LMFDB - Embedded newform 950.2.n.a.39.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.14
Character	$\chi$	$=$	950.39
Dual form			950.2.n.a.609.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-1.78167 - 0.578899i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.452104 - 2.18989i) q^{5} +(-0.578899 - 1.78167i) q^{6} -4.62971i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.412164 + 0.299454i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-1.78167 - 0.578899i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.452104 - 2.18989i) q^{5} +(-0.578899 - 1.78167i) q^{6} -4.62971i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.412164 + 0.299454i) q^{9} +(2.03740 - 0.921423i) q^{10} +(-1.66981 + 1.21319i) q^{11} +(1.10113 - 1.51558i) q^{12} +(0.120083 - 0.165281i) q^{13} +(3.74551 - 2.72127i) q^{14} +(-2.07322 + 3.63993i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-7.34351 + 2.38605i) q^{17} +0.509462i q^{18} +(0.309017 + 0.951057i) q^{19} +(1.94300 + 1.10669i) q^{20} +(-2.68013 + 8.24859i) q^{21} +(-1.96298 - 0.637810i) q^{22} +(3.34422 + 4.60293i) q^{23} +1.87336 q^{24} +(-4.59120 - 1.98011i) q^{25} +0.204298 q^{26} +(2.74241 + 3.77460i) q^{27} +(4.40311 + 1.43066i) q^{28} +(-2.29817 + 7.07304i) q^{29} +(-4.16337 + 0.462223i) q^{30} +(0.930922 + 2.86508i) q^{31} -1.00000i q^{32} +(3.67735 - 1.19484i) q^{33} +(-6.24677 - 4.53854i) q^{34} +(-10.1385 - 2.09311i) q^{35} +(-0.412164 + 0.299454i) q^{36} +(2.09837 - 2.88815i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(-0.309629 + 0.224959i) q^{39} +(0.246735 + 2.22241i) q^{40} +(6.24877 + 4.54000i) q^{41} +(-8.24859 + 2.68013i) q^{42} -9.51033i q^{43} +(-0.637810 - 1.96298i) q^{44} +(0.842112 - 0.767207i) q^{45} +(-1.75816 + 5.41106i) q^{46} +(-8.97884 - 2.91740i) q^{47} +(1.10113 + 1.51558i) q^{48} -14.4342 q^{49} +(-1.09670 - 4.87824i) q^{50} +14.4650 q^{51} +(0.120083 + 0.165281i) q^{52} +(-8.36014 - 2.71637i) q^{53} +(-1.44177 + 4.43731i) q^{54} +(1.90181 + 4.20517i) q^{55} +(1.43066 + 4.40311i) q^{56} -1.87336i q^{57} +(-7.07304 + 2.29817i) q^{58} +(-3.73244 - 2.71177i) q^{59} +(-2.82111 - 3.09655i) q^{60} +(-2.93132 + 2.12973i) q^{61} +(-1.77072 + 2.43719i) q^{62} +(1.38639 - 1.90820i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.307655 - 0.337693i) q^{65} +(3.12814 + 2.27273i) q^{66} +(0.615998 - 0.200150i) q^{67} -7.72143i q^{68} +(-3.29366 - 10.1368i) q^{69} +(-4.26592 - 9.43254i) q^{70} +(2.53132 - 7.79060i) q^{71} +(-0.484527 - 0.157432i) q^{72} +(-0.0392713 - 0.0540524i) q^{73} +3.56995 q^{74} +(7.03371 + 6.18575i) q^{75} -1.00000 q^{76} +(5.61669 + 7.73071i) q^{77} +(-0.363991 - 0.118268i) q^{78} +(1.52921 - 4.70642i) q^{79} +(-1.65294 + 1.50591i) q^{80} +(-3.17324 - 9.76624i) q^{81} +7.72390i q^{82} +(12.1253 - 3.93975i) q^{83} +(-7.01667 - 5.09791i) q^{84} +(1.90515 + 17.1602i) q^{85} +(7.69402 - 5.59003i) q^{86} +(8.18915 - 11.2714i) q^{87} +(1.21319 - 1.66981i) q^{88} +(-8.13660 + 5.91159i) q^{89} +(1.11566 + 0.230330i) q^{90} +(-0.765200 - 0.555950i) q^{91} +(-5.41106 + 1.75816i) q^{92} -5.64353i q^{93} +(-2.91740 - 8.97884i) q^{94} +(2.22241 - 0.246735i) q^{95} +(-0.578899 + 1.78167i) q^{96} +(-11.5818 - 3.76315i) q^{97} +(-8.48419 - 11.6775i) q^{98} -1.05153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−1.78167	−	0.578899i	−1.02865	−	0.334227i	−0.254391	−	0.967101i	$-0.581875\pi$
$3$	−1.78167	−	0.578899i	−1.02865	−	0.334227i	−0.774255	+	0.632874i	$0.781875\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	0.452104	−	2.18989i	0.202187	−	0.979347i
$5$	0.452104	−	2.18989i	0.202187	−	0.979347i
$6$	−0.578899	−	1.78167i	−0.236334	−	0.727363i
$7$		−	4.62971i		−	1.74986i	−0.484246	−	0.874932i	$-0.660906\pi$
$7$		−	4.62971i		−	1.74986i	0.484246	−	0.874932i	$-0.339094\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	0.412164	+	0.299454i	0.137388	+	0.0998181i
$10$	2.03740	−	0.921423i	0.644281	−	0.291379i
$11$	−1.66981	+	1.21319i	−0.503466	+	0.365789i	−0.810339	−	0.585961i	$-0.800717\pi$
$11$	−1.66981	+	1.21319i	−0.503466	+	0.365789i	0.306873	+	0.951750i	$0.400717\pi$
$12$	1.10113	−	1.51558i	0.317869	−	0.437509i
$13$	0.120083	−	0.165281i	0.0333051	−	0.0458406i	−0.792040	−	0.610470i	$-0.790981\pi$
$13$	0.120083	−	0.165281i	0.0333051	−	0.0458406i	0.825345	+	0.564629i	$0.190981\pi$
$14$	3.74551	−	2.72127i	1.00103	−	0.727291i
$15$	−2.07322	+	3.63993i	−0.535304	+	0.939825i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−7.34351	+	2.38605i	−1.78106	+	0.578703i	−0.999009	−	0.0445073i	$-0.985828\pi$
$17$	−7.34351	+	2.38605i	−1.78106	+	0.578703i	−0.782055	+	0.623210i	$0.785828\pi$
$18$			0.509462i			0.120081i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	1.94300	+	1.10669i	0.434467	+	0.247463i
$21$	−2.68013	+	8.24859i	−0.584852	+	1.79999i
$22$	−1.96298	−	0.637810i	−0.418508	−	0.135981i
$23$	3.34422	+	4.60293i	0.697318	+	0.959776i	0.999978	+	0.00667754i	$0.00212554\pi$
$23$	3.34422	+	4.60293i	0.697318	+	0.959776i	−0.302659	+	0.953099i	$0.597874\pi$
$24$	1.87336			0.382397
$25$	−4.59120	−	1.98011i	−0.918241	−	0.396023i
$26$	0.204298			0.0400661
$27$	2.74241	+	3.77460i	0.527777	+	0.726422i
$28$	4.40311	+	1.43066i	0.832110	+	0.270369i
$29$	−2.29817	+	7.07304i	−0.426760	+	1.31343i	0.474540	+	0.880234i	$0.342615\pi$
$29$	−2.29817	+	7.07304i	−0.426760	+	1.31343i	−0.901299	+	0.433197i	$0.857385\pi$
$30$	−4.16337	+	0.462223i	−0.760124	+	0.0843899i
$31$	0.930922	+	2.86508i	0.167199	+	0.514584i	0.999192	−	0.0402019i	$-0.0128001\pi$
$31$	0.930922	+	2.86508i	0.167199	+	0.514584i	−0.831993	+	0.554786i	$0.812800\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.67735	−	1.19484i	0.640145	−	0.207996i
$34$	−6.24677	−	4.53854i	−1.07131	−	0.778353i
$35$	−10.1385	−	2.09311i	−1.71372	−	0.353800i
$36$	−0.412164	+	0.299454i	−0.0686939	+	0.0499091i
$37$	2.09837	−	2.88815i	0.344969	−	0.474809i	−0.600915	−	0.799313i	$-0.705197\pi$
$37$	2.09837	−	2.88815i	0.344969	−	0.474809i	0.945885	+	0.324503i	$0.105197\pi$
$38$	−0.587785	+	0.809017i	−0.0953514	+	0.131240i
$39$	−0.309629	+	0.224959i	−0.0495804	+	0.0360222i
$40$	0.246735	+	2.22241i	0.0390123	+	0.351394i
$41$	6.24877	+	4.54000i	0.975894	+	0.709028i	0.956787	−	0.290789i	$-0.0939179\pi$
$41$	6.24877	+	4.54000i	0.975894	+	0.709028i	0.0191064	+	0.999817i	$0.493918\pi$
$42$	−8.24859	+	2.68013i	−1.27279	+	0.413553i
$43$		−	9.51033i		−	1.45031i	−0.688585	−	0.725156i	$-0.741768\pi$
$43$		−	9.51033i		−	1.45031i	0.688585	−	0.725156i	$-0.258232\pi$
$44$	−0.637810	−	1.96298i	−0.0961534	−	0.295930i
$45$	0.842112	−	0.767207i	0.125535	−	0.114368i
$46$	−1.75816	+	5.41106i	−0.259227	+	0.797818i
$47$	−8.97884	−	2.91740i	−1.30970	−	0.425547i	−0.430753	−	0.902470i	$-0.641752\pi$
$47$	−8.97884	−	2.91740i	−1.30970	−	0.425547i	−0.878945	+	0.476923i	$0.841752\pi$
$48$	1.10113	+	1.51558i	0.158935	+	0.218755i
$49$	−14.4342			−2.06202
$50$	−1.09670	−	4.87824i	−0.155096	−	0.689888i
$51$	14.4650			2.02550
$52$	0.120083	+	0.165281i	0.0166526	+	0.0229203i
$53$	−8.36014	−	2.71637i	−1.14835	−	0.373123i	−0.327831	−	0.944736i	$-0.606318\pi$
$53$	−8.36014	−	2.71637i	−1.14835	−	0.373123i	−0.820523	+	0.571614i	$0.806318\pi$
$54$	−1.44177	+	4.43731i	−0.196200	+	0.603841i
$55$	1.90181	+	4.20517i	0.256440	+	0.567026i
$56$	1.43066	+	4.40311i	0.191180	+	0.588391i
$57$		−	1.87336i		−	0.248132i
$58$	−7.07304	+	2.29817i	−0.928736	+	0.301765i
$59$	−3.73244	−	2.71177i	−0.485922	−	0.353043i	0.317692	−	0.948194i	$-0.397092\pi$
$59$	−3.73244	−	2.71177i	−0.485922	−	0.353043i	−0.803614	+	0.595151i	$0.797092\pi$
$60$	−2.82111	−	3.09655i	−0.364204	−	0.399763i
$61$	−2.93132	+	2.12973i	−0.375317	+	0.272684i	−0.759412	−	0.650610i	$-0.774513\pi$
$61$	−2.93132	+	2.12973i	−0.375317	+	0.272684i	0.384095	+	0.923294i	$0.374513\pi$
$62$	−1.77072	+	2.43719i	−0.224881	+	0.309523i
$63$	1.38639	−	1.90820i	0.174668	−	0.240410i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−0.307655	−	0.337693i	−0.0381599	−	0.0418856i
$66$	3.12814	+	2.27273i	0.385048	+	0.279754i
$67$	0.615998	−	0.200150i	0.0752562	−	0.0244522i	−0.271147	−	0.962538i	$-0.587403\pi$
$67$	0.615998	−	0.200150i	0.0752562	−	0.0244522i	0.346403	+	0.938086i	$0.387403\pi$
$68$		−	7.72143i		−	0.936361i
$69$	−3.29366	−	10.1368i	−0.396510	−	1.22033i
$70$	−4.26592	−	9.43254i	−0.509874	−	1.12740i
$71$	2.53132	−	7.79060i	0.300412	−	0.924574i	−0.680937	−	0.732342i	$-0.738427\pi$
$71$	2.53132	−	7.79060i	0.300412	−	0.924574i	0.981349	−	0.192232i	$-0.0615727\pi$
$72$	−0.484527	−	0.157432i	−0.0571021	−	0.0185536i
$73$	−0.0392713	−	0.0540524i	−0.00459636	−	0.00632635i	0.806713	−	0.590944i	$-0.201245\pi$
$73$	−0.0392713	−	0.0540524i	−0.00459636	−	0.00632635i	−0.811309	+	0.584618i	$0.801245\pi$
$74$	3.56995			0.414999
$75$	7.03371	+	6.18575i	0.812183	+	0.714269i
$76$	−1.00000			−0.114708
$77$	5.61669	+	7.73071i	0.640082	+	0.880997i
$78$	−0.363991	−	0.118268i	−0.0412139	−	0.0133912i
$79$	1.52921	−	4.70642i	0.172049	−	0.529513i	−0.827437	−	0.561558i	$-0.810202\pi$
$79$	1.52921	−	4.70642i	0.172049	−	0.529513i	0.999486	+	0.0320451i	$0.0102020\pi$
$80$	−1.65294	+	1.50591i	−0.184805	+	0.168366i
$81$	−3.17324	−	9.76624i	−0.352583	−	1.08514i
$82$			7.72390i			0.852962i
$83$	12.1253	−	3.93975i	1.33092	−	0.432443i	0.444691	−	0.895684i	$-0.353313\pi$
$83$	12.1253	−	3.93975i	1.33092	−	0.432443i	0.886233	+	0.463240i	$0.153313\pi$
$84$	−7.01667	−	5.09791i	−0.765582	−	0.556228i
$85$	1.90515	+	17.1602i	0.206642	+	1.86129i
$86$	7.69402	−	5.59003i	0.829667	−	0.602788i
$87$	8.18915	−	11.2714i	0.877969	−	1.20842i
$88$	1.21319	−	1.66981i	0.129326	−	0.178002i
$89$	−8.13660	+	5.91159i	−0.862478	+	0.626627i	−0.928558	−	0.371187i	$-0.878951\pi$
$89$	−8.13660	+	5.91159i	−0.862478	+	0.626627i	0.0660800	+	0.997814i	$0.478951\pi$
$90$	1.11566	+	0.230330i	0.117601	+	0.0242789i
$91$	−0.765200	−	0.555950i	−0.0802148	−	0.0582794i
$92$	−5.41106	+	1.75816i	−0.564142	+	0.183301i
$93$		−	5.64353i		−	0.585207i
$94$	−2.91740	−	8.97884i	−0.300907	−	0.926096i
$95$	2.22241	−	0.246735i	0.228015	−	0.0253145i
$96$	−0.578899	+	1.78167i	−0.0590836	+	0.181841i
$97$	−11.5818	−	3.76315i	−1.17595	−	0.382090i	−0.345091	−	0.938569i	$-0.612152\pi$
$97$	−11.5818	−	3.76315i	−1.17595	−	0.382090i	−0.830861	+	0.556479i	$0.812152\pi$
$98$	−8.48419	−	11.6775i	−0.857033	−	1.17960i
$99$	−1.05153			−0.105682
$100$	3.30196	−	3.75460i	0.330196	−	0.375460i
$101$	0.678131			0.0674766			0.0337383	−	0.999431i	$-0.489259\pi$
$101$	0.678131			0.0674766			0.0337383	+	0.999431i	$0.489259\pi$
$102$	8.50230	+	11.7024i	0.841853	+	1.15871i
$103$	13.8117	+	4.48769i	1.36091	+	0.442185i	0.896345	−	0.443356i	$-0.146212\pi$
$103$	13.8117	+	4.48769i	1.36091	+	0.442185i	0.464560	+	0.885541i	$0.346212\pi$
$104$	−0.0631315	+	0.194299i	−0.00619056	+	0.0190526i
$105$	16.8518	+	9.59841i	1.64457	+	0.936709i
$106$	−2.71637	−	8.36014i	−0.263838	−	0.812009i
$107$		−	12.0523i		−	1.16514i	−0.812781	−	0.582569i	$-0.802048\pi$
$107$		−	12.0523i		−	1.16514i	0.812781	−	0.582569i	$-0.197952\pi$
$108$	−4.43731	+	1.44177i	−0.426980	+	0.138734i
$109$	−15.1220	−	10.9868i	−1.44842	−	1.05234i	−0.986196	−	0.165580i	$-0.947051\pi$
$109$	−15.1220	−	10.9868i	−1.44842	−	1.05234i	−0.462227	−	0.886762i	$-0.652949\pi$
$110$	−2.28420	+	4.01034i	−0.217790	+	0.382371i
$111$	−5.41054	+	3.93099i	−0.513545	+	0.373113i
$112$	−2.72127	+	3.74551i	−0.257136	+	0.353917i
$113$	−1.48903	+	2.04947i	−0.140076	+	0.192798i	−0.873291	−	0.487198i	$-0.838019\pi$
$113$	−1.48903	+	2.04947i	−0.140076	+	0.192798i	0.733215	+	0.679997i	$0.238019\pi$
$114$	1.51558	−	1.10113i	0.141947	−	0.103130i
$115$	11.5918	−	5.24246i	1.08094	−	0.488862i
$116$	−6.01669	−	4.37138i	−0.558636	−	0.405873i
$117$	0.0989879	−	0.0321631i	0.00915144	−	0.00297348i
$118$		−	4.61355i		−	0.424711i
$119$	11.0467	+	33.9983i	1.01265	+	3.11662i
$120$	0.846953	−	4.10244i	0.0773158	−	0.374499i
$121$	−2.08275	+	6.41005i	−0.189341	+	0.582732i
$122$	−3.44597	−	1.11966i	−0.311984	−	0.101370i
$123$	−8.50503	−	11.7062i	−0.766872	−	1.05551i
$124$	−3.01253			−0.270533
$125$	−6.41193	+	9.15899i	−0.573500	+	0.819205i
$126$	2.35866			0.210126
$127$	−2.09512	−	2.88369i	−0.185912	−	0.255886i	0.705880	−	0.708331i	$-0.250552\pi$
$127$	−2.09512	−	2.88369i	−0.185912	−	0.255886i	−0.891792	+	0.452445i	$0.850552\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−5.50552	+	16.9442i	−0.484734	+	1.49186i
$130$	0.0923640	−	0.447389i	0.00810086	−	0.0392386i
$131$	1.85691	+	5.71497i	0.162239	+	0.499319i	0.998822	−	0.0485202i	$-0.0154505\pi$
$131$	1.85691	+	5.71497i	0.162239	+	0.499319i	−0.836584	+	0.547839i	$0.815451\pi$
$132$			3.86660i			0.336544i
$133$	4.40311	−	1.43066i	0.381798	−	0.124054i
$134$	0.523999	+	0.380708i	0.0452667	+	0.0328881i
$135$	9.50580	−	4.29905i	0.818129	−	0.370003i
$136$	6.24677	−	4.53854i	0.535656	−	0.389177i
$137$	6.77931	−	9.33091i	0.579195	−	0.797194i	−0.414412	−	0.910090i	$-0.636013\pi$
$137$	6.77931	−	9.33091i	0.579195	−	0.797194i	0.993607	+	0.112896i	$0.0360126\pi$
$138$	6.26492	−	8.62292i	0.533305	−	0.734031i
$139$	−3.62171	+	2.63133i	−0.307189	+	0.223186i	−0.730690	−	0.682710i	$-0.760801\pi$
$139$	−3.62171	+	2.63133i	−0.307189	+	0.223186i	0.423500	+	0.905896i	$0.360801\pi$
$140$	5.12364	−	8.99551i	0.433027	−	0.760259i
$141$	14.3084	+	10.3957i	1.20499	+	0.875474i
$142$	7.79060	−	2.53132i	0.653773	−	0.212424i
$143$			0.421670i			0.0352618i
$144$	−0.157432	−	0.484527i	−0.0131194	−	0.0403773i
$145$	14.4501	+	8.23049i	1.20002	+	0.683505i
$146$	0.0206462	−	0.0635424i	0.00170869	−	0.00525880i
$147$	25.7169	+	8.35592i	2.12109	+	0.689185i
$148$	2.09837	+	2.88815i	0.172485	+	0.237405i
$149$	−21.2226			−1.73862			−0.869311	−	0.494266i	$-0.835437\pi$
$149$	−21.2226			−1.73862			−0.869311	+	0.494266i	$0.835437\pi$
$150$	−0.870064	+	9.32628i	−0.0710404	+	0.761488i
$151$	−18.0349			−1.46766			−0.733829	−	0.679334i	$-0.762269\pi$
$151$	−18.0349			−1.46766			−0.733829	+	0.679334i	$0.762269\pi$
$152$	−0.587785	−	0.809017i	−0.0476757	−	0.0656199i
$153$	−3.74124	−	1.21560i	−0.302462	−	0.0982757i
$154$	−2.95287	+	9.08800i	−0.237949	+	0.732332i
$155$	6.69508	−	0.743296i	0.537762	−	0.0597030i
$156$	−0.118268	−	0.363991i	−0.00946900	−	0.0291426i
$157$			11.7140i			0.934881i	0.884024	+	0.467441i	$0.154824\pi$
$157$			11.7140i			0.934881i	−0.884024	+	0.467441i	$0.845176\pi$
$158$	4.70642	−	1.52921i	0.374422	−	0.121657i
$159$	13.3225	+	9.67935i	1.05654	+	0.767622i
$160$	−2.18989	−	0.452104i	−0.173126	−	0.0357420i
$161$	21.3102	−	15.4828i	1.67948	−	1.22021i
$162$	6.03587	−	8.30766i	0.474223	−	0.652712i
$163$	−0.113457	+	0.156160i	−0.00888661	+	0.0122314i	−0.813437	−	0.581653i	$-0.802406\pi$
$163$	−0.113457	+	0.156160i	−0.00888661	+	0.0122314i	0.804551	+	0.593884i	$0.202406\pi$
$164$	−6.24877	+	4.54000i	−0.487947	+	0.354514i
$165$	−0.954025	−	8.59318i	−0.0742708	−	0.668978i
$166$	10.3144	+	7.49384i	0.800552	+	0.581635i
$167$	−3.45815	+	1.12362i	−0.267600	+	0.0869483i	−0.439743	−	0.898123i	$-0.644931\pi$
$167$	−3.45815	+	1.12362i	−0.267600	+	0.0869483i	0.172144	+	0.985072i	$0.444931\pi$
$168$		−	8.67309i		−	0.669143i
$169$	4.00432	+	12.3240i	0.308025	+	0.948003i
$170$	−12.7631	+	11.6278i	−0.978883	+	0.891812i
$171$	−0.157432	+	0.484527i	−0.0120392	+	0.0370527i
$172$	9.04486	+	2.93885i	0.689664	+	0.224085i
$173$	6.87977	+	9.46920i	0.523060	+	0.719930i	0.986053	−	0.166432i	$-0.0532246\pi$
$173$	6.87977	+	9.46920i	0.523060	+	0.719930i	−0.462993	+	0.886362i	$0.653225\pi$
$174$	13.9322			1.05620
$175$	−9.16735	+	21.2559i	−0.692986	+	1.60680i
$176$	2.06399			0.155579
$177$	5.08012	+	6.99218i	0.381845	+	0.525565i
$178$	−9.56515	−	3.10790i	−0.716938	−	0.232947i
$179$	−1.35831	+	4.18044i	−0.101525	+	0.312461i	−0.988899	−	0.148589i	$-0.952527\pi$
$179$	−1.35831	+	4.18044i	−0.101525	+	0.312461i	0.887374	+	0.461049i	$0.152527\pi$
$180$	0.469430	+	1.03798i	0.0349892	+	0.0773662i
$181$	−2.35287	−	7.24140i	−0.174888	−	0.538249i	0.824741	−	0.565511i	$-0.191321\pi$
$181$	−2.35287	−	7.24140i	−0.174888	−	0.538249i	−0.999628	+	0.0272621i	$0.991321\pi$
$182$		−	0.945839i		−	0.0701103i
$183$	6.45554	−	2.09753i	0.477207	−	0.155054i
$184$	−4.60293	−	3.34422i	−0.339332	−	0.246539i
$185$	−5.37604	−	5.90093i	−0.395255	−	0.433845i
$186$	4.56572	−	3.31719i	0.334774	−	0.243228i
$187$	9.36753	−	12.8933i	0.685021	−	0.942851i
$188$	5.54923	−	7.63785i	0.404719	−	0.557048i
$189$	17.4753	−	12.6965i	1.27114	−	0.923538i
$190$	1.50591	+	1.65294i	0.109251	+	0.119917i
$191$	−12.5605	−	9.12572i	−0.908844	−	0.660314i	0.0318779	−	0.999492i	$-0.489851\pi$
$191$	−12.5605	−	9.12572i	−0.908844	−	0.660314i	−0.940722	+	0.339178i	$0.889851\pi$
$192$	−1.78167	+	0.578899i	−0.128581	+	0.0417784i
$193$		−	26.4651i		−	1.90500i	−0.304545	−	0.952498i	$-0.598504\pi$
$193$		−	26.4651i		−	1.90500i	0.304545	−	0.952498i	$-0.401496\pi$
$194$	−3.76315	−	11.5818i	−0.270178	−	0.831524i
$195$	0.352649	+	0.779758i	0.0252537	+	0.0558396i
$196$	4.46040	−	13.7277i	0.318600	−	0.980551i
$197$	−8.33021	−	2.70665i	−0.593503	−	0.192841i	−0.00316239	−	0.999995i	$-0.501007\pi$
$197$	−8.33021	−	2.70665i	−0.593503	−	0.192841i	−0.590341	+	0.807154i	$0.701007\pi$
$198$	−0.618072	−	0.850703i	−0.0439245	−	0.0604569i
$199$	−17.5777			−1.24605			−0.623025	−	0.782202i	$-0.714096\pi$
$199$	−17.5777			−1.24605			−0.623025	+	0.782202i	$0.714096\pi$
$200$	4.97838	+	0.464441i	0.352025	+	0.0328409i
$201$	−1.21337			−0.0855846
$202$	0.398596	+	0.548620i	0.0280451	+	0.0386008i
$203$	32.7461	+	10.6399i	2.29833	+	0.746771i
$204$	−4.46992	+	13.7570i	−0.312957	+	0.963184i
$205$	12.7672	−	11.6315i	0.891698	−	0.812382i
$206$	4.48769	+	13.8117i	0.312672	+	0.962306i
$207$			2.89860i			0.201467i
$208$	−0.194299	+	0.0631315i	−0.0134722	+	0.00437738i
$209$	−1.66981	−	1.21319i	−0.115503	−	0.0839178i
$210$	2.13996	+	19.2752i	0.147671	+	1.33011i
$211$	3.30762	−	2.40313i	0.227706	−	0.165438i	−0.468082	−	0.883685i	$-0.655055\pi$
$211$	3.30762	−	2.40313i	0.227706	−	0.165438i	0.695789	+	0.718247i	$0.255055\pi$
$212$	5.16685	−	7.11156i	0.354861	−	0.488424i
$213$	−9.01994	+	12.4149i	−0.618036	+	0.850654i
$214$	9.75050	−	7.08415i	0.666530	−	0.484263i
$215$	−20.8265	−	4.29966i	−1.42036	−	0.293234i
$216$	−3.77460	−	2.74241i	−0.256829	−	0.186597i
$217$	13.2645	−	4.30989i	0.900452	−	0.292575i
$218$		−	18.6918i		−	1.26597i
$219$	0.0386776	+	0.119037i	0.00261359	+	0.00804381i
$220$	−4.58705	+	0.509260i	−0.309259	+	0.0343343i
$221$	−0.487466	+	1.50026i	−0.0327905	+	0.100919i
$222$	−6.36047	−	2.06664i	−0.426887	−	0.138704i
$223$	8.65002	+	11.9057i	0.579248	+	0.797267i	0.993613	−	0.112844i	$-0.0359961\pi$
$223$	8.65002	+	11.9057i	0.579248	+	0.797267i	−0.414365	+	0.910111i	$0.635996\pi$
$224$	−4.62971			−0.309335
$225$	−1.29937	−	2.19099i	−0.0866248	−	0.146066i
$226$	−2.53329			−0.168512
$227$	−7.10783	−	9.78308i	−0.471763	−	0.649326i	0.505133	−	0.863042i	$-0.331443\pi$
$227$	−7.10783	−	9.78308i	−0.471763	−	0.649326i	−0.976896	+	0.213715i	$0.931443\pi$
$228$	1.78167	+	0.578899i	0.117994	+	0.0383385i
$229$	8.33376	−	25.6487i	0.550710	−	1.69491i	−0.156301	−	0.987710i	$-0.549957\pi$
$229$	8.33376	−	25.6487i	0.550710	−	1.69491i	0.707011	−	0.707203i	$-0.250043\pi$
$230$	11.0547	+	6.29654i	0.728928	+	0.415181i
$231$	−5.53178	−	17.0251i	−0.363964	−	1.12017i
$232$		−	7.43704i		−	0.488265i
$233$	0.866515	−	0.281548i	0.0567673	−	0.0184448i	−0.280496	−	0.959855i	$-0.590499\pi$
$233$	0.866515	−	0.281548i	0.0567673	−	0.0184448i	0.337263	+	0.941410i	$0.390499\pi$
$234$	0.0842042	+	0.0611779i	0.00550460	+	0.00399932i
$235$	−10.4481	+	18.3437i	−0.681562	+	1.19661i
$236$	3.73244	−	2.71177i	0.242961	−	0.176522i
$237$	−5.44908	+	7.50001i	−0.353956	+	0.487178i
$238$	−21.0121	+	28.9207i	−1.36201	+	1.87465i
$239$	−1.97362	+	1.43392i	−0.127663	+	0.0927524i	−0.649784	−	0.760119i	$-0.725141\pi$
$239$	−1.97362	+	1.43392i	−0.127663	+	0.0927524i	0.522121	+	0.852871i	$0.325141\pi$
$240$	3.81677	−	1.72615i	0.246371	−	0.111423i
$241$	21.2031	+	15.4049i	1.36581	+	0.992319i	0.998051	+	0.0623982i	$0.0198749\pi$
$241$	21.2031	+	15.4049i	1.36581	+	0.992319i	0.367759	+	0.929921i	$0.380125\pi$
$242$	−6.41005	+	2.08275i	−0.412054	+	0.133884i
$243$			5.24019i			0.336158i
$244$	−1.11966	−	3.44597i	−0.0716792	−	0.220606i
$245$	−6.52575	+	31.6092i	−0.416915	+	2.01944i
$246$	4.47136	−	13.7614i	0.285083	−	0.877396i
$247$	0.194299	+	0.0631315i	0.0123629	+	0.00401696i
$248$	−1.77072	−	2.43719i	−0.112441	−	0.154761i
$249$	−23.8840			−1.51358
$250$	−11.1786	+	0.196162i	−0.706998	+	0.0124064i
$251$	16.4595			1.03891			0.519456	−	0.854497i	$-0.326135\pi$
$251$	16.4595			1.03891			0.519456	+	0.854497i	$0.326135\pi$
$252$	1.38639	+	1.90820i	0.0873341	+	0.120205i
$253$	−11.1684	−	3.62884i	−0.702152	−	0.228143i
$254$	1.10147	−	3.38998i	0.0691124	−	0.212706i
$255$	6.53968	−	31.6767i	0.409531	−	1.98367i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			2.63423i			0.164319i	0.996619	+	0.0821595i	$0.0261817\pi$
$257$			2.63423i			0.164319i	−0.996619	+	0.0821595i	$0.973818\pi$
$258$	−16.9442	+	5.50552i	−1.05490	+	0.342758i
$259$	−13.3713	−	9.71481i	−0.830852	−	0.603649i
$260$	0.416236	−	0.188245i	0.0258138	−	0.0116744i
$261$	−3.06528	+	2.22705i	−0.189736	+	0.137851i
$262$	−3.53204	+	4.86144i	−0.218210	+	0.300341i
$263$	9.98564	−	13.7441i	0.615741	−	0.847495i	−0.381293	−	0.924454i	$-0.624521\pi$
$263$	9.98564	−	13.7441i	0.615741	−	0.847495i	0.997034	+	0.0769594i	$0.0245212\pi$
$264$	−3.12814	+	2.27273i	−0.192524	+	0.139877i
$265$	−9.72821	+	17.0797i	−0.597599	+	1.04920i
$266$	3.74551	+	2.72127i	0.229652	+	0.166852i
$267$	17.9189	−	5.82221i	1.09662	−	0.356314i
$268$			0.647699i			0.0395645i
$269$	−5.34385	−	16.4467i	−0.325820	−	1.00277i	−0.971069	−	0.238799i	$-0.923246\pi$
$269$	−5.34385	−	16.4467i	−0.325820	−	1.00277i	0.645249	−	0.763972i	$-0.276754\pi$
$270$	9.06537	+	5.16344i	0.551701	+	0.314237i
$271$	−7.28919	+	22.4338i	−0.442786	+	1.36276i	0.442107	+	0.896963i	$0.354231\pi$
$271$	−7.28919	+	22.4338i	−0.442786	+	1.36276i	−0.884893	+	0.465794i	$0.845769\pi$
$272$	7.34351	+	2.38605i	0.445266	+	0.144676i
$273$	1.04149	+	1.43349i	0.0630340	+	0.0867589i
$274$	11.5336			0.696773
$275$	10.0687	−	2.26357i	0.607164	−	0.136499i
$276$	10.6585			0.641567
$277$	−11.1869	−	15.3974i	−0.672155	−	0.925143i	0.327651	−	0.944799i	$-0.393743\pi$
$277$	−11.1869	−	15.3974i	−0.672155	−	0.925143i	−0.999807	+	0.0196561i	$0.993743\pi$
$278$	−4.25757	−	1.38337i	−0.255352	−	0.0829690i
$279$	−0.474269	+	1.45965i	−0.0283938	+	0.0873870i
$280$	10.2891	−	1.14231i	0.614893	−	0.0682661i
$281$	1.04496	+	3.21607i	0.0623373	+	0.191854i	0.977375	−	0.211514i	$-0.0678393\pi$
$281$	1.04496	+	3.21607i	0.0623373	+	0.191854i	−0.915038	+	0.403368i	$0.867839\pi$
$282$			17.6862i			1.05320i
$283$	−5.97905	+	1.94271i	−0.355418	+	0.115482i	−0.481283	−	0.876565i	$-0.659829\pi$
$283$	−5.97905	+	1.94271i	−0.355418	+	0.115482i	0.125866	+	0.992047i	$0.459829\pi$
$284$	6.62708	+	4.81486i	0.393245	+	0.285709i
$285$	−4.10244	−	0.846953i	−0.243007	−	0.0501691i
$286$	−0.341138	+	0.247851i	−0.0201719	+	0.0146558i
$287$	21.0188	−	28.9300i	1.24070	−	1.70768i
$288$	0.299454	−	0.412164i	0.0176455	−	0.0242870i
$289$	34.4807	−	25.0517i	2.02827	−	1.47363i
$290$	1.83498	+	16.5282i	0.107754	+	0.970568i
$291$	18.4564	+	13.4094i	1.08193	+	0.786071i
$292$	0.0635424	−	0.0206462i	0.00371854	−	0.00120823i
$293$			6.49657i			0.379534i	0.981829	+	0.189767i	$0.0607732\pi$
$293$			6.49657i			0.379534i	−0.981829	+	0.189767i	$0.939227\pi$
$294$	8.35592	+	25.7169i	0.487327	+	1.49984i
$295$	−7.62593	+	6.94761i	−0.443999	+	0.404505i
$296$	−1.10318	+	3.39523i	−0.0641208	+	0.197344i
$297$	−9.15858	−	2.97580i	−0.531435	−	0.172674i
$298$	−12.4743	−	17.1694i	−0.722618	−	0.994598i
$299$	1.16236			0.0672210
$300$	−8.05653	+	4.77796i	−0.465144	+	0.275855i
$301$	−44.0300			−2.53785
$302$	−10.6006	−	14.5905i	−0.609998	−	0.839590i
$303$	−1.20820	−	0.392569i	−0.0694095	−	0.0225525i
$304$	0.309017	−	0.951057i	0.0177233	−	0.0545468i
$305$	3.33860	+	7.38212i	0.191168	+	0.422699i
$306$	−1.21560	−	3.74124i	−0.0694914	−	0.213873i
$307$		−	3.05405i		−	0.174304i	−0.996195	−	0.0871520i	$-0.972223\pi$
$307$		−	3.05405i		−	0.174304i	0.996195	−	0.0871520i	$-0.0277766\pi$
$308$	−9.08800	+	2.95287i	−0.517837	+	0.168255i
$309$	−22.0099	−	15.9911i	−1.25210	−	0.909704i
$310$	4.53661	+	4.97953i	0.257662	+	0.282819i
$311$	−0.296452	+	0.215385i	−0.0168103	+	0.0122134i	−0.596159	−	0.802867i	$-0.703307\pi$
$311$	−0.296452	+	0.215385i	−0.0168103	+	0.0122134i	0.579348	+	0.815080i	$0.303307\pi$
$312$	0.224959	−	0.309629i	0.0127358	−	0.0175293i
$313$	−11.4142	+	15.7103i	−0.645170	+	0.888000i	−0.998878	−	0.0473557i	$-0.984921\pi$
$313$	−11.4142	+	15.7103i	−0.645170	+	0.888000i	0.353708	+	0.935356i	$0.384921\pi$
$314$	−9.47685	+	6.88533i	−0.534810	+	0.388562i
$315$	−3.55194	−	3.89873i	−0.200129	−	0.219669i
$316$	4.00352	+	2.90873i	0.225215	+	0.163629i
$317$	−21.0127	+	6.82746i	−1.18019	+	0.383468i	−0.832439	−	0.554117i	$-0.813056\pi$
$317$	−21.0127	+	6.82746i	−1.18019	+	0.383468i	−0.347755	+	0.937585i	$0.613056\pi$
$318$			16.4675i			0.923451i
$319$	−4.74341	−	14.5987i	−0.265580	−	0.817372i
$320$	−0.921423	−	2.03740i	−0.0515091	−	0.113894i
$321$	−6.97705	+	21.4732i	−0.389421	+	1.19851i
$322$	25.0516	+	8.13977i	1.39607	+	0.453612i
$323$	−4.53854	−	6.24677i	−0.252531	−	0.347579i
$324$	10.2688			0.570491
$325$	−0.878601	+	0.521058i	−0.0487360	+	0.0289031i
$326$	−0.193024			−0.0106906
$327$	20.5821	+	28.3289i	1.13819	+	1.56659i
$328$	−7.34587	−	2.38682i	−0.405608	−	0.131790i
$329$	−13.5067	+	41.5694i	−0.744649	+	2.29179i
$330$	6.39126	−	5.82277i	0.351828	−	0.320533i
$331$	−7.45281	−	22.9374i	−0.409643	−	1.26075i	−0.916955	−	0.398990i	$-0.869361\pi$
$331$	−7.45281	−	22.9374i	−0.409643	−	1.26075i	0.507312	−	0.861762i	$-0.330639\pi$
$332$			12.7493i			0.699708i
$333$	1.72974	−	0.562026i	0.0947891	−	0.0307989i
$334$	−2.94168	−	2.13725i	−0.160961	−	0.116945i
$335$	−0.159810	−	1.43945i	−0.00873136	−	0.0786458i
$336$	7.01667	−	5.09791i	0.382791	−	0.278114i
$337$	3.74975	−	5.16109i	0.204262	−	0.281142i	−0.694580	−	0.719416i	$-0.744410\pi$
$337$	3.74975	−	5.16109i	0.204262	−	0.281142i	0.898842	+	0.438273i	$0.144410\pi$
$338$	−7.61668	+	10.4835i	−0.414293	+	0.570225i
$339$	3.83939	−	2.78948i	0.208527	−	0.151504i
$340$	−16.9090	−	3.49089i	−0.917022	−	0.189320i
$341$	−5.03034	−	3.65475i	−0.272408	−	0.197916i
$342$	−0.484527	+	0.157432i	−0.0262002	+	0.00851297i
$343$			34.4180i			1.85840i
$344$	2.93885	+	9.04486i	0.158452	+	0.487666i
$345$	−23.6876	+	2.62983i	−1.27530	+	0.141585i
$346$	−3.61691	+	11.1317i	−0.194446	+	0.598444i
$347$	9.30005	+	3.02177i	0.499253	+	0.162217i	0.547809	−	0.836603i	$-0.315462\pi$
$347$	9.30005	+	3.02177i	0.499253	+	0.162217i	−0.0485562	+	0.998820i	$0.515462\pi$
$348$	8.18915	+	11.2714i	0.438985	+	0.604210i
$349$	−2.56146			−0.137112			−0.0685560	−	0.997647i	$-0.521839\pi$
$349$	−2.56146			−0.137112			−0.0685560	+	0.997647i	$0.521839\pi$
$350$	−22.5848	+	5.07738i	−1.20721	+	0.271397i
$351$	0.953185			0.0508773
$352$	1.21319	+	1.66981i	0.0646630	+	0.0890010i
$353$	−29.6525	−	9.63469i	−1.57824	−	0.512803i	−0.616641	−	0.787245i	$-0.711507\pi$
$353$	−29.6525	−	9.63469i	−1.57824	−	0.512803i	−0.961604	+	0.274442i	$0.911507\pi$
$354$	−2.67078	+	8.21981i	−0.141950	+	0.436878i
$355$	−15.9161	−	9.06547i	−0.844739	−	0.481145i
$356$	−3.10790	−	9.56515i	−0.164719	−	0.506952i
$357$		−	66.9686i		−	3.54435i
$358$	−4.18044	+	1.35831i	−0.220943	+	0.0717888i
$359$	28.6175	+	20.7918i	1.51037	+	1.09735i	0.966012	+	0.258498i	$0.0832276\pi$
$359$	28.6175	+	20.7918i	1.51037	+	1.09735i	0.544360	+	0.838851i	$0.316772\pi$
$360$	−0.563816	+	0.989884i	−0.0297157	+	0.0521715i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	4.47543	−	6.15990i	0.235223	−	0.323757i
$363$	7.42154	−	10.2149i	0.389530	−	0.536142i
$364$	0.765200	−	0.555950i	0.0401074	−	0.0291397i
$365$	−0.136123	+	0.0615625i	−0.00712502	+	0.00322233i
$366$	5.49141	+	3.98974i	0.287040	+	0.208547i
$367$	−3.43434	+	1.11588i	−0.179271	+	0.0582487i	−0.397277	−	0.917699i	$-0.630045\pi$
$367$	−3.43434	+	1.11588i	−0.179271	+	0.0582487i	0.218006	+	0.975947i	$0.430045\pi$
$368$		−	5.68953i		−	0.296587i
$369$	1.21599	+	3.74244i	0.0633021	+	0.194824i
$370$	1.61399	−	7.81779i	0.0839074	−	0.406428i
$371$	−12.5760	+	38.7050i	−0.652914	+	2.00946i
$372$	5.36732	+	1.74395i	0.278283	+	0.0904195i
$373$	−14.7302	−	20.2743i	−0.762700	−	1.04977i	−0.996985	−	0.0775980i	$-0.975275\pi$
$373$	−14.7302	−	20.2743i	−0.762700	−	1.04977i	0.234285	−	0.972168i	$-0.424725\pi$
$374$	15.9370			0.824082
$375$	16.7261	−	12.6064i	0.863730	−	0.650993i
$376$	9.44091			0.486878
$377$	0.893064	+	1.22920i	0.0459951	+	0.0633069i
$378$	20.5434	+	6.67497i	1.05664	+	0.343323i
$379$	8.13678	−	25.0424i	0.417958	−	1.28634i	−0.491620	−	0.870810i	$-0.663595\pi$
$379$	8.13678	−	25.0424i	0.417958	−	1.28634i	0.909578	−	0.415533i	$-0.136405\pi$
$380$	−0.452104	+	2.18989i	−0.0231925	+	0.112339i
$381$	2.06345	+	6.35064i	0.105714	+	0.325353i
$382$		−	15.5256i		−	0.794359i
$383$	−8.58356	+	2.78897i	−0.438599	+	0.142510i	−0.519989	−	0.854173i	$-0.674064\pi$
$383$	−8.58356	+	2.78897i	−0.438599	+	0.142510i	0.0813899	+	0.996682i	$0.474064\pi$
$384$	−1.51558	−	1.10113i	−0.0773415	−	0.0561919i
$385$	19.4687	−	8.80483i	0.992218	−	0.448736i
$386$	21.4107	−	15.5558i	1.08977	−	0.791768i
$387$	2.84791	−	3.91981i	0.144767	−	0.199255i
$388$	7.15794	−	9.85205i	0.363389	−	0.500162i
$389$	11.5630	−	8.40098i	0.586265	−	0.425946i	−0.254712	−	0.967017i	$-0.581981\pi$
$389$	11.5630	−	8.40098i	0.586265	−	0.425946i	0.840977	+	0.541070i	$0.181981\pi$
$390$	−0.423555	+	0.743629i	−0.0214475	+	0.0376551i
$391$	−35.5412	−	25.8222i	−1.79739	−	1.30588i
$392$	13.7277	−	4.46040i	0.693354	−	0.225284i
$393$		−	11.2571i		−	0.567847i
$394$	−2.70665	−	8.33021i	−0.136359	−	0.419670i
$395$	−9.61516	−	5.47658i	−0.483791	−	0.275557i
$396$	0.324940	−	1.00006i	0.0163288	−	0.0502550i
$397$	−0.987672	−	0.320914i	−0.0495698	−	0.0161062i	0.284127	−	0.958787i	$-0.408296\pi$
$397$	−0.987672	−	0.320914i	−0.0495698	−	0.0161062i	−0.333697	+	0.942680i	$0.608296\pi$
$398$	−10.3319	−	14.2206i	−0.517892	−	0.712817i
$399$	−8.67309			−0.434197
$400$	2.55048	+	4.30059i	0.127524	+	0.215029i
$401$	35.4919			1.77238			0.886191	−	0.463321i	$-0.153342\pi$
$401$	35.4919			1.77238			0.886191	+	0.463321i	$0.153342\pi$
$402$	−0.713201	−	0.981637i	−0.0355712	−	0.0489596i
$403$	0.585331	+	0.190185i	0.0291574	+	0.00947381i
$404$	−0.209554	+	0.644941i	−0.0104257	+	0.0320870i
$405$	−22.8216	+	2.53368i	−1.13401	+	0.125900i
$406$	10.6399	+	32.7461i	0.528047	+	1.62516i
$407$			7.36836i			0.365236i
$408$	−13.7570	+	4.46992i	−0.681074	+	0.221294i
$409$	3.34477	+	2.43012i	0.165388	+	0.120162i	0.667401	−	0.744699i	$-0.267407\pi$
$409$	3.34477	+	2.43012i	0.165388	+	0.120162i	−0.502012	+	0.864860i	$0.667407\pi$
$410$	16.9145	+	3.49201i	0.835346	+	0.172458i
$411$	−17.4801	+	12.7001i	−0.862231	+	0.626447i
$412$	−8.53609	+	11.7489i	−0.420543	+	0.578828i
$413$	−12.5547	+	17.2801i	−0.617777	+	0.850297i
$414$	−2.34502	+	1.70375i	−0.115251	+	0.0837349i
$415$	−3.14570	−	28.3342i	−0.154416	−	1.39087i
$416$	−0.165281	−	0.120083i	−0.00810354	−	0.00588757i
$417$	7.97595	−	2.59154i	0.390584	−	0.126908i
$418$		−	2.06399i		−	0.100953i
$419$	−11.8623	−	36.5085i	−0.579513	−	1.78356i	−0.620269	−	0.784389i	$-0.712976\pi$
$419$	−11.8623	−	36.5085i	−0.579513	−	1.78356i	0.0407555	−	0.999169i	$-0.487024\pi$
$420$	−14.3361	+	13.0609i	−0.699531	+	0.637308i
$421$	0.712286	−	2.19219i	0.0347147	−	0.106841i	−0.932198	−	0.361950i	$-0.882111\pi$
$421$	0.712286	−	2.19219i	0.0347147	−	0.106841i	0.966912	+	0.255109i	$0.0821113\pi$
$422$	3.88835	+	1.26340i	0.189282	+	0.0615013i
$423$	−2.82712	−	3.89120i	−0.137459	−	0.189197i
$424$	8.79037			0.426898
$425$	38.4402	+	3.58615i	1.86462	+	0.173954i
$426$	−15.3456			−0.743498
$427$	9.86002	+	13.5712i	0.477160	+	0.656754i
$428$	11.4624	+	3.72436i	0.554056	+	0.180024i
$429$	0.244104	−	0.751276i	0.0117855	−	0.0362719i
$430$	−8.76303	−	19.3763i	−0.422591	−	0.934408i
$431$	9.89862	+	30.4648i	0.476800	+	1.46744i	0.843515	+	0.537106i	$0.180482\pi$
$431$	9.89862	+	30.4648i	0.476800	+	1.46744i	−0.366715	+	0.930333i	$0.619518\pi$
$432$		−	4.66566i		−	0.224477i
$433$	5.84170	−	1.89808i	0.280734	−	0.0912161i	−0.165266	−	0.986249i	$-0.552848\pi$
$433$	5.84170	−	1.89808i	0.280734	−	0.0912161i	0.446000	+	0.895033i	$0.352848\pi$
$434$	11.2834	+	8.19791i	0.541623	+	0.393512i
$435$	−20.9807	−	23.0292i	−1.00595	−	1.10416i
$436$	15.1220	−	10.9868i	0.724212	−	0.526171i
$437$	−3.34422	+	4.60293i	−0.159976	+	0.220188i
$438$	−0.0735692	+	0.101259i	−0.00351527	+	0.00483836i
$439$	9.49136	−	6.89587i	0.452998	−	0.329122i	−0.337780	−	0.941225i	$-0.609676\pi$
$439$	9.49136	−	6.89587i	0.452998	−	0.329122i	0.790778	+	0.612103i	$0.209676\pi$
$440$	−3.10820	−	3.41167i	−0.148178	−	0.162645i
$441$	−5.94924	−	4.32238i	−0.283297	−	0.205827i
$442$	−1.50026	+	0.487466i	−0.0713603	+	0.0231864i
$443$		−	0.276529i		−	0.0131383i	−0.999978	−	0.00656915i	$-0.997909\pi$
$443$		−	0.276529i		−	0.0131383i	0.999978	−	0.00656915i	$-0.00209104\pi$
$444$	−2.06664	−	6.36047i	−0.0980785	−	0.301854i
$445$	9.26711	+	20.4909i	0.439303	+	0.971361i
$446$	−4.54758	+	13.9960i	−0.215334	+	0.662731i
$447$	37.8116	+	12.2857i	1.78843	+	0.581095i
$448$	−2.72127	−	3.74551i	−0.128568	−	0.176959i
$449$	0.371473			0.0175309			0.00876545	−	0.999962i	$-0.497210\pi$
$449$	0.371473			0.0175309			0.00876545	+	0.999962i	$0.497210\pi$
$450$	1.00879	−	2.33904i	0.0475550	−	0.110264i
$451$	−15.9421			−0.750684
$452$	−1.48903	−	2.04947i	−0.0700381	−	0.0963991i
$453$	32.1322	+	10.4404i	1.50970	+	0.490531i
$454$	3.73681	−	11.5007i	0.175377	−	0.539755i
$455$	−1.56342	+	1.42435i	−0.0732942	+	0.0667747i
$456$	0.578899	+	1.78167i	0.0271094	+	0.0834342i
$457$			1.20175i			0.0562157i	0.999605	+	0.0281079i	$0.00894819\pi$
$457$			1.20175i			0.0562157i	−0.999605	+	0.0281079i	$0.991052\pi$
$458$	25.6487	−	8.33376i	1.19848	−	0.389411i
$459$	−29.1453	−	21.1753i	−1.36039	−	0.988379i
$460$	1.40381	+	12.6445i	0.0654528	+	0.589552i
$461$	15.9058	−	11.5562i	0.740806	−	0.538227i	−0.152157	−	0.988356i	$-0.548622\pi$
$461$	15.9058	−	11.5562i	0.740806	−	0.538227i	0.892963	+	0.450129i	$0.148622\pi$
$462$	10.5221	−	14.4824i	0.489531	−	0.673781i
$463$	−8.19090	+	11.2738i	−0.380664	+	0.523938i	−0.955760	−	0.294147i	$-0.904964\pi$
$463$	−8.19090	+	11.2738i	−0.380664	+	0.523938i	0.575097	+	0.818085i	$0.304964\pi$
$464$	6.01669	−	4.37138i	0.279318	−	0.202936i
$465$	−12.3587	−	2.55147i	−0.573121	−	0.118321i
$466$	0.737102	+	0.535536i	0.0341456	+	0.0248082i
$467$	8.60130	−	2.79473i	0.398021	−	0.129325i	−0.103165	−	0.994664i	$-0.532897\pi$
$467$	8.60130	−	2.79473i	0.398021	−	0.129325i	0.501186	+	0.865339i	$0.332897\pi$
$468$			0.104082i			0.00481120i
$469$	−0.926635	−	2.85189i	−0.0427880	−	0.131688i
$470$	−20.9816	+	2.32940i	−0.967809	+	0.107447i
$471$	6.78124	−	20.8705i	0.312463	−	0.961662i
$472$	4.38774	+	1.42566i	0.201962	+	0.0656215i
$473$	11.5378	+	15.8804i	0.530508	+	0.730182i
$474$	−9.27053			−0.425809
$475$	0.464441	−	4.97838i	0.0213100	−	0.228424i
$476$	−35.7479			−1.63850
$477$	−2.63231	−	3.62307i	−0.120525	−	0.165889i
$478$	−2.32013	−	0.753855i	−0.106120	−	0.0344805i
$479$	−7.37610	+	22.7013i	−0.337023	+	1.03725i	0.628695	+	0.777652i	$0.283590\pi$
$479$	−7.37610	+	22.7013i	−0.337023	+	1.03725i	−0.965717	+	0.259597i	$0.916410\pi$
$480$	3.63993	+	2.07322i	0.166139	+	0.0946292i
$481$	−0.225377	−	0.693638i	−0.0102763	−	0.0316272i
$482$			26.2084i			1.19376i
$483$	−46.9306	+	15.2487i	−2.13542	+	0.693839i
$484$	−5.45271	−	3.96163i	−0.247851	−	0.180074i
$485$	−13.4770	+	23.6615i	−0.611961	+	1.07441i
$486$	−4.23940	+	3.08011i	−0.192303	+	0.139716i
$487$	−13.0834	+	18.0078i	−0.592866	+	0.816010i	−0.995032	−	0.0995570i	$-0.968257\pi$
$487$	−13.0834	+	18.0078i	−0.592866	+	0.816010i	0.402166	+	0.915567i	$0.368257\pi$
$488$	2.12973	−	2.93132i	0.0964083	−	0.132695i
$489$	0.292543	−	0.212545i	0.0132292	−	0.00961160i
$490$	−29.4081	+	13.3000i	−1.32852	+	0.600831i
$491$	3.39826	+	2.46898i	0.153361	+	0.111423i	0.661820	−	0.749663i	$-0.269784\pi$
$491$	3.39826	+	2.46898i	0.153361	+	0.111423i	−0.508458	+	0.861087i	$0.669784\pi$
$492$	13.7614	−	4.47136i	0.620413	−	0.201584i
$493$		−	57.4245i		−	2.58627i
$494$	0.0631315	+	0.194299i	0.00284042	+	0.00874192i
$495$	−0.475400	+	2.30273i	−0.0213676	+	0.103500i
$496$	0.930922	−	2.86508i	0.0417996	−	0.128646i
$497$	−36.0682	−	11.7193i	−1.61788	−	0.525681i
$498$	−14.0386	−	19.3225i	−0.629086	−	0.865863i
$499$	10.2246			0.457714			0.228857	−	0.973460i	$-0.426501\pi$
$499$	10.2246			0.457714			0.228857	+	0.973460i	$0.426501\pi$
$500$	−6.72933	−	8.92839i	−0.300945	−	0.399290i
$501$	6.81173			0.304326
$502$	9.67463	+	13.3160i	0.431800	+	0.594322i
$503$	−12.4321	−	4.03942i	−0.554319	−	0.180109i	0.0184447	−	0.999830i	$-0.494129\pi$
$503$	−12.4321	−	4.03942i	−0.554319	−	0.180109i	−0.572763	+	0.819721i	$0.694129\pi$
$504$	−0.728866	+	2.24322i	−0.0324663	+	0.0999209i
$505$	0.306586	−	1.48503i	0.0136429	−	0.0660830i
$506$	−3.62884	−	11.1684i	−0.161321	−	0.496496i
$507$		−	24.2754i		−	1.07811i
$508$	3.38998	−	1.10147i	0.150406	−	0.0488699i
$509$	15.0385	+	10.9261i	0.666570	+	0.484292i	0.868875	−	0.495031i	$-0.164843\pi$
$509$	15.0385	+	10.9261i	0.666570	+	0.484292i	−0.202305	+	0.979323i	$0.564843\pi$
$510$	29.4709	−	13.3284i	1.30499	−	0.590190i
$511$	−0.250247	+	0.181815i	−0.0110703	+	0.00804301i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−2.74241	+	3.77460i	−0.121080	+	0.166653i
$514$	−2.13114	+	1.54836i	−0.0940006	+	0.0682954i
$515$	16.0719	−	28.2171i	0.708210	−	1.24339i
$516$	−14.4136	−	10.4721i	−0.634525	−	0.461009i
$517$	18.5323	−	6.02150i	0.815048	−	0.264825i
$518$		−	16.5278i		−	0.726191i
$519$	−6.77576	−	20.8537i	−0.297423	−	0.915374i
$520$	0.396950	+	0.226094i	0.0174074	+	0.00991489i
$521$	−11.6465	+	35.8442i	−0.510242	+	1.57036i	0.281533	+	0.959552i	$0.409157\pi$
$521$	−11.6465	+	35.8442i	−0.510242	+	1.57036i	−0.791775	+	0.610813i	$0.790843\pi$
$522$	−3.60345	−	1.17083i	−0.157719	−	0.0512459i
$523$	−18.8738	−	25.9776i	−0.825294	−	1.13592i	−0.988781	−	0.149375i	$-0.952274\pi$
$523$	−18.8738	−	25.9776i	−0.825294	−	1.13592i	0.163486	−	0.986546i	$-0.447726\pi$
$524$	−6.00907			−0.262508
$525$	28.6382	−	32.5640i	1.24987	−	1.42121i
$526$	16.9886			0.740738
$527$	−13.6725	−	18.8185i	−0.595582	−	0.819749i
$528$	−3.67735	−	1.19484i	−0.160036	−	0.0519989i
$529$	−2.89572	+	8.91210i	−0.125901	+	0.387483i
$530$	−19.5358	+	2.16889i	−0.848583	+	0.0942107i
$531$	−0.726322	−	2.23539i	−0.0315197	−	0.0970076i
$532$			4.62971i			0.200723i
$533$	1.50075	−	0.487622i	0.0650045	−	0.0211212i
$534$	15.2427	+	11.0745i	0.659618	+	0.479241i
$535$	−26.3931	−	5.44889i	−1.14107	−	0.235576i
$536$	−0.523999	+	0.380708i	−0.0226333	+	0.0164441i
$537$	4.84010	−	6.66183i	0.208866	−	0.287479i
$538$	10.1646	−	13.9904i	0.438227	−	0.603168i
$539$	24.1023	−	17.5113i	1.03816	−	0.754266i
$540$	1.15118	+	10.3690i	0.0495390	+	0.446212i
$541$	−11.2805	−	8.19579i	−0.484988	−	0.352365i	0.318265	−	0.948002i	$-0.396900\pi$
$541$	−11.2805	−	8.19579i	−0.484988	−	0.352365i	−0.803254	+	0.595637i	$0.796900\pi$
$542$	−22.4338	+	7.28919i	−0.963614	+	0.313097i
$543$			14.2638i			0.612120i
$544$	2.38605	+	7.34351i	0.102301	+	0.314851i
$545$	−30.8965	+	28.1483i	−1.32346	+	1.20574i
$546$	−0.547545	+	1.68517i	−0.0234328	+	0.0721187i
$547$	13.5552	+	4.40434i	0.579577	+	0.188316i	0.584111	−	0.811674i	$-0.301443\pi$
$547$	13.5552	+	4.40434i	0.579577	+	0.188316i	−0.00453382	+	0.999990i	$0.501443\pi$
$548$	6.77931	+	9.33091i	0.289598	+	0.398597i
$549$	−1.84594			−0.0787828
$550$	7.74948	+	6.81523i	0.330439	+	0.290602i
$551$	−7.43704			−0.316828
$552$	6.26492	+	8.62292i	0.266653	+	0.367016i
$553$	−21.7893	−	7.07978i	−0.926576	−	0.301063i
$554$	5.88130	−	18.1008i	0.249872	−	0.769028i
$555$	6.16228	+	13.6257i	0.261574	+	0.578378i
$556$	−1.38337	−	4.25757i	−0.0586680	−	0.180561i
$557$			29.4715i			1.24875i	0.781126	+	0.624373i	$0.214646\pi$
$557$			29.4715i			1.24875i	−0.781126	+	0.624373i	$0.785354\pi$
$558$	−1.45965	+	0.474269i	−0.0617920	+	0.0200774i
$559$	−1.57187	−	1.14203i	−0.0664831	−	0.0483028i
$560$	6.97194	+	7.65264i	0.294618	+	0.323383i
$561$	−24.1537	+	17.5487i	−1.01977	+	0.740907i
$562$	−1.98764	+	2.73575i	−0.0838435	+	0.115401i
$563$	7.24786	−	9.97582i	0.305461	−	0.420431i	−0.628498	−	0.777811i	$-0.716330\pi$
$563$	7.24786	−	9.97582i	0.305461	−	0.420431i	0.933959	+	0.357380i	$0.116330\pi$
$564$	−14.3084	+	10.3957i	−0.602493	+	0.437737i
$565$	3.81492	+	4.18738i	0.160495	+	0.176164i
$566$	−5.08608	−	3.69525i	−0.213784	−	0.155323i
$567$	−45.2148	+	14.6912i	−1.89884	+	0.616972i
$568$			8.19152i			0.343709i
$569$	3.27032	+	10.0650i	0.137099	+	0.421948i	0.995911	−	0.0903441i	$-0.0287967\pi$
$569$	3.27032	+	10.0650i	0.137099	+	0.421948i	−0.858812	+	0.512292i	$0.828797\pi$
$570$	−1.72615	−	3.81677i	−0.0723006	−	0.159867i
$571$	5.15290	−	15.8590i	0.215642	−	0.663679i	−0.783465	−	0.621436i	$-0.786550\pi$
$571$	5.15290	−	15.8590i	0.215642	−	0.663679i	0.999107	−	0.0422429i	$-0.0134503\pi$
$572$	−0.401032	−	0.130303i	−0.0167680	−	0.00544825i
$573$	17.0957	+	23.5302i	0.714184	+	0.982990i
$574$	35.7594			1.49257
$575$	−6.23968	−	27.7549i	−0.260213	−	1.15746i
$576$	0.509462			0.0212276
$577$	−25.9594	−	35.7301i	−1.08071	−	1.48746i	−0.858742	−	0.512408i	$-0.828753\pi$
$577$	−25.9594	−	35.7301i	−1.08071	−	1.48746i	−0.221963	−	0.975055i	$-0.571247\pi$
$578$	40.5344	+	13.1704i	1.68601	+	0.547818i
$579$	−15.3206	+	47.1519i	−0.636702	+	1.95957i
$580$	−12.2930	+	11.1995i	−0.510439	+	0.465036i
$581$	−18.2399	−	56.1365i	−0.756717	−	2.32894i
$582$			22.8134i			0.945645i
$583$	17.2553	−	5.60658i	0.714641	−	0.232201i
$584$	0.0540524	+	0.0392713i	0.00223670	+	0.00162506i
$585$	−0.0256807	−	0.231313i	−0.00106177	−	0.00956363i
$586$	−5.25584	+	3.81859i	−0.217117	+	0.157744i
$587$	0.0429258	−	0.0590823i	0.00177174	−	0.00243859i	−0.808130	−	0.589004i	$-0.799520\pi$
$587$	0.0429258	−	0.0590823i	0.00177174	−	0.00243859i	0.809902	+	0.586565i	$0.199520\pi$
$588$	−15.8939	+	21.8761i	−0.655454	+	0.902155i
$589$	−2.43719	+	1.77072i	−0.100422	+	0.0729612i
$590$	−10.1031	−	2.08581i	−0.415940	−	0.0858712i
$591$	13.2748	+	9.64470i	0.546052	+	0.396730i
$592$	−3.39523	+	1.10318i	−0.139543	+	0.0453403i
$593$			44.6850i			1.83499i	0.397742	+	0.917497i	$0.369794\pi$
$593$			44.6850i			1.83499i	−0.397742	+	0.917497i	$0.630206\pi$
$594$	−2.97580	−	9.15858i	−0.122099	−	0.375781i
$595$	79.4467	−	8.82027i	3.25700	−	0.361596i
$596$	6.55814	−	20.1839i	0.268632	−	0.826764i
$597$	31.3176	+	10.1757i	1.28174	+	0.416464i
$598$	0.683218	+	0.940368i	0.0279388	+	0.0384545i
$599$	32.8863			1.34370			0.671849	−	0.740688i	$-0.265501\pi$
$599$	32.8863			1.34370			0.671849	+	0.740688i	$0.265501\pi$
$600$	−8.60096	−	3.70946i	−0.351133	−	0.151438i
$601$	45.6102			1.86048			0.930239	−	0.366954i	$-0.119599\pi$
$601$	45.6102			1.86048			0.930239	+	0.366954i	$0.119599\pi$
$602$	−25.8802	−	35.6210i	−1.05480	−	1.45180i
$603$	0.313828	+	0.101969i	0.0127801	+	0.00415249i
$604$	5.57309	−	17.1522i	0.226766	−	0.697913i
$605$	13.0957	+	7.45900i	0.532414	+	0.303251i
$606$	−0.392569	−	1.20820i	−0.0159470	−	0.0490800i
$607$		−	21.7976i		−	0.884739i	−0.896833	−	0.442369i	$-0.854138\pi$
$607$		−	21.7976i		−	0.884739i	0.896833	−	0.442369i	$-0.145862\pi$
$608$	0.951057	−	0.309017i	0.0385704	−	0.0125323i
$609$	−52.1833	−	37.9134i	−2.11457	−	1.53633i
$610$	−4.00988	+	7.04009i	−0.162355	+	0.285045i
$611$	−1.56040	+	1.13370i	−0.0631269	+	0.0458644i
$612$	2.31221	−	3.18249i	0.0934657	−	0.128645i
$613$	−9.89758	+	13.6229i	−0.399760	+	0.550222i	−0.960684	−	0.277645i	$-0.910446\pi$
$613$	−9.89758	+	13.6229i	−0.399760	+	0.550222i	0.560924	+	0.827867i	$0.310446\pi$
$614$	2.47078	−	1.79513i	0.0997126	−	0.0724454i
$615$	−29.4803	+	13.3326i	−1.18876	+	0.537624i
$616$	−7.73071	−	5.61669i	−0.311479	−	0.226303i
$617$	−21.2309	+	6.89834i	−0.854724	+	0.277717i	−0.703423	−	0.710771i	$-0.748346\pi$
$617$	−21.2309	+	6.89834i	−0.854724	+	0.277717i	−0.151300	+	0.988488i	$0.548346\pi$
$618$		−	27.2057i		−	1.09438i
$619$	−2.02127	−	6.22083i	−0.0812418	−	0.250036i	0.902183	−	0.431354i	$-0.141964\pi$
$619$	−2.02127	−	6.22083i	−0.0812418	−	0.250036i	−0.983425	+	0.181317i	$0.941964\pi$
$620$	−1.36198	+	6.59709i	−0.0546983	+	0.264946i
$621$	−8.20299	+	25.2462i	−0.329175	+	1.01310i
$622$	−0.348501	−	0.113235i	−0.0139736	−	0.00454030i
$623$	27.3689	+	37.6701i	1.09651	+	1.50922i
$624$	0.382723			0.0153212
$625$	17.1583	+	18.1822i	0.686332	+	0.727289i
$626$	−19.4190			−0.776141
$627$	2.27273	+	3.12814i	0.0907640	+	0.124926i
$628$	−11.1407	−	3.61983i	−0.444562	−	0.144447i
$629$	−8.51809	+	26.2160i	−0.339639	+	1.04530i
$630$	1.06636	−	5.16520i	0.0424848	−	0.205786i
$631$	−1.97446	−	6.07677i	−0.0786021	−	0.241912i	0.904032	−	0.427464i	$-0.140593\pi$
$631$	−1.97446	−	6.07677i	−0.0786021	−	0.241912i	−0.982635	+	0.185551i	$0.940593\pi$
$632$			4.94862i			0.196846i
$633$	−7.28425	+	2.36680i	−0.289523	+	0.0940718i
$634$	−17.8745	−	12.9866i	−0.709887	−	0.515763i
$635$	−7.26216	+	3.28435i	−0.288190	+	0.130335i
$636$	−13.3225	+	9.67935i	−0.528271	+	0.383811i
$637$	−1.73330	+	2.38569i	−0.0686760	+	0.0945244i
$638$	9.02251	−	12.4184i	0.357205	−	0.491650i
$639$	3.37625	−	2.45299i	0.133562	−	0.0970387i
$640$	1.10669	−	1.94300i	0.0437457	−	0.0768037i
$641$	27.7712	+	20.1770i	1.09690	+	0.796942i	0.980551	−	0.196267i	$-0.0628818\pi$
$641$	27.7712	+	20.1770i	1.09690	+	0.796942i	0.116346	+	0.993209i	$0.462882\pi$
$642$	−21.4732	+	6.97705i	−0.847478	+	0.275362i
$643$		−	26.4649i		−	1.04368i	−0.853045	−	0.521838i	$-0.825247\pi$
$643$		−	26.4649i		−	1.04368i	0.853045	−	0.521838i	$-0.174753\pi$
$644$	8.13977	+	25.0516i	0.320752	+	0.987173i
$645$	34.6169	+	19.7170i	1.36304	+	0.776357i
$646$	2.38605	−	7.34351i	0.0938780	−	0.288927i
$647$	2.34364	+	0.761495i	0.0921380	+	0.0299375i	0.354723	−	0.934971i	$-0.384575\pi$
$647$	2.34364	+	0.761495i	0.0921380	+	0.0299375i	−0.262585	+	0.964909i	$0.584575\pi$
$648$	6.03587	+	8.30766i	0.237111	+	0.326356i
$649$	9.52234			0.373784
$650$	−0.937973	−	0.404533i	−0.0367903	−	0.0158671i
$651$	−26.1279			−1.02403
$652$	−0.113457	−	0.156160i	−0.00444331	−	0.00611568i
$653$	10.5292	+	3.42115i	0.412040	+	0.133880i	0.507699	−	0.861534i	$-0.330496\pi$
$653$	10.5292	+	3.42115i	0.412040	+	0.133880i	−0.0956597	+	0.995414i	$0.530496\pi$
$654$	−10.8207	+	33.3026i	−0.423121	+	1.30223i
$655$	13.3546	−	1.48265i	0.521809	−	0.0579319i
$656$	−2.38682	−	7.34587i	−0.0931895	−	0.286808i
$657$		−	0.0340384i		−	0.00132796i
$658$	−41.5694	+	13.5067i	−1.62054	+	0.526546i
$659$	−7.53076	−	5.47142i	−0.293357	−	0.213136i	0.431365	−	0.902177i	$-0.358032\pi$
$659$	−7.53076	−	5.47142i	−0.293357	−	0.213136i	−0.724722	+	0.689041i	$0.758032\pi$
$660$	8.46741	+	1.74811i	0.329593	+	0.0680449i
$661$	24.6265	−	17.8922i	0.957859	−	0.695925i	0.00520618	−	0.999986i	$-0.498343\pi$
$661$	24.6265	−	17.8922i	0.957859	−	0.695925i	0.952652	+	0.304061i	$0.0983428\pi$
$662$	14.1761	−	19.5117i	0.550969	−	0.758344i
$663$	1.73700	−	2.39078i	0.0674596	−	0.0928502i
$664$	−10.3144	+	7.49384i	−0.400276	+	0.290818i
$665$	−1.14231	−	10.2891i	−0.0442969	−	0.398995i
$666$	1.47140	+	1.06904i	0.0570158	+	0.0414244i
$667$	−40.2423	+	13.0755i	−1.55819	+	0.506286i
$668$		−	3.63611i		−	0.140685i
$669$	−8.51924	−	26.2195i	−0.329373	−	1.01371i
$670$	1.07061	−	0.975379i	0.0413612	−	0.0376822i
$671$	2.31098	−	7.11247i	0.0892145	−	0.274574i
$672$	8.24859	+	2.68013i	0.318196	+	0.103388i
$673$	0.540259	+	0.743602i	0.0208254	+	0.0286638i	0.819303	−	0.573361i	$-0.194361\pi$
$673$	0.540259	+	0.743602i	0.0208254	+	0.0286638i	−0.798477	+	0.602025i	$0.794361\pi$
$674$	6.37946			0.245727
$675$	−5.11681	−	22.7602i	−0.196946	−	0.876042i
$676$	−12.9583			−0.498395
$677$	−0.227897	−	0.313674i	−0.00875881	−	0.0120555i	0.804615	−	0.593797i	$-0.202372\pi$
$677$	−0.227897	−	0.313674i	−0.00875881	−	0.0120555i	−0.813374	+	0.581741i	$0.802372\pi$
$678$	4.51348	+	1.46652i	0.173339	+	0.0563213i
$679$	−17.4223	+	53.6202i	−0.668605	+	2.05776i
$680$	−7.11470	−	15.7316i	−0.272836	−	0.603279i
$681$	7.00037	+	21.5449i	0.268255	+	0.825603i
$682$		−	6.21784i		−	0.238093i
$683$	−24.7310	+	8.03560i	−0.946307	+	0.307474i	−0.741214	−	0.671269i	$-0.765750\pi$
$683$	−24.7310	+	8.03560i	−0.946307	+	0.307474i	−0.205093	+	0.978743i	$0.565750\pi$
$684$	−0.412164	−	0.299454i	−0.0157595	−	0.0114499i
$685$	−17.3687	−	19.0645i	−0.663623	−	0.728415i
$686$	−27.8448	+	20.2304i	−1.06312	+	0.772401i
$687$	−29.6960	+	40.8730i	−1.13297	+	1.55940i
$688$	−5.59003	+	7.69402i	−0.213118	+	0.293332i
$689$	−1.45288	+	1.05558i	−0.0553502	+	0.0402143i
$690$	−16.0508	−	17.6179i	−0.611044	−	0.670702i
$691$	15.3903	+	11.1817i	0.585475	+	0.425373i	0.840694	−	0.541511i	$-0.182147\pi$
$691$	15.3903	+	11.1817i	0.585475	+	0.425373i	−0.255219	+	0.966883i	$0.582147\pi$
$692$	−11.1317	+	3.61691i	−0.423164	+	0.137494i
$693$			4.86826i			0.184930i
$694$	3.02177	+	9.30005i	0.114705	+	0.353025i
$695$	4.12491	+	9.12077i	0.156467	+	0.345970i
$696$	−4.30529	+	13.2503i	−0.163192	+	0.502252i
$697$	−56.7206	−	18.4296i	−2.14844	−	0.698072i
$698$	−1.50559	−	2.07227i	−0.0569874	−	0.0784365i
$699$	−1.70683			−0.0645582
$700$	−17.3827	−	15.2871i	−0.657005	−	0.577798i
$701$	17.9418			0.677654			0.338827	−	0.940849i	$-0.389970\pi$
$701$	17.9418			0.677654			0.338827	+	0.940849i	$0.389970\pi$
$702$	0.560268	+	0.771143i	0.0211460	+	0.0291049i
$703$	3.39523	+	1.10318i	0.128053	+	0.0416071i
$704$	−0.637810	+	1.96298i	−0.0240384	+	0.0739824i
$705$	29.2342	−	26.6339i	1.10103	−	1.00309i
$706$	−9.63469	−	29.6525i	−0.362606	−	1.11599i
$707$		−	3.13955i		−	0.118075i
$708$	−8.21981	+	2.67078i	−0.308919	+	0.100374i
$709$	−11.6407	−	8.45746i	−0.437175	−	0.317626i	0.347336	−	0.937741i	$-0.387086\pi$
$709$	−11.6407	−	8.45746i	−0.437175	−	0.317626i	−0.784512	+	0.620114i	$0.787086\pi$
$710$	−2.02114	−	18.2049i	−0.0758519	−	0.683220i
$711$	2.03964	−	1.48189i	0.0764925	−	0.0555751i
$712$	5.91159	−	8.13660i	0.221546	−	0.304932i
$713$	−10.0746	+	13.8664i	−0.377295	+	0.519302i
$714$	54.1787	−	39.3632i	2.02759	−	1.47313i
$715$	0.923409	+	0.190639i	0.0345335	+	0.00712949i
$716$	−3.55609	−	2.58365i	−0.132897	−	0.0965557i
$717$	4.34642	−	1.41224i	0.162320	−	0.0527410i
$718$			35.3731i			1.32011i
$719$	4.49999	+	13.8496i	0.167821	+	0.516501i	0.999233	−	0.0391557i	$-0.0124668\pi$
$719$	4.49999	+	13.8496i	0.167821	+	0.516501i	−0.831412	+	0.555657i	$0.812467\pi$
$720$	−1.13224	+	0.125702i	−0.0421959	+	0.00468465i
$721$	20.7767	−	63.9440i	0.773764	−	2.38140i
$722$	−0.951057	−	0.309017i	−0.0353947	−	0.0115004i
$723$	−28.8589	−	39.7209i	−1.07328	−	1.47724i
$724$	7.61406			0.282974
$725$	24.5568	−	27.9231i	0.912017	−	1.03704i
$726$	12.6263			0.468605
$727$	13.8606	+	19.0775i	0.514061	+	0.707544i	0.984598	−	0.174836i	$-0.0559396\pi$
$727$	13.8606	+	19.0775i	0.514061	+	0.707544i	−0.470536	+	0.882381i	$0.655940\pi$
$728$	0.899547	+	0.292280i	0.0333394	+	0.0108326i
$729$	−6.48619	+	19.9624i	−0.240229	+	0.739350i
$730$	−0.129816	−	0.0739406i	−0.00480472	−	0.00273666i
$731$	22.6921	+	69.8392i	0.839299	+	2.58310i
$732$			6.78775i			0.250883i
$733$	26.0016	−	8.44842i	0.960389	−	0.312049i	0.213459	−	0.976952i	$-0.431527\pi$
$733$	26.0016	−	8.44842i	0.960389	−	0.312049i	0.746930	+	0.664902i	$0.231527\pi$
$734$	−2.92142	−	2.12254i	−0.107832	−	0.0783443i
$735$	29.9252	−	52.5393i	1.10381	−	1.93794i
$736$	4.60293	−	3.34422i	0.169666	−	0.123270i
$737$	−0.785779	+	1.08153i	−0.0289445	+	0.0398387i
$738$	−2.31296	+	3.18351i	−0.0851411	+	0.117187i
$739$	−15.0634	+	10.9442i	−0.554117	+	0.402590i	−0.829301	−	0.558802i	$-0.811261\pi$
$739$	−15.0634	+	10.9442i	−0.554117	+	0.402590i	0.275184	+	0.961392i	$0.411261\pi$
$740$	7.27341	−	3.28944i	0.267376	−	0.120922i
$741$	−0.309629	−	0.224959i	−0.0113745	−	0.00826407i
$742$	−38.7050	+	12.5760i	−1.42090	+	0.461680i
$743$		−	33.0121i		−	1.21110i	−0.795808	−	0.605549i	$-0.792954\pi$
$743$		−	33.0121i		−	1.21110i	0.795808	−	0.605549i	$-0.207046\pi$
$744$	1.74395	+	5.36732i	0.0639362	+	0.196776i
$745$	−9.59483	+	46.4750i	−0.351527	+	1.70271i
$746$	7.74411	−	23.8339i	0.283532	−	0.872622i
$747$	6.17738	+	2.00715i	0.226018	+	0.0734379i
$748$	9.36753	+	12.8933i	0.342511	+	0.471425i
$749$	−55.7985			−2.03883
$750$	20.0301	+	6.12179i	0.731397	+	0.223536i
$751$	−10.4136			−0.379997			−0.189999	−	0.981784i	$-0.560848\pi$
$751$	−10.4136			−0.379997			−0.189999	+	0.981784i	$0.560848\pi$
$752$	5.54923	+	7.63785i	0.202359	+	0.278524i
$753$	−29.3253	−	9.52837i	−1.06867	−	0.347233i
$754$	−0.469512	+	1.44501i	−0.0170986	+	0.0526241i
$755$	−8.15365	+	39.4943i	−0.296742	+	1.43735i
$756$	6.67497	+	20.5434i	0.242766	+	0.747158i
$757$			1.46402i			0.0532108i	0.999646	+	0.0266054i	$0.00846977\pi$
$757$			1.46402i			0.0532108i	−0.999646	+	0.0266054i	$0.991530\pi$
$758$	25.0424	−	8.13678i	0.909582	−	0.295541i
$759$	17.7977	+	12.9308i	0.646014	+	0.469357i
$760$	−2.03740	+	0.921423i	−0.0739041	+	0.0334235i
$761$	−31.0766	+	22.5784i	−1.12652	+	0.818468i	−0.985185	−	0.171494i	$-0.945141\pi$
$761$	−31.0766	+	22.5784i	−1.12652	+	0.818468i	−0.141339	+	0.989961i	$0.545141\pi$
$762$	−3.92491	+	5.40217i	−0.142184	+	0.195700i
$763$	−50.8655	+	70.0103i	−1.84145	+	2.53454i
$764$	12.5605	−	9.12572i	0.454422	−	0.330157i
$765$	−4.35347	+	7.64332i	−0.157400	+	0.276345i
$766$	−7.30161	−	5.30493i	−0.263818	−	0.191675i
$767$	−0.896407	+	0.291260i	−0.0323674	+	0.0105168i
$768$		−	1.87336i		−	0.0675989i
$769$	0.750147	+	2.30872i	0.0270510	+	0.0832544i	0.963671	−	0.267094i	$-0.0860633\pi$
$769$	0.750147	+	2.30872i	0.0270510	+	0.0832544i	−0.936620	+	0.350348i	$0.886063\pi$
$770$	18.5667	+	10.5752i	0.669097	+	0.381103i
$771$	1.52496	−	4.69333i	0.0549199	−	0.169026i
$772$	25.1698	+	8.17815i	0.905880	+	0.294338i
$773$	−3.90434	−	5.37386i	−0.140429	−	0.193284i	0.733009	−	0.680219i	$-0.238115\pi$
$773$	−3.90434	−	5.37386i	−0.140429	−	0.193284i	−0.873439	+	0.486934i	$0.838115\pi$
$774$	4.84515			0.174155
$775$	1.39914	−	14.9975i	0.0502586	−	0.538726i
$776$	12.1778			0.437158
$777$	18.1993	+	25.0492i	0.652896	+	0.898635i
$778$	13.5931	+	4.41665i	0.487335	+	0.158345i
$779$	−2.38682	+	7.34587i	−0.0855166	+	0.263193i
$780$	−0.850568	+	0.0944312i	−0.0304552	+	0.00338118i
$781$	5.22463	+	16.0798i	0.186952	+	0.575379i
$782$		−	43.9313i		−	1.57098i
$783$	−33.0004	+	10.7225i	−1.17934	+	0.383191i
$784$	11.6775	+	8.48419i	0.417053	+	0.303007i
$785$	25.6524	+	5.29596i	0.915573	+	0.189021i
$786$	9.10721	−	6.61678i	0.324843	−	0.236013i
$787$	−13.0343	+	17.9402i	−0.464622	+	0.639498i	−0.975459	−	0.220180i	$-0.929336\pi$
$787$	−13.0343	+	17.9402i	−0.464622	+	0.639498i	0.510837	+	0.859678i	$0.329336\pi$
$788$	5.14835	−	7.08610i	0.183403	−	0.252432i
$789$	−25.7475	+	18.7067i	−0.916635	+	0.665975i
$790$	−1.22100	−	10.9979i	−0.0434412	−	0.391287i
$791$	9.48846	+	6.89377i	0.337371	+	0.245114i
$792$	1.00006	−	0.324940i	0.0355357	−	0.0115462i
$793$			0.740235i			0.0262865i
$794$	−0.320914	−	0.987672i	−0.0113888	−	0.0350512i
$795$	27.2198	−	24.7986i	0.965388	−	0.879517i
$796$	5.43180	−	16.7174i	0.192525	−	0.592532i
$797$	51.3222	+	16.6756i	1.81792	+	0.590679i	0.999879	+	0.0155246i	$0.00494183\pi$
$797$	51.3222	+	16.6756i	1.81792	+	0.590679i	0.818045	+	0.575155i	$0.195058\pi$
$798$	−5.09791	−	7.01667i	−0.180464	−	0.248388i
$799$	72.8973			2.57892
$800$	−1.98011	+	4.59120i	−0.0700076	+	0.162324i
$801$	−5.12386			−0.181043
$802$	20.8616	+	28.7136i	0.736649	+	1.01391i
$803$	0.131151	+	0.0426136i	0.00462822	+	0.00150380i
$804$	0.374952	−	1.15398i	0.0132235	−	0.0406979i
$805$	−24.2710	−	53.6667i	−0.855442	−	1.89150i
$806$	0.190185	+	0.585331i	0.00669900	+	0.0206174i
$807$			32.3960i			1.14039i
$808$	−0.644941	+	0.209554i	−0.0226890	+	0.00737209i
$809$	26.0437	+	18.9218i	0.915647	+	0.665256i	0.942437	−	0.334385i	$-0.108529\pi$
$809$	26.0437	+	18.9218i	0.915647	+	0.665256i	−0.0267900	+	0.999641i	$0.508529\pi$
$810$	−15.4640	−	16.9738i	−0.543349	−	0.596398i
$811$	−27.8939	+	20.2661i	−0.979486	+	0.711638i	−0.957594	−	0.288122i	$-0.906969\pi$
$811$	−27.8939	+	20.2661i	−0.979486	+	0.711638i	−0.0218922	+	0.999760i	$0.506969\pi$
$812$	−20.2382	+	27.8555i	−0.710222	+	0.977536i
$813$	25.9738	−	35.7499i	0.910941	−	1.25380i
$814$	−5.96113	+	4.33102i	−0.208938	+	0.151802i
$815$	0.290678	+	0.319058i	0.0101820	+	0.0111761i
$816$	−11.7024	−	8.50230i	−0.409666	−	0.297640i
$817$	9.04486	−	2.93885i	0.316440	−	0.102817i
$818$			4.13437i			0.144555i
$819$	−0.148906	−	0.458285i	−0.00520319	−	0.0160138i
$820$	7.11698	+	15.7366i	0.248536	+	0.549547i
$821$	5.60988	−	17.2654i	0.195786	−	0.602567i	−0.804181	−	0.594385i	$-0.797395\pi$
$821$	5.60988	−	17.2654i	0.195786	−	0.602567i	0.999967	−	0.00818226i	$-0.00260452\pi$
$822$	−20.5491	−	6.67681i	−0.716733	−	0.232881i
$823$	17.6152	+	24.2453i	0.614029	+	0.845138i	0.996901	−	0.0786633i	$-0.0250652\pi$
$823$	17.6152	+	24.2453i	0.614029	+	0.845138i	−0.382873	+	0.923801i	$0.625065\pi$
$824$	−14.5225			−0.505914
$825$	−19.2494	−	1.79581i	−0.670178	−	0.0625220i
$826$	−21.3594			−0.743187
$827$	−27.6522	−	38.0600i	−0.961562	−	1.32348i	−0.946196	−	0.323595i	$-0.895108\pi$
$827$	−27.6522	−	38.0600i	−0.961562	−	1.32348i	−0.0153668	−	0.999882i	$-0.504892\pi$
$828$	−2.75673	−	0.895717i	−0.0958031	−	0.0311283i
$829$	−3.75462	+	11.5555i	−0.130403	+	0.401340i	−0.994847	−	0.101390i	$-0.967671\pi$
$829$	−3.75462	+	11.5555i	−0.130403	+	0.401340i	0.864443	+	0.502730i	$0.167671\pi$
$830$	21.0738	−	19.1993i	0.731484	−	0.666419i
$831$	11.0178	+	33.9092i	0.382202	+	1.17630i
$832$		−	0.204298i		−	0.00708276i
$833$	105.998	−	34.4407i	3.67260	−	1.19330i
$834$	6.78475	+	4.92941i	0.234937	+	0.170692i
$835$	0.897157	+	8.08094i	0.0310474	+	0.279653i
$836$	1.66981	−	1.21319i	0.0577515	−	0.0419589i
$837$	−8.26158	+	11.3711i	−0.285562	+	0.393042i
$838$	22.5635	−	31.0560i	0.779444	−	1.07281i
$839$	29.5777	−	21.4895i	1.02114	−	0.741900i	0.0546216	−	0.998507i	$-0.482605\pi$
$839$	29.5777	−	21.4895i	1.02114	−	0.741900i	0.966516	+	0.256607i	$0.0826048\pi$
$840$	−18.9931	−	3.92114i	−0.655323	−	0.135292i
$841$	−21.2849	−	15.4644i	−0.733960	−	0.533253i
$842$	2.19219	−	0.712286i	0.0755479	−	0.0245470i
$843$		−	6.33489i		−	0.218185i
$844$	1.26340	+	3.88835i	0.0434880	+	0.133842i
$845$	28.7986	−	3.19726i	0.990703	−	0.109989i
$846$	1.48631	−	4.57438i	0.0511002	−	0.157270i
$847$	29.6766	+	9.64252i	1.01970	+	0.331321i
$848$	5.16685	+	7.11156i	0.177430	+	0.244212i
$849$	11.7773			0.404196
$850$	19.6933	+	33.2067i	0.675476	+	1.13898i
$851$	20.3113			0.696264
$852$	−9.01994	−	12.4149i	−0.309018	−	0.425327i
$853$	−24.3132	−	7.89982i	−0.832467	−	0.270485i	−0.138383	−	0.990379i	$-0.544190\pi$
$853$	−24.3132	−	7.89982i	−0.832467	−	0.270485i	−0.694084	+	0.719894i	$0.744190\pi$
$854$	−5.18372	+	15.9538i	−0.177383	+	0.545929i
$855$	0.989884	+	0.563816i	0.0338533	+	0.0192821i
$856$	3.72436	+	11.4624i	0.127296	+	0.391777i
$857$			0.459788i			0.0157061i	0.999969	+	0.00785304i	$0.00249972\pi$
$857$			0.459788i			0.0157061i	−0.999969	+	0.00785304i	$0.997500\pi$
$858$	0.751276	−	0.244104i	0.0256481	−	0.00833358i
$859$	6.67976	+	4.85313i	0.227910	+	0.165587i	0.695880	−	0.718158i	$-0.255014\pi$
$859$	6.67976	+	4.85313i	0.227910	+	0.165587i	−0.467970	+	0.883744i	$0.655014\pi$
$860$	10.5250	−	18.4785i	0.358899	−	0.630113i
$861$	−54.1961	+	39.3758i	−1.84700	+	1.34192i
$862$	−18.8283	+	25.9149i	−0.641294	+	0.882666i
$863$	20.3788	−	28.0490i	0.693703	−	0.954800i	−0.306293	−	0.951937i	$-0.599089\pi$
$863$	20.3788	−	28.0490i	0.693703	−	0.954800i	0.999996	−	0.00286268i	$-0.000911221\pi$
$864$	3.77460	−	2.74241i	0.128415	−	0.0932986i
$865$	23.8468	−	10.7849i	0.810817	−	0.366696i
$866$	4.96925	+	3.61037i	0.168862	+	0.122685i
$867$	−75.9354	+	24.6729i	−2.57890	+	0.837936i
$868$			13.9471i			0.473396i
$869$	3.15628	+	9.71402i	0.107069	+	0.329526i
$870$	6.29882	−	30.5100i	0.213550	−	1.03438i
$871$	0.0408902	−	0.125847i	0.00138551	−	0.00426417i
$872$	17.7770	+	5.77608i	0.602004	+	0.195603i
$873$	−3.64670	−	5.01925i	−0.123422	−	0.169876i
$874$	−5.68953			−0.192451
$875$	42.4034	+	29.6853i	1.43350	+	1.00355i
$876$	−0.125163			−0.00422888
$877$	−16.4277	−	22.6108i	−0.554725	−	0.763513i	0.435919	−	0.899986i	$-0.356423\pi$
$877$	−16.4277	−	22.6108i	−0.554725	−	0.763513i	−0.990644	+	0.136473i	$0.956423\pi$
$878$	11.1578	+	3.62538i	0.376556	+	0.122350i
$879$	3.76086	−	11.5747i	0.126851	−	0.390406i
$880$	0.933141	−	4.51991i	0.0314562	−	0.152366i
$881$	−9.61304	−	29.5859i	−0.323872	−	0.996775i	−0.971947	−	0.235199i	$-0.924426\pi$
$881$	−9.61304	−	29.5859i	−0.323872	−	0.996775i	0.648076	−	0.761576i	$-0.275574\pi$
$882$		−	7.35366i		−	0.247611i
$883$	26.2850	−	8.54051i	0.884560	−	0.287411i	0.168711	−	0.985666i	$-0.446040\pi$
$883$	26.2850	−	8.54051i	0.884560	−	0.287411i	0.715850	+	0.698255i	$0.246040\pi$
$884$	−1.27620	−	0.927215i	−0.0429233	−	0.0311856i
$885$	17.6088	−	7.96369i	0.591914	−	0.267696i
$886$	0.223717	−	0.162540i	0.00751591	−	0.00546063i
$887$	30.5085	−	41.9913i	1.02437	−	1.40993i	0.115284	−	0.993333i	$-0.463222\pi$
$887$	30.5085	−	41.9913i	1.02437	−	1.40993i	0.909091	−	0.416599i	$-0.136778\pi$
$888$	3.93099	−	5.41054i	0.131915	−	0.181566i
$889$	−13.3506	+	9.69980i	−0.447766	+	0.325321i
$890$	−11.1304	+	19.5415i	−0.373092	+	0.655032i
$891$	17.1470	+	12.4580i	0.574445	+	0.417359i
$892$	−13.9960	+	4.54758i	−0.468622	+	0.152264i
$893$		−	9.44091i		−	0.315928i
$894$	12.2857	+	37.8116i	0.410896	+	1.26461i
$895$	8.54059	+	4.86453i	0.285480	+	0.162603i
$896$	1.43066	−	4.40311i	0.0477949	−	0.147098i
$897$	−2.07094	−	0.672888i	−0.0691466	−	0.0224671i
$898$	0.218346	+	0.300528i	0.00728631	+	0.0100287i
$899$	−22.4043			−0.747224
$900$	2.48528	−	0.558725i	0.0828427	−	0.0186242i
$901$	67.8742			2.26122
$902$	−9.37053	−	12.8974i	−0.312004	−	0.429437i
$903$	78.4468	+	25.4889i	2.61055	+	0.848218i
$904$	0.782829	−	2.40930i	0.0260365	−	0.0801321i
$905$	−16.9216	+	1.87866i	−0.562493	+	0.0624486i
$906$	10.4404	+	32.1322i	0.346858	+	1.06752i
$907$		−	33.8971i		−	1.12554i	−0.826615	−	0.562768i	$-0.809736\pi$
$907$		−	33.8971i		−	1.12554i	0.826615	−	0.562768i	$-0.190264\pi$
$908$	11.5007	−	3.73681i	0.381664	−	0.124010i
$909$	0.279501	+	0.203069i	0.00927046	+	0.00673539i
$910$	−2.07128	−	0.427618i	−0.0686623	−	0.0141754i
$911$	−31.6406	+	22.9882i	−1.04830	+	0.761633i	−0.971888	−	0.235443i	$-0.924346\pi$
$911$	−31.6406	+	22.9882i	−1.04830	+	0.761633i	−0.0764104	+	0.997076i	$0.524346\pi$
$912$	−1.10113	+	1.51558i	−0.0364621	+	0.0501858i
$913$	−15.4673	+	21.2889i	−0.511891	+	0.704558i
$914$	−0.972240	+	0.706374i	−0.0321588	+	0.0233648i
$915$	−1.67478	−	15.0852i	−0.0553664	−	0.498701i
$916$	21.8181	+	15.8518i	0.720889	+	0.523757i
$917$	26.4586	−	8.59693i	0.873741	−	0.283896i
$918$		−	36.0256i		−	1.18902i
$919$	−8.96541	−	27.5927i	−0.295742	−	0.910199i	−0.982971	−	0.183759i	$-0.941173\pi$
$919$	−8.96541	−	27.5927i	−0.295742	−	0.910199i	0.687230	−	0.726440i	$-0.258827\pi$
$920$	−9.40447	+	8.56795i	−0.310056	+	0.282477i
$921$	−1.76799	+	5.44130i	−0.0582571	+	0.179297i
$922$	18.6984	+	6.07547i	0.615798	+	0.200085i
$923$	−0.983665	−	1.35390i	−0.0323777	−	0.0445641i
$924$	17.9012			0.588906
$925$	−15.3529	+	9.10509i	−0.504800	+	0.299374i
$926$	−13.9352			−0.457939
$927$	4.34882	+	5.98563i	0.142834	+	0.196594i
$928$	7.07304	+	2.29817i	0.232184	+	0.0754412i
$929$	14.0822	−	43.3405i	0.462021	−	1.42196i	−0.400669	−	0.916223i	$-0.631222\pi$
$929$	14.0822	−	43.3405i	0.462021	−	1.42196i	0.862690	−	0.505733i	$-0.168778\pi$
$930$	−5.20008	−	11.4981i	−0.170517	−	0.377038i
$931$	−4.46040	−	13.7277i	−0.146184	−	0.449908i
$932$			0.911108i			0.0298443i
$933$	0.652866	−	0.212129i	0.0213739	−	0.00694479i
$934$	7.31671	+	5.31590i	0.239410	+	0.173942i
$935$	−23.9997	−	26.3429i	−0.784876	−	0.861506i
$936$	−0.0842042	+	0.0611779i	−0.00275230	+	0.00199966i
$937$	22.6880	−	31.2274i	0.741185	−	1.02015i	−0.257364	−	0.966314i	$-0.582854\pi$
$937$	22.6880	−	31.2274i	0.741185	−	1.02015i	0.998550	−	0.0538396i	$-0.0171460\pi$
$938$	1.76257	−	2.42596i	0.0575498	−	0.0792105i
$939$	29.4310	−	21.3829i	0.960445	−	0.697804i
$940$	−14.2172	−	15.6053i	−0.463714	−	0.508988i
$941$	−42.2431	−	30.6914i	−1.37709	−	1.00051i	−0.997146	−	0.0755004i	$-0.975945\pi$
$941$	−42.2431	−	30.6914i	−1.37709	−	1.00051i	−0.379940	−	0.925011i	$-0.624055\pi$
$942$	20.8705	−	6.78124i	0.679998	−	0.220945i
$943$			43.9454i			1.43106i
$944$	1.42566	+	4.38774i	0.0464014	+	0.142809i
$945$	−19.9033	−	44.0091i	−0.647455	−	1.43161i
$946$	−6.06578	+	18.6685i	−0.197215	+	0.606967i
$947$	−2.34760	−	0.762781i	−0.0762868	−	0.0247871i	0.270625	−	0.962685i	$-0.412770\pi$
$947$	−2.34760	−	0.762781i	−0.0762868	−	0.0247871i	−0.346912	+	0.937898i	$0.612770\pi$
$948$	−5.44908	−	7.50001i	−0.176978	−	0.243589i
$949$	−0.0136496			−0.000443086
$950$	4.30059	−	2.55048i	0.139529	−	0.0827485i
$951$	41.3901			1.34217
$952$	−21.0121	−	28.9207i	−0.681006	−	0.937325i
$953$	13.1082	+	4.25912i	0.424617	+	0.137966i	0.513527	−	0.858073i	$-0.328339\pi$
$953$	13.1082	+	4.25912i	0.424617	+	0.137966i	−0.0889105	+	0.996040i	$0.528339\pi$
$954$	1.38389	−	4.25917i	0.0448051	−	0.137896i
$955$	−25.6629	+	23.3802i	−0.830433	+	0.756567i
$956$	−0.753855	−	2.32013i	−0.0243814	−	0.0750383i
$957$			28.7560i			0.929550i
$958$	−22.7013	+	7.37610i	−0.733446	+	0.238311i
$959$	−43.1994	−	31.3862i	−1.39498	−	1.01351i
$960$	0.462223	+	4.16337i	0.0149182	+	0.134372i
$961$	17.7374	−	12.8870i	0.572176	−	0.415710i
$962$	0.428692	−	0.590044i	0.0138216	−	0.0190238i
$963$	3.60911	−	4.96751i	0.116302	−	0.160076i
$964$	−21.2031	+	15.4049i	−0.682905	+	0.496160i
$965$	−57.9555	−	11.9650i	−1.86565	−	0.385166i
$966$	−39.9216	−	29.0047i	−1.28446	−	0.933211i
$967$	−15.4767	+	5.02867i	−0.497696	+	0.161711i	−0.547099	−	0.837068i	$-0.684268\pi$
$967$	−15.4767	+	5.02867i	−0.497696	+	0.161711i	0.0494036	+	0.998779i	$0.484268\pi$
$968$		−	6.73992i		−	0.216629i
$969$	4.46992	+	13.7570i	0.143595	+	0.441939i
$970$	−27.0641	+	3.00469i	−0.868977	+	0.0964749i
$971$	−1.72461	+	5.30780i	−0.0553453	+	0.170335i	−0.974908	−	0.222608i	$-0.928543\pi$
$971$	−1.72461	+	5.30780i	−0.0553453	+	0.170335i	0.919563	+	0.392943i	$0.128543\pi$
$972$	−4.98372	−	1.61931i	−0.159853	−	0.0519393i
$973$	12.1823	+	16.7674i	0.390545	+	0.537540i
$974$	−22.2588			−0.713219
$975$	1.86701	−	0.419730i	0.0597923	−	0.0134421i
$976$	3.62331			0.115979
$977$	−0.0686120	−	0.0944363i	−0.00219509	−	0.00302129i	0.807918	−	0.589295i	$-0.200594\pi$
$977$	−0.0686120	−	0.0944363i	−0.00219509	−	0.00302129i	−0.810113	+	0.586274i	$0.800594\pi$
$978$	0.343904	+	0.111741i	0.0109969	+	0.00357309i
$979$	6.41470	−	19.7424i	0.205015	−	0.630970i
$980$	−28.0456	−	15.9741i	−0.895883	−	0.510275i
$981$	−2.94270	−	9.05669i	−0.0939531	−	0.289158i
$982$			4.20048i			0.134043i
$983$	40.4078	−	13.1293i	1.28881	−	0.418759i	0.417134	−	0.908845i	$-0.363035\pi$
$983$	40.4078	−	13.1293i	1.28881	−	0.418759i	0.871674	+	0.490086i	$0.163035\pi$
$984$	11.7062	+	8.50503i	0.373179	+	0.271130i
$985$	−9.69338	+	17.0185i	−0.308857	+	0.542255i
$986$	46.4574	−	33.7533i	1.47951	−	1.07492i
$987$	48.1289	−	66.2438i	1.53196	−	2.10856i
$988$	−0.120083	+	0.165281i	−0.00382036	+	0.00525827i
$989$	43.7753	−	31.8046i	1.39197	−	1.01133i
$990$	−2.14238	+	0.968901i	−0.0680892	+	0.0307937i
$991$	48.5407	+	35.2669i	1.54194	+	1.12029i	0.949101	+	0.314971i	$0.101995\pi$
$991$	48.5407	+	35.2669i	1.54194	+	1.12029i	0.592843	+	0.805318i	$0.298005\pi$
$992$	2.86508	−	0.930922i	0.0909665	−	0.0295568i
$993$			45.1812i			1.43378i
$994$	−11.7193	−	36.0682i	−0.371712	−	1.14401i
$995$	−7.94695	+	38.4931i	−0.251935	+	1.22031i
$996$	7.38055	−	22.7150i	0.233862	−	0.719752i
$997$	26.5486	+	8.62616i	0.840802	+	0.273193i	0.697588	−	0.716499i	$-0.254256\pi$
$997$	26.5486	+	8.62616i	0.840802	+	0.273193i	0.143213	+	0.989692i	$0.454256\pi$
$998$	6.00985	+	8.27184i	0.190238	+	0.261841i
$999$	16.6562			0.526979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.a.39.14	✓	88
25.9	even	10	inner	950.2.n.a.609.14	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.a.39.14	✓	88	1.1	even	1	trivial
950.2.n.a.609.14	yes	88	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-1.78167 - 0.578899i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.452104 - 2.18989i) q^{5} +(-0.578899 - 1.78167i) q^{6} -4.62971i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.412164 + 0.299454i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-1.78167 - 0.578899i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.452104 - 2.18989i) q^{5} +(-0.578899 - 1.78167i) q^{6} -4.62971i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.412164 + 0.299454i) q^{9} +(2.03740 - 0.921423i) q^{10} +(-1.66981 + 1.21319i) q^{11} +(1.10113 - 1.51558i) q^{12} +(0.120083 - 0.165281i) q^{13} +(3.74551 - 2.72127i) q^{14} +(-2.07322 + 3.63993i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-7.34351 + 2.38605i) q^{17} +0.509462i q^{18} +(0.309017 + 0.951057i) q^{19} +(1.94300 + 1.10669i) q^{20} +(-2.68013 + 8.24859i) q^{21} +(-1.96298 - 0.637810i) q^{22} +(3.34422 + 4.60293i) q^{23} +1.87336 q^{24} +(-4.59120 - 1.98011i) q^{25} +0.204298 q^{26} +(2.74241 + 3.77460i) q^{27} +(4.40311 + 1.43066i) q^{28} +(-2.29817 + 7.07304i) q^{29} +(-4.16337 + 0.462223i) q^{30} +(0.930922 + 2.86508i) q^{31} -1.00000i q^{32} +(3.67735 - 1.19484i) q^{33} +(-6.24677 - 4.53854i) q^{34} +(-10.1385 - 2.09311i) q^{35} +(-0.412164 + 0.299454i) q^{36} +(2.09837 - 2.88815i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(-0.309629 + 0.224959i) q^{39} +(0.246735 + 2.22241i) q^{40} +(6.24877 + 4.54000i) q^{41} +(-8.24859 + 2.68013i) q^{42} -9.51033i q^{43} +(-0.637810 - 1.96298i) q^{44} +(0.842112 - 0.767207i) q^{45} +(-1.75816 + 5.41106i) q^{46} +(-8.97884 - 2.91740i) q^{47} +(1.10113 + 1.51558i) q^{48} -14.4342 q^{49} +(-1.09670 - 4.87824i) q^{50} +14.4650 q^{51} +(0.120083 + 0.165281i) q^{52} +(-8.36014 - 2.71637i) q^{53} +(-1.44177 + 4.43731i) q^{54} +(1.90181 + 4.20517i) q^{55} +(1.43066 + 4.40311i) q^{56} -1.87336i q^{57} +(-7.07304 + 2.29817i) q^{58} +(-3.73244 - 2.71177i) q^{59} +(-2.82111 - 3.09655i) q^{60} +(-2.93132 + 2.12973i) q^{61} +(-1.77072 + 2.43719i) q^{62} +(1.38639 - 1.90820i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.307655 - 0.337693i) q^{65} +(3.12814 + 2.27273i) q^{66} +(0.615998 - 0.200150i) q^{67} -7.72143i q^{68} +(-3.29366 - 10.1368i) q^{69} +(-4.26592 - 9.43254i) q^{70} +(2.53132 - 7.79060i) q^{71} +(-0.484527 - 0.157432i) q^{72} +(-0.0392713 - 0.0540524i) q^{73} +3.56995 q^{74} +(7.03371 + 6.18575i) q^{75} -1.00000 q^{76} +(5.61669 + 7.73071i) q^{77} +(-0.363991 - 0.118268i) q^{78} +(1.52921 - 4.70642i) q^{79} +(-1.65294 + 1.50591i) q^{80} +(-3.17324 - 9.76624i) q^{81} +7.72390i q^{82} +(12.1253 - 3.93975i) q^{83} +(-7.01667 - 5.09791i) q^{84} +(1.90515 + 17.1602i) q^{85} +(7.69402 - 5.59003i) q^{86} +(8.18915 - 11.2714i) q^{87} +(1.21319 - 1.66981i) q^{88} +(-8.13660 + 5.91159i) q^{89} +(1.11566 + 0.230330i) q^{90} +(-0.765200 - 0.555950i) q^{91} +(-5.41106 + 1.75816i) q^{92} -5.64353i q^{93} +(-2.91740 - 8.97884i) q^{94} +(2.22241 - 0.246735i) q^{95} +(-0.578899 + 1.78167i) q^{96} +(-11.5818 - 3.76315i) q^{97} +(-8.48419 - 11.6775i) q^{98} -1.05153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

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