LMFDB - Embedded newform 110.2.g.a.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,2,Mod(31,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	110.31
Dual form			110.2.g.a.71.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.381966 - 1.17557i) q^{6} +(-0.309017 - 0.224514i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.454915 + 1.40008i) q^{9} -1.00000 q^{10} +(3.04508 + 1.31433i) q^{11} -1.23607 q^{12} +(0.190983 - 0.587785i) q^{13} +(-0.309017 + 0.224514i) q^{14} +(-1.00000 - 0.726543i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.236068 - 0.726543i) q^{17} +(1.19098 + 0.865300i) q^{18} +(-5.73607 + 4.16750i) q^{19} +(-0.309017 + 0.951057i) q^{20} -0.472136 q^{21} +(2.19098 - 2.48990i) q^{22} +6.85410 q^{23} +(-0.381966 + 1.17557i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.500000 - 0.363271i) q^{26} +(1.70820 + 5.25731i) q^{27} +(0.118034 + 0.363271i) q^{28} +(-2.61803 - 1.90211i) q^{29} +(-1.00000 + 0.726543i) q^{30} +(-0.854102 + 2.62866i) q^{31} +1.00000 q^{32} +(4.00000 - 0.898056i) q^{33} -0.763932 q^{34} +(-0.118034 + 0.363271i) q^{35} +(1.19098 - 0.865300i) q^{36} +(-4.73607 - 3.44095i) q^{37} +(2.19098 + 6.74315i) q^{38} +(-0.236068 - 0.726543i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-3.92705 + 2.85317i) q^{41} +(-0.145898 + 0.449028i) q^{42} -4.76393 q^{43} +(-1.69098 - 2.85317i) q^{44} +1.47214 q^{45} +(2.11803 - 6.51864i) q^{46} +(3.50000 - 2.54290i) q^{47} +(1.00000 + 0.726543i) q^{48} +(-2.11803 - 6.51864i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-0.763932 - 0.555029i) q^{51} +(-0.500000 + 0.363271i) q^{52} +(3.73607 - 11.4984i) q^{53} +5.52786 q^{54} +(0.309017 - 3.30220i) q^{55} +0.381966 q^{56} +(-2.70820 + 8.33499i) q^{57} +(-2.61803 + 1.90211i) q^{58} +(-3.73607 - 2.71441i) q^{59} +(0.381966 + 1.17557i) q^{60} +(-2.76393 - 8.50651i) q^{61} +(2.23607 + 1.62460i) q^{62} +(0.454915 - 0.330515i) q^{63} +(0.309017 - 0.951057i) q^{64} -0.618034 q^{65} +(0.381966 - 4.08174i) q^{66} +5.23607 q^{67} +(-0.236068 + 0.726543i) q^{68} +(6.85410 - 4.97980i) q^{69} +(0.309017 + 0.224514i) q^{70} +(2.70820 + 8.33499i) q^{71} +(-0.454915 - 1.40008i) q^{72} +(-9.47214 - 6.88191i) q^{73} +(-4.73607 + 3.44095i) q^{74} +(-0.381966 + 1.17557i) q^{75} +7.09017 q^{76} +(-0.645898 - 1.08981i) q^{77} -0.763932 q^{78} +(-3.23607 + 9.95959i) q^{79} +(0.809017 - 0.587785i) q^{80} +(1.95492 + 1.42033i) q^{81} +(1.50000 + 4.61653i) q^{82} +(0.708204 + 2.17963i) q^{83} +(0.381966 + 0.277515i) q^{84} +(-0.618034 + 0.449028i) q^{85} +(-1.47214 + 4.53077i) q^{86} -4.00000 q^{87} +(-3.23607 + 0.726543i) q^{88} +17.0344 q^{89} +(0.454915 - 1.40008i) q^{90} +(-0.190983 + 0.138757i) q^{91} +(-5.54508 - 4.02874i) q^{92} +(1.05573 + 3.24920i) q^{93} +(-1.33688 - 4.11450i) q^{94} +(5.73607 + 4.16750i) q^{95} +(1.00000 - 0.726543i) q^{96} +(-3.70820 + 11.4127i) q^{97} -6.85410 q^{98} +(-3.22542 + 3.66547i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 4 q^{3} - q^{4} + q^{5} - 6 q^{6} + q^{7} - q^{8} - 13 q^{9} - 4 q^{10} + q^{11} + 4 q^{12} + 3 q^{13} + q^{14} - 4 q^{15} - q^{16} + 8 q^{17} + 7 q^{18} - 14 q^{19} + q^{20} + 16 q^{21}+ \cdots + 43 q^{99}+O(q^{100}) $ 4 * q - q^2 + 4 * q^3 - q^4 + q^5 - 6 * q^6 + q^7 - q^8 - 13 * q^9 - 4 * q^10 + q^11 + 4 * q^12 + 3 * q^13 + q^14 - 4 * q^15 - q^16 + 8 * q^17 + 7 * q^18 - 14 * q^19 + q^20 + 16 * q^21 + 11 * q^22 + 14 * q^23 - 6 * q^24 - q^25 - 2 * q^26 - 20 * q^27 - 4 * q^28 - 6 * q^29 - 4 * q^30 + 10 * q^31 + 4 * q^32 + 16 * q^33 - 12 * q^34 + 4 * q^35 + 7 * q^36 - 10 * q^37 + 11 * q^38 + 8 * q^39 + q^40 - 9 * q^41 - 14 * q^42 - 28 * q^43 - 9 * q^44 - 12 * q^45 + 4 * q^46 + 14 * q^47 + 4 * q^48 - 4 * q^49 - q^50 - 12 * q^51 - 2 * q^52 + 6 * q^53 + 40 * q^54 - q^55 + 6 * q^56 + 16 * q^57 - 6 * q^58 - 6 * q^59 + 6 * q^60 - 20 * q^61 + 13 * q^63 - q^64 + 2 * q^65 + 6 * q^66 + 12 * q^67 + 8 * q^68 + 14 * q^69 - q^70 - 16 * q^71 - 13 * q^72 - 20 * q^73 - 10 * q^74 - 6 * q^75 + 6 * q^76 - 16 * q^77 - 12 * q^78 - 4 * q^79 + q^80 + 19 * q^81 + 6 * q^82 - 24 * q^83 + 6 * q^84 + 2 * q^85 + 12 * q^86 - 16 * q^87 - 4 * q^88 + 10 * q^89 + 13 * q^90 - 3 * q^91 - 11 * q^92 + 40 * q^93 - 21 * q^94 + 14 * q^95 + 4 * q^96 + 12 * q^97 - 14 * q^98 + 43 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	1.00000	−	0.726543i	0.577350	−	0.419470i	−0.260418	−	0.965496i	$-0.583860\pi$
$3$	1.00000	−	0.726543i	0.577350	−	0.419470i	0.837768	+	0.546027i	$0.183860\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	−0.381966	−	1.17557i	−0.155937	−	0.479925i
$7$	−0.309017	−	0.224514i	−0.116797	−	0.0848583i	0.527853	−	0.849336i	$-0.322997\pi$
$7$	−0.309017	−	0.224514i	−0.116797	−	0.0848583i	−0.644651	+	0.764477i	$0.722997\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.454915	+	1.40008i	−0.151638	+	0.466695i
$10$	−1.00000			−0.316228
$11$	3.04508	+	1.31433i	0.918128	+	0.396285i
$11$	3.04508	+	1.31433i	0.918128	+	0.396285i
$12$	−1.23607			−0.356822
$13$	0.190983	−	0.587785i	0.0529692	−	0.163022i	−0.921073	−	0.389391i	$-0.872685\pi$
$13$	0.190983	−	0.587785i	0.0529692	−	0.163022i	0.974042	+	0.226369i	$0.0726855\pi$
$14$	−0.309017	+	0.224514i	−0.0825883	+	0.0600039i
$15$	−1.00000	−	0.726543i	−0.258199	−	0.187592i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.236068	−	0.726543i	−0.0572549	−	0.176212i	0.918339	−	0.395794i	$-0.129531\pi$
$17$	−0.236068	−	0.726543i	−0.0572549	−	0.176212i	−0.975594	+	0.219582i	$0.929531\pi$
$18$	1.19098	+	0.865300i	0.280717	+	0.203953i
$19$	−5.73607	+	4.16750i	−1.31594	+	0.956089i	−0.315971	+	0.948769i	$0.602330\pi$
$19$	−5.73607	+	4.16750i	−1.31594	+	0.956089i	−0.999973	+	0.00732062i	$0.997670\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	−0.472136			−0.103029
$22$	2.19098	−	2.48990i	0.467119	−	0.530848i
$23$	6.85410			1.42918			0.714590	−	0.699544i	$-0.246614\pi$
$23$	6.85410			1.42918			0.714590	+	0.699544i	$0.246614\pi$
$24$	−0.381966	+	1.17557i	−0.0779685	+	0.239962i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−0.500000	−	0.363271i	−0.0980581	−	0.0712434i
$27$	1.70820	+	5.25731i	0.328744	+	1.01177i
$28$	0.118034	+	0.363271i	0.0223063	+	0.0686518i
$29$	−2.61803	−	1.90211i	−0.486157	−	0.353214i	0.317548	−	0.948242i	$-0.397141\pi$
$29$	−2.61803	−	1.90211i	−0.486157	−	0.353214i	−0.803704	+	0.595029i	$0.797141\pi$
$30$	−1.00000	+	0.726543i	−0.182574	+	0.132648i
$31$	−0.854102	+	2.62866i	−0.153401	+	0.472120i	−0.997995	−	0.0632866i	$-0.979842\pi$
$31$	−0.854102	+	2.62866i	−0.153401	+	0.472120i	0.844594	+	0.535407i	$0.179842\pi$
$32$	1.00000			0.176777
$33$	4.00000	−	0.898056i	0.696311	−	0.156331i
$34$	−0.763932			−0.131013
$35$	−0.118034	+	0.363271i	−0.0199514	+	0.0614041i
$36$	1.19098	−	0.865300i	0.198497	−	0.144217i
$37$	−4.73607	−	3.44095i	−0.778605	−	0.565689i	0.125955	−	0.992036i	$-0.459800\pi$
$37$	−4.73607	−	3.44095i	−0.778605	−	0.565689i	−0.904560	+	0.426346i	$0.859800\pi$
$38$	2.19098	+	6.74315i	0.355424	+	1.09388i
$39$	−0.236068	−	0.726543i	−0.0378011	−	0.116340i
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	−3.92705	+	2.85317i	−0.613302	+	0.445590i	−0.850576	−	0.525853i	$-0.823746\pi$
$41$	−3.92705	+	2.85317i	−0.613302	+	0.445590i	0.237273	+	0.971443i	$0.423746\pi$
$42$	−0.145898	+	0.449028i	−0.0225126	+	0.0692865i
$43$	−4.76393			−0.726493			−0.363246	−	0.931693i	$-0.618332\pi$
$43$	−4.76393			−0.726493			−0.363246	+	0.931693i	$0.618332\pi$
$44$	−1.69098	−	2.85317i	−0.254925	−	0.430131i
$45$	1.47214			0.219453
$46$	2.11803	−	6.51864i	0.312287	−	0.961121i
$47$	3.50000	−	2.54290i	0.510527	−	0.370920i	−0.302496	−	0.953151i	$-0.597820\pi$
$47$	3.50000	−	2.54290i	0.510527	−	0.370920i	0.813024	+	0.582231i	$0.197820\pi$
$48$	1.00000	+	0.726543i	0.144338	+	0.104867i
$49$	−2.11803	−	6.51864i	−0.302576	−	0.931234i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	−0.763932	−	0.555029i	−0.106972	−	0.0777196i
$52$	−0.500000	+	0.363271i	−0.0693375	+	0.0503767i
$53$	3.73607	−	11.4984i	0.513188	−	1.57943i	−0.273366	−	0.961910i	$-0.588137\pi$
$53$	3.73607	−	11.4984i	0.513188	−	1.57943i	0.786554	−	0.617521i	$-0.211863\pi$
$54$	5.52786			0.752247
$55$	0.309017	−	3.30220i	0.0416678	−	0.445268i
$56$	0.381966			0.0510424
$57$	−2.70820	+	8.33499i	−0.358710	+	1.10400i
$58$	−2.61803	+	1.90211i	−0.343765	+	0.249760i
$59$	−3.73607	−	2.71441i	−0.486395	−	0.353386i	0.317401	−	0.948291i	$-0.397190\pi$
$59$	−3.73607	−	2.71441i	−0.486395	−	0.353386i	−0.803796	+	0.594905i	$0.797190\pi$
$60$	0.381966	+	1.17557i	0.0493116	+	0.151765i
$61$	−2.76393	−	8.50651i	−0.353885	−	1.08915i	−0.956653	−	0.291230i	$-0.905935\pi$
$61$	−2.76393	−	8.50651i	−0.353885	−	1.08915i	0.602768	−	0.797917i	$-0.294065\pi$
$62$	2.23607	+	1.62460i	0.283981	+	0.206324i
$63$	0.454915	−	0.330515i	0.0573139	−	0.0416410i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−0.618034			−0.0766577
$66$	0.381966	−	4.08174i	0.0470168	−	0.502428i
$67$	5.23607			0.639688			0.319844	−	0.947470i	$-0.396370\pi$
$67$	5.23607			0.639688			0.319844	+	0.947470i	$0.396370\pi$
$68$	−0.236068	+	0.726543i	−0.0286274	+	0.0881062i
$69$	6.85410	−	4.97980i	0.825137	−	0.599497i
$70$	0.309017	+	0.224514i	0.0369346	+	0.0268346i
$71$	2.70820	+	8.33499i	0.321405	+	0.989182i	0.973037	+	0.230647i	$0.0740843\pi$
$71$	2.70820	+	8.33499i	0.321405	+	0.989182i	−0.651633	+	0.758535i	$0.725916\pi$
$72$	−0.454915	−	1.40008i	−0.0536123	−	0.165002i
$73$	−9.47214	−	6.88191i	−1.10863	−	0.805467i	−0.126182	−	0.992007i	$-0.540272\pi$
$73$	−9.47214	−	6.88191i	−1.10863	−	0.805467i	−0.982447	+	0.186540i	$0.940272\pi$
$74$	−4.73607	+	3.44095i	−0.550557	+	0.400003i
$75$	−0.381966	+	1.17557i	−0.0441056	+	0.135743i
$76$	7.09017			0.813298
$77$	−0.645898	−	1.08981i	−0.0736069	−	0.124196i
$78$	−0.763932			−0.0864983
$79$	−3.23607	+	9.95959i	−0.364086	+	1.12054i	0.586465	+	0.809974i	$0.300519\pi$
$79$	−3.23607	+	9.95959i	−0.364086	+	1.12054i	−0.950551	+	0.310567i	$0.899481\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	1.95492	+	1.42033i	0.217213	+	0.157814i
$82$	1.50000	+	4.61653i	0.165647	+	0.509810i
$83$	0.708204	+	2.17963i	0.0777355	+	0.239245i	0.982371	−	0.186940i	$-0.0598571\pi$
$83$	0.708204	+	2.17963i	0.0777355	+	0.239245i	−0.904636	+	0.426185i	$0.859857\pi$
$84$	0.381966	+	0.277515i	0.0416759	+	0.0302793i
$85$	−0.618034	+	0.449028i	−0.0670352	+	0.0487039i
$86$	−1.47214	+	4.53077i	−0.158745	+	0.488565i
$87$	−4.00000			−0.428845
$88$	−3.23607	+	0.726543i	−0.344966	+	0.0774497i
$89$	17.0344			1.80565			0.902824	−	0.430011i	$-0.141490\pi$
$89$	17.0344			1.80565			0.902824	+	0.430011i	$0.141490\pi$
$90$	0.454915	−	1.40008i	0.0479523	−	0.147582i
$91$	−0.190983	+	0.138757i	−0.0200205	+	0.0145457i
$92$	−5.54508	−	4.02874i	−0.578115	−	0.420025i
$93$	1.05573	+	3.24920i	0.109474	+	0.336926i
$94$	−1.33688	−	4.11450i	−0.137889	−	0.424378i
$95$	5.73607	+	4.16750i	0.588508	+	0.427576i
$96$	1.00000	−	0.726543i	0.102062	−	0.0741524i
$97$	−3.70820	+	11.4127i	−0.376511	+	1.15878i	0.565942	+	0.824445i	$0.308512\pi$
$97$	−3.70820	+	11.4127i	−0.376511	+	1.15878i	−0.942454	+	0.334337i	$0.891488\pi$
$98$	−6.85410			−0.692369
$99$	−3.22542	+	3.66547i	−0.324167	+	0.368393i
$100$	1.00000			0.100000
$101$	−3.00000	+	9.23305i	−0.298511	+	0.918723i	0.683508	+	0.729943i	$0.260453\pi$
$101$	−3.00000	+	9.23305i	−0.298511	+	0.918723i	−0.982019	+	0.188780i	$0.939547\pi$
$102$	−0.763932	+	0.555029i	−0.0756405	+	0.0549561i
$103$	−3.50000	−	2.54290i	−0.344865	−	0.250559i	0.401847	−	0.915707i	$-0.368369\pi$
$103$	−3.50000	−	2.54290i	−0.344865	−	0.250559i	−0.746712	+	0.665148i	$0.768369\pi$
$104$	0.190983	+	0.587785i	0.0187274	+	0.0576371i
$105$	0.145898	+	0.449028i	0.0142382	+	0.0438206i
$106$	−9.78115	−	7.10642i	−0.950030	−	0.690237i
$107$	13.3262	−	9.68208i	1.28830	−	0.936002i	0.288527	−	0.957472i	$-0.406835\pi$
$107$	13.3262	−	9.68208i	1.28830	−	0.936002i	0.999769	+	0.0214700i	$0.00683465\pi$
$108$	1.70820	−	5.25731i	0.164372	−	0.505885i
$109$	16.4721			1.57774			0.788872	−	0.614557i	$-0.210665\pi$
$109$	16.4721			1.57774			0.788872	+	0.614557i	$0.210665\pi$
$110$	−3.04508	−	1.31433i	−0.290337	−	0.125316i
$111$	−7.23607			−0.686817
$112$	0.118034	−	0.363271i	0.0111532	−	0.0343259i
$113$	−15.9443	+	11.5842i	−1.49991	+	1.08975i	−0.529494	+	0.848314i	$0.677618\pi$
$113$	−15.9443	+	11.5842i	−1.49991	+	1.08975i	−0.970417	+	0.241435i	$0.922382\pi$
$114$	7.09017	+	5.15131i	0.664055	+	0.482464i
$115$	−2.11803	−	6.51864i	−0.197508	−	0.607866i
$116$	1.00000	+	3.07768i	0.0928477	+	0.285756i
$117$	0.736068	+	0.534785i	0.0680495	+	0.0494409i
$118$	−3.73607	+	2.71441i	−0.343933	+	0.249882i
$119$	−0.0901699	+	0.277515i	−0.00826587	+	0.0254397i
$120$	1.23607			0.112837
$121$	7.54508	+	8.00448i	0.685917	+	0.727680i
$122$	−8.94427			−0.809776
$123$	−1.85410	+	5.70634i	−0.167179	+	0.514523i
$124$	2.23607	−	1.62460i	0.200805	−	0.145893i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	−0.173762	−	0.534785i	−0.0154800	−	0.0476424i
$127$	−1.42705	−	4.39201i	−0.126630	−	0.389728i	0.867564	−	0.497325i	$-0.165684\pi$
$127$	−1.42705	−	4.39201i	−0.126630	−	0.389728i	−0.994195	+	0.107597i	$0.965684\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−4.76393	+	3.46120i	−0.419441	+	0.304742i
$130$	−0.190983	+	0.587785i	−0.0167503	+	0.0515522i
$131$	−15.4164			−1.34694			−0.673469	−	0.739216i	$-0.735196\pi$
$131$	−15.4164			−1.34694			−0.673469	+	0.739216i	$0.735196\pi$
$132$	−3.76393	−	1.62460i	−0.327608	−	0.141403i
$133$	2.70820			0.234831
$134$	1.61803	−	4.97980i	0.139777	−	0.430189i
$135$	4.47214	−	3.24920i	0.384900	−	0.279646i
$136$	0.618034	+	0.449028i	0.0529960	+	0.0385038i
$137$	−0.236068	−	0.726543i	−0.0201686	−	0.0620727i	0.940466	−	0.339889i	$-0.110389\pi$
$137$	−0.236068	−	0.726543i	−0.0201686	−	0.0620727i	−0.960634	+	0.277816i	$0.910389\pi$
$138$	−2.61803	−	8.05748i	−0.222862	−	0.685898i
$139$	12.0172	+	8.73102i	1.01929	+	0.740556i	0.966137	−	0.258031i	$-0.0830736\pi$
$139$	12.0172	+	8.73102i	1.01929	+	0.740556i	0.0531507	+	0.998587i	$0.483074\pi$
$140$	0.309017	−	0.224514i	0.0261167	−	0.0189749i
$141$	1.65248	−	5.08580i	0.139164	−	0.428301i
$142$	8.76393			0.735453
$143$	1.35410	−	1.53884i	0.113236	−	0.128684i
$144$	−1.47214			−0.122678
$145$	−1.00000	+	3.07768i	−0.0830455	+	0.255588i
$146$	−9.47214	+	6.88191i	−0.783920	+	0.569551i
$147$	−6.85410	−	4.97980i	−0.565317	−	0.410727i
$148$	1.80902	+	5.56758i	0.148700	+	0.457652i
$149$	−1.23607	−	3.80423i	−0.101263	−	0.311654i	0.887572	−	0.460668i	$-0.152390\pi$
$149$	−1.23607	−	3.80423i	−0.101263	−	0.311654i	−0.988835	+	0.149014i	$0.952390\pi$
$150$	1.00000	+	0.726543i	0.0816497	+	0.0593219i
$151$	15.0902	−	10.9637i	1.22802	−	0.892209i	0.231280	−	0.972887i	$-0.425709\pi$
$151$	15.0902	−	10.9637i	1.22802	−	0.892209i	0.996740	+	0.0806779i	$0.0257085\pi$
$152$	2.19098	−	6.74315i	0.177712	−	0.546942i
$153$	1.12461			0.0909195
$154$	−1.23607	+	0.277515i	−0.0996052	+	0.0223628i
$155$	2.76393			0.222004
$156$	−0.236068	+	0.726543i	−0.0189006	+	0.0581700i
$157$	−5.16312	+	3.75123i	−0.412062	+	0.299380i	−0.774436	−	0.632652i	$-0.781966\pi$
$157$	−5.16312	+	3.75123i	−0.412062	+	0.299380i	0.362374	+	0.932033i	$0.381966\pi$
$158$	8.47214	+	6.15537i	0.674007	+	0.489695i
$159$	−4.61803	−	14.2128i	−0.366234	−	1.12715i
$160$	−0.309017	−	0.951057i	−0.0244299	−	0.0751876i
$161$	−2.11803	−	1.53884i	−0.166924	−	0.121278i
$162$	1.95492	−	1.42033i	0.153593	−	0.111592i
$163$	−0.854102	+	2.62866i	−0.0668984	+	0.205892i	−0.978918	−	0.204255i	$-0.934523\pi$
$163$	−0.854102	+	2.62866i	−0.0668984	+	0.205892i	0.912019	+	0.410147i	$0.134523\pi$
$164$	4.85410			0.379042
$165$	−2.09017	−	3.52671i	−0.162720	−	0.274554i
$166$	2.29180			0.177878
$167$	5.89919	−	18.1558i	0.456493	−	1.40494i	−0.412881	−	0.910785i	$-0.635477\pi$
$167$	5.89919	−	18.1558i	0.456493	−	1.40494i	0.869374	−	0.494155i	$-0.164523\pi$
$168$	0.381966	−	0.277515i	0.0294693	−	0.0214107i
$169$	10.2082	+	7.41669i	0.785246	+	0.570515i
$170$	0.236068	+	0.726543i	0.0181056	+	0.0557233i
$171$	−3.22542	−	9.92684i	−0.246654	−	0.759124i
$172$	3.85410	+	2.80017i	0.293873	+	0.213511i
$173$	8.39919	−	6.10237i	0.638578	−	0.463954i	−0.220783	−	0.975323i	$-0.570861\pi$
$173$	8.39919	−	6.10237i	0.638578	−	0.463954i	0.859361	+	0.511369i	$0.170861\pi$
$174$	−1.23607	+	3.80423i	−0.0937061	+	0.288398i
$175$	0.381966			0.0288739
$176$	−0.309017	+	3.30220i	−0.0232930	+	0.248913i
$177$	−5.70820			−0.429055
$178$	5.26393	−	16.2007i	0.394548	−	1.21430i
$179$	11.3992	−	8.28199i	0.852015	−	0.619025i	−0.0736857	−	0.997282i	$-0.523476\pi$
$179$	11.3992	−	8.28199i	0.852015	−	0.619025i	0.925701	+	0.378256i	$0.123476\pi$
$180$	−1.19098	−	0.865300i	−0.0887706	−	0.0644956i
$181$	−3.56231	−	10.9637i	−0.264784	−	0.814922i	−0.991743	−	0.128241i	$-0.959067\pi$
$181$	−3.56231	−	10.9637i	−0.264784	−	0.814922i	0.726959	−	0.686681i	$-0.240933\pi$
$182$	0.0729490	+	0.224514i	0.00540734	+	0.0166421i
$183$	−8.94427	−	6.49839i	−0.661180	−	0.480375i
$184$	−5.54508	+	4.02874i	−0.408789	+	0.297003i
$185$	−1.80902	+	5.56758i	−0.133002	+	0.409337i
$186$	3.41641			0.250503
$187$	0.236068	−	2.52265i	0.0172630	−	0.184475i
$188$	−4.32624			−0.315523
$189$	0.652476	−	2.00811i	0.0474606	−	0.146069i
$190$	5.73607	−	4.16750i	0.416138	−	0.302342i
$191$	1.14590	+	0.832544i	0.0829143	+	0.0602407i	0.628470	−	0.777834i	$-0.283681\pi$
$191$	1.14590	+	0.832544i	0.0829143	+	0.0602407i	−0.545556	+	0.838074i	$0.683681\pi$
$192$	−0.381966	−	1.17557i	−0.0275660	−	0.0848395i
$193$	6.61803	+	20.3682i	0.476377	+	1.46614i	0.844092	+	0.536198i	$0.180140\pi$
$193$	6.61803	+	20.3682i	0.476377	+	1.46614i	−0.367716	+	0.929938i	$0.619860\pi$
$194$	9.70820	+	7.05342i	0.697008	+	0.506406i
$195$	−0.618034	+	0.449028i	−0.0442583	+	0.0321556i
$196$	−2.11803	+	6.51864i	−0.151288	+	0.465617i
$197$	−16.0902			−1.14638			−0.573189	−	0.819423i	$-0.694294\pi$
$197$	−16.0902			−1.14638			−0.573189	+	0.819423i	$0.694294\pi$
$198$	2.48936	+	4.20025i	0.176911	+	0.298499i
$199$	−11.7082			−0.829973			−0.414986	−	0.909828i	$-0.636214\pi$
$199$	−11.7082			−0.829973			−0.414986	+	0.909828i	$0.636214\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	5.23607	−	3.80423i	0.369324	−	0.268329i
$202$	7.85410	+	5.70634i	0.552613	+	0.401497i
$203$	0.381966	+	1.17557i	0.0268088	+	0.0825089i
$204$	0.291796	+	0.898056i	0.0204298	+	0.0628765i
$205$	3.92705	+	2.85317i	0.274277	+	0.199274i
$206$	−3.50000	+	2.54290i	−0.243857	+	0.177172i
$207$	−3.11803	+	9.59632i	−0.216718	+	0.666990i
$208$	0.618034			0.0428529
$209$	−22.9443	+	5.15131i	−1.58709	+	0.356324i
$210$	0.472136			0.0325805
$211$	0.944272	−	2.90617i	0.0650064	−	0.200069i	−0.913278	−	0.407337i	$-0.866457\pi$
$211$	0.944272	−	2.90617i	0.0650064	−	0.200069i	0.978284	+	0.207268i	$0.0664573\pi$
$212$	−9.78115	+	7.10642i	−0.671772	+	0.488071i
$213$	8.76393	+	6.36737i	0.600495	+	0.436285i
$214$	−5.09017	−	15.6659i	−0.347957	−	1.07090i
$215$	1.47214	+	4.53077i	0.100399	+	0.308996i
$216$	−4.47214	−	3.24920i	−0.304290	−	0.221080i
$217$	0.854102	−	0.620541i	0.0579802	−	0.0421251i
$218$	5.09017	−	15.6659i	0.344750	−	1.06103i
$219$	−14.4721			−0.977936
$220$	−2.19098	+	2.48990i	−0.147716	+	0.167869i
$221$	−0.472136			−0.0317593
$222$	−2.23607	+	6.88191i	−0.150075	+	0.461884i
$223$	−20.4894	+	14.8864i	−1.37207	+	0.996866i	−0.374496	+	0.927228i	$0.622184\pi$
$223$	−20.4894	+	14.8864i	−1.37207	+	0.996866i	−0.997572	+	0.0696380i	$0.977816\pi$
$224$	−0.309017	−	0.224514i	−0.0206471	−	0.0150010i
$225$	−0.454915	−	1.40008i	−0.0303277	−	0.0933390i
$226$	6.09017	+	18.7436i	0.405112	+	1.24681i
$227$	6.09017	+	4.42477i	0.404219	+	0.293682i	0.771257	−	0.636524i	$-0.219628\pi$
$227$	6.09017	+	4.42477i	0.404219	+	0.293682i	−0.367038	+	0.930206i	$0.619628\pi$
$228$	7.09017	−	5.15131i	0.469558	−	0.341154i
$229$	−1.79837	+	5.53483i	−0.118840	+	0.365752i	−0.992729	−	0.120375i	$-0.961590\pi$
$229$	−1.79837	+	5.53483i	−0.118840	+	0.365752i	0.873889	+	0.486126i	$0.161590\pi$
$230$	−6.85410			−0.451946
$231$	−1.43769	−	0.620541i	−0.0945933	−	0.0408286i
$232$	3.23607			0.212458
$233$	3.32624	−	10.2371i	0.217909	−	0.670655i	−0.781025	−	0.624500i	$-0.785303\pi$
$233$	3.32624	−	10.2371i	0.217909	−	0.670655i	0.998934	−	0.0461557i	$-0.0146970\pi$
$234$	0.736068	−	0.534785i	0.0481183	−	0.0349600i
$235$	−3.50000	−	2.54290i	−0.228315	−	0.165880i
$236$	1.42705	+	4.39201i	0.0928931	+	0.285896i
$237$	4.00000	+	12.3107i	0.259828	+	0.799668i
$238$	0.236068	+	0.171513i	0.0153020	+	0.0111176i
$239$	−14.9443	+	10.8576i	−0.966665	+	0.702323i	−0.954689	−	0.297605i	$-0.903812\pi$
$239$	−14.9443	+	10.8576i	−0.966665	+	0.702323i	−0.0119756	+	0.999928i	$0.503812\pi$
$240$	0.381966	−	1.17557i	0.0246558	−	0.0758827i
$241$	4.85410			0.312680			0.156340	−	0.987703i	$-0.450030\pi$
$241$	4.85410			0.312680			0.156340	+	0.987703i	$0.450030\pi$
$242$	9.94427	−	4.70228i	0.639242	−	0.302274i
$243$	−13.5967			−0.872232
$244$	−2.76393	+	8.50651i	−0.176943	+	0.544573i
$245$	−5.54508	+	4.02874i	−0.354262	+	0.257387i
$246$	4.85410	+	3.52671i	0.309486	+	0.224855i
$247$	1.35410	+	4.16750i	0.0861594	+	0.265172i
$248$	−0.854102	−	2.62866i	−0.0542355	−	0.166920i
$249$	2.29180	+	1.66509i	0.145237	+	0.105521i
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	5.88197	−	18.1028i	0.371266	−	1.14264i	−0.574697	−	0.818366i	$-0.694880\pi$
$251$	5.88197	−	18.1028i	0.371266	−	1.14264i	0.945963	−	0.324274i	$-0.105120\pi$
$252$	−0.562306			−0.0354219
$253$	20.8713	+	9.00854i	1.31217	+	0.566362i
$254$	−4.61803			−0.289761
$255$	−0.291796	+	0.898056i	−0.0182730	+	0.0562384i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	9.70820	+	7.05342i	0.605581	+	0.439980i	0.847856	−	0.530227i	$-0.177893\pi$
$257$	9.70820	+	7.05342i	0.605581	+	0.439980i	−0.242274	+	0.970208i	$0.577893\pi$
$258$	1.81966	+	5.60034i	0.113287	+	0.348662i
$259$	0.690983	+	2.12663i	0.0429356	+	0.132142i
$260$	0.500000	+	0.363271i	0.0310087	+	0.0225291i
$261$	3.85410	−	2.80017i	0.238563	−	0.173326i
$262$	−4.76393	+	14.6619i	−0.294317	+	0.905814i
$263$	1.20163			0.0740954			0.0370477	−	0.999313i	$-0.488205\pi$
$263$	1.20163			0.0740954			0.0370477	+	0.999313i	$0.488205\pi$
$264$	−2.70820	+	3.07768i	−0.166678	+	0.189418i
$265$	−12.0902			−0.742693
$266$	0.836881	−	2.57565i	0.0513125	−	0.157924i
$267$	17.0344	−	12.3762i	1.04249	−	0.757414i
$268$	−4.23607	−	3.07768i	−0.258759	−	0.187999i
$269$	−9.76393	−	30.0503i	−0.595317	−	1.83220i	−0.553140	−	0.833089i	$-0.686570\pi$
$269$	−9.76393	−	30.0503i	−0.595317	−	1.83220i	−0.0421778	−	0.999110i	$-0.513430\pi$
$270$	−1.70820	−	5.25731i	−0.103958	−	0.319950i
$271$	10.8541	+	7.88597i	0.659340	+	0.479038i	0.866440	−	0.499281i	$-0.166403\pi$
$271$	10.8541	+	7.88597i	0.659340	+	0.479038i	−0.207100	+	0.978320i	$0.566403\pi$
$272$	0.618034	−	0.449028i	0.0374738	−	0.0272263i
$273$	−0.0901699	+	0.277515i	−0.00545733	+	0.0167959i
$274$	−0.763932			−0.0461508
$275$	−3.23607	+	0.726543i	−0.195142	+	0.0438122i
$276$	−8.47214			−0.509963
$277$	0.500000	−	1.53884i	0.0300421	−	0.0924600i	−0.934911	−	0.354882i	$-0.884521\pi$
$277$	0.500000	−	1.53884i	0.0300421	−	0.0924600i	0.964953	+	0.262422i	$0.0845211\pi$
$278$	12.0172	−	8.73102i	0.720745	−	0.523652i
$279$	−3.29180	−	2.39163i	−0.197075	−	0.143183i
$280$	−0.118034	−	0.363271i	−0.00705388	−	0.0217096i
$281$	5.56231	+	17.1190i	0.331819	+	1.02123i	0.968268	+	0.249916i	$0.0804029\pi$
$281$	5.56231	+	17.1190i	0.331819	+	1.02123i	−0.636448	+	0.771319i	$0.719597\pi$
$282$	−4.32624	−	3.14320i	−0.257624	−	0.187175i
$283$	23.3262	−	16.9475i	1.38660	−	1.00742i	0.390372	−	0.920657i	$-0.372346\pi$
$283$	23.3262	−	16.9475i	1.38660	−	1.00742i	0.996229	−	0.0867675i	$-0.0276537\pi$
$284$	2.70820	−	8.33499i	0.160702	−	0.494591i
$285$	8.76393			0.519131
$286$	−1.04508	−	1.76336i	−0.0617972	−	0.104269i
$287$	1.85410			0.109444
$288$	−0.454915	+	1.40008i	−0.0268061	+	0.0825008i
$289$	13.2812	−	9.64932i	0.781244	−	0.567607i
$290$	2.61803	+	1.90211i	0.153736	+	0.111696i
$291$	4.58359	+	14.1068i	0.268695	+	0.826958i
$292$	3.61803	+	11.1352i	0.211729	+	0.651636i
$293$	−15.1631	−	11.0167i	−0.885839	−	0.643600i	0.0489509	−	0.998801i	$-0.484412\pi$
$293$	−15.1631	−	11.0167i	−0.885839	−	0.643600i	−0.934790	+	0.355202i	$0.884412\pi$
$294$	−6.85410	+	4.97980i	−0.399739	+	0.290428i
$295$	−1.42705	+	4.39201i	−0.0830861	+	0.255713i
$296$	5.85410			0.340263
$297$	−1.70820	+	18.2541i	−0.0991200	+	1.05921i
$298$	−4.00000			−0.231714
$299$	1.30902	−	4.02874i	0.0757024	−	0.232988i
$300$	1.00000	−	0.726543i	0.0577350	−	0.0419470i
$301$	1.47214	+	1.06957i	0.0848525	+	0.0616490i
$302$	−5.76393	−	17.7396i	−0.331677	−	1.02080i
$303$	3.70820	+	11.4127i	0.213031	+	0.655641i
$304$	−5.73607	−	4.16750i	−0.328986	−	0.239022i
$305$	−7.23607	+	5.25731i	−0.414336	+	0.301033i
$306$	0.347524	−	1.06957i	0.0198666	−	0.0611432i
$307$	−9.05573			−0.516838			−0.258419	−	0.966033i	$-0.583201\pi$
$307$	−9.05573			−0.516838			−0.258419	+	0.966033i	$0.583201\pi$
$308$	−0.118034	+	1.26133i	−0.00672561	+	0.0718708i
$309$	−5.34752			−0.304210
$310$	0.854102	−	2.62866i	0.0485097	−	0.149298i
$311$	−5.23607	+	3.80423i	−0.296910	+	0.215718i	−0.726260	−	0.687421i	$-0.758743\pi$
$311$	−5.23607	+	3.80423i	−0.296910	+	0.215718i	0.429349	+	0.903138i	$0.358743\pi$
$312$	0.618034	+	0.449028i	0.0349893	+	0.0254212i
$313$	0.180340	+	0.555029i	0.0101934	+	0.0313721i	0.956024	−	0.293289i	$-0.0947498\pi$
$313$	0.180340	+	0.555029i	0.0101934	+	0.0313721i	−0.945830	+	0.324661i	$0.894750\pi$
$314$	1.97214	+	6.06961i	0.111294	+	0.342528i
$315$	−0.454915	−	0.330515i	−0.0256316	−	0.0186224i
$316$	8.47214	−	6.15537i	0.476595	−	0.346266i
$317$	9.51722	−	29.2910i	0.534540	−	1.64515i	−0.210100	−	0.977680i	$-0.567379\pi$
$317$	9.51722	−	29.2910i	0.534540	−	1.64515i	0.744640	−	0.667466i	$-0.232621\pi$
$318$	−14.9443			−0.838033
$319$	−5.47214	−	9.23305i	−0.306381	−	0.516952i
$320$	−1.00000			−0.0559017
$321$	6.29180	−	19.3642i	0.351174	−	1.08080i
$322$	−2.11803	+	1.53884i	−0.118033	+	0.0857563i
$323$	4.38197	+	3.18368i	0.243819	+	0.177145i
$324$	−0.746711	−	2.29814i	−0.0414839	−	0.127674i
$325$	0.190983	+	0.587785i	0.0105938	+	0.0326045i
$326$	2.23607	+	1.62460i	0.123844	+	0.0899782i
$327$	16.4721	−	11.9677i	0.910911	−	0.661816i
$328$	1.50000	−	4.61653i	0.0828236	−	0.254905i
$329$	−1.65248			−0.0911039
$330$	−4.00000	+	0.898056i	−0.220193	+	0.0494364i
$331$	−16.6180			−0.913410			−0.456705	−	0.889618i	$-0.650970\pi$
$331$	−16.6180			−0.913410			−0.456705	+	0.889618i	$0.650970\pi$
$332$	0.708204	−	2.17963i	0.0388677	−	0.119623i
$333$	6.97214	−	5.06555i	0.382071	−	0.277591i
$334$	−15.4443	−	11.2209i	−0.845073	−	0.613981i
$335$	−1.61803	−	4.97980i	−0.0884026	−	0.272075i
$336$	−0.145898	−	0.449028i	−0.00795939	−	0.0244965i
$337$	−6.94427	−	5.04531i	−0.378279	−	0.274835i	0.382357	−	0.924015i	$-0.375113\pi$
$337$	−6.94427	−	5.04531i	−0.378279	−	0.274835i	−0.760635	+	0.649179i	$0.775113\pi$
$338$	10.2082	−	7.41669i	0.555253	−	0.403415i
$339$	−7.52786	+	23.1684i	−0.408857	+	1.25833i
$340$	0.763932			0.0414300
$341$	−6.05573	+	6.88191i	−0.327936	+	0.372676i
$342$	−10.4377			−0.564406
$343$	−1.63525	+	5.03280i	−0.0882955	+	0.271746i
$344$	3.85410	−	2.80017i	0.207799	−	0.150975i
$345$	−6.85410	−	4.97980i	−0.369012	−	0.268103i
$346$	−3.20820	−	9.87384i	−0.172474	−	0.530821i
$347$	4.05573	+	12.4822i	0.217723	+	0.670082i	0.998949	+	0.0458341i	$0.0145946\pi$
$347$	4.05573	+	12.4822i	0.217723	+	0.670082i	−0.781226	+	0.624248i	$0.785405\pi$
$348$	3.23607	+	2.35114i	0.173471	+	0.126034i
$349$	−10.5623	+	7.67396i	−0.565387	+	0.410778i	−0.833427	−	0.552630i	$-0.813624\pi$
$349$	−10.5623	+	7.67396i	−0.565387	+	0.410778i	0.268039	+	0.963408i	$0.413624\pi$
$350$	0.118034	−	0.363271i	0.00630918	−	0.0194177i
$351$	3.41641			0.182354
$352$	3.04508	+	1.31433i	0.162304	+	0.0700539i
$353$	−1.70820			−0.0909185			−0.0454593	−	0.998966i	$-0.514475\pi$
$353$	−1.70820			−0.0909185			−0.0454593	+	0.998966i	$0.514475\pi$
$354$	−1.76393	+	5.42882i	−0.0937519	+	0.288539i
$355$	7.09017	−	5.15131i	0.376307	−	0.273403i
$356$	−13.7812	−	10.0126i	−0.730400	−	0.530666i
$357$	0.111456	+	0.343027i	0.00589889	+	0.0181549i
$358$	−4.35410	−	13.4005i	−0.230121	−	0.708241i
$359$	17.4164	+	12.6538i	0.919203	+	0.667840i	0.943325	−	0.331869i	$-0.107679\pi$
$359$	17.4164	+	12.6538i	0.919203	+	0.667840i	−0.0241226	+	0.999709i	$0.507679\pi$
$360$	−1.19098	+	0.865300i	−0.0627703	+	0.0456053i
$361$	9.66312	−	29.7400i	0.508585	−	1.56526i
$362$	−11.5279			−0.605891
$363$	13.3607	+	2.52265i	0.701254	+	0.132405i
$364$	0.236068			0.0123733
$365$	−3.61803	+	11.1352i	−0.189377	+	0.582841i
$366$	−8.94427	+	6.49839i	−0.467525	+	0.339676i
$367$	−1.23607	−	0.898056i	−0.0645222	−	0.0468781i	0.555057	−	0.831813i	$-0.312697\pi$
$367$	−1.23607	−	0.898056i	−0.0645222	−	0.0468781i	−0.619579	+	0.784934i	$0.712697\pi$
$368$	2.11803	+	6.51864i	0.110410	+	0.339808i
$369$	−2.20820	−	6.79615i	−0.114955	−	0.353794i
$370$	4.73607	+	3.44095i	0.246216	+	0.178887i
$371$	−3.73607	+	2.71441i	−0.193967	+	0.140925i
$372$	1.05573	−	3.24920i	0.0547370	−	0.168463i
$373$	36.0344			1.86579			0.932896	−	0.360145i	$-0.117273\pi$
$373$	36.0344			1.86579			0.932896	+	0.360145i	$0.117273\pi$
$374$	−2.32624	−	1.00406i	−0.120287	−	0.0519186i
$375$	1.23607			0.0638303
$376$	−1.33688	+	4.11450i	−0.0689444	+	0.212189i
$377$	−1.61803	+	1.17557i	−0.0833330	+	0.0605450i
$378$	−1.70820	−	1.24108i	−0.0878605	−	0.0638344i
$379$	1.64590	+	5.06555i	0.0845441	+	0.260200i	0.984388	−	0.176012i	$-0.0563198\pi$
$379$	1.64590	+	5.06555i	0.0845441	+	0.260200i	−0.899844	+	0.436212i	$0.856320\pi$
$380$	−2.19098	−	6.74315i	−0.112395	−	0.345916i
$381$	−4.61803	−	3.35520i	−0.236589	−	0.171892i
$382$	1.14590	−	0.832544i	0.0586292	−	0.0425966i
$383$	−2.82624	+	8.69827i	−0.144414	+	0.444461i	−0.996935	−	0.0782321i	$-0.975072\pi$
$383$	−2.82624	+	8.69827i	−0.144414	+	0.444461i	0.852521	+	0.522693i	$0.175072\pi$
$384$	−1.23607			−0.0630778
$385$	−0.836881	+	0.951057i	−0.0426514	+	0.0484703i
$386$	21.4164			1.09007
$387$	2.16718	−	6.66991i	0.110164	−	0.339050i
$388$	9.70820	−	7.05342i	0.492859	−	0.358083i
$389$	8.23607	+	5.98385i	0.417585	+	0.303393i	0.776665	−	0.629913i	$-0.216910\pi$
$389$	8.23607	+	5.98385i	0.417585	+	0.303393i	−0.359080	+	0.933307i	$0.616910\pi$
$390$	0.236068	+	0.726543i	0.0119538	+	0.0367899i
$391$	−1.61803	−	4.97980i	−0.0818275	−	0.251839i
$392$	5.54508	+	4.02874i	0.280069	+	0.203482i
$393$	−15.4164	+	11.2007i	−0.777655	+	0.564999i
$394$	−4.97214	+	15.3027i	−0.250493	+	0.770937i
$395$	10.4721			0.526910
$396$	4.76393	−	1.06957i	0.239397	−	0.0537479i
$397$	−17.7984			−0.893275			−0.446637	−	0.894715i	$-0.647379\pi$
$397$	−17.7984			−0.893275			−0.446637	+	0.894715i	$0.647379\pi$
$398$	−3.61803	+	11.1352i	−0.181356	+	0.558155i
$399$	2.70820	−	1.96763i	0.135580	−	0.0985045i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	9.80902	+	30.1891i	0.489839	+	1.50757i	0.824848	+	0.565354i	$0.191261\pi$
$401$	9.80902	+	30.1891i	0.489839	+	1.50757i	−0.335009	+	0.942215i	$0.608739\pi$
$402$	−2.00000	−	6.15537i	−0.0997509	−	0.307002i
$403$	1.38197	+	1.00406i	0.0688406	+	0.0500156i
$404$	7.85410	−	5.70634i	0.390756	−	0.283901i
$405$	0.746711	−	2.29814i	0.0371044	−	0.114196i
$406$	1.23607			0.0613450
$407$	−9.89919	−	16.7027i	−0.490684	−	0.827924i
$408$	0.944272			0.0467484
$409$	−2.37132	+	7.29818i	−0.117254	+	0.360872i	−0.992411	−	0.122969i	$-0.960759\pi$
$409$	−2.37132	+	7.29818i	−0.117254	+	0.360872i	0.875156	+	0.483841i	$0.160759\pi$
$410$	3.92705	−	2.85317i	0.193943	−	0.140908i
$411$	−0.763932	−	0.555029i	−0.0376820	−	0.0273776i
$412$	1.33688	+	4.11450i	0.0658634	+	0.202707i
$413$	0.545085	+	1.67760i	0.0268219	+	0.0825493i
$414$	8.16312	+	5.93085i	0.401195	+	0.291486i
$415$	1.85410	−	1.34708i	0.0910143	−	0.0661257i
$416$	0.190983	−	0.587785i	0.00936371	−	0.0288185i
$417$	18.3607			0.899126
$418$	−2.19098	+	23.4131i	−0.107164	+	1.14517i
$419$	0.618034			0.0301929			0.0150965	−	0.999886i	$-0.495194\pi$
$419$	0.618034			0.0301929			0.0150965	+	0.999886i	$0.495194\pi$
$420$	0.145898	−	0.449028i	0.00711910	−	0.0219103i
$421$	−10.2361	+	7.43694i	−0.498875	+	0.362454i	−0.808587	−	0.588376i	$-0.799767\pi$
$421$	−10.2361	+	7.43694i	−0.498875	+	0.362454i	0.309712	+	0.950830i	$0.399767\pi$
$422$	−2.47214	−	1.79611i	−0.120342	−	0.0874334i
$423$	1.96807	+	6.05710i	0.0956909	+	0.294506i
$424$	3.73607	+	11.4984i	0.181440	+	0.558413i
$425$	0.618034	+	0.449028i	0.0299791	+	0.0217811i
$426$	8.76393	−	6.36737i	0.424614	−	0.308500i
$427$	−1.05573	+	3.24920i	−0.0510903	+	0.157240i
$428$	−16.4721			−0.796211
$429$	0.236068	−	2.52265i	0.0113975	−	0.121795i
$430$	4.76393			0.229737
$431$	−1.18034	+	3.63271i	−0.0568550	+	0.174982i	−0.975451	−	0.220216i	$-0.929324\pi$
$431$	−1.18034	+	3.63271i	−0.0568550	+	0.174982i	0.918596	+	0.395197i	$0.129324\pi$
$432$	−4.47214	+	3.24920i	−0.215166	+	0.156327i
$433$	−14.9443	−	10.8576i	−0.718176	−	0.521785i	0.167625	−	0.985851i	$-0.446390\pi$
$433$	−14.9443	−	10.8576i	−0.718176	−	0.521785i	−0.885801	+	0.464066i	$0.846390\pi$
$434$	−0.326238	−	1.00406i	−0.0156599	−	0.0481963i
$435$	1.23607	+	3.80423i	0.0592649	+	0.182399i
$436$	−13.3262	−	9.68208i	−0.638211	−	0.463687i
$437$	−39.3156	+	28.5645i	−1.88072	+	1.36642i
$438$	−4.47214	+	13.7638i	−0.213687	+	0.657661i
$439$	27.1246			1.29459			0.647294	−	0.762241i	$-0.275901\pi$
$439$	27.1246			1.29459			0.647294	+	0.762241i	$0.275901\pi$
$440$	1.69098	+	2.85317i	0.0806145	+	0.136020i
$441$	10.0902			0.480484
$442$	−0.145898	+	0.449028i	−0.00693966	+	0.0213581i
$443$	−26.4164	+	19.1926i	−1.25508	+	0.911870i	−0.998505	−	0.0546540i	$-0.982594\pi$
$443$	−26.4164	+	19.1926i	−1.25508	+	0.911870i	−0.256576	+	0.966524i	$0.582594\pi$
$444$	5.85410	+	4.25325i	0.277823	+	0.201851i
$445$	−5.26393	−	16.2007i	−0.249534	−	0.767988i
$446$	7.82624	+	24.0867i	0.370583	+	1.14054i
$447$	−4.00000	−	2.90617i	−0.189194	−	0.137457i
$448$	−0.309017	+	0.224514i	−0.0145997	+	0.0106073i
$449$	3.04508	−	9.37181i	0.143706	−	0.442283i	−0.853136	−	0.521689i	$-0.825302\pi$
$449$	3.04508	−	9.37181i	0.143706	−	0.442283i	0.996842	+	0.0794057i	$0.0253023\pi$
$450$	−1.47214			−0.0693972
$451$	−15.7082	+	3.52671i	−0.739670	+	0.166066i
$452$	19.7082			0.926996
$453$	7.12461	−	21.9273i	0.334743	−	1.03023i
$454$	6.09017	−	4.42477i	0.285826	−	0.207665i
$455$	0.190983	+	0.138757i	0.00895342	+	0.00650504i
$456$	−2.70820	−	8.33499i	−0.126823	−	0.390322i
$457$	−10.6738	−	32.8505i	−0.499298	−	1.53668i	−0.810151	−	0.586222i	$-0.800615\pi$
$457$	−10.6738	−	32.8505i	−0.499298	−	1.53668i	0.310853	−	0.950458i	$-0.399385\pi$
$458$	4.70820	+	3.42071i	0.220000	+	0.159839i
$459$	3.41641	−	2.48217i	0.159464	−	0.115858i
$460$	−2.11803	+	6.51864i	−0.0987538	+	0.303933i
$461$	−38.5410			−1.79503			−0.897517	−	0.440980i	$-0.854631\pi$
$461$	−38.5410			−1.79503			−0.897517	+	0.440980i	$0.854631\pi$
$462$	−1.03444	+	1.17557i	−0.0481266	+	0.0546925i
$463$	−22.5066			−1.04597			−0.522985	−	0.852342i	$-0.675182\pi$
$463$	−22.5066			−1.04597			−0.522985	+	0.852342i	$0.675182\pi$
$464$	1.00000	−	3.07768i	0.0464238	−	0.142878i
$465$	2.76393	−	2.00811i	0.128174	−	0.0931241i
$466$	−8.70820	−	6.32688i	−0.403400	−	0.293087i
$467$	3.94427	+	12.1392i	0.182519	+	0.561736i	0.999897	−	0.0143661i	$-0.00457302\pi$
$467$	3.94427	+	12.1392i	0.182519	+	0.561736i	−0.817378	+	0.576102i	$0.804573\pi$
$468$	−0.281153	−	0.865300i	−0.0129963	−	0.0399985i
$469$	−1.61803	−	1.17557i	−0.0747139	−	0.0542828i
$470$	−3.50000	+	2.54290i	−0.161443	+	0.117295i
$471$	−2.43769	+	7.50245i	−0.112323	+	0.345695i
$472$	4.61803			0.212562
$473$	−14.5066	−	6.26137i	−0.667013	−	0.287898i
$474$	12.9443			0.594550
$475$	2.19098	−	6.74315i	0.100529	−	0.309397i
$476$	0.236068	−	0.171513i	0.0108202	−	0.00786130i
$477$	14.3992	+	10.4616i	0.659293	+	0.479005i
$478$	5.70820	+	17.5680i	0.261087	+	0.803544i
$479$	6.05573	+	18.6376i	0.276693	+	0.851574i	0.988766	+	0.149469i	$0.0477564\pi$
$479$	6.05573	+	18.6376i	0.276693	+	0.851574i	−0.712073	+	0.702105i	$0.752244\pi$
$480$	−1.00000	−	0.726543i	−0.0456435	−	0.0331620i
$481$	−2.92705	+	2.12663i	−0.133462	+	0.0969658i
$482$	1.50000	−	4.61653i	0.0683231	−	0.210277i
$483$	−3.23607			−0.147246
$484$	−1.39919	−	10.9106i	−0.0635994	−	0.495939i
$485$	12.0000			0.544892
$486$	−4.20163	+	12.9313i	−0.190590	+	0.586575i
$487$	−15.4164	+	11.2007i	−0.698584	+	0.507551i	−0.879471	−	0.475953i	$-0.842103\pi$
$487$	−15.4164	+	11.2007i	−0.698584	+	0.507551i	0.180887	+	0.983504i	$0.442103\pi$
$488$	7.23607	+	5.25731i	0.327561	+	0.237987i
$489$	1.05573	+	3.24920i	0.0477417	+	0.146934i
$490$	2.11803	+	6.51864i	0.0956830	+	0.294482i
$491$	15.7361	+	11.4329i	0.710159	+	0.515961i	0.883225	−	0.468950i	$-0.155367\pi$
$491$	15.7361	+	11.4329i	0.710159	+	0.515961i	−0.173066	+	0.984910i	$0.555367\pi$
$492$	4.85410	−	3.52671i	0.218840	−	0.158996i
$493$	−0.763932	+	2.35114i	−0.0344058	+	0.105890i
$494$	4.38197			0.197154
$495$	4.48278	+	1.93487i	0.201486	+	0.0869659i
$496$	−2.76393			−0.124104
$497$	1.03444	−	3.18368i	0.0464011	−	0.142808i
$498$	2.29180	−	1.66509i	0.102698	−	0.0746143i
$499$	−9.54508	−	6.93491i	−0.427297	−	0.310449i	0.353270	−	0.935521i	$-0.385070\pi$
$499$	−9.54508	−	6.93491i	−0.427297	−	0.310449i	−0.780567	+	0.625072i	$0.785070\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	−7.29180	−	22.4418i	−0.325773	−	1.00263i
$502$	−15.3992	−	11.1882i	−0.687299	−	0.499352i
$503$	24.6803	−	17.9313i	1.10044	−	0.799518i	0.119310	−	0.992857i	$-0.461932\pi$
$503$	24.6803	−	17.9313i	1.10044	−	0.799518i	0.981132	+	0.193339i	$0.0619318\pi$
$504$	−0.173762	+	0.534785i	−0.00773998	+	0.0238212i
$505$	9.70820			0.432009
$506$	15.0172	−	17.0660i	0.667597	−	0.758677i
$507$	15.5967			0.692676
$508$	−1.42705	+	4.39201i	−0.0633151	+	0.194864i
$509$	−7.38197	+	5.36331i	−0.327200	+	0.237725i	−0.739242	−	0.673440i	$-0.764816\pi$
$509$	−7.38197	+	5.36331i	−0.327200	+	0.237725i	0.412042	+	0.911165i	$0.364816\pi$
$510$	0.763932	+	0.555029i	0.0338275	+	0.0245771i
$511$	1.38197	+	4.25325i	0.0611346	+	0.188153i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−31.7082	−	23.0374i	−1.39995	−	1.01712i
$514$	9.70820	−	7.05342i	0.428211	−	0.311113i
$515$	−1.33688	+	4.11450i	−0.0589100	+	0.181306i
$516$	5.88854			0.259229
$517$	14.0000	−	3.14320i	0.615719	−	0.138238i
$518$	2.23607			0.0982472
$519$	3.96556	−	12.2047i	0.174069	−	0.535728i
$520$	0.500000	−	0.363271i	0.0219265	−	0.0159305i
$521$	5.16312	+	3.75123i	0.226200	+	0.164344i	0.695113	−	0.718900i	$-0.255354\pi$
$521$	5.16312	+	3.75123i	0.226200	+	0.164344i	−0.468913	+	0.883244i	$0.655354\pi$
$522$	−1.47214	−	4.53077i	−0.0644336	−	0.198306i
$523$	−11.9443	−	36.7607i	−0.522287	−	1.60743i	−0.769620	−	0.638502i	$-0.779554\pi$
$523$	−11.9443	−	36.7607i	−0.522287	−	1.60743i	0.247333	−	0.968930i	$-0.420446\pi$
$524$	12.4721	+	9.06154i	0.544848	+	0.395855i
$525$	0.381966	−	0.277515i	0.0166704	−	0.0121117i
$526$	0.371323	−	1.14281i	0.0161904	−	0.0498291i
$527$	2.11146			0.0919765
$528$	2.09017	+	3.52671i	0.0909630	+	0.153480i
$529$	23.9787			1.04255
$530$	−3.73607	+	11.4984i	−0.162284	+	0.499460i
$531$	5.50000	−	3.99598i	0.238680	−	0.173411i
$532$	−2.19098	−	1.59184i	−0.0949912	−	0.0690151i
$533$	0.927051	+	2.85317i	0.0401550	+	0.123584i
$534$	−6.50658	−	20.0252i	−0.281567	−	0.866575i
$535$	−13.3262	−	9.68208i	−0.576144	−	0.418593i
$536$	−4.23607	+	3.07768i	−0.182970	+	0.132936i
$537$	5.38197	−	16.5640i	0.232249	−	0.714789i
$538$	−31.5967			−1.36223
$539$	2.11803	−	22.6336i	0.0912302	−	0.974898i
$540$	−5.52786			−0.237881
$541$	−2.47214	+	7.60845i	−0.106285	+	0.327113i	−0.990030	−	0.140857i	$-0.955014\pi$
$541$	−2.47214	+	7.60845i	−0.106285	+	0.327113i	0.883745	+	0.467970i	$0.155014\pi$
$542$	10.8541	−	7.88597i	0.466224	−	0.338731i
$543$	−11.5279	−	8.37548i	−0.494708	−	0.359426i
$544$	−0.236068	−	0.726543i	−0.0101213	−	0.0311503i
$545$	−5.09017	−	15.6659i	−0.218039	−	0.671055i
$546$	0.236068	+	0.171513i	0.0101028	+	0.00734010i
$547$	−27.1803	+	19.7477i	−1.16215	+	0.844350i	−0.990048	−	0.140730i	$-0.955055\pi$
$547$	−27.1803	+	19.7477i	−1.16215	+	0.844350i	−0.172099	+	0.985080i	$0.555055\pi$
$548$	−0.236068	+	0.726543i	−0.0100843	+	0.0310364i
$549$	13.1672			0.561962
$550$	−0.309017	+	3.30220i	−0.0131765	+	0.140806i
$551$	22.9443			0.977459
$552$	−2.61803	+	8.05748i	−0.111431	+	0.342949i
$553$	3.23607	−	2.35114i	0.137612	−	0.0999807i
$554$	−1.30902	−	0.951057i	−0.0556148	−	0.0404065i
$555$	2.23607	+	6.88191i	0.0949158	+	0.292121i
$556$	−4.59017	−	14.1271i	−0.194667	−	0.599122i
$557$	14.7361	+	10.7064i	0.624387	+	0.453644i	0.854451	−	0.519532i	$-0.173894\pi$
$557$	14.7361	+	10.7064i	0.624387	+	0.453644i	−0.230064	+	0.973176i	$0.573894\pi$
$558$	−3.29180	+	2.39163i	−0.139353	+	0.101246i
$559$	−0.909830	+	2.80017i	−0.0384817	+	0.118435i
$560$	−0.381966			−0.0161410
$561$	−1.59675	−	2.69417i	−0.0674147	−	0.113748i
$562$	18.0000			0.759284
$563$	−3.67376	+	11.3067i	−0.154831	+	0.476520i	−0.998144	−	0.0609030i	$-0.980602\pi$
$563$	−3.67376	+	11.3067i	−0.154831	+	0.476520i	0.843313	+	0.537423i	$0.180602\pi$
$564$	−4.32624	+	3.14320i	−0.182167	+	0.132352i
$565$	15.9443	+	11.5842i	0.670781	+	0.487351i
$566$	−8.90983	−	27.4216i	−0.374508	−	1.15262i
$567$	−0.285218	−	0.877812i	−0.0119780	−	0.0368646i
$568$	−7.09017	−	5.15131i	−0.297497	−	0.216144i
$569$	5.92705	−	4.30625i	0.248475	−	0.180528i	−0.456576	−	0.889685i	$-0.650924\pi$
$569$	5.92705	−	4.30625i	0.248475	−	0.180528i	0.705051	+	0.709157i	$0.250924\pi$
$570$	2.70820	−	8.33499i	0.113434	−	0.349115i
$571$	−17.9098			−0.749503			−0.374752	−	0.927125i	$-0.622272\pi$
$571$	−17.9098			−0.749503			−0.374752	+	0.927125i	$0.622272\pi$
$572$	−2.00000	+	0.449028i	−0.0836242	+	0.0187748i
$573$	1.75078			0.0731397
$574$	0.572949	−	1.76336i	0.0239144	−	0.0736010i
$575$	−5.54508	+	4.02874i	−0.231246	+	0.168010i
$576$	1.19098	+	0.865300i	0.0496243	+	0.0360542i
$577$	−0.909830	−	2.80017i	−0.0378767	−	0.116573i	0.930330	−	0.366722i	$-0.119520\pi$
$577$	−0.909830	−	2.80017i	−0.0378767	−	0.116573i	−0.968207	+	0.250150i	$0.919520\pi$
$578$	−5.07295	−	15.6129i	−0.211007	−	0.649412i
$579$	21.4164	+	15.5599i	0.890036	+	0.646649i
$580$	2.61803	−	1.90211i	0.108708	−	0.0789809i
$581$	0.270510	−	0.832544i	0.0112226	−	0.0345397i
$582$	14.8328			0.614840
$583$	26.4894	−	30.1033i	1.09708	−	1.24675i
$584$	11.7082			0.484489
$585$	0.281153	−	0.865300i	0.0116242	−	0.0357757i
$586$	−15.1631	+	11.0167i	−0.626383	+	0.455094i
$587$	20.4164	+	14.8334i	0.842675	+	0.612239i	0.923117	−	0.384520i	$-0.125633\pi$
$587$	20.4164	+	14.8334i	0.842675	+	0.612239i	−0.0804414	+	0.996759i	$0.525633\pi$
$588$	2.61803	+	8.05748i	0.107966	+	0.332285i
$589$	−6.05573	−	18.6376i	−0.249522	−	0.767950i
$590$	3.73607	+	2.71441i	0.153811	+	0.111751i
$591$	−16.0902	+	11.6902i	−0.661861	+	0.480870i
$592$	1.80902	−	5.56758i	0.0743501	−	0.228826i
$593$	−6.29180			−0.258373			−0.129187	−	0.991620i	$-0.541237\pi$
$593$	−6.29180			−0.258373			−0.129187	+	0.991620i	$0.541237\pi$
$594$	16.8328	+	7.26543i	0.690659	+	0.298104i
$595$	0.291796			0.0119625
$596$	−1.23607	+	3.80423i	−0.0506313	+	0.155827i
$597$	−11.7082	+	8.50651i	−0.479185	+	0.348148i
$598$	−3.42705	−	2.48990i	−0.140143	−	0.101820i
$599$	2.32624	+	7.15942i	0.0950475	+	0.292526i	0.987266	−	0.159078i	$-0.0508520\pi$
$599$	2.32624	+	7.15942i	0.0950475	+	0.292526i	−0.892219	+	0.451604i	$0.850852\pi$
$600$	−0.381966	−	1.17557i	−0.0155937	−	0.0479925i
$601$	−1.97214	−	1.43284i	−0.0804451	−	0.0584468i	0.546836	−	0.837240i	$-0.315832\pi$
$601$	−1.97214	−	1.43284i	−0.0804451	−	0.0584468i	−0.627281	+	0.778793i	$0.715832\pi$
$602$	1.47214	−	1.06957i	0.0599998	−	0.0435924i
$603$	−2.38197	+	7.33094i	−0.0970012	+	0.298539i
$604$	−18.6525			−0.758958
$605$	5.28115	−	9.64932i	0.214709	−	0.392301i
$606$	12.0000			0.487467
$607$	−3.81966	+	11.7557i	−0.155035	+	0.477149i	−0.998164	−	0.0605616i	$-0.980711\pi$
$607$	−3.81966	+	11.7557i	−0.155035	+	0.477149i	0.843129	+	0.537711i	$0.180711\pi$
$608$	−5.73607	+	4.16750i	−0.232628	+	0.169014i
$609$	1.23607	+	0.898056i	0.0500880	+	0.0363911i
$610$	2.76393	+	8.50651i	0.111908	+	0.344418i
$611$	−0.826238	−	2.54290i	−0.0334260	−	0.102875i
$612$	−0.909830	−	0.661030i	−0.0367777	−	0.0267206i
$613$	−16.5623	+	12.0332i	−0.668945	+	0.486017i	−0.869672	−	0.493630i	$-0.835670\pi$
$613$	−16.5623	+	12.0332i	−0.668945	+	0.486017i	0.200727	+	0.979647i	$0.435670\pi$
$614$	−2.79837	+	8.61251i	−0.112933	+	0.347573i
$615$	6.00000			0.241943
$616$	1.16312	+	0.502029i	0.0468634	+	0.0202273i
$617$	15.0557			0.606121			0.303060	−	0.952971i	$-0.401992\pi$
$617$	15.0557			0.606121			0.303060	+	0.952971i	$0.401992\pi$
$618$	−1.65248	+	5.08580i	−0.0664723	+	0.204581i
$619$	15.9721	−	11.6044i	0.641974	−	0.466422i	−0.218554	−	0.975825i	$-0.570134\pi$
$619$	15.9721	−	11.6044i	0.641974	−	0.466422i	0.860528	+	0.509403i	$0.170134\pi$
$620$	−2.23607	−	1.62460i	−0.0898027	−	0.0652454i
$621$	11.7082	+	36.0341i	0.469834	+	1.44600i
$622$	2.00000	+	6.15537i	0.0801927	+	0.246808i
$623$	−5.26393	−	3.82447i	−0.210895	−	0.153224i
$624$	0.618034	−	0.449028i	0.0247412	−	0.0179755i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	0.583592			0.0233250
$627$	−19.2016	+	21.8213i	−0.766839	+	0.871459i
$628$	6.38197			0.254668
$629$	−1.38197	+	4.25325i	−0.0551026	+	0.169588i
$630$	−0.454915	+	0.330515i	−0.0181242	+	0.0131680i
$631$	15.7082	+	11.4127i	0.625334	+	0.454332i	0.854781	−	0.518990i	$-0.173692\pi$
$631$	15.7082	+	11.4127i	0.625334	+	0.454332i	−0.229447	+	0.973321i	$0.573692\pi$
$632$	−3.23607	−	9.95959i	−0.128724	−	0.396171i
$633$	−1.16718	−	3.59222i	−0.0463914	−	0.142778i
$634$	−24.9164	−	18.1028i	−0.989557	−	0.718955i
$635$	−3.73607	+	2.71441i	−0.148261	+	0.107718i
$636$	−4.61803	+	14.2128i	−0.183117	+	0.563576i
$637$	−4.23607			−0.167839
$638$	−10.4721	+	2.35114i	−0.414596	+	0.0930826i
$639$	−12.9017			−0.510383
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	25.2082	−	18.3148i	0.995664	−	0.723392i	0.0345100	−	0.999404i	$-0.489013\pi$
$641$	25.2082	−	18.3148i	0.995664	−	0.723392i	0.961154	+	0.276012i	$0.0890129\pi$
$642$	−16.4721	−	11.9677i	−0.650103	−	0.472328i
$643$	4.14590	+	12.7598i	0.163498	+	0.503196i	0.998922	−	0.0464097i	$-0.0147780\pi$
$643$	4.14590	+	12.7598i	0.163498	+	0.503196i	−0.835424	+	0.549606i	$0.814778\pi$
$644$	0.809017	+	2.48990i	0.0318797	+	0.0981157i
$645$	4.76393	+	3.46120i	0.187580	+	0.136285i
$646$	4.38197	−	3.18368i	0.172406	−	0.125260i
$647$	−7.70820	+	23.7234i	−0.303041	+	0.932664i	0.677360	+	0.735651i	$0.263124\pi$
$647$	−7.70820	+	23.7234i	−0.303041	+	0.932664i	−0.980401	+	0.197012i	$0.936876\pi$
$648$	−2.41641			−0.0949255
$649$	−7.80902	−	13.1760i	−0.306531	−	0.517205i
$650$	0.618034			0.0242413
$651$	0.403252	−	1.24108i	0.0158047	−	0.0486419i
$652$	2.23607	−	1.62460i	0.0875712	−	0.0636242i
$653$	−0.972136	−	0.706298i	−0.0380426	−	0.0276396i	0.568601	−	0.822613i	$-0.307485\pi$
$653$	−0.972136	−	0.706298i	−0.0380426	−	0.0276396i	−0.606644	+	0.794974i	$0.707485\pi$
$654$	−6.29180	−	19.3642i	−0.246029	−	0.757198i
$655$	4.76393	+	14.6619i	0.186142	+	0.572887i
$656$	−3.92705	−	2.85317i	−0.153326	−	0.111398i
$657$	13.9443	−	10.1311i	0.544018	−	0.395252i
$658$	−0.510643	+	1.57160i	−0.0199069	+	0.0612673i
$659$	−15.6180			−0.608392			−0.304196	−	0.952609i	$-0.598388\pi$
$659$	−15.6180			−0.608392			−0.304196	+	0.952609i	$0.598388\pi$
$660$	−0.381966	+	4.08174i	−0.0148680	+	0.158882i
$661$	−20.1803			−0.784924			−0.392462	−	0.919768i	$-0.628377\pi$
$661$	−20.1803			−0.784924			−0.392462	+	0.919768i	$0.628377\pi$
$662$	−5.13525	+	15.8047i	−0.199587	+	0.614267i
$663$	−0.472136	+	0.343027i	−0.0183362	+	0.0133221i
$664$	−1.85410	−	1.34708i	−0.0719531	−	0.0522770i
$665$	−0.836881	−	2.57565i	−0.0324529	−	0.0998796i
$666$	−2.66312	−	8.19624i	−0.103194	−	0.317598i
$667$	−17.9443	−	13.0373i	−0.694805	−	0.504805i
$668$	−15.4443	+	11.2209i	−0.597557	+	0.434150i
$669$	−9.67376	+	29.7728i	−0.374009	+	1.15108i
$670$	−5.23607			−0.202287
$671$	2.76393	−	29.5358i	0.106700	−	1.14022i
$672$	−0.472136			−0.0182130
$673$	−1.23607	+	3.80423i	−0.0476469	+	0.146642i	−0.972049	−	0.234776i	$-0.924564\pi$
$673$	−1.23607	+	3.80423i	−0.0476469	+	0.146642i	0.924403	+	0.381418i	$0.124564\pi$
$674$	−6.94427	+	5.04531i	−0.267483	+	0.194338i
$675$	−4.47214	−	3.24920i	−0.172133	−	0.125062i
$676$	−3.89919	−	12.0005i	−0.149969	−	0.461556i
$677$	−3.09017	−	9.51057i	−0.118765	−	0.365521i	0.873949	−	0.486018i	$-0.161551\pi$
$677$	−3.09017	−	9.51057i	−0.118765	−	0.365521i	−0.992714	+	0.120497i	$0.961551\pi$
$678$	19.7082	+	14.3188i	0.756889	+	0.549912i
$679$	3.70820	−	2.69417i	0.142308	−	0.103393i
$680$	0.236068	−	0.726543i	0.00905279	−	0.0278616i
$681$	9.30495			0.356567
$682$	4.67376	+	7.88597i	0.178968	+	0.301969i
$683$	29.0132			1.11016			0.555079	−	0.831798i	$-0.312688\pi$
$683$	29.0132			1.11016			0.555079	+	0.831798i	$0.312688\pi$
$684$	−3.22542	+	9.92684i	−0.123327	+	0.379562i
$685$	−0.618034	+	0.449028i	−0.0236139	+	0.0171565i
$686$	4.28115	+	3.11044i	0.163455	+	0.118757i
$687$	2.22291	+	6.84142i	0.0848094	+	0.261016i
$688$	−1.47214	−	4.53077i	−0.0561247	−	0.172734i
$689$	−6.04508	−	4.39201i	−0.230299	−	0.167322i
$690$	−6.85410	+	4.97980i	−0.260931	+	0.189578i
$691$	−8.88197	+	27.3359i	−0.337886	+	1.03991i	0.627397	+	0.778700i	$0.284120\pi$
$691$	−8.88197	+	27.3359i	−0.337886	+	1.03991i	−0.965283	+	0.261206i	$0.915880\pi$
$692$	−10.3820			−0.394663
$693$	1.81966	−	0.408539i	0.0691232	−	0.0155191i
$694$	13.1246			0.498203
$695$	4.59017	−	14.1271i	0.174115	−	0.535871i
$696$	3.23607	−	2.35114i	0.122663	−	0.0891198i
$697$	3.00000	+	2.17963i	0.113633	+	0.0825593i
$698$	4.03444	+	12.4167i	0.152706	+	0.469980i
$699$	−4.11146	−	12.6538i	−0.155510	−	0.478609i
$700$	−0.309017	−	0.224514i	−0.0116797	−	0.00848583i
$701$	−22.7984	+	16.5640i	−0.861083	+	0.625613i	−0.928179	−	0.372133i	$-0.878626\pi$
$701$	−22.7984	+	16.5640i	−0.861083	+	0.625613i	0.0670966	+	0.997746i	$0.478626\pi$
$702$	1.05573	−	3.24920i	0.0398459	−	0.122633i
$703$	41.5066			1.56545
$704$	2.19098	−	2.48990i	0.0825758	−	0.0938416i
$705$	−5.34752			−0.201399
$706$	−0.527864	+	1.62460i	−0.0198664	+	0.0611426i
$707$	3.00000	−	2.17963i	0.112827	−	0.0819733i
$708$	4.61803	+	3.35520i	0.173556	+	0.126096i
$709$	15.7984	+	48.6224i	0.593320	+	1.82605i	0.562915	+	0.826515i	$0.309680\pi$
$709$	15.7984	+	48.6224i	0.593320	+	1.82605i	0.0304053	+	0.999538i	$0.490320\pi$
$710$	−2.70820	−	8.33499i	−0.101637	−	0.312807i
$711$	−12.4721	−	9.06154i	−0.467742	−	0.339834i
$712$	−13.7812	+	10.0126i	−0.516471	+	0.375238i
$713$	−5.85410	+	18.0171i	−0.219238	+	0.674745i
$714$	0.360680			0.0134981
$715$	−1.88197	−	0.812299i	−0.0703815	−	0.0303783i
$716$	−14.0902			−0.526574
$717$	−7.05573	+	21.7153i	−0.263501	+	0.810973i
$718$	17.4164	−	12.6538i	0.649975	−	0.472234i
$719$	−37.3607	−	27.1441i	−1.39332	−	1.01230i	−0.995492	−	0.0948441i	$-0.969765\pi$
$719$	−37.3607	−	27.1441i	−1.39332	−	1.01230i	−0.397826	−	0.917461i	$-0.630235\pi$
$720$	0.454915	+	1.40008i	0.0169537	+	0.0521781i
$721$	0.510643	+	1.57160i	0.0190173	+	0.0585294i
$722$	−25.2984	−	18.3803i	−0.941508	−	0.684046i
$723$	4.85410	−	3.52671i	0.180526	−	0.131160i
$724$	−3.56231	+	10.9637i	−0.132392	+	0.407461i
$725$	3.23607			0.120185
$726$	6.52786	−	11.9272i	0.242272	−	0.442661i
$727$	15.7984			0.585929			0.292965	−	0.956123i	$-0.405358\pi$
$727$	15.7984			0.585929			0.292965	+	0.956123i	$0.405358\pi$
$728$	0.0729490	−	0.224514i	0.00270367	−	0.00832104i
$729$	−19.4615	+	14.1396i	−0.720796	+	0.523689i
$730$	9.47214	+	6.88191i	0.350579	+	0.254711i
$731$	1.12461	+	3.46120i	0.0415953	+	0.128017i
$732$	3.41641	+	10.5146i	0.126274	+	0.388632i
$733$	35.7984	+	26.0090i	1.32224	+	0.960666i	0.999901	+	0.0140425i	$0.00447000\pi$
$733$	35.7984	+	26.0090i	1.32224	+	0.960666i	0.322342	+	0.946623i	$0.395530\pi$
$734$	−1.23607	+	0.898056i	−0.0456241	+	0.0331479i
$735$	−2.61803	+	8.05748i	−0.0965676	+	0.297205i
$736$	6.85410			0.252646
$737$	15.9443	+	6.88191i	0.587315	+	0.253498i
$738$	−7.14590			−0.263044
$739$	−7.77051	+	23.9152i	−0.285843	+	0.879734i	0.700302	+	0.713847i	$0.253049\pi$
$739$	−7.77051	+	23.9152i	−0.285843	+	0.879734i	−0.986145	+	0.165887i	$0.946951\pi$
$740$	4.73607	−	3.44095i	0.174101	−	0.126492i
$741$	4.38197	+	3.18368i	0.160976	+	0.116956i
$742$	1.42705	+	4.39201i	0.0523887	+	0.161236i
$743$	7.64590	+	23.5317i	0.280501	+	0.863293i	0.987711	+	0.156290i	$0.0499533\pi$
$743$	7.64590	+	23.5317i	0.280501	+	0.863293i	−0.707210	+	0.707003i	$0.750047\pi$
$744$	−2.76393	−	2.00811i	−0.101331	−	0.0736210i
$745$	−3.23607	+	2.35114i	−0.118560	+	0.0861391i
$746$	11.1353	−	34.2708i	0.407691	−	1.25474i
$747$	−3.37384			−0.123442
$748$	−1.67376	+	1.90211i	−0.0611988	+	0.0695481i
$749$	−6.29180			−0.229897
$750$	0.381966	−	1.17557i	0.0139474	−	0.0429258i
$751$	−5.61803	+	4.08174i	−0.205005	+	0.148945i	−0.685551	−	0.728025i	$-0.740439\pi$
$751$	−5.61803	+	4.08174i	−0.205005	+	0.148945i	0.480546	+	0.876970i	$0.340439\pi$
$752$	3.50000	+	2.54290i	0.127632	+	0.0927300i
$753$	−7.27051	−	22.3763i	−0.264952	−	0.815439i
$754$	0.618034	+	1.90211i	0.0225075	+	0.0692709i
$755$	−15.0902	−	10.9637i	−0.549188	−	0.399008i
$756$	−1.70820	+	1.24108i	−0.0621268	+	0.0451377i
$757$	14.4615	−	44.5079i	0.525612	−	1.61767i	−0.237491	−	0.971390i	$-0.576325\pi$
$757$	14.4615	−	44.5079i	0.525612	−	1.61767i	0.763103	−	0.646277i	$-0.223675\pi$
$758$	5.32624			0.193458
$759$	27.4164	−	6.15537i	0.995153	−	0.223426i
$760$	−7.09017			−0.257187
$761$	10.3262	−	31.7809i	0.374326	−	1.15206i	−0.569607	−	0.821918i	$-0.692904\pi$
$761$	10.3262	−	31.7809i	0.374326	−	1.15206i	0.943932	−	0.330139i	$-0.107096\pi$
$762$	−4.61803	+	3.35520i	−0.167294	+	0.121546i
$763$	−5.09017	−	3.69822i	−0.184277	−	0.133885i
$764$	−0.437694	−	1.34708i	−0.0158352	−	0.0487358i
$765$	−0.347524	−	1.06957i	−0.0125648	−	0.0386704i
$766$	7.39919	+	5.37582i	0.267343	+	0.194236i
$767$	−2.30902	+	1.67760i	−0.0833738	+	0.0605746i
$768$	−0.381966	+	1.17557i	−0.0137830	+	0.0424197i
$769$	−20.9098			−0.754028			−0.377014	−	0.926208i	$-0.623049\pi$
$769$	−20.9098			−0.754028			−0.377014	+	0.926208i	$0.623049\pi$
$770$	0.645898	+	1.08981i	0.0232765	+	0.0392742i
$771$	14.8328			0.534191
$772$	6.61803	−	20.3682i	0.238188	−	0.733068i
$773$	14.1074	−	10.2496i	0.507408	−	0.368653i	−0.304432	−	0.952534i	$-0.598467\pi$
$773$	14.1074	−	10.2496i	0.507408	−	0.368653i	0.811839	+	0.583881i	$0.198467\pi$
$774$	−5.67376	−	4.12223i	−0.203939	−	0.148170i
$775$	−0.854102	−	2.62866i	−0.0306802	−	0.0944241i
$776$	−3.70820	−	11.4127i	−0.133117	−	0.409691i
$777$	2.23607	+	1.62460i	0.0802185	+	0.0582821i
$778$	8.23607	−	5.98385i	0.295277	−	0.214532i
$779$	10.6353	−	32.7319i	0.381048	−	1.17274i
$780$	0.763932			0.0273532
$781$	−2.70820	+	28.9402i	−0.0969072	+	1.03556i
$782$	−5.23607			−0.187241
$783$	5.52786	−	17.0130i	0.197550	−	0.607996i
$784$	5.54508	−	4.02874i	0.198039	−	0.143884i
$785$	5.16312	+	3.75123i	0.184280	+	0.133887i
$786$	5.88854	+	18.1231i	0.210037	+	0.646429i
$787$	−11.1246	−	34.2380i	−0.396550	−	1.22045i	−0.927748	−	0.373207i	$-0.878258\pi$
$787$	−11.1246	−	34.2380i	−0.396550	−	1.22045i	0.531199	−	0.847247i	$-0.321742\pi$
$788$	13.0172	+	9.45756i	0.463719	+	0.336912i
$789$	1.20163	−	0.873032i	0.0427790	−	0.0310808i
$790$	3.23607	−	9.95959i	0.115134	−	0.354346i
$791$	7.52786			0.267660
$792$	0.454915	−	4.86128i	0.0161647	−	0.172738i
$793$	−5.52786			−0.196300
$794$	−5.50000	+	16.9273i	−0.195188	+	0.600726i
$795$	−12.0902	+	8.78402i	−0.428794	+	0.311537i
$796$	9.47214	+	6.88191i	0.335731	+	0.243923i
$797$	2.46149	+	7.57570i	0.0871905	+	0.268345i	0.985140	−	0.171754i	$-0.0549434\pi$
$797$	2.46149	+	7.57570i	0.0871905	+	0.268345i	−0.897949	+	0.440099i	$0.854943\pi$
$798$	−1.03444	−	3.18368i	−0.0366188	−	0.112701i
$799$	−2.67376	−	1.94260i	−0.0945909	−	0.0687243i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$	−7.74922	+	23.8497i	−0.273805	+	0.842686i
$802$	31.7426			1.12087
$803$	−19.7984	−	33.4055i	−0.698669	−	1.17885i
$804$	−6.47214			−0.228255
$805$	−0.809017	+	2.48990i	−0.0285141	+	0.0877574i
$806$	1.38197	−	1.00406i	0.0486777	−	0.0353664i
$807$	−31.5967	−	22.9564i	−1.11226	−	0.808103i
$808$	−3.00000	−	9.23305i	−0.105540	−	0.324818i
$809$	6.19098	+	19.0539i	0.217663	+	0.669899i	0.998954	+	0.0457313i	$0.0145618\pi$
$809$	6.19098	+	19.0539i	0.217663	+	0.669899i	−0.781290	+	0.624168i	$0.785438\pi$
$810$	−1.95492	−	1.42033i	−0.0686887	−	0.0499053i
$811$	35.9058	−	26.0871i	1.26082	−	0.916041i	0.262024	−	0.965061i	$-0.415610\pi$
$811$	35.9058	−	26.0871i	1.26082	−	0.916041i	0.998798	+	0.0490206i	$0.0156100\pi$
$812$	0.381966	−	1.17557i	0.0134044	−	0.0412544i
$813$	16.5836			0.581612
$814$	−18.9443	+	4.25325i	−0.663996	+	0.149076i
$815$	2.76393			0.0968163
$816$	0.291796	−	0.898056i	0.0102149	−	0.0314382i
$817$	27.3262	−	19.8537i	0.956024	−	0.694592i
$818$	6.20820	+	4.51052i	0.217065	+	0.157707i
$819$	−0.107391	−	0.330515i	−0.00375254	−	0.0115491i
$820$	−1.50000	−	4.61653i	−0.0523823	−	0.161216i
$821$	−16.4721	−	11.9677i	−0.574882	−	0.417676i	0.261994	−	0.965070i	$-0.415620\pi$
$821$	−16.4721	−	11.9677i	−0.574882	−	0.417676i	−0.836875	+	0.547394i	$0.815620\pi$
$822$	−0.763932	+	0.555029i	−0.0266452	+	0.0193589i
$823$	3.71885	−	11.4454i	0.129631	−	0.398963i	−0.865085	−	0.501624i	$-0.832736\pi$
$823$	3.71885	−	11.4454i	0.129631	−	0.398963i	0.994716	+	0.102662i	$0.0327359\pi$
$824$	4.32624			0.150712
$825$	−2.70820	+	3.07768i	−0.0942876	+	0.107151i
$826$	1.76393			0.0613750
$827$	6.79837	−	20.9232i	0.236403	−	0.727572i	−0.760530	−	0.649303i	$-0.775061\pi$
$827$	6.79837	−	20.9232i	0.236403	−	0.727572i	0.996932	−	0.0782692i	$-0.0249394\pi$
$828$	8.16312	−	5.93085i	0.283688	−	0.206111i
$829$	−4.00000	−	2.90617i	−0.138926	−	0.100935i	0.516152	−	0.856497i	$-0.327364\pi$
$829$	−4.00000	−	2.90617i	−0.138926	−	0.100935i	−0.655078	+	0.755562i	$0.727364\pi$
$830$	−0.708204	−	2.17963i	−0.0245821	−	0.0756560i
$831$	−0.618034	−	1.90211i	−0.0214394	−	0.0659836i
$832$	−0.500000	−	0.363271i	−0.0173344	−	0.0125942i
$833$	−4.23607	+	3.07768i	−0.146771	+	0.106635i
$834$	5.67376	−	17.4620i	0.196466	−	0.604661i
$835$	−19.0902			−0.660643
$836$	21.5902	+	9.31881i	0.746712	+	0.322298i
$837$	−15.2786			−0.528107
$838$	0.190983	−	0.587785i	0.00659740	−	0.0203047i
$839$	−11.7639	+	8.54700i	−0.406136	+	0.295075i	−0.772036	−	0.635579i	$-0.780761\pi$
$839$	−11.7639	+	8.54700i	−0.406136	+	0.295075i	0.365900	+	0.930654i	$0.380761\pi$
$840$	−0.381966	−	0.277515i	−0.0131791	−	0.00957516i
$841$	−5.72542	−	17.6210i	−0.197428	−	0.607622i
$842$	3.90983	+	12.0332i	0.134742	+	0.414692i
$843$	18.0000	+	13.0778i	0.619953	+	0.450422i
$844$	−2.47214	+	1.79611i	−0.0850944	+	0.0618247i
$845$	3.89919	−	12.0005i	0.134136	−	0.412828i
$846$	6.36881			0.218964
$847$	−0.534442	−	4.16750i	−0.0183636	−	0.143197i
$848$	12.0902			0.415178
$849$	11.0132	−	33.8950i	0.377971	−	1.16327i
$850$	0.618034	−	0.449028i	0.0211984	−	0.0154015i
$851$	−32.4615	−	23.5847i	−1.11277	−	0.808472i
$852$	−3.34752	−	10.3026i	−0.114684	−	0.352962i
$853$	13.9164	+	42.8303i	0.476489	+	1.46648i	0.843939	+	0.536439i	$0.180231\pi$
$853$	13.9164	+	42.8303i	0.476489	+	1.46648i	−0.367451	+	0.930043i	$0.619769\pi$
$854$	2.76393	+	2.00811i	0.0945798	+	0.0687163i
$855$	−8.44427	+	6.13512i	−0.288788	+	0.209817i
$856$	−5.09017	+	15.6659i	−0.173978	+	0.535451i
$857$	22.0000			0.751506			0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000			0.751506			0.375753	+	0.926720i	$0.377384\pi$
$858$	−2.32624	−	1.00406i	−0.0794165	−	0.0342779i
$859$	−42.0902			−1.43610			−0.718049	−	0.695993i	$-0.754965\pi$
$859$	−42.0902			−1.43610			−0.718049	+	0.695993i	$0.754965\pi$
$860$	1.47214	−	4.53077i	0.0501994	−	0.154498i
$861$	1.85410	−	1.34708i	0.0631876	−	0.0459085i
$862$	3.09017	+	2.24514i	0.105252	+	0.0764698i
$863$	−9.51722	−	29.2910i	−0.323970	−	0.997077i	−0.971903	−	0.235380i	$-0.924367\pi$
$863$	−9.51722	−	29.2910i	−0.323970	−	0.997077i	0.647933	−	0.761697i	$-0.275633\pi$
$864$	1.70820	+	5.25731i	0.0581143	+	0.178857i
$865$	−8.39919	−	6.10237i	−0.285581	−	0.207487i
$866$	−14.9443	+	10.8576i	−0.507827	+	0.368958i
$867$	6.27051	−	19.2986i	0.212958	−	0.655416i
$868$	−1.05573			−0.0358337
$869$	−22.9443	+	26.0746i	−0.778331	+	0.884519i
$870$	4.00000			0.135613
$871$	1.00000	−	3.07768i	0.0338837	−	0.104283i
$872$	−13.3262	+	9.68208i	−0.451283	+	0.327877i
$873$	−14.2918	−	10.3836i	−0.483704	−	0.351432i
$874$	15.0172	+	46.2183i	0.507965	+	1.56336i
$875$	−0.118034	−	0.363271i	−0.00399028	−	0.0122808i
$876$	11.7082	+	8.50651i	0.395584	+	0.287408i
$877$	−3.73607	+	2.71441i	−0.126158	+	0.0916592i	−0.649075	−	0.760725i	$-0.724844\pi$
$877$	−3.73607	+	2.71441i	−0.126158	+	0.0916592i	0.522917	+	0.852384i	$0.324844\pi$
$878$	8.38197	−	25.7970i	0.282878	−	0.870608i
$879$	−23.1672			−0.781410
$880$	3.23607	−	0.726543i	0.109088	−	0.0244917i
$881$	28.4508			0.958533			0.479267	−	0.877669i	$-0.340903\pi$
$881$	28.4508			0.958533			0.479267	+	0.877669i	$0.340903\pi$
$882$	3.11803	−	9.59632i	0.104990	−	0.323125i
$883$	0.527864	−	0.383516i	0.0177640	−	0.0129063i	−0.578868	−	0.815421i	$-0.696505\pi$
$883$	0.527864	−	0.383516i	0.0177640	−	0.0129063i	0.596632	+	0.802515i	$0.296505\pi$
$884$	0.381966	+	0.277515i	0.0128469	+	0.00933382i
$885$	1.76393	+	5.42882i	0.0592939	+	0.182488i
$886$	10.0902	+	31.0543i	0.338986	+	1.04329i
$887$	−11.1074	−	8.06999i	−0.372950	−	0.270964i	0.385483	−	0.922715i	$-0.374035\pi$
$887$	−11.1074	−	8.06999i	−0.372950	−	0.270964i	−0.758433	+	0.651751i	$0.774035\pi$
$888$	5.85410	−	4.25325i	0.196451	−	0.142730i
$889$	−0.545085	+	1.67760i	−0.0182816	+	0.0562649i
$890$	−17.0344			−0.570996
$891$	4.08610	+	6.89442i	0.136890	+	0.230972i
$892$	25.3262			0.847985
$893$	−9.47871	+	29.1725i	−0.317193	+	0.976220i
$894$	−4.00000	+	2.90617i	−0.133780	+	0.0971969i
$895$	−11.3992	−	8.28199i	−0.381033	−	0.276837i
$896$	0.118034	+	0.363271i	0.00394324	+	0.0121360i
$897$	−1.61803	−	4.97980i	−0.0540246	−	0.166271i
$898$	−7.97214	−	5.79210i	−0.266034	−	0.193285i
$899$	7.23607	−	5.25731i	0.241336	−	0.175341i
$900$	−0.454915	+	1.40008i	−0.0151638	+	0.0466695i
$901$	−9.23607			−0.307698
$902$	−1.50000	+	16.0292i	−0.0499445	+	0.533714i
$903$	2.24922			0.0748495
$904$	6.09017	−	18.7436i	0.202556	−	0.623403i
$905$	−9.32624	+	6.77591i	−0.310015	+	0.225239i
$906$	−18.6525	−	13.5518i	−0.619687	−	0.450229i
$907$	5.76393	+	17.7396i	0.191388	+	0.589032i	1.00000		0.000689472i	$0.000219466\pi$
$907$	5.76393	+	17.7396i	0.191388	+	0.589032i	−0.808612	+	0.588343i	$0.799781\pi$
$908$	−2.32624	−	7.15942i	−0.0771989	−	0.237594i
$909$	−11.5623	−	8.40051i	−0.383497	−	0.278627i
$910$	0.190983	−	0.138757i	0.00633102	−	0.00459976i
$911$	−0.944272	+	2.90617i	−0.0312851	+	0.0962857i	−0.965480	−	0.260478i	$-0.916120\pi$
$911$	−0.944272	+	2.90617i	−0.0312851	+	0.0962857i	0.934195	+	0.356764i	$0.116120\pi$
$912$	−8.76393			−0.290203
$913$	−0.708204	+	7.56796i	−0.0234381	+	0.250463i
$914$	−34.5410			−1.14252
$915$	−3.41641	+	10.5146i	−0.112943	+	0.347603i
$916$	4.70820	−	3.42071i	0.155563	−	0.113023i
$917$	4.76393	+	3.46120i	0.157319	+	0.114299i
$918$	−1.30495	−	4.01623i	−0.0430698	−	0.132555i
$919$	−3.70820	−	11.4127i	−0.122322	−	0.376470i	0.871081	−	0.491139i	$-0.163419\pi$
$919$	−3.70820	−	11.4127i	−0.122322	−	0.376470i	−0.993404	+	0.114669i	$0.963419\pi$
$920$	5.54508	+	4.02874i	0.182816	+	0.132824i
$921$	−9.05573	+	6.57937i	−0.298396	+	0.216798i
$922$	−11.9098	+	36.6547i	−0.392229	+	1.20716i
$923$	5.41641			0.178283
$924$	0.798374	+	1.34708i	0.0262646	+	0.0443158i
$925$	5.85410			0.192482
$926$	−6.95492	+	21.4050i	−0.228553	+	0.703413i
$927$	5.15248	−	3.74349i	0.169230	−	0.122952i
$928$	−2.61803	−	1.90211i	−0.0859412	−	0.0624399i
$929$	6.09675	+	18.7639i	0.200028	+	0.615622i	0.999881	+	0.0154266i	$0.00491063\pi$
$929$	6.09675	+	18.7639i	0.200028	+	0.615622i	−0.799853	+	0.600196i	$0.795089\pi$
$930$	−1.05573	−	3.24920i	−0.0346187	−	0.106545i
$931$	39.3156	+	28.5645i	1.28852	+	0.936162i
$932$	−8.70820	+	6.32688i	−0.285247	+	0.207244i
$933$	−2.47214	+	7.60845i	−0.0809341	+	0.249090i
$934$	12.7639			0.417649
$935$	−2.47214	+	0.555029i	−0.0808475	+	0.0181514i
$936$	−0.909830			−0.0297387
$937$	−7.97871	+	24.5560i	−0.260653	+	0.802208i	0.732010	+	0.681294i	$0.238583\pi$
$937$	−7.97871	+	24.5560i	−0.260653	+	0.802208i	−0.992663	+	0.120914i	$0.961417\pi$
$938$	−1.61803	+	1.17557i	−0.0528307	+	0.0383837i
$939$	0.583592	+	0.424005i	0.0190448	+	0.0138369i
$940$	1.33688	+	4.11450i	0.0436043	+	0.134200i
$941$	−0.639320	−	1.96763i	−0.0208412	−	0.0641428i	0.940095	−	0.340913i	$-0.110736\pi$
$941$	−0.639320	−	1.96763i	−0.0208412	−	0.0641428i	−0.960936	+	0.276770i	$0.910736\pi$
$942$	6.38197	+	4.63677i	0.207936	+	0.151074i
$943$	−26.9164	+	19.5559i	−0.876519	+	0.636828i
$944$	1.42705	−	4.39201i	0.0464466	−	0.142948i
$945$	−2.11146			−0.0686857
$946$	−10.4377	+	11.8617i	−0.339359	+	0.385657i
$947$	−43.9574			−1.42842			−0.714212	−	0.699929i	$-0.753215\pi$
$947$	−43.9574			−1.42842			−0.714212	+	0.699929i	$0.753215\pi$
$948$	4.00000	−	12.3107i	0.129914	−	0.399834i
$949$	−5.85410	+	4.25325i	−0.190032	+	0.138066i
$950$	−5.73607	−	4.16750i	−0.186103	−	0.135211i
$951$	−11.7639	−	36.2057i	−0.381472	−	1.17405i
$952$	−0.0901699	−	0.277515i	−0.00292242	−	0.00899430i
$953$	−1.85410	−	1.34708i	−0.0600603	−	0.0436363i	0.557350	−	0.830278i	$-0.311818\pi$
$953$	−1.85410	−	1.34708i	−0.0600603	−	0.0436363i	−0.617410	+	0.786641i	$0.711818\pi$
$954$	14.3992	−	10.4616i	0.466191	−	0.338708i
$955$	0.437694	−	1.34708i	0.0141634	−	0.0435906i
$956$	18.4721			0.597432
$957$	−12.1803	−	5.25731i	−0.393734	−	0.169945i
$958$	19.5967			0.633142
$959$	−0.0901699	+	0.277515i	−0.00291174	+	0.00896141i
$960$	−1.00000	+	0.726543i	−0.0322749	+	0.0234491i
$961$	18.8992	+	13.7311i	0.609651	+	0.442938i
$962$	1.11803	+	3.44095i	0.0360469	+	0.110941i
$963$	7.49342	+	23.0624i	0.241472	+	0.743175i
$964$	−3.92705	−	2.85317i	−0.126482	−	0.0918944i
$965$	17.3262	−	12.5882i	0.557751	−	0.405230i
$966$	−1.00000	+	3.07768i	−0.0321745	+	0.0990228i
$967$	15.0902			0.485267			0.242634	−	0.970118i	$-0.421989\pi$
$967$	15.0902			0.485267			0.242634	+	0.970118i	$0.421989\pi$
$968$	−10.8090	−	2.04087i	−0.347415	−	0.0655961i
$969$	6.69505			0.215076
$970$	3.70820	−	11.4127i	0.119063	−	0.366439i
$971$	42.3435	−	30.7643i	1.35887	−	0.987274i	0.360350	−	0.932817i	$-0.382657\pi$
$971$	42.3435	−	30.7643i	1.35887	−	0.987274i	0.998516	−	0.0544570i	$-0.0173428\pi$
$972$	11.0000	+	7.99197i	0.352825	+	0.256342i
$973$	−1.75329	−	5.39607i	−0.0562079	−	0.172990i
$974$	5.88854	+	18.1231i	0.188681	+	0.580701i
$975$	0.618034	+	0.449028i	0.0197929	+	0.0143804i
$976$	7.23607	−	5.25731i	0.231621	−	0.168282i
$977$	5.61803	−	17.2905i	0.179737	−	0.553173i	−0.820081	−	0.572247i	$-0.806072\pi$
$977$	5.61803	−	17.2905i	0.179737	−	0.553173i	0.999818	+	0.0190740i	$0.00607182\pi$
$978$	3.41641			0.109245
$979$	51.8713	+	22.3888i	1.65781	+	0.715550i
$980$	6.85410			0.218946
$981$	−7.49342	+	23.0624i	−0.239247	+	0.736325i
$982$	15.7361	−	11.4329i	0.502158	−	0.364839i
$983$	15.3992	+	11.1882i	0.491158	+	0.356847i	0.805629	−	0.592420i	$-0.201827\pi$
$983$	15.3992	+	11.1882i	0.491158	+	0.356847i	−0.314472	+	0.949267i	$0.601827\pi$
$984$	−1.85410	−	5.70634i	−0.0591066	−	0.181911i
$985$	4.97214	+	15.3027i	0.158425	+	0.487583i
$986$	2.00000	+	1.45309i	0.0636930	+	0.0462757i
$987$	−1.65248	+	1.20059i	−0.0525989	+	0.0382153i
$988$	1.35410	−	4.16750i	0.0430797	−	0.132586i
$989$	−32.6525			−1.03829
$990$	3.22542	−	3.66547i	0.102511	−	0.116496i
$991$	−34.7214			−1.10296			−0.551480	−	0.834188i	$-0.685937\pi$
$991$	−34.7214			−1.10296			−0.551480	+	0.834188i	$0.685937\pi$
$992$	−0.854102	+	2.62866i	−0.0271178	+	0.0834599i
$993$	−16.6180	+	12.0737i	−0.527357	+	0.383148i
$994$	−2.70820	−	1.96763i	−0.0858990	−	0.0624093i
$995$	3.61803	+	11.1352i	0.114699	+	0.353008i
$996$	−0.875388	−	2.69417i	−0.0277377	−	0.0853680i
$997$	35.2148	+	25.5850i	1.11526	+	0.810286i	0.983484	−	0.180993i	$-0.0579311\pi$
$997$	35.2148	+	25.5850i	1.11526	+	0.810286i	0.131779	+	0.991279i	$0.457931\pi$
$998$	−9.54508	+	6.93491i	−0.302144	+	0.219521i
$999$	10.0000	−	30.7768i	0.316386	−	0.973736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.g.a.31.1	✓	4
3.2	odd	2		990.2.n.f.361.1		4
4.3	odd	2		880.2.bo.a.801.1		4
5.2	odd	4		550.2.ba.a.449.2		8
5.3	odd	4		550.2.ba.a.449.1		8
5.4	even	2		550.2.h.f.251.1		4
11.4	even	5		1210.2.a.t.1.1		2
11.5	even	5	inner	110.2.g.a.71.1	yes	4
11.7	odd	10		1210.2.a.p.1.1		2
33.5	odd	10		990.2.n.f.181.1		4
44.7	even	10		9680.2.a.bi.1.2		2
44.15	odd	10		9680.2.a.bh.1.2		2
44.27	odd	10		880.2.bo.a.401.1		4
55.4	even	10		6050.2.a.bu.1.2		2
55.27	odd	20		550.2.ba.a.49.1		8
55.29	odd	10		6050.2.a.cm.1.2		2
55.38	odd	20		550.2.ba.a.49.2		8
55.49	even	10		550.2.h.f.401.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.a.31.1	✓	4	1.1	even	1	trivial
110.2.g.a.71.1	yes	4	11.5	even	5	inner
550.2.h.f.251.1		4	5.4	even	2
550.2.h.f.401.1		4	55.49	even	10
550.2.ba.a.49.1		8	55.27	odd	20
550.2.ba.a.49.2		8	55.38	odd	20
550.2.ba.a.449.1		8	5.3	odd	4
550.2.ba.a.449.2		8	5.2	odd	4
880.2.bo.a.401.1		4	44.27	odd	10
880.2.bo.a.801.1		4	4.3	odd	2
990.2.n.f.181.1		4	33.5	odd	10
990.2.n.f.361.1		4	3.2	odd	2
1210.2.a.p.1.1		2	11.7	odd	10
1210.2.a.t.1.1		2	11.4	even	5
6050.2.a.bu.1.2		2	55.4	even	10
6050.2.a.cm.1.2		2	55.29	odd	10
9680.2.a.bh.1.2		2	44.15	odd	10
9680.2.a.bi.1.2		2	44.7	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.381966 - 1.17557i) q^{6} +(-0.309017 - 0.224514i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.454915 + 1.40008i) q^{9} -1.00000 q^{10} +(3.04508 + 1.31433i) q^{11} -1.23607 q^{12} +(0.190983 - 0.587785i) q^{13} +(-0.309017 + 0.224514i) q^{14} +(-1.00000 - 0.726543i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.236068 - 0.726543i) q^{17} +(1.19098 + 0.865300i) q^{18} +(-5.73607 + 4.16750i) q^{19} +(-0.309017 + 0.951057i) q^{20} -0.472136 q^{21} +(2.19098 - 2.48990i) q^{22} +6.85410 q^{23} +(-0.381966 + 1.17557i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.500000 - 0.363271i) q^{26} +(1.70820 + 5.25731i) q^{27} +(0.118034 + 0.363271i) q^{28} +(-2.61803 - 1.90211i) q^{29} +(-1.00000 + 0.726543i) q^{30} +(-0.854102 + 2.62866i) q^{31} +1.00000 q^{32} +(4.00000 - 0.898056i) q^{33} -0.763932 q^{34} +(-0.118034 + 0.363271i) q^{35} +(1.19098 - 0.865300i) q^{36} +(-4.73607 - 3.44095i) q^{37} +(2.19098 + 6.74315i) q^{38} +(-0.236068 - 0.726543i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-3.92705 + 2.85317i) q^{41} +(-0.145898 + 0.449028i) q^{42} -4.76393 q^{43} +(-1.69098 - 2.85317i) q^{44} +1.47214 q^{45} +(2.11803 - 6.51864i) q^{46} +(3.50000 - 2.54290i) q^{47} +(1.00000 + 0.726543i) q^{48} +(-2.11803 - 6.51864i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-0.763932 - 0.555029i) q^{51} +(-0.500000 + 0.363271i) q^{52} +(3.73607 - 11.4984i) q^{53} +5.52786 q^{54} +(0.309017 - 3.30220i) q^{55} +0.381966 q^{56} +(-2.70820 + 8.33499i) q^{57} +(-2.61803 + 1.90211i) q^{58} +(-3.73607 - 2.71441i) q^{59} +(0.381966 + 1.17557i) q^{60} +(-2.76393 - 8.50651i) q^{61} +(2.23607 + 1.62460i) q^{62} +(0.454915 - 0.330515i) q^{63} +(0.309017 - 0.951057i) q^{64} -0.618034 q^{65} +(0.381966 - 4.08174i) q^{66} +5.23607 q^{67} +(-0.236068 + 0.726543i) q^{68} +(6.85410 - 4.97980i) q^{69} +(0.309017 + 0.224514i) q^{70} +(2.70820 + 8.33499i) q^{71} +(-0.454915 - 1.40008i) q^{72} +(-9.47214 - 6.88191i) q^{73} +(-4.73607 + 3.44095i) q^{74} +(-0.381966 + 1.17557i) q^{75} +7.09017 q^{76} +(-0.645898 - 1.08981i) q^{77} -0.763932 q^{78} +(-3.23607 + 9.95959i) q^{79} +(0.809017 - 0.587785i) q^{80} +(1.95492 + 1.42033i) q^{81} +(1.50000 + 4.61653i) q^{82} +(0.708204 + 2.17963i) q^{83} +(0.381966 + 0.277515i) q^{84} +(-0.618034 + 0.449028i) q^{85} +(-1.47214 + 4.53077i) q^{86} -4.00000 q^{87} +(-3.23607 + 0.726543i) q^{88} +17.0344 q^{89} +(0.454915 - 1.40008i) q^{90} +(-0.190983 + 0.138757i) q^{91} +(-5.54508 - 4.02874i) q^{92} +(1.05573 + 3.24920i) q^{93} +(-1.33688 - 4.11450i) q^{94} +(5.73607 + 4.16750i) q^{95} +(1.00000 - 0.726543i) q^{96} +(-3.70820 + 11.4127i) q^{97} -6.85410 q^{98} +(-3.22542 + 3.66547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 4 q^{3} - q^{4} + q^{5} - 6 q^{6} + q^{7} - q^{8} - 13 q^{9} - 4 q^{10} + q^{11} + 4 q^{12} + 3 q^{13} + q^{14} - 4 q^{15} - q^{16} + 8 q^{17} + 7 q^{18} - 14 q^{19} + q^{20} + 16 q^{21}+ \cdots + 43 q^{99}+O(q^{100}) \) 4 * q - q^2 + 4 * q^3 - q^4 + q^5 - 6 * q^6 + q^7 - q^8 - 13 * q^9 - 4 * q^10 + q^11 + 4 * q^12 + 3 * q^13 + q^14 - 4 * q^15 - q^16 + 8 * q^17 + 7 * q^18 - 14 * q^19 + q^20 + 16 * q^21 + 11 * q^22 + 14 * q^23 - 6 * q^24 - q^25 - 2 * q^26 - 20 * q^27 - 4 * q^28 - 6 * q^29 - 4 * q^30 + 10 * q^31 + 4 * q^32 + 16 * q^33 - 12 * q^34 + 4 * q^35 + 7 * q^36 - 10 * q^37 + 11 * q^38 + 8 * q^39 + q^40 - 9 * q^41 - 14 * q^42 - 28 * q^43 - 9 * q^44 - 12 * q^45 + 4 * q^46 + 14 * q^47 + 4 * q^48 - 4 * q^49 - q^50 - 12 * q^51 - 2 * q^52 + 6 * q^53 + 40 * q^54 - q^55 + 6 * q^56 + 16 * q^57 - 6 * q^58 - 6 * q^59 + 6 * q^60 - 20 * q^61 + 13 * q^63 - q^64 + 2 * q^65 + 6 * q^66 + 12 * q^67 + 8 * q^68 + 14 * q^69 - q^70 - 16 * q^71 - 13 * q^72 - 20 * q^73 - 10 * q^74 - 6 * q^75 + 6 * q^76 - 16 * q^77 - 12 * q^78 - 4 * q^79 + q^80 + 19 * q^81 + 6 * q^82 - 24 * q^83 + 6 * q^84 + 2 * q^85 + 12 * q^86 - 16 * q^87 - 4 * q^88 + 10 * q^89 + 13 * q^90 - 3 * q^91 - 11 * q^92 + 40 * q^93 - 21 * q^94 + 14 * q^95 + 4 * q^96 + 12 * q^97 - 14 * q^98 + 43 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more