LMFDB - Embedded newform 273.2.k.b.22.1

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			22.1
Root			$1.06421 + 1.84326i$ of defining polynomial
Character	$\chi$	$=$	273.22
Dual form			273.2.k.b.211.1

$q$-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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	0.194093	+	0.980983i	$0.437824\pi$
$2$	−1.06421	+	1.84326i	−0.752510	+	1.30339i	−0.946603	+	0.322402i	$0.895510\pi$
$3$	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	−0.812103	−	0.583513i	$-0.801678\pi$
$11$	0.329293	−	0.570353i	0.0992857	−	0.171968i	0.911389	+	0.411546i	$0.135011\pi$
$12$	−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	−0.951040	−	0.309067i	$-0.899983\pi$
$17$	−3.06421	−	5.30737i	−0.743180	−	1.28723i	0.207860	−	0.978159i	$-0.433350\pi$
$18$	2.12842			0.501673
$19$	−2.62842	−	4.55256i	−0.603001	−	1.04443i	−0.992364	−	0.123344i	$-0.960638\pi$
$19$	−2.62842	−	4.55256i	−0.603001	−	1.04443i	0.389363	−	0.921084i	$-0.372695\pi$
$20$	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	−0.621214	−	0.783641i	$-0.713360\pi$
$23$	1.76508	−	3.05721i	0.368045	−	0.637473i	0.989260	+	0.146167i	$0.0466938\pi$
$24$	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	−0.903647	−	0.428278i	$-0.859121\pi$
$29$	−0.435790	+	0.754811i	−0.0809243	+	0.140165i	0.822723	+	0.568443i	$0.192454\pi$
$30$	−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	−0.919840	−	0.392295i	$-0.871681\pi$
$37$	−0.731042	+	1.26620i	−0.120183	+	0.208162i	0.799657	+	0.600457i	$0.205015\pi$
$38$	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	0.0839729	+	0.996468i	$0.473239\pi$
$41$	−5.25684	+	9.10511i	−0.820980	+	1.42198i	−0.904953	+	0.425511i	$0.860094\pi$
$42$	1.06421	−	1.84326i	0.164211	−	0.284422i
$43$	1.76508	+	3.05721i	0.269173	+	0.466221i	0.968648	−	0.248436i	$-0.0799164\pi$
$43$	1.76508	+	3.05721i	0.269173	+	0.466221i	−0.699476	+	0.714656i	$0.746583\pi$
$44$	−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	−0.820497	−	0.571651i	$-0.806303\pi$
$59$	−6.95384	−	12.0444i	−0.905313	−	1.56805i	−0.0848156	−	0.996397i	$-0.527030\pi$
$60$	6.72667			0.868409
$61$	−4.09825	−	7.09838i	−0.524727	−	0.908854i	−0.999585	−	0.0287920i	$-0.990834\pi$
$61$	−4.09825	−	7.09838i	−0.524727	−	0.908854i	0.474858	−	0.880062i	$-0.342499\pi$
$62$	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	0.0897858	+	0.995961i	$0.471382\pi$
$67$	−6.69263	+	11.5920i	−0.817635	+	1.41618i	−0.907421	+	0.420224i	$0.861952\pi$
$68$	−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	0.710932	−	0.703261i	$-0.248273\pi$
$71$	−2.13666	−	3.70081i	−0.253575	−	0.439206i	−0.964508	+	0.264055i	$0.914940\pi$
$72$	−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	−0.495764	−	0.868457i	$-0.665112\pi$
$89$	4.75684	−	8.23909i	0.504224	−	0.873341i	0.999988	−	0.00488415i	$-0.00155468\pi$
$90$	−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	0.780550	−	0.625093i	$-0.214939\pi$
$97$	−1.48788	−	2.57708i	−0.151071	−	0.261663i	−0.931622	+	0.363430i	$0.881606\pi$
$98$	−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	−0.539222	−	0.842164i	$-0.681282\pi$
$101$	4.62017	−	8.00237i	0.459724	−	0.796266i	0.998946	+	0.0458978i	$0.0146149\pi$
$102$	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	−0.999622	−	0.0275068i	$-0.991243\pi$
$107$	−4.92367	+	8.52805i	−0.475989	+	0.824437i	0.523632	+	0.851944i	$0.324577\pi$
$108$	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	−0.989036	−	0.147676i	$-0.952821\pi$
$113$	−6.61630	−	11.4598i	−0.622409	−	1.07804i	0.366627	−	0.930368i	$-0.380513\pi$
$114$	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	−0.461664	−	0.887055i	$-0.652747\pi$
$127$	6.05596	−	10.4892i	0.537380	−	0.930769i	0.999044	−	0.0437145i	$-0.0139192\pi$
$128$	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	0.824931	−	0.565234i	$-0.191214\pi$
$137$	−0.901749	−	1.56187i	−0.0770416	−	0.133440i	−0.901972	+	0.431794i	$0.857881\pi$
$138$	7.51368			0.639607
$139$	0.564210	+	0.977240i	0.0478556	+	0.0828884i	0.888961	−	0.457983i	$-0.151428\pi$
$139$	0.564210	+	0.977240i	0.0478556	+	0.0828884i	−0.841105	+	0.540871i	$0.818095\pi$
$140$	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	−0.996871	−	0.0790466i	$-0.974812\pi$
$149$	−6.91980	−	11.9854i	−0.566892	−	0.981885i	0.429979	−	0.902839i	$-0.358521\pi$
$150$	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	0.900266	+	0.435341i	$0.143372\pi$
$163$	10.5603	+	18.2910i	0.827149	+	1.43266i	−0.0731162	+	0.997323i	$0.523294\pi$
$164$	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	−0.694756	−	0.719246i	$-0.744488\pi$
$167$	3.56034	−	6.16668i	0.275507	−	0.477192i	0.970263	+	0.242053i	$0.0778209\pi$
$168$	−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	0.939990	−	0.341203i	$-0.110834\pi$
$173$	2.29525	+	3.97549i	0.174505	+	0.302251i	−0.765485	+	0.643454i	$0.777501\pi$
$174$	−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	0.131292	+	0.991344i	$0.458088\pi$
$179$	−10.6081	+	18.3737i	−0.792883	+	1.37331i	−0.924175	+	0.381970i	$0.875246\pi$
$180$	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	0.904638	−	0.426181i	$-0.140141\pi$
$191$	1.15034	+	1.99245i	0.0832358	+	0.144169i	−0.821402	+	0.570349i	$0.806808\pi$
$192$	−5.76508	+	9.98542i	−0.416059	+	0.720635i
$193$	11.6124	−	20.1133i	0.835881	−	1.44779i	−0.0574307	−	0.998349i	$-0.518291\pi$
$193$	11.6124	−	20.1133i	0.835881	−	1.44779i	0.893311	−	0.449438i	$-0.148376\pi$
$194$	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	−0.590429	−	0.807089i	$-0.701042\pi$
$197$	5.66683	−	9.81524i	0.403745	−	0.699307i	0.994175	+	0.107782i	$0.0343749\pi$
$198$	0.700874	−	1.21395i	0.0498090	−	0.0862717i
$199$	7.90718	+	13.6956i	0.560525	+	0.970858i	0.997451	+	0.0713602i	$0.0227340\pi$
$199$	7.90718	+	13.6956i	0.560525	+	0.970858i	−0.436926	+	0.899498i	$0.643933\pi$
$200$	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	−0.957033	−	0.289978i	$-0.906352\pi$
$211$	−3.30300	+	5.72096i	−0.227388	+	0.393847i	0.729645	+	0.683826i	$0.239685\pi$
$212$	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	−0.653918	−	0.756565i	$-0.726876\pi$
$223$	4.90175	−	8.49008i	0.328245	−	0.568538i	0.982164	+	0.188027i	$0.0602094\pi$
$224$	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	0.998864	+	0.0476522i	$0.0151739\pi$
$227$	8.14647	+	14.1101i	0.540700	+	0.936520i	−0.458164	+	0.888868i	$0.651493\pi$
$228$	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	−0.717596	−	0.696459i	$-0.754758\pi$
$241$	−14.9335	−	25.8655i	−0.961950	−	1.66615i	−0.244353	−	0.969686i	$-0.578576\pi$
$242$	−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	0.982172	+	0.187982i	$0.0601946\pi$
$251$	10.3595	+	17.9431i	0.653883	+	1.13256i	−0.328289	+	0.944577i	$0.606472\pi$
$252$	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	−0.982941	−	0.183921i	$-0.941121\pi$
$257$	−5.32542	+	9.22390i	−0.332191	+	0.575371i	0.650751	+	0.759292i	$0.274454\pi$
$258$	−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	−0.226840	−	0.973932i	$-0.572839\pi$
$263$	11.8391	−	20.5059i	0.730030	−	1.26445i	0.956870	−	0.290517i	$-0.0938272\pi$
$264$	−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	0.873213	−	0.487338i	$-0.162032\pi$
$269$	0.238790	+	0.413597i	0.0145593	+	0.0252174i	−0.858654	+	0.512556i	$0.828699\pi$
$270$	−2.82929	+	4.90048i	−0.172185	+	0.298234i
$271$	10.3210	−	17.8766i	0.626959	−	1.08592i	−0.361200	−	0.932489i	$-0.617633\pi$
$271$	10.3210	−	17.8766i	0.626959	−	1.08592i	0.988159	−	0.153436i	$-0.0490340\pi$
$272$	−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	0.924783	+	0.380495i	$0.124247\pi$
$277$	13.1800	+	22.8284i	0.791910	+	1.37163i	−0.132873	+	0.991133i	$0.542420\pi$
$278$	−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	−0.886332	−	0.463050i	$-0.846755\pi$
$283$	−0.709120	+	1.22823i	−0.0421528	+	0.0730108i	0.844179	+	0.536061i	$0.180088\pi$
$284$	−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	−0.834319	−	0.551282i	$-0.814139\pi$
$293$	−15.3128	−	26.5226i	−0.894583	−	1.54946i	−0.0602641	−	0.998182i	$-0.519194\pi$
$294$	−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	−0.982046	−	0.188643i	$-0.939591\pi$
$331$	−11.9056	−	20.6211i	−0.654392	−	1.13344i	0.327654	−	0.944798i	$-0.393742\pi$
$332$	−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	0.999512	+	0.0312340i	$0.00994372\pi$
$347$	9.81330	+	16.9971i	0.526806	+	0.912454i	−0.472707	+	0.881220i	$0.656723\pi$
$348$	1.10262	−	1.90980i	0.0591068	−	0.102376i
$349$	−13.5400	+	23.4519i	−0.724778	+	1.25535i	0.234287	+	0.972167i	$0.424724\pi$
$349$	−13.5400	+	23.4519i	−0.724778	+	1.25535i	−0.959065	+	0.283185i	$0.908609\pi$
$350$	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	−0.842890	−	0.538086i	$-0.819148\pi$
$353$	0.837042	−	1.44980i	0.0445512	−	0.0771650i	0.887441	+	0.460921i	$0.152481\pi$
$354$	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	−0.997389	−	0.0722110i	$-0.976994\pi$
$367$	−8.35559	+	14.4723i	−0.436158	+	0.755448i	0.561231	+	0.827659i	$0.310328\pi$
$368$	−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	0.574489	−	0.818512i	$-0.305201\pi$
$373$	−8.14259	−	14.1034i	−0.421607	−	0.730246i	−0.996097	+	0.0882664i	$0.971867\pi$
$374$	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	0.259039	+	0.965867i	$0.416594\pi$
$379$	−13.7628	+	23.8378i	−0.706946	+	1.22447i	−0.965985	+	0.258599i	$0.916739\pi$
$380$	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	0.666205	−	0.745768i	$-0.267917\pi$
$383$	−6.12067	−	10.6013i	−0.312752	−	0.541702i	−0.978957	+	0.204067i	$0.934584\pi$
$384$	−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	0.855654	−	0.517548i	$-0.173155\pi$
$397$	−0.406120	−	0.703421i	−0.0203826	−	0.0353037i	−0.876037	+	0.482244i	$0.839822\pi$
$398$	−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	−0.718019	−	0.696024i	$-0.754951\pi$
$401$	4.88138	−	8.45480i	0.243765	−	0.422213i	0.961784	+	0.273811i	$0.0882842\pi$
$402$	−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	0.533847	−	0.845581i	$-0.320746\pi$
$409$	−9.41155	−	16.3013i	−0.465371	−	0.806047i	−0.999218	+	0.0395345i	$0.987413\pi$
$410$	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	−0.671577	−	0.740935i	$-0.734383\pi$
$419$	6.26121	−	10.8447i	0.305880	−	0.529800i	0.977457	+	0.211135i	$0.0677160\pi$
$420$	−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	−0.876522	−	0.481363i	$-0.840142\pi$
$431$	−0.444036	+	0.769093i	−0.0213885	+	0.0370459i	0.855133	+	0.518409i	$0.173475\pi$
$432$	−1.32929	+	2.30240i	−0.0639557	+	0.110774i
$433$	−13.4154	−	23.2362i	−0.644704	−	1.11666i	−0.984370	−	0.176114i	$-0.943647\pi$
$433$	−13.4154	−	23.2362i	−0.644704	−	1.11666i	0.339666	−	0.940546i	$-0.389686\pi$
$434$	−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	−0.100376	−	0.994950i	$-0.532004\pi$
$439$	17.0021	−	29.4484i	0.811464	−	1.40550i	0.911840	−	0.410547i	$-0.134662\pi$
$440$	−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	0.575454	−	0.817834i	$-0.304826\pi$
$449$	−8.91105	−	15.4344i	−0.420539	−	0.728394i	−0.995992	+	0.0894402i	$0.971492\pi$
$450$	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	0.238390	−	0.971170i	$-0.423381\pi$
$457$	20.5279	−	35.5553i	0.960252	−	1.66321i	0.721863	−	0.692036i	$-0.243286\pi$
$458$	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	0.891518	+	0.452984i	$0.149641\pi$
$461$	17.9938	+	31.1662i	0.838055	+	1.45155i	−0.0534633	+	0.998570i	$0.517026\pi$
$462$	−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	−0.917871	−	0.396878i	$-0.870094\pi$
$479$	−2.52192	+	4.36810i	−0.115230	+	0.199583i	0.802642	+	0.596461i	$0.203427\pi$
$480$	−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	0.972142	−	0.234393i	$-0.0753104\pi$
$487$	6.24704	+	10.8202i	0.283080	+	0.490309i	−0.689062	+	0.724703i	$0.741977\pi$
$488$	−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	−0.865256	−	0.501330i	$-0.832844\pi$
$491$	0.0340418	−	0.0589622i	0.00153629	−	0.00266093i	0.866793	+	0.498669i	$0.166178\pi$
$492$	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	0.999958	+	0.00915539i	$0.00291429\pi$
$503$	11.3912	+	19.7301i	0.507908	+	0.879722i	−0.492050	+	0.870567i	$0.663752\pi$
$504$	−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	0.420886	+	0.907114i	$0.361719\pi$
$509$	−12.9758	+	22.4747i	−0.575140	+	0.996173i	−0.996026	+	0.0890589i	$0.971614\pi$
$510$	−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	−0.474792	−	0.880098i	$-0.657477\pi$
$523$	12.0016	−	20.7873i	0.524791	−	0.908965i	0.999583	−	0.0288673i	$-0.00919002\pi$
$524$	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	−0.942734	−	0.333544i	$-0.891755\pi$
$557$	−4.30737	+	7.46059i	−0.182509	+	0.316115i	0.760225	+	0.649660i	$0.225089\pi$
$558$	−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	−0.947026	−	0.321158i	$-0.895928\pi$
$563$	−17.8347	−	30.8906i	−0.751644	−	1.30189i	0.195382	−	0.980727i	$-0.437405\pi$
$564$	−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	−0.721810	−	0.692092i	$-0.756689\pi$
$569$	5.68826	−	9.85235i	0.238464	−	0.413032i	0.960274	+	0.279060i	$0.0900227\pi$
$570$	−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	−0.213690	+	0.976901i	$0.568548\pi$
$587$	−23.0861	+	39.9864i	−0.952867	+	1.65041i	−0.739176	+	0.673512i	$0.764785\pi$
$588$	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	−0.891863	−	0.452306i	$-0.850602\pi$
$601$	−1.32929	+	2.30240i	−0.0542230	+	0.0939170i	0.837640	+	0.546223i	$0.183935\pi$
$602$	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	−0.817165	−	0.576404i	$-0.804455\pi$
$607$	−22.3649	−	38.7371i	−0.907763	−	1.57229i	−0.0905981	−	0.995888i	$-0.528878\pi$
$608$	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	0.00484892	−	0.999988i	$-0.498457\pi$
$613$	21.5016	−	37.2418i	0.868440	−	1.50418i	0.863591	−	0.504193i	$-0.168210\pi$
$614$	−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	0.702455	−	0.711729i	$-0.252087\pi$
$617$	−6.58613	−	11.4075i	−0.265148	−	0.459249i	−0.967602	+	0.252479i	$0.918754\pi$
$618$	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	0.818520	−	0.574478i	$-0.194795\pi$
$631$	−2.21687	−	3.83973i	−0.0882521	−	0.152857i	−0.906772	+	0.421620i	$0.861461\pi$
$632$	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	0.962486	−	0.271330i	$-0.0874635\pi$
$641$	6.23492	+	10.7992i	0.246264	+	0.426542i	−0.716222	+	0.697873i	$0.754130\pi$
$642$	−20.9593			−0.827196
$643$	−19.0137	−	32.9327i	−0.749826	−	1.29874i	−0.947906	−	0.318551i	$-0.896804\pi$
$643$	−19.0137	−	32.9327i	−0.749826	−	1.29874i	0.198079	−	0.980186i	$-0.436530\pi$
$644$	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	−0.960598	−	0.277941i	$-0.910348\pi$
$647$	−6.09438	+	10.5558i	−0.239595	+	0.414990i	0.721003	+	0.692932i	$0.243681\pi$
$648$	−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	−0.955315	−	0.295589i	$-0.904484\pi$
$653$	−5.66451	+	9.81123i	−0.221670	+	0.383943i	0.733645	+	0.679532i	$0.237817\pi$
$654$	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	−0.902871	−	0.429911i	$-0.858545\pi$
$659$	−21.1465	−	36.6268i	−0.823749	−	1.42678i	0.0791219	−	0.996865i	$-0.474788\pi$
$660$	2.21505	−	3.83658i	0.0862206	−	0.149339i
$661$	7.67663	−	13.2963i	0.298586	−	0.517167i	−0.677226	−	0.735775i	$-0.736818\pi$
$661$	7.67663	−	13.2963i	0.298586	−	0.517167i	0.975813	+	0.218608i	$0.0701515\pi$
$662$	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	0.201582	+	0.979472i	$0.435392\pi$
$673$	−19.3907	+	33.5857i	−0.747456	+	1.29463i	−0.949038	+	0.315160i	$0.897942\pi$
$674$	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	0.812517	−	0.582938i	$-0.198097\pi$
$683$	−2.57633	−	4.46233i	−0.0985805	−	0.170746i	−0.911097	+	0.412191i	$0.864764\pi$
$684$	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	−0.999057	−	0.0434196i	$-0.986175\pi$
$691$	−12.1426	+	21.0316i	−0.461926	+	0.800079i	0.537131	+	0.843499i	$0.319508\pi$
$692$	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	−0.990318	−	0.138819i	$-0.955669\pi$
$709$	−16.3858	−	28.3810i	−0.615380	−	1.06587i	0.374938	−	0.927050i	$-0.377664\pi$
$710$	−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	0.865639	+	0.500668i	$0.166912\pi$
$719$	23.2321	+	40.2392i	0.866411	+	1.50067i	0.000772041		1.00000i	$0.499754\pi$
$720$	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	−0.0929182	−	0.995674i	$-0.529620\pi$
$739$	22.1777	−	38.4129i	0.815820	−	1.41304i	0.908738	−	0.417367i	$-0.137047\pi$
$740$	−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	−0.683787	−	0.729682i	$-0.739668\pi$
$743$	7.90562	−	13.6929i	0.290029	−	0.502345i	0.973816	+	0.227336i	$0.0730017\pi$
$744$	−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	−0.743078	−	0.669205i	$-0.766635\pi$
$751$	5.70038	−	9.87334i	0.208010	−	0.360283i	0.951087	+	0.308922i	$0.0999681\pi$
$752$	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	−0.871635	−	0.490155i	$-0.836940\pi$
$757$	−0.311743	+	0.539955i	−0.0113305	+	0.0196250i	0.860305	+	0.509780i	$0.170273\pi$
$758$	−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	0.981182	+	0.193087i	$0.0618499\pi$
$761$	18.1465	+	31.4306i	0.657809	+	1.13936i	−0.323373	+	0.946272i	$0.604817\pi$
$762$	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	0.353428	+	0.935462i	$0.385016\pi$
$769$	−17.5653	+	30.4239i	−0.633420	+	1.09712i	−0.986848	+	0.161653i	$0.948317\pi$
$770$	−1.86334	+	3.22739i	−0.0671499	+	0.116307i
$771$	5.32542	+	9.22390i	0.191790	+	0.332191i
$772$	−58.7628			−2.11492
$773$	25.8951	+	44.8516i	0.931381	+	1.61320i	0.780964	+	0.624576i	$0.214728\pi$
$773$	25.8951	+	44.8516i	0.931381	+	1.61320i	0.150416	+	0.988623i	$0.451939\pi$
$774$	3.75684	+	6.50703i	0.135037	+	0.233891i
$775$	−12.2336			−0.439444
$776$	−1.67895	−	2.90803i	−0.0602709	−	0.104392i
$777$	0.731042	−	1.26620i	0.0262260	−	0.0454247i
$778$	2.94841	−	5.10679i	0.105706	−	0.183087i
$779$	55.2687			1.98021
$780$	22.3951	−	9.31056i	0.801872	−	0.333372i
$781$	−2.81436			−0.100706
$782$	23.0235	−	39.8778i	0.823318	−	1.42603i
$783$	0.435790	−	0.754811i	0.0155739	−	0.0269748i
$784$	1.32929	+	2.30240i	0.0474748	+	0.0822287i
$785$	−19.5905			−0.699215
$786$	−3.55596	−	6.15911i	−0.126837	−	0.219688i
$787$	16.0021	+	27.7164i	0.570412	+	0.987982i	0.996524	+	0.0833115i	$0.0265496\pi$
$787$	16.0021	+	27.7164i	0.570412	+	0.987982i	−0.426112	+	0.904670i	$0.640117\pi$
$788$	−28.6761			−1.02154
$789$	−11.8391	−	20.5059i	−0.421483	−	0.730030i
$790$	13.7365	−	23.7923i	0.488722	−	0.846491i
$791$	−6.61630	+	11.4598i	−0.235249	+	0.407462i
$792$	−0.743162			−0.0264071
$793$	−23.4693	−	17.9601i	−0.833421	−	0.637782i
$794$	1.72879			0.0613524
$795$	2.57838	−	4.46589i	0.0914458	−	0.158389i
$796$	20.0065	−	34.6523i	0.709111	−	1.22822i
$797$	−7.51318	−	13.0132i	−0.266130	−	0.460951i	0.701729	−	0.712444i	$-0.252412\pi$
$797$	−7.51318	−	13.0132i	−0.266130	−	0.460951i	−0.967859	+	0.251493i	$0.919079\pi$
$798$	−11.1888			−0.396078
$799$	−26.7166	−	46.2745i	−0.945166	−	1.63707i
$800$	8.18488	+	14.1766i	0.289379	+	0.501220i
$801$	−9.51368			−0.336149
$802$	10.3896	+	17.9954i	0.366871	+	0.635438i
$803$	−1.14259	+	1.97903i	−0.0403212	+	0.0698384i
$804$	16.9335	−	29.3296i	0.597198	−	1.03438i
$805$	9.38526			0.330787
$806$	5.86665	−	45.0150i	0.206644	−	1.58559i
$807$	0.477581			0.0168116
$808$	5.21349	−	9.03003i	0.183410	−	0.317675i
$809$	26.2365	−	45.4429i	0.922425	−	1.59769i	0.126775	−	0.991932i	$-0.459537\pi$
$809$	26.2365	−	45.4429i	0.922425	−	1.59769i	0.795651	−	0.605756i	$-0.207129\pi$
$810$	2.82929	+	4.90048i	0.0994112	+	0.172185i
$811$	−29.6627			−1.04160			−0.520799	−	0.853679i	$-0.674366\pi$
$811$	−29.6627			−1.04160			−0.520799	+	0.853679i	$0.674366\pi$
$812$	−1.10262	−	1.90980i	−0.0386945	−	0.0670208i
$813$	−10.3210	−	17.8766i	−0.361975	−	0.626959i
$814$	−2.04947			−0.0718340
$815$	−28.0756	−	48.6283i	−0.983444	−	1.70338i
$816$	−8.14647	+	14.1101i	−0.285183	+	0.493952i
$817$	9.27876	−	16.0713i	0.324623	−	0.562263i
$818$	40.0634			1.40079
$819$	−0.465958	+	3.57532i	−0.0162819	+	0.124932i
$820$	−70.7220			−2.46972
$821$	2.88807	−	5.00229i	0.100794	−	0.174581i	−0.811218	−	0.584744i	$-0.801195\pi$
$821$	2.88807	−	5.00229i	0.100794	−	0.174581i	0.912012	+	0.410163i	$0.134528\pi$
$822$	1.91930	−	3.32432i	0.0669432	−	0.115949i
$823$	5.62842	+	9.74871i	0.196194	+	0.339819i	0.947291	−	0.320373i	$-0.103808\pi$
$823$	5.62842	+	9.74871i	0.196194	+	0.339819i	−0.751097	+	0.660192i	$0.770475\pi$
$824$	15.0954			0.525874
$825$	−0.681006	−	1.17954i	−0.0237096	−	0.0410662i
$826$	−14.8007	−	25.6355i	−0.514982	−	0.891974i
$827$	20.0644			0.697709			0.348855	−	0.937177i	$-0.386571\pi$
$827$	20.0644			0.697709			0.348855	+	0.937177i	$0.386571\pi$
$828$	4.46596	+	7.73527i	0.155203	+	0.268819i
$829$	15.8308	−	27.4198i	0.549828	−	0.952330i	−0.448458	−	0.893804i	$-0.648027\pi$
$829$	15.8308	−	27.4198i	0.549828	−	0.952330i	0.998286	−	0.0585262i	$-0.0186401\pi$
$830$	44.8587	−	77.6975i	1.55707	−	2.69692i
$831$	26.3600			0.914419
$832$	−38.3873	+	15.9592i	−1.33084	+	0.553286i
$833$	6.12842			0.212337
$834$	−1.20087	+	2.07998i	−0.0415829	+	0.0720237i
$835$	−9.46546	+	16.3947i	−0.327566	+	0.567361i
$836$	4.37983	+	7.58608i	0.151479	+	0.262370i
$837$	5.91542			0.204467
$838$	13.3265	+	23.0821i	0.460356	+	0.797359i
$839$	6.02530	+	10.4361i	0.208016	+	0.360295i	0.951090	−	0.308915i	$-0.0999659\pi$
$839$	6.02530	+	10.4361i	0.208016	+	0.360295i	−0.743073	+	0.669210i	$0.766633\pi$
$840$	3.00000			0.103510
$841$	14.1202	+	24.4569i	0.486903	+	0.843340i
$842$	−29.3478	+	50.8319i	−1.01139	+	1.75178i
$843$	0.102623	−	0.177748i	0.00353452	−	0.00612197i
$844$	16.7143			0.575329
$845$	−24.3750	+	24.5024i	−0.838524	+	0.842908i
$846$	18.5575			0.638021
$847$	5.28313	−	9.15065i	0.181531	−	0.314420i
$848$	−2.57838	+	4.46589i	−0.0885420	+	0.153359i
$849$	0.709120	+	1.22823i	0.0243369	+	0.0421528i
$850$	26.9758			0.925261
$851$	2.58070	+	4.46991i	0.0884653	+	0.153226i
$852$	5.40612	+	9.36367i	0.185211	+	0.320794i
$853$	36.1764			1.23866			0.619328	−	0.785133i	$-0.287405\pi$
$853$	36.1764			1.23866			0.619328	+	0.785133i	$0.287405\pi$
$854$	−8.72280	−	15.1083i	−0.298488	−	0.516996i
$855$	6.98788	−	12.1034i	0.238980	−	0.413926i
$856$	−5.55596	+	9.62321i	−0.189899	+	0.328915i
$857$	−30.6869			−1.04825			−0.524123	−	0.851643i	$-0.675607\pi$
$857$	−30.6869			−1.04825			−0.524123	+	0.851643i	$0.675607\pi$
$858$	4.66683	−	1.94020i	0.159323	−	0.0662372i
$859$	−5.93291			−0.202428			−0.101214	−	0.994865i	$-0.532273\pi$
$859$	−5.93291			−0.202428			−0.101214	+	0.994865i	$0.532273\pi$
$860$	−11.8731	+	20.5649i	−0.404871	+	0.701256i
$861$	5.25684	−	9.10511i	0.179153	−	0.310301i
$862$	−0.945095	−	1.63695i	−0.0321901	−	0.0557548i
$863$	16.8299			0.572895			0.286447	−	0.958096i	$-0.407526\pi$
$863$	16.8299			0.572895			0.286447	+	0.958096i	$0.407526\pi$
$864$	−3.95771	−	6.85496i	−0.134644	−	0.233210i
$865$	−6.10213	−	10.5692i	−0.207478	−	0.359363i
$866$	57.1073			1.94058
$867$	10.2788	+	17.8033i	0.349085	+	0.604633i
$868$	7.48351	−	12.9618i	0.254007	−	0.439953i
$869$	1.59875	−	2.76911i	0.0542338	−	0.0939358i
$870$	4.93192			0.167208
$871$	−6.23697	+	47.8565i	−0.211332	+	1.62156i
$872$	7.13716			0.241695
$873$	−1.48788	+	2.57708i	−0.0503571	+	0.0872211i
$874$	19.7491	−	34.2064i	0.668023	−	1.15705i
$875$	−3.89738	−	6.75046i	−0.131755	−	0.228207i
$876$	8.77926			0.296624
$877$	25.9340	+	44.9190i	0.875728	+	1.51681i	0.855985	+	0.517000i	$0.172951\pi$
$877$	25.9340	+	44.9190i	0.875728	+	1.51681i	0.0197427	+	0.999805i	$0.493715\pi$
$878$	36.1875	+	62.6786i	1.22127	+	2.11530i
$879$	−30.6256			−1.03298
$880$	2.32747	+	4.03130i	0.0784591	+	0.135895i
$881$	8.13047	−	14.0824i	0.273923	−	0.474448i	−0.695940	−	0.718100i	$-0.745012\pi$
$881$	8.13047	−	14.0824i	0.273923	−	0.474448i	0.969863	+	0.243652i	$0.0783455\pi$
$882$	−1.06421	+	1.84326i	−0.0358338	+	0.0620660i
$883$	−21.5049			−0.723699			−0.361849	−	0.932237i	$-0.617855\pi$
$883$	−21.5049			−0.723699			−0.361849	+	0.932237i	$0.617855\pi$
$884$	−7.22511	+	55.4386i	−0.243007	+	1.86460i
$885$	36.9748			1.24289
$886$	22.3133	−	38.6478i	0.749630	−	1.29840i
$887$	−0.317174	+	0.549361i	−0.0106496	+	0.0184457i	−0.871301	−	0.490749i	$-0.836723\pi$
$887$	−0.317174	+	0.549361i	−0.0106496	+	0.0184457i	0.860651	+	0.509195i	$0.170057\pi$
$888$	0.824922	+	1.42881i	0.0276826	+	0.0479476i
$889$	−12.1119			−0.406221
$890$	−26.9170	−	46.6216i	−0.902259	−	1.56276i
$891$	0.329293	+	0.570353i	0.0110317	+	0.0191075i
$892$	−24.8045			−0.830516
$893$	−22.9170	−	39.6934i	−0.766888	−	1.32829i
$894$	14.7282	−	25.5100i	0.492586	−	0.853183i
$895$	28.2024	−	48.8480i	0.942703	−	1.63281i
$896$	−8.71018			−0.290987
$897$	−10.1081	−	7.73527i	−0.337498	−	0.258273i
$898$	37.9329			1.26584
$899$	2.57789	−	4.46503i	0.0859773	−	0.148917i
$900$	−2.61630	+	4.53156i	−0.0872100	+	0.151052i
$901$	5.94354	+	10.2945i	0.198008	+	0.342960i
$902$	−14.7375			−0.490706
$903$	−1.76508	−	3.05721i	−0.0587383	−	0.101738i
$904$	−7.46596	−	12.9314i	−0.248314	−	0.430093i
$905$	46.8386			1.55697
$906$	−8.06034	−	13.9609i	−0.267787	−	0.463820i
$907$	12.1766	−	21.0905i	0.404319	−	0.700300i	−0.589923	−	0.807459i	$-0.700842\pi$
$907$	12.1766	−	21.0905i	0.404319	−	0.700300i	0.994242	+	0.107159i	$0.0341754\pi$
$908$	20.6119	−	35.7009i	0.684031	−	1.18478i
$909$	−9.24035			−0.306483
$910$	−18.8391	+	7.83220i	−0.624510	+	0.259635i
$911$	−2.71217			−0.0898582			−0.0449291	−	0.998990i	$-0.514306\pi$
$911$	−2.71217			−0.0898582			−0.0449291	+	0.998990i	$0.514306\pi$
$912$	−6.98788	+	12.1034i	−0.231392	+	0.400782i
$913$	5.22098	−	9.04300i	0.172789	−	0.299279i
$914$	43.6919	+	75.6765i	1.44520	+	2.50316i
$915$	21.7911			0.720392
$916$	29.3397	+	50.8178i	0.969410	+	1.67907i
$917$	1.67071	+	2.89375i	0.0551716	+	0.0955600i
$918$	−13.0438			−0.430511
$919$	−2.48788	−	4.30913i	−0.0820676	−	0.142145i	0.822070	−	0.569386i	$-0.192819\pi$
$919$	−2.48788	−	4.30913i	−0.0820676	−	0.142145i	−0.904138	+	0.427241i	$0.859486\pi$
$920$	−5.29525	+	9.17164i	−0.174579	+	0.302380i
$921$	2.23929	−	3.87856i	0.0737870	−	0.127803i
$922$	−76.5967			−2.52258
$923$	−12.2360	−	9.36367i	−0.402752	−	0.308209i
$924$	1.66633			0.0548184
$925$	−1.51186	+	2.61861i	−0.0497095	+	0.0860994i
$926$	13.9972	−	24.2438i	0.459976	−	0.796702i
$927$	−6.68875	−	11.5853i	−0.219688	−	0.380510i
$928$	−6.89893			−0.226469
$929$	−25.3167	−	43.8498i	−0.830613	−	1.43866i	−0.897553	−	0.440907i	$-0.854657\pi$
$929$	−25.3167	−	43.8498i	−0.830613	−	1.43866i	0.0669395	−	0.997757i	$-0.478677\pi$
$930$	16.7365	+	28.9884i	0.548811	+	0.950568i
$931$	5.25684			0.172286
$932$	3.29807	+	5.71242i	0.108032	+	0.187117i
$933$	0.337539	−	0.584635i	0.0110505	−	0.0191401i
$934$	−20.7233	+	35.8938i	−0.678087	+	1.17448i
$935$	10.7303			0.350919
$936$	−3.23104	−	2.47258i	−0.105610	−	0.0808188i
$937$	19.5018			0.637097			0.318548	−	0.947907i	$-0.396805\pi$
$937$	19.5018			0.637097			0.318548	+	0.947907i	$0.396805\pi$
$938$	−14.2447	+	24.6726i	−0.465107	+	0.805588i
$939$	5.01212	−	8.68125i	0.163564	−	0.283302i
$940$	29.3247	+	50.7918i	0.956465	+	1.65665i
$941$	−9.95827			−0.324630			−0.162315	−	0.986739i	$-0.551896\pi$
$941$	−9.95827			−0.324630			−0.162315	+	0.986739i	$0.551896\pi$
$942$	7.84191	+	13.5826i	0.255503	+	0.442545i
$943$	18.5575	+	32.1426i	0.604316	+	1.04671i
$944$	−36.9748			−1.20343
$945$	−1.32929	−	2.30240i	−0.0432419	−	0.0748972i
$946$	−2.47420	+	4.28545i	−0.0804433	+	0.139332i
$947$	−30.0093	+	51.9776i	−0.975171	+	1.68905i	−0.295803	+	0.955249i	$0.595587\pi$
$947$	−30.0093	+	51.9776i	−0.975171	+	1.68905i	−0.679368	+	0.733797i	$0.737746\pi$
$948$	−12.2842			−0.398972
$949$	−11.5521	+	4.80269i	−0.374997	+	0.155902i
$950$	23.1393			0.750737
$951$	13.5779	−	23.5176i	0.440293	−	0.762610i
$952$	−3.45771	+	5.98893i	−0.112065	+	0.194102i
$953$	0.799623	+	1.38499i	0.0259023	+	0.0448642i	0.878686	−	0.477400i	$-0.158421\pi$
$953$	0.799623	+	1.38499i	0.0259023	+	0.0448642i	−0.852784	+	0.522264i	$0.825087\pi$
$954$	−4.12842			−0.133663
$955$	−3.05828	−	5.29710i	−0.0989637	−	0.171410i
$956$	−19.9164	−	34.4963i	−0.644143	−	1.11569i
$957$	0.574012			0.0185552
$958$	−5.36771	−	9.29714i	−0.173423	−	0.300377i
$959$	−0.901749	+	1.56187i	−0.0291190	+	0.0504356i
$960$	15.3270	−	26.5471i	0.494676	−	0.856804i
$961$	3.99225			0.128782
$962$	−8.91049	−	6.81882i	−0.287286	−	0.219848i
$963$	9.84734			0.317326
$964$	−37.7842	+	65.4441i	−1.21695	+	2.10781i
$965$	−30.8726	+	53.4730i	−0.993825	+	1.72136i
$966$	−3.75684	−	6.50703i	−0.120874	−	0.209360i
$967$	29.7705			0.957355			0.478678	−	0.877991i	$-0.341116\pi$
$967$	29.7705			0.957355			0.478678	+	0.877991i	$0.341116\pi$
$968$	5.96159	+	10.3258i	0.191613	+	0.331883i
$969$	16.1081	+	27.9000i	0.517465	+	0.896276i
$970$	−16.8386			−0.540655
$971$	−18.0905	−	31.3337i	−0.580552	−	1.00555i	−0.995414	−	0.0956610i	$-0.969504\pi$
$971$	−18.0905	−	31.3337i	−0.580552	−	1.00555i	0.414862	−	0.909884i	$-0.363830\pi$
$972$	1.26508	−	2.19119i	0.0405776	−	0.0702824i
$973$	0.564210	−	0.977240i	0.0180877	−	0.0313289i
$974$	−26.5926			−0.852083
$975$	0.963640	−	7.39405i	0.0308612	−	0.236799i
$976$	−21.7911			−0.697517
$977$	2.15034	−	3.72450i	0.0687955	−	0.119157i	−0.829576	−	0.558394i	$-0.811418\pi$
$977$	2.15034	−	3.72450i	0.0687955	−	0.119157i	0.898371	+	0.439237i	$0.144751\pi$
$978$	−22.4768	+	38.9310i	−0.718729	+	1.24488i
$979$	−3.13279	−	5.42615i	−0.100124	−	0.173421i
$980$	−6.72667			−0.214876
$981$	−3.16246	−	5.47754i	−0.100970	−	0.174884i
$982$	0.0724553	+	0.125496i	0.00231214	+	0.00400474i
$983$	7.42599			0.236852			0.118426	−	0.992963i	$-0.462215\pi$
$983$	7.42599			0.236852			0.118426	+	0.992963i	$0.462215\pi$
$984$	5.93192	+	10.2744i	0.189103	+	0.327535i
$985$	−15.0658	+	26.0947i	−0.480035	+	0.831445i
$986$	−5.68438	+	9.84564i	−0.181028	+	0.313549i
$987$	−8.71892			−0.277526
$988$	−6.19756	+	47.5541i	−0.197171	+	1.51290i
$989$	12.4621			0.396271
$990$	−1.86334	+	3.22739i	−0.0592207	+	0.102573i
$991$	−5.13822	+	8.89966i	−0.163221	+	0.282707i	−0.936022	−	0.351941i	$-0.885522\pi$
$991$	−5.13822	+	8.89966i	−0.163221	+	0.282707i	0.772801	+	0.634648i	$0.218855\pi$
$992$	−23.4116	−	40.5500i	−0.743317	−	1.28746i
$993$	−23.8112			−0.755627
$994$	−4.54772	−	7.87688i	−0.144245	−	0.249839i
$995$	−21.0219	−	36.4110i	−0.666440	−	1.15431i
$996$	−40.1160			−1.27113
$997$	11.6947	+	20.2558i	0.370374	+	0.641507i	0.989623	−	0.143688i	$-0.0458961\pi$
$997$	11.6947	+	20.2558i	0.370374	+	0.641507i	−0.619249	+	0.785195i	$0.712563\pi$
$998$	2.28158	−	3.95180i	0.0722220	−	0.125092i
$999$	0.731042	−	1.26620i	0.0231291	−	0.0400609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.k.b.22.1	✓	6
3.2	odd	2		819.2.o.f.568.3		6
13.3	even	3	inner	273.2.k.b.211.1	yes	6
13.4	even	6		3549.2.a.l.1.1		3
13.9	even	3		3549.2.a.m.1.3		3
39.29	odd	6		819.2.o.f.757.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.b.22.1	✓	6	1.1	even	1	trivial
273.2.k.b.211.1	yes	6	13.3	even	3	inner
819.2.o.f.568.3		6	3.2	odd	2
819.2.o.f.757.3		6	39.29	odd	6
3549.2.a.l.1.1		3	13.4	even	6
3549.2.a.m.1.3		3	13.9	even	3

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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