LMFDB - Embedded newform 154.2.e.f.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(23,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("154.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.e (of order $3$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			23.2
Root			$-1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	154.23
Dual form			154.2.e.f.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.32288 + 2.29129i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.82288 + 3.15731i) q^{5} +2.64575 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.32288 + 2.29129i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.82288 + 3.15731i) q^{5} +2.64575 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +(1.82288 + 3.15731i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.32288 - 2.29129i) q^{12} +5.00000 q^{13} +(-1.32288 - 2.29129i) q^{14} -9.64575 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{18} +(0.177124 - 0.306788i) q^{19} +3.64575 q^{20} +7.00000 q^{21} -1.00000 q^{22} +(1.82288 - 3.15731i) q^{23} +(-1.32288 - 2.29129i) q^{24} +(-4.14575 - 7.18065i) q^{25} +(2.50000 - 4.33013i) q^{26} -2.64575 q^{27} -2.64575 q^{28} -4.29150 q^{29} +(-4.82288 + 8.35347i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.32288 - 2.29129i) q^{33} -6.00000 q^{34} +(4.82288 + 8.35347i) q^{35} +4.00000 q^{36} +(0.822876 - 1.42526i) q^{37} +(-0.177124 - 0.306788i) q^{38} +(6.61438 + 11.4564i) q^{39} +(1.82288 - 3.15731i) q^{40} -4.93725 q^{41} +(3.50000 - 6.06218i) q^{42} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-7.29150 - 12.6293i) q^{45} +(-1.82288 - 3.15731i) q^{46} +(-6.64575 + 11.5108i) q^{47} -2.64575 q^{48} +(-3.50000 - 6.06218i) q^{49} -8.29150 q^{50} +(7.93725 - 13.7477i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(1.82288 + 3.15731i) q^{53} +(-1.32288 + 2.29129i) q^{54} +3.64575 q^{55} +(-1.32288 + 2.29129i) q^{56} +0.937254 q^{57} +(-2.14575 + 3.71655i) q^{58} +(0.322876 + 0.559237i) q^{59} +(4.82288 + 8.35347i) q^{60} +(-1.85425 + 3.21165i) q^{61} +4.00000 q^{62} +(5.29150 + 9.16515i) q^{63} +1.00000 q^{64} +(-9.11438 + 15.7866i) q^{65} +(-1.32288 - 2.29129i) q^{66} +(-1.96863 - 3.40976i) q^{67} +(-3.00000 + 5.19615i) q^{68} +9.64575 q^{69} +9.64575 q^{70} +9.64575 q^{71} +(2.00000 - 3.46410i) q^{72} +(-2.82288 - 4.88936i) q^{73} +(-0.822876 - 1.42526i) q^{74} +(10.9686 - 18.9982i) q^{75} -0.354249 q^{76} -2.64575 q^{77} +13.2288 q^{78} +(-1.32288 + 2.29129i) q^{79} +(-1.82288 - 3.15731i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-2.46863 + 4.27579i) q^{82} +13.2915 q^{83} +(-3.50000 - 6.06218i) q^{84} +21.8745 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-5.67712 - 9.83307i) q^{87} +(0.500000 + 0.866025i) q^{88} +(7.29150 - 12.6293i) q^{89} -14.5830 q^{90} +(6.61438 - 11.4564i) q^{91} -3.64575 q^{92} +(-5.29150 + 9.16515i) q^{93} +(6.64575 + 11.5108i) q^{94} +(0.645751 + 1.11847i) q^{95} +(-1.32288 + 2.29129i) q^{96} -5.70850 q^{97} -7.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 - 8 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 28 q^{15} - 2 q^{16} - 12 q^{17} + 8 q^{18} + 6 q^{19} + 4 q^{20} + 28 q^{21} - 4 q^{22} + 2 q^{23} - 6 q^{25} + 10 q^{26} + 4 q^{29} - 14 q^{30} + 8 q^{31} + 2 q^{32} - 24 q^{34} + 14 q^{35} + 16 q^{36} - 2 q^{37} - 6 q^{38} + 2 q^{40} + 12 q^{41} + 14 q^{42} - 16 q^{43} - 2 q^{44} - 8 q^{45} - 2 q^{46} - 16 q^{47} - 14 q^{49} - 12 q^{50} - 10 q^{52} + 2 q^{53} + 4 q^{55} - 28 q^{57} + 2 q^{58} - 4 q^{59} + 14 q^{60} - 18 q^{61} + 16 q^{62} + 4 q^{64} - 10 q^{65} + 8 q^{67} - 12 q^{68} + 28 q^{69} + 28 q^{70} + 28 q^{71} + 8 q^{72} - 6 q^{73} + 2 q^{74} + 28 q^{75} - 12 q^{76} - 2 q^{80} + 10 q^{81} + 6 q^{82} + 32 q^{83} - 14 q^{84} + 24 q^{85} - 8 q^{86} - 28 q^{87} + 2 q^{88} + 8 q^{89} - 16 q^{90} - 4 q^{92} + 16 q^{94} - 8 q^{95} - 44 q^{97} - 28 q^{98} + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 - 8 * q^9 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 28 * q^15 - 2 * q^16 - 12 * q^17 + 8 * q^18 + 6 * q^19 + 4 * q^20 + 28 * q^21 - 4 * q^22 + 2 * q^23 - 6 * q^25 + 10 * q^26 + 4 * q^29 - 14 * q^30 + 8 * q^31 + 2 * q^32 - 24 * q^34 + 14 * q^35 + 16 * q^36 - 2 * q^37 - 6 * q^38 + 2 * q^40 + 12 * q^41 + 14 * q^42 - 16 * q^43 - 2 * q^44 - 8 * q^45 - 2 * q^46 - 16 * q^47 - 14 * q^49 - 12 * q^50 - 10 * q^52 + 2 * q^53 + 4 * q^55 - 28 * q^57 + 2 * q^58 - 4 * q^59 + 14 * q^60 - 18 * q^61 + 16 * q^62 + 4 * q^64 - 10 * q^65 + 8 * q^67 - 12 * q^68 + 28 * q^69 + 28 * q^70 + 28 * q^71 + 8 * q^72 - 6 * q^73 + 2 * q^74 + 28 * q^75 - 12 * q^76 - 2 * q^80 + 10 * q^81 + 6 * q^82 + 32 * q^83 - 14 * q^84 + 24 * q^85 - 8 * q^86 - 28 * q^87 + 2 * q^88 + 8 * q^89 - 16 * q^90 - 4 * q^92 + 16 * q^94 - 8 * q^95 - 44 * q^97 - 28 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.32288	+	2.29129i	0.763763	+	1.32288i	0.940898	+	0.338689i	$0.109984\pi$
$3$	1.32288	+	2.29129i	0.763763	+	1.32288i	−0.177136	+	0.984186i	$0.556683\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.82288	+	3.15731i	−0.815215	+	1.41199i	0.0939588	+	0.995576i	$0.470048\pi$
$5$	−1.82288	+	3.15731i	−0.815215	+	1.41199i	−0.909174	+	0.416417i	$0.863286\pi$
$6$	2.64575			1.08012
$7$	1.32288	−	2.29129i	0.500000	−	0.866025i
$7$	1.32288	−	2.29129i	0.500000	−	0.866025i
$8$	−1.00000			−0.353553
$9$	−2.00000	+	3.46410i	−0.666667	+	1.15470i
$10$	1.82288	+	3.15731i	0.576444	+	0.998430i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	1.32288	−	2.29129i	0.381881	−	0.661438i
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.32288	−	2.29129i	−0.353553	−	0.612372i
$15$	−9.64575			−2.49052
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	2.00000	+	3.46410i	0.471405	+	0.816497i
$19$	0.177124	−	0.306788i	0.0406351	−	0.0703821i	−0.844993	−	0.534778i	$-0.820395\pi$
$19$	0.177124	−	0.306788i	0.0406351	−	0.0703821i	0.885628	+	0.464396i	$0.153729\pi$
$20$	3.64575			0.815215
$21$	7.00000			1.52753
$22$	−1.00000			−0.213201
$23$	1.82288	−	3.15731i	0.380096	−	0.658345i	−0.610980	−	0.791646i	$-0.709224\pi$
$23$	1.82288	−	3.15731i	0.380096	−	0.658345i	0.991076	+	0.133301i	$0.0425577\pi$
$24$	−1.32288	−	2.29129i	−0.270031	−	0.467707i
$25$	−4.14575	−	7.18065i	−0.829150	−	1.43613i
$26$	2.50000	−	4.33013i	0.490290	−	0.849208i
$27$	−2.64575			−0.509175
$28$	−2.64575			−0.500000
$29$	−4.29150			−0.796912			−0.398456	−	0.917187i	$-0.630454\pi$
$29$	−4.29150			−0.796912			−0.398456	+	0.917187i	$0.630454\pi$
$30$	−4.82288	+	8.35347i	−0.880533	+	1.52513i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.32288	−	2.29129i	0.230283	−	0.398862i
$34$	−6.00000			−1.02899
$35$	4.82288	+	8.35347i	0.815215	+	1.41199i
$36$	4.00000			0.666667
$37$	0.822876	−	1.42526i	0.135280	−	0.234312i	−0.790424	−	0.612560i	$-0.790140\pi$
$37$	0.822876	−	1.42526i	0.135280	−	0.234312i	0.925704	+	0.378248i	$0.123473\pi$
$38$	−0.177124	−	0.306788i	−0.0287334	−	0.0497676i
$39$	6.61438	+	11.4564i	1.05915	+	1.83450i
$40$	1.82288	−	3.15731i	0.288222	−	0.499215i
$41$	−4.93725			−0.771070			−0.385535	−	0.922693i	$-0.625983\pi$
$41$	−4.93725			−0.771070			−0.385535	+	0.922693i	$0.625983\pi$
$42$	3.50000	−	6.06218i	0.540062	−	0.935414i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−7.29150	−	12.6293i	−1.08695	−	1.88266i
$46$	−1.82288	−	3.15731i	−0.268768	−	0.465520i
$47$	−6.64575	+	11.5108i	−0.969382	+	1.67902i	−0.272034	+	0.962288i	$0.587696\pi$
$47$	−6.64575	+	11.5108i	−0.969382	+	1.67902i	−0.697349	+	0.716732i	$0.745637\pi$
$48$	−2.64575			−0.381881
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$	−8.29150			−1.17260
$51$	7.93725	−	13.7477i	1.11144	−	1.92507i
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	1.82288	+	3.15731i	0.250391	+	0.433690i	0.963634	−	0.267227i	$-0.0861074\pi$
$53$	1.82288	+	3.15731i	0.250391	+	0.433690i	−0.713242	+	0.700918i	$0.752774\pi$
$54$	−1.32288	+	2.29129i	−0.180021	+	0.311805i
$55$	3.64575			0.491593
$56$	−1.32288	+	2.29129i	−0.176777	+	0.306186i
$57$	0.937254			0.124142
$58$	−2.14575	+	3.71655i	−0.281751	+	0.488007i
$59$	0.322876	+	0.559237i	0.0420348	+	0.0728065i	0.886277	−	0.463155i	$-0.153283\pi$
$59$	0.322876	+	0.559237i	0.0420348	+	0.0728065i	−0.844243	+	0.535961i	$0.819949\pi$
$60$	4.82288	+	8.35347i	0.622631	+	1.07843i
$61$	−1.85425	+	3.21165i	−0.237412	+	0.411210i	−0.959971	−	0.280099i	$-0.909633\pi$
$61$	−1.85425	+	3.21165i	−0.237412	+	0.411210i	0.722559	+	0.691310i	$0.242966\pi$
$62$	4.00000			0.508001
$63$	5.29150	+	9.16515i	0.666667	+	1.15470i
$64$	1.00000			0.125000
$65$	−9.11438	+	15.7866i	−1.13050	+	1.95808i
$66$	−1.32288	−	2.29129i	−0.162835	−	0.282038i
$67$	−1.96863	−	3.40976i	−0.240506	−	0.416569i	0.720352	−	0.693608i	$-0.243980\pi$
$67$	−1.96863	−	3.40976i	−0.240506	−	0.416569i	−0.960859	+	0.277039i	$0.910647\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	9.64575			1.16121
$70$	9.64575			1.15289
$71$	9.64575			1.14474			0.572370	−	0.819995i	$-0.306024\pi$
$71$	9.64575			1.14474			0.572370	+	0.819995i	$0.306024\pi$
$72$	2.00000	−	3.46410i	0.235702	−	0.408248i
$73$	−2.82288	−	4.88936i	−0.330393	−	0.572257i	0.652196	−	0.758050i	$-0.273848\pi$
$73$	−2.82288	−	4.88936i	−0.330393	−	0.572257i	−0.982589	+	0.185793i	$0.940514\pi$
$74$	−0.822876	−	1.42526i	−0.0956574	−	0.165683i
$75$	10.9686	−	18.9982i	1.26655	−	2.19373i
$76$	−0.354249			−0.0406351
$77$	−2.64575			−0.301511
$78$	13.2288			1.49786
$79$	−1.32288	+	2.29129i	−0.148835	+	0.257790i	−0.930797	−	0.365536i	$-0.880886\pi$
$79$	−1.32288	+	2.29129i	−0.148835	+	0.257790i	0.781962	+	0.623326i	$0.214219\pi$
$80$	−1.82288	−	3.15731i	−0.203804	−	0.352998i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	−2.46863	+	4.27579i	−0.272614	+	0.472182i
$83$	13.2915			1.45893			0.729466	−	0.684017i	$-0.239769\pi$
$83$	13.2915			1.45893			0.729466	+	0.684017i	$0.239769\pi$
$84$	−3.50000	−	6.06218i	−0.381881	−	0.661438i
$85$	21.8745			2.37262
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	−5.67712	−	9.83307i	−0.608652	−	1.05422i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	7.29150	−	12.6293i	0.772898	−	1.33870i	−0.163071	−	0.986614i	$-0.552140\pi$
$89$	7.29150	−	12.6293i	0.772898	−	1.33870i	0.935968	−	0.352084i	$-0.114527\pi$
$90$	−14.5830			−1.53718
$91$	6.61438	−	11.4564i	0.693375	−	1.20096i
$92$	−3.64575			−0.380096
$93$	−5.29150	+	9.16515i	−0.548703	+	0.950382i
$94$	6.64575	+	11.5108i	0.685457	+	1.18725i
$95$	0.645751	+	1.11847i	0.0662527	+	0.114753i
$96$	−1.32288	+	2.29129i	−0.135015	+	0.233854i
$97$	−5.70850			−0.579610			−0.289805	−	0.957086i	$-0.593590\pi$
$97$	−5.70850			−0.579610			−0.289805	+	0.957086i	$0.593590\pi$
$98$	−7.00000			−0.707107
$99$	4.00000			0.402015
$100$	−4.14575	+	7.18065i	−0.414575	+	0.718065i
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$	−7.93725	−	13.7477i	−0.785905	−	1.36123i
$103$	−6.46863	+	11.2040i	−0.637373	+	1.10396i	0.348634	+	0.937259i	$0.386646\pi$
$103$	−6.46863	+	11.2040i	−0.637373	+	1.10396i	−0.986007	+	0.166703i	$0.946688\pi$
$104$	−5.00000			−0.490290
$105$	−12.7601	+	22.1012i	−1.24526	+	2.15686i
$106$	3.64575			0.354107
$107$	−2.46863	+	4.27579i	−0.238651	+	0.413356i	−0.960327	−	0.278875i	$-0.910039\pi$
$107$	−2.46863	+	4.27579i	−0.238651	+	0.413356i	0.721676	+	0.692231i	$0.243372\pi$
$108$	1.32288	+	2.29129i	0.127294	+	0.220479i
$109$	−5.29150	−	9.16515i	−0.506834	−	0.877862i	−0.999969	−	0.00790932i	$-0.997482\pi$
$109$	−5.29150	−	9.16515i	−0.506834	−	0.877862i	0.493135	−	0.869953i	$-0.335851\pi$
$110$	1.82288	−	3.15731i	0.173804	−	0.301038i
$111$	4.35425			0.413287
$112$	1.32288	+	2.29129i	0.125000	+	0.216506i
$113$	−7.70850			−0.725154			−0.362577	−	0.931954i	$-0.618103\pi$
$113$	−7.70850			−0.725154			−0.362577	+	0.931954i	$0.618103\pi$
$114$	0.468627	−	0.811686i	0.0438909	−	0.0760213i
$115$	6.64575	+	11.5108i	0.619720	+	1.07339i
$116$	2.14575	+	3.71655i	0.199228	+	0.345073i
$117$	−10.0000	+	17.3205i	−0.924500	+	1.60128i
$118$	0.645751			0.0594462
$119$	−15.8745			−1.45521
$120$	9.64575			0.880533
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	1.85425	+	3.21165i	0.167876	+	0.290769i
$123$	−6.53137	−	11.3127i	−0.588914	−	1.02003i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	12.0000			1.07331
$126$	10.5830			0.942809
$127$	0.0627461			0.00556781			0.00278391	−	0.999996i	$-0.499114\pi$
$127$	0.0627461			0.00556781			0.00278391	+	0.999996i	$0.499114\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−5.29150	−	9.16515i	−0.465891	−	0.806947i
$130$	9.11438	+	15.7866i	0.799384	+	1.38457i
$131$	−7.82288	+	13.5496i	−0.683488	+	1.18384i	0.290422	+	0.956899i	$0.406204\pi$
$131$	−7.82288	+	13.5496i	−0.683488	+	1.18384i	−0.973909	+	0.226937i	$0.927129\pi$
$132$	−2.64575			−0.230283
$133$	−0.468627	−	0.811686i	−0.0406351	−	0.0703821i
$134$	−3.93725			−0.340127
$135$	4.82288	−	8.35347i	0.415087	−	0.718952i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−9.43725	−	16.3458i	−0.806279	−	1.39652i	−0.915424	−	0.402490i	$-0.868145\pi$
$137$	−9.43725	−	16.3458i	−0.806279	−	1.39652i	0.109145	−	0.994026i	$-0.465189\pi$
$138$	4.82288	−	8.35347i	0.410550	−	0.711094i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	4.82288	−	8.35347i	0.407607	−	0.705997i
$141$	−35.1660			−2.96151
$142$	4.82288	−	8.35347i	0.404727	−	0.701007i
$143$	−2.50000	−	4.33013i	−0.209061	−	0.362103i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	7.82288	−	13.5496i	0.649654	−	1.12523i
$146$	−5.64575			−0.467246
$147$	9.26013	−	16.0390i	0.763763	−	1.32288i
$148$	−1.64575			−0.135280
$149$	2.35425	−	4.07768i	0.192868	−	0.334056i	−0.753332	−	0.657641i	$-0.771555\pi$
$149$	2.35425	−	4.07768i	0.192868	−	0.334056i	0.946199	+	0.323584i	$0.104888\pi$
$150$	−10.9686	−	18.9982i	−0.895585	−	1.55120i
$151$	1.67712	+	2.90486i	0.136482	+	0.236395i	0.926163	−	0.377124i	$-0.123087\pi$
$151$	1.67712	+	2.90486i	0.136482	+	0.236395i	−0.789680	+	0.613519i	$0.789754\pi$
$152$	−0.177124	+	0.306788i	−0.0143667	+	0.0248838i
$153$	24.0000			1.94029
$154$	−1.32288	+	2.29129i	−0.106600	+	0.184637i
$155$	−14.5830			−1.17134
$156$	6.61438	−	11.4564i	0.529574	−	0.917249i
$157$	10.5830	+	18.3303i	0.844616	+	1.46292i	0.885954	+	0.463772i	$0.153504\pi$
$157$	10.5830	+	18.3303i	0.844616	+	1.46292i	−0.0413387	+	0.999145i	$0.513162\pi$
$158$	1.32288	+	2.29129i	0.105242	+	0.182285i
$159$	−4.82288	+	8.35347i	−0.382479	+	0.662473i
$160$	−3.64575			−0.288222
$161$	−4.82288	−	8.35347i	−0.380096	−	0.658345i
$162$	5.00000			0.392837
$163$	2.32288	−	4.02334i	0.181942	−	0.315132i	−0.760600	−	0.649221i	$-0.775095\pi$
$163$	2.32288	−	4.02334i	0.181942	−	0.315132i	0.942542	+	0.334089i	$0.108428\pi$
$164$	2.46863	+	4.27579i	0.192767	+	0.333883i
$165$	4.82288	+	8.35347i	0.375460	+	0.650316i
$166$	6.64575	−	11.5108i	0.515810	−	0.893410i
$167$	15.2288			1.17844			0.589218	−	0.807974i	$-0.299436\pi$
$167$	15.2288			1.17844			0.589218	+	0.807974i	$0.299436\pi$
$168$	−7.00000			−0.540062
$169$	12.0000			0.923077
$170$	10.9373	−	18.9439i	0.838849	−	1.45293i
$171$	0.708497	+	1.22715i	0.0541801	+	0.0938428i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−5.14575	+	8.91270i	−0.391224	+	0.677620i	−0.992611	−	0.121338i	$-0.961282\pi$
$173$	−5.14575	+	8.91270i	−0.391224	+	0.677620i	0.601387	+	0.798958i	$0.294615\pi$
$174$	−11.3542			−0.860763
$175$	−21.9373			−1.65830
$176$	1.00000			0.0753778
$177$	−0.854249	+	1.47960i	−0.0642093	+	0.111214i
$178$	−7.29150	−	12.6293i	−0.546521	−	0.946603i
$179$	2.03137	+	3.51844i	0.151832	+	0.262981i	0.931901	−	0.362713i	$-0.118149\pi$
$179$	2.03137	+	3.51844i	0.151832	+	0.262981i	−0.780069	+	0.625693i	$0.784816\pi$
$180$	−7.29150	+	12.6293i	−0.543477	+	0.941329i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−6.61438	−	11.4564i	−0.490290	−	0.849208i
$183$	−9.81176			−0.725306
$184$	−1.82288	+	3.15731i	−0.134384	+	0.232760i
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$	5.29150	+	9.16515i	0.387992	+	0.672022i
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$	13.2915			0.969382
$189$	−3.50000	+	6.06218i	−0.254588	+	0.440959i
$190$	1.29150			0.0936954
$191$	6.64575	−	11.5108i	0.480870	−	0.832891i	−0.518889	−	0.854841i	$-0.673654\pi$
$191$	6.64575	−	11.5108i	0.480870	−	0.832891i	0.999759	+	0.0219507i	$0.00698768\pi$
$192$	1.32288	+	2.29129i	0.0954703	+	0.165359i
$193$	5.76013	+	9.97684i	0.414623	+	0.718148i	0.995389	−	0.0959224i	$-0.0305801\pi$
$193$	5.76013	+	9.97684i	0.414623	+	0.718148i	−0.580766	+	0.814071i	$0.697247\pi$
$194$	−2.85425	+	4.94370i	−0.204923	+	0.354937i
$195$	−48.2288			−3.45373
$196$	−3.50000	+	6.06218i	−0.250000	+	0.433013i
$197$	18.8745			1.34475			0.672377	−	0.740209i	$-0.265274\pi$
$197$	18.8745			1.34475			0.672377	+	0.740209i	$0.265274\pi$
$198$	2.00000	−	3.46410i	0.142134	−	0.246183i
$199$	11.1144	+	19.2507i	0.787877	+	1.36464i	0.927265	+	0.374406i	$0.122153\pi$
$199$	11.1144	+	19.2507i	0.787877	+	1.36464i	−0.139388	+	0.990238i	$0.544513\pi$
$200$	4.14575	+	7.18065i	0.293149	+	0.507749i
$201$	5.20850	−	9.02138i	0.367379	−	0.636319i
$202$	−3.00000			−0.211079
$203$	−5.67712	+	9.83307i	−0.398456	+	0.690146i
$204$	−15.8745			−1.11144
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$	6.46863	+	11.2040i	0.450691	+	0.780619i
$207$	7.29150	+	12.6293i	0.506794	+	0.877794i
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$	−0.354249			−0.0245039
$210$	12.7601	+	22.1012i	0.880533	+	1.52513i
$211$	−14.9373			−1.02832			−0.514161	−	0.857693i	$-0.671897\pi$
$211$	−14.9373			−1.02832			−0.514161	+	0.857693i	$0.671897\pi$
$212$	1.82288	−	3.15731i	0.125196	−	0.216845i
$213$	12.7601	+	22.1012i	0.874310	+	1.51435i
$214$	2.46863	+	4.27579i	0.168752	+	0.292287i
$215$	7.29150	−	12.6293i	0.497276	−	0.861308i
$216$	2.64575			0.180021
$217$	10.5830			0.718421
$218$	−10.5830			−0.716772
$219$	7.46863	−	12.9360i	0.504683	−	0.874137i
$220$	−1.82288	−	3.15731i	−0.122898	−	0.212866i
$221$	−15.0000	−	25.9808i	−1.00901	−	1.74766i
$222$	2.17712	−	3.77089i	0.146119	−	0.253086i
$223$	−12.3542			−0.827302			−0.413651	−	0.910436i	$-0.635747\pi$
$223$	−12.3542			−0.827302			−0.413651	+	0.910436i	$0.635747\pi$
$224$	2.64575			0.176777
$225$	33.1660			2.21107
$226$	−3.85425	+	6.67575i	−0.256381	+	0.444065i
$227$	6.64575	+	11.5108i	0.441094	+	0.763997i	0.997771	−	0.0667318i	$-0.0212572\pi$
$227$	6.64575	+	11.5108i	0.441094	+	0.763997i	−0.556677	+	0.830729i	$0.687924\pi$
$228$	−0.468627	−	0.811686i	−0.0310356	−	0.0537552i
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	−0.470787	−	0.882247i	$-0.656030\pi$
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	0.999442	−	0.0334101i	$-0.0106368\pi$
$230$	13.2915			0.876416
$231$	−3.50000	−	6.06218i	−0.230283	−	0.398862i
$232$	4.29150			0.281751
$233$	−8.46863	+	14.6681i	−0.554798	+	0.960939i	0.443121	+	0.896462i	$0.353871\pi$
$233$	−8.46863	+	14.6681i	−0.554798	+	0.960939i	−0.997919	+	0.0644769i	$0.979462\pi$
$234$	10.0000	+	17.3205i	0.653720	+	1.13228i
$235$	−24.2288	−	41.9654i	−1.58051	−	2.73752i
$236$	0.322876	−	0.559237i	0.0210174	−	0.0364032i
$237$	−7.00000			−0.454699
$238$	−7.93725	+	13.7477i	−0.514496	+	0.891133i
$239$	9.22876			0.596959			0.298479	−	0.954416i	$-0.403521\pi$
$239$	9.22876			0.596959			0.298479	+	0.954416i	$0.403521\pi$
$240$	4.82288	−	8.35347i	0.311315	−	0.539214i
$241$	−11.4059	−	19.7556i	−0.734717	−	1.27257i	−0.954847	−	0.297097i	$-0.903981\pi$
$241$	−11.4059	−	19.7556i	−0.734717	−	1.27257i	0.220130	−	0.975471i	$-0.429352\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$	−10.5830	+	18.3303i	−0.678900	+	1.17589i
$244$	3.70850			0.237412
$245$	25.5203			1.63043
$246$	−13.0627			−0.832850
$247$	0.885622	−	1.53394i	0.0563508	−	0.0976024i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$	17.5830	+	30.4547i	1.11428	+	1.92999i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	7.29150			0.460236			0.230118	−	0.973163i	$-0.426089\pi$
$251$	7.29150			0.460236			0.230118	+	0.973163i	$0.426089\pi$
$252$	5.29150	−	9.16515i	0.333333	−	0.577350i
$253$	−3.64575			−0.229206
$254$	0.0313730	−	0.0543397i	0.00196852	−	0.00340958i
$255$	28.9373	+	50.1208i	1.81212	+	3.13869i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.208497	−	0.361128i	0.0130057	−	0.0225265i	−0.859449	−	0.511221i	$-0.829193\pi$
$257$	0.208497	−	0.361128i	0.0130057	−	0.0225265i	0.872455	+	0.488694i	$0.162527\pi$
$258$	−10.5830			−0.658869
$259$	−2.17712	−	3.77089i	−0.135280	−	0.234312i
$260$	18.2288			1.13050
$261$	8.58301	−	14.8662i	0.531275	−	0.920195i
$262$	7.82288	+	13.5496i	0.483299	+	0.837098i
$263$	−2.03137	−	3.51844i	−0.125260	−	0.216956i	0.796575	−	0.604540i	$-0.206643\pi$
$263$	−2.03137	−	3.51844i	−0.125260	−	0.216956i	−0.921834	+	0.387584i	$0.873310\pi$
$264$	−1.32288	+	2.29129i	−0.0814174	+	0.141019i
$265$	−13.2915			−0.816491
$266$	−0.937254			−0.0574667
$267$	38.5830			2.36124
$268$	−1.96863	+	3.40976i	−0.120253	+	0.208284i
$269$	−13.2915	−	23.0216i	−0.810397	−	1.40365i	−0.912586	−	0.408884i	$-0.865918\pi$
$269$	−13.2915	−	23.0216i	−0.810397	−	1.40365i	0.102189	−	0.994765i	$-0.467415\pi$
$270$	−4.82288	−	8.35347i	−0.293511	−	0.508376i
$271$	8.96863	−	15.5341i	0.544805	−	0.943630i	−0.453814	−	0.891097i	$-0.649937\pi$
$271$	8.96863	−	15.5341i	0.544805	−	0.943630i	0.998619	−	0.0525339i	$-0.0167298\pi$
$272$	6.00000			0.363803
$273$	35.0000			2.11830
$274$	−18.8745			−1.14025
$275$	−4.14575	+	7.18065i	−0.249998	+	0.433010i
$276$	−4.82288	−	8.35347i	−0.290303	−	0.502820i
$277$	5.85425	+	10.1399i	0.351748	+	0.609245i	0.986556	−	0.163425i	$-0.0522542\pi$
$277$	5.85425	+	10.1399i	0.351748	+	0.609245i	−0.634808	+	0.772670i	$0.718921\pi$
$278$	−2.00000	+	3.46410i	−0.119952	+	0.207763i
$279$	−16.0000			−0.957895
$280$	−4.82288	−	8.35347i	−0.288222	−	0.499215i
$281$	−7.06275			−0.421328			−0.210664	−	0.977559i	$-0.567563\pi$
$281$	−7.06275			−0.421328			−0.210664	+	0.977559i	$0.567563\pi$
$282$	−17.5830	+	30.4547i	−1.04705	+	1.81355i
$283$	3.82288	+	6.62141i	0.227246	+	0.393602i	0.956991	−	0.290118i	$-0.0936944\pi$
$283$	3.82288	+	6.62141i	0.227246	+	0.393602i	−0.729745	+	0.683720i	$0.760361\pi$
$284$	−4.82288	−	8.35347i	−0.286185	−	0.495687i
$285$	−1.70850	+	2.95920i	−0.101203	+	0.175288i
$286$	−5.00000			−0.295656
$287$	−6.53137	+	11.3127i	−0.385535	+	0.667766i
$288$	−4.00000			−0.235702
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	−7.82288	−	13.5496i	−0.459375	−	0.795661i
$291$	−7.55163	−	13.0798i	−0.442685	−	0.766752i
$292$	−2.82288	+	4.88936i	−0.165196	+	0.286128i
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$	−9.26013	−	16.0390i	−0.540062	−	0.935414i
$295$	−2.35425			−0.137070
$296$	−0.822876	+	1.42526i	−0.0478287	+	0.0828417i
$297$	1.32288	+	2.29129i	0.0767610	+	0.132954i
$298$	−2.35425	−	4.07768i	−0.136378	−	0.236214i
$299$	9.11438	−	15.7866i	0.527098	−	0.912961i
$300$	−21.9373			−1.26655
$301$	−5.29150	+	9.16515i	−0.304997	+	0.528271i
$302$	3.35425			0.193015
$303$	3.96863	−	6.87386i	0.227992	−	0.394893i
$304$	0.177124	+	0.306788i	0.0101588	+	0.0175955i
$305$	−6.76013	−	11.7089i	−0.387084	−	0.670449i
$306$	12.0000	−	20.7846i	0.685994	−	1.18818i
$307$	−4.22876			−0.241348			−0.120674	−	0.992692i	$-0.538506\pi$
$307$	−4.22876			−0.241348			−0.120674	+	0.992692i	$0.538506\pi$
$308$	1.32288	+	2.29129i	0.0753778	+	0.130558i
$309$	−34.2288			−1.94721
$310$	−7.29150	+	12.6293i	−0.414130	+	0.717293i
$311$	−8.46863	−	14.6681i	−0.480212	−	0.831751i	0.519531	−	0.854452i	$-0.326107\pi$
$311$	−8.46863	−	14.6681i	−0.480212	−	0.831751i	−0.999742	+	0.0227007i	$0.992774\pi$
$312$	−6.61438	−	11.4564i	−0.374465	−	0.648593i
$313$	−1.20850	+	2.09318i	−0.0683083	+	0.118313i	−0.898157	−	0.439675i	$-0.855093\pi$
$313$	−1.20850	+	2.09318i	−0.0683083	+	0.118313i	0.829848	+	0.557989i	$0.188427\pi$
$314$	21.1660			1.19447
$315$	−38.5830			−2.17391
$316$	2.64575			0.148835
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$	4.82288	+	8.35347i	0.270453	+	0.468439i
$319$	2.14575	+	3.71655i	0.120139	+	0.208087i
$320$	−1.82288	+	3.15731i	−0.101902	+	0.176499i
$321$	−13.0627			−0.729091
$322$	−9.64575			−0.537537
$323$	−2.12549			−0.118266
$324$	2.50000	−	4.33013i	0.138889	−	0.240563i
$325$	−20.7288	−	35.9033i	−1.14982	−	1.99155i
$326$	−2.32288	−	4.02334i	−0.128652	−	0.222832i
$327$	14.0000	−	24.2487i	0.774202	−	1.34096i
$328$	4.93725			0.272614
$329$	17.5830	+	30.4547i	0.969382	+	1.67902i
$330$	9.64575			0.530981
$331$	7.67712	−	13.2972i	0.421973	−	0.730879i	−0.574159	−	0.818743i	$-0.694671\pi$
$331$	7.67712	−	13.2972i	0.421973	−	0.730879i	0.996132	+	0.0878650i	$0.0280044\pi$
$332$	−6.64575	−	11.5108i	−0.364733	−	0.631736i
$333$	3.29150	+	5.70105i	0.180373	+	0.312416i
$334$	7.61438	−	13.1885i	0.416640	−	0.721642i
$335$	14.3542			0.784256
$336$	−3.50000	+	6.06218i	−0.190941	+	0.330719i
$337$	24.9373			1.35842			0.679209	−	0.733945i	$-0.262323\pi$
$337$	24.9373			1.35842			0.679209	+	0.733945i	$0.262323\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	−10.1974	−	17.6624i	−0.553846	−	0.959289i
$340$	−10.9373	−	18.9439i	−0.593156	−	1.02738i
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$	1.41699			0.0766223
$343$	−18.5203			−1.00000
$344$	4.00000			0.215666
$345$	−17.5830	+	30.4547i	−0.946637	+	1.63962i
$346$	5.14575	+	8.91270i	0.276637	+	0.479150i
$347$	−13.4059	−	23.2197i	−0.719665	−	1.24650i	−0.961132	−	0.276088i	$-0.910962\pi$
$347$	−13.4059	−	23.2197i	−0.719665	−	1.24650i	0.241467	−	0.970409i	$-0.422371\pi$
$348$	−5.67712	+	9.83307i	−0.304326	+	0.527108i
$349$	29.8745			1.59915			0.799573	−	0.600569i	$-0.205059\pi$
$349$	29.8745			1.59915			0.799573	+	0.600569i	$0.205059\pi$
$350$	−10.9686	+	18.9982i	−0.586298	+	1.01550i
$351$	−13.2288			−0.706099
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	17.5830	+	30.4547i	0.935849	+	1.62094i	0.773113	+	0.634268i	$0.218699\pi$
$353$	17.5830	+	30.4547i	0.935849	+	1.62094i	0.162736	+	0.986670i	$0.447968\pi$
$354$	0.854249	+	1.47960i	0.0454028	+	0.0786400i
$355$	−17.5830	+	30.4547i	−0.933209	+	1.61637i
$356$	−14.5830			−0.772898
$357$	−21.0000	−	36.3731i	−1.11144	−	1.92507i
$358$	4.06275			0.214723
$359$	5.03137	−	8.71459i	0.265546	−	0.459939i	−0.702161	−	0.712018i	$-0.747781\pi$
$359$	5.03137	−	8.71459i	0.265546	−	0.459939i	0.967706	+	0.252080i	$0.0811145\pi$
$360$	7.29150	+	12.6293i	0.384296	+	0.665620i
$361$	9.43725	+	16.3458i	0.496698	+	0.860305i
$362$	−5.00000	+	8.66025i	−0.262794	+	0.455173i
$363$	−2.64575			−0.138866
$364$	−13.2288			−0.693375
$365$	20.5830			1.07736
$366$	−4.90588	+	8.49723i	−0.256435	+	0.444158i
$367$	4.88562	+	8.46215i	0.255027	+	0.441720i	0.964903	−	0.262607i	$-0.0845822\pi$
$367$	4.88562	+	8.46215i	0.255027	+	0.441720i	−0.709876	+	0.704327i	$0.751249\pi$
$368$	1.82288	+	3.15731i	0.0950240	+	0.164586i
$369$	9.87451	−	17.1031i	0.514046	−	0.890354i
$370$	6.00000			0.311925
$371$	9.64575			0.500782
$372$	10.5830			0.548703
$373$	5.43725	−	9.41760i	0.281530	−	0.487625i	−0.690232	−	0.723589i	$-0.742491\pi$
$373$	5.43725	−	9.41760i	0.281530	−	0.487625i	0.971762	+	0.235964i	$0.0758247\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$	15.8745	+	27.4955i	0.819756	+	1.41986i
$376$	6.64575	−	11.5108i	0.342728	−	0.593623i
$377$	−21.4575			−1.10512
$378$	3.50000	+	6.06218i	0.180021	+	0.311805i
$379$	21.9373			1.12684			0.563421	−	0.826170i	$-0.309485\pi$
$379$	21.9373			1.12684			0.563421	+	0.826170i	$0.309485\pi$
$380$	0.645751	−	1.11847i	0.0331263	−	0.0573765i
$381$	0.0830052	+	0.143769i	0.00425249	+	0.00736552i
$382$	−6.64575	−	11.5108i	−0.340026	−	0.588943i
$383$	17.0516	−	29.5343i	0.871298	−	1.50913i	0.0106427	−	0.999943i	$-0.496612\pi$
$383$	17.0516	−	29.5343i	0.871298	−	1.50913i	0.860655	−	0.509189i	$-0.170054\pi$
$384$	2.64575			0.135015
$385$	4.82288	−	8.35347i	0.245797	−	0.425732i
$386$	11.5203			0.586366
$387$	8.00000	−	13.8564i	0.406663	−	0.704361i
$388$	2.85425	+	4.94370i	0.144903	+	0.250979i
$389$	10.4059	+	18.0235i	0.527599	+	0.913828i	0.999482	+	0.0321675i	$0.0102410\pi$
$389$	10.4059	+	18.0235i	0.527599	+	0.913828i	−0.471883	+	0.881661i	$0.656426\pi$
$390$	−24.1144	+	41.7673i	−1.22108	+	2.11497i
$391$	−21.8745			−1.10624
$392$	3.50000	+	6.06218i	0.176777	+	0.306186i
$393$	−41.3948			−2.08809
$394$	9.43725	−	16.3458i	0.475442	−	0.823490i
$395$	−4.82288	−	8.35347i	−0.242665	−	0.420308i
$396$	−2.00000	−	3.46410i	−0.100504	−	0.174078i
$397$	−15.5830	+	26.9906i	−0.782089	+	1.35462i	0.148634	+	0.988892i	$0.452512\pi$
$397$	−15.5830	+	26.9906i	−0.782089	+	1.35462i	−0.930723	+	0.365725i	$0.880821\pi$
$398$	22.2288			1.11423
$399$	1.23987	−	2.14752i	0.0620712	−	0.107510i
$400$	8.29150			0.414575
$401$	−0.208497	+	0.361128i	−0.0104119	+	0.0180339i	−0.871184	−	0.490956i	$-0.836648\pi$
$401$	−0.208497	+	0.361128i	−0.0104119	+	0.0180339i	0.860773	+	0.508990i	$0.169981\pi$
$402$	−5.20850	−	9.02138i	−0.259776	−	0.449946i
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$	−1.50000	+	2.59808i	−0.0746278	+	0.129259i
$405$	−18.2288			−0.905794
$406$	5.67712	+	9.83307i	0.281751	+	0.488007i
$407$	−1.64575			−0.0815769
$408$	−7.93725	+	13.7477i	−0.392953	+	0.680614i
$409$	−9.46863	−	16.4001i	−0.468193	−	0.810935i	0.531146	−	0.847280i	$-0.321762\pi$
$409$	−9.46863	−	16.4001i	−0.468193	−	0.810935i	−0.999339	+	0.0363456i	$0.988428\pi$
$410$	−9.00000	−	15.5885i	−0.444478	−	0.769859i
$411$	24.9686	−	43.2469i	1.23161	−	2.13321i
$412$	12.9373			0.637373
$413$	1.70850			0.0840697
$414$	14.5830			0.716716
$415$	−24.2288	+	41.9654i	−1.18934	+	2.06000i
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$	−5.29150	−	9.16515i	−0.259126	−	0.448819i
$418$	−0.177124	+	0.306788i	−0.00866343	+	0.0150055i
$419$	21.8745			1.06864			0.534320	−	0.845282i	$-0.320568\pi$
$419$	21.8745			1.06864			0.534320	+	0.845282i	$0.320568\pi$
$420$	25.5203			1.24526
$421$	−33.1660			−1.61641			−0.808206	−	0.588900i	$-0.799561\pi$
$421$	−33.1660			−1.61641			−0.808206	+	0.588900i	$0.799561\pi$
$422$	−7.46863	+	12.9360i	−0.363567	+	0.629717i
$423$	−26.5830	−	46.0431i	−1.29251	−	2.23869i
$424$	−1.82288	−	3.15731i	−0.0885267	−	0.153333i
$425$	−24.8745	+	43.0839i	−1.20659	+	2.08988i
$426$	25.5203			1.23646
$427$	4.90588	+	8.49723i	0.237412	+	0.411210i
$428$	4.93725			0.238651
$429$	6.61438	−	11.4564i	0.319345	−	0.553122i
$430$	−7.29150	−	12.6293i	−0.351627	−	0.609037i
$431$	−1.38562	−	2.39997i	−0.0667430	−	0.115602i	0.830723	−	0.556686i	$-0.187927\pi$
$431$	−1.38562	−	2.39997i	−0.0667430	−	0.115602i	−0.897466	+	0.441084i	$0.854594\pi$
$432$	1.32288	−	2.29129i	0.0636469	−	0.110240i
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$	5.29150	−	9.16515i	0.254000	−	0.439941i
$435$	41.3948			1.98473
$436$	−5.29150	+	9.16515i	−0.253417	+	0.438931i
$437$	−0.645751	−	1.11847i	−0.0308905	−	0.0535039i
$438$	−7.46863	−	12.9360i	−0.356865	−	0.618108i
$439$	5.96863	−	10.3380i	0.284867	−	0.493404i	−0.687710	−	0.725986i	$-0.741384\pi$
$439$	5.96863	−	10.3380i	0.284867	−	0.493404i	0.972577	+	0.232581i	$0.0747172\pi$
$440$	−3.64575			−0.173804
$441$	28.0000			1.33333
$442$	−30.0000			−1.42695
$443$	9.22876	−	15.9847i	0.438471	−	0.759455i	−0.559100	−	0.829100i	$-0.688853\pi$
$443$	9.22876	−	15.9847i	0.438471	−	0.759455i	0.997572	+	0.0696451i	$0.0221867\pi$
$444$	−2.17712	−	3.77089i	−0.103322	−	0.178959i
$445$	26.5830	+	46.0431i	1.26016	+	2.18265i
$446$	−6.17712	+	10.6991i	−0.292495	+	0.506617i
$447$	12.4575			0.589220
$448$	1.32288	−	2.29129i	0.0625000	−	0.108253i
$449$	9.87451			0.466007			0.233003	−	0.972476i	$-0.425145\pi$
$449$	9.87451			0.466007			0.233003	+	0.972476i	$0.425145\pi$
$450$	16.5830	−	28.7226i	0.781730	−	1.35400i
$451$	2.46863	+	4.27579i	0.116243	+	0.201339i
$452$	3.85425	+	6.67575i	0.181289	+	0.314001i
$453$	−4.43725	+	7.68555i	−0.208480	+	0.361099i
$454$	13.2915			0.623801
$455$	24.1144	+	41.7673i	1.13050	+	1.95808i
$456$	−0.937254			−0.0438909
$457$	19.5830	−	33.9188i	0.916054	−	1.58665i	0.110704	−	0.993853i	$-0.464689\pi$
$457$	19.5830	−	33.9188i	0.916054	−	1.58665i	0.805350	−	0.592799i	$-0.201977\pi$
$458$	−8.00000	−	13.8564i	−0.373815	−	0.647467i
$459$	7.93725	+	13.7477i	0.370479	+	0.641689i
$460$	6.64575	−	11.5108i	0.309860	−	0.536693i
$461$	−32.1660			−1.49812			−0.749060	−	0.662502i	$-0.769495\pi$
$461$	−32.1660			−1.49812			−0.749060	+	0.662502i	$0.769495\pi$
$462$	−7.00000			−0.325669
$463$	−22.4575			−1.04369			−0.521845	−	0.853041i	$-0.674756\pi$
$463$	−22.4575			−1.04369			−0.521845	+	0.853041i	$0.674756\pi$
$464$	2.14575	−	3.71655i	0.0996140	−	0.172537i
$465$	−19.2915	−	33.4139i	−0.894622	−	1.54953i
$466$	8.46863	+	14.6681i	0.392302	+	0.679486i
$467$	−5.35425	+	9.27383i	−0.247765	+	0.429142i	−0.962905	−	0.269839i	$-0.913029\pi$
$467$	−5.35425	+	9.27383i	−0.247765	+	0.429142i	0.715140	+	0.698981i	$0.246363\pi$
$468$	20.0000			0.924500
$469$	−10.4170			−0.481012
$470$	−48.4575			−2.23518
$471$	−28.0000	+	48.4974i	−1.29017	+	2.23464i
$472$	−0.322876	−	0.559237i	−0.0148616	−	0.0257410i
$473$	2.00000	+	3.46410i	0.0919601	+	0.159280i
$474$	−3.50000	+	6.06218i	−0.160760	+	0.278445i
$475$	−2.93725			−0.134770
$476$	7.93725	+	13.7477i	0.363803	+	0.630126i
$477$	−14.5830			−0.667710
$478$	4.61438	−	7.99234i	0.211057	−	0.365561i
$479$	12.9686	+	22.4623i	0.592552	+	1.02633i	0.993887	+	0.110399i	$0.0352127\pi$
$479$	12.9686	+	22.4623i	0.592552	+	1.02633i	−0.401336	+	0.915931i	$0.631454\pi$
$480$	−4.82288	−	8.35347i	−0.220133	−	0.381282i
$481$	4.11438	−	7.12631i	0.187600	−	0.324932i
$482$	−22.8118			−1.03905
$483$	12.7601	−	22.1012i	0.580606	−	1.00564i
$484$	1.00000			0.0454545
$485$	10.4059	−	18.0235i	0.472507	−	0.818406i
$486$	10.5830	+	18.3303i	0.480055	+	0.831479i
$487$	15.2915	+	26.4857i	0.692924	+	1.20018i	0.970875	+	0.239585i	$0.0770113\pi$
$487$	15.2915	+	26.4857i	0.692924	+	1.20018i	−0.277951	+	0.960595i	$0.589655\pi$
$488$	1.85425	−	3.21165i	0.0839379	−	0.145385i
$489$	12.2915			0.555841
$490$	12.7601	−	22.1012i	0.576444	−	0.998430i
$491$	10.7085			0.483268			0.241634	−	0.970367i	$-0.422317\pi$
$491$	10.7085			0.483268			0.241634	+	0.970367i	$0.422317\pi$
$492$	−6.53137	+	11.3127i	−0.294457	+	0.510015i
$493$	12.8745	+	22.2993i	0.579839	+	1.00431i
$494$	−0.885622	−	1.53394i	−0.0398460	−	0.0690153i
$495$	−7.29150	+	12.6293i	−0.327729	+	0.567643i
$496$	−4.00000			−0.179605
$497$	12.7601	−	22.1012i	0.572370	−	0.991374i
$498$	35.1660			1.57583
$499$	−8.93725	+	15.4798i	−0.400086	+	0.692970i	−0.993736	−	0.111754i	$-0.964353\pi$
$499$	−8.93725	+	15.4798i	−0.400086	+	0.692970i	0.593650	+	0.804724i	$0.297687\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$	20.1458	+	34.8935i	0.900046	+	1.55893i
$502$	3.64575	−	6.31463i	0.162718	−	0.281836i
$503$	−19.9373			−0.888958			−0.444479	−	0.895789i	$-0.646611\pi$
$503$	−19.9373			−0.888958			−0.444479	+	0.895789i	$0.646611\pi$
$504$	−5.29150	−	9.16515i	−0.235702	−	0.408248i
$505$	10.9373			0.486701
$506$	−1.82288	+	3.15731i	−0.0810367	+	0.140360i
$507$	15.8745	+	27.4955i	0.705012	+	1.22112i
$508$	−0.0313730	−	0.0543397i	−0.00139195	−	0.00241093i
$509$	−10.2915	+	17.8254i	−0.456163	+	0.790097i	−0.998754	−	0.0498996i	$-0.984110\pi$
$509$	−10.2915	+	17.8254i	−0.456163	+	0.790097i	0.542591	+	0.839997i	$0.317443\pi$
$510$	57.8745			2.56273
$511$	−14.9373			−0.660785
$512$	−1.00000			−0.0441942
$513$	−0.468627	+	0.811686i	−0.0206904	+	0.0358368i
$514$	−0.208497	−	0.361128i	−0.00919643	−	0.0159287i
$515$	−23.5830	−	40.8470i	−1.03919	−	1.79993i
$516$	−5.29150	+	9.16515i	−0.232945	+	0.403473i
$517$	13.2915			0.584560
$518$	−4.35425			−0.191315
$519$	−27.2288			−1.19521
$520$	9.11438	−	15.7866i	0.399692	−	0.692287i
$521$	1.06275	+	1.84073i	0.0465598	+	0.0806439i	0.888366	−	0.459136i	$-0.151841\pi$
$521$	1.06275	+	1.84073i	0.0465598	+	0.0806439i	−0.841806	+	0.539780i	$0.818508\pi$
$522$	−8.58301	−	14.8662i	−0.375668	−	0.650676i
$523$	−7.76013	+	13.4409i	−0.339327	+	0.587731i	−0.984306	−	0.176469i	$-0.943533\pi$
$523$	−7.76013	+	13.4409i	−0.339327	+	0.587731i	0.644979	+	0.764200i	$0.276866\pi$
$524$	15.6458			0.683488
$525$	−29.0203	−	50.2646i	−1.26655	−	2.19373i
$526$	−4.06275			−0.177144
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$	1.32288	+	2.29129i	0.0575708	+	0.0997155i
$529$	4.85425	+	8.40781i	0.211054	+	0.365557i
$530$	−6.64575	+	11.5108i	−0.288673	+	0.499996i
$531$	−2.58301			−0.112093
$532$	−0.468627	+	0.811686i	−0.0203176	+	0.0351910i
$533$	−24.6863			−1.06928
$534$	19.2915	−	33.4139i	0.834825	−	1.44596i
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$	1.96863	+	3.40976i	0.0850317	+	0.147279i
$537$	−5.37451	+	9.30892i	−0.231927	+	0.401710i
$538$	−26.5830			−1.14607
$539$	−3.50000	+	6.06218i	−0.150756	+	0.261116i
$540$	−9.64575			−0.415087
$541$	4.14575	−	7.18065i	0.178240	−	0.308720i	−0.763038	−	0.646354i	$-0.776293\pi$
$541$	4.14575	−	7.18065i	0.178240	−	0.308720i	0.941278	+	0.337633i	$0.109626\pi$
$542$	−8.96863	−	15.5341i	−0.385236	−	0.667247i
$543$	−13.2288	−	22.9129i	−0.567700	−	0.983286i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	38.5830			1.65271
$546$	17.5000	−	30.3109i	0.748931	−	1.29719i
$547$	27.5203			1.17668			0.588341	−	0.808613i	$-0.299781\pi$
$547$	27.5203			1.17668			0.588341	+	0.808613i	$0.299781\pi$
$548$	−9.43725	+	16.3458i	−0.403140	+	0.698258i
$549$	−7.41699	−	12.8466i	−0.316550	−	0.548280i
$550$	4.14575	+	7.18065i	0.176775	+	0.306184i
$551$	−0.760130	+	1.31658i	−0.0323826	+	0.0560883i
$552$	−9.64575			−0.410550
$553$	3.50000	+	6.06218i	0.148835	+	0.257790i
$554$	11.7085			0.497446
$555$	−7.93725	+	13.7477i	−0.336918	+	0.583559i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−15.8745	−	27.4955i	−0.672624	−	1.16502i	−0.977157	−	0.212518i	$-0.931834\pi$
$557$	−15.8745	−	27.4955i	−0.672624	−	1.16502i	0.304533	−	0.952502i	$-0.401500\pi$
$558$	−8.00000	+	13.8564i	−0.338667	+	0.586588i
$559$	−20.0000			−0.845910
$560$	−9.64575			−0.407607
$561$	−15.8745			−0.670222
$562$	−3.53137	+	6.11652i	−0.148962	+	0.258010i
$563$	−6.53137	−	11.3127i	−0.275265	−	0.476772i	0.694937	−	0.719070i	$-0.255432\pi$
$563$	−6.53137	−	11.3127i	−0.275265	−	0.476772i	−0.970202	+	0.242298i	$0.922099\pi$
$564$	17.5830	+	30.4547i	0.740378	+	1.28237i
$565$	14.0516	−	24.3381i	0.591157	−	1.02391i
$566$	7.64575			0.321375
$567$	13.2288			0.555556
$568$	−9.64575			−0.404727
$569$	20.5830	−	35.6508i	0.862884	−	1.49456i	−0.00624806	−	0.999980i	$-0.501989\pi$
$569$	20.5830	−	35.6508i	0.862884	−	1.49456i	0.869133	−	0.494579i	$-0.164678\pi$
$570$	1.70850	+	2.95920i	0.0715611	+	0.123947i
$571$	22.4686	+	38.9168i	0.940283	+	1.62862i	0.764932	+	0.644112i	$0.222773\pi$
$571$	22.4686	+	38.9168i	0.940283	+	1.62862i	0.175351	+	0.984506i	$0.443894\pi$
$572$	−2.50000	+	4.33013i	−0.104530	+	0.181052i
$573$	35.1660			1.46908
$574$	6.53137	+	11.3127i	0.272614	+	0.472182i
$575$	−30.2288			−1.26063
$576$	−2.00000	+	3.46410i	−0.0833333	+	0.144338i
$577$	12.7288	+	22.0469i	0.529905	+	0.917823i	0.999391	+	0.0348828i	$0.0111058\pi$
$577$	12.7288	+	22.0469i	0.529905	+	0.917823i	−0.469486	+	0.882940i	$0.655561\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	−15.2399	+	26.3962i	−0.633347	+	1.09699i
$580$	−15.6458			−0.649654
$581$	17.5830	−	30.4547i	0.729466	−	1.26347i
$582$	−15.1033			−0.626050
$583$	1.82288	−	3.15731i	0.0754958	−	0.130763i
$584$	2.82288	+	4.88936i	0.116811	+	0.202323i
$585$	−36.4575	−	63.1463i	−1.50733	−	2.61078i
$586$	6.00000	−	10.3923i	0.247858	−	0.429302i
$587$	−7.93725			−0.327606			−0.163803	−	0.986493i	$-0.552376\pi$
$587$	−7.93725			−0.327606			−0.163803	+	0.986493i	$0.552376\pi$
$588$	−18.5203			−0.763763
$589$	1.41699			0.0583863
$590$	−1.17712	+	2.03884i	−0.0484614	+	0.0839377i
$591$	24.9686	+	43.2469i	1.02707	+	1.77894i
$592$	0.822876	+	1.42526i	0.0338200	+	0.0585779i
$593$	−11.4686	+	19.8642i	−0.470960	+	0.815727i	−0.999448	−	0.0332139i	$-0.989426\pi$
$593$	−11.4686	+	19.8642i	−0.470960	+	0.815727i	0.528488	+	0.848941i	$0.322759\pi$
$594$	2.64575			0.108556
$595$	28.9373	−	50.1208i	1.18631	−	2.05475i
$596$	−4.70850			−0.192868
$597$	−29.4059	+	50.9325i	−1.20350	+	2.08453i
$598$	−9.11438	−	15.7866i	−0.372715	−	0.645561i
$599$	9.87451	+	17.1031i	0.403461	+	0.698816i	0.994141	−	0.108090i	$-0.0344736\pi$
$599$	9.87451	+	17.1031i	0.403461	+	0.698816i	−0.590680	+	0.806906i	$0.701140\pi$
$600$	−10.9686	+	18.9982i	−0.447792	+	0.775599i
$601$	−24.5830			−1.00276			−0.501381	−	0.865227i	$-0.667174\pi$
$601$	−24.5830			−1.00276			−0.501381	+	0.865227i	$0.667174\pi$
$602$	5.29150	+	9.16515i	0.215666	+	0.373544i
$603$	15.7490			0.641350
$604$	1.67712	−	2.90486i	0.0682412	−	0.118197i
$605$	−1.82288	−	3.15731i	−0.0741104	−	0.128363i
$606$	−3.96863	−	6.87386i	−0.161214	−	0.279232i
$607$	−10.6458	+	18.4390i	−0.432098	+	0.748415i	−0.997054	−	0.0767058i	$-0.975560\pi$
$607$	−10.6458	+	18.4390i	−0.432098	+	0.748415i	0.564956	+	0.825121i	$0.308893\pi$
$608$	0.354249			0.0143667
$609$	−30.0405			−1.21730
$610$	−13.5203			−0.547419
$611$	−33.2288	+	57.5539i	−1.34429	+	2.32838i
$612$	−12.0000	−	20.7846i	−0.485071	−	0.840168i
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	−2.11438	+	3.66221i	−0.0853294	+	0.147795i
$615$	47.6235			1.92037
$616$	2.64575			0.106600
$617$	−16.2915			−0.655871			−0.327936	−	0.944700i	$-0.606353\pi$
$617$	−16.2915			−0.655871			−0.327936	+	0.944700i	$0.606353\pi$
$618$	−17.1144	+	29.6430i	−0.688441	+	1.19242i
$619$	−17.2915	−	29.9498i	−0.695004	−	1.20378i	−0.970179	−	0.242388i	$-0.922069\pi$
$619$	−17.2915	−	29.9498i	−0.695004	−	1.20378i	0.275175	−	0.961394i	$-0.411264\pi$
$620$	7.29150	+	12.6293i	0.292834	+	0.507203i
$621$	−4.82288	+	8.35347i	−0.193535	+	0.335213i
$622$	−16.9373			−0.679122
$623$	−19.2915	−	33.4139i	−0.772898	−	1.33870i
$624$	−13.2288			−0.529574
$625$	−1.14575	+	1.98450i	−0.0458301	+	0.0793800i
$626$	1.20850	+	2.09318i	0.0483013	+	0.0836603i
$627$	−0.468627	−	0.811686i	−0.0187152	−	0.0324156i
$628$	10.5830	−	18.3303i	0.422308	−	0.731459i
$629$	−9.87451			−0.393722
$630$	−19.2915	+	33.4139i	−0.768592	+	1.33124i
$631$	34.8118			1.38583			0.692917	−	0.721017i	$-0.256325\pi$
$631$	34.8118			1.38583			0.692917	+	0.721017i	$0.256325\pi$
$632$	1.32288	−	2.29129i	0.0526212	−	0.0911425i
$633$	−19.7601	−	34.2255i	−0.785395	−	1.36034i
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$	−0.114378	+	0.198109i	−0.00453896	+	0.00786172i
$636$	9.64575			0.382479
$637$	−17.5000	−	30.3109i	−0.693375	−	1.20096i
$638$	4.29150			0.169902
$639$	−19.2915	+	33.4139i	−0.763160	+	1.32183i
$640$	1.82288	+	3.15731i	0.0720555	+	0.124804i
$641$	9.43725	+	16.3458i	0.372749	+	0.645620i	0.989987	−	0.141156i	$-0.0450819\pi$
$641$	9.43725	+	16.3458i	0.372749	+	0.645620i	−0.617238	+	0.786776i	$0.711749\pi$
$642$	−6.53137	+	11.3127i	−0.257773	+	0.446475i
$643$	6.52026			0.257134			0.128567	−	0.991701i	$-0.458962\pi$
$643$	6.52026			0.257134			0.128567	+	0.991701i	$0.458962\pi$
$644$	−4.82288	+	8.35347i	−0.190048	+	0.329173i
$645$	38.5830			1.51920
$646$	−1.06275	+	1.84073i	−0.0418132	+	0.0724226i
$647$	−19.4059	−	33.6120i	−0.762924	−	1.32142i	−0.941337	−	0.337467i	$-0.890430\pi$
$647$	−19.4059	−	33.6120i	−0.762924	−	1.32142i	0.178413	−	0.983956i	$-0.442904\pi$
$648$	−2.50000	−	4.33013i	−0.0982093	−	0.170103i
$649$	0.322876	−	0.559237i	0.0126740	−	0.0219520i
$650$	−41.4575			−1.62610
$651$	14.0000	+	24.2487i	0.548703	+	0.950382i
$652$	−4.64575			−0.181942
$653$	−1.17712	+	2.03884i	−0.0460644	+	0.0797859i	−0.888138	−	0.459576i	$-0.848001\pi$
$653$	−1.17712	+	2.03884i	−0.0460644	+	0.0797859i	0.842074	+	0.539362i	$0.181335\pi$
$654$	−14.0000	−	24.2487i	−0.547443	−	0.948200i
$655$	−28.5203	−	49.3985i	−1.11438	−	1.93016i
$656$	2.46863	−	4.27579i	0.0963837	−	0.166941i
$657$	22.5830			0.881047
$658$	35.1660			1.37091
$659$	14.5830			0.568073			0.284037	−	0.958813i	$-0.408326\pi$
$659$	14.5830			0.568073			0.284037	+	0.958813i	$0.408326\pi$
$660$	4.82288	−	8.35347i	0.187730	−	0.325158i
$661$	−14.2915	−	24.7536i	−0.555875	−	0.962804i	−0.997835	−	0.0657690i	$-0.979050\pi$
$661$	−14.2915	−	24.7536i	−0.555875	−	0.962804i	0.441960	−	0.897035i	$-0.354283\pi$
$662$	−7.67712	−	13.2972i	−0.298380	−	0.516809i
$663$	39.6863	−	68.7386i	1.54129	−	2.66959i
$664$	−13.2915			−0.515810
$665$	3.41699			0.132505
$666$	6.58301			0.255086
$667$	−7.82288	+	13.5496i	−0.302903	+	0.524643i
$668$	−7.61438	−	13.1885i	−0.294609	−	0.510278i
$669$	−16.3431	−	28.3071i	−0.631862	−	1.09442i
$670$	7.17712	−	12.4311i	0.277277	−	0.480257i
$671$	3.70850			0.143165
$672$	3.50000	+	6.06218i	0.135015	+	0.233854i
$673$	−14.9373			−0.575789			−0.287894	−	0.957662i	$-0.592955\pi$
$673$	−14.9373			−0.575789			−0.287894	+	0.957662i	$0.592955\pi$
$674$	12.4686	−	21.5963i	0.480274	−	0.831858i
$675$	10.9686	+	18.9982i	0.422183	+	0.731242i
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	1.06275	−	1.84073i	0.0408446	−	0.0707450i	−0.844880	−	0.534955i	$-0.820328\pi$
$677$	1.06275	−	1.84073i	0.0408446	−	0.0707450i	0.885725	+	0.464210i	$0.153662\pi$
$678$	−20.3948			−0.783256
$679$	−7.55163	+	13.0798i	−0.289805	+	0.501957i
$680$	−21.8745			−0.838849
$681$	−17.5830	+	30.4547i	−0.673782	+	1.16703i
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	6.96863	+	12.0700i	0.266647	+	0.461846i	0.967994	−	0.250974i	$-0.0807509\pi$
$683$	6.96863	+	12.0700i	0.266647	+	0.461846i	−0.701347	+	0.712820i	$0.747418\pi$
$684$	0.708497	−	1.22715i	0.0270901	−	0.0469214i
$685$	68.8118			2.62916
$686$	−9.26013	+	16.0390i	−0.353553	+	0.612372i
$687$	42.3320			1.61507
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	9.11438	+	15.7866i	0.347230	+	0.601420i
$690$	17.5830	+	30.4547i	0.669374	+	1.15939i
$691$	9.38562	−	16.2564i	0.357046	−	0.618422i	−0.630420	−	0.776254i	$-0.717117\pi$
$691$	9.38562	−	16.2564i	0.357046	−	0.618422i	0.987466	+	0.157833i	$0.0504506\pi$
$692$	10.2915			0.391224
$693$	5.29150	−	9.16515i	0.201008	−	0.348155i
$694$	−26.8118			−1.01776
$695$	7.29150	−	12.6293i	0.276582	−	0.479055i
$696$	5.67712	+	9.83307i	0.215191	+	0.372721i
$697$	14.8118	+	25.6547i	0.561035	+	0.971742i
$698$	14.9373	−	25.8721i	0.565383	−	0.979273i
$699$	−44.8118			−1.69494
$700$	10.9686	+	18.9982i	0.414575	+	0.718065i
$701$	−6.87451			−0.259647			−0.129823	−	0.991537i	$-0.541441\pi$
$701$	−6.87451			−0.259647			−0.129823	+	0.991537i	$0.541441\pi$
$702$	−6.61438	+	11.4564i	−0.249644	+	0.432395i
$703$	−0.291503	−	0.504897i	−0.0109942	−	0.0190426i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	64.1033	−	111.030i	2.41427	−	4.18164i
$706$	35.1660			1.32349
$707$	−7.93725			−0.298511
$708$	1.70850			0.0642093
$709$	3.40588	−	5.89916i	0.127911	−	0.221548i	−0.794956	−	0.606667i	$-0.792506\pi$
$709$	3.40588	−	5.89916i	0.127911	−	0.221548i	0.922867	+	0.385119i	$0.125840\pi$
$710$	17.5830	+	30.4547i	0.659878	+	1.14294i
$711$	−5.29150	−	9.16515i	−0.198447	−	0.343720i
$712$	−7.29150	+	12.6293i	−0.273261	+	0.473301i
$713$	14.5830			0.546138
$714$	−42.0000			−1.57181
$715$	18.2288			0.681717
$716$	2.03137	−	3.51844i	0.0759160	−	0.131490i
$717$	12.2085	+	21.1457i	0.455935	+	0.789702i
$718$	−5.03137	−	8.71459i	−0.187769	−	0.325226i
$719$	1.93725	−	3.35542i	0.0722474	−	0.125136i	−0.827639	−	0.561261i	$-0.810316\pi$
$719$	1.93725	−	3.35542i	0.0722474	−	0.125136i	0.899886	+	0.436125i	$0.143650\pi$
$720$	14.5830			0.543477
$721$	17.1144	+	29.6430i	0.637373	+	1.10396i
$722$	18.8745			0.702436
$723$	30.1771	−	52.2683i	1.12230	−	1.94388i
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	17.7915	+	30.8158i	0.660760	+	1.14447i
$726$	−1.32288	+	2.29129i	−0.0490965	+	0.0850377i
$727$	−17.2915			−0.641306			−0.320653	−	0.947197i	$-0.603902\pi$
$727$	−17.2915			−0.641306			−0.320653	+	0.947197i	$0.603902\pi$
$728$	−6.61438	+	11.4564i	−0.245145	+	0.424604i
$729$	−41.0000			−1.51852
$730$	10.2915	−	17.8254i	0.380906	−	0.659748i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	4.90588	+	8.49723i	0.181327	+	0.314067i
$733$	−20.7288	+	35.9033i	−0.765634	+	1.32612i	0.174277	+	0.984697i	$0.444241\pi$
$733$	−20.7288	+	35.9033i	−0.765634	+	1.32612i	−0.939911	+	0.341420i	$0.889092\pi$
$734$	9.77124			0.360663
$735$	33.7601	+	58.4743i	1.24526	+	2.15686i
$736$	3.64575			0.134384
$737$	−1.96863	+	3.40976i	−0.0725153	+	0.125600i
$738$	−9.87451	−	17.1031i	−0.363486	−	0.629576i
$739$	3.93725	+	6.81952i	0.144834	+	0.250860i	0.929311	−	0.369298i	$-0.120402\pi$
$739$	3.93725	+	6.81952i	0.144834	+	0.250860i	−0.784477	+	0.620158i	$0.787068\pi$
$740$	3.00000	−	5.19615i	0.110282	−	0.191014i
$741$	4.68627			0.172154
$742$	4.82288	−	8.35347i	0.177053	−	0.306665i
$743$	−34.7085			−1.27333			−0.636666	−	0.771140i	$-0.719687\pi$
$743$	−34.7085			−1.27333			−0.636666	+	0.771140i	$0.719687\pi$
$744$	5.29150	−	9.16515i	0.193996	−	0.336011i
$745$	8.58301	+	14.8662i	0.314457	+	0.544655i
$746$	−5.43725	−	9.41760i	−0.199072	−	0.344803i
$747$	−26.5830	+	46.0431i	−0.972621	+	1.68463i
$748$	6.00000			0.219382
$749$	6.53137	+	11.3127i	0.238651	+	0.413356i
$750$	31.7490			1.15931
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	−6.64575	−	11.5108i	−0.242346	−	0.419755i
$753$	9.64575	+	16.7069i	0.351511	+	0.608834i
$754$	−10.7288	+	18.5828i	−0.390718	+	0.676744i
$755$	−12.2288			−0.445050
$756$	7.00000			0.254588
$757$	19.1660			0.696600			0.348300	−	0.937383i	$-0.386759\pi$
$757$	19.1660			0.696600			0.348300	+	0.937383i	$0.386759\pi$
$758$	10.9686	−	18.9982i	0.398398	−	0.690046i
$759$	−4.82288	−	8.35347i	−0.175059	−	0.303212i
$760$	−0.645751	−	1.11847i	−0.0234239	−	0.0405713i
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$	0.166010			0.00601393
$763$	−28.0000			−1.01367
$764$	−13.2915			−0.480870
$765$	−43.7490	+	75.7755i	−1.58175	+	2.73967i
$766$	−17.0516	−	29.5343i	−0.616101	−	1.06712i
$767$	1.61438	+	2.79619i	0.0582918	+	0.100964i
$768$	1.32288	−	2.29129i	0.0477352	−	0.0826797i
$769$	−15.1660			−0.546900			−0.273450	−	0.961886i	$-0.588165\pi$
$769$	−15.1660			−0.546900			−0.273450	+	0.961886i	$0.588165\pi$
$770$	−4.82288	−	8.35347i	−0.173804	−	0.301038i
$771$	1.10326			0.0397331
$772$	5.76013	−	9.97684i	0.207312	−	0.359074i
$773$	−1.29150	−	2.23695i	−0.0464521	−	0.0804574i	0.841864	−	0.539689i	$-0.181458\pi$
$773$	−1.29150	−	2.23695i	−0.0464521	−	0.0804574i	−0.888317	+	0.459232i	$0.848125\pi$
$774$	−8.00000	−	13.8564i	−0.287554	−	0.498058i
$775$	16.5830	−	28.7226i	0.595679	−	1.03175i
$776$	5.70850			0.204923
$777$	5.76013	−	9.97684i	0.206643	−	0.357917i
$778$	20.8118			0.746138
$779$	−0.874508	+	1.51469i	−0.0313325	+	0.0542695i
$780$	24.1144	+	41.7673i	0.863433	+	1.49551i
$781$	−4.82288	−	8.35347i	−0.172576	−	0.298911i
$782$	−10.9373	+	18.9439i	−0.391115	+	0.677432i
$783$	11.3542			0.405768
$784$	7.00000			0.250000
$785$	−77.1660			−2.75417
$786$	−20.6974	+	35.8489i	−0.738251	+	1.27869i
$787$	0.405881	+	0.703006i	0.0144681	+	0.0250595i	0.873169	−	0.487418i	$-0.162061\pi$
$787$	0.405881	+	0.703006i	0.0144681	+	0.0250595i	−0.858701	+	0.512477i	$0.828728\pi$
$788$	−9.43725	−	16.3458i	−0.336188	−	0.582295i
$789$	5.37451	−	9.30892i	0.191338	−	0.331406i
$790$	−9.64575			−0.343180
$791$	−10.1974	+	17.6624i	−0.362577	+	0.628002i
$792$	−4.00000			−0.142134
$793$	−9.27124	+	16.0583i	−0.329232	+	0.570246i
$794$	15.5830	+	26.9906i	0.553020	+	0.957859i
$795$	−17.5830	−	30.4547i	−0.623605	−	1.08012i
$796$	11.1144	−	19.2507i	0.393939	−	0.682322i
$797$	−35.1660			−1.24564			−0.622822	−	0.782364i	$-0.714014\pi$
$797$	−35.1660			−1.24564			−0.622822	+	0.782364i	$0.714014\pi$
$798$	−1.23987	−	2.14752i	−0.0438909	−	0.0760213i
$799$	79.7490			2.82132
$800$	4.14575	−	7.18065i	0.146574	−	0.253874i
$801$	29.1660	+	50.5170i	1.03053	+	1.78493i
$802$	0.208497	+	0.361128i	0.00736230	+	0.0127519i
$803$	−2.82288	+	4.88936i	−0.0996171	+	0.172542i
$804$	−10.4170			−0.367379
$805$	35.1660			1.23944
$806$	20.0000			0.704470
$807$	35.1660	−	60.9093i	1.23790	−	2.14411i
$808$	1.50000	+	2.59808i	0.0527698	+	0.0914000i
$809$	−25.2915	−	43.8062i	−0.889202	−	1.54014i	−0.840821	−	0.541314i	$-0.817927\pi$
$809$	−25.2915	−	43.8062i	−0.889202	−	1.54014i	−0.0483813	−	0.998829i	$-0.515406\pi$
$810$	−9.11438	+	15.7866i	−0.320247	+	0.554683i
$811$	27.7490			0.974400			0.487200	−	0.873290i	$-0.338018\pi$
$811$	27.7490			0.974400			0.487200	+	0.873290i	$0.338018\pi$
$812$	11.3542			0.398456
$813$	47.4575			1.66441
$814$	−0.822876	+	1.42526i	−0.0288418	+	0.0499554i
$815$	8.46863	+	14.6681i	0.296643	+	0.513801i
$816$	7.93725	+	13.7477i	0.277859	+	0.481267i
$817$	−0.708497	+	1.22715i	−0.0247872	+	0.0429327i
$818$	−18.9373			−0.662126
$819$	26.4575	+	45.8258i	0.924500	+	1.60128i
$820$	−18.0000			−0.628587
$821$	3.85425	−	6.67575i	0.134514	−	0.232985i	−0.790898	−	0.611949i	$-0.790386\pi$
$821$	3.85425	−	6.67575i	0.134514	−	0.232985i	0.925412	+	0.378963i	$0.123719\pi$
$822$	−24.9686	−	43.2469i	−0.870881	−	1.50841i
$823$	21.9373	+	37.9964i	0.764685	+	1.32447i	0.940413	+	0.340034i	$0.110439\pi$
$823$	21.9373	+	37.9964i	0.764685	+	1.32447i	−0.175729	+	0.984439i	$0.556228\pi$
$824$	6.46863	−	11.2040i	0.225345	−	0.390310i
$825$	−21.9373			−0.763757
$826$	0.854249	−	1.47960i	0.0297231	−	0.0514819i
$827$	−35.3948			−1.23080			−0.615398	−	0.788216i	$-0.711005\pi$
$827$	−35.3948			−1.23080			−0.615398	+	0.788216i	$0.711005\pi$
$828$	7.29150	−	12.6293i	0.253397	−	0.438897i
$829$	−21.6974	−	37.5810i	−0.753581	−	1.30524i	−0.946077	−	0.323943i	$-0.894991\pi$
$829$	−21.6974	−	37.5810i	−0.753581	−	1.30524i	0.192495	−	0.981298i	$-0.438342\pi$
$830$	24.2288	+	41.9654i	0.840992	+	1.45664i
$831$	−15.4889	+	26.8275i	−0.537304	+	0.930637i
$832$	5.00000			0.173344
$833$	−21.0000	+	36.3731i	−0.727607	+	1.26025i
$834$	−10.5830			−0.366460
$835$	−27.7601	+	48.0820i	−0.960679	+	1.66394i
$836$	0.177124	+	0.306788i	0.00612597	+	0.0106105i
$837$	−5.29150	−	9.16515i	−0.182901	−	0.316794i
$838$	10.9373	−	18.9439i	0.377821	−	0.654405i
$839$	27.8745			0.962335			0.481167	−	0.876629i	$-0.340213\pi$
$839$	27.8745			0.962335			0.481167	+	0.876629i	$0.340213\pi$
$840$	12.7601	−	22.1012i	0.440266	−	0.762564i
$841$	−10.5830			−0.364931
$842$	−16.5830	+	28.7226i	−0.571488	+	0.989846i
$843$	−9.34313	−	16.1828i	−0.321795	−	0.557365i
$844$	7.46863	+	12.9360i	0.257081	+	0.445277i
$845$	−21.8745	+	37.8878i	−0.752506	+	1.30338i
$846$	−53.1660			−1.82789
$847$	1.32288	+	2.29129i	0.0454545	+	0.0787296i
$848$	−3.64575			−0.125196
$849$	−10.1144	+	17.5186i	−0.347125	+	0.601237i
$850$	24.8745	+	43.0839i	0.853189	+	1.47777i
$851$	−3.00000	−	5.19615i	−0.102839	−	0.178122i
$852$	12.7601	−	22.1012i	0.437155	−	0.757174i
$853$	−3.16601			−0.108402			−0.0542011	−	0.998530i	$-0.517261\pi$
$853$	−3.16601			−0.108402			−0.0542011	+	0.998530i	$0.517261\pi$
$854$	9.81176			0.335752
$855$	−5.16601			−0.176674
$856$	2.46863	−	4.27579i	0.0843759	−	0.146143i
$857$	−18.0000	−	31.1769i	−0.614868	−	1.06498i	−0.990408	−	0.138177i	$-0.955876\pi$
$857$	−18.0000	−	31.1769i	−0.614868	−	1.06498i	0.375539	−	0.926806i	$-0.377458\pi$
$858$	−6.61438	−	11.4564i	−0.225811	−	0.391116i
$859$	−18.9059	+	32.7459i	−0.645060	+	1.11728i	0.339227	+	0.940704i	$0.389834\pi$
$859$	−18.9059	+	32.7459i	−0.645060	+	1.11728i	−0.984288	+	0.176573i	$0.943499\pi$
$860$	−14.5830			−0.497276
$861$	−34.5608			−1.17783
$862$	−2.77124			−0.0943889
$863$	24.7601	−	42.8858i	0.842845	−	1.45985i	−0.0446353	−	0.999003i	$-0.514213\pi$
$863$	24.7601	−	42.8858i	0.842845	−	1.45985i	0.887480	−	0.460846i	$-0.152454\pi$
$864$	−1.32288	−	2.29129i	−0.0450051	−	0.0779512i
$865$	−18.7601	−	32.4935i	−0.637864	−	1.10481i
$866$	−8.00000	+	13.8564i	−0.271851	+	0.470860i
$867$	−50.2693			−1.70723
$868$	−5.29150	−	9.16515i	−0.179605	−	0.311086i
$869$	2.64575			0.0897510
$870$	20.6974	−	35.8489i	0.701707	−	1.21539i
$871$	−9.84313	−	17.0488i	−0.333522	−	0.577677i
$872$	5.29150	+	9.16515i	0.179193	+	0.310371i
$873$	11.4170	−	19.7748i	0.386407	−	0.669276i
$874$	−1.29150			−0.0436857
$875$	15.8745	−	27.4955i	0.536656	−	0.929516i
$876$	−14.9373			−0.504683
$877$	−4.43725	+	7.68555i	−0.149835	+	0.259523i	−0.931167	−	0.364594i	$-0.881208\pi$
$877$	−4.43725	+	7.68555i	−0.149835	+	0.259523i	0.781331	+	0.624117i	$0.214541\pi$
$878$	−5.96863	−	10.3380i	−0.201431	−	0.348889i
$879$	15.8745	+	27.4955i	0.535434	+	0.927399i
$880$	−1.82288	+	3.15731i	−0.0614491	+	0.106433i
$881$	6.87451			0.231608			0.115804	−	0.993272i	$-0.463056\pi$
$881$	6.87451			0.231608			0.115804	+	0.993272i	$0.463056\pi$
$882$	14.0000	−	24.2487i	0.471405	−	0.816497i
$883$	6.06275			0.204028			0.102014	−	0.994783i	$-0.467471\pi$
$883$	6.06275			0.204028			0.102014	+	0.994783i	$0.467471\pi$
$884$	−15.0000	+	25.9808i	−0.504505	+	0.873828i
$885$	−3.11438	−	5.39426i	−0.104689	−	0.181326i
$886$	−9.22876	−	15.9847i	−0.310046	−	0.537016i
$887$	6.55163	−	11.3478i	0.219982	−	0.381020i	−0.734820	−	0.678262i	$-0.762733\pi$
$887$	6.55163	−	11.3478i	0.219982	−	0.381020i	0.954802	+	0.297242i	$0.0960667\pi$
$888$	−4.35425			−0.146119
$889$	0.0830052	−	0.143769i	0.00278391	−	0.00482187i
$890$	53.1660			1.78213
$891$	2.50000	−	4.33013i	0.0837532	−	0.145065i
$892$	6.17712	+	10.6991i	0.206825	+	0.358232i
$893$	2.35425	+	4.07768i	0.0787819	+	0.136454i
$894$	6.22876	−	10.7885i	0.208321	−	0.360822i
$895$	−14.8118			−0.495103
$896$	−1.32288	−	2.29129i	−0.0441942	−	0.0765466i
$897$	48.2288			1.61031
$898$	4.93725	−	8.55157i	0.164758	−	0.285370i
$899$	−8.58301	−	14.8662i	−0.286259	−	0.495816i
$900$	−16.5830	−	28.7226i	−0.552767	−	0.957420i
$901$	10.9373	−	18.9439i	0.364373	−	0.631112i
$902$	4.93725			0.164393
$903$	−28.0000			−0.931782
$904$	7.70850			0.256381
$905$	18.2288	−	31.5731i	0.605944	−	1.04953i
$906$	4.43725	+	7.68555i	0.147418	+	0.255335i
$907$	5.22876	+	9.05647i	0.173618	+	0.300715i	0.939682	−	0.342049i	$-0.111121\pi$
$907$	5.22876	+	9.05647i	0.173618	+	0.300715i	−0.766064	+	0.642764i	$0.777788\pi$
$908$	6.64575	−	11.5108i	0.220547	−	0.381999i
$909$	12.0000			0.398015
$910$	48.2288			1.59877
$911$	−1.29150			−0.0427894			−0.0213947	−	0.999771i	$-0.506811\pi$
$911$	−1.29150			−0.0427894			−0.0213947	+	0.999771i	$0.506811\pi$
$912$	−0.468627	+	0.811686i	−0.0155178	+	0.0268776i
$913$	−6.64575	−	11.5108i	−0.219942	−	0.380951i
$914$	−19.5830	−	33.9188i	−0.647748	−	1.12193i
$915$	17.8856	−	30.9788i	0.591280	−	1.02413i
$916$	−16.0000			−0.528655
$917$	20.6974	+	35.8489i	0.683488	+	1.18384i
$918$	15.8745			0.523937
$919$	17.6458	−	30.5633i	0.582080	−	1.00819i	−0.413153	−	0.910662i	$-0.635573\pi$
$919$	17.6458	−	30.5633i	0.582080	−	1.00819i	0.995233	−	0.0975298i	$-0.0310941\pi$
$920$	−6.64575	−	11.5108i	−0.219104	−	0.379499i
$921$	−5.59412	−	9.68930i	−0.184332	−	0.319273i
$922$	−16.0830	+	27.8566i	−0.529666	+	0.917408i
$923$	48.2288			1.58747
$924$	−3.50000	+	6.06218i	−0.115142	+	0.199431i
$925$	−13.6458			−0.448670
$926$	−11.2288	+	19.4488i	−0.369000	+	0.639126i
$927$	−25.8745	−	44.8160i	−0.849830	−	1.47195i
$928$	−2.14575	−	3.71655i	−0.0704377	−	0.122002i
$929$	−17.7915	+	30.8158i	−0.583720	+	1.01103i	0.411313	+	0.911494i	$0.365070\pi$
$929$	−17.7915	+	30.8158i	−0.583720	+	1.01103i	−0.995034	+	0.0995392i	$0.968263\pi$
$930$	−38.5830			−1.26519
$931$	−2.47974			−0.0812702
$932$	16.9373			0.554798
$933$	22.4059	−	38.8081i	0.733536	−	1.27052i
$934$	5.35425	+	9.27383i	0.175196	+	0.303449i
$935$	−10.9373	−	18.9439i	−0.357686	−	0.619531i
$936$	10.0000	−	17.3205i	0.326860	−	0.566139i
$937$	−46.6863			−1.52517			−0.762587	−	0.646886i	$-0.776071\pi$
$937$	−46.6863			−1.52517			−0.762587	+	0.646886i	$0.776071\pi$
$938$	−5.20850	+	9.02138i	−0.170063	+	0.294559i
$939$	−6.39477			−0.208685
$940$	−24.2288	+	41.9654i	−0.790255	+	1.36876i
$941$	22.3118	+	38.6451i	0.727343	+	1.25979i	0.958002	+	0.286760i	$0.0925782\pi$
$941$	22.3118	+	38.6451i	0.727343	+	1.25979i	−0.230660	+	0.973034i	$0.574088\pi$
$942$	28.0000	+	48.4974i	0.912289	+	1.58013i
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$	−0.645751			−0.0210174
$945$	−12.7601	−	22.1012i	−0.415087	−	0.718952i
$946$	4.00000			0.130051
$947$	16.9373	−	29.3362i	0.550387	−	0.953298i	−0.447860	−	0.894104i	$-0.647814\pi$
$947$	16.9373	−	29.3362i	0.550387	−	0.953298i	0.998246	−	0.0591941i	$-0.0188531\pi$
$948$	3.50000	+	6.06218i	0.113675	+	0.196890i
$949$	−14.1144	−	24.4468i	−0.458172	−	0.793577i
$950$	−1.46863	+	2.54374i	−0.0476486	+	0.0825297i
$951$	−31.7490			−1.02953
$952$	15.8745			0.514496
$953$	−25.5203			−0.826682			−0.413341	−	0.910576i	$-0.635638\pi$
$953$	−25.5203			−0.826682			−0.413341	+	0.910576i	$0.635638\pi$
$954$	−7.29150	+	12.6293i	−0.236071	+	0.408887i
$955$	24.2288	+	41.9654i	0.784024	+	1.35797i
$956$	−4.61438	−	7.99234i	−0.149240	−	0.258491i
$957$	−5.67712	+	9.83307i	−0.183515	+	0.317858i
$958$	25.9373			0.837995
$959$	−49.9373			−1.61256
$960$	−9.64575			−0.311315
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−4.11438	−	7.12631i	−0.132653	−	0.229762i
$963$	−9.87451	−	17.1031i	−0.318202	−	0.551141i
$964$	−11.4059	+	19.7556i	−0.367359	+	0.636284i
$965$	−42.0000			−1.35203
$966$	−12.7601	−	22.1012i	−0.410550	−	0.711094i
$967$	−26.3320			−0.846781			−0.423390	−	0.905947i	$-0.639160\pi$
$967$	−26.3320			−0.846781			−0.423390	+	0.905947i	$0.639160\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	−2.81176	−	4.87011i	−0.0903268	−	0.156451i
$970$	−10.4059	−	18.0235i	−0.334113	−	0.578700i
$971$	12.9686	−	22.4623i	0.416183	−	0.720850i	−0.579369	−	0.815066i	$-0.696701\pi$
$971$	12.9686	−	22.4623i	0.416183	−	0.720850i	0.995552	+	0.0942153i	$0.0300342\pi$
$972$	21.1660			0.678900
$973$	−5.29150	+	9.16515i	−0.169638	+	0.293821i
$974$	30.5830			0.979943
$975$	54.8431	−	94.9911i	1.75639	−	3.04215i
$976$	−1.85425	−	3.21165i	−0.0593531	−	0.102803i
$977$	−18.2288	−	31.5731i	−0.583190	−	1.01011i	−0.995098	−	0.0988890i	$-0.968471\pi$
$977$	−18.2288	−	31.5731i	−0.583190	−	1.01011i	0.411909	−	0.911225i	$-0.364862\pi$
$978$	6.14575	−	10.6448i	0.196519	−	0.340382i
$979$	−14.5830			−0.466075
$980$	−12.7601	−	22.1012i	−0.407607	−	0.705997i
$981$	42.3320			1.35156
$982$	5.35425	−	9.27383i	0.170861	−	0.295940i
$983$	18.6458	+	32.2954i	0.594707	+	1.03006i	0.993588	+	0.113060i	$0.0360653\pi$
$983$	18.6458	+	32.2954i	0.594707	+	1.03006i	−0.398881	+	0.917003i	$0.630601\pi$
$984$	6.53137	+	11.3127i	0.208213	+	0.360635i
$985$	−34.4059	+	59.5927i	−1.09626	+	1.89878i
$986$	25.7490			0.820016
$987$	−46.5203	+	80.5755i	−1.48076	+	2.56474i
$988$	−1.77124			−0.0563508
$989$	−7.29150	+	12.6293i	−0.231856	+	0.401587i
$990$	7.29150	+	12.6293i	0.231739	+	0.401384i
$991$	−28.3431	−	49.0917i	−0.900349	−	1.55945i	−0.827041	−	0.562141i	$-0.809978\pi$
$991$	−28.3431	−	49.0917i	−0.900349	−	1.55945i	−0.0733083	−	0.997309i	$-0.523356\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	40.6235			1.28915
$994$	−12.7601	−	22.1012i	−0.404727	−	0.701007i
$995$	−81.0405			−2.56916
$996$	17.5830	−	30.4547i	0.557139	−	0.964993i
$997$	21.2915	+	36.8780i	0.674309	+	1.16794i	0.976670	+	0.214744i	$0.0688916\pi$
$997$	21.2915	+	36.8780i	0.674309	+	1.16794i	−0.302362	+	0.953193i	$0.597775\pi$
$998$	8.93725	+	15.4798i	0.282904	+	0.490004i
$999$	−2.17712	+	3.77089i	−0.0688812	+	0.119306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.e.f.23.2	✓	4
3.2	odd	2		1386.2.k.s.793.2		4
4.3	odd	2		1232.2.q.g.177.1		4
7.2	even	3		1078.2.a.s.1.1		2
7.3	odd	6		1078.2.e.v.67.1		4
7.4	even	3	inner	154.2.e.f.67.2	yes	4
7.5	odd	6		1078.2.a.n.1.2		2
7.6	odd	2		1078.2.e.v.177.1		4
21.2	odd	6		9702.2.a.cz.1.1		2
21.5	even	6		9702.2.a.dr.1.2		2
21.11	odd	6		1386.2.k.s.991.2		4
28.11	odd	6		1232.2.q.g.529.1		4
28.19	even	6		8624.2.a.bk.1.1		2
28.23	odd	6		8624.2.a.ca.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.f.23.2	✓	4	1.1	even	1	trivial
154.2.e.f.67.2	yes	4	7.4	even	3	inner
1078.2.a.n.1.2		2	7.5	odd	6
1078.2.a.s.1.1		2	7.2	even	3
1078.2.e.v.67.1		4	7.3	odd	6
1078.2.e.v.177.1		4	7.6	odd	2
1232.2.q.g.177.1		4	4.3	odd	2
1232.2.q.g.529.1		4	28.11	odd	6
1386.2.k.s.793.2		4	3.2	odd	2
1386.2.k.s.991.2		4	21.11	odd	6
8624.2.a.bk.1.1		2	28.19	even	6
8624.2.a.ca.1.2		2	28.23	odd	6
9702.2.a.cz.1.1		2	21.2	odd	6
9702.2.a.dr.1.2		2	21.5	even	6

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.32288 + 2.29129i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.82288 + 3.15731i) q^{5} +2.64575 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.32288 + 2.29129i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.82288 + 3.15731i) q^{5} +2.64575 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +(1.82288 + 3.15731i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.32288 - 2.29129i) q^{12} +5.00000 q^{13} +(-1.32288 - 2.29129i) q^{14} -9.64575 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{18} +(0.177124 - 0.306788i) q^{19} +3.64575 q^{20} +7.00000 q^{21} -1.00000 q^{22} +(1.82288 - 3.15731i) q^{23} +(-1.32288 - 2.29129i) q^{24} +(-4.14575 - 7.18065i) q^{25} +(2.50000 - 4.33013i) q^{26} -2.64575 q^{27} -2.64575 q^{28} -4.29150 q^{29} +(-4.82288 + 8.35347i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.32288 - 2.29129i) q^{33} -6.00000 q^{34} +(4.82288 + 8.35347i) q^{35} +4.00000 q^{36} +(0.822876 - 1.42526i) q^{37} +(-0.177124 - 0.306788i) q^{38} +(6.61438 + 11.4564i) q^{39} +(1.82288 - 3.15731i) q^{40} -4.93725 q^{41} +(3.50000 - 6.06218i) q^{42} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-7.29150 - 12.6293i) q^{45} +(-1.82288 - 3.15731i) q^{46} +(-6.64575 + 11.5108i) q^{47} -2.64575 q^{48} +(-3.50000 - 6.06218i) q^{49} -8.29150 q^{50} +(7.93725 - 13.7477i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(1.82288 + 3.15731i) q^{53} +(-1.32288 + 2.29129i) q^{54} +3.64575 q^{55} +(-1.32288 + 2.29129i) q^{56} +0.937254 q^{57} +(-2.14575 + 3.71655i) q^{58} +(0.322876 + 0.559237i) q^{59} +(4.82288 + 8.35347i) q^{60} +(-1.85425 + 3.21165i) q^{61} +4.00000 q^{62} +(5.29150 + 9.16515i) q^{63} +1.00000 q^{64} +(-9.11438 + 15.7866i) q^{65} +(-1.32288 - 2.29129i) q^{66} +(-1.96863 - 3.40976i) q^{67} +(-3.00000 + 5.19615i) q^{68} +9.64575 q^{69} +9.64575 q^{70} +9.64575 q^{71} +(2.00000 - 3.46410i) q^{72} +(-2.82288 - 4.88936i) q^{73} +(-0.822876 - 1.42526i) q^{74} +(10.9686 - 18.9982i) q^{75} -0.354249 q^{76} -2.64575 q^{77} +13.2288 q^{78} +(-1.32288 + 2.29129i) q^{79} +(-1.82288 - 3.15731i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-2.46863 + 4.27579i) q^{82} +13.2915 q^{83} +(-3.50000 - 6.06218i) q^{84} +21.8745 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-5.67712 - 9.83307i) q^{87} +(0.500000 + 0.866025i) q^{88} +(7.29150 - 12.6293i) q^{89} -14.5830 q^{90} +(6.61438 - 11.4564i) q^{91} -3.64575 q^{92} +(-5.29150 + 9.16515i) q^{93} +(6.64575 + 11.5108i) q^{94} +(0.645751 + 1.11847i) q^{95} +(-1.32288 + 2.29129i) q^{96} -5.70850 q^{97} -7.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 - 8 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 28 q^{15} - 2 q^{16} - 12 q^{17} + 8 q^{18} + 6 q^{19} + 4 q^{20} + 28 q^{21} - 4 q^{22} + 2 q^{23} - 6 q^{25} + 10 q^{26} + 4 q^{29} - 14 q^{30} + 8 q^{31} + 2 q^{32} - 24 q^{34} + 14 q^{35} + 16 q^{36} - 2 q^{37} - 6 q^{38} + 2 q^{40} + 12 q^{41} + 14 q^{42} - 16 q^{43} - 2 q^{44} - 8 q^{45} - 2 q^{46} - 16 q^{47} - 14 q^{49} - 12 q^{50} - 10 q^{52} + 2 q^{53} + 4 q^{55} - 28 q^{57} + 2 q^{58} - 4 q^{59} + 14 q^{60} - 18 q^{61} + 16 q^{62} + 4 q^{64} - 10 q^{65} + 8 q^{67} - 12 q^{68} + 28 q^{69} + 28 q^{70} + 28 q^{71} + 8 q^{72} - 6 q^{73} + 2 q^{74} + 28 q^{75} - 12 q^{76} - 2 q^{80} + 10 q^{81} + 6 q^{82} + 32 q^{83} - 14 q^{84} + 24 q^{85} - 8 q^{86} - 28 q^{87} + 2 q^{88} + 8 q^{89} - 16 q^{90} - 4 q^{92} + 16 q^{94} - 8 q^{95} - 44 q^{97} - 28 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 - 8 * q^9 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 28 * q^15 - 2 * q^16 - 12 * q^17 + 8 * q^18 + 6 * q^19 + 4 * q^20 + 28 * q^21 - 4 * q^22 + 2 * q^23 - 6 * q^25 + 10 * q^26 + 4 * q^29 - 14 * q^30 + 8 * q^31 + 2 * q^32 - 24 * q^34 + 14 * q^35 + 16 * q^36 - 2 * q^37 - 6 * q^38 + 2 * q^40 + 12 * q^41 + 14 * q^42 - 16 * q^43 - 2 * q^44 - 8 * q^45 - 2 * q^46 - 16 * q^47 - 14 * q^49 - 12 * q^50 - 10 * q^52 + 2 * q^53 + 4 * q^55 - 28 * q^57 + 2 * q^58 - 4 * q^59 + 14 * q^60 - 18 * q^61 + 16 * q^62 + 4 * q^64 - 10 * q^65 + 8 * q^67 - 12 * q^68 + 28 * q^69 + 28 * q^70 + 28 * q^71 + 8 * q^72 - 6 * q^73 + 2 * q^74 + 28 * q^75 - 12 * q^76 - 2 * q^80 + 10 * q^81 + 6 * q^82 + 32 * q^83 - 14 * q^84 + 24 * q^85 - 8 * q^86 - 28 * q^87 + 2 * q^88 + 8 * q^89 - 16 * q^90 - 4 * q^92 + 16 * q^94 - 8 * q^95 - 44 * q^97 - 28 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more