LMFDB - Embedded newform 187.2.m.a.10.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [187,2,Mod(10,187)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("187.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(187, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.m (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			10.3
Character	$\chi$	$=$	187.10
Dual form			187.2.m.a.131.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.58527 - 0.656642i) q^{2} +(2.26689 + 1.51468i) q^{3} +(0.667703 + 0.667703i) q^{4} +(-3.74296 + 0.744522i) q^{5} +(-2.59903 - 3.88972i) q^{6} +(-0.334093 + 1.67960i) q^{7} +(0.693234 + 1.67362i) q^{8} +(1.69645 + 4.09559i) q^{9} +(6.42251 + 1.27752i) q^{10} +(-1.97510 + 2.66439i) q^{11} +(0.502247 + 2.52496i) q^{12} +(-2.69751 - 2.69751i) q^{13} +(1.63253 - 2.44325i) q^{14} +(-9.61258 - 3.98166i) q^{15} -4.99689i q^{16} +(1.14497 + 3.96094i) q^{17} -7.60660i q^{18} +(4.05978 + 1.68161i) q^{19} +(-2.99630 - 2.00207i) q^{20} +(-3.30141 + 3.30141i) q^{21} +(4.88063 - 2.92686i) q^{22} +(-3.79941 + 2.53868i) q^{23} +(-0.963517 + 4.84393i) q^{24} +(8.83606 - 3.66002i) q^{25} +(2.50500 + 6.04759i) q^{26} +(-0.762214 + 3.83191i) q^{27} +(-1.34455 + 0.898398i) q^{28} +(6.63760 - 1.32030i) q^{29} +(12.6241 + 12.6241i) q^{30} +(-2.57365 + 3.85173i) q^{31} +(-1.89470 + 4.57422i) q^{32} +(-8.51304 + 3.04821i) q^{33} +(0.785829 - 7.03101i) q^{34} -6.53542i q^{35} +(-1.60191 + 3.86736i) q^{36} +(4.11189 + 2.74748i) q^{37} +(-5.33164 - 5.33164i) q^{38} +(-2.02907 - 10.2008i) q^{39} +(-3.84079 - 5.74815i) q^{40} +(1.90465 - 9.57533i) q^{41} +(7.40150 - 3.06580i) q^{42} +(-3.15691 + 1.30764i) q^{43} +(-3.09780 + 0.460240i) q^{44} +(-9.39901 - 14.0666i) q^{45} +(7.69011 - 1.52966i) q^{46} +(-3.85758 + 3.85758i) q^{47} +(7.56872 - 11.3274i) q^{48} +(3.75772 + 1.55650i) q^{49} -16.4109 q^{50} +(-3.40406 + 10.7133i) q^{51} -3.60227i q^{52} +(3.09054 - 7.46123i) q^{53} +(3.72451 - 5.57413i) q^{54} +(5.40903 - 11.4432i) q^{55} +(-3.04261 + 0.605213i) q^{56} +(6.65593 + 9.96131i) q^{57} +(-11.3894 - 2.26549i) q^{58} +(1.06069 - 0.439353i) q^{59} +(-3.75978 - 9.07691i) q^{60} +(0.936098 + 0.186202i) q^{61} +(6.60915 - 4.41609i) q^{62} +(-7.44573 + 1.48105i) q^{63} +(-1.05943 + 1.05943i) q^{64} +(12.1050 + 8.08833i) q^{65} +(15.4971 + 0.757767i) q^{66} -2.35465i q^{67} +(-1.88023 + 3.40923i) q^{68} -12.4581 q^{69} +(-4.29143 + 10.3604i) q^{70} +(1.01745 + 0.679835i) q^{71} +(-5.67841 + 5.67841i) q^{72} +(0.172856 + 0.869007i) q^{73} +(-4.71436 - 7.05554i) q^{74} +(25.5741 + 5.08700i) q^{75} +(1.58791 + 3.83354i) q^{76} +(-3.81524 - 4.20753i) q^{77} +(-3.48166 + 17.5035i) q^{78} +(-0.991979 + 0.662819i) q^{79} +(3.72030 + 18.7032i) q^{80} +(1.87191 - 1.87191i) q^{81} +(-9.30696 + 13.9289i) q^{82} +(-0.486489 + 1.17449i) q^{83} -4.40873 q^{84} +(-7.23458 - 13.9732i) q^{85} +5.86323 q^{86} +(17.0465 + 7.06090i) q^{87} +(-5.82837 - 1.45851i) q^{88} +(-4.19632 - 4.19632i) q^{89} +(5.66328 + 28.4712i) q^{90} +(5.43196 - 3.62952i) q^{91} +(-4.23196 - 0.841789i) q^{92} +(-11.6683 + 4.83318i) q^{93} +(8.64836 - 3.58227i) q^{94} +(-16.4476 - 3.27163i) q^{95} +(-11.2236 + 7.49935i) q^{96} +(3.39119 + 17.0486i) q^{97} +(-4.93495 - 4.93495i) q^{98} +(-14.2629 - 3.56921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9} - 64 q^{12} + 16 q^{14} - 16 q^{15} - 16 q^{20} + 8 q^{22} - 32 q^{23} + 16 q^{26} + 32 q^{27} - 80 q^{31} - 16 q^{34} + 16 q^{36} + 16 q^{37} + 80 q^{38}+ \cdots - 112 q^{99}+O(q^{100}) $ 128 * q - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^9 - 64 * q^12 + 16 * q^14 - 16 * q^15 - 16 * q^20 + 8 * q^22 - 32 * q^23 + 16 * q^26 + 32 * q^27 - 80 * q^31 - 16 * q^34 + 16 * q^36 + 16 * q^37 + 80 * q^38 - 112 * q^42 - 72 * q^44 - 16 * q^45 - 16 * q^47 + 32 * q^48 + 48 * q^49 - 16 * q^53 - 8 * q^55 - 16 * q^56 - 128 * q^58 + 48 * q^59 + 112 * q^60 + 48 * q^64 + 72 * q^66 - 192 * q^69 + 128 * q^70 - 16 * q^71 + 48 * q^75 + 8 * q^77 - 16 * q^78 + 112 * q^80 - 16 * q^82 + 32 * q^86 - 168 * q^88 - 16 * q^89 + 144 * q^91 - 176 * q^92 + 48 * q^93 + 48 * q^97 - 112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$-1$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

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

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

$2$	−1.58527	−	0.656642i	−1.12096	−	0.464316i	−0.256260	−	0.966608i	$-0.582490\pi$
$2$	−1.58527	−	0.656642i	−1.12096	−	0.464316i	−0.864698	+	0.502292i	$0.832490\pi$
$3$	2.26689	+	1.51468i	1.30879	+	0.874504i	0.997131	−	0.0756916i	$-0.0241164\pi$
$3$	2.26689	+	1.51468i	1.30879	+	0.874504i	0.311656	+	0.950195i	$0.399116\pi$
$4$	0.667703	+	0.667703i	0.333851	+	0.333851i
$5$	−3.74296	+	0.744522i	−1.67390	+	0.332960i	−0.938660	−	0.344843i	$-0.887932\pi$
$5$	−3.74296	+	0.744522i	−1.67390	+	0.332960i	−0.735243	+	0.677803i	$0.762932\pi$
$6$	−2.59903	−	3.88972i	−1.06105	−	1.58797i
$7$	−0.334093	+	1.67960i	−0.126275	+	0.634829i	0.864864	+	0.502006i	$0.167404\pi$
$7$	−0.334093	+	1.67960i	−0.126275	+	0.634829i	−0.991140	+	0.132823i	$0.957596\pi$
$8$	0.693234	+	1.67362i	0.245095	+	0.591712i
$9$	1.69645	+	4.09559i	0.565484	+	1.36520i
$10$	6.42251	+	1.27752i	2.03098	+	0.403986i
$11$	−1.97510	+	2.66439i	−0.595515	+	0.803344i
$11$	−1.97510	+	2.66439i	−0.595515	+	0.803344i
$12$	0.502247	+	2.52496i	0.144986	+	0.728894i
$13$	−2.69751	−	2.69751i	−0.748155	−	0.748155i	0.225978	−	0.974132i	$-0.427442\pi$
$13$	−2.69751	−	2.69751i	−0.748155	−	0.748155i	−0.974132	+	0.225978i	$0.927442\pi$
$14$	1.63253	−	2.44325i	0.436311	−	0.652985i
$15$	−9.61258	−	3.98166i	−2.48196	−	1.02806i
$16$		−	4.99689i		−	1.24922i
$17$	1.14497	+	3.96094i	0.277696	+	0.960669i
$17$	1.14497	+	3.96094i	0.277696	+	0.960669i
$18$		−	7.60660i		−	1.79289i
$19$	4.05978	+	1.68161i	0.931377	+	0.385789i	0.796201	−	0.605033i	$-0.206840\pi$
$19$	4.05978	+	1.68161i	0.931377	+	0.385789i	0.135176	+	0.990822i	$0.456840\pi$
$20$	−2.99630	−	2.00207i	−0.669994	−	0.447676i
$21$	−3.30141	+	3.30141i	−0.720428	+	0.720428i
$22$	4.88063	−	2.92686i	1.04055	−	0.624008i
$23$	−3.79941	+	2.53868i	−0.792231	+	0.529352i	−0.884587	−	0.466374i	$-0.845560\pi$
$23$	−3.79941	+	2.53868i	−0.792231	+	0.529352i	0.0923567	+	0.995726i	$0.470560\pi$
$24$	−0.963517	+	4.84393i	−0.196677	+	0.988762i
$25$	8.83606	−	3.66002i	1.76721	−	0.732003i
$26$	2.50500	+	6.04759i	0.491270	+	1.18603i
$27$	−0.762214	+	3.83191i	−0.146688	+	0.737451i
$28$	−1.34455	+	0.898398i	−0.254096	+	0.169781i
$29$	6.63760	−	1.32030i	1.23257	−	0.245174i	0.464520	−	0.885563i	$-0.346227\pi$
$29$	6.63760	−	1.32030i	1.23257	−	0.245174i	0.768051	+	0.640389i	$0.221227\pi$
$30$	12.6241	+	12.6241i	2.30483	+	2.30483i
$31$	−2.57365	+	3.85173i	−0.462241	+	0.691792i	−0.987227	−	0.159319i	$-0.949070\pi$
$31$	−2.57365	+	3.85173i	−0.462241	+	0.691792i	0.524987	+	0.851110i	$0.324070\pi$
$32$	−1.89470	+	4.57422i	−0.334939	+	0.808615i
$33$	−8.51304	+	3.04821i	−1.48193	+	0.530626i
$34$	0.785829	−	7.03101i	0.134769	−	1.20581i
$35$		−	6.53542i		−	1.10469i
$36$	−1.60191	+	3.86736i	−0.266986	+	0.644561i
$37$	4.11189	+	2.74748i	0.675990	+	0.451682i	0.845592	−	0.533830i	$-0.179248\pi$
$37$	4.11189	+	2.74748i	0.675990	+	0.451682i	−0.169601	+	0.985513i	$0.554248\pi$
$38$	−5.33164	−	5.33164i	−0.864906	−	0.864906i
$39$	−2.02907	−	10.2008i	−0.324911	−	1.63344i
$40$	−3.84079	−	5.74815i	−0.607283	−	0.908863i
$41$	1.90465	−	9.57533i	0.297457	−	1.49542i	−0.485995	−	0.873962i	$-0.661543\pi$
$41$	1.90465	−	9.57533i	0.297457	−	1.49542i	0.783451	−	0.621453i	$-0.213457\pi$
$42$	7.40150	−	3.06580i	1.14208	−	0.473063i
$43$	−3.15691	+	1.30764i	−0.481425	+	0.199413i	−0.610179	−	0.792264i	$-0.708902\pi$
$43$	−3.15691	+	1.30764i	−0.481425	+	0.199413i	0.128754	+	0.991677i	$0.458902\pi$
$44$	−3.09780	+	0.460240i	−0.467011	+	0.0693838i
$45$	−9.39901	−	14.0666i	−1.40112	−	2.09693i
$46$	7.69011	−	1.52966i	1.13384	−	0.225536i
$47$	−3.85758	+	3.85758i	−0.562685	+	0.562685i	−0.930069	−	0.367384i	$-0.880253\pi$
$47$	−3.85758	+	3.85758i	−0.562685	+	0.562685i	0.367384	+	0.930069i	$0.380253\pi$
$48$	7.56872	−	11.3274i	1.09245	−	1.63497i
$49$	3.75772	+	1.55650i	0.536817	+	0.222357i
$50$	−16.4109			−2.32085
$51$	−3.40406	+	10.7133i	−0.476664	+	1.50016i
$52$		−	3.60227i		−	0.499545i
$53$	3.09054	−	7.46123i	0.424519	−	1.02488i	−0.556479	−	0.830861i	$-0.687848\pi$
$53$	3.09054	−	7.46123i	0.424519	−	1.02488i	0.980998	−	0.194017i	$-0.0621518\pi$
$54$	3.72451	−	5.57413i	0.506842	−	0.758543i
$55$	5.40903	−	11.4432i	0.729354	−	1.54300i
$56$	−3.04261	+	0.605213i	−0.406586	+	0.0808749i
$57$	6.65593	+	9.96131i	0.881600	+	1.31941i
$58$	−11.3894	−	2.26549i	−1.49550	−	0.297473i
$59$	1.06069	−	0.439353i	0.138090	−	0.0571989i	−0.312568	−	0.949895i	$-0.601189\pi$
$59$	1.06069	−	0.439353i	0.138090	−	0.0571989i	0.450658	+	0.892696i	$0.351189\pi$
$60$	−3.75978	−	9.07691i	−0.485386	−	1.17182i
$61$	0.936098	+	0.186202i	0.119855	+	0.0238407i	0.254653	−	0.967032i	$-0.418039\pi$
$61$	0.936098	+	0.186202i	0.119855	+	0.0238407i	−0.134798	+	0.990873i	$0.543039\pi$
$62$	6.60915	−	4.41609i	0.839362	−	0.560844i
$63$	−7.44573	+	1.48105i	−0.938074	+	0.186595i
$64$	−1.05943	+	1.05943i	−0.132428	+	0.132428i
$65$	12.1050	+	8.08833i	1.50144	+	1.00323i
$66$	15.4971	+	0.757767i	1.90756	+	0.0932747i
$67$		−	2.35465i		−	0.287667i	−0.989602	−	0.143833i	$-0.954057\pi$
$67$		−	2.35465i		−	0.287667i	0.989602	−	0.143833i	$-0.0459430\pi$
$68$	−1.88023	+	3.40923i	−0.228011	+	0.413430i
$69$	−12.4581			−1.49978
$70$	−4.29143	+	10.3604i	−0.512924	+	1.23831i
$71$	1.01745	+	0.679835i	0.120749	+	0.0806816i	0.614478	−	0.788934i	$-0.289367\pi$
$71$	1.01745	+	0.679835i	0.120749	+	0.0806816i	−0.493729	+	0.869616i	$0.664367\pi$
$72$	−5.67841	+	5.67841i	−0.669207	+	0.669207i
$73$	0.172856	+	0.869007i	0.0202313	+	0.101710i	0.989582	−	0.143973i	$-0.0459879\pi$
$73$	0.172856	+	0.869007i	0.0202313	+	0.101710i	−0.969350	+	0.245683i	$0.920988\pi$
$74$	−4.71436	−	7.05554i	−0.548034	−	0.820190i
$75$	25.5741	+	5.08700i	2.95304	+	0.587397i
$76$	1.58791	+	3.83354i	0.182145	+	0.439737i
$77$	−3.81524	−	4.20753i	−0.434787	−	0.479493i
$78$	−3.48166	+	17.5035i	−0.394220	+	1.98188i
$79$	−0.991979	+	0.662819i	−0.111606	+	0.0745730i	−0.610121	−	0.792308i	$-0.708879\pi$
$79$	−0.991979	+	0.662819i	−0.111606	+	0.0745730i	0.498514	+	0.866881i	$0.333879\pi$
$80$	3.72030	+	18.7032i	0.415942	+	2.09108i
$81$	1.87191	−	1.87191i	0.207990	−	0.207990i
$82$	−9.30696	+	13.9289i	−1.02778	+	1.53818i
$83$	−0.486489	+	1.17449i	−0.0533991	+	0.128917i	−0.948328	−	0.317293i	$-0.897226\pi$
$83$	−0.486489	+	1.17449i	−0.0533991	+	0.128917i	0.894929	+	0.446209i	$0.147226\pi$
$84$	−4.40873			−0.481032
$85$	−7.23458	−	13.9732i	−0.784701	−	1.51561i
$86$	5.86323			0.632248
$87$	17.0465	+	7.06090i	1.82758	+	0.757008i
$88$	−5.82837	−	1.45851i	−0.621307	−	0.155478i
$89$	−4.19632	−	4.19632i	−0.444809	−	0.444809i	0.448816	−	0.893624i	$-0.351846\pi$
$89$	−4.19632	−	4.19632i	−0.444809	−	0.444809i	−0.893624	+	0.448816i	$0.851846\pi$
$90$	5.66328	+	28.4712i	0.596962	+	3.00113i
$91$	5.43196	−	3.62952i	0.569424	−	0.380477i
$92$	−4.23196	−	0.841789i	−0.441212	−	0.0877625i
$93$	−11.6683	+	4.83318i	−1.20995	+	0.501177i
$94$	8.64836	−	3.58227i	0.892010	−	0.369483i
$95$	−16.4476	−	3.27163i	−1.68749	−	0.335662i
$96$	−11.2236	+	7.49935i	−1.14550	+	0.765399i
$97$	3.39119	+	17.0486i	0.344323	+	1.73103i	0.633491	+	0.773750i	$0.281621\pi$
$97$	3.39119	+	17.0486i	0.344323	+	1.73103i	−0.289169	+	0.957278i	$0.593379\pi$
$98$	−4.93495	−	4.93495i	−0.498506	−	0.498506i
$99$	−14.2629	−	3.56921i	−1.43348	−	0.358719i
$100$	8.34366	+	3.45606i	0.834366	+	0.345606i
$101$	−0.100954			−0.0100453			−0.00502266	−	0.999987i	$-0.501599\pi$
$101$	−0.100954			−0.0100453			−0.00502266	+	0.999987i	$0.501599\pi$
$102$	12.4312	−	14.7482i	1.23087	−	1.46029i
$103$	10.2360			1.00859			0.504293	−	0.863533i	$-0.331753\pi$
$103$	10.2360			1.00859			0.504293	+	0.863533i	$0.331753\pi$
$104$	2.64459	−	6.38460i	0.259323	−	0.626062i
$105$	9.89910	−	14.8150i	0.966053	−	1.44580i
$106$	−9.79872	+	9.79872i	−0.951736	+	0.951736i
$107$	2.20443	+	11.0824i	0.213110	+	1.07138i	0.928125	+	0.372269i	$0.121420\pi$
$107$	2.20443	+	11.0824i	0.213110	+	1.07138i	−0.715014	+	0.699110i	$0.753580\pi$
$108$	−3.06751	+	2.04964i	−0.295171	+	0.197227i
$109$	−2.19542	+	11.0371i	−0.210283	+	1.05716i	0.721018	+	0.692916i	$0.243674\pi$
$109$	−2.19542	+	11.0371i	−0.210283	+	1.05716i	−0.931302	+	0.364249i	$0.881326\pi$
$110$	−16.0889	+	14.5888i	−1.53402	+	1.39099i
$111$	5.15962	+	12.4564i	0.489730	+	1.18231i
$112$	8.39278	+	1.66943i	0.793043	+	0.157746i
$113$	7.38057	+	11.0458i	0.694305	+	1.03910i	0.996313	+	0.0857959i	$0.0273433\pi$
$113$	7.38057	+	11.0458i	0.694305	+	1.03910i	−0.302007	+	0.953306i	$0.597657\pi$
$114$	−4.01047	−	20.1620i	−0.375615	−	1.88834i
$115$	12.3309	−	12.3309i	1.14987	−	1.14987i
$116$	5.31351	+	3.55037i	0.493347	+	0.329644i
$117$	6.47171	−	15.6241i	0.598310	−	1.44445i
$118$	−1.96999			−0.181352
$119$	−7.03532	+	0.599767i	−0.644927	+	0.0549806i
$120$		−	18.8480i		−	1.72058i
$121$	−3.19795	−	10.5249i	−0.290723	−	0.956807i
$122$	−1.36170	−	0.909862i	−0.123283	−	0.0823750i
$123$	18.8212	−	18.8212i	1.69705	−	1.69705i
$124$	−4.29024	+	0.853382i	−0.385275	+	0.0766360i
$125$	−14.4824	+	9.67684i	−1.29535	+	0.865523i
$126$	12.7760	+	2.54131i	1.13818	+	0.226398i
$127$	4.55122	+	10.9876i	0.403855	+	0.974993i	0.986721	+	0.162424i	$0.0519313\pi$
$127$	4.55122	+	10.9876i	0.403855	+	0.974993i	−0.582866	+	0.812568i	$0.698069\pi$
$128$	11.5236	−	4.77322i	1.01855	−	0.421897i
$129$	−9.13702	−	1.81747i	−0.804470	−	0.160019i
$130$	−13.8787	−	20.7709i	−1.21724	−	1.82173i
$131$	−1.97413	+	0.392679i	−0.172480	+	0.0343085i	−0.280575	−	0.959832i	$-0.590525\pi$
$131$	−1.97413	+	0.392679i	−0.172480	+	0.0343085i	0.108094	+	0.994141i	$0.465525\pi$
$132$	−7.71948	−	3.64888i	−0.671894	−	0.317594i
$133$	−4.18078	+	6.25698i	−0.362520	+	0.542549i
$134$	−1.54617	+	3.73277i	−0.133568	+	0.322463i
$135$		−	14.9102i		−	1.28326i
$136$	−5.83536	+	4.66210i	−0.500378	+	0.399772i
$137$	−10.3732			−0.886244			−0.443122	−	0.896461i	$-0.646129\pi$
$137$	−10.3732			−0.886244			−0.443122	+	0.896461i	$0.646129\pi$
$138$	19.7495	+	8.18053i	1.68119	+	0.696373i
$139$	−6.43385	+	9.62893i	−0.545712	+	0.816715i	−0.997139	−	0.0755926i	$-0.975915\pi$
$139$	−6.43385	+	9.62893i	−0.545712	+	0.816715i	0.451427	+	0.892308i	$0.350915\pi$
$140$	4.36372	−	4.36372i	0.368801	−	0.368801i
$141$	−14.5877	+	2.90167i	−1.22851	+	0.244365i
$142$	−1.16652	−	1.74582i	−0.0978923	−	0.146506i
$143$	12.5151	−	1.85936i	1.04656	−	0.155488i
$144$	20.4653	−	8.47699i	1.70544	−	0.706415i
$145$	−23.8613	+	9.88367i	−1.98157	+	0.820794i
$146$	0.296602	−	1.49112i	0.0245470	−	0.123406i
$147$	6.16072	+	9.22016i	0.508127	+	0.760466i
$148$	0.911022	+	4.58002i	0.0748855	+	0.376475i
$149$	−9.18258	−	9.18258i	−0.752266	−	0.752266i	0.222636	−	0.974902i	$-0.428534\pi$
$149$	−9.18258	−	9.18258i	−0.752266	−	0.752266i	−0.974902	+	0.222636i	$0.928534\pi$
$150$	−37.2016	−	24.8573i	−3.03750	−	2.02959i
$151$	−0.482852	+	1.16571i	−0.0392940	+	0.0948640i	−0.942308	−	0.334747i	$-0.891349\pi$
$151$	−0.482852	+	1.16571i	−0.0392940	+	0.0948640i	0.903014	+	0.429611i	$0.141349\pi$
$152$			7.96026i			0.645662i
$153$	−14.2800	+	11.4089i	−1.15447	+	0.922352i
$154$	3.28536	+	9.17534i	0.264742	+	0.739370i
$155$	6.76536	−	16.3330i	0.543407	−	1.31190i
$156$	5.45630	−	8.16593i	0.436854	−	0.653798i
$157$	−4.83960	−	4.83960i	−0.386242	−	0.386242i	0.487103	−	0.873345i	$-0.338054\pi$
$157$	−4.83960	−	4.83960i	−0.386242	−	0.386242i	−0.873345	+	0.487103i	$0.838054\pi$
$158$	2.00779	−	0.399375i	0.159732	−	0.0317726i
$159$	18.3073	−	12.2326i	1.45186	−	0.970105i
$160$	3.68620	−	18.5318i	0.291420	−	1.46507i
$161$	−2.99461	−	7.22964i	−0.236009	−	0.569775i
$162$	−4.19667	+	1.73832i	−0.329721	+	0.136575i
$163$	−0.515309	+	2.59063i	−0.0403621	+	0.202914i	−0.995705	−	0.0925867i	$-0.970486\pi$
$163$	−0.515309	+	2.59063i	−0.0403621	+	0.202914i	0.955343	+	0.295501i	$0.0954865\pi$
$164$	7.66521	−	5.12173i	0.598553	−	0.399940i
$165$	29.5945	−	17.7475i	2.30393	−	1.38164i
$166$	1.54244	−	1.54244i	0.119716	−	0.119716i
$167$	5.91349	+	3.95127i	0.457600	+	0.305758i	0.762922	−	0.646491i	$-0.223764\pi$
$167$	5.91349	+	3.95127i	0.457600	+	0.305758i	−0.305322	+	0.952249i	$0.598764\pi$
$168$	−7.81395	−	3.23664i	−0.602859	−	0.249713i
$169$			1.55312i			0.119471i
$170$	2.29341	+	26.9019i	0.175896	+	2.06328i
$171$			19.4800i			1.48967i
$172$	−2.98099	−	1.23477i	−0.227299	−	0.0941501i
$173$	9.52006	−	14.2478i	0.723797	−	1.08324i	−0.268966	−	0.963150i	$-0.586682\pi$
$173$	9.52006	−	14.2478i	0.723797	−	1.08324i	0.992763	−	0.120089i	$-0.0383179\pi$
$174$	−22.3869	−	22.3869i	−1.69715	−	1.69715i
$175$	3.19529	+	16.0638i	0.241542	+	1.21431i
$176$	13.3137	+	9.86937i	1.00356	+	0.743932i
$177$	3.06995	+	0.610651i	0.230751	+	0.0458993i
$178$	3.89684	+	9.40780i	0.292080	+	0.705144i
$179$	−3.54414	−	8.55632i	−0.264902	−	0.639529i	0.734327	−	0.678796i	$-0.237498\pi$
$179$	−3.54414	−	8.55632i	−0.264902	−	0.639529i	−0.999229	+	0.0392665i	$0.987498\pi$
$180$	3.11657	−	15.6681i	0.232295	−	1.16783i
$181$	−5.39035	−	8.06723i	−0.400662	−	0.599632i	0.575203	−	0.818011i	$-0.304923\pi$
$181$	−5.39035	−	8.06723i	−0.400662	−	0.599632i	−0.975864	+	0.218379i	$0.929923\pi$
$182$	−10.9944	+	2.18693i	−0.814962	+	0.162106i
$183$	1.83999	+	1.83999i	0.136016	+	0.136016i
$184$	−6.88265	−	4.59884i	−0.507396	−	0.339031i
$185$	−17.4362	−	7.22231i	−1.28193	−	0.530995i
$186$	21.6712			1.58901
$187$	−12.8149	−	4.77261i	−0.937120	−	0.349008i
$188$	−5.15143			−0.375706
$189$	−6.18142	−	2.56043i	−0.449632	−	0.186244i
$190$	23.9257	+	15.9866i	1.73575	+	1.15979i
$191$	15.3377	+	15.3377i	1.10980	+	1.10980i	0.993176	+	0.116623i	$0.0372069\pi$
$191$	15.3377	+	15.3377i	1.10980	+	1.10980i	0.116623	+	0.993176i	$0.462793\pi$
$192$	−4.00629	+	0.796901i	−0.289129	+	0.0575114i
$193$	3.48759	+	5.21955i	0.251043	+	0.375712i	0.935492	−	0.353349i	$-0.114957\pi$
$193$	3.48759	+	5.21955i	0.251043	+	0.375712i	−0.684449	+	0.729061i	$0.739957\pi$
$194$	5.81890	−	29.2536i	0.417773	−	2.10028i
$195$	15.1895	+	36.6706i	1.08774	+	2.62604i
$196$	1.46976	+	3.54832i	0.104983	+	0.253451i
$197$	18.1627	+	3.61278i	1.29404	+	0.257400i	0.793636	−	0.608393i	$-0.208185\pi$
$197$	18.1627	+	3.61278i	1.29404	+	0.257400i	0.500402	+	0.865793i	$0.333185\pi$
$198$	20.2670	+	15.0238i	1.44031	+	1.06770i
$199$	0.173014	+	0.869800i	0.0122646	+	0.0616585i	0.986433	−	0.164165i	$-0.0524928\pi$
$199$	0.173014	+	0.869800i	0.0122646	+	0.0616585i	−0.974168	+	0.225823i	$0.927493\pi$
$200$	12.2509	+	12.2509i	0.866270	+	0.866270i
$201$	3.56656	−	5.33773i	0.251566	−	0.376495i
$202$	0.160040	+	0.0662908i	0.0112604	+	0.00466420i
$203$			11.5896i			0.813431i
$204$	−9.42617	+	4.88038i	−0.659964	+	0.341695i
$205$			37.2582i			2.60222i
$206$	−16.2269	−	6.72141i	−1.13058	−	0.468303i
$207$	−16.8429	−	11.2541i	−1.17066	−	0.782212i
$208$	−13.4792	+	13.4792i	−0.934613	+	0.934613i
$209$	−12.4989	+	7.49547i	−0.864570	+	0.518473i
$210$	−25.4210	+	16.9857i	−1.75421	+	1.17213i
$211$	4.76873	−	23.9740i	0.328293	−	1.65044i	−0.365902	−	0.930653i	$-0.619239\pi$
$211$	4.76873	−	23.9740i	0.328293	−	1.65044i	0.694195	−	0.719787i	$-0.255761\pi$
$212$	7.04545	−	2.91832i	0.483883	−	0.200431i
$213$	1.27670	+	3.08222i	0.0874778	+	0.211190i
$214$	3.78256	−	19.0162i	0.258570	−	1.29992i
$215$	10.8426	−	7.24483i	0.739462	−	0.494093i
$216$	−6.94154	+	1.38076i	−0.472312	+	0.0939486i
$217$	−5.60953	−	5.60953i	−0.380800	−	0.380800i
$218$	10.7278	−	16.0553i	0.726577	−	1.08740i
$219$	−0.924426	+	2.23176i	−0.0624669	+	0.150808i
$220$	11.2523	−	4.02904i	0.758629	−	0.271638i
$221$	7.59611	−	13.7732i	0.510970	−	0.926489i
$222$		−	23.1349i		−	1.55271i
$223$	3.62978	−	8.76306i	0.243068	−	0.586818i	−0.754517	−	0.656281i	$-0.772129\pi$
$223$	3.62978	−	8.76306i	0.243068	−	0.586818i	0.997585	+	0.0694632i	$0.0221286\pi$
$224$	−7.04985	−	4.71056i	−0.471038	−	0.314737i
$225$	29.9799	+	29.9799i	1.99866	+	1.99866i
$226$	−4.44709	−	22.3570i	−0.295816	−	1.48717i
$227$	−4.02871	−	6.02940i	−0.267395	−	0.400185i	0.673337	−	0.739336i	$-0.264860\pi$
$227$	−4.02871	−	6.02940i	−0.267395	−	0.400185i	−0.940732	+	0.339151i	$0.889860\pi$
$228$	−2.20701	+	11.0954i	−0.146163	+	0.734809i
$229$	−2.70985	+	1.12246i	−0.179072	+	0.0741741i	−0.470418	−	0.882444i	$-0.655897\pi$
$229$	−2.70985	+	1.12246i	−0.179072	+	0.0741741i	0.291346	+	0.956618i	$0.405897\pi$
$230$	−27.6449	+	11.4509i	−1.82285	+	0.755050i
$231$	−2.27563	−	15.3169i	−0.149725	−	1.00778i
$232$	6.81108	+	10.1935i	0.447170	+	0.669237i
$233$	−27.9334	+	5.55630i	−1.82998	+	0.364005i	−0.985240	−	0.171178i	$-0.945243\pi$
$233$	−27.9334	+	5.55630i	−1.82998	+	0.364005i	−0.844736	+	0.535182i	$0.820243\pi$
$234$	−20.5189	+	20.5189i	−1.34136	+	1.34136i
$235$	11.5667	−	17.3108i	0.754529	−	1.12923i
$236$	1.00158	+	0.414870i	0.0651976	+	0.0270057i
$237$	−3.25267			−0.211283
$238$	11.5467	+	3.66889i	0.748464	+	0.237819i
$239$		−	0.544255i		−	0.0352049i	−0.999845	−	0.0176025i	$-0.994397\pi$
$239$		−	0.544255i		−	0.0352049i	0.999845	−	0.0176025i	$-0.00560333\pi$
$240$	−19.8959	+	48.0331i	−1.28428	+	3.10052i
$241$	10.3493	−	15.4888i	0.666657	−	0.997722i	−0.331863	−	0.943328i	$-0.607677\pi$
$241$	10.3493	−	15.4888i	0.666657	−	0.997722i	0.998520	−	0.0543947i	$-0.0173229\pi$
$242$	−1.84145	+	18.7847i	−0.118373	+	1.20753i
$243$	18.5745	−	3.69470i	1.19155	−	0.237015i
$244$	0.500708	+	0.749362i	0.0320545	+	0.0479730i
$245$	−15.2238	−	3.02821i	−0.972616	−	0.193465i
$246$	−42.1956	+	17.4780i	−2.69029	+	1.11436i
$247$	−6.41512	−	15.4875i	−0.408184	−	0.985444i
$248$	−8.23046	−	1.63714i	−0.522635	−	0.103959i
$249$	−2.88179	+	1.92555i	−0.182626	+	0.122027i
$250$	29.3128	−	5.83069i	1.85391	−	0.368765i
$251$	14.8179	−	14.8179i	0.935297	−	0.935297i	−0.0627330	−	0.998030i	$-0.519982\pi$
$251$	14.8179	−	14.8179i	0.935297	−	0.935297i	0.998030	+	0.0627330i	$0.0199816\pi$
$252$	−5.96043	−	3.98263i	−0.375472	−	0.250882i
$253$	0.740172	−	15.1373i	0.0465342	−	0.951671i
$254$		−	20.4069i		−	1.28044i
$255$	4.76501	−	42.6337i	0.298397	−	2.66983i
$256$	−18.4058			−1.15036
$257$	−6.53787	+	15.7838i	−0.407821	+	0.984567i	0.577889	+	0.816116i	$0.303877\pi$
$257$	−6.53787	+	15.7838i	−0.407821	+	0.984567i	−0.985710	+	0.168452i	$0.946123\pi$
$258$	13.2913	+	8.88094i	0.827478	+	0.552903i
$259$	−5.98841	+	5.98841i	−0.372102	+	0.372102i
$260$	2.68197	+	13.4832i	0.166329	+	0.836190i
$261$	16.6678	+	24.9451i	1.03171	+	1.54406i
$262$	3.38738	+	0.673793i	0.209273	+	0.0416271i
$263$	−3.53223	−	8.52755i	−0.217807	−	0.525831i	0.776777	−	0.629776i	$-0.216853\pi$
$263$	−3.53223	−	8.52755i	−0.217807	−	0.525831i	−0.994583	+	0.103945i	$0.966853\pi$
$264$	−11.0031	−	12.1344i	−0.677192	−	0.746822i
$265$	−6.01274	+	30.2281i	−0.369360	+	1.85690i
$266$	10.7363	−	7.17376i	0.658284	−	0.439851i
$267$	−3.15648	−	15.8687i	−0.193173	−	0.971147i
$268$	1.57221	−	1.57221i	0.0960380	−	0.0960380i
$269$	17.0481	−	25.5143i	1.03944	−	1.55563i	0.225876	−	0.974156i	$-0.427475\pi$
$269$	17.0481	−	25.5143i	1.03944	−	1.55563i	0.813564	−	0.581476i	$-0.197525\pi$
$270$	−9.79065	+	23.6367i	−0.595840	+	1.43849i
$271$	−27.7812			−1.68759			−0.843793	−	0.536669i	$-0.819683\pi$
$271$	−27.7812			−1.68759			−0.843793	+	0.536669i	$0.819683\pi$
$272$	19.7924	−	5.72129i	1.20009	−	0.346904i
$273$	17.8112			1.07798
$274$	16.4444	+	6.81149i	0.993443	+	0.411497i
$275$	−7.70040	+	30.7716i	−0.464352	+	1.85560i
$276$	−8.31832	−	8.31832i	−0.500704	−	0.500704i
$277$	0.706960	+	3.55413i	0.0424771	+	0.213547i	0.996195	−	0.0871574i	$-0.0277783\pi$
$277$	0.706960	+	3.55413i	0.0424771	+	0.213547i	−0.953717	+	0.300704i	$0.902778\pi$
$278$	16.5222	−	11.0398i	0.990934	−	0.662121i
$279$	−20.1412	−	4.00633i	−1.20582	−	0.239853i
$280$	10.9378	−	4.53058i	0.653657	−	0.270754i
$281$	24.5959	−	10.1879i	1.46727	−	0.607762i	0.501033	−	0.865428i	$-0.332953\pi$
$281$	24.5959	−	10.1879i	1.46727	−	0.607762i	0.966234	+	0.257666i	$0.0829534\pi$
$282$	25.0309	+	4.97895i	1.49057	+	0.296492i
$283$	−1.08414	+	0.724398i	−0.0644453	+	0.0430610i	−0.587376	−	0.809314i	$-0.699839\pi$
$283$	−1.08414	+	0.724398i	−0.0644453	+	0.0430610i	0.522930	+	0.852376i	$0.324839\pi$
$284$	0.225423	+	1.13328i	0.0133764	+	0.0672477i
$285$	−32.3293	−	32.3293i	−1.91502	−	1.91502i
$286$	−21.0608	−	5.27032i	−1.24535	−	0.311641i
$287$	15.4464	+	6.39810i	0.911772	+	0.377668i
$288$	−21.9484			−1.29332
$289$	−14.3781	+	9.07031i	−0.845770	+	0.533548i
$290$	44.3167			2.60237
$291$	−18.1359	+	43.7839i	−1.06314	+	2.56666i
$292$	−0.464822	+	0.695655i	−0.0272016	+	0.0407101i
$293$	0.830100	−	0.830100i	0.0484950	−	0.0484950i	−0.682443	−	0.730938i	$-0.739083\pi$
$293$	0.830100	−	0.830100i	0.0484950	−	0.0484950i	0.730938	+	0.682443i	$0.239083\pi$
$294$	−3.71208	−	18.6619i	−0.216493	−	1.08838i
$295$	−3.64302	+	2.43419i	−0.212105	+	0.141724i
$296$	−1.74772	+	8.78636i	−0.101584	+	0.510697i
$297$	−8.70425	−	9.59925i	−0.505072	−	0.557005i
$298$	8.52724	+	20.5866i	0.493970	+	1.19255i
$299$	17.0971	+	3.40082i	0.988748	+	0.196674i
$300$	13.6793	+	20.4725i	0.789774	+	1.18198i
$301$	−1.14160	−	5.73923i	−0.0658009	−	0.330803i
$302$	1.53091	−	1.53091i	0.0880938	−	0.0880938i
$303$	−0.228852	−	0.152914i	−0.0131472	−	0.00878466i
$304$	8.40285	−	20.2863i	0.481937	−	1.16350i
$305$	−3.64241			−0.208564
$306$	30.1293	−	8.70933i	1.72238	−	0.497879i
$307$		−	25.5552i		−	1.45851i	−0.684240	−	0.729257i	$-0.739866\pi$
$307$		−	25.5552i		−	1.45851i	0.684240	−	0.729257i	$-0.260134\pi$
$308$	0.261935	−	5.35683i	0.0149251	−	0.305234i
$309$	23.2039	+	15.5044i	1.32002	+	0.882012i
$310$	−21.4499	+	21.4499i	−1.21827	+	1.21827i
$311$	−16.7089	+	3.32360i	−0.947474	+	0.188464i	−0.644560	−	0.764554i	$-0.722959\pi$
$311$	−16.7089	+	3.32360i	−0.947474	+	0.188464i	−0.302914	+	0.953018i	$0.597959\pi$
$312$	15.6656	−	10.4674i	0.886892	−	0.592602i
$313$	−18.2043	−	3.62106i	−1.02897	−	0.204674i	−0.348390	−	0.937350i	$-0.613271\pi$
$313$	−18.2043	−	3.62106i	−1.02897	−	0.204674i	−0.680578	+	0.732675i	$0.738271\pi$
$314$	4.49421	+	10.8500i	0.253623	+	0.612300i
$315$	26.7664	−	11.0870i	1.50812	−	0.624683i
$316$	−1.10491	−	0.219781i	−0.0621562	−	0.0123636i
$317$	−5.92888	−	8.87319i	−0.332999	−	0.498368i	0.626753	−	0.779218i	$-0.284384\pi$
$317$	−5.92888	−	8.87319i	−0.332999	−	0.498368i	−0.959752	+	0.280850i	$0.909384\pi$
$318$	−37.0545	+	7.37061i	−2.07792	+	0.413323i
$319$	−9.59213	+	20.2929i	−0.537056	+	1.13618i
$320$	3.17663	−	4.75416i	0.177579	−	0.265765i
$321$	−11.7892	+	28.4616i	−0.658008	+	1.58857i
$322$			13.4273i			0.748277i
$323$	−2.01245	+	18.0059i	−0.111976	+	1.00188i
$324$	2.49976			0.138875
$325$	−33.7083	−	13.9624i	−1.86980	−	0.774496i
$326$	2.51802	−	3.76849i	0.139461	−	0.208717i
$327$	−21.6945	+	21.6945i	−1.19971	+	1.19971i
$328$	17.3458	−	3.45029i	0.957761	−	0.190510i
$329$	−5.19039	−	7.76797i	−0.286156	−	0.428262i
$330$	−58.5692	+	8.70162i	−3.22413	+	0.479009i
$331$	−10.0776	+	4.17427i	−0.553914	+	0.229439i	−0.642040	−	0.766671i	$-0.721912\pi$
$331$	−10.0776	+	4.17427i	−0.553914	+	0.229439i	0.0881269	+	0.996109i	$0.471912\pi$
$332$	−1.10904	+	0.459379i	−0.0608664	+	0.0252117i
$333$	−4.27693	+	21.5016i	−0.234374	+	1.17828i
$334$	−6.77994	−	10.1469i	−0.370982	−	0.555213i
$335$	1.75309	+	8.81338i	0.0957816	+	0.481527i
$336$	16.4968	+	16.4968i	0.899975	+	0.899975i
$337$	23.9951	+	16.0330i	1.30710	+	0.873376i	0.997006	−	0.0773306i	$-0.0246397\pi$
$337$	23.9951	+	16.0330i	1.30710	+	0.873376i	0.310093	+	0.950706i	$0.399640\pi$
$338$	1.01985	−	2.46213i	0.0554723	−	0.133922i
$339$			36.2188i			1.96714i
$340$	4.49939	−	14.1605i	0.244014	−	0.767960i
$341$	−5.17931	−	14.4648i	−0.280475	−	0.783311i
$342$	12.7914	−	30.8811i	0.691678	−	1.66986i
$343$	−10.5296	+	15.7587i	−0.568547	+	0.850891i
$344$	−4.37696	−	4.37696i	−0.235990	−	0.235990i
$345$	46.6303	−	9.27534i	2.51049	−	0.499367i
$346$	−24.4476	+	16.3354i	−1.31431	+	0.878195i
$347$	0.608721	−	3.06024i	0.0326778	−	0.164283i	−0.961001	−	0.276546i	$-0.910810\pi$
$347$	0.608721	−	3.06024i	0.0326778	−	0.164283i	0.993678	+	0.112264i	$0.0358101\pi$
$348$	6.66742	+	16.0966i	0.357411	+	0.862867i
$349$	6.32852	−	2.62136i	0.338758	−	0.140318i	−0.206818	−	0.978379i	$-0.566311\pi$
$349$	6.32852	−	2.62136i	0.338758	−	0.140318i	0.545576	+	0.838061i	$0.316311\pi$
$350$	5.48277	−	27.5637i	0.293066	−	1.47334i
$351$	12.3927	−	8.28053i	0.661473	−	0.441982i
$352$	−8.44527	−	14.0828i	−0.450135	−	0.750614i
$353$	0.604835	−	0.604835i	0.0321921	−	0.0321921i	−0.690828	−	0.723020i	$-0.742754\pi$
$353$	0.604835	−	0.604835i	0.0321921	−	0.0321921i	0.723020	+	0.690828i	$0.242754\pi$
$354$	−4.46573	−	2.98391i	−0.237351	−	0.158593i
$355$	−4.31441	−	1.78709i	−0.228985	−	0.0948488i
$356$		−	5.60379i		−	0.297000i
$357$	−16.8567	−	9.29669i	−0.892152	−	0.492033i
$358$			15.8913i			0.839884i
$359$	31.5649	+	13.0746i	1.66593	+	0.690052i	0.998507	−	0.0546248i	$-0.0173963\pi$
$359$	31.5649	+	13.0746i	1.66593	+	0.690052i	0.667425	+	0.744677i	$0.267396\pi$
$360$	17.0264	−	25.4818i	0.897369	−	1.34301i
$361$	0.218931	+	0.218931i	0.0115227	+	0.0115227i
$362$	3.24790	+	16.3283i	0.170706	+	0.858196i
$363$	8.69249	−	28.7026i	0.456237	−	1.50650i
$364$	6.05037	+	1.20349i	0.317126	+	0.0630802i
$365$	−1.29399	−	3.12396i	−0.0677304	−	0.163516i
$366$	−1.70867	−	4.12511i	−0.0893139	−	0.215623i
$367$	1.60325	−	8.06007i	0.0836888	−	0.420732i	−0.916115	−	0.400916i	$-0.868692\pi$
$367$	1.60325	−	8.06007i	0.0836888	−	0.420732i	0.999804	−	0.0198162i	$-0.00630810\pi$
$368$	12.6855	+	18.9852i	0.661279	+	0.989673i
$369$	42.4478	−	8.44339i	2.20974	−	0.439546i
$370$	22.8987	+	22.8987i	1.19045	+	1.19045i
$371$	11.4994	+	7.68362i	0.597017	+	0.398914i
$372$	−11.0181	−	4.56384i	−0.571262	−	0.236624i
$373$	9.18124			0.475387			0.237693	−	0.971340i	$-0.423609\pi$
$373$	9.18124			0.475387			0.237693	+	0.971340i	$0.423609\pi$
$374$	17.1813	+	15.9807i	0.888422	+	0.826343i
$375$	−47.4874			−2.45224
$376$	−9.13030	−	3.78189i	−0.470859	−	0.195036i
$377$	−21.4665	−	14.3435i	−1.10558	−	0.738726i
$378$	8.11797	+	8.11797i	0.417543	+	0.417543i
$379$	15.2312	−	3.02967i	0.782373	−	0.155624i	0.212286	−	0.977208i	$-0.431909\pi$
$379$	15.2312	−	3.02967i	0.782373	−	0.155624i	0.570087	+	0.821584i	$0.306909\pi$
$380$	−8.79762	−	13.1666i	−0.451309	−	0.675431i
$381$	−6.32567	+	31.8013i	−0.324074	+	1.62923i
$382$	−14.2431	−	34.3859i	−0.728741	−	1.75934i
$383$	6.40480	+	15.4625i	0.327270	+	0.790099i	0.998793	+	0.0491158i	$0.0156403\pi$
$383$	6.40480	+	15.4625i	0.327270	+	0.790099i	−0.671523	+	0.740983i	$0.734360\pi$
$384$	33.3526	+	6.63424i	1.70202	+	0.338552i
$385$	17.4129	+	12.9081i	0.887444	+	0.657858i
$386$	−2.10142	−	10.5645i	−0.106959	−	0.537720i
$387$	−10.7111	−	10.7111i	−0.544476	−	0.544476i
$388$	−9.11912	+	13.6477i	−0.462953	+	0.692859i
$389$	5.89143	+	2.44031i	0.298707	+	0.123729i	0.527003	−	0.849863i	$-0.323315\pi$
$389$	5.89143	+	2.44031i	0.298707	+	0.123729i	−0.228296	+	0.973592i	$0.573315\pi$
$390$		−	68.1070i		−	3.44873i
$391$	−14.4058	−	12.1425i	−0.728531	−	0.614073i
$392$			7.36799i			0.372140i
$393$	−5.06991	−	2.10002i	−0.255743	−	0.105932i
$394$	−26.4205	−	17.6536i	−1.33105	−	0.889378i
$395$	3.21946	−	3.21946i	0.161988	−	0.161988i
$396$	−7.14022	−	11.9066i	−0.358810	−	0.598327i
$397$	6.26404	−	4.18550i	0.314383	−	0.210064i	−0.388360	−	0.921508i	$-0.626958\pi$
$397$	6.26404	−	4.18550i	0.314383	−	0.210064i	0.702743	+	0.711444i	$0.251958\pi$
$398$	0.296873	−	1.49248i	0.0148809	−	0.0748113i
$399$	−18.9547	+	7.85130i	−0.948923	+	0.393057i
$400$	−18.2887	−	44.1529i	−0.914435	−	2.20764i
$401$	6.37904	−	32.0696i	0.318554	−	1.60148i	−0.407076	−	0.913394i	$-0.633452\pi$
$401$	6.37904	−	32.0696i	0.318554	−	1.60148i	0.725630	−	0.688085i	$-0.241548\pi$
$402$	−9.15896	+	6.11982i	−0.456807	+	0.305229i
$403$	17.3325	−	3.44765i	0.863395	−	0.171740i
$404$	−0.0674074	−	0.0674074i	−0.00335364	−	0.00335364i
$405$	−5.61281	+	8.40017i	−0.278903	+	0.417408i
$406$	7.61023	−	18.3727i	0.377689	−	0.911823i
$407$	−15.4417	+	5.52913i	−0.765419	+	0.274069i
$408$	−20.2897	+	1.72971i	−1.00449	+	0.0856336i
$409$		−	5.04860i		−	0.249637i	−0.992180	−	0.124819i	$-0.960165\pi$
$409$		−	5.04860i		−	0.249637i	0.992180	−	0.124819i	$-0.0398349\pi$
$410$	24.4653	−	59.0644i	1.20825	−	2.91698i
$411$	−23.5149	−	15.7122i	−1.15990	−	0.775024i
$412$	6.83463	+	6.83463i	0.336718	+	0.336718i
$413$	0.383567	+	1.92832i	0.0188741	+	0.0948866i
$414$	19.3107	+	28.9006i	0.949071	+	1.42039i
$415$	0.946478	−	4.75826i	0.0464608	−	0.233574i
$416$	17.4500	−	7.22802i	0.855556	−	0.354383i
$417$	−29.1696	+	12.0824i	−1.42844	+	0.591680i
$418$	24.7361	−	3.67504i	1.20988	−	0.179752i
$419$	−6.06070	−	9.07048i	−0.296085	−	0.443122i	0.653364	−	0.757044i	$-0.273357\pi$
$419$	−6.06070	−	9.07048i	−0.296085	−	0.443122i	−0.949449	+	0.313922i	$0.898357\pi$
$420$	16.5017	−	3.28239i	0.805200	−	0.160164i
$421$	17.2128	−	17.2128i	0.838899	−	0.838899i	−0.149815	−	0.988714i	$-0.547868\pi$
$421$	17.2128	−	17.2128i	0.838899	−	0.838899i	0.988714	+	0.149815i	$0.0478678\pi$
$422$	−23.3021	+	34.8741i	−1.13433	+	1.69764i
$423$	−22.3432	−	9.25488i	−1.08637	−	0.449987i
$424$	14.6297			0.710481
$425$	24.6141	+	30.8085i	1.19396	+	1.49443i
$426$		−	5.72449i		−	0.277353i
$427$	−0.625488	+	1.51006i	−0.0302695	+	0.0730770i
$428$	−5.92786	+	8.87167i	−0.286534	+	0.428828i
$429$	31.1866	+	14.7414i	1.50570	+	0.711723i
$430$	−21.9458	+	4.36530i	−1.05832	+	0.210513i
$431$	−1.29787	−	1.94240i	−0.0625162	−	0.0935621i	0.798894	−	0.601471i	$-0.205419\pi$
$431$	−1.29787	−	1.94240i	−0.0625162	−	0.0935621i	−0.861411	+	0.507909i	$0.830419\pi$
$432$	19.1476	+	3.80870i	0.921242	+	0.183246i
$433$	−17.6562	+	7.31345i	−0.848504	+	0.351462i	−0.764201	−	0.644978i	$-0.776866\pi$
$433$	−17.6562	+	7.31345i	−0.848504	+	0.351462i	−0.0843031	+	0.996440i	$0.526866\pi$
$434$	5.20919	+	12.5761i	0.250049	+	0.603672i
$435$	−69.0614	−	13.7372i	−3.31124	−	0.658647i
$436$	−8.83540	+	5.90363i	−0.423139	+	0.282733i
$437$	−19.6938	+	3.91734i	−0.942083	+	0.187392i
$438$	2.93094	−	2.93094i	0.140046	−	0.140046i
$439$	−10.4964	−	7.01345i	−0.500964	−	0.334734i	0.279279	−	0.960210i	$-0.409905\pi$
$439$	−10.4964	−	7.01345i	−0.500964	−	0.334734i	−0.780243	+	0.625476i	$0.784905\pi$
$440$	22.9013	+	1.11981i	1.09178	+	0.0533849i
$441$			18.0306i			0.858601i
$442$	−21.0860	+	16.8464i	−1.00296	+	0.801304i
$443$	29.4887			1.40105			0.700524	−	0.713629i	$-0.252950\pi$
$443$	29.4887			1.40105			0.700524	+	0.713629i	$0.252950\pi$
$444$	−4.87210	+	11.7623i	−0.231219	+	0.558213i
$445$	18.8309	+	12.5824i	0.892671	+	0.596464i
$446$	−11.5084	+	11.5084i	−0.544938	+	0.544938i
$447$	−6.90714	−	34.7246i	−0.326697	−	1.64242i
$448$	−1.42546	−	2.13336i	−0.0673469	−	0.100792i
$449$	15.7406	+	3.13101i	0.742846	+	0.147761i	0.551983	−	0.833855i	$-0.313871\pi$
$449$	15.7406	+	3.13101i	0.742846	+	0.147761i	0.190863	+	0.981617i	$0.438871\pi$
$450$	−27.8403	−	67.2124i	−1.31240	−	3.16842i
$451$	21.7505	+	23.9870i	1.02419	+	1.12950i
$452$	−2.44729	+	12.3033i	−0.115111	+	0.578700i
$453$	−2.86025	+	1.91116i	−0.134386	+	0.0897941i
$454$	2.42746	+	12.2037i	0.113926	+	0.572747i
$455$	−17.6294	+	17.6294i	−0.826477	+	0.826477i
$456$	−12.0573	+	18.0450i	−0.564634	+	0.845034i
$457$	5.47047	−	13.2069i	0.255898	−	0.617792i	−0.742762	−	0.669556i	$-0.766484\pi$
$457$	5.47047	−	13.2069i	0.255898	−	0.617792i	0.998659	+	0.0517642i	$0.0164844\pi$
$458$	5.03291			0.235172
$459$	−16.0507	+	1.36833i	−0.749181	+	0.0638684i
$460$	16.4668			0.767768
$461$	−1.81256	−	0.750787i	−0.0844194	−	0.0349677i	0.340074	−	0.940399i	$-0.389548\pi$
$461$	−1.81256	−	0.750787i	−0.0844194	−	0.0349677i	−0.424494	+	0.905431i	$0.639548\pi$
$462$	−6.45022	+	25.7757i	−0.300091	+	1.19920i
$463$	−19.5298	−	19.5298i	−0.907626	−	0.907626i	0.0884539	−	0.996080i	$-0.471807\pi$
$463$	−19.5298	−	19.5298i	−0.907626	−	0.907626i	−0.996080	+	0.0884539i	$0.971807\pi$
$464$	−6.59740	−	33.1674i	−0.306277	−	1.53976i
$465$	40.0757	−	26.7777i	1.85847	−	1.24179i
$466$	47.9306	+	9.53398i	2.22034	+	0.441653i
$467$	−19.3670	+	8.02208i	−0.896198	+	0.371218i	−0.782757	−	0.622327i	$-0.786187\pi$
$467$	−19.3670	+	8.02208i	−0.896198	+	0.371218i	−0.113441	+	0.993545i	$0.536187\pi$
$468$	14.7534	−	6.11107i	0.681978	−	0.282484i
$469$	3.95488	+	0.786674i	0.182619	+	0.0363252i
$470$	−29.7034	+	19.8472i	−1.37012	+	0.915483i
$471$	−3.64035	−	18.3013i	−0.167739	−	0.843279i
$472$	1.47062	+	1.47062i	0.0676906	+	0.0676906i
$473$	2.75117	−	10.9940i	0.126499	−	0.505503i
$474$	5.15637	+	2.13584i	0.236840	+	0.0981022i
$475$	42.0272			1.92834
$476$	−5.09797	−	4.29704i	−0.233665	−	0.196954i
$477$	35.8011			1.63922
$478$	−0.357381	+	0.862793i	−0.0163462	+	0.0394632i
$479$	−16.7936	+	25.1334i	−0.767319	+	1.14837i	0.217714	+	0.976013i	$0.430140\pi$
$479$	−16.7936	+	25.1334i	−0.767319	+	1.14837i	−0.985034	+	0.172362i	$0.944860\pi$
$480$	36.4260	−	36.4260i	1.66261	−	1.66261i
$481$	−3.68052	−	18.5032i	−0.167817	−	0.843674i
$482$	−26.5771	+	17.7582i	−1.21055	+	0.808866i
$483$	4.16217	−	20.9247i	0.189385	−	0.952105i
$484$	4.89221	−	9.16277i	0.222373	−	0.416490i
$485$	−25.3862	−	61.2876i	−1.15273	−	2.78293i
$486$	−31.8718	−	6.33969i	−1.44573	−	0.287574i
$487$	19.1826	+	28.7087i	0.869245	+	1.30092i	0.952547	+	0.304393i	$0.0984536\pi$
$487$	19.1826	+	28.7087i	0.869245	+	1.30092i	−0.0833012	+	0.996524i	$0.526546\pi$
$488$	0.337306	+	1.69575i	0.0152691	+	0.0767630i
$489$	−5.09214	+	5.09214i	−0.230274	+	0.230274i
$490$	22.1455	+	14.7972i	1.00043	+	0.668468i
$491$	−13.0301	+	31.4573i	−0.588038	+	1.41965i	0.297337	+	0.954772i	$0.403901\pi$
$491$	−13.0301	+	31.4573i	−0.588038	+	1.41965i	−0.885375	+	0.464877i	$0.846099\pi$
$492$	25.1340			1.13313
$493$	12.8295	+	24.7794i	0.577811	+	1.11601i
$494$			28.7643i			1.29417i
$495$	56.0429	+	2.74035i	2.51894	+	0.123170i
$496$	19.2467	+	12.8602i	0.864203	+	0.577442i
$497$	−1.48177	+	1.48177i	−0.0664666	+	0.0664666i
$498$	5.83283	−	1.16022i	0.261375	−	0.0519908i
$499$	1.31090	−	0.875916i	0.0586840	−	0.0392114i	−0.525882	−	0.850557i	$-0.676265\pi$
$499$	1.31090	−	0.875916i	0.0586840	−	0.0392114i	0.584566	+	0.811346i	$0.301265\pi$
$500$	−16.1312	−	3.20870i	−0.721409	−	0.143497i
$501$	7.42028	+	17.9141i	0.331514	+	0.800345i
$502$	−33.2205	+	13.7604i	−1.48270	+	0.614156i
$503$	−5.24656	−	1.04360i	−0.233932	−	0.0465320i	0.0767318	−	0.997052i	$-0.475551\pi$
$503$	−5.24656	−	1.04360i	−0.233932	−	0.0465320i	−0.310664	+	0.950520i	$0.600551\pi$
$504$	−7.64034	−	11.4346i	−0.340328	−	0.509337i
$505$	0.377868	−	0.0751626i	0.0168149	−	0.00334469i
$506$	−11.1131	+	23.5107i	−0.494039	+	1.04518i
$507$	−2.35249	+	3.52075i	−0.104478	+	0.156362i
$508$	−4.29760	+	10.3753i	−0.190675	+	0.460330i
$509$		−	6.32559i		−	0.280377i	−0.990125	−	0.140188i	$-0.955229\pi$
$509$		−	6.32559i		−	0.280377i	0.990125	−	0.140188i	$-0.0447708\pi$
$510$	−35.5490	+	64.4573i	−1.57413	+	2.85422i
$511$	−1.51733			−0.0671229
$512$	6.13113	+	2.53960i	0.270960	+	0.112235i
$513$	−9.53821	+	14.2749i	−0.421122	+	0.630254i
$514$	20.7286	−	20.7286i	0.914301	−	0.914301i
$515$	−38.3131	+	7.62095i	−1.68828	+	0.335819i
$516$	−4.88729	−	7.31434i	−0.215151	−	0.321996i
$517$	−2.65898	−	17.8972i	−0.116942	−	0.787117i
$518$	13.4255	−	5.56103i	0.589884	−	0.244338i
$519$	43.1618	−	17.8782i	1.89459	−	0.784765i
$520$	−5.14512	+	25.8663i	−0.225629	+	1.13431i
$521$	−14.3169	−	21.4267i	−0.627235	−	0.938723i	−0.999942	−	0.0107739i	$-0.996570\pi$
$521$	−14.3169	−	21.4267i	−0.627235	−	0.938723i	0.372707	−	0.927949i	$-0.378430\pi$
$522$	−10.0430	−	50.4896i	−0.439570	−	2.20987i
$523$	15.2364	+	15.2364i	0.666243	+	0.666243i	0.956844	−	0.290601i	$-0.0938553\pi$
$523$	15.2364	+	15.2364i	0.666243	+	0.666243i	−0.290601	+	0.956844i	$0.593855\pi$
$524$	−1.58032	−	1.05594i	−0.0690367	−	0.0461289i
$525$	−17.0883	+	41.2547i	−0.745793	+	1.80050i
$526$			15.8379i			0.690566i
$527$	−18.2032	−	5.78394i	−0.792945	−	0.251952i
$528$	15.2316	+	42.5388i	0.662870	+	1.85126i
$529$	−0.811142	+	1.95827i	−0.0352670	+	0.0851422i
$530$	29.3809	−	43.9716i	1.27622	−	1.91000i
$531$	3.59882	+	3.59882i	0.156176	+	0.156176i
$532$	−6.96932	+	1.38628i	−0.302159	+	0.0601031i
$533$	−30.9674	+	20.6917i	−1.34135	+	0.896258i
$534$	−5.41616	+	27.2289i	−0.234380	+	1.17831i
$535$	−16.5022	−	39.8399i	−0.713453	−	1.72243i
$536$	3.94079	−	1.63233i	0.170216	−	0.0705058i
$537$	4.92596	−	24.7645i	0.212571	−	1.06867i
$538$	−43.7796	+	29.2526i	−1.88747	+	1.26117i
$539$	−11.5690	+	6.93779i	−0.498312	+	0.298832i
$540$	9.95557	−	9.95557i	0.428419	−	0.428419i
$541$	33.6592	+	22.4903i	1.44712	+	0.966936i	0.997271	+	0.0738317i	$0.0235228\pi$
$541$	33.6592	+	22.4903i	1.44712	+	0.966936i	0.449851	+	0.893104i	$0.351477\pi$
$542$	44.0408	+	18.2423i	1.89171	+	0.783574i
$543$		−	26.4522i		−	1.13517i
$544$	−20.2876	−	2.26747i	−0.869823	−	0.0972168i
$545$		−	42.9461i		−	1.83961i
$546$	−28.2356	−	11.6956i	−1.20837	−	0.500525i
$547$	12.9074	−	19.3174i	0.551882	−	0.825950i	−0.445719	−	0.895173i	$-0.647052\pi$
$547$	12.9074	−	19.3174i	0.551882	−	0.825950i	0.997601	+	0.0692226i	$0.0220519\pi$
$548$	−6.92623	−	6.92623i	−0.295874	−	0.295874i
$549$	0.825439	+	4.14976i	0.0352289	+	0.177107i
$550$	32.4132	−	43.7250i	1.38210	−	1.86444i
$551$	29.1674	+	5.80176i	1.24257	+	0.247163i
$552$	−8.63639	−	20.8501i	−0.367589	−	0.887439i
$553$	−0.781858	−	1.88757i	−0.0332480	−	0.0802677i
$554$	1.21306	−	6.09849i	0.0515382	−	0.259100i
$555$	−28.5863	−	42.7825i	−1.21342	−	1.81602i
$556$	−10.7252	+	2.13337i	−0.454848	+	0.0904749i
$557$	−26.7241	−	26.7241i	−1.13233	−	1.13233i	−0.989788	−	0.142547i	$-0.954471\pi$
$557$	−26.7241	−	26.7241i	−1.13233	−	1.13233i	−0.142547	−	0.989788i	$-0.545529\pi$
$558$	29.2986	+	19.5767i	1.24031	+	0.828748i
$559$	12.0432	+	4.98845i	0.509372	+	0.210989i
$560$	−32.6568			−1.38000
$561$	−21.8210	−	30.2295i	−0.921281	−	1.27629i
$562$	−45.6811			−1.92694
$563$	−34.9083	−	14.4595i	−1.47121	−	0.609395i	−0.504075	−	0.863660i	$-0.668167\pi$
$563$	−34.9083	−	14.4595i	−1.47121	−	0.609395i	−0.967135	+	0.254265i	$0.918167\pi$
$564$	−11.6777	−	7.80279i	−0.491720	−	0.328557i
$565$	−35.8490	−	35.8490i	−1.50818	−	1.50818i
$566$	2.19433	−	0.436479i	0.0922345	−	0.0183466i
$567$	2.51867	+	3.76945i	0.105774	+	0.158302i
$568$	−0.432455	+	2.17410i	−0.0181454	+	0.0912231i
$569$	10.9465	+	26.4271i	0.458899	+	1.10788i	0.968844	+	0.247674i	$0.0796660\pi$
$569$	10.9465	+	26.4271i	0.458899	+	1.10788i	−0.509944	+	0.860207i	$0.670334\pi$
$570$	30.0220	+	72.4796i	1.25749	+	3.03584i
$571$	22.6379	+	4.50296i	0.947368	+	0.188443i	0.644513	−	0.764594i	$-0.277060\pi$
$571$	22.6379	+	4.50296i	0.947368	+	0.188443i	0.302855	+	0.953037i	$0.402060\pi$
$572$	9.59785	+	7.11485i	0.401306	+	0.297487i
$573$	11.5371	+	58.0007i	0.481968	+	2.42301i
$574$	−20.2855	−	20.2855i	−0.846701	−	0.846701i
$575$	−24.2802	+	36.3378i	−1.01255	+	1.51539i
$576$	−6.13624	−	2.54172i	−0.255677	−	0.105905i
$577$			40.1749i			1.67250i	0.548347	+	0.836251i	$0.315257\pi$
$577$			40.1749i			1.67250i	−0.548347	+	0.836251i	$0.684743\pi$
$578$	28.7492	−	4.93767i	1.19581	−	0.205380i
$579$			17.1147i			0.711264i
$580$	−22.5316	−	9.33289i	−0.935574	−	0.387527i
$581$	−1.81014	−	1.20949i	−0.0750971	−	0.0501783i
$582$	57.5007	−	57.5007i	2.38348	−	2.38348i
$583$	13.7755	+	22.9711i	0.570523	+	0.951366i
$584$	−1.33455	+	0.891720i	−0.0552242	+	0.0368996i
$585$	−12.5909	+	63.2988i	−0.520570	+	2.61708i
$586$	−1.86102	+	0.770858i	−0.0768779	+	0.0318439i
$587$	1.55341	+	3.75027i	0.0641162	+	0.154790i	0.952690	−	0.303943i	$-0.0983033\pi$
$587$	1.55341	+	3.75027i	0.0641162	+	0.154790i	−0.888574	+	0.458733i	$0.848303\pi$
$588$	−2.04280	+	10.2699i	−0.0842437	+	0.423522i
$589$	−16.9256	+	11.3093i	−0.697406	+	0.465992i
$590$	7.37358	−	1.46670i	0.303566	−	0.0603829i
$591$	35.7005	+	35.7005i	1.46852	+	1.46852i
$592$	13.7288	−	20.5467i	0.564252	−	0.844463i
$593$	9.81815	−	23.7031i	0.403183	−	0.973370i	−0.583705	−	0.811966i	$-0.698398\pi$
$593$	9.81815	−	23.7031i	0.403183	−	0.973370i	0.986888	−	0.161404i	$-0.0516024\pi$
$594$	7.49536	+	20.9330i	0.307538	+	0.858892i
$595$	25.8864	−	7.48285i	1.06124	−	0.306767i
$596$		−	12.2625i		−	0.502290i
$597$	−0.925270	+	2.23380i	−0.0378688	+	0.0914233i
$598$	−24.8704	−	16.6179i	−1.01703	−	0.679555i
$599$	32.8696	+	32.8696i	1.34302	+	1.34302i	0.893042	+	0.449974i	$0.148567\pi$
$599$	32.8696	+	32.8696i	1.34302	+	1.34302i	0.449974	+	0.893042i	$0.351433\pi$
$600$	9.21515	+	46.3277i	0.376207	+	1.89132i
$601$	−1.79477	−	2.68606i	−0.0732101	−	0.109567i	0.793058	−	0.609146i	$-0.208488\pi$
$601$	−1.79477	−	2.68606i	−0.0732101	−	0.109567i	−0.866268	+	0.499580i	$0.833488\pi$
$602$	−1.95886	+	9.84787i	−0.0798373	+	0.401369i
$603$	9.64371	−	3.99456i	0.392722	−	0.162671i
$604$	−1.10075	+	0.455945i	−0.0447888	+	0.0185521i
$605$	19.8058	+	37.0133i	0.805221	+	1.50480i
$606$	0.262383	+	0.392684i	0.0106586	+	0.0159517i
$607$	−2.30266	+	0.458028i	−0.0934623	+	0.0185908i	−0.241600	−	0.970376i	$-0.577672\pi$
$607$	−2.30266	+	0.458028i	−0.0934623	+	0.0185908i	0.148138	+	0.988967i	$0.452672\pi$
$608$	−15.3841	+	15.3841i	−0.623910	+	0.623910i
$609$	−17.5546	+	26.2723i	−0.711348	+	1.06461i
$610$	5.77422	+	2.39176i	0.233791	+	0.0968396i
$611$	20.8117			0.841951
$612$	−17.1525	−	1.91707i	−0.693350	−	0.0774931i
$613$		−	0.0835286i		−	0.00337369i	−0.999999	−	0.00168685i	$-0.999463\pi$
$613$		−	0.0835286i		−	0.00337369i	0.999999	−	0.00168685i	$-0.000536940\pi$
$614$	−16.7806	+	40.5121i	−0.677212	+	1.63493i
$615$	−56.4343	+	84.4600i	−2.27565	+	3.40575i
$616$	4.39694	−	9.30205i	0.177158	−	0.374790i
$617$	15.7762	−	3.13808i	0.635125	−	0.126334i	0.132981	−	0.991119i	$-0.457545\pi$
$617$	15.7762	−	3.13808i	0.635125	−	0.126334i	0.502143	+	0.864784i	$0.332545\pi$
$618$	−26.6038	−	39.8153i	−1.07016	−	1.60161i
$619$	−20.4770	−	4.07313i	−0.823041	−	0.163713i	−0.234433	−	0.972132i	$-0.575323\pi$
$619$	−20.4770	−	4.07313i	−0.823041	−	0.163713i	−0.588607	+	0.808419i	$0.700323\pi$
$620$	15.4229	−	6.38836i	0.619397	−	0.256563i
$621$	−6.83204	−	16.4940i	−0.274160	−	0.661881i
$622$	28.6706	+	5.70294i	1.14959	+	0.228667i
$623$	8.45010	−	5.64617i	0.338546	−	0.226209i
$624$	−50.9724	+	10.1390i	−2.04053	+	0.405887i
$625$	13.1884	−	13.1884i	0.527536	−	0.527536i
$626$	26.4811	+	17.6941i	1.05840	+	0.707198i
$627$	−39.6870	−	1.94059i	−1.58494	−	0.0774996i
$628$		−	6.46283i		−	0.257895i
$629$	−6.17460	+	19.4327i	−0.246197	+	0.774833i
$630$	−49.7123			−1.98059
$631$	−3.40516	+	8.22079i	−0.135557	+	0.327265i	−0.977052	−	0.213001i	$-0.931676\pi$
$631$	−3.40516	+	8.22079i	−0.135557	+	0.327265i	0.841495	+	0.540266i	$0.181676\pi$
$632$	−1.79698	−	1.20070i	−0.0714800	−	0.0477614i
$633$	47.1233	−	47.1233i	1.87298	−	1.87298i
$634$	3.57239	+	17.9596i	0.141878	+	0.713267i
$635$	−25.2155	−	37.7377i	−1.00065	−	1.49758i
$636$	20.3916	+	4.05613i	0.808578	+	0.160836i
$637$	−5.93782	−	14.3352i	−0.235265	−	0.567980i
$638$	28.5313	−	25.8712i	1.12957	−	1.02425i
$639$	−1.05828	+	5.32035i	−0.0418650	+	0.210470i
$640$	−39.5786	+	26.4456i	−1.56448	+	1.04535i
$641$	2.98979	+	15.0307i	0.118090	+	0.593677i	0.993832	+	0.110898i	$0.0353727\pi$
$641$	2.98979	+	15.0307i	0.118090	+	0.593677i	−0.875742	+	0.482779i	$0.839627\pi$
$642$	37.3782	−	37.3782i	1.47520	−	1.47520i
$643$	4.16523	−	6.23371i	0.164261	−	0.245834i	−0.740204	−	0.672383i	$-0.765271\pi$
$643$	4.16523	−	6.23371i	0.164261	−	0.245834i	0.904464	+	0.426549i	$0.140271\pi$
$644$	2.82774	−	6.82676i	0.111428	−	0.269012i
$645$	35.5527			1.39988
$646$	15.0137	−	27.2229i	0.590708	−	1.07107i
$647$	32.5159			1.27833			0.639166	−	0.769068i	$-0.279279\pi$
$647$	32.5159			1.27833			0.639166	+	0.769068i	$0.279279\pi$
$648$	4.43053	+	1.83519i	0.174048	+	0.0720929i
$649$	−0.924366	+	3.69386i	−0.0362845	+	0.144997i
$650$	44.2686	+	44.2686i	1.73636	+	1.73636i
$651$	−4.21950	−	21.2128i	−0.165375	−	0.831397i
$652$	−2.07385	+	1.38570i	−0.0812181	+	0.0542682i
$653$	−16.5294	−	3.28790i	−0.646845	−	0.128665i	−0.139244	−	0.990258i	$-0.544467\pi$
$653$	−16.5294	−	3.28790i	−0.646845	−	0.128665i	−0.507600	+	0.861593i	$0.669467\pi$
$654$	48.6373	−	20.1462i	1.90187	−	0.787780i
$655$	7.09673	−	2.93956i	0.277292	−	0.114858i
$656$	−47.8469	−	9.51734i	−1.86811	−	0.371590i
$657$	−3.26586	+	2.18218i	−0.127413	+	0.0851348i
$658$	3.12742	+	15.7226i	0.121919	+	0.612931i
$659$	8.17464	+	8.17464i	0.318439	+	0.318439i	0.848167	−	0.529729i	$-0.177706\pi$
$659$	8.17464	+	8.17464i	0.318439	+	0.318439i	−0.529729	+	0.848167i	$0.677706\pi$
$660$	31.6104	+	7.91030i	1.23043	+	0.307908i
$661$	−33.0715	−	13.6987i	−1.28633	−	0.532817i	−0.368443	−	0.929650i	$-0.620109\pi$
$661$	−33.0715	−	13.6987i	−1.28633	−	0.532817i	−0.917891	+	0.396833i	$0.870109\pi$
$662$	18.7167			0.727446
$663$	38.0816	−	19.7167i	1.47897	−	0.765731i
$664$	−2.30289			−0.0893695
$665$	10.9901	−	26.5323i	0.426176	−	1.02888i
$666$	20.8990	−	31.2775i	0.809818	−	1.21198i
$667$	−21.8671	+	21.8671i	−0.846698	+	0.846698i
$668$	1.31018	+	6.58673i	0.0506924	+	0.254848i
$669$	21.5016	−	14.3669i	0.831298	−	0.555456i
$670$	3.00811	−	15.1228i	0.116213	−	0.584244i
$671$	−2.34500	+	2.12636i	−0.0905278	+	0.0820874i
$672$	−8.84619	−	21.3566i	−0.341249	−	0.823849i
$673$	−23.2107	−	4.61689i	−0.894706	−	0.177968i	−0.273738	−	0.961804i	$-0.588260\pi$
$673$	−23.2107	−	4.61689i	−0.894706	−	0.177968i	−0.620968	+	0.783836i	$0.713260\pi$
$674$	−27.5109	−	41.1730i	−1.05968	−	1.58592i
$675$	7.28988	+	36.6487i	0.280588	+	1.41061i
$676$	−1.03702	+	1.03702i	−0.0398855	+	0.0398855i
$677$	−8.43429	−	5.63561i	−0.324156	−	0.216594i	0.382835	−	0.923817i	$-0.374948\pi$
$677$	−8.43429	−	5.63561i	−0.324156	−	0.216594i	−0.706991	+	0.707223i	$0.749948\pi$
$678$	23.7828	−	57.4167i	0.913373	−	2.20508i
$679$	−29.7679			−1.14239
$680$	18.3705	−	21.7946i	0.704476	−	0.835785i
$681$		−	19.7702i		−	0.757595i
$682$	−1.28754	+	26.3316i	−0.0493026	+	1.00829i
$683$	−38.4279	−	25.6767i	−1.47040	−	0.982492i	−0.994693	−	0.102890i	$-0.967191\pi$
$683$	−38.4279	−	25.6767i	−1.47040	−	0.982492i	−0.475710	−	0.879602i	$-0.657809\pi$
$684$	−13.0068	+	13.0068i	−0.497329	+	0.497329i
$685$	38.8266	−	7.72309i	1.48349	−	0.295084i
$686$	27.0402	−	18.0677i	1.03240	−	0.689828i
$687$	−7.84309	−	1.56009i	−0.299233	−	0.0595211i
$688$	6.53412	+	15.7748i	0.249111	+	0.601407i
$689$	−28.4635	+	11.7900i	−1.08437	+	0.449162i
$690$	−80.0124	−	15.9154i	−3.04602	−	0.605891i
$691$	−0.103603	−	0.155053i	−0.00394126	−	0.00589851i	0.829494	−	0.558516i	$-0.188629\pi$
$691$	−0.103603	−	0.155053i	−0.00394126	−	0.00589851i	−0.833435	+	0.552617i	$0.813629\pi$
$692$	15.8698	−	3.15671i	0.603281	−	0.120000i
$693$	10.7600	−	22.7636i	0.408738	−	0.864716i
$694$	−2.97447	+	4.45162i	−0.112910	+	0.168981i
$695$	16.9127	−	40.8309i	0.641535	−	1.54880i
$696$			33.4242i			1.26694i
$697$	40.1081	−	3.41925i	1.51920	−	0.129513i
$698$	−11.7537			−0.444885
$699$	−71.7378	−	29.7148i	−2.71337	−	1.12392i
$700$	−8.59235	+	12.8594i	−0.324760	+	0.486038i
$701$	−16.4993	+	16.4993i	−0.623170	+	0.623170i	−0.946341	−	0.323171i	$-0.895251\pi$
$701$	−16.4993	+	16.4993i	−0.623170	+	0.623170i	0.323171	+	0.946341i	$0.395251\pi$
$702$	−25.0832	+	4.98935i	−0.946703	+	0.188311i
$703$	12.0732	+	18.0688i	0.455348	+	0.681476i
$704$	−0.730251	−	4.91520i	−0.0275224	−	0.185248i
$705$	52.4408	−	21.7217i	1.97504	−	0.818087i
$706$	−1.35599	+	0.561669i	−0.0510333	+	0.0211387i
$707$	0.0337281	−	0.169563i	0.00126848	−	0.00637706i
$708$	1.64208	+	2.45755i	0.0617131	+	0.0923602i
$709$	−6.39654	−	32.1576i	−0.240227	−	1.20770i	−0.892967	−	0.450121i	$-0.851381\pi$
$709$	−6.39654	−	32.1576i	−0.240227	−	1.20770i	0.652740	−	0.757582i	$-0.273619\pi$
$710$	5.66605	+	5.66605i	0.212643	+	0.212643i
$711$	−4.39748	−	2.93830i	−0.164918	−	0.110195i
$712$	4.11399	−	9.93206i	0.154178	−	0.372220i
$713$		−	21.1680i		−	0.792747i
$714$	20.6179	+	25.8066i	0.771607	+	0.965789i
$715$	−45.4591	+	16.2773i	−1.70007	+	0.608736i
$716$	3.34664	−	8.07951i	0.125070	−	0.301946i
$717$	0.824374	−	1.23376i	0.0307868	−	0.0460757i
$718$	−41.4537	−	41.4537i	−1.54704	−	1.54704i
$719$	−30.6917	+	6.10496i	−1.14461	+	0.227677i	−0.730737	−	0.682659i	$-0.760823\pi$
$719$	−30.6917	+	6.10496i	−1.14461	+	0.227677i	−0.413871	+	0.910336i	$0.635823\pi$
$720$	−70.2894	+	46.9659i	−2.61953	+	1.75031i
$721$	−3.41979	+	17.1924i	−0.127360	+	0.640280i
$722$	−0.203307	−	0.490826i	−0.00756629	−	0.0182666i
$723$	46.9213	−	19.4355i	1.74502	−	0.722812i
$724$	1.78736	−	8.98566i	0.0664267	−	0.333949i
$725$	53.8179	−	35.9600i	1.99875	−	1.33552i
$726$	−32.6273	+	39.7936i	−1.21091	+	1.47688i
$727$	2.76644	−	2.76644i	0.102602	−	0.102602i	−0.653943	−	0.756544i	$-0.726886\pi$
$727$	2.76644	−	2.76644i	0.102602	−	0.102602i	0.756544	+	0.653943i	$0.226886\pi$
$728$	9.84004	+	6.57490i	0.364696	+	0.243682i
$729$	40.3652	+	16.7198i	1.49501	+	0.619253i
$730$			5.80203i			0.214743i
$731$	−8.79404	−	11.0071i	−0.325259	−	0.407114i
$732$			2.45713i			0.0908183i
$733$	−2.26167	−	0.936816i	−0.0835369	−	0.0346021i	0.340524	−	0.940236i	$-0.389396\pi$
$733$	−2.26167	−	0.936816i	−0.0835369	−	0.0346021i	−0.424061	+	0.905634i	$0.639396\pi$
$734$	−7.83417	+	11.7247i	−0.289164	+	0.432765i
$735$	−29.9239	−	29.9239i	−1.10376	−	1.10376i
$736$	−4.41374	−	22.1894i	−0.162693	−	0.817911i
$737$	6.27372	+	4.65068i	0.231095	+	0.171310i
$738$	−72.8357	−	14.4879i	−2.68112	−	0.533308i
$739$	−7.96527	−	19.2299i	−0.293007	−	0.707382i	−1.00000		0.000160989i	$-0.999949\pi$
$739$	−7.96527	−	19.2299i	−0.293007	−	0.707382i	0.706993	−	0.707221i	$-0.250051\pi$
$740$	−6.81984	−	16.4646i	−0.250702	−	0.605249i
$741$	8.91628	−	44.8252i	0.327548	−	1.64669i
$742$	−13.1842	−	19.7316i	−0.484009	−	0.724370i
$743$	35.4268	−	7.04683i	1.29968	−	0.258523i	0.503719	−	0.863867i	$-0.331965\pi$
$743$	35.4268	−	7.04683i	1.29968	−	0.258523i	0.795964	+	0.605344i	$0.206965\pi$
$744$	−16.1778	−	16.1778i	−0.593105	−	0.593105i
$745$	41.2067	+	27.5334i	1.50970	+	1.00875i
$746$	−14.5548	−	6.02879i	−0.532888	−	0.220730i
$747$	−5.63553			−0.206193
$748$	−5.36987	−	11.7432i	−0.196342	−	0.429375i
$749$	−19.3505			−0.707053
$750$	75.2805	+	31.1822i	2.74886	+	1.13861i
$751$	28.3773	+	18.9611i	1.03550	+	0.691901i	0.952466	−	0.304645i	$-0.0985378\pi$
$751$	28.3773	+	18.9611i	1.03550	+	0.691901i	0.0830377	+	0.996546i	$0.473538\pi$
$752$	19.2759	+	19.2759i	0.702920	+	0.702920i
$753$	56.0349	−	11.1460i	2.04203	−	0.406184i
$754$	24.6118	+	36.8341i	0.896308	+	1.34142i
$755$	0.939403	−	4.72270i	0.0341884	−	0.171877i
$756$	−2.41775	−	5.83696i	−0.0879326	−	0.212288i
$757$	18.2374	+	44.0289i	0.662848	+	1.60026i	0.793320	+	0.608805i	$0.208351\pi$
$757$	18.2374	+	44.0289i	0.662848	+	1.60026i	−0.130472	+	0.991452i	$0.541649\pi$
$758$	−26.1350	−	5.19858i	−0.949266	−	0.188821i
$759$	24.6060	−	33.1933i	0.893143	−	1.20484i
$760$	−5.92658	−	29.7949i	−0.214980	−	1.08078i
$761$	8.04981	+	8.04981i	0.291805	+	0.291805i	0.837793	−	0.545988i	$-0.183845\pi$
$761$	8.04981	+	8.04981i	0.291805	+	0.291805i	−0.545988	+	0.837793i	$0.683845\pi$
$762$	30.9100	−	46.2601i	1.11975	−	1.67583i
$763$	−17.8045	−	7.37486i	−0.644565	−	0.266988i
$764$			20.4821i			0.741016i
$765$	44.9554	−	53.3348i	1.62537	−	1.92832i
$766$		−	28.7180i		−	1.03763i
$767$	−4.04639	−	1.67607i	−0.146107	−	0.0605193i
$768$	−41.7239	−	27.8790i	−1.50558	−	1.00600i
$769$	11.7503	−	11.7503i	0.423726	−	0.423726i	−0.462758	−	0.886485i	$-0.653140\pi$
$769$	11.7503	−	11.7503i	0.423726	−	0.423726i	0.886485	+	0.462758i	$0.153140\pi$
$770$	−19.1282	−	31.8969i	−0.689333	−	1.14949i
$771$	−38.7281	+	25.8773i	−1.39476	+	0.931948i
$772$	−1.15643	+	5.81379i	−0.0416210	+	0.209243i
$773$	−31.5544	+	13.0703i	−1.13493	+	0.470105i	−0.869455	−	0.494011i	$-0.835530\pi$
$773$	−31.5544	+	13.0703i	−1.13493	+	0.470105i	−0.265479	+	0.964117i	$0.585530\pi$
$774$	9.94667	+	24.0134i	0.357526	+	0.863144i
$775$	−8.64348	+	43.4537i	−0.310483	+	1.56090i
$776$	−26.1820	+	17.4942i	−0.939879	+	0.628007i
$777$	−22.6456	+	4.50449i	−0.812407	+	0.161598i
$778$	−7.73712	−	7.73712i	−0.277389	−	0.277389i
$779$	23.8345	−	35.6708i	0.853959	−	1.27804i
$780$	−14.3430	+	34.6271i	−0.513562	+	1.23985i
$781$	−3.82090	+	1.36813i	−0.136723	+	0.0489555i
$782$	14.8638	+	28.7086i	0.531529	+	1.02662i
$783$			26.4410i			0.944925i
$784$	7.77766	−	18.7769i	0.277774	−	0.670605i
$785$	21.7176	+	14.5113i	0.775136	+	0.517929i
$786$	6.65823	+	6.65823i	0.237491	+	0.237491i
$787$	0.325696	+	1.63739i	0.0116098	+	0.0583665i	0.986156	−	0.165821i	$-0.0530273\pi$
$787$	0.325696	+	1.63739i	0.0116098	+	0.0583665i	−0.974546	+	0.224187i	$0.928027\pi$
$788$	9.71501	+	14.5395i	0.346083	+	0.517950i
$789$	4.90940	−	24.6812i	0.174779	−	0.878674i
$790$	−7.21775	+	2.98969i	−0.256796	+	0.106368i
$791$	−21.0183	+	8.70607i	−0.747326	+	0.309552i
$792$	−3.91407	−	26.3449i	−0.139080	−	0.936127i
$793$	−2.02285	−	3.02741i	−0.0718336	−	0.107507i
$794$	−12.6786	+	2.52193i	−0.449946	+	0.0894999i
$795$	−59.4162	+	59.4162i	−2.10728	+	2.10728i
$796$	−0.465246	+	0.696290i	−0.0164902	+	0.0246793i
$797$	5.78594	+	2.39662i	0.204949	+	0.0848925i	0.482796	−	0.875733i	$-0.339621\pi$
$797$	5.78594	+	2.39662i	0.204949	+	0.0848925i	−0.277848	+	0.960625i	$0.589621\pi$
$798$	35.2039			1.24621
$799$	−19.6964	−	10.8628i	−0.696810	−	0.384299i
$800$			47.3527i			1.67417i
$801$	10.0676	−	24.3053i	0.355720	−	0.858784i
$802$	−31.1708	+	46.6504i	−1.10068	+	1.64728i
$803$	−2.65678	−	1.25582i	−0.0937558	−	0.0443169i
$804$	5.94542	−	1.18262i	0.209679	−	0.0417077i
$805$	16.5913	+	24.8307i	0.584768	+	0.875167i
$806$	−29.7407	−	5.91579i	−1.04757	−	0.208375i
$807$	77.2921	−	32.0154i	2.72081	−	1.12700i
$808$	−0.0699849	−	0.168958i	−0.00246206	−	0.00594394i
$809$	0.895958	+	0.178217i	0.0315002	+	0.00626578i	0.210815	−	0.977526i	$-0.432388\pi$
$809$	0.895958	+	0.178217i	0.0315002	+	0.00626578i	−0.179315	+	0.983792i	$0.557388\pi$
$810$	14.4138	−	9.63096i	0.506448	−	0.338397i
$811$	43.9274	−	8.73770i	1.54250	−	0.306822i	0.650729	−	0.759310i	$-0.274463\pi$
$811$	43.9274	−	8.73770i	1.54250	−	0.306822i	0.891771	+	0.452488i	$0.149463\pi$
$812$	−7.73841	+	7.73841i	−0.271565	+	0.271565i
$813$	−62.9767	−	42.0797i	−2.20869	−	1.47580i
$814$	28.1101	+	1.37451i	0.985257	+	0.0481765i
$815$		−	10.0803i		−	0.353098i
$816$	53.5331	+	17.0097i	1.87403	+	0.595460i
$817$	−15.0153			−0.525319
$818$	−3.31512	+	8.00341i	−0.115911	+	0.279833i
$819$	24.0801	+	16.0898i	0.841426	+	0.562223i
$820$	−24.8774	+	24.8774i	−0.868755	+	0.868755i
$821$	−3.01078	−	15.1362i	−0.105077	−	0.528257i	−0.997089	−	0.0762459i	$-0.975707\pi$
$821$	−3.01078	−	15.1362i	−0.105077	−	0.528257i	0.892012	−	0.452011i	$-0.149293\pi$
$822$	26.9603	+	40.3490i	0.940349	+	1.40733i
$823$	7.61506	+	1.51473i	0.265444	+	0.0528001i	0.326018	−	0.945364i	$-0.394293\pi$
$823$	7.61506	+	1.51473i	0.265444	+	0.0528001i	−0.0605737	+	0.998164i	$0.519293\pi$
$824$	7.09597	+	17.1312i	0.247200	+	0.596793i
$825$	−64.0652	+	58.0920i	−2.23046	+	2.02251i
$826$	0.658159	−	3.30879i	0.0229003	−	0.115127i
$827$	33.8350	−	22.6078i	1.17656	−	0.786151i	0.195660	−	0.980672i	$-0.437315\pi$
$827$	33.8350	−	22.6078i	1.17656	−	0.786151i	0.980898	+	0.194521i	$0.0623151\pi$
$828$	−3.73168	−	18.7604i	−0.129685	−	0.651970i
$829$	3.88265	−	3.88265i	0.134850	−	0.134850i	−0.636460	−	0.771310i	$-0.719602\pi$
$829$	3.88265	−	3.88265i	0.134850	−	0.134850i	0.771310	+	0.636460i	$0.219602\pi$
$830$	−4.62490	+	6.92166i	−0.160533	+	0.240254i
$831$	−3.78079	+	9.12762i	−0.131154	+	0.316634i
$832$	5.71562			0.198154
$833$	−1.86272	+	16.6662i	−0.0645395	+	0.577451i
$834$	54.1757			1.87595
$835$	−25.0758	−	10.3867i	−0.867783	−	0.359448i
$836$	−13.3503	−	3.34083i	−0.461731	−	0.115545i
$837$	−12.7978	−	12.7978i	−0.442358	−	0.442358i
$838$	3.65181	+	18.3589i	0.126150	+	0.634198i
$839$	−7.17962	+	4.79727i	−0.247868	+	0.165620i	−0.673298	−	0.739371i	$-0.735123\pi$
$839$	−7.17962	+	4.79727i	−0.247868	+	0.165620i	0.425430	+	0.904991i	$0.360123\pi$
$840$	31.6571	+	6.29698i	1.09227	+	0.217267i
$841$	15.5220	−	6.42943i	0.535242	−	0.221704i
$842$	−38.5896	+	15.9843i	−1.32989	+	0.550856i
$843$	71.1876	+	14.1601i	2.45183	+	0.487699i
$844$	19.1916	−	12.8234i	0.660603	−	0.441401i
$845$	−1.15633	−	5.81328i	−0.0397791	−	0.199983i
$846$	29.3430	+	29.3430i	1.00883	+	1.00883i
$847$	18.7460	−	1.85499i	0.644120	−	0.0637381i
$848$	−37.2830	−	15.4431i	−1.28030	−	0.530319i
$849$	−3.55485			−0.122002
$850$	−18.7900	−	65.0026i	−0.644491	−	2.22957i
$851$	−22.5977			−0.774639
$852$	−1.20555	+	2.91046i	−0.0413015	+	0.0997106i
$853$	2.20406	−	3.29861i	0.0754656	−	0.112942i	−0.791817	−	0.610759i	$-0.790865\pi$
$853$	2.20406	−	3.29861i	0.0754656	−	0.112942i	0.867283	+	0.497816i	$0.165865\pi$
$854$	1.98314	−	1.98314i	0.0678617	−	0.0678617i
$855$	−14.5033	−	72.9128i	−0.496001	−	2.49357i
$856$	−17.0195	+	11.3721i	−0.581716	+	0.388690i
$857$	−10.4428	+	52.4998i	−0.356721	+	1.79336i	0.219015	+	0.975722i	$0.429716\pi$
$857$	−10.4428	+	52.4998i	−0.356721	+	1.79336i	−0.575736	+	0.817636i	$0.695284\pi$
$858$	−39.7595	−	43.8476i	−1.35737	−	1.49693i
$859$	6.97417	+	16.8371i	0.237956	+	0.574475i	0.997071	−	0.0764804i	$-0.0243683\pi$
$859$	6.97417	+	16.8371i	0.237956	+	0.574475i	−0.759116	+	0.650956i	$0.774368\pi$
$860$	12.0771	+	2.40228i	0.411824	+	0.0819169i
$861$	25.3241	+	37.9002i	0.863043	+	1.29163i
$862$	0.782018	+	3.93147i	0.0266357	+	0.133906i
$863$	27.3990	−	27.3990i	0.932671	−	0.932671i	−0.0652007	−	0.997872i	$-0.520769\pi$
$863$	27.3990	−	27.3990i	0.932671	−	0.932671i	0.997872	+	0.0652007i	$0.0207688\pi$
$864$	−16.0838	−	10.7469i	−0.547183	−	0.365616i
$865$	−25.0254	+	60.4168i	−0.850891	+	2.05423i
$866$	32.7923			1.11433
$867$	−46.3321	−	1.21692i	−1.57352	−	0.0413286i
$868$		−	7.49100i		−	0.254261i
$869$	0.193250	−	3.95215i	0.00655556	−	0.134068i
$870$	100.461	+	67.1259i	3.40594	+	2.27578i
$871$	−6.35171	+	6.35171i	−0.215219	+	0.215219i
$872$	−19.9938	+	3.97702i	−0.677077	+	0.134679i
$873$	−64.0714	+	42.8111i	−2.16849	+	1.44894i
$874$	33.7924	+	6.72173i	1.14305	+	0.227366i
$875$	−11.4147	−	27.5576i	−0.385889	−	0.931618i
$876$	−2.10739	+	0.872911i	−0.0712023	+	0.0294929i
$877$	−13.5372	−	2.69271i	−0.457118	−	0.0909264i	−0.0388397	−	0.999245i	$-0.512366\pi$
$877$	−13.5372	−	2.69271i	−0.457118	−	0.0909264i	−0.418278	+	0.908319i	$0.637366\pi$
$878$	12.0343	+	18.0106i	0.406138	+	0.607828i
$879$	3.13908	−	0.624402i	0.105879	−	0.0210606i
$880$	−57.1806	−	27.0284i	−1.92756	−	0.911126i
$881$	−7.90109	+	11.8248i	−0.266195	+	0.398388i	−0.940354	−	0.340198i	$-0.889506\pi$
$881$	−7.90109	+	11.8248i	−0.266195	+	0.398388i	0.674159	+	0.738586i	$0.264506\pi$
$882$	11.8397	−	28.5835i	0.398662	−	0.962456i
$883$		−	27.4196i		−	0.922743i	−0.887207	−	0.461372i	$-0.847358\pi$
$883$		−	27.4196i		−	0.922743i	0.887207	−	0.461372i	$-0.152642\pi$
$884$	14.2684	−	4.12449i	0.479897	−	0.138722i
$885$	−11.9453			−0.401538
$886$	−46.7476	−	19.3635i	−1.57052	−	0.650529i
$887$	−29.4338	+	44.0507i	−0.988289	+	1.47908i	−0.114115	+	0.993468i	$0.536403\pi$
$887$	−29.4338	+	44.0507i	−0.988289	+	1.47908i	−0.874175	+	0.485612i	$0.838597\pi$
$888$	−17.2704	+	17.2704i	−0.579558	+	0.579558i
$889$	−19.9753	+	3.97334i	−0.669951	+	0.133261i
$890$	−21.5900	−	32.3118i	−0.723699	−	1.08309i
$891$	1.29029	+	8.68471i	0.0432262	+	0.290949i
$892$	8.27473	−	3.42750i	0.277058	−	0.114761i
$893$	−22.1478	+	9.17394i	−0.741149	+	0.306994i
$894$	−11.8519	+	59.5835i	−0.396386	+	1.99277i
$895$	19.6360	+	29.3873i	0.656358	+	0.982309i
$896$	4.16716	+	20.9497i	0.139215	+	0.699881i
$897$	33.6059	+	33.6059i	1.12207	+	1.12207i
$898$	−22.8973	−	15.2995i	−0.764092	−	0.510550i
$899$	−11.9974	+	28.9642i	−0.400135	+	0.966012i
$900$			40.0353i			1.33451i
$901$	33.0921	+	3.69857i	1.10246	+	0.123217i
$902$	−18.7297	−	52.3083i	−0.623631	−	1.74167i
$903$	6.10523	−	14.7393i	0.203169	−	0.490494i
$904$	−13.3700	+	20.0096i	−0.444678	+	0.665508i
$905$	26.1821	+	26.1821i	0.870322	+	0.870322i
$906$	5.78923	−	1.15155i	0.192334	−	0.0382577i
$907$	6.63109	−	4.43075i	0.220182	−	0.147121i	−0.440588	−	0.897709i	$-0.645230\pi$
$907$	6.63109	−	4.43075i	0.220182	−	0.147121i	0.660770	+	0.750589i	$0.270230\pi$
$908$	1.33586	−	6.71583i	0.0443321	−	0.222873i
$909$	−0.171264	−	0.413467i	−0.00568046	−	0.0137138i
$910$	39.5236	−	16.3712i	1.31019	−	0.542700i
$911$	−0.251199	+	1.26286i	−0.00832259	+	0.0418405i	−0.984723	−	0.174126i	$-0.944290\pi$
$911$	−0.251199	+	1.26286i	−0.00832259	+	0.0418405i	0.976401	+	0.215966i	$0.0692901\pi$
$912$	49.7756	−	33.2590i	1.64824	−	1.10132i
$913$	−2.16843	−	3.61593i	−0.0717645	−	0.119670i
$914$	−17.3444	+	17.3444i	−0.573701	+	0.573701i
$915$	−8.25693	−	5.51710i	−0.272966	−	0.182390i
$916$	−2.55884	−	1.05991i	−0.0845465	−	0.0350203i
$917$		−	3.44694i		−	0.113828i
$918$	26.3432	+	8.37036i	0.869456	+	0.276263i
$919$		−	7.94953i		−	0.262231i	−0.991367	−	0.131115i	$-0.958144\pi$
$919$		−	7.94953i		−	0.262231i	0.991367	−	0.131115i	$-0.0418558\pi$
$920$	29.1855	+	12.0890i	0.962216	+	0.398563i
$921$	38.7081	−	57.9308i	1.27548	−	1.90888i
$922$	2.38041	+	2.38041i	0.0783946	+	0.0783946i
$923$	−0.910707	−	4.57843i	−0.0299763	−	0.150701i
$924$	8.70768	−	11.7466i	0.286462	−	0.386434i
$925$	46.3887	+	9.22728i	1.52525	+	0.303391i
$926$	18.1360	+	43.7842i	0.595986	+	1.43884i
$927$	17.3649	+	41.9226i	0.570339	+	1.37692i
$928$	−6.53694	+	32.8634i	−0.214585	+	1.07879i
$929$	8.25226	+	12.3504i	0.270748	+	0.405203i	0.941782	−	0.336224i	$-0.109150\pi$
$929$	8.25226	+	12.3504i	0.270748	+	0.405203i	−0.671034	+	0.741426i	$0.734150\pi$
$930$	−81.1144	+	16.1346i	−2.65984	+	0.529076i
$931$	12.6381	+	12.6381i	0.414196	+	0.414196i
$932$	−22.3611	−	14.9412i	−0.732464	−	0.489417i
$933$	−42.9113	−	17.7745i	−1.40485	−	0.581910i
$934$	35.9697			1.17696
$935$	51.5191	+	8.32272i	1.68485	+	0.272182i
$936$	30.6351			1.00134
$937$	25.1264	+	10.4077i	0.820843	+	0.340004i	0.753271	−	0.657710i	$-0.228475\pi$
$937$	25.1264	+	10.4077i	0.820843	+	0.340004i	0.0675720	+	0.997714i	$0.478475\pi$
$938$	−5.75300	−	3.84403i	−0.187842	−	0.125512i
$939$	−35.7823	−	35.7823i	−1.16771	−	1.16771i
$940$	19.2816	−	3.83535i	0.628896	−	0.125095i
$941$	18.1807	+	27.2094i	0.592674	+	0.887000i	0.999650	−	0.0264391i	$-0.00841680\pi$
$941$	18.1807	+	27.2094i	0.592674	+	0.887000i	−0.406976	+	0.913439i	$0.633417\pi$
$942$	−6.24644	+	31.4030i	−0.203520	+	1.02316i
$943$	17.0722	+	41.2159i	0.555946	+	1.34217i
$944$	−2.19540	−	5.30017i	−0.0714542	−	0.172506i
$945$	25.0431	+	4.98139i	0.814653	+	0.162045i
$946$	−11.5805	+	15.6219i	−0.376513	+	0.507912i
$947$	5.17936	+	26.0384i	0.168306	+	0.846134i	0.969000	+	0.247060i	$0.0794644\pi$
$947$	5.17936	+	26.0384i	0.168306	+	0.846134i	−0.800694	+	0.599074i	$0.795536\pi$
$948$	−2.17181	−	2.17181i	−0.0705372	−	0.0705372i
$949$	1.87787	−	2.81044i	0.0609583	−	0.0912306i
$950$	−66.6246	−	27.5968i	−2.16159	−	0.895359i
$951$		−	29.0949i		−	0.943467i
$952$	−5.88090	−	11.3586i	−0.190601	−	0.368136i
$953$		−	40.1487i		−	1.30055i	−0.759701	−	0.650273i	$-0.774655\pi$
$953$		−	40.1487i		−	1.30055i	0.759701	−	0.650273i	$-0.225345\pi$
$954$	−56.7546	−	23.5085i	−1.83750	−	0.761117i
$955$	−68.8278	−	45.9893i	−2.22722	−	1.48818i
$956$	0.363400	−	0.363400i	0.0117532	−	0.0117532i
$957$	−52.4816	+	31.4726i	−1.69649	+	1.01736i
$958$	43.1261	−	28.8160i	1.39334	−	0.931001i
$959$	3.46562	−	17.4229i	0.111911	−	0.562614i
$960$	14.4021	−	5.96554i	0.464826	−	0.192537i
$961$	3.65099	+	8.81426i	0.117774	+	0.284331i
$962$	−6.31536	+	31.7494i	−0.203615	+	1.02364i
$963$	−41.6494	+	27.8292i	−1.34213	+	0.896785i
$964$	17.2522	−	3.43167i	0.555655	−	0.110527i
$965$	−16.9400	−	16.9400i	−0.545318	−	0.545318i
$966$	−20.3382	+	30.4383i	−0.654371	+	0.979335i
$967$	5.88266	−	14.2020i	0.189174	−	0.456705i	−0.800627	−	0.599162i	$-0.795500\pi$
$967$	5.88266	−	14.2020i	0.189174	−	0.456705i	0.989801	+	0.142457i	$0.0455003\pi$
$968$	15.3977	−	12.6483i	0.494900	−	0.406533i
$969$	−31.8353	+	37.7691i	−1.02270	+	1.21332i
$970$			113.827i			3.65478i
$971$	18.8104	−	45.4123i	0.603654	−	1.45735i	−0.266140	−	0.963934i	$-0.585748\pi$
$971$	18.8104	−	45.4123i	0.603654	−	1.45735i	0.869794	−	0.493415i	$-0.164252\pi$
$972$	14.8692	+	9.93528i	0.476930	+	0.318674i
$973$	−14.0233	−	14.0233i	−0.449565	−	0.449565i
$974$	−11.5583	−	58.1073i	−0.370351	−	1.86188i
$975$	−55.2641	−	82.7086i	−1.76987	−	2.64880i
$976$	0.930429	−	4.67758i	0.0297823	−	0.149726i
$977$	−28.1225	+	11.6487i	−0.899720	+	0.372676i	−0.784112	−	0.620619i	$-0.786881\pi$
$977$	−28.1225	+	11.6487i	−0.899720	+	0.372676i	−0.115608	+	0.993295i	$0.536881\pi$
$978$	11.4161	−	4.72872i	0.365048	−	0.151208i
$979$	19.4688	−	2.89248i	0.622225	−	0.0924440i
$980$	−8.14306	−	12.1869i	−0.260120	−	0.389298i
$981$	−48.9280	+	9.73239i	−1.56215	+	0.310731i
$982$	41.3124	−	41.3124i	1.31833	−	1.31833i
$983$	28.3293	−	42.3978i	0.903565	−	1.35228i	−0.0321351	−	0.999484i	$-0.510231\pi$
$983$	28.3293	−	42.3978i	0.903565	−	1.35228i	0.935700	−	0.352797i	$-0.114769\pi$
$984$	44.5470	+	18.4520i	1.42011	+	0.588228i
$985$	−70.6721			−2.25180
$986$	−4.06703	−	47.7066i	−0.129521	−	1.51929i
$987$		−	25.4709i		−	0.810748i
$988$	6.05763	−	14.6244i	0.192719	−	0.465264i
$989$	8.67472	−	12.9826i	0.275840	−	0.412824i
$990$	−87.0440	−	41.1444i	−2.76644	−	1.30765i
$991$	21.3663	−	4.25001i	0.678722	−	0.135006i	0.156321	−	0.987706i	$-0.450037\pi$
$991$	21.3663	−	4.25001i	0.678722	−	0.135006i	0.522401	+	0.852700i	$0.325037\pi$
$992$	−12.7424	−	19.0703i	−0.404571	−	0.605483i
$993$	−29.1674	−	5.80176i	−0.925600	−	0.184113i
$994$	3.32201	−	1.37602i	0.105368	−	0.0436448i
$995$	−1.29517	−	3.12682i	−0.0410596	−	0.0991267i
$996$	−3.20988	−	0.638484i	−0.101709	−	0.0202311i
$997$	34.0517	−	22.7526i	1.07843	−	0.720584i	0.116310	−	0.993213i	$-0.462893\pi$
$997$	34.0517	−	22.7526i	1.07843	−	0.720584i	0.962119	+	0.272629i	$0.0878933\pi$
$998$	−2.65330	+	0.527774i	−0.0839887	+	0.0167064i
$999$	−13.6622	+	13.6622i	−0.432254	+	0.432254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.m.a.10.3	✓	128
11.10	odd	2	inner	187.2.m.a.10.14	yes	128
17.12	odd	16	inner	187.2.m.a.131.14	yes	128
187.131	even	16	inner	187.2.m.a.131.3	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.m.a.10.3	✓	128	1.1	even	1	trivial
187.2.m.a.10.14	yes	128	11.10	odd	2	inner
187.2.m.a.131.3	yes	128	187.131	even	16	inner
187.2.m.a.131.14	yes	128	17.12	odd	16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.m (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58527 - 0.656642i) q^{2} +(2.26689 + 1.51468i) q^{3} +(0.667703 + 0.667703i) q^{4} +(-3.74296 + 0.744522i) q^{5} +(-2.59903 - 3.88972i) q^{6} +(-0.334093 + 1.67960i) q^{7} +(0.693234 + 1.67362i) q^{8} +(1.69645 + 4.09559i) q^{9} +(6.42251 + 1.27752i) q^{10} +(-1.97510 + 2.66439i) q^{11} +(0.502247 + 2.52496i) q^{12} +(-2.69751 - 2.69751i) q^{13} +(1.63253 - 2.44325i) q^{14} +(-9.61258 - 3.98166i) q^{15} -4.99689i q^{16} +(1.14497 + 3.96094i) q^{17} -7.60660i q^{18} +(4.05978 + 1.68161i) q^{19} +(-2.99630 - 2.00207i) q^{20} +(-3.30141 + 3.30141i) q^{21} +(4.88063 - 2.92686i) q^{22} +(-3.79941 + 2.53868i) q^{23} +(-0.963517 + 4.84393i) q^{24} +(8.83606 - 3.66002i) q^{25} +(2.50500 + 6.04759i) q^{26} +(-0.762214 + 3.83191i) q^{27} +(-1.34455 + 0.898398i) q^{28} +(6.63760 - 1.32030i) q^{29} +(12.6241 + 12.6241i) q^{30} +(-2.57365 + 3.85173i) q^{31} +(-1.89470 + 4.57422i) q^{32} +(-8.51304 + 3.04821i) q^{33} +(0.785829 - 7.03101i) q^{34} -6.53542i q^{35} +(-1.60191 + 3.86736i) q^{36} +(4.11189 + 2.74748i) q^{37} +(-5.33164 - 5.33164i) q^{38} +(-2.02907 - 10.2008i) q^{39} +(-3.84079 - 5.74815i) q^{40} +(1.90465 - 9.57533i) q^{41} +(7.40150 - 3.06580i) q^{42} +(-3.15691 + 1.30764i) q^{43} +(-3.09780 + 0.460240i) q^{44} +(-9.39901 - 14.0666i) q^{45} +(7.69011 - 1.52966i) q^{46} +(-3.85758 + 3.85758i) q^{47} +(7.56872 - 11.3274i) q^{48} +(3.75772 + 1.55650i) q^{49} -16.4109 q^{50} +(-3.40406 + 10.7133i) q^{51} -3.60227i q^{52} +(3.09054 - 7.46123i) q^{53} +(3.72451 - 5.57413i) q^{54} +(5.40903 - 11.4432i) q^{55} +(-3.04261 + 0.605213i) q^{56} +(6.65593 + 9.96131i) q^{57} +(-11.3894 - 2.26549i) q^{58} +(1.06069 - 0.439353i) q^{59} +(-3.75978 - 9.07691i) q^{60} +(0.936098 + 0.186202i) q^{61} +(6.60915 - 4.41609i) q^{62} +(-7.44573 + 1.48105i) q^{63} +(-1.05943 + 1.05943i) q^{64} +(12.1050 + 8.08833i) q^{65} +(15.4971 + 0.757767i) q^{66} -2.35465i q^{67} +(-1.88023 + 3.40923i) q^{68} -12.4581 q^{69} +(-4.29143 + 10.3604i) q^{70} +(1.01745 + 0.679835i) q^{71} +(-5.67841 + 5.67841i) q^{72} +(0.172856 + 0.869007i) q^{73} +(-4.71436 - 7.05554i) q^{74} +(25.5741 + 5.08700i) q^{75} +(1.58791 + 3.83354i) q^{76} +(-3.81524 - 4.20753i) q^{77} +(-3.48166 + 17.5035i) q^{78} +(-0.991979 + 0.662819i) q^{79} +(3.72030 + 18.7032i) q^{80} +(1.87191 - 1.87191i) q^{81} +(-9.30696 + 13.9289i) q^{82} +(-0.486489 + 1.17449i) q^{83} -4.40873 q^{84} +(-7.23458 - 13.9732i) q^{85} +5.86323 q^{86} +(17.0465 + 7.06090i) q^{87} +(-5.82837 - 1.45851i) q^{88} +(-4.19632 - 4.19632i) q^{89} +(5.66328 + 28.4712i) q^{90} +(5.43196 - 3.62952i) q^{91} +(-4.23196 - 0.841789i) q^{92} +(-11.6683 + 4.83318i) q^{93} +(8.64836 - 3.58227i) q^{94} +(-16.4476 - 3.27163i) q^{95} +(-11.2236 + 7.49935i) q^{96} +(3.39119 + 17.0486i) q^{97} +(-4.93495 - 4.93495i) q^{98} +(-14.2629 - 3.56921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9} - 64 q^{12} + 16 q^{14} - 16 q^{15} - 16 q^{20} + 8 q^{22} - 32 q^{23} + 16 q^{26} + 32 q^{27} - 80 q^{31} - 16 q^{34} + 16 q^{36} + 16 q^{37} + 80 q^{38}+ \cdots - 112 q^{99}+O(q^{100}) \) 128 * q - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^9 - 64 * q^12 + 16 * q^14 - 16 * q^15 - 16 * q^20 + 8 * q^22 - 32 * q^23 + 16 * q^26 + 32 * q^27 - 80 * q^31 - 16 * q^34 + 16 * q^36 + 16 * q^37 + 80 * q^38 - 112 * q^42 - 72 * q^44 - 16 * q^45 - 16 * q^47 + 32 * q^48 + 48 * q^49 - 16 * q^53 - 8 * q^55 - 16 * q^56 - 128 * q^58 + 48 * q^59 + 112 * q^60 + 48 * q^64 + 72 * q^66 - 192 * q^69 + 128 * q^70 - 16 * q^71 + 48 * q^75 + 8 * q^77 - 16 * q^78 + 112 * q^80 - 16 * q^82 + 32 * q^86 - 168 * q^88 - 16 * q^89 + 144 * q^91 - 176 * q^92 + 48 * q^93 + 48 * q^97 - 112 * q^99

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