LMFDB - Embedded newform 605.2.g.m.511.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(81,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,3,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			511.1
Root			$-0.227943 + 0.701538i$ of defining polynomial
Character	$\chi$	$=$	605.511
Dual form			605.2.g.m.251.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.227943 - 0.701538i) q^{2} +(2.27460 + 1.65259i) q^{3} +(1.17784 - 0.855749i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.640877 - 1.97242i) q^{6} +(-0.834404 + 0.606230i) q^{7} +(-2.06235 - 1.49838i) q^{8} +(1.51569 + 4.66481i) q^{9} +0.737640 q^{10} +4.09331 q^{12} +(1.06580 + 3.28018i) q^{13} +(0.615490 + 0.447180i) q^{14} +(-2.27460 + 1.65259i) q^{15} +(0.318714 - 0.980901i) q^{16} +(0.741089 - 2.28084i) q^{17} +(2.92705 - 2.12663i) q^{18} +(6.20420 + 4.50761i) q^{19} +(0.449894 + 1.38463i) q^{20} -2.89979 q^{21} +2.45589 q^{23} +(-2.21480 - 6.81645i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(2.05823 - 1.49539i) q^{26} +(-1.65499 + 5.09355i) q^{27} +(-0.464011 + 1.42808i) q^{28} +(4.81714 - 3.49986i) q^{29} +(1.67784 + 1.21902i) q^{30} +(-1.13972 - 3.50769i) q^{31} -5.85919 q^{32} -1.76902 q^{34} +(-0.318714 - 0.980901i) q^{35} +(5.77714 + 4.19734i) q^{36} +(-4.82059 + 3.50236i) q^{37} +(1.74805 - 5.37996i) q^{38} +(-2.99655 + 9.22244i) q^{39} +(2.06235 - 1.49838i) q^{40} +(-3.18450 - 2.31367i) q^{41} +(0.660987 + 2.03431i) q^{42} -7.64941 q^{43} -4.90488 q^{45} +(-0.559803 - 1.72290i) q^{46} +(-4.72704 - 3.43439i) q^{47} +(2.34598 - 1.70445i) q^{48} +(-1.83440 + 5.64571i) q^{49} +(-0.227943 + 0.701538i) q^{50} +(5.45498 - 3.96328i) q^{51} +(4.06235 + 2.95147i) q^{52} +(-3.66124 - 11.2681i) q^{53} +3.95056 q^{54} +2.62920 q^{56} +(6.66281 + 20.5060i) q^{57} +(-3.55332 - 2.58164i) q^{58} +(-2.38361 + 1.73179i) q^{59} +(-1.26490 + 3.89297i) q^{60} +(0.766476 - 2.35897i) q^{61} +(-2.20098 + 1.59911i) q^{62} +(-4.09265 - 2.97348i) q^{63} +(0.698136 + 2.14864i) q^{64} -3.44899 q^{65} -6.14702 q^{67} +(-1.07894 - 3.32064i) q^{68} +(5.58616 + 4.05858i) q^{69} +(-0.615490 + 0.447180i) q^{70} +(0.625187 - 1.92413i) q^{71} +(3.86380 - 11.8916i) q^{72} +(0.668140 - 0.485432i) q^{73} +(3.55586 + 2.58348i) q^{74} +(-0.868820 - 2.67395i) q^{75} +11.1649 q^{76} +7.15293 q^{78} +(-3.73236 - 11.4870i) q^{79} +(0.834404 + 0.606230i) q^{80} +(-0.277637 + 0.201715i) q^{81} +(-0.897243 + 2.76143i) q^{82} +(0.497523 - 1.53122i) q^{83} +(-3.41548 + 2.48149i) q^{84} +(1.94020 + 1.40964i) q^{85} +(1.74363 + 5.36635i) q^{86} +16.7409 q^{87} +8.16116 q^{89} +(1.11803 + 3.44095i) q^{90} +(-2.87785 - 2.09088i) q^{91} +(2.89263 - 2.10162i) q^{92} +(3.20438 - 9.86208i) q^{93} +(-1.33186 + 4.09904i) q^{94} +(-6.20420 + 4.50761i) q^{95} +(-13.3273 - 9.68286i) q^{96} +(0.754861 + 2.32322i) q^{97} +4.37882 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - q^{8} + 5 q^{9} + 2 q^{10} + 16 q^{12} + 3 q^{13} + 14 q^{14} - 5 q^{15} - q^{16} + 12 q^{17} + 10 q^{18} + 5 q^{19} + 2 q^{20} - 20 q^{21}+ \cdots + 16 q^{98}+O(q^{100}) $ 8 * q + 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - q^8 + 5 * q^9 + 2 * q^10 + 16 * q^12 + 3 * q^13 + 14 * q^14 - 5 * q^15 - q^16 + 12 * q^17 + 10 * q^18 + 5 * q^19 + 2 * q^20 - 20 * q^21 + 10 * q^23 - 2 * q^24 - 2 * q^25 + 5 * q^26 + 5 * q^27 + 19 * q^28 + 21 * q^29 + 7 * q^30 + 15 * q^31 + 16 * q^32 + 4 * q^34 + q^35 + 15 * q^36 - 31 * q^37 - 20 * q^38 - 14 * q^39 + q^40 + 3 * q^41 - 21 * q^42 - 38 * q^43 - 7 * q^46 - 5 * q^47 + 5 * q^48 - 4 * q^49 + 3 * q^50 + 6 * q^51 + 17 * q^52 - 2 * q^53 + 16 * q^54 + 22 * q^56 + 40 * q^57 + 2 * q^58 + 18 * q^59 + 4 * q^60 + 6 * q^61 - 5 * q^62 - 30 * q^63 + 29 * q^64 + 2 * q^65 - 38 * q^67 - 14 * q^68 + 9 * q^69 - 14 * q^70 + 15 * q^71 + 5 * q^72 - 2 * q^73 - 20 * q^74 - 5 * q^75 - 16 * q^78 - 3 * q^79 - 4 * q^80 - 12 * q^81 - 22 * q^82 - 38 * q^83 - 17 * q^84 + 13 * q^85 + 2 * q^86 + 38 * q^87 - 16 * q^89 - 36 * q^91 + q^92 + 40 * q^93 - 18 * q^94 - 5 * q^95 - 17 * q^96 - 56 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.227943	−	0.701538i	−0.161180	−	0.496062i	0.837554	−	0.546354i	$-0.183985\pi$
$2$	−0.227943	−	0.701538i	−0.161180	−	0.496062i	−0.998735	+	0.0502922i	$0.983985\pi$
$3$	2.27460	+	1.65259i	1.31324	+	0.954126i	0.999990	+	0.00445538i	$0.00141820\pi$
$3$	2.27460	+	1.65259i	1.31324	+	0.954126i	0.313251	+	0.949670i	$0.398582\pi$
$4$	1.17784	−	0.855749i	0.588919	−	0.427874i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	0.640877	−	1.97242i	0.261637	−	0.805235i
$7$	−0.834404	+	0.606230i	−0.315375	+	0.229133i	−0.734199	−	0.678934i	$-0.762442\pi$
$7$	−0.834404	+	0.606230i	−0.315375	+	0.229133i	0.418824	+	0.908067i	$0.362442\pi$
$8$	−2.06235	−	1.49838i	−0.729150	−	0.529758i
$9$	1.51569	+	4.66481i	0.505230	+	1.55494i
$10$	0.737640			0.233262
$11$		0			0
$11$		0			0
$12$	4.09331			1.18164
$13$	1.06580	+	3.28018i	0.295599	+	0.909759i	0.983020	+	0.183500i	$0.0587427\pi$
$13$	1.06580	+	3.28018i	0.295599	+	0.909759i	−0.687421	+	0.726259i	$0.741257\pi$
$14$	0.615490	+	0.447180i	0.164497	+	0.119514i
$15$	−2.27460	+	1.65259i	−0.587299	+	0.426698i
$16$	0.318714	−	0.980901i	0.0796785	−	0.245225i
$17$	0.741089	−	2.28084i	0.179741	−	0.553185i	−0.820078	−	0.572252i	$-0.806070\pi$
$17$	0.741089	−	2.28084i	0.179741	−	0.553185i	0.999818	+	0.0190677i	$0.00606982\pi$
$18$	2.92705	−	2.12663i	0.689913	−	0.501251i
$19$	6.20420	+	4.50761i	1.42334	+	1.03412i	0.991209	+	0.132306i	$0.0422383\pi$
$19$	6.20420	+	4.50761i	1.42334	+	1.03412i	0.432131	+	0.901811i	$0.357762\pi$
$20$	0.449894	+	1.38463i	0.100599	+	0.309613i
$21$	−2.89979			−0.632786
$22$		0			0
$23$	2.45589			0.512088			0.256044	−	0.966665i	$-0.417581\pi$
$23$	2.45589			0.512088			0.256044	+	0.966665i	$0.417581\pi$
$24$	−2.21480	−	6.81645i	−0.452094	−	1.39140i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	2.05823	−	1.49539i	0.403652	−	0.293271i
$27$	−1.65499	+	5.09355i	−0.318504	+	0.980254i
$28$	−0.464011	+	1.42808i	−0.0876899	+	0.269882i
$29$	4.81714	−	3.49986i	0.894521	−	0.649907i	−0.0425320	−	0.999095i	$-0.513542\pi$
$29$	4.81714	−	3.49986i	0.894521	−	0.649907i	0.937053	+	0.349188i	$0.113542\pi$
$30$	1.67784	+	1.21902i	0.306330	+	0.222562i
$31$	−1.13972	−	3.50769i	−0.204699	−	0.629999i	−0.999726	−	0.0234246i	$-0.992543\pi$
$31$	−1.13972	−	3.50769i	−0.204699	−	0.629999i	0.795026	−	0.606575i	$-0.207457\pi$
$32$	−5.85919			−1.03577
$33$		0			0
$34$	−1.76902			−0.303384
$35$	−0.318714	−	0.980901i	−0.0538725	−	0.165802i
$36$	5.77714	+	4.19734i	0.962857	+	0.699557i
$37$	−4.82059	+	3.50236i	−0.792500	+	0.575785i	−0.908704	−	0.417440i	$-0.862927\pi$
$37$	−4.82059	+	3.50236i	−0.792500	+	0.575785i	0.116204	+	0.993225i	$0.462927\pi$
$38$	1.74805	−	5.37996i	0.283572	−	0.872744i
$39$	−2.99655	+	9.22244i	−0.479832	+	1.47677i
$40$	2.06235	−	1.49838i	0.326086	−	0.236915i
$41$	−3.18450	−	2.31367i	−0.497335	−	0.361335i	0.310663	−	0.950520i	$-0.399449\pi$
$41$	−3.18450	−	2.31367i	−0.497335	−	0.361335i	−0.807998	+	0.589185i	$0.799449\pi$
$42$	0.660987	+	2.03431i	0.101993	+	0.313901i
$43$	−7.64941			−1.16652			−0.583262	−	0.812284i	$-0.698224\pi$
$43$	−7.64941			−1.16652			−0.583262	+	0.812284i	$0.698224\pi$
$44$		0			0
$45$	−4.90488			−0.731176
$46$	−0.559803	−	1.72290i	−0.0825385	−	0.254027i
$47$	−4.72704	−	3.43439i	−0.689509	−	0.500958i	0.186989	−	0.982362i	$-0.440127\pi$
$47$	−4.72704	−	3.43439i	−0.689509	−	0.500958i	−0.876499	+	0.481404i	$0.840127\pi$
$48$	2.34598	−	1.70445i	0.338613	−	0.246017i
$49$	−1.83440	+	5.64571i	−0.262058	+	0.806531i
$50$	−0.227943	+	0.701538i	−0.0322361	+	0.0992124i
$51$	5.45498	−	3.96328i	0.763850	−	0.554970i
$52$	4.06235	+	2.95147i	0.563346	+	0.409295i
$53$	−3.66124	−	11.2681i	−0.502910	−	1.54780i	−0.804256	−	0.594284i	$-0.797436\pi$
$53$	−3.66124	−	11.2681i	−0.502910	−	1.54780i	0.301345	−	0.953515i	$-0.402564\pi$
$54$	3.95056			0.537603
$55$		0			0
$56$	2.62920			0.351341
$57$	6.66281	+	20.5060i	0.882511	+	2.71609i
$58$	−3.55332	−	2.58164i	−0.466573	−	0.338985i
$59$	−2.38361	+	1.73179i	−0.310319	+	0.225460i	−0.732033	−	0.681269i	$-0.761428\pi$
$59$	−2.38361	+	1.73179i	−0.310319	+	0.225460i	0.421714	+	0.906729i	$0.361428\pi$
$60$	−1.26490	+	3.89297i	−0.163298	+	0.502581i
$61$	0.766476	−	2.35897i	0.0981372	−	0.302035i	−0.889921	−	0.456114i	$-0.849241\pi$
$61$	0.766476	−	2.35897i	0.0981372	−	0.302035i	0.988059	+	0.154079i	$0.0492409\pi$
$62$	−2.20098	+	1.59911i	−0.279525	+	0.203087i
$63$	−4.09265	−	2.97348i	−0.515625	−	0.374624i
$64$	0.698136	+	2.14864i	0.0872670	+	0.268580i
$65$	−3.44899			−0.427794
$66$		0			0
$67$	−6.14702			−0.750978			−0.375489	−	0.926827i	$-0.622525\pi$
$67$	−6.14702			−0.750978			−0.375489	+	0.926827i	$0.622525\pi$
$68$	−1.07894	−	3.32064i	−0.130841	−	0.402687i
$69$	5.58616	+	4.05858i	0.672495	+	0.488596i
$70$	−0.615490	+	0.447180i	−0.0735651	+	0.0534482i
$71$	0.625187	−	1.92413i	0.0741960	−	0.228352i	−0.907080	−	0.420958i	$-0.861694\pi$
$71$	0.625187	−	1.92413i	0.0741960	−	0.228352i	0.981276	+	0.192606i	$0.0616940\pi$
$72$	3.86380	−	11.8916i	0.455353	−	1.40143i
$73$	0.668140	−	0.485432i	0.0781999	−	0.0568156i	−0.547998	−	0.836479i	$-0.684610\pi$
$73$	0.668140	−	0.485432i	0.0781999	−	0.0568156i	0.626198	+	0.779664i	$0.284610\pi$
$74$	3.55586	+	2.58348i	0.413361	+	0.300324i
$75$	−0.868820	−	2.67395i	−0.100323	−	0.308762i
$76$	11.1649			1.28070
$77$		0			0
$78$	7.15293			0.809910
$79$	−3.73236	−	11.4870i	−0.419924	−	1.29239i	−0.907772	−	0.419464i	$-0.862218\pi$
$79$	−3.73236	−	11.4870i	−0.419924	−	1.29239i	0.487848	−	0.872928i	$-0.337782\pi$
$80$	0.834404	+	0.606230i	0.0932892	+	0.0677786i
$81$	−0.277637	+	0.201715i	−0.0308486	+	0.0224128i
$82$	−0.897243	+	2.76143i	−0.0990840	+	0.304949i
$83$	0.497523	−	1.53122i	0.0546102	−	0.168073i	−0.920031	−	0.391845i	$-0.871837\pi$
$83$	0.497523	−	1.53122i	0.0546102	−	0.168073i	0.974642	+	0.223772i	$0.0718370\pi$
$84$	−3.41548	+	2.48149i	−0.372659	+	0.270753i
$85$	1.94020	+	1.40964i	0.210444	+	0.152896i
$86$	1.74363	+	5.36635i	0.188021	+	0.578669i
$87$	16.7409			1.79481
$88$		0			0
$89$	8.16116			0.865081			0.432541	−	0.901614i	$-0.357617\pi$
$89$	8.16116			0.865081			0.432541	+	0.901614i	$0.357617\pi$
$90$	1.11803	+	3.44095i	0.117851	+	0.362708i
$91$	−2.87785	−	2.09088i	−0.301681	−	0.219184i
$92$	2.89263	−	2.10162i	0.301578	−	0.219109i
$93$	3.20438	−	9.86208i	0.332279	−	1.02265i
$94$	−1.33186	+	4.09904i	−0.137371	+	0.422784i
$95$	−6.20420	+	4.50761i	−0.636537	+	0.462471i
$96$	−13.3273	−	9.68286i	−1.36021	−	0.988253i
$97$	0.754861	+	2.32322i	0.0766445	+	0.235888i	0.982037	−	0.188688i	$-0.0604234\pi$
$97$	0.754861	+	2.32322i	0.0766445	+	0.235888i	−0.905393	+	0.424575i	$0.860423\pi$
$98$	4.37882			0.442328
$99$		0			0
$100$	−1.45589			−0.145589
$101$	−2.32496	−	7.15550i	−0.231342	−	0.711999i	−0.997586	−	0.0694479i	$-0.977876\pi$
$101$	−2.32496	−	7.15550i	−0.231342	−	0.711999i	0.766243	−	0.642551i	$-0.222124\pi$
$102$	−4.02381	−	2.92347i	−0.398417	−	0.289467i
$103$	7.67135	−	5.57356i	0.755881	−	0.549180i	−0.141763	−	0.989901i	$-0.545277\pi$
$103$	7.67135	−	5.57356i	0.755881	−	0.549180i	0.897644	+	0.440721i	$0.145277\pi$
$104$	2.71693	−	8.36185i	0.266417	−	0.819947i
$105$	0.896084	−	2.75786i	0.0874488	−	0.269140i
$106$	−7.07047	+	5.13700i	−0.686745	+	0.498949i
$107$	3.75932	+	2.73131i	0.363427	+	0.264046i	0.754480	−	0.656323i	$-0.227889\pi$
$107$	3.75932	+	2.73131i	0.363427	+	0.264046i	−0.391053	+	0.920368i	$0.627889\pi$
$108$	2.40948	+	7.41563i	0.231853	+	0.713569i
$109$	−5.32826			−0.510355			−0.255178	−	0.966894i	$-0.582134\pi$
$109$	−5.32826			−0.510355			−0.255178	+	0.966894i	$0.582134\pi$
$110$		0			0
$111$	−16.7529			−1.59012
$112$	0.328715	+	1.01168i	0.0310607	+	0.0955949i
$113$	−0.246670	−	0.179216i	−0.0232047	−	0.0168592i	0.576122	−	0.817363i	$-0.304565\pi$
$113$	−0.246670	−	0.179216i	−0.0232047	−	0.0168592i	−0.599327	+	0.800504i	$0.704565\pi$
$114$	12.8670	−	9.34843i	1.20511	−	0.875561i
$115$	−0.758911	+	2.33569i	−0.0707688	+	0.217804i
$116$	2.67881	−	8.24453i	0.248721	−	0.765485i
$117$	−13.6860	+	9.94348i	−1.26527	+	0.919275i
$118$	1.75824	+	1.27744i	0.161859	+	0.117598i
$119$	0.764345	+	2.35241i	0.0700673	+	0.215645i
$120$	7.16724			0.654276
$121$		0			0
$122$	−1.82962			−0.165646
$123$	−3.41990	−	10.5254i	−0.308362	−	0.949040i
$124$	−4.34410	−	3.15617i	−0.390112	−	0.283433i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	−1.15312	+	3.54893i	−0.102728	+	0.316164i
$127$	−3.68038	+	11.3270i	−0.326581	+	1.00511i	0.644141	+	0.764907i	$0.277215\pi$
$127$	−3.68038	+	11.3270i	−0.326581	+	1.00511i	−0.970722	+	0.240206i	$0.922785\pi$
$128$	−8.13215	+	5.90835i	−0.718787	+	0.522230i
$129$	−17.3994	−	12.6414i	−1.53193	−	1.11301i
$130$	0.786174	+	2.41960i	0.0689520	+	0.212213i
$131$	−11.1875			−0.977452			−0.488726	−	0.872437i	$-0.662538\pi$
$131$	−11.1875			−0.977452			−0.488726	+	0.872437i	$0.662538\pi$
$132$		0			0
$133$	−7.90945			−0.685837
$134$	1.40117	+	4.31236i	0.121043	+	0.372531i
$135$	−4.33283	−	3.14799i	−0.372911	−	0.270936i
$136$	−4.94595	+	3.59344i	−0.424112	+	0.308135i
$137$	−1.32298	+	4.07170i	−0.113030	+	0.347869i	−0.991531	−	0.129871i	$-0.958544\pi$
$137$	−1.32298	+	4.07170i	−0.113030	+	0.347869i	0.878501	+	0.477740i	$0.158544\pi$
$138$	1.57392	−	4.84403i	0.133981	−	0.412351i
$139$	4.81624	−	3.49920i	0.408508	−	0.296798i	−0.364490	−	0.931207i	$-0.618757\pi$
$139$	4.81624	−	3.49920i	0.408508	−	0.296798i	0.772997	+	0.634409i	$0.218757\pi$
$140$	−1.21480	−	0.882602i	−0.102669	−	0.0745935i
$141$	−5.07646	−	15.6238i	−0.427515	−	1.31576i
$142$	−1.49235			−0.125236
$143$		0			0
$144$	5.05879			0.421566
$145$	1.83998	+	5.66289i	0.152802	+	0.470277i
$146$	−0.492847	−	0.358074i	−0.0407883	−	0.0296345i
$147$	−13.5026	+	9.81022i	−1.11368	+	0.809133i
$148$	−2.68073	+	8.25043i	−0.220354	+	0.678181i
$149$	−1.16946	+	3.59922i	−0.0958057	+	0.294860i	−0.987463	−	0.157852i	$-0.949543\pi$
$149$	−1.16946	+	3.59922i	−0.0958057	+	0.294860i	0.891657	+	0.452711i	$0.149543\pi$
$150$	−1.67784	+	1.21902i	−0.136995	+	0.0995326i
$151$	19.7049	+	14.3165i	1.60356	+	1.16506i	0.880214	+	0.474576i	$0.157399\pi$
$151$	19.7049	+	14.3165i	1.60356	+	1.16506i	0.723350	+	0.690481i	$0.242601\pi$
$152$	−6.04108	−	18.5925i	−0.489996	−	1.50805i
$153$	11.7629			0.950978
$154$		0			0
$155$	3.68820			0.296243
$156$	4.36264	+	13.4268i	0.349291	+	1.07501i
$157$	−5.85089	−	4.25092i	−0.466952	−	0.339260i	0.329300	−	0.944225i	$-0.393187\pi$
$157$	−5.85089	−	4.25092i	−0.466952	−	0.339260i	−0.796252	+	0.604965i	$0.793187\pi$
$158$	−7.20782	+	5.23679i	−0.573423	+	0.416616i
$159$	10.2938	−	31.6811i	0.816352	−	2.51247i
$160$	1.81059	−	5.57242i	0.143140	−	0.440539i
$161$	−2.04920	+	1.48883i	−0.161500	+	0.117336i
$162$	0.204796	+	0.148793i	0.0160903	+	0.0116903i
$163$	5.77527	+	17.7744i	0.452354	+	1.39220i	0.874214	+	0.485541i	$0.161377\pi$
$163$	5.77527	+	17.7744i	0.452354	+	1.39220i	−0.421860	+	0.906661i	$0.638623\pi$
$164$	−5.73074			−0.447496
$165$		0			0
$166$	−1.18761			−0.0921767
$167$	2.42680	+	7.46891i	0.187791	+	0.577962i	0.999985	−	0.00542559i	$-0.00172703\pi$
$167$	2.42680	+	7.46891i	0.187791	+	0.577962i	−0.812194	+	0.583387i	$0.801727\pi$
$168$	5.98037	+	4.34499i	0.461395	+	0.335223i
$169$	0.893540	−	0.649194i	0.0687338	−	0.0499380i
$170$	0.546657	−	1.68244i	0.0419267	−	0.129037i
$171$	−11.6235	+	35.7736i	−0.888874	+	2.73567i
$172$	−9.00976	+	6.54598i	−0.686988	+	0.499126i
$173$	−9.06478	−	6.58595i	−0.689183	−	0.500721i	0.187209	−	0.982320i	$-0.440056\pi$
$173$	−9.06478	−	6.58595i	−0.689183	−	0.500721i	−0.876391	+	0.481600i	$0.840056\pi$
$174$	−3.81598	−	11.7444i	−0.289289	−	0.890339i
$175$	1.03138			0.0779650
$176$		0			0
$177$	−8.28370			−0.622641
$178$	−1.86028	−	5.72536i	−0.139434	−	0.429134i
$179$	−1.18491	−	0.860888i	−0.0885643	−	0.0643458i	0.542622	−	0.839977i	$-0.317432\pi$
$179$	−1.18491	−	0.860888i	−0.0885643	−	0.0643458i	−0.631186	+	0.775631i	$0.717432\pi$
$180$	−5.77714	+	4.19734i	−0.430603	+	0.312851i
$181$	2.87046	−	8.83437i	0.213360	−	0.656653i	−0.785906	−	0.618345i	$-0.787803\pi$
$181$	2.87046	−	8.83437i	0.213360	−	0.656653i	0.999266	−	0.0383078i	$-0.0121967\pi$
$182$	−0.810844	+	2.49552i	−0.0601038	+	0.184980i
$183$	5.64185	−	4.09904i	0.417057	−	0.303010i
$184$	−5.06489	−	3.67986i	−0.373389	−	0.271283i
$185$	−1.84130	−	5.66694i	−0.135375	−	0.416642i
$186$	−7.64904			−0.560855
$187$		0			0
$188$	−8.50666			−0.620412
$189$	−1.70693	−	5.25338i	−0.124161	−	0.382127i
$190$	4.57646	+	3.32500i	0.332012	+	0.241221i
$191$	3.61870	−	2.62914i	0.261840	−	0.190238i	−0.449118	−	0.893473i	$-0.648262\pi$
$191$	3.61870	−	2.62914i	0.261840	−	0.190238i	0.710958	+	0.703235i	$0.248262\pi$
$192$	−1.96285	+	6.04104i	−0.141657	+	0.435974i
$193$	−7.00418	+	21.5567i	−0.504172	+	1.55168i	0.297986	+	0.954570i	$0.403685\pi$
$193$	−7.00418	+	21.5567i	−0.504172	+	1.55168i	−0.802158	+	0.597112i	$0.796315\pi$
$194$	1.45776	−	1.05913i	0.104661	−	0.0760409i
$195$	−7.84507	−	5.69978i	−0.561797	−	0.408170i
$196$	2.67068	+	8.21952i	0.190763	+	0.587109i
$197$	−11.2080			−0.798535			−0.399267	−	0.916835i	$-0.630735\pi$
$197$	−11.2080			−0.798535			−0.399267	+	0.916835i	$0.630735\pi$
$198$		0			0
$199$	−7.81979			−0.554330			−0.277165	−	0.960822i	$-0.589395\pi$
$199$	−7.81979			−0.554330			−0.277165	+	0.960822i	$0.589395\pi$
$200$	0.787747	+	2.42443i	0.0557021	+	0.171433i
$201$	−13.9820	−	10.1585i	−0.986215	−	0.716527i
$202$	−4.48989	+	3.26210i	−0.315908	+	0.229520i
$203$	−1.89772	+	5.84059i	−0.133194	+	0.409929i
$204$	3.03351	−	9.33619i	0.212388	−	0.653664i
$205$	3.18450	−	2.31367i	0.222415	−	0.161594i
$206$	−5.65870	−	4.11128i	−0.394260	−	0.286447i
$207$	3.72236	+	11.4563i	0.258722	+	0.796265i
$208$	3.55722			0.246649
$209$		0			0
$210$	−2.13900			−0.147605
$211$	−7.03539	−	21.6527i	−0.484336	−	1.49063i	−0.832940	−	0.553363i	$-0.813344\pi$
$211$	−7.03539	−	21.6527i	−0.484336	−	1.49063i	0.348604	−	0.937270i	$-0.386656\pi$
$212$	−13.9550	−	10.1389i	−0.958437	−	0.696345i
$213$	4.60185	−	3.34344i	0.315314	−	0.229089i
$214$	1.05920	−	3.25989i	0.0724056	−	0.222842i
$215$	2.36380	−	7.27502i	0.161210	−	0.496153i
$216$	11.0453	−	8.02485i	0.751535	−	0.546022i
$217$	3.07745	+	2.23590i	0.208911	+	0.151783i
$218$	1.21454	+	3.73798i	0.0822592	+	0.253168i
$219$	2.32197			0.156905
$220$		0			0
$221$	8.27142			0.556396
$222$	3.81871	+	11.7528i	0.256295	+	0.788796i
$223$	12.9788	+	9.42965i	0.869124	+	0.631456i	0.930352	−	0.366668i	$-0.119501\pi$
$223$	12.9788	+	9.42965i	0.869124	+	0.631456i	−0.0612274	+	0.998124i	$0.519501\pi$
$224$	4.88893	−	3.55202i	0.326655	−	0.237329i
$225$	1.51569	−	4.66481i	0.101046	−	0.310988i
$226$	−0.0695001	+	0.213899i	−0.00462308	+	0.0142284i
$227$	19.5428	−	14.1987i	1.29710	−	0.942398i	0.297177	−	0.954822i	$-0.403955\pi$
$227$	19.5428	−	14.1987i	1.29710	−	0.942398i	0.999923	+	0.0124240i	$0.00395478\pi$
$228$	25.3957	+	18.4511i	1.68187	+	1.22195i
$229$	−4.63967	−	14.2794i	−0.306598	−	0.943611i	−0.979076	−	0.203494i	$-0.934770\pi$
$229$	−4.63967	−	14.2794i	−0.306598	−	0.943611i	0.672478	−	0.740117i	$-0.265230\pi$
$230$	1.81156			0.119451
$231$		0			0
$232$	−15.1787			−0.996534
$233$	3.53081	+	10.8667i	0.231311	+	0.711902i	0.997589	+	0.0693934i	$0.0221064\pi$
$233$	3.53081	+	10.8667i	0.231311	+	0.711902i	−0.766278	+	0.642509i	$0.777894\pi$
$234$	10.0954	+	7.33471i	0.659955	+	0.479485i
$235$	4.72704	−	3.43439i	0.308358	−	0.224035i
$236$	−1.32552	+	4.07953i	−0.0862841	+	0.265555i
$237$	10.4938	−	32.2965i	0.681644	−	2.09788i
$238$	1.47608	−	1.07243i	0.0956799	−	0.0695155i
$239$	−22.1725	−	16.1093i	−1.43422	−	1.04202i	−0.989211	−	0.146495i	$-0.953201\pi$
$239$	−22.1725	−	16.1093i	−1.43422	−	1.04202i	−0.445008	−	0.895526i	$-0.646799\pi$
$240$	0.896084	+	2.75786i	0.0578419	+	0.178019i
$241$	10.9387			0.704624			0.352312	−	0.935883i	$-0.385396\pi$
$241$	10.9387			0.704624			0.352312	+	0.935883i	$0.385396\pi$
$242$		0			0
$243$	15.1022			0.968804
$244$	−1.11590	−	3.43439i	−0.0714383	−	0.219865i
$245$	−4.80253	−	3.48924i	−0.306822	−	0.222920i
$246$	−6.60440	+	4.79837i	−0.421081	+	0.305933i
$247$	−8.17339	+	25.1551i	−0.520060	+	1.60058i
$248$	−2.90537	+	8.94180i	−0.184491	+	0.567805i
$249$	3.66215	−	2.66071i	0.232079	−	0.168615i
$250$	−0.596764	−	0.433574i	−0.0377426	−	0.0274216i
$251$	5.32471	+	16.3878i	0.336093	+	1.03439i	0.966181	+	0.257863i	$0.0830184\pi$
$251$	5.32471	+	16.3878i	0.336093	+	1.03439i	−0.630089	+	0.776523i	$0.716982\pi$
$252$	−7.36503			−0.463953
$253$		0			0
$254$	8.78527			0.551237
$255$	2.08362	+	6.41272i	0.130481	+	0.401580i
$256$	9.65409	+	7.01411i	0.603381	+	0.438382i
$257$	−14.9631	+	10.8713i	−0.933373	+	0.678135i	−0.946816	−	0.321774i	$-0.895721\pi$
$257$	−14.9631	+	10.8713i	−0.933373	+	0.678135i	0.0134434	+	0.999910i	$0.495721\pi$
$258$	−4.90233	+	15.0878i	−0.305206	+	0.939327i
$259$	1.89908	−	5.84477i	0.118003	−	0.363176i
$260$	−4.06235	+	2.95147i	−0.251936	+	0.183042i
$261$	23.6275	+	17.1664i	1.46250	+	1.06257i
$262$	2.55011	+	7.84842i	0.157546	+	0.484877i
$263$	3.69135			0.227618			0.113809	−	0.993503i	$-0.463695\pi$
$263$	3.69135			0.227618			0.113809	+	0.993503i	$0.463695\pi$
$264$		0			0
$265$	11.8480			0.727819
$266$	1.80291	+	5.54878i	0.110543	+	0.340217i
$267$	18.5634	+	13.4871i	1.13606	+	0.825396i
$268$	−7.24018	+	5.26030i	−0.442265	+	0.321324i
$269$	−3.07320	+	9.45835i	−0.187377	+	0.576686i	−0.999981	−	0.00612956i	$-0.998049\pi$
$269$	−3.07320	+	9.45835i	−0.187377	+	0.576686i	0.812605	+	0.582815i	$0.198049\pi$
$270$	−1.22079	+	3.75721i	−0.0742949	+	0.228656i
$271$	−1.01423	+	0.736878i	−0.0616098	+	0.0447622i	−0.618164	−	0.786049i	$-0.712123\pi$
$271$	−1.01423	+	0.736878i	−0.0616098	+	0.0447622i	0.556554	+	0.830811i	$0.312123\pi$
$272$	−2.00108	−	1.45387i	−0.121333	−	0.0881538i
$273$	−3.09058	−	9.51183i	−0.187051	−	0.575682i
$274$	3.15802			0.190783
$275$		0			0
$276$	10.0527			0.605102
$277$	−2.50097	−	7.69720i	−0.150269	−	0.462480i	0.847382	−	0.530984i	$-0.178177\pi$
$277$	−2.50097	−	7.69720i	−0.150269	−	0.462480i	−0.997651	+	0.0685038i	$0.978177\pi$
$278$	−3.55265	−	2.58115i	−0.213074	−	0.154807i
$279$	14.6353	−	10.6331i	0.876190	−	0.636589i
$280$	−0.812466	+	2.50051i	−0.0485541	+	0.149434i
$281$	7.83984	−	24.1285i	0.467686	−	1.43939i	−0.387888	−	0.921707i	$-0.626795\pi$
$281$	7.83984	−	24.1285i	0.467686	−	1.43939i	0.855573	−	0.517681i	$-0.173205\pi$
$282$	−9.80350	+	7.12266i	−0.583790	+	0.424148i
$283$	16.5383	+	12.0157i	0.983097	+	0.714262i	0.958399	−	0.285433i	$-0.0921374\pi$
$283$	16.5383	+	12.0157i	0.983097	+	0.714262i	0.0246985	+	0.999695i	$0.492137\pi$
$284$	−0.910201	−	2.80131i	−0.0540105	−	0.166227i
$285$	−21.5613			−1.27718
$286$		0			0
$287$	4.05977			0.239641
$288$	−8.88072	−	27.3320i	−0.523301	−	1.61056i
$289$	9.10028	+	6.61174i	0.535311	+	0.388926i
$290$	3.55332	−	2.58164i	0.208658	−	0.151599i
$291$	−2.12234	+	6.53189i	−0.124414	+	0.382906i
$292$	0.371552	−	1.14352i	0.0217435	−	0.0669195i
$293$	−2.06224	+	1.49830i	−0.120477	+	0.0875319i	−0.646392	−	0.763005i	$-0.723723\pi$
$293$	−2.06224	+	1.49830i	−0.120477	+	0.0875319i	0.525915	+	0.850537i	$0.323723\pi$
$294$	9.96007	+	7.23641i	0.580883	+	0.422036i
$295$	−0.910456	−	2.80210i	−0.0530088	−	0.163144i
$296$	15.1896			0.882878
$297$		0			0
$298$	2.79156			0.161711
$299$	2.61747	+	8.05576i	0.151372	+	0.465877i
$300$	−3.31156	−	2.40599i	−0.191193	−	0.138910i
$301$	6.38270	−	4.63730i	0.367893	−	0.267290i
$302$	5.55193	−	17.0871i	0.319478	−	0.983252i
$303$	6.53677	−	20.1181i	0.375528	−	1.15576i
$304$	6.39888	−	4.64906i	0.367001	−	0.266642i
$305$	2.00666	+	1.45792i	0.114901	+	0.0834805i
$306$	−2.68129	−	8.25215i	−0.153279	−	0.471744i
$307$	8.99273			0.513242			0.256621	−	0.966512i	$-0.417391\pi$
$307$	8.99273			0.513242			0.256621	+	0.966512i	$0.417391\pi$
$308$		0			0
$309$	26.6601			1.51664
$310$	−0.840701	−	2.58741i	−0.0477486	−	0.146955i
$311$	16.2800	+	11.8281i	0.923154	+	0.670710i	0.944307	−	0.329066i	$-0.106734\pi$
$311$	16.2800	+	11.8281i	0.923154	+	0.670710i	−0.0211533	+	0.999776i	$0.506734\pi$
$312$	19.9987	−	14.5299i	1.13220	−	0.822593i
$313$	2.19551	−	6.75709i	0.124098	−	0.381933i	−0.869638	−	0.493690i	$-0.835648\pi$
$313$	2.19551	−	6.75709i	0.124098	−	0.381933i	0.993736	+	0.111757i	$0.0356477\pi$
$314$	−1.64851	+	5.07359i	−0.0930307	+	0.286319i
$315$	4.09265	−	2.97348i	0.230595	−	0.167537i
$316$	−14.2261	−	10.3359i	−0.800283	−	0.581439i
$317$	0.708647	+	2.18099i	0.0398016	+	0.122497i	0.968983	−	0.247127i	$-0.0794865\pi$
$317$	0.708647	+	2.18099i	0.0398016	+	0.122497i	−0.929181	+	0.369624i	$0.879487\pi$
$318$	−24.5719			−1.37792
$319$		0			0
$320$	−2.25922			−0.126294
$321$	4.03722	+	12.4253i	0.225335	+	0.693511i
$322$	1.51157	+	1.09822i	0.0842367	+	0.0612015i
$323$	14.8790	−	10.8102i	0.827890	−	0.601497i
$324$	−0.154394	+	0.475175i	−0.00857743	+	0.0263986i
$325$	1.06580	−	3.28018i	0.0591197	−	0.181952i
$326$	11.1530	−	8.10314i	0.617708	−	0.448791i
$327$	−12.1197	−	8.80546i	−0.670219	−	0.486943i
$328$	3.10077	+	9.54319i	0.171211	+	0.526935i
$329$	6.02629			0.332240
$330$		0			0
$331$	15.3951			0.846192			0.423096	−	0.906085i	$-0.360943\pi$
$331$	15.3951			0.846192			0.423096	+	0.906085i	$0.360943\pi$
$332$	−0.724337	−	2.22928i	−0.0397532	−	0.122348i
$333$	−23.6444	−	17.1787i	−1.29570	−	0.941385i
$334$	4.68655	−	3.40498i	0.256437	−	0.186312i
$335$	1.89953	−	5.84616i	0.103783	−	0.319410i
$336$	−0.924203	+	2.84440i	−0.0504194	+	0.155175i
$337$	15.7733	−	11.4600i	0.859225	−	0.624263i	−0.0684492	−	0.997655i	$-0.521805\pi$
$337$	15.7733	−	11.4600i	0.859225	−	0.624263i	0.927674	+	0.373391i	$0.121805\pi$
$338$	−0.659111	−	0.478872i	−0.0358509	−	0.0260472i
$339$	−0.264904	−	0.815290i	−0.0143876	−	0.0442805i
$340$	3.49153			0.189355
$341$		0			0
$342$	27.7460			1.50033
$343$	−4.12296	−	12.6892i	−0.222619	−	0.685151i
$344$	15.7757	+	11.4618i	0.850571	+	0.617976i
$345$	−5.58616	+	4.05858i	−0.300749	+	0.218507i
$346$	−2.55403	+	7.86051i	−0.137306	+	0.422584i
$347$	−0.670272	+	2.06288i	−0.0359821	+	0.110741i	−0.967434	−	0.253122i	$-0.918543\pi$
$347$	−0.670272	+	2.06288i	−0.0359821	+	0.110741i	0.931452	+	0.363864i	$0.118543\pi$
$348$	19.7181	−	14.3260i	1.05700	−	0.767955i
$349$	20.2675	+	14.7252i	1.08490	+	0.788222i	0.978530	−	0.206105i	$-0.0660787\pi$
$349$	20.2675	+	14.7252i	1.08490	+	0.788222i	0.106365	+	0.994327i	$0.466079\pi$
$350$	−0.235096	−	0.723552i	−0.0125664	−	0.0386755i
$351$	−18.4717			−0.985944
$352$		0			0
$353$	−23.2532			−1.23764			−0.618821	−	0.785532i	$-0.712389\pi$
$353$	−23.2532			−1.23764			−0.618821	+	0.785532i	$0.712389\pi$
$354$	1.88821	+	5.81133i	0.100357	+	0.308868i
$355$	1.63676	+	1.18918i	0.0868702	+	0.0631149i
$356$	9.61252	−	6.98390i	0.509463	−	0.370146i
$357$	−2.14900	+	6.61395i	−0.113737	+	0.350047i
$358$	−0.333853	+	1.02749i	−0.0176447	+	0.0543047i
$359$	−8.18917	+	5.94978i	−0.432208	+	0.314018i	−0.782531	−	0.622611i	$-0.786072\pi$
$359$	−8.18917	+	5.94978i	−0.432208	+	0.314018i	0.350323	+	0.936629i	$0.386072\pi$
$360$	10.1156	+	7.34938i	0.533137	+	0.387346i
$361$	12.3022	+	37.8621i	0.647482	+	1.99274i
$362$	−6.85194			−0.360130
$363$		0			0
$364$	−5.17891			−0.271448
$365$	0.255207	+	0.785446i	0.0133581	+	0.0411121i
$366$	−4.16165	−	3.02362i	−0.217533	−	0.158047i
$367$	−3.00084	+	2.18024i	−0.156643	+	0.113808i	−0.663346	−	0.748313i	$-0.730864\pi$
$367$	−3.00084	+	2.18024i	−0.156643	+	0.113808i	0.506703	+	0.862121i	$0.330864\pi$
$368$	0.782725	−	2.40898i	0.0408024	−	0.125577i
$369$	5.96614	−	18.3619i	0.310585	−	0.955882i
$370$	−3.55586	+	2.58348i	−0.184860	+	0.134309i
$371$	9.88604	+	7.18263i	0.513258	+	0.372904i
$372$	−4.66522	−	14.3581i	−0.241880	−	0.744431i
$373$	−9.34017			−0.483616			−0.241808	−	0.970324i	$-0.577740\pi$
$373$	−9.34017			−0.483616			−0.241808	+	0.970324i	$0.577740\pi$
$374$		0			0
$375$	2.81156			0.145188
$376$	4.60276	+	14.1658i	0.237369	+	0.730547i
$377$	16.6143	+	12.0710i	0.855678	+	0.621687i
$378$	−3.29636	+	2.39495i	−0.169547	+	0.123183i
$379$	−3.03198	+	9.33148i	−0.155742	+	0.479326i	−0.998235	−	0.0593816i	$-0.981087\pi$
$379$	−3.03198	+	9.33148i	−0.155742	+	0.479326i	0.842493	+	0.538707i	$0.181087\pi$
$380$	−3.45015	+	10.6185i	−0.176989	+	0.544716i
$381$	−27.0904	+	19.6823i	−1.38788	+	1.00836i
$382$	−2.66930	−	1.93936i	−0.136573	−	0.0992263i
$383$	−5.57677	−	17.1635i	−0.284960	−	0.877015i	−0.986411	−	0.164298i	$-0.947464\pi$
$383$	−5.57677	−	17.1635i	−0.284960	−	0.877015i	0.701451	−	0.712718i	$-0.252536\pi$
$384$	−28.2615			−1.44221
$385$		0			0
$386$	16.7194			0.850993
$387$	−11.5941	−	35.6831i	−0.589363	−	1.81387i
$388$	2.87720	+	2.09041i	0.146068	+	0.106124i
$389$	−25.2345	+	18.3339i	−1.27944	+	0.929567i	−0.999536	−	0.0304614i	$-0.990302\pi$
$389$	−25.2345	+	18.3339i	−1.27944	+	0.929567i	−0.279903	+	0.960028i	$0.590302\pi$
$390$	−2.21038	+	6.80284i	−0.111927	+	0.344475i
$391$	1.82003	−	5.60148i	0.0920429	−	0.283279i
$392$	12.2426	−	8.89478i	0.618346	−	0.449254i
$393$	−25.4470	−	18.4883i	−1.28363	−	0.932612i
$394$	2.55478	+	7.86281i	0.128708	+	0.396123i
$395$	12.0782			0.607719
$396$		0			0
$397$	−10.6212			−0.533062			−0.266531	−	0.963826i	$-0.585877\pi$
$397$	−10.6212			−0.533062			−0.266531	+	0.963826i	$0.585877\pi$
$398$	1.78247	+	5.48588i	0.0893472	+	0.274982i
$399$	−17.9908	−	13.0711i	−0.900669	−	0.654374i
$400$	−0.834404	+	0.606230i	−0.0417202	+	0.0303115i
$401$	−8.51895	+	26.2186i	−0.425416	+	1.30930i	0.477179	+	0.878806i	$0.341659\pi$
$401$	−8.51895	+	26.2186i	−0.425416	+	1.30930i	−0.902595	+	0.430490i	$0.858341\pi$
$402$	−3.93948	+	12.1245i	−0.196483	+	0.604714i
$403$	10.2912	−	7.47696i	0.512639	−	0.372454i
$404$	−8.86173	−	6.43843i	−0.440888	−	0.320324i
$405$	−0.106048	−	0.326382i	−0.00526956	−	0.0162181i
$406$	4.52997			0.224818
$407$		0			0
$408$	−17.1886			−0.850961
$409$	4.44001	+	13.6649i	0.219544	+	0.675688i	0.998800	+	0.0489814i	$0.0155975\pi$
$409$	4.44001	+	13.6649i	0.219544	+	0.675688i	−0.779255	+	0.626707i	$0.784402\pi$
$410$	−2.34901	−	1.70666i	−0.116010	−	0.0842859i
$411$	−9.73812	+	7.07516i	−0.480346	+	0.348992i
$412$	4.26603	−	13.1295i	0.210172	−	0.646844i
$413$	0.939026	−	2.89003i	0.0462065	−	0.142209i
$414$	7.18851	−	5.22276i	0.353296	−	0.256684i
$415$	1.30253	+	0.946345i	0.0639388	+	0.0464542i
$416$	−6.24470	−	19.2192i	−0.306172	−	0.942300i
$417$	16.7378			0.819652
$418$		0			0
$419$	−31.4707			−1.53744			−0.768722	−	0.639584i	$-0.779107\pi$
$419$	−31.4707			−1.53744			−0.768722	+	0.639584i	$0.779107\pi$
$420$	−1.30460	−	4.01513i	−0.0636578	−	0.195919i
$421$	−21.4965	−	15.6181i	−1.04768	−	0.761182i	−0.0759078	−	0.997115i	$-0.524185\pi$
$421$	−21.4965	−	15.6181i	−1.04768	−	0.761182i	−0.971769	+	0.235933i	$0.924185\pi$
$422$	−13.5865	+	9.87118i	−0.661381	+	0.480521i
$423$	8.85609	−	27.2562i	0.430598	−	1.32524i
$424$	−9.33324	+	28.7248i	−0.453262	+	1.39500i
$425$	−1.94020	+	1.40964i	−0.0941134	+	0.0683774i
$426$	−3.39451	−	2.46626i	−0.164465	−	0.119491i
$427$	0.790528	+	2.43300i	0.0382563	+	0.117741i
$428$	6.76518			0.327008
$429$		0			0
$430$	−5.64252			−0.272106
$431$	−1.19549	−	3.67935i	−0.0575849	−	0.177228i	0.918127	−	0.396287i	$-0.129701\pi$
$431$	−1.19549	−	3.67935i	−0.0575849	−	0.177228i	−0.975712	+	0.219059i	$0.929701\pi$
$432$	4.46880	+	3.24677i	0.215005	+	0.156210i
$433$	−32.4730	+	23.5930i	−1.56055	+	1.13381i	−0.624995	+	0.780629i	$0.714899\pi$
$433$	−32.4730	+	23.5930i	−1.56055	+	1.13381i	−0.935556	+	0.353178i	$0.885101\pi$
$434$	0.867082	−	2.66860i	0.0416213	−	0.128097i
$435$	−5.17323	+	15.9216i	−0.248037	+	0.763380i
$436$	−6.27583	+	4.55966i	−0.300558	+	0.218368i
$437$	15.2368	+	11.0702i	0.728875	+	0.529559i
$438$	−0.529279	−	1.62895i	−0.0252899	−	0.0778344i
$439$	1.02336			0.0488425			0.0244212	−	0.999702i	$-0.492226\pi$
$439$	1.02336			0.0488425			0.0244212	+	0.999702i	$0.492226\pi$
$440$		0			0
$441$	−29.1166			−1.38650
$442$	−1.88541	−	5.80271i	−0.0896800	−	0.276007i
$443$	13.0032	+	9.44738i	0.617801	+	0.448858i	0.852153	−	0.523293i	$-0.175297\pi$
$443$	13.0032	+	9.44738i	0.617801	+	0.448858i	−0.234352	+	0.972152i	$0.575297\pi$
$444$	−19.7322	+	14.3363i	−0.936448	+	0.680370i
$445$	−2.52194	+	7.76173i	−0.119551	+	0.367941i
$446$	3.65682	−	11.2545i	0.173156	−	0.532918i
$447$	−8.60810	+	6.25415i	−0.407149	+	0.295811i
$448$	−1.88510	−	1.36960i	−0.0890625	−	0.0647077i
$449$	11.0758	+	34.0879i	0.522700	+	1.60871i	0.768820	+	0.639466i	$0.220844\pi$
$449$	11.0758	+	34.0879i	0.522700	+	1.60871i	−0.246120	+	0.969239i	$0.579156\pi$
$450$	−3.61803			−0.170556
$451$		0			0
$452$	−0.443901			−0.0208793
$453$	21.1615	+	65.1285i	0.994256	+	3.06000i
$454$	−14.4155	−	10.4735i	−0.676555	−	0.491546i
$455$	2.87785	−	2.09088i	0.134916	−	0.0980220i
$456$	16.9849	−	52.2740i	0.795389	−	2.44795i
$457$	−7.77254	+	23.9214i	−0.363584	+	1.11900i	0.587279	+	0.809384i	$0.300199\pi$
$457$	−7.77254	+	23.9214i	−0.363584	+	1.11900i	−0.950863	+	0.309612i	$0.899801\pi$
$458$	−8.95997	+	6.50980i	−0.418672	+	0.304183i
$459$	10.3911	+	7.54955i	0.485013	+	0.352383i
$460$	1.10489	+	3.40050i	0.0515157	+	0.158549i
$461$	6.65631			0.310015			0.155008	−	0.987913i	$-0.450460\pi$
$461$	6.65631			0.310015			0.155008	+	0.987913i	$0.450460\pi$
$462$		0			0
$463$	38.7730			1.80194			0.900968	−	0.433886i	$-0.142858\pi$
$463$	38.7730			1.80194			0.900968	+	0.433886i	$0.142858\pi$
$464$	−1.89772	−	5.84059i	−0.0880996	−	0.271143i
$465$	8.38919	+	6.09510i	0.389039	+	0.282654i
$466$	6.81858	−	4.95399i	0.315865	−	0.229489i
$467$	6.96815	−	21.4458i	0.322448	−	0.992392i	−0.650132	−	0.759821i	$-0.725286\pi$
$467$	6.96815	−	21.4458i	0.322448	−	0.992392i	0.972580	−	0.232571i	$-0.0747136\pi$
$468$	−7.61079	+	23.4236i	−0.351809	+	1.08276i
$469$	5.12909	−	3.72651i	0.236840	−	0.172074i
$470$	−3.48685	−	2.53335i	−0.160837	−	0.116855i
$471$	−6.28339	−	19.3383i	−0.289523	−	0.891062i
$472$	7.51071			0.345708
$473$		0			0
$474$	−25.0492			−1.15055
$475$	−2.36979	−	7.29347i	−0.108734	−	0.334647i
$476$	2.91335	+	2.11667i	0.133533	+	0.0970174i
$477$	47.0145	−	34.1580i	2.15265	−	1.56399i
$478$	−6.24718	+	19.2268i	−0.285739	+	0.879415i
$479$	−0.504274	+	1.55200i	−0.0230409	+	0.0709125i	−0.961916	−	0.273346i	$-0.911870\pi$
$479$	−0.504274	+	1.55200i	−0.0230409	+	0.0709125i	0.938875	+	0.344258i	$0.111870\pi$
$480$	13.3273	−	9.68286i	0.608306	−	0.441960i
$481$	−16.6262	−	12.0796i	−0.758088	−	0.550783i
$482$	−2.49341	−	7.67392i	−0.113572	−	0.349537i
$483$	−7.12155			−0.324042
$484$		0			0
$485$	−2.44278			−0.110921
$486$	−3.44244	−	10.5947i	−0.156152	−	0.480587i
$487$	−0.849710	−	0.617350i	−0.0385040	−	0.0279748i	0.568367	−	0.822775i	$-0.307575\pi$
$487$	−0.849710	−	0.617350i	−0.0385040	−	0.0279748i	−0.606871	+	0.794800i	$0.707575\pi$
$488$	−5.11538	+	3.71654i	−0.231562	+	0.168240i
$489$	−16.2375	+	49.9739i	−0.734286	+	2.25990i
$490$	−1.35313	+	4.16451i	−0.0611282	+	0.188133i
$491$	11.2567	−	8.17850i	0.508009	−	0.369090i	−0.304058	−	0.952653i	$-0.598342\pi$
$491$	11.2567	−	8.17850i	0.508009	−	0.369090i	0.812068	+	0.583563i	$0.198342\pi$
$492$	−13.0352	−	9.47059i	−0.587670	−	0.426967i
$493$	−4.41268	−	13.5808i	−0.198737	−	0.611650i
$494$	19.5103			0.877811
$495$		0			0
$496$	−3.80394			−0.170802
$497$	0.644805	+	1.98451i	0.0289235	+	0.0890173i
$498$	−2.70135	−	1.96264i	−0.121050	−	0.0879482i
$499$	−14.0504	+	10.2082i	−0.628984	+	0.456983i	−0.856048	−	0.516896i	$-0.827087\pi$
$499$	−14.0504	+	10.2082i	−0.628984	+	0.456983i	0.227064	+	0.973880i	$0.427087\pi$
$500$	0.449894	−	1.38463i	0.0201199	−	0.0619226i
$501$	−6.82309	+	20.9993i	−0.304833	+	0.938179i
$502$	10.2829	−	7.47096i	0.458948	−	0.333445i
$503$	−29.0062	−	21.0742i	−1.29332	−	0.939653i	−0.293454	−	0.955973i	$-0.594805\pi$
$503$	−29.0062	−	21.0742i	−1.29332	−	0.939653i	−0.999867	+	0.0163204i	$0.994805\pi$
$504$	3.98504	+	12.2647i	0.177508	+	0.546313i
$505$	7.52373			0.334802
$506$		0			0
$507$	3.10530			0.137911
$508$	5.35822	+	16.4909i	0.237732	+	0.731665i
$509$	−1.73031	−	1.25715i	−0.0766947	−	0.0557220i	0.548777	−	0.835969i	$-0.315094\pi$
$509$	−1.73031	−	1.25715i	−0.0766947	−	0.0557220i	−0.625472	+	0.780247i	$0.715094\pi$
$510$	4.02381	−	2.92347i	0.178178	−	0.129454i
$511$	−0.263215	+	0.810093i	−0.0116440	+	0.0358364i
$512$	−3.49234	+	10.7483i	−0.154341	+	0.475013i
$513$	−33.2277	+	24.1413i	−1.46704	+	1.06586i
$514$	11.0374	+	8.01913i	0.486838	+	0.353709i
$515$	2.93020	+	9.01821i	0.129120	+	0.397390i
$516$	−31.3115			−1.37841
$517$		0			0
$518$	−4.53321			−0.199178
$519$	−9.73486	−	29.9608i	−0.427313	−	1.31513i
$520$	7.11301	+	5.16791i	0.311926	+	0.226628i
$521$	10.3030	−	7.48558i	0.451383	−	0.327949i	−0.338758	−	0.940873i	$-0.610007\pi$
$521$	10.3030	−	7.48558i	0.451383	−	0.327949i	0.790142	+	0.612924i	$0.210007\pi$
$522$	6.65713	−	20.4885i	0.291374	−	0.896758i
$523$	7.38821	−	22.7386i	0.323064	−	0.994289i	−0.649243	−	0.760581i	$-0.724914\pi$
$523$	7.38821	−	22.7386i	0.323064	−	0.994289i	0.972307	−	0.233708i	$-0.0750859\pi$
$524$	−13.1770	+	9.57365i	−0.575640	+	0.418227i
$525$	2.34598	+	1.70445i	0.102387	+	0.0743884i
$526$	−0.841418	−	2.58962i	−0.0366876	−	0.112913i
$527$	−8.84510			−0.385299
$528$		0			0
$529$	−16.9686			−0.737766
$530$	−2.70068	−	8.31184i	−0.117310	−	0.361043i
$531$	−11.6913	−	8.49422i	−0.507359	−	0.368618i
$532$	−9.31605	+	6.76851i	−0.403902	+	0.293452i
$533$	4.19525	−	12.9116i	0.181716	−	0.559265i
$534$	5.23030	−	16.0972i	0.226337	−	0.696594i
$535$	−3.75932	+	2.73131i	−0.162530	+	0.118085i
$536$	12.6773	+	9.21058i	0.547575	+	0.397837i
$537$	−1.27250	−	3.91635i	−0.0549124	−	0.169003i
$538$	7.33590			0.316273
$539$		0			0
$540$	−7.79726			−0.335540
$541$	0.407657	+	1.25464i	0.0175265	+	0.0539412i	0.959437	−	0.281922i	$-0.0909720\pi$
$541$	0.407657	+	1.25464i	0.0175265	+	0.0539412i	−0.941911	+	0.335863i	$0.890972\pi$
$542$	0.748134	+	0.543551i	0.0321351	+	0.0233475i
$543$	21.1288	−	15.3509i	0.906722	−	0.658772i
$544$	−4.34218	+	13.3639i	−0.186170	+	0.572971i
$545$	1.64652	−	5.06748i	0.0705293	−	0.217067i
$546$	−5.96843	+	4.33632i	−0.255425	+	0.185577i
$547$	−7.54108	−	5.47891i	−0.322433	−	0.234261i	0.414780	−	0.909922i	$-0.363859\pi$
$547$	−7.54108	−	5.47891i	−0.322433	−	0.234261i	−0.737213	+	0.675660i	$0.763859\pi$
$548$	1.92610	+	5.92794i	0.0822791	+	0.253229i
$549$	12.1659			0.519228
$550$		0			0
$551$	45.6625			1.94529
$552$	−5.43929	−	16.7404i	−0.231512	−	0.712520i
$553$	10.0781	+	7.32216i	0.428564	+	0.311370i
$554$	−4.82980	+	3.50905i	−0.205198	+	0.149085i
$555$	5.17693	−	15.9330i	0.219749	−	0.676316i
$556$	2.67831	−	8.24298i	0.113585	−	0.349580i
$557$	−31.8083	+	23.1101i	−1.34776	+	0.979205i	−0.348640	+	0.937257i	$0.613356\pi$
$557$	−31.8083	+	23.1101i	−1.34776	+	0.979205i	−0.999120	+	0.0419481i	$0.986644\pi$
$558$	−10.7956	−	7.84343i	−0.457012	−	0.332039i
$559$	−8.15272	−	25.0915i	−0.344823	−	1.06126i
$560$	−1.06374			−0.0449514
$561$		0			0
$562$	−18.7141			−0.789407
$563$	6.17446	+	19.0030i	0.260222	+	0.800882i	0.992756	+	0.120151i	$0.0383378\pi$
$563$	6.17446	+	19.0030i	0.260222	+	0.800882i	−0.732533	+	0.680731i	$0.761662\pi$
$564$	−19.3493	−	14.0581i	−0.814751	−	0.591951i
$565$	0.246670	−	0.179216i	0.0103775	−	0.00753968i
$566$	4.65971	−	14.3411i	0.195862	−	0.602802i
$567$	0.109376	−	0.336624i	0.00459335	−	0.0141369i
$568$	−4.17243	+	3.03145i	−0.175071	+	0.127197i
$569$	27.9635	+	20.3166i	1.17229	+	0.851718i	0.991281	−	0.131764i	$-0.0420640\pi$
$569$	27.9635	+	20.3166i	1.17229	+	0.851718i	0.181008	+	0.983482i	$0.442064\pi$
$570$	4.91476	+	15.1261i	0.205857	+	0.633562i
$571$	3.15090			0.131861			0.0659306	−	0.997824i	$-0.478998\pi$
$571$	3.15090			0.131861			0.0659306	+	0.997824i	$0.478998\pi$
$572$		0			0
$573$	12.5760			0.525370
$574$	−0.925399	−	2.84808i	−0.0386254	−	0.118877i
$575$	−1.98685	−	1.44353i	−0.0828575	−	0.0601995i
$576$	−8.96485	+	6.51335i	−0.373536	+	0.271389i
$577$	8.44314	−	25.9853i	0.351493	−	1.08178i	−0.606523	−	0.795066i	$-0.707436\pi$
$577$	8.44314	−	25.9853i	0.351493	−	1.08178i	0.958015	−	0.286717i	$-0.0925639\pi$
$578$	2.56404	−	7.89129i	0.106650	−	0.328234i
$579$	−51.5561	+	37.4577i	−2.14260	+	1.55669i
$580$	7.01321	+	5.09540i	0.291208	+	0.211575i
$581$	0.513135	+	1.57927i	0.0212884	+	0.0655190i
$582$	5.06614			0.209998
$583$		0			0
$584$	−2.10530			−0.0871180
$585$	−5.22760	−	16.0889i	−0.216135	−	0.665194i
$586$	1.52119	+	1.10521i	0.0628398	+	0.0456558i
$587$	37.3506	−	27.1368i	1.54162	−	1.12005i	0.592316	−	0.805706i	$-0.298214\pi$
$587$	37.3506	−	27.1368i	1.54162	−	1.12005i	0.949307	−	0.314349i	$-0.101786\pi$
$588$	−7.50879	+	23.1097i	−0.309657	+	0.953027i
$589$	8.74027	−	26.8998i	0.360137	−	1.10839i
$590$	−1.75824	+	1.27744i	−0.0723857	+	0.0525913i
$591$	−25.4936	−	18.5222i	−1.04867	−	0.761902i
$592$	1.89908	+	5.84477i	0.0780518	+	0.240219i
$593$	39.4265			1.61905			0.809525	−	0.587085i	$-0.199725\pi$
$593$	39.4265			1.61905			0.809525	+	0.587085i	$0.199725\pi$
$594$		0			0
$595$	−2.47347			−0.101402
$596$	1.70260	+	5.24006i	0.0697411	+	0.214641i
$597$	−17.7869	−	12.9229i	−0.727970	−	0.528901i
$598$	5.05478	−	3.67251i	0.206705	−	0.150180i
$599$	0.324081	−	0.997418i	0.0132416	−	0.0407534i	−0.944217	−	0.329323i	$-0.893180\pi$
$599$	0.324081	−	0.997418i	0.0132416	−	0.0407534i	0.957459	+	0.288569i	$0.0931796\pi$
$600$	−2.21480	+	6.81645i	−0.0904187	+	0.278280i
$601$	−22.0455	+	16.0170i	−0.899256	+	0.653348i	−0.938275	−	0.345891i	$-0.887577\pi$
$601$	−22.0455	+	16.0170i	−0.899256	+	0.653348i	0.0390187	+	0.999238i	$0.487577\pi$
$602$	−4.70814	−	3.42066i	−0.191889	−	0.139416i
$603$	−9.31697	−	28.6747i	−0.379416	−	1.16772i
$604$	35.4605			1.44287
$605$		0			0
$606$	−15.6036			−0.633854
$607$	6.77418	+	20.8488i	0.274955	+	0.846225i	0.989231	+	0.146361i	$0.0467562\pi$
$607$	6.77418	+	20.8488i	0.274955	+	0.846225i	−0.714276	+	0.699864i	$0.753244\pi$
$608$	−36.3516	−	26.4110i	−1.47425	−	1.07111i
$609$	−13.9687	+	10.1488i	−0.566040	+	0.411252i
$610$	0.565384	−	1.74007i	0.0228917	−	0.0704535i
$611$	6.22738	−	19.1659i	0.251933	−	0.775370i
$612$	13.8548	−	10.0661i	0.560049	−	0.406899i
$613$	−8.56915	−	6.22586i	−0.346105	−	0.251460i	0.401128	−	0.916022i	$-0.368618\pi$
$613$	−8.56915	−	6.22586i	−0.346105	−	0.251460i	−0.747233	+	0.664562i	$0.768618\pi$
$614$	−2.04983	−	6.30874i	−0.0827245	−	0.254600i
$615$	11.0670			0.446265
$616$		0			0
$617$	4.60402			0.185351			0.0926755	−	0.995696i	$-0.470458\pi$
$617$	4.60402			0.185351			0.0926755	+	0.995696i	$0.470458\pi$
$618$	−6.07699	−	18.7031i	−0.244453	−	0.752348i
$619$	−29.9366	−	21.7502i	−1.20326	−	0.874216i	−0.208654	−	0.977989i	$-0.566908\pi$
$619$	−29.9366	−	21.7502i	−1.20326	−	0.874216i	−0.994601	+	0.103773i	$0.966908\pi$
$620$	4.34410	−	3.15617i	0.174463	−	0.126755i
$621$	−4.06448	+	12.5092i	−0.163102	+	0.501976i
$622$	4.58695	−	14.1172i	0.183920	−	0.566047i
$623$	−6.80971	+	4.94754i	−0.272825	+	0.198219i
$624$	8.09125	+	5.87864i	0.323909	+	0.235334i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−5.24081			−0.209465
$627$		0			0
$628$	−10.5291			−0.420157
$629$	4.41584	+	13.5906i	0.176071	+	0.541891i
$630$	−3.01890	−	2.19336i	−0.120276	−	0.0873856i
$631$	20.0965	−	14.6009i	0.800028	−	0.581254i	−0.110895	−	0.993832i	$-0.535372\pi$
$631$	20.0965	−	14.6009i	0.800028	−	0.581254i	0.910922	+	0.412578i	$0.135372\pi$
$632$	−9.51455	+	29.2828i	−0.378468	+	1.16481i
$633$	19.7804	−	60.8779i	0.786201	−	2.41968i
$634$	1.36852	−	0.994285i	0.0543507	−	0.0394881i
$635$	−9.63536	−	7.00050i	−0.382368	−	0.277806i
$636$	−14.9866	−	46.1241i	−0.594258	−	1.82894i
$637$	−20.4741			−0.811213
$638$		0			0
$639$	9.92328			0.392559
$640$	−3.10621	−	9.55992i	−0.122784	−	0.377889i
$641$	35.9440	+	26.1149i	1.41970	+	1.03147i	0.991820	+	0.127641i	$0.0407405\pi$
$641$	35.9440	+	26.1149i	1.41970	+	1.03147i	0.427883	+	0.903834i	$0.359260\pi$
$642$	7.79654	−	5.66452i	0.307705	−	0.223561i
$643$	7.99148	−	24.5952i	0.315153	−	0.969942i	−0.660538	−	0.750793i	$-0.729672\pi$
$643$	7.99148	−	24.5952i	0.315153	−	0.969942i	0.975691	−	0.219149i	$-0.0703282\pi$
$644$	−1.13956	+	3.50720i	−0.0449049	+	0.138203i
$645$	17.3994	−	12.6414i	0.685099	−	0.497754i
$646$	−10.9753	−	7.97406i	−0.431819	−	0.313735i
$647$	6.02166	+	18.5328i	0.236736	+	0.728598i	0.996886	+	0.0788509i	$0.0251251\pi$
$647$	6.02166	+	18.5328i	0.236736	+	0.728598i	−0.760151	+	0.649747i	$0.774875\pi$
$648$	0.874831			0.0343666
$649$		0			0
$650$	−2.54411			−0.0997883
$651$	3.30494	+	10.1716i	0.129531	+	0.398654i
$652$	22.0128	+	15.9932i	0.862087	+	0.626343i
$653$	13.5347	−	9.83353i	0.529653	−	0.384816i	−0.290575	−	0.956852i	$-0.593847\pi$
$653$	13.5347	−	9.83353i	0.529653	−	0.384816i	0.820228	+	0.572037i	$0.193847\pi$
$654$	−3.41476	+	10.5096i	−0.133528	+	0.410956i
$655$	3.45711	−	10.6399i	0.135081	−	0.415735i
$656$	−3.28443	+	2.38628i	−0.128235	+	0.0931684i
$657$	3.27714	+	2.38099i	0.127854	+	0.0928911i
$658$	−1.37365	−	4.22767i	−0.0535506	−	0.164812i
$659$	−1.66127			−0.0647137			−0.0323569	−	0.999476i	$-0.510301\pi$
$659$	−1.66127			−0.0647137			−0.0323569	+	0.999476i	$0.510301\pi$
$660$		0			0
$661$	−44.0130			−1.71191			−0.855953	−	0.517053i	$-0.827029\pi$
$661$	−44.0130			−1.71191			−0.855953	+	0.517053i	$0.827029\pi$
$662$	−3.50921	−	10.8002i	−0.136389	−	0.419763i
$663$	18.8142	+	13.6693i	0.730682	+	0.530871i
$664$	−3.32042	+	2.41242i	−0.128857	+	0.0936202i
$665$	2.44416	−	7.52234i	0.0947803	−	0.291704i
$666$	−6.66189	+	20.5032i	−0.258143	+	0.794483i
$667$	11.8304	−	8.59526i	0.458073	−	0.332810i
$668$	9.24988	+	6.72043i	0.357889	+	0.260021i
$669$	13.9382	+	42.8974i	0.538882	+	1.65851i
$670$	−4.53429			−0.175175
$671$		0			0
$672$	16.9904			0.655419
$673$	−11.9265	−	36.7059i	−0.459732	−	1.41491i	−0.865489	−	0.500928i	$-0.832992\pi$
$673$	−11.9265	−	36.7059i	−0.459732	−	1.41491i	0.405757	−	0.913981i	$-0.367008\pi$
$674$	−11.6350	−	8.45332i	−0.448163	−	0.325610i
$675$	4.33283	−	3.14799i	0.166771	−	0.121166i
$676$	0.496897	−	1.52929i	0.0191114	−	0.0588189i
$677$	−11.9277	+	36.7097i	−0.458419	+	1.41087i	0.408656	+	0.912689i	$0.365998\pi$
$677$	−11.9277	+	36.7097i	−0.458419	+	1.41087i	−0.867074	+	0.498179i	$0.834002\pi$
$678$	−0.511574	+	0.371680i	−0.0196469	+	0.0142743i
$679$	−2.03827	−	1.48089i	−0.0782215	−	0.0568313i
$680$	−1.88919	−	5.81432i	−0.0724470	−	0.222969i
$681$	67.9167			2.60257
$682$		0			0
$683$	−0.748158			−0.0286275			−0.0143137	−	0.999898i	$-0.504556\pi$
$683$	−0.748158			−0.0286275			−0.0143137	+	0.999898i	$0.504556\pi$
$684$	16.9226	+	52.0823i	0.647050	+	1.99141i
$685$	−3.46360	−	2.51645i	−0.132337	−	0.0961487i
$686$	−7.96213	+	5.78483i	−0.303996	+	0.220866i
$687$	13.0447	−	40.1475i	0.497687	−	1.53172i
$688$	−2.43797	+	7.50331i	−0.0929469	+	0.286061i
$689$	33.0594	−	24.0191i	1.25946	−	0.915055i
$690$	4.12058	+	2.99378i	0.156868	+	0.113971i
$691$	1.61364	+	4.96627i	0.0613857	+	0.188926i	0.977047	−	0.213026i	$-0.0683319\pi$
$691$	1.61364	+	4.96627i	0.0613857	+	0.188926i	−0.915661	+	0.401952i	$0.868332\pi$
$692$	−16.3128			−0.620118
$693$		0			0
$694$	1.59998			0.0607342
$695$	1.83964	+	5.66183i	0.0697815	+	0.214765i
$696$	−34.5256	−	25.0843i	−1.30869	−	0.950818i
$697$	−7.63711	+	5.54869i	−0.289276	+	0.210171i
$698$	5.71044	−	17.5749i	0.216143	−	0.665221i
$699$	−9.92709	+	30.5524i	−0.375477	+	1.15560i
$700$	1.21480	−	0.882602i	0.0459150	−	0.0333592i
$701$	11.4540	+	8.32185i	0.432613	+	0.314312i	0.782693	−	0.622408i	$-0.213845\pi$
$701$	11.4540	+	8.32185i	0.432613	+	0.314312i	−0.350080	+	0.936720i	$0.613845\pi$
$702$	4.21049	+	12.9586i	0.158915	+	0.489090i
$703$	−45.6952			−1.72343
$704$		0			0
$705$	16.4278			0.618706
$706$	5.30041	+	16.3130i	0.199483	+	0.613947i
$707$	6.27783	+	4.56111i	0.236102	+	0.171538i
$708$	−9.75685	+	7.08876i	−0.366685	+	0.266412i
$709$	−5.31953	+	16.3718i	−0.199779	+	0.614857i	0.800108	+	0.599855i	$0.204775\pi$
$709$	−5.31953	+	16.3718i	−0.199779	+	0.614857i	−0.999887	+	0.0150013i	$0.995225\pi$
$710$	0.461163	−	1.41931i	0.0173071	−	0.0532659i
$711$	47.9278	−	34.8216i	1.79743	−	1.30591i
$712$	−16.8312	−	12.2285i	−0.630774	−	0.458284i
$713$	−2.79902	−	8.61448i	−0.104824	−	0.322615i
$714$	5.12978			0.191977
$715$		0			0
$716$	−2.13233			−0.0796891
$717$	−23.8115	−	73.2843i	−0.889257	−	2.73685i
$718$	6.04066	+	4.38880i	0.225436	+	0.163789i
$719$	21.4842	−	15.6092i	0.801226	−	0.582125i	−0.110048	−	0.993926i	$-0.535100\pi$
$719$	21.4842	−	15.6092i	0.801226	−	0.582125i	0.911273	+	0.411802i	$0.135100\pi$
$720$	−1.56325	+	4.81120i	−0.0582590	+	0.179303i
$721$	−3.02214	+	9.30121i	−0.112551	+	0.346395i
$722$	23.7575	−	17.2608i	0.884163	−	0.642382i
$723$	24.8812	+	18.0772i	0.925342	+	0.672300i
$724$	−4.17906	−	12.8618i	−0.155314	−	0.478006i
$725$	−5.95431			−0.221138
$726$		0			0
$727$	44.1917			1.63898			0.819490	−	0.573094i	$-0.194257\pi$
$727$	44.1917			1.63898			0.819490	+	0.573094i	$0.194257\pi$
$728$	2.80219	+	8.62424i	0.103856	+	0.319636i
$729$	35.1843	+	25.5629i	1.30312	+	0.946773i
$730$	0.492847	−	0.358074i	0.0182411	−	0.0132529i
$731$	−5.66890	+	17.4471i	−0.209672	+	0.645303i
$732$	3.13743	−	9.65601i	0.115963	−	0.356896i
$733$	−20.1934	+	14.6714i	−0.745861	+	0.541900i	−0.894541	−	0.446986i	$-0.852498\pi$
$733$	−20.1934	+	14.6714i	−0.745861	+	0.541900i	0.148680	+	0.988885i	$0.452498\pi$
$734$	2.21354	+	1.60823i	0.0817033	+	0.0593610i
$735$	−5.15754	−	15.8733i	−0.190239	−	0.585494i
$736$	−14.3895			−0.530404
$737$		0			0
$738$	−14.2415			−0.524237
$739$	6.56174	+	20.1950i	0.241377	+	0.742883i	0.996211	+	0.0869672i	$0.0277175\pi$
$739$	6.56174	+	20.1950i	0.241377	+	0.742883i	−0.754834	+	0.655916i	$0.772282\pi$
$740$	−7.01823	−	5.09905i	−0.257995	−	0.187445i
$741$	−60.1624	+	43.7105i	−2.21012	+	1.60575i
$742$	2.78543	−	8.57266i	0.102256	−	0.314712i
$743$	−9.47222	+	29.1525i	−0.347502	+	1.06950i	0.612729	+	0.790293i	$0.290072\pi$
$743$	−9.47222	+	29.1525i	−0.347502	+	1.06950i	−0.960231	+	0.279208i	$0.909928\pi$
$744$	−21.3857	+	15.5376i	−0.784039	+	0.569637i
$745$	−3.06168	−	2.22444i	−0.112171	−	0.0814972i
$746$	2.12903	+	6.55248i	0.0779493	+	0.239903i
$747$	7.89694			0.288934
$748$		0			0
$749$	−4.79259			−0.175118
$750$	−0.640877	−	1.97242i	−0.0234015	−	0.0720224i
$751$	24.5191	+	17.8142i	0.894716	+	0.650049i	0.937103	−	0.349052i	$-0.113496\pi$
$751$	24.5191	+	17.8142i	0.894716	+	0.650049i	−0.0423872	+	0.999101i	$0.513496\pi$
$752$	−4.87537	+	3.54217i	−0.177787	+	0.129169i
$753$	−14.9707	+	46.0752i	−0.545564	+	1.67907i
$754$	4.68113	−	14.4070i	0.170477	−	0.524673i
$755$	−19.7049	+	14.3165i	−0.717136	+	0.521030i
$756$	−6.50606	−	4.72693i	−0.236623	−	0.171917i
$757$	−10.7752	−	33.1627i	−0.391632	−	1.20532i	−0.931553	−	0.363605i	$-0.881546\pi$
$757$	−10.7752	−	33.1627i	−0.391632	−	1.20532i	0.539921	−	0.841716i	$-0.318454\pi$
$758$	7.23750			0.262878
$759$		0			0
$760$	19.5493			0.709129
$761$	−0.831169	−	2.55807i	−0.0301298	−	0.0927301i	0.934861	−	0.355015i	$-0.115524\pi$
$761$	−0.831169	−	2.55807i	−0.0301298	−	0.0927301i	−0.964991	+	0.262285i	$0.915524\pi$
$762$	19.9830	+	14.5185i	0.723907	+	0.525949i
$763$	4.44592	−	3.23015i	0.160953	−	0.116939i
$764$	2.01236	−	6.19340i	0.0728045	−	0.224069i
$765$	−3.63495	+	11.1872i	−0.131422	+	0.404475i
$766$	−10.7697	+	7.82463i	−0.389124	+	0.282715i
$767$	−8.22103	−	5.97293i	−0.296844	−	0.215670i
$768$	10.3677	+	31.9086i	0.374113	+	1.15140i
$769$	−32.5735			−1.17463			−0.587315	−	0.809359i	$-0.699815\pi$
$769$	−32.5735			−1.17463			−0.587315	+	0.809359i	$0.699815\pi$
$770$		0			0
$771$	−52.0010			−1.87277
$772$	10.1973	+	31.3841i	0.367009	+	1.12954i
$773$	−33.7067	−	24.4893i	−1.21234	−	0.880820i	−0.216903	−	0.976193i	$-0.569595\pi$
$773$	−33.7067	−	24.4893i	−1.21234	−	0.880820i	−0.995442	+	0.0953734i	$0.969595\pi$
$774$	−22.3902	+	16.2675i	−0.804800	+	0.584721i
$775$	−1.13972	+	3.50769i	−0.0409398	+	0.126000i
$776$	1.92429	−	5.92237i	0.0690781	−	0.212601i
$777$	13.9787	−	10.1561i	0.501483	−	0.364348i
$778$	18.6140	+	13.5238i	0.667343	+	0.484853i
$779$	−9.32811	−	28.7090i	−0.334214	−	1.02861i
$780$	−14.1178			−0.505498
$781$		0			0
$782$	−4.34451			−0.155359
$783$	9.85436	+	30.3286i	0.352166	+	1.08386i
$784$	4.95323	+	3.59874i	0.176901	+	0.128526i
$785$	5.85089	−	4.25092i	0.208827	−	0.151722i
$786$	−7.16978	+	22.0663i	−0.255738	+	0.787079i
$787$	−11.1001	+	34.1627i	−0.395677	+	1.21777i	0.532757	+	0.846268i	$0.321156\pi$
$787$	−11.1001	+	34.1627i	−0.395677	+	1.21777i	−0.928433	+	0.371499i	$0.878844\pi$
$788$	−13.2012	+	9.59120i	−0.470272	+	0.341672i
$789$	8.39634	+	6.10030i	0.298918	+	0.217176i
$790$	−2.75314	−	8.47330i	−0.0979524	−	0.301466i
$791$	0.314468			0.0111812
$792$		0			0
$793$	8.55476			0.303789
$794$	2.42103	+	7.45116i	0.0859190	+	0.264432i
$795$	26.9495	+	19.5800i	0.955802	+	0.694430i
$796$	−9.21044	+	6.69178i	−0.326456	+	0.237184i
$797$	−9.80193	+	30.1672i	−0.347202	+	1.06858i	0.613192	+	0.789934i	$0.289885\pi$
$797$	−9.80193	+	30.1672i	−0.347202	+	1.06858i	−0.960394	+	0.278645i	$0.910115\pi$
$798$	−5.06899	+	15.6007i	−0.179440	+	0.552260i
$799$	−11.3365	+	8.23642i	−0.401055	+	0.291383i
$800$	4.74018	+	3.44395i	0.167591	+	0.121762i
$801$	12.3698	+	38.0703i	0.437065	+	1.34515i
$802$	20.3352			0.718061
$803$		0			0
$804$	−25.1617			−0.887384
$805$	−0.782725	−	2.40898i	−0.0275874	−	0.0849054i
$806$	−7.59117	−	5.51531i	−0.267388	−	0.194268i
$807$	−22.6211	+	16.4352i	−0.796301	+	0.578547i
$808$	−5.92680	+	18.2408i	−0.208504	+	0.641709i
$809$	−2.63150	+	8.09893i	−0.0925187	+	0.284743i	−0.986599	−	0.163163i	$-0.947830\pi$
$809$	−2.63150	+	8.09893i	−0.0925187	+	0.284743i	0.894080	+	0.447906i	$0.147830\pi$
$810$	−0.204796	+	0.148793i	−0.00719581	+	0.00522806i
$811$	−7.30566	−	5.30788i	−0.256537	−	0.186385i	0.452082	−	0.891976i	$-0.350681\pi$
$811$	−7.30566	−	5.30788i	−0.256537	−	0.186385i	−0.708619	+	0.705592i	$0.750681\pi$
$812$	2.76287	+	8.50324i	0.0969577	+	0.298405i
$813$	−3.52472			−0.123617
$814$		0			0
$815$	−18.6892			−0.654653
$816$	−2.14900	−	6.61395i	−0.0752301	−	0.231534i
$817$	−47.4585	−	34.4806i	−1.66036	−	1.20632i
$818$	8.57440	−	6.22967i	0.299797	−	0.217815i
$819$	5.39164	−	16.5938i	0.188399	−	0.579833i
$820$	1.77090	−	5.45026i	0.0618424	−	0.190331i
$821$	43.9479	−	31.9300i	1.53379	−	1.11436i	0.579707	−	0.814825i	$-0.303167\pi$
$821$	43.9479	−	31.9300i	1.53379	−	1.11436i	0.954084	−	0.299539i	$-0.0968328\pi$
$822$	7.18323	+	5.21892i	0.250544	+	0.182031i
$823$	5.51887	+	16.9853i	0.192376	+	0.592072i	0.999997	+	0.00237039i	$0.000754519\pi$
$823$	5.51887	+	16.9853i	0.192376	+	0.592072i	−0.807621	+	0.589701i	$0.799245\pi$
$824$	−24.1723			−0.842083
$825$		0			0
$826$	−2.24151			−0.0779920
$827$	−16.0533	−	49.4068i	−0.558226	−	1.71804i	−0.687267	−	0.726404i	$-0.741190\pi$
$827$	−16.0533	−	49.4068i	−0.558226	−	1.71804i	0.129041	−	0.991639i	$-0.458810\pi$
$828$	14.1880	+	10.3082i	0.493068	+	0.358235i
$829$	15.9749	−	11.6064i	0.554830	−	0.403107i	−0.274733	−	0.961520i	$-0.588590\pi$
$829$	15.9749	−	11.6064i	0.554830	−	0.403107i	0.829563	+	0.558413i	$0.188590\pi$
$830$	0.366993	−	1.12949i	0.0127385	−	0.0392051i
$831$	7.03163	−	21.6411i	0.243925	−	0.750723i
$832$	−6.30387	+	4.58003i	−0.218547	+	0.158784i
$833$	11.5175	+	8.36796i	0.399058	+	0.289933i
$834$	−3.81526	−	11.7422i	−0.132112	−	0.406598i
$835$	−7.85328			−0.271774
$836$		0			0
$837$	19.7528			0.682757
$838$	7.17353	+	22.0779i	0.247806	+	0.762667i
$839$	3.33032	+	2.41962i	0.114975	+	0.0835344i	0.643787	−	0.765205i	$-0.277362\pi$
$839$	3.33032	+	2.41962i	0.114975	+	0.0835344i	−0.528812	+	0.848739i	$0.677362\pi$
$840$	−5.98037	+	4.34499i	−0.206342	+	0.149916i
$841$	1.99435	−	6.13799i	0.0687708	−	0.211655i
$842$	−6.05673	+	18.6407i	−0.208729	+	0.642400i
$843$	57.7072	−	41.9267i	1.98754	−	1.44403i
$844$	−26.8158	−	19.4828i	−0.923038	−	0.670627i
$845$	0.341302	+	1.05042i	0.0117411	+	0.0361355i
$846$	−21.1400			−0.726807
$847$		0			0
$848$	−12.2198			−0.419630
$849$	17.7608	+	54.6620i	0.609548	+	1.87600i
$850$	1.43117	+	1.03980i	0.0490886	+	0.0356650i
$851$	−11.8388	+	8.60141i	−0.405830	+	0.294853i
$852$	2.55909	−	7.87606i	0.0876729	−	0.269829i
$853$	1.70047	−	5.23352i	0.0582231	−	0.179192i	−0.917715	−	0.397239i	$-0.869968\pi$
$853$	1.70047	−	5.23352i	0.0582231	−	0.179192i	0.975938	+	0.218046i	$0.0699684\pi$
$854$	1.52664	−	1.10917i	0.0522406	−	0.0379550i
$855$	−30.4308	−	22.1093i	−1.04071	−	0.756121i
$856$	−3.66048	−	11.2658i	−0.125113	−	0.385058i
$857$	−26.9281			−0.919847			−0.459924	−	0.887959i	$-0.652123\pi$
$857$	−26.9281			−0.919847			−0.459924	+	0.887959i	$0.652123\pi$
$858$		0			0
$859$	19.1519			0.653456			0.326728	−	0.945118i	$-0.394054\pi$
$859$	19.1519			0.653456			0.326728	+	0.945118i	$0.394054\pi$
$860$	−3.44142	−	10.5916i	−0.117352	−	0.361171i
$861$	9.23437	+	6.70916i	0.314706	+	0.228648i
$862$	−2.30870	+	1.67737i	−0.0786346	+	0.0571314i
$863$	1.53319	−	4.71867i	0.0521904	−	0.160625i	−0.921564	−	0.388226i	$-0.873088\pi$
$863$	1.53319	−	4.71867i	0.0521904	−	0.160625i	0.973755	+	0.227600i	$0.0730880\pi$
$864$	9.69693	−	29.8441i	0.329896	−	1.01532i
$865$	9.06478	−	6.58595i	0.308212	−	0.223929i
$866$	23.9534	+	17.4031i	0.813969	+	0.591383i
$867$	9.77298	+	30.0781i	0.331908	+	1.02151i
$868$	5.53810			0.187975
$869$		0			0
$870$	12.3488			0.418663
$871$	−6.55147	−	20.1633i	−0.221988	−	0.683209i
$872$	10.9887	+	7.98378i	0.372125	+	0.270365i
$873$	−9.69327	+	7.04257i	−0.328068	+	0.238355i
$874$	4.29302	−	13.2126i	0.145214	−	0.446922i
$875$	−0.318714	+	0.980901i	−0.0107745	+	0.0331605i
$876$	2.73491	−	1.98703i	0.0924040	−	0.0671354i
$877$	22.0096	+	15.9909i	0.743211	+	0.539974i	0.893715	−	0.448635i	$-0.148090\pi$
$877$	22.0096	+	15.9909i	0.743211	+	0.539974i	−0.150504	+	0.988609i	$0.548090\pi$
$878$	−0.233269	−	0.717928i	−0.00787245	−	0.0242289i
$879$	−7.16686			−0.241732
$880$		0			0
$881$	10.3570			0.348935			0.174467	−	0.984663i	$-0.444180\pi$
$881$	10.3570			0.348935			0.174467	+	0.984663i	$0.444180\pi$
$882$	6.63694	+	20.4264i	0.223477	+	0.687792i
$883$	−5.98260	−	4.34661i	−0.201330	−	0.146275i	0.482552	−	0.875867i	$-0.339710\pi$
$883$	−5.98260	−	4.34661i	−0.201330	−	0.146275i	−0.683882	+	0.729592i	$0.739710\pi$
$884$	9.74238	−	7.07826i	0.327672	−	0.238067i
$885$	2.55980	−	7.87826i	0.0860468	−	0.264825i
$886$	3.66370	−	11.2757i	0.123084	−	0.378815i
$887$	14.6101	−	10.6148i	0.490558	−	0.356411i	−0.314841	−	0.949144i	$-0.601951\pi$
$887$	14.6101	−	10.6148i	0.490558	−	0.356411i	0.805399	+	0.592733i	$0.201951\pi$
$888$	34.5503	+	25.1023i	1.15943	+	0.842377i
$889$	−3.79587	−	11.6825i	−0.127309	−	0.391818i
$890$	6.02000			0.201791
$891$		0			0
$892$	23.3563			0.782027
$893$	−13.8466	−	42.6153i	−0.463357	−	1.42607i
$894$	6.34968	+	4.61331i	0.212365	+	0.154292i
$895$	1.18491	−	0.860888i	0.0396072	−	0.0287763i
$896$	3.20368	−	9.85991i	0.107027	−	0.329396i
$897$	−7.35919	+	22.6493i	−0.245716	+	0.756237i
$898$	21.3893	−	15.5402i	0.713769	−	0.518583i
$899$	−17.7666	−	12.9082i	−0.592549	−	0.430512i
$900$	−2.20667	−	6.79144i	−0.0735558	−	0.226381i
$901$	−28.4141			−0.946612
$902$		0			0
$903$	22.1817			0.738160
$904$	0.240184	+	0.739212i	0.00798841	+	0.0245858i
$905$	7.51496	+	5.45994i	0.249806	+	0.181494i
$906$	40.8665	−	29.6912i	1.35770	−	0.986425i
$907$	8.12624	−	25.0100i	0.269827	−	0.830443i	−0.720715	−	0.693232i	$-0.756186\pi$
$907$	8.12624	−	25.0100i	0.269827	−	0.830443i	0.990542	−	0.137211i	$-0.0438138\pi$
$908$	10.8677	−	33.4474i	0.360658	−	1.10999i
$909$	29.8551	−	21.6910i	0.990233	−	0.719446i
$910$	−2.12282	−	1.54232i	−0.0703707	−	0.0511273i
$911$	8.85298	+	27.2467i	0.293312	+	0.902723i	0.983783	+	0.179362i	$0.0574035\pi$
$911$	8.85298	+	27.2467i	0.293312	+	0.902723i	−0.690471	+	0.723360i	$0.742597\pi$
$912$	22.2379			0.736371
$913$		0			0
$914$	18.5535			0.613694
$915$	2.15499	+	6.63239i	0.0712419	+	0.219260i
$916$	−17.6844	−	12.8485i	−0.584308	−	0.424525i
$917$	9.33485	−	6.78217i	0.308264	−	0.223967i
$918$	2.92772	−	9.01059i	0.0966291	−	0.297394i
$919$	12.0074	−	36.9550i	0.396088	−	1.21903i	−0.532023	−	0.846730i	$-0.678568\pi$
$919$	12.0074	−	36.9550i	0.396088	−	1.21903i	0.928111	−	0.372303i	$-0.121432\pi$
$920$	5.06489	−	3.67986i	0.166985	−	0.121321i
$921$	20.4549	+	14.8613i	0.674011	+	0.489697i
$922$	−1.51726	−	4.66965i	−0.0499684	−	0.153787i
$923$	6.97781			0.229677
$924$		0			0
$925$	5.95858			0.195917
$926$	−8.83806	−	27.2007i	−0.290437	−	0.893872i
$927$	37.6270	+	27.3376i	1.23583	+	0.897886i
$928$	−28.2245	+	20.5063i	−0.926516	+	0.673153i
$929$	2.29331	−	7.05810i	0.0752412	−	0.231569i	−0.906362	−	0.422503i	$-0.861152\pi$
$929$	2.29331	−	7.05810i	0.0752412	−	0.231569i	0.981603	+	0.190934i	$0.0611517\pi$
$930$	2.36368	−	7.27467i	0.0775082	−	0.238546i
$931$	−36.8297	+	26.7583i	−1.20704	+	0.876969i
$932$	13.4579	+	9.77773i	0.440828	+	0.320280i
$933$	17.4834	+	53.8084i	0.572382	+	1.76161i
$934$	−16.6334			−0.544260
$935$		0			0
$936$	43.1245			1.40957
$937$	−4.61547	−	14.2049i	−0.150781	−	0.464055i	0.846928	−	0.531707i	$-0.178449\pi$
$937$	−4.61547	−	14.2049i	−0.150781	−	0.464055i	−0.997709	+	0.0676518i	$0.978449\pi$
$938$	−3.78343	−	2.74882i	−0.123533	−	0.0897522i
$939$	16.1606	−	11.7414i	0.527383	−	0.383166i
$940$	2.62870	−	8.09031i	0.0857388	−	0.263877i
$941$	−16.1742	+	49.7791i	−0.527265	+	1.62275i	0.232529	+	0.972589i	$0.425300\pi$
$941$	−16.1742	+	49.7791i	−0.527265	+	1.62275i	−0.759794	+	0.650164i	$0.774700\pi$
$942$	−12.1343	+	8.81607i	−0.395356	+	0.287243i
$943$	−7.82077	−	5.68212i	−0.254679	−	0.185035i
$944$	0.939026	+	2.89003i	0.0305627	+	0.0940623i
$945$	5.52373			0.179687
$946$		0			0
$947$	−3.69553			−0.120088			−0.0600442	−	0.998196i	$-0.519124\pi$
$947$	−3.69553			−0.120088			−0.0600442	+	0.998196i	$0.519124\pi$
$948$	−15.2777	−	47.0201i	−0.496198	−	1.52714i
$949$	2.30441	+	1.67425i	0.0748043	+	0.0543485i
$950$	−4.57646	+	3.32500i	−0.148480	+	0.107877i
$951$	−1.99240	+	6.13199i	−0.0646081	+	0.198843i
$952$	1.94847	−	5.99677i	0.0631502	−	0.194356i
$953$	−34.9112	+	25.3645i	−1.13088	+	0.821635i	−0.985823	−	0.167787i	$-0.946338\pi$
$953$	−34.9112	+	25.3645i	−1.13088	+	0.821635i	−0.145061	+	0.989423i	$0.546338\pi$
$954$	−34.6798	−	25.1963i	−1.12280	−	0.815762i
$955$	1.38222	+	4.25404i	0.0447276	+	0.137657i
$956$	−39.9011			−1.29049
$957$		0			0
$958$	1.20373			0.0388907
$959$	−1.36449	−	4.19947i	−0.0440617	−	0.135608i
$960$	−5.13881	−	3.73357i	−0.165854	−	0.120500i
$961$	14.0746	−	10.2258i	0.454020	−	0.329865i
$962$	−4.68448	+	14.4173i	−0.151034	+	0.464834i
$963$	−7.04308	+	21.6764i	−0.226960	+	0.698511i
$964$	12.8840	−	9.36079i	0.414966	−	0.301491i
$965$	−18.3372	−	13.3227i	−0.590295	−	0.428874i
$966$	1.62331	+	4.99604i	0.0522291	+	0.160745i
$967$	−29.2144			−0.939471			−0.469736	−	0.882807i	$-0.655651\pi$
$967$	−29.2144			−0.939471			−0.469736	+	0.882807i	$0.655651\pi$
$968$		0			0
$969$	51.7087			1.66112
$970$	0.556816	+	1.71370i	0.0178783	+	0.0550237i
$971$	21.3618	+	15.5203i	0.685533	+	0.498069i	0.875189	−	0.483782i	$-0.160737\pi$
$971$	21.3618	+	15.5203i	0.685533	+	0.498069i	−0.189656	+	0.981851i	$0.560737\pi$
$972$	17.7879	−	12.9237i	0.570547	−	0.414526i
$973$	−1.89737	+	5.83949i	−0.0608268	+	0.187206i
$974$	−0.239409	+	0.736824i	−0.00767115	+	0.0236094i
$975$	7.84507	−	5.69978i	0.251243	−	0.182539i
$976$	−2.06963	−	1.50367i	−0.0662472	−	0.0481314i
$977$	−4.89588	−	15.0680i	−0.156633	−	0.482067i	0.841690	−	0.539961i	$-0.181561\pi$
$977$	−4.89588	−	15.0680i	−0.156633	−	0.482067i	−0.998323	+	0.0578948i	$0.981561\pi$
$978$	38.7598			1.23940
$979$		0			0
$980$	−8.64252			−0.276075
$981$	−8.07600	−	24.8554i	−0.257847	−	0.793571i
$982$	−8.30342	−	6.03279i	−0.264973	−	0.192514i
$983$	−28.3997	+	20.6336i	−0.905809	+	0.658109i	−0.939951	−	0.341308i	$-0.889130\pi$
$983$	−28.3997	+	20.6336i	−0.905809	+	0.658109i	0.0341426	+	0.999417i	$0.489130\pi$
$984$	−8.71801	+	26.8313i	−0.277920	+	0.855350i
$985$	3.46345	−	10.6594i	0.110355	−	0.339637i
$986$	−8.52162	+	6.19132i	−0.271384	+	0.197172i
$987$	13.7074	+	9.95901i	0.436312	+	0.316999i
$988$	11.8995	+	36.6230i	0.378574	+	1.16513i
$989$	−18.7861			−0.597363
$990$		0			0
$991$	18.9700			0.602600			0.301300	−	0.953529i	$-0.402579\pi$
$991$	18.9700			0.602600			0.301300	+	0.953529i	$0.402579\pi$
$992$	6.67782	+	20.5522i	0.212021	+	0.652533i
$993$	35.0177	+	25.4419i	1.11125	+	0.807373i
$994$	1.24523	−	0.904710i	0.0394962	−	0.0286957i
$995$	2.41645	−	7.43707i	0.0766066	−	0.235771i
$996$	2.03652	−	6.26776i	0.0645295	−	0.198601i
$997$	−24.3795	+	17.7127i	−0.772106	+	0.560968i	−0.902599	−	0.430481i	$-0.858344\pi$
$997$	−24.3795	+	17.7127i	−0.772106	+	0.560968i	0.130494	+	0.991449i	$0.458344\pi$
$998$	10.3642	+	7.53000i	0.328072	+	0.238358i
$999$	−9.86141	−	30.3503i	−0.312001	−	0.960241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.m.511.1		8
11.2	odd	10		605.2.g.e.251.2		8
11.3	even	5		605.2.a.j.1.2		4
11.4	even	5		55.2.g.b.36.2	yes	8
11.5	even	5		55.2.g.b.26.2	✓	8
11.6	odd	10		605.2.g.k.81.1		8
11.7	odd	10		605.2.g.k.366.1		8
11.8	odd	10		605.2.a.k.1.3		4
11.9	even	5	inner	605.2.g.m.251.1		8
11.10	odd	2		605.2.g.e.511.2		8
33.5	odd	10		495.2.n.e.136.1		8
33.8	even	10		5445.2.a.bi.1.2		4
33.14	odd	10		5445.2.a.bp.1.3		4
33.26	odd	10		495.2.n.e.91.1		8
44.3	odd	10		9680.2.a.cn.1.4		4
44.15	odd	10		880.2.bo.h.641.2		8
44.19	even	10		9680.2.a.cm.1.4		4
44.27	odd	10		880.2.bo.h.81.2		8
55.4	even	10		275.2.h.a.201.1		8
55.14	even	10		3025.2.a.bd.1.3		4
55.19	odd	10		3025.2.a.w.1.2		4
55.27	odd	20		275.2.z.a.224.2		16
55.37	odd	20		275.2.z.a.124.3		16
55.38	odd	20		275.2.z.a.224.3		16
55.48	odd	20		275.2.z.a.124.2		16
55.49	even	10		275.2.h.a.26.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.2	✓	8	11.5	even	5
55.2.g.b.36.2	yes	8	11.4	even	5
275.2.h.a.26.1		8	55.49	even	10
275.2.h.a.201.1		8	55.4	even	10
275.2.z.a.124.2		16	55.48	odd	20
275.2.z.a.124.3		16	55.37	odd	20
275.2.z.a.224.2		16	55.27	odd	20
275.2.z.a.224.3		16	55.38	odd	20
495.2.n.e.91.1		8	33.26	odd	10
495.2.n.e.136.1		8	33.5	odd	10
605.2.a.j.1.2		4	11.3	even	5
605.2.a.k.1.3		4	11.8	odd	10
605.2.g.e.251.2		8	11.2	odd	10
605.2.g.e.511.2		8	11.10	odd	2
605.2.g.k.81.1		8	11.6	odd	10
605.2.g.k.366.1		8	11.7	odd	10
605.2.g.m.251.1		8	11.9	even	5	inner
605.2.g.m.511.1		8	1.1	even	1	trivial
880.2.bo.h.81.2		8	44.27	odd	10
880.2.bo.h.641.2		8	44.15	odd	10
3025.2.a.w.1.2		4	55.19	odd	10
3025.2.a.bd.1.3		4	55.14	even	10
5445.2.a.bi.1.2		4	33.8	even	10
5445.2.a.bp.1.3		4	33.14	odd	10
9680.2.a.cm.1.4		4	44.19	even	10
9680.2.a.cn.1.4		4	44.3	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.227943 - 0.701538i) q^{2} +(2.27460 + 1.65259i) q^{3} +(1.17784 - 0.855749i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.640877 - 1.97242i) q^{6} +(-0.834404 + 0.606230i) q^{7} +(-2.06235 - 1.49838i) q^{8} +(1.51569 + 4.66481i) q^{9} +0.737640 q^{10} +4.09331 q^{12} +(1.06580 + 3.28018i) q^{13} +(0.615490 + 0.447180i) q^{14} +(-2.27460 + 1.65259i) q^{15} +(0.318714 - 0.980901i) q^{16} +(0.741089 - 2.28084i) q^{17} +(2.92705 - 2.12663i) q^{18} +(6.20420 + 4.50761i) q^{19} +(0.449894 + 1.38463i) q^{20} -2.89979 q^{21} +2.45589 q^{23} +(-2.21480 - 6.81645i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(2.05823 - 1.49539i) q^{26} +(-1.65499 + 5.09355i) q^{27} +(-0.464011 + 1.42808i) q^{28} +(4.81714 - 3.49986i) q^{29} +(1.67784 + 1.21902i) q^{30} +(-1.13972 - 3.50769i) q^{31} -5.85919 q^{32} -1.76902 q^{34} +(-0.318714 - 0.980901i) q^{35} +(5.77714 + 4.19734i) q^{36} +(-4.82059 + 3.50236i) q^{37} +(1.74805 - 5.37996i) q^{38} +(-2.99655 + 9.22244i) q^{39} +(2.06235 - 1.49838i) q^{40} +(-3.18450 - 2.31367i) q^{41} +(0.660987 + 2.03431i) q^{42} -7.64941 q^{43} -4.90488 q^{45} +(-0.559803 - 1.72290i) q^{46} +(-4.72704 - 3.43439i) q^{47} +(2.34598 - 1.70445i) q^{48} +(-1.83440 + 5.64571i) q^{49} +(-0.227943 + 0.701538i) q^{50} +(5.45498 - 3.96328i) q^{51} +(4.06235 + 2.95147i) q^{52} +(-3.66124 - 11.2681i) q^{53} +3.95056 q^{54} +2.62920 q^{56} +(6.66281 + 20.5060i) q^{57} +(-3.55332 - 2.58164i) q^{58} +(-2.38361 + 1.73179i) q^{59} +(-1.26490 + 3.89297i) q^{60} +(0.766476 - 2.35897i) q^{61} +(-2.20098 + 1.59911i) q^{62} +(-4.09265 - 2.97348i) q^{63} +(0.698136 + 2.14864i) q^{64} -3.44899 q^{65} -6.14702 q^{67} +(-1.07894 - 3.32064i) q^{68} +(5.58616 + 4.05858i) q^{69} +(-0.615490 + 0.447180i) q^{70} +(0.625187 - 1.92413i) q^{71} +(3.86380 - 11.8916i) q^{72} +(0.668140 - 0.485432i) q^{73} +(3.55586 + 2.58348i) q^{74} +(-0.868820 - 2.67395i) q^{75} +11.1649 q^{76} +7.15293 q^{78} +(-3.73236 - 11.4870i) q^{79} +(0.834404 + 0.606230i) q^{80} +(-0.277637 + 0.201715i) q^{81} +(-0.897243 + 2.76143i) q^{82} +(0.497523 - 1.53122i) q^{83} +(-3.41548 + 2.48149i) q^{84} +(1.94020 + 1.40964i) q^{85} +(1.74363 + 5.36635i) q^{86} +16.7409 q^{87} +8.16116 q^{89} +(1.11803 + 3.44095i) q^{90} +(-2.87785 - 2.09088i) q^{91} +(2.89263 - 2.10162i) q^{92} +(3.20438 - 9.86208i) q^{93} +(-1.33186 + 4.09904i) q^{94} +(-6.20420 + 4.50761i) q^{95} +(-13.3273 - 9.68286i) q^{96} +(0.754861 + 2.32322i) q^{97} +4.37882 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - q^{8} + 5 q^{9} + 2 q^{10} + 16 q^{12} + 3 q^{13} + 14 q^{14} - 5 q^{15} - q^{16} + 12 q^{17} + 10 q^{18} + 5 q^{19} + 2 q^{20} - 20 q^{21}+ \cdots + 16 q^{98}+O(q^{100}) \) 8 * q + 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - q^8 + 5 * q^9 + 2 * q^10 + 16 * q^12 + 3 * q^13 + 14 * q^14 - 5 * q^15 - q^16 + 12 * q^17 + 10 * q^18 + 5 * q^19 + 2 * q^20 - 20 * q^21 + 10 * q^23 - 2 * q^24 - 2 * q^25 + 5 * q^26 + 5 * q^27 + 19 * q^28 + 21 * q^29 + 7 * q^30 + 15 * q^31 + 16 * q^32 + 4 * q^34 + q^35 + 15 * q^36 - 31 * q^37 - 20 * q^38 - 14 * q^39 + q^40 + 3 * q^41 - 21 * q^42 - 38 * q^43 - 7 * q^46 - 5 * q^47 + 5 * q^48 - 4 * q^49 + 3 * q^50 + 6 * q^51 + 17 * q^52 - 2 * q^53 + 16 * q^54 + 22 * q^56 + 40 * q^57 + 2 * q^58 + 18 * q^59 + 4 * q^60 + 6 * q^61 - 5 * q^62 - 30 * q^63 + 29 * q^64 + 2 * q^65 - 38 * q^67 - 14 * q^68 + 9 * q^69 - 14 * q^70 + 15 * q^71 + 5 * q^72 - 2 * q^73 - 20 * q^74 - 5 * q^75 - 16 * q^78 - 3 * q^79 - 4 * q^80 - 12 * q^81 - 22 * q^82 - 38 * q^83 - 17 * q^84 + 13 * q^85 + 2 * q^86 + 38 * q^87 - 16 * q^89 - 36 * q^91 + q^92 + 40 * q^93 - 18 * q^94 - 5 * q^95 - 17 * q^96 - 56 * q^97 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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