9.19253	−	7.71345i	0.336337	−	0.282220i
$748$	9.00000	+	15.5885i	0.329073	+	0.569970i
$749$	−4.50000	+	7.79423i	−0.164426	+	0.284795i
$750$		0			0
$751$	−6.94593	−	39.3923i	−0.253460	−	1.43745i	−0.799994	−	0.600008i	$-0.795164\pi$
$751$	−6.94593	−	39.3923i	−0.253460	−	1.43745i	0.546533	−	0.837437i	$-0.315947\pi$
$752$		0			0
$753$	−3.00000	−	5.19615i	−0.109326	−	0.189358i
$754$	−34.4720	+	28.9254i	−1.25540	+	1.05340i
$755$		0			0
$756$	−4.69846	−	1.71010i	−0.170881	−	0.0621958i
$757$	1.53209	+	1.28558i	0.0556847	+	0.0467250i	0.670205	−	0.742176i	$-0.266206\pi$
$757$	1.53209	+	1.28558i	0.0556847	+	0.0467250i	−0.614521	+	0.788901i	$0.710651\pi$
$758$	1.21554	−	6.89365i	0.0441503	−	0.250389i
$759$	−18.0000			−0.653359
$760$		0			0
$761$	−21.0000			−0.761249			−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000			−0.761249			−0.380625	+	0.924730i	$0.624291\pi$
$762$	−0.347296	+	1.96962i	−0.0125812	+	0.0713516i
$763$	−8.42649	−	7.07066i	−0.305059	−	0.255975i
$764$	−2.81908	−	1.02606i	−0.101991	−	0.0371216i
$765$		0			0
$766$	−13.7888	+	11.5702i	−0.498210	+	0.418047i
$767$	−22.5000	−	38.9711i	−0.812428	−	1.40717i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	0.868241	+	4.92404i	0.0313096	+	0.177565i	0.996452	−	0.0841584i	$-0.0268202\pi$
$769$	0.868241	+	4.92404i	0.0313096	+	0.177565i	−0.965143	+	0.261724i	$0.915709\pi$
$770$		0			0
$771$	−6.00000	+	10.3923i	−0.216085	+	0.374270i
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	39.0683	−	32.7822i	1.40519	−	1.17909i	0.446447	−	0.894810i	$-0.352689\pi$
$773$	39.0683	−	32.7822i	1.40519	−	1.17909i	0.958740	−	0.284283i	$-0.0917554\pi$
$774$	−15.0351	+	5.47232i	−0.540425	+	0.196699i
$775$	−18.7939	−	6.84040i	−0.675095	−	0.245715i
$776$	7.66044	+	6.42788i	0.274994	+	0.230747i
$777$	−0.347296	+	1.96962i	−0.0124592	+

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.347296 - 1.96962i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.347296 - 1.96962i) q^{9} +(3.00000 - 5.19615i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(3.83022 - 3.21394i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.520945 - 2.95442i) q^{17} +2.00000 q^{18} +(-0.173648 + 0.984808i) q^{21} +(4.59627 + 3.85673i) q^{22} +(-2.81908 - 1.02606i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-3.83022 + 3.21394i) q^{25} +(2.50000 + 4.33013i) q^{26} +(2.50000 - 4.33013i) q^{27} +(-0.173648 - 0.984808i) q^{28} +(1.56283 + 8.86327i) q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(5.63816 - 2.05212i) q^{33} +(2.81908 + 1.02606i) q^{34} +(-0.347296 + 1.96962i) q^{36} +2.00000 q^{37} +5.00000 q^{39} +(-0.939693 - 0.342020i) q^{42} +(-7.51754 + 2.73616i) q^{43} +(-4.59627 + 3.85673i) q^{44} +(1.50000 - 2.59808i) q^{46} +(0.173648 + 0.984808i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-2.50000 - 4.33013i) q^{50} +(2.29813 - 1.92836i) q^{51} +(-4.69846 + 1.71010i) q^{52} +(2.81908 + 1.02606i) q^{53} +(3.83022 + 3.21394i) q^{54} +1.00000 q^{56} -9.00000 q^{58} +(1.56283 - 8.86327i) q^{59} +(9.39693 + 3.42020i) q^{61} +(-3.75877 + 1.36808i) q^{62} +(1.53209 - 1.28558i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.04189 + 5.90885i) q^{66} +(0.868241 + 4.92404i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-1.50000 - 2.59808i) q^{69} +(5.63816 - 2.05212i) q^{71} +(-1.87939 - 0.684040i) q^{72} +(-5.36231 - 4.49951i) q^{73} +(-0.347296 + 1.96962i) q^{74} -5.00000 q^{75} +6.00000 q^{77} +(-0.868241 + 4.92404i) q^{78} +(-7.66044 - 6.42788i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(3.00000 + 5.19615i) q^{83} +(0.500000 - 0.866025i) q^{84} +(-1.38919 - 7.87846i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(-9.19253 + 7.71345i) q^{89} +(4.69846 + 1.71010i) q^{91} +(2.29813 + 1.92836i) q^{92} +(-0.694593 + 3.93923i) q^{93} -1.00000 q^{96} +(-1.73648 + 9.84808i) q^{97} +(4.59627 + 3.85673i) q^{98} +(-11.2763 - 4.10424i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^7 + 3 * q^8	\( 6 q + 3 q^{7} + 3 q^{8} + 18 q^{11} - 3 q^{12} + 12 q^{18} + 15 q^{26} + 15 q^{27} + 12 q^{31} + 12 q^{37} + 30 q^{39} + 9 q^{46} + 18 q^{49} - 15 q^{50} + 6 q^{56} - 54 q^{58} - 3 q^{64} - 9 q^{68} - 9 q^{69} - 30 q^{75} + 36 q^{77} + 18 q^{83} + 3 q^{84} - 27 q^{87} - 18 q^{88} - 6 q^{96}+O(q^{100}) \) 6 * q + 3 * q^7 + 3 * q^8 + 18 * q^11 - 3 * q^12 + 12 * q^18 + 15 * q^26 + 15 * q^27 + 12 * q^31 + 12 * q^37 + 30 * q^39 + 9 * q^46 + 18 * q^49 - 15 * q^50 + 6 * q^56 - 54 * q^58 - 3 * q^64 - 9 * q^68 - 9 * q^69 - 30 * q^75 + 36 * q^77 + 18 * q^83 + 3 * q^84 - 27 * q^87 - 18 * q^88 - 6 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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