LMFDB - Embedded newform 154.2.f.c.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(15,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("154.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.22969619113$
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			141.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	154.141
Dual form			154.2.f.c.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.500000 + 0.363271i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.618034 + 1.90211i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 2.48990i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.500000 + 0.363271i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.618034 + 1.90211i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 2.48990i) q^{9} -2.00000 q^{10} +(-3.04508 + 1.31433i) q^{11} +0.618034 q^{12} +(-0.381966 + 1.17557i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-1.00000 - 0.726543i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.263932 + 0.812299i) q^{17} +(-2.11803 - 1.53884i) q^{18} +(5.54508 - 4.02874i) q^{19} +(0.618034 - 1.90211i) q^{20} -0.618034 q^{21} +(-0.309017 - 3.30220i) q^{22} -0.472136 q^{23} +(-0.190983 + 0.587785i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-1.00000 - 0.726543i) q^{26} +(-1.07295 - 3.30220i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(6.47214 + 4.70228i) q^{29} +(1.00000 - 0.726543i) q^{30} +(1.38197 - 4.25325i) q^{31} -1.00000 q^{32} +(1.04508 - 1.76336i) q^{33} -0.854102 q^{34} +(-0.618034 + 1.90211i) q^{35} +(2.11803 - 1.53884i) q^{36} +(-4.61803 - 3.35520i) q^{37} +(2.11803 + 6.51864i) q^{38} +(-0.236068 - 0.726543i) q^{39} +(1.61803 + 1.17557i) q^{40} +(4.73607 - 3.44095i) q^{41} +(0.190983 - 0.587785i) q^{42} +1.85410 q^{43} +(3.23607 + 0.726543i) q^{44} -5.23607 q^{45} +(0.145898 - 0.449028i) q^{46} +(9.47214 - 6.88191i) q^{47} +(-0.500000 - 0.363271i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-0.427051 - 0.310271i) q^{51} +(1.00000 - 0.726543i) q^{52} +(-4.00000 + 12.3107i) q^{53} +3.47214 q^{54} +(-4.38197 - 4.97980i) q^{55} +1.00000 q^{56} +(-1.30902 + 4.02874i) q^{57} +(-6.47214 + 4.70228i) q^{58} +(-8.78115 - 6.37988i) q^{59} +(0.381966 + 1.17557i) q^{60} +(-0.763932 - 2.35114i) q^{61} +(3.61803 + 2.62866i) q^{62} +(-2.11803 + 1.53884i) q^{63} +(0.309017 - 0.951057i) q^{64} -2.47214 q^{65} +(1.35410 + 1.53884i) q^{66} -10.0902 q^{67} +(0.263932 - 0.812299i) q^{68} +(0.236068 - 0.171513i) q^{69} +(-1.61803 - 1.17557i) q^{70} +(0.472136 + 1.45309i) q^{71} +(0.809017 + 2.48990i) q^{72} +(3.73607 + 2.71441i) q^{73} +(4.61803 - 3.35520i) q^{74} +(-0.190983 + 0.587785i) q^{75} -6.85410 q^{76} +(-3.23607 - 0.726543i) q^{77} +0.763932 q^{78} +(1.00000 - 3.07768i) q^{79} +(-1.61803 + 1.17557i) q^{80} +(-4.61803 - 3.35520i) q^{81} +(1.80902 + 5.56758i) q^{82} +(4.95492 + 15.2497i) q^{83} +(0.500000 + 0.363271i) q^{84} +(-1.38197 + 1.00406i) q^{85} +(-0.572949 + 1.76336i) q^{86} -4.94427 q^{87} +(-1.69098 + 2.85317i) q^{88} +0.326238 q^{89} +(1.61803 - 4.97980i) q^{90} +(-1.00000 + 0.726543i) q^{91} +(0.381966 + 0.277515i) q^{92} +(0.854102 + 2.62866i) q^{93} +(3.61803 + 11.1352i) q^{94} +(11.0902 + 8.05748i) q^{95} +(0.500000 - 0.363271i) q^{96} +(-3.04508 + 9.37181i) q^{97} -1.00000 q^{98} +(-0.809017 - 8.64527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} + q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^6 + q^7 + q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} + q^{7} + q^{8} - q^{9} - 8 q^{10} - q^{11} - 2 q^{12} - 6 q^{13} - q^{14} - 4 q^{15} - q^{16} + 10 q^{17} - 4 q^{18} + 11 q^{19} - 2 q^{20} + 2 q^{21} + q^{22} + 16 q^{23} - 3 q^{24} + q^{25} - 4 q^{26} - 11 q^{27} + q^{28} + 8 q^{29} + 4 q^{30} + 10 q^{31} - 4 q^{32} - 7 q^{33} + 10 q^{34} + 2 q^{35} + 4 q^{36} - 14 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 10 q^{41} + 3 q^{42} - 6 q^{43} + 4 q^{44} - 12 q^{45} + 14 q^{46} + 20 q^{47} - 2 q^{48} - q^{49} - q^{50} + 5 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 22 q^{55} + 4 q^{56} - 3 q^{57} - 8 q^{58} - 15 q^{59} + 6 q^{60} - 12 q^{61} + 10 q^{62} - 4 q^{63} - q^{64} + 8 q^{65} - 8 q^{66} - 18 q^{67} + 10 q^{68} - 8 q^{69} - 2 q^{70} - 16 q^{71} + q^{72} + 6 q^{73} + 14 q^{74} - 3 q^{75} - 14 q^{76} - 4 q^{77} + 12 q^{78} + 4 q^{79} - 2 q^{80} - 14 q^{81} + 5 q^{82} + 31 q^{83} + 2 q^{84} - 10 q^{85} - 9 q^{86} + 16 q^{87} - 9 q^{88} - 30 q^{89} + 2 q^{90} - 4 q^{91} + 6 q^{92} - 10 q^{93} + 10 q^{94} + 22 q^{95} + 2 q^{96} - q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^6 + q^7 + q^8 - q^9 - 8 * q^10 - q^11 - 2 * q^12 - 6 * q^13 - q^14 - 4 * q^15 - q^16 + 10 * q^17 - 4 * q^18 + 11 * q^19 - 2 * q^20 + 2 * q^21 + q^22 + 16 * q^23 - 3 * q^24 + q^25 - 4 * q^26 - 11 * q^27 + q^28 + 8 * q^29 + 4 * q^30 + 10 * q^31 - 4 * q^32 - 7 * q^33 + 10 * q^34 + 2 * q^35 + 4 * q^36 - 14 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 + 10 * q^41 + 3 * q^42 - 6 * q^43 + 4 * q^44 - 12 * q^45 + 14 * q^46 + 20 * q^47 - 2 * q^48 - q^49 - q^50 + 5 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 22 * q^55 + 4 * q^56 - 3 * q^57 - 8 * q^58 - 15 * q^59 + 6 * q^60 - 12 * q^61 + 10 * q^62 - 4 * q^63 - q^64 + 8 * q^65 - 8 * q^66 - 18 * q^67 + 10 * q^68 - 8 * q^69 - 2 * q^70 - 16 * q^71 + q^72 + 6 * q^73 + 14 * q^74 - 3 * q^75 - 14 * q^76 - 4 * q^77 + 12 * q^78 + 4 * q^79 - 2 * q^80 - 14 * q^81 + 5 * q^82 + 31 * q^83 + 2 * q^84 - 10 * q^85 - 9 * q^86 + 16 * q^87 - 9 * q^88 - 30 * q^89 + 2 * q^90 - 4 * q^91 + 6 * q^92 - 10 * q^93 + 10 * q^94 + 22 * q^95 + 2 * q^96 - q^97 - 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−0.500000	+	0.363271i	−0.288675	+	0.209735i	−0.722692	−	0.691170i	$-0.757096\pi$
$3$	−0.500000	+	0.363271i	−0.288675	+	0.209735i	0.434017	+	0.900905i	$0.357096\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.618034	+	1.90211i	0.276393	+	0.850651i	0.988847	+	0.148932i	$0.0475836\pi$
$5$	0.618034	+	1.90211i	0.276393	+	0.850651i	−0.712454	+	0.701719i	$0.752416\pi$
$6$	−0.190983	−	0.587785i	−0.0779685	−	0.239962i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.809017	+	2.48990i	−0.269672	+	0.829966i
$10$	−2.00000			−0.632456
$11$	−3.04508	+	1.31433i	−0.918128	+	0.396285i
$11$	−3.04508	+	1.31433i	−0.918128	+	0.396285i
$12$	0.618034			0.178411
$13$	−0.381966	+	1.17557i	−0.105938	+	0.326045i	−0.989950	−	0.141421i	$-0.954833\pi$
$13$	−0.381966	+	1.17557i	−0.105938	+	0.326045i	0.884011	+	0.467466i	$0.154833\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	−1.00000	−	0.726543i	−0.258199	−	0.187592i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.263932	+	0.812299i	0.0640129	+	0.197012i	0.977948	−	0.208849i	$-0.0669718\pi$
$17$	0.263932	+	0.812299i	0.0640129	+	0.197012i	−0.913935	+	0.405861i	$0.866972\pi$
$18$	−2.11803	−	1.53884i	−0.499225	−	0.362708i
$19$	5.54508	−	4.02874i	1.27213	−	0.924256i	0.272844	−	0.962058i	$-0.412036\pi$
$19$	5.54508	−	4.02874i	1.27213	−	0.924256i	0.999285	+	0.0378018i	$0.0120356\pi$
$20$	0.618034	−	1.90211i	0.138197	−	0.425325i
$21$	−0.618034			−0.134866
$22$	−0.309017	−	3.30220i	−0.0658826	−	0.704031i
$23$	−0.472136			−0.0984472			−0.0492236	−	0.998788i	$-0.515675\pi$
$23$	−0.472136			−0.0984472			−0.0492236	+	0.998788i	$0.515675\pi$
$24$	−0.190983	+	0.587785i	−0.0389842	+	0.119981i
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$	−1.00000	−	0.726543i	−0.196116	−	0.142487i
$27$	−1.07295	−	3.30220i	−0.206489	−	0.635508i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	6.47214	+	4.70228i	1.20185	+	0.873192i	0.994465	−	0.105069i	$-0.0335062\pi$
$29$	6.47214	+	4.70228i	1.20185	+	0.873192i	0.207380	+	0.978260i	$0.433506\pi$
$30$	1.00000	−	0.726543i	0.182574	−	0.132648i
$31$	1.38197	−	4.25325i	0.248208	−	0.763907i	−0.746884	−	0.664955i	$-0.768451\pi$
$31$	1.38197	−	4.25325i	0.248208	−	0.763907i	0.995092	−	0.0989523i	$-0.0315491\pi$
$32$	−1.00000			−0.176777
$33$	1.04508	−	1.76336i	0.181926	−	0.306961i
$34$	−0.854102			−0.146477
$35$	−0.618034	+	1.90211i	−0.104467	+	0.321516i
$36$	2.11803	−	1.53884i	0.353006	−	0.256474i
$37$	−4.61803	−	3.35520i	−0.759200	−	0.551591i	0.139465	−	0.990227i	$-0.455462\pi$
$37$	−4.61803	−	3.35520i	−0.759200	−	0.551591i	−0.898665	+	0.438636i	$0.855462\pi$
$38$	2.11803	+	6.51864i	0.343590	+	1.05746i
$39$	−0.236068	−	0.726543i	−0.0378011	−	0.116340i
$40$	1.61803	+	1.17557i	0.255834	+	0.185874i
$41$	4.73607	−	3.44095i	0.739650	−	0.537387i	−0.152952	−	0.988234i	$-0.548878\pi$
$41$	4.73607	−	3.44095i	0.739650	−	0.537387i	0.892601	+	0.450847i	$0.148878\pi$
$42$	0.190983	−	0.587785i	0.0294693	−	0.0906972i
$43$	1.85410			0.282748			0.141374	−	0.989956i	$-0.454848\pi$
$43$	1.85410			0.282748			0.141374	+	0.989956i	$0.454848\pi$
$44$	3.23607	+	0.726543i	0.487856	+	0.109530i
$45$	−5.23607			−0.780547
$46$	0.145898	−	0.449028i	0.0215115	−	0.0662056i
$47$	9.47214	−	6.88191i	1.38165	−	1.00383i	0.384929	−	0.922946i	$-0.374226\pi$
$47$	9.47214	−	6.88191i	1.38165	−	1.00383i	0.996724	−	0.0808837i	$-0.0257742\pi$
$48$	−0.500000	−	0.363271i	−0.0721688	−	0.0524337i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	−0.427051	−	0.310271i	−0.0597991	−	0.0434466i
$52$	1.00000	−	0.726543i	0.138675	−	0.100753i
$53$	−4.00000	+	12.3107i	−0.549442	+	1.69101i	0.160744	+	0.986996i	$0.448610\pi$
$53$	−4.00000	+	12.3107i	−0.549442	+	1.69101i	−0.710187	+	0.704013i	$0.751390\pi$
$54$	3.47214			0.472498
$55$	−4.38197	−	4.97980i	−0.590864	−	0.671476i
$56$	1.00000			0.133631
$57$	−1.30902	+	4.02874i	−0.173384	+	0.533620i
$58$	−6.47214	+	4.70228i	−0.849833	+	0.617440i
$59$	−8.78115	−	6.37988i	−1.14321	−	0.830590i	−0.155646	−	0.987813i	$-0.549746\pi$
$59$	−8.78115	−	6.37988i	−1.14321	−	0.830590i	−0.987563	+	0.157223i	$0.949746\pi$
$60$	0.381966	+	1.17557i	0.0493116	+	0.151765i
$61$	−0.763932	−	2.35114i	−0.0978115	−	0.301033i	0.890165	−	0.455639i	$-0.150589\pi$
$61$	−0.763932	−	2.35114i	−0.0978115	−	0.301033i	−0.987976	+	0.154606i	$0.950589\pi$
$62$	3.61803	+	2.62866i	0.459491	+	0.333840i
$63$	−2.11803	+	1.53884i	−0.266847	+	0.193876i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−2.47214			−0.306631
$66$	1.35410	+	1.53884i	0.166678	+	0.189418i
$67$	−10.0902			−1.23271			−0.616355	−	0.787468i	$-0.711391\pi$
$67$	−10.0902			−1.23271			−0.616355	+	0.787468i	$0.711391\pi$
$68$	0.263932	−	0.812299i	0.0320065	−	0.0985058i
$69$	0.236068	−	0.171513i	0.0284192	−	0.0206478i
$70$	−1.61803	−	1.17557i	−0.193392	−	0.140508i
$71$	0.472136	+	1.45309i	0.0560322	+	0.172449i	0.975156	−	0.221520i	$-0.0711017\pi$
$71$	0.472136	+	1.45309i	0.0560322	+	0.172449i	−0.919124	+	0.393969i	$0.871102\pi$
$72$	0.809017	+	2.48990i	0.0953436	+	0.293437i
$73$	3.73607	+	2.71441i	0.437274	+	0.317698i	0.784551	−	0.620065i	$-0.212894\pi$
$73$	3.73607	+	2.71441i	0.437274	+	0.317698i	−0.347277	+	0.937763i	$0.612894\pi$
$74$	4.61803	−	3.35520i	0.536836	−	0.390034i
$75$	−0.190983	+	0.587785i	−0.0220528	+	0.0678716i
$76$	−6.85410			−0.786219
$77$	−3.23607	−	0.726543i	−0.368784	−	0.0827972i
$78$	0.763932			0.0864983
$79$	1.00000	−	3.07768i	0.112509	−	0.346266i	−0.878911	−	0.476987i	$-0.841729\pi$
$79$	1.00000	−	3.07768i	0.112509	−	0.346266i	0.991419	+	0.130720i	$0.0417290\pi$
$80$	−1.61803	+	1.17557i	−0.180902	+	0.131433i
$81$	−4.61803	−	3.35520i	−0.513115	−	0.372800i
$82$	1.80902	+	5.56758i	0.199773	+	0.614837i
$83$	4.95492	+	15.2497i	0.543873	+	1.67387i	0.723655	+	0.690161i	$0.242460\pi$
$83$	4.95492	+	15.2497i	0.543873	+	1.67387i	−0.179783	+	0.983706i	$0.557540\pi$
$84$	0.500000	+	0.363271i	0.0545545	+	0.0396361i
$85$	−1.38197	+	1.00406i	−0.149895	+	0.108905i
$86$	−0.572949	+	1.76336i	−0.0617827	+	0.190148i
$87$	−4.94427			−0.530082
$88$	−1.69098	+	2.85317i	−0.180259	+	0.304149i
$89$	0.326238			0.0345812			0.0172906	−	0.999851i	$-0.494496\pi$
$89$	0.326238			0.0345812			0.0172906	+	0.999851i	$0.494496\pi$
$90$	1.61803	−	4.97980i	0.170556	−	0.524917i
$91$	−1.00000	+	0.726543i	−0.104828	+	0.0761624i
$92$	0.381966	+	0.277515i	0.0398227	+	0.0289329i
$93$	0.854102	+	2.62866i	0.0885662	+	0.272579i
$94$	3.61803	+	11.1352i	0.373172	+	1.14850i
$95$	11.0902	+	8.05748i	1.13783	+	0.826680i
$96$	0.500000	−	0.363271i	0.0510310	−	0.0370762i
$97$	−3.04508	+	9.37181i	−0.309182	+	0.951563i	0.668902	+	0.743351i	$0.266765\pi$
$97$	−3.04508	+	9.37181i	−0.309182	+	0.951563i	−0.978084	+	0.208212i	$0.933235\pi$
$98$	−1.00000			−0.101015
$99$	−0.809017	−	8.64527i	−0.0813093	−	0.868882i
$100$	−1.00000			−0.100000
$101$	3.90983	−	12.0332i	0.389043	−	1.19735i	−0.544462	−	0.838785i	$-0.683266\pi$
$101$	3.90983	−	12.0332i	0.389043	−	1.19735i	0.933505	−	0.358565i	$-0.116734\pi$
$102$	0.427051	−	0.310271i	0.0422843	−	0.0307214i
$103$	−3.00000	−	2.17963i	−0.295599	−	0.214765i	0.430094	−	0.902784i	$-0.358480\pi$
$103$	−3.00000	−	2.17963i	−0.295599	−	0.214765i	−0.725693	+	0.688019i	$0.758480\pi$
$104$	0.381966	+	1.17557i	0.0374548	+	0.115274i
$105$	−0.381966	−	1.17557i	−0.0372761	−	0.114724i
$106$	−10.4721	−	7.60845i	−1.01714	−	0.738998i
$107$	−6.73607	+	4.89404i	−0.651200	+	0.473125i	−0.863680	−	0.504041i	$-0.831846\pi$
$107$	−6.73607	+	4.89404i	−0.651200	+	0.473125i	0.212480	+	0.977166i	$0.431846\pi$
$108$	−1.07295	+	3.30220i	−0.103245	+	0.317754i
$109$	12.1803			1.16666			0.583332	−	0.812233i	$-0.301748\pi$
$109$	12.1803			1.16666			0.583332	+	0.812233i	$0.301748\pi$
$110$	6.09017	−	2.62866i	0.580675	−	0.250632i
$111$	3.52786			0.334850
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	−1.92705	+	1.40008i	−0.181282	+	0.131709i	−0.674725	−	0.738069i	$-0.735738\pi$
$113$	−1.92705	+	1.40008i	−0.181282	+	0.131709i	0.493444	+	0.869778i	$0.335738\pi$
$114$	−3.42705	−	2.48990i	−0.320973	−	0.233200i
$115$	−0.291796	−	0.898056i	−0.0272101	−	0.0837441i
$116$	−2.47214	−	7.60845i	−0.229532	−	0.706427i
$117$	−2.61803	−	1.90211i	−0.242037	−	0.175850i
$118$	8.78115	−	6.37988i	0.808371	−	0.587316i
$119$	−0.263932	+	0.812299i	−0.0241946	+	0.0744633i
$120$	−1.23607			−0.112837
$121$	7.54508	−	8.00448i	0.685917	−	0.727680i
$122$	2.47214			0.223817
$123$	−1.11803	+	3.44095i	−0.100810	+	0.310260i
$124$	−3.61803	+	2.62866i	−0.324909	+	0.236060i
$125$	9.70820	+	7.05342i	0.868328	+	0.630877i
$126$	−0.809017	−	2.48990i	−0.0720730	−	0.221818i
$127$	−4.09017	−	12.5882i	−0.362944	−	1.11703i	−0.951259	−	0.308394i	$-0.900208\pi$
$127$	−4.09017	−	12.5882i	−0.362944	−	1.11703i	0.588315	−	0.808632i	$-0.299792\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−0.927051	+	0.673542i	−0.0816223	+	0.0593021i
$130$	0.763932	−	2.35114i	0.0670013	−	0.206209i
$131$	−4.56231			−0.398611			−0.199305	−	0.979937i	$-0.563869\pi$
$131$	−4.56231			−0.398611			−0.199305	+	0.979937i	$0.563869\pi$
$132$	−1.88197	+	0.812299i	−0.163804	+	0.0707016i
$133$	6.85410			0.594326
$134$	3.11803	−	9.59632i	0.269357	−	0.828996i
$135$	5.61803	−	4.08174i	0.483523	−	0.351300i
$136$	0.690983	+	0.502029i	0.0592513	+	0.0430486i
$137$	−1.13525	−	3.49396i	−0.0969914	−	0.298509i	0.890776	−	0.454442i	$-0.150161\pi$
$137$	−1.13525	−	3.49396i	−0.0969914	−	0.298509i	−0.987768	+	0.155934i	$0.950161\pi$
$138$	0.0901699	+	0.277515i	0.00767578	+	0.0236236i
$139$	4.47214	+	3.24920i	0.379322	+	0.275593i	0.761066	−	0.648675i	$-0.224676\pi$
$139$	4.47214	+	3.24920i	0.379322	+	0.275593i	−0.381744	+	0.924268i	$0.624676\pi$
$140$	1.61803	−	1.17557i	0.136749	−	0.0993538i
$141$	−2.23607	+	6.88191i	−0.188311	+	0.579561i
$142$	−1.52786			−0.128216
$143$	−0.381966	−	4.08174i	−0.0319416	−	0.341332i
$144$	−2.61803			−0.218169
$145$	−4.94427	+	15.2169i	−0.410599	+	1.26370i
$146$	−3.73607	+	2.71441i	−0.309199	+	0.224646i
$147$	−0.500000	−	0.363271i	−0.0412393	−	0.0299621i
$148$	1.76393	+	5.42882i	0.144994	+	0.446247i
$149$	−4.70820	−	14.4904i	−0.385711	−	1.18710i	−0.935963	−	0.352098i	$-0.885468\pi$
$149$	−4.70820	−	14.4904i	−0.385711	−	1.18710i	0.550252	−	0.834999i	$-0.314532\pi$
$150$	−0.500000	−	0.363271i	−0.0408248	−	0.0296610i
$151$	12.7082	−	9.23305i	1.03418	−	0.751375i	0.0650382	−	0.997883i	$-0.479283\pi$
$151$	12.7082	−	9.23305i	1.03418	−	0.751375i	0.969141	+	0.246508i	$0.0792831\pi$
$152$	2.11803	−	6.51864i	0.171795	−	0.528731i
$153$	−2.23607			−0.180775
$154$	1.69098	−	2.85317i	0.136263	−	0.229915i
$155$	8.94427			0.718421
$156$	−0.236068	+	0.726543i	−0.0189006	+	0.0581700i
$157$	5.85410	−	4.25325i	0.467208	−	0.339447i	−0.329144	−	0.944280i	$-0.606760\pi$
$157$	5.85410	−	4.25325i	0.467208	−	0.339447i	0.796352	+	0.604833i	$0.206760\pi$
$158$	2.61803	+	1.90211i	0.208280	+	0.151324i
$159$	−2.47214	−	7.60845i	−0.196053	−	0.603390i
$160$	−0.618034	−	1.90211i	−0.0488599	−	0.150375i
$161$	−0.381966	−	0.277515i	−0.0301031	−	0.0218712i
$162$	4.61803	−	3.35520i	0.362827	−	0.263609i
$163$	−3.17376	+	9.76784i	−0.248588	+	0.765076i	0.746437	+	0.665456i	$0.231763\pi$
$163$	−3.17376	+	9.76784i	−0.248588	+	0.765076i	−0.995026	+	0.0996202i	$0.968237\pi$
$164$	−5.85410			−0.457129
$165$	4.00000	+	0.898056i	0.311400	+	0.0699136i
$166$	−16.0344			−1.24451
$167$	2.32624	−	7.15942i	0.180010	−	0.554013i	−0.819817	−	0.572625i	$-0.805925\pi$
$167$	2.32624	−	7.15942i	0.180010	−	0.554013i	0.999827	+	0.0186126i	$0.00592492\pi$
$168$	−0.500000	+	0.363271i	−0.0385758	+	0.0280270i
$169$	9.28115	+	6.74315i	0.713935	+	0.518704i
$170$	−0.527864	−	1.62460i	−0.0404853	−	0.124601i
$171$	5.54508	+	17.0660i	0.424043	+	1.30507i
$172$	−1.50000	−	1.08981i	−0.114374	−	0.0830975i
$173$	−12.7082	+	9.23305i	−0.966187	+	0.701976i	−0.954579	−	0.297957i	$-0.903695\pi$
$173$	−12.7082	+	9.23305i	−0.966187	+	0.701976i	−0.0116075	+	0.999933i	$0.503695\pi$
$174$	1.52786	−	4.70228i	0.115827	−	0.356479i
$175$	1.00000			0.0755929
$176$	−2.19098	−	2.48990i	−0.165152	−	0.187683i
$177$	6.70820			0.504219
$178$	−0.100813	+	0.310271i	−0.00755626	+	0.0232558i
$179$	−10.9271	+	7.93897i	−0.816726	+	0.593386i	−0.915773	−	0.401697i	$-0.868421\pi$
$179$	−10.9271	+	7.93897i	−0.816726	+	0.593386i	0.0990467	+	0.995083i	$0.468421\pi$
$180$	4.23607	+	3.07768i	0.315738	+	0.229397i
$181$	−7.18034	−	22.0988i	−0.533710	−	1.64259i	−0.746419	−	0.665476i	$-0.768229\pi$
$181$	−7.18034	−	22.0988i	−0.533710	−	1.64259i	0.212709	−	0.977116i	$-0.431771\pi$
$182$	−0.381966	−	1.17557i	−0.0283132	−	0.0871391i
$183$	1.23607	+	0.898056i	0.0913728	+	0.0663862i
$184$	−0.381966	+	0.277515i	−0.0281589	+	0.0204586i
$185$	3.52786	−	10.8576i	0.259374	−	0.798270i
$186$	−2.76393			−0.202661
$187$	−1.87132	−	2.12663i	−0.136845	−	0.155514i
$188$	−11.7082			−0.853909
$189$	1.07295	−	3.30220i	0.0780456	−	0.240200i
$190$	−11.0902	+	8.05748i	−0.804565	+	0.584551i
$191$	−2.85410	−	2.07363i	−0.206516	−	0.150042i	0.479720	−	0.877422i	$-0.340738\pi$
$191$	−2.85410	−	2.07363i	−0.206516	−	0.150042i	−0.686236	+	0.727379i	$0.740738\pi$
$192$	0.190983	+	0.587785i	0.0137830	+	0.0424197i
$193$	−2.90983	−	8.95554i	−0.209454	−	0.644634i	−0.999501	−	0.0315871i	$-0.989944\pi$
$193$	−2.90983	−	8.95554i	−0.209454	−	0.644634i	0.790047	−	0.613046i	$-0.210056\pi$
$194$	−7.97214	−	5.79210i	−0.572366	−	0.415848i
$195$	1.23607	−	0.898056i	0.0885167	−	0.0643111i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−12.4721			−0.888603			−0.444301	−	0.895877i	$-0.646548\pi$
$197$	−12.4721			−0.888603			−0.444301	+	0.895877i	$0.646548\pi$
$198$	8.47214	+	1.90211i	0.602088	+	0.135177i
$199$	2.18034			0.154560			0.0772801	−	0.997009i	$-0.475376\pi$
$199$	2.18034			0.154560			0.0772801	+	0.997009i	$0.475376\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	5.04508	−	3.66547i	0.355853	−	0.258542i
$202$	10.2361	+	7.43694i	0.720207	+	0.523261i
$203$	2.47214	+	7.60845i	0.173510	+	0.534009i
$204$	0.163119	+	0.502029i	0.0114206	+	0.0351490i
$205$	9.47214	+	6.88191i	0.661563	+	0.480653i
$206$	3.00000	−	2.17963i	0.209020	−	0.151862i
$207$	0.381966	−	1.17557i	0.0265485	−	0.0817078i
$208$	−1.23607			−0.0857059
$209$	−11.5902	+	19.5559i	−0.801709	+	1.35271i
$210$	1.23607			0.0852968
$211$	−8.37132	+	25.7643i	−0.576306	+	1.77369i	0.0553842	+	0.998465i	$0.482362\pi$
$211$	−8.37132	+	25.7643i	−0.576306	+	1.77369i	−0.631690	+	0.775221i	$0.717638\pi$
$212$	10.4721	−	7.60845i	0.719229	−	0.522551i
$213$	−0.763932	−	0.555029i	−0.0523438	−	0.0380300i
$214$	−2.57295	−	7.91872i	−0.175883	−	0.541313i
$215$	1.14590	+	3.52671i	0.0781496	+	0.240520i
$216$	−2.80902	−	2.04087i	−0.191129	−	0.138864i
$217$	3.61803	−	2.62866i	0.245608	−	0.178445i
$218$	−3.76393	+	11.5842i	−0.254926	+	0.784580i
$219$	−2.85410			−0.192862
$220$	0.618034	+	6.60440i	0.0416678	+	0.445268i
$221$	−1.05573			−0.0710160
$222$	−1.09017	+	3.35520i	−0.0731674	+	0.225186i
$223$	−7.61803	+	5.53483i	−0.510141	+	0.370639i	−0.812877	−	0.582435i	$-0.802100\pi$
$223$	−7.61803	+	5.53483i	−0.510141	+	0.370639i	0.302736	+	0.953074i	$0.402100\pi$
$224$	−0.809017	−	0.587785i	−0.0540547	−	0.0392731i
$225$	0.809017	+	2.48990i	0.0539345	+	0.165993i
$226$	−0.736068	−	2.26538i	−0.0489625	−	0.150691i
$227$	5.07295	+	3.68571i	0.336703	+	0.244629i	0.743270	−	0.668992i	$-0.233274\pi$
$227$	5.07295	+	3.68571i	0.336703	+	0.244629i	−0.406566	+	0.913621i	$0.633274\pi$
$228$	3.42705	−	2.48990i	0.226962	−	0.164898i
$229$	−8.41641	+	25.9030i	−0.556172	+	1.71172i	0.136656	+	0.990619i	$0.456364\pi$
$229$	−8.41641	+	25.9030i	−0.556172	+	1.71172i	−0.692828	+	0.721103i	$0.743636\pi$
$230$	0.944272			0.0622634
$231$	1.88197	−	0.812299i	0.123824	−	0.0534454i
$232$	8.00000			0.525226
$233$	5.89919	−	18.1558i	0.386469	−	1.18943i	−0.548941	−	0.835861i	$-0.684969\pi$
$233$	5.89919	−	18.1558i	0.386469	−	1.18943i	0.935409	−	0.353567i	$-0.115031\pi$
$234$	2.61803	−	1.90211i	0.171146	−	0.124345i
$235$	18.9443	+	13.7638i	1.23579	+	0.897853i
$236$	3.35410	+	10.3229i	0.218333	+	0.671961i
$237$	0.618034	+	1.90211i	0.0401456	+	0.123556i
$238$	−0.690983	−	0.502029i	−0.0447898	−	0.0325417i
$239$	−11.0902	+	8.05748i	−0.717363	+	0.521195i	−0.885541	−	0.464562i	$-0.846212\pi$
$239$	−11.0902	+	8.05748i	−0.717363	+	0.521195i	0.168177	+	0.985757i	$0.446212\pi$
$240$	0.381966	−	1.17557i	0.0246558	−	0.0758827i
$241$	17.7984			1.14649			0.573247	−	0.819383i	$-0.305684\pi$
$241$	17.7984			1.14649			0.573247	+	0.819383i	$0.305684\pi$
$242$	5.28115	+	9.64932i	0.339485	+	0.620282i
$243$	13.9443			0.894525
$244$	−0.763932	+	2.35114i	−0.0489057	+	0.150516i
$245$	−1.61803	+	1.17557i	−0.103372	+	0.0751044i
$246$	−2.92705	−	2.12663i	−0.186622	−	0.135589i
$247$	2.61803	+	8.05748i	0.166582	+	0.512685i
$248$	−1.38197	−	4.25325i	−0.0877549	−	0.270082i
$249$	−8.01722	−	5.82485i	−0.508071	−	0.369135i
$250$	−9.70820	+	7.05342i	−0.614001	+	0.446098i
$251$	4.00000	−	12.3107i	0.252478	−	0.777047i	−0.741838	−	0.670579i	$-0.766046\pi$
$251$	4.00000	−	12.3107i	0.252478	−	0.777047i	0.994316	−	0.106468i	$-0.0339541\pi$
$252$	2.61803			0.164921
$253$	1.43769	−	0.620541i	0.0903871	−	0.0390131i
$254$	13.2361			0.830505
$255$	0.326238	−	1.00406i	0.0204298	−	0.0628765i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−18.9164	−	13.7436i	−1.17997	−	0.857301i	−0.187804	−	0.982206i	$-0.560137\pi$
$257$	−18.9164	−	13.7436i	−1.17997	−	0.857301i	−0.992169	+	0.124906i	$0.960137\pi$
$258$	−0.354102	−	1.08981i	−0.0220454	−	0.0678488i
$259$	−1.76393	−	5.42882i	−0.109605	−	0.337331i
$260$	2.00000	+	1.45309i	0.124035	+	0.0901165i
$261$	−16.9443	+	12.3107i	−1.04882	+	0.762015i
$262$	1.40983	−	4.33901i	0.0870996	−	0.268065i
$263$	4.94427			0.304877			0.152438	−	0.988313i	$-0.451287\pi$
$263$	4.94427			0.304877			0.152438	+	0.988313i	$0.451287\pi$
$264$	−0.190983	−	2.04087i	−0.0117542	−	0.125607i
$265$	−25.8885			−1.59032
$266$	−2.11803	+	6.51864i	−0.129865	+	0.399683i
$267$	−0.163119	+	0.118513i	−0.00998272	+	0.00725287i
$268$	8.16312	+	5.93085i	0.498642	+	0.362285i
$269$	−9.09017	−	27.9767i	−0.554237	−	1.70577i	−0.697949	−	0.716148i	$-0.745904\pi$
$269$	−9.09017	−	27.9767i	−0.554237	−	1.70577i	0.143711	−	0.989620i	$-0.454096\pi$
$270$	2.14590	+	6.60440i	0.130595	+	0.401931i
$271$	−10.2361	−	7.43694i	−0.621797	−	0.451762i	0.231752	−	0.972775i	$-0.425554\pi$
$271$	−10.2361	−	7.43694i	−0.621797	−	0.451762i	−0.853549	+	0.521013i	$0.825554\pi$
$272$	−0.690983	+	0.502029i	−0.0418970	+	0.0304400i
$273$	0.236068	−	0.726543i	0.0142875	−	0.0439724i
$274$	3.67376			0.221940
$275$	−1.69098	+	2.85317i	−0.101970	+	0.172053i
$276$	−0.291796			−0.0175641
$277$	5.79837	−	17.8456i	0.348391	−	1.07224i	−0.611353	−	0.791358i	$-0.709374\pi$
$277$	5.79837	−	17.8456i	0.348391	−	1.07224i	0.959744	−	0.280878i	$-0.0906256\pi$
$278$	−4.47214	+	3.24920i	−0.268221	+	0.194874i
$279$	9.47214	+	6.88191i	0.567082	+	0.412009i
$280$	0.618034	+	1.90211i	0.0369346	+	0.113673i
$281$	−4.57295	−	14.0741i	−0.272799	−	0.839590i	−0.989793	−	0.142510i	$-0.954483\pi$
$281$	−4.57295	−	14.0741i	−0.272799	−	0.839590i	0.716994	−	0.697079i	$-0.245517\pi$
$282$	−5.85410	−	4.25325i	−0.348607	−	0.253278i
$283$	−23.4164	+	17.0130i	−1.39196	+	1.01132i	−0.396314	+	0.918115i	$0.629711\pi$
$283$	−23.4164	+	17.0130i	−1.39196	+	1.01132i	−0.995647	+	0.0932038i	$0.970289\pi$
$284$	0.472136	−	1.45309i	0.0280161	−	0.0862247i
$285$	−8.47214			−0.501846
$286$	4.00000	+	0.898056i	0.236525	+	0.0531032i
$287$	5.85410			0.345557
$288$	0.809017	−	2.48990i	0.0476718	−	0.146719i
$289$	13.1631	−	9.56357i	0.774301	−	0.562563i
$290$	−12.9443	−	9.40456i	−0.760114	−	0.552255i
$291$	−1.88197	−	5.79210i	−0.110323	−	0.339539i
$292$	−1.42705	−	4.39201i	−0.0835118	−	0.257023i
$293$	−3.09017	−	2.24514i	−0.180530	−	0.131162i	0.493850	−	0.869547i	$-0.335589\pi$
$293$	−3.09017	−	2.24514i	−0.180530	−	0.131162i	−0.674380	+	0.738384i	$0.735589\pi$
$294$	0.500000	−	0.363271i	0.0291606	−	0.0211864i
$295$	6.70820	−	20.6457i	0.390567	−	1.20204i
$296$	−5.70820			−0.331783
$297$	7.60739	+	8.64527i	0.441426	+	0.501649i
$298$	15.2361			0.882602
$299$	0.180340	−	0.555029i	0.0104293	−	0.0320982i
$300$	0.500000	−	0.363271i	0.0288675	−	0.0209735i
$301$	1.50000	+	1.08981i	0.0864586	+	0.0628158i
$302$	4.85410	+	14.9394i	0.279322	+	0.859665i
$303$	2.41641	+	7.43694i	0.138819	+	0.427241i
$304$	5.54508	+	4.02874i	0.318032	+	0.231064i
$305$	4.00000	−	2.90617i	0.229039	−	0.166407i
$306$	0.690983	−	2.12663i	0.0395009	−	0.121571i
$307$	−15.3820			−0.877895			−0.438948	−	0.898513i	$-0.644649\pi$
$307$	−15.3820			−0.877895			−0.438948	+	0.898513i	$0.644649\pi$
$308$	2.19098	+	2.48990i	0.124843	+	0.141875i
$309$	2.29180			0.130376
$310$	−2.76393	+	8.50651i	−0.156981	+	0.483137i
$311$	14.3262	−	10.4086i	0.812366	−	0.590219i	−0.102149	−	0.994769i	$-0.532572\pi$
$311$	14.3262	−	10.4086i	0.812366	−	0.590219i	0.914516	+	0.404550i	$0.132572\pi$
$312$	−0.618034	−	0.449028i	−0.0349893	−	0.0254212i
$313$	4.26393	+	13.1230i	0.241012	+	0.741758i	0.996267	+	0.0863268i	$0.0275129\pi$
$313$	4.26393	+	13.1230i	0.241012	+	0.741758i	−0.755255	+	0.655431i	$0.772487\pi$
$314$	2.23607	+	6.88191i	0.126189	+	0.388369i
$315$	−4.23607	−	3.07768i	−0.238675	−	0.173408i
$316$	−2.61803	+	1.90211i	−0.147276	+	0.107002i
$317$	3.70820	−	11.4127i	0.208273	−	0.641000i	−0.791290	−	0.611442i	$-0.790590\pi$
$317$	3.70820	−	11.4127i	0.208273	−	0.641000i	0.999563	−	0.0295583i	$-0.00941007\pi$
$318$	8.00000			0.448618
$319$	−25.8885	−	5.81234i	−1.44948	−	0.325429i
$320$	2.00000			0.111803
$321$	1.59017	−	4.89404i	0.0887546	−	0.273159i
$322$	0.381966	−	0.277515i	0.0212861	−	0.0154653i
$323$	4.73607	+	3.44095i	0.263522	+	0.191460i
$324$	1.76393	+	5.42882i	0.0979962	+	0.301601i
$325$	0.381966	+	1.17557i	0.0211877	+	0.0652089i
$326$	−8.30902	−	6.03685i	−0.460194	−	0.334350i
$327$	−6.09017	+	4.42477i	−0.336787	+	0.244690i
$328$	1.80902	−	5.56758i	0.0998863	−	0.307418i
$329$	11.7082			0.645494
$330$	−2.09017	+	3.52671i	−0.115060	+	0.194139i
$331$	29.2705			1.60885			0.804426	−	0.594052i	$-0.202473\pi$
$331$	29.2705			1.60885			0.804426	+	0.594052i	$0.202473\pi$
$332$	4.95492	−	15.2497i	0.271936	−	0.836934i
$333$	12.0902	−	8.78402i	0.662537	−	0.481361i
$334$	6.09017	+	4.42477i	0.333239	+	0.242113i
$335$	−6.23607	−	19.1926i	−0.340713	−	1.04861i
$336$	−0.190983	−	0.587785i	−0.0104190	−	0.0320663i
$337$	−20.8713	−	15.1639i	−1.13693	−	0.826030i	−0.150244	−	0.988649i	$-0.548006\pi$
$337$	−20.8713	−	15.1639i	−1.13693	−	0.826030i	−0.986689	+	0.162618i	$0.948006\pi$
$338$	−9.28115	+	6.74315i	−0.504828	+	0.366779i
$339$	0.454915	−	1.40008i	0.0247076	−	0.0760422i
$340$	1.70820			0.0926404
$341$	1.38197	+	14.7679i	0.0748377	+	0.799725i
$342$	−17.9443			−0.970315
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	1.50000	−	1.08981i	0.0808746	−	0.0587588i
$345$	0.472136	+	0.343027i	0.0254189	+	0.0184679i
$346$	−4.85410	−	14.9394i	−0.260958	−	0.803147i
$347$	5.82624	+	17.9313i	0.312769	+	0.962604i	0.976663	+	0.214777i	$0.0689025\pi$
$347$	5.82624	+	17.9313i	0.312769	+	0.962604i	−0.663894	+	0.747826i	$0.731098\pi$
$348$	4.00000	+	2.90617i	0.214423	+	0.155787i
$349$	25.4164	−	18.4661i	1.36051	−	0.988468i	0.362097	−	0.932141i	$-0.382061\pi$
$349$	25.4164	−	18.4661i	1.36051	−	0.988468i	0.998412	−	0.0563272i	$-0.0179390\pi$
$350$	−0.309017	+	0.951057i	−0.0165177	+	0.0508361i
$351$	4.29180			0.229079
$352$	3.04508	−	1.31433i	0.162304	−	0.0700539i
$353$	−32.2705			−1.71759			−0.858793	−	0.512323i	$-0.828785\pi$
$353$	−32.2705			−1.71759			−0.858793	+	0.512323i	$0.828785\pi$
$354$	−2.07295	+	6.37988i	−0.110176	+	0.339087i
$355$	−2.47214	+	1.79611i	−0.131207	+	0.0953277i
$356$	−0.263932	−	0.191758i	−0.0139884	−	0.0101631i
$357$	−0.163119	−	0.502029i	−0.00863317	−	0.0265702i
$358$	−4.17376	−	12.8455i	−0.220590	−	0.678907i
$359$	−10.3262	−	7.50245i	−0.544998	−	0.395964i	0.280940	−	0.959725i	$-0.409354\pi$
$359$	−10.3262	−	7.50245i	−0.544998	−	0.395964i	−0.825938	+	0.563761i	$0.809354\pi$
$360$	−4.23607	+	3.07768i	−0.223260	+	0.162208i
$361$	8.64590	−	26.6093i	0.455047	−	1.40049i
$362$	23.2361			1.22126
$363$	−0.864745	+	6.74315i	−0.0453873	+	0.353924i
$364$	1.23607			0.0647876
$365$	−2.85410	+	8.78402i	−0.149391	+	0.459777i
$366$	−1.23607	+	0.898056i	−0.0646103	+	0.0469421i
$367$	9.70820	+	7.05342i	0.506764	+	0.368186i	0.811595	−	0.584221i	$-0.198600\pi$
$367$	9.70820	+	7.05342i	0.506764	+	0.368186i	−0.304831	+	0.952407i	$0.598600\pi$
$368$	−0.145898	−	0.449028i	−0.00760546	−	0.0234072i
$369$	4.73607	+	14.5761i	0.246550	+	0.758802i
$370$	9.23607	+	6.71040i	0.480160	+	0.348857i
$371$	−10.4721	+	7.60845i	−0.543686	+	0.395011i
$372$	0.854102	−	2.62866i	0.0442831	−	0.136289i
$373$	21.5279			1.11467			0.557335	−	0.830288i	$-0.311824\pi$
$373$	21.5279			1.11467			0.557335	+	0.830288i	$0.311824\pi$
$374$	2.60081	−	1.12257i	0.134485	−	0.0580467i
$375$	−7.41641			−0.382982
$376$	3.61803	−	11.1352i	0.186586	−	0.574252i
$377$	−8.00000	+	5.81234i	−0.412021	+	0.299351i
$378$	2.80902	+	2.04087i	0.144480	+	0.104971i
$379$	−1.89919	−	5.84510i	−0.0975547	−	0.300242i	0.890356	−	0.455264i	$-0.150455\pi$
$379$	−1.89919	−	5.84510i	−0.0975547	−	0.300242i	−0.987911	+	0.155022i	$0.950455\pi$
$380$	−4.23607	−	13.0373i	−0.217306	−	0.668798i
$381$	6.61803	+	4.80828i	0.339052	+	0.246336i
$382$	2.85410	−	2.07363i	0.146029	−	0.106096i
$383$	10.7082	−	32.9565i	0.547164	−	1.68400i	−0.168626	−	0.985680i	$-0.553933\pi$
$383$	10.7082	−	32.9565i	0.547164	−	1.68400i	0.715789	−	0.698316i	$-0.246067\pi$
$384$	−0.618034			−0.0315389
$385$	−0.618034	−	6.60440i	−0.0314979	−	0.336591i
$386$	9.41641			0.479283
$387$	−1.50000	+	4.61653i	−0.0762493	+	0.234671i
$388$	7.97214	−	5.79210i	0.404724	−	0.294049i
$389$	2.00000	+	1.45309i	0.101404	+	0.0736743i	0.637332	−	0.770589i	$-0.280038\pi$
$389$	2.00000	+	1.45309i	0.101404	+	0.0736743i	−0.535928	+	0.844264i	$0.680038\pi$
$390$	0.472136	+	1.45309i	0.0239075	+	0.0735798i
$391$	−0.124612	−	0.383516i	−0.00630189	−	0.0193952i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$	2.28115	−	1.65735i	0.115069	−	0.0836025i
$394$	3.85410	−	11.8617i	0.194167	−	0.597584i
$395$	6.47214			0.325649
$396$	−4.42705	+	7.46969i	−0.222468	+	0.375366i
$397$	17.5967			0.883155			0.441578	−	0.897223i	$-0.354419\pi$
$397$	17.5967			0.883155			0.441578	+	0.897223i	$0.354419\pi$
$398$	−0.673762	+	2.07363i	−0.0337726	+	0.103942i
$399$	−3.42705	+	2.48990i	−0.171567	+	0.124651i
$400$	0.809017	+	0.587785i	0.0404508	+	0.0293893i
$401$	6.28115	+	19.3314i	0.313666	+	0.965364i	0.976300	+	0.216421i	$0.0694384\pi$
$401$	6.28115	+	19.3314i	0.313666	+	0.965364i	−0.662634	+	0.748943i	$0.730562\pi$
$402$	1.92705	+	5.93085i	0.0961126	+	0.295804i
$403$	4.47214	+	3.24920i	0.222773	+	0.161854i
$404$	−10.2361	+	7.43694i	−0.509263	+	0.370002i
$405$	3.52786	−	10.8576i	0.175301	−	0.539521i
$406$	−8.00000			−0.397033
$407$	18.4721	+	4.14725i	0.915630	+	0.205572i
$408$	−0.527864			−0.0261332
$409$	−8.14590	+	25.0705i	−0.402789	+	1.23966i	0.519939	+	0.854203i	$0.325955\pi$
$409$	−8.14590	+	25.0705i	−0.402789	+	1.23966i	−0.922728	+	0.385453i	$0.874045\pi$
$410$	−9.47214	+	6.88191i	−0.467795	+	0.339873i
$411$	1.83688	+	1.33457i	0.0906067	+	0.0658296i
$412$	1.14590	+	3.52671i	0.0564543	+	0.173749i
$413$	−3.35410	−	10.3229i	−0.165045	−	0.507955i
$414$	1.00000	+	0.726543i	0.0491473	+	0.0357076i
$415$	−25.9443	+	18.8496i	−1.27355	+	0.925291i
$416$	0.381966	−	1.17557i	0.0187274	−	0.0576371i
$417$	−3.41641			−0.167302
$418$	−15.0172	−	17.0660i	−0.734516	−	0.834726i
$419$	−26.5066			−1.29493			−0.647466	−	0.762095i	$-0.724171\pi$
$419$	−26.5066			−1.29493			−0.647466	+	0.762095i	$0.724171\pi$
$420$	−0.381966	+	1.17557i	−0.0186380	+	0.0573620i
$421$	−3.61803	+	2.62866i	−0.176332	+	0.128113i	−0.672451	−	0.740142i	$-0.734758\pi$
$421$	−3.61803	+	2.62866i	−0.176332	+	0.128113i	0.496118	+	0.868255i	$0.334758\pi$
$422$	−21.9164	−	15.9232i	−1.06687	−	0.775129i
$423$	9.47214	+	29.1522i	0.460551	+	1.41743i
$424$	4.00000	+	12.3107i	0.194257	+	0.597862i
$425$	0.690983	+	0.502029i	0.0335176	+	0.0243520i
$426$	0.763932	−	0.555029i	0.0370126	−	0.0268912i
$427$	0.763932	−	2.35114i	0.0369693	−	0.113780i
$428$	8.32624			0.402464
$429$	1.67376	+	1.90211i	0.0808100	+	0.0918349i
$430$	−3.70820			−0.178825
$431$	−2.05573	+	6.32688i	−0.0990209	+	0.304755i	−0.988281	−	0.152647i	$-0.951220\pi$
$431$	−2.05573	+	6.32688i	−0.0990209	+	0.304755i	0.889260	+	0.457402i	$0.151220\pi$
$432$	2.80902	−	2.04087i	0.135149	−	0.0981914i
$433$	25.4894	+	18.5191i	1.22494	+	0.889971i	0.996501	−	0.0835868i	$-0.0266376\pi$
$433$	25.4894	+	18.5191i	1.22494	+	0.889971i	0.228440	+	0.973558i	$0.426638\pi$
$434$	1.38197	+	4.25325i	0.0663365	+	0.204163i
$435$	−3.05573	−	9.40456i	−0.146511	−	0.450914i
$436$	−9.85410	−	7.15942i	−0.471926	−	0.342874i
$437$	−2.61803	+	1.90211i	−0.125238	+	0.0909904i
$438$	0.881966	−	2.71441i	0.0421420	−	0.129700i
$439$	0.944272			0.0450676			0.0225338	−	0.999746i	$-0.492827\pi$
$439$	0.944272			0.0450676			0.0225338	+	0.999746i	$0.492827\pi$
$440$	−6.47214	−	1.45309i	−0.308547	−	0.0692731i
$441$	−2.61803			−0.124668
$442$	0.326238	−	1.00406i	0.0155176	−	0.0477581i
$443$	−16.9164	+	12.2905i	−0.803723	+	0.583939i	−0.912004	−	0.410182i	$-0.865465\pi$
$443$	−16.9164	+	12.2905i	−0.803723	+	0.583939i	0.108281	+	0.994120i	$0.465465\pi$
$444$	−2.85410	−	2.07363i	−0.135450	−	0.0984100i
$445$	0.201626	+	0.620541i	0.00955799	+	0.0294165i
$446$	−2.90983	−	8.95554i	−0.137784	−	0.424057i
$447$	7.61803	+	5.53483i	0.360321	+	0.261788i
$448$	0.809017	−	0.587785i	0.0382225	−	0.0277702i
$449$	−7.02786	+	21.6295i	−0.331665	+	1.02076i	0.636676	+	0.771131i	$0.280309\pi$
$449$	−7.02786	+	21.6295i	−0.331665	+	1.02076i	−0.968341	+	0.249630i	$0.919691\pi$
$450$	−2.61803			−0.123415
$451$	−9.89919	+	16.7027i	−0.466135	+	0.786502i
$452$	2.38197			0.112038
$453$	−3.00000	+	9.23305i	−0.140952	+	0.433807i
$454$	−5.07295	+	3.68571i	−0.238085	+	0.172979i
$455$	−2.00000	−	1.45309i	−0.0937614	−	0.0681217i
$456$	1.30902	+	4.02874i	0.0613003	+	0.188663i
$457$	−2.77458	−	8.53926i	−0.129789	−	0.399450i	0.864954	−	0.501851i	$-0.167347\pi$
$457$	−2.77458	−	8.53926i	−0.129789	−	0.399450i	−0.994743	+	0.102401i	$0.967347\pi$
$458$	−22.0344	−	16.0090i	−1.02960	−	0.748050i
$459$	2.39919	−	1.74311i	0.111984	−	0.0813615i
$460$	−0.291796	+	0.898056i	−0.0136051	+	0.0418721i
$461$	35.0132			1.63073			0.815363	−	0.578951i	$-0.196538\pi$
$461$	35.0132			1.63073			0.815363	+	0.578951i	$0.196538\pi$
$462$	0.190983	+	2.04087i	0.00888533	+	0.0949499i
$463$	29.2361			1.35872			0.679358	−	0.733807i	$-0.262259\pi$
$463$	29.2361			1.35872			0.679358	+	0.733807i	$0.262259\pi$
$464$	−2.47214	+	7.60845i	−0.114766	+	0.353214i
$465$	−4.47214	+	3.24920i	−0.207390	+	0.150678i
$466$	15.4443	+	11.2209i	0.715442	+	0.519799i
$467$	−4.29180	−	13.2088i	−0.198601	−	0.611230i	−0.999916	−	0.0129873i	$-0.995866\pi$
$467$	−4.29180	−	13.2088i	−0.198601	−	0.611230i	0.801315	−	0.598243i	$-0.204134\pi$
$468$	1.00000	+	3.07768i	0.0462250	+	0.142266i
$469$	−8.16312	−	5.93085i	−0.376938	−	0.273861i
$470$	−18.9443	+	13.7638i	−0.873834	+	0.634878i
$471$	−1.38197	+	4.25325i	−0.0636776	+	0.195980i
$472$	−10.8541			−0.499601
$473$	−5.64590	+	2.43690i	−0.259599	+	0.112049i
$474$	−2.00000			−0.0918630
$475$	2.11803	−	6.51864i	0.0971821	−	0.299096i
$476$	0.690983	−	0.502029i	0.0316712	−	0.0230104i
$477$	−27.4164	−	19.9192i	−1.25531	−	0.912037i
$478$	−4.23607	−	13.0373i	−0.193753	−	0.596311i
$479$	7.00000	+	21.5438i	0.319838	+	0.984361i	0.973717	+	0.227761i	$0.0731406\pi$
$479$	7.00000	+	21.5438i	0.319838	+	0.984361i	−0.653879	+	0.756599i	$0.726859\pi$
$480$	1.00000	+	0.726543i	0.0456435	+	0.0331620i
$481$	5.70820	−	4.14725i	0.260272	−	0.189098i
$482$	−5.50000	+	16.9273i	−0.250518	+	0.771016i
$483$	0.291796			0.0132772
$484$	−10.8090	+	2.04087i	−0.491319	+	0.0927668i
$485$	−19.7082			−0.894903
$486$	−4.30902	+	13.2618i	−0.195461	+	0.601567i
$487$	−35.0344	+	25.4540i	−1.58756	+	1.15343i	−0.680245	+	0.732985i	$0.738126\pi$
$487$	−35.0344	+	25.4540i	−1.58756	+	1.15343i	−0.907317	+	0.420446i	$0.861874\pi$
$488$	−2.00000	−	1.45309i	−0.0905357	−	0.0657781i
$489$	−1.96149	−	6.03685i	−0.0887018	−	0.272996i
$490$	−0.618034	−	1.90211i	−0.0279199	−	0.0859287i
$491$	−5.50000	−	3.99598i	−0.248212	−	0.180336i	0.456722	−	0.889609i	$-0.349023\pi$
$491$	−5.50000	−	3.99598i	−0.248212	−	0.180336i	−0.704934	+	0.709273i	$0.749023\pi$
$492$	2.92705	−	2.12663i	0.131962	−	0.0958758i
$493$	−2.11146	+	6.49839i	−0.0950952	+	0.292673i
$494$	−8.47214			−0.381179
$495$	15.9443	−	6.88191i	0.716642	−	0.309319i
$496$	4.47214			0.200805
$497$	−0.472136	+	1.45309i	−0.0211782	+	0.0651798i
$498$	8.01722	−	5.82485i	0.359260	−	0.261018i
$499$	4.26393	+	3.09793i	0.190880	+	0.138682i	0.679121	−	0.734027i	$-0.262361\pi$
$499$	4.26393	+	3.09793i	0.190880	+	0.138682i	−0.488241	+	0.872709i	$0.662361\pi$
$500$	−3.70820	−	11.4127i	−0.165836	−	0.510390i
$501$	1.43769	+	4.42477i	0.0642314	+	0.197684i
$502$	10.4721	+	7.60845i	0.467394	+	0.339582i
$503$	22.3262	−	16.2210i	0.995478	−	0.723257i	0.0343639	−	0.999409i	$-0.489059\pi$
$503$	22.3262	−	16.2210i	0.995478	−	0.723257i	0.961114	+	0.276152i	$0.0890595\pi$
$504$	−0.809017	+	2.48990i	−0.0360365	+	0.110909i
$505$	25.3050			1.12606
$506$	0.145898	+	1.55909i	0.00648596	+	0.0693098i
$507$	−7.09017			−0.314886
$508$	−4.09017	+	12.5882i	−0.181472	+	0.558513i
$509$	−5.09017	+	3.69822i	−0.225618	+	0.163921i	−0.694852	−	0.719153i	$-0.744530\pi$
$509$	−5.09017	+	3.69822i	−0.225618	+	0.163921i	0.469234	+	0.883074i	$0.344530\pi$
$510$	0.854102	+	0.620541i	0.0378203	+	0.0274780i
$511$	1.42705	+	4.39201i	0.0631290	+	0.194291i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−19.2533	−	13.9883i	−0.850053	−	0.617600i
$514$	18.9164	−	13.7436i	0.834367	−	0.606203i
$515$	2.29180	−	7.05342i	0.100989	−	0.310811i
$516$	1.14590			0.0504453
$517$	−19.7984	+	33.4055i	−0.870731	+	1.46917i
$518$	5.70820			0.250804
$519$	3.00000	−	9.23305i	0.131685	−	0.405286i
$520$	−2.00000	+	1.45309i	−0.0877058	+	0.0637220i
$521$	4.54508	+	3.30220i	0.199124	+	0.144672i	0.682879	−	0.730531i	$-0.260728\pi$
$521$	4.54508	+	3.30220i	0.199124	+	0.144672i	−0.483755	+	0.875203i	$0.660728\pi$
$522$	−6.47214	−	19.9192i	−0.283278	−	0.871839i
$523$	−10.1180	−	31.1401i	−0.442431	−	1.36166i	−0.885277	−	0.465064i	$-0.846031\pi$
$523$	−10.1180	−	31.1401i	−0.442431	−	1.36166i	0.442846	−	0.896598i	$-0.353969\pi$
$524$	3.69098	+	2.68166i	0.161241	+	0.117149i
$525$	−0.500000	+	0.363271i	−0.0218218	+	0.0158545i
$526$	−1.52786	+	4.70228i	−0.0666180	+	0.205029i
$527$	3.81966			0.166387
$528$	2.00000	+	0.449028i	0.0870388	+	0.0195414i
$529$	−22.7771			−0.990308
$530$	8.00000	−	24.6215i	0.347498	−	1.06949i
$531$	22.9894	−	16.7027i	0.997653	−	0.724837i
$532$	−5.54508	−	4.02874i	−0.240410	−	0.174668i
$533$	2.23607	+	6.88191i	0.0968549	+	0.298089i
$534$	−0.0623059	−	0.191758i	−0.00269624	−	0.00829817i
$535$	−13.4721	−	9.78808i	−0.582451	−	0.423176i
$536$	−8.16312	+	5.93085i	−0.352593	+	0.256174i
$537$	2.57953	−	7.93897i	0.111315	−	0.342592i
$538$	29.4164			1.26823
$539$	−2.19098	−	2.48990i	−0.0943723	−	0.107248i
$540$	−6.94427			−0.298834
$541$	−7.65248	+	23.5519i	−0.329006	+	1.01258i	0.640594	+	0.767880i	$0.278688\pi$
$541$	−7.65248	+	23.5519i	−0.329006	+	1.01258i	−0.969600	+	0.244696i	$0.921312\pi$
$542$	10.2361	−	7.43694i	0.439677	−	0.319444i
$543$	11.6180	+	8.44100i	0.498578	+	0.362238i
$544$	−0.263932	−	0.812299i	−0.0113160	−	0.0348270i
$545$	7.52786	+	23.1684i	0.322458	+	0.992425i
$546$	0.618034	+	0.449028i	0.0264494	+	0.0192166i
$547$	12.7812	−	9.28605i	0.546483	−	0.397043i	−0.280004	−	0.959999i	$-0.590336\pi$
$547$	12.7812	−	9.28605i	0.546483	−	0.397043i	0.826487	+	0.562956i	$0.190336\pi$
$548$	−1.13525	+	3.49396i	−0.0484957	+	0.149254i
$549$	6.47214			0.276224
$550$	−2.19098	−	2.48990i	−0.0934238	−	0.106170i
$551$	54.8328			2.33596
$552$	0.0901699	−	0.277515i	0.00383789	−	0.0118118i
$553$	2.61803	−	1.90211i	0.111330	−	0.0808861i
$554$	15.1803	+	11.0292i	0.644951	+	0.468584i
$555$	2.18034	+	6.71040i	0.0925503	+	0.284840i
$556$	−1.70820	−	5.25731i	−0.0724440	−	0.222960i
$557$	14.4721	+	10.5146i	0.613204	+	0.445519i	0.850541	−	0.525909i	$-0.176275\pi$
$557$	14.4721	+	10.5146i	0.613204	+	0.445519i	−0.237337	+	0.971427i	$0.576275\pi$
$558$	−9.47214	+	6.88191i	−0.400987	+	0.291334i
$559$	−0.708204	+	2.17963i	−0.0299538	+	0.0921884i
$560$	−2.00000			−0.0845154
$561$	1.70820	+	0.383516i	0.0721204	+	0.0161920i
$562$	14.7984			0.624232
$563$	12.9549	−	39.8711i	0.545985	−	1.68037i	−0.172653	−	0.984983i	$-0.555234\pi$
$563$	12.9549	−	39.8711i	0.545985	−	1.68037i	0.718637	−	0.695385i	$-0.244766\pi$
$564$	5.85410	−	4.25325i	0.246502	−	0.179094i
$565$	−3.85410	−	2.80017i	−0.162143	−	0.117804i
$566$	−8.94427	−	27.5276i	−0.375956	−	1.15707i
$567$	−1.76393	−	5.42882i	−0.0740782	−	0.227989i
$568$	1.23607	+	0.898056i	0.0518643	+	0.0376816i
$569$	7.45492	−	5.41631i	0.312526	−	0.227064i	−0.420453	−	0.907314i	$-0.638129\pi$
$569$	7.45492	−	5.41631i	0.312526	−	0.227064i	0.732980	+	0.680250i	$0.238129\pi$
$570$	2.61803	−	8.05748i	0.109657	−	0.337491i
$571$	−34.8328			−1.45771			−0.728854	−	0.684669i	$-0.759947\pi$
$571$	−34.8328			−1.45771			−0.728854	+	0.684669i	$0.759947\pi$
$572$	−2.09017	+	3.52671i	−0.0873944	+	0.147459i
$573$	2.18034			0.0910850
$574$	−1.80902	+	5.56758i	−0.0755069	+	0.232386i
$575$	−0.381966	+	0.277515i	−0.0159291	+	0.0115732i
$576$	2.11803	+	1.53884i	0.0882514	+	0.0641184i
$577$	7.08359	+	21.8011i	0.294894	+	0.907590i	0.983257	+	0.182224i	$0.0583295\pi$
$577$	7.08359	+	21.8011i	0.294894	+	0.907590i	−0.688363	+	0.725366i	$0.741670\pi$
$578$	5.02786	+	15.4742i	0.209132	+	0.643641i
$579$	4.70820	+	3.42071i	0.195666	+	0.142160i
$580$	12.9443	−	9.40456i	0.537482	−	0.390503i
$581$	−4.95492	+	15.2497i	−0.205565	+	0.632663i
$582$	6.09017			0.252446
$583$	−4.00000	−	42.7445i	−0.165663	−	1.77030i
$584$	4.61803			0.191096
$585$	2.00000	−	6.15537i	0.0826898	−	0.254493i
$586$	3.09017	−	2.24514i	0.127654	−	0.0927459i
$587$	−2.16312	−	1.57160i	−0.0892815	−	0.0648668i	0.542249	−	0.840218i	$-0.317573\pi$
$587$	−2.16312	−	1.57160i	−0.0892815	−	0.0648668i	−0.631530	+	0.775351i	$0.717573\pi$
$588$	0.190983	+	0.587785i	0.00787601	+	0.0242399i
$589$	−9.47214	−	29.1522i	−0.390293	−	1.20120i
$590$	17.5623	+	12.7598i	0.723029	+	0.525311i
$591$	6.23607	−	4.53077i	0.256518	−	0.186371i
$592$	1.76393	−	5.42882i	0.0724972	−	0.223123i
$593$	0.0901699			0.00370284			0.00185142	−	0.999998i	$-0.499411\pi$
$593$	0.0901699			0.00370284			0.00185142	+	0.999998i	$0.499411\pi$
$594$	−10.5729	+	4.56352i	−0.433813	+	0.187244i
$595$	−1.70820			−0.0700295
$596$	−4.70820	+	14.4904i	−0.192856	+	0.593548i
$597$	−1.09017	+	0.792055i	−0.0446177	+	0.0324166i
$598$	0.472136	+	0.343027i	0.0193071	+	0.0140274i
$599$	−2.00000	−	6.15537i	−0.0817178	−	0.251501i	0.901847	−	0.432055i	$-0.142211\pi$
$599$	−2.00000	−	6.15537i	−0.0817178	−	0.251501i	−0.983565	+	0.180553i	$0.942211\pi$
$600$	0.190983	+	0.587785i	0.00779685	+	0.0239962i
$601$	−23.2082	−	16.8617i	−0.946682	−	0.687805i	0.00333749	−	0.999994i	$-0.498938\pi$
$601$	−23.2082	−	16.8617i	−0.946682	−	0.687805i	−0.950020	+	0.312189i	$0.898938\pi$
$602$	−1.50000	+	1.08981i	−0.0611354	+	0.0444175i
$603$	8.16312	−	25.1235i	0.332428	−	1.02311i
$604$	−15.7082			−0.639158
$605$	19.8885	+	9.40456i	0.808584	+	0.382350i
$606$	−7.81966			−0.317652
$607$	−0.909830	+	2.80017i	−0.0369289	+	0.113655i	−0.967822	−	0.251637i	$-0.919031\pi$
$607$	−0.909830	+	2.80017i	−0.0369289	+	0.113655i	0.930893	+	0.365293i	$0.119031\pi$
$608$	−5.54508	+	4.02874i	−0.224883	+	0.163387i
$609$	−4.00000	−	2.90617i	−0.162088	−	0.117764i
$610$	1.52786	+	4.70228i	0.0618614	+	0.190390i
$611$	4.47214	+	13.7638i	0.180923	+	0.556825i
$612$	1.80902	+	1.31433i	0.0731252	+	0.0531286i
$613$	−6.61803	+	4.80828i	−0.267300	+	0.194205i	−0.713359	−	0.700799i	$-0.752827\pi$
$613$	−6.61803	+	4.80828i	−0.267300	+	0.194205i	0.446059	+	0.895003i	$0.352827\pi$
$614$	4.75329	−	14.6291i	0.191827	−	0.590383i
$615$	−7.23607			−0.291786
$616$	−3.04508	+	1.31433i	−0.122690	+	0.0529558i
$617$	30.1591			1.21416			0.607079	−	0.794642i	$-0.292341\pi$
$617$	30.1591			1.21416			0.607079	+	0.794642i	$0.292341\pi$
$618$	−0.708204	+	2.17963i	−0.0284881	+	0.0876775i
$619$	−12.1631	+	8.83702i	−0.488877	+	0.355190i	−0.804752	−	0.593611i	$-0.797702\pi$
$619$	−12.1631	+	8.83702i	−0.488877	+	0.355190i	0.315875	+	0.948801i	$0.397702\pi$
$620$	−7.23607	−	5.25731i	−0.290607	−	0.211139i
$621$	0.506578	+	1.55909i	0.0203283	+	0.0625640i
$622$	5.47214	+	16.8415i	0.219413	+	0.675283i
$623$	0.263932	+	0.191758i	0.0105742	+	0.00768262i
$624$	0.618034	−	0.449028i	0.0247412	−	0.0179755i
$625$	−5.87132	+	18.0701i	−0.234853	+	0.722803i
$626$	−13.7984			−0.551494
$627$	−1.30902	−	13.9883i	−0.0522771	−	0.558640i
$628$	−7.23607			−0.288751
$629$	1.50658	−	4.63677i	0.0600712	−	0.184880i
$630$	4.23607	−	3.07768i	0.168769	−	0.122618i
$631$	−24.8885	−	18.0826i	−0.990797	−	0.719856i	−0.0307017	−	0.999529i	$-0.509774\pi$
$631$	−24.8885	−	18.0826i	−0.990797	−	0.719856i	−0.960096	+	0.279672i	$0.909774\pi$
$632$	−1.00000	−	3.07768i	−0.0397779	−	0.122424i
$633$	−5.17376	−	15.9232i	−0.205639	−	0.632890i
$634$	9.70820	+	7.05342i	0.385562	+	0.280127i
$635$	21.4164	−	15.5599i	0.849884	−	0.617477i
$636$	−2.47214	+	7.60845i	−0.0980266	+	0.301695i
$637$	−1.23607			−0.0489748
$638$	13.5279	−	22.8254i	0.535573	−	0.903665i
$639$	−4.00000			−0.158238
$640$	−0.618034	+	1.90211i	−0.0244299	+	0.0751876i
$641$	11.7361	−	8.52675i	0.463547	−	0.336786i	−0.331374	−	0.943499i	$-0.607512\pi$
$641$	11.7361	−	8.52675i	0.463547	−	0.336786i	0.794921	+	0.606713i	$0.207512\pi$
$642$	4.16312	+	3.02468i	0.164305	+	0.119375i
$643$	−5.13525	−	15.8047i	−0.202515	−	0.623276i	−0.999806	−	0.0196818i	$-0.993735\pi$
$643$	−5.13525	−	15.8047i	−0.202515	−	0.623276i	0.797292	−	0.603594i	$-0.206265\pi$
$644$	0.145898	+	0.449028i	0.00574919	+	0.0176942i
$645$	−1.85410	−	1.34708i	−0.0730052	−	0.0530414i
$646$	−4.73607	+	3.44095i	−0.186338	+	0.135383i
$647$	−3.27051	+	10.0656i	−0.128577	+	0.395719i	−0.994536	−	0.104396i	$-0.966709\pi$
$647$	−3.27051	+	10.0656i	−0.128577	+	0.395719i	0.865959	+	0.500115i	$0.166709\pi$
$648$	−5.70820			−0.224239
$649$	35.1246	+	7.88597i	1.37876	+	0.309551i
$650$	−1.23607			−0.0484826
$651$	−0.854102	+	2.62866i	−0.0334749	+	0.103025i
$652$	8.30902	−	6.03685i	0.325406	−	0.236421i
$653$	−31.0344	−	22.5478i	−1.21447	−	0.882365i	−0.218842	−	0.975760i	$-0.570228\pi$
$653$	−31.0344	−	22.5478i	−1.21447	−	0.882365i	−0.995629	+	0.0933950i	$0.970228\pi$
$654$	−2.32624	−	7.15942i	−0.0909631	−	0.279956i
$655$	−2.81966	−	8.67802i	−0.110173	−	0.339078i
$656$	4.73607	+	3.44095i	0.184912	+	0.134347i
$657$	−9.78115	+	7.10642i	−0.381599	+	0.277248i
$658$	−3.61803	+	11.1352i	−0.141046	+	0.434094i
$659$	−21.5066			−0.837777			−0.418889	−	0.908038i	$-0.637580\pi$
$659$	−21.5066			−0.837777			−0.418889	+	0.908038i	$0.637580\pi$
$660$	−2.70820	−	3.07768i	−0.105417	−	0.119799i
$661$	7.52786			0.292800			0.146400	−	0.989225i	$-0.453231\pi$
$661$	7.52786			0.292800			0.146400	+	0.989225i	$0.453231\pi$
$662$	−9.04508	+	27.8379i	−0.351547	+	1.08195i
$663$	0.527864	−	0.383516i	0.0205005	−	0.0148945i
$664$	12.9721	+	9.42481i	0.503417	+	0.365754i
$665$	4.23607	+	13.0373i	0.164268	+	0.505564i
$666$	4.61803	+	14.2128i	0.178945	+	0.550737i
$667$	−3.05573	−	2.22012i	−0.118318	−	0.0859633i
$668$	−6.09017	+	4.42477i	−0.235636	+	0.171199i
$669$	1.79837	−	5.53483i	0.0695292	−	0.213989i
$670$	20.1803			0.779635
$671$	5.41641	+	6.15537i	0.209098	+	0.237625i
$672$	0.618034			0.0238412
$673$	−2.62461	+	8.07772i	−0.101171	+	0.311373i	−0.988813	−	0.149162i	$-0.952342\pi$
$673$	−2.62461	+	8.07772i	−0.101171	+	0.311373i	0.887641	+	0.460535i	$0.152342\pi$
$674$	20.8713	−	15.1639i	0.803933	−	0.584092i
$675$	−2.80902	−	2.04087i	−0.108119	−	0.0785531i
$676$	−3.54508	−	10.9106i	−0.136349	−	0.419640i
$677$	−0.0344419	−	0.106001i	−0.00132371	−	0.00407395i	0.950392	−	0.311053i	$-0.100682\pi$
$677$	−0.0344419	−	0.106001i	−0.00132371	−	0.00407395i	−0.951716	+	0.306979i	$0.900682\pi$
$678$	1.19098	+	0.865300i	0.0457394	+	0.0332316i
$679$	−7.97214	+	5.79210i	−0.305942	+	0.222280i
$680$	−0.527864	+	1.62460i	−0.0202427	+	0.0623005i
$681$	−3.87539			−0.148505
$682$	−14.4721	−	3.24920i	−0.554167	−	0.124418i
$683$	−20.3607			−0.779080			−0.389540	−	0.921010i	$-0.627366\pi$
$683$	−20.3607			−0.779080			−0.389540	+	0.921010i	$0.627366\pi$
$684$	5.54508	−	17.0660i	0.212022	−	0.652535i
$685$	5.94427	−	4.31877i	0.227119	−	0.165012i
$686$	−0.809017	−	0.587785i	−0.0308884	−	0.0224417i
$687$	−5.20163	−	16.0090i	−0.198454	−	0.610780i
$688$	0.572949	+	1.76336i	0.0218435	+	0.0672273i
$689$	−12.9443	−	9.40456i	−0.493137	−	0.358285i
$690$	−0.472136	+	0.343027i	−0.0179739	+	0.0130588i
$691$	−4.11803	+	12.6740i	−0.156657	+	0.482142i	−0.998325	−	0.0578540i	$-0.981574\pi$
$691$	−4.11803	+	12.6740i	−0.156657	+	0.482142i	0.841668	+	0.539996i	$0.181574\pi$
$692$	15.7082			0.597136
$693$	4.42705	−	7.46969i	0.168170	−	0.283750i
$694$	−18.8541			−0.715692
$695$	−3.41641	+	10.5146i	−0.129592	+	0.398842i
$696$	−4.00000	+	2.90617i	−0.151620	+	0.110158i
$697$	4.04508	+	2.93893i	0.153219	+	0.111320i
$698$	9.70820	+	29.8788i	0.367461	+	1.13093i
$699$	3.64590	+	11.2209i	0.137901	+	0.424414i
$700$	−0.809017	−	0.587785i	−0.0305780	−	0.0222162i
$701$	−7.18034	+	5.21682i	−0.271198	+	0.197037i	−0.715069	−	0.699054i	$-0.753605\pi$
$701$	−7.18034	+	5.21682i	−0.271198	+	0.197037i	0.443871	+	0.896091i	$0.353605\pi$
$702$	−1.32624	+	4.08174i	−0.0500556	+	0.154055i
$703$	−39.1246			−1.47561
$704$	0.309017	+	3.30220i	0.0116465	+	0.124456i
$705$	−14.4721			−0.545052
$706$	9.97214	−	30.6911i	0.375306	−	1.15507i
$707$	10.2361	−	7.43694i	0.384967	−	0.279695i
$708$	−5.42705	−	3.94298i	−0.203961	−	0.148186i
$709$	12.5623	+	38.6628i	0.471787	+	1.45201i	0.850242	+	0.526392i	$0.176456\pi$
$709$	12.5623	+	38.6628i	0.471787	+	1.45201i	−0.378455	+	0.925620i	$0.623544\pi$
$710$	−0.944272	−	2.90617i	−0.0354379	−	0.109067i
$711$	6.85410	+	4.97980i	0.257049	+	0.186757i
$712$	0.263932	−	0.191758i	0.00989127	−	0.00718643i
$713$	−0.652476	+	2.00811i	−0.0244354	+	0.0752045i
$714$	0.527864			0.0197548
$715$	7.52786	−	3.24920i	0.281526	−	0.121513i
$716$	13.5066			0.504765
$717$	2.61803	−	8.05748i	0.0977723	−	0.300912i
$718$	10.3262	−	7.50245i	0.385372	−	0.279989i
$719$	−4.85410	−	3.52671i	−0.181027	−	0.131524i	0.493581	−	0.869700i	$-0.335688\pi$
$719$	−4.85410	−	3.52671i	−0.181027	−	0.131524i	−0.674609	+	0.738176i	$0.735688\pi$
$720$	−1.61803	−	4.97980i	−0.0603006	−	0.185586i
$721$	−1.14590	−	3.52671i	−0.0426755	−	0.131342i
$722$	22.6353	+	16.4455i	0.842397	+	0.612037i
$723$	−8.89919	+	6.46564i	−0.330964	+	0.240460i
$724$	−7.18034	+	22.0988i	−0.266855	+	0.821296i
$725$	8.00000			0.297113
$726$	−6.14590	−	2.90617i	−0.228096	−	0.107858i
$727$	−38.4721			−1.42685			−0.713426	−	0.700730i	$-0.752858\pi$
$727$	−38.4721			−1.42685			−0.713426	+	0.700730i	$0.752858\pi$
$728$	−0.381966	+	1.17557i	−0.0141566	+	0.0435695i
$729$	6.88197	−	5.00004i	0.254888	−	0.185187i
$730$	−7.47214	−	5.42882i	−0.276556	−	0.200930i
$731$	0.489357	+	1.50609i	0.0180995	+	0.0557046i
$732$	−0.472136	−	1.45309i	−0.0174506	−	0.0537076i
$733$	7.00000	+	5.08580i	0.258551	+	0.187848i	0.709508	−	0.704697i	$-0.248917\pi$
$733$	7.00000	+	5.08580i	0.258551	+	0.187848i	−0.450957	+	0.892546i	$0.648917\pi$
$734$	−9.70820	+	7.05342i	−0.358336	+	0.260347i
$735$	0.381966	−	1.17557i	0.0140890	−	0.0433616i
$736$	0.472136			0.0174032
$737$	30.7254	−	13.2618i	1.13179	−	0.488504i
$738$	−15.3262			−0.564167
$739$	6.35410	−	19.5559i	0.233739	−	0.719376i	−0.763547	−	0.645753i	$-0.776544\pi$
$739$	6.35410	−	19.5559i	0.233739	−	0.719376i	0.997286	−	0.0736233i	$-0.0234563\pi$
$740$	−9.23607	+	6.71040i	−0.339525	+	0.246679i
$741$	−4.23607	−	3.07768i	−0.155616	−	0.113062i
$742$	−4.00000	−	12.3107i	−0.146845	−	0.451941i
$743$	4.61803	+	14.2128i	0.169419	+	0.521419i	0.999335	−	0.0364703i	$-0.0116114\pi$
$743$	4.61803	+	14.2128i	0.169419	+	0.521419i	−0.829916	+	0.557889i	$0.811611\pi$
$744$	2.23607	+	1.62460i	0.0819782	+	0.0595607i
$745$	24.6525	−	17.9111i	0.903197	−	0.656211i
$746$	−6.65248	+	20.4742i	−0.243564	+	0.749614i
$747$	−41.9787			−1.53592
$748$	0.263932	+	2.82041i	0.00965031	+	0.103125i
$749$	−8.32624			−0.304234
$750$	2.29180	−	7.05342i	0.0836846	−	0.257555i
$751$	−39.7984	+	28.9152i	−1.45226	+	1.05513i	−0.466967	+	0.884275i	$0.654653\pi$
$751$	−39.7984	+	28.9152i	−1.45226	+	1.05513i	−0.985296	+	0.170856i	$0.945347\pi$
$752$	9.47214	+	6.88191i	0.345413	+	0.250957i
$753$	2.47214	+	7.60845i	0.0900896	+	0.277267i
$754$	−3.05573	−	9.40456i	−0.111283	−	0.342494i
$755$	25.4164	+	18.4661i	0.924998	+	0.672050i
$756$	−2.80902	+	2.04087i	−0.102163	+	0.0742257i
$757$	−13.6180	+	41.9120i	−0.494956	+	1.52332i	0.322070	+	0.946716i	$0.395621\pi$
$757$	−13.6180	+	41.9120i	−0.494956	+	1.52332i	−0.817026	+	0.576602i	$0.804379\pi$
$758$	6.14590			0.223229
$759$	−0.493422	+	0.832544i	−0.0179101	+	0.0302194i
$760$	13.7082			0.497249
$761$	−10.6803	+	32.8707i	−0.387162	+	1.19156i	0.547738	+	0.836650i	$0.315489\pi$
$761$	−10.6803	+	32.8707i	−0.387162	+	1.19156i	−0.934900	+	0.354912i	$0.884511\pi$
$762$	−6.61803	+	4.80828i	−0.239746	+	0.174186i
$763$	9.85410	+	7.15942i	0.356742	+	0.259189i
$764$	1.09017	+	3.35520i	0.0394410	+	0.121387i
$765$	−1.38197	−	4.25325i	−0.0499651	−	0.153777i
$766$	28.0344	+	20.3682i	1.01293	+	0.735933i
$767$	10.8541	−	7.88597i	0.391919	−	0.284746i
$768$	0.190983	−	0.587785i	0.00689151	−	0.0212099i
$769$	−49.4164			−1.78200			−0.891001	−	0.454002i	$-0.849996\pi$
$769$	−49.4164			−1.78200			−0.891001	+	0.454002i	$0.849996\pi$
$770$	6.47214	+	1.45309i	0.233240	+	0.0523656i
$771$	14.4508			0.520435
$772$	−2.90983	+	8.95554i	−0.104727	+	0.322317i
$773$	−18.4721	+	13.4208i	−0.664397	+	0.482712i	−0.868145	−	0.496311i	$-0.834688\pi$
$773$	−18.4721	+	13.4208i	−0.664397	+	0.482712i	0.203748	+	0.979023i	$0.434688\pi$
$774$	−3.92705	−	2.85317i	−0.141155	−	0.102555i
$775$	−1.38197	−	4.25325i	−0.0496417	−	0.152781i
$776$	3.04508	+	9.37181i	0.109312	+	0.336428i
$777$	2.85410	+	2.07363i	0.102390	+	0.0743909i
$778$	−2.00000	+	1.45309i	−0.0717035	+	0.0520956i
$779$	12.3992	−	38.1608i	0.444247	−	1.36725i
$780$	−1.52786			−0.0547063
$781$	−3.34752	−	3.80423i	−0.119784	−	0.136126i
$782$	0.403252			0.0144203
$783$	8.58359	−	26.4176i	0.306753	−	0.944087i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	11.7082	+	8.50651i	0.417884	+	0.303610i
$786$	0.871323	+	2.68166i	0.0310791	+	0.0956515i
$787$	3.35410	+	10.3229i	0.119561	+	0.367970i	0.992871	−	0.119194i	$-0.0380311\pi$
$787$	3.35410	+	10.3229i	0.119561	+	0.367970i	−0.873310	+	0.487165i	$0.838031\pi$
$788$	10.0902	+	7.33094i	0.359447	+	0.261154i
$789$	−2.47214	+	1.79611i	−0.0880104	+	0.0639433i
$790$	−2.00000	+	6.15537i	−0.0711568	+	0.218998i
$791$	−2.38197			−0.0846930
$792$	−5.73607	−	6.51864i	−0.203822	−	0.231630i
$793$	3.05573			0.108512
$794$	−5.43769	+	16.7355i	−0.192977	+	0.593921i
$795$	12.9443	−	9.40456i	0.459086	−	0.333546i
$796$	−1.76393	−	1.28157i	−0.0625209	−	0.0454241i
$797$	−3.34752	−	10.3026i	−0.118575	−	0.364938i	0.874101	−	0.485745i	$-0.161452\pi$
$797$	−3.34752	−	10.3026i	−0.118575	−	0.364938i	−0.992676	+	0.120807i	$0.961452\pi$
$798$	−1.30902	−	4.02874i	−0.0463387	−	0.142616i
$799$	8.09017	+	5.87785i	0.286210	+	0.207943i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$	−0.263932	+	0.812299i	−0.00932558	+	0.0287012i
$802$	−20.3262			−0.717744
$803$	−14.9443	−	3.35520i	−0.527372	−	0.118402i
$804$	−6.23607			−0.219929
$805$	0.291796	−	0.898056i	0.0102845	−	0.0316523i
$806$	−4.47214	+	3.24920i	−0.157524	+	0.114448i
$807$	14.7082	+	10.6861i	0.517753	+	0.376170i
$808$	−3.90983	−	12.0332i	−0.137547	−	0.423327i
$809$	17.4443	+	53.6879i	0.613308	+	1.88757i	0.424044	+	0.905641i	$0.360610\pi$
$809$	17.4443	+	53.6879i	0.613308	+	1.88757i	0.189264	+	0.981926i	$0.439390\pi$
$810$	9.23607	+	6.71040i	0.324522	+	0.235779i
$811$	45.3885	−	32.9767i	1.59381	−	1.15797i	0.695570	−	0.718459i	$-0.255152\pi$
$811$	45.3885	−	32.9767i	1.59381	−	1.15797i	0.898238	−	0.439510i	$-0.144848\pi$
$812$	2.47214	−	7.60845i	0.0867550	−	0.267004i
$813$	7.81966			0.274247
$814$	−9.65248	+	16.2865i	−0.338319	+	0.570841i
$815$	−20.5410			−0.719521
$816$	0.163119	−	0.502029i	0.00571031	−	0.0175745i
$817$	10.2812	−	7.46969i	0.359692	−	0.261332i
$818$	−21.3262	−	15.4944i	−0.745654	−	0.541750i
$819$	−1.00000	−	3.07768i	−0.0349428	−	0.107543i
$820$	−3.61803	−	11.1352i	−0.126347	−	0.388857i
$821$	5.00000	+	3.63271i	0.174501	+	0.126783i	0.671608	−	0.740907i	$-0.265604\pi$
$821$	5.00000	+	3.63271i	0.174501	+	0.126783i	−0.497106	+	0.867690i	$0.665604\pi$
$822$	−1.83688	+	1.33457i	−0.0640686	+	0.0465486i
$823$	−7.00000	+	21.5438i	−0.244005	+	0.750969i	0.751794	+	0.659398i	$0.229189\pi$
$823$	−7.00000	+	21.5438i	−0.244005	+	0.750969i	−0.995799	+	0.0915710i	$0.970811\pi$
$824$	−3.70820			−0.129181
$825$	−0.190983	−	2.04087i	−0.00664917	−	0.0710540i
$826$	10.8541			0.377663
$827$	5.59017	−	17.2048i	0.194389	−	0.598269i	−0.805594	−	0.592468i	$-0.798154\pi$
$827$	5.59017	−	17.2048i	0.194389	−	0.598269i	0.999983	−	0.00580052i	$-0.00184637\pi$
$828$	−1.00000	+	0.726543i	−0.0347524	+	0.0252491i
$829$	25.7984	+	18.7436i	0.896015	+	0.650993i	0.937439	−	0.348149i	$-0.113190\pi$
$829$	25.7984	+	18.7436i	0.896015	+	0.650993i	−0.0414247	+	0.999142i	$0.513190\pi$
$830$	−9.90983	−	30.4993i	−0.343975	−	1.05865i
$831$	3.58359	+	11.0292i	0.124313	+	0.382597i
$832$	1.00000	+	0.726543i	0.0346688	+	0.0251883i
$833$	−0.690983	+	0.502029i	−0.0239411	+	0.0173943i
$834$	1.05573	−	3.24920i	0.0365569	−	0.112510i
$835$	15.0557			0.521025
$836$	20.8713	−	9.00854i	0.721850	−	0.311567i
$837$	−15.5279			−0.536721
$838$	8.19098	−	25.2093i	0.282953	−	0.870839i
$839$	−15.0000	+	10.8981i	−0.517858	+	0.376246i	−0.815796	−	0.578340i	$-0.803701\pi$
$839$	−15.0000	+	10.8981i	−0.517858	+	0.376246i	0.297939	+	0.954585i	$0.403701\pi$
$840$	−1.00000	−	0.726543i	−0.0345033	−	0.0250681i
$841$	10.8156	+	33.2870i	0.372952	+	1.14783i
$842$	−1.38197	−	4.25325i	−0.0476257	−	0.146577i
$843$	7.39919	+	5.37582i	0.254842	+	0.185153i
$844$	21.9164	−	15.9232i	0.754394	−	0.548099i
$845$	−7.09017	+	21.8213i	−0.243909	+	0.750676i
$846$	−30.6525			−1.05385
$847$	10.8090	−	2.04087i	0.371402	−	0.0701251i
$848$	−12.9443			−0.444508
$849$	5.52786	−	17.0130i	0.189716	−	0.583885i
$850$	−0.690983	+	0.502029i	−0.0237005	+	0.0172194i
$851$	2.18034	+	1.58411i	0.0747411	+	0.0543026i
$852$	0.291796	+	0.898056i	0.00999677	+	0.0307669i
$853$	−9.29180	−	28.5972i	−0.318145	−	0.979150i	−0.974440	−	0.224646i	$-0.927878\pi$
$853$	−9.29180	−	28.5972i	−0.318145	−	0.979150i	0.656295	−	0.754504i	$-0.272122\pi$
$854$	2.00000	+	1.45309i	0.0684386	+	0.0497235i
$855$	−29.0344	+	21.0948i	−0.992957	+	0.721425i
$856$	−2.57295	+	7.91872i	−0.0879416	+	0.270656i
$857$	−4.90983			−0.167717			−0.0838583	−	0.996478i	$-0.526724\pi$
$857$	−4.90983			−0.167717			−0.0838583	+	0.996478i	$0.526724\pi$
$858$	−2.32624	+	1.00406i	−0.0794165	+	0.0342779i
$859$	27.6180			0.942315			0.471158	−	0.882049i	$-0.343836\pi$
$859$	27.6180			0.942315			0.471158	+	0.882049i	$0.343836\pi$
$860$	1.14590	−	3.52671i	0.0390748	−	0.120260i
$861$	−2.92705	+	2.12663i	−0.0997536	+	0.0724753i
$862$	−5.38197	−	3.91023i	−0.183310	−	0.133183i
$863$	12.4377	+	38.2793i	0.423384	+	1.30304i	0.904533	+	0.426403i	$0.140220\pi$
$863$	12.4377	+	38.2793i	0.423384	+	1.30304i	−0.481149	+	0.876639i	$0.659780\pi$
$864$	1.07295	+	3.30220i	0.0365025	+	0.112343i
$865$	−25.4164	−	18.4661i	−0.864184	−	0.627866i
$866$	−25.4894	+	18.5191i	−0.866164	+	0.629305i
$867$	−3.10739	+	9.56357i	−0.105533	+	0.324796i
$868$	−4.47214			−0.151794
$869$	1.00000	+	10.6861i	0.0339227	+	0.362502i
$870$	9.88854			0.335253
$871$	3.85410	−	11.8617i	0.130591	−	0.401919i
$872$	9.85410	−	7.15942i	0.333702	−	0.242449i
$873$	−20.8713	−	15.1639i	−0.706387	−	0.513220i
$874$	−1.00000	−	3.07768i	−0.0338255	−	0.104104i
$875$	3.70820	+	11.4127i	0.125360	+	0.385819i
$876$	2.30902	+	1.67760i	0.0780145	+	0.0566808i
$877$	24.7082	−	17.9516i	0.834337	−	0.606181i	−0.0864462	−	0.996257i	$-0.527551\pi$
$877$	24.7082	−	17.9516i	0.834337	−	0.606181i	0.920783	+	0.390075i	$0.127551\pi$
$878$	−0.291796	+	0.898056i	−0.00984764	+	0.0303079i
$879$	2.36068			0.0796238
$880$	3.38197	−	5.70634i	0.114006	−	0.192361i
$881$	−21.9230			−0.738604			−0.369302	−	0.929309i	$-0.620403\pi$
$881$	−21.9230			−0.738604			−0.369302	+	0.929309i	$0.620403\pi$
$882$	0.809017	−	2.48990i	0.0272410	−	0.0838392i
$883$	−0.972136	+	0.706298i	−0.0327150	+	0.0237688i	−0.604023	−	0.796967i	$-0.706436\pi$
$883$	−0.972136	+	0.706298i	−0.0327150	+	0.0237688i	0.571308	+	0.820736i	$0.306436\pi$
$884$	0.854102	+	0.620541i	0.0287266	+	0.0208711i
$885$	4.14590	+	12.7598i	0.139363	+	0.428915i
$886$	−6.46149	−	19.8864i	−0.217078	−	0.668098i
$887$	2.85410	+	2.07363i	0.0958314	+	0.0696256i	0.634669	−	0.772784i	$-0.281136\pi$
$887$	2.85410	+	2.07363i	0.0958314	+	0.0696256i	−0.538838	+	0.842410i	$0.681136\pi$
$888$	2.85410	−	2.07363i	0.0957774	−	0.0695863i
$889$	4.09017	−	12.5882i	0.137180	−	0.422196i
$890$	−0.652476			−0.0218710
$891$	18.4721	+	4.14725i	0.618840	+	0.138938i
$892$	9.41641			0.315285
$893$	24.7984	−	76.3215i	0.829846	−	2.55400i
$894$	−7.61803	+	5.53483i	−0.254785	+	0.185112i
$895$	−21.8541	−	15.8779i	−0.730502	−	0.530741i
$896$	0.309017	+	0.951057i	0.0103235	+	0.0317726i
$897$	0.111456	+	0.343027i	0.00372141	+	0.0114533i
$898$	−18.3992	−	13.3678i	−0.613989	−	0.446089i
$899$	28.9443	−	21.0292i	0.965346	−	0.701365i
$900$	0.809017	−	2.48990i	0.0269672	−	0.0829966i
$901$	−11.0557			−0.368320
$902$	−12.8262	−	14.5761i	−0.427067	−	0.485332i
$903$	−1.14590			−0.0381331
$904$	−0.736068	+	2.26538i	−0.0244813	+	0.0753456i
$905$	37.5967	−	27.3156i	1.24976	−	0.908002i
$906$	−7.85410	−	5.70634i	−0.260935	−	0.189580i
$907$	13.5902	+	41.8262i	0.451254	+	1.38882i	0.875477	+	0.483260i	$0.160547\pi$
$907$	13.5902	+	41.8262i	0.451254	+	1.38882i	−0.424223	+	0.905558i	$0.639453\pi$
$908$	−1.93769	−	5.96361i	−0.0643046	−	0.197909i
$909$	26.7984	+	19.4702i	0.888846	+	0.645784i
$910$	2.00000	−	1.45309i	0.0662994	−	0.0481693i
$911$	−3.79837	+	11.6902i	−0.125846	+	0.387313i	−0.994054	−	0.108886i	$-0.965272\pi$
$911$	−3.79837	+	11.6902i	−0.125846	+	0.387313i	0.868208	+	0.496200i	$0.165272\pi$
$912$	−4.23607			−0.140270
$913$	−35.1312	−	39.9241i	−1.16267	−	1.32130i
$914$	8.97871			0.296989
$915$	−0.944272	+	2.90617i	−0.0312167	+	0.0960750i
$916$	22.0344	−	16.0090i	0.728038	−	0.528951i
$917$	−3.69098	−	2.68166i	−0.121887	−	0.0885561i
$918$	0.916408	+	2.82041i	0.0302460	+	0.0930875i
$919$	−9.29180	−	28.5972i	−0.306508	−	0.943335i	−0.979110	−	0.203330i	$-0.934823\pi$
$919$	−9.29180	−	28.5972i	−0.306508	−	0.943335i	0.672602	−	0.740004i	$-0.265177\pi$
$920$	−0.763932	−	0.555029i	−0.0251861	−	0.0182988i
$921$	7.69098	−	5.58783i	0.253427	−	0.184125i
$922$	−10.8197	+	33.2995i	−0.356327	+	1.09666i
$923$	−1.88854			−0.0621622
$924$	−2.00000	−	0.449028i	−0.0657952	−	0.0147719i
$925$	−5.70820			−0.187685
$926$	−9.03444	+	27.8052i	−0.296890	+	0.913734i
$927$	7.85410	−	5.70634i	0.257963	−	0.187421i
$928$	−6.47214	−	4.70228i	−0.212458	−	0.154360i
$929$	−7.62461	−	23.4661i	−0.250155	−	0.769899i	−0.994746	−	0.102377i	$-0.967355\pi$
$929$	−7.62461	−	23.4661i	−0.250155	−	0.769899i	0.744590	−	0.667522i	$-0.232645\pi$
$930$	−1.70820	−	5.25731i	−0.0560142	−	0.172394i
$931$	5.54508	+	4.02874i	0.181733	+	0.132037i
$932$	−15.4443	+	11.2209i	−0.505894	+	0.367553i
$933$	−3.38197	+	10.4086i	−0.110721	+	0.340763i
$934$	13.8885			0.454447
$935$	2.88854	−	4.87380i	0.0944655	−	0.159390i
$936$	−3.23607			−0.105774
$937$	−10.1525	+	31.2461i	−0.331667	+	1.02077i	0.636674	+	0.771133i	$0.280310\pi$
$937$	−10.1525	+	31.2461i	−0.331667	+	1.02077i	−0.968341	+	0.249633i	$0.919690\pi$
$938$	8.16312	−	5.93085i	0.266535	−	0.193649i
$939$	−6.89919	−	5.01255i	−0.225146	−	0.163578i
$940$	−7.23607	−	22.2703i	−0.236015	−	0.726378i
$941$	−12.0344	−	37.0382i	−0.392312	−	1.20741i	−0.931036	−	0.364929i	$-0.881093\pi$
$941$	−12.0344	−	37.0382i	−0.392312	−	1.20741i	0.538724	−	0.842482i	$-0.318907\pi$
$942$	−3.61803	−	2.62866i	−0.117882	−	0.0856462i
$943$	−2.23607	+	1.62460i	−0.0728164	+	0.0529042i
$944$	3.35410	−	10.3229i	0.109167	−	0.335981i
$945$	6.94427			0.225897
$946$	−0.572949	−	6.12261i	−0.0186282	−	0.199063i
$947$	6.27051			0.203764			0.101882	−	0.994796i	$-0.467514\pi$
$947$	6.27051			0.203764			0.101882	+	0.994796i	$0.467514\pi$
$948$	0.618034	−	1.90211i	0.0200728	−	0.0617778i
$949$	−4.61803	+	3.35520i	−0.149908	+	0.108914i
$950$	5.54508	+	4.02874i	0.179906	+	0.130710i
$951$	2.29180	+	7.05342i	0.0743166	+	0.228723i
$952$	0.263932	+	0.812299i	0.00855409	+	0.0263268i
$953$	5.44427	+	3.95550i	0.176357	+	0.128131i	0.672462	−	0.740132i	$-0.265237\pi$
$953$	5.44427	+	3.95550i	0.176357	+	0.128131i	−0.496105	+	0.868263i	$0.665237\pi$
$954$	27.4164	−	19.9192i	0.887639	−	0.644907i
$955$	2.18034	−	6.71040i	0.0705541	−	0.217143i
$956$	13.7082			0.443355
$957$	15.0557	−	6.49839i	0.486683	−	0.210063i
$958$	−22.6525			−0.731868
$959$	1.13525	−	3.49396i	0.0366593	−	0.112826i
$960$	−1.00000	+	0.726543i	−0.0322749	+	0.0234491i
$961$	8.89919	+	6.46564i	0.287071	+	0.208569i
$962$	2.18034	+	6.71040i	0.0702970	+	0.216352i
$963$	−6.73607	−	20.7315i	−0.217067	−	0.668063i
$964$	−14.3992	−	10.4616i	−0.463767	−	0.336946i
$965$	15.2361	−	11.0697i	0.490466	−	0.356345i
$966$	−0.0901699	+	0.277515i	−0.00290117	+	0.00892888i
$967$	−8.47214			−0.272446			−0.136223	−	0.990678i	$-0.543496\pi$
$967$	−8.47214			−0.272446			−0.136223	+	0.990678i	$0.543496\pi$
$968$	1.39919	−	10.9106i	0.0449716	−	0.350682i
$969$	−3.61803			−0.116228
$970$	6.09017	−	18.7436i	0.195544	−	0.601821i
$971$	−27.8885	+	20.2622i	−0.894986	+	0.650245i	−0.937173	−	0.348864i	$-0.886567\pi$
$971$	−27.8885	+	20.2622i	−0.894986	+	0.650245i	0.0421873	+	0.999110i	$0.486567\pi$
$972$	−11.2812	−	8.19624i	−0.361843	−	0.262894i
$973$	1.70820	+	5.25731i	0.0547625	+	0.168542i
$974$	−13.3820	−	41.1855i	−0.428786	−	1.31967i
$975$	−0.618034	−	0.449028i	−0.0197929	−	0.0143804i
$976$	2.00000	−	1.45309i	0.0640184	−	0.0465121i
$977$	−11.2705	+	34.6871i	−0.360576	+	1.10974i	0.592130	+	0.805842i	$0.298287\pi$
$977$	−11.2705	+	34.6871i	−0.360576	+	1.10974i	−0.952706	+	0.303895i	$0.901713\pi$
$978$	6.34752			0.202971
$979$	−0.993422	+	0.428784i	−0.0317499	+	0.0137040i
$980$	2.00000			0.0638877
$981$	−9.85410	+	30.3278i	−0.314617	+	0.968292i
$982$	5.50000	−	3.99598i	0.175512	−	0.127517i
$983$	12.7082	+	9.23305i	0.405329	+	0.294489i	0.771708	−	0.635977i	$-0.219403\pi$
$983$	12.7082	+	9.23305i	0.405329	+	0.294489i	−0.366379	+	0.930466i	$0.619403\pi$
$984$	1.11803	+	3.44095i	0.0356416	+	0.109694i
$985$	−7.70820	−	23.7234i	−0.245604	−	0.755891i
$986$	−5.52786	−	4.01623i	−0.176043	−	0.127903i
$987$	−5.85410	+	4.25325i	−0.186338	+	0.135383i
$988$	2.61803	−	8.05748i	0.0832908	−	0.256343i
$989$	−0.875388			−0.0278357
$990$	1.61803	+	17.2905i	0.0514245	+	0.549529i
$991$	28.7639			0.913716			0.456858	−	0.889540i	$-0.348975\pi$
$991$	28.7639			0.913716			0.456858	+	0.889540i	$0.348975\pi$
$992$	−1.38197	+	4.25325i	−0.0438775	+	0.135041i
$993$	−14.6353	+	10.6331i	−0.464436	+	0.337432i
$994$	−1.23607	−	0.898056i	−0.0392057	−	0.0284846i
$995$	1.34752	+	4.14725i	0.0427194	+	0.131477i
$996$	3.06231	+	9.42481i	0.0970329	+	0.298636i
$997$	1.85410	+	1.34708i	0.0587200	+	0.0426626i	0.616758	−	0.787153i	$-0.288446\pi$
$997$	1.85410	+	1.34708i	0.0587200	+	0.0426626i	−0.558038	+	0.829815i	$0.688446\pi$
$998$	−4.26393	+	3.09793i	−0.134972	+	0.0980632i
$999$	−6.12461	+	18.8496i	−0.193774	+	0.596375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.f.c.141.1	yes	4
11.4	even	5		1694.2.a.m.1.2		2
11.5	even	5	inner	154.2.f.c.71.1	✓	4
11.7	odd	10		1694.2.a.r.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.f.c.71.1	✓	4	11.5	even	5	inner
154.2.f.c.141.1	yes	4	1.1	even	1	trivial
1694.2.a.m.1.2		2	11.4	even	5
1694.2.a.r.1.2		2	11.7	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.500000 + 0.363271i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.618034 + 1.90211i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 2.48990i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.500000 + 0.363271i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.618034 + 1.90211i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 2.48990i) q^{9} -2.00000 q^{10} +(-3.04508 + 1.31433i) q^{11} +0.618034 q^{12} +(-0.381966 + 1.17557i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-1.00000 - 0.726543i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.263932 + 0.812299i) q^{17} +(-2.11803 - 1.53884i) q^{18} +(5.54508 - 4.02874i) q^{19} +(0.618034 - 1.90211i) q^{20} -0.618034 q^{21} +(-0.309017 - 3.30220i) q^{22} -0.472136 q^{23} +(-0.190983 + 0.587785i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-1.00000 - 0.726543i) q^{26} +(-1.07295 - 3.30220i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(6.47214 + 4.70228i) q^{29} +(1.00000 - 0.726543i) q^{30} +(1.38197 - 4.25325i) q^{31} -1.00000 q^{32} +(1.04508 - 1.76336i) q^{33} -0.854102 q^{34} +(-0.618034 + 1.90211i) q^{35} +(2.11803 - 1.53884i) q^{36} +(-4.61803 - 3.35520i) q^{37} +(2.11803 + 6.51864i) q^{38} +(-0.236068 - 0.726543i) q^{39} +(1.61803 + 1.17557i) q^{40} +(4.73607 - 3.44095i) q^{41} +(0.190983 - 0.587785i) q^{42} +1.85410 q^{43} +(3.23607 + 0.726543i) q^{44} -5.23607 q^{45} +(0.145898 - 0.449028i) q^{46} +(9.47214 - 6.88191i) q^{47} +(-0.500000 - 0.363271i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-0.427051 - 0.310271i) q^{51} +(1.00000 - 0.726543i) q^{52} +(-4.00000 + 12.3107i) q^{53} +3.47214 q^{54} +(-4.38197 - 4.97980i) q^{55} +1.00000 q^{56} +(-1.30902 + 4.02874i) q^{57} +(-6.47214 + 4.70228i) q^{58} +(-8.78115 - 6.37988i) q^{59} +(0.381966 + 1.17557i) q^{60} +(-0.763932 - 2.35114i) q^{61} +(3.61803 + 2.62866i) q^{62} +(-2.11803 + 1.53884i) q^{63} +(0.309017 - 0.951057i) q^{64} -2.47214 q^{65} +(1.35410 + 1.53884i) q^{66} -10.0902 q^{67} +(0.263932 - 0.812299i) q^{68} +(0.236068 - 0.171513i) q^{69} +(-1.61803 - 1.17557i) q^{70} +(0.472136 + 1.45309i) q^{71} +(0.809017 + 2.48990i) q^{72} +(3.73607 + 2.71441i) q^{73} +(4.61803 - 3.35520i) q^{74} +(-0.190983 + 0.587785i) q^{75} -6.85410 q^{76} +(-3.23607 - 0.726543i) q^{77} +0.763932 q^{78} +(1.00000 - 3.07768i) q^{79} +(-1.61803 + 1.17557i) q^{80} +(-4.61803 - 3.35520i) q^{81} +(1.80902 + 5.56758i) q^{82} +(4.95492 + 15.2497i) q^{83} +(0.500000 + 0.363271i) q^{84} +(-1.38197 + 1.00406i) q^{85} +(-0.572949 + 1.76336i) q^{86} -4.94427 q^{87} +(-1.69098 + 2.85317i) q^{88} +0.326238 q^{89} +(1.61803 - 4.97980i) q^{90} +(-1.00000 + 0.726543i) q^{91} +(0.381966 + 0.277515i) q^{92} +(0.854102 + 2.62866i) q^{93} +(3.61803 + 11.1352i) q^{94} +(11.0902 + 8.05748i) q^{95} +(0.500000 - 0.363271i) q^{96} +(-3.04508 + 9.37181i) q^{97} -1.00000 q^{98} +(-0.809017 - 8.64527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} + q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^6 + q^7 + q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} + q^{7} + q^{8} - q^{9} - 8 q^{10} - q^{11} - 2 q^{12} - 6 q^{13} - q^{14} - 4 q^{15} - q^{16} + 10 q^{17} - 4 q^{18} + 11 q^{19} - 2 q^{20} + 2 q^{21} + q^{22} + 16 q^{23} - 3 q^{24} + q^{25} - 4 q^{26} - 11 q^{27} + q^{28} + 8 q^{29} + 4 q^{30} + 10 q^{31} - 4 q^{32} - 7 q^{33} + 10 q^{34} + 2 q^{35} + 4 q^{36} - 14 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 10 q^{41} + 3 q^{42} - 6 q^{43} + 4 q^{44} - 12 q^{45} + 14 q^{46} + 20 q^{47} - 2 q^{48} - q^{49} - q^{50} + 5 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 22 q^{55} + 4 q^{56} - 3 q^{57} - 8 q^{58} - 15 q^{59} + 6 q^{60} - 12 q^{61} + 10 q^{62} - 4 q^{63} - q^{64} + 8 q^{65} - 8 q^{66} - 18 q^{67} + 10 q^{68} - 8 q^{69} - 2 q^{70} - 16 q^{71} + q^{72} + 6 q^{73} + 14 q^{74} - 3 q^{75} - 14 q^{76} - 4 q^{77} + 12 q^{78} + 4 q^{79} - 2 q^{80} - 14 q^{81} + 5 q^{82} + 31 q^{83} + 2 q^{84} - 10 q^{85} - 9 q^{86} + 16 q^{87} - 9 q^{88} - 30 q^{89} + 2 q^{90} - 4 q^{91} + 6 q^{92} - 10 q^{93} + 10 q^{94} + 22 q^{95} + 2 q^{96} - q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^6 + q^7 + q^8 - q^9 - 8 * q^10 - q^11 - 2 * q^12 - 6 * q^13 - q^14 - 4 * q^15 - q^16 + 10 * q^17 - 4 * q^18 + 11 * q^19 - 2 * q^20 + 2 * q^21 + q^22 + 16 * q^23 - 3 * q^24 + q^25 - 4 * q^26 - 11 * q^27 + q^28 + 8 * q^29 + 4 * q^30 + 10 * q^31 - 4 * q^32 - 7 * q^33 + 10 * q^34 + 2 * q^35 + 4 * q^36 - 14 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 + 10 * q^41 + 3 * q^42 - 6 * q^43 + 4 * q^44 - 12 * q^45 + 14 * q^46 + 20 * q^47 - 2 * q^48 - q^49 - q^50 + 5 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 22 * q^55 + 4 * q^56 - 3 * q^57 - 8 * q^58 - 15 * q^59 + 6 * q^60 - 12 * q^61 + 10 * q^62 - 4 * q^63 - q^64 + 8 * q^65 - 8 * q^66 - 18 * q^67 + 10 * q^68 - 8 * q^69 - 2 * q^70 - 16 * q^71 + q^72 + 6 * q^73 + 14 * q^74 - 3 * q^75 - 14 * q^76 - 4 * q^77 + 12 * q^78 + 4 * q^79 - 2 * q^80 - 14 * q^81 + 5 * q^82 + 31 * q^83 + 2 * q^84 - 10 * q^85 - 9 * q^86 + 16 * q^87 - 9 * q^88 - 30 * q^89 + 2 * q^90 - 4 * q^91 + 6 * q^92 - 10 * q^93 + 10 * q^94 + 22 * q^95 + 2 * q^96 - q^97 - 4 * q^98 - q^99

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