LMFDB - Embedded newform 722.2.i.b.501.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(7,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("722.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, 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:	$612$
Relative dimension:	$17$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			501.13
Character	$\chi$	$=$	722.501
Dual form			722.2.i.b.49.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.926494 - 0.376309i) q^{2} +(1.98560 + 0.444982i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.00459569 - 0.166723i) q^{5} +(-1.67219 - 1.15947i) q^{6} +(-0.556362 - 2.19703i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(1.03151 + 0.486781i) q^{9} +O(q^{10})$	\(q+(-0.926494 - 0.376309i) q^{2} +(1.98560 + 0.444982i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.00459569 - 0.166723i) q^{5} +(-1.67219 - 1.15947i) q^{6} +(-0.556362 - 2.19703i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(1.03151 + 0.486781i) q^{9} +(-0.0584816 + 0.156197i) q^{10} +(0.477849 - 5.76678i) q^{11} +(1.11296 + 1.70351i) q^{12} +(-1.18856 - 3.80005i) q^{13} +(-0.311295 + 2.24490i) q^{14} +(0.0650636 - 0.333090i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(-4.57094 + 4.44668i) q^{17} +(-0.772507 - 0.839166i) q^{18} +(-2.26471 - 3.72439i) q^{19} +(0.112961 - 0.122709i) q^{20} +(-0.127073 - 4.60998i) q^{21} +(-2.61282 + 5.16307i) q^{22} +(-1.18158 + 0.264799i) q^{23} +(-0.390102 - 1.99710i) q^{24} +(4.96463 - 0.273906i) q^{25} +(-0.328797 + 3.96799i) q^{26} +(-2.98579 - 2.32393i) q^{27} +(1.13319 - 1.96274i) q^{28} +(3.96102 + 1.12007i) q^{29} +(-0.185626 + 0.284121i) q^{30} +(-1.74514 - 1.35830i) q^{31} +(0.350638 - 0.936511i) q^{32} +(3.51493 - 11.2379i) q^{33} +(5.90827 - 2.39973i) q^{34} +(-0.363738 + 0.102855i) q^{35} +(0.399937 + 1.06818i) q^{36} +(-0.382861 + 4.62044i) q^{37} +(0.696713 + 4.30286i) q^{38} +(-0.669051 - 8.07425i) q^{39} +(-0.150834 + 0.0711805i) q^{40} +(-0.796165 - 0.693381i) q^{41} +(-1.61704 + 4.31893i) q^{42} +(-0.148613 - 0.396927i) q^{43} +(4.36367 - 3.80032i) q^{44} +(0.0764171 - 0.174213i) q^{45} +(1.19438 + 0.199306i) q^{46} +(6.60022 + 4.57649i) q^{47} +(-0.390102 + 1.99710i) q^{48} +(1.63893 - 0.886946i) q^{49} +(-4.70278 - 1.61446i) q^{50} +(-11.0547 + 6.79532i) q^{51} +(1.79782 - 3.55259i) q^{52} +(9.15312 + 6.34663i) q^{53} +(1.89180 + 3.27669i) q^{54} +(-0.963651 - 0.0531661i) q^{55} +(-1.78849 + 1.39204i) q^{56} +(-2.83950 - 8.40289i) q^{57} +(-3.24837 - 2.52831i) q^{58} +(8.44825 + 7.35759i) q^{59} +(0.278899 - 0.193384i) q^{60} +(1.86467 + 2.53697i) q^{61} +(1.10572 + 1.91517i) q^{62} +(0.495577 - 2.53708i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(-0.628093 + 0.215625i) q^{65} +(-7.48547 + 9.08911i) q^{66} +(0.653808 + 0.0723634i) q^{67} -6.37702 q^{68} -2.46398 q^{69} +(0.375706 + 0.0415832i) q^{70} +(6.98466 - 9.50297i) q^{71} +(0.0314285 - 1.14017i) q^{72} +(-0.990741 + 0.963807i) q^{73} +(2.09343 - 4.13674i) q^{74} +(9.97964 + 1.66531i) q^{75} +(0.973706 - 4.24875i) q^{76} +(-12.9356 + 2.15857i) q^{77} +(-2.41854 + 7.73251i) q^{78} +(-3.09211 - 8.25867i) q^{79} +(0.166533 - 0.00918789i) q^{80} +(-7.06978 - 8.58435i) q^{81} +(0.476717 + 0.942018i) q^{82} +(-2.65030 + 1.43427i) q^{83} +(3.12344 - 3.39296i) q^{84} +(0.762370 + 0.741645i) q^{85} +(-0.0116785 + 0.423675i) q^{86} +(7.36657 + 3.98659i) q^{87} +(-5.47301 + 1.87889i) q^{88} +(-4.60596 - 4.48074i) q^{89} +(-0.136358 + 0.132651i) q^{90} +(-7.68753 + 4.72551i) q^{91} +(-1.03158 - 0.634111i) q^{92} +(-2.86072 - 3.47359i) q^{93} +(-4.39289 - 6.72382i) q^{94} +(-0.610534 + 0.394695i) q^{95} +(1.11296 - 1.70351i) q^{96} +(12.3525 - 1.36718i) q^{97} +(-1.85223 + 0.205005i) q^{98} +(3.30006 - 5.71588i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9}+O(q^{10}) $ 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21} + 33 q^{22} + 39 q^{23} + 20 q^{25} - 8 q^{26} + 158 q^{27} - 37 q^{28} - 42 q^{29} - 29 q^{30} + 12 q^{31} + 17 q^{32} + 60 q^{33} - q^{34} - 14 q^{35} + 23 q^{36} - 6 q^{37} + 76 q^{38} - 108 q^{39} + q^{40} + 8 q^{41} + 11 q^{42} + 7 q^{43} - 5 q^{44} - 101 q^{45} - 21 q^{46} + 105 q^{47} - 62 q^{49} - 78 q^{50} - 3 q^{51} + 4 q^{52} + 146 q^{53} - 79 q^{54} + 4 q^{55} - 21 q^{56} - 28 q^{57} + 8 q^{58} - 4 q^{59} - 14 q^{60} - 93 q^{61} - 6 q^{62} - 95 q^{63} - 34 q^{64} - 76 q^{65} - 16 q^{66} - 6 q^{67} + 78 q^{68} + 38 q^{69} + 81 q^{70} - 151 q^{71} + 23 q^{72} + 7 q^{73} - 35 q^{74} - 12 q^{75} - 7 q^{76} + 78 q^{77} - 3 q^{78} - 10 q^{79} + q^{80} + 58 q^{81} - 30 q^{82} + 67 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 109 q^{87} + 10 q^{88} - 25 q^{89} - 73 q^{90} + 37 q^{91} + q^{92} + 56 q^{93} - 39 q^{94} - 29 q^{95} - 153 q^{97} + 164 q^{98} - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$363$
$\chi(n)$	$e\left(\frac{7}{57}\right)$

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 $

$2$	−0.926494	−	0.376309i	−0.655130	−	0.266091i
$2$	−0.926494	−	0.376309i	−0.655130	−	0.266091i
$3$	1.98560	+	0.444982i	1.14638	+	0.256911i	0.750168	−	0.661247i	$-0.229972\pi$
$3$	1.98560	+	0.444982i	1.14638	+	0.256911i	0.396216	+	0.918157i	$0.370323\pi$
$4$	0.716783	+	0.697297i	0.358391	+	0.348648i
$5$	−0.00459569	−	0.166723i	−0.00205525	−	0.0745608i	−0.999953	−	0.00974523i	$-0.996898\pi$
$5$	−0.00459569	−	0.166723i	−0.00205525	−	0.0745608i	0.997897	−	0.0648156i	$-0.0206459\pi$
$6$	−1.67219	−	1.15947i	−0.682669	−	0.473352i
$7$	−0.556362	−	2.19703i	−0.210285	−	0.830398i	−0.981126	−	0.193370i	$-0.938058\pi$
$7$	−0.556362	−	2.19703i	−0.210285	−	0.830398i	0.770841	−	0.637028i	$-0.219836\pi$
$8$	−0.401695	−	0.915773i	−0.142021	−	0.323775i
$9$	1.03151	+	0.486781i	0.343836	+	0.162260i
$10$	−0.0584816	+	0.156197i	−0.0184935	+	0.0493939i
$11$	0.477849	−	5.76678i	0.144077	−	1.73875i	−0.415166	−	0.909746i	$-0.636276\pi$
$11$	0.477849	−	5.76678i	0.144077	−	1.73875i	0.559243	−	0.829004i	$-0.311092\pi$
$12$	1.11296	+	1.70351i	0.321283	+	0.491760i
$13$	−1.18856	−	3.80005i	−0.329648	−	1.05394i	−0.960556	−	0.278086i	$-0.910300\pi$
$13$	−1.18856	−	3.80005i	−0.329648	−	1.05394i	0.630908	−	0.775857i	$-0.282682\pi$
$14$	−0.311295	+	2.24490i	−0.0831970	+	0.599974i
$15$	0.0650636	−	0.333090i	0.0167994	−	0.0860034i
$16$	0.0275543	+	0.999620i	0.00688859	+	0.249905i
$17$	−4.57094	+	4.44668i	−1.10862	+	1.07848i	−0.112217	+	0.993684i	$0.535795\pi$
$17$	−4.57094	+	4.44668i	−1.10862	+	1.07848i	−0.996398	+	0.0847942i	$0.972977\pi$
$18$	−0.772507	−	0.839166i	−0.182082	−	0.197793i
$19$	−2.26471	−	3.72439i	−0.519559	−	0.854434i
$19$	−2.26471	−	3.72439i	−0.519559	−	0.854434i
$20$	0.112961	−	0.122709i	0.0252589	−	0.0274385i
$21$	−0.127073	−	4.60998i	−0.0277296	−	1.00598i
$22$	−2.61282	+	5.16307i	−0.557055	+	1.10077i
$23$	−1.18158	+	0.264799i	−0.246377	+	0.0552144i	−0.340120	−	0.940382i	$-0.610468\pi$
$23$	−1.18158	+	0.264799i	−0.246377	+	0.0552144i	0.0937428	+	0.995596i	$0.470117\pi$
$24$	−0.390102	−	1.99710i	−0.0796292	−	0.407657i
$25$	4.96463	−	0.273906i	0.992926	−	0.0547813i
$26$	−0.328797	+	3.96799i	−0.0644824	+	0.778187i
$27$	−2.98579	−	2.32393i	−0.574615	−	0.447241i
$28$	1.13319	−	1.96274i	0.214152	−	0.370923i
$29$	3.96102	+	1.12007i	0.735543	+	0.207992i	0.619217	−	0.785220i	$-0.287450\pi$
$29$	3.96102	+	1.12007i	0.735543	+	0.207992i	0.116325	+	0.993211i	$0.462889\pi$
$30$	−0.185626	+	0.284121i	−0.0338905	+	0.0518732i
$31$	−1.74514	−	1.35830i	−0.313436	−	0.243957i	0.445261	−	0.895401i	$-0.353111\pi$
$31$	−1.74514	−	1.35830i	−0.313436	−	0.243957i	−0.758697	+	0.651444i	$0.774164\pi$
$32$	0.350638	−	0.936511i	0.0619845	−	0.165553i
$33$	3.51493	−	11.2379i	0.611871	−	1.95626i
$34$	5.90827	−	2.39973i	1.01326	−	0.411551i
$35$	−0.363738	+	0.102855i	−0.0614829	+	0.0173857i
$36$	0.399937	+	1.06818i	0.0666562	+	0.178031i
$37$	−0.382861	+	4.62044i	−0.0629419	+	0.759596i	0.889905	+	0.456145i	$0.150770\pi$
$37$	−0.382861	+	4.62044i	−0.0629419	+	0.759596i	−0.952847	+	0.303451i	$0.901861\pi$
$38$	0.696713	+	4.30286i	0.113022	+	0.698016i
$39$	−0.669051	−	8.07425i	−0.107134	−	1.29291i
$40$	−0.150834	+	0.0711805i	−0.0238490	+	0.0112546i
$41$	−0.796165	−	0.693381i	−0.124340	−	0.108288i	0.592346	−	0.805683i	$-0.298202\pi$
$41$	−0.796165	−	0.693381i	−0.124340	−	0.108288i	−0.716686	+	0.697396i	$0.754342\pi$
$42$	−1.61704	+	4.31893i	−0.249515	+	0.666426i
$43$	−0.148613	−	0.396927i	−0.0226632	−	0.0605308i	0.924690	−	0.380720i	$-0.124324\pi$
$43$	−0.148613	−	0.396927i	−0.0226632	−	0.0605308i	−0.947354	+	0.320189i	$0.896254\pi$
$44$	4.36367	−	3.80032i	0.657848	−	0.572920i
$45$	0.0764171	−	0.174213i	0.0113916	−	0.0259702i
$46$	1.19438	+	0.199306i	0.176101	+	0.0293861i
$47$	6.60022	+	4.57649i	0.962742	+	0.667550i	0.943188	−	0.332259i	$-0.107811\pi$
$47$	6.60022	+	4.57649i	0.962742	+	0.667550i	0.0195534	+	0.999809i	$0.493776\pi$
$48$	−0.390102	+	1.99710i	−0.0563063	+	0.288257i
$49$	1.63893	−	0.886946i	0.234133	−	0.126707i
$50$	−4.70278	−	1.61446i	−0.665073	−	0.228320i
$51$	−11.0547	+	6.79532i	−1.54797	+	0.951535i
$52$	1.79782	−	3.55259i	0.249313	−	0.492655i
$53$	9.15312	+	6.34663i	1.25728	+	0.871777i	0.995630	−	0.0933860i	$-0.0297691\pi$
$53$	9.15312	+	6.34663i	1.25728	+	0.871777i	0.261648	+	0.965163i	$0.415734\pi$
$54$	1.89180	+	3.27669i	0.257441	+	0.445901i
$55$	−0.963651	−	0.0531661i	−0.129939	−	0.00716892i
$56$	−1.78849	+	1.39204i	−0.238997	+	0.186019i
$57$	−2.83950	−	8.40289i	−0.376101	−	1.11299i
$58$	−3.24837	−	2.52831i	−0.426532	−	0.331983i
$59$	8.44825	+	7.35759i	1.09987	+	0.957877i	0.999313	−	0.0370549i	$-0.0117976\pi$
$59$	8.44825	+	7.35759i	1.09987	+	0.957877i	0.100556	+	0.994931i	$0.467938\pi$
$60$	0.278899	−	0.193384i	0.0360057	−	0.0249658i
$61$	1.86467	+	2.53697i	0.238746	+	0.324826i	0.908600	−	0.417667i	$-0.137152\pi$
$61$	1.86467	+	2.53697i	0.238746	+	0.324826i	−0.669854	+	0.742493i	$0.733643\pi$
$62$	1.10572	+	1.91517i	0.140427	+	0.243226i
$63$	0.495577	−	2.53708i	0.0624368	−	0.319642i
$64$	−0.677282	+	0.735724i	−0.0846602	+	0.0919655i
$65$	−0.628093	+	0.215625i	−0.0779054	+	0.0267449i
$66$	−7.48547	+	9.08911i	−0.921398	+	1.11879i
$67$	0.653808	+	0.0723634i	0.0798753	+	0.00884060i	0.149857	−	0.988708i	$-0.452119\pi$
$67$	0.653808	+	0.0723634i	0.0798753	+	0.00884060i	−0.0699817	+	0.997548i	$0.522294\pi$
$68$	−6.37702			−0.773328
$69$	−2.46398			−0.296628
$70$	0.375706	+	0.0415832i	0.0449055	+	0.00497014i
$71$	6.98466	−	9.50297i	0.828926	−	1.12779i	−0.161104	−	0.986938i	$-0.551505\pi$
$71$	6.98466	−	9.50297i	0.828926	−	1.12779i	0.990030	−	0.140857i	$-0.0449859\pi$
$72$	0.0314285	−	1.14017i	0.00370388	−	0.134370i
$73$	−0.990741	+	0.963807i	−0.115957	+	0.112805i	−0.752991	−	0.658031i	$-0.771389\pi$
$73$	−0.990741	+	0.963807i	−0.115957	+	0.112805i	0.637033	+	0.770836i	$0.280161\pi$
$74$	2.09343	−	4.13674i	0.243357	−	0.480886i
$75$	9.97964	+	1.66531i	1.15235	+	0.192293i
$76$	0.973706	−	4.24875i	0.111692	−	0.487365i
$77$	−12.9356	+	2.15857i	−1.47415	+	0.245992i
$78$	−2.41854	+	7.73251i	−0.273846	+	0.875534i
$79$	−3.09211	−	8.25867i	−0.347890	−	0.929173i	−0.987095	−	0.160136i	$-0.948807\pi$
$79$	−3.09211	−	8.25867i	−0.347890	−	0.929173i	0.639205	−	0.769036i	$-0.279264\pi$
$80$	0.166533	−	0.00918789i	0.0186190	−	0.00102724i
$81$	−7.06978	−	8.58435i	−0.785531	−	0.953817i
$82$	0.476717	+	0.942018i	0.0526445	+	0.104028i
$83$	−2.65030	+	1.43427i	−0.290908	+	0.157432i	−0.614847	−	0.788646i	$-0.710782\pi$
$83$	−2.65030	+	1.43427i	−0.290908	+	0.157432i	0.323939	+	0.946078i	$0.394993\pi$
$84$	3.12344	−	3.39296i	0.340795	−	0.370202i
$85$	0.762370	+	0.741645i	0.0826907	+	0.0804427i
$86$	−0.0116785	+	0.423675i	−0.00125933	+	0.0456861i
$87$	7.36657	+	3.98659i	0.789779	+	0.427407i
$88$	−5.47301	+	1.87889i	−0.583425	+	0.200290i
$89$	−4.60596	−	4.48074i	−0.488230	−	0.474958i	0.411496	−	0.911411i	$-0.365006\pi$
$89$	−4.60596	−	4.48074i	−0.488230	−	0.474958i	−0.899727	+	0.436453i	$0.856234\pi$
$90$	−0.136358	+	0.132651i	−0.0143734	+	0.0139827i
$91$	−7.68753	+	4.72551i	−0.805872	+	0.495368i
$92$	−1.03158	−	0.634111i	−0.107550	−	0.0661107i
$93$	−2.86072	−	3.47359i	−0.296643	−	0.360194i
$94$	−4.39289	−	6.72382i	−0.453092	−	0.693509i
$95$	−0.610534	+	0.394695i	−0.0626395	+	0.0404948i
$96$	1.11296	−	1.70351i	0.113591	−	0.173863i
$97$	12.3525	−	1.36718i	1.25421	−	0.138816i	0.541755	−	0.840536i	$-0.317760\pi$
$97$	12.3525	−	1.36718i	1.25421	−	0.138816i	0.712452	+	0.701721i	$0.247585\pi$
$98$	−1.85223	+	0.205005i	−0.187103	+	0.0207086i
$99$	3.30006	−	5.71588i	0.331669	−	0.574467i
$100$	3.74956	+	3.26549i	0.374956	+	0.326549i
$101$	1.51135	+	0.713223i	0.150385	+	0.0709683i	0.500491	−	0.865742i	$-0.333153\pi$
$101$	1.51135	+	0.713223i	0.150385	+	0.0709683i	−0.350106	+	0.936710i	$0.613855\pi$
$102$	12.7993	−	2.13582i	1.26732	−	0.211478i
$103$	4.56488	−	18.0263i	0.449791	−	1.77618i	−0.163732	−	0.986505i	$-0.552353\pi$
$103$	4.56488	−	18.0263i	0.449791	−	1.77618i	0.613522	−	0.789678i	$-0.289752\pi$
$104$	−3.00254	+	2.61492i	−0.294423	+	0.256414i
$105$	−0.768005	+	0.0423720i	−0.0749496	+	0.00413509i
$106$	−6.09202	−	9.32453i	−0.591709	−	0.905678i
$107$	−11.7066	+	9.11164i	−1.13172	+	0.880855i	−0.993974	−	0.109612i	$-0.965039\pi$
$107$	−11.7066	+	9.11164i	−1.13172	+	0.880855i	−0.137749	+	0.990467i	$0.543987\pi$
$108$	−0.519690	−	3.74773i	−0.0500072	−	0.360626i
$109$	2.66998	−	1.85132i	0.255737	−	0.177324i	−0.434999	−	0.900431i	$-0.643251\pi$
$109$	2.66998	−	1.85132i	0.255737	−	0.177324i	0.690736	+	0.723107i	$0.257286\pi$
$110$	0.872810	+	0.411889i	0.0832192	+	0.0392721i
$111$	−2.81622	+	9.00397i	−0.267304	+	0.854619i
$112$	2.18086	−	0.616689i	0.206072	−	0.0582716i
$113$	−2.28094	+	9.00723i	−0.214573	+	0.847329i	0.764634	+	0.644465i	$0.222920\pi$
$113$	−2.28094	+	9.00723i	−0.214573	+	0.847329i	−0.979207	+	0.202864i	$0.934975\pi$
$114$	−0.531306	+	8.85376i	−0.0497614	+	0.829231i
$115$	0.0495783	+	0.195780i	0.00462320	+	0.0182566i
$116$	2.05817	+	3.56485i	0.191096	+	0.330988i
$117$	0.623777	−	4.49835i	0.0576682	−	0.415873i
$118$	−5.05853	−	9.99592i	−0.465675	−	0.920199i
$119$	12.3126	+	7.56851i	1.12869	+	0.693804i
$120$	−0.331170	+	0.0742170i	−0.0302316	+	0.00677505i
$121$	−22.1774	−	3.70076i	−2.01613	−	0.336433i
$122$	−0.772916	−	3.05218i	−0.0699766	−	0.276331i
$123$	−1.27232	−	1.73105i	−0.114721	−	0.156084i
$124$	−0.303750	−	2.19048i	−0.0272775	−	0.196711i
$125$	−0.137348	−	1.65754i	−0.0122848	−	0.148255i
$126$	−1.41388	+	2.16410i	−0.125958	+	0.192793i
$127$	6.14102	−	10.6366i	0.544927	−	0.943842i	−0.453684	−	0.891162i	$-0.649891\pi$
$127$	6.14102	−	10.6366i	0.544927	−	0.943842i	0.998611	−	0.0526791i	$-0.0167760\pi$
$128$	0.904357	−	0.426776i	0.0799346	−	0.0377221i
$129$	−0.118459	−	0.854267i	−0.0104298	−	0.0752140i
$130$	0.663066	+	0.0365824i	0.0581547	+	0.00320849i
$131$	−2.18434	+	15.7523i	−0.190846	+	1.37628i	0.617034	+	0.786937i	$0.288334\pi$
$131$	−2.18434	+	15.7523i	−0.190846	+	1.37628i	−0.807880	+	0.589347i	$0.799385\pi$
$132$	10.3556	−	5.60415i	0.901336	−	0.487779i
$133$	−6.92259	+	7.04773i	−0.600265	+	0.611116i
$134$	−0.578518	−	0.313078i	−0.0499763	−	0.0270458i
$135$	−0.373731	+	0.508480i	−0.0321657	+	0.0437630i
$136$	5.90827	+	2.39973i	0.506630	+	0.205775i
$137$	−7.01388	−	0.776296i	−0.599236	−	0.0663234i	−0.194727	−	0.980857i	$-0.562382\pi$
$137$	−7.01388	−	0.776296i	−0.599236	−	0.0663234i	−0.404509	+	0.914534i	$0.632558\pi$
$138$	2.28286	+	0.927218i	0.194330	+	0.0789301i
$139$	−9.93135	+	12.0590i	−0.842366	+	1.02283i	0.157013	+	0.987597i	$0.449814\pi$
$139$	−9.93135	+	12.0590i	−0.842366	+	1.02283i	−0.999379	+	0.0352320i	$0.988783\pi$
$140$	−0.332442	−	0.179908i	−0.0280964	−	0.0152050i
$141$	11.0689	+	12.0241i	0.932171	+	1.01261i
$142$	−10.0473	+	6.17605i	−0.843151	+	0.518283i
$143$	−22.4820	+	5.03833i	−1.88004	+	0.421326i
$144$	−0.458173	+	1.04453i	−0.0381811	+	0.0870442i
$145$	0.168538	−	0.665541i	0.0139963	−	0.0552701i
$146$	1.28060	−	0.520137i	0.105984	−	0.0430468i
$147$	3.64893	−	1.03182i	0.300959	−	0.0851031i
$148$	−3.49625	+	3.04489i	−0.287390	+	0.250288i
$149$	−2.58287	−	13.2229i	−0.211597	−	1.08326i	−0.924263	−	0.381756i	$-0.875320\pi$
$149$	−2.58287	−	13.2229i	−0.211597	−	1.08326i	0.712666	−	0.701503i	$-0.247487\pi$
$150$	−8.61940	−	5.29833i	−0.703771	−	0.432607i
$151$	5.85379	+	2.00961i	0.476375	+	0.163540i	0.552422	−	0.833564i	$-0.313704\pi$
$151$	5.85379	+	2.00961i	0.476375	+	0.163540i	−0.0760472	+	0.997104i	$0.524230\pi$
$152$	−2.50098	+	3.57003i	−0.202856	+	0.289568i
$153$	−6.87952	+	2.36174i	−0.556176	+	0.190936i
$154$	12.7971	+	2.86789i	1.03122	+	0.231101i
$155$	−0.218439	+	0.297197i	−0.0175455	+	0.0238715i
$156$	5.15058	−	6.25401i	0.412377	−	0.500721i
$157$	15.1369	+	3.39226i	1.20806	+	0.270732i	0.775776	−	0.631008i	$-0.217359\pi$
$157$	15.1369	+	3.39226i	1.20806	+	0.270732i	0.432279	+	0.901740i	$0.357709\pi$
$158$	−0.242989	+	8.81520i	−0.0193312	+	0.701300i
$159$	15.3503	+	16.6748i	1.21735	+	1.32240i
$160$	−0.157749	−	0.0541554i	−0.0124712	−	0.00428136i
$161$	1.23916	+	2.44865i	0.0976595	+	0.192980i
$162$	3.31973	+	10.6138i	0.260823	+	0.833897i
$163$	16.4005	−	12.7650i	1.28458	−	0.999832i	0.285443	−	0.958396i	$-0.407859\pi$
$163$	16.4005	−	12.7650i	1.28458	−	0.999832i	0.999141	−	0.0414359i	$-0.0131932\pi$
$164$	−0.0871850	−	1.05217i	−0.00680801	−	0.0821604i
$165$	−1.88976	−	0.534374i	−0.147118	−	0.0416010i
$166$	2.99522	−	0.331511i	0.232474	−	0.0257302i
$167$	18.5766	+	5.25298i	1.43750	+	0.406487i	0.899673	−	0.436565i	$-0.143805\pi$
$167$	18.5766	+	5.25298i	1.43750	+	0.406487i	0.537831	+	0.843052i	$0.319244\pi$
$168$	−4.17065	+	1.96818i	−0.321773	+	0.151848i
$169$	−2.34456	+	1.62568i	−0.180351	+	0.125053i
$170$	−0.427244	−	0.974017i	−0.0327681	−	0.0747037i
$171$	−0.523102	−	4.94416i	−0.0400026	−	0.378089i
$172$	0.170253	−	0.388138i	0.0129817	−	0.0295952i
$173$	2.29852	+	11.7671i	0.174753	+	0.894638i	0.960963	+	0.276678i	$0.0892336\pi$
$173$	2.29852	+	11.7671i	0.174753	+	0.894638i	−0.786210	+	0.617960i	$0.787959\pi$
$174$	−5.32489	−	6.46566i	−0.403679	−	0.490160i
$175$	−3.36391	−	10.7550i	−0.254288	−	0.813004i
$176$	5.77776	+	0.318768i	0.435515	+	0.0240280i
$177$	13.5008	+	18.3685i	1.01478	+	1.38066i
$178$	2.58125	+	5.88465i	0.193473	+	0.441073i
$179$	−9.54825	+	1.59332i	−0.713670	+	0.119090i	−0.510281	−	0.860008i	$-0.670459\pi$
$179$	−9.54825	+	1.59332i	−0.713670	+	0.119090i	−0.203389	+	0.979098i	$0.565196\pi$
$180$	0.176253	−	0.0715877i	0.0131371	−	0.00533584i
$181$	9.99971	−	4.06153i	0.743272	−	0.301891i	0.0269274	−	0.999637i	$-0.491428\pi$
$181$	9.99971	−	4.06153i	0.743272	−	0.301891i	0.716345	+	0.697746i	$0.245814\pi$
$182$	8.90070	−	1.48526i	0.659764	−	0.110095i
$183$	2.57357	+	5.86714i	0.190243	+	0.433711i
$184$	0.717133	+	0.975694i	0.0528677	+	0.0719291i
$185$	0.772094	+	0.0425976i	0.0567655	+	0.00313184i
$186$	1.34330	+	4.29477i	0.0984956	+	0.314908i
$187$	23.4588	+	28.4844i	1.71548	+	2.08299i
$188$	1.53975	+	7.88267i	0.112298	+	0.574903i
$189$	−3.44456	+	7.85280i	−0.250555	+	0.571207i
$190$	0.714184	−	0.135933i	0.0518123	−	0.00986159i
$191$	4.02133	+	9.16772i	0.290974	+	0.663353i	0.999086	−	0.0427468i	$-0.0136109\pi$
$191$	4.02133	+	9.16772i	0.290974	+	0.663353i	−0.708112	+	0.706100i	$0.750453\pi$
$192$	−1.67219	+	1.15947i	−0.120680	+	0.0836777i
$193$	−2.51821	+	1.18837i	−0.181265	+	0.0855409i	−0.515260	−	0.857034i	$-0.672305\pi$
$193$	−2.51821	+	1.18837i	−0.181265	+	0.0855409i	0.333996	+	0.942575i	$0.391603\pi$
$194$	−11.9590	−	3.38169i	−0.858607	−	0.242791i
$195$	−1.34309	+	0.148653i	−0.0961805	+	0.0106453i
$196$	1.79322	+	0.507075i	0.128087	+	0.0362197i
$197$	−0.122315	−	1.47612i	−0.00871457	−	0.105169i	0.990839	−	0.135049i	$-0.0431192\pi$
$197$	−0.122315	−	1.47612i	−0.00871457	−	0.105169i	−0.999554	+	0.0298797i	$0.990488\pi$
$198$	−5.20843	+	4.05388i	−0.370147	+	0.288097i
$199$	5.08690	+	16.2637i	0.360601	+	1.15290i	0.940952	+	0.338539i	$0.109933\pi$
$199$	5.08690	+	16.2637i	0.360601	+	1.15290i	−0.580352	+	0.814366i	$0.697085\pi$
$200$	−2.24511	−	4.43645i	−0.158753	−	0.313704i
$201$	1.26600	+	0.434617i	0.0892966	+	0.0306556i
$202$	−1.13186	−	1.22953i	−0.0796377	−	0.0865096i
$203$	0.257059	−	9.32562i	0.0180420	−	0.654531i
$204$	−12.6622	−	2.83766i	−0.886531	−	0.198676i
$205$	−0.111944	+	0.135926i	−0.00781848	+	0.00949346i
$206$	−11.0128	+	14.9834i	−0.767297	+	1.04395i
$207$	−1.34771	−	0.302030i	−0.0936726	−	0.0209925i
$208$	3.76585	−	1.29282i	0.261115	−	0.0896409i
$209$	−22.5599	+	11.2804i	−1.56050	+	0.780279i
$210$	0.727497	+	0.249750i	0.0502021	+	0.0172344i
$211$	−20.6153	−	12.6722i	−1.41922	−	0.872390i	−0.419838	−	0.907599i	$-0.637913\pi$
$211$	−20.6153	−	12.6722i	−1.41922	−	0.872390i	−0.999380	+	0.0352095i	$0.988790\pi$
$212$	2.13531	+	10.9316i	0.146654	+	0.750785i
$213$	18.0974	−	15.7610i	1.24001	−	1.07993i
$214$	14.2749	−	4.03656i	0.975814	−	0.275934i
$215$	−0.0654939	+	0.0266013i	−0.00446665	+	0.00181420i
$216$	−0.928818	+	3.66782i	−0.0631980	+	0.249563i
$217$	−2.01328	+	4.58982i	−0.136671	+	0.311577i
$218$	−3.17038	+	0.710500i	−0.214726	+	0.0481211i
$219$	−2.39609	+	1.47287i	−0.161913	+	0.0995273i
$220$	−0.653656	−	0.710059i	−0.0440695	−	0.0478722i
$221$	22.3304	+	12.0846i	1.50211	+	0.812900i
$222$	5.99749	−	7.28235i	0.402525	−	0.488759i
$223$	−15.9359	−	6.47262i	−1.06715	−	0.433439i	−0.225937	−	0.974142i	$-0.572544\pi$
$223$	−15.9359	−	6.47262i	−1.06715	−	0.433439i	−0.841214	+	0.540703i	$0.818158\pi$
$224$	−2.25262	−	0.249320i	−0.150510	−	0.0166584i
$225$	5.25440	+	2.13415i	0.350293	+	0.142277i
$226$	5.50279	−	7.48681i	0.366040	−	0.498015i
$227$	4.99446	+	2.70287i	0.331494	+	0.179396i	0.633166	−	0.774016i	$-0.281755\pi$
$227$	4.99446	+	2.70287i	0.331494	+	0.179396i	−0.301672	+	0.953412i	$0.597545\pi$
$228$	3.82401	−	8.00302i	0.253251	−	0.530013i
$229$	−10.6178	+	5.74608i	−0.701645	+	0.379711i	−0.787264	−	0.616617i	$-0.788503\pi$
$229$	−10.6178	+	5.74608i	−0.701645	+	0.379711i	0.0856183	+	0.996328i	$0.472713\pi$
$230$	0.0277400	−	0.200046i	0.00182912	−	0.0131906i
$231$	−26.6454	−	1.47007i	−1.75314	−	0.0967235i
$232$	−0.565393	−	4.07732i	−0.0371199	−	0.267689i
$233$	7.02052	−	3.31307i	0.459930	−	0.217046i	−0.182783	−	0.983153i	$-0.558511\pi$
$233$	7.02052	−	3.31307i	0.459930	−	0.217046i	0.642713	+	0.766107i	$0.277809\pi$
$234$	−2.27070	+	3.93296i	−0.148440	+	0.257106i
$235$	0.732674	−	1.12144i	0.0477944	−	0.0731548i
$236$	0.925136	+	11.1647i	0.0602212	+	0.726762i
$237$	−2.46473	−	17.7743i	−0.160101	−	1.15457i
$238$	−8.55942	−	11.6455i	−0.554825	−	0.754866i
$239$	2.24631	+	8.87047i	0.145302	+	0.573783i	0.998626	+	0.0524029i	$0.0166880\pi$
$239$	2.24631	+	8.87047i	0.145302	+	0.573783i	−0.853324	+	0.521380i	$0.825417\pi$
$240$	0.334756	+	0.0558609i	0.0216084	+	0.00360580i
$241$	−7.26264	+	1.62760i	−0.467828	+	0.104843i	−0.446219	−	0.894924i	$-0.647230\pi$
$241$	−7.26264	+	1.62760i	−0.467828	+	0.104843i	−0.0216088	+	0.999767i	$0.506879\pi$
$242$	19.1546	+	11.7743i	1.23131	+	0.756881i
$243$	−5.09257	−	10.0632i	−0.326689	−	0.645554i
$244$	−0.432461	+	3.11868i	−0.0276855	+	0.199653i
$245$	−0.155406	−	0.269172i	−0.00992855	−	0.0171968i
$246$	0.527385	+	2.08260i	0.0336249	+	0.132782i
$247$	−11.4611	+	13.0327i	−0.729254	+	0.829249i
$248$	−0.542877	+	2.14377i	−0.0344728	+	0.136130i
$249$	−5.90065	+	1.66855i	−0.373939	+	0.105740i
$250$	−0.496497	+	1.58739i	−0.0314012	+	0.100395i
$251$	−13.8988	−	6.55899i	−0.877282	−	0.414000i	−0.0654265	−	0.997857i	$-0.520841\pi$
$251$	−13.8988	−	6.55899i	−0.877282	−	0.414000i	−0.811856	+	0.583858i	$0.801543\pi$
$252$	2.12432	−	1.47297i	0.133819	−	0.0927883i
$253$	0.962420	+	6.94047i	0.0605068	+	0.436344i
$254$	−9.69225	+	7.54378i	−0.608146	+	0.473339i
$255$	1.18374	+	1.81185i	0.0741287	+	0.113462i
$256$	−0.998482	+	0.0550878i	−0.0624051	+	0.00344299i
$257$	−17.3430	+	15.1040i	−1.08183	+	0.942164i	−0.998521	−	0.0543598i	$-0.982688\pi$
$257$	−17.3430	+	15.1040i	−1.08183	+	0.942164i	−0.0833059	+	0.996524i	$0.526548\pi$
$258$	−0.211717	+	0.836051i	−0.0131809	+	0.0520502i
$259$	10.3642	−	1.72949i	0.644003	−	0.107465i
$260$	−0.600561	−	0.283411i	−0.0372452	−	0.0175764i
$261$	3.54060	+	3.08351i	0.219158	+	0.190864i
$262$	7.95151	−	13.7724i	0.491246	−	0.850862i
$263$	24.2438	−	2.68331i	1.49494	−	0.165460i	0.674960	−	0.737855i	$-0.264161\pi$
$263$	24.2438	−	2.68331i	1.49494	−	0.165460i	0.819978	+	0.572395i	$0.193986\pi$
$264$	−11.7033	+	1.29532i	−0.720286	+	0.0797212i
$265$	1.01607	−	1.55520i	0.0624164	−	0.0955354i
$266$	9.06587	−	3.92465i	0.555864	−	0.240635i
$267$	−7.15172	−	10.9465i	−0.437678	−	0.669916i
$268$	0.418179	+	0.507767i	0.0255444	+	0.0310168i
$269$	−14.9182	−	9.17018i	−0.909579	−	0.559116i	−0.0119794	−	0.999928i	$-0.503813\pi$
$269$	−14.9182	−	9.17018i	−0.909579	−	0.559116i	−0.897599	+	0.440812i	$0.854690\pi$
$270$	0.537605	−	0.330465i	0.0327176	−	0.0201115i
$271$	6.49018	−	6.31374i	0.394250	−	0.383533i	−0.473284	−	0.880910i	$-0.656932\pi$
$271$	6.49018	−	6.31374i	0.394250	−	0.383533i	0.867534	+	0.497377i	$0.165704\pi$
$272$	−4.57094	−	4.44668i	−0.277154	−	0.269619i
$273$	−17.3671	+	5.96213i	−1.05110	+	0.360845i
$274$	6.20619	+	3.35862i	0.374930	+	0.202902i
$275$	0.792787	−	28.7608i	0.0478068	−	1.73434i
$276$	−1.76614	−	1.71812i	−0.106309	−	0.103419i
$277$	−11.0968	+	12.0544i	−0.666744	+	0.724277i	−0.973798	−	0.227415i	$-0.926972\pi$
$277$	−11.0968	+	12.0544i	−0.666744	+	0.724277i	0.307054	+	0.951692i	$0.400657\pi$
$278$	13.7392	−	7.43530i	0.824025	−	0.445940i
$279$	−1.13893	−	2.25060i	−0.0681862	−	0.134740i
$280$	0.240304	+	0.291785i	0.0143609	+	0.0174375i
$281$	7.93775	−	0.437938i	0.473527	−	0.0261252i	0.183247	−	0.983067i	$-0.441339\pi$
$281$	7.93775	−	0.437938i	0.473527	−	0.0261252i	0.290280	+	0.956942i	$0.406252\pi$
$282$	−5.73052	−	15.3055i	−0.341248	−	0.911432i
$283$	9.67234	−	30.9242i	0.574961	−	1.83825i	0.0303903	−	0.999538i	$-0.490325\pi$
$283$	9.67234	−	30.9242i	0.574961	−	1.83825i	0.544571	−	0.838715i	$-0.316693\pi$
$284$	11.6329	−	1.94118i	0.690284	−	0.115188i
$285$	−1.38791	+	0.512027i	−0.0822125	+	0.0303299i
$286$	22.7254	+	3.79220i	1.34378	+	0.224237i
$287$	−1.08042	+	2.13497i	−0.0637751	+	0.126023i
$288$	0.817562	−	0.795336i	0.0481753	−	0.0468656i
$289$	0.652113	−	23.6574i	0.0383596	−	1.39161i
$290$	−0.406598	+	0.553197i	−0.0238763	+	0.0324848i
$291$	25.1355	+	2.78199i	1.47347	+	0.163083i
$292$	−1.38221			−0.0808874
$293$	−27.4869			−1.60580			−0.802900	−	0.596114i	$-0.796711\pi$
$293$	−27.4869			−1.60580			−0.802900	+	0.596114i	$0.796711\pi$
$294$	−3.76900	−	0.417153i	−0.219813	−	0.0243288i
$295$	1.18785	−	1.44233i	0.0691595	−	0.0839758i
$296$	4.38507	−	1.50540i	0.254877	−	0.0874994i
$297$	−14.8284	+	16.1079i	−0.860429	+	0.934675i
$298$	−2.58287	+	13.2229i	−0.149622	+	0.765980i
$299$	2.41064	+	4.17534i	0.139411	+	0.241466i
$300$	5.99202	+	8.15243i	0.345949	+	0.470681i
$301$	−0.789377	+	0.547342i	−0.0454989	+	0.0315483i
$302$	−4.66727	−	4.06473i	−0.268571	−	0.233899i
$303$	2.68356	+	2.08870i	0.154166	+	0.119992i
$304$	3.66058	−	2.36647i	0.209948	−	0.135726i
$305$	0.414402	−	0.322542i	0.0237286	−	0.0184687i
$306$	7.26258	+	0.400688i	0.415174	+	0.0229058i
$307$	2.49222	+	4.31666i	0.142239	+	0.246365i	0.928339	−	0.371734i	$-0.121237\pi$
$307$	2.49222	+	4.31666i	0.142239	+	0.246365i	−0.786101	+	0.618098i	$0.787903\pi$
$308$	−10.7772	−	7.47274i	−0.614088	−	0.425799i
$309$	17.0854	−	33.7616i	0.971953	−	1.92063i
$310$	0.314221	−	0.193151i	0.0178465	−	0.0109702i
$311$	27.5181	+	9.44698i	1.56041	+	0.535689i	0.963750	−	0.266806i	$-0.0859684\pi$
$311$	27.5181	+	9.44698i	1.56041	+	0.535689i	0.596659	+	0.802495i	$0.296495\pi$
$312$	−7.12542	+	3.85609i	−0.403398	+	0.218308i
$313$	−4.58562	+	23.4758i	−0.259194	+	1.32693i	0.593632	+	0.804736i	$0.297693\pi$
$313$	−4.58562	+	23.4758i	−0.259194	+	1.32693i	−0.852827	+	0.522194i	$0.825114\pi$
$314$	−12.7477	−	8.83906i	−0.719395	−	0.498817i
$315$	−0.425267	−	0.0709645i	−0.0239611	−	0.00399840i
$316$	3.54237	−	8.07579i	0.199274	−	0.454299i
$317$	−6.45207	+	5.61911i	−0.362384	+	0.315601i	−0.818705	−	0.574215i	$-0.805307\pi$
$317$	−6.45207	+	5.61911i	−0.362384	+	0.315601i	0.456320	+	0.889816i	$0.349167\pi$
$318$	−7.94703	−	21.2256i	−0.445647	−	1.19027i
$319$	8.35196	−	22.3071i	0.467620	−	1.24896i
$320$	0.125775	+	0.109537i	0.00703102	+	0.00612332i
$321$	−27.2992	+	12.8828i	−1.52369	+	0.719047i
$322$	−0.226626	−	2.73496i	−0.0126293	−	0.152414i
$323$	26.9130	+	6.95355i	1.49748	+	0.386906i
$324$	0.918351	−	11.0828i	0.0510195	−	0.615714i
$325$	−6.94163	−	18.5403i	−0.385053	−	1.02843i
$326$	−19.9985	+	5.65504i	−1.10762	+	0.313204i
$327$	6.12530	−	2.48788i	0.338730	−	0.137580i
$328$	−0.315164	+	1.00763i	−0.0174020	+	0.0556373i
$329$	6.38256	−	17.0471i	0.351882	−	0.939834i
$330$	1.54976	+	1.20623i	0.0853117	+	0.0664008i
$331$	12.6190	−	19.3148i	0.693604	−	1.06164i	−0.300560	−	0.953763i	$-0.597174\pi$
$331$	12.6190	−	19.3148i	0.693604	−	1.06164i	0.994164	−	0.107877i	$-0.0344053\pi$
$332$	−2.89980	−	0.819986i	−0.159147	−	0.0450026i
$333$	−2.64407	+	4.57966i	−0.144894	+	0.250964i
$334$	−15.2344	−	11.8574i	−0.833590	−	0.648809i
$335$	0.00905995	−	0.109337i	0.000494998	−	0.00597374i
$336$	4.60472	−	0.254050i	0.251208	−	0.0138595i
$337$	−0.179290	−	0.917863i	−0.00976653	−	0.0499992i	0.976250	−	0.216648i	$-0.0695124\pi$
$337$	−0.179290	−	0.917863i	−0.00976653	−	0.0499992i	−0.986016	+	0.166649i	$0.946705\pi$
$338$	2.78399	−	0.623906i	0.151429	−	0.0339360i
$339$	−8.53709	+	16.8697i	−0.463671	+	0.916239i
$340$	0.0293068	+	1.06320i	0.00158939	+	0.0576599i
$341$	−8.66691	+	9.41478i	−0.469340	+	0.509839i
$342$	−1.37588	+	4.77758i	−0.0743993	+	0.258342i
$343$	−13.6053	−	14.7793i	−0.734618	−	0.798007i
$344$	−0.303798	+	0.295540i	−0.0163797	+	0.0159344i
$345$	0.0113237	+	0.410802i	0.000609646	+	0.0221168i
$346$	2.29852	−	11.7671i	0.123569	−	0.632605i
$347$	2.93277	−	21.1496i	0.157439	−	1.13537i	−0.732987	−	0.680243i	$-0.761874\pi$
$347$	2.93277	−	21.1496i	0.157439	−	1.13537i	0.890426	−	0.455128i	$-0.150407\pi$
$348$	2.50039	+	7.99420i	0.134035	+	0.428534i
$349$	−6.01650	−	9.20894i	−0.322056	−	0.492943i	0.639034	−	0.769178i	$-0.279334\pi$
$349$	−6.01650	−	9.20894i	−0.322056	−	0.492943i	−0.961090	+	0.276235i	$0.910913\pi$
$350$	−0.930573	+	11.2303i	−0.0497412	+	0.600287i
$351$	−5.28225	+	14.1083i	−0.281946	+	0.753044i
$352$	−5.23310	−	2.46956i	−0.278925	−	0.131628i
$353$	−1.63825	−	3.73482i	−0.0871950	−	0.198785i	0.866766	−	0.498715i	$-0.166195\pi$
$353$	−1.63825	−	3.73482i	−0.0871950	−	0.198785i	−0.953961	+	0.299930i	$0.903037\pi$
$354$	−5.59618	−	22.0988i	−0.297434	−	1.17454i
$355$	−1.61646	−	1.12083i	−0.0857930	−	0.0594875i
$356$	−0.177061	−	6.42344i	−0.00938421	−	0.340442i
$357$	21.0799	+	20.5069i	1.11567	+	1.08534i
$358$	9.44598	+	2.11689i	0.499236	+	0.111881i
$359$	31.3853	+	12.7476i	1.65645	+	0.672793i	0.996886	−	0.0788537i	$-0.0251260\pi$
$359$	31.3853	+	12.7476i	1.65645	+	0.672793i	0.659566	+	0.751646i	$0.270740\pi$
$360$	−0.190236			−0.0100263
$361$	−8.74221	+	16.8693i	−0.460116	+	0.887859i
$362$	−10.7931			−0.567271
$363$	−42.3886	−	17.2168i	−2.22483	−	0.903647i
$364$	−8.80537	−	1.97333i	−0.461527	−	0.103431i
$365$	0.165242	+	0.160750i	0.00864916	+	0.00841404i
$366$	−0.176534	−	6.40433i	−0.00922758	−	0.334759i
$367$	17.6217	+	12.2186i	0.919847	+	0.637808i	0.932133	−	0.362117i	$-0.117946\pi$
$367$	17.6217	+	12.2186i	0.919847	+	0.637808i	−0.0122855	+	0.999925i	$0.503911\pi$
$368$	−0.297256	−	1.17384i	−0.0154956	−	0.0611906i
$369$	−0.483727	−	1.10279i	−0.0251818	−	0.0574088i
$370$	−0.699311	−	0.330013i	−0.0363554	−	0.0171565i
$371$	8.85126	−	23.6407i	0.459535	−	1.22736i
$372$	0.371603	−	4.48458i	0.0192667	−	0.232515i
$373$	−0.363783	−	0.556811i	−0.0188360	−	0.0288306i	0.827624	−	0.561282i	$-0.189692\pi$
$373$	−0.363783	−	0.556811i	−0.0188360	−	0.0288306i	−0.846460	+	0.532452i	$0.821271\pi$
$374$	−11.0155	−	35.2184i	−0.569597	−	1.82110i
$375$	0.464860	−	3.35233i	0.0240053	−	0.173113i
$376$	1.53975	−	7.88267i	0.0794066	−	0.406517i
$377$	−0.451603	−	16.3833i	−0.0232588	−	0.843784i
$378$	6.14645	−	5.97935i	0.316139	−	0.307545i
$379$	−24.5641	−	26.6837i	−1.26177	−	1.37065i	−0.898504	−	0.438965i	$-0.855345\pi$
$379$	−24.5641	−	26.6837i	−1.26177	−	1.37065i	−0.363268	−	0.931685i	$-0.618339\pi$
$380$	−0.712840	−	0.142813i	−0.0365679	−	0.00732616i
$381$	16.9267	−	18.3872i	0.867179	−	0.942007i
$382$	−0.275844	−	10.0071i	−0.0141134	−	0.512008i
$383$	7.13474	−	14.0986i	0.364568	−	0.720406i	−0.634032	−	0.773307i	$-0.718601\pi$
$383$	7.13474	−	14.0986i	0.364568	−	0.720406i	0.998600	+	0.0529009i	$0.0168467\pi$
$384$	1.98560	−	0.444982i	0.101327	−	0.0227079i
$385$	0.419332	+	2.14675i	0.0213711	+	0.109408i
$386$	2.78030	−	0.153394i	0.141514	−	0.00780752i
$387$	0.0399211	−	0.481776i	0.00202930	−	0.0244900i
$388$	9.80739	+	7.63340i	0.497895	+	0.387527i
$389$	−1.80035	+	3.11830i	−0.0912813	+	0.158104i	−0.908051	−	0.418861i	$-0.862430\pi$
$389$	−1.80035	+	3.11830i	−0.0912813	+	0.158104i	0.816769	+	0.576964i	$0.195763\pi$
$390$	1.30030	+	0.367691i	0.0658434	+	0.0186187i
$391$	4.22347	−	6.46450i	0.213590	−	0.326924i
$392$	−1.47059	−	1.14461i	−0.0742762	−	0.0578115i
$393$	−11.3467	+	30.3057i	−0.572365	+	1.52872i
$394$	−0.442154	+	1.41364i	−0.0222754	+	0.0712184i
$395$	−1.36270	+	0.553481i	−0.0685649	+	0.0278486i
$396$	6.35109	−	1.79592i	0.319154	−	0.0902482i
$397$	12.8948	+	34.4404i	0.647170	+	1.72851i	0.684298	+	0.729203i	$0.260109\pi$
$397$	12.8948	+	34.4404i	0.647170	+	1.72851i	−0.0371282	+	0.999311i	$0.511821\pi$
$398$	1.40721	−	16.9825i	0.0705370	−	0.851255i
$399$	−16.8816	+	10.9135i	−0.845136	+	0.546359i
$400$	0.410600	+	4.95520i	0.0205300	+	0.247760i
$401$	8.35303	−	3.94189i	0.417130	−	0.196848i	−0.206707	−	0.978403i	$-0.566275\pi$
$401$	8.35303	−	3.94189i	0.417130	−	0.196848i	0.623837	+	0.781554i	$0.285573\pi$
$402$	−1.00939	−	0.879077i	−0.0503437	−	0.0438444i
$403$	−3.08738	+	8.24604i	−0.153794	+	0.410764i
$404$	0.585981	+	1.56508i	0.0291536	+	0.0778659i
$405$	−1.39872	+	1.21815i	−0.0695029	+	0.0605301i
$406$	−3.74748	+	8.54340i	−0.185984	+	0.424002i
$407$	26.4621	+	4.41575i	1.31168	+	0.218881i
$408$	10.6636	+	7.39398i	0.527927	+	0.366057i
$409$	4.73531	−	24.2421i	0.234146	−	1.19870i	−0.660120	−	0.751161i	$-0.729494\pi$
$409$	4.73531	−	24.2421i	0.234146	−	1.19870i	0.894266	−	0.447537i	$-0.147699\pi$
$410$	0.154865	−	0.0838089i	0.00764825	−	0.00413903i
$411$	−13.5813	−	4.66246i	−0.669916	−	0.229982i
$412$	15.8417	−	9.73785i	0.780464	−	0.479750i
$413$	11.4645	−	22.6545i	0.564132	−	1.11476i
$414$	1.13499	+	0.786986i	0.0557818	+	0.0386783i
$415$	0.251306	+	0.435275i	0.0123361	+	0.0213668i
$416$	−3.97554	−	0.219337i	−0.194917	−	0.0107539i
$417$	−25.0857	+	19.5250i	−1.22845	+	0.956142i
$418$	25.1466	−	1.96167i	1.22996	−	0.0959486i
$419$	−17.4346	−	13.5699i	−0.851737	−	0.662934i	0.0912261	−	0.995830i	$-0.470921\pi$
$419$	−17.4346	−	13.5699i	−0.851737	−	0.662934i	−0.942963	+	0.332896i	$0.891974\pi$
$420$	−0.580039	−	0.505156i	−0.0283030	−	0.0246491i
$421$	−12.1984	+	8.45820i	−0.594515	+	0.412227i	−0.828481	−	0.560017i	$-0.810794\pi$
$421$	−12.1984	+	8.45820i	−0.594515	+	0.412227i	0.233966	+	0.972245i	$0.424830\pi$
$422$	14.3313	+	19.4985i	0.697637	+	0.949170i
$423$	4.58044	+	7.93356i	0.222709	+	0.385743i
$424$	2.13531	−	10.9316i	0.103700	−	0.530885i
$425$	−21.4751	+	23.3281i	−1.04169	+	1.13158i
$426$	−22.6981	+	7.79227i	−1.09973	+	0.377537i
$427$	4.53636	−	5.50819i	0.219530	−	0.266560i
$428$	−14.7446	−	1.63193i	−0.712708	−	0.0788826i
$429$	−46.8821			−2.26349
$430$	0.0706901			0.00340898
$431$	−23.8277	−	2.63725i	−1.14774	−	0.127032i	−0.484050	−	0.875041i	$-0.660835\pi$
$431$	−23.8277	−	2.63725i	−1.14774	−	0.127032i	−0.663689	+	0.748009i	$0.731010\pi$
$432$	2.24078	−	3.04869i	0.107809	−	0.146680i
$433$	0.602752	−	21.8667i	0.0289664	−	1.05085i	−0.835911	−	0.548864i	$-0.815060\pi$
$433$	0.602752	−	21.8667i	0.0289664	−	1.05085i	0.864878	−	0.501982i	$-0.167396\pi$
$434$	3.59249	−	3.49483i	0.172445	−	0.167757i
$435$	0.630802	−	1.24650i	0.0302446	−	0.0597650i
$436$	3.20471	+	0.534772i	0.153478	+	0.0256109i
$437$	3.66216	+	3.80099i	0.175185	+	0.181826i
$438$	2.77422	−	0.462935i	0.132557	−	0.0221199i
$439$	2.97483	−	9.51105i	0.141981	−	0.453938i	−0.856034	−	0.516920i	$-0.827079\pi$
$439$	2.97483	−	9.51105i	0.141981	−	0.453938i	0.998015	+	0.0629819i	$0.0200610\pi$
$440$	0.338406	+	0.903843i	0.0161329	+	0.0430890i
$441$	2.12232	−	0.117092i	0.101063	−	0.00557580i
$442$	−16.1415	−	19.5995i	−0.767771	−	0.932253i
$443$	−4.36915	−	8.63368i	−0.207585	−	0.410198i	0.764569	−	0.644541i	$-0.222952\pi$
$443$	−4.36915	−	8.63368i	−0.207585	−	0.410198i	−0.972154	+	0.234343i	$0.924706\pi$
$444$	−8.29706	+	4.49014i	−0.393761	+	0.213093i
$445$	−0.725876	+	0.788511i	−0.0344098	+	0.0373790i
$446$	12.3289	+	11.9937i	0.583788	+	0.567918i
$447$	0.755402	−	27.4046i	0.0357293	−	1.29619i
$448$	1.99322	+	1.07868i	0.0941707	+	0.0509626i
$449$	−7.27254	+	2.49667i	−0.343212	+	0.117825i	−0.490916	−	0.871207i	$-0.663338\pi$
$449$	−7.27254	+	2.49667i	−0.343212	+	0.117825i	0.147704	+	0.989032i	$0.452812\pi$
$450$	−4.06507	−	3.95456i	−0.191629	−	0.186420i
$451$	−4.37902	+	4.25998i	−0.206200	+	0.200595i
$452$	−7.91565	+	4.86573i	−0.372321	+	0.228865i
$453$	10.7290	+	6.59511i	0.504094	+	0.309865i
$454$	−3.61023	−	4.38366i	−0.169436	−	0.205735i
$455$	0.823180	+	1.25997i	0.0385913	+	0.0590684i
$456$	−6.55453	+	5.97574i	−0.306944	+	0.279840i
$457$	−5.59766	+	8.56785i	−0.261847	+	0.400787i	−0.943752	−	0.330654i	$-0.892731\pi$
$457$	−5.59766	+	8.56785i	−0.261847	+	0.400787i	0.681905	+	0.731441i	$0.261152\pi$
$458$	11.9996	−	1.32812i	0.560707	−	0.0620590i
$459$	23.9816	−	2.65429i	1.11937	−	0.123891i
$460$	−0.100980	+	0.174903i	−0.00470822	+	0.00815488i
$461$	21.7477	+	18.9401i	1.01289	+	0.882127i	0.993052	−	0.117676i	$-0.0375445\pi$
$461$	21.7477	+	18.9401i	1.01289	+	0.882127i	0.0198385	+	0.999803i	$0.493685\pi$
$462$	24.1336	+	11.3889i	1.12280	+	0.529861i
$463$	−12.1089	+	2.02062i	−0.562750	+	0.0939063i	−0.439130	−	0.898423i	$-0.644713\pi$
$463$	−12.1089	+	2.02062i	−0.562750	+	0.0939063i	−0.123619	+	0.992330i	$0.539450\pi$
$464$	−1.01050	+	3.99038i	−0.0469113	+	0.185249i
$465$	−0.565980	+	0.492912i	−0.0262467	+	0.0228583i
$466$	−7.75121	+	0.427646i	−0.359068	+	0.0198103i
$467$	6.41518	+	9.81916i	0.296859	+	0.454377i	0.954180	−	0.299234i	$-0.0967313\pi$
$467$	6.41518	+	9.81916i	0.296859	+	0.454377i	−0.657320	+	0.753611i	$0.728310\pi$
$468$	3.58380	−	2.78938i	0.165661	−	0.128939i
$469$	−0.204770	−	1.47669i	−0.00945539	−	0.0681873i
$470$	−1.10083	+	0.763297i	−0.0507774	+	0.0352083i
$471$	28.5463	+	13.4713i	1.31534	+	0.620725i
$472$	3.34426	−	10.6922i	0.153932	−	0.492148i
$473$	−2.36001	+	0.667346i	−0.108513	+	0.0306846i
$474$	−4.40509	+	17.3953i	−0.202332	+	0.798992i
$475$	−12.2636	−	17.8699i	−0.562691	−	0.819928i
$476$	3.54794	+	14.0105i	0.162619	+	0.642170i
$477$	6.35211	+	11.0022i	0.290843	+	0.503755i
$478$	1.25685	−	9.06375i	0.0574870	−	0.414566i
$479$	1.80363	+	3.56407i	0.0824100	+	0.162847i	0.929736	−	0.368226i	$-0.120035\pi$
$479$	1.80363	+	3.56407i	0.0824100	+	0.162847i	−0.847326	+	0.531073i	$0.821789\pi$
$480$	−0.289128	−	0.177727i	−0.0131968	−	0.00811207i
$481$	18.0130	−	4.03680i	0.821320	−	0.184062i
$482$	7.34127	+	1.22504i	0.334386	+	0.0557991i
$483$	1.37087	+	5.41342i	0.0623765	+	0.246319i
$484$	−13.3159	−	18.1169i	−0.605267	−	0.823495i
$485$	−0.284708	−	2.05316i	−0.0129279	−	0.0932294i
$486$	0.931363	+	11.2399i	0.0422475	+	0.509851i
$487$	−17.5019	+	26.7887i	−0.793087	+	1.21391i	0.180044	+	0.983659i	$0.442376\pi$
$487$	−17.5019	+	26.7887i	−0.793087	+	1.21391i	−0.973131	+	0.230252i	$0.926045\pi$
$488$	1.57426	−	2.72670i	0.0712634	−	0.123432i
$489$	38.2449	−	18.0482i	1.72949	−	0.816168i
$490$	0.0426913	+	0.307867i	0.00192859	+	0.0139080i
$491$	−15.2975	−	0.843989i	−0.690369	−	0.0380887i	−0.293493	−	0.955961i	$-0.594818\pi$
$491$	−15.2975	−	0.843989i	−0.690369	−	0.0380887i	−0.396875	+	0.917872i	$0.629906\pi$
$492$	0.295082	−	2.12797i	0.0133033	−	0.0959365i
$493$	−23.0862	+	12.4936i	−1.03975	+	0.562684i
$494$	15.5230	−	7.76176i	0.698412	−	0.349218i
$495$	−0.968135	−	0.523928i	−0.0435144	−	0.0235488i
$496$	1.30970	−	1.78190i	0.0588070	−	0.0800099i
$497$	−24.7643	−	10.0584i	−1.11083	−	0.451180i
$498$	6.09481	+	0.674573i	0.273115	+	0.0302284i
$499$	25.2516	+	10.2563i	1.13042	+	0.459135i	0.863381	−	0.504552i	$-0.168342\pi$
$499$	25.2516	+	10.2563i	1.13042	+	0.459135i	0.267034	+	0.963687i	$0.413956\pi$
$500$	1.05735	−	1.28387i	0.0472862	−	0.0574164i
$501$	34.5482	+	18.6966i	1.54350	+	0.835301i
$502$	10.4089	+	11.3071i	0.464573	+	0.504660i
$503$	7.81465	−	4.80365i	0.348438	−	0.214184i	−0.338387	−	0.941007i	$-0.609881\pi$
$503$	7.81465	−	4.80365i	0.348438	−	0.214184i	0.686825	+	0.726823i	$0.259004\pi$
$504$	−2.52246	+	0.565296i	−0.112359	+	0.0251803i
$505$	0.111965	−	0.255255i	0.00498238	−	0.0113587i
$506$	1.72009	−	6.79247i	0.0764672	−	0.301962i
$507$	−5.37876	+	2.18466i	−0.238879	+	0.0970243i
$508$	11.8186	−	3.34198i	0.524366	−	0.148277i
$509$	20.6366	−	17.9724i	0.914700	−	0.796613i	−0.0648331	−	0.997896i	$-0.520651\pi$
$509$	20.6366	−	17.9724i	0.914700	−	0.796613i	0.979533	+	0.201283i	$0.0645111\pi$
$510$	−0.414912	−	2.12412i	−0.0183726	−	0.0940576i
$511$	2.66872	+	1.64046i	0.118057	+	0.0725695i
$512$	0.945817	+	0.324699i	0.0417996	+	0.0143498i
$513$	−1.89330	+	16.3833i	−0.0835914	+	0.723339i
$514$	21.7520	−	7.46747i	0.959439	−	0.329376i
$515$	−3.02638	−	0.678227i	−0.133358	−	0.0298862i
$516$	0.510768	−	0.694925i	0.0224853	−	0.0305924i
$517$	29.5455	−	35.8752i	1.29941	−	1.57779i
$518$	−10.2532	−	2.29780i	−0.450501	−	0.100960i
$519$	−0.672238	+	24.3876i	−0.0295080	+	1.07050i
$520$	0.449765	+	0.488576i	0.0197235	+	0.0214255i
$521$	−27.9858	−	9.60754i	−1.22608	−	0.420914i	−0.365780	−	0.930701i	$-0.619198\pi$
$521$	−27.9858	−	9.60754i	−1.22608	−	0.420914i	−0.860300	+	0.509788i	$0.829724\pi$
$522$	−2.11999	−	4.18921i	−0.0927894	−	0.183357i
$523$	11.9155	+	38.0960i	0.521028	+	1.66582i	0.726507	+	0.687159i	$0.241142\pi$
$523$	11.9155	+	38.0960i	0.521028	+	1.66582i	−0.205478	+	0.978662i	$0.565875\pi$
$524$	−12.5497	+	9.76783i	−0.548237	+	0.426710i
$525$	−1.89357	−	22.8520i	−0.0826423	−	0.997344i
$526$	−23.4715	−	6.63711i	−1.02341	−	0.289392i
$527$	14.0168	−	1.55138i	0.610583	−	0.0675793i
$528$	11.3304	+	3.20394i	0.493094	+	0.139434i
$529$	−19.4742	+	9.19009i	−0.846704	+	0.399569i
$530$	−1.52662	+	1.05853i	−0.0663120	+	0.0459797i
$531$	5.13291	+	11.7019i	0.222750	+	0.507818i
$532$	−9.87635	+	0.224590i	−0.428194	+	0.00973722i
$533$	−1.68859	+	3.84959i	−0.0731409	+	0.166744i
$534$	2.50675	+	12.8331i	0.108478	+	0.555344i
$535$	1.57292	+	1.90989i	0.0680033	+	0.0825718i
$536$	−0.196363	−	0.627808i	−0.00848159	−	0.0271172i
$537$	−19.6680	−	1.08511i	−0.848735	−	0.0468260i
$538$	10.3708	+	14.1100i	0.447117	+	0.608324i
$539$	−4.33166	−	9.87520i	−0.186578	−	0.425355i
$540$	−0.622445	+	0.103868i	−0.0267858	+	0.00446976i
$541$	−10.2023	+	4.14383i	−0.438633	+	0.178157i	−0.584931	−	0.811083i	$-0.698878\pi$
$541$	−10.2023	+	4.14383i	−0.438633	+	0.178157i	0.146298	+	0.989241i	$0.453264\pi$
$542$	−8.38903	+	3.40733i	−0.360340	+	0.146357i
$543$	21.6627	−	3.61486i	0.929635	−	0.155129i
$544$	2.56162	+	5.83991i	0.109829	+	0.250384i
$545$	−0.320928	−	0.436638i	−0.0137470	−	0.0187035i
$546$	18.3341	+	1.01152i	0.784628	+	0.0432891i
$547$	11.3319	+	36.2300i	0.484516	+	1.54908i	0.799909	+	0.600122i	$0.204881\pi$
$547$	11.3319	+	36.2300i	0.484516	+	1.54908i	−0.315393	+	0.948961i	$0.602136\pi$
$548$	−4.48612	−	5.44719i	−0.191637	−	0.232692i
$549$	0.688471	+	3.52459i	0.0293832	+	0.150426i
$550$	−11.5575	+	26.3484i	−0.492813	+	1.12350i
$551$	−4.79897	−	17.2890i	−0.204443	−	0.736537i
$552$	0.989769	+	2.25645i	0.0421274	+	0.0960407i
$553$	−16.4242	+	11.3883i	−0.698427	+	0.484278i
$554$	14.8173	−	6.99246i	0.629527	−	0.297081i
$555$	1.51411	+	0.428150i	0.0642704	+	0.0181739i
$556$	−15.5273	+	1.71856i	−0.658504	+	0.0728832i
$557$	−32.3663	−	9.15233i	−1.37141	−	0.387797i	−0.494801	−	0.869007i	$-0.664759\pi$
$557$	−32.3663	−	9.15233i	−1.37141	−	0.387797i	−0.876605	+	0.481210i	$0.840198\pi$
$558$	0.208296	+	2.51376i	0.00881786	+	0.106416i
$559$	−1.33171	+	1.03651i	−0.0563252	+	0.0438397i
$560$	−0.112839	−	0.360766i	−0.00476831	−	0.0152451i
$561$	33.9046	+	66.9973i	1.43145	+	2.82863i
$562$	−7.51908	−	2.58130i	−0.317173	−	0.108886i
$563$	−3.05469	−	3.31827i	−0.128740	−	0.139849i	0.668024	−	0.744140i	$-0.267140\pi$
$563$	−3.05469	−	3.31827i	−0.128740	−	0.139849i	−0.796763	+	0.604291i	$0.793456\pi$
$564$	−0.450325	+	16.3370i	−0.0189621	+	0.687910i
$565$	1.51220	+	0.338891i	0.0636186	+	0.0142573i
$566$	−20.5984	+	25.0113i	−0.865817	+	1.05130i
$567$	−14.9267	+	20.3085i	−0.626862	+	0.852877i
$568$	−11.5083	−	2.57906i	−0.482876	−	0.108215i
$569$	−11.5613	+	3.96899i	−0.484674	+	0.166389i	−0.556198	−	0.831050i	$-0.687740\pi$
$569$	−11.5613	+	3.96899i	−0.484674	+	0.166389i	0.0715235	+	0.997439i	$0.477214\pi$
$570$	1.47857	+	0.0478919i	0.0619304	+	0.00200597i
$571$	32.1845	+	11.0490i	1.34688	+	0.462384i	0.901431	−	0.432923i	$-0.142518\pi$
$571$	32.1845	+	11.0490i	1.34688	+	0.462384i	0.445449	+	0.895307i	$0.353044\pi$
$572$	−19.6279	−	12.0652i	−0.820684	−	0.504473i
$573$	3.90527	+	19.9928i	0.163145	+	0.835211i
$574$	1.80441	−	1.57146i	0.0753146	−	0.0655916i
$575$	−5.79360	+	1.63827i	−0.241610	+	0.0683207i
$576$	−1.05676	+	0.429218i	−0.0440316	+	0.0178841i
$577$	6.70316	−	26.4702i	0.279056	−	1.10197i	−0.658064	−	0.752962i	$-0.728624\pi$
$577$	6.70316	−	26.4702i	0.279056	−	1.10197i	0.937120	−	0.349007i	$-0.113481\pi$
$578$	−9.50670	+	21.6731i	−0.395426	+	0.901482i
$579$	−5.52895	+	1.23907i	−0.229775	+	0.0514939i
$580$	0.584884	−	0.359527i	0.0242860	−	0.0149285i
$581$	4.62566	+	5.02481i	0.191905	+	0.208464i
$582$	−22.2410	−	12.0362i	−0.921918	−	0.498917i
$583$	40.9735	−	49.7513i	1.69695	−	2.06049i
$584$	1.28060	+	0.520137i	0.0529918	+	0.0215234i
$585$	−0.752846	−	0.0833249i	−0.0311263	−	0.00344506i
$586$	25.4664	+	10.3436i	1.05201	+	0.427289i
$587$	−18.8547	+	25.6528i	−0.778217	+	1.05880i	0.218338	+	0.975873i	$0.429936\pi$
$587$	−18.8547	+	25.6528i	−0.778217	+	1.05880i	−0.996555	+	0.0829295i	$0.973572\pi$
$588$	3.33498	+	1.80480i	0.137532	+	0.0744287i
$589$	−1.10660	+	9.57573i	−0.0455968	+	0.394561i
$590$	−1.64330	+	0.889311i	−0.0676537	+	0.0366124i
$591$	0.413980	−	2.98541i	0.0170288	−	0.122803i
$592$	−4.62924	−	0.255402i	−0.190261	−	0.0104970i
$593$	3.85126	+	27.7733i	0.158152	+	1.14051i	0.888979	+	0.457948i	$0.151416\pi$
$593$	3.85126	+	27.7733i	0.158152	+	1.14051i	−0.730827	+	0.682563i	$0.760865\pi$
$594$	19.7999	−	9.34382i	0.812401	−	0.383381i
$595$	1.20526	−	2.08757i	0.0494108	−	0.0855821i
$596$	7.36890	−	11.2789i	0.301842	−	0.462003i
$597$	2.86345	+	34.5567i	0.117193	+	1.41431i
$598$	−0.662219	−	4.77558i	−0.0270801	−	0.195288i
$599$	−19.2347	−	26.1698i	−0.785910	−	1.06927i	−0.995801	−	0.0915447i	$-0.970820\pi$
$599$	−19.2347	−	26.1698i	−0.785910	−	1.06927i	0.209891	−	0.977725i	$-0.432689\pi$
$600$	−2.48373	−	9.80803i	−0.101398	−	0.400411i
$601$	−1.03542	−	0.172781i	−0.0422357	−	0.00704790i	0.143439	−	0.989659i	$-0.454184\pi$
$601$	−1.03542	−	0.172781i	−0.0422357	−	0.00704790i	−0.185675	+	0.982611i	$0.559447\pi$
$602$	0.937323	−	0.210059i	0.0382024	−	0.00856136i
$603$	0.639183	+	0.392905i	0.0260296	+	0.0160003i
$604$	2.79460	+	5.52229i	0.113711	+	0.224699i
$605$	−0.515081	+	3.71450i	−0.0209410	+	0.151016i
$606$	−1.70030	−	2.94501i	−0.0690701	−	0.119633i
$607$	3.03504	+	11.9851i	0.123189	+	0.486461i	0.999984	+	0.00559784i	$0.00178186\pi$
$607$	3.03504	+	11.9851i	0.123189	+	0.486461i	−0.876796	+	0.480863i	$0.840323\pi$
$608$	−4.28203	+	0.815011i	−0.173659	+	0.0330531i
$609$	4.66015	−	18.4025i	0.188839	−	0.745708i
$610$	−0.505316	+	0.142890i	−0.0204597	+	0.00578544i
$611$	9.54611	−	30.5206i	0.386194	−	1.23473i
$612$	−6.57796	−	3.10421i	−0.265898	−	0.125480i
$613$	−18.3084	+	12.6948i	−0.739470	+	0.512737i	−0.878613	−	0.477535i	$-0.841530\pi$
$613$	−18.3084	+	12.6948i	−0.739470	+	0.512737i	0.139142	+	0.990272i	$0.455565\pi$
$614$	−0.684631	−	4.93720i	−0.0276295	−	0.199249i
$615$	−0.282759	+	0.220080i	−0.0114020	+	0.00887450i
$616$	7.17294	+	10.9790i	0.289006	+	0.442357i
$617$	36.3229	−	2.00399i	1.46231	−	0.0806777i	0.693637	−	0.720324i	$-0.256007\pi$
$617$	36.3229	−	2.00399i	1.46231	−	0.0806777i	0.768669	+	0.639647i	$0.220919\pi$
$618$	−28.5343	+	24.8506i	−1.14782	+	0.999636i
$619$	−7.84796	+	30.9909i	−0.315436	+	1.24563i	0.585141	+	0.810932i	$0.301039\pi$
$619$	−7.84796	+	30.9909i	−0.315436	+	1.24563i	−0.900577	+	0.434697i	$0.856855\pi$
$620$	−0.363808	+	0.0607089i	−0.0146109	+	0.00243813i
$621$	4.14333	+	1.95529i	0.166266	+	0.0784629i
$622$	−21.9404	−	19.1079i	−0.879729	−	0.766157i
$623$	−7.28173	+	12.6123i	−0.291736	+	0.505302i
$624$	8.05275	−	0.891278i	0.322368	−	0.0356797i
$625$	24.4343	−	2.70439i	0.977372	−	0.108176i
$626$	13.0827	−	20.0246i	0.522890	−	0.800343i
$627$	−49.8145	+	12.3595i	−1.98940	+	0.493590i
$628$	8.48445	+	12.9864i	0.338566	+	0.518215i
$629$	−18.7956	−	22.8222i	−0.749429	−	0.909982i
$630$	0.367303	+	0.225780i	0.0146337	+	0.00899530i
$631$	−1.59387	+	0.979746i	−0.0634508	+	0.0390031i	−0.555035	−	0.831827i	$-0.687295\pi$
$631$	−1.59387	+	0.979746i	−0.0634508	+	0.0390031i	0.491584	+	0.870830i	$0.336418\pi$
$632$	−6.32098	+	6.14915i	−0.251435	+	0.244600i
$633$	−35.2948	−	34.3353i	−1.40284	−	1.36471i
$634$	8.09233	−	2.77810i	0.321387	−	0.110332i
$635$	−1.80158	−	0.974967i	−0.0714936	−	0.0386904i
$636$	−0.624506	+	22.6559i	−0.0247633	+	0.898365i
$637$	−5.31841	−	5.17383i	−0.210723	−	0.204995i
$638$	−16.1324	+	17.5245i	−0.638688	+	0.693801i
$639$	11.8306	−	6.40240i	0.468011	−	0.253275i
$640$	−0.0753096	−	0.148816i	−0.00297687	−	0.00588246i
$641$	6.75876	+	8.20670i	0.266955	+	0.324145i	0.888188	−	0.459481i	$-0.151964\pi$
$641$	6.75876	+	8.20670i	0.266955	+	0.324145i	−0.621233	+	0.783626i	$0.713368\pi$
$642$	30.1404	−	1.66289i	1.18955	−	0.0656292i
$643$	13.5712	+	36.2472i	0.535197	+	1.42945i	0.872762	+	0.488146i	$0.162327\pi$
$643$	13.5712	+	36.2472i	0.535197	+	1.42945i	−0.337564	+	0.941302i	$0.609603\pi$
$644$	−0.819225	+	2.61921i	−0.0322820	+	0.103211i
$645$	−0.141882	+	0.0236759i	−0.00558658	+	0.000932236i
$646$	−22.3181	−	16.5700i	−0.878092	−	0.651940i
$647$	−28.5155	−	4.75839i	−1.12106	−	0.187072i	−0.425096	−	0.905148i	$-0.639760\pi$
$647$	−28.5155	−	4.75839i	−1.12106	−	0.187072i	−0.695964	+	0.718077i	$0.745023\pi$
$648$	−5.02143	+	9.92261i	−0.197260	+	0.389797i
$649$	46.4666	−	45.2034i	1.82397	−	1.77439i
$650$	−0.545498	+	19.7897i	−0.0213962	+	0.776214i
$651$	−6.03996	+	8.21766i	−0.236725	+	0.322075i
$652$	20.6566	+	2.28627i	0.808973	+	0.0895371i
$653$	1.92333			0.0752658			0.0376329	−	0.999292i	$-0.488018\pi$
$653$	1.92333			0.0752658			0.0376329	+	0.999292i	$0.488018\pi$
$654$	−6.61126			−0.258521
$655$	2.63631	+	0.291786i	0.103009	+	0.0114010i
$656$	0.671180	−	0.814969i	0.0262052	−	0.0318192i
$657$	−1.49112	+	0.511902i	−0.0581742	+	0.0199712i
$658$	−12.3284	+	13.3922i	−0.480610	+	0.522081i
$659$	7.53281	−	38.5638i	0.293437	−	1.50223i	−0.485003	−	0.874513i	$-0.661181\pi$
$659$	7.53281	−	38.5638i	0.293437	−	1.50223i	0.778439	−	0.627720i	$-0.216012\pi$
$660$	−0.981932	−	1.70076i	−0.0382217	−	0.0662018i
$661$	6.35052	+	8.64019i	0.247007	+	0.336065i	0.911553	−	0.411182i	$-0.134884\pi$
$661$	6.35052	+	8.64019i	0.247007	+	0.336065i	−0.664547	+	0.747247i	$0.731375\pi$
$662$	−18.9598	+	13.1464i	−0.736894	+	0.510951i
$663$	38.9618	+	33.9318i	1.51315	+	1.31780i
$664$	2.37808	+	1.85094i	0.0922875	+	0.0718302i
$665$	1.20683	+	1.12177i	0.0467990	+	0.0435002i
$666$	4.17308	−	3.24804i	0.161704	−	0.125859i
$667$	−4.97687	−	0.274582i	−0.192705	−	0.0106318i
$668$	9.65253	+	16.7187i	0.373468	+	0.646865i
$669$	−28.7621	−	19.9432i	−1.11201	−	0.771050i
$670$	−0.0495387	+	0.0978911i	−0.00191385	+	0.00378186i
$671$	15.5212	−	9.54083i	0.599188	−	0.368320i
$672$	−4.36185	−	1.49743i	−0.168262	−	0.0577644i
$673$	33.2766	−	18.0084i	1.28272	−	0.694172i	0.315695	−	0.948861i	$-0.397762\pi$
$673$	33.2766	−	18.0084i	1.28272	−	0.694172i	0.967023	+	0.254689i	$0.0819730\pi$
$674$	−0.179290	+	0.917863i	−0.00690598	+	0.0353547i
$675$	−15.4599	−	10.7196i	−0.595051	−	0.412599i
$676$	−2.81413	−	0.469595i	−0.108236	−	0.0180613i
$677$	10.4282	−	23.7739i	0.400789	−	0.913706i	−0.593284	−	0.804993i	$-0.702169\pi$
$677$	10.4282	−	23.7739i	0.400789	−	0.913706i	0.994073	−	0.108713i	$-0.0346731\pi$
$678$	14.2578	−	12.4171i	0.547568	−	0.476877i
$679$	−9.87619	−	26.3781i	−0.379013	−	1.01230i
$680$	0.372938	−	0.996074i	0.0143015	−	0.0381977i
$681$	8.71426	+	7.58925i	0.333931	+	0.290821i
$682$	11.5727	−	5.46129i	0.443142	−	0.209124i
$683$	1.21508	+	14.6638i	0.0464936	+	0.561094i	0.979528	+	0.201307i	$0.0645190\pi$
$683$	1.21508	+	14.6638i	0.0464936	+	0.561094i	−0.933035	+	0.359787i	$0.882849\pi$
$684$	3.07260	−	3.90865i	0.117484	−	0.149451i
$685$	−0.0971928	+	1.17294i	−0.00371355	+	0.0448158i
$686$	7.04365	+	18.8127i	0.268928	+	0.718274i
$687$	−23.6396	+	6.68464i	−0.901907	+	0.255035i
$688$	0.392682	−	0.159493i	0.0149708	−	0.00608063i
$689$	13.2384	−	42.3257i	0.504345	−	1.61248i
$690$	0.144097	−	0.384867i	0.00548569	−	0.0146516i
$691$	10.8135	+	8.41645i	0.411363	+	0.320177i	0.798665	−	0.601776i	$-0.205540\pi$
$691$	10.8135	+	8.41645i	0.411363	+	0.320177i	−0.387301	+	0.921953i	$0.626593\pi$
$692$	−6.55764	+	10.0372i	−0.249284	+	0.381558i
$693$	−14.3940	−	4.07022i	−0.546781	−	0.154615i
$694$	−10.6760	+	18.4914i	−0.405255	+	0.701923i
$695$	2.05615	+	1.60037i	0.0779942	+	0.0607053i
$696$	0.691694	−	8.34750i	0.0262186	−	0.316411i
$697$	6.72247	−	0.370889i	0.254632	−	0.0140484i
$698$	2.10884	+	10.7961i	0.0798209	+	0.408638i
$699$	15.4142	−	3.45440i	0.583018	−	0.130657i
$700$	5.08826	−	10.0547i	0.192318	−	0.380031i
$701$	−0.507125	−	18.3976i	−0.0191538	−	0.694866i	−0.946877	−	0.321596i	$-0.895781\pi$
$701$	−0.507125	−	18.3976i	−0.0191538	−	0.694866i	0.927723	−	0.373269i	$-0.121763\pi$
$702$	10.2031	−	11.0835i	0.385089	−	0.418319i
$703$	18.0754	−	9.03802i	0.681727	−	0.340875i
$704$	3.91912	+	4.25730i	0.147707	+	0.160453i
$705$	1.95382	−	1.90070i	0.0735850	−	0.0715846i
$706$	0.112376	+	4.07678i	0.00422931	+	0.153432i
$707$	0.726111	−	3.71728i	0.0273082	−	0.139803i
$708$	−3.13116	+	22.5803i	−0.117676	+	0.848620i
$709$	3.24614	+	10.3785i	0.121911	+	0.389772i	0.995251	−	0.0973389i	$-0.0310331\pi$
$709$	3.24614	+	10.3785i	0.121911	+	0.389772i	−0.873340	+	0.487111i	$0.838051\pi$
$710$	1.07586	+	1.64673i	0.0403765	+	0.0618008i
$711$	0.830618	−	10.0241i	0.0311506	−	0.375932i
$712$	−2.25315	+	6.01791i	−0.0844405	+	0.225531i
$713$	2.42171	+	1.14283i	0.0906936	+	0.0427993i
$714$	−11.8135	−	26.9321i	−0.442109	−	1.00791i
$715$	0.943326	+	3.72511i	0.0352784	+	0.139311i
$716$	−7.95504	−	5.51590i	−0.297294	−	0.206139i
$717$	0.513057	+	18.6127i	0.0191605	+	0.695106i
$718$	−24.2812	−	23.6212i	−0.906168	−	0.881534i
$719$	14.2626	+	3.19632i	0.531905	+	0.119203i	0.476355	−	0.879253i	$-0.341958\pi$
$719$	14.2626	+	3.19632i	0.531905	+	0.119203i	0.0555504	+	0.998456i	$0.482309\pi$
$720$	0.176253	+	0.0715877i	0.00656856	+	0.00266792i
$721$	−42.1439			−1.56952
$722$	14.4477	−	12.3395i	0.537687	−	0.459230i
$723$	−15.1449			−0.563245
$724$	9.99971	+	4.06153i	0.371636	+	0.150946i
$725$	19.9718	+	4.47578i	0.741734	+	0.166226i
$726$	32.7940	+	31.9025i	1.21710	+	1.18401i
$727$	0.0500806	+	1.81683i	0.00185739	+	0.0673825i	0.999981	+	0.00615257i	$0.00195844\pi$
$727$	0.0500806	+	1.81683i	0.00185739	+	0.0673825i	−0.998124	+	0.0612299i	$0.980498\pi$
$728$	7.41554	+	5.14182i	0.274838	+	0.190569i
$729$	2.55616	+	10.0941i	0.0946728	+	0.373854i
$730$	−0.0926041	−	0.211116i	−0.00342743	−	0.00781375i
$731$	2.44431	+	1.15350i	0.0904060	+	0.0426636i
$732$	−2.24645	+	6.00000i	−0.0830312	+	0.221766i
$733$	1.62440	−	19.6036i	0.0599988	−	0.724077i	−0.898499	−	0.438976i	$-0.855341\pi$
$733$	1.62440	−	19.6036i	0.0599988	−	0.724077i	0.958497	−	0.285101i	$-0.0920272\pi$
$734$	−11.7284	−	17.9517i	−0.432905	−	0.662610i
$735$	−0.188798	−	0.603620i	−0.00696390	−	0.0222648i
$736$	−0.166320	+	1.19942i	−0.00613065	+	0.0442110i
$737$	0.729725	−	3.73579i	0.0268798	−	0.137609i
$738$	0.0331813	+	1.20376i	0.00122142	+	0.0443109i
$739$	−5.37326	+	5.22719i	−0.197659	+	0.192285i	−0.789466	−	0.613794i	$-0.789643\pi$
$739$	−5.37326	+	5.22719i	−0.197659	+	0.192285i	0.591808	+	0.806079i	$0.298415\pi$
$740$	0.523720	+	0.568912i	0.0192523	+	0.0209136i
$741$	−28.5565	+	20.7776i	−1.04905	+	0.763284i
$742$	−17.0969	+	18.5721i	−0.627645	+	0.681804i
$743$	−0.898442	−	32.5938i	−0.0329607	−	1.19575i	−0.817595	−	0.575793i	$-0.804693\pi$
$743$	−0.898442	−	32.5938i	−0.0329607	−	1.19575i	0.784635	−	0.619958i	$-0.212850\pi$
$744$	−2.03188	+	4.01510i	−0.0744922	+	0.147201i
$745$	−2.19269	+	0.491392i	−0.0803338	+	0.0180032i
$746$	0.127509	+	0.652777i	0.00466845	+	0.0238999i
$747$	−3.43199	+	0.189348i	−0.125570	+	0.00692788i
$748$	−3.04725	+	36.7749i	−0.111419	+	1.34462i
$749$	26.5316	+	20.6504i	0.969445	+	0.754549i
$750$	−1.69220	+	2.93098i	−0.0617905	+	0.107024i
$751$	2.53981	+	0.718190i	0.0926790	+	0.0262071i	0.318127	−	0.948048i	$-0.396946\pi$
$751$	2.53981	+	0.718190i	0.0926790	+	0.0262071i	−0.225448	+	0.974255i	$0.572385\pi$
$752$	−4.39289	+	6.72382i	−0.160192	+	0.245193i
$753$	−24.6787	−	19.2082i	−0.899342	−	0.699986i
$754$	−5.74679	+	15.3490i	−0.209286	+	0.558978i
$755$	0.308146	−	0.985198i	0.0112146	−	0.0358550i
$756$	−7.94473	+	3.22687i	−0.288947	+	0.117360i
$757$	29.9960	−	8.48207i	1.09022	−	0.308286i	0.320880	−	0.947120i	$-0.396021\pi$
$757$	29.9960	−	8.48207i	1.09022	−	0.308286i	0.769345	+	0.638834i	$0.220583\pi$
$758$	12.7171	+	33.9660i	0.461908	+	1.23370i
$759$	−1.17741	+	14.2092i	−0.0427373	+	0.515762i
$760$	0.606700	+	0.400564i	0.0220073	+	0.0145300i
$761$	−0.0511326	−	0.617079i	−0.00185356	−	0.0223691i	0.995595	−	0.0937587i	$-0.0298882\pi$
$761$	−0.0511326	−	0.617079i	−0.00185356	−	0.0223691i	−0.997449	+	0.0713896i	$0.977257\pi$
$762$	−22.6017	+	10.6660i	−0.818775	+	0.386389i
$763$	−5.55287	−	4.83600i	−0.201027	−	0.175075i
$764$	−3.51020	+	9.37533i	−0.126995	+	0.339187i
$765$	0.425373	+	1.13612i	0.0153794	+	0.0410765i
$766$	−11.9157	+	10.3774i	−0.430533	+	0.374952i
$767$	17.9179	−	40.8487i	0.646978	−	1.47496i
$768$	−2.00709	−	0.334925i	−0.0724248	−	0.0120856i
$769$	−4.38713	−	3.04197i	−0.158204	−	0.109696i	0.488060	−	0.872810i	$-0.337705\pi$
$769$	−4.38713	−	3.04197i	−0.158204	−	0.109696i	−0.646264	+	0.763114i	$0.723670\pi$
$770$	0.419332	−	2.14675i	0.0151117	−	0.0773634i
$771$	−41.1572	+	22.2732i	−1.48224	+	0.802149i
$772$	−2.63366	−	0.904135i	−0.0947874	−	0.0325405i
$773$	−11.7800	+	7.24114i	−0.423697	+	0.260446i	−0.719072	−	0.694936i	$-0.755433\pi$
$773$	−11.7800	+	7.24114i	−0.423697	+	0.260446i	0.295375	+	0.955381i	$0.404556\pi$
$774$	−0.218283	+	0.431340i	−0.00784604	+	0.0155042i
$775$	−9.03602	−	6.26544i	−0.324584	−	0.225061i
$776$	−6.21397	−	10.7629i	−0.223069	−	0.386366i
$777$	21.3488	+	1.17785i	0.765883	+	0.0422550i
$778$	2.84146	−	2.21159i	0.101871	−	0.0792895i
$779$	−0.779343	+	4.53554i	−0.0279229	+	0.162502i
$780$	−1.06636	−	0.829979i	−0.0381817	−	0.0297180i
$781$	−51.4639	−	44.8200i	−1.84152	−	1.60378i
$782$	−6.34568	+	4.39999i	−0.226921	+	0.157343i
$783$	−9.22380	−	12.5494i	−0.329632	−	0.448480i
$784$	0.931769	+	1.61387i	0.0332775	+	0.0576383i
$785$	0.496003	−	2.53926i	0.0177031	−	0.0906300i
$786$	21.9170	−	23.8082i	0.781752	−	0.849209i
$787$	−13.7149	+	4.70834i	−0.488885	+	0.167834i	−0.558110	−	0.829767i	$-0.688473\pi$
$787$	−13.7149	+	4.70834i	−0.488885	+	0.167834i	0.0692258	+	0.997601i	$0.477947\pi$
$788$	0.941621	−	1.14335i	0.0335438	−	0.0407300i
$789$	49.3324	+	5.46011i	1.75628	+	0.194385i
$790$	1.47081			0.0523292
$791$	21.0582			0.748742
$792$	−6.56007	−	0.726068i	−0.233102	−	0.0257997i
$793$	7.42433	−	10.1012i	0.263646	−	0.358703i
$794$	1.01332	−	36.7612i	0.0359612	−	1.30461i
$795$	2.70953	−	2.63587i	0.0960972	−	0.0934848i
$796$	−7.69444	+	15.2046i	−0.272722	+	0.538914i
$797$	−41.0868	−	6.85618i	−1.45537	−	0.242858i	−0.616571	−	0.787299i	$-0.711479\pi$
$797$	−41.0868	−	6.85618i	−1.45537	−	0.242858i	−0.838799	+	0.544441i	$0.816742\pi$
$798$	19.7475	−	3.75861i	0.699055	−	0.133053i
$799$	−50.5194	+	8.43020i	−1.78725	+	0.298239i
$800$	1.48427	−	4.74548i	0.0524769	−	0.167778i
$801$	−2.56995	−	6.86402i	−0.0908046	−	0.242528i
$802$	−9.22240	+	0.508814i	−0.325654	+	0.0179668i
$803$	5.08464	+	6.17394i	0.179433	+	0.217874i
$804$	0.604387	+	1.19430i	0.0213151	+	0.0421198i
$805$	0.402551	−	0.217850i	0.0141881	−	0.00767819i
$806$	5.96350	−	6.47809i	0.210055	−	0.228181i
$807$	−25.5409	−	24.8466i	−0.899084	−	0.874642i
$808$	0.0460484	−	1.67055i	0.00161998	−	0.0587698i
$809$	30.2928	+	16.3937i	1.06504	+	0.576370i	0.911301	−	0.411741i	$-0.135079\pi$
$809$	30.2928	+	16.3937i	1.06504	+	0.576370i	0.153738	+	0.988112i	$0.450869\pi$
$810$	1.75430	−	0.602254i	0.0616400	−	0.0211610i
$811$	−29.9642	−	29.1496i	−1.05218	−	1.02358i	−0.999688	−	0.0249602i	$-0.992054\pi$
$811$	−29.9642	−	29.1496i	−1.05218	−	1.02358i	−0.0524965	−	0.998621i	$-0.516718\pi$
$812$	6.68698	−	6.50520i	0.234667	−	0.228288i
$813$	15.6964	−	9.64853i	0.550496	−	0.338389i
$814$	−22.8553	−	14.0491i	−0.801078	−	0.492421i
$815$	−2.20359	−	2.67567i	−0.0771884	−	0.0937247i
$816$	−7.09734	−	10.8633i	−0.248457	−	0.380291i
$817$	−1.14175	+	1.45242i	−0.0399447	+	0.0508136i
$818$	−13.5098	+	20.6783i	−0.472359	+	0.722999i
$819$	−10.2300	+	1.13226i	−0.357467	+	0.0395644i
$820$	−0.175020	+	0.0193712i	−0.00611196	+	0.000676471i
$821$	18.6175	−	32.2465i	0.649755	−	1.12541i	−0.333426	−	0.942776i	$-0.608205\pi$
$821$	18.6175	−	32.2465i	0.649755	−	1.12541i	0.983181	−	0.182633i	$-0.0584619\pi$
$822$	10.8285	+	9.43051i	0.377686	+	0.328927i
$823$	31.9957	+	15.0991i	1.11530	+	0.526323i	0.893633	−	0.448799i	$-0.148148\pi$
$823$	31.9957	+	15.0991i	1.11530	+	0.526323i	0.221668	+	0.975122i	$0.428850\pi$
$824$	−18.3417	+	3.06068i	−0.638963	+	0.106624i
$825$	14.3722	−	56.7546i	0.500376	−	1.97594i
$826$	−19.1469	+	16.6751i	−0.666206	+	0.580200i
$827$	17.7327	−	0.978342i	0.616628	−	0.0340203i	0.255918	−	0.966698i	$-0.417622\pi$
$827$	17.7327	−	0.978342i	0.616628	−	0.0340203i	0.360710	+	0.932678i	$0.382535\pi$
$828$	−0.755413	−	1.15625i	−0.0262524	−	0.0401823i
$829$	25.8315	−	20.1055i	0.897166	−	0.698293i	−0.0567426	−	0.998389i	$-0.518071\pi$
$829$	25.8315	−	20.1055i	0.897166	−	0.698293i	0.953909	+	0.300096i	$0.0970188\pi$
$830$	−0.0690356	−	0.497848i	−0.00239626	−	0.0172806i
$831$	−27.3978	+	18.9972i	−0.950419	+	0.659006i
$832$	3.60078	+	1.69925i	0.124834	+	0.0589108i
$833$	−3.54750	+	11.3420i	−0.122914	+	0.392977i
$834$	30.5892	−	8.64979i	1.05922	−	0.299518i
$835$	0.790420	−	3.12130i	0.0273536	−	0.108017i
$836$	−24.0363	−	7.64541i	−0.831314	−	0.264422i
$837$	2.05403	+	8.11117i	0.0709976	+	0.280363i
$838$	11.0466	+	19.1333i	0.381598	+	0.660947i
$839$	2.06685	−	14.9050i	0.0713555	−	0.514579i	−0.920845	−	0.389928i	$-0.872500\pi$
$839$	2.06685	−	14.9050i	0.0713555	−	0.514579i	0.992201	−	0.124650i	$-0.0397809\pi$
$840$	0.347307	+	0.686298i	0.0119832	+	0.0236795i
$841$	−10.2705	−	6.31328i	−0.354157	−	0.217699i
$842$	14.4847	−	3.24609i	0.499174	−	0.111868i
$843$	15.9560	+	2.66259i	0.549555	+	0.0917046i
$844$	−5.94042	−	23.4582i	−0.204478	−	0.807465i
$845$	0.281814	+	0.383422i	0.00969470	+	0.0131901i
$846$	−1.25828	−	9.07406i	−0.0432606	−	0.311973i
$847$	4.20803	+	50.7834i	0.144590	+	1.74494i
$848$	−6.09202	+	9.32453i	−0.209201	+	0.320206i
$849$	32.9661	−	57.0989i	1.13139	−	1.95963i
$850$	28.6751	−	13.5321i	0.983548	−	0.464148i
$851$	−0.771107	−	5.56082i	−0.0264332	−	0.190623i
$852$	23.9620	+	1.32202i	0.820923	+	0.0452916i
$853$	−4.24930	+	30.6437i	−0.145493	+	1.04922i	0.767442	+	0.641118i	$0.221529\pi$
$853$	−4.24930	+	30.6437i	−0.145493	+	1.04922i	−0.912936	+	0.408103i	$0.866190\pi$
$854$	−6.27569	+	3.39623i	−0.214750	+	0.116217i
$855$	−0.821902	+	0.109935i	−0.0281084	+	0.00375970i
$856$	13.0467	+	7.06052i	0.445927	+	0.241324i
$857$	−24.8797	+	33.8500i	−0.849874	+	1.15629i	0.136314	+	0.990666i	$0.456474\pi$
$857$	−24.8797	+	33.8500i	−0.849874	+	1.15629i	−0.986188	+	0.165629i	$0.947035\pi$
$858$	43.4360	+	17.6422i	1.48288	+	0.602294i
$859$	11.6312	+	1.28734i	0.396852	+	0.0439236i	0.306220	−	0.951961i	$-0.400936\pi$
$859$	11.6312	+	1.28734i	0.396852	+	0.0439236i	0.0906323	+	0.995884i	$0.471111\pi$
$860$	−0.0654939	−	0.0266013i	−0.00223332	−	0.000907098i
$861$	−3.09530	+	3.75841i	−0.105487	+	0.128086i
$862$	21.0838	+	11.4100i	0.718116	+	0.388625i
$863$	33.3989	+	36.2808i	1.13691	+	1.23501i	0.968424	+	0.249310i	$0.0802037\pi$
$863$	33.3989	+	36.2808i	1.13691	+	1.23501i	0.168486	+	0.985704i	$0.446112\pi$
$864$	−3.22332	+	1.98137i	−0.109659	+	0.0674074i
$865$	1.95129	−	0.437294i	0.0663458	−	0.0148684i
$866$	−8.78709	+	20.0326i	−0.298598	+	0.680734i
$867$	11.8220	−	46.6839i	0.401495	−	1.58547i
$868$	−4.64356	+	1.88605i	−0.157613	+	0.0640167i
$869$	−49.1035	+	13.8851i	−1.66572	+	0.471021i
$870$	−1.05350	+	0.917497i	−0.0357171	+	0.0311060i
$871$	−0.502107	−	2.57051i	−0.0170133	−	0.0870984i
$872$	−2.76791	−	1.70143i	−0.0937331	−	0.0576175i
$873$	13.4072	+	4.60271i	0.453766	+	0.155778i
$874$	−1.96262	−	4.89970i	−0.0663865	−	0.165735i
$875$	−3.56525	+	1.22395i	−0.120527	+	0.0413771i
$876$	−2.74450	−	0.615057i	−0.0927281	−	0.0207809i
$877$	−12.2014	+	16.6007i	−0.412013	+	0.560564i	−0.961453	−	0.274969i	$-0.911332\pi$
$877$	−12.2014	+	16.6007i	−0.412013	+	0.560564i	0.549440	+	0.835533i	$0.314841\pi$
$878$	−6.33526	+	7.69248i	−0.213805	+	0.259609i
$879$	−54.5778	−	12.2312i	−1.84086	−	0.412547i
$880$	0.0265932	−	0.964750i	0.000896455	−	0.0325217i
$881$	3.75297	+	4.07681i	0.126441	+	0.137351i	0.795732	−	0.605649i	$-0.207086\pi$
$881$	3.75297	+	4.07681i	0.126441	+	0.137351i	−0.669291	+	0.743000i	$0.733402\pi$
$882$	−2.01038	−	0.690165i	−0.0676931	−	0.0232391i
$883$	−8.33531	−	16.4710i	−0.280505	−	0.554294i	0.707867	−	0.706346i	$-0.249658\pi$
$883$	−8.33531	−	16.4710i	−0.280505	−	0.554294i	−0.988373	+	0.152052i	$0.951412\pi$
$884$	7.57949	+	24.2330i	0.254926	+	0.815044i
$885$	3.00041	−	2.33531i	0.100858	−	0.0785007i
$886$	0.799059	+	9.64320i	0.0268449	+	0.323970i
$887$	53.0033	+	14.9879i	1.77968	+	0.503245i	0.993407	−	0.114638i	$-0.0365707\pi$
$887$	53.0033	+	14.9879i	1.77968	+	0.503245i	0.786270	+	0.617883i	$0.212009\pi$
$888$	9.37685	−	1.03783i	0.314667	−	0.0348273i
$889$	−26.7854	−	7.57419i	−0.898354	−	0.254030i
$890$	0.969244	−	0.457397i	0.0324891	−	0.0153320i
$891$	−52.8824	+	36.6678i	−1.77163	+	1.22842i
$892$	−6.90927	−	15.7516i	−0.231339	−	0.527401i
$893$	2.09709	−	34.9462i	0.0701765	−	1.16943i
$894$	−11.0125	+	25.1059i	−0.368312	+	0.839667i
$895$	0.309524	+	1.58459i	0.0103463	+	0.0529670i
$896$	−1.44079	−	1.74945i	−0.0481334	−	0.0584451i
$897$	2.92859	+	9.36324i	0.0977829	+	0.312629i
$898$	7.67748	+	0.423578i	0.256201	+	0.0141350i
$899$	−5.39115	−	7.33492i	−0.179805	−	0.244633i
$900$	2.27812	+	5.19360i	0.0759374	+	0.173120i
$901$	−70.0598	+	11.6909i	−2.33403	+	0.389481i
$902$	5.66021	−	2.29898i	0.188464	−	0.0765476i
$903$	−1.81094	+	0.735540i	−0.0602643	+	0.0244773i
$904$	9.16483	−	1.52934i	0.304818	−	0.0508651i
$905$	−0.723106	−	1.64852i	−0.0240369	−	0.0547985i
$906$	−7.45858	−	10.1478i	−0.247795	−	0.337137i
$907$	−33.3258	−	1.83864i	−1.10657	−	0.0610509i	−0.507426	−	0.861695i	$-0.669403\pi$
$907$	−33.3258	−	1.83864i	−1.10657	−	0.0610509i	−0.599140	+	0.800645i	$0.704491\pi$
$908$	1.69524	+	5.41999i	0.0562586	+	0.179869i
$909$	1.21179	+	1.47139i	0.0401924	+	0.0488030i
$910$	−0.288533	−	1.47713i	−0.00956477	−	0.0489663i
$911$	0.657079	−	1.49799i	0.0217700	−	0.0496306i	−0.904552	−	0.426363i	$-0.859795\pi$
$911$	0.657079	−	1.49799i	0.0217700	−	0.0496306i	0.926322	+	0.376733i	$0.122952\pi$
$912$	8.32146	−	3.06996i	0.275551	−	0.101657i
$913$	7.00468	+	15.9691i	0.231821	+	0.528499i
$914$	8.41036	−	5.83161i	0.278190	−	0.192893i
$915$	0.966360	−	0.456036i	0.0319469	−	0.0150761i
$916$	−11.6174	−	3.28508i	−0.383849	−	0.108542i
$917$	35.8235	−	3.96494i	1.18299	−	0.130934i
$918$	−23.2177	−	6.56533i	−0.766297	−	0.216688i
$919$	2.61573	+	31.5672i	0.0862851	+	1.04131i	0.892908	+	0.450240i	$0.148661\pi$
$919$	2.61573	+	31.5672i	0.0862851	+	1.04131i	−0.806623	+	0.591067i	$0.798707\pi$
$920$	0.159375	−	0.124047i	0.00525444	−	0.00408969i
$921$	3.02771	+	9.68013i	0.0997664	+	0.318971i
$922$	−13.0218	−	25.7317i	−0.428849	−	0.847429i
$923$	−44.4134	−	15.2472i	−1.46189	−	0.501866i
$924$	−18.0739	−	19.6335i	−0.594588	−	0.645895i
$925$	−0.635194	+	23.0437i	−0.0208851	+	0.757671i
$926$	11.9792	+	2.68461i	0.393662	+	0.0882217i
$927$	13.4836	−	16.3722i	0.442858	−	0.537733i
$928$	2.43784	−	3.31680i	0.0800260	−	0.108879i
$929$	−30.8937	−	6.92343i	−1.01359	−	0.227150i	−0.319920	−	0.947445i	$-0.603656\pi$
$929$	−30.8937	−	6.92343i	−1.01359	−	0.227150i	−0.693669	+	0.720294i	$0.744007\pi$
$930$	0.709864	−	0.243697i	0.0232774	−	0.00799113i
$931$	−7.01504	−	4.09536i	−0.229909	−	0.134220i
$932$	7.34238	+	2.52064i	0.240508	+	0.0825664i
$933$	50.4361	+	31.0030i	1.65120	+	1.01499i
$934$	−2.24858	−	11.5115i	−0.0735759	−	0.376667i
$935$	4.64120	−	4.04203i	0.151784	−	0.132188i
$936$	−4.37004	+	1.23573i	−0.142839	+	0.0403911i
$937$	4.26753	−	1.73332i	0.139414	−	0.0566252i	−0.305536	−	0.952181i	$-0.598836\pi$
$937$	4.26753	−	1.73332i	0.139414	−	0.0566252i	0.444950	+	0.895555i	$0.353221\pi$
$938$	−0.365975	+	1.44520i	−0.0119495	+	0.0471876i
$939$	−19.5515	+	44.5729i	−0.638039	+	1.45458i
$940$	1.30715	−	0.292938i	0.0426344	−	0.00955459i
$941$	44.1180	−	27.1192i	1.43821	−	0.884062i	0.438315	−	0.898822i	$-0.355576\pi$
$941$	44.1180	−	27.1192i	1.43821	−	0.884062i	0.999891	+	0.0147599i	$0.00469839\pi$
$942$	−21.3786	−	23.2233i	−0.696551	−	0.756656i
$943$	1.12434	+	0.608464i	0.0366136	+	0.0198143i
$944$	−7.12201	+	8.64778i	−0.231802	+	0.281461i
$945$	1.32507	+	0.538198i	0.0431046	+	0.0175076i
$946$	2.43766	+	0.269800i	0.0792552	+	0.00877196i
$947$	55.7321	+	22.6364i	1.81105	+	0.735585i	0.985133	+	0.171794i	$0.0549563\pi$
$947$	55.7321	+	22.6364i	1.81105	+	0.735585i	0.825917	+	0.563791i	$0.190658\pi$
$948$	10.6273	−	14.4590i	0.345159	−	0.469605i
$949$	4.84007	+	2.61932i	0.157115	+	0.0850266i
$950$	4.63750	+	21.1713i	0.150460	+	0.686887i
$951$	−15.3116	+	8.28623i	−0.496513	+	0.268699i
$952$	1.98513	−	14.3158i	0.0643386	−	0.463976i
$953$	7.89196	+	0.435412i	0.255646	+	0.0141044i	0.182457	−	0.983214i	$-0.441595\pi$
$953$	7.89196	+	0.435412i	0.255646	+	0.0141044i	0.0731883	+	0.997318i	$0.476683\pi$
$954$	−1.74497	−	12.5838i	−0.0564955	−	0.407416i
$955$	1.50999	−	0.712581i	0.0488621	−	0.0230586i
$956$	−4.57524	+	7.92455i	−0.147974	+	0.256298i
$957$	26.5099	−	40.5764i	0.856943	−	1.31165i
$958$	−0.329860	−	3.98082i	−0.0106573	−	0.128614i
$959$	2.19672	+	15.8416i	0.0709357	+	0.511551i
$960$	0.200996	+	0.273464i	0.00648710	+	0.00882602i
$961$	−6.40951	−	25.3106i	−0.206758	−	0.816470i
$962$	−18.2080	−	3.03837i	−0.587049	−	0.0979611i
$963$	−16.5109	+	3.70017i	−0.532055	+	0.119236i
$964$	−6.34065	−	3.89758i	−0.204219	−	0.125533i
$965$	0.209702	+	0.414382i	0.00675054	+	0.0133394i
$966$	0.767024	−	5.53138i	0.0246786	−	0.177969i
$967$	22.6731	+	39.2710i	0.729118	+	1.26287i	0.957257	+	0.289240i	$0.0934026\pi$
$967$	22.6731	+	39.2710i	0.729118	+	1.26287i	−0.228139	+	0.973629i	$0.573264\pi$
$968$	5.51952	+	21.7961i	0.177404	+	0.700553i
$969$	50.3442	+	25.7828i	1.61729	+	0.828262i
$970$	−0.508845	+	2.00938i	−0.0163380	+	0.0645174i
$971$	48.1289	−	13.6096i	1.54453	−	0.436752i	0.609931	−	0.792454i	$-0.291197\pi$
$971$	48.1289	−	13.6096i	1.54453	−	0.436752i	0.934599	+	0.355703i	$0.115758\pi$
$972$	3.36677	−	10.7642i	0.107989	−	0.345261i
$973$	32.0193	+	15.1103i	1.02649	+	0.484413i
$974$	26.2962	−	18.2334i	0.842586	−	0.584236i
$975$	−5.53318	−	39.9024i	−0.177204	−	1.27790i
$976$	−2.48463	+	1.93386i	−0.0795309	+	0.0619014i
$977$	19.4767	+	29.8112i	0.623114	+	0.953746i	0.999626	+	0.0273349i	$0.00870206\pi$
$977$	19.4767	+	29.8112i	0.623114	+	0.953746i	−0.376513	+	0.926411i	$0.622877\pi$
$978$	−42.2254	+	2.32964i	−1.35022	+	0.0744936i
$979$	−28.0404	+	24.4204i	−0.896176	+	0.780480i
$980$	0.0763001	−	0.301302i	0.00243732	−	0.00962474i
$981$	3.65529	−	0.609960i	0.116704	−	0.0194745i
$982$	13.8555	+	6.53856i	0.442146	+	0.208654i
$983$	18.3131	+	15.9489i	0.584097	+	0.508690i	0.897550	−	0.440913i	$-0.145345\pi$
$983$	18.3131	+	15.9489i	0.584097	+	0.508690i	−0.313453	+	0.949604i	$0.601486\pi$
$984$	−1.07417	+	1.86051i	−0.0342432	+	0.0593110i
$985$	−0.245541	+	0.0271765i	−0.00782359	+	0.000865915i
$986$	26.0907	−	2.88771i	0.830896	−	0.0919635i
$987$	20.2588	−	31.0084i	0.644845	−	0.987009i
$988$	−17.3028	+	1.34978i	−0.550474	+	0.0429423i
$989$	0.280705	+	0.429650i	0.00892589	+	0.0136621i
$990$	0.699812	+	0.849735i	0.0222415	+	0.0270063i
$991$	8.89865	+	5.46998i	0.282675	+	0.173760i	0.657753	−	0.753233i	$-0.271507\pi$
$991$	8.89865	+	5.46998i	0.282675	+	0.173760i	−0.375078	+	0.926993i	$0.622384\pi$
$992$	−1.88397	+	1.15807i	−0.0598162	+	0.0367689i
$993$	33.6510	−	32.7362i	1.06788	−	1.03885i
$994$	19.1589	+	18.6381i	0.607683	+	0.591163i
$995$	2.68816	−	0.922846i	0.0852204	−	0.0292562i
$996$	−5.39296	−	2.91852i	−0.170882	−	0.0924769i
$997$	0.140837	−	5.10931i	0.00446036	−	0.161813i	−0.994111	−	0.108371i	$-0.965437\pi$
$997$	0.140837	−	5.10931i	0.00446036	−	0.161813i	0.998571	−	0.0534428i	$-0.0170195\pi$
$998$	−19.5359	−	19.0048i	−0.618398	−	0.601587i
$999$	11.8807	−	12.9059i	0.375890	−	0.408325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.b.501.13	yes	612
361.49	even	57	inner	722.2.i.b.49.13	✓	612

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.b.49.13	✓	612	361.49	even	57	inner
722.2.i.b.501.13	yes	612	1.1	even	1	trivial

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.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.926494 - 0.376309i) q^{2} +(1.98560 + 0.444982i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.00459569 - 0.166723i) q^{5} +(-1.67219 - 1.15947i) q^{6} +(-0.556362 - 2.19703i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(1.03151 + 0.486781i) q^{9} +O(q^{10})\)	\(q+(-0.926494 - 0.376309i) q^{2} +(1.98560 + 0.444982i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.00459569 - 0.166723i) q^{5} +(-1.67219 - 1.15947i) q^{6} +(-0.556362 - 2.19703i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(1.03151 + 0.486781i) q^{9} +(-0.0584816 + 0.156197i) q^{10} +(0.477849 - 5.76678i) q^{11} +(1.11296 + 1.70351i) q^{12} +(-1.18856 - 3.80005i) q^{13} +(-0.311295 + 2.24490i) q^{14} +(0.0650636 - 0.333090i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(-4.57094 + 4.44668i) q^{17} +(-0.772507 - 0.839166i) q^{18} +(-2.26471 - 3.72439i) q^{19} +(0.112961 - 0.122709i) q^{20} +(-0.127073 - 4.60998i) q^{21} +(-2.61282 + 5.16307i) q^{22} +(-1.18158 + 0.264799i) q^{23} +(-0.390102 - 1.99710i) q^{24} +(4.96463 - 0.273906i) q^{25} +(-0.328797 + 3.96799i) q^{26} +(-2.98579 - 2.32393i) q^{27} +(1.13319 - 1.96274i) q^{28} +(3.96102 + 1.12007i) q^{29} +(-0.185626 + 0.284121i) q^{30} +(-1.74514 - 1.35830i) q^{31} +(0.350638 - 0.936511i) q^{32} +(3.51493 - 11.2379i) q^{33} +(5.90827 - 2.39973i) q^{34} +(-0.363738 + 0.102855i) q^{35} +(0.399937 + 1.06818i) q^{36} +(-0.382861 + 4.62044i) q^{37} +(0.696713 + 4.30286i) q^{38} +(-0.669051 - 8.07425i) q^{39} +(-0.150834 + 0.0711805i) q^{40} +(-0.796165 - 0.693381i) q^{41} +(-1.61704 + 4.31893i) q^{42} +(-0.148613 - 0.396927i) q^{43} +(4.36367 - 3.80032i) q^{44} +(0.0764171 - 0.174213i) q^{45} +(1.19438 + 0.199306i) q^{46} +(6.60022 + 4.57649i) q^{47} +(-0.390102 + 1.99710i) q^{48} +(1.63893 - 0.886946i) q^{49} +(-4.70278 - 1.61446i) q^{50} +(-11.0547 + 6.79532i) q^{51} +(1.79782 - 3.55259i) q^{52} +(9.15312 + 6.34663i) q^{53} +(1.89180 + 3.27669i) q^{54} +(-0.963651 - 0.0531661i) q^{55} +(-1.78849 + 1.39204i) q^{56} +(-2.83950 - 8.40289i) q^{57} +(-3.24837 - 2.52831i) q^{58} +(8.44825 + 7.35759i) q^{59} +(0.278899 - 0.193384i) q^{60} +(1.86467 + 2.53697i) q^{61} +(1.10572 + 1.91517i) q^{62} +(0.495577 - 2.53708i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(-0.628093 + 0.215625i) q^{65} +(-7.48547 + 9.08911i) q^{66} +(0.653808 + 0.0723634i) q^{67} -6.37702 q^{68} -2.46398 q^{69} +(0.375706 + 0.0415832i) q^{70} +(6.98466 - 9.50297i) q^{71} +(0.0314285 - 1.14017i) q^{72} +(-0.990741 + 0.963807i) q^{73} +(2.09343 - 4.13674i) q^{74} +(9.97964 + 1.66531i) q^{75} +(0.973706 - 4.24875i) q^{76} +(-12.9356 + 2.15857i) q^{77} +(-2.41854 + 7.73251i) q^{78} +(-3.09211 - 8.25867i) q^{79} +(0.166533 - 0.00918789i) q^{80} +(-7.06978 - 8.58435i) q^{81} +(0.476717 + 0.942018i) q^{82} +(-2.65030 + 1.43427i) q^{83} +(3.12344 - 3.39296i) q^{84} +(0.762370 + 0.741645i) q^{85} +(-0.0116785 + 0.423675i) q^{86} +(7.36657 + 3.98659i) q^{87} +(-5.47301 + 1.87889i) q^{88} +(-4.60596 - 4.48074i) q^{89} +(-0.136358 + 0.132651i) q^{90} +(-7.68753 + 4.72551i) q^{91} +(-1.03158 - 0.634111i) q^{92} +(-2.86072 - 3.47359i) q^{93} +(-4.39289 - 6.72382i) q^{94} +(-0.610534 + 0.394695i) q^{95} +(1.11296 - 1.70351i) q^{96} +(12.3525 - 1.36718i) q^{97} +(-1.85223 + 0.205005i) q^{98} +(3.30006 - 5.71588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9}+O(q^{10}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21} + 33 q^{22} + 39 q^{23} + 20 q^{25} - 8 q^{26} + 158 q^{27} - 37 q^{28} - 42 q^{29} - 29 q^{30} + 12 q^{31} + 17 q^{32} + 60 q^{33} - q^{34} - 14 q^{35} + 23 q^{36} - 6 q^{37} + 76 q^{38} - 108 q^{39} + q^{40} + 8 q^{41} + 11 q^{42} + 7 q^{43} - 5 q^{44} - 101 q^{45} - 21 q^{46} + 105 q^{47} - 62 q^{49} - 78 q^{50} - 3 q^{51} + 4 q^{52} + 146 q^{53} - 79 q^{54} + 4 q^{55} - 21 q^{56} - 28 q^{57} + 8 q^{58} - 4 q^{59} - 14 q^{60} - 93 q^{61} - 6 q^{62} - 95 q^{63} - 34 q^{64} - 76 q^{65} - 16 q^{66} - 6 q^{67} + 78 q^{68} + 38 q^{69} + 81 q^{70} - 151 q^{71} + 23 q^{72} + 7 q^{73} - 35 q^{74} - 12 q^{75} - 7 q^{76} + 78 q^{77} - 3 q^{78} - 10 q^{79} + q^{80} + 58 q^{81} - 30 q^{82} + 67 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 109 q^{87} + 10 q^{88} - 25 q^{89} - 73 q^{90} + 37 q^{91} + q^{92} + 56 q^{93} - 39 q^{94} - 29 q^{95} - 153 q^{97} + 164 q^{98} - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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