LMFDB - Embedded newform 273.2.cc.a.50.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (of order $12$, degree $4$, 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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.2
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.46820 - 0.661352i) q^{2} +(1.55028 - 0.772424i) q^{3} +(3.92257 + 2.26470i) q^{4} +(2.12589 - 2.12589i) q^{5} +(-4.33724 + 0.881217i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-4.57023 - 4.57023i) q^{8} +(1.80672 - 2.39494i) q^{9} +O(q^{10})$	\(q+(-2.46820 - 0.661352i) q^{2} +(1.55028 - 0.772424i) q^{3} +(3.92257 + 2.26470i) q^{4} +(2.12589 - 2.12589i) q^{5} +(-4.33724 + 0.881217i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-4.57023 - 4.57023i) q^{8} +(1.80672 - 2.39494i) q^{9} +(-6.65309 + 3.84116i) q^{10} +(0.380509 - 1.42008i) q^{11} +(7.83038 + 0.481022i) q^{12} +(2.61617 + 2.48106i) q^{13} +2.55527i q^{14} +(1.65363 - 4.93781i) q^{15} +(3.72831 + 6.45763i) q^{16} +(-4.01657 + 6.95691i) q^{17} +(-6.04325 + 4.71632i) q^{18} +(2.18321 - 0.584989i) q^{19} +(13.1535 - 3.52446i) q^{20} +(-1.14735 - 1.29754i) q^{21} +(-1.87834 + 3.25339i) q^{22} +(-0.558002 - 0.966487i) q^{23} +(-10.6153 - 3.55497i) q^{24} -4.03883i q^{25} +(-4.81639 - 7.85395i) q^{26} +(0.951010 - 5.10838i) q^{27} +(1.17229 - 4.37506i) q^{28} +(1.56425 - 0.903119i) q^{29} +(-7.34713 + 11.0939i) q^{30} +(-4.01042 - 4.01042i) q^{31} +(-1.58581 - 5.91834i) q^{32} +(-0.507008 - 2.49543i) q^{33} +(14.5147 - 14.5147i) q^{34} +(-2.60368 - 1.50323i) q^{35} +(12.5108 - 5.30266i) q^{36} +(-6.69521 - 1.79398i) q^{37} -5.77548 q^{38} +(5.97222 + 1.82553i) q^{39} -19.4316 q^{40} +(-8.75726 - 2.34650i) q^{41} +(1.97375 + 3.96138i) q^{42} +(5.32638 + 3.07519i) q^{43} +(4.70862 - 4.70862i) q^{44} +(-1.25049 - 8.93229i) q^{45} +(0.738071 + 2.75452i) q^{46} +(4.21433 + 4.21433i) q^{47} +(10.7679 + 7.13128i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-2.67109 + 9.96865i) q^{50} +(-0.853122 + 13.8876i) q^{51} +(4.64329 + 15.6570i) q^{52} +4.87531i q^{53} +(-5.72572 + 11.9796i) q^{54} +(-2.21001 - 3.82785i) q^{55} +(-3.23164 + 5.59737i) q^{56} +(2.93272 - 2.59326i) q^{57} +(-4.45816 + 1.19456i) q^{58} +(10.8376 - 2.90392i) q^{59} +(17.6691 - 15.6239i) q^{60} +(4.67806 - 8.10263i) q^{61} +(7.24623 + 12.5508i) q^{62} +(-2.78095 - 1.12530i) q^{63} +0.743175i q^{64} +(10.8362 - 0.287246i) q^{65} +(-0.398961 + 6.49453i) q^{66} +(-0.941798 + 3.51484i) q^{67} +(-31.5106 + 18.1927i) q^{68} +(-1.61160 - 1.06731i) q^{69} +(5.43222 + 5.43222i) q^{70} +(1.95774 + 7.30640i) q^{71} +(-19.2026 + 2.68830i) q^{72} +(-10.5269 + 10.5269i) q^{73} +(15.3387 + 8.85579i) q^{74} +(-3.11969 - 6.26131i) q^{75} +(9.88862 + 2.64965i) q^{76} -1.47017 q^{77} +(-13.5333 - 8.45551i) q^{78} -6.82850 q^{79} +(21.6542 + 5.80223i) q^{80} +(-2.47151 - 8.65400i) q^{81} +(20.0628 + 11.5833i) q^{82} +(1.67181 - 1.67181i) q^{83} +(-1.56202 - 7.68807i) q^{84} +(6.25084 + 23.3284i) q^{85} +(-11.1128 - 11.1128i) q^{86} +(1.72743 - 2.60835i) q^{87} +(-8.22910 + 4.75107i) q^{88} +(-1.30042 + 4.85323i) q^{89} +(-2.82092 + 22.8737i) q^{90} +(1.71940 - 3.16917i) q^{91} -5.05482i q^{92} +(-9.31502 - 3.11952i) q^{93} +(-7.61466 - 13.1890i) q^{94} +(3.39764 - 5.88489i) q^{95} +(-7.02992 - 7.95015i) q^{96} +(3.45015 - 0.924465i) q^{97} +(2.46820 - 0.661352i) q^{98} +(-2.71353 - 3.47698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−2.46820	−	0.661352i	−1.74528	−	0.467647i	−0.761672	−	0.647963i	$-0.775621\pi$
$2$	−2.46820	−	0.661352i	−1.74528	−	0.467647i	−0.983609	+	0.180316i	$0.942288\pi$
$3$	1.55028	−	0.772424i	0.895053	−	0.445959i
$3$	1.55028	−	0.772424i	0.895053	−	0.445959i
$4$	3.92257	+	2.26470i	1.96129	+	1.13235i
$5$	2.12589	−	2.12589i	0.950728	−	0.950728i	−0.0481140	−	0.998842i	$-0.515321\pi$
$5$	2.12589	−	2.12589i	0.950728	−	0.950728i	0.998842	+	0.0481140i	$0.0153211\pi$
$6$	−4.33724	+	0.881217i	−1.77067	+	0.359755i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$8$	−4.57023	−	4.57023i	−1.61582	−	1.61582i
$9$	1.80672	−	2.39494i	0.602241	−	0.798314i
$10$	−6.65309	+	3.84116i	−2.10389	+	1.21468i
$11$	0.380509	−	1.42008i	0.114728	−	0.428170i	−0.884539	−	0.466467i	$-0.845527\pi$
$11$	0.380509	−	1.42008i	0.114728	−	0.428170i	0.999266	+	0.0382972i	$0.0121934\pi$
$12$	7.83038	+	0.481022i	2.26044	+	0.138859i
$13$	2.61617	+	2.48106i	0.725596	+	0.688121i
$13$	2.61617	+	2.48106i	0.725596	+	0.688121i
$14$			2.55527i			0.682924i
$15$	1.65363	−	4.93781i	0.426966	−	1.27494i
$16$	3.72831	+	6.45763i	0.932078	+	1.61441i
$17$	−4.01657	+	6.95691i	−0.974162	+	1.68730i	−0.291491	+	0.956574i	$0.594151\pi$
$17$	−4.01657	+	6.95691i	−0.974162	+	1.68730i	−0.682672	+	0.730725i	$0.739182\pi$
$18$	−6.04325	+	4.71632i	−1.42441	+	1.11165i
$19$	2.18321	−	0.584989i	0.500863	−	0.134206i	0.000462375	−	1.00000i	$-0.499853\pi$
$19$	2.18321	−	0.584989i	0.500863	−	0.134206i	0.500400	+	0.865794i	$0.333186\pi$
$20$	13.1535	−	3.52446i	2.94120	−	0.788093i
$21$	−1.14735	−	1.29754i	−0.250371	−	0.283145i
$22$	−1.87834	+	3.25339i	−0.400464	+	0.693624i
$23$	−0.558002	−	0.966487i	−0.116351	−	0.201527i	0.801968	−	0.597367i	$-0.203787\pi$
$23$	−0.558002	−	0.966487i	−0.116351	−	0.201527i	−0.918319	+	0.395841i	$0.870453\pi$
$24$	−10.6153	−	3.55497i	−2.16684	−	0.725655i
$25$		−	4.03883i		−	0.807767i
$26$	−4.81639	−	7.85395i	−0.944571	−	1.54029i
$27$	0.951010	−	5.10838i	0.183022	−	0.983109i
$28$	1.17229	−	4.37506i	0.221543	−	0.826809i
$29$	1.56425	−	0.903119i	0.290474	−	0.167705i	−0.347682	−	0.937613i	$-0.613031\pi$
$29$	1.56425	−	0.903119i	0.290474	−	0.167705i	0.638155	+	0.769908i	$0.279698\pi$
$30$	−7.34713	+	11.0939i	−1.34140	+	2.02545i
$31$	−4.01042	−	4.01042i	−0.720294	−	0.720294i	0.248371	−	0.968665i	$-0.420105\pi$
$31$	−4.01042	−	4.01042i	−0.720294	−	0.720294i	−0.968665	+	0.248371i	$0.920105\pi$
$32$	−1.58581	−	5.91834i	−0.280335	−	1.04622i
$33$	−0.507008	−	2.49543i	−0.0882588	−	0.434399i
$34$	14.5147	−	14.5147i	2.48925	−	2.48925i
$35$	−2.60368	−	1.50323i	−0.440101	−	0.254093i
$36$	12.5108	−	5.30266i	2.08514	−	0.883776i
$37$	−6.69521	−	1.79398i	−1.10069	−	0.294928i	−0.337642	−	0.941275i	$-0.609629\pi$
$37$	−6.69521	−	1.79398i	−1.10069	−	0.294928i	−0.763044	+	0.646347i	$0.776296\pi$
$38$	−5.77548			−0.936907
$39$	5.97222	+	1.82553i	0.956321	+	0.292319i
$40$	−19.4316			−3.07241
$41$	−8.75726	−	2.34650i	−1.36765	−	0.366462i	−0.501033	−	0.865428i	$-0.667046\pi$
$41$	−8.75726	−	2.34650i	−1.36765	−	0.366462i	−0.866621	+	0.498967i	$0.833713\pi$
$42$	1.97375	+	3.96138i	0.304556	+	0.611253i
$43$	5.32638	+	3.07519i	0.812265	+	0.468962i	0.847742	−	0.530409i	$-0.177962\pi$
$43$	5.32638	+	3.07519i	0.812265	+	0.468962i	−0.0354767	+	0.999371i	$0.511295\pi$
$44$	4.70862	−	4.70862i	0.709851	−	0.709851i
$45$	−1.25049	−	8.93229i	−0.186413	−	1.33155i
$46$	0.738071	+	2.75452i	0.108823	+	0.406132i
$47$	4.21433	+	4.21433i	0.614724	+	0.614724i	0.944173	−	0.329449i	$-0.106863\pi$
$47$	4.21433	+	4.21433i	0.614724	+	0.614724i	−0.329449	+	0.944173i	$0.606863\pi$
$48$	10.7679	+	7.13128i	1.55422	+	1.02931i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−2.67109	+	9.96865i	−0.377749	+	1.40978i
$51$	−0.853122	+	13.8876i	−0.119461	+	1.94466i
$52$	4.64329	+	15.6570i	0.643908	+	2.17123i
$53$			4.87531i			0.669675i	0.942276	+	0.334838i	$0.108682\pi$
$53$			4.87531i			0.669675i	−0.942276	+	0.334838i	$0.891318\pi$
$54$	−5.72572	+	11.9796i	−0.779172	+	1.63021i
$55$	−2.21001	−	3.82785i	−0.297998	−	0.516148i
$56$	−3.23164	+	5.59737i	−0.431846	+	0.747979i
$57$	2.93272	−	2.59326i	0.388449	−	0.343486i
$58$	−4.45816	+	1.19456i	−0.585385	+	0.156853i
$59$	10.8376	−	2.90392i	1.41093	−	0.378058i	0.528674	−	0.848825i	$-0.322690\pi$
$59$	10.8376	−	2.90392i	1.41093	−	0.378058i	0.882257	+	0.470767i	$0.156023\pi$
$60$	17.6691	−	15.6239i	2.28108	−	2.01704i
$61$	4.67806	−	8.10263i	0.598964	−	1.03744i	−0.394011	−	0.919106i	$-0.628913\pi$
$61$	4.67806	−	8.10263i	0.598964	−	1.03744i	0.992974	−	0.118330i	$-0.0377540\pi$
$62$	7.24623	+	12.5508i	0.920272	+	1.59396i
$63$	−2.78095	−	1.12530i	−0.350367	−	0.141775i
$64$			0.743175i			0.0928968i
$65$	10.8362	−	0.287246i	1.34406	−	0.0356284i
$66$	−0.398961	+	6.49453i	−0.0491087	+	0.799421i
$67$	−0.941798	+	3.51484i	−0.115059	+	0.429406i	−0.999291	−	0.0376415i	$-0.988016\pi$
$67$	−0.941798	+	3.51484i	−0.115059	+	0.429406i	0.884232	+	0.467047i	$0.154682\pi$
$68$	−31.5106	+	18.1927i	−3.82122	+	2.20618i
$69$	−1.61160	−	1.06731i	−0.194013	−	0.128489i
$70$	5.43222	+	5.43222i	0.649275	+	0.649275i
$71$	1.95774	+	7.30640i	0.232341	+	0.867110i	0.979329	+	0.202272i	$0.0648326\pi$
$71$	1.95774	+	7.30640i	0.232341	+	0.867110i	−0.746988	+	0.664838i	$0.768501\pi$
$72$	−19.2026	+	2.68830i	−2.26305	+	0.316820i
$73$	−10.5269	+	10.5269i	−1.23207	+	1.23207i	−0.268909	+	0.963165i	$0.586663\pi$
$73$	−10.5269	+	10.5269i	−1.23207	+	1.23207i	−0.963165	+	0.268909i	$0.913337\pi$
$74$	15.3387	+	8.85579i	1.78308	+	1.02946i
$75$	−3.11969	−	6.26131i	−0.360231	−	0.722994i
$76$	9.88862	+	2.64965i	1.13430	+	0.303935i
$77$	−1.47017			−0.167542
$78$	−13.5333	−	8.45551i	−1.53235	−	0.957399i
$79$	−6.82850			−0.768267			−0.384133	−	0.923278i	$-0.625500\pi$
$79$	−6.82850			−0.768267			−0.384133	+	0.923278i	$0.625500\pi$
$80$	21.6542	+	5.80223i	2.42101	+	0.648709i
$81$	−2.47151	−	8.65400i	−0.274612	−	0.961555i
$82$	20.0628	+	11.5833i	2.21556	+	1.27916i
$83$	1.67181	−	1.67181i	0.183505	−	0.183505i	−0.609376	−	0.792881i	$-0.708580\pi$
$83$	1.67181	−	1.67181i	0.183505	−	0.183505i	0.792881	+	0.609376i	$0.208580\pi$
$84$	−1.56202	−	7.68807i	−0.170430	−	0.838837i
$85$	6.25084	+	23.3284i	0.677999	+	2.53033i
$86$	−11.1128	−	11.1128i	−1.19832	−	1.19832i
$87$	1.72743	−	2.60835i	0.185200	−	0.279644i
$88$	−8.22910	+	4.75107i	−0.877225	+	0.506466i
$89$	−1.30042	+	4.85323i	−0.137844	+	0.514442i	0.862126	+	0.506694i	$0.169133\pi$
$89$	−1.30042	+	4.85323i	−0.137844	+	0.514442i	−0.999970	+	0.00774733i	$0.997534\pi$
$90$	−2.82092	+	22.8737i	−0.297351	+	2.41110i
$91$	1.71940	−	3.16917i	0.180242	−	0.332220i
$92$		−	5.05482i		−	0.527001i
$93$	−9.31502	−	3.11952i	−0.965923	−	0.323480i
$94$	−7.61466	−	13.1890i	−0.785392	−	1.36034i
$95$	3.39764	−	5.88489i	0.348591	−	0.603777i
$96$	−7.02992	−	7.95015i	−0.717488	−	0.811409i
$97$	3.45015	−	0.924465i	0.350310	−	0.0938652i	−0.0793733	−	0.996845i	$-0.525292\pi$
$97$	3.45015	−	0.924465i	0.350310	−	0.0938652i	0.429683	+	0.902980i	$0.358625\pi$
$98$	2.46820	−	0.661352i	0.249326	−	0.0668066i
$99$	−2.71353	−	3.47698i	−0.272720	−	0.349450i
$100$	9.14674	−	15.8426i	0.914674	−	1.58426i
$101$	0.921061	+	1.59532i	0.0916490	+	0.158741i	0.908205	−	0.418525i	$-0.137453\pi$
$101$	0.921061	+	1.59532i	0.0916490	+	0.158741i	−0.816556	+	0.577266i	$0.804120\pi$
$102$	11.2903	−	33.7133i	1.11791	−	3.33811i
$103$			8.86524i			0.873518i	0.899579	+	0.436759i	$0.143874\pi$
$103$			8.86524i			0.873518i	−0.899579	+	0.436759i	$0.856126\pi$
$104$	−0.617519	−	23.2955i	−0.0605527	−	2.28431i
$105$	−5.19755	−	0.319287i	−0.507229	−	0.0311592i
$106$	3.22430	−	12.0332i	0.313171	−	1.16877i
$107$	8.80632	−	5.08433i	0.851339	−	0.491521i	−0.00976347	−	0.999952i	$-0.503108\pi$
$107$	8.80632	−	5.08433i	0.851339	−	0.491521i	0.861102	+	0.508432i	$0.169775\pi$
$108$	15.2993	−	17.8842i	1.47218	−	1.72091i
$109$	3.45876	+	3.45876i	0.331289	+	0.331289i	0.853076	−	0.521787i	$-0.174734\pi$
$109$	3.45876	+	3.45876i	0.331289	+	0.331289i	−0.521787	+	0.853076i	$0.674734\pi$
$110$	2.92319	+	10.9095i	0.278715	+	1.04018i
$111$	−11.7652	+	2.39038i	−1.11670	+	0.226885i
$112$	5.27263	−	5.27263i	0.498217	−	0.498217i
$113$	−11.6603	−	6.73208i	−1.09691	−	0.633301i	−0.161502	−	0.986872i	$-0.551634\pi$
$113$	−11.6603	−	6.73208i	−1.09691	−	0.633301i	−0.935408	+	0.353571i	$0.884967\pi$
$114$	−8.95360	+	4.46112i	−0.838582	+	0.417822i
$115$	−3.24090	−	0.868396i	−0.302215	−	0.0809784i
$116$	8.18117			0.759602
$117$	10.6687	−	1.78301i	0.986320	−	0.164839i
$118$	−28.6698			−2.63927
$119$	7.75943	+	2.07913i	0.711305	+	0.190594i
$120$	−30.1244	+	15.0095i	−2.74997	+	1.37017i
$121$	7.65444	+	4.41930i	0.695859	+	0.401754i
$122$	−16.9051	+	16.9051i	−1.53051	+	1.53051i
$123$	−15.3887	+	3.12659i	−1.38755	+	0.281915i
$124$	−6.64878	−	24.8136i	−0.597078	−	2.22832i
$125$	2.04334	+	2.04334i	0.182761	+	0.182761i
$126$	6.11972	+	4.61666i	0.545188	+	0.411285i
$127$	7.79947	−	4.50303i	0.692091	−	0.399579i	−0.112304	−	0.993674i	$-0.535823\pi$
$127$	7.79947	−	4.50303i	0.692091	−	0.399579i	0.804395	+	0.594095i	$0.202490\pi$
$128$	−2.68013	+	10.0024i	−0.236892	+	0.884094i
$129$	10.6327	+	0.653171i	0.936158	+	0.0575085i
$130$	−26.9358	−	6.45754i	−2.36242	−	0.566363i
$131$			7.57076i			0.661461i	0.943725	+	0.330730i	$0.107295\pi$
$131$			7.57076i			0.661461i	−0.943725	+	0.330730i	$0.892705\pi$
$132$	3.66262	−	10.9367i	0.318790	−	0.951919i
$133$	−1.13011	−	1.95741i	−0.0979932	−	0.169729i
$134$	4.64909	−	8.05246i	0.401620	−	0.695627i
$135$	−8.83813	−	12.8816i	−0.760665	−	1.10867i
$136$	50.1514	−	13.4380i	4.30044	−	1.15230i
$137$	−17.1677	+	4.60008i	−1.46674	+	0.393011i	−0.901811	−	0.432130i	$-0.857762\pi$
$137$	−17.1677	+	4.60008i	−1.46674	+	0.393011i	−0.564927	+	0.825141i	$0.691096\pi$
$138$	3.27187	+	3.70017i	0.278520	+	0.314979i
$139$	−4.84756	+	8.39621i	−0.411164	+	0.712157i	−0.995017	−	0.0997019i	$-0.968211\pi$
$139$	−4.84756	+	8.39621i	−0.411164	+	0.712157i	0.583853	+	0.811859i	$0.301544\pi$
$140$	−6.80873	−	11.7931i	−0.575443	−	0.996697i
$141$	9.78864	+	3.27814i	0.824352	+	0.276069i
$142$		−	19.3284i		−	1.62200i
$143$	4.51877	−	2.77111i	0.377878	−	0.231732i
$144$	22.2017	+	2.73804i	1.85014	+	0.228170i
$145$	1.40549	−	5.24536i	0.116720	−	0.435603i
$146$	32.9443	−	19.0204i	2.72649	−	1.57414i
$147$	−0.956368	+	1.44408i	−0.0788799	+	0.119106i
$148$	−22.1996	−	22.1996i	−1.82480	−	1.82480i
$149$	2.71898	+	10.1474i	0.222748	+	0.831306i	0.983294	+	0.182023i	$0.0582644\pi$
$149$	2.71898	+	10.1474i	0.222748	+	0.831306i	−0.760547	+	0.649283i	$0.775069\pi$
$150$	3.55909	+	17.5174i	0.290598	+	1.43029i
$151$	−8.34949	+	8.34949i	−0.679472	+	0.679472i	−0.959881	−	0.280409i	$-0.909530\pi$
$151$	−8.34949	+	8.34949i	−0.679472	+	0.679472i	0.280409	+	0.959881i	$0.409530\pi$
$152$	−12.6513	−	7.30424i	−1.02616	−	0.592452i
$153$	9.40457	+	22.1887i	0.760315	+	1.79385i
$154$	3.62868	+	0.972302i	0.292407	+	0.0783503i
$155$	−17.0515			−1.36961
$156$	19.2922	+	20.6860i	1.54461	+	1.65621i
$157$	10.3032			0.822284			0.411142	−	0.911571i	$-0.365130\pi$
$157$	10.3032			0.822284			0.411142	+	0.911571i	$0.365130\pi$
$158$	16.8541	+	4.51605i	1.34084	+	0.359277i
$159$	3.76581	+	7.55809i	0.298648	+	0.599395i
$160$	−15.9530	−	9.21048i	−1.26120	−	0.728153i
$161$	−0.789134	+	0.789134i	−0.0621924	+	0.0621924i
$162$	0.376834	+	22.9943i	0.0296069	+	1.80660i
$163$	0.239946	+	0.895490i	0.0187940	+	0.0701402i	0.974686	−	0.223578i	$-0.0717738\pi$
$163$	0.239946	+	0.895490i	0.0187940	+	0.0701402i	−0.955892	+	0.293719i	$0.905107\pi$
$164$	−29.0368	−	29.0368i	−2.26740	−	2.26740i
$165$	−6.38286	−	4.22717i	−0.496905	−	0.329085i
$166$	−5.23202	+	3.02071i	−0.406083	+	0.234452i
$167$	3.18488	−	11.8861i	0.246453	−	0.919777i	−0.726194	−	0.687490i	$-0.758713\pi$
$167$	3.18488	−	11.8861i	0.246453	−	0.919777i	0.972647	−	0.232287i	$-0.0746208\pi$
$168$	−0.686402	+	11.1737i	−0.0529570	+	0.862067i
$169$	0.688726	+	12.9817i	0.0529789	+	0.998596i
$170$		−	61.7133i		−	4.73319i
$171$	2.54344	−	6.28558i	0.194502	−	0.480670i
$172$	13.9287	+	24.1253i	1.06206	+	1.83953i
$173$	3.29038	−	5.69910i	0.250163	−	0.433295i	−0.713408	−	0.700749i	$-0.752849\pi$
$173$	3.29038	−	5.69910i	0.250163	−	0.433295i	0.963570	+	0.267455i	$0.0861826\pi$
$174$	−5.98867	+	5.29549i	−0.454000	+	0.401450i
$175$	−3.90121	+	1.04533i	−0.294904	+	0.0790193i
$176$	10.5890	−	2.83731i	0.798175	−	0.213870i
$177$	14.5582	−	12.8731i	1.09426	−	0.967600i
$178$	6.41939	−	11.1187i	0.481154	−	0.833383i
$179$	2.44684	+	4.23805i	0.182885	+	0.316767i	0.942862	−	0.333184i	$-0.108123\pi$
$179$	2.44684	+	4.23805i	0.182885	+	0.316767i	−0.759976	+	0.649951i	$0.774790\pi$
$180$	15.3238	−	37.8695i	1.14217	−	2.82263i
$181$			2.54202i			0.188947i	0.995527	+	0.0944736i	$0.0301168\pi$
$181$			2.54202i			0.188947i	−0.995527	+	0.0944736i	$0.969883\pi$
$182$	−6.33976	+	6.68502i	−0.469934	+	0.495527i
$183$	0.993621	−	16.1748i	0.0734506	−	1.19567i
$184$	−1.86687	+	6.96727i	−0.137628	+	0.513634i
$185$	−18.0471	+	10.4195i	−1.32685	+	0.766057i
$186$	20.9282	+	13.8601i	1.53453	+	1.01627i
$187$	8.35102	+	8.35102i	0.610687	+	0.610687i
$188$	6.98683	+	26.0752i	0.509567	+	1.90173i
$189$	−5.18046	+	0.403541i	−0.376823	+	0.0293533i
$190$	−12.2781	+	12.2781i	−0.890743	+	0.890743i
$191$	18.8492	+	10.8826i	1.36388	+	0.787438i	0.990138	−	0.140093i	$-0.0447402\pi$
$191$	18.8492	+	10.8826i	1.36388	+	0.787438i	0.373745	+	0.927531i	$0.378073\pi$
$192$	0.574046	+	1.15213i	0.0414282	+	0.0831476i
$193$	−10.6918	−	2.86487i	−0.769614	−	0.206218i	−0.147413	−	0.989075i	$-0.547095\pi$
$193$	−10.6918	−	2.86487i	−0.769614	−	0.206218i	−0.622201	+	0.782857i	$0.713761\pi$
$194$	−9.12706			−0.655285
$195$	16.5772	−	8.81542i	1.18712	−	0.631285i
$196$	−4.52939			−0.323528
$197$	0.669079	+	0.179279i	0.0476699	+	0.0127731i	0.282575	−	0.959245i	$-0.408811\pi$
$197$	0.669079	+	0.179279i	0.0476699	+	0.0127731i	−0.234905	+	0.972018i	$0.575478\pi$
$198$	4.39803	+	10.3765i	0.312554	+	0.737425i
$199$	−12.9539	−	7.47892i	−0.918276	−	0.530167i	−0.0351911	−	0.999381i	$-0.511204\pi$
$199$	−12.9539	−	7.47892i	−0.918276	−	0.530167i	−0.883085	+	0.469214i	$0.844537\pi$
$200$	−18.4584	+	18.4584i	−1.30521	+	1.30521i
$201$	1.25490	+	6.17644i	0.0885135	+	0.435653i
$202$	−1.21829	−	4.54672i	−0.0857186	−	0.319906i
$203$	−1.27720	−	1.27720i	−0.0896421	−	0.0896421i
$204$	−34.7977	+	52.5432i	−2.43633	+	3.67876i
$205$	−23.6054	+	13.6286i	−1.64867	+	0.951861i
$206$	5.86304	−	21.8812i	0.408498	−	1.52453i
$207$	−3.32284	−	0.409792i	−0.230953	−	0.0284825i
$208$	−6.26782	+	26.1444i	−0.434595	+	1.81279i
$209$		−	3.32292i		−	0.229851i
$210$	12.6174	+	4.22548i	0.870686	+	0.291586i
$211$	−11.5575	−	20.0182i	−0.795652	−	1.37811i	−0.922424	−	0.386178i	$-0.873795\pi$
$211$	−11.5575	−	20.0182i	−0.795652	−	1.37811i	0.126772	−	0.991932i	$-0.459538\pi$
$212$	−11.0411	+	19.1238i	−0.758306	+	1.31342i
$213$	8.67868	+	9.81474i	0.594654	+	0.672495i
$214$	−25.0983	+	6.72506i	−1.71568	+	0.459716i
$215$	17.8608	−	4.78579i	1.21810	−	0.326388i
$216$	−27.6928	+	19.0002i	−1.88426	+	1.29280i
$217$	−2.83580	+	4.91175i	−0.192507	+	0.333431i
$218$	−6.24946	−	10.8244i	−0.423267	−	0.733119i
$219$	−8.18835	+	24.4507i	−0.553318	+	1.65223i
$220$		−	20.0200i		−	1.34975i
$221$	−27.7685	+	8.23514i	−1.86791	+	0.553956i
$222$	30.6196	+	1.88097i	2.05505	+	0.126243i
$223$	3.26006	−	12.1667i	0.218310	−	0.814742i	−0.766666	−	0.642047i	$-0.778086\pi$
$223$	3.26006	−	12.1667i	0.218310	−	0.814742i	0.984975	−	0.172696i	$-0.0552478\pi$
$224$	−5.30624	+	3.06356i	−0.354538	+	0.204693i
$225$	−9.67278	−	7.29705i	−0.644852	−	0.486470i
$226$	24.3277	+	24.3277i	1.61825	+	1.61825i
$227$	−1.17717	−	4.39325i	−0.0781315	−	0.291591i	0.915794	−	0.401649i	$-0.131563\pi$
$227$	−1.17717	−	4.39325i	−0.0781315	−	0.291591i	−0.993925	+	0.110059i	$0.964896\pi$
$228$	17.3768	−	3.53052i	1.15080	−	0.233814i
$229$	10.1200	−	10.1200i	0.668750	−	0.668750i	−0.288676	−	0.957427i	$-0.593215\pi$
$229$	10.1200	−	10.1200i	0.668750	−	0.668750i	0.957427	+	0.288676i	$0.0932151\pi$
$230$	7.42487	+	4.28675i	0.489581	+	0.282660i
$231$	−2.27918	+	1.13560i	−0.149959	+	0.0747168i
$232$	−11.2764	−	3.02151i	−0.740334	−	0.198372i
$233$	−22.2155			−1.45539			−0.727694	−	0.685902i	$-0.759408\pi$
$233$	−22.2155			−1.45539			−0.727694	+	0.685902i	$0.759408\pi$
$234$	−27.5116	−	2.65494i	−1.79849	−	0.173559i
$235$	17.9184			1.16887
$236$	49.0876	+	13.1530i	3.19533	+	0.856187i
$237$	−10.5861	+	5.27450i	−0.687640	+	0.342616i
$238$	−17.7768	−	10.2634i	−1.15230	−	0.665279i
$239$	4.70120	−	4.70120i	0.304095	−	0.304095i	−0.538518	−	0.842614i	$-0.681016\pi$
$239$	4.70120	−	4.70120i	0.304095	−	0.304095i	0.842614	+	0.538518i	$0.181016\pi$
$240$	38.0518	−	7.73117i	2.45623	−	0.499045i
$241$	1.62020	+	6.04667i	0.104366	+	0.389500i	0.998273	−	0.0587538i	$-0.0187127\pi$
$241$	1.62020	+	6.04667i	0.104366	+	0.389500i	−0.893906	+	0.448254i	$0.852046\pi$
$242$	−15.9700	−	15.9700i	−1.02659	−	1.02659i
$243$	−10.5161	−	11.5070i	−0.674607	−	0.738177i
$244$	36.7000	−	21.1888i	2.34948	−	1.35647i
$245$	−0.778130	+	2.90402i	−0.0497129	+	0.185531i
$246$	40.0501	+	2.46029i	2.55350	+	0.156862i
$247$	7.16305	+	3.88623i	0.455774	+	0.247275i
$248$			36.6571i			2.32773i
$249$	1.30042	−	3.88312i	0.0824110	−	0.246083i
$250$	−3.69200	−	6.39472i	−0.233502	−	0.404438i
$251$	6.94283	−	12.0253i	0.438227	−	0.759032i	−0.559326	−	0.828948i	$-0.688940\pi$
$251$	6.94283	−	12.0253i	0.438227	−	0.759032i	0.997553	+	0.0699160i	$0.0222731\pi$
$252$	−8.36001	−	10.7121i	−0.526631	−	0.674799i
$253$	−1.58481	+	0.424649i	−0.0996363	+	0.0266975i
$254$	−22.2287	+	5.95617i	−1.39475	+	0.373723i
$255$	27.7100	+	31.3373i	1.73527	+	1.96242i
$256$	13.9734	−	24.2026i	0.873335	−	1.51266i
$257$	−4.17898	−	7.23820i	−0.260677	−	0.451507i	0.705745	−	0.708466i	$-0.250613\pi$
$257$	−4.17898	−	7.23820i	−0.260677	−	0.451507i	−0.966422	+	0.256960i	$0.917279\pi$
$258$	−25.8117	−	8.64412i	−1.60697	−	0.538160i
$259$			6.93139i			0.430696i
$260$	43.1561	+	23.4139i	2.67643	+	1.45207i
$261$	0.663243	−	5.37797i	0.0410537	−	0.332888i
$262$	5.00694	−	18.6862i	0.309330	−	1.15443i
$263$	4.51049	−	2.60413i	0.278129	−	0.160578i	−0.354447	−	0.935076i	$-0.615331\pi$
$263$	4.51049	−	2.60413i	0.278129	−	0.160578i	0.632576	+	0.774498i	$0.281998\pi$
$264$	−9.08754	+	13.7218i	−0.559300	+	0.844520i
$265$	10.3644	+	10.3644i	0.636679	+	0.636679i
$266$	1.49480	+	5.57869i	0.0916524	+	0.342051i
$267$	1.73274	+	8.52834i	0.106042	+	0.521926i
$268$	−11.6543	+	11.6543i	−0.711900	+	0.711900i
$269$	19.2457	+	11.1115i	1.17343	+	0.677479i	0.954485	−	0.298259i	$-0.0964058\pi$
$269$	19.2457	+	11.1115i	1.17343	+	0.677479i	0.218943	+	0.975738i	$0.429739\pi$
$270$	13.2950	+	37.6395i	0.809106	+	2.29067i
$271$	11.5907	+	3.10572i	0.704084	+	0.188659i	0.593059	−	0.805159i	$-0.297920\pi$
$271$	11.5907	+	3.10572i	0.704084	+	0.188659i	0.111025	+	0.993818i	$0.464587\pi$
$272$	−59.9002			−3.63198
$273$	0.217602	−	6.24121i	0.0131699	−	0.377735i
$274$	45.4156			2.74366
$275$	−5.73546	−	1.53681i	−0.345861	−	0.0926732i
$276$	−3.90446	−	7.83638i	−0.235021	−	0.471694i
$277$	−7.07853	−	4.08679i	−0.425308	−	0.245552i	0.272038	−	0.962287i	$-0.412302\pi$
$277$	−7.07853	−	4.08679i	−0.425308	−	0.245552i	−0.697346	+	0.716735i	$0.745636\pi$
$278$	17.5176	−	17.5176i	1.05064	−	1.05064i
$279$	−16.8505	+	2.35902i	−1.00881	+	0.141231i
$280$	5.02928	+	18.7695i	0.300557	+	1.12169i
$281$	−9.33069	−	9.33069i	−0.556623	−	0.556623i	0.371722	−	0.928344i	$-0.378768\pi$
$281$	−9.33069	−	9.33069i	−0.556623	−	0.556623i	−0.928344	+	0.371722i	$0.878768\pi$
$282$	−21.9923	−	14.5648i	−1.30962	−	0.867323i
$283$	26.2854	−	15.1759i	1.56250	−	0.902111i	0.565500	−	0.824748i	$-0.308683\pi$
$283$	26.2854	−	15.1759i	1.56250	−	0.902111i	0.997003	−	0.0773629i	$-0.0246500\pi$
$284$	−8.86739	+	33.0936i	−0.526183	+	1.96374i
$285$	0.721661	−	11.7476i	0.0427475	−	0.695870i
$286$	−12.9859	+	3.85115i	−0.767872	+	0.227723i
$287$			9.06618i			0.535160i
$288$	−17.0392	−	6.89486i	−1.00405	−	0.406284i
$289$	−23.7657	−	41.1635i	−1.39799	−	2.42138i
$290$	−6.93805	+	12.0171i	−0.407417	+	0.705666i
$291$	4.63461	−	4.09816i	0.271686	−	0.240238i
$292$	−65.1325	+	17.4522i	−3.81159	+	1.02131i
$293$	−14.8490	+	3.97877i	−0.867486	+	0.232442i	−0.665001	−	0.746843i	$-0.731569\pi$
$293$	−14.8490	+	3.97877i	−0.867486	+	0.232442i	−0.202486	+	0.979285i	$0.564902\pi$
$294$	3.31555	−	2.93178i	0.193367	−	0.170985i
$295$	16.8661	−	29.2129i	0.981981	−	1.70084i
$296$	22.3998	+	38.7976i	1.30196	+	2.25506i
$297$	−6.89243	−	3.29429i	−0.399940	−	0.191154i
$298$		−	26.8440i		−	1.55503i
$299$	0.938080	−	3.91293i	0.0542505	−	0.226291i
$300$	1.94277	−	31.6256i	0.112166	−	1.82591i
$301$	1.59183	−	5.94080i	0.0917518	−	0.342422i
$302$	26.1302	−	15.0863i	1.50362	−	0.868117i
$303$	2.66017	+	1.76175i	0.152823	+	0.101210i
$304$	11.9173	+	11.9173i	0.683506	+	0.683506i
$305$	−7.28028	−	27.1704i	−0.416867	−	1.55577i
$306$	−8.53783	−	60.9858i	−0.488075	−	3.48633i
$307$	−11.5632	+	11.5632i	−0.659949	+	0.659949i	−0.955368	−	0.295419i	$-0.904541\pi$
$307$	−11.5632	+	11.5632i	−0.659949	+	0.659949i	0.295419	+	0.955368i	$0.404541\pi$
$308$	−5.76686	−	3.32950i	−0.328597	−	0.189716i
$309$	6.84772	+	13.7436i	0.389553	+	0.781845i
$310$	42.0864	+	11.2770i	2.39035	+	0.640492i
$311$	−7.32969			−0.415629			−0.207814	−	0.978168i	$-0.566635\pi$
$311$	−7.32969			−0.415629			−0.207814	+	0.978168i	$0.566635\pi$
$312$	−18.9513	−	35.6375i	−1.07291	−	2.01758i
$313$	1.28087			0.0723988			0.0361994	−	0.999345i	$-0.488475\pi$
$313$	1.28087			0.0723988			0.0361994	+	0.999345i	$0.488475\pi$
$314$	−25.4303	−	6.81404i	−1.43512	−	0.384538i
$315$	−8.30428	+	3.51973i	−0.467893	+	0.198314i
$316$	−26.7853	−	15.4645i	−1.50679	−	0.869946i
$317$	19.3797	−	19.3797i	1.08847	−	1.08847i	0.0927880	−	0.995686i	$-0.470422\pi$
$317$	19.3797	−	19.3797i	1.08847	−	1.08847i	0.995686	−	0.0927880i	$-0.0295779\pi$
$318$	−4.29621	−	21.1454i	−0.240919	−	1.18577i
$319$	−0.687289	−	2.56500i	−0.0384808	−	0.143612i
$320$	1.57991	+	1.57991i	0.0883196	+	0.0883196i
$321$	9.72498	−	14.6843i	0.542796	−	0.819600i
$322$	2.46963	−	1.42584i	0.137627	−	0.0794592i
$323$	−4.69931	+	17.5381i	−0.261476	+	0.975843i
$324$	9.90402	−	39.5431i	0.550223	−	2.19684i
$325$	10.0206	−	10.5663i	0.555841	−	0.586112i
$326$		−	2.36894i		−	0.131203i
$327$	8.03367	+	2.69041i	0.444263	+	0.148780i
$328$	29.2986	+	50.7467i	1.61775	+	2.80202i
$329$	2.97998	−	5.16148i	0.164292	−	0.284562i
$330$	12.9585	+	14.6548i	0.713343	+	0.806721i
$331$	−4.95745	+	1.32834i	−0.272486	+	0.0730124i	−0.392474	−	0.919763i	$-0.628381\pi$
$331$	−4.95745	+	1.32834i	−0.272486	+	0.0730124i	0.119989	+	0.992775i	$0.461714\pi$
$332$	10.3439	−	2.77165i	0.567697	−	0.152114i
$333$	−16.3929	+	12.7934i	−0.898323	+	0.701076i
$334$	−15.7218	+	27.2310i	−0.860261	+	1.49002i
$335$	5.47000	+	9.47432i	0.298858	+	0.517638i
$336$	4.10134	−	12.2468i	0.223746	−	0.668115i
$337$			9.99760i			0.544604i	0.962212	+	0.272302i	$0.0877850\pi$
$337$			9.99760i			0.544604i	−0.962212	+	0.272302i	$0.912215\pi$
$338$	6.88559	−	32.4970i	0.374527	−	1.76760i
$339$	−23.2767	−	1.42990i	−1.26422	−	0.0776613i
$340$	−28.3125	+	105.664i	−1.53546	+	5.73042i
$341$	−7.22112	+	4.16911i	−0.391045	+	0.225770i
$342$	−10.4347	+	13.8320i	−0.564244	+	0.747946i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−10.2885	−	38.3971i	−0.554717	−	2.07023i
$345$	−5.69506	+	1.15709i	−0.306612	+	0.0622958i
$346$	−11.8904	+	11.8904i	−0.639233	+	0.639233i
$347$	−12.3108	−	7.10766i	−0.660880	−	0.381559i	0.131732	−	0.991285i	$-0.457946\pi$
$347$	−12.3108	−	7.10766i	−0.660880	−	0.381559i	−0.792612	+	0.609726i	$0.791279\pi$
$348$	12.6831	−	6.31933i	0.679884	−	0.338752i
$349$	−4.41926	−	1.18414i	−0.236557	−	0.0633854i	0.138593	−	0.990349i	$-0.455742\pi$
$349$	−4.41926	−	1.18414i	−0.236557	−	0.0633854i	−0.375150	+	0.926964i	$0.622409\pi$
$350$	10.3203			0.551643
$351$	15.1622	−	11.0049i	0.809298	−	0.587398i
$352$	−9.00792			−0.480124
$353$	23.8051	+	6.37855i	1.26702	+	0.339496i	0.828887	−	0.559416i	$-0.188975\pi$
$353$	23.8051	+	6.37855i	1.26702	+	0.339496i	0.438129	+	0.898912i	$0.355641\pi$
$354$	−44.4461	+	22.1452i	−2.36229	+	1.17701i
$355$	19.6946	+	11.3707i	1.04528	+	0.603492i
$356$	−16.0921	+	16.0921i	−0.852879	+	0.852879i
$357$	13.6352	−	2.77033i	0.721653	−	0.146622i
$358$	−3.23645	−	12.0786i	−0.171052	−	0.638373i
$359$	−8.64329	−	8.64329i	−0.456176	−	0.456176i	0.441222	−	0.897398i	$-0.354545\pi$
$359$	−8.64329	−	8.64329i	−0.456176	−	0.456176i	−0.897398	+	0.441222i	$0.854545\pi$
$360$	−35.1076	+	46.5377i	−1.85033	+	2.45275i
$361$	−12.0303	+	6.94569i	−0.633173	+	0.365563i
$362$	1.68117	−	6.27422i	0.0883605	−	0.329766i
$363$	15.2801	+	0.938660i	0.801997	+	0.0492669i
$364$	13.9217	−	8.53739i	0.729695	−	0.447481i
$365$			44.7579i			2.34274i
$366$	−13.1497	+	39.2654i	−0.687345	+	2.05244i
$367$	9.62012	+	16.6625i	0.502166	+	0.869778i	0.999997	+	0.00250325i	$0.000796811\pi$
$367$	9.62012	+	16.6625i	0.502166	+	0.869778i	−0.497831	+	0.867274i	$0.665870\pi$
$368$	4.16081	−	7.20674i	0.216897	−	0.375677i
$369$	−21.4417	+	16.7337i	−1.11621	+	0.871119i
$370$	51.4348	−	13.7819i	2.67397	−	0.716488i
$371$	4.70919	−	1.26182i	0.244489	−	0.0655106i
$372$	−29.4740	−	33.3323i	−1.52816	−	1.72820i
$373$	−5.08940	+	8.81510i	−0.263519	+	0.456429i	−0.967175	−	0.254113i	$-0.918217\pi$
$373$	−5.08940	+	8.81510i	−0.263519	+	0.456429i	0.703655	+	0.710541i	$0.251550\pi$
$374$	−15.0890	−	26.1349i	−0.780234	−	1.35141i
$375$	4.74606	+	1.58942i	0.245085	+	0.0820771i
$376$		−	38.5210i		−	1.98657i
$377$	6.33303	+	1.51827i	0.326168	+	0.0781949i
$378$	13.0533	+	2.43009i	0.671389	+	0.124990i
$379$	2.06543	−	7.70828i	0.106094	−	0.395948i	−0.892373	−	0.451299i	$-0.850961\pi$
$379$	2.06543	−	7.70828i	0.106094	−	0.395948i	0.998467	+	0.0553505i	$0.0176276\pi$
$380$	26.6550	−	15.3893i	1.36737	−	0.789453i
$381$	8.61310	−	13.0054i	0.441262	−	0.666289i
$382$	−39.3265	−	39.3265i	−2.01212	−	2.01212i
$383$	−9.81073	−	36.6141i	−0.501305	−	1.87089i	−0.491383	−	0.870944i	$-0.663508\pi$
$383$	−9.81073	−	36.6141i	−0.501305	−	1.87089i	−0.00992170	−	0.999951i	$-0.503158\pi$
$384$	3.57113	+	17.5767i	0.182239	+	0.896955i
$385$	−3.12543	+	3.12543i	−0.159287	+	0.159287i
$386$	24.4949	+	14.1421i	1.24676	+	0.719815i
$387$	16.9882	−	7.20037i	0.863558	−	0.366015i
$388$	15.6271	+	4.18727i	0.793346	+	0.212576i
$389$	12.3518			0.626260			0.313130	−	0.949710i	$-0.398622\pi$
$389$	12.3518			0.626260			0.313130	+	0.949710i	$0.398622\pi$
$390$	−46.7459	+	10.7949i	−2.36707	+	0.546619i
$391$	8.96502			0.453381
$392$	6.24305	+	1.67282i	0.315322	+	0.0844902i
$393$	5.84784	+	11.7368i	0.294984	+	0.592043i
$394$	−1.53285	−	0.884993i	−0.0772240	−	0.0445853i
$395$	−14.5167	+	14.5167i	−0.730413	+	0.730413i
$396$	−2.76971	−	19.7840i	−0.139183	−	0.994186i
$397$	8.51392	+	31.7744i	0.427301	+	1.59471i	0.758845	+	0.651271i	$0.225764\pi$
$397$	8.51392	+	31.7744i	0.427301	+	1.59471i	−0.331544	+	0.943440i	$0.607570\pi$
$398$	27.0265	+	27.0265i	1.35472	+	1.35472i
$399$	−3.26394	−	2.16161i	−0.163401	−	0.108216i
$400$	26.0813	−	15.0580i	1.30406	−	0.752902i
$401$	−1.65736	+	6.18536i	−0.0827647	+	0.308882i	−0.994882	−	0.101048i	$-0.967780\pi$
$401$	−1.65736	+	6.18536i	−0.0827647	+	0.308882i	0.912117	+	0.409930i	$0.134447\pi$
$402$	0.987468	−	16.0746i	0.0492504	−	0.801729i
$403$	−0.541879	−	20.4421i	−0.0269929	−	1.01829i
$404$			8.34369i			0.415114i
$405$	−23.6516	−	13.1433i	−1.17526	−	0.653096i
$406$	2.30771	+	3.99707i	0.114530	+	0.198371i
$407$	−5.09517	+	8.82510i	−0.252558	+	0.437444i
$408$	67.3687	−	59.5708i	3.33525	−	2.94919i
$409$	−20.2784	+	5.43357i	−1.00270	+	0.268673i	−0.722576	−	0.691291i	$-0.757042\pi$
$409$	−20.2784	+	5.43357i	−1.00270	+	0.268673i	−0.280124	+	0.959964i	$0.590376\pi$
$410$	67.2761	−	18.0266i	3.32253	−	0.890269i
$411$	−23.0615	+	20.3922i	−1.13754	+	1.00587i
$412$	−20.0771	+	34.7745i	−0.989127	+	1.71322i
$413$	−5.60994	−	9.71670i	−0.276047	−	0.478127i
$414$	7.93041	+	3.20901i	0.389758	+	0.157714i
$415$		−	7.10818i		−	0.348927i
$416$	10.5350	−	19.4179i	0.516519	−	0.952041i
$417$	−1.02962	+	16.7608i	−0.0504208	+	0.820781i
$418$	−2.19762	+	8.20163i	−0.107489	+	0.401155i
$419$	−14.2429	+	8.22311i	−0.695809	+	0.401725i	−0.805785	−	0.592209i	$-0.798256\pi$
$419$	−14.2429	+	8.22311i	−0.695809	+	0.401725i	0.109976	+	0.993934i	$0.464923\pi$
$420$	−19.6647	−	13.0233i	−0.959538	−	0.635473i
$421$	−8.53586	−	8.53586i	−0.416013	−	0.416013i	0.467814	−	0.883827i	$-0.345042\pi$
$421$	−8.53586	−	8.53586i	−0.416013	−	0.416013i	−0.883827	+	0.467814i	$0.845042\pi$
$422$	15.2872	+	57.0525i	0.744168	+	2.77727i
$423$	17.7072	−	2.47896i	0.860955	−	0.120531i
$424$	22.2813	−	22.2813i	1.08208	−	1.08208i
$425$	28.0978	+	16.2223i	1.36294	+	0.786896i
$426$	−14.9297	−	29.9644i	−0.723347	−	1.45178i
$427$	−9.03731	−	2.42154i	−0.437346	−	0.117187i
$428$	46.0579			2.22629
$429$	4.86488	−	7.78639i	0.234879	−	0.375930i
$430$	−47.2492			−2.27856
$431$	−12.2262	−	3.27599i	−0.588914	−	0.157799i	−0.0479570	−	0.998849i	$-0.515271\pi$
$431$	−12.2262	−	3.27599i	−0.588914	−	0.157799i	−0.540957	+	0.841050i	$0.681938\pi$
$432$	36.5337	−	12.9044i	1.75773	−	0.620862i
$433$	−31.8379	−	18.3816i	−1.53003	−	0.883365i	−0.999359	−	0.0357896i	$-0.988605\pi$
$433$	−31.8379	−	18.3816i	−1.53003	−	0.883365i	−0.530674	−	0.847576i	$-0.678061\pi$
$434$	10.2477	−	10.2477i	0.491906	−	0.491906i
$435$	−1.87274	−	9.21739i	−0.0897910	−	0.441940i
$436$	5.73419	+	21.4003i	0.274618	+	1.02489i
$437$	−1.78362	−	1.78362i	−0.0853221	−	0.0853221i
$438$	36.3810	−	54.9339i	1.73835	−	2.62484i
$439$	5.45196	−	3.14769i	0.260208	−	0.150231i	−0.364222	−	0.931312i	$-0.618665\pi$
$439$	5.45196	−	3.14769i	0.260208	−	0.150231i	0.624429	+	0.781081i	$0.285332\pi$
$440$	−7.39391	+	27.5944i	−0.352491	+	1.31551i
$441$	−0.367196	+	2.97744i	−0.0174855	+	0.141783i
$442$	73.9846	−	1.96119i	3.51909	−	0.0932843i
$443$			0.0920773i			0.00437472i	0.999998	+	0.00218736i	$0.000696260\pi$
$443$			0.0920773i			0.00437472i	−0.999998	+	0.00218736i	$0.999304\pi$
$444$	−51.5631	−	17.2681i	−2.44708	−	0.819506i
$445$	7.55290	+	13.0820i	0.358042	+	0.620146i
$446$	−16.0929	+	27.8738i	−0.762023	+	1.31986i
$447$	12.0533	+	13.6311i	0.570100	+	0.644727i
$448$	0.717851	−	0.192348i	0.0339153	−	0.00908758i
$449$	−16.1589	+	4.32977i	−0.762586	+	0.204334i	−0.619094	−	0.785317i	$-0.712500\pi$
$449$	−16.1589	+	4.32977i	−0.762586	+	0.204334i	−0.143492	+	0.989651i	$0.545833\pi$
$450$	19.0484	+	24.4077i	0.897951	+	1.15059i
$451$	−6.66443	+	11.5431i	−0.313816	+	0.543544i
$452$	−30.4923	−	52.8142i	−1.43424	−	2.48417i
$453$	−6.49469	+	19.3934i	−0.305147	+	0.911181i
$454$			11.6220i			0.545445i
$455$	−3.08206	−	10.3926i	−0.144489	−	0.487212i
$456$	−25.2550	−	1.55142i	−1.18267	−	0.0726520i
$457$	−4.68835	+	17.4972i	−0.219312	+	0.818483i	0.765292	+	0.643683i	$0.222595\pi$
$457$	−4.68835	+	17.4972i	−0.219312	+	0.818483i	−0.984604	+	0.174800i	$0.944072\pi$
$458$	−31.6712	+	18.2853i	−1.47990	+	0.854418i
$459$	31.7188	+	27.1343i	1.48051	+	1.26652i
$460$	−10.7460	−	10.7460i	−0.501035	−	0.501035i
$461$	−4.15065	−	15.4904i	−0.193315	−	0.721461i	−0.992697	−	0.120638i	$-0.961506\pi$
$461$	−4.15065	−	15.4904i	−0.193315	−	0.721461i	0.799382	−	0.600824i	$-0.205161\pi$
$462$	6.37649	−	1.29554i	0.296661	−	0.0602740i
$463$	−16.2694	+	16.2694i	−0.756102	+	0.756102i	−0.975610	−	0.219509i	$-0.929554\pi$
$463$	−16.2694	+	16.2694i	−0.756102	+	0.756102i	0.219509	+	0.975610i	$0.429554\pi$
$464$	11.6640	+	6.73422i	0.541488	+	0.312628i
$465$	−26.4345	+	13.1710i	−1.22587	+	0.610788i
$466$	54.8323	+	14.6923i	2.54006	+	0.680607i
$467$	−24.2357			−1.12149			−0.560746	−	0.827988i	$-0.689486\pi$
$467$	−24.2357			−1.12149			−0.560746	+	0.827988i	$0.689486\pi$
$468$	45.8867	+	17.1674i	2.12111	+	0.793562i
$469$	3.63883			0.168025
$470$	−44.2263	−	11.8504i	−2.04001	−	0.546618i
$471$	15.9728	−	7.95843i	0.735988	−	0.366705i
$472$	−62.8018	−	36.2586i	−2.89068	−	1.66894i
$473$	6.39374	−	6.39374i	0.293984	−	0.293984i
$474$	29.6169	−	6.01739i	1.36035	−	0.276388i
$475$	−2.36267	−	8.81762i	−0.108407	−	0.404580i
$476$	25.7283	+	25.7283i	1.17925	+	1.17925i
$477$	11.6761	+	8.80833i	0.534612	+	0.403306i
$478$	−14.7126	+	8.49435i	−0.672941	+	0.388523i
$479$	3.81791	−	14.2486i	0.174445	−	0.651037i	−0.822201	−	0.569198i	$-0.807254\pi$
$479$	3.81791	−	14.2486i	0.174445	−	0.651037i	0.996646	−	0.0818395i	$-0.0260795\pi$
$480$	−31.8460	−	1.95631i	−1.45357	−	0.0892929i
$481$	−13.0649	−	21.3046i	−0.595707	−	0.971404i
$482$		−	15.9959i		−	0.728594i
$483$	−0.613831	+	1.83292i	−0.0279303	+	0.0834008i
$484$	20.0167	+	34.6700i	0.909852	+	1.57591i
$485$	5.36934	−	9.29996i	0.243809	−	0.422290i
$486$	18.3456	+	35.3565i	0.832172	+	1.60380i
$487$	−8.72851	+	2.33880i	−0.395526	+	0.105981i	−0.451100	−	0.892474i	$-0.648968\pi$
$487$	−8.72851	+	2.33880i	−0.395526	+	0.105981i	0.0555732	+	0.998455i	$0.482301\pi$
$488$	−58.4107	+	15.6511i	−2.64413	+	0.708492i
$489$	1.06368	+	1.20292i	0.0481013	+	0.0543979i
$490$	3.84116	−	6.65309i	0.173526	−	0.300556i
$491$	−14.0196	−	24.2827i	−0.632697	−	1.09586i	−0.986998	−	0.160732i	$-0.948614\pi$
$491$	−14.0196	−	24.2827i	−0.632697	−	1.09586i	0.354301	−	0.935132i	$-0.384719\pi$
$492$	−67.4439	−	22.5864i	−3.04061	−	1.01827i
$493$			14.5098i			0.653488i
$494$	−15.1097	−	14.3293i	−0.679816	−	0.644705i
$495$	−13.1604	−	1.62302i	−0.591515	−	0.0729491i
$496$	10.9457	−	40.8500i	0.491477	−	1.83422i
$497$	6.55074	−	3.78207i	0.293841	−	0.169649i
$498$	−5.77781	+	8.72427i	−0.258910	+	0.390944i
$499$	12.6796	+	12.6796i	0.567615	+	0.567615i	0.931460	−	0.363845i	$-0.118536\pi$
$499$	12.6796	+	12.6796i	0.567615	+	0.567615i	−0.363845	+	0.931460i	$0.618536\pi$
$500$	3.38759	+	12.6427i	0.151498	+	0.565397i
$501$	−4.24369	−	20.8869i	−0.189594	−	0.933157i
$502$	−25.0893	+	25.0893i	−1.11979	+	1.11979i
$503$	−1.96436	−	1.13412i	−0.0875863	−	0.0505680i	0.455567	−	0.890201i	$-0.349436\pi$
$503$	−1.96436	−	1.13412i	−0.0875863	−	0.0505680i	−0.543153	+	0.839633i	$0.682770\pi$
$504$	7.56670	+	17.8525i	0.337047	+	0.795213i
$505$	5.34956	+	1.43341i	0.238052	+	0.0637859i
$506$	4.19247			0.186378
$507$	11.0951	+	19.5933i	0.492752	+	0.870170i
$508$	40.7920			1.80985
$509$	36.7791	+	9.85493i	1.63020	+	0.436812i	0.953977	−	0.299881i	$-0.0969469\pi$
$509$	36.7791	+	9.85493i	1.63020	+	0.436812i	0.676228	+	0.736693i	$0.263614\pi$
$510$	−47.6688	−	95.6727i	−2.11081	−	4.23646i
$511$	12.8927	+	7.44361i	0.570340	+	0.329286i
$512$	−35.8510	+	35.8510i	−1.58440	+	1.58440i
$513$	−0.912094	−	11.7090i	−0.0402700	−	0.516965i
$514$	5.52755	+	20.6291i	0.243810	+	0.909911i
$515$	18.8465	+	18.8465i	0.830478	+	0.830478i
$516$	40.2283	+	26.6420i	1.77095	+	1.17285i
$517$	7.58827	−	4.38109i	0.333732	−	0.192680i
$518$	4.58409	−	17.1081i	0.201413	−	0.751685i
$519$	0.698877	−	11.3768i	0.0306773	−	0.499384i
$520$	−50.8365	−	48.2110i	−2.22933	−	2.11419i
$521$		−	15.7132i		−	0.688407i	−0.938895	−	0.344203i	$-0.888149\pi$
$521$		−	15.7132i		−	0.688407i	0.938895	−	0.344203i	$-0.111851\pi$
$522$	−5.19375	+	12.8353i	−0.227324	+	0.561784i
$523$	−1.80059	−	3.11872i	−0.0787345	−	0.136372i	0.823970	−	0.566634i	$-0.191755\pi$
$523$	−1.80059	−	3.11872i	−0.0787345	−	0.136372i	−0.902704	+	0.430262i	$0.858421\pi$
$524$	−17.1455	+	29.6969i	−0.749004	+	1.29731i
$525$	−5.24053	+	4.63394i	−0.228715	+	0.202242i
$526$	−12.8550	+	3.44450i	−0.560506	+	0.150187i
$527$	44.0083	−	11.7920i	1.91703	−	0.513668i
$528$	14.2243	−	12.5778i	0.619032	−	0.547379i
$529$	10.8773	−	18.8400i	0.472925	−	0.819130i
$530$	−18.7269	−	32.4359i	−0.813443	−	1.40892i
$531$	12.6258	−	31.2019i	0.547911	−	1.35405i
$532$		−	10.2375i		−	0.443850i
$533$	−17.0887	−	27.8661i	−0.740194	−	1.20701i
$534$	1.36348	−	22.1956i	0.0590036	−	0.960497i
$535$	7.91254	−	29.5300i	0.342089	−	1.27669i
$536$	20.3678	−	11.7594i	0.879757	−	0.507928i
$537$	7.06686	+	4.68016i	0.304957	+	0.201964i
$538$	−40.1535	−	40.1535i	−1.73114	−	1.73114i
$539$	0.380509	+	1.42008i	0.0163897	+	0.0611671i
$540$	−5.49521	−	70.5447i	−0.236476	−	3.03576i
$541$	−1.47591	+	1.47591i	−0.0634542	+	0.0634542i	−0.738122	−	0.674668i	$-0.764287\pi$
$541$	−1.47591	+	1.47591i	−0.0634542	+	0.0634542i	0.674668	+	0.738122i	$0.264287\pi$
$542$	−26.5542	−	15.3310i	−1.14060	−	0.658525i
$543$	1.96352	+	3.94084i	0.0842627	+	0.169118i
$544$	47.5429	+	12.7391i	2.03839	+	0.546184i
$545$	14.7059			0.629932
$546$	−4.66472	+	15.2606i	−0.199632	+	0.653095i
$547$	−35.9891			−1.53878			−0.769391	−	0.638778i	$-0.779440\pi$
$547$	−35.9891			−1.53878			−0.769391	+	0.638778i	$0.779440\pi$
$548$	−77.7594	−	20.8356i	−3.32172	−	0.890052i
$549$	−10.9534	−	25.8429i	−0.467479	−	1.10295i
$550$	13.1399	+	7.58631i	0.560286	+	0.323482i
$551$	2.88677	−	2.88677i	0.122980	−	0.122980i
$552$	2.48751	+	12.2432i	0.105875	+	0.521106i
$553$	1.76735	+	6.59583i	0.0751552	+	0.280483i
$554$	14.7684	+	14.7684i	0.627450	+	0.627450i
$555$	−19.9298	+	30.0931i	−0.845971	+	1.27738i
$556$	−38.0298	+	21.9565i	−1.61282	+	0.931163i
$557$	7.81926	−	29.1819i	0.331313	−	1.23648i	−0.576499	−	0.817098i	$-0.695582\pi$
$557$	7.81926	−	29.1819i	0.331313	−	1.23648i	0.907812	−	0.419378i	$-0.137752\pi$
$558$	43.1504	+	5.32157i	1.82670	+	0.225280i
$559$	6.30502	+	21.2603i	0.266674	+	0.899213i
$560$		−	22.4181i		−	0.947337i
$561$	19.3969	+	6.49587i	0.818939	+	0.274256i
$562$	16.8591	+	29.2009i	0.711160	+	1.23177i
$563$	15.2651	−	26.4399i	0.643346	−	1.11431i	−0.341334	−	0.939942i	$-0.610879\pi$
$563$	15.2651	−	26.4399i	0.643346	−	1.11431i	0.984681	−	0.174367i	$-0.0557878\pi$
$564$	30.9727	+	35.0270i	1.30418	+	1.47490i
$565$	−39.1003	+	10.4769i	−1.64496	+	0.440766i
$566$	−74.9141	+	20.0732i	−3.14887	+	0.843738i
$567$	−7.71945	+	4.62711i	−0.324186	+	0.194320i
$568$	24.4446	−	42.3393i	1.02567	−	1.77652i
$569$	−2.73370	−	4.73491i	−0.114603	−	0.198498i	0.803018	−	0.595955i	$-0.203226\pi$
$569$	−2.73370	−	4.73491i	−0.114603	−	0.198498i	−0.917621	+	0.397457i	$0.869893\pi$
$570$	−9.55053	+	28.5182i	−0.400028	+	1.19450i
$571$			7.26480i			0.304022i	0.988379	+	0.152011i	$0.0485750\pi$
$571$			7.26480i			0.304022i	−0.988379	+	0.152011i	$0.951425\pi$
$572$	24.0009	−	0.636218i	1.00353	−	0.0266016i
$573$	37.6276	+	2.31147i	1.57191	+	0.0965631i
$574$	5.99594	−	22.3771i	0.250266	−	0.934004i
$575$	−3.90348	+	2.25368i	−0.162786	+	0.0939848i
$576$	1.77986	+	1.34271i	0.0741609	+	0.0559463i
$577$	27.7641	+	27.7641i	1.15583	+	1.15583i	0.985363	+	0.170472i	$0.0545292\pi$
$577$	27.7641	+	27.7641i	1.15583	+	1.15583i	0.170472	+	0.985363i	$0.445471\pi$
$578$	31.4350	+	117.317i	1.30753	+	4.87975i
$579$	−18.7882	+	3.81728i	−0.780811	+	0.158641i
$580$	17.3923	−	17.3923i	0.722175	−	0.722175i
$581$	−2.04754	−	1.18215i	−0.0849463	−	0.0490438i
$582$	−14.1495	+	7.04996i	−0.586515	+	0.292230i
$583$	6.92332	+	1.85510i	0.286735	+	0.0768303i
$584$	96.2203			3.98162
$585$	18.8900	−	26.4710i	0.781005	−	1.09444i
$586$	39.2816			1.62271
$587$	−8.62152	−	2.31013i	−0.355848	−	0.0953493i	0.0764662	−	0.997072i	$-0.475636\pi$
$587$	−8.62152	−	2.31013i	−0.355848	−	0.0953493i	−0.432314	+	0.901723i	$0.642303\pi$
$588$	−7.02182	+	3.49861i	−0.289575	+	0.144280i
$589$	−11.1017	−	6.40954i	−0.457436	−	0.264101i
$590$	−60.9489	+	60.9489i	−2.50923	+	2.50923i
$591$	1.17574	−	0.238880i	0.0483634	−	0.00982621i
$592$	−13.3770	−	49.9237i	−0.549792	−	2.05185i
$593$	15.1795	+	15.1795i	0.623348	+	0.623348i	0.946386	−	0.323038i	$-0.104704\pi$
$593$	15.1795	+	15.1795i	0.623348	+	0.623348i	−0.323038	+	0.946386i	$0.604704\pi$
$594$	14.8332	+	12.6893i	0.608614	+	0.520648i
$595$	20.9157	−	12.0757i	0.857461	−	0.495055i
$596$	−12.3153	+	45.9615i	−0.504456	+	1.88266i
$597$	−25.8590	−	1.58853i	−1.05834	−	0.0650140i
$598$	−4.90319	+	9.03750i	−0.200506	+	0.369571i
$599$			35.4683i			1.44920i	0.689172	+	0.724598i	$0.257974\pi$
$599$			35.4683i			1.44920i	−0.689172	+	0.724598i	$0.742026\pi$
$600$	−14.3579	+	42.8734i	−0.586160	+	1.75030i
$601$	0.623201	+	1.07942i	0.0254209	+	0.0440303i	0.878456	−	0.477823i	$-0.158574\pi$
$601$	0.623201	+	1.07942i	0.0254209	+	0.0440303i	−0.853035	+	0.521854i	$0.825241\pi$
$602$	−7.85793	+	13.6103i	−0.320265	+	0.554715i
$603$	6.71627	+	8.60589i	0.273508	+	0.350459i
$604$	−51.6606	+	13.8424i	−2.10204	+	0.563239i
$605$	25.6675	−	6.87758i	1.04353	−	0.279613i
$606$	−5.40069	−	6.10765i	−0.219388	−	0.248106i
$607$	15.8593	−	27.4691i	0.643708	−	1.11494i	−0.340890	−	0.940103i	$-0.610728\pi$
$607$	15.8593	−	27.4691i	0.643708	−	1.11494i	0.984598	−	0.174832i	$-0.0559383\pi$
$608$	−6.92433	−	11.9933i	−0.280819	−	0.486392i
$609$	−2.96656	−	0.993478i	−0.120211	−	0.0402577i
$610$			71.8767i			2.91020i
$611$	0.569431	+	21.4814i	0.0230367	+	0.869045i
$612$	−13.3605	+	108.335i	−0.540068	+	4.37919i
$613$	−2.68470	+	10.0194i	−0.108434	+	0.404682i	−0.998712	−	0.0507358i	$-0.983843\pi$
$613$	−2.68470	+	10.0194i	−0.108434	+	0.404682i	0.890278	+	0.455418i	$0.150510\pi$
$614$	36.1877	−	20.8930i	1.46042	−	0.843173i
$615$	−26.0679	+	39.3614i	−1.05116	+	1.58721i
$616$	6.71903	+	6.71903i	0.270717	+	0.270717i
$617$	−0.693287	−	2.58738i	−0.0279107	−	0.104164i	0.950565	−	0.310525i	$-0.100505\pi$
$617$	−0.693287	−	2.58738i	−0.0279107	−	0.104164i	−0.978476	+	0.206360i	$0.933838\pi$
$618$	−7.81220	−	38.4507i	−0.314253	−	1.54671i
$619$	19.1080	−	19.1080i	0.768014	−	0.768014i	−0.209743	−	0.977757i	$-0.567263\pi$
$619$	19.1080	−	19.1080i	0.768014	−	0.768014i	0.977757	+	0.209743i	$0.0672626\pi$
$620$	−66.8856	−	38.6164i	−2.68619	−	1.55087i
$621$	−5.46785	+	1.93135i	−0.219417	+	0.0775023i
$622$	18.0911	+	4.84751i	0.725389	+	0.194367i
$623$	5.02444			0.201300
$624$	10.4777	+	45.3725i	0.419444	+	1.81636i
$625$	28.8820			1.15528
$626$	−3.16143	−	0.847103i	−0.126356	−	0.0338571i
$627$	−2.56670	−	5.15145i	−0.102504	−	0.205729i
$628$	40.4150	+	23.3336i	1.61273	+	0.931112i
$629$	39.3724	−	39.3724i	1.56988	−	1.56988i
$630$	22.8244	−	3.19535i	0.909345	−	0.127306i
$631$	−6.92269	−	25.8358i	−0.275588	−	1.02851i	−0.955446	−	0.295165i	$-0.904625\pi$
$631$	−6.92269	−	25.8358i	−0.275588	−	1.02851i	0.679859	−	0.733343i	$-0.262041\pi$
$632$	31.2078	+	31.2078i	1.24138	+	1.24138i
$633$	−33.3799	−	22.1065i	−1.32673	−	0.878653i
$634$	−60.6499	+	35.0162i	−2.40871	+	1.39067i
$635$	7.00788	−	26.1538i	0.278099	−	1.03788i
$636$	−2.34513	+	38.1755i	−0.0929906	+	1.51376i
$637$	−3.50620	−	0.840571i	−0.138921	−	0.0333046i
$638$			6.78547i			0.268639i
$639$	21.0355	+	8.51195i	0.832152	+	0.336728i
$640$	15.5663	+	26.9616i	0.615313	+	1.06575i
$641$	−5.04894	+	8.74503i	−0.199421	+	0.345408i	−0.948341	−	0.317253i	$-0.897240\pi$
$641$	−5.04894	+	8.74503i	−0.199421	+	0.345408i	0.748920	+	0.662661i	$0.230573\pi$
$642$	−33.7147	+	29.8122i	−1.33061	+	1.17659i
$643$	2.44852	−	0.656078i	0.0965601	−	0.0258732i	−0.210215	−	0.977655i	$-0.567417\pi$
$643$	2.44852	−	0.656078i	0.0965601	−	0.0258732i	0.306776	+	0.951782i	$0.400750\pi$
$644$	−4.88258	+	1.30828i	−0.192401	+	0.0515536i
$645$	23.9926	−	21.2154i	0.944707	−	0.835357i
$646$	23.1977	−	40.1795i	0.912700	−	1.58084i
$647$	6.86148	+	11.8844i	0.269753	+	0.467225i	0.968798	−	0.247852i	$-0.0797247\pi$
$647$	6.86148	+	11.8844i	0.269753	+	0.467225i	−0.699045	+	0.715078i	$0.746391\pi$
$648$	−28.2554	+	50.8461i	−1.10998	+	1.99742i
$649$		−	16.4952i		−	0.647492i
$650$	−31.7208	+	19.4526i	−1.24419	+	0.762993i
$651$	−0.602325	+	9.80501i	−0.0236070	+	0.384289i
$652$	−1.08681	+	4.05603i	−0.0425628	+	0.158846i
$653$	−24.5202	+	14.1567i	−0.959548	+	0.553996i	−0.896034	−	0.443985i	$-0.853564\pi$
$653$	−24.5202	+	14.1567i	−0.959548	+	0.553996i	−0.0635144	+	0.997981i	$0.520231\pi$
$654$	−18.0494	−	11.9536i	−0.705787	−	0.467421i
$655$	16.0946	+	16.0946i	0.628869	+	0.628869i
$656$	−17.4970	−	65.2996i	−0.683142	−	2.54952i
$657$	6.19211	+	44.2303i	0.241577	+	1.72559i
$658$	−10.7688	+	10.7688i	−0.419810	+	0.419810i
$659$	−10.2429	−	5.91375i	−0.399007	−	0.230367i	0.287048	−	0.957916i	$-0.407326\pi$
$659$	−10.2429	−	5.91375i	−0.399007	−	0.230367i	−0.686055	+	0.727549i	$0.740659\pi$
$660$	−15.4640	−	31.0366i	−0.601934	−	1.20810i
$661$	−7.01399	−	1.87939i	−0.272813	−	0.0731000i	0.119819	−	0.992796i	$-0.461769\pi$
$661$	−7.01399	−	1.87939i	−0.272813	−	0.0731000i	−0.392632	+	0.919696i	$0.628435\pi$
$662$	13.1145			0.509708
$663$	−36.6879	+	34.2158i	−1.42484	+	1.32883i
$664$	−15.2811			−0.593022
$665$	−6.56375	−	1.75875i	−0.254531	−	0.0682014i
$666$	48.9218	−	20.7353i	1.89568	−	0.803476i
$667$	−1.74571	−	1.00788i	−0.0675940	−	0.0390254i
$668$	39.4114	−	39.4114i	1.52487	−	1.52487i
$669$	−4.34385	−	21.3799i	−0.167943	−	0.826595i
$670$	−7.23520	−	27.0021i	−0.279520	−	1.04318i
$671$	−9.72633	−	9.72633i	−0.375481	−	0.375481i
$672$	−5.85978	+	8.84803i	−0.226046	+	0.341320i
$673$	−4.00671	+	2.31327i	−0.154447	+	0.0891701i	−0.575232	−	0.817990i	$-0.695088\pi$
$673$	−4.00671	+	2.31327i	−0.154447	+	0.0891701i	0.420785	+	0.907161i	$0.361755\pi$
$674$	6.61194	−	24.6761i	0.254682	−	0.950487i
$675$	−20.6319	−	3.84097i	−0.794123	−	0.147839i
$676$	−26.6981	+	52.4816i	−1.02685	+	2.01852i
$677$			10.5748i			0.406422i	0.979135	+	0.203211i	$0.0651377\pi$
$677$			10.5748i			0.406422i	−0.979135	+	0.203211i	$0.934862\pi$
$678$	56.5060	+	18.9234i	2.17010	+	0.726749i
$679$	−1.78593	−	3.09332i	−0.0685377	−	0.118711i
$680$	78.0486	−	135.184i	2.99303	−	5.18408i
$681$	−5.21839	−	5.90149i	−0.199969	−	0.226146i
$682$	20.5804	−	5.51450i	0.788065	−	0.211161i
$683$	−41.3449	+	11.0783i	−1.58202	+	0.423901i	−0.939550	−	0.342411i	$-0.888756\pi$
$683$	−41.3449	+	11.0783i	−1.58202	+	0.423901i	−0.642469	+	0.766312i	$0.722090\pi$
$684$	24.2118	−	18.8955i	0.925759	−	0.722488i
$685$	−26.7175	+	46.2760i	−1.02082	+	1.76812i
$686$	−1.27763	−	2.21293i	−0.0487803	−	0.0844899i
$687$	7.87190	−	23.5058i	0.300332	−	0.896803i
$688$			45.8610i			1.74844i
$689$	−12.0959	+	12.7547i	−0.460818	+	0.485914i
$690$	14.8218	+	0.910507i	0.564256	+	0.0346624i
$691$	2.96869	−	11.0793i	0.112934	−	0.421477i	−0.886190	−	0.463323i	$-0.846657\pi$
$691$	2.96869	−	11.0793i	0.112934	−	0.421477i	0.999124	+	0.0418458i	$0.0133238\pi$
$692$	25.8135	−	14.9034i	0.981281	−	0.566543i
$693$	−2.65619	+	3.52098i	−0.100900	+	0.133751i
$694$	25.6849	+	25.6849i	0.974986	+	0.974986i
$695$	7.54406	+	28.1548i	0.286163	+	1.06797i
$696$	−19.8155	+	4.02601i	−0.751105	+	0.152605i
$697$	51.4986	−	51.4986i	1.95065	−	1.95065i
$698$	10.1245	+	5.84537i	0.383217	+	0.221251i
$699$	−34.4402	+	17.1598i	−1.30265	+	0.649043i
$700$	−17.6701	−	4.73470i	−0.667868	−	0.178955i
$701$	−29.9920			−1.13278			−0.566390	−	0.824137i	$-0.691660\pi$
$701$	−29.9920			−1.13278			−0.566390	+	0.824137i	$0.691660\pi$
$702$	−44.7014	+	17.1348i	−1.68715	+	0.646710i
$703$	−15.6665			−0.590874
$704$	1.05537	+	0.282784i	0.0397756	+	0.0106578i
$705$	27.7786	−	13.8406i	1.04620	−	0.521268i
$706$	−54.5372	−	31.4871i	−2.05253	−	1.18503i
$707$	1.30258	−	1.30258i	0.0489884	−	0.0489884i
$708$	86.2591	−	17.5257i	3.24182	−	0.658655i
$709$	4.75701	+	17.7534i	0.178653	+	0.666744i	0.995900	+	0.0904561i	$0.0288325\pi$
$709$	4.75701	+	17.7534i	0.178653	+	0.666744i	−0.817247	+	0.576288i	$0.804501\pi$
$710$	−41.0901	−	41.0901i	−1.54208	−	1.54208i
$711$	−12.3372	+	16.3539i	−0.462682	+	0.613318i
$712$	28.1236	−	16.2372i	1.05398	−	0.608514i
$713$	−1.63820	+	6.11385i	−0.0613511	+	0.228965i
$714$	−35.4867	−	2.17995i	−1.32805	−	0.0815828i
$715$	3.71534	−	15.4975i	0.138946	−	0.579573i
$716$			22.1654i			0.828361i
$717$	3.65685	−	10.9195i	0.136567	−	0.407796i
$718$	15.6171	+	27.0496i	0.582826	+	1.00948i
$719$	10.6960	−	18.5261i	0.398895	−	0.690906i	−0.594695	−	0.803951i	$-0.702727\pi$
$719$	10.6960	−	18.5261i	0.398895	−	0.690906i	0.993590	+	0.113046i	$0.0360606\pi$
$720$	53.0192	−	41.3776i	1.97591	−	1.54205i
$721$	8.56316	−	2.29449i	0.318909	−	0.0854514i
$722$	34.2867	−	9.18709i	1.27602	−	0.341908i
$723$	7.18235	+	8.12254i	0.267115	+	0.302080i
$724$	−5.75692	+	9.97127i	−0.213954	+	0.370579i
$725$	−3.64755	−	6.31774i	−0.135467	−	0.234635i
$726$	−37.0935	−	12.4223i	−1.37667	−	0.461035i
$727$		−	36.1327i		−	1.34009i	−0.742321	−	0.670044i	$-0.766275\pi$
$727$		−	36.1327i		−	1.34009i	0.742321	−	0.670044i	$-0.233725\pi$
$728$	−22.3419	+	6.62580i	−0.828046	+	0.245568i
$729$	−25.1912	−	9.71625i	−0.933006	−	0.359861i
$730$	29.6007	−	110.471i	1.09557	−	4.08873i
$731$	−42.7876	+	24.7034i	−1.58256	+	0.913689i
$732$	40.5285	−	61.1965i	1.49798	−	2.26189i
$733$	−9.79712	−	9.79712i	−0.361865	−	0.361865i	0.502634	−	0.864499i	$-0.332364\pi$
$733$	−9.79712	−	9.79712i	−0.361865	−	0.361865i	−0.864499	+	0.502634i	$0.832364\pi$
$734$	−12.7246	−	47.4888i	−0.469673	−	1.75284i
$735$	1.03682	+	5.10309i	0.0382436	+	0.188230i
$736$	−4.83512	+	4.83512i	−0.178225	+	0.178225i
$737$	4.63298	+	2.67485i	0.170658	+	0.0985295i
$738$	63.9891	−	27.1215i	2.35547	−	0.998357i
$739$	−32.0696	−	8.59303i	−1.17970	−	0.316100i	−0.384893	−	0.922961i	$-0.625762\pi$
$739$	−32.0696	−	8.59303i	−1.17970	−	0.316100i	−0.794807	+	0.606862i	$0.792428\pi$
$740$	−94.3880			−3.46977
$741$	14.1065	+	0.491830i	0.518216	+	0.0180678i
$742$	−12.4577			−0.457338
$743$	−19.0654	−	5.10855i	−0.699441	−	0.187415i	−0.108461	−	0.994101i	$-0.534592\pi$
$743$	−19.0654	−	5.10855i	−0.699441	−	0.187415i	−0.590980	+	0.806686i	$0.701259\pi$
$744$	28.3148	+	56.8287i	1.03807	+	2.08344i
$745$	27.3525	+	15.7920i	1.00212	+	0.578573i
$746$	18.3915	−	18.3915i	0.673362	−	0.673362i
$747$	−0.983394	−	7.02439i	−0.0359805	−	0.257009i
$748$	13.8449	+	51.6700i	0.506221	+	1.88924i
$749$	−7.19033	−	7.19033i	−0.262729	−	0.262729i
$750$	−10.6631	−	7.06181i	−0.389360	−	0.257861i
$751$	−1.95961	+	1.13138i	−0.0715072	+	0.0412847i	−0.535327	−	0.844645i	$-0.679812\pi$
$751$	−1.95961	+	1.13138i	−0.0715072	+	0.0412847i	0.463820	+	0.885929i	$0.346478\pi$
$752$	−11.5022	+	42.9270i	−0.419444	+	1.56539i
$753$	1.47466	−	24.0054i	0.0537396	−	0.874806i
$754$	−14.6271	−	7.93576i	−0.532687	−	0.289003i
$755$			35.5002i			1.29199i
$756$	−21.2346	−	10.1493i	−0.772296	−	0.369125i
$757$	−5.03650	−	8.72348i	−0.183055	−	0.317060i	0.759865	−	0.650081i	$-0.225265\pi$
$757$	−5.03650	−	8.72348i	−0.183055	−	0.317060i	−0.942919	+	0.333021i	$0.891932\pi$
$758$	−10.1958	+	17.6596i	−0.370327	+	0.641426i
$759$	−2.12889	+	1.88247i	−0.0772738	+	0.0683294i
$760$	−42.4233	+	11.3673i	−1.53886	+	0.412335i
$761$	12.8603	−	3.44591i	0.466185	−	0.124914i	−0.0180775	−	0.999837i	$-0.505755\pi$
$761$	12.8603	−	3.44591i	0.466185	−	0.124914i	0.484263	+	0.874923i	$0.339088\pi$
$762$	−29.8600	+	26.4037i	−1.08171	+	0.956506i
$763$	2.44571	−	4.23610i	0.0885408	−	0.153357i
$764$	49.2917	+	85.3757i	1.78331	+	3.08878i
$765$	67.1638	+	27.1776i	2.42831	+	0.982609i
$766$			96.8593i			3.49967i
$767$	35.5577	+	19.2915i	1.28392	+	0.696574i
$768$	2.96795	−	48.3141i	0.107097	−	1.74338i
$769$	−3.38647	+	12.6385i	−0.122119	+	0.455755i	−0.999721	−	0.0236359i	$-0.992476\pi$
$769$	−3.38647	+	12.6385i	−0.122119	+	0.455755i	0.877601	+	0.479391i	$0.159142\pi$
$770$	9.78119	−	5.64717i	0.352490	−	0.203510i
$771$	−12.0695	−	7.99328i	−0.434674	−	0.287871i
$772$	−35.4514	−	35.4514i	−1.27592	−	1.27592i
$773$	3.83426	+	14.3096i	0.137909	+	0.514682i	0.999969	+	0.00787630i	$0.00250713\pi$
$773$	3.83426	+	14.3096i	0.137909	+	0.514682i	−0.862060	+	0.506806i	$0.830826\pi$
$774$	−46.6922	+	6.53677i	−1.67832	+	0.234959i
$775$	−16.1974	+	16.1974i	−0.581829	+	0.581829i
$776$	−19.9930	−	11.5430i	−0.717707	−	0.414368i
$777$	5.35397	+	10.7456i	0.192073	+	0.385496i
$778$	−30.4866	−	8.16887i	−1.09300	−	0.292868i
$779$	−20.4916			−0.734188
$780$	84.9894	+	2.96319i	3.04311	+	0.106099i
$781$	11.1206			0.397926
$782$	−22.1275	−	5.92904i	−0.791277	−	0.212022i
$783$	−3.12586	−	8.84966i	−0.111709	−	0.316261i
$784$	−6.45763	−	3.72831i	−0.230630	−	0.133154i
$785$	21.9035	−	21.9035i	0.781768	−	0.781768i
$786$	−6.67149	−	32.8362i	−0.237964	−	1.17123i
$787$	−13.6623	−	50.9883i	−0.487007	−	1.81754i	−0.570846	−	0.821057i	$-0.693385\pi$
$787$	−13.6623	−	50.9883i	−0.487007	−	1.81754i	0.0838385	−	0.996479i	$-0.473282\pi$
$788$	2.21850	+	2.21850i	0.0790307	+	0.0790307i
$789$	4.98102	−	7.52114i	0.177329	−	0.267760i
$790$	45.4306	−	26.2294i	1.61635	−	0.933200i
$791$	−3.48478	+	13.0054i	−0.123905	+	0.462418i
$792$	−3.48915	+	28.2921i	−0.123981	+	1.00532i
$793$	32.3417	−	9.59137i	1.14849	−	0.340600i
$794$		−	84.0562i		−	2.98304i
$795$	24.0734	+	8.06198i	0.853795	+	0.285929i
$796$	−33.8750	−	58.6732i	−1.20067	−	2.07962i
$797$	5.18457	−	8.97993i	0.183647	−	0.318086i	−0.759473	−	0.650539i	$-0.774543\pi$
$797$	5.18457	−	8.97993i	0.183647	−	0.318086i	0.943120	+	0.332453i	$0.107876\pi$
$798$	6.62647	+	7.49389i	0.234575	+	0.265281i
$799$	−46.2459	+	12.3916i	−1.63606	+	0.438382i
$800$	−23.9032	+	6.40484i	−0.845106	+	0.226445i
$801$	9.27372	+	11.8829i	0.327671	+	0.419861i
$802$	8.18140	−	14.1706i	0.288895	−	0.500381i
$803$	10.9434	+	18.9545i	0.386184	+	0.668890i
$804$	−9.06535	+	27.0695i	−0.319710	+	0.954667i
$805$			3.35523i			0.118256i
$806$	−12.1819	+	50.8134i	−0.429090	+	1.78983i
$807$	38.4189	+	2.36008i	1.35241	+	0.0830788i
$808$	3.08154	−	11.5005i	0.108408	−	0.404585i
$809$	4.01101	−	2.31576i	0.141020	−	0.0814177i	−0.427830	−	0.903859i	$-0.640722\pi$
$809$	4.01101	−	2.31576i	0.141020	−	0.0814177i	0.568850	+	0.822441i	$0.307389\pi$
$810$	49.6846	+	48.0823i	1.74574	+	1.68944i
$811$	−30.1490	−	30.1490i	−1.05868	−	1.05868i	−0.998168	−	0.0605080i	$-0.980728\pi$
$811$	−30.1490	−	30.1490i	−1.05868	−	1.05868i	−0.0605080	−	0.998168i	$-0.519272\pi$
$812$	−2.11744	−	7.90240i	−0.0743076	−	0.277320i
$813$	20.3677	−	4.13820i	0.714327	−	0.145133i
$814$	18.4124	−	18.4124i	0.645354	−	0.645354i
$815$	2.41381	+	1.39362i	0.0845522	+	0.0488163i
$816$	−92.8620	+	46.2683i	−3.25082	+	1.61972i
$817$	13.4276	+	3.59790i	0.469771	+	0.125875i
$818$	53.6445			1.87564
$819$	−4.48351	−	9.84368i	−0.156667	−	0.343966i
$820$	−123.458			−4.31135
$821$	27.0505	+	7.24817i	0.944070	+	0.252963i	0.697844	−	0.716250i	$-0.254143\pi$
$821$	27.0505	+	7.24817i	0.944070	+	0.252963i	0.246226	+	0.969212i	$0.420809\pi$
$822$	70.4069	−	35.0801i	2.45572	−	1.22356i
$823$	33.6775	+	19.4437i	1.17393	+	0.677766i	0.954601	−	0.297886i	$-0.0962815\pi$
$823$	33.6775	+	19.4437i	1.17393	+	0.677766i	0.219324	+	0.975652i	$0.429615\pi$
$824$	40.5162	−	40.5162i	1.41145	−	1.41145i
$825$	−10.0786	+	2.04772i	−0.350893	+	0.0712925i
$826$	7.42029	+	27.6929i	0.258185	+	0.963559i
$827$	−14.2159	−	14.2159i	−0.494334	−	0.494334i	0.415335	−	0.909669i	$-0.363664\pi$
$827$	−14.2159	−	14.2159i	−0.494334	−	0.494334i	−0.909669	+	0.415335i	$0.863664\pi$
$828$	−12.1060	−	9.13266i	−0.420713	−	0.317382i
$829$	16.3626	−	9.44695i	0.568296	−	0.328106i	−0.188172	−	0.982136i	$-0.560256\pi$
$829$	16.3626	−	9.44695i	0.568296	−	0.328106i	0.756469	+	0.654030i	$0.226923\pi$
$830$	−4.70101	+	17.5444i	−0.163174	+	0.608975i
$831$	−14.1304	−	0.868036i	−0.490179	−	0.0301118i
$832$	−1.84386	+	1.94427i	−0.0639243	+	0.0674055i
$833$		−	8.03315i		−	0.278332i
$834$	13.6261	−	40.6881i	0.471834	−	1.40891i
$835$	−18.4979	−	32.0393i	−0.640147	−	1.10877i
$836$	7.52541	−	13.0344i	0.260272	−	0.450804i
$837$	−24.3007	+	16.6728i	−0.839957	+	0.576297i
$838$	40.5926	−	10.8767i	1.40225	−	0.375731i
$839$	22.1013	−	5.92204i	0.763023	−	0.204451i	0.143736	−	0.989616i	$-0.454088\pi$
$839$	22.1013	−	5.92204i	0.763023	−	0.204451i	0.619287	+	0.785165i	$0.287422\pi$
$840$	22.2948	+	25.2132i	0.769244	+	0.869939i
$841$	−12.8688	+	22.2893i	−0.443750	+	0.768598i
$842$	15.4230	+	26.7134i	0.531512	+	0.920605i
$843$	−21.6724	−	7.25792i	−0.746438	−	0.249976i
$844$		−	104.697i		−	3.60382i
$845$	29.0619	+	26.1336i	0.999761	+	0.899024i
$846$	−45.3444	−	5.59214i	−1.55897	−	0.192262i
$847$	2.28760	−	8.53742i	0.0786027	−	0.293349i
$848$	−31.4829	+	18.1767i	−1.08113	+	0.624190i
$849$	29.0274	−	43.8302i	0.996218	−	1.50425i
$850$	−58.6224	−	58.6224i	−2.01073	−	2.01073i
$851$	2.00208	+	7.47188i	0.0686306	+	0.256133i
$852$	11.8153	+	58.1536i	0.404787	+	1.99231i
$853$	35.3567	−	35.3567i	1.21059	−	1.21059i	0.239756	−	0.970833i	$-0.422933\pi$
$853$	35.3567	−	35.3567i	1.21059	−	1.21059i	0.970833	−	0.239756i	$-0.0770674\pi$
$854$	20.7044	+	11.9537i	0.708490	+	0.409047i
$855$	−7.95538	−	18.7695i	−0.272068	−	0.641905i
$856$	−63.4835	−	17.0103i	−2.16982	−	0.581402i
$857$	−24.2300			−0.827682			−0.413841	−	0.910349i	$-0.635813\pi$
$857$	−24.2300			−0.827682			−0.413841	+	0.910349i	$0.635813\pi$
$858$	−17.1570	+	16.0010i	−0.585732	+	0.546264i
$859$	−41.6159			−1.41992			−0.709958	−	0.704244i	$-0.751286\pi$
$859$	−41.6159			−1.41992			−0.709958	+	0.704244i	$0.751286\pi$
$860$	80.8987	+	21.6767i	2.75862	+	0.739171i
$861$	7.00293	+	14.0551i	0.238659	+	0.478996i
$862$	28.0100	+	16.1716i	0.954025	+	0.550807i
$863$	−21.1693	+	21.1693i	−0.720611	+	0.720611i	−0.968730	−	0.248118i	$-0.920188\pi$
$863$	−21.1693	+	21.1693i	−0.720611	+	0.720611i	0.248118	+	0.968730i	$0.420188\pi$
$864$	−31.7413	+	2.47255i	−1.07986	+	0.0841177i
$865$	−5.12068	−	19.1107i	−0.174109	−	0.649782i
$866$	66.4256	+	66.4256i	2.25724	+	2.25724i
$867$	−68.6392	−	45.4576i	−2.33111	−	1.54382i
$868$	−22.2472	+	12.8445i	−0.755121	+	0.435969i
$869$	−2.59831	+	9.69701i	−0.0881415	+	0.328948i
$870$	−1.47365	+	23.9889i	−0.0499612	+	0.813300i
$871$	−11.1844	+	6.85877i	−0.378969	+	0.232401i
$872$		−	31.6147i		−	1.07061i
$873$	4.01943	−	9.93317i	0.136037	−	0.336187i
$874$	3.22273	+	5.58193i	0.109010	+	0.188812i
$875$	1.44486	−	2.50256i	0.0488451	−	0.0846021i
$876$	−87.4929	+	77.3656i	−2.95611	+	2.61394i
$877$	−21.5905	+	5.78516i	−0.729060	+	0.195351i	−0.604211	−	0.796825i	$-0.706511\pi$
$877$	−21.5905	+	5.78516i	−0.729060	+	0.195351i	−0.124849	+	0.992176i	$0.539845\pi$
$878$	−15.5383	+	4.16346i	−0.524391	+	0.140510i
$879$	−19.9467	+	17.6379i	−0.672787	+	0.594912i
$880$	16.4792	−	28.5429i	0.555515	−	0.962180i
$881$	4.09989	+	7.10122i	0.138129	+	0.239246i	0.926788	−	0.375584i	$-0.122558\pi$
$881$	4.09989	+	7.10122i	0.138129	+	0.239246i	−0.788659	+	0.614830i	$0.789225\pi$
$882$	2.87545	−	7.10608i	0.0968215	−	0.239274i
$883$			19.9644i			0.671855i	0.941888	+	0.335928i	$0.109050\pi$
$883$			19.9644i			0.671855i	−0.941888	+	0.335928i	$0.890950\pi$
$884$	−127.574	−	30.5844i	−4.29078	−	1.02867i
$885$	3.58236	−	58.3159i	0.120420	−	1.96027i
$886$	0.0608955	−	0.227265i	0.00204582	−	0.00763512i
$887$	0.820404	−	0.473660i	0.0275465	−	0.0159040i	−0.486164	−	0.873868i	$-0.661604\pi$
$887$	0.820404	−	0.473660i	0.0275465	−	0.0159040i	0.513710	+	0.857964i	$0.328271\pi$
$888$	64.6940	+	42.8449i	2.17099	+	1.43778i
$889$	−6.36824	−	6.36824i	−0.213584	−	0.213584i
$890$	−9.99025	−	37.2841i	−0.334874	−	1.24977i
$891$	−13.2298	+	0.216811i	−0.443214	+	0.00726346i
$892$	40.3417	−	40.3417i	1.35074	−	1.35074i
$893$	11.6661	+	6.73544i	0.390392	+	0.225393i
$894$	−20.7349	−	41.6156i	−0.693480	−	1.39183i
$895$	14.2114	+	3.80792i	0.475033	+	0.127285i
$896$	10.3552			0.345944
$897$	−1.56816	−	6.79073i	−0.0523593	−	0.226736i
$898$	42.7469			1.42648
$899$	−9.89519	−	2.65141i	−0.330023	−	0.0884294i
$900$	−21.4165	−	50.5291i	−0.713885	−	1.68430i
$901$	−33.9171	−	19.5821i	−1.12994	−	0.652373i
$902$	24.0832	−	24.0832i	0.801883	−	0.801883i
$903$	−2.12103	−	10.4395i	−0.0705836	−	0.347404i
$904$	22.5231	+	84.0575i	0.749108	+	2.79571i
$905$	5.40407	+	5.40407i	0.179637	+	0.179637i
$906$	28.8560	−	43.5715i	0.958678	−	1.44756i
$907$	4.88169	−	2.81845i	0.162094	−	0.0935850i	−0.416759	−	0.909017i	$-0.636834\pi$
$907$	4.88169	−	2.81845i	0.162094	−	0.0935850i	0.578853	+	0.815432i	$0.303501\pi$
$908$	5.33186	−	19.8988i	0.176944	−	0.660364i
$909$	5.48481	+	0.676420i	0.181920	+	0.0224354i
$910$	0.733989	+	27.6893i	0.0243315	+	0.917891i
$911$			50.9761i			1.68891i	0.535625	+	0.844456i	$0.320076\pi$
$911$			50.9761i			1.68891i	−0.535625	+	0.844456i	$0.679924\pi$
$912$	27.6804	+	9.26995i	0.916590	+	0.306959i
$913$	−1.73796	−	3.01024i	−0.0575182	−	0.0996244i
$914$	23.1436	−	40.0858i	0.765521	−	1.32592i
$915$	−32.2735	−	36.4982i	−1.06693	−	1.20659i
$916$	62.6153	−	16.7777i	2.06887	−	0.554352i
$917$	7.31280	−	1.95946i	0.241490	−	0.0647070i
$918$	−60.3429	−	87.9501i	−1.99161	−	2.90279i
$919$	6.17819	−	10.7009i	0.203800	−	0.352991i	−0.745950	−	0.666002i	$-0.768004\pi$
$919$	6.17819	−	10.7009i	0.203800	−	0.352991i	0.949750	+	0.313011i	$0.101338\pi$
$920$	10.8429	+	18.7804i	0.357479	+	0.619172i
$921$	−8.99451	+	26.8579i	−0.296379	+	0.884999i
$922$			40.9785i			1.34956i
$923$	−13.0058	+	23.9721i	−0.428091	+	0.789050i
$924$	−11.5120	−	0.707186i	−0.378717	−	0.0232647i
$925$	−7.24557	+	27.0409i	−0.238233	+	0.889098i
$926$	50.9158	−	29.3963i	1.67320	−	0.966021i
$927$	21.2317	+	16.0170i	0.697342	+	0.526068i
$928$	−7.82558	−	7.82558i	−0.256887	−	0.256887i
$929$	5.59629	+	20.8856i	0.183608	+	0.685235i	0.994924	+	0.100627i	$0.0320850\pi$
$929$	5.59629	+	20.8856i	0.183608	+	0.685235i	−0.811316	+	0.584608i	$0.801248\pi$
$930$	73.9563	−	15.0260i	2.42512	−	0.492723i
$931$	−1.59822	+	1.59822i	−0.0523796	+	0.0523796i
$932$	−87.1420	−	50.3114i	−2.85443	−	1.64801i
$933$	−11.3631	+	5.66163i	−0.372010	+	0.185353i
$934$	59.8184	+	16.0283i	1.95732	+	0.524462i
$935$	35.5067			1.16119
$936$	−56.9071	−	40.6096i	−1.86007	−	1.32737i
$937$	−10.4641			−0.341848			−0.170924	−	0.985284i	$-0.554675\pi$
$937$	−10.4641			−0.341848			−0.170924	+	0.985284i	$0.554675\pi$
$938$	−8.98135	−	2.40655i	−0.293252	−	0.0785765i
$939$	1.98570	−	0.989371i	0.0648008	−	0.0322869i
$940$	70.2863	+	40.5798i	2.29249	+	1.32357i
$941$	15.8998	−	15.8998i	0.518319	−	0.518319i	−0.398744	−	0.917062i	$-0.630554\pi$
$941$	15.8998	−	15.8998i	0.518319	−	0.518319i	0.917062	+	0.398744i	$0.130554\pi$
$942$	−44.6874	+	9.07934i	−1.45599	+	0.295821i
$943$	2.61870	+	9.77313i	0.0852767	+	0.318257i
$944$	59.1583	+	59.1583i	1.92544	+	1.92544i
$945$	−10.1552	+	11.8710i	−0.330349	+	0.386163i
$946$	−20.0095	+	11.5525i	−0.650566	+	0.375604i
$947$	11.9659	−	44.6573i	0.388839	−	1.45117i	−0.443186	−	0.896430i	$-0.646152\pi$
$947$	11.9659	−	44.6573i	0.388839	−	1.45117i	0.832025	−	0.554738i	$-0.187181\pi$
$948$	−53.4698	−	3.28466i	−1.73662	−	0.106681i
$949$	−53.6578	+	1.42236i	−1.74181	+	0.0461719i
$950$			23.3262i			0.756802i
$951$	15.0746	−	45.0133i	0.488827	−	1.45966i
$952$	−25.9603	−	44.9645i	−0.841377	−	1.45731i
$953$	1.22793	−	2.12683i	0.0397765	−	0.0688949i	−0.845452	−	0.534052i	$-0.820669\pi$
$953$	1.22793	−	2.12683i	0.0397765	−	0.0688949i	0.885228	+	0.465157i	$0.154002\pi$
$954$	−22.9935	−	29.4627i	−0.744443	−	0.953891i
$955$	63.2067	−	16.9362i	2.04532	−	0.548042i
$956$	29.0876	−	7.79400i	0.940760	−	0.252076i
$957$	−3.04676	−	3.44558i	−0.0984876	−	0.111380i
$958$	−18.8467	+	32.6435i	−0.608911	+	1.05466i
$959$	8.88667	+	15.3922i	0.286966	+	0.497039i
$960$	3.66966	+	1.22894i	0.118438	+	0.0396638i
$961$			1.16701i			0.0376456i
$962$	18.1569	+	61.2244i	0.585403	+	1.97395i
$963$	3.73389	−	30.2766i	0.120323	−	0.975650i
$964$	−7.33853	+	27.3877i	−0.236358	+	0.882100i
$965$	−28.8201	+	16.6393i	−0.927751	+	0.535637i
$966$	2.72726	−	4.11806i	0.0877483	−	0.132496i
$967$	29.8022	+	29.8022i	0.958375	+	0.958375i	0.999168	−	0.0407929i	$-0.0129884\pi$
$967$	29.8022	+	29.8022i	0.958375	+	0.958375i	−0.0407929	+	0.999168i	$0.512988\pi$
$968$	−14.7854	−	55.1798i	−0.475220	−	1.77355i
$969$	6.26158	+	30.8187i	0.201151	+	0.990040i
$970$	−19.4031	+	19.4031i	−0.622997	+	0.622997i
$971$	−53.5146	−	30.8967i	−1.71736	−	0.991521i	−0.923655	−	0.383224i	$-0.874814\pi$
$971$	−53.5146	−	30.8967i	−1.71736	−	0.991521i	−0.793710	−	0.608297i	$-0.791853\pi$
$972$	−15.1901	−	68.9529i	−0.487222	−	2.21167i
$973$	9.36476	+	2.50928i	0.300220	+	0.0804438i
$974$	23.0905			0.739866
$975$	7.37301	−	24.1208i	0.236125	−	0.772484i
$976$	69.7651			2.23313
$977$	−7.69427	−	2.06167i	−0.246161	−	0.0659588i	0.133629	−	0.991031i	$-0.457337\pi$
$977$	−7.69427	−	2.06167i	−0.246161	−	0.0659588i	−0.379790	+	0.925073i	$0.624004\pi$
$978$	−1.82982	−	3.67251i	−0.0585113	−	0.117434i
$979$	6.39715	+	3.69340i	0.204454	+	0.118041i
$980$	−9.62900	+	9.62900i	−0.307587	+	0.307587i
$981$	14.5326	−	2.03452i	0.463989	−	0.0649571i
$982$	18.5438	+	69.2065i	0.591757	+	2.20847i
$983$	20.2622	+	20.2622i	0.646263	+	0.646263i	0.952088	−	0.305824i	$-0.0989321\pi$
$983$	20.2622	+	20.2622i	0.646263	+	0.646263i	−0.305824	+	0.952088i	$0.598932\pi$
$984$	84.6190	+	56.0405i	2.69756	+	1.78651i
$985$	1.80352	−	1.04126i	0.0574648	−	0.0331773i
$986$	9.59607	−	35.8130i	0.305601	−	1.14052i
$987$	0.632950	−	10.3035i	0.0201470	−	0.327965i
$988$	19.2964	+	31.4662i	0.613901	+	1.00107i
$989$		−	6.86384i		−	0.218257i
$990$	31.4090	+	12.7096i	0.998245	+	0.403936i
$991$	20.5812	+	35.6477i	0.653783	+	1.13239i	0.982197	+	0.187852i	$0.0601526\pi$
$991$	20.5812	+	35.6477i	0.653783	+	1.13239i	−0.328414	+	0.944534i	$0.606514\pi$
$992$	−17.3753	+	30.0949i	−0.551665	+	0.955513i
$993$	−6.65938	+	5.88855i	−0.211329	+	0.186868i
$994$	−18.6698	+	5.00256i	−0.592170	+	0.158672i
$995$	−43.4379	+	11.6392i	−1.37707	+	0.368986i
$996$	13.8951	−	12.2867i	0.440283	−	0.389320i
$997$	23.4671	−	40.6463i	0.743212	−	1.28728i	−0.207814	−	0.978168i	$-0.566635\pi$
$997$	23.4671	−	40.6463i	0.743212	−	1.28728i	0.951026	−	0.309112i	$-0.100032\pi$
$998$	−22.9100	−	39.6813i	−0.725204	−	1.25609i
$999$	−15.5315	+	32.4956i	−0.491396	+	1.02812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.2	✓	112
3.2	odd	2	inner	273.2.cc.a.50.27	yes	112
13.6	odd	12	inner	273.2.cc.a.71.27	yes	112
39.32	even	12	inner	273.2.cc.a.71.2	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.2	✓	112	1.1	even	1	trivial
273.2.cc.a.50.27	yes	112	3.2	odd	2	inner
273.2.cc.a.71.2	yes	112	39.32	even	12	inner
273.2.cc.a.71.27	yes	112	13.6	odd	12	inner

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.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.46820 - 0.661352i) q^{2} +(1.55028 - 0.772424i) q^{3} +(3.92257 + 2.26470i) q^{4} +(2.12589 - 2.12589i) q^{5} +(-4.33724 + 0.881217i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-4.57023 - 4.57023i) q^{8} +(1.80672 - 2.39494i) q^{9} +O(q^{10})\)	\(q+(-2.46820 - 0.661352i) q^{2} +(1.55028 - 0.772424i) q^{3} +(3.92257 + 2.26470i) q^{4} +(2.12589 - 2.12589i) q^{5} +(-4.33724 + 0.881217i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-4.57023 - 4.57023i) q^{8} +(1.80672 - 2.39494i) q^{9} +(-6.65309 + 3.84116i) q^{10} +(0.380509 - 1.42008i) q^{11} +(7.83038 + 0.481022i) q^{12} +(2.61617 + 2.48106i) q^{13} +2.55527i q^{14} +(1.65363 - 4.93781i) q^{15} +(3.72831 + 6.45763i) q^{16} +(-4.01657 + 6.95691i) q^{17} +(-6.04325 + 4.71632i) q^{18} +(2.18321 - 0.584989i) q^{19} +(13.1535 - 3.52446i) q^{20} +(-1.14735 - 1.29754i) q^{21} +(-1.87834 + 3.25339i) q^{22} +(-0.558002 - 0.966487i) q^{23} +(-10.6153 - 3.55497i) q^{24} -4.03883i q^{25} +(-4.81639 - 7.85395i) q^{26} +(0.951010 - 5.10838i) q^{27} +(1.17229 - 4.37506i) q^{28} +(1.56425 - 0.903119i) q^{29} +(-7.34713 + 11.0939i) q^{30} +(-4.01042 - 4.01042i) q^{31} +(-1.58581 - 5.91834i) q^{32} +(-0.507008 - 2.49543i) q^{33} +(14.5147 - 14.5147i) q^{34} +(-2.60368 - 1.50323i) q^{35} +(12.5108 - 5.30266i) q^{36} +(-6.69521 - 1.79398i) q^{37} -5.77548 q^{38} +(5.97222 + 1.82553i) q^{39} -19.4316 q^{40} +(-8.75726 - 2.34650i) q^{41} +(1.97375 + 3.96138i) q^{42} +(5.32638 + 3.07519i) q^{43} +(4.70862 - 4.70862i) q^{44} +(-1.25049 - 8.93229i) q^{45} +(0.738071 + 2.75452i) q^{46} +(4.21433 + 4.21433i) q^{47} +(10.7679 + 7.13128i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-2.67109 + 9.96865i) q^{50} +(-0.853122 + 13.8876i) q^{51} +(4.64329 + 15.6570i) q^{52} +4.87531i q^{53} +(-5.72572 + 11.9796i) q^{54} +(-2.21001 - 3.82785i) q^{55} +(-3.23164 + 5.59737i) q^{56} +(2.93272 - 2.59326i) q^{57} +(-4.45816 + 1.19456i) q^{58} +(10.8376 - 2.90392i) q^{59} +(17.6691 - 15.6239i) q^{60} +(4.67806 - 8.10263i) q^{61} +(7.24623 + 12.5508i) q^{62} +(-2.78095 - 1.12530i) q^{63} +0.743175i q^{64} +(10.8362 - 0.287246i) q^{65} +(-0.398961 + 6.49453i) q^{66} +(-0.941798 + 3.51484i) q^{67} +(-31.5106 + 18.1927i) q^{68} +(-1.61160 - 1.06731i) q^{69} +(5.43222 + 5.43222i) q^{70} +(1.95774 + 7.30640i) q^{71} +(-19.2026 + 2.68830i) q^{72} +(-10.5269 + 10.5269i) q^{73} +(15.3387 + 8.85579i) q^{74} +(-3.11969 - 6.26131i) q^{75} +(9.88862 + 2.64965i) q^{76} -1.47017 q^{77} +(-13.5333 - 8.45551i) q^{78} -6.82850 q^{79} +(21.6542 + 5.80223i) q^{80} +(-2.47151 - 8.65400i) q^{81} +(20.0628 + 11.5833i) q^{82} +(1.67181 - 1.67181i) q^{83} +(-1.56202 - 7.68807i) q^{84} +(6.25084 + 23.3284i) q^{85} +(-11.1128 - 11.1128i) q^{86} +(1.72743 - 2.60835i) q^{87} +(-8.22910 + 4.75107i) q^{88} +(-1.30042 + 4.85323i) q^{89} +(-2.82092 + 22.8737i) q^{90} +(1.71940 - 3.16917i) q^{91} -5.05482i q^{92} +(-9.31502 - 3.11952i) q^{93} +(-7.61466 - 13.1890i) q^{94} +(3.39764 - 5.88489i) q^{95} +(-7.02992 - 7.95015i) q^{96} +(3.45015 - 0.924465i) q^{97} +(2.46820 - 0.661352i) q^{98} +(-2.71353 - 3.47698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

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