LMFDB - Embedded newform 418.2.f.f.267.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 24 x^{14} - 62 x^{13} + 148 x^{12} - 232 x^{11} + 432 x^{10} - 356 x^{9} + 424 x^{8} + \cdots + 16 $ x^16 - 6x^15 + 24x^14 - 62x^13 + 148x^12 - 232x^11 + 432x^10 - 356x^9 + 424x^8 - 320x^7 + 712x^6 - 936x^5 + 968x^4 - 336x^3 + 208x^2 - 80*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			267.3
Root			$0.870631 - 0.632551i$ of defining polynomial
Character	$\chi$	$=$	418.267
Dual form			418.2.f.f.191.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.636445 + 1.95878i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.58981 - 1.15506i) q^{5} +(-1.66623 - 1.21059i) q^{6} +(1.27470 - 3.92313i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.00469 + 0.729952i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.636445 + 1.95878i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.58981 - 1.15506i) q^{5} +(-1.66623 - 1.21059i) q^{6} +(1.27470 - 3.92313i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.00469 + 0.729952i) q^{9} +1.96511 q^{10} +(-2.95516 - 1.50566i) q^{11} +2.05958 q^{12} +(3.85890 - 2.80365i) q^{13} +(1.27470 + 3.92313i) q^{14} +(1.25068 - 3.84921i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.67144 - 4.12054i) q^{17} +(0.383758 - 1.18109i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-1.58981 + 1.15506i) q^{20} +8.49580 q^{21} +(3.27578 - 0.518898i) q^{22} +3.10979 q^{23} +(-1.66623 + 1.21059i) q^{24} +(-0.351768 - 1.08263i) q^{25} +(-1.47397 + 4.53640i) q^{26} +(2.92946 + 2.12838i) q^{27} +(-3.33721 - 2.42462i) q^{28} +(-0.208859 + 0.642803i) q^{29} +(1.25068 + 3.84921i) q^{30} +(0.656300 - 0.476830i) q^{31} +1.00000 q^{32} +(1.06845 - 6.74677i) q^{33} +7.01028 q^{34} +(-6.55798 + 4.76465i) q^{35} +(0.383758 + 1.18109i) q^{36} +(-3.63206 + 11.1783i) q^{37} +(0.809017 + 0.587785i) q^{38} +(7.94770 + 5.77434i) q^{39} +(0.607252 - 1.86893i) q^{40} +(2.55747 + 7.87108i) q^{41} +(-6.87325 + 4.99371i) q^{42} +7.01961 q^{43} +(-2.34516 + 2.34525i) q^{44} +2.44041 q^{45} +(-2.51587 + 1.82789i) q^{46} +(-1.86705 - 5.74618i) q^{47} +(0.636445 - 1.95878i) q^{48} +(-8.10293 - 5.88712i) q^{49} +(0.920940 + 0.669102i) q^{50} +(4.46166 - 13.7316i) q^{51} +(-1.47397 - 4.53640i) q^{52} +(3.98840 - 2.89774i) q^{53} -3.62101 q^{54} +(2.95901 + 5.80710i) q^{55} +4.12502 q^{56} +(1.66623 - 1.21059i) q^{57} +(-0.208859 - 0.642803i) q^{58} +(1.88652 - 5.80612i) q^{59} +(-3.27433 - 2.37894i) q^{60} +(2.99976 + 2.17945i) q^{61} +(-0.250684 + 0.771527i) q^{62} +(1.58301 + 4.87200i) q^{63} +(-0.809017 + 0.587785i) q^{64} -9.37329 q^{65} +(3.10126 + 6.08627i) q^{66} -12.3789 q^{67} +(-5.67144 + 4.12054i) q^{68} +(1.97921 + 6.09138i) q^{69} +(2.50493 - 7.70937i) q^{70} +(-7.01781 - 5.09874i) q^{71} +(-1.00469 - 0.729952i) q^{72} +(3.07971 - 9.47837i) q^{73} +(-3.63206 - 11.1783i) q^{74} +(1.89675 - 1.37807i) q^{75} -1.00000 q^{76} +(-9.67384 + 9.67421i) q^{77} -9.82390 q^{78} +(11.6248 - 8.44593i) q^{79} +(0.607252 + 1.86893i) q^{80} +(-3.45585 + 10.6360i) q^{81} +(-6.69554 - 4.86459i) q^{82} +(2.01931 + 1.46711i) q^{83} +(2.62535 - 8.07999i) q^{84} +(4.25701 + 13.1017i) q^{85} +(-5.67898 + 4.12602i) q^{86} -1.39203 q^{87} +(0.518771 - 3.27580i) q^{88} +8.51163 q^{89} +(-1.97433 + 1.43444i) q^{90} +(-6.08014 - 18.7127i) q^{91} +(0.960977 - 2.95758i) q^{92} +(1.35170 + 0.982069i) q^{93} +(4.88799 + 3.55134i) q^{94} +(-0.607252 + 1.86893i) q^{95} +(0.636445 + 1.95878i) q^{96} +(-11.5332 + 8.37934i) q^{97} +10.0158 q^{98} +(4.06809 - 0.644403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9	$ 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9} + 4 q^{10} + 2 q^{11} - 14 q^{13} + 6 q^{14} - 10 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{19} + 4 q^{20} + 28 q^{21} + 2 q^{22} + 24 q^{23} - 4 q^{26} - 18 q^{27} - 14 q^{28} - 22 q^{29} - 10 q^{30} - 24 q^{31} + 16 q^{32} + 2 q^{33} + 8 q^{34} - 20 q^{35} + 6 q^{37} + 4 q^{38} + 72 q^{39} - 6 q^{40} - 14 q^{41} - 22 q^{42} + 56 q^{43} + 12 q^{44} - 56 q^{45} + 4 q^{46} - 38 q^{47} - 36 q^{49} + 56 q^{51} - 4 q^{52} + 22 q^{53} - 48 q^{54} - 6 q^{55} + 16 q^{56} - 22 q^{58} - 28 q^{59} + 12 q^{61} + 26 q^{62} - 20 q^{63} - 4 q^{64} - 32 q^{65} + 12 q^{66} - 44 q^{67} + 8 q^{68} + 64 q^{69} - 20 q^{70} + 16 q^{71} - 20 q^{72} + 12 q^{73} + 6 q^{74} + 32 q^{75} - 16 q^{76} - 12 q^{77} - 8 q^{78} + 48 q^{79} - 6 q^{80} - 64 q^{81} + 6 q^{82} + 14 q^{83} + 8 q^{84} + 6 q^{85} - 14 q^{86} + 84 q^{87} - 8 q^{88} - 56 q^{89} + 34 q^{90} + 26 q^{91} - 16 q^{92} - 46 q^{93} + 32 q^{94} + 6 q^{95} - 24 q^{97} + 64 q^{98} - 56 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9 + 4 * q^10 + 2 * q^11 - 14 * q^13 + 6 * q^14 - 10 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^19 + 4 * q^20 + 28 * q^21 + 2 * q^22 + 24 * q^23 - 4 * q^26 - 18 * q^27 - 14 * q^28 - 22 * q^29 - 10 * q^30 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 8 * q^34 - 20 * q^35 + 6 * q^37 + 4 * q^38 + 72 * q^39 - 6 * q^40 - 14 * q^41 - 22 * q^42 + 56 * q^43 + 12 * q^44 - 56 * q^45 + 4 * q^46 - 38 * q^47 - 36 * q^49 + 56 * q^51 - 4 * q^52 + 22 * q^53 - 48 * q^54 - 6 * q^55 + 16 * q^56 - 22 * q^58 - 28 * q^59 + 12 * q^61 + 26 * q^62 - 20 * q^63 - 4 * q^64 - 32 * q^65 + 12 * q^66 - 44 * q^67 + 8 * q^68 + 64 * q^69 - 20 * q^70 + 16 * q^71 - 20 * q^72 + 12 * q^73 + 6 * q^74 + 32 * q^75 - 16 * q^76 - 12 * q^77 - 8 * q^78 + 48 * q^79 - 6 * q^80 - 64 * q^81 + 6 * q^82 + 14 * q^83 + 8 * q^84 + 6 * q^85 - 14 * q^86 + 84 * q^87 - 8 * q^88 - 56 * q^89 + 34 * q^90 + 26 * q^91 - 16 * q^92 - 46 * q^93 + 32 * q^94 + 6 * q^95 - 24 * q^97 + 64 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.636445	+	1.95878i	0.367452	+	1.13090i	0.948431	+	0.316982i	$0.102670\pi$
$3$	0.636445	+	1.95878i	0.367452	+	1.13090i	−0.580980	+	0.813918i	$0.697330\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.58981	−	1.15506i	−0.710983	−	0.516560i	0.172507	−	0.985008i	$-0.444813\pi$
$5$	−1.58981	−	1.15506i	−0.710983	−	0.516560i	−0.883491	+	0.468449i	$0.844813\pi$
$6$	−1.66623	−	1.21059i	−0.680238	−	0.494222i
$7$	1.27470	−	3.92313i	0.481792	−	1.48280i	−0.354783	−	0.934949i	$-0.615445\pi$
$7$	1.27470	−	3.92313i	0.481792	−	1.48280i	0.836574	−	0.547853i	$-0.184555\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−1.00469	+	0.729952i	−0.334898	+	0.243317i
$10$	1.96511			0.621422
$11$	−2.95516	−	1.50566i	−0.891015	−	0.453973i
$11$	−2.95516	−	1.50566i	−0.891015	−	0.453973i
$12$	2.05958			0.594549
$13$	3.85890	−	2.80365i	1.07027	−	0.777593i	0.0943052	−	0.995543i	$-0.469937\pi$
$13$	3.85890	−	2.80365i	1.07027	−	0.777593i	0.975960	+	0.217950i	$0.0699370\pi$
$14$	1.27470	+	3.92313i	0.340678	+	1.04850i
$15$	1.25068	−	3.84921i	0.322925	−	0.993862i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.67144	−	4.12054i	−1.37553	−	0.999378i	−0.997283	−	0.0736720i	$-0.976528\pi$
$17$	−5.67144	−	4.12054i	−1.37553	−	0.999378i	−0.378243	−	0.925706i	$-0.623472\pi$
$18$	0.383758	−	1.18109i	0.0904527	−	0.278385i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−1.58981	+	1.15506i	−0.355492	+	0.258280i
$21$	8.49580			1.85394
$22$	3.27578	−	0.518898i	0.698399	−	0.110629i
$23$	3.10979			0.648435			0.324218	−	0.945982i	$-0.394899\pi$
$23$	3.10979			0.648435			0.324218	+	0.945982i	$0.394899\pi$
$24$	−1.66623	+	1.21059i	−0.340119	+	0.247111i
$25$	−0.351768	−	1.08263i	−0.0703536	−	0.216526i
$26$	−1.47397	+	4.53640i	−0.289069	+	0.889662i
$27$	2.92946	+	2.12838i	0.563775	+	0.409606i
$28$	−3.33721	−	2.42462i	−0.630673	−	0.458211i
$29$	−0.208859	+	0.642803i	−0.0387842	+	0.119365i	−0.968574	−	0.248725i	$-0.919988\pi$
$29$	−0.208859	+	0.642803i	−0.0387842	+	0.119365i	0.929790	+	0.368091i	$0.119988\pi$
$30$	1.25068	+	3.84921i	0.228343	+	0.702766i
$31$	0.656300	−	0.476830i	0.117875	−	0.0856412i	−0.527286	−	0.849688i	$-0.676790\pi$
$31$	0.656300	−	0.476830i	0.117875	−	0.0856412i	0.645161	+	0.764047i	$0.276790\pi$
$32$	1.00000			0.176777
$33$	1.06845	−	6.74677i	0.185993	−	1.17446i
$34$	7.01028			1.20225
$35$	−6.55798	+	4.76465i	−1.10850	+	0.805373i
$36$	0.383758	+	1.18109i	0.0639597	+	0.196848i
$37$	−3.63206	+	11.1783i	−0.597107	+	1.83771i	−0.0531592	+	0.998586i	$0.516929\pi$
$37$	−3.63206	+	11.1783i	−0.597107	+	1.83771i	−0.543947	+	0.839119i	$0.683071\pi$
$38$	0.809017	+	0.587785i	0.131240	+	0.0953514i
$39$	7.94770	+	5.77434i	1.27265	+	0.924635i
$40$	0.607252	−	1.86893i	0.0960150	−	0.295504i
$41$	2.55747	+	7.87108i	0.399409	+	1.22926i	0.925474	+	0.378811i	$0.123667\pi$
$41$	2.55747	+	7.87108i	0.399409	+	1.22926i	−0.526065	+	0.850445i	$0.676333\pi$
$42$	−6.87325	+	4.99371i	−1.06057	+	0.770546i
$43$	7.01961			1.07048			0.535240	−	0.844700i	$-0.320221\pi$
$43$	7.01961			1.07048			0.535240	+	0.844700i	$0.320221\pi$
$44$	−2.34516	+	2.34525i	−0.353547	+	0.353560i
$45$	2.44041			0.363794
$46$	−2.51587	+	1.82789i	−0.370945	+	0.269507i
$47$	−1.86705	−	5.74618i	−0.272337	−	0.838167i	−0.989912	−	0.141685i	$-0.954748\pi$
$47$	−1.86705	−	5.74618i	−0.272337	−	0.838167i	0.717575	−	0.696481i	$-0.245252\pi$
$48$	0.636445	−	1.95878i	0.0918629	−	0.282725i
$49$	−8.10293	−	5.88712i	−1.15756	−	0.841018i
$50$	0.920940	+	0.669102i	0.130241	+	0.0946254i
$51$	4.46166	−	13.7316i	0.624758	−	1.92281i
$52$	−1.47397	−	4.53640i	−0.204402	−	0.629086i
$53$	3.98840	−	2.89774i	0.547848	−	0.398035i	−0.279143	−	0.960250i	$-0.590050\pi$
$53$	3.98840	−	2.89774i	0.547848	−	0.398035i	0.826992	+	0.562214i	$0.190050\pi$
$54$	−3.62101			−0.492757
$55$	2.95901	+	5.80710i	0.398993	+	0.783030i
$56$	4.12502			0.551229
$57$	1.66623	−	1.21059i	0.220698	−	0.160347i
$58$	−0.208859	−	0.642803i	−0.0274246	−	0.0844041i
$59$	1.88652	−	5.80612i	0.245604	−	0.755893i	−0.749932	−	0.661515i	$-0.769914\pi$
$59$	1.88652	−	5.80612i	0.245604	−	0.755893i	0.995536	−	0.0943778i	$-0.0300862\pi$
$60$	−3.27433	−	2.37894i	−0.422715	−	0.307120i
$61$	2.99976	+	2.17945i	0.384080	+	0.279050i	0.763025	−	0.646369i	$-0.223713\pi$
$61$	2.99976	+	2.17945i	0.384080	+	0.279050i	−0.378945	+	0.925419i	$0.623713\pi$
$62$	−0.250684	+	0.771527i	−0.0318369	+	0.0979840i
$63$	1.58301	+	4.87200i	0.199441	+	0.613815i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−9.37329			−1.16261
$66$	3.10126	+	6.08627i	0.381739	+	0.749169i
$67$	−12.3789			−1.51233			−0.756164	−	0.654383i	$-0.772929\pi$
$67$	−12.3789			−1.51233			−0.756164	+	0.654383i	$0.772929\pi$
$68$	−5.67144	+	4.12054i	−0.687763	+	0.499689i
$69$	1.97921	+	6.09138i	0.238269	+	0.733316i
$70$	2.50493	−	7.70937i	0.299396	−	0.921446i
$71$	−7.01781	−	5.09874i	−0.832861	−	0.605109i	0.0875065	−	0.996164i	$-0.472110\pi$
$71$	−7.01781	−	5.09874i	−0.832861	−	0.605109i	−0.920367	+	0.391055i	$0.872110\pi$
$72$	−1.00469	−	0.729952i	−0.118404	−	0.0860256i
$73$	3.07971	−	9.47837i	0.360453	−	1.10936i	−0.592327	−	0.805698i	$-0.701791\pi$
$73$	3.07971	−	9.47837i	0.360453	−	1.10936i	0.952780	−	0.303662i	$-0.0982094\pi$
$74$	−3.63206	−	11.1783i	−0.422218	−	1.29945i
$75$	1.89675	−	1.37807i	0.219018	−	0.159126i
$76$	−1.00000			−0.114708
$77$	−9.67384	+	9.67421i	−1.10244	+	1.10248i
$78$	−9.82390			−1.11234
$79$	11.6248	−	8.44593i	1.30790	−	0.950242i	0.307896	−	0.951420i	$-0.400375\pi$
$79$	11.6248	−	8.44593i	1.30790	−	0.950242i	0.999999	+	0.00117819i	$0.000375028\pi$
$80$	0.607252	+	1.86893i	0.0678929	+	0.208953i
$81$	−3.45585	+	10.6360i	−0.383983	+	1.18178i
$82$	−6.69554	−	4.86459i	−0.739398	−	0.537204i
$83$	2.01931	+	1.46711i	0.221648	+	0.161036i	0.693068	−	0.720872i	$-0.256259\pi$
$83$	2.01931	+	1.46711i	0.221648	+	0.161036i	−0.471420	+	0.881909i	$0.656259\pi$
$84$	2.62535	−	8.07999i	0.286449	−	0.881599i
$85$	4.25701	+	13.1017i	0.461738	+	1.42108i
$86$	−5.67898	+	4.12602i	−0.612381	+	0.444921i
$87$	−1.39203			−0.149242
$88$	0.518771	−	3.27580i	0.0553012	−	0.349202i
$89$	8.51163			0.902231			0.451116	−	0.892466i	$-0.351026\pi$
$89$	8.51163			0.902231			0.451116	+	0.892466i	$0.351026\pi$
$90$	−1.97433	+	1.43444i	−0.208113	+	0.151203i
$91$	−6.08014	−	18.7127i	−0.637372	−	1.96163i
$92$	0.960977	−	2.95758i	0.100189	−	0.308349i
$93$	1.35170	+	0.982069i	0.140165	+	0.101836i
$94$	4.88799	+	3.55134i	0.504158	+	0.366292i
$95$	−0.607252	+	1.86893i	−0.0623028	+	0.191748i
$96$	0.636445	+	1.95878i	0.0649569	+	0.199917i
$97$	−11.5332	+	8.37934i	−1.17102	+	0.850793i	−0.991130	−	0.132895i	$-0.957573\pi$
$97$	−11.5332	+	8.37934i	−1.17102	+	0.850793i	−0.179886	+	0.983688i	$0.557573\pi$
$98$	10.0158			1.01175
$99$	4.06809	−	0.644403i	0.408858	−	0.0647649i
$100$	−1.13834			−0.113834
$101$	9.72357	−	7.06459i	0.967531	−	0.702953i	0.0126437	−	0.999920i	$-0.495975\pi$
$101$	9.72357	−	7.06459i	0.967531	−	0.702953i	0.954888	+	0.296967i	$0.0959753\pi$
$102$	4.46166	+	13.7316i	0.441770	+	1.35963i
$103$	−2.19522	+	6.75620i	−0.216302	+	0.665708i	0.782757	+	0.622328i	$0.213813\pi$
$103$	−2.19522	+	6.75620i	−0.216302	+	0.665708i	−0.999059	+	0.0433808i	$0.986187\pi$
$104$	3.85890	+	2.80365i	0.378396	+	0.274921i
$105$	−13.5067	−	9.81318i	−1.31812	−	0.957669i
$106$	−1.52343	+	4.68864i	−0.147969	+	0.455401i
$107$	2.65552	+	8.17284i	0.256719	+	0.790098i	0.993486	+	0.113952i	$0.0363511\pi$
$107$	2.65552	+	8.17284i	0.256719	+	0.790098i	−0.736768	+	0.676146i	$0.763649\pi$
$108$	2.92946	−	2.12838i	0.281887	−	0.204803i
$109$	−10.3108			−0.987591			−0.493795	−	0.869578i	$-0.664391\pi$
$109$	−10.3108			−0.987591			−0.493795	+	0.869578i	$0.664391\pi$
$110$	−5.80722	−	2.95878i	−0.553697	−	0.282109i
$111$	−24.2074			−2.29767
$112$	−3.33721	+	2.42462i	−0.315337	+	0.229106i
$113$	−0.894368	−	2.75258i	−0.0841351	−	0.258941i	0.900135	−	0.435611i	$-0.143468\pi$
$113$	−0.894368	−	2.75258i	−0.0841351	−	0.258941i	−0.984270	+	0.176670i	$0.943468\pi$
$114$	−0.636445	+	1.95878i	−0.0596085	+	0.183456i
$115$	−4.94396	−	3.59200i	−0.461027	−	0.334956i
$116$	0.546801	+	0.397274i	0.0507692	+	0.0368860i
$117$	−1.83047	+	5.63362i	−0.169227	+	0.520828i
$118$	1.88652	+	5.80612i	0.173669	+	0.534497i
$119$	−23.3948	+	16.9973i	−2.14460	+	1.55814i
$120$	4.04730			0.369466
$121$	6.46598	+	8.89894i	0.587817	+	0.808994i
$122$	−3.70791			−0.335698
$123$	−13.7900	+	10.0190i	−1.24340	+	0.903384i
$124$	−0.250684	−	0.771527i	−0.0225121	−	0.0692852i
$125$	−3.72752	+	11.4721i	−0.333400	+	1.02610i
$126$	−4.14437	−	3.01106i	−0.369210	−	0.268247i
$127$	2.01364	+	1.46299i	0.178682	+	0.129820i	0.673531	−	0.739159i	$-0.264777\pi$
$127$	2.01364	+	1.46299i	0.178682	+	0.129820i	−0.494849	+	0.868979i	$0.664777\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	4.46760	+	13.7498i	0.393350	+	1.21061i
$130$	7.58315	−	5.50948i	0.665086	−	0.483214i
$131$	3.29365			0.287767			0.143884	−	0.989595i	$-0.454041\pi$
$131$	3.29365			0.287767			0.143884	+	0.989595i	$0.454041\pi$
$132$	−6.08639	−	3.10102i	−0.529753	−	0.269910i
$133$	−4.12502			−0.357684
$134$	10.0148	−	7.27615i	0.865144	−	0.628564i
$135$	−2.19887	−	6.76742i	−0.189248	−	0.582447i
$136$	2.16630	−	6.66718i	0.185758	−	0.571706i
$137$	4.13250	+	3.00244i	0.353063	+	0.256515i	0.750153	−	0.661264i	$-0.229980\pi$
$137$	4.13250	+	3.00244i	0.353063	+	0.256515i	−0.397090	+	0.917780i	$0.629980\pi$
$138$	−5.18164	−	3.76468i	−0.441090	−	0.320471i
$139$	5.69708	−	17.5338i	0.483220	−	1.48720i	−0.351323	−	0.936254i	$-0.614268\pi$
$139$	5.69708	−	17.5338i	0.483220	−	1.48720i	0.834543	−	0.550943i	$-0.185732\pi$
$140$	2.50493	+	7.70937i	0.211705	+	0.651561i
$141$	10.0672	−	7.31426i	0.847812	−	0.615972i
$142$	8.67449			0.727947
$143$	−15.6250	+	2.47507i	−1.30663	+	0.206976i
$144$	1.24187			0.103489
$145$	1.07452	−	0.780687i	0.0892343	−	0.0648325i
$146$	3.07971	+	9.47837i	0.254879	+	0.784436i
$147$	6.37449	−	19.6187i	0.525759	−	1.61812i
$148$	9.50885	+	6.90858i	0.781623	+	0.567882i
$149$	2.61290	+	1.89838i	0.214057	+	0.155522i	0.689647	−	0.724145i	$-0.257766\pi$
$149$	2.61290	+	1.89838i	0.214057	+	0.155522i	−0.475590	+	0.879667i	$0.657766\pi$
$150$	−0.724494	+	2.22976i	−0.0591547	+	0.182059i
$151$	−2.09665	−	6.45283i	−0.170623	−	0.525124i	0.828783	−	0.559570i	$-0.189034\pi$
$151$	−2.09665	−	6.45283i	−0.170623	−	0.525124i	−0.999407	+	0.0344454i	$0.989034\pi$
$152$	0.809017	−	0.587785i	0.0656199	−	0.0476757i
$153$	8.70585			0.703826
$154$	2.13994	−	13.5127i	0.172441	−	1.08889i
$155$	−1.59416			−0.128046
$156$	7.94770	−	5.77434i	0.636326	−	0.462318i
$157$	2.11327	+	6.50398i	0.168658	+	0.519074i	0.999287	−	0.0377508i	$-0.0120193\pi$
$157$	2.11327	+	6.50398i	0.168658	+	0.519074i	−0.830630	+	0.556825i	$0.812019\pi$
$158$	−4.44029	+	13.6658i	−0.353251	+	1.08719i
$159$	8.21442	+	5.96813i	0.651446	+	0.473303i
$160$	−1.58981	−	1.15506i	−0.125685	−	0.0913157i
$161$	3.96405	−	12.2001i	0.312411	−	0.961501i
$162$	−3.45585	−	10.6360i	−0.271517	−	0.835644i
$163$	15.0120	−	10.9069i	1.17583	−	0.854292i	0.184136	−	0.982901i	$-0.441051\pi$
$163$	15.0120	−	10.9069i	1.17583	−	0.854292i	0.991695	+	0.128609i	$0.0410512\pi$
$164$	8.27614			0.646258
$165$	−9.49157	+	9.49194i	−0.738918	+	0.738947i
$166$	−2.49600			−0.193727
$167$	−6.35415	+	4.61656i	−0.491699	+	0.357240i	−0.805837	−	0.592137i	$-0.798284\pi$
$167$	−6.35415	+	4.61656i	−0.491699	+	0.357240i	0.314138	+	0.949377i	$0.398284\pi$
$168$	2.62535	+	8.07999i	0.202550	+	0.623385i
$169$	3.01339	−	9.27427i	0.231799	−	0.713405i
$170$	−11.1450	−	8.09732i	−0.854782	−	0.621036i
$171$	1.00469	+	0.729952i	0.0768308	+	0.0558208i
$172$	2.16918	−	6.67605i	0.165398	−	0.509044i
$173$	6.94151	+	21.3638i	0.527754	+	1.62426i	0.758806	+	0.651317i	$0.225783\pi$
$173$	6.94151	+	21.3638i	0.527754	+	1.62426i	−0.231052	+	0.972941i	$0.574217\pi$
$174$	1.12618	−	0.818217i	0.0853754	−	0.0620289i
$175$	−4.69569			−0.354961
$176$	1.50577	+	2.95511i	0.113502	+	0.222749i
$177$	12.5736			0.945087
$178$	−6.88605	+	5.00301i	−0.516132	+	0.374992i
$179$	−2.65936	−	8.18465i	−0.198770	−	0.611750i	−0.999912	−	0.0132759i	$-0.995774\pi$
$179$	−2.65936	−	8.18465i	−0.198770	−	0.611750i	0.801142	−	0.598474i	$-0.204226\pi$
$180$	0.754127	−	2.32096i	0.0562093	−	0.172995i
$181$	8.03940	+	5.84096i	0.597564	+	0.434155i	0.845013	−	0.534745i	$-0.179592\pi$
$181$	8.03940	+	5.84096i	0.597564	+	0.434155i	−0.247450	+	0.968901i	$0.579592\pi$
$182$	15.9180	+	11.5651i	1.17992	+	0.857263i
$183$	−2.35988	+	7.26296i	−0.174447	+	0.536894i
$184$	0.960977	+	2.95758i	0.0708442	+	0.218036i
$185$	18.6859	−	13.5761i	1.37382	−	0.998137i
$186$	−1.67080			−0.122509
$187$	10.5559	+	20.7161i	0.771924	+	1.51491i
$188$	−6.04189			−0.440650
$189$	12.0841	−	8.77960i	0.878987	−	0.638622i
$190$	−0.607252	−	1.86893i	−0.0440547	−	0.135586i
$191$	−2.50725	+	7.71651i	−0.181418	+	0.558347i	−0.999868	−	0.0162301i	$-0.994834\pi$
$191$	−2.50725	+	7.71651i	−0.181418	+	0.558347i	0.818450	+	0.574577i	$0.194834\pi$
$192$	−1.66623	−	1.21059i	−0.120250	−	0.0873668i
$193$	13.9252	+	10.1173i	1.00236	+	0.728256i	0.962593	−	0.270953i	$-0.0873388\pi$
$193$	13.9252	+	10.1173i	1.00236	+	0.728256i	0.0397659	+	0.999209i	$0.487339\pi$
$194$	4.40528	−	13.5581i	0.316281	−	0.973411i
$195$	−5.96559	−	18.3602i	−0.427204	−	1.31480i
$196$	−8.10293	+	5.88712i	−0.578781	+	0.420509i
$197$	18.5503			1.32165			0.660826	−	0.750539i	$-0.270206\pi$
$197$	18.5503			1.32165			0.660826	+	0.750539i	$0.270206\pi$
$198$	−2.91238	+	2.91250i	−0.206974	+	0.206982i
$199$	−13.4114			−0.950710			−0.475355	−	0.879794i	$-0.657680\pi$
$199$	−13.4114			−0.950710			−0.475355	+	0.879794i	$0.657680\pi$
$200$	0.920940	−	0.669102i	0.0651203	−	0.0473127i
$201$	−7.87851	−	24.2476i	−0.555707	−	1.71029i
$202$	−3.71407	+	11.4307i	−0.261321	+	0.804264i
$203$	2.25556	+	1.63876i	0.158309	+	0.115019i
$204$	−11.6808	−	8.48658i	−0.817818	−	0.594180i
$205$	5.02570	−	15.4675i	0.351010	−	1.08030i
$206$	−2.19522	−	6.75620i	−0.152948	−	0.470727i
$207$	−3.12438	+	2.26999i	−0.217159	+	0.157776i
$208$	−4.76986			−0.330730
$209$	−0.518771	+	3.27580i	−0.0358841	+	0.226592i
$210$	16.6952			1.15208
$211$	8.58584	−	6.23798i	0.591074	−	0.429440i	−0.251626	−	0.967825i	$-0.580965\pi$
$211$	8.58584	−	6.23798i	0.591074	−	0.429440i	0.842699	+	0.538384i	$0.180965\pi$
$212$	−1.52343	−	4.68864i	−0.104630	−	0.322017i
$213$	5.52084	−	16.9914i	0.378281	−	1.16423i
$214$	−6.95223	−	5.05109i	−0.475245	−	0.345286i
$215$	−11.1598	−	8.10809i	−0.761094	−	0.552967i
$216$	−1.11895	+	3.44379i	−0.0761352	+	0.234320i
$217$	−1.03408	−	3.18256i	−0.0701977	−	0.216046i
$218$	8.34157	−	6.06051i	0.564963	−	0.410469i
$219$	20.5261			1.38702
$220$	6.43727	−	1.01969i	0.434001	−	0.0687476i
$221$	−33.4381			−2.24929
$222$	19.5842	−	14.2288i	1.31441	−	0.954973i
$223$	6.64038	+	20.4370i	0.444673	+	1.36856i	0.882842	+	0.469670i	$0.155627\pi$
$223$	6.64038	+	20.4370i	0.444673	+	1.36856i	−0.438170	+	0.898892i	$0.644373\pi$
$224$	1.27470	−	3.92313i	0.0851695	−	0.262125i
$225$	1.14369	+	0.830937i	0.0762458	+	0.0553958i
$226$	2.34149	+	1.70119i	0.155753	+	0.113161i
$227$	−3.90497	+	12.0182i	−0.259182	+	0.797679i	0.733795	+	0.679371i	$0.237747\pi$
$227$	−3.90497	+	12.0182i	−0.259182	+	0.797679i	−0.992977	+	0.118308i	$0.962253\pi$
$228$	−0.636445	−	1.95878i	−0.0421496	−	0.129723i
$229$	11.4826	−	8.34260i	0.758792	−	0.551295i	−0.139748	−	0.990187i	$-0.544629\pi$
$229$	11.4826	−	8.34260i	0.758792	−	0.551295i	0.898540	+	0.438892i	$0.144629\pi$
$230$	6.11107			0.402952
$231$	−25.1065	−	12.7918i	−1.65189	−	0.841637i
$232$	−0.675883			−0.0443739
$233$	−6.00718	+	4.36447i	−0.393544	+	0.285926i	−0.766906	−	0.641759i	$-0.778205\pi$
$233$	−6.00718	+	4.36447i	−0.393544	+	0.285926i	0.373362	+	0.927686i	$0.378205\pi$
$234$	−1.83047	−	5.63362i	−0.119662	−	0.368281i
$235$	−3.66895	+	11.2919i	−0.239336	+	0.736601i
$236$	−4.93898	−	3.58838i	−0.321500	−	0.233584i
$237$	23.9423	+	17.3951i	1.55522	+	1.12993i
$238$	8.93601	−	27.5022i	0.579236	−	1.78270i
$239$	−1.69441	−	5.21485i	−0.109602	−	0.337321i	0.881181	−	0.472779i	$-0.156749\pi$
$239$	−1.69441	−	5.21485i	−0.109602	−	0.337321i	−0.990783	+	0.135459i	$0.956749\pi$
$240$	−3.27433	+	2.37894i	−0.211357	+	0.153560i
$241$	−13.6790			−0.881139			−0.440570	−	0.897718i	$-0.645224\pi$
$241$	−13.6790			−0.881139			−0.440570	+	0.897718i	$0.645224\pi$
$242$	−10.4618	−	3.39878i	−0.672507	−	0.218482i
$243$	−12.1700			−0.780706
$244$	2.99976	−	2.17945i	0.192040	−	0.139525i
$245$	6.08210	+	18.7188i	0.388571	+	1.19590i
$246$	5.26731	−	16.2111i	0.335831	−	1.03358i
$247$	−3.85890	−	2.80365i	−0.245536	−	0.178392i
$248$	0.656300	+	0.476830i	0.0416751	+	0.0302787i
$249$	−1.58857	+	4.88910i	−0.100671	+	0.309834i
$250$	−3.72752	−	11.4721i	−0.235749	−	0.725562i
$251$	6.70197	−	4.86927i	0.423025	−	0.307345i	−0.355829	−	0.934551i	$-0.615801\pi$
$251$	6.70197	−	4.86927i	0.423025	−	0.307345i	0.778854	+	0.627206i	$0.215801\pi$
$252$	5.12273			0.322702
$253$	−9.18993	−	4.68228i	−0.577766	−	0.294372i
$254$	−2.48900			−0.156173
$255$	−22.9540	+	16.6771i	−1.43744	+	1.04436i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	5.89873	−	18.1544i	0.367952	−	1.13244i	−0.580159	−	0.814503i	$-0.697010\pi$
$257$	5.89873	−	18.1544i	0.367952	−	1.13244i	0.948111	−	0.317938i	$-0.102990\pi$
$258$	−11.6963	−	8.49787i	−0.728181	−	0.529055i
$259$	39.2242	+	28.4980i	2.43727	+	1.77078i
$260$	−2.89651	+	8.91453i	−0.179634	+	0.552856i
$261$	−0.259376	−	0.798276i	−0.0160549	−	0.0494121i
$262$	−2.66462	+	1.93596i	−0.164621	+	0.119604i
$263$	−20.9903			−1.29431			−0.647157	−	0.762357i	$-0.724042\pi$
$263$	−20.9903			−1.29431			−0.647157	+	0.762357i	$0.724042\pi$
$264$	6.74673	−	1.06871i	0.415233	−	0.0657747i
$265$	−9.68785			−0.595120
$266$	3.33721	−	2.42462i	0.204617	−	0.148663i
$267$	5.41719	+	16.6724i	0.331526	+	1.02033i
$268$	−3.82530	+	11.7731i	−0.233667	+	0.719154i
$269$	20.9581	+	15.2269i	1.27784	+	0.928403i	0.999485	−	0.0320757i	$-0.0102118\pi$
$269$	20.9581	+	15.2269i	1.27784	+	0.928403i	0.278352	+	0.960479i	$0.410212\pi$
$270$	5.75671	+	4.18249i	0.350342	+	0.254539i
$271$	3.30284	−	10.1651i	0.200633	−	0.617486i	−0.799231	−	0.601024i	$-0.794760\pi$
$271$	3.30284	−	10.1651i	0.200633	−	0.617486i	0.999864	−	0.0164622i	$-0.00524031\pi$
$272$	2.16630	+	6.66718i	0.131351	+	0.404257i
$273$	32.7844	−	23.8193i	1.98420	−	1.44161i
$274$	−5.10805			−0.308589
$275$	−0.590540	+	3.72899i	−0.0356109	+	0.224867i
$276$	6.40485			0.385527
$277$	−18.9707	+	13.7830i	−1.13984	+	0.828143i	−0.987097	−	0.160123i	$-0.948811\pi$
$277$	−18.9707	+	13.7830i	−1.13984	+	0.828143i	−0.152743	+	0.988266i	$0.548811\pi$
$278$	5.69708	+	17.5338i	0.341688	+	1.05161i
$279$	−0.311317	+	0.958135i	−0.0186381	+	0.0573620i
$280$	−6.55798	−	4.76465i	−0.391914	−	0.284742i
$281$	−13.3990	−	9.73492i	−0.799315	−	0.580736i	0.111398	−	0.993776i	$-0.464467\pi$
$281$	−13.3990	−	9.73492i	−0.799315	−	0.580736i	−0.910713	+	0.413040i	$0.864467\pi$
$282$	−3.84533	+	11.8347i	−0.228986	+	0.704747i
$283$	−0.482193	−	1.48404i	−0.0286634	−	0.0882168i	0.935701	−	0.352793i	$-0.114768\pi$
$283$	−0.482193	−	1.48404i	−0.0286634	−	0.0882168i	−0.964365	+	0.264576i	$0.914768\pi$
$284$	−7.01781	+	5.09874i	−0.416430	+	0.302554i
$285$	−4.04730			−0.239741
$286$	11.1861	−	11.1865i	0.661447	−	0.661473i
$287$	34.1392			2.01517
$288$	−1.00469	+	0.729952i	−0.0592021	+	0.0430128i
$289$	9.93307	+	30.5708i	0.584298	+	1.79828i
$290$	−0.410431	+	1.26318i	−0.0241014	+	0.0741763i
$291$	−23.7535	−	17.2579i	−1.39245	−	1.01168i
$292$	−8.06279	−	5.85796i	−0.471839	−	0.342811i
$293$	0.702176	−	2.16108i	0.0410216	−	0.126251i	−0.928448	−	0.371461i	$-0.878857\pi$
$293$	0.702176	−	2.16108i	0.0410216	−	0.126251i	0.969470	+	0.245210i	$0.0788569\pi$
$294$	6.37449	+	19.6187i	0.371768	+	1.14418i
$295$	−9.70564	+	7.05156i	−0.565084	+	0.410558i
$296$	−11.7536			−0.683163
$297$	−5.45242	−	10.7005i	−0.316382	−	0.620904i
$298$	−3.22972			−0.187093
$299$	12.0003	−	8.71876i	0.693998	−	0.504219i
$300$	−0.724494	−	2.22976i	−0.0418287	−	0.128735i
$301$	8.94790	−	27.5388i	0.515749	−	1.58731i
$302$	5.48911	+	3.98807i	0.315863	+	0.229488i
$303$	20.0265	+	14.5501i	1.15049	+	0.835880i
$304$	−0.309017	+	0.951057i	−0.0177233	+	0.0545468i
$305$	−2.25164	−	6.92982i	−0.128928	−	0.396800i
$306$	−7.04318	+	5.11717i	−0.402632	+	0.292529i
$307$	−15.9893			−0.912556			−0.456278	−	0.889837i	$-0.650818\pi$
$307$	−15.9893			−0.912556			−0.456278	+	0.889837i	$0.650818\pi$
$308$	6.21134	+	12.1899i	0.353924	+	0.694582i
$309$	−14.6310			−0.832330
$310$	1.28970	−	0.937023i	0.0732501	−	0.0532193i
$311$	3.77957	+	11.6323i	0.214320	+	0.659608i	0.999201	+	0.0399625i	$0.0127238\pi$
$311$	3.77957	+	11.6323i	0.214320	+	0.659608i	−0.784881	+	0.619646i	$0.787276\pi$
$312$	−3.03575	+	9.34309i	−0.171866	+	0.528948i
$313$	23.2932	+	16.9235i	1.31661	+	0.956574i	0.999968	+	0.00802959i	$0.00255593\pi$
$313$	23.2932	+	16.9235i	1.31661	+	0.956574i	0.316644	+	0.948545i	$0.397444\pi$
$314$	−5.53262	−	4.01968i	−0.312224	−	0.226844i
$315$	3.11079	−	9.57402i	0.175273	−	0.539435i
$316$	−4.44029	−	13.6658i	−0.249786	−	0.768762i
$317$	−8.33870	+	6.05842i	−0.468348	+	0.340275i	−0.796797	−	0.604247i	$-0.793474\pi$
$317$	−8.33870	+	6.05842i	−0.468348	+	0.340275i	0.328449	+	0.944522i	$0.393474\pi$
$318$	−10.1536			−0.569385
$319$	1.58505	−	1.58512i	0.0887460	−	0.0887495i
$320$	1.96511			0.109853
$321$	−14.3187	+	10.4031i	−0.799191	+	0.580646i
$322$	3.96405	+	12.2001i	0.220908	+	0.679884i
$323$	−2.16630	+	6.66718i	−0.120536	+	0.370972i
$324$	9.04753	+	6.57342i	0.502641	+	0.365190i
$325$	−4.39275	−	3.19152i	−0.243666	−	0.177034i
$326$	−5.73408	+	17.6477i	−0.317581	+	0.977415i
$327$	−6.56223	−	20.1965i	−0.362892	−	1.11687i
$328$	−6.69554	+	4.86459i	−0.369699	+	0.268602i
$329$	−24.9229			−1.37405
$330$	2.09962	−	13.2581i	0.115580	−	0.729837i
$331$	−1.18204			−0.0649706			−0.0324853	−	0.999472i	$-0.510342\pi$
$331$	−1.18204			−0.0649706			−0.0324853	+	0.999472i	$0.510342\pi$
$332$	2.01931	−	1.46711i	0.110824	−	0.0805182i
$333$	−4.51054	−	13.8820i	−0.247176	−	0.760729i
$334$	2.42707	−	7.46975i	0.132803	−	0.408726i
$335$	19.6801	+	14.2984i	1.07524	+	0.781207i
$336$	−6.87325	−	4.99371i	−0.374966	−	0.272429i
$337$	−1.18201	+	3.63785i	−0.0643882	+	0.198167i	−0.978075	−	0.208252i	$-0.933223\pi$
$337$	−1.18201	+	3.63785i	−0.0643882	+	0.198167i	0.913687	+	0.406419i	$0.133223\pi$
$338$	3.01339	+	9.27427i	0.163907	+	0.504454i
$339$	4.82248	−	3.50373i	0.261921	−	0.190297i
$340$	13.7760			0.747107
$341$	−2.65742	+	0.420946i	−0.143907	+	0.0227955i
$342$	−1.24187			−0.0671525
$343$	−10.0643	+	7.31212i	−0.543419	+	0.394817i
$344$	2.16918	+	6.67605i	0.116954	+	0.359948i
$345$	3.88936	−	11.9702i	0.209396	−	0.644455i
$346$	−18.1731	−	13.2035i	−0.976993	−	0.709827i
$347$	12.7126	+	9.23623i	0.682447	+	0.495827i	0.874169	−	0.485622i	$-0.161407\pi$
$347$	12.7126	+	9.23623i	0.682447	+	0.495827i	−0.191721	+	0.981449i	$0.561407\pi$
$348$	−0.430162	+	1.32390i	−0.0230591	+	0.0709687i
$349$	8.92950	+	27.4822i	0.477985	+	1.47109i	0.841889	+	0.539651i	$0.181444\pi$
$349$	8.92950	+	27.4822i	0.477985	+	1.47109i	−0.363904	+	0.931437i	$0.618556\pi$
$350$	3.79890	−	2.76006i	0.203060	−	0.147531i
$351$	17.2717			0.921896
$352$	−2.95516	−	1.50566i	−0.157511	−	0.0802519i
$353$	22.1628			1.17960			0.589802	−	0.807548i	$-0.299206\pi$
$353$	22.1628			1.17960			0.589802	+	0.807548i	$0.299206\pi$
$354$	−10.1722	+	7.39056i	−0.540648	+	0.392804i
$355$	5.26760	+	16.2120i	0.279575	+	0.860444i
$356$	2.63024	−	8.09504i	0.139402	−	0.429036i
$357$	−48.1834	−	35.0073i	−2.55014	−	1.85278i
$358$	6.96228	+	5.05839i	0.367968	+	0.267344i
$359$	7.34559	−	22.6074i	0.387685	−	1.19317i	−0.546828	−	0.837245i	$-0.684165\pi$
$359$	7.34559	−	22.6074i	0.387685	−	1.19317i	0.934514	−	0.355928i	$-0.115835\pi$
$360$	0.754127	+	2.32096i	0.0397460	+	0.122326i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−9.93724			−0.522290
$363$	−13.3158	+	18.3291i	−0.698897	+	0.962028i
$364$	−19.6757			−1.03129
$365$	−15.8443	+	11.5115i	−0.829326	+	0.602541i
$366$	−2.35988	−	7.26296i	−0.123353	−	0.379641i
$367$	7.06991	−	21.7589i	0.369046	−	1.13581i	−0.578362	−	0.815780i	$-0.696308\pi$
$367$	7.06991	−	21.7589i	0.369046	−	1.13581i	0.947408	−	0.320027i	$-0.103692\pi$
$368$	−2.51587	−	1.82789i	−0.131149	−	0.0952852i
$369$	−8.31498	−	6.04118i	−0.432860	−	0.314491i
$370$	−7.13739	+	21.9666i	−0.371055	+	1.14199i
$371$	−6.28418	−	19.3407i	−0.326259	−	1.00412i
$372$	1.35170	−	0.982069i	0.0700825	−	0.0509179i
$373$	−0.861889			−0.0446269			−0.0223135	−	0.999751i	$-0.507103\pi$
$373$	−0.861889			−0.0446269			−0.0223135	+	0.999751i	$0.507103\pi$
$374$	−20.7165	−	10.5551i	−1.07123	−	0.545791i
$375$	−24.8437			−1.28292
$376$	4.88799	−	3.55134i	0.252079	−	0.183146i
$377$	0.996229	+	3.06608i	0.0513084	+	0.157911i
$378$	−4.61571	+	14.2057i	−0.237406	+	0.730662i
$379$	−22.1284	−	16.0772i	−1.13666	−	0.825830i	−0.150007	−	0.988685i	$-0.547930\pi$
$379$	−22.1284	−	16.0772i	−1.13666	−	0.825830i	−0.986650	+	0.162855i	$0.947930\pi$
$380$	1.58981	+	1.15506i	0.0815554	+	0.0592534i
$381$	−1.58411	+	4.87539i	−0.0811564	+	0.249774i
$382$	−2.50725	−	7.71651i	−0.128282	−	0.394811i
$383$	−9.15035	+	6.64812i	−0.467561	+	0.339703i	−0.796490	−	0.604652i	$-0.793312\pi$
$383$	−9.15035	+	6.64812i	−0.467561	+	0.339703i	0.328929	+	0.944355i	$0.393312\pi$
$384$	2.05958			0.105102
$385$	26.5539	−	4.20624i	1.35331	−	0.214370i
$386$	−17.2125			−0.876093
$387$	−7.05255	+	5.12398i	−0.358501	+	0.260466i
$388$	4.40528	+	13.5581i	0.223644	+	0.688306i
$389$	−4.73958	+	14.5869i	−0.240306	+	0.739587i	0.756067	+	0.654495i	$0.227119\pi$
$389$	−4.73958	+	14.5869i	−0.240306	+	0.739587i	−0.996373	+	0.0850925i	$0.972881\pi$
$390$	15.6181	+	11.3472i	0.790854	+	0.574589i
$391$	−17.6370	−	12.8140i	−0.891940	−	0.648032i
$392$	3.09504	−	9.52557i	0.156323	−	0.481114i
$393$	2.09623	+	6.45152i	0.105741	+	0.325436i
$394$	−15.0075	+	10.9036i	−0.756067	+	0.549314i
$395$	−28.2368			−1.42075
$396$	0.644245	−	4.06811i	0.0323745	−	0.204430i
$397$	−14.1783			−0.711591			−0.355795	−	0.934564i	$-0.615790\pi$
$397$	−14.1783			−0.711591			−0.355795	+	0.934564i	$0.615790\pi$
$398$	10.8501	−	7.88303i	0.543864	−	0.395141i
$399$	−2.62535	−	8.07999i	−0.131432	−	0.404505i
$400$	−0.351768	+	1.08263i	−0.0175884	+	0.0541315i
$401$	−15.0977	−	10.9691i	−0.753942	−	0.547771i	0.143104	−	0.989708i	$-0.454292\pi$
$401$	−15.0977	−	10.9691i	−0.753942	−	0.547771i	−0.897046	+	0.441936i	$0.854292\pi$
$402$	20.6262	+	14.9858i	1.02874	+	0.747425i
$403$	1.19573	−	3.68007i	0.0595635	−	0.183318i
$404$	−3.71407	−	11.4307i	−0.184782	−	0.568701i
$405$	17.7794	−	12.9175i	0.883465	−	0.641875i
$406$	−2.78803			−0.138368
$407$	27.5641	−	27.5651i	1.36630	−	1.36635i
$408$	14.4382			0.714799
$409$	−20.9734	+	15.2381i	−1.03707	+	0.753475i	−0.969711	−	0.244254i	$-0.921457\pi$
$409$	−20.9734	+	15.2381i	−1.03707	+	0.753475i	−0.0673577	+	0.997729i	$0.521457\pi$
$410$	5.02570	+	15.4675i	0.248202	+	0.763887i
$411$	−3.25099	+	10.0055i	−0.160360	+	0.493536i
$412$	5.74717	+	4.17556i	0.283143	+	0.205715i
$413$	−20.3734	−	14.8021i	−1.00251	−	0.728365i
$414$	1.19341	−	3.67293i	0.0586528	−	0.180515i
$415$	−1.51570	−	4.66485i	−0.0744028	−	0.228988i
$416$	3.85890	−	2.80365i	0.189198	−	0.137460i
$417$	37.9707			1.85943
$418$	−1.50577	−	2.95511i	−0.0736498	−	0.144539i
$419$	6.07570			0.296818			0.148409	−	0.988926i	$-0.452585\pi$
$419$	6.07570			0.296818			0.148409	+	0.988926i	$0.452585\pi$
$420$	−13.5067	+	9.81318i	−0.659059	+	0.478834i
$421$	1.09786	+	3.37887i	0.0535065	+	0.164676i	0.974239	−	0.225519i	$-0.0724077\pi$
$421$	1.09786	+	3.37887i	0.0535065	+	0.164676i	−0.920732	+	0.390195i	$0.872408\pi$
$422$	−3.27950	+	10.0933i	−0.159644	+	0.491332i
$423$	6.07025	+	4.41029i	0.295145	+	0.214436i
$424$	3.98840	+	2.89774i	0.193694	+	0.140727i
$425$	−2.46599	+	7.58955i	−0.119618	+	0.368147i
$426$	5.52084	+	16.9914i	0.267485	+	0.823235i
$427$	12.3741	−	8.99029i	0.598823	−	0.435070i
$428$	8.59343			0.415379
$429$	−14.7926	−	29.0307i	−0.714192	−	1.40161i
$430$	13.7943			0.665220
$431$	24.0098	−	17.4441i	1.15651	−	0.840253i	0.167176	−	0.985927i	$-0.446535\pi$
$431$	24.0098	−	17.4441i	1.15651	−	0.840253i	0.989333	+	0.145674i	$0.0465351\pi$
$432$	−1.11895	−	3.44379i	−0.0538357	−	0.165689i
$433$	−6.74472	+	20.7581i	−0.324131	+	0.997572i	0.647701	+	0.761895i	$0.275731\pi$
$433$	−6.74472	+	20.7581i	−0.324131	+	0.997572i	−0.971831	+	0.235677i	$0.924269\pi$
$434$	2.70725	+	1.96693i	0.129952	+	0.0944157i
$435$	2.21307	+	1.60789i	0.106108	+	0.0770922i
$436$	−3.18620	+	9.80611i	−0.152591	+	0.469627i
$437$	−0.960977	−	2.95758i	−0.0459698	−	0.141480i
$438$	−16.6060	+	12.0649i	−0.793463	+	0.576485i
$439$	21.6449			1.03305			0.516527	−	0.856271i	$-0.327224\pi$
$439$	21.6449			1.03305			0.516527	+	0.856271i	$0.327224\pi$
$440$	−4.60850	+	4.60868i	−0.219702	+	0.219710i
$441$	12.4383			0.592299
$442$	27.0520	−	19.6544i	1.28673	−	0.934864i
$443$	−2.56932	−	7.90757i	−0.122072	−	0.375700i	0.871284	−	0.490779i	$-0.163288\pi$
$443$	−2.56932	−	7.90757i	−0.122072	−	0.375700i	−0.993356	+	0.115079i	$0.963288\pi$
$444$	−7.48051	+	23.0227i	−0.355009	+	1.09261i
$445$	−13.5318	−	9.83146i	−0.641471	−	0.466056i
$446$	−17.3847	−	12.6308i	−0.823191	−	0.598083i
$447$	−2.05554	+	6.32630i	−0.0972237	+	0.299224i
$448$	1.27470	+	3.92313i	0.0602239	+	0.185350i
$449$	2.79095	−	2.02774i	0.131713	−	0.0956951i	−0.519978	−	0.854180i	$-0.674060\pi$
$449$	2.79095	−	2.02774i	0.131713	−	0.0956951i	0.651691	+	0.758485i	$0.274060\pi$
$450$	−1.41367			−0.0666413
$451$	4.29342	−	27.1110i	0.202169	−	1.27661i
$452$	−2.89424			−0.136133
$453$	11.3053	−	8.21375i	0.531167	−	0.385916i
$454$	−3.90497	−	12.0182i	−0.183269	−	0.564044i
$455$	−11.9481	+	36.7726i	−0.560138	+	1.72393i
$456$	1.66623	+	1.21059i	0.0780286	+	0.0566911i
$457$	−32.9884	−	23.9675i	−1.54313	−	1.12115i	−0.948332	−	0.317279i	$-0.897231\pi$
$457$	−32.9884	−	23.9675i	−1.54313	−	1.12115i	−0.594801	−	0.803873i	$-0.702769\pi$
$458$	−4.38597	+	13.4986i	−0.204943	+	0.630749i
$459$	−7.84419	−	24.1419i	−0.366135	−	1.12685i
$460$	−4.94396	+	3.59200i	−0.230513	+	0.167478i
$461$	39.4014			1.83510			0.917552	−	0.397616i	$-0.130162\pi$
$461$	39.4014			1.83510			0.917552	+	0.397616i	$0.130162\pi$
$462$	27.8304	−	4.40845i	1.29479	−	0.205100i
$463$	4.81281			0.223670			0.111835	−	0.993727i	$-0.464327\pi$
$463$	4.81281			0.223670			0.111835	+	0.993727i	$0.464327\pi$
$464$	0.546801	−	0.397274i	0.0253846	−	0.0184430i
$465$	−1.01459	−	3.12260i	−0.0470507	−	0.144807i
$466$	2.29454	−	7.06187i	0.106293	−	0.327135i
$467$	−3.75772	−	2.73014i	−0.173886	−	0.126336i	0.497438	−	0.867500i	$-0.334274\pi$
$467$	−3.75772	−	2.73014i	−0.173886	−	0.126336i	−0.671324	+	0.741164i	$0.734274\pi$
$468$	4.79224	+	3.48177i	0.221521	+	0.160945i
$469$	−15.7794	+	48.5641i	−0.728627	+	2.24248i
$470$	−3.66895	−	11.2919i	−0.169236	−	0.520855i
$471$	−11.3949	+	8.27886i	−0.525048	+	0.381470i
$472$	6.10492			0.281002
$473$	−20.7441	−	10.5691i	−0.953815	−	0.485970i
$474$	−29.5943			−1.35931
$475$	−0.920940	+	0.669102i	−0.0422556	+	0.0307005i
$476$	8.93601	+	27.5022i	0.409582	+	1.26056i
$477$	−1.89190	+	5.82268i	−0.0866242	+	0.266602i
$478$	4.43602	+	3.22296i	0.202899	+	0.147415i
$479$	23.2091	+	16.8624i	1.06045	+	0.770462i	0.974171	−	0.225809i	$-0.0725027\pi$
$479$	23.2091	+	16.8624i	1.06045	+	0.770462i	0.0862780	+	0.996271i	$0.472503\pi$
$480$	1.25068	−	3.84921i	0.0570857	−	0.175692i
$481$	17.3244	+	53.3190i	0.789925	+	2.43114i
$482$	11.0665	−	8.04029i	0.504066	−	0.366225i
$483$	26.4201			1.20216
$484$	10.4615	−	3.39959i	0.475522	−	0.154527i
$485$	28.0142			1.27206
$486$	9.84574	−	7.15335i	0.446612	−	0.324482i
$487$	−6.21877	−	19.1394i	−0.281799	−	0.867289i	−0.987340	−	0.158619i	$-0.949296\pi$
$487$	−6.21877	−	19.1394i	−0.281799	−	0.867289i	0.705541	−	0.708670i	$-0.250704\pi$
$488$	−1.14581	+	3.52643i	−0.0518682	+	0.159634i
$489$	30.9184	+	22.4636i	1.39818	+	1.01584i
$490$	−15.9231	−	11.5688i	−0.719334	−	0.522627i
$491$	3.56010	−	10.9569i	0.160665	−	0.494476i	−0.838026	−	0.545631i	$-0.816290\pi$
$491$	3.56010	−	10.9569i	0.160665	−	0.494476i	0.998691	+	0.0511546i	$0.0162901\pi$
$492$	5.26731	+	16.2111i	0.237469	+	0.730853i
$493$	3.83323	−	2.78500i	0.172640	−	0.125430i
$494$	4.76986			0.214606
$495$	−7.21180	−	3.67442i	−0.324146	−	0.165153i
$496$	−0.811231			−0.0364254
$497$	−28.9486	+	21.0324i	−1.29852	+	0.943431i
$498$	−1.58857	−	4.88910i	−0.0711854	−	0.219086i
$499$	−0.528565	+	1.62676i	−0.0236618	+	0.0728236i	−0.962190	−	0.272379i	$-0.912190\pi$
$499$	−0.528565	+	1.62676i	−0.0236618	+	0.0728236i	0.938528	+	0.345202i	$0.112190\pi$
$500$	9.75878	+	7.09017i	0.436426	+	0.317082i
$501$	−13.0869	−	9.50817i	−0.584678	−	0.424794i
$502$	−2.55993	+	7.87864i	−0.114255	+	0.351641i
$503$	−6.89858	−	21.2316i	−0.307592	−	0.946672i	−0.978697	−	0.205309i	$-0.934180\pi$
$503$	−6.89858	−	21.2316i	−0.307592	−	0.946672i	0.671105	−	0.741363i	$-0.265820\pi$
$504$	−4.14437	+	3.01106i	−0.184605	+	0.134123i
$505$	−23.6186			−1.05102
$506$	10.1870	−	1.61366i	0.452867	−	0.0717360i
$507$	20.0841			0.891965
$508$	2.01364	−	1.46299i	0.0893408	−	0.0649099i
$509$	−2.78143	−	8.56038i	−0.123285	−	0.379432i	0.870300	−	0.492522i	$-0.163925\pi$
$509$	−2.78143	−	8.56038i	−0.123285	−	0.379432i	−0.993585	+	0.113090i	$0.963925\pi$
$510$	8.76765	−	26.9841i	0.388238	−	1.19487i
$511$	−33.2591	−	24.1642i	−1.47130	−	1.06896i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	1.11895	−	3.44379i	0.0494030	−	0.152047i
$514$	5.89873	+	18.1544i	0.260182	+	0.800757i
$515$	11.2938	−	8.20544i	0.497665	−	0.361575i
$516$	14.4574			0.636454
$517$	−3.13436	+	19.7920i	−0.137849	+	0.870453i
$518$	−48.4838			−2.13025
$519$	−37.4290	+	27.1938i	−1.64295	+	1.19367i
$520$	−2.89651	−	8.91453i	−0.127020	−	0.390928i
$521$	7.56158	−	23.2721i	0.331279	−	1.01957i	−0.637247	−	0.770659i	$-0.719927\pi$
$521$	7.56158	−	23.2721i	0.331279	−	1.01957i	0.968526	−	0.248912i	$-0.0800730\pi$
$522$	0.679054	+	0.493362i	0.0297214	+	0.0215939i
$523$	−2.48550	−	1.80582i	−0.108683	−	0.0789630i	0.532116	−	0.846671i	$-0.321397\pi$
$523$	−2.48550	−	1.80582i	−0.108683	−	0.0789630i	−0.640799	+	0.767708i	$0.721397\pi$
$524$	1.01779	−	3.13244i	0.0444625	−	0.136841i
$525$	−2.98855	−	9.19781i	−0.130431	−	0.401426i
$526$	16.9815	−	12.3378i	0.740427	−	0.537952i
$527$	−5.68696			−0.247728
$528$	−4.83005	+	4.83024i	−0.210201	+	0.210209i
$529$	−13.3292			−0.579531
$530$	7.83764	−	5.69438i	0.340445	−	0.247348i
$531$	2.34281	+	7.21044i	0.101669	+	0.312906i
$532$	−1.27470	+	3.92313i	−0.0552653	+	0.170089i
$533$	31.9368	+	23.2034i	1.38333	+	1.00505i
$534$	−14.1824	−	10.3041i	−0.613731	−	0.445902i
$535$	5.21838	−	16.0605i	0.225610	−	0.694357i
$536$	−3.82530	−	11.7731i	−0.165228	−	0.508519i
$537$	14.3394	−	10.4182i	0.618790	−	0.449577i
$538$	−25.9056			−1.11687
$539$	15.0815	+	29.5977i	0.649606	+	1.27486i
$540$	−7.11569			−0.306210
$541$	11.4877	−	8.34628i	0.493894	−	0.358835i	−0.312786	−	0.949824i	$-0.601262\pi$
$541$	11.4877	−	8.34628i	0.493894	−	0.358835i	0.806680	+	0.590989i	$0.201262\pi$
$542$	3.30284	+	10.1651i	0.141869	+	0.436629i
$543$	−6.32451	+	19.4648i	−0.271411	+	0.835316i
$544$	−5.67144	−	4.12054i	−0.243161	−	0.176667i
$545$	16.3921	+	11.9096i	0.702161	+	0.510150i
$546$	−12.5225	+	38.5404i	−0.535915	+	1.64938i
$547$	4.60778	+	14.1813i	0.197015	+	0.606348i	0.999947	+	0.0102787i	$0.00327186\pi$
$547$	4.60778	+	14.1813i	0.197015	+	0.606348i	−0.802933	+	0.596070i	$0.796728\pi$
$548$	4.13250	−	3.00244i	0.176532	−	0.128258i
$549$	−4.60473			−0.196525
$550$	−1.71409	−	3.36393i	−0.0730890	−	0.143438i
$551$	0.675883			0.0287936
$552$	−5.18164	+	3.76468i	−0.220545	+	0.160235i
$553$	−18.3163	−	56.3717i	−0.778887	−	2.39717i
$554$	7.24617	−	22.3014i	0.307860	−	0.947497i
$555$	38.4852	+	27.9611i	1.63360	+	1.18688i
$556$	−14.9151	−	10.8365i	−0.632543	−	0.459569i
$557$	−2.06206	+	6.34638i	−0.0873725	+	0.268905i	−0.985191	−	0.171461i	$-0.945151\pi$
$557$	−2.06206	+	6.34638i	−0.0873725	+	0.268905i	0.897818	+	0.440366i	$0.145151\pi$
$558$	−0.311317	−	0.958135i	−0.0131791	−	0.0405611i
$559$	27.0879	−	19.6805i	1.14570	−	0.832398i
$560$	8.10611			0.342546
$561$	−33.8600	+	33.8613i	−1.42957	+	1.42963i
$562$	16.5620			0.698627
$563$	33.1391	−	24.0769i	1.39665	−	1.01472i	0.401546	−	0.915839i	$-0.368473\pi$
$563$	33.1391	−	24.0769i	1.39665	−	1.01472i	0.995099	−	0.0988833i	$-0.0315271\pi$
$564$	−3.84533	−	11.8347i	−0.161918	−	0.498332i
$565$	−1.75753	+	5.40913i	−0.0739399	+	0.227564i
$566$	1.26240	+	0.917185i	0.0530625	+	0.0385522i
$567$	37.3212	+	27.1155i	1.56734	+	1.13874i
$568$	2.68056	−	8.24993i	0.112474	−	0.346159i
$569$	−7.44178	−	22.9034i	−0.311976	−	0.960162i	−0.976982	−	0.213324i	$-0.931571\pi$
$569$	−7.44178	−	22.9034i	−0.311976	−	0.960162i	0.665006	−	0.746838i	$-0.268429\pi$
$570$	3.27433	−	2.37894i	0.137147	−	0.0996430i
$571$	32.6098			1.36468			0.682339	−	0.731036i	$-0.260963\pi$
$571$	32.6098			1.36468			0.682339	+	0.731036i	$0.260963\pi$
$572$	−2.47446	+	15.6251i	−0.103463	+	0.653319i
$573$	−16.7107			−0.698097
$574$	−27.6192	+	20.0665i	−1.15280	+	0.837561i
$575$	−1.09392	−	3.36675i	−0.0456198	−	0.140403i
$576$	0.383758	−	1.18109i	0.0159899	−	0.0492120i
$577$	−2.26922	−	1.64868i	−0.0944689	−	0.0686356i	0.539548	−	0.841955i	$-0.318595\pi$
$577$	−2.26922	−	1.64868i	−0.0944689	−	0.0686356i	−0.634017	+	0.773319i	$0.718595\pi$
$578$	−26.0051	−	18.8938i	−1.08167	−	0.785879i
$579$	−10.9548	+	33.7155i	−0.455267	+	1.40117i
$580$	−0.410431	−	1.26318i	−0.0170422	−	0.0524506i
$581$	8.32967	−	6.05186i	0.345573	−	0.251074i
$582$	29.3609			1.21705
$583$	−16.1494	+	2.55813i	−0.668839	+	0.105947i
$584$	9.96615			0.412402
$585$	9.41728	−	6.84205i	0.389356	−	0.282884i
$586$	0.702176	+	2.16108i	0.0290066	+	0.0892732i
$587$	−1.58279	+	4.87133i	−0.0653288	+	0.201061i	−0.978393	−	0.206755i	$-0.933710\pi$
$587$	−1.58279	+	4.87133i	−0.0653288	+	0.201061i	0.913064	+	0.407816i	$0.133710\pi$
$588$	−16.6886	−	12.1250i	−0.688228	−	0.500027i
$589$	−0.656300	−	0.476830i	−0.0270424	−	0.0196474i
$590$	3.70722	−	11.4097i	0.152624	−	0.469728i
$591$	11.8062	+	36.3359i	0.485644	+	1.49466i
$592$	9.50885	−	6.90858i	0.390811	−	0.283941i
$593$	−40.3565			−1.65724			−0.828621	−	0.559810i	$-0.810874\pi$
$593$	−40.3565			−1.65724			−0.828621	+	0.559810i	$0.810874\pi$
$594$	10.7007	+	5.45201i	0.439054	+	0.223699i
$595$	56.8261			2.32964
$596$	2.61290	−	1.89838i	0.107029	−	0.0777608i
$597$	−8.53563	−	26.2700i	−0.349340	−	1.07516i
$598$	−4.58372	+	14.1073i	−0.187442	+	0.576888i
$599$	11.6010	+	8.42859i	0.474002	+	0.344383i	0.798999	−	0.601332i	$-0.205363\pi$
$599$	11.6010	+	8.42859i	0.474002	+	0.344383i	−0.324997	+	0.945715i	$0.605363\pi$
$600$	1.89675	+	1.37807i	0.0774345	+	0.0562595i
$601$	1.36308	−	4.19514i	0.0556014	−	0.171123i	−0.919399	−	0.393326i	$-0.871325\pi$
$601$	1.36308	−	4.19514i	0.0556014	−	0.171123i	0.975001	+	0.222202i	$0.0713245\pi$
$602$	8.94790	+	27.5388i	0.364689	+	1.12240i
$603$	12.4370	−	9.03602i	0.506475	−	0.367975i
$604$	−6.78491			−0.276074
$605$	−0.000838142	−	21.6162i	−3.40753e−5	−	0.878824i
$606$	−24.7541			−1.00557
$607$	−16.1654	+	11.7448i	−0.656132	+	0.476708i	−0.865354	−	0.501160i	$-0.832907\pi$
$607$	−16.1654	+	11.7448i	−0.656132	+	0.476708i	0.209223	+	0.977868i	$0.432907\pi$
$608$	−0.309017	−	0.951057i	−0.0125323	−	0.0385704i
$609$	−1.77443	+	5.46112i	−0.0719034	+	0.221296i
$610$	5.89486	+	4.28286i	0.238676	+	0.173408i
$611$	−23.3150	−	16.9394i	−0.943226	−	0.685293i
$612$	2.69026	−	8.27975i	0.108747	−	0.334689i
$613$	−9.82448	−	30.2366i	−0.396807	−	1.22125i	−0.927545	−	0.373710i	$-0.878085\pi$
$613$	−9.82448	−	30.2366i	−0.396807	−	1.22125i	0.530739	−	0.847536i	$-0.321915\pi$
$614$	12.9356	−	9.39825i	0.522038	−	0.379283i
$615$	33.4960			1.35069
$616$	−12.1901	−	6.21087i	−0.491153	−	0.250243i
$617$	11.2190			0.451658			0.225829	−	0.974167i	$-0.427491\pi$
$617$	11.2190			0.451658			0.225829	+	0.974167i	$0.427491\pi$
$618$	11.8368	−	8.59990i	0.476144	−	0.345939i
$619$	13.2064	+	40.6450i	0.530809	+	1.63366i	0.752535	+	0.658552i	$0.228831\pi$
$619$	13.2064	+	40.6450i	0.530809	+	1.63366i	−0.221726	+	0.975109i	$0.571169\pi$
$620$	−0.492622	+	1.51613i	−0.0197842	+	0.0608894i
$621$	9.11000	+	6.61880i	0.365572	+	0.265603i
$622$	−9.89504	−	7.18917i	−0.396755	−	0.288259i
$623$	10.8498	−	33.3922i	0.434687	−	1.33783i
$624$	−3.03575	−	9.34309i	−0.121527	−	0.374023i
$625$	14.5724	−	10.5875i	0.582895	−	0.423498i
$626$	−28.7920			−1.15076
$627$	−6.74673	+	1.06871i	−0.269439	+	0.0426802i
$628$	6.83869			0.272894
$629$	66.6597	−	48.4311i	2.65790	−	1.93108i
$630$	3.11079	+	9.57402i	0.123937	+	0.381438i
$631$	−9.10889	+	28.0343i	−0.362619	+	1.11603i	0.588839	+	0.808250i	$0.299585\pi$
$631$	−9.10889	+	28.0343i	−0.362619	+	1.11603i	−0.951458	+	0.307777i	$0.900415\pi$
$632$	11.6248	+	8.44593i	0.462411	+	0.335961i
$633$	17.6832	+	12.8476i	0.702845	+	0.510647i
$634$	3.18510	−	9.80272i	0.126496	−	0.389316i
$635$	−1.51145	−	4.65176i	−0.0599800	−	0.184599i
$636$	8.21442	−	5.96813i	0.325723	−	0.236652i
$637$	−47.7738			−1.89287
$638$	−0.350628	+	2.21406i	−0.0138815	+	0.0876554i
$639$	10.7726			0.426156
$640$	−1.58981	+	1.15506i	−0.0628426	+	0.0456578i
$641$	2.98080	+	9.17396i	0.117734	+	0.362350i	0.992508	−	0.122183i	$-0.0389896\pi$
$641$	2.98080	+	9.17396i	0.117734	+	0.362350i	−0.874773	+	0.484533i	$0.838990\pi$
$642$	5.46925	−	16.8326i	0.215854	−	0.664330i
$643$	4.91545	+	3.57128i	0.193846	+	0.140838i	0.680475	−	0.732771i	$-0.261773\pi$
$643$	4.91545	+	3.57128i	0.193846	+	0.140838i	−0.486629	+	0.873609i	$0.661773\pi$
$644$	−10.3780	−	7.54007i	−0.408951	−	0.297120i
$645$	8.77932	−	27.0200i	0.345685	−	1.06391i
$646$	−2.16630	−	6.66718i	−0.0852318	−	0.262317i
$647$	−32.3835	+	23.5280i	−1.27313	+	0.924980i	−0.999322	−	0.0368060i	$-0.988282\pi$
$647$	−32.3835	+	23.5280i	−1.27313	+	0.924980i	−0.273803	+	0.961786i	$0.588282\pi$
$648$	−11.1834			−0.439324
$649$	−14.3170	+	14.3176i	−0.561992	+	0.562014i
$650$	5.42974			0.212972
$651$	5.57580	−	4.05105i	0.218533	−	0.158773i
$652$	−5.73408	−	17.6477i	−0.224564	−	0.691136i
$653$	−1.42893	+	4.39779i	−0.0559183	+	0.172099i	−0.975115	−	0.221700i	$-0.928839\pi$
$653$	−1.42893	+	4.39779i	−0.0559183	+	0.172099i	0.919197	+	0.393799i	$0.128839\pi$
$654$	17.1801	+	12.4821i	0.671796	+	0.488089i
$655$	−5.23626	−	3.80437i	−0.204598	−	0.148649i
$656$	2.55747	−	7.87108i	0.0998523	−	0.307314i
$657$	3.82459	+	11.7709i	0.149212	+	0.459226i
$658$	20.1631	−	14.6493i	0.786038	−	0.571090i
$659$	−37.9621			−1.47879			−0.739397	−	0.673270i	$-0.764889\pi$
$659$	−37.9621			−1.47879			−0.739397	+	0.673270i	$0.764889\pi$
$660$	6.09432	+	11.9602i	0.237221	+	0.465550i
$661$	−18.2744			−0.710791			−0.355396	−	0.934716i	$-0.615654\pi$
$661$	−18.2744			−0.710791			−0.355396	+	0.934716i	$0.615654\pi$
$662$	0.956288	−	0.694784i	0.0371672	−	0.0270035i
$663$	−21.2815	−	65.4977i	−0.826504	−	2.54372i
$664$	−0.771306	+	2.37384i	−0.0299325	+	0.0921227i
$665$	6.55798	+	4.76465i	0.254308	+	0.184765i
$666$	11.8087	+	8.57955i	0.457579	+	0.332451i
$667$	−0.649508	+	1.99898i	−0.0251490	+	0.0774008i
$668$	2.42707	+	7.46975i	0.0939061	+	0.289013i
$669$	−35.8053	+	26.0140i	−1.38431	+	1.00576i
$670$	−24.3260			−0.939794
$671$	−5.58327	−	10.9573i	−0.215540	−	0.423000i
$672$	8.49580			0.327733
$673$	−20.0143	+	14.5413i	−0.771496	+	0.560525i	−0.902415	−	0.430869i	$-0.858207\pi$
$673$	−20.0143	+	14.5413i	−0.771496	+	0.560525i	0.130919	+	0.991393i	$0.458207\pi$
$674$	−1.18201	−	3.63785i	−0.0455294	−	0.140125i
$675$	1.27376	−	3.92022i	0.0490269	−	0.150889i
$676$	−7.88916	−	5.73181i	−0.303429	−	0.220454i
$677$	−11.4196	−	8.29682i	−0.438890	−	0.318873i	0.346303	−	0.938123i	$-0.387437\pi$
$677$	−11.4196	−	8.29682i	−0.438890	−	0.318873i	−0.785194	+	0.619250i	$0.787437\pi$
$678$	−1.84202	+	5.66916i	−0.0707424	+	0.217723i
$679$	18.1719	+	55.9272i	0.697372	+	2.14629i
$680$	−11.1450	+	8.09732i	−0.427391	+	0.310518i
$681$	−26.0264			−0.997332
$682$	1.90247	−	1.90254i	0.0728493	−	0.0728521i
$683$	7.29411			0.279101			0.139551	−	0.990215i	$-0.455434\pi$
$683$	7.29411			0.279101			0.139551	+	0.990215i	$0.455434\pi$
$684$	1.00469	−	0.729952i	0.0384154	−	0.0279104i
$685$	−3.10187	−	9.54659i	−0.118517	−	0.364756i
$686$	3.84421	−	11.8313i	0.146773	−	0.451719i
$687$	23.6493	+	17.1823i	0.902279	+	0.655544i
$688$	−5.67898	−	4.12602i	−0.216509	−	0.157303i
$689$	7.26655	−	22.3642i	0.276834	−	0.852006i
$690$	3.88936	+	11.9702i	0.148065	+	0.455699i
$691$	0.0706045	−	0.0512972i	0.00268592	−	0.00195144i	−0.586441	−	0.809992i	$-0.699472\pi$
$691$	0.0706045	−	0.0512972i	0.00268592	−	0.00195144i	0.589127	+	0.808040i	$0.299472\pi$
$692$	22.4632			0.853923
$693$	2.65752	−	16.7810i	0.100951	−	0.637459i
$694$	−15.7136			−0.596481
$695$	−29.3099	+	21.2949i	−1.11179	+	0.807761i
$696$	−0.430162	−	1.32390i	−0.0163053	−	0.0501824i
$697$	17.9286	−	55.1785i	0.679093	−	2.09003i
$698$	−23.3777	−	16.9849i	−0.884861	−	0.642889i
$699$	−12.3723	−	8.98898i	−0.467962	−	0.339995i
$700$	−1.45105	+	4.46587i	−0.0548445	+	0.168794i
$701$	−9.94488	−	30.6072i	−0.375613	−	1.15602i	−0.943064	−	0.332611i	$-0.892071\pi$
$701$	−9.94488	−	30.6072i	−0.375613	−	1.15602i	0.567451	−	0.823407i	$-0.307929\pi$
$702$	−13.9731	+	10.1521i	−0.527381	+	0.383165i
$703$	11.7536			0.443295
$704$	3.27578	−	0.518898i	0.123461	−	0.0195567i
$705$	−24.4534			−0.920967
$706$	−17.9301	+	13.0269i	−0.674806	+	0.490276i
$707$	−15.3206	−	47.1520i	−0.576191	−	1.77333i
$708$	3.88545	−	11.9582i	0.146024	−	0.449416i
$709$	−9.17829	−	6.66842i	−0.344698	−	0.250438i	0.401943	−	0.915664i	$-0.368335\pi$
$709$	−9.17829	−	6.66842i	−0.344698	−	0.250438i	−0.746641	+	0.665227i	$0.768335\pi$
$710$	−13.7908	−	10.0196i	−0.517558	−	0.376028i
$711$	−5.51426	+	16.9711i	−0.206801	+	0.636467i
$712$	2.63024	+	8.09504i	0.0985724	+	0.303375i
$713$	2.04095	−	1.48284i	0.0764343	−	0.0555328i
$714$	59.5580			2.22890
$715$	27.6996	+	14.1130i	1.03591	+	0.527796i
$716$	−8.60585			−0.321616
$717$	9.13633	−	6.63793i	0.341203	−	0.247898i
$718$	7.34559	+	22.6074i	0.274135	+	0.843700i
$719$	12.7693	−	39.2999i	0.476215	−	1.46564i	−0.368097	−	0.929787i	$-0.619991\pi$
$719$	12.7693	−	39.2999i	0.476215	−	1.46564i	0.844312	−	0.535852i	$-0.180009\pi$
$720$	−1.97433	−	1.43444i	−0.0735790	−	0.0534582i
$721$	23.7072	+	17.2243i	0.882901	+	0.641465i
$722$	0.309017	−	0.951057i	0.0115004	−	0.0353947i
$723$	−8.70591	−	26.7940i	−0.323776	−	0.996481i
$724$	8.03940	−	5.84096i	0.298782	−	0.217078i
$725$	0.769388			0.0285743
$726$	−0.000878435	−	22.6554i	−3.26018e−5	−	0.840820i
$727$	37.0528			1.37421			0.687107	−	0.726556i	$-0.258880\pi$
$727$	37.0528			1.37421			0.687107	+	0.726556i	$0.258880\pi$
$728$	15.9180	−	11.5651i	0.589961	−	0.428632i
$729$	2.62202	+	8.06973i	0.0971117	+	0.298879i
$730$	6.05197	−	18.6260i	0.223993	−	0.689381i
$731$	−39.8113	−	28.9246i	−1.47247	−	1.06981i
$732$	6.17825	+	4.48876i	0.228355	+	0.165909i
$733$	−4.61237	+	14.1954i	−0.170362	+	0.524320i	−0.999391	−	0.0348852i	$-0.988893\pi$
$733$	−4.61237	+	14.1954i	−0.170362	+	0.524320i	0.829030	+	0.559205i	$0.188893\pi$
$734$	7.06991	+	21.7589i	0.260955	+	0.803137i
$735$	−32.7950	+	23.8270i	−1.20966	+	0.878870i
$736$	3.10979			0.114628
$737$	36.5818	+	18.6385i	1.34751	+	0.686556i
$738$	10.2779			0.378334
$739$	−4.69205	+	3.40898i	−0.172600	+	0.125401i	−0.670731	−	0.741700i	$-0.734020\pi$
$739$	−4.69205	+	3.40898i	−0.172600	+	0.125401i	0.498132	+	0.867101i	$0.334020\pi$
$740$	−7.13739	−	21.9666i	−0.262376	−	0.807509i
$741$	3.03575	−	9.34309i	0.111521	−	0.343227i
$742$	16.4522	+	11.9532i	0.603980	+	0.438817i
$743$	3.31675	+	2.40976i	0.121680	+	0.0884054i	0.646961	−	0.762523i	$-0.276040\pi$
$743$	3.31675	+	2.40976i	0.121680	+	0.0884054i	−0.525281	+	0.850929i	$0.676040\pi$
$744$	−0.516304	+	1.58902i	−0.0189286	+	0.0582563i
$745$	−1.96126	−	6.03612i	−0.0718548	−	0.221146i
$746$	0.697283	−	0.506605i	0.0255293	−	0.0185481i
$747$	−3.09970			−0.113412
$748$	22.9642	−	3.63762i	0.839653	−	0.133005i
$749$	35.4481			1.29524
$750$	20.0990	−	14.6028i	0.733911	−	0.533218i
$751$	8.82916	+	27.1733i	0.322180	+	0.991569i	0.972697	+	0.232078i	$0.0745523\pi$
$751$	8.82916	+	27.1733i	0.322180	+	0.991569i	−0.650517	+	0.759492i	$0.725448\pi$
$752$	−1.86705	+	5.74618i	−0.0680842	+	0.209542i
$753$	13.8032	+	10.0286i	0.503018	+	0.365464i
$754$	−2.60816	−	1.89494i	−0.0949836	−	0.0690096i
$755$	−4.12015	+	12.6805i	−0.149948	+	0.461492i
$756$	−4.61571	−	14.2057i	−0.167872	−	0.516656i
$757$	−19.7454	+	14.3459i	−0.717658	+	0.521409i	−0.885635	−	0.464382i	$-0.846277\pi$
$757$	−19.7454	+	14.3459i	−0.717658	+	0.521409i	0.167977	+	0.985791i	$0.446277\pi$
$758$	27.3522			0.993475
$759$	3.32265	−	20.9810i	0.120605	−	0.761563i
$760$	−1.96511			−0.0712820
$761$	10.1631	−	7.38395i	0.368414	−	0.267668i	−0.388139	−	0.921601i	$-0.626882\pi$
$761$	10.1631	−	7.38395i	0.368414	−	0.267668i	0.756553	+	0.653933i	$0.226882\pi$
$762$	−1.58411	−	4.87539i	−0.0573862	−	0.176617i
$763$	−13.1431	+	40.4504i	−0.475813	+	1.46440i
$764$	6.56406	+	4.76907i	0.237479	+	0.172539i
$765$	−13.8406	−	10.0558i	−0.500409	−	0.363568i
$766$	3.49512	−	10.7569i	0.126284	−	0.388662i
$767$	−8.99845	−	27.6944i	−0.324915	−	0.999986i
$768$	−1.66623	+	1.21059i	−0.0601251	+	0.0436834i
$769$	−4.12912			−0.148900			−0.0744500	−	0.997225i	$-0.523720\pi$
$769$	−4.12912			−0.148900			−0.0744500	+	0.997225i	$0.523720\pi$
$770$	−19.0101	+	19.0109i	−0.685078	+	0.685105i
$771$	39.3147			1.41588
$772$	13.9252	−	10.1173i	0.501179	−	0.364128i
$773$	0.453830	+	1.39675i	0.0163231	+	0.0502375i	0.958886	−	0.283790i	$-0.0915920\pi$
$773$	0.453830	+	1.39675i	0.0163231	+	0.0502375i	−0.942563	+	0.334028i	$0.891592\pi$
$774$	2.69383	−	8.29077i	0.0968279	−	0.298006i
$775$	−0.747096	−	0.542797i	−0.0268365	−	0.0194978i
$776$	−11.5332	−	8.37934i	−0.414017	−	0.300801i
$777$	−30.8572	+	94.9688i	−1.10700	+	3.40699i
$778$	−4.73958	−	14.5869i	−0.169922	−	0.522967i
$779$	6.69554	−	4.86459i	0.239893	−	0.174292i
$780$	−19.3050			−0.691231
$781$	13.0618	+	25.6340i	0.467389	+	0.917258i
$782$	21.8005			0.779584
$783$	−1.97997	+	1.43853i	−0.0707584	+	0.0514090i
$784$	3.09504	+	9.52557i	0.110537	+	0.340199i
$785$	4.15281	−	12.7810i	0.148220	−	0.456175i
$786$	−5.48799	−	3.98726i	−0.195750	−	0.142221i
$787$	5.57236	+	4.04856i	0.198633	+	0.144316i	0.682656	−	0.730740i	$-0.260825\pi$
$787$	5.57236	+	4.04856i	0.198633	+	0.144316i	−0.484023	+	0.875055i	$0.660825\pi$
$788$	5.73235	−	17.6424i	0.204207	−	0.628483i
$789$	−13.3591	−	41.1152i	−0.475598	−	1.46374i
$790$	22.8441	−	16.5972i	0.812755	−	0.590501i
$791$	−11.9388			−0.424494
$792$	1.86997	+	3.66985i	0.0664466	+	0.130402i
$793$	17.6862			0.628055
$794$	11.4705	−	8.33382i	0.407073	−	0.295756i
$795$	−6.16579	−	18.9763i	−0.218678	−	0.673021i
$796$	−4.14435	+	12.7550i	−0.146893	+	0.452089i
$797$	30.5336	+	22.1839i	1.08156	+	0.785796i	0.977953	−	0.208823i	$-0.0669633\pi$
$797$	30.5336	+	22.1839i	1.08156	+	0.785796i	0.103602	+	0.994619i	$0.466963\pi$
$798$	6.87325	+	4.99371i	0.243310	+	0.176775i
$799$	−13.0885	+	40.2824i	−0.463039	+	1.42509i
$800$	−0.351768	−	1.08263i	−0.0124369	−	0.0382768i
$801$	−8.55157	+	6.21308i	−0.302155	+	0.219528i
$802$	18.6618			0.658970
$803$	−23.3722	+	23.3732i	−0.824789	+	0.824821i
$804$	−25.4954			−0.899153
$805$	−20.3939	+	14.8171i	−0.718792	+	0.522233i
$806$	1.19573	+	3.68007i	0.0421177	+	0.129625i
$807$	−16.4875	+	50.7433i	−0.580388	+	1.78625i
$808$	9.72357	+	7.06459i	0.342074	+	0.248531i
$809$	−39.8703	−	28.9675i	−1.40177	−	1.01844i	−0.994456	−	0.105154i	$-0.966467\pi$
$809$	−39.8703	−	28.9675i	−1.40177	−	1.01844i	−0.407311	−	0.913290i	$-0.633533\pi$
$810$	−6.79112	+	20.9009i	−0.238616	+	0.734384i
$811$	−6.81658	−	20.9793i	−0.239363	−	0.736682i	−0.996513	−	0.0834412i	$-0.973409\pi$
$811$	−6.81658	−	20.9793i	−0.239363	−	0.736682i	0.757150	−	0.653241i	$-0.226591\pi$
$812$	2.25556	−	1.63876i	0.0791547	−	0.0575093i
$813$	22.0132			0.772038
$814$	−6.09742	+	38.5024i	−0.213714	+	1.34951i
$815$	−36.4643			−1.27729
$816$	−11.6808	+	8.48658i	−0.408909	+	0.297090i
$817$	−2.16918	−	6.67605i	−0.0758900	−	0.233565i
$818$	8.01113	−	24.6557i	0.280103	−	0.862068i
$819$	19.7681	+	14.3623i	0.690752	+	0.501861i
$820$	−13.1575	−	9.55946i	−0.459479	−	0.333831i
$821$	−1.82446	+	5.61511i	−0.0636740	+	0.195969i	−0.977833	−	0.209388i	$-0.932853\pi$
$821$	−1.82446	+	5.61511i	−0.0636740	+	0.195969i	0.914159	+	0.405357i	$0.132853\pi$
$822$	−3.25099	−	10.0055i	−0.113391	−	0.348983i
$823$	−22.7907	+	16.5584i	−0.794433	+	0.577190i	−0.909276	−	0.416194i	$-0.863364\pi$
$823$	−22.7907	+	16.5584i	−0.794433	+	0.577190i	0.114843	+	0.993384i	$0.463364\pi$
$824$	−7.10389			−0.247476
$825$	−7.68011	+	1.21656i	−0.267387	+	0.0423553i
$826$	25.1829			0.876225
$827$	28.9988	−	21.0689i	1.00839	−	0.732636i	0.0445166	−	0.999009i	$-0.485825\pi$
$827$	28.9988	−	21.0689i	1.00839	−	0.732636i	0.963870	+	0.266373i	$0.0858253\pi$
$828$	1.19341	+	3.67293i	0.0414738	+	0.127643i
$829$	−0.333939	+	1.02776i	−0.0115982	+	0.0356955i	−0.956688	−	0.291115i	$-0.905974\pi$
$829$	−0.333939	+	1.02776i	−0.0115982	+	0.0356955i	0.945090	+	0.326810i	$0.105974\pi$
$830$	3.96816	+	2.88303i	0.137737	+	0.100072i
$831$	−39.0717	−	28.3873i	−1.35538	−	0.984743i
$832$	−1.47397	+	4.53640i	−0.0511006	+	0.157272i
$833$	21.6971	+	66.7769i	0.751761	+	2.31368i
$834$	−30.7189	+	22.3186i	−1.06371	+	0.772830i
$835$	15.4343			0.534125
$836$	2.95516	+	1.50566i	0.102206	+	0.0520743i
$837$	2.93748			0.101534
$838$	−4.91535	+	3.57121i	−0.169798	+	0.123365i
$839$	−3.28517	−	10.1107i	−0.113417	−	0.349060i	0.878197	−	0.478299i	$-0.158747\pi$
$839$	−3.28517	−	10.1107i	−0.113417	−	0.349060i	−0.991613	+	0.129239i	$0.958747\pi$
$840$	5.15910	−	15.8781i	0.178006	−	0.547845i
$841$	23.0919	+	16.7773i	0.796273	+	0.578526i
$842$	−2.87424	−	2.08826i	−0.0990529	−	0.0719661i
$843$	10.5408	−	32.4413i	0.363045	−	1.11734i
$844$	−3.27950	−	10.0933i	−0.112885	−	0.347424i
$845$	−15.5031	+	11.2636i	−0.533322	+	0.387481i
$846$	−7.50324			−0.257967
$847$	43.1538	−	14.0234i	1.48278	−	0.481849i
$848$	−4.92993			−0.169294
$849$	2.60001	−	1.88902i	0.0892320	−	0.0648309i
$850$	−2.46599	−	7.58955i	−0.0845829	−	0.260319i
$851$	−11.2949	+	34.7622i	−0.387185	+	1.19163i
$852$	−14.4537	−	10.5013i	−0.495177	−	0.359767i
$853$	41.1127	+	29.8701i	1.40767	+	1.02273i	0.993656	+	0.112465i	$0.0358747\pi$
$853$	41.1127	+	29.8701i	1.40767	+	1.02273i	0.414017	+	0.910269i	$0.364125\pi$
$854$	−4.72647	+	14.5466i	−0.161737	+	0.497774i
$855$	−0.754127	−	2.32096i	−0.0257906	−	0.0793753i
$856$	−6.95223	+	5.05109i	−0.237622	+	0.172643i
$857$	−15.0596			−0.514427			−0.257214	−	0.966355i	$-0.582804\pi$
$857$	−15.0596			−0.514427			−0.257214	+	0.966355i	$0.582804\pi$
$858$	29.0312	+	14.7914i	0.991110	+	0.504972i
$859$	3.74888			0.127910			0.0639551	−	0.997953i	$-0.479629\pi$
$859$	3.74888			0.127910			0.0639551	+	0.997953i	$0.479629\pi$
$860$	−11.1598	+	8.10809i	−0.380547	+	0.276484i
$861$	21.7277	+	66.8711i	0.740479	+	2.27896i
$862$	−9.17091	+	28.2252i	−0.312362	+	0.961353i
$863$	18.2791	+	13.2805i	0.622228	+	0.452075i	0.853699	−	0.520767i	$-0.174354\pi$
$863$	18.2791	+	13.2805i	0.622228	+	0.452075i	−0.231471	+	0.972842i	$0.574354\pi$
$864$	2.92946	+	2.12838i	0.0996623	+	0.0724089i
$865$	13.6408	−	41.9822i	0.463802	−	1.42744i
$866$	−6.74472	−	20.7581i	−0.229195	−	0.705390i
$867$	−53.5596	+	38.9133i	−1.81898	+	1.32157i
$868$	−3.34634			−0.113582
$869$	−47.0700	+	7.45609i	−1.59674	+	0.252930i
$870$	−2.73550			−0.0927421
$871$	−47.7690	+	34.7062i	−1.61859	+	1.17598i
$872$	−3.18620	−	9.80611i	−0.107898	−	0.332077i
$873$	5.47078	−	16.8373i	0.185158	−	0.569857i
$874$	2.51587	+	1.82789i	0.0851006	+	0.0618292i
$875$	40.2552	+	29.2471i	1.36087	+	0.988732i
$876$	6.34291	−	19.5215i	0.214307	−	0.659569i
$877$	−6.16275	−	18.9670i	−0.208101	−	0.640470i	−0.999572	−	0.0292623i	$-0.990684\pi$
$877$	−6.16275	−	18.9670i	−0.208101	−	0.640470i	0.791471	−	0.611207i	$-0.209316\pi$
$878$	−17.5111	+	12.7226i	−0.590971	+	0.429365i
$879$	4.67996			0.157851
$880$	1.01944	−	6.43731i	0.0343654	−	0.217002i
$881$	−11.0913			−0.373676			−0.186838	−	0.982391i	$-0.559824\pi$
$881$	−11.0913			−0.373676			−0.186838	+	0.982391i	$0.559824\pi$
$882$	−10.0628	+	7.31103i	−0.338831	+	0.246175i
$883$	−2.94852	−	9.07460i	−0.0992255	−	0.305385i	0.889106	−	0.457701i	$-0.151327\pi$
$883$	−2.94852	−	9.07460i	−0.0992255	−	0.305385i	−0.988332	+	0.152316i	$0.951327\pi$
$884$	−10.3329	+	31.8015i	−0.347534	+	1.06960i
$885$	−19.9895	−	14.5233i	−0.671941	−	0.488194i
$886$	6.72658	+	4.88715i	0.225984	+	0.164187i
$887$	−8.93586	+	27.5017i	−0.300037	+	0.923418i	0.681446	+	0.731868i	$0.261351\pi$
$887$	−8.93586	+	27.5017i	−0.300037	+	0.923418i	−0.981483	+	0.191550i	$0.938649\pi$
$888$	−7.48051	−	23.0227i	−0.251030	−	0.772590i
$889$	8.30630	−	6.03488i	0.278584	−	0.202403i
$890$	16.7263			0.560666
$891$	26.2268	−	26.2278i	0.878631	−	0.878665i
$892$	21.4887			0.719496
$893$	−4.88799	+	3.55134i	−0.163571	+	0.118841i
$894$	−2.05554	−	6.32630i	−0.0687475	−	0.211583i
$895$	−5.22592	+	16.0837i	−0.174683	+	0.537620i
$896$	−3.33721	−	2.42462i	−0.111488	−	0.0810010i
$897$	24.7157	+	17.9570i	0.825232	+	0.599566i
$898$	−1.06605	+	3.28096i	−0.0355745	+	0.109487i
$899$	0.169433	+	0.521462i	0.00565091	+	0.0173917i
$900$	1.14369	−	0.830937i	0.0381229	−	0.0276979i
$901$	−34.5602			−1.15137
$902$	12.4620	+	24.4569i	0.414939	+	0.814324i
$903$	59.6372			1.98460
$904$	2.34149	−	1.70119i	0.0778767	−	0.0565807i
$905$	−6.03441	−	18.5720i	−0.200591	−	0.617354i
$906$	−4.31822	+	13.2901i	−0.143463	+	0.441535i
$907$	19.7119	+	14.3215i	0.654522	+	0.475538i	0.864809	−	0.502102i	$-0.167440\pi$
$907$	19.7119	+	14.3215i	0.654522	+	0.475538i	−0.210287	+	0.977640i	$0.567440\pi$
$908$	10.2233	+	7.42769i	0.339273	+	0.246496i
$909$	−4.61239	+	14.1955i	−0.152983	+	0.470834i
$910$	−11.9481	−	36.7726i	−0.396077	−	1.21900i
$911$	−0.749069	+	0.544231i	−0.0248178	+	0.0180312i	−0.600125	−	0.799906i	$-0.704883\pi$
$911$	−0.749069	+	0.544231i	−0.0248178	+	0.0180312i	0.575307	+	0.817937i	$0.304883\pi$
$912$	−2.05958			−0.0681995
$913$	−3.75841	−	7.37594i	−0.124385	−	0.244108i
$914$	40.7759			1.34875
$915$	12.1409	−	8.82090i	0.401367	−	0.291610i
$916$	−4.38597	−	13.4986i	−0.144916	−	0.446007i
$917$	4.19841	−	12.9214i	0.138644	−	0.426702i
$918$	20.5364	+	14.9205i	0.677801	+	0.492451i
$919$	−9.09400	−	6.60717i	−0.299983	−	0.217951i	0.427603	−	0.903966i	$-0.359358\pi$
$919$	−9.09400	−	6.60717i	−0.299983	−	0.217951i	−0.727587	+	0.686016i	$0.759358\pi$
$920$	1.88843	−	5.81198i	0.0622595	−	0.191615i
$921$	−10.1763	−	31.3194i	−0.335320	−	1.03201i
$922$	−31.8764	+	23.1595i	−1.04979	+	0.762719i
$923$	−41.3761			−1.36191
$924$	−19.9240	+	19.9248i	−0.655453	+	0.655478i
$925$	13.3796			0.439920
$926$	−3.89365	+	2.82890i	−0.127953	+	0.0929634i
$927$	−2.72618	−	8.39031i	−0.0895394	−	0.275574i
$928$	−0.208859	+	0.642803i	−0.00685614	+	0.0211010i
$929$	−41.9826	−	30.5022i	−1.37740	−	1.00074i	−0.997117	−	0.0758749i	$-0.975825\pi$
$929$	−41.9826	−	30.5022i	−1.37740	−	1.00074i	−0.380288	−	0.924868i	$-0.624175\pi$
$930$	2.65624	+	1.92987i	0.0871016	+	0.0632830i
$931$	−3.09504	+	9.52557i	−0.101436	+	0.312188i
$932$	2.29454	+	7.06187i	0.0751602	+	0.231319i
$933$	−20.3796	+	14.8067i	−0.667199	+	0.484749i
$934$	4.64479			0.151982
$935$	7.14658	−	45.1274i	0.233718	−	1.47582i
$936$	−5.92353			−0.193617
$937$	3.57138	−	2.59476i	0.116672	−	0.0847671i	−0.527919	−	0.849295i	$-0.677028\pi$
$937$	3.57138	−	2.59476i	0.116672	−	0.0847671i	0.644591	+	0.764527i	$0.277028\pi$
$938$	−15.7794	−	48.5641i	−0.515217	−	1.58567i
$939$	−18.3245	+	56.3971i	−0.597999	+	1.84045i
$940$	9.60544	+	6.97876i	0.313295	+	0.227622i
$941$	−5.74944	−	4.17721i	−0.187426	−	0.136173i	0.490115	−	0.871658i	$-0.336955\pi$
$941$	−5.74944	−	4.17721i	−0.187426	−	0.136173i	−0.677542	+	0.735484i	$0.736955\pi$
$942$	4.35245	−	13.3955i	0.141811	−	0.436448i
$943$	7.95318	+	24.4774i	0.258991	+	0.797093i
$944$	−4.93898	+	3.58838i	−0.160750	+	0.116792i
$945$	−29.3523			−0.954831
$946$	22.9947	−	3.64246i	0.747623	−	0.118427i
$947$	−22.6251			−0.735218			−0.367609	−	0.929980i	$-0.619824\pi$
$947$	−22.6251			−0.735218			−0.367609	+	0.929980i	$0.619824\pi$
$948$	23.9423	−	17.3951i	0.777609	−	0.564966i
$949$	−14.6898	−	45.2105i	−0.476850	−	1.46759i
$950$	0.351768	−	1.08263i	0.0114129	−	0.0351252i
$951$	−17.1742	−	12.4778i	−0.556912	−	0.404620i
$952$	−23.3948	−	16.9973i	−0.758229	−	0.550886i
$953$	7.18422	−	22.1108i	0.232720	−	0.716238i	−0.764696	−	0.644391i	$-0.777111\pi$
$953$	7.18422	−	22.1108i	0.232720	−	0.716238i	0.997416	−	0.0718464i	$-0.0228892\pi$
$954$	−1.89190	−	5.82268i	−0.0612526	−	0.188516i
$955$	12.8991	−	9.37174i	0.417405	−	0.303262i
$956$	−5.48322			−0.177340
$957$	4.11369	+	2.09593i	0.132977	+	0.0677517i
$958$	−28.6880			−0.926867
$959$	17.0466	−	12.3851i	0.550465	−	0.399936i
$960$	1.25068	+	3.84921i	0.0403657	+	0.124233i
$961$	−9.37616	+	28.8569i	−0.302457	+	0.930867i
$962$	−45.3559	−	32.9530i	−1.46233	−	1.06245i
$963$	−8.63376	−	6.27279i	−0.278219	−	0.202138i
$964$	−4.22703	+	13.0095i	−0.136144	+	0.419007i
$965$	−10.4523	−	32.1690i	−0.336472	−	1.03556i
$966$	−21.3743	+	15.5294i	−0.687708	+	0.499649i
$967$	31.0356			0.998036			0.499018	−	0.866592i	$-0.333694\pi$
$967$	31.0356			0.998036			0.499018	+	0.866592i	$0.333694\pi$
$968$	−6.46529	+	8.89944i	−0.207802	+	0.286039i
$969$	−14.4382			−0.463823
$970$	−22.6639	+	16.4663i	−0.727695	+	0.528702i
$971$	12.2202	+	37.6099i	0.392165	+	1.20696i	0.931147	+	0.364643i	$0.118809\pi$
$971$	12.2202	+	37.6099i	0.392165	+	1.20696i	−0.538982	+	0.842317i	$0.681191\pi$
$972$	−3.76074	+	11.5744i	−0.120626	+	0.371248i
$973$	−61.5252	−	44.7007i	−1.97241	−	1.43304i
$974$	16.2809	+	11.8288i	0.521675	+	0.379019i
$975$	3.45573	−	10.6357i	0.110672	−	0.340614i
$976$	−1.14581	−	3.52643i	−0.0366764	−	0.112878i
$977$	−0.678878	+	0.493234i	−0.0217192	+	0.0157799i	−0.598592	−	0.801054i	$-0.704273\pi$
$977$	−0.678878	+	0.493234i	−0.0217192	+	0.0157799i	0.576873	+	0.816834i	$0.304273\pi$
$978$	−38.2173			−1.22205
$979$	−25.1533	−	12.8156i	−0.803902	−	0.409589i
$980$	19.6821			0.628721
$981$	10.3591	−	7.52635i	0.330742	−	0.240298i
$982$	3.56010	+	10.9569i	0.113607	+	0.349647i
$983$	−7.46369	+	22.9709i	−0.238055	+	0.732657i	0.758647	+	0.651502i	$0.225861\pi$
$983$	−7.46369	+	22.9709i	−0.238055	+	0.732657i	−0.996701	+	0.0811550i	$0.974139\pi$
$984$	−13.7900	−	10.0190i	−0.439609	−	0.319395i
$985$	−29.4914	−	21.4267i	−0.939673	−	0.682712i
$986$	−1.46416	+	4.50623i	−0.0466284	+	0.143508i
$987$	−15.8621	−	48.8184i	−0.504895	−	1.55391i
$988$	−3.85890	+	2.80365i	−0.122768	+	0.0891960i
$989$	21.8295			0.694138
$990$	7.99424	−	1.26632i	0.254074	−	0.0402464i
$991$	25.2153			0.800992			0.400496	−	0.916299i	$-0.368838\pi$
$991$	25.2153			0.800992			0.400496	+	0.916299i	$0.368838\pi$
$992$	0.656300	−	0.476830i	0.0208375	−	0.0151394i
$993$	−0.752301	−	2.31535i	−0.0238736	−	0.0734753i
$994$	11.0574	−	34.0311i	0.350719	−	1.07940i
$995$	21.3216	+	15.4910i	0.675939	+	0.491098i
$996$	4.15892	+	3.02163i	0.131780	+	0.0957441i
$997$	9.88430	−	30.4207i	0.313039	−	0.963435i	−0.663515	−	0.748163i	$-0.730936\pi$
$997$	9.88430	−	30.4207i	0.313039	−	0.963435i	0.976554	−	0.215272i	$-0.0690638\pi$
$998$	−0.528565	−	1.62676i	−0.0167314	−	0.0514941i
$999$	−34.4317	+	25.0161i	−1.08937	+	0.791473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.f.267.3	yes	16
11.2	odd	10		4598.2.a.bx.1.6		8
11.4	even	5	inner	418.2.f.f.191.3	✓	16
11.9	even	5		4598.2.a.ca.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.191.3	✓	16	11.4	even	5	inner
418.2.f.f.267.3	yes	16	1.1	even	1	trivial
4598.2.a.bx.1.6		8	11.2	odd	10
4598.2.a.ca.1.6		8	11.9	even	5

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.636445 + 1.95878i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.58981 - 1.15506i) q^{5} +(-1.66623 - 1.21059i) q^{6} +(1.27470 - 3.92313i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.00469 + 0.729952i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.636445 + 1.95878i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.58981 - 1.15506i) q^{5} +(-1.66623 - 1.21059i) q^{6} +(1.27470 - 3.92313i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.00469 + 0.729952i) q^{9} +1.96511 q^{10} +(-2.95516 - 1.50566i) q^{11} +2.05958 q^{12} +(3.85890 - 2.80365i) q^{13} +(1.27470 + 3.92313i) q^{14} +(1.25068 - 3.84921i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.67144 - 4.12054i) q^{17} +(0.383758 - 1.18109i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-1.58981 + 1.15506i) q^{20} +8.49580 q^{21} +(3.27578 - 0.518898i) q^{22} +3.10979 q^{23} +(-1.66623 + 1.21059i) q^{24} +(-0.351768 - 1.08263i) q^{25} +(-1.47397 + 4.53640i) q^{26} +(2.92946 + 2.12838i) q^{27} +(-3.33721 - 2.42462i) q^{28} +(-0.208859 + 0.642803i) q^{29} +(1.25068 + 3.84921i) q^{30} +(0.656300 - 0.476830i) q^{31} +1.00000 q^{32} +(1.06845 - 6.74677i) q^{33} +7.01028 q^{34} +(-6.55798 + 4.76465i) q^{35} +(0.383758 + 1.18109i) q^{36} +(-3.63206 + 11.1783i) q^{37} +(0.809017 + 0.587785i) q^{38} +(7.94770 + 5.77434i) q^{39} +(0.607252 - 1.86893i) q^{40} +(2.55747 + 7.87108i) q^{41} +(-6.87325 + 4.99371i) q^{42} +7.01961 q^{43} +(-2.34516 + 2.34525i) q^{44} +2.44041 q^{45} +(-2.51587 + 1.82789i) q^{46} +(-1.86705 - 5.74618i) q^{47} +(0.636445 - 1.95878i) q^{48} +(-8.10293 - 5.88712i) q^{49} +(0.920940 + 0.669102i) q^{50} +(4.46166 - 13.7316i) q^{51} +(-1.47397 - 4.53640i) q^{52} +(3.98840 - 2.89774i) q^{53} -3.62101 q^{54} +(2.95901 + 5.80710i) q^{55} +4.12502 q^{56} +(1.66623 - 1.21059i) q^{57} +(-0.208859 - 0.642803i) q^{58} +(1.88652 - 5.80612i) q^{59} +(-3.27433 - 2.37894i) q^{60} +(2.99976 + 2.17945i) q^{61} +(-0.250684 + 0.771527i) q^{62} +(1.58301 + 4.87200i) q^{63} +(-0.809017 + 0.587785i) q^{64} -9.37329 q^{65} +(3.10126 + 6.08627i) q^{66} -12.3789 q^{67} +(-5.67144 + 4.12054i) q^{68} +(1.97921 + 6.09138i) q^{69} +(2.50493 - 7.70937i) q^{70} +(-7.01781 - 5.09874i) q^{71} +(-1.00469 - 0.729952i) q^{72} +(3.07971 - 9.47837i) q^{73} +(-3.63206 - 11.1783i) q^{74} +(1.89675 - 1.37807i) q^{75} -1.00000 q^{76} +(-9.67384 + 9.67421i) q^{77} -9.82390 q^{78} +(11.6248 - 8.44593i) q^{79} +(0.607252 + 1.86893i) q^{80} +(-3.45585 + 10.6360i) q^{81} +(-6.69554 - 4.86459i) q^{82} +(2.01931 + 1.46711i) q^{83} +(2.62535 - 8.07999i) q^{84} +(4.25701 + 13.1017i) q^{85} +(-5.67898 + 4.12602i) q^{86} -1.39203 q^{87} +(0.518771 - 3.27580i) q^{88} +8.51163 q^{89} +(-1.97433 + 1.43444i) q^{90} +(-6.08014 - 18.7127i) q^{91} +(0.960977 - 2.95758i) q^{92} +(1.35170 + 0.982069i) q^{93} +(4.88799 + 3.55134i) q^{94} +(-0.607252 + 1.86893i) q^{95} +(0.636445 + 1.95878i) q^{96} +(-11.5332 + 8.37934i) q^{97} +10.0158 q^{98} +(4.06809 - 0.644403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9	\( 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9} + 4 q^{10} + 2 q^{11} - 14 q^{13} + 6 q^{14} - 10 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{19} + 4 q^{20} + 28 q^{21} + 2 q^{22} + 24 q^{23} - 4 q^{26} - 18 q^{27} - 14 q^{28} - 22 q^{29} - 10 q^{30} - 24 q^{31} + 16 q^{32} + 2 q^{33} + 8 q^{34} - 20 q^{35} + 6 q^{37} + 4 q^{38} + 72 q^{39} - 6 q^{40} - 14 q^{41} - 22 q^{42} + 56 q^{43} + 12 q^{44} - 56 q^{45} + 4 q^{46} - 38 q^{47} - 36 q^{49} + 56 q^{51} - 4 q^{52} + 22 q^{53} - 48 q^{54} - 6 q^{55} + 16 q^{56} - 22 q^{58} - 28 q^{59} + 12 q^{61} + 26 q^{62} - 20 q^{63} - 4 q^{64} - 32 q^{65} + 12 q^{66} - 44 q^{67} + 8 q^{68} + 64 q^{69} - 20 q^{70} + 16 q^{71} - 20 q^{72} + 12 q^{73} + 6 q^{74} + 32 q^{75} - 16 q^{76} - 12 q^{77} - 8 q^{78} + 48 q^{79} - 6 q^{80} - 64 q^{81} + 6 q^{82} + 14 q^{83} + 8 q^{84} + 6 q^{85} - 14 q^{86} + 84 q^{87} - 8 q^{88} - 56 q^{89} + 34 q^{90} + 26 q^{91} - 16 q^{92} - 46 q^{93} + 32 q^{94} + 6 q^{95} - 24 q^{97} + 64 q^{98} - 56 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9 + 4 * q^10 + 2 * q^11 - 14 * q^13 + 6 * q^14 - 10 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^19 + 4 * q^20 + 28 * q^21 + 2 * q^22 + 24 * q^23 - 4 * q^26 - 18 * q^27 - 14 * q^28 - 22 * q^29 - 10 * q^30 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 8 * q^34 - 20 * q^35 + 6 * q^37 + 4 * q^38 + 72 * q^39 - 6 * q^40 - 14 * q^41 - 22 * q^42 + 56 * q^43 + 12 * q^44 - 56 * q^45 + 4 * q^46 - 38 * q^47 - 36 * q^49 + 56 * q^51 - 4 * q^52 + 22 * q^53 - 48 * q^54 - 6 * q^55 + 16 * q^56 - 22 * q^58 - 28 * q^59 + 12 * q^61 + 26 * q^62 - 20 * q^63 - 4 * q^64 - 32 * q^65 + 12 * q^66 - 44 * q^67 + 8 * q^68 + 64 * q^69 - 20 * q^70 + 16 * q^71 - 20 * q^72 + 12 * q^73 + 6 * q^74 + 32 * q^75 - 16 * q^76 - 12 * q^77 - 8 * q^78 + 48 * q^79 - 6 * q^80 - 64 * q^81 + 6 * q^82 + 14 * q^83 + 8 * q^84 + 6 * q^85 - 14 * q^86 + 84 * q^87 - 8 * q^88 - 56 * q^89 + 34 * q^90 + 26 * q^91 - 16 * q^92 - 46 * q^93 + 32 * q^94 + 6 * q^95 - 24 * q^97 + 64 * q^98 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more