LMFDB - Embedded newform 380.2.n.b.31.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(31,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("380.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.n (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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.11
Character	$\chi$	$=$	380.31
Dual form			380.2.n.b.331.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0671334 + 1.41262i) q^{2} +(1.38246 + 2.39450i) q^{3} +(-1.99099 + 0.189668i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.28970 + 2.11365i) q^{6} +2.18272i q^{7} +(-0.401590 - 2.79977i) q^{8} +(-2.32241 + 4.02254i) q^{9} +O(q^{10})$	\(q+(0.0671334 + 1.41262i) q^{2} +(1.38246 + 2.39450i) q^{3} +(-1.99099 + 0.189668i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.28970 + 2.11365i) q^{6} +2.18272i q^{7} +(-0.401590 - 2.79977i) q^{8} +(-2.32241 + 4.02254i) q^{9} +(1.18980 - 0.764449i) q^{10} +2.17298i q^{11} +(-3.20663 - 4.50520i) q^{12} +(-4.38226 - 2.53010i) q^{13} +(-3.08336 + 0.146534i) q^{14} +(1.38246 - 2.39450i) q^{15} +(3.92805 - 0.755252i) q^{16} +(1.50270 + 2.60275i) q^{17} +(-5.83823 - 3.01064i) q^{18} +(3.96739 + 1.80549i) q^{19} +(1.15975 + 1.62941i) q^{20} +(-5.22653 + 3.01754i) q^{21} +(-3.06959 + 0.145880i) q^{22} +(-4.62252 - 2.66881i) q^{23} +(6.14887 - 4.83219i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.27987 - 6.36032i) q^{26} -4.54783 q^{27} +(-0.413992 - 4.34577i) q^{28} +(7.07391 + 4.08413i) q^{29} +(3.47532 + 1.79214i) q^{30} +1.63029 q^{31} +(1.33059 + 5.49814i) q^{32} +(-5.20320 + 3.00407i) q^{33} +(-3.57582 + 2.29748i) q^{34} +(1.89029 - 1.09136i) q^{35} +(3.86095 - 8.44930i) q^{36} +1.65367i q^{37} +(-2.28413 + 5.72562i) q^{38} -13.9911i q^{39} +(-2.22388 + 1.74767i) q^{40} +(3.52888 - 2.03740i) q^{41} +(-4.61350 - 7.18052i) q^{42} +(10.2968 - 5.94484i) q^{43} +(-0.412144 - 4.32637i) q^{44} +4.64483 q^{45} +(3.45969 - 6.70902i) q^{46} +(-0.310910 - 0.179504i) q^{47} +(7.23884 + 8.36160i) q^{48} +2.23572 q^{49} +(-1.25693 - 0.648170i) q^{50} +(-4.15486 + 7.19643i) q^{51} +(9.20490 + 4.20622i) q^{52} +(-9.75968 - 5.63476i) q^{53} +(-0.305311 - 6.42435i) q^{54} +(1.88186 - 1.08649i) q^{55} +(6.11113 - 0.876560i) q^{56} +(1.16153 + 11.9959i) q^{57} +(-5.29442 + 10.2669i) q^{58} +(2.15002 + 3.72394i) q^{59} +(-2.29831 + 5.02962i) q^{60} +(-4.18333 + 7.24574i) q^{61} +(0.109447 + 2.30298i) q^{62} +(-8.78009 - 5.06919i) q^{63} +(-7.67745 + 2.24872i) q^{64} +5.06020i q^{65} +(-4.59291 - 7.14846i) q^{66} +(-4.10768 + 7.11471i) q^{67} +(-3.48552 - 4.89704i) q^{68} -14.7581i q^{69} +(1.66858 + 2.59700i) q^{70} +(3.24775 + 5.62526i) q^{71} +(12.1948 + 4.88682i) q^{72} +(-2.49186 - 4.31602i) q^{73} +(-2.33601 + 0.111017i) q^{74} -2.76493 q^{75} +(-8.24147 - 2.84223i) q^{76} -4.74302 q^{77} +(19.7641 - 0.939268i) q^{78} +(3.74126 + 6.48006i) q^{79} +(-2.61809 - 3.02417i) q^{80} +(0.680033 + 1.17785i) q^{81} +(3.11498 + 4.84819i) q^{82} +0.827326i q^{83} +(9.83361 - 6.99918i) q^{84} +(1.50270 - 2.60275i) q^{85} +(9.08905 + 14.1463i) q^{86} +22.5846i q^{87} +(6.08385 - 0.872647i) q^{88} +(-14.4063 - 8.31749i) q^{89} +(0.311823 + 6.56137i) q^{90} +(5.52251 - 9.56526i) q^{91} +(9.70956 + 4.43683i) q^{92} +(2.25382 + 3.90372i) q^{93} +(0.232698 - 0.451248i) q^{94} +(-0.420092 - 4.33861i) q^{95} +(-11.3258 + 10.7871i) q^{96} +(12.9391 - 7.47039i) q^{97} +(0.150091 + 3.15822i) q^{98} +(-8.74090 - 5.04656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9	$ 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} - 18 q^{14} + 9 q^{16} - 12 q^{17} - 2 q^{20} + 12 q^{21} + 20 q^{24} - 20 q^{25} + 34 q^{26} + 12 q^{28} + 10 q^{30} - 12 q^{32} - 6 q^{33} - 27 q^{34} - 6 q^{36} + 12 q^{38} + 36 q^{41} - 21 q^{42} + 28 q^{44} + 44 q^{45} + 36 q^{48} - 60 q^{49} + 15 q^{52} - 66 q^{53} - 31 q^{54} + 28 q^{57} + 2 q^{58} + 3 q^{60} + 4 q^{61} - 57 q^{62} - 80 q^{64} + 18 q^{66} - 20 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} + 30 q^{76} + 12 q^{77} + 144 q^{78} + 9 q^{80} + 16 q^{81} - 41 q^{82} - 12 q^{85} + 18 q^{86} - 18 q^{89} + 39 q^{90} + 40 q^{92} - 8 q^{93} - 160 q^{96} - 18 q^{97} - 66 q^{98}+O(q^{100}) $ 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 - 18 * q^14 + 9 * q^16 - 12 * q^17 - 2 * q^20 + 12 * q^21 + 20 * q^24 - 20 * q^25 + 34 * q^26 + 12 * q^28 + 10 * q^30 - 12 * q^32 - 6 * q^33 - 27 * q^34 - 6 * q^36 + 12 * q^38 + 36 * q^41 - 21 * q^42 + 28 * q^44 + 44 * q^45 + 36 * q^48 - 60 * q^49 + 15 * q^52 - 66 * q^53 - 31 * q^54 + 28 * q^57 + 2 * q^58 + 3 * q^60 + 4 * q^61 - 57 * q^62 - 80 * q^64 + 18 * q^66 - 20 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 + 30 * q^76 + 12 * q^77 + 144 * q^78 + 9 * q^80 + 16 * q^81 - 41 * q^82 - 12 * q^85 + 18 * q^86 - 18 * q^89 + 39 * q^90 + 40 * q^92 - 8 * q^93 - 160 * q^96 - 18 * q^97 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	0.0671334	+	1.41262i	0.0474705	+	0.998873i
$2$	0.0671334	+	1.41262i	0.0474705	+	0.998873i
$3$	1.38246	+	2.39450i	0.798166	+	1.38246i	0.920809	+	0.390013i	$0.127530\pi$
$3$	1.38246	+	2.39450i	0.798166	+	1.38246i	−0.122643	+	0.992451i	$0.539137\pi$
$4$	−1.99099	+	0.189668i	−0.995493	+	0.0948339i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−3.28970	+	2.11365i	−1.34302	+	0.862892i
$7$			2.18272i			0.824992i	0.910959	+	0.412496i	$0.135343\pi$
$7$			2.18272i			0.824992i	−0.910959	+	0.412496i	$0.864657\pi$
$8$	−0.401590	−	2.79977i	−0.141983	−	0.989869i
$9$	−2.32241	+	4.02254i	−0.774138	+	1.34085i
$10$	1.18980	−	0.764449i	0.376247	−	0.241740i
$11$			2.17298i			0.655178i	0.944820	+	0.327589i	$0.106236\pi$
$11$			2.17298i			0.655178i	−0.944820	+	0.327589i	$0.893764\pi$
$12$	−3.20663	−	4.50520i	−0.925673	−	1.30054i
$13$	−4.38226	−	2.53010i	−1.21542	−	0.701723i	−0.251485	−	0.967861i	$-0.580919\pi$
$13$	−4.38226	−	2.53010i	−1.21542	−	0.701723i	−0.963935	+	0.266138i	$0.914252\pi$
$14$	−3.08336	+	0.146534i	−0.824062	+	0.0391627i
$15$	1.38246	−	2.39450i	0.356951	−	0.618257i
$16$	3.92805	−	0.755252i	0.982013	−	0.188813i
$17$	1.50270	+	2.60275i	0.364459	+	0.631261i	0.988689	−	0.149979i	$-0.0479207\pi$
$17$	1.50270	+	2.60275i	0.364459	+	0.631261i	−0.624231	+	0.781240i	$0.714587\pi$
$18$	−5.83823	−	3.01064i	−1.37608	−	0.709614i
$19$	3.96739	+	1.80549i	0.910182	+	0.414209i
$19$	3.96739	+	1.80549i	0.910182	+	0.414209i
$20$	1.15975	+	1.62941i	0.259328	+	0.364347i
$21$	−5.22653	+	3.01754i	−1.14052	+	0.658481i
$22$	−3.06959	+	0.145880i	−0.654440	+	0.0311016i
$23$	−4.62252	−	2.66881i	−0.963862	−	0.556486i	−0.0665022	−	0.997786i	$-0.521184\pi$
$23$	−4.62252	−	2.66881i	−0.963862	−	0.556486i	−0.897359	+	0.441301i	$0.854517\pi$
$24$	6.14887	−	4.83219i	1.25513	−	0.986367i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.27987	−	6.36032i	0.643236	−	1.24736i
$27$	−4.54783			−0.875230
$28$	−0.413992	−	4.34577i	−0.0782372	−	0.821274i
$29$	7.07391	+	4.08413i	1.31359	+	0.758403i	0.982689	−	0.185261i	$-0.0593132\pi$
$29$	7.07391	+	4.08413i	1.31359	+	0.758403i	0.330904	+	0.943665i	$0.392647\pi$
$30$	3.47532	+	1.79214i	0.634504	+	0.327199i
$31$	1.63029			0.292808			0.146404	−	0.989225i	$-0.453230\pi$
$31$	1.63029			0.292808			0.146404	+	0.989225i	$0.453230\pi$
$32$	1.33059	+	5.49814i	0.235217	+	0.971943i
$33$	−5.20320	+	3.00407i	−0.905760	+	0.522941i
$34$	−3.57582	+	2.29748i	−0.613248	+	0.394014i
$35$	1.89029	−	1.09136i	0.319518	−	0.184474i
$36$	3.86095	−	8.44930i	0.643491	−	1.40822i
$37$			1.65367i			0.271862i	0.990718	+	0.135931i	$0.0434026\pi$
$37$			1.65367i			0.271862i	−0.990718	+	0.135931i	$0.956597\pi$
$38$	−2.28413	+	5.72562i	−0.370535	+	0.928819i
$39$		−	13.9911i		−	2.24037i
$40$	−2.22388	+	1.74767i	−0.351626	+	0.276331i
$41$	3.52888	−	2.03740i	0.551119	−	0.318189i	−0.198454	−	0.980110i	$-0.563592\pi$
$41$	3.52888	−	2.03740i	0.551119	−	0.318189i	0.749573	+	0.661922i	$0.230259\pi$
$42$	−4.61350	−	7.18052i	−0.711879	−	1.10798i
$43$	10.2968	−	5.94484i	1.57024	−	0.906580i	0.574104	−	0.818783i	$-0.305351\pi$
$43$	10.2968	−	5.94484i	1.57024	−	0.906580i	0.996138	−	0.0877972i	$-0.0279827\pi$
$44$	−0.412144	−	4.32637i	−0.0621331	−	0.652226i
$45$	4.64483			0.692410
$46$	3.45969	−	6.70902i	0.510103	−	0.989192i
$47$	−0.310910	−	0.179504i	−0.0453509	−	0.0261833i	0.477153	−	0.878820i	$-0.341669\pi$
$47$	−0.310910	−	0.179504i	−0.0453509	−	0.0261833i	−0.522504	+	0.852637i	$0.675002\pi$
$48$	7.23884	+	8.36160i	1.04484	+	1.20689i
$49$	2.23572			0.319388
$50$	−1.25693	−	0.648170i	−0.177757	−	0.0916651i
$51$	−4.15486	+	7.19643i	−0.581797	+	1.00770i
$52$	9.20490	+	4.20622i	1.27649	+	0.583298i
$53$	−9.75968	−	5.63476i	−1.34060	−	0.773993i	−0.353701	−	0.935359i	$-0.615077\pi$
$53$	−9.75968	−	5.63476i	−1.34060	−	0.773993i	−0.986895	+	0.161365i	$0.948410\pi$
$54$	−0.305311	−	6.42435i	−0.0415476	−	0.874243i
$55$	1.88186	−	1.08649i	0.253749	−	0.146502i
$56$	6.11113	−	0.876560i	0.816634	−	0.117135i
$57$	1.16153	+	11.9959i	0.153848	+	1.58890i
$58$	−5.29442	+	10.2669i	−0.695191	+	1.34811i
$59$	2.15002	+	3.72394i	0.279908	+	0.484816i	0.971362	−	0.237606i	$-0.0763626\pi$
$59$	2.15002	+	3.72394i	0.279908	+	0.484816i	−0.691453	+	0.722421i	$0.743029\pi$
$60$	−2.29831	+	5.02962i	−0.296710	+	0.649321i
$61$	−4.18333	+	7.24574i	−0.535621	+	0.927722i	0.463512	+	0.886091i	$0.346589\pi$
$61$	−4.18333	+	7.24574i	−0.535621	+	0.927722i	−0.999133	+	0.0416319i	$0.986744\pi$
$62$	0.109447	+	2.30298i	0.0138998	+	0.292478i
$63$	−8.78009	−	5.06919i	−1.10619	−	0.638657i
$64$	−7.67745	+	2.24872i	−0.959681	+	0.281090i
$65$			5.06020i			0.627640i
$66$	−4.59291	−	7.14846i	−0.565348	−	0.879915i
$67$	−4.10768	+	7.11471i	−0.501833	+	0.869200i	0.498165	+	0.867082i	$0.334007\pi$
$67$	−4.10768	+	7.11471i	−0.501833	+	0.869200i	−0.999998	+	0.00211743i	$0.999326\pi$
$68$	−3.48552	−	4.89704i	−0.422681	−	0.593853i
$69$		−	14.7581i		−	1.77667i
$70$	1.66858	+	2.59700i	0.199434	+	0.310401i
$71$	3.24775	+	5.62526i	0.385437	+	0.667596i	0.991830	−	0.127569i	$-0.0407175\pi$
$71$	3.24775	+	5.62526i	0.385437	+	0.667596i	−0.606393	+	0.795165i	$0.707384\pi$
$72$	12.1948	+	4.88682i	1.43718	+	0.575917i
$73$	−2.49186	−	4.31602i	−0.291650	−	0.505152i	0.682550	−	0.730839i	$-0.260871\pi$
$73$	−2.49186	−	4.31602i	−0.291650	−	0.505152i	−0.974200	+	0.225686i	$0.927538\pi$
$74$	−2.33601	+	0.111017i	−0.271556	+	0.0129054i
$75$	−2.76493			−0.319266
$76$	−8.24147	−	2.84223i	−0.945361	−	0.326026i
$77$	−4.74302			−0.540517
$78$	19.7641	−	0.939268i	2.23784	−	0.106351i
$79$	3.74126	+	6.48006i	0.420925	+	0.729063i	0.996030	−	0.0890162i	$-0.0283723\pi$
$79$	3.74126	+	6.48006i	0.420925	+	0.729063i	−0.575105	+	0.818079i	$0.695039\pi$
$80$	−2.61809	−	3.02417i	−0.292712	−	0.338112i
$81$	0.680033	+	1.17785i	0.0755592	+	0.130872i
$82$	3.11498	+	4.84819i	0.343992	+	0.535393i
$83$			0.827326i			0.0908108i	0.998969	+	0.0454054i	$0.0144580\pi$
$83$			0.827326i			0.0908108i	−0.998969	+	0.0454054i	$0.985542\pi$
$84$	9.83361	−	6.99918i	1.07294	−	0.763673i
$85$	1.50270	−	2.60275i	0.162991	−	0.282308i
$86$	9.08905	+	14.1463i	0.980098	+	1.52544i
$87$			22.5846i			2.42133i
$88$	6.08385	−	0.872647i	0.648541	−	0.0930245i
$89$	−14.4063	−	8.31749i	−1.52707	−	0.881652i	−0.999483	−	0.0321483i	$-0.989765\pi$
$89$	−14.4063	−	8.31749i	−1.52707	−	0.881652i	−0.527583	−	0.849504i	$-0.676902\pi$
$90$	0.311823	+	6.56137i	0.0328690	+	0.691629i
$91$	5.52251	−	9.56526i	0.578916	−	1.00271i
$92$	9.70956	+	4.43683i	1.01229	+	0.462571i
$93$	2.25382	+	3.90372i	0.233710	+	0.404797i
$94$	0.232698	−	0.451248i	0.0240010	−	0.0465427i
$95$	−0.420092	−	4.33861i	−0.0431006	−	0.445132i
$96$	−11.3258	+	10.7871i	−1.15593	+	1.10095i
$97$	12.9391	−	7.47039i	1.31377	−	0.758503i	0.331048	−	0.943614i	$-0.392598\pi$
$97$	12.9391	−	7.47039i	1.31377	−	0.758503i	0.982718	+	0.185111i	$0.0592643\pi$
$98$	0.150091	+	3.15822i	0.0151615	+	0.319028i
$99$	−8.74090	−	5.04656i	−0.878493	−	0.507198i
$100$	0.831236	−	1.81908i	0.0831236	−	0.181908i
$101$	2.26854	−	3.92923i	0.225728	−	0.390973i	−0.730809	−	0.682581i	$-0.760857\pi$
$101$	2.26854	−	3.92923i	0.225728	−	0.390973i	0.956538	+	0.291609i	$0.0941906\pi$
$102$	−10.4447	−	5.38612i	−1.03418	−	0.533305i
$103$	17.9724			1.77088			0.885438	−	0.464757i	$-0.153858\pi$
$103$	17.9724			1.77088			0.885438	+	0.464757i	$0.153858\pi$
$104$	−5.32383	+	13.2854i	−0.522044	+	1.30274i
$105$	5.22653	+	3.01754i	0.510057	+	0.294481i
$106$	7.30456	−	14.1650i	0.709482	−	1.37583i
$107$	−13.8396			−1.33792			−0.668961	−	0.743297i	$-0.733261\pi$
$107$	−13.8396			−1.33792			−0.668961	+	0.743297i	$0.733261\pi$
$108$	9.05466	−	0.862576i	0.871285	−	0.0830014i
$109$	6.20653	−	3.58334i	0.594478	−	0.343222i	−0.172388	−	0.985029i	$-0.555148\pi$
$109$	6.20653	−	3.58334i	0.594478	−	0.343222i	0.766866	+	0.641807i	$0.221815\pi$
$110$	1.66113	+	2.58541i	0.158383	+	0.246509i
$111$	−3.95971	+	2.28614i	−0.375840	+	0.216991i
$112$	1.64851	+	8.57385i	0.155769	+	0.810153i
$113$		−	3.59380i		−	0.338076i	−0.985610	−	0.169038i	$-0.945934\pi$
$113$		−	3.59380i		−	0.338076i	0.985610	−	0.169038i	$-0.0540661\pi$
$114$	−16.8677	+	2.44612i	−1.57981	+	0.229100i
$115$			5.33762i			0.497736i
$116$	−14.8587	−	6.78975i	−1.37959	−	0.630412i
$117$	20.3548	−	11.7519i	1.88181	−	1.08646i
$118$	−5.11617	+	3.28716i	−0.470982	+	0.302607i
$119$	−5.68109	+	3.27998i	−0.520785	+	0.300675i
$120$	−7.25923	−	2.90898i	−0.662674	−	0.265552i
$121$	6.27815			0.570741
$122$	−10.5163	−	5.42302i	−0.952103	−	0.490978i
$123$	9.75710	+	5.63327i	0.879769	+	0.507935i
$124$	−3.24588	+	0.309213i	−0.291489	+	0.0277682i
$125$	1.00000			0.0894427
$126$	6.57139	−	12.7432i	0.585426	−	1.13526i
$127$	7.38413	−	12.7897i	0.655236	−	1.13490i	−0.326599	−	0.945163i	$-0.605903\pi$
$127$	7.38413	−	12.7897i	0.655236	−	1.13490i	0.981835	−	0.189739i	$-0.0607642\pi$
$128$	−3.69200	−	10.6944i	−0.326330	−	0.945256i
$129$	28.4698	+	16.4371i	2.50663	+	1.44720i
$130$	−7.14813	+	0.339708i	−0.626933	+	0.0297944i
$131$	−3.92080	+	2.26367i	−0.342561	+	0.197778i	−0.661404	−	0.750030i	$-0.730039\pi$
$131$	−3.92080	+	2.26367i	−0.342561	+	0.197778i	0.318843	+	0.947808i	$0.396706\pi$
$132$	9.78972	−	6.96794i	0.852086	−	0.606481i
$133$	−3.94089	+	8.65972i	−0.341719	+	0.750893i
$134$	−10.3261	−	5.32495i	−0.892042	−	0.460006i
$135$	2.27391	+	3.93853i	0.195707	+	0.338975i
$136$	6.68365	−	5.25246i	0.573118	−	0.450395i
$137$	−2.88771	+	5.00166i	−0.246714	+	0.427320i	−0.962612	−	0.270884i	$-0.912684\pi$
$137$	−2.88771	+	5.00166i	−0.246714	+	0.427320i	0.715898	+	0.698204i	$0.246017\pi$
$138$	20.8476	−	0.990764i	1.77467	−	0.0843394i
$139$	−7.50843	−	4.33499i	−0.636857	−	0.367689i	0.146546	−	0.989204i	$-0.453184\pi$
$139$	−7.50843	−	4.33499i	−0.636857	−	0.367689i	−0.783403	+	0.621514i	$0.786518\pi$
$140$	−3.55655	+	2.53141i	−0.300584	+	0.213944i
$141$		−	0.992631i		−	0.0835946i
$142$	−7.72832	+	4.96547i	−0.648546	+	0.416693i
$143$	5.49786	−	9.52257i	0.459754	−	0.796317i
$144$	−6.08453	+	17.5547i	−0.507044	+	1.46290i
$145$		−	8.16825i		−	0.678336i
$146$	5.92961	−	3.80979i	0.490738	−	0.315301i
$147$	3.09080	+	5.35342i	0.254925	+	0.441543i
$148$	−0.313648	−	3.29244i	−0.0257817	−	0.270637i
$149$	−10.3988	−	18.0113i	−0.851907	−	1.47555i	−0.879485	−	0.475926i	$-0.842113\pi$
$149$	−10.3988	−	18.0113i	−0.851907	−	1.47555i	0.0275781	−	0.999620i	$-0.491221\pi$
$150$	−0.185619	−	3.90579i	−0.0151557	−	0.318906i
$151$	13.8156			1.12430			0.562151	−	0.827035i	$-0.309974\pi$
$151$	13.8156			1.12430			0.562151	+	0.827035i	$0.309974\pi$
$152$	3.46171	−	11.8329i	0.280781	−	0.959772i
$153$	−13.9596			−1.12856
$154$	−0.318415	−	6.70008i	−0.0256586	−	0.539908i
$155$	−0.815144	−	1.41187i	−0.0654740	−	0.113404i
$156$	2.65366	+	27.8561i	0.212463	+	2.23027i
$157$	−10.7080	−	18.5468i	−0.854589	−	1.48019i	−0.877026	−	0.480444i	$-0.840476\pi$
$157$	−10.7080	−	18.5468i	−0.854589	−	1.48019i	0.0224363	−	0.999748i	$-0.492858\pi$
$158$	−8.90269	+	5.72001i	−0.708260	+	0.455059i
$159$		−	31.1594i		−	2.47110i
$160$	4.09624	−	3.90139i	0.323836	−	0.308432i
$161$	5.82528	−	10.0897i	0.459096	−	0.795178i
$162$	−1.61820	+	1.03970i	−0.127138	+	0.0816866i
$163$			13.9029i			1.08896i	0.838773	+	0.544481i	$0.183273\pi$
$163$			13.9029i			1.08896i	−0.838773	+	0.544481i	$0.816727\pi$
$164$	−6.63953	+	4.72575i	−0.518460	+	0.369019i
$165$	5.20320	+	3.00407i	0.405068	+	0.233866i
$166$	−1.16870	+	0.0555412i	−0.0907084	+	0.00431083i
$167$	3.32755	−	5.76348i	0.257494	−	0.445992i	−0.708076	−	0.706136i	$-0.750437\pi$
$167$	3.32755	−	5.76348i	0.257494	−	0.445992i	0.965570	+	0.260144i	$0.0837701\pi$
$168$	10.5473	+	13.4213i	0.813745	+	1.03547i
$169$	6.30280	+	10.9168i	0.484831	+	0.839752i
$170$	3.77758	+	1.94801i	0.289727	+	0.149406i
$171$	−16.4766	+	11.7659i	−1.26000	+	0.899759i
$172$	−19.3732	+	13.7891i	−1.47719	+	1.05141i
$173$	−10.7277	+	6.19363i	−0.815611	+	0.470893i	−0.848901	−	0.528553i	$-0.822735\pi$
$173$	−10.7277	+	6.19363i	−0.815611	+	0.470893i	0.0332896	+	0.999446i	$0.489402\pi$
$174$	−31.9035	+	1.51618i	−2.41860	+	0.114941i
$175$	−1.89029	−	1.09136i	−0.142893	−	0.0824992i
$176$	1.64115	+	8.53558i	0.123706	+	0.643394i
$177$	−5.94464	+	10.2964i	−0.446827	+	0.773926i
$178$	10.7823	−	20.9090i	0.808167	−	1.56720i
$179$	−8.20196			−0.613043			−0.306522	−	0.951864i	$-0.599165\pi$
$179$	−8.20196			−0.613043			−0.306522	+	0.951864i	$0.599165\pi$
$180$	−9.24779	+	0.880974i	−0.689289	+	0.0656639i
$181$	−4.15238	−	2.39738i	−0.308644	−	0.178196i	0.337676	−	0.941263i	$-0.390359\pi$
$181$	−4.15238	−	2.39738i	−0.308644	−	0.178196i	−0.646320	+	0.763067i	$0.723693\pi$
$182$	13.8828	+	7.15905i	1.02906	+	0.530664i
$183$	−23.1332			−1.71006
$184$	−5.61571	+	14.0138i	−0.413996	+	1.03311i
$185$	1.43212	−	0.826836i	0.105292	−	0.0607902i
$186$	−5.36317	+	3.44585i	−0.393247	+	0.252662i
$187$	−5.65574	+	3.26534i	−0.413588	+	0.238785i
$188$	0.653064	+	0.298420i	0.0476296	+	0.0217645i
$189$		−	9.92665i		−	0.722057i
$190$	6.10060	−	0.884696i	0.442584	−	0.0641826i
$191$		−	2.08371i		−	0.150772i	−0.997154	−	0.0753861i	$-0.975981\pi$
$191$		−	2.08371i		−	0.150772i	0.997154	−	0.0753861i	$-0.0240189\pi$
$192$	−15.9984	−	15.2749i	−1.15458	−	1.10237i
$193$	14.5234	−	8.38512i	1.04542	−	0.603574i	0.124057	−	0.992275i	$-0.460410\pi$
$193$	14.5234	−	8.38512i	1.04542	−	0.603574i	0.921364	+	0.388701i	$0.127076\pi$
$194$	11.4215	+	17.7765i	0.820013	+	1.27628i
$195$	−12.1166	+	6.99554i	−0.867690	+	0.500961i
$196$	−4.45128	+	0.424044i	−0.317949	+	0.0302888i
$197$	2.20542			0.157130			0.0785648	−	0.996909i	$-0.474966\pi$
$197$	2.20542			0.157130			0.0785648	+	0.996909i	$0.474966\pi$
$198$	6.54206	−	12.6864i	0.464924	−	0.901580i
$199$	20.3102	+	11.7261i	1.43975	+	0.831243i	0.997832	−	0.0658103i	$-0.0209632\pi$
$199$	20.3102	+	11.7261i	1.43975	+	0.831243i	0.441923	+	0.897053i	$0.354297\pi$
$200$	2.62547	+	1.05210i	0.185649	+	0.0743946i
$201$	−22.7149			−1.60218
$202$	5.70280	+	2.94080i	0.401247	+	0.206914i
$203$	−8.91452	+	15.4404i	−0.625677	+	1.08370i
$204$	6.90734	−	15.1160i	0.483611	−	1.05833i
$205$	−3.52888	−	2.03740i	−0.246468	−	0.142298i
$206$	1.20655	+	25.3882i	0.0840643	+	1.76888i
$207$	21.4708	−	12.3962i	1.49232	−	0.861593i
$208$	−19.1246	−	6.62865i	−1.32605	−	0.459614i
$209$	−3.92330	+	8.62106i	−0.271381	+	0.596332i
$210$	−3.91176	+	7.58567i	−0.269937	+	0.523461i
$211$	−13.5923	−	23.5425i	−0.935730	−	1.62073i	−0.773326	−	0.634008i	$-0.781409\pi$
$211$	−13.5923	−	23.5425i	−0.935730	−	1.62073i	−0.162404	−	0.986724i	$-0.551925\pi$
$212$	20.5001	+	9.36762i	1.40795	+	0.643371i
$213$	−8.97979	+	15.5534i	−0.615285	+	1.06570i
$214$	−0.929097	−	19.5501i	−0.0635118	−	1.33641i
$215$	−10.2968	−	5.94484i	−0.702234	−	0.405435i
$216$	1.82636	+	12.7329i	0.124268	+	0.866363i
$217$			3.55847i			0.241565i
$218$	5.47857	+	8.52691i	0.371055	+	0.577515i
$219$	6.88981	−	11.9335i	0.465570	−	0.806391i
$220$	−3.54068	+	2.52011i	−0.238712	+	0.169906i
$221$		−	15.2079i		−	1.02300i
$222$	−3.49528	−	5.44009i	−0.234588	−	0.365115i
$223$	−5.83141	−	10.1003i	−0.390500	−	0.676365i	0.602016	−	0.798484i	$-0.294364\pi$
$223$	−5.83141	−	10.1003i	−0.390500	−	0.676365i	−0.992515	+	0.122119i	$0.961031\pi$
$224$	−12.0009	+	2.90430i	−0.801845	+	0.194052i
$225$	−2.32241	−	4.02254i	−0.154828	−	0.268169i
$226$	5.07667	−	0.241264i	0.337695	−	0.0160486i
$227$	18.2541			1.21157			0.605784	−	0.795629i	$-0.292859\pi$
$227$	18.2541			1.21157			0.605784	+	0.795629i	$0.292859\pi$
$228$	−4.58782	−	23.6634i	−0.303836	−	1.56715i
$229$	12.6355			0.834974			0.417487	−	0.908683i	$-0.362911\pi$
$229$	12.6355			0.834974			0.417487	+	0.908683i	$0.362911\pi$
$230$	−7.54003	+	0.358333i	−0.497175	+	0.0236278i
$231$	−6.55705	−	11.3571i	−0.431422	−	0.747245i
$232$	8.59381	−	21.4455i	0.564211	−	1.40797i
$233$	−5.05480	−	8.75517i	−0.331151	−	0.573571i	0.651587	−	0.758574i	$-0.274104\pi$
$233$	−5.05480	−	8.75517i	−0.331151	−	0.573571i	−0.982738	+	0.185004i	$0.940770\pi$
$234$	17.9674	+	27.9647i	1.17457	+	1.82811i
$235$			0.359008i			0.0234191i
$236$	−4.98697	−	7.00652i	−0.324624	−	0.456086i
$237$	−10.3443	+	17.9169i	−0.671936	+	1.16383i
$238$	−5.01476	−	7.80503i	−0.325058	−	0.505925i
$239$		−	16.7508i		−	1.08352i	−0.840533	−	0.541760i	$-0.817758\pi$
$239$		−	16.7508i		−	1.08352i	0.840533	−	0.541760i	$-0.182242\pi$
$240$	3.62194	−	10.4498i	0.233795	−	0.674533i
$241$	−11.4567	−	6.61455i	−0.737993	−	0.426081i	0.0833459	−	0.996521i	$-0.473439\pi$
$241$	−11.4567	−	6.61455i	−0.737993	−	0.426081i	−0.821339	+	0.570440i	$0.806773\pi$
$242$	0.421474	+	8.86864i	0.0270934	+	0.570098i
$243$	−8.70198	+	15.0723i	−0.558232	+	0.966887i
$244$	6.95467	−	15.2196i	0.445227	−	0.974336i
$245$	−1.11786	−	1.93619i	−0.0714174	−	0.123699i
$246$	−7.30263	+	14.1613i	−0.465599	+	0.902889i
$247$	−12.8181	−	17.9500i	−0.815594	−	1.14213i
$248$	−0.654708	−	4.56444i	−0.0415740	−	0.289842i
$249$	−1.98103	+	1.14375i	−0.125543	+	0.0724821i
$250$	0.0671334	+	1.41262i	0.00424589	+	0.0893419i
$251$	−1.63502	−	0.943979i	−0.103201	−	0.0595834i	0.447511	−	0.894278i	$-0.352311\pi$
$251$	−1.63502	−	0.943979i	−0.103201	−	0.0595834i	−0.550712	+	0.834695i	$0.685644\pi$
$252$	18.4425	+	8.42738i	1.16177	+	0.530875i
$253$	5.79928	−	10.0446i	0.364597	−	0.631501i
$254$	18.5627	+	9.57236i	1.16473	+	0.600623i
$255$	8.30972			0.520375
$256$	14.8592	−	5.93334i	0.928699	−	0.370834i
$257$	9.93205	+	5.73427i	0.619544	+	0.357694i	0.776691	−	0.629881i	$-0.216896\pi$
$257$	9.93205	+	5.73427i	0.619544	+	0.357694i	−0.157147	+	0.987575i	$0.550230\pi$
$258$	−21.3080	+	41.3205i	−1.32658	+	2.57250i
$259$	−3.60951			−0.224284
$260$	−0.959756	−	10.0748i	−0.0595216	−	0.624812i
$261$	−32.8571	+	18.9701i	−2.03380	+	1.17422i
$262$	−3.46092	−	5.38662i	−0.213817	−	0.332787i
$263$	−11.5681	+	6.67887i	−0.713322	+	0.411837i	−0.812290	−	0.583254i	$-0.801779\pi$
$263$	−11.5681	+	6.67887i	−0.713322	+	0.411837i	0.0989677	+	0.995091i	$0.468446\pi$
$264$	10.5003	+	13.3614i	0.646246	+	0.822335i
$265$			11.2695i			0.692281i
$266$	−12.4975	−	4.98563i	−0.766268	−	0.305688i
$267$		−	45.9945i		−	2.81482i
$268$	6.82890	−	14.9444i	0.417141	−	0.912873i
$269$	20.0598	−	11.5815i	1.22307	−	0.706138i	0.257496	−	0.966279i	$-0.417103\pi$
$269$	20.0598	−	11.5815i	1.22307	−	0.706138i	0.965570	+	0.260142i	$0.0837693\pi$
$270$	−5.41099	+	3.47658i	−0.329303	+	0.211578i
$271$	−18.2451	+	10.5338i	−1.10831	+	0.639885i	−0.938392	−	0.345572i	$-0.887685\pi$
$271$	−18.2451	+	10.5338i	−1.10831	+	0.639885i	−0.169922	+	0.985458i	$0.554351\pi$
$272$	7.86842	+	9.08884i	0.477093	+	0.551092i
$273$	30.5387			1.84828
$274$	−7.25930	−	3.74345i	−0.438550	−	0.226150i
$275$	−1.88186	−	1.08649i	−0.113480	−	0.0655178i
$276$	2.79914	+	29.3833i	0.168489	+	1.76866i
$277$	−24.5511			−1.47513			−0.737566	−	0.675275i	$-0.764025\pi$
$277$	−24.5511			−1.47513			−0.737566	+	0.675275i	$0.764025\pi$
$278$	5.61963	−	10.8976i	0.337043	−	0.653593i
$279$	−3.78620	+	6.55790i	−0.226674	+	0.392611i
$280$	−3.81469	−	4.85411i	−0.227971	−	0.290089i
$281$	5.01344	+	2.89451i	0.299077	+	0.172672i	0.642028	−	0.766681i	$-0.278093\pi$
$281$	5.01344	+	2.89451i	0.299077	+	0.172672i	−0.342951	+	0.939353i	$0.611427\pi$
$282$	1.40221	−	0.0666387i	0.0835004	−	0.00396828i
$283$	−14.1273	+	8.15640i	−0.839781	+	0.484848i	−0.857190	−	0.515001i	$-0.827792\pi$
$283$	−14.1273	+	8.15640i	−0.839781	+	0.484848i	0.0174087	+	0.999848i	$0.494458\pi$
$284$	−7.53315	−	10.5838i	−0.447010	−	0.628035i
$285$	9.80803	−	7.00388i	0.580977	−	0.414874i
$286$	13.8209	+	7.12710i	0.817244	+	0.421434i
$287$	4.44708	+	7.70257i	0.262503	+	0.454669i
$288$	−25.2066	−	7.41662i	−1.48532	−	0.437028i
$289$	3.98378	−	6.90011i	0.234340	−	0.405889i
$290$	11.5386	−	0.548362i	0.677572	−	0.0322009i
$291$	35.7757	+	20.6551i	2.09721	+	1.21082i
$292$	5.77986	+	8.12052i	0.338241	+	0.475217i
$293$			9.21300i			0.538229i	0.963108	+	0.269115i	$0.0867311\pi$
$293$			9.21300i			0.538229i	−0.963108	+	0.269115i	$0.913269\pi$
$294$	−7.35485	+	4.72551i	−0.428943	+	0.275598i
$295$	2.15002	−	3.72394i	0.125179	−	0.216816i
$296$	4.62991	−	0.664098i	0.269108	−	0.0385999i
$297$		−	9.88234i		−	0.573432i
$298$	24.7450	−	15.8988i	1.43344	−	0.920991i
$299$	13.5047	+	23.3909i	0.780998	+	1.35273i
$300$	5.50493	−	0.524418i	0.317827	−	0.0302773i
$301$	12.9759	+	22.4750i	0.747921	+	1.29544i
$302$	0.927491	+	19.5163i	0.0533711	+	1.12303i
$303$	12.5447			0.720674
$304$	16.9477	+	4.09569i	0.972019	+	0.234904i
$305$	8.36666			0.479074
$306$	−0.937153	−	19.7196i	−0.0535735	−	1.12729i
$307$	−0.206707	−	0.358027i	−0.0117974	−	0.0204337i	0.860066	−	0.510182i	$-0.170422\pi$
$307$	−0.206707	−	0.358027i	−0.0117974	−	0.0204337i	−0.871864	+	0.489748i	$0.837089\pi$
$308$	9.44328	−	0.899597i	0.538081	−	0.0512593i
$309$	24.8462	+	43.0349i	1.41345	+	2.44817i
$310$	1.93971	−	1.24627i	0.110168	−	0.0707835i
$311$		−	4.30800i		−	0.244284i	−0.992513	−	0.122142i	$-0.961024\pi$
$311$		−	4.30800i		−	0.244284i	0.992513	−	0.122142i	$-0.0389764\pi$
$312$	−39.1718	+	5.61868i	−2.21767	+	0.318095i
$313$	11.4791	−	19.8824i	0.648838	−	1.12382i	−0.334563	−	0.942374i	$-0.608589\pi$
$313$	11.4791	−	19.8824i	0.648838	−	1.12382i	0.983401	−	0.181447i	$-0.0580781\pi$
$314$	25.4806	−	16.3714i	1.43796	−	0.923891i
$315$			10.1384i			0.571233i
$316$	−8.67786	−	12.1921i	−0.488168	−	0.685859i
$317$	12.5590	+	7.25094i	0.705383	+	0.407253i	0.809349	−	0.587328i	$-0.199820\pi$
$317$	12.5590	+	7.25094i	0.705383	+	0.407253i	−0.103966	+	0.994581i	$0.533153\pi$
$318$	44.0163	−	2.09183i	2.46831	−	0.117304i
$319$	−8.87473	+	15.3715i	−0.496889	+	0.860638i
$320$	5.78617	+	5.52451i	0.323457	+	0.308829i
$321$	−19.1327	−	33.1388i	−1.06788	−	1.84963i
$322$	14.6439	+	7.55155i	0.816075	+	0.420831i
$323$	1.26255	+	13.0393i	0.0702500	+	0.725524i
$324$	−1.57734	−	2.21611i	−0.0876298	−	0.123117i
$325$	4.38226	−	2.53010i	0.243084	−	0.140345i
$326$	−19.6395	+	0.933351i	−1.08773	+	0.0516935i
$327$	17.1606	+	9.90769i	0.948984	+	0.547896i
$328$	−7.12142	−	9.06187i	−0.393215	−	0.500358i
$329$	0.391808	−	0.678631i	0.0216011	−	0.0374141i
$330$	−3.89430	+	7.55181i	−0.214374	+	0.415713i
$331$	11.0317			0.606359			0.303179	−	0.952934i	$-0.401952\pi$
$331$	11.0317			0.606359			0.303179	+	0.952934i	$0.401952\pi$
$332$	−0.156917	−	1.64719i	−0.00861194	−	0.0904015i
$333$	−6.65196	−	3.84051i	−0.364525	−	0.210459i
$334$	8.36500	+	4.31364i	0.457712	+	0.236032i
$335$	8.21535			0.448853
$336$	−18.2511	+	15.8004i	−0.995678	+	0.861982i
$337$	−17.1575	+	9.90587i	−0.934627	+	0.539607i	−0.888272	−	0.459318i	$-0.848094\pi$
$337$	−17.1575	+	9.90587i	−0.934627	+	0.539607i	−0.0463550	+	0.998925i	$0.514761\pi$
$338$	−14.9981	+	9.63634i	−0.815790	+	0.524148i
$339$	8.60534	−	4.96830i	0.467378	−	0.269841i
$340$	−2.49820	+	5.46706i	−0.135484	+	0.296493i
$341$			3.54259i			0.191842i
$342$	−17.7268	−	22.4853i	−0.958558	−	1.21586i
$343$			20.1590i			1.08848i
$344$	−20.7793	−	26.4412i	−1.12034	−	1.42561i
$345$	−12.7809	+	7.37907i	−0.688102	+	0.397276i
$346$	−9.46943	−	14.7383i	−0.509080	−	0.792338i
$347$	−17.6766	+	10.2056i	−0.948932	+	0.547866i	−0.892749	−	0.450554i	$-0.851226\pi$
$347$	−17.6766	+	10.2056i	−0.948932	+	0.547866i	−0.0561829	+	0.998420i	$0.517893\pi$
$348$	−4.28358	−	44.9657i	−0.229624	−	2.41041i
$349$	−3.44772			−0.184552			−0.0922762	−	0.995733i	$-0.529414\pi$
$349$	−3.44772			−0.184552			−0.0922762	+	0.995733i	$0.529414\pi$
$350$	1.41478	−	2.74353i	0.0756230	−	0.146648i
$351$	19.9298	+	11.5065i	1.06377	+	0.614169i
$352$	−11.9474	+	2.89134i	−0.636796	+	0.154109i
$353$	−31.8847			−1.69705			−0.848526	−	0.529154i	$-0.822509\pi$
$353$	−31.8847			−1.69705			−0.848526	+	0.529154i	$0.822509\pi$
$354$	−14.9440	−	7.70628i	−0.794265	−	0.409584i
$355$	3.24775	−	5.62526i	0.172373	−	0.298558i
$356$	30.2603	+	13.8276i	1.60379	+	0.732861i
$357$	−15.7078	−	9.06891i	−0.831346	−	0.479978i
$358$	−0.550625	−	11.5862i	−0.0291014	−	0.612352i
$359$	14.6161	−	8.43860i	0.771408	−	0.445372i	−0.0619688	−	0.998078i	$-0.519738\pi$
$359$	14.6161	−	8.43860i	0.771408	−	0.445372i	0.833377	+	0.552706i	$0.186405\pi$
$360$	−1.86532	−	13.0045i	−0.0983108	−	0.685395i
$361$	12.4804	+	14.3262i	0.656862	+	0.754010i
$362$	3.10782	−	6.02668i	0.163343	−	0.316755i
$363$	8.67932	+	15.0330i	0.455546	+	0.789029i
$364$	−9.18101	+	20.0917i	−0.481216	+	1.05309i
$365$	−2.49186	+	4.31602i	−0.130430	+	0.225911i
$366$	−1.55301	−	32.6784i	−0.0811772	−	1.70813i
$367$	−2.53795	−	1.46528i	−0.132480	−	0.0764873i	0.432295	−	0.901732i	$-0.357704\pi$
$367$	−2.53795	−	1.46528i	−0.132480	−	0.0764873i	−0.564775	+	0.825245i	$0.691037\pi$
$368$	−20.1731	−	6.99207i	−1.05160	−	0.364487i
$369$			18.9267i			0.985287i
$370$	1.26415	+	1.96754i	0.0657199	+	0.102287i
$371$	12.2991	−	21.3027i	0.638538	−	1.10598i
$372$	−5.22773	−	7.34478i	−0.271045	−	0.380809i
$373$			4.27609i			0.221408i	0.993853	+	0.110704i	$0.0353105\pi$
$373$			4.27609i			0.221408i	−0.993853	+	0.110704i	$0.964689\pi$
$374$	−4.99237	−	7.77019i	−0.258149	−	0.401787i
$375$	1.38246	+	2.39450i	0.0713901	+	0.123651i
$376$	−0.377712	+	0.942564i	−0.0194790	+	0.0486090i
$377$	−20.6665	−	35.7954i	−1.06438	−	1.84356i
$378$	14.0226	−	0.666409i	0.721243	−	0.0342764i
$379$	18.2739			0.938667			0.469334	−	0.883021i	$-0.344494\pi$
$379$	18.2739			0.938667			0.469334	+	0.883021i	$0.344494\pi$
$380$	1.65929	+	8.55843i	0.0851199	+	0.439038i
$381$	40.8332			2.09195
$382$	2.94349	−	0.139887i	0.150602	−	0.00715722i
$383$	11.3931	+	19.7334i	0.582160	+	1.00833i	0.995223	+	0.0976278i	$0.0311255\pi$
$383$	11.3931	+	19.7334i	0.582160	+	1.00833i	−0.413063	+	0.910702i	$0.635541\pi$
$384$	20.5035	−	23.6250i	1.04632	−	1.20561i
$385$	2.37151	+	4.10757i	0.120863	+	0.209341i
$386$	12.8200	+	19.9532i	0.652520	+	1.01559i
$387$			55.2255i			2.80727i
$388$	−24.3447	+	17.3276i	−1.23591	+	0.879674i
$389$	5.83415	−	10.1050i	0.295803	−	0.512346i	−0.679368	−	0.733797i	$-0.737746\pi$
$389$	5.83415	−	10.1050i	0.295803	−	0.512346i	0.975171	+	0.221452i	$0.0710795\pi$
$390$	−10.6955	−	16.6466i	−0.541586	−	0.842931i
$391$		−	16.0417i		−	0.811264i
$392$	−0.897842	−	6.25950i	−0.0453478	−	0.316152i
$393$	−10.8407	−	6.25889i	−0.546842	−	0.315719i
$394$	0.148057	+	3.11542i	0.00745902	+	0.156953i
$395$	3.74126	−	6.48006i	0.188243	−	0.326047i
$396$	18.3602	+	8.38976i	0.922634	+	0.421601i
$397$	10.7828	+	18.6764i	0.541174	+	0.937341i	0.998837	+	0.0482151i	$0.0153533\pi$
$397$	10.7828	+	18.6764i	0.541174	+	0.937341i	−0.457663	+	0.889126i	$0.651313\pi$
$398$	−15.2011	+	29.4779i	−0.761960	+	1.47759i
$399$	−26.1838	+	2.53529i	−1.31083	+	0.126923i
$400$	−1.30996	+	3.77942i	−0.0654979	+	0.188971i
$401$	11.1929	−	6.46224i	0.558948	−	0.322709i	−0.193775	−	0.981046i	$-0.562073\pi$
$401$	11.1929	−	6.46224i	0.558948	−	0.322709i	0.752723	+	0.658337i	$0.228740\pi$
$402$	−1.52493	−	32.0875i	−0.0760564	−	1.60038i
$403$	−7.14435	−	4.12479i	−0.355885	−	0.205471i
$404$	−3.77138	+	8.25330i	−0.187633	+	0.410617i
$405$	0.680033	−	1.17785i	0.0337911	−	0.0585279i
$406$	−22.4099	−	11.5563i	−1.11218	−	0.573527i
$407$	−3.59340			−0.178118
$408$	21.8169	+	8.74265i	1.08010	+	0.432826i
$409$	−16.0872	−	9.28793i	−0.795459	−	0.459259i	0.0464217	−	0.998922i	$-0.485218\pi$
$409$	−16.0872	−	9.28793i	−0.795459	−	0.459259i	−0.841881	+	0.539663i	$0.818552\pi$
$410$	2.64117	−	5.12174i	0.130438	−	0.252945i
$411$	−15.9686			−0.787673
$412$	−35.7829	+	3.40879i	−1.76289	+	0.167939i
$413$	−8.12833	+	4.69289i	−0.399969	+	0.230922i
$414$	18.9525	+	29.4979i	0.931463	+	1.44974i
$415$	0.716485	−	0.413663i	0.0351709	−	0.0203059i
$416$	8.07986	−	27.4608i	0.396148	−	1.34638i
$417$		−	23.9719i		−	1.17391i
$418$	−12.4417	−	4.96337i	−0.608542	−	0.242766i
$419$			15.9107i			0.777289i	0.921388	+	0.388644i	$0.127056\pi$
$419$			15.9107i			0.777289i	−0.921388	+	0.388644i	$0.872944\pi$
$420$	−10.9783	−	5.01657i	−0.535685	−	0.244784i
$421$	−14.6473	+	8.45663i	−0.713867	+	0.412151i	−0.812491	−	0.582974i	$-0.801889\pi$
$421$	−14.6473	+	8.45663i	−0.713867	+	0.412151i	0.0986244	+	0.995125i	$0.468556\pi$
$422$	32.3441	−	20.7812i	1.57449	−	1.01161i
$423$	1.44412	−	0.833765i	0.0702157	−	0.0405390i
$424$	−11.8566	+	29.5878i	−0.575809	+	1.43691i
$425$	−3.00540			−0.145783
$426$	−22.5739	−	11.6409i	−1.09371	−	0.564002i
$427$	−15.8155	−	9.13106i	−0.765364	−	0.441883i
$428$	27.5544	−	2.62492i	1.33189	−	0.126880i
$429$	30.4024			1.46784
$430$	7.70654	−	14.9445i	0.371642	−	0.720688i
$431$	−9.69484	+	16.7920i	−0.466984	+	0.808840i	−0.999289	−	0.0377126i	$-0.987993\pi$
$431$	−9.69484	+	16.7920i	−0.466984	+	0.808840i	0.532304	+	0.846553i	$0.321326\pi$
$432$	−17.8641	+	3.43475i	−0.859487	+	0.165255i
$433$	31.2255	+	18.0280i	1.50060	+	0.866372i	1.00000		0.000692918i	$0.000220563\pi$
$433$	31.2255	+	18.0280i	1.50060	+	0.866372i	0.500600	+	0.865679i	$0.333113\pi$
$434$	−5.02676	+	0.238892i	−0.241292	+	0.0114672i
$435$	19.5589	−	11.2923i	0.937776	−	0.541425i
$436$	−11.6775	+	8.31157i	−0.559250	+	0.398052i
$437$	−13.5208	−	18.9341i	−0.646788	−	0.905743i
$438$	17.3200	+	8.93154i	0.827582	+	0.426765i
$439$	10.3371	+	17.9044i	0.493364	+	0.854531i	0.999971	−	0.00764596i	$-0.00243381\pi$
$439$	10.3371	+	17.9044i	0.493364	+	0.854531i	−0.506607	+	0.862177i	$0.669100\pi$
$440$	−3.79766	−	4.83245i	−0.181046	−	0.230378i
$441$	−5.19226	+	8.99326i	−0.247250	+	0.428250i
$442$	21.4830	−	1.02096i	1.02184	−	0.0485621i
$443$	−31.9909	−	18.4699i	−1.51993	−	0.877534i	−0.999724	−	0.0234946i	$-0.992521\pi$
$443$	−31.9909	−	18.4699i	−1.51993	−	0.877534i	−0.520209	−	0.854039i	$-0.674146\pi$
$444$	7.45013	−	5.30271i	0.353568	−	0.251655i
$445$			16.6350i			0.788573i
$446$	13.8764	−	8.91562i	0.657066	−	0.422167i
$447$	28.7521	−	49.8000i	1.35993	−	2.35546i
$448$	−4.90834	−	16.7578i	−0.231897	−	0.791729i
$449$			23.3017i			1.09967i	0.835272	+	0.549837i	$0.185310\pi$
$449$			23.3017i			1.09967i	−0.835272	+	0.549837i	$0.814690\pi$
$450$	5.52640	−	3.55073i	0.260517	−	0.167383i
$451$	4.42723	+	7.66819i	0.208470	+	0.361081i
$452$	0.681628	+	7.15520i	0.0320611	+	0.336552i
$453$	19.0996	+	33.0815i	0.897379	+	1.55431i
$454$	1.22546	+	25.7861i	0.0575137	+	1.21020i
$455$	−11.0450			−0.517798
$456$	33.1194	−	8.06946i	1.55096	−	0.377887i
$457$	−20.3308			−0.951034			−0.475517	−	0.879706i	$-0.657739\pi$
$457$	−20.3308			−0.951034			−0.475517	+	0.879706i	$0.657739\pi$
$458$	0.848261	+	17.8491i	0.0396366	+	0.834033i
$459$	−6.83403	−	11.8369i	−0.318985	−	0.552498i
$460$	−1.01238	−	10.6271i	−0.0472022	−	0.495493i
$461$	4.86101	+	8.41951i	0.226400	+	0.392136i	0.956738	−	0.290949i	$-0.0939711\pi$
$461$	4.86101	+	8.41951i	0.226400	+	0.392136i	−0.730339	+	0.683085i	$0.760638\pi$
$462$	15.6031	−	10.0251i	0.725923	−	0.466408i
$463$			0.171279i			0.00796003i	0.999992	+	0.00398001i	$0.00126688\pi$
$463$			0.171279i			0.00796003i	−0.999992	+	0.00398001i	$0.998733\pi$
$464$	30.8712	+	10.7001i	1.43316	+	0.496738i
$465$	2.25382	−	3.90372i	0.104518	−	0.181031i
$466$	12.0284	−	7.72828i	0.557204	−	0.358005i
$467$		−	4.88083i		−	0.225858i	−0.993603	−	0.112929i	$-0.963977\pi$
$467$		−	4.88083i		−	0.225858i	0.993603	−	0.112929i	$-0.0360233\pi$
$468$	−38.2972	+	27.2585i	−1.77029	+	1.26002i
$469$	−15.5294	−	8.96592i	−0.717083	−	0.414008i
$470$	−0.507142	+	0.0241014i	−0.0233927	+	0.00111172i
$471$	29.6068	−	51.2804i	1.36421	−	2.36288i
$472$	9.56276	−	7.51505i	0.440162	−	0.345908i
$473$	12.9180	+	22.3747i	0.593971	+	1.02879i
$474$	−26.0042	−	13.4098i	−1.19441	−	0.615931i
$475$	−3.54730	+	2.53311i	−0.162761	+	0.116227i
$476$	10.6889	−	7.60792i	0.489924	−	0.348708i
$477$	45.3320	−	26.1725i	2.07561	−	1.19835i
$478$	23.6625	−	1.12454i	1.08230	−	0.0514352i
$479$	−9.28818	−	5.36254i	−0.424388	−	0.245020i	0.272565	−	0.962137i	$-0.412128\pi$
$479$	−9.28818	−	5.36254i	−0.424388	−	0.245020i	−0.696953	+	0.717117i	$0.745461\pi$
$480$	15.0048	+	4.41489i	0.684871	+	0.201511i
$481$	4.18395	−	7.24682i	0.190772	−	0.330427i
$482$	8.57471	−	16.6281i	0.390567	−	0.757388i
$483$	32.2130			1.46574
$484$	−12.4997	+	1.19076i	−0.568169	+	0.0541256i
$485$	−12.9391	−	7.47039i	−0.587534	−	0.339213i
$486$	−21.8756	−	11.2807i	−0.992296	−	0.511705i
$487$	4.63382			0.209978			0.104989	−	0.994473i	$-0.466519\pi$
$487$	4.63382			0.209978			0.104989	+	0.994473i	$0.466519\pi$
$488$	21.9664	+	8.80256i	0.994373	+	0.398473i
$489$	−33.2905	+	19.2203i	−1.50545	+	0.869172i
$490$	2.66005	−	1.70909i	0.120169	−	0.0772089i
$491$	−18.3657	+	10.6034i	−0.828833	+	0.478527i	−0.853453	−	0.521170i	$-0.825496\pi$
$491$	−18.3657	+	10.6034i	−0.828833	+	0.478527i	0.0246202	+	0.999697i	$0.492162\pi$
$492$	−20.4947	−	9.36515i	−0.923973	−	0.422214i
$493$			24.5489i			1.10563i
$494$	24.4960	−	19.3121i	1.10213	−	0.868892i
$495$			10.0931i			0.453652i
$496$	6.40386	−	1.23128i	0.287542	−	0.0552860i
$497$	−12.2784	+	7.08893i	−0.550761	+	0.317982i
$498$	−1.74867	−	2.72166i	−0.0783600	−	0.121960i
$499$	0.173776	−	0.100330i	0.00777929	−	0.00449138i	−0.496105	−	0.868262i	$-0.665237\pi$
$499$	0.173776	−	0.100330i	0.00777929	−	0.00449138i	0.503885	+	0.863771i	$0.331904\pi$
$500$	−1.99099	+	0.189668i	−0.0890396	+	0.00848220i
$501$	18.4009			0.822090
$502$	1.22372	−	2.37303i	0.0546172	−	0.105914i
$503$	−9.70051	−	5.60059i	−0.432525	−	0.249718i	0.267897	−	0.963448i	$-0.413671\pi$
$503$	−9.70051	−	5.60059i	−0.432525	−	0.249718i	−0.700422	+	0.713729i	$0.747005\pi$
$504$	−10.6666	+	26.6180i	−0.475127	+	1.18566i
$505$	−4.53708			−0.201897
$506$	14.5786	+	7.51784i	0.648097	+	0.334209i
$507$	−17.4268	+	30.1841i	−0.773951	+	1.34052i
$508$	−12.2759	+	26.8646i	−0.544656	+	1.19193i
$509$	−4.70571	−	2.71684i	−0.208577	−	0.120422i	0.392073	−	0.919934i	$-0.371758\pi$
$509$	−4.70571	−	2.71684i	−0.208577	−	0.120422i	−0.600650	+	0.799512i	$0.705091\pi$
$510$	0.557860	+	11.7385i	0.0247024	+	0.519788i
$511$	9.42069	−	5.43904i	0.416747	−	0.240609i
$512$	9.37909	+	20.5921i	0.414501	+	0.910049i
$513$	−18.0430	−	8.21107i	−0.796618	−	0.362528i
$514$	−7.43357	+	14.4152i	−0.327881	+	0.635825i
$515$	−8.98621	−	15.5646i	−0.395980	−	0.685857i
$516$	−59.8006	−	27.3261i	−2.63257	−	1.20297i
$517$	0.390059	−	0.675601i	0.0171548	−	0.0297129i
$518$	−0.242319	−	5.09886i	−0.0106469	−	0.224031i
$519$	−29.6613	−	17.1249i	−1.30199	−	0.751702i
$520$	14.1674	−	2.03212i	0.621282	−	0.0891146i
$521$		−	28.5989i		−	1.25294i	−0.779445	−	0.626470i	$-0.784499\pi$
$521$		−	28.5989i		−	1.25294i	0.779445	−	0.626470i	$-0.215501\pi$
$522$	−29.0033	−	45.1410i	−1.26944	−	1.97577i
$523$	22.3991	−	38.7963i	0.979443	−	1.69645i	0.315028	−	0.949082i	$-0.397986\pi$
$523$	22.3991	−	38.7963i	0.979443	−	1.69645i	0.664416	−	0.747363i	$-0.268681\pi$
$524$	7.37690	−	5.25059i	0.322262	−	0.229373i
$525$		−	6.03507i		−	0.263392i
$526$	−10.2113	−	15.8930i	−0.445234	−	0.692968i
$527$	2.44984	+	4.24324i	0.106717	+	0.184839i
$528$	−18.1696	+	15.7299i	−0.790731	+	0.684554i
$529$	2.74511	+	4.75468i	0.119353	+	0.206725i
$530$	−15.9195	+	0.756560i	−0.691500	+	0.0328629i
$531$	−19.9729			−0.866751
$532$	6.20379	−	17.9888i	0.268969	−	0.779915i
$533$	−20.6193			−0.893121
$534$	64.9727	−	3.08777i	2.81164	−	0.133621i
$535$	6.91979	+	11.9854i	0.299169	+	0.518175i
$536$	21.5692	+	8.64337i	0.931646	+	0.373337i
$537$	−11.3389	−	19.6396i	−0.489310	−	0.847510i
$538$	17.7070	+	27.5593i	0.763401	+	1.18817i
$539$			4.85817i			0.209256i
$540$	−5.27434	−	7.41028i	−0.226972	−	0.318888i
$541$	−21.4447	+	37.1434i	−0.921981	+	1.59692i	−0.125636	+	0.992076i	$0.540097\pi$
$541$	−21.4447	+	37.1434i	−0.921981	+	1.59692i	−0.796345	+	0.604842i	$0.793236\pi$
$542$	−16.1052	−	25.0663i	−0.691776	−	1.07669i
$543$		−	13.2572i		−	0.568919i
$544$	−12.3108	+	11.7253i	−0.527823	+	0.502716i
$545$	−6.20653	−	3.58334i	−0.265859	−	0.153494i
$546$	2.05016	+	43.1395i	0.0877389	+	1.84620i
$547$	4.41258	−	7.64282i	0.188668	−	0.326783i	−0.756138	−	0.654412i	$-0.772916\pi$
$547$	4.41258	−	7.64282i	0.188668	−	0.326783i	0.944807	+	0.327629i	$0.106250\pi$
$548$	4.80073	−	10.5059i	0.205077	−	0.448791i
$549$	−19.4309	−	33.6552i	−0.829289	−	1.43637i
$550$	1.40846	−	2.73129i	0.0600570	−	0.116462i
$551$	20.6911	+	28.9752i	0.881471	+	1.23439i
$552$	−41.3194	+	5.92672i	−1.75867	+	0.252258i
$553$	−14.1442	+	8.16614i	−0.601471	+	0.347260i
$554$	−1.64820	−	34.6814i	−0.0700252	−	1.47347i
$555$	3.95971	+	2.28614i	0.168081	+	0.0970413i
$556$	15.7714	+	7.20681i	0.668856	+	0.305637i
$557$	−20.0537	+	34.7340i	−0.849702	+	1.47173i	0.0317722	+	0.999495i	$0.489885\pi$
$557$	−20.0537	+	34.7340i	−0.849702	+	1.47173i	−0.881474	+	0.472232i	$0.843448\pi$
$558$	−9.51799	−	4.90821i	−0.402929	−	0.207781i
$559$	−60.1641			−2.54467
$560$	6.60092	−	5.71457i	0.278940	−	0.241485i
$561$	−15.6377	−	9.02843i	−0.660224	−	0.381181i
$562$	−3.75227	+	7.27640i	−0.158280	+	0.306936i
$563$	−6.87673			−0.289819			−0.144910	−	0.989445i	$-0.546289\pi$
$563$	−6.87673			−0.289819			−0.144910	+	0.989445i	$0.546289\pi$
$564$	0.188270	+	1.97631i	0.00792760	+	0.0832179i
$565$	−3.11232	+	1.79690i	−0.130936	+	0.0755961i
$566$	−12.4703	−	19.4089i	−0.524166	−	0.815818i
$567$	−2.57093	+	1.48432i	−0.107969	+	0.0623358i
$568$	14.4452	−	11.3520i	0.606107	−	0.476319i
$569$		−	12.3097i		−	0.516050i	−0.966138	−	0.258025i	$-0.916928\pi$
$569$		−	12.3097i		−	0.516050i	0.966138	−	0.258025i	$-0.0830718\pi$
$570$	10.5523	+	13.3848i	0.441986	+	0.560628i
$571$			7.15670i			0.299499i	0.988724	+	0.149749i	$0.0478467\pi$
$571$			7.15670i			0.299499i	−0.988724	+	0.149749i	$0.952153\pi$
$572$	−9.14003	+	20.0021i	−0.382164	+	0.836328i
$573$	4.98945	−	2.88066i	0.208437	−	0.120341i
$574$	−10.5823	+	6.79914i	−0.441695	+	0.283790i
$575$	4.62252	−	2.66881i	0.192772	−	0.111297i
$576$	8.78465	−	36.1053i	0.366027	−	1.50439i
$577$	35.3209			1.47043			0.735215	−	0.677834i	$-0.237081\pi$
$577$	35.3209			1.47043			0.735215	+	0.677834i	$0.237081\pi$
$578$	10.0147	+	5.16433i	0.416555	+	0.214808i
$579$	40.1563	+	23.1842i	1.66884	+	0.963504i
$580$	1.54925	+	16.2629i	0.0643293	+	0.675279i
$581$	−1.80582			−0.0749182
$582$	−26.7760	+	51.9240i	−1.10990	+	2.15232i
$583$	12.2442	−	21.2076i	0.507104	−	0.878329i
$584$	−11.0832	+	8.70990i	−0.458625	+	0.360418i
$585$	−20.3548	−	11.7519i	−0.841569	−	0.485880i
$586$	−13.0145	+	0.618500i	−0.537623	+	0.0255500i
$587$	−21.0448	+	12.1502i	−0.868613	+	0.501494i	−0.866887	−	0.498504i	$-0.833883\pi$
$587$	−21.0448	+	12.1502i	−0.868613	+	0.501494i	−0.00172609	+	0.999999i	$0.500549\pi$
$588$	−7.16911	−	10.0724i	−0.295649	−	0.415377i
$589$	6.46799	+	2.94348i	0.266509	+	0.121284i
$590$	5.40485	+	2.78715i	0.222514	+	0.114745i
$591$	3.04891	+	5.28087i	0.125416	+	0.217226i
$592$	1.24894	+	6.49571i	0.0513311	+	0.266972i
$593$	13.7573	−	23.8284i	0.564946	−	0.978515i	−0.432109	−	0.901821i	$-0.642230\pi$
$593$	13.7573	−	23.8284i	0.564946	−	0.978515i	0.997055	−	0.0766934i	$-0.0244363\pi$
$594$	13.9600	−	0.663435i	0.572785	−	0.0272211i
$595$	5.68109	+	3.27998i	0.232902	+	0.134466i
$596$	24.1201	+	33.8880i	0.987999	+	1.38811i
$597$			64.8438i			2.65388i
$598$	−32.1358	+	20.6473i	−1.31413	+	0.844332i
$599$	−13.3675	+	23.1532i	−0.546182	+	0.946016i	0.452349	+	0.891841i	$0.350586\pi$
$599$	−13.3675	+	23.1532i	−0.546182	+	0.946016i	−0.998531	+	0.0541747i	$0.982747\pi$
$600$	1.11037	+	7.74117i	0.0453306	+	0.316032i
$601$			6.93661i			0.282950i	0.989942	+	0.141475i	$0.0451845\pi$
$601$			6.93661i			0.282950i	−0.989942	+	0.141475i	$0.954815\pi$
$602$	−30.8775	+	19.8389i	−1.25847	+	0.808573i
$603$	−19.0794	−	33.0466i	−0.776975	−	1.34576i
$604$	−27.5068	+	2.62038i	−1.11923	+	0.106622i
$605$	−3.13908	−	5.43704i	−0.127622	−	0.221047i
$606$	0.842168	+	17.7209i	0.0342107	+	0.719862i
$607$	3.37786			0.137103			0.0685516	−	0.997648i	$-0.478162\pi$
$607$	3.37786			0.137103			0.0685516	+	0.997648i	$0.478162\pi$
$608$	−4.64790	+	24.2156i	−0.188497	+	0.982074i
$609$	−49.2960			−1.99757
$610$	0.561682	+	11.8189i	0.0227419	+	0.478534i
$611$	0.908326	+	1.57327i	0.0367469	+	0.0636475i
$612$	27.7933	−	2.64768i	1.12348	−	0.107026i
$613$	7.47134	+	12.9407i	0.301765	+	0.522672i	0.976536	−	0.215355i	$-0.0690910\pi$
$613$	7.47134	+	12.9407i	0.301765	+	0.522672i	−0.674771	+	0.738027i	$0.735758\pi$
$614$	0.491878	−	0.316034i	0.0198506	−	0.0127541i
$615$		−	11.2665i		−	0.454311i
$616$	1.90475	+	13.2794i	0.0767445	+	0.535041i
$617$	−0.978279	+	1.69443i	−0.0393840	+	0.0682152i	−0.885046	−	0.465504i	$-0.845873\pi$
$617$	−0.978279	+	1.69443i	−0.0393840	+	0.0682152i	0.845661	+	0.533720i	$0.179206\pi$
$618$	−59.1240	+	37.9874i	−2.37832	+	1.52808i
$619$			4.32563i			0.173862i	0.996214	+	0.0869309i	$0.0277059\pi$
$619$			4.32563i			0.173862i	−0.996214	+	0.0869309i	$0.972294\pi$
$620$	1.89073	+	2.65641i	0.0759334	+	0.106684i
$621$	21.0224	+	12.1373i	0.843600	+	0.487053i
$622$	6.08556	−	0.289210i	0.244009	−	0.0115963i
$623$	18.1548	−	31.4450i	0.727356	−	1.25982i
$624$	−10.5668	−	54.9577i	−0.423010	−	2.20007i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	28.8569	+	14.8809i	1.15335	+	0.594758i
$627$	−26.0669	+	2.52397i	−1.04101	+	0.100798i
$628$	24.8371	+	34.8954i	0.991110	+	1.39248i
$629$	−4.30410	+	2.48498i	−0.171616	+	0.0990825i
$630$	−14.3217	+	0.680623i	−0.570589	+	0.0271167i
$631$	−27.3094	−	15.7671i	−1.08717	−	0.627679i	−0.154350	−	0.988016i	$-0.549328\pi$
$631$	−27.3094	−	15.7671i	−1.08717	−	0.627679i	−0.932822	+	0.360337i	$0.882662\pi$
$632$	16.6402	−	13.0770i	0.661913	−	0.520175i
$633$	37.5816	−	65.0933i	1.49374	−	2.58723i
$634$	−9.39969	+	18.2279i	−0.373309	+	0.723921i
$635$	−14.7683			−0.586061
$636$	5.90993	+	62.0379i	0.234344	+	2.45996i
$637$	−9.79749	−	5.65659i	−0.388191	−	0.224122i
$638$	−22.3098	−	11.5047i	−0.883255	−	0.455474i
$639$	−30.1704			−1.19352
$640$	−7.41558	+	8.54454i	−0.293127	+	0.337753i
$641$	23.2718	−	13.4360i	0.919181	−	0.530689i	0.0358072	−	0.999359i	$-0.488600\pi$
$641$	23.2718	−	13.4360i	0.919181	−	0.530689i	0.883374	+	0.468669i	$0.155266\pi$
$642$	45.5281	−	29.2520i	1.79685	−	1.15448i
$643$	−7.20688	+	4.16089i	−0.284212	+	0.164090i	−0.635329	−	0.772242i	$-0.719135\pi$
$643$	−7.20688	+	4.16089i	−0.284212	+	0.164090i	0.351117	+	0.936332i	$0.385802\pi$
$644$	−9.68436	+	21.1933i	−0.381617	+	0.835132i
$645$		−	32.8741i		−	1.29442i
$646$	−18.3348	+	2.65887i	−0.721371	+	0.104612i
$647$			4.26130i			0.167529i	0.996486	+	0.0837645i	$0.0266943\pi$
$647$			4.26130i			0.167529i	−0.996486	+	0.0837645i	$0.973306\pi$
$648$	3.02462	−	2.37695i	0.118818	−	0.0933755i
$649$	−8.09205	+	4.67195i	−0.317641	+	0.183390i
$650$	3.86826	+	6.02061i	0.151726	+	0.236148i
$651$	−8.52075	+	4.91946i	−0.333954	+	0.192809i
$652$	−2.63694	−	27.6805i	−0.103270	−	1.08405i
$653$	8.36559			0.327371			0.163685	−	0.986513i	$-0.447662\pi$
$653$	8.36559			0.327371			0.163685	+	0.986513i	$0.447662\pi$
$654$	−12.8437	+	24.9066i	−0.502230	+	0.973924i
$655$	3.92080	+	2.26367i	0.153198	+	0.0884490i
$656$	12.3229	−	10.6682i	0.481128	−	0.416524i
$657$	23.1485			0.903109
$658$	0.984950	+	0.507916i	0.0383974	+	0.0198006i
$659$	−1.32499	+	2.29495i	−0.0516142	+	0.0893985i	−0.890678	−	0.454634i	$-0.849770\pi$
$659$	−1.32499	+	2.29495i	−0.0516142	+	0.0893985i	0.839064	+	0.544033i	$0.183103\pi$
$660$	−10.9293	−	4.99418i	−0.425421	−	0.194398i
$661$	−28.2689	−	16.3211i	−1.09953	−	0.634815i	−0.163434	−	0.986554i	$-0.552257\pi$
$661$	−28.2689	−	16.3211i	−1.09953	−	0.634815i	−0.936098	+	0.351739i	$0.885591\pi$
$662$	0.740597	+	15.5836i	0.0287841	+	0.605675i
$663$	36.4154	−	21.0244i	1.41426	−	0.816521i
$664$	2.31632	−	0.332246i	0.0898908	−	0.0128936i
$665$	9.46998	−	0.916946i	0.367230	−	0.0355576i
$666$	4.97861	−	9.65451i	0.192917	−	0.374105i
$667$	−21.7995	−	37.7579i	−0.844081	−	1.46199i
$668$	−5.53196	+	12.1061i	−0.214038	+	0.468401i
$669$	16.1234	−	27.9266i	0.623367	−	1.07970i
$670$	0.551524	+	11.6052i	0.0213072	+	0.448347i
$671$	−15.7449	−	9.09030i	−0.607824	−	0.350927i
$672$	−23.5452	−	24.7211i	−0.908275	−	0.953636i
$673$		−	35.9561i		−	1.38601i	−0.720935	−	0.693003i	$-0.756287\pi$
$673$		−	35.9561i		−	1.38601i	0.720935	−	0.693003i	$-0.243713\pi$
$674$	−15.1451	−	23.5720i	−0.583366	−	0.907958i
$675$	2.27391	−	3.93853i	0.0875230	−	0.151594i
$676$	−14.6194	−	20.5397i	−0.562283	−	0.789989i
$677$			43.5015i			1.67190i	0.548805	+	0.835950i	$0.315083\pi$
$677$			43.5015i			1.67190i	−0.548805	+	0.835950i	$0.684917\pi$
$678$	7.59602	+	11.8225i	0.291723	+	0.454042i
$679$	16.3058	+	28.2425i	0.625759	+	1.08385i
$680$	−7.89059	−	3.16198i	−0.302590	−	0.121256i
$681$	25.2357	+	43.7095i	0.967033	+	1.67495i
$682$	−5.00432	+	0.237826i	−0.191626	+	0.00910682i
$683$	26.1006			0.998711			0.499356	−	0.866397i	$-0.333570\pi$
$683$	26.1006			0.998711			0.499356	+	0.866397i	$0.333570\pi$
$684$	30.5731	−	26.5508i	1.16899	−	1.01519i
$685$	5.77542			0.220667
$686$	−28.4770	+	1.35334i	−1.08726	+	0.0516709i
$687$	17.4681	+	30.2556i	0.666448	+	1.15432i
$688$	35.9564	−	31.1283i	1.37082	−	1.18676i
$689$	28.5130	+	49.3859i	1.08626	+	1.88145i
$690$	−11.2818	−	17.5592i	−0.429493	−	0.668467i
$691$			35.7207i			1.35888i	0.733732	+	0.679439i	$0.237777\pi$
$691$			35.7207i			1.35888i	−0.733732	+	0.679439i	$0.762223\pi$
$692$	20.1839	−	14.3661i	0.767278	−	0.546119i
$693$	11.0152	−	19.0790i	0.418435	−	0.724750i
$694$	−15.6033	−	24.2852i	−0.592295	−	0.921855i
$695$			8.66999i			0.328871i
$696$	63.2318	−	9.06976i	2.39680	−	0.343788i
$697$	10.6057	+	6.12321i	0.401720	+	0.231933i
$698$	−0.231457	−	4.87032i	−0.00876079	−	0.184344i
$699$	13.9762	−	24.2074i	0.528627	−	0.915609i
$700$	3.97055	+	1.81436i	0.150073	+	0.0685763i
$701$	−17.1309	−	29.6716i	−0.647026	−	1.12068i	−0.983830	−	0.179107i	$-0.942679\pi$
$701$	−17.1309	−	29.6716i	−0.647026	−	1.12068i	0.336804	−	0.941575i	$-0.390654\pi$
$702$	−14.9163	+	28.9256i	−0.562979	+	1.09173i
$703$	−2.98569	+	6.56077i	−0.112608	+	0.247444i
$704$	−4.88643	−	16.6830i	−0.184164	−	0.628762i
$705$	−0.859644	+	0.496316i	−0.0323761	+	0.0186923i
$706$	−2.14053	−	45.0409i	−0.0805598	−	1.69514i
$707$	8.57642	+	4.95160i	0.322549	+	0.186224i
$708$	9.88280	−	21.6275i	0.371418	−	0.812813i
$709$	0.650040	−	1.12590i	0.0244128	−	0.0422842i	−0.853561	−	0.520993i	$-0.825562\pi$
$709$	0.650040	−	1.12590i	0.0244128	−	0.0422842i	0.877974	+	0.478709i	$0.158895\pi$
$710$	8.16439	+	4.21019i	0.306404	+	0.158006i
$711$	−34.7550			−1.30342
$712$	−17.5016	+	43.6746i	−0.655902	+	1.63678i
$713$	−7.53604	−	4.35093i	−0.282227	−	0.162944i
$714$	11.7564	−	22.7980i	0.439972	−	0.853193i
$715$	−10.9957			−0.411216
$716$	16.3300	−	1.55565i	0.610280	−	0.0581373i
$717$	40.1098	−	23.1574i	1.49793	−	0.864829i
$718$	12.9018	+	20.0805i	0.481489	+	0.749396i
$719$	15.9031	−	9.18168i	0.593087	−	0.342419i	−0.173230	−	0.984881i	$-0.555421\pi$
$719$	15.9031	−	9.18168i	0.593087	−	0.342419i	0.766317	+	0.642463i	$0.222087\pi$
$720$	18.2451	−	3.50801i	0.679956	−	0.130736i
$721$			39.2288i			1.46096i
$722$	−19.3996	+	18.5918i	−0.721979	+	0.691915i
$723$		−	36.5775i		−	1.36033i
$724$	8.72204	+	3.98557i	0.324152	+	0.148123i
$725$	−7.07391	+	4.08413i	−0.262719	+	0.151681i
$726$	−20.6533	+	13.2698i	−0.766515	+	0.492488i
$727$	7.98924	−	4.61259i	0.296305	−	0.171072i	−0.344477	−	0.938795i	$-0.611944\pi$
$727$	7.98924	−	4.61259i	0.296305	−	0.171072i	0.640782	+	0.767723i	$0.278610\pi$
$728$	−28.9983	−	11.6204i	−1.07475	−	0.430682i
$729$	−44.0405			−1.63113
$730$	−6.26418	−	3.23030i	−0.231848	−	0.119559i
$731$	30.9459	+	17.8666i	1.14458	+	0.660822i
$732$	46.0579	−	4.38763i	1.70235	−	0.162171i
$733$	9.19832			0.339748			0.169874	−	0.985466i	$-0.445664\pi$
$733$	9.19832			0.339748			0.169874	+	0.985466i	$0.445664\pi$
$734$	1.89951	−	3.68352i	0.0701121	−	0.135961i
$735$	3.09080	−	5.35342i	0.114006	−	0.197464i
$736$	8.52284	−	28.9663i	0.314156	−	1.06771i
$737$	−15.4601	−	8.92590i	−0.569481	−	0.328790i
$738$	−26.7363	+	1.27062i	−0.984176	+	0.0467720i
$739$	−25.4237	+	14.6784i	−0.935227	+	0.539954i	−0.888461	−	0.458952i	$-0.848225\pi$
$739$	−25.4237	+	14.6784i	−0.935227	+	0.539954i	−0.0467663	+	0.998906i	$0.514892\pi$
$740$	−2.69451	+	1.91785i	−0.0990522	+	0.0705015i
$741$	25.2608	−	55.5081i	0.927979	−	2.03914i
$742$	30.9183	+	15.9438i	1.13505	+	0.585317i
$743$	9.29972	+	16.1076i	0.341174	+	0.590930i	0.984651	−	0.174535i	$-0.0558423\pi$
$743$	9.29972	+	16.1076i	0.341174	+	0.590930i	−0.643477	+	0.765465i	$0.722509\pi$
$744$	10.0244	−	7.87787i	0.367513	−	0.288817i
$745$	−10.3988	+	18.0113i	−0.380984	+	0.659884i
$746$	−6.04049	+	0.287069i	−0.221158	+	0.0105103i
$747$	−3.32795	−	1.92139i	−0.121763	−	0.0703001i
$748$	10.6412	−	7.57396i	0.389079	−	0.276931i
$749$		−	30.2080i		−	1.10378i
$750$	−3.28970	+	2.11365i	−0.120123	+	0.0771794i
$751$	−12.8124	+	22.1917i	−0.467530	+	0.809786i	−0.999312	−	0.0370957i	$-0.988189\pi$
$751$	−12.8124	+	22.1917i	−0.467530	+	0.809786i	0.531782	+	0.846881i	$0.321523\pi$
$752$	−1.35684	−	0.470286i	−0.0494789	−	0.0171496i
$753$		−	5.22007i		−	0.190230i
$754$	49.1779	−	31.5969i	1.79095	−	1.15069i
$755$	−6.90782	−	11.9647i	−0.251401	−	0.435440i
$756$	1.88277	+	19.7638i	0.0684755	+	0.718803i
$757$	−3.08640	−	5.34580i	−0.112177	−	0.194296i	0.804471	−	0.593992i	$-0.202449\pi$
$757$	−3.08640	−	5.34580i	−0.112177	−	0.194296i	−0.916648	+	0.399696i	$0.869116\pi$
$758$	1.22679	+	25.8141i	0.0445590	+	0.937609i
$759$	32.0692			1.16404
$760$	−11.9784	+	2.91850i	−0.434503	+	0.105865i
$761$	33.0112			1.19666			0.598328	−	0.801251i	$-0.295832\pi$
$761$	33.0112			1.19666			0.598328	+	0.801251i	$0.295832\pi$
$762$	2.74127	+	57.6818i	0.0993057	+	2.08959i
$763$	7.82145	+	13.5471i	0.283156	+	0.490440i
$764$	0.395213	+	4.14864i	0.0142983	+	0.150093i
$765$	6.97979	+	12.0893i	0.252355	+	0.437091i
$766$	−27.1109	+	17.4189i	−0.979558	+	0.629369i
$767$		−	21.7590i		−	0.785673i
$768$	34.7497	+	27.3777i	1.25392	+	0.987907i
$769$	21.2189	−	36.7522i	0.765174	−	1.32532i	−0.174981	−	0.984572i	$-0.555986\pi$
$769$	21.2189	−	36.7522i	0.765174	−	1.32532i	0.940155	−	0.340748i	$-0.110680\pi$
$770$	−5.64323	+	3.62579i	−0.203368	+	0.130665i
$771$			31.7097i			1.14200i
$772$	−27.3256	+	19.4493i	−0.983470	+	0.699995i
$773$	24.1948	+	13.9689i	0.870226	+	0.502425i	0.867423	−	0.497571i	$-0.165775\pi$
$773$	24.1948	+	13.9689i	0.870226	+	0.502425i	0.00280270	+	0.999996i	$0.499108\pi$
$774$	−78.0126	+	3.70747i	−2.80411	+	0.133262i
$775$	−0.815144	+	1.41187i	−0.0292808	+	0.0507159i
$776$	−26.1116	−	33.2265i	−0.937352	−	1.19276i
$777$	−4.99002	−	8.64296i	−0.179016	−	0.310065i
$778$	14.6662	+	7.56304i	0.525810	+	0.271148i
$779$	17.6790	−	1.71179i	0.633415	−	0.0613314i
$780$	22.7972	−	16.2262i	0.816271	−	0.580990i
$781$	−12.2236	+	7.05729i	−0.437394	+	0.252530i
$782$	22.6608	−	1.07693i	0.810349	−	0.0385111i
$783$	−32.1709	−	18.5739i	−1.14970	−	0.663777i
$784$	8.78201	−	1.68853i	0.313643	−	0.0603046i
$785$	−10.7080	+	18.5468i	−0.382184	+	0.661962i
$786$	8.11366	−	15.7340i	0.289405	−	0.561213i
$787$	−20.9075			−0.745271			−0.372635	−	0.927978i	$-0.621546\pi$
$787$	−20.9075			−0.745271			−0.372635	+	0.927978i	$0.621546\pi$
$788$	−4.39096	+	0.418297i	−0.156422	+	0.0149012i
$789$	−31.9851	−	18.4666i	−1.13870	−	0.657428i
$790$	9.40501	+	4.84995i	0.334615	+	0.172553i
$791$	7.84427			0.278910
$792$	−10.6190	+	26.4992i	−0.377328	+	0.941607i
$793$	36.6649	−	21.1685i	1.30201	−	0.751715i
$794$	−25.6587	+	16.4858i	−0.910594	+	0.585060i
$795$	−26.9848	+	15.5797i	−0.957053	+	0.552555i
$796$	−42.6615	−	19.4944i	−1.51210	−	0.690959i
$797$		−	44.4387i		−	1.57410i	−0.616890	−	0.787049i	$-0.711608\pi$
$797$		−	44.4387i		−	1.57410i	0.616890	−	0.787049i	$-0.288392\pi$
$798$	−5.33921	−	36.8176i	−0.189006	−	1.30333i
$799$		−	1.07896i		−	0.0381710i
$800$	−5.42682	−	1.59675i	−0.191867	−	0.0564536i
$801$	66.9148	−	38.6333i	2.36432	−	1.36504i
$802$	9.88011	+	15.3775i	0.348879	+	0.542999i
$803$	9.37864	−	5.41476i	0.330965	−	0.191083i
$804$	45.2250	−	4.30828i	1.59496	−	0.151941i
$805$	−11.6506			−0.410628
$806$	5.34714	−	10.3692i	0.188345	−	0.365238i
$807$	55.4638	+	32.0221i	1.95242	+	1.12723i
$808$	−11.9120	−	4.77346i	−0.419061	−	0.167930i
$809$	8.29205			0.291533			0.145767	−	0.989319i	$-0.453435\pi$
$809$	8.29205			0.291533			0.145767	+	0.989319i	$0.453435\pi$
$810$	1.70951	+	0.881555i	0.0600660	+	0.0309747i
$811$	10.6956	−	18.5253i	0.375573	−	0.650512i	−0.614839	−	0.788652i	$-0.710779\pi$
$811$	10.6956	−	18.5253i	0.375573	−	0.650512i	0.990413	+	0.138140i	$0.0441125\pi$
$812$	14.8201	−	32.4324i	0.520085	−	1.13815i
$813$	−50.4465	−	29.1253i	−1.76924	−	1.02147i
$814$	−0.241237	−	5.07610i	−0.00845535	−	0.177917i
$815$	12.0403	−	6.95147i	0.421753	−	0.243499i
$816$	−10.8854	+	31.4059i	−0.381065	+	1.09943i
$817$	51.5847	−	4.99477i	1.80472	−	0.174745i
$818$	12.0403	−	23.3486i	0.420980	−	0.816364i
$819$	25.6511	+	44.4290i	0.896321	+	1.55247i
$820$	7.41238	+	3.38712i	0.258852	+	0.118283i
$821$	8.56684	−	14.8382i	0.298985	−	0.517857i	−0.676919	−	0.736057i	$-0.736685\pi$
$821$	8.56684	−	14.8382i	0.298985	−	0.517857i	0.975904	+	0.218201i	$0.0700187\pi$
$822$	−1.07203	−	22.5576i	−0.0373912	−	0.786785i
$823$	4.75672	+	2.74630i	0.165809	+	0.0957298i	0.580608	−	0.814183i	$-0.302815\pi$
$823$	4.75672	+	2.74630i	0.165809	+	0.0957298i	−0.414799	+	0.909913i	$0.636148\pi$
$824$	−7.21755	−	50.3187i	−0.251435	−	1.75294i
$825$		−	6.00814i		−	0.209176i
$826$	−7.17495	−	11.1672i	−0.249649	−	0.388556i
$827$	3.78281	−	6.55202i	0.131541	−	0.227836i	−0.792730	−	0.609573i	$-0.791341\pi$
$827$	3.78281	−	6.55202i	0.131541	−	0.227836i	0.924271	+	0.381737i	$0.124674\pi$
$828$	−40.3969	+	28.7529i	−1.40389	+	0.999233i
$829$		−	20.9352i		−	0.727111i	−0.931573	−	0.363555i	$-0.881563\pi$
$829$		−	20.9352i		−	0.727111i	0.931573	−	0.363555i	$-0.118437\pi$
$830$	0.632448	+	0.984350i	0.0219526	+	0.0341673i
$831$	−33.9410	−	58.7876i	−1.17740	−	2.03932i
$832$	39.3341	+	9.57023i	1.36366	+	0.331788i
$833$	3.35962	+	5.81902i	0.116404	+	0.201617i
$834$	33.8632	−	1.60931i	1.17259	−	0.0557260i
$835$	−6.65510			−0.230309
$836$	6.17610	−	17.9085i	0.213605	−	0.619380i
$837$	−7.41427			−0.256275
$838$	−22.4758	+	1.06814i	−0.776412	+	0.0368982i
$839$	−7.78062	−	13.4764i	−0.268617	−	0.465258i	0.699888	−	0.714253i	$-0.253233\pi$
$839$	−7.78062	−	13.4764i	−0.268617	−	0.465258i	−0.968505	+	0.248995i	$0.919900\pi$
$840$	6.34950	−	15.8449i	0.219078	−	0.546701i
$841$	18.8602	+	32.6668i	0.650351	+	1.12644i
$842$	−12.9293	−	20.1234i	−0.445574	−	0.693497i
$843$			16.0062i			0.551284i
$844$	31.5273	+	44.2948i	1.08521	+	1.52469i
$845$	6.30280	−	10.9168i	0.216823	−	0.375548i
$846$	1.27474	+	1.98402i	0.0438265	+	0.0682121i
$847$			13.7035i			0.470857i
$848$	−42.5922	−	14.7626i	−1.46262	−	0.506950i
$849$	−39.0610	−	22.5519i	−1.34057	−	0.773978i
$850$	−0.201763	−	4.24549i	−0.00692041	−	0.145619i
$851$	4.41334	−	7.64413i	0.151287	−	0.262037i
$852$	14.9286	−	32.6699i	0.511447	−	1.11925i
$853$	5.31920	+	9.21312i	0.182126	+	0.315451i	0.942604	−	0.333912i	$-0.108369\pi$
$853$	5.31920	+	9.21312i	0.182126	+	0.315451i	−0.760478	+	0.649363i	$0.775035\pi$
$854$	11.8370	−	22.9542i	0.405053	−	0.785477i
$855$	18.4278	+	8.38620i	0.630219	+	0.286802i
$856$	5.55784	+	38.7477i	0.189963	+	1.32437i
$857$	41.1589	−	23.7631i	1.40596	−	0.811732i	0.410966	−	0.911651i	$-0.365191\pi$
$857$	41.1589	−	23.7631i	1.40596	−	0.811732i	0.994996	+	0.0999183i	$0.0318581\pi$
$858$	2.04101	+	42.9469i	0.0696790	+	1.46618i
$859$	−19.8002	−	11.4317i	−0.675574	−	0.390043i	0.122611	−	0.992455i	$-0.460873\pi$
$859$	−19.8002	−	11.4317i	−0.675574	−	0.390043i	−0.798185	+	0.602412i	$0.794207\pi$
$860$	21.6283	+	9.88313i	0.737518	+	0.337012i
$861$	−12.2959	+	21.2971i	−0.419042	+	0.725802i
$862$	−24.3715	−	12.5678i	−0.830096	−	0.428062i
$863$	−36.5702			−1.24486			−0.622431	−	0.782674i	$-0.713855\pi$
$863$	−36.5702			−1.24486			−0.622431	+	0.782674i	$0.713855\pi$
$864$	−6.05128	−	25.0046i	−0.205869	−	0.850673i
$865$	10.7277	+	6.19363i	0.364752	+	0.210590i
$866$	−23.3705	+	45.3200i	−0.794161	+	1.54004i
$867$	22.0297			0.748168
$868$	−0.674927	−	7.08486i	−0.0229085	−	0.240476i
$869$	−14.0810	+	8.12969i	−0.477666	+	0.275781i
$870$	17.2648	+	26.8711i	0.585331	+	0.911017i
$871$	36.0018	−	20.7857i	1.21988	−	0.704295i
$872$	−12.5250	−	15.9378i	−0.424151	−	0.539724i
$873$			69.3973i			2.34874i
$874$	25.8390	−	20.3709i	0.874019	−	0.689055i
$875$			2.18272i			0.0737895i
$876$	−11.4541	+	25.0662i	−0.386998	+	0.846908i
$877$	19.3735	−	11.1853i	0.654197	−	0.377701i	−0.135865	−	0.990727i	$-0.543381\pi$
$877$	19.3735	−	11.1853i	0.654197	−	0.377701i	0.790062	+	0.613027i	$0.210048\pi$
$878$	−24.5982	+	15.8044i	−0.830148	+	0.533373i
$879$	−22.0605	+	12.7366i	−0.744083	+	0.429596i
$880$	6.57146	−	5.68907i	0.221524	−	0.191778i
$881$	−44.2302			−1.49015			−0.745077	−	0.666978i	$-0.767587\pi$
$881$	−44.2302			−1.49015			−0.745077	+	0.666978i	$0.767587\pi$
$882$	−13.0526	−	6.73094i	−0.439505	−	0.226642i
$883$	−14.0382	−	8.10497i	−0.472424	−	0.272754i	0.244830	−	0.969566i	$-0.421268\pi$
$883$	−14.0382	−	8.10497i	−0.472424	−	0.272754i	−0.717254	+	0.696812i	$0.754601\pi$
$884$	2.88445	+	30.2788i	0.0970147	+	1.01839i
$885$	11.8893			0.399654
$886$	23.9433	−	46.4309i	0.804392	−	1.55988i
$887$	22.2717	−	38.5757i	0.747811	−	1.29525i	−0.201059	−	0.979579i	$-0.564438\pi$
$887$	22.2717	−	38.5757i	0.747811	−	1.29525i	0.948870	−	0.315667i	$-0.102228\pi$
$888$	7.99086	+	10.1682i	0.268156	+	0.341223i
$889$	27.9164	+	16.1175i	0.936285	+	0.540564i
$890$	−23.4989	+	1.11676i	−0.787684	+	0.0374339i
$891$	−2.55945	+	1.47770i	−0.0857448	+	0.0495048i
$892$	13.5259	+	19.0035i	0.452882	+	0.636285i
$893$	−0.909408	−	1.27351i	−0.0304322	−	0.0426163i
$894$	72.2787	+	37.2725i	2.41736	+	1.24658i
$895$	4.10098	+	7.10310i	0.137081	+	0.237431i
$896$	23.3428	−	8.05861i	0.779829	−	0.269219i
$897$	−37.3396	+	64.6740i	−1.24673	+	2.15940i
$898$	−32.9164	+	1.56432i	−1.09843	+	0.0522020i
$899$	11.5325	+	6.65830i	0.384631	+	0.222067i
$900$	5.38684	+	7.56833i	0.179561	+	0.252278i
$901$		−	33.8694i		−	1.12835i
$902$	−10.5350	+	6.76879i	−0.350778	+	0.225376i
$903$	−35.8776	+	62.1417i	−1.19393	+	2.06795i
$904$	−10.0618	+	1.44323i	−0.334651	+	0.0480012i
$905$			4.79476i			0.159383i
$906$	−45.4494	+	29.2014i	−1.50996	+	0.970151i
$907$	−12.5852	−	21.7982i	−0.417885	−	0.723799i	0.577841	−	0.816149i	$-0.303895\pi$
$907$	−12.5852	−	21.7982i	−0.417885	−	0.723799i	−0.995727	+	0.0923507i	$0.970562\pi$
$908$	−36.3437	+	3.46222i	−1.20611	+	0.114898i
$909$	10.5370	+	18.2506i	0.349489	+	0.605333i
$910$	−0.741489	−	15.6024i	−0.0245801	−	0.517214i
$911$	−45.7359			−1.51530			−0.757649	−	0.652662i	$-0.773652\pi$
$911$	−45.7359			−1.51530			−0.757649	+	0.652662i	$0.773652\pi$
$912$	13.6225	+	46.2434i	0.451086	+	1.53127i
$913$	−1.79776			−0.0594973
$914$	−1.36487	−	28.7197i	−0.0451460	−	0.949962i
$915$	11.5666	+	20.0340i	0.382380	+	0.662302i
$916$	−25.1570	+	2.39654i	−0.831211	+	0.0791839i
$917$	−4.94097	−	8.55801i	−0.163165	−	0.282610i
$918$	16.2622	−	10.4485i	0.536733	−	0.344853i
$919$			31.8418i			1.05037i	0.850990	+	0.525183i	$0.176003\pi$
$919$			31.8418i			1.05037i	−0.850990	+	0.525183i	$0.823997\pi$
$920$	14.9441	−	2.14354i	0.492693	−	0.0706703i
$921$	0.571529	−	0.989918i	0.0188325	−	0.0326189i
$922$	−11.5672	+	7.43198i	−0.380946	+	0.244759i
$923$		−	32.8685i		−	1.08188i
$924$	15.2091	+	21.3683i	0.500342	+	0.702964i
$925$	−1.43212	−	0.826836i	−0.0470879	−	0.0271862i
$926$	−0.241952	+	0.0114986i	−0.00795105	+	0.000377866i
$927$	−41.7394	+	72.2948i	−1.37090	+	2.37447i
$928$	−13.0426	+	44.3276i	−0.428146	+	1.45513i
$929$	11.8751	+	20.5683i	0.389609	+	0.674823i	0.992397	−	0.123079i	$-0.0392768\pi$
$929$	11.8751	+	20.5683i	0.389609	+	0.674823i	−0.602788	+	0.797902i	$0.705943\pi$
$930$	5.66578	+	2.92171i	0.185788	+	0.0958067i
$931$	8.86997	+	4.03657i	0.290701	+	0.132293i
$932$	11.7246	+	16.4727i	0.384053	+	0.539581i
$933$	10.3155	−	5.95565i	0.337714	−	0.194979i
$934$	6.89476	−	0.327667i	0.225603	−	0.0107216i
$935$	5.65574	+	3.26534i	0.184962	+	0.106788i
$936$	−41.0769	−	52.2695i	−1.34264	−	1.70848i
$937$	−0.291481	+	0.504861i	−0.00952228	+	0.0164931i	−0.870747	−	0.491731i	$-0.836364\pi$
$937$	−0.291481	+	0.504861i	−0.00952228	+	0.0164931i	0.861225	+	0.508224i	$0.169698\pi$
$938$	11.6229	−	22.5391i	0.379501	−	0.735927i
$939$	63.4779			2.07152
$940$	−0.0680922	−	0.714780i	−0.00222092	−	0.0233135i
$941$	38.3502	+	22.1415i	1.25018	+	0.721792i	0.971145	−	0.238489i	$-0.0766520\pi$
$941$	38.3502	+	22.1415i	1.25018	+	0.721792i	0.279035	+	0.960281i	$0.409985\pi$
$942$	74.4273	+	38.3805i	2.42497	+	1.25050i
$943$	−21.7498			−0.708270
$944$	11.2579	+	13.0040i	0.366413	+	0.423245i
$945$	−8.59673	+	4.96332i	−0.279652	+	0.161457i
$946$	−30.7397	+	19.7503i	−0.999433	+	0.642139i
$947$	−12.5413	+	7.24073i	−0.407538	+	0.235292i	−0.689731	−	0.724065i	$-0.742271\pi$
$947$	−12.5413	+	7.24073i	−0.407538	+	0.235292i	0.282193	+	0.959358i	$0.408938\pi$
$948$	17.1971	−	37.6343i	0.558537	−	1.22230i
$949$			25.2186i			0.818630i
$950$	−3.81647	−	4.84093i	−0.123823	−	0.157060i
$951$			40.0966i			1.30022i
$952$	11.4647	+	14.5886i	0.371572	+	0.472818i
$953$	−18.3631	+	10.6019i	−0.594838	+	0.343430i	−0.767008	−	0.641637i	$-0.778256\pi$
$953$	−18.3631	+	10.6019i	−0.594838	+	0.343430i	0.172170	+	0.985067i	$0.444922\pi$
$954$	40.0150	+	62.2799i	1.29553	+	2.01638i
$955$	−1.80455	+	1.04186i	−0.0583938	+	0.0337137i
$956$	3.17709	+	33.3507i	0.102754	+	1.07864i
$957$	−49.0760			−1.58640
$958$	6.95167	−	13.4807i	0.224598	−	0.435541i
$959$	−10.9172	−	6.30307i	−0.352536	−	0.203537i
$960$	−5.22924	+	21.4924i	−0.168773	+	0.693665i
$961$	−28.3422			−0.914263
$962$	10.5179	+	5.42383i	0.339110	+	0.174871i
$963$	32.1412	−	55.6702i	1.03574	−	1.79395i
$964$	24.0648	+	10.9965i	0.775074	+	0.354174i
$965$	−14.5234	−	8.38512i	−0.467526	−	0.269926i
$966$	2.16256	+	45.5046i	0.0695794	+	1.46409i
$967$	−19.4740	+	11.2433i	−0.626242	+	0.361561i	−0.779295	−	0.626657i	$-0.784423\pi$
$967$	−19.4740	+	11.2433i	−0.626242	+	0.361561i	0.153053	+	0.988218i	$0.451089\pi$
$968$	−2.52124	−	17.5774i	−0.0810358	−	0.564959i
$969$	−29.4771	+	21.0495i	−0.946940	+	0.676207i
$970$	9.68417	−	18.7795i	0.310940	−	0.602974i
$971$	−7.24627	−	12.5509i	−0.232544	−	0.402778i	0.726012	−	0.687682i	$-0.241372\pi$
$971$	−7.24627	−	12.5509i	−0.232544	−	0.402778i	−0.958556	+	0.284904i	$0.908038\pi$
$972$	14.4668	−	31.6592i	0.464023	−	1.01547i
$973$	9.46210	−	16.3888i	0.303341	−	0.525402i
$974$	0.311084	+	6.54582i	0.00996777	+	0.209742i
$975$	12.1166	+	6.99554i	0.388043	+	0.224037i
$976$	−10.9600	+	31.6211i	−0.350821	+	1.01217i
$977$		−	28.3116i		−	0.905769i	−0.891569	−	0.452884i	$-0.850395\pi$
$977$		−	28.3116i		−	0.905769i	0.891569	−	0.452884i	$-0.149605\pi$
$978$	−29.3859	−	45.7365i	−0.939657	−	1.46249i
$979$	18.0737	−	31.3046i	0.577639	−	1.00050i
$980$	2.59287	+	3.64290i	0.0828263	+	0.116368i
$981$			33.2880i			1.06280i
$982$	−16.2116	−	25.2319i	−0.517332	−	0.805182i
$983$	26.5194	+	45.9330i	0.845839	+	1.46504i	0.884891	+	0.465799i	$0.154233\pi$
$983$	26.5194	+	45.9330i	0.845839	+	1.46504i	−0.0390516	+	0.999237i	$0.512434\pi$
$984$	11.8535	−	29.5799i	0.377876	−	0.942974i
$985$	−1.10271	−	1.90995i	−0.0351353	−	0.0608561i
$986$	−34.6782	+	1.64805i	−1.10438	+	0.0524846i
$987$	2.16664			0.0689649
$988$	28.9251	+	33.3071i	0.920231	+	1.05964i
$989$	−63.4626			−2.01799
$990$	−14.2577	+	0.677585i	−0.453141	+	0.0215351i
$991$	12.4689	+	21.5969i	0.396089	+	0.686047i	0.993240	−	0.116083i	$-0.0370338\pi$
$991$	12.4689	+	21.5969i	0.396089	+	0.686047i	−0.597150	+	0.802129i	$0.703700\pi$
$992$	2.16924	+	8.96355i	0.0688734	+	0.284593i
$993$	15.2510	+	26.4154i	0.483975	+	0.838269i
$994$	−10.8383	−	16.8688i	−0.343769	−	0.535046i
$995$		−	23.4522i		−	0.743486i
$996$	3.72727	−	2.65292i	0.118103	−	0.0840611i
$997$	6.61929	−	11.4649i	0.209635	−	0.363099i	−0.741965	−	0.670439i	$-0.766106\pi$
$997$	6.61929	−	11.4649i	0.209635	−	0.363099i	0.951600	+	0.307341i	$0.0994391\pi$
$998$	0.153394	+	0.238744i	0.00485560	+	0.00755731i
$999$		−	7.52062i		−	0.237942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.b.31.11	yes	40
4.3	odd	2	inner	380.2.n.b.31.4	✓	40
19.8	odd	6	inner	380.2.n.b.331.4	yes	40
76.27	even	6	inner	380.2.n.b.331.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.b.31.4	✓	40	4.3	odd	2	inner
380.2.n.b.31.11	yes	40	1.1	even	1	trivial
380.2.n.b.331.4	yes	40	19.8	odd	6	inner
380.2.n.b.331.11	yes	40	76.27	even	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0671334 + 1.41262i) q^{2} +(1.38246 + 2.39450i) q^{3} +(-1.99099 + 0.189668i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.28970 + 2.11365i) q^{6} +2.18272i q^{7} +(-0.401590 - 2.79977i) q^{8} +(-2.32241 + 4.02254i) q^{9} +O(q^{10})\)	\(q+(0.0671334 + 1.41262i) q^{2} +(1.38246 + 2.39450i) q^{3} +(-1.99099 + 0.189668i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.28970 + 2.11365i) q^{6} +2.18272i q^{7} +(-0.401590 - 2.79977i) q^{8} +(-2.32241 + 4.02254i) q^{9} +(1.18980 - 0.764449i) q^{10} +2.17298i q^{11} +(-3.20663 - 4.50520i) q^{12} +(-4.38226 - 2.53010i) q^{13} +(-3.08336 + 0.146534i) q^{14} +(1.38246 - 2.39450i) q^{15} +(3.92805 - 0.755252i) q^{16} +(1.50270 + 2.60275i) q^{17} +(-5.83823 - 3.01064i) q^{18} +(3.96739 + 1.80549i) q^{19} +(1.15975 + 1.62941i) q^{20} +(-5.22653 + 3.01754i) q^{21} +(-3.06959 + 0.145880i) q^{22} +(-4.62252 - 2.66881i) q^{23} +(6.14887 - 4.83219i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.27987 - 6.36032i) q^{26} -4.54783 q^{27} +(-0.413992 - 4.34577i) q^{28} +(7.07391 + 4.08413i) q^{29} +(3.47532 + 1.79214i) q^{30} +1.63029 q^{31} +(1.33059 + 5.49814i) q^{32} +(-5.20320 + 3.00407i) q^{33} +(-3.57582 + 2.29748i) q^{34} +(1.89029 - 1.09136i) q^{35} +(3.86095 - 8.44930i) q^{36} +1.65367i q^{37} +(-2.28413 + 5.72562i) q^{38} -13.9911i q^{39} +(-2.22388 + 1.74767i) q^{40} +(3.52888 - 2.03740i) q^{41} +(-4.61350 - 7.18052i) q^{42} +(10.2968 - 5.94484i) q^{43} +(-0.412144 - 4.32637i) q^{44} +4.64483 q^{45} +(3.45969 - 6.70902i) q^{46} +(-0.310910 - 0.179504i) q^{47} +(7.23884 + 8.36160i) q^{48} +2.23572 q^{49} +(-1.25693 - 0.648170i) q^{50} +(-4.15486 + 7.19643i) q^{51} +(9.20490 + 4.20622i) q^{52} +(-9.75968 - 5.63476i) q^{53} +(-0.305311 - 6.42435i) q^{54} +(1.88186 - 1.08649i) q^{55} +(6.11113 - 0.876560i) q^{56} +(1.16153 + 11.9959i) q^{57} +(-5.29442 + 10.2669i) q^{58} +(2.15002 + 3.72394i) q^{59} +(-2.29831 + 5.02962i) q^{60} +(-4.18333 + 7.24574i) q^{61} +(0.109447 + 2.30298i) q^{62} +(-8.78009 - 5.06919i) q^{63} +(-7.67745 + 2.24872i) q^{64} +5.06020i q^{65} +(-4.59291 - 7.14846i) q^{66} +(-4.10768 + 7.11471i) q^{67} +(-3.48552 - 4.89704i) q^{68} -14.7581i q^{69} +(1.66858 + 2.59700i) q^{70} +(3.24775 + 5.62526i) q^{71} +(12.1948 + 4.88682i) q^{72} +(-2.49186 - 4.31602i) q^{73} +(-2.33601 + 0.111017i) q^{74} -2.76493 q^{75} +(-8.24147 - 2.84223i) q^{76} -4.74302 q^{77} +(19.7641 - 0.939268i) q^{78} +(3.74126 + 6.48006i) q^{79} +(-2.61809 - 3.02417i) q^{80} +(0.680033 + 1.17785i) q^{81} +(3.11498 + 4.84819i) q^{82} +0.827326i q^{83} +(9.83361 - 6.99918i) q^{84} +(1.50270 - 2.60275i) q^{85} +(9.08905 + 14.1463i) q^{86} +22.5846i q^{87} +(6.08385 - 0.872647i) q^{88} +(-14.4063 - 8.31749i) q^{89} +(0.311823 + 6.56137i) q^{90} +(5.52251 - 9.56526i) q^{91} +(9.70956 + 4.43683i) q^{92} +(2.25382 + 3.90372i) q^{93} +(0.232698 - 0.451248i) q^{94} +(-0.420092 - 4.33861i) q^{95} +(-11.3258 + 10.7871i) q^{96} +(12.9391 - 7.47039i) q^{97} +(0.150091 + 3.15822i) q^{98} +(-8.74090 - 5.04656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9	\( 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} - 18 q^{14} + 9 q^{16} - 12 q^{17} - 2 q^{20} + 12 q^{21} + 20 q^{24} - 20 q^{25} + 34 q^{26} + 12 q^{28} + 10 q^{30} - 12 q^{32} - 6 q^{33} - 27 q^{34} - 6 q^{36} + 12 q^{38} + 36 q^{41} - 21 q^{42} + 28 q^{44} + 44 q^{45} + 36 q^{48} - 60 q^{49} + 15 q^{52} - 66 q^{53} - 31 q^{54} + 28 q^{57} + 2 q^{58} + 3 q^{60} + 4 q^{61} - 57 q^{62} - 80 q^{64} + 18 q^{66} - 20 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} + 30 q^{76} + 12 q^{77} + 144 q^{78} + 9 q^{80} + 16 q^{81} - 41 q^{82} - 12 q^{85} + 18 q^{86} - 18 q^{89} + 39 q^{90} + 40 q^{92} - 8 q^{93} - 160 q^{96} - 18 q^{97} - 66 q^{98}+O(q^{100}) \) 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 - 18 * q^14 + 9 * q^16 - 12 * q^17 - 2 * q^20 + 12 * q^21 + 20 * q^24 - 20 * q^25 + 34 * q^26 + 12 * q^28 + 10 * q^30 - 12 * q^32 - 6 * q^33 - 27 * q^34 - 6 * q^36 + 12 * q^38 + 36 * q^41 - 21 * q^42 + 28 * q^44 + 44 * q^45 + 36 * q^48 - 60 * q^49 + 15 * q^52 - 66 * q^53 - 31 * q^54 + 28 * q^57 + 2 * q^58 + 3 * q^60 + 4 * q^61 - 57 * q^62 - 80 * q^64 + 18 * q^66 - 20 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 + 30 * q^76 + 12 * q^77 + 144 * q^78 + 9 * q^80 + 16 * q^81 - 41 * q^82 - 12 * q^85 + 18 * q^86 - 18 * q^89 + 39 * q^90 + 40 * q^92 - 8 * q^93 - 160 * q^96 - 18 * q^97 - 66 * q^98

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