LMFDB - Embedded newform 722.2.e.e.423.1

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			423.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	722.423
Dual form			722.2.e.e.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.87939 + 0.684040i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.87939 + 0.684040i) q^{9} +(3.00000 - 5.19615i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.868241 - 4.92404i) q^{13} +(-0.766044 - 0.642788i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-2.81908 + 1.02606i) q^{17} -2.00000 q^{18} +(-0.939693 + 0.342020i) q^{21} +(-1.04189 + 5.90885i) q^{22} +(2.29813 - 1.92836i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(-0.868241 - 4.92404i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-2.50000 + 4.33013i) q^{27} +(0.939693 + 0.342020i) q^{28} +(8.45723 + 3.07818i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.173648 + 0.984808i) q^{32} +(4.59627 + 3.85673i) q^{33} +(2.29813 - 1.92836i) q^{34} +(1.87939 - 0.684040i) q^{36} -2.00000 q^{37} +5.00000 q^{39} +(0.766044 - 0.642788i) q^{42} +(6.12836 + 5.14230i) q^{43} +(-1.04189 - 5.90885i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(0.939693 + 0.342020i) q^{48} +(3.00000 - 5.19615i) q^{49} +(2.50000 + 4.33013i) q^{50} +(-0.520945 - 2.95442i) q^{51} +(-3.83022 - 3.21394i) q^{52} +(2.29813 - 1.92836i) q^{53} +(0.868241 - 4.92404i) q^{54} -1.00000 q^{56} -9.00000 q^{58} +(8.45723 - 3.07818i) q^{59} +(-7.66044 + 6.42788i) q^{61} +(3.06418 + 2.57115i) q^{62} +(0.347296 + 1.96962i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-5.63816 - 2.05212i) q^{66} +(4.69846 + 1.71010i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(1.50000 + 2.59808i) q^{69} +(4.59627 + 3.85673i) q^{71} +(-1.53209 + 1.28558i) q^{72} +(-1.21554 + 6.89365i) q^{73} +(1.87939 - 0.684040i) q^{74} +5.00000 q^{75} +6.00000 q^{77} +(-4.69846 + 1.71010i) q^{78} +(1.73648 - 9.84808i) q^{79} +(0.766044 + 0.642788i) q^{81} +(3.00000 + 5.19615i) q^{83} +(-0.500000 + 0.866025i) q^{84} +(-7.51754 - 2.73616i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(3.00000 + 5.19615i) q^{88} +(2.08378 + 11.8177i) q^{89} +(3.83022 - 3.21394i) q^{91} +(0.520945 - 2.95442i) q^{92} +(3.75877 - 1.36808i) q^{93} -1.00000 q^{96} +(-9.39693 + 3.42020i) q^{97} +(-1.04189 + 5.90885i) q^{98} +(9.19253 - 7.71345i) 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 $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i	0.892754	+	0.450545i	$0.148770\pi$
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i	−0.993010	+	0.118034i	$0.962341\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$5$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$6$	−0.173648	−	0.984808i	−0.0708916	−	0.402046i
$7$	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
$9$	1.87939	+	0.684040i	0.626462	+	0.228013i
$10$		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
$13$	−0.868241	−	4.92404i	−0.240807	−	1.36568i	−0.830033	−	0.557714i	$-0.811678\pi$
$13$	−0.868241	−	4.92404i	−0.240807	−	1.36568i	0.589226	−	0.807968i	$-0.299433\pi$
$14$	−0.766044	−	0.642788i	−0.204734	−	0.171792i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.81908	+	1.02606i	−0.683727	+	0.248856i	−0.660447	−	0.750873i	$-0.729633\pi$
$17$	−2.81908	+	1.02606i	−0.683727	+	0.248856i	−0.0232799	+	0.999729i	$0.507411\pi$
$18$	−2.00000			−0.471405
$19$		0			0
$19$		0			0
$20$		0			0
$21$	−0.939693	+	0.342020i	−0.205058	+	0.0746349i
$22$	−1.04189	+	5.90885i	−0.222131	+	1.25977i
$23$	2.29813	−	1.92836i	0.479194	−	0.402091i	−0.370941	−	0.928656i	$-0.620965\pi$
$23$	2.29813	−	1.92836i	0.479194	−	0.402091i	0.850135	+	0.526565i	$0.176520\pi$
$24$	−0.766044	−	0.642788i	−0.156368	−	0.131208i
$25$	−0.868241	−	4.92404i	−0.173648	−	0.984808i
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$	−2.50000	+	4.33013i	−0.481125	+	0.833333i
$28$	0.939693	+	0.342020i	0.177585	+	0.0646357i
$29$	8.45723	+	3.07818i	1.57047	+	0.571604i	0.973104	−	0.230366i	$-0.0739923\pi$
$29$	8.45723	+	3.07818i	1.57047	+	0.571604i	0.597365	+	0.801970i	$0.296214\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	4.59627	+	3.85673i	0.800107	+	0.671370i
$34$	2.29813	−	1.92836i	0.394127	−	0.330711i
$35$		0			0
$36$	1.87939	−	0.684040i	0.313231	−	0.114007i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		0			0
$39$	5.00000			0.800641
$40$		0			0
$41$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$41$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$42$	0.766044	−	0.642788i	0.118203	−	0.0991843i
$43$	6.12836	+	5.14230i	0.934565	+	0.784194i	0.976631	−	0.214921i	$-0.0689495\pi$
$43$	6.12836	+	5.14230i	0.934565	+	0.784194i	−0.0420659	+	0.999115i	$0.513394\pi$
$44$	−1.04189	−	5.90885i	−0.157071	−	0.890792i
$45$		0			0
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$47$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$48$	0.939693	+	0.342020i	0.135633	+	0.0493664i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	2.50000	+	4.33013i	0.353553	+	0.612372i
$51$	−0.520945	−	2.95442i	−0.0729468	−	0.413702i
$52$	−3.83022	−	3.21394i	−0.531156	−	0.445693i
$53$	2.29813	−	1.92836i	0.315673	−	0.264881i	−0.471159	−	0.882048i	$-0.656164\pi$
$53$	2.29813	−	1.92836i	0.315673	−	0.264881i	0.786832	+	0.617167i	$0.211720\pi$
$54$	0.868241	−	4.92404i	0.118153	−	0.670077i
$55$		0			0
$56$	−1.00000			−0.133631
$57$		0			0
$58$	−9.00000			−1.18176
$59$	8.45723	−	3.07818i	1.10104	−	0.400745i	0.273339	−	0.961918i	$-0.411872\pi$
$59$	8.45723	−	3.07818i	1.10104	−	0.400745i	0.827699	+	0.561173i	$0.189650\pi$
$60$		0			0
$61$	−7.66044	+	6.42788i	−0.980819	+	0.823005i	−0.984213	−	0.176989i	$-0.943364\pi$
$61$	−7.66044	+	6.42788i	−0.980819	+	0.823005i	0.00339342	+	0.999994i	$0.498920\pi$
$62$	3.06418	+	2.57115i	0.389151	+	0.326536i
$63$	0.347296	+	1.96962i	0.0437552	+	0.248148i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−5.63816	−	2.05212i	−0.694009	−	0.252599i
$67$	4.69846	+	1.71010i	0.574009	+	0.208922i	0.612682	−	0.790330i	$-0.290091\pi$
$67$	4.69846	+	1.71010i	0.574009	+	0.208922i	−0.0386729	+	0.999252i	$0.512313\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$		0			0
$71$	4.59627	+	3.85673i	0.545476	+	0.457709i	0.873406	−	0.486993i	$-0.161906\pi$
$71$	4.59627	+	3.85673i	0.545476	+	0.457709i	−0.327929	+	0.944702i	$0.606351\pi$
$72$	−1.53209	+	1.28558i	−0.180558	+	0.151506i
$73$	−1.21554	+	6.89365i	−0.142268	+	0.806841i	0.827252	+	0.561830i	$0.189903\pi$
$73$	−1.21554	+	6.89365i	−0.142268	+	0.806841i	−0.969520	+	0.245011i	$0.921208\pi$
$74$	1.87939	−	0.684040i	0.218474	−	0.0795181i
$75$	5.00000			0.577350
$76$		0			0
$77$	6.00000			0.683763
$78$	−4.69846	+	1.71010i	−0.531996	+	0.193631i
$79$	1.73648	−	9.84808i	0.195369	−	1.10800i	−0.716522	−	0.697564i	$-0.754267\pi$
$79$	1.73648	−	9.84808i	0.195369	−	1.10800i	0.911892	−	0.410431i	$-0.134622\pi$
$80$		0			0
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$		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
$86$	−7.51754	−	2.73616i	−0.810637	−	0.295048i
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	2.08378	+	11.8177i	0.220880	+	1.25267i	0.870406	+	0.492334i	$0.163856\pi$
$89$	2.08378	+	11.8177i	0.220880	+	1.25267i	−0.649526	+	0.760339i	$0.725033\pi$
$90$		0			0
$91$	3.83022	−	3.21394i	0.401516	−	0.336912i
$92$	0.520945	−	2.95442i	0.0543122	−	0.308020i
$93$	3.75877	−	1.36808i	0.389766	−	0.141863i
$94$		0			0
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−9.39693	+	3.42020i	−0.954113	+	0.347269i	−0.771724	−	0.635958i	$-0.780605\pi$
$97$	−9.39693	+	3.42020i	−0.954113	+	0.347269i	−0.182389	+	0.983226i	$0.558383\pi$
$98$	−1.04189	+	5.90885i	−0.105247	+	0.596884i
$99$	9.19253	−	7.71345i	0.923884	−	0.775231i
$100$	−3.83022	−	3.21394i	−0.383022	−	0.321394i
$101$	3.12567	+	17.7265i	0.311016	+	1.76386i	0.593741	+	0.804656i	$0.297650\pi$
$101$	3.12567	+	17.7265i	0.311016	+	1.76386i	−0.282726	+	0.959201i	$0.591239\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	−0.282194	−	0.959357i	$-0.591062\pi$
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	0.971925	−	0.235291i	$-0.0756043\pi$
$104$	4.69846	+	1.71010i	0.460722	+	0.167689i
$105$		0			0
$106$	−1.50000	+	2.59808i	−0.145693	+	0.252347i
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	0.562267	−	0.826956i	$-0.309929\pi$
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	−0.997298	+	0.0734594i	$0.976596\pi$
$108$	0.868241	+	4.92404i	0.0835465	+	0.473816i
$109$	−8.42649	−	7.07066i	−0.807111	−	0.677247i	0.142805	−	0.989751i	$-0.454388\pi$
$109$	−8.42649	−	7.07066i	−0.807111	−	0.677247i	−0.949916	+	0.312504i	$0.898832\pi$
$110$		0			0
$111$	0.347296	−	1.96962i	0.0329639	−	0.186948i
$112$	0.939693	−	0.342020i	0.0887926	−	0.0323179i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$		0			0
$116$	8.45723	−	3.07818i	0.785234	−	0.285802i
$117$	1.73648	−	9.84808i	0.160538	−	0.910455i
$118$	−6.89440	+	5.78509i	−0.634681	+	0.532561i
$119$	−2.29813	−	1.92836i	−0.210670	−	0.176773i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	5.00000	−	8.66025i	0.452679	−	0.784063i
$123$		0			0
$124$	−3.75877	−	1.36808i	−0.337548	−	0.122857i
$125$		0			0
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	−0.347296	−	1.96962i	−0.0308176	−	0.174775i	0.965514	−	0.260351i	$-0.0838382\pi$
$127$	−0.347296	−	1.96962i	−0.0308176	−	0.174775i	−0.996332	+	0.0855756i	$0.972727\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−6.12836	+	5.14230i	−0.539572	+	0.452754i
$130$		0			0
$131$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$131$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$132$	6.00000			0.522233
$133$		0			0
$134$	−5.00000			−0.431934
$135$		0			0
$136$	0.520945	−	2.95442i	0.0446706	−	0.253340i
$137$	−6.89440	+	5.78509i	−0.589028	+	0.494253i	−0.887898	−	0.460040i	$-0.847835\pi$
$137$	−6.89440	+	5.78509i	−0.589028	+	0.494253i	0.298870	+	0.954294i	$0.403390\pi$
$138$	−2.29813	−	1.92836i	−0.195630	−	0.164153i
$139$	−0.694593	−	3.93923i	−0.0589146	−	0.334121i	0.941077	−	0.338192i	$-0.109815\pi$
$139$	−0.694593	−	3.93923i	−0.0589146	−	0.334121i	−0.999992	+	0.00407080i	$0.998704\pi$
$140$		0			0
$141$		0			0
$142$	−5.63816	−	2.05212i	−0.473144	−	0.172210i
$143$	−28.1908	−	10.2606i	−2.35743	−	0.858035i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$		0			0
$146$	−1.21554	−	6.89365i	−0.100599	−	0.570523i
$147$	4.59627	+	3.85673i	0.379094	+	0.318097i
$148$	−1.53209	+	1.28558i	−0.125937	+	0.105674i
$149$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$149$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$150$	−4.69846	+	1.71010i	−0.383628	+	0.139629i
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	−5.63816	+	2.05212i	−0.454336	+	0.165365i
$155$		0			0
$156$	3.83022	−	3.21394i	0.306663	−	0.257321i
$157$	−16.8530	−	14.1413i	−1.34501	−	1.12860i	−0.980307	−	0.197478i	$-0.936725\pi$
$157$	−16.8530	−	14.1413i	−1.34501	−	1.12860i	−0.364707	−	0.931122i	$-0.618831\pi$
$158$	1.73648	+	9.84808i	0.138147	+	0.783471i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$		0			0
$161$	2.81908	+	1.02606i	0.222174	+	0.0808649i
$162$	−0.939693	−	0.342020i	−0.0738292	−	0.0268716i
$163$	−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
$166$	−4.59627	−	3.85673i	−0.356739	−	0.299340i
$167$	−9.19253	+	7.71345i	−0.711340	+	0.596885i	−0.924975	−	0.380029i	$-0.875914\pi$
$167$	−9.19253	+	7.71345i	−0.711340	+	0.596885i	0.213635	+	0.976914i	$0.431470\pi$
$168$	0.173648	−	0.984808i	0.0133972	−	0.0759796i
$169$	−11.2763	+	4.10424i	−0.867409	+	0.315711i
$170$		0			0
$171$		0			0
$172$	8.00000			0.609994
$173$	5.63816	−	2.05212i	0.428661	−	0.156020i	−0.118674	−	0.992933i	$-0.537864\pi$
$173$	5.63816	−	2.05212i	0.428661	−	0.156020i	0.547335	+	0.836913i	$0.315642\pi$
$174$	1.56283	−	8.86327i	0.118478	−	0.671923i
$175$	3.83022	−	3.21394i	0.289538	−	0.242951i
$176$	−4.59627	−	3.85673i	−0.346457	−	0.290712i
$177$	1.56283	+	8.86327i	0.117470	+	0.666204i
$178$	−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
$181$	1.87939	+	0.684040i	0.139694	+	0.0508443i	0.410921	−	0.911671i	$-0.365207\pi$
$181$	1.87939	+	0.684040i	0.139694	+	0.0508443i	−0.271227	+	0.962515i	$0.587429\pi$
$182$	−2.50000	+	4.33013i	−0.185312	+	0.320970i
$183$	−5.00000	−	8.66025i	−0.369611	−	0.640184i
$184$	0.520945	+	2.95442i	0.0384045	+	0.217803i
$185$		0			0
$186$	−3.06418	+	2.57115i	−0.224676	+	0.188526i
$187$	−3.12567	+	17.7265i	−0.228571	+	1.29629i
$188$		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	$0.465384\pi$
$192$	0.939693	−	0.342020i	0.0678165	−	0.0246832i
$193$	−2.43107	+	13.7873i	−0.174993	+	0.992432i	0.763160	+	0.646210i	$0.223647\pi$
$193$	−2.43107	+	13.7873i	−0.174993	+	0.992432i	−0.938152	+	0.346222i	$0.887464\pi$
$194$	7.66044	−	6.42788i	0.549988	−	0.461495i
$195$		0			0
$196$	−1.04189	−	5.90885i	−0.0744206	−	0.422060i
$197$		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
$199$	−10.3366	−	3.76222i	−0.732743	−	0.266697i	−0.0514178	−	0.998677i	$-0.516374\pi$
$199$	−10.3366	−	3.76222i	−0.732743	−	0.266697i	−0.681326	+	0.731980i	$0.738596\pi$
$200$	4.69846	+	1.71010i	0.332232	+	0.120922i
$201$	−2.50000	+	4.33013i	−0.176336	+	0.305424i
$202$	−9.00000	−	15.5885i	−0.633238	−	1.09680i
$203$	1.56283	+	8.86327i	0.109689	+	0.622080i
$204$	−2.29813	−	1.92836i	−0.160902	−	0.135012i
$205$		0			0
$206$	−2.43107	+	13.7873i	−0.169381	+	0.960607i
$207$	5.63816	−	2.05212i	0.391879	−	0.142632i
$208$	−5.00000			−0.346688
$209$		0			0
$210$		0			0
$211$	4.69846	−	1.71010i	0.323456	−	0.117728i	−0.175189	−	0.984535i	$-0.556054\pi$
$211$	4.69846	−	1.71010i	0.323456	−	0.117728i	0.498644	+	0.866807i	$0.333831\pi$
$212$	0.520945	−	2.95442i	0.0357786	−	0.202911i
$213$	−4.59627	+	3.85673i	−0.314931	+	0.264258i
$214$	6.89440	+	5.78509i	0.471291	+	0.395461i
$215$		0			0
$216$	−2.50000	−	4.33013i	−0.170103	−	0.294628i
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$	10.3366	+	3.76222i	0.700084	+	0.254810i
$219$	−6.57785	−	2.39414i	−0.444490	−	0.161781i
$220$		0			0
$221$	7.50000	+	12.9904i	0.504505	+	0.873828i
$222$	0.347296	+	1.96962i	0.0233090	+	0.132192i
$223$	−19.9172	−	16.7125i	−1.33375	−	1.11915i	−0.983185	−	0.182612i	$-0.941545\pi$
$223$	−19.9172	−	16.7125i	−1.33375	−	1.11915i	−0.350566	−	0.936538i	$-0.614011\pi$
$224$	−0.766044	+	0.642788i	−0.0511835	+	0.0429481i
$225$	1.73648	−	9.84808i	0.115765	−	0.656539i
$226$	5.63816	−	2.05212i	0.375045	−	0.136505i
$227$	15.0000			0.995585			0.497792	−	0.867296i	$-0.334144\pi$
$227$	15.0000			0.995585			0.497792	+	0.867296i	$0.334144\pi$
$228$		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
$231$	−1.04189	+	5.90885i	−0.0685513	+	0.388774i
$232$	−6.89440	+	5.78509i	−0.452640	+	0.379810i
$233$	−4.59627	−	3.85673i	−0.301111	−	0.252662i	0.479695	−	0.877435i	$-0.340747\pi$
$233$	−4.59627	−	3.85673i	−0.301111	−	0.252662i	−0.780807	+	0.624773i	$0.785192\pi$
$234$	1.73648	+	9.84808i	0.113517	+	0.643789i
$235$		0			0
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	9.39693	+	3.42020i	0.610396	+	0.222166i
$238$	2.81908	+	1.02606i	0.182734	+	0.0665096i
$239$	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
$241$	−1.38919	−	7.87846i	−0.0894853	−	0.507496i	−0.996298	−	0.0859632i	$-0.972603\pi$
$241$	−1.38919	−	7.87846i	−0.0894853	−	0.507496i	0.906813	−	0.421533i	$-0.138508\pi$
$242$	19.1511	+	16.0697i	1.23108	+	1.03300i
$243$	−12.2567	+	10.2846i	−0.786268	+	0.659758i
$244$	−1.73648	+	9.84808i	−0.111167	+	0.630459i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	4.00000			0.254000
$249$	−5.63816	+	2.05212i	−0.357304	+	0.130048i
$250$		0			0
$251$	4.59627	−	3.85673i	0.290114	−	0.243434i	−0.486101	−	0.873902i	$-0.661581\pi$
$251$	4.59627	−	3.85673i	0.290114	−	0.243434i	0.776215	+	0.630468i	$0.217137\pi$
$252$	1.53209	+	1.28558i	0.0965125	+	0.0809836i
$253$	−3.12567	−	17.7265i	−0.196509	−	1.11446i
$254$	1.00000	+	1.73205i	0.0627456	+	0.108679i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	11.2763	+	4.10424i	0.703397	+	0.256016i	0.668861	−	0.743388i	$-0.266782\pi$
$257$	11.2763	+	4.10424i	0.703397	+	0.256016i	0.0345364	+	0.999403i	$0.489005\pi$
$258$	4.00000	−	6.92820i	0.249029	−	0.431331i
$259$	−1.00000	−	1.73205i	−0.0621370	−	0.107624i
$260$		0			0
$261$	13.7888	+	11.5702i	0.853505	+	0.716176i
$262$		0			0
$263$	4.16756	−	23.6354i	0.256983	−	1.45742i	−0.533950	−	0.845516i	$-0.679293\pi$
$263$	4.16756	−	23.6354i	0.256983	−	1.45742i	0.790932	−	0.611904i	$-0.209596\pi$
$264$	−5.63816	+	2.05212i	−0.347004	+	0.126299i
$265$		0			0
$266$		0			0
$267$	−12.0000			−0.734388
$268$	4.69846	−	1.71010i	0.287004	−	0.104461i
$269$	1.04189	−	5.90885i	0.0635251	−	0.360269i	−0.936431	−	0.350853i	$-0.885892\pi$
$269$	1.04189	−	5.90885i	0.0635251	−	0.360269i	0.999956	−	0.00941580i	$-0.00299719\pi$
$270$		0			0
$271$	8.42649	+	7.07066i	0.511873	+	0.429512i	0.861788	−	0.507269i	$-0.169345\pi$
$271$	8.42649	+	7.07066i	0.511873	+	0.429512i	−0.349915	+	0.936782i	$0.613789\pi$
$272$	0.520945	+	2.95442i	0.0315869	+	0.179138i
$273$	2.50000	+	4.33013i	0.151307	+	0.262071i
$274$	4.50000	−	7.79423i	0.271855	−	0.470867i
$275$	−28.1908	−	10.2606i	−1.69997	−	0.618738i
$276$	2.81908	+	1.02606i	0.169689	+	0.0617616i
$277$	−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
$279$	−1.38919	−	7.87846i	−0.0831684	−	0.471671i
$280$		0			0
$281$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$281$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$282$		0			0
$283$	20.6732	−	7.52444i	1.22890	−	0.447282i	0.355677	−	0.934609i	$-0.384250\pi$
$283$	20.6732	−	7.52444i	1.22890	−	0.447282i	0.873219	+	0.487327i	$0.162028\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	30.0000			1.77394
$287$		0			0
$288$	−0.347296	+	1.96962i	−0.0204646	+	0.116061i
$289$	−6.12836	+	5.14230i	−0.360492	+	0.302488i
$290$		0			0
$291$	−1.73648	−	9.84808i	−0.101794	−	0.577305i
$292$	3.50000	+	6.06218i	0.204822	+	0.354762i
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	0.377244	+	0.926114i	$0.376872\pi$
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	−0.990660	+	0.136355i	$0.956461\pi$
$294$	−5.63816	−	2.05212i	−0.328824	−	0.119682i
$295$		0			0
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	15.0000	+	25.9808i	0.870388	+	1.50756i
$298$		0			0
$299$	−11.4907	−	9.64181i	−0.664522	−	0.557601i
$300$	3.83022	−	3.21394i	0.221138	−	0.185557i
$301$	−1.38919	+	7.87846i	−0.0800713	+	0.454107i
$302$	−9.39693	+	3.42020i	−0.540732	+	0.196810i
$303$	−18.0000			−1.03407
$304$		0			0
$305$		0			0
$306$	5.63816	−	2.05212i	0.322312	−	0.117312i
$307$	−3.47296	+	19.6962i	−0.198212	+	1.12412i	0.709557	+	0.704649i	$0.248895\pi$
$307$	−3.47296	+	19.6962i	−0.198212	+	1.12412i	−0.907769	+	0.419470i	$0.862216\pi$
$308$	4.59627	−	3.85673i	0.261897	−	0.219757i
$309$	10.7246	+	8.99903i	0.610102	+	0.511937i
$310$		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
$313$	17.8542	+	6.49838i	1.00918	+	0.367310i	0.793117	−	0.609070i	$-0.208457\pi$
$313$	17.8542	+	6.49838i	1.00918	+	0.367310i	0.216060	+	0.976380i	$0.430679\pi$
$314$	20.6732	+	7.52444i	1.16666	+	0.424629i
$315$		0			0
$316$	−5.00000	−	8.66025i	−0.281272	−	0.487177i
$317$	1.56283	+	8.86327i	0.0877775	+	0.497811i	0.996723	+	0.0808951i	$0.0257779\pi$
$317$	1.56283	+	8.86327i	0.0877775	+	0.497811i	−0.908945	+	0.416916i	$0.863111\pi$
$318$	−2.29813	−	1.92836i	−0.128873	−	0.108137i
$319$	41.3664	−	34.7105i	2.31607	−	1.94342i
$320$		0			0
$321$	8.45723	−	3.07818i	0.472037	−	0.171807i
$322$	−3.00000			−0.167183
$323$		0			0
$324$	1.00000			0.0555556
$325$	−23.4923	+	8.55050i	−1.30312	+	0.474297i
$326$	3.47296	−	19.6962i	0.192350	−	1.09087i
$327$	8.42649	−	7.07066i	0.465986	−	0.391009i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.500000	+	0.866025i	−0.0274825	+	0.0476011i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−0.500000	+	0.866025i	−0.0274825	+	0.0476011i	0.851957	+	0.523612i	$0.175416\pi$
$332$	5.63816	+	2.05212i	0.309434	+	0.112625i
$333$	−3.75877	−	1.36808i	−0.205979	−	0.0749704i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$		0			0
$336$	0.173648	+	0.984808i	0.00947328	+	0.0537257i
$337$	3.06418	+	2.57115i	0.166916	+	0.140059i	0.722420	−	0.691455i	$-0.243030\pi$
$337$	3.06418	+	2.57115i	0.166916	+	0.140059i	−0.555503	+	0.831514i	$0.687474\pi$
$338$	9.19253	−	7.71345i	0.500008	−	0.419556i
$339$	1.04189	−	5.90885i	0.0565876	−	0.320924i
$340$		0			0
$341$	−24.0000			−1.29967
$342$		0			0
$343$	13.0000			0.701934
$344$	−7.51754	+	2.73616i	−0.405319	+	0.147524i
$345$		0			0
$346$	−4.59627	+	3.85673i	−0.247097	+	0.207339i
$347$	13.7888	+	11.5702i	0.740222	+	0.621120i	0.932897	−	0.360143i	$-0.117272\pi$
$347$	13.7888	+	11.5702i	0.740222	+	0.621120i	−0.192676	+	0.981263i	$0.561717\pi$
$348$	1.56283	+	8.86327i	0.0837767	+	0.475121i
$349$	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
$351$	23.4923	+	8.55050i	1.25393	+	0.456392i
$352$	5.63816	+	2.05212i	0.300515	+	0.109378i
$353$	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
$356$	9.19253	+	7.71345i	0.487203	+	0.408812i
$357$	2.29813	−	1.92836i	0.121630	−	0.102060i
$358$		0			0
$359$	−19.7335	+	7.18242i	−1.04150	+	0.379074i	−0.805447	−	0.592667i	$-0.798075\pi$
$359$	−19.7335	+	7.18242i	−1.04150	+	0.379074i	−0.236049	+	0.971741i	$0.575853\pi$
$360$		0			0
$361$		0			0
$362$	−2.00000			−0.105118
$363$	23.4923	−	8.55050i	1.23303	−	0.448785i
$364$	0.868241	−	4.92404i	0.0455082	−	0.258090i
$365$		0			0
$366$	7.66044	+	6.42788i	0.400418	+	0.335990i
$367$	−4.86215	−	27.5746i	−0.253802	−	1.43938i	−0.799129	−	0.601160i	$-0.794706\pi$
$367$	−4.86215	−	27.5746i	−0.253802	−	1.43938i	0.545327	−	0.838224i	$-0.316406\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$		0			0
$370$		0			0
$371$	2.81908	+	1.02606i	0.146359	+	0.0532704i
$372$	2.00000	−	3.46410i	0.103695	−	0.179605i
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	0.993484	+	0.113975i	$0.0363585\pi$
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	−0.398036	+	0.917370i	$0.630308\pi$
$374$	−3.12567	−	17.7265i	−0.161624	−	0.916618i
$375$		0			0
$376$		0			0
$377$	7.81417	−	44.3163i	0.402450	−	2.28241i
$378$	4.69846	−	1.71010i	0.241663	−	0.0879581i
$379$	7.00000			0.359566			0.179783	−	0.983706i	$-0.442460\pi$
$379$	7.00000			0.359566			0.179783	+	0.983706i	$0.442460\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	−2.81908	+	1.02606i	−0.144237	+	0.0524978i
$383$	−3.12567	+	17.7265i	−0.159714	+	0.905784i	0.794634	+	0.607088i	$0.207663\pi$
$383$	−3.12567	+	17.7265i	−0.159714	+	0.905784i	−0.954348	+	0.298696i	$0.903449\pi$
$384$	−0.766044	+	0.642788i	−0.0390920	+	0.0328021i
$385$		0			0
$386$	−2.43107	−	13.7873i	−0.123738	−	0.701756i
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	−16.9145	−	6.15636i	−0.857598	−	0.312140i	−0.124464	−	0.992224i	$-0.539721\pi$
$389$	−16.9145	−	6.15636i	−0.857598	−	0.312140i	−0.733134	+	0.680084i	$0.761943\pi$
$390$		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
$396$	2.08378	−	11.8177i	0.104714	−	0.593861i
$397$	−18.7939	+	6.84040i	−0.943236	+	0.343310i	−0.767443	−	0.641117i	$-0.778471\pi$
$397$	−18.7939	+	6.84040i	−0.943236	+	0.343310i	−0.175793	+	0.984427i	$0.556249\pi$
$398$	11.0000			0.551380
$399$		0			0
$400$	−5.00000			−0.250000
$401$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$401$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$402$	0.868241	−	4.92404i	0.0433039	−	0.245589i
$403$	−15.3209	+	12.8558i	−0.763188	+	0.640391i
$404$	13.7888	+	11.5702i	0.686018	+	0.575638i
$405$		0			0
$406$	−4.50000	−	7.79423i	−0.223331	−	0.386821i
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$	2.81908	+	1.02606i	0.139565	+	0.0507976i
$409$	30.0702	+	10.9446i	1.48687	+	0.541178i	0.952624	−	0.304149i	$-0.0983721\pi$
$409$	30.0702	+	10.9446i	1.48687	+	0.541178i	0.534249	+	0.845327i	$0.320594\pi$
$410$		0			0
$411$	−4.50000	−	7.79423i	−0.221969	−	0.384461i
$412$	−2.43107	−	13.7873i	−0.119770	−	0.679252i
$413$	6.89440	+	5.78509i	0.339251	+	0.284666i
$414$	−4.59627	+	3.85673i	−0.225894	+	0.189548i
$415$		0			0
$416$	4.69846	−	1.71010i	0.230361	−	0.0838446i
$417$	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
$421$	−2.95202	+	16.7417i	−0.143873	+	0.815942i	0.824393	+	0.566018i	$0.191517\pi$
$421$	−2.95202	+	16.7417i	−0.143873	+	0.815942i	−0.968265	+	0.249924i	$0.919594\pi$
$422$	−3.83022	+	3.21394i	−0.186452	+	0.156452i
$423$		0			0
$424$	0.520945	+	2.95442i	0.0252993	+	0.143479i
$425$	7.50000	+	12.9904i	0.363803	+	0.630126i
$426$	3.00000	−	5.19615i	0.145350	−	0.251754i
$427$	−9.39693	−	3.42020i	−0.454749	−	0.165515i
$428$	−8.45723	−	3.07818i	−0.408796	−	0.148790i
$429$	15.0000	−	25.9808i	0.724207	−	1.25436i
$430$		0			0
$431$	−1.04189	−	5.90885i	−0.0501860	−	0.284619i	0.949378	−	0.314135i	$-0.101715\pi$
$431$	−1.04189	−	5.90885i	−0.0501860	−	0.284619i	−0.999564	+	0.0295160i	$0.990603\pi$
$432$	3.83022	+	3.21394i	0.184282	+	0.154631i
$433$	−1.53209	+	1.28558i	−0.0736275	+	0.0617808i	−0.678859	−	0.734269i	$-0.737525\pi$
$433$	−1.53209	+	1.28558i	−0.0736275	+	0.0617808i	0.605231	+	0.796050i	$0.293081\pi$
$434$	−0.694593	+	3.93923i	−0.0333415	+	0.189089i
$435$		0			0
$436$	−11.0000			−0.526804
$437$		0			0
$438$	7.00000			0.334473
$439$	−26.3114	+	9.57656i	−1.25577	+	0.457064i	−0.882349	−	0.470596i	$-0.844039\pi$
$439$	−26.3114	+	9.57656i	−1.25577	+	0.457064i	−0.373425	+	0.927660i	$0.621817\pi$
$440$		0			0
$441$	9.19253	−	7.71345i	0.437740	−	0.367307i
$442$	−11.4907	−	9.64181i	−0.546555	−	0.458614i
$443$	−3.12567	−	17.7265i	−0.148505	−	0.842213i	−0.964486	−	0.264134i	$-0.914914\pi$
$443$	−3.12567	−	17.7265i	−0.148505	−	0.842213i	0.815981	−	0.578079i	$-0.196197\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$		0			0
$446$	24.4320	+	8.89252i	1.15689	+	0.421073i
$447$		0			0
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	0.571660	−	0.820491i	$-0.306300\pi$
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	−0.996396	+	0.0848262i	$0.972967\pi$
$450$	1.73648	+	9.84808i	0.0818585	+	0.464243i
$451$		0			0
$452$	−4.59627	+	3.85673i	−0.216190	+	0.181405i
$453$	−1.73648	+	9.84808i	−0.0815870	+	0.462703i
$454$	−14.0954	+	5.13030i	−0.661529	+	0.240777i
$455$		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	$0.369839\pi$
$458$	20.6732	−	7.52444i	0.965997	−	0.351594i
$459$	2.60472	−	14.7721i	0.121578	−	0.689503i
$460$		0			0
$461$	−9.19253	−	7.71345i	−0.428139	−	0.359251i	0.403110	−	0.915152i	$-0.367929\pi$
$461$	−9.19253	−	7.71345i	−0.428139	−	0.359251i	−0.831249	+	0.555900i	$0.812374\pi$
$462$	−1.04189	−	5.90885i	−0.0484731	−	0.274904i
$463$	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
$466$	5.63816	+	2.05212i	0.261183	+	0.0950627i
$467$	−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
$469$	0.868241	+	4.92404i	0.0400916	+	0.227371i
$470$		0			0
$471$	16.8530	−	14.1413i	0.776544	−	0.651598i
$472$	−1.56283	+	8.86327i	−0.0719352	+	0.407965i
$473$	45.1052	−	16.4170i	2.07394	−	0.754853i
$474$	−10.0000			−0.459315
$475$		0			0
$476$	−3.00000			−0.137505
$477$	5.63816	−	2.05212i	0.258153	−	0.0939602i
$478$	−3.64661	+	20.6810i	−0.166792	+	0.945925i
$479$	27.5776	−	23.1404i	1.26005	−	1.05731i	0.264376	−	0.964420i	$-0.414834\pi$
$479$	27.5776	−	23.1404i	1.26005	−	1.05731i	0.995676	−	0.0928902i	$-0.0296105\pi$
$480$		0			0
$481$	1.73648	+	9.84808i	0.0791768	+	0.449034i
$482$	4.00000	+	6.92820i	0.182195	+	0.315571i
$483$	−1.50000	+	2.59808i	−0.0682524	+	0.118217i
$484$	−23.4923	−	8.55050i	−1.06783	−	0.388659i
$485$		0			0
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	0.887793	−	0.460243i	$-0.152238\pi$
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	−0.842479	+	0.538730i	$0.818904\pi$
$488$	−1.73648	−	9.84808i	−0.0786068	−	0.445802i
$489$	−15.3209	−	12.8558i	−0.692835	−	0.581357i
$490$		0			0
$491$	−6.25133	+	35.4531i	−0.282119	+	1.59998i	0.433280	+	0.901259i	$0.357356\pi$
$491$	−6.25133	+	35.4531i	−0.282119	+	1.59998i	−0.715399	+	0.698716i	$0.753755\pi$
$492$		0			0
$493$	−27.0000			−1.21602
$494$		0			0
$495$		0			0
$496$	−3.75877	+	1.36808i	−0.168774	+	0.0614286i
$497$	−1.04189	+	5.90885i	−0.0467351	+	0.265048i
$498$	4.59627	−	3.85673i	0.205964	−	0.172824i
$499$	−3.06418	−	2.57115i	−0.137171	−	0.115101i	0.571620	−	0.820518i	$-0.306315\pi$
$499$	−3.06418	−	2.57115i	−0.137171	−	0.115101i	−0.708792	+	0.705418i	$0.750759\pi$
$500$		0			0
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	−3.00000	+	5.19615i	−0.133897	+	0.231916i
$503$	19.7335	+	7.18242i	0.879875	+	0.320248i	0.742159	−	0.670223i	$-0.233802\pi$
$503$	19.7335	+	7.18242i	0.879875	+	0.320248i	0.137716	+	0.990472i	$0.456024\pi$
$504$	−1.87939	−	0.684040i	−0.0837145	−	0.0304696i
$505$		0			0
$506$	9.00000	+	15.5885i	0.400099	+	0.692991i
$507$	−2.08378	−	11.8177i	−0.0925438	−	0.524842i
$508$	−1.53209	−	1.28558i	−0.0679755	−	0.0570382i
$509$	−22.9813	+	19.2836i	−1.01863	+	0.854732i	−0.989455	−	0.144843i	$-0.953732\pi$
$509$	−22.9813	+	19.2836i	−1.01863	+	0.854732i	−0.0291750	+	0.999574i	$0.509288\pi$
$510$		0			0
$511$	−6.57785	+	2.39414i	−0.290987	+	0.105911i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−12.0000			−0.529297
$515$		0			0
$516$	−1.38919	+	7.87846i	−0.0611555	+	0.346830i
$517$		0			0
$518$	1.53209	+	1.28558i	0.0673161	+	0.0564849i
$519$	1.04189	+	5.90885i	0.0457339	+	0.259370i
$520$		0			0
$521$	−18.0000	+	31.1769i	−0.788594	+	1.36589i	0.138234	+	0.990400i	$0.455857\pi$
$521$	−18.0000	+	31.1769i	−0.788594	+	1.36589i	−0.926828	+	0.375486i	$0.877476\pi$
$522$	−16.9145	−	6.15636i	−0.740326	−	0.269457i
$523$	10.3366	+	3.76222i	0.451989	+	0.164510i	0.557976	−	0.829857i	$-0.311578\pi$
$523$	10.3366	+	3.76222i	0.451989	+	0.164510i	−0.105987	+	0.994367i	$0.533800\pi$
$524$		0			0
$525$	2.50000	+	4.33013i	0.109109	+	0.188982i
$526$	4.16756	+	23.6354i	0.181714	+	1.03055i
$527$	9.19253	+	7.71345i	0.400433	+	0.336003i
$528$	4.59627	−	3.85673i	0.200027	−	0.167842i
$529$	−2.43107	+	13.7873i	−0.105699	+	0.599448i
$530$		0			0
$531$	18.0000			0.781133
$532$		0			0
$533$		0			0
$534$	11.2763	−	4.10424i	0.487974	−	0.177608i
$535$		0			0
$536$	−3.83022	+	3.21394i	−0.165440	+	0.138821i
$537$		0			0
$538$	1.04189	+	5.90885i	0.0449190	+	0.254748i
$539$	−18.0000	−	31.1769i	−0.775315	−	1.34288i
$540$		0			0
$541$	−1.87939	−	0.684040i	−0.0808011	−	0.0294092i	0.301303	−	0.953528i	$-0.402578\pi$
$541$	−1.87939	−	0.684040i	−0.0808011	−	0.0294092i	−0.382104	+	0.924119i	$0.624801\pi$
$542$	−10.3366	−	3.76222i	−0.443996	−	0.161601i
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$	−3.83022	−	3.21394i	−0.163918	−	0.137544i
$547$	−33.7060	+	28.2827i	−1.44116	+	1.20928i	−0.502437	+	0.864614i	$0.667563\pi$
$547$	−33.7060	+	28.2827i	−1.44116	+	1.20928i	−0.938726	+	0.344665i	$0.887992\pi$
$548$	−1.56283	+	8.86327i	−0.0667609	+	0.378620i
$549$	−18.7939	+	6.84040i	−0.802102	+	0.291941i
$550$	30.0000			1.27920
$551$		0			0
$552$	−3.00000			−0.127688
$553$	9.39693	−	3.42020i	0.399598	−	0.145442i
$554$	1.38919	−	7.87846i	0.0590208	−	0.334724i
$555$		0			0
$556$	−3.06418	−	2.57115i	−0.129950	−	0.109041i
$557$	4.16756	+	23.6354i	0.176585	+	1.00146i	0.936298	+	0.351205i	$0.114228\pi$
$557$	4.16756	+	23.6354i	0.176585	+	1.00146i	−0.759713	+	0.650258i	$0.774661\pi$
$558$	4.00000	+	6.92820i	0.169334	+	0.293294i
$559$	20.0000	−	34.6410i	0.845910	−	1.46516i
$560$		0			0
$561$	−16.9145	−	6.15636i	−0.714129	−	0.259922i
$562$		0			0
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	0.711445	−	0.702742i	$-0.248041\pi$
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	−0.964315	+	0.264758i	$0.914708\pi$
$564$		0			0
$565$		0			0
$566$	−16.8530	+	14.1413i	−0.708383	+	0.594404i
$567$	−0.173648	+	0.984808i	−0.00729254	+	0.0413580i
$568$	−5.63816	+	2.05212i	−0.236572	+	0.0861051i
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−28.1908	+	10.2606i	−1.17872	+	0.429017i
$573$	−0.520945	+	2.95442i	−0.0217628	+	0.123423i
$574$		0			0
$575$	−11.4907	−	9.64181i	−0.479194	−	0.402091i
$576$	−0.347296	−	1.96962i	−0.0144707	−	0.0820673i
$577$	−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
$579$	−13.1557	−	4.78828i	−0.546732	−	0.198994i
$580$		0			0
$581$	−3.00000	+	5.19615i	−0.124461	+	0.215573i
$582$	5.00000	+	8.66025i	0.207257	+	0.358979i
$583$	−3.12567	−	17.7265i	−0.129452	−	0.734158i
$584$	−5.36231	−	4.49951i	−0.221894	−	0.186191i
$585$		0			0
$586$	3.64661	−	20.6810i	0.150640	−	0.854323i
$587$	11.2763	−	4.10424i	0.465423	−	0.169400i	−0.0986548	−	0.995122i	$-0.531454\pi$
$587$	11.2763	−	4.10424i	0.465423	−	0.169400i	0.564078	+	0.825722i	$0.309232\pi$
$588$	6.00000			0.247436
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.347296	+	1.96962i	−0.0142738	+	0.0809507i
$593$	−22.9813	+	19.2836i	−0.943730	+	0.791884i	−0.978231	−	0.207521i	$-0.933460\pi$
$593$	−22.9813	+	19.2836i	−0.943730	+	0.791884i	0.0345003	+	0.999405i	$0.489016\pi$
$594$	−22.9813	−	19.2836i	−0.942936	−	0.791217i
$595$		0			0
$596$		0			0
$597$	5.50000	−	9.52628i	0.225100	−	0.389885i
$598$	14.0954	+	5.13030i	0.576403	+	0.209794i
$599$	−22.5526	−	8.20848i	−0.921475	−	0.335390i	−0.162650	−	0.986684i	$-0.552004\pi$
$599$	−22.5526	−	8.20848i	−0.921475	−	0.335390i	−0.758825	+	0.651294i	$0.774226\pi$
$600$	−2.50000	+	4.33013i	−0.102062	+	0.176777i
$601$	−14.0000	−	24.2487i	−0.571072	−	0.989126i	−0.996456	−	0.0841128i	$-0.973194\pi$
$601$	−14.0000	−	24.2487i	−0.571072	−	0.989126i	0.425384	−	0.905013i	$-0.360139\pi$
$602$	−1.38919	−	7.87846i	−0.0566190	−	0.321102i
$603$	7.66044	+	6.42788i	0.311957	+	0.261763i
$604$	7.66044	−	6.42788i	0.311699	−	0.261547i
$605$		0			0
$606$	16.9145	−	6.15636i	0.687103	−	0.250085i
$607$	22.0000			0.892952			0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000			0.892952			0.446476	+	0.894795i	$0.352679\pi$
$608$		0			0
$609$	−9.00000			−0.364698
$610$		0			0
$611$		0			0
$612$	−4.59627	+	3.85673i	−0.185793	+	0.155899i
$613$	1.53209	+	1.28558i	0.0618805	+	0.0519239i	0.673203	−	0.739457i	$-0.264918\pi$
$613$	1.53209	+	1.28558i	0.0618805	+	0.0519239i	−0.611323	+	0.791381i	$0.709362\pi$
$614$	−3.47296	−	19.6962i	−0.140157	−	0.794872i
$615$		0			0
$616$	−3.00000	+	5.19615i	−0.120873	+	0.209359i
$617$	5.63816	+	2.05212i	0.226984	+	0.0826153i	0.453008	−	0.891506i	$-0.350351\pi$
$617$	5.63816	+	2.05212i	0.226984	+	0.0826153i	−0.226025	+	0.974122i	$0.572573\pi$
$618$	−13.1557	−	4.78828i	−0.529200	−	0.192613i
$619$	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
$621$	2.60472	+	14.7721i	0.104524	+	0.592785i
$622$	−16.0869	−	13.4985i	−0.645027	−	0.541242i
$623$	−9.19253	+	7.71345i	−0.368291	+	0.309033i
$624$	0.868241	−	4.92404i	0.0347575	−	0.197119i
$625$	−23.4923	+	8.55050i	−0.939693	+	0.342020i
$626$	−19.0000			−0.759393
$627$		0			0
$628$	−22.0000			−0.877896
$629$	5.63816	−	2.05212i	0.224808	−	0.0818234i
$630$		0			0
$631$	−12.2567	+	10.2846i	−0.487932	+	0.409424i	−0.853284	−	0.521446i	$-0.825393\pi$
$631$	−12.2567	+	10.2846i	−0.487932	+	0.409424i	0.365352	+	0.930869i	$0.380948\pi$
$632$	7.66044	+	6.42788i	0.304716	+	0.255687i
$633$	0.868241	+	4.92404i	0.0345095	+	0.195713i
$634$	−4.50000	−	7.79423i	−0.178718	−	0.309548i
$635$		0			0
$636$	2.81908	+	1.02606i	0.111784	+	0.0406859i
$637$	−28.1908	−	10.2606i	−1.11696	−	0.406540i
$638$	−27.0000	+	46.7654i	−1.06894	+	1.85146i
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$		0			0
$641$	−4.59627	−	3.85673i	−0.181542	−	0.152332i	0.547488	−	0.836813i	$-0.315584\pi$
$641$	−4.59627	−	3.85673i	−0.181542	−	0.152332i	−0.729030	+	0.684482i	$0.760029\pi$
$642$	−6.89440	+	5.78509i	−0.272100	+	0.228319i
$643$	−3.82026	+	21.6658i	−0.150656	+	0.854415i	0.811994	+	0.583666i	$0.198382\pi$
$643$	−3.82026	+	21.6658i	−0.150656	+	0.854415i	−0.962650	+	0.270748i	$0.912729\pi$
$644$	2.81908	−	1.02606i	0.111087	−	0.0404324i
$645$		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	$0.321914\pi$
$648$	−0.939693	+	0.342020i	−0.0369146	+	0.0134358i
$649$	9.37700	−	53.1796i	0.368080	−	2.08748i
$650$	19.1511	−	16.0697i	0.751168	−	0.630305i
$651$	3.06418	+	2.57115i	0.120095	+	0.100771i
$652$	3.47296	+	19.6962i	0.136012	+	0.771361i
$653$	−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
$659$	7.81417	+	44.3163i	0.304397	+	1.72632i	0.626330	+	0.779558i	$0.284556\pi$
$659$	7.81417	+	44.3163i	0.304397	+	1.72632i	−0.321934	+	0.946762i	$0.604333\pi$
$660$		0			0
$661$	9.95858	−	8.35624i	0.387344	−	0.325020i	−0.428234	−	0.903668i	$-0.640864\pi$
$661$	9.95858	−	8.35624i	0.387344	−	0.325020i	0.815577	+	0.578648i	$0.196420\pi$
$662$	0.173648	−	0.984808i	0.00674903	−	0.0382756i
$663$	−14.0954	+	5.13030i	−0.547420	+	0.199244i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	4.00000			0.154997
$667$	25.3717	−	9.23454i	0.982396	−	0.357563i
$668$	−2.08378	+	11.8177i	−0.0806238	+	0.457240i
$669$	19.9172	−	16.7125i	0.770042	−	0.646142i
$670$		0			0
$671$	10.4189	+	59.0885i	0.402217	+	2.28108i
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	22.0000	−	38.1051i	0.848038	−	1.46884i	−0.0349191	−	0.999390i	$-0.511117\pi$
$673$	22.0000	−	38.1051i	0.848038	−	1.46884i	0.882957	−	0.469454i	$-0.155549\pi$
$674$	−3.75877	−	1.36808i	−0.144782	−	0.0526965i
$675$	23.4923	+	8.55050i	0.904220	+	0.329109i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	−0.986695	−	0.162581i	$-0.948018\pi$
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	0.352549	−	0.935793i	$-0.385315\pi$
$678$	1.04189	+	5.90885i	0.0400135	+	0.226928i
$679$	−7.66044	−	6.42788i	−0.293981	−	0.246679i
$680$		0			0
$681$	−2.60472	+	14.7721i	−0.0998132	+	0.566069i
$682$	22.5526	−	8.20848i	0.863585	−	0.314319i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$		0			0
$685$		0			0
$686$	−12.2160	+	4.44626i	−0.466409	+	0.169759i
$687$	3.82026	−	21.6658i	0.145752	−	0.826601i
$688$	6.12836	−	5.14230i	0.233641	−	0.196048i
$689$	−11.4907	−	9.64181i	−0.437760	−	0.367324i
$690$		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
$693$	11.2763	+	4.10424i	0.428352	+	0.155907i
$694$	−16.9145	−	6.15636i	−0.642064	−	0.233692i
$695$		0			0
$696$	−4.50000	−	7.79423i	−0.170572	−	0.295439i
$697$		0			0
$698$	−7.66044	−	6.42788i	−0.289952	−	0.243299i
$699$	4.59627	−	3.85673i	0.173847	−	0.145875i
$700$	0.868241	−	4.92404i	0.0328164	−	0.186111i
$701$	−11.2763	+	4.10424i	−0.425900	+	0.155015i	−0.546072	−	0.837738i	$-0.683878\pi$
$701$	−11.2763	+	4.10424i	−0.425900	+	0.155015i	0.120172	+	0.992753i	$0.461655\pi$
$702$	−25.0000			−0.943564
$703$		0			0
$704$	−6.00000			−0.226134
$705$		0			0
$706$	−2.60472	+	14.7721i	−0.0980300	+	0.555956i
$707$	−13.7888	+	11.5702i	−0.518581	+	0.435141i
$708$	6.89440	+	5.78509i	0.259107	+	0.217417i
$709$	−1.73648	−	9.84808i	−0.0652149	−	0.369852i	−0.999897	−	0.0143670i	$-0.995427\pi$
$709$	−1.73648	−	9.84808i	−0.0652149	−	0.369852i	0.934682	−	0.355485i	$-0.115684\pi$
$710$		0			0
$711$	10.0000	−	17.3205i	0.375029	−	0.649570i
$712$	−11.2763	−	4.10424i	−0.422598	−	0.153813i
$713$	−11.2763	−	4.10424i	−0.422301	−	0.153705i
$714$	−1.50000	+	2.59808i	−0.0561361	+	0.0972306i
$715$		0			0
$716$		0			0
$717$	16.0869	+	13.4985i	0.600778	+	0.504112i
$718$	16.0869	−	13.4985i	0.600359	−	0.503761i
$719$	6.77228	−	38.4075i	0.252563	−	1.43236i	−0.549687	−	0.835371i	$-0.685253\pi$
$719$	6.77228	−	38.4075i	0.252563	−	1.43236i	0.802251	−	0.596988i	$-0.203636\pi$
$720$		0			0
$721$	14.0000			0.521387
$722$		0			0
$723$	8.00000			0.297523
$724$	1.87939	−	0.684040i	0.0698468	−	0.0254222i
$725$	7.81417	−	44.3163i	0.290211	−	1.64587i
$726$	−19.1511	+	16.0697i	−0.710764	+	0.596402i
$727$	−28.3436	−	23.7831i	−1.05121	−	0.882068i	−0.0579875	−	0.998317i	$-0.518468\pi$
$727$	−28.3436	−	23.7831i	−1.05121	−	0.882068i	−0.993220	+	0.116249i	$0.962913\pi$
$728$	0.868241	+	4.92404i	0.0321791	+	0.182497i
$729$	−6.50000	−	11.2583i	−0.240741	−	0.416975i
$730$		0			0
$731$	−22.5526	−	8.20848i	−0.834139	−	0.303602i
$732$	−9.39693	−	3.42020i	−0.347320	−	0.126414i
$733$	−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
$736$	2.29813	+	1.92836i	0.0847103	+	0.0710804i
$737$	22.9813	−	19.2836i	0.846528	−	0.710322i
$738$		0			0
$739$	15.0351	−	5.47232i	0.553074	−	0.201303i	−0.0503375	−	0.998732i	$-0.516030\pi$
$739$	15.0351	−	5.47232i	0.553074	−	0.201303i	0.603412	+	0.797430i	$0.293807\pi$
$740$		0			0
$741$		0			0
$742$	−3.00000			−0.110133
$743$	−33.8289	+	12.3127i	−1.24106	+	0.451710i	−0.877373	−	0.479810i	$-0.840706\pi$
$743$	−33.8289	+	12.3127i	−1.24106	+	0.451710i	−0.363691	+	0.931520i	$0.618483\pi$
$744$	−0.694593	+	3.93923i	−0.0254650	+	0.144419i
$745$		0			0
$746$	−17.6190	−	14.7841i	−0.645078	−	0.541285i
$747$	2.08378	+	11.8177i	0.0762415	+	0.432387i
$748$	9.00000	+	15.5885i	0.329073	+	0.569970i
$749$	4.50000	−	7.79423i	0.164426	−	0.284795i
$750$		0			0
$751$	−37.5877	−	13.6808i	−1.37159	−	0.499220i	−0.451975	−	0.892030i	$-0.649281\pi$
$751$	−37.5877	−	13.6808i	−1.37159	−	0.499220i	−0.919619	+	0.392811i	$0.871503\pi$
$752$		0			0
$753$	3.00000	+	5.19615i	0.109326	+	0.189358i
$754$	7.81417	+	44.3163i	0.284575	+	1.61391i
$755$		0			0
$756$	−3.83022	+	3.21394i	−0.139304	+	0.116890i
$757$	0.347296	−	1.96962i	0.0126227	−	0.0715869i	−0.977846	−	0.209327i	$-0.932873\pi$
$757$	0.347296	−	1.96962i	0.0126227	−	0.0715869i	0.990468	+	0.137740i	$0.0439838\pi$
$758$	−6.57785	+	2.39414i	−0.238918	+	0.0869591i
$759$	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	$0.624291\pi$
$762$	−1.87939	+	0.684040i	−0.0680829	+	0.0247802i
$763$	1.91013	−	10.8329i	0.0691513	−	0.392177i
$764$	2.29813	−	1.92836i	0.0831435	−	0.0697657i
$765$		0			0
$766$	−3.12567	−	17.7265i	−0.112935	−	0.640486i
$767$	−22.5000	−	38.9711i	−0.812428	−	1.40717i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−4.69846	−	1.71010i	−0.169431	−	0.0616678i	0.255912	−	0.966700i	$-0.417624\pi$
$769$	−4.69846	−	1.71010i	−0.169431	−	0.0616678i	−0.425343	+	0.905032i	$0.639846\pi$
$770$		0			0
$771$	−6.00000	+	10.3923i	−0.216085	+	0.374270i
$772$	7.00000	+	12.1244i	0.251936	+	0.436365i
$773$	−8.85606	−	50.2252i	−0.318530	−	1.80647i	−0.551704	−	0.834040i	$-0.686022\pi$
$773$	−8.85606	−	50.2252i	−0.318530	−	1.80647i	0.233174	−	0.972435i	$-0.425089\pi$
$774$	−12.2567	−	10.2846i	−0.440558	−	0.369672i
$775$	−15.3209	+	12.8558i	−0.550343	+	0.461792i
$776$	1.73648	−	9.84808i	0.0623361	−	0.353525i
$777$	1.87939	−	0.684040i	0.0674226	−	0.0245398i

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)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.87939 + 0.684040i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.87939 + 0.684040i) q^{9} +(3.00000 - 5.19615i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.868241 - 4.92404i) q^{13} +(-0.766044 - 0.642788i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-2.81908 + 1.02606i) q^{17} -2.00000 q^{18} +(-0.939693 + 0.342020i) q^{21} +(-1.04189 + 5.90885i) q^{22} +(2.29813 - 1.92836i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(-0.868241 - 4.92404i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-2.50000 + 4.33013i) q^{27} +(0.939693 + 0.342020i) q^{28} +(8.45723 + 3.07818i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.173648 + 0.984808i) q^{32} +(4.59627 + 3.85673i) q^{33} +(2.29813 - 1.92836i) q^{34} +(1.87939 - 0.684040i) q^{36} -2.00000 q^{37} +5.00000 q^{39} +(0.766044 - 0.642788i) q^{42} +(6.12836 + 5.14230i) q^{43} +(-1.04189 - 5.90885i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(0.939693 + 0.342020i) q^{48} +(3.00000 - 5.19615i) q^{49} +(2.50000 + 4.33013i) q^{50} +(-0.520945 - 2.95442i) q^{51} +(-3.83022 - 3.21394i) q^{52} +(2.29813 - 1.92836i) q^{53} +(0.868241 - 4.92404i) q^{54} -1.00000 q^{56} -9.00000 q^{58} +(8.45723 - 3.07818i) q^{59} +(-7.66044 + 6.42788i) q^{61} +(3.06418 + 2.57115i) q^{62} +(0.347296 + 1.96962i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-5.63816 - 2.05212i) q^{66} +(4.69846 + 1.71010i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(1.50000 + 2.59808i) q^{69} +(4.59627 + 3.85673i) q^{71} +(-1.53209 + 1.28558i) q^{72} +(-1.21554 + 6.89365i) q^{73} +(1.87939 - 0.684040i) q^{74} +5.00000 q^{75} +6.00000 q^{77} +(-4.69846 + 1.71010i) q^{78} +(1.73648 - 9.84808i) q^{79} +(0.766044 + 0.642788i) q^{81} +(3.00000 + 5.19615i) q^{83} +(-0.500000 + 0.866025i) q^{84} +(-7.51754 - 2.73616i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(3.00000 + 5.19615i) q^{88} +(2.08378 + 11.8177i) q^{89} +(3.83022 - 3.21394i) q^{91} +(0.520945 - 2.95442i) q^{92} +(3.75877 - 1.36808i) q^{93} -1.00000 q^{96} +(-9.39693 + 3.42020i) q^{97} +(-1.04189 + 5.90885i) q^{98} +(9.19253 - 7.71345i) 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

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