LMFDB - Embedded newform 143.2.e.c.133.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("143.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 9x^{10} - 2x^{9} + 59x^{8} - 13x^{7} + 175x^{6} - 50x^{5} + 380x^{4} - 64x^{3} + 280x^{2} + 48x + 144 $ x^12 + 9x^10 - 2x^9 + 59x^8 - 13x^7 + 175x^6 - 50x^5 + 380x^4 - 64x^3 + 280x^2 + 48x + 144
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			133.3
Root			$-0.903935 - 1.56566i$ of defining polynomial
Character	$\chi$	$=$	143.133
Dual form			143.2.e.c.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.134198 - 0.232438i) q^{2} +(-1.17558 - 2.03617i) q^{3} +(0.963982 - 1.66967i) q^{4} -2.80787 q^{5} +(-0.315522 + 0.546500i) q^{6} +(-1.19233 + 2.06518i) q^{7} -1.05425 q^{8} +(-1.26400 + 2.18931i) q^{9} +O(q^{10})$	\(q+(-0.134198 - 0.232438i) q^{2} +(-1.17558 - 2.03617i) q^{3} +(0.963982 - 1.66967i) q^{4} -2.80787 q^{5} +(-0.315522 + 0.546500i) q^{6} +(-1.19233 + 2.06518i) q^{7} -1.05425 q^{8} +(-1.26400 + 2.18931i) q^{9} +(0.376811 + 0.652655i) q^{10} +(0.500000 + 0.866025i) q^{11} -4.53297 q^{12} +(1.15941 - 3.41405i) q^{13} +0.640034 q^{14} +(3.30089 + 5.71731i) q^{15} +(-1.78649 - 3.09428i) q^{16} +(0.918197 - 1.59036i) q^{17} +0.678504 q^{18} +(4.00924 - 6.94420i) q^{19} +(-2.70674 + 4.68820i) q^{20} +5.60675 q^{21} +(0.134198 - 0.232438i) q^{22} +(-2.83500 - 4.91036i) q^{23} +(1.23936 + 2.14663i) q^{24} +2.88414 q^{25} +(-0.949146 + 0.188668i) q^{26} -1.10976 q^{27} +(2.29877 + 3.98159i) q^{28} +(2.35255 + 4.07474i) q^{29} +(0.885945 - 1.53450i) q^{30} +2.36542 q^{31} +(-1.53373 + 2.65651i) q^{32} +(1.17558 - 2.03617i) q^{33} -0.492881 q^{34} +(3.34792 - 5.79876i) q^{35} +(2.43694 + 4.22091i) q^{36} +(4.85504 + 8.40917i) q^{37} -2.15213 q^{38} +(-8.31459 + 1.65275i) q^{39} +2.96020 q^{40} +(1.76127 + 3.05061i) q^{41} +(-0.752415 - 1.30322i) q^{42} +(0.709691 - 1.22922i) q^{43} +1.92796 q^{44} +(3.54914 - 6.14729i) q^{45} +(-0.760901 + 1.31792i) q^{46} -9.28956 q^{47} +(-4.20033 + 7.27518i) q^{48} +(0.656686 + 1.13741i) q^{49} +(-0.387045 - 0.670382i) q^{50} -4.31767 q^{51} +(-4.58268 - 5.22691i) q^{52} +11.3543 q^{53} +(0.148928 + 0.257951i) q^{54} +(-1.40394 - 2.43169i) q^{55} +(1.25702 - 2.17722i) q^{56} -18.8528 q^{57} +(0.631416 - 1.09364i) q^{58} +(4.36291 - 7.55678i) q^{59} +12.7280 q^{60} +(3.96207 - 6.86251i) q^{61} +(-0.317434 - 0.549812i) q^{62} +(-3.01421 - 5.22077i) q^{63} -6.32265 q^{64} +(-3.25548 + 9.58622i) q^{65} -0.631044 q^{66} +(0.331554 + 0.574268i) q^{67} +(-1.77025 - 3.06616i) q^{68} +(-6.66555 + 11.5451i) q^{69} -1.79713 q^{70} +(-1.77031 + 3.06627i) q^{71} +(1.33257 - 2.30808i) q^{72} -2.81169 q^{73} +(1.30307 - 2.25699i) q^{74} +(-3.39055 - 5.87260i) q^{75} +(-7.72967 - 13.3882i) q^{76} -2.38467 q^{77} +(1.49996 + 1.71083i) q^{78} +9.63788 q^{79} +(5.01622 + 8.68835i) q^{80} +(5.09661 + 8.82759i) q^{81} +(0.472718 - 0.818772i) q^{82} +3.79517 q^{83} +(5.40481 - 9.36140i) q^{84} +(-2.57818 + 4.46554i) q^{85} -0.380956 q^{86} +(5.53125 - 9.58040i) q^{87} +(-0.527125 - 0.913007i) q^{88} +(-1.53569 - 2.65989i) q^{89} -1.90515 q^{90} +(5.66824 + 6.46508i) q^{91} -10.9315 q^{92} +(-2.78075 - 4.81639i) q^{93} +(1.24664 + 2.15924i) q^{94} +(-11.2574 + 19.4984i) q^{95} +7.21214 q^{96} +(0.765158 - 1.32529i) q^{97} +(0.176252 - 0.305277i) q^{98} -2.52800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - 34 q^{12} - 4 q^{13} + 24 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{17} + 12 q^{18} + 10 q^{19} + 15 q^{20} - 24 q^{21} - 3 q^{23} + 14 q^{24} - 12 q^{25} - 3 q^{26} + 20 q^{27} + 16 q^{28} - 3 q^{29} - 19 q^{30} - 10 q^{31} - q^{32} + q^{33} + 10 q^{34} + 13 q^{35} - 20 q^{36} + 25 q^{37} - 54 q^{38} - 12 q^{39} - 16 q^{40} + 24 q^{41} - 13 q^{42} + 8 q^{43} - 16 q^{44} + 27 q^{45} + 18 q^{46} - 20 q^{47} + 28 q^{48} + q^{49} - 26 q^{50} - 34 q^{51} - 39 q^{52} + 20 q^{53} + 47 q^{54} - 6 q^{55} - 15 q^{56} + 6 q^{58} - 4 q^{59} + 122 q^{60} + 21 q^{61} + 5 q^{62} + 6 q^{63} - 54 q^{64} - 32 q^{65} + 24 q^{66} + 21 q^{67} - 14 q^{68} - 5 q^{69} - 62 q^{70} - 3 q^{71} - 50 q^{72} - 26 q^{73} + 38 q^{74} + 23 q^{75} + 8 q^{76} + 6 q^{77} + 36 q^{78} - 8 q^{79} + 44 q^{80} - 34 q^{81} + 33 q^{82} - 16 q^{83} + 47 q^{84} - 13 q^{85} + 22 q^{86} + 51 q^{87} + 3 q^{88} - 9 q^{89} - 140 q^{90} - 19 q^{91} + 30 q^{92} - 21 q^{93} - 10 q^{94} - 27 q^{95} + 38 q^{96} + 15 q^{97} + 21 q^{98} - 14 q^{99}+O(q^{100}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - 34 * q^12 - 4 * q^13 + 24 * q^14 - 4 * q^15 - 8 * q^16 - 2 * q^17 + 12 * q^18 + 10 * q^19 + 15 * q^20 - 24 * q^21 - 3 * q^23 + 14 * q^24 - 12 * q^25 - 3 * q^26 + 20 * q^27 + 16 * q^28 - 3 * q^29 - 19 * q^30 - 10 * q^31 - q^32 + q^33 + 10 * q^34 + 13 * q^35 - 20 * q^36 + 25 * q^37 - 54 * q^38 - 12 * q^39 - 16 * q^40 + 24 * q^41 - 13 * q^42 + 8 * q^43 - 16 * q^44 + 27 * q^45 + 18 * q^46 - 20 * q^47 + 28 * q^48 + q^49 - 26 * q^50 - 34 * q^51 - 39 * q^52 + 20 * q^53 + 47 * q^54 - 6 * q^55 - 15 * q^56 + 6 * q^58 - 4 * q^59 + 122 * q^60 + 21 * q^61 + 5 * q^62 + 6 * q^63 - 54 * q^64 - 32 * q^65 + 24 * q^66 + 21 * q^67 - 14 * q^68 - 5 * q^69 - 62 * q^70 - 3 * q^71 - 50 * q^72 - 26 * q^73 + 38 * q^74 + 23 * q^75 + 8 * q^76 + 6 * q^77 + 36 * q^78 - 8 * q^79 + 44 * q^80 - 34 * q^81 + 33 * q^82 - 16 * q^83 + 47 * q^84 - 13 * q^85 + 22 * q^86 + 51 * q^87 + 3 * q^88 - 9 * q^89 - 140 * q^90 - 19 * q^91 + 30 * q^92 - 21 * q^93 - 10 * q^94 - 27 * q^95 + 38 * q^96 + 15 * q^97 + 21 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.134198	−	0.232438i	−0.0948923	−	0.164358i	0.814671	−	0.579923i	$-0.196917\pi$
$2$	−0.134198	−	0.232438i	−0.0948923	−	0.164358i	−0.909564	+	0.415565i	$0.863584\pi$
$3$	−1.17558	−	2.03617i	−0.678724	−	1.17558i	−0.975365	−	0.220596i	$-0.929200\pi$
$3$	−1.17558	−	2.03617i	−0.678724	−	1.17558i	0.296641	−	0.954989i	$-0.404133\pi$
$4$	0.963982	−	1.66967i	0.481991	−	0.834833i
$5$	−2.80787			−1.25572			−0.627859	−	0.778327i	$-0.716069\pi$
$5$	−2.80787			−1.25572			−0.627859	+	0.778327i	$0.716069\pi$
$6$	−0.315522	+	0.546500i	−0.128811	+	0.223108i
$7$	−1.19233	+	2.06518i	−0.450659	+	0.780565i	−0.998427	−	0.0560655i	$-0.982144\pi$
$7$	−1.19233	+	2.06518i	−0.450659	+	0.780565i	0.547768	+	0.836630i	$0.315478\pi$
$8$	−1.05425			−0.372733
$9$	−1.26400	+	2.18931i	−0.421333	+	0.729769i
$10$	0.376811	+	0.652655i	0.119158	+	0.206388i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−4.53297			−1.30856
$13$	1.15941	−	3.41405i	0.321563	−	0.946888i
$13$	1.15941	−	3.41405i	0.321563	−	0.946888i
$14$	0.640034			0.171056
$15$	3.30089	+	5.71731i	0.852286	+	1.47620i
$16$	−1.78649	−	3.09428i	−0.446621	−	0.773571i
$17$	0.918197	−	1.59036i	0.222695	−	0.385720i	−0.732930	−	0.680304i	$-0.761848\pi$
$17$	0.918197	−	1.59036i	0.222695	−	0.385720i	0.955626	+	0.294584i	$0.0951811\pi$
$18$	0.678504			0.159925
$19$	4.00924	−	6.94420i	0.919782	−	1.59311i	0.120038	−	0.992769i	$-0.461698\pi$
$19$	4.00924	−	6.94420i	0.919782	−	1.59311i	0.799745	−	0.600340i	$-0.204968\pi$
$20$	−2.70674	+	4.68820i	−0.605245	+	1.04831i
$21$	5.60675			1.22349
$22$	0.134198	−	0.232438i	0.0286111	−	0.0495559i
$23$	−2.83500	−	4.91036i	−0.591137	−	1.02388i	−0.994080	−	0.108655i	$-0.965346\pi$
$23$	−2.83500	−	4.91036i	−0.591137	−	1.02388i	0.402942	−	0.915225i	$-0.367988\pi$
$24$	1.23936	+	2.14663i	0.252983	+	0.438180i
$25$	2.88414			0.576827
$26$	−0.949146	+	0.188668i	−0.186143	+	0.0370009i
$27$	−1.10976			−0.213574
$28$	2.29877	+	3.98159i	0.434427	+	0.752450i
$29$	2.35255	+	4.07474i	0.436858	+	0.756660i	0.997445	−	0.0714351i	$-0.0227579\pi$
$29$	2.35255	+	4.07474i	0.436858	+	0.756660i	−0.560587	+	0.828095i	$0.689425\pi$
$30$	0.885945	−	1.53450i	0.161751	−	0.280160i
$31$	2.36542			0.424841			0.212421	−	0.977178i	$-0.431865\pi$
$31$	2.36542			0.424841			0.212421	+	0.977178i	$0.431865\pi$
$32$	−1.53373	+	2.65651i	−0.271129	+	0.469609i
$33$	1.17558	−	2.03617i	0.204643	−	0.354452i
$34$	−0.492881			−0.0845283
$35$	3.34792	−	5.79876i	0.565901	−	0.980169i
$36$	2.43694	+	4.22091i	0.406157	+	0.703484i
$37$	4.85504	+	8.40917i	0.798163	+	1.38246i	0.920811	+	0.390009i	$0.127528\pi$
$37$	4.85504	+	8.40917i	0.798163	+	1.38246i	−0.122647	+	0.992450i	$0.539138\pi$
$38$	−2.15213			−0.349121
$39$	−8.31459	+	1.65275i	−1.33140	+	0.264652i
$40$	2.96020			0.468048
$41$	1.76127	+	3.05061i	0.275065	+	0.476426i	0.970151	−	0.242500i	$-0.0779674\pi$
$41$	1.76127	+	3.05061i	0.275065	+	0.476426i	−0.695087	+	0.718926i	$0.744634\pi$
$42$	−0.752415	−	1.30322i	−0.116100	−	0.201091i
$43$	0.709691	−	1.22922i	0.108227	−	0.187454i	−0.806825	−	0.590790i	$-0.798816\pi$
$43$	0.709691	−	1.22922i	0.108227	−	0.187454i	0.915052	+	0.403336i	$0.132149\pi$
$44$	1.92796			0.290651
$45$	3.54914	−	6.14729i	0.529075	−	0.916384i
$46$	−0.760901	+	1.31792i	−0.112189	+	0.194317i
$47$	−9.28956			−1.35502			−0.677510	−	0.735513i	$-0.736941\pi$
$47$	−9.28956			−1.35502			−0.677510	+	0.735513i	$0.736941\pi$
$48$	−4.20033	+	7.27518i	−0.606265	+	1.05008i
$49$	0.656686	+	1.13741i	0.0938123	+	0.162488i
$50$	−0.387045	−	0.670382i	−0.0547365	−	0.0948064i
$51$	−4.31767			−0.604595
$52$	−4.58268	−	5.22691i	−0.635503	−	0.724843i
$53$	11.3543			1.55963			0.779814	−	0.626012i	$-0.215314\pi$
$53$	11.3543			1.55963			0.779814	+	0.626012i	$0.215314\pi$
$54$	0.148928	+	0.257951i	0.0202665	+	0.0351026i
$55$	−1.40394	−	2.43169i	−0.189307	−	0.327889i
$56$	1.25702	−	2.17722i	0.167976	−	0.290943i
$57$	−18.8528			−2.49711
$58$	0.631416	−	1.09364i	0.0829089	−	0.143602i
$59$	4.36291	−	7.55678i	0.568002	−	0.983809i	−0.428761	−	0.903418i	$-0.641050\pi$
$59$	4.36291	−	7.55678i	0.568002	−	0.983809i	0.996763	−	0.0803910i	$-0.0256169\pi$
$60$	12.7280			1.64318
$61$	3.96207	−	6.86251i	0.507291	−	0.878654i	−0.492673	−	0.870214i	$-0.663980\pi$
$61$	3.96207	−	6.86251i	0.507291	−	0.878654i	0.999964	−	0.00843957i	$-0.00268643\pi$
$62$	−0.317434	−	0.549812i	−0.0403142	−	0.0698262i
$63$	−3.01421	−	5.22077i	−0.379755	−	0.657755i
$64$	−6.32265			−0.790331
$65$	−3.25548	+	9.58622i	−0.403792	+	1.18902i
$66$	−0.631044			−0.0776762
$67$	0.331554	+	0.574268i	0.0405058	+	0.0701580i	0.885568	−	0.464511i	$-0.153770\pi$
$67$	0.331554	+	0.574268i	0.0405058	+	0.0701580i	−0.845062	+	0.534669i	$0.820436\pi$
$68$	−1.77025	−	3.06616i	−0.214674	−	0.371827i
$69$	−6.66555	+	11.5451i	−0.802438	+	1.38986i
$70$	−1.79713			−0.214799
$71$	−1.77031	+	3.06627i	−0.210097	+	0.363899i	−0.951745	−	0.306891i	$-0.900711\pi$
$71$	−1.77031	+	3.06627i	−0.210097	+	0.363899i	0.741647	+	0.670790i	$0.234045\pi$
$72$	1.33257	−	2.30808i	0.157045	−	0.272009i
$73$	−2.81169			−0.329084			−0.164542	−	0.986370i	$-0.552615\pi$
$73$	−2.81169			−0.329084			−0.164542	+	0.986370i	$0.552615\pi$
$74$	1.30307	−	2.25699i	0.151479	−	0.262370i
$75$	−3.39055	−	5.87260i	−0.391507	−	0.678109i
$76$	−7.72967	−	13.3882i	−0.886653	−	1.53573i
$77$	−2.38467			−0.271758
$78$	1.49996	+	1.71083i	0.169837	+	0.193713i
$79$	9.63788			1.08435			0.542173	−	0.840267i	$-0.317602\pi$
$79$	9.63788			1.08435			0.542173	+	0.840267i	$0.317602\pi$
$80$	5.01622	+	8.68835i	0.560830	+	0.971387i
$81$	5.09661	+	8.82759i	0.566290	+	0.980844i
$82$	0.472718	−	0.818772i	0.0522030	−	0.0904183i
$83$	3.79517			0.416574			0.208287	−	0.978068i	$-0.433211\pi$
$83$	3.79517			0.416574			0.208287	+	0.978068i	$0.433211\pi$
$84$	5.40481	−	9.36140i	0.589713	−	1.02141i
$85$	−2.57818	+	4.46554i	−0.279643	+	0.484355i
$86$	−0.380956			−0.0410796
$87$	5.53125	−	9.58040i	0.593012	−	1.02713i
$88$	−0.527125	−	0.913007i	−0.0561917	−	0.0973269i
$89$	−1.53569	−	2.65989i	−0.162783	−	0.281948i	0.773083	−	0.634305i	$-0.218714\pi$
$89$	−1.53569	−	2.65989i	−0.162783	−	0.281948i	−0.935866	+	0.352357i	$0.885380\pi$
$90$	−1.90515			−0.200820
$91$	5.66824	+	6.46508i	0.594193	+	0.677725i
$92$	−10.9315			−1.13969
$93$	−2.78075	−	4.81639i	−0.288350	−	0.499437i
$94$	1.24664	+	2.15924i	0.128581	+	0.222709i
$95$	−11.2574	+	19.4984i	−1.15499	+	2.00050i
$96$	7.21214			0.736086
$97$	0.765158	−	1.32529i	0.0776900	−	0.134563i	−0.824563	−	0.565770i	$-0.808579\pi$
$97$	0.765158	−	1.32529i	0.0776900	−	0.134563i	0.902253	+	0.431207i	$0.141912\pi$
$98$	0.176252	−	0.305277i	0.0178041	−	0.0308376i
$99$	−2.52800			−0.254073
$100$	2.78026	−	4.81554i	0.278026	−	0.481554i
$101$	3.34904	+	5.80071i	0.333242	+	0.577192i	0.983146	−	0.182825i	$-0.0585241\pi$
$101$	3.34904	+	5.80071i	0.333242	+	0.577192i	−0.649904	+	0.760017i	$0.725191\pi$
$102$	0.579423	+	1.00359i	0.0573714	+	0.0993702i
$103$	−14.6760			−1.44607			−0.723034	−	0.690812i	$-0.757253\pi$
$103$	−14.6760			−1.44607			−0.723034	+	0.690812i	$0.757253\pi$
$104$	−1.22231	+	3.59926i	−0.119857	+	0.352937i
$105$	−15.7430			−1.53636
$106$	−1.52372	−	2.63916i	−0.147997	−	0.256338i
$107$	−8.64052	−	14.9658i	−0.835311	−	1.44680i	−0.893777	−	0.448511i	$-0.851954\pi$
$107$	−8.64052	−	14.9658i	−0.835311	−	1.44680i	0.0584665	−	0.998289i	$-0.481379\pi$
$108$	−1.06979	+	1.85293i	−0.102941	+	0.178299i
$109$	−8.75670			−0.838740			−0.419370	−	0.907815i	$-0.637749\pi$
$109$	−8.75670			−0.838740			−0.419370	+	0.907815i	$0.637749\pi$
$110$	−0.376811	+	0.652655i	−0.0359275	+	0.0622282i
$111$	11.4150	−	19.7714i	1.08347	−	1.87662i
$112$	8.52034			0.805096
$113$	1.22190	−	2.11639i	0.114946	−	0.199093i	−0.802812	−	0.596232i	$-0.796664\pi$
$113$	1.22190	−	2.11639i	0.114946	−	0.199093i	0.917758	+	0.397139i	$0.129997\pi$
$114$	2.53001	+	4.38210i	0.236957	+	0.410421i
$115$	7.96030	+	13.7876i	0.742302	+	1.28570i
$116$	9.07127			0.842246
$117$	6.00892	+	6.85366i	0.555525	+	0.633621i
$118$	−2.34197			−0.215596
$119$	2.18959	+	3.79249i	0.200720	+	0.347657i
$120$	−3.47996	−	6.02747i	−0.317675	−	0.550230i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−2.12681			−0.192552
$123$	4.14105	−	7.17251i	0.373386	−	0.646723i
$124$	2.28022	−	3.94945i	0.204770	−	0.354671i
$125$	5.94107			0.531385
$126$	−0.809002	+	1.40123i	−0.0720716	+	0.124832i
$127$	8.75815	+	15.1696i	0.777160	+	1.34608i	0.933572	+	0.358389i	$0.116674\pi$
$127$	8.75815	+	15.1696i	0.777160	+	1.34608i	−0.156412	+	0.987692i	$0.549993\pi$
$128$	3.91596	+	6.78263i	0.346125	+	0.599506i
$129$	−3.33721			−0.293825
$130$	2.66508	−	0.529756i	0.233743	−	0.0464627i
$131$	1.60414			0.140154			0.0700771	−	0.997542i	$-0.477675\pi$
$131$	1.60414			0.140154			0.0700771	+	0.997542i	$0.477675\pi$
$132$	−2.26648	−	3.92567i	−0.197272	−	0.341685i
$133$	9.56069	+	16.5596i	0.829017	+	1.43590i
$134$	0.0889877	−	0.154131i	0.00768737	−	0.0133149i
$135$	3.11607			0.268189
$136$	−0.968009	+	1.67664i	−0.0830061	+	0.143771i
$137$	0.968908	−	1.67820i	0.0827794	−	0.143378i	−0.821663	−	0.569973i	$-0.806954\pi$
$137$	0.968908	−	1.67820i	0.0827794	−	0.143378i	0.904443	+	0.426595i	$0.140287\pi$
$138$	3.57801			0.304581
$139$	6.14479	−	10.6431i	0.521195	−	0.902735i	−0.478502	−	0.878087i	$-0.658820\pi$
$139$	6.14479	−	10.6431i	0.521195	−	0.902735i	0.999696	−	0.0246487i	$-0.00784673\pi$
$140$	−6.45466	−	11.1798i	−0.545518	−	0.944865i
$141$	10.9207	+	18.9151i	0.919685	+	1.59294i
$142$	0.950289			0.0797465
$143$	3.53636	−	0.702948i	0.295726	−	0.0587835i
$144$	9.03245			0.752704
$145$	−6.60566	−	11.4413i	−0.548570	−	0.950152i
$146$	0.377324	+	0.653544i	0.0312275	+	0.0540877i
$147$	1.54398	−	2.67425i	0.127345	−	0.220568i
$148$	18.7207			1.53883
$149$	−2.88372	+	4.99475i	−0.236243	+	0.409186i	−0.959633	−	0.281254i	$-0.909250\pi$
$149$	−2.88372	+	4.99475i	−0.236243	+	0.409186i	0.723390	+	0.690440i	$0.242583\pi$
$150$	−0.910009	+	1.57618i	−0.0743019	+	0.128695i
$151$	0.712761			0.0580036			0.0290018	−	0.999579i	$-0.490767\pi$
$151$	0.712761			0.0580036			0.0290018	+	0.999579i	$0.490767\pi$
$152$	−4.22674	+	7.32092i	−0.342834	+	0.593805i
$153$	2.32120	+	4.02043i	0.187658	+	0.325033i
$154$	0.320017	+	0.554286i	0.0257877	+	0.0446656i
$155$	−6.64178			−0.533481
$156$	−5.25557	+	15.4758i	−0.420783	+	1.23906i
$157$	7.27705			0.580772			0.290386	−	0.956910i	$-0.406216\pi$
$157$	7.27705			0.580772			0.290386	+	0.956910i	$0.406216\pi$
$158$	−1.29338	−	2.24021i	−0.102896	−	0.178221i
$159$	−13.3479	−	23.1192i	−1.05856	−	1.83347i
$160$	4.30653	−	7.45913i	0.340461	−	0.589696i
$161$	13.5210			1.06561
$162$	1.36791	−	2.36929i	0.107473	−	0.186149i
$163$	−7.70189	+	13.3401i	−0.603258	+	1.04487i	0.389066	+	0.921210i	$0.372798\pi$
$163$	−7.70189	+	13.3401i	−0.603258	+	1.04487i	−0.992324	+	0.123664i	$0.960535\pi$
$164$	6.79134			0.530314
$165$	−3.30089	+	5.71731i	−0.256974	+	0.445092i
$166$	−0.509304	−	0.882141i	−0.0395297	−	0.0684674i
$167$	−1.19185	−	2.06434i	−0.0922279	−	0.159743i	0.816220	−	0.577741i	$-0.196065\pi$
$167$	−1.19185	−	2.06434i	−0.0922279	−	0.159743i	−0.908448	+	0.417997i	$0.862732\pi$
$168$	−5.91091			−0.456037
$169$	−10.3115	−	7.91658i	−0.793195	−	0.608968i
$170$	1.38395			0.106144
$171$	10.1353	+	17.5549i	0.775068	+	1.34246i
$172$	−1.36826	−	2.36989i	−0.104329	−	0.180703i
$173$	−2.55445	+	4.42443i	−0.194211	+	0.336384i	−0.946642	−	0.322288i	$-0.895548\pi$
$173$	−2.55445	+	4.42443i	−0.194211	+	0.336384i	0.752430	+	0.658672i	$0.228881\pi$
$174$	−2.96913			−0.225089
$175$	−3.43885	+	5.95626i	−0.259953	+	0.450251i
$176$	1.78649	−	3.09428i	0.134661	−	0.233240i
$177$	−20.5159			−1.54207
$178$	−0.412173	+	0.713904i	−0.0308937	+	0.0535094i
$179$	−12.1531	−	21.0497i	−0.908364	−	1.57333i	−0.816337	−	0.577575i	$-0.803999\pi$
$179$	−12.1531	−	21.0497i	−0.908364	−	1.57333i	−0.0920263	−	0.995757i	$-0.529334\pi$
$180$	−6.84262	−	11.8518i	−0.510018	−	0.883378i
$181$	−2.00442			−0.148988			−0.0744938	−	0.997221i	$-0.523734\pi$
$181$	−2.00442			−0.148988			−0.0744938	+	0.997221i	$0.523734\pi$
$182$	0.742063	−	2.18511i	0.0550054	−	0.161971i
$183$	−18.6310			−1.37724
$184$	2.98879	+	5.17674i	0.220337	+	0.381634i
$185$	−13.6323	−	23.6119i	−1.00227	−	1.73598i
$186$	−0.746341	+	1.29270i	−0.0547244	+	0.0947854i
$187$	1.83639			0.134290
$188$	−8.95496	+	15.5104i	−0.653108	+	1.13122i
$189$	1.32321	−	2.29186i	0.0962491	−	0.166708i
$190$	6.04289			0.438398
$191$	1.58514	−	2.74554i	0.114697	−	0.198660i	−0.802962	−	0.596030i	$-0.796744\pi$
$191$	1.58514	−	2.74554i	0.114697	−	0.198660i	0.917658	+	0.397370i	$0.130077\pi$
$192$	7.43280	+	12.8740i	0.536416	+	0.929100i
$193$	−12.0376	−	20.8498i	−0.866488	−	1.50080i	−0.865562	−	0.500802i	$-0.833038\pi$
$193$	−12.0376	−	20.8498i	−0.866488	−	1.50080i	−0.000926311	−	1.00000i	$-0.500295\pi$
$194$	−0.410730			−0.0294887
$195$	23.3463	−	4.64071i	1.67186	−	0.332328i
$196$	2.53213			0.180867
$197$	−1.30520	−	2.26067i	−0.0929917	−	0.161066i	0.815777	−	0.578367i	$-0.196310\pi$
$197$	−1.30520	−	2.26067i	−0.0929917	−	0.161066i	−0.908769	+	0.417300i	$0.862976\pi$
$198$	0.339252	+	0.587601i	0.0241096	+	0.0417590i
$199$	−8.52647	+	14.7683i	−0.604425	+	1.04690i	0.387717	+	0.921779i	$0.373264\pi$
$199$	−8.52647	+	14.7683i	−0.604425	+	1.04690i	−0.992142	+	0.125117i	$0.960069\pi$
$200$	−3.04060			−0.215003
$201$	0.779539	−	1.35020i	0.0549845	−	0.0952359i
$202$	0.898868	−	1.55689i	0.0632442	−	0.109542i
$203$	−11.2201			−0.787497
$204$	−4.16216	+	7.20907i	−0.291409	+	0.504736i
$205$	−4.94543	−	8.56573i	−0.345403	−	0.598256i
$206$	1.96949	+	3.41126i	0.137221	+	0.237673i
$207$	14.3337			0.996262
$208$	−12.6353	+	2.51161i	−0.876102	+	0.174149i
$209$	8.01848			0.554650
$210$	2.11268	+	3.65927i	0.145789	+	0.252514i
$211$	10.1890	+	17.6479i	0.701442	+	1.21493i	0.967960	+	0.251103i	$0.0807933\pi$
$211$	10.1890	+	17.6479i	0.701442	+	1.21493i	−0.266519	+	0.963830i	$0.585873\pi$
$212$	10.9453	−	18.9578i	0.751726	−	1.30203i
$213$	8.32460			0.570392
$214$	−2.31908	+	4.01677i	−0.158529	+	0.274580i
$215$	−1.99272	+	3.45149i	−0.135902	+	0.235390i
$216$	1.16997			0.0796062
$217$	−2.82036	+	4.88501i	−0.191459	+	0.331616i
$218$	1.17513	+	2.03539i	0.0795900	+	0.137854i
$219$	3.30538	+	5.72509i	0.223357	+	0.386866i
$220$	−5.41347			−0.364976
$221$	−4.36502	−	4.97866i	−0.293623	−	0.334901i
$222$	−6.12749			−0.411250
$223$	−0.509039	−	0.881682i	−0.0340878	−	0.0590418i	0.848478	−	0.529230i	$-0.177519\pi$
$223$	−0.509039	−	0.881682i	−0.0340878	−	0.0590418i	−0.882566	+	0.470189i	$0.844186\pi$
$224$	−3.65744	−	6.33488i	−0.244373	−	0.423267i
$225$	−3.64554	+	6.31426i	−0.243036	+	0.420951i
$226$	−0.655905			−0.0436301
$227$	−0.0114153	+	0.0197719i	−0.000757660	+	0.00131231i	−0.866404	−	0.499344i	$-0.833575\pi$
$227$	−0.0114153	+	0.0197719i	−0.000757660	+	0.00131231i	0.865646	+	0.500656i	$0.166908\pi$
$228$	−18.1737	+	31.4779i	−1.20359	+	2.08467i
$229$	−21.4247			−1.41578			−0.707891	−	0.706322i	$-0.750353\pi$
$229$	−21.4247			−1.41578			−0.707891	+	0.706322i	$0.750353\pi$
$230$	2.13651	−	3.70055i	0.140877	−	0.244007i
$231$	2.80338	+	4.85559i	0.184449	+	0.319474i
$232$	−2.48018	−	4.29579i	−0.162832	−	0.282033i
$233$	27.0674			1.77324			0.886621	−	0.462496i	$-0.153046\pi$
$233$	27.0674			1.77324			0.886621	+	0.462496i	$0.153046\pi$
$234$	0.786665	−	2.31645i	0.0514259	−	0.151431i
$235$	26.0839			1.70152
$236$	−8.41153	−	14.5692i	−0.547544	−	0.948374i
$237$	−11.3301	−	19.6244i	−0.735972	−	1.27474i
$238$	0.587678	−	1.01789i	0.0380935	−	0.0659799i
$239$	29.1026			1.88249			0.941245	−	0.337726i	$-0.109658\pi$
$239$	29.1026			1.88249			0.941245	+	0.337726i	$0.109658\pi$
$240$	11.7940	−	20.4278i	0.761298	−	1.31861i
$241$	−5.90258	+	10.2236i	−0.380219	+	0.658558i	−0.991093	−	0.133169i	$-0.957485\pi$
$241$	−5.90258	+	10.2236i	−0.380219	+	0.658558i	0.610875	+	0.791727i	$0.290818\pi$
$242$	0.268396			0.0172531
$243$	10.3184	−	17.8719i	0.661923	−	1.14648i
$244$	−7.63873	−	13.2307i	−0.489019	−	0.847006i
$245$	−1.84389	−	3.19371i	−0.117802	−	0.204039i
$246$	−2.22288			−0.141726
$247$	−19.0595	−	21.7389i	−1.21273	−	1.38322i
$248$	−2.49374			−0.158353
$249$	−4.46154	−	7.72762i	−0.282739	−	0.489718i
$250$	−0.797279	−	1.38093i	−0.0504244	−	0.0873376i
$251$	7.47739	−	12.9512i	0.471969	−	0.817474i	−0.527517	−	0.849545i	$-0.676877\pi$
$251$	7.47739	−	12.9512i	0.471969	−	0.817474i	0.999486	+	0.0320706i	$0.0102101\pi$
$252$	−11.6226			−0.732154
$253$	2.83500	−	4.91036i	0.178235	−	0.308711i
$254$	2.35065	−	4.07145i	0.147493	−	0.255466i
$255$	12.1235			0.759201
$256$	−5.27162	+	9.13071i	−0.329476	+	0.570669i
$257$	6.27337	+	10.8658i	0.391322	+	0.677789i	0.992624	−	0.121232i	$-0.0386846\pi$
$257$	6.27337	+	10.8658i	0.391322	+	0.677789i	−0.601302	+	0.799022i	$0.705351\pi$
$258$	0.447846	+	0.775692i	0.0278817	+	0.0482925i
$259$	−23.1553			−1.43880
$260$	12.8676	+	14.6765i	0.798013	+	0.910198i
$261$	−11.8945			−0.736250
$262$	−0.215272	−	0.372862i	−0.0132996	−	0.0230355i
$263$	13.1504	+	22.7771i	0.810888	+	1.40450i	0.912243	+	0.409649i	$0.134349\pi$
$263$	13.1504	+	22.7771i	0.810888	+	1.40450i	−0.101355	+	0.994850i	$0.532318\pi$
$264$	−1.23936	+	2.14663i	−0.0762773	+	0.132116i
$265$	−31.8813			−1.95845
$266$	2.56605	−	4.44453i	0.157335	−	0.272512i
$267$	−3.61066	+	6.25385i	−0.220969	+	0.382730i
$268$	1.27845			0.0780936
$269$	−10.7170	+	18.5624i	−0.653429	+	1.13177i	0.328856	+	0.944380i	$0.393337\pi$
$269$	−10.7170	+	18.5624i	−0.653429	+	1.13177i	−0.982285	+	0.187392i	$0.939996\pi$
$270$	−0.418170	−	0.724292i	−0.0254490	−	0.0440790i
$271$	−1.21707	−	2.10802i	−0.0739316	−	0.128053i	0.826690	−	0.562658i	$-0.190221\pi$
$271$	−1.21707	−	2.10802i	−0.0739316	−	0.128053i	−0.900621	+	0.434605i	$0.856888\pi$
$272$	−6.56138			−0.397842
$273$	6.50053	−	19.1418i	0.393430	−	1.15851i
$274$	−0.520102			−0.0314205
$275$	1.44207	+	2.49774i	0.0869600	+	0.150619i
$276$	12.8509	+	22.2585i	0.773536	+	1.33980i
$277$	2.82864	−	4.89935i	0.169956	−	0.294373i	−0.768448	−	0.639912i	$-0.778971\pi$
$277$	2.82864	−	4.89935i	0.169956	−	0.294373i	0.938404	+	0.345539i	$0.112304\pi$
$278$	−3.29847			−0.197829
$279$	−2.98988	+	5.17862i	−0.178999	+	0.310036i
$280$	−3.52954	+	6.11334i	−0.210930	+	0.365342i
$281$	17.9567			1.07121			0.535604	−	0.844469i	$-0.320084\pi$
$281$	17.9567			1.07121			0.535604	+	0.844469i	$0.320084\pi$
$282$	2.93106	−	5.07674i	0.174542	−	0.302316i
$283$	7.18650	+	12.4474i	0.427193	+	0.739920i	0.996622	−	0.0821203i	$-0.0261692\pi$
$283$	7.18650	+	12.4474i	0.427193	+	0.739920i	−0.569430	+	0.822040i	$0.692836\pi$
$284$	3.41310	+	5.91166i	0.202530	+	0.350792i
$285$	52.9362			3.13567
$286$	−0.637964	−	0.727650i	−0.0377236	−	0.0430268i
$287$	−8.40009			−0.495842
$288$	−3.87727	−	6.71564i	−0.228471	−	0.395723i
$289$	6.81383	+	11.8019i	0.400813	+	0.694229i
$290$	−1.77293	+	3.07081i	−0.104110	+	0.180324i
$291$	−3.59803			−0.210920
$292$	−2.71042	+	4.69459i	−0.158615	+	0.274730i
$293$	13.5653	−	23.4957i	0.792491	−	1.37263i	−0.131929	−	0.991259i	$-0.542117\pi$
$293$	13.5653	−	23.4957i	0.792491	−	1.37263i	0.924420	−	0.381376i	$-0.124550\pi$
$294$	−0.828796			−0.0483363
$295$	−12.2505	+	21.2185i	−0.713251	+	1.23539i
$296$	−5.11842	−	8.86537i	−0.297502	−	0.515289i
$297$	−0.554881	−	0.961083i	−0.0321975	−	0.0557677i
$298$	1.54796			0.0896707
$299$	−20.0511	+	3.98571i	−1.15959	+	0.230499i
$300$	−13.0737			−0.754810
$301$	1.69237	+	2.93128i	0.0975469	+	0.168956i
$302$	−0.0956510	−	0.165672i	−0.00550410	−	0.00953338i
$303$	7.87416	−	13.6384i	0.452358	−	0.783508i
$304$	−28.6498			−1.64318
$305$	−11.1250	+	19.2690i	−0.637014	+	1.10334i
$306$	0.623000	−	1.07907i	0.0356145	−	0.0616862i
$307$	10.2326			0.584008			0.292004	−	0.956417i	$-0.405678\pi$
$307$	10.2326			0.584008			0.292004	+	0.956417i	$0.405678\pi$
$308$	−2.29877	+	3.98159i	−0.130985	+	0.226872i
$309$	17.2529	+	29.8829i	0.981482	+	1.69998i
$310$	0.891314	+	1.54380i	0.0506232	+	0.0876820i
$311$	−8.44726			−0.479000			−0.239500	−	0.970896i	$-0.576984\pi$
$311$	−8.44726			−0.479000			−0.239500	+	0.970896i	$0.576984\pi$
$312$	8.76565	−	1.74241i	0.496257	−	0.0986445i
$313$	20.9335			1.18323			0.591617	−	0.806219i	$-0.298490\pi$
$313$	20.9335			1.18323			0.591617	+	0.806219i	$0.298490\pi$
$314$	−0.976565	−	1.69146i	−0.0551108	−	0.0954547i
$315$	8.46352	+	14.6592i	0.476865	+	0.825954i
$316$	9.29074	−	16.0920i	0.522645	−	0.905248i
$317$	23.0814			1.29638			0.648189	−	0.761480i	$-0.275527\pi$
$317$	23.0814			1.29638			0.648189	+	0.761480i	$0.275527\pi$
$318$	−3.58252	+	6.20511i	−0.200898	+	0.347965i
$319$	−2.35255	+	4.07474i	−0.131718	+	0.228142i
$320$	17.7532			0.992432
$321$	−20.3153	+	35.1872i	−1.13389	+	1.96396i
$322$	−1.81449	−	3.14280i	−0.101118	−	0.175141i
$323$	−7.36254	−	12.7523i	−0.409663	−	0.709557i
$324$	19.6522			1.09179
$325$	3.34390	−	9.84660i	0.185486	−	0.546191i
$326$	4.13431			0.228978
$327$	10.2942	+	17.8302i	0.569273	+	0.986010i
$328$	−1.85682	−	3.21611i	−0.102526	−	0.177580i
$329$	11.0762	−	19.1846i	0.610653	−	1.05768i
$330$	1.77189			0.0975394
$331$	−1.65132	+	2.86017i	−0.0907648	+	0.157209i	−0.907833	−	0.419332i	$-0.862264\pi$
$331$	−1.65132	+	2.86017i	−0.0907648	+	0.157209i	0.817068	+	0.576541i	$0.195598\pi$
$332$	3.65848	−	6.33667i	0.200785	−	0.347770i
$333$	−24.5470			−1.34517
$334$	−0.319887	+	0.554060i	−0.0175034	+	0.0303168i
$335$	−0.930961	−	1.61247i	−0.0508638	−	0.0880987i
$336$	−10.0164	−	17.3489i	−0.546438	−	0.946459i
$337$	22.5110			1.22625			0.613127	−	0.789985i	$-0.289912\pi$
$337$	22.5110			1.22625			0.613127	+	0.789985i	$0.289912\pi$
$338$	−0.456326	+	3.45918i	−0.0248208	+	0.188155i
$339$	−5.74577			−0.312068
$340$	4.97063	+	8.60939i	0.269570	+	0.466910i
$341$	1.18271	+	2.04851i	0.0640472	+	0.110933i
$342$	2.72028	−	4.71167i	0.147096	−	0.254778i
$343$	−19.8246			−1.07043
$344$	−0.748191	+	1.29591i	−0.0403398	+	0.0698705i
$345$	18.7160	−	32.4171i	1.00764	−	1.74528i
$346$	1.37121			0.0737166
$347$	15.3883	−	26.6533i	0.826088	−	1.43083i	−0.0749978	−	0.997184i	$-0.523895\pi$
$347$	15.3883	−	26.6533i	0.826088	−	1.43083i	0.901085	−	0.433642i	$-0.142772\pi$
$348$	−10.6640	−	18.4707i	−0.571653	−	0.990132i
$349$	15.2402	+	26.3967i	0.815787	+	1.41298i	0.908762	+	0.417315i	$0.137029\pi$
$349$	15.2402	+	26.3967i	0.815787	+	1.41298i	−0.0929752	+	0.995668i	$0.529638\pi$
$350$	1.84595			0.0986700
$351$	−1.28667	+	3.78879i	−0.0686774	+	0.202231i
$352$	−3.06747			−0.163497
$353$	2.03503	+	3.52477i	0.108313	+	0.187604i	0.915087	−	0.403256i	$-0.132122\pi$
$353$	2.03503	+	3.52477i	0.108313	+	0.187604i	−0.806774	+	0.590861i	$0.798788\pi$
$354$	2.75319	+	4.76866i	0.146330	+	0.253452i
$355$	4.97081	−	8.60969i	0.263823	−	0.456955i
$356$	−5.92151			−0.313839
$357$	5.14810	−	8.91677i	0.272466	−	0.471926i
$358$	−3.26184	+	5.64967i	−0.172393	+	0.298594i
$359$	−29.7361			−1.56941			−0.784705	−	0.619870i	$-0.787185\pi$
$359$	−29.7361			−1.56941			−0.784705	+	0.619870i	$0.787185\pi$
$360$	−3.74168	+	6.48078i	−0.197204	+	0.341567i
$361$	−22.6480	−	39.2275i	−1.19200	−	2.06460i
$362$	0.268990	+	0.465904i	0.0141378	+	0.0244874i
$363$	2.35117			0.123404
$364$	16.2586	−	3.23184i	0.852182	−	0.169394i
$365$	7.89487			0.413237
$366$	2.50024	+	4.33054i	0.130690	+	0.226361i
$367$	3.15018	+	5.45627i	0.164438	+	0.284815i	0.936456	−	0.350786i	$-0.114086\pi$
$367$	3.15018	+	5.45627i	0.164438	+	0.284815i	−0.772018	+	0.635601i	$0.780752\pi$
$368$	−10.1294	+	17.5446i	−0.528029	+	0.914573i
$369$	−8.90498			−0.463575
$370$	−3.65886	+	6.33733i	−0.190215	+	0.329462i
$371$	−13.5381	+	23.4486i	−0.702861	+	1.21739i
$372$	−10.7224			−0.555928
$373$	3.50044	−	6.06294i	0.181246	−	0.313927i	−0.761059	−	0.648683i	$-0.775320\pi$
$373$	3.50044	−	6.06294i	0.181246	−	0.313927i	0.942305	+	0.334755i	$0.108654\pi$
$374$	−0.246440	−	0.426847i	−0.0127431	−	0.0220717i
$375$	−6.98423	−	12.0970i	−0.360664	−	0.624688i
$376$	9.79351			0.505062
$377$	16.6390	−	3.30744i	0.856950	−	0.170342i
$378$	−0.710286			−0.0365332
$379$	−3.46628	−	6.00378i	−0.178051	−	0.308393i	0.763162	−	0.646207i	$-0.223646\pi$
$379$	−3.46628	−	6.00378i	−0.178051	−	0.308393i	−0.941213	+	0.337814i	$0.890313\pi$
$380$	21.7039	+	37.5923i	1.11339	+	1.92844i
$381$	20.5919	−	35.6662i	1.05495	−	1.82724i
$382$	−0.850889			−0.0435353
$383$	−2.95524	+	5.11862i	−0.151006	+	0.261549i	−0.931597	−	0.363492i	$-0.881584\pi$
$383$	−2.95524	+	5.11862i	−0.151006	+	0.261549i	0.780592	+	0.625041i	$0.214918\pi$
$384$	9.20707	−	15.9471i	0.469847	−	0.813798i
$385$	6.69583			0.341251
$386$	−3.23085	+	5.59600i	−0.164446	+	0.284829i
$387$	1.79409	+	3.10746i	0.0911990	+	0.157961i
$388$	−1.47520	−	2.55512i	−0.0748917	−	0.129716i
$389$	−1.83318			−0.0929457			−0.0464728	−	0.998920i	$-0.514798\pi$
$389$	−1.83318			−0.0929457			−0.0464728	+	0.998920i	$0.514798\pi$
$390$	−4.21170	−	4.80378i	−0.213268	−	0.243249i
$391$	−10.4123			−0.526575
$392$	−0.692311	−	1.19912i	−0.0349670	−	0.0605646i
$393$	−1.88580	−	3.26630i	−0.0951261	−	0.164763i
$394$	−0.350310	+	0.606755i	−0.0176484	+	0.0305679i
$395$	−27.0619			−1.36163
$396$	−2.43694	+	4.22091i	−0.122461	+	0.212109i
$397$	−4.69260	+	8.12782i	−0.235515	+	0.407924i	−0.959422	−	0.281973i	$-0.909011\pi$
$397$	−4.69260	+	8.12782i	−0.235515	+	0.407924i	0.723907	+	0.689897i	$0.242344\pi$
$398$	4.57694			0.229421
$399$	22.4788	−	38.9344i	1.12535	−	1.94916i
$400$	−5.15247	−	8.92434i	−0.257623	−	0.446217i
$401$	−5.76867	−	9.99163i	−0.288074	−	0.498958i	0.685276	−	0.728283i	$-0.259681\pi$
$401$	−5.76867	−	9.99163i	−0.288074	−	0.498958i	−0.973350	+	0.229325i	$0.926348\pi$
$402$	−0.418450			−0.0208704
$403$	2.74249	−	8.07566i	0.136613	−	0.402277i
$404$	12.9136			0.642478
$405$	−14.3106	−	24.7867i	−0.711101	−	1.23166i
$406$	1.50571	+	2.60797i	0.0747274	+	0.129432i
$407$	−4.85504	+	8.40917i	−0.240655	+	0.416827i
$408$	4.55190			0.225353
$409$	−17.3892	+	30.1191i	−0.859843	+	1.48929i	0.0122354	+	0.999925i	$0.496105\pi$
$409$	−17.3892	+	30.1191i	−0.859843	+	1.48929i	−0.872078	+	0.489366i	$0.837228\pi$
$410$	−1.32733	+	2.29901i	−0.0655523	+	0.113540i
$411$	−4.55613			−0.224738
$412$	−14.1474	+	24.5040i	−0.696992	+	1.20723i
$413$	10.4041	+	18.0204i	0.511951	+	0.886725i
$414$	−1.92355	−	3.33169i	−0.0945376	−	0.163744i
$415$	−10.6563			−0.523100
$416$	7.29123	+	8.31624i	0.357482	+	0.407737i
$417$	−28.8949			−1.41499
$418$	−1.07606	−	1.86380i	−0.0526320	−	0.0911613i
$419$	6.17269	+	10.6914i	0.301556	+	0.522310i	0.976489	−	0.215569i	$-0.0691607\pi$
$419$	6.17269	+	10.6914i	0.301556	+	0.522310i	−0.674933	+	0.737879i	$0.735827\pi$
$420$	−15.1760	+	26.2856i	−0.740513	+	1.28261i
$421$	2.52324			0.122975			0.0614875	−	0.998108i	$-0.480416\pi$
$421$	2.52324			0.122975			0.0614875	+	0.998108i	$0.480416\pi$
$422$	2.73469	−	4.73663i	0.133123	−	0.230576i
$423$	11.7420	−	20.3377i	0.570914	−	0.988853i
$424$	−11.9702			−0.581325
$425$	2.64821	−	4.58683i	0.128457	−	0.222494i
$426$	−1.11715	−	1.93495i	−0.0541259	−	0.0937487i
$427$	9.44821	+	16.3648i	0.457231	+	0.791947i
$428$	−33.3172			−1.61045
$429$	−5.58862	−	6.37427i	−0.269821	−	0.307753i
$430$	1.06968			0.0515843
$431$	−7.95709	−	13.7821i	−0.383280	−	0.663860i	0.608249	−	0.793746i	$-0.291872\pi$
$431$	−7.95709	−	13.7821i	−0.383280	−	0.663860i	−0.991529	+	0.129886i	$0.958539\pi$
$432$	1.98258	+	3.43392i	0.0953867	+	0.165215i
$433$	1.05516	−	1.82759i	0.0507077	−	0.0878283i	−0.839557	−	0.543271i	$-0.817186\pi$
$433$	1.05516	−	1.82759i	0.0507077	−	0.0878283i	0.890265	+	0.455443i	$0.150519\pi$
$434$	1.51395			0.0726718
$435$	−15.5310	+	26.9005i	−0.744656	+	1.28978i
$436$	−8.44130	+	14.6208i	−0.404265	+	0.700208i
$437$	−45.4647			−2.17487
$438$	0.887152	−	1.53659i	0.0423897	−	0.0734212i
$439$	8.78185	+	15.2106i	0.419135	+	0.725963i	0.995853	−	0.0909808i	$-0.0290002\pi$
$439$	8.78185	+	15.2106i	0.419135	+	0.725963i	−0.576718	+	0.816943i	$0.695667\pi$
$440$	1.48010	+	2.56361i	0.0705609	+	0.122215i
$441$	−3.32020			−0.158105
$442$	−0.571451	+	1.68272i	−0.0271812	+	0.0800389i
$443$	−32.3904			−1.53892			−0.769458	−	0.638697i	$-0.779474\pi$
$443$	−32.3904			−1.53892			−0.769458	+	0.638697i	$0.779474\pi$
$444$	−22.0077	−	38.1185i	−1.04444	−	1.80902i
$445$	4.31202	+	7.46863i	0.204409	+	0.354047i
$446$	−0.136624	+	0.236640i	−0.00646934	+	0.0112052i
$447$	13.5602			0.641377
$448$	7.53870	−	13.0574i	0.356170	−	0.616904i
$449$	−11.8301	+	20.4903i	−0.558297	+	0.966999i	0.439342	+	0.898320i	$0.355212\pi$
$449$	−11.8301	+	20.4903i	−0.558297	+	0.966999i	−0.997639	+	0.0686787i	$0.978122\pi$
$450$	1.95690			0.0922490
$451$	−1.76127	+	3.05061i	−0.0829351	+	0.143648i
$452$	−2.35577	−	4.08032i	−0.110806	−	0.191922i
$453$	−0.837910	−	1.45130i	−0.0393685	−	0.0681882i
$454$	0.00612764			0.000287584
$455$	−15.9157	−	18.1531i	−0.746138	−	0.851031i
$456$	19.8755			0.930758
$457$	−1.76225	−	3.05231i	−0.0824348	−	0.142781i	0.821860	−	0.569689i	$-0.192936\pi$
$457$	−1.76225	−	3.05231i	−0.0824348	−	0.142781i	−0.904295	+	0.426908i	$0.859603\pi$
$458$	2.87515	+	4.97990i	0.134347	+	0.232695i
$459$	−1.01898	+	1.76493i	−0.0475620	+	0.0823797i
$460$	30.6943			1.43113
$461$	7.07243	−	12.2498i	0.329396	−	0.570530i	−0.652996	−	0.757361i	$-0.726488\pi$
$461$	7.07243	−	12.2498i	0.329396	−	0.570530i	0.982392	+	0.186831i	$0.0598216\pi$
$462$	0.752415	−	1.30322i	0.0350055	−	0.0606313i
$463$	8.79709			0.408836			0.204418	−	0.978884i	$-0.434470\pi$
$463$	8.79709			0.408836			0.204418	+	0.978884i	$0.434470\pi$
$464$	8.40560	−	14.5589i	0.390220	−	0.675881i
$465$	7.80797	+	13.5238i	0.362086	+	0.627152i
$466$	−3.63239	−	6.29148i	−0.168267	−	0.291447i
$467$	5.12967			0.237373			0.118686	−	0.992932i	$-0.462132\pi$
$467$	5.12967			0.237373			0.118686	+	0.992932i	$0.462132\pi$
$468$	17.2358	−	3.42609i	0.796726	−	0.158371i
$469$	−1.58129			−0.0730172
$470$	−3.50040	−	6.06287i	−0.161462	−	0.279660i
$471$	−8.55479	−	14.8173i	−0.394184	−	0.682746i
$472$	−4.59959	+	7.96673i	−0.211713	+	0.366699i
$473$	1.41938			0.0652632
$474$	−3.04096	+	5.26710i	−0.139676	+	0.241926i
$475$	11.5632	−	20.0280i	0.530556	−	0.918949i
$476$	8.44291			0.386980
$477$	−14.3518	+	24.8580i	−0.657122	+	1.13817i
$478$	−3.90551	−	6.76454i	−0.178634	−	0.309403i
$479$	11.9389	+	20.6788i	0.545503	+	0.944839i	0.998575	+	0.0533648i	$0.0169946\pi$
$479$	11.9389	+	20.6788i	0.545503	+	0.944839i	−0.453072	+	0.891474i	$0.649672\pi$
$480$	−20.2508			−0.924316
$481$	34.3384	−	6.82568i	1.56569	−	0.311224i
$482$	3.16846			0.144319
$483$	−15.8951	−	27.5311i	−0.723253	−	1.25271i
$484$	0.963982	+	1.66967i	0.0438174	+	0.0758939i
$485$	−2.14846	+	3.72125i	−0.0975567	+	0.168973i
$486$	−5.53881			−0.251245
$487$	6.66290	−	11.5405i	0.301925	−	0.522949i	−0.674647	−	0.738140i	$-0.735704\pi$
$487$	6.66290	−	11.5405i	0.301925	−	0.522949i	0.976572	+	0.215191i	$0.0690375\pi$
$488$	−4.17701	+	7.23479i	−0.189084	+	0.327504i
$489$	36.2169			1.63778
$490$	−0.494892	+	0.857179i	−0.0223570	+	0.0387234i
$491$	−1.99224	−	3.45067i	−0.0899088	−	0.155727i	0.817564	−	0.575838i	$-0.195324\pi$
$491$	−1.99224	−	3.45067i	−0.0899088	−	0.155727i	−0.907472	+	0.420112i	$0.861991\pi$
$492$	−7.98379	−	13.8283i	−0.359937	−	0.623429i
$493$	8.64043			0.389145
$494$	−2.49520	+	7.34748i	−0.112264	+	0.330579i
$495$	7.09828			0.319044
$496$	−4.22578	−	7.31927i	−0.189743	−	0.328645i
$497$	−4.22160	−	7.31203i	−0.189365	−	0.327989i
$498$	−1.19746	+	2.07406i	−0.0536595	+	0.0929410i
$499$	3.44227			0.154097			0.0770485	−	0.997027i	$-0.475450\pi$
$499$	3.44227			0.154097			0.0770485	+	0.997027i	$0.475450\pi$
$500$	5.72708	−	9.91960i	0.256123	−	0.443618i
$501$	−2.80223	+	4.85361i	−0.125195	+	0.216843i
$502$	−4.01380			−0.179145
$503$	14.1758	−	24.5531i	0.632065	−	1.09477i	−0.355063	−	0.934842i	$-0.615541\pi$
$503$	14.1758	−	24.5531i	0.632065	−	1.09477i	0.987129	−	0.159927i	$-0.0511260\pi$
$504$	3.17773	+	5.50399i	0.141547	+	0.245167i
$505$	−9.40367	−	16.2876i	−0.418458	−	0.724790i
$506$	−1.52180			−0.0676524
$507$	−3.99745	+	30.3027i	−0.177533	+	1.34579i
$508$	33.7708			1.49834
$509$	−17.2089	−	29.8067i	−0.762771	−	1.32116i	−0.941417	−	0.337245i	$-0.890505\pi$
$509$	−17.2089	−	29.8067i	−0.762771	−	1.32116i	0.178646	−	0.983913i	$-0.442828\pi$
$510$	−1.62694	−	2.81795i	−0.0720423	−	0.124781i
$511$	3.35247	−	5.80666i	0.148305	−	0.256871i
$512$	18.4936			0.817309
$513$	−4.44930	+	7.70642i	−0.196442	+	0.340247i
$514$	1.68375	−	2.91633i	0.0742668	−	0.128634i
$515$	41.2083			1.81585
$516$	−3.21701	+	5.57202i	−0.141621	+	0.245294i
$517$	−4.64478	−	8.04499i	−0.204277	−	0.353818i
$518$	3.10739	+	5.38216i	0.136531	+	0.236479i
$519$	12.0119			0.527263
$520$	3.43208	−	10.1063i	0.150507	−	0.443189i
$521$	−28.8248			−1.26284			−0.631420	−	0.775441i	$-0.717527\pi$
$521$	−28.8248			−1.26284			−0.631420	+	0.775441i	$0.717527\pi$
$522$	1.59622	+	2.76473i	0.0698645	+	0.121009i
$523$	4.66882	+	8.08663i	0.204153	+	0.353604i	0.949863	−	0.312668i	$-0.101223\pi$
$523$	4.66882	+	8.08663i	0.204153	+	0.353604i	−0.745709	+	0.666271i	$0.767889\pi$
$524$	1.54636	−	2.67838i	0.0675531	−	0.117005i
$525$	16.1706			0.705744
$526$	3.52951	−	6.11329i	0.153894	−	0.266552i
$527$	2.17192	−	3.76187i	0.0946102	−	0.163870i
$528$	−8.40066			−0.365592
$529$	−4.57440	+	7.92309i	−0.198887	+	0.344482i
$530$	4.27840	+	7.41041i	0.185842	+	0.321888i
$531$	11.0294	+	19.1035i	0.478636	+	0.829021i
$532$	36.8653			1.59831
$533$	12.4570	−	2.47617i	0.539573	−	0.107255i
$534$	1.93818			0.0838731
$535$	24.2615	+	42.0221i	1.04891	+	1.81677i
$536$	−0.349541	−	0.605422i	−0.0150979	−	0.0261502i
$537$	−28.5739	+	49.4915i	−1.23306	+	2.13572i
$538$	5.75282			0.248022
$539$	−0.656686	+	1.13741i	−0.0282855	+	0.0489919i
$540$	3.00384	−	5.20280i	0.129264	−	0.223893i
$541$	−10.7783			−0.463395			−0.231697	−	0.972788i	$-0.574428\pi$
$541$	−10.7783			−0.463395			−0.231697	+	0.972788i	$0.574428\pi$
$542$	−0.326656	+	0.565785i	−0.0140311	+	0.0243025i
$543$	2.35637	+	4.08135i	0.101121	+	0.175148i
$544$	2.81654	+	4.87839i	0.120758	+	0.209159i
$545$	24.5877			1.05322
$546$	−5.32162	+	1.05782i	−0.227744	+	0.0452704i
$547$	−19.4925			−0.833439			−0.416719	−	0.909035i	$-0.636820\pi$
$547$	−19.4925			−0.833439			−0.416719	+	0.909035i	$0.636820\pi$
$548$	−1.86802	−	3.23551i	−0.0797979	−	0.138214i
$549$	10.0161	+	17.3484i	0.427476	+	0.740411i
$550$	0.387045	−	0.670382i	0.0165037	−	0.0285852i
$551$	37.7278			1.60726
$552$	7.02716	−	12.1714i	0.299096	−	0.518049i
$553$	−11.4916	+	19.9040i	−0.488671	+	0.846402i
$554$	−1.51839			−0.0645102
$555$	−32.0519	+	55.5155i	−1.36053	+	2.35650i
$556$	−11.8469	−	20.5195i	−0.502422	−	0.870220i
$557$	−6.03230	−	10.4482i	−0.255597	−	0.442706i	0.709461	−	0.704745i	$-0.248939\pi$
$557$	−6.03230	−	10.4482i	−0.255597	−	0.442706i	−0.965057	+	0.262039i	$0.915605\pi$
$558$	1.60494			0.0679427
$559$	−3.37380	−	3.84809i	−0.142697	−	0.162757i
$560$	−23.9240			−1.01097
$561$	−2.15884	−	3.73921i	−0.0911461	−	0.157870i
$562$	−2.40976	−	4.17382i	−0.101649	−	0.176062i
$563$	−10.4590	+	18.1156i	−0.440796	+	0.763481i	−0.997749	−	0.0670633i	$-0.978637\pi$
$563$	−10.4590	+	18.1156i	−0.440796	+	0.763481i	0.556953	+	0.830544i	$0.311970\pi$
$564$	42.1093			1.77312
$565$	−3.43093	+	5.94254i	−0.144340	+	0.250005i
$566$	1.92883	−	3.34083i	0.0810746	−	0.140425i
$567$	−24.3074			−1.02082
$568$	1.86635	−	3.23261i	0.0783103	−	0.135637i
$569$	−5.54414	−	9.60273i	−0.232422	−	0.402567i	0.726098	−	0.687591i	$-0.241332\pi$
$569$	−5.54414	−	9.60273i	−0.232422	−	0.402567i	−0.958520	+	0.285024i	$0.907998\pi$
$570$	−7.10393	−	12.3044i	−0.297551	−	0.515373i
$571$	−12.6344			−0.528732			−0.264366	−	0.964422i	$-0.585163\pi$
$571$	−12.6344			−0.528732			−0.264366	+	0.964422i	$0.585163\pi$
$572$	2.23530	−	6.58217i	0.0934627	−	0.275214i
$573$	−7.45385			−0.311389
$574$	1.12728	+	1.95250i	0.0470516	+	0.0814957i
$575$	−8.17651	−	14.1621i	−0.340984	−	0.590602i
$576$	7.99181	−	13.8422i	0.332992	−	0.576759i
$577$	−21.3084			−0.887082			−0.443541	−	0.896254i	$-0.646278\pi$
$577$	−21.3084			−0.887082			−0.443541	+	0.896254i	$0.646278\pi$
$578$	1.82880	−	3.16758i	0.0760682	−	0.131754i
$579$	−28.3025	+	49.0214i	−1.17621	+	2.03726i
$580$	−25.4710			−1.05762
$581$	−4.52511	+	7.83771i	−0.187733	+	0.325163i
$582$	0.482848	+	0.836318i	0.0200147	+	0.0346665i
$583$	5.67713	+	9.83308i	0.235123	+	0.407244i
$584$	2.96423			0.122661
$585$	−16.8723	−	19.2442i	−0.697583	−	0.795650i
$586$	−7.28172			−0.300805
$587$	10.8380	+	18.7720i	0.447334	+	0.774805i	0.998212	−	0.0597810i	$-0.0190402\pi$
$587$	10.8380	+	18.7720i	0.447334	+	0.774805i	−0.550878	+	0.834586i	$0.685707\pi$
$588$	−2.97674	−	5.15586i	−0.122759	−	0.212624i
$589$	9.48352	−	16.4259i	0.390761	−	0.676819i
$590$	6.57596			0.270728
$591$	−3.06875	+	5.31522i	−0.126231	+	0.218639i
$592$	17.3469	−	30.0457i	0.712954	−	1.23487i
$593$	3.39934			0.139594			0.0697971	−	0.997561i	$-0.477765\pi$
$593$	3.39934			0.139594			0.0697971	+	0.997561i	$0.477765\pi$
$594$	−0.148928	+	0.257951i	−0.00611059	+	0.0105838i
$595$	−6.14809	−	10.6488i	−0.252047	−	0.436559i
$596$	5.55971	+	9.62969i	0.227734	+	0.394448i
$597$	40.0943			1.64095
$598$	3.61725	+	4.12577i	0.147920	+	0.168715i
$599$	12.5139			0.511305			0.255653	−	0.966769i	$-0.417710\pi$
$599$	12.5139			0.511305			0.255653	+	0.966769i	$0.417710\pi$
$600$	3.57448	+	6.19118i	0.145928	+	0.252754i
$601$	−16.6554	−	28.8480i	−0.679387	−	1.17673i	−0.975166	−	0.221477i	$-0.928912\pi$
$601$	−16.6554	−	28.8480i	−0.679387	−	1.17673i	0.295779	−	0.955257i	$-0.404421\pi$
$602$	0.454227	−	0.786743i	0.0185129	−	0.0320653i
$603$	−1.67633			−0.0682656
$604$	0.687088	−	1.19007i	0.0279572	−	0.0484233i
$605$	1.40394	−	2.43169i	0.0570781	−	0.0988621i
$606$	−4.22678			−0.171701
$607$	12.8594	−	22.2731i	0.521945	−	0.904036i	−0.477729	−	0.878507i	$-0.658540\pi$
$607$	12.8594	−	22.2731i	0.521945	−	0.904036i	0.999674	−	0.0255286i	$-0.00812690\pi$
$608$	12.2982	+	21.3011i	0.498759	+	0.863875i
$609$	13.1902	+	22.8461i	0.534493	+	0.925769i
$610$	5.97180			0.241791
$611$	−10.7704	+	31.7150i	−0.435724	+	1.28305i
$612$	8.95037			0.361797
$613$	18.5817	+	32.1844i	0.750508	+	1.29992i	0.947577	+	0.319528i	$0.103524\pi$
$613$	18.5817	+	32.1844i	0.750508	+	1.29992i	−0.197069	+	0.980390i	$0.563142\pi$
$614$	−1.37320	−	2.37845i	−0.0554179	−	0.0959866i
$615$	−11.6275	+	20.1395i	−0.468867	+	0.812102i
$616$	2.51403			0.101293
$617$	1.70556	−	2.95411i	0.0686632	−	0.118928i	−0.829650	−	0.558284i	$-0.811460\pi$
$617$	1.70556	−	2.95411i	0.0686632	−	0.118928i	0.898313	+	0.439356i	$0.144793\pi$
$618$	4.63060	−	8.02044i	0.186270	−	0.322629i
$619$	0.940405			0.0377981			0.0188990	−	0.999821i	$-0.493984\pi$
$619$	0.940405			0.0377981			0.0188990	+	0.999821i	$0.493984\pi$
$620$	−6.40256	+	11.0896i	−0.257133	+	0.445367i
$621$	3.14617	+	5.44933i	0.126252	+	0.218674i
$622$	1.13361	+	1.96346i	0.0454534	+	0.0787276i
$623$	7.32421			0.293438
$624$	19.9680	+	22.7751i	0.799358	+	0.911733i
$625$	−31.1024			−1.24410
$626$	−2.80924	−	4.86574i	−0.112280	−	0.194474i
$627$	−9.42640	−	16.3270i	−0.376454	−	0.652037i
$628$	7.01494	−	12.1502i	0.279927	−	0.484847i
$629$	17.8315			0.710990
$630$	2.27157	−	3.93448i	0.0905016	−	0.156753i
$631$	8.41513	−	14.5754i	0.335001	−	0.580239i	−0.648484	−	0.761228i	$-0.724597\pi$
$631$	8.41513	−	14.5754i	0.335001	−	0.580239i	0.983485	+	0.180989i	$0.0579299\pi$
$632$	−10.1607			−0.404172
$633$	23.9561	−	41.4932i	0.952171	−	1.64921i
$634$	−3.09747	−	5.36498i	−0.123016	−	0.213070i
$635$	−24.5918	−	42.5942i	−0.975894	−	1.69030i
$636$	−51.4685			−2.04086
$637$	4.64456	−	0.923232i	0.184024	−	0.0365798i
$638$	1.26283			0.0499960
$639$	−4.47534	−	7.75152i	−0.177042	−	0.306645i
$640$	−10.9955	−	19.0448i	−0.434635	−	0.752810i
$641$	−10.8312	+	18.7603i	−0.427808	+	0.740986i	−0.996678	−	0.0814420i	$-0.974047\pi$
$641$	−10.8312	+	18.7603i	−0.427808	+	0.740986i	0.568870	+	0.822428i	$0.307381\pi$
$642$	10.9051			0.430390
$643$	−1.71425	+	2.96916i	−0.0676033	+	0.117092i	−0.897846	−	0.440310i	$-0.854869\pi$
$643$	−1.71425	+	2.96916i	−0.0676033	+	0.117092i	0.830243	+	0.557402i	$0.188202\pi$
$644$	13.0340	−	22.5756i	0.513613	−	0.889603i
$645$	9.37044			0.368961
$646$	−1.97608	+	3.42266i	−0.0777477	+	0.134663i
$647$	22.5782	+	39.1065i	0.887639	+	1.53744i	0.842659	+	0.538448i	$0.180989\pi$
$647$	22.5782	+	39.1065i	0.887639	+	1.53744i	0.0449804	+	0.998988i	$0.485677\pi$
$648$	−5.37310	−	9.30648i	−0.211075	−	0.365593i
$649$	8.72582			0.342518
$650$	−2.73747	+	0.544145i	−0.107372	+	0.0213431i
$651$	13.2623			0.519790
$652$	14.8490	+	25.7192i	0.581530	+	1.00724i
$653$	−14.3241	−	24.8101i	−0.560545	−	0.970893i	−0.997449	−	0.0713844i	$-0.977258\pi$
$653$	−14.3241	−	24.8101i	−0.560545	−	0.970893i	0.436904	−	0.899508i	$-0.356075\pi$
$654$	2.76293	−	4.78554i	0.108039	−	0.187129i
$655$	−4.50421			−0.175994
$656$	6.29298	−	10.8998i	0.245699	−	0.425564i
$657$	3.55397	−	6.15567i	0.138654	−	0.240155i
$658$	−5.94564			−0.231785
$659$	9.50013	−	16.4547i	0.370072	−	0.640984i	−0.619504	−	0.784994i	$-0.712666\pi$
$659$	9.50013	−	16.4547i	0.370072	−	0.640984i	0.989576	+	0.144009i	$0.0459996\pi$
$660$	6.36399	+	11.0228i	0.247718	+	0.429060i
$661$	−18.4711	−	31.9929i	−0.718442	−	1.24438i	−0.961617	−	0.274395i	$-0.911522\pi$
$661$	−18.4711	−	31.9929i	−0.718442	−	1.24438i	0.243175	−	0.969982i	$-0.421811\pi$
$662$	0.886415			0.0344515
$663$	−5.00596	+	14.7408i	−0.194415	+	0.572484i
$664$	−4.00106			−0.155271
$665$	−26.8452	−	46.4972i	−1.04101	−	1.80308i
$666$	3.29416	+	5.70566i	0.127646	+	0.221090i
$667$	13.3390	−	23.1037i	0.516486	−	0.894580i
$668$	−4.59567			−0.177812
$669$	−1.19684	+	2.07298i	−0.0462724	+	0.0801462i
$670$	−0.249866	+	0.432781i	−0.00965317	+	0.0167198i
$671$	7.92414			0.305908
$672$	−8.59927	+	14.8944i	−0.331724	+	0.574563i
$673$	17.3176	+	29.9949i	0.667544	+	1.15622i	0.978589	+	0.205825i	$0.0659876\pi$
$673$	17.3176	+	29.9949i	0.667544	+	1.15622i	−0.311045	+	0.950395i	$0.600679\pi$
$674$	−3.02093	−	5.23241i	−0.116362	−	0.201545i
$675$	−3.20071			−0.123195
$676$	−23.1582	+	9.58537i	−0.890699	+	0.368668i
$677$	−29.3445			−1.12780			−0.563900	−	0.825843i	$-0.690700\pi$
$677$	−29.3445			−1.12780			−0.563900	+	0.825843i	$0.690700\pi$
$678$	0.771071	+	1.33553i	0.0296128	+	0.0512909i
$679$	1.82465	+	3.16038i	0.0700235	+	0.121284i
$680$	2.71804	−	4.70779i	0.104232	−	0.180535i
$681$	0.0536786			0.00205697
$682$	0.317434	−	0.549812i	0.0121552	−	0.0210534i
$683$	−19.2890	+	33.4095i	−0.738073	+	1.27838i	0.215288	+	0.976551i	$0.430931\pi$
$683$	−19.2890	+	33.4095i	−0.738073	+	1.27838i	−0.953362	+	0.301830i	$0.902402\pi$
$684$	39.0811			1.49430
$685$	−2.72057	+	4.71216i	−0.103948	+	0.180043i
$686$	2.66042	+	4.60799i	0.101575	+	0.175934i
$687$	25.1865	+	43.6243i	0.960925	+	1.66437i
$688$	−5.07141			−0.193346
$689$	13.1642	−	38.7641i	0.501518	−	1.47679i
$690$	−10.0466			−0.382468
$691$	−4.79080	−	8.29791i	−0.182251	−	0.315667i	0.760396	−	0.649460i	$-0.225005\pi$
$691$	−4.79080	−	8.29791i	−0.182251	−	0.315667i	−0.942647	+	0.333792i	$0.891672\pi$
$692$	4.92488	+	8.53015i	0.187216	+	0.324268i
$693$	3.01421	−	5.22077i	0.114500	−	0.198321i
$694$	−8.26032			−0.313557
$695$	−17.2538	+	29.8844i	−0.654473	+	1.13358i
$696$	−5.83132	+	10.1001i	−0.221035	+	0.382845i
$697$	6.46878			0.245023
$698$	4.09039	−	7.08477i	0.154824	−	0.268163i
$699$	−31.8200	−	55.1138i	−1.20354	−	2.08460i
$700$	6.62998	+	11.4835i	0.250590	+	0.434034i
$701$	−15.9373			−0.601943			−0.300971	−	0.953633i	$-0.597311\pi$
$701$	−15.9373			−0.601943			−0.300971	+	0.953633i	$0.597311\pi$
$702$	1.05333	−	0.209377i	0.0397552	−	0.00790243i
$703$	77.8600			2.93655
$704$	−3.16132	−	5.47557i	−0.119147	−	0.206368i
$705$	−30.6638	−	53.1112i	−1.15487	−	2.00029i
$706$	0.546193	−	0.946033i	0.0205562	−	0.0356044i
$707$	−15.9727			−0.600714
$708$	−19.7769	+	34.2546i	−0.743262	+	1.28737i
$709$	15.3120	−	26.5212i	0.575054	−	0.996023i	−0.420982	−	0.907069i	$-0.638314\pi$
$709$	15.3120	−	26.5212i	0.575054	−	0.996023i	0.996036	−	0.0889538i	$-0.0283523\pi$
$710$	−2.66829			−0.100139
$711$	−12.1823	+	21.1003i	−0.456870	+	0.791323i
$712$	1.61900	+	2.80419i	0.0606746	+	0.105091i
$713$	−6.70594	−	11.6150i	−0.251140	−	0.434986i
$714$	−2.76346			−0.103420
$715$	−9.92965	+	1.97379i	−0.371348	+	0.0738154i
$716$	−46.8614			−1.75129
$717$	−34.2125	−	59.2578i	−1.27769	−	2.21302i
$718$	3.99052	+	6.91178i	0.148925	+	0.257945i
$719$	−17.8179	+	30.8616i	−0.664497	+	1.15094i	0.314924	+	0.949117i	$0.398021\pi$
$719$	−17.8179	+	30.8616i	−0.664497	+	1.15094i	−0.979421	+	0.201826i	$0.935312\pi$
$720$	−25.3620			−0.945184
$721$	17.4987	−	30.3086i	0.651685	−	1.12875i
$722$	−6.07863	+	10.5285i	−0.226223	+	0.391830i
$723$	27.7559			1.03225
$724$	−1.93223	+	3.34672i	−0.0718107	+	0.124380i
$725$	6.78508	+	11.7521i	0.251992	+	0.436462i
$726$	−0.315522	−	0.546500i	−0.0117101	−	0.0202825i
$727$	23.1160			0.857325			0.428663	−	0.903465i	$-0.358985\pi$
$727$	23.1160			0.857325			0.428663	+	0.903465i	$0.358985\pi$
$728$	−5.97573	−	6.81581i	−0.221475	−	0.252611i
$729$	−17.9407			−0.664471
$730$	−1.05948	−	1.83507i	−0.0392130	−	0.0679189i
$731$	−1.30327	−	2.25733i	−0.0482033	−	0.0834905i
$732$	−17.9599	+	31.1075i	−0.663818	+	1.14977i
$733$	−4.90763			−0.181267			−0.0906337	−	0.995884i	$-0.528889\pi$
$733$	−4.90763			−0.181267			−0.0906337	+	0.995884i	$0.528889\pi$
$734$	0.845495	−	1.46444i	0.0312078	−	0.0540535i
$735$	−4.33529	+	7.50895i	−0.159910	+	0.276972i
$736$	17.3925			0.641097
$737$	−0.331554	+	0.574268i	−0.0122129	+	0.0211534i
$738$	1.19503	+	2.06985i	0.0439897	+	0.0761923i
$739$	−4.73066	−	8.19374i	−0.174020	−	0.301412i	0.765802	−	0.643077i	$-0.222342\pi$
$739$	−4.73066	−	8.19374i	−0.174020	−	0.301412i	−0.939822	+	0.341665i	$0.889009\pi$
$740$	−52.5652			−1.93234
$741$	−21.8581	+	64.3645i	−0.802979	+	2.36449i
$742$	7.26712			0.266784
$743$	15.1360	+	26.2163i	0.555285	+	0.961782i	0.997881	+	0.0650610i	$0.0207242\pi$
$743$	15.1360	+	26.2163i	0.555285	+	0.961782i	−0.442596	+	0.896721i	$0.645942\pi$
$744$	2.93160	+	5.07768i	0.107478	+	0.186157i
$745$	8.09711	−	14.0246i	0.296655	−	0.513822i
$746$	−1.87901			−0.0687954
$747$	−4.79709	+	8.30880i	−0.175516	+	0.304003i
$748$	1.77025	−	3.06616i	0.0647268	−	0.112110i
$749$	41.2095			1.50576
$750$	−1.87454	+	3.24680i	−0.0684485	+	0.118556i
$751$	−26.8774	−	46.5530i	−0.980771	−	1.69874i	−0.659403	−	0.751790i	$-0.729191\pi$
$751$	−26.8774	−	46.5530i	−0.980771	−	1.69874i	−0.321368	−	0.946954i	$-0.604143\pi$
$752$	16.5957	+	28.7445i	0.605181	+	1.04820i
$753$	−35.1612			−1.28135
$754$	−3.00169	−	3.42367i	−0.109315	−	0.124683i
$755$	−2.00134			−0.0728362
$756$	−2.55109	−	4.41862i	−0.0927824	−	0.160704i
$757$	10.7975	+	18.7019i	0.392443	+	0.679731i	0.992771	−	0.120023i	$-0.0382967\pi$
$757$	10.7975	+	18.7019i	0.392443	+	0.679731i	−0.600328	+	0.799754i	$0.704963\pi$
$758$	−0.930336	+	1.61139i	−0.0337913	+	0.0585283i
$759$	−13.3311			−0.483888
$760$	11.8681	−	20.5562i	0.430502	−	0.745652i
$761$	4.27236	−	7.39994i	0.154873	−	0.268248i	−0.778140	−	0.628091i	$-0.783837\pi$
$761$	4.27236	−	7.39994i	0.154873	−	0.268248i	0.933013	+	0.359843i	$0.117170\pi$
$762$	−11.0536			−0.400428
$763$	10.4409	−	18.0842i	0.377986	−	0.654691i
$764$	−3.05609	−	5.29330i	−0.110565	−	0.191505i
$765$	−6.51762	−	11.2889i	−0.235645	−	0.408149i
$766$	1.58635			0.0573170
$767$	−20.7409	−	23.6566i	−0.748909	−	0.854191i
$768$	24.7889			0.894494
$769$	12.2280	+	21.1795i	0.440954	+	0.763754i	0.997760	−	0.0668880i	$-0.0213070\pi$
$769$	12.2280	+	21.1795i	0.440954	+	0.763754i	−0.556807	+	0.830642i	$0.687974\pi$
$770$	−0.898567	−	1.55636i	−0.0323821	−	0.0560875i
$771$	14.7497	−	25.5473i	0.531199	−	0.920064i
$772$	−46.4163			−1.67056
$773$	−0.752970	+	1.30418i	−0.0270824	+	0.0469082i	−0.879249	−	0.476363i	$-0.841955\pi$
$773$	−0.752970	+	1.30418i	−0.0270824	+	0.0469082i	0.852167	+	0.523271i	$0.175288\pi$
$774$	0.481528	−	0.834031i	0.0173082	−	0.0299786i
$775$	6.82218			0.245060
$776$	−0.806667	+	1.39719i	−0.0289577	+	0.0501561i
$777$	27.2210	+	47.1481i	0.976548	+	1.69143i
$778$	0.246008	+	0.426099i	0.00881983	+	0.0152764i
$779$	28.2454			1.01200
$780$	14.7570	−	43.4540i	0.528384	−	1.55590i
$781$	−3.54062			−0.126693
$782$	1.39731	+	2.42022i	0.0499679	+	0.0865469i
$783$	−2.61078	−	4.52200i	−0.0933015	−	0.161603i
$784$	2.34632	−	4.06394i	0.0837971	−	0.145141i
$785$	−20.4330			−0.729286
$786$	−0.506141	+	0.876662i	−0.0180535	+	0.0312695i
$787$	−5.29788	+	9.17620i	−0.188849	+	0.327096i	−0.944867	−	0.327455i	$-0.893809\pi$
$787$	−5.29788	+	9.17620i	−0.188849	+	0.327096i	0.756018	+	0.654551i	$0.227142\pi$
$788$	−5.03276			−0.179285
$789$	30.9188	−	53.5529i	1.10074	−	1.90653i
$790$	3.63165	+	6.29021i	0.129208	+	0.223796i
$791$	2.91382	+	5.04688i	0.103603	+	0.179446i
$792$	2.66514			0.0947015
$793$	−18.8353	−	21.4832i	−0.668861	−	0.762890i
$794$	2.51895			0.0893942
$795$	37.4791	+	64.9158i	1.32925	+	2.30233i
$796$	16.4387	+	28.4727i	0.582655	+	1.00919i
$797$	−1.87305	+	3.24422i	−0.0663470	+	0.114916i	−0.897291	−	0.441440i	$-0.854468\pi$
$797$	−1.87305	+	3.24422i	−0.0663470	+	0.114916i	0.830944	+	0.556356i	$0.187801\pi$
$798$	−12.0664			−0.427147
$799$	−8.52964	+	14.7738i	−0.301757	+	0.522659i
$800$	−4.42350	+	7.66173i	−0.156394	+	0.270883i
$801$	7.76443			0.274343
$802$	−1.54829	+	2.68171i	−0.0546719	+	0.0946945i
$803$	−1.40585	−	2.43500i	−0.0496113	−	0.0859292i
$804$	−1.50292	−	2.60314i	−0.0530040	−	0.0918057i
$805$	−37.9653			−1.33810
$806$	−2.24512	+	0.446279i	−0.0790811	+	0.0157195i
$807$	50.3951			1.77399
$808$	−3.53072	−	6.11539i	−0.124210	−	0.215139i
$809$	13.1394	+	22.7581i	0.461956	+	0.800131i	0.999058	−	0.0433858i	$-0.0138145\pi$
$809$	13.1394	+	22.7581i	0.461956	+	0.800131i	−0.537102	+	0.843517i	$0.680481\pi$
$810$	−3.84091	+	6.65266i	−0.134956	+	0.233751i
$811$	8.17124			0.286931			0.143465	−	0.989655i	$-0.454175\pi$
$811$	8.17124			0.286931			0.143465	+	0.989655i	$0.454175\pi$
$812$	−10.8160	+	18.7338i	−0.379566	+	0.657428i
$813$	−2.86153	+	4.95632i	−0.100358	+	0.173826i
$814$	2.60615			0.0913454
$815$	21.6259	−	37.4572i	0.757522	−	1.31207i
$816$	7.71346	+	13.3601i	0.270025	+	0.467697i
$817$	−5.69064	−	9.85648i	−0.199090	−	0.344834i
$818$	9.33441			0.326370
$819$	−21.3187	+	4.23767i	−0.744935	+	0.148076i
$820$	−19.0692			−0.665925
$821$	27.9142	+	48.3489i	0.974214	+	1.68739i	0.682505	+	0.730881i	$0.260890\pi$
$821$	27.9142	+	48.3489i	0.974214	+	1.68739i	0.291708	+	0.956507i	$0.405776\pi$
$822$	0.611424	+	1.05902i	0.0213259	+	0.0369375i
$823$	15.2445	−	26.4043i	0.531391	−	0.920396i	−0.467938	−	0.883761i	$-0.655003\pi$
$823$	15.2445	−	26.4043i	0.531391	−	0.920396i	0.999329	−	0.0366346i	$-0.0116638\pi$
$824$	15.4722			0.538998
$825$	3.39055	−	5.87260i	0.118044	−	0.204458i
$826$	2.79241	−	4.83660i	0.0971604	−	0.168287i
$827$	3.15547			0.109726			0.0548631	−	0.998494i	$-0.482528\pi$
$827$	3.15547			0.109726			0.0548631	+	0.998494i	$0.482528\pi$
$828$	13.8174	−	23.9325i	0.480189	−	0.831712i
$829$	7.93696	+	13.7472i	0.275662	+	0.477461i	0.970302	−	0.241897i	$-0.0777696\pi$
$829$	7.93696	+	13.7472i	0.275662	+	0.477461i	−0.694640	+	0.719358i	$0.744436\pi$
$830$	1.43006	+	2.47694i	0.0496381	+	0.0859758i
$831$	−13.3012			−0.461414
$832$	−7.33054	+	21.5859i	−0.254141	+	0.748355i
$833$	2.41187			0.0835663
$834$	3.87764	+	6.71626i	0.134272	+	0.232565i
$835$	3.34655	+	5.79640i	0.115812	+	0.200593i
$836$	7.72967	−	13.3882i	0.267336	−	0.463040i
$837$	−2.62505			−0.0907350
$838$	1.65673	−	2.86953i	0.0572306	−	0.0991264i
$839$	−15.2475	+	26.4094i	−0.526401	+	0.911753i	0.473126	+	0.880995i	$0.343126\pi$
$839$	−15.2475	+	26.4094i	−0.526401	+	0.911753i	−0.999527	+	0.0307583i	$0.990208\pi$
$840$	16.5971			0.572654
$841$	3.43099	−	5.94265i	0.118310	−	0.204919i
$842$	−0.338613	−	0.586495i	−0.0116694	−	0.0202120i
$843$	−21.1096	−	36.5630i	−0.727055	−	1.25930i
$844$	39.2882			1.35235
$845$	28.9534	+	22.2287i	0.996029	+	0.764692i
$846$	−6.30300			−0.216702
$847$	−1.19233	−	2.06518i	−0.0409690	−	0.0709604i
$848$	−20.2842	−	35.1333i	−0.696563	−	1.20648i
$849$	16.8967	−	29.2659i	0.579892	−	1.00440i
$850$	−1.42154			−0.0487583
$851$	27.5280	−	47.6799i	0.943649	−	1.63445i
$852$	8.02477	−	13.8993i	0.274924	−	0.476182i
$853$	−33.0339			−1.13106			−0.565530	−	0.824728i	$-0.691328\pi$
$853$	−33.0339			−1.13106			−0.565530	+	0.824728i	$0.691328\pi$
$854$	2.53586	−	4.39224i	0.0867754	−	0.150299i
$855$	−28.4587	−	49.2919i	−0.973267	−	1.68575i
$856$	9.10927	+	15.7777i	0.311348	+	0.539271i
$857$	−2.25150			−0.0769098			−0.0384549	−	0.999260i	$-0.512244\pi$
$857$	−2.25150			−0.0769098			−0.0384549	+	0.999260i	$0.512244\pi$
$858$	−0.731639	+	2.15442i	−0.0249778	+	0.0735507i
$859$	14.7807			0.504309			0.252155	−	0.967687i	$-0.418861\pi$
$859$	14.7807			0.504309			0.252155	+	0.967687i	$0.418861\pi$
$860$	3.84189	+	6.65435i	0.131007	+	0.226911i
$861$	9.87502	+	17.1040i	0.336540	+	0.582904i
$862$	−2.13565	+	3.69906i	−0.0727406	+	0.125990i
$863$	−42.7490			−1.45519			−0.727597	−	0.686005i	$-0.759363\pi$
$863$	−42.7490			−1.45519			−0.727597	+	0.686005i	$0.759363\pi$
$864$	1.70208	−	2.94809i	0.0579060	−	0.100296i
$865$	7.17256	−	12.4232i	0.243874	−	0.422403i
$866$	−0.566400			−0.0192471
$867$	16.0205	−	27.7483i	0.544083	−	0.942380i
$868$	5.43756	+	9.41812i	0.184563	+	0.319672i
$869$	4.81894	+	8.34665i	0.163471	+	0.283141i
$870$	8.33693			0.282648
$871$	2.34499	−	0.466130i	0.0794570	−	0.0157942i
$872$	9.23175			0.312626
$873$	1.93432	+	3.35033i	0.0654667	+	0.113392i
$874$	6.10127	+	10.5677i	0.206378	+	0.357458i
$875$	−7.08373	+	12.2694i	−0.239474	+	0.414781i
$876$	12.7453			0.430624
$877$	16.7639	−	29.0360i	0.566078	−	0.980475i	−0.430871	−	0.902414i	$-0.641794\pi$
$877$	16.7639	−	29.0360i	0.566078	−	0.980475i	0.996949	−	0.0780617i	$-0.0248731\pi$
$878$	2.35701	−	4.08246i	0.0795453	−	0.137777i
$879$	−63.7884			−2.15153
$880$	−5.01622	+	8.68835i	−0.169097	+	0.292884i
$881$	−11.1873	−	19.3769i	−0.376909	−	0.652825i	0.613702	−	0.789538i	$-0.289680\pi$
$881$	−11.1873	−	19.3769i	−0.376909	−	0.652825i	−0.990611	+	0.136713i	$0.956346\pi$
$882$	0.445564	+	0.771739i	0.0150029	+	0.0259858i
$883$	10.7284			0.361041			0.180520	−	0.983571i	$-0.442222\pi$
$883$	10.7284			0.361041			0.180520	+	0.983571i	$0.442222\pi$
$884$	−12.5205	+	2.48879i	−0.421110	+	0.0837070i
$885$	57.6059			1.93640
$886$	4.34673	+	7.52876i	0.146031	+	0.252934i
$887$	2.75829	+	4.77749i	0.0926142	+	0.160412i	0.908610	−	0.417645i	$-0.137144\pi$
$887$	2.75829	+	4.77749i	0.0926142	+	0.160412i	−0.815996	+	0.578057i	$0.803811\pi$
$888$	−12.0343	+	20.8440i	−0.403844	+	0.699478i
$889$	−41.7705			−1.40094
$890$	1.15733	−	2.00455i	0.0387937	−	0.0671927i
$891$	−5.09661	+	8.82759i	−0.170743	+	0.295735i
$892$	−1.96282			−0.0657200
$893$	−37.2440	+	64.5086i	−1.24632	+	2.15870i
$894$	−1.81975	−	3.15191i	−0.0608617	−	0.105416i
$895$	34.1243	+	59.1050i	1.14065	+	1.97566i
$896$	−18.6765			−0.623938
$897$	31.6874	+	36.1420i	1.05801	+	1.20675i
$898$	6.35030			0.211912
$899$	5.56476	+	9.63845i	0.185595	+	0.321460i
$900$	7.02847	+	12.1737i	0.234282	+	0.405789i
$901$	10.4254	−	18.0574i	0.347322	−	0.601579i
$902$	0.945437			0.0314796
$903$	3.97906	−	6.89193i	0.132415	−	0.229349i
$904$	−1.28818	+	2.23120i	−0.0428444	+	0.0742087i
$905$	5.62816			0.187086
$906$	−0.224892	+	0.389524i	−0.00747153	+	0.0129411i
$907$	8.76282	+	15.1777i	0.290965	+	0.503966i	0.974038	−	0.226384i	$-0.0726904\pi$
$907$	8.76282	+	15.1777i	0.290965	+	0.503966i	−0.683073	+	0.730350i	$0.739357\pi$
$908$	0.0220083	+	0.0381195i	0.000730370	+	0.00126504i
$909$	−16.9327			−0.561622
$910$	−2.08362	+	6.13551i	−0.0690712	+	0.203390i
$911$	27.8447			0.922537			0.461268	−	0.887261i	$-0.347394\pi$
$911$	27.8447			0.922537			0.461268	+	0.887261i	$0.347394\pi$
$912$	33.6802	+	58.3359i	1.11526	+	1.93169i
$913$	1.89759	+	3.28671i	0.0628009	+	0.108774i
$914$	−0.472982	+	0.819229i	−0.0156449	+	0.0270977i
$915$	52.3134			1.72943
$916$	−20.6530	+	35.7720i	−0.682394	+	1.18194i
$917$	−1.91267	+	3.31284i	−0.0631618	+	0.109400i
$918$	0.546981			0.0180531
$919$	−23.4408	+	40.6007i	−0.773241	+	1.33929i	0.162537	+	0.986702i	$0.448032\pi$
$919$	−23.4408	+	40.6007i	−0.773241	+	1.33929i	−0.935778	+	0.352590i	$0.885301\pi$
$920$	−8.39214	−	14.5356i	−0.276681	−	0.479225i
$921$	−12.0293	−	20.8354i	−0.396380	−	0.686551i
$922$	−3.79642			−0.125028
$923$	8.41589	+	9.59901i	0.277013	+	0.315955i
$924$	10.8096			0.355610
$925$	14.0026	+	24.2532i	0.460403	+	0.797441i
$926$	−1.18055	−	2.04478i	−0.0387954	−	0.0671955i
$927$	18.5504	−	32.1303i	0.609276	−	1.05530i
$928$	−14.4328			−0.473779
$929$	1.73354	−	3.00258i	0.0568756	−	0.0985114i	−0.836186	−	0.548446i	$-0.815220\pi$
$929$	1.73354	−	3.00258i	0.0568756	−	0.0985114i	0.893061	+	0.449935i	$0.148553\pi$
$930$	2.09563	−	3.62974i	0.0687184	−	0.119024i
$931$	10.5312			0.345147
$932$	26.0925	−	45.1935i	0.854687	−	1.48036i
$933$	9.93047	+	17.2001i	0.325109	+	0.563105i
$934$	−0.688391	−	1.19233i	−0.0225249	−	0.0390142i
$935$	−5.15636			−0.168631
$936$	−6.33491	−	7.22547i	−0.207063	−	0.236172i
$937$	13.4020			0.437825			0.218913	−	0.975744i	$-0.429749\pi$
$937$	13.4020			0.437825			0.218913	+	0.975744i	$0.429749\pi$
$938$	0.212206	+	0.367551i	0.00692877	+	0.0120010i
$939$	−24.6091	−	42.6243i	−0.803089	−	1.39099i
$940$	25.1444	−	43.5513i	0.820119	−	1.42049i
$941$	−11.9245			−0.388728			−0.194364	−	0.980930i	$-0.562264\pi$
$941$	−11.9245			−0.388728			−0.194364	+	0.980930i	$0.562264\pi$
$942$	−2.29607	+	3.97691i	−0.0748100	+	0.129575i
$943$	9.98640	−	17.2970i	0.325202	−	0.563266i
$944$	−31.1771			−1.01473
$945$	−3.71539	+	6.43525i	−0.120862	+	0.209339i
$946$	−0.190478	−	0.329918i	−0.00619298	−	0.0107266i
$947$	21.0637	+	36.4833i	0.684477	+	1.18555i	0.973601	+	0.228257i	$0.0733027\pi$
$947$	21.0637	+	36.4833i	0.684477	+	1.18555i	−0.289124	+	0.957292i	$0.593364\pi$
$948$	−43.6882			−1.41893
$949$	−3.25991	+	9.59928i	−0.105821	+	0.311606i
$950$	−6.20703			−0.201383
$951$	−27.1341	−	46.9976i	−0.879883	−	1.52400i
$952$	−2.30838	−	3.99823i	−0.0748149	−	0.129583i
$953$	−12.1110	+	20.9769i	−0.392314	+	0.679508i	−0.992754	−	0.120161i	$-0.961659\pi$
$953$	−12.1110	+	20.9769i	−0.392314	+	0.679508i	0.600440	+	0.799670i	$0.294992\pi$
$954$	7.70391			0.249423
$955$	−4.45086	+	7.70912i	−0.144027	+	0.249461i
$956$	28.0544	−	48.5916i	0.907343	−	1.57156i
$957$	11.0625			0.357600
$958$	3.20436	−	5.55011i	0.103528	−	0.179316i
$959$	2.31052	+	4.00194i	0.0746106	+	0.129229i
$960$	−20.8704	−	36.1485i	−0.673588	−	1.16669i
$961$	−25.4048			−0.819510
$962$	−6.19468	−	7.06554i	−0.199725	−	0.227802i
$963$	43.6864			1.40777
$964$	11.3800	+	19.7107i	0.366524	+	0.634838i
$965$	33.8001	+	58.5435i	1.08806	+	1.88458i
$966$	−4.26618	+	7.38925i	−0.137262	+	0.237745i
$967$	−30.0551			−0.966506			−0.483253	−	0.875481i	$-0.660545\pi$
$967$	−30.0551			−0.966506			−0.483253	+	0.875481i	$0.660545\pi$
$968$	0.527125	−	0.913007i	0.0169424	−	0.0293452i
$969$	−17.3106	+	29.9828i	−0.556096	+	0.963186i
$970$	1.15328			0.0370295
$971$	−12.1208	+	20.9939i	−0.388976	+	0.673726i	−0.992312	−	0.123761i	$-0.960504\pi$
$971$	−12.1208	+	20.9939i	−0.388976	+	0.673726i	0.603336	+	0.797487i	$0.293838\pi$
$972$	−19.8934	−	34.4564i	−0.638081	−	1.10519i
$973$	14.6533	+	25.3802i	0.469762	+	0.813652i
$974$	−3.57659			−0.114601
$975$	−23.9804	+	4.76676i	−0.767988	+	0.152658i
$976$	−28.3127			−0.906268
$977$	16.5682	+	28.6970i	0.530064	+	0.918098i	0.999385	+	0.0350703i	$0.0111655\pi$
$977$	16.5682	+	28.6970i	0.530064	+	0.918098i	−0.469321	+	0.883028i	$0.655501\pi$
$978$	−4.86023	−	8.41817i	−0.155413	−	0.269183i
$979$	1.53569	−	2.65989i	0.0490808	−	0.0850105i
$980$	−7.10990			−0.227117
$981$	11.0685	−	19.1711i	0.353388	−	0.612087i
$982$	−0.534710	+	0.926146i	−0.0170633	+	0.0295545i
$983$	13.2214			0.421696			0.210848	−	0.977519i	$-0.432378\pi$
$983$	13.2214			0.421696			0.210848	+	0.977519i	$0.432378\pi$
$984$	−4.36570	+	7.56161i	−0.139173	+	0.241055i
$985$	3.66483	+	6.34768i	0.116771	+	0.202254i
$986$	−1.15953	−	2.00836i	−0.0369269	−	0.0639592i
$987$	−52.0842			−1.65786
$988$	−54.6698	+	10.8671i	−1.73928	+	0.345729i
$989$	−8.04788			−0.255908
$990$	−0.952575	−	1.64991i	−0.0302748	−	0.0524375i
$991$	−3.22583	−	5.58730i	−0.102472	−	0.177487i	0.810231	−	0.586111i	$-0.199342\pi$
$991$	−3.22583	−	5.58730i	−0.102472	−	0.177487i	−0.912703	+	0.408625i	$0.866009\pi$
$992$	−3.62792	+	6.28374i	−0.115187	+	0.199509i
$993$	7.76507			0.246417
$994$	−1.13306	+	1.96252i	−0.0359385	+	0.0622473i
$995$	23.9412	−	41.4674i	0.758988	−	1.31461i
$996$	−17.2034			−0.545110
$997$	3.43607	−	5.95146i	0.108822	−	0.188485i	−0.806472	−	0.591273i	$-0.798626\pi$
$997$	3.43607	−	5.95146i	0.108822	−	0.188485i	0.915293	+	0.402788i	$0.131959\pi$
$998$	−0.461945	−	0.800113i	−0.0146226	−	0.0253271i
$999$	−5.38794	−	9.33219i	−0.170467	−	0.295257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.e.c.133.3	yes	12
13.3	even	3		1859.2.a.k.1.4		6
13.9	even	3	inner	143.2.e.c.100.3	✓	12
13.10	even	6		1859.2.a.l.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.c.100.3	✓	12	13.9	even	3	inner
143.2.e.c.133.3	yes	12	1.1	even	1	trivial
1859.2.a.k.1.4		6	13.3	even	3
1859.2.a.l.1.3		6	13.10	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.134198 - 0.232438i) q^{2} +(-1.17558 - 2.03617i) q^{3} +(0.963982 - 1.66967i) q^{4} -2.80787 q^{5} +(-0.315522 + 0.546500i) q^{6} +(-1.19233 + 2.06518i) q^{7} -1.05425 q^{8} +(-1.26400 + 2.18931i) q^{9} +O(q^{10})\)	\(q+(-0.134198 - 0.232438i) q^{2} +(-1.17558 - 2.03617i) q^{3} +(0.963982 - 1.66967i) q^{4} -2.80787 q^{5} +(-0.315522 + 0.546500i) q^{6} +(-1.19233 + 2.06518i) q^{7} -1.05425 q^{8} +(-1.26400 + 2.18931i) q^{9} +(0.376811 + 0.652655i) q^{10} +(0.500000 + 0.866025i) q^{11} -4.53297 q^{12} +(1.15941 - 3.41405i) q^{13} +0.640034 q^{14} +(3.30089 + 5.71731i) q^{15} +(-1.78649 - 3.09428i) q^{16} +(0.918197 - 1.59036i) q^{17} +0.678504 q^{18} +(4.00924 - 6.94420i) q^{19} +(-2.70674 + 4.68820i) q^{20} +5.60675 q^{21} +(0.134198 - 0.232438i) q^{22} +(-2.83500 - 4.91036i) q^{23} +(1.23936 + 2.14663i) q^{24} +2.88414 q^{25} +(-0.949146 + 0.188668i) q^{26} -1.10976 q^{27} +(2.29877 + 3.98159i) q^{28} +(2.35255 + 4.07474i) q^{29} +(0.885945 - 1.53450i) q^{30} +2.36542 q^{31} +(-1.53373 + 2.65651i) q^{32} +(1.17558 - 2.03617i) q^{33} -0.492881 q^{34} +(3.34792 - 5.79876i) q^{35} +(2.43694 + 4.22091i) q^{36} +(4.85504 + 8.40917i) q^{37} -2.15213 q^{38} +(-8.31459 + 1.65275i) q^{39} +2.96020 q^{40} +(1.76127 + 3.05061i) q^{41} +(-0.752415 - 1.30322i) q^{42} +(0.709691 - 1.22922i) q^{43} +1.92796 q^{44} +(3.54914 - 6.14729i) q^{45} +(-0.760901 + 1.31792i) q^{46} -9.28956 q^{47} +(-4.20033 + 7.27518i) q^{48} +(0.656686 + 1.13741i) q^{49} +(-0.387045 - 0.670382i) q^{50} -4.31767 q^{51} +(-4.58268 - 5.22691i) q^{52} +11.3543 q^{53} +(0.148928 + 0.257951i) q^{54} +(-1.40394 - 2.43169i) q^{55} +(1.25702 - 2.17722i) q^{56} -18.8528 q^{57} +(0.631416 - 1.09364i) q^{58} +(4.36291 - 7.55678i) q^{59} +12.7280 q^{60} +(3.96207 - 6.86251i) q^{61} +(-0.317434 - 0.549812i) q^{62} +(-3.01421 - 5.22077i) q^{63} -6.32265 q^{64} +(-3.25548 + 9.58622i) q^{65} -0.631044 q^{66} +(0.331554 + 0.574268i) q^{67} +(-1.77025 - 3.06616i) q^{68} +(-6.66555 + 11.5451i) q^{69} -1.79713 q^{70} +(-1.77031 + 3.06627i) q^{71} +(1.33257 - 2.30808i) q^{72} -2.81169 q^{73} +(1.30307 - 2.25699i) q^{74} +(-3.39055 - 5.87260i) q^{75} +(-7.72967 - 13.3882i) q^{76} -2.38467 q^{77} +(1.49996 + 1.71083i) q^{78} +9.63788 q^{79} +(5.01622 + 8.68835i) q^{80} +(5.09661 + 8.82759i) q^{81} +(0.472718 - 0.818772i) q^{82} +3.79517 q^{83} +(5.40481 - 9.36140i) q^{84} +(-2.57818 + 4.46554i) q^{85} -0.380956 q^{86} +(5.53125 - 9.58040i) q^{87} +(-0.527125 - 0.913007i) q^{88} +(-1.53569 - 2.65989i) q^{89} -1.90515 q^{90} +(5.66824 + 6.46508i) q^{91} -10.9315 q^{92} +(-2.78075 - 4.81639i) q^{93} +(1.24664 + 2.15924i) q^{94} +(-11.2574 + 19.4984i) q^{95} +7.21214 q^{96} +(0.765158 - 1.32529i) q^{97} +(0.176252 - 0.305277i) q^{98} -2.52800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - 34 q^{12} - 4 q^{13} + 24 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{17} + 12 q^{18} + 10 q^{19} + 15 q^{20} - 24 q^{21} - 3 q^{23} + 14 q^{24} - 12 q^{25} - 3 q^{26} + 20 q^{27} + 16 q^{28} - 3 q^{29} - 19 q^{30} - 10 q^{31} - q^{32} + q^{33} + 10 q^{34} + 13 q^{35} - 20 q^{36} + 25 q^{37} - 54 q^{38} - 12 q^{39} - 16 q^{40} + 24 q^{41} - 13 q^{42} + 8 q^{43} - 16 q^{44} + 27 q^{45} + 18 q^{46} - 20 q^{47} + 28 q^{48} + q^{49} - 26 q^{50} - 34 q^{51} - 39 q^{52} + 20 q^{53} + 47 q^{54} - 6 q^{55} - 15 q^{56} + 6 q^{58} - 4 q^{59} + 122 q^{60} + 21 q^{61} + 5 q^{62} + 6 q^{63} - 54 q^{64} - 32 q^{65} + 24 q^{66} + 21 q^{67} - 14 q^{68} - 5 q^{69} - 62 q^{70} - 3 q^{71} - 50 q^{72} - 26 q^{73} + 38 q^{74} + 23 q^{75} + 8 q^{76} + 6 q^{77} + 36 q^{78} - 8 q^{79} + 44 q^{80} - 34 q^{81} + 33 q^{82} - 16 q^{83} + 47 q^{84} - 13 q^{85} + 22 q^{86} + 51 q^{87} + 3 q^{88} - 9 q^{89} - 140 q^{90} - 19 q^{91} + 30 q^{92} - 21 q^{93} - 10 q^{94} - 27 q^{95} + 38 q^{96} + 15 q^{97} + 21 q^{98} - 14 q^{99}+O(q^{100}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - 34 * q^12 - 4 * q^13 + 24 * q^14 - 4 * q^15 - 8 * q^16 - 2 * q^17 + 12 * q^18 + 10 * q^19 + 15 * q^20 - 24 * q^21 - 3 * q^23 + 14 * q^24 - 12 * q^25 - 3 * q^26 + 20 * q^27 + 16 * q^28 - 3 * q^29 - 19 * q^30 - 10 * q^31 - q^32 + q^33 + 10 * q^34 + 13 * q^35 - 20 * q^36 + 25 * q^37 - 54 * q^38 - 12 * q^39 - 16 * q^40 + 24 * q^41 - 13 * q^42 + 8 * q^43 - 16 * q^44 + 27 * q^45 + 18 * q^46 - 20 * q^47 + 28 * q^48 + q^49 - 26 * q^50 - 34 * q^51 - 39 * q^52 + 20 * q^53 + 47 * q^54 - 6 * q^55 - 15 * q^56 + 6 * q^58 - 4 * q^59 + 122 * q^60 + 21 * q^61 + 5 * q^62 + 6 * q^63 - 54 * q^64 - 32 * q^65 + 24 * q^66 + 21 * q^67 - 14 * q^68 - 5 * q^69 - 62 * q^70 - 3 * q^71 - 50 * q^72 - 26 * q^73 + 38 * q^74 + 23 * q^75 + 8 * q^76 + 6 * q^77 + 36 * q^78 - 8 * q^79 + 44 * q^80 - 34 * q^81 + 33 * q^82 - 16 * q^83 + 47 * q^84 - 13 * q^85 + 22 * q^86 + 51 * q^87 + 3 * q^88 - 9 * q^89 - 140 * q^90 - 19 * q^91 + 30 * q^92 - 21 * q^93 - 10 * q^94 - 27 * q^95 + 38 * q^96 + 15 * q^97 + 21 * q^98 - 14 * q^99

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