LMFDB - Embedded newform 855.2.w.a.56.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(56,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 3]))

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

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

chi := DirichletCharacter("855.56");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.w (of order $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$80$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			56.15
Character	$\chi$	$=$	855.56
Dual form			855.2.w.a.626.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965535 + 1.67236i) q^{2} +(1.70969 - 0.277442i) q^{3} +(-0.864515 - 1.49738i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.18678 + 3.12708i) q^{6} +(-0.855216 + 1.48128i) q^{7} -0.523262 q^{8} +(2.84605 - 0.948678i) q^{9} +O(q^{10})$	\(q+(-0.965535 + 1.67236i) q^{2} +(1.70969 - 0.277442i) q^{3} +(-0.864515 - 1.49738i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.18678 + 3.12708i) q^{6} +(-0.855216 + 1.48128i) q^{7} -0.523262 q^{8} +(2.84605 - 0.948678i) q^{9} -1.93107i q^{10} +(-2.91134 - 1.68086i) q^{11} +(-1.89349 - 2.32020i) q^{12} +(-4.16547 + 2.40493i) q^{13} +(-1.65148 - 2.86045i) q^{14} +(-1.34191 + 1.09511i) q^{15} +(2.23426 - 3.86985i) q^{16} -6.00654i q^{17} +(-1.16144 + 5.67559i) q^{18} +(-3.85049 + 2.04298i) q^{19} +(1.49738 + 0.864515i) q^{20} +(-1.05118 + 2.76979i) q^{21} +(5.62199 - 3.24586i) q^{22} +(-8.14126 + 4.70036i) q^{23} +(-0.894614 + 0.145175i) q^{24} +(0.500000 - 0.866025i) q^{25} -9.28819i q^{26} +(4.60265 - 2.41156i) q^{27} +2.95739 q^{28} +(0.442996 - 0.767292i) q^{29} +(-0.535760 - 3.30152i) q^{30} +(1.11455 - 0.643489i) q^{31} +(3.79124 + 6.56663i) q^{32} +(-5.44381 - 2.06602i) q^{33} +(10.0451 + 5.79952i) q^{34} -1.71043i q^{35} +(-3.88099 - 3.44148i) q^{36} +11.7946i q^{37} +(0.301191 - 8.41195i) q^{38} +(-6.45441 + 5.26736i) q^{39} +(0.453159 - 0.261631i) q^{40} +(-0.459908 - 0.796585i) q^{41} +(-3.61712 - 4.43228i) q^{42} +(4.14003 - 7.17074i) q^{43} +5.81252i q^{44} +(-1.99041 + 2.24461i) q^{45} -18.1534i q^{46} +(-7.36162 - 4.25023i) q^{47} +(2.74622 - 7.23610i) q^{48} +(2.03721 + 3.52856i) q^{49} +(0.965535 + 1.67236i) q^{50} +(-1.66647 - 10.2693i) q^{51} +(7.20222 + 4.15820i) q^{52} -3.83217 q^{53} +(-0.411040 + 10.0257i) q^{54} +3.36172 q^{55} +(0.447502 - 0.775097i) q^{56} +(-6.01631 + 4.56114i) q^{57} +(0.855456 + 1.48169i) q^{58} +(0.717415 + 1.24260i) q^{59} +(2.79991 + 1.06261i) q^{60} +(0.254297 - 0.440456i) q^{61} +2.48524i q^{62} +(-1.02873 + 5.02712i) q^{63} -5.70528 q^{64} +(2.40493 - 4.16547i) q^{65} +(8.71131 - 7.10918i) q^{66} +(-7.51967 + 4.34148i) q^{67} +(-8.99409 + 5.19274i) q^{68} +(-12.6149 + 10.2949i) q^{69} +(2.86045 + 1.65148i) q^{70} -12.0984 q^{71} +(-1.48923 + 0.496408i) q^{72} -3.46459 q^{73} +(-19.7247 - 11.3880i) q^{74} +(0.614571 - 1.61935i) q^{75} +(6.38792 + 3.99947i) q^{76} +(4.97964 - 2.87500i) q^{77} +(-2.57694 - 15.8799i) q^{78} +(6.38865 + 3.68849i) q^{79} +4.46852i q^{80} +(7.20002 - 5.39997i) q^{81} +1.77623 q^{82} +(0.0729891 + 0.0421403i) q^{83} +(5.05620 - 0.820504i) q^{84} +(3.00327 + 5.20182i) q^{85} +(7.99469 + 13.8472i) q^{86} +(0.544505 - 1.43473i) q^{87} +(1.52339 + 0.879532i) q^{88} +14.3029 q^{89} +(-1.83196 - 5.49592i) q^{90} -8.22695i q^{91} +(14.0765 + 8.12706i) q^{92} +(1.72701 - 1.40939i) q^{93} +(14.2158 - 8.20750i) q^{94} +(2.31313 - 3.69451i) q^{95} +(8.30370 + 10.1750i) q^{96} +(1.88374 + 1.08758i) q^{97} -7.86800 q^{98} +(-9.88041 - 2.02190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 80 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{9}+O(q^{10}) $ 160 * q - 80 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^9	$ 160 q - 80 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{9} - 12 q^{11} - 80 q^{16} + 8 q^{19} + 20 q^{24} + 80 q^{25} - 32 q^{28} + 16 q^{30} - 100 q^{36} - 66 q^{38} + 8 q^{39} + 8 q^{42} - 28 q^{43} - 8 q^{45} + 36 q^{47} - 84 q^{49} - 8 q^{54} + 30 q^{57} + 28 q^{61} - 12 q^{63} + 136 q^{64} + 40 q^{66} - 84 q^{68} + 128 q^{73} - 84 q^{74} - 16 q^{76} - 84 q^{81} + 24 q^{82} + 60 q^{83} - 36 q^{87} - 120 q^{92} + 40 q^{93} - 12 q^{95} + 44 q^{96} + 84 q^{99}+O(q^{100}) $ 160 * q - 80 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^9 - 12 * q^11 - 80 * q^16 + 8 * q^19 + 20 * q^24 + 80 * q^25 - 32 * q^28 + 16 * q^30 - 100 * q^36 - 66 * q^38 + 8 * q^39 + 8 * q^42 - 28 * q^43 - 8 * q^45 + 36 * q^47 - 84 * q^49 - 8 * q^54 + 30 * q^57 + 28 * q^61 - 12 * q^63 + 136 * q^64 + 40 * q^66 - 84 * q^68 + 128 * q^73 - 84 * q^74 - 16 * q^76 - 84 * q^81 + 24 * q^82 + 60 * q^83 - 36 * q^87 - 120 * q^92 + 40 * q^93 - 12 * q^95 + 44 * q^96 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.965535	+	1.67236i	−0.682736	+	1.18253i	0.291406	+	0.956599i	$0.405877\pi$
$2$	−0.965535	+	1.67236i	−0.682736	+	1.18253i	−0.974143	+	0.225934i	$0.927456\pi$
$3$	1.70969	−	0.277442i	0.987088	−	0.160181i
$3$	1.70969	−	0.277442i	0.987088	−	0.160181i
$4$	−0.864515	−	1.49738i	−0.432257	−	0.748692i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−1.18678	+	3.12708i	−0.484501	+	1.27663i
$7$	−0.855216	+	1.48128i	−0.323241	+	0.559870i	−0.981155	−	0.193223i	$-0.938106\pi$
$7$	−0.855216	+	1.48128i	−0.323241	+	0.559870i	0.657914	+	0.753093i	$0.271439\pi$
$8$	−0.523262			−0.185001
$9$	2.84605	−	0.948678i	0.948684	−	0.316226i
$10$		−	1.93107i		−	0.610658i
$11$	−2.91134	−	1.68086i	−0.877801	−	0.506799i	−0.00786840	−	0.999969i	$-0.502505\pi$
$11$	−2.91134	−	1.68086i	−0.877801	−	0.506799i	−0.869933	+	0.493170i	$0.835838\pi$
$12$	−1.89349	−	2.32020i	−0.546602	−	0.669785i
$13$	−4.16547	+	2.40493i	−1.15529	+	0.667009i	−0.950171	−	0.311728i	$-0.899092\pi$
$13$	−4.16547	+	2.40493i	−1.15529	+	0.667009i	−0.205121	+	0.978737i	$0.565759\pi$
$14$	−1.65148	−	2.86045i	−0.441377	−	0.764487i
$15$	−1.34191	+	1.09511i	−0.346480	+	0.282757i
$16$	2.23426	−	3.86985i	0.558564	−	0.967462i
$17$		−	6.00654i		−	1.45680i	−0.685152	−	0.728400i	$-0.740264\pi$
$17$		−	6.00654i		−	1.45680i	0.685152	−	0.728400i	$-0.259736\pi$
$18$	−1.16144	+	5.67559i	−0.273753	+	1.33775i
$19$	−3.85049	+	2.04298i	−0.883362	+	0.468691i
$19$	−3.85049	+	2.04298i	−0.883362	+	0.468691i
$20$	1.49738	+	0.864515i	0.334825	+	0.193311i
$21$	−1.05118	+	2.76979i	−0.229387	+	0.604418i
$22$	5.62199	−	3.24586i	1.19861	−	0.692020i
$23$	−8.14126	+	4.70036i	−1.69757	+	0.980093i	−0.749515	+	0.661988i	$0.769713\pi$
$23$	−8.14126	+	4.70036i	−1.69757	+	0.980093i	−0.948055	+	0.318105i	$0.896954\pi$
$24$	−0.894614	+	0.145175i	−0.182612	+	0.0296337i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		−	9.28819i		−	1.82156i
$27$	4.60265	−	2.41156i	0.885781	−	0.464104i
$28$	2.95739			0.558894
$29$	0.442996	−	0.767292i	0.0822623	−	0.142482i	−0.821959	−	0.569547i	$-0.807119\pi$
$29$	0.442996	−	0.767292i	0.0822623	−	0.142482i	0.904221	+	0.427064i	$0.140452\pi$
$30$	−0.535760	−	3.30152i	−0.0978160	−	0.602773i
$31$	1.11455	−	0.643489i	0.200180	−	0.115574i	−0.396559	−	0.918009i	$-0.629796\pi$
$31$	1.11455	−	0.643489i	0.200180	−	0.115574i	0.596739	+	0.802435i	$0.296463\pi$
$32$	3.79124	+	6.56663i	0.670204	+	1.16083i
$33$	−5.44381	−	2.06602i	−0.947646	−	0.359647i
$34$	10.0451	+	5.79952i	1.72272	+	0.994610i
$35$		−	1.71043i		−	0.289116i
$36$	−3.88099	−	3.44148i	−0.646831	−	0.573581i
$37$			11.7946i			1.93901i	0.245067	+	0.969506i	$0.421190\pi$
$37$			11.7946i			1.93901i	−0.245067	+	0.969506i	$0.578810\pi$
$38$	0.301191	−	8.41195i	0.0488597	−	1.36460i
$39$	−6.45441	+	5.26736i	−1.03353	+	0.843452i
$40$	0.453159	−	0.261631i	0.0716507	−	0.0413675i
$41$	−0.459908	−	0.796585i	−0.0718256	−	0.124406i	0.827876	−	0.560911i	$-0.189549\pi$
$41$	−0.459908	−	0.796585i	−0.0718256	−	0.124406i	−0.899701	+	0.436506i	$0.856216\pi$
$42$	−3.61712	−	4.43228i	−0.558134	−	0.683915i
$43$	4.14003	−	7.17074i	0.631349	−	1.09353i	−0.355928	−	0.934514i	$-0.615835\pi$
$43$	4.14003	−	7.17074i	0.631349	−	1.09353i	0.987276	−	0.159014i	$-0.0508316\pi$
$44$			5.81252i			0.876270i
$45$	−1.99041	+	2.24461i	−0.296713	+	0.334606i
$46$		−	18.1534i		−	2.67658i
$47$	−7.36162	−	4.25023i	−1.07380	−	0.619960i	−0.144585	−	0.989492i	$-0.546185\pi$
$47$	−7.36162	−	4.25023i	−1.07380	−	0.619960i	−0.929218	+	0.369532i	$0.879518\pi$
$48$	2.74622	−	7.23610i	0.396383	−	1.04444i
$49$	2.03721	+	3.52856i	0.291030	+	0.504079i
$50$	0.965535	+	1.67236i	0.136547	+	0.236507i
$51$	−1.66647	−	10.2693i	−0.233352	−	1.43799i
$52$	7.20222	+	4.15820i	0.998768	+	0.576639i
$53$	−3.83217			−0.526390			−0.263195	−	0.964743i	$-0.584776\pi$
$53$	−3.83217			−0.526390			−0.263195	+	0.964743i	$0.584776\pi$
$54$	−0.411040	+	10.0257i	−0.0559355	+	1.36433i
$55$	3.36172			0.453295
$56$	0.447502	−	0.775097i	0.0598000	−	0.103577i
$57$	−6.01631	+	4.56114i	−0.796880	+	0.604138i
$58$	0.855456	+	1.48169i	0.112327	+	0.194556i
$59$	0.717415	+	1.24260i	0.0933995	+	0.161773i	0.908940	−	0.416928i	$-0.136893\pi$
$59$	0.717415	+	1.24260i	0.0933995	+	0.161773i	−0.815540	+	0.578701i	$0.803560\pi$
$60$	2.79991	+	1.06261i	0.361467	+	0.137183i
$61$	0.254297	−	0.440456i	0.0325594	−	0.0563946i	−0.849287	−	0.527932i	$-0.822968\pi$
$61$	0.254297	−	0.440456i	0.0325594	−	0.0563946i	0.881846	+	0.471538i	$0.156301\pi$
$62$			2.48524i			0.315626i
$63$	−1.02873	+	5.02712i	−0.129608	+	0.633357i
$64$	−5.70528			−0.713160
$65$	2.40493	−	4.16547i	0.298295	−	0.516663i
$66$	8.71131	−	7.10918i	1.07229	−	0.875080i
$67$	−7.51967	+	4.34148i	−0.918674	+	0.530397i	−0.883212	−	0.468974i	$-0.844624\pi$
$67$	−7.51967	+	4.34148i	−0.918674	+	0.530397i	−0.0354620	+	0.999371i	$0.511290\pi$
$68$	−8.99409	+	5.19274i	−1.09069	+	0.629713i
$69$	−12.6149	+	10.2949i	−1.51866	+	1.23936i
$70$	2.86045	+	1.65148i	0.341889	+	0.197390i
$71$	−12.0984			−1.43582			−0.717909	−	0.696137i	$-0.754901\pi$
$71$	−12.0984			−1.43582			−0.717909	+	0.696137i	$0.754901\pi$
$72$	−1.48923	+	0.496408i	−0.175508	+	0.0585022i
$73$	−3.46459			−0.405500			−0.202750	−	0.979231i	$-0.564988\pi$
$73$	−3.46459			−0.405500			−0.202750	+	0.979231i	$0.564988\pi$
$74$	−19.7247	−	11.3880i	−2.29295	−	1.32383i
$75$	0.614571	−	1.61935i	0.0709645	−	0.186987i
$76$	6.38792	+	3.99947i	0.732745	+	0.458770i
$77$	4.97964	−	2.87500i	0.567483	−	0.327636i
$78$	−2.57694	−	15.8799i	−0.291780	−	1.79804i
$79$	6.38865	+	3.68849i	0.718780	+	0.414988i	0.814303	−	0.580440i	$-0.197119\pi$
$79$	6.38865	+	3.68849i	0.718780	+	0.414988i	−0.0955237	+	0.995427i	$0.530453\pi$
$80$			4.46852i			0.499595i
$81$	7.20002	−	5.39997i	0.800002	−	0.599997i
$82$	1.77623			0.196152
$83$	0.0729891	+	0.0421403i	0.00801159	+	0.00462550i	0.504000	−	0.863703i	$-0.331861\pi$
$83$	0.0729891	+	0.0421403i	0.00801159	+	0.00462550i	−0.495989	+	0.868329i	$0.665194\pi$
$84$	5.05620	−	0.820504i	0.551677	−	0.0895243i
$85$	3.00327	+	5.20182i	0.325750	+	0.564216i
$86$	7.99469	+	13.8472i	0.862089	+	1.49318i
$87$	0.544505	−	1.43473i	0.0583771	−	0.153820i
$88$	1.52339	+	0.879532i	0.162394	+	0.0937584i
$89$	14.3029			1.51611			0.758054	−	0.652191i	$-0.226150\pi$
$89$	14.3029			1.51611			0.758054	+	0.652191i	$0.226150\pi$
$90$	−1.83196	−	5.49592i	−0.193106	−	0.579321i
$91$		−	8.22695i		−	0.862418i
$92$	14.0765	+	8.12706i	1.46757	+	0.847305i
$93$	1.72701	−	1.40939i	0.179082	−	0.146147i
$94$	14.2158	−	8.20750i	1.46625	−	0.846538i
$95$	2.31313	−	3.69451i	0.237322	−	0.379049i
$96$	8.30370	+	10.1750i	0.847493	+	1.03848i
$97$	1.88374	+	1.08758i	0.191265	+	0.110427i	0.592575	−	0.805516i	$-0.298112\pi$
$97$	1.88374	+	1.08758i	0.191265	+	0.110427i	−0.401310	+	0.915942i	$0.631445\pi$
$98$	−7.86800			−0.794788
$99$	−9.88041	−	2.02190i	−0.993019	−	0.203208i
$100$	−1.72903			−0.172903
$101$	−3.36834	−	1.94471i	−0.335163	−	0.193506i	0.322968	−	0.946410i	$-0.395319\pi$
$101$	−3.36834	−	1.94471i	−0.335163	−	0.193506i	−0.658131	+	0.752904i	$0.728653\pi$
$102$	18.7829	+	7.12844i	1.85979	+	0.705820i
$103$	−4.63258	+	2.67462i	−0.456462	+	0.263538i	−0.710555	−	0.703641i	$-0.751556\pi$
$103$	−4.63258	+	2.67462i	−0.456462	+	0.263538i	0.254093	+	0.967180i	$0.418223\pi$
$104$	2.17963	−	1.25841i	0.213731	−	0.123397i
$105$	−0.474546	−	2.92430i	−0.0463109	−	0.285382i
$106$	3.70010	−	6.40876i	0.359385	−	0.622473i
$107$	5.59545			0.540932			0.270466	−	0.962729i	$-0.412822\pi$
$107$	5.59545			0.540932			0.270466	+	0.962729i	$0.412822\pi$
$108$	−7.59009	−	4.80711i	−0.730356	−	0.462564i
$109$		−	16.9857i		−	1.62694i	−0.581609	−	0.813468i	$-0.697577\pi$
$109$		−	16.9857i		−	1.62694i	0.581609	−	0.813468i	$-0.302423\pi$
$110$	−3.24586	+	5.62199i	−0.309481	+	0.536036i
$111$	3.27231	+	20.1650i	0.310594	+	1.91397i
$112$	3.82154	+	6.61911i	0.361102	+	0.625447i
$113$	6.15379	+	10.6587i	0.578899	+	1.00268i	0.995606	+	0.0936421i	$0.0298509\pi$
$113$	6.15379	+	10.6587i	0.578899	+	1.00268i	−0.416707	+	0.909041i	$0.636816\pi$
$114$	−1.81889	−	14.4653i	−0.170354	−	1.35480i
$115$	4.70036	−	8.14126i	0.438311	−	0.759176i
$116$	−1.53191			−0.142234
$117$	−9.57363	+	10.7963i	−0.885082	+	0.998114i
$118$	−2.77076			−0.255069
$119$	8.89735	+	5.13689i	0.815619	+	0.470898i
$120$	0.702171	−	0.573033i	0.0640992	−	0.0523105i
$121$	0.150590	+	0.260829i	0.0136900	+	0.0237117i
$122$	0.491065	+	0.850550i	0.0444590	+	0.0770052i
$123$	−1.00731	−	1.23431i	−0.0908257	−	0.111294i
$124$	−1.92710	−	1.11261i	−0.173059	−	0.0999154i
$125$			1.00000i			0.0894427i
$126$	−7.41385	−	6.57426i	−0.660478	−	0.585682i
$127$		−	3.69364i		−	0.327757i	−0.986480	−	0.163879i	$-0.947599\pi$
$127$		−	3.69364i		−	0.327757i	0.986480	−	0.163879i	$-0.0524006\pi$
$128$	−2.07384	+	3.59200i	−0.183303	+	0.317491i
$129$	5.08868	−	13.4083i	0.448034	−	1.18054i
$130$	4.64409	+	8.04381i	0.407314	+	0.705489i
$131$	2.43807	−	1.40762i	0.213015	−	0.122984i	−0.389697	−	0.920943i	$-0.627420\pi$
$131$	2.43807	−	1.40762i	0.213015	−	0.122984i	0.602712	+	0.797959i	$0.294087\pi$
$132$	1.61264	+	9.93758i	0.140362	+	0.864955i
$133$	0.266778	−	7.45082i	0.0231326	−	0.646068i
$134$		−	16.7674i		−	1.44848i
$135$	−2.78023	+	4.38979i	−0.239284	+	0.377813i
$136$			3.14300i			0.269510i
$137$	−0.127922	−	0.0738559i	−0.0109291	−	0.00630994i	0.494525	−	0.869163i	$-0.335342\pi$
$137$	−0.127922	−	0.0738559i	−0.0109291	−	0.00630994i	−0.505455	+	0.862853i	$0.668675\pi$
$138$	−5.03653	−	31.0367i	−0.428738	−	2.64202i
$139$	7.92463	+	13.7259i	0.672158	+	1.16421i	0.977291	+	0.211902i	$0.0679658\pi$
$139$	7.92463	+	13.7259i	0.672158	+	1.16421i	−0.305133	+	0.952310i	$0.598701\pi$
$140$	−2.56117	+	1.47869i	−0.216459	+	0.124972i
$141$	−13.7653	−	5.22414i	−1.15924	−	0.439952i
$142$	11.6814	−	20.2328i	0.980285	−	1.69790i
$143$	16.1694			1.35216
$144$	2.68757	−	13.1334i	0.223964	−	1.09445i
$145$			0.885992i			0.0735776i
$146$	3.34519	−	5.79403i	0.276850	−	0.479517i
$147$	4.46196	+	5.46751i	0.368017	+	0.450953i
$148$	17.6610	−	10.1966i	1.45172	−	0.838152i
$149$	−16.2898	+	9.40494i	−1.33452	+	0.770483i	−0.985988	−	0.166816i	$-0.946651\pi$
$149$	−16.2898	+	9.40494i	−1.33452	+	0.770483i	−0.348527	+	0.937299i	$0.613318\pi$
$150$	2.11474	+	2.59132i	0.172668	+	0.211581i
$151$	−14.8368	−	8.56605i	−1.20740	−	0.697095i	−0.245213	−	0.969469i	$-0.578858\pi$
$151$	−14.8368	−	8.56605i	−1.20740	−	0.697095i	−0.962191	+	0.272374i	$0.912191\pi$
$152$	2.01481	−	1.06901i	0.163423	−	0.0867085i
$153$	−5.69827	−	17.0949i	−0.460678	−	1.38204i
$154$			11.1036i			0.894757i
$155$	−0.643489	+	1.11455i	−0.0516862	+	0.0895232i
$156$	13.4672	+	5.11102i	1.07824	+	0.409209i
$157$	8.00841	+	13.8710i	0.639140	+	1.10702i	0.985622	+	0.168967i	$0.0540431\pi$
$157$	8.00841	+	13.8710i	0.639140	+	1.10702i	−0.346481	+	0.938057i	$0.612624\pi$
$158$	−12.3369	+	7.12273i	−0.981474	+	0.566654i
$159$	−6.55181	+	1.06321i	−0.519593	+	0.0843178i
$160$	−6.56663	−	3.79124i	−0.519138	−	0.299724i
$161$		−	16.0793i		−	1.26723i
$162$	2.07880	+	17.2549i	0.163326	+	1.35567i
$163$	24.6417			1.93009			0.965043	−	0.262093i	$-0.0844128\pi$
$163$	24.6417			1.93009			0.965043	+	0.262093i	$0.0844128\pi$
$164$	−0.795195	+	1.37732i	−0.0620943	+	0.107551i
$165$	5.74749	−	0.932684i	0.447441	−	0.0726093i
$166$	−0.140947	+	0.0813758i	−0.0109396	+	0.00631599i
$167$	1.10268	+	1.90989i	0.0853276	+	0.147792i	0.905531	−	0.424281i	$-0.139473\pi$
$167$	1.10268	+	1.90989i	0.0853276	+	0.147792i	−0.820203	+	0.572072i	$0.806140\pi$
$168$	0.550044	−	1.44933i	0.0424368	−	0.111818i
$169$	5.06741	−	8.77701i	0.389801	−	0.675155i
$170$	−11.5990			−0.889606
$171$	−9.02055	+	9.46729i	−0.689819	+	0.723982i
$172$	−14.3165			−1.09162
$173$	−8.49069	+	14.7063i	−0.645535	+	1.11810i	0.338643	+	0.940915i	$0.390032\pi$
$173$	−8.49069	+	14.7063i	−0.645535	+	1.11810i	−0.984178	+	0.177184i	$0.943301\pi$
$174$	1.87365	+	2.29589i	0.142041	+	0.174051i
$175$	0.855216	+	1.48128i	0.0646482	+	0.111974i
$176$	−13.0094	+	7.51096i	−0.980617	+	0.566160i
$177$	1.57130	+	1.92541i	0.118106	+	0.144723i
$178$	−13.8100	+	23.9196i	−1.03510	+	1.79285i
$179$	−15.9807			−1.19445			−0.597225	−	0.802074i	$-0.703730\pi$
$179$	−15.9807			−1.19445			−0.597225	+	0.802074i	$0.703730\pi$
$180$	5.08178	+	1.03992i	0.378773	+	0.0775110i
$181$		−	19.5348i		−	1.45201i	−0.687689	−	0.726005i	$-0.741375\pi$
$181$		−	19.5348i		−	1.45201i	0.687689	−	0.726005i	$-0.258625\pi$
$182$	13.7584	+	7.94340i	1.01984	+	0.588804i
$183$	0.312567	−	0.823593i	0.0231056	−	0.0608818i
$184$	4.26002	−	2.45952i	0.314053	−	0.181318i
$185$	−5.89728	−	10.2144i	−0.433576	−	0.750976i
$186$	0.689511	+	4.24898i	0.0505574	+	0.311551i
$187$	−10.0962	+	17.4871i	−0.738304	+	1.27878i
$188$			14.6976i			1.07193i
$189$	−0.364076	+	8.88020i	−0.0264826	+	0.645940i
$190$	3.94513	+	7.43556i	0.286210	+	0.539432i
$191$	18.5900	+	10.7330i	1.34513	+	0.776609i	0.987555	−	0.157276i	$-0.0502712\pi$
$191$	18.5900	+	10.7330i	1.34513	+	0.776609i	0.357572	+	0.933885i	$0.383605\pi$
$192$	−9.75424	+	1.58289i	−0.703952	+	0.114235i
$193$	−15.0158	+	8.66939i	−1.08086	+	0.624036i	−0.931129	−	0.364690i	$-0.881175\pi$
$193$	−15.0158	+	8.66939i	−1.08086	+	0.624036i	−0.149733	+	0.988726i	$0.547842\pi$
$194$	−3.63763	+	2.10019i	−0.261167	+	0.150785i
$195$	2.95600	−	7.78887i	0.211684	−	0.557773i
$196$	3.52240	−	6.10098i	0.251600	−	0.435784i
$197$			19.3741i			1.38035i	0.723644	+	0.690173i	$0.242466\pi$
$197$			19.3741i			1.38035i	−0.723644	+	0.690173i	$0.757534\pi$
$198$	12.9212	−	14.5713i	0.918270	−	1.03554i
$199$	−23.4887			−1.66507			−0.832535	−	0.553973i	$-0.813111\pi$
$199$	−23.4887			−1.66507			−0.832535	+	0.553973i	$0.813111\pi$
$200$	−0.261631	+	0.453159i	−0.0185001	+	0.0320432i
$201$	−11.6518	+	9.50885i	−0.821852	+	0.670702i
$202$	6.50450	−	3.75538i	0.457655	−	0.264227i
$203$	0.757714	+	1.31240i	0.0531811	+	0.0921124i
$204$	−13.9364	+	11.3733i	−0.975742	+	0.796290i
$205$	0.796585	+	0.459908i	0.0556359	+	0.0321214i
$206$		−	10.3298i		−	0.719709i
$207$	−18.7113	+	21.1009i	−1.30053	+	1.46661i
$208$			21.4930i			1.49027i
$209$	14.6440	+	0.524332i	1.01295	+	0.0362688i
$210$	5.34866	+	2.02990i	0.369093	+	0.140077i
$211$	−12.4228	+	7.17230i	−0.855220	+	0.493761i	−0.862409	−	0.506213i	$-0.831045\pi$
$211$	−12.4228	+	7.17230i	−0.855220	+	0.493761i	0.00718893	+	0.999974i	$0.497712\pi$
$212$	3.31297	+	5.73823i	0.227536	+	0.394104i
$213$	−20.6845	+	3.35661i	−1.41728	+	0.229991i
$214$	−5.40260	+	9.35758i	−0.369314	+	0.639671i
$215$			8.28006i			0.564695i
$216$	−2.40839	+	1.26188i	−0.163870	+	0.0858599i
$217$			2.20129i			0.149433i
$218$	28.4062	+	16.4003i	1.92391	+	1.11077i
$219$	−5.92337	+	0.961225i	−0.400264	+	0.0649535i
$220$	−2.90626	−	5.03379i	−0.195940	−	0.339378i
$221$	14.4453	+	25.0200i	0.971698	+	1.68303i
$222$	−36.8825	−	13.9975i	−2.47539	−	0.939453i
$223$	19.3801	+	11.1891i	1.29778	+	0.749276i	0.980021	−	0.198894i	$-0.0637349\pi$
$223$	19.3801	+	11.1891i	1.29778	+	0.749276i	0.317763	+	0.948170i	$0.397068\pi$
$224$	−12.9693			−0.866550
$225$	0.601446	−	2.93909i	0.0400964	−	0.195939i
$226$	−23.7668			−1.58094
$227$	−5.69015	+	9.85562i	−0.377668	+	0.654141i	−0.990723	−	0.135900i	$-0.956607\pi$
$227$	−5.69015	+	9.85562i	−0.377668	+	0.654141i	0.613054	+	0.790041i	$0.289941\pi$
$228$	12.0310	+	5.06555i	0.796770	+	0.335475i
$229$	4.34386	+	7.52379i	0.287050	+	0.497186i	0.973104	−	0.230365i	$-0.0739919\pi$
$229$	4.34386	+	7.52379i	0.287050	+	0.497186i	−0.686054	+	0.727551i	$0.740659\pi$
$230$	9.07672	+	15.7213i	0.598501	+	1.03663i
$231$	7.71598	−	6.29691i	0.507674	−	0.414306i
$232$	−0.231803	+	0.401495i	−0.0152186	+	0.0263594i
$233$		−	11.5577i		−	0.757170i	−0.925567	−	0.378585i	$-0.876411\pi$
$233$		−	11.5577i		−	0.757170i	0.925567	−	0.378585i	$-0.123589\pi$
$234$	−8.81150	−	26.4347i	−0.576026	−	1.72809i
$235$	8.50047			0.554509
$236$	1.24043	−	2.14849i	0.0807453	−	0.139855i
$237$	11.9459	+	4.53368i	0.775972	+	0.294494i
$238$	−17.1814	+	9.91969i	−1.11370	+	0.642998i
$239$	12.6078	−	7.27913i	0.815532	−	0.470848i	−0.0333410	−	0.999444i	$-0.510615\pi$
$239$	12.6078	−	7.27913i	0.815532	−	0.470848i	0.848873	+	0.528596i	$0.177281\pi$
$240$	1.23975	+	7.63976i	0.0800258	+	0.493144i
$241$	−4.92431	−	2.84305i	−0.317203	−	0.183137i	0.332942	−	0.942947i	$-0.391959\pi$
$241$	−4.92431	−	2.84305i	−0.317203	−	0.183137i	−0.650145	+	0.759810i	$0.725292\pi$
$242$	−0.581598			−0.0373865
$243$	10.8116	−	11.2298i	0.693564	−	0.720395i
$244$	−0.879375			−0.0562962
$245$	−3.52856	−	2.03721i	−0.225431	−	0.130153i
$246$	3.03680	−	0.492801i	0.193619	−	0.0314199i
$247$	11.1258	−	17.7701i	0.707920	−	1.13069i
$248$	−0.583205	+	0.336713i	−0.0370335	+	0.0213813i
$249$	0.136480	+	0.0517964i	0.00864906	+	0.00328246i
$250$	−1.67236	−	0.965535i	−0.105769	−	0.0610658i
$251$			7.93249i			0.500694i	0.968156	+	0.250347i	$0.0805447\pi$
$251$			7.93249i			0.500694i	−0.968156	+	0.250347i	$0.919455\pi$
$252$	8.41687	−	2.80561i	0.530213	−	0.176737i
$253$	31.6026			1.98684
$254$	6.17708	+	3.56634i	0.387584	+	0.223772i
$255$	6.57785	+	8.06024i	0.411921	+	0.504752i
$256$	−9.71001	−	16.8182i	−0.606876	−	1.05114i
$257$	2.98451	+	5.16932i	0.186168	+	0.322453i	0.943970	−	0.330032i	$-0.107060\pi$
$257$	2.98451	+	5.16932i	0.186168	+	0.322453i	−0.757801	+	0.652485i	$0.773726\pi$
$258$	17.5102	+	21.4563i	1.09014	+	1.33581i
$259$	−17.4710	−	10.0869i	−1.08559	−	0.626768i
$260$	−8.31640			−0.515761
$261$	0.532877	−	2.60401i	0.0329842	−	0.161184i
$262$			5.43642i			0.335863i
$263$	−12.8939	−	7.44429i	−0.795071	−	0.459034i	0.0466739	−	0.998910i	$-0.485138\pi$
$263$	−12.8939	−	7.44429i	−0.795071	−	0.459034i	−0.841745	+	0.539876i	$0.818471\pi$
$264$	2.84854	+	1.08107i	0.175316	+	0.0665352i
$265$	3.31876	−	1.91609i	0.203870	−	0.117704i
$266$	12.2028	+	7.64018i	0.748204	+	0.468449i
$267$	24.4535	−	3.96824i	1.49653	−	0.242852i
$268$	13.0017	+	7.50655i	0.794207	+	0.458536i
$269$	8.62693			0.525993			0.262997	−	0.964797i	$-0.415289\pi$
$269$	8.62693			0.525993			0.262997	+	0.964797i	$0.415289\pi$
$270$	−4.65688	−	8.88804i	−0.283409	−	0.540909i
$271$	−29.6880			−1.80342			−0.901708	−	0.432345i	$-0.857686\pi$
$271$	−29.6880			−1.80342			−0.901708	+	0.432345i	$0.857686\pi$
$272$	−23.2444	−	13.4202i	−1.40940	−	0.813717i
$273$	−2.28250	−	14.0655i	−0.138143	−	0.851283i
$274$	0.247027	−	0.142621i	0.0149234	−	0.00861605i
$275$	−2.91134	+	1.68086i	−0.175560	+	0.101360i
$276$	26.3212	+	9.98931i	1.58435	+	0.601286i
$277$	−8.18381	+	14.1748i	−0.491717	+	0.851679i	−0.999955	−	0.00953788i	$-0.996964\pi$
$277$	−8.18381	+	14.1748i	−0.491717	+	0.851679i	0.508237	+	0.861217i	$0.330297\pi$
$278$	−30.6060			−1.83563
$279$	2.56162	−	2.88876i	0.153360	−	0.172945i
$280$			0.895005i			0.0534868i
$281$	−6.90667	+	11.9627i	−0.412017	+	0.713635i	−0.995110	−	0.0987704i	$-0.968509\pi$
$281$	−6.90667	+	11.9627i	−0.412017	+	0.713635i	0.583093	+	0.812406i	$0.301842\pi$
$282$	22.0274	−	17.9763i	1.31172	−	1.07047i
$283$	−5.30862	−	9.19480i	−0.315565	−	0.546574i	0.663993	−	0.747739i	$-0.268861\pi$
$283$	−5.30862	−	9.19480i	−0.315565	−	0.546574i	−0.979557	+	0.201165i	$0.935527\pi$
$284$	10.4593	+	18.1160i	0.620643	+	1.07498i
$285$	2.92971	−	6.95822i	0.173541	−	0.412169i
$286$	−15.6122	+	27.0410i	−0.923166	+	1.59897i
$287$	1.57328			0.0928680
$288$	17.0197	+	15.0923i	1.00290	+	0.889322i
$289$	−19.0785			−1.12227
$290$	−1.48169	−	0.855456i	−0.0870080	−	0.0502341i
$291$	3.52234	+	1.33679i	0.206483	+	0.0783638i
$292$	2.99519	+	5.18783i	0.175280	+	0.303595i
$293$	−10.8245	−	18.7487i	−0.632376	−	1.09531i	−0.987065	−	0.160323i	$-0.948746\pi$
$293$	−10.8245	−	18.7487i	−0.632376	−	1.09531i	0.354688	−	0.934985i	$-0.384587\pi$
$294$	−13.4518	+	2.18291i	−0.784525	+	0.127310i
$295$	−1.24260	−	0.717415i	−0.0723469	−	0.0417695i
$296$		−	6.17165i		−	0.358720i
$297$	−17.4534	−	0.715564i	−1.01275	−	0.0415212i
$298$		−	36.3232i		−	2.10415i
$299$	22.6081	−	39.1584i	1.30746	−	2.26459i
$300$	−2.95610	+	0.479706i	−0.170670	+	0.0276958i
$301$	7.08124	+	12.2651i	0.408156	+	0.706946i
$302$	28.6510	−	16.5416i	1.64868	−	0.951864i
$303$	−6.29835	−	2.39033i	−0.361831	−	0.137321i
$304$	−0.696960	+	19.4653i	−0.0399734	+	1.11641i
$305$			0.508594i			0.0291220i
$306$	34.0907	+	6.97621i	1.94883	+	0.398803i
$307$			7.36315i			0.420237i	0.977676	+	0.210119i	$0.0673851\pi$
$307$			7.36315i			0.420237i	−0.977676	+	0.210119i	$0.932615\pi$
$308$	−8.60995	−	4.97096i	−0.490597	−	0.283247i
$309$	−7.17821	+	5.85804i	−0.408354	+	0.333252i
$310$	−1.24262	−	2.15228i	−0.0705761	−	0.122241i
$311$	17.9746	−	10.3776i	1.01924	−	0.588461i	0.105359	−	0.994434i	$-0.466401\pi$
$311$	17.9746	−	10.3776i	1.01924	−	0.588461i	0.913885	+	0.405974i	$0.133068\pi$
$312$	3.37735	−	2.75621i	0.191205	−	0.156040i
$313$	1.53005	−	2.65012i	0.0864835	−	0.149794i	−0.819539	−	0.573024i	$-0.805770\pi$
$313$	1.53005	−	2.65012i	0.0864835	−	0.149794i	0.906022	+	0.423230i	$0.139104\pi$
$314$	−30.9296			−1.74546
$315$	−1.62265	−	4.86798i	−0.0914259	−	0.274279i
$316$		−	12.7550i		−	0.717526i
$317$	4.28835	−	7.42764i	0.240858	−	0.417178i	−0.720101	−	0.693869i	$-0.755905\pi$
$317$	4.28835	−	7.42764i	0.240858	−	0.417178i	0.960959	+	0.276691i	$0.0892380\pi$
$318$	4.54794	−	11.9835i	0.255036	−	0.672003i
$319$	−2.57942	+	1.48923i	−0.144420	+	0.0833809i
$320$	4.94092	−	2.85264i	0.276206	−	0.159468i
$321$	9.56646	−	1.55241i	0.533948	−	0.0866473i
$322$	26.8903	+	15.5251i	1.49854	+	0.865180i
$323$	12.2712	+	23.1281i	0.682790	+	1.28688i
$324$	−14.3104	−	6.11283i	−0.795020	−	0.339602i
$325$			4.80987i			0.266803i
$326$	−23.7924	+	41.2096i	−1.31774	+	2.28239i
$327$	−4.71255	−	29.0402i	−0.260605	−	1.60593i
$328$	0.240653	+	0.416823i	0.0132878	+	0.0230152i
$329$	12.5915	−	7.26973i	0.694194	−	0.400793i
$330$	−3.98962	+	10.5124i	−0.219621	+	0.578688i
$331$	−5.88287	−	3.39647i	−0.323352	−	0.186687i	0.329534	−	0.944144i	$-0.393108\pi$
$331$	−5.88287	−	3.39647i	−0.323352	−	0.186687i	−0.652885	+	0.757457i	$0.726442\pi$
$332$		−	0.145724i		−	0.00799762i
$333$	11.1892	+	33.5679i	0.613166	+	1.83951i
$334$	−4.25869			−0.233025
$335$	4.34148	−	7.51967i	0.237201	−	0.410843i
$336$	8.37006	+	10.2563i	0.456624	+	0.559529i
$337$	−13.9983	+	8.08191i	−0.762535	+	0.440250i	−0.830205	−	0.557458i	$-0.811777\pi$
$337$	−13.9983	+	8.08191i	−0.762535	+	0.440250i	0.0676704	+	0.997708i	$0.478443\pi$
$338$	9.78552	+	16.9490i	0.532262	+	0.921905i
$339$	13.4782	+	16.5157i	0.732036	+	0.897007i
$340$	5.19274	−	8.99409i	0.281616	−	0.487773i
$341$	−4.32646			−0.234291
$342$	−7.12302	−	24.2266i	−0.385169	−	1.31002i
$343$	−18.9420			−1.02277
$344$	−2.16632	+	3.75218i	−0.116800	+	0.202304i
$345$	5.77741	−	15.2231i	0.311045	−	0.819583i
$346$	−16.3961	−	28.3989i	−0.881460	−	1.52673i
$347$	2.38950	−	1.37958i	0.128275	−	0.0740598i	−0.434489	−	0.900677i	$-0.643071\pi$
$347$	2.38950	−	1.37958i	0.128275	−	0.0740598i	0.562765	+	0.826617i	$0.309738\pi$
$348$	−2.61908	+	0.425016i	−0.140397	+	0.0227832i
$349$	5.14353	−	8.90885i	0.275327	−	0.476880i	−0.694891	−	0.719115i	$-0.744547\pi$
$349$	5.14353	−	8.90885i	0.275327	−	0.476880i	0.970217	+	0.242235i	$0.0778806\pi$
$350$	−3.30296			−0.176551
$351$	−13.3726	+	21.1143i	−0.713774	+	1.12700i
$352$		−	25.4902i		−	1.35863i
$353$	−7.62665	−	4.40325i	−0.405926	−	0.234361i	0.283112	−	0.959087i	$-0.408633\pi$
$353$	−7.62665	−	4.40325i	−0.405926	−	0.234361i	−0.689038	+	0.724726i	$0.741967\pi$
$354$	−4.73712	+	0.768725i	−0.251775	+	0.0408573i
$355$	10.4775	−	6.04921i	0.556090	−	0.321059i
$356$	−12.3651	−	21.4170i	−0.655349	−	1.13510i
$357$	16.6369	+	6.31396i	0.880516	+	0.334170i
$358$	15.4299	−	26.7253i	0.815494	−	1.41248i
$359$		−	19.2603i		−	1.01652i	−0.861204	−	0.508260i	$-0.830289\pi$
$359$		−	19.2603i		−	1.01652i	0.861204	−	0.508260i	$-0.169711\pi$
$360$	1.04151	−	1.17452i	0.0548923	−	0.0619025i
$361$	10.6525	−	15.7329i	0.560657	−	0.828048i
$362$	32.6691	+	18.8615i	1.71705	+	0.991340i
$363$	0.329826	+	0.404155i	0.0173114	+	0.0212126i
$364$	−12.3189	+	7.11232i	−0.645686	+	0.372787i
$365$	3.00043	−	1.73230i	0.157049	−	0.0906726i
$366$	1.07555	+	1.31793i	0.0562197	+	0.0688894i
$367$	8.14102	−	14.1007i	0.424958	−	0.736049i	−0.571459	−	0.820631i	$-0.693622\pi$
$367$	8.14102	−	14.1007i	0.424958	−	0.736049i	0.996417	+	0.0845821i	$0.0269555\pi$
$368$			42.0073i			2.18978i
$369$	−2.06463	−	1.83082i	−0.107480	−	0.0953085i
$370$	22.7761			1.18407
$371$	3.27734	−	5.67651i	0.170151	−	0.294710i
$372$	−3.60342	−	1.36756i	−0.186829	−	0.0709045i
$373$	11.7058	−	6.75836i	0.606104	−	0.349935i	−0.165335	−	0.986237i	$-0.552870\pi$
$373$	11.7058	−	6.75836i	0.606104	−	0.349935i	0.771439	+	0.636303i	$0.219537\pi$
$374$	−19.4964	−	33.7687i	−1.00813	−	1.74614i
$375$	0.277442	+	1.70969i	0.0143271	+	0.0882878i
$376$	3.85206	+	2.22399i	0.198655	+	0.114693i
$377$			4.26150i			0.219479i
$378$	−14.4993	−	9.18301i	−0.745765	−	0.472323i
$379$			34.0873i			1.75095i	0.483265	+	0.875474i	$0.339451\pi$
$379$			34.0873i			1.75095i	−0.483265	+	0.875474i	$0.660549\pi$
$380$	−7.53184	−	0.269679i	−0.386375	−	0.0138342i
$381$	−1.02477	−	6.31496i	−0.0525006	−	0.323525i
$382$	−35.8986	+	20.7261i	−1.83673	+	1.06044i
$383$	−12.6610	−	21.9295i	−0.646947	−	1.12054i	−0.983848	−	0.179005i	$-0.942712\pi$
$383$	−12.6610	−	21.9295i	−0.646947	−	1.12054i	0.336901	−	0.941540i	$-0.390621\pi$
$384$	−2.54904	+	6.71655i	−0.130080	+	0.342753i
$385$	−2.87500	+	4.97964i	−0.146523	+	0.253786i
$386$		−	33.4824i		−	1.70421i
$387$	4.98001	−	24.3359i	0.253148	−	1.23706i
$388$		−	3.76091i		−	0.190931i
$389$	22.6370	+	13.0695i	1.14774	+	0.662649i	0.948336	−	0.317268i	$-0.102765\pi$
$389$	22.6370	+	13.0695i	1.14774	+	0.662649i	0.199406	+	0.979917i	$0.436099\pi$
$390$	10.1716	+	12.4639i	0.515061	+	0.631135i
$391$	28.2329	+	48.9008i	1.42780	+	2.47302i
$392$	−1.06600	−	1.84636i	−0.0538410	−	0.0932553i
$393$	3.77780	−	3.08301i	0.190565	−	0.155517i
$394$	−32.4004	−	18.7064i	−1.63231	−	0.942413i
$395$	−7.37698			−0.371176
$396$	5.51421	+	16.5427i	0.277099	+	0.831303i
$397$	−1.61422			−0.0810155			−0.0405077	−	0.999179i	$-0.512898\pi$
$397$	−1.61422			−0.0810155			−0.0405077	+	0.999179i	$0.512898\pi$
$398$	22.6792	−	39.2814i	1.13680	−	1.96900i
$399$	−1.61107	−	12.8126i	−0.0806542	−	0.641431i
$400$	−2.23426	−	3.86985i	−0.111713	−	0.193492i
$401$	−2.62279	−	4.54280i	−0.130976	−	0.226857i	0.793077	−	0.609121i	$-0.208478\pi$
$401$	−2.62279	−	4.54280i	−0.130976	−	0.226857i	−0.924053	+	0.382264i	$0.875144\pi$
$402$	−4.65199	−	28.6670i	−0.232020	−	1.42978i
$403$	−3.09509	+	5.36086i	−0.154178	+	0.267043i
$404$			6.72494i			0.334578i
$405$	−3.53541	+	8.27652i	−0.175676	+	0.411264i
$406$	−2.92640			−0.145235
$407$	19.8250	−	34.3379i	0.982689	−	1.70207i
$408$	0.872000	+	5.37354i	0.0431704	+	0.266030i
$409$	15.7868	−	9.11452i	0.780608	−	0.450684i	−0.0560380	−	0.998429i	$-0.517847\pi$
$409$	15.7868	−	9.11452i	0.780608	−	0.450684i	0.836646	+	0.547745i	$0.184513\pi$
$410$	−1.53826	+	0.888115i	−0.0759693	+	0.0438609i
$411$	−0.239198	−	0.0907794i	−0.0117987	−	0.00447782i
$412$	8.00988	+	4.62450i	0.394618	+	0.227833i
$413$	−2.45418			−0.120762
$414$	−17.2218	−	51.6656i	−0.846404	−	2.53923i
$415$	−0.0842805			−0.00413717
$416$	−31.5846	−	18.2354i	−1.54856	−	0.894063i
$417$	17.3568	+	21.2683i	0.849964	+	1.04151i
$418$	−15.0162	+	23.9838i	−0.734466	+	1.17308i
$419$	−14.6820	+	8.47665i	−0.717262	+	0.414112i	−0.813744	−	0.581223i	$-0.802574\pi$
$419$	−14.6820	+	8.47665i	−0.717262	+	0.414112i	0.0964818	+	0.995335i	$0.469241\pi$
$420$	−3.96855	+	3.23868i	−0.193645	+	0.158031i
$421$	12.2171	+	7.05357i	0.595427	+	0.343770i	0.767241	−	0.641359i	$-0.221629\pi$
$421$	12.2171	+	7.05357i	0.595427	+	0.343770i	−0.171813	+	0.985130i	$0.554963\pi$
$422$		−	27.7004i		−	1.34843i
$423$	−24.9837	−	5.11258i	−1.21475	−	0.248582i
$424$	2.00523			0.0973827
$425$	−5.20182	−	3.00327i	−0.252325	−	0.145680i
$426$	14.3581	−	37.8327i	0.695654	−	1.83300i
$427$	0.434958	+	0.753369i	0.0210491	+	0.0364581i
$428$	−4.83735	−	8.37853i	−0.233822	−	0.404992i
$429$	27.6447	−	4.48608i	1.33470	−	0.216590i
$430$	−13.8472	−	7.99469i	−0.667771	−	0.385538i
$431$	31.5854			1.52141			0.760707	−	0.649096i	$-0.224853\pi$
$431$	31.5854			1.52141			0.760707	+	0.649096i	$0.224853\pi$
$432$	0.951152	−	23.1996i	0.0457623	−	1.11619i
$433$		−	29.3764i		−	1.41174i	−0.708342	−	0.705869i	$-0.750557\pi$
$433$		−	29.3764i		−	1.41174i	0.708342	−	0.705869i	$-0.249443\pi$
$434$	−3.68133	−	2.12542i	−0.176710	−	0.102023i
$435$	0.245812	+	1.51477i	0.0117858	+	0.0726276i
$436$	−25.4341	+	14.6844i	−1.21807	+	0.703255i
$437$	21.7451	−	34.7311i	1.04021	−	1.66141i
$438$	4.11171	−	10.8341i	0.196465	−	0.517672i
$439$	−6.23386	−	3.59912i	−0.297526	−	0.171777i	0.343805	−	0.939041i	$-0.388284\pi$
$439$	−6.23386	−	3.59912i	−0.297526	−	0.171777i	−0.641331	+	0.767264i	$0.721617\pi$
$440$	−1.75906			−0.0838601
$441$	9.14547	+	8.10979i	0.435499	+	0.386181i
$442$	−55.7899			−2.65365
$443$	−11.5235	−	6.65309i	−0.547497	−	0.316098i	0.200615	−	0.979670i	$-0.435706\pi$
$443$	−11.5235	−	6.65309i	−0.547497	−	0.316098i	−0.748112	+	0.663572i	$0.769039\pi$
$444$	27.3657	−	22.3328i	1.29872	−	1.05987i
$445$	−12.3867	+	7.15147i	−0.587186	+	0.339012i
$446$	−37.4242	+	21.6069i	−1.77209	+	1.02312i
$447$	−25.2412	+	20.5990i	−1.19387	+	0.974298i
$448$	4.87925	−	8.45111i	0.230523	−	0.399277i
$449$	25.1176			1.18537			0.592687	−	0.805433i	$-0.298067\pi$
$449$	25.1176			1.18537			0.592687	+	0.805433i	$0.298067\pi$
$450$	4.33449	+	3.84363i	0.204330	+	0.181190i
$451$			3.09217i			0.145605i
$452$	10.6401	−	18.4292i	0.500467	−	0.866835i
$453$	−27.7429	−	10.5289i	−1.30348	−	0.494690i
$454$	−10.9881	−	19.0319i	−0.515696	−	0.893211i
$455$	4.11347	+	7.12475i	0.192843	+	0.334013i
$456$	3.14811	−	2.38667i	0.147424	−	0.111766i
$457$	4.96093	−	8.59258i	0.232062	−	0.401944i	−0.726353	−	0.687322i	$-0.758786\pi$
$457$	4.96093	−	8.59258i	0.232062	−	0.401944i	0.958415	+	0.285379i	$0.0921193\pi$
$458$	−16.7766			−0.783919
$459$	−14.4851	−	27.6460i	−0.676107	−	1.29041i
$460$	−16.2541			−0.757852
$461$	0.689808	+	0.398261i	0.0321276	+	0.0185489i	0.515978	−	0.856602i	$-0.327429\pi$
$461$	0.689808	+	0.398261i	0.0321276	+	0.0185489i	−0.483850	+	0.875151i	$0.660762\pi$
$462$	3.08062	+	18.9837i	0.143323	+	0.883203i
$463$	−1.09893	−	1.90340i	−0.0510715	−	0.0884584i	0.839359	−	0.543577i	$-0.182930\pi$
$463$	−1.09893	−	1.90340i	−0.0510715	−	0.0884584i	−0.890431	+	0.455118i	$0.849597\pi$
$464$	−1.97953	−	3.42865i	−0.0918976	−	0.159171i
$465$	−0.790939	+	2.08407i	−0.0366789	+	0.0966464i
$466$	19.3286	+	11.1594i	0.895379	+	0.516947i
$467$			32.5093i			1.50435i	0.658963	+	0.752175i	$0.270995\pi$
$467$			32.5093i			1.50435i	−0.658963	+	0.752175i	$0.729005\pi$
$468$	24.4427	+	5.00187i	1.12986	+	0.231212i
$469$		−	14.8516i		−	0.685784i
$470$	−8.20750	+	14.2158i	−0.378584	+	0.655726i
$471$	17.5403	+	21.4931i	0.808212	+	0.990351i
$472$	−0.375396	−	0.650206i	−0.0172790	−	0.0299281i
$473$	−24.1060	+	13.9176i	−1.10840	+	0.639933i
$474$	−19.1161	+	15.6004i	−0.878033	+	0.716551i
$475$	−0.155971	+	4.35611i	−0.00715645	+	0.199872i
$476$		−	17.7637i		−	0.814196i
$477$	−10.9066	+	3.63550i	−0.499377	+	0.166458i
$478$			28.1130i			1.28586i
$479$	−0.323529	−	0.186789i	−0.0147824	−	0.00853463i	0.492591	−	0.870261i	$-0.336050\pi$
$479$	−0.323529	−	0.186789i	−0.0147824	−	0.00853463i	−0.507373	+	0.861727i	$0.669383\pi$
$480$	−12.2787	−	4.65998i	−0.560445	−	0.212698i
$481$	−28.3651	−	49.1298i	−1.29334	−	2.24013i
$482$	9.50919	−	5.49014i	0.433132	−	0.250069i
$483$	−4.46107	−	27.4905i	−0.202986	−	1.25086i
$484$	0.260374	−	0.450981i	0.0118352	−	0.0204991i
$485$	−2.17515			−0.0987687
$486$	8.34133	+	28.9236i	0.378370	+	1.31200i
$487$		−	1.68514i		−	0.0763610i	−0.999271	−	0.0381805i	$-0.987844\pi$
$487$		−	1.68514i		−	0.0763610i	0.999271	−	0.0381805i	$-0.0121562\pi$
$488$	−0.133064	+	0.230474i	−0.00602353	+	0.0104331i
$489$	42.1295	−	6.83664i	1.90516	−	0.309164i
$490$	6.81389	−	3.93400i	0.307820	−	0.177720i
$491$	−7.27267	+	4.19888i	−0.328211	+	0.189493i	−0.655047	−	0.755589i	$-0.727351\pi$
$491$	−7.27267	+	4.19888i	−0.328211	+	0.189493i	0.326836	+	0.945081i	$0.394018\pi$
$492$	−0.977408	+	2.57540i	−0.0440650	+	0.116108i
$493$	−4.60877	−	2.66087i	−0.207568	−	0.119840i
$494$	18.9756	+	35.7640i	0.853751	+	1.60910i
$495$	9.56764	−	3.18919i	0.430033	−	0.143344i
$496$		−	5.75088i		−	0.258222i
$497$	10.3468	−	17.9211i	0.464115	−	0.803871i
$498$	−0.218398	+	0.178232i	−0.00978665	+	0.00798675i
$499$	−9.13283	−	15.8185i	−0.408842	−	0.708134i	0.585919	−	0.810370i	$-0.300734\pi$
$499$	−9.13283	−	15.8185i	−0.408842	−	0.708134i	−0.994760	+	0.102236i	$0.967400\pi$
$500$	1.49738	−	0.864515i	0.0669650	−	0.0386623i
$501$	2.41511	+	2.95938i	0.107899	+	0.132215i
$502$	−13.2659	−	7.65909i	−0.592088	−	0.341842i
$503$		−	9.72835i		−	0.433766i	−0.976198	−	0.216883i	$-0.930411\pi$
$503$		−	9.72835i		−	0.433766i	0.976198	−	0.216883i	$-0.0695890\pi$
$504$	0.538297	−	2.63050i	0.0239777	−	0.117172i
$505$	3.88943			0.173077
$506$	−30.5134	+	52.8508i	−1.35649	+	2.34950i
$507$	6.22857	−	16.4118i	0.276620	−	0.728876i
$508$	−5.53079	+	3.19321i	−0.245389	+	0.141676i
$509$	7.73415	+	13.3959i	0.342810	+	0.593765i	0.984953	−	0.172820i	$-0.0552878\pi$
$509$	7.73415	+	13.3959i	0.342810	+	0.593765i	−0.642143	+	0.766585i	$0.721955\pi$
$510$	−19.8307	+	3.21807i	−0.878119	+	0.142498i
$511$	2.96297	−	5.13202i	0.131074	−	0.227027i
$512$	29.2061			1.29074
$513$	−12.7957	+	18.6888i	−0.564943	+	0.825130i
$514$	−11.5266			−0.508416
$515$	2.67462	−	4.63258i	0.117858	−	0.204136i
$516$	−24.4767	+	3.97199i	−1.07753	+	0.174857i
$517$	14.2881	+	24.7477i	0.628390	+	1.08840i
$518$	33.7377	−	19.4785i	1.48235	−	0.855835i
$519$	−10.4363	+	27.4988i	−0.458101	+	1.20706i
$520$	−1.25841	+	2.17963i	−0.0551850	+	0.0955832i
$521$	−7.23358			−0.316909			−0.158454	−	0.987366i	$-0.550651\pi$
$521$	−7.23358			−0.316909			−0.158454	+	0.987366i	$0.550651\pi$
$522$	3.84032	+	3.40542i	0.168086	+	0.149051i
$523$			14.7477i			0.644871i	0.946591	+	0.322435i	$0.104501\pi$
$523$			14.7477i			0.644871i	−0.946591	+	0.322435i	$0.895499\pi$
$524$	−4.21549	−	2.43382i	−0.184155	−	0.106322i
$525$	1.87312	+	2.29525i	0.0817496	+	0.100173i
$526$	24.8990	−	14.3754i	1.08565	−	0.626799i
$527$	−3.86514	−	6.69462i	−0.168368	−	0.291622i
$528$	−20.1581	+	16.4507i	−0.877267	+	0.715926i
$529$	32.6868	−	56.6151i	1.42116	−	2.46153i
$530$			7.40019i			0.321444i
$531$	3.22063	+	2.85591i	0.139763	+	0.123936i
$532$	−11.3874	+	6.04188i	−0.493705	+	0.261949i
$533$	3.83147	+	2.21210i	0.165959	+	0.0958166i
$534$	−16.9744	+	44.7265i	−0.734556	+	1.93550i
$535$	−4.84580	+	2.79772i	−0.209502	+	0.120956i
$536$	3.93476	−	2.27174i	0.169956	−	0.0981240i
$537$	−27.3219	+	4.43371i	−1.17903	+	0.191329i
$538$	−8.32960	+	14.4273i	−0.359115	+	0.622005i
$539$		−	13.6971i		−	0.589975i
$540$	8.97676	+	0.368035i	0.386298	+	0.0158377i
$541$	13.5810			0.583892			0.291946	−	0.956435i	$-0.405697\pi$
$541$	13.5810			0.583892			0.291946	+	0.956435i	$0.405697\pi$
$542$	28.6648	−	49.6489i	1.23126	−	2.13260i
$543$	−5.41978	−	33.3984i	−0.232585	−	1.43326i
$544$	39.4427	−	22.7723i	1.69109	−	0.976353i
$545$	8.49286	+	14.7101i	0.363794	+	0.630110i
$546$	25.7263	+	9.76357i	1.10099	+	0.417842i
$547$	−30.9145	−	17.8485i	−1.32181	−	0.763146i	−0.337791	−	0.941221i	$-0.609680\pi$
$547$	−30.9145	−	17.8485i	−1.32181	−	0.763146i	−0.984017	+	0.178075i	$0.943013\pi$
$548$			0.255398i			0.0109101i
$549$	0.305892	−	1.49481i	0.0130552	−	0.0637967i
$550$		−	6.49172i		−	0.276808i
$551$	−0.138189	+	3.85948i	−0.00588706	+	0.164419i
$552$	6.60091	−	5.38692i	0.280954	−	0.229282i
$553$	−10.9274	+	6.30891i	−0.464678	+	0.268282i
$554$	−15.8035	−	27.3725i	−0.671426	−	1.16294i
$555$	−12.9164	−	15.8272i	−0.548270	−	0.671828i
$556$	13.7019	−	23.7324i	0.581091	−	1.00648i
$557$		−	34.3362i		−	1.45487i	−0.686175	−	0.727436i	$-0.740712\pi$
$557$		−	34.3362i		−	1.45487i	0.686175	−	0.727436i	$-0.259288\pi$
$558$	2.35769	+	7.07313i	0.0998092	+	0.299429i
$559$			39.8260i			1.68446i
$560$	−6.61911	−	3.82154i	−0.279708	−	0.161490i
$561$	−12.4096	+	32.6985i	−0.523934	+	1.38053i
$562$	−13.3373	−	23.1008i	−0.562598	−	0.974449i
$563$	3.25436	+	5.63671i	0.137155	+	0.237559i	0.926419	−	0.376495i	$-0.122871\pi$
$563$	3.25436	+	5.63671i	0.137155	+	0.237559i	−0.789264	+	0.614054i	$0.789538\pi$
$564$	4.07772	+	25.1282i	0.171703	+	1.05809i
$565$	−10.6587	−	6.15379i	−0.448414	−	0.258892i
$566$	20.5026			0.861790
$567$	1.84129	+	15.2834i	0.0773268	+	0.641841i
$568$	6.33065			0.265628
$569$	−16.5702	+	28.7005i	−0.694660	+	1.20319i	0.275635	+	0.961262i	$0.411112\pi$
$569$	−16.5702	+	28.7005i	−0.694660	+	1.20319i	−0.970295	+	0.241924i	$0.922222\pi$
$570$	8.80788	+	11.6179i	0.368921	+	0.486621i
$571$	−10.9987	−	19.0503i	−0.460280	−	0.797229i	0.538694	−	0.842501i	$-0.318918\pi$
$571$	−10.9987	−	19.0503i	−0.460280	−	0.797229i	−0.998975	+	0.0452725i	$0.985584\pi$
$572$	−13.9787	−	24.2119i	−0.584480	−	1.01235i
$573$	34.7609	+	13.1923i	1.45216	+	0.551117i
$574$	−1.51906	+	2.63109i	−0.0634043	+	0.109820i
$575$			9.40072i			0.392037i
$576$	−16.2375	+	5.41248i	−0.676564	+	0.225520i
$577$	18.7840			0.781990			0.390995	−	0.920393i	$-0.372131\pi$
$577$	18.7840			0.781990			0.390995	+	0.920393i	$0.372131\pi$
$578$	18.4210	−	31.9061i	0.766211	−	1.32712i
$579$	−23.2671	+	18.9879i	−0.966947	+	0.789112i
$580$	1.32667	−	0.765953i	0.0550870	−	0.0318045i
$581$	−0.124843	+	0.0720780i	−0.00517935	+	0.00299030i
$582$	−5.63653	+	4.59989i	−0.233642	+	0.190672i
$583$	11.1568	+	6.44135i	0.462065	+	0.266774i
$584$	1.81289			0.0750180
$585$	2.89288	−	14.1366i	0.119606	−	0.584478i
$586$	41.8059			1.72699
$587$	−5.99649	−	3.46208i	−0.247502	−	0.142895i	0.371118	−	0.928586i	$-0.378974\pi$
$587$	−5.99649	−	3.46208i	−0.247502	−	0.142895i	−0.618620	+	0.785691i	$0.712308\pi$
$588$	4.32953	−	11.4080i	0.178547	−	0.470459i
$589$	−2.97694	+	4.75476i	−0.122663	+	0.195916i
$590$	2.39955	−	1.38538i	0.0987878	−	0.0570351i
$591$	5.37519	+	33.1236i	0.221106	+	1.36252i
$592$	45.6431	+	26.3521i	1.87592	+	1.08306i
$593$		−	6.51537i		−	0.267554i	−0.991011	−	0.133777i	$-0.957289\pi$
$593$		−	6.51537i		−	0.267554i	0.991011	−	0.133777i	$-0.0427106\pi$
$594$	18.0485	−	28.4973i	0.740539	−	1.16926i
$595$	−10.2738			−0.421184
$596$	28.1656	+	16.2614i	1.15371	+	0.666094i
$597$	−40.1583	+	6.51676i	−1.64357	+	0.266713i
$598$	43.6578	+	75.6176i	1.78530	+	3.09223i
$599$	−11.6035	−	20.0979i	−0.474108	−	0.821178i	0.525453	−	0.850823i	$-0.323896\pi$
$599$	−11.6035	−	20.0979i	−0.474108	−	0.821178i	−0.999561	+	0.0296442i	$0.990563\pi$
$600$	−0.321582	+	0.847346i	−0.0131285	+	0.0345928i
$601$	−7.47621	−	4.31639i	−0.304961	−	0.176069i	0.339708	−	0.940531i	$-0.389672\pi$
$601$	−7.47621	−	4.31639i	−0.304961	−	0.176069i	−0.644669	+	0.764461i	$0.723005\pi$
$602$	−27.3487			−1.11465
$603$	−17.2827	+	19.4898i	−0.703806	+	0.793687i
$604$			29.6219i			1.20530i
$605$	−0.260829	−	0.150590i	−0.0106042	−	0.00612233i
$606$	10.0788	−	8.22514i	0.409422	−	0.334123i
$607$	−6.30622	+	3.64090i	−0.255962	+	0.147780i	−0.622491	−	0.782627i	$-0.713879\pi$
$607$	−6.30622	+	3.64090i	−0.255962	+	0.147780i	0.366529	+	0.930406i	$0.380546\pi$
$608$	−28.0136	−	17.5393i	−1.13610	−	0.711312i
$609$	1.65957	+	2.03357i	0.0672491	+	0.0824044i
$610$	−0.850550	−	0.491065i	−0.0344378	−	0.0198827i
$611$	40.8861			1.65407
$612$	−20.6714	+	23.3113i	−0.835592	+	0.942304i
$613$	−13.3449			−0.538995			−0.269498	−	0.963001i	$-0.586858\pi$
$613$	−13.3449			−0.538995			−0.269498	+	0.963001i	$0.586858\pi$
$614$	−12.3138	−	7.10938i	−0.496945	−	0.286911i
$615$	1.48951	+	0.565293i	0.0600628	+	0.0227948i
$616$	−2.60566	+	1.50438i	−0.104985	+	0.0606131i
$617$	−33.9326	+	19.5910i	−1.36607	+	0.788703i	−0.990424	−	0.138058i	$-0.955914\pi$
$617$	−33.9326	+	19.5910i	−1.36607	+	0.788703i	−0.375650	+	0.926761i	$0.622581\pi$
$618$	−2.86591	−	17.6607i	−0.115284	−	0.710416i
$619$	4.80423	−	8.32118i	0.193098	−	0.334456i	−0.753177	−	0.657818i	$-0.771480\pi$
$619$	4.80423	−	8.32118i	0.193098	−	0.334456i	0.946276	+	0.323362i	$0.104813\pi$
$620$	2.22522			0.0893670
$621$	−26.1362	+	41.2672i	−1.04881	+	1.65600i
$622$			40.0798i			1.60705i
$623$	−12.2321	+	21.1866i	−0.490069	+	0.848824i
$624$	5.96306	+	36.7462i	0.238713	+	1.47103i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.95463	+	5.11757i	0.118091	+	0.204539i
$627$	25.1822	−	3.16643i	1.00568	−	0.126455i
$628$	13.8468	−	23.9833i	0.552546	−	0.957038i
$629$	70.8444			2.82475
$630$	9.70771	+	1.98655i	0.386764	+	0.0791462i
$631$	−10.1272			−0.403157			−0.201579	−	0.979472i	$-0.564607\pi$
$631$	−10.1272			−0.403157			−0.201579	+	0.979472i	$0.564607\pi$
$632$	−3.34294	−	1.93005i	−0.132975	−	0.0767732i
$633$	−19.2492	+	15.7090i	−0.765085	+	0.624376i
$634$	8.28110	+	14.3433i	0.328884	+	0.569645i
$635$	1.84682	+	3.19878i	0.0732888	+	0.126940i
$636$	7.25617	+	8.89142i	0.287726	+	0.352568i
$637$	−16.9719	−	9.79872i	−0.672450	−	0.388239i
$638$		−	5.75161i		−	0.227709i
$639$	−34.4327	+	11.4775i	−1.36214	+	0.454043i
$640$		−	4.14768i		−	0.163951i
$641$	−10.6642	+	18.4710i	−0.421211	+	0.729559i	−0.996058	−	0.0887016i	$-0.971728\pi$
$641$	−10.6642	+	18.4710i	−0.421211	+	0.729559i	0.574847	+	0.818261i	$0.305062\pi$
$642$	−6.64056	+	17.4974i	−0.262082	+	0.690569i
$643$	8.82363	+	15.2830i	0.347970	+	0.602702i	0.985889	−	0.167402i	$-0.0535378\pi$
$643$	8.82363	+	15.2830i	0.347970	+	0.602702i	−0.637919	+	0.770104i	$0.720204\pi$
$644$	−24.0769	+	13.9008i	−0.948761	+	0.547767i
$645$	2.29724	+	14.1563i	0.0904537	+	0.557404i
$646$	−50.5267	−	1.80912i	−1.98795	−	0.0711788i
$647$		−	3.82797i		−	0.150493i	−0.997165	−	0.0752466i	$-0.976026\pi$
$647$		−	3.82797i		−	0.150493i	0.997165	−	0.0752466i	$-0.0239744\pi$
$648$	−3.76750	+	2.82560i	−0.148001	+	0.111000i
$649$		−	4.82350i		−	0.189339i
$650$	−8.04381	−	4.64409i	−0.315504	−	0.182156i
$651$	0.610730	+	3.76351i	0.0239364	+	0.147503i
$652$	−21.3031	−	36.8980i	−0.834294	−	1.44504i
$653$	26.2044	−	15.1291i	1.02546	−	0.592049i	0.109778	−	0.993956i	$-0.464986\pi$
$653$	26.2044	−	15.1291i	1.02546	−	0.592049i	0.915680	+	0.401907i	$0.131653\pi$
$654$	53.1157	+	20.1583i	2.07699	+	0.788252i
$655$	−1.40762	+	2.43807i	−0.0550003	+	0.0952632i
$656$	−4.11022			−0.160477
$657$	−9.86041	+	3.28678i	−0.384691	+	0.128230i
$658$			28.0767i			1.09454i
$659$	−5.19669	+	9.00092i	−0.202434	+	0.350626i	−0.949312	−	0.314335i	$-0.898219\pi$
$659$	−5.19669	+	9.00092i	−0.202434	+	0.350626i	0.746878	+	0.664961i	$0.231552\pi$
$660$	−6.36538	−	7.79988i	−0.247772	−	0.303610i
$661$	−17.1268	+	9.88814i	−0.666154	+	0.384604i	−0.794618	−	0.607110i	$-0.792329\pi$
$661$	−17.1268	+	9.88814i	−0.666154	+	0.384604i	0.128464	+	0.991714i	$0.458995\pi$
$662$	11.3602	−	6.55883i	0.441528	−	0.254916i
$663$	31.6386	+	38.7687i	1.22874	+	1.50565i
$664$	−0.0381925	−	0.0220504i	−0.00148215	−	0.000855722i
$665$	3.49437	+	6.58599i	0.135506	+	0.255394i
$666$	−66.9410	−	13.6986i	−2.59391	−	0.530810i
$667$			8.32896i			0.322499i
$668$	1.90656	−	3.30226i	0.0737670	−	0.127768i
$669$	36.2381	+	13.7530i	1.40105	+	0.531720i
$670$	8.38371	+	14.5210i	0.323891	+	0.560995i
$671$	−1.48069	+	0.854876i	−0.0571614	+	0.0330021i
$672$	−22.1735	+	3.59824i	−0.855360	+	0.138805i
$673$	15.8964	+	9.17777i	0.612760	+	0.353777i	0.774045	−	0.633131i	$-0.218231\pi$
$673$	15.8964	+	9.17777i	0.612760	+	0.353777i	−0.161285	+	0.986908i	$0.551564\pi$
$674$		−	31.2135i		−	1.20230i
$675$	0.212856	−	5.19179i	0.00819285	−	0.199832i
$676$	−17.5234			−0.673977
$677$	−11.7829	+	20.4086i	−0.452854	+	0.784367i	−0.998562	−	0.0536090i	$-0.982928\pi$
$677$	−11.7829	+	20.4086i	−0.452854	+	0.784367i	0.545708	+	0.837976i	$0.316261\pi$
$678$	−40.6337	+	6.59391i	−1.56053	+	0.253237i
$679$	−3.22201	+	1.86023i	−0.123649	+	0.0713889i
$680$	−1.57150	−	2.72192i	−0.0602642	−	0.104381i
$681$	−6.99400	+	18.4287i	−0.268011	+	0.706190i
$682$	4.17735	−	7.23538i	0.159959	−	0.277057i
$683$	−24.6383			−0.942757			−0.471378	−	0.881931i	$-0.656243\pi$
$683$	−24.6383			−0.942757			−0.471378	+	0.881931i	$0.656243\pi$
$684$	21.9746	+	5.32261i	0.840219	+	0.203515i
$685$	0.147712			0.00564378
$686$	18.2892	−	31.6778i	0.698285	−	1.20947i
$687$	9.51406	+	11.6581i	0.362984	+	0.444786i
$688$	−18.4998	−	32.0426i	−0.705298	−	1.22161i
$689$	15.9628	−	9.21612i	0.608134	−	0.351106i
$690$	19.8801	+	24.3603i	0.756823	+	0.927380i
$691$	16.5194	−	28.6125i	0.628429	−	1.08847i	−0.359438	−	0.933169i	$-0.617032\pi$
$691$	16.5194	−	28.6125i	0.628429	−	1.08847i	0.987867	−	0.155302i	$-0.0496350\pi$
$692$	29.3613			1.11615
$693$	11.4449	−	12.9065i	0.434755	−	0.490276i
$694$			5.32813i			0.202253i
$695$	−13.7259	−	7.92463i	−0.520651	−	0.300598i
$696$	−0.284919	+	0.750742i	−0.0107998	+	0.0284568i
$697$	−4.78472	+	2.76246i	−0.181234	+	0.104636i
$698$	9.93251	+	17.2036i	0.375951	+	0.651166i
$699$	−3.20659	−	19.7600i	−0.121285	−	0.747393i
$700$	1.47869	−	2.56117i	0.0558894	−	0.0968032i
$701$		−	4.78761i		−	0.180826i	−0.995904	−	0.0904128i	$-0.971181\pi$
$701$		−	4.78761i		−	0.180826i	0.995904	−	0.0904128i	$-0.0288186\pi$
$702$	−22.3990	−	42.7503i	−0.845395	−	1.61351i
$703$	−24.0960	−	45.4147i	−0.908798	−	1.71285i
$704$	16.6100	+	9.58979i	0.626013	+	0.361429i
$705$	14.5331	−	2.35839i	0.547349	−	0.0888220i
$706$	14.7276	−	8.50298i	0.554280	−	0.320014i
$707$	5.76132	−	3.32630i	0.216677	−	0.125098i
$708$	1.52467	−	4.01739i	0.0573005	−	0.150983i
$709$	11.8940	−	20.6011i	0.446689	−	0.773689i	−0.551479	−	0.834189i	$-0.685936\pi$
$709$	11.8940	−	20.6011i	0.446689	−	0.773689i	0.998168	+	0.0605001i	$0.0192696\pi$
$710$			23.3629i			0.876793i
$711$	21.6816	+	4.43686i	0.813125	+	0.166395i
$712$	−7.48419			−0.280482
$713$	−6.04925	+	10.4776i	−0.226546	+	0.392390i
$714$	−26.6227	+	21.7264i	−0.996328	+	0.813090i
$715$	−14.0031	+	8.08472i	−0.523688	+	0.302351i
$716$	13.8155	+	23.9292i	0.516310	+	0.894275i
$717$	19.5359	−	15.9430i	0.729581	−	0.595401i
$718$	32.2101	+	18.5965i	1.20207	+	0.694015i
$719$			19.5293i			0.728320i	0.931336	+	0.364160i	$0.118644\pi$
$719$			19.5293i			0.728320i	−0.931336	+	0.364160i	$0.881356\pi$
$720$	4.23918	+	12.7176i	0.157985	+	0.473958i
$721$		−	9.14952i		−	0.340746i
$722$	16.0257	+	33.0054i	0.596415	+	1.22833i
$723$	−9.20782	−	3.49452i	−0.342442	−	0.129963i
$724$	−29.2511	+	16.8881i	−1.08711	+	0.627642i
$725$	−0.442996	−	0.767292i	−0.0164525	−	0.0284965i
$726$	−0.994349	+	0.161360i	−0.0369038	+	0.00598862i
$727$	−15.4279	+	26.7219i	−0.572189	+	0.991061i	0.424151	+	0.905591i	$0.360572\pi$
$727$	−15.4279	+	26.7219i	−0.572189	+	0.991061i	−0.996341	+	0.0854697i	$0.972761\pi$
$728$			4.30485i			0.159548i
$729$	15.3688	−	22.1991i	0.569215	−	0.822189i
$730$			6.69037i			0.247622i
$731$	−43.0713	−	24.8673i	−1.59305	−	0.919749i
$732$	−1.50345	+	0.243976i	−0.0555693	+	0.00901760i
$733$	−20.9317	−	36.2547i	−0.773128	−	1.33910i	−0.935841	−	0.352424i	$-0.885358\pi$
$733$	−20.9317	−	36.2547i	−0.773128	−	1.33910i	0.162712	−	0.986674i	$-0.447976\pi$
$734$	15.7209	+	27.2294i	0.580268	+	1.00505i
$735$	−6.59793	−	2.50402i	−0.243368	−	0.0923623i
$736$	−61.7310	−	35.6404i	−2.27544	−	1.31372i
$737$	29.1897			1.07522
$738$	5.05524	−	1.68507i	0.186086	−	0.0620283i
$739$	15.4239			0.567379			0.283689	−	0.958916i	$-0.408442\pi$
$739$	15.4239			0.567379			0.283689	+	0.958916i	$0.408442\pi$
$740$	−10.1966	+	17.6610i	−0.374833	+	0.649230i
$741$	14.0915	−	33.4681i	0.517665	−	1.22948i
$742$	6.32876	+	10.9617i	0.232336	+	0.402418i
$743$	−24.1552	−	41.8380i	−0.886167	−	1.53489i	−0.844370	−	0.535760i	$-0.820025\pi$
$743$	−24.1552	−	41.8380i	−0.886167	−	1.53489i	−0.0417969	−	0.999126i	$-0.513308\pi$
$744$	−0.903678	+	0.737480i	−0.0331305	+	0.0270373i
$745$	9.40494	−	16.2898i	0.344570	−	0.596813i
$746$			26.1017i			0.955652i
$747$	0.247708	+	0.0506902i	0.00906317	+	0.00185466i
$748$	34.9131			1.27655
$749$	−4.78532	+	8.28841i	−0.174852	+	0.302852i
$750$	−3.12708	−	1.18678i	−0.114185	−	0.0433351i
$751$	−35.6639	+	20.5905i	−1.30139	+	0.751359i	−0.980643	−	0.195805i	$-0.937268\pi$
$751$	−35.6639	+	20.5905i	−1.30139	+	0.751359i	−0.320750	+	0.947164i	$0.603935\pi$
$752$	−32.8955	+	18.9922i	−1.19958	+	0.692575i
$753$	2.20081	+	13.5621i	0.0802018	+	0.494229i
$754$	−7.12675	−	4.11463i	−0.259541	−	0.149846i
$755$	17.1321			0.623501
$756$	13.6118	−	7.13190i	0.495057	−	0.259385i
$757$	49.3904			1.79513			0.897563	−	0.440887i	$-0.145336\pi$
$757$	49.3904			1.79513			0.897563	+	0.440887i	$0.145336\pi$
$758$	−57.0061	−	32.9125i	−2.07055	−	1.19544i
$759$	54.0305	−	8.76790i	1.96118	−	0.318255i
$760$	−1.21037	+	1.93320i	−0.0439049	+	0.0701246i
$761$	−10.5209	+	6.07423i	−0.381381	+	0.220191i	−0.678419	−	0.734675i	$-0.737335\pi$
$761$	−10.5209	+	6.07423i	−0.381381	+	0.220191i	0.297038	+	0.954866i	$0.404001\pi$
$762$	11.5503	+	4.38353i	0.418424	+	0.158799i
$763$	25.1606	+	14.5265i	0.910873	+	0.525893i
$764$		−	37.1152i		−	1.34278i
$765$	13.4823	+	11.9555i	0.487454	+	0.432252i
$766$	48.8985			1.76678
$767$	−5.97674	−	3.45067i	−0.215808	−	0.124597i
$768$	−21.2672	−	26.0599i	−0.767413	−	0.940357i
$769$	1.44465	+	2.50220i	0.0520954	+	0.0902318i	0.890897	−	0.454205i	$-0.150077\pi$
$769$	1.44465	+	2.50220i	0.0520954	+	0.0902318i	−0.838802	+	0.544437i	$0.816743\pi$
$770$	−5.55182	−	9.61604i	−0.200074	−	0.346538i
$771$	6.53675	+	8.00988i	0.235415	+	0.288469i
$772$	25.9628	+	14.9896i	0.934421	+	0.539488i
$773$	10.5183			0.378316			0.189158	−	0.981947i	$-0.439424\pi$
$773$	10.5183			0.378316			0.189158	+	0.981947i	$0.439424\pi$
$774$	35.8898	+	31.8255i	1.29003	+	1.14394i
$775$		−	1.28698i		−	0.0462296i
$776$	−0.985690	−	0.569088i	−0.0353842	−	0.0204291i
$777$	−32.6684	−	12.3982i	−1.17197	−	0.444783i
$778$	−43.7136	+	25.2381i	−1.56721	+	0.904829i
$779$	3.39828	+	2.12766i	0.121756	+	0.0762312i
$780$	−14.2184	+	2.30732i	−0.509102	+	0.0826154i
$781$	35.2226	+	20.3358i	1.26036	+	0.727671i
$782$	−109.039			−3.89924
$783$	0.188589	−	4.59989i	0.00673962	−	0.164386i
$784$	18.2066			0.650237
$785$	−13.8710	−	8.00841i	−0.495076	−	0.285832i
$786$	1.50829	+	9.29458i	0.0537990	+	0.331527i
$787$	8.81021	−	5.08658i	0.314050	−	0.181317i	−0.334687	−	0.942329i	$-0.608631\pi$
$787$	8.81021	−	5.08658i	0.314050	−	0.181317i	0.648737	+	0.761012i	$0.275297\pi$
$788$	29.0104	−	16.7492i	1.03345	−	0.596665i
$789$	−24.1098	−	9.15008i	−0.858333	−	0.325752i
$790$	7.12273	−	12.3369i	0.253415	−	0.438928i
$791$	−21.0513			−0.748496
$792$	5.17005	+	1.05798i	0.183710	+	0.0375938i
$793$			2.44627i			0.0868696i
$794$	1.55859	−	2.69955i	0.0553122	−	0.0958035i
$795$	5.14243	−	4.19667i	0.182383	−	0.148841i
$796$	20.3063	+	35.1716i	0.719739	+	1.24662i
$797$	−11.4968	−	19.9131i	−0.407238	−	0.705356i	0.587341	−	0.809339i	$-0.300175\pi$
$797$	−11.4968	−	19.9131i	−0.407238	−	0.705356i	−0.994579	+	0.103983i	$0.966841\pi$
$798$	22.9827	+	9.67672i	0.813580	+	0.342552i
$799$	−25.5292	+	44.2179i	−0.903158	+	1.56432i
$800$	7.58249			0.268081
$801$	40.7069	−	13.5689i	1.43831	−	0.479433i
$802$	10.1296			0.357688
$803$	10.0866	+	5.82350i	0.355948	+	0.205507i
$804$	24.3115	+	9.22662i	0.857401	+	0.325398i
$805$	8.03964	+	13.9251i	0.283360	+	0.490794i
$806$	−5.97684	−	10.3522i	−0.210525	−	0.364641i
$807$	14.7493	−	2.39347i	0.519201	−	0.0842543i
$808$	1.76253	+	1.01760i	0.0620055	+	0.0357989i
$809$			0.203482i			0.00715406i	0.999994	+	0.00357703i	$0.00113861\pi$
$809$			0.203482i			0.00715406i	−0.999994	+	0.00357703i	$0.998861\pi$
$810$	−10.4277	−	13.9037i	−0.366393	−	0.488528i
$811$		−	20.9546i		−	0.735816i	−0.929862	−	0.367908i	$-0.880074\pi$
$811$		−	20.9546i		−	0.735816i	0.929862	−	0.367908i	$-0.119926\pi$
$812$	1.31011	−	2.26918i	0.0459759	−	0.0796325i
$813$	−50.7571	+	8.23670i	−1.78013	+	0.288874i
$814$	38.2835	+	66.3089i	1.34183	+	2.32413i
$815$	−21.3403	+	12.3208i	−0.747519	+	0.431580i
$816$	−43.4639	−	16.4953i	−1.52154	−	0.577450i
$817$	−1.29145	+	36.0688i	−0.0451822	+	1.26189i
$818$			35.2015i			1.23079i
$819$	−7.80472	−	23.4143i	−0.272719	−	0.818162i
$820$		−	1.59039i		−	0.0555389i
$821$	20.5413	+	11.8595i	0.716897	+	0.413900i	0.813609	−	0.581412i	$-0.197500\pi$
$821$	20.5413	+	11.8595i	0.716897	+	0.413900i	−0.0967128	+	0.995312i	$0.530833\pi$
$822$	0.382769	−	0.312373i	0.0133506	−	0.0108952i
$823$	−6.73781	−	11.6702i	−0.234865	−	0.406798i	0.724368	−	0.689413i	$-0.242132\pi$
$823$	−6.73781	−	11.6702i	−0.234865	−	0.406798i	−0.959233	+	0.282615i	$0.908798\pi$
$824$	2.42406	−	1.39953i	0.0844460	−	0.0487549i
$825$	−4.51113	+	3.68147i	−0.157057	+	0.128172i
$826$	2.36959	−	4.10426i	0.0824488	−	0.142805i
$827$	−23.0971			−0.803164			−0.401582	−	0.915823i	$-0.631540\pi$
$827$	−23.0971			−0.803164			−0.401582	+	0.915823i	$0.631540\pi$
$828$	47.7724	+	9.77598i	1.66020	+	0.339739i
$829$			1.37224i			0.0476597i	0.999716	+	0.0238298i	$0.00758599\pi$
$829$			1.37224i			0.0476597i	−0.999716	+	0.0238298i	$0.992414\pi$
$830$	0.0813758	−	0.140947i	0.00282460	−	0.00489234i
$831$	−10.0591	+	26.5049i	−0.348945	+	0.919446i
$832$	23.7652	−	13.7208i	0.823909	−	0.475684i
$833$	21.1944	−	12.2366i	0.734343	−	0.423973i
$834$	−52.3267	+	8.49140i	−1.81192	+	0.294033i
$835$	−1.90989	−	1.10268i	−0.0660945	−	0.0381597i
$836$	−11.8749	−	22.3810i	−0.410700	−	0.774064i
$837$	3.57810	−	5.64956i	0.123677	−	0.195278i
$838$		−	32.7380i		−	1.13092i
$839$	−11.4512	+	19.8340i	−0.395339	+	0.684747i	−0.993144	−	0.116894i	$-0.962706\pi$
$839$	−11.4512	+	19.8340i	−0.395339	+	0.684747i	0.597806	+	0.801641i	$0.296039\pi$
$840$	0.248312	+	1.53018i	0.00856758	+	0.0527961i
$841$	14.1075	+	24.4349i	0.486466	+	0.842584i
$842$	−23.5922	+	13.6209i	−0.813039	+	0.469409i
$843$	−8.48928	+	22.3687i	−0.292386	+	0.770418i
$844$	21.4794	+	12.4011i	0.739350	+	0.426864i
$845$			10.1348i			0.348648i
$846$	32.6726	−	36.8452i	1.12331	−	1.26676i
$847$	−0.515146			−0.0177006
$848$	−8.56206	+	14.8299i	−0.294023	+	0.509262i
$849$	−11.6271	−	14.2474i	−0.399041	−	0.488969i
$850$	10.0451	−	5.79952i	0.344543	−	0.198922i
$851$	−55.4386	−	96.0225i	−1.90041	−	3.29161i
$852$	22.9082	+	28.0708i	0.784821	+	0.961689i
$853$	27.5726	−	47.7572i	0.944069	−	1.63518i	0.186465	−	0.982462i	$-0.440297\pi$
$853$	27.5726	−	47.7572i	0.944069	−	1.63518i	0.757604	−	0.652714i	$-0.226370\pi$
$854$	−1.67987			−0.0574839
$855$	3.07838	−	12.7092i	0.105278	−	0.434645i
$856$	−2.92789			−0.100073
$857$	4.97618	−	8.61899i	0.169983	−	0.294419i	−0.768431	−	0.639933i	$-0.778962\pi$
$857$	4.97618	−	8.61899i	0.169983	−	0.294419i	0.938414	+	0.345514i	$0.112295\pi$
$858$	−19.1896	+	50.5632i	−0.655121	+	1.72620i
$859$	−16.4444	−	28.4825i	−0.561074	−	0.971809i	−0.997403	−	0.0720221i	$-0.977055\pi$
$859$	−16.4444	−	28.4825i	−0.561074	−	0.971809i	0.436329	−	0.899787i	$-0.356279\pi$
$860$	12.3984	−	7.15823i	0.422783	−	0.244094i
$861$	2.68982	−	0.436495i	0.0916689	−	0.0148757i
$862$	−30.4968	+	52.8219i	−1.03872	+	1.79912i
$863$	−13.0514			−0.444276			−0.222138	−	0.975015i	$-0.571304\pi$
$863$	−13.0514			−0.444276			−0.222138	+	0.975015i	$0.571304\pi$
$864$	33.2856	+	21.0811i	1.13240	+	0.717194i
$865$		−	16.9814i		−	0.577384i
$866$	49.1277	+	28.3639i	1.66943	+	0.963845i
$867$	−32.6183	+	5.29319i	−1.10777	+	0.179766i
$868$	3.29617	−	1.90304i	0.111879	−	0.0645935i
$869$	−12.3997	−	21.4769i	−0.420630	−	0.728553i
$870$	−2.77057	−	1.05148i	−0.0939311	−	0.0356484i
$871$	20.8820	−	36.1686i	0.707558	−	1.22553i
$872$			8.88799i			0.300985i
$873$	6.39298	+	1.30824i	0.216370	+	0.0442772i
$874$	37.0871	+	69.8996i	1.25449	+	2.36439i
$875$	−1.48128	−	0.855216i	−0.0500763	−	0.0289116i
$876$	6.56016	+	8.03856i	0.221647	+	0.271598i
$877$	3.37853	−	1.95060i	0.114085	−	0.0658670i	−0.441872	−	0.897078i	$-0.645685\pi$
$877$	3.37853	−	1.95060i	0.114085	−	0.0658670i	0.555957	+	0.831211i	$0.312352\pi$
$878$	12.0380	−	6.95015i	0.406263	−	0.234556i
$879$	−23.7082	−	29.0511i	−0.799659	−	0.979870i
$880$	7.51096	−	13.0094i	0.253194	−	0.438545i
$881$		−	13.6643i		−	0.460361i	−0.973148	−	0.230180i	$-0.926068\pi$
$881$		−	13.6643i		−	0.460361i	0.973148	−	0.230180i	$-0.0739316\pi$
$882$	−22.3927	+	7.46420i	−0.754002	+	0.251333i
$883$	−18.9449			−0.637546			−0.318773	−	0.947831i	$-0.603271\pi$
$883$	−18.9449			−0.637546			−0.318773	+	0.947831i	$0.603271\pi$
$884$	24.9764	−	43.2604i	0.840047	−	1.45500i
$885$	−2.32350	−	0.881805i	−0.0781035	−	0.0296416i
$886$	22.2527	−	12.8476i	0.747593	−	0.431623i
$887$	−6.51471	−	11.2838i	−0.218743	−	0.378873i	0.735681	−	0.677328i	$-0.236862\pi$
$887$	−6.51471	−	11.2838i	−0.218743	−	0.378873i	−0.954424	+	0.298455i	$0.903529\pi$
$888$	−1.71228	−	10.5516i	−0.0574602	−	0.354088i
$889$	5.47130	+	3.15886i	0.183502	+	0.105945i
$890$		−	27.6200i		−	0.925824i
$891$	−30.0383	+	3.61891i	−1.00632	+	0.121238i
$892$		−	38.6925i		−	1.29552i
$893$	37.0289	+	1.32583i	1.23913	+	0.0443671i
$894$	−10.0776	−	62.1012i	−0.337045	−	2.07698i
$895$	13.8397	−	7.99033i	0.462609	−	0.267087i
$896$	−3.54716	−	6.14386i	−0.118502	−	0.205252i
$897$	27.7886	−	73.2210i	0.927833	−	2.44478i
$898$	−24.2519	+	42.0056i	−0.809298	+	1.40174i
$899$		−	1.14025i		−	0.0380295i
$900$	−4.92091	+	1.64029i	−0.164030	+	0.0546764i
$901$			23.0181i			0.766844i
$902$	−5.17121	−	2.98560i	−0.172182	−	0.0994095i
$903$	15.5095	+	19.0048i	0.516125	+	0.632439i
$904$	−3.22004	−	5.57728i	−0.107097	−	0.185498i
$905$	9.76740	+	16.9176i	0.324679	+	0.562361i
$906$	44.3948	−	36.2300i	1.47492	−	1.20366i
$907$	28.6950	+	16.5670i	0.952800	+	0.550099i	0.893950	−	0.448167i	$-0.147923\pi$
$907$	28.6950	+	16.5670i	0.952800	+	0.550099i	0.0588506	+	0.998267i	$0.481256\pi$
$908$	19.6769			0.653000
$909$	−11.4314	−	2.33928i	−0.379155	−	0.0775891i
$910$	−15.8868			−0.526643
$911$	−1.92801	+	3.33941i	−0.0638777	+	0.110639i	−0.896196	−	0.443659i	$-0.853680\pi$
$911$	−1.92801	+	3.33941i	−0.0638777	+	0.110639i	0.832318	+	0.554299i	$0.187013\pi$
$912$	4.20892	+	33.4730i	0.139371	+	1.10840i
$913$	−0.141664	−	0.245369i	−0.00468839	−	0.00812053i
$914$	9.57989	+	16.5929i	0.316875	+	0.548843i
$915$	0.141106	+	0.869536i	0.00466480	+	0.0287460i
$916$	7.51067	−	13.0089i	0.248159	−	0.429825i
$917$			4.81527i			0.159014i
$918$	60.2198	+	2.46893i	1.98755	+	0.0814869i
$919$	−50.0985			−1.65260			−0.826299	−	0.563232i	$-0.809558\pi$
$919$	−50.0985			−1.65260			−0.826299	+	0.563232i	$0.809558\pi$
$920$	−2.45952	+	4.26002i	−0.0810880	+	0.140449i
$921$	2.04285	+	12.5887i	0.0673142	+	0.414811i
$922$	−1.33207	+	0.769069i	−0.0438693	+	0.0253279i
$923$	50.3955	−	29.0959i	1.65879	−	0.957703i
$924$	−16.0995	−	6.11001i	−0.529633	−	0.201005i
$925$	10.2144	+	5.89728i	0.335847	+	0.193901i
$926$	4.24421			0.139473
$927$	−10.6472	+	12.0069i	−0.349700	+	0.394360i
$928$	6.71803			0.220530
$929$	40.5633	+	23.4192i	1.33084	+	0.768360i	0.985428	−	0.170092i	$-0.0544066\pi$
$929$	40.5633	+	23.4192i	1.33084	+	0.768360i	0.345410	+	0.938452i	$0.387740\pi$
$930$	−2.72163	−	3.33497i	−0.0892456	−	0.109358i
$931$	−15.0530	−	9.42467i	−0.493343	−	0.308881i
$932$	−17.3063	+	9.99180i	−0.566887	+	0.327292i
$933$	27.8517	−	22.7294i	0.911822	−	0.744126i
$934$	−54.3671	−	31.3889i	−1.77895	−	1.02707i
$935$		−	20.1923i		−	0.660359i
$936$	5.00952	−	5.64927i	0.163741	−	0.184652i
$937$	−10.0638			−0.328769			−0.164385	−	0.986396i	$-0.552564\pi$
$937$	−10.0638			−0.328769			−0.164385	+	0.986396i	$0.552564\pi$
$938$	24.8372	+	14.3398i	0.810963	+	0.468210i
$939$	1.88065	−	4.95538i	0.0613726	−	0.161713i
$940$	−7.34878	−	12.7285i	−0.239691	−	0.415157i
$941$	19.7767	+	34.2543i	0.644703	+	1.11666i	0.984370	+	0.176112i	$0.0563522\pi$
$941$	19.7767	+	34.2543i	0.644703	+	1.11666i	−0.339667	+	0.940546i	$0.610314\pi$
$942$	−52.8799	+	8.58117i	−1.72292	+	0.279590i
$943$	7.48847	+	4.32347i	0.243858	+	0.140792i
$944$	6.41156			0.208679
$945$	−4.12480	−	7.87252i	−0.134180	−	0.256093i
$946$		−	53.7518i		−	1.74762i
$947$	−18.1920	−	10.5032i	−0.591162	−	0.341307i	0.174395	−	0.984676i	$-0.444203\pi$
$947$	−18.1920	−	10.5032i	−0.591162	−	0.341307i	−0.765557	+	0.643368i	$0.777536\pi$
$948$	−3.53878	−	21.8071i	−0.114934	−	0.708261i
$949$	14.4317	−	8.33212i	0.468471	−	0.270472i
$950$	−7.13436	−	4.46681i	−0.231469	−	0.144923i
$951$	5.27099	−	13.8887i	0.170923	−	0.450372i
$952$	−4.65565	−	2.68794i	−0.150890	−	0.0871166i
$953$	−3.22382			−0.104430			−0.0522149	−	0.998636i	$-0.516628\pi$
$953$	−3.22382			−0.104430			−0.0522149	+	0.998636i	$0.516628\pi$
$954$	4.45082	−	21.7499i	0.144101	−	0.704177i
$955$	−21.4659			−0.694621
$956$	−21.7993	−	12.5858i	−0.705040	−	0.407055i
$957$	−3.99683	+	3.26176i	−0.129199	+	0.105438i
$958$	0.624757	−	0.360703i	0.0201850	−	0.0116538i
$959$	0.218802	−	0.126326i	0.00706549	−	0.00407926i
$960$	7.65598	−	6.24794i	0.247096	−	0.201651i
$961$	−14.6718	+	25.4124i	−0.473285	+	0.819754i
$962$	109.550			3.53203
$963$	15.9249	−	5.30828i	0.513174	−	0.171057i
$964$			9.83145i			0.316650i
$965$	8.66939	−	15.0158i	0.279077	−	0.483376i
$966$	50.2812	+	19.0826i	1.61777	+	0.613971i
$967$	−6.81815	−	11.8094i	−0.219257	−	0.379764i	0.735324	−	0.677716i	$-0.237030\pi$
$967$	−6.81815	−	11.8094i	−0.219257	−	0.379764i	−0.954581	+	0.297952i	$0.903697\pi$
$968$	−0.0787978	−	0.136482i	−0.00253266	−	0.00438669i
$969$	27.3967	+	36.1372i	0.880108	+	1.16089i
$970$	2.10019	−	3.63763i	0.0674330	−	0.116797i
$971$	−57.9502			−1.85971			−0.929855	−	0.367927i	$-0.880068\pi$
$971$	−57.9502			−1.85971			−0.929855	+	0.367927i	$0.880068\pi$
$972$	−26.1622	−	6.48073i	−0.839152	−	0.207870i
$973$	−27.1091			−0.869076
$974$	2.81815	+	1.62706i	0.0902995	+	0.0521344i
$975$	1.33446	+	8.22336i	0.0427369	+	0.263358i
$976$	−1.13633	−	1.96818i	−0.0363731	−	0.0630000i
$977$	−9.94607	−	17.2271i	−0.318203	−	0.551143i	0.661910	−	0.749583i	$-0.269746\pi$
$977$	−9.94607	−	17.2271i	−0.318203	−	0.551143i	−0.980113	+	0.198440i	$0.936413\pi$
$978$	−29.2442	+	77.0566i	−0.935127	+	2.46400i
$979$	−41.6407	−	24.0413i	−1.33084	−	0.768362i
$980$			7.04480i			0.225038i
$981$	−16.1140	−	48.3422i	−0.514480	−	1.54345i
$982$		−	16.2167i		−	0.517494i
$983$	−4.83389	+	8.37254i	−0.154177	+	0.267043i	−0.932759	−	0.360500i	$-0.882606\pi$
$983$	−4.83389	+	8.37254i	−0.154177	+	0.267043i	0.778582	+	0.627543i	$0.215939\pi$
$984$	0.527085	+	0.645869i	0.0168029	+	0.0205896i
$985$	−9.68705	−	16.7785i	−0.308655	−	0.534606i
$986$	8.89985	−	5.13833i	0.283429	−	0.163638i
$987$	19.5107	−	15.9224i	0.621031	−	0.506815i
$988$	−36.2271	−	1.29712i	−1.15254	−	0.0412669i
$989$			77.8385i			2.47512i
$990$	−3.90442	+	19.0798i	−0.124091	+	0.606395i
$991$		−	22.9071i		−	0.727666i	−0.931464	−	0.363833i	$-0.881468\pi$
$991$		−	22.9071i		−	0.727666i	0.931464	−	0.363833i	$-0.118532\pi$
$992$	8.45110	+	4.87925i	0.268323	+	0.154916i
$993$	−11.0002	−	4.17475i	−0.349080	−	0.132482i
$994$	19.9803	+	34.6069i	0.633737	+	1.09766i
$995$	20.3418	−	11.7443i	0.644879	−	0.372321i
$996$	−0.0404299	−	0.249142i	−0.00128107	−	0.00789435i
$997$	20.0754	−	34.7716i	0.635794	−	1.10123i	−0.350552	−	0.936543i	$-0.614006\pi$
$997$	20.0754	−	34.7716i	0.635794	−	1.10123i	0.986346	−	0.164685i	$-0.0526606\pi$
$998$	35.2723			1.11652
$999$	28.4432	+	54.2862i	0.899904	+	1.71754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.w.a.56.15	✓	160
9.5	odd	6	inner	855.2.w.a.626.66	yes	160
19.18	odd	2	inner	855.2.w.a.56.66	yes	160
171.113	even	6	inner	855.2.w.a.626.15	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.w.a.56.15	✓	160	1.1	even	1	trivial
855.2.w.a.56.66	yes	160	19.18	odd	2	inner
855.2.w.a.626.15	yes	160	171.113	even	6	inner
855.2.w.a.626.66	yes	160	9.5	odd	6	inner

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965535 + 1.67236i) q^{2} +(1.70969 - 0.277442i) q^{3} +(-0.864515 - 1.49738i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.18678 + 3.12708i) q^{6} +(-0.855216 + 1.48128i) q^{7} -0.523262 q^{8} +(2.84605 - 0.948678i) q^{9} +O(q^{10})\)	\(q+(-0.965535 + 1.67236i) q^{2} +(1.70969 - 0.277442i) q^{3} +(-0.864515 - 1.49738i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.18678 + 3.12708i) q^{6} +(-0.855216 + 1.48128i) q^{7} -0.523262 q^{8} +(2.84605 - 0.948678i) q^{9} -1.93107i q^{10} +(-2.91134 - 1.68086i) q^{11} +(-1.89349 - 2.32020i) q^{12} +(-4.16547 + 2.40493i) q^{13} +(-1.65148 - 2.86045i) q^{14} +(-1.34191 + 1.09511i) q^{15} +(2.23426 - 3.86985i) q^{16} -6.00654i q^{17} +(-1.16144 + 5.67559i) q^{18} +(-3.85049 + 2.04298i) q^{19} +(1.49738 + 0.864515i) q^{20} +(-1.05118 + 2.76979i) q^{21} +(5.62199 - 3.24586i) q^{22} +(-8.14126 + 4.70036i) q^{23} +(-0.894614 + 0.145175i) q^{24} +(0.500000 - 0.866025i) q^{25} -9.28819i q^{26} +(4.60265 - 2.41156i) q^{27} +2.95739 q^{28} +(0.442996 - 0.767292i) q^{29} +(-0.535760 - 3.30152i) q^{30} +(1.11455 - 0.643489i) q^{31} +(3.79124 + 6.56663i) q^{32} +(-5.44381 - 2.06602i) q^{33} +(10.0451 + 5.79952i) q^{34} -1.71043i q^{35} +(-3.88099 - 3.44148i) q^{36} +11.7946i q^{37} +(0.301191 - 8.41195i) q^{38} +(-6.45441 + 5.26736i) q^{39} +(0.453159 - 0.261631i) q^{40} +(-0.459908 - 0.796585i) q^{41} +(-3.61712 - 4.43228i) q^{42} +(4.14003 - 7.17074i) q^{43} +5.81252i q^{44} +(-1.99041 + 2.24461i) q^{45} -18.1534i q^{46} +(-7.36162 - 4.25023i) q^{47} +(2.74622 - 7.23610i) q^{48} +(2.03721 + 3.52856i) q^{49} +(0.965535 + 1.67236i) q^{50} +(-1.66647 - 10.2693i) q^{51} +(7.20222 + 4.15820i) q^{52} -3.83217 q^{53} +(-0.411040 + 10.0257i) q^{54} +3.36172 q^{55} +(0.447502 - 0.775097i) q^{56} +(-6.01631 + 4.56114i) q^{57} +(0.855456 + 1.48169i) q^{58} +(0.717415 + 1.24260i) q^{59} +(2.79991 + 1.06261i) q^{60} +(0.254297 - 0.440456i) q^{61} +2.48524i q^{62} +(-1.02873 + 5.02712i) q^{63} -5.70528 q^{64} +(2.40493 - 4.16547i) q^{65} +(8.71131 - 7.10918i) q^{66} +(-7.51967 + 4.34148i) q^{67} +(-8.99409 + 5.19274i) q^{68} +(-12.6149 + 10.2949i) q^{69} +(2.86045 + 1.65148i) q^{70} -12.0984 q^{71} +(-1.48923 + 0.496408i) q^{72} -3.46459 q^{73} +(-19.7247 - 11.3880i) q^{74} +(0.614571 - 1.61935i) q^{75} +(6.38792 + 3.99947i) q^{76} +(4.97964 - 2.87500i) q^{77} +(-2.57694 - 15.8799i) q^{78} +(6.38865 + 3.68849i) q^{79} +4.46852i q^{80} +(7.20002 - 5.39997i) q^{81} +1.77623 q^{82} +(0.0729891 + 0.0421403i) q^{83} +(5.05620 - 0.820504i) q^{84} +(3.00327 + 5.20182i) q^{85} +(7.99469 + 13.8472i) q^{86} +(0.544505 - 1.43473i) q^{87} +(1.52339 + 0.879532i) q^{88} +14.3029 q^{89} +(-1.83196 - 5.49592i) q^{90} -8.22695i q^{91} +(14.0765 + 8.12706i) q^{92} +(1.72701 - 1.40939i) q^{93} +(14.2158 - 8.20750i) q^{94} +(2.31313 - 3.69451i) q^{95} +(8.30370 + 10.1750i) q^{96} +(1.88374 + 1.08758i) q^{97} -7.86800 q^{98} +(-9.88041 - 2.02190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 80 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{9}+O(q^{10}) \) 160 * q - 80 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^9	\( 160 q - 80 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{9} - 12 q^{11} - 80 q^{16} + 8 q^{19} + 20 q^{24} + 80 q^{25} - 32 q^{28} + 16 q^{30} - 100 q^{36} - 66 q^{38} + 8 q^{39} + 8 q^{42} - 28 q^{43} - 8 q^{45} + 36 q^{47} - 84 q^{49} - 8 q^{54} + 30 q^{57} + 28 q^{61} - 12 q^{63} + 136 q^{64} + 40 q^{66} - 84 q^{68} + 128 q^{73} - 84 q^{74} - 16 q^{76} - 84 q^{81} + 24 q^{82} + 60 q^{83} - 36 q^{87} - 120 q^{92} + 40 q^{93} - 12 q^{95} + 44 q^{96} + 84 q^{99}+O(q^{100}) \) 160 * q - 80 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^9 - 12 * q^11 - 80 * q^16 + 8 * q^19 + 20 * q^24 + 80 * q^25 - 32 * q^28 + 16 * q^30 - 100 * q^36 - 66 * q^38 + 8 * q^39 + 8 * q^42 - 28 * q^43 - 8 * q^45 + 36 * q^47 - 84 * q^49 - 8 * q^54 + 30 * q^57 + 28 * q^61 - 12 * q^63 + 136 * q^64 + 40 * q^66 - 84 * q^68 + 128 * q^73 - 84 * q^74 - 16 * q^76 - 84 * q^81 + 24 * q^82 + 60 * q^83 - 36 * q^87 - 120 * q^92 + 40 * q^93 - 12 * q^95 + 44 * q^96 + 84 * q^99

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