LMFDB - Embedded newform 841.2.e.d.270.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(63,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.63"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,4,-2,6,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			270.1
Root			$-0.433884 + 0.900969i$ of defining polynomial
Character	$\chi$	$=$	841.270
Dual form			841.2.e.d.651.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.193096 - 0.400969i) q^{2} +(-0.974928 + 0.777479i) q^{3} +(1.12349 - 1.40881i) q^{4} +(0.623490 - 0.300257i) q^{5} +(0.500000 + 0.240787i) q^{6} +(0.222521 + 0.279032i) q^{7} +(-1.64960 - 0.376510i) q^{8} +(-0.321552 + 1.40881i) q^{9} +(-0.240787 - 0.192021i) q^{10} +(-4.81517 + 1.09903i) q^{11} +2.24698i q^{12} +(-1.25786 - 5.51107i) q^{13} +(0.0689153 - 0.143104i) q^{14} +(-0.374414 + 0.777479i) q^{15} +(-0.634375 - 2.77938i) q^{16} -4.49396i q^{17} +(0.626980 - 0.143104i) q^{18} +(1.84270 + 1.46950i) q^{19} +(0.277479 - 1.21572i) q^{20} +(-0.433884 - 0.0990311i) q^{21} +(1.37047 + 1.71851i) q^{22} +(-2.06853 - 0.996152i) q^{23} +(1.90097 - 0.915458i) q^{24} +(-2.81886 + 3.53474i) q^{25} +(-1.96688 + 1.56853i) q^{26} +(-2.40496 - 4.99396i) q^{27} +0.643104 q^{28} +0.384043 q^{30} +(-2.90356 - 6.02930i) q^{31} +(-3.63770 + 2.90097i) q^{32} +(3.83997 - 4.81517i) q^{33} +(-1.80194 + 0.867767i) q^{34} +(0.222521 + 0.107160i) q^{35} +(1.62349 + 2.03579i) q^{36} +(4.81517 + 1.09903i) q^{37} +(0.233406 - 1.02262i) q^{38} +(5.51107 + 4.39493i) q^{39} +(-1.14156 + 0.260553i) q^{40} +3.10992i q^{41} +(0.0440730 + 0.193096i) q^{42} +(1.47773 - 3.06853i) q^{43} +(-3.86147 + 8.01842i) q^{44} +(0.222521 + 0.974928i) q^{45} +1.02177i q^{46} +(-6.28345 + 1.43416i) q^{47} +(2.77938 + 2.21648i) q^{48} +(1.52930 - 6.70031i) q^{49} +(1.96163 + 0.447730i) q^{50} +(3.49396 + 4.38129i) q^{51} +(-9.17725 - 4.41953i) q^{52} +(4.22737 - 2.03579i) q^{53} +(-1.53803 + 1.92863i) q^{54} +(-2.67222 + 2.13102i) q^{55} +(-0.262012 - 0.544073i) q^{56} -2.93900 q^{57} -12.4940 q^{59} +(0.674671 + 1.40097i) q^{60} +(-1.28463 + 1.02446i) q^{61} +(-1.85690 + 2.32847i) q^{62} +(-0.464656 + 0.223767i) q^{63} +(-3.27144 - 1.57544i) q^{64} +(-2.43900 - 3.05841i) q^{65} +(-2.67222 - 0.609916i) q^{66} +(-0.516926 + 2.26480i) q^{67} +(-6.33114 - 5.04892i) q^{68} +(2.79116 - 0.637063i) q^{69} -0.109916i q^{70} +(-1.63222 - 7.15122i) q^{71} +(1.06086 - 2.20291i) q^{72} +(2.44088 - 5.06853i) q^{73} +(-0.489115 - 2.14295i) q^{74} -5.63773i q^{75} +(4.14050 - 0.945042i) q^{76} +(-1.37814 - 1.09903i) q^{77} +(0.698062 - 3.05841i) q^{78} +(-4.54792 - 1.03803i) q^{79} +(-1.23005 - 1.54244i) q^{80} +(2.32155 + 1.11800i) q^{81} +(1.24698 - 0.600514i) q^{82} +(2.77748 - 3.48285i) q^{83} +(-0.626980 + 0.500000i) q^{84} +(-1.34934 - 2.80194i) q^{85} -1.51573 q^{86} +8.35690 q^{88} +(-2.46443 - 5.11745i) q^{89} +(0.347948 - 0.277479i) q^{90} +(1.25786 - 1.57731i) q^{91} +(-3.72737 + 1.79500i) q^{92} +(7.51842 + 3.62068i) q^{93} +(1.78836 + 2.24254i) q^{94} +(1.59013 + 0.362937i) q^{95} +(1.29105 - 5.65647i) q^{96} +(-0.141202 - 0.112605i) q^{97} +(-2.98192 + 0.680604i) q^{98} -7.13706i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 2 q^{5} + 6 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{13} + 8 q^{16} + 4 q^{20} - 12 q^{22} - 14 q^{23} + 14 q^{24} - 48 q^{25} + 24 q^{28} - 36 q^{30} - 2 q^{33} - 4 q^{34} + 2 q^{35} + 10 q^{36}+ \cdots + 4 q^{96}+O(q^{100}) $ 12 * q + 4 * q^4 - 2 * q^5 + 6 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^13 + 8 * q^16 + 4 * q^20 - 12 * q^22 - 14 * q^23 + 14 * q^24 - 48 * q^25 + 24 * q^28 - 36 * q^30 - 2 * q^33 - 4 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^38 + 8 * q^42 + 2 * q^45 - 44 * q^49 + 4 * q^51 - 20 * q^52 + 6 * q^53 + 12 * q^54 + 4 * q^57 - 112 * q^59 - 6 * q^62 - 30 * q^63 - 2 * q^64 + 10 * q^65 - 38 * q^67 - 42 * q^71 - 12 * q^74 + 26 * q^78 + 36 * q^80 + 36 * q^81 - 4 * q^82 + 34 * q^83 + 32 * q^86 + 84 * q^88 - 10 * q^91 + 34 * q^93 + 16 * q^94 + 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{14}\right)$

Coefficient data

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

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

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

$2$	−0.193096	−	0.400969i	−0.136540	−	0.283528i	0.821476	−	0.570243i	$-0.193151\pi$
$2$	−0.193096	−	0.400969i	−0.136540	−	0.283528i	−0.958016	+	0.286715i	$0.907437\pi$
$3$	−0.974928	+	0.777479i	−0.562875	+	0.448878i	−0.863130	−	0.504981i	$-0.831499\pi$
$3$	−0.974928	+	0.777479i	−0.562875	+	0.448878i	0.300256	+	0.953859i	$0.402928\pi$
$4$	1.12349	−	1.40881i	0.561745	−	0.704406i
$5$	0.623490	−	0.300257i	0.278833	−	0.134279i	−0.289241	−	0.957256i	$-0.593403\pi$
$5$	0.623490	−	0.300257i	0.278833	−	0.134279i	0.568074	+	0.822977i	$0.307689\pi$
$6$	0.500000	+	0.240787i	0.204124	+	0.0983010i
$7$	0.222521	+	0.279032i	0.0841050	+	0.105464i	0.822104	−	0.569338i	$-0.192800\pi$
$7$	0.222521	+	0.279032i	0.0841050	+	0.105464i	−0.737999	+	0.674802i	$0.764229\pi$
$8$	−1.64960	−	0.376510i	−0.583221	−	0.133116i
$9$	−0.321552	+	1.40881i	−0.107184	+	0.469604i
$10$	−0.240787	−	0.192021i	−0.0761436	−	0.0607225i
$11$	−4.81517	+	1.09903i	−1.45183	+	0.331370i	−0.874454	−	0.485109i	$-0.838780\pi$
$11$	−4.81517	+	1.09903i	−1.45183	+	0.331370i	−0.577375	+	0.816479i	$0.695923\pi$
$12$			2.24698i			0.648647i
$13$	−1.25786	−	5.51107i	−0.348869	−	1.52849i	−0.779753	−	0.626087i	$-0.784655\pi$
$13$	−1.25786	−	5.51107i	−0.348869	−	1.52849i	0.430884	−	0.902407i	$-0.358202\pi$
$14$	0.0689153	−	0.143104i	0.0184184	−	0.0382462i
$15$	−0.374414	+	0.777479i	−0.0966733	+	0.200744i
$16$	−0.634375	−	2.77938i	−0.158594	−	0.694845i
$17$		−	4.49396i		−	1.08995i	−0.838454	−	0.544973i	$-0.816540\pi$
$17$		−	4.49396i		−	1.08995i	0.838454	−	0.544973i	$-0.183460\pi$
$18$	0.626980	−	0.143104i	0.147781	−	0.0337300i
$19$	1.84270	+	1.46950i	0.422743	+	0.337127i	0.811643	−	0.584153i	$-0.198573\pi$
$19$	1.84270	+	1.46950i	0.422743	+	0.337127i	−0.388900	+	0.921280i	$0.627145\pi$
$20$	0.277479	−	1.21572i	0.0620462	−	0.271842i
$21$	−0.433884	−	0.0990311i	−0.0946812	−	0.0216104i
$22$	1.37047	+	1.71851i	0.292185	+	0.366388i
$23$	−2.06853	−	0.996152i	−0.431319	−	0.207712i	0.205611	−	0.978634i	$-0.434082\pi$
$23$	−2.06853	−	0.996152i	−0.431319	−	0.207712i	−0.636930	+	0.770922i	$0.719796\pi$
$24$	1.90097	−	0.915458i	0.388034	−	0.186867i
$25$	−2.81886	+	3.53474i	−0.563773	+	0.706949i
$26$	−1.96688	+	1.56853i	−0.385736	+	0.307614i
$27$	−2.40496	−	4.99396i	−0.462836	−	0.961088i
$28$	0.643104			0.121535
$29$		0			0
$29$		0			0
$30$	0.384043			0.0701163
$31$	−2.90356	−	6.02930i	−0.521495	−	1.08289i	−0.980872	−	0.194654i	$-0.937642\pi$
$31$	−2.90356	−	6.02930i	−0.521495	−	1.08289i	0.459377	−	0.888241i	$-0.348073\pi$
$32$	−3.63770	+	2.90097i	−0.643061	+	0.512824i
$33$	3.83997	−	4.81517i	0.668453	−	0.838214i
$34$	−1.80194	+	0.867767i	−0.309030	+	0.148821i
$35$	0.222521	+	0.107160i	0.0376129	+	0.0181134i
$36$	1.62349	+	2.03579i	0.270582	+	0.339299i
$37$	4.81517	+	1.09903i	0.791609	+	0.180680i	0.599162	−	0.800628i	$-0.295501\pi$
$37$	4.81517	+	1.09903i	0.791609	+	0.180680i	0.192447	+	0.981307i	$0.438358\pi$
$38$	0.233406	−	1.02262i	0.0378635	−	0.165891i
$39$	5.51107	+	4.39493i	0.882477	+	0.703752i
$40$	−1.14156	+	0.260553i	−0.180496	+	0.0411971i
$41$			3.10992i			0.485687i	0.970065	+	0.242844i	$0.0780802\pi$
$41$			3.10992i			0.485687i	−0.970065	+	0.242844i	$0.921920\pi$
$42$	0.0440730	+	0.193096i	0.00680061	+	0.0297954i
$43$	1.47773	−	3.06853i	0.225351	−	0.467947i	−0.757383	−	0.652971i	$-0.773522\pi$
$43$	1.47773	−	3.06853i	0.225351	−	0.467947i	0.982734	+	0.185025i	$0.0592365\pi$
$44$	−3.86147	+	8.01842i	−0.582138	+	1.20882i
$45$	0.222521	+	0.974928i	0.0331715	+	0.145334i
$46$			1.02177i			0.150652i
$47$	−6.28345	+	1.43416i	−0.916536	+	0.209193i	−0.654673	−	0.755912i	$-0.727194\pi$
$47$	−6.28345	+	1.43416i	−0.916536	+	0.209193i	−0.261862	+	0.965105i	$0.584337\pi$
$48$	2.77938	+	2.21648i	0.401169	+	0.319921i
$49$	1.52930	−	6.70031i	0.218472	−	0.957188i
$50$	1.96163	+	0.447730i	0.277417	+	0.0633186i
$51$	3.49396	+	4.38129i	0.489252	+	0.613503i
$52$	−9.17725	−	4.41953i	−1.27266	−	0.612879i
$53$	4.22737	−	2.03579i	0.580673	−	0.279638i	−0.120401	−	0.992725i	$-0.538418\pi$
$53$	4.22737	−	2.03579i	0.580673	−	0.279638i	0.701075	+	0.713088i	$0.252704\pi$
$54$	−1.53803	+	1.92863i	−0.209300	+	0.262453i
$55$	−2.67222	+	2.13102i	−0.360322	+	0.287347i
$56$	−0.262012	−	0.544073i	−0.0350128	−	0.0727048i
$57$	−2.93900			−0.389280
$58$		0			0
$59$	−12.4940			−1.62657			−0.813287	−	0.581862i	$-0.802324\pi$
$59$	−12.4940			−1.62657			−0.813287	+	0.581862i	$0.802324\pi$
$60$	0.674671	+	1.40097i	0.0870997	+	0.180864i
$61$	−1.28463	+	1.02446i	−0.164480	+	0.131168i	−0.702271	−	0.711910i	$-0.747830\pi$
$61$	−1.28463	+	1.02446i	−0.164480	+	0.131168i	0.537791	+	0.843078i	$0.319259\pi$
$62$	−1.85690	+	2.32847i	−0.235826	+	0.295716i
$63$	−0.464656	+	0.223767i	−0.0585412	+	0.0281919i
$64$	−3.27144	−	1.57544i	−0.408930	−	0.196930i
$65$	−2.43900	−	3.05841i	−0.302521	−	0.379349i
$66$	−2.67222	−	0.609916i	−0.328927	−	0.0750755i
$67$	−0.516926	+	2.26480i	−0.0631526	+	0.276689i	−0.996639	−	0.0819245i	$-0.973893\pi$
$67$	−0.516926	+	2.26480i	−0.0631526	+	0.276689i	0.933486	+	0.358614i	$0.116751\pi$
$68$	−6.33114	−	5.04892i	−0.767764	−	0.612271i
$69$	2.79116	−	0.637063i	0.336016	−	0.0766934i
$70$		−	0.109916i		−	0.0131375i
$71$	−1.63222	−	7.15122i	−0.193709	−	0.848694i	−0.974587	−	0.224010i	$-0.928085\pi$
$71$	−1.63222	−	7.15122i	−0.193709	−	0.848694i	0.780878	−	0.624683i	$-0.214772\pi$
$72$	1.06086	−	2.20291i	0.125024	−	0.259615i
$73$	2.44088	−	5.06853i	0.285683	−	0.593227i	−0.707903	−	0.706310i	$-0.750358\pi$
$73$	2.44088	−	5.06853i	0.285683	−	0.593227i	0.993586	+	0.113083i	$0.0360727\pi$
$74$	−0.489115	−	2.14295i	−0.0568584	−	0.249113i
$75$		−	5.63773i		−	0.650989i
$76$	4.14050	−	0.945042i	0.474948	−	0.108404i
$77$	−1.37814	−	1.09903i	−0.157054	−	0.125246i
$78$	0.698062	−	3.05841i	0.0790400	−	0.346297i
$79$	−4.54792	−	1.03803i	−0.511681	−	0.116788i	−0.0411178	−	0.999154i	$-0.513092\pi$
$79$	−4.54792	−	1.03803i	−0.511681	−	0.116788i	−0.470563	+	0.882367i	$0.655949\pi$
$80$	−1.23005	−	1.54244i	−0.137524	−	0.172450i
$81$	2.32155	+	1.11800i	0.257950	+	0.124222i
$82$	1.24698	−	0.600514i	0.137706	−	0.0663156i
$83$	2.77748	−	3.48285i	0.304868	−	0.382292i	−0.605671	−	0.795715i	$-0.707095\pi$
$83$	2.77748	−	3.48285i	0.304868	−	0.382292i	0.910539	+	0.413423i	$0.135667\pi$
$84$	−0.626980	+	0.500000i	−0.0684091	+	0.0545545i
$85$	−1.34934	−	2.80194i	−0.146357	−	0.303913i
$86$	−1.51573			−0.163445
$87$		0			0
$88$	8.35690			0.890848
$89$	−2.46443	−	5.11745i	−0.261229	−	0.542449i	0.728561	−	0.684981i	$-0.240190\pi$
$89$	−2.46443	−	5.11745i	−0.261229	−	0.542449i	−0.989790	+	0.142533i	$0.954475\pi$
$90$	0.347948	−	0.277479i	0.0366769	−	0.0292489i
$91$	1.25786	−	1.57731i	0.131860	−	0.165347i
$92$	−3.72737	+	1.79500i	−0.388605	+	0.187142i
$93$	7.51842	+	3.62068i	0.779624	+	0.375447i
$94$	1.78836	+	2.24254i	0.184456	+	0.231300i
$95$	1.59013	+	0.362937i	0.163144	+	0.0372365i
$96$	1.29105	−	5.65647i	0.131768	−	0.577311i
$97$	−0.141202	−	0.112605i	−0.0143369	−	0.0114333i	0.616295	−	0.787515i	$-0.288633\pi$
$97$	−0.141202	−	0.112605i	−0.0143369	−	0.0114333i	−0.630632	+	0.776082i	$0.717204\pi$
$98$	−2.98192	+	0.680604i	−0.301219	+	0.0687514i
$99$		−	7.13706i		−	0.717302i
$100$	1.81282	+	7.94250i	0.181282	+	0.794250i
$101$	−1.40124	+	2.90970i	−0.139428	+	0.289526i	−0.958977	−	0.283484i	$-0.908510\pi$
$101$	−1.40124	+	2.90970i	−0.139428	+	0.289526i	0.819549	+	0.573009i	$0.194224\pi$
$102$	1.08209	−	2.24698i	0.107143	−	0.222484i
$103$	3.03803	+	13.3105i	0.299346	+	1.31152i	0.871104	+	0.491099i	$0.163405\pi$
$103$	3.03803	+	13.3105i	0.299346	+	1.31152i	−0.571758	+	0.820423i	$0.693738\pi$
$104$			9.56465i			0.937891i
$105$	−0.300257	+	0.0685317i	−0.0293021	+	0.00668801i
$106$	−1.63258	−	1.30194i	−0.158570	−	0.126455i
$107$	−3.61476	+	15.8373i	−0.349452	+	1.53105i	0.428976	+	0.903316i	$0.358874\pi$
$107$	−3.61476	+	15.8373i	−0.349452	+	1.53105i	−0.778428	+	0.627734i	$0.783983\pi$
$108$	−9.73750	−	2.22252i	−0.936991	−	0.213862i
$109$	−3.40850	−	4.27413i	−0.326475	−	0.409387i	0.591323	−	0.806435i	$-0.298606\pi$
$109$	−3.40850	−	4.27413i	−0.326475	−	0.409387i	−0.917798	+	0.397048i	$0.870035\pi$
$110$	1.37047	+	0.659983i	0.130669	+	0.0629269i
$111$	−5.54892	+	2.67222i	−0.526680	+	0.253636i
$112$	0.634375	−	0.795481i	0.0599428	−	0.0751659i
$113$	8.34571	−	6.65548i	0.785098	−	0.626095i	−0.146655	−	0.989188i	$-0.546851\pi$
$113$	8.34571	−	6.65548i	0.785098	−	0.626095i	0.931753	+	0.363093i	$0.118279\pi$
$114$	0.567511	+	1.17845i	0.0531522	+	0.110372i
$115$	−1.58881			−0.148157
$116$		0			0
$117$	8.16852			0.755180
$118$	2.41254	+	5.00969i	0.222092	+	0.461179i
$119$	1.25396	−	1.00000i	0.114950	−	0.0916698i
$120$	0.910362	−	1.14156i	0.0831043	−	0.104210i
$121$	12.0673	−	5.81132i	1.09703	−	0.528302i
$122$	0.658834	+	0.317278i	0.0596480	+	0.0287250i
$123$	−2.41789	−	3.03194i	−0.218014	−	0.273381i
$124$	−11.7563	−	2.68329i	−1.05574	−	0.240967i
$125$	−1.46615	+	6.42361i	−0.131136	+	0.574546i
$126$	0.179447	+	0.143104i	0.0159864	+	0.0127487i
$127$	1.01084	−	0.230718i	0.0896976	−	0.0204729i	−0.177437	−	0.984132i	$-0.556780\pi$
$127$	1.01084	−	0.230718i	0.0896976	−	0.0204729i	0.267134	+	0.963659i	$0.413923\pi$
$128$			10.9215i			0.965337i
$129$	0.945042	+	4.14050i	0.0832063	+	0.364551i
$130$	−0.755365	+	1.56853i	−0.0662499	+	0.137569i
$131$	3.48052	−	7.22737i	0.304094	−	0.631458i	−0.691790	−	0.722099i	$-0.743177\pi$
$131$	3.48052	−	7.22737i	0.304094	−	0.631458i	0.995884	+	0.0906414i	$0.0288917\pi$
$132$	−2.46950	−	10.8196i	−0.214942	−	0.941724i
$133$			0.841166i			0.0729384i
$134$	1.00793	−	0.230054i	0.0870720	−	0.0198736i
$135$	−2.99894	−	2.39158i	−0.258108	−	0.205834i
$136$	−1.69202	+	7.41323i	−0.145090	+	0.635679i
$137$	16.8005	+	3.83459i	1.43536	+	0.327611i	0.868289	−	0.496058i	$-0.165220\pi$
$137$	16.8005	+	3.83459i	1.43536	+	0.327611i	0.567070	+	0.823670i	$0.308077\pi$
$138$	−0.794405	−	0.996152i	−0.0676242	−	0.0847981i
$139$	15.0172	+	7.23191i	1.27374	+	0.613403i	0.943775	−	0.330589i	$-0.107247\pi$
$139$	15.0172	+	7.23191i	1.27374	+	0.613403i	0.329969	+	0.943992i	$0.392962\pi$
$140$	0.400969	−	0.193096i	0.0338881	−	0.0163196i
$141$	5.01089	−	6.28345i	0.421993	−	0.529162i
$142$	−2.55224	+	2.03534i	−0.214179	+	0.170802i
$143$	12.1137	+	25.1543i	1.01300	+	2.10351i
$144$	4.11960			0.343300
$145$		0			0
$146$	−2.50365			−0.207203
$147$	3.71839	+	7.72132i	0.306688	+	0.636844i
$148$	6.95812	−	5.54892i	0.571954	−	0.456118i
$149$	−11.6012	+	14.5474i	−0.950406	+	1.19177i	0.0309396	+	0.999521i	$0.490150\pi$
$149$	−11.6012	+	14.5474i	−0.950406	+	1.19177i	−0.981346	+	0.192251i	$0.938421\pi$
$150$	−2.26055	+	1.08863i	−0.184573	+	0.0888859i
$151$	−6.78232	−	3.26619i	−0.551938	−	0.265799i	0.137060	−	0.990563i	$-0.456235\pi$
$151$	−6.78232	−	3.26619i	−0.551938	−	0.265799i	−0.688998	+	0.724764i	$0.741949\pi$
$152$	−2.48643	−	3.11788i	−0.201676	−	0.252893i
$153$	6.33114	+	1.44504i	0.511843	+	0.116825i
$154$	−0.174563	+	0.764811i	−0.0140667	+	0.0616302i
$155$	−3.62068	−	2.88740i	−0.290820	−	0.231921i
$156$	12.3833	−	2.82640i	0.991454	−	0.226293i
$157$		−	18.2392i		−	1.45565i	−0.685764	−	0.727824i	$-0.740532\pi$
$157$		−	18.2392i		−	1.45565i	0.685764	−	0.727824i	$-0.259468\pi$
$158$	0.461968	+	2.02401i	0.0367522	+	0.161022i
$159$	−2.53859	+	5.27144i	−0.201323	+	0.418052i
$160$	−1.39703	+	2.90097i	−0.110445	+	0.229342i
$161$	−0.182333	−	0.798852i	−0.0143698	−	0.0629584i
$162$		−	1.14675i		−	0.0900973i
$163$	12.3238	−	2.81282i	0.965273	−	0.220317i	0.289296	−	0.957240i	$-0.406579\pi$
$163$	12.3238	−	2.81282i	0.965273	−	0.220317i	0.675977	+	0.736922i	$0.263722\pi$
$164$	4.38129	+	3.49396i	0.342121	+	0.272832i
$165$	0.948394	−	4.15519i	0.0738324	−	0.323481i
$166$	−1.93284	−	0.441157i	−0.150017	−	0.0342404i
$167$	0.496648	+	0.622776i	0.0384317	+	0.0481919i	0.800676	−	0.599098i	$-0.204474\pi$
$167$	0.496648	+	0.622776i	0.0384317	+	0.0481919i	−0.762244	+	0.647290i	$0.775902\pi$
$168$	0.678448	+	0.326723i	0.0523434	+	0.0252073i
$169$	−17.0770	+	8.22386i	−1.31362	+	0.632605i
$170$	−0.862937	+	1.08209i	−0.0661842	+	0.0829924i
$171$	−2.66277	+	2.12349i	−0.203627	+	0.162387i
$172$	−2.66277	−	5.52930i	−0.203034	−	0.421605i
$173$	9.15346			0.695924			0.347962	−	0.937509i	$-0.386874\pi$
$173$	9.15346			0.695924			0.347962	+	0.937509i	$0.386874\pi$
$174$		0			0
$175$	−1.61356			−0.121974
$176$	6.10925	+	12.6860i	0.460502	+	0.956242i
$177$	12.1807	−	9.71379i	0.915558	−	0.730133i
$178$	−1.57606	+	1.97632i	−0.118131	+	0.148132i
$179$	3.06853	−	1.47773i	0.229353	−	0.110450i	−0.315678	−	0.948866i	$-0.602232\pi$
$179$	3.06853	−	1.47773i	0.229353	−	0.110450i	0.545031	+	0.838416i	$0.316518\pi$
$180$	1.62349	+	0.781831i	0.121008	+	0.0582743i
$181$	7.90246	+	9.90937i	0.587385	+	0.736558i	0.983353	−	0.181707i	$-0.0581621\pi$
$181$	7.90246	+	9.90937i	0.587385	+	0.736558i	−0.395967	+	0.918265i	$0.629591\pi$
$182$	−0.875342	−	0.199791i	−0.0648847	−	0.0148095i
$183$	0.455927	−	1.99755i	0.0337031	−	0.147663i
$184$	3.03719	+	2.42208i	0.223904	+	0.178558i
$185$	3.33220	−	0.760553i	0.244988	−	0.0559170i
$186$		−	3.71379i		−	0.272308i
$187$	4.93900	+	21.6392i	0.361176	+	1.58241i
$188$	−5.03894	+	10.4635i	−0.367502	+	0.763126i
$189$	0.858322	−	1.78232i	0.0624337	−	0.129645i
$190$	−0.161522	−	0.707674i	−0.0117180	−	0.0513401i
$191$			10.6703i			0.772072i	0.922484	+	0.386036i	$0.126156\pi$
$191$			10.6703i			0.772072i	−0.922484	+	0.386036i	$0.873844\pi$
$192$	4.41429	−	1.00753i	0.318574	−	0.0727124i
$193$	−17.7701	−	14.1712i	−1.27912	−	1.02007i	−0.998178	−	0.0603421i	$-0.980781\pi$
$193$	−17.7701	−	14.1712i	−1.27912	−	1.02007i	−0.280945	−	0.959724i	$-0.590648\pi$
$194$	−0.0178854	+	0.0783611i	−0.00128410	+	0.00562600i
$195$	4.75570	+	1.08546i	0.340563	+	0.0777312i
$196$	−7.72132	−	9.68223i	−0.551523	−	0.691588i
$197$	17.6211	+	8.48587i	1.25545	+	0.604593i	0.938968	−	0.344005i	$-0.111784\pi$
$197$	17.6211	+	8.48587i	1.25545	+	0.604593i	0.316483	+	0.948598i	$0.397498\pi$
$198$	−2.86174	+	1.37814i	−0.203375	+	0.0979402i
$199$	−0.545565	+	0.684117i	−0.0386741	+	0.0484958i	−0.800792	−	0.598942i	$-0.795588\pi$
$199$	−0.545565	+	0.684117i	−0.0386741	+	0.0484958i	0.762118	+	0.647438i	$0.224159\pi$
$200$	5.98086	−	4.76958i	0.422911	−	0.337260i
$201$	−1.25687	−	2.60992i	−0.0886527	−	0.184089i
$202$	1.43727			0.101126
$203$		0			0
$204$	10.0978			0.706990
$205$	0.933774	+	1.93900i	0.0652176	+	0.135426i
$206$	4.75046	−	3.78836i	0.330980	−	0.263948i
$207$	2.06853	−	2.59386i	0.143773	−	0.180286i
$208$	−14.5194	+	6.99216i	−1.00674	+	0.484819i
$209$	−10.4879	−	5.05072i	−0.725464	−	0.349365i
$210$	0.0854576	+	0.107160i	0.00589713	+	0.00739477i
$211$	17.8107	+	4.06518i	1.22614	+	0.279858i	0.786088	−	0.618114i	$-0.212103\pi$
$211$	17.8107	+	4.06518i	1.22614	+	0.279858i	0.440052	+	0.897972i	$0.354960\pi$
$212$	1.88135	−	8.24275i	0.129212	−	0.566115i
$213$	7.15122	+	5.70291i	0.489993	+	0.390757i
$214$	7.04826	−	1.60872i	0.481809	−	0.109970i
$215$		−	2.35690i		−	0.160739i
$216$	2.08695	+	9.14352i	0.141999	+	0.622138i
$217$	1.03627	−	2.15183i	0.0703465	−	0.146076i
$218$	−1.05562	+	2.19202i	−0.0714957	+	0.148462i
$219$	1.56100	+	6.83918i	0.105483	+	0.462149i
$220$			6.15883i			0.415228i
$221$	−24.7665	+	5.65279i	−1.66598	+	0.380248i
$222$	2.14295	+	1.70895i	0.143826	+	0.114697i
$223$	0.404617	−	1.77274i	0.0270951	−	0.118712i	−0.959572	−	0.281464i	$-0.909180\pi$
$223$	0.404617	−	1.77274i	0.0270951	−	0.118712i	0.986667	+	0.162752i	$0.0520372\pi$
$224$	−1.61893	−	0.369510i	−0.108169	−	0.0246889i
$225$	−4.07338	−	5.10785i	−0.271558	−	0.340523i
$226$	−4.28017	−	2.06122i	−0.284713	−	0.137110i
$227$	12.4840	−	6.01199i	0.828594	−	0.399030i	0.0290066	−	0.999579i	$-0.490766\pi$
$227$	12.4840	−	6.01199i	0.828594	−	0.399030i	0.799588	+	0.600549i	$0.205051\pi$
$228$	−3.30194	+	4.14050i	−0.218676	+	0.274211i
$229$	9.98586	−	7.96346i	0.659884	−	0.526240i	−0.235308	−	0.971921i	$-0.575610\pi$
$229$	9.98586	−	7.96346i	0.659884	−	0.526240i	0.895192	+	0.445681i	$0.147038\pi$
$230$	0.306794	+	0.637063i	0.0202294	+	0.0420067i
$231$	2.19806			0.144622
$232$		0			0
$233$	−8.86592			−0.580826			−0.290413	−	0.956901i	$-0.593793\pi$
$233$	−8.86592			−0.580826			−0.290413	+	0.956901i	$0.593793\pi$
$234$	−1.57731	−	3.27532i	−0.103112	−	0.214115i
$235$	−3.48705	+	2.78083i	−0.227470	+	0.181401i
$236$	−14.0368	+	17.6016i	−0.913720	+	1.14577i
$237$	5.24094	−	2.52390i	0.340436	−	0.163945i
$238$	−0.643104	−	0.309703i	−0.0416862	−	0.0200750i
$239$	−15.9393	−	19.9872i	−1.03103	−	1.29287i	−0.955268	−	0.295741i	$-0.904433\pi$
$239$	−15.9393	−	19.9872i	−1.03103	−	1.29287i	−0.0757593	−	0.997126i	$-0.524138\pi$
$240$	2.39843	+	0.547425i	0.154818	+	0.0353362i
$241$	2.16541	−	9.48727i	0.139486	−	0.611129i	−0.856062	−	0.516873i	$-0.827096\pi$
$241$	2.16541	−	9.48727i	0.139486	−	0.611129i	0.995548	−	0.0942554i	$-0.0300470\pi$
$242$	−4.66032	−	3.71648i	−0.299577	−	0.238904i
$243$	13.0791	−	2.98523i	0.839028	−	0.191503i
$244$			2.96077i			0.189544i
$245$	−1.05831	−	4.63676i	−0.0676130	−	0.296232i
$246$	−0.748828	+	1.55496i	−0.0477436	+	0.0991405i
$247$	5.78065	−	12.0036i	0.367814	−	0.763774i
$248$	2.51961	+	11.0392i	0.159996	+	0.700987i
$249$			5.55496i			0.352031i
$250$	2.85878	−	0.652497i	0.180805	−	0.0412676i
$251$	7.63092	+	6.08546i	0.481660	+	0.384111i	0.834003	−	0.551760i	$-0.186044\pi$
$251$	7.63092	+	6.08546i	0.481660	+	0.384111i	−0.352343	+	0.935871i	$0.614615\pi$
$252$	−0.206791	+	0.906013i	−0.0130266	+	0.0570734i
$253$	11.0551	+	2.52326i	0.695030	+	0.158636i
$254$	−0.287700	−	0.360765i	−0.0180519	−	0.0226364i
$255$	3.49396	+	1.68260i	0.218800	+	0.105369i
$256$	−2.16368	+	1.04197i	−0.135230	+	0.0651233i
$257$	10.1984	−	12.7883i	0.636156	−	0.797714i	−0.354360	−	0.935109i	$-0.615301\pi$
$257$	10.1984	−	12.7883i	0.636156	−	0.797714i	0.990516	+	0.137394i	$0.0438728\pi$
$258$	1.47773	−	1.17845i	0.0919993	−	0.0733670i
$259$	0.764811	+	1.58815i	0.0475230	+	0.0986826i
$260$	−7.04892			−0.437155
$261$		0			0
$262$	−3.57002			−0.220557
$263$	10.2932	+	21.3741i	0.634708	+	1.31798i	0.931743	+	0.363118i	$0.118288\pi$
$263$	10.2932	+	21.3741i	0.634708	+	1.31798i	−0.297035	+	0.954867i	$0.595998\pi$
$264$	−8.14737	+	6.49731i	−0.501436	+	0.399882i
$265$	2.02446	−	2.53859i	0.124362	−	0.155944i
$266$	0.337282	−	0.162426i	0.0206801	−	0.00995899i
$267$	6.38135	+	3.07310i	0.390533	+	0.188071i
$268$	2.60992	+	3.27273i	0.159426	+	0.199914i
$269$	−24.7188	−	5.64191i	−1.50713	−	0.343993i	−0.612383	−	0.790561i	$-0.709789\pi$
$269$	−24.7188	−	5.64191i	−1.50713	−	0.343993i	−0.894750	+	0.446568i	$0.852646\pi$
$270$	−0.379863	+	1.66429i	−0.0231177	+	0.101285i
$271$	−0.940887	−	0.750332i	−0.0571548	−	0.0455794i	0.594496	−	0.804099i	$-0.297352\pi$
$271$	−0.940887	−	0.750332i	−0.0571548	−	0.0455794i	−0.651651	+	0.758519i	$0.725923\pi$
$272$	−12.4904	+	2.85086i	−0.757342	+	0.172858i
$273$			2.51573i			0.152259i
$274$	−1.70655	−	7.47690i	−0.103097	−	0.451696i
$275$	9.68851	−	20.1184i	0.584239	−	1.21319i
$276$	2.23833	−	4.64795i	0.134732	−	0.279774i
$277$	−2.37316	−	10.3975i	−0.142589	−	0.624724i	−0.994828	−	0.101572i	$-0.967613\pi$
$277$	−2.37316	−	10.3975i	−0.142589	−	0.624724i	0.852239	−	0.523153i	$-0.175244\pi$
$278$		−	7.41789i		−	0.444896i
$279$	9.42780	−	2.15183i	0.564427	−	0.128827i
$280$	−0.326723	−	0.260553i	−0.0195255	−	0.0155710i
$281$	3.62253	−	15.8713i	0.216102	−	0.946805i	−0.744225	−	0.667929i	$-0.767181\pi$
$281$	3.62253	−	15.8713i	0.216102	−	0.946805i	0.960327	−	0.278876i	$-0.0899618\pi$
$282$	−3.48705	−	0.795897i	−0.207651	−	0.0473950i
$283$	3.27144	+	4.10225i	0.194467	+	0.243854i	0.869499	−	0.493935i	$-0.164442\pi$
$283$	3.27144	+	4.10225i	0.194467	+	0.243854i	−0.675032	+	0.737788i	$0.735870\pi$
$284$	−11.9085	−	5.73483i	−0.706640	−	0.340300i
$285$	−1.83244	+	0.882455i	−0.108544	+	0.0522721i
$286$	7.74698	−	9.71441i	0.458089	−	0.574425i
$287$	−0.867767	+	0.692021i	−0.0512227	+	0.0408487i
$288$	−2.91721	−	6.05765i	−0.171898	−	0.356950i
$289$	−3.19567			−0.187981
$290$		0			0
$291$	0.225209			0.0132020
$292$	−4.39831	−	9.13318i	−0.257391	−	0.534479i
$293$	5.28813	−	4.21714i	0.308936	−	0.246368i	−0.456732	−	0.889604i	$-0.650980\pi$
$293$	5.28813	−	4.21714i	0.308936	−	0.246368i	0.765668	+	0.643236i	$0.222409\pi$
$294$	2.37800	−	2.98192i	0.138688	−	0.173909i
$295$	−7.78986	+	3.75140i	−0.453543	+	0.218415i
$296$	−7.52930	−	3.62592i	−0.437632	−	0.210752i
$297$	17.0688	+	21.4036i	0.990434	+	1.24196i
$298$	8.07321	+	1.84266i	0.467669	+	0.106742i
$299$	−2.88793	+	12.6528i	−0.167013	+	0.731733i
$300$	−7.94250	−	6.33393i	−0.458560	−	0.365690i
$301$	1.18505	−	0.270479i	0.0683049	−	0.0155901i
$302$			3.35019i			0.192782i
$303$	−0.896125	−	3.92618i	−0.0514810	−	0.225553i
$304$	2.91534	−	6.05376i	0.167206	−	0.347207i
$305$	−0.493353	+	1.02446i	−0.0282493	+	0.0586603i
$306$	−0.643104	−	2.81762i	−0.0367638	−	0.161073i
$307$		−	4.51812i		−	0.257863i	−0.991654	−	0.128931i	$-0.958845\pi$
$307$		−	4.51812i		−	0.257863i	0.991654	−	0.128931i	$-0.0411547\pi$
$308$	−3.09666	+	0.706791i	−0.176448	+	0.0402732i
$309$	−13.3105	−	10.6148i	−0.757207	−	0.603853i
$310$	−0.458615	+	2.00933i	−0.0260476	+	0.114122i
$311$	−12.3002	−	2.80745i	−0.697482	−	0.159196i	−0.140944	−	0.990018i	$-0.545014\pi$
$311$	−12.3002	−	2.80745i	−0.697482	−	0.159196i	−0.556538	+	0.830822i	$0.687871\pi$
$312$	−7.43631	−	9.32484i	−0.420998	−	0.527915i
$313$	−17.3349	−	8.34804i	−0.979826	−	0.471859i	−0.125781	−	0.992058i	$-0.540144\pi$
$313$	−17.3349	−	8.34804i	−0.979826	−	0.471859i	−0.854045	+	0.520199i	$0.825858\pi$
$314$	−7.31336	+	3.52193i	−0.412717	+	0.198754i
$315$	−0.222521	+	0.279032i	−0.0125376	+	0.0157217i
$316$	−6.57193	+	5.24094i	−0.369700	+	0.294826i
$317$	−1.24451	−	2.58426i	−0.0698989	−	0.145147i	0.863092	−	0.505047i	$-0.168525\pi$
$317$	−1.24451	−	2.58426i	−0.0698989	−	0.145147i	−0.932991	+	0.359901i	$0.882811\pi$
$318$	2.60388			0.146018
$319$		0			0
$320$	−2.51275			−0.140467
$321$	−8.78904	−	18.2506i	−0.490556	−	1.01865i
$322$	−0.285107	+	0.227365i	−0.0158884	+	0.0126706i
$323$	6.60388	−	8.28100i	0.367449	−	0.460767i
$324$	4.18329	−	2.01457i	0.232405	−	0.111920i
$325$	23.0260	+	11.0887i	1.27725	+	0.615091i
$326$	−3.50753	−	4.39831i	−0.194264	−	0.243600i
$327$	6.64609	+	1.51693i	0.367529	+	0.0838862i
$328$	1.17092	−	5.13011i	0.0646530	−	0.283263i
$329$	−1.79838	−	1.43416i	−0.0991477	−	0.0790676i
$330$	−1.84923	+	0.422075i	−0.101797	+	0.0232345i
$331$			3.13408i			0.172265i	0.996284	+	0.0861323i	$0.0274508\pi$
$331$			3.13408i			0.172265i	−0.996284	+	0.0861323i	$0.972549\pi$
$332$	−1.78621	−	7.82589i	−0.0980309	−	0.429501i
$333$	−3.09666	+	6.43027i	−0.169696	+	0.352377i
$334$	0.153813	−	0.319396i	0.00841628	−	0.0174766i
$335$	0.357724	+	1.56729i	0.0195445	+	0.0856302i
$336$			1.26875i			0.0692160i
$337$	4.85762	−	1.10872i	0.264611	−	0.0603958i	−0.0881567	−	0.996107i	$-0.528098\pi$
$337$	4.85762	−	1.10872i	0.264611	−	0.0603958i	0.352768	+	0.935711i	$0.385240\pi$
$338$	6.59502	+	5.25936i	0.358722	+	0.286071i
$339$	−2.96197	+	12.9772i	−0.160872	+	0.704826i
$340$	−5.46337	−	1.24698i	−0.296293	−	0.0676270i
$341$	20.6075	+	25.8410i	1.11596	+	1.39937i
$342$	1.36563	+	0.657650i	0.0738445	+	0.0355617i
$343$	4.46077	−	2.14819i	0.240859	−	0.115992i
$344$	−3.59299	+	4.50547i	−0.193721	+	0.242919i
$345$	1.54898	−	1.23527i	0.0833940	−	0.0665045i
$346$	−1.76750	−	3.67025i	−0.0950214	−	0.197314i
$347$	−20.1172			−1.07995			−0.539974	−	0.841682i	$-0.681566\pi$
$347$	−20.1172			−1.07995			−0.539974	+	0.841682i	$0.681566\pi$
$348$		0			0
$349$	20.4892			1.09676			0.548380	−	0.836229i	$-0.315245\pi$
$349$	20.4892			1.09676			0.548380	+	0.836229i	$0.315245\pi$
$350$	0.311573	+	0.646989i	0.0166543	+	0.0345830i
$351$	−24.4969	+	19.5356i	−1.30755	+	1.04274i
$352$	14.3279	−	17.9666i	0.763679	−	0.957623i
$353$	16.2153	−	7.80887i	0.863052	−	0.415624i	0.0506467	−	0.998717i	$-0.483872\pi$
$353$	16.2153	−	7.80887i	0.863052	−	0.415624i	0.812406	+	0.583092i	$0.198157\pi$
$354$	−6.24698	−	3.00839i	−0.332023	−	0.159894i
$355$	−3.16487	−	3.96863i	−0.167974	−	0.210633i
$356$	−9.97829	−	2.27748i	−0.528848	−	0.120706i
$357$	−0.445042	+	1.94986i	−0.0235541	+	0.103197i
$358$	−1.18505	−	0.945042i	−0.0626316	−	0.0499470i
$359$	−23.0362	+	5.25786i	−1.21580	+	0.277499i	−0.781868	−	0.623444i	$-0.785733\pi$
$359$	−23.0362	+	5.25786i	−1.21580	+	0.277499i	−0.433937	+	0.900943i	$0.642876\pi$
$360$		−	1.69202i		−	0.0891774i
$361$	−2.99180	−	13.1079i	−0.157463	−	0.689892i
$362$	2.44741	−	5.08211i	0.128633	−	0.267110i
$363$	−7.24660	+	15.0477i	−0.380348	+	0.789801i
$364$	−0.808938	−	3.54419i	−0.0423999	−	0.185766i
$365$		−	3.89307i		−	0.203772i
$366$	−0.888992	+	0.202907i	−0.0464684	+	0.0106061i
$367$	23.1759	+	18.4822i	1.20977	+	0.964762i	0.999916	−	0.0129705i	$-0.00412876\pi$
$367$	23.1759	+	18.4822i	1.20977	+	0.964762i	0.209857	+	0.977732i	$0.432700\pi$
$368$	−1.45646	+	6.38117i	−0.0759232	+	0.332641i
$369$	−4.38129	−	1.00000i	−0.228081	−	0.0520579i
$370$	−0.948394	−	1.18925i	−0.0493047	−	0.0618261i
$371$	1.50873	+	0.726566i	0.0783293	+	0.0377214i
$372$	13.5477	−	6.52424i	0.702417	−	0.338266i
$373$	−15.7044	+	19.6927i	−0.813143	+	1.01965i	0.186167	+	0.982518i	$0.440393\pi$
$373$	−15.7044	+	19.6927i	−0.813143	+	1.01965i	−0.999310	+	0.0371310i	$0.988178\pi$
$374$	7.72293	−	6.15883i	0.399343	−	0.318466i
$375$	−3.56484	−	7.40246i	−0.184087	−	0.382261i
$376$	10.9051			0.562390
$377$		0			0
$378$	−0.880395			−0.0452826
$379$	−11.6745	−	24.2424i	−0.599681	−	1.24525i	−0.951057	−	0.309016i	$-0.900000\pi$
$379$	−11.6745	−	24.2424i	−0.599681	−	1.24525i	0.351376	−	0.936234i	$-0.385714\pi$
$380$	2.29780	−	1.83244i	0.117875	−	0.0940020i
$381$	−0.806118	+	1.01084i	−0.0412987	+	0.0517869i
$382$	4.27844	−	2.06039i	0.218904	−	0.105419i
$383$	−17.7213	−	8.53414i	−0.905517	−	0.436074i	−0.0776388	−	0.996982i	$-0.524738\pi$
$383$	−17.7213	−	8.53414i	−0.905517	−	0.436074i	−0.827879	+	0.560907i	$0.810452\pi$
$384$	−8.49127	−	10.6477i	−0.433318	−	0.543364i
$385$	−1.18925	−	0.271438i	−0.0606097	−	0.0138338i
$386$	−2.25086	+	9.86168i	−0.114566	+	0.501946i
$387$	3.84782	+	3.06853i	0.195596	+	0.155982i
$388$	−0.317278	+	0.0724165i	−0.0161073	+	0.00367639i
$389$			24.8552i			1.26021i	0.776511	+	0.630103i	$0.216988\pi$
$389$			24.8552i			1.26021i	−0.776511	+	0.630103i	$0.783012\pi$
$390$	−0.483074	−	2.11649i	−0.0244614	−	0.107172i
$391$	−4.47667	+	9.29590i	−0.226395	+	0.470114i
$392$	−5.04547	+	10.4770i	−0.254835	+	0.529170i
$393$	2.22587	+	9.75219i	0.112280	+	0.491933i
$394$		−	8.70410i		−	0.438506i
$395$	−3.14726	+	0.718341i	−0.158356	+	0.0361436i
$396$	−10.0548	−	8.01842i	−0.505272	−	0.402941i
$397$	0.888887	−	3.89447i	0.0446120	−	0.195458i	−0.947711	−	0.319129i	$-0.896610\pi$
$397$	0.888887	−	3.89447i	0.0446120	−	0.195458i	0.992323	+	0.123671i	$0.0394668\pi$
$398$	0.379656	+	0.0866540i	0.0190304	+	0.00434357i
$399$	−0.653989	−	0.820077i	−0.0327404	−	0.0410552i
$400$	11.6126	+	5.59234i	0.580630	+	0.279617i
$401$	22.4405	−	10.8068i	1.12062	−	0.539664i	0.220539	−	0.975378i	$-0.429218\pi$
$401$	22.4405	−	10.8068i	1.12062	−	0.539664i	0.900085	+	0.435714i	$0.143504\pi$
$402$	−0.803798	+	1.00793i	−0.0400898	+	0.0502710i
$403$	−29.5756	+	23.5858i	−1.47327	+	1.17489i
$404$	2.52494	+	5.24309i	0.125621	+	0.260854i
$405$	1.78315			0.0886055
$406$		0			0
$407$	−24.3937			−1.20915
$408$	−4.11403	−	8.54288i	−0.203675	−	0.422935i
$409$	0.221434	−	0.176587i	0.0109492	−	0.00873169i	−0.618000	−	0.786178i	$-0.712057\pi$
$409$	0.221434	−	0.176587i	0.0109492	−	0.00873169i	0.628949	+	0.777446i	$0.283485\pi$
$410$	0.597171	−	0.748828i	0.0294922	−	0.0369820i
$411$	−19.3605	+	9.32355i	−0.954985	+	0.459897i
$412$	22.1652	+	10.6742i	1.09200	+	0.525879i
$413$	−2.78017	−	3.48622i	−0.136803	−	0.171546i
$414$	−1.43948	−	0.328552i	−0.0707467	−	0.0161475i
$415$	0.685981	−	3.00548i	0.0336735	−	0.147533i
$416$	20.5632	+	16.3986i	1.00819	+	0.804006i
$417$	−20.2634	+	4.62498i	−0.992301	+	0.226486i
$418$			5.18060i			0.253392i
$419$	−5.89426	−	25.8245i	−0.287954	−	1.26161i	−0.887328	−	0.461139i	$-0.847441\pi$
$419$	−5.89426	−	25.8245i	−0.287954	−	1.26161i	0.599374	−	0.800469i	$-0.295416\pi$
$420$	−0.240787	+	0.500000i	−0.0117492	+	0.0243975i
$421$	−7.62859	+	15.8409i	−0.371795	+	0.772040i	−0.999982	−	0.00602261i	$-0.998083\pi$
$421$	−7.62859	+	15.8409i	−0.371795	+	0.772040i	0.628187	+	0.778062i	$0.283797\pi$
$422$	−1.80917	−	7.92651i	−0.0880693	−	0.385857i
$423$		−	9.31336i		−	0.452831i
$424$	−7.73995	+	1.76659i	−0.375885	+	0.0857934i
$425$	15.8850	+	12.6679i	0.770535	+	0.614481i
$426$	0.905813	−	3.96863i	0.0438868	−	0.192281i
$427$	−0.571714	−	0.130490i	−0.0276672	−	0.00631486i
$428$	18.2506	+	22.8856i	0.882177	+	1.10622i
$429$	−31.3669	−	15.1055i	−1.51441	−	0.729300i
$430$	−0.945042	+	0.455108i	−0.0455740	+	0.0219473i
$431$	−17.3300	+	21.7312i	−0.834759	+	1.04675i	0.163428	+	0.986555i	$0.447745\pi$
$431$	−17.3300	+	21.7312i	−0.834759	+	1.04675i	−0.998186	+	0.0601992i	$0.980826\pi$
$432$	−12.3545	+	9.85235i	−0.594404	+	0.474021i
$433$	−2.54933	−	5.29374i	−0.122513	−	0.254401i	0.830688	−	0.556738i	$-0.187947\pi$
$433$	−2.54933	−	5.29374i	−0.122513	−	0.254401i	−0.953201	+	0.302337i	$0.902233\pi$
$434$	−1.06292			−0.0510217
$435$		0			0
$436$	−9.85086			−0.471770
$437$	−2.34783	−	4.87531i	−0.112312	−	0.233218i
$438$	2.44088	−	1.94653i	0.116630	−	0.0930090i
$439$	9.81431	−	12.3068i	0.468412	−	0.587370i	−0.490370	−	0.871515i	$-0.663138\pi$
$439$	9.81431	−	12.3068i	0.468412	−	0.587370i	0.958781	+	0.284145i	$0.0917097\pi$
$440$	5.21044	−	2.50922i	0.248398	−	0.119622i
$441$	8.94773	+	4.30900i	0.426082	+	0.205190i
$442$	7.04892	+	8.83906i	0.335283	+	0.420431i
$443$	−6.56960	−	1.49947i	−0.312131	−	0.0712419i	0.0635859	−	0.997976i	$-0.479746\pi$
$443$	−6.56960	−	1.49947i	−0.312131	−	0.0712419i	−0.375717	+	0.926735i	$0.622603\pi$
$444$	−2.46950	+	10.8196i	−0.117197	+	0.513475i
$445$	−3.07310	−	2.45071i	−0.145679	−	0.116175i
$446$	−0.788944	+	0.180071i	−0.0373576	+	0.00852663i
$447$		−	23.2024i		−	1.09743i
$448$	−0.288364	−	1.26341i	−0.0136239	−	0.0596903i
$449$	−5.34547	+	11.1000i	−0.252269	+	0.523841i	−0.988191	−	0.153224i	$-0.951034\pi$
$449$	−5.34547	+	11.1000i	−0.252269	+	0.523841i	0.735923	+	0.677065i	$0.236749\pi$
$450$	−1.26154	+	2.61960i	−0.0594693	+	0.123489i
$451$	−3.41789	−	14.9748i	−0.160942	−	0.705135i
$452$		−	19.2349i		−	0.904733i
$453$	9.15167	−	2.08881i	0.429983	−	0.0981409i
$454$	−4.82124	−	3.84481i	−0.226272	−	0.180446i
$455$	0.310667	−	1.36112i	0.0145643	−	0.0638103i
$456$	4.84817	+	1.10656i	0.227037	+	0.0518196i
$457$	−8.51842	−	10.6818i	−0.398475	−	0.499672i	0.541602	−	0.840635i	$-0.317818\pi$
$457$	−8.51842	−	10.6818i	−0.398475	−	0.499672i	−0.940076	+	0.340964i	$0.889247\pi$
$458$	−5.12133	−	2.46630i	−0.239304	−	0.115243i
$459$	−22.4426	+	10.8078i	−1.04753	+	0.504465i
$460$	−1.78501	+	2.23833i	−0.0832266	+	0.104363i
$461$	−9.07565	+	7.23759i	−0.422695	+	0.337088i	−0.811624	−	0.584180i	$-0.801416\pi$
$461$	−9.07565	+	7.23759i	−0.422695	+	0.337088i	0.388929	+	0.921268i	$0.372845\pi$
$462$	−0.424438	−	0.881355i	−0.0197466	−	0.0410043i
$463$	7.24267			0.336595			0.168298	−	0.985736i	$-0.446173\pi$
$463$	7.24267			0.336595			0.168298	+	0.985736i	$0.446173\pi$
$464$		0			0
$465$	5.77479			0.267800
$466$	1.71198	+	3.55496i	0.0793058	+	0.164680i
$467$	−1.61322	+	1.28650i	−0.0746511	+	0.0595323i	−0.660104	−	0.751174i	$-0.729488\pi$
$467$	−1.61322	+	1.28650i	−0.0746511	+	0.0595323i	0.585453	+	0.810706i	$0.300917\pi$
$468$	9.17725	−	11.5079i	0.424219	−	0.531953i
$469$	−0.746980	+	0.359726i	−0.0344923	+	0.0166106i
$470$	1.78836	+	0.861231i	0.0824911	+	0.0397256i
$471$	14.1806	+	17.7819i	0.653408	+	0.819347i
$472$	20.6100	+	4.70410i	0.948653	+	0.216524i
$473$	−3.74309	+	16.3996i	−0.172108	+	0.754053i
$474$	−2.02401	−	1.61410i	−0.0929660	−	0.0741379i
$475$	−10.3886	+	2.37113i	−0.476662	+	0.108795i
$476$		−	2.89008i		−	0.132467i
$477$	1.50873	+	6.61017i	0.0690800	+	0.302659i
$478$	−4.93644	+	10.2506i	−0.225788	+	0.468853i
$479$	−1.68738	+	3.50388i	−0.0770985	+	0.160097i	−0.935955	−	0.352120i	$-0.885461\pi$
$479$	−1.68738	+	3.50388i	−0.0770985	+	0.160097i	0.858857	+	0.512216i	$0.171175\pi$
$480$	−0.893436	−	3.91440i	−0.0407796	−	0.178667i
$481$		−	27.9191i		−	1.27300i
$482$	−4.22223	+	0.963697i	−0.192317	+	0.0438952i
$483$	0.798852	+	0.637063i	0.0363490	+	0.0289874i
$484$	5.37047	−	23.5296i	0.244112	−	1.06953i
$485$	−0.121848	−	0.0278111i	−0.00553284	−	0.00126284i
$486$	−3.72252	−	4.66789i	−0.168857	−	0.211740i
$487$	−8.87047	−	4.27179i	−0.401959	−	0.193573i	0.221971	−	0.975053i	$-0.428751\pi$
$487$	−8.87047	−	4.27179i	−0.401959	−	0.193573i	−0.623931	+	0.781480i	$0.714465\pi$
$488$	2.50484	−	1.20627i	0.113389	−	0.0546053i
$489$	−9.82789	+	12.3238i	−0.444432	+	0.557301i
$490$	−1.65484	+	1.31969i	−0.0747581	+	0.0596176i
$491$	−3.38047	−	7.01961i	−0.152558	−	0.316791i	0.810657	−	0.585521i	$-0.199110\pi$
$491$	−3.38047	−	7.01961i	−0.152558	−	0.316791i	−0.963215	+	0.268731i	$0.913396\pi$
$492$	−6.98792			−0.315040
$493$		0			0
$494$	−5.92931			−0.266772
$495$	−2.14295	−	4.44989i	−0.0963185	−	0.200008i
$496$	−14.9158	+	11.8949i	−0.669738	+	0.534098i
$497$	1.63222	−	2.04674i	0.0732150	−	0.0918087i
$498$	2.22737	−	1.07264i	0.0998106	−	0.0480663i
$499$	−18.5286	−	8.92292i	−0.829456	−	0.399445i	−0.0295448	−	0.999563i	$-0.509406\pi$
$499$	−18.5286	−	8.92292i	−0.829456	−	0.399445i	−0.799911	+	0.600119i	$0.795120\pi$
$500$	7.40246	+	9.28239i	0.331048	+	0.415121i
$501$	−0.968391	−	0.221029i	−0.0432645	−	0.00987485i
$502$	0.966575	−	4.23484i	0.0431404	−	0.189010i
$503$	6.43830	+	5.13437i	0.287070	+	0.228930i	0.756427	−	0.654078i	$-0.226943\pi$
$503$	6.43830	+	5.13437i	0.287070	+	0.228930i	−0.469358	+	0.883008i	$0.655514\pi$
$504$	0.850747	−	0.194177i	0.0378953	−	0.00864935i
$505$			2.23490i			0.0994517i
$506$	−1.12296	−	4.92000i	−0.0499215	−	0.218721i
$507$	10.2550	−	21.2947i	0.455440	−	0.945731i
$508$	0.810631	−	1.68329i	0.0359659	−	0.0746840i
$509$	−1.76151	−	7.71769i	−0.0780777	−	0.342081i	0.920768	−	0.390110i	$-0.127563\pi$
$509$	−1.76151	−	7.71769i	−0.0780777	−	0.342081i	−0.998846	+	0.0480294i	$0.984706\pi$
$510$		−	1.72587i		−	0.0764230i
$511$	1.95743	−	0.446771i	0.0865916	−	0.0197640i
$512$	17.9132	+	14.2853i	0.791659	+	0.631327i
$513$	2.90701	−	12.7364i	0.128348	−	0.562328i
$514$	−7.09699	−	1.61984i	−0.313035	−	0.0714482i
$515$	5.89075	+	7.38676i	0.259577	+	0.325500i
$516$	6.89493	+	3.32042i	0.303532	+	0.146173i
$517$	28.6797	−	13.8114i	1.26133	−	0.607425i
$518$	0.489115	−	0.613331i	0.0214905	−	0.0269482i
$519$	−8.92396	+	7.11662i	−0.391718	+	0.312385i
$520$	2.87185	+	5.96346i	0.125939	+	0.261515i
$521$	3.52542			0.154451			0.0772257	−	0.997014i	$-0.475394\pi$
$521$	3.52542			0.154451			0.0772257	+	0.997014i	$0.475394\pi$
$522$		0			0
$523$	10.0301			0.438587			0.219294	−	0.975659i	$-0.429625\pi$
$523$	10.0301			0.438587			0.219294	+	0.975659i	$0.429625\pi$
$524$	−6.27167	−	13.0233i	−0.273979	−	0.568924i
$525$	1.57311	−	1.25451i	0.0686561	−	0.0547514i
$526$	6.58277	−	8.25453i	0.287022	−	0.359915i
$527$	−27.0954	+	13.0485i	−1.18030	+	0.568401i
$528$	−15.8192	−	7.61811i	−0.688441	−	0.331535i
$529$	−11.0538	−	13.8610i	−0.480598	−	0.602651i
$530$	−1.40881	−	0.321552i	−0.0611949	−	0.0139673i
$531$	4.01746	−	17.6016i	0.174343	−	0.763846i
$532$	1.18505	+	0.945042i	0.0513782	+	0.0409728i
$533$	17.1390	−	3.91185i	0.742370	−	0.169441i
$534$		−	3.15213i		−	0.136406i
$535$	2.50149	+	10.9598i	0.108149	+	0.473831i
$536$	1.70544	−	3.54138i	0.0736638	−	0.152965i
$537$	−1.84270	+	3.82640i	−0.0795182	+	0.165121i
$538$	2.51089	+	11.0009i	0.108252	+	0.474283i
$539$			33.9439i			1.46207i
$540$	−6.73856	+	1.53803i	−0.289981	+	0.0661864i
$541$	−6.42990	−	5.12767i	−0.276443	−	0.220456i	0.475447	−	0.879744i	$-0.342286\pi$
$541$	−6.42990	−	5.12767i	−0.276443	−	0.220456i	−0.751890	+	0.659288i	$0.770858\pi$
$542$	−0.119178	+	0.522153i	−0.00511913	+	0.0224284i
$543$	−15.4087	−	3.51693i	−0.661249	−	0.150926i
$544$	13.0368	+	16.3477i	0.558950	+	0.700901i
$545$	−3.40850	−	1.64145i	−0.146004	−	0.0703119i
$546$	1.00873	−	0.485778i	0.0431696	−	0.0207894i
$547$	16.1253	−	20.2205i	0.689467	−	0.864564i	−0.306721	−	0.951800i	$-0.599232\pi$
$547$	16.1253	−	20.2205i	0.689467	−	0.864564i	0.996188	+	0.0872352i	$0.0278032\pi$
$548$	24.2774	−	19.3605i	1.03708	−	0.827041i
$549$	−1.03019	−	2.13922i	−0.0439676	−	0.0912997i
$550$	−9.93767			−0.423744
$551$		0			0
$552$	−4.84415			−0.206181
$553$	−0.722362	−	1.50000i	−0.0307180	−	0.0637865i
$554$	−3.71082	+	2.95928i	−0.157658	+	0.125728i
$555$	−2.65734	+	3.33220i	−0.112798	+	0.141444i
$556$	27.0601	−	13.0315i	1.14760	−	0.552657i
$557$	20.7310	+	9.98353i	0.878401	+	0.423016i	0.818040	−	0.575161i	$-0.195061\pi$
$557$	20.7310	+	9.98353i	0.878401	+	0.423016i	0.0603609	+	0.998177i	$0.480775\pi$
$558$	−2.68329	−	3.36474i	−0.113593	−	0.142441i
$559$	−18.7697	−	4.28405i	−0.793872	−	0.181196i
$560$	0.156678	−	0.686450i	0.00662084	−	0.0290078i
$561$	−21.6392	−	17.2567i	−0.913607	−	0.728577i
$562$	−7.06341	+	1.61218i	−0.297952	+	0.0680056i
$563$			43.1159i			1.81712i	0.417757	+	0.908559i	$0.362816\pi$
$563$			43.1159i			1.81712i	−0.417757	+	0.908559i	$0.637184\pi$
$564$	−3.22252	−	14.1188i	−0.135693	−	0.594508i
$565$	3.20511	−	6.65548i	0.134840	−	0.279998i
$566$	1.01317	−	2.10388i	0.0425868	−	0.0884325i
$567$	0.204636	+	0.896567i	0.00859388	+	0.0376523i
$568$			12.4112i			0.520762i
$569$	−23.7027	+	5.40999i	−0.993670	+	0.226799i	−0.688293	−	0.725433i	$-0.741640\pi$
$569$	−23.7027	+	5.40999i	−0.993670	+	0.226799i	−0.305377	+	0.952231i	$0.598783\pi$
$570$	0.707674	+	0.564351i	0.0296412	+	0.0236381i
$571$	−4.11410	+	18.0250i	−0.172170	+	0.754324i	0.812933	+	0.582357i	$0.197869\pi$
$571$	−4.11410	+	18.0250i	−0.172170	+	0.754324i	−0.985103	+	0.171967i	$0.944988\pi$
$572$	49.0472	+	11.1947i	2.05077	+	0.468074i
$573$	−8.29590	−	10.4027i	−0.346566	−	0.434580i
$574$	0.445042	+	0.214321i	0.0185757	+	0.00894558i
$575$	9.35205	−	4.50371i	0.390008	−	0.187818i
$576$	3.27144	−	4.10225i	0.136310	−	0.170927i
$577$	29.5987	−	23.6042i	1.23221	−	0.982654i	0.232260	−	0.972654i	$-0.425388\pi$
$577$	29.5987	−	23.6042i	1.23221	−	0.982654i	0.999950	−	0.0100007i	$-0.00318338\pi$
$578$	0.617072	+	1.28136i	0.0256668	+	0.0532977i
$579$	28.3424			1.17787
$580$		0			0
$581$	1.58987			0.0659591
$582$	−0.0434871	−	0.0903019i	−0.00180260	−	0.00374314i
$583$	−18.1181	+	14.4487i	−0.750374	+	0.598404i
$584$	−5.93482	+	7.44203i	−0.245585	+	0.307953i
$585$	5.09299	−	2.45265i	0.210569	−	0.101405i
$586$	−2.71206	−	1.30606i	−0.112034	−	0.0539529i
$587$	−9.00030	−	11.2860i	−0.371482	−	0.465824i	0.560592	−	0.828092i	$-0.310574\pi$
$587$	−9.00030	−	11.2860i	−0.371482	−	0.465824i	−0.932074	+	0.362269i	$0.882002\pi$
$588$	15.0555	+	3.43631i	0.620877	+	0.141711i
$589$	3.50969	−	15.3770i	0.144614	−	0.633596i
$590$	3.00839	+	2.39911i	0.123853	+	0.0987697i
$591$	−23.7769	+	5.42692i	−0.978050	+	0.223234i
$592$		−	14.0804i		−	0.578700i
$593$	−2.89320	−	12.6759i	−0.118809	−	0.520538i	−0.998950	−	0.0458241i	$-0.985409\pi$
$593$	−2.89320	−	12.6759i	−0.118809	−	0.520538i	0.880140	−	0.474714i	$-0.157449\pi$
$594$	5.28626	−	10.9770i	0.216898	−	0.450393i
$595$	0.481575	−	1.00000i	0.0197426	−	0.0409960i
$596$	7.46077	+	32.6878i	0.305605	+	1.33894i
$597$		−	1.09113i		−	0.0446570i
$598$	5.63104	−	1.28525i	0.230270	−	0.0525577i
$599$	−9.45510	−	7.54019i	−0.386325	−	0.308084i	0.410999	−	0.911636i	$-0.365180\pi$
$599$	−9.45510	−	7.54019i	−0.386325	−	0.308084i	−0.797323	+	0.603552i	$0.793751\pi$
$600$	−2.12266	+	9.29999i	−0.0866573	+	0.379670i
$601$	−21.7869	−	4.97272i	−0.888707	−	0.202842i	−0.246289	−	0.969196i	$-0.579211\pi$
$601$	−21.7869	−	4.97272i	−0.888707	−	0.202842i	−0.642418	+	0.766355i	$0.722068\pi$
$602$	−0.337282	−	0.422938i	−0.0137466	−	0.0172377i
$603$	−3.02446	−	1.45650i	−0.123165	−	0.0593134i
$604$	−12.2213	+	5.88548i	−0.497279	+	0.239477i
$605$	5.77897	−	7.24660i	0.234949	−	0.294616i
$606$	−1.40124	+	1.11745i	−0.0569214	+	0.0453933i
$607$	−17.9926	−	37.3620i	−0.730297	−	1.51648i	−0.851789	−	0.523886i	$-0.824482\pi$
$607$	−17.9926	−	37.3620i	−0.730297	−	1.51648i	0.121491	−	0.992593i	$-0.461232\pi$
$608$	−10.9661			−0.444736
$609$		0			0
$610$	0.506041			0.0204890
$611$	15.8075	+	32.8245i	0.639502	+	1.32794i
$612$	9.14877	−	7.29590i	0.369817	−	0.294919i
$613$	−16.0764	+	20.1591i	−0.649318	+	0.814219i	−0.992134	−	0.125184i	$-0.960048\pi$
$613$	−16.0764	+	20.1591i	−0.649318	+	0.814219i	0.342816	+	0.939403i	$0.388619\pi$
$614$	−1.81163	+	0.872433i	−0.0731113	+	0.0352085i
$615$	−2.41789	−	1.16440i	−0.0974989	−	0.0469530i
$616$	1.85958	+	2.33184i	0.0749248	+	0.0939527i
$617$	−8.64306	−	1.97272i	−0.347956	−	0.0794188i	0.0449710	−	0.998988i	$-0.485680\pi$
$617$	−8.64306	−	1.97272i	−0.347956	−	0.0794188i	−0.392927	+	0.919570i	$0.628538\pi$
$618$	−1.68598	+	7.38676i	−0.0678201	+	0.297139i
$619$	23.0259	+	18.3626i	0.925490	+	0.738054i	0.965297	−	0.261153i	$-0.0841029\pi$
$619$	23.0259	+	18.3626i	0.925490	+	0.738054i	−0.0398069	+	0.999207i	$0.512674\pi$
$620$	−8.13559	+	1.85690i	−0.326733	+	0.0745747i
$621$			12.7259i			0.510672i
$622$	1.24943	+	5.47412i	0.0500976	+	0.219492i
$623$	0.879546	−	1.82640i	0.0352383	−	0.0731730i
$624$	8.71909	−	18.1054i	0.349043	−	0.724795i
$625$	−4.01560	−	17.5935i	−0.160624	−	0.703739i
$626$			8.56273i			0.342235i
$627$	14.1518	−	3.23005i	0.565168	−	0.128996i
$628$	−25.6956	−	20.4916i	−1.02537	−	0.817703i
$629$	4.93900	−	21.6392i	0.196931	−	0.862811i
$630$	0.154851	+	0.0353438i	0.00616942	+	0.00140813i
$631$	−14.8210	−	18.5850i	−0.590015	−	0.739856i	0.393769	−	0.919209i	$-0.371171\pi$
$631$	−14.8210	−	18.5850i	−0.590015	−	0.739856i	−0.983785	+	0.179353i	$0.942599\pi$
$632$	7.11141	+	3.42467i	0.282877	+	0.136226i
$633$	−20.5248	+	9.88420i	−0.815786	+	0.392862i
$634$	−0.795897	+	0.998023i	−0.0316091	+	0.0396366i
$635$	0.560974	−	0.447362i	0.0222616	−	0.0177530i
$636$	4.57438	+	9.49880i	0.181386	+	0.376652i
$637$	−38.8495			−1.53927
$638$		0			0
$639$	10.5996			0.419312
$640$	3.27927	+	6.80947i	0.129624	+	0.269168i
$641$	22.2552	−	17.7479i	0.879028	−	0.701001i	−0.0761300	−	0.997098i	$-0.524256\pi$
$641$	22.2552	−	17.7479i	0.879028	−	0.701001i	0.955158	+	0.296096i	$0.0956850\pi$
$642$	−5.62080	+	7.04826i	−0.221835	+	0.278173i
$643$	−17.4308	+	8.39423i	−0.687404	+	0.331036i	−0.744774	−	0.667317i	$-0.767443\pi$
$643$	−17.4308	+	8.39423i	−0.687404	+	0.331036i	0.0573702	+	0.998353i	$0.481728\pi$
$644$	−1.33028	−	0.640630i	−0.0524204	−	0.0252443i
$645$	1.83244	+	2.29780i	0.0721521	+	0.0904759i
$646$	−4.59561	−	1.04892i	−0.180812	−	0.0412691i
$647$	5.05443	−	22.1449i	0.198710	−	0.870605i	−0.772996	−	0.634411i	$-0.781243\pi$
$647$	5.05443	−	22.1449i	0.198710	−	0.870605i	0.971706	−	0.236194i	$-0.0759002\pi$
$648$	−3.40869	−	2.71834i	−0.133906	−	0.106787i
$649$	60.1605	−	13.7313i	2.36151	−	0.538999i
$650$		−	11.3739i		−	0.446120i
$651$	0.662718	+	2.90356i	0.0259740	+	0.113799i
$652$	9.88291	−	20.5221i	0.387044	−	0.803706i
$653$	9.94949	−	20.6603i	0.389354	−	0.808501i	−0.610510	−	0.792008i	$-0.709036\pi$
$653$	9.94949	−	20.6603i	0.389354	−	0.808501i	0.999864	−	0.0164928i	$-0.00525006\pi$
$654$	−0.675096	−	2.95779i	−0.0263983	−	0.115659i
$655$		−	5.55124i		−	0.216905i
$656$	8.64363	−	1.97285i	0.337477	−	0.0770270i
$657$	6.35574	+	5.06853i	0.247961	+	0.197742i
$658$	−0.227792	+	0.998023i	−0.00888027	+	0.0389070i
$659$	−18.6974	−	4.26755i	−0.728346	−	0.166240i	−0.157759	−	0.987478i	$-0.550427\pi$
$659$	−18.6974	−	4.26755i	−0.728346	−	0.166240i	−0.570587	+	0.821237i	$0.693284\pi$
$660$	−4.78836	−	6.00442i	−0.186387	−	0.233722i
$661$	3.05107	+	1.46932i	0.118673	+	0.0571499i	0.492278	−	0.870438i	$-0.336164\pi$
$661$	3.05107	+	1.46932i	0.118673	+	0.0571499i	−0.373605	+	0.927588i	$0.621879\pi$
$662$	1.25667	−	0.605180i	0.0488418	−	0.0235210i
$663$	19.7506	−	24.7665i	0.767051	−	0.961851i
$664$	−5.89305	+	4.69955i	−0.228695	+	0.182378i
$665$	0.252566	+	0.524459i	0.00979409	+	0.0203376i
$666$	3.17629			0.123079
$667$		0			0
$668$	1.43535			0.0555355
$669$	0.983797	+	2.04288i	0.0380358	+	0.0789822i
$670$	0.559360	−	0.446074i	0.0216099	−	0.0172334i
$671$	5.05980	−	6.34479i	0.195332	−	0.244938i
$672$	1.86563	−	0.898438i	0.0719680	−	0.0346580i
$673$	4.29805	+	2.06983i	0.165678	+	0.0797862i	0.514885	−	0.857259i	$-0.327835\pi$
$673$	4.29805	+	2.06983i	0.165678	+	0.0797862i	−0.349207	+	0.937046i	$0.613549\pi$
$674$	−1.38255	−	1.73366i	−0.0532539	−	0.0667782i
$675$	24.4316	+	5.57636i	0.940374	+	0.214634i
$676$	−7.59999	+	33.2977i	−0.292307	+	1.28068i
$677$	−33.6892	−	26.8662i	−1.29478	−	1.03255i	−0.996959	−	0.0779309i	$-0.975169\pi$
$677$	−33.6892	−	26.8662i	−1.29478	−	1.03255i	−0.297821	−	0.954622i	$-0.596260\pi$
$678$	5.77541	−	1.31820i	0.221803	−	0.0506252i
$679$		−	0.0644568i		−	0.00247362i
$680$	1.17092	+	5.13011i	0.0449025	+	0.196731i
$681$	−7.49683	+	15.5673i	−0.287279	+	0.596542i
$682$	6.38220	−	13.2528i	0.244387	−	0.507475i
$683$	−5.21432	−	22.8454i	−0.199521	−	0.874157i	−0.971223	−	0.238173i	$-0.923452\pi$
$683$	−5.21432	−	22.8454i	−0.199521	−	0.874157i	0.771702	−	0.635984i	$-0.219406\pi$
$684$			6.13706i			0.234656i
$685$	11.6263	−	2.65362i	0.444217	−	0.101390i
$686$	−1.72272	−	1.37382i	−0.0657737	−	0.0524528i
$687$	−3.54407	+	15.5276i	−0.135215	+	0.592415i
$688$	−9.46604	−	2.16056i	−0.360890	−	0.0823707i
$689$	−16.5368	−	20.7365i	−0.630003	−	0.789999i
$690$	−0.794405	−	0.382565i	−0.0302425	−	0.0145640i
$691$	−38.8657	+	18.7167i	−1.47852	+	0.712018i	−0.987278	−	0.159005i	$-0.949171\pi$
$691$	−38.8657	+	18.7167i	−1.47852	+	0.712018i	−0.491243	+	0.871023i	$0.663457\pi$
$692$	10.2838	−	12.8955i	0.390932	−	0.490213i
$693$	1.99147	−	1.58815i	0.0756498	−	0.0603287i
$694$	3.88456	+	8.06638i	0.147456	+	0.306195i
$695$	11.5345			0.437529
$696$		0			0
$697$	13.9758			0.529373
$698$	−3.95639	−	8.21552i	−0.149751	−	0.310962i
$699$	8.64363	−	6.89307i	0.326932	−	0.260720i
$700$	−1.81282	+	2.27321i	−0.0685183	+	0.0859192i
$701$	3.81186	−	1.83570i	0.143972	−	0.0693333i	−0.360511	−	0.932755i	$-0.617398\pi$
$701$	3.81186	−	1.83570i	0.143972	−	0.0693333i	0.504483	+	0.863422i	$0.331683\pi$
$702$	12.5635	+	6.05024i	0.474177	+	0.228352i
$703$	7.25786	+	9.10107i	0.273736	+	0.343254i
$704$	17.4840	+	3.99061i	0.658953	+	0.150402i
$705$	1.23759	−	5.42222i	0.0466102	−	0.204213i
$706$	−6.26223	−	4.99396i	−0.235682	−	0.187950i
$707$	−1.12370	+	0.256478i	−0.0422613	+	0.00964586i
$708$		−	28.0737i		−	1.05507i
$709$	3.18287	+	13.9450i	0.119535	+	0.523717i	0.998871	+	0.0475144i	$0.0151300\pi$
$709$	3.18287	+	13.9450i	0.119535	+	0.523717i	−0.879336	+	0.476203i	$0.842013\pi$
$710$	−0.980170	+	2.03534i	−0.0367851	+	0.0763851i
$711$	2.92478	−	6.07338i	0.109688	−	0.227769i
$712$	2.13856	+	9.36962i	0.0801457	+	0.351141i
$713$			15.3642i			0.575393i
$714$	0.867767	−	0.198062i	0.0324754	−	0.00741229i
$715$	15.1055	+	12.0462i	0.564913	+	0.450503i
$716$	1.36563	−	5.98319i	0.0510358	−	0.223602i
$717$	31.0793	+	7.09365i	1.16068	+	0.264917i
$718$	6.55645	+	8.22153i	0.244685	+	0.306825i
$719$	21.1194	+	10.1706i	0.787620	+	0.379298i	0.784051	−	0.620696i	$-0.213150\pi$
$719$	21.1194	+	10.1706i	0.787620	+	0.379298i	0.00356825	+	0.999994i	$0.498864\pi$
$720$	2.56853	−	1.23694i	0.0957235	−	0.0460980i
$721$	−3.03803	+	3.80957i	−0.113142	+	0.141876i
$722$	−4.67817	+	3.73072i	−0.174104	+	0.138843i
$723$	5.26504	+	10.9330i	0.195809	+	0.406601i
$724$	22.8388			0.848796
$725$		0			0
$726$	7.43296			0.275863
$727$	22.5609	+	46.8482i	0.836738	+	1.73750i	0.657146	+	0.753763i	$0.271763\pi$
$727$	22.5609	+	46.8482i	0.836738	+	1.73750i	0.179592	+	0.983741i	$0.442522\pi$
$728$	−2.66885	+	2.12833i	−0.0989140	+	0.0788813i
$729$	−15.2500	+	19.1228i	−0.564813	+	0.708254i
$730$	−1.56100	+	0.751737i	−0.0577752	+	0.0278231i
$731$	−13.7899	−	6.64084i	−0.510036	−	0.245621i
$732$	−2.30194	−	2.88654i	−0.0850821	−	0.106690i
$733$	−33.3331	−	7.60806i	−1.23119	−	0.281010i	−0.443041	−	0.896501i	$-0.646101\pi$
$733$	−33.3331	−	7.60806i	−1.23119	−	0.281010i	−0.788144	+	0.615491i	$0.788958\pi$
$734$	2.93559	−	12.8617i	0.108355	−	0.474733i
$735$	4.63676	+	3.69769i	0.171030	+	0.136391i
$736$	10.4145	−	2.37704i	0.383884	−	0.0876190i
$737$		−	11.4735i		−	0.422632i
$738$	0.445042	+	1.94986i	0.0163822	+	0.0717752i
$739$	−17.2569	+	35.8342i	−0.634804	+	1.31818i	0.296881	+	0.954915i	$0.404054\pi$
$739$	−17.2569	+	35.8342i	−0.634804	+	1.31818i	−0.931684	+	0.363269i	$0.881661\pi$
$740$	2.67222	−	5.54892i	0.0982327	−	0.203982i
$741$	3.69687	+	16.1970i	0.135808	+	0.595013i
$742$		−	0.745251i		−	0.0273590i
$743$	6.99824	−	1.59730i	0.256740	−	0.0585993i	−0.0922133	−	0.995739i	$-0.529394\pi$
$743$	6.99824	−	1.59730i	0.256740	−	0.0585993i	0.348954	+	0.937140i	$0.386537\pi$
$744$	−11.0392	−	8.80343i	−0.404715	−	0.322749i
$745$	−2.86526	+	12.5535i	−0.104975	+	0.459925i
$746$	10.9286	+	2.49439i	0.400125	+	0.0913260i
$747$	4.01357	+	5.03286i	0.146849	+	0.184143i
$748$	36.0344	+	17.3533i	1.31755	+	0.634499i
$749$	−5.22348	+	2.51550i	−0.190862	+	0.0919142i
$750$	−2.27980	+	2.85878i	−0.0832465	+	0.104388i
$751$	21.2412	−	16.9393i	0.775103	−	0.618124i	−0.153947	−	0.988079i	$-0.549198\pi$
$751$	21.2412	−	16.9393i	0.775103	−	0.618124i	0.929050	+	0.369955i	$0.120627\pi$
$752$	7.97213	+	16.5543i	0.290714	+	0.603673i
$753$	−12.1709			−0.443533
$754$		0			0
$755$	−5.20941			−0.189590
$756$	−1.54664	−	3.21164i	−0.0562508	−	0.116806i
$757$	18.5236	−	14.7721i	0.673253	−	0.536901i	−0.226111	−	0.974101i	$-0.572601\pi$
$757$	18.5236	−	14.7721i	0.673253	−	0.536901i	0.899364	+	0.437200i	$0.144030\pi$
$758$	−7.46615	+	9.36225i	−0.271183	+	0.340052i
$759$	−12.7397	+	6.13514i	−0.462423	+	0.222691i
$760$	−2.48643	−	1.19740i	−0.0901922	−	0.0434343i
$761$	−8.88740	−	11.1444i	−0.322168	−	0.403986i	0.594204	−	0.804315i	$-0.297467\pi$
$761$	−8.88740	−	11.1444i	−0.322168	−	0.403986i	−0.916372	+	0.400329i	$0.868896\pi$
$762$	0.560974	+	0.128039i	0.0203219	+	0.00463835i
$763$	0.434157	−	1.90216i	0.0157175	−	0.0688630i
$764$	15.0324	+	11.9879i	0.543852	+	0.433708i
$765$	4.38129	−	1.00000i	0.158406	−	0.0361551i
$766$			8.75361i			0.316281i
$767$	15.7157	+	68.8550i	0.567461	+	2.48621i
$768$	1.29932	−	2.69806i	0.0468851	−	0.0973579i
$769$	−19.3975	+	40.2793i	−0.699491	+	1.45251i	0.183453	+	0.983029i	$0.441273\pi$
$769$	−19.3975	+	40.2793i	−0.699491	+	1.45251i	−0.882944	+	0.469479i	$0.844442\pi$
$770$	0.120801	+	0.529265i	0.00435338	+	0.0190734i
$771$			20.3967i			0.734570i
$772$	−39.9291	+	9.11356i	−1.43708	+	0.328004i
$773$	−17.9420	−	14.3083i	−0.645329	−	0.514633i	0.245251	−	0.969460i	$-0.421130\pi$
$773$	−17.9420	−	14.3083i	−0.645329	−	0.514633i	−0.890580	+	0.454827i	$0.849701\pi$
$774$	0.487386	−	2.13538i	0.0175187	−	0.0767546i
$775$	29.4968	+	6.73245i	1.05956	+	0.241837i
$776$	0.190530	+	0.238916i	0.00683961	+	0.00857660i
$777$	−1.98039	−	0.953703i	−0.0710459	−	0.0342139i
$778$	9.96615	−	4.79944i	0.357304	−	0.172068i
$779$	−4.57002	+	5.73063i	−0.163738	+	0.205321i
$780$	6.87219	−	5.48039i	0.246064	−	0.196229i
$781$	15.7188	+	32.6405i	0.562464	+	1.16797i
$782$	4.59179			0.164202
$783$		0			0
$784$	−19.5929			−0.699745
$785$	−5.47645	−	11.3720i	−0.195463	−	0.405883i
$786$	3.48052	−	2.77562i	0.124146	−	0.0990030i
$787$	−8.93631	+	11.2058i	−0.318545	+	0.399443i	−0.915164	−	0.403082i	$-0.867939\pi$
$787$	−8.93631	+	11.2058i	−0.318545	+	0.399443i	0.596619	+	0.802525i	$0.296510\pi$
$788$	31.7521	−	15.2910i	1.13112	−	0.544720i
$789$	−26.6531	−	12.8355i	−0.948875	−	0.456954i
$790$	0.895756	+	1.12324i	0.0318696	+	0.0399632i
$791$	3.71419	+	0.847740i	0.132061	+	0.0301422i
$792$	−2.68718	+	11.7733i	−0.0954847	+	0.418346i
$793$	7.26175	+	5.79105i	0.257872	+	0.205646i
$794$	−1.73320	+	0.395592i	−0.0615090	+	0.0140390i
$795$			4.04892i			0.143600i
$796$	0.350855	+	1.53720i	0.0124357	+	0.0544845i
$797$	−4.42270	+	9.18382i	−0.156660	+	0.325308i	−0.964495	−	0.264101i	$-0.914925\pi$
$797$	−4.42270	+	9.18382i	−0.156660	+	0.325308i	0.807835	+	0.589409i	$0.200639\pi$
$798$	−0.202542	+	0.420583i	−0.00716992	+	0.0148885i
$799$	6.44504	+	28.2376i	0.228009	+	0.998974i
$800$		−	21.0358i		−	0.743727i
$801$	8.00197	−	1.82640i	0.282736	−	0.0645325i
$802$	−8.66636	−	6.91119i	−0.306020	−	0.244043i
$803$	−6.18276	+	27.0884i	−0.218185	+	0.955930i
$804$	−5.08896	−	1.16152i	−0.179474	−	0.0409637i
$805$	−0.353543	−	0.443330i	−0.0124608	−	0.0156253i
$806$	15.1681	+	7.30457i	0.534273	+	0.257292i
$807$	28.4855	−	13.7179i	1.00274	−	0.482893i
$808$	3.40701	−	4.27225i	0.119858	−	0.150297i
$809$	−7.01526	+	5.59448i	−0.246643	+	0.196692i	−0.739006	−	0.673698i	$-0.764705\pi$
$809$	−7.01526	+	5.59448i	−0.246643	+	0.196692i	0.492363	+	0.870390i	$0.336133\pi$
$810$	−0.344320	−	0.714988i	−0.0120982	−	0.0251221i
$811$	28.5628			1.00298			0.501489	−	0.865164i	$-0.332786\pi$
$811$	28.5628			1.00298			0.501489	+	0.865164i	$0.332786\pi$
$812$		0			0
$813$	1.50066			0.0526306
$814$	4.71034	+	9.78113i	0.165097	+	0.342828i
$815$	6.83918	−	5.45407i	0.239566	−	0.191048i
$816$	9.96077	−	12.4904i	0.348697	−	0.437252i
$817$	7.23221	−	3.48285i	0.253023	−	0.121849i
$818$	−0.113564	−	0.0546896i	−0.00397068	−	0.00191218i
$819$	1.81767	+	2.27928i	0.0635144	+	0.0796446i
$820$	3.78077	+	0.862937i	0.132030	+	0.0301351i
$821$	2.52230	−	11.0509i	0.0880290	−	0.385680i	−0.911651	−	0.410965i	$-0.865192\pi$
$821$	2.52230	−	11.0509i	0.0880290	−	0.385680i	0.999680	+	0.0252844i	$0.00804914\pi$
$822$	7.47690	+	5.96263i	0.260787	+	0.207971i
$823$	−5.52996	+	1.26218i	−0.192762	+	0.0439967i	−0.317812	−	0.948154i	$-0.602948\pi$
$823$	−5.52996	+	1.26218i	−0.192762	+	0.0439967i	0.125050	+	0.992150i	$0.460091\pi$
$824$		−	23.1008i		−	0.804755i
$825$	6.19604	+	27.1466i	0.215718	+	0.945124i
$826$	−0.861025	+	1.78794i	−0.0299589	+	0.0622103i
$827$	−1.25966	+	2.61572i	−0.0438028	+	0.0909575i	−0.921722	−	0.387852i	$-0.873217\pi$
$827$	−1.25966	+	2.61572i	−0.0438028	+	0.0909575i	0.877919	+	0.478809i	$0.158931\pi$
$828$	−1.33028	−	5.82834i	−0.0462305	−	0.202549i
$829$			45.2137i			1.57034i	0.619282	+	0.785169i	$0.287424\pi$
$829$			45.2137i			1.57034i	−0.619282	+	0.785169i	$0.712576\pi$
$830$	−1.33756	+	0.305290i	−0.0464275	+	0.0105968i
$831$	10.3975	+	8.29172i	0.360685	+	0.287636i
$832$	−4.56734	+	20.0108i	−0.158344	+	0.693750i
$833$	−30.1109	−	6.87263i	−1.04328	−	0.238122i
$834$	5.76726	+	7.23191i	0.199704	+	0.250421i
$835$	0.496648	+	0.239173i	0.0171872	+	0.00827692i
$836$	−18.8986	+	9.10107i	−0.653621	+	0.314767i
$837$	−23.1271	+	29.0005i	−0.799391	+	1.00240i
$838$	−9.21664	+	7.35003i	−0.318384	+	0.253902i
$839$	19.7962	+	41.1073i	0.683442	+	1.41918i	0.896902	+	0.442229i	$0.145812\pi$
$839$	19.7962	+	41.1073i	0.683442	+	1.41918i	−0.213460	+	0.976952i	$0.568473\pi$
$840$	0.521106			0.0179799
$841$		0			0
$842$	7.82477			0.269659
$843$	8.80793	+	18.2899i	0.303361	+	0.629936i
$844$	25.7372	−	20.5248i	0.885912	−	0.706491i
$845$	−8.17808	+	10.2550i	−0.281334	+	0.352782i
$846$	−3.73437	+	1.79838i	−0.128390	+	0.0618294i
$847$	4.30678	+	2.07404i	0.147983	+	0.0712648i
$848$	−8.33997	−	10.4580i	−0.286396	−	0.359129i
$849$	−6.37883	−	1.45593i	−0.218921	−	0.0499673i
$850$	2.01208	−	8.81551i	0.0690138	−	0.302369i
$851$	−8.86553	−	7.07002i	−0.303906	−	0.242357i
$852$	16.0686	−	3.66756i	0.550503	−	0.125649i
$853$		−	36.9288i		−	1.26442i	−0.774797	−	0.632210i	$-0.782148\pi$
$853$		−	36.9288i		−	1.26442i	0.774797	−	0.632210i	$-0.217852\pi$
$854$	0.0580735	+	0.254437i	0.00198724	+	0.00870665i
$855$	−1.02262	+	2.12349i	−0.0349728	+	0.0726218i
$856$	11.9258	−	24.7642i	0.407616	−	0.846423i
$857$	−7.91066	−	34.6589i	−0.270223	−	1.18392i	−0.909750	−	0.415156i	$-0.863727\pi$
$857$	−7.91066	−	34.6589i	−0.270223	−	1.18392i	0.639527	−	0.768768i	$-0.279130\pi$
$858$			15.4940i			0.528955i
$859$	41.3186	−	9.43070i	1.40977	−	0.321771i	0.551161	−	0.834399i	$-0.314185\pi$
$859$	41.3186	−	9.43070i	1.40977	−	0.321771i	0.858611	+	0.512628i	$0.171328\pi$
$860$	−3.32042	−	2.64795i	−0.113225	−	0.0902943i
$861$	0.307979	−	1.34934i	0.0104959	−	0.0459855i
$862$	12.0599	+	2.75259i	0.410762	+	0.0937537i
$863$	−31.0371	−	38.9193i	−1.05652	−	1.32483i	−0.943550	−	0.331231i	$-0.892536\pi$
$863$	−31.0371	−	38.9193i	−1.05652	−	1.32483i	−0.112966	−	0.993599i	$-0.536035\pi$
$864$	23.2359	+	11.1898i	0.790500	+	0.380685i
$865$	5.70709	−	2.74839i	0.194047	−	0.0934480i
$866$	−1.63036	+	2.04440i	−0.0554018	+	0.0694717i
$867$	3.11555	−	2.48457i	0.105810	−	0.0843803i
$868$	−1.86729	−	3.87747i	−0.0633800	−	0.131610i
$869$	23.0398			0.781572
$870$		0			0
$871$	13.1317			0.444950
$872$	4.01341	+	8.33393i	0.135911	+	0.282222i
$873$	0.204042	−	0.162718i	0.00690579	−	0.00550719i
$874$	−1.50149	+	1.88281i	−0.0507887	+	0.0636870i
$875$	−2.11865	+	1.02029i	−0.0716233	+	0.0344920i
$876$	11.3889	+	5.48460i	0.384795	+	0.185307i
$877$	13.6501	+	17.1167i	0.460931	+	0.577990i	0.956925	−	0.290337i	$-0.0937674\pi$
$877$	13.6501	+	17.1167i	0.460931	+	0.577990i	−0.495993	+	0.868326i	$0.665196\pi$
$878$	−6.82974	−	1.55884i	−0.230492	−	0.0526084i
$879$	−1.87681	+	8.22282i	−0.0633031	+	0.277349i
$880$	7.61811	+	6.07524i	0.256806	+	0.204796i
$881$	32.6901	−	7.46130i	1.10136	−	0.251378i	0.367055	−	0.930199i	$-0.380366\pi$
$881$	32.6901	−	7.46130i	1.10136	−	0.251378i	0.734303	+	0.678822i	$0.237509\pi$
$882$		−	4.41981i		−	0.148823i
$883$	−3.58868	−	15.7230i	−0.120769	−	0.529122i	−0.998730	−	0.0503898i	$-0.983954\pi$
$883$	−3.58868	−	15.7230i	−0.120769	−	0.529122i	0.877961	−	0.478732i	$-0.158904\pi$
$884$	−19.8612	+	41.2422i	−0.668004	+	1.38713i
$885$	4.67792	−	9.71379i	0.157246	−	0.326526i
$886$	0.667326	+	2.92375i	0.0224192	+	0.0982252i
$887$		−	52.7391i		−	1.77081i	−0.464823	−	0.885403i	$-0.653882\pi$
$887$		−	52.7391i		−	1.77081i	0.464823	−	0.885403i	$-0.346118\pi$
$888$	10.1596	−	2.31886i	0.340934	−	0.0778160i
$889$	0.289311	+	0.230718i	0.00970317	+	0.00773802i
$890$	−0.389256	+	1.70544i	−0.0130479	+	0.0571665i
$891$	−12.4074	−	2.83190i	−0.415663	−	0.0948724i
$892$	−2.04288	−	2.56169i	−0.0684006	−	0.0857716i
$893$	−13.6860	−	6.59082i	−0.457984	−	0.220553i
$894$	−9.30343	+	4.48030i	−0.311153	+	0.149844i
$895$	1.46950	−	1.84270i	0.0491200	−	0.0615945i
$896$	−3.04746	+	2.43027i	−0.101809	+	0.0811897i
$897$	−7.02180	−	14.5809i	−0.234451	−	0.486842i
$898$	5.48294			0.182968
$899$		0			0
$900$	−11.7724			−0.392413
$901$	−9.14877	−	18.9976i	−0.304790	−	0.632902i
$902$	−5.34444	+	4.26205i	−0.177950	+	0.141911i
$903$	−0.945042	+	1.18505i	−0.0314490	+	0.0394358i
$904$	−16.2729	+	7.83663i	−0.541230	+	0.260642i
$905$	7.90246	+	3.80562i	0.262687	+	0.126503i
$906$	−2.60470	−	3.26619i	−0.0865355	−	0.108512i
$907$	29.0954	+	6.64084i	0.966098	+	0.220506i	0.676336	−	0.736593i	$-0.263567\pi$
$907$	29.0954	+	6.64084i	0.966098	+	0.220506i	0.289762	+	0.957099i	$0.406424\pi$
$908$	5.55592	−	24.3421i	0.184380	−	0.807820i
$909$	−3.64865	−	2.90970i	−0.121018	−	0.0965086i
$910$	−0.605756	+	0.138260i	−0.0200806	+	0.00458327i
$911$		−	9.34050i		−	0.309465i	−0.987956	−	0.154732i	$-0.950548\pi$
$911$		−	9.34050i		−	0.309465i	0.987956	−	0.154732i	$-0.0494515\pi$
$912$	1.86443	+	8.16860i	0.0617374	+	0.270489i
$913$	−9.54627	+	19.8230i	−0.315936	+	0.656047i
$914$	−2.63818	+	5.47823i	−0.0872631	+	0.181204i
$915$	−0.315511	−	1.38235i	−0.0104305	−	0.0456989i
$916$		−	23.0151i		−	0.760439i
$917$	2.79116	−	0.637063i	0.0921721	−	0.0210377i
$918$	8.66719	+	6.91185i	0.286060	+	0.228125i
$919$	4.09903	−	17.9590i	0.135215	−	0.592414i	−0.861234	−	0.508209i	$-0.830308\pi$
$919$	4.09903	−	17.9590i	0.135215	−	0.592414i	0.996448	−	0.0842049i	$-0.0268350\pi$
$920$	2.62090	+	0.598203i	0.0864085	+	0.0197222i
$921$	3.51275	+	4.40484i	0.115749	+	0.145145i
$922$	4.65452	+	2.24150i	0.153289	+	0.0738199i
$923$	−37.3577	+	17.9905i	−1.22964	+	0.592166i
$924$	2.46950	−	3.09666i	0.0812406	−	0.101872i
$925$	−17.4581	+	13.9224i	−0.574019	+	0.457765i
$926$	−1.39853	−	2.90408i	−0.0459587	−	0.0954341i
$927$	−19.7289			−0.647981
$928$		0			0
$929$	−4.84654			−0.159010			−0.0795050	−	0.996834i	$-0.525334\pi$
$929$	−4.84654			−0.159010			−0.0795050	+	0.996834i	$0.525334\pi$
$930$	−1.11509	−	2.31551i	−0.0365653	−	0.0759286i
$931$	12.6642	−	10.0993i	0.415051	−	0.330992i
$932$	−9.96077	+	12.4904i	−0.326276	+	0.409137i
$933$	14.1746	−	6.82611i	0.464054	−	0.223477i
$934$	0.827356	+	0.398434i	0.0270719	+	0.0130371i
$935$	9.57673	+	12.0088i	0.313193	+	0.392731i
$936$	−13.4748	−	3.07553i	−0.440437	−	0.100527i
$937$	−9.94989	+	43.5933i	−0.325049	+	1.42413i	0.503394	+	0.864057i	$0.332084\pi$
$937$	−9.94989	+	43.5933i	−0.325049	+	1.42413i	−0.828443	+	0.560074i	$0.810773\pi$
$938$	0.288478	+	0.230054i	0.00941915	+	0.00751152i
$939$	23.3907	−	5.33877i	0.763326	−	0.174224i
$940$			8.03684i			0.262133i
$941$	3.02297	+	13.2445i	0.0985459	+	0.431758i	0.999999	−	0.00111821i	$-0.000355936\pi$
$941$	3.02297	+	13.2445i	0.0985459	+	0.431758i	−0.901453	+	0.432876i	$0.857499\pi$
$942$	4.39177	−	9.11960i	0.143092	−	0.297133i
$943$	3.09795	−	6.43296i	0.100883	−	0.209486i
$944$	7.92585	+	34.7254i	0.257965	+	1.13022i
$945$		−	1.36898i		−	0.0445328i
$946$	7.29850	−	1.66583i	0.237295	−	0.0541609i
$947$	−11.7365	−	9.35958i	−0.381387	−	0.304146i	0.413966	−	0.910292i	$-0.364143\pi$
$947$	−11.7365	−	9.35958i	−0.381387	−	0.304146i	−0.795353	+	0.606147i	$0.792715\pi$
$948$	2.33244	−	10.2191i	0.0757540	−	0.331900i
$949$	−31.0033	−	7.07630i	−1.00641	−	0.229706i
$950$	2.95675	+	3.70765i	0.0959298	+	0.120292i
$951$	3.22252	+	1.55188i	0.104497	+	0.0503233i
$952$	−2.44504	+	1.17747i	−0.0792443	+	0.0381620i
$953$	32.3247	−	40.5339i	1.04710	−	1.31302i	0.0989849	−	0.995089i	$-0.468440\pi$
$953$	32.3247	−	40.5339i	1.04710	−	1.31302i	0.948114	−	0.317931i	$-0.102988\pi$
$954$	2.35914	−	1.88135i	0.0763801	−	0.0609111i
$955$	3.20382	+	6.65279i	0.103673	+	0.215279i
$956$	−46.0659			−1.48988
$957$		0			0
$958$	1.73078			0.0559188
$959$	2.66848	+	5.54115i	0.0861696	+	0.178933i
$960$	2.44975	−	1.95361i	0.0790652	−	0.0630524i
$961$	−8.59365	+	10.7761i	−0.277215	+	0.347616i
$962$	−11.1947	+	5.39109i	−0.360932	+	0.173816i
$963$	−21.1494	−	10.1850i	−0.681531	−	0.328208i
$964$	−10.9330	−	13.7095i	−0.352127	−	0.441553i
$965$	−15.3345	−	3.50000i	−0.493635	−	0.112669i
$966$	0.101187	−	0.443330i	0.00325564	−	0.0142639i
$967$	−32.5437	−	25.9527i	−1.04653	−	0.834583i	−0.0600094	−	0.998198i	$-0.519113\pi$
$967$	−32.5437	−	25.9527i	−1.04653	−	0.834583i	−0.986524	+	0.163615i	$0.947685\pi$
$968$	−22.0943	+	5.04288i	−0.710137	+	0.162084i
$969$			13.2078i			0.424294i
$970$	0.0123771	+	0.0542276i	0.000397404	+	0.00174114i
$971$	24.1990	−	50.2497i	0.776583	−	1.61259i	−0.0137446	−	0.999906i	$-0.504375\pi$
$971$	24.1990	−	50.2497i	0.776583	−	1.61259i	0.790327	−	0.612685i	$-0.209911\pi$
$972$	10.4887	−	21.7799i	0.336424	−	0.698592i
$973$	1.32371	+	5.79954i	0.0424361	+	0.185925i
$974$			4.38165i			0.140397i
$975$	−31.0699	+	7.09150i	−0.995033	+	0.227110i
$976$	3.66230	+	2.92058i	0.117227	+	0.0934856i
$977$	−10.8943	+	47.7309i	−0.348538	+	1.52705i	0.431962	+	0.901892i	$0.357821\pi$
$977$	−10.8943	+	47.7309i	−0.348538	+	1.52705i	−0.780501	+	0.625155i	$0.785036\pi$
$978$	6.83918	+	1.56100i	0.218693	+	0.0499152i
$979$	17.4909	+	21.9329i	0.559012	+	0.700978i
$980$	−7.72132	−	3.71839i	−0.246649	−	0.118780i
$981$	7.11745	−	3.42758i	0.227243	−	0.109434i
$982$	−2.16189	+	2.71092i	−0.0689887	+	0.0865091i
$983$	−4.04466	+	3.22550i	−0.129004	+	0.102878i	−0.685867	−	0.727727i	$-0.740577\pi$
$983$	−4.04466	+	3.22550i	−0.129004	+	0.102878i	0.556862	+	0.830605i	$0.312005\pi$
$984$	2.84700	+	5.91185i	0.0907590	+	0.188463i
$985$	13.5345			0.431246
$986$		0			0
$987$	2.86831			0.0912994
$988$	−10.4164	−	21.6298i	−0.331389	−	0.688136i
$989$	−6.11345	+	4.87531i	−0.194396	+	0.155026i
$990$	−1.37047	+	1.71851i	−0.0435564	+	0.0546180i
$991$	−15.1838	+	7.31214i	−0.482330	+	0.232278i	−0.659216	−	0.751953i	$-0.729112\pi$
$991$	−15.1838	+	7.31214i	−0.482330	+	0.232278i	0.176886	+	0.984231i	$0.443398\pi$
$992$	28.0531	+	13.5097i	0.890687	+	0.428932i
$993$	−2.43668	−	3.05550i	−0.0773257	−	0.0969634i
$994$	−1.13585	−	0.259251i	−0.0360271	−	0.00822295i
$995$	−0.134743	+	0.590349i	−0.00427165	+	0.0187153i
$996$	7.82589	+	6.24094i	0.247973	+	0.197752i
$997$	−37.2517	+	8.50245i	−1.17977	+	0.269275i	−0.767054	−	0.641583i	$-0.778278\pi$
$997$	−37.2517	+	8.50245i	−1.17977	+	0.269275i	−0.412719	+	0.910858i	$0.635421\pi$
$998$			9.15239i			0.289714i
$999$	−6.09179	−	26.6899i	−0.192736	−	0.844431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.d.270.1		12
29.2	odd	28		841.2.d.a.645.1		6
29.3	odd	28		841.2.d.c.574.1		6
29.4	even	14		841.2.b.c.840.3		6
29.5	even	14		841.2.e.b.196.1		12
29.6	even	14		841.2.e.c.63.2		12
29.7	even	7		841.2.e.c.267.2		12
29.8	odd	28		841.2.d.e.605.1		6
29.9	even	14		841.2.e.b.236.2		12
29.10	odd	28		841.2.a.e.1.2		3
29.11	odd	28		841.2.d.d.190.1		6
29.12	odd	4		29.2.d.a.20.1	yes	6
29.13	even	14	inner	841.2.e.d.651.1		12
29.14	odd	28		841.2.d.c.778.1		6
29.15	odd	28		841.2.d.b.778.1		6
29.16	even	7	inner	841.2.e.d.651.2		12
29.17	odd	4		841.2.d.d.571.1		6
29.18	odd	28		29.2.d.a.16.1	✓	6
29.19	odd	28		841.2.a.f.1.2		3
29.20	even	7		841.2.e.b.236.1		12
29.21	odd	28		841.2.d.a.605.1		6
29.22	even	14		841.2.e.c.267.1		12
29.23	even	7		841.2.e.c.63.1		12
29.24	even	7		841.2.e.b.196.2		12
29.25	even	7		841.2.b.c.840.4		6
29.26	odd	28		841.2.d.b.574.1		6
29.27	odd	28		841.2.d.e.645.1		6
29.28	even	2	inner	841.2.e.d.270.2		12
87.41	even	4		261.2.k.a.136.1		6
87.47	even	28		261.2.k.a.190.1		6
87.68	even	28		7569.2.a.r.1.2		3
87.77	even	28		7569.2.a.p.1.2		3
116.47	even	28		464.2.u.f.161.1		6
116.99	even	4		464.2.u.f.49.1		6
145.12	even	4		725.2.r.b.49.2		12
145.18	even	28		725.2.r.b.74.2		12
145.47	even	28		725.2.r.b.74.1		12
145.99	odd	4		725.2.l.b.426.1		6
145.128	even	4		725.2.r.b.49.1		12
145.134	odd	28		725.2.l.b.451.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.16.1	✓	6	29.18	odd	28
29.2.d.a.20.1	yes	6	29.12	odd	4
261.2.k.a.136.1		6	87.41	even	4
261.2.k.a.190.1		6	87.47	even	28
464.2.u.f.49.1		6	116.99	even	4
464.2.u.f.161.1		6	116.47	even	28
725.2.l.b.426.1		6	145.99	odd	4
725.2.l.b.451.1		6	145.134	odd	28
725.2.r.b.49.1		12	145.128	even	4
725.2.r.b.49.2		12	145.12	even	4
725.2.r.b.74.1		12	145.47	even	28
725.2.r.b.74.2		12	145.18	even	28
841.2.a.e.1.2		3	29.10	odd	28
841.2.a.f.1.2		3	29.19	odd	28
841.2.b.c.840.3		6	29.4	even	14
841.2.b.c.840.4		6	29.25	even	7
841.2.d.a.605.1		6	29.21	odd	28
841.2.d.a.645.1		6	29.2	odd	28
841.2.d.b.574.1		6	29.26	odd	28
841.2.d.b.778.1		6	29.15	odd	28
841.2.d.c.574.1		6	29.3	odd	28
841.2.d.c.778.1		6	29.14	odd	28
841.2.d.d.190.1		6	29.11	odd	28
841.2.d.d.571.1		6	29.17	odd	4
841.2.d.e.605.1		6	29.8	odd	28
841.2.d.e.645.1		6	29.27	odd	28
841.2.e.b.196.1		12	29.5	even	14
841.2.e.b.196.2		12	29.24	even	7
841.2.e.b.236.1		12	29.20	even	7
841.2.e.b.236.2		12	29.9	even	14
841.2.e.c.63.1		12	29.23	even	7
841.2.e.c.63.2		12	29.6	even	14
841.2.e.c.267.1		12	29.22	even	14
841.2.e.c.267.2		12	29.7	even	7
841.2.e.d.270.1		12	1.1	even	1	trivial
841.2.e.d.270.2		12	29.28	even	2	inner
841.2.e.d.651.1		12	29.13	even	14	inner
841.2.e.d.651.2		12	29.16	even	7	inner
7569.2.a.p.1.2		3	87.77	even	28
7569.2.a.r.1.2		3	87.68	even	28

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.193096 - 0.400969i) q^{2} +(-0.974928 + 0.777479i) q^{3} +(1.12349 - 1.40881i) q^{4} +(0.623490 - 0.300257i) q^{5} +(0.500000 + 0.240787i) q^{6} +(0.222521 + 0.279032i) q^{7} +(-1.64960 - 0.376510i) q^{8} +(-0.321552 + 1.40881i) q^{9} +(-0.240787 - 0.192021i) q^{10} +(-4.81517 + 1.09903i) q^{11} +2.24698i q^{12} +(-1.25786 - 5.51107i) q^{13} +(0.0689153 - 0.143104i) q^{14} +(-0.374414 + 0.777479i) q^{15} +(-0.634375 - 2.77938i) q^{16} -4.49396i q^{17} +(0.626980 - 0.143104i) q^{18} +(1.84270 + 1.46950i) q^{19} +(0.277479 - 1.21572i) q^{20} +(-0.433884 - 0.0990311i) q^{21} +(1.37047 + 1.71851i) q^{22} +(-2.06853 - 0.996152i) q^{23} +(1.90097 - 0.915458i) q^{24} +(-2.81886 + 3.53474i) q^{25} +(-1.96688 + 1.56853i) q^{26} +(-2.40496 - 4.99396i) q^{27} +0.643104 q^{28} +0.384043 q^{30} +(-2.90356 - 6.02930i) q^{31} +(-3.63770 + 2.90097i) q^{32} +(3.83997 - 4.81517i) q^{33} +(-1.80194 + 0.867767i) q^{34} +(0.222521 + 0.107160i) q^{35} +(1.62349 + 2.03579i) q^{36} +(4.81517 + 1.09903i) q^{37} +(0.233406 - 1.02262i) q^{38} +(5.51107 + 4.39493i) q^{39} +(-1.14156 + 0.260553i) q^{40} +3.10992i q^{41} +(0.0440730 + 0.193096i) q^{42} +(1.47773 - 3.06853i) q^{43} +(-3.86147 + 8.01842i) q^{44} +(0.222521 + 0.974928i) q^{45} +1.02177i q^{46} +(-6.28345 + 1.43416i) q^{47} +(2.77938 + 2.21648i) q^{48} +(1.52930 - 6.70031i) q^{49} +(1.96163 + 0.447730i) q^{50} +(3.49396 + 4.38129i) q^{51} +(-9.17725 - 4.41953i) q^{52} +(4.22737 - 2.03579i) q^{53} +(-1.53803 + 1.92863i) q^{54} +(-2.67222 + 2.13102i) q^{55} +(-0.262012 - 0.544073i) q^{56} -2.93900 q^{57} -12.4940 q^{59} +(0.674671 + 1.40097i) q^{60} +(-1.28463 + 1.02446i) q^{61} +(-1.85690 + 2.32847i) q^{62} +(-0.464656 + 0.223767i) q^{63} +(-3.27144 - 1.57544i) q^{64} +(-2.43900 - 3.05841i) q^{65} +(-2.67222 - 0.609916i) q^{66} +(-0.516926 + 2.26480i) q^{67} +(-6.33114 - 5.04892i) q^{68} +(2.79116 - 0.637063i) q^{69} -0.109916i q^{70} +(-1.63222 - 7.15122i) q^{71} +(1.06086 - 2.20291i) q^{72} +(2.44088 - 5.06853i) q^{73} +(-0.489115 - 2.14295i) q^{74} -5.63773i q^{75} +(4.14050 - 0.945042i) q^{76} +(-1.37814 - 1.09903i) q^{77} +(0.698062 - 3.05841i) q^{78} +(-4.54792 - 1.03803i) q^{79} +(-1.23005 - 1.54244i) q^{80} +(2.32155 + 1.11800i) q^{81} +(1.24698 - 0.600514i) q^{82} +(2.77748 - 3.48285i) q^{83} +(-0.626980 + 0.500000i) q^{84} +(-1.34934 - 2.80194i) q^{85} -1.51573 q^{86} +8.35690 q^{88} +(-2.46443 - 5.11745i) q^{89} +(0.347948 - 0.277479i) q^{90} +(1.25786 - 1.57731i) q^{91} +(-3.72737 + 1.79500i) q^{92} +(7.51842 + 3.62068i) q^{93} +(1.78836 + 2.24254i) q^{94} +(1.59013 + 0.362937i) q^{95} +(1.29105 - 5.65647i) q^{96} +(-0.141202 - 0.112605i) q^{97} +(-2.98192 + 0.680604i) q^{98} -7.13706i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 2 q^{5} + 6 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{13} + 8 q^{16} + 4 q^{20} - 12 q^{22} - 14 q^{23} + 14 q^{24} - 48 q^{25} + 24 q^{28} - 36 q^{30} - 2 q^{33} - 4 q^{34} + 2 q^{35} + 10 q^{36}+ \cdots + 4 q^{96}+O(q^{100}) \) 12 * q + 4 * q^4 - 2 * q^5 + 6 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^13 + 8 * q^16 + 4 * q^20 - 12 * q^22 - 14 * q^23 + 14 * q^24 - 48 * q^25 + 24 * q^28 - 36 * q^30 - 2 * q^33 - 4 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^38 + 8 * q^42 + 2 * q^45 - 44 * q^49 + 4 * q^51 - 20 * q^52 + 6 * q^53 + 12 * q^54 + 4 * q^57 - 112 * q^59 - 6 * q^62 - 30 * q^63 - 2 * q^64 + 10 * q^65 - 38 * q^67 - 42 * q^71 - 12 * q^74 + 26 * q^78 + 36 * q^80 + 36 * q^81 - 4 * q^82 + 34 * q^83 + 32 * q^86 + 84 * q^88 - 10 * q^91 + 34 * q^93 + 16 * q^94 + 4 * q^96

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