LMFDB - Embedded newform 925.2.t.b.843.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(82,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			843.12
Character	$\chi$	$=$	925.843
Dual form			925.2.t.b.282.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.567972 + 0.983757i) q^{2} +(-0.273625 - 1.02118i) q^{3} +(0.354815 - 0.614557i) q^{4} +(0.849185 - 0.849185i) q^{6} +(0.422839 + 1.57806i) q^{7} +3.07799 q^{8} +(1.63013 - 0.941157i) q^{9} -1.92257i q^{11} +(-0.724662 - 0.194173i) q^{12} +(-0.763528 + 1.32247i) q^{13} +(-1.31226 + 1.31226i) q^{14} +(1.03858 + 1.79888i) q^{16} +(-1.14334 + 0.660110i) q^{17} +(1.85174 + 1.06910i) q^{18} +(2.17790 - 0.583566i) q^{19} +(1.49579 - 0.863592i) q^{21} +(1.89134 - 1.09196i) q^{22} +4.57925 q^{23} +(-0.842216 - 3.14319i) q^{24} -1.73465 q^{26} +(-3.64981 - 3.64981i) q^{27} +(1.11984 + 0.300059i) q^{28} +(0.241089 - 0.241089i) q^{29} +(-1.00617 - 1.00617i) q^{31} +(1.89822 - 3.28781i) q^{32} +(-1.96329 + 0.526063i) q^{33} +(-1.29878 - 0.749849i) q^{34} -1.33575i q^{36} +(-1.71804 - 5.83510i) q^{37} +(1.81107 + 1.81107i) q^{38} +(1.55940 + 0.417841i) q^{39} +(6.76304 + 3.90464i) q^{41} +(1.69913 + 0.980993i) q^{42} -5.46568 q^{43} +(-1.18153 - 0.682155i) q^{44} +(2.60089 + 4.50487i) q^{46} +(-1.79140 + 1.79140i) q^{47} +(1.55280 - 1.55280i) q^{48} +(3.75071 - 2.16547i) q^{49} +(0.986942 + 0.986942i) q^{51} +(0.541822 + 0.938463i) q^{52} +(0.870548 - 3.24893i) q^{53} +(1.51754 - 5.66352i) q^{54} +(1.30149 + 4.85724i) q^{56} +(-1.19186 - 2.06436i) q^{57} +(0.374105 + 0.100241i) q^{58} +(-1.40987 + 5.26170i) q^{59} +(10.4583 - 2.80230i) q^{61} +(0.418352 - 1.56131i) q^{62} +(2.17448 + 2.17448i) q^{63} +8.46687 q^{64} +(-1.63261 - 1.63261i) q^{66} +(9.45477 - 2.53340i) q^{67} +0.936868i q^{68} +(-1.25300 - 4.67625i) q^{69} +(1.65295 - 2.86299i) q^{71} +(5.01753 - 2.89687i) q^{72} +(-1.78634 + 1.78634i) q^{73} +(4.76452 - 5.00430i) q^{74} +(0.414116 - 1.54550i) q^{76} +(3.03392 - 0.812936i) q^{77} +(0.474644 + 1.77140i) q^{78} +(-12.3408 + 3.30670i) q^{79} +(0.0950223 - 0.164583i) q^{81} +8.87092i q^{82} +(-2.29888 + 8.57952i) q^{83} -1.22566i q^{84} +(-3.10436 - 5.37690i) q^{86} +(-0.312164 - 0.180228i) q^{87} -5.91764i q^{88} +(-16.4223 - 4.40035i) q^{89} +(-2.40978 - 0.645698i) q^{91} +(1.62479 - 2.81421i) q^{92} +(-0.752174 + 1.30280i) q^{93} +(-2.77976 - 0.744835i) q^{94} +(-3.87685 - 1.03880i) q^{96} +15.4196i q^{97} +(4.26060 + 2.45986i) q^{98} +(-1.80944 - 3.13404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) $ 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.567972	+	0.983757i	0.401617	+	0.695621i	0.993921	−	0.110093i	$-0.0351149\pi$
$2$	0.567972	+	0.983757i	0.401617	+	0.695621i	−0.592304	+	0.805714i	$0.701782\pi$
$3$	−0.273625	−	1.02118i	−0.157978	−	0.589581i	−0.998832	−	0.0483191i	$-0.984614\pi$
$3$	−0.273625	−	1.02118i	−0.157978	−	0.589581i	0.840854	−	0.541262i	$-0.182053\pi$
$4$	0.354815	−	0.614557i	0.177407	−	0.307279i
$5$		0			0
$5$		0			0
$6$	0.849185	−	0.849185i	0.346678	−	0.346678i
$7$	0.422839	+	1.57806i	0.159818	+	0.596449i	0.998644	+	0.0520501i	$0.0165756\pi$
$7$	0.422839	+	1.57806i	0.159818	+	0.596449i	−0.838826	+	0.544399i	$0.816758\pi$
$8$	3.07799			1.08823
$9$	1.63013	−	0.941157i	0.543377	−	0.313719i
$10$		0			0
$11$		−	1.92257i		−	0.579676i	−0.957076	−	0.289838i	$-0.906399\pi$
$11$		−	1.92257i		−	0.579676i	0.957076	−	0.289838i	$-0.0936014\pi$
$12$	−0.724662	−	0.194173i	−0.209192	−	0.0560528i
$13$	−0.763528	+	1.32247i	−0.211764	+	0.366787i	−0.952267	−	0.305267i	$-0.901254\pi$
$13$	−0.763528	+	1.32247i	−0.211764	+	0.366787i	0.740502	+	0.672054i	$0.234588\pi$
$14$	−1.31226	+	1.31226i	−0.350717	+	0.350717i
$15$		0			0
$16$	1.03858	+	1.79888i	0.259646	+	0.449720i
$17$	−1.14334	+	0.660110i	−0.277302	+	0.160100i	−0.632201	−	0.774804i	$-0.717848\pi$
$17$	−1.14334	+	0.660110i	−0.277302	+	0.160100i	0.354899	+	0.934904i	$0.384515\pi$
$18$	1.85174	+	1.06910i	0.436459	+	0.251990i
$19$	2.17790	−	0.583566i	0.499644	−	0.133879i	−0.000190628	−	1.00000i	$-0.500061\pi$
$19$	2.17790	−	0.583566i	0.499644	−	0.133879i	0.499835	+	0.866121i	$0.333394\pi$
$20$		0			0
$21$	1.49579	−	0.863592i	0.326407	−	0.188451i
$22$	1.89134	−	1.09196i	0.403235	−	0.232808i
$23$	4.57925			0.954839			0.477420	−	0.878675i	$-0.341572\pi$
$23$	4.57925			0.954839			0.477420	+	0.878675i	$0.341572\pi$
$24$	−0.842216	−	3.14319i	−0.171917	−	0.641601i
$25$		0			0
$26$	−1.73465			−0.340193
$27$	−3.64981	−	3.64981i	−0.702407	−	0.702407i
$28$	1.11984	+	0.300059i	0.211629	+	0.0567058i
$29$	0.241089	−	0.241089i	0.0447691	−	0.0447691i	−0.684368	−	0.729137i	$-0.739922\pi$
$29$	0.241089	−	0.241089i	0.0447691	−	0.0447691i	0.729137	+	0.684368i	$0.239922\pi$
$30$		0			0
$31$	−1.00617	−	1.00617i	−0.180714	−	0.180714i	0.610953	−	0.791667i	$-0.290787\pi$
$31$	−1.00617	−	1.00617i	−0.180714	−	0.180714i	−0.791667	+	0.610953i	$0.790787\pi$
$32$	1.89822	−	3.28781i	0.335560	−	0.581208i
$33$	−1.96329	+	0.526063i	−0.341766	+	0.0915758i
$34$	−1.29878	−	0.749849i	−0.222738	−	0.128598i
$35$		0			0
$36$		−	1.33575i		−	0.222624i
$37$	−1.71804	−	5.83510i	−0.282443	−	0.959284i
$37$	−1.71804	−	5.83510i	−0.282443	−	0.959284i
$38$	1.81107	+	1.81107i	0.293795	+	0.293795i
$39$	1.55940	+	0.417841i	0.249704	+	0.0669081i
$40$		0			0
$41$	6.76304	+	3.90464i	1.05621	+	0.609803i	0.924381	−	0.381470i	$-0.124582\pi$
$41$	6.76304	+	3.90464i	1.05621	+	0.609803i	0.131828	+	0.991273i	$0.457915\pi$
$42$	1.69913	+	0.980993i	0.262181	+	0.151370i
$43$	−5.46568			−0.833509			−0.416754	−	0.909019i	$-0.636832\pi$
$43$	−5.46568			−0.833509			−0.416754	+	0.909019i	$0.636832\pi$
$44$	−1.18153	−	0.682155i	−0.178122	−	0.102839i
$45$		0			0
$46$	2.60089	+	4.50487i	0.383480	+	0.664207i
$47$	−1.79140	+	1.79140i	−0.261302	+	0.261302i	−0.825583	−	0.564281i	$-0.809154\pi$
$47$	−1.79140	+	1.79140i	−0.261302	+	0.261302i	0.564281	+	0.825583i	$0.309154\pi$
$48$	1.55280	−	1.55280i	0.224128	−	0.224128i
$49$	3.75071	−	2.16547i	0.535816	−	0.309353i
$50$		0			0
$51$	0.986942	+	0.986942i	0.138200	+	0.138200i
$52$	0.541822	+	0.938463i	0.0751372	+	0.130141i
$53$	0.870548	−	3.24893i	0.119579	−	0.446275i	−0.880010	−	0.474956i	$-0.842464\pi$
$53$	0.870548	−	3.24893i	0.119579	−	0.446275i	0.999589	+	0.0286809i	$0.00913067\pi$
$54$	1.51754	−	5.66352i	0.206511	−	0.770708i
$55$		0			0
$56$	1.30149	+	4.85724i	0.173919	+	0.649076i
$57$	−1.19186	−	2.06436i	−0.157865	−	0.273431i
$58$	0.374105	+	0.100241i	0.0491223	+	0.0131623i
$59$	−1.40987	+	5.26170i	−0.183549	+	0.685016i	0.811387	+	0.584509i	$0.198713\pi$
$59$	−1.40987	+	5.26170i	−0.183549	+	0.685016i	−0.994936	+	0.100506i	$0.967954\pi$
$60$		0			0
$61$	10.4583	−	2.80230i	1.33905	−	0.358797i	0.482968	−	0.875638i	$-0.339559\pi$
$61$	10.4583	−	2.80230i	1.33905	−	0.358797i	0.856081	+	0.516841i	$0.172892\pi$
$62$	0.418352	−	1.56131i	0.0531307	−	0.198287i
$63$	2.17448	+	2.17448i	0.273959	+	0.273959i
$64$	8.46687			1.05836
$65$		0			0
$66$	−1.63261	−	1.63261i	−0.200961	−	0.200961i
$67$	9.45477	−	2.53340i	1.15508	−	0.309504i	0.370083	−	0.928999i	$-0.379329\pi$
$67$	9.45477	−	2.53340i	1.15508	−	0.309504i	0.785001	+	0.619495i	$0.212662\pi$
$68$			0.936868i			0.113612i
$69$	−1.25300	−	4.67625i	−0.150843	−	0.562955i
$70$		0			0
$71$	1.65295	−	2.86299i	0.196169	−	0.339774i	−0.751114	−	0.660172i	$-0.770483\pi$
$71$	1.65295	−	2.86299i	0.196169	−	0.339774i	0.947283	+	0.320398i	$0.103817\pi$
$72$	5.01753	−	2.89687i	0.591321	−	0.341399i
$73$	−1.78634	+	1.78634i	−0.209075	+	0.209075i	−0.803874	−	0.594799i	$-0.797232\pi$
$73$	−1.78634	+	1.78634i	−0.209075	+	0.209075i	0.594799	+	0.803874i	$0.297232\pi$
$74$	4.76452	−	5.00430i	0.553864	−	0.581739i
$75$		0			0
$76$	0.414116	−	1.54550i	0.0475023	−	0.177281i
$77$	3.03392	−	0.812936i	0.345747	−	0.0926427i
$78$	0.474644	+	1.77140i	0.0537429	+	0.200571i
$79$	−12.3408	+	3.30670i	−1.38844	+	0.372032i	−0.874181	−	0.485600i	$-0.838601\pi$
$79$	−12.3408	+	3.30670i	−1.38844	+	0.372032i	−0.514263	+	0.857633i	$0.671934\pi$
$80$		0			0
$81$	0.0950223	−	0.164583i	0.0105580	−	0.0182871i
$82$			8.87092i			0.979629i
$83$	−2.29888	+	8.57952i	−0.252334	+	0.941725i	0.717220	+	0.696847i	$0.245414\pi$
$83$	−2.29888	+	8.57952i	−0.252334	+	0.941725i	−0.969554	+	0.244878i	$0.921252\pi$
$84$		−	1.22566i		−	0.133731i
$85$		0			0
$86$	−3.10436	−	5.37690i	−0.334751	−	0.579806i
$87$	−0.312164	−	0.180228i	−0.0334675	−	0.0193225i
$88$		−	5.91764i		−	0.630823i
$89$	−16.4223	−	4.40035i	−1.74076	−	0.466436i	−0.758146	−	0.652085i	$-0.773894\pi$
$89$	−16.4223	−	4.40035i	−1.74076	−	0.466436i	−0.982616	+	0.185650i	$0.940561\pi$
$90$		0			0
$91$	−2.40978	−	0.645698i	−0.252613	−	0.0676876i
$92$	1.62479	−	2.81421i	0.169396	−	0.293402i
$93$	−0.752174	+	1.30280i	−0.0779968	+	0.135094i
$94$	−2.77976	−	0.744835i	−0.286711	−	0.0768239i
$95$		0			0
$96$	−3.87685	−	1.03880i	−0.395680	−	0.106022i
$97$			15.4196i			1.56563i	0.622256	+	0.782814i	$0.286216\pi$
$97$			15.4196i			1.56563i	−0.622256	+	0.782814i	$0.713784\pi$
$98$	4.26060	+	2.45986i	0.430385	+	0.248483i
$99$	−1.80944	−	3.13404i	−0.181855	−	0.314983i
$100$		0			0
$101$			0.767212i			0.0763405i	0.999271	+	0.0381702i	$0.0121529\pi$
$101$			0.767212i			0.0763405i	−0.999271	+	0.0381702i	$0.987847\pi$
$102$	−0.410355	+	1.53147i	−0.0406312	+	0.151638i
$103$			4.78539i			0.471518i	0.971812	+	0.235759i	$0.0757576\pi$
$103$			4.78539i			0.471518i	−0.971812	+	0.235759i	$0.924242\pi$
$104$	−2.35013	+	4.07054i	−0.230449	+	0.399150i
$105$		0			0
$106$	3.69061	−	0.988895i	0.358463	−	0.0960500i
$107$	−3.36743	−	12.5674i	−0.325542	−	1.21494i	−0.913766	−	0.406240i	$-0.866840\pi$
$107$	−3.36743	−	12.5674i	−0.325542	−	1.21494i	0.588225	−	0.808698i	$-0.299827\pi$
$108$	−3.53803	+	0.948011i	−0.340447	+	0.0912224i
$109$	−3.42875	+	12.7963i	−0.328414	+	1.22566i	0.582421	+	0.812888i	$0.302106\pi$
$109$	−3.42875	+	12.7963i	−0.328414	+	1.22566i	−0.910835	+	0.412771i	$0.864561\pi$
$110$		0			0
$111$	−5.48861	+	3.35106i	−0.520955	+	0.318069i
$112$	−2.39958	+	2.39958i	−0.226739	+	0.226739i
$113$	−12.6175	+	7.28470i	−1.18695	+	0.685287i	−0.957612	−	0.288060i	$-0.906990\pi$
$113$	−12.6175	+	7.28470i	−1.18695	+	0.685287i	−0.229339	+	0.973347i	$0.573657\pi$
$114$	1.35388	−	2.34499i	0.126803	−	0.219629i
$115$		0			0
$116$	−0.0626210	−	0.233705i	−0.00581421	−	0.0216989i
$117$			2.87440i			0.265738i
$118$	−5.97701	+	1.60153i	−0.550228	+	0.147433i
$119$	−1.52514	−	1.52514i	−0.139810	−	0.139810i
$120$		0			0
$121$	7.30374			0.663976
$122$	8.69681	+	8.69681i	0.787372	+	0.787372i
$123$	2.13682	−	7.97471i	0.192670	−	0.719056i
$124$	−0.975357	+	0.261346i	−0.0875896	+	0.0234696i
$125$		0			0
$126$	−0.904116	+	3.37421i	−0.0805450	+	0.300598i
$127$	−4.94102	−	1.32394i	−0.438445	−	0.117481i	0.0328428	−	0.999461i	$-0.489544\pi$
$127$	−4.94102	−	1.32394i	−0.438445	−	0.117481i	−0.471288	+	0.881980i	$0.656211\pi$
$128$	1.01252	+	1.75373i	0.0894947	+	0.155009i
$129$	1.49555	+	5.58146i	0.131676	+	0.491421i
$130$		0			0
$131$	−0.824339	+	3.07647i	−0.0720228	+	0.268793i	−0.992542	−	0.121905i	$-0.961100\pi$
$131$	−0.824339	+	3.07647i	−0.0720228	+	0.268793i	0.920519	+	0.390698i	$0.127766\pi$
$132$	−0.373310	+	1.39321i	−0.0324924	+	0.121263i
$133$	1.84180	+	3.19009i	0.159704	+	0.276616i
$134$	7.86230	+	7.86230i	0.679199	+	0.679199i
$135$		0			0
$136$	−3.51920	+	2.03181i	−0.301769	+	0.174227i
$137$	−15.2791	+	15.2791i	−1.30538	+	1.30538i	−0.380674	+	0.924709i	$0.624308\pi$
$137$	−15.2791	+	15.2791i	−1.30538	+	1.30538i	−0.924709	+	0.380674i	$0.875692\pi$
$138$	3.88863	−	3.88863i	0.331022	−	0.331022i
$139$	8.97537	+	15.5458i	0.761281	+	1.31858i	0.942191	+	0.335077i	$0.108762\pi$
$139$	8.97537	+	15.5458i	0.761281	+	1.31858i	−0.180910	+	0.983500i	$0.557904\pi$
$140$		0			0
$141$	2.31952	+	1.33917i	0.195339	+	0.112779i
$142$	3.75532			0.315139
$143$	2.54253	+	1.46793i	0.212617	+	0.122755i
$144$	3.38605	+	1.95494i	0.282171	+	0.162912i
$145$		0			0
$146$	−2.77191	−	0.742732i	−0.229405	−	0.0614689i
$147$	−3.23763	−	3.23763i	−0.267036	−	0.267036i
$148$	−4.19559	−	1.01455i	−0.344875	−	0.0833952i
$149$		−	16.8891i		−	1.38361i	−0.722084	−	0.691805i	$-0.756816\pi$
$149$		−	16.8891i		−	1.38361i	0.722084	−	0.691805i	$-0.243184\pi$
$150$		0			0
$151$	−19.2569	−	11.1180i	−1.56711	−	0.904770i	−0.996504	−	0.0835434i	$-0.973376\pi$
$151$	−19.2569	−	11.1180i	−1.56711	−	0.904770i	−0.570603	−	0.821226i	$-0.693290\pi$
$152$	6.70355	−	1.79621i	0.543730	−	0.145692i
$153$	−1.24253	+	2.15213i	−0.100453	+	0.173990i
$154$	2.52291	+	2.52291i	0.203302	+	0.203302i
$155$		0			0
$156$	0.810087	−	0.810087i	0.0648588	−	0.0648588i
$157$	5.03393	+	1.34884i	0.401751	+	0.107649i	0.454036	−	0.890983i	$-0.349984\pi$
$157$	5.03393	+	1.34884i	0.401751	+	0.107649i	−0.0522849	+	0.998632i	$0.516650\pi$
$158$	−10.2622	−	10.2622i	−0.816417	−	0.816417i
$159$	−3.55596			−0.282006
$160$		0			0
$161$	1.93628	+	7.22631i	0.152601	+	0.569513i
$162$	0.215880			0.0169611
$163$	12.7064	−	7.33603i	0.995241	−	0.574603i	0.0884042	−	0.996085i	$-0.471823\pi$
$163$	12.7064	−	7.33603i	0.995241	−	0.574603i	0.906837	+	0.421482i	$0.138490\pi$
$164$	4.79925	−	2.77085i	0.374759	−	0.216367i
$165$		0			0
$166$	−9.74586	+	2.61140i	−0.756426	+	0.202684i
$167$	−18.6925	−	10.7921i	−1.44647	−	0.835120i	−0.448201	−	0.893933i	$-0.647935\pi$
$167$	−18.6925	−	10.7921i	−1.44647	−	0.835120i	−0.998269	+	0.0588131i	$0.981268\pi$
$168$	4.60401	−	2.65813i	0.355207	−	0.205079i
$169$	5.33405	+	9.23885i	0.410312	+	0.710681i
$170$		0			0
$171$	3.00103	−	3.00103i	0.229495	−	0.229495i
$172$	−1.93930	+	3.35897i	−0.147871	+	0.256119i
$173$	0.797367	+	0.213654i	0.0606227	+	0.0162438i	0.289003	−	0.957328i	$-0.406676\pi$
$173$	0.797367	+	0.213654i	0.0606227	+	0.0162438i	−0.228380	+	0.973572i	$0.573343\pi$
$174$		−	0.409458i		−	0.0310409i
$175$		0			0
$176$	3.45847	−	1.99675i	0.260692	−	0.150510i
$177$	5.75894			0.432869
$178$	−4.99855	−	18.6548i	−0.374657	−	1.39824i
$179$	−16.5150	+	16.5150i	−1.23439	+	1.23439i	−0.272124	+	0.962262i	$0.587726\pi$
$179$	−16.5150	+	16.5150i	−1.23439	+	1.23439i	−0.962262	+	0.272124i	$0.912274\pi$
$180$		0			0
$181$	−10.0502	+	17.4074i	−0.747024	+	1.29388i	0.202219	+	0.979340i	$0.435185\pi$
$181$	−10.0502	+	17.4074i	−0.747024	+	1.29388i	−0.949243	+	0.314544i	$0.898148\pi$
$182$	−0.733478	−	2.73738i	−0.0543690	−	0.202908i
$183$	−5.72332	−	9.91307i	−0.423080	−	0.732796i
$184$	14.0949			1.03909
$185$		0			0
$186$	−1.70886			−0.125299
$187$	1.26911	+	2.19816i	0.0928063	+	0.160745i
$188$	0.465302	+	1.73653i	0.0339356	+	0.126649i
$189$	4.21633	−	7.30289i	0.306693	−	0.531207i
$190$		0			0
$191$	−12.5389	+	12.5389i	−0.907285	+	0.907285i	−0.996052	−	0.0887670i	$-0.971707\pi$
$191$	−12.5389	+	12.5389i	−0.907285	+	0.907285i	0.0887670	+	0.996052i	$0.471707\pi$
$192$	−2.31675	−	8.64623i	−0.167197	−	0.623988i
$193$	17.1943			1.23767			0.618837	−	0.785519i	$-0.287604\pi$
$193$	17.1943			1.23767			0.618837	+	0.785519i	$0.287604\pi$
$194$	−15.1692	+	8.75793i	−1.08908	+	0.628783i
$195$		0			0
$196$		−	3.07337i		−	0.219526i
$197$	−8.61235	−	2.30767i	−0.613604	−	0.164415i	−0.0613857	−	0.998114i	$-0.519552\pi$
$197$	−8.61235	−	2.30767i	−0.613604	−	0.164415i	−0.552219	+	0.833699i	$0.686219\pi$
$198$	2.05542	−	3.56009i	0.146072	−	0.253005i
$199$	7.61077	−	7.61077i	0.539513	−	0.539513i	−0.383873	−	0.923386i	$-0.625410\pi$
$199$	7.61077	−	7.61077i	0.539513	−	0.539513i	0.923386	+	0.383873i	$0.125410\pi$
$200$		0			0
$201$	−5.17413	−	8.96186i	−0.364955	−	0.632121i
$202$	−0.754750	+	0.435755i	−0.0531041	+	0.0306596i
$203$	0.482393	+	0.278510i	0.0338574	+	0.0195476i
$204$	0.956714	−	0.256351i	0.0669834	−	0.0179481i
$205$		0			0
$206$	−4.70766	+	2.71797i	−0.327998	+	0.189370i
$207$	7.46478	−	4.30979i	0.518838	−	0.299551i
$208$	−3.17195			−0.219935
$209$	−1.12195	−	4.18716i	−0.0776066	−	0.289632i
$210$		0			0
$211$	1.64325			0.113126			0.0565629	−	0.998399i	$-0.481986\pi$
$211$	1.64325			0.113126			0.0565629	+	0.998399i	$0.481986\pi$
$212$	−1.68777	−	1.68777i	−0.115917	−	0.115917i
$213$	−3.37593	−	0.904577i	−0.231315	−	0.0619806i
$214$	10.4507	−	10.4507i	0.714393	−	0.714393i
$215$		0			0
$216$	−11.2341	−	11.2341i	−0.764383	−	0.764383i
$217$	1.16235	−	2.01325i	0.0789054	−	0.136668i
$218$	−14.5358	+	3.89487i	−0.984491	+	0.263794i
$219$	2.31297	+	1.33539i	0.156296	+	0.0902374i
$220$		0			0
$221$		−	2.01605i		−	0.135614i
$222$	−6.41401	−	3.49615i	−0.430480	−	0.234646i
$223$	13.8186	+	13.8186i	0.925365	+	0.925365i	0.997402	−	0.0720369i	$-0.0229499\pi$
$223$	13.8186	+	13.8186i	0.925365	+	0.925365i	−0.0720369	+	0.997402i	$0.522950\pi$
$224$	5.99098	+	1.60528i	0.400289	+	0.107257i
$225$		0			0
$226$	−14.3327	−	8.27502i	−0.953400	−	0.550446i
$227$	−18.4016	−	10.6242i	−1.22136	−	0.705151i	−0.256150	−	0.966637i	$-0.582454\pi$
$227$	−18.4016	−	10.6242i	−1.22136	−	0.705151i	−0.965207	+	0.261487i	$0.915787\pi$
$228$	−1.69155			−0.112026
$229$	−3.48912	−	2.01445i	−0.230568	−	0.133118i	0.380266	−	0.924877i	$-0.375832\pi$
$229$	−3.48912	−	2.01445i	−0.230568	−	0.133118i	−0.610834	+	0.791759i	$0.709166\pi$
$230$		0			0
$231$	−1.66031	−	2.87575i	−0.109241	−	0.189210i
$232$	0.742069	−	0.742069i	0.0487192	−	0.0487192i
$233$	−2.25220	+	2.25220i	−0.147547	+	0.147547i	−0.777021	−	0.629475i	$-0.783270\pi$
$233$	−2.25220	+	2.25220i	−0.147547	+	0.147547i	0.629475	+	0.777021i	$0.283270\pi$
$234$	−2.82771	+	1.63258i	−0.184853	+	0.106725i
$235$		0			0
$236$	2.73338	+	2.73338i	0.177928	+	0.177928i
$237$	6.75349	+	11.6974i	0.438686	+	0.759827i
$238$	0.634131	−	2.36661i	0.0411046	−	0.153404i
$239$	−5.13865	+	19.1777i	−0.332392	+	1.24050i	0.574277	+	0.818661i	$0.305283\pi$
$239$	−5.13865	+	19.1777i	−0.332392	+	1.24050i	−0.906669	+	0.421843i	$0.861383\pi$
$240$		0			0
$241$	2.89066	+	10.7881i	0.186204	+	0.694922i	0.994370	+	0.105967i	$0.0337939\pi$
$241$	2.89066	+	10.7881i	0.186204	+	0.694922i	−0.808166	+	0.588955i	$0.799539\pi$
$242$	4.14832	+	7.18510i	0.266664	+	0.461876i
$243$	−15.1513	−	4.05977i	−0.971955	−	0.260435i
$244$	1.98859	−	7.42153i	0.127307	−	0.475114i
$245$		0			0
$246$	9.05883	−	2.42731i	0.577570	−	0.154759i
$247$	−0.891138	+	3.32577i	−0.0567017	+	0.211614i
$248$	−3.09699	−	3.09699i	−0.196659	−	0.196659i
$249$	9.39030			0.595086
$250$		0			0
$251$	−6.77562	−	6.77562i	−0.427673	−	0.427673i	0.460162	−	0.887835i	$-0.347791\pi$
$251$	−6.77562	−	6.77562i	−0.427673	−	0.427673i	−0.887835	+	0.460162i	$0.847791\pi$
$252$	2.10788	−	0.564805i	0.132784	−	0.0355794i
$253$		−	8.80391i		−	0.553497i
$254$	−1.50393	−	5.61273i	−0.0943647	−	0.352174i
$255$		0			0
$256$	7.31671	−	12.6729i	0.457294	−	0.792057i
$257$	−0.306484	+	0.176949i	−0.0191180	+	0.0110378i	−0.509529	−	0.860454i	$-0.670180\pi$
$257$	−0.306484	+	0.176949i	−0.0191180	+	0.0110378i	0.490411	+	0.871492i	$0.336847\pi$
$258$	−4.64137	+	4.64137i	−0.288959	+	0.288959i
$259$	8.48166	−	5.17846i	0.527025	−	0.321774i
$260$		0			0
$261$	0.166104	−	0.619909i	0.0102816	−	0.0383714i
$262$	−3.49470	+	0.936403i	−0.215904	+	0.0578512i
$263$	−5.22227	−	19.4898i	−0.322019	−	1.20179i	−0.917275	−	0.398255i	$-0.869616\pi$
$263$	−5.22227	−	19.4898i	−0.322019	−	1.20179i	0.595256	−	0.803536i	$-0.297051\pi$
$264$	−6.04300	+	1.61922i	−0.371921	+	0.0996559i
$265$		0			0
$266$	−2.09218	+	3.62377i	−0.128280	+	0.222187i
$267$			17.9742i			1.10001i
$268$	1.79777	−	6.70939i	0.109817	−	0.409841i
$269$			6.49930i			0.396269i	0.980175	+	0.198135i	$0.0634883\pi$
$269$			6.49930i			0.396269i	−0.980175	+	0.198135i	$0.936512\pi$
$270$		0			0
$271$	−2.12937	−	3.68817i	−0.129350	−	0.224040i	0.794075	−	0.607820i	$-0.207956\pi$
$271$	−2.12937	−	3.68817i	−0.129350	−	0.224040i	−0.923425	+	0.383779i	$0.874622\pi$
$272$	−2.37492	−	1.37116i	−0.144001	−	0.0831388i
$273$			2.63751i			0.159629i
$274$	−23.7091	−	6.35282i	−1.43232	−	0.383788i
$275$		0			0
$276$	−3.31841	−	0.889165i	−0.199745	−	0.0535214i
$277$	−0.285590	+	0.494657i	−0.0171595	+	0.0297211i	−0.874478	−	0.485066i	$-0.838796\pi$
$277$	−0.285590	+	0.494657i	−0.0171595	+	0.0297211i	0.857318	+	0.514787i	$0.172129\pi$
$278$	−10.1955	+	17.6592i	−0.611487	+	1.05913i
$279$	−2.58716	−	0.693228i	−0.154889	−	0.0415025i
$280$		0			0
$281$	30.2609	+	8.10837i	1.80521	+	0.483705i	0.994772	−	0.102118i	$-0.0325620\pi$
$281$	30.2609	+	8.10837i	1.80521	+	0.483705i	0.810439	+	0.585823i	$0.199229\pi$
$282$			3.04245i			0.181176i
$283$	−0.533664	−	0.308111i	−0.0317230	−	0.0183153i	0.484055	−	0.875038i	$-0.339164\pi$
$283$	−0.533664	−	0.308111i	−0.0317230	−	0.0183153i	−0.515778	+	0.856722i	$0.672497\pi$
$284$	−1.17298	−	2.03166i	−0.0696036	−	0.120557i
$285$		0			0
$286$			3.33498i			0.197202i
$287$	−3.30207	+	12.3235i	−0.194915	+	0.727433i
$288$		−	7.14608i		−	0.421087i
$289$	−7.62851	+	13.2130i	−0.448736	+	0.777233i
$290$		0			0
$291$	15.7463	−	4.21920i	0.923063	−	0.247334i
$292$	0.463988	+	1.73163i	0.0271528	+	0.101336i
$293$	9.54988	−	2.55888i	0.557910	−	0.149492i	0.0311641	−	0.999514i	$-0.490079\pi$
$293$	9.54988	−	2.55888i	0.557910	−	0.149492i	0.526746	+	0.850023i	$0.323412\pi$
$294$	1.34616	−	5.02393i	0.0785096	−	0.293002i
$295$		0			0
$296$	−5.28810	−	17.9604i	−0.307364	−	1.04393i
$297$	−7.01701	+	7.01701i	−0.407168	+	0.407168i
$298$	16.6148	−	9.59255i	0.962469	−	0.555682i
$299$	−3.49638	+	6.05591i	−0.202201	+	0.350222i
$300$		0			0
$301$	−2.31110	−	8.62515i	−0.133210	−	0.497146i
$302$		−	25.2589i		−	1.45348i
$303$	0.783464	−	0.209929i	0.0450089	−	0.0120601i
$304$	3.31170	+	3.31170i	0.189939	+	0.189939i
$305$		0			0
$306$	−2.82290			−0.161375
$307$	12.7533	+	12.7533i	0.727869	+	0.727869i	0.970195	−	0.242326i	$-0.0779104\pi$
$307$	12.7533	+	12.7533i	0.727869	+	0.727869i	−0.242326	+	0.970195i	$0.577910\pi$
$308$	0.576883	−	2.15296i	0.0328710	−	0.122676i
$309$	4.88676	−	1.30940i	0.277998	−	0.0744893i
$310$		0			0
$311$	6.30945	−	23.5472i	0.357776	−	1.33524i	−0.519179	−	0.854665i	$-0.673762\pi$
$311$	6.30945	−	23.5472i	0.357776	−	1.33524i	0.876955	−	0.480572i	$-0.159571\pi$
$312$	4.79983	+	1.28611i	0.271737	+	0.0728116i
$313$	−0.462994	−	0.801929i	−0.0261700	−	0.0453277i	0.852644	−	0.522493i	$-0.174998\pi$
$313$	−0.462994	−	0.801929i	−0.0261700	−	0.0453277i	−0.878814	+	0.477165i	$0.841664\pi$
$314$	1.53220	+	5.71826i	0.0864673	+	0.322700i
$315$		0			0
$316$	−2.34653	+	8.75737i	−0.132003	+	0.492640i
$317$	6.85107	−	25.5685i	0.384794	−	1.43607i	−0.453696	−	0.891156i	$-0.649895\pi$
$317$	6.85107	−	25.5685i	0.384794	−	1.43607i	0.838491	−	0.544916i	$-0.183438\pi$
$318$	−2.01969	−	3.49820i	−0.113258	−	0.196169i
$319$	−0.463509	−	0.463509i	−0.0259515	−	0.0259515i
$320$		0			0
$321$	−11.9122	+	6.87752i	−0.664875	+	0.383866i
$322$	−6.00918	+	6.00918i	−0.334878	+	0.334878i
$323$	−2.10487	+	2.10487i	−0.117118	+	0.117118i
$324$	−0.0674306	−	0.116793i	−0.00374615	−	0.00648852i
$325$		0			0
$326$	14.4338	+	8.33333i	0.799412	+	0.461540i
$327$	14.0055			0.774507
$328$	20.8166	+	12.0184i	1.14940	+	0.663608i
$329$	−3.58440	−	2.06945i	−0.197614	−	0.114093i
$330$		0			0
$331$	−9.40727	−	2.52067i	−0.517070	−	0.138549i	−0.00915915	−	0.999958i	$-0.502915\pi$
$331$	−9.40727	−	2.52067i	−0.517070	−	0.138549i	−0.507911	+	0.861410i	$0.669582\pi$
$332$	4.45693	+	4.45693i	0.244606	+	0.244606i
$333$	−8.29237	−	7.89503i	−0.454419	−	0.432645i
$334$		−	24.5185i		−	1.34159i
$335$		0			0
$336$	3.10700	+	1.79382i	0.169501	+	0.0978612i
$337$	19.1912	−	5.14226i	1.04541	−	0.280117i	0.305057	−	0.952334i	$-0.401325\pi$
$337$	19.1912	−	5.14226i	1.04541	−	0.280117i	0.740354	+	0.672217i	$0.234658\pi$
$338$	−6.05919	+	10.4948i	−0.329576	+	0.570843i
$339$	10.8915	+	10.8915i	0.591544	+	0.591544i
$340$		0			0
$341$	−1.93444	+	1.93444i	−0.104756	+	0.104756i
$342$	4.65679	+	1.24778i	0.251810	+	0.0674724i
$343$	13.0897	+	13.0897i	0.706778	+	0.706778i
$344$	−16.8233			−0.907052
$345$		0			0
$346$	0.242699	+	0.905765i	0.0130476	+	0.0486942i
$347$	10.3295			0.554517			0.277258	−	0.960795i	$-0.410574\pi$
$347$	10.3295			0.554517			0.277258	+	0.960795i	$0.410574\pi$
$348$	−0.221521	+	0.127895i	−0.0118748	+	0.00685589i
$349$	13.7141	−	7.91783i	0.734098	−	0.423832i	−0.0858212	−	0.996311i	$-0.527351\pi$
$349$	13.7141	−	7.91783i	0.734098	−	0.423832i	0.819920	+	0.572479i	$0.194018\pi$
$350$		0			0
$351$	7.61350	−	2.04003i	0.406378	−	0.108889i
$352$	−6.32103	−	3.64945i	−0.336912	−	0.194516i
$353$	−7.53835	+	4.35227i	−0.401226	+	0.231648i	−0.687013	−	0.726645i	$-0.741078\pi$
$353$	−7.53835	+	4.35227i	−0.401226	+	0.231648i	0.285787	+	0.958293i	$0.407745\pi$
$354$	3.27092	+	5.66540i	0.173847	+	0.301113i
$355$		0			0
$356$	−8.53114	+	8.53114i	−0.452150	+	0.452150i
$357$	−1.14013	+	1.97477i	−0.0603422	+	0.104516i
$358$	−25.6268	−	6.86667i	−1.35442	−	0.362915i
$359$		−	9.85969i		−	0.520375i	−0.965558	−	0.260187i	$-0.916216\pi$
$359$		−	9.85969i		−	0.520375i	0.965558	−	0.260187i	$-0.0837843\pi$
$360$		0			0
$361$	−12.0518	+	6.95810i	−0.634305	+	0.366216i
$362$	−22.8329			−1.20007
$363$	−1.99849	−	7.45845i	−0.104893	−	0.391467i
$364$	−1.25184	+	1.25184i	−0.0656144	+	0.0656144i
$365$		0			0
$366$	6.50137	−	11.2607i	0.339832	−	0.588606i
$367$	−5.24797	−	19.5857i	−0.273942	−	1.02236i	−0.956547	−	0.291577i	$-0.905820\pi$
$367$	−5.24797	−	19.5857i	−0.273942	−	1.02236i	0.682606	−	0.730787i	$-0.260847\pi$
$368$	4.75593	+	8.23752i	0.247920	+	0.429410i
$369$	14.6995			0.765227
$370$		0			0
$371$	5.49510			0.285291
$372$	0.533765	+	0.924507i	0.0276744	+	0.0479335i
$373$	0.616084	+	2.29926i	0.0318996	+	0.119051i	0.980040	−	0.198802i	$-0.0637049\pi$
$373$	0.616084	+	2.29926i	0.0318996	+	0.119051i	−0.948140	+	0.317853i	$0.897038\pi$
$374$	−1.44163	+	2.49698i	−0.0745452	+	0.129116i
$375$		0			0
$376$	−5.51390	+	5.51390i	−0.284358	+	0.284358i
$377$	0.134754	+	0.502910i	0.00694021	+	0.0259012i
$378$	9.57903			0.492692
$379$	−14.3987	+	8.31312i	−0.739614	+	0.427016i	−0.821929	−	0.569590i	$-0.807102\pi$
$379$	−14.3987	+	8.31312i	−0.739614	+	0.427016i	0.0823151	+	0.996606i	$0.473769\pi$
$380$		0			0
$381$			5.40795i			0.277058i
$382$	−19.4570	−	5.21350i	−0.995508	−	0.266746i
$383$	−4.50352	+	7.80032i	−0.230119	+	0.398578i	−0.957843	−	0.287292i	$-0.907245\pi$
$383$	−4.50352	+	7.80032i	−0.230119	+	0.398578i	0.727724	+	0.685870i	$0.240578\pi$
$384$	1.51383	−	1.51383i	0.0772523	−	0.0772523i
$385$		0			0
$386$	9.76590	+	16.9150i	0.497071	+	0.860953i
$387$	−8.90978	+	5.14406i	−0.452910	+	0.261487i
$388$	9.47625	+	5.47112i	0.481084	+	0.277754i
$389$	11.4603	−	3.07078i	0.581061	−	0.155695i	0.0436964	−	0.999045i	$-0.486087\pi$
$389$	11.4603	−	3.07078i	0.581061	−	0.155695i	0.537365	+	0.843350i	$0.319420\pi$
$390$		0			0
$391$	−5.23566	+	3.02281i	−0.264779	+	0.152870i
$392$	11.5446	−	6.66530i	0.583093	−	0.336649i
$393$	3.36720			0.169853
$394$	−2.62139	−	9.78315i	−0.132064	−	0.492868i
$395$		0			0
$396$	−2.56806			−0.129050
$397$	−1.62569	−	1.62569i	−0.0815913	−	0.0815913i	0.665133	−	0.746725i	$-0.268375\pi$
$397$	−1.62569	−	1.62569i	−0.0815913	−	0.0815913i	−0.746725	+	0.665133i	$0.768375\pi$
$398$	11.8099	+	3.16444i	0.591974	+	0.158619i
$399$	2.75371	−	2.75371i	0.137858	−	0.137858i
$400$		0			0
$401$	16.9699	+	16.9699i	0.847436	+	0.847436i	0.989813	−	0.142377i	$-0.0454744\pi$
$401$	16.9699	+	16.9699i	0.847436	+	0.847436i	−0.142377	+	0.989813i	$0.545474\pi$
$402$	5.87753	−	10.1802i	0.293144	−	0.507741i
$403$	2.09888	−	0.562392i	0.104552	−	0.0280147i
$404$	0.471496	+	0.272218i	0.0234578	+	0.0135434i
$405$		0			0
$406$			0.632744i			0.0314026i
$407$	−11.2184	+	3.30304i	−0.556074	+	0.163726i
$408$	3.03780	+	3.03780i	0.150393	+	0.150393i
$409$	24.9023	+	6.67256i	1.23134	+	0.329937i	0.815102	−	0.579318i	$-0.196681\pi$
$409$	24.9023	+	6.67256i	1.23134	+	0.329937i	0.416240	+	0.909255i	$0.363348\pi$
$410$		0			0
$411$	19.7835	+	11.4220i	0.975850	+	0.563407i
$412$	2.94089	+	1.69793i	0.144887	+	0.0836508i
$413$	−8.89941			−0.437911
$414$	8.47957	+	4.89568i	0.416748	+	0.240610i
$415$		0			0
$416$	2.89868	+	5.02066i	0.142120	+	0.246158i
$417$	13.4192	−	13.4192i	0.657142	−	0.657142i
$418$	3.48191	−	3.48191i	0.170306	−	0.170306i
$419$	−29.0354	+	16.7636i	−1.41847	+	0.818955i	−0.996165	−	0.0874987i	$-0.972113\pi$
$419$	−29.0354	+	16.7636i	−1.41847	+	0.818955i	−0.422306	+	0.906453i	$0.638779\pi$
$420$		0			0
$421$	−0.954366	−	0.954366i	−0.0465130	−	0.0465130i	0.683468	−	0.729981i	$-0.260471\pi$
$421$	−0.954366	−	0.954366i	−0.0465130	−	0.0465130i	−0.729981	+	0.683468i	$0.760471\pi$
$422$	0.933319	+	1.61656i	0.0454333	+	0.0786927i
$423$	−1.23423	+	4.60620i	−0.0600102	+	0.223961i
$424$	2.67954	−	10.0002i	0.130130	−	0.485651i
$425$		0			0
$426$	−1.02755	−	3.83487i	−0.0497849	−	0.185800i
$427$	8.84436	+	15.3189i	0.428009	+	0.741333i
$428$	−8.91821	−	2.38963i	−0.431078	−	0.115507i
$429$	0.803327	−	2.99806i	0.0387850	−	0.144748i
$430$		0			0
$431$	−12.1677	+	3.26032i	−0.586097	+	0.157044i	−0.539669	−	0.841877i	$-0.681451\pi$
$431$	−12.1677	+	3.26032i	−0.586097	+	0.157044i	−0.0464282	+	0.998922i	$0.514784\pi$
$432$	2.77494	−	10.3562i	0.133509	−	0.498263i
$433$	13.7322	+	13.7322i	0.659928	+	0.659928i	0.955363	−	0.295435i	$-0.0954646\pi$
$433$	13.7322	+	13.7322i	0.659928	+	0.659928i	−0.295435	+	0.955363i	$0.595465\pi$
$434$	2.64073			0.126759
$435$		0			0
$436$	6.64746	+	6.64746i	0.318356	+	0.318356i
$437$	9.97314	−	2.67230i	0.477080	−	0.127833i
$438$			3.03386i			0.144963i
$439$	−8.00818	−	29.8869i	−0.382210	−	1.42643i	−0.842519	−	0.538667i	$-0.818928\pi$
$439$	−8.00818	−	29.8869i	−0.382210	−	1.42643i	0.460309	−	0.887759i	$-0.347739\pi$
$440$		0			0
$441$	4.07610	−	7.06001i	0.194100	−	0.336191i
$442$	1.98330	−	1.14506i	0.0943361	−	0.0544650i
$443$	13.3025	−	13.3025i	0.632023	−	0.632023i	−0.316552	−	0.948575i	$-0.602525\pi$
$443$	13.3025	−	13.3025i	0.632023	−	0.632023i	0.948575	+	0.316552i	$0.102525\pi$
$444$	0.111980	+	4.56207i	0.00531432	+	0.216506i
$445$		0			0
$446$	−5.74558	+	21.4428i	−0.272061	+	1.01535i
$447$	−17.2469	+	4.62129i	−0.815750	+	0.218580i
$448$	3.58012	+	13.3612i	0.169145	+	0.631257i
$449$	−28.3423	+	7.59430i	−1.33756	+	0.358397i	−0.855527	−	0.517758i	$-0.826767\pi$
$449$	−28.3423	+	7.59430i	−1.33756	+	0.358397i	−0.482029	+	0.876155i	$0.660100\pi$
$450$		0			0
$451$	7.50694	−	13.0024i	0.353488	−	0.612259i
$452$			10.3389i			0.486300i
$453$	−6.08433	+	22.7070i	−0.285867	+	1.06687i
$454$		−	24.1369i		−	1.13280i
$455$		0			0
$456$	−3.66852	−	6.35407i	−0.171794	−	0.297556i
$457$	5.55747	+	3.20861i	0.259968	+	0.150092i	0.624320	−	0.781169i	$-0.285376\pi$
$457$	5.55747	+	3.20861i	0.259968	+	0.150092i	−0.364352	+	0.931261i	$0.618710\pi$
$458$		−	4.57660i		−	0.213850i
$459$	6.58228	+	1.76372i	0.307234	+	0.0823232i
$460$		0			0
$461$	25.3037	+	6.78010i	1.17851	+	0.315781i	0.794335	−	0.607479i	$-0.207819\pi$
$461$	25.3037	+	6.78010i	1.17851	+	0.315781i	0.384175	+	0.923260i	$0.374486\pi$
$462$	1.88602	−	3.26669i	0.0877458	−	0.151980i
$463$	−19.1066	+	33.0936i	−0.887960	+	1.53799i	−0.0456763	+	0.998956i	$0.514544\pi$
$463$	−19.1066	+	33.0936i	−0.887960	+	1.53799i	−0.842283	+	0.539035i	$0.818789\pi$
$464$	0.684081	+	0.183299i	0.0317576	+	0.00850944i
$465$		0			0
$466$	−3.49481	−	0.936431i	−0.161894	−	0.0433793i
$467$			13.5181i			0.625544i	0.949828	+	0.312772i	$0.101258\pi$
$467$			13.5181i			0.625544i	−0.949828	+	0.312772i	$0.898742\pi$
$468$	1.76648	+	1.01988i	0.0816556	+	0.0471439i
$469$	7.99569	+	13.8489i	0.369207	+	0.639485i
$470$		0			0
$471$		−	5.50964i		−	0.253871i
$472$	−4.33956	+	16.1955i	−0.199745	+	0.745457i
$473$			10.5081i			0.483165i
$474$	−7.67159	+	13.2876i	−0.352368	+	0.610319i
$475$		0			0
$476$	−1.47843	+	0.396144i	−0.0677637	+	0.0181572i
$477$	−1.63865	−	6.11551i	−0.0750284	−	0.280010i
$478$	−21.7848	+	5.83723i	−0.996415	+	0.266989i
$479$	−0.466920	+	1.74257i	−0.0213341	+	0.0796200i	−0.975772	−	0.218789i	$-0.929789\pi$
$479$	−0.466920	+	1.74257i	−0.0213341	+	0.0796200i	0.954438	+	0.298409i	$0.0964560\pi$
$480$		0			0
$481$	9.02850	+	2.18321i	0.411664	+	0.0995457i
$482$	−8.97105	+	8.97105i	−0.408620	+	0.408620i
$483$	6.84957	−	3.95460i	0.311666	−	0.179941i
$484$	2.59147	−	4.48856i	0.117794	−	0.204026i
$485$		0			0
$486$	−4.61168	−	17.2110i	−0.209190	−	0.780708i
$487$			4.70678i			0.213285i	0.994297	+	0.106642i	$0.0340100\pi$
$487$			4.70678i			0.213285i	−0.994297	+	0.106642i	$0.965990\pi$
$488$	32.1906	−	8.62544i	1.45720	−	0.390455i
$489$	−10.9682	−	10.9682i	−0.496000	−	0.496000i
$490$		0			0
$491$	22.3671			1.00941			0.504707	−	0.863291i	$-0.331601\pi$
$491$	22.3671			1.00941			0.504707	+	0.863291i	$0.331601\pi$
$492$	−4.14274	−	4.14274i	−0.186769	−	0.186769i
$493$	−0.116502	+	0.434793i	−0.00524700	+	0.0195821i
$494$	−3.77789	+	1.01228i	−0.169975	+	0.0455448i
$495$		0			0
$496$	0.764990	−	2.85498i	0.0343491	−	0.128192i
$497$	5.21689	+	1.39786i	0.234009	+	0.0627026i
$498$	5.33343	+	9.23777i	0.238997	+	0.413954i
$499$	−4.04934	−	15.1123i	−0.181273	−	0.676521i	−0.995398	−	0.0958307i	$-0.969449\pi$
$499$	−4.04934	−	15.1123i	−0.181273	−	0.676521i	0.814124	−	0.580691i	$-0.197217\pi$
$500$		0			0
$501$	−5.90600	+	22.0415i	−0.263860	+	0.984741i
$502$	2.81720	−	10.5139i	0.125738	−	0.469260i
$503$	−5.10938	−	8.84970i	−0.227816	−	0.394589i	0.729345	−	0.684146i	$-0.239825\pi$
$503$	−5.10938	−	8.84970i	−0.227816	−	0.394589i	−0.957161	+	0.289558i	$0.906492\pi$
$504$	6.69303	+	6.69303i	0.298131	+	0.298131i
$505$		0			0
$506$	8.66091	−	5.00038i	0.385024	−	0.222294i
$507$	7.97503	−	7.97503i	0.354183	−	0.354183i
$508$	−2.56679	+	2.56679i	−0.113883	+	0.113883i
$509$	−3.43610	−	5.95149i	−0.152302	−	0.263795i	0.779771	−	0.626065i	$-0.215335\pi$
$509$	−3.43610	−	5.95149i	−0.152302	−	0.263795i	−0.932073	+	0.362269i	$0.882002\pi$
$510$		0			0
$511$	−3.57427	−	2.06361i	−0.158117	−	0.0912886i
$512$	20.6728			0.913618
$513$	−10.0788	−	5.81902i	−0.444991	−	0.256916i
$514$	−0.348149	−	0.201004i	−0.0153562	−	0.00886591i
$515$		0			0
$516$	3.96077	+	1.06129i	0.174363	+	0.0467205i
$517$	3.44408	+	3.44408i	0.151471	+	0.151471i
$518$	9.91170	+	5.40267i	0.435495	+	0.237379i
$519$		−	0.872719i		−	0.0383081i
$520$		0			0
$521$	−19.6337	−	11.3355i	−0.860166	−	0.496617i	0.00390182	−	0.999992i	$-0.498758\pi$
$521$	−19.6337	−	11.3355i	−0.860166	−	0.496617i	−0.864068	+	0.503375i	$0.832091\pi$
$522$	0.704182	−	0.188685i	0.0308212	−	0.00825852i
$523$	4.24004	−	7.34396i	0.185404	−	0.321129i	−0.758309	−	0.651896i	$-0.773974\pi$
$523$	4.24004	−	7.34396i	0.185404	−	0.321129i	0.943713	+	0.330767i	$0.107307\pi$
$524$	1.59818	+	1.59818i	0.0698169	+	0.0698169i
$525$		0			0
$526$	16.2071	−	16.2071i	0.706663	−	0.706663i
$527$	1.81459	+	0.486218i	0.0790448	+	0.0211800i
$528$	−2.98537	−	2.98537i	−0.129921	−	0.129921i
$529$	−2.03048			−0.0882817
$530$		0			0
$531$	2.65382	+	9.90418i	0.115166	+	0.429805i
$532$	2.61399			0.113331
$533$	−10.3275	+	5.96260i	−0.447335	+	0.258269i
$534$	−17.6823	+	10.2089i	−0.765187	+	0.441781i
$535$		0			0
$536$	29.1017	−	7.79777i	1.25700	−	0.336813i
$537$	21.3837	+	12.3459i	0.922776	+	0.532765i
$538$	−6.39373	+	3.69142i	−0.275653	+	0.159148i
$539$	−4.16327	−	7.21099i	−0.179325	−	0.310599i
$540$		0			0
$541$	−9.87420	+	9.87420i	−0.424525	+	0.424525i	−0.886758	−	0.462233i	$-0.847048\pi$
$541$	−9.87420	+	9.87420i	−0.424525	+	0.424525i	0.462233	+	0.886758i	$0.347048\pi$
$542$	2.41884	−	4.18956i	0.103898	−	0.179957i
$543$	20.5262	+	5.49997i	0.880862	+	0.236026i
$544$			5.01213i			0.214893i
$545$		0			0
$546$	−2.59466	+	1.49803i	−0.111041	+	0.0641098i
$547$	−16.2777			−0.695983			−0.347992	−	0.937498i	$-0.613136\pi$
$547$	−16.2777			−0.695983			−0.347992	+	0.937498i	$0.613136\pi$
$548$	3.96864	+	14.8112i	0.169532	+	0.632701i
$549$	14.4110	−	14.4110i	0.615047	−	0.615047i
$550$		0			0
$551$	0.384376	−	0.665758i	0.0163750	−	0.0283623i
$552$	−3.85672	−	14.3935i	−0.164153	−	0.612626i
$553$	−10.4363	−	18.0762i	−0.443797	−	0.768679i
$554$	−0.648830			−0.0275661
$555$		0			0
$556$	12.7384			0.540227
$557$	6.36833	+	11.0303i	0.269835	+	0.467368i	0.968819	−	0.247769i	$-0.0796975\pi$
$557$	6.36833	+	11.0303i	0.269835	+	0.467368i	−0.698984	+	0.715137i	$0.746364\pi$
$558$	−0.787469	−	2.93887i	−0.0333362	−	0.124412i
$559$	4.17320	−	7.22819i	0.176508	−	0.305720i
$560$		0			0
$561$	1.89746	−	1.89746i	0.0801109	−	0.0801109i
$562$	9.21066	+	34.3747i	0.388528	+	1.45001i
$563$	9.88042			0.416410			0.208205	−	0.978085i	$-0.433238\pi$
$563$	9.88042			0.416410			0.208205	+	0.978085i	$0.433238\pi$
$564$	1.64600	−	0.950317i	0.0693090	−	0.0400156i
$565$		0			0
$566$		−	0.699994i		−	0.0294229i
$567$	0.299901	+	0.0803582i	0.0125947	+	0.00337473i
$568$	5.08776	−	8.81225i	0.213478	−	0.369754i
$569$	28.2430	−	28.2430i	1.18401	−	1.18401i	0.205312	−	0.978697i	$-0.434179\pi$
$569$	28.2430	−	28.2430i	1.18401	−	1.18401i	0.978697	−	0.205312i	$-0.0658210\pi$
$570$		0			0
$571$	−18.9395	−	32.8041i	−0.792592	−	1.37281i	−0.924357	−	0.381529i	$-0.875398\pi$
$571$	−18.9395	−	32.8041i	−0.792592	−	1.37281i	0.131765	−	0.991281i	$-0.457936\pi$
$572$	1.80426	−	1.04169i	0.0754398	−	0.0435552i
$573$	16.2355	+	9.37358i	0.678249	+	0.391587i
$574$	−13.9988	+	3.75097i	−0.584299	+	0.156562i
$575$		0			0
$576$	13.8021	−	7.96865i	0.575088	−	0.332027i
$577$	23.5713	−	13.6089i	0.981288	−	0.566547i	0.0786291	−	0.996904i	$-0.474946\pi$
$577$	23.5713	−	13.6089i	0.981288	−	0.566547i	0.902659	+	0.430357i	$0.141612\pi$
$578$	−17.3311			−0.720880
$579$	−4.70480	−	17.5586i	−0.195525	−	0.729709i
$580$		0			0
$581$	−14.5110			−0.602019
$582$	13.0941	+	13.0941i	0.542769	+	0.542769i
$583$	−6.24629	−	1.67369i	−0.258695	−	0.0693171i
$584$	−5.49833	+	5.49833i	−0.227522	+	0.227522i
$585$		0			0
$586$	7.94139	+	7.94139i	0.328056	+	0.328056i
$587$	−6.06864	+	10.5112i	−0.250480	+	0.433843i	−0.963658	−	0.267139i	$-0.913922\pi$
$587$	−6.06864	+	10.5112i	−0.250480	+	0.433843i	0.713178	+	0.700983i	$0.247255\pi$
$588$	−3.13847	+	0.840951i	−0.129428	+	0.0346802i
$589$	−2.77851	−	1.60418i	−0.114487	−	0.0660989i
$590$		0			0
$591$			9.42622i			0.387743i
$592$	8.71231	−	9.15077i	0.358074	−	0.376095i
$593$	22.9652	+	22.9652i	0.943070	+	0.943070i	0.998465	−	0.0553950i	$-0.0176418\pi$
$593$	22.9652	+	22.9652i	0.943070	+	0.943070i	−0.0553950	+	0.998465i	$0.517642\pi$
$594$	−10.8885	−	2.91757i	−0.446761	−	0.119709i
$595$		0			0
$596$	−10.3793	−	5.99251i	−0.425154	−	0.245463i
$597$	−9.85449	−	5.68949i	−0.403317	−	0.232855i
$598$	−7.94340			−0.324830
$599$	−2.59862	−	1.50032i	−0.106177	−	0.0613013i	0.445971	−	0.895047i	$-0.352858\pi$
$599$	−2.59862	−	1.50032i	−0.106177	−	0.0613013i	−0.552148	+	0.833746i	$0.686192\pi$
$600$		0			0
$601$	7.76062	+	13.4418i	0.316562	+	0.548302i	0.979768	−	0.200135i	$-0.0641380\pi$
$601$	7.76062	+	13.4418i	0.316562	+	0.548302i	−0.663206	+	0.748437i	$0.730805\pi$
$602$	7.17241	−	7.17241i	0.292326	−	0.292326i
$603$	13.0282	−	13.0282i	0.530549	−	0.530549i
$604$	−13.6653	+	7.88966i	−0.556033	+	0.321026i
$605$		0			0
$606$	0.651505	+	0.651505i	0.0264656	+	0.0264656i
$607$	−18.5157	−	32.0701i	−0.751529	−	1.30169i	−0.947081	−	0.320994i	$-0.895983\pi$
$607$	−18.5157	−	32.0701i	−0.751529	−	1.30169i	0.195552	−	0.980693i	$-0.437350\pi$
$608$	2.21547	−	8.26824i	0.0898492	−	0.335322i
$609$	0.152415	−	0.568820i	0.00617616	−	0.0230497i
$610$		0			0
$611$	−1.00129	−	3.73685i	−0.0405077	−	0.151177i
$612$	0.881739	+	1.52722i	0.0356422	+	0.0617341i
$613$	−16.8361	−	4.51123i	−0.680005	−	0.182207i	−0.0977478	−	0.995211i	$-0.531164\pi$
$613$	−16.8361	−	4.51123i	−0.680005	−	0.182207i	−0.582258	+	0.813004i	$0.697831\pi$
$614$	−5.30262	+	19.7897i	−0.213996	+	0.798645i
$615$		0			0
$616$	9.33837	−	2.50221i	0.376254	−	0.100817i
$617$	6.18875	−	23.0967i	0.249150	−	0.929839i	−0.722103	−	0.691786i	$-0.756824\pi$
$617$	6.18875	−	23.0967i	0.249150	−	0.929839i	0.971252	−	0.238053i	$-0.0765092\pi$
$618$	4.06368	+	4.06368i	0.163465	+	0.163465i
$619$	−6.37727			−0.256324			−0.128162	−	0.991753i	$-0.540908\pi$
$619$	−6.37727			−0.256324			−0.128162	+	0.991753i	$0.540908\pi$
$620$		0			0
$621$	−16.7134	−	16.7134i	−0.670686	−	0.670686i
$622$	26.7483	−	7.16718i	1.07251	−	0.287378i
$623$		−	27.7760i		−	1.11282i
$624$	0.867925	+	3.23914i	0.0347448	+	0.129669i
$625$		0			0
$626$	0.525936	−	0.910947i	0.0210206	−	0.0364088i
$627$	−3.96886	+	2.29142i	−0.158501	+	0.0915107i
$628$	2.61505	−	2.61505i	0.104352	−	0.104352i
$629$	5.81612	+	5.53743i	0.231904	+	0.220792i
$630$		0			0
$631$	−5.89535	+	22.0017i	−0.234690	+	0.875876i	0.743598	+	0.668627i	$0.233118\pi$
$631$	−5.89535	+	22.0017i	−0.234690	+	0.875876i	−0.978288	+	0.207249i	$0.933549\pi$
$632$	−37.9847	+	10.1780i	−1.51095	+	0.404858i
$633$	−0.449634	−	1.67806i	−0.0178714	−	0.0666968i
$634$	29.0445	−	7.78244i	1.15350	−	0.309080i
$635$		0			0
$636$	−1.26171	+	2.18534i	−0.0500299	+	0.0866544i
$637$			6.61359i			0.262040i
$638$	0.192720	−	0.719241i	0.00762986	−	0.0284750i
$639$		−	6.22273i		−	0.246168i
$640$		0			0
$641$	−11.7520	−	20.3550i	−0.464175	−	0.803976i	0.534988	−	0.844859i	$-0.320316\pi$
$641$	−11.7520	−	20.3550i	−0.464175	−	0.803976i	−0.999164	+	0.0408839i	$0.986983\pi$
$642$	−13.5316	−	7.81249i	−0.534051	−	0.308334i
$643$		−	24.3699i		−	0.961055i	−0.876980	−	0.480527i	$-0.840445\pi$
$643$		−	24.3699i		−	0.961055i	0.876980	−	0.480527i	$-0.159555\pi$
$644$	5.12800	+	1.37404i	0.202072	+	0.0541449i
$645$		0			0
$646$	−3.26619	−	0.875173i	−0.128507	−	0.0344332i
$647$	−20.7661	+	35.9680i	−0.816400	+	1.41405i	0.0919177	+	0.995767i	$0.470700\pi$
$647$	−20.7661	+	35.9680i	−0.816400	+	1.41405i	−0.908318	+	0.418280i	$0.862633\pi$
$648$	0.292478	−	0.506586i	0.0114896	−	0.0199006i
$649$	10.1160	+	2.71057i	0.397087	+	0.106399i
$650$		0			0
$651$	−2.37394	−	0.636096i	−0.0930422	−	0.0249306i
$652$		−	10.4117i		−	0.407755i
$653$	−0.642043	−	0.370684i	−0.0251251	−	0.0145060i	0.487385	−	0.873187i	$-0.337951\pi$
$653$	−0.642043	−	0.370684i	−0.0251251	−	0.0145060i	−0.512510	+	0.858681i	$0.671284\pi$
$654$	7.95475	+	13.7780i	0.311055	+	0.538763i
$655$		0			0
$656$			16.2212i			0.633331i
$657$	−1.23074	+	4.59319i	−0.0480158	+	0.179197i
$658$		−	4.70157i		−	0.183286i
$659$	15.9185	−	27.5717i	0.620098	−	1.07404i	−0.369369	−	0.929283i	$-0.620426\pi$
$659$	15.9185	−	27.5717i	0.620098	−	1.07404i	0.989467	−	0.144759i	$-0.0462406\pi$
$660$		0			0
$661$	46.6955	−	12.5120i	1.81624	−	0.486661i	0.819932	−	0.572461i	$-0.194011\pi$
$661$	46.6955	−	12.5120i	1.81624	−	0.486661i	0.996312	+	0.0858000i	$0.0273446\pi$
$662$	−2.86334	−	10.6861i	−0.111287	−	0.415329i
$663$	−2.05876	+	0.551642i	−0.0799555	+	0.0214240i
$664$	−7.07592	+	26.4077i	−0.274599	+	1.02482i
$665$		0			0
$666$	3.05696	−	12.6418i	0.118455	−	0.489861i
$667$	1.10401	−	1.10401i	0.0427473	−	0.0427473i
$668$	−13.2648	+	7.65841i	−0.513229	+	0.296313i
$669$	10.3302	−	17.8925i	0.399390	−	0.691764i
$670$		0			0
$671$	−5.38760	−	20.1068i	−0.207986	−	0.776214i
$672$		−	6.55714i		−	0.252947i
$673$	16.5351	−	4.43056i	0.637380	−	0.170785i	0.0743635	−	0.997231i	$-0.476307\pi$
$673$	16.5351	−	4.43056i	0.637380	−	0.170785i	0.563016	+	0.826446i	$0.309641\pi$
$674$	15.9588	+	15.9588i	0.614710	+	0.614710i
$675$		0			0
$676$	7.57040			0.291169
$677$	−31.1728	−	31.1728i	−1.19807	−	1.19807i	−0.974745	−	0.223322i	$-0.928310\pi$
$677$	−31.1728	−	31.1728i	−1.19807	−	1.19807i	−0.223322	−	0.974745i	$-0.571690\pi$
$678$	−4.52851	+	16.9006i	−0.173916	+	0.649064i
$679$	−24.3331	+	6.52002i	−0.933817	+	0.250216i
$680$		0			0
$681$	−5.81408	+	21.6984i	−0.222796	+	0.831486i
$682$	−3.00172	−	0.804309i	−0.114942	−	0.0307986i
$683$	−18.4398	−	31.9387i	−0.705580	−	1.22210i	−0.966482	−	0.256736i	$-0.917353\pi$
$683$	−18.4398	−	31.9387i	−0.705580	−	1.22210i	0.260901	−	0.965365i	$-0.415980\pi$
$684$	−0.779496	−	2.90912i	−0.0298048	−	0.111233i
$685$		0			0
$686$	−5.44250	+	20.3117i	−0.207796	+	0.775503i
$687$	−1.10241	+	4.11424i	−0.0420595	+	0.156968i
$688$	−5.67657	−	9.83210i	−0.216417	−	0.374845i
$689$	3.63192	+	3.63192i	0.138365	+	0.138365i
$690$		0			0
$691$	−0.520289	+	0.300389i	−0.0197927	+	0.0114273i	−0.509864	−	0.860255i	$-0.670304\pi$
$691$	−0.520289	+	0.300389i	−0.0197927	+	0.0114273i	0.490071	+	0.871683i	$0.336971\pi$
$692$	0.414220	−	0.414220i	0.0157463	−	0.0157463i
$693$	4.18059	−	4.18059i	0.158807	−	0.158807i
$694$	5.86687	+	10.1617i	0.222703	+	0.385734i
$695$		0			0
$696$	−0.960837	−	0.554740i	−0.0364204	−	0.0210274i
$697$	−10.3100			−0.390518
$698$	15.5785	+	8.99422i	0.589653	+	0.340436i
$699$	2.91617	+	1.68365i	0.110300	+	0.0636816i
$700$		0			0
$701$	−6.15868	−	1.65021i	−0.232610	−	0.0623277i	0.140631	−	0.990062i	$-0.455087\pi$
$701$	−6.15868	−	1.65021i	−0.232610	−	0.0623277i	−0.373241	+	0.927734i	$0.621754\pi$
$702$	6.33115	+	6.33115i	0.238954	+	0.238954i
$703$	−7.14687	−	11.7057i	−0.269549	−	0.441487i
$704$		−	16.2781i		−	0.613505i
$705$		0			0
$706$	−8.56315	−	4.94394i	−0.322278	−	0.186067i
$707$	−1.21070	+	0.324407i	−0.0455332	+	0.0122006i
$708$	2.04336	−	3.53920i	0.0767941	−	0.133011i
$709$	−0.102970	−	0.102970i	−0.00386711	−	0.00386711i	0.705171	−	0.709038i	$-0.250870\pi$
$709$	−0.102970	−	0.102970i	−0.00386711	−	0.00386711i	−0.709038	+	0.705171i	$0.750870\pi$
$710$		0			0
$711$	−17.0049	+	17.0049i	−0.637735	+	0.637735i
$712$	−50.5477	−	13.5442i	−1.89436	−	0.507591i
$713$	−4.60752	−	4.60752i	−0.172553	−	0.172553i
$714$	−2.59025			−0.0969378
$715$		0			0
$716$	4.28964	+	16.0091i	0.160311	+	0.598290i
$717$	20.9900			0.783887
$718$	9.69954	−	5.60003i	0.361984	−	0.208991i
$719$	−15.6399	+	9.02972i	−0.583271	+	0.336752i	−0.762432	−	0.647068i	$-0.775995\pi$
$719$	−15.6399	+	9.02972i	−0.583271	+	0.336752i	0.179161	+	0.983820i	$0.442662\pi$
$720$		0			0
$721$	−7.55161	+	2.02345i	−0.281237	+	0.0753571i
$722$	−13.6902	−	7.90402i	−0.509495	−	0.294157i
$723$	10.2257	−	5.90379i	0.380297	−	0.219564i
$724$	7.13191	+	12.3528i	0.265055	+	0.459089i
$725$		0			0
$726$	6.20222	−	6.20222i	0.230186	−	0.230186i
$727$	9.79831	−	16.9712i	0.363399	−	0.629426i	−0.625119	−	0.780530i	$-0.714949\pi$
$727$	9.79831	−	16.9712i	0.363399	−	0.629426i	0.988518	+	0.151104i	$0.0482828\pi$
$728$	−7.41727	−	1.98745i	−0.274902	−	0.0736599i
$729$			16.0130i			0.593073i
$730$		0			0
$731$	6.24916	−	3.60795i	0.231134	−	0.133445i
$732$	−8.12287			−0.300230
$733$	−7.89548	−	29.4663i	−0.291626	−	1.08836i	−0.943860	−	0.330346i	$-0.892835\pi$
$733$	−7.89548	−	29.4663i	−0.291626	−	1.08836i	0.652234	−	0.758018i	$-0.273832\pi$
$734$	16.2868	−	16.2868i	0.601158	−	0.601158i
$735$		0			0
$736$	8.69240	−	15.0557i	0.320406	−	0.554960i
$737$	−4.87063	−	18.1774i	−0.179412	−	0.669574i
$738$	8.34892	+	14.4608i	0.307328	+	0.532308i
$739$	52.1459			1.91822			0.959110	−	0.283035i	$-0.0913412\pi$
$739$	52.1459			1.91822			0.959110	+	0.283035i	$0.0913412\pi$
$740$		0			0
$741$	3.64006			0.133721
$742$	3.12106	+	5.40584i	0.114578	+	0.198455i
$743$	6.78290	+	25.3141i	0.248841	+	0.928686i	0.971414	+	0.237392i	$0.0762924\pi$
$743$	6.78290	+	25.3141i	0.248841	+	0.928686i	−0.722573	+	0.691294i	$0.757041\pi$
$744$	−2.31518	+	4.01001i	−0.0848787	+	0.147014i
$745$		0			0
$746$	−1.91199	+	1.91199i	−0.0700030	+	0.0700030i
$747$	4.32721	+	16.1494i	0.158324	+	0.590874i
$748$	1.80119			0.0658581
$749$	18.4082	−	10.6280i	0.672621	−	0.388338i
$750$		0			0
$751$		−	53.1233i		−	1.93850i	−0.246087	−	0.969248i	$-0.579145\pi$
$751$		−	53.1233i		−	1.93850i	0.246087	−	0.969248i	$-0.420855\pi$
$752$	−5.08302	−	1.36199i	−0.185359	−	0.0496667i
$753$	−5.06517	+	8.77313i	−0.184585	+	0.319711i
$754$	−0.418205	+	0.418205i	−0.0152301	+	0.0152301i
$755$		0			0
$756$	−2.99203	−	5.18235i	−0.108819	−	0.188480i
$757$	12.9392	−	7.47044i	0.470282	−	0.271518i	−0.246075	−	0.969251i	$-0.579141\pi$
$757$	12.9392	−	7.47044i	0.470282	−	0.271518i	0.716358	+	0.697733i	$0.245808\pi$
$758$	−16.3562	−	9.44324i	−0.594083	−	0.342994i
$759$	−8.99041	+	2.40897i	−0.326331	+	0.0874402i
$760$		0			0
$761$	−33.1931	+	19.1641i	−1.20325	+	0.694697i	−0.961277	−	0.275586i	$-0.911128\pi$
$761$	−33.1931	+	19.1641i	−1.20325	+	0.694697i	−0.241974	+	0.970283i	$0.577795\pi$
$762$	−5.32011	+	3.07157i	−0.192727	+	0.111271i
$763$	−21.6430			−0.783530
$764$	3.25689	+	12.1549i	0.117830	+	0.439749i
$765$		0			0
$766$	−10.2315			−0.369679
$767$	−5.88197	−	5.88197i	−0.212385	−	0.212385i
$768$	−14.9434	−	4.00407i	−0.539224	−	0.144485i
$769$	−22.4800	+	22.4800i	−0.810650	+	0.810650i	−0.984731	−	0.174081i	$-0.944304\pi$
$769$	−22.4800	+	22.4800i	−0.810650	+	0.810650i	0.174081	+	0.984731i	$0.444304\pi$
$770$		0			0
$771$	0.264559	+	0.264559i	0.00952786	+	0.00952786i
$772$	6.10080	−	10.5669i	0.219573	−	0.380311i
$773$	29.6256	−	7.93815i	1.06556	−	0.285515i	0.316891	−	0.948462i	$-0.397361\pi$
$773$	29.6256	−	7.93815i	1.06556	−	0.285515i	0.748667	+	0.662947i	$0.230694\pi$
$774$	−10.1210	−	5.84337i	−0.363792	−	0.210036i
$775$		0			0
$776$			47.4615i			1.70377i
$777$	−7.60896	−	7.24437i	−0.272970	−	0.259890i
$778$	9.53005	+	9.53005i	0.341669	+	0.341669i
$779$	17.0078	+	4.55724i	0.609369	+	0.163280i
$780$		0			0
$781$	−5.50429	−	3.17790i	−0.196959	−	0.113714i
$782$	−5.94742	−	3.43375i	−0.212679	−	0.122790i
$783$	−1.75986			−0.0628922
$784$	7.79085	+	4.49805i	0.278245	+	0.160645i
$785$		0			0
$786$	1.91248	+	3.31251i	0.0682159	+	0.118153i
$787$	17.9843	−	17.9843i	0.641072	−	0.641072i	−0.309747	−	0.950819i	$-0.600244\pi$
$787$	17.9843	−	17.9843i	0.641072	−	0.641072i	0.950819	+	0.309747i	$0.100244\pi$
$788$	−4.47398	+	4.47398i	−0.159379	+	0.159379i
$789$	−18.4737	+	10.6658i	−0.657681	+	0.379712i
$790$		0			0
$791$	−16.8308	−	16.8308i	−0.598435	−	0.598435i
$792$	−5.56943	−	9.64653i	−0.197901	−	0.342775i
$793$	−4.27926	+	15.9704i	−0.151961	+	0.567126i
$794$	0.675939	−	2.52264i	0.0239882	−	0.0895251i
$795$		0			0
$796$	−1.97684	−	7.37767i	−0.0700672	−	0.261494i
$797$	14.1009	+	24.4236i	0.499481	+	0.865127i	1.00000		0.000599033i	$-0.000190678\pi$
$797$	14.1009	+	24.4236i	0.499481	+	0.865127i	−0.500519	+	0.865726i	$0.666857\pi$
$798$	4.27301	+	1.14495i	0.151263	+	0.0405307i
$799$	0.865665	−	3.23070i	0.0306250	−	0.114294i
$800$		0			0
$801$	−30.9119	+	8.28283i	−1.09222	+	0.292659i
$802$	−7.05582	+	26.3327i	−0.249150	+	0.929839i
$803$	3.43435	+	3.43435i	0.121196	+	0.121196i
$804$	−7.34343			−0.258983
$805$		0			0
$806$	1.74536	+	1.74536i	0.0614777	+	0.0614777i
$807$	6.63697	−	1.77837i	0.233633	−	0.0626017i
$808$			2.36147i			0.0830763i
$809$	0.812619	+	3.03273i	0.0285701	+	0.106625i	0.978739	−	0.205112i	$-0.0657558\pi$
$809$	0.812619	+	3.03273i	0.0285701	+	0.106625i	−0.950168	+	0.311737i	$0.899089\pi$
$810$		0			0
$811$	−10.5095	+	18.2030i	−0.369038	+	0.639192i	−0.989415	−	0.145111i	$-0.953646\pi$
$811$	−10.5095	+	18.2030i	−0.369038	+	0.639192i	0.620377	+	0.784303i	$0.286979\pi$
$812$	0.342321	−	0.197639i	0.0120131	−	0.00693577i
$813$	−3.18365	+	3.18365i	−0.111655	+	0.111655i
$814$	−9.62111	−	9.16011i	−0.337220	−	0.321062i
$815$		0			0
$816$	−0.750368	+	2.80041i	−0.0262681	+	0.0980340i
$817$	−11.9037	+	3.18959i	−0.416458	+	0.111590i
$818$	7.57966	+	28.2877i	0.265017	+	0.989056i
$819$	−4.53596	+	1.21541i	−0.158499	+	0.0424697i
$820$		0			0
$821$	2.11926	−	3.67067i	0.0739627	−	0.128107i	−0.826672	−	0.562684i	$-0.809769\pi$
$821$	2.11926	−	3.67067i	0.0739627	−	0.128107i	0.900635	+	0.434577i	$0.143102\pi$
$822$			25.9496i			0.905096i
$823$	0.244554	−	0.912687i	0.00852461	−	0.0318143i	−0.961533	−	0.274691i	$-0.911424\pi$
$823$	0.244554	−	0.912687i	0.00852461	−	0.0318143i	0.970057	+	0.242877i	$0.0780911\pi$
$824$			14.7294i			0.513122i
$825$		0			0
$826$	−5.05462	−	8.75486i	−0.175873	−	0.304621i
$827$	20.7030	+	11.9529i	0.719912	+	0.415642i	0.814720	−	0.579854i	$-0.196890\pi$
$827$	20.7030	+	11.9529i	0.719912	+	0.415642i	−0.0948080	+	0.995496i	$0.530224\pi$
$828$		−	6.11671i		−	0.212570i
$829$	−2.51032	−	0.672639i	−0.0871871	−	0.0233617i	0.214962	−	0.976622i	$-0.431037\pi$
$829$	−2.51032	−	0.672639i	−0.0871871	−	0.0233617i	−0.302149	+	0.953261i	$0.597704\pi$
$830$		0			0
$831$	0.583280	+	0.156289i	0.0202338	+	0.00542162i
$832$	−6.46469	+	11.1972i	−0.224123	+	0.388192i
$833$	−2.85890	+	4.95177i	−0.0990551	+	0.171569i
$834$	20.8230	+	5.57951i	0.721041	+	0.193202i
$835$		0			0
$836$	−2.97133	−	0.796165i	−0.102766	−	0.0275360i
$837$			7.34470i			0.253870i
$838$	−32.9826	−	19.0425i	−1.13936	−	0.657812i
$839$	−18.2196	−	31.5573i	−0.629012	−	1.08948i	−0.987750	−	0.156042i	$-0.950126\pi$
$839$	−18.2196	−	31.5573i	−0.629012	−	1.08948i	0.358739	−	0.933438i	$-0.383207\pi$
$840$		0			0
$841$			28.8838i			0.995991i
$842$	0.396811	−	1.48092i	0.0136750	−	0.0510358i
$843$		−	33.1205i		−	1.14073i
$844$	0.583049	−	1.00987i	0.0200694	−	0.0347611i
$845$		0			0
$846$	−5.23239	+	1.40201i	−0.179893	+	0.0482022i
$847$	3.08830	+	11.5257i	0.106115	+	0.396028i
$848$	6.74857	−	1.80827i	0.231747	−	0.0620964i
$849$	−0.168614	+	0.629276i	−0.00578681	+	0.0215967i
$850$		0			0
$851$	−7.86732	−	26.7204i	−0.269688	−	0.915962i
$852$	−1.75374	+	1.75374i	−0.0600822	+	0.0600822i
$853$	22.4827	−	12.9804i	0.769792	−	0.444440i	−0.0630083	−	0.998013i	$-0.520069\pi$
$853$	22.4827	−	12.9804i	0.769792	−	0.444440i	0.832800	+	0.553573i	$0.186736\pi$
$854$	−10.0467	+	17.4014i	−0.343791	+	0.595464i
$855$		0			0
$856$	−10.3649	−	38.6824i	−0.354265	−	1.32214i
$857$			40.2792i			1.37591i	0.725753	+	0.687955i	$0.241491\pi$
$857$			40.2792i			1.37591i	−0.725753	+	0.687955i	$0.758509\pi$
$858$	3.40563	−	0.912535i	0.116266	−	0.0311534i
$859$	3.69657	+	3.69657i	0.126125	+	0.126125i	0.767352	−	0.641226i	$-0.221574\pi$
$859$	3.69657	+	3.69657i	0.126125	+	0.126125i	−0.641226	+	0.767352i	$0.721574\pi$
$860$		0			0
$861$	13.4881			0.459672
$862$	−10.1183	−	10.1183i	−0.344630	−	0.344630i
$863$	1.83795	−	6.85933i	0.0625646	−	0.233494i	−0.927562	−	0.373669i	$-0.878100\pi$
$863$	1.83795	−	6.85933i	0.0625646	−	0.233494i	0.990127	+	0.140174i	$0.0447663\pi$
$864$	−18.9280	+	5.07175i	−0.643944	+	0.172544i
$865$		0			0
$866$	−5.70964	+	21.3087i	−0.194021	+	0.724098i
$867$	15.5802	+	4.17471i	0.529132	+	0.141780i
$868$	−0.824838	−	1.42866i	−0.0279968	−	0.0484919i
$869$	6.35735	+	23.7259i	0.215658	+	0.804847i
$870$		0			0
$871$	−3.86864	+	14.4380i	−0.131084	+	0.489212i
$872$	−10.5536	+	39.3867i	−0.357391	+	1.33380i
$873$	14.5123	+	25.1360i	0.491167	+	0.850726i
$874$	8.29336	+	8.29336i	0.280527	+	0.280527i
$875$		0			0
$876$	1.64135	−	0.947633i	0.0554560	−	0.0320176i
$877$	26.8398	−	26.8398i	0.906315	−	0.906315i	−0.0896576	−	0.995973i	$-0.528577\pi$
$877$	26.8398	−	26.8398i	0.906315	−	0.906315i	0.995973	+	0.0896576i	$0.0285773\pi$
$878$	24.8531	−	24.8531i	0.838750	−	0.838750i
$879$	−5.22618	−	9.05201i	−0.176275	−	0.305317i
$880$		0			0
$881$	−3.79357	−	2.19022i	−0.127809	−	0.0737904i	0.434733	−	0.900560i	$-0.356843\pi$
$881$	−3.79357	−	2.19022i	−0.127809	−	0.0737904i	−0.562541	+	0.826769i	$0.690176\pi$
$882$	9.26045			0.311815
$883$	−50.6657	−	29.2518i	−1.70504	−	0.984402i	−0.940483	−	0.339840i	$-0.889627\pi$
$883$	−50.6657	−	29.2518i	−1.70504	−	0.984402i	−0.764552	−	0.644562i	$-0.777040\pi$
$884$	−1.23898	−	0.715324i	−0.0416713	−	0.0240590i
$885$		0			0
$886$	20.6420	+	5.53099i	0.693480	+	0.185817i
$887$	−2.53298	−	2.53298i	−0.0850491	−	0.0850491i	0.663302	−	0.748351i	$-0.269154\pi$
$887$	−2.53298	−	2.53298i	−0.0850491	−	0.0850491i	−0.748351	+	0.663302i	$0.769154\pi$
$888$	−16.8939	+	10.3145i	−0.566921	+	0.346133i
$889$		−	8.35702i		−	0.280286i
$890$		0			0
$891$	−0.316423	−	0.182687i	−0.0106006	−	0.00612024i
$892$	13.3954	−	3.58929i	0.448511	−	0.120178i
$893$	−2.85608	+	4.94688i	−0.0955752	+	0.165541i
$894$	−14.3420	−	14.3420i	−0.479668	−	0.479668i
$895$		0			0
$896$	−2.33935	+	2.33935i	−0.0781523	+	0.0781523i
$897$	7.14090	+	1.91340i	0.238428	+	0.0638865i
$898$	−23.5686	−	23.5686i	−0.786494	−	0.786494i
$899$	−0.485155			−0.0161808
$900$		0			0
$901$	1.14932	+	4.28931i	0.0382893	+	0.142898i
$902$	17.0549			0.567867
$903$	−8.17549	+	4.72012i	−0.272063	+	0.157076i
$904$	−38.8364	+	22.4222i	−1.29168	+	0.745752i
$905$		0			0
$906$	−25.7939	+	6.91146i	−0.856946	+	0.229618i
$907$	10.6371	+	6.14134i	0.353200	+	0.203920i	0.666094	−	0.745868i	$-0.267965\pi$
$907$	10.6371	+	6.14134i	0.353200	+	0.203920i	−0.312894	+	0.949788i	$0.601298\pi$
$908$	−13.0583	+	7.53922i	−0.433355	+	0.250198i
$909$	0.722067	+	1.25066i	0.0239495	+	0.0414817i
$910$		0			0
$911$	−8.69751	+	8.69751i	−0.288161	+	0.288161i	−0.836353	−	0.548191i	$-0.815317\pi$
$911$	−8.69751	+	8.69751i	−0.288161	+	0.288161i	0.548191	+	0.836353i	$0.315317\pi$
$912$	2.47568	−	4.28801i	0.0819781	−	0.141990i
$913$	16.4947	+	4.41974i	0.545895	+	0.146272i
$914$			7.28961i			0.241119i
$915$		0			0
$916$	−2.47599	+	1.42951i	−0.0818089	+	0.0472324i
$917$	−5.20341			−0.171832
$918$	2.00348	+	7.47710i	0.0661248	+	0.246781i
$919$	25.2847	−	25.2847i	0.834065	−	0.834065i	−0.154005	−	0.988070i	$-0.549217\pi$
$919$	25.2847	−	25.2847i	0.834065	−	0.834065i	0.988070	+	0.154005i	$0.0492173\pi$
$920$		0			0
$921$	9.53382	−	16.5131i	0.314150	−	0.544124i
$922$	7.70182	+	28.7436i	0.253646	+	0.946620i
$923$	2.52414	+	4.37194i	0.0830832	+	0.143904i
$924$	−2.35642			−0.0775204
$925$		0			0
$926$	−43.4081			−1.42648
$927$	4.50380	+	7.80081i	0.147924	+	0.256212i
$928$	−0.335015	−	1.25029i	−0.0109974	−	0.0410428i
$929$	−6.26098	+	10.8443i	−0.205416	+	0.355791i	−0.950265	−	0.311442i	$-0.899188\pi$
$929$	−6.26098	+	10.8443i	−0.205416	+	0.355791i	0.744849	+	0.667233i	$0.232521\pi$
$930$		0			0
$931$	6.90497	−	6.90497i	0.226301	−	0.226301i
$932$	0.584992	+	2.18322i	0.0191621	+	0.0715138i
$933$	−25.7724			−0.843751
$934$	−13.2985	+	7.67791i	−0.435141	+	0.251229i
$935$		0			0
$936$			8.84736i			0.289185i
$937$	−11.8419	−	3.17302i	−0.386857	−	0.103658i	0.0601478	−	0.998189i	$-0.480843\pi$
$937$	−11.8419	−	3.17302i	−0.386857	−	0.103658i	−0.447005	+	0.894531i	$0.647509\pi$
$938$	−9.08266	+	15.7316i	−0.296559	+	0.513656i
$939$	−0.692230	+	0.692230i	−0.0225901	+	0.0225901i
$940$		0			0
$941$	−13.7869	−	23.8796i	−0.449440	−	0.778452i	0.548910	−	0.835881i	$-0.315043\pi$
$941$	−13.7869	−	23.8796i	−0.449440	−	0.778452i	−0.998350	+	0.0574293i	$0.981710\pi$
$942$	5.42015	−	3.12932i	0.176598	−	0.101959i
$943$	30.9696	+	17.8803i	1.00851	+	0.582264i
$944$	−10.9294	+	2.92853i	−0.355723	+	0.0953157i
$945$		0			0
$946$	−10.3375	+	5.96833i	−0.336100	+	0.194047i
$947$	−7.76600	+	4.48370i	−0.252361	+	0.145701i	−0.620845	−	0.783933i	$-0.713210\pi$
$947$	−7.76600	+	4.48370i	−0.252361	+	0.145701i	0.368484	+	0.929634i	$0.379877\pi$
$948$	9.58495			0.311305
$949$	−0.998457	−	3.72629i	−0.0324113	−	0.120961i
$950$		0			0
$951$	−27.9848			−0.907469
$952$	−4.69437	−	4.69437i	−0.152145	−	0.152145i
$953$	−35.9483	−	9.63231i	−1.16448	−	0.312021i	−0.375725	−	0.926731i	$-0.622606\pi$
$953$	−35.9483	−	9.63231i	−1.16448	−	0.312021i	−0.788753	+	0.614710i	$0.789273\pi$
$954$	5.08547	−	5.08547i	0.164648	−	0.164648i
$955$		0			0
$956$	9.96253	+	9.96253i	0.322211	+	0.322211i
$957$	−0.346500	+	0.600156i	−0.0112008	+	0.0194003i
$958$	−1.97946	+	0.530395i	−0.0639535	+	0.0171363i
$959$	−30.5719	−	17.6507i	−0.987219	−	0.569971i
$960$		0			0
$961$		−	28.9752i		−	0.934685i
$962$	2.98019	+	10.1219i	0.0960852	+	0.326342i
$963$	−17.3173	−	17.3173i	−0.558041	−	0.558041i
$964$	7.65555	+	2.05130i	0.246569	+	0.0660679i
$965$		0			0
$966$	7.78074	+	4.49221i	0.250341	+	0.144535i
$967$	−48.6411	−	28.0830i	−1.56419	−	0.903087i	−0.996825	−	0.0796228i	$-0.974628\pi$
$967$	−48.6411	−	28.0830i	−1.56419	−	0.903087i	−0.567368	−	0.823464i	$-0.692038\pi$
$968$	22.4808			0.722561
$969$	2.72541	+	1.57351i	0.0875526	+	0.0505485i
$970$		0			0
$971$	−19.7612	−	34.2274i	−0.634167	−	1.09841i	−0.986691	−	0.162607i	$-0.948010\pi$
$971$	−19.7612	−	34.2274i	−0.634167	−	1.09841i	0.352523	−	0.935803i	$-0.385324\pi$
$972$	−7.87086	+	7.87086i	−0.252458	+	0.252458i
$973$	−20.7370	+	20.7370i	−0.664798	+	0.664798i
$974$	−4.63033	+	2.67332i	−0.148365	+	0.0856588i
$975$		0			0
$976$	15.9028	+	15.9028i	0.509037	+	0.509037i
$977$	3.00331	+	5.20188i	0.0960843	+	0.166423i	0.910061	−	0.414475i	$-0.136035\pi$
$977$	3.00331	+	5.20188i	0.0960843	+	0.166423i	−0.813976	+	0.580898i	$0.802702\pi$
$978$	4.56042	−	17.0197i	0.145826	−	0.544231i
$979$	−8.45996	+	31.5730i	−0.270381	+	1.00908i
$980$		0			0
$981$	6.45397	+	24.0866i	0.206060	+	0.769025i
$982$	12.7039	+	22.0038i	0.405398	+	0.702169i
$983$	−23.1064	−	6.19133i	−0.736979	−	0.197473i	−0.129244	−	0.991613i	$-0.541255\pi$
$983$	−23.1064	−	6.19133i	−0.736979	−	0.197473i	−0.607735	+	0.794140i	$0.707922\pi$
$984$	6.57710	−	24.5461i	0.209670	−	0.782501i
$985$		0			0
$986$	−0.493901	+	0.132340i	−0.0157290	+	0.00421457i
$987$	−1.13251	+	4.22658i	−0.0360482	+	0.134534i
$988$	1.72769	+	1.72769i	0.0549651	+	0.0549651i
$989$	−25.0287			−0.795867
$990$		0			0
$991$	18.5888	+	18.5888i	0.590492	+	0.590492i	0.937764	−	0.347272i	$-0.112892\pi$
$991$	18.5888	+	18.5888i	0.590492	+	0.590492i	−0.347272	+	0.937764i	$0.612892\pi$
$992$	−5.21804	+	1.39817i	−0.165673	+	0.0443919i
$993$			10.2963i			0.326742i
$994$	1.58789	+	5.92610i	0.0503649	+	0.187964i
$995$		0			0
$996$	3.33182	−	5.77087i	0.105573	−	0.182857i
$997$	−44.7129	+	25.8150i	−1.41607	+	0.817569i	−0.995951	−	0.0898999i	$-0.971345\pi$
$997$	−44.7129	+	25.8150i	−1.41607	+	0.817569i	−0.420120	+	0.907469i	$0.638012\pi$
$998$	12.5670	−	12.5670i	0.397800	−	0.397800i
$999$	−15.0265	+	27.5675i	−0.475417	+	0.872198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.t.b.843.12		68
5.2	odd	4		925.2.y.b.732.6		68
5.3	odd	4		185.2.u.a.177.12	yes	68
5.4	even	2		185.2.p.a.103.6	yes	68
37.23	odd	12		925.2.y.b.393.6		68
185.23	even	12		185.2.p.a.97.6	✓	68
185.97	even	12	inner	925.2.t.b.282.12		68
185.134	odd	12		185.2.u.a.23.12	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.6	✓	68	185.23	even	12
185.2.p.a.103.6	yes	68	5.4	even	2
185.2.u.a.23.12	yes	68	185.134	odd	12
185.2.u.a.177.12	yes	68	5.3	odd	4
925.2.t.b.282.12		68	185.97	even	12	inner
925.2.t.b.843.12		68	1.1	even	1	trivial
925.2.y.b.393.6		68	37.23	odd	12
925.2.y.b.732.6		68	5.2	odd	4

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.567972 + 0.983757i) q^{2} +(-0.273625 - 1.02118i) q^{3} +(0.354815 - 0.614557i) q^{4} +(0.849185 - 0.849185i) q^{6} +(0.422839 + 1.57806i) q^{7} +3.07799 q^{8} +(1.63013 - 0.941157i) q^{9} -1.92257i q^{11} +(-0.724662 - 0.194173i) q^{12} +(-0.763528 + 1.32247i) q^{13} +(-1.31226 + 1.31226i) q^{14} +(1.03858 + 1.79888i) q^{16} +(-1.14334 + 0.660110i) q^{17} +(1.85174 + 1.06910i) q^{18} +(2.17790 - 0.583566i) q^{19} +(1.49579 - 0.863592i) q^{21} +(1.89134 - 1.09196i) q^{22} +4.57925 q^{23} +(-0.842216 - 3.14319i) q^{24} -1.73465 q^{26} +(-3.64981 - 3.64981i) q^{27} +(1.11984 + 0.300059i) q^{28} +(0.241089 - 0.241089i) q^{29} +(-1.00617 - 1.00617i) q^{31} +(1.89822 - 3.28781i) q^{32} +(-1.96329 + 0.526063i) q^{33} +(-1.29878 - 0.749849i) q^{34} -1.33575i q^{36} +(-1.71804 - 5.83510i) q^{37} +(1.81107 + 1.81107i) q^{38} +(1.55940 + 0.417841i) q^{39} +(6.76304 + 3.90464i) q^{41} +(1.69913 + 0.980993i) q^{42} -5.46568 q^{43} +(-1.18153 - 0.682155i) q^{44} +(2.60089 + 4.50487i) q^{46} +(-1.79140 + 1.79140i) q^{47} +(1.55280 - 1.55280i) q^{48} +(3.75071 - 2.16547i) q^{49} +(0.986942 + 0.986942i) q^{51} +(0.541822 + 0.938463i) q^{52} +(0.870548 - 3.24893i) q^{53} +(1.51754 - 5.66352i) q^{54} +(1.30149 + 4.85724i) q^{56} +(-1.19186 - 2.06436i) q^{57} +(0.374105 + 0.100241i) q^{58} +(-1.40987 + 5.26170i) q^{59} +(10.4583 - 2.80230i) q^{61} +(0.418352 - 1.56131i) q^{62} +(2.17448 + 2.17448i) q^{63} +8.46687 q^{64} +(-1.63261 - 1.63261i) q^{66} +(9.45477 - 2.53340i) q^{67} +0.936868i q^{68} +(-1.25300 - 4.67625i) q^{69} +(1.65295 - 2.86299i) q^{71} +(5.01753 - 2.89687i) q^{72} +(-1.78634 + 1.78634i) q^{73} +(4.76452 - 5.00430i) q^{74} +(0.414116 - 1.54550i) q^{76} +(3.03392 - 0.812936i) q^{77} +(0.474644 + 1.77140i) q^{78} +(-12.3408 + 3.30670i) q^{79} +(0.0950223 - 0.164583i) q^{81} +8.87092i q^{82} +(-2.29888 + 8.57952i) q^{83} -1.22566i q^{84} +(-3.10436 - 5.37690i) q^{86} +(-0.312164 - 0.180228i) q^{87} -5.91764i q^{88} +(-16.4223 - 4.40035i) q^{89} +(-2.40978 - 0.645698i) q^{91} +(1.62479 - 2.81421i) q^{92} +(-0.752174 + 1.30280i) q^{93} +(-2.77976 - 0.744835i) q^{94} +(-3.87685 - 1.03880i) q^{96} +15.4196i q^{97} +(4.26060 + 2.45986i) q^{98} +(-1.80944 - 3.13404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) \) 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

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Database

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