LMFDB - Embedded newform 273.2.k.b.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.k (of order $3$, degree $2$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.6040683.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 5x^{4} - 2x^{3} + 25x^{2} - 5x + 1 $ x^6 + 5x^4 - 2x^3 + 25x^2 - 5x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$1.06421 - 1.84326i$ of defining polynomial
Character	$\chi$	$=$	273.211
Dual form			273.2.k.b.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06421 - 1.84326i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.26508 + 2.19119i) q^{4} -2.65859 q^{5} +(1.06421 - 1.84326i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.12842 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.06421 - 1.84326i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.26508 + 2.19119i) q^{4} -2.65859 q^{5} +(1.06421 - 1.84326i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.12842 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.82929 + 4.90048i) q^{10} +(0.329293 + 0.570353i) q^{11} -2.53017 q^{12} +(3.32929 + 1.38413i) q^{13} +2.12842 q^{14} +(-1.32929 - 2.30240i) q^{15} +(1.32929 + 2.30240i) q^{16} +(-3.06421 + 5.30737i) q^{17} +2.12842 q^{18} +(-2.62842 + 4.55256i) q^{19} +(3.36334 - 5.82547i) q^{20} -1.00000 q^{21} +(0.700874 - 1.21395i) q^{22} +(1.76508 + 3.05721i) q^{23} +(0.564210 + 0.977240i) q^{24} +2.06808 q^{25} +(-0.991754 - 7.60977i) q^{26} -1.00000 q^{27} +(-1.26508 - 2.19119i) q^{28} +(-0.435790 - 0.754811i) q^{29} +(-2.82929 + 4.90048i) q^{30} -5.91542 q^{31} +(3.95771 - 6.85496i) q^{32} +(-0.329293 + 0.570353i) q^{33} +13.0438 q^{34} +(1.32929 - 2.30240i) q^{35} +(-1.26508 - 2.19119i) q^{36} +(-0.731042 - 1.26620i) q^{37} +11.1888 q^{38} +(0.465958 + 3.57532i) q^{39} -3.00000 q^{40} +(-5.25684 - 9.10511i) q^{41} +(1.06421 + 1.84326i) q^{42} +(1.76508 - 3.05721i) q^{43} -1.66633 q^{44} +(1.32929 - 2.30240i) q^{45} +(3.75684 - 6.50703i) q^{46} +8.71892 q^{47} +(-1.32929 + 2.30240i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.20087 - 3.81203i) q^{50} -6.12842 q^{51} +(-7.24472 + 5.54408i) q^{52} -1.93966 q^{53} +(1.06421 + 1.84326i) q^{54} +(-0.875455 - 1.51633i) q^{55} +(-0.564210 + 0.977240i) q^{56} -5.25684 q^{57} +(-0.927545 + 1.60655i) q^{58} +(-6.95384 + 12.0444i) q^{59} +6.72667 q^{60} +(-4.09825 + 7.09838i) q^{61} +(6.29525 + 10.9037i) q^{62} +(-0.500000 - 0.866025i) q^{63} -11.5302 q^{64} +(-8.85122 - 3.67982i) q^{65} +1.40175 q^{66} +(-6.69263 - 11.5920i) q^{67} +(-7.75296 - 13.4285i) q^{68} +(-1.76508 + 3.05721i) q^{69} -5.65859 q^{70} +(-2.13666 + 3.70081i) q^{71} +(-0.564210 + 0.977240i) q^{72} -3.46983 q^{73} +(-1.55596 + 2.69501i) q^{74} +(1.03404 + 1.79101i) q^{75} +(-6.65034 - 11.5187i) q^{76} -0.658587 q^{77} +(6.09438 - 4.66377i) q^{78} +4.85509 q^{79} +(-3.53404 - 6.12114i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-11.1888 + 19.3795i) q^{82} +15.8551 q^{83} +(1.26508 - 2.19119i) q^{84} +(8.14647 - 14.1101i) q^{85} -7.51368 q^{86} +(0.435790 - 0.754811i) q^{87} +(0.371581 + 0.643597i) q^{88} +(4.75684 + 8.23909i) q^{89} -5.65859 q^{90} +(-2.86334 + 2.19119i) q^{91} -8.93192 q^{92} +(-2.95771 - 5.12291i) q^{93} +(-9.27876 - 16.0713i) q^{94} +(6.98788 - 12.1034i) q^{95} +7.91542 q^{96} +(-1.48788 + 2.57708i) q^{97} +(-1.06421 + 1.84326i) q^{98} -0.658587 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} - 8 q^{11} - 8 q^{12} + 10 q^{13} + 2 q^{15} - 2 q^{16} - 12 q^{17} - 3 q^{19} + 11 q^{20} - 6 q^{21} + 7 q^{22} + 7 q^{23} - 3 q^{24} + 14 q^{25} + 16 q^{26} - 6 q^{27} - 4 q^{28} - 9 q^{29} - 7 q^{30} + 10 q^{31} + q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{35} - 4 q^{36} + 40 q^{38} + 2 q^{39} - 18 q^{40} - 6 q^{41} + 7 q^{43} - 6 q^{44} - 2 q^{45} - 3 q^{46} + 18 q^{47} + 2 q^{48} - 3 q^{49} - 16 q^{50} - 24 q^{51} + 12 q^{52} - 26 q^{53} - 26 q^{55} + 3 q^{56} - 6 q^{57} + 10 q^{58} - 11 q^{59} + 22 q^{60} - 19 q^{61} + 27 q^{62} - 3 q^{63} - 62 q^{64} - 14 q^{65} + 14 q^{66} - 21 q^{67} - 13 q^{68} - 7 q^{69} - 14 q^{70} - 22 q^{71} + 3 q^{72} - 28 q^{73} + 19 q^{74} + 7 q^{75} + 2 q^{76} + 16 q^{77} + 23 q^{78} - 2 q^{79} - 22 q^{80} - 3 q^{81} - 40 q^{82} + 64 q^{83} + 4 q^{84} - q^{85} + 6 q^{86} + 9 q^{87} + 15 q^{88} + 3 q^{89} - 14 q^{90} - 8 q^{91} - 52 q^{92} + 5 q^{93} - q^{94} + 12 q^{95} + 2 q^{96} + 21 q^{97} + 16 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 - 8 * q^11 - 8 * q^12 + 10 * q^13 + 2 * q^15 - 2 * q^16 - 12 * q^17 - 3 * q^19 + 11 * q^20 - 6 * q^21 + 7 * q^22 + 7 * q^23 - 3 * q^24 + 14 * q^25 + 16 * q^26 - 6 * q^27 - 4 * q^28 - 9 * q^29 - 7 * q^30 + 10 * q^31 + q^32 + 8 * q^33 + 20 * q^34 - 2 * q^35 - 4 * q^36 + 40 * q^38 + 2 * q^39 - 18 * q^40 - 6 * q^41 + 7 * q^43 - 6 * q^44 - 2 * q^45 - 3 * q^46 + 18 * q^47 + 2 * q^48 - 3 * q^49 - 16 * q^50 - 24 * q^51 + 12 * q^52 - 26 * q^53 - 26 * q^55 + 3 * q^56 - 6 * q^57 + 10 * q^58 - 11 * q^59 + 22 * q^60 - 19 * q^61 + 27 * q^62 - 3 * q^63 - 62 * q^64 - 14 * q^65 + 14 * q^66 - 21 * q^67 - 13 * q^68 - 7 * q^69 - 14 * q^70 - 22 * q^71 + 3 * q^72 - 28 * q^73 + 19 * q^74 + 7 * q^75 + 2 * q^76 + 16 * q^77 + 23 * q^78 - 2 * q^79 - 22 * q^80 - 3 * q^81 - 40 * q^82 + 64 * q^83 + 4 * q^84 - q^85 + 6 * q^86 + 9 * q^87 + 15 * q^88 + 3 * q^89 - 14 * q^90 - 8 * q^91 - 52 * q^92 + 5 * q^93 - q^94 + 12 * q^95 + 2 * q^96 + 21 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.06421	−	1.84326i	−0.752510	−	1.30339i	−0.946603	−	0.322402i	$-0.895510\pi$
$2$	−1.06421	−	1.84326i	−0.752510	−	1.30339i	0.194093	−	0.980983i	$-0.437824\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.26508	+	2.19119i	−0.632542	+	1.09559i
$5$	−2.65859			−1.18896			−0.594478	−	0.804112i	$-0.702641\pi$
$5$	−2.65859			−1.18896			−0.594478	+	0.804112i	$0.702641\pi$
$6$	1.06421	−	1.84326i	0.434462	−	0.752510i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	1.12842			0.398956
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.82929	+	4.90048i	0.894701	+	1.54967i
$11$	0.329293	+	0.570353i	0.0992857	+	0.171968i	0.911389	−	0.411546i	$-0.135011\pi$
$11$	0.329293	+	0.570353i	0.0992857	+	0.171968i	−0.812103	+	0.583513i	$0.801678\pi$
$12$	−2.53017			−0.730397
$13$	3.32929	+	1.38413i	0.923380	+	0.383888i
$13$	3.32929	+	1.38413i	0.923380	+	0.383888i
$14$	2.12842			0.568844
$15$	−1.32929	−	2.30240i	−0.343222	−	0.594478i
$16$	1.32929	+	2.30240i	0.332323	+	0.575601i
$17$	−3.06421	+	5.30737i	−0.743180	+	1.28723i	0.207860	+	0.978159i	$0.433350\pi$
$17$	−3.06421	+	5.30737i	−0.743180	+	1.28723i	−0.951040	+	0.309067i	$0.899983\pi$
$18$	2.12842			0.501673
$19$	−2.62842	+	4.55256i	−0.603001	+	1.04443i	0.389363	+	0.921084i	$0.372695\pi$
$19$	−2.62842	+	4.55256i	−0.603001	+	1.04443i	−0.992364	+	0.123344i	$0.960638\pi$
$20$	3.36334	−	5.82547i	0.752065	−	1.30261i
$21$	−1.00000			−0.218218
$22$	0.700874	−	1.21395i	0.149427	−	0.258815i
$23$	1.76508	+	3.05721i	0.368045	+	0.637473i	0.989260	−	0.146167i	$-0.0466938\pi$
$23$	1.76508	+	3.05721i	0.368045	+	0.637473i	−0.621214	+	0.783641i	$0.713360\pi$
$24$	0.564210	+	0.977240i	0.115169	+	0.199478i
$25$	2.06808			0.413617
$26$	−0.991754	−	7.60977i	−0.194499	−	1.49240i
$27$	−1.00000			−0.192450
$28$	−1.26508	−	2.19119i	−0.239078	−	0.414096i
$29$	−0.435790	−	0.754811i	−0.0809243	−	0.140165i	0.822723	−	0.568443i	$-0.192454\pi$
$29$	−0.435790	−	0.754811i	−0.0809243	−	0.140165i	−0.903647	+	0.428278i	$0.859121\pi$
$30$	−2.82929	+	4.90048i	−0.516556	+	0.894701i
$31$	−5.91542			−1.06244			−0.531221	−	0.847233i	$-0.678267\pi$
$31$	−5.91542			−1.06244			−0.531221	+	0.847233i	$0.678267\pi$
$32$	3.95771	−	6.85496i	0.699631	−	1.21180i
$33$	−0.329293	+	0.570353i	−0.0573226	+	0.0992857i
$34$	13.0438			2.23700
$35$	1.32929	−	2.30240i	0.224692	−	0.389177i
$36$	−1.26508	−	2.19119i	−0.210847	−	0.365198i
$37$	−0.731042	−	1.26620i	−0.120183	−	0.208162i	0.799657	−	0.600457i	$-0.205015\pi$
$37$	−0.731042	−	1.26620i	−0.120183	−	0.208162i	−0.919840	+	0.392295i	$0.871681\pi$
$38$	11.1888			1.81506
$39$	0.465958	+	3.57532i	0.0746130	+	0.572509i
$40$	−3.00000			−0.474342
$41$	−5.25684	−	9.10511i	−0.820980	−	1.42198i	−0.904953	−	0.425511i	$-0.860094\pi$
$41$	−5.25684	−	9.10511i	−0.820980	−	1.42198i	0.0839729	−	0.996468i	$-0.473239\pi$
$42$	1.06421	+	1.84326i	0.164211	+	0.284422i
$43$	1.76508	−	3.05721i	0.269173	−	0.466221i	−0.699476	−	0.714656i	$-0.746583\pi$
$43$	1.76508	−	3.05721i	0.269173	−	0.466221i	0.968648	+	0.248436i	$0.0799164\pi$
$44$	−1.66633			−0.251209
$45$	1.32929	−	2.30240i	0.198159	−	0.343222i
$46$	3.75684	−	6.50703i	0.553916	−	0.959410i
$47$	8.71892			1.27179			0.635893	−	0.771777i	$-0.280632\pi$
$47$	8.71892			1.27179			0.635893	+	0.771777i	$0.280632\pi$
$48$	−1.32929	+	2.30240i	−0.191867	+	0.332323i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.20087	−	3.81203i	−0.311251	−	0.539102i
$51$	−6.12842			−0.858150
$52$	−7.24472	+	5.54408i	−1.00466	+	0.768825i
$53$	−1.93966			−0.266433			−0.133217	−	0.991087i	$-0.542531\pi$
$53$	−1.93966			−0.266433			−0.133217	+	0.991087i	$0.542531\pi$
$54$	1.06421	+	1.84326i	0.144821	+	0.250837i
$55$	−0.875455	−	1.51633i	−0.118046	−	0.204462i
$56$	−0.564210	+	0.977240i	−0.0753957	+	0.130589i
$57$	−5.25684			−0.696285
$58$	−0.927545	+	1.60655i	−0.121793	+	0.210951i
$59$	−6.95384	+	12.0444i	−0.905313	+	1.56805i	−0.0848156	+	0.996397i	$0.527030\pi$
$59$	−6.95384	+	12.0444i	−0.905313	+	1.56805i	−0.820497	+	0.571651i	$0.806303\pi$
$60$	6.72667			0.868409
$61$	−4.09825	+	7.09838i	−0.524727	+	0.908854i	0.474858	+	0.880062i	$0.342499\pi$
$61$	−4.09825	+	7.09838i	−0.524727	+	0.908854i	−0.999585	+	0.0287920i	$0.990834\pi$
$62$	6.29525	+	10.9037i	0.799498	+	1.38477i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	−11.5302			−1.44127
$65$	−8.85122	−	3.67982i	−1.09786	−	0.456425i
$66$	1.40175			0.172543
$67$	−6.69263	−	11.5920i	−0.817635	−	1.41618i	−0.907421	−	0.420224i	$-0.861952\pi$
$67$	−6.69263	−	11.5920i	−0.817635	−	1.41618i	0.0897858	−	0.995961i	$-0.471382\pi$
$68$	−7.75296	−	13.4285i	−0.940185	−	1.62845i
$69$	−1.76508	+	3.05721i	−0.212491	+	0.368045i
$70$	−5.65859			−0.676330
$71$	−2.13666	+	3.70081i	−0.253575	+	0.439206i	−0.964508	−	0.264055i	$-0.914940\pi$
$71$	−2.13666	+	3.70081i	−0.253575	+	0.439206i	0.710932	+	0.703261i	$0.248273\pi$
$72$	−0.564210	+	0.977240i	−0.0664927	+	0.115169i
$73$	−3.46983			−0.406113			−0.203057	−	0.979167i	$-0.565088\pi$
$73$	−3.46983			−0.406113			−0.203057	+	0.979167i	$0.565088\pi$
$74$	−1.55596	+	2.69501i	−0.180877	+	0.313288i
$75$	1.03404	+	1.79101i	0.119401	+	0.206808i
$76$	−6.65034	−	11.5187i	−0.762846	−	1.32129i
$77$	−0.658587			−0.0750529
$78$	6.09438	−	4.66377i	0.690052	−	0.528068i
$79$	4.85509			0.546240			0.273120	−	0.961980i	$-0.411944\pi$
$79$	4.85509			0.546240			0.273120	+	0.961980i	$0.411944\pi$
$80$	−3.53404	−	6.12114i	−0.395118	−	0.684364i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−11.1888	+	19.3795i	−1.23559	+	2.14011i
$83$	15.8551			1.74032			0.870161	−	0.492767i	$-0.164015\pi$
$83$	15.8551			1.74032			0.870161	+	0.492767i	$0.164015\pi$
$84$	1.26508	−	2.19119i	0.138032	−	0.239078i
$85$	8.14647	−	14.1101i	0.883608	−	1.53045i
$86$	−7.51368			−0.810221
$87$	0.435790	−	0.754811i	0.0467216	−	0.0809243i
$88$	0.371581	+	0.643597i	0.0396107	+	0.0686077i
$89$	4.75684	+	8.23909i	0.504224	+	0.873341i	0.999988	+	0.00488415i	$0.00155468\pi$
$89$	4.75684	+	8.23909i	0.504224	+	0.873341i	−0.495764	+	0.868457i	$0.665112\pi$
$90$	−5.65859			−0.596467
$91$	−2.86334	+	2.19119i	−0.300159	+	0.229699i
$92$	−8.93192			−0.931217
$93$	−2.95771	−	5.12291i	−0.306700	−	0.531221i
$94$	−9.27876	−	16.0713i	−0.957031	−	1.65763i
$95$	6.98788	−	12.1034i	0.716941	−	1.24178i
$96$	7.91542			0.807865
$97$	−1.48788	+	2.57708i	−0.151071	+	0.261663i	−0.931622	−	0.363430i	$-0.881606\pi$
$97$	−1.48788	+	2.57708i	−0.151071	+	0.261663i	0.780550	+	0.625093i	$0.214939\pi$
$98$	−1.06421	+	1.84326i	−0.107501	+	0.186198i
$99$	−0.658587			−0.0661905
$100$	−2.61630	+	4.53156i	−0.261630	+	0.453156i
$101$	4.62017	+	8.00237i	0.459724	+	0.796266i	0.998946	−	0.0458978i	$-0.0146149\pi$
$101$	4.62017	+	8.00237i	0.459724	+	0.796266i	−0.539222	+	0.842164i	$0.681282\pi$
$102$	6.52192	+	11.2963i	0.645767	+	1.11850i
$103$	13.3775			1.31813			0.659063	−	0.752088i	$-0.270953\pi$
$103$	13.3775			1.31813			0.659063	+	0.752088i	$0.270953\pi$
$104$	3.75684	+	1.56187i	0.368388	+	0.153154i
$105$	2.65859			0.259452
$106$	2.06421	+	3.57532i	0.200494	+	0.347265i
$107$	−4.92367	−	8.52805i	−0.475989	−	0.824437i	0.523632	−	0.851944i	$-0.324577\pi$
$107$	−4.92367	−	8.52805i	−0.475989	−	0.824437i	−0.999622	+	0.0275068i	$0.991243\pi$
$108$	1.26508	−	2.19119i	0.121733	−	0.210847i
$109$	6.32492			0.605818			0.302909	−	0.953020i	$-0.402042\pi$
$109$	6.32492			0.605818			0.302909	+	0.953020i	$0.402042\pi$
$110$	−1.86334	+	3.22739i	−0.177662	+	0.307720i
$111$	0.731042	−	1.26620i	0.0693874	−	0.120183i
$112$	−2.65859			−0.251213
$113$	−6.61630	+	11.4598i	−0.622409	+	1.07804i	0.366627	+	0.930368i	$0.380513\pi$
$113$	−6.61630	+	11.4598i	−0.622409	+	1.07804i	−0.989036	+	0.147676i	$0.952821\pi$
$114$	5.59438	+	9.68975i	0.523961	+	0.907528i
$115$	−4.69263	−	8.12787i	−0.437590	−	0.757928i
$116$	2.20525			0.204752
$117$	−2.86334	+	2.19119i	−0.264715	+	0.202576i
$118$	29.6014			2.72503
$119$	−3.06421	−	5.30737i	−0.280896	−	0.486525i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	5.28313	−	9.15065i	0.480285	−	0.831878i
$122$	17.4456			1.57945
$123$	5.25684	−	9.10511i	0.473993	−	0.820980i
$124$	7.48351	−	12.9618i	0.672039	−	1.16401i
$125$	7.79475			0.697184
$126$	−1.06421	+	1.84326i	−0.0948073	+	0.164211i
$127$	6.05596	+	10.4892i	0.537380	+	0.930769i	0.999044	+	0.0437145i	$0.0139192\pi$
$127$	6.05596	+	10.4892i	0.537380	+	0.930769i	−0.461664	+	0.887055i	$0.652747\pi$
$128$	4.35509	+	7.54324i	0.384939	+	0.666734i
$129$	3.53017			0.310814
$130$	2.63666	+	20.2312i	0.231251	+	1.77440i
$131$	−3.34141			−0.291941			−0.145970	−	0.989289i	$-0.546630\pi$
$131$	−3.34141			−0.291941			−0.145970	+	0.989289i	$0.546630\pi$
$132$	−0.833167	−	1.44309i	−0.0725179	−	0.125605i
$133$	−2.62842	−	4.55256i	−0.227913	−	0.394757i
$134$	−14.2447	+	24.6726i	−1.23056	+	2.13139i
$135$	2.65859			0.228815
$136$	−3.45771	+	5.98893i	−0.296496	+	0.513547i
$137$	−0.901749	+	1.56187i	−0.0770416	+	0.133440i	−0.901972	−	0.431794i	$-0.857881\pi$
$137$	−0.901749	+	1.56187i	−0.0770416	+	0.133440i	0.824931	+	0.565234i	$0.191214\pi$
$138$	7.51368			0.639607
$139$	0.564210	−	0.977240i	0.0478556	−	0.0828884i	−0.841105	−	0.540871i	$-0.818095\pi$
$139$	0.564210	−	0.977240i	0.0478556	−	0.0828884i	0.888961	+	0.457983i	$0.151428\pi$
$140$	3.36334	+	5.82547i	0.284254	+	0.492342i
$141$	4.35946	+	7.55081i	0.367133	+	0.635893i
$142$	9.09544			0.763272
$143$	0.306874	+	2.35466i	0.0256621	+	0.196906i
$144$	−2.65859			−0.221549
$145$	1.15859	+	2.00673i	0.0962154	+	0.166650i
$146$	3.69263	+	6.39582i	0.305604	+	0.529322i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$	3.69932			0.304082
$149$	−6.91980	+	11.9854i	−0.566892	+	0.981885i	0.429979	+	0.902839i	$0.358521\pi$
$149$	−6.91980	+	11.9854i	−0.566892	+	0.981885i	−0.996871	+	0.0790466i	$0.974812\pi$
$150$	2.20087	−	3.81203i	0.179701	−	0.311251i
$151$	−7.57401			−0.616364			−0.308182	−	0.951327i	$-0.599721\pi$
$151$	−7.57401			−0.616364			−0.308182	+	0.951327i	$0.599721\pi$
$152$	−2.96596	+	5.13719i	−0.240571	+	0.416681i
$153$	−3.06421	−	5.30737i	−0.247727	−	0.429075i
$154$	0.700874	+	1.21395i	0.0564781	+	0.0978229i
$155$	15.7267			1.26320
$156$	−8.42367	−	3.50207i	−0.674433	−	0.280390i
$157$	7.36877			0.588092			0.294046	−	0.955791i	$-0.404998\pi$
$157$	7.36877			0.588092			0.294046	+	0.955791i	$0.404998\pi$
$158$	−5.16683	−	8.94922i	−0.411051	−	0.711961i
$159$	−0.969832	−	1.67980i	−0.0769127	−	0.133217i
$160$	−10.5219	+	18.2245i	−0.831831	+	1.44077i
$161$	−3.53017			−0.278216
$162$	−1.06421	+	1.84326i	−0.0836122	+	0.144821i
$163$	10.5603	−	18.2910i	0.827149	−	1.43266i	−0.0731162	−	0.997323i	$-0.523294\pi$
$163$	10.5603	−	18.2910i	0.827149	−	1.43266i	0.900266	−	0.435341i	$-0.143372\pi$
$164$	26.6014			2.07722
$165$	0.875455	−	1.51633i	0.0681541	−	0.118046i
$166$	−16.8731	−	29.2251i	−1.30961	−	2.26831i
$167$	3.56034	+	6.16668i	0.275507	+	0.477192i	0.970263	−	0.242053i	$-0.0778209\pi$
$167$	3.56034	+	6.16668i	0.275507	+	0.477192i	−0.694756	+	0.719246i	$0.744488\pi$
$168$	−1.12842			−0.0870594
$169$	9.16839	+	9.21632i	0.705261	+	0.708948i
$170$	−34.6782			−2.65970
$171$	−2.62842	−	4.55256i	−0.201000	−	0.348143i
$172$	4.46596	+	7.73527i	0.340526	+	0.589809i
$173$	2.29525	−	3.97549i	0.174505	−	0.302251i	−0.765485	−	0.643454i	$-0.777501\pi$
$173$	2.29525	−	3.97549i	0.174505	−	0.302251i	0.939990	+	0.341203i	$0.110834\pi$
$174$	−1.85509			−0.140634
$175$	−1.03404	+	1.79101i	−0.0781662	+	0.135388i
$176$	−0.875455	+	1.51633i	−0.0659899	+	0.114298i
$177$	−13.9077			−1.04536
$178$	10.1245	−	17.5362i	0.758867	−	1.31440i
$179$	−10.6081	−	18.3737i	−0.792883	−	1.37331i	−0.924175	−	0.381970i	$-0.875246\pi$
$179$	−10.6081	−	18.3737i	−0.792883	−	1.37331i	0.131292	−	0.991344i	$-0.458088\pi$
$180$	3.36334	+	5.82547i	0.250688	+	0.434205i
$181$	−17.6179			−1.30952			−0.654762	−	0.755835i	$-0.727231\pi$
$181$	−17.6179			−1.30952			−0.654762	+	0.755835i	$0.727231\pi$
$182$	7.08613	+	2.94600i	0.525259	+	0.218372i
$183$	−8.19650			−0.605903
$184$	1.99175	+	3.44982i	0.146834	+	0.254324i
$185$	1.94354	+	3.36631i	0.142892	+	0.247496i
$186$	−6.29525	+	10.9037i	−0.461590	+	0.799498i
$187$	−4.03610			−0.295149
$188$	−11.0302	+	19.1048i	−0.804458	+	1.39336i
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$	−29.7463			−2.15802
$191$	1.15034	−	1.99245i	0.0832358	−	0.144169i	−0.821402	−	0.570349i	$-0.806808\pi$
$191$	1.15034	−	1.99245i	0.0832358	−	0.144169i	0.904638	+	0.426181i	$0.140141\pi$
$192$	−5.76508	−	9.98542i	−0.416059	−	0.720635i
$193$	11.6124	+	20.1133i	0.835881	+	1.44779i	0.893311	+	0.449438i	$0.148376\pi$
$193$	11.6124	+	20.1133i	0.835881	+	1.44779i	−0.0574307	+	0.998349i	$0.518291\pi$
$194$	6.33367			0.454731
$195$	−1.23879	−	9.50529i	−0.0887116	−	0.680688i
$196$	2.53017			0.180726
$197$	5.66683	+	9.81524i	0.403745	+	0.699307i	0.994175	−	0.107782i	$-0.0343749\pi$
$197$	5.66683	+	9.81524i	0.403745	+	0.699307i	−0.590429	+	0.807089i	$0.701042\pi$
$198$	0.700874	+	1.21395i	0.0498090	+	0.0862717i
$199$	7.90718	−	13.6956i	0.560525	−	0.970858i	−0.436926	−	0.899498i	$-0.643933\pi$
$199$	7.90718	−	13.6956i	0.560525	−	0.970858i	0.997451	−	0.0713602i	$-0.0227340\pi$
$200$	2.33367			0.165015
$201$	6.69263	−	11.5920i	0.472062	−	0.817635i
$202$	9.83367	−	17.0324i	0.691894	−	1.19840i
$203$	0.871581			0.0611730
$204$	7.75296	−	13.4285i	0.542816	−	0.940185i
$205$	13.9758	+	24.2067i	0.976109	+	1.69067i
$206$	−14.2365	−	24.6583i	−0.991902	−	1.71802i
$207$	−3.53017			−0.245364
$208$	1.23879	+	9.50529i	0.0858946	+	0.659073i
$209$	−3.46208			−0.239477
$210$	−2.82929	−	4.90048i	−0.195240	−	0.338165i
$211$	−3.30300	−	5.72096i	−0.227388	−	0.393847i	0.729645	−	0.683826i	$-0.239685\pi$
$211$	−3.30300	−	5.72096i	−0.227388	−	0.393847i	−0.957033	+	0.289978i	$0.906352\pi$
$212$	2.45384	−	4.25017i	0.168530	−	0.291903i
$213$	−4.27333			−0.292804
$214$	−10.4796	+	18.1513i	−0.716373	+	1.24079i
$215$	−4.69263	+	8.12787i	−0.320035	+	0.554316i
$216$	−1.12842			−0.0767792
$217$	2.95771	−	5.12291i	0.200783	−	0.347766i
$218$	−6.73104	−	11.6585i	−0.455884	−	0.789614i
$219$	−1.73492	−	3.00496i	−0.117235	−	0.203057i
$220$	4.43010			0.298677
$221$	−17.5477	+	13.4285i	−1.18039	+	0.903301i
$222$	−3.11193			−0.208859
$223$	4.90175	+	8.49008i	0.328245	+	0.568538i	0.982164	−	0.188027i	$-0.0602094\pi$
$223$	4.90175	+	8.49008i	0.328245	+	0.568538i	−0.653918	+	0.756565i	$0.726876\pi$
$224$	3.95771	+	6.85496i	0.264436	+	0.458016i
$225$	−1.03404	+	1.79101i	−0.0689361	+	0.119401i
$226$	28.1645			1.87348
$227$	8.14647	−	14.1101i	0.540700	−	0.936520i	−0.458164	−	0.888868i	$-0.651493\pi$
$227$	8.14647	−	14.1101i	0.540700	−	0.936520i	0.998864	−	0.0476522i	$-0.0151739\pi$
$228$	6.65034	−	11.5187i	0.440430	−	0.762846i
$229$	−23.1919			−1.53256			−0.766281	−	0.642506i	$-0.777895\pi$
$229$	−23.1919			−1.53256			−0.766281	+	0.642506i	$0.777895\pi$
$230$	−9.98788	+	17.2995i	−0.658581	+	1.14070i
$231$	−0.329293	−	0.570353i	−0.0216659	−	0.0375265i
$232$	−0.491754	−	0.851743i	−0.0322852	−	0.0559197i
$233$	−2.60699			−0.170790			−0.0853949	−	0.996347i	$-0.527215\pi$
$233$	−2.60699			−0.170790			−0.0853949	+	0.996347i	$0.527215\pi$
$234$	7.08613	+	2.94600i	0.463235	+	0.192586i
$235$	−23.1800			−1.51210
$236$	−17.5944	−	30.4744i	−1.14530	−	1.98371i
$237$	2.42754	+	4.20463i	0.157686	+	0.273120i
$238$	−6.52192	+	11.2963i	−0.422753	+	0.732230i
$239$	15.7432			1.01834			0.509170	−	0.860666i	$-0.329952\pi$
$239$	15.7432			1.01834			0.509170	+	0.860666i	$0.329952\pi$
$240$	3.53404	−	6.12114i	0.228121	−	0.395118i
$241$	−14.9335	+	25.8655i	−0.961950	+	1.66615i	−0.244353	+	0.969686i	$0.578576\pi$
$241$	−14.9335	+	25.8655i	−0.961950	+	1.66615i	−0.717596	+	0.696459i	$0.754758\pi$
$242$	−22.4894			−1.44568
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−10.3693	−	17.9601i	−0.663824	−	1.14978i
$245$	1.32929	+	2.30240i	0.0849254	+	0.147095i
$246$	−22.3775			−1.42674
$247$	−15.0521	+	11.5187i	−0.957742	+	0.732919i
$248$	−6.67508			−0.423868
$249$	7.92754	+	13.7309i	0.502388	+	0.870161i
$250$	−8.29525	−	14.3678i	−0.524638	−	0.908699i
$251$	10.3595	−	17.9431i	0.653883	−	1.13256i	−0.328289	−	0.944577i	$-0.606472\pi$
$251$	10.3595	−	17.9431i	0.653883	−	1.13256i	0.982172	−	0.187982i	$-0.0601946\pi$
$252$	2.53017			0.159386
$253$	−1.16246	+	2.01344i	−0.0730833	+	0.126584i
$254$	12.8896	−	22.3255i	0.808767	−	1.40083i
$255$	16.2929			1.02030
$256$	−2.26071	+	3.91567i	−0.141295	+	0.244729i
$257$	−5.32542	−	9.22390i	−0.332191	−	0.575371i	0.650751	−	0.759292i	$-0.274454\pi$
$257$	−5.32542	−	9.22390i	−0.332191	−	0.575371i	−0.982941	+	0.183921i	$0.941121\pi$
$258$	−3.75684	−	6.50703i	−0.233891	−	0.405110i
$259$	1.46208			0.0908495
$260$	19.2607	−	14.7394i	1.19450	−	0.914099i
$261$	0.871581			0.0539495
$262$	3.55596	+	6.15911i	0.219688	+	0.380511i
$263$	11.8391	+	20.5059i	0.730030	+	1.26445i	0.956870	+	0.290517i	$0.0938272\pi$
$263$	11.8391	+	20.5059i	0.730030	+	1.26445i	−0.226840	+	0.973932i	$0.572839\pi$
$264$	−0.371581	+	0.643597i	−0.0228692	+	0.0396107i
$265$	5.15677			0.316778
$266$	−5.59438	+	9.68975i	−0.343013	+	0.594116i
$267$	−4.75684	+	8.23909i	−0.291114	+	0.504224i
$268$	33.8669			2.06875
$269$	0.238790	−	0.413597i	0.0145593	−	0.0252174i	−0.858654	−	0.512556i	$-0.828699\pi$
$269$	0.238790	−	0.413597i	0.0145593	−	0.0252174i	0.873213	+	0.487338i	$0.162032\pi$
$270$	−2.82929	−	4.90048i	−0.172185	−	0.298234i
$271$	10.3210	+	17.8766i	0.626959	+	1.08592i	0.988159	+	0.153436i	$0.0490340\pi$
$271$	10.3210	+	17.8766i	0.626959	+	1.08592i	−0.361200	+	0.932489i	$0.617633\pi$
$272$	−16.2929			−0.987904
$273$	−3.32929	−	1.38413i	−0.201498	−	0.0837711i
$274$	3.83860			0.231898
$275$	0.681006	+	1.17954i	0.0410662	+	0.0711288i
$276$	−4.46596	−	7.73527i	−0.268819	−	0.465608i
$277$	13.1800	−	22.8284i	0.791910	−	1.37163i	−0.132873	−	0.991133i	$-0.542420\pi$
$277$	13.1800	−	22.8284i	0.791910	−	1.37163i	0.924783	−	0.380495i	$-0.124247\pi$
$278$	−2.40175			−0.144047
$279$	2.95771	−	5.12291i	0.177074	−	0.306700i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	0.205246			0.0122439			0.00612197	−	0.999981i	$-0.498051\pi$
$281$	0.205246			0.0122439			0.00612197	+	0.999981i	$0.498051\pi$
$282$	9.27876	−	16.0713i	0.552542	−	0.957031i
$283$	−0.709120	−	1.22823i	−0.0421528	−	0.0730108i	0.844179	−	0.536061i	$-0.180088\pi$
$283$	−0.709120	−	1.22823i	−0.0421528	−	0.0730108i	−0.886332	+	0.463050i	$0.846755\pi$
$284$	−5.40612	−	9.36367i	−0.320794	−	0.555632i
$285$	13.9758			0.827853
$286$	4.01368	−	3.07150i	0.237334	−	0.181621i
$287$	10.5137			0.620603
$288$	3.95771	+	6.85496i	0.233210	+	0.403932i
$289$	−10.2788	−	17.8033i	−0.604633	−	1.04725i
$290$	2.46596	−	4.27116i	0.144806	−	0.250811i
$291$	−2.97576			−0.174442
$292$	4.38963	−	7.60306i	0.256884	−	0.444935i
$293$	−15.3128	+	26.5226i	−0.894583	+	1.54946i	−0.0602641	+	0.998182i	$0.519194\pi$
$293$	−15.3128	+	26.5226i	−0.894583	+	1.54946i	−0.834319	+	0.551282i	$0.814139\pi$
$294$	−2.12842			−0.124132
$295$	18.4874	−	32.0211i	1.07638	−	1.86434i
$296$	−0.824922	−	1.42881i	−0.0479476	−	0.0830477i
$297$	−0.329293	−	0.570353i	−0.0191075	−	0.0330952i
$298$	29.4565			1.70637
$299$	1.64491	+	12.6215i	0.0951276	+	0.729918i
$300$	−5.23260			−0.302104
$301$	1.76508	+	3.05721i	0.101738	+	0.176215i
$302$	8.06034	+	13.9609i	0.463820	+	0.803360i
$303$	−4.62017	+	8.00237i	−0.265422	+	0.459724i
$304$	−13.9758			−0.801565
$305$	10.8956	−	18.8717i	0.623878	−	1.08059i
$306$	−6.52192	+	11.2963i	−0.372833	+	0.645767i
$307$	4.47858			0.255606			0.127803	−	0.991800i	$-0.459208\pi$
$307$	4.47858			0.255606			0.127803	+	0.991800i	$0.459208\pi$
$308$	0.833167	−	1.44309i	0.0474741	−	0.0822276i
$309$	6.68875	+	11.5853i	0.380510	+	0.659063i
$310$	−16.7365	−	28.9884i	−0.950568	−	1.64643i
$311$	0.675078			0.0382802			0.0191401	−	0.999817i	$-0.493907\pi$
$311$	0.675078			0.0382802			0.0191401	+	0.999817i	$0.493907\pi$
$312$	0.525796	+	4.03445i	0.0297673	+	0.228406i
$313$	10.0242			0.566604			0.283302	−	0.959031i	$-0.408570\pi$
$313$	10.0242			0.566604			0.283302	+	0.959031i	$0.408570\pi$
$314$	−7.84191	−	13.5826i	−0.442545	−	0.766510i
$315$	1.32929	+	2.30240i	0.0748972	+	0.129726i
$316$	−6.14210	+	10.6384i	−0.345520	+	0.598458i
$317$	27.1558			1.52522			0.762610	−	0.646859i	$-0.223918\pi$
$317$	27.1558			1.52522			0.762610	+	0.646859i	$0.223918\pi$
$318$	−2.06421	+	3.57532i	−0.115755	+	0.200494i
$319$	0.287006	−	0.497109i	0.0160692	−	0.0278327i
$320$	30.6540			1.71361
$321$	4.92367	−	8.52805i	0.274812	−	0.475989i
$322$	3.75684	+	6.50703i	0.209360	+	0.362623i
$323$	−16.1081	−	27.9000i	−0.896276	−	1.55240i
$324$	2.53017			0.140565
$325$	6.88526	+	2.86249i	0.381925	+	0.158782i
$326$	−44.9536			−2.48975
$327$	3.16246	+	5.47754i	0.174884	+	0.302909i
$328$	−5.93192	−	10.2744i	−0.327535	−	0.567308i
$329$	−4.35946	+	7.55081i	−0.240345	+	0.416290i
$330$	−3.72667			−0.205146
$331$	−11.9056	+	20.6211i	−0.654392	+	1.13344i	0.327654	+	0.944798i	$0.393742\pi$
$331$	−11.9056	+	20.6211i	−0.654392	+	1.13344i	−0.982046	+	0.188643i	$0.939591\pi$
$332$	−20.0580	+	34.7415i	−1.10083	+	1.90669i
$333$	1.46208			0.0801217
$334$	7.57789	−	13.1253i	0.414643	−	0.718184i
$335$	17.7929	+	30.8183i	0.972132	+	1.68378i
$336$	−1.32929	−	2.30240i	−0.0725189	−	0.125606i
$337$	−21.4894			−1.17060			−0.585302	−	0.810815i	$-0.699024\pi$
$337$	−21.4894			−1.17060			−0.585302	+	0.810815i	$0.699024\pi$
$338$	7.23104	−	26.7079i	0.393317	−	1.45272i
$339$	−13.2326			−0.718696
$340$	20.6119	+	35.7009i	1.11784	+	1.93615i
$341$	−1.94791	−	3.37388i	−0.105485	−	0.182706i
$342$	−5.59438	+	9.68975i	−0.302509	+	0.523961i
$343$	1.00000			0.0539949
$344$	1.99175	−	3.44982i	0.107388	−	0.186002i
$345$	4.69263	−	8.12787i	0.252643	−	0.437590i
$346$	−9.77051			−0.525266
$347$	9.81330	−	16.9971i	0.526806	−	0.912454i	−0.472707	−	0.881220i	$-0.656723\pi$
$347$	9.81330	−	16.9971i	0.526806	−	0.912454i	0.999512	−	0.0312340i	$-0.00994372\pi$
$348$	1.10262	+	1.90980i	0.0591068	+	0.102376i
$349$	−13.5400	−	23.4519i	−0.724778	−	1.25535i	−0.959065	−	0.283185i	$-0.908609\pi$
$349$	−13.5400	−	23.4519i	−0.724778	−	1.25535i	0.234287	−	0.972167i	$-0.424724\pi$
$350$	4.40175			0.235283
$351$	−3.32929	−	1.38413i	−0.177705	−	0.0738792i
$352$	5.21299			0.277854
$353$	0.837042	+	1.44980i	0.0445512	+	0.0771650i	0.887441	−	0.460921i	$-0.152481\pi$
$353$	0.837042	+	1.44980i	0.0445512	+	0.0771650i	−0.842890	+	0.538086i	$0.819148\pi$
$354$	14.8007	+	25.6355i	0.786647	+	1.36251i
$355$	5.68051	−	9.83893i	0.301490	−	0.522196i
$356$	−24.0712			−1.27577
$357$	3.06421	−	5.30737i	0.162175	−	0.280896i
$358$	−22.5784	+	39.1069i	−1.19330	+	2.06686i
$359$	20.1207			1.06193			0.530964	−	0.847394i	$-0.321830\pi$
$359$	20.1207			1.06193			0.530964	+	0.847394i	$0.321830\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	−4.31717	−	7.47756i	−0.227220	−	0.393556i
$362$	18.7491	+	32.4744i	0.985430	+	1.70682i
$363$	10.5663			0.554585
$364$	−1.17895	−	9.04615i	−0.0617939	−	0.474147i
$365$	9.22485			0.482851
$366$	8.72280	+	15.1083i	0.455948	+	0.789725i
$367$	−8.35559	−	14.4723i	−0.436158	−	0.755448i	0.561231	−	0.827659i	$-0.310328\pi$
$367$	−8.35559	−	14.4723i	−0.436158	−	0.755448i	−0.997389	+	0.0722110i	$0.976994\pi$
$368$	−4.69263	+	8.12787i	−0.244620	+	0.423695i
$369$	10.5137			0.547320
$370$	4.13666	−	7.16491i	0.215055	−	0.372486i
$371$	0.969832	−	1.67980i	0.0503512	−	0.0872108i
$372$	14.9670			0.776004
$373$	−8.14259	+	14.1034i	−0.421607	+	0.730246i	−0.996097	−	0.0882664i	$-0.971867\pi$
$373$	−8.14259	+	14.1034i	−0.421607	+	0.730246i	0.574489	+	0.818512i	$0.305201\pi$
$374$	4.29525	+	7.43959i	0.222102	+	0.384692i
$375$	3.89738	+	6.75046i	0.201260	+	0.348592i
$376$	9.83860			0.507387
$377$	−0.406120	−	3.11618i	−0.0209163	−	0.160491i
$378$	−2.12842			−0.109474
$379$	−13.7628	−	23.8378i	−0.706946	−	1.22447i	−0.965985	−	0.258599i	$-0.916739\pi$
$379$	−13.7628	−	23.8378i	−0.706946	−	1.22447i	0.259039	−	0.965867i	$-0.416594\pi$
$380$	17.6805	+	30.6235i	0.906991	+	1.57095i
$381$	−6.05596	+	10.4892i	−0.310256	+	0.537380i
$382$	−4.89682			−0.250543
$383$	−6.12067	+	10.6013i	−0.312752	+	0.541702i	−0.978957	−	0.204067i	$-0.934584\pi$
$383$	−6.12067	+	10.6013i	−0.312752	+	0.541702i	0.666205	+	0.745768i	$0.267917\pi$
$384$	−4.35509	+	7.54324i	−0.222245	+	0.384939i
$385$	1.75091			0.0892346
$386$	24.7161	−	42.8096i	1.25802	−	2.17895i
$387$	1.76508	+	3.05721i	0.0897243	+	0.155407i
$388$	−3.76459	−	6.52045i	−0.191118	−	0.331026i
$389$	−2.77051			−0.140471			−0.0702353	−	0.997530i	$-0.522375\pi$
$389$	−2.77051			−0.140471			−0.0702353	+	0.997530i	$0.522375\pi$
$390$	−16.2024	+	12.3990i	−0.820442	+	0.627850i
$391$	−21.6343			−1.09410
$392$	−0.564210	−	0.977240i	−0.0284969	−	0.0493581i
$393$	−1.67071	−	2.89375i	−0.0842760	−	0.145970i
$394$	12.0614	−	20.8909i	0.607644	−	1.05247i
$395$	−12.9077			−0.649456
$396$	0.833167	−	1.44309i	0.0418682	−	0.0725179i
$397$	−0.406120	+	0.703421i	−0.0203826	+	0.0353037i	−0.876037	−	0.482244i	$-0.839822\pi$
$397$	−0.406120	+	0.703421i	−0.0203826	+	0.0353037i	0.855654	+	0.517548i	$0.173155\pi$
$398$	−33.6596			−1.68720
$399$	2.62842	−	4.55256i	0.131586	−	0.227913i
$400$	2.74909	+	4.76156i	0.137454	+	0.238078i
$401$	4.88138	+	8.45480i	0.243765	+	0.422213i	0.961784	−	0.273811i	$-0.0882842\pi$
$401$	4.88138	+	8.45480i	0.243765	+	0.422213i	−0.718019	+	0.696024i	$0.754951\pi$
$402$	−28.4894			−1.42092
$403$	−19.6942	−	8.18770i	−0.981037	−	0.407858i
$404$	−23.3796			−1.16318
$405$	1.32929	+	2.30240i	0.0660531	+	0.114407i
$406$	−0.927545	−	1.60655i	−0.0460333	−	0.0797320i
$407$	0.481455	−	0.833904i	0.0238648	−	0.0413351i
$408$	−6.91542			−0.342365
$409$	−9.41155	+	16.3013i	−0.465371	+	0.806047i	−0.999218	−	0.0395345i	$-0.987413\pi$
$409$	−9.41155	+	16.3013i	−0.465371	+	0.806047i	0.533847	+	0.845581i	$0.320746\pi$
$410$	29.7463	−	51.5221i	1.46906	−	2.54449i
$411$	−1.80350			−0.0889600
$412$	−16.9237	+	29.3127i	−0.833769	+	1.44413i
$413$	−6.95384	−	12.0444i	−0.342176	−	0.592666i
$414$	3.75684	+	6.50703i	0.184639	+	0.319803i
$415$	−42.1521			−2.06917
$416$	22.6645	−	17.3442i	1.11122	−	0.850369i
$417$	1.12842			0.0552589
$418$	3.68438	+	6.38154i	0.180209	+	0.312131i
$419$	6.26121	+	10.8447i	0.305880	+	0.529800i	0.977457	−	0.211135i	$-0.0677160\pi$
$419$	6.26121	+	10.8447i	0.305880	+	0.529800i	−0.671577	+	0.740935i	$0.734383\pi$
$420$	−3.36334	+	5.82547i	−0.164114	+	0.284254i
$421$	27.5771			1.34403			0.672013	−	0.740539i	$-0.265430\pi$
$421$	27.5771			1.34403			0.672013	+	0.740539i	$0.265430\pi$
$422$	−7.03017	+	12.1766i	−0.342223	+	0.592748i
$423$	−4.35946	+	7.55081i	−0.211964	+	0.367133i
$424$	−2.18875			−0.106295
$425$	−6.33704	+	10.9761i	−0.307392	+	0.532418i
$426$	4.54772	+	7.87688i	0.220338	+	0.381636i
$427$	−4.09825	−	7.09838i	−0.198328	−	0.343515i
$428$	24.9154			1.20433
$429$	−1.88575	+	1.44309i	−0.0910451	+	0.0696730i
$430$	19.9758			0.963317
$431$	−0.444036	−	0.769093i	−0.0213885	−	0.0370459i	0.855133	−	0.518409i	$-0.173475\pi$
$431$	−0.444036	−	0.769093i	−0.0213885	−	0.0370459i	−0.876522	+	0.481363i	$0.840142\pi$
$432$	−1.32929	−	2.30240i	−0.0639557	−	0.110774i
$433$	−13.4154	+	23.2362i	−0.644704	+	1.11666i	0.339666	+	0.940546i	$0.389686\pi$
$433$	−13.4154	+	23.2362i	−0.644704	+	1.11666i	−0.984370	+	0.176114i	$0.943647\pi$
$434$	−12.5905			−0.604363
$435$	−1.15859	+	2.00673i	−0.0555500	+	0.0962154i
$436$	−8.00156	+	13.8591i	−0.383205	+	0.663731i
$437$	−18.5575			−0.887727
$438$	−3.69263	+	6.39582i	−0.176441	+	0.305604i
$439$	17.0021	+	29.4484i	0.811464	+	1.40550i	0.911840	+	0.410547i	$0.134662\pi$
$439$	17.0021	+	29.4484i	0.811464	+	1.40550i	−0.100376	+	0.994950i	$0.532004\pi$
$440$	−0.987880	−	1.71106i	−0.0470953	−	0.0815715i
$441$	1.00000			0.0476190
$442$	43.4268	+	18.0543i	2.06560	+	0.858757i
$443$	−20.9670			−0.996173			−0.498087	−	0.867127i	$-0.665964\pi$
$443$	−20.9670			−0.996173			−0.498087	+	0.867127i	$0.665964\pi$
$444$	1.84966	+	3.20370i	0.0877809	+	0.152041i
$445$	−12.6465	−	21.9043i	−0.599500	−	1.03836i
$446$	10.4330	−	18.0704i	0.494016	−	0.855660i
$447$	−13.8396			−0.654590
$448$	5.76508	−	9.98542i	0.272375	−	0.471767i
$449$	−8.91105	+	15.4344i	−0.420539	+	0.728394i	−0.995992	−	0.0894402i	$-0.971492\pi$
$449$	−8.91105	+	15.4344i	−0.420539	+	0.728394i	0.575454	+	0.817834i	$0.304826\pi$
$450$	4.40175			0.207500
$451$	3.46208	−	5.99651i	0.163023	−	0.282364i
$452$	−16.7403	−	28.9951i	−0.787400	−	1.36382i
$453$	−3.78701	−	6.55929i	−0.177929	−	0.308182i
$454$	−34.6782			−1.62753
$455$	7.61243	−	5.82547i	0.356876	−	0.273102i
$456$	−5.93192			−0.277787
$457$	20.5279	+	35.5553i	0.960252	+	1.66321i	0.721863	+	0.692036i	$0.243286\pi$
$457$	20.5279	+	35.5553i	0.960252	+	1.66321i	0.238390	+	0.971170i	$0.423381\pi$
$458$	24.6810	+	42.7488i	1.15327	+	1.99752i
$459$	3.06421	−	5.30737i	0.143025	−	0.247727i
$460$	23.7463			1.10718
$461$	17.9938	−	31.1662i	0.838055	−	1.45155i	−0.0534633	−	0.998570i	$-0.517026\pi$
$461$	17.9938	−	31.1662i	0.838055	−	1.45155i	0.891518	−	0.452984i	$-0.149641\pi$
$462$	−0.700874	+	1.21395i	−0.0326076	+	0.0564781i
$463$	−13.1527			−0.611256			−0.305628	−	0.952151i	$-0.598866\pi$
$463$	−13.1527			−0.611256			−0.305628	+	0.952151i	$0.598866\pi$
$464$	1.15859	−	2.00673i	0.0537860	−	0.0931602i
$465$	7.86334	+	13.6197i	0.364653	+	0.631598i
$466$	2.77439	+	4.80538i	0.128521	+	0.222605i
$467$	19.4729			0.901100			0.450550	−	0.892751i	$-0.351228\pi$
$467$	19.4729			0.901100			0.450550	+	0.892751i	$0.351228\pi$
$468$	−1.17895	−	9.04615i	−0.0544971	−	0.418158i
$469$	13.3853			0.618074
$470$	24.6684	+	42.7269i	1.13787	+	1.97085i
$471$	3.68438	+	6.38154i	0.169767	+	0.294046i
$472$	−7.84684	+	13.5911i	−0.361180	+	0.625583i
$473$	2.32492			0.106900
$474$	5.16683	−	8.94922i	0.237320	−	0.411051i
$475$	−5.43579	+	9.41507i	−0.249411	+	0.431993i
$476$	15.5059			0.710713
$477$	0.969832	−	1.67980i	0.0444056	−	0.0769127i
$478$	−16.7540	−	29.0188i	−0.766311	−	1.32729i
$479$	−2.52192	−	4.36810i	−0.115230	−	0.199583i	0.802642	−	0.596461i	$-0.203427\pi$
$479$	−2.52192	−	4.36810i	−0.115230	−	0.199583i	−0.917871	+	0.396878i	$0.870094\pi$
$480$	−21.0438			−0.960516
$481$	−0.681270	−	5.22741i	−0.0310632	−	0.238349i
$482$	63.5694			2.89551
$483$	−1.76508	−	3.05721i	−0.0803141	−	0.139108i
$484$	13.3672	+	23.1527i	0.607600	+	1.05239i
$485$	3.95566	−	6.85140i	0.179617	−	0.311106i
$486$	−2.12842			−0.0965470
$487$	6.24704	−	10.8202i	0.283080	−	0.490309i	−0.689062	−	0.724703i	$-0.741977\pi$
$487$	6.24704	−	10.8202i	0.283080	−	0.490309i	0.972142	+	0.234393i	$0.0753104\pi$
$488$	−4.62454	+	8.00995i	−0.209343	+	0.362593i
$489$	21.1207			0.955110
$490$	2.82929	−	4.90048i	0.127814	−	0.221381i
$491$	0.0340418	+	0.0589622i	0.00153629	+	0.00266093i	0.866793	−	0.498669i	$-0.166178\pi$
$491$	0.0340418	+	0.0589622i	0.00153629	+	0.00266093i	−0.865256	+	0.501330i	$0.832844\pi$
$492$	13.3007	+	23.0375i	0.599641	+	1.03861i
$493$	5.34141			0.240565
$494$	37.2506	+	15.4866i	1.67599	+	0.696777i
$495$	1.75091			0.0786976
$496$	−7.86334	−	13.6197i	−0.353074	−	0.611542i
$497$	−2.13666	−	3.70081i	−0.0958425	−	0.166004i
$498$	16.8731	−	29.2251i	0.756103	−	1.30961i
$499$	−2.14392			−0.0959748			−0.0479874	−	0.998848i	$-0.515281\pi$
$499$	−2.14392			−0.0959748			−0.0479874	+	0.998848i	$0.515281\pi$
$500$	−9.86102	+	17.0798i	−0.440998	+	0.763831i
$501$	−3.56034	+	6.16668i	−0.159064	+	0.275507i
$502$	−44.0985			−1.96821
$503$	11.3912	−	19.7301i	0.507908	−	0.879722i	−0.492050	−	0.870567i	$-0.663752\pi$
$503$	11.3912	−	19.7301i	0.507908	−	0.879722i	0.999958	−	0.00915539i	$-0.00291429\pi$
$504$	−0.564210	−	0.977240i	−0.0251319	−	0.0435297i
$505$	−12.2831	−	21.2750i	−0.546592	−	0.946725i
$506$	4.94841			0.219984
$507$	−3.39738	+	12.5482i	−0.150883	+	0.557286i
$508$	−30.6452			−1.35966
$509$	−12.9758	−	22.4747i	−0.575140	−	0.996173i	−0.996026	−	0.0890589i	$-0.971614\pi$
$509$	−12.9758	−	22.4747i	−0.575140	−	0.996173i	0.420886	−	0.907114i	$-0.361719\pi$
$510$	−17.3391	−	30.0322i	−0.767788	−	1.32985i
$511$	1.73492	−	3.00496i	0.0767482	−	0.132932i
$512$	27.0438			1.19518
$513$	2.62842	−	4.55256i	0.116048	−	0.201000i
$514$	−11.3347	+	19.6323i	−0.499953	+	0.865944i
$515$	−35.5653			−1.56719
$516$	−4.46596	+	7.73527i	−0.196603	+	0.340526i
$517$	2.87108	+	4.97286i	0.126270	+	0.218706i
$518$	−1.55596	−	2.69501i	−0.0683651	−	0.118412i
$519$	4.59050			0.201501
$520$	−9.98788	−	4.15238i	−0.437998	−	0.182094i
$521$	−11.0077			−0.482258			−0.241129	−	0.970493i	$-0.577518\pi$
$521$	−11.0077			−0.482258			−0.241129	+	0.970493i	$0.577518\pi$
$522$	−0.927545	−	1.60655i	−0.0405975	−	0.0703170i
$523$	12.0016	+	20.7873i	0.524791	+	0.908965i	0.999583	+	0.0288673i	$0.00919002\pi$
$523$	12.0016	+	20.7873i	0.524791	+	0.908965i	−0.474792	+	0.880098i	$0.657477\pi$
$524$	4.22717	−	7.32167i	0.184665	−	0.319849i
$525$	−2.06808			−0.0902586
$526$	25.1986	−	43.6452i	1.09871	−	1.90302i
$527$	18.1261	−	31.3953i	0.789585	−	1.36760i
$528$	−1.75091			−0.0761986
$529$	5.26896	−	9.12610i	0.229085	−	0.396787i
$530$	−5.48788	−	9.50529i	−0.238378	−	0.412883i
$531$	−6.95384	−	12.0444i	−0.301771	−	0.522682i
$532$	13.3007			0.576658
$533$	−4.89893	−	37.5897i	−0.212196	−	1.62819i
$534$	20.2491			0.876264
$535$	13.0900	+	22.6726i	0.565930	+	0.980220i
$536$	−7.55209	−	13.0806i	−0.326201	−	0.564996i
$537$	10.6081	−	18.3737i	0.457771	−	0.792883i
$538$	−1.01649			−0.0438241
$539$	0.329293	−	0.570353i	0.0141837	−	0.0245668i
$540$	−3.36334	+	5.82547i	−0.144735	+	0.250688i
$541$	−7.12842			−0.306475			−0.153237	−	0.988189i	$-0.548970\pi$
$541$	−7.12842			−0.306475			−0.153237	+	0.988189i	$0.548970\pi$
$542$	21.9675	−	38.0489i	0.943586	−	1.63434i
$543$	−8.80893	−	15.2575i	−0.378027	−	0.654762i
$544$	24.2545	+	42.0101i	1.03990	+	1.80117i
$545$	−16.8154			−0.720291
$546$	0.991754	+	7.60977i	0.0424432	+	0.325668i
$547$	29.6540			1.26791			0.633956	−	0.773369i	$-0.281430\pi$
$547$	29.6540			1.26791			0.633956	+	0.773369i	$0.281430\pi$
$548$	−2.28158	−	3.95180i	−0.0974641	−	0.168813i
$549$	−4.09825	−	7.09838i	−0.174909	−	0.302951i
$550$	1.44947	−	2.51055i	0.0618055	−	0.107050i
$551$	4.58176			0.195190
$552$	−1.99175	+	3.44982i	−0.0847747	+	0.146834i
$553$	−2.42754	+	4.20463i	−0.103230	+	0.178799i
$554$	−56.1052			−2.38368
$555$	−1.94354	+	3.36631i	−0.0824986	+	0.142892i
$556$	1.42754	+	2.47258i	0.0605414	+	0.104861i
$557$	−4.30737	−	7.46059i	−0.182509	−	0.316115i	0.760225	−	0.649660i	$-0.225089\pi$
$557$	−4.30737	−	7.46059i	−0.182509	−	0.316115i	−0.942734	+	0.333544i	$0.891755\pi$
$558$	−12.5905			−0.532998
$559$	10.1081	−	7.73527i	0.427525	−	0.327167i
$560$	7.06808			0.298681
$561$	−2.01805	−	3.49536i	−0.0852020	−	0.147574i
$562$	−0.218425	−	0.378323i	−0.00921369	−	0.0159586i
$563$	−17.8347	+	30.8906i	−0.751644	+	1.30189i	0.195382	+	0.980727i	$0.437405\pi$
$563$	−17.8347	+	30.8906i	−0.751644	+	1.30189i	−0.947026	+	0.321158i	$0.895928\pi$
$564$	−22.0603			−0.928908
$565$	17.5900	−	30.4668i	0.740017	−	1.28175i
$566$	−1.50930	+	2.61419i	−0.0634408	+	0.109883i
$567$	1.00000			0.0419961
$568$	−2.41105	+	4.17607i	−0.101166	+	0.175224i
$569$	5.68826	+	9.85235i	0.238464	+	0.413032i	0.960274	−	0.279060i	$-0.0900227\pi$
$569$	5.68826	+	9.85235i	0.238464	+	0.413032i	−0.721810	+	0.692092i	$0.756689\pi$
$570$	−14.8731	−	25.7610i	−0.622967	−	1.07901i
$571$	24.6266			1.03059			0.515296	−	0.857013i	$-0.327682\pi$
$571$	24.6266			1.03059			0.515296	+	0.857013i	$0.327682\pi$
$572$	−5.54772	−	2.30642i	−0.231962	−	0.0964362i
$573$	2.30068			0.0961124
$574$	−11.1888	−	19.3795i	−0.467010	−	0.808884i
$575$	3.65034	+	6.32258i	0.152230	+	0.263670i
$576$	5.76508	−	9.98542i	0.240212	−	0.416059i
$577$	−18.0438			−0.751175			−0.375588	−	0.926787i	$-0.622559\pi$
$577$	−18.0438			−0.751175			−0.375588	+	0.926787i	$0.622559\pi$
$578$	−21.8775	+	37.8930i	−0.909984	+	1.57614i
$579$	−11.6124	+	20.1133i	−0.482596	+	0.835881i
$580$	−5.86284			−0.243441
$581$	−7.92754	+	13.7309i	−0.328890	+	0.569654i
$582$	3.16683	+	5.48511i	0.131269	+	0.227365i
$583$	−0.638719	−	1.10629i	−0.0264530	−	0.0458180i
$584$	−3.91542			−0.162021
$585$	7.61243	−	5.82547i	0.314735	−	0.240853i
$586$	65.1841			2.69273
$587$	−23.0861	−	39.9864i	−0.952867	−	1.65041i	−0.739176	−	0.673512i	$-0.764785\pi$
$587$	−23.0861	−	39.9864i	−0.952867	−	1.65041i	−0.213690	−	0.976901i	$-0.568548\pi$
$588$	1.26508	+	2.19119i	0.0521712	+	0.0903631i
$589$	15.5482	−	26.9303i	0.640653	−	1.10964i
$590$	−78.6978			−3.23994
$591$	−5.66683	+	9.81524i	−0.233102	+	0.403745i
$592$	1.94354	−	3.36631i	0.0798789	−	0.138354i
$593$	−37.8505			−1.55433			−0.777166	−	0.629296i	$-0.783343\pi$
$593$	−37.8505			−1.55433			−0.777166	+	0.629296i	$0.783343\pi$
$594$	−0.700874	+	1.21395i	−0.0287572	+	0.0498090i
$595$	8.14647	+	14.1101i	0.333973	+	0.578457i
$596$	−17.5082	−	30.3252i	−0.717166	−	1.24217i
$597$	15.8144			0.647239
$598$	21.5142	−	16.4639i	0.879780	−	0.673258i
$599$	−3.68283			−0.150476			−0.0752381	−	0.997166i	$-0.523972\pi$
$599$	−3.68283			−0.150476			−0.0752381	+	0.997166i	$0.523972\pi$
$600$	1.16683	+	2.02101i	0.0476357	+	0.0825075i
$601$	−1.32929	−	2.30240i	−0.0542230	−	0.0939170i	0.837640	−	0.546223i	$-0.183935\pi$
$601$	−1.32929	−	2.30240i	−0.0542230	−	0.0939170i	−0.891863	+	0.452306i	$0.850602\pi$
$602$	3.75684	−	6.50703i	0.153117	−	0.265207i
$603$	13.3853			0.545090
$604$	9.58176	−	16.5961i	0.389876	−	0.675286i
$605$	−14.0457	+	24.3278i	−0.571037	+	0.989066i
$606$	19.6673			0.798931
$607$	−22.3649	+	38.7371i	−0.907763	+	1.57229i	−0.0905981	+	0.995888i	$0.528878\pi$
$607$	−22.3649	+	38.7371i	−0.907763	+	1.57229i	−0.817165	+	0.576404i	$0.804455\pi$
$608$	20.8051	+	36.0354i	0.843756	+	1.46143i
$609$	0.435790	+	0.754811i	0.0176591	+	0.0305865i
$610$	−46.3806			−1.87790
$611$	29.0279	+	12.0681i	1.17434	+	0.488223i
$612$	15.5059			0.626790
$613$	21.5016	+	37.2418i	0.868440	+	1.50418i	0.863591	+	0.504193i	$0.168210\pi$
$613$	21.5016	+	37.2418i	0.868440	+	1.50418i	0.00484892	+	0.999988i	$0.498457\pi$
$614$	−4.76614	−	8.25520i	−0.192346	−	0.333153i
$615$	−13.9758	+	24.2067i	−0.563557	+	0.976109i
$616$	−0.743162			−0.0299428
$617$	−6.58613	+	11.4075i	−0.265148	+	0.459249i	−0.967602	−	0.252479i	$-0.918754\pi$
$617$	−6.58613	+	11.4075i	−0.265148	+	0.459249i	0.702455	+	0.711729i	$0.252087\pi$
$618$	14.2365	−	24.6583i	0.572675	−	0.991902i
$619$	24.7705			0.995611			0.497806	−	0.867289i	$-0.334139\pi$
$619$	24.7705			0.995611			0.497806	+	0.867289i	$0.334139\pi$
$620$	−19.8956	+	34.4601i	−0.799025	+	1.38395i
$621$	−1.76508	−	3.05721i	−0.0708304	−	0.122682i
$622$	−0.718425	−	1.24435i	−0.0288062	−	0.0498938i
$623$	−9.51368			−0.381157
$624$	−7.61243	+	5.82547i	−0.304741	+	0.233205i
$625$	−31.0634			−1.24254
$626$	−10.6679	−	18.4773i	−0.426375	−	0.738503i
$627$	−1.73104	−	2.99825i	−0.0691312	−	0.119739i
$628$	−9.32211	+	16.1464i	−0.371993	+	0.644310i
$629$	8.96026			0.357269
$630$	2.82929	−	4.90048i	0.112722	−	0.195240i
$631$	−2.21687	+	3.83973i	−0.0882521	+	0.152857i	−0.906772	−	0.421620i	$-0.861461\pi$
$631$	−2.21687	+	3.83973i	−0.0882521	+	0.152857i	0.818520	+	0.574478i	$0.194795\pi$
$632$	5.47858			0.217926
$633$	3.30300	−	5.72096i	0.131282	−	0.227388i
$634$	−28.8994	−	50.0553i	−1.14774	−	1.98795i
$635$	−16.1003	−	27.8865i	−0.638921	−	1.10664i
$636$	4.90768			0.194602
$637$	−0.465958	−	3.57532i	−0.0184619	−	0.141659i
$638$	−1.22174			−0.0483690
$639$	−2.13666	−	3.70081i	−0.0845252	−	0.146402i
$640$	−11.5784	−	20.0543i	−0.457676	−	0.792718i
$641$	6.23492	−	10.7992i	0.246264	−	0.426542i	−0.716222	−	0.697873i	$-0.754130\pi$
$641$	6.23492	−	10.7992i	0.246264	−	0.426542i	0.962486	+	0.271330i	$0.0874635\pi$
$642$	−20.9593			−0.827196
$643$	−19.0137	+	32.9327i	−0.749826	+	1.29874i	0.198079	+	0.980186i	$0.436530\pi$
$643$	−19.0137	+	32.9327i	−0.749826	+	1.29874i	−0.947906	+	0.318551i	$0.896804\pi$
$644$	4.46596	−	7.73527i	0.175983	−	0.304812i
$645$	−9.38526			−0.369544
$646$	−34.2847	+	59.3828i	−1.34891	+	2.33639i
$647$	−6.09438	−	10.5558i	−0.239595	−	0.414990i	0.721003	−	0.692932i	$-0.243681\pi$
$647$	−6.09438	−	10.5558i	−0.239595	−	0.414990i	−0.960598	+	0.277941i	$0.910348\pi$
$648$	−0.564210	−	0.977240i	−0.0221642	−	0.0383896i
$649$	−9.15941			−0.359538
$650$	−2.05103	−	15.7376i	−0.0804480	−	0.617281i
$651$	5.91542			0.231844
$652$	26.7194	+	46.2794i	1.04641	+	1.81244i
$653$	−5.66451	−	9.81123i	−0.221670	−	0.383943i	0.733645	−	0.679532i	$-0.237817\pi$
$653$	−5.66451	−	9.81123i	−0.221670	−	0.383943i	−0.955315	+	0.295589i	$0.904484\pi$
$654$	6.73104	−	11.6585i	0.263205	−	0.455884i
$655$	8.88344			0.347105
$656$	13.9758	−	24.2067i	0.545662	−	0.945114i
$657$	1.73492	−	3.00496i	0.0676855	−	0.117235i
$658$	18.5575			0.723447
$659$	−21.1465	+	36.6268i	−0.823749	+	1.42678i	0.0791219	+	0.996865i	$0.474788\pi$
$659$	−21.1465	+	36.6268i	−0.823749	+	1.42678i	−0.902871	+	0.429911i	$0.858545\pi$
$660$	2.21505	+	3.83658i	0.0862206	+	0.149339i
$661$	7.67663	+	13.2963i	0.298586	+	0.517167i	0.975813	−	0.218608i	$-0.0701515\pi$
$661$	7.67663	+	13.2963i	0.298586	+	0.517167i	−0.677226	+	0.735775i	$0.736818\pi$
$662$	50.6803			1.96975
$663$	−20.4033	−	8.48251i	−0.792399	−	0.329433i
$664$	17.8912			0.694313
$665$	6.98788	+	12.1034i	0.270978	+	0.469348i
$666$	−1.55596	−	2.69501i	−0.0602924	−	0.104429i
$667$	1.53841	−	2.66461i	0.0595676	−	0.103174i
$668$	−18.0165			−0.697079
$669$	−4.90175	+	8.49008i	−0.189513	+	0.328245i
$670$	37.8708	−	65.5942i	1.46308	−	2.53412i
$671$	−5.39811			−0.208392
$672$	−3.95771	+	6.85496i	−0.152672	+	0.264436i
$673$	−19.3907	−	33.5857i	−0.747456	−	1.29463i	−0.949038	−	0.315160i	$-0.897942\pi$
$673$	−19.3907	−	33.5857i	−0.747456	−	1.29463i	0.201582	−	0.979472i	$-0.435392\pi$
$674$	22.8693	+	39.6107i	0.880891	+	1.52575i
$675$	−2.06808			−0.0796006
$676$	−31.7935	+	8.43025i	−1.22283	+	0.324241i
$677$	−21.4729			−0.825272			−0.412636	−	0.910896i	$-0.635392\pi$
$677$	−21.4729			−0.825272			−0.412636	+	0.910896i	$0.635392\pi$
$678$	14.0823	+	24.3912i	0.540826	+	0.936738i
$679$	−1.48788	−	2.57708i	−0.0570996	−	0.0988994i
$680$	9.19263	−	15.9221i	0.352521	−	0.610585i
$681$	16.2929			0.624347
$682$	−4.14597	+	7.18103i	−0.158757	+	0.274976i
$683$	−2.57633	+	4.46233i	−0.0985805	+	0.170746i	−0.911097	−	0.412191i	$-0.864764\pi$
$683$	−2.57633	+	4.46233i	−0.0985805	+	0.170746i	0.812517	+	0.582938i	$0.198097\pi$
$684$	13.3007			0.508564
$685$	2.39738	−	4.15238i	0.0915991	−	0.158654i
$686$	−1.06421	−	1.84326i	−0.0406317	−	0.0703762i
$687$	−11.5959	−	20.0847i	−0.442412	−	0.766281i
$688$	9.38526			0.357810
$689$	−6.45771	−	2.68474i	−0.246019	−	0.102280i
$690$	−19.9758			−0.760464
$691$	−12.1426	−	21.0316i	−0.461926	−	0.800079i	0.537131	−	0.843499i	$-0.319508\pi$
$691$	−12.1426	−	21.0316i	−0.461926	−	0.800079i	−0.999057	+	0.0434196i	$0.986175\pi$
$692$	5.80737	+	10.0587i	0.220763	+	0.382373i
$693$	0.329293	−	0.570353i	0.0125088	−	0.0216659i
$694$	−41.7736			−1.58571
$695$	−1.50000	+	2.59808i	−0.0568982	+	0.0985506i
$696$	0.491754	−	0.851743i	0.0186399	−	0.0322852i
$697$	64.4322			2.44054
$698$	−28.8187	+	49.9155i	−1.09081	+	1.88933i
$699$	−1.30350	−	2.25772i	−0.0493028	−	0.0853949i
$700$	−2.61630	−	4.53156i	−0.0988868	−	0.171277i
$701$	−1.31307			−0.0495938			−0.0247969	−	0.999693i	$-0.507894\pi$
$701$	−1.31307			−0.0495938			−0.0247969	+	0.999693i	$0.507894\pi$
$702$	0.991754	+	7.60977i	0.0374314	+	0.287212i
$703$	7.68594			0.289881
$704$	−3.79681	−	6.57626i	−0.143098	−	0.247852i
$705$	−11.5900	−	20.0745i	−0.436505	−	0.756049i
$706$	1.78158	−	3.08578i	0.0670505	−	0.116135i
$707$	−9.24035			−0.347519
$708$	17.5944	−	30.4744i	0.661237	−	1.14530i
$709$	−16.3858	+	28.3810i	−0.615380	+	1.06587i	0.374938	+	0.927050i	$0.377664\pi$
$709$	−16.3858	+	28.3810i	−0.615380	+	1.06587i	−0.990318	+	0.138819i	$0.955669\pi$
$710$	−24.1810			−0.907497
$711$	−2.42754	+	4.20463i	−0.0910400	+	0.157686i
$712$	5.36771	+	9.29714i	0.201163	+	0.348425i
$713$	−10.4412	−	18.0847i	−0.391027	−	0.677278i
$714$	−13.0438			−0.488154
$715$	−0.815851	−	6.26006i	−0.0305111	−	0.234113i
$716$	53.6803			2.00613
$717$	7.87158	+	13.6340i	0.293970	+	0.509170i
$718$	−21.4126	−	37.0877i	−0.799111	−	1.38410i
$719$	23.2321	−	40.2392i	0.866411	−	1.50067i	0.000772041	−	1.00000i	$-0.499754\pi$
$719$	23.2321	−	40.2392i	0.866411	−	1.50067i	0.865639	−	0.500668i	$-0.166912\pi$
$720$	7.06808			0.263412
$721$	−6.68875	+	11.5853i	−0.249102	+	0.431458i
$722$	−9.18875	+	15.9154i	−0.341970	+	0.592309i
$723$	−29.8669			−1.11076
$724$	22.2881	−	38.6041i	0.828329	−	1.43471i
$725$	−0.901251	−	1.56101i	−0.0334716	−	0.0579746i
$726$	−11.2447	−	19.4764i	−0.417331	−	0.722838i
$727$	19.5059			0.723435			0.361717	−	0.932288i	$-0.382191\pi$
$727$	19.5059			0.723435			0.361717	+	0.932288i	$0.382191\pi$
$728$	−3.23104	+	2.47258i	−0.119750	+	0.0916399i
$729$	1.00000			0.0370370
$730$	−9.81717	−	17.0038i	−0.363350	−	0.629340i
$731$	10.8172	+	18.7359i	0.400088	+	0.692972i
$732$	10.3693	−	17.9601i	0.383259	−	0.663824i
$733$	−21.6849			−0.800952			−0.400476	−	0.916307i	$-0.631155\pi$
$733$	−21.6849			−0.800952			−0.400476	+	0.916307i	$0.631155\pi$
$734$	−17.7842	+	30.8031i	−0.656426	+	1.13696i
$735$	−1.32929	+	2.30240i	−0.0490317	+	0.0849254i
$736$	27.9428			1.02998
$737$	4.40768	−	7.63432i	0.162359	−	0.281214i
$738$	−11.1888	−	19.3795i	−0.411864	−	0.713369i
$739$	22.1777	+	38.4129i	0.815820	+	1.41304i	0.908738	+	0.417367i	$0.137047\pi$
$739$	22.1777	+	38.4129i	0.815820	+	1.41304i	−0.0929182	+	0.995674i	$0.529620\pi$
$740$	−9.83496			−0.361540
$741$	−17.5016	−	7.27613i	−0.642936	−	0.267295i
$742$	−4.12842			−0.151559
$743$	7.90562	+	13.6929i	0.290029	+	0.502345i	0.973816	−	0.227336i	$-0.0730017\pi$
$743$	7.90562	+	13.6929i	0.290029	+	0.502345i	−0.683787	+	0.729682i	$0.739668\pi$
$744$	−3.33754	−	5.78079i	−0.122360	−	0.211934i
$745$	18.3969	−	31.8643i	0.674010	−	1.16742i
$746$	34.6617			1.26905
$747$	−7.92754	+	13.7309i	−0.290054	+	0.502388i
$748$	5.10600	−	8.84385i	0.186694	−	0.323363i
$749$	9.84734			0.359814
$750$	8.29525	−	14.3678i	0.302900	−	0.524638i
$751$	5.70038	+	9.87334i	0.208010	+	0.360283i	0.951087	−	0.308922i	$-0.0999681\pi$
$751$	5.70038	+	9.87334i	0.208010	+	0.360283i	−0.743078	+	0.669205i	$0.766635\pi$
$752$	11.5900	+	20.0745i	0.422644	+	0.732041i
$753$	20.7189			0.755039
$754$	−5.31174	+	4.06485i	−0.193442	+	0.148033i
$755$	20.1362			0.732830
$756$	1.26508	+	2.19119i	0.0460107	+	0.0796928i
$757$	−0.311743	−	0.539955i	−0.0113305	−	0.0196250i	0.860305	−	0.509780i	$-0.170273\pi$
$757$	−0.311743	−	0.539955i	−0.0113305	−	0.0196250i	−0.871635	+	0.490155i	$0.836940\pi$
$758$	−29.2929	+	50.7368i	−1.06397	+	1.84285i
$759$	−2.32492			−0.0843893
$760$	7.88526	−	13.6577i	0.286028	−	0.495416i
$761$	18.1465	−	31.4306i	0.657809	−	1.13936i	−0.323373	−	0.946272i	$-0.604817\pi$
$761$	18.1465	−	31.4306i	0.657809	−	1.13936i	0.981182	−	0.193087i	$-0.0618499\pi$
$762$	25.7793			0.933884
$763$	−3.16246	+	5.47754i	−0.114489	+	0.198300i
$764$	2.91056	+	5.04123i	0.105300	+	0.182385i
$765$	8.14647	+	14.1101i	0.294536	+	0.510152i
$766$	26.0547			0.941395
$767$	−39.8223	+	30.4744i	−1.43790	+	1.10037i
$768$	−4.52142			−0.163153
$769$	−17.5653	−	30.4239i	−0.633420	−	1.09712i	−0.986848	−	0.161653i	$-0.948317\pi$
$769$	−17.5653	−	30.4239i	−0.633420	−	1.09712i	0.353428	−	0.935462i	$-0.385016\pi$
$770$	−1.86334	−	3.22739i	−0.0671499	−	0.116307i
$771$	5.32542	−	9.22390i	0.191790	−	0.332191i
$772$	−58.7628

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06421 - 1.84326i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.26508 + 2.19119i) q^{4} -2.65859 q^{5} +(1.06421 - 1.84326i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.12842 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.06421 - 1.84326i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.26508 + 2.19119i) q^{4} -2.65859 q^{5} +(1.06421 - 1.84326i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.12842 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.82929 + 4.90048i) q^{10} +(0.329293 + 0.570353i) q^{11} -2.53017 q^{12} +(3.32929 + 1.38413i) q^{13} +2.12842 q^{14} +(-1.32929 - 2.30240i) q^{15} +(1.32929 + 2.30240i) q^{16} +(-3.06421 + 5.30737i) q^{17} +2.12842 q^{18} +(-2.62842 + 4.55256i) q^{19} +(3.36334 - 5.82547i) q^{20} -1.00000 q^{21} +(0.700874 - 1.21395i) q^{22} +(1.76508 + 3.05721i) q^{23} +(0.564210 + 0.977240i) q^{24} +2.06808 q^{25} +(-0.991754 - 7.60977i) q^{26} -1.00000 q^{27} +(-1.26508 - 2.19119i) q^{28} +(-0.435790 - 0.754811i) q^{29} +(-2.82929 + 4.90048i) q^{30} -5.91542 q^{31} +(3.95771 - 6.85496i) q^{32} +(-0.329293 + 0.570353i) q^{33} +13.0438 q^{34} +(1.32929 - 2.30240i) q^{35} +(-1.26508 - 2.19119i) q^{36} +(-0.731042 - 1.26620i) q^{37} +11.1888 q^{38} +(0.465958 + 3.57532i) q^{39} -3.00000 q^{40} +(-5.25684 - 9.10511i) q^{41} +(1.06421 + 1.84326i) q^{42} +(1.76508 - 3.05721i) q^{43} -1.66633 q^{44} +(1.32929 - 2.30240i) q^{45} +(3.75684 - 6.50703i) q^{46} +8.71892 q^{47} +(-1.32929 + 2.30240i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.20087 - 3.81203i) q^{50} -6.12842 q^{51} +(-7.24472 + 5.54408i) q^{52} -1.93966 q^{53} +(1.06421 + 1.84326i) q^{54} +(-0.875455 - 1.51633i) q^{55} +(-0.564210 + 0.977240i) q^{56} -5.25684 q^{57} +(-0.927545 + 1.60655i) q^{58} +(-6.95384 + 12.0444i) q^{59} +6.72667 q^{60} +(-4.09825 + 7.09838i) q^{61} +(6.29525 + 10.9037i) q^{62} +(-0.500000 - 0.866025i) q^{63} -11.5302 q^{64} +(-8.85122 - 3.67982i) q^{65} +1.40175 q^{66} +(-6.69263 - 11.5920i) q^{67} +(-7.75296 - 13.4285i) q^{68} +(-1.76508 + 3.05721i) q^{69} -5.65859 q^{70} +(-2.13666 + 3.70081i) q^{71} +(-0.564210 + 0.977240i) q^{72} -3.46983 q^{73} +(-1.55596 + 2.69501i) q^{74} +(1.03404 + 1.79101i) q^{75} +(-6.65034 - 11.5187i) q^{76} -0.658587 q^{77} +(6.09438 - 4.66377i) q^{78} +4.85509 q^{79} +(-3.53404 - 6.12114i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-11.1888 + 19.3795i) q^{82} +15.8551 q^{83} +(1.26508 - 2.19119i) q^{84} +(8.14647 - 14.1101i) q^{85} -7.51368 q^{86} +(0.435790 - 0.754811i) q^{87} +(0.371581 + 0.643597i) q^{88} +(4.75684 + 8.23909i) q^{89} -5.65859 q^{90} +(-2.86334 + 2.19119i) q^{91} -8.93192 q^{92} +(-2.95771 - 5.12291i) q^{93} +(-9.27876 - 16.0713i) q^{94} +(6.98788 - 12.1034i) q^{95} +7.91542 q^{96} +(-1.48788 + 2.57708i) q^{97} +(-1.06421 + 1.84326i) q^{98} -0.658587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} - 8 q^{11} - 8 q^{12} + 10 q^{13} + 2 q^{15} - 2 q^{16} - 12 q^{17} - 3 q^{19} + 11 q^{20} - 6 q^{21} + 7 q^{22} + 7 q^{23} - 3 q^{24} + 14 q^{25} + 16 q^{26} - 6 q^{27} - 4 q^{28} - 9 q^{29} - 7 q^{30} + 10 q^{31} + q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{35} - 4 q^{36} + 40 q^{38} + 2 q^{39} - 18 q^{40} - 6 q^{41} + 7 q^{43} - 6 q^{44} - 2 q^{45} - 3 q^{46} + 18 q^{47} + 2 q^{48} - 3 q^{49} - 16 q^{50} - 24 q^{51} + 12 q^{52} - 26 q^{53} - 26 q^{55} + 3 q^{56} - 6 q^{57} + 10 q^{58} - 11 q^{59} + 22 q^{60} - 19 q^{61} + 27 q^{62} - 3 q^{63} - 62 q^{64} - 14 q^{65} + 14 q^{66} - 21 q^{67} - 13 q^{68} - 7 q^{69} - 14 q^{70} - 22 q^{71} + 3 q^{72} - 28 q^{73} + 19 q^{74} + 7 q^{75} + 2 q^{76} + 16 q^{77} + 23 q^{78} - 2 q^{79} - 22 q^{80} - 3 q^{81} - 40 q^{82} + 64 q^{83} + 4 q^{84} - q^{85} + 6 q^{86} + 9 q^{87} + 15 q^{88} + 3 q^{89} - 14 q^{90} - 8 q^{91} - 52 q^{92} + 5 q^{93} - q^{94} + 12 q^{95} + 2 q^{96} + 21 q^{97} + 16 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 - 8 * q^11 - 8 * q^12 + 10 * q^13 + 2 * q^15 - 2 * q^16 - 12 * q^17 - 3 * q^19 + 11 * q^20 - 6 * q^21 + 7 * q^22 + 7 * q^23 - 3 * q^24 + 14 * q^25 + 16 * q^26 - 6 * q^27 - 4 * q^28 - 9 * q^29 - 7 * q^30 + 10 * q^31 + q^32 + 8 * q^33 + 20 * q^34 - 2 * q^35 - 4 * q^36 + 40 * q^38 + 2 * q^39 - 18 * q^40 - 6 * q^41 + 7 * q^43 - 6 * q^44 - 2 * q^45 - 3 * q^46 + 18 * q^47 + 2 * q^48 - 3 * q^49 - 16 * q^50 - 24 * q^51 + 12 * q^52 - 26 * q^53 - 26 * q^55 + 3 * q^56 - 6 * q^57 + 10 * q^58 - 11 * q^59 + 22 * q^60 - 19 * q^61 + 27 * q^62 - 3 * q^63 - 62 * q^64 - 14 * q^65 + 14 * q^66 - 21 * q^67 - 13 * q^68 - 7 * q^69 - 14 * q^70 - 22 * q^71 + 3 * q^72 - 28 * q^73 + 19 * q^74 + 7 * q^75 + 2 * q^76 + 16 * q^77 + 23 * q^78 - 2 * q^79 - 22 * q^80 - 3 * q^81 - 40 * q^82 + 64 * q^83 + 4 * q^84 - q^85 + 6 * q^86 + 9 * q^87 + 15 * q^88 + 3 * q^89 - 14 * q^90 - 8 * q^91 - 52 * q^92 + 5 * q^93 - q^94 + 12 * q^95 + 2 * q^96 + 21 * q^97 + 16 * q^99

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