LMFDB - Embedded newform 62.2.d.a.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(33,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("62.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.d (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:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.511890625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 7x^{6} - 5x^{5} + 16x^{4} + 15x^{3} + 63x^{2} + 81x + 81 $ x^8 - 3x^7 + 7x^6 - 5x^5 + 16x^4 + 15x^3 + 63x^2 + 81*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			39.2
Root			$2.20109 - 1.59918i$ of defining polynomial
Character	$\chi$	$=$	62.39
Dual form			62.2.d.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.649758 + 1.99975i) q^{3} +(-0.809017 - 0.587785i) q^{4} +0.681481 q^{5} +2.10266 q^{6} +(-2.28414 - 1.65953i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-1.14976 + 0.835348i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.649758 + 1.99975i) q^{3} +(-0.809017 - 0.587785i) q^{4} +0.681481 q^{5} +2.10266 q^{6} +(-2.28414 - 1.65953i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-1.14976 + 0.835348i) q^{9} +(0.210589 - 0.648127i) q^{10} +(-3.87045 - 2.81205i) q^{11} +(0.649758 - 1.99975i) q^{12} +(0.978381 + 3.01115i) q^{13} +(-2.28414 + 1.65953i) q^{14} +(0.442798 + 1.36279i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.33547 - 1.69682i) q^{17} +(0.439168 + 1.35162i) q^{18} +(-2.34074 + 7.20406i) q^{19} +(-0.551330 - 0.400565i) q^{20} +(1.83450 - 5.64600i) q^{21} +(-3.87045 + 2.81205i) q^{22} +(3.31912 - 2.41148i) q^{23} +(-1.70109 - 1.23591i) q^{24} -4.53558 q^{25} +3.16611 q^{26} +(2.68571 + 1.95129i) q^{27} +(0.872464 + 2.68517i) q^{28} +(1.71059 - 5.26465i) q^{29} +1.43292 q^{30} +(4.02548 - 3.84649i) q^{31} +1.00000 q^{32} +(3.10853 - 9.56708i) q^{33} +(-0.892071 - 2.74551i) q^{34} +(-1.55660 - 1.13094i) q^{35} +1.42118 q^{36} +5.44541 q^{37} +(6.12814 + 4.45235i) q^{38} +(-5.38583 + 3.91303i) q^{39} +(-0.551330 + 0.400565i) q^{40} +(-2.81325 + 8.65829i) q^{41} +(-4.80277 - 3.48942i) q^{42} +(-2.98463 + 9.18573i) q^{43} +(1.47838 + 4.54999i) q^{44} +(-0.783538 + 0.569274i) q^{45} +(-1.26779 - 3.90186i) q^{46} +(-1.07882 - 3.32027i) q^{47} +(-1.70109 + 1.23591i) q^{48} +(0.300156 + 0.923786i) q^{49} +(-1.40157 + 4.31360i) q^{50} +(4.91070 + 3.56783i) q^{51} +(0.978381 - 3.01115i) q^{52} +(2.73281 - 1.98550i) q^{53} +(2.68571 - 1.95129i) q^{54} +(-2.63764 - 1.91636i) q^{55} +2.82335 q^{56} -15.9272 q^{57} +(-4.47838 - 3.25373i) q^{58} +(-0.870452 - 2.67897i) q^{59} +(0.442798 - 1.36279i) q^{60} -1.26682 q^{61} +(-2.41429 - 5.01709i) q^{62} +4.01249 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.666748 + 2.05204i) q^{65} +(-8.13824 - 5.91278i) q^{66} +2.70169 q^{67} -2.88680 q^{68} +(6.97898 + 5.07053i) q^{69} +(-1.55660 + 1.13094i) q^{70} +(-5.58104 + 4.05486i) q^{71} +(0.439168 - 1.35162i) q^{72} +(-1.32966 - 0.966055i) q^{73} +(1.68273 - 5.17890i) q^{74} +(-2.94703 - 9.07003i) q^{75} +(6.12814 - 4.45235i) q^{76} +(4.17399 + 12.8462i) q^{77} +(2.05720 + 6.33142i) q^{78} +(-6.70267 + 4.86977i) q^{79} +(0.210589 + 0.648127i) q^{80} +(-3.47452 + 10.6935i) q^{81} +(7.36518 + 5.35112i) q^{82} +(4.92118 - 15.1458i) q^{83} +(-4.80277 + 3.48942i) q^{84} +(1.59158 - 1.15635i) q^{85} +(7.81385 + 5.67710i) q^{86} +11.6394 q^{87} +4.78414 q^{88} +(-8.11662 - 5.89707i) q^{89} +(0.299285 + 0.921105i) q^{90} +(2.76232 - 8.50153i) q^{91} -4.10266 q^{92} +(10.3076 + 5.55066i) q^{93} -3.49114 q^{94} +(-1.59517 + 4.90943i) q^{95} +(0.649758 + 1.99975i) q^{96} +(-0.366592 - 0.266345i) q^{97} +0.971326 q^{98} +6.79912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8} + q^{10} - 2 q^{11} - 4 q^{12} - 11 q^{13} + 2 q^{14} + 21 q^{15} - 2 q^{16} - 7 q^{17} - 5 q^{18} - 14 q^{19} + q^{20} - 7 q^{21} - 2 q^{22} + 3 q^{23} + q^{24} + 14 q^{26} + 5 q^{27} + 2 q^{28} + 13 q^{29} - 14 q^{30} + 15 q^{31} + 8 q^{32} + 2 q^{33} + 3 q^{34} - 28 q^{35} + 10 q^{36} + 52 q^{37} + 21 q^{38} - 16 q^{39} + q^{40} - 11 q^{41} - 17 q^{42} - 22 q^{43} - 7 q^{44} - 19 q^{45} + 8 q^{46} - 10 q^{47} + q^{48} - 10 q^{49} - 15 q^{50} + 28 q^{51} - 11 q^{52} + 7 q^{53} + 5 q^{54} - 7 q^{55} - 8 q^{56} - 20 q^{57} - 17 q^{58} + 22 q^{59} + 21 q^{60} + 4 q^{61} + 5 q^{62} + 66 q^{63} - 2 q^{64} - 18 q^{66} - 26 q^{67} + 8 q^{68} + 4 q^{69} - 28 q^{70} - 15 q^{71} - 5 q^{72} - 29 q^{73} - 23 q^{74} - 34 q^{75} + 21 q^{76} + 34 q^{77} - q^{78} - 2 q^{79} + q^{80} - 45 q^{81} + 9 q^{82} + 38 q^{83} - 17 q^{84} + 25 q^{85} + 18 q^{86} - 20 q^{87} + 18 q^{88} + q^{89} + 46 q^{90} + 38 q^{91} - 22 q^{92} + 21 q^{93} - 20 q^{94} - 12 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} + 14 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8 + q^10 - 2 * q^11 - 4 * q^12 - 11 * q^13 + 2 * q^14 + 21 * q^15 - 2 * q^16 - 7 * q^17 - 5 * q^18 - 14 * q^19 + q^20 - 7 * q^21 - 2 * q^22 + 3 * q^23 + q^24 + 14 * q^26 + 5 * q^27 + 2 * q^28 + 13 * q^29 - 14 * q^30 + 15 * q^31 + 8 * q^32 + 2 * q^33 + 3 * q^34 - 28 * q^35 + 10 * q^36 + 52 * q^37 + 21 * q^38 - 16 * q^39 + q^40 - 11 * q^41 - 17 * q^42 - 22 * q^43 - 7 * q^44 - 19 * q^45 + 8 * q^46 - 10 * q^47 + q^48 - 10 * q^49 - 15 * q^50 + 28 * q^51 - 11 * q^52 + 7 * q^53 + 5 * q^54 - 7 * q^55 - 8 * q^56 - 20 * q^57 - 17 * q^58 + 22 * q^59 + 21 * q^60 + 4 * q^61 + 5 * q^62 + 66 * q^63 - 2 * q^64 - 18 * q^66 - 26 * q^67 + 8 * q^68 + 4 * q^69 - 28 * q^70 - 15 * q^71 - 5 * q^72 - 29 * q^73 - 23 * q^74 - 34 * q^75 + 21 * q^76 + 34 * q^77 - q^78 - 2 * q^79 + q^80 - 45 * q^81 + 9 * q^82 + 38 * q^83 - 17 * q^84 + 25 * q^85 + 18 * q^86 - 20 * q^87 + 18 * q^88 + q^89 + 46 * q^90 + 38 * q^91 - 22 * q^92 + 21 * q^93 - 20 * q^94 - 12 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.649758	+	1.99975i	0.375138	+	1.15456i	0.943386	+	0.331698i	$0.107621\pi$
$3$	0.649758	+	1.99975i	0.375138	+	1.15456i	−0.568248	+	0.822857i	$0.692379\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.681481			0.304768			0.152384	−	0.988321i	$-0.451305\pi$
$5$	0.681481			0.304768			0.152384	+	0.988321i	$0.451305\pi$
$6$	2.10266			0.858407
$7$	−2.28414	−	1.65953i	−0.863324	−	0.627242i	0.0654631	−	0.997855i	$-0.479148\pi$
$7$	−2.28414	−	1.65953i	−0.863324	−	0.627242i	−0.928787	+	0.370613i	$0.879148\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−1.14976	+	0.835348i	−0.383253	+	0.278449i
$10$	0.210589	−	0.648127i	0.0665942	−	0.204956i
$11$	−3.87045	−	2.81205i	−1.16699	−	0.847864i	−0.176340	−	0.984329i	$-0.556426\pi$
$11$	−3.87045	−	2.81205i	−1.16699	−	0.847864i	−0.990645	+	0.136465i	$0.956426\pi$
$12$	0.649758	−	1.99975i	0.187569	−	0.577278i
$13$	0.978381	+	3.01115i	0.271354	+	0.835142i	0.990161	+	0.139932i	$0.0446885\pi$
$13$	0.978381	+	3.01115i	0.271354	+	0.835142i	−0.718807	+	0.695210i	$0.755312\pi$
$14$	−2.28414	+	1.65953i	−0.610462	+	0.443527i
$15$	0.442798	+	1.36279i	0.114330	+	0.351871i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.33547	−	1.69682i	0.566435	−	0.411539i	−0.267373	−	0.963593i	$-0.586156\pi$
$17$	2.33547	−	1.69682i	0.566435	−	0.411539i	0.833808	+	0.552054i	$0.186156\pi$
$18$	0.439168	+	1.35162i	0.103513	+	0.318580i
$19$	−2.34074	+	7.20406i	−0.537003	+	1.65272i	0.202279	+	0.979328i	$0.435165\pi$
$19$	−2.34074	+	7.20406i	−0.537003	+	1.65272i	−0.739282	+	0.673396i	$0.764835\pi$
$20$	−0.551330	−	0.400565i	−0.123281	−	0.0895690i
$21$	1.83450	−	5.64600i	0.400320	−	1.23206i
$22$	−3.87045	+	2.81205i	−0.825183	+	0.599531i
$23$	3.31912	−	2.41148i	0.692085	−	0.502829i	−0.185260	−	0.982690i	$-0.559313\pi$
$23$	3.31912	−	2.41148i	0.692085	−	0.502829i	0.877345	+	0.479861i	$0.159313\pi$
$24$	−1.70109	−	1.23591i	−0.347233	−	0.252280i
$25$	−4.53558			−0.907117
$26$	3.16611			0.620925
$27$	2.68571	+	1.95129i	0.516866	+	0.375525i
$28$	0.872464	+	2.68517i	0.164880	+	0.507449i
$29$	1.71059	−	5.26465i	0.317648	−	0.977621i	−0.657002	−	0.753889i	$-0.728176\pi$
$29$	1.71059	−	5.26465i	0.317648	−	0.977621i	0.974651	−	0.223733i	$-0.0718243\pi$
$30$	1.43292			0.261615
$31$	4.02548	−	3.84649i	0.722997	−	0.690851i
$31$	4.02548	−	3.84649i	0.722997	−	0.690851i
$32$	1.00000			0.176777
$33$	3.10853	−	9.56708i	0.541126	−	1.66541i
$34$	−0.892071	−	2.74551i	−0.152989	−	0.470851i
$35$	−1.55660	−	1.13094i	−0.263113	−	0.191163i
$36$	1.42118			0.236863
$37$	5.44541			0.895220			0.447610	−	0.894229i	$-0.352275\pi$
$37$	5.44541			0.895220			0.447610	+	0.894229i	$0.352275\pi$
$38$	6.12814	+	4.45235i	0.994115	+	0.722267i
$39$	−5.38583	+	3.91303i	−0.862422	+	0.626586i
$40$	−0.551330	+	0.400565i	−0.0871729	+	0.0633348i
$41$	−2.81325	+	8.65829i	−0.439356	+	1.35220i	0.449201	+	0.893431i	$0.351709\pi$
$41$	−2.81325	+	8.65829i	−0.439356	+	1.35220i	−0.888557	+	0.458767i	$0.848291\pi$
$42$	−4.80277	−	3.48942i	−0.741084	−	0.538429i
$43$	−2.98463	+	9.18573i	−0.455151	+	1.40081i	0.415806	+	0.909453i	$0.363499\pi$
$43$	−2.98463	+	9.18573i	−0.455151	+	1.40081i	−0.870958	+	0.491358i	$0.836501\pi$
$44$	1.47838	+	4.54999i	0.222874	+	0.685937i
$45$	−0.783538	+	0.569274i	−0.116803	+	0.0848623i
$46$	−1.26779	−	3.90186i	−0.186926	−	0.575298i
$47$	−1.07882	−	3.32027i	−0.157362	−	0.484311i	0.841030	−	0.540988i	$-0.181950\pi$
$47$	−1.07882	−	3.32027i	−0.157362	−	0.484311i	−0.998393	+	0.0566767i	$0.981950\pi$
$48$	−1.70109	+	1.23591i	−0.245531	+	0.178389i
$49$	0.300156	+	0.923786i	0.0428795	+	0.131969i
$50$	−1.40157	+	4.31360i	−0.198212	+	0.610035i
$51$	4.91070	+	3.56783i	0.687636	+	0.499597i
$52$	0.978381	−	3.01115i	0.135677	−	0.417571i
$53$	2.73281	−	1.98550i	0.375380	−	0.272730i	−0.384058	−	0.923309i	$-0.625474\pi$
$53$	2.73281	−	1.98550i	0.375380	−	0.272730i	0.759439	+	0.650579i	$0.225474\pi$
$54$	2.68571	−	1.95129i	0.365479	−	0.265536i
$55$	−2.63764	−	1.91636i	−0.355659	−	0.258402i
$56$	2.82335			0.377287
$57$	−15.9272			−2.10961
$58$	−4.47838	−	3.25373i	−0.588040	−	0.427236i
$59$	−0.870452	−	2.67897i	−0.113323	−	0.348773i	0.878270	−	0.478164i	$-0.158698\pi$
$59$	−0.870452	−	2.67897i	−0.113323	−	0.348773i	−0.991594	+	0.129391i	$0.958698\pi$
$60$	0.442798	−	1.36279i	0.0571649	−	0.175936i
$61$	−1.26682			−0.162199			−0.0810996	−	0.996706i	$-0.525843\pi$
$61$	−1.26682			−0.162199			−0.0810996	+	0.996706i	$0.525843\pi$
$62$	−2.41429	−	5.01709i	−0.306615	−	0.637171i
$63$	4.01249			0.505526
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.666748	+	2.05204i	0.0826999	+	0.254524i
$66$	−8.13824	−	5.91278i	−1.00175	−	0.727813i
$67$	2.70169			0.330064			0.165032	−	0.986288i	$-0.447227\pi$
$67$	2.70169			0.330064			0.165032	+	0.986288i	$0.447227\pi$
$68$	−2.88680			−0.350076
$69$	6.97898	+	5.07053i	0.840171	+	0.610420i
$70$	−1.55660	+	1.13094i	−0.186049	+	0.135173i
$71$	−5.58104	+	4.05486i	−0.662348	+	0.481224i	−0.867455	−	0.497516i	$-0.834246\pi$
$71$	−5.58104	+	4.05486i	−0.662348	+	0.481224i	0.205107	+	0.978740i	$0.434246\pi$
$72$	0.439168	−	1.35162i	0.0517565	−	0.159290i
$73$	−1.32966	−	0.966055i	−0.155625	−	0.113068i	0.507248	−	0.861800i	$-0.330663\pi$
$73$	−1.32966	−	0.966055i	−0.155625	−	0.113068i	−0.662873	+	0.748732i	$0.730663\pi$
$74$	1.68273	−	5.17890i	0.195613	−	0.602034i
$75$	−2.94703	−	9.07003i	−0.340294	−	1.04732i
$76$	6.12814	−	4.45235i	0.702946	−	0.510720i
$77$	4.17399	+	12.8462i	0.475671	+	1.46396i
$78$	2.05720	+	6.33142i	0.232932	+	0.716892i
$79$	−6.70267	+	4.86977i	−0.754109	+	0.547892i	−0.897098	−	0.441832i	$-0.854329\pi$
$79$	−6.70267	+	4.86977i	−0.754109	+	0.547892i	0.142989	+	0.989724i	$0.454329\pi$
$80$	0.210589	+	0.648127i	0.0235446	+	0.0724628i
$81$	−3.47452	+	10.6935i	−0.386058	+	1.18816i
$82$	7.36518	+	5.35112i	0.813348	+	0.590932i
$83$	4.92118	−	15.1458i	0.540170	−	1.66247i	−0.192037	−	0.981388i	$-0.561509\pi$
$83$	4.92118	−	15.1458i	0.540170	−	1.66247i	0.732206	−	0.681083i	$-0.238491\pi$
$84$	−4.80277	+	3.48942i	−0.524025	+	0.380727i
$85$	1.59158	−	1.15635i	0.172631	−	0.125424i
$86$	7.81385	+	5.67710i	0.842589	+	0.612177i
$87$	11.6394			1.24788
$88$	4.78414			0.509991
$89$	−8.11662	−	5.89707i	−0.860360	−	0.625088i	0.0676226	−	0.997711i	$-0.478459\pi$
$89$	−8.11662	−	5.89707i	−0.860360	−	0.625088i	−0.927983	+	0.372623i	$0.878459\pi$
$90$	0.299285	+	0.921105i	0.0315474	+	0.0970929i
$91$	2.76232	−	8.50153i	0.289569	−	0.891203i
$92$	−4.10266			−0.427732
$93$	10.3076	+	5.55066i	1.06885	+	0.575576i
$94$	−3.49114			−0.360084
$95$	−1.59517	+	4.90943i	−0.163661	+	0.503697i
$96$	0.649758	+	1.99975i	0.0663156	+	0.204098i
$97$	−0.366592	−	0.266345i	−0.0372218	−	0.0270432i	0.569019	−	0.822324i	$-0.307323\pi$
$97$	−0.366592	−	0.266345i	−0.0372218	−	0.0270432i	−0.606241	+	0.795281i	$0.707323\pi$
$98$	0.971326			0.0981188
$99$	6.79912			0.683337
$100$	3.66936	+	2.66595i	0.366936	+	0.266595i
$101$	−6.16735	+	4.48084i	−0.613674	+	0.445861i	−0.850706	−	0.525641i	$-0.823825\pi$
$101$	−6.16735	+	4.48084i	−0.613674	+	0.445861i	0.237032	+	0.971502i	$0.423825\pi$
$102$	4.91070	−	3.56783i	0.486232	−	0.353268i
$103$	5.19907	−	16.0011i	0.512280	−	1.57664i	−0.275897	−	0.961187i	$-0.588975\pi$
$103$	5.19907	−	16.0011i	0.512280	−	1.57664i	0.788177	−	0.615449i	$-0.211025\pi$
$104$	−2.56143	−	1.86099i	−0.251169	−	0.182485i
$105$	1.25017	−	3.84764i	0.122005	−	0.375491i
$106$	−1.04384	−	3.21261i	−0.101387	−	0.312036i
$107$	6.62710	−	4.81487i	0.640666	−	0.465471i	−0.219413	−	0.975632i	$-0.570414\pi$
$107$	6.62710	−	4.81487i	0.640666	−	0.465471i	0.860079	+	0.510161i	$0.170414\pi$
$108$	−1.02585	−	3.15725i	−0.0987126	−	0.303806i
$109$	−4.70858	−	14.4915i	−0.451000	−	1.38803i	−0.875768	−	0.482733i	$-0.839644\pi$
$109$	−4.70858	−	14.4915i	−0.451000	−	1.38803i	0.424768	−	0.905302i	$-0.360356\pi$
$110$	−2.63764	+	1.91636i	−0.251489	+	0.182718i
$111$	3.53820	+	10.8895i	0.335831	+	1.03358i
$112$	0.872464	−	2.68517i	0.0824401	−	0.253725i
$113$	3.98365	+	2.89429i	0.374750	+	0.272272i	0.759178	−	0.650883i	$-0.225601\pi$
$113$	3.98365	+	2.89429i	0.374750	+	0.272272i	−0.384428	+	0.923155i	$0.625601\pi$
$114$	−4.92178	+	15.1477i	−0.460967	+	1.41871i
$115$	2.26192	−	1.64338i	0.210925	−	0.153246i
$116$	−4.47838	+	3.25373i	−0.415807	+	0.302102i
$117$	−3.64026	−	2.64480i	−0.336542	−	0.244512i
$118$	−2.81684			−0.259311
$119$	−8.15046			−0.747152
$120$	−1.15926	−	0.842251i	−0.105825	−	0.0768867i
$121$	3.67360	+	11.3062i	0.333963	+	1.02783i
$122$	−0.391468	+	1.20481i	−0.0354418	+	0.109079i
$123$	−19.1423			−1.72601
$124$	−5.51759	+	0.745763i	−0.495495	+	0.0669715i
$125$	−6.49832			−0.581228
$126$	1.23993	−	3.81610i	0.110462	−	0.339966i
$127$	1.13015	+	3.47825i	0.100285	+	0.308645i	0.988595	−	0.150599i	$-0.0481204\pi$
$127$	1.13015	+	3.47825i	0.100285	+	0.308645i	−0.888310	+	0.459244i	$0.848120\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−20.3084			−1.78806
$130$	2.15764			0.189238
$131$	0.607929	+	0.441687i	0.0531150	+	0.0385903i	0.614026	−	0.789286i	$-0.289549\pi$
$131$	0.607929	+	0.441687i	0.0531150	+	0.0385903i	−0.560911	+	0.827876i	$0.689549\pi$
$132$	−8.13824	+	5.91278i	−0.708343	+	0.514641i
$133$	17.3019	−	12.5706i	1.50027	−	1.09001i
$134$	0.834868	−	2.56946i	0.0721216	−	0.221968i
$135$	1.83026	+	1.32976i	0.157524	+	0.114448i
$136$	−0.892071	+	2.74551i	−0.0764944	+	0.235426i
$137$	1.04247	+	3.20839i	0.0890642	+	0.274111i	0.985661	−	0.168736i	$-0.0539685\pi$
$137$	1.04247	+	3.20839i	0.0890642	+	0.274111i	−0.896597	+	0.442847i	$0.853968\pi$
$138$	6.97898	−	5.07053i	0.594091	−	0.431632i
$139$	4.42379	+	13.6150i	0.375221	+	1.15481i	0.943329	+	0.331858i	$0.107676\pi$
$139$	4.42379	+	13.6150i	0.375221	+	1.15481i	−0.568108	+	0.822954i	$0.692324\pi$
$140$	0.594568	+	1.82989i	0.0502502	+	0.154654i
$141$	5.93873	−	4.31474i	0.500132	−	0.363367i
$142$	2.13177	+	6.56091i	0.178894	+	0.550579i
$143$	4.68071	−	14.4058i	0.391421	−	1.20467i
$144$	−1.14976	−	0.835348i	−0.0958131	−	0.0696123i
$145$	1.16573	−	3.58776i	0.0968090	−	0.297947i
$146$	−1.32966	+	0.966055i	−0.110043	+	0.0799513i
$147$	−1.65231	+	1.20047i	−0.136280	+	0.0990135i
$148$	−4.40543	−	3.20073i	−0.362124	−	0.263099i
$149$	−21.6499			−1.77363			−0.886813	−	0.462128i	$-0.847086\pi$
$149$	−21.6499			−1.77363			−0.886813	+	0.462128i	$0.847086\pi$
$150$	−9.53679			−0.778676
$151$	−1.54606	−	1.12328i	−0.125817	−	0.0914111i	0.523097	−	0.852273i	$-0.324776\pi$
$151$	−1.54606	−	1.12328i	−0.125817	−	0.0914111i	−0.648914	+	0.760862i	$0.724776\pi$
$152$	−2.34074	−	7.20406i	−0.189859	−	0.584326i
$153$	−1.26779	+	3.90186i	−0.102495	+	0.315447i
$154$	13.5073			1.08845
$155$	2.74329	−	2.62131i	0.220346	−	0.210549i
$156$	6.65725			0.533006
$157$	−3.44988	+	10.6176i	−0.275330	+	0.847379i	0.713802	+	0.700348i	$0.246972\pi$
$157$	−3.44988	+	10.6176i	−0.275330	+	0.847379i	−0.989132	+	0.147031i	$0.953028\pi$
$158$	2.56019	+	7.87946i	0.203678	+	0.626856i
$159$	5.74617	+	4.17484i	0.455701	+	0.331086i
$160$	0.681481			0.0538758
$161$	−11.5833			−0.912889
$162$	9.09641	+	6.60893i	0.714682	+	0.519247i
$163$	0.676212	−	0.491297i	0.0529650	−	0.0384813i	−0.560988	−	0.827824i	$-0.689579\pi$
$163$	0.676212	−	0.491297i	0.0529650	−	0.0384813i	0.613953	+	0.789343i	$0.289579\pi$
$164$	7.36518	−	5.35112i	0.575124	−	0.417852i
$165$	2.11841	−	6.51979i	0.164918	−	0.507565i
$166$	−12.8838	−	9.36064i	−0.999978	−	0.726526i
$167$	−3.00911	+	9.26107i	−0.232852	+	0.716643i	0.764548	+	0.644567i	$0.222962\pi$
$167$	−3.00911	+	9.26107i	−0.232852	+	0.716643i	−0.997399	+	0.0720761i	$0.977038\pi$
$168$	1.83450	+	5.64600i	0.141534	+	0.435598i
$169$	2.40744	−	1.74911i	0.185188	−	0.134547i
$170$	−0.607929	−	1.87101i	−0.0466261	−	0.143500i
$171$	−3.32661	−	10.2383i	−0.254392	−	0.782939i
$172$	7.81385	−	5.67710i	0.595801	−	0.432874i
$173$	4.87284	+	14.9970i	0.370475	+	1.14020i	0.946481	+	0.322759i	$0.104610\pi$
$173$	4.87284	+	14.9970i	0.370475	+	1.14020i	−0.576006	+	0.817445i	$0.695390\pi$
$174$	3.59679	−	11.0698i	0.272672	−	0.839197i
$175$	10.3599	+	7.52692i	0.783136	+	0.568981i
$176$	1.47838	−	4.54999i	0.111437	−	0.342968i
$177$	4.79169	−	3.48137i	0.360166	−	0.261676i
$178$	−8.11662	+	5.89707i	−0.608367	+	0.442004i
$179$	13.5437	+	9.84006i	1.01230	+	0.735480i	0.964691	−	0.263386i	$-0.0848392\pi$
$179$	13.5437	+	9.84006i	1.01230	+	0.735480i	0.0476112	+	0.998866i	$0.484839\pi$
$180$	0.968507			0.0721882
$181$	18.9657			1.40971			0.704854	−	0.709352i	$-0.251012\pi$
$181$	18.9657			1.40971			0.704854	+	0.709352i	$0.251012\pi$
$182$	−7.23184	−	5.25424i	−0.536059	−	0.389470i
$183$	−0.823123	−	2.53331i	−0.0608470	−	0.187268i
$184$	−1.26779	+	3.90186i	−0.0934628	+	0.287649i
$185$	3.71095			0.272834
$186$	8.46421	−	8.08787i	0.620626	−	0.593031i
$187$	−13.8109			−1.00995
$188$	−1.07882	+	3.32027i	−0.0786811	+	0.242156i
$189$	−2.89634	−	8.91402i	−0.210678	−	0.648400i
$190$	4.17621	+	3.03420i	0.302974	+	0.220124i
$191$	3.11764			0.225584			0.112792	−	0.993619i	$-0.464021\pi$
$191$	3.11764			0.225584			0.112792	+	0.993619i	$0.464021\pi$
$192$	2.10266			0.151746
$193$	−14.9505	−	10.8622i	−1.07616	−	0.781877i	−0.0991521	−	0.995072i	$-0.531613\pi$
$193$	−14.9505	−	10.8622i	−1.07616	−	0.781877i	−0.977010	+	0.213195i	$0.931613\pi$
$194$	−0.366592	+	0.266345i	−0.0263198	+	0.0191224i
$195$	−3.67034	+	2.66666i	−0.262838	+	0.190963i
$196$	0.300156	−	0.923786i	0.0214397	−	0.0659847i
$197$	15.6552	+	11.3742i	1.11539	+	0.810376i	0.983503	−	0.180890i	$-0.0578977\pi$
$197$	15.6552	+	11.3742i	1.11539	+	0.810376i	0.131883	+	0.991265i	$0.457898\pi$
$198$	2.10104	−	6.46635i	0.149315	−	0.459543i
$199$	−0.387070	−	1.19128i	−0.0274386	−	0.0844474i	0.936399	−	0.350936i	$-0.114137\pi$
$199$	−0.387070	−	1.19128i	−0.0274386	−	0.0844474i	−0.963838	+	0.266489i	$0.914137\pi$
$200$	3.66936	−	2.66595i	0.259463	−	0.188511i
$201$	1.75544	+	5.40270i	0.123819	+	0.381077i
$202$	2.35572	+	7.25016i	0.165748	+	0.510119i
$203$	−12.6441	+	9.18644i	−0.887439	+	0.644762i
$204$	−1.87572	−	5.77288i	−0.131327	−	0.404182i
$205$	−1.91718	+	5.90046i	−0.133901	+	0.412106i
$206$	−13.6114	−	9.88923i	−0.948348	−	0.689015i
$207$	−1.80176	+	5.54524i	−0.125231	+	0.385421i
$208$	−2.56143	+	1.86099i	−0.177604	+	0.129037i
$209$	29.3179	−	21.3007i	2.02796	−	1.47340i
$210$	−3.27300	−	2.37797i	−0.225858	−	0.164096i
$211$	12.1746			0.838132			0.419066	−	0.907956i	$-0.362358\pi$
$211$	12.1746			0.838132			0.419066	+	0.907956i	$0.362358\pi$
$212$	−3.37794			−0.231998
$213$	−11.7350	−	8.52600i	−0.804071	−	0.584192i
$214$	−2.53133	−	7.79062i	−0.173038	−	0.532556i
$215$	−2.03397	+	6.25991i	−0.138715	+	0.426922i
$216$	−3.31972			−0.225879
$217$	−15.5781	+	2.10555i	−1.05751	+	0.142934i
$218$	−15.2373			−1.03200
$219$	1.06791	−	3.28669i	0.0721627	−	0.222094i
$220$	1.00749	+	3.10073i	0.0679249	+	0.209051i
$221$	7.39435	+	5.37231i	0.497398	+	0.361381i
$222$	11.4499			0.768464
$223$	1.52189			0.101913			0.0509566	−	0.998701i	$-0.483773\pi$
$223$	1.52189			0.101913			0.0509566	+	0.998701i	$0.483773\pi$
$224$	−2.28414	−	1.65953i	−0.152616	−	0.110882i
$225$	5.21482	−	3.78879i	0.347655	−	0.252586i
$226$	3.98365	−	2.89429i	0.264988	−	0.192525i
$227$	0.703100	−	2.16392i	0.0466664	−	0.143624i	−0.925008	−	0.379947i	$-0.875942\pi$
$227$	0.703100	−	2.16392i	0.0466664	−	0.143624i	0.971675	+	0.236323i	$0.0759422\pi$
$228$	12.8854	+	9.36178i	0.853356	+	0.619999i
$229$	2.02222	−	6.22376i	0.133632	−	0.411278i	−0.861743	−	0.507346i	$-0.830627\pi$
$229$	2.02222	−	6.22376i	0.133632	−	0.411278i	0.995375	+	0.0960682i	$0.0306267\pi$
$230$	−0.863976	−	2.65905i	−0.0569689	−	0.175332i
$231$	−22.9771	+	16.6939i	−1.51178	+	1.09838i
$232$	1.71059	+	5.26465i	0.112306	+	0.345641i
$233$	5.82883	+	17.9393i	0.381859	+	1.17524i	0.938733	+	0.344645i	$0.112001\pi$
$233$	5.82883	+	17.9393i	0.381859	+	1.17524i	−0.556874	+	0.830597i	$0.687999\pi$
$234$	−3.64026	+	2.64480i	−0.237971	+	0.172896i
$235$	−0.735197	−	2.26270i	−0.0479589	−	0.147602i
$236$	−0.870452	+	2.67897i	−0.0566616	+	0.174386i
$237$	−14.0934	−	10.2395i	−0.915466	−	0.665125i
$238$	−2.51863	+	7.75155i	−0.163259	+	0.502458i
$239$	2.40543	−	1.74765i	0.155594	−	0.113046i	−0.507264	−	0.861791i	$-0.669343\pi$
$239$	2.40543	−	1.74765i	0.155594	−	0.113046i	0.662858	+	0.748745i	$0.269343\pi$
$240$	−1.15926	+	0.842251i	−0.0748299	+	0.0543671i
$241$	−3.56372	−	2.58919i	−0.229559	−	0.166784i	0.467060	−	0.884226i	$-0.345313\pi$
$241$	−3.56372	−	2.58919i	−0.229559	−	0.166784i	−0.696619	+	0.717441i	$0.745313\pi$
$242$	11.8880			0.764190
$243$	−13.6827			−0.877745
$244$	1.02488	+	0.744616i	0.0656110	+	0.0476691i
$245$	0.204551	+	0.629543i	0.0130683	+	0.0402200i
$246$	−5.91531	+	18.2054i	−0.377146	+	1.16074i
$247$	−23.9826			−1.52598
$248$	−0.995768	+	5.47800i	−0.0632313	+	0.347853i
$249$	33.4854			2.12205
$250$	−2.00809	+	6.18027i	−0.127003	+	0.390875i
$251$	−4.92077	−	15.1446i	−0.310596	−	0.955917i	−0.977529	−	0.210799i	$-0.932393\pi$
$251$	−4.92077	−	15.1446i	−0.310596	−	0.955917i	0.666933	−	0.745117i	$-0.267607\pi$
$252$	−3.24617	−	2.35848i	−0.204490	−	0.148570i
$253$	−19.6277			−1.23398
$254$	3.65725			0.229476
$255$	3.34655	+	2.43141i	0.209569	+	0.152261i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−13.7712	+	10.0054i	−0.859025	+	0.624118i	−0.927620	−	0.373526i	$-0.878148\pi$
$257$	−13.7712	+	10.0054i	−0.859025	+	0.624118i	0.0685946	+	0.997645i	$0.478148\pi$
$258$	−6.27565	+	19.3145i	−0.390705	+	1.20247i
$259$	−12.4381	−	9.03680i	−0.772865	−	0.561520i
$260$	0.666748	−	2.05204i	0.0413500	−	0.127262i
$261$	2.43105	+	7.48201i	0.150478	+	0.463125i
$262$	0.607929	−	0.441687i	0.0375580	−	0.0272875i
$263$	−7.65536	−	23.5608i	−0.472050	−	1.45282i	−0.849895	−	0.526951i	$-0.823335\pi$
$263$	−7.65536	−	23.5608i	−0.472050	−	1.45282i	0.377846	−	0.925869i	$-0.376665\pi$
$264$	3.10853	+	9.56708i	0.191317	+	0.588813i
$265$	1.86236	−	1.35308i	0.114404	−	0.0831193i
$266$	−6.60874	−	20.3396i	−0.405208	−	1.24710i
$267$	6.51882	−	20.0629i	0.398945	−	1.22783i
$268$	−2.18571	−	1.58801i	−0.133514	−	0.0970034i
$269$	−1.45676	+	4.48345i	−0.0888203	+	0.273361i	−0.985594	−	0.169129i	$-0.945905\pi$
$269$	−1.45676	+	4.48345i	−0.0888203	+	0.273361i	0.896774	+	0.442490i	$0.145905\pi$
$270$	1.83026	−	1.32976i	0.111386	−	0.0809269i
$271$	−4.82080	+	3.50252i	−0.292843	+	0.212763i	−0.724500	−	0.689275i	$-0.757929\pi$
$271$	−4.82080	+	3.50252i	−0.292843	+	0.212763i	0.431657	+	0.902038i	$0.357929\pi$
$272$	2.33547	+	1.69682i	0.141609	+	0.102885i
$273$	18.7958			1.13757
$274$	3.37350			0.203801
$275$	17.5548	+	12.7543i	1.05859	+	0.769112i
$276$	−2.66573	−	8.20429i	−0.160458	−	0.493840i
$277$	1.51232	−	4.65445i	0.0908667	−	0.279659i	−0.895288	−	0.445488i	$-0.853030\pi$
$277$	1.51232	−	4.65445i	0.0908667	−	0.279659i	0.986154	+	0.165829i	$0.0530301\pi$
$278$	14.3157			0.858599
$279$	−1.41516	+	7.78521i	−0.0847236	+	0.466088i
$280$	1.92406			0.114985
$281$	8.38518	−	25.8069i	0.500218	−	1.53951i	−0.308446	−	0.951242i	$-0.599809\pi$
$281$	8.38518	−	25.8069i	0.500218	−	1.53951i	0.808664	−	0.588271i	$-0.200191\pi$
$282$	−2.26839	−	6.98140i	−0.135081	−	0.415736i
$283$	6.88321	+	5.00094i	0.409164	+	0.297275i	0.773263	−	0.634085i	$-0.218623\pi$
$283$	6.88321	+	5.00094i	0.409164	+	0.297275i	−0.364099	+	0.931360i	$0.618623\pi$
$284$	6.89855			0.409353
$285$	−10.8541			−0.642942
$286$	−12.2543	−	8.90324i	−0.724610	−	0.526460i
$287$	20.7945	−	15.1081i	1.22746	−	0.891803i
$288$	−1.14976	+	0.835348i	−0.0677501	+	0.0492233i
$289$	−2.67806	+	8.24222i	−0.157533	+	0.484836i
$290$	−3.05193	−	2.21736i	−0.179216	−	0.130208i
$291$	0.294426	−	0.906151i	0.0172596	−	0.0531195i
$292$	0.507885	+	1.56311i	0.0297217	+	0.0914741i
$293$	−6.71287	+	4.87719i	−0.392170	+	0.284928i	−0.766344	−	0.642430i	$-0.777926\pi$
$293$	−6.71287	+	4.87719i	−0.392170	+	0.284928i	0.374174	+	0.927358i	$0.377926\pi$
$294$	0.631127	+	1.94241i	0.0368081	+	0.113284i
$295$	−0.593196	−	1.82567i	−0.0345372	−	0.106295i
$296$	−4.40543	+	3.20073i	−0.256061	+	0.186039i
$297$	−4.90782	−	15.1047i	−0.284780	−	0.876464i
$298$	−6.69018	+	20.5902i	−0.387551	+	1.19276i
$299$	10.5087	+	7.63501i	0.607734	+	0.441544i
$300$	−2.94703	+	9.07003i	−0.170147	+	0.523658i
$301$	22.0613	−	16.0284i	1.27159	−	0.923864i
$302$	−1.54606	+	1.12328i	−0.0889658	+	0.0646374i
$303$	−12.9678	−	9.42169i	−0.744983	−	0.541262i
$304$	−7.57480			−0.434444
$305$	−0.863312			−0.0494331
$306$	3.31912	+	2.41148i	0.189742	+	0.137855i
$307$	6.66148	+	20.5019i	0.380191	+	1.17011i	0.939909	+	0.341424i	$0.110909\pi$
$307$	6.66148	+	20.5019i	0.380191	+	1.17011i	−0.559719	+	0.828683i	$0.689091\pi$
$308$	4.17399	−	12.8462i	0.237835	−	0.731982i
$309$	35.3763			2.01249
$310$	−1.64530	−	3.41905i	−0.0934465	−	0.194189i
$311$	1.81086			0.102685			0.0513423	−	0.998681i	$-0.483650\pi$
$311$	1.81086			0.102685			0.0513423	+	0.998681i	$0.483650\pi$
$312$	2.05720	−	6.33142i	0.116466	−	0.358446i
$313$	−0.687726	−	2.11660i	−0.0388726	−	0.119638i	0.929737	−	0.368224i	$-0.120034\pi$
$313$	−0.687726	−	2.11660i	−0.0388726	−	0.119638i	−0.968610	+	0.248586i	$0.920034\pi$
$314$	9.03189	+	6.56205i	0.509699	+	0.370318i
$315$	2.73444			0.154068
$316$	8.28495			0.466065
$317$	−4.02222	−	2.92232i	−0.225910	−	0.164134i	0.469073	−	0.883160i	$-0.344588\pi$
$317$	−4.02222	−	2.92232i	−0.225910	−	0.164134i	−0.694983	+	0.719026i	$0.744588\pi$
$318$	5.74617	−	4.17484i	0.322229	−	0.234113i
$319$	−21.4252	+	15.5663i	−1.19958	+	0.871547i
$320$	0.210589	−	0.648127i	0.0117723	−	0.0362314i
$321$	13.9345	+	10.1240i	0.777750	+	0.565069i
$322$	−3.57942	+	11.0163i	−0.199474	+	0.613916i
$323$	6.75725	+	20.7967i	0.375984	+	1.15716i
$324$	9.09641	−	6.60893i	0.505356	−	0.367163i
$325$	−4.43753	−	13.6573i	−0.246150	−	0.757571i
$326$	−0.258290	−	0.794935i	−0.0143054	−	0.0440274i
$327$	25.9199	−	18.8319i	1.43338	−	1.04141i
$328$	−2.81325	−	8.65829i	−0.155336	−	0.478074i
$329$	−3.04589	+	9.37430i	−0.167926	+	0.516822i
$330$	−5.54606	−	4.02945i	−0.305301	−	0.221814i
$331$	−7.93491	+	24.4211i	−0.436142	+	1.34231i	0.455769	+	0.890098i	$0.349364\pi$
$331$	−7.93491	+	24.4211i	−0.436142	+	1.34231i	−0.891912	+	0.452210i	$0.850636\pi$
$332$	−12.8838	+	9.36064i	−0.707091	+	0.513732i
$333$	−6.26091	+	4.54881i	−0.343096	+	0.249273i
$334$	7.87794	+	5.72366i	0.431062	+	0.313185i
$335$	1.84115			0.100593
$336$	5.93655			0.323866
$337$	16.0982	+	11.6960i	0.876925	+	0.637123i	0.932436	−	0.361335i	$-0.117679\pi$
$337$	16.0982	+	11.6960i	0.876925	+	0.637123i	−0.0555113	+	0.998458i	$0.517679\pi$
$338$	−0.919562	−	2.83012i	−0.0500176	−	0.153938i
$339$	−3.19945	+	9.84689i	−0.173770	+	0.534809i
$340$	−1.96730			−0.106692
$341$	−26.3969	+	3.56783i	−1.42947	+	0.193209i
$342$	−10.7651			−0.582112
$343$	−5.25980	+	16.1880i	−0.284003	+	0.874070i
$344$	−2.98463	−	9.18573i	−0.160920	−	0.495262i
$345$	4.75605	+	3.45547i	0.256057	+	0.186036i
$346$	15.7688			0.847738
$347$	−5.99282			−0.321711			−0.160856	−	0.986978i	$-0.551425\pi$
$347$	−5.99282			−0.321711			−0.160856	+	0.986978i	$0.551425\pi$
$348$	−9.41651	−	6.84150i	−0.504778	−	0.366743i
$349$	1.09158	−	0.793079i	0.0584309	−	0.0424526i	−0.558186	−	0.829716i	$-0.688503\pi$
$349$	1.09158	−	0.793079i	0.0584309	−	0.0424526i	0.616617	+	0.787263i	$0.288503\pi$
$350$	10.3599	−	7.52692i	0.553761	−	0.402331i
$351$	−3.24796	+	9.99618i	−0.173363	+	0.533557i
$352$	−3.87045	−	2.81205i	−0.206296	−	0.149883i
$353$	−0.677225	+	2.08429i	−0.0360451	+	0.110935i	−0.967460	−	0.253023i	$-0.918575\pi$
$353$	−0.677225	+	2.08429i	−0.0360451	+	0.110935i	0.931415	+	0.363959i	$0.118575\pi$
$354$	−1.83026	−	5.63297i	−0.0972774	−	0.299389i
$355$	−3.80337	+	2.76331i	−0.201862	+	0.146661i
$356$	3.10027	+	9.54166i	0.164314	+	0.505707i
$357$	−5.29582	−	16.2989i	−0.280285	−	0.862628i
$358$	13.5437	−	9.84006i	0.715805	−	0.520063i
$359$	−10.2794	−	31.6366i	−0.542524	−	1.66972i	−0.726804	−	0.686845i	$-0.758995\pi$
$359$	−10.2794	−	31.6366i	−0.542524	−	1.66972i	0.184280	−	0.982874i	$-0.441005\pi$
$360$	0.299285	−	0.921105i	0.0157737	−	0.0485465i
$361$	−31.0481	−	22.5577i	−1.63411	−	1.18725i
$362$	5.86072	−	18.0374i	0.308033	−	0.948027i
$363$	−20.2225	+	14.6925i	−1.06141	+	0.771158i
$364$	−7.23184	+	5.25424i	−0.379051	+	0.275397i
$365$	−0.906139	−	0.658348i	−0.0474295	−	0.0344595i
$366$	−2.66368			−0.139233
$367$	34.3764			1.79443			0.897217	−	0.441590i	$-0.145586\pi$
$367$	34.3764			1.79443			0.897217	+	0.441590i	$0.145586\pi$
$368$	3.31912	+	2.41148i	0.173021	+	0.125707i
$369$	−3.99813	−	12.3050i	−0.208134	−	0.640572i
$370$	1.14675	−	3.52932i	0.0596165	−	0.183481i
$371$	−9.53712			−0.495143
$372$	−5.07644	−	10.5492i	−0.263201	−	0.546952i
$373$	−26.7020			−1.38258			−0.691289	−	0.722578i	$-0.742957\pi$
$373$	−26.7020			−1.38258			−0.691289	+	0.722578i	$0.742957\pi$
$374$	−4.26779	+	13.1349i	−0.220682	+	0.679190i
$375$	−4.22233	−	12.9950i	−0.218040	−	0.671059i
$376$	2.82439	+	2.05204i	0.145657	+	0.105826i
$377$	17.5262			0.902648
$378$	−9.37276			−0.482083
$379$	−16.0099	−	11.6319i	−0.822375	−	0.597491i	0.0950166	−	0.995476i	$-0.469710\pi$
$379$	−16.0099	−	11.6319i	−0.822375	−	0.597491i	−0.917392	+	0.397985i	$0.869710\pi$
$380$	4.17621	−	3.03420i	0.214235	−	0.155651i
$381$	−6.22130	+	4.52004i	−0.318727	+	0.231568i
$382$	0.963403	−	2.96505i	0.0492920	−	0.151705i
$383$	17.5454	+	12.7474i	0.896526	+	0.651364i	0.937571	−	0.347793i	$-0.113069\pi$
$383$	17.5454	+	12.7474i	0.896526	+	0.651364i	−0.0410456	+	0.999157i	$0.513069\pi$
$384$	0.649758	−	1.99975i	0.0331578	−	0.102049i
$385$	2.84450	+	8.75446i	0.144969	+	0.446169i
$386$	−14.9505	+	10.8622i	−0.760961	+	0.552871i
$387$	−4.24169	−	13.0546i	−0.215617	−	0.663601i
$388$	0.140026	+	0.430955i	0.00710873	+	0.0218784i
$389$	−20.1061	+	14.6080i	−1.01942	+	0.740654i	−0.966164	−	0.257927i	$-0.916961\pi$
$389$	−20.1061	+	14.6080i	−1.01942	+	0.740654i	−0.0532578	+	0.998581i	$0.516961\pi$
$390$	1.40194	+	4.31474i	0.0709902	+	0.218485i
$391$	3.65986	−	11.2639i	0.185087	−	0.569640i
$392$	−0.785820	−	0.570931i	−0.0396899	−	0.0288364i
$393$	−0.488255	+	1.50270i	−0.0246292	+	0.0758009i
$394$	15.6552	−	11.3742i	0.788697	−	0.573022i
$395$	−4.56774	+	3.31866i	−0.229828	+	0.166980i
$396$	−5.50060	−	3.99642i	−0.276416	−	0.200828i
$397$	−32.0356			−1.60782			−0.803912	−	0.594749i	$-0.797251\pi$
$397$	−32.0356			−1.60782			−0.803912	+	0.594749i	$0.797251\pi$
$398$	−1.25258			−0.0627863
$399$	36.3800	+	26.4316i	1.82128	+	1.32324i
$400$	−1.40157	−	4.31360i	−0.0700786	−	0.215680i
$401$	1.22455	−	3.76879i	0.0611513	−	0.188204i	−0.915814	−	0.401603i	$-0.868453\pi$
$401$	1.22455	−	3.76879i	0.0611513	−	0.188204i	0.976965	+	0.213398i	$0.0684533\pi$
$402$	5.68074			0.283329
$403$	15.5208	+	8.35797i	0.773147	+	0.416340i
$404$	7.62327			0.379272
$405$	−2.36782	+	7.28740i	−0.117658	+	0.362114i
$406$	4.82960	+	14.8640i	0.239689	+	0.737687i
$407$	−21.0762	−	15.3128i	−1.04471	−	0.759025i
$408$	−6.06996			−0.300508
$409$	24.8853			1.23050			0.615249	−	0.788333i	$-0.289056\pi$
$409$	24.8853			1.23050			0.615249	+	0.788333i	$0.289056\pi$
$410$	5.01923	+	3.64669i	0.247882	+	0.180097i
$411$	−5.73862	+	4.16935i	−0.283065	+	0.205659i
$412$	−13.6114	+	9.88923i	−0.670583	+	0.487207i
$413$	−2.45759	+	7.56369i	−0.120930	+	0.372185i
$414$	4.71706	+	3.42715i	0.231831	+	0.168435i
$415$	3.35369	−	10.3216i	0.164626	−	0.506667i
$416$	0.978381	+	3.01115i	0.0479691	+	0.147634i
$417$	−24.3523	+	17.6930i	−1.19254	+	0.866428i
$418$	−11.1984	−	34.4652i	−0.547733	−	1.68575i
$419$	−1.21671	−	3.74464i	−0.0594400	−	0.182938i	0.916928	−	0.399053i	$-0.130661\pi$
$419$	−1.21671	−	3.74464i	−0.0594400	−	0.182938i	−0.976368	+	0.216116i	$0.930661\pi$
$420$	−3.27300	+	2.37797i	−0.159706	+	0.116033i
$421$	8.94722	+	27.5367i	0.436061	+	1.34206i	0.891996	+	0.452044i	$0.149305\pi$
$421$	8.94722	+	27.5367i	0.436061	+	1.34206i	−0.455935	+	0.890013i	$0.650695\pi$
$422$	3.76215	−	11.5787i	0.183139	−	0.563643i
$423$	4.01396	+	2.91632i	0.195166	+	0.141796i
$424$	−1.04384	+	3.21261i	−0.0506934	+	0.156018i
$425$	−10.5927	+	7.69606i	−0.513823	+	0.373314i
$426$	−11.7350	+	8.52600i	−0.568564	+	0.413086i
$427$	2.89359	+	2.10231i	0.140030	+	0.101738i
$428$	−8.19155			−0.395953
$429$	31.8492			1.53769
$430$	5.32499	+	3.86883i	0.256794	+	0.186572i
$431$	0.739452	+	2.27580i	0.0356182	+	0.109621i	0.967285	−	0.253693i	$-0.0816452\pi$
$431$	0.739452	+	2.27580i	0.0356182	+	0.109621i	−0.931667	+	0.363314i	$0.881645\pi$
$432$	−1.02585	+	3.15725i	−0.0493563	+	0.151903i
$433$	18.1536			0.872407			0.436204	−	0.899848i	$-0.356323\pi$
$433$	18.1536			0.872407			0.436204	+	0.899848i	$0.356323\pi$
$434$	−2.81140	+	15.4663i	−0.134952	+	0.742407i
$435$	7.93207			0.380313
$436$	−4.70858	+	14.4915i	−0.225500	+	0.694017i
$437$	9.60326	+	29.5558i	0.459386	+	1.41385i
$438$	−2.79582	−	2.03129i	−0.133590	−	0.0970586i
$439$	25.6177			1.22267			0.611333	−	0.791373i	$-0.290634\pi$
$439$	25.6177			1.22267			0.611333	+	0.791373i	$0.290634\pi$
$440$	3.26030			0.155429
$441$	−1.11679	−	0.811395i	−0.0531805	−	0.0386379i
$442$	7.39435	−	5.37231i	0.351713	−	0.255535i
$443$	2.35242	−	1.70914i	0.111767	−	0.0812035i	−0.530498	−	0.847686i	$-0.677995\pi$
$443$	2.35242	−	1.70914i	0.111767	−	0.0812035i	0.642265	+	0.766483i	$0.277995\pi$
$444$	3.53820	−	10.8895i	0.167915	−	0.516791i
$445$	−5.53133	−	4.01874i	−0.262210	−	0.190507i
$446$	0.470289	−	1.44740i	0.0222688	−	0.0685364i
$447$	−14.0672	−	43.2943i	−0.665354	−	2.04775i
$448$	−2.28414	+	1.65953i	−0.107916	+	0.0784052i
$449$	−4.59806	−	14.1514i	−0.216996	−	0.667844i	−0.999006	−	0.0445783i	$-0.985806\pi$
$449$	−4.59806	−	14.1514i	−0.216996	−	0.667844i	0.782010	−	0.623266i	$-0.214194\pi$
$450$	−1.99188	−	6.13039i	−0.0938983	−	0.288989i
$451$	35.2361	−	25.6005i	1.65920	−	1.20548i
$452$	−1.52162	−	4.68306i	−0.0715709	−	0.220273i
$453$	1.24171	−	3.82159i	0.0583406	−	0.179554i
$454$	−1.84074	−	1.33738i	−0.0863902	−	0.0627662i
$455$	1.88247	−	5.79364i	0.0882514	−	0.271610i
$456$	12.8854	−	9.36178i	0.603414	−	0.438406i
$457$	−2.56778	+	1.86560i	−0.120116	+	0.0872691i	−0.646221	−	0.763150i	$-0.723652\pi$
$457$	−2.56778	+	1.86560i	−0.120116	+	0.0872691i	0.526106	+	0.850419i	$0.323652\pi$
$458$	−5.29425	−	3.84649i	−0.247384	−	0.179735i
$459$	9.58338			0.447314
$460$	−2.79589			−0.130359
$461$	−10.6879	−	7.76521i	−0.497785	−	0.361662i	0.310385	−	0.950611i	$-0.399542\pi$
$461$	−10.6879	−	7.76521i	−0.497785	−	0.361662i	−0.808170	+	0.588949i	$0.799542\pi$
$462$	8.77649	+	27.0112i	0.408319	+	1.25668i
$463$	3.32362	−	10.2291i	0.154462	−	0.475385i	−0.843644	−	0.536903i	$-0.819594\pi$
$463$	3.32362	−	10.2291i	0.154462	−	0.475385i	0.998106	+	0.0615181i	$0.0195942\pi$
$464$	5.53558			0.256983
$465$	7.02444	+	3.78267i	0.325751	+	0.175417i
$466$	18.8625			0.873788
$467$	−7.04002	+	21.6670i	−0.325773	+	1.00263i	0.645317	+	0.763915i	$0.276725\pi$
$467$	−7.04002	+	21.6670i	−0.325773	+	1.00263i	−0.971090	+	0.238712i	$0.923275\pi$
$468$	1.39045	+	4.27938i	0.0642738	+	0.197814i
$469$	−6.17104	−	4.48352i	−0.284952	−	0.207030i
$470$	−2.37915			−0.109742
$471$	−23.4742			−1.08163
$472$	2.27887	+	1.65570i	0.104894	+	0.0762096i
$473$	37.3826	−	27.1600i	1.71885	−	1.24882i
$474$	−14.0934	+	10.2395i	−0.647333	+	0.470315i
$475$	10.6166	−	32.6746i	0.487124	−	1.49921i
$476$	6.59386	+	4.79072i	0.302229	+	0.219582i
$477$	−1.48348	+	4.56570i	−0.0679241	+	0.209049i
$478$	−0.918793	−	2.82775i	−0.0420246	−	0.129338i
$479$	10.4545	−	7.59567i	0.477680	−	0.347055i	−0.322747	−	0.946485i	$-0.604606\pi$
$479$	10.4545	−	7.59567i	0.477680	−	0.347055i	0.800427	+	0.599430i	$0.204606\pi$
$480$	0.442798	+	1.36279i	0.0202109	+	0.0622026i
$481$	5.32769	+	16.3969i	0.242922	+	0.747636i
$482$	−3.56372	+	2.58919i	−0.162323	+	0.117934i
$483$	−7.52631	−	23.1636i	−0.342459	−	1.05398i
$484$	3.67360	−	11.3062i	0.166982	−	0.513917i
$485$	−0.249826	−	0.181509i	−0.0113440	−	0.00824189i
$486$	−4.22818	+	13.0130i	−0.191794	+	0.590282i
$487$	−7.65100	+	5.55878i	−0.346700	+	0.251892i	−0.747483	−	0.664281i	$-0.768738\pi$
$487$	−7.65100	+	5.55878i	−0.346700	+	0.251892i	0.400783	+	0.916173i	$0.368738\pi$
$488$	1.02488	−	0.744616i	0.0463939	−	0.0337072i
$489$	1.42184	+	1.03303i	0.0642980	+	0.0467152i
$490$	0.661941			0.0299034
$491$	−20.4282			−0.921910			−0.460955	−	0.887424i	$-0.652493\pi$
$491$	−20.4282			−0.921910			−0.460955	+	0.887424i	$0.652493\pi$
$492$	15.4865	+	11.2516i	0.698184	+	0.507260i
$493$	−4.93813	−	15.1980i	−0.222402	−	0.684484i
$494$	−7.41104	+	22.8088i	−0.333438	+	1.02622i
$495$	4.63347			0.208259
$496$	4.90218	+	2.63983i	0.220114	+	0.118532i
$497$	19.4770			0.873664
$498$	10.3476	−	31.8465i	0.463685	−	1.42708i
$499$	4.94689	+	15.2250i	0.221453	+	0.681563i	0.998632	+	0.0522832i	$0.0166499\pi$
$499$	4.94689	+	15.2250i	0.221453	+	0.681563i	−0.777179	+	0.629279i	$0.783350\pi$
$500$	5.25725	+	3.81962i	0.235111	+	0.170818i
$501$	−20.4750			−0.914756
$502$	−15.9239			−0.710720
$503$	−17.8039	−	12.9353i	−0.793837	−	0.576757i	0.115262	−	0.993335i	$-0.463229\pi$
$503$	−17.8039	−	12.9353i	−0.793837	−	0.576757i	−0.909100	+	0.416578i	$0.863229\pi$
$504$	−3.24617	+	2.35848i	−0.144596	+	0.105055i
$505$	−4.20293	+	3.05361i	−0.187028	+	0.135884i
$506$	−6.06529	+	18.6671i	−0.269635	+	0.829852i
$507$	5.06204	+	3.67779i	0.224813	+	0.163336i
$508$	1.13015	−	3.47825i	0.0501424	−	0.154322i
$509$	−9.61086	−	29.5792i	−0.425994	−	1.31107i	−0.902040	−	0.431653i	$-0.857930\pi$
$509$	−9.61086	−	29.5792i	−0.425994	−	1.31107i	0.476046	−	0.879420i	$-0.342070\pi$
$510$	3.34655	−	2.43141i	0.148188	−	0.107665i
$511$	1.43394	+	4.41321i	0.0634337	+	0.195229i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−20.3437	+	14.7806i	−0.898198	+	0.652579i
$514$	5.26014	+	16.1890i	0.232015	+	0.714068i
$515$	3.54307	−	10.9045i	0.156126	−	0.480508i
$516$	16.4299	+	11.9370i	0.723285	+	0.525497i
$517$	−5.16123	+	15.8846i	−0.226991	+	0.698606i
$518$	−12.4381	+	9.03680i	−0.546498	+	0.397054i
$519$	−26.8242	+	19.4889i	−1.17745	+	0.855468i
$520$	−1.74557	−	1.26823i	−0.0765483	−	0.0556156i
$521$	−2.75924			−0.120884			−0.0604422	−	0.998172i	$-0.519251\pi$
$521$	−2.75924			−0.120884			−0.0604422	+	0.998172i	$0.519251\pi$
$522$	7.86705			0.344332
$523$	−7.06691	−	5.13441i	−0.309014	−	0.224512i	0.422459	−	0.906382i	$-0.361167\pi$
$523$	−7.06691	−	5.13441i	−0.309014	−	0.224512i	−0.731473	+	0.681870i	$0.761167\pi$
$524$	−0.232208	−	0.714664i	−0.0101441	−	0.0312202i
$525$	−8.32051	+	25.6079i	−0.363137	+	1.11762i
$526$	−24.7733			−1.08017
$527$	2.87458	−	15.8139i	0.125219	−	0.688864i
$528$	10.0594			0.437780
$529$	−1.90607	+	5.86629i	−0.0828727	+	0.255056i
$530$	−0.711358	−	2.18934i	−0.0308994	−	0.0950986i
$531$	3.23868	+	2.35304i	0.140547	+	0.102113i
$532$	−21.3863			−0.927215
$533$	−28.8238			−1.24850
$534$	−17.0665	−	12.3995i	−0.738540	−	0.536580i
$535$	4.51625	−	3.28124i	0.195254	−	0.141861i
$536$	−2.18571	+	1.58801i	−0.0944084	+	0.0685917i
$537$	−10.8775	+	33.4776i	−0.469400	+	1.44466i
$538$	3.81385	+	2.77093i	0.164427	+	0.119463i
$539$	1.43599	−	4.41952i	0.0618525	−	0.190362i
$540$	−0.699098	−	2.15160i	−0.0300844	−	0.0925903i
$541$	34.5270	−	25.0853i	1.48443	−	1.07850i	0.508337	−	0.861159i	$-0.330261\pi$
$541$	34.5270	−	25.0853i	1.48443	−	1.07850i	0.976095	−	0.217344i	$-0.0697394\pi$
$542$	1.84138	+	5.66719i	0.0790941	+	0.243427i
$543$	12.3231	+	37.9266i	0.528835	+	1.62759i
$544$	2.33547	−	1.69682i	0.100132	−	0.0727505i
$545$	−3.20881	−	9.87569i	−0.137450	−	0.423028i
$546$	5.80821	−	17.8758i	0.248568	−	0.765015i
$547$	0.962466	+	0.699272i	0.0411521	+	0.0298987i	0.608171	−	0.793806i	$-0.291903\pi$
$547$	0.962466	+	0.699272i	0.0411521	+	0.0298987i	−0.567019	+	0.823705i	$0.691903\pi$
$548$	1.04247	−	3.20839i	0.0445321	−	0.137056i
$549$	1.45653	−	1.05823i	0.0621633	−	0.0451642i
$550$	17.5548	−	12.7543i	0.748537	−	0.543844i
$551$	33.9228	+	24.6464i	1.44516	+	1.04997i
$552$	−8.62650			−0.367168
$553$	23.3913			0.994701
$554$	−3.95932	−	2.87661i	−0.168215	−	0.122215i
$555$	2.41122	+	7.42096i	0.102350	+	0.315002i
$556$	4.42379	−	13.6150i	0.187611	−	0.577406i
$557$	−2.38907			−0.101228			−0.0506141	−	0.998718i	$-0.516118\pi$
$557$	−2.38907			−0.101228			−0.0506141	+	0.998718i	$0.516118\pi$
$558$	6.96687	+	3.75166i	0.294931	+	0.158821i
$559$	−30.5797			−1.29338
$560$	0.594568	−	1.82989i	0.0251251	−	0.0773271i
$561$	−8.97371	−	27.6183i	−0.378871	−	1.16604i
$562$	−21.9527	−	15.9496i	−0.926019	−	0.672792i
$563$	1.91688			0.0807869			0.0403934	−	0.999184i	$-0.487139\pi$
$563$	1.91688			0.0807869			0.0403934	+	0.999184i	$0.487139\pi$
$564$	−7.34068			−0.309098
$565$	2.71478	+	1.97241i	0.114212	+	0.0829797i
$566$	6.88321	−	5.00094i	0.289323	−	0.210205i
$567$	25.6824	−	18.6594i	1.07856	−	0.783619i
$568$	2.13177	−	6.56091i	0.0894470	−	0.275290i
$569$	−2.21065	−	1.60613i	−0.0926753	−	0.0673326i	0.540483	−	0.841355i	$-0.318242\pi$
$569$	−2.21065	−	1.60613i	−0.0926753	−	0.0673326i	−0.633158	+	0.774023i	$0.718242\pi$
$570$	−3.35410	+	10.3229i	−0.140488	+	0.432377i
$571$	−10.8416	−	33.3669i	−0.453705	−	1.39636i	−0.872649	−	0.488348i	$-0.837600\pi$
$571$	−10.8416	−	33.3669i	−0.453705	−	1.39636i	0.418944	−	0.908012i	$-0.362400\pi$
$572$	−12.2543	+	8.90324i	−0.512377	+	0.372263i
$573$	2.02571	+	6.23449i	0.0846252	+	0.260450i
$574$	−7.94280	−	24.4454i	−0.331526	−	1.02033i
$575$	−15.0542	+	10.9375i	−0.627802	+	0.456125i
$576$	0.439168	+	1.35162i	0.0182987	+	0.0563175i
$577$	−6.46351	+	19.8926i	−0.269079	+	0.828141i	0.721646	+	0.692262i	$0.243386\pi$
$577$	−6.46351	+	19.8926i	−0.269079	+	0.828141i	−0.990725	+	0.135879i	$0.956614\pi$
$578$	7.01125	+	5.09397i	0.291629	+	0.211881i
$579$	12.0074	−	36.9551i	0.499012	−	1.53580i
$580$	−3.05193	+	2.21736i	−0.126725	+	0.0920708i
$581$	−36.3756	+	26.4284i	−1.50911	+	1.09643i
$582$	−0.770818	−	0.560032i	−0.0319514	−	0.0232141i
$583$	−16.1605			−0.669301
$584$	1.64355			0.0680106
$585$	−2.48077	−	1.80238i	−0.102567	−	0.0745193i
$586$	2.56409	+	7.89145i	0.105922	+	0.325993i
$587$	4.63663	−	14.2701i	0.191374	−	0.588989i	−0.808626	−	0.588323i	$-0.799788\pi$
$587$	4.63663	−	14.2701i	0.191374	−	0.588989i	1.00000		0.000665373i	$-0.000211795\pi$
$588$	2.04237			0.0842259
$589$	18.2878	+	38.0034i	0.753535	+	1.56590i
$590$	−1.91962			−0.0790297
$591$	−12.5734	+	38.6969i	−0.517200	+	1.59178i
$592$	1.68273	+	5.17890i	0.0691596	+	0.212851i
$593$	18.3091	+	13.3024i	0.751866	+	0.546262i	0.896405	−	0.443237i	$-0.146170\pi$
$593$	18.3091	+	13.3024i	0.751866	+	0.546262i	−0.144539	+	0.989499i	$0.546170\pi$
$594$	−15.8820			−0.651648
$595$	−5.55439			−0.227708
$596$	17.5151	+	12.7255i	0.717447	+	0.521256i
$597$	2.13075	−	1.54808i	0.0872060	−	0.0633588i
$598$	10.5087	−	7.63501i	0.429732	−	0.312219i
$599$	−13.3017	+	40.9384i	−0.543493	+	1.67270i	0.181055	+	0.983473i	$0.442049\pi$
$599$	−13.3017	+	40.9384i	−0.543493	+	1.67270i	−0.724547	+	0.689225i	$0.757951\pi$
$600$	7.71542	+	5.60558i	0.314981	+	0.228847i
$601$	10.6827	−	32.8780i	0.435757	−	1.34112i	−0.456551	−	0.889697i	$-0.650915\pi$
$601$	10.6827	−	32.8780i	0.435757	−	1.34112i	0.892308	−	0.451426i	$-0.149085\pi$
$602$	−8.42665	−	25.9346i	−0.343445	−	1.05701i
$603$	−3.10629	+	2.25685i	−0.126498	+	0.0919061i
$604$	0.590543	+	1.81750i	0.0240288	+	0.0739531i
$605$	2.50349	+	7.70494i	0.101781	+	0.313250i
$606$	−12.9678	+	9.42169i	−0.526783	+	0.382730i
$607$	−4.42417	−	13.6162i	−0.179571	−	0.552664i	0.820241	−	0.572018i	$-0.193839\pi$
$607$	−4.42417	−	13.6162i	−0.179571	−	0.552664i	−0.999813	+	0.0193537i	$0.993839\pi$
$608$	−2.34074	+	7.20406i	−0.0949296	+	0.292163i
$609$	−26.5861	−	19.3160i	−1.07732	−	0.782722i
$610$	−0.266778	+	0.821058i	−0.0108015	+	0.0332437i
$611$	8.94232	−	6.49698i	0.361768	−	0.262840i
$612$	3.31912	−	2.41148i	0.134168	−	0.0974784i
$613$	−20.8857	−	15.1743i	−0.843564	−	0.612885i	0.0798001	−	0.996811i	$-0.474572\pi$
$613$	−20.8857	−	15.1743i	−0.843564	−	0.612885i	−0.923364	+	0.383926i	$0.874572\pi$
$614$	21.5570			0.869970
$615$	−13.0451			−0.526031
$616$	−10.9277	−	7.93941i	−0.440288	−	0.319888i
$617$	−8.25792	−	25.4153i	−0.332451	−	1.02318i	−0.967964	−	0.251089i	$-0.919211\pi$
$617$	−8.25792	−	25.4153i	−0.332451	−	1.02318i	0.635513	−	0.772090i	$-0.280789\pi$
$618$	10.9319	−	33.6449i	0.439745	−	1.35340i
$619$	22.2550			0.894504			0.447252	−	0.894408i	$-0.352403\pi$
$619$	22.2550			0.894504			0.447252	+	0.894408i	$0.352403\pi$
$620$	−3.76014	+	0.508223i	−0.151011	+	0.0204107i
$621$	13.6197			0.546540
$622$	0.559588	−	1.72223i	0.0224374	−	0.0690553i
$623$	8.75317	+	26.9395i	0.350688	+	1.07931i
$624$	−5.38583	−	3.91303i	−0.215606	−	0.156647i
$625$	18.2494			0.729977
$626$	−2.22553			−0.0889500
$627$	61.6455	+	44.7881i	2.46189	+	1.78866i
$628$	9.03189	−	6.56205i	0.360412	−	0.261854i
$629$	12.7176	−	9.23988i	0.507084	−	0.368418i
$630$	0.844987	−	2.60060i	0.0336651	−	0.103611i
$631$	21.2115	+	15.4111i	0.844418	+	0.613505i	0.923601	−	0.383355i	$-0.125231\pi$
$631$	21.2115	+	15.4111i	0.844418	+	0.613505i	−0.0791836	+	0.996860i	$0.525231\pi$
$632$	2.56019	−	7.87946i	0.101839	−	0.313428i
$633$	7.91052	+	24.3461i	0.314415	+	0.967670i
$634$	−4.02222	+	2.92232i	−0.159743	+	0.116060i
$635$	0.770177	+	2.37036i	0.0305635	+	0.0940649i
$636$	−2.19484	−	6.75503i	−0.0870312	−	0.267854i
$637$	−2.48799	+	1.80763i	−0.0985777	+	0.0716209i
$638$	8.18370	+	25.1868i	0.323996	+	0.997157i
$639$	3.02962	−	9.32422i	0.119850	−	0.368860i
$640$	−0.551330	−	0.400565i	−0.0217932	−	0.0158337i
$641$	0.820738	−	2.52597i	0.0324172	−	0.0997699i	−0.933539	−	0.358477i	$-0.883296\pi$
$641$	0.820738	−	2.52597i	0.0324172	−	0.0997699i	0.965956	+	0.258707i	$0.0832963\pi$
$642$	13.9345	−	10.1240i	0.549952	−	0.399564i
$643$	−12.9551	+	9.41242i	−0.510898	+	0.371189i	−0.813164	−	0.582034i	$-0.802257\pi$
$643$	−12.9551	+	9.41242i	−0.510898	+	0.371189i	0.302266	+	0.953224i	$0.402257\pi$
$644$	9.37105	+	6.80847i	0.369271	+	0.268291i
$645$	−13.8398			−0.544942
$646$	21.8669			0.860343
$647$	−17.3388	−	12.5974i	−0.681660	−	0.495255i	0.192248	−	0.981346i	$-0.438422\pi$
$647$	−17.3388	−	12.5974i	−0.681660	−	0.495255i	−0.873908	+	0.486091i	$0.838422\pi$
$648$	−3.47452	−	10.6935i	−0.136492	−	0.420079i
$649$	−4.16436	+	12.8166i	−0.163466	+	0.503095i
$650$	−14.3601			−0.563251
$651$	−14.3326	−	29.7842i	−0.561738	−	1.16734i
$652$	−0.835844			−0.0327342
$653$	14.7967	−	45.5397i	0.579041	−	1.78210i	−0.0429463	−	0.999077i	$-0.513674\pi$
$653$	14.7967	−	45.5397i	0.579041	−	1.78210i	0.621987	−	0.783027i	$-0.286326\pi$
$654$	−9.90053	−	30.4707i	−0.387142	−	1.19150i
$655$	0.414293	+	0.301001i	0.0161877	+	0.0117611i
$656$	−9.10387			−0.355446
$657$	2.33578			0.0911274
$658$	7.97426	+	5.79364i	0.310869	+	0.225859i
$659$	−29.3954	+	21.3570i	−1.14508	+	0.831951i	−0.987819	−	0.155606i	$-0.950267\pi$
$659$	−29.3954	+	21.3570i	−1.14508	+	0.831951i	−0.157263	+	0.987557i	$0.550267\pi$
$660$	−5.54606	+	4.02945i	−0.215880	+	0.156846i
$661$	8.02084	−	24.6856i	0.311974	−	0.960158i	−0.665008	−	0.746837i	$-0.731572\pi$
$661$	8.02084	−	24.6856i	0.311974	−	0.960158i	0.976982	−	0.213322i	$-0.0684283\pi$
$662$	20.7739	+	15.0931i	0.807399	+	0.586610i
$663$	−5.93873	+	18.2775i	−0.230641	+	0.709841i
$664$	4.92118	+	15.1458i	0.190979	+	0.587772i
$665$	11.7909	−	8.56661i	0.457232	−	0.332199i
$666$	2.39145	+	7.36014i	0.0926669	+	0.285199i
$667$	−7.01797	−	21.5991i	−0.271737	−	0.836320i
$668$	7.87794	−	5.72366i	0.304807	−	0.221455i
$669$	0.988858	+	3.04339i	0.0382315	+	0.117664i
$670$	0.568947	−	1.75104i	0.0219803	−	0.0676485i
$671$	4.90315	+	3.56235i	0.189284	+	0.137523i
$672$	1.83450	−	5.64600i	0.0707672	−	0.217799i
$673$	10.4172	−	7.56852i	0.401553	−	0.291745i	−0.368620	−	0.929580i	$-0.620170\pi$
$673$	10.4172	−	7.56852i	0.401553	−	0.291745i	0.770173	+	0.637835i	$0.220170\pi$
$674$	16.0982	−	11.6960i	0.620079	−	0.450514i
$675$	−12.1813	−	8.85022i	−0.468858	−	0.340645i
$676$	−2.97577			−0.114453
$677$	6.90655			0.265440			0.132720	−	0.991154i	$-0.457629\pi$
$677$	6.90655			0.265440			0.132720	+	0.991154i	$0.457629\pi$
$678$	8.37626	+	6.08571i	0.321688	+	0.233720i
$679$	0.395342	+	1.21674i	0.0151718	+	0.0466941i
$680$	−0.607929	+	1.87101i	−0.0233130	+	0.0717501i
$681$	4.78414			0.183329
$682$	−4.76389	+	26.2075i	−0.182419	+	1.00354i
$683$	1.51496			0.0579684			0.0289842	−	0.999580i	$-0.490773\pi$
$683$	1.51496			0.0579684			0.0289842	+	0.999580i	$0.490773\pi$
$684$	−3.32661	+	10.2383i	−0.127196	+	0.391469i
$685$	0.710423	+	2.18646i	0.0271439	+	0.0835403i
$686$	13.7703	+	10.0047i	0.525754	+	0.381983i
$687$	13.7599			0.524973
$688$	−9.65845			−0.368225
$689$	8.65237	+	6.28632i	0.329629	+	0.239490i
$690$	4.75605	−	3.45547i	0.181060	−	0.131548i
$691$	1.70743	−	1.24052i	0.0649538	−	0.0471917i	−0.554835	−	0.831961i	$-0.687218\pi$
$691$	1.70743	−	1.24052i	0.0649538	−	0.0471917i	0.619788	+	0.784769i	$0.287218\pi$
$692$	4.87284	−	14.9970i	0.185237	−	0.570102i
$693$	−15.5301	−	11.2833i	−0.589942	−	0.428618i
$694$	−1.85188	+	5.69951i	−0.0702965	+	0.216350i
$695$	3.01473	+	9.27839i	0.114355	+	0.351950i
$696$	−9.41651	+	6.84150i	−0.356932	+	0.259326i
$697$	8.12129	+	24.9948i	0.307616	+	0.946744i
$698$	−0.416946	−	1.28323i	−0.0157817	−	0.0485709i
$699$	−32.0867	+	23.3124i	−1.21363	+	0.881755i
$700$	−3.95713	−	12.1788i	−0.149566	−	0.460316i
$701$	14.4917	−	44.6008i	0.547343	−	1.68455i	−0.168009	−	0.985785i	$-0.553734\pi$
$701$	14.4917	−	44.6008i	0.547343	−	1.68455i	0.715352	−	0.698764i	$-0.246266\pi$
$702$	8.50326	+	6.17798i	0.320935	+	0.233173i
$703$	−12.7463	+	39.2291i	−0.480736	+	1.47955i
$704$	−3.87045	+	2.81205i	−0.145873	+	0.105983i
$705$	4.04714	−	2.94042i	0.152424	−	0.110742i
$706$	1.77300	+	1.28816i	0.0667277	+	0.0484805i
$707$	21.5232			0.809462
$708$	−5.92286			−0.222595
$709$	−10.1969	−	7.40845i	−0.382951	−	0.278230i	0.379610	−	0.925147i	$-0.376058\pi$
$709$	−10.1969	−	7.40845i	−0.382951	−	0.278230i	−0.762561	+	0.646917i	$0.776058\pi$
$710$	1.45276	+	4.47114i	0.0545211	+	0.167799i
$711$	3.63849	−	11.1981i	0.136454	−	0.419962i
$712$	10.0327			0.375991
$713$	4.08530	−	22.4744i	0.152996	−	0.841671i
$714$	−17.1376			−0.641360
$715$	3.18982	−	9.81725i	0.119292	−	0.367144i
$716$	−5.17322	−	15.9215i	−0.193332	−	0.595016i
$717$	5.05781	+	3.67471i	0.188887	+	0.137235i
$718$	−33.2647			−1.24143
$719$	5.24499			0.195605			0.0978026	−	0.995206i	$-0.468819\pi$
$719$	5.24499			0.195605			0.0978026	+	0.995206i	$0.468819\pi$
$720$	−0.783538	−	0.569274i	−0.0292007	−	0.0212156i
$721$	−38.4297	+	27.9208i	−1.43120	+	1.03982i
$722$	−31.0481	+	22.5577i	−1.15549	+	0.839512i
$723$	2.86218	−	8.80888i	0.106446	−	0.327606i
$724$	−15.3436	−	11.1478i	−0.570239	−	0.414303i
$725$	−7.75852	+	23.8783i	−0.288144	+	0.886817i
$726$	7.72432	+	23.7730i	0.286677	+	0.882300i
$727$	9.30207	−	6.75835i	0.344995	−	0.250653i	−0.401772	−	0.915740i	$-0.631605\pi$
$727$	9.30207	−	6.75835i	0.344995	−	0.250653i	0.746766	+	0.665087i	$0.231605\pi$
$728$	2.76232	+	8.50153i	0.102378	+	0.315088i
$729$	1.53313	+	4.71850i	0.0567827	+	0.174759i
$730$	−0.906139	+	0.658348i	−0.0335377	+	0.0243666i
$731$	8.61602	+	26.5174i	0.318675	+	0.980781i
$732$	−0.823123	+	2.53331i	−0.0304235	+	0.0936340i
$733$	38.7815	+	28.1764i	1.43243	+	1.04072i	0.989558	+	0.144133i	$0.0460392\pi$
$733$	38.7815	+	28.1764i	1.43243	+	1.04072i	0.442869	+	0.896587i	$0.353961\pi$
$734$	10.6229	−	32.6939i	0.392098	−	1.20675i
$735$	−1.12602	+	0.818101i	−0.0415338	+	0.0301761i
$736$	3.31912	−	2.41148i	0.122344	−	0.0888884i
$737$	−10.4568	−	7.59728i	−0.385180	−	0.279849i
$738$	−12.9382			−0.476262
$739$	−35.7604			−1.31547			−0.657733	−	0.753251i	$-0.728485\pi$
$739$	−35.7604			−1.31547			−0.657733	+	0.753251i	$0.728485\pi$
$740$	−3.00222	−	2.18124i	−0.110364	−	0.0801840i
$741$	−15.5829	−	47.9592i	−0.572452	−	1.76183i
$742$	−2.94713	+	9.07034i	−0.108193	+	0.332983i
$743$	10.2110			0.374604			0.187302	−	0.982302i	$-0.440026\pi$
$743$	10.2110			0.374604			0.187302	+	0.982302i	$0.440026\pi$
$744$	−11.6016	+	1.56809i	−0.425336	+	0.0574888i
$745$	−14.7540			−0.540544
$746$	−8.25138	+	25.3951i	−0.302104	+	0.929782i
$747$	6.99387	+	21.5249i	0.255892	+	0.787556i
$748$	11.1732	+	8.11782i	0.408534	+	0.296817i
$749$	−23.1276			−0.845065
$750$	−13.6638			−0.498930
$751$	−29.9202	−	21.7383i	−1.09180	−	0.793241i	−0.112100	−	0.993697i	$-0.535758\pi$
$751$	−29.9202	−	21.7383i	−1.09180	−	0.793241i	−0.979703	+	0.200456i	$0.935758\pi$
$752$	2.82439	−	2.05204i	0.102995	−	0.0748302i
$753$	27.0880	−	19.6806i	0.987142	−	0.717201i
$754$	5.41591	−	16.6685i	0.197236	−	0.607029i
$755$	−1.05361	−	0.765493i	−0.0383448	−	0.0278592i
$756$	−2.89634	+	8.91402i	−0.105339	+	0.324200i
$757$	7.18760	+	22.1212i	0.261238	+	0.804007i	0.992536	+	0.121950i	$0.0389146\pi$
$757$	7.18760	+	22.1212i	0.261238	+	0.804007i	−0.731299	+	0.682057i	$0.761085\pi$
$758$	−16.0099	+	11.6319i	−0.581507	+	0.422490i
$759$	−12.7533	−	39.2505i	−0.462914	−	1.42470i
$760$	−1.59517	−	4.90943i	−0.0578629	−	0.178084i
$761$	14.7467	−	10.7141i	0.534566	−	0.388385i	−0.287497	−	0.957781i	$-0.592823\pi$
$761$	14.7467	−	10.7141i	0.534566	−	0.388385i	0.822063	+	0.569397i	$0.192823\pi$
$762$	2.37632	+	7.31357i	0.0860851	+	0.264943i
$763$	−13.2940	+	40.9147i	−0.481274	+	1.48121i
$764$	−2.52222	−	1.83250i	−0.0912508	−	0.0662976i
$765$	−0.863976	+	2.65905i	−0.0312371	+	0.0961380i
$766$	17.5454	−	12.7474i	0.633939	−	0.460584i
$767$	7.21515	−	5.24211i	0.260524	−	0.189282i
$768$	−1.70109	−	1.23591i	−0.0613827	−	0.0445971i
$769$	−0.305539			−0.0110180			−0.00550901	−	0.999985i	$-0.501754\pi$
$769$	−0.305539			−0.0110180			−0.00550901	+	0.999985i	$0.501754\pi$
$770$	9.20499			0.331725
$771$	−28.9562	−	21.0379i	−1.04283	−	0.757661i
$772$	5.71059	+	17.5754i	0.205529	+	0.632552i
$773$	−7.39728	+	22.7665i	−0.266062	+	0.818853i	0.725385	+	0.688343i	$0.241662\pi$
$773$	−7.39728	+	22.7665i	−0.266062	+	0.818853i	−0.991447	+	0.130510i	$0.958338\pi$
$774$	−13.7264			−0.493385
$775$	−18.2579	+	17.4461i	−0.655843	+	0.626682i
$776$	0.453133			0.0162665
$777$	9.98959	−	30.7448i	0.358374	−	1.10296i
$778$	7.67986	+	23.6362i	0.275336	+	0.847399i
$779$	−55.7897	−	40.5336i	−1.99888	−	1.45227i
$780$	4.53679			0.162443
$781$	33.0036			1.18096
$782$	−9.58164	−	6.96147i	−0.342639	−	0.248942i
$783$	14.8670	−	10.8015i	0.531303	−	0.386014i
$784$	−0.785820	+	0.570931i	−0.0280650	+	0.0203904i
$785$	−2.35103	+	7.23571i	−0.0839117	+	0.258254i
$786$	1.27827	+	0.928717i	0.0455943	+	0.0331262i
$787$	−0.355846	+	1.09518i	−0.0126845	+	0.0390390i	−0.957198	−	0.289432i	$-0.906533\pi$
$787$	−0.355846	+	1.09518i	−0.0126845	+	0.0390390i	0.944514	+	0.328471i	$0.106533\pi$
$788$	−5.97975	−	18.4038i	−0.213020	−	0.655608i
$789$	42.1415	−	30.6176i	1.50028	−	1.09002i
$790$	1.74472	+	5.36970i	0.0620744	+	0.191045i
$791$	−4.29607	−	13.2219i	−0.152751	−	0.470118i
$792$	−5.50060	+	3.99642i	−0.195455	+	0.142007i
$793$	−1.23943	−	3.81457i	−0.0440134	−	0.135459i
$794$	−9.89956	+	30.4677i	−0.351322	+	1.08126i
$795$	3.91591	+	2.84507i	0.138883	+	0.100904i
$796$	−0.387070	+	1.19128i	−0.0137193	+	0.0422237i
$797$	14.1282	−	10.2648i	0.500448	−	0.363597i	−0.308740	−	0.951146i	$-0.599907\pi$
$797$	14.1282	−	10.2648i	0.500448	−	0.363597i	0.809188	+	0.587550i	$0.199907\pi$
$798$	36.3800	−	26.4316i	1.28784	−	0.935670i
$799$	−8.15346	−	5.92383i	−0.288449	−	0.209570i
$800$	−4.53558			−0.160357
$801$	14.2583			0.503791
$802$	−3.20592	−	2.32924i	−0.113205	−	0.0822483i
$803$	2.42979	+	7.47814i	0.0857456	+	0.263898i
$804$	1.75544	−	5.40270i	0.0619097	−	0.190539i
$805$	−7.89378			−0.278219
$806$	12.7451	−	12.1784i	0.448927	−	0.428966i
$807$	−9.91232			−0.348930
$808$	2.35572	−	7.25016i	0.0828739	−	0.255060i
$809$	−9.93268	−	30.5696i	−0.349214	−	1.07477i	−0.959289	−	0.282427i	$-0.908860\pi$
$809$	−9.93268	−	30.5696i	−0.349214	−	1.07477i	0.610074	−	0.792344i	$-0.291140\pi$
$810$	6.19904	+	4.50386i	0.217812	+	0.158250i
$811$	33.5238			1.17718			0.588591	−	0.808431i	$-0.299683\pi$
$811$	33.5238			1.17718			0.588591	+	0.808431i	$0.299683\pi$
$812$	15.6289			0.548467
$813$	−10.1365	−	7.36460i	−0.355503	−	0.258288i
$814$	−21.0762	+	15.3128i	−0.738721	+	0.536712i
$815$	0.460826	−	0.334809i	0.0161420	−	0.0117279i
$816$	−1.87572	+	5.77288i	−0.0656634	+	0.202091i
$817$	−59.1883	−	43.0028i	−2.07074	−	1.50448i
$818$	7.68997	−	23.6673i	0.268873	−	0.827507i
$819$	3.92574	+	12.0822i	0.137177	+	0.422186i
$820$	5.01923	−	3.64669i	0.175279	−	0.127348i
$821$	13.3049	+	40.9481i	0.464342	+	1.42910i	0.859808	+	0.510618i	$0.170583\pi$
$821$	13.3049	+	40.9481i	0.464342	+	1.42910i	−0.395465	+	0.918481i	$0.629417\pi$
$822$	2.19196	+	6.74615i	0.0764533	+	0.235299i
$823$	35.1370	−	25.5285i	1.22480	−	0.889868i	0.228310	−	0.973589i	$-0.426680\pi$
$823$	35.1370	−	25.5285i	1.22480	−	0.889868i	0.996489	+	0.0837201i	$0.0266802\pi$
$824$	5.19907	+	16.0011i	0.181118	+	0.557425i
$825$	−14.0990	+	43.3923i	−0.490864	+	1.51073i
$826$	6.43406	+	4.67462i	0.223870	+	0.162651i
$827$	−12.0893	+	37.2071i	−0.420387	+	1.29382i	0.486956	+	0.873426i	$0.338107\pi$
$827$	−12.0893	+	37.2071i	−0.420387	+	1.29382i	−0.907343	+	0.420391i	$0.861893\pi$
$828$	4.71706	−	3.42715i	0.163929	−	0.119102i
$829$	−11.6109	+	8.43583i	−0.403264	+	0.292988i	−0.770869	−	0.636994i	$-0.780178\pi$
$829$	−11.6109	+	8.43583i	−0.403264	+	0.292988i	0.367605	+	0.929982i	$0.380178\pi$
$830$	−8.78008	−	6.37910i	−0.304761	−	0.221422i
$831$	10.2904			0.356969
$832$	3.16611			0.109765
$833$	2.26850	+	1.64817i	0.0785990	+	0.0571055i
$834$	9.30173	+	28.6278i	0.322093	+	0.991299i
$835$	−2.05065	+	6.31125i	−0.0709656	+	0.218410i
$836$	−36.2389			−1.25335
$837$	18.3169	−	2.47573i	0.633124	−	0.0855736i
$838$	−3.93735			−0.136013
$839$	−5.95770	+	18.3359i	−0.205683	+	0.633026i	0.794002	+	0.607915i	$0.207994\pi$
$839$	−5.95770	+	18.3359i	−0.205683	+	0.633026i	−0.999685	+	0.0251108i	$0.992006\pi$
$840$	1.25017	+	3.84764i	0.0431351	+	0.132756i
$841$	−1.32896	−	0.965544i	−0.0458261	−	0.0332946i
$842$	28.9538			0.997814
$843$	57.0557			1.96510
$844$	−9.84944	−	7.15603i	−0.339032	−	0.246321i
$845$	1.64063	−	1.19199i	0.0564393	−	0.0410056i
$846$	4.01396	−	2.91632i	0.138003	−	0.100265i
$847$	10.3719	−	31.9213i	0.356381	−	1.09683i
$848$	2.73281	+	1.98550i	0.0938451	+	0.0681825i
$849$	−5.52821	+	17.0141i	−0.189728	+	0.583922i
$850$	4.04606	+	12.4525i	0.138779	+	0.427117i
$851$	18.0740	−	13.1315i	0.619568	−	0.450143i
$852$	4.48238	+	13.7954i	0.153564	+	0.472621i
$853$	12.9782	+	39.9428i	0.444365	+	1.36762i	0.883179	+	0.469037i	$0.155399\pi$
$853$	12.9782	+	39.9428i	0.444365	+	1.36762i	−0.438813	+	0.898578i	$0.644601\pi$
$854$	2.89359	−	2.10231i	0.0990165	−	0.0719397i
$855$	−2.26702	−	6.97718i	−0.0775305	−	0.238614i
$856$	−2.53133	+	7.79062i	−0.0865190	+	0.266278i
$857$	−24.2518	−	17.6200i	−0.828426	−	0.601887i	0.0906874	−	0.995879i	$-0.471094\pi$
$857$	−24.2518	−	17.6200i	−0.828426	−	0.601887i	−0.919114	+	0.393992i	$0.871094\pi$
$858$	9.84195	−	30.2904i	0.335999	−	1.03410i
$859$	−26.0628	+	18.9358i	−0.889253	+	0.646080i	−0.935683	−	0.352842i	$-0.885215\pi$
$859$	−26.0628	+	18.9358i	−0.889253	+	0.646080i	0.0464302	+	0.998922i	$0.485215\pi$
$860$	5.32499	−	3.86883i	0.181581	−	0.131926i
$861$	43.7238	+	31.7672i	1.49010	+	1.08262i
$862$	2.39292			0.0815031
$863$	−51.4871			−1.75264			−0.876321	−	0.481728i	$-0.840009\pi$
$863$	−51.4871			−1.75264			−0.876321	+	0.481728i	$0.840009\pi$
$864$	2.68571	+	1.95129i	0.0913698	+	0.0663841i
$865$	3.32075	+	10.2202i	0.112909	+	0.347498i
$866$	5.60978	−	17.2651i	0.190628	−	0.586693i
$867$	−18.2224			−0.618867
$868$	13.8406	+	7.45316i	0.469780	+	0.252977i
$869$	39.6364			1.34457
$870$	2.45114	−	7.54384i	0.0831015	−	0.255760i
$871$	2.64328	+	8.13519i	0.0895642	+	0.275650i
$872$	12.3272	+	8.95624i	0.417452	+	0.303297i
$873$	0.643982			0.0217955
$874$	31.0768			1.05119
$875$	14.8431	+	10.7841i	0.501788	+	0.364570i
$876$	−2.79582	+	2.03129i	−0.0944621	+	0.0686308i
$877$	12.0611	−	8.76292i	0.407275	−	0.295903i	−0.365223	−	0.930920i	$-0.619007\pi$
$877$	12.0611	−	8.76292i	0.407275	−	0.295903i	0.772498	+	0.635017i	$0.219007\pi$
$878$	7.91631	−	24.3639i	0.267162	−	0.822241i
$879$	−14.1149	−	10.2551i	−0.476083	−	0.345895i
$880$	1.00749	−	3.10073i	0.0339624	−	0.104526i
$881$	11.6082	+	35.7264i	0.391090	+	1.20365i	0.931965	+	0.362549i	$0.118093\pi$
$881$	11.6082	+	35.7264i	0.391090	+	1.20365i	−0.540875	+	0.841103i	$0.681907\pi$
$882$	−1.11679	+	0.811395i	−0.0376043	+	0.0273211i
$883$	−2.02481	−	6.23174i	−0.0681404	−	0.209715i	0.911188	−	0.411990i	$-0.135166\pi$
$883$	−2.02481	−	6.23174i	−0.0681404	−	0.209715i	−0.979329	+	0.202276i	$0.935166\pi$
$884$	−2.82439	−	8.69258i	−0.0949946	−	0.292363i
$885$	3.26545	−	2.37249i	0.109767	−	0.0797503i
$886$	−0.898546	−	2.76544i	−0.0301872	−	0.0929068i
$887$	3.54458	−	10.9091i	0.119016	−	0.366292i	−0.873748	−	0.486379i	$-0.838317\pi$
$887$	3.54458	−	10.9091i	0.119016	−	0.366292i	0.992763	+	0.120087i	$0.0383174\pi$
$888$	−9.26312	−	6.73005i	−0.310850	−	0.225846i
$889$	3.19082	−	9.82033i	0.107017	−	0.329363i
$890$	−5.53133	+	4.01874i	−0.185411	+	0.134709i
$891$	43.5185	−	31.6181i	1.45793	−	1.05925i
$892$	−1.23123	−	0.894543i	−0.0412247	−	0.0299515i
$893$	26.4447			0.884937
$894$	−45.5223			−1.52249
$895$	9.22976	+	6.70581i	0.308517	+	0.224151i
$896$	0.872464	+	2.68517i	0.0291470	+	0.0897052i
$897$	−8.44000	+	25.9757i	−0.281803	+	0.867302i
$898$	−14.8796			−0.496539
$899$	−13.3645	−	27.7725i	−0.445732	−	0.926265i
$900$	−6.44587			−0.214862
$901$	3.01336	−	9.27417i	0.100390	−	0.308967i
$902$	−13.4590	−	41.4225i	−0.448135	−	1.37922i
$903$	46.3873	+	33.7024i	1.54367	+	1.12154i
$904$	−4.92406			−0.163772
$905$	12.9248			0.429634
$906$	−3.25084	−	2.36187i	−0.108002	−	0.0784680i
$907$	−23.0526	+	16.7487i	−0.765450	+	0.556132i	−0.900577	−	0.434696i	$-0.856856\pi$
$907$	−23.0526	+	16.7487i	−0.765450	+	0.556132i	0.135127	+	0.990828i	$0.456856\pi$
$908$	−1.84074	+	1.33738i	−0.0610871	+	0.0443824i
$909$	3.34790	−	10.3038i	0.111043	−	0.341754i
$910$	−4.92836	−	3.58066i	−0.163374	−	0.118698i
$911$	8.33259	−	25.6451i	0.276071	−	0.849659i	−0.712863	−	0.701303i	$-0.752602\pi$
$911$	8.33259	−	25.6451i	0.276071	−	0.849659i	0.988934	−	0.148356i	$-0.0473981\pi$
$912$	−4.92178	−	15.1477i	−0.162976	−	0.501590i
$913$	−61.6380	+	44.7826i	−2.03992	+	1.48209i
$914$	0.980805	+	3.01861i	0.0324421	+	0.0998466i
$915$	−0.560943	−	1.72641i	−0.0185442	−	0.0570732i
$916$	−5.29425	+	3.84649i	−0.174927	+	0.127092i
$917$	−0.655606	−	2.01775i	−0.0216500	−	0.0666319i
$918$	2.96143	−	9.11434i	0.0977417	−	0.300818i
$919$	−20.8514	−	15.1494i	−0.687824	−	0.499733i	0.188120	−	0.982146i	$-0.439761\pi$
$919$	−20.8514	−	15.1494i	−0.687824	−	0.499733i	−0.875944	+	0.482413i	$0.839761\pi$
$920$	−0.863976	+	2.65905i	−0.0284845	+	0.0876661i
$921$	−36.6703	+	26.6426i	−1.20833	+	0.877902i
$922$	−10.6879	+	7.76521i	−0.351987	+	0.255734i
$923$	−17.6702	−	12.8381i	−0.581621	−	0.422572i
$924$	28.4013			0.934334
$925$	−24.6981			−0.812069
$926$	−8.70136	−	6.32191i	−0.285944	−	0.207751i
$927$	7.38881	+	22.7404i	0.242680	+	0.746894i
$928$	1.71059	−	5.26465i	0.0561528	−	0.172821i
$929$	14.6336			0.480113			0.240056	−	0.970759i	$-0.422834\pi$
$929$	14.6336			0.480113			0.240056	+	0.970759i	$0.422834\pi$
$930$	5.76820	−	5.51173i	0.189147	−	0.180737i
$931$	−7.35760			−0.241136
$932$	5.82883	−	17.9393i	0.190930	−	0.587621i
$933$	1.17662	+	3.62127i	0.0385209	+	0.118555i
$934$	18.4310	+	13.3909i	0.603081	+	0.438164i
$935$	−9.41185			−0.307800
$936$	4.49960			0.147074
$937$	−1.98312	−	1.44082i	−0.0647856	−	0.0470695i	0.554921	−	0.831903i	$-0.312748\pi$
$937$	−1.98312	−	1.44082i	−0.0647856	−	0.0470695i	−0.619707	+	0.784833i	$0.712748\pi$
$938$	−6.17104	+	4.48352i	−0.201492	+	0.146392i
$939$	3.78582	−	2.75056i	0.123546	−	0.0897611i
$940$	−0.735197	+	2.26270i	−0.0239795	+	0.0738012i
$941$	−43.5938	−	31.6728i	−1.42112	−	1.03250i	−0.991586	−	0.129451i	$-0.958678\pi$
$941$	−43.5938	−	31.6728i	−1.42112	−	1.03250i	−0.429532	−	0.903051i	$-0.641322\pi$
$942$	−7.25392	+	22.3253i	−0.236345	+	0.727396i
$943$	11.5418	+	35.5220i	0.375853	+	1.15676i
$944$	2.27887	−	1.65570i	0.0741710	−	0.0538884i
$945$	−1.97380	−	6.07474i	−0.0642078	−	0.197611i
$946$	−14.2789	−	43.9458i	−0.464246	−	1.42880i
$947$	20.7483	−	15.0746i	0.674231	−	0.489857i	−0.197208	−	0.980362i	$-0.563187\pi$
$947$	20.7483	−	15.0746i	0.674231	−	0.489857i	0.871439	+	0.490504i	$0.163187\pi$
$948$	5.38321	+	16.5678i	0.174839	+	0.538098i
$949$	1.60802	−	4.94897i	0.0521985	−	0.160650i
$950$	−27.7947	−	20.1940i	−0.901779	−	0.655180i
$951$	3.23043	−	9.94223i	0.104754	−	0.322399i
$952$	6.59386	−	4.79072i	0.213708	−	0.155268i
$953$	40.7432	−	29.6017i	1.31980	−	0.958892i	0.319867	−	0.947463i	$-0.396362\pi$
$953$	40.7432	−	29.6017i	1.31980	−	0.958892i	0.999935	−	0.0114293i	$-0.00363814\pi$
$954$	3.88381	+	2.82176i	0.125743	+	0.0913577i
$955$	2.12461			0.0687508
$956$	−2.97328			−0.0961627
$957$	−45.0499	−	32.7307i	−1.45626	−	1.05803i
$958$	−3.99328	−	12.2901i	−0.129017	−	0.397074i
$959$	2.94326	−	9.05842i	0.0950428	−	0.292512i
$960$	1.43292			0.0462474
$961$	1.40896	−	30.9680i	0.0454502	−	0.998967i
$962$	17.2408			0.555864
$963$	−3.59747	+	11.0719i	−0.115927	+	0.356786i
$964$	1.36122	+	4.18940i	0.0438419	+	0.134931i
$965$	−10.1885	−	7.40238i	−0.327979	−	0.238291i
$966$	−24.3557			−0.783630
$967$	7.68546			0.247148			0.123574	−	0.992335i	$-0.460564\pi$
$967$	7.68546			0.247148			0.123574	+	0.992335i	$0.460564\pi$
$968$	−9.61760	−	6.98760i	−0.309121	−	0.224590i
$969$	−37.1976	+	27.0256i	−1.19496	+	0.868188i
$970$	−0.249826	+	0.181509i	−0.00802141	+	0.00582790i
$971$	−9.38068	+	28.8708i	−0.301040	+	0.926507i	0.680085	+	0.733134i	$0.261943\pi$
$971$	−9.38068	+	28.8708i	−0.301040	+	0.926507i	−0.981125	+	0.193374i	$0.938057\pi$
$972$	11.0695	+	8.04248i	0.355055	+	0.257963i
$973$	12.4899	−	38.4401i	0.400409	−	1.23233i
$974$	2.92242	+	8.99429i	0.0936405	+	0.288196i
$975$	24.4279	−	17.7479i	0.782318	−	0.568387i
$976$	−0.391468	−	1.20481i	−0.0125306	−	0.0385651i
$977$	6.33564	+	19.4991i	0.202695	+	0.623831i	0.999800	+	0.0199905i	$0.00636361\pi$
$977$	6.33564	+	19.4991i	0.202695	+	0.623831i	−0.797105	+	0.603840i	$0.793636\pi$
$978$	1.42184	−	1.03303i	0.0454655	−	0.0330326i
$979$	14.8322	+	45.6487i	0.474038	+	1.45894i
$980$	0.204551	−	0.629543i	0.00653414	−	0.0201100i
$981$	17.5192	+	12.7284i	0.559344	+	0.406387i
$982$	−6.31265	+	19.4283i	−0.201445	+	0.619983i
$983$	−42.7228	+	31.0399i	−1.36264	+	0.990020i	−0.364373	+	0.931253i	$0.618717\pi$
$983$	−42.7228	+	31.0399i	−1.36264	+	0.990020i	−0.998272	+	0.0587665i	$0.981283\pi$
$984$	15.4865	−	11.2516i	0.493691	−	0.358687i
$985$	10.6687	+	7.75128i	0.339934	+	0.246976i
$986$	−15.9801			−0.508911
$987$	−20.7253			−0.659695
$988$	19.4023	+	14.0966i	0.617271	+	0.448473i
$989$	12.2449	+	37.6859i	0.389365	+	1.19834i
$990$	1.43182	−	4.40669i	0.0455063	−	0.140054i
$991$	14.7962			0.470018			0.235009	−	0.971993i	$-0.424488\pi$
$991$	14.7962			0.470018			0.235009	+	0.971993i	$0.424488\pi$
$992$	4.02548	−	3.84649i	0.127809	−	0.122126i
$993$	−53.9919			−1.71338
$994$	6.01873	−	18.5238i	0.190903	−	0.587538i
$995$	−0.263781	−	0.811833i	−0.00836241	−	0.0257369i
$996$	−27.0903	−	19.6822i	−0.858388	−	0.623656i
$997$	12.7205			0.402862			0.201431	−	0.979503i	$-0.435441\pi$
$997$	12.7205			0.402862			0.201431	+	0.979503i	$0.435441\pi$
$998$	16.0085			0.506739
$999$	14.6248	+	10.6256i	0.462709	+	0.336178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.d.a.39.2	yes	8
3.2	odd	2		558.2.i.i.163.1		8
4.3	odd	2		496.2.n.e.225.1		8
31.2	even	5		1922.2.a.r.1.3		4
31.4	even	5	inner	62.2.d.a.35.2	✓	8
31.29	odd	10		1922.2.a.n.1.2		4
93.35	odd	10		558.2.i.i.469.1		8
124.35	odd	10		496.2.n.e.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.d.a.35.2	✓	8	31.4	even	5	inner
62.2.d.a.39.2	yes	8	1.1	even	1	trivial
496.2.n.e.97.1		8	124.35	odd	10
496.2.n.e.225.1		8	4.3	odd	2
558.2.i.i.163.1		8	3.2	odd	2
558.2.i.i.469.1		8	93.35	odd	10
1922.2.a.n.1.2		4	31.29	odd	10
1922.2.a.r.1.3		4	31.2	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.649758 + 1.99975i) q^{3} +(-0.809017 - 0.587785i) q^{4} +0.681481 q^{5} +2.10266 q^{6} +(-2.28414 - 1.65953i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-1.14976 + 0.835348i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.649758 + 1.99975i) q^{3} +(-0.809017 - 0.587785i) q^{4} +0.681481 q^{5} +2.10266 q^{6} +(-2.28414 - 1.65953i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-1.14976 + 0.835348i) q^{9} +(0.210589 - 0.648127i) q^{10} +(-3.87045 - 2.81205i) q^{11} +(0.649758 - 1.99975i) q^{12} +(0.978381 + 3.01115i) q^{13} +(-2.28414 + 1.65953i) q^{14} +(0.442798 + 1.36279i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.33547 - 1.69682i) q^{17} +(0.439168 + 1.35162i) q^{18} +(-2.34074 + 7.20406i) q^{19} +(-0.551330 - 0.400565i) q^{20} +(1.83450 - 5.64600i) q^{21} +(-3.87045 + 2.81205i) q^{22} +(3.31912 - 2.41148i) q^{23} +(-1.70109 - 1.23591i) q^{24} -4.53558 q^{25} +3.16611 q^{26} +(2.68571 + 1.95129i) q^{27} +(0.872464 + 2.68517i) q^{28} +(1.71059 - 5.26465i) q^{29} +1.43292 q^{30} +(4.02548 - 3.84649i) q^{31} +1.00000 q^{32} +(3.10853 - 9.56708i) q^{33} +(-0.892071 - 2.74551i) q^{34} +(-1.55660 - 1.13094i) q^{35} +1.42118 q^{36} +5.44541 q^{37} +(6.12814 + 4.45235i) q^{38} +(-5.38583 + 3.91303i) q^{39} +(-0.551330 + 0.400565i) q^{40} +(-2.81325 + 8.65829i) q^{41} +(-4.80277 - 3.48942i) q^{42} +(-2.98463 + 9.18573i) q^{43} +(1.47838 + 4.54999i) q^{44} +(-0.783538 + 0.569274i) q^{45} +(-1.26779 - 3.90186i) q^{46} +(-1.07882 - 3.32027i) q^{47} +(-1.70109 + 1.23591i) q^{48} +(0.300156 + 0.923786i) q^{49} +(-1.40157 + 4.31360i) q^{50} +(4.91070 + 3.56783i) q^{51} +(0.978381 - 3.01115i) q^{52} +(2.73281 - 1.98550i) q^{53} +(2.68571 - 1.95129i) q^{54} +(-2.63764 - 1.91636i) q^{55} +2.82335 q^{56} -15.9272 q^{57} +(-4.47838 - 3.25373i) q^{58} +(-0.870452 - 2.67897i) q^{59} +(0.442798 - 1.36279i) q^{60} -1.26682 q^{61} +(-2.41429 - 5.01709i) q^{62} +4.01249 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.666748 + 2.05204i) q^{65} +(-8.13824 - 5.91278i) q^{66} +2.70169 q^{67} -2.88680 q^{68} +(6.97898 + 5.07053i) q^{69} +(-1.55660 + 1.13094i) q^{70} +(-5.58104 + 4.05486i) q^{71} +(0.439168 - 1.35162i) q^{72} +(-1.32966 - 0.966055i) q^{73} +(1.68273 - 5.17890i) q^{74} +(-2.94703 - 9.07003i) q^{75} +(6.12814 - 4.45235i) q^{76} +(4.17399 + 12.8462i) q^{77} +(2.05720 + 6.33142i) q^{78} +(-6.70267 + 4.86977i) q^{79} +(0.210589 + 0.648127i) q^{80} +(-3.47452 + 10.6935i) q^{81} +(7.36518 + 5.35112i) q^{82} +(4.92118 - 15.1458i) q^{83} +(-4.80277 + 3.48942i) q^{84} +(1.59158 - 1.15635i) q^{85} +(7.81385 + 5.67710i) q^{86} +11.6394 q^{87} +4.78414 q^{88} +(-8.11662 - 5.89707i) q^{89} +(0.299285 + 0.921105i) q^{90} +(2.76232 - 8.50153i) q^{91} -4.10266 q^{92} +(10.3076 + 5.55066i) q^{93} -3.49114 q^{94} +(-1.59517 + 4.90943i) q^{95} +(0.649758 + 1.99975i) q^{96} +(-0.366592 - 0.266345i) q^{97} +0.971326 q^{98} +6.79912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8} + q^{10} - 2 q^{11} - 4 q^{12} - 11 q^{13} + 2 q^{14} + 21 q^{15} - 2 q^{16} - 7 q^{17} - 5 q^{18} - 14 q^{19} + q^{20} - 7 q^{21} - 2 q^{22} + 3 q^{23} + q^{24} + 14 q^{26} + 5 q^{27} + 2 q^{28} + 13 q^{29} - 14 q^{30} + 15 q^{31} + 8 q^{32} + 2 q^{33} + 3 q^{34} - 28 q^{35} + 10 q^{36} + 52 q^{37} + 21 q^{38} - 16 q^{39} + q^{40} - 11 q^{41} - 17 q^{42} - 22 q^{43} - 7 q^{44} - 19 q^{45} + 8 q^{46} - 10 q^{47} + q^{48} - 10 q^{49} - 15 q^{50} + 28 q^{51} - 11 q^{52} + 7 q^{53} + 5 q^{54} - 7 q^{55} - 8 q^{56} - 20 q^{57} - 17 q^{58} + 22 q^{59} + 21 q^{60} + 4 q^{61} + 5 q^{62} + 66 q^{63} - 2 q^{64} - 18 q^{66} - 26 q^{67} + 8 q^{68} + 4 q^{69} - 28 q^{70} - 15 q^{71} - 5 q^{72} - 29 q^{73} - 23 q^{74} - 34 q^{75} + 21 q^{76} + 34 q^{77} - q^{78} - 2 q^{79} + q^{80} - 45 q^{81} + 9 q^{82} + 38 q^{83} - 17 q^{84} + 25 q^{85} + 18 q^{86} - 20 q^{87} + 18 q^{88} + q^{89} + 46 q^{90} + 38 q^{91} - 22 q^{92} + 21 q^{93} - 20 q^{94} - 12 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} + 14 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8 + q^10 - 2 * q^11 - 4 * q^12 - 11 * q^13 + 2 * q^14 + 21 * q^15 - 2 * q^16 - 7 * q^17 - 5 * q^18 - 14 * q^19 + q^20 - 7 * q^21 - 2 * q^22 + 3 * q^23 + q^24 + 14 * q^26 + 5 * q^27 + 2 * q^28 + 13 * q^29 - 14 * q^30 + 15 * q^31 + 8 * q^32 + 2 * q^33 + 3 * q^34 - 28 * q^35 + 10 * q^36 + 52 * q^37 + 21 * q^38 - 16 * q^39 + q^40 - 11 * q^41 - 17 * q^42 - 22 * q^43 - 7 * q^44 - 19 * q^45 + 8 * q^46 - 10 * q^47 + q^48 - 10 * q^49 - 15 * q^50 + 28 * q^51 - 11 * q^52 + 7 * q^53 + 5 * q^54 - 7 * q^55 - 8 * q^56 - 20 * q^57 - 17 * q^58 + 22 * q^59 + 21 * q^60 + 4 * q^61 + 5 * q^62 + 66 * q^63 - 2 * q^64 - 18 * q^66 - 26 * q^67 + 8 * q^68 + 4 * q^69 - 28 * q^70 - 15 * q^71 - 5 * q^72 - 29 * q^73 - 23 * q^74 - 34 * q^75 + 21 * q^76 + 34 * q^77 - q^78 - 2 * q^79 + q^80 - 45 * q^81 + 9 * q^82 + 38 * q^83 - 17 * q^84 + 25 * q^85 + 18 * q^86 - 20 * q^87 + 18 * q^88 + q^89 + 46 * q^90 + 38 * q^91 - 22 * q^92 + 21 * q^93 - 20 * q^94 - 12 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 + 14 * q^99

Introduction

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