LMFDB - Embedded newform 725.2.l.b.451.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [725,2,Mod(226,725)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(725, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("725.226"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.l (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 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:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			451.1
Root			$-0.623490 - 0.781831i$ of defining polynomial
Character	$\chi$	$=$	725.451
Dual form			725.2.l.b.426.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.400969 - 0.193096i) q^{2} +(0.777479 - 0.974928i) q^{3} +(-1.12349 - 1.40881i) q^{4} +(-0.500000 + 0.240787i) q^{6} +(-0.222521 + 0.279032i) q^{7} +(0.376510 + 1.64960i) q^{8} +(0.321552 + 1.40881i) q^{9} +(-1.09903 + 4.81517i) q^{11} -2.24698 q^{12} +(-1.25786 + 5.51107i) q^{13} +(0.143104 - 0.0689153i) q^{14} +(-0.634375 + 2.77938i) q^{16} -4.49396 q^{17} +(0.143104 - 0.626980i) q^{18} +(-1.46950 - 1.84270i) q^{19} +(0.0990311 + 0.433884i) q^{21} +(1.37047 - 1.71851i) q^{22} +(2.06853 - 0.996152i) q^{23} +(1.90097 + 0.915458i) q^{24} +(1.56853 - 1.96688i) q^{26} +(4.99396 + 2.40496i) q^{27} +0.643104 q^{28} +(-5.09783 - 1.73553i) q^{29} +(6.02930 + 2.90356i) q^{31} +(2.90097 - 3.63770i) q^{32} +(3.83997 + 4.81517i) q^{33} +(1.80194 + 0.867767i) q^{34} +(1.62349 - 2.03579i) q^{36} +(-1.09903 - 4.81517i) q^{37} +(0.233406 + 1.02262i) q^{38} +(4.39493 + 5.51107i) q^{39} +3.10992 q^{41} +(0.0440730 - 0.193096i) q^{42} +(-3.06853 + 1.47773i) q^{43} +(8.01842 - 3.86147i) q^{44} -1.02177 q^{46} +(-1.43416 + 6.28345i) q^{47} +(2.21648 + 2.77938i) q^{48} +(1.52930 + 6.70031i) q^{49} +(-3.49396 + 4.38129i) q^{51} +(9.17725 - 4.41953i) q^{52} +(-4.22737 - 2.03579i) q^{53} +(-1.53803 - 1.92863i) q^{54} +(-0.544073 - 0.262012i) q^{56} -2.93900 q^{57} +(1.70895 + 1.68027i) q^{58} -12.4940 q^{59} +(-1.02446 + 1.28463i) q^{61} +(-1.85690 - 2.32847i) q^{62} +(-0.464656 - 0.223767i) q^{63} +(3.27144 - 1.57544i) q^{64} +(-0.609916 - 2.67222i) q^{66} +(-0.516926 - 2.26480i) q^{67} +(5.04892 + 6.33114i) q^{68} +(0.637063 - 2.79116i) q^{69} +(1.63222 - 7.15122i) q^{71} +(-2.20291 + 1.06086i) q^{72} +(5.06853 - 2.44088i) q^{73} +(-0.489115 + 2.14295i) q^{74} +(-0.945042 + 4.14050i) q^{76} +(-1.09903 - 1.37814i) q^{77} +(-0.698062 - 3.05841i) q^{78} +(1.03803 + 4.54792i) q^{79} +(2.32155 - 1.11800i) q^{81} +(-1.24698 - 0.600514i) q^{82} +(-2.77748 - 3.48285i) q^{83} +(0.500000 - 0.626980i) q^{84} +1.51573 q^{86} +(-5.65548 + 3.62068i) q^{87} -8.35690 q^{88} +(5.11745 + 2.46443i) q^{89} +(-1.25786 - 1.57731i) q^{91} +(-3.72737 - 1.79500i) q^{92} +(7.51842 - 3.62068i) q^{93} +(1.78836 - 2.24254i) q^{94} +(-1.29105 - 5.65647i) q^{96} +(0.112605 + 0.141202i) q^{97} +(0.680604 - 2.98192i) q^{98} -7.13706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 3 q^{6} - q^{7} + 7 q^{8} + 6 q^{9} - 11 q^{11} - 4 q^{12} + 5 q^{13} + 9 q^{14} + 4 q^{16} - 8 q^{17} + 9 q^{18} + q^{19} + 5 q^{21} - 6 q^{22} + 7 q^{23} + 7 q^{24}+ \cdots - 32 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 3 * q^6 - q^7 + 7 * q^8 + 6 * q^9 - 11 * q^11 - 4 * q^12 + 5 * q^13 + 9 * q^14 + 4 * q^16 - 8 * q^17 + 9 * q^18 + q^19 + 5 * q^21 - 6 * q^22 + 7 * q^23 + 7 * q^24 + 4 * q^26 + 11 * q^27 + 12 * q^28 + 6 * q^29 + 5 * q^31 + 13 * q^32 - q^33 + 2 * q^34 + 5 * q^36 - 11 * q^37 - 2 * q^38 + 3 * q^39 + 20 * q^41 + 4 * q^42 - 13 * q^43 + 20 * q^44 - 11 * q^47 - 6 * q^48 - 22 * q^49 - 2 * q^51 + 10 * q^52 - 3 * q^53 + 6 * q^54 - 7 * q^56 + 2 * q^57 + 16 * q^58 - 56 * q^59 + 3 * q^61 - 3 * q^62 - 15 * q^63 + q^64 - 5 * q^66 - 19 * q^67 + 12 * q^68 - 7 * q^69 + 21 * q^71 + 25 * q^73 - 6 * q^74 - 5 * q^76 - 11 * q^77 - 13 * q^78 - 9 * q^79 + 18 * q^81 + 2 * q^82 - 17 * q^83 + 3 * q^84 - 16 * q^86 + 5 * q^87 - 42 * q^88 + 7 * q^89 + 5 * q^91 + 17 * q^93 + 8 * q^94 - 2 * q^96 - q^97 - 19 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.400969	−	0.193096i	−0.283528	−	0.136540i	0.286715	−	0.958016i	$-0.407437\pi$
$2$	−0.400969	−	0.193096i	−0.283528	−	0.136540i	−0.570243	+	0.821476i	$0.693151\pi$
$3$	0.777479	−	0.974928i	0.448878	−	0.562875i	−0.504981	−	0.863130i	$-0.668501\pi$
$3$	0.777479	−	0.974928i	0.448878	−	0.562875i	0.953859	+	0.300256i	$0.0970720\pi$
$4$	−1.12349	−	1.40881i	−0.561745	−	0.704406i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.240787i	−0.204124	+	0.0983010i
$7$	−0.222521	+	0.279032i	−0.0841050	+	0.105464i	−0.822104	−	0.569338i	$-0.807200\pi$
$7$	−0.222521	+	0.279032i	−0.0841050	+	0.105464i	0.737999	+	0.674802i	$0.235771\pi$
$8$	0.376510	+	1.64960i	0.133116	+	0.583221i
$9$	0.321552	+	1.40881i	0.107184	+	0.469604i
$10$		0			0
$11$	−1.09903	+	4.81517i	−0.331370	+	1.45183i	0.485109	+	0.874454i	$0.338780\pi$
$11$	−1.09903	+	4.81517i	−0.331370	+	1.45183i	−0.816479	+	0.577375i	$0.804077\pi$
$12$	−2.24698			−0.648647
$13$	−1.25786	+	5.51107i	−0.348869	+	1.52849i	0.430884	+	0.902407i	$0.358202\pi$
$13$	−1.25786	+	5.51107i	−0.348869	+	1.52849i	−0.779753	+	0.626087i	$0.784655\pi$
$14$	0.143104	−	0.0689153i	0.0382462	−	0.0184184i
$15$		0			0
$16$	−0.634375	+	2.77938i	−0.158594	+	0.694845i
$17$	−4.49396			−1.08995			−0.544973	−	0.838454i	$-0.683460\pi$
$17$	−4.49396			−1.08995			−0.544973	+	0.838454i	$0.683460\pi$
$18$	0.143104	−	0.626980i	0.0337300	−	0.147781i
$19$	−1.46950	−	1.84270i	−0.337127	−	0.422743i	0.584153	−	0.811643i	$-0.301427\pi$
$19$	−1.46950	−	1.84270i	−0.337127	−	0.422743i	−0.921280	+	0.388900i	$0.872855\pi$
$20$		0			0
$21$	0.0990311	+	0.433884i	0.0216104	+	0.0946812i
$22$	1.37047	−	1.71851i	0.292185	−	0.366388i
$23$	2.06853	−	0.996152i	0.431319	−	0.207712i	−0.205611	−	0.978634i	$-0.565918\pi$
$23$	2.06853	−	0.996152i	0.431319	−	0.207712i	0.636930	+	0.770922i	$0.280204\pi$
$24$	1.90097	+	0.915458i	0.388034	+	0.186867i
$25$		0			0
$26$	1.56853	−	1.96688i	0.307614	−	0.385736i
$27$	4.99396	+	2.40496i	0.961088	+	0.462836i
$28$	0.643104			0.121535
$29$	−5.09783	−	1.73553i	−0.946644	−	0.322281i
$29$	−5.09783	−	1.73553i	−0.946644	−	0.322281i
$30$		0			0
$31$	6.02930	+	2.90356i	1.08289	+	0.521495i	0.888241	−	0.459377i	$-0.151927\pi$
$31$	6.02930	+	2.90356i	1.08289	+	0.521495i	0.194654	+	0.980872i	$0.437642\pi$
$32$	2.90097	−	3.63770i	0.512824	−	0.643061i
$33$	3.83997	+	4.81517i	0.668453	+	0.838214i
$34$	1.80194	+	0.867767i	0.309030	+	0.148821i
$35$		0			0
$36$	1.62349	−	2.03579i	0.270582	−	0.339299i
$37$	−1.09903	−	4.81517i	−0.180680	−	0.791609i	−0.981307	−	0.192447i	$-0.938358\pi$
$37$	−1.09903	−	4.81517i	−0.180680	−	0.791609i	0.800628	−	0.599162i	$-0.204499\pi$
$38$	0.233406	+	1.02262i	0.0378635	+	0.165891i
$39$	4.39493	+	5.51107i	0.703752	+	0.882477i
$40$		0			0
$41$	3.10992			0.485687			0.242844	−	0.970065i	$-0.421920\pi$
$41$	3.10992			0.485687			0.242844	+	0.970065i	$0.421920\pi$
$42$	0.0440730	−	0.193096i	0.00680061	−	0.0297954i
$43$	−3.06853	+	1.47773i	−0.467947	+	0.225351i	−0.652971	−	0.757383i	$-0.726478\pi$
$43$	−3.06853	+	1.47773i	−0.467947	+	0.225351i	0.185025	+	0.982734i	$0.440764\pi$
$44$	8.01842	−	3.86147i	1.20882	−	0.582138i
$45$		0			0
$46$	−1.02177			−0.150652
$47$	−1.43416	+	6.28345i	−0.209193	+	0.916536i	0.755912	+	0.654673i	$0.227194\pi$
$47$	−1.43416	+	6.28345i	−0.209193	+	0.916536i	−0.965105	+	0.261862i	$0.915663\pi$
$48$	2.21648	+	2.77938i	0.319921	+	0.401169i
$49$	1.52930	+	6.70031i	0.218472	+	0.957188i
$50$		0			0
$51$	−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	$-0.461582\pi$
$53$	−4.22737	−	2.03579i	−0.580673	−	0.279638i	−0.701075	+	0.713088i	$0.747296\pi$
$54$	−1.53803	−	1.92863i	−0.209300	−	0.262453i
$55$		0			0
$56$	−0.544073	−	0.262012i	−0.0727048	−	0.0350128i
$57$	−2.93900			−0.389280
$58$	1.70895	+	1.68027i	0.224396	+	0.220630i
$59$	−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			0
$61$	−1.02446	+	1.28463i	−0.131168	+	0.164480i	−0.843078	−	0.537791i	$-0.819259\pi$
$61$	−1.02446	+	1.28463i	−0.131168	+	0.164480i	0.711910	+	0.702271i	$0.247830\pi$
$62$	−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
$65$		0			0
$66$	−0.609916	−	2.67222i	−0.0750755	−	0.328927i
$67$	−0.516926	−	2.26480i	−0.0631526	−	0.276689i	0.933486	−	0.358614i	$-0.116751\pi$
$67$	−0.516926	−	2.26480i	−0.0631526	−	0.276689i	−0.996639	+	0.0819245i	$0.973893\pi$
$68$	5.04892	+	6.33114i	0.612271	+	0.767764i
$69$	0.637063	−	2.79116i	0.0766934	−	0.336016i
$70$		0			0
$71$	1.63222	−	7.15122i	0.193709	−	0.848694i	−0.780878	−	0.624683i	$-0.785228\pi$
$71$	1.63222	−	7.15122i	0.193709	−	0.848694i	0.974587	−	0.224010i	$-0.0719148\pi$
$72$	−2.20291	+	1.06086i	−0.259615	+	0.125024i
$73$	5.06853	−	2.44088i	0.593227	−	0.285683i	−0.113083	−	0.993586i	$-0.536073\pi$
$73$	5.06853	−	2.44088i	0.593227	−	0.285683i	0.706310	+	0.707903i	$0.250358\pi$
$74$	−0.489115	+	2.14295i	−0.0568584	+	0.249113i
$75$		0			0
$76$	−0.945042	+	4.14050i	−0.108404	+	0.474948i
$77$	−1.09903	−	1.37814i	−0.125246	−	0.157054i
$78$	−0.698062	−	3.05841i	−0.0790400	−	0.346297i
$79$	1.03803	+	4.54792i	0.116788	+	0.511681i	0.999154	+	0.0411178i	$0.0130919\pi$
$79$	1.03803	+	4.54792i	0.116788	+	0.511681i	−0.882367	+	0.470563i	$0.844051\pi$
$80$		0			0
$81$	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	$-0.292905\pi$
$83$	−2.77748	−	3.48285i	−0.304868	−	0.382292i	−0.910539	+	0.413423i	$0.864333\pi$
$84$	0.500000	−	0.626980i	0.0545545	−	0.0684091i
$85$		0			0
$86$	1.51573			0.163445
$87$	−5.65548	+	3.62068i	−0.606331	+	0.388178i
$88$	−8.35690			−0.890848
$89$	5.11745	+	2.46443i	0.542449	+	0.261229i	0.684981	−	0.728561i	$-0.259810\pi$
$89$	5.11745	+	2.46443i	0.542449	+	0.261229i	−0.142533	+	0.989790i	$0.545525\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	−1.29105	−	5.65647i	−0.131768	−	0.577311i
$97$	0.112605	+	0.141202i	0.0114333	+	0.0143369i	0.787515	−	0.616295i	$-0.211367\pi$
$97$	0.112605	+	0.141202i	0.0114333	+	0.0143369i	−0.776082	+	0.630632i	$0.782796\pi$
$98$	0.680604	−	2.98192i	0.0687514	−	0.301219i
$99$	−7.13706			−0.717302
$100$		0			0
$101$	−2.90970	+	1.40124i	−0.289526	+	0.139428i	−0.573009	−	0.819549i	$-0.694224\pi$
$101$	−2.90970	+	1.40124i	−0.289526	+	0.139428i	0.283484	+	0.958977i	$0.408510\pi$
$102$	2.24698	−	1.08209i	0.222484	−	0.107143i
$103$	−3.03803	+	13.3105i	−0.299346	+	1.31152i	0.571758	+	0.820423i	$0.306262\pi$
$103$	−3.03803	+	13.3105i	−0.299346	+	1.31152i	−0.871104	+	0.491099i	$0.836595\pi$
$104$	−9.56465			−0.937891
$105$		0			0
$106$	1.30194	+	1.63258i	0.126455	+	0.158570i
$107$	3.61476	+	15.8373i	0.349452	+	1.53105i	0.778428	+	0.627734i	$0.216017\pi$
$107$	3.61476	+	15.8373i	0.349452	+	1.53105i	−0.428976	+	0.903316i	$0.641126\pi$
$108$	−2.22252	−	9.73750i	−0.213862	−	0.936991i
$109$	3.40850	−	4.27413i	0.326475	−	0.409387i	−0.591323	−	0.806435i	$-0.701394\pi$
$109$	3.40850	−	4.27413i	0.326475	−	0.409387i	0.917798	+	0.397048i	$0.129965\pi$
$110$		0			0
$111$	−5.54892	−	2.67222i	−0.526680	−	0.253636i
$112$	−0.634375	−	0.795481i	−0.0599428	−	0.0751659i
$113$	6.65548	−	8.34571i	0.626095	−	0.785098i	−0.363093	−	0.931753i	$-0.618279\pi$
$113$	6.65548	−	8.34571i	0.626095	−	0.785098i	0.989188	+	0.146655i	$0.0468506\pi$
$114$	1.17845	+	0.567511i	0.110372	+	0.0531522i
$115$		0			0
$116$	3.28232	+	9.13174i	0.304756	+	0.847861i
$117$	−8.16852			−0.755180
$118$	5.00969	+	2.41254i	0.461179	+	0.222092i
$119$	1.00000	−	1.25396i	0.0916698	−	0.114950i
$120$		0			0
$121$	−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
$124$	−2.68329	−	11.7563i	−0.240967	−	1.05574i
$125$		0			0
$126$	0.143104	+	0.179447i	0.0127487	+	0.0159864i
$127$	−0.230718	+	1.01084i	−0.0204729	+	0.0896976i	−0.984132	−	0.177437i	$-0.943220\pi$
$127$	−0.230718	+	1.01084i	−0.0204729	+	0.0896976i	0.963659	+	0.267134i	$0.0860767\pi$
$128$	−10.9215			−0.965337
$129$	−0.945042	+	4.14050i	−0.0832063	+	0.364551i
$130$		0			0
$131$	−7.22737	+	3.48052i	−0.631458	+	0.304094i	−0.722099	−	0.691790i	$-0.756823\pi$
$131$	−7.22737	+	3.48052i	−0.631458	+	0.304094i	0.0906414	+	0.995884i	$0.471108\pi$
$132$	2.46950	−	10.8196i	0.214942	−	0.941724i
$133$	0.841166			0.0729384
$134$	−0.230054	+	1.00793i	−0.0198736	+	0.0870720i
$135$		0			0
$136$	−1.69202	−	7.41323i	−0.145090	−	0.635679i
$137$	3.83459	+	16.8005i	0.327611	+	1.43536i	0.823670	+	0.567070i	$0.191923\pi$
$137$	3.83459	+	16.8005i	0.327611	+	1.43536i	−0.496058	+	0.868289i	$0.665220\pi$
$138$	−0.794405	+	0.996152i	−0.0676242	+	0.0847981i
$139$	15.0172	−	7.23191i	1.27374	−	0.613403i	0.329969	−	0.943992i	$-0.392962\pi$
$139$	15.0172	−	7.23191i	1.27374	−	0.613403i	0.943775	+	0.330589i	$0.107247\pi$
$140$		0			0
$141$	5.01089	+	6.28345i	0.421993	+	0.529162i
$142$	−2.03534	+	2.55224i	−0.170802	+	0.214179i
$143$	−25.1543	−	12.1137i	−2.10351	−	1.01300i
$144$	−4.11960			−0.343300
$145$		0			0
$146$	−2.50365			−0.207203
$147$	7.72132	+	3.71839i	0.636844	+	0.306688i
$148$	−5.54892	+	6.95812i	−0.456118	+	0.571954i
$149$	11.6012	+	14.5474i	0.950406	+	1.19177i	0.981346	+	0.192251i	$0.0615786\pi$
$149$	11.6012	+	14.5474i	0.950406	+	1.19177i	−0.0309396	+	0.999521i	$0.509850\pi$
$150$		0			0
$151$	6.78232	−	3.26619i	0.551938	−	0.265799i	−0.137060	−	0.990563i	$-0.543765\pi$
$151$	6.78232	−	3.26619i	0.551938	−	0.265799i	0.688998	+	0.724764i	$0.258051\pi$
$152$	2.48643	−	3.11788i	0.201676	−	0.252893i
$153$	−1.44504	−	6.33114i	−0.116825	−	0.511843i
$154$	0.174563	+	0.764811i	0.0140667	+	0.0616302i
$155$		0			0
$156$	2.82640	−	12.3833i	0.226293	−	0.991454i
$157$	18.2392			1.45565			0.727824	−	0.685764i	$-0.240532\pi$
$157$	18.2392			1.45565			0.727824	+	0.685764i	$0.240532\pi$
$158$	0.461968	−	2.02401i	0.0367522	−	0.161022i
$159$	−5.27144	+	2.53859i	−0.418052	+	0.201323i
$160$		0			0
$161$	−0.182333	+	0.798852i	−0.0143698	+	0.0629584i
$162$	−1.14675			−0.0900973
$163$	2.81282	−	12.3238i	0.220317	−	0.965273i	−0.736922	−	0.675977i	$-0.763722\pi$
$163$	2.81282	−	12.3238i	0.220317	−	0.965273i	0.957240	−	0.289296i	$-0.0934211\pi$
$164$	−3.49396	−	4.38129i	−0.272832	−	0.342121i
$165$		0			0
$166$	0.441157	+	1.93284i	0.0342404	+	0.150017i
$167$	0.496648	−	0.622776i	0.0384317	−	0.0481919i	−0.762244	−	0.647290i	$-0.775902\pi$
$167$	0.496648	−	0.622776i	0.0384317	−	0.0481919i	0.800676	+	0.599098i	$0.204474\pi$
$168$	−0.678448	+	0.326723i	−0.0523434	+	0.0252073i
$169$	−17.0770	−	8.22386i	−1.31362	−	0.632605i
$170$		0			0
$171$	2.12349	−	2.66277i	0.162387	−	0.203627i
$172$	5.52930	+	2.66277i	0.421605	+	0.203034i
$173$	9.15346			0.695924			0.347962	−	0.937509i	$-0.386874\pi$
$173$	9.15346			0.695924			0.347962	+	0.937509i	$0.386874\pi$
$174$	2.96681	−	0.359726i	0.224913	−	0.0272708i
$175$		0			0
$176$	−12.6860	−	6.10925i	−0.956242	−	0.460502i
$177$	−9.71379	+	12.1807i	−0.730133	+	0.915558i
$178$	−1.57606	−	1.97632i	−0.118131	−	0.148132i
$179$	−3.06853	−	1.47773i	−0.229353	−	0.110450i	0.315678	−	0.948866i	$-0.397768\pi$
$179$	−3.06853	−	1.47773i	−0.229353	−	0.110450i	−0.545031	+	0.838416i	$0.683482\pi$
$180$		0			0
$181$	7.90246	−	9.90937i	0.587385	−	0.736558i	−0.395967	−	0.918265i	$-0.629591\pi$
$181$	7.90246	−	9.90937i	0.587385	−	0.736558i	0.983353	+	0.181707i	$0.0581621\pi$
$182$	0.199791	+	0.875342i	0.0148095	+	0.0648847i
$183$	0.455927	+	1.99755i	0.0337031	+	0.147663i
$184$	2.42208	+	3.03719i	0.178558	+	0.223904i
$185$		0			0
$186$	−3.71379			−0.272308
$187$	4.93900	−	21.6392i	0.361176	−	1.58241i
$188$	10.4635	−	5.03894i	0.763126	−	0.367502i
$189$	−1.78232	+	0.858322i	−0.129645	+	0.0624337i
$190$		0			0
$191$	−10.6703			−0.772072			−0.386036	−	0.922484i	$-0.626156\pi$
$191$	−10.6703			−0.772072			−0.386036	+	0.922484i	$0.626156\pi$
$192$	1.00753	−	4.41429i	0.0727124	−	0.318574i
$193$	−14.1712	−	17.7701i	−1.02007	−	1.27912i	−0.959724	−	0.280945i	$-0.909352\pi$
$193$	−14.1712	−	17.7701i	−1.02007	−	1.27912i	−0.0603421	−	0.998178i	$-0.519219\pi$
$194$	−0.0178854	−	0.0783611i	−0.00128410	−	0.00562600i
$195$		0			0
$196$	7.72132	−	9.68223i	0.551523	−	0.691588i
$197$	−17.6211	+	8.48587i	−1.25545	+	0.604593i	−0.938968	−	0.344005i	$-0.888216\pi$
$197$	−17.6211	+	8.48587i	−1.25545	+	0.604593i	−0.316483	+	0.948598i	$0.602502\pi$
$198$	2.86174	+	1.37814i	0.203375	+	0.0979402i
$199$	−0.545565	−	0.684117i	−0.0386741	−	0.0484958i	0.762118	−	0.647438i	$-0.224159\pi$
$199$	−0.545565	−	0.684117i	−0.0386741	−	0.0484958i	−0.800792	+	0.598942i	$0.795588\pi$
$200$		0			0
$201$	−2.60992	−	1.25687i	−0.184089	−	0.0886527i
$202$	1.43727			0.101126
$203$	1.61865	−	1.03627i	0.113607	−	0.0727318i
$204$	10.0978			0.706990
$205$		0			0
$206$	3.78836	−	4.75046i	0.263948	−	0.330980i
$207$	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			0
$211$	4.06518	+	17.8107i	0.279858	+	1.22614i	0.897972	+	0.440052i	$0.145040\pi$
$211$	4.06518	+	17.8107i	0.279858	+	1.22614i	−0.618114	+	0.786088i	$0.712103\pi$
$212$	1.88135	+	8.24275i	0.129212	+	0.566115i
$213$	−5.70291	−	7.15122i	−0.390757	−	0.489993i
$214$	1.60872	−	7.04826i	0.109970	−	0.481809i
$215$		0			0
$216$	−2.08695	+	9.14352i	−0.141999	+	0.622138i
$217$	−2.15183	+	1.03627i	−0.146076	+	0.0703465i
$218$	−2.19202	+	1.05562i	−0.148462	+	0.0714957i
$219$	1.56100	−	6.83918i	0.105483	−	0.462149i
$220$		0			0
$221$	5.65279	−	24.7665i	0.380248	−	1.66598i
$222$	1.70895	+	2.14295i	0.114697	+	0.143826i
$223$	−0.404617	−	1.77274i	−0.0270951	−	0.118712i	0.959572	−	0.281464i	$-0.0908200\pi$
$223$	−0.404617	−	1.77274i	−0.0270951	−	0.118712i	−0.986667	+	0.162752i	$0.947963\pi$
$224$	0.369510	+	1.61893i	0.0246889	+	0.108169i
$225$		0			0
$226$	−4.28017	+	2.06122i	−0.284713	+	0.137110i
$227$	−12.4840	−	6.01199i	−0.828594	−	0.399030i	−0.0290066	−	0.999579i	$-0.509234\pi$
$227$	−12.4840	−	6.01199i	−0.828594	−	0.399030i	−0.799588	+	0.600549i	$0.794949\pi$
$228$	3.30194	+	4.14050i	0.218676	+	0.274211i
$229$	−7.96346	+	9.98586i	−0.526240	+	0.659884i	−0.971921	−	0.235308i	$-0.924390\pi$
$229$	−7.96346	+	9.98586i	−0.526240	+	0.659884i	0.445681	+	0.895192i	$0.352962\pi$
$230$		0			0
$231$	−2.19806			−0.144622
$232$	0.943550	−	9.06283i	0.0619471	−	0.595004i
$233$	8.86592			0.580826			0.290413	−	0.956901i	$-0.406207\pi$
$233$	8.86592			0.580826			0.290413	+	0.956901i	$0.406207\pi$
$234$	3.27532	+	1.57731i	0.214115	+	0.103112i
$235$		0			0
$236$	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	−0.0757593	+	0.997126i	$0.524138\pi$
$239$	−15.9393	+	19.9872i	−1.03103	+	1.29287i	−0.955268	+	0.295741i	$0.904433\pi$
$240$		0			0
$241$	−2.16541	−	9.48727i	−0.139486	−	0.611129i	−0.995548	−	0.0942554i	$-0.969953\pi$
$241$	−2.16541	−	9.48727i	−0.139486	−	0.611129i	0.856062	−	0.516873i	$-0.172904\pi$
$242$	3.71648	+	4.66032i	0.238904	+	0.299577i
$243$	−2.98523	+	13.0791i	−0.191503	+	0.839028i
$244$	2.96077			0.189544
$245$		0			0
$246$	−1.55496	+	0.748828i	−0.0991405	+	0.0477436i
$247$	12.0036	−	5.78065i	0.763774	−	0.367814i
$248$	−2.51961	+	11.0392i	−0.159996	+	0.700987i
$249$	−5.55496			−0.352031
$250$		0			0
$251$	−6.08546	−	7.63092i	−0.384111	−	0.481660i	0.551760	−	0.834003i	$-0.313956\pi$
$251$	−6.08546	−	7.63092i	−0.384111	−	0.481660i	−0.935871	+	0.352343i	$0.885385\pi$
$252$	0.206791	+	0.906013i	0.0130266	+	0.0570734i
$253$	2.52326	+	11.0551i	0.158636	+	0.695030i
$254$	0.287700	−	0.360765i	0.0180519	−	0.0226364i
$255$		0			0
$256$	−2.16368	−	1.04197i	−0.135230	−	0.0651233i
$257$	−10.1984	−	12.7883i	−0.636156	−	0.797714i	0.354360	−	0.935109i	$-0.384699\pi$
$257$	−10.1984	−	12.7883i	−0.636156	−	0.797714i	−0.990516	+	0.137394i	$0.956127\pi$
$258$	1.17845	−	1.47773i	0.0733670	−	0.0919993i
$259$	1.58815	+	0.764811i	0.0986826	+	0.0475230i
$260$		0			0
$261$	0.805823	−	7.73995i	0.0498792	−	0.479091i
$262$	3.57002			0.220557
$263$	21.3741	+	10.2932i	1.31798	+	0.634708i	0.954867	−	0.297035i	$-0.0959979\pi$
$263$	21.3741	+	10.2932i	1.31798	+	0.634708i	0.363118	+	0.931743i	$0.381712\pi$
$264$	−6.49731	+	8.14737i	−0.399882	+	0.501436i
$265$		0			0
$266$	−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
$269$	−5.64191	−	24.7188i	−0.343993	−	1.50713i	−0.790561	−	0.612383i	$-0.790211\pi$
$269$	−5.64191	−	24.7188i	−0.343993	−	1.50713i	0.446568	−	0.894750i	$-0.352646\pi$
$270$		0			0
$271$	−0.750332	−	0.940887i	−0.0455794	−	0.0571548i	0.758519	−	0.651651i	$-0.225923\pi$
$271$	−0.750332	−	0.940887i	−0.0455794	−	0.0571548i	−0.804099	+	0.594496i	$0.797352\pi$
$272$	2.85086	−	12.4904i	0.172858	−	0.757342i
$273$	−2.51573			−0.152259
$274$	1.70655	−	7.47690i	0.103097	−	0.451696i
$275$		0			0
$276$	−4.64795	+	2.23833i	−0.279774	+	0.134732i
$277$	2.37316	−	10.3975i	0.142589	−	0.624724i	−0.852239	−	0.523153i	$-0.824756\pi$
$277$	2.37316	−	10.3975i	0.142589	−	0.624724i	0.994828	−	0.101572i	$-0.0323871\pi$
$278$	−7.41789			−0.444896
$279$	−2.15183	+	9.42780i	−0.128827	+	0.564427i
$280$		0			0
$281$	3.62253	+	15.8713i	0.216102	+	0.946805i	0.960327	+	0.278876i	$0.0899618\pi$
$281$	3.62253	+	15.8713i	0.216102	+	0.946805i	−0.744225	+	0.667929i	$0.767181\pi$
$282$	−0.795897	−	3.48705i	−0.0473950	−	0.207651i
$283$	3.27144	−	4.10225i	0.194467	−	0.243854i	−0.675032	−	0.737788i	$-0.735870\pi$
$283$	3.27144	−	4.10225i	0.194467	−	0.243854i	0.869499	+	0.493935i	$0.164442\pi$
$284$	−11.9085	+	5.73483i	−0.706640	+	0.340300i
$285$		0			0
$286$	7.74698	+	9.71441i	0.458089	+	0.574425i
$287$	−0.692021	+	0.867767i	−0.0408487	+	0.0512227i
$288$	6.05765	+	2.91721i	0.356950	+	0.171898i
$289$	3.19567			0.187981
$290$		0			0
$291$	0.225209			0.0132020
$292$	−9.13318	−	4.39831i	−0.534479	−	0.257391i
$293$	−4.21714	+	5.28813i	−0.246368	+	0.308936i	−0.889604	−	0.456732i	$-0.849020\pi$
$293$	−4.21714	+	5.28813i	−0.246368	+	0.308936i	0.643236	+	0.765668i	$0.277591\pi$
$294$	−2.37800	−	2.98192i	−0.138688	−	0.173909i
$295$		0			0
$296$	7.52930	−	3.62592i	0.437632	−	0.210752i
$297$	−17.0688	+	21.4036i	−0.990434	+	1.24196i
$298$	−1.84266	−	8.07321i	−0.106742	−	0.467669i
$299$	2.88793	+	12.6528i	0.167013	+	0.731733i
$300$		0			0
$301$	0.270479	−	1.18505i	0.0155901	−	0.0683049i
$302$	−3.35019			−0.192782
$303$	−0.896125	+	3.92618i	−0.0514810	+	0.225553i
$304$	6.05376	−	2.91534i	0.347207	−	0.167206i
$305$		0			0
$306$	−0.643104	+	2.81762i	−0.0367638	+	0.161073i
$307$	−4.51812			−0.257863			−0.128931	−	0.991654i	$-0.541155\pi$
$307$	−4.51812			−0.257863			−0.128931	+	0.991654i	$0.541155\pi$
$308$	−0.706791	+	3.09666i	−0.0402732	+	0.176448i
$309$	10.6148	+	13.3105i	0.603853	+	0.757207i
$310$		0			0
$311$	2.80745	+	12.3002i	0.159196	+	0.697482i	0.990018	+	0.140944i	$0.0450136\pi$
$311$	2.80745	+	12.3002i	0.159196	+	0.697482i	−0.830822	+	0.556538i	$0.812129\pi$
$312$	−7.43631	+	9.32484i	−0.420998	+	0.527915i
$313$	17.3349	−	8.34804i	0.979826	−	0.471859i	0.125781	−	0.992058i	$-0.459856\pi$
$313$	17.3349	−	8.34804i	0.979826	−	0.471859i	0.854045	+	0.520199i	$0.174142\pi$
$314$	−7.31336	−	3.52193i	−0.412717	−	0.198754i
$315$		0			0
$316$	5.24094	−	6.57193i	0.294826	−	0.369700i
$317$	2.58426	+	1.24451i	0.145147	+	0.0698989i	0.505047	−	0.863092i	$-0.331475\pi$
$317$	2.58426	+	1.24451i	0.145147	+	0.0698989i	−0.359901	+	0.932991i	$0.617189\pi$
$318$	2.60388			0.146018
$319$	13.9596	−	22.6395i	0.781586	−	1.26757i
$320$		0			0
$321$	18.2506	+	8.78904i	1.01865	+	0.490556i
$322$	0.227365	−	0.285107i	0.0126706	−	0.0158884i
$323$	6.60388	+	8.28100i	0.367449	+	0.460767i
$324$	−4.18329	−	2.01457i	−0.232405	−	0.111920i
$325$		0			0
$326$	−3.50753	+	4.39831i	−0.194264	+	0.243600i
$327$	−1.51693	−	6.64609i	−0.0838862	−	0.367529i
$328$	1.17092	+	5.13011i	0.0646530	+	0.283263i
$329$	−1.43416	−	1.79838i	−0.0790676	−	0.0991477i
$330$		0			0
$331$	3.13408			0.172265			0.0861323	−	0.996284i	$-0.472549\pi$
$331$	3.13408			0.172265			0.0861323	+	0.996284i	$0.472549\pi$
$332$	−1.78621	+	7.82589i	−0.0980309	+	0.429501i
$333$	6.43027	−	3.09666i	0.352377	−	0.169696i
$334$	−0.319396	+	0.153813i	−0.0174766	+	0.00841628i
$335$		0			0
$336$	−1.26875			−0.0692160
$337$	1.10872	−	4.85762i	0.0603958	−	0.264611i	−0.935711	−	0.352768i	$-0.885240\pi$
$337$	1.10872	−	4.85762i	0.0603958	−	0.264611i	0.996107	+	0.0881567i	$0.0280976\pi$
$338$	5.25936	+	6.59502i	0.286071	+	0.358722i
$339$	−2.96197	−	12.9772i	−0.160872	−	0.704826i
$340$		0			0
$341$	−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
$345$		0			0
$346$	−3.67025	−	1.76750i	−0.197314	−	0.0950214i
$347$	−20.1172			−1.07995			−0.539974	−	0.841682i	$-0.681566\pi$
$347$	−20.1172			−1.07995			−0.539974	+	0.841682i	$0.681566\pi$
$348$	11.4547	+	3.89971i	0.614038	+	0.209046i
$349$	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			0
$351$	−19.5356	+	24.4969i	−1.04274	+	1.30755i
$352$	14.3279	+	17.9666i	0.763679	+	0.957623i
$353$	16.2153	+	7.80887i	0.863052	+	0.415624i	0.812406	−	0.583092i	$-0.198157\pi$
$353$	16.2153	+	7.80887i	0.863052	+	0.415624i	0.0506467	+	0.998717i	$0.483872\pi$
$354$	6.24698	−	3.00839i	0.332023	−	0.159894i
$355$		0			0
$356$	−2.27748	−	9.97829i	−0.120706	−	0.528848i
$357$	−0.445042	−	1.94986i	−0.0235541	−	0.103197i
$358$	0.945042	+	1.18505i	0.0499470	+	0.0626316i
$359$	−5.25786	+	23.0362i	−0.277499	+	1.21580i	0.623444	+	0.781868i	$0.285733\pi$
$359$	−5.25786	+	23.0362i	−0.277499	+	1.21580i	−0.900943	+	0.433937i	$0.857124\pi$
$360$		0			0
$361$	2.99180	−	13.1079i	0.157463	−	0.689892i
$362$	−5.08211	+	2.44741i	−0.267110	+	0.128633i
$363$	−15.0477	+	7.24660i	−0.789801	+	0.380348i
$364$	−0.808938	+	3.54419i	−0.0423999	+	0.185766i
$365$		0			0
$366$	0.202907	−	0.888992i	0.0106061	−	0.0464684i
$367$	18.4822	+	23.1759i	0.964762	+	1.20977i	0.977732	+	0.209857i	$0.0672998\pi$
$367$	18.4822	+	23.1759i	0.964762	+	1.20977i	−0.0129705	+	0.999916i	$0.504129\pi$
$368$	1.45646	+	6.38117i	0.0759232	+	0.332641i
$369$	1.00000	+	4.38129i	0.0520579	+	0.228081i
$370$		0			0
$371$	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	0.999310	+	0.0371310i	$0.0118219\pi$
$373$	15.7044	+	19.6927i	0.813143	+	1.01965i	−0.186167	+	0.982518i	$0.559607\pi$
$374$	−6.15883	+	7.72293i	−0.318466	+	0.399343i
$375$		0			0
$376$	−10.9051			−0.562390
$377$	15.9770	−	25.9114i	0.822859	−	1.33451i
$378$	0.880395			0.0452826
$379$	24.2424	+	11.6745i	1.24525	+	0.599681i	0.936234	−	0.351376i	$-0.114286\pi$
$379$	24.2424	+	11.6745i	1.24525	+	0.599681i	0.309016	+	0.951057i	$0.400000\pi$
$380$		0			0
$381$	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	−0.827879	−	0.560907i	$-0.810452\pi$
$383$	−17.7213	+	8.53414i	−0.905517	+	0.436074i	−0.0776388	+	0.996982i	$0.524738\pi$
$384$	−8.49127	+	10.6477i	−0.433318	+	0.543364i
$385$		0			0
$386$	2.25086	+	9.86168i	0.114566	+	0.501946i
$387$	−3.06853	−	3.84782i	−0.155982	−	0.195596i
$388$	0.0724165	−	0.317278i	0.00367639	−	0.0161073i
$389$	24.8552			1.26021			0.630103	−	0.776511i	$-0.283012\pi$
$389$	24.8552			1.26021			0.630103	+	0.776511i	$0.283012\pi$
$390$		0			0
$391$	−9.29590	+	4.47667i	−0.470114	+	0.226395i
$392$	−10.4770	+	5.04547i	−0.529170	+	0.254835i
$393$	−2.22587	+	9.75219i	−0.112280	+	0.491933i
$394$	8.70410			0.438506
$395$		0			0
$396$	8.01842	+	10.0548i	0.402941	+	0.505272i
$397$	−0.888887	−	3.89447i	−0.0446120	−	0.195458i	0.947711	−	0.319129i	$-0.103390\pi$
$397$	−0.888887	−	3.89447i	−0.0446120	−	0.195458i	−0.992323	+	0.123671i	$0.960533\pi$
$398$	0.0866540	+	0.379656i	0.00434357	+	0.0190304i
$399$	0.653989	−	0.820077i	0.0327404	−	0.0410552i
$400$		0			0
$401$	22.4405	+	10.8068i	1.12062	+	0.539664i	0.900085	−	0.435714i	$-0.143504\pi$
$401$	22.4405	+	10.8068i	1.12062	+	0.539664i	0.220539	+	0.975378i	$0.429218\pi$
$402$	0.803798	+	1.00793i	0.0400898	+	0.0502710i
$403$	−23.5858	+	29.5756i	−1.17489	+	1.47327i
$404$	5.24309	+	2.52494i	0.260854	+	0.125621i
$405$		0			0
$406$	−0.849126	+	0.102957i	−0.0421414	+	0.00510965i
$407$	24.3937			1.20915
$408$	−8.54288	−	4.11403i	−0.422935	−	0.203675i
$409$	0.176587	−	0.221434i	0.00873169	−	0.0109492i	−0.777446	−	0.628949i	$-0.783485\pi$
$409$	0.176587	−	0.221434i	0.00873169	−	0.0109492i	0.786178	+	0.618000i	$0.212057\pi$
$410$		0			0
$411$	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
$414$	−0.328552	−	1.43948i	−0.0161475	−	0.0707467i
$415$		0			0
$416$	16.3986	+	20.5632i	0.804006	+	1.00819i
$417$	4.62498	−	20.2634i	0.226486	−	0.992301i
$418$	−5.18060			−0.253392
$419$	5.89426	−	25.8245i	0.287954	−	1.26161i	−0.599374	−	0.800469i	$-0.704584\pi$
$419$	5.89426	−	25.8245i	0.287954	−	1.26161i	0.887328	−	0.461139i	$-0.152559\pi$
$420$		0			0
$421$	15.8409	−	7.62859i	0.772040	−	0.371795i	−0.00602261	−	0.999982i	$-0.501917\pi$
$421$	15.8409	−	7.62859i	0.772040	−	0.371795i	0.778062	+	0.628187i	$0.216203\pi$
$422$	1.80917	−	7.92651i	0.0880693	−	0.385857i
$423$	−9.31336			−0.452831
$424$	1.76659	−	7.73995i	0.0857934	−	0.375885i
$425$		0			0
$426$	0.905813	+	3.96863i	0.0438868	+	0.192281i
$427$	−0.130490	−	0.571714i	−0.00631486	−	0.0276672i
$428$	18.2506	−	22.8856i	0.882177	−	1.10622i
$429$	−31.3669	+	15.1055i	−1.51441	+	0.729300i
$430$		0			0
$431$	−17.3300	−	21.7312i	−0.834759	−	1.04675i	−0.998186	−	0.0601992i	$-0.980826\pi$
$431$	−17.3300	−	21.7312i	−0.834759	−	1.04675i	0.163428	−	0.986555i	$-0.447745\pi$
$432$	−9.85235	+	12.3545i	−0.474021	+	0.594404i
$433$	5.29374	+	2.54933i	0.254401	+	0.122513i	0.556738	−	0.830688i	$-0.312053\pi$
$433$	5.29374	+	2.54933i	0.254401	+	0.122513i	−0.302337	+	0.953201i	$0.597767\pi$
$434$	1.06292			0.0510217
$435$		0			0
$436$	−9.85086			−0.471770
$437$	−4.87531	−	2.34783i	−0.233218	−	0.112312i
$438$	−1.94653	+	2.44088i	−0.0930090	+	0.116630i
$439$	−9.81431	−	12.3068i	−0.468412	−	0.587370i	0.490370	−	0.871515i	$-0.336862\pi$
$439$	−9.81431	−	12.3068i	−0.468412	−	0.587370i	−0.958781	+	0.284145i	$0.908290\pi$
$440$		0			0
$441$	−8.94773	+	4.30900i	−0.426082	+	0.205190i
$442$	−7.04892	+	8.83906i	−0.335283	+	0.420431i
$443$	1.49947	+	6.56960i	0.0712419	+	0.312131i	0.997976	−	0.0635859i	$-0.0202537\pi$
$443$	1.49947	+	6.56960i	0.0712419	+	0.312131i	−0.926735	+	0.375717i	$0.877397\pi$
$444$	2.46950	+	10.8196i	0.117197	+	0.513475i
$445$		0			0
$446$	−0.180071	+	0.788944i	−0.00852663	+	0.0373576i
$447$	23.2024			1.09743
$448$	−0.288364	+	1.26341i	−0.0136239	+	0.0596903i
$449$	−11.1000	+	5.34547i	−0.523841	+	0.252269i	−0.677065	−	0.735923i	$-0.736749\pi$
$449$	−11.1000	+	5.34547i	−0.523841	+	0.252269i	0.153224	+	0.988191i	$0.451034\pi$
$450$		0			0
$451$	−3.41789	+	14.9748i	−0.160942	+	0.705135i
$452$	−19.2349			−0.904733
$453$	2.08881	−	9.15167i	0.0981409	−	0.429983i
$454$	3.84481	+	4.82124i	0.180446	+	0.226272i
$455$		0			0
$456$	−1.10656	−	4.84817i	−0.0518196	−	0.227037i
$457$	−8.51842	+	10.6818i	−0.398475	+	0.499672i	−0.940076	−	0.340964i	$-0.889247\pi$
$457$	−8.51842	+	10.6818i	−0.398475	+	0.499672i	0.541602	+	0.840635i	$0.317818\pi$
$458$	5.12133	−	2.46630i	0.239304	−	0.115243i
$459$	−22.4426	−	10.8078i	−1.04753	−	0.504465i
$460$		0			0
$461$	7.23759	−	9.07565i	0.337088	−	0.422695i	−0.584180	−	0.811624i	$-0.698584\pi$
$461$	7.23759	−	9.07565i	0.337088	−	0.422695i	0.921268	+	0.388929i	$0.127155\pi$
$462$	0.881355	+	0.424438i	0.0410043	+	0.0197466i
$463$	7.24267			0.336595			0.168298	−	0.985736i	$-0.446173\pi$
$463$	7.24267			0.336595			0.168298	+	0.985736i	$0.446173\pi$
$464$	8.05765	−	13.0678i	0.374067	−	0.606659i
$465$		0			0
$466$	−3.55496	−	1.71198i	−0.164680	−	0.0793058i
$467$	1.28650	−	1.61322i	0.0595323	−	0.0746511i	−0.751174	−	0.660104i	$-0.770512\pi$
$467$	1.28650	−	1.61322i	0.0595323	−	0.0746511i	0.810706	+	0.585453i	$0.199083\pi$
$468$	9.17725	+	11.5079i	0.424219	+	0.531953i
$469$	0.746980	+	0.359726i	0.0344923	+	0.0166106i
$470$		0			0
$471$	14.1806	−	17.7819i	0.653408	−	0.819347i
$472$	−4.70410	−	20.6100i	−0.216524	−	0.948653i
$473$	−3.74309	−	16.3996i	−0.172108	−	0.754053i
$474$	−1.61410	−	2.02401i	−0.0741379	−	0.0929660i
$475$		0			0
$476$	−2.89008			−0.132467
$477$	1.50873	−	6.61017i	0.0690800	−	0.302659i
$478$	10.2506	−	4.93644i	0.468853	−	0.225788i
$479$	3.50388	−	1.68738i	0.160097	−	0.0770985i	−0.352120	−	0.935955i	$-0.614539\pi$
$479$	3.50388	−	1.68738i	0.160097	−	0.0770985i	0.512216	+	0.858857i	$0.328825\pi$
$480$		0			0
$481$	27.9191			1.27300
$482$	−0.963697	+	4.22223i	−0.0438952	+	0.192317i
$483$	0.637063	+	0.798852i	0.0289874	+	0.0363490i
$484$	5.37047	+	23.5296i	0.244112	+	1.06953i
$485$		0			0
$486$	3.72252	−	4.66789i	0.168857	−	0.211740i
$487$	8.87047	−	4.27179i	0.401959	−	0.193573i	−0.221971	−	0.975053i	$-0.571249\pi$
$487$	8.87047	−	4.27179i	0.401959	−	0.193573i	0.623931	+	0.781480i	$0.285535\pi$
$488$	−2.50484	−	1.20627i	−0.113389	−	0.0546053i
$489$	−9.82789	−	12.3238i	−0.444432	−	0.557301i
$490$		0			0
$491$	−7.01961	−	3.38047i	−0.316791	−	0.152558i	0.268731	−	0.963215i	$-0.413396\pi$
$491$	−7.01961	−	3.38047i	−0.316791	−	0.152558i	−0.585521	+	0.810657i	$0.699110\pi$
$492$	−6.98792			−0.315040
$493$	22.9095	+	7.79942i	1.03179	+	0.351268i
$494$	−5.92931			−0.266772
$495$		0			0
$496$	−11.8949	+	14.9158i	−0.534098	+	0.669738i
$497$	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	$-0.490594\pi$
$499$	18.5286	−	8.92292i	0.829456	−	0.399445i	0.799911	+	0.600119i	$0.204880\pi$
$500$		0			0
$501$	−0.221029	−	0.968391i	−0.00987485	−	0.0432645i
$502$	0.966575	+	4.23484i	0.0431404	+	0.189010i
$503$	−5.13437	−	6.43830i	−0.228930	−	0.287070i	0.654078	−	0.756427i	$-0.273057\pi$
$503$	−5.13437	−	6.43830i	−0.228930	−	0.287070i	−0.883008	+	0.469358i	$0.844486\pi$
$504$	0.194177	−	0.850747i	0.00864935	−	0.0378953i
$505$		0			0
$506$	1.12296	−	4.92000i	0.0499215	−	0.218721i
$507$	−21.2947	+	10.2550i	−0.945731	+	0.455440i
$508$	1.68329	−	0.810631i	0.0746840	−	0.0359659i
$509$	−1.76151	+	7.71769i	−0.0780777	+	0.342081i	−0.998846	−	0.0480294i	$-0.984706\pi$
$509$	−1.76151	+	7.71769i	−0.0780777	+	0.342081i	0.920768	+	0.390110i	$0.127563\pi$
$510$		0			0
$511$	−0.446771	+	1.95743i	−0.0197640	+	0.0865916i
$512$	14.2853	+	17.9132i	0.631327	+	0.791659i
$513$	−2.90701	−	12.7364i	−0.128348	−	0.562328i
$514$	1.61984	+	7.09699i	0.0714482	+	0.313035i
$515$		0			0
$516$	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
$519$	7.11662	−	8.92396i	0.312385	−	0.391718i
$520$		0			0
$521$	−3.52542			−0.154451			−0.0772257	−	0.997014i	$-0.524606\pi$
$521$	−3.52542			−0.154451			−0.0772257	+	0.997014i	$0.524606\pi$
$522$	−1.81767	+	2.94788i	−0.0795571	+	0.129025i
$523$	−10.0301			−0.438587			−0.219294	−	0.975659i	$-0.570375\pi$
$523$	−10.0301			−0.438587			−0.219294	+	0.975659i	$0.570375\pi$
$524$	13.0233	+	6.27167i	0.568924	+	0.273979i
$525$		0			0
$526$	−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
$530$		0			0
$531$	−4.01746	−	17.6016i	−0.174343	−	0.763846i
$532$	−0.945042	−	1.18505i	−0.0409728	−	0.0513782i
$533$	−3.91185	+	17.1390i	−0.169441	+	0.742370i
$534$	−3.15213			−0.136406
$535$		0			0
$536$	3.54138	−	1.70544i	0.152965	−	0.0736638i
$537$	−3.82640	+	1.84270i	−0.165121	+	0.0795182i
$538$	−2.51089	+	11.0009i	−0.108252	+	0.474283i
$539$	−33.9439			−1.46207
$540$		0			0
$541$	5.12767	+	6.42990i	0.220456	+	0.276443i	0.879744	−	0.475447i	$-0.157714\pi$
$541$	5.12767	+	6.42990i	0.220456	+	0.276443i	−0.659288	+	0.751890i	$0.729142\pi$
$542$	0.119178	+	0.522153i	0.00511913	+	0.0224284i
$543$	−3.51693	−	15.4087i	−0.150926	−	0.661249i
$544$	−13.0368	+	16.3477i	−0.558950	+	0.700901i
$545$		0			0
$546$	1.00873	+	0.485778i	0.0431696	+	0.0207894i
$547$	−16.1253	−	20.2205i	−0.689467	−	0.864564i	0.306721	−	0.951800i	$-0.400768\pi$
$547$	−16.1253	−	20.2205i	−0.689467	−	0.864564i	−0.996188	+	0.0872352i	$0.972197\pi$
$548$	19.3605	−	24.2774i	0.827041	−	1.03708i
$549$	−2.13922	−	1.03019i	−0.0912997	−	0.0439676i
$550$		0			0
$551$	4.29321	+	11.9441i	0.182897	+	0.508837i
$552$	4.84415			0.206181
$553$	−1.50000	−	0.722362i	−0.0637865	−	0.0307180i
$554$	−2.95928	+	3.71082i	−0.125728	+	0.157658i
$555$		0			0
$556$	−27.0601	−	13.0315i	−1.14760	−	0.552657i
$557$	20.7310	−	9.98353i	0.878401	−	0.423016i	0.0603609	−	0.998177i	$-0.480775\pi$
$557$	20.7310	−	9.98353i	0.878401	−	0.423016i	0.818040	+	0.575161i	$0.195061\pi$
$558$	2.68329	−	3.36474i	0.113593	−	0.142441i
$559$	−4.28405	−	18.7697i	−0.181196	−	0.793872i
$560$		0			0
$561$	−17.2567	−	21.6392i	−0.728577	−	0.913607i
$562$	1.61218	−	7.06341i	0.0680056	−	0.297952i
$563$	−43.1159			−1.81712			−0.908559	−	0.417757i	$-0.862816\pi$
$563$	−43.1159			−1.81712			−0.908559	+	0.417757i	$0.862816\pi$
$564$	3.22252	−	14.1188i	0.135693	−	0.594508i
$565$		0			0
$566$	−2.10388	+	1.01317i	−0.0884325	+	0.0425868i
$567$	−0.204636	+	0.896567i	−0.00859388	+	0.0376523i
$568$	12.4112			0.520762
$569$	5.40999	−	23.7027i	0.226799	−	0.993670i	−0.725433	−	0.688293i	$-0.758360\pi$
$569$	5.40999	−	23.7027i	0.226799	−	0.993670i	0.952231	−	0.305377i	$-0.0987825\pi$
$570$		0			0
$571$	−4.11410	−	18.0250i	−0.172170	−	0.754324i	−0.985103	−	0.171967i	$-0.944988\pi$
$571$	−4.11410	−	18.0250i	−0.172170	−	0.754324i	0.812933	−	0.582357i	$-0.197869\pi$
$572$	11.1947	+	49.0472i	0.468074	+	2.05077i
$573$	−8.29590	+	10.4027i	−0.346566	+	0.434580i
$574$	0.445042	−	0.214321i	0.0185757	−	0.00894558i
$575$		0			0
$576$	3.27144	+	4.10225i	0.136310	+	0.170927i
$577$	23.6042	−	29.5987i	0.982654	−	1.23221i	0.0100007	−	0.999950i	$-0.496817\pi$
$577$	23.6042	−	29.5987i	0.982654	−	1.23221i	0.972654	−	0.232260i	$-0.0746119\pi$
$578$	−1.28136	−	0.617072i	−0.0532977	−	0.0256668i
$579$	−28.3424			−1.17787
$580$		0			0
$581$	1.58987			0.0659591
$582$	−0.0903019	−	0.0434871i	−0.00374314	−	0.00180260i
$583$	14.4487	−	18.1181i	0.598404	−	0.750374i
$584$	5.93482	+	7.44203i	0.245585	+	0.307953i
$585$		0			0
$586$	2.71206	−	1.30606i	0.112034	−	0.0539529i
$587$	9.00030	−	11.2860i	0.371482	−	0.465824i	−0.560592	−	0.828092i	$-0.689426\pi$
$587$	9.00030	−	11.2860i	0.371482	−	0.465824i	0.932074	+	0.362269i	$0.117998\pi$
$588$	−3.43631	−	15.0555i	−0.141711	−	0.620877i
$589$	−3.50969	−	15.3770i	−0.144614	−	0.633596i
$590$		0			0
$591$	−5.42692	+	23.7769i	−0.223234	+	0.978050i
$592$	14.0804			0.578700
$593$	−2.89320	+	12.6759i	−0.118809	+	0.520538i	0.880140	+	0.474714i	$0.157449\pi$
$593$	−2.89320	+	12.6759i	−0.118809	+	0.520538i	−0.998950	+	0.0458241i	$0.985409\pi$
$594$	10.9770	−	5.28626i	0.450393	−	0.216898i
$595$		0			0
$596$	7.46077	−	32.6878i	0.305605	−	1.33894i
$597$	−1.09113			−0.0446570
$598$	1.28525	−	5.63104i	0.0525577	−	0.230270i
$599$	7.54019	+	9.45510i	0.308084	+	0.386325i	0.911636	−	0.410999i	$-0.134820\pi$
$599$	7.54019	+	9.45510i	0.308084	+	0.386325i	−0.603552	+	0.797323i	$0.706249\pi$
$600$		0			0
$601$	4.97272	+	21.7869i	0.202842	+	0.888707i	0.969196	+	0.246289i	$0.0792113\pi$
$601$	4.97272	+	21.7869i	0.202842	+	0.888707i	−0.766355	+	0.642418i	$0.777932\pi$
$602$	−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
$605$		0			0
$606$	1.11745	−	1.40124i	0.0453933	−	0.0569214i
$607$	37.3620	+	17.9926i	1.51648	+	0.730297i	0.992593	−	0.121491i	$-0.0387676\pi$
$607$	37.3620	+	17.9926i	1.51648	+	0.730297i	0.523886	+	0.851789i	$0.324482\pi$
$608$	−10.9661			−0.444736
$609$	0.248176	−	2.38374i	0.0100566	−	0.0965940i
$610$		0			0
$611$	−32.8245	−	15.8075i	−1.32794	−	0.639502i
$612$	−7.29590	+	9.14877i	−0.294919	+	0.369817i
$613$	−16.0764	−	20.1591i	−0.649318	−	0.814219i	0.342816	−	0.939403i	$-0.388619\pi$
$613$	−16.0764	−	20.1591i	−0.649318	−	0.814219i	−0.992134	+	0.125184i	$0.960048\pi$
$614$	1.81163	+	0.872433i	0.0731113	+	0.0352085i
$615$		0			0
$616$	1.85958	−	2.33184i	0.0749248	−	0.0939527i
$617$	1.97272	+	8.64306i	0.0794188	+	0.347956i	0.998988	−	0.0449710i	$-0.0143195\pi$
$617$	1.97272	+	8.64306i	0.0794188	+	0.347956i	−0.919570	+	0.392927i	$0.871462\pi$
$618$	−1.68598	−	7.38676i	−0.0678201	−	0.297139i
$619$	18.3626	+	23.0259i	0.738054	+	0.925490i	0.999207	−	0.0398069i	$-0.0126743\pi$
$619$	18.3626	+	23.0259i	0.738054	+	0.925490i	−0.261153	+	0.965297i	$0.584103\pi$
$620$		0			0
$621$	12.7259			0.510672
$622$	1.24943	−	5.47412i	0.0500976	−	0.219492i
$623$	−1.82640	+	0.879546i	−0.0731730	+	0.0352383i
$624$	−18.1054	+	8.71909i	−0.724795	+	0.349043i
$625$		0			0
$626$	−8.56273			−0.342235
$627$	3.23005	−	14.1518i	0.128996	−	0.565168i
$628$	−20.4916	−	25.6956i	−0.817703	−	1.02537i
$629$	4.93900	+	21.6392i	0.196931	+	0.862811i
$630$		0			0
$631$	14.8210	−	18.5850i	0.590015	−	0.739856i	−0.393769	−	0.919209i	$-0.628829\pi$
$631$	14.8210	−	18.5850i	0.590015	−	0.739856i	0.983785	+	0.179353i	$0.0574005\pi$
$632$	−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			0
$636$	9.49880	+	4.57438i	0.376652	+	0.181386i
$637$	−38.8495			−1.53927
$638$	−9.96897	+	6.38220i	−0.394675	+	0.252674i
$639$	10.5996			0.419312
$640$		0			0
$641$	17.7479	−	22.2552i	0.701001	−	0.879028i	−0.296096	−	0.955158i	$-0.595685\pi$
$641$	17.7479	−	22.2552i	0.701001	−	0.879028i	0.997098	+	0.0761300i	$0.0242564\pi$
$642$	−5.62080	−	7.04826i	−0.221835	−	0.278173i
$643$	−17.4308	−	8.39423i	−0.687404	−	0.331036i	0.0573702	−	0.998353i	$-0.481728\pi$
$643$	−17.4308	−	8.39423i	−0.687404	−	0.331036i	−0.744774	+	0.667317i	$0.767443\pi$
$644$	1.33028	−	0.640630i	0.0524204	−	0.0252443i
$645$		0			0
$646$	−1.04892	−	4.59561i	−0.0412691	−	0.180812i
$647$	5.05443	+	22.1449i	0.198710	+	0.870605i	0.971706	+	0.236194i	$0.0759002\pi$
$647$	5.05443	+	22.1449i	0.198710	+	0.870605i	−0.772996	+	0.634411i	$0.781243\pi$
$648$	2.71834	+	3.40869i	0.106787	+	0.133906i
$649$	13.7313	−	60.1605i	0.538999	−	2.36151i
$650$		0			0
$651$	−0.662718	+	2.90356i	−0.0259740	+	0.113799i
$652$	−20.5221	+	9.88291i	−0.803706	+	0.387044i
$653$	20.6603	−	9.94949i	0.808501	−	0.389354i	0.0164928	−	0.999864i	$-0.494750\pi$
$653$	20.6603	−	9.94949i	0.808501	−	0.389354i	0.792008	+	0.610510i	$0.209036\pi$
$654$	−0.675096	+	2.95779i	−0.0263983	+	0.115659i
$655$		0			0
$656$	−1.97285	+	8.64363i	−0.0770270	+	0.337477i
$657$	5.06853	+	6.35574i	0.197742	+	0.247961i
$658$	0.227792	+	0.998023i	0.00888027	+	0.0389070i
$659$	4.26755	+	18.6974i	0.166240	+	0.728346i	0.987478	+	0.157759i	$0.0504271\pi$
$659$	4.26755	+	18.6974i	0.166240	+	0.728346i	−0.821237	+	0.570587i	$0.806716\pi$
$660$		0			0
$661$	3.05107	−	1.46932i	0.118673	−	0.0571499i	−0.373605	−	0.927588i	$-0.621879\pi$
$661$	3.05107	−	1.46932i	0.118673	−	0.0571499i	0.492278	+	0.870438i	$0.336164\pi$
$662$	−1.25667	−	0.605180i	−0.0488418	−	0.0235210i
$663$	−19.7506	−	24.7665i	−0.767051	−	0.961851i
$664$	4.69955	−	5.89305i	0.182378	−	0.228695i
$665$		0			0
$666$	−3.17629			−0.123079
$667$	−12.2739	+	1.48821i	−0.475247	+	0.0576238i
$668$	−1.43535			−0.0555355
$669$	−2.04288	−	0.983797i	−0.0789822	−	0.0380358i
$670$		0			0
$671$	−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	−0.349207	−	0.937046i	$-0.613549\pi$
$673$	4.29805	−	2.06983i	0.165678	−	0.0797862i	0.514885	+	0.857259i	$0.327835\pi$
$674$	−1.38255	+	1.73366i	−0.0532539	+	0.0667782i
$675$		0			0
$676$	7.59999	+	33.2977i	0.292307	+	1.28068i
$677$	26.8662	+	33.6892i	1.03255	+	1.29478i	0.954622	+	0.297821i	$0.0962599\pi$
$677$	26.8662	+	33.6892i	1.03255	+	1.29478i	0.0779309	+	0.996959i	$0.475169\pi$
$678$	−1.31820	+	5.77541i	−0.0506252	+	0.221803i
$679$	−0.0644568			−0.00247362
$680$		0			0
$681$	−15.5673	+	7.49683i	−0.596542	+	0.287279i
$682$	13.2528	−	6.38220i	0.507475	−	0.244387i
$683$	5.21432	−	22.8454i	0.199521	−	0.874157i	−0.771702	−	0.635984i	$-0.780594\pi$
$683$	5.21432	−	22.8454i	0.199521	−	0.874157i	0.971223	−	0.238173i	$-0.0765484\pi$
$684$	−6.13706			−0.234656
$685$		0			0
$686$	1.37382	+	1.72272i	0.0524528	+	0.0657737i
$687$	3.54407	+	15.5276i	0.135215	+	0.592415i
$688$	−2.16056	−	9.46604i	−0.0823707	−	0.360890i
$689$	16.5368	−	20.7365i	0.630003	−	0.789999i
$690$		0			0
$691$	−38.8657	−	18.7167i	−1.47852	−	0.712018i	−0.491243	−	0.871023i	$-0.663457\pi$
$691$	−38.8657	−	18.7167i	−1.47852	−	0.712018i	−0.987278	+	0.159005i	$0.949171\pi$
$692$	−10.2838	−	12.8955i	−0.390932	−	0.490213i
$693$	1.58815	−	1.99147i	0.0603287	−	0.0756498i
$694$	8.06638	+	3.88456i	0.306195	+	0.147456i
$695$		0			0
$696$	−8.10202	−	7.96605i	−0.307106	−	0.301952i
$697$	−13.9758			−0.529373
$698$	−8.21552	−	3.95639i	−0.310962	−	0.149751i
$699$	6.89307	−	8.64363i	0.260720	−	0.326932i
$700$		0			0
$701$	−3.81186	−	1.83570i	−0.143972	−	0.0693333i	0.360511	−	0.932755i	$-0.382602\pi$
$701$	−3.81186	−	1.83570i	−0.143972	−	0.0693333i	−0.504483	+	0.863422i	$0.668317\pi$
$702$	12.5635	−	6.05024i	0.474177	−	0.228352i
$703$	−7.25786	+	9.10107i	−0.273736	+	0.343254i
$704$	3.99061	+	17.4840i	0.150402	+	0.658953i
$705$		0			0
$706$	−4.99396	−	6.26223i	−0.187950	−	0.235682i
$707$	0.256478	−	1.12370i	0.00964586	−	0.0422613i
$708$	28.0737			1.05507
$709$	−3.18287	+	13.9450i	−0.119535	+	0.523717i	0.879336	+	0.476203i	$0.157987\pi$
$709$	−3.18287	+	13.9450i	−0.119535	+	0.523717i	−0.998871	+	0.0475144i	$0.984870\pi$
$710$		0			0
$711$	−6.07338	+	2.92478i	−0.227769	+	0.109688i
$712$	−2.13856	+	9.36962i	−0.0801457	+	0.351141i
$713$	15.3642			0.575393
$714$	−0.198062	+	0.867767i	−0.00741229	+	0.0324754i
$715$		0			0
$716$	1.36563	+	5.98319i	0.0510358	+	0.223602i
$717$	7.09365	+	31.0793i	0.264917	+	1.16068i
$718$	6.55645	−	8.22153i	0.244685	−	0.306825i
$719$	21.1194	−	10.1706i	0.787620	−	0.379298i	0.00356825	−	0.999994i	$-0.498864\pi$
$719$	21.1194	−	10.1706i	0.787620	−	0.379298i	0.784051	+	0.620696i	$0.213150\pi$
$720$		0			0
$721$	−3.03803	−	3.80957i	−0.113142	−	0.141876i
$722$	−3.73072	+	4.67817i	−0.138843	+	0.174104i
$723$	−10.9330	−	5.26504i	−0.406601	−	0.195809i
$724$	−22.8388			−0.848796
$725$		0			0
$726$	7.43296			0.275863
$727$	46.8482	+	22.5609i	1.73750	+	0.836738i	0.983741	+	0.179592i	$0.0574778\pi$
$727$	46.8482	+	22.5609i	1.73750	+	0.836738i	0.753763	+	0.657146i	$0.228237\pi$
$728$	2.12833	−	2.66885i	0.0788813	−	0.0989140i
$729$	15.2500	+	19.1228i	0.564813	+	0.708254i
$730$		0			0
$731$	13.7899	−	6.64084i	0.510036	−	0.245621i
$732$	2.30194	−	2.88654i	0.0850821	−	0.106690i
$733$	7.60806	+	33.3331i	0.281010	+	1.23119i	0.896501	+	0.443041i	$0.146101\pi$
$733$	7.60806	+	33.3331i	0.281010	+	1.23119i	−0.615491	+	0.788144i	$0.711042\pi$
$734$	−2.93559	−	12.8617i	−0.108355	−	0.474733i
$735$		0			0
$736$	2.37704	−	10.4145i	0.0876190	−	0.383884i
$737$	11.4735			0.422632
$738$	0.445042	−	1.94986i	0.0163822	−	0.0717752i
$739$	−35.8342	+	17.2569i	−1.31818	+	0.634804i	−0.954915	−	0.296881i	$-0.904054\pi$
$739$	−35.8342	+	17.2569i	−1.31818	+	0.634804i	−0.363269	+	0.931684i	$0.618339\pi$
$740$		0			0
$741$	3.69687	−	16.1970i	0.135808	−	0.595013i
$742$	−0.745251			−0.0273590
$743$	1.59730	−	6.99824i	0.0585993	−	0.256740i	−0.937140	−	0.348954i	$-0.886537\pi$
$743$	1.59730	−	6.99824i	0.0585993	−	0.256740i	0.995739	+	0.0922133i	$0.0293942\pi$
$744$	8.80343	+	11.0392i	0.322749	+	0.404715i
$745$		0			0
$746$	−2.49439	−	10.9286i	−0.0913260	−	0.400125i
$747$	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
$750$		0			0
$751$	−16.9393	+	21.2412i	−0.618124	+	0.775103i	−0.988079	−	0.153947i	$-0.950802\pi$
$751$	−16.9393	+	21.2412i	−0.618124	+	0.775103i	0.369955	+	0.929050i	$0.379373\pi$
$752$	−16.5543	−	7.97213i	−0.603673	−	0.290714i
$753$	−12.1709			−0.443533
$754$	−11.4097	+	7.30457i	−0.415517	+	0.266017i
$755$		0			0
$756$	3.21164	+	1.54664i	0.116806	+	0.0562508i
$757$	−14.7721	+	18.5236i	−0.536901	+	0.673253i	−0.974101	−	0.226111i	$-0.927399\pi$
$757$	−14.7721	+	18.5236i	−0.536901	+	0.673253i	0.437200	+	0.899364i	$0.355970\pi$
$758$	−7.46615	−	9.36225i	−0.271183	−	0.340052i
$759$	12.7397	+	6.13514i	0.462423	+	0.222691i
$760$		0			0
$761$	−8.88740	+	11.1444i	−0.322168	+	0.403986i	−0.916372	−	0.400329i	$-0.868896\pi$
$761$	−8.88740	+	11.1444i	−0.322168	+	0.403986i	0.594204	+	0.804315i	$0.297467\pi$
$762$	−0.128039	−	0.560974i	−0.00463835	−	0.0203219i
$763$	0.434157	+	1.90216i	0.0157175	+	0.0688630i
$764$	11.9879	+	15.0324i	0.433708	+	0.543852i
$765$		0			0
$766$	8.75361			0.316281
$767$	15.7157	−	68.8550i	0.567461	−	2.48621i
$768$	−2.69806	+	1.29932i	−0.0973579	+	0.0468851i
$769$	40.2793	−	19.3975i	1.45251	−	0.699491i	0.469479	−	0.882944i	$-0.344442\pi$
$769$	40.2793	−	19.3975i	1.45251	−	0.699491i	0.983029	+	0.183453i	$0.0587275\pi$
$770$		0			0
$771$	−20.3967			−0.734570
$772$	−9.11356	+	39.9291i	−0.328004	+	1.43708i
$773$	−14.3083	−	17.9420i	−0.514633	−	0.645329i	0.454827	−	0.890580i	$-0.349701\pi$
$773$	−14.3083	−	17.9420i	−0.514633	−	0.645329i	−0.969460	+	0.245251i	$0.921130\pi$
$774$	0.487386	+	2.13538i	0.0175187	+	0.0767546i
$775$		0			0
$776$	−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
$780$		0			0
$781$	32.6405	+	15.7188i	1.16797	+	0.562464i
$782$	4.59179			0.164202
$783$	−21.2845	−	20.9273i	−0.760645	−	0.747881i
$784$	−19.5929			−0.699745
$785$		0			0
$786$	2.77562	−	3.48052i	0.0990030	−	0.124146i
$787$	−8.93631	−	11.2058i	−0.318545	−	0.399443i	0.596619	−	0.802525i	$-0.296510\pi$
$787$	−8.93631	−	11.2058i	−0.318545	−	0.399443i	−0.915164	+	0.403082i	$0.867939\pi$
$788$	31.7521	+	15.2910i	1.13112	+	0.544720i
$789$	26.6531	−	12.8355i	0.948875	−	0.456954i
$790$		0			0
$791$	0.847740	+	3.71419i	0.0301422	+	0.132061i
$792$	−2.68718	−	11.7733i	−0.0954847	−	0.418346i
$793$	−5.79105	−	7.26175i	−0.205646	−	0.257872i
$794$	−0.395592	+	1.73320i	−0.0140390	+	0.0615090i
$795$		0			0
$796$	−0.350855	+	1.53720i	−0.0124357	+	0.0544845i
$797$	9.18382	−	4.42270i	0.325308	−	0.156660i	−0.264101	−	0.964495i	$-0.585075\pi$
$797$	9.18382	−	4.42270i	0.325308	−	0.156660i	0.589409	+	0.807835i	$0.299361\pi$
$798$	−0.420583	+	0.202542i	−0.0148885	+	0.00716992i
$799$	6.44504	−	28.2376i	0.228009	−	0.998974i
$800$		0			0
$801$	−1.82640	+	8.00197i	−0.0645325	+	0.282736i
$802$	−6.91119	−	8.66636i	−0.244043	−	0.306020i
$803$	6.18276	+	27.0884i	0.218185	+	0.955930i
$804$	1.16152	+	5.08896i	0.0409637	+	0.179474i
$805$		0			0
$806$	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
$809$	5.59448	−	7.01526i	0.196692	−	0.246643i	−0.673698	−	0.739006i	$-0.735295\pi$
$809$	5.59448	−	7.01526i	0.196692	−	0.246643i	0.870390	+	0.492363i	$0.163867\pi$
$810$		0			0
$811$	−28.5628			−1.00298			−0.501489	−	0.865164i	$-0.667214\pi$
$811$	−28.5628			−1.00298			−0.501489	+	0.865164i	$0.667214\pi$
$812$	−3.27844	−	1.11613i	−0.115051	−	0.0391685i
$813$	−1.50066			−0.0526306
$814$	−9.78113	−	4.71034i	−0.342828	−	0.165097i
$815$		0			0
$816$	−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
$820$		0			0
$821$	−2.52230	−	11.0509i	−0.0880290	−	0.385680i	0.911651	−	0.410965i	$-0.134808\pi$
$821$	−2.52230	−	11.0509i	−0.0880290	−	0.385680i	−0.999680	+	0.0252844i	$0.991951\pi$
$822$	−5.96263	−	7.47690i	−0.207971	−	0.260787i
$823$	1.26218	−	5.52996i	0.0439967	−	0.192762i	−0.948154	−	0.317812i	$-0.897052\pi$
$823$	1.26218	−	5.52996i	0.0439967	−	0.192762i	0.992150	+	0.125050i	$0.0399091\pi$
$824$	−23.1008			−0.804755
$825$		0			0
$826$	−1.78794	+	0.861025i	−0.0622103	+	0.0299589i
$827$	−2.61572	+	1.25966i	−0.0909575	+	0.0438028i	−0.478809	−	0.877919i	$-0.658931\pi$
$827$	−2.61572	+	1.25966i	−0.0909575	+	0.0438028i	0.387852	+	0.921722i	$0.373217\pi$
$828$	1.33028	−	5.82834i	0.0462305	−	0.202549i
$829$	−45.2137			−1.57034			−0.785169	−	0.619282i	$-0.787424\pi$
$829$	−45.2137			−1.57034			−0.785169	+	0.619282i	$0.787424\pi$
$830$		0			0
$831$	−8.29172	−	10.3975i	−0.287636	−	0.360685i
$832$	4.56734	+	20.0108i	0.158344	+	0.693750i
$833$	−6.87263	−	30.1109i	−0.238122	−	1.04328i
$834$	−5.76726	+	7.23191i	−0.199704	+	0.250421i
$835$		0			0
$836$	−18.8986	−	9.10107i	−0.653621	−	0.314767i
$837$	23.1271	+	29.0005i	0.799391	+	1.00240i
$838$	−7.35003	+	9.21664i	−0.253902	+	0.318384i
$839$	41.1073	+	19.7962i	1.41918	+	0.683442i	0.976952	−	0.213460i	$-0.0684734\pi$
$839$	41.1073	+	19.7962i	1.41918	+	0.683442i	0.442229	+	0.896902i	$0.354188\pi$
$840$		0			0
$841$	22.9758	+	17.6949i	0.792270	+	0.610170i
$842$	−7.82477			−0.269659
$843$	18.2899	+	8.80793i	0.629936	+	0.303361i
$844$	20.5248	−	25.7372i	0.706491	−	0.885912i
$845$		0			0
$846$	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
$849$	−1.45593	−	6.37883i	−0.0499673	−	0.218921i
$850$		0			0
$851$	−7.07002	−	8.86553i	−0.242357	−	0.303906i
$852$	−3.66756	+	16.0686i	−0.125649	+	0.550503i
$853$	36.9288			1.26442			0.632210	−	0.774797i	$-0.282148\pi$
$853$	36.9288			1.26442			0.632210	+	0.774797i	$0.282148\pi$
$854$	−0.0580735	+	0.254437i	−0.00198724	+	0.00870665i
$855$		0			0
$856$	−24.7642	+	11.9258i	−0.846423	+	0.407616i
$857$	7.91066	−	34.6589i	0.270223	−	1.18392i	−0.639527	−	0.768768i	$-0.720870\pi$
$857$	7.91066	−	34.6589i	0.270223	−	1.18392i	0.909750	−	0.415156i	$-0.136273\pi$
$858$	15.4940			0.528955
$859$	−9.43070	+	41.3186i	−0.321771	+	1.40977i	0.512628	+	0.858611i	$0.328672\pi$
$859$	−9.43070	+	41.3186i	−0.321771	+	1.40977i	−0.834399	+	0.551161i	$0.814185\pi$
$860$		0			0
$861$	0.307979	+	1.34934i	0.0104959	+	0.0459855i
$862$	2.75259	+	12.0599i	0.0937537	+	0.410762i
$863$	−31.0371	+	38.9193i	−1.05652	+	1.32483i	−0.112966	+	0.993599i	$0.536035\pi$
$863$	−31.0371	+	38.9193i	−1.05652	+	1.32483i	−0.943550	+	0.331231i	$0.892536\pi$
$864$	23.2359	−	11.1898i	0.790500	−	0.380685i
$865$		0			0
$866$	−1.63036	−	2.04440i	−0.0554018	−	0.0694717i
$867$	2.48457	−	3.11555i	0.0843803	−	0.105810i
$868$	3.87747	+	1.86729i	0.131610	+	0.0633800i
$869$	−23.0398			−0.781572
$870$		0			0
$871$	13.1317			0.444950
$872$	8.33393	+	4.01341i	0.282222	+	0.135911i
$873$	−0.162718	+	0.204042i	−0.00550719	+	0.00690579i
$874$	1.50149	+	1.88281i	0.0507887	+	0.0636870i
$875$		0			0
$876$	−11.3889	+	5.48460i	−0.384795	+	0.185307i
$877$	−13.6501	+	17.1167i	−0.460931	+	0.577990i	−0.956925	−	0.290337i	$-0.906233\pi$
$877$	−13.6501	+	17.1167i	−0.460931	+	0.577990i	0.495993	+	0.868326i	$0.334804\pi$
$878$	1.55884	+	6.82974i	0.0526084	+	0.230492i
$879$	1.87681	+	8.22282i	0.0633031	+	0.277349i
$880$		0			0
$881$	7.46130	−	32.6901i	0.251378	−	1.10136i	−0.678822	−	0.734303i	$-0.737509\pi$
$881$	7.46130	−	32.6901i	0.251378	−	1.10136i	0.930199	−	0.367055i	$-0.119634\pi$
$882$	4.41981			0.148823
$883$	−3.58868	+	15.7230i	−0.120769	+	0.529122i	0.877961	+	0.478732i	$0.158904\pi$
$883$	−3.58868	+	15.7230i	−0.120769	+	0.529122i	−0.998730	+	0.0503898i	$0.983954\pi$
$884$	−41.2422	+	19.8612i	−1.38713	+	0.668004i
$885$		0			0
$886$	0.667326	−	2.92375i	0.0224192	−	0.0982252i
$887$	−52.7391			−1.77081			−0.885403	−	0.464823i	$-0.846118\pi$
$887$	−52.7391			−1.77081			−0.885403	+	0.464823i	$0.846118\pi$
$888$	2.31886	−	10.1596i	0.0778160	−	0.340934i
$889$	−0.230718	−	0.289311i	−0.00773802	−	0.00970317i
$890$		0			0
$891$	2.83190	+	12.4074i	0.0948724	+	0.415663i
$892$	−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
$895$		0			0
$896$	2.43027	−	3.04746i	0.0811897	−	0.101809i
$897$	14.5809	+	7.02180i	0.486842	+	0.234451i
$898$	5.48294			0.182968
$899$	−25.6972	−	25.2659i	−0.857048	−	0.842666i
$900$		0			0
$901$	18.9976	+	9.14877i	0.632902	+	0.304790i
$902$	4.26205	−	5.34444i	0.141911	−	0.177950i
$903$	−0.945042	−	1.18505i	−0.0314490	−	0.0394358i
$904$	16.2729	+	7.83663i	0.541230	+	0.260642i
$905$		0			0
$906$	−2.60470	+	3.26619i	−0.0865355	+	0.108512i
$907$	−6.64084	−	29.0954i	−0.220506	−	0.966098i	−0.957099	−	0.289762i	$-0.906424\pi$
$907$	−6.64084	−	29.0954i	−0.220506	−	0.966098i	0.736593	−	0.676336i	$-0.236433\pi$
$908$	5.55592	+	24.3421i	0.184380	+	0.807820i
$909$	−2.90970	−	3.64865i	−0.0965086	−	0.121018i
$910$		0			0
$911$	−9.34050			−0.309465			−0.154732	−	0.987956i	$-0.549452\pi$
$911$	−9.34050			−0.309465			−0.154732	+	0.987956i	$0.549452\pi$
$912$	1.86443	−	8.16860i	0.0617374	−	0.270489i
$913$	19.8230	−	9.54627i	0.656047	−	0.315936i
$914$	5.47823	−	2.63818i	0.181204	−	0.0872631i
$915$		0			0
$916$	23.0151			0.760439
$917$	0.637063	−	2.79116i	0.0210377	−	0.0921721i
$918$	6.91185	+	8.66719i	0.228125	+	0.286060i
$919$	4.09903	+	17.9590i	0.135215	+	0.592414i	0.996448	+	0.0842049i	$0.0268350\pi$
$919$	4.09903	+	17.9590i	0.135215	+	0.592414i	−0.861234	+	0.508209i	$0.830308\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	−2.90408	−	1.39853i	−0.0954341	−	0.0459587i
$927$	−19.7289			−0.647981
$928$	−21.1020	+	13.5097i	−0.692708	+	0.443476i
$929$	−4.84654			−0.159010			−0.0795050	−	0.996834i	$-0.525334\pi$
$929$	−4.84654			−0.159010			−0.0795050	+	0.996834i	$0.525334\pi$
$930$		0			0
$931$	10.0993	−	12.6642i	0.330992	−	0.415051i
$932$	−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
$935$		0			0
$936$	−3.07553	−	13.4748i	−0.100527	−	0.440437i
$937$	−9.94989	−	43.5933i	−0.325049	−	1.42413i	−0.828443	−	0.560074i	$-0.810773\pi$
$937$	−9.94989	−	43.5933i	−0.325049	−	1.42413i	0.503394	−	0.864057i	$-0.332084\pi$
$938$	−0.230054	−	0.288478i	−0.00751152	−	0.00941915i
$939$	5.33877	−	23.3907i	0.174224	−	0.763326i
$940$		0			0
$941$	−3.02297	+	13.2445i	−0.0985459	+	0.431758i	−0.999999	−	0.00111821i	$-0.999644\pi$
$941$	−3.02297	+	13.2445i	−0.0985459	+	0.431758i	0.901453	+	0.432876i	$0.142501\pi$
$942$	−9.11960	+	4.39177i	−0.297133	+	0.143092i
$943$	6.43296	−	3.09795i	0.209486	−	0.100883i
$944$	7.92585	−	34.7254i	0.257965	−	1.13022i
$945$		0			0
$946$	−1.66583	+	7.29850i	−0.0541609	+	0.237295i
$947$	−9.35958	−	11.7365i	−0.304146	−	0.381387i	0.606147	−	0.795353i	$-0.292715\pi$
$947$	−9.35958	−	11.7365i	−0.304146	−	0.381387i	−0.910292	+	0.413966i	$0.864143\pi$
$948$	−2.33244	−	10.2191i	−0.0757540	−	0.331900i
$949$	7.07630	+	31.0033i	0.229706	+	1.00641i
$950$		0			0
$951$	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	−0.948114	−	0.317931i	$-0.897012\pi$
$953$	−32.3247	−	40.5339i	−1.04710	−	1.31302i	−0.0989849	−	0.995089i	$-0.531560\pi$
$954$	−1.88135	+	2.35914i	−0.0609111	+	0.0763801i
$955$		0			0
$956$	46.0659			1.48988
$957$	−11.2186	−	31.2113i	−0.362647	−	1.00892i
$958$	−1.73078			−0.0559188
$959$	−5.54115	−	2.66848i	−0.178933	−	0.0861696i
$960$		0			0
$961$	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
$965$		0			0
$966$	−0.101187	−	0.443330i	−0.00325564	−	0.0142639i
$967$	25.9527	+	32.5437i	0.834583	+	1.04653i	0.998198	+	0.0600094i	$0.0191131\pi$
$967$	25.9527	+	32.5437i	0.834583	+	1.04653i	−0.163615	+	0.986524i	$0.552315\pi$
$968$	5.04288	−	22.0943i	0.162084	−	0.710137i
$969$	13.2078			0.424294
$970$		0			0
$971$	50.2497	−	24.1990i	1.61259	−	0.776583i	0.612685	−	0.790327i	$-0.290089\pi$
$971$	50.2497	−	24.1990i	1.61259	−	0.776583i	0.999906	+	0.0137446i	$0.00437519\pi$
$972$	21.7799	−	10.4887i	0.698592	−	0.336424i
$973$	−1.32371	+	5.79954i	−0.0424361	+	0.185925i
$974$	−4.38165			−0.140397
$975$		0			0
$976$	−2.92058	−	3.66230i	−0.0934856	−	0.117227i
$977$	10.8943	+	47.7309i	0.348538	+	1.52705i	0.780501	+	0.625155i	$0.214964\pi$
$977$	10.8943	+	47.7309i	0.348538	+	1.52705i	−0.431962	+	0.901892i	$0.642179\pi$
$978$	1.56100	+	6.83918i	0.0499152	+	0.218693i
$979$	−17.4909	+	21.9329i	−0.559012	+	0.700978i
$980$		0			0
$981$	7.11745	+	3.42758i	0.227243	+	0.109434i
$982$	2.16189	+	2.71092i	0.0689887	+	0.0865091i
$983$	−3.22550	+	4.04466i	−0.102878	+	0.129004i	−0.830605	−	0.556862i	$-0.812005\pi$
$983$	−3.22550	+	4.04466i	−0.102878	+	0.129004i	0.727727	+	0.685867i	$0.240577\pi$
$984$	5.91185	+	2.84700i	0.188463	+	0.0907590i
$985$		0			0
$986$	−7.67994	−	7.55106i	−0.244579	−	0.240475i
$987$	−2.86831			−0.0912994
$988$	−21.6298	−	10.4164i	−0.688136	−	0.331389i
$989$	−4.87531	+	6.11345i	−0.155026	+	0.194396i
$990$		0			0
$991$	15.1838	+	7.31214i	0.482330	+	0.232278i	0.659216	−	0.751953i	$-0.270888\pi$
$991$	15.1838	+	7.31214i	0.482330	+	0.232278i	−0.176886	+	0.984231i	$0.556602\pi$
$992$	28.0531	−	13.5097i	0.890687	−	0.428932i
$993$	2.43668	−	3.05550i	0.0773257	−	0.0969634i
$994$	−0.259251	−	1.13585i	−0.00822295	−	0.0360271i
$995$		0			0
$996$	6.24094	+	7.82589i	0.197752	+	0.247973i
$997$	8.50245	−	37.2517i	0.269275	−	1.17977i	−0.641583	−	0.767054i	$-0.721722\pi$
$997$	8.50245	−	37.2517i	0.269275	−	1.17977i	0.910858	−	0.412719i	$-0.135421\pi$
$998$	−9.15239			−0.289714
$999$	6.09179	−	26.6899i	0.192736	−	0.844431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.l.b.451.1		6
5.2	odd	4		725.2.r.b.74.2		12
5.3	odd	4		725.2.r.b.74.1		12
5.4	even	2		29.2.d.a.16.1	✓	6
15.14	odd	2		261.2.k.a.190.1		6
20.19	odd	2		464.2.u.f.161.1		6
29.20	even	7	inner	725.2.l.b.426.1		6
145.4	even	14		841.2.d.c.778.1		6
145.9	even	14		841.2.d.d.571.1		6
145.14	odd	28		841.2.e.b.236.1		12
145.19	odd	28		841.2.e.c.63.1		12
145.24	even	14		841.2.d.b.574.1		6
145.34	even	14		841.2.d.c.574.1		6
145.39	odd	28		841.2.e.c.63.2		12
145.44	odd	28		841.2.e.b.236.2		12
145.49	even	14		29.2.d.a.20.1	yes	6
145.54	even	14		841.2.d.b.778.1		6
145.64	even	14		841.2.d.a.605.1		6
145.69	odd	28		841.2.e.b.196.2		12
145.74	even	14		841.2.d.e.645.1		6
145.78	odd	28		725.2.r.b.49.2		12
145.79	odd	28		841.2.e.d.270.1		12
145.84	odd	28		841.2.b.c.840.3		6
145.89	odd	28		841.2.e.c.267.2		12
145.94	even	14		841.2.a.e.1.2		3
145.99	odd	4		841.2.e.d.651.1		12
145.104	odd	4		841.2.e.d.651.2		12
145.107	odd	28		725.2.r.b.49.1		12
145.109	even	14		841.2.a.f.1.2		3
145.114	odd	28		841.2.e.c.267.1		12
145.119	odd	28		841.2.b.c.840.4		6
145.124	odd	28		841.2.e.d.270.2		12
145.129	even	14		841.2.d.a.645.1		6
145.134	odd	28		841.2.e.b.196.1		12
145.139	even	14		841.2.d.e.605.1		6
145.144	even	2		841.2.d.d.190.1		6
435.194	odd	14		261.2.k.a.136.1		6
435.239	odd	14		7569.2.a.r.1.2		3
435.254	odd	14		7569.2.a.p.1.2		3
580.339	odd	14		464.2.u.f.49.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.16.1	✓	6	5.4	even	2
29.2.d.a.20.1	yes	6	145.49	even	14
261.2.k.a.136.1		6	435.194	odd	14
261.2.k.a.190.1		6	15.14	odd	2
464.2.u.f.49.1		6	580.339	odd	14
464.2.u.f.161.1		6	20.19	odd	2
725.2.l.b.426.1		6	29.20	even	7	inner
725.2.l.b.451.1		6	1.1	even	1	trivial
725.2.r.b.49.1		12	145.107	odd	28
725.2.r.b.49.2		12	145.78	odd	28
725.2.r.b.74.1		12	5.3	odd	4
725.2.r.b.74.2		12	5.2	odd	4
841.2.a.e.1.2		3	145.94	even	14
841.2.a.f.1.2		3	145.109	even	14
841.2.b.c.840.3		6	145.84	odd	28
841.2.b.c.840.4		6	145.119	odd	28
841.2.d.a.605.1		6	145.64	even	14
841.2.d.a.645.1		6	145.129	even	14
841.2.d.b.574.1		6	145.24	even	14
841.2.d.b.778.1		6	145.54	even	14
841.2.d.c.574.1		6	145.34	even	14
841.2.d.c.778.1		6	145.4	even	14
841.2.d.d.190.1		6	145.144	even	2
841.2.d.d.571.1		6	145.9	even	14
841.2.d.e.605.1		6	145.139	even	14
841.2.d.e.645.1		6	145.74	even	14
841.2.e.b.196.1		12	145.134	odd	28
841.2.e.b.196.2		12	145.69	odd	28
841.2.e.b.236.1		12	145.14	odd	28
841.2.e.b.236.2		12	145.44	odd	28
841.2.e.c.63.1		12	145.19	odd	28
841.2.e.c.63.2		12	145.39	odd	28
841.2.e.c.267.1		12	145.114	odd	28
841.2.e.c.267.2		12	145.89	odd	28
841.2.e.d.270.1		12	145.79	odd	28
841.2.e.d.270.2		12	145.124	odd	28
841.2.e.d.651.1		12	145.99	odd	4
841.2.e.d.651.2		12	145.104	odd	4
7569.2.a.p.1.2		3	435.254	odd	14
7569.2.a.r.1.2		3	435.239	odd	14

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.l (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.400969 - 0.193096i) q^{2} +(0.777479 - 0.974928i) q^{3} +(-1.12349 - 1.40881i) q^{4} +(-0.500000 + 0.240787i) q^{6} +(-0.222521 + 0.279032i) q^{7} +(0.376510 + 1.64960i) q^{8} +(0.321552 + 1.40881i) q^{9} +(-1.09903 + 4.81517i) q^{11} -2.24698 q^{12} +(-1.25786 + 5.51107i) q^{13} +(0.143104 - 0.0689153i) q^{14} +(-0.634375 + 2.77938i) q^{16} -4.49396 q^{17} +(0.143104 - 0.626980i) q^{18} +(-1.46950 - 1.84270i) q^{19} +(0.0990311 + 0.433884i) q^{21} +(1.37047 - 1.71851i) q^{22} +(2.06853 - 0.996152i) q^{23} +(1.90097 + 0.915458i) q^{24} +(1.56853 - 1.96688i) q^{26} +(4.99396 + 2.40496i) q^{27} +0.643104 q^{28} +(-5.09783 - 1.73553i) q^{29} +(6.02930 + 2.90356i) q^{31} +(2.90097 - 3.63770i) q^{32} +(3.83997 + 4.81517i) q^{33} +(1.80194 + 0.867767i) q^{34} +(1.62349 - 2.03579i) q^{36} +(-1.09903 - 4.81517i) q^{37} +(0.233406 + 1.02262i) q^{38} +(4.39493 + 5.51107i) q^{39} +3.10992 q^{41} +(0.0440730 - 0.193096i) q^{42} +(-3.06853 + 1.47773i) q^{43} +(8.01842 - 3.86147i) q^{44} -1.02177 q^{46} +(-1.43416 + 6.28345i) q^{47} +(2.21648 + 2.77938i) q^{48} +(1.52930 + 6.70031i) q^{49} +(-3.49396 + 4.38129i) q^{51} +(9.17725 - 4.41953i) q^{52} +(-4.22737 - 2.03579i) q^{53} +(-1.53803 - 1.92863i) q^{54} +(-0.544073 - 0.262012i) q^{56} -2.93900 q^{57} +(1.70895 + 1.68027i) q^{58} -12.4940 q^{59} +(-1.02446 + 1.28463i) q^{61} +(-1.85690 - 2.32847i) q^{62} +(-0.464656 - 0.223767i) q^{63} +(3.27144 - 1.57544i) q^{64} +(-0.609916 - 2.67222i) q^{66} +(-0.516926 - 2.26480i) q^{67} +(5.04892 + 6.33114i) q^{68} +(0.637063 - 2.79116i) q^{69} +(1.63222 - 7.15122i) q^{71} +(-2.20291 + 1.06086i) q^{72} +(5.06853 - 2.44088i) q^{73} +(-0.489115 + 2.14295i) q^{74} +(-0.945042 + 4.14050i) q^{76} +(-1.09903 - 1.37814i) q^{77} +(-0.698062 - 3.05841i) q^{78} +(1.03803 + 4.54792i) q^{79} +(2.32155 - 1.11800i) q^{81} +(-1.24698 - 0.600514i) q^{82} +(-2.77748 - 3.48285i) q^{83} +(0.500000 - 0.626980i) q^{84} +1.51573 q^{86} +(-5.65548 + 3.62068i) q^{87} -8.35690 q^{88} +(5.11745 + 2.46443i) q^{89} +(-1.25786 - 1.57731i) q^{91} +(-3.72737 - 1.79500i) q^{92} +(7.51842 - 3.62068i) q^{93} +(1.78836 - 2.24254i) q^{94} +(-1.29105 - 5.65647i) q^{96} +(0.112605 + 0.141202i) q^{97} +(0.680604 - 2.98192i) q^{98} -7.13706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 3 q^{6} - q^{7} + 7 q^{8} + 6 q^{9} - 11 q^{11} - 4 q^{12} + 5 q^{13} + 9 q^{14} + 4 q^{16} - 8 q^{17} + 9 q^{18} + q^{19} + 5 q^{21} - 6 q^{22} + 7 q^{23} + 7 q^{24}+ \cdots - 32 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 3 * q^6 - q^7 + 7 * q^8 + 6 * q^9 - 11 * q^11 - 4 * q^12 + 5 * q^13 + 9 * q^14 + 4 * q^16 - 8 * q^17 + 9 * q^18 + q^19 + 5 * q^21 - 6 * q^22 + 7 * q^23 + 7 * q^24 + 4 * q^26 + 11 * q^27 + 12 * q^28 + 6 * q^29 + 5 * q^31 + 13 * q^32 - q^33 + 2 * q^34 + 5 * q^36 - 11 * q^37 - 2 * q^38 + 3 * q^39 + 20 * q^41 + 4 * q^42 - 13 * q^43 + 20 * q^44 - 11 * q^47 - 6 * q^48 - 22 * q^49 - 2 * q^51 + 10 * q^52 - 3 * q^53 + 6 * q^54 - 7 * q^56 + 2 * q^57 + 16 * q^58 - 56 * q^59 + 3 * q^61 - 3 * q^62 - 15 * q^63 + q^64 - 5 * q^66 - 19 * q^67 + 12 * q^68 - 7 * q^69 + 21 * q^71 + 25 * q^73 - 6 * q^74 - 5 * q^76 - 11 * q^77 - 13 * q^78 - 9 * q^79 + 18 * q^81 + 2 * q^82 - 17 * q^83 + 3 * q^84 - 16 * q^86 + 5 * q^87 - 42 * q^88 + 7 * q^89 + 5 * q^91 + 17 * q^93 + 8 * q^94 - 2 * q^96 - q^97 - 19 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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