LMFDB - Embedded newform 605.2.m.c.457.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(112,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.112"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,6,0,-2,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			457.3
Character	$\chi$	$=$	605.457
Dual form			605.2.m.c.233.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.435114 + 0.221702i) q^{2} +(1.12533 - 0.178235i) q^{3} +(-1.03540 - 1.42510i) q^{4} +(-1.14075 + 1.92320i) q^{5} +(0.529164 + 0.171936i) q^{6} +(-0.456227 + 2.88051i) q^{7} +(-0.287355 - 1.81429i) q^{8} +(-1.61856 + 0.525902i) q^{9} +(-0.922733 + 0.583903i) q^{10} +(-1.41917 - 1.41917i) q^{12} +(-1.32861 + 2.60754i) q^{13} +(-0.837124 + 1.15220i) q^{14} +(-0.940946 + 2.36756i) q^{15} +(-0.811484 + 2.49749i) q^{16} +(2.39167 + 4.69392i) q^{17} +(-0.820851 - 0.130010i) q^{18} +(3.31646 + 2.40955i) q^{19} +(3.92189 - 0.365584i) q^{20} +3.32285i q^{21} +(-2.12046 + 2.12046i) q^{23} +(-0.646740 - 1.99046i) q^{24} +(-2.39737 - 4.38778i) q^{25} +(-1.15619 + 0.840024i) q^{26} +(-4.77322 + 2.43208i) q^{27} +(4.57740 - 2.33230i) q^{28} +(2.13957 - 1.55449i) q^{29} +(-0.934311 + 0.821549i) q^{30} +(-2.08297 - 6.41071i) q^{31} +(-3.50456 + 3.50456i) q^{32} +2.57262i q^{34} +(-5.01934 - 4.16336i) q^{35} +(2.42532 + 1.76210i) q^{36} +(-1.14895 - 0.181976i) q^{37} +(0.908835 + 1.78369i) q^{38} +(-1.03037 + 3.17117i) q^{39} +(3.81703 + 1.51701i) q^{40} +(2.08980 - 2.87636i) q^{41} +(-0.736681 + 1.44582i) q^{42} +(5.07292 + 5.07292i) q^{43} +(0.834964 - 3.71273i) q^{45} +(-1.39275 + 0.452533i) q^{46} +(0.575943 + 3.63636i) q^{47} +(-0.468049 + 2.95515i) q^{48} +(-1.43178 - 0.465213i) q^{49} +(-0.0703494 - 2.44068i) q^{50} +(3.52805 + 4.85594i) q^{51} +(5.09166 - 0.806440i) q^{52} +(1.31668 + 0.670880i) q^{53} -2.61609 q^{54} +5.35716 q^{56} +(4.16159 + 2.12044i) q^{57} +(1.27559 - 0.202033i) q^{58} +(-0.943564 - 1.29870i) q^{59} +(4.34827 - 1.11042i) q^{60} +(-6.59851 - 2.14398i) q^{61} +(0.514937 - 3.25119i) q^{62} +(-0.776433 - 4.90220i) q^{63} +(2.69314 - 0.875053i) q^{64} +(-3.49920 - 5.52974i) q^{65} +(1.31471 + 1.31471i) q^{67} +(4.21298 - 8.26845i) q^{68} +(-2.00829 + 2.76417i) q^{69} +(-1.26096 - 2.92433i) q^{70} +(0.887847 - 2.73251i) q^{71} +(1.41924 + 2.78541i) q^{72} +(-14.6197 - 2.31553i) q^{73} +(-0.459581 - 0.333905i) q^{74} +(-3.47990 - 4.51043i) q^{75} -7.22113i q^{76} +(-1.15138 + 1.15138i) q^{78} +(4.71123 + 14.4997i) q^{79} +(-3.87746 - 4.40966i) q^{80} +(-0.807503 + 0.586685i) q^{81} +(1.54699 - 0.788233i) q^{82} +(5.95431 - 3.03387i) q^{83} +(4.73540 - 3.44047i) q^{84} +(-11.7556 - 0.754947i) q^{85} +(1.08262 + 3.33197i) q^{86} +(2.13066 - 2.13066i) q^{87} -11.1726i q^{89} +(1.18642 - 1.43035i) q^{90} +(-6.90490 - 5.01670i) q^{91} +(5.21741 + 0.826356i) q^{92} +(-3.48665 - 6.84294i) q^{93} +(-0.555586 + 1.70992i) q^{94} +(-8.41729 + 3.62950i) q^{95} +(-3.31916 + 4.56843i) q^{96} +(-4.57097 + 8.97103i) q^{97} +(-0.519848 - 0.519848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{3} - 2 q^{5} - 20 q^{7} + 20 q^{8} + 12 q^{12} + 20 q^{13} + 4 q^{15} + 12 q^{16} - 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} + 20 q^{28} - 40 q^{30} + 32 q^{31}+ \cdots - 38 q^{97}+O(q^{100}) $ 32 * q + 6 * q^3 - 2 * q^5 - 20 * q^7 + 20 * q^8 + 12 * q^12 + 20 * q^13 + 4 * q^15 + 12 * q^16 - 30 * q^18 + 16 * q^20 - 24 * q^23 - 24 * q^25 - 20 * q^26 + 24 * q^27 + 20 * q^28 - 40 * q^30 + 32 * q^31 - 30 * q^35 - 36 * q^36 - 8 * q^37 + 10 * q^38 + 50 * q^40 - 20 * q^42 - 28 * q^45 - 20 * q^46 + 42 * q^47 + 26 * q^48 - 80 * q^50 + 100 * q^51 + 20 * q^52 - 34 * q^53 - 80 * q^56 + 40 * q^57 + 90 * q^58 - 86 * q^60 - 10 * q^62 + 10 * q^63 - 8 * q^67 + 70 * q^68 + 10 * q^70 - 36 * q^71 + 70 * q^72 - 30 * q^73 + 4 * q^75 + 60 * q^78 - 102 * q^80 + 8 * q^81 + 20 * q^82 + 60 * q^83 - 60 * q^85 - 80 * q^86 - 130 * q^90 - 60 * q^91 + 42 * q^92 - 8 * q^93 + 30 * q^95 - 38 * q^97

Character values

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

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.435114	+	0.221702i	0.307672	+	0.156767i	0.601009	−	0.799243i	$-0.294766\pi$
$2$	0.435114	+	0.221702i	0.307672	+	0.156767i	−0.293337	+	0.956009i	$0.594766\pi$
$3$	1.12533	−	0.178235i	0.649712	−	0.102904i	0.177125	−	0.984188i	$-0.443320\pi$
$3$	1.12533	−	0.178235i	0.649712	−	0.102904i	0.472587	+	0.881284i	$0.343320\pi$
$4$	−1.03540	−	1.42510i	−0.517699	−	0.712552i
$5$	−1.14075	+	1.92320i	−0.510160	+	0.860079i
$5$	−1.14075	+	1.92320i	−0.510160	+	0.860079i
$6$	0.529164	+	0.171936i	0.216030	+	0.0701924i
$7$	−0.456227	+	2.88051i	−0.172438	+	1.08873i	0.737914	+	0.674894i	$0.235811\pi$
$7$	−0.456227	+	2.88051i	−0.172438	+	1.08873i	−0.910352	+	0.413835i	$0.864189\pi$
$8$	−0.287355	−	1.81429i	−0.101595	−	0.641447i
$9$	−1.61856	+	0.525902i	−0.539520	+	0.175301i
$10$	−0.922733	+	0.583903i	−0.291794	+	0.184646i
$11$		0			0
$11$		0			0
$12$	−1.41917	−	1.41917i	−0.409680	−	0.409680i
$13$	−1.32861	+	2.60754i	−0.368490	+	0.723203i	−0.998577	−	0.0533216i	$-0.983019\pi$
$13$	−1.32861	+	2.60754i	−0.368490	+	0.723203i	0.630087	+	0.776524i	$0.283019\pi$
$14$	−0.837124	+	1.15220i	−0.223731	+	0.307939i
$15$	−0.940946	+	2.36756i	−0.242951	+	0.611302i
$16$	−0.811484	+	2.49749i	−0.202871	+	0.624373i
$17$	2.39167	+	4.69392i	0.580065	+	1.13844i	0.975511	+	0.219952i	$0.0705902\pi$
$17$	2.39167	+	4.69392i	0.580065	+	1.13844i	−0.395446	+	0.918489i	$0.629410\pi$
$18$	−0.820851	−	0.130010i	−0.193476	−	0.0306437i
$19$	3.31646	+	2.40955i	0.760847	+	0.552788i	0.899170	−	0.437599i	$-0.144171\pi$
$19$	3.31646	+	2.40955i	0.760847	+	0.552788i	−0.138323	+	0.990387i	$0.544171\pi$
$20$	3.92189	−	0.365584i	0.876960	−	0.0817470i
$21$			3.32285i			0.725105i
$22$		0			0
$23$	−2.12046	+	2.12046i	−0.442147	+	0.442147i	−0.892733	−	0.450586i	$-0.851215\pi$
$23$	−2.12046	+	2.12046i	−0.442147	+	0.442147i	0.450586	+	0.892733i	$0.351215\pi$
$24$	−0.646740	−	1.99046i	−0.132015	−	0.406301i
$25$	−2.39737	−	4.38778i	−0.479473	−	0.877556i
$26$	−1.15619	+	0.840024i	−0.226748	+	0.164742i
$27$	−4.77322	+	2.43208i	−0.918607	+	0.468054i
$28$	4.57740	−	2.33230i	0.865047	−	0.440763i
$29$	2.13957	−	1.55449i	0.397307	−	0.288661i	−0.371136	−	0.928579i	$-0.621032\pi$
$29$	2.13957	−	1.55449i	0.397307	−	0.288661i	0.768443	+	0.639918i	$0.221032\pi$
$30$	−0.934311	+	0.821549i	−0.170581	+	0.149994i
$31$	−2.08297	−	6.41071i	−0.374112	−	1.15140i	−0.944076	−	0.329728i	$-0.893043\pi$
$31$	−2.08297	−	6.41071i	−0.374112	−	1.15140i	0.569964	−	0.821670i	$-0.306957\pi$
$32$	−3.50456	+	3.50456i	−0.619524	+	0.619524i
$33$		0			0
$34$			2.57262i			0.441201i
$35$	−5.01934	−	4.16336i	−0.848423	−	0.703736i
$36$	2.42532	+	1.76210i	0.404220	+	0.293683i
$37$	−1.14895	−	0.181976i	−0.188887	−	0.0299167i	0.0612742	−	0.998121i	$-0.480484\pi$
$37$	−1.14895	−	0.181976i	−0.188887	−	0.0299167i	−0.250161	+	0.968204i	$0.580484\pi$
$38$	0.908835	+	1.78369i	0.147433	+	0.289353i
$39$	−1.03037	+	3.17117i	−0.164992	+	0.507793i
$40$	3.81703	+	1.51701i	0.603525	+	0.239861i
$41$	2.08980	−	2.87636i	0.326372	−	0.449212i	−0.614028	−	0.789285i	$-0.710452\pi$
$41$	2.08980	−	2.87636i	0.326372	−	0.449212i	0.940399	+	0.340073i	$0.110452\pi$
$42$	−0.736681	+	1.44582i	−0.113672	+	0.223094i
$43$	5.07292	+	5.07292i	0.773613	+	0.773613i	0.978736	−	0.205123i	$-0.0657595\pi$
$43$	5.07292	+	5.07292i	0.773613	+	0.773613i	−0.205123	+	0.978736i	$0.565759\pi$
$44$		0			0
$45$	0.834964	−	3.71273i	0.124469	−	0.553461i
$46$	−1.39275	+	0.452533i	−0.205350	+	0.0667224i
$47$	0.575943	+	3.63636i	0.0840099	+	0.530417i	0.993421	+	0.114519i	$0.0365328\pi$
$47$	0.575943	+	3.63636i	0.0840099	+	0.530417i	−0.909411	+	0.415898i	$0.863467\pi$
$48$	−0.468049	+	2.95515i	−0.0675571	+	0.426539i
$49$	−1.43178	−	0.465213i	−0.204540	−	0.0664590i
$50$	−0.0703494	−	2.44068i	−0.00994891	−	0.345165i
$51$	3.52805	+	4.85594i	0.494026	+	0.679968i
$52$	5.09166	−	0.806440i	0.706086	−	0.111833i
$53$	1.31668	+	0.670880i	0.180859	+	0.0921524i	0.542076	−	0.840330i	$-0.317639\pi$
$53$	1.31668	+	0.670880i	0.180859	+	0.0921524i	−0.361217	+	0.932482i	$0.617639\pi$
$54$	−2.61609			−0.356005
$55$		0			0
$56$	5.35716			0.715881
$57$	4.16159	+	2.12044i	0.551216	+	0.280859i
$58$	1.27559	−	0.202033i	0.167493	−	0.0265282i
$59$	−0.943564	−	1.29870i	−0.122842	−	0.169077i	0.743167	−	0.669106i	$-0.233323\pi$
$59$	−0.943564	−	1.29870i	−0.122842	−	0.169077i	−0.866009	+	0.500029i	$0.833323\pi$
$60$	4.34827	−	1.11042i	0.561360	−	0.143355i
$61$	−6.59851	−	2.14398i	−0.844852	−	0.274509i	−0.145564	−	0.989349i	$-0.546500\pi$
$61$	−6.59851	−	2.14398i	−0.844852	−	0.274509i	−0.699288	+	0.714840i	$0.746500\pi$
$62$	0.514937	−	3.25119i	0.0653971	−	0.412901i
$63$	−0.776433	−	4.90220i	−0.0978213	−	0.617619i
$64$	2.69314	−	0.875053i	0.336642	−	0.109382i
$65$	−3.49920	−	5.52974i	−0.434023	−	0.685880i
$66$		0			0
$67$	1.31471	+	1.31471i	0.160617	+	0.160617i	0.782840	−	0.622223i	$-0.213770\pi$
$67$	1.31471	+	1.31471i	0.160617	+	0.160617i	−0.622223	+	0.782840i	$0.713770\pi$
$68$	4.21298	−	8.26845i	0.510899	−	1.00270i
$69$	−2.00829	+	2.76417i	−0.241770	+	0.332767i
$70$	−1.26096	−	2.92433i	−0.150713	−	0.349524i
$71$	0.887847	−	2.73251i	0.105368	−	0.324289i	−0.884449	−	0.466638i	$-0.845465\pi$
$71$	0.887847	−	2.73251i	0.105368	−	0.324289i	0.989817	+	0.142348i	$0.0454653\pi$
$72$	1.41924	+	2.78541i	0.167259	+	0.328264i
$73$	−14.6197	−	2.31553i	−1.71110	−	0.271012i	−0.777385	−	0.629025i	$-0.783454\pi$
$73$	−14.6197	−	2.31553i	−1.71110	−	0.271012i	−0.933716	+	0.358013i	$0.883454\pi$
$74$	−0.459581	−	0.333905i	−0.0534252	−	0.0388157i
$75$	−3.47990	−	4.51043i	−0.401824	−	0.520819i
$76$		−	7.22113i		−	0.828321i
$77$		0			0
$78$	−1.15138	+	1.15138i	−0.130368	+	0.130368i
$79$	4.71123	+	14.4997i	0.530055	+	1.63134i	0.754098	+	0.656762i	$0.228074\pi$
$79$	4.71123	+	14.4997i	0.530055	+	1.63134i	−0.224043	+	0.974579i	$0.571926\pi$
$80$	−3.87746	−	4.40966i	−0.433513	−	0.493015i
$81$	−0.807503	+	0.586685i	−0.0897226	+	0.0651873i
$82$	1.54699	−	0.788233i	0.170837	−	0.0870457i
$83$	5.95431	−	3.03387i	0.653571	−	0.333011i	−0.0955691	−	0.995423i	$-0.530467\pi$
$83$	5.95431	−	3.03387i	0.653571	−	0.333011i	0.749140	+	0.662412i	$0.230467\pi$
$84$	4.73540	−	3.44047i	0.516675	−	0.375386i
$85$	−11.7556	−	0.754947i	−1.27508	−	0.0818855i
$86$	1.08262	+	3.33197i	0.116742	+	0.359296i
$87$	2.13066	−	2.13066i	0.228431	−	0.228431i
$88$		0			0
$89$		−	11.1726i		−	1.18429i	−0.805830	−	0.592147i	$-0.798281\pi$
$89$		−	11.1726i		−	1.18429i	0.805830	−	0.592147i	$-0.201719\pi$
$90$	1.18642	−	1.43035i	0.125060	−	0.150772i
$91$	−6.90490	−	5.01670i	−0.723830	−	0.525894i
$92$	5.21741	+	0.826356i	0.543952	+	0.0861536i
$93$	−3.48665	−	6.84294i	−0.361549	−	0.709580i
$94$	−0.555586	+	1.70992i	−0.0573043	+	0.176364i
$95$	−8.41729	+	3.62950i	−0.863595	+	0.372379i
$96$	−3.31916	+	4.56843i	−0.338761	+	0.466264i
$97$	−4.57097	+	8.97103i	−0.464112	+	0.910871i	0.533758	+	0.845637i	$0.320779\pi$
$97$	−4.57097	+	8.97103i	−0.464112	+	0.910871i	−0.997870	+	0.0652335i	$0.979221\pi$
$98$	−0.519848	−	0.519848i	−0.0525126	−	0.0525126i
$99$		0			0
$100$	−3.77081	+	7.95960i	−0.377081	+	0.795960i
$101$	−1.81570	+	0.589955i	−0.180668	+	0.0587027i	−0.397954	−	0.917405i	$-0.630280\pi$
$101$	−1.81570	+	0.589955i	−0.180668	+	0.0587027i	0.217286	+	0.976108i	$0.430280\pi$
$102$	0.458533	+	2.89506i	0.0454015	+	0.286654i
$103$	0.965408	−	6.09534i	0.0951244	−	0.600592i	−0.893368	−	0.449325i	$-0.851665\pi$
$103$	0.965408	−	6.09534i	0.0951244	−	0.600592i	0.988493	−	0.151267i	$-0.0483354\pi$
$104$	5.11261	+	1.66119i	0.501333	+	0.162893i
$105$	−6.39049	−	3.79055i	−0.623648	−	0.369920i
$106$	0.424169	+	0.583818i	0.0411989	+	0.0567054i
$107$	−0.430167	+	0.0681317i	−0.0415858	+	0.00658654i	−0.177193	−	0.984176i	$-0.556702\pi$
$107$	−0.430167	+	0.0681317i	−0.0415858	+	0.00658654i	0.135607	+	0.990763i	$0.456702\pi$
$108$	8.40815	+	4.28417i	0.809075	+	0.412244i
$109$	9.46672			0.906748			0.453374	−	0.891320i	$-0.350220\pi$
$109$	9.46672			0.906748			0.453374	+	0.891320i	$0.350220\pi$
$110$		0			0
$111$	−1.32539			−0.125801
$112$	−6.82382	−	3.47691i	−0.644790	−	0.328537i
$113$	20.0170	−	3.17038i	1.88304	−	0.298244i	0.894251	−	0.447566i	$-0.147709\pi$
$113$	20.0170	−	3.17038i	1.88304	−	0.298244i	0.988789	+	0.149322i	$0.0477090\pi$
$114$	1.34066	+	1.84526i	0.125564	+	0.172825i
$115$	−1.65914	−	6.49700i	−0.154716	−	0.605848i
$116$	−4.43060	−	1.43959i	−0.411371	−	0.133663i
$117$	0.779122	−	4.91919i	0.0720299	−	0.454779i
$118$	−0.122633	−	0.774274i	−0.0112893	−	0.0712777i
$119$	−14.6120	+	4.74773i	−1.33948	+	0.435223i
$120$	4.56582	+	1.02682i	0.416800	+	0.0937351i
$121$		0			0
$122$	−2.39578	−	2.39578i	−0.216903	−	0.216903i
$123$	1.83905	−	3.60934i	0.165822	−	0.325444i
$124$	−6.97923	+	9.60608i	−0.626753	+	0.862652i
$125$	11.1734	+	0.394766i	0.999376	+	0.0353090i
$126$	0.748989	−	2.30515i	0.0667253	−	0.205359i
$127$	−4.28099	−	8.40191i	−0.379876	−	0.745549i	0.619341	−	0.785122i	$-0.287400\pi$
$127$	−4.28099	−	8.40191i	−0.379876	−	0.745549i	−0.999217	+	0.0395736i	$0.987400\pi$
$128$	11.1562	+	1.76696i	0.986075	+	0.156179i
$129$	6.61291	+	4.80456i	0.582234	+	0.423018i
$130$	−0.296600	−	3.18185i	−0.0260135	−	0.279066i
$131$		−	7.51676i		−	0.656743i	−0.944549	−	0.328371i	$-0.893500\pi$
$131$		−	7.51676i		−	0.656743i	0.944549	−	0.328371i	$-0.106500\pi$
$132$		0			0
$133$	−8.45377	+	8.45377i	−0.733035	+	0.733035i
$134$	0.280575	+	0.863521i	0.0242380	+	0.0745968i
$135$	0.767702	−	11.9542i	0.0660733	−	1.02886i
$136$	7.82885	−	5.68799i	0.671318	−	0.487741i
$137$	13.6942	−	6.97753i	1.16997	−	0.596131i	0.242547	−	0.970140i	$-0.422017\pi$
$137$	13.6942	−	6.97753i	1.16997	−	0.596131i	0.927425	+	0.374009i	$0.122017\pi$
$138$	−1.48666	+	0.757489i	−0.126553	+	0.0644818i
$139$	3.36744	−	2.44659i	0.285623	−	0.207517i	−0.435743	−	0.900071i	$-0.643514\pi$
$139$	3.36744	−	2.44659i	0.285623	−	0.207517i	0.721366	+	0.692554i	$0.243514\pi$
$140$	−0.736206	+	11.4638i	−0.0622208	+	0.968869i
$141$	1.29626	+	3.98947i	0.109164	+	0.335974i
$142$	0.992116	−	0.992116i	0.0832565	−	0.0832565i
$143$		0			0
$144$		−	4.46910i		−	0.372425i
$145$	0.548865	+	5.88809i	0.0455808	+	0.488979i
$146$	−5.84786	−	4.24872i	−0.483972	−	0.351626i
$147$	−1.69415	−	0.268327i	−0.139731	−	0.0221312i
$148$	0.930290	+	1.82580i	0.0764693	+	0.150080i
$149$	−5.55533	+	17.0976i	−0.455111	+	1.40069i	0.415895	+	0.909413i	$0.363468\pi$
$149$	−5.55533	+	17.0976i	−0.455111	+	1.40069i	−0.871005	+	0.491273i	$0.836532\pi$
$150$	−0.514183	−	2.73405i	−0.0419829	−	0.223234i
$151$	−10.4580	+	14.3942i	−0.851058	+	1.17138i	0.132571	+	0.991173i	$0.457677\pi$
$151$	−10.4580	+	14.3942i	−0.851058	+	1.17138i	−0.983629	+	0.180207i	$0.942323\pi$
$152$	3.41861	−	6.70939i	0.277286	−	0.544204i
$153$	−6.33960	−	6.33960i	−0.512526	−	0.512526i
$154$		0			0
$155$	14.7052	+	3.30708i	1.18115	+	0.265631i
$156$	5.58609	−	1.81503i	0.447245	−	0.145319i
$157$	3.35784	+	21.2006i	0.267985	+	1.69199i	0.643720	+	0.765261i	$0.277390\pi$
$157$	3.35784	+	21.2006i	0.267985	+	1.69199i	−0.375735	+	0.926727i	$0.622610\pi$
$158$	−1.16468	+	7.35350i	−0.0926569	+	0.585013i
$159$	1.60127	+	0.520286i	0.126989	+	0.0412613i
$160$	−2.74212	−	10.7378i	−0.216783	−	0.848896i
$161$	−5.14060	−	7.07543i	−0.405136	−	0.557622i
$162$	−0.481425	+	0.0762502i	−0.0378243	+	0.00599078i
$163$	9.28876	+	4.73286i	0.727552	+	0.370706i	0.778205	−	0.628010i	$-0.216130\pi$
$163$	9.28876	+	4.73286i	0.727552	+	0.370706i	−0.0506534	+	0.998716i	$0.516130\pi$
$164$	−6.26288			−0.489049
$165$		0			0
$166$	3.26342			0.253290
$167$	10.0620	+	5.12686i	0.778623	+	0.396728i	0.797673	−	0.603090i	$-0.206064\pi$
$167$	10.0620	+	5.12686i	0.778623	+	0.396728i	−0.0190498	+	0.999819i	$0.506064\pi$
$168$	6.02860	−	0.954836i	0.465117	−	0.0736672i
$169$	2.60712	+	3.58840i	0.200548	+	0.276031i
$170$	−4.94766	−	2.93473i	−0.379468	−	0.225083i
$171$	−6.63507	−	2.15586i	−0.507396	−	0.164863i
$172$	1.97694	−	12.4819i	0.150741	−	0.951738i
$173$	−2.06528	−	13.0397i	−0.157020	−	0.991387i	−0.932803	−	0.360387i	$-0.882645\pi$
$173$	−2.06528	−	13.0397i	−0.157020	−	0.991387i	0.775783	−	0.631000i	$-0.217355\pi$
$174$	1.39945	−	0.454709i	0.106092	−	0.0344714i
$175$	13.7328	−	4.90381i	1.03810	−	0.370693i
$176$		0			0
$177$	−1.29330	−	1.29330i	−0.0972104	−	0.0972104i
$178$	2.47698	−	4.86135i	0.185658	−	0.364374i
$179$	1.30884	−	1.80147i	0.0978276	−	0.134648i	−0.757297	−	0.653071i	$-0.773480\pi$
$179$	1.30884	−	1.80147i	0.0978276	−	0.134648i	0.855125	+	0.518422i	$0.173480\pi$
$180$	−6.15555	+	2.65425i	−0.458807	+	0.197836i
$181$	1.33951	−	4.12258i	0.0995647	−	0.306429i	−0.888852	−	0.458195i	$-0.848496\pi$
$181$	1.33951	−	4.12258i	0.0995647	−	0.306429i	0.988416	+	0.151766i	$0.0484961\pi$
$182$	−1.89221	−	3.71366i	−0.140260	−	0.275275i
$183$	−7.80766	−	1.23661i	−0.577159	−	0.0914130i
$184$	4.45646	+	3.23780i	0.328534	+	0.238694i
$185$	1.66065	−	2.00207i	0.122093	−	0.147195i
$186$		−	3.75045i		−	0.274996i
$187$		0			0
$188$	4.58586	−	4.58586i	0.334458	−	0.334458i
$189$	−4.82794	−	14.8589i	−0.351181	−	1.08082i
$190$	−4.46714	−	0.286880i	−0.324081	−	0.0208125i
$191$	3.29900	−	2.39686i	0.238707	−	0.173431i	−0.462000	−	0.886880i	$-0.652868\pi$
$191$	3.29900	−	2.39686i	0.238707	−	0.173431i	0.700707	+	0.713449i	$0.252868\pi$
$192$	2.87471	−	1.46474i	0.207465	−	0.105708i
$193$	18.6227	−	9.48874i	1.34049	−	0.683015i	0.371113	−	0.928588i	$-0.378976\pi$
$193$	18.6227	−	9.48874i	1.34049	−	0.683015i	0.969378	+	0.245573i	$0.0789761\pi$
$194$	−3.97778	+	2.89003i	−0.285588	+	0.207492i
$195$	−4.92337	−	5.59913i	−0.352570	−	0.400962i
$196$	0.819484	+	2.52211i	0.0585346	+	0.180151i
$197$	0.213782	−	0.213782i	0.0152313	−	0.0152313i	−0.699450	−	0.714681i	$-0.746572\pi$
$197$	0.213782	−	0.213782i	0.0152313	−	0.0152313i	0.714681	+	0.699450i	$0.246572\pi$
$198$		0			0
$199$			11.0815i			0.785549i	0.919635	+	0.392775i	$0.128485\pi$
$199$			11.0815i			0.785549i	−0.919635	+	0.392775i	$0.871515\pi$
$200$	−7.27180	+	5.61036i	−0.514194	+	0.396712i
$201$	1.71381	+	1.24516i	0.120883	+	0.0878267i
$202$	−0.920828	−	0.145845i	−0.0647892	−	0.0102616i
$203$	3.50158	+	6.87223i	0.245762	+	0.482336i
$204$	3.26729	−	10.0557i	0.228756	−	0.704038i
$205$	3.14786	+	7.30031i	0.219856	+	0.509876i
$206$	1.77141	−	2.43814i	0.123420	−	0.169873i
$207$	2.31694	−	4.54726i	0.161039	−	0.316056i
$208$	−5.43417	−	5.43417i	−0.376792	−	0.376792i
$209$		0			0
$210$	−1.94022	−	3.06610i	−0.133888	−	0.211581i
$211$	−8.42206	+	2.73649i	−0.579799	+	0.188388i	−0.584210	−	0.811602i	$-0.698596\pi$
$211$	−8.42206	+	2.73649i	−0.579799	+	0.188388i	0.00441172	+	0.999990i	$0.498596\pi$
$212$	−0.407211	−	2.57103i	−0.0279673	−	0.176579i
$213$	0.512094	−	3.23323i	0.0350881	−	0.221538i
$214$	−0.202276	−	0.0657236i	−0.0138273	−	0.00449277i
$215$	−15.5432	+	3.96927i	−1.06004	+	0.270702i
$216$	5.78409	+	7.96112i	0.393558	+	0.541686i
$217$	19.4164	−	3.07526i	1.31807	−	0.208762i
$218$	4.11910	+	2.09879i	0.278981	+	0.142148i
$219$	−16.8647			−1.13961
$220$		0			0
$221$	−15.4172			−1.03707
$222$	−0.576696	−	0.293842i	−0.0387053	−	0.0197214i
$223$	−6.10610	+	0.967112i	−0.408895	+	0.0647626i	−0.357494	−	0.933916i	$-0.616369\pi$
$223$	−6.10610	+	0.967112i	−0.408895	+	0.0647626i	−0.0514011	+	0.998678i	$0.516369\pi$
$224$	−8.49602	−	11.6938i	−0.567664	−	0.781323i
$225$	6.18782	+	5.84111i	0.412522	+	0.389407i
$226$	9.41254	+	3.05832i	0.626113	+	0.203436i
$227$	−0.518849	+	3.27588i	−0.0344372	+	0.217428i	−0.998906	−	0.0467700i	$-0.985107\pi$
$227$	−0.518849	+	3.27588i	−0.0344372	+	0.217428i	0.964468	+	0.264198i	$0.0851072\pi$
$228$	−1.28706	−	8.12619i	−0.0852377	−	0.538170i
$229$	−5.07862	+	1.65014i	−0.335604	+	0.109044i	−0.471971	−	0.881614i	$-0.656457\pi$
$229$	−5.07862	+	1.65014i	−0.335604	+	0.109044i	0.136367	+	0.990658i	$0.456457\pi$
$230$	0.718477	−	3.19477i	0.0473750	−	0.210657i
$231$		0			0
$232$	−3.43509	−	3.43509i	−0.225525	−	0.225525i
$233$	2.00585	−	3.93669i	0.131407	−	0.257901i	−0.815922	−	0.578162i	$-0.803770\pi$
$233$	2.00585	−	3.93669i	0.131407	−	0.257901i	0.947330	+	0.320260i	$0.103770\pi$
$234$	1.42960	−	1.96767i	0.0934557	−	0.128631i
$235$	−7.65044	−	3.04054i	−0.499060	−	0.198343i
$236$	−0.873824	+	2.68935i	−0.0568811	+	0.175062i
$237$	7.88607	+	15.4773i	0.512255	+	1.00536i
$238$	−7.41046	−	1.17370i	−0.480349	−	0.0760798i
$239$	−8.45656	−	6.14405i	−0.547009	−	0.397426i	0.279672	−	0.960096i	$-0.409774\pi$
$239$	−8.45656	−	6.14405i	−0.547009	−	0.397426i	−0.826682	+	0.562670i	$0.809774\pi$
$240$	−5.14940	−	4.27124i	−0.332392	−	0.275708i
$241$			27.8579i			1.79449i	0.441536	+	0.897243i	$0.354434\pi$
$241$			27.8579i			1.79449i	−0.441536	+	0.897243i	$0.645566\pi$
$242$		0			0
$243$	10.5600	−	10.5600i	0.677425	−	0.677425i
$244$	3.77668	+	11.6234i	0.241777	+	0.744114i
$245$	2.52800	−	2.22290i	0.161508	−	0.142016i
$246$	1.60039	−	1.16275i	0.102037	−	0.0741345i
$247$	−10.6893	+	5.44646i	−0.680142	+	0.346550i
$248$	−11.0323	+	5.62125i	−0.700553	+	0.356949i
$249$	6.15985	−	4.47539i	0.390365	−	0.283616i
$250$	4.77417	+	2.64892i	0.301945	+	0.167532i
$251$	−3.07357	−	9.45946i	−0.194002	−	0.597076i	−0.999987	−	0.00514015i	$-0.998364\pi$
$251$	−3.07357	−	9.45946i	−0.194002	−	0.597076i	0.805985	−	0.591936i	$-0.201636\pi$
$252$	−6.18223	+	6.18223i	−0.389444	+	0.389444i
$253$		0			0
$254$		−	4.60489i		−	0.288936i
$255$	−13.3636	+	1.24570i	−0.836859	+	0.0780089i
$256$	−0.119374	−	0.0867302i	−0.00746087	−	0.00542064i
$257$	−4.18826	−	0.663355i	−0.261257	−	0.0413790i	0.0244320	−	0.999701i	$-0.492222\pi$
$257$	−4.18826	−	0.663355i	−0.261257	−	0.0413790i	−0.285689	+	0.958323i	$0.592222\pi$
$258$	1.81219	+	3.55662i	0.112822	+	0.221426i
$259$	1.04837	−	3.22655i	0.0651425	−	0.200488i
$260$	−4.25738	+	10.7122i	−0.264032	+	0.664343i
$261$	−2.64551	+	3.64123i	−0.163753	+	0.225386i
$262$	1.66648	−	3.27065i	0.102955	−	0.202061i
$263$	16.1830	+	16.1830i	0.997884	+	0.997884i	0.999998	−	0.00211364i	$-0.000672793\pi$
$263$	16.1830	+	16.1830i	0.997884	+	0.997884i	−0.00211364	+	0.999998i	$0.500673\pi$
$264$		0			0
$265$	−2.79223	+	1.76692i	−0.171526	+	0.108541i
$266$	−5.55257	+	1.80414i	−0.340450	+	0.110619i
$267$	−1.99135	−	12.5729i	−0.121869	−	0.769450i
$268$	0.512349	−	3.23484i	0.0312967	−	0.197599i
$269$	−21.7521	−	7.06768i	−1.32625	−	0.430924i	−0.441611	−	0.897206i	$-0.645593\pi$
$269$	−21.7521	−	7.06768i	−1.32625	−	0.430924i	−0.884636	+	0.466283i	$0.845593\pi$
$270$	2.98431	−	5.03126i	0.181619	−	0.306192i
$271$	0.817223	+	1.12481i	0.0496428	+	0.0683274i	0.833117	−	0.553097i	$-0.186554\pi$
$271$	0.817223	+	1.12481i	0.0496428	+	0.0683274i	−0.783474	+	0.621425i	$0.786554\pi$
$272$	−13.6638	+	2.16414i	−0.828490	+	0.131220i
$273$	−8.66448	−	4.41477i	−0.524398	−	0.267194i
$274$	7.50545			0.453421
$275$		0			0
$276$	6.01861			0.362278
$277$	12.7020	+	6.47199i	0.763189	+	0.388864i	0.791843	−	0.610725i	$-0.209122\pi$
$277$	12.7020	+	6.47199i	0.763189	+	0.388864i	−0.0286534	+	0.999589i	$0.509122\pi$
$278$	2.00763	−	0.317978i	0.120410	−	0.0190711i
$279$	6.74281	+	9.28068i	0.403682	+	0.555620i
$280$	−6.11120	+	10.3029i	−0.365214	+	0.615714i
$281$	24.1347	+	7.84184i	1.43976	+	0.467805i	0.921821	−	0.387615i	$-0.126701\pi$
$281$	24.1347	+	7.84184i	1.43976	+	0.467805i	0.517935	+	0.855420i	$0.326701\pi$
$282$	−0.320452	+	2.02325i	−0.0190826	+	0.120483i
$283$	1.15929	+	7.31948i	0.0689128	+	0.435098i	0.997888	+	0.0649564i	$0.0206908\pi$
$283$	1.15929	+	7.31948i	0.0689128	+	0.435098i	−0.928975	+	0.370142i	$0.879309\pi$
$284$	−4.81338	+	1.56396i	−0.285622	+	0.0928042i
$285$	−8.82536	+	5.58466i	−0.522769	+	0.330807i
$286$		0			0
$287$	7.33195	+	7.33195i	0.432791	+	0.432791i
$288$	3.82928	−	7.51539i	0.225643	−	0.442848i
$289$	−6.32041	+	8.69930i	−0.371789	+	0.511724i
$290$	−1.06658	+	2.68367i	−0.0626317	+	0.157591i
$291$	−3.54491	+	10.9101i	−0.207807	+	0.639563i
$292$	11.8373	+	23.2320i	0.692726	+	1.35955i
$293$	14.4967	+	2.29605i	0.846906	+	0.134137i	0.564781	−	0.825241i	$-0.308961\pi$
$293$	14.4967	+	2.29605i	0.846906	+	0.134137i	0.282125	+	0.959378i	$0.408961\pi$
$294$	−0.677659	−	0.492348i	−0.0395219	−	0.0287143i
$295$	3.57404	−	0.333158i	0.208088	−	0.0193972i
$296$			2.13682i			0.124200i
$297$		0			0
$298$	−6.20775	+	6.20775i	−0.359606	+	0.359606i
$299$	−2.71194	−	8.34648i	−0.156835	−	0.482689i
$300$	−2.82474	+	9.62930i	−0.163087	+	0.555948i
$301$	−16.9270	+	12.2982i	−0.975655	+	0.708855i
$302$	−7.74161	+	3.94455i	−0.445480	+	0.226983i
$303$	−1.93811	+	0.987518i	−0.111342	+	0.0567314i
$304$	−8.70907	+	6.32751i	−0.499499	+	0.362908i
$305$	11.6506	−	10.2445i	0.667109	−	0.586596i
$306$	−1.35295	−	4.16395i	−0.0773429	−	0.238037i
$307$	−0.874954	+	0.874954i	−0.0499363	+	0.0499363i	−0.731634	−	0.681698i	$-0.761242\pi$
$307$	−0.874954	+	0.874954i	−0.0499363	+	0.0499363i	0.681698	+	0.731634i	$0.261242\pi$
$308$		0			0
$309$		−	7.03137i		−	0.400001i
$310$	5.66525	+	4.69912i	0.321765	+	0.266892i
$311$	−11.4450	−	8.31532i	−0.648989	−	0.471518i	0.213937	−	0.976847i	$-0.431371\pi$
$311$	−11.4450	−	8.31532i	−0.648989	−	0.471518i	−0.862927	+	0.505329i	$0.831371\pi$
$312$	6.04948	+	0.958144i	0.342485	+	0.0542442i
$313$	0.335793	+	0.659031i	0.0189802	+	0.0372506i	0.900302	−	0.435266i	$-0.143346\pi$
$313$	0.335793	+	0.659031i	0.0189802	+	0.0372506i	−0.881322	+	0.472517i	$0.843346\pi$
$314$	−3.23915	+	9.96909i	−0.182796	+	0.562588i
$315$	10.3136	+	4.09897i	0.581106	+	0.230951i
$316$	15.7855	−	21.7269i	0.888006	−	1.22224i
$317$	−7.74784	+	15.2060i	−0.435162	+	0.854054i	0.564430	+	0.825481i	$0.309096\pi$
$317$	−7.74784	+	15.2060i	−0.435162	+	0.854054i	−0.999592	+	0.0285725i	$0.990904\pi$
$318$	0.581389	+	0.581389i	0.0326027	+	0.0326027i
$319$		0			0
$320$	−1.38930	+	6.17765i	−0.0776644	+	0.345341i
$321$	−0.471938	+	0.153342i	−0.0263410	+	0.00855871i
$322$	−0.668112	−	4.21829i	−0.0372324	−	0.235076i
$323$	−3.37834	+	21.3300i	−0.187976	+	1.18683i
$324$	1.67217	+	0.543322i	0.0928986	+	0.0301846i
$325$	14.6265	−	0.421589i	0.811333	−	0.0233856i
$326$	2.99238	+	4.11866i	0.165733	+	0.228112i
$327$	10.6532	−	1.68731i	0.589125	−	0.0933082i
$328$	−5.81905	−	2.96496i	−0.321304	−	0.163712i
$329$	−10.7373			−0.591967
$330$		0			0
$331$	−14.9189			−0.820016			−0.410008	−	0.912082i	$-0.634474\pi$
$331$	−14.9189			−0.820016			−0.410008	+	0.912082i	$0.634474\pi$
$332$	−10.4887	−	5.34424i	−0.575640	−	0.293303i
$333$	1.95535	−	0.309697i	0.107153	−	0.0169713i
$334$	3.24149	+	4.46153i	0.177367	+	0.244124i
$335$	−4.02820	+	1.02869i	−0.220084	+	0.0562031i
$336$	−8.29879	−	2.69644i	−0.452736	−	0.147103i
$337$	−1.47636	+	9.32134i	−0.0804222	+	0.507766i	0.914290	+	0.405061i	$0.132750\pi$
$337$	−1.47636	+	9.32134i	−0.0804222	+	0.507766i	−0.994712	+	0.102705i	$0.967250\pi$
$338$	0.338842	+	2.13936i	0.0184306	+	0.116366i
$339$	21.9607	−	7.13547i	1.19274	−	0.387546i
$340$	11.0959	+	17.5346i	0.601758	+	0.950950i
$341$		0			0
$342$	−2.40905	−	2.40905i	−0.130267	−	0.130267i
$343$	−7.27490	+	14.2778i	−0.392808	+	0.770928i
$344$	7.74600	−	10.6615i	0.417636	−	0.574827i
$345$	−3.02509	−	7.01557i	−0.162865	−	0.377706i
$346$	1.99228	−	6.13161i	0.107106	−	0.329637i
$347$	−8.73452	−	17.1425i	−0.468894	−	0.920255i	−0.997451	−	0.0713577i	$-0.977267\pi$
$347$	−8.73452	−	17.1425i	−0.468894	−	0.920255i	0.528557	−	0.848898i	$-0.322733\pi$
$348$	−5.24250	−	0.830330i	−0.281027	−	0.0445104i
$349$	12.0325	+	8.74209i	0.644082	+	0.467953i	0.861250	−	0.508181i	$-0.169682\pi$
$349$	12.0325	+	8.74209i	0.644082	+	0.467953i	−0.217168	+	0.976134i	$0.569682\pi$
$350$	7.06250	+	0.910865i	0.377507	+	0.0486878i
$351$		−	15.6777i		−	0.836813i
$352$		0			0
$353$	1.78406	−	1.78406i	0.0949560	−	0.0949560i	−0.658033	−	0.752989i	$-0.728611\pi$
$353$	1.78406	−	1.78406i	0.0949560	−	0.0949560i	0.752989	+	0.658033i	$0.228611\pi$
$354$	−0.276006	−	0.849460i	−0.0146696	−	0.0451483i
$355$	4.24234	+	4.82462i	0.225160	+	0.256064i
$356$	−15.9221	+	11.5681i	−0.843870	+	0.613108i
$357$	−15.5972	+	7.94716i	−0.825490	+	0.420608i
$358$	0.968885	−	0.493672i	0.0512072	−	0.0260914i
$359$	−6.87015	+	4.99146i	−0.362593	+	0.263439i	−0.754133	−	0.656722i	$-0.771942\pi$
$359$	−6.87015	+	4.99146i	−0.362593	+	0.263439i	0.391540	+	0.920161i	$0.371942\pi$
$360$	−6.97589	−	0.447992i	−0.367662	−	0.0236112i
$361$	−0.678357	−	2.08777i	−0.0357030	−	0.109883i
$362$	1.49682	−	1.49682i	0.0786711	−	0.0786711i
$363$		0			0
$364$			15.0345i			0.788021i
$365$	21.1306	−	25.4750i	1.10603	−	1.33342i
$366$	−3.12306	−	2.26904i	−0.163245	−	0.118604i
$367$	−20.9681	−	3.32102i	−1.09453	−	0.173356i	−0.417038	−	0.908889i	$-0.636932\pi$
$367$	−20.9681	−	3.32102i	−1.09453	−	0.173356i	−0.677489	+	0.735533i	$0.736932\pi$
$368$	−3.57512	−	7.01656i	−0.186366	−	0.365764i
$369$	−1.86978	+	5.75459i	−0.0973368	+	0.299572i
$370$	1.16643	−	0.502962i	0.0606400	−	0.0261477i
$371$	−2.53318	+	3.48662i	−0.131516	+	0.181016i
$372$	−6.14182	+	12.0540i	−0.318439	+	0.624971i
$373$	2.57445	+	2.57445i	0.133300	+	0.133300i	0.770609	−	0.637309i	$-0.219952\pi$
$373$	2.57445	+	2.57445i	0.133300	+	0.133300i	−0.637309	+	0.770609i	$0.719952\pi$
$374$		0			0
$375$	12.6441	−	1.54725i	0.652940	−	0.0798995i
$376$	6.43190	−	2.08985i	0.331700	−	0.107776i
$377$	1.21074	+	7.64432i	0.0623563	+	0.393702i
$378$	1.19353	−	7.53567i	0.0613887	−	0.387593i
$379$	15.7712	+	5.12437i	0.810112	+	0.263221i	0.684645	−	0.728877i	$-0.259957\pi$
$379$	15.7712	+	5.12437i	0.810112	+	0.263221i	0.125467	+	0.992098i	$0.459957\pi$
$380$	13.8877	+	8.23752i	0.712422	+	0.422576i
$381$	−6.31506	−	8.69193i	−0.323530	−	0.445301i
$382$	1.96683	−	0.311515i	0.100632	−	0.0159385i
$383$	−10.1043	−	5.14840i	−0.516306	−	0.263071i	0.176365	−	0.984325i	$-0.443566\pi$
$383$	−10.1043	−	5.14840i	−0.516306	−	0.263071i	−0.692671	+	0.721254i	$0.743566\pi$
$384$	12.8694			0.656736
$385$		0			0
$386$	10.2067			0.519505
$387$	−10.8787	−	5.54297i	−0.552995	−	0.281765i
$388$	17.5174	−	2.77449i	0.889312	−	0.140853i
$389$	0.480555	+	0.661427i	0.0243651	+	0.0335357i	0.821026	−	0.570891i	$-0.193402\pi$
$389$	0.480555	+	0.661427i	0.0243651	+	0.0335357i	−0.796661	+	0.604427i	$0.793402\pi$
$390$	−0.900892	−	3.52778i	−0.0456184	−	0.178636i
$391$	−15.0247	−	4.88183i	−0.759833	−	0.246885i
$392$	−0.432601	+	2.73134i	−0.0218497	+	0.137953i
$393$	−1.33975	−	8.45887i	−0.0675816	−	0.426694i
$394$	0.140415	−	0.0456237i	0.00707402	−	0.00229849i
$395$	−33.2601	−	7.47992i	−1.67350	−	0.376356i
$396$		0			0
$397$	11.8504	+	11.8504i	0.594752	+	0.594752i	0.938911	−	0.344159i	$-0.111836\pi$
$397$	11.8504	+	11.8504i	0.594752	+	0.594752i	−0.344159	+	0.938911i	$0.611836\pi$
$398$	−2.45679	+	4.82173i	−0.123148	+	0.241691i
$399$	−8.00656	+	11.0201i	−0.400829	+	0.551694i
$400$	12.9039	−	2.42679i	0.645194	−	0.121339i
$401$	−8.79392	+	27.0649i	−0.439148	+	1.35156i	0.449629	+	0.893216i	$0.351556\pi$
$401$	−8.79392	+	27.0649i	−0.439148	+	1.35156i	−0.888776	+	0.458342i	$0.848444\pi$
$402$	0.469651	+	0.921741i	0.0234240	+	0.0459723i
$403$	19.4837	+	3.08591i	0.970551	+	0.153720i
$404$	2.72071	+	1.97671i	0.135361	+	0.0983452i
$405$	−0.207150	−	2.22225i	−0.0102934	−	0.110424i
$406$			3.76651i			0.186929i
$407$		0			0
$408$	7.79627	−	7.79627i	0.385973	−	0.385973i
$409$	0.748644	+	2.30409i	0.0370181	+	0.113930i	0.967858	−	0.251497i	$-0.0809229\pi$
$409$	0.748644	+	2.30409i	0.0370181	+	0.113930i	−0.930840	+	0.365427i	$0.880923\pi$
$410$	−0.248811	+	3.87435i	−0.0122879	+	0.191341i
$411$	14.1669	−	10.2928i	0.698801	−	0.507708i
$412$	−9.68608	+	4.93530i	−0.477199	+	0.243145i
$413$	4.17141	−	2.12544i	0.205262	−	0.104586i
$414$	2.01627	−	1.46490i	0.0990941	−	0.0719961i
$415$	−0.957663	+	14.9122i	−0.0470098	+	0.732012i
$416$	−4.48210	−	13.7945i	−0.219753	−	0.676330i
$417$	3.35343	−	3.35343i	0.164218	−	0.164218i
$418$		0			0
$419$		−	16.4371i		−	0.803006i	−0.915858	−	0.401503i	$-0.868488\pi$
$419$		−	16.4371i		−	0.803006i	0.915858	−	0.401503i	$-0.131512\pi$
$420$	1.21478	+	13.0318i	0.0592751	+	0.635889i
$421$	10.0871	+	7.32873i	0.491617	+	0.357180i	0.805806	−	0.592180i	$-0.201733\pi$
$421$	10.0871	+	7.32873i	0.491617	+	0.357180i	−0.314189	+	0.949360i	$0.601733\pi$
$422$	−4.27124	−	0.676498i	−0.207921	−	0.0329314i
$423$	−2.84457	−	5.58277i	−0.138308	−	0.271444i
$424$	0.838815	−	2.58161i	0.0407364	−	0.125374i
$425$	14.8622	−	21.7472i	0.720921	−	1.05489i
$426$	0.939632	−	1.29329i	0.0455253	−	0.0626602i
$427$	9.18618	−	18.0289i	0.444550	−	0.872479i
$428$	0.542488	+	0.542488i	0.0262222	+	0.0262222i
$429$		0			0
$430$	−7.64304	−	1.71886i	−0.368580	−	0.0828907i
$431$	−18.8644	+	6.12941i	−0.908666	+	0.295243i	−0.725809	−	0.687896i	$-0.758534\pi$
$431$	−18.8644	+	6.12941i	−0.908666	+	0.295243i	−0.182857	+	0.983140i	$0.558534\pi$
$432$	−2.20070	−	13.8947i	−0.105881	−	0.668508i
$433$	4.47800	−	28.2730i	0.215199	−	1.35871i	−0.609341	−	0.792908i	$-0.708566\pi$
$433$	4.47800	−	28.2730i	0.215199	−	1.35871i	0.824540	−	0.565803i	$-0.191434\pi$
$434$	9.13013	+	2.96656i	0.438260	+	0.142399i
$435$	1.66712	+	6.52824i	0.0799324	+	0.313005i
$436$	−9.80183	−	13.4911i	−0.469422	−	0.646104i
$437$	−12.1418	+	1.92307i	−0.580820	+	0.0919929i
$438$	−7.33807	−	3.73893i	−0.350626	−	0.178653i
$439$	−3.12279			−0.149043			−0.0745214	−	0.997219i	$-0.523743\pi$
$439$	−3.12279			−0.149043			−0.0745214	+	0.997219i	$0.523743\pi$
$440$		0			0
$441$	2.56208			0.122004
$442$	−6.70823	−	3.41802i	−0.319078	−	0.162578i
$443$	−31.3472	+	4.96491i	−1.48935	+	0.235890i	−0.847441	−	0.530890i	$-0.821858\pi$
$443$	−31.3472	+	4.96491i	−1.48935	+	0.235890i	−0.641910	+	0.766780i	$0.721858\pi$
$444$	1.37231	+	1.88882i	0.0651269	+	0.0896395i
$445$	21.4871	+	12.7452i	1.01859	+	0.604179i
$446$	−2.87126	−	0.932929i	−0.135958	−	0.0441755i
$447$	−3.20422	+	20.2306i	−0.151554	+	0.956876i
$448$	1.29191	+	8.15682i	0.0610372	+	0.385373i
$449$	33.2818	−	10.8139i	1.57067	−	0.510341i	0.611036	−	0.791603i	$-0.290753\pi$
$449$	33.2818	−	10.8139i	1.57067	−	0.510341i	0.959631	+	0.281262i	$0.0907530\pi$
$450$	1.39743	+	3.91340i	0.0658753	+	0.184479i
$451$		0			0
$452$	−25.2437	−	25.2437i	−1.18736	−	1.18736i
$453$	−9.20317	+	18.0622i	−0.432402	+	0.848638i
$454$	−0.952026	+	1.31035i	−0.0446808	+	0.0614978i
$455$	17.5249	−	7.55666i	0.821580	−	0.354262i
$456$	2.65122	−	8.15963i	0.124155	−	0.382110i
$457$	−2.31538	−	4.54419i	−0.108309	−	0.212568i	0.830490	−	0.557033i	$-0.188060\pi$
$457$	−2.31538	−	4.54419i	−0.108309	−	0.212568i	−0.938799	+	0.344465i	$0.888060\pi$
$458$	−2.57562	−	0.407937i	−0.120351	−	0.0190617i
$459$	−22.8319	−	16.5884i	−1.06570	−	0.774279i
$460$	−7.54101	+	9.09143i	−0.351602	+	0.423890i
$461$			12.4703i			0.580801i	0.956905	+	0.290400i	$0.0937885\pi$
$461$			12.4703i			0.580801i	−0.956905	+	0.290400i	$0.906211\pi$
$462$		0			0
$463$	−19.2728	+	19.2728i	−0.895684	+	0.895684i	−0.995051	−	0.0993669i	$-0.968318\pi$
$463$	−19.2728	+	19.2728i	−0.895684	+	0.895684i	0.0993669	+	0.995051i	$0.468318\pi$
$464$	2.14609	+	6.60498i	0.0996297	+	0.306629i
$465$	17.1377	+	1.10059i	0.794743	+	0.0510384i
$466$	1.74554	−	1.26821i	0.0808607	−	0.0587487i
$467$	35.3668	−	18.0203i	1.63658	−	0.833879i	0.638655	−	0.769493i	$-0.279491\pi$
$467$	35.3668	−	18.0203i	1.63658	−	0.833879i	0.997925	−	0.0643861i	$-0.0205089\pi$
$468$	−7.81705	+	3.98299i	−0.361343	+	0.184114i
$469$	−4.38683	+	3.18722i	−0.202565	+	0.147172i
$470$	−2.65472	−	3.01909i	−0.122453	−	0.139260i
$471$	7.55738	+	23.2592i	0.348226	+	1.07173i
$472$	−2.08508	+	2.08508i	−0.0959738	+	0.0959738i
$473$		0			0
$474$			8.48273i			0.389625i
$475$	2.62180	−	20.3285i	0.120296	−	0.932733i
$476$	21.8952	+	15.9078i	1.00357	+	0.729134i
$477$	−2.48393	−	0.393417i	−0.113732	−	0.0180133i
$478$	−2.31742	−	4.54819i	−0.105996	−	0.208029i
$479$	11.8215	−	36.3828i	0.540138	−	1.66237i	−0.192141	−	0.981367i	$-0.561543\pi$
$479$	11.8215	−	36.3828i	0.540138	−	1.66237i	0.732278	−	0.681006i	$-0.238457\pi$
$480$	−4.99965	−	11.5949i	−0.228202	−	0.529230i
$481$	2.00102	−	2.75417i	0.0912389	−	0.125580i
$482$	−6.17614	+	12.1214i	−0.281316	+	0.552113i
$483$	−7.04599	−	7.04599i	−0.320603	−	0.320603i
$484$		0			0
$485$	−12.0387	−	19.0246i	−0.546650	−	0.863863i
$486$	6.93598	−	2.25364i	0.314622	−	0.102227i
$487$	−4.25177	−	26.8446i	−0.192666	−	1.21645i	−0.874532	−	0.484968i	$-0.838831\pi$
$487$	−4.25177	−	26.8446i	−0.192666	−	1.21645i	0.681866	−	0.731477i	$-0.261169\pi$
$488$	−1.99369	+	12.5877i	−0.0902501	+	0.569817i
$489$	11.2965	+	3.67046i	0.510846	+	0.165984i
$490$	1.59279	−	0.406752i	0.0719549	−	0.0183752i
$491$	−2.33461	−	3.21331i	−0.105359	−	0.145015i	0.753082	−	0.657927i	$-0.228567\pi$
$491$	−2.33461	−	3.21331i	−0.105359	−	0.145015i	−0.858441	+	0.512912i	$0.828567\pi$
$492$	−7.04784	+	1.11627i	−0.317741	+	0.0503253i
$493$	12.4138	+	6.32512i	0.559087	+	0.284869i
$494$	−5.85854			−0.263588
$495$		0			0
$496$	17.7010			0.794798
$497$	7.46596	+	3.80409i	0.334894	+	0.170637i
$498$	3.67244	−	0.581657i	0.164566	−	0.0260647i
$499$	−3.77656	−	5.19799i	−0.169062	−	0.232694i	0.716076	−	0.698022i	$-0.245936\pi$
$499$	−3.77656	−	5.19799i	−0.169062	−	0.232694i	−0.885138	+	0.465328i	$0.845936\pi$
$500$	−11.0063	−	16.3319i	−0.492217	−	0.730387i
$501$	12.2369	+	3.97602i	0.546706	+	0.177636i
$502$	0.759827	−	4.79736i	0.0339127	−	0.214117i
$503$	6.37107	+	40.2254i	0.284072	+	1.79356i	0.555937	+	0.831224i	$0.312360\pi$
$503$	6.37107	+	40.2254i	0.284072	+	1.79356i	−0.271865	+	0.962335i	$0.587640\pi$
$504$	−8.67089	+	2.81734i	−0.386232	+	0.125494i
$505$	0.936660	−	4.16493i	0.0416808	−	0.185337i
$506$		0			0
$507$	3.57347	+	3.57347i	0.158703	+	0.158703i
$508$	−7.54106	+	14.8002i	−0.334581	+	0.656651i
$509$	5.45800	−	7.51230i	0.241922	−	0.332977i	−0.670740	−	0.741693i	$-0.734023\pi$
$509$	5.45800	−	7.51230i	0.241922	−	0.332977i	0.912662	+	0.408716i	$0.134023\pi$
$510$	−6.09085	−	2.42070i	−0.269707	−	0.107190i
$511$	13.3398	−	41.0556i	0.590117	−	1.81619i
$512$	−10.2886	−	20.1924i	−0.454695	−	0.892388i
$513$	−21.6904	−	3.43542i	−0.957654	−	0.151678i
$514$	−1.67530	−	1.21718i	−0.0738944	−	0.0536875i
$515$	10.6213	+	8.80995i	0.468028	+	0.388213i
$516$		−	14.3987i		−	0.633868i
$517$		0			0
$518$	1.17149	−	1.17149i	0.0514723	−	0.0514723i
$519$	−4.64826	−	14.3059i	−0.204036	−	0.627958i
$520$	−9.02702	+	7.93755i	−0.395861	+	0.348085i
$521$	11.9792	−	8.70338i	0.524817	−	0.381302i	−0.293598	−	0.955929i	$-0.594853\pi$
$521$	11.9792	−	8.70338i	0.524817	−	0.381302i	0.818416	+	0.574627i	$0.194853\pi$
$522$	−1.95836	+	0.997836i	−0.0857152	+	0.0436741i
$523$	−34.6096	+	17.6345i	−1.51337	+	0.771102i	−0.996390	−	0.0848935i	$-0.972945\pi$
$523$	−34.6096	+	17.6345i	−1.51337	+	0.771102i	−0.516983	+	0.855996i	$0.672945\pi$
$524$	−10.7122	+	7.78284i	−0.467963	+	0.339995i
$525$	14.5799	−	7.96609i	0.636321	−	0.347669i
$526$	3.45364	+	10.6292i	0.150586	+	0.463456i
$527$	25.1096	−	25.1096i	1.09379	−	1.09379i
$528$		0			0
$529$			14.0073i			0.609011i
$530$	−1.60667	+	0.149768i	−0.0697892	+	0.00650549i
$531$	2.21021	+	1.60581i	0.0959148	+	0.0696862i
$532$	20.8005	+	3.29448i	0.901817	+	0.142834i
$533$	4.72371	+	9.27081i	0.204607	+	0.401563i
$534$	1.92097	−	5.91214i	0.0831285	−	0.255843i
$535$	0.359683	−	0.905016i	0.0155505	−	0.0391273i
$536$	2.00747	−	2.76304i	0.0867095	−	0.119345i
$537$	1.15180	−	2.26054i	0.0497039	−	0.0975495i
$538$	−7.89771	−	7.89771i	−0.340495	−	0.340495i
$539$		0			0
$540$	−17.8309	+	11.2833i	−0.767320	+	0.485558i
$541$	16.5674	−	5.38306i	0.712286	−	0.231436i	0.0696106	−	0.997574i	$-0.477824\pi$
$541$	16.5674	−	5.38306i	0.712286	−	0.231436i	0.642676	+	0.766138i	$0.277824\pi$
$542$	0.106213	+	0.670600i	0.00456222	+	0.0288047i
$543$	0.772603	−	4.87803i	0.0331556	−	0.209336i
$544$	−24.8318	−	8.06835i	−1.06466	−	0.345928i
$545$	−10.7992	+	18.2064i	−0.462586	+	0.779875i
$546$	−2.79127	−	3.84186i	−0.119455	−	0.164416i
$547$	−38.7239	+	6.13326i	−1.65571	+	0.262239i	−0.913176	−	0.407565i	$-0.866378\pi$
$547$	−38.7239	+	6.13326i	−1.65571	+	0.262239i	−0.742538	+	0.669804i	$0.766378\pi$
$548$	−24.1226	−	12.2911i	−1.03047	−	0.525049i
$549$	11.8076			0.503936
$550$		0			0
$551$	10.8414			0.461858
$552$	5.59209	+	2.84931i	0.238015	+	0.121275i
$553$	−43.9158	+	6.95558i	−1.86749	+	0.295781i
$554$	4.09197	+	5.63211i	0.173851	+	0.239285i
$555$	1.51194	−	2.54899i	0.0641785	−	0.108199i
$556$	−6.97329	−	2.26576i	−0.295733	−	0.0960896i
$557$	5.74133	−	36.2493i	0.243268	−	1.53593i	−0.499459	−	0.866338i	$-0.666468\pi$
$557$	5.74133	−	36.2493i	0.243268	−	1.53593i	0.742727	−	0.669595i	$-0.233532\pi$
$558$	0.876348	+	5.53305i	0.0370988	+	0.234232i
$559$	−19.9678	+	6.48793i	−0.844548	+	0.274410i
$560$	14.4711	−	9.15725i	0.611514	−	0.386964i
$561$		0			0
$562$	8.76280	+	8.76280i	0.369636	+	0.369636i
$563$	7.66381	−	15.0411i	0.322991	−	0.633906i	−0.671231	−	0.741248i	$-0.734234\pi$
$563$	7.66381	−	15.0411i	0.322991	−	0.633906i	0.994222	+	0.107342i	$0.0342341\pi$
$564$	4.34326	−	5.97799i	0.182884	−	0.251719i
$565$	−16.7372	+	42.1132i	−0.704138	+	1.77172i
$566$	−1.11832	+	3.44182i	−0.0470063	+	0.144671i
$567$	−1.32155	−	2.59368i	−0.0554997	−	0.108924i
$568$	−5.21268	−	0.825608i	−0.218719	−	0.0346417i
$569$	2.14294	+	1.55694i	0.0898368	+	0.0652703i	0.631797	−	0.775134i	$-0.282318\pi$
$569$	2.14294	+	1.55694i	0.0898368	+	0.0652703i	−0.541960	+	0.840404i	$0.682318\pi$
$570$	−5.07816	+	0.473367i	−0.212701	+	0.0198272i
$571$		−	29.8675i		−	1.24992i	−0.780658	−	0.624959i	$-0.785116\pi$
$571$		−	29.8675i		−	1.24992i	0.780658	−	0.624959i	$-0.214884\pi$
$572$		0			0
$573$	3.28527	−	3.28527i	0.137244	−	0.137244i
$574$	1.56473	+	4.81574i	0.0653105	+	0.201005i
$575$	14.3877	+	4.22060i	0.600007	+	0.176011i
$576$	−3.89881	+	2.83265i	−0.162450	+	0.118027i
$577$	0.319779	−	0.162935i	0.0133126	−	0.00678309i	−0.447322	−	0.894373i	$-0.647622\pi$
$577$	0.319779	−	0.162935i	0.0133126	−	0.00678309i	0.460634	+	0.887590i	$0.347622\pi$
$578$	−4.67875	+	2.38394i	−0.194610	+	0.0991589i
$579$	19.2655	−	13.9972i	0.800649	−	0.581705i
$580$	7.82284	−	6.87870i	0.324826	−	0.285623i
$581$	6.02257	+	18.5356i	0.249858	+	0.768985i
$582$	−3.96123	+	3.96123i	−0.164198	+	0.164198i
$583$		0			0
$584$			27.1896i			1.12511i
$585$	8.57177	+	7.10998i	0.354399	+	0.293961i
$586$	5.79867	+	4.21298i	0.239541	+	0.174037i
$587$	25.5288	+	4.04336i	1.05368	+	0.166887i	0.659164	−	0.752000i	$-0.270910\pi$
$587$	25.5288	+	4.04336i	1.05368	+	0.166887i	0.394521	+	0.918887i	$0.370910\pi$
$588$	1.37172	+	2.69216i	0.0565690	+	0.111023i
$589$	8.53884	−	26.2798i	0.351837	−	1.08284i
$590$	1.62897	+	0.647408i	0.0670638	+	0.0266534i
$591$	0.202473	−	0.278680i	0.00832861	−	0.0114634i
$592$	1.38684	−	2.72183i	0.0569989	−	0.111867i
$593$	−9.56872	−	9.56872i	−0.392940	−	0.392940i	0.482794	−	0.875734i	$-0.339622\pi$
$593$	−9.56872	−	9.56872i	−0.392940	−	0.392940i	−0.875734	+	0.482794i	$0.839622\pi$
$594$		0			0
$595$	7.53787	−	33.5177i	0.309022	−	1.37409i
$596$	30.1178	−	9.78585i	1.23367	−	0.400844i
$597$	1.97512	+	12.4704i	0.0808364	+	0.510381i
$598$	0.670427	−	4.23291i	0.0274158	−	0.173096i
$599$	−10.7687	−	3.49896i	−0.439997	−	0.142964i	0.0806373	−	0.996744i	$-0.474304\pi$
$599$	−10.7687	−	3.49896i	−0.439997	−	0.142964i	−0.520634	+	0.853780i	$0.674304\pi$
$600$	−7.18324	+	7.60962i	−0.293254	+	0.310662i
$601$	9.69211	+	13.3401i	0.395350	+	0.544152i	0.959569	−	0.281473i	$-0.0908229\pi$
$601$	9.69211	+	13.3401i	0.395350	+	0.544152i	−0.564220	+	0.825625i	$0.690823\pi$
$602$	−10.0917	+	1.59837i	−0.411307	+	0.0651446i
$603$	−2.81934	−	1.43653i	−0.114812	−	0.0584999i
$604$	31.3413			1.27526
$605$		0			0
$606$	−1.06223			−0.0431503
$607$	4.44109	+	2.26285i	0.180258	+	0.0918461i	0.541791	−	0.840513i	$-0.317746\pi$
$607$	4.44109	+	2.26285i	0.180258	+	0.0918461i	−0.361533	+	0.932359i	$0.617746\pi$
$608$	−20.0671	+	3.17832i	−0.813828	+	0.128898i
$609$	5.16532	+	7.10945i	0.209309	+	0.288090i
$610$	7.34053	−	1.87456i	0.297210	−	0.0758987i
$611$	−10.2472	−	3.32951i	−0.414556	−	0.134697i
$612$	−2.47057	+	15.5986i	−0.0998670	+	0.630536i
$613$	2.85957	+	18.0546i	0.115497	+	0.729218i	0.975675	+	0.219224i	$0.0703525\pi$
$613$	2.85957	+	18.0546i	0.115497	+	0.729218i	−0.860178	+	0.509994i	$0.829648\pi$
$614$	−0.574683	+	0.186726i	−0.0231923	+	0.00753565i
$615$	4.84357	+	7.65423i	0.195312	+	0.308648i
$616$		0			0
$617$	15.4942	+	15.4942i	0.623773	+	0.623773i	0.946494	−	0.322721i	$-0.104598\pi$
$617$	15.4942	+	15.4942i	0.623773	+	0.623773i	−0.322721	+	0.946494i	$0.604598\pi$
$618$	1.55887	−	3.05945i	0.0627068	−	0.123069i
$619$	28.9283	−	39.8164i	1.16273	−	1.60036i	0.462106	−	0.886825i	$-0.347094\pi$
$619$	28.9283	−	39.8164i	1.16273	−	1.60036i	0.700622	−	0.713533i	$-0.252906\pi$
$620$	−10.5128	−	24.3806i	−0.422205	−	0.979148i
$621$	4.96431	−	15.2786i	0.199211	−	0.613109i
$622$	−3.13638	−	6.15549i	−0.125757	−	0.246813i
$623$	32.1828	+	5.09725i	1.28938	+	0.204217i
$624$	−7.08383	−	5.14670i	−0.283580	−	0.206033i
$625$	−13.5053	+	21.0382i	−0.540210	+	0.841530i
$626$			0.361199i			0.0144364i
$627$		0			0
$628$	26.7363	−	26.7363i	1.06689	−	1.06689i
$629$	−1.89374	−	5.82832i	−0.0755082	−	0.232390i
$630$	3.57885	+	4.07006i	0.142585	+	0.162155i
$631$	7.32346	−	5.32080i	0.291542	−	0.211818i	−0.432394	−	0.901685i	$-0.642331\pi$
$631$	7.32346	−	5.32080i	0.291542	−	0.211818i	0.723936	+	0.689867i	$0.242331\pi$
$632$	24.9528	−	12.7141i	0.992568	−	0.505739i
$633$	−8.98990	+	4.58058i	−0.357316	+	0.182062i
$634$	−6.74238	+	4.89863i	−0.267774	+	0.194549i
$635$	21.0421	+	1.35132i	0.835029	+	0.0536256i
$636$	−0.916496	−	2.82068i	−0.0363414	−	0.111847i
$637$	3.11534	−	3.11534i	0.123434	−	0.123434i
$638$		0			0
$639$			4.88965i			0.193432i
$640$	−16.1246	+	19.4398i	−0.637382	+	0.768427i
$641$	22.5944	+	16.4158i	0.892426	+	0.648385i	0.936509	−	0.350643i	$-0.114037\pi$
$641$	22.5944	+	16.4158i	0.892426	+	0.648385i	−0.0440836	+	0.999028i	$0.514037\pi$
$642$	−0.239343	−	0.0379082i	−0.00944611	−	0.00149612i
$643$	−4.37166	−	8.57987i	−0.172401	−	0.338357i	0.788597	−	0.614910i	$-0.210808\pi$
$643$	−4.37166	−	8.57987i	−0.172401	−	0.338357i	−0.960999	+	0.276553i	$0.910808\pi$
$644$	−4.76065	+	14.6518i	−0.187596	+	0.577361i
$645$	−16.7838	+	7.23711i	−0.660861	+	0.284961i
$646$	−6.19886	+	8.53199i	−0.243891	+	0.335687i
$647$	14.0516	−	27.5778i	0.552425	−	1.08420i	−0.430910	−	0.902395i	$-0.641807\pi$
$647$	14.0516	−	27.5778i	0.552425	−	1.08420i	0.983335	−	0.181801i	$-0.0581926\pi$
$648$	1.29645	+	1.29645i	0.0509296	+	0.0509296i
$649$		0			0
$650$	6.45766	+	3.05928i	0.253290	+	0.119995i
$651$	21.3018	−	6.92139i	0.834885	−	0.271270i
$652$	−2.87275	−	18.1378i	−0.112506	−	0.710332i
$653$	0.955876	−	6.03516i	0.0374063	−	0.236174i	−0.961901	−	0.273399i	$-0.911852\pi$
$653$	0.955876	−	6.03516i	0.0374063	−	0.236174i	0.999307	+	0.0372253i	$0.0118519\pi$
$654$	5.00945	+	1.62767i	0.195885	+	0.0636468i
$655$	14.4562	+	8.57477i	0.564851	+	0.335044i
$656$	5.48785	+	7.55337i	0.214264	+	0.294910i
$657$	24.8805	−	3.94069i	0.970682	−	0.153741i
$658$	−4.67195	−	2.38048i	−0.182132	−	0.0928008i
$659$	12.0647			0.469975			0.234988	−	0.971998i	$-0.424495\pi$
$659$	12.0647			0.469975			0.234988	+	0.971998i	$0.424495\pi$
$660$		0			0
$661$	−29.6228			−1.15219			−0.576097	−	0.817382i	$-0.695425\pi$
$661$	−29.6228			−1.15219			−0.576097	+	0.817382i	$0.695425\pi$
$662$	−6.49141	−	3.30754i	−0.252296	−	0.128551i
$663$	−17.3495	+	2.74789i	−0.673799	+	0.106719i
$664$	−7.21531	−	9.93103i	−0.280008	−	0.385399i
$665$	−6.61460	−	25.9019i	−0.256503	−	1.00443i
$666$	0.919461	+	0.298751i	0.0356284	+	0.0115764i
$667$	−1.24064	+	7.83310i	−0.0480378	+	0.303299i
$668$	−3.11190	−	19.6478i	−0.120403	−	0.760195i
$669$	−6.69903	+	2.17665i	−0.259000	+	0.0841541i
$670$	−1.98079	−	0.445463i	−0.0765244	−	0.0172097i
$671$		0			0
$672$	−11.6451	−	11.6451i	−0.449220	−	0.449220i
$673$	−2.28621	+	4.48693i	−0.0881267	+	0.172958i	−0.930863	−	0.365368i	$-0.880943\pi$
$673$	−2.28621	+	4.48693i	−0.0881267	+	0.172958i	0.842736	+	0.538326i	$0.180943\pi$
$674$	−2.70894	+	3.72853i	−0.104344	+	0.143618i
$675$	22.1146	+	15.1133i	0.851191	+	0.581710i
$676$	2.41443	−	7.43084i	0.0928626	−	0.285802i
$677$	−16.5280	−	32.4380i	−0.635223	−	1.24670i	−0.954267	−	0.298956i	$-0.903362\pi$
$677$	−16.5280	−	32.4380i	−0.635223	−	1.24670i	0.319044	−	0.947740i	$-0.396638\pi$
$678$	11.1374	+	1.76398i	0.427728	+	0.0677454i
$679$	−23.7557	−	17.2595i	−0.911661	−	0.662360i
$680$	2.00834	+	21.5450i	0.0770165	+	0.826213i
$681$			3.77894i			0.144809i
$682$		0			0
$683$	−8.07353	+	8.07353i	−0.308925	+	0.308925i	−0.844492	−	0.535567i	$-0.820098\pi$
$683$	−8.07353	+	8.07353i	−0.308925	+	0.308925i	0.535567	+	0.844492i	$0.320098\pi$
$684$	3.79761	+	11.6878i	0.145205	+	0.446895i
$685$	−2.20250	+	34.2962i	−0.0841534	+	1.31039i
$686$	−6.33082	+	4.59961i	−0.241712	+	0.175614i
$687$	−5.42103	+	2.76215i	−0.206825	+	0.105383i
$688$	−16.7862	+	8.55298i	−0.639967	+	0.326079i
$689$	−3.49870	+	2.54195i	−0.133290	+	0.0968407i
$690$	0.239107	−	3.72324i	0.00910263	−	0.141741i
$691$	−3.67098	−	11.2981i	−0.139651	−	0.429801i	0.856634	−	0.515925i	$-0.172552\pi$
$691$	−3.67098	−	11.2981i	−0.139651	−	0.429801i	−0.996284	+	0.0861243i	$0.972552\pi$
$692$	−16.4445	+	16.4445i	−0.625125	+	0.625125i
$693$		0			0
$694$		−	9.39538i		−	0.356644i
$695$	0.863855	+	9.26721i	0.0327679	+	0.351525i
$696$	−4.47789	−	3.25338i	−0.169734	−	0.123319i
$697$	18.4995	+	2.93003i	0.700719	+	0.110983i
$698$	3.29735	+	6.47142i	0.124807	+	0.244947i
$699$	1.55559	−	4.78761i	0.0588378	−	0.181084i
$700$	−21.2073	−	14.4932i	−0.801561	−	0.547793i
$701$	15.6038	−	21.4768i	0.589348	−	0.811169i	−0.405333	−	0.914169i	$-0.632844\pi$
$701$	15.6038	−	21.4768i	0.589348	−	0.811169i	0.994681	+	0.103001i	$0.0328444\pi$
$702$	3.47577	−	6.82157i	0.131184	−	0.257464i
$703$	−3.37197	−	3.37197i	−0.127176	−	0.127176i
$704$		0			0
$705$	−9.15124	−	2.05804i	−0.344655	−	0.0775102i
$706$	1.17180	−	0.380741i	0.0441012	−	0.0143294i
$707$	−0.871000	−	5.49928i	−0.0327573	−	0.206822i
$708$	−0.504006	+	3.18217i	−0.0189417	+	0.119593i
$709$	16.9867	+	5.51933i	0.637950	+	0.207283i	0.610094	−	0.792329i	$-0.291132\pi$
$709$	16.9867	+	5.51933i	0.637950	+	0.207283i	0.0278567	+	0.999612i	$0.491132\pi$
$710$	0.776275	+	3.03979i	0.0291331	+	0.114081i
$711$	−15.2508	−	20.9909i	−0.571950	−	0.787222i
$712$	−20.2703	+	3.21050i	−0.759662	+	0.120319i
$713$	18.0105	+	9.17683i	0.674500	+	0.343675i
$714$	−8.54844			−0.319917
$715$		0			0
$716$	−3.92246			−0.146589
$717$	−10.6115	−	5.40685i	−0.396295	−	0.201923i
$718$	−4.09591	+	0.648729i	−0.152858	+	0.0242103i
$719$	−19.2585	−	26.5071i	−0.718222	−	0.988547i	−0.999581	−	0.0289450i	$-0.990785\pi$
$719$	−19.2585	−	26.5071i	−0.718222	−	0.988547i	0.281359	−	0.959603i	$-0.409215\pi$
$720$	8.59495	+	5.09814i	0.320315	+	0.189996i
$721$	17.1172	+	5.56173i	0.637479	+	0.207130i
$722$	0.167699	−	1.05881i	0.00624111	−	0.0394048i
$723$	4.96527	+	31.3495i	0.184660	+	1.16590i
$724$	−7.26202	+	2.35957i	−0.269891	+	0.0876929i
$725$	−11.9501	−	5.66127i	−0.443814	−	0.210254i
$726$		0			0
$727$	0.964903	+	0.964903i	0.0357863	+	0.0357863i	0.724773	−	0.688987i	$-0.241944\pi$
$727$	0.964903	+	0.964903i	0.0357863	+	0.0357863i	−0.688987	+	0.724773i	$0.741944\pi$
$728$	−7.11758	+	13.9690i	−0.263795	+	0.517727i
$729$	11.7614	−	16.1882i	0.435609	−	0.599564i
$730$	14.8421	−	6.39984i	0.549330	−	0.236869i
$731$	−11.6791	+	35.9446i	−0.431968	+	1.32946i
$732$	6.32174	+	12.4071i	0.233658	+	0.458580i
$733$	11.6481	+	1.84488i	0.430233	+	0.0681422i	0.367796	−	0.929907i	$-0.380113\pi$
$733$	11.6481	+	1.84488i	0.430233	+	0.0681422i	0.0624374	+	0.998049i	$0.480113\pi$
$734$	−8.38724	−	6.09369i	−0.309579	−	0.224922i
$735$	2.44865	−	2.95208i	0.0903198	−	0.108889i
$736$		−	14.8626i		−	0.547842i
$737$		0			0
$738$	−2.08937	+	2.08937i	−0.0769107	+	0.0769107i
$739$	−13.3170	−	40.9856i	−0.489875	−	1.50768i	−0.824794	−	0.565434i	$-0.808709\pi$
$739$	−13.3170	−	40.9856i	−0.489875	−	1.50768i	0.334919	−	0.942247i	$-0.391291\pi$
$740$	−4.57259	−	0.293652i	−0.168092	−	0.0107949i
$741$	−11.0583	+	8.03430i	−0.406235	+	0.295147i
$742$	−1.87521	+	0.955467i	−0.0688411	+	0.0350763i
$743$	33.7816	−	17.2126i	1.23933	−	0.631468i	0.293443	−	0.955977i	$-0.405199\pi$
$743$	33.7816	−	17.2126i	1.23933	−	0.631468i	0.945883	+	0.324509i	$0.105199\pi$
$744$	−11.4131	+	8.29213i	−0.418426	+	0.304004i
$745$	−26.5447	−	30.1881i	−0.972522	−	1.10601i
$746$	0.549420	+	1.69094i	0.0201157	+	0.0619098i
$747$	−8.04189	+	8.04189i	−0.294237	+	0.294237i
$748$		0			0
$749$		−	1.27018i		−	0.0464114i
$750$	5.84467	+	2.13000i	0.213417	+	0.0777765i
$751$	−28.2437	−	20.5203i	−1.03063	−	0.748795i	−0.0621941	−	0.998064i	$-0.519810\pi$
$751$	−28.2437	−	20.5203i	−1.03063	−	0.748795i	−0.968434	+	0.249269i	$0.919810\pi$
$752$	−9.54914	−	1.51244i	−0.348221	−	0.0551528i
$753$	−5.14480	−	10.0972i	−0.187487	−	0.367964i
$754$	−1.16795	+	3.59457i	−0.0425341	+	0.130907i
$755$	−15.7528	−	36.5329i	−0.573305	−	1.32957i
$756$	−16.1766	+	22.2652i	−0.588337	+	0.809777i
$757$	15.6517	−	30.7182i	0.568870	−	1.11647i	−0.410019	−	0.912077i	$-0.634478\pi$
$757$	15.6517	−	30.7182i	0.568870	−	1.11647i	0.978889	−	0.204393i	$-0.0655221\pi$
$758$	5.72618	+	5.72618i	0.207984	+	0.207984i
$759$		0			0
$760$	9.00370	+	14.2284i	0.326598	+	0.516119i
$761$	−13.2335	+	4.29984i	−0.479716	+	0.155869i	−0.538886	−	0.842379i	$-0.681155\pi$
$761$	−13.2335	+	4.29984i	−0.479716	+	0.155869i	0.0591701	+	0.998248i	$0.481155\pi$
$762$	−0.820754	−	5.18204i	−0.0297328	−	0.187725i
$763$	−4.31898	+	27.2690i	−0.156358	+	0.987203i
$764$	−6.83155	−	2.21970i	−0.247157	−	0.0803061i
$765$	19.4242	−	4.96038i	0.702284	−	0.179343i
$766$	−3.25512	−	4.48028i	−0.117612	−	0.161879i
$767$	4.64006	−	0.734913i	0.167543	−	0.0265362i
$768$	−0.149794	−	0.0763239i	−0.00540523	−	0.00275410i
$769$	−13.3273			−0.480596			−0.240298	−	0.970699i	$-0.577245\pi$
$769$	−13.3273			−0.480596			−0.240298	+	0.970699i	$0.577245\pi$
$770$		0			0
$771$	−4.83143			−0.174000
$772$	−32.8043	−	16.7146i	−1.18065	−	0.601573i
$773$	−12.3457	+	1.95537i	−0.444045	+	0.0703298i	−0.374453	−	0.927246i	$-0.622170\pi$
$773$	−12.3457	+	1.95537i	−0.444045	+	0.0703298i	−0.0695917	+	0.997576i	$0.522170\pi$
$774$	−3.50458	−	4.82364i	−0.125970	−	0.173382i
$775$	−23.1352	+	24.5084i	−0.831040	+	0.880369i
$776$	17.5895	+	5.71518i	0.631427	+	0.205163i
$777$	0.604680	−	3.81780i	0.0216928	−	0.136963i
$778$	0.0624567	+	0.394336i	0.00223918	+	0.0141376i
$779$	13.8614	−	4.50386i	0.496638	−	0.161367i
$780$	−2.88168	+	12.8136i	−0.103181	+	0.458802i
$781$		0			0
$782$	−5.45516	−	5.45516i	−0.195076	−	0.195076i
$783$	−6.43199	+	12.6235i	−0.229861	+	0.451127i
$784$	2.32373	−	3.19834i	0.0829904	−	0.114227i
$785$	−44.6033	−	17.7268i	−1.59196	−	0.632697i
$786$	1.29240	−	3.97760i	0.0460984	−	0.141876i
$787$	−2.85686	−	5.60690i	−0.101836	−	0.199864i	0.834467	−	0.551058i	$-0.185776\pi$
$787$	−2.85686	−	5.60690i	−0.101836	−	0.199864i	−0.936303	+	0.351194i	$0.885776\pi$
$788$	−0.526011	−	0.0833119i	−0.0187384	−	0.00296786i
$789$	21.0956	+	15.3269i	0.751024	+	0.545651i
$790$	−12.8136	−	10.6284i	−0.455888	−	0.378142i
$791$			59.1055i			2.10155i
$792$		0			0
$793$	14.3574	−	14.3574i	0.509846	−	0.509846i
$794$	2.52901	+	7.78350i	0.0897512	+	0.276226i
$795$	−2.82727	+	2.48605i	−0.100273	+	0.0881711i
$796$	15.7923	−	11.4738i	0.559744	−	0.406678i
$797$	1.57581	−	0.802918i	0.0558182	−	0.0284408i	−0.425859	−	0.904790i	$-0.640028\pi$
$797$	1.57581	−	0.802918i	0.0558182	−	0.0284408i	0.481677	+	0.876349i	$0.340028\pi$
$798$	−5.92693	+	3.01992i	−0.209811	+	0.106904i
$799$	−15.6913	+	11.4004i	−0.555118	+	0.403317i
$800$	23.7789	+	6.97552i	0.840712	+	0.246622i
$801$	5.87569	+	18.0835i	0.207607	+	0.638950i
$802$	−9.82669	+	9.82669i	−0.346992	+	0.346992i
$803$		0			0
$804$		−	3.73160i		−	0.131603i
$805$	19.4716	−	1.81507i	0.686283	−	0.0639727i
$806$	7.79346	+	5.66228i	0.274513	+	0.199445i
$807$	−25.7381	−	4.07651i	−0.906023	−	0.143500i
$808$	1.59210	+	3.12466i	0.0560097	+	0.109925i
$809$	−5.70252	+	17.5505i	−0.200490	+	0.617044i	0.799379	+	0.600828i	$0.205162\pi$
$809$	−5.70252	+	17.5505i	−0.200490	+	0.617044i	−0.999869	+	0.0162167i	$0.994838\pi$
$810$	0.402542	−	1.01286i	0.0141439	−	0.0355882i
$811$	7.66716	−	10.5529i	0.269230	−	0.370564i	−0.652899	−	0.757445i	$-0.726448\pi$
$811$	7.66716	−	10.5529i	0.269230	−	0.370564i	0.922130	+	0.386881i	$0.126448\pi$
$812$	6.16811	−	12.1056i	0.216458	−	0.424823i
$813$	1.12013	+	1.12013i	0.0392847	+	0.0392847i
$814$		0			0
$815$	−19.6984	+	12.4651i	−0.690004	+	0.436633i
$816$	−14.9906	+	4.87075i	−0.524777	+	0.170510i
$817$	4.60068	+	29.0476i	0.160957	+	1.01625i
$818$	−0.185075	+	1.16852i	−0.00647099	+	0.0408562i
$819$	13.8143	+	4.48853i	0.482710	+	0.156842i
$820$	7.14440	−	12.0448i	0.249493	−	0.420621i
$821$	15.3089	+	21.0709i	0.534283	+	0.735378i	0.987776	−	0.155882i	$-0.0498220\pi$
$821$	15.3089	+	21.0709i	0.534283	+	0.735378i	−0.453492	+	0.891260i	$0.649822\pi$
$822$	8.44614	−	1.33774i	0.294593	−	0.0466590i
$823$	−4.47662	−	2.28095i	−0.156045	−	0.0795089i	0.374224	−	0.927338i	$-0.377909\pi$
$823$	−4.47662	−	2.28095i	−0.156045	−	0.0795089i	−0.530269	+	0.847829i	$0.677909\pi$
$824$	−11.3361			−0.394912
$825$		0			0
$826$	2.28625			0.0795488
$827$	−10.8443	−	5.52543i	−0.377092	−	0.192138i	0.255164	−	0.966898i	$-0.417871\pi$
$827$	−10.8443	−	5.52543i	−0.377092	−	0.192138i	−0.632255	+	0.774760i	$0.717871\pi$
$828$	−8.87927	+	1.40634i	−0.308576	+	0.0488736i
$829$	6.47245	+	8.90857i	0.224798	+	0.309407i	0.906487	−	0.422235i	$-0.138754\pi$
$829$	6.47245	+	8.90857i	0.224798	+	0.309407i	−0.681689	+	0.731642i	$0.738754\pi$
$830$	−3.72275	+	6.27619i	−0.129219	+	0.217850i
$831$	15.4475	+	5.01921i	0.535869	+	0.174114i
$832$	−1.29639	+	8.18508i	−0.0449442	+	0.283766i
$833$	−1.24067	−	7.83329i	−0.0429867	−	0.271407i
$834$	2.20259	−	0.715663i	0.0762693	−	0.0247814i
$835$	−21.3382	+	13.5028i	−0.738440	+	0.467283i
$836$		0			0
$837$	25.5338	+	25.5338i	0.882578	+	0.882578i
$838$	3.64414	−	7.15202i	0.125885	−	0.247062i
$839$	−5.46148	+	7.51708i	−0.188551	+	0.259518i	−0.892819	−	0.450416i	$-0.851276\pi$
$839$	−5.46148	+	7.51708i	−0.188551	+	0.259518i	0.704268	+	0.709935i	$0.251276\pi$
$840$	−5.04080	+	12.6834i	−0.173924	+	0.437619i
$841$	−6.80018	+	20.9288i	−0.234489	+	0.721683i
$842$	2.76426	+	5.42516i	0.0952626	+	0.186963i
$843$	28.5573	+	4.52303i	0.983566	+	0.155782i
$844$	12.6200	+	9.16895i	0.434397	+	0.315608i
$845$	−9.87528	+	0.920536i	−0.339720	+	0.0316674i
$846$		−	3.05979i		−	0.105198i
$847$		0			0
$848$	−2.74398	+	2.74398i	−0.0942286	+	0.0942286i
$849$	2.60918	+	8.03024i	0.0895469	+	0.275597i
$850$	11.2881	−	6.16752i	0.387179	−	0.211544i
$851$	2.82219	−	2.05044i	0.0967435	−	0.0702882i
$852$	−5.13791	+	2.61790i	−0.176022	+	0.0896877i
$853$	−24.0984	+	12.2787i	−0.825113	+	0.420416i	−0.814949	−	0.579532i	$-0.803235\pi$
$853$	−24.0984	+	12.2787i	−0.825113	+	0.420416i	−0.0101637	+	0.999948i	$0.503235\pi$
$854$	7.99407	−	5.80803i	0.273551	−	0.198747i
$855$	11.7151	−	10.3012i	0.400649	−	0.352295i
$856$	0.247221	+	0.760867i	0.00844983	+	0.0260059i
$857$	33.1497	−	33.1497i	1.13237	−	1.13237i	0.142591	−	0.989782i	$-0.454457\pi$
$857$	33.1497	−	33.1497i	1.13237	−	1.13237i	0.989782	−	0.142591i	$-0.0455432\pi$
$858$		0			0
$859$		−	47.2517i		−	1.61221i	−0.591775	−	0.806103i	$-0.701573\pi$
$859$		−	47.2517i		−	1.61221i	0.591775	−	0.806103i	$-0.298427\pi$
$860$	21.7500	+	18.0408i	0.741669	+	0.615188i
$861$	9.55771	+	6.94409i	0.325726	+	0.236654i
$862$	−9.56706	−	1.51527i	−0.325855	−	0.0516104i
$863$	7.06437	+	13.8646i	0.240474	+	0.471957i	0.979427	−	0.201801i	$-0.0646793\pi$
$863$	7.06437	+	13.8646i	0.240474	+	0.471957i	−0.738953	+	0.673757i	$0.764679\pi$
$864$	8.20467	−	25.2514i	0.279129	−	0.859070i
$865$	27.4338	+	10.9031i	0.932777	+	0.370716i
$866$	8.21659	−	11.3092i	0.279211	−	0.384301i
$867$	−5.56205	+	10.9161i	−0.188897	+	0.370732i
$868$	−24.4863	−	24.4863i	−0.831118	−	0.831118i
$869$		0			0
$870$	−0.721933	+	3.21013i	−0.0244758	+	0.108834i
$871$	−5.17490	+	1.68143i	−0.175345	+	0.0569729i
$872$	−2.72031	−	17.1753i	−0.0921212	−	0.581630i
$873$	2.68050	−	16.9240i	0.0907213	−	0.572792i
$874$	−5.70941	−	1.85510i	−0.193124	−	0.0627496i
$875$	−6.23472	+	32.0049i	−0.210772	+	1.08196i
$876$	17.4617	+	24.0340i	0.589976	+	0.812032i
$877$	28.7727	−	4.55715i	0.971586	−	0.153884i	0.349588	−	0.936903i	$-0.386321\pi$
$877$	28.7727	−	4.55715i	0.971586	−	0.153884i	0.621997	+	0.783019i	$0.286321\pi$
$878$	−1.35877	−	0.692328i	−0.0458563	−	0.0233650i
$879$	16.7229			0.564048
$880$		0			0
$881$	4.18815			0.141102			0.0705512	−	0.997508i	$-0.477524\pi$
$881$	4.18815			0.141102			0.0705512	+	0.997508i	$0.477524\pi$
$882$	1.11479	+	0.568016i	0.0375371	+	0.0191261i
$883$	45.1550	−	7.15185i	1.51959	−	0.240679i	0.659843	−	0.751404i	$-0.270623\pi$
$883$	45.1550	−	7.15185i	1.51959	−	0.240679i	0.859744	+	0.510725i	$0.170623\pi$
$884$	15.9629	+	21.9711i	0.536892	+	0.738968i
$885$	3.96261	−	1.01193i	0.133202	−	0.0340158i
$886$	−14.7403	−	4.78942i	−0.495211	−	0.160904i
$887$	−5.39049	+	34.0342i	−0.180995	+	1.14276i	0.715142	+	0.698979i	$0.246362\pi$
$887$	−5.39049	+	34.0342i	−0.180995	+	1.14276i	−0.896137	+	0.443777i	$0.853638\pi$
$888$	0.380858	+	2.40464i	0.0127807	+	0.0806945i
$889$	26.1549	−	8.49823i	0.877206	−	0.285021i
$890$	6.52371	+	10.3093i	0.218675	+	0.345569i
$891$		0			0
$892$	7.70048	+	7.70048i	0.257831	+	0.257831i
$893$	−6.85189	+	13.4476i	−0.229290	+	0.450006i
$894$	−5.87936	+	8.09224i	−0.196635	+	0.270645i
$895$	1.97151	+	4.57220i	0.0659004	+	0.152832i
$896$	−10.1795	+	31.3293i	−0.340073	+	1.04664i
$897$	−4.53947	−	8.90922i	−0.151569	−	0.297470i
$898$	16.8789	+	2.67335i	0.563255	+	0.0892108i
$899$	−14.4220	−	10.4782i	−0.481001	−	0.349467i
$900$	1.91732	−	14.8662i	0.0639106	−	0.495539i
$901$			7.78489i			0.259352i
$902$		0			0
$903$	−16.8566	+	16.8566i	−0.560951	+	0.560951i
$904$	−11.5039	−	35.4055i	−0.382616	−	1.17757i
$905$	6.40048	+	7.27897i	0.212759	+	0.241961i
$906$	−8.00885	+	5.81877i	−0.266076	+	0.193316i
$907$	−34.3152	+	17.4845i	−1.13942	+	0.580563i	−0.918771	−	0.394791i	$-0.870817\pi$
$907$	−34.3152	+	17.4845i	−1.13942	+	0.580563i	−0.220648	+	0.975354i	$0.570817\pi$
$908$	5.20568	−	2.65243i	0.172757	−	0.0880239i
$909$	2.62855	−	1.90976i	0.0871836	−	0.0633426i
$910$	9.30064	+	0.597288i	0.308313	+	0.0197999i
$911$	−11.3933	−	35.0649i	−0.377476	−	1.16175i	−0.941793	−	0.336193i	$-0.890861\pi$
$911$	−11.3933	−	35.0649i	−0.377476	−	1.16175i	0.564317	−	0.825558i	$-0.309139\pi$
$912$	−8.67283	+	8.67283i	−0.287186	+	0.287186i
$913$		0			0
$914$		−	2.49056i		−	0.0823805i
$915$	11.2849	−	13.6050i	0.373066	−	0.449767i
$916$	7.61001	+	5.52900i	0.251442	+	0.182683i
$917$	21.6521	+	3.42935i	0.715015	+	0.113247i
$918$	−6.25682	−	12.2797i	−0.206506	−	0.405291i
$919$	−9.39535	+	28.9159i	−0.309924	+	0.953848i	0.667870	+	0.744278i	$0.267206\pi$
$919$	−9.39535	+	28.9159i	−0.309924	+	0.953848i	−0.977794	+	0.209570i	$0.932794\pi$
$920$	−11.3106	+	4.87710i	−0.372901	+	0.160793i
$921$	−0.828668	+	1.14056i	−0.0273056	+	0.0375829i
$922$	−2.76469	+	5.42601i	−0.0910502	+	0.178696i
$923$	5.94554	+	5.94554i	0.195700	+	0.195700i
$924$		0			0
$925$	1.95599	+	5.47762i	0.0643126	+	0.180103i
$926$	−12.6587	+	4.11306i	−0.415990	+	0.135163i
$927$	1.64298	+	10.3734i	0.0539626	+	0.340707i
$928$	−2.05045	+	12.9460i	−0.0673092	+	0.424974i
$929$	−22.1568	−	7.19917i	−0.726940	−	0.236197i	−0.0779103	−	0.996960i	$-0.524825\pi$
$929$	−22.1568	−	7.19917i	−0.726940	−	0.236197i	−0.649029	+	0.760763i	$0.724825\pi$
$930$	7.21286	+	4.27834i	0.236519	+	0.140292i
$931$	−3.62748	−	4.99280i	−0.118886	−	0.163632i
$932$	−7.68704	+	1.21751i	−0.251797	+	0.0398808i
$933$	−14.3616	−	7.31760i	−0.470177	−	0.239567i
$934$	19.3837			0.634254
$935$		0			0
$936$	−9.14869			−0.299034
$937$	−7.16683	−	3.65168i	−0.234130	−	0.119295i	0.332990	−	0.942930i	$-0.391942\pi$
$937$	−7.16683	−	3.65168i	−0.234130	−	0.119295i	−0.567120	+	0.823635i	$0.691942\pi$
$938$	−2.61538	+	0.414236i	−0.0853953	+	0.0135253i
$939$	0.495342	+	0.681780i	0.0161649	+	0.0222491i
$940$	3.58817	+	14.0508i	0.117033	+	0.458288i
$941$	45.5460	+	14.7988i	1.48476	+	0.482427i	0.935531	−	0.353245i	$-0.114922\pi$
$941$	45.5460	+	14.7988i	1.48476	+	0.482427i	0.549228	+	0.835673i	$0.314922\pi$
$942$	−1.86829	+	11.7959i	−0.0608721	+	0.384331i
$943$	1.66788	+	10.5306i	0.0543136	+	0.342922i
$944$	4.00919	−	1.30266i	0.130488	−	0.0423981i
$945$	34.0840	+	7.66523i	1.10875	+	0.249350i
$946$		0			0
$947$	9.38618	+	9.38618i	0.305010	+	0.305010i	0.842970	−	0.537960i	$-0.180805\pi$
$947$	9.38618	+	9.38618i	0.305010	+	0.305010i	−0.537960	+	0.842970i	$0.680805\pi$
$948$	13.8915	−	27.2636i	0.451175	−	0.885481i
$949$	25.4617	−	35.0450i	0.826521	−	1.13761i
$950$	5.64763	−	8.26393i	0.183233	−	0.268117i
$951$	−6.00866	+	18.4928i	−0.194844	+	0.599669i
$952$	12.8126	+	25.1461i	0.415257	+	0.814989i
$953$	−52.5908	−	8.32956i	−1.70358	−	0.269821i	−0.772602	−	0.634890i	$-0.781045\pi$
$953$	−52.5908	−	8.32956i	−1.70358	−	0.269821i	−0.930980	+	0.365069i	$0.881045\pi$
$954$	−0.993573	−	0.721873i	−0.0321681	−	0.0233715i
$955$	0.846295	+	9.07884i	0.0273855	+	0.293784i
$956$			18.4130i			0.595519i
$957$		0			0
$958$	13.2098	−	13.2098i	0.426790	−	0.426790i
$959$	13.8512	+	42.6295i	0.447277	+	1.37658i
$960$	−0.462355	+	7.19954i	−0.0149224	+	0.232364i
$961$	−11.6790	+	8.48526i	−0.376741	+	0.273718i
$962$	1.48128	−	0.754749i	0.0477583	−	0.0243341i
$963$	0.660420	−	0.336501i	0.0212817	−	0.0108436i
$964$	39.7004	−	28.8440i	1.27866	−	0.929004i
$965$	−2.99519	+	46.6394i	−0.0964184	+	1.50138i
$966$	−1.50370	−	4.62791i	−0.0483807	−	0.148901i
$967$	−38.6475	+	38.6475i	−1.24282	+	1.24282i	−0.283994	+	0.958826i	$0.591660\pi$
$967$	−38.6475	+	38.6475i	−1.24282	+	1.24282i	−0.958826	+	0.283994i	$0.908340\pi$
$968$		0			0
$969$			24.6055i			0.790443i
$970$	−1.02043	−	10.9469i	−0.0327639	−	0.351483i
$971$	−6.69055	−	4.86097i	−0.214710	−	0.155996i	0.475232	−	0.879860i	$-0.342364\pi$
$971$	−6.69055	−	4.86097i	−0.214710	−	0.155996i	−0.689942	+	0.723865i	$0.742364\pi$
$972$	−25.9829	−	4.11529i	−0.833403	−	0.131998i
$973$	5.51110	+	10.8161i	0.176678	+	0.346750i
$974$	4.10149	−	12.6231i	0.131420	−	0.404470i
$975$	16.3846	−	3.08139i	0.524726	−	0.0986835i
$976$	10.7092	−	14.7399i	0.342792	−	0.471813i
$977$	−24.8581	+	48.7867i	−0.795280	+	1.56083i	0.0322997	+	0.999478i	$0.489717\pi$
$977$	−24.8581	+	48.7867i	−0.795280	+	1.56083i	−0.827580	+	0.561348i	$0.810283\pi$
$978$	4.10153	+	4.10153i	0.131152	+	0.131152i
$979$		0			0
$980$	−5.78535	−	1.30108i	−0.184806	−	0.0415614i
$981$	−15.3225	+	4.97857i	−0.489208	+	0.158953i
$982$	−0.303424	−	1.91574i	−0.00968265	−	0.0611338i
$983$	−2.13363	+	13.4712i	−0.0680521	+	0.429664i	0.930015	+	0.367521i	$0.119793\pi$
$983$	−2.13363	+	13.4712i	−0.0680521	+	0.429664i	−0.998067	+	0.0621429i	$0.980207\pi$
$984$	−7.07684	−	2.29941i	−0.225602	−	0.0733024i
$985$	0.167272	+	0.655017i	0.00532974	+	0.0208706i
$986$	3.99911	+	5.50430i	0.127357	+	0.175293i
$987$	−12.0831	+	1.91377i	−0.384608	+	0.0609160i
$988$	18.8294	+	9.59407i	0.599044	+	0.305228i
$989$	−21.5139			−0.684102
$990$		0			0
$991$	6.43457			0.204401			0.102200	−	0.994764i	$-0.467412\pi$
$991$	6.43457			0.204401			0.102200	+	0.994764i	$0.467412\pi$
$992$	29.7666	+	15.1668i	0.945090	+	0.481547i
$993$	−16.7887	+	2.65908i	−0.532775	+	0.0843832i
$994$	2.40517	+	3.31043i	0.0762872	+	0.105000i
$995$	−21.3120	−	12.6413i	−0.675635	−	0.400756i
$996$	−12.7558	−	4.14461i	−0.404183	−	0.131327i
$997$	−3.32838	+	21.0146i	−0.105411	+	0.665538i	0.877237	+	0.480058i	$0.159384\pi$
$997$	−3.32838	+	21.0146i	−0.105411	+	0.665538i	−0.982648	+	0.185481i	$0.940616\pi$
$998$	−0.490831	−	3.09899i	−0.0155370	−	0.0980967i
$999$	5.92680	−	1.92573i	0.187516	−	0.0609275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.c.457.3		32
5.3	odd	4	inner	605.2.m.c.578.3		32
11.2	odd	10	inner	605.2.m.c.112.3		32
11.3	even	5		605.2.e.b.362.9		32
11.4	even	5		55.2.l.a.52.2	yes	32
11.5	even	5		605.2.m.e.282.2		32
11.6	odd	10		55.2.l.a.7.3	✓	32
11.7	odd	10		605.2.m.e.602.3		32
11.8	odd	10		605.2.e.b.362.8		32
11.9	even	5		605.2.m.d.112.2		32
11.10	odd	2		605.2.m.d.457.2		32
33.17	even	10		495.2.bj.a.172.2		32
33.26	odd	10		495.2.bj.a.217.3		32
44.15	odd	10		880.2.cm.a.657.3		32
44.39	even	10		880.2.cm.a.337.2		32
55.3	odd	20		605.2.e.b.483.8		32
55.4	even	10		275.2.bm.b.107.3		32
55.8	even	20		605.2.e.b.483.9		32
55.13	even	20	inner	605.2.m.c.233.3		32
55.17	even	20		275.2.bm.b.18.3		32
55.18	even	20		605.2.m.e.118.2		32
55.28	even	20		55.2.l.a.18.2	yes	32
55.37	odd	20		275.2.bm.b.118.2		32
55.38	odd	20		605.2.m.e.403.3		32
55.39	odd	10		275.2.bm.b.7.2		32
55.43	even	4		605.2.m.d.578.2		32
55.48	odd	20		55.2.l.a.8.3	yes	32
55.53	odd	20		605.2.m.d.233.2		32
165.83	odd	20		495.2.bj.a.73.3		32
165.158	even	20		495.2.bj.a.118.2		32
220.83	odd	20		880.2.cm.a.513.3		32
220.103	even	20		880.2.cm.a.833.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	11.6	odd	10
55.2.l.a.8.3	yes	32	55.48	odd	20
55.2.l.a.18.2	yes	32	55.28	even	20
55.2.l.a.52.2	yes	32	11.4	even	5
275.2.bm.b.7.2		32	55.39	odd	10
275.2.bm.b.18.3		32	55.17	even	20
275.2.bm.b.107.3		32	55.4	even	10
275.2.bm.b.118.2		32	55.37	odd	20
495.2.bj.a.73.3		32	165.83	odd	20
495.2.bj.a.118.2		32	165.158	even	20
495.2.bj.a.172.2		32	33.17	even	10
495.2.bj.a.217.3		32	33.26	odd	10
605.2.e.b.362.8		32	11.8	odd	10
605.2.e.b.362.9		32	11.3	even	5
605.2.e.b.483.8		32	55.3	odd	20
605.2.e.b.483.9		32	55.8	even	20
605.2.m.c.112.3		32	11.2	odd	10	inner
605.2.m.c.233.3		32	55.13	even	20	inner
605.2.m.c.457.3		32	1.1	even	1	trivial
605.2.m.c.578.3		32	5.3	odd	4	inner
605.2.m.d.112.2		32	11.9	even	5
605.2.m.d.233.2		32	55.53	odd	20
605.2.m.d.457.2		32	11.10	odd	2
605.2.m.d.578.2		32	55.43	even	4
605.2.m.e.118.2		32	55.18	even	20
605.2.m.e.282.2		32	11.5	even	5
605.2.m.e.403.3		32	55.38	odd	20
605.2.m.e.602.3		32	11.7	odd	10
880.2.cm.a.337.2		32	44.39	even	10
880.2.cm.a.513.3		32	220.83	odd	20
880.2.cm.a.657.3		32	44.15	odd	10
880.2.cm.a.833.2		32	220.103	even	20

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.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.435114 + 0.221702i) q^{2} +(1.12533 - 0.178235i) q^{3} +(-1.03540 - 1.42510i) q^{4} +(-1.14075 + 1.92320i) q^{5} +(0.529164 + 0.171936i) q^{6} +(-0.456227 + 2.88051i) q^{7} +(-0.287355 - 1.81429i) q^{8} +(-1.61856 + 0.525902i) q^{9} +(-0.922733 + 0.583903i) q^{10} +(-1.41917 - 1.41917i) q^{12} +(-1.32861 + 2.60754i) q^{13} +(-0.837124 + 1.15220i) q^{14} +(-0.940946 + 2.36756i) q^{15} +(-0.811484 + 2.49749i) q^{16} +(2.39167 + 4.69392i) q^{17} +(-0.820851 - 0.130010i) q^{18} +(3.31646 + 2.40955i) q^{19} +(3.92189 - 0.365584i) q^{20} +3.32285i q^{21} +(-2.12046 + 2.12046i) q^{23} +(-0.646740 - 1.99046i) q^{24} +(-2.39737 - 4.38778i) q^{25} +(-1.15619 + 0.840024i) q^{26} +(-4.77322 + 2.43208i) q^{27} +(4.57740 - 2.33230i) q^{28} +(2.13957 - 1.55449i) q^{29} +(-0.934311 + 0.821549i) q^{30} +(-2.08297 - 6.41071i) q^{31} +(-3.50456 + 3.50456i) q^{32} +2.57262i q^{34} +(-5.01934 - 4.16336i) q^{35} +(2.42532 + 1.76210i) q^{36} +(-1.14895 - 0.181976i) q^{37} +(0.908835 + 1.78369i) q^{38} +(-1.03037 + 3.17117i) q^{39} +(3.81703 + 1.51701i) q^{40} +(2.08980 - 2.87636i) q^{41} +(-0.736681 + 1.44582i) q^{42} +(5.07292 + 5.07292i) q^{43} +(0.834964 - 3.71273i) q^{45} +(-1.39275 + 0.452533i) q^{46} +(0.575943 + 3.63636i) q^{47} +(-0.468049 + 2.95515i) q^{48} +(-1.43178 - 0.465213i) q^{49} +(-0.0703494 - 2.44068i) q^{50} +(3.52805 + 4.85594i) q^{51} +(5.09166 - 0.806440i) q^{52} +(1.31668 + 0.670880i) q^{53} -2.61609 q^{54} +5.35716 q^{56} +(4.16159 + 2.12044i) q^{57} +(1.27559 - 0.202033i) q^{58} +(-0.943564 - 1.29870i) q^{59} +(4.34827 - 1.11042i) q^{60} +(-6.59851 - 2.14398i) q^{61} +(0.514937 - 3.25119i) q^{62} +(-0.776433 - 4.90220i) q^{63} +(2.69314 - 0.875053i) q^{64} +(-3.49920 - 5.52974i) q^{65} +(1.31471 + 1.31471i) q^{67} +(4.21298 - 8.26845i) q^{68} +(-2.00829 + 2.76417i) q^{69} +(-1.26096 - 2.92433i) q^{70} +(0.887847 - 2.73251i) q^{71} +(1.41924 + 2.78541i) q^{72} +(-14.6197 - 2.31553i) q^{73} +(-0.459581 - 0.333905i) q^{74} +(-3.47990 - 4.51043i) q^{75} -7.22113i q^{76} +(-1.15138 + 1.15138i) q^{78} +(4.71123 + 14.4997i) q^{79} +(-3.87746 - 4.40966i) q^{80} +(-0.807503 + 0.586685i) q^{81} +(1.54699 - 0.788233i) q^{82} +(5.95431 - 3.03387i) q^{83} +(4.73540 - 3.44047i) q^{84} +(-11.7556 - 0.754947i) q^{85} +(1.08262 + 3.33197i) q^{86} +(2.13066 - 2.13066i) q^{87} -11.1726i q^{89} +(1.18642 - 1.43035i) q^{90} +(-6.90490 - 5.01670i) q^{91} +(5.21741 + 0.826356i) q^{92} +(-3.48665 - 6.84294i) q^{93} +(-0.555586 + 1.70992i) q^{94} +(-8.41729 + 3.62950i) q^{95} +(-3.31916 + 4.56843i) q^{96} +(-4.57097 + 8.97103i) q^{97} +(-0.519848 - 0.519848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{3} - 2 q^{5} - 20 q^{7} + 20 q^{8} + 12 q^{12} + 20 q^{13} + 4 q^{15} + 12 q^{16} - 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} + 20 q^{28} - 40 q^{30} + 32 q^{31}+ \cdots - 38 q^{97}+O(q^{100}) \) 32 * q + 6 * q^3 - 2 * q^5 - 20 * q^7 + 20 * q^8 + 12 * q^12 + 20 * q^13 + 4 * q^15 + 12 * q^16 - 30 * q^18 + 16 * q^20 - 24 * q^23 - 24 * q^25 - 20 * q^26 + 24 * q^27 + 20 * q^28 - 40 * q^30 + 32 * q^31 - 30 * q^35 - 36 * q^36 - 8 * q^37 + 10 * q^38 + 50 * q^40 - 20 * q^42 - 28 * q^45 - 20 * q^46 + 42 * q^47 + 26 * q^48 - 80 * q^50 + 100 * q^51 + 20 * q^52 - 34 * q^53 - 80 * q^56 + 40 * q^57 + 90 * q^58 - 86 * q^60 - 10 * q^62 + 10 * q^63 - 8 * q^67 + 70 * q^68 + 10 * q^70 - 36 * q^71 + 70 * q^72 - 30 * q^73 + 4 * q^75 + 60 * q^78 - 102 * q^80 + 8 * q^81 + 20 * q^82 + 60 * q^83 - 60 * q^85 - 80 * q^86 - 130 * q^90 - 60 * q^91 + 42 * q^92 - 8 * q^93 + 30 * q^95 - 38 * q^97

Introduction

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