LMFDB - Embedded newform 143.2.h.c.27.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(14,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.6
Character	$\chi$	$=$	143.27
Dual form			143.2.h.c.53.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.481645 + 1.48235i) q^{2} +(-1.52980 - 1.11146i) q^{3} +(-0.347348 + 0.252363i) q^{4} +(1.25281 - 3.85574i) q^{5} +(0.910760 - 2.80303i) q^{6} +(0.257053 - 0.186760i) q^{7} +(1.98054 + 1.43894i) q^{8} +(0.177882 + 0.547464i) q^{9} +O(q^{10})$	\(q+(0.481645 + 1.48235i) q^{2} +(-1.52980 - 1.11146i) q^{3} +(-0.347348 + 0.252363i) q^{4} +(1.25281 - 3.85574i) q^{5} +(0.910760 - 2.80303i) q^{6} +(0.257053 - 0.186760i) q^{7} +(1.98054 + 1.43894i) q^{8} +(0.177882 + 0.547464i) q^{9} +6.31897 q^{10} +(-2.23215 + 2.45306i) q^{11} +0.811864 q^{12} +(0.309017 + 0.951057i) q^{13} +(0.400652 + 0.291090i) q^{14} +(-6.20206 + 4.50606i) q^{15} +(-1.44445 + 4.44557i) q^{16} +(0.908878 - 2.79724i) q^{17} +(-0.725858 + 0.527367i) q^{18} +(1.91090 + 1.38835i) q^{19} +(0.537887 + 1.65545i) q^{20} -0.600816 q^{21} +(-4.71140 - 2.12733i) q^{22} +5.05215 q^{23} +(-1.43049 - 4.40259i) q^{24} +(-9.25215 - 6.72208i) q^{25} +(-1.26096 + 0.916143i) q^{26} +(-1.41663 + 4.35994i) q^{27} +(-0.0421554 + 0.129741i) q^{28} +(-1.24624 + 0.905446i) q^{29} +(-9.66676 - 7.02331i) q^{30} +(1.76388 + 5.42866i) q^{31} -2.38946 q^{32} +(6.14123 - 1.27173i) q^{33} +4.58424 q^{34} +(-0.398060 - 1.22510i) q^{35} +(-0.199946 - 0.145270i) q^{36} +(-4.17075 + 3.03023i) q^{37} +(-1.13765 + 3.50132i) q^{38} +(0.584331 - 1.79839i) q^{39} +(8.02943 - 5.83372i) q^{40} +(5.15952 + 3.74861i) q^{41} +(-0.289380 - 0.890620i) q^{42} -4.12956 q^{43} +(0.156273 - 1.41538i) q^{44} +2.33373 q^{45} +(2.43334 + 7.48906i) q^{46} +(-6.86743 - 4.98948i) q^{47} +(7.15082 - 5.19538i) q^{48} +(-2.13192 + 6.56138i) q^{49} +(5.50823 - 16.9526i) q^{50} +(-4.49943 + 3.26903i) q^{51} +(-0.347348 - 0.252363i) q^{52} +(-1.91824 - 5.90374i) q^{53} -7.14527 q^{54} +(6.66190 + 11.6798i) q^{55} +0.777839 q^{56} +(-1.38019 - 4.24779i) q^{57} +(-1.94243 - 1.41126i) q^{58} +(9.82758 - 7.14016i) q^{59} +(1.01711 - 3.13034i) q^{60} +(-3.77392 + 11.6149i) q^{61} +(-7.19762 + 5.22938i) q^{62} +(0.147969 + 0.107506i) q^{63} +(1.73804 + 5.34914i) q^{64} +4.05417 q^{65} +(4.84304 + 8.49094i) q^{66} -5.94398 q^{67} +(0.390222 + 1.20098i) q^{68} +(-7.72878 - 5.61529i) q^{69} +(1.62431 - 1.18013i) q^{70} +(0.0667988 - 0.205585i) q^{71} +(-0.435469 + 1.34023i) q^{72} +(12.0659 - 8.76640i) q^{73} +(-6.50068 - 4.72302i) q^{74} +(6.68258 + 20.5669i) q^{75} -1.01411 q^{76} +(-0.115649 + 1.04744i) q^{77} +2.94728 q^{78} +(3.67720 + 11.3172i) q^{79} +(15.3314 + 11.1389i) q^{80} +(8.41018 - 6.11035i) q^{81} +(-3.07170 + 9.45372i) q^{82} +(0.966175 - 2.97358i) q^{83} +(0.208692 - 0.151624i) q^{84} +(-9.64678 - 7.00880i) q^{85} +(-1.98898 - 6.12146i) q^{86} +2.91287 q^{87} +(-7.95068 + 1.64643i) q^{88} +2.04425 q^{89} +(1.12403 + 3.45941i) q^{90} +(0.257053 + 0.186760i) q^{91} +(-1.75485 + 1.27498i) q^{92} +(3.33538 - 10.2653i) q^{93} +(4.08849 - 12.5831i) q^{94} +(7.74711 - 5.62861i) q^{95} +(3.65539 + 2.65580i) q^{96} +(-4.08269 - 12.5652i) q^{97} -10.7531 q^{98} +(-1.74002 - 0.785669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.481645	+	1.48235i	0.340574	+	1.04818i	0.963911	+	0.266226i	$0.0857768\pi$
$2$	0.481645	+	1.48235i	0.340574	+	1.04818i	−0.623336	+	0.781954i	$0.714223\pi$
$3$	−1.52980	−	1.11146i	−0.883230	−	0.641704i	0.0508741	−	0.998705i	$-0.483799\pi$
$3$	−1.52980	−	1.11146i	−0.883230	−	0.641704i	−0.934104	+	0.357001i	$0.883799\pi$
$4$	−0.347348	+	0.252363i	−0.173674	+	0.126181i
$5$	1.25281	−	3.85574i	0.560272	−	1.72434i	−0.121324	−	0.992613i	$-0.538714\pi$
$5$	1.25281	−	3.85574i	0.560272	−	1.72434i	0.681597	−	0.731728i	$-0.261286\pi$
$6$	0.910760	−	2.80303i	0.371816	−	1.14433i
$7$	0.257053	−	0.186760i	0.0971568	−	0.0705885i	−0.538146	−	0.842851i	$-0.680875\pi$
$7$	0.257053	−	0.186760i	0.0971568	−	0.0705885i	0.635303	+	0.772263i	$0.280875\pi$
$8$	1.98054	+	1.43894i	0.700226	+	0.508744i
$9$	0.177882	+	0.547464i	0.0592940	+	0.182488i
$10$	6.31897			1.99823
$11$	−2.23215	+	2.45306i	−0.673020	+	0.739625i
$11$	−2.23215	+	2.45306i	−0.673020	+	0.739625i
$12$	0.811864			0.234365
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	0.400652	+	0.291090i	0.107079	+	0.0777972i
$15$	−6.20206	+	4.50606i	−1.60137	+	1.16346i
$16$	−1.44445	+	4.44557i	−0.361114	+	1.11139i
$17$	0.908878	−	2.79724i	0.220435	−	0.678430i	−0.778288	−	0.627908i	$-0.783911\pi$
$17$	0.908878	−	2.79724i	0.220435	−	0.678430i	0.998723	−	0.0505221i	$-0.0160885\pi$
$18$	−0.725858	+	0.527367i	−0.171086	+	0.124301i
$19$	1.91090	+	1.38835i	0.438391	+	0.318509i	0.784995	−	0.619502i	$-0.212665\pi$
$19$	1.91090	+	1.38835i	0.438391	+	0.318509i	−0.346605	+	0.938011i	$0.612665\pi$
$20$	0.537887	+	1.65545i	0.120275	+	0.370169i
$21$	−0.600816			−0.131109
$22$	−4.71140	−	2.12733i	−1.00447	−	0.453549i
$23$	5.05215			1.05345			0.526723	−	0.850037i	$-0.323420\pi$
$23$	5.05215			1.05345			0.526723	+	0.850037i	$0.323420\pi$
$24$	−1.43049	−	4.40259i	−0.291997	−	0.898675i
$25$	−9.25215	−	6.72208i	−1.85043	−	1.34442i
$26$	−1.26096	+	0.916143i	−0.247295	+	0.179670i
$27$	−1.41663	+	4.35994i	−0.272631	+	0.839071i
$28$	−0.0421554	+	0.129741i	−0.00796663	+	0.0245188i
$29$	−1.24624	+	0.905446i	−0.231421	+	0.168137i	−0.697453	−	0.716631i	$-0.745683\pi$
$29$	−1.24624	+	0.905446i	−0.231421	+	0.168137i	0.466032	+	0.884768i	$0.345683\pi$
$30$	−9.66676	−	7.02331i	−1.76490	−	1.28228i
$31$	1.76388	+	5.42866i	0.316802	+	0.975017i	0.975006	+	0.222177i	$0.0713163\pi$
$31$	1.76388	+	5.42866i	0.316802	+	0.975017i	−0.658204	+	0.752839i	$0.728684\pi$
$32$	−2.38946			−0.422400
$33$	6.14123	−	1.27173i	1.06905	−	0.221379i
$34$	4.58424			0.786191
$35$	−0.398060	−	1.22510i	−0.0672845	−	0.207080i
$36$	−0.199946	−	0.145270i	−0.0333244	−	0.0242116i
$37$	−4.17075	+	3.03023i	−0.685668	+	0.498167i	−0.875233	−	0.483701i	$-0.839292\pi$
$37$	−4.17075	+	3.03023i	−0.685668	+	0.498167i	0.189566	+	0.981868i	$0.439292\pi$
$38$	−1.13765	+	3.50132i	−0.184551	+	0.567988i
$39$	0.584331	−	1.79839i	0.0935679	−	0.287972i
$40$	8.02943	−	5.83372i	1.26956	−	0.922393i
$41$	5.15952	+	3.74861i	0.805782	+	0.585435i	0.912605	−	0.408843i	$-0.134068\pi$
$41$	5.15952	+	3.74861i	0.805782	+	0.585435i	−0.106822	+	0.994278i	$0.534068\pi$
$42$	−0.289380	−	0.890620i	−0.0446523	−	0.137426i
$43$	−4.12956			−0.629753			−0.314876	−	0.949133i	$-0.601963\pi$
$43$	−4.12956			−0.629753			−0.314876	+	0.949133i	$0.601963\pi$
$44$	0.156273	−	1.41538i	0.0235590	−	0.213376i
$45$	2.33373			0.347892
$46$	2.43334	+	7.48906i	0.358777	+	1.10420i
$47$	−6.86743	−	4.98948i	−1.00172	−	0.727790i	−0.0392613	−	0.999229i	$-0.512500\pi$
$47$	−6.86743	−	4.98948i	−1.00172	−	0.727790i	−0.962456	+	0.271439i	$0.912500\pi$
$48$	7.15082	−	5.19538i	1.03213	−	0.749888i
$49$	−2.13192	+	6.56138i	−0.304560	+	0.937340i
$50$	5.50823	−	16.9526i	0.778981	−	2.39746i
$51$	−4.49943	+	3.26903i	−0.630046	+	0.457755i
$52$	−0.347348	−	0.252363i	−0.0481685	−	0.0349964i
$53$	−1.91824	−	5.90374i	−0.263491	−	0.810941i	−0.992037	−	0.125945i	$-0.959804\pi$
$53$	−1.91824	−	5.90374i	−0.263491	−	0.810941i	0.728547	−	0.684996i	$-0.240196\pi$
$54$	−7.14527			−0.972349
$55$	6.66190	+	11.6798i	0.898291	+	1.57491i
$56$	0.777839			0.103943
$57$	−1.38019	−	4.24779i	−0.182811	−	0.562634i
$58$	−1.94243	−	1.41126i	−0.255054	−	0.185308i
$59$	9.82758	−	7.14016i	1.27944	−	0.929569i	0.279906	−	0.960027i	$-0.409697\pi$
$59$	9.82758	−	7.14016i	1.27944	−	0.929569i	0.999536	+	0.0304579i	$0.00969656\pi$
$60$	1.01711	−	3.13034i	0.131308	−	0.404125i
$61$	−3.77392	+	11.6149i	−0.483201	+	1.48714i	0.351367	+	0.936238i	$0.385717\pi$
$61$	−3.77392	+	11.6149i	−0.483201	+	1.48714i	−0.834569	+	0.550904i	$0.814283\pi$
$62$	−7.19762	+	5.22938i	−0.914098	+	0.664131i
$63$	0.147969	+	0.107506i	0.0186424	+	0.0135445i
$64$	1.73804	+	5.34914i	0.217255	+	0.668642i
$65$	4.05417			0.502858
$66$	4.84304	+	8.49094i	0.596137	+	1.04516i
$67$	−5.94398			−0.726172			−0.363086	−	0.931756i	$-0.618277\pi$
$67$	−5.94398			−0.726172			−0.363086	+	0.931756i	$0.618277\pi$
$68$	0.390222	+	1.20098i	0.0473214	+	0.145640i
$69$	−7.72878	−	5.61529i	−0.930436	−	0.676001i
$70$	1.62431	−	1.18013i	0.194142	−	0.141052i
$71$	0.0667988	−	0.205585i	0.00792755	−	0.0243985i	−0.947014	−	0.321191i	$-0.895917\pi$
$71$	0.0667988	−	0.205585i	0.00792755	−	0.0243985i	0.954942	+	0.296792i	$0.0959169\pi$
$72$	−0.435469	+	1.34023i	−0.0513205	+	0.157948i
$73$	12.0659	−	8.76640i	1.41221	−	1.02603i	0.419212	−	0.907888i	$-0.362306\pi$
$73$	12.0659	−	8.76640i	1.41221	−	1.02603i	0.992997	−	0.118141i	$-0.0376935\pi$
$74$	−6.50068	−	4.72302i	−0.755689	−	0.549040i
$75$	6.68258	+	20.5669i	0.771638	+	2.37486i
$76$	−1.01411			−0.116327
$77$	−0.115649	+	1.04744i	−0.0131794	+	0.119367i
$78$	2.94728			0.333714
$79$	3.67720	+	11.3172i	0.413717	+	1.27329i	0.913394	+	0.407078i	$0.133452\pi$
$79$	3.67720	+	11.3172i	0.413717	+	1.27329i	−0.499677	+	0.866212i	$0.666548\pi$
$80$	15.3314	+	11.1389i	1.71410	+	1.24537i
$81$	8.41018	−	6.11035i	0.934464	−	0.678928i
$82$	−3.07170	+	9.45372i	−0.339213	+	1.04399i
$83$	0.966175	−	2.97358i	0.106052	−	0.326393i	−0.883924	−	0.467630i	$-0.845108\pi$
$83$	0.966175	−	2.97358i	0.106052	−	0.326393i	0.989976	+	0.141237i	$0.0451080\pi$
$84$	0.208692	−	0.151624i	0.0227702	−	0.0165435i
$85$	−9.64678	−	7.00880i	−1.04634	−	0.760211i
$86$	−1.98898	−	6.12146i	−0.214478	−	0.660094i
$87$	2.91287			0.312292
$88$	−7.95068	+	1.64643i	−0.847545	+	0.175510i
$89$	2.04425			0.216690			0.108345	−	0.994113i	$-0.465445\pi$
$89$	2.04425			0.216690			0.108345	+	0.994113i	$0.465445\pi$
$90$	1.12403	+	3.45941i	0.118483	+	0.364654i
$91$	0.257053	+	0.186760i	0.0269464	+	0.0195777i
$92$	−1.75485	+	1.27498i	−0.182956	+	0.132925i
$93$	3.33538	−	10.2653i	0.345863	−	1.06446i
$94$	4.08849	−	12.5831i	0.421696	−	1.29785i
$95$	7.74711	−	5.62861i	0.794837	−	0.577483i
$96$	3.65539	+	2.65580i	0.373077	+	0.271056i
$97$	−4.08269	−	12.5652i	−0.414534	−	1.27581i	−0.912667	−	0.408704i	$-0.865981\pi$
$97$	−4.08269	−	12.5652i	−0.414534	−	1.27581i	0.498133	−	0.867101i	$-0.334019\pi$
$98$	−10.7531			−1.08623
$99$	−1.74002	−	0.785669i	−0.174879	−	0.0789627i
$100$	4.91012			0.491012
$101$	−3.99465	−	12.2943i	−0.397483	−	1.22333i	−0.927011	−	0.375034i	$-0.877631\pi$
$101$	−3.99465	−	12.2943i	−0.397483	−	1.22333i	0.529528	−	0.848292i	$-0.322369\pi$
$102$	−7.01297	−	5.09522i	−0.694388	−	0.504502i
$103$	0.655749	−	0.476429i	0.0646128	−	0.0469440i	−0.555010	−	0.831844i	$-0.687286\pi$
$103$	0.655749	−	0.476429i	0.0646128	−	0.0469440i	0.619623	+	0.784900i	$0.287286\pi$
$104$	−0.756498	+	2.32826i	−0.0741807	+	0.228305i
$105$	−0.752706	+	2.31659i	−0.0734566	+	0.226076i
$106$	7.82750	−	5.68701i	0.760274	−	0.552371i
$107$	−5.77033	−	4.19239i	−0.557839	−	0.405293i	0.272829	−	0.962063i	$-0.412041\pi$
$107$	−5.77033	−	4.19239i	−0.557839	−	0.405293i	−0.830667	+	0.556769i	$0.812041\pi$
$108$	−0.608224	−	1.87192i	−0.0585264	−	0.180126i
$109$	4.92737			0.471956			0.235978	−	0.971758i	$-0.424171\pi$
$109$	4.92737			0.471956			0.235978	+	0.971758i	$0.424171\pi$
$110$	−14.1049	+	15.5008i	−1.34485	+	1.47794i
$111$	9.74841			0.925278
$112$	0.458953	+	1.41251i	0.0433670	+	0.133470i
$113$	11.0049	+	7.99551i	1.03525	+	0.752154i	0.969353	−	0.245672i	$-0.0790087\pi$
$113$	11.0049	+	7.99551i	1.03525	+	0.752154i	0.0658984	+	0.997826i	$0.479009\pi$
$114$	5.63196	−	4.09186i	0.527481	−	0.383238i
$115$	6.32937	−	19.4798i	0.590217	−	1.81650i
$116$	0.204377	−	0.629009i	0.0189760	−	0.0584020i
$117$	−0.465701	+	0.338351i	−0.0430540	+	0.0312806i
$118$	15.3176	+	11.1289i	1.41010	+	1.02450i
$119$	−0.288782	−	0.888779i	−0.0264726	−	0.0814743i
$120$	−18.7674			−1.71322
$121$	−1.03498	−	10.9512i	−0.0940893	−	0.995564i
$122$	−19.0351			−1.72336
$123$	−3.72659	−	11.4693i	−0.336015	−	1.03415i
$124$	−1.98267	−	1.44050i	−0.178049	−	0.129360i
$125$	−21.1103	+	15.3375i	−1.88816	+	1.37183i
$126$	−0.0880929	+	0.271122i	−0.00784794	+	0.0241535i
$127$	−1.81211	+	5.57711i	−0.160799	+	0.494888i	−0.998702	−	0.0509306i	$-0.983781\pi$
$127$	−1.81211	+	5.57711i	−0.160799	+	0.494888i	0.837903	+	0.545819i	$0.183781\pi$
$128$	−10.9584	+	7.96174i	−0.968595	+	0.703725i
$129$	6.31740	+	4.58986i	0.556216	+	0.404115i
$130$	1.95267	+	6.00970i	0.171260	+	0.527086i
$131$	−19.1307			−1.67145			−0.835727	−	0.549145i	$-0.814954\pi$
$131$	−19.1307			−1.67145			−0.835727	+	0.549145i	$0.814954\pi$
$132$	−1.81221	+	1.99155i	−0.157732	+	0.173342i
$133$	0.750490			0.0650757
$134$	−2.86289	−	8.81106i	−0.247316	−	0.761160i
$135$	15.0360	+	10.9243i	1.29410	+	0.940217i
$136$	5.82514	−	4.23221i	0.499501	−	0.362909i
$137$	−1.56836	+	4.82693i	−0.133994	+	0.412392i	−0.995432	−	0.0954707i	$-0.969564\pi$
$137$	−1.56836	+	4.82693i	−0.133994	+	0.412392i	0.861438	+	0.507863i	$0.169564\pi$
$138$	4.60130	−	14.1613i	0.391688	−	1.20549i
$139$	−13.8721	+	10.0787i	−1.17662	+	0.854864i	−0.991786	−	0.127906i	$-0.959174\pi$
$139$	−13.8721	+	10.0787i	−1.17662	+	0.854864i	−0.184833	+	0.982770i	$0.559174\pi$
$140$	0.447436	+	0.325081i	0.0378152	+	0.0274744i
$141$	4.96016	+	15.2658i	0.417721	+	1.28561i
$142$	0.336923			0.0282739
$143$	−3.02277	−	1.36487i	−0.252777	−	0.114136i
$144$	−2.69073			−0.224228
$145$	1.92987	+	5.93953i	0.160267	+	0.493251i
$146$	18.8064	+	13.6636i	1.55643	+	1.13081i
$147$	10.5542	−	7.66804i	0.870492	−	0.632449i
$148$	0.683984	−	2.10509i	0.0562231	−	0.173037i
$149$	−1.94833	+	5.99635i	−0.159614	+	0.491240i	−0.998599	−	0.0529136i	$-0.983149\pi$
$149$	−1.94833	+	5.99635i	−0.159614	+	0.491240i	0.838985	+	0.544154i	$0.183149\pi$
$150$	−27.2687	+	19.8119i	−2.22648	+	1.61763i
$151$	−14.9894	−	10.8905i	−1.21982	−	0.886253i	−0.223737	−	0.974650i	$-0.571826\pi$
$151$	−14.9894	−	10.8905i	−1.21982	−	0.886253i	−0.996085	+	0.0883971i	$0.971826\pi$
$152$	1.78685	+	5.49936i	0.144933	+	0.446057i
$153$	1.69306			0.136876
$154$	−1.60838	+	0.333063i	−0.129607	+	0.0268390i
$155$	23.1413			1.85876
$156$	0.250880	+	0.772129i	0.0200865	+	0.0618198i
$157$	−10.3883	−	7.54754i	−0.829077	−	0.602360i	0.0902212	−	0.995922i	$-0.471243\pi$
$157$	−10.3883	−	7.54754i	−0.829077	−	0.602360i	−0.919298	+	0.393562i	$0.871243\pi$
$158$	−15.0050	+	10.9018i	−1.19374	+	0.867300i
$159$	−3.62727	+	11.1636i	−0.287661	+	0.885330i
$160$	−2.99353	+	9.21313i	−0.236659	+	0.728362i
$161$	1.29867	−	0.943539i	0.102349	−	0.0743613i
$162$	13.1084	+	9.52382i	1.02989	+	0.748262i
$163$	−2.04203	−	6.28474i	−0.159944	−	0.492259i	0.838684	−	0.544619i	$-0.183326\pi$
$163$	−2.04203	−	6.28474i	−0.159944	−	0.492259i	−0.998628	+	0.0523602i	$0.983326\pi$
$164$	−2.73816			−0.213814
$165$	2.79033	−	25.2722i	0.217227	−	1.96744i
$166$	4.87324			0.378237
$167$	−0.549944	−	1.69255i	−0.0425559	−	0.130974i	0.927521	−	0.373770i	$-0.121935\pi$
$167$	−0.549944	−	1.69255i	−0.0425559	−	0.130974i	−0.970077	+	0.242797i	$0.921935\pi$
$168$	−1.18994	−	0.864541i	−0.0918057	−	0.0667008i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	5.74317	−	17.6757i	0.440481	−	1.35566i
$171$	−0.420157	+	1.29311i	−0.0321302	+	0.0988867i
$172$	1.43439	−	1.04215i	0.109372	−	0.0794631i
$173$	−1.22803	−	0.892218i	−0.0933656	−	0.0678341i	0.540123	−	0.841586i	$-0.318378\pi$
$173$	−1.22803	−	0.892218i	−0.0933656	−	0.0678341i	−0.633489	+	0.773752i	$0.718378\pi$
$174$	1.40297	+	4.31789i	0.106359	+	0.327338i
$175$	−3.63370			−0.274682
$176$	−7.68100	−	13.4665i	−0.578978	−	1.01508i
$177$	−22.9703			−1.72655
$178$	0.984600	+	3.03029i	0.0737989	+	0.227130i
$179$	−17.8779	−	12.9891i	−1.33626	−	0.970848i	−0.999573	−	0.0292303i	$-0.990694\pi$
$179$	−17.8779	−	12.9891i	−1.33626	−	0.970848i	−0.336685	−	0.941617i	$-0.609306\pi$
$180$	−0.810617	+	0.588947i	−0.0604198	+	0.0438975i
$181$	2.13013	−	6.55586i	0.158331	−	0.487294i	−0.840152	−	0.542351i	$-0.817534\pi$
$181$	2.13013	−	6.55586i	0.158331	−	0.487294i	0.998483	+	0.0550576i	$0.0175342\pi$
$182$	−0.153035	+	0.470994i	−0.0113437	+	0.0349124i
$183$	18.6829	−	13.5739i	1.38108	−	1.00342i
$184$	10.0060	+	7.26977i	0.737650	+	0.535934i
$185$	6.45864	+	19.8776i	0.474849	+	1.46143i
$186$	16.8232			1.23353
$187$	4.83303	+	8.47339i	0.353426	+	0.619636i
$188$	3.64454			0.265806
$189$	0.450113	+	1.38530i	0.0327409	+	0.100766i
$190$	12.0749	+	8.77295i	0.876007	+	0.636456i
$191$	−0.937118	+	0.680856i	−0.0678075	+	0.0492650i	−0.621173	−	0.783674i	$-0.713343\pi$
$191$	−0.937118	+	0.680856i	−0.0678075	+	0.0492650i	0.553365	+	0.832939i	$0.313343\pi$
$192$	3.28652	−	10.1149i	0.237184	−	0.729978i
$193$	−0.185805	+	0.571850i	−0.0133746	+	0.0411626i	−0.957521	−	0.288363i	$-0.906889\pi$
$193$	−0.185805	+	0.571850i	−0.0133746	+	0.0411626i	0.944147	+	0.329526i	$0.106889\pi$
$194$	16.6597	−	12.1040i	1.19609	−	0.869013i
$195$	−6.20206	−	4.50606i	−0.444139	−	0.322686i
$196$	−0.915331	−	2.81710i	−0.0653808	−	0.201221i
$197$	22.2918			1.58822			0.794112	−	0.607771i	$-0.207936\pi$
$197$	22.2918			1.58822			0.794112	+	0.607771i	$0.207936\pi$
$198$	0.326565	−	2.95773i	0.0232080	−	0.210197i
$199$	−0.0260657			−0.00184775			−0.000923873	−	1.00000i	$-0.500294\pi$
$199$	−0.0260657			−0.00184775			−0.000923873		1.00000i	$0.500294\pi$
$200$	−8.65153	−	26.6267i	−0.611755	−	1.88279i
$201$	9.09309	+	6.60652i	0.641377	+	0.465988i
$202$	16.3004	−	11.8429i	1.14689	−	0.833267i
$203$	−0.151248	+	0.465495i	−0.0106156	+	0.0326713i
$204$	0.737885	−	2.27098i	0.0516623	−	0.159000i
$205$	20.9176	−	15.1975i	1.46095	−	1.06144i
$206$	1.02207	+	0.742580i	0.0712112	+	0.0517380i
$207$	0.898686	+	2.76587i	0.0624630	+	0.192241i
$208$	−4.67435			−0.324108
$209$	−7.67113	+	1.58854i	−0.530623	+	0.109881i
$210$	−3.79654			−0.261986
$211$	3.99818	+	12.3051i	0.275246	+	0.847121i	0.989154	+	0.146881i	$0.0469235\pi$
$211$	3.99818	+	12.3051i	0.275246	+	0.847121i	−0.713908	+	0.700240i	$0.753076\pi$
$212$	2.15618	+	1.56656i	0.148087	+	0.107592i
$213$	−0.330690	+	0.240260i	−0.0226585	+	0.0164623i
$214$	3.43534	−	10.5729i	0.234835	−	0.722748i
$215$	−5.17355	+	15.9225i	−0.352833	+	1.08591i
$216$	−9.07940	+	6.59657i	−0.617775	+	0.448840i
$217$	1.46727	+	1.06603i	0.0996045	+	0.0723669i
$218$	2.37324	+	7.30409i	0.160736	+	0.494695i
$219$	−28.2020			−1.90571
$220$	−5.26155	−	2.37574i	−0.354734	−	0.160172i
$221$	2.94119			0.197846
$222$	4.69527	+	14.4506i	0.315126	+	0.969858i
$223$	−9.53240	−	6.92569i	−0.638337	−	0.463779i	0.220942	−	0.975287i	$-0.429087\pi$
$223$	−9.53240	−	6.92569i	−0.638337	−	0.463779i	−0.859278	+	0.511508i	$0.829087\pi$
$224$	−0.614216	+	0.446254i	−0.0410391	+	0.0298166i
$225$	2.03431	−	6.26095i	0.135621	−	0.417397i
$226$	−6.55171	+	20.1641i	−0.435813	+	1.34129i
$227$	7.57872	−	5.50627i	0.503018	−	0.365464i	−0.307151	−	0.951661i	$-0.599376\pi$
$227$	7.57872	−	5.50627i	0.503018	−	0.365464i	0.810168	+	0.586197i	$0.199376\pi$
$228$	1.55139	+	1.12715i	0.102743	+	0.0746475i
$229$	−0.401156	−	1.23463i	−0.0265091	−	0.0815867i	0.936927	−	0.349526i	$-0.113657\pi$
$229$	−0.401156	−	1.23463i	−0.0265091	−	0.0815867i	−0.963436	+	0.267939i	$0.913657\pi$
$230$	31.9244			2.10503
$231$	1.34111	−	1.47384i	0.0882388	−	0.0969713i
$232$	−3.77111			−0.247586
$233$	0.512762	+	1.57812i	0.0335921	+	0.103386i	0.966447	−	0.256867i	$-0.0826903\pi$
$233$	0.512762	+	1.57812i	0.0335921	+	0.103386i	−0.932855	+	0.360253i	$0.882690\pi$
$234$	−0.725858	−	0.527367i	−0.0474508	−	0.0344750i
$235$	−27.8417	+	20.2282i	−1.81619	+	1.31954i
$236$	−1.61168	+	4.96023i	−0.104911	+	0.322884i
$237$	6.95334	−	21.4002i	0.451668	−	1.39009i
$238$	1.17839	−	0.856152i	0.0763838	−	0.0554961i
$239$	−6.81796	−	4.95353i	−0.441017	−	0.320418i	0.345022	−	0.938595i	$-0.387871\pi$
$239$	−6.81796	−	4.95353i	−0.441017	−	0.320418i	−0.786039	+	0.618177i	$0.787871\pi$
$240$	−11.0734	−	34.0805i	−0.714787	−	2.19989i
$241$	28.0294			1.80553			0.902767	−	0.430129i	$-0.141532\pi$
$241$	28.0294			1.80553			0.902767	+	0.430129i	$0.141532\pi$
$242$	15.7350	−	6.80880i	1.01149	−	0.437686i
$243$	−5.90439			−0.378767
$244$	−1.62032	−	4.98682i	−0.103730	−	0.319249i
$245$	22.6281	+	16.4403i	1.44566	+	1.05033i
$246$	15.2066	−	11.0482i	0.969535	−	0.704408i
$247$	−0.729899	+	2.24640i	−0.0464424	+	0.142935i
$248$	−4.31812	+	13.2898i	−0.274201	+	0.843903i
$249$	−4.78308	+	3.47511i	−0.303116	+	0.220226i
$250$	−32.9033	−	23.9056i	−2.08099	−	1.51193i
$251$	5.55676	+	17.1020i	0.350740	+	1.07947i	0.958439	+	0.285299i	$0.0920928\pi$
$251$	5.55676	+	17.1020i	0.350740	+	1.07947i	−0.607699	+	0.794168i	$0.707907\pi$
$252$	−0.0785273			−0.00494675
$253$	−11.2772	+	12.3932i	−0.708990	+	0.779155i
$254$	−9.14002			−0.573496
$255$	6.96761	+	21.4441i	0.436329	+	1.34288i
$256$	−7.97966	−	5.79756i	−0.498729	−	0.362348i
$257$	7.02928	−	5.10707i	0.438475	−	0.318570i	−0.346554	−	0.938030i	$-0.612648\pi$
$257$	7.02928	−	5.10707i	0.438475	−	0.318570i	0.785029	+	0.619460i	$0.212648\pi$
$258$	−3.76104	+	11.5753i	−0.234152	+	0.720646i
$259$	−0.506179	+	1.55786i	−0.0314524	+	0.0968006i
$260$	−1.40821	+	1.02312i	−0.0873332	+	0.0634513i
$261$	−0.717383	−	0.521209i	−0.0444049	−	0.0322620i
$262$	−9.21419	−	28.3584i	−0.569255	−	1.75199i
$263$	1.03556			0.0638554			0.0319277	−	0.999490i	$-0.489835\pi$
$263$	1.03556			0.0638554			0.0319277	+	0.999490i	$0.489835\pi$
$264$	13.9929	+	6.31819i	0.861202	+	0.388858i
$265$	−25.1665			−1.54597
$266$	0.361470	+	1.11249i	0.0221631	+	0.0682111i
$267$	−3.12728	−	2.27211i	−0.191387	−	0.139051i
$268$	2.06463	−	1.50004i	0.126117	−	0.0916295i
$269$	−3.76903	+	11.5999i	−0.229802	+	0.707258i	0.767966	+	0.640490i	$0.221269\pi$
$269$	−3.76903	+	11.5999i	−0.229802	+	0.707258i	−0.997769	+	0.0667680i	$0.978731\pi$
$270$	−8.95165	+	27.5503i	−0.544780	+	1.67666i
$271$	22.8629	−	16.6108i	1.38882	−	1.00904i	0.392826	−	0.919613i	$-0.371497\pi$
$271$	22.8629	−	16.6108i	1.38882	−	1.00904i	0.995994	−	0.0894240i	$-0.0285026\pi$
$272$	11.1225	+	8.08097i	0.674400	+	0.489981i
$273$	−0.185662	−	0.571410i	−0.0112368	−	0.0345833i
$274$	−7.91059			−0.477896
$275$	37.1419	−	7.69134i	2.23974	−	0.463805i
$276$	4.10166			0.246891
$277$	1.11195	+	3.42223i	0.0668105	+	0.205622i	0.978888	−	0.204395i	$-0.0655228\pi$
$277$	1.11195	+	3.42223i	0.0668105	+	0.205622i	−0.912078	+	0.410017i	$0.865523\pi$
$278$	−21.6216	−	15.7090i	−1.29678	−	0.942164i
$279$	−2.65824	+	1.93132i	−0.159144	+	0.115625i
$280$	0.974483	−	2.99915i	0.0582365	−	0.179233i
$281$	−5.42712	+	16.7030i	−0.323755	+	0.996415i	0.648245	+	0.761432i	$0.275503\pi$
$281$	−5.42712	+	16.7030i	−0.323755	+	0.996415i	−0.971999	+	0.234983i	$0.924497\pi$
$282$	−20.2402	+	14.7054i	−1.20529	+	0.875693i
$283$	−4.36875	−	3.17408i	−0.259695	−	0.188680i	0.450317	−	0.892869i	$-0.351311\pi$
$283$	−4.36875	−	3.17408i	−0.259695	−	0.188680i	−0.710013	+	0.704189i	$0.751311\pi$
$284$	0.0286797	+	0.0882671i	0.00170183	+	0.00523769i
$285$	−18.1075			−1.07260
$286$	0.567311	−	5.13819i	0.0335458	−	0.303827i
$287$	2.02636			0.119612
$288$	−0.425041	−	1.30814i	−0.0250458	−	0.0770830i
$289$	6.75481	+	4.90765i	0.397342	+	0.288686i
$290$	−7.87495	+	5.72149i	−0.462433	+	0.335977i
$291$	−7.72010	+	23.7600i	−0.452560	+	1.39284i
$292$	−1.97875	+	6.08998i	−0.115798	+	0.356389i
$293$	−0.266813	+	0.193851i	−0.0155874	+	0.0113249i	−0.595552	−	0.803317i	$-0.703067\pi$
$293$	−0.266813	+	0.193851i	−0.0155874	+	0.0113249i	0.579964	+	0.814642i	$0.303067\pi$
$294$	16.4501	+	11.9517i	0.959388	+	0.697036i
$295$	−15.2186	−	46.8379i	−0.886058	−	2.72701i
$296$	−12.6207			−0.733561
$297$	−7.53305	−	13.2071i	−0.437112	−	0.766356i
$298$	−9.82710			−0.569269
$299$	1.56120	+	4.80488i	0.0902866	+	0.277874i
$300$	−7.51149	−	5.45742i	−0.433676	−	0.315084i
$301$	−1.06152	+	0.771236i	−0.0611848	+	0.0444533i
$302$	8.92389	−	27.4649i	0.513512	−	1.58043i
$303$	−7.55363	+	23.2477i	−0.433945	+	1.33554i
$304$	−8.93222	+	6.48964i	−0.512298	+	0.372206i
$305$	40.0562	+	29.1026i	2.29361	+	1.66641i
$306$	0.815454	+	2.50971i	0.0466164	+	0.143471i
$307$	9.63977			0.550170			0.275085	−	0.961420i	$-0.411294\pi$
$307$	9.63977			0.550170			0.275085	+	0.961420i	$0.411294\pi$
$308$	−0.224165	−	0.393012i	−0.0127730	−	0.0223939i
$309$	−1.53270			−0.0871921
$310$	11.1459	+	34.3036i	0.633045	+	1.94831i
$311$	−20.8601	−	15.1557i	−1.18287	−	0.859404i	−0.190375	−	0.981711i	$-0.560970\pi$
$311$	−20.8601	−	15.1557i	−1.18287	−	0.859404i	−0.992492	+	0.122308i	$0.960970\pi$
$312$	3.74507	−	2.72095i	0.212023	−	0.154044i
$313$	−3.68421	+	11.3388i	−0.208244	+	0.640908i	0.791321	+	0.611401i	$0.209394\pi$
$313$	−3.68421	+	11.3388i	−0.208244	+	0.640908i	−0.999565	+	0.0295072i	$0.990606\pi$
$314$	6.18463	−	19.0343i	0.349019	−	1.07417i
$315$	0.599892	−	0.435847i	0.0338001	−	0.0245572i
$316$	−4.13332	−	3.00303i	−0.232517	−	0.168934i
$317$	−6.54178	−	20.1335i	−0.367423	−	1.13081i	−0.948450	−	0.316927i	$-0.897349\pi$
$317$	−6.54178	−	20.1335i	−0.367423	−	1.13081i	0.581027	−	0.813884i	$-0.302651\pi$
$318$	−18.2954			−1.02596
$319$	0.560687	−	5.07819i	0.0313924	−	0.284324i
$320$	22.8023			1.27469
$321$	4.16775	+	12.8270i	0.232621	+	0.715935i
$322$	2.02415	+	1.47063i	0.112802	+	0.0819552i
$323$	5.62032	−	4.08340i	0.312723	−	0.227207i
$324$	−1.37923	+	4.24483i	−0.0766239	+	0.235824i
$325$	3.53401	−	10.8766i	0.196031	−	0.603323i
$326$	8.33265	−	6.05402i	0.461503	−	0.335301i
$327$	−7.53788	−	5.47659i	−0.416846	−	0.302856i
$328$	4.82458	+	14.8485i	0.266393	+	0.819873i
$329$	−2.69712			−0.148697
$330$	38.8063	−	8.03601i	2.13622	−	0.442368i
$331$	1.19187			0.0655113			0.0327557	−	0.999463i	$-0.489572\pi$
$331$	1.19187			0.0655113			0.0327557	+	0.999463i	$0.489572\pi$
$332$	0.414823	+	1.27669i	0.0227664	+	0.0700676i
$333$	−2.40084	−	1.74431i	−0.131565	−	0.0955878i
$334$	2.24408	−	1.63042i	0.122791	−	0.0892126i
$335$	−7.44666	+	22.9185i	−0.406854	+	1.25217i
$336$	0.867851	−	2.67097i	0.0473452	−	0.145713i
$337$	−19.0592	+	13.8473i	−1.03822	+	0.754310i	−0.969937	−	0.243356i	$-0.921752\pi$
$337$	−19.0592	+	13.8473i	−1.03822	+	0.754310i	−0.0682814	+	0.997666i	$0.521752\pi$
$338$	−1.26096	−	0.916143i	−0.0685873	−	0.0498316i
$339$	−7.94852	−	24.4630i	−0.431705	−	1.32865i
$340$	5.11955			0.277646
$341$	−17.2541	−	7.79071i	−0.934360	−	0.421891i
$342$	−2.11921			−0.114594
$343$	1.36468	+	4.20006i	0.0736860	+	0.226782i
$344$	−8.17876	−	5.94221i	−0.440969	−	0.320383i
$345$	−31.3338	+	22.7653i	−1.68695	+	1.22564i
$346$	0.731104	−	2.25011i	0.0393044	−	0.120967i
$347$	−2.87260	+	8.84097i	−0.154209	+	0.474608i	−0.998080	−	0.0619390i	$-0.980272\pi$
$347$	−2.87260	+	8.84097i	−0.154209	+	0.474608i	0.843870	+	0.536547i	$0.180272\pi$
$348$	−1.01178	+	0.735099i	−0.0542370	+	0.0394055i
$349$	−25.5903	−	18.5924i	−1.36982	−	0.995230i	−0.997751	−	0.0670228i	$-0.978650\pi$
$349$	−25.5903	−	18.5924i	−1.36982	−	0.995230i	−0.372065	−	0.928207i	$-0.621350\pi$
$350$	−1.75016	−	5.38642i	−0.0935497	−	0.287916i
$351$	−4.58431			−0.244693
$352$	5.33363	−	5.86148i	0.284284	−	0.312418i
$353$	−30.3634			−1.61608			−0.808039	−	0.589129i	$-0.799471\pi$
$353$	−30.3634			−1.61608			−0.808039	+	0.589129i	$0.799471\pi$
$354$	−11.0635	−	34.0500i	−0.588019	−	1.80974i
$355$	−0.708999	−	0.515118i	−0.0376297	−	0.0273396i
$356$	−0.710064	+	0.515892i	−0.0376333	+	0.0273422i
$357$	−0.546068	+	1.68062i	−0.0289010	+	0.0889481i
$358$	10.6435	−	32.7574i	0.562528	−	1.73128i
$359$	2.36848	−	1.72080i	0.125004	−	0.0908204i	−0.523527	−	0.852009i	$-0.675384\pi$
$359$	2.36848	−	1.72080i	0.125004	−	0.0908204i	0.648530	+	0.761189i	$0.275384\pi$
$360$	4.62204	+	3.35811i	0.243603	+	0.176988i
$361$	−4.14730	−	12.7641i	−0.218279	−	0.671793i
$362$	10.7441			0.564695
$363$	−10.5886	+	17.9035i	−0.555755	+	0.939689i
$364$	−0.136418			−0.00715024
$365$	−18.6847	−	57.5057i	−0.978003	−	3.00999i
$366$	29.1199	+	21.1568i	1.52212	+	1.10589i
$367$	−5.92541	+	4.30507i	−0.309304	+	0.224723i	−0.731598	−	0.681736i	$-0.761225\pi$
$367$	−5.92541	+	4.30507i	−0.309304	+	0.224723i	0.422294	+	0.906459i	$0.361225\pi$
$368$	−7.29760	+	22.4597i	−0.380414	+	1.17079i
$369$	−1.13445	+	3.49146i	−0.0590569	+	0.181758i
$370$	−26.3549	+	19.1479i	−1.37012	+	0.995454i
$371$	−1.59567	−	1.15932i	−0.0828431	−	0.0601890i
$372$	1.43203	+	4.40734i	0.0742473	+	0.228510i
$373$	24.3961			1.26318			0.631590	−	0.775302i	$-0.282402\pi$
$373$	24.3961			1.26318			0.631590	+	0.775302i	$0.282402\pi$
$374$	−10.2327	+	11.2454i	−0.529122	+	0.581487i
$375$	49.3417			2.54799
$376$	−6.42161	−	19.7637i	−0.331169	−	1.01923i
$377$	−1.24624	−	0.905446i	−0.0641846	−	0.0466328i
$378$	−1.83671	+	1.33445i	−0.0944703	+	0.0686367i
$379$	0.0669026	−	0.205905i	0.00343655	−	0.0105766i	−0.949324	−	0.314301i	$-0.898230\pi$
$379$	0.0669026	−	0.205905i	0.00343655	−	0.0105766i	0.952760	+	0.303724i	$0.0982300\pi$
$380$	−1.27049	+	3.91017i	−0.0651748	+	0.200587i
$381$	8.97092	−	6.51775i	0.459594	−	0.333915i
$382$	−1.46063	−	1.06121i	−0.0747321	−	0.0542960i
$383$	0.594339	+	1.82919i	0.0303693	+	0.0934670i	0.965092	−	0.261910i	$-0.0843524\pi$
$383$	0.594339	+	1.82919i	0.0303693	+	0.0934670i	−0.934723	+	0.355377i	$0.884352\pi$
$384$	25.6133			1.30708
$385$	3.89378	+	1.75815i	0.198445	+	0.0896038i
$386$	−0.937174			−0.0477009
$387$	−0.734575	−	2.26079i	−0.0373405	−	0.114922i
$388$	4.58911	+	3.33418i	0.232977	+	0.169267i
$389$	−10.4926	+	7.62332i	−0.531996	+	0.386517i	−0.821104	−	0.570779i	$-0.806641\pi$
$389$	−10.4926	+	7.62332i	−0.531996	+	0.386517i	0.289108	+	0.957296i	$0.406641\pi$
$390$	3.69237	−	11.3640i	0.186971	−	0.575436i
$391$	4.59179	−	14.1321i	0.232217	−	0.714690i
$392$	−13.6638	+	9.92734i	−0.690127	+	0.501406i
$393$	29.2661	+	21.2631i	1.47628	+	1.07258i
$394$	10.7367	+	33.0443i	0.540909	+	1.66475i
$395$	48.2432			2.42738
$396$	0.802666	−	0.166216i	0.0403355	−	0.00835267i
$397$	−1.33036			−0.0667690			−0.0333845	−	0.999443i	$-0.510629\pi$
$397$	−1.33036			−0.0667690			−0.0333845	+	0.999443i	$0.510629\pi$
$398$	−0.0125544	−	0.0386385i	−0.000629295	−	0.00193677i
$399$	−1.14810	−	0.834143i	−0.0574768	−	0.0417594i
$400$	43.2478	−	31.4214i	2.16239	−	1.57107i
$401$	−4.14754	+	12.7648i	−0.207118	+	0.637445i	0.792501	+	0.609870i	$0.208778\pi$
$401$	−4.14754	+	12.7648i	−0.207118	+	0.637445i	−0.999620	+	0.0275746i	$0.991222\pi$
$402$	−5.41353	+	16.6611i	−0.270003	+	0.830982i
$403$	−4.61790	+	3.35510i	−0.230034	+	0.167129i
$404$	4.49015	+	3.26229i	0.223393	+	0.162305i
$405$	−13.0236	−	40.0826i	−0.647149	−	1.99172i
$406$	−0.762874			−0.0378608
$407$	1.87643	−	16.9950i	0.0930113	−	0.842413i
$408$	−13.6152			−0.674055
$409$	10.2866	+	31.6590i	0.508642	+	1.56544i	0.794560	+	0.607185i	$0.207701\pi$
$409$	10.2866	+	31.6590i	0.508642	+	1.56544i	−0.285918	+	0.958254i	$0.592299\pi$
$410$	32.6029	+	23.6874i	1.61014	+	1.16984i
$411$	7.76424	−	5.64105i	0.382982	−	0.278252i
$412$	−0.107540	+	0.330973i	−0.00529810	+	0.0163059i
$413$	1.19271	−	3.67079i	0.0586896	−	0.180628i
$414$	−3.66714	+	2.66434i	−0.180230	+	0.130945i
$415$	−10.2549	−	7.45065i	−0.503395	−	0.365738i
$416$	−0.738383	−	2.27251i	−0.0362022	−	0.111419i
$417$	32.4237			1.58779
$418$	−6.04953	−	10.6062i	−0.295892	−	0.518766i
$419$	1.72585			0.0843135			0.0421567	−	0.999111i	$-0.486577\pi$
$419$	1.72585			0.0843135			0.0421567	+	0.999111i	$0.486577\pi$
$420$	−0.323171	−	0.994618i	−0.0157691	−	0.0485324i
$421$	15.5918	+	11.3281i	0.759896	+	0.552097i	0.898878	−	0.438198i	$-0.144383\pi$
$421$	15.5918	+	11.3281i	0.759896	+	0.552097i	−0.138983	+	0.990295i	$0.544383\pi$
$422$	−16.3148	+	11.8534i	−0.794194	+	0.577015i
$423$	1.50997	−	4.64721i	0.0734172	−	0.225955i
$424$	4.69600	−	14.4528i	0.228058	−	0.701891i
$425$	−27.2123	+	19.7709i	−1.31999	+	0.959030i
$426$	−0.515424	−	0.374478i	−0.0249724	−	0.0181435i
$427$	1.19911	+	3.69047i	0.0580288	+	0.178594i
$428$	3.06231			0.148022
$429$	3.10723	+	5.44767i	0.150018	+	0.263016i
$430$	−26.0946			−1.25839
$431$	3.02244	+	9.30212i	0.145586	+	0.448067i	0.997086	−	0.0762874i	$-0.0243067\pi$
$431$	3.02244	+	9.30212i	0.145586	+	0.448067i	−0.851500	+	0.524355i	$0.824307\pi$
$432$	−17.3362	−	12.5955i	−0.834087	−	0.606000i
$433$	−6.22322	+	4.52143i	−0.299069	+	0.217286i	−0.727192	−	0.686434i	$-0.759175\pi$
$433$	−6.22322	+	4.52143i	−0.299069	+	0.217286i	0.428123	+	0.903720i	$0.359175\pi$
$434$	−0.873531	+	2.68845i	−0.0419308	+	0.129050i
$435$	3.64926	−	11.2313i	0.174969	−	0.538498i
$436$	−1.71151	+	1.24348i	−0.0819664	+	0.0595521i
$437$	9.65416	+	7.01416i	0.461821	+	0.335533i
$438$	−13.5833	−	41.8052i	−0.649037	−	1.99753i
$439$	−3.90125			−0.186197			−0.0930983	−	0.995657i	$-0.529677\pi$
$439$	−3.90125			−0.186197			−0.0930983	+	0.995657i	$0.529677\pi$
$440$	−3.61246	+	32.7184i	−0.172217	+	1.55979i
$441$	−3.97135			−0.189112
$442$	1.41661	+	4.35988i	0.0673812	+	0.207378i
$443$	19.7418	+	14.3433i	0.937961	+	0.681469i	0.947929	−	0.318481i	$-0.103173\pi$
$443$	19.7418	+	14.3433i	0.937961	+	0.681469i	−0.00996770	+	0.999950i	$0.503173\pi$
$444$	−3.38609	+	2.46014i	−0.160697	+	0.116753i
$445$	2.56104	−	7.88209i	0.121405	−	0.373647i
$446$	5.67507	−	17.4661i	0.268723	−	0.827043i
$447$	9.64529	−	7.00771i	0.456206	−	0.331453i
$448$	1.44577	+	1.05041i	0.0683063	+	0.0496274i
$449$	1.35807	+	4.17972i	0.0640915	+	0.197253i	0.977975	−	0.208724i	$-0.0669311\pi$
$449$	1.35807	+	4.17972i	0.0640915	+	0.197253i	−0.913883	+	0.405978i	$0.866931\pi$
$450$	10.2607			0.483696
$451$	−20.7124	+	4.28913i	−0.975309	+	0.201967i
$452$	−5.84029			−0.274704
$453$	10.8265	+	33.3204i	0.508671	+	1.56553i
$454$	11.8125	+	8.58226i	0.554387	+	0.402786i
$455$	1.04214	−	0.757156i	0.0488561	−	0.0354960i
$456$	3.37882	−	10.3989i	0.158228	−	0.486975i
$457$	−0.502034	+	1.54510i	−0.0234842	+	0.0722769i	−0.962112	−	0.272655i	$-0.912098\pi$
$457$	−0.502034	+	1.54510i	−0.0234842	+	0.0722769i	0.938628	+	0.344932i	$0.112098\pi$
$458$	1.63694	−	1.18931i	0.0764892	−	0.0555727i
$459$	10.9082	+	7.92531i	0.509153	+	0.369922i
$460$	2.71749	+	8.36356i	0.126703	+	0.389953i
$461$	23.2291			1.08189			0.540945	−	0.841058i	$-0.318067\pi$
$461$	23.2291			1.08189			0.540945	+	0.841058i	$0.318067\pi$
$462$	2.83068	+	1.27813i	0.131695	+	0.0594642i
$463$	9.97505			0.463580			0.231790	−	0.972766i	$-0.425542\pi$
$463$	9.97505			0.463580			0.231790	+	0.972766i	$0.425542\pi$
$464$	−2.22509	−	6.84813i	−0.103297	−	0.317916i
$465$	−35.4016	−	25.7208i	−1.64171	−	1.19277i
$466$	−2.09235	+	1.52018i	−0.0969265	+	0.0704212i
$467$	6.76078	−	20.8075i	0.312851	−	0.962858i	−0.663778	−	0.747929i	$-0.731048\pi$
$467$	6.76078	−	20.8075i	0.312851	−	0.962858i	0.976630	−	0.214928i	$-0.0689518\pi$
$468$	0.0763727	−	0.235051i	0.00353033	−	0.0108652i
$469$	−1.52792	+	1.11010i	−0.0705526	+	0.0512595i
$470$	−43.3951	−	31.5284i	−2.00167	−	1.45430i
$471$	7.50319	+	23.0925i	0.345729	+	1.06404i
$472$	29.7382			1.36881
$473$	9.21782	−	10.1301i	0.423836	−	0.465781i
$474$	35.0716			1.61089
$475$	−8.34733	−	25.6904i	−0.383002	−	1.17876i
$476$	0.324603	+	0.235838i	0.0148781	+	0.0108096i
$477$	2.89086	−	2.10034i	0.132364	−	0.0961678i
$478$	4.05904	−	12.4924i	0.185656	−	0.571391i
$479$	5.96014	−	18.3434i	0.272326	−	0.838133i	−0.717589	−	0.696467i	$-0.754754\pi$
$479$	5.96014	−	18.3434i	0.272326	−	0.838133i	0.989915	−	0.141666i	$-0.0452458\pi$
$480$	14.8196	−	10.7670i	0.676417	−	0.491446i
$481$	−4.17075	−	3.03023i	−0.190170	−	0.138167i
$482$	13.5002	+	41.5495i	0.614919	+	1.89253i
$483$	−3.03541			−0.138116
$484$	3.12317	+	3.54268i	0.141962	+	0.161031i
$485$	−53.5631			−2.43218
$486$	−2.84382	−	8.75237i	−0.128998	−	0.397016i
$487$	−12.8706	−	9.35107i	−0.583224	−	0.423737i	0.256661	−	0.966502i	$-0.417378\pi$
$487$	−12.8706	−	9.35107i	−0.583224	−	0.423737i	−0.839885	+	0.542764i	$0.817378\pi$
$488$	−24.1877	+	17.5734i	−1.09492	+	0.795509i
$489$	−3.86136	+	11.8840i	−0.174617	+	0.537414i
$490$	−13.4716	+	41.4612i	−0.608583	+	1.87303i
$491$	3.93388	−	2.85813i	0.177534	−	0.128986i	−0.495470	−	0.868625i	$-0.665004\pi$
$491$	3.93388	−	2.85813i	0.177534	−	0.128986i	0.673003	+	0.739640i	$0.265004\pi$
$492$	4.18883	+	3.04337i	0.188847	+	0.137206i
$493$	1.40007	+	4.30897i	0.0630559	+	0.194066i
$494$	−3.68150			−0.165639
$495$	−5.20925	+	5.72478i	−0.234138	+	0.257310i
$496$	−26.6814			−1.19803
$497$	−0.0212243	−	0.0653216i	−0.000952039	−	0.00293008i
$498$	−7.45508	−	5.41644i	−0.334070	−	0.242716i
$499$	21.2346	−	15.4279i	0.950593	−	0.690646i	−0.000353942	−	1.00000i	$-0.500113\pi$
$499$	21.2346	−	15.4279i	0.950593	−	0.690646i	0.950947	+	0.309354i	$0.100113\pi$
$500$	3.46199	−	10.6549i	0.154825	−	0.476502i
$501$	−1.03991	+	3.20051i	−0.0464597	+	0.142988i
$502$	−22.6747	+	16.4741i	−1.01202	+	0.735277i
$503$	31.5735	+	22.9395i	1.40779	+	1.02282i	0.993639	+	0.112614i	$0.0359224\pi$
$503$	31.5735	+	22.9395i	1.40779	+	1.02282i	0.414154	+	0.910207i	$0.364078\pi$
$504$	0.138364	+	0.425839i	0.00616320	+	0.0189684i
$505$	−52.4081			−2.33213
$506$	−23.8027	−	10.7476i	−1.05816	−	0.477789i
$507$	1.89094			0.0839794
$508$	−0.778022	−	2.39450i	−0.0345191	−	0.106239i
$509$	−8.32218	−	6.04642i	−0.368874	−	0.268003i	0.387870	−	0.921714i	$-0.373211\pi$
$509$	−8.32218	−	6.04642i	−0.368874	−	0.268003i	−0.756744	+	0.653711i	$0.773211\pi$
$510$	−28.4318	+	20.6569i	−1.25898	+	0.914703i
$511$	1.46437	−	4.50685i	0.0647797	−	0.199372i
$512$	−3.62081	+	11.1437i	−0.160019	+	0.492488i
$513$	−8.76016	+	6.36463i	−0.386771	+	0.281005i
$514$	10.9561	+	7.96007i	0.483252	+	0.351103i
$515$	−1.01546	−	3.12527i	−0.0447466	−	0.137716i
$516$	−3.35265			−0.147592
$517$	27.5686	−	5.70891i	1.21247	−	0.251078i
$518$	−2.55309			−0.112176
$519$	0.886975	+	2.72983i	0.0389339	+	0.119826i
$520$	8.02943	+	5.83372i	0.352114	+	0.255826i
$521$	35.5157	−	25.8036i	1.55597	−	1.13048i	0.616750	−	0.787159i	$-0.288449\pi$
$521$	35.5157	−	25.8036i	1.55597	−	1.13048i	0.939219	−	0.343319i	$-0.111551\pi$
$522$	0.427091	−	1.31445i	0.0186933	−	0.0575319i
$523$	8.10232	−	24.9364i	0.354290	−	1.09039i	−0.602130	−	0.798398i	$-0.705681\pi$
$523$	8.10232	−	24.9364i	0.354290	−	1.09039i	0.956420	−	0.291994i	$-0.0943187\pi$
$524$	6.64499	−	4.82787i	0.290288	−	0.210907i
$525$	5.55884	+	4.03873i	0.242608	+	0.176265i
$526$	0.498772	+	1.53506i	0.0217475	+	0.0669319i
$527$	16.7884			0.731315
$528$	−3.21717	+	29.1383i	−0.140010	+	1.26808i
$529$	2.52424			0.109750
$530$	−12.1213	−	37.3056i	−0.526516	−	1.62045i
$531$	5.65713	+	4.11014i	0.245498	+	0.178365i
$532$	−0.260681	+	0.189396i	−0.0113020	+	0.00821135i
$533$	−1.97076	+	6.06538i	−0.0853632	+	0.262721i
$534$	1.86182	−	5.73008i	0.0805687	−	0.247965i
$535$	−23.3939	+	16.9966i	−1.01141	+	0.734829i
$536$	−11.7723	−	8.55305i	−0.508485	−	0.369436i
$537$	12.9127	+	39.7413i	0.557225	+	1.71496i
$538$	−19.0104			−0.819599
$539$	−11.3367	−	19.8757i	−0.488305	−	0.856109i
$540$	−7.97963			−0.343389
$541$	−6.08430	−	18.7256i	−0.261585	−	0.805075i	−0.992461	−	0.122564i	$-0.960888\pi$
$541$	−6.08430	−	18.7256i	−0.261585	−	0.805075i	0.730876	−	0.682510i	$-0.239112\pi$
$542$	35.6349	+	25.8903i	1.53065	+	1.11208i
$543$	−10.5453	+	7.66159i	−0.452541	+	0.328790i
$544$	−2.17172	+	6.68388i	−0.0931119	+	0.286569i
$545$	6.17304	−	18.9987i	0.264424	−	0.813813i
$546$	0.757606	−	0.550433i	0.0324226	−	0.0235564i
$547$	2.20183	+	1.59973i	0.0941437	+	0.0683994i	0.633861	−	0.773447i	$-0.281469\pi$
$547$	2.20183	+	1.59973i	0.0941437	+	0.0683994i	−0.539718	+	0.841846i	$0.681469\pi$
$548$	−0.673370	−	2.07242i	−0.0287649	−	0.0885293i
$549$	−7.03008			−0.300036
$550$	29.2905	+	51.3528i	1.24895	+	2.18969i
$551$	−3.63852			−0.155006
$552$	−7.22705	−	22.2426i	−0.307604	−	0.946706i
$553$	3.05884	+	2.22238i	0.130075	+	0.0945051i
$554$	−4.53737	+	3.29659i	−0.192775	+	0.140059i
$555$	12.2129	−	37.5874i	0.518407	−	1.59549i
$556$	2.27496	−	7.00162i	0.0964800	−	0.296935i
$557$	−32.4915	+	23.6065i	−1.37671	+	1.00024i	−0.379531	+	0.925179i	$0.623915\pi$
$557$	−32.4915	+	23.6065i	−1.37671	+	1.00024i	−0.997179	+	0.0750598i	$0.976085\pi$
$558$	−4.14322	−	3.01023i	−0.175397	−	0.127433i
$559$	−1.27611	−	3.92745i	−0.0539735	−	0.166113i
$560$	6.02127			0.254445
$561$	2.02431	−	18.3343i	0.0854663	−	0.774076i
$562$	−27.3736			−1.15469
$563$	−8.08363	−	24.8788i	−0.340684	−	1.04852i	−0.963854	−	0.266432i	$-0.914155\pi$
$563$	−8.08363	−	24.8788i	−0.340684	−	1.04852i	0.623170	−	0.782087i	$-0.285845\pi$
$564$	−5.57542	−	4.05078i	−0.234767	−	0.170569i
$565$	44.6156	−	32.4151i	1.87699	−	1.36372i
$566$	2.60092	−	8.00480i	0.109325	−	0.336467i
$567$	1.02069	−	3.14137i	0.0428650	−	0.131925i
$568$	0.428123	−	0.311050i	0.0179637	−	0.0130514i
$569$	−2.27369	−	1.65194i	−0.0953182	−	0.0692527i	0.539105	−	0.842238i	$-0.318762\pi$
$569$	−2.27369	−	1.65194i	−0.0953182	−	0.0692527i	−0.634424	+	0.772986i	$0.718762\pi$
$570$	−8.72139	−	26.8417i	−0.365299	−	1.12427i
$571$	18.5767			0.777412			0.388706	−	0.921362i	$-0.372922\pi$
$571$	18.5767			0.777412			0.388706	+	0.921362i	$0.372922\pi$
$572$	1.39439	−	0.288751i	0.0583025	−	0.0120733i
$573$	2.19035			0.0915031
$574$	0.975986	+	3.00378i	0.0407369	+	0.125375i
$575$	−46.7433	−	33.9610i	−1.94933	−	1.41627i
$576$	−2.61929	+	1.90303i	−0.109137	+	0.0792928i
$577$	−0.890985	+	2.74217i	−0.0370922	+	0.114158i	−0.967888	−	0.251381i	$-0.919115\pi$
$577$	−0.890985	+	2.74217i	−0.0370922	+	0.114158i	0.930796	+	0.365539i	$0.119115\pi$
$578$	−4.02145	+	12.3767i	−0.167270	+	0.514804i
$579$	0.919835	−	0.668299i	0.0382270	−	0.0277736i
$580$	−2.16925	−	1.57605i	−0.0900733	−	0.0654421i
$581$	−0.306987	−	0.944810i	−0.0127360	−	0.0391973i
$582$	−38.9390			−1.61408
$583$	18.7640	+	8.47250i	0.777126	+	0.350895i
$584$	36.5114			1.51085
$585$	0.721163	+	2.21951i	0.0298164	+	0.0917655i
$586$	−0.415865	−	0.302144i	−0.0171792	−	0.0124814i
$587$	−29.8567	+	21.6922i	−1.23232	+	0.895332i	−0.997062	−	0.0766007i	$-0.975593\pi$
$587$	−29.8567	+	21.6922i	−1.23232	+	0.895332i	−0.235257	+	0.971933i	$0.575593\pi$
$588$	−1.73083	+	5.32695i	−0.0713783	+	0.219680i
$589$	−4.16629	+	12.8225i	−0.171669	+	0.528343i
$590$	62.1002	−	45.1185i	2.55663	−	1.85750i
$591$	−34.1020	−	24.7765i	−1.40277	−	1.01917i
$592$	−7.44665	−	22.9184i	−0.306055	−	0.941941i
$593$	−19.5389			−0.802368			−0.401184	−	0.915997i	$-0.631401\pi$
$593$	−19.5389			−0.802368			−0.401184	+	0.915997i	$0.631401\pi$
$594$	15.9493	−	17.5278i	0.654410	−	0.719173i
$595$	−3.78869			−0.155321
$596$	−0.836507	−	2.57451i	−0.0342647	−	0.105456i
$597$	0.0398752	+	0.0289711i	0.00163198	+	0.00118571i
$598$	−6.37058	+	4.62849i	−0.260512	+	0.189273i
$599$	2.39385	−	7.36750i	0.0978099	−	0.301028i	−0.890166	−	0.455637i	$-0.849412\pi$
$599$	2.39385	−	7.36750i	0.0978099	−	0.301028i	0.987976	+	0.154609i	$0.0494117\pi$
$600$	−16.3595	+	50.3493i	−0.667873	+	2.05550i
$601$	18.7353	−	13.6120i	0.764231	−	0.555246i	−0.135974	−	0.990712i	$-0.543416\pi$
$601$	18.7353	−	13.6120i	0.764231	−	0.555246i	0.900205	+	0.435466i	$0.143416\pi$
$602$	−1.65452	−	1.20208i	−0.0674331	−	0.0489930i
$603$	−1.05733	−	3.25411i	−0.0430576	−	0.132518i
$604$	7.95489			0.323680
$605$	−43.5217	−	9.72912i	−1.76941	−	0.395545i
$606$	−38.0994			−1.54768
$607$	−1.38068	−	4.24930i	−0.0560401	−	0.172474i	0.919119	−	0.393981i	$-0.128902\pi$
$607$	−1.38068	−	4.24930i	−0.0560401	−	0.172474i	−0.975159	+	0.221507i	$0.928902\pi$
$608$	−4.56601	−	3.31740i	−0.185176	−	0.134538i
$609$	0.748760	−	0.544006i	0.0303413	−	0.0220442i
$610$	−23.8473	+	73.3945i	−0.965550	+	2.97166i
$611$	2.62312	−	8.07314i	0.106120	−	0.326604i
$612$	−0.588080	+	0.427265i	−0.0237717	+	0.0172712i
$613$	30.9550	+	22.4901i	1.25026	+	0.908367i	0.998237	−	0.0593542i	$-0.0189041\pi$
$613$	30.9550	+	22.4901i	1.25026	+	0.908367i	0.252023	+	0.967721i	$0.418904\pi$
$614$	4.64294	+	14.2895i	0.187374	+	0.576678i
$615$	−48.8912			−1.97148
$616$	−1.73626	+	1.90808i	−0.0699558	+	0.0768789i
$617$	27.6662			1.11380			0.556900	−	0.830580i	$-0.311991\pi$
$617$	27.6662			1.11380			0.556900	+	0.830580i	$0.311991\pi$
$618$	−0.738216	−	2.27200i	−0.0296954	−	0.0913931i
$619$	32.9208	+	23.9184i	1.32320	+	0.961361i	0.999886	+	0.0150693i	$0.00479689\pi$
$619$	32.9208	+	23.9184i	1.32320	+	0.961361i	0.323314	+	0.946292i	$0.395203\pi$
$620$	−8.03809	+	5.84001i	−0.322817	+	0.234541i
$621$	−7.15703	+	22.0271i	−0.287202	+	0.883916i
$622$	12.4190	−	38.2217i	0.497955	−	1.53255i
$623$	0.525479	−	0.381783i	0.0210529	−	0.0152958i
$624$	7.15082	+	5.19538i	0.286262	+	0.207981i
$625$	15.0204	+	46.2282i	0.600818	+	1.84913i
$626$	−18.5826			−0.742710
$627$	13.5009	+	6.09604i	0.539173	+	0.243452i
$628$	5.51307			0.219996
$629$	4.68557	+	14.4207i	0.186826	+	0.574991i
$630$	0.935014	+	0.679327i	0.0372518	+	0.0270650i
$631$	7.29617	−	5.30098i	0.290456	−	0.211029i	−0.433009	−	0.901390i	$-0.642548\pi$
$631$	7.29617	−	5.30098i	0.290456	−	0.211029i	0.723465	+	0.690361i	$0.242548\pi$
$632$	−9.00206	+	27.7055i	−0.358083	+	1.10207i
$633$	7.56031	−	23.2682i	0.300495	−	0.924829i
$634$	26.6941	−	19.3944i	1.06016	−	0.770251i
$635$	19.2337	+	13.9741i	0.763265	+	0.554544i
$636$	−1.55735	−	4.79304i	−0.0617530	−	0.190056i
$637$	−6.89904			−0.273350
$638$	7.79771	−	1.61475i	0.308714	−	0.0639286i
$639$	0.124433			0.00492249
$640$	16.9697	+	52.2273i	0.670785	+	2.06447i
$641$	12.3881	+	9.00046i	0.489299	+	0.355497i	0.804915	−	0.593390i	$-0.202211\pi$
$641$	12.3881	+	9.00046i	0.489299	+	0.355497i	−0.315616	+	0.948887i	$0.602211\pi$
$642$	−17.0068	+	12.3561i	−0.671204	+	0.487658i
$643$	1.92334	−	5.91943i	0.0758491	−	0.233439i	−0.905943	−	0.423401i	$-0.860836\pi$
$643$	1.92334	−	5.91943i	0.0758491	−	0.233439i	0.981792	+	0.189961i	$0.0608363\pi$
$644$	−0.212976	+	0.655472i	−0.00839242	+	0.0258292i
$645$	25.6118	−	18.6081i	1.00846	−	0.732692i
$646$	8.76003	+	6.36454i	0.344659	+	0.250409i
$647$	−2.53901	−	7.81426i	−0.0998186	−	0.307210i	0.888661	−	0.458565i	$-0.151636\pi$
$647$	−2.53901	−	7.81426i	−0.0998186	−	0.307210i	−0.988479	+	0.151355i	$0.951636\pi$
$648$	25.4491			0.999736
$649$	−4.42146	+	40.0456i	−0.173557	+	1.57193i
$650$	17.8250			0.699154
$651$	−1.05977	−	3.26163i	−0.0415355	−	0.127833i
$652$	2.29533	+	1.66765i	0.0898920	+	0.0653104i
$653$	−20.7148	+	15.0502i	−0.810633	+	0.588959i	−0.914014	−	0.405683i	$-0.867034\pi$
$653$	−20.7148	+	15.0502i	−0.810633	+	0.588959i	0.103381	+	0.994642i	$0.467034\pi$
$654$	4.48765	−	13.8116i	0.175481	−	0.540075i
$655$	−23.9670	+	73.7630i	−0.936470	+	2.88216i
$656$	−24.1174	+	17.5223i	−0.941628	+	0.684133i
$657$	6.94560	+	5.04627i	0.270974	+	0.196874i
$658$	−1.29906	−	3.99808i	−0.0506425	−	0.155862i
$659$	−44.6751			−1.74029			−0.870147	−	0.492792i	$-0.835976\pi$
$659$	−44.6751			−1.74029			−0.870147	+	0.492792i	$0.835976\pi$
$660$	5.40856	+	9.48243i	0.210528	+	0.369103i
$661$	32.1613			1.25093			0.625464	−	0.780253i	$-0.284910\pi$
$661$	32.1613			1.25093			0.625464	+	0.780253i	$0.284910\pi$
$662$	0.574060	+	1.76678i	0.0223115	+	0.0686677i
$663$	−4.49943	−	3.26903i	−0.174743	−	0.126958i
$664$	6.19236	−	4.49902i	0.240310	−	0.174596i
$665$	0.940219	−	2.89370i	0.0364601	−	0.112213i
$666$	1.42933	−	4.39903i	0.0553855	−	0.170459i
$667$	−6.29619	+	4.57445i	−0.243790	+	0.177123i
$668$	0.618159	+	0.449119i	0.0239173	+	0.0173769i
$669$	6.88500	+	21.1898i	0.266189	+	0.819247i
$670$	−37.5598			−1.45106
$671$	−20.0681	−	35.1840i	−0.774722	−	1.35826i
$672$	1.43562			0.0553804
$673$	7.54348	+	23.2164i	0.290780	+	0.894928i	0.984606	+	0.174786i	$0.0559234\pi$
$673$	7.54348	+	23.2164i	0.290780	+	0.894928i	−0.693827	+	0.720142i	$0.744077\pi$
$674$	−29.7063	−	21.5829i	−1.14424	−	0.831341i
$675$	42.4147	−	30.8161i	1.63254	−	1.18611i
$676$	0.132675	−	0.408332i	0.00510288	−	0.0157051i
$677$	−0.517122	+	1.59154i	−0.0198746	+	0.0611677i	−0.960502	−	0.278273i	$-0.910238\pi$
$677$	−0.517122	+	1.59154i	−0.0198746	+	0.0611677i	0.940627	+	0.339441i	$0.110238\pi$
$678$	32.4344	−	23.5650i	1.24564	−	0.905008i
$679$	−3.39614	−	2.46744i	−0.130332	−	0.0946918i
$680$	−9.02054	−	27.7624i	−0.345922	−	1.06464i
$681$	−17.7139			−0.678800
$682$	3.23823	−	29.3289i	0.123998	−	1.12306i
$683$	39.4883			1.51098			0.755488	−	0.655163i	$-0.227400\pi$
$683$	39.4883			1.51098			0.755488	+	0.655163i	$0.227400\pi$
$684$	−0.180393	−	0.555191i	−0.00689748	−	0.0212283i
$685$	16.6465	+	12.0944i	0.636032	+	0.462104i
$686$	−5.56867	+	4.04588i	−0.212613	+	0.154472i
$687$	−0.758560	+	2.33461i	−0.0289409	+	0.0890708i
$688$	5.96497	−	18.3583i	0.227412	−	0.699903i
$689$	5.02202	−	3.64871i	0.191324	−	0.139005i
$690$	−48.8379	−	35.4828i	−1.85923	−	1.35081i
$691$	1.70402	+	5.24443i	0.0648239	+	0.199508i	0.978223	−	0.207559i	$-0.0665518\pi$
$691$	1.70402	+	5.24443i	0.0648239	+	0.199508i	−0.913399	+	0.407066i	$0.866552\pi$
$692$	0.651717			0.0247746
$693$	−0.594008	+	0.123007i	−0.0225645	+	0.00467266i
$694$	−14.4890			−0.549994
$695$	21.4818	+	66.1140i	0.814849	+	2.50785i
$696$	5.76904	+	4.19145i	0.218675	+	0.158877i
$697$	15.1751	−	11.0254i	0.574799	−	0.417616i
$698$	15.2351	−	46.8887i	0.576656	−	1.77476i
$699$	0.969599	−	2.98412i	0.0366736	−	0.112870i
$700$	1.26216	−	0.917012i	0.0477051	−	0.0346598i
$701$	−24.6165	−	17.8849i	−0.929752	−	0.675504i	0.0161801	−	0.999869i	$-0.494849\pi$
$701$	−24.6165	−	17.8849i	−0.929752	−	0.675504i	−0.945932	+	0.324365i	$0.894849\pi$
$702$	−2.20801	−	6.79556i	−0.0833360	−	0.256482i
$703$	−12.1769			−0.459261
$704$	−17.0013	−	7.67658i	−0.640761	−	0.289322i
$705$	65.0751			2.45087
$706$	−14.6244	−	45.0091i	−0.550395	−	1.69394i
$707$	−3.32291	−	2.41424i	−0.124971	−	0.0907967i
$708$	7.97867	−	5.79684i	0.299857	−	0.217859i
$709$	2.96496	−	9.12522i	0.111352	−	0.342705i	−0.879817	−	0.475313i	$-0.842335\pi$
$709$	2.96496	−	9.12522i	0.111352	−	0.342705i	0.991169	+	0.132608i	$0.0423350\pi$
$710$	0.422100	−	1.29909i	0.0158411	−	0.0487539i
$711$	−5.54168	+	4.02626i	−0.207829	+	0.150997i
$712$	4.04870	+	2.94156i	0.151732	+	0.110239i
$713$	8.91139	+	27.4264i	0.333734	+	1.02713i
$714$	−2.75429			−0.103077
$715$	−9.04953	+	9.94511i	−0.338433	+	0.371926i
$716$	9.48780			0.354576
$717$	4.92443	+	15.1558i	0.183906	+	0.566005i
$718$	3.69160	+	2.68210i	0.137769	+	0.100095i
$719$	14.0920	−	10.2384i	0.525542	−	0.381828i	−0.293146	−	0.956068i	$-0.594702\pi$
$719$	14.0920	−	10.2384i	0.525542	−	0.381828i	0.818687	+	0.574239i	$0.194702\pi$
$720$	−3.37097	+	10.3748i	−0.125629	+	0.386645i
$721$	0.0795842	−	0.244935i	0.00296387	−	0.00912185i
$722$	16.9233	−	12.2955i	0.629820	−	0.457591i
$723$	−42.8794	−	31.1537i	−1.59470	−	1.15862i
$724$	0.914561	+	2.81473i	0.0339894	+	0.104609i
$725$	17.6169			0.654274
$726$	−31.6392	−	7.07283i	−1.17424	−	0.262497i
$727$	4.02873			0.149417			0.0747086	−	0.997205i	$-0.476197\pi$
$727$	4.02873			0.149417			0.0747086	+	0.997205i	$0.476197\pi$
$728$	0.240366	+	0.739769i	0.00890854	+	0.0274177i
$729$	−16.1980	−	11.7685i	−0.599927	−	0.435872i
$730$	76.2442	−	55.3946i	2.82192	−	2.05025i
$731$	−3.75327	+	11.5514i	−0.138820	+	0.427243i
$732$	−3.06391	+	9.42976i	−0.113246	+	0.348534i
$733$	27.4460	−	19.9407i	1.01374	−	0.736527i	0.0487519	−	0.998811i	$-0.484476\pi$
$733$	27.4460	−	19.9407i	1.01374	−	0.736527i	0.964991	+	0.262284i	$0.0844756\pi$
$734$	−9.23556	−	6.71003i	−0.340891	−	0.247672i
$735$	−16.3437	−	50.3007i	−0.602846	−	1.85537i
$736$	−12.0719			−0.444976
$737$	13.2679	−	14.5809i	0.488728	−	0.537095i
$738$	−5.72197			−0.210629
$739$	−0.111221	−	0.342304i	−0.00409134	−	0.0125919i	0.948990	−	0.315306i	$-0.102107\pi$
$739$	−0.111221	−	0.342304i	−0.00409134	−	0.0125919i	−0.953081	+	0.302714i	$0.902107\pi$
$740$	−7.25977	−	5.27453i	−0.266875	−	0.193896i
$741$	3.61339	−	2.62528i	0.132741	−	0.0964421i
$742$	0.949975	−	2.92372i	0.0348747	−	0.107333i
$743$	7.84593	−	24.1473i	0.287839	−	0.885879i	−0.697694	−	0.716396i	$-0.745790\pi$
$743$	7.84593	−	24.1473i	0.287839	−	0.885879i	0.985533	−	0.169483i	$-0.0542096\pi$
$744$	21.3770	−	15.5313i	0.783718	−	0.569404i
$745$	20.6795	+	15.0245i	0.757639	+	0.550457i
$746$	11.7502	+	36.1635i	0.430207	+	1.32404i
$747$	1.79979			0.0658510
$748$	−3.81711	−	1.72354i	−0.139567	−	0.0630187i
$749$	−2.26625			−0.0828069
$750$	23.7652	+	73.1417i	0.867781	+	2.67076i
$751$	−11.1710	−	8.11618i	−0.407634	−	0.296164i	0.365009	−	0.931004i	$-0.381066\pi$
$751$	−11.1710	−	8.11618i	−0.407634	−	0.296164i	−0.772643	+	0.634840i	$0.781066\pi$
$752$	32.1008	−	23.3226i	1.17059	−	0.850487i
$753$	10.5075	−	32.3387i	0.382914	−	1.17849i
$754$	0.741944	−	2.28347i	0.0270200	−	0.0831590i
$755$	−60.7697	+	44.1517i	−2.21163	+	1.60685i
$756$	−0.505945	−	0.367590i	−0.0184010	−	0.0133691i
$757$	−6.22718	−	19.1653i	−0.226331	−	0.696574i	−0.998154	−	0.0607371i	$-0.980655\pi$
$757$	−6.22718	−	19.1653i	−0.226331	−	0.696574i	0.771823	−	0.635837i	$-0.219345\pi$
$758$	0.337447			0.0122566
$759$	31.0264	−	6.42496i	1.12619	−	0.233211i
$760$	23.4427			0.850356
$761$	13.5349	+	41.6561i	0.490639	+	1.51003i	0.823644	+	0.567107i	$0.191937\pi$
$761$	13.5349	+	41.6561i	0.490639	+	1.51003i	−0.333005	+	0.942925i	$0.608063\pi$
$762$	13.9824	+	10.1588i	0.506529	+	0.368015i
$763$	1.26659	−	0.920234i	0.0458538	−	0.0333147i
$764$	0.153683	−	0.472987i	0.00556005	−	0.0171121i
$765$	2.12108	−	6.52801i	0.0766877	−	0.236021i
$766$	−2.42524	+	1.76204i	−0.0876273	+	0.0636650i
$767$	9.82758	+	7.14016i	0.354853	+	0.257816i
$768$	5.76349	+	17.7382i	0.207972	+	0.640073i
$769$	20.9060			0.753888			0.376944	−	0.926236i	$-0.376975\pi$
$769$	20.9060			0.753888			0.376944	+	0.926236i	$0.376975\pi$
$770$	−0.730781	+	6.61875i	−0.0263355	+	0.238523i
$771$	−16.4297			−0.591702
$772$	−0.0797746	−	0.245521i	−0.00287115	−	0.00883649i
$773$	−24.2938	−	17.6505i	−0.873788	−	0.634844i	0.0578128	−	0.998327i	$-0.481587\pi$
$773$	−24.2938	−	17.6505i	−0.873788	−	0.634844i	−0.931601	+	0.363483i	$0.881587\pi$
$774$	2.99748	−	2.17779i	0.107742	−	0.0782792i
$775$	20.1722	−	62.0837i	0.724608	−	2.23011i
$776$	9.99474	−	30.7607i	0.358790	−	1.10424i
$777$	2.50585	−	1.82061i	0.0898970	−	0.0653140i
$778$	−16.3541	−	11.8820i	−0.586324	−	0.425989i
$779$	4.65495	+	14.3265i	0.166781	+	0.513298i
$780$	3.29144			0.117852
$781$	0.355208	+	0.622759i	0.0127103	+	0.0222841i
$782$	23.1603			0.828211
$783$	−2.18223	−	6.71621i	−0.0779865	−	0.240018i
$784$	−26.0896	−	18.9552i	−0.931773	−	0.676973i
$785$	−42.1159	+	30.5990i	−1.50318	+	1.09213i
$786$	−17.4234	+	53.6238i	−0.621474	+	1.91270i
$787$	−15.7037	+	48.3309i	−0.559775	+	1.72281i	0.123214	+	0.992380i	$0.460680\pi$
$787$	−15.7037	+	48.3309i	−0.559775	+	1.72281i	−0.682988	+	0.730429i	$0.739320\pi$
$788$	−7.74300	+	5.62562i	−0.275833	+	0.200404i
$789$	−1.58420	−	1.15099i	−0.0563990	−	0.0409763i
$790$	23.2361	+	71.5134i	0.826703	+	2.54433i
$791$	4.32207			0.153675
$792$	−2.31564	−	4.05984i	−0.0822827	−	0.144260i
$793$	−12.2127			−0.433685
$794$	−0.640762	−	1.97206i	−0.0227398	−	0.0699859i
$795$	38.4997	+	27.9717i	1.36544	+	0.992052i
$796$	0.00905385	−	0.00657801i	0.000320905	−	0.000233151i
$797$	6.29216	−	19.3653i	0.222880	−	0.685954i	−0.775620	−	0.631200i	$-0.782563\pi$
$797$	6.29216	−	19.3653i	0.222880	−	0.685954i	0.998500	−	0.0547535i	$-0.0174373\pi$
$798$	0.683516	−	2.10365i	0.0241962	−	0.0744683i
$799$	−20.1984	+	14.6750i	−0.714568	+	0.519164i
$800$	22.1076	+	16.0621i	0.781622	+	0.567882i
$801$	0.363634	+	1.11915i	0.0128484	+	0.0395432i
$802$	−20.9196			−0.738696
$803$	−5.42849	+	49.1663i	−0.191567	+	1.73504i
$804$	−4.82570			−0.170189
$805$	−2.01106	−	6.18941i	−0.0708806	−	0.218148i
$806$	−7.19762	−	5.22938i	−0.253525	−	0.184197i
$807$	18.6587	−	13.5564i	0.656818	−	0.477207i
$808$	9.77922	−	30.0973i	0.344032	−	1.05882i
$809$	9.10066	−	28.0090i	0.319962	−	0.984743i	−0.653701	−	0.756753i	$-0.726785\pi$
$809$	9.10066	−	28.0090i	0.319962	−	0.984743i	0.973663	−	0.227990i	$-0.0732153\pi$
$810$	53.1437	−	38.6112i	1.86728	−	1.35666i
$811$	−27.7672	−	20.1741i	−0.975039	−	0.708407i	−0.0184443	−	0.999830i	$-0.505871\pi$
$811$	−27.7672	−	20.1741i	−0.975039	−	0.708407i	−0.956594	+	0.291423i	$0.905871\pi$
$812$	−0.0649378	−	0.199858i	−0.00227887	−	0.00701364i
$813$	−53.4379			−1.87415
$814$	26.0964	−	5.40404i	0.914677	−	0.189411i
$815$	−26.7906			−0.938434
$816$	−8.03348	−	24.7245i	−0.281228	−	0.865531i
$817$	−7.89119	−	5.73328i	−0.276078	−	0.200582i
$818$	−41.9753	+	30.4968i	−1.46763	+	1.06630i
$819$	−0.0565192	+	0.173948i	−0.00197494	+	0.00607825i
$820$	−3.43039	+	10.5576i	−0.119794	+	0.368689i
$821$	−17.7010	+	12.8605i	−0.617770	+	0.448836i	−0.852142	−	0.523311i	$-0.824697\pi$
$821$	−17.7010	+	12.8605i	−0.617770	+	0.448836i	0.234372	+	0.972147i	$0.424697\pi$
$822$	12.1016	+	8.79234i	0.422092	+	0.306668i
$823$	−8.47837	−	26.0937i	−0.295537	−	0.909571i	−0.983040	−	0.183389i	$-0.941293\pi$
$823$	−8.47837	−	26.0937i	−0.295537	−	0.909571i	0.687503	−	0.726182i	$-0.258707\pi$
$824$	1.98429			0.0691260
$825$	−65.3682	−	29.5156i	−2.27583	−	1.02760i
$826$	6.01587			0.209319
$827$	10.7622	+	33.1227i	0.374238	+	1.15179i	0.943991	+	0.329971i	$0.107039\pi$
$827$	10.7622	+	33.1227i	0.374238	+	1.15179i	−0.569753	+	0.821816i	$0.692961\pi$
$828$	−1.01016	−	0.733924i	−0.0351055	−	0.0255056i
$829$	−37.8810	+	27.5221i	−1.31566	+	0.955883i	−0.315685	+	0.948864i	$0.602234\pi$
$829$	−37.8810	+	27.5221i	−1.31566	+	0.955883i	−0.999975	+	0.00701875i	$0.997766\pi$
$830$	6.10523	−	18.7900i	0.211916	−	0.652210i
$831$	2.10262	−	6.47121i	0.0729392	−	0.224484i
$832$	−4.55025	+	3.30595i	−0.157751	+	0.114613i
$833$	16.4161	+	11.9270i	0.568784	+	0.413246i
$834$	15.6167	+	48.0633i	0.540762	+	1.66429i
$835$	−7.21502			−0.249686
$836$	2.26366	−	2.48768i	0.0782903	−	0.0860383i
$837$	−26.1674			−0.904478
$838$	0.831248	+	2.55832i	0.0287150	+	0.0883757i
$839$	−9.95087	−	7.22973i	−0.343542	−	0.249598i	0.402613	−	0.915370i	$-0.368102\pi$
$839$	−9.95087	−	7.22973i	−0.343542	−	0.249598i	−0.746155	+	0.665772i	$0.768102\pi$
$840$	−4.82421	+	3.50499i	−0.166451	+	0.120934i
$841$	−8.22821	+	25.3238i	−0.283731	+	0.873236i
$842$	−9.28249	+	28.5686i	−0.319896	+	0.984538i
$843$	26.8671	−	19.5201i	0.925354	−	0.672309i
$844$	−4.49412	−	3.26517i	−0.154694	−	0.112392i
$845$	1.25281	+	3.85574i	0.0430979	+	0.132642i
$846$	7.61606			0.261845
$847$	−2.31129	−	2.62174i	−0.0794168	−	0.0900842i
$848$	29.0163			0.996425
$849$	3.15543	+	9.71142i	0.108294	+	0.333295i
$850$	−42.4141	−	30.8157i	−1.45479	−	1.05697i
$851$	−21.0713	+	15.3092i	−0.722314	+	0.524792i
$852$	0.0542315	−	0.166907i	0.00185794	−	0.00571816i
$853$	3.51372	−	10.8141i	0.120307	−	0.370268i	−0.872710	−	0.488240i	$-0.837639\pi$
$853$	3.51372	−	10.8141i	0.120307	−	0.370268i	0.993017	+	0.117971i	$0.0376391\pi$
$854$	−4.89303	+	3.55499i	−0.167436	+	0.121649i
$855$	4.45953	+	3.24004i	0.152513	+	0.110807i
$856$	−5.39573	−	16.6064i	−0.184422	−	0.567594i
$857$	−1.63010			−0.0556831			−0.0278415	−	0.999612i	$-0.508863\pi$
$857$	−1.63010			−0.0556831			−0.0278415	+	0.999612i	$0.508863\pi$
$858$	−6.57878	+	7.22985i	−0.224596	+	0.246823i
$859$	7.88765			0.269123			0.134562	−	0.990905i	$-0.457037\pi$
$859$	7.88765			0.269123			0.134562	+	0.990905i	$0.457037\pi$
$860$	−2.22124	−	6.83627i	−0.0757436	−	0.233115i
$861$	−3.09992	−	2.25223i	−0.105645	−	0.0767557i
$862$	−12.3333	+	8.96063i	−0.420072	+	0.305200i
$863$	15.9496	−	49.0878i	0.542931	−	1.67097i	−0.182929	−	0.983126i	$-0.558558\pi$
$863$	15.9496	−	49.0878i	0.542931	−	1.67097i	0.725860	−	0.687843i	$-0.241442\pi$
$864$	3.38498	−	10.4179i	0.115159	−	0.354424i
$865$	−4.97865	+	3.61720i	−0.169279	+	0.122989i
$866$	−9.69973	−	7.04726i	−0.329610	−	0.239476i
$867$	−4.87882	−	15.0155i	−0.165693	−	0.509951i
$868$	−0.778678			−0.0264300
$869$	−35.9699	−	16.2415i	−1.22020	−	0.550954i
$870$	18.4063			0.624033
$871$	−1.83679	−	5.65306i	−0.0622373	−	0.191547i
$872$	9.75883	+	7.09021i	0.330476	+	0.240105i
$873$	6.15277	−	4.47025i	0.208240	−	0.151295i
$874$	−5.74756	+	17.6892i	−0.194414	+	0.598345i
$875$	−2.56203	+	7.88511i	−0.0866124	+	0.266566i
$876$	9.79589	−	7.11713i	0.330972	−	0.240465i
$877$	−23.1770	−	16.8390i	−0.782630	−	0.568614i	0.123137	−	0.992390i	$-0.460705\pi$
$877$	−23.1770	−	16.8390i	−0.782630	−	0.568614i	−0.905767	+	0.423776i	$0.860705\pi$
$878$	−1.87902	−	5.78303i	−0.0634138	−	0.195168i
$879$	0.623630			0.0210345
$880$	−61.5463	+	12.7450i	−2.07473	+	0.429634i
$881$	−4.98437			−0.167928			−0.0839638	−	0.996469i	$-0.526758\pi$
$881$	−4.98437			−0.167928			−0.0839638	+	0.996469i	$0.526758\pi$
$882$	−1.91278	−	5.88693i	−0.0644067	−	0.198223i
$883$	38.0135	+	27.6185i	1.27926	+	0.929435i	0.999530	−	0.0306447i	$-0.00975603\pi$
$883$	38.0135	+	27.6185i	1.27926	+	0.929435i	0.279727	+	0.960080i	$0.409756\pi$
$884$	−1.02162	+	0.742247i	−0.0343606	+	0.0249645i
$885$	−28.7773	+	88.5674i	−0.967338	+	2.97716i
$886$	−11.7532	+	36.1726i	−0.394857	+	1.21524i
$887$	12.7915	−	9.29359i	0.429498	−	0.312048i	−0.351950	−	0.936019i	$-0.614481\pi$
$887$	12.7915	−	9.29359i	0.429498	−	0.312048i	0.781448	+	0.623970i	$0.214481\pi$
$888$	19.3071	+	14.0274i	0.647903	+	0.470729i
$889$	0.575771	+	1.77204i	0.0193107	+	0.0594323i
$890$	12.9175			0.432997
$891$	−3.78376	+	34.2699i	−0.126761	+	1.14808i
$892$	5.05884			0.169383
$893$	−6.19582	−	19.0688i	−0.207335	−	0.638113i
$894$	15.0335	+	10.9225i	0.502795	+	0.365302i
$895$	−72.4800	+	52.6598i	−2.42274	+	1.76022i
$896$	−1.32995	+	4.09318i	−0.0444306	+	0.136743i
$897$	2.95213	−	9.08572i	0.0985688	−	0.303363i
$898$	−5.54171	+	4.02629i	−0.184929	+	0.134359i
$899$	−7.11358	−	5.16832i	−0.237251	−	0.172373i
$900$	0.873420	+	2.68811i	0.0291140	+	0.0896037i
$901$	−18.2576			−0.608249
$902$	−16.3340	−	28.6372i	−0.543863	−	0.953515i
$903$	2.48111			0.0825661
$904$	10.2905	+	31.6708i	0.342256	+	1.05336i
$905$	−22.6091	−	16.4265i	−0.751552	−	0.546034i
$906$	−44.1780	+	32.0972i	−1.46772	+	1.06636i
$907$	1.11336	−	3.42658i	0.0369686	−	0.113778i	−0.930869	−	0.365353i	$-0.880948\pi$
$907$	1.11336	−	3.42658i	0.0369686	−	0.113778i	0.967838	+	0.251575i	$0.0809484\pi$
$908$	−1.24288	+	3.82518i	−0.0412463	+	0.126943i
$909$	6.02010	−	4.37386i	0.199674	−	0.145072i
$910$	1.62431	+	1.18013i	0.0538453	+	0.0391209i
$911$	−2.94250	−	9.05609i	−0.0974894	−	0.300041i	0.890405	−	0.455169i	$-0.150421\pi$
$911$	−2.94250	−	9.05609i	−0.0974894	−	0.300041i	−0.987894	+	0.155128i	$0.950421\pi$
$912$	20.8775			0.691323
$913$	5.13772	+	9.00757i	0.170034	+	0.298107i
$914$	−2.53219			−0.0837573
$915$	−28.9316	−	89.0422i	−0.956448	−	2.94364i
$916$	0.450916	+	0.327609i	0.0148987	+	0.0108245i
$917$	−4.91759	+	3.57284i	−0.162393	+	0.117986i
$918$	−6.49418	+	19.9870i	−0.214340	+	0.659670i
$919$	−4.68539	+	14.4201i	−0.154557	+	0.475677i	−0.998116	−	0.0613599i	$-0.980456\pi$
$919$	−4.68539	+	14.4201i	−0.154557	+	0.475677i	0.843559	+	0.537036i	$0.180456\pi$
$920$	40.5659	−	29.4729i	1.33742	−	0.971691i
$921$	−14.7469	−	10.7143i	−0.485927	−	0.353047i
$922$	11.1882	+	34.4337i	0.368464	+	1.13401i
$923$	0.216165			0.00711517
$924$	−0.0938911	+	0.850380i	−0.00308879	+	0.0279755i
$925$	58.9579			1.93852
$926$	4.80443	+	14.7865i	0.157883	+	0.485915i
$927$	0.377474	+	0.274251i	0.0123979	+	0.00900758i
$928$	2.97784	−	2.16352i	0.0977522	−	0.0710212i
$929$	13.5798	−	41.7944i	0.445539	−	1.37123i	−0.436352	−	0.899776i	$-0.643730\pi$
$929$	13.5798	−	41.7944i	0.445539	−	1.37123i	0.881891	−	0.471453i	$-0.156270\pi$
$930$	21.0762	−	64.8658i	0.691116	−	2.12703i
$931$	−13.1834	+	9.57829i	−0.432068	+	0.313916i
$932$	−0.576365	−	0.418754i	−0.0188795	−	0.0137167i
$933$	15.0667	+	46.3705i	0.493261	+	1.51810i
$934$	34.1004			1.11580
$935$	38.7261	−	8.01940i	1.26648	−	0.262263i
$936$	−1.40921			−0.0460614
$937$	−10.4633	−	32.2027i	−0.341821	−	1.05202i	−0.963264	−	0.268556i	$-0.913453\pi$
$937$	−10.4633	−	32.2027i	−0.341821	−	1.05202i	0.621443	−	0.783459i	$-0.286547\pi$
$938$	−2.38146	−	1.73023i	−0.0777576	−	0.0564942i
$939$	18.2388	−	13.2513i	0.595201	−	0.432439i
$940$	4.56591	−	14.0524i	0.148924	−	0.458339i
$941$	−1.87561	+	5.77255i	−0.0611433	+	0.188180i	−0.976962	−	0.213411i	$-0.931543\pi$
$941$	−1.87561	+	5.77255i	−0.0611433	+	0.188180i	0.915819	+	0.401591i	$0.131543\pi$
$942$	−30.6172	+	22.2447i	−0.997563	+	0.724772i
$943$	26.0667	+	18.9386i	0.848849	+	0.616725i
$944$	17.5466	+	54.0029i	0.571093	+	1.75764i
$945$	5.90528			0.192099
$946$	19.4560	+	8.78495i	0.632570	+	0.285623i
$947$	8.29917			0.269687			0.134843	−	0.990867i	$-0.456947\pi$
$947$	8.29917			0.269687			0.134843	+	0.990867i	$0.456947\pi$
$948$	2.98538	+	9.18807i	0.0969608	+	0.298415i
$949$	12.0659	+	8.76640i	0.391676	+	0.284569i
$950$	34.0618	−	24.7473i	1.10511	−	0.802910i
$951$	−12.3701	+	38.0712i	−0.401128	+	1.23454i
$952$	0.706961	−	2.17580i	0.0229127	−	0.0705181i
$953$	36.0622	−	26.2007i	1.16817	−	0.848724i	0.177380	−	0.984142i	$-0.443238\pi$
$953$	36.0622	−	26.2007i	1.16817	−	0.848724i	0.990788	+	0.135419i	$0.0432379\pi$
$954$	4.50580	+	3.27366i	0.145881	+	0.105989i
$955$	1.45118	+	4.46627i	0.0469590	+	0.144525i
$956$	3.61829			0.117024
$957$	−6.50197	+	7.14543i	−0.210179	+	0.230979i
$958$	30.0621			0.971262
$959$	0.498324	+	1.53368i	0.0160917	+	0.0495252i
$960$	−34.8830	−	25.3440i	−1.12584	−	0.817973i
$961$	−1.27958	+	0.929671i	−0.0412769	+	0.0299894i
$962$	2.48304	−	7.64201i	0.0800564	−	0.246388i
$963$	1.26875	−	3.90480i	0.0408847	−	0.125830i
$964$	−9.73596	+	7.07359i	−0.313574	+	0.227825i
$965$	1.97213	+	1.43283i	0.0634850	+	0.0461246i
$966$	−1.46199	−	4.49955i	−0.0470388	−	0.144771i
$967$	−2.58658			−0.0831788			−0.0415894	−	0.999135i	$-0.513242\pi$
$967$	−2.58658			−0.0831788			−0.0415894	+	0.999135i	$0.513242\pi$
$968$	13.7083	−	23.1785i	0.440603	−	0.744987i
$969$	−13.1365			−0.422006
$970$	−25.7984	−	79.3993i	−0.828337	−	2.54936i
$971$	47.8743	+	34.7827i	1.53636	+	1.11623i	0.952568	+	0.304327i	$0.0984315\pi$
$971$	47.8743	+	34.7827i	1.53636	+	1.11623i	0.583792	+	0.811904i	$0.301569\pi$
$972$	2.05087	−	1.49005i	0.0657818	−	0.0477933i
$973$	−1.68357	+	5.18151i	−0.0539729	+	0.166112i
$974$	7.66248	−	23.5827i	0.245522	−	0.755638i
$975$	−17.4952	+	12.7110i	−0.560295	+	0.407078i
$976$	−46.1838	−	33.5545i	−1.47831	−	1.07405i
$977$	13.5646	+	41.7476i	0.433970	+	1.33562i	0.894138	+	0.447791i	$0.147789\pi$
$977$	13.5646	+	41.7476i	0.433970	+	1.33562i	−0.460168	+	0.887832i	$0.652211\pi$
$978$	−19.4761			−0.622777
$979$	−4.56307	+	5.01465i	−0.145836	+	0.160269i
$980$	−12.0087			−0.383605
$981$	0.876489	+	2.69756i	0.0279841	+	0.0861263i
$982$	6.13149	+	4.45479i	0.195664	+	0.142158i
$983$	15.4413	−	11.2188i	0.492502	−	0.357824i	−0.313644	−	0.949541i	$-0.601550\pi$
$983$	15.4413	−	11.2188i	0.492502	−	0.357824i	0.806146	+	0.591717i	$0.201550\pi$
$984$	9.12297	−	28.0776i	0.290830	−	0.895082i
$985$	27.9273	−	85.9515i	0.889838	−	2.73864i
$986$	−5.71307	+	4.15079i	−0.181941	+	0.132188i
$987$	4.12606	+	2.99776i	0.131334	+	0.0954196i
$988$	−0.313379	−	0.964480i	−0.00996990	−	0.0306842i
$989$	−20.8632			−0.663411
$990$	−10.9951	−	4.96462i	−0.349449	−	0.157786i
$991$	−13.7241			−0.435960			−0.217980	−	0.975953i	$-0.569947\pi$
$991$	−13.7241			−0.435960			−0.217980	+	0.975953i	$0.569947\pi$
$992$	−4.21471	−	12.9716i	−0.133817	−	0.411847i
$993$	−1.82333	−	1.32473i	−0.0578616	−	0.0420389i
$994$	0.0866070	−	0.0629237i	0.00274701	−	0.00199582i
$995$	−0.0326553	+	0.100503i	−0.00103524	+	0.00318614i
$996$	0.784403	−	2.41414i	0.0248548	−	0.0764951i
$997$	21.1892	−	15.3948i	0.671068	−	0.487559i	−0.199315	−	0.979936i	$-0.563872\pi$
$997$	21.1892	−	15.3948i	0.671068	−	0.487559i	0.870382	+	0.492376i	$0.163872\pi$
$998$	33.0971	+	24.0464i	1.04767	+	0.761176i
$999$	−7.30320	−	22.4770i	−0.231063	−	0.711139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.c.27.6	✓	28
11.3	even	5		1573.2.a.s.1.11		14
11.8	odd	10		1573.2.a.r.1.4		14
11.9	even	5	inner	143.2.h.c.53.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.27.6	✓	28	1.1	even	1	trivial
143.2.h.c.53.6	yes	28	11.9	even	5	inner
1573.2.a.r.1.4		14	11.8	odd	10
1573.2.a.s.1.11		14	11.3	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.481645 + 1.48235i) q^{2} +(-1.52980 - 1.11146i) q^{3} +(-0.347348 + 0.252363i) q^{4} +(1.25281 - 3.85574i) q^{5} +(0.910760 - 2.80303i) q^{6} +(0.257053 - 0.186760i) q^{7} +(1.98054 + 1.43894i) q^{8} +(0.177882 + 0.547464i) q^{9} +O(q^{10})\)	\(q+(0.481645 + 1.48235i) q^{2} +(-1.52980 - 1.11146i) q^{3} +(-0.347348 + 0.252363i) q^{4} +(1.25281 - 3.85574i) q^{5} +(0.910760 - 2.80303i) q^{6} +(0.257053 - 0.186760i) q^{7} +(1.98054 + 1.43894i) q^{8} +(0.177882 + 0.547464i) q^{9} +6.31897 q^{10} +(-2.23215 + 2.45306i) q^{11} +0.811864 q^{12} +(0.309017 + 0.951057i) q^{13} +(0.400652 + 0.291090i) q^{14} +(-6.20206 + 4.50606i) q^{15} +(-1.44445 + 4.44557i) q^{16} +(0.908878 - 2.79724i) q^{17} +(-0.725858 + 0.527367i) q^{18} +(1.91090 + 1.38835i) q^{19} +(0.537887 + 1.65545i) q^{20} -0.600816 q^{21} +(-4.71140 - 2.12733i) q^{22} +5.05215 q^{23} +(-1.43049 - 4.40259i) q^{24} +(-9.25215 - 6.72208i) q^{25} +(-1.26096 + 0.916143i) q^{26} +(-1.41663 + 4.35994i) q^{27} +(-0.0421554 + 0.129741i) q^{28} +(-1.24624 + 0.905446i) q^{29} +(-9.66676 - 7.02331i) q^{30} +(1.76388 + 5.42866i) q^{31} -2.38946 q^{32} +(6.14123 - 1.27173i) q^{33} +4.58424 q^{34} +(-0.398060 - 1.22510i) q^{35} +(-0.199946 - 0.145270i) q^{36} +(-4.17075 + 3.03023i) q^{37} +(-1.13765 + 3.50132i) q^{38} +(0.584331 - 1.79839i) q^{39} +(8.02943 - 5.83372i) q^{40} +(5.15952 + 3.74861i) q^{41} +(-0.289380 - 0.890620i) q^{42} -4.12956 q^{43} +(0.156273 - 1.41538i) q^{44} +2.33373 q^{45} +(2.43334 + 7.48906i) q^{46} +(-6.86743 - 4.98948i) q^{47} +(7.15082 - 5.19538i) q^{48} +(-2.13192 + 6.56138i) q^{49} +(5.50823 - 16.9526i) q^{50} +(-4.49943 + 3.26903i) q^{51} +(-0.347348 - 0.252363i) q^{52} +(-1.91824 - 5.90374i) q^{53} -7.14527 q^{54} +(6.66190 + 11.6798i) q^{55} +0.777839 q^{56} +(-1.38019 - 4.24779i) q^{57} +(-1.94243 - 1.41126i) q^{58} +(9.82758 - 7.14016i) q^{59} +(1.01711 - 3.13034i) q^{60} +(-3.77392 + 11.6149i) q^{61} +(-7.19762 + 5.22938i) q^{62} +(0.147969 + 0.107506i) q^{63} +(1.73804 + 5.34914i) q^{64} +4.05417 q^{65} +(4.84304 + 8.49094i) q^{66} -5.94398 q^{67} +(0.390222 + 1.20098i) q^{68} +(-7.72878 - 5.61529i) q^{69} +(1.62431 - 1.18013i) q^{70} +(0.0667988 - 0.205585i) q^{71} +(-0.435469 + 1.34023i) q^{72} +(12.0659 - 8.76640i) q^{73} +(-6.50068 - 4.72302i) q^{74} +(6.68258 + 20.5669i) q^{75} -1.01411 q^{76} +(-0.115649 + 1.04744i) q^{77} +2.94728 q^{78} +(3.67720 + 11.3172i) q^{79} +(15.3314 + 11.1389i) q^{80} +(8.41018 - 6.11035i) q^{81} +(-3.07170 + 9.45372i) q^{82} +(0.966175 - 2.97358i) q^{83} +(0.208692 - 0.151624i) q^{84} +(-9.64678 - 7.00880i) q^{85} +(-1.98898 - 6.12146i) q^{86} +2.91287 q^{87} +(-7.95068 + 1.64643i) q^{88} +2.04425 q^{89} +(1.12403 + 3.45941i) q^{90} +(0.257053 + 0.186760i) q^{91} +(-1.75485 + 1.27498i) q^{92} +(3.33538 - 10.2653i) q^{93} +(4.08849 - 12.5831i) q^{94} +(7.74711 - 5.62861i) q^{95} +(3.65539 + 2.65580i) q^{96} +(-4.08269 - 12.5652i) q^{97} -10.7531 q^{98} +(-1.74002 - 0.785669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

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