LMFDB - Embedded newform 399.2.ck.a.10.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(10,399)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("399.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.ck (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [78] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			10.9
Character	$\chi$	$=$	399.10
Dual form			399.2.ck.a.40.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.623350 + 0.742879i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.183992 - 1.04347i) q^{4} +(-1.88728 + 0.332779i) q^{5} +(0.623350 - 0.742879i) q^{6} +(-2.31983 - 1.27216i) q^{7} +(2.56954 - 1.48352i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-1.42365 - 1.19459i) q^{10} -1.47652 q^{11} -1.05956 q^{12} +(-1.81773 - 1.52525i) q^{13} +(-0.501009 - 2.51635i) q^{14} +(0.655447 + 1.80082i) q^{15} +(0.712468 + 0.259317i) q^{16} +(1.16444 - 3.19928i) q^{17} +(-0.839837 - 0.484880i) q^{18} +(-2.24114 - 3.73862i) q^{19} +2.03055i q^{20} +(-0.849994 + 2.50550i) q^{21} +(-0.920389 - 1.09688i) q^{22} +(1.33540 + 1.12053i) q^{23} +(-1.90718 - 2.27289i) q^{24} +(-1.24737 + 0.454005i) q^{25} -2.30112i q^{26} +(0.500000 + 0.866025i) q^{27} +(-1.75428 + 2.18660i) q^{28} +(4.88893 + 0.862050i) q^{29} +(-0.929223 + 1.60946i) q^{30} +(-2.04014 - 3.53363i) q^{31} +(-1.77810 - 4.88530i) q^{32} +(0.256395 + 1.45409i) q^{33} +(3.10253 - 1.12923i) q^{34} +(4.80153 + 1.62893i) q^{35} +(0.183992 + 1.04347i) q^{36} +(0.921832 - 0.532220i) q^{37} +(1.38033 - 3.99537i) q^{38} +(-1.18644 + 2.05497i) q^{39} +(-4.35576 + 3.65491i) q^{40} +(1.68041 - 1.41003i) q^{41} +(-2.39113 + 0.930358i) q^{42} +(4.25739 + 1.54956i) q^{43} +(-0.271667 + 1.54070i) q^{44} +(1.65965 - 0.958199i) q^{45} +1.69053i q^{46} +(1.44230 + 3.96270i) q^{47} +(0.131659 - 0.746674i) q^{48} +(3.76324 + 5.90237i) q^{49} +(-1.11482 - 0.643640i) q^{50} +(-3.35288 - 0.591203i) q^{51} +(-1.92600 + 1.61611i) q^{52} +(13.5404 + 2.38753i) q^{53} +(-0.331678 + 0.911277i) q^{54} +(2.78661 - 0.491355i) q^{55} +(-7.84816 + 0.172674i) q^{56} +(-3.29266 + 2.85629i) q^{57} +(2.40711 + 4.16924i) q^{58} +(-2.04703 - 0.745056i) q^{59} +(1.99970 - 0.352601i) q^{60} +(0.0745948 - 0.0888986i) q^{61} +(1.35334 - 3.71827i) q^{62} +(2.61503 + 0.402006i) q^{63} +(3.27900 - 5.67939i) q^{64} +(3.93814 + 2.27368i) q^{65} +(-0.920389 + 1.09688i) q^{66} +(1.86318 - 2.22045i) q^{67} +(-3.12410 - 1.80370i) q^{68} +(0.871621 - 1.50969i) q^{69} +(1.78294 + 4.58235i) q^{70} +(0.0303899 - 0.0834955i) q^{71} +(-1.90718 + 2.27289i) q^{72} +(-1.48467 + 0.261788i) q^{73} +(0.969999 + 0.353051i) q^{74} +(0.663710 + 1.14958i) q^{75} +(-4.31348 + 1.65068i) q^{76} +(3.42528 + 1.87836i) q^{77} +(-2.26616 + 0.399585i) q^{78} +(4.50961 - 12.3900i) q^{79} +(-1.43092 - 0.252310i) q^{80} +(0.766044 - 0.642788i) q^{81} +(2.09496 + 0.369398i) q^{82} +(-5.79148 - 3.34371i) q^{83} +(2.45801 + 1.34793i) q^{84} +(-1.13298 + 6.42545i) q^{85} +(1.50271 + 4.12865i) q^{86} -4.96435i q^{87} +(-3.79397 + 2.19045i) q^{88} +(0.491187 - 2.78566i) q^{89} +(1.74637 + 0.635626i) q^{90} +(2.27646 + 5.85076i) q^{91} +(1.41494 - 1.18728i) q^{92} +(-3.12568 + 2.62276i) q^{93} +(-2.04475 + 3.54160i) q^{94} +(5.47380 + 6.31004i) q^{95} +(-4.50231 + 2.59941i) q^{96} +(-0.981335 - 5.56543i) q^{97} +(-2.03894 + 6.47488i) q^{98} +(1.38747 - 0.505000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 6 q^{7} + 12 q^{10} + 6 q^{11} + 72 q^{12} + 3 q^{13} - 15 q^{14} + 18 q^{19} + 9 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{24} + 18 q^{25} + 39 q^{27} - 9 q^{28} - 6 q^{29} - 18 q^{31} - 51 q^{32} - 12 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) $ 78 * q - 6 * q^7 + 12 * q^10 + 6 * q^11 + 72 * q^12 + 3 * q^13 - 15 * q^14 + 18 * q^19 + 9 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^24 + 18 * q^25 + 39 * q^27 - 9 * q^28 - 6 * q^29 - 18 * q^31 - 51 * q^32 - 12 * q^33 + 30 * q^34 + 33 * q^35 + 18 * q^37 - 57 * q^38 - 18 * q^40 - 63 * q^41 - 27 * q^42 - 51 * q^43 - 36 * q^44 + 9 * q^45 - 84 * q^47 + 18 * q^49 - 27 * q^50 - 18 * q^51 + 18 * q^52 - 45 * q^53 + 30 * q^55 + 33 * q^56 - 6 * q^57 - 18 * q^58 - 24 * q^59 + 66 * q^61 + 171 * q^62 + 6 * q^63 + 18 * q^64 - 99 * q^65 - 12 * q^66 - 24 * q^67 - 12 * q^69 - 150 * q^70 - 66 * q^71 - 9 * q^72 + 3 * q^73 + 18 * q^74 - 36 * q^75 - 12 * q^76 + 21 * q^77 + 75 * q^78 + 45 * q^79 + 78 * q^80 - 24 * q^82 - 72 * q^83 - 9 * q^84 + 60 * q^85 - 9 * q^86 - 108 * q^88 + 48 * q^89 - 33 * q^90 - 54 * q^91 - 102 * q^92 + 9 * q^93 - 66 * q^94 - 84 * q^95 + 75 * q^97 - 39 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.623350	+	0.742879i	0.440775	+	0.525295i	0.939999	−	0.341178i	$-0.110826\pi$
$2$	0.623350	+	0.742879i	0.440775	+	0.525295i	−0.499224	+	0.866473i	$0.666381\pi$
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	0.183992	−	1.04347i	0.0919958	−	0.521734i
$5$	−1.88728	+	0.332779i	−0.844019	+	0.148823i	−0.578906	−	0.815394i	$-0.696520\pi$
$5$	−1.88728	+	0.332779i	−0.844019	+	0.148823i	−0.265113	+	0.964217i	$0.585409\pi$
$6$	0.623350	−	0.742879i	0.254482	−	0.303279i
$7$	−2.31983	−	1.27216i	−0.876814	−	0.480830i
$7$	−2.31983	−	1.27216i	−0.876814	−	0.480830i
$8$	2.56954	−	1.48352i	0.908468	−	0.524504i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−1.42365	−	1.19459i	−0.450198	−	0.377761i
$11$	−1.47652			−0.445188			−0.222594	−	0.974911i	$-0.571452\pi$
$11$	−1.47652			−0.445188			−0.222594	+	0.974911i	$0.571452\pi$
$12$	−1.05956			−0.305870
$13$	−1.81773	−	1.52525i	−0.504147	−	0.423029i	0.354917	−	0.934898i	$-0.384509\pi$
$13$	−1.81773	−	1.52525i	−0.504147	−	0.423029i	−0.859064	+	0.511868i	$0.828954\pi$
$14$	−0.501009	−	2.51635i	−0.133900	−	0.672524i
$15$	0.655447	+	1.80082i	0.169236	+	0.464971i
$16$	0.712468	+	0.259317i	0.178117	+	0.0648293i
$17$	1.16444	−	3.19928i	0.282419	−	0.775939i	−0.714654	−	0.699478i	$-0.753416\pi$
$17$	1.16444	−	3.19928i	0.282419	−	0.775939i	0.997073	−	0.0764607i	$-0.0243620\pi$
$18$	−0.839837	−	0.484880i	−0.197951	−	0.114287i
$19$	−2.24114	−	3.73862i	−0.514152	−	0.857699i
$19$	−2.24114	−	3.73862i	−0.514152	−	0.857699i
$20$			2.03055i			0.454044i
$21$	−0.849994	+	2.50550i	−0.185484	+	0.546744i
$22$	−0.920389	−	1.09688i	−0.196228	−	0.233855i
$23$	1.33540	+	1.12053i	0.278450	+	0.233648i	0.771308	−	0.636463i	$-0.219603\pi$
$23$	1.33540	+	1.12053i	0.278450	+	0.233648i	−0.492857	+	0.870110i	$0.664047\pi$
$24$	−1.90718	−	2.27289i	−0.389301	−	0.463951i
$25$	−1.24737	+	0.454005i	−0.249473	+	0.0908009i
$26$		−	2.30112i		−	0.451287i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−1.75428	+	2.18660i	−0.331528	+	0.413229i
$29$	4.88893	+	0.862050i	0.907851	+	0.160079i	0.608027	−	0.793916i	$-0.291961\pi$
$29$	4.88893	+	0.862050i	0.907851	+	0.160079i	0.299824	+	0.953995i	$0.403072\pi$
$30$	−0.929223	+	1.60946i	−0.169652	+	0.293846i
$31$	−2.04014	−	3.53363i	−0.366420	−	0.634659i	0.622583	−	0.782554i	$-0.286083\pi$
$31$	−2.04014	−	3.53363i	−0.366420	−	0.634659i	−0.989003	+	0.147895i	$0.952750\pi$
$32$	−1.77810	−	4.88530i	−0.314327	−	0.863607i
$33$	0.256395	+	1.45409i	0.0446326	+	0.253124i
$34$	3.10253	−	1.12923i	0.532080	−	0.193661i
$35$	4.80153	+	1.62893i	0.811606	+	0.275339i
$36$	0.183992	+	1.04347i	0.0306653	+	0.173911i
$37$	0.921832	−	0.532220i	0.151548	−	0.0874964i	−0.422308	−	0.906452i	$-0.638780\pi$
$37$	0.921832	−	0.532220i	0.151548	−	0.0874964i	0.573857	+	0.818956i	$0.305447\pi$
$38$	1.38033	−	3.99537i	0.223920	−	0.648134i
$39$	−1.18644	+	2.05497i	−0.189982	+	0.329058i
$40$	−4.35576	+	3.65491i	−0.688706	+	0.577893i
$41$	1.68041	−	1.41003i	0.262435	−	0.220209i	−0.502070	−	0.864827i	$-0.667428\pi$
$41$	1.68041	−	1.41003i	0.262435	−	0.220209i	0.764505	+	0.644618i	$0.222983\pi$
$42$	−2.39113	+	0.930358i	−0.368959	+	0.143557i
$43$	4.25739	+	1.54956i	0.649247	+	0.236306i	0.645587	−	0.763687i	$-0.276613\pi$
$43$	4.25739	+	1.54956i	0.649247	+	0.236306i	0.00365977	+	0.999993i	$0.498835\pi$
$44$	−0.271667	+	1.54070i	−0.0409554	+	0.232269i
$45$	1.65965	−	0.958199i	0.247406	−	0.142840i
$46$			1.69053i			0.249255i
$47$	1.44230	+	3.96270i	0.210382	+	0.578019i	0.999336	−	0.0364330i	$-0.0115995\pi$
$47$	1.44230	+	3.96270i	0.210382	+	0.578019i	−0.788955	+	0.614452i	$0.789377\pi$
$48$	0.131659	−	0.746674i	0.0190033	−	0.107773i
$49$	3.76324	+	5.90237i	0.537606	+	0.843196i
$50$	−1.11482	−	0.643640i	−0.157659	−	0.0910244i
$51$	−3.35288	−	0.591203i	−0.469497	−	0.0827849i
$52$	−1.92600	+	1.61611i	−0.267088	+	0.224114i
$53$	13.5404	+	2.38753i	1.85991	+	0.327953i	0.987100	−	0.160105i	$-0.0511833\pi$
$53$	13.5404	+	2.38753i	1.85991	+	0.327953i	0.872811	+	0.488058i	$0.162294\pi$
$54$	−0.331678	+	0.911277i	−0.0451356	+	0.124009i
$55$	2.78661	−	0.491355i	0.375747	−	0.0662543i
$56$	−7.84816	+	0.172674i	−1.04875	+	0.0230745i
$57$	−3.29266	+	2.85629i	−0.436123	+	0.378325i
$58$	2.40711	+	4.16924i	0.316069	+	0.547448i
$59$	−2.04703	−	0.745056i	−0.266500	−	0.0969981i	0.205314	−	0.978696i	$-0.434178\pi$
$59$	−2.04703	−	0.745056i	−0.266500	−	0.0969981i	−0.471814	+	0.881698i	$0.656401\pi$
$60$	1.99970	−	0.352601i	0.258160	−	0.0455206i
$61$	0.0745948	−	0.0888986i	0.00955089	−	0.0113823i	−0.761248	−	0.648461i	$-0.775413\pi$
$61$	0.0745948	−	0.0888986i	0.00955089	−	0.0113823i	0.770799	+	0.637079i	$0.219857\pi$
$62$	1.35334	−	3.71827i	0.171874	−	0.472220i
$63$	2.61503	+	0.402006i	0.329463	+	0.0506480i
$64$	3.27900	−	5.67939i	0.409875	−	0.709924i
$65$	3.93814	+	2.27368i	0.488466	+	0.282016i
$66$	−0.920389	+	1.09688i	−0.113292	+	0.135016i
$67$	1.86318	−	2.22045i	0.227624	−	0.271271i	−0.640129	−	0.768267i	$-0.721119\pi$
$67$	1.86318	−	2.22045i	0.227624	−	0.271271i	0.867753	+	0.496996i	$0.165564\pi$
$68$	−3.12410	−	1.80370i	−0.378852	−	0.218730i
$69$	0.871621	−	1.50969i	0.104931	−	0.181746i
$70$	1.78294	+	4.58235i	0.213102	+	0.547695i
$71$	0.0303899	−	0.0834955i	0.00360661	−	0.00990909i	−0.937876	−	0.346970i	$-0.887211\pi$
$71$	0.0303899	−	0.0834955i	0.00360661	−	0.00990909i	0.941483	+	0.337061i	$0.109433\pi$
$72$	−1.90718	+	2.27289i	−0.224763	+	0.267862i
$73$	−1.48467	+	0.261788i	−0.173768	+	0.0306399i	−0.259855	−	0.965648i	$-0.583675\pi$
$73$	−1.48467	+	0.261788i	−0.173768	+	0.0306399i	0.0860872	+	0.996288i	$0.472564\pi$
$74$	0.969999	+	0.353051i	0.112760	+	0.0410413i
$75$	0.663710	+	1.14958i	0.0766387	+	0.132742i
$76$	−4.31348	+	1.65068i	−0.494790	+	0.189346i
$77$	3.42528	+	1.87836i	0.390347	+	0.214059i
$78$	−2.26616	+	0.399585i	−0.256592	+	0.0452441i
$79$	4.50961	−	12.3900i	0.507370	−	1.39399i	−0.376570	−	0.926388i	$-0.622896\pi$
$79$	4.50961	−	12.3900i	0.507370	−	1.39399i	0.883940	−	0.467600i	$-0.154881\pi$
$80$	−1.43092	−	0.252310i	−0.159982	−	0.0282092i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	2.09496	+	0.369398i	0.231350	+	0.0407932i
$83$	−5.79148	−	3.34371i	−0.635697	−	0.367020i	0.147258	−	0.989098i	$-0.452955\pi$
$83$	−5.79148	−	3.34371i	−0.635697	−	0.367020i	−0.782955	+	0.622078i	$0.786289\pi$
$84$	2.45801	+	1.34793i	0.268191	+	0.147071i
$85$	−1.13298	+	6.42545i	−0.122889	+	0.696937i
$86$	1.50271	+	4.12865i	0.162041	+	0.445204i
$87$		−	4.96435i		−	0.532234i
$88$	−3.79397	+	2.19045i	−0.404439	+	0.233503i
$89$	0.491187	−	2.78566i	0.0520657	−	0.295279i	−0.947645	−	0.319325i	$-0.896544\pi$
$89$	0.491187	−	2.78566i	0.0520657	−	0.295279i	0.999711	+	0.0240462i	$0.00765487\pi$
$90$	1.74637	+	0.635626i	0.184083	+	0.0670009i
$91$	2.27646	+	5.85076i	0.238638	+	0.613327i
$92$	1.41494	−	1.18728i	0.147518	−	0.123782i
$93$	−3.12568	+	2.62276i	−0.324118	+	0.271967i
$94$	−2.04475	+	3.54160i	−0.210899	+	0.365289i
$95$	5.47380	+	6.31004i	0.561600	+	0.647396i
$96$	−4.50231	+	2.59941i	−0.459516	+	0.265301i
$97$	−0.981335	−	5.56543i	−0.0996394	−	0.565083i	−0.993227	−	0.116194i	$-0.962931\pi$
$97$	−0.981335	−	5.56543i	−0.0996394	−	0.565083i	0.893587	−	0.448890i	$-0.148180\pi$
$98$	−2.03894	+	6.47488i	−0.205964	+	0.654062i
$99$	1.38747	−	0.505000i	0.139446	−	0.0507544i
$100$	0.244234	+	1.38512i	0.0244234	+	0.138512i
$101$	3.66500	+	10.0695i	0.364681	+	1.00195i	0.977353	+	0.211616i	$0.0678725\pi$
$101$	3.66500	+	10.0695i	0.364681	+	1.00195i	−0.612672	+	0.790337i	$0.709905\pi$
$102$	−1.65082	−	2.85931i	−0.163456	−	0.283114i
$103$	−9.69914	+	16.7994i	−0.955685	+	1.65530i	−0.222892	+	0.974843i	$0.571550\pi$
$103$	−9.69914	+	16.7994i	−0.955685	+	1.65530i	−0.732793	+	0.680452i	$0.761783\pi$
$104$	−6.93346	−	1.22256i	−0.679882	−	0.119882i
$105$	0.770403	−	5.01144i	0.0751836	−	0.489067i
$106$	6.66673	+	11.5471i	0.647530	+	1.12156i
$107$		−	10.6893i		−	1.03337i	−0.856174	−	0.516687i	$-0.827165\pi$
$107$		−	10.6893i		−	1.03337i	0.856174	−	0.516687i	$-0.172835\pi$
$108$	0.995665	−	0.362393i	0.0958079	−	0.0348712i
$109$	−1.30701	−	1.55763i	−0.125189	−	0.149194i	0.699809	−	0.714330i	$-0.253268\pi$
$109$	−1.30701	−	1.55763i	−0.125189	−	0.149194i	−0.824998	+	0.565136i	$0.808824\pi$
$110$	2.10205	+	1.76383i	0.200423	+	0.168175i
$111$	−0.684209	−	0.815409i	−0.0649422	−	0.0773952i
$112$	−1.32291	−	1.50794i	−0.125004	−	0.142487i
$113$			2.51093i			0.236208i	0.993001	+	0.118104i	$0.0376817\pi$
$113$			2.51093i			0.236208i	−0.993001	+	0.118104i	$0.962318\pi$
$114$	−4.17436	−	0.665576i	−0.390965	−	0.0623369i
$115$	−2.89317	−	1.67037i	−0.269790	−	0.155763i
$116$	1.79904	−	4.94283i	0.167037	−	0.458930i
$117$	2.22977	+	0.811571i	0.206143	+	0.0750297i
$118$	−0.722526	−	1.98512i	−0.0665139	−	0.182745i
$119$	−6.77129	+	5.94044i	−0.620723	+	0.544559i
$120$	4.35576	+	3.65491i	0.397624	+	0.333646i
$121$	−8.81989			−0.801808
$122$	0.112540			0.0101889
$123$	−1.68041	−	1.41003i	−0.151517	−	0.127138i
$124$	−4.06260	+	1.47866i	−0.364832	+	0.132788i
$125$	10.5013	−	6.06293i	0.939265	−	0.542285i
$126$	1.33144	+	2.19324i	0.118614	+	0.195390i
$127$	−4.57515	+	5.45246i	−0.405979	+	0.483827i	−0.929833	−	0.367981i	$-0.880049\pi$
$127$	−4.57515	+	5.45246i	−0.405979	+	0.483827i	0.523854	+	0.851808i	$0.324494\pi$
$128$	−3.97662	+	0.701185i	−0.351487	+	0.0619766i
$129$	0.786735	−	4.46179i	0.0692681	−	0.392839i
$130$	0.765764	+	4.34286i	0.0671619	+	0.380894i
$131$	−10.9582	−	13.0595i	−0.957422	−	1.14101i	−0.989933	−	0.141539i	$-0.954795\pi$
$131$	−10.9582	−	13.0595i	−0.957422	−	1.14101i	0.0325110	−	0.999471i	$-0.489650\pi$
$132$	1.56447			0.136170
$133$	0.442952	+	11.5241i	0.0384088	+	0.999262i
$134$	2.81094			0.242828
$135$	−1.23184	−	1.46805i	−0.106020	−	0.126349i
$136$	−1.75412	−	9.94814i	−0.150415	−	0.853046i
$137$	−0.632295	+	3.58592i	−0.0540206	+	0.306366i	−0.999832	−	0.0183517i	$-0.994158\pi$
$137$	−0.632295	+	3.58592i	−0.0540206	+	0.306366i	0.945811	+	0.324718i	$0.105269\pi$
$138$	1.66484	−	0.293557i	0.141721	−	0.0249892i
$139$	1.00100	−	1.19294i	0.0849034	−	0.101184i	−0.721920	−	0.691976i	$-0.756740\pi$
$139$	1.00100	−	1.19294i	0.0849034	−	0.101184i	0.806824	+	0.590792i	$0.201185\pi$
$140$	2.58317	−	4.71053i	0.218318	−	0.398112i
$141$	3.65204	−	2.10851i	0.307557	−	0.177568i
$142$	0.0809706	−	0.0294709i	0.00679490	−	0.00247314i
$143$	2.68391	+	2.25207i	0.224440	+	0.188327i
$144$	−0.758192			−0.0631827
$145$	−9.51366			−0.790067
$146$	−1.11995	−	0.939747i	−0.0926875	−	0.0777740i
$147$	5.15922	−	4.73101i	0.425526	−	0.390207i
$148$	−0.385745	−	1.05983i	−0.0317081	−	0.0871172i
$149$	9.18262	+	3.34220i	0.752270	+	0.273804i	0.689561	−	0.724228i	$-0.257804\pi$
$149$	9.18262	+	3.34220i	0.752270	+	0.273804i	0.0627092	+	0.998032i	$0.480026\pi$
$150$	−0.440276	+	1.20965i	−0.0359484	+	0.0987673i
$151$	−16.1640	−	9.33227i	−1.31540	−	0.759449i	−0.332419	−	0.943132i	$-0.607865\pi$
$151$	−16.1640	−	9.33227i	−1.31540	−	0.759449i	−0.982986	+	0.183682i	$0.941198\pi$
$152$	−11.3050	−	6.28175i	−0.916958	−	0.509517i
$153$			3.40460i			0.275246i
$154$	0.739750	+	3.71545i	0.0596107	+	0.299399i
$155$	5.02624	+	5.99004i	0.403718	+	0.481132i
$156$	1.92600	+	1.61611i	0.154203	+	0.129392i
$157$	8.26984	+	9.85561i	0.660005	+	0.786563i	0.987386	−	0.158329i	$-0.0506107\pi$
$157$	8.26984	+	9.85561i	0.660005	+	0.786563i	−0.327381	+	0.944892i	$0.606166\pi$
$158$	12.0154	−	4.37324i	0.955891	−	0.347916i
$159$		−	13.7492i		−	1.09039i
$160$	4.98151	+	8.62822i	0.393823	+	0.682121i
$161$	−1.67241	−	4.29829i	−0.131805	−	0.338753i
$162$	0.955027	+	0.168397i	0.0750340	+	0.0132305i
$163$	11.3972	−	19.7405i	0.892698	−	1.54620i	0.0560707	−	0.998427i	$-0.482143\pi$
$163$	11.3972	−	19.7405i	0.892698	−	1.54620i	0.836628	−	0.547772i	$-0.184524\pi$
$164$	−1.16214	−	2.01288i	−0.0907477	−	0.157180i
$165$	−0.967780	−	2.65895i	−0.0753416	−	0.206999i
$166$	−1.12614	−	6.38667i	−0.0874056	−	0.495702i
$167$	17.2875	−	6.29213i	1.33775	−	0.486900i	0.428644	−	0.903474i	$-0.358992\pi$
$167$	17.2875	−	6.29213i	1.33775	−	0.486900i	0.909102	+	0.416574i	$0.136769\pi$
$168$	1.53287	+	7.69895i	0.118263	+	0.593987i
$169$	−1.27969	−	7.25751i	−0.0984381	−	0.558270i
$170$	−5.47957	+	3.16363i	−0.420264	+	0.242640i
$171$	3.38466	+	2.74664i	0.258832	+	0.210041i
$172$	2.40025	−	4.15735i	0.183017	−	0.316995i
$173$	−0.834513	+	0.700240i	−0.0634468	+	0.0532382i	−0.673960	−	0.738768i	$-0.735408\pi$
$173$	−0.834513	+	0.700240i	−0.0634468	+	0.0532382i	0.610513	+	0.792006i	$0.290963\pi$
$174$	3.68791	−	3.09452i	0.279580	−	0.234595i
$175$	3.47125	+	0.533631i	0.262402	+	0.0403387i
$176$	−1.05197	−	0.382887i	−0.0792954	−	0.0288612i
$177$	−0.378275	+	2.14530i	−0.0284329	+	0.161251i
$178$	2.37559	−	1.37155i	0.178058	−	0.102802i
$179$			22.8167i			1.70540i	0.522399	+	0.852701i	$0.325037\pi$
$179$			22.8167i			1.70540i	−0.522399	+	0.852701i	$0.674963\pi$
$180$	−0.694488	−	1.90809i	−0.0517641	−	0.142221i
$181$	3.23658	−	18.3556i	0.240573	−	1.36436i	−0.589979	−	0.807418i	$-0.700864\pi$
$181$	3.23658	−	18.3556i	0.240573	−	1.36436i	0.830552	−	0.556940i	$-0.188025\pi$
$182$	−2.92738	+	5.33821i	−0.216992	+	0.395694i
$183$	−0.100501	−	0.0580245i	−0.00742927	−	0.00428929i
$184$	5.09370	+	0.898157i	0.375513	+	0.0662130i
$185$	−1.56265	+	1.31122i	−0.114888	+	0.0964025i
$186$	−3.89678	−	0.687108i	−0.285726	−	0.0503812i
$187$	−1.71932	+	4.72380i	−0.125729	+	0.345438i
$188$	4.40032	−	0.775895i	0.320926	−	0.0565879i
$189$	−0.0581972	−	2.64511i	−0.00423322	−	0.192404i
$190$	−1.27551	+	7.99973i	−0.0925351	+	0.580362i
$191$	−9.88500	−	17.1213i	−0.715254	−	1.23886i	−0.962862	−	0.269996i	$-0.912978\pi$
$191$	−9.88500	−	17.1213i	−0.715254	−	1.23886i	0.247608	−	0.968860i	$-0.420356\pi$
$192$	−6.16250	−	2.24297i	−0.444740	−	0.161872i
$193$	−18.5177	+	3.26517i	−1.33293	+	0.235032i	−0.794309	−	0.607514i	$-0.792167\pi$
$193$	−18.5177	+	3.26517i	−1.33293	+	0.235032i	−0.538624	+	0.842546i	$0.681056\pi$
$194$	3.52273	−	4.19822i	0.252917	−	0.301415i
$195$	1.55529	−	4.27313i	0.111377	−	0.306005i
$196$	6.85134	−	2.84083i	0.489382	−	0.202917i
$197$	−2.16279	+	3.74606i	−0.154092	+	0.266896i	−0.932728	−	0.360580i	$-0.882579\pi$
$197$	−2.16279	+	3.74606i	−0.154092	+	0.266896i	0.778636	+	0.627476i	$0.215912\pi$
$198$	1.24004	+	0.715935i	0.0881255	+	0.0508793i
$199$	16.3833	−	19.5249i	1.16138	−	1.38408i	0.252207	−	0.967673i	$-0.418844\pi$
$199$	16.3833	−	19.5249i	1.16138	−	1.38408i	0.909177	−	0.416410i	$-0.136712\pi$
$200$	−2.53163	+	3.01708i	−0.179013	+	0.213340i
$201$	−2.51025	−	1.44930i	−0.177060	−	0.102225i
$202$	−5.19585	+	8.99948i	−0.365579	+	0.633201i
$203$	−10.2448	−	8.21928i	−0.719046	−	0.576881i
$204$	−1.23380	+	3.38984i	−0.0863834	+	0.237336i
$205$	−2.70217	+	3.22032i	−0.188728	+	0.224917i
$206$	−18.5259	+	3.26662i	−1.29076	+	0.227596i
$207$	−1.63811	−	0.596224i	−0.113857	−	0.0414404i
$208$	−0.899547	−	1.55806i	−0.0623724	−	0.108032i
$209$	3.30908	+	5.52015i	0.228894	+	0.381837i
$210$	4.20313	−	2.55156i	0.290043	−	0.176075i
$211$	18.6072	−	3.28095i	1.28097	−	0.225870i	0.508579	−	0.861015i	$-0.330171\pi$
$211$	18.6072	−	3.28095i	1.28097	−	0.225870i	0.772393	+	0.635145i	$0.219060\pi$
$212$	4.98262	−	13.6896i	0.342208	−	0.940209i
$213$	−0.0875041	−	0.0154293i	−0.00599569	−	0.00105720i
$214$	7.94087	−	6.66318i	0.542826	−	0.455485i
$215$	−8.55057	−	1.50770i	−0.583144	−	0.102824i
$216$	2.56954	+	1.48352i	0.174835	+	0.100941i
$217$	0.237461	+	10.7928i	0.0161199	+	0.732663i
$218$	0.342409	−	1.94190i	0.0231909	−	0.131522i
$219$	0.515621	+	1.41666i	0.0348425	+	0.0957289i
$220$		−	2.99814i		−	0.202135i
$221$	−6.99635	+	4.03934i	−0.470625	+	0.271716i
$222$	0.179249	−	1.01657i	0.0120304	−	0.0682277i
$223$	13.8598	+	5.04455i	0.928121	+	0.337808i	0.761464	−	0.648207i	$-0.224481\pi$
$223$	13.8598	+	5.04455i	0.928121	+	0.337808i	0.166656	+	0.986015i	$0.446703\pi$
$224$	−2.08996	+	13.5951i	−0.139641	+	0.908360i
$225$	1.01686	−	0.853249i	0.0677909	−	0.0568833i
$226$	−1.86532	+	1.56519i	−0.124079	+	0.104115i
$227$	−8.49796	+	14.7189i	−0.564029	+	0.976927i	0.433110	+	0.901341i	$0.357416\pi$
$227$	−8.49796	+	14.7189i	−0.564029	+	0.976927i	−0.997139	+	0.0755862i	$0.975917\pi$
$228$	2.37463	+	3.96131i	0.157264	+	0.262344i
$229$	25.9166	−	14.9629i	1.71262	−	0.988779i	0.781616	−	0.623760i	$-0.214396\pi$
$229$	25.9166	−	14.9629i	1.71262	−	0.988779i	0.931000	−	0.365020i	$-0.118938\pi$
$230$	−0.562572	−	3.19050i	−0.0370949	−	0.210376i
$231$	1.25503	−	3.69942i	0.0825751	−	0.243404i
$232$	13.8411	−	5.03776i	0.908716	−	0.330745i
$233$	0.289203	+	1.64015i	0.0189463	+	0.107450i	0.992814	−	0.119665i	$-0.0381819\pi$
$233$	0.289203	+	1.64015i	0.0189463	+	0.107450i	−0.973868	+	0.227115i	$0.927071\pi$
$234$	0.787029	+	2.16234i	0.0514497	+	0.141357i
$235$	−4.04074	−	6.99876i	−0.263589	−	0.456549i
$236$	−1.15408	+	1.99892i	−0.0751240	+	0.130119i
$237$	−12.9849	−	2.28959i	−0.843459	−	0.148725i
$238$	−8.63391	−	1.32728i	−0.559653	−	0.0860348i
$239$	−8.01354	−	13.8799i	−0.518353	−	0.897813i	−0.999773	−	0.0213231i	$-0.993212\pi$
$239$	−8.01354	−	13.8799i	−0.518353	−	0.897813i	0.481420	−	0.876490i	$-0.340121\pi$
$240$			1.45300i			0.0937906i
$241$	1.95316	−	0.710893i	0.125814	−	0.0457926i	−0.278346	−	0.960481i	$-0.589786\pi$
$241$	1.95316	−	0.710893i	0.125814	−	0.0457926i	0.404160	+	0.914688i	$0.367564\pi$
$242$	−5.49788	−	6.55211i	−0.353417	−	0.421186i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	−0.0790381	−	0.0941939i	−0.00505989	−	0.00603015i
$245$	−9.06649	−	9.88712i	−0.579237	−	0.631665i
$246$		−	2.12728i		−	0.135630i
$247$	−1.62858	+	10.2141i	−0.103624	+	0.649908i
$248$	−10.4844	−	6.05319i	−0.665762	−	0.384378i
$249$	−2.28723	+	6.28412i	−0.144947	+	0.398240i
$250$	11.0500	+	4.02187i	0.698864	+	0.254366i
$251$	−5.55427	−	15.2602i	−0.350582	−	0.963217i	−0.982184	−	0.187924i	$-0.939824\pi$
$251$	−5.55427	−	15.2602i	−0.350582	−	0.963217i	0.631601	−	0.775293i	$-0.282398\pi$
$252$	0.900624	−	2.65474i	0.0567340	−	0.167233i
$253$	−1.97175	−	1.65449i	−0.123963	−	0.104017i
$254$	−6.90244			−0.433098
$255$	6.52457			0.408584
$256$	−13.0472	−	10.9479i	−0.815447	−	0.684241i
$257$	−15.3650	+	5.59241i	−0.958443	+	0.348845i	−0.773423	−	0.633890i	$-0.781457\pi$
$257$	−15.3650	+	5.59241i	−0.958443	+	0.348845i	−0.185020	+	0.982735i	$0.559235\pi$
$258$	3.80499	−	2.19681i	0.236888	−	0.136767i
$259$	−2.81556	+	0.0619475i	−0.174951	+	0.00384923i
$260$	3.09710	−	3.69098i	0.192074	−	0.228905i
$261$	−4.88893	+	0.862050i	−0.302617	+	0.0533595i
$262$	2.87082	−	16.2812i	0.177360	−	1.00586i
$263$	4.47505	+	25.3793i	0.275943	+	1.56495i	0.735950	+	0.677036i	$0.236736\pi$
$263$	4.47505	+	25.3793i	0.275943	+	1.56495i	−0.460007	+	0.887915i	$0.652153\pi$
$264$	2.81599	+	3.35596i	0.173312	+	0.206545i
$265$	−26.3490			−1.61861
$266$	−8.28487	+	7.51258i	−0.507978	+	0.460626i
$267$	−2.82863			−0.173109
$268$	−1.97416	−	2.35271i	−0.120591	−	0.143715i
$269$	5.38393	+	30.5338i	0.328264	+	1.86168i	0.485666	+	0.874145i	$0.338577\pi$
$269$	5.38393	+	30.5338i	0.328264	+	1.86168i	−0.157401	+	0.987535i	$0.550312\pi$
$270$	0.322716	−	1.83021i	0.0196399	−	0.111383i
$271$	16.5694	−	2.92163i	1.00652	−	0.177476i	0.353996	−	0.935247i	$-0.384822\pi$
$271$	16.5694	−	2.92163i	1.00652	−	0.177476i	0.652521	+	0.757771i	$0.273711\pi$
$272$	1.65925	−	1.97742i	0.100607	−	0.119899i
$273$	5.36657	−	3.25785i	0.324800	−	0.197174i
$274$	−3.05805	+	1.76556i	−0.184743	+	0.106662i
$275$	1.84176	−	0.670347i	0.111062	−	0.0404234i
$276$	−1.41494	−	1.18728i	−0.0851696	−	0.0714658i
$277$	−23.0159			−1.38289			−0.691446	−	0.722428i	$-0.743026\pi$
$277$	−23.0159			−1.38289			−0.691446	+	0.722428i	$0.743026\pi$
$278$	1.51018			0.0905747
$279$	3.12568	+	2.62276i	0.187129	+	0.157020i
$280$	14.7542	−	2.93759i	0.881735	−	0.175554i
$281$	5.45077	+	14.9759i	0.325166	+	0.893386i	0.989316	+	0.145787i	$0.0465713\pi$
$281$	5.45077	+	14.9759i	0.325166	+	0.893386i	−0.664150	+	0.747599i	$0.731206\pi$
$282$	3.84287	+	1.39869i	0.228839	+	0.0832907i
$283$	3.85096	−	10.5804i	0.228916	−	0.628941i	−0.771054	−	0.636770i	$-0.780270\pi$
$283$	3.85096	−	10.5804i	0.228916	−	0.628941i	0.999969	+	0.00782944i	$0.00249221\pi$
$284$	−0.0815334	−	0.0470733i	−0.00483812	−	0.00279329i
$285$	5.26366	−	6.48636i	0.311792	−	0.384219i
$286$			3.39765i			0.200907i
$287$	−5.69203	+	1.13329i	−0.335990	+	0.0668960i
$288$	3.34174	+	3.98253i	0.196914	+	0.234673i
$289$	4.14330	+	3.47664i	0.243724	+	0.204508i
$290$	−5.93034	−	7.06750i	−0.348242	−	0.415018i
$291$	−5.31047	+	1.93285i	−0.311305	+	0.113306i
$292$			1.59737i			0.0934793i
$293$	6.41166	+	11.1053i	0.374573	+	0.648780i	0.990263	−	0.139209i	$-0.0444559\pi$
$293$	6.41166	+	11.1053i	0.374573	+	0.648780i	−0.615690	+	0.787989i	$0.711123\pi$
$294$	6.73057	+	0.883609i	0.392535	+	0.0515331i
$295$	4.11125	+	0.724925i	0.239367	+	0.0422068i
$296$	1.57912	−	2.73512i	0.0917845	−	0.158975i
$297$	−0.738260	−	1.27870i	−0.0428382	−	0.0741979i
$298$	3.24113	+	8.90494i	0.187754	+	0.515849i
$299$	−0.718295	−	4.07365i	−0.0415401	−	0.235585i
$300$	1.32167	−	0.481047i	0.0763065	−	0.0277733i
$301$	−7.90515	−	9.01080i	−0.455645	−	0.519374i
$302$	−3.14305	−	17.8251i	−0.180862	−	1.02572i
$303$	9.28011	−	5.35787i	0.533128	−	0.307802i
$304$	−0.627249	−	3.24481i	−0.0359752	−	0.186103i
$305$	−0.111198	+	0.192601i	−0.00636718	+	0.0110283i
$306$	−2.52921	+	2.12226i	−0.144585	+	0.121321i
$307$	8.97007	−	7.52678i	0.511949	−	0.429576i	−0.349866	−	0.936800i	$-0.613773\pi$
$307$	8.97007	−	7.52678i	0.511949	−	0.429576i	0.861814	+	0.507224i	$0.169328\pi$
$308$	2.59023	−	3.22856i	0.147592	−	0.183965i
$309$	18.2284	+	6.63461i	1.03698	+	0.377430i
$310$	−1.31677	+	7.46779i	−0.0747876	+	0.424142i
$311$	−16.9810	+	9.80396i	−0.962902	+	0.555932i	−0.897065	−	0.441899i	$-0.854305\pi$
$311$	−16.9810	+	9.80396i	−0.962902	+	0.555932i	−0.0658369	+	0.997830i	$0.520972\pi$
$312$			7.04042i			0.398585i
$313$	2.42657	+	6.66693i	0.137158	+	0.376837i	0.989188	−	0.146656i	$-0.0468509\pi$
$313$	2.42657	+	6.66693i	0.137158	+	0.376837i	−0.852030	+	0.523493i	$0.824629\pi$
$314$	−2.16653	+	12.2870i	−0.122264	+	0.693395i
$315$	−5.06908	+	0.111529i	−0.285611	+	0.00628395i
$316$	−12.0989	−	6.98529i	−0.680615	−	0.392953i
$317$	−6.87691	−	1.21258i	−0.386246	−	0.0681055i	−0.0228462	−	0.999739i	$-0.507273\pi$
$317$	−6.87691	−	1.21258i	−0.386246	−	0.0681055i	−0.363399	+	0.931633i	$0.618384\pi$
$318$	10.2140	−	8.57059i	0.572774	−	0.480615i
$319$	−7.21860	−	1.27283i	−0.404164	−	0.0712650i
$320$	−4.29842	+	11.8098i	−0.240289	+	0.660188i
$321$	−10.5269	+	1.85618i	−0.587555	+	0.103602i
$322$	2.15061	−	3.92174i	0.119849	−	0.218550i
$323$	−14.5706	+	2.81661i	−0.810728	+	0.156720i
$324$	−0.529782	−	0.917610i	−0.0294324	−	0.0509783i
$325$	2.95985	+	1.07730i	0.164183	+	0.0597576i
$326$	21.7693	−	3.83851i	1.20569	−	0.212596i
$327$	−1.30701	+	1.55763i	−0.0722778	+	0.0861373i
$328$	2.22605	−	6.11604i	0.122913	−	0.337702i
$329$	1.69526	−	11.0276i	0.0934629	−	0.607973i
$330$	1.37202	−	2.37640i	0.0755270	−	0.130817i
$331$	−19.9511	−	11.5188i	−1.09661	−	0.633130i	−0.161284	−	0.986908i	$-0.551564\pi$
$331$	−19.9511	−	11.5188i	−1.09661	−	0.633130i	−0.935329	+	0.353778i	$0.884897\pi$
$332$	−4.55464	+	5.42800i	−0.249968	+	0.297900i
$333$	−0.684209	+	0.815409i	−0.0374944	+	0.0446841i
$334$	15.4504	+	8.92032i	0.845411	+	0.488098i
$335$	−2.77743	+	4.81065i	−0.151747	+	0.262834i
$336$	−1.25531	+	1.56467i	−0.0684828	+	0.0853596i
$337$	−5.31277	+	14.5967i	−0.289405	+	0.795134i	0.706745	+	0.707468i	$0.250163\pi$
$337$	−5.31277	+	14.5967i	−0.289405	+	0.795134i	−0.996150	+	0.0876653i	$0.972059\pi$
$338$	4.59376	−	5.47463i	0.249867	−	0.297780i
$339$	2.47278	−	0.436018i	0.134303	−	0.0236812i
$340$	6.49629	+	2.36446i	0.352311	+	0.128231i
$341$	3.01231	+	5.21747i	0.163126	+	0.282542i
$342$	0.0694056	+	4.22652i	0.00375302	+	0.228544i
$343$	−1.22135	−	18.4799i	−0.0659469	−	0.997823i
$344$	13.2383	−	2.33428i	0.713764	−	0.125856i
$345$	−1.14260	+	3.13927i	−0.0615156	+	0.169013i
$346$	−1.04039	−	0.183448i	−0.0559316	−	0.00986224i
$347$	7.70722	−	6.46712i	0.413745	−	0.347173i	−0.412033	−	0.911169i	$-0.635181\pi$
$347$	7.70722	−	6.46712i	0.413745	−	0.347173i	0.825778	+	0.563996i	$0.190737\pi$
$348$	−5.18014	−	0.913398i	−0.277684	−	0.0489633i
$349$	−21.5419	−	12.4372i	−1.15311	−	0.665750i	−0.203469	−	0.979081i	$-0.565222\pi$
$349$	−21.5419	−	12.4372i	−1.15311	−	0.665750i	−0.949644	+	0.313331i	$0.898555\pi$
$350$	1.76738	+	2.91136i	0.0944703	+	0.155619i
$351$	0.412045	−	2.33682i	0.0219933	−	0.124730i
$352$	2.62540	+	7.21324i	0.139935	+	0.384467i
$353$			7.87928i			0.419372i	0.977769	+	0.209686i	$0.0672442\pi$
$353$			7.87928i			0.419372i	−0.977769	+	0.209686i	$0.932756\pi$
$354$	−1.82950	+	1.05626i	−0.0972368	+	0.0561397i
$355$	−0.0295688	+	0.167693i	−0.00156935	+	0.00890021i
$356$	−2.81637	−	1.02507i	−0.149267	−	0.0543288i
$357$	7.02601	+	5.63687i	0.371856	+	0.298335i
$358$	−16.9501	+	14.2228i	−0.895839	+	0.751699i
$359$	−4.49593	+	3.77253i	−0.237286	+	0.199107i	−0.753674	−	0.657248i	$-0.771720\pi$
$359$	−4.49593	+	3.77253i	−0.237286	+	0.199107i	0.516389	+	0.856354i	$0.327276\pi$
$360$	2.84302	−	4.92425i	0.149840	−	0.259531i
$361$	−8.95461	+	16.7575i	−0.471295	+	0.881975i
$362$	15.6535	−	9.03755i	0.822730	−	0.475003i
$363$	1.53156	+	8.68589i	0.0803859	+	0.455891i
$364$	6.52393	−	1.29892i	0.341947	−	0.0680821i
$365$	2.71488	−	0.988135i	0.142103	−	0.0517214i
$366$	−0.0195423	−	0.110830i	−0.00102149	−	0.00579317i
$367$	6.61017	+	18.1613i	0.345048	+	0.948012i	0.983906	+	0.178687i	$0.0571851\pi$
$367$	6.61017	+	18.1613i	0.345048	+	0.948012i	−0.638858	+	0.769325i	$0.720593\pi$
$368$	0.660856	+	1.14464i	0.0344495	+	0.0596683i
$369$	−1.09681	+	1.89972i	−0.0570975	+	0.0988957i
$370$	−1.94815	−	0.343512i	−0.101280	−	0.0178583i
$371$	−28.3740	−	22.7641i	−1.47311	−	1.18185i
$372$	2.16166	+	3.74411i	0.112077	+	0.194123i
$373$			31.3988i			1.62577i	0.582425	+	0.812884i	$0.302104\pi$
$373$			31.3988i			1.62577i	−0.582425	+	0.812884i	$0.697896\pi$
$374$	−4.58095	+	1.66733i	−0.236875	+	0.0862156i
$375$	−7.79435	−	9.28894i	−0.402498	−	0.479679i
$376$	9.58480	+	8.04260i	0.494298	+	0.414765i
$377$	−7.57189	−	9.02383i	−0.389972	−	0.464751i
$378$	1.92872	−	1.69206i	0.0992027	−	0.0870303i
$379$		−	7.04674i		−	0.361967i	−0.983486	−	0.180983i	$-0.942072\pi$
$379$		−	7.04674i		−	0.361967i	0.983486	−	0.180983i	$-0.0579280\pi$
$380$	7.59145	−	4.55074i	0.389433	−	0.233448i
$381$	6.16409	+	3.55884i	0.315796	+	0.182325i
$382$	6.55727	−	18.0159i	0.335499	−	0.921776i
$383$	23.3682	+	8.50532i	1.19406	+	0.434601i	0.861146	−	0.508357i	$-0.169747\pi$
$383$	23.3682	+	8.50532i	1.19406	+	0.434601i	0.332911	+	0.942958i	$0.391969\pi$
$384$	1.38106	+	3.79444i	0.0704772	+	0.193634i
$385$	−7.08955	−	2.40514i	−0.361317	−	0.122577i
$386$	−13.9686	−	11.7211i	−0.710984	−	0.596587i
$387$	−4.53062			−0.230305
$388$	−5.98790			−0.303990
$389$	27.1129	+	22.7504i	1.37468	+	1.15349i	0.971134	+	0.238533i	$0.0766664\pi$
$389$	27.1129	+	22.7504i	1.37468	+	1.15349i	0.403545	+	0.914960i	$0.367778\pi$
$390$	4.14391	−	1.50826i	0.209835	−	0.0763737i
$391$	5.13990	−	2.96752i	0.259936	−	0.150074i
$392$	18.4261	+	9.58351i	0.930658	+	0.484040i
$393$	−10.9582	+	13.0595i	−0.552768	+	0.658763i
$394$	−4.13105	+	0.728415i	−0.208119	+	0.0366970i
$395$	−4.38776	+	24.8842i	−0.220772	+	1.25206i
$396$	−0.271667	−	1.54070i	−0.0136518	−	0.0774231i
$397$	7.47634	+	8.90996i	0.375227	+	0.447178i	0.920302	−	0.391209i	$-0.127943\pi$
$397$	7.47634	+	8.90996i	0.375227	+	0.447178i	−0.545075	+	0.838387i	$0.683499\pi$
$398$	24.7172			1.23896
$399$	11.2721	−	2.43735i	0.564309	−	0.122020i
$400$	−1.00644			−0.0503220
$401$	4.50284	+	5.36628i	0.224861	+	0.267979i	0.866666	−	0.498889i	$-0.166258\pi$
$401$	4.50284	+	5.36628i	0.224861	+	0.267979i	−0.641805	+	0.766868i	$0.721814\pi$
$402$	−0.488115	−	2.76823i	−0.0243449	−	0.138067i
$403$	−1.68126	+	9.53491i	−0.0837496	+	0.474968i
$404$	11.1815	−	1.97161i	0.556302	−	0.0980911i
$405$	−1.23184	+	1.46805i	−0.0612105	+	0.0729478i
$406$	−0.280175	−	12.7342i	−0.0139048	−	0.631986i
$407$	−1.36110	+	0.785834i	−0.0674674	+	0.0389523i
$408$	−9.49240	+	3.45495i	−0.469944	+	0.171046i
$409$	12.5876	+	10.5623i	0.622417	+	0.522270i	0.898562	−	0.438846i	$-0.144613\pi$
$409$	12.5876	+	10.5623i	0.622417	+	0.522270i	−0.276145	+	0.961116i	$0.589057\pi$
$410$	−4.07671			−0.201334
$411$	3.64124			0.179609
$412$	15.7451	+	13.2117i	0.775705	+	0.650893i
$413$	3.80093	+	4.33254i	0.187031	+	0.213190i
$414$	−0.578194	−	1.58858i	−0.0284167	−	0.0780743i
$415$	12.0429	+	4.38325i	0.591161	+	0.215165i
$416$	−4.21921	+	11.5922i	−0.206864	+	0.568354i
$417$	−1.34864	−	0.778637i	−0.0660431	−	0.0381300i
$418$	−2.03809	+	5.89924i	−0.0996863	+	0.288541i
$419$			26.8351i			1.31098i	0.755204	+	0.655490i	$0.227538\pi$
$419$			26.8351i			1.31098i	−0.755204	+	0.655490i	$0.772462\pi$
$420$	−5.08753	−	1.72595i	−0.248246	−	0.0842179i
$421$	14.8361	+	17.6810i	0.723069	+	0.861720i	0.994925	−	0.100618i	$-0.0320819\pi$
$421$	14.8361	+	17.6810i	0.723069	+	0.861720i	−0.271856	+	0.962338i	$0.587637\pi$
$422$	14.0361	+	11.7777i	0.683269	+	0.573330i
$423$	−2.71064	−	3.23042i	−0.131796	−	0.157068i
$424$	38.3344	−	13.9526i	1.86168	−	0.677597i
$425$			4.51934i			0.219220i
$426$	−0.0430836	−	0.0746229i	−0.00208741	−	0.00361549i
$427$	−0.286140	+	0.111334i	−0.0138473	+	0.00538782i
$428$	−11.1539	−	1.96674i	−0.539146	−	0.0950661i
$429$	1.75180	−	3.03420i	0.0845776	−	0.146493i
$430$	−4.20996	−	7.29187i	−0.203022	−	0.351645i
$431$	−6.67711	−	18.3452i	−0.321625	−	0.883658i	−0.990155	−	0.139973i	$-0.955298\pi$
$431$	−6.67711	−	18.3452i	−0.321625	−	0.883658i	0.668530	−	0.743685i	$-0.266924\pi$
$432$	0.131659	+	0.746674i	0.00633443	+	0.0359244i
$433$	32.0425	−	11.6625i	1.53986	−	0.560464i	0.573850	−	0.818960i	$-0.305449\pi$
$433$	32.0425	−	11.6625i	1.53986	−	0.560464i	0.966012	+	0.258496i	$0.0832269\pi$
$434$	−7.86973	+	6.90410i	−0.377759	+	0.331407i
$435$	1.65203	+	9.36913i	0.0792088	+	0.449215i
$436$	−1.86582	+	1.07723i	−0.0893565	+	0.0515900i
$437$	1.19644	−	7.50383i	0.0572335	−	0.358957i
$438$	−0.730994	+	1.26612i	−0.0349282	+	0.0604975i
$439$	−23.2524	+	19.5110i	−1.10977	+	0.931211i	−0.998043	−	0.0625274i	$-0.980084\pi$
$439$	−23.2524	+	19.5110i	−1.10977	+	0.931211i	−0.111731	+	0.993738i	$0.535639\pi$
$440$	6.43136	−	5.39655i	0.306603	−	0.257271i
$441$	−5.55502	−	4.25931i	−0.264525	−	0.202824i
$442$	−7.36192	−	2.67952i	−0.350171	−	0.127452i
$443$	−2.17493	+	12.3346i	−0.103334	+	0.586037i	0.888539	+	0.458802i	$0.151721\pi$
$443$	−2.17493	+	12.3346i	−0.103334	+	0.586037i	−0.991873	+	0.127235i	$0.959390\pi$
$444$	−0.976741	+	0.563922i	−0.0463541	+	0.0267625i
$445$			5.42078i			0.256970i
$446$	4.89201	+	13.4407i	0.231643	+	0.636435i
$447$	1.69688	−	9.62348i	0.0802597	−	0.455175i
$448$	−14.8318	+	9.00384i	−0.700737	+	0.425392i
$449$	−31.5658	−	18.2245i	−1.48968	−	0.860069i	−0.489753	−	0.871861i	$-0.662913\pi$
$449$	−31.5658	−	18.2245i	−1.48968	−	0.860069i	−0.999930	+	0.0117916i	$0.996247\pi$
$450$	1.26772	+	0.223534i	0.0597610	+	0.0105375i
$451$	−2.48115	+	2.08193i	−0.116833	+	0.0980344i
$452$	2.62007	+	0.461989i	0.123238	+	0.0217302i
$453$	−6.38365	+	17.5389i	−0.299930	+	0.824051i
$454$	−16.2316	+	2.86206i	−0.761785	+	0.134323i
$455$	−6.24334	−	10.2845i	−0.292692	−	0.482144i
$456$	−4.22322	+	12.2241i	−0.197770	+	0.572445i
$457$	−1.24486	−	2.15616i	−0.0582321	−	0.100861i	0.835440	−	0.549582i	$-0.185213\pi$
$457$	−1.24486	−	2.15616i	−0.0582321	−	0.100861i	−0.893672	+	0.448721i	$0.851880\pi$
$458$	27.2708	+	9.92575i	1.27428	+	0.463800i
$459$	3.35288	−	0.591203i	0.156499	−	0.0275950i
$460$	−2.27530	+	2.71160i	−0.106086	+	0.126429i
$461$	1.82945	−	5.02637i	0.0852060	−	0.234102i	−0.889771	−	0.456407i	$-0.849136\pi$
$461$	1.82945	−	5.02637i	0.0852060	−	0.234102i	0.974977	+	0.222306i	$0.0713583\pi$
$462$	3.53054	−	1.37369i	0.164256	−	0.0639099i
$463$	16.7619	−	29.0324i	0.778991	−	1.34925i	−0.153534	−	0.988143i	$-0.549065\pi$
$463$	16.7619	−	29.0324i	0.778991	−	1.34925i	0.932524	−	0.361108i	$-0.117601\pi$
$464$	3.25966	+	1.88196i	0.151326	+	0.0873680i
$465$	5.02624	−	5.99004i	0.233086	−	0.277782i
$466$	−1.03816	+	1.23723i	−0.0480919	+	0.0573137i
$467$	−11.0491	−	6.37921i	−0.511292	−	0.295195i	0.222072	−	0.975030i	$-0.428718\pi$
$467$	−11.0491	−	6.37921i	−0.511292	−	0.295195i	−0.733365	+	0.679835i	$0.762051\pi$
$468$	1.25711	−	2.17737i	0.0581098	−	0.100649i
$469$	−7.14702	+	2.78082i	−0.330019	+	0.128406i
$470$	2.68044	−	7.36446i	0.123640	−	0.339697i
$471$	8.26984	−	9.85561i	0.381054	−	0.454123i
$472$	−6.36521	+	1.12236i	−0.292983	+	0.0516607i
$473$	−6.28613	−	2.28796i	−0.289037	−	0.105201i
$474$	−6.39324	−	11.0734i	−0.293651	−	0.508619i
$475$	4.49287	+	3.64595i	0.206147	+	0.167288i
$476$	4.95279	+	8.15861i	0.227011	+	0.373949i
$477$	−13.5404	+	2.38753i	−0.619970	+	0.109318i
$478$	5.31582	−	14.6051i	0.243140	−	0.668022i
$479$	16.4792	+	2.90572i	0.752953	+	0.132766i	0.536935	−	0.843623i	$-0.319582\pi$
$479$	16.4792	+	2.90572i	0.752953	+	0.132766i	0.216018	+	0.976389i	$0.430693\pi$
$480$	7.63211	−	6.40410i	0.348357	−	0.292306i
$481$	−2.48741	−	0.438598i	−0.113416	−	0.0199983i
$482$	1.74561	+	1.00783i	0.0795104	+	0.0459053i
$483$	−3.94258	+	2.39339i	−0.179393	+	0.108903i
$484$	−1.62278	+	9.20327i	−0.0737629	+	0.418330i
$485$	3.70411	+	10.1770i	0.168195	+	0.462112i
$486$		−	0.969760i		−	0.0439892i
$487$	−12.5730	+	7.25905i	−0.569739	+	0.328939i	−0.757045	−	0.653363i	$-0.773358\pi$
$487$	−12.5730	+	7.25905i	−0.569739	+	0.328939i	0.187306	+	0.982302i	$0.440024\pi$
$488$	0.0597910	−	0.339091i	0.00270661	−	0.0153499i
$489$	−21.4197	−	7.79615i	−0.968634	−	0.352554i
$490$	1.69335	−	12.8984i	0.0764976	−	0.582692i
$491$	30.7586	−	25.8096i	1.38812	−	1.16477i	0.422022	−	0.906586i	$-0.361320\pi$
$491$	30.7586	−	25.8096i	1.38812	−	1.16477i	0.966096	−	0.258184i	$-0.0831239\pi$
$492$	−1.78050	+	1.49402i	−0.0802711	+	0.0673554i
$493$	8.45081	−	14.6372i	0.380605	−	0.659228i
$494$	−8.60302	+	5.15712i	−0.387068	+	0.232030i
$495$	−2.45050	+	1.41480i	−0.110142	+	0.0635905i
$496$	−0.537205	−	3.04664i	−0.0241212	−	0.136798i
$497$	−0.176719	+	0.155035i	−0.00792691	+	0.00695426i
$498$	−6.09409	+	2.21807i	−0.273083	+	0.0993940i
$499$	−0.0703216	−	0.398814i	−0.00314803	−	0.0178533i	0.983193	−	0.182568i	$-0.0584409\pi$
$499$	−0.0703216	−	0.398814i	−0.00314803	−	0.0178533i	−0.986341	+	0.164714i	$0.947330\pi$
$500$	−4.39432	−	12.0733i	−0.196520	−	0.539934i
$501$	−9.19848	−	15.9322i	−0.410958	−	0.711800i
$502$	7.87426	−	13.6386i	0.351445	−	0.608721i
$503$	−7.68572	−	1.35520i	−0.342689	−	0.0604254i	−0.000345090	−	1.00000i	$-0.500110\pi$
$503$	−7.68572	−	1.35520i	−0.342689	−	0.0604254i	−0.342344	+	0.939575i	$0.611221\pi$
$504$	7.31580	−	2.84649i	0.325872	−	0.126793i
$505$	−10.2678	−	17.7844i	−0.456912	−	0.791394i
$506$		−	2.49610i		−	0.110965i
$507$	−6.92504	+	2.52051i	−0.307552	+	0.111940i
$508$	4.84767	+	5.77723i	0.215081	+	0.256323i
$509$	−10.6974	−	8.97622i	−0.474156	−	0.397864i	0.374152	−	0.927367i	$-0.377934\pi$
$509$	−10.6974	−	8.97622i	−0.474156	−	0.397864i	−0.848308	+	0.529503i	$0.822378\pi$
$510$	4.06709	+	4.84697i	0.180094	+	0.214627i
$511$	3.77723	+	1.28143i	0.167095	+	0.0566871i
$512$		−	8.44089i		−	0.373038i
$513$	2.11717	−	3.81019i	0.0934755	−	0.168224i
$514$	−13.7323	−	7.92833i	−0.605704	−	0.349704i
$515$	12.7145	−	34.9329i	0.560270	−	1.53933i
$516$	−4.51099	−	1.64186i	−0.198585	−	0.0722791i
$517$	−2.12959	−	5.85100i	−0.0936593	−	0.257327i
$518$	−1.80110	−	2.05301i	−0.0791358	−	0.0902040i
$519$	0.834513	+	0.700240i	0.0366311	+	0.0307371i
$520$	13.4922			0.591674
$521$	2.42093			0.106063			0.0530314	−	0.998593i	$-0.483112\pi$
$521$	2.42093			0.106063			0.0530314	+	0.998593i	$0.483112\pi$
$522$	−3.68791	−	3.09452i	−0.161415	−	0.135444i
$523$	3.84929	−	1.40103i	0.168318	−	0.0612626i	−0.256487	−	0.966548i	$-0.582565\pi$
$523$	3.84929	−	1.40103i	0.168318	−	0.0612626i	0.424805	+	0.905285i	$0.360343\pi$
$524$	−15.6433	+	9.03169i	−0.683383	+	0.394551i
$525$	−0.0772522	−	3.51117i	−0.00337156	−	0.153240i
$526$	−16.0642	+	19.1446i	−0.700433	+	0.834743i
$527$	−13.6807	+	2.41227i	−0.595940	+	0.105080i
$528$	−0.194397	+	1.10248i	−0.00846003	+	0.0479792i
$529$	−3.46621	−	19.6579i	−0.150705	−	0.854689i
$530$	−16.4247	−	19.5741i	−0.713441	−	0.850246i
$531$	2.17840			0.0945344
$532$	12.1065	+	1.65812i	0.524882	+	0.0718887i
$533$	−5.20517			−0.225461
$534$	−1.76323	−	2.10133i	−0.0763023	−	0.0909335i
$535$	3.55718	+	20.1737i	0.153790	+	0.872187i
$536$	1.49342	−	8.46959i	0.0645058	−	0.365831i
$537$	22.4701	−	3.96208i	0.969656	−	0.170976i
$538$	−19.3269	+	23.0329i	−0.833240	+	0.993017i
$539$	−5.55650	−	8.71497i	−0.239335	−	0.375380i
$540$	−1.75851	+	1.01527i	−0.0756740	+	0.0436904i
$541$	24.4139	−	8.88594i	1.04964	−	0.382036i	0.241111	−	0.970498i	$-0.422488\pi$
$541$	24.4139	−	8.88594i	1.04964	−	0.382036i	0.808526	+	0.588461i	$0.200266\pi$
$542$	12.4989	+	10.4878i	0.536875	+	0.450492i
$543$	−18.6387			−0.799865
$544$	−17.6999			−0.758878
$545$	2.98504	+	2.50475i	0.127865	+	0.107292i
$546$	5.76544	+	1.95594i	0.246738	+	0.0837064i
$547$	−8.52803	−	23.4306i	−0.364632	−	1.00182i	−0.977371	−	0.211533i	$-0.932154\pi$
$547$	−8.52803	−	23.4306i	−0.364632	−	1.00182i	0.612739	−	0.790285i	$-0.290068\pi$
$548$	3.62546	+	1.31956i	0.154872	+	0.0563687i
$549$	−0.0396911	+	0.109050i	−0.00169397	+	0.00465415i
$550$	1.64605	+	0.950347i	0.0701878	+	0.0405229i
$551$	−7.73388	−	20.2098i	−0.329474	−	0.860968i
$552$		−	5.17228i		−	0.220147i
$553$	−26.2236	+	23.0059i	−1.11514	+	0.978310i
$554$	−14.3470	−	17.0981i	−0.609544	−	0.726427i
$555$	1.56265	+	1.31122i	0.0663307	+	0.0556580i
$556$	−1.06062	−	1.26400i	−0.0449803	−	0.0536055i
$557$	26.6743	−	9.70865i	1.13023	−	0.411369i	0.291852	−	0.956464i	$-0.405729\pi$
$557$	26.6743	−	9.70865i	1.13023	−	0.411369i	0.838374	+	0.545095i	$0.183506\pi$
$558$			3.95690i			0.167509i
$559$	−5.37530	−	9.31029i	−0.227351	−	0.393783i
$560$	2.99852	+	2.40567i	0.126711	+	0.101658i
$561$	4.95059	+	0.872923i	0.209014	+	0.0368548i
$562$	−7.72753	+	13.3845i	−0.325966	+	0.564590i
$563$	5.37382	+	9.30773i	0.226480	+	0.392274i	0.956762	−	0.290871i	$-0.0939450\pi$
$563$	5.37382	+	9.30773i	0.226480	+	0.392274i	−0.730283	+	0.683145i	$0.760612\pi$
$564$	−1.52821	−	4.19873i	−0.0643494	−	0.176799i
$565$	−0.835584	−	4.73883i	−0.0351533	−	0.199364i
$566$	10.2605	−	3.73451i	0.431280	−	0.156973i
$567$	−2.59482	+	0.516632i	−0.108972	+	0.0216965i
$568$	−0.0457795	−	0.259629i	−0.00192087	−	0.0108938i
$569$	18.6443	−	10.7643i	0.781610	−	0.451263i	−0.0553907	−	0.998465i	$-0.517640\pi$
$569$	18.6443	−	10.7643i	0.781610	−	0.451263i	0.837000	+	0.547202i	$0.184307\pi$
$570$	8.09969	−	0.133009i	0.339259	−	0.00557112i
$571$	−1.61553	+	2.79819i	−0.0676080	+	0.117100i	−0.897848	−	0.440306i	$-0.854870\pi$
$571$	−1.61553	+	2.79819i	−0.0676080	+	0.117100i	0.830240	+	0.557406i	$0.188203\pi$
$572$	2.84378	−	2.38621i	0.118904	−	0.0997725i
$573$	−15.1447	+	12.7079i	−0.632679	+	0.530881i
$574$	−4.39003	−	3.52206i	−0.183236	−	0.147008i
$575$	−2.17446	−	0.791440i	−0.0906814	−	0.0330053i
$576$	−1.13878	+	6.45837i	−0.0474494	+	0.269099i
$577$	−5.66927	+	3.27316i	−0.236015	+	0.136263i	−0.613344	−	0.789816i	$-0.710176\pi$
$577$	−5.66927	+	3.27316i	−0.236015	+	0.136263i	0.377329	+	0.926079i	$0.376843\pi$
$578$			5.24514i			0.218169i
$579$	6.43113	+	17.6694i	0.267268	+	0.734314i
$580$	−1.75043	+	9.92720i	−0.0726828	+	0.412204i
$581$	9.18153	+	15.1245i	0.380914	+	0.627470i
$582$	−4.74616	−	2.74019i	−0.196734	−	0.113585i
$583$	−19.9926	−	3.52524i	−0.828009	−	0.146000i
$584$	−3.42655	+	2.87522i	−0.141792	+	0.118977i
$585$	−4.47828	−	0.789642i	−0.185154	−	0.0326477i
$586$	−4.25321	+	11.6856i	−0.175698	+	0.482728i
$587$	−35.2898	+	6.22255i	−1.45657	+	0.256832i	−0.845172	−	0.534494i	$-0.820502\pi$
$587$	−35.2898	+	6.22255i	−1.45657	+	0.256832i	−0.611395	+	0.791326i	$0.709391\pi$
$588$	−3.98740	−	6.25395i	−0.164438	−	0.257908i
$589$	−8.63867	+	15.5467i	−0.355950	+	0.640589i
$590$	2.02422	+	3.50605i	0.0833358	+	0.144342i
$591$	4.06472	+	1.47944i	0.167200	+	0.0608559i
$592$	0.794789	−	0.140143i	0.0326656	−	0.00575983i
$593$	13.0801	−	15.5882i	0.537134	−	0.640132i	−0.427409	−	0.904059i	$-0.640573\pi$
$593$	13.0801	−	15.5882i	0.537134	−	0.640132i	0.964543	+	0.263927i	$0.0850178\pi$
$594$	0.489729	−	1.34552i	0.0200938	−	0.0552073i
$595$	10.8025	−	13.4646i	0.442859	−	0.551996i
$596$	5.17700	−	8.96683i	0.212058	−	0.367296i
$597$	−22.0732	−	12.7440i	−0.903396	−	0.521576i
$598$	2.57848	−	3.07292i	0.105442	−	0.125661i
$599$	−5.06610	+	6.03754i	−0.206995	+	0.246687i	−0.859547	−	0.511057i	$-0.829254\pi$
$599$	−5.06610	+	6.03754i	−0.206995	+	0.246687i	0.652552	+	0.757744i	$0.273699\pi$
$600$	3.41085	+	1.96926i	0.139248	+	0.0803946i
$601$	−18.0191	+	31.2101i	−0.735016	+	1.27309i	0.219700	+	0.975567i	$0.429492\pi$
$601$	−18.0191	+	31.2101i	−0.735016	+	1.27309i	−0.954716	+	0.297518i	$0.903841\pi$
$602$	1.76626	−	11.4895i	0.0719874	−	0.468275i
$603$	−0.991377	+	2.72379i	−0.0403720	+	0.110921i
$604$	−12.7120	+	15.1495i	−0.517242	+	0.616425i
$605$	16.6456	−	2.93507i	0.676741	−	0.119328i
$606$	9.76501	+	3.55417i	0.396676	+	0.144378i
$607$	−8.95689	−	15.5138i	−0.363549	−	0.629686i	0.624993	−	0.780630i	$-0.285102\pi$
$607$	−8.95689	−	15.5138i	−0.363549	−	0.629686i	−0.988542	+	0.150945i	$0.951768\pi$
$608$	−14.2793	+	17.5963i	−0.579103	+	0.713623i
$609$	−6.31542	+	11.5164i	−0.255914	+	0.466670i
$610$	−0.212394	+	0.0374508i	−0.00859959	+	0.00151634i
$611$	3.42240	−	9.40298i	0.138456	−	0.380404i
$612$	3.55259	+	0.626418i	0.143605	+	0.0253214i
$613$	2.31658	−	1.94384i	0.0935657	−	0.0785109i	−0.594805	−	0.803870i	$-0.702771\pi$
$613$	2.31658	−	1.94384i	0.0935657	−	0.0785109i	0.688371	+	0.725359i	$0.258326\pi$
$614$	11.1830	+	1.97186i	0.451308	+	0.0795778i
$615$	3.64063	+	2.10192i	0.146804	+	0.0847575i
$616$	11.5880	−	0.254956i	0.466893	−	0.0102725i
$617$	−2.96008	+	16.7875i	−0.119168	+	0.675838i	0.865433	+	0.501025i	$0.167043\pi$
$617$	−2.96008	+	16.7875i	−0.119168	+	0.675838i	−0.984602	+	0.174814i	$0.944068\pi$
$618$	6.43398	+	17.6772i	0.258813	+	0.711082i
$619$		−	29.9091i		−	1.20215i	−0.799193	−	0.601075i	$-0.794739\pi$
$619$		−	29.9091i		−	1.20215i	0.799193	−	0.601075i	$-0.205261\pi$
$620$	7.17520	−	4.14261i	0.288163	−	0.166371i
$621$	−0.302711	+	1.71676i	−0.0121474	+	0.0688911i
$622$	−17.8682	−	6.50351i	−0.716451	−	0.260767i
$623$	−4.68326	+	5.83739i	−0.187631	+	0.233870i
$624$	−1.37819	+	1.15644i	−0.0551716	+	0.0462945i
$625$	−12.7170	+	10.6708i	−0.508680	+	0.426833i
$626$	−3.44013	+	5.95848i	−0.137495	+	0.238149i
$627$	4.86167	−	4.21738i	0.194156	−	0.168426i
$628$	11.8056	−	6.81596i	0.471094	−	0.271986i
$629$	−0.629300	−	3.56894i	−0.0250918	−	0.142303i
$630$	−3.24267	−	3.69620i	−0.129191	−	0.147260i
$631$	−31.5850	+	11.4960i	−1.25738	+	0.457649i	−0.882889	−	0.469581i	$-0.844405\pi$
$631$	−31.5850	+	11.4960i	−1.25738	+	0.457649i	−0.374491	+	0.927230i	$0.622183\pi$
$632$	−6.79331	−	38.5268i	−0.270223	−	1.53251i
$633$	−6.46221	−	17.7548i	−0.256850	−	0.705689i
$634$	−3.38591	−	5.86458i	−0.134472	−	0.232912i
$635$	6.82015	−	11.8128i	0.270649	−	0.468778i
$636$	−14.3469	−	2.52974i	−0.568891	−	0.100311i
$637$	2.16207	−	16.4688i	0.0856644	−	0.652518i
$638$	−3.55415	−	6.15597i	−0.140710	−	0.243717i
$639$			0.0888540i			0.00351501i
$640$	7.27166	−	2.64667i	0.287438	−	0.104619i
$641$	−15.5435	−	18.5240i	−0.613930	−	0.731653i	0.366084	−	0.930582i	$-0.380698\pi$
$641$	−15.5435	−	18.5240i	−0.613930	−	0.731653i	−0.980014	+	0.198928i	$0.936254\pi$
$642$	−7.94087	−	6.66318i	−0.313401	−	0.262975i
$643$	25.0957	+	29.9079i	0.989678	+	1.17945i	0.983763	+	0.179470i	$0.0574382\pi$
$643$	25.0957	+	29.9079i	0.989678	+	1.17945i	0.00591456	+	0.999983i	$0.498117\pi$
$644$	−4.79284	+	0.954259i	−0.188864	+	0.0376031i
$645$			8.68248i			0.341872i
$646$	−11.1750	−	9.06844i	−0.439673	−	0.356793i
$647$	23.9290	+	13.8154i	0.940747	+	0.543141i	0.890195	−	0.455581i	$-0.150568\pi$
$647$	23.9290	+	13.8154i	0.940747	+	0.543141i	0.0505529	+	0.998721i	$0.483902\pi$
$648$	1.01479	−	2.78811i	0.0398647	−	0.109527i
$649$	3.02247	+	1.10009i	0.118642	+	0.0431823i
$650$	1.04472	+	2.87034i	0.0409772	+	0.112584i
$651$	10.5876	−	2.10800i	0.414961	−	0.0826192i
$652$	−18.5016	−	15.5247i	−0.724580	−	0.607995i
$653$	5.51552			0.215839			0.107919	−	0.994160i	$-0.465581\pi$
$653$	5.51552			0.215839			0.107919	+	0.994160i	$0.465581\pi$
$654$	−1.97186			−0.0771057
$655$	25.0271	+	21.0003i	0.977891	+	0.820548i
$656$	1.56288	−	0.568841i	0.0610202	−	0.0222095i
$657$	1.30560	−	0.753788i	0.0509363	−	0.0294081i
$658$	9.24894	−	5.61469i	0.360561	−	0.218883i
$659$	30.8916	−	36.8151i	1.20336	−	1.43411i	0.332139	−	0.943230i	$-0.392230\pi$
$659$	30.8916	−	36.8151i	1.20336	−	1.43411i	0.871225	−	0.490884i	$-0.163326\pi$
$660$	−2.95260	+	0.520622i	−0.114930	+	0.0202652i
$661$	−5.89504	+	33.4324i	−0.229290	+	1.30037i	0.625021	+	0.780608i	$0.285090\pi$
$661$	−5.89504	+	33.4324i	−0.229290	+	1.30037i	−0.854311	+	0.519762i	$0.826021\pi$
$662$	−3.87946	−	22.0015i	−0.150780	−	0.855114i
$663$	5.19288	+	6.18863i	0.201675	+	0.240347i
$664$	−19.8419			−0.770014
$665$	−4.67094	−	21.6017i	−0.181131	−	0.837680i
$666$	−1.03225			−0.0399989
$667$	5.56272	+	6.62939i	0.215389	+	0.256691i
$668$	−3.38488	−	19.1966i	−0.130965	−	0.742740i
$669$	2.56119	−	14.5252i	0.0990212	−	0.561577i
$670$	−5.30504	+	0.935421i	−0.204952	+	0.0361385i
$671$	−0.110141	+	0.131261i	−0.00425194	+	0.00506726i
$672$	13.7515	−	0.302557i	0.530474	−	0.0116714i
$673$	10.1319	−	5.84968i	0.390557	−	0.225488i	−0.291844	−	0.956466i	$-0.594269\pi$
$673$	10.1319	−	5.84968i	0.390557	−	0.225488i	0.682402	+	0.730977i	$0.260936\pi$
$674$	−14.1553	+	5.15211i	−0.545242	+	0.198452i
$675$	−1.01686	−	0.853249i	−0.0391391	−	0.0328416i
$676$	−7.80843			−0.300324
$677$	16.3198			0.627220			0.313610	−	0.949552i	$-0.398462\pi$
$677$	16.3198			0.627220			0.313610	+	0.949552i	$0.398462\pi$
$678$	1.86532	+	1.56519i	0.0716371	+	0.0601106i
$679$	−4.80355	+	14.1593i	−0.184344	+	0.543383i
$680$	6.62106	+	18.1912i	0.253906	+	0.697601i
$681$	15.9709	+	5.81295i	0.612008	+	0.222753i
$682$	−1.99823	+	5.49010i	−0.0765162	+	0.210227i
$683$	42.7379	+	24.6747i	1.63532	+	0.944152i	0.982415	+	0.186712i	$0.0597832\pi$
$683$	42.7379	+	24.6747i	1.63532	+	0.944152i	0.652905	+	0.757440i	$0.273550\pi$
$684$	3.48878	−	3.02643i	0.133397	−	0.115718i
$685$		−	6.97806i		−	0.266618i
$686$	12.9670	−	12.4268i	0.495084	−	0.474457i
$687$	−19.2360	−	22.9246i	−0.733899	−	0.874627i
$688$	2.63143	+	2.20803i	0.100322	+	0.0841803i
$689$	−20.9711	−	24.9924i	−0.798935	−	0.952133i
$690$	−3.04434	+	1.10805i	−0.115896	+	0.0421828i
$691$		−	30.0687i		−	1.14387i	−0.820300	−	0.571933i	$-0.806194\pi$
$691$		−	30.0687i		−	1.14387i	0.820300	−	0.571933i	$-0.193806\pi$
$692$	0.577134	+	0.999626i	0.0219393	+	0.0380001i
$693$	−3.86115	−	0.593569i	−0.146673	−	0.0225478i
$694$	9.60859	+	1.69425i	0.364737	+	0.0643130i
$695$	−1.49218	+	2.58453i	−0.0566015	+	0.0980367i
$696$	−7.36472	−	12.7561i	−0.279159	−	0.483517i
$697$	−2.55434	−	7.01798i	−0.0967524	−	0.265825i
$698$	−4.18879	−	23.7558i	−0.158548	−	0.899171i
$699$	1.56502	−	0.569619i	0.0591943	−	0.0215450i
$700$	1.19551	−	3.52395i	0.0451859	−	0.133193i
$701$	−6.14470	−	34.8483i	−0.232082	−	1.31620i	−0.848672	−	0.528919i	$-0.822597\pi$
$701$	−6.14470	−	34.8483i	−0.232082	−	1.31620i	0.616590	−	0.787285i	$-0.288514\pi$
$702$	1.99283	−	1.15056i	0.0752144	−	0.0434251i
$703$	−4.05572	−	2.25361i	−0.152964	−	0.0849963i
$704$	−4.84151	+	8.38574i	−0.182471	+	0.316049i
$705$	−6.19077	+	5.19467i	−0.233158	+	0.195643i
$706$	−5.85336	+	4.91155i	−0.220294	+	0.184849i
$707$	4.30779	−	28.0220i	0.162011	−	1.05388i
$708$	2.16896	+	0.789435i	0.0815144	+	0.0296688i
$709$	6.99088	−	39.6472i	0.262548	−	1.48898i	−0.513380	−	0.858161i	$-0.671607\pi$
$709$	6.99088	−	39.6472i	0.262548	−	1.48898i	0.775928	−	0.630821i	$-0.217282\pi$
$710$	−0.143007	+	0.0825652i	−0.00536696	+	0.00309862i
$711$			13.1852i			0.494484i
$712$	−2.87046	−	7.88653i	−0.107575	−	0.295560i
$713$	1.23515	−	7.00486i	0.0462566	−	0.262334i
$714$	0.192147	+	8.73322i	0.00719091	+	0.326833i
$715$	−5.81474	−	3.35714i	−0.217459	−	0.125550i
$716$	23.8085	+	4.19808i	0.889766	+	0.156890i
$717$	−12.2775	+	10.3020i	−0.458510	+	0.384735i
$718$	−5.60507	−	0.988325i	−0.209179	−	0.0368840i
$719$	−13.1347	+	36.0872i	−0.489840	+	1.34582i	0.410985	+	0.911642i	$0.365185\pi$
$719$	−13.1347	+	36.0872i	−0.489840	+	1.34582i	−0.900825	+	0.434182i	$0.857037\pi$
$720$	1.43092	−	0.252310i	0.0533274	−	0.00940305i
$721$	43.8718	−	26.6330i	1.63387	−	0.991865i
$722$	−18.0307	+	3.79361i	−0.671033	+	0.141184i
$723$	−1.03926	−	1.80004i	−0.0386503	−	0.0669443i
$724$	−18.5579	−	6.75454i	−0.689701	−	0.251030i
$725$	−6.48966	+	1.14430i	−0.241020	+	0.0424983i
$726$	−5.49788	+	6.55211i	−0.204045	+	0.243172i
$727$	−14.4633	+	39.7377i	−0.536416	+	1.47379i	0.314894	+	0.949127i	$0.398031\pi$
$727$	−14.4633	+	39.7377i	−0.536416	+	1.47379i	−0.851310	+	0.524663i	$0.824191\pi$
$728$	14.5292	+	11.6566i	0.538488	+	0.432021i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	2.42639	+	1.40087i	0.0898046	+	0.0518487i
$731$	9.91498	−	11.8162i	0.366719	−	0.437038i
$732$	−0.0790381	+	0.0941939i	−0.00292133	+	0.00348151i
$733$	39.5119	+	22.8122i	1.45940	+	0.842588i	0.998982	−	0.0451117i	$-0.0143644\pi$
$733$	39.5119	+	22.8122i	1.45940	+	0.842588i	0.460423	+	0.887700i	$0.347698\pi$
$734$	−9.37121	+	16.2314i	−0.345898	+	0.599112i
$735$	−8.16254	+	10.6456i	−0.301080	+	0.392670i
$736$	3.09966	−	8.51626i	0.114255	−	0.313913i
$737$	−2.75102	+	3.27854i	−0.101335	+	0.120767i
$738$	−2.09496	+	0.369398i	−0.0771166	+	0.0135977i
$739$	35.6116	+	12.9616i	1.30999	+	0.476798i	0.900238	−	0.435397i	$-0.143392\pi$
$739$	35.6116	+	12.9616i	1.30999	+	0.476798i	0.409755	+	0.912196i	$0.365614\pi$
$740$	1.08070	+	1.87182i	0.0397273	+	0.0688096i
$741$	10.3417	−	0.169826i	0.379913	−	0.00623872i
$742$	−0.775971	−	35.2685i	−0.0284868	−	1.29475i
$743$	40.2438	−	7.09606i	1.47640	−	0.260329i	0.623262	−	0.782013i	$-0.285807\pi$
$743$	40.2438	−	7.09606i	1.47640	−	0.260329i	0.853139	+	0.521684i	$0.174696\pi$
$744$	−4.14063	+	11.3763i	−0.151803	+	0.417075i
$745$	−18.4424	−	3.25190i	−0.675678	−	0.119140i
$746$	−23.3255	+	19.5724i	−0.854008	+	0.716598i
$747$	6.58582	+	1.16126i	0.240963	+	0.0424882i
$748$	4.61279	+	2.66320i	0.168660	+	0.0973761i
$749$	−13.5985	+	24.7974i	−0.496877	+	0.906077i
$750$	2.04196	−	11.5805i	0.0745618	−	0.422861i
$751$	0.435943	+	1.19774i	0.0159078	+	0.0437063i	0.947392	−	0.320075i	$-0.103708\pi$
$751$	0.435943	+	1.19774i	0.0159078	+	0.0437063i	−0.931485	+	0.363781i	$0.881486\pi$
$752$			3.19731i			0.116594i
$753$	−14.0639	+	8.11980i	−0.512517	+	0.295902i
$754$	1.98368	−	11.2500i	0.0722413	−	0.409701i
$755$	33.6116	+	12.2336i	1.22325	+	0.445227i
$756$	−2.77080	−	0.425951i	−0.100773	−	0.0154917i
$757$	−13.2805	+	11.1437i	−0.482688	+	0.405024i	−0.851397	−	0.524521i	$-0.824244\pi$
$757$	−13.2805	+	11.1437i	−0.482688	+	0.405024i	0.368709	+	0.929545i	$0.379800\pi$
$758$	5.23488	−	4.39258i	0.190139	−	0.159546i
$759$	−1.28697	+	2.22909i	−0.0467139	+	0.0809109i
$760$	23.4262	+	8.09337i	0.849757	+	0.293577i
$761$	11.2690	−	6.50619i	0.408503	−	0.235849i	−0.281644	−	0.959519i	$-0.590880\pi$
$761$	11.2690	−	6.50619i	0.408503	−	0.235849i	0.690146	+	0.723670i	$0.257546\pi$
$762$	1.19860	+	6.79758i	0.0434206	+	0.246250i
$763$	1.05049	+	5.27617i	0.0380303	+	0.191010i
$764$	−19.6843	+	7.16450i	−0.712153	+	0.259203i
$765$	−1.13298	−	6.42545i	−0.0409630	−	0.232312i
$766$	8.24812	+	22.6615i	0.298017	+	0.818794i
$767$	2.58453	+	4.47654i	0.0933221	+	0.161639i
$768$	−8.51593	+	14.7500i	−0.307292	+	0.532245i
$769$	−17.8258	−	3.14316i	−0.642813	−	0.113345i	−0.157267	−	0.987556i	$-0.550268\pi$
$769$	−17.8258	−	3.14316i	−0.642813	−	0.113345i	−0.485547	+	0.874211i	$0.661379\pi$
$770$	−2.63254	−	6.76593i	−0.0948701	−	0.243827i
$771$	8.17555	+	14.1605i	0.294435	+	0.509977i
$772$			19.9234i			0.717058i
$773$	37.9222	−	13.8026i	1.36397	−	0.496443i	0.446688	−	0.894690i	$-0.352603\pi$
$773$	37.9222	−	13.8026i	1.36397	−	0.496443i	0.917278	+	0.398246i	$0.130381\pi$
$774$	−2.82416	−	3.36571i	−0.101513	−	0.120978i
$775$	4.14909	+	3.48150i	0.149040	+	0.125059i
$776$	−10.7780	−	12.8447i	−0.386908	−	0.461099i
$777$	0.549924	+	2.76203i	0.0197284	+	0.0990873i
$778$			34.3231i			1.23054i
$779$	−9.03758	−	3.12234i	−0.323805	−	0.111869i
$780$	−4.17271	−	2.40912i	−0.149407	−	0.0862602i
$781$	−0.0448713	+	0.123283i	−0.00160562	+	0.00441140i
$782$	5.40847	+	1.96852i	0.193406	+	0.0703942i
$783$	1.69791	+	4.66496i	0.0606782	+	0.166712i
$784$	1.15060	+	5.18112i	0.0410929	+	0.185040i
$785$	−18.8873	−	15.8483i	−0.674115	−	0.565650i
$786$	−16.5324			−0.589691
$787$	−12.1571			−0.433352			−0.216676	−	0.976244i	$-0.569522\pi$
$787$	−12.1571			−0.433352			−0.216676	+	0.976244i	$0.569522\pi$
$788$	3.51096	+	2.94605i	0.125073	+	0.104949i
$789$	24.2166	−	8.81412i	0.862134	−	0.313791i
$790$	−21.2211	+	12.2520i	−0.755012	+	0.435907i
$791$	3.19429	−	5.82493i	0.113576	−	0.207111i
$792$	2.81599	−	3.35596i	0.100062	−	0.119249i
$793$	−0.271186	+	0.0478174i	−0.00963010	+	0.00169805i
$794$	−1.95865	+	11.1080i	−0.0695098	+	0.394210i
$795$	4.57546	+	25.9487i	0.162275	+	0.920306i
$796$	−17.3592	−	20.6879i	−0.615281	−	0.733263i
$797$	11.9282			0.422517			0.211259	−	0.977430i	$-0.432244\pi$
$797$	11.9282			0.422517			0.211259	+	0.977430i	$0.432244\pi$
$798$	8.83710	+	6.85446i	0.312830	+	0.242645i
$799$	14.3572			0.507923
$800$	4.43589	+	5.28649i	0.156833	+	0.186906i
$801$	0.491187	+	2.78566i	0.0173552	+	0.0984264i
$802$	−1.17965	+	6.69014i	−0.0416549	+	0.236237i
$803$	2.19215	−	0.386535i	0.0773592	−	0.0136405i
$804$	−1.97416	+	2.35271i	−0.0696232	+	0.0829737i
$805$	4.58670	+	7.55555i	0.161660	+	0.266298i
$806$	−8.13130	+	4.69461i	−0.286413	+	0.165361i
$807$	29.1350	−	10.6043i	1.02560	−	0.373288i
$808$	24.3557	+	20.4368i	0.856830	+	0.718966i
$809$	19.1711			0.674020			0.337010	−	0.941501i	$-0.390584\pi$
$809$	19.1711			0.674020			0.337010	+	0.941501i	$0.390584\pi$
$810$	−1.85845			−0.0652991
$811$	27.0802	+	22.7230i	0.950914	+	0.797911i	0.979451	−	0.201681i	$-0.0646405\pi$
$811$	27.0802	+	22.7230i	0.950914	+	0.797911i	−0.0285374	+	0.999593i	$0.509085\pi$
$812$	−10.4615	+	9.17787i	−0.367127	+	0.322080i
$813$	−5.75448	−	15.8103i	−0.201818	−	0.554492i
$814$	−1.43222	−	0.521287i	−0.0501994	−	0.0182711i
$815$	−14.9405	+	41.0488i	−0.523344	+	1.43788i
$816$	−2.23551	−	1.29067i	−0.0782584	−	0.0451825i
$817$	−3.74816	−	19.3896i	−0.131132	−	0.678356i
$818$			15.9351i			0.557156i
$819$	−4.14025	−	4.71932i	−0.144672	−	0.164907i
$820$	2.86313	+	3.41214i	0.0999848	+	0.119157i
$821$	33.9608	+	28.4965i	1.18524	+	0.994535i	0.999930	+	0.0118550i	$0.00377367\pi$
$821$	33.9608	+	28.4965i	1.18524	+	0.994535i	0.185311	+	0.982680i	$0.440671\pi$
$822$	2.26977	+	2.70500i	0.0791672	+	0.0943478i
$823$	13.0060	−	4.73380i	0.453361	−	0.165010i	−0.105239	−	0.994447i	$-0.533561\pi$
$823$	13.0060	−	4.73380i	0.453361	−	0.165010i	0.558600	+	0.829437i	$0.311339\pi$
$824$			57.5556i			2.00504i
$825$	−0.979981	−	1.69738i	−0.0341186	−	0.0590951i
$826$	−0.849247	+	5.52432i	−0.0295491	+	0.192216i
$827$	−6.84495	−	1.20695i	−0.238022	−	0.0419697i	0.0533644	−	0.998575i	$-0.483006\pi$
$827$	−6.84495	−	1.20695i	−0.238022	−	0.0419697i	−0.291387	+	0.956605i	$0.594117\pi$
$828$	−0.923539	+	1.59962i	−0.0320952	+	0.0555905i
$829$	−10.4191	−	18.0464i	−0.361871	−	0.626778i	0.626398	−	0.779503i	$-0.284528\pi$
$829$	−10.4191	−	18.0464i	−0.361871	−	0.626778i	−0.988269	+	0.152725i	$0.951195\pi$
$830$	4.25070	+	11.6787i	0.147544	+	0.405374i
$831$	3.99667	+	22.6663i	0.138643	+	0.786284i
$832$	−14.6228	+	5.32228i	−0.506956	+	0.184517i
$833$	23.2654	−	5.16669i	0.806099	−	0.179015i
$834$	−0.262240	−	1.48724i	−0.00908064	−	0.0514989i
$835$	−30.5325	+	17.6279i	−1.05662	+	0.610040i
$836$	6.36894	−	2.43726i	0.220275	−	0.0842944i
$837$	2.04014	−	3.53363i	0.0705176	−	0.122140i
$838$	−19.9352	+	16.7276i	−0.688651	+	0.577847i
$839$	−31.8362	+	26.7137i	−1.09911	+	0.922260i	−0.997365	−	0.0725503i	$-0.976886\pi$
$839$	−31.8362	+	26.7137i	−1.09911	+	0.922260i	−0.101742	+	0.994811i	$0.532442\pi$
$840$	−5.45501	−	14.0200i	−0.188216	−	0.483735i
$841$	−4.09261	−	1.48959i	−0.141125	−	0.0513651i
$842$	−3.88676	+	22.0429i	−0.133947	+	0.759650i
$843$	13.8018	−	7.96850i	0.475361	−	0.274450i
$844$		−	20.0197i		−	0.689105i
$845$	4.83029	+	13.2711i	0.166167	+	0.456540i
$846$	0.710133	−	4.02736i	0.0244149	−	0.138464i
$847$	20.4607	+	11.2203i	0.703037	+	0.385533i
$848$	9.02794	+	5.21228i	0.310021	+	0.178991i
$849$	−11.0884	−	1.95518i	−0.380553	−	0.0671017i
$850$	−3.35732	+	2.81713i	−0.115155	+	0.0966267i
$851$	1.82739	+	0.322218i	0.0626420	+	0.0110455i
$852$	−0.0322000	+	0.0884689i	−0.00110316	+	0.00303089i
$853$	26.3030	−	4.63792i	0.900596	−	0.158799i	0.295866	−	0.955230i	$-0.404392\pi$
$853$	26.3030	−	4.63792i	0.900596	−	0.158799i	0.604730	+	0.796430i	$0.293281\pi$
$854$	−0.261073	−	0.143168i	−0.00893374	−	0.00489911i
$855$	−7.30184	−	4.05735i	−0.249718	−	0.138758i
$856$	−15.8578	−	27.4666i	−0.542009	−	0.938788i
$857$	−21.3113	−	7.75669i	−0.727981	−	0.264963i	−0.0486709	−	0.998815i	$-0.515499\pi$
$857$	−21.3113	−	7.75669i	−0.727981	−	0.264963i	−0.679310	+	0.733852i	$0.737721\pi$
$858$	3.34603	−	0.589995i	0.114232	−	0.0201421i
$859$	−16.2709	+	19.3909i	−0.555155	+	0.661608i	−0.968514	−	0.248961i	$-0.919911\pi$
$859$	−16.2709	+	19.3909i	−0.555155	+	0.661608i	0.413359	+	0.910568i	$0.364355\pi$
$860$	−3.14647	+	8.64484i	−0.107294	+	0.294787i
$861$	2.10448	+	5.40876i	0.0717206	+	0.184330i
$862$	9.46611	−	16.3958i	0.322417	−	0.558442i
$863$	−47.8349	−	27.6175i	−1.62832	−	0.940110i	−0.984595	−	0.174851i	$-0.944056\pi$
$863$	−47.8349	−	27.6175i	−1.62832	−	0.940110i	−0.643723	−	0.765259i	$-0.722611\pi$
$864$	3.34174	−	3.98253i	0.113688	−	0.135488i
$865$	1.34194	−	1.59926i	0.0456272	−	0.0543764i
$866$	28.6375	+	16.5339i	0.973142	+	0.561844i
$867$	2.70435	−	4.68407i	0.0918444	−	0.159079i
$868$	11.3056	+	1.73800i	0.383738	+	0.0589916i
$869$	−6.65852	+	18.2941i	−0.225875	+	0.620586i
$870$	−5.93034	+	7.06750i	−0.201057	+	0.239611i
$871$	−6.77350	+	1.19435i	−0.229511	+	0.0404690i
$872$	−5.66919	−	2.06342i	−0.191983	−	0.0698761i
$873$	2.82564	+	4.89415i	0.0956335	+	0.165642i
$874$	6.32024	−	3.78870i	0.213785	−	0.128155i
$875$	−32.0742	+	0.705691i	−1.08431	+	0.0238567i
$876$	1.57311	−	0.277381i	0.0531504	−	0.00937184i
$877$	−9.44553	+	25.9514i	−0.318953	+	0.876316i	0.671812	+	0.740722i	$0.265516\pi$
$877$	−9.44553	+	25.9514i	−0.318953	+	0.876316i	−0.990765	+	0.135594i	$0.956706\pi$
$878$	−28.9887	−	5.11149i	−0.978321	−	0.172504i
$879$	9.82324	−	8.24268i	0.331330	−	0.278019i
$880$	2.11279	+	0.372541i	0.0712220	+	0.0125584i
$881$	6.29696	+	3.63555i	0.212150	+	0.122485i	0.602310	−	0.798262i	$-0.294247\pi$
$881$	6.29696	+	3.63555i	0.212150	+	0.122485i	−0.390160	+	0.920747i	$0.627580\pi$
$882$	−0.298566	−	6.78175i	−0.0100532	−	0.228354i
$883$	−1.02893	+	5.83537i	−0.0346263	+	0.196376i	−0.997214	−	0.0745951i	$-0.976234\pi$
$883$	−1.02893	+	5.83537i	−0.0346263	+	0.196376i	0.962588	+	0.270971i	$0.0873447\pi$
$884$	2.92766	+	8.04367i	0.0984677	+	0.270538i
$885$		−	4.17468i		−	0.140330i
$886$	−10.5189	+	6.07309i	−0.353389	+	0.204029i
$887$	−0.130700	+	0.741235i	−0.00438847	+	0.0248882i	−0.986923	−	0.161190i	$-0.948467\pi$
$887$	−0.130700	+	0.741235i	−0.00438847	+	0.0248882i	0.982535	+	0.186078i	$0.0595779\pi$
$888$	−2.96778	−	1.08018i	−0.0995921	−	0.0362485i
$889$	17.5500	−	6.82848i	0.588607	−	0.229020i
$890$	−4.02699	+	3.37904i	−0.134985	+	0.113266i
$891$	−1.13108	+	0.949089i	−0.0378926	+	0.0317957i
$892$	7.81391	−	13.5341i	0.261629	−	0.453155i
$893$	11.5826	−	14.2732i	0.387598	−	0.477634i
$894$	8.20684	−	4.73822i	0.274478	−	0.158470i
$895$	−7.59293	−	43.0616i	−0.253804	−	1.43939i
$896$	10.1171	+	3.43224i	0.337989	+	0.114663i
$897$	−3.88703	+	1.41476i	−0.129784	+	0.0472376i
$898$	−6.13792	−	34.8099i	−0.204825	−	1.16162i
$899$	−6.92794	−	19.0344i	−0.231060	−	0.634831i
$900$	−0.703244	−	1.21805i	−0.0234415	−	0.0406018i
$901$	23.4053	−	40.5392i	0.779745	−	1.35056i
$902$	−3.09325	−	0.545424i	−0.102994	−	0.0181606i
$903$	−7.50119	+	9.34977i	−0.249624	+	0.311141i
$904$	3.72502	+	6.45192i	0.123892	+	0.214588i
$905$			35.7192i			1.18735i
$906$	−17.0086	+	6.19061i	−0.565072	+	0.205669i
$907$	5.72498	+	6.82277i	0.190095	+	0.226546i	0.852671	−	0.522448i	$-0.174981\pi$
$907$	5.72498	+	6.82277i	0.190095	+	0.226546i	−0.662576	+	0.748995i	$0.730537\pi$
$908$	13.7951	+	11.5755i	0.457808	+	0.384146i
$909$	−6.88795	−	8.20874i	−0.228459	−	0.272267i
$910$	3.74835	−	11.0489i	0.124257	−	0.366267i
$911$			42.3514i			1.40317i	0.712588	+	0.701583i	$0.247523\pi$
$911$			42.3514i			1.40317i	−0.712588	+	0.701583i	$0.752477\pi$
$912$	−3.08660	+	1.18118i	−0.102207	+	0.0391126i
$913$	8.55123	+	4.93706i	0.283004	+	0.163393i
$914$	0.825785	−	2.26883i	0.0273145	−	0.0750461i
$915$	0.208984	+	0.0760639i	0.00690879	+	0.00251459i
$916$	−10.8449	−	29.7962i	−0.358326	−	0.984493i
$917$	8.80750	+	44.2363i	0.290849	+	1.46081i
$918$	2.52921	+	2.12226i	0.0834763	+	0.0700449i
$919$	−6.12833			−0.202155			−0.101077	−	0.994879i	$-0.532229\pi$
$919$	−6.12833			−0.202155			−0.101077	+	0.994879i	$0.532229\pi$
$920$	−9.91214			−0.326794
$921$	−8.97007	−	7.52678i	−0.295574	−	0.248016i
$922$	4.87438	−	1.77413i	0.160529	−	0.0584278i
$923$	−0.182592	+	0.105420i	−0.00601010	+	0.00346993i
$924$	−3.62930	−	1.99025i	−0.119395	−	0.0654743i
$925$	−0.908233	+	1.08239i	−0.0298625	+	0.0355888i
$926$	32.0161	−	5.64530i	1.05211	−	0.185516i
$927$	3.36848	−	19.1036i	0.110635	−	0.627444i
$928$	−4.48165	−	25.4167i	−0.147117	−	0.834343i
$929$	−35.1403	−	41.8786i	−1.15292	−	1.37399i	−0.915368	−	0.402617i	$-0.868101\pi$
$929$	−35.1403	−	41.8786i	−1.15292	−	1.37399i	−0.237548	−	0.971376i	$-0.576344\pi$
$930$	7.58299			0.248656
$931$	13.6328	−	27.2974i	0.446797	−	0.894635i
$932$	1.76466			0.0578033
$933$	12.6037	+	15.0205i	0.412628	+	0.491750i
$934$	−2.14848	−	12.1846i	−0.0703005	−	0.398694i
$935$	1.67287	−	9.48730i	0.0547086	−	0.310268i
$936$	6.93346	−	1.22256i	0.226627	−	0.0399605i
$937$	7.62264	−	9.08431i	0.249021	−	0.296772i	−0.627025	−	0.778999i	$-0.715728\pi$
$937$	7.62264	−	9.08431i	0.249021	−	0.296772i	0.876046	+	0.482227i	$0.160172\pi$
$938$	−6.52091	−	3.57595i	−0.212915	−	0.116759i
$939$	6.14428	−	3.54740i	0.200511	−	0.115765i
$940$	−8.04644	+	2.92867i	−0.262446	+	0.0955225i
$941$	−35.9865	−	30.1962i	−1.17313	−	0.984370i	−0.173126	−	0.984900i	$-0.555387\pi$
$941$	−35.9865	−	30.1962i	−1.17313	−	0.984370i	−1.00000		0.000530142i	$0.999831\pi$
$942$	12.4765			0.406507
$943$	3.82400			0.124527
$944$	−1.26523	−	1.06166i	−0.0411798	−	0.0345540i
$945$	0.990072	+	4.97271i	0.0322070	+	0.161762i
$946$	−2.21878	−	6.09604i	−0.0721386	−	0.198199i
$947$	−0.535492	−	0.194903i	−0.0174012	−	0.00633351i	0.333305	−	0.942819i	$-0.391836\pi$
$947$	−0.535492	−	0.194903i	−0.0174012	−	0.00633351i	−0.350706	+	0.936486i	$0.614058\pi$
$948$	−4.77822	+	13.1281i	−0.155189	+	0.426379i
$949$	3.09802	+	1.78864i	0.100566	+	0.0580618i
$950$	0.0921304	+	5.61037i	0.00298910	+	0.182024i
$951$			6.98299i			0.226439i
$952$	−8.58630	+	25.3095i	−0.278284	+	0.820286i
$953$	−2.30103	−	2.74226i	−0.0745376	−	0.0888304i	0.727487	−	0.686121i	$-0.240688\pi$
$953$	−2.30103	−	2.74226i	−0.0745376	−	0.0888304i	−0.802025	+	0.597291i	$0.796244\pi$
$954$	−10.2140	−	8.57059i	−0.330691	−	0.277483i
$955$	24.3534	+	29.0233i	0.788058	+	0.939171i
$956$	−15.9576	+	5.80809i	−0.516106	+	0.187847i
$957$			7.32996i			0.236944i
$958$	8.11369	+	14.0533i	0.262142	+	0.454042i
$959$	6.02867	−	7.51436i	0.194676	−	0.242651i
$960$	12.3768	+	2.18236i	0.399459	+	0.0704355i
$961$	7.17564	−	12.4286i	0.231472	−	0.400922i
$962$	−1.22470	−	2.12125i	−0.0394860	−	0.0683917i
$963$	3.65596	+	10.0447i	0.117812	+	0.323685i
$964$	−0.382428	−	2.16886i	−0.0123172	−	0.0698542i
$965$	33.8615	−	12.3246i	1.09004	−	0.396743i
$966$	−4.23561	−	1.43694i	−0.136278	−	0.0462327i
$967$	5.58594	+	31.6794i	0.179632	+	1.01874i	0.932661	+	0.360755i	$0.117481\pi$
$967$	5.58594	+	31.6794i	0.179632	+	1.01874i	−0.753029	+	0.657987i	$0.771408\pi$
$968$	−22.6630	+	13.0845i	−0.728417	+	0.420552i
$969$	5.30397	+	13.8601i	0.170388	+	0.445251i
$970$	−5.25130	+	9.09552i	−0.168609	+	0.292040i
$971$	28.1230	−	23.5980i	0.902511	−	0.757296i	−0.0681688	−	0.997674i	$-0.521716\pi$
$971$	28.1230	−	23.5980i	0.902511	−	0.757296i	0.970680	+	0.240377i	$0.0772712\pi$
$972$	−0.811674	+	0.681075i	−0.0260345	+	0.0218455i
$973$	−3.83975	+	1.49400i	−0.123097	+	0.0478954i
$974$	−13.2300	−	4.81533i	−0.423917	−	0.154293i
$975$	0.546957	−	3.10195i	0.0175167	−	0.0993419i
$976$	0.0761993	−	0.0439937i	0.00243908	−	0.00140820i
$977$			40.6274i			1.29978i	0.760026	+	0.649892i	$0.225186\pi$
$977$			40.6274i			1.29978i	−0.760026	+	0.649892i	$0.774814\pi$
$978$	−7.56040	−	20.7720i	−0.241755	−	0.664216i
$979$	−0.725247	+	4.11308i	−0.0231790	+	0.131455i
$980$	−11.9851	+	7.64144i	−0.382848	+	0.244097i
$981$	1.76093	+	1.01667i	0.0562221	+	0.0324599i
$982$	38.3468	+	6.76157i	1.22370	+	0.215770i
$983$	4.76870	−	4.00142i	0.152098	−	0.127625i	−0.563563	−	0.826073i	$-0.690570\pi$
$983$	4.76870	−	4.00142i	0.152098	−	0.127625i	0.715661	+	0.698447i	$0.246125\pi$
$984$	−6.40967	−	1.13020i	−0.204333	−	0.0360294i
$985$	2.83519	−	7.78961i	0.0903366	−	0.248198i
$986$	16.1415	−	2.84618i	0.514050	−	0.0906409i
$987$	−11.1545	+	0.245418i	−0.355051	+	0.00781175i
$988$	10.3584	+	3.57867i	0.329546	+	0.113853i
$989$	3.94899	+	6.83985i	0.125571	+	0.217495i
$990$	−2.57855	−	0.938515i	−0.0819516	−	0.0298280i
$991$	−37.2428	+	6.56692i	−1.18306	+	0.208605i	−0.730362	−	0.683060i	$-0.760649\pi$
$991$	−37.2428	+	6.56692i	−1.18306	+	0.208605i	−0.452696	+	0.891665i	$0.649538\pi$
$992$	−13.6352	+	16.2499i	−0.432920	+	0.515933i
$993$	−7.87932	+	21.6482i	−0.250043	+	0.686986i
$994$	−0.225330	−	0.0346397i	−0.00714703	−	0.00109870i
$995$	−24.4225	+	42.3010i	−0.774246	+	1.34103i
$996$	6.13645	+	3.54288i	0.194441	+	0.112260i
$997$	11.3507	−	13.5272i	0.359479	−	0.428411i	−0.555747	−	0.831352i	$-0.687568\pi$
$997$	11.3507	−	13.5272i	0.359479	−	0.428411i	0.915226	+	0.402941i	$0.132012\pi$
$998$	0.252435	−	0.300841i	0.00799071	−	0.00952295i
$999$	0.921832	+	0.532220i	0.0291655	+	0.0168387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.ck.a.10.9	yes	78
7.5	odd	6		399.2.cd.a.124.9	✓	78
19.2	odd	18		399.2.cd.a.325.9	yes	78
133.40	even	18	inner	399.2.ck.a.40.9	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.cd.a.124.9	✓	78	7.5	odd	6
399.2.cd.a.325.9	yes	78	19.2	odd	18
399.2.ck.a.10.9	yes	78	1.1	even	1	trivial
399.2.ck.a.40.9	yes	78	133.40	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623350 + 0.742879i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.183992 - 1.04347i) q^{4} +(-1.88728 + 0.332779i) q^{5} +(0.623350 - 0.742879i) q^{6} +(-2.31983 - 1.27216i) q^{7} +(2.56954 - 1.48352i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-1.42365 - 1.19459i) q^{10} -1.47652 q^{11} -1.05956 q^{12} +(-1.81773 - 1.52525i) q^{13} +(-0.501009 - 2.51635i) q^{14} +(0.655447 + 1.80082i) q^{15} +(0.712468 + 0.259317i) q^{16} +(1.16444 - 3.19928i) q^{17} +(-0.839837 - 0.484880i) q^{18} +(-2.24114 - 3.73862i) q^{19} +2.03055i q^{20} +(-0.849994 + 2.50550i) q^{21} +(-0.920389 - 1.09688i) q^{22} +(1.33540 + 1.12053i) q^{23} +(-1.90718 - 2.27289i) q^{24} +(-1.24737 + 0.454005i) q^{25} -2.30112i q^{26} +(0.500000 + 0.866025i) q^{27} +(-1.75428 + 2.18660i) q^{28} +(4.88893 + 0.862050i) q^{29} +(-0.929223 + 1.60946i) q^{30} +(-2.04014 - 3.53363i) q^{31} +(-1.77810 - 4.88530i) q^{32} +(0.256395 + 1.45409i) q^{33} +(3.10253 - 1.12923i) q^{34} +(4.80153 + 1.62893i) q^{35} +(0.183992 + 1.04347i) q^{36} +(0.921832 - 0.532220i) q^{37} +(1.38033 - 3.99537i) q^{38} +(-1.18644 + 2.05497i) q^{39} +(-4.35576 + 3.65491i) q^{40} +(1.68041 - 1.41003i) q^{41} +(-2.39113 + 0.930358i) q^{42} +(4.25739 + 1.54956i) q^{43} +(-0.271667 + 1.54070i) q^{44} +(1.65965 - 0.958199i) q^{45} +1.69053i q^{46} +(1.44230 + 3.96270i) q^{47} +(0.131659 - 0.746674i) q^{48} +(3.76324 + 5.90237i) q^{49} +(-1.11482 - 0.643640i) q^{50} +(-3.35288 - 0.591203i) q^{51} +(-1.92600 + 1.61611i) q^{52} +(13.5404 + 2.38753i) q^{53} +(-0.331678 + 0.911277i) q^{54} +(2.78661 - 0.491355i) q^{55} +(-7.84816 + 0.172674i) q^{56} +(-3.29266 + 2.85629i) q^{57} +(2.40711 + 4.16924i) q^{58} +(-2.04703 - 0.745056i) q^{59} +(1.99970 - 0.352601i) q^{60} +(0.0745948 - 0.0888986i) q^{61} +(1.35334 - 3.71827i) q^{62} +(2.61503 + 0.402006i) q^{63} +(3.27900 - 5.67939i) q^{64} +(3.93814 + 2.27368i) q^{65} +(-0.920389 + 1.09688i) q^{66} +(1.86318 - 2.22045i) q^{67} +(-3.12410 - 1.80370i) q^{68} +(0.871621 - 1.50969i) q^{69} +(1.78294 + 4.58235i) q^{70} +(0.0303899 - 0.0834955i) q^{71} +(-1.90718 + 2.27289i) q^{72} +(-1.48467 + 0.261788i) q^{73} +(0.969999 + 0.353051i) q^{74} +(0.663710 + 1.14958i) q^{75} +(-4.31348 + 1.65068i) q^{76} +(3.42528 + 1.87836i) q^{77} +(-2.26616 + 0.399585i) q^{78} +(4.50961 - 12.3900i) q^{79} +(-1.43092 - 0.252310i) q^{80} +(0.766044 - 0.642788i) q^{81} +(2.09496 + 0.369398i) q^{82} +(-5.79148 - 3.34371i) q^{83} +(2.45801 + 1.34793i) q^{84} +(-1.13298 + 6.42545i) q^{85} +(1.50271 + 4.12865i) q^{86} -4.96435i q^{87} +(-3.79397 + 2.19045i) q^{88} +(0.491187 - 2.78566i) q^{89} +(1.74637 + 0.635626i) q^{90} +(2.27646 + 5.85076i) q^{91} +(1.41494 - 1.18728i) q^{92} +(-3.12568 + 2.62276i) q^{93} +(-2.04475 + 3.54160i) q^{94} +(5.47380 + 6.31004i) q^{95} +(-4.50231 + 2.59941i) q^{96} +(-0.981335 - 5.56543i) q^{97} +(-2.03894 + 6.47488i) q^{98} +(1.38747 - 0.505000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 6 q^{7} + 12 q^{10} + 6 q^{11} + 72 q^{12} + 3 q^{13} - 15 q^{14} + 18 q^{19} + 9 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{24} + 18 q^{25} + 39 q^{27} - 9 q^{28} - 6 q^{29} - 18 q^{31} - 51 q^{32} - 12 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) \) 78 * q - 6 * q^7 + 12 * q^10 + 6 * q^11 + 72 * q^12 + 3 * q^13 - 15 * q^14 + 18 * q^19 + 9 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^24 + 18 * q^25 + 39 * q^27 - 9 * q^28 - 6 * q^29 - 18 * q^31 - 51 * q^32 - 12 * q^33 + 30 * q^34 + 33 * q^35 + 18 * q^37 - 57 * q^38 - 18 * q^40 - 63 * q^41 - 27 * q^42 - 51 * q^43 - 36 * q^44 + 9 * q^45 - 84 * q^47 + 18 * q^49 - 27 * q^50 - 18 * q^51 + 18 * q^52 - 45 * q^53 + 30 * q^55 + 33 * q^56 - 6 * q^57 - 18 * q^58 - 24 * q^59 + 66 * q^61 + 171 * q^62 + 6 * q^63 + 18 * q^64 - 99 * q^65 - 12 * q^66 - 24 * q^67 - 12 * q^69 - 150 * q^70 - 66 * q^71 - 9 * q^72 + 3 * q^73 + 18 * q^74 - 36 * q^75 - 12 * q^76 + 21 * q^77 + 75 * q^78 + 45 * q^79 + 78 * q^80 - 24 * q^82 - 72 * q^83 - 9 * q^84 + 60 * q^85 - 9 * q^86 - 108 * q^88 + 48 * q^89 - 33 * q^90 - 54 * q^91 - 102 * q^92 + 9 * q^93 - 66 * q^94 - 84 * q^95 + 75 * q^97 - 39 * q^98 - 6 * q^99

Introduction

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