LMFDB - Embedded newform 294.2.j.a.251.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,2,Mod(41,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.41"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.j (of order $14$, degree $6$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.14
Character	$\chi$	$=$	294.251
Dual form			294.2.j.a.41.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.781831 + 0.623490i) q^{2} +(-0.913887 + 1.47133i) q^{3} +(0.222521 + 0.974928i) q^{4} +(3.14996 + 1.51694i) q^{5} +(-1.63186 + 0.580532i) q^{6} +(2.47808 - 0.926885i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-1.32962 - 2.68926i) q^{9} +(1.51694 + 3.14996i) q^{10} +(-1.47826 - 1.17888i) q^{11} +(-1.63780 - 0.563572i) q^{12} +(-0.731696 - 0.583508i) q^{13} +(2.51534 + 0.820391i) q^{14} +(-5.11062 + 3.24831i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-1.24123 + 5.43819i) q^{17} +(0.637185 - 2.93155i) q^{18} -6.71507i q^{19} +(-0.777975 + 3.40853i) q^{20} +(-0.900933 + 4.49314i) q^{21} +(-0.420736 - 1.84336i) q^{22} +(-5.84179 + 1.33335i) q^{23} +(-0.929101 - 1.46177i) q^{24} +(4.50368 + 5.64743i) q^{25} +(-0.208252 - 0.912410i) q^{26} +(5.17191 + 0.501368i) q^{27} +(1.45507 + 2.20970i) q^{28} +(-0.519155 - 0.118494i) q^{29} +(-6.02094 - 0.646788i) q^{30} -5.34122i q^{31} +(-0.974928 - 0.222521i) q^{32} +(3.08548 - 1.09765i) q^{33} +(-4.36109 + 3.47785i) q^{34} +(9.21188 + 0.839452i) q^{35} +(2.32596 - 1.89470i) q^{36} +(0.612916 - 2.68536i) q^{37} +(4.18678 - 5.25005i) q^{38} +(1.52722 - 0.543305i) q^{39} +(-2.73343 + 2.17984i) q^{40} +(1.61381 + 0.777171i) q^{41} +(-3.50581 + 2.95116i) q^{42} +(-9.41518 + 4.53411i) q^{43} +(0.820375 - 1.70353i) q^{44} +(-0.108807 - 10.4880i) q^{45} +(-5.39863 - 2.59984i) q^{46} +(7.08465 - 8.88387i) q^{47} +(0.184998 - 1.72214i) q^{48} +(5.28177 - 4.59379i) q^{49} +7.22334i q^{50} +(-6.86702 - 6.79615i) q^{51} +(0.406061 - 0.843194i) q^{52} +(5.46957 - 1.24839i) q^{53} +(3.73096 + 3.61662i) q^{54} +(-2.86818 - 5.95585i) q^{55} +(-0.240105 + 2.63483i) q^{56} +(9.88008 + 6.13682i) q^{57} +(-0.332012 - 0.416330i) q^{58} +(-0.981235 + 0.472538i) q^{59} +(-4.30409 - 4.25967i) q^{60} +(4.27189 + 0.975031i) q^{61} +(3.33020 - 4.17593i) q^{62} +(-5.78754 - 5.43179i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-1.41966 - 2.94796i) q^{65} +(3.09670 + 1.06559i) q^{66} -9.15032 q^{67} -5.57804 q^{68} +(3.37694 - 9.81373i) q^{69} +(6.67875 + 6.39982i) q^{70} +(-5.70374 + 1.30184i) q^{71} +(2.99984 - 0.0311217i) q^{72} +(1.01364 - 0.808350i) q^{73} +(2.15349 - 1.71735i) q^{74} +(-12.4251 + 1.46528i) q^{75} +(6.54671 - 1.49424i) q^{76} +(-4.75594 - 1.55117i) q^{77} +(1.53277 + 0.527433i) q^{78} +15.3224 q^{79} -3.49619 q^{80} +(-5.46422 + 7.15139i) q^{81} +(0.777171 + 1.61381i) q^{82} +(9.92846 + 12.4499i) q^{83} +(-4.58097 + 0.121473i) q^{84} +(-12.1592 + 15.2472i) q^{85} +(-10.1881 - 2.32536i) q^{86} +(0.648792 - 0.655558i) q^{87} +(1.70353 - 0.820375i) q^{88} +(6.59006 + 8.26368i) q^{89} +(6.45409 - 8.26769i) q^{90} +(-2.35405 - 0.767783i) q^{91} +(-2.59984 - 5.39863i) q^{92} +(7.85869 + 4.88127i) q^{93} +(11.0780 - 2.52848i) q^{94} +(10.1864 - 21.1522i) q^{95} +(1.21838 - 1.23108i) q^{96} +7.02844i q^{97} +(6.99364 - 0.298440i) q^{98} +(-1.20477 + 5.54289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{9}{14}\right)$

Coefficient data

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

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

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

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$	−0.913887	+	1.47133i	−0.527633	+	0.849472i
$3$	−0.913887	+	1.47133i	−0.527633	+	0.849472i
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	3.14996	+	1.51694i	1.40870	+	0.678396i	0.974907	−	0.222614i	$-0.0714591\pi$
$5$	3.14996	+	1.51694i	1.40870	+	0.678396i	0.433797	+	0.901010i	$0.357173\pi$
$6$	−1.63186	+	0.580532i	−0.666206	+	0.237001i
$7$	2.47808	−	0.926885i	0.936627	−	0.350329i
$7$	2.47808	−	0.926885i	0.936627	−	0.350329i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$	−1.32962	−	2.68926i	−0.443207	−	0.896419i
$10$	1.51694	+	3.14996i	0.479698	+	0.996104i
$11$	−1.47826	−	1.17888i	−0.445713	−	0.355445i	0.374767	−	0.927119i	$-0.377723\pi$
$11$	−1.47826	−	1.17888i	−0.445713	−	0.355445i	−0.820481	+	0.571674i	$0.806294\pi$
$12$	−1.63780	−	0.563572i	−0.472792	−	0.162689i
$13$	−0.731696	−	0.583508i	−0.202936	−	0.161836i	0.516749	−	0.856137i	$-0.327142\pi$
$13$	−0.731696	−	0.583508i	−0.202936	−	0.161836i	−0.719685	+	0.694301i	$0.755714\pi$
$14$	2.51534	+	0.820391i	0.672254	+	0.219259i
$15$	−5.11062	+	3.24831i	−1.31956	+	0.838711i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−1.24123	+	5.43819i	−0.301043	+	1.31895i	0.567513	+	0.823364i	$0.307906\pi$
$17$	−1.24123	+	5.43819i	−0.301043	+	1.31895i	−0.868556	+	0.495591i	$0.834952\pi$
$18$	0.637185	−	2.93155i	0.150186	−	0.690973i
$19$		−	6.71507i		−	1.54054i	−0.637716	−	0.770271i	$-0.720121\pi$
$19$		−	6.71507i		−	1.54054i	0.637716	−	0.770271i	$-0.279879\pi$
$20$	−0.777975	+	3.40853i	−0.173961	+	0.762171i
$21$	−0.900933	+	4.49314i	−0.196600	+	0.980484i
$22$	−0.420736	−	1.84336i	−0.0897012	−	0.393007i
$23$	−5.84179	+	1.33335i	−1.21810	+	0.278023i	−0.782806	−	0.622266i	$-0.786212\pi$
$23$	−5.84179	+	1.33335i	−1.21810	+	0.278023i	−0.435292	+	0.900289i	$0.643355\pi$
$24$	−0.929101	−	1.46177i	−0.189652	−	0.298382i
$25$	4.50368	+	5.64743i	0.900736	+	1.12949i
$26$	−0.208252	−	0.912410i	−0.0408415	−	0.178938i
$27$	5.17191	+	0.501368i	0.995334	+	0.0964883i
$28$	1.45507	+	2.20970i	0.274982	+	0.417594i
$29$	−0.519155	−	0.118494i	−0.0964047	−	0.0220037i	0.174046	−	0.984737i	$-0.444316\pi$
$29$	−0.519155	−	0.118494i	−0.0964047	−	0.0220037i	−0.270451	+	0.962734i	$0.587173\pi$
$30$	−6.02094	−	0.646788i	−1.09927	−	0.118087i
$31$		−	5.34122i		−	0.959311i	−0.877457	−	0.479656i	$-0.840762\pi$
$31$		−	5.34122i		−	0.959311i	0.877457	−	0.479656i	$-0.159238\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$	3.08548	−	1.09765i	0.537113	−	0.191077i
$34$	−4.36109	+	3.47785i	−0.747921	+	0.596447i
$35$	9.21188	+	0.839452i	1.55709	+	0.141893i
$36$	2.32596	−	1.89470i	0.387661	−	0.315783i
$37$	0.612916	−	2.68536i	0.100763	−	0.441470i	−0.899229	−	0.437478i	$-0.855872\pi$
$37$	0.612916	−	2.68536i	0.100763	−	0.441470i	0.999992	−	0.00399278i	$-0.00127095\pi$
$38$	4.18678	−	5.25005i	0.679185	−	0.851671i
$39$	1.52722	−	0.543305i	0.244551	−	0.0869985i
$40$	−2.73343	+	2.17984i	−0.432193	+	0.344663i
$41$	1.61381	+	0.777171i	0.252035	+	0.121374i	0.555636	−	0.831425i	$-0.312475\pi$
$41$	1.61381	+	0.777171i	0.252035	+	0.121374i	−0.303601	+	0.952799i	$0.598189\pi$
$42$	−3.50581	+	2.95116i	−0.540958	+	0.455373i
$43$	−9.41518	+	4.53411i	−1.43580	+	0.691445i	−0.980066	−	0.198670i	$-0.936338\pi$
$43$	−9.41518	+	4.53411i	−1.43580	+	0.691445i	−0.455735	+	0.890116i	$0.650623\pi$
$44$	0.820375	−	1.70353i	0.123676	−	0.256816i
$45$	−0.108807	−	10.4880i	−0.0162200	−	1.56346i
$46$	−5.39863	−	2.59984i	−0.795984	−	0.383326i
$47$	7.08465	−	8.88387i	1.03340	−	1.29584i	0.0791429	−	0.996863i	$-0.474782\pi$
$47$	7.08465	−	8.88387i	1.03340	−	1.29584i	0.954259	−	0.298982i	$-0.0966469\pi$
$48$	0.184998	−	1.72214i	0.0267021	−	0.248570i
$49$	5.28177	−	4.59379i	0.754539	−	0.656256i
$50$			7.22334i			1.02153i
$51$	−6.86702	−	6.79615i	−0.961576	−	0.951652i
$52$	0.406061	−	0.843194i	0.0563105	−	0.116930i
$53$	5.46957	−	1.24839i	0.751304	−	0.171480i	0.170313	−	0.985390i	$-0.445522\pi$
$53$	5.46957	−	1.24839i	0.751304	−	0.171480i	0.580991	+	0.813910i	$0.302665\pi$
$54$	3.73096	+	3.61662i	0.507720	+	0.492159i
$55$	−2.86818	−	5.95585i	−0.386746	−	0.803086i
$56$	−0.240105	+	2.63483i	−0.0320854	+	0.352094i
$57$	9.88008	+	6.13682i	1.30865	+	0.812841i
$58$	−0.332012	−	0.416330i	−0.0435953	−	0.0546668i
$59$	−0.981235	+	0.472538i	−0.127746	+	0.0615192i	−0.496665	−	0.867942i	$-0.665442\pi$
$59$	−0.981235	+	0.472538i	−0.127746	+	0.0615192i	0.368919	+	0.929462i	$0.379728\pi$
$60$	−4.30409	−	4.25967i	−0.555656	−	0.549921i
$61$	4.27189	+	0.975031i	0.546960	+	0.124840i	0.487067	−	0.873365i	$-0.338067\pi$
$61$	4.27189	+	0.975031i	0.546960	+	0.124840i	0.0598930	+	0.998205i	$0.480924\pi$
$62$	3.33020	−	4.17593i	0.422935	−	0.530344i
$63$	−5.78754	−	5.43179i	−0.729161	−	0.684342i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−1.41966	−	2.94796i	−0.176088	−	0.365650i
$66$	3.09670	+	1.06559i	0.381178	+	0.131165i
$67$	−9.15032			−1.11789			−0.558945	−	0.829205i	$-0.688794\pi$
$67$	−9.15032			−1.11789			−0.558945	+	0.829205i	$0.688794\pi$
$68$	−5.57804			−0.676437
$69$	3.37694	−	9.81373i	0.406536	−	1.18143i
$70$	6.67875	+	6.39982i	0.798263	+	0.764925i
$71$	−5.70374	+	1.30184i	−0.676909	+	0.154500i	−0.547136	−	0.837044i	$-0.684282\pi$
$71$	−5.70374	+	1.30184i	−0.676909	+	0.154500i	−0.129773	+	0.991544i	$0.541425\pi$
$72$	2.99984	−	0.0311217i	0.353534	−	0.00366773i
$73$	1.01364	−	0.808350i	0.118637	−	0.0946102i	−0.562374	−	0.826883i	$-0.690112\pi$
$73$	1.01364	−	0.808350i	0.118637	−	0.0946102i	0.681011	+	0.732273i	$0.261540\pi$
$74$	2.15349	−	1.71735i	0.250338	−	0.199638i
$75$	−12.4251	+	1.46528i	−1.43473	+	0.169196i
$76$	6.54671	−	1.49424i	0.750959	−	0.171402i
$77$	−4.75594	−	1.55117i	−0.541990	−	0.176772i
$78$	1.53277	+	0.527433i	0.173553	+	0.0597200i
$79$	15.3224			1.72390			0.861950	−	0.506993i	$-0.169243\pi$
$79$	15.3224			1.72390			0.861950	+	0.506993i	$0.169243\pi$
$80$	−3.49619			−0.390886
$81$	−5.46422	+	7.15139i	−0.607135	+	0.794599i
$82$	0.777171	+	1.61381i	0.0858242	+	0.178216i
$83$	9.92846	+	12.4499i	1.08979	+	1.36655i	0.924886	+	0.380244i	$0.124160\pi$
$83$	9.92846	+	12.4499i	1.08979	+	1.36655i	0.164904	+	0.986310i	$0.447269\pi$
$84$	−4.58097	+	0.121473i	−0.499824	+	0.0132538i
$85$	−12.1592	+	15.2472i	−1.31885	+	1.65379i
$86$	−10.1881	−	2.32536i	−1.09861	−	0.250750i
$87$	0.648792	−	0.655558i	0.0695578	−	0.0702832i
$88$	1.70353	−	0.820375i	0.181596	−	0.0874522i
$89$	6.59006	+	8.26368i	0.698545	+	0.875948i	0.996914	−	0.0785028i	$-0.0250140\pi$
$89$	6.59006	+	8.26368i	0.698545	+	0.875948i	−0.298369	+	0.954451i	$0.596443\pi$
$90$	6.45409	−	8.26769i	0.680321	−	0.871491i
$91$	−2.35405	−	0.767783i	−0.246771	−	0.0804855i
$92$	−2.59984	−	5.39863i	−0.271052	−	0.562846i
$93$	7.85869	+	4.88127i	0.814908	+	0.506164i
$94$	11.0780	−	2.52848i	1.14261	−	0.260793i
$95$	10.1864	−	21.1522i	1.04510	−	2.17017i
$96$	1.21838	−	1.23108i	0.124350	−	0.125647i
$97$			7.02844i			0.713630i	0.934175	+	0.356815i	$0.116137\pi$
$97$			7.02844i			0.713630i	−0.934175	+	0.356815i	$0.883863\pi$
$98$	6.99364	−	0.298440i	0.706464	−	0.0301470i
$99$	−1.20477	+	5.54289i	−0.121084	+	0.557082i
$100$	−4.50368	+	5.64743i	−0.450368	+	0.564743i
$101$	−14.8915	−	7.17135i	−1.48176	−	0.713576i	−0.493982	−	0.869472i	$-0.664459\pi$
$101$	−14.8915	−	7.17135i	−1.48176	−	0.713576i	−0.987773	+	0.155896i	$0.950174\pi$
$102$	−1.13152	−	9.59497i	−0.112038	−	0.950043i
$103$	0.0466493	−	0.0968682i	0.00459649	−	0.00954471i	−0.898658	−	0.438650i	$-0.855457\pi$
$103$	0.0466493	−	0.0968682i	0.00459649	−	0.00954471i	0.903254	+	0.429105i	$0.141171\pi$
$104$	0.843194	−	0.406061i	0.0826819	−	0.0398175i
$105$	−9.65373	+	12.7865i	−0.942107	+	1.24784i
$106$	5.05464	+	2.43419i	0.490951	+	0.236429i
$107$	−9.83286	+	7.84144i	−0.950578	+	0.758061i	−0.970340	−	0.241744i	$-0.922281\pi$
$107$	−9.83286	+	7.84144i	−0.950578	+	0.758061i	0.0197619	+	0.999805i	$0.493709\pi$
$108$	0.662060	+	5.15380i	0.0637068	+	0.495925i
$109$	−2.56680	+	3.21867i	−0.245855	+	0.308292i	−0.889413	−	0.457105i	$-0.848886\pi$
$109$	−2.56680	+	3.21867i	−0.245855	+	0.308292i	0.643558	+	0.765398i	$0.277458\pi$
$110$	1.47097	−	6.44475i	0.140252	−	0.614483i
$111$	3.39091	+	3.35592i	0.321851	+	0.318530i
$112$	−1.83051	+	1.91029i	−0.172967	+	0.180506i
$113$	0.409927	−	0.326906i	0.0385627	−	0.0307528i	−0.604019	−	0.796970i	$-0.706435\pi$
$113$	0.409927	−	0.326906i	0.0385627	−	0.0307528i	0.642582	+	0.766217i	$0.277863\pi$
$114$	3.89832	+	10.9581i	0.365111	+	1.02632i
$115$	−20.4240	−	4.66165i	−1.90455	−	0.434701i
$116$		−	0.532506i		−	0.0494419i
$117$	−0.596326	+	2.74356i	−0.0551303	+	0.253643i
$118$	−1.06178	−	0.242345i	−0.0977451	−	0.0223097i
$119$	1.96470	+	14.6268i	0.180104	+	1.34083i
$120$	−0.709213	−	6.01390i	−0.0647420	−	0.548992i
$121$	−1.65222	−	7.23883i	−0.150201	−	0.658075i
$122$	2.73198	+	3.42579i	0.247342	+	0.310156i
$123$	−2.61832	+	1.66420i	−0.236086	+	0.150056i
$124$	5.20730	−	1.18853i	0.467630	−	0.106733i
$125$	1.72970	+	7.57832i	0.154709	+	0.677826i
$126$	−1.13821	−	7.85522i	−0.101400	−	0.699799i
$127$	2.25720	−	9.88945i	0.200294	−	0.877547i	−0.770463	−	0.637484i	$-0.779975\pi$
$127$	2.25720	−	9.88945i	0.200294	−	0.877547i	0.970758	−	0.240062i	$-0.0771678\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.93324	−	17.9965i	0.170212	−	1.58450i
$130$	0.728087	−	3.18996i	0.0638575	−	0.279778i
$131$	−4.46922	+	2.15226i	−0.390477	+	0.188044i	−0.618813	−	0.785539i	$-0.712386\pi$
$131$	−4.46922	+	2.15226i	−0.390477	+	0.188044i	0.228335	+	0.973583i	$0.426672\pi$
$132$	1.75672	+	2.76387i	0.152903	+	0.240564i
$133$	−6.22410	−	16.6405i	−0.539698	−	1.44291i
$134$	−7.15401	−	5.70513i	−0.618012	−	0.492848i
$135$	15.5307	+	9.42476i	1.33667	+	0.811154i
$136$	−4.36109	−	3.47785i	−0.373960	−	0.298223i
$137$	0.306633	+	0.636730i	0.0261974	+	0.0543995i	0.913657	−	0.406486i	$-0.133246\pi$
$137$	0.306633	+	0.636730i	0.0261974	+	0.0543995i	−0.887459	+	0.460886i	$0.847532\pi$
$138$	8.75896	−	5.56720i	0.745612	−	0.473911i
$139$	2.79825	−	5.81062i	0.237344	−	0.492851i	−0.747942	−	0.663765i	$-0.768958\pi$
$139$	2.79825	−	5.81062i	0.237344	−	0.492851i	0.985286	+	0.170914i	$0.0546720\pi$
$140$	1.23143	+	9.16771i	0.104075	+	0.774813i
$141$	6.59653	+	18.5427i	0.555528	+	1.56158i
$142$	−5.27105	−	2.53840i	−0.442336	−	0.213018i
$143$	0.393756	+	1.72516i	0.0329275	+	0.144265i
$144$	2.36477	+	1.84604i	0.197064	+	0.153836i
$145$	−1.45557	−	1.16078i	−0.120878	−	0.0963973i
$146$	1.29649			0.107299
$147$	1.93204	+	11.9694i	0.159352	+	0.987222i
$148$	2.75442			0.226412
$149$	−8.44769	−	6.73681i	−0.692062	−	0.551901i	0.213067	−	0.977038i	$-0.431655\pi$
$149$	−8.44769	−	6.73681i	−0.692062	−	0.551901i	−0.905129	+	0.425137i	$0.860226\pi$
$150$	−10.6279	−	6.60132i	−0.867765	−	0.538995i
$151$	−0.671380	−	2.94151i	−0.0546361	−	0.239377i	0.940235	−	0.340526i	$-0.110605\pi$
$151$	−0.671380	−	2.94151i	−0.0546361	−	0.239377i	−0.994871	+	0.101149i	$0.967748\pi$
$152$	6.05007	+	2.91356i	0.490725	+	0.236321i
$153$	16.2751	−	3.89274i	1.31576	−	0.314709i
$154$	−2.75120	−	4.17803i	−0.221698	−	0.336676i
$155$	8.10231	−	16.8246i	0.650793	−	1.35139i
$156$	0.869522	+	1.36803i	0.0696175	+	0.109530i
$157$	9.20064	+	19.1053i	0.734291	+	1.52477i	0.847264	+	0.531172i	$0.178248\pi$
$157$	9.20064	+	19.1053i	0.734291	+	1.52477i	−0.112973	+	0.993598i	$0.536037\pi$
$158$	11.9795	+	9.55333i	0.953038	+	0.760022i
$159$	−3.16177	+	9.18843i	−0.250745	+	0.728690i
$160$	−2.73343	−	2.17984i	−0.216097	−	0.172331i
$161$	−13.2406	+	8.71882i	−1.04350	+	0.687139i
$162$	−8.73091	+	2.18430i	−0.685965	+	0.171615i
$163$	−6.52790	+	3.14367i	−0.511305	+	0.246231i	−0.671702	−	0.740821i	$-0.734437\pi$
$163$	−6.52790	+	3.14367i	−0.511305	+	0.246231i	0.160398	+	0.987052i	$0.448722\pi$
$164$	−0.398579	+	1.74629i	−0.0311238	+	0.136362i
$165$	11.3842	+	1.22293i	0.886260	+	0.0952047i
$166$			15.9240i			1.23594i
$167$	0.192314	−	0.842585i	0.0148817	−	0.0652012i	−0.966942	−	0.254997i	$-0.917925\pi$
$167$	0.192314	−	0.842585i	0.0148817	−	0.0652012i	0.981824	+	0.189796i	$0.0607826\pi$
$168$	−3.65728	−	2.76121i	−0.282165	−	0.213032i
$169$	−2.69787	−	11.8202i	−0.207529	−	0.909243i
$170$	−19.0129	+	4.33958i	−1.45823	+	0.332831i
$171$	−18.0586	+	8.92850i	−1.38097	+	0.682779i
$172$	−6.51550	−	8.17018i	−0.496803	−	0.622971i
$173$	−4.85722	−	21.2809i	−0.369288	−	1.61795i	−0.728740	−	0.684791i	$-0.759894\pi$
$173$	−4.85722	−	21.2809i	−0.369288	−	1.61795i	0.359452	−	0.933163i	$-0.382964\pi$
$174$	0.915980	−	0.108021i	0.0694403	−	0.00818902i
$175$	16.3950	+	9.82041i	1.23935	+	0.742353i
$176$	1.84336	+	0.420736i	0.138949	+	0.0317142i
$177$	0.201479	−	1.87557i	0.0151441	−	0.140976i
$178$			10.5696i			0.792228i
$179$	−4.81319	−	1.09858i	−0.359755	−	0.0821116i	0.0388234	−	0.999246i	$-0.487639\pi$
$179$	−4.81319	−	1.09858i	−0.359755	−	0.0821116i	−0.398578	+	0.917134i	$0.630496\pi$
$180$	10.2008	−	2.43988i	0.760325	−	0.181858i
$181$	−18.5737	+	14.8120i	−1.38057	+	1.10097i	−0.397528	+	0.917590i	$0.630132\pi$
$181$	−18.5737	+	14.8120i	−1.38057	+	1.10097i	−0.983043	+	0.183378i	$0.941297\pi$
$182$	−1.36176	−	2.06800i	−0.100941	−	0.153290i
$183$	−5.33862	+	5.39429i	−0.394642	+	0.398757i
$184$	1.33335	−	5.84179i	0.0982959	−	0.430663i
$185$	6.00419	−	7.52901i	0.441437	−	0.553544i
$186$	3.10075	+	8.71615i	0.227358	+	0.639099i
$187$	8.24582	−	6.57582i	0.602994	−	0.480872i
$188$	10.2376	+	4.93017i	0.746654	+	0.359570i
$189$	13.2811	−	3.55133i	0.966059	−	0.258321i
$190$	21.1522	−	10.1864i	1.53454	−	0.738996i
$191$	−6.99491	+	14.5251i	−0.506134	+	1.05100i	0.478777	+	0.877936i	$0.341080\pi$
$191$	−6.99491	+	14.5251i	−0.506134	+	1.05100i	−0.984911	+	0.173061i	$0.944634\pi$
$192$	1.72013	−	0.202853i	0.124140	−	0.0146397i
$193$	10.4512	+	5.03302i	0.752292	+	0.362285i	0.770408	−	0.637551i	$-0.220053\pi$
$193$	10.4512	+	5.03302i	0.752292	+	0.362285i	−0.0181163	+	0.999836i	$0.505767\pi$
$194$	−4.38216	+	5.49506i	−0.314621	+	0.394522i
$195$	5.63484	+	0.605312i	0.403519	+	0.0433473i
$196$	5.65392	+	4.12713i	0.403851	+	0.294795i
$197$			15.3394i			1.09289i	0.837497	+	0.546443i	$0.184018\pi$
$197$			15.3394i			1.09289i	−0.837497	+	0.546443i	$0.815982\pi$
$198$	−4.39786	+	3.58244i	−0.312543	+	0.254593i
$199$	−10.9339	+	22.7045i	−0.775085	+	1.60948i	0.0175977	+	0.999845i	$0.494398\pi$
$199$	−10.9339	+	22.7045i	−0.775085	+	1.60948i	−0.792682	+	0.609635i	$0.791316\pi$
$200$	−7.04223	+	1.60734i	−0.497961	+	0.113656i
$201$	8.36236	−	13.4631i	0.589835	−	0.949616i
$202$	−7.17135	−	14.8915i	−0.504574	−	1.04776i
$203$	−1.39634	+	0.187560i	−0.0980037	+	0.0131641i
$204$	5.09770	−	8.20714i	0.356911	−	0.574615i
$205$	3.90452	+	4.89611i	0.272703	+	0.341959i
$206$	0.0968682	−	0.0466493i	0.00674913	−	0.00325021i
$207$	11.3531	+	13.9372i	0.789094	+	0.968705i
$208$	0.912410	+	0.208252i	0.0632643	+	0.0144397i
$209$	−7.91624	+	9.92665i	−0.547577	+	0.686640i
$210$	−15.5199	+	3.97792i	−1.07097	+	0.274503i
$211$	5.21715	+	6.54210i	0.359163	+	0.450377i	0.928281	−	0.371880i	$-0.121287\pi$
$211$	5.21715	+	6.54210i	0.359163	+	0.450377i	−0.569118	+	0.822256i	$0.692715\pi$
$212$	2.43419	+	5.05464i	0.167181	+	0.347154i
$213$	3.29714	−	9.58181i	0.225916	−	0.656535i
$214$	−12.5767			−0.859725
$215$	−36.5354			−2.49169
$216$	−2.69572	+	4.44219i	−0.183421	+	0.302253i
$217$	−4.95069	−	13.2360i	−0.336075	−	0.898516i
$218$	−4.01361	+	0.916081i	−0.271836	+	0.0620448i
$219$	0.262998	+	2.23014i	0.0177717	+	0.150699i
$220$	5.16829	−	4.12157i	0.348446	−	0.277876i
$221$	4.08143	−	3.25483i	0.274547	−	0.218944i
$222$	0.558743	+	4.73796i	0.0375004	+	0.317991i
$223$	−0.338200	+	0.0771919i	−0.0226475	+	0.00516915i	−0.233830	−	0.972278i	$-0.575126\pi$
$223$	−0.338200	+	0.0771919i	−0.0226475	+	0.00516915i	0.211182	+	0.977447i	$0.432269\pi$
$224$	−2.62220	+	0.352221i	−0.175203	+	0.0235337i
$225$	9.19922	−	19.6205i	0.613281	−	1.30803i
$226$	0.524317			0.0348770
$227$	12.4355			0.825373			0.412687	−	0.910873i	$-0.364590\pi$
$227$	12.4355			0.825373			0.412687	+	0.910873i	$0.364590\pi$
$228$	−3.78443	+	10.9979i	−0.250630	+	0.728356i
$229$	−1.56484	−	3.24941i	−0.103407	−	0.214727i	0.842845	−	0.538156i	$-0.180879\pi$
$229$	−1.56484	−	3.24941i	−0.103407	−	0.214727i	−0.946253	+	0.323428i	$0.895165\pi$
$230$	−13.0616	−	16.3788i	−0.861259	−	1.07998i
$231$	6.62867	−	5.57996i	0.436135	−	0.367134i
$232$	0.332012	−	0.416330i	0.0217977	−	0.0273334i
$233$	12.4633	+	2.84467i	0.816499	+	0.186361i	0.610321	−	0.792154i	$-0.291040\pi$
$233$	12.4633	+	2.84467i	0.816499	+	0.186361i	0.206178	+	0.978515i	$0.433897\pi$
$234$	−2.17681	+	1.77320i	−0.142303	+	0.115918i
$235$	35.7926	−	17.2368i	2.33485	−	1.12441i
$236$	−0.679036	−	0.851484i	−0.0442015	−	0.0554269i
$237$	−14.0029	+	22.5442i	−0.909586	+	1.46441i
$238$	−7.58356	+	12.6606i	−0.491570	+	0.820667i
$239$	−10.5814	−	21.9726i	−0.684457	−	1.42129i	−0.896060	−	0.443933i	$-0.853583\pi$
$239$	−10.5814	−	21.9726i	−0.684457	−	1.42129i	0.211603	−	0.977356i	$-0.432132\pi$
$240$	3.19512	−	5.14405i	0.206244	−	0.332047i
$241$	0.779823	−	0.177990i	0.0502328	−	0.0114653i	−0.197331	−	0.980337i	$-0.563227\pi$
$241$	0.779823	−	0.177990i	0.0502328	−	0.0114653i	0.247563	+	0.968872i	$0.420370\pi$
$242$	3.22158	−	6.68968i	0.207091	−	0.430029i
$243$	−5.52837	−	14.5752i	−0.354645	−	0.935001i
$244$			4.38175i			0.280513i
$245$	23.6059	−	6.45812i	1.50812	−	0.412594i
$246$	−3.08470	−	0.331368i	−0.196673	−	0.0211272i
$247$	−3.91830	+	4.91339i	−0.249315	+	0.312632i
$248$	4.81227	+	2.31747i	0.305580	+	0.147159i
$249$	−27.3914	+	3.23024i	−1.73586	+	0.204708i
$250$	−3.37267	+	7.00342i	−0.213306	+	0.442935i
$251$	−17.4679	+	8.41209i	−1.10256	+	0.530967i	−0.894464	−	0.447141i	$-0.852442\pi$
$251$	−17.4679	+	8.41209i	−1.10256	+	0.530967i	−0.208100	+	0.978108i	$0.566728\pi$
$252$	4.00776	−	6.85112i	0.252465	−	0.431580i
$253$	10.2076	+	4.91570i	0.641744	+	0.309048i
$254$	7.93072	−	6.32454i	0.497618	−	0.396837i
$255$	−11.3215	−	31.8245i	−0.708979	−	1.99292i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	5.63841	−	24.7035i	0.351714	−	1.54096i	−0.421507	−	0.906825i	$-0.638499\pi$
$257$	5.63841	−	24.7035i	0.351714	−	1.54096i	0.773222	−	0.634136i	$-0.218644\pi$
$258$	12.7321	−	12.8649i	0.792666	−	0.800932i
$259$	−0.970164	−	7.22264i	−0.0602830	−	0.448793i
$260$	2.55815	−	2.04005i	0.158650	−	0.126519i
$261$	0.371619	+	1.55369i	0.0230026	+	0.0961712i
$262$	−4.83609	−	1.10381i	−0.298775	−	0.0681933i
$263$		−	15.8937i		−	0.980048i	−0.871709	−	0.490024i	$-0.836988\pi$
$263$		−	15.8937i		−	0.980048i	0.871709	−	0.490024i	$-0.163012\pi$
$264$	−0.349788	+	3.25618i	−0.0215280	+	0.200404i
$265$	19.1227	+	4.36462i	1.17470	+	0.268117i
$266$	5.50898	−	16.8907i	0.337777	−	1.03564i
$267$	−18.1812	+	2.14409i	−1.11267	+	0.131216i
$268$	−2.03614	−	8.92090i	−0.124377	−	0.544931i
$269$	2.62574	+	3.29258i	0.160094	+	0.200752i	0.855408	−	0.517954i	$-0.173306\pi$
$269$	2.62574	+	3.29258i	0.160094	+	0.200752i	−0.695314	+	0.718706i	$0.744735\pi$
$270$	6.26618	+	17.0518i	0.381348	+	1.03774i
$271$	9.72437	−	2.21952i	0.590714	−	0.134827i	0.0832931	−	0.996525i	$-0.473456\pi$
$271$	9.72437	−	2.21952i	0.590714	−	0.134827i	0.507421	+	0.861699i	$0.330599\pi$
$272$	−1.24123	−	5.43819i	−0.0752607	−	0.329739i
$273$	3.28099	−	2.76191i	0.198575	−	0.167159i
$274$	−0.157259	+	0.688998i	−0.00950038	+	0.0416239i
$275$		−	13.6577i		−	0.823589i
$276$	10.3191	+	1.10851i	0.621138	+	0.0667246i
$277$	3.14104	−	13.7618i	0.188727	−	0.826866i	−0.788562	−	0.614955i	$-0.789174\pi$
$277$	3.14104	−	13.7618i	0.188727	−	0.826866i	0.977289	−	0.211911i	$-0.0679687\pi$
$278$	5.81062	−	2.79825i	0.348498	−	0.167828i
$279$	−14.3639	+	7.10180i	−0.859945	+	0.425173i
$280$	−4.75320	+	7.93539i	−0.284058	+	0.474230i
$281$	−14.2433	−	11.3587i	−0.849684	−	0.677600i	0.0985641	−	0.995131i	$-0.468575\pi$
$281$	−14.2433	−	11.3587i	−0.849684	−	0.677600i	−0.948248	+	0.317530i	$0.897146\pi$
$282$	−6.40381	+	18.6101i	−0.381341	+	1.10822i
$283$	5.75856	+	4.59230i	0.342311	+	0.272984i	0.779522	−	0.626375i	$-0.215462\pi$
$283$	5.75856	+	4.59230i	0.342311	+	0.272984i	−0.437211	+	0.899359i	$0.644034\pi$
$284$	−2.53840	−	5.27105i	−0.150626	−	0.312779i
$285$	21.8127	+	34.3182i	1.29207	+	2.03283i
$286$	−0.767768	+	1.59429i	−0.0453990	+	0.0942721i
$287$	4.71951	+	0.430075i	0.278584	+	0.0253865i
$288$	0.697868	+	2.91770i	0.0411223	+	0.171927i
$289$	−12.7168	−	6.12408i	−0.748046	−	0.360240i
$290$	−0.414277	−	1.81506i	−0.0243272	−	0.106584i
$291$	−10.3412	−	6.42320i	−0.606209	−	0.376535i
$292$	1.01364	+	0.808350i	0.0593187	+	0.0473051i
$293$	6.26961			0.366274			0.183137	−	0.983087i	$-0.441375\pi$
$293$	6.26961			0.366274			0.183137	+	0.983087i	$0.441375\pi$
$294$	−5.95229	+	10.5627i	−0.347145	+	0.616028i
$295$	−3.80766			−0.221691
$296$	2.15349	+	1.71735i	0.125169	+	0.0998191i
$297$	−7.05439	−	6.83819i	−0.409337	−	0.396792i
$298$	−2.40434	−	10.5341i	−0.139280	−	0.610224i
$299$	5.05244	+	2.43313i	0.292190	+	0.140711i
$300$	−4.19338	−	11.7875i	−0.242105	−	0.680552i
$301$	−19.1290	+	19.9627i	−1.10258	+	1.15063i
$302$	1.30909	−	2.71836i	0.0753299	−	0.156424i
$303$	24.1605	−	15.3564i	1.38799	−	0.882205i
$304$	2.91356	+	6.05007i	0.167104	+	0.346995i
$305$	11.9772	+	9.55151i	0.685813	+	0.546918i
$306$	15.1514	+	7.10387i	0.866150	+	0.406101i
$307$	9.18514	+	7.32491i	0.524224	+	0.418054i	0.849519	−	0.527558i	$-0.176892\pi$
$307$	9.18514	+	7.32491i	0.524224	+	0.418054i	−0.325295	+	0.945612i	$0.605464\pi$
$308$	0.453983	−	4.98187i	0.0258681	−	0.283868i
$309$	0.0998929	+	0.157163i	0.00568271	+	0.00894069i
$310$	16.8246	−	8.10231i	0.955574	−	0.460180i
$311$	−7.19171	+	31.5090i	−0.407805	+	1.78671i	0.186485	+	0.982458i	$0.440290\pi$
$311$	−7.19171	+	31.5090i	−0.407805	+	1.78671i	−0.594289	+	0.804251i	$0.702567\pi$
$312$	−0.173135	+	1.61171i	−0.00980183	+	0.0912451i
$313$			3.86197i			0.218292i	0.994026	+	0.109146i	$0.0348116\pi$
$313$			3.86197i			0.218292i	−0.994026	+	0.109146i	$0.965188\pi$
$314$	−4.71862	+	20.6736i	−0.266287	+	1.16668i
$315$	−9.99080	−	25.8893i	−0.562918	−	1.45869i
$316$	3.40955	+	14.9382i	0.191802	+	0.840339i
$317$	10.8251	−	2.47075i	0.607996	−	0.138771i	0.0925714	−	0.995706i	$-0.470491\pi$
$317$	10.8251	−	2.47075i	0.607996	−	0.138771i	0.515425	+	0.856935i	$0.327634\pi$
$318$	−8.20087	+	5.21247i	−0.459882	+	0.292301i
$319$	0.627759	+	0.787184i	0.0351477	+	0.0440739i
$320$	−0.777975	−	3.40853i	−0.0434901	−	0.190543i
$321$	−2.55122	−	21.6336i	−0.142395	−	1.20747i
$322$	−15.7880	−	1.43871i	−0.879830	−	0.0801764i
$323$	36.5178	+	8.33496i	2.03191	+	0.463769i
$324$	−8.18799	−	3.73588i	−0.454888	−	0.207549i
$325$		−	6.76014i		−	0.374985i
$326$	−7.06376	−	1.61226i	−0.391226	−	0.0892947i
$327$	−2.38995	−	6.71811i	−0.132165	−	0.371512i
$328$	−1.40041	+	1.11679i	−0.0773249	+	0.0616646i
$329$	9.32201	−	28.5816i	0.513939	−	1.57575i
$330$	8.13805	+	8.05406i	0.447985	+	0.443361i
$331$	2.54914	−	11.1685i	0.140113	−	0.613877i	−0.855294	−	0.518144i	$-0.826623\pi$
$331$	2.54914	−	11.1685i	0.140113	−	0.613877i	0.995407	−	0.0957333i	$-0.0305196\pi$
$332$	−9.92846	+	12.4499i	−0.544895	+	0.683277i
$333$	−8.03657	+	1.92222i	−0.440401	+	0.105337i
$334$	0.675700	−	0.538853i	0.0369727	−	0.0294847i
$335$	−28.8231	−	13.8805i	−1.57477	−	0.758372i
$336$	−1.13779	−	4.43908i	−0.0620714	−	0.242172i
$337$	−12.5010	+	6.02017i	−0.680973	+	0.327940i	−0.742194	−	0.670185i	$-0.766215\pi$
$337$	−12.5010	+	6.02017i	−0.680973	+	0.327940i	0.0612209	+	0.998124i	$0.480501\pi$
$338$	5.26047	−	10.9235i	0.286132	−	0.594159i
$339$	0.106359	+	0.901894i	0.00577665	+	0.0489841i
$340$	−17.5706	−	8.46155i	−0.952900	−	0.458892i
$341$	−6.29664	+	7.89573i	−0.340982	+	0.427578i
$342$	−19.6856	−	4.27875i	−1.06447	−	0.231368i
$343$	8.83074	−	16.2794i	0.476815	−	0.879004i
$344$		−	10.4501i		−	0.563429i
$345$	25.5241	−	25.7902i	1.37417	−	1.38850i
$346$	9.47088	−	19.6665i	0.509157	−	1.05728i
$347$	−21.4836	+	4.90348i	−1.15330	+	0.263233i	−0.756072	−	0.654488i	$-0.772884\pi$
$347$	−21.4836	+	4.90348i	−1.15330	+	0.263233i	−0.397226	+	0.917721i	$0.630027\pi$
$348$	0.783492	+	0.486650i	0.0419996	+	0.0260872i
$349$	−1.23408	−	2.56259i	−0.0660588	−	0.137173i	0.865325	−	0.501211i	$-0.167112\pi$
$349$	−1.23408	−	2.56259i	−0.0660588	−	0.137173i	−0.931384	+	0.364038i	$0.881398\pi$
$350$	6.69520	+	17.9000i	0.357874	+	0.956796i
$351$	−3.49171	−	3.38470i	−0.186374	−	0.180662i
$352$	1.17888	+	1.47826i	0.0628343	+	0.0787917i
$353$	−9.16301	+	4.41267i	−0.487698	+	0.234863i	−0.661539	−	0.749911i	$-0.730096\pi$
$353$	−9.16301	+	4.41267i	−0.487698	+	0.234863i	0.173841	+	0.984774i	$0.444382\pi$
$354$	1.32692	−	1.34076i	0.0705250	−	0.0712604i
$355$	−19.9413	−	4.55148i	−1.05838	−	0.241568i
$356$	−6.59006	+	8.26368i	−0.349273	+	0.437974i
$357$	−23.3163	−	10.4765i	−1.23403	−	0.554474i
$358$	−3.07815	−	3.85988i	−0.162685	−	0.204001i
$359$	1.98772	+	4.12754i	0.104908	+	0.217843i	0.946815	−	0.321780i	$-0.104281\pi$
$359$	1.98772	+	4.12754i	0.104908	+	0.217843i	−0.841907	+	0.539623i	$0.818567\pi$
$360$	9.49657	+	4.45254i	0.500513	+	0.234670i
$361$	−26.0922			−1.37327
$362$	−23.7566			−1.24862
$363$	12.1606	+	4.18452i	0.638268	+	0.219630i
$364$	0.224708	−	2.46587i	0.0117779	−	0.129247i
$365$	4.41914	−	1.00864i	0.231308	−	0.0527946i
$366$	−7.53718	+	0.888852i	−0.393975	+	0.0464611i
$367$	12.9265	−	10.3086i	0.674759	−	0.538103i	−0.225071	−	0.974342i	$-0.572261\pi$
$367$	12.9265	−	10.3086i	0.674759	−	0.538103i	0.899830	+	0.436240i	$0.143690\pi$
$368$	4.68475	−	3.73597i	0.244210	−	0.194751i
$369$	−0.0557451	−	5.37330i	−0.00290197	−	0.279723i
$370$	9.38853	−	2.14287i	0.488086	−	0.111402i
$371$	12.3969	−	8.16328i	0.643616	−	0.423817i
$372$	−3.01016	+	8.74784i	−0.156070	+	0.453555i
$373$	−4.86997			−0.252158			−0.126079	−	0.992020i	$-0.540239\pi$
$373$	−4.86997			−0.252158			−0.126079	+	0.992020i	$0.540239\pi$
$374$	10.5468			0.545362
$375$	−12.7310	−	4.38077i	−0.657424	−	0.226222i
$376$	4.93017	+	10.2376i	0.254254	+	0.527964i
$377$	0.310722	+	0.389633i	0.0160030	+	0.0200671i
$378$	12.5978	+	5.50410i	0.647962	+	0.283100i
$379$	−2.11183	+	2.64815i	−0.108477	+	0.136026i	−0.833106	−	0.553113i	$-0.813440\pi$
$379$	−2.11183	+	2.64815i	−0.108477	+	0.136026i	0.724629	+	0.689139i	$0.242011\pi$
$380$	22.8885	+	5.22416i	1.17416	+	0.267994i
$381$	12.4878	+	12.3589i	0.639770	+	0.633167i
$382$	−14.5251	+	6.99491i	−0.743168	+	0.357891i
$383$	20.5992	+	25.8306i	1.05257	+	1.31988i	0.945496	+	0.325633i	$0.105577\pi$
$383$	20.5992	+	25.8306i	1.05257	+	1.31988i	0.107076	+	0.994251i	$0.465851\pi$
$384$	1.47133	+	0.913887i	0.0750835	+	0.0466366i
$385$	−12.6280	−	12.1006i	−0.643581	−	0.616703i
$386$	5.03302	+	10.4512i	0.256174	+	0.531950i
$387$	24.7120	+	19.2912i	1.25618	+	0.980626i
$388$	−6.85223	+	1.56398i	−0.347869	+	0.0793988i
$389$	−4.17306	+	8.66545i	−0.211583	+	0.439356i	−0.979568	−	0.201111i	$-0.935545\pi$
$389$	−4.17306	+	8.66545i	−0.211583	+	0.439356i	0.767986	+	0.640467i	$0.221259\pi$
$390$	4.02809	+	3.98652i	0.203970	+	0.201865i
$391$		−	33.4238i		−	1.69031i
$392$	1.84719	+	6.75188i	0.0932971	+	0.341021i
$393$	0.917674	−	8.54262i	0.0462905	−	0.430918i
$394$	−9.56394	+	11.9928i	−0.481825	+	0.604189i
$395$	48.2648	+	23.2431i	2.42846	+	1.16949i
$396$	−5.67201	+	0.0588440i	−0.285029	+	0.00295702i
$397$	−4.66293	+	9.68268i	−0.234026	+	0.485960i	−0.984599	−	0.174827i	$-0.944063\pi$
$397$	−4.66293	+	9.68268i	−0.234026	+	0.485960i	0.750573	+	0.660787i	$0.229778\pi$
$398$	−22.7045	+	10.9339i	−1.13807	+	0.548068i
$399$	30.1718	+	6.04983i	1.51048	+	0.302870i
$400$	−6.50800	−	3.13409i	−0.325400	−	0.156704i
$401$	−3.93361	+	3.13695i	−0.196435	+	0.156652i	−0.716768	−	0.697312i	$-0.754379\pi$
$401$	−3.93361	+	3.13695i	−0.196435	+	0.156652i	0.520333	+	0.853964i	$0.325808\pi$
$402$	14.9321	−	5.31206i	0.744744	−	0.264941i
$403$	−3.11664	+	3.90815i	−0.155251	+	0.194679i
$404$	3.67789	−	16.1139i	0.182982	−	0.801695i
$405$	−28.0603	+	14.2377i	−1.39433	+	0.707476i
$406$	−1.20864	−	0.723962i	−0.0599839	−	0.0359297i
$407$	−4.07176	+	3.24712i	−0.201830	+	0.160954i
$408$	9.10261	−	3.23824i	0.450646	−	0.160317i
$409$	25.9226	+	5.91665i	1.28179	+	0.292560i	0.808577	−	0.588390i	$-0.200238\pi$
$409$	25.9226	+	5.91665i	1.28179	+	0.292560i	0.473210	+	0.880949i	$0.343095\pi$
$410$			6.26236i			0.309276i
$411$	−1.21707	−	0.130741i	−0.0600335	−	0.00644898i
$412$	0.104820	+	0.0239245i	0.00516411	+	0.00117867i
$413$	−1.99359	+	2.08048i	−0.0980983	+	0.102374i
$414$	0.186482	+	17.9751i	0.00916509	+	0.883428i
$415$	12.3885	+	54.2775i	0.608127	+	2.66438i
$416$	0.583508	+	0.731696i	0.0286088	+	0.0358744i
$417$	5.99206	+	9.42740i	0.293432	+	0.461662i
$418$	−12.3783	+	2.82527i	−0.605444	+	0.138189i
$419$	−1.32239	−	5.79375i	−0.0646028	−	0.283043i	0.932300	−	0.361686i	$-0.117799\pi$
$419$	−1.32239	−	5.79375i	−0.0646028	−	0.283043i	−0.996903	+	0.0786423i	$0.974941\pi$
$420$	−14.6141	−	6.56641i	−0.713096	−	0.320408i
$421$	0.130906	−	0.573538i	0.00637998	−	0.0279525i	−0.971638	−	0.236474i	$-0.924008\pi$
$421$	0.130906	−	0.573538i	0.00637998	−	0.0279525i	0.978018	+	0.208522i	$0.0668652\pi$
$422$			8.36766i			0.407331i
$423$	−33.3109	−	7.24027i	−1.61963	−	0.352034i
$424$	−1.24839	+	5.46957i	−0.0606274	+	0.265626i
$425$	−36.3019	+	17.4821i	−1.76090	+	0.848006i
$426$	8.55197	−	5.43563i	0.414344	−	0.263357i
$427$	11.4898	−	1.54334i	0.556032	−	0.0746876i
$428$	−9.83286	−	7.84144i	−0.475289	−	0.379030i
$429$	−2.89812	−	0.997255i	−0.139923	−	0.0481479i
$430$	−28.5645	−	22.7794i	−1.37750	−	1.09852i
$431$	14.4900	+	30.0888i	0.697958	+	1.44932i	0.884338	+	0.466847i	$0.154610\pi$
$431$	14.4900	+	30.0888i	0.697958	+	1.44932i	−0.186380	+	0.982478i	$0.559676\pi$
$432$	−4.87726	+	1.79229i	−0.234657	+	0.0862316i
$433$	−14.3080	+	29.7109i	−0.687598	+	1.42781i	0.205821	+	0.978590i	$0.434013\pi$
$433$	−14.3080	+	29.7109i	−0.687598	+	1.42781i	−0.893420	+	0.449223i	$0.851701\pi$
$434$	4.38189	−	13.4350i	0.210337	−	0.644901i
$435$	3.03811	−	1.08080i	0.145666	−	0.0518205i
$436$	−3.70914	−	1.78623i	−0.177635	−	0.0855447i
$437$	8.95354	+	39.2280i	0.428306	+	1.87653i
$438$	−1.18485	+	1.90757i	−0.0566142	+	0.0911472i
$439$	18.0534	+	14.3971i	0.861642	+	0.687136i	0.951110	−	0.308853i	$-0.0999453\pi$
$439$	18.0534	+	14.3971i	0.861642	+	0.687136i	−0.0894681	+	0.995990i	$0.528517\pi$
$440$	6.61049			0.315143
$441$	−19.3766	−	8.09604i	−0.922697	−	0.385526i
$442$	5.22035			0.248307
$443$	−19.7092	−	15.7176i	−0.936414	−	0.746765i	0.0311178	−	0.999516i	$-0.490093\pi$
$443$	−19.7092	−	15.7176i	−0.936414	−	0.746765i	−0.967531	+	0.252751i	$0.918665\pi$
$444$	−2.51723	+	4.05266i	−0.119462	+	0.192331i
$445$	8.22292	+	36.0270i	0.389804	+	1.70784i
$446$	−0.312544	−	0.150513i	−0.0147994	−	0.00712700i
$447$	17.6323	−	6.27265i	0.833979	−	0.296686i
$448$	−2.26973	−	1.35954i	−0.107234	−	0.0642322i
$449$	12.5440	−	26.0480i	0.591990	−	1.22928i	−0.362763	−	0.931881i	$-0.618167\pi$
$449$	12.5440	−	26.0480i	0.591990	−	1.22928i	0.954753	−	0.297399i	$-0.0961192\pi$
$450$	19.4254	−	9.60430i	0.915723	−	0.452751i
$451$	−1.46945	−	3.05135i	−0.0691938	−	0.143682i
$452$	0.409927	+	0.326906i	0.0192814	+	0.0153764i
$453$	4.94149	+	1.70038i	0.232172	+	0.0798911i
$454$	9.72247	+	7.75341i	0.456298	+	0.363886i
$455$	−6.25047	−	5.98943i	−0.293026	−	0.280789i
$456$	−9.81589	+	6.23898i	−0.459671	+	0.292167i
$457$	−1.14333	+	0.550596i	−0.0534825	+	0.0257558i	−0.460434	−	0.887694i	$-0.652306\pi$
$457$	−1.14333	+	0.550596i	−0.0534825	+	0.0257558i	0.406951	+	0.913450i	$0.366592\pi$
$458$	0.802539	−	3.51615i	0.0375002	−	0.164299i
$459$	−9.14607	+	27.5035i	−0.426902	+	1.28375i
$460$		−	20.9493i		−	0.976764i
$461$	0.971716	−	4.25737i	0.0452573	−	0.198285i	−0.947245	−	0.320510i	$-0.896146\pi$
$461$	0.971716	−	4.25737i	0.0452573	−	0.198285i	0.992502	+	0.122225i	$0.0390028\pi$
$462$	8.66155	−	0.229677i	0.402972	−	0.0106856i
$463$	7.77329	+	34.0570i	0.361255	+	1.58276i	0.750013	+	0.661423i	$0.230047\pi$
$463$	7.77329	+	34.0570i	0.361255	+	1.58276i	−0.388758	+	0.921340i	$0.627096\pi$
$464$	0.519155	−	0.118494i	0.0241012	−	0.00550093i
$465$	17.3500	+	27.2970i	0.804585	+	1.26587i
$466$	7.97059	+	9.99481i	0.369231	+	0.463000i
$467$	0.310204	+	1.35909i	0.0143545	+	0.0628914i	0.981598	−	0.190959i	$-0.0611599\pi$
$467$	0.310204	+	1.35909i	0.0143545	+	0.0628914i	−0.967243	+	0.253851i	$0.918303\pi$
$468$	−2.80747	+	0.0291260i	−0.129775	+	0.00134635i
$469$	−22.6752	+	8.48129i	−1.04704	+	0.391629i
$470$	38.7308	+	8.84005i	1.78652	+	0.407761i
$471$	−36.5186	−	3.92294i	−1.68269	−	0.180759i
$472$		−	1.08909i		−	0.0501294i
$473$	19.2633	+	4.39672i	0.885726	+	0.202161i
$474$	−25.0040	+	8.89513i	−1.14847	+	0.408567i
$475$	37.9229	−	30.2425i	1.74002	−	1.38762i
$476$	−13.8228	+	5.17020i	−0.633569	+	0.236976i
$477$	−10.6297	−	13.0492i	−0.486701	−	0.597482i
$478$	5.42678	−	23.7763i	0.248215	−	1.08750i
$479$	17.4124	−	21.8344i	0.795592	−	0.997641i	−0.204233	−	0.978922i	$-0.565470\pi$
$479$	17.4124	−	21.8344i	0.795592	−	0.997641i	0.999825	−	0.0187185i	$-0.00595862\pi$
$480$	5.70531	−	2.02965i	0.260410	−	0.0926405i
$481$	−2.01540	+	1.60723i	−0.0918942	+	0.0732832i
$482$	0.720665	+	0.347054i	0.0328254	+	0.0158079i
$483$	−0.727869	−	27.4493i	−0.0331192	−	1.24898i
$484$	6.68968	−	3.22158i	0.304076	−	0.146436i
$485$	−10.6617	+	22.1393i	−0.484124	+	1.00529i
$486$	4.76525	−	14.8423i	0.216156	−	0.673258i
$487$	20.9148	+	10.0720i	0.947739	+	0.456407i	0.842893	−	0.538081i	$-0.180851\pi$
$487$	20.9148	+	10.0720i	0.947739	+	0.456407i	0.104846	+	0.994488i	$0.466565\pi$
$488$	−2.73198	+	3.42579i	−0.123671	+	0.155078i
$489$	1.34039	−	12.4777i	0.0606144	−	0.564259i
$490$	22.4824	+	9.66885i	1.01565	+	0.436794i
$491$			24.1230i			1.08865i	0.838873	+	0.544327i	$0.183215\pi$
$491$			24.1230i			1.08865i	−0.838873	+	0.544327i	$0.816785\pi$
$492$	−2.20511	−	2.18235i	−0.0994140	−	0.0983880i
$493$	1.28878	−	2.67619i	0.0580439	−	0.120529i
$494$	−6.12690	+	1.39842i	−0.275662	+	0.0629181i
$495$	−12.2032	+	15.6323i	−0.548494	+	0.702620i
$496$	2.31747	+	4.81227i	0.104057	+	0.216077i
$497$	−12.9277	+	8.51278i	−0.579885	+	0.381850i
$498$	−23.4295	−	14.5528i	−1.04990	−	0.652124i
$499$	−16.0286	−	20.0992i	−0.717539	−	0.899765i	0.280657	−	0.959808i	$-0.409448\pi$
$499$	−16.0286	−	20.0992i	−0.717539	−	0.899765i	−0.998196	+	0.0600429i	$0.980876\pi$
$500$	−7.00342	+	3.37267i	−0.313203	+	0.150830i
$501$	1.06397	+	1.05299i	0.0475345	+	0.0470439i
$502$	−18.9018	−	4.31421i	−0.843629	−	0.192553i
$503$	17.4154	−	21.8382i	0.776512	−	0.973716i	−0.223487	−	0.974707i	$-0.571744\pi$
$503$	17.4154	−	21.8382i	0.776512	−	0.973716i	1.00000		0.000991148i	$0.000315492\pi$
$504$	7.40500	−	2.85763i	0.329845	−	0.127289i
$505$	−36.0290	−	45.1789i	−1.60327	−	2.01043i
$506$	4.91570	+	10.2076i	0.218530	+	0.453782i
$507$	19.8569	+	6.83283i	0.881876	+	0.303457i
$508$	10.1438			0.450057
$509$	−23.5371			−1.04326			−0.521631	−	0.853171i	$-0.674676\pi$
$509$	−23.5371			−1.04326			−0.521631	+	0.853171i	$0.674676\pi$
$510$	10.9907	−	31.9402i	0.486678	−	1.41434i
$511$	1.76263	−	2.94268i	0.0779743	−	0.130177i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	3.36672	−	34.7297i	0.148644	−	1.53335i
$514$	19.8107	−	15.7985i	0.873810	−	0.696841i
$515$	0.293886	−	0.234367i	0.0129502	−	0.0103274i
$516$	17.9755	−	2.11983i	0.791326	−	0.0933202i
$517$	−20.9460	+	4.78078i	−0.921202	+	0.210258i
$518$	3.74474	−	6.25178i	0.164534	−	0.274687i
$519$	35.7501	+	12.3017i	1.56926	+	0.539986i
$520$	3.27199			0.143486
$521$	8.87883			0.388988			0.194494	−	0.980904i	$-0.437693\pi$
$521$	8.87883			0.388988			0.194494	+	0.980904i	$0.437693\pi$
$522$	−0.678169	+	1.44643i	−0.0296826	+	0.0633084i
$523$	−1.67184	−	3.47161i	−0.0731044	−	0.151803i	0.861214	−	0.508243i	$-0.169705\pi$
$523$	−1.67184	−	3.47161i	−0.0731044	−	0.151803i	−0.934318	+	0.356440i	$0.883990\pi$
$524$	−3.09279	−	3.87824i	−0.135109	−	0.169422i
$525$	−29.4322	+	15.1477i	−1.28453	+	0.661100i
$526$	9.90957	−	12.4262i	0.432078	−	0.541808i
$527$	29.0466	+	6.62969i	1.26529	+	0.288794i
$528$	−2.30367	+	2.32769i	−0.100254	+	0.101300i
$529$	11.6264	−	5.59899i	0.505497	−	0.243434i
$530$	12.2294	+	15.3352i	0.531211	+	0.666118i
$531$	2.57545	+	2.01050i	0.111765	+	0.0872482i
$532$	14.8383	−	9.77090i	0.643321	−	0.423622i
$533$	−0.727335	−	1.51033i	−0.0315044	−	0.0654195i
$534$	−15.5514	−	9.65945i	−0.672976	−	0.418005i
$535$	−42.8681	+	9.78436i	−1.85335	+	0.423015i
$536$	3.97017	−	8.24415i	0.171485	−	0.356093i
$537$	6.01508	−	6.07781i	0.259570	−	0.262277i
$538$			4.21137i			0.181565i
$539$	−13.2234	+	0.564282i	−0.569570	+	0.0243053i
$540$	−5.73254	+	17.2386i	−0.246689	+	0.741830i
$541$	−1.60716	+	2.01531i	−0.0690972	+	0.0866451i	−0.815179	−	0.579209i	$-0.803361\pi$
$541$	−1.60716	+	2.01531i	−0.0690972	+	0.0866451i	0.746082	+	0.665854i	$0.231933\pi$
$542$	8.98667	+	4.32775i	0.386011	+	0.185893i
$543$	−4.81911	−	40.8645i	−0.206808	−	1.75366i
$544$	2.42022	−	5.02564i	0.103766	−	0.215473i
$545$	−12.9678	+	6.24498i	−0.555481	+	0.267506i
$546$	4.28721	−	0.113683i	0.183476	−	0.00486520i
$547$	−2.74349	−	1.32120i	−0.117303	−	0.0564902i	0.374312	−	0.927303i	$-0.377879\pi$
$547$	−2.74349	−	1.32120i	−0.117303	−	0.0564902i	−0.491615	+	0.870813i	$0.663593\pi$
$548$	−0.552534	+	0.440631i	−0.0236031	+	0.0188228i
$549$	−3.05788	−	12.7846i	−0.130507	−	0.545635i
$550$	8.51542	−	10.6780i	0.363099	−	0.455311i
$551$	−0.795694	+	3.48616i	−0.0338977	+	0.148516i
$552$	7.37667	+	7.30054i	0.313972	+	0.310731i
$553$	37.9700	−	14.2021i	1.61465	−	0.603933i
$554$	11.0361	−	8.80100i	0.468879	−	0.373919i
$555$	5.59051	+	15.7148i	0.237304	+	0.667056i
$556$	6.28761	+	1.43511i	0.266654	+	0.0608620i
$557$			6.39084i			0.270789i	0.990792	+	0.135394i	$0.0432301\pi$
$557$			6.39084i			0.270789i	−0.990792	+	0.135394i	$0.956770\pi$
$558$	−15.6581	−	3.40335i	−0.662858	−	0.144075i
$559$	9.53474	+	2.17624i	0.403276	+	0.0920452i
$560$	−8.66384	+	3.24056i	−0.366114	+	0.136939i
$561$	2.13945	+	18.1419i	0.0903278	+	0.765951i
$562$	−4.05386	−	17.7611i	−0.171002	−	0.749207i
$563$	−6.82612	−	8.55968i	−0.287686	−	0.360747i	0.616897	−	0.787044i	$-0.288389\pi$
$563$	−6.82612	−	8.55968i	−0.287686	−	0.360747i	−0.904584	+	0.426296i	$0.859818\pi$
$564$	−16.6099	+	10.5573i	−0.699404	+	0.444542i
$565$	1.78715	−	0.407906i	0.0751860	−	0.0171607i
$566$	1.63897	+	7.18081i	0.0688912	+	0.301832i
$567$	−6.91226	+	22.7864i	−0.290288	+	0.956939i
$568$	1.30184	−	5.70374i	0.0546240	−	0.239324i
$569$		−	36.1358i		−	1.51489i	−0.652897	−	0.757447i	$-0.726447\pi$
$569$		−	36.1358i		−	1.51489i	0.652897	−	0.757447i	$-0.273553\pi$
$570$	−4.34322	+	40.4310i	−0.181918	+	1.69347i
$571$	−7.19005	+	31.5016i	−0.300894	+	1.31830i	0.567887	+	0.823107i	$0.307761\pi$
$571$	−7.19005	+	31.5016i	−0.300894	+	1.31830i	−0.868781	+	0.495196i	$0.835096\pi$
$572$	−1.59429	+	0.767768i	−0.0666604	+	0.0321020i
$573$	−14.9786	−	23.5661i	−0.625741	−	0.984488i
$574$	3.42171	+	3.27881i	0.142819	+	0.136855i
$575$	−33.8396	−	26.9861i	−1.41121	−	1.12540i
$576$	−1.27354	+	2.71626i	−0.0530642	+	0.113178i
$577$	10.6004	+	8.45354i	0.441300	+	0.351925i	0.818795	−	0.574087i	$-0.194643\pi$
$577$	10.6004	+	8.45354i	0.441300	+	0.351925i	−0.377494	+	0.926012i	$0.623214\pi$
$578$	−6.12408	−	12.7168i	−0.254728	−	0.528949i
$579$	−16.9564	+	10.7775i	−0.704685	+	0.447898i
$580$	0.807780	−	1.67737i	0.0335412	−	0.0696491i
$581$	36.1431	+	21.6493i	1.49947	+	0.898165i
$582$	−4.08024	−	11.4695i	−0.169131	−	0.475425i
$583$	−9.55717	−	4.60249i	−0.395818	−	0.190616i
$584$	0.288497	+	1.26399i	0.0119381	+	0.0523042i
$585$	−6.04022	+	7.73752i	−0.249732	+	0.319907i
$586$	4.90177	+	3.90903i	0.202490	+	0.161481i
$587$	−10.2207			−0.421854			−0.210927	−	0.977502i	$-0.567648\pi$
$587$	−10.2207			−0.421854			−0.210927	+	0.977502i	$0.567648\pi$
$588$	−11.2394	+	4.54705i	−0.463506	+	0.187517i
$589$	−35.8667			−1.47786
$590$	−2.97695	−	2.37404i	−0.122559	−	0.0977376i
$591$	−22.5693	−	14.0185i	−0.928376	−	0.576642i
$592$	0.612916	+	2.68536i	0.0251907	+	0.110368i
$593$	−7.72484	−	3.72009i	−0.317221	−	0.152766i	0.268497	−	0.963281i	$-0.413473\pi$
$593$	−7.72484	−	3.72009i	−0.317221	−	0.152766i	−0.585718	+	0.810515i	$0.699187\pi$
$594$	−1.25180	−	9.74466i	−0.0513622	−	0.399828i
$595$	−15.9992	+	49.0540i	−0.655902	+	2.01102i
$596$	4.68811	−	9.73497i	0.192033	−	0.398760i
$597$	−23.4134	−	36.8367i	−0.958249	−	1.50763i
$598$	2.43313	+	5.05244i	0.0994979	+	0.206610i
$599$	−12.3013	−	9.80999i	−0.502619	−	0.400825i	0.339092	−	0.940753i	$-0.389880\pi$
$599$	−12.3013	−	9.80999i	−0.502619	−	0.400825i	−0.841711	+	0.539928i	$0.818452\pi$
$600$	4.07087	−	11.8304i	0.166193	−	0.482973i
$601$	−19.3083	−	15.3979i	−0.787603	−	0.628092i	0.144821	−	0.989458i	$-0.453739\pi$
$601$	−19.3083	−	15.3979i	−0.787603	−	0.628092i	−0.932424	+	0.361365i	$0.882311\pi$
$602$	−27.4022	+	3.68073i	−1.11683	+	0.150015i
$603$	12.1665	+	24.6076i	0.495456	+	1.00210i
$604$	2.71836	−	1.30909i	0.110609	−	0.0532663i
$605$	5.77646	−	25.3083i	0.234846	−	1.02893i
$606$	28.4641	+	3.05770i	1.15627	+	0.124210i
$607$		−	27.8162i		−	1.12903i	−0.825424	−	0.564513i	$-0.809064\pi$
$607$		−	27.8162i		−	1.12903i	0.825424	−	0.564513i	$-0.190936\pi$
$608$	−1.49424	+	6.54671i	−0.0605996	+	0.265504i
$609$	1.00013	−	2.22588i	0.0405274	−	0.0901973i
$610$	3.40889	+	14.9353i	0.138022	+	0.604714i
$611$	−10.3676	+	2.36634i	−0.419429	+	0.0957319i
$612$	7.41668	+	15.0008i	0.299802	+	0.606371i
$613$	9.11335	+	11.4278i	0.368085	+	0.461564i	0.931036	−	0.364926i	$-0.118906\pi$
$613$	9.11335	+	11.4278i	0.368085	+	0.461564i	−0.562952	+	0.826490i	$0.690334\pi$
$614$	2.61423	+	11.4537i	0.105502	+	0.462233i
$615$	−10.7721	+	1.27034i	−0.434372	+	0.0512251i
$616$	3.46108	−	3.61193i	0.139451	−	0.145529i
$617$	−23.6239	−	5.39201i	−0.951063	−	0.217074i	−0.281276	−	0.959627i	$-0.590758\pi$
$617$	−23.6239	−	5.39201i	−0.951063	−	0.217074i	−0.669787	+	0.742553i	$0.733615\pi$
$618$	−0.0198902	+	0.185157i	−0.000800099	+	0.00744812i
$619$			28.5393i			1.14709i	0.819173	+	0.573546i	$0.194433\pi$
$619$			28.5393i			1.14709i	−0.819173	+	0.573546i	$0.805567\pi$
$620$	18.2057	+	4.15534i	0.731159	+	0.166882i
$621$	−30.8817	+	3.96708i	−1.23924	+	0.159194i
$622$	−25.2682	+	20.1507i	−1.01316	+	0.807971i
$623$	23.9902	+	14.3698i	0.961146	+	0.575715i
$624$	−1.14025	+	1.15214i	−0.0456464	+	0.0461224i
$625$	1.98935	−	8.71593i	0.0795742	−	0.348637i
$626$	−2.40790	+	3.01941i	−0.0962391	+	0.120680i
$627$	−7.37082	−	20.7192i	−0.294362	−	0.827446i
$628$	−16.5790	+	13.2213i	−0.661573	+	0.527587i
$629$	13.8427	+	6.66631i	0.551946	+	0.265803i
$630$	8.33057	−	26.4702i	0.331898	−	1.05460i
$631$	26.3497	−	12.6894i	1.04897	−	0.505156i	0.171695	−	0.985150i	$-0.445076\pi$
$631$	26.3497	−	12.6894i	1.04897	−	0.505156i	0.877272	+	0.479994i	$0.159361\pi$
$632$	−6.64812	+	13.8050i	−0.264448	+	0.549132i
$633$	−14.3935	+	1.69741i	−0.572089	+	0.0674658i
$634$	10.0039	+	4.81761i	0.397304	+	0.191332i
$635$	22.1118	−	27.7273i	0.877480	−	1.10032i
$636$	−9.66162	−	1.03788i	−0.383108	−	0.0411547i
$637$	−6.54516	+	0.279303i	−0.259329	+	0.0110664i
$638$			1.00685i			0.0398614i
$639$	11.0848	+	13.6079i	0.438508	+	0.538319i
$640$	1.51694	−	3.14996i	0.0599623	−	0.124513i
$641$	41.7094	−	9.51990i	1.64742	−	0.376013i	0.704678	−	0.709528i	$-0.251092\pi$
$641$	41.7094	−	9.51990i	1.64742	−	0.376013i	0.942745	+	0.333514i	$0.108234\pi$
$642$	11.4937	−	18.5045i	0.453619	−	0.730313i
$643$	−2.21459	−	4.59865i	−0.0873350	−	0.181353i	0.852727	−	0.522357i	$-0.174947\pi$
$643$	−2.21459	−	4.59865i	−0.0873350	−	0.181353i	−0.940062	+	0.341004i	$0.889233\pi$
$644$	−11.4465	−	10.9685i	−0.451056	−	0.432219i
$645$	33.3892	−	53.7556i	1.31470	−	2.11662i
$646$	23.3540	+	29.2850i	0.918852	+	1.15220i
$647$	−25.1785	+	12.1253i	−0.989871	+	0.476697i	−0.857489	−	0.514502i	$-0.827977\pi$
$647$	−25.1785	+	12.1253i	−0.989871	+	0.476697i	−0.132382	+	0.991199i	$0.542262\pi$
$648$	−4.07234	−	8.02596i	−0.159977	−	0.315289i
$649$	2.00759	+	0.458219i	0.0788047	+	0.0179867i
$650$	4.21488	−	5.28529i	0.165321	−	0.207306i
$651$	23.9989	+	4.81208i	0.940589	+	0.188600i
$652$	−4.51745	−	5.66470i	−0.176917	−	0.221847i
$653$	10.2505	+	21.2853i	0.401131	+	0.832958i	0.999496	+	0.0317341i	$0.0101030\pi$
$653$	10.2505	+	21.2853i	0.401131	+	0.832958i	−0.598365	+	0.801224i	$0.704183\pi$
$654$	2.32013	−	6.74254i	0.0907243	−	0.263654i
$655$	−17.3427			−0.677635
$656$	−1.79120			−0.0699345
$657$	−3.52162	−	1.65114i	−0.137391	−	0.0644170i
$658$	25.1086	−	16.5338i	0.978834	−	0.644555i
$659$	34.6272	−	7.90343i	1.34888	−	0.307874i	0.513759	−	0.857935i	$-0.328253\pi$
$659$	34.6272	−	7.90343i	1.34888	−	0.307874i	0.835124	+	0.550061i	$0.185396\pi$
$660$	1.34096	+	11.3709i	0.0521968	+	0.442612i
$661$	28.2365	−	22.5179i	1.09827	−	0.875844i	0.105330	−	0.994437i	$-0.466410\pi$
$661$	28.2365	−	22.5179i	1.09827	−	0.875844i	0.992943	+	0.118594i	$0.0378386\pi$
$662$	8.95645	−	7.14253i	0.348102	−	0.277602i
$663$	1.05896	+	8.97968i	0.0411268	+	0.348742i
$664$	−15.5248	+	3.54343i	−0.602478	+	0.137512i
$665$	5.63698	−	61.8584i	0.218593	−	2.39877i
$666$	−7.48173	−	3.50787i	−0.289911	−	0.135927i
$667$	3.19079			0.123548
$668$	0.864253			0.0334390
$669$	0.195502	−	0.568148i	0.00755854	−	0.0219659i
$670$	−13.8805	−	28.8231i	−0.536250	−	1.11353i
$671$	−5.16554	−	6.47738i	−0.199413	−	0.250057i
$672$	1.87816	−	4.18001i	0.0724517	−	0.161247i
$673$	18.7379	−	23.4966i	0.722294	−	0.905728i	−0.276171	−	0.961108i	$-0.589066\pi$
$673$	18.7379	−	23.4966i	0.722294	−	0.905728i	0.998465	+	0.0553805i	$0.0176372\pi$
$674$	−13.5272	−	3.08749i	−0.521048	−	0.118926i
$675$	20.4612	+	31.4660i	0.787551	+	1.21113i
$676$	10.9235	−	5.26047i	0.420134	−	0.202326i
$677$	−20.0772	−	25.1760i	−0.771630	−	0.967594i	0.228352	−	0.973579i	$-0.426666\pi$
$677$	−20.0772	−	25.1760i	−0.771630	−	0.967594i	−0.999982	+	0.00598501i	$0.998095\pi$
$678$	−0.479166	+	0.771443i	−0.0184023	+	0.0296271i
$679$	6.51456	+	17.4171i	0.250006	+	0.668405i
$680$	−8.46155	−	17.5706i	−0.324486	−	0.673802i
$681$	−11.3646	+	18.2967i	−0.435494	+	0.701132i
$682$	−9.84582	+	2.24724i	−0.377016	+	0.0860514i
$683$	−17.3665	+	36.0619i	−0.664511	+	1.37987i	0.247170	+	0.968972i	$0.420499\pi$
$683$	−17.3665	+	36.0619i	−0.664511	+	1.37987i	−0.911681	+	0.410899i	$0.865215\pi$
$684$	−12.7230	−	15.6190i	−0.486478	−	0.597208i
$685$			2.47082i			0.0944050i
$686$	17.0542	−	7.22185i	0.651131	−	0.275732i
$687$	6.21104	+	0.667209i	0.236966	+	0.0254556i
$688$	6.51550	−	8.17018i	0.248401	−	0.311485i
$689$	−4.73051	−	2.27809i	−0.180218	−	0.0867885i
$690$	36.0355	−	4.24962i	1.37185	−	0.161780i
$691$	12.8577	−	26.6993i	0.489130	−	1.01569i	−0.499638	−	0.866234i	$-0.666534\pi$
$691$	12.8577	−	26.6993i	0.489130	−	1.01569i	0.988768	−	0.149455i	$-0.0477520\pi$
$692$	19.6665	−	9.47088i	0.747607	−	0.360029i
$693$	2.15210	+	14.8524i	0.0817515	+	0.564197i
$694$	−19.8538	−	9.56109i	−0.753640	−	0.362934i
$695$	17.6287	−	14.0584i	0.668696	−	0.533267i
$696$	0.309137	+	0.868978i	0.0117178	+	0.0329385i
$697$	−6.22952	+	7.81157i	−0.235960	+	0.295884i
$698$	0.632909	−	2.77295i	0.0239559	−	0.104958i
$699$	−15.5755	+	15.7379i	−0.589120	+	0.595264i
$700$	−5.92596	+	18.1692i	−0.223980	+	0.686731i
$701$	7.44619	−	5.93814i	0.281239	−	0.224280i	−0.472703	−	0.881222i	$-0.656722\pi$
$701$	7.44619	−	5.93814i	0.281239	−	0.224280i	0.753942	+	0.656942i	$0.228150\pi$
$702$	−0.619605	−	4.82331i	−0.0233855	−	0.182044i
$703$	−18.0324	−	4.11577i	−0.680104	−	0.155229i
$704$			1.89077i			0.0712611i
$705$	−7.34938	+	68.4152i	−0.276793	+	2.57667i
$706$	−9.91518	−	2.26308i	−0.373163	−	0.0851720i
$707$	−43.5493	−	3.96852i	−1.63784	−	0.149251i
$708$	1.87338	−	0.220925i	0.0704058	−	0.00830288i
$709$	9.17508	+	40.1987i	0.344577	+	1.50969i	0.789291	+	0.614020i	$0.210448\pi$
$709$	9.17508	+	40.1987i	0.344577	+	1.50969i	−0.444713	+	0.895673i	$0.646694\pi$
$710$	−12.7530	−	15.9917i	−0.478610	−	0.600159i
$711$	−20.3729	−	41.2058i	−0.764044	−	1.54534i
$712$	−10.3046	+	2.35197i	−0.386183	+	0.0881436i
$713$	7.12172	+	31.2023i	0.266710	+	1.16853i
$714$	−11.6974	−	22.7283i	−0.437765	−	0.850586i
$715$	−1.37665	+	6.03148i	−0.0514836	+	0.225565i
$716$		−	4.93697i		−	0.184503i
$717$	41.9992	+	4.51168i	1.56849	+	0.168492i
$718$	−1.01942	+	4.46637i	−0.0380444	+	0.166683i
$719$	−13.2937	+	6.40189i	−0.495770	+	0.238750i	−0.665024	−	0.746822i	$-0.731579\pi$
$719$	−13.2937	+	6.40189i	−0.495770	+	0.238750i	0.169254	+	0.985573i	$0.445864\pi$
$720$	4.64861	+	9.40215i	0.173243	+	0.350398i
$721$	0.0258150	−	0.283286i	0.000961401	−	0.0105501i
$722$	−20.3997	−	16.2682i	−0.759197	−	0.605440i
$723$	−0.450789	+	1.31004i	−0.0167650	+	0.0487209i
$724$	−18.5737	−	14.8120i	−0.690285	−	0.550484i
$725$	−1.66892	−	3.46555i	−0.0619822	−	0.128707i
$726$	6.89857	+	10.8536i	0.256030	+	0.402816i
$727$	4.49126	−	9.32620i	0.166572	−	0.345890i	−0.800929	−	0.598760i	$-0.795660\pi$
$727$	4.49126	−	9.32620i	0.166572	−	0.345890i	0.967500	+	0.252870i	$0.0813746\pi$
$728$	1.71313	−	1.78779i	0.0634929	−	0.0662601i
$729$	26.4973	+	5.18606i	0.981380	+	0.192076i
$730$	4.08390	+	1.96670i	0.151152	+	0.0727909i
$731$	−12.9709	−	56.8294i	−0.479748	−	2.10191i
$732$	−6.44700	−	4.00442i	−0.238288	−	0.148008i
$733$	−25.1654	−	20.0687i	−0.929503	−	0.741254i	0.0366215	−	0.999329i	$-0.488340\pi$
$733$	−25.1654	−	20.0687i	−0.929503	−	0.741254i	−0.966125	+	0.258075i	$0.916912\pi$
$734$	16.5337			0.610268
$735$	−12.0711	+	40.6340i	−0.445248	+	1.49881i
$736$	5.99202			0.220869
$737$	13.5266	+	10.7871i	0.498258	+	0.397348i
$738$	3.30662	−	4.23577i	0.121718	−	0.155921i
$739$	−0.272894	−	1.19563i	−0.0100386	−	0.0439818i	0.969661	−	0.244455i	$-0.0786091\pi$
$739$	−0.272894	−	1.19563i	−0.0100386	−	0.0439818i	−0.979699	+	0.200473i	$0.935752\pi$
$740$	8.67630	+	4.17829i	0.318947	+	0.153597i
$741$	−3.64833	−	10.2554i	−0.134025	−	0.376741i
$742$	14.7820	+	1.34704i	0.542665	+	0.0494515i
$743$	3.78240	−	7.85423i	0.138763	−	0.288144i	−0.819994	−	0.572372i	$-0.806023\pi$
$743$	3.78240	−	7.85423i	0.138763	−	0.288144i	0.958757	+	0.284229i	$0.0917375\pi$
$744$	−7.80763	+	4.96253i	−0.286242	+	0.181935i
$745$	−16.3905	−	34.0353i	−0.600503	−	1.24696i
$746$	−3.80750	−	3.03638i	−0.139402	−	0.111170i
$747$	20.2799	−	43.2538i	0.742002	−	1.58257i
$748$	8.24582	+	6.57582i	0.301497	+	0.240436i
$749$	−17.0985	+	28.5457i	−0.624766	+	1.04304i
$750$	−7.22210	−	11.3626i	−0.263714	−	0.414905i
$751$	−16.8476	+	8.11337i	−0.614777	+	0.296061i	−0.715239	−	0.698880i	$-0.753682\pi$
$751$	−16.8476	+	8.11337i	−0.614777	+	0.296061i	0.100462	+	0.994941i	$0.467968\pi$
$752$	−2.52848	+	11.0780i	−0.0922042	+	0.403973i
$753$	3.58672	−	33.3887i	0.130707	−	1.21675i
$754$			0.498359i			0.0181492i
$755$	2.34727	−	10.2841i	0.0854260	−	0.374276i
$756$	6.41762	+	12.1579i	0.233407	+	0.442178i
$757$	−3.31118	−	14.5072i	−0.120347	−	0.527274i	−0.998779	−	0.0494064i	$-0.984267\pi$
$757$	−3.31118	−	14.5072i	−0.120347	−	0.527274i	0.878432	−	0.477867i	$-0.158590\pi$
$758$	−3.30219	+	0.753702i	−0.119941	+	0.0273757i
$759$	−16.5612	+	10.5263i	−0.601133	+	0.382080i
$760$	14.6378	+	18.3552i	0.530968	+	0.665812i
$761$	8.41521	+	36.8694i	0.305051	+	1.33652i	0.862396	+	0.506235i	$0.168963\pi$
$761$	8.41521	+	36.8694i	0.305051	+	1.33652i	−0.557345	+	0.830281i	$0.688180\pi$
$762$	2.05770	+	17.4486i	0.0745425	+	0.632097i
$763$	−3.37741	+	10.3552i	−0.122270	+	0.374885i
$764$	−15.7174	−	3.58740i	−0.568636	−	0.129788i
$765$	57.1708	+	12.4263i	2.06701	+	0.449275i
$766$			33.0386i			1.19373i
$767$	0.993696	+	0.226805i	0.0358803	+	0.00818944i
$768$	0.580532	+	1.63186i	0.0209482	+	0.0588848i
$769$	25.7798	−	20.5587i	0.929645	−	0.741367i	−0.0365092	−	0.999333i	$-0.511624\pi$
$769$	25.7798	−	20.5587i	0.929645	−	0.741367i	0.966154	+	0.257966i	$0.0830524\pi$
$770$	−2.32835	−	17.3340i	−0.0839080	−	0.624675i
$771$	31.1941	+	30.8721i	1.12343	+	1.11183i
$772$	−2.58123	+	11.3091i	−0.0929003	+	0.407023i
$773$	−9.18431	+	11.5168i	−0.330337	+	0.414229i	−0.919068	−	0.394100i	$-0.871056\pi$
$773$	−9.18431	+	11.5168i	−0.330337	+	0.414229i	0.588731	+	0.808329i	$0.299628\pi$
$774$	7.29276	+	30.4901i	0.262133	+	1.09595i
$775$	30.1642	−	24.0551i	1.08353	−	0.864086i
$776$	−6.33241	−	3.04953i	−0.227320	−	0.109472i
$777$	11.5135	+	5.17325i	0.413045	+	0.185589i
$778$	−8.66545	+	4.17306i	−0.310672	+	0.149612i
$779$	5.21876	−	10.8369i	0.186981	−	0.388271i
$780$	0.663735	+	5.62826i	0.0237655	+	0.201524i
$781$	9.96634	+	4.79954i	0.356624	+	0.171741i
$782$	20.8394	−	26.1318i	0.745215	−	0.934470i
$783$	−2.62561	−	0.873126i	−0.0938318	−	0.0312030i
$784$	−2.76554	+	6.43054i	−0.0987693	+	0.229662i
$785$			74.1378i			2.64609i
$786$	6.04370	−	6.10673i	0.215572	−	0.217820i
$787$	18.5806	−	38.5829i	0.662325	−	1.37533i	−0.250954	−	0.967999i	$-0.580744\pi$
$787$	18.5806	−	38.5829i	0.662325	−	1.37533i	0.913280	−	0.407333i	$-0.133541\pi$
$788$	−14.9548	+	3.41333i	−0.532742	+	0.121595i
$789$	23.3849	+	14.5251i	0.832524	+	0.517106i
$790$	23.2431	+	48.2648i	0.826952	+	1.71718i
$791$	0.712829	−	1.19006i	0.0253453	−	0.0423135i
$792$	−4.47124	−	3.49043i	−0.158879	−	0.124027i
$793$	−2.55679	−	3.20611i	−0.0907942	−	0.113852i
$794$	−9.68268	+	4.66293i	−0.343626	+	0.165481i
$795$	−23.8977	+	24.1470i	−0.847566	+	0.856404i
$796$	−24.5683	−	5.60755i	−0.870800	−	0.198754i
$797$	15.6893	−	19.6738i	0.555744	−	0.696881i	−0.422020	−	0.906586i	$-0.638679\pi$
$797$	15.6893	−	19.6738i	0.555744	−	0.696881i	0.977765	+	0.209705i	$0.0672504\pi$
$798$	19.8172	+	23.5417i	0.701522	+	0.833368i
$799$	39.5185	+	49.5546i	1.39806	+	1.75312i
$800$	−3.13409	−	6.50800i	−0.110807	−	0.230093i
$801$	13.4609	−	28.7099i	0.475617	−	1.01442i
$802$	−5.03127			−0.177660
$803$	−2.45137			−0.0865070
$804$	14.9864	+	5.15687i	0.528529	+	0.181869i
$805$	−54.9332	+	7.37876i	−1.93614	+	0.260067i
$806$	−4.87338	+	1.11232i	−0.171658	+	0.0391797i
$807$	−7.24410	+	0.854289i	−0.255004	+	0.0300724i
$808$	12.9223	−	10.3052i	0.454606	−	0.362536i
$809$	−20.2571	+	16.1545i	−0.712202	+	0.567962i	−0.911163	−	0.412045i	$-0.864815\pi$
$809$	−20.2571	+	16.1545i	−0.712202	+	0.567962i	0.198962	+	0.980007i	$0.436243\pi$
$810$	−30.8155	−	6.36383i	−1.08274	−	0.223602i
$811$	9.44028	−	2.15468i	0.331493	−	0.0756612i	−0.0535350	−	0.998566i	$-0.517049\pi$
$811$	9.44028	−	2.15468i	0.331493	−	0.0756612i	0.385028	+	0.922905i	$0.374192\pi$
$812$	−0.493572	−	1.31959i	−0.0173210	−	0.0463086i
$813$	−5.62133	+	16.3362i	−0.197149	+	0.572934i
$814$	−5.20797			−0.182539
$815$	−25.3314			−0.887319
$816$	9.13571	+	3.14363i	0.319814	+	0.110049i
$817$	30.4469	+	63.2236i	1.06520	+	2.21191i
$818$	16.5781	+	20.7883i	0.579640	+	0.726845i
$819$	1.06522	+	7.35150i	0.0372220	+	0.256882i
$820$	−3.90452	+	4.89611i	−0.136352	+	0.170980i
$821$	−18.1075	−	4.13292i	−0.631956	−	0.144240i	−0.105468	−	0.994423i	$-0.533634\pi$
$821$	−18.1075	−	4.13292i	−0.631956	−	0.144240i	−0.526488	+	0.850183i	$0.676491\pi$
$822$	−0.870026	−	0.861047i	−0.0303456	−	0.0300325i
$823$	−9.91019	+	4.77250i	−0.345448	+	0.166359i	−0.598560	−	0.801078i	$-0.704260\pi$
$823$	−9.91019	+	4.77250i	−0.345448	+	0.166359i	0.253112	+	0.967437i	$0.418546\pi$
$824$	0.0670349	+	0.0840591i	0.00233527	+	0.00292834i
$825$	20.0949	+	12.4816i	0.699616	+	0.434553i
$826$	−2.85581	+	0.383600i	−0.0993664	+	0.0133471i
$827$	−3.97464	−	8.25342i	−0.138212	−	0.287000i	0.820362	−	0.571845i	$-0.193772\pi$
$827$	−3.97464	−	8.25342i	−0.138212	−	0.287000i	−0.958574	+	0.284845i	$0.908058\pi$
$828$	−11.0615	+	14.1698i	−0.384414	+	0.492434i
$829$	16.6757	−	3.80612i	0.579171	−	0.132192i	0.0771074	−	0.997023i	$-0.475432\pi$
$829$	16.6757	−	3.80612i	0.579171	−	0.132192i	0.502063	+	0.864831i	$0.332574\pi$
$830$	−24.1558	+	50.1600i	−0.838459	+	1.74108i
$831$	17.3776	+	17.1982i	0.602822	+	0.596600i
$832$			0.935874i			0.0324456i
$833$	18.4260	+	34.4252i	0.638423	+	1.19276i
$834$	−1.19311	+	11.1066i	−0.0413140	+	0.384591i
$835$	1.88393	−	2.36238i	0.0651962	−	0.0817534i
$836$	−11.4393	−	5.50887i	−0.395636	−	0.190528i
$837$	2.67791	−	27.6243i	0.0925623	−	0.954835i
$838$	2.57846	−	5.35423i	0.0890715	−	0.184959i
$839$	3.29152	−	1.58511i	0.113636	−	0.0547242i	−0.376202	−	0.926538i	$-0.622770\pi$
$839$	3.29152	−	1.58511i	0.113636	−	0.0547242i	0.489838	+	0.871813i	$0.337056\pi$
$840$	−7.33168	−	14.2456i	−0.252967	−	0.491519i
$841$	−25.8726	−	12.4596i	−0.892159	−	0.429641i
$842$	0.459942	−	0.366791i	0.0158506	−	0.0126405i
$843$	29.7291	−	10.5761i	1.02392	−	0.364259i
$844$	−5.21715	+	6.54210i	−0.179582	+	0.225188i
$845$	9.43228	−	41.3255i	0.324480	−	1.42164i
$846$	−21.5293	−	26.4297i	−0.740192	−	0.908671i
$847$	−10.8039	−	16.4070i	−0.371226	−	0.563751i
$848$	−4.38626	+	3.49792i	−0.150625	+	0.120119i
$849$	−12.0195	+	4.27590i	−0.412507	+	0.146748i
$850$	−39.2819	−	8.96583i	−1.34736	−	0.307526i
$851$			16.5045i			0.565769i
$852$	10.0753	+	1.08232i	0.345173	+	0.0370795i
$853$	15.3949	+	3.51378i	0.527111	+	0.120310i	0.477791	−	0.878473i	$-0.341438\pi$
$853$	15.3949	+	3.51378i	0.527111	+	0.120310i	0.0493196	+	0.998783i	$0.484295\pi$
$854$	9.94537	+	5.95716i	0.340324	+	0.203850i
$855$	−70.4277	+	0.730649i	−2.40858	+	0.0249877i
$856$	−2.79858	−	12.2614i	−0.0956534	−	0.419085i
$857$	−11.8969	−	14.9183i	−0.406391	−	0.509598i	0.535951	−	0.844249i	$-0.319953\pi$
$857$	−11.8969	−	14.9183i	−0.406391	−	0.509598i	−0.942342	+	0.334651i	$0.891382\pi$
$858$	−1.64407	−	2.58664i	−0.0561275	−	0.0883063i
$859$	29.7891	−	6.79917i	1.01639	−	0.231985i	0.318298	−	0.947991i	$-0.396889\pi$
$859$	29.7891	−	6.79917i	1.01639	−	0.231985i	0.698094	+	0.716006i	$0.254032\pi$
$860$	−8.12989	−	35.6194i	−0.277227	−	1.21461i
$861$	−4.94588	+	6.55091i	−0.168555	+	0.223254i
$862$	−7.43131	+	32.5587i	−0.253111	+	1.10895i
$863$			2.81501i			0.0958240i	0.998852	+	0.0479120i	$0.0152567\pi$
$863$			2.81501i			0.0958240i	−0.998852	+	0.0479120i	$0.984743\pi$
$864$	−4.93067	−	1.63966i	−0.167745	−	0.0557822i
$865$	16.9818	−	74.4019i	0.577397	−	2.52974i
$866$	−29.7109	+	14.3080i	−1.00962	+	0.486205i
$867$	20.6322	−	13.1139i	0.700708	−	0.445370i
$868$	11.8025	−	7.77185i	0.400602	−	0.263794i
$869$	−22.6505	−	18.0632i	−0.768365	−	0.612751i
$870$	3.04916	+	1.04923i	0.103376	+	0.0355721i
$871$	6.69525	+	5.33928i	0.226860	+	0.180915i
$872$	−1.78623	−	3.70914i	−0.0604892	−	0.125607i
$873$	18.9013	−	9.34517i	0.639712	−	0.316286i
$874$	−17.4581	+	36.2522i	−0.590530	+	1.22625i
$875$	11.3106	+	17.1765i	0.382367	+	0.580670i
$876$	−2.11570	+	0.752656i	−0.0714829	+	0.0254299i
$877$	7.64504	+	3.68166i	0.258155	+	0.124321i	0.558485	−	0.829514i	$-0.311383\pi$
$877$	7.64504	+	3.68166i	0.258155	+	0.124321i	−0.300331	+	0.953835i	$0.597097\pi$
$878$	5.13827	+	22.5122i	0.173408	+	0.759750i
$879$	−5.72971	+	9.22465i	−0.193258	+	0.311140i
$880$	5.16829	+	4.12157i	0.174223	+	0.138938i
$881$	−49.1472			−1.65581			−0.827905	−	0.560868i	$-0.810467\pi$
$881$	−49.1472			−1.65581			−0.827905	+	0.560868i	$0.810467\pi$
$882$	−10.1015	−	18.4109i	−0.340134	−	0.619926i
$883$	12.3776			0.416540			0.208270	−	0.978071i	$-0.433217\pi$
$883$	12.3776			0.416540			0.208270	+	0.978071i	$0.433217\pi$
$884$	4.08143	+	3.25483i	0.137273	+	0.109472i
$885$	3.47977	−	5.60232i	0.116971	−	0.188320i
$886$	−5.60954	−	24.5770i	−0.188456	−	0.825681i
$887$	23.2903	+	11.2160i	0.782011	+	0.376597i	0.781901	−	0.623403i	$-0.214250\pi$
$887$	23.2903	+	11.2160i	0.782011	+	0.376597i	0.000110765		1.00000i	$0.499965\pi$
$888$	−4.49484	+	1.59903i	−0.150837	+	0.0536599i
$889$	−3.57285	−	26.5990i	−0.119829	−	0.892103i
$890$	−16.0335	+	33.2939i	−0.537444	+	1.11601i
$891$	16.5082	−	4.13000i	0.553044	−	0.138360i
$892$	−0.150513	−	0.312544i	−0.00503955	−	0.0104647i
$893$	−59.6558	−	47.5739i	−1.99630	−	1.59200i
$894$	17.6964	+	6.08940i	0.591857	+	0.203660i
$895$	−13.4949	−	10.7618i	−0.451083	−	0.359727i
$896$	−0.926885	−	2.47808i	−0.0309650	−	0.0827869i
$897$	−8.19729	+	5.21020i	−0.273699	+	0.173963i
$898$	26.0480	−	12.5440i	0.869233	−	0.418600i
$899$	−0.632901	+	2.77292i	−0.0211084	+	0.0924821i
$900$	21.1756	+	4.60261i	0.705853	+	0.153420i
$901$			31.2941i			1.04256i
$902$	0.753621	−	3.30183i	0.0250928	−	0.109939i
$903$	−11.8900	−	46.3887i	−0.395673	−	1.54372i
$904$	0.116671	+	0.511171i	0.00388044	+	0.0170013i
$905$	−80.9752	+	18.4821i	−2.69171	+	0.614365i
$906$	2.80324	+	4.41038i	0.0931315	+	0.146525i
$907$	−20.8470	−	26.1414i	−0.692215	−	0.868010i	0.304200	−	0.952608i	$-0.401611\pi$
$907$	−20.8470	−	26.1414i	−0.692215	−	0.868010i	−0.996415	+	0.0845982i	$0.973039\pi$
$908$	2.76716	+	12.1237i	0.0918314	+	0.402340i
$909$	0.514388	+	49.5822i	0.0170612	+	1.64454i
$910$	−1.15246	−	8.57983i	−0.0382038	−	0.284419i
$911$	44.8646	+	10.2400i	1.48643	+	0.339268i	0.887228	−	0.461330i	$-0.152628\pi$
$911$	44.8646	+	10.2400i	1.48643	+	0.339268i	0.599201	+	0.800598i	$0.295485\pi$
$912$	−11.5643	−	1.24227i	−0.382933	−	0.0411358i
$913$		−	30.1087i		−	0.996451i
$914$	−1.23718	−	0.282378i	−0.0409222	−	0.00934023i
$915$	−24.9992	+	8.89342i	−0.826449	+	0.294008i
$916$	2.81974	−	2.24866i	0.0931667	−	0.0742980i
$917$	−9.08019	+	9.47593i	−0.299854	+	0.312923i
$918$	−24.2988	+	15.8006i	−0.801981	+	0.521498i
$919$	−6.75190	+	29.5820i	−0.222724	+	0.975820i	0.732692	+	0.680560i	$0.238263\pi$
$919$	−6.75190	+	29.5820i	−0.222724	+	0.975820i	−0.955417	+	0.295260i	$0.904594\pi$
$920$	13.0616	−	16.3788i	0.430630	−	0.539992i
$921$	−19.1715	+	6.82023i	−0.631723	+	0.224734i
$922$	3.41414	−	2.72269i	0.112439	−	0.0896670i
$923$	4.93304	+	2.37563i	0.162373	+	0.0781947i
$924$	6.91508	+	5.22082i	0.227489	+	0.171752i
$925$	17.9258	−	8.63259i	0.589396	−	0.283838i
$926$	−15.1568	+	31.4734i	−0.498083	+	1.03428i
$927$	−0.322529	+	0.00334607i	−0.0105933	+	0.000109899i
$928$	0.479771	+	0.231046i	0.0157493	+	0.00758445i
$929$	1.04602	−	1.31166i	0.0343187	−	0.0430342i	−0.764376	−	0.644771i	$-0.776953\pi$
$929$	1.04602	−	1.31166i	0.0343187	−	0.0430342i	0.798695	+	0.601737i	$0.205524\pi$
$930$	−3.45463	+	32.1591i	−0.113282	+	1.05454i
$931$	−30.8476	−	35.4675i	−1.01099	−	1.16240i
$932$			12.7838i			0.418748i
$933$	−39.7876	−	39.3770i	−1.30259	−	1.28915i
$934$	−0.604854	+	1.25599i	−0.0197914	+	0.0410973i
$935$	35.9491	−	8.20515i	1.17566	−	0.268337i
$936$	−2.21313	−	1.72766i	−0.0723384	−	0.0564703i
$937$	−14.8287	−	30.7920i	−0.484431	−	1.00593i	−0.989725	−	0.142984i	$-0.954330\pi$
$937$	−14.8287	−	30.7920i	−0.484431	−	1.00593i	0.505294	−	0.862947i	$-0.331384\pi$
$938$	−23.0162	−	7.50683i	−0.751506	−	0.245107i
$939$	−5.68224	−	3.52941i	−0.185433	−	0.115178i
$940$	24.7693	+	31.0597i	0.807884	+	1.01305i
$941$	7.21806	−	3.47603i	0.235302	−	0.113315i	−0.312518	−	0.949912i	$-0.601172\pi$
$941$	7.21806	−	3.47603i	0.235302	−	0.113315i	0.547820	+	0.836596i	$0.315458\pi$
$942$	−26.1055	−	25.8360i	−0.850562	−	0.841783i
$943$	−10.4638	−	2.38829i	−0.340748	−	0.0777735i
$944$	0.679036	−	0.851484i	0.0221007	−	0.0277134i
$945$	47.2221	+	8.96011i	1.53614	+	0.291472i
$946$	12.3193	+	15.4479i	0.400536	+	0.502256i
$947$	3.81956	+	7.93140i	0.124119	+	0.257736i	0.953765	−	0.300555i	$-0.0971718\pi$
$947$	3.81956	+	7.93140i	0.124119	+	0.257736i	−0.829646	+	0.558290i	$0.811457\pi$
$948$	−25.0949	−	8.63526i	−0.815046	−	0.280460i
$949$	−1.21335			−0.0393872
$950$	48.5052			1.57372
$951$	−6.25760	+	18.1852i	−0.202916	+	0.589696i
$952$	−14.0307	−	4.57617i	−0.454738	−	0.148315i
$953$	−5.81440	+	1.32710i	−0.188347	+	0.0429889i	−0.315654	−	0.948874i	$-0.602224\pi$
$953$	−5.81440	+	1.32710i	−0.188347	+	0.0429889i	0.127307	+	0.991863i	$0.459367\pi$
$954$	−0.174600	−	16.8298i	−0.00565288	−	0.544885i
$955$	−44.0673	+	35.1425i	−1.42599	+	1.13719i
$956$	19.0671	−	15.2055i	0.616674	−	0.491781i
$957$	−1.73191	+	0.204242i	−0.0559846	+	0.00660221i
$958$	27.2271	−	6.21441i	0.879668	−	0.200778i
$959$	1.35004	+	1.29365i	0.0435950	+	0.0417743i
$960$	5.72606	+	1.97036i	0.184808	+	0.0635930i
$961$	2.47138			0.0797219
$962$	−2.57779			−0.0831113
$963$	34.1616	+	16.0169i	1.10084	+	0.516139i
$964$	0.347054	+	0.720665i	0.0111779	+	0.0232111i
$965$	25.2860	+	31.7076i	0.813984	+	1.02070i
$966$	16.5453	−	21.9145i	0.532335	−	0.705088i
$967$	2.27991	−	2.85892i	0.0733169	−	0.0919365i	−0.743820	−	0.668379i	$-0.766988\pi$
$967$	2.27991	−	2.85892i	0.0733169	−	0.0919365i	0.817137	+	0.576443i	$0.195560\pi$
$968$	7.23883	+	1.65222i	0.232665	+	0.0531042i
$969$	−45.6366	+	46.1125i	−1.46606	+	1.48135i
$970$	−22.1393	+	10.6617i	−0.710850	+	0.342327i
$971$	20.4671	+	25.6649i	0.656819	+	0.823625i	0.992993	−	0.118175i	$-0.0377044\pi$
$971$	20.4671	+	25.6649i	0.656819	+	0.823625i	−0.336174	+	0.941800i	$0.609133\pi$
$972$	12.9796	−	8.63305i	0.416321	−	0.276905i
$973$	1.54851	−	16.9929i	0.0496429	−	0.544766i
$974$	10.0720	+	20.9148i	0.322729	+	0.670153i
$975$	9.94639	+	6.17800i	0.318539	+	0.197854i
$976$	−4.27189	+	0.975031i	−0.136740	+	0.0312100i
$977$	15.4660	−	32.1155i	0.494801	−	1.02747i	−0.492751	−	0.870171i	$-0.664009\pi$
$977$	15.4660	−	32.1155i	0.494801	−	1.02747i	0.987552	−	0.157295i	$-0.0502772\pi$
$978$	8.82765	−	8.91970i	0.282277	−	0.285221i
$979$		−	19.9848i		−	0.638716i
$980$	11.5490	+	21.5769i	0.368919	+	0.689250i
$981$	12.0687	+	2.62318i	0.385324	+	0.0837518i
$982$	−15.0404	+	18.8601i	−0.479959	+	0.601850i
$983$	25.3959	+	12.2300i	0.810002	+	0.390077i	0.792577	−	0.609772i	$-0.208739\pi$
$983$	25.3959	+	12.2300i	0.810002	+	0.390077i	0.0174252	+	0.999848i	$0.494453\pi$
$984$	−0.363350	−	3.08109i	−0.0115832	−	0.0982217i
$985$	−23.2689	+	48.3184i	−0.741409	+	1.53955i
$986$	2.67619	−	1.28878i	0.0852271	−	0.0410432i
$987$	33.5337	+	39.8361i	1.06739	+	1.26800i
$988$	−5.66211	−	2.72673i	−0.180136	−	0.0867487i
$989$	48.9559	−	39.0411i	1.55671	−	1.24143i
$990$	−19.2874	+	4.61325i	−0.612995	+	0.146619i
$991$	−1.69684	+	2.12777i	−0.0539018	+	0.0675907i	−0.808052	−	0.589112i	$-0.799478\pi$
$991$	−1.69684	+	2.12777i	−0.0539018	+	0.0675907i	0.754150	+	0.656702i	$0.228049\pi$
$992$	−1.18853	+	5.20730i	−0.0377360	+	0.165332i
$993$	14.1029	+	13.9574i	0.447543	+	0.442924i
$994$	−15.4149	−	1.40471i	−0.488931	−	0.0445548i
$995$	−68.8827	+	54.9322i	−2.18373	+	1.74147i
$996$	−9.24441	−	25.9858i	−0.292920	−	0.823393i
$997$	56.3565	+	12.8630i	1.78483	+	0.407375i	0.982007	−	0.188844i	$-0.0604741\pi$
$997$	56.3565	+	12.8630i	1.78483	+	0.407375i	0.802821	+	0.596220i	$0.203331\pi$
$998$		−	25.7079i		−	0.813769i
$999$	4.51630	−	13.5811i	0.142889	−	0.429688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.j.a.251.14	yes	120
3.2	odd	2	inner	294.2.j.a.251.4	yes	120
49.41	odd	14	inner	294.2.j.a.41.4	✓	120
147.41	even	14	inner	294.2.j.a.41.14	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.4	✓	120	49.41	odd	14	inner
294.2.j.a.41.14	yes	120	147.41	even	14	inner
294.2.j.a.251.4	yes	120	3.2	odd	2	inner
294.2.j.a.251.14	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(-0.913887 + 1.47133i) q^{3} +(0.222521 + 0.974928i) q^{4} +(3.14996 + 1.51694i) q^{5} +(-1.63186 + 0.580532i) q^{6} +(2.47808 - 0.926885i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-1.32962 - 2.68926i) q^{9} +(1.51694 + 3.14996i) q^{10} +(-1.47826 - 1.17888i) q^{11} +(-1.63780 - 0.563572i) q^{12} +(-0.731696 - 0.583508i) q^{13} +(2.51534 + 0.820391i) q^{14} +(-5.11062 + 3.24831i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-1.24123 + 5.43819i) q^{17} +(0.637185 - 2.93155i) q^{18} -6.71507i q^{19} +(-0.777975 + 3.40853i) q^{20} +(-0.900933 + 4.49314i) q^{21} +(-0.420736 - 1.84336i) q^{22} +(-5.84179 + 1.33335i) q^{23} +(-0.929101 - 1.46177i) q^{24} +(4.50368 + 5.64743i) q^{25} +(-0.208252 - 0.912410i) q^{26} +(5.17191 + 0.501368i) q^{27} +(1.45507 + 2.20970i) q^{28} +(-0.519155 - 0.118494i) q^{29} +(-6.02094 - 0.646788i) q^{30} -5.34122i q^{31} +(-0.974928 - 0.222521i) q^{32} +(3.08548 - 1.09765i) q^{33} +(-4.36109 + 3.47785i) q^{34} +(9.21188 + 0.839452i) q^{35} +(2.32596 - 1.89470i) q^{36} +(0.612916 - 2.68536i) q^{37} +(4.18678 - 5.25005i) q^{38} +(1.52722 - 0.543305i) q^{39} +(-2.73343 + 2.17984i) q^{40} +(1.61381 + 0.777171i) q^{41} +(-3.50581 + 2.95116i) q^{42} +(-9.41518 + 4.53411i) q^{43} +(0.820375 - 1.70353i) q^{44} +(-0.108807 - 10.4880i) q^{45} +(-5.39863 - 2.59984i) q^{46} +(7.08465 - 8.88387i) q^{47} +(0.184998 - 1.72214i) q^{48} +(5.28177 - 4.59379i) q^{49} +7.22334i q^{50} +(-6.86702 - 6.79615i) q^{51} +(0.406061 - 0.843194i) q^{52} +(5.46957 - 1.24839i) q^{53} +(3.73096 + 3.61662i) q^{54} +(-2.86818 - 5.95585i) q^{55} +(-0.240105 + 2.63483i) q^{56} +(9.88008 + 6.13682i) q^{57} +(-0.332012 - 0.416330i) q^{58} +(-0.981235 + 0.472538i) q^{59} +(-4.30409 - 4.25967i) q^{60} +(4.27189 + 0.975031i) q^{61} +(3.33020 - 4.17593i) q^{62} +(-5.78754 - 5.43179i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-1.41966 - 2.94796i) q^{65} +(3.09670 + 1.06559i) q^{66} -9.15032 q^{67} -5.57804 q^{68} +(3.37694 - 9.81373i) q^{69} +(6.67875 + 6.39982i) q^{70} +(-5.70374 + 1.30184i) q^{71} +(2.99984 - 0.0311217i) q^{72} +(1.01364 - 0.808350i) q^{73} +(2.15349 - 1.71735i) q^{74} +(-12.4251 + 1.46528i) q^{75} +(6.54671 - 1.49424i) q^{76} +(-4.75594 - 1.55117i) q^{77} +(1.53277 + 0.527433i) q^{78} +15.3224 q^{79} -3.49619 q^{80} +(-5.46422 + 7.15139i) q^{81} +(0.777171 + 1.61381i) q^{82} +(9.92846 + 12.4499i) q^{83} +(-4.58097 + 0.121473i) q^{84} +(-12.1592 + 15.2472i) q^{85} +(-10.1881 - 2.32536i) q^{86} +(0.648792 - 0.655558i) q^{87} +(1.70353 - 0.820375i) q^{88} +(6.59006 + 8.26368i) q^{89} +(6.45409 - 8.26769i) q^{90} +(-2.35405 - 0.767783i) q^{91} +(-2.59984 - 5.39863i) q^{92} +(7.85869 + 4.88127i) q^{93} +(11.0780 - 2.52848i) q^{94} +(10.1864 - 21.1522i) q^{95} +(1.21838 - 1.23108i) q^{96} +7.02844i q^{97} +(6.99364 - 0.298440i) q^{98} +(-1.20477 + 5.54289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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