LMFDB - Embedded newform 925.2.y.b.393.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] 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([9, 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("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (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			393.6
Character	$\chi$	$=$	925.393
Dual form			925.2.y.b.732.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.983757 - 0.567972i) q^{2} +(-1.02118 - 0.273625i) q^{3} +(-0.354815 - 0.614557i) q^{4} +(0.849185 + 0.849185i) q^{6} +(-1.57806 - 0.422839i) q^{7} +3.07799i q^{8} +(-1.63013 - 0.941157i) q^{9} +1.92257i q^{11} +(0.194173 + 0.724662i) q^{12} +(1.32247 - 0.763528i) q^{13} +(1.31226 + 1.31226i) q^{14} +(1.03858 - 1.79888i) q^{16} +(-0.660110 + 1.14334i) q^{17} +(1.06910 + 1.85174i) q^{18} +(-2.17790 - 0.583566i) q^{19} +(1.49579 + 0.863592i) q^{21} +(1.09196 - 1.89134i) q^{22} +4.57925i q^{23} +(0.842216 - 3.14319i) q^{24} -1.73465 q^{26} +(3.64981 + 3.64981i) q^{27} +(0.300059 + 1.11984i) q^{28} +(-0.241089 - 0.241089i) q^{29} +(-1.00617 + 1.00617i) q^{31} +(3.28781 - 1.89822i) q^{32} +(0.526063 - 1.96329i) q^{33} +(1.29878 - 0.749849i) q^{34} +1.33575i q^{36} +(5.83510 + 1.71804i) q^{37} +(1.81107 + 1.81107i) q^{38} +(-1.55940 + 0.417841i) q^{39} +(6.76304 - 3.90464i) q^{41} +(-0.980993 - 1.69913i) q^{42} -5.46568i 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} +(-0.938463 - 0.541822i) q^{52} +(-3.24893 + 0.870548i) q^{53} +(-1.51754 - 5.66352i) q^{54} +(1.30149 - 4.85724i) q^{56} +(2.06436 + 1.19186i) q^{57} +(0.100241 + 0.374105i) q^{58} +(1.40987 + 5.26170i) q^{59} +(10.4583 + 2.80230i) q^{61} +(1.56131 - 0.418352i) q^{62} +(2.17448 + 2.17448i) q^{63} -8.46687 q^{64} +(-1.63261 + 1.63261i) q^{66} +(2.53340 - 9.45477i) q^{67} +0.936868 q^{68} +(1.25300 - 4.67625i) q^{69} +(1.65295 + 2.86299i) q^{71} +(2.89687 - 5.01753i) q^{72} +(1.78634 - 1.78634i) q^{73} +(-4.76452 - 5.00430i) q^{74} +(0.414116 + 1.54550i) q^{76} +(0.812936 - 3.03392i) q^{77} +(1.77140 + 0.474644i) q^{78} +(12.3408 + 3.30670i) q^{79} +(0.0950223 + 0.164583i) q^{81} -8.87092 q^{82} +(8.57952 - 2.29888i) q^{83} -1.22566i q^{84} +(-3.10436 + 5.37690i) q^{86} +(0.180228 + 0.312164i) q^{87} -5.91764 q^{88} +(16.4223 - 4.40035i) q^{89} +(-2.40978 + 0.645698i) q^{91} +(2.81421 - 1.62479i) q^{92} +(1.30280 - 0.752174i) q^{93} +(2.77976 - 0.744835i) q^{94} +(-3.87685 + 1.03880i) q^{96} -15.4196 q^{97} +(2.45986 + 4.26060i) q^{98} +(1.80944 - 3.13404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.983757	−	0.567972i	−0.695621	−	0.401617i	0.110093	−	0.993921i	$-0.464885\pi$
$2$	−0.983757	−	0.567972i	−0.695621	−	0.401617i	−0.805714	+	0.592304i	$0.798218\pi$
$3$	−1.02118	−	0.273625i	−0.589581	−	0.157978i	−0.0483191	−	0.998832i	$-0.515386\pi$
$3$	−1.02118	−	0.273625i	−0.589581	−	0.157978i	−0.541262	+	0.840854i	$0.682053\pi$
$4$	−0.354815	−	0.614557i	−0.177407	−	0.307279i
$5$		0			0
$5$		0			0
$6$	0.849185	+	0.849185i	0.346678	+	0.346678i
$7$	−1.57806	−	0.422839i	−0.596449	−	0.159818i	−0.0520501	−	0.998644i	$-0.516576\pi$
$7$	−1.57806	−	0.422839i	−0.596449	−	0.159818i	−0.544399	+	0.838826i	$0.683242\pi$
$8$			3.07799i			1.08823i
$9$	−1.63013	−	0.941157i	−0.543377	−	0.313719i
$10$		0			0
$11$			1.92257i			0.579676i	0.957076	+	0.289838i	$0.0936014\pi$
$11$			1.92257i			0.579676i	−0.957076	+	0.289838i	$0.906399\pi$
$12$	0.194173	+	0.724662i	0.0560528	+	0.209192i
$13$	1.32247	−	0.763528i	0.366787	−	0.211764i	−0.305267	−	0.952267i	$-0.598746\pi$
$13$	1.32247	−	0.763528i	0.366787	−	0.211764i	0.672054	+	0.740502i	$0.265412\pi$
$14$	1.31226	+	1.31226i	0.350717	+	0.350717i
$15$		0			0
$16$	1.03858	−	1.79888i	0.259646	−	0.449720i
$17$	−0.660110	+	1.14334i	−0.160100	+	0.277302i	−0.934904	−	0.354899i	$-0.884515\pi$
$17$	−0.660110	+	1.14334i	−0.160100	+	0.277302i	0.774804	+	0.632201i	$0.217848\pi$
$18$	1.06910	+	1.85174i	0.251990	+	0.436459i
$19$	−2.17790	−	0.583566i	−0.499644	−	0.133879i	0.000190628	−	1.00000i	$-0.499939\pi$
$19$	−2.17790	−	0.583566i	−0.499644	−	0.133879i	−0.499835	+	0.866121i	$0.666606\pi$
$20$		0			0
$21$	1.49579	+	0.863592i	0.326407	+	0.188451i
$22$	1.09196	−	1.89134i	0.232808	−	0.403235i
$23$			4.57925i			0.954839i	0.878675	+	0.477420i	$0.158428\pi$
$23$			4.57925i			0.954839i	−0.878675	+	0.477420i	$0.841572\pi$
$24$	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
$28$	0.300059	+	1.11984i	0.0567058	+	0.211629i
$29$	−0.241089	−	0.241089i	−0.0447691	−	0.0447691i	0.684368	−	0.729137i	$-0.260078\pi$
$29$	−0.241089	−	0.241089i	−0.0447691	−	0.0447691i	−0.729137	+	0.684368i	$0.760078\pi$
$30$		0			0
$31$	−1.00617	+	1.00617i	−0.180714	+	0.180714i	−0.791667	−	0.610953i	$-0.790787\pi$
$31$	−1.00617	+	1.00617i	−0.180714	+	0.180714i	0.610953	+	0.791667i	$0.290787\pi$
$32$	3.28781	−	1.89822i	0.581208	−	0.335560i
$33$	0.526063	−	1.96329i	0.0915758	−	0.341766i
$34$	1.29878	−	0.749849i	0.222738	−	0.128598i
$35$		0			0
$36$			1.33575i			0.222624i
$37$	5.83510	+	1.71804i	0.959284	+	0.282443i
$37$	5.83510	+	1.71804i	0.959284	+	0.282443i
$38$	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	0.131828	−	0.991273i	$-0.457915\pi$
$41$	6.76304	−	3.90464i	1.05621	−	0.609803i	0.924381	+	0.381470i	$0.124582\pi$
$42$	−0.980993	−	1.69913i	−0.151370	−	0.262181i
$43$		−	5.46568i		−	0.833509i	−0.909019	−	0.416754i	$-0.863168\pi$
$43$		−	5.46568i		−	0.833509i	0.909019	−	0.416754i	$-0.136832\pi$
$44$	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
$52$	−0.938463	−	0.541822i	−0.130141	−	0.0751372i
$53$	−3.24893	+	0.870548i	−0.446275	+	0.119579i	−0.474956	−	0.880010i	$-0.657536\pi$
$53$	−3.24893	+	0.870548i	−0.446275	+	0.119579i	0.0286809	+	0.999589i	$0.490869\pi$
$54$	−1.51754	−	5.66352i	−0.206511	−	0.770708i
$55$		0			0
$56$	1.30149	−	4.85724i	0.173919	−	0.649076i
$57$	2.06436	+	1.19186i	0.273431	+	0.157865i
$58$	0.100241	+	0.374105i	0.0131623	+	0.0491223i
$59$	1.40987	+	5.26170i	0.183549	+	0.685016i	0.994936	+	0.100506i	$0.0320463\pi$
$59$	1.40987	+	5.26170i	0.183549	+	0.685016i	−0.811387	+	0.584509i	$0.801287\pi$
$60$		0			0
$61$	10.4583	+	2.80230i	1.33905	+	0.358797i	0.856081	−	0.516841i	$-0.172892\pi$
$61$	10.4583	+	2.80230i	1.33905	+	0.358797i	0.482968	+	0.875638i	$0.339559\pi$
$62$	1.56131	−	0.418352i	0.198287	−	0.0531307i
$63$	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
$67$	2.53340	−	9.45477i	0.309504	−	1.15508i	−0.619495	−	0.785001i	$-0.712662\pi$
$67$	2.53340	−	9.45477i	0.309504	−	1.15508i	0.928999	−	0.370083i	$-0.120671\pi$
$68$	0.936868			0.113612
$69$	1.25300	−	4.67625i	0.150843	−	0.562955i
$70$		0			0
$71$	1.65295	+	2.86299i	0.196169	+	0.339774i	0.947283	−	0.320398i	$-0.103817\pi$
$71$	1.65295	+	2.86299i	0.196169	+	0.339774i	−0.751114	+	0.660172i	$0.770483\pi$
$72$	2.89687	−	5.01753i	0.341399	−	0.591321i
$73$	1.78634	−	1.78634i	0.209075	−	0.209075i	−0.594799	−	0.803874i	$-0.702768\pi$
$73$	1.78634	−	1.78634i	0.209075	−	0.209075i	0.803874	+	0.594799i	$0.202768\pi$
$74$	−4.76452	−	5.00430i	−0.553864	−	0.581739i
$75$		0			0
$76$	0.414116	+	1.54550i	0.0475023	+	0.177281i
$77$	0.812936	−	3.03392i	0.0926427	−	0.345747i
$78$	1.77140	+	0.474644i	0.200571	+	0.0537429i
$79$	12.3408	+	3.30670i	1.38844	+	0.372032i	0.874181	−	0.485600i	$-0.161399\pi$
$79$	12.3408	+	3.30670i	1.38844	+	0.372032i	0.514263	+	0.857633i	$0.328066\pi$
$80$		0			0
$81$	0.0950223	+	0.164583i	0.0105580	+	0.0182871i
$82$	−8.87092			−0.979629
$83$	8.57952	−	2.29888i	0.941725	−	0.252334i	0.244878	−	0.969554i	$-0.421252\pi$
$83$	8.57952	−	2.29888i	0.941725	−	0.252334i	0.696847	+	0.717220i	$0.254586\pi$
$84$		−	1.22566i		−	0.133731i
$85$		0			0
$86$	−3.10436	+	5.37690i	−0.334751	+	0.579806i
$87$	0.180228	+	0.312164i	0.0193225	+	0.0334675i
$88$	−5.91764			−0.630823
$89$	16.4223	−	4.40035i	1.74076	−	0.466436i	0.758146	−	0.652085i	$-0.226106\pi$
$89$	16.4223	−	4.40035i	1.74076	−	0.466436i	0.982616	+	0.185650i	$0.0594390\pi$
$90$		0			0
$91$	−2.40978	+	0.645698i	−0.252613	+	0.0676876i
$92$	2.81421	−	1.62479i	0.293402	−	0.169396i
$93$	1.30280	−	0.752174i	0.135094	−	0.0779968i
$94$	2.77976	−	0.744835i	0.286711	−	0.0768239i
$95$		0			0
$96$	−3.87685	+	1.03880i	−0.395680	+	0.106022i
$97$	−15.4196			−1.56563			−0.782814	−	0.622256i	$-0.786216\pi$
$97$	−15.4196			−1.56563			−0.782814	+	0.622256i	$0.786216\pi$
$98$	2.45986	+	4.26060i	0.248483	+	0.430385i
$99$	1.80944	−	3.13404i	0.181855	−	0.314983i
$100$		0			0
$101$		−	0.767212i		−	0.0763405i	−0.999271	−	0.0381702i	$-0.987847\pi$
$101$		−	0.767212i		−	0.0763405i	0.999271	−	0.0381702i	$-0.0121529\pi$
$102$	−1.53147	+	0.410355i	−0.151638	+	0.0406312i
$103$	4.78539			0.471518			0.235759	−	0.971812i	$-0.424242\pi$
$103$	4.78539			0.471518			0.235759	+	0.971812i	$0.424242\pi$
$104$	2.35013	+	4.07054i	0.230449	+	0.399150i
$105$		0			0
$106$	3.69061	+	0.988895i	0.358463	+	0.0960500i
$107$	12.5674	+	3.36743i	1.21494	+	0.325542i	0.808698	−	0.588225i	$-0.200173\pi$
$107$	12.5674	+	3.36743i	1.21494	+	0.325542i	0.406240	+	0.913766i	$0.366840\pi$
$108$	0.948011	−	3.53803i	0.0912224	−	0.340447i
$109$	3.42875	+	12.7963i	0.328414	+	1.22566i	0.910835	+	0.412771i	$0.135439\pi$
$109$	3.42875	+	12.7963i	0.328414	+	1.22566i	−0.582421	+	0.812888i	$0.697894\pi$
$110$		0			0
$111$	−5.48861	−	3.35106i	−0.520955	−	0.318069i
$112$	−2.39958	+	2.39958i	−0.226739	+	0.226739i
$113$	7.28470	−	12.6175i	0.685287	−	1.18695i	−0.288060	−	0.957612i	$-0.593010\pi$
$113$	7.28470	−	12.6175i	0.685287	−	1.18695i	0.973347	−	0.229339i	$-0.0736565\pi$
$114$	−1.35388	−	2.34499i	−0.126803	−	0.219629i
$115$		0			0
$116$	−0.0626210	+	0.233705i	−0.00581421	+	0.0216989i
$117$	−2.87440			−0.265738
$118$	1.60153	−	5.97701i	0.147433	−	0.550228i
$119$	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
$123$	−7.97471	+	2.13682i	−0.719056	+	0.192670i
$124$	0.975357	+	0.261346i	0.0875896	+	0.0234696i
$125$		0			0
$126$	−0.904116	−	3.37421i	−0.0805450	−	0.300598i
$127$	1.32394	+	4.94102i	0.117481	+	0.438445i	0.999461	−	0.0328428i	$-0.0104561\pi$
$127$	1.32394	+	4.94102i	0.117481	+	0.438445i	−0.881980	+	0.471288i	$0.843789\pi$
$128$	1.75373	+	1.01252i	0.155009	+	0.0894947i
$129$	−1.49555	+	5.58146i	−0.131676	+	0.491421i
$130$		0			0
$131$	−0.824339	−	3.07647i	−0.0720228	−	0.268793i	0.920519	−	0.390698i	$-0.127766\pi$
$131$	−0.824339	−	3.07647i	−0.0720228	−	0.268793i	−0.992542	+	0.121905i	$0.961100\pi$
$132$	−1.39321	+	0.373310i	−0.121263	+	0.0324924i
$133$	3.19009	+	1.84180i	0.276616	+	0.159704i
$134$	−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	0.180910	+	0.983500i	$0.442096\pi$
$139$	−8.97537	+	15.5458i	−0.761281	+	1.31858i	−0.942191	+	0.335077i	$0.891238\pi$
$140$		0			0
$141$	2.31952	−	1.33917i	0.195339	−	0.112779i
$142$		−	3.75532i		−	0.315139i
$143$	1.46793	+	2.54253i	0.122755	+	0.212617i
$144$	−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
$148$	−1.01455	−	4.19559i	−0.0833952	−	0.344875i
$149$		−	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	−0.570603	+	0.821226i	$0.693290\pi$
$151$	−19.2569	+	11.1180i	−1.56711	+	0.904770i	−0.996504	+	0.0835434i	$0.973376\pi$
$152$	1.79621	−	6.70355i	0.145692	−	0.543730i
$153$	2.15213	−	1.24253i	0.173990	−	0.100453i
$154$	−2.52291	+	2.52291i	−0.203302	+	0.203302i
$155$		0			0
$156$	0.810087	+	0.810087i	0.0648588	+	0.0648588i
$157$	−1.34884	−	5.03393i	−0.107649	−	0.401751i	0.890983	−	0.454036i	$-0.150016\pi$
$157$	−1.34884	−	5.03393i	−0.107649	−	0.401751i	−0.998632	+	0.0522849i	$0.983350\pi$
$158$	−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
$162$		−	0.215880i		−	0.0169611i
$163$	−7.33603	+	12.7064i	−0.574603	+	0.995241i	0.421482	+	0.906837i	$0.361510\pi$
$163$	−7.33603	+	12.7064i	−0.574603	+	0.995241i	−0.996085	+	0.0884042i	$0.971823\pi$
$164$	−4.79925	−	2.77085i	−0.374759	−	0.216367i
$165$		0			0
$166$	−9.74586	−	2.61140i	−0.756426	−	0.202684i
$167$	10.7921	+	18.6925i	0.835120	+	1.44647i	0.893933	+	0.448201i	$0.147935\pi$
$167$	10.7921	+	18.6925i	0.835120	+	1.44647i	−0.0588131	+	0.998269i	$0.518732\pi$
$168$	−2.65813	+	4.60401i	−0.205079	+	0.355207i
$169$	−5.33405	+	9.23885i	−0.410312	+	0.710681i
$170$		0			0
$171$	3.00103	+	3.00103i	0.229495	+	0.229495i
$172$	−3.35897	+	1.93930i	−0.256119	+	0.147871i
$173$	0.213654	+	0.797367i	0.0162438	+	0.0606227i	0.973572	−	0.228380i	$-0.0733429\pi$
$173$	0.213654	+	0.797367i	0.0162438	+	0.0606227i	−0.957328	+	0.289003i	$0.906676\pi$
$174$		−	0.409458i		−	0.0310409i
$175$		0			0
$176$	3.45847	+	1.99675i	0.260692	+	0.150510i
$177$		−	5.75894i		−	0.432869i
$178$	−18.6548	−	4.99855i	−1.39824	−	0.374657i
$179$	16.5150	+	16.5150i	1.23439	+	1.23439i	0.962262	+	0.272124i	$0.0877261\pi$
$179$	16.5150	+	16.5150i	1.23439	+	1.23439i	0.272124	+	0.962262i	$0.412274\pi$
$180$		0			0
$181$	−10.0502	−	17.4074i	−0.747024	−	1.29388i	−0.949243	−	0.314544i	$-0.898148\pi$
$181$	−10.0502	−	17.4074i	−0.747024	−	1.29388i	0.202219	−	0.979340i	$-0.435185\pi$
$182$	2.73738	+	0.733478i	0.202908	+	0.0543690i
$183$	−9.91307	−	5.72332i	−0.732796	−	0.423080i
$184$	−14.0949			−1.03909
$185$		0			0
$186$	−1.70886			−0.125299
$187$	−2.19816	−	1.26911i	−0.160745	−	0.0928063i
$188$	1.73653	+	0.465302i	0.126649	+	0.0339356i
$189$	−4.21633	−	7.30289i	−0.306693	−	0.531207i
$190$		0			0
$191$	−12.5389	−	12.5389i	−0.907285	−	0.907285i	0.0887670	−	0.996052i	$-0.471707\pi$
$191$	−12.5389	−	12.5389i	−0.907285	−	0.907285i	−0.996052	+	0.0887670i	$0.971707\pi$
$192$	8.64623	+	2.31675i	0.623988	+	0.167197i
$193$			17.1943i			1.23767i	0.785519	+	0.618837i	$0.212396\pi$
$193$			17.1943i			1.23767i	−0.785519	+	0.618837i	$0.787604\pi$
$194$	15.1692	+	8.75793i	1.08908	+	0.628783i
$195$		0			0
$196$			3.07337i			0.219526i
$197$	2.30767	+	8.61235i	0.164415	+	0.613604i	0.998114	+	0.0613857i	$0.0195520\pi$
$197$	2.30767	+	8.61235i	0.164415	+	0.613604i	−0.833699	+	0.552219i	$0.813781\pi$
$198$	−3.56009	+	2.05542i	−0.253005	+	0.146072i
$199$	−7.61077	−	7.61077i	−0.539513	−	0.539513i	0.383873	−	0.923386i	$-0.374590\pi$
$199$	−7.61077	−	7.61077i	−0.539513	−	0.539513i	−0.923386	+	0.383873i	$0.874590\pi$
$200$		0			0
$201$	−5.17413	+	8.96186i	−0.364955	+	0.632121i
$202$	−0.435755	+	0.754750i	−0.0306596	+	0.0531041i
$203$	0.278510	+	0.482393i	0.0195476	+	0.0338574i
$204$	−0.956714	−	0.256351i	−0.0669834	−	0.0179481i
$205$		0			0
$206$	−4.70766	−	2.71797i	−0.327998	−	0.189370i
$207$	4.30979	−	7.46478i	0.299551	−	0.518838i
$208$		−	3.17195i		−	0.219935i
$209$	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
$213$	−0.904577	−	3.37593i	−0.0619806	−	0.231315i
$214$	−10.4507	−	10.4507i	−0.714393	−	0.714393i
$215$		0			0
$216$	−11.2341	+	11.2341i	−0.764383	+	0.764383i
$217$	2.01325	−	1.16235i	0.136668	−	0.0789054i
$218$	3.89487	−	14.5358i	0.263794	−	0.984491i
$219$	−2.31297	+	1.33539i	−0.156296	+	0.0902374i
$220$		0			0
$221$			2.01605i			0.135614i
$222$	3.49615	+	6.41401i	0.234646	+	0.430480i
$223$	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
$227$	10.6242	+	18.4016i	0.705151	+	1.22136i	0.966637	+	0.256150i	$0.0824539\pi$
$227$	10.6242	+	18.4016i	0.705151	+	1.22136i	−0.261487	+	0.965207i	$0.584213\pi$
$228$		−	1.69155i		−	0.112026i
$229$	3.48912	−	2.01445i	0.230568	−	0.133118i	−0.380266	−	0.924877i	$-0.624168\pi$
$229$	3.48912	−	2.01445i	0.230568	−	0.133118i	0.610834	+	0.791759i	$0.290834\pi$
$230$		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	−0.629475	−	0.777021i	$-0.716730\pi$
$233$	2.25220	−	2.25220i	0.147547	−	0.147547i	0.777021	+	0.629475i	$0.216730\pi$
$234$	2.82771	+	1.63258i	0.184853	+	0.106725i
$235$		0			0
$236$	2.73338	−	2.73338i	0.177928	−	0.177928i
$237$	−11.6974	−	6.75349i	−0.759827	−	0.438686i
$238$	−2.36661	+	0.634131i	−0.153404	+	0.0411046i
$239$	5.13865	+	19.1777i	0.332392	+	1.24050i	0.906669	+	0.421843i	$0.138617\pi$
$239$	5.13865	+	19.1777i	0.332392	+	1.24050i	−0.574277	+	0.818661i	$0.694717\pi$
$240$		0			0
$241$	2.89066	−	10.7881i	0.186204	−	0.694922i	−0.808166	−	0.588955i	$-0.799539\pi$
$241$	2.89066	−	10.7881i	0.186204	−	0.694922i	0.994370	−	0.105967i	$-0.0337939\pi$
$242$	−7.18510	−	4.14832i	−0.461876	−	0.266664i
$243$	−4.05977	−	15.1513i	−0.260435	−	0.971955i
$244$	−1.98859	−	7.42153i	−0.127307	−	0.475114i
$245$		0			0
$246$	9.05883	+	2.42731i	0.577570	+	0.154759i
$247$	−3.32577	+	0.891138i	−0.211614	+	0.0567017i
$248$	−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	−0.887835	−	0.460162i	$-0.847791\pi$
$251$	−6.77562	+	6.77562i	−0.427673	+	0.427673i	0.460162	+	0.887835i	$0.347791\pi$
$252$	0.564805	−	2.10788i	0.0355794	−	0.132784i
$253$	−8.80391			−0.553497
$254$	1.50393	−	5.61273i	0.0943647	−	0.352174i
$255$		0			0
$256$	7.31671	+	12.6729i	0.457294	+	0.792057i
$257$	−0.176949	+	0.306484i	−0.0110378	+	0.0191180i	−0.871492	−	0.490411i	$-0.836847\pi$
$257$	−0.176949	+	0.306484i	−0.0110378	+	0.0191180i	0.860454	+	0.509529i	$0.170180\pi$
$258$	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
$262$	−0.936403	+	3.49470i	−0.0578512	+	0.215904i
$263$	−19.4898	−	5.22227i	−1.20179	−	0.322019i	−0.398255	−	0.917275i	$-0.630384\pi$
$263$	−19.4898	−	5.22227i	−1.20179	−	0.322019i	−0.803536	+	0.595256i	$0.797051\pi$
$264$	6.04300	+	1.61922i	0.371921	+	0.0996559i
$265$		0			0
$266$	−2.09218	−	3.62377i	−0.128280	−	0.222187i
$267$	−17.9742			−1.10001
$268$	−6.70939	+	1.79777i	−0.409841	+	0.109817i
$269$			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	−0.923425	−	0.383779i	$-0.874622\pi$
$271$	−2.12937	+	3.68817i	−0.129350	+	0.224040i	0.794075	+	0.607820i	$0.207956\pi$
$272$	1.37116	+	2.37492i	0.0831388	+	0.144001i
$273$	2.63751			0.159629
$274$	23.7091	−	6.35282i	1.43232	−	0.383788i
$275$		0			0
$276$	−3.31841	+	0.889165i	−0.199745	+	0.0535214i
$277$	−0.494657	+	0.285590i	−0.0297211	+	0.0171595i	−0.514787	−	0.857318i	$-0.672129\pi$
$277$	−0.494657	+	0.285590i	−0.0297211	+	0.0171595i	0.485066	+	0.874478i	$0.338796\pi$
$278$	17.6592	−	10.1955i	1.05913	−	0.611487i
$279$	2.58716	−	0.693228i	0.154889	−	0.0415025i
$280$		0			0
$281$	30.2609	−	8.10837i	1.80521	−	0.483705i	0.810439	−	0.585823i	$-0.199229\pi$
$281$	30.2609	−	8.10837i	1.80521	−	0.483705i	0.994772	+	0.102118i	$0.0325620\pi$
$282$	−3.04245			−0.181176
$283$	−0.308111	−	0.533664i	−0.0183153	−	0.0317230i	0.856722	−	0.515778i	$-0.172497\pi$
$283$	−0.308111	−	0.533664i	−0.0183153	−	0.0317230i	−0.875038	+	0.484055i	$0.839164\pi$
$284$	1.17298	−	2.03166i	0.0696036	−	0.120557i
$285$		0			0
$286$		−	3.33498i		−	0.197202i
$287$	−12.3235	+	3.30207i	−0.727433	+	0.194915i
$288$	−7.14608			−0.421087
$289$	7.62851	+	13.2130i	0.448736	+	0.777233i
$290$		0			0
$291$	15.7463	+	4.21920i	0.923063	+	0.247334i
$292$	−1.73163	−	0.463988i	−0.101336	−	0.0271528i
$293$	−2.55888	+	9.54988i	−0.149492	+	0.557910i	0.850023	+	0.526746i	$0.176588\pi$
$293$	−2.55888	+	9.54988i	−0.149492	+	0.557910i	−0.999514	+	0.0311641i	$0.990079\pi$
$294$	−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
$298$	−9.59255	+	16.6148i	−0.555682	+	0.962469i
$299$	3.49638	+	6.05591i	0.202201	+	0.350222i
$300$		0			0
$301$	−2.31110	+	8.62515i	−0.133210	+	0.497146i
$302$	25.2589			1.45348
$303$	−0.209929	+	0.783464i	−0.0120601	+	0.0450089i
$304$	−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	0.242326	−	0.970195i	$-0.422090\pi$
$307$	−12.7533	−	12.7533i	−0.727869	−	0.727869i	−0.970195	+	0.242326i	$0.922090\pi$
$308$	−2.15296	+	0.576883i	−0.122676	+	0.0328710i
$309$	−4.88676	−	1.30940i	−0.277998	−	0.0744893i
$310$		0			0
$311$	6.30945	+	23.5472i	0.357776	+	1.33524i	0.876955	+	0.480572i	$0.159571\pi$
$311$	6.30945	+	23.5472i	0.357776	+	1.33524i	−0.519179	+	0.854665i	$0.673762\pi$
$312$	−1.28611	−	4.79983i	−0.0728116	−	0.271737i
$313$	−0.801929	−	0.462994i	−0.0453277	−	0.0261700i	0.477165	−	0.878814i	$-0.341664\pi$
$313$	−0.801929	−	0.462994i	−0.0453277	−	0.0261700i	−0.522493	+	0.852644i	$0.674998\pi$
$314$	−1.53220	+	5.71826i	−0.0864673	+	0.322700i
$315$		0			0
$316$	−2.34653	−	8.75737i	−0.132003	−	0.492640i
$317$	25.5685	−	6.85107i	1.43607	−	0.384794i	0.544916	−	0.838491i	$-0.316562\pi$
$317$	25.5685	−	6.85107i	1.43607	−	0.384794i	0.891156	+	0.453696i	$0.149895\pi$
$318$	−3.49820	−	2.01969i	−0.196169	−	0.113258i
$319$	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
$327$		−	14.0055i		−	0.774507i
$328$	12.0184	+	20.8166i	0.663608	+	1.14940i
$329$	3.58440	−	2.06945i	0.197614	−	0.114093i
$330$		0			0
$331$	−9.40727	+	2.52067i	−0.517070	+	0.138549i	−0.507911	−	0.861410i	$-0.669582\pi$
$331$	−9.40727	+	2.52067i	−0.517070	+	0.138549i	−0.00915915	+	0.999958i	$0.502915\pi$
$332$	−4.45693	−	4.45693i	−0.244606	−	0.244606i
$333$	−7.89503	−	8.29237i	−0.432645	−	0.454419i
$334$		−	24.5185i		−	1.34159i
$335$		0			0
$336$	3.10700	−	1.79382i	0.169501	−	0.0978612i
$337$	5.14226	−	19.1912i	0.280117	−	1.04541i	−0.672217	−	0.740354i	$-0.734658\pi$
$337$	5.14226	−	19.1912i	0.280117	−	1.04541i	0.952334	−	0.305057i	$-0.0986754\pi$
$338$	10.4948	−	6.05919i	0.570843	−	0.329576i
$339$	−10.8915	+	10.8915i	−0.591544	+	0.591544i
$340$		0			0
$341$	−1.93444	−	1.93444i	−0.104756	−	0.104756i
$342$	−1.24778	−	4.65679i	−0.0674724	−	0.251810i
$343$	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
$347$		−	10.3295i		−	0.554517i	−0.960795	−	0.277258i	$-0.910574\pi$
$347$		−	10.3295i		−	0.554517i	0.960795	−	0.277258i	$-0.0894258\pi$
$348$	0.127895	−	0.221521i	0.00685589	−	0.0118748i
$349$	−13.7141	−	7.91783i	−0.734098	−	0.423832i	0.0858212	−	0.996311i	$-0.472649\pi$
$349$	−13.7141	−	7.91783i	−0.734098	−	0.423832i	−0.819920	+	0.572479i	$0.805982\pi$
$350$		0			0
$351$	7.61350	+	2.04003i	0.406378	+	0.108889i
$352$	3.64945	+	6.32103i	0.194516	+	0.336912i
$353$	4.35227	−	7.53835i	0.231648	−	0.401226i	−0.726645	−	0.687013i	$-0.758922\pi$
$353$	4.35227	−	7.53835i	0.231648	−	0.401226i	0.958293	+	0.285787i	$0.0922550\pi$
$354$	−3.27092	+	5.66540i	−0.173847	+	0.301113i
$355$		0			0
$356$	−8.53114	−	8.53114i	−0.452150	−	0.452150i
$357$	−1.97477	+	1.14013i	−0.104516	+	0.0603422i
$358$	−6.86667	−	25.6268i	−0.362915	−	1.35442i
$359$		−	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
$362$			22.8329i			1.20007i
$363$	−7.45845	−	1.99849i	−0.391467	−	0.104893i
$364$	1.25184	+	1.25184i	0.0656144	+	0.0656144i
$365$		0			0
$366$	6.50137	+	11.2607i	0.339832	+	0.588606i
$367$	19.5857	+	5.24797i	1.02236	+	0.273942i	0.730787	−	0.682606i	$-0.239153\pi$
$367$	19.5857	+	5.24797i	1.02236	+	0.273942i	0.291577	+	0.956547i	$0.405820\pi$
$368$	8.23752	+	4.75593i	0.429410	+	0.247920i
$369$	−14.6995			−0.765227
$370$		0			0
$371$	5.49510			0.285291
$372$	−0.924507	−	0.533765i	−0.0479335	−	0.0276744i
$373$	2.29926	+	0.616084i	0.119051	+	0.0318996i	0.317853	−	0.948140i	$-0.397038\pi$
$373$	2.29926	+	0.616084i	0.119051	+	0.0318996i	−0.198802	+	0.980040i	$0.563705\pi$
$374$	1.44163	+	2.49698i	0.0745452	+	0.129116i
$375$		0			0
$376$	−5.51390	−	5.51390i	−0.284358	−	0.284358i
$377$	−0.502910	−	0.134754i	−0.0259012	−	0.00694021i
$378$			9.57903i			0.492692i
$379$	14.3987	+	8.31312i	0.739614	+	0.427016i	0.821929	−	0.569590i	$-0.192898\pi$
$379$	14.3987	+	8.31312i	0.739614	+	0.427016i	−0.0823151	+	0.996606i	$0.526231\pi$
$380$		0			0
$381$		−	5.40795i		−	0.277058i
$382$	5.21350	+	19.4570i	0.266746	+	0.995508i
$383$	7.80032	−	4.50352i	0.398578	−	0.230119i	−0.287292	−	0.957843i	$-0.592755\pi$
$383$	7.80032	−	4.50352i	0.398578	−	0.230119i	0.685870	+	0.727724i	$0.259422\pi$
$384$	−1.51383	−	1.51383i	−0.0772523	−	0.0772523i
$385$		0			0
$386$	9.76590	−	16.9150i	0.497071	−	0.860953i
$387$	−5.14406	+	8.90978i	−0.261487	+	0.452910i
$388$	5.47112	+	9.47625i	0.277754	+	0.481084i
$389$	−11.4603	−	3.07078i	−0.581061	−	0.155695i	−0.0436964	−	0.999045i	$-0.513913\pi$
$389$	−11.4603	−	3.07078i	−0.581061	−	0.155695i	−0.537365	+	0.843350i	$0.680580\pi$
$390$		0			0
$391$	−5.23566	−	3.02281i	−0.264779	−	0.152870i
$392$	6.66530	−	11.5446i	0.336649	−	0.583093i
$393$			3.36720i			0.169853i
$394$	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	0.746725	−	0.665133i	$-0.231625\pi$
$397$	1.62569	+	1.62569i	0.0815913	+	0.0815913i	−0.665133	+	0.746725i	$0.731625\pi$
$398$	3.16444	+	11.8099i	0.158619	+	0.591974i
$399$	−2.75371	−	2.75371i	−0.137858	−	0.137858i
$400$		0			0
$401$	16.9699	−	16.9699i	0.847436	−	0.847436i	−0.142377	−	0.989813i	$-0.545474\pi$
$401$	16.9699	−	16.9699i	0.847436	−	0.847436i	0.989813	+	0.142377i	$0.0454744\pi$
$402$	10.1802	−	5.87753i	0.507741	−	0.293144i
$403$	−0.562392	+	2.09888i	−0.0280147	+	0.104552i
$404$	−0.471496	+	0.272218i	−0.0234578	+	0.0135434i
$405$		0			0
$406$		−	0.632744i		−	0.0314026i
$407$	−3.30304	+	11.2184i	−0.163726	+	0.556074i
$408$	3.03780	+	3.03780i	0.150393	+	0.150393i
$409$	−24.9023	+	6.67256i	−1.23134	+	0.329937i	−0.815102	−	0.579318i	$-0.803319\pi$
$409$	−24.9023	+	6.67256i	−1.23134	+	0.329937i	−0.416240	+	0.909255i	$0.636652\pi$
$410$		0			0
$411$	19.7835	−	11.4220i	0.975850	−	0.563407i
$412$	−1.69793	−	2.94089i	−0.0836508	−	0.144887i
$413$		−	8.89941i		−	0.437911i
$414$	−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	$-0.0278874\pi$
$419$	29.0354	+	16.7636i	1.41847	+	0.818955i	0.422306	+	0.906453i	$0.361221\pi$
$420$		0			0
$421$	−0.954366	+	0.954366i	−0.0465130	+	0.0465130i	−0.729981	−	0.683468i	$-0.760471\pi$
$421$	−0.954366	+	0.954366i	−0.0465130	+	0.0465130i	0.683468	+	0.729981i	$0.260471\pi$
$422$	−1.61656	−	0.933319i	−0.0786927	−	0.0454333i
$423$	4.60620	−	1.23423i	0.223961	−	0.0600102i
$424$	−2.67954	−	10.0002i	−0.130130	−	0.485651i
$425$		0			0
$426$	−1.02755	+	3.83487i	−0.0497849	+	0.185800i
$427$	−15.3189	−	8.84436i	−0.741333	−	0.428009i
$428$	−2.38963	−	8.91821i	−0.115507	−	0.431078i
$429$	−0.803327	−	2.99806i	−0.0387850	−	0.144748i
$430$		0			0
$431$	−12.1677	−	3.26032i	−0.586097	−	0.157044i	−0.0464282	−	0.998922i	$-0.514784\pi$
$431$	−12.1677	−	3.26032i	−0.586097	−	0.157044i	−0.539669	+	0.841877i	$0.681451\pi$
$432$	10.3562	−	2.77494i	0.498263	−	0.133509i
$433$	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
$437$	2.67230	−	9.97314i	0.127833	−	0.477080i
$438$	3.03386			0.144963
$439$	8.00818	−	29.8869i	0.382210	−	1.42643i	−0.460309	−	0.887759i	$-0.652261\pi$
$439$	8.00818	−	29.8869i	0.382210	−	1.42643i	0.842519	−	0.538667i	$-0.181072\pi$
$440$		0			0
$441$	4.07610	+	7.06001i	0.194100	+	0.336191i
$442$	1.14506	−	1.98330i	0.0544650	−	0.0943361i
$443$	−13.3025	+	13.3025i	−0.632023	+	0.632023i	−0.948575	−	0.316552i	$-0.897475\pi$
$443$	−13.3025	+	13.3025i	−0.632023	+	0.632023i	0.316552	+	0.948575i	$0.397475\pi$
$444$	−0.111980	+	4.56207i	−0.00531432	+	0.216506i
$445$		0			0
$446$	−5.74558	−	21.4428i	−0.272061	−	1.01535i
$447$	−4.62129	+	17.2469i	−0.218580	+	0.815750i
$448$	13.3612	+	3.58012i	0.631257	+	0.169145i
$449$	28.3423	+	7.59430i	1.33756	+	0.358397i	0.855527	−	0.517758i	$-0.173233\pi$
$449$	28.3423	+	7.59430i	1.33756	+	0.358397i	0.482029	+	0.876155i	$0.339900\pi$
$450$		0			0
$451$	7.50694	+	13.0024i	0.353488	+	0.612259i
$452$	−10.3389			−0.486300
$453$	22.7070	−	6.08433i	1.06687	−	0.285867i
$454$		−	24.1369i		−	1.13280i
$455$		0			0
$456$	−3.66852	+	6.35407i	−0.171794	+	0.297556i
$457$	−3.20861	−	5.55747i	−0.150092	−	0.259968i	0.781169	−	0.624320i	$-0.214624\pi$
$457$	−3.20861	−	5.55747i	−0.150092	−	0.259968i	−0.931261	+	0.364352i	$0.881290\pi$
$458$	−4.57660			−0.213850
$459$	−6.58228	+	1.76372i	−0.307234	+	0.0823232i
$460$		0			0
$461$	25.3037	−	6.78010i	1.17851	−	0.315781i	0.384175	−	0.923260i	$-0.374486\pi$
$461$	25.3037	−	6.78010i	1.17851	−	0.315781i	0.794335	+	0.607479i	$0.207819\pi$
$462$	3.26669	−	1.88602i	0.151980	−	0.0877458i
$463$	33.0936	−	19.1066i	1.53799	−	0.887960i	0.539035	−	0.842283i	$-0.318789\pi$
$463$	33.0936	−	19.1066i	1.53799	−	0.887960i	0.998956	−	0.0456763i	$-0.0145443\pi$
$464$	−0.684081	+	0.183299i	−0.0317576	+	0.00850944i
$465$		0			0
$466$	−3.49481	+	0.936431i	−0.161894	+	0.0433793i
$467$	−13.5181			−0.625544			−0.312772	−	0.949828i	$-0.601258\pi$
$467$	−13.5181			−0.625544			−0.312772	+	0.949828i	$0.601258\pi$
$468$	1.01988	+	1.76648i	0.0471439	+	0.0816556i
$469$	−7.99569	+	13.8489i	−0.369207	+	0.639485i
$470$		0			0
$471$			5.50964i			0.253871i
$472$	−16.1955	+	4.33956i	−0.745457	+	0.199745i
$473$	10.5081			0.483165
$474$	7.67159	+	13.2876i	0.352368	+	0.610319i
$475$		0			0
$476$	−1.47843	−	0.396144i	−0.0677637	−	0.0181572i
$477$	6.11551	+	1.63865i	0.280010	+	0.0750284i
$478$	5.83723	−	21.7848i	0.266989	−	0.996415i
$479$	0.466920	+	1.74257i	0.0213341	+	0.0796200i	0.975772	−	0.218789i	$-0.0702107\pi$
$479$	0.466920	+	1.74257i	0.0213341	+	0.0796200i	−0.954438	+	0.298409i	$0.903544\pi$
$480$		0			0
$481$	9.02850	−	2.18321i	0.411664	−	0.0995457i
$482$	−8.97105	+	8.97105i	−0.408620	+	0.408620i
$483$	−3.95460	+	6.84957i	−0.179941	+	0.311666i
$484$	−2.59147	−	4.48856i	−0.117794	−	0.204026i
$485$		0			0
$486$	−4.61168	+	17.2110i	−0.209190	+	0.780708i
$487$	−4.70678			−0.213285			−0.106642	−	0.994297i	$-0.534010\pi$
$487$	−4.70678			−0.213285			−0.106642	+	0.994297i	$0.534010\pi$
$488$	−8.62544	+	32.1906i	−0.390455	+	1.45720i
$489$	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
$493$	0.434793	−	0.116502i	0.0195821	−	0.00524700i
$494$	3.77789	+	1.01228i	0.169975	+	0.0455448i
$495$		0			0
$496$	0.764990	+	2.85498i	0.0343491	+	0.128192i
$497$	−1.39786	−	5.21689i	−0.0627026	−	0.234009i
$498$	9.23777	+	5.33343i	0.413954	+	0.238997i
$499$	4.04934	−	15.1123i	0.181273	−	0.676521i	−0.814124	−	0.580691i	$-0.802783\pi$
$499$	4.04934	−	15.1123i	0.181273	−	0.676521i	0.995398	−	0.0958307i	$-0.0305507\pi$
$500$		0			0
$501$	−5.90600	−	22.0415i	−0.263860	−	0.984741i
$502$	10.5139	−	2.81720i	0.469260	−	0.125738i
$503$	−8.84970	−	5.10938i	−0.394589	−	0.227816i	0.289558	−	0.957161i	$-0.406492\pi$
$503$	−8.84970	−	5.10938i	−0.394589	−	0.227816i	−0.684146	+	0.729345i	$0.739825\pi$
$504$	−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	$-0.784665\pi$
$509$	3.43610	−	5.95149i	0.152302	−	0.263795i	0.932073	+	0.362269i	$0.117998\pi$
$510$		0			0
$511$	−3.57427	+	2.06361i	−0.158117	+	0.0912886i
$512$		−	20.6728i		−	0.913618i
$513$	−5.81902	−	10.0788i	−0.256916	−	0.444991i
$514$	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
$518$	5.40267	+	9.91170i	0.237379	+	0.435495i
$519$		−	0.872719i		−	0.0383081i
$520$		0			0
$521$	−19.6337	+	11.3355i	−0.860166	+	0.496617i	−0.864068	−	0.503375i	$-0.832091\pi$
$521$	−19.6337	+	11.3355i	−0.860166	+	0.496617i	0.00390182	+	0.999992i	$0.498758\pi$
$522$	0.188685	−	0.704182i	0.00825852	−	0.0308212i
$523$	−7.34396	+	4.24004i	−0.321129	+	0.185404i	−0.651896	−	0.758309i	$-0.726026\pi$
$523$	−7.34396	+	4.24004i	−0.321129	+	0.185404i	0.330767	+	0.943713i	$0.392693\pi$
$524$	−1.59818	+	1.59818i	−0.0698169	+	0.0698169i
$525$		0			0
$526$	16.2071	+	16.2071i	0.706663	+	0.706663i
$527$	−0.486218	−	1.81459i	−0.0211800	−	0.0790448i
$528$	−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
$532$		−	2.61399i		−	0.113331i
$533$	5.96260	−	10.3275i	0.258269	−	0.447335i
$534$	17.6823	+	10.2089i	0.765187	+	0.441781i
$535$		0			0
$536$	29.1017	+	7.79777i	1.25700	+	0.336813i
$537$	−12.3459	−	21.3837i	−0.532765	−	0.922776i
$538$	3.69142	−	6.39373i	0.159148	−	0.275653i
$539$	4.16327	−	7.21099i	0.179325	−	0.310599i
$540$		0			0
$541$	−9.87420	−	9.87420i	−0.424525	−	0.424525i	0.462233	−	0.886758i	$-0.347048\pi$
$541$	−9.87420	−	9.87420i	−0.424525	−	0.424525i	−0.886758	+	0.462233i	$0.847048\pi$
$542$	4.18956	−	2.41884i	0.179957	−	0.103898i
$543$	5.49997	+	20.5262i	0.236026	+	0.880862i
$544$			5.01213i			0.214893i
$545$		0			0
$546$	−2.59466	−	1.49803i	−0.111041	−	0.0641098i
$547$			16.2777i			0.695983i	0.937498	+	0.347992i	$0.113136\pi$
$547$			16.2777i			0.695983i	−0.937498	+	0.347992i	$0.886864\pi$
$548$	14.8112	+	3.96864i	0.632701	+	0.169532i
$549$	−14.4110	−	14.4110i	−0.615047	−	0.615047i
$550$		0			0
$551$	0.384376	+	0.665758i	0.0163750	+	0.0283623i
$552$	14.3935	+	3.85672i	0.612626	+	0.164153i
$553$	−18.0762	−	10.4363i	−0.768679	−	0.443797i
$554$	0.648830			0.0275661
$555$		0			0
$556$	12.7384			0.540227
$557$	−11.0303	−	6.36833i	−0.467368	−	0.269835i	0.247769	−	0.968819i	$-0.420302\pi$
$557$	−11.0303	−	6.36833i	−0.467368	−	0.269835i	−0.715137	+	0.698984i	$0.753636\pi$
$558$	−2.93887	−	0.787469i	−0.124412	−	0.0333362i
$559$	−4.17320	−	7.22819i	−0.176508	−	0.305720i
$560$		0			0
$561$	1.89746	+	1.89746i	0.0801109	+	0.0801109i
$562$	−34.3747	−	9.21066i	−1.45001	−	0.388528i
$563$			9.88042i			0.416410i	0.978085	+	0.208205i	$0.0667622\pi$
$563$			9.88042i			0.416410i	−0.978085	+	0.208205i	$0.933238\pi$
$564$	−1.64600	−	0.950317i	−0.0693090	−	0.0400156i
$565$		0			0
$566$			0.699994i			0.0294229i
$567$	−0.0803582	−	0.299901i	−0.00337473	−	0.0125947i
$568$	−8.81225	+	5.08776i	−0.369754	+	0.213478i
$569$	−28.2430	−	28.2430i	−1.18401	−	1.18401i	−0.978697	−	0.205312i	$-0.934179\pi$
$569$	−28.2430	−	28.2430i	−1.18401	−	1.18401i	−0.205312	−	0.978697i	$-0.565821\pi$
$570$		0			0
$571$	−18.9395	+	32.8041i	−0.792592	+	1.37281i	0.131765	+	0.991281i	$0.457936\pi$
$571$	−18.9395	+	32.8041i	−0.792592	+	1.37281i	−0.924357	+	0.381529i	$0.875398\pi$
$572$	1.04169	−	1.80426i	0.0435552	−	0.0754398i
$573$	9.37358	+	16.2355i	0.391587	+	0.678249i
$574$	13.9988	+	3.75097i	0.584299	+	0.156562i
$575$		0			0
$576$	13.8021	+	7.96865i	0.575088	+	0.332027i
$577$	13.6089	−	23.5713i	0.566547	−	0.981288i	−0.430357	−	0.902659i	$-0.641612\pi$
$577$	13.6089	−	23.5713i	0.566547	−	0.981288i	0.996904	−	0.0786291i	$-0.0250543\pi$
$578$		−	17.3311i		−	0.720880i
$579$	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
$583$	−1.67369	−	6.24629i	−0.0693171	−	0.258695i
$584$	5.49833	+	5.49833i	0.227522	+	0.227522i
$585$		0			0
$586$	7.94139	−	7.94139i	0.328056	−	0.328056i
$587$	−10.5112	+	6.06864i	−0.433843	+	0.250480i	−0.700983	−	0.713178i	$-0.747255\pi$
$587$	−10.5112	+	6.06864i	−0.433843	+	0.250480i	0.267139	+	0.963658i	$0.413922\pi$
$588$	0.840951	−	3.13847i	0.0346802	−	0.129428i
$589$	2.77851	−	1.60418i	0.114487	−	0.0660989i
$590$		0			0
$591$		−	9.42622i		−	0.387743i
$592$	9.15077	−	8.71231i	0.376095	−	0.358074i
$593$	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
$597$	5.68949	+	9.85449i	0.232855	+	0.403317i
$598$		−	7.94340i		−	0.324830i
$599$	2.59862	−	1.50032i	0.106177	−	0.0613013i	−0.445971	−	0.895047i	$-0.647142\pi$
$599$	2.59862	−	1.50032i	0.106177	−	0.0613013i	0.552148	+	0.833746i	$0.313808\pi$
$600$		0			0
$601$	7.76062	−	13.4418i	0.316562	−	0.548302i	−0.663206	−	0.748437i	$-0.730805\pi$
$601$	7.76062	−	13.4418i	0.316562	−	0.548302i	0.979768	+	0.200135i	$0.0641380\pi$
$602$	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
$607$	32.0701	+	18.5157i	1.30169	+	0.751529i	0.980693	−	0.195552i	$-0.0626499\pi$
$607$	32.0701	+	18.5157i	1.30169	+	0.751529i	0.320994	+	0.947081i	$0.395983\pi$
$608$	−8.26824	+	2.21547i	−0.335322	+	0.0898492i
$609$	−0.152415	−	0.568820i	−0.00617616	−	0.0230497i
$610$		0			0
$611$	−1.00129	+	3.73685i	−0.0405077	+	0.151177i
$612$	−1.52722	−	0.881739i	−0.0617341	−	0.0356422i
$613$	−4.51123	−	16.8361i	−0.182207	−	0.680005i	−0.995211	−	0.0977478i	$-0.968836\pi$
$613$	−4.51123	−	16.8361i	−0.182207	−	0.680005i	0.813004	−	0.582258i	$-0.197831\pi$
$614$	5.30262	+	19.7897i	0.213996	+	0.798645i
$615$		0			0
$616$	9.33837	+	2.50221i	0.376254	+	0.100817i
$617$	23.0967	−	6.18875i	0.929839	−	0.249150i	0.238053	−	0.971252i	$-0.423491\pi$
$617$	23.0967	−	6.18875i	0.929839	−	0.249150i	0.691786	+	0.722103i	$0.256824\pi$
$618$	4.06368	+	4.06368i	0.163465	+	0.163465i
$619$	6.37727			0.256324			0.128162	−	0.991753i	$-0.459092\pi$
$619$	6.37727			0.256324			0.128162	+	0.991753i	$0.459092\pi$
$620$		0			0
$621$	−16.7134	+	16.7134i	−0.670686	+	0.670686i
$622$	7.16718	−	26.7483i	0.287378	−	1.07251i
$623$	−27.7760			−1.11282
$624$	−0.867925	+	3.23914i	−0.0347448	+	0.129669i
$625$		0			0
$626$	0.525936	+	0.910947i	0.0210206	+	0.0364088i
$627$	−2.29142	+	3.96886i	−0.0915107	+	0.158501i
$628$	−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	−0.978288	−	0.207249i	$-0.933549\pi$
$631$	−5.89535	−	22.0017i	−0.234690	−	0.875876i	0.743598	−	0.668627i	$-0.233118\pi$
$632$	−10.1780	+	37.9847i	−0.404858	+	1.51095i
$633$	−1.67806	−	0.449634i	−0.0666968	−	0.0178714i
$634$	−29.0445	−	7.78244i	−1.15350	−	0.309080i
$635$		0			0
$636$	−1.26171	−	2.18534i	−0.0500299	−	0.0866544i
$637$	−6.61359			−0.262040
$638$	−0.719241	+	0.192720i	−0.0284750	+	0.00762986i
$639$		−	6.22273i		−	0.246168i
$640$		0			0
$641$	−11.7520	+	20.3550i	−0.464175	+	0.803976i	−0.999164	−	0.0408839i	$-0.986983\pi$
$641$	−11.7520	+	20.3550i	−0.464175	+	0.803976i	0.534988	+	0.844859i	$0.320316\pi$
$642$	7.81249	+	13.5316i	0.308334	+	0.534051i
$643$	−24.3699			−0.961055			−0.480527	−	0.876980i	$-0.659555\pi$
$643$	−24.3699			−0.961055			−0.480527	+	0.876980i	$0.659555\pi$
$644$	−5.12800	+	1.37404i	−0.202072	+	0.0541449i
$645$		0			0
$646$	−3.26619	+	0.875173i	−0.128507	+	0.0344332i
$647$	−35.9680	+	20.7661i	−1.41405	+	0.816400i	−0.995767	−	0.0919177i	$-0.970700\pi$
$647$	−35.9680	+	20.7661i	−1.41405	+	0.816400i	−0.418280	+	0.908318i	$0.637367\pi$
$648$	−0.506586	+	0.292478i	−0.0199006	+	0.0114896i
$649$	−10.1160	+	2.71057i	−0.397087	+	0.106399i
$650$		0			0
$651$	−2.37394	+	0.636096i	−0.0930422	+	0.0249306i
$652$	10.4117			0.407755
$653$	−0.370684	−	0.642043i	−0.0145060	−	0.0251251i	0.858681	−	0.512510i	$-0.171284\pi$
$653$	−0.370684	−	0.642043i	−0.0145060	−	0.0251251i	−0.873187	+	0.487385i	$0.837951\pi$
$654$	−7.95475	+	13.7780i	−0.311055	+	0.538763i
$655$		0			0
$656$		−	16.2212i		−	0.633331i
$657$	−4.59319	+	1.23074i	−0.179197	+	0.0480158i
$658$	−4.70157			−0.183286
$659$	−15.9185	−	27.5717i	−0.620098	−	1.07404i	−0.989467	−	0.144759i	$-0.953759\pi$
$659$	−15.9185	−	27.5717i	−0.620098	−	1.07404i	0.369369	−	0.929283i	$-0.379574\pi$
$660$		0			0
$661$	46.6955	+	12.5120i	1.81624	+	0.486661i	0.996312	−	0.0858000i	$-0.0273446\pi$
$661$	46.6955	+	12.5120i	1.81624	+	0.486661i	0.819932	+	0.572461i	$0.194011\pi$
$662$	10.6861	+	2.86334i	0.415329	+	0.111287i
$663$	0.551642	−	2.05876i	0.0214240	−	0.0799555i
$664$	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
$668$	7.65841	−	13.2648i	0.296313	−	0.513229i
$669$	−10.3302	−	17.8925i	−0.399390	−	0.691764i
$670$		0			0
$671$	−5.38760	+	20.1068i	−0.207986	+	0.776214i
$672$	6.55714			0.252947
$673$	−4.43056	+	16.5351i	−0.170785	+	0.637380i	0.826446	+	0.563016i	$0.190359\pi$
$673$	−4.43056	+	16.5351i	−0.170785	+	0.637380i	−0.997231	+	0.0743635i	$0.976307\pi$
$674$	−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	$0.0716902\pi$
$677$	31.1728	+	31.1728i	1.19807	+	1.19807i	0.223322	+	0.974745i	$0.428310\pi$
$678$	16.9006	−	4.52851i	0.649064	−	0.173916i
$679$	24.3331	+	6.52002i	0.933817	+	0.250216i
$680$		0			0
$681$	−5.81408	−	21.6984i	−0.222796	−	0.831486i
$682$	0.804309	+	3.00172i	0.0307986	+	0.114942i
$683$	−31.9387	−	18.4398i	−1.22210	−	0.705580i	−0.256736	−	0.966482i	$-0.582647\pi$
$683$	−31.9387	−	18.4398i	−1.22210	−	0.705580i	−0.965365	+	0.260901i	$0.915980\pi$
$684$	0.779496	−	2.90912i	0.0298048	−	0.111233i
$685$		0			0
$686$	−5.44250	−	20.3117i	−0.207796	−	0.775503i
$687$	−4.11424	+	1.10241i	−0.156968	+	0.0420595i
$688$	−9.83210	−	5.67657i	−0.374845	−	0.216417i
$689$	−3.63192	+	3.63192i	−0.138365	+	0.138365i
$690$		0			0
$691$	−0.520289	−	0.300389i	−0.0197927	−	0.0114273i	0.490071	−	0.871683i	$-0.336971\pi$
$691$	−0.520289	−	0.300389i	−0.0197927	−	0.0114273i	−0.509864	+	0.860255i	$0.670304\pi$
$692$	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
$697$			10.3100i			0.390518i
$698$	8.99422	+	15.5785i	0.340436	+	0.589653i
$699$	−2.91617	+	1.68365i	−0.110300	+	0.0636816i
$700$		0			0
$701$	−6.15868	+	1.65021i	−0.232610	+	0.0623277i	−0.373241	−	0.927734i	$-0.621754\pi$
$701$	−6.15868	+	1.65021i	−0.232610	+	0.0623277i	0.140631	+	0.990062i	$0.455087\pi$
$702$	−6.33115	−	6.33115i	−0.238954	−	0.238954i
$703$	−11.7057	−	7.14687i	−0.441487	−	0.269549i
$704$		−	16.2781i		−	0.613505i
$705$		0			0
$706$	−8.56315	+	4.94394i	−0.322278	+	0.186067i
$707$	−0.324407	+	1.21070i	−0.0122006	+	0.0455332i
$708$	−3.53920	+	2.04336i	−0.133011	+	0.0767941i
$709$	0.102970	−	0.102970i	0.00386711	−	0.00386711i	−0.705171	−	0.709038i	$-0.749130\pi$
$709$	0.102970	−	0.102970i	0.00386711	−	0.00386711i	0.709038	+	0.705171i	$0.249130\pi$
$710$		0			0
$711$	−17.0049	−	17.0049i	−0.637735	−	0.637735i
$712$	13.5442	+	50.5477i	0.507591	+	1.89436i
$713$	−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
$717$		−	20.9900i		−	0.783887i
$718$	−5.60003	+	9.69954i	−0.208991	+	0.361984i
$719$	15.6399	+	9.02972i	0.583271	+	0.336752i	0.762432	−	0.647068i	$-0.224005\pi$
$719$	15.6399	+	9.02972i	0.583271	+	0.336752i	−0.179161	+	0.983820i	$0.557338\pi$
$720$		0			0
$721$	−7.55161	−	2.02345i	−0.281237	−	0.0753571i
$722$	7.90402	+	13.6902i	0.294157	+	0.509495i
$723$	−5.90379	+	10.2257i	−0.219564	+	0.380297i
$724$	−7.13191	+	12.3528i	−0.265055	+	0.459089i
$725$		0			0
$726$	6.20222	+	6.20222i	0.230186	+	0.230186i
$727$	16.9712	−	9.79831i	0.629426	−	0.363399i	−0.151104	−	0.988518i	$-0.548283\pi$
$727$	16.9712	−	9.79831i	0.629426	−	0.363399i	0.780530	+	0.625119i	$0.214949\pi$
$728$	−1.98745	−	7.41727i	−0.0736599	−	0.274902i
$729$			16.0130i			0.593073i
$730$		0			0
$731$	6.24916	+	3.60795i	0.231134	+	0.133445i
$732$			8.12287i			0.300230i
$733$	−29.4663	−	7.89548i	−1.08836	−	0.291626i	−0.330346	−	0.943860i	$-0.607165\pi$
$733$	−29.4663	−	7.89548i	−1.08836	−	0.291626i	−0.758018	+	0.652234i	$0.773832\pi$
$734$	−16.2868	−	16.2868i	−0.601158	−	0.601158i
$735$		0			0
$736$	8.69240	+	15.0557i	0.320406	+	0.554960i
$737$	18.1774	+	4.87063i	0.669574	+	0.179412i
$738$	14.4608	+	8.34892i	0.532308	+	0.307328i
$739$	−52.1459			−1.91822			−0.959110	−	0.283035i	$-0.908659\pi$
$739$	−52.1459			−1.91822			−0.959110	+	0.283035i	$0.908659\pi$
$740$		0			0
$741$	3.64006			0.133721
$742$	−5.40584	−	3.12106i	−0.198455	−	0.114578i
$743$	25.3141	+	6.78290i	0.928686	+	0.248841i	0.691294	−	0.722573i	$-0.257041\pi$
$743$	25.3141	+	6.78290i	0.928686	+	0.248841i	0.237392	+	0.971414i	$0.423708\pi$
$744$	2.31518	+	4.01001i	0.0848787	+	0.147014i
$745$		0			0
$746$	−1.91199	−	1.91199i	−0.0700030	−	0.0700030i
$747$	−16.1494	−	4.32721i	−0.590874	−	0.158324i
$748$			1.80119i			0.0658581i
$749$	−18.4082	−	10.6280i	−0.672621	−	0.388338i
$750$		0			0
$751$			53.1233i			1.93850i	0.246087	+	0.969248i	$0.420855\pi$
$751$			53.1233i			1.93850i	−0.246087	+	0.969248i	$0.579145\pi$
$752$	1.36199	+	5.08302i	0.0496667	+	0.185359i
$753$	8.77313	−	5.06517i	0.319711	−	0.184585i
$754$	0.418205	+	0.418205i	0.0152301	+	0.0152301i
$755$		0			0
$756$	−2.99203	+	5.18235i	−0.108819	+	0.188480i
$757$	7.47044	−	12.9392i	0.271518	−	0.470282i	−0.697733	−	0.716358i	$-0.745808\pi$
$757$	7.47044	−	12.9392i	0.271518	−	0.470282i	0.969251	+	0.246075i	$0.0791411\pi$
$758$	−9.44324	−	16.3562i	−0.342994	−	0.594083i
$759$	8.99041	+	2.40897i	0.326331	+	0.0874402i
$760$		0			0
$761$	−33.1931	−	19.1641i	−1.20325	−	0.694697i	−0.241974	−	0.970283i	$-0.577795\pi$
$761$	−33.1931	−	19.1641i	−1.20325	−	0.694697i	−0.961277	+	0.275586i	$0.911128\pi$
$762$	−3.07157	+	5.32011i	−0.111271	+	0.192727i
$763$		−	21.6430i		−	0.783530i
$764$	−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
$768$	−4.00407	−	14.9434i	−0.144485	−	0.539224i
$769$	22.4800	+	22.4800i	0.810650	+	0.810650i	0.984731	−	0.174081i	$-0.0556955\pi$
$769$	22.4800	+	22.4800i	0.810650	+	0.810650i	−0.174081	+	0.984731i	$0.555696\pi$
$770$		0			0
$771$	0.264559	−	0.264559i	0.00952786	−	0.00952786i
$772$	10.5669	−	6.10080i	0.380311	−	0.219573i
$773$	−7.93815	+	29.6256i	−0.285515	+	1.06556i	0.662947	+	0.748667i	$0.269306\pi$
$773$	−7.93815	+	29.6256i	−0.285515	+	1.06556i	−0.948462	+	0.316891i	$0.897361\pi$
$774$	10.1210	−	5.84337i	0.363792	−	0.210036i
$775$		0			0
$776$		−	47.4615i		−	1.70377i
$777$	7.24437	+	7.60896i	0.259890	+	0.272970i
$778$	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
$782$	3.43375	+	5.94742i	0.122790	+	0.212679i
$783$		−	1.75986i		−	0.0628922i
$784$	−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
$792$	9.64653	+	5.56943i	0.342775	+	0.197901i
$793$	15.9704	−	4.27926i	0.567126	−	0.151961i
$794$	−0.675939	−	2.52264i	−0.0239882	−	0.0895251i
$795$		0			0
$796$	−1.97684	+	7.37767i	−0.0700672	+	0.261494i
$797$	−24.4236	−	14.1009i	−0.865127	−	0.499481i	0.000599033	−	1.00000i	$-0.499809\pi$
$797$	−24.4236	−	14.1009i	−0.865127	−	0.499481i	−0.865726	+	0.500519i	$0.833143\pi$
$798$	1.14495	+	4.27301i	0.0405307	+	0.151263i
$799$	−0.865665	−	3.23070i	−0.0306250	−	0.114294i
$800$		0			0
$801$	−30.9119	−	8.28283i	−1.09222	−	0.292659i
$802$	−26.3327	+	7.05582i	−0.929839	+	0.249150i
$803$	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
$807$	1.77837	−	6.63697i	0.0626017	−	0.233633i
$808$	2.36147			0.0830763
$809$	−0.812619	+	3.03273i	−0.0285701	+	0.106625i	−0.978739	−	0.205112i	$-0.934244\pi$
$809$	−0.812619	+	3.03273i	−0.0285701	+	0.106625i	0.950168	+	0.311737i	$0.100911\pi$
$810$		0			0
$811$	−10.5095	−	18.2030i	−0.369038	−	0.639192i	0.620377	−	0.784303i	$-0.286979\pi$
$811$	−10.5095	−	18.2030i	−0.369038	−	0.639192i	−0.989415	+	0.145111i	$0.953646\pi$
$812$	0.197639	−	0.342321i	0.00693577	−	0.0120131i
$813$	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
$817$	−3.18959	+	11.9037i	−0.111590	+	0.416458i
$818$	28.2877	+	7.57966i	0.989056	+	0.265017i
$819$	4.53596	+	1.21541i	0.158499	+	0.0424697i
$820$		0			0
$821$	2.11926	+	3.67067i	0.0739627	+	0.128107i	0.900635	−	0.434577i	$-0.143102\pi$
$821$	2.11926	+	3.67067i	0.0739627	+	0.128107i	−0.826672	+	0.562684i	$0.809769\pi$
$822$	−25.9496			−0.905096
$823$	−0.912687	+	0.244554i	−0.0318143	+	0.00852461i	−0.274691	−	0.961533i	$-0.588576\pi$
$823$	−0.912687	+	0.244554i	−0.0318143	+	0.00852461i	0.242877	+	0.970057i	$0.421909\pi$
$824$			14.7294i			0.513122i
$825$		0			0
$826$	−5.05462	+	8.75486i	−0.175873	+	0.304621i
$827$	−11.9529	−	20.7030i	−0.415642	−	0.719912i	0.579854	−	0.814720i	$-0.303110\pi$
$827$	−11.9529	−	20.7030i	−0.415642	−	0.719912i	−0.995496	+	0.0948080i	$0.969776\pi$
$828$	−6.11671			−0.212570
$829$	2.51032	−	0.672639i	0.0871871	−	0.0233617i	−0.214962	−	0.976622i	$-0.568963\pi$
$829$	2.51032	−	0.672639i	0.0871871	−	0.0233617i	0.302149	+	0.953261i	$0.402296\pi$
$830$		0			0
$831$	0.583280	−	0.156289i	0.0202338	−	0.00542162i
$832$	−11.1972	+	6.46469i	−0.388192	+	0.224123i
$833$	4.95177	−	2.85890i	0.171569	−	0.0990551i
$834$	−20.8230	+	5.57951i	−0.721041	+	0.193202i
$835$		0			0
$836$	−2.97133	+	0.796165i	−0.102766	+	0.0275360i
$837$	−7.34470			−0.253870
$838$	−19.0425	−	32.9826i	−0.657812	−	1.13936i
$839$	18.2196	−	31.5573i	0.629012	−	1.08948i	−0.358739	−	0.933438i	$-0.616793\pi$
$839$	18.2196	−	31.5573i	0.629012	−	1.08948i	0.987750	−	0.156042i	$-0.0498736\pi$
$840$		0			0
$841$		−	28.8838i		−	0.995991i
$842$	1.48092	−	0.396811i	0.0510358	−	0.0136750i
$843$	−33.1205			−1.14073
$844$	−0.583049	−	1.00987i	−0.0200694	−	0.0347611i
$845$		0			0
$846$	−5.23239	−	1.40201i	−0.179893	−	0.0482022i
$847$	−11.5257	−	3.08830i	−0.396028	−	0.106115i
$848$	−1.80827	+	6.74857i	−0.0620964	+	0.231747i
$849$	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
$853$	−12.9804	+	22.4827i	−0.444440	+	0.769792i	−0.998013	−	0.0630083i	$-0.979931\pi$
$853$	−12.9804	+	22.4827i	−0.444440	+	0.769792i	0.553573	+	0.832800i	$0.313264\pi$
$854$	10.0467	+	17.4014i	0.343791	+	0.595464i
$855$		0			0
$856$	−10.3649	+	38.6824i	−0.354265	+	1.32214i
$857$	−40.2792			−1.37591			−0.687955	−	0.725753i	$-0.741491\pi$
$857$	−40.2792			−1.37591			−0.687955	+	0.725753i	$0.741491\pi$
$858$	−0.912535	+	3.40563i	−0.0311534	+	0.116266i
$859$	−3.69657	+	3.69657i	−0.126125	+	0.126125i	−0.767352	−	0.641226i	$-0.778426\pi$
$859$	−3.69657	+	3.69657i	−0.126125	+	0.126125i	0.641226	+	0.767352i	$0.278426\pi$
$860$		0			0
$861$	13.4881			0.459672
$862$	10.1183	+	10.1183i	0.344630	+	0.344630i
$863$	−6.85933	+	1.83795i	−0.233494	+	0.0625646i	−0.373669	−	0.927562i	$-0.621900\pi$
$863$	−6.85933	+	1.83795i	−0.233494	+	0.0625646i	0.140174	+	0.990127i	$0.455234\pi$
$864$	18.9280	+	5.07175i	0.643944	+	0.172544i
$865$		0			0
$866$	−5.70964	−	21.3087i	−0.194021	−	0.724098i
$867$	−4.17471	−	15.5802i	−0.141780	−	0.529132i
$868$	−1.42866	−	0.824838i	−0.0484919	−	0.0279968i
$869$	−6.35735	+	23.7259i	−0.215658	+	0.804847i
$870$		0			0
$871$	−3.86864	−	14.4380i	−0.131084	−	0.489212i
$872$	−39.3867	+	10.5536i	−1.33380	+	0.357391i
$873$	25.1360	+	14.5123i	0.850726	+	0.491167i
$874$	−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	−0.562541	−	0.826769i	$-0.690176\pi$
$881$	−3.79357	+	2.19022i	−0.127809	+	0.0737904i	0.434733	+	0.900560i	$0.356843\pi$
$882$		−	9.26045i		−	0.311815i
$883$	−29.2518	−	50.6657i	−0.984402	−	1.70504i	−0.644562	−	0.764552i	$-0.722960\pi$
$883$	−29.2518	−	50.6657i	−0.984402	−	1.70504i	−0.339840	−	0.940483i	$-0.610373\pi$
$884$	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	0.748351	−	0.663302i	$-0.230846\pi$
$887$	2.53298	+	2.53298i	0.0850491	+	0.0850491i	−0.663302	+	0.748351i	$0.730846\pi$
$888$	10.3145	−	16.8939i	0.346133	−	0.566921i
$889$		−	8.35702i		−	0.280286i
$890$		0			0
$891$	−0.316423	+	0.182687i	−0.0106006	+	0.00612024i
$892$	3.58929	−	13.3954i	0.120178	−	0.448511i
$893$	4.94688	−	2.85608i	0.165541	−	0.0955752i
$894$	14.3420	−	14.3420i	0.479668	−	0.479668i
$895$		0			0
$896$	−2.33935	−	2.33935i	−0.0781523	−	0.0781523i
$897$	−1.91340	−	7.14090i	−0.0638865	−	0.238428i
$898$	−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
$902$		−	17.0549i		−	0.567867i
$903$	4.72012	−	8.17549i	0.157076	−	0.272063i
$904$	38.8364	+	22.4222i	1.29168	+	0.745752i
$905$		0			0
$906$	−25.7939	−	6.91146i	−0.856946	−	0.229618i
$907$	−6.14134	−	10.6371i	−0.203920	−	0.353200i	0.745868	−	0.666094i	$-0.232035\pi$
$907$	−6.14134	−	10.6371i	−0.203920	−	0.353200i	−0.949788	+	0.312894i	$0.898702\pi$
$908$	7.53922	−	13.0583i	0.250198	−	0.433355i
$909$	−0.722067	+	1.25066i	−0.0239495	+	0.0414817i
$910$		0			0
$911$	−8.69751	−	8.69751i	−0.288161	−	0.288161i	0.548191	−	0.836353i	$-0.315317\pi$
$911$	−8.69751	−	8.69751i	−0.288161	−	0.288161i	−0.836353	+	0.548191i	$0.815317\pi$
$912$	4.28801	−	2.47568i	0.141990	−	0.0819781i
$913$	4.41974	+	16.4947i	0.146272	+	0.545895i
$914$			7.28961i			0.241119i
$915$		0			0
$916$	−2.47599	−	1.42951i	−0.0818089	−	0.0472324i
$917$			5.20341i			0.171832i
$918$	7.47710	+	2.00348i	0.246781	+	0.0661248i
$919$	−25.2847	−	25.2847i	−0.834065	−	0.834065i	0.154005	−	0.988070i	$-0.450783\pi$
$919$	−25.2847	−	25.2847i	−0.834065	−	0.834065i	−0.988070	+	0.154005i	$0.950783\pi$
$920$		0			0
$921$	9.53382	+	16.5131i	0.314150	+	0.544124i
$922$	−28.7436	−	7.70182i	−0.946620	−	0.253646i
$923$	4.37194	+	2.52414i	0.143904	+	0.0830832i
$924$	2.35642			0.0775204
$925$		0			0
$926$	−43.4081			−1.42648
$927$	−7.80081	−	4.50380i	−0.256212	−	0.147924i
$928$	−1.25029	−	0.335015i	−0.0410428	−	0.0109974i
$929$	6.26098	+	10.8443i	0.205416	+	0.355791i	0.950265	−	0.311442i	$-0.100812\pi$
$929$	6.26098	+	10.8443i	0.205416	+	0.355791i	−0.744849	+	0.667233i	$0.767479\pi$
$930$		0			0
$931$	6.90497	+	6.90497i	0.226301	+	0.226301i
$932$	−2.18322	−	0.584992i	−0.0715138	−	0.0191621i
$933$		−	25.7724i		−	0.843751i
$934$	13.2985	+	7.67791i	0.435141	+	0.251229i
$935$		0			0
$936$		−	8.84736i		−	0.289185i
$937$	3.17302	+	11.8419i	0.103658	+	0.386857i	0.998189	−	0.0601478i	$-0.0191572\pi$
$937$	3.17302	+	11.8419i	0.103658	+	0.386857i	−0.894531	+	0.447005i	$0.852491\pi$
$938$	15.7316	−	9.08266i	0.513656	−	0.296559i
$939$	0.692230	+	0.692230i	0.0225901	+	0.0225901i
$940$		0			0
$941$	−13.7869	+	23.8796i	−0.449440	+	0.778452i	−0.998350	−	0.0574293i	$-0.981710\pi$
$941$	−13.7869	+	23.8796i	−0.449440	+	0.778452i	0.548910	+	0.835881i	$0.315043\pi$
$942$	3.12932	−	5.42015i	0.101959	−	0.176598i
$943$	17.8803	+	30.9696i	0.582264	+	1.00851i
$944$	10.9294	+	2.92853i	0.355723	+	0.0953157i
$945$		0			0
$946$	−10.3375	−	5.96833i	−0.336100	−	0.194047i
$947$	−4.48370	+	7.76600i	−0.145701	+	0.252361i	−0.929634	−	0.368484i	$-0.879877\pi$
$947$	−4.48370	+	7.76600i	−0.145701	+	0.252361i	0.783933	+	0.620845i	$0.213210\pi$
$948$			9.58495i			0.311305i
$949$	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
$953$	−9.63231	−	35.9483i	−0.312021	−	1.16448i	−0.926731	−	0.375725i	$-0.877394\pi$
$953$	−9.63231	−	35.9483i	−0.312021	−	1.16448i	0.614710	−	0.788753i	$-0.289273\pi$
$954$	−5.08547	−	5.08547i	−0.164648	−	0.164648i
$955$		0			0
$956$	9.96253	−	9.96253i	0.322211	−	0.322211i
$957$	−0.600156	+	0.346500i	−0.0194003	+	0.0112008i
$958$	0.530395	−	1.97946i	0.0171363	−	0.0639535i
$959$	30.5719	−	17.6507i	0.987219	−	0.569971i
$960$		0			0
$961$			28.9752i			0.934685i
$962$	−10.1219	−	2.98019i	−0.326342	−	0.0960852i
$963$	−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
$967$	28.0830	+	48.6411i	0.903087	+	1.56419i	0.823464	+	0.567368i	$0.192038\pi$
$967$	28.0830	+	48.6411i	0.903087	+	1.56419i	0.0796228	+	0.996825i	$0.474628\pi$
$968$			22.4808i			0.722561i
$969$	−2.72541	+	1.57351i	−0.0875526	+	0.0505485i
$970$		0			0
$971$	−19.7612	+	34.2274i	−0.634167	+	1.09841i	0.352523	+	0.935803i	$0.385324\pi$
$971$	−19.7612	+	34.2274i	−0.634167	+	1.09841i	−0.986691	+	0.162607i	$0.948010\pi$
$972$	−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
$977$	−5.20188	−	3.00331i	−0.166423	−	0.0960843i	0.414475	−	0.910061i	$-0.363965\pi$
$977$	−5.20188	−	3.00331i	−0.166423	−	0.0960843i	−0.580898	+	0.813976i	$0.697298\pi$
$978$	−17.0197	+	4.56042i	−0.544231	+	0.145826i
$979$	8.45996	+	31.5730i	0.270381	+	1.00908i
$980$		0			0
$981$	6.45397	−	24.0866i	0.206060	−	0.769025i
$982$	−22.0038	−	12.7039i	−0.702169	−	0.405398i
$983$	−6.19133	−	23.1064i	−0.197473	−	0.736979i	−0.991613	−	0.129244i	$-0.958745\pi$
$983$	−6.19133	−	23.1064i	−0.197473	−	0.736979i	0.794140	−	0.607735i	$-0.207922\pi$
$984$	−6.57710	−	24.5461i	−0.209670	−	0.782501i
$985$		0			0
$986$	−0.493901	−	0.132340i	−0.0157290	−	0.00421457i
$987$	−4.22658	+	1.13251i	−0.134534	+	0.0360482i
$988$	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	−0.347272	−	0.937764i	$-0.612892\pi$
$991$	18.5888	−	18.5888i	0.590492	−	0.590492i	0.937764	+	0.347272i	$0.112892\pi$
$992$	−1.39817	+	5.21804i	−0.0443919	+	0.165673i
$993$	10.2963			0.326742
$994$	−1.58789	+	5.92610i	−0.0503649	+	0.187964i
$995$		0			0
$996$	3.33182	+	5.77087i	0.105573	+	0.182857i
$997$	−25.8150	+	44.7129i	−0.817569	+	1.41607i	0.0898999	+	0.995951i	$0.471345\pi$
$997$	−25.8150	+	44.7129i	−0.817569	+	1.41607i	−0.907469	+	0.420120i	$0.861988\pi$
$998$	−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.y.b.393.6		68
5.2	odd	4		925.2.t.b.282.12		68
5.3	odd	4		185.2.p.a.97.6	✓	68
5.4	even	2		185.2.u.a.23.12	yes	68
37.29	odd	12		925.2.t.b.843.12		68
185.29	odd	12		185.2.p.a.103.6	yes	68
185.103	even	12		185.2.u.a.177.12	yes	68
185.177	even	12	inner	925.2.y.b.732.6		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.6	✓	68	5.3	odd	4
185.2.p.a.103.6	yes	68	185.29	odd	12
185.2.u.a.23.12	yes	68	5.4	even	2
185.2.u.a.177.12	yes	68	185.103	even	12
925.2.t.b.282.12		68	5.2	odd	4
925.2.t.b.843.12		68	37.29	odd	12
925.2.y.b.393.6		68	1.1	even	1	trivial
925.2.y.b.732.6		68	185.177	even	12	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.983757 - 0.567972i) q^{2} +(-1.02118 - 0.273625i) q^{3} +(-0.354815 - 0.614557i) q^{4} +(0.849185 + 0.849185i) q^{6} +(-1.57806 - 0.422839i) q^{7} +3.07799i q^{8} +(-1.63013 - 0.941157i) q^{9} +1.92257i q^{11} +(0.194173 + 0.724662i) q^{12} +(1.32247 - 0.763528i) q^{13} +(1.31226 + 1.31226i) q^{14} +(1.03858 - 1.79888i) q^{16} +(-0.660110 + 1.14334i) q^{17} +(1.06910 + 1.85174i) q^{18} +(-2.17790 - 0.583566i) q^{19} +(1.49579 + 0.863592i) q^{21} +(1.09196 - 1.89134i) q^{22} +4.57925i q^{23} +(0.842216 - 3.14319i) q^{24} -1.73465 q^{26} +(3.64981 + 3.64981i) q^{27} +(0.300059 + 1.11984i) q^{28} +(-0.241089 - 0.241089i) q^{29} +(-1.00617 + 1.00617i) q^{31} +(3.28781 - 1.89822i) q^{32} +(0.526063 - 1.96329i) q^{33} +(1.29878 - 0.749849i) q^{34} +1.33575i q^{36} +(5.83510 + 1.71804i) q^{37} +(1.81107 + 1.81107i) q^{38} +(-1.55940 + 0.417841i) q^{39} +(6.76304 - 3.90464i) q^{41} +(-0.980993 - 1.69913i) q^{42} -5.46568i 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} +(-0.938463 - 0.541822i) q^{52} +(-3.24893 + 0.870548i) q^{53} +(-1.51754 - 5.66352i) q^{54} +(1.30149 - 4.85724i) q^{56} +(2.06436 + 1.19186i) q^{57} +(0.100241 + 0.374105i) q^{58} +(1.40987 + 5.26170i) q^{59} +(10.4583 + 2.80230i) q^{61} +(1.56131 - 0.418352i) q^{62} +(2.17448 + 2.17448i) q^{63} -8.46687 q^{64} +(-1.63261 + 1.63261i) q^{66} +(2.53340 - 9.45477i) q^{67} +0.936868 q^{68} +(1.25300 - 4.67625i) q^{69} +(1.65295 + 2.86299i) q^{71} +(2.89687 - 5.01753i) q^{72} +(1.78634 - 1.78634i) q^{73} +(-4.76452 - 5.00430i) q^{74} +(0.414116 + 1.54550i) q^{76} +(0.812936 - 3.03392i) q^{77} +(1.77140 + 0.474644i) q^{78} +(12.3408 + 3.30670i) q^{79} +(0.0950223 + 0.164583i) q^{81} -8.87092 q^{82} +(8.57952 - 2.29888i) q^{83} -1.22566i q^{84} +(-3.10436 + 5.37690i) q^{86} +(0.180228 + 0.312164i) q^{87} -5.91764 q^{88} +(16.4223 - 4.40035i) q^{89} +(-2.40978 + 0.645698i) q^{91} +(2.81421 - 1.62479i) q^{92} +(1.30280 - 0.752174i) q^{93} +(2.77976 - 0.744835i) q^{94} +(-3.87685 + 1.03880i) q^{96} -15.4196 q^{97} +(2.45986 + 4.26060i) q^{98} +(1.80944 - 3.13404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

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