LMFDB - Embedded newform 605.2.m.c.233.3

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)

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")

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);

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			233.3
Character	$\chi$	$=$	605.233
Dual form			605.2.m.c.457.3

$q$-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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

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	−0.293337	−	0.956009i	$-0.594766\pi$
$2$	0.435114	−	0.221702i	0.307672	−	0.156767i	0.601009	+	0.799243i	$0.294766\pi$
$3$	1.12533	+	0.178235i	0.649712	+	0.102904i	0.472587	−	0.881284i	$-0.343320\pi$
$3$	1.12533	+	0.178235i	0.649712	+	0.102904i	0.177125	+	0.984188i	$0.443320\pi$
$4$	−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	−0.910352	−	0.413835i	$-0.864189\pi$
$7$	−0.456227	−	2.88051i	−0.172438	−	1.08873i	0.737914	−	0.674894i	$-0.235811\pi$
$8$	−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	0.630087	−	0.776524i	$-0.283019\pi$
$13$	−1.32861	−	2.60754i	−0.368490	−	0.723203i	−0.998577	+	0.0533216i	$0.983019\pi$
$14$	−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	−0.395446	−	0.918489i	$-0.629410\pi$
$17$	2.39167	−	4.69392i	0.580065	−	1.13844i	0.975511	−	0.219952i	$-0.0705902\pi$
$18$	−0.820851	+	0.130010i	−0.193476	+	0.0306437i
$19$	3.31646	−	2.40955i	0.760847	−	0.552788i	−0.138323	−	0.990387i	$-0.544171\pi$
$19$	3.31646	−	2.40955i	0.760847	−	0.552788i	0.899170	+	0.437599i	$0.144171\pi$
$20$	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	0.450586	−	0.892733i	$-0.351215\pi$
$23$	−2.12046	−	2.12046i	−0.442147	−	0.442147i	−0.892733	+	0.450586i	$0.851215\pi$
$24$	−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	0.768443	−	0.639918i	$-0.221032\pi$
$29$	2.13957	+	1.55449i	0.397307	+	0.288661i	−0.371136	+	0.928579i	$0.621032\pi$
$30$	−0.934311	−	0.821549i	−0.170581	−	0.149994i
$31$	−2.08297	+	6.41071i	−0.374112	+	1.15140i	0.569964	+	0.821670i	$0.306957\pi$
$31$	−2.08297	+	6.41071i	−0.374112	+	1.15140i	−0.944076	+	0.329728i	$0.893043\pi$
$32$	−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	−0.250161	−	0.968204i	$-0.580484\pi$
$37$	−1.14895	+	0.181976i	−0.188887	+	0.0299167i	0.0612742	+	0.998121i	$0.480484\pi$
$38$	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	0.940399	−	0.340073i	$-0.110452\pi$
$41$	2.08980	+	2.87636i	0.326372	+	0.449212i	−0.614028	+	0.789285i	$0.710452\pi$
$42$	−0.736681	−	1.44582i	−0.113672	−	0.223094i
$43$	5.07292	−	5.07292i	0.773613	−	0.773613i	−0.205123	−	0.978736i	$-0.565759\pi$
$43$	5.07292	−	5.07292i	0.773613	−	0.773613i	0.978736	+	0.205123i	$0.0657595\pi$
$44$		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	−0.909411	−	0.415898i	$-0.863467\pi$
$47$	0.575943	−	3.63636i	0.0840099	−	0.530417i	0.993421	−	0.114519i	$-0.0365328\pi$
$48$	−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	−0.361217	−	0.932482i	$-0.617639\pi$
$53$	1.31668	−	0.670880i	0.180859	−	0.0921524i	0.542076	+	0.840330i	$0.317639\pi$
$54$	−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	−0.866009	−	0.500029i	$-0.833323\pi$
$59$	−0.943564	+	1.29870i	−0.122842	+	0.169077i	0.743167	+	0.669106i	$0.233323\pi$
$60$	4.34827	+	1.11042i	0.561360	+	0.143355i
$61$	−6.59851	+	2.14398i	−0.844852	+	0.274509i	−0.699288	−	0.714840i	$-0.746500\pi$
$61$	−6.59851	+	2.14398i	−0.844852	+	0.274509i	−0.145564	+	0.989349i	$0.546500\pi$
$62$	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	−0.622223	−	0.782840i	$-0.713770\pi$
$67$	1.31471	−	1.31471i	0.160617	−	0.160617i	0.782840	+	0.622223i	$0.213770\pi$
$68$	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	0.989817	−	0.142348i	$-0.0454653\pi$
$71$	0.887847	+	2.73251i	0.105368	+	0.324289i	−0.884449	+	0.466638i	$0.845465\pi$
$72$	1.41924	−	2.78541i	0.167259	−	0.328264i
$73$	−14.6197	+	2.31553i	−1.71110	+	0.271012i	−0.933716	−	0.358013i	$-0.883454\pi$
$73$	−14.6197	+	2.31553i	−1.71110	+	0.271012i	−0.777385	+	0.629025i	$0.783454\pi$
$74$	−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	−0.224043	−	0.974579i	$-0.571926\pi$
$79$	4.71123	−	14.4997i	0.530055	−	1.63134i	0.754098	−	0.656762i	$-0.228074\pi$
$80$	−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	0.749140	−	0.662412i	$-0.230467\pi$
$83$	5.95431	+	3.03387i	0.653571	+	0.333011i	−0.0955691	+	0.995423i	$0.530467\pi$
$84$	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	$0.201719\pi$
$89$			11.1726i			1.18429i	−0.805830	+	0.592147i	$0.798281\pi$
$90$	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	−0.997870	−	0.0652335i	$-0.979221\pi$
$97$	−4.57097	−	8.97103i	−0.464112	−	0.910871i	0.533758	−	0.845637i	$-0.320779\pi$
$98$	−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	0.217286	−	0.976108i	$-0.430280\pi$
$101$	−1.81570	−	0.589955i	−0.180668	−	0.0587027i	−0.397954	+	0.917405i	$0.630280\pi$
$102$	0.458533	−	2.89506i	0.0454015	−	0.286654i
$103$	0.965408	+	6.09534i	0.0951244	+	0.600592i	0.988493	+	0.151267i	$0.0483354\pi$
$103$	0.965408	+	6.09534i	0.0951244	+	0.600592i	−0.893368	+	0.449325i	$0.851665\pi$
$104$	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	0.135607	−	0.990763i	$-0.456702\pi$
$107$	−0.430167	−	0.0681317i	−0.0415858	−	0.00658654i	−0.177193	+	0.984176i	$0.556702\pi$
$108$	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	0.988789	−	0.149322i	$-0.0477090\pi$
$113$	20.0170	+	3.17038i	1.88304	+	0.298244i	0.894251	+	0.447566i	$0.147709\pi$
$114$	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	−0.999217	−	0.0395736i	$-0.987400\pi$
$127$	−4.28099	+	8.40191i	−0.379876	+	0.745549i	0.619341	+	0.785122i	$0.287400\pi$
$128$	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	$0.106500\pi$
$131$			7.51676i			0.656743i	−0.944549	+	0.328371i	$0.893500\pi$
$132$		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	0.927425	−	0.374009i	$-0.122017\pi$
$137$	13.6942	+	6.97753i	1.16997	+	0.596131i	0.242547	+	0.970140i	$0.422017\pi$
$138$	−1.48666	−	0.757489i	−0.126553	−	0.0644818i
$139$	3.36744	+	2.44659i	0.285623	+	0.207517i	0.721366	−	0.692554i	$-0.243514\pi$
$139$	3.36744	+	2.44659i	0.285623	+	0.207517i	−0.435743	+	0.900071i	$0.643514\pi$
$140$	−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	−0.871005	−	0.491273i	$-0.836532\pi$
$149$	−5.55533	−	17.0976i	−0.455111	−	1.40069i	0.415895	−	0.909413i	$-0.363468\pi$
$150$	−0.514183	+	2.73405i	−0.0419829	+	0.223234i
$151$	−10.4580	−	14.3942i	−0.851058	−	1.17138i	−0.983629	−	0.180207i	$-0.942323\pi$
$151$	−10.4580	−	14.3942i	−0.851058	−	1.17138i	0.132571	−	0.991173i	$-0.457677\pi$
$152$	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	−0.375735	−	0.926727i	$-0.622610\pi$
$157$	3.35784	−	21.2006i	0.267985	−	1.69199i	0.643720	−	0.765261i	$-0.277390\pi$
$158$	−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	−0.0506534	−	0.998716i	$-0.516130\pi$
$163$	9.28876	−	4.73286i	0.727552	−	0.370706i	0.778205	+	0.628010i	$0.216130\pi$
$164$	−6.26288			−0.489049
$165$		0			0
$166$	3.26342			0.253290
$167$	10.0620	−	5.12686i	0.778623	−	0.396728i	−0.0190498	−	0.999819i	$-0.506064\pi$
$167$	10.0620	−	5.12686i	0.778623	−	0.396728i	0.797673	+	0.603090i	$0.206064\pi$
$168$	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	0.775783	+	0.631000i	$0.217355\pi$
$173$	−2.06528	+	13.0397i	−0.157020	+	0.991387i	−0.932803	+	0.360387i	$0.882645\pi$
$174$	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	0.855125	−	0.518422i	$-0.173480\pi$
$179$	1.30884	+	1.80147i	0.0978276	+	0.134648i	−0.757297	+	0.653071i	$0.773480\pi$
$180$	−6.15555	−	2.65425i	−0.458807	−	0.197836i
$181$	1.33951	+	4.12258i	0.0995647	+	0.306429i	0.988416	−	0.151766i	$-0.0484961\pi$
$181$	1.33951	+	4.12258i	0.0995647	+	0.306429i	−0.888852	+	0.458195i	$0.848496\pi$
$182$	−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	0.700707	−	0.713449i	$-0.252868\pi$
$191$	3.29900	+	2.39686i	0.238707	+	0.173431i	−0.462000	+	0.886880i	$0.652868\pi$
$192$	2.87471	+	1.46474i	0.207465	+	0.105708i
$193$	18.6227	+	9.48874i	1.34049	+	0.683015i	0.969378	−	0.245573i	$-0.0789761\pi$
$193$	18.6227	+	9.48874i	1.34049	+	0.683015i	0.371113	+	0.928588i	$0.378976\pi$
$194$	−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	0.714681	−	0.699450i	$-0.246572\pi$
$197$	0.213782	+	0.213782i	0.0152313	+	0.0152313i	−0.699450	+	0.714681i	$0.746572\pi$
$198$		0			0
$199$		−	11.0815i		−	0.785549i	−0.919635	−	0.392775i	$-0.871515\pi$
$199$		−	11.0815i		−	0.785549i	0.919635	−	0.392775i	$-0.128485\pi$
$200$	−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	0.00441172	−	0.999990i	$-0.498596\pi$
$211$	−8.42206	−	2.73649i	−0.579799	−	0.188388i	−0.584210	+	0.811602i	$0.698596\pi$
$212$	−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	−0.0514011	−	0.998678i	$-0.516369\pi$
$223$	−6.10610	−	0.967112i	−0.408895	−	0.0647626i	−0.357494	+	0.933916i	$0.616369\pi$
$224$	−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	0.964468	−	0.264198i	$-0.0851072\pi$
$227$	−0.518849	−	3.27588i	−0.0344372	−	0.217428i	−0.998906	+	0.0467700i	$0.985107\pi$
$228$	−1.28706	+	8.12619i	−0.0852377	+	0.538170i
$229$	−5.07862	−	1.65014i	−0.335604	−	0.109044i	0.136367	−	0.990658i	$-0.456457\pi$
$229$	−5.07862	−	1.65014i	−0.335604	−	0.109044i	−0.471971	+	0.881614i	$0.656457\pi$
$230$	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	0.947330	−	0.320260i	$-0.103770\pi$
$233$	2.00585	+	3.93669i	0.131407	+	0.257901i	−0.815922	+	0.578162i	$0.803770\pi$
$234$	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	−0.826682	−	0.562670i	$-0.809774\pi$
$239$	−8.45656	+	6.14405i	−0.547009	+	0.397426i	0.279672	+	0.960096i	$0.409774\pi$
$240$	−5.14940	+	4.27124i	−0.332392	+	0.275708i
$241$		−	27.8579i		−	1.79449i	−0.441536	−	0.897243i	$-0.645566\pi$
$241$		−	27.8579i		−	1.79449i	0.441536	−	0.897243i	$-0.354434\pi$
$242$		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	0.805985	+	0.591936i	$0.201636\pi$
$251$	−3.07357	+	9.45946i	−0.194002	+	0.597076i	−0.999987	+	0.00514015i	$0.998364\pi$
$252$	−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	−0.285689	−	0.958323i	$-0.592222\pi$
$257$	−4.18826	+	0.663355i	−0.261257	+	0.0413790i	0.0244320	+	0.999701i	$0.492222\pi$
$258$	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	−0.00211364	−	0.999998i	$-0.500673\pi$
$263$	16.1830	−	16.1830i	0.997884	−	0.997884i	0.999998	+	0.00211364i	$0.000672793\pi$
$264$		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	−0.884636	−	0.466283i	$-0.845593\pi$
$269$	−21.7521	+	7.06768i	−1.32625	+	0.430924i	−0.441611	+	0.897206i	$0.645593\pi$
$270$	2.98431	+	5.03126i	0.181619	+	0.306192i
$271$	0.817223	−	1.12481i	0.0496428	−	0.0683274i	−0.783474	−	0.621425i	$-0.786554\pi$
$271$	0.817223	−	1.12481i	0.0496428	−	0.0683274i	0.833117	+	0.553097i	$0.186554\pi$
$272$	−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	−0.0286534	−	0.999589i	$-0.509122\pi$
$277$	12.7020	−	6.47199i	0.763189	−	0.388864i	0.791843	+	0.610725i	$0.209122\pi$
$278$	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	0.517935	−	0.855420i	$-0.326701\pi$
$281$	24.1347	−	7.84184i	1.43976	−	0.467805i	0.921821	+	0.387615i	$0.126701\pi$
$282$	−0.320452	−	2.02325i	−0.0190826	−	0.120483i
$283$	1.15929	−	7.31948i	0.0689128	−	0.435098i	−0.928975	−	0.370142i	$-0.879309\pi$
$283$	1.15929	−	7.31948i	0.0689128	−	0.435098i	0.997888	−	0.0649564i	$-0.0206908\pi$
$284$	−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	0.282125	−	0.959378i	$-0.408961\pi$
$293$	14.4967	−	2.29605i	0.846906	−	0.134137i	0.564781	+	0.825241i	$0.308961\pi$
$294$	−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	0.681698	−	0.731634i	$-0.261242\pi$
$307$	−0.874954	−	0.874954i	−0.0499363	−	0.0499363i	−0.731634	+	0.681698i	$0.761242\pi$
$308$		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	−0.862927	−	0.505329i	$-0.831371\pi$
$311$	−11.4450	+	8.31532i	−0.648989	+	0.471518i	0.213937	+	0.976847i	$0.431371\pi$
$312$	6.04948	−	0.958144i	0.342485	−	0.0542442i
$313$	0.335793	−	0.659031i	0.0189802	−	0.0372506i	−0.881322	−	0.472517i	$-0.843346\pi$
$313$	0.335793	−	0.659031i	0.0189802	−	0.0372506i	0.900302	+	0.435266i	$0.143346\pi$
$314$	−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	−0.999592	−	0.0285725i	$-0.990904\pi$
$317$	−7.74784	−	15.2060i	−0.435162	−	0.854054i	0.564430	−	0.825481i	$-0.309096\pi$
$318$	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	−0.994712	−	0.102705i	$-0.967250\pi$
$337$	−1.47636	−	9.32134i	−0.0804222	−	0.507766i	0.914290	−	0.405061i	$-0.132750\pi$
$338$	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	0.528557	+	0.848898i	$0.322733\pi$
$347$	−8.73452	+	17.1425i	−0.468894	+	0.920255i	−0.997451	+	0.0713577i	$0.977267\pi$
$348$	−5.24250	+	0.830330i	−0.281027	+	0.0445104i
$349$	12.0325	−	8.74209i	0.644082	−	0.467953i	−0.217168	−	0.976134i	$-0.569682\pi$
$349$	12.0325	−	8.74209i	0.644082	−	0.467953i	0.861250	+	0.508181i	$0.169682\pi$
$350$	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	0.752989	−	0.658033i	$-0.228611\pi$
$353$	1.78406	+	1.78406i	0.0949560	+	0.0949560i	−0.658033	+	0.752989i	$0.728611\pi$
$354$	−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	0.391540	−	0.920161i	$-0.371942\pi$
$359$	−6.87015	−	4.99146i	−0.362593	−	0.263439i	−0.754133	+	0.656722i	$0.771942\pi$
$360$	−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	−0.677489	−	0.735533i	$-0.736932\pi$
$367$	−20.9681	+	3.32102i	−1.09453	+	0.173356i	−0.417038	+	0.908889i	$0.636932\pi$
$368$	−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	−0.637309	−	0.770609i	$-0.719952\pi$
$373$	2.57445	−	2.57445i	0.133300	−	0.133300i	0.770609	+	0.637309i	$0.219952\pi$
$374$		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	0.125467	−	0.992098i	$-0.459957\pi$
$379$	15.7712	−	5.12437i	0.810112	−	0.263221i	0.684645	+	0.728877i	$0.259957\pi$
$380$	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	−0.692671	−	0.721254i	$-0.743566\pi$
$383$	−10.1043	+	5.14840i	−0.516306	+	0.263071i	0.176365	+	0.984325i	$0.443566\pi$
$384$	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	−0.796661	−	0.604427i	$-0.793402\pi$
$389$	0.480555	−	0.661427i	0.0243651	−	0.0335357i	0.821026	+	0.570891i	$0.193402\pi$
$390$	−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	−0.344159	−	0.938911i	$-0.611836\pi$
$397$	11.8504	−	11.8504i	0.594752	−	0.594752i	0.938911	+	0.344159i	$0.111836\pi$
$398$	−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	−0.888776	−	0.458342i	$-0.848444\pi$
$401$	−8.79392	−	27.0649i	−0.439148	−	1.35156i	0.449629	−	0.893216i	$-0.351556\pi$
$402$	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	−0.930840	−	0.365427i	$-0.880923\pi$
$409$	0.748644	−	2.30409i	0.0370181	−	0.113930i	0.967858	+	0.251497i	$0.0809229\pi$
$410$	−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	$0.131512\pi$
$419$			16.4371i			0.803006i	−0.915858	+	0.401503i	$0.868488\pi$
$420$	1.21478	−	13.0318i	0.0592751	−	0.635889i
$421$	10.0871	−	7.32873i	0.491617	−	0.357180i	−0.314189	−	0.949360i	$-0.601733\pi$
$421$	10.0871	−	7.32873i	0.491617	−	0.357180i	0.805806	+	0.592180i	$0.201733\pi$
$422$	−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	−0.182857	−	0.983140i	$-0.558534\pi$
$431$	−18.8644	−	6.12941i	−0.908666	−	0.295243i	−0.725809	+	0.687896i	$0.758534\pi$
$432$	−2.20070	+	13.8947i	−0.105881	+	0.668508i
$433$	4.47800	+	28.2730i	0.215199	+	1.35871i	0.824540	+	0.565803i	$0.191434\pi$
$433$	4.47800	+	28.2730i	0.215199	+	1.35871i	−0.609341	+	0.792908i	$0.708566\pi$
$434$	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	−0.641910	−	0.766780i	$-0.721858\pi$
$443$	−31.3472	−	4.96491i	−1.48935	−	0.235890i	−0.847441	+	0.530890i	$0.821858\pi$
$444$	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	0.959631	−	0.281262i	$-0.0907530\pi$
$449$	33.2818	+	10.8139i	1.57067	+	0.510341i	0.611036	+	0.791603i	$0.290753\pi$
$450$	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	−0.938799	−	0.344465i	$-0.888060\pi$
$457$	−2.31538	+	4.54419i	−0.108309	+	0.212568i	0.830490	+	0.557033i	$0.188060\pi$
$458$	−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	$-0.906211\pi$
$461$		−	12.4703i		−	0.580801i	0.956905	−	0.290400i	$-0.0937885\pi$
$462$		0			0
$463$	−19.2728	−	19.2728i	−0.895684	−	0.895684i	0.0993669	−	0.995051i	$-0.468318\pi$
$463$	−19.2728	−	19.2728i	−0.895684	−	0.895684i	−0.995051	+	0.0993669i	$0.968318\pi$
$464$	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	0.997925	+	0.0643861i	$0.0205089\pi$
$467$	35.3668	+	18.0203i	1.63658	+	0.833879i	0.638655	+	0.769493i	$0.279491\pi$
$468$	−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	0.732278	+	0.681006i	$0.238457\pi$
$479$	11.8215	+	36.3828i	0.540138	+	1.66237i	−0.192141	+	0.981367i	$0.561543\pi$
$480$	−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	0.681866	+	0.731477i	$0.261169\pi$
$487$	−4.25177	+	26.8446i	−0.192666	+	1.21645i	−0.874532	+	0.484968i	$0.838831\pi$
$488$	−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	−0.858441	−	0.512912i	$-0.828567\pi$
$491$	−2.33461	+	3.21331i	−0.105359	+	0.145015i	0.753082	+	0.657927i	$0.228567\pi$
$492$	−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	−0.885138	−	0.465328i	$-0.845936\pi$
$499$	−3.77656	+	5.19799i	−0.169062	+	0.232694i	0.716076	+	0.698022i	$0.245936\pi$
$500$	−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	−0.271865	−	0.962335i	$-0.587640\pi$
$503$	6.37107	−	40.2254i	0.284072	−	1.79356i	0.555937	−	0.831224i	$-0.312360\pi$
$504$	−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	0.912662	−	0.408716i	$-0.134023\pi$
$509$	5.45800	+	7.51230i	0.241922	+	0.332977i	−0.670740	+	0.741693i	$0.734023\pi$
$510$	−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	0.818416	−	0.574627i	$-0.194853\pi$
$521$	11.9792	+	8.70338i	0.524817	+	0.381302i	−0.293598	+	0.955929i	$0.594853\pi$
$522$	−1.95836	−	0.997836i	−0.0857152	−	0.0436741i
$523$	−34.6096	−	17.6345i	−1.51337	−	0.771102i	−0.516983	−	0.855996i	$-0.672945\pi$
$523$	−34.6096	−	17.6345i	−1.51337	−	0.771102i	−0.996390	+	0.0848935i	$0.972945\pi$
$524$	−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	0.642676	−	0.766138i	$-0.277824\pi$
$541$	16.5674	+	5.38306i	0.712286	+	0.231436i	0.0696106	+	0.997574i	$0.477824\pi$
$542$	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	−0.742538	−	0.669804i	$-0.766378\pi$
$547$	−38.7239	−	6.13326i	−1.65571	−	0.262239i	−0.913176	+	0.407565i	$0.866378\pi$
$548$	−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	0.742727	+	0.669595i	$0.233532\pi$
$557$	5.74133	+	36.2493i	0.243268	+	1.53593i	−0.499459	+	0.866338i	$0.666468\pi$
$558$	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	0.994222	−	0.107342i	$-0.0342341\pi$
$563$	7.66381	+	15.0411i	0.322991	+	0.633906i	−0.671231	+	0.741248i	$0.734234\pi$
$564$	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	−0.541960	−	0.840404i	$-0.682318\pi$
$569$	2.14294	−	1.55694i	0.0898368	−	0.0652703i	0.631797	+	0.775134i	$0.282318\pi$
$570$	−5.07816	−	0.473367i	−0.212701	−	0.0198272i
$571$			29.8675i			1.24992i	0.780658	+	0.624959i	$0.214884\pi$
$571$			29.8675i			1.24992i	−0.780658	+	0.624959i	$0.785116\pi$
$572$		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	0.460634	−	0.887590i	$-0.347622\pi$
$577$	0.319779	+	0.162935i	0.0133126	+	0.00678309i	−0.447322	+	0.894373i	$0.647622\pi$
$578$	−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	0.394521	−	0.918887i	$-0.370910\pi$
$587$	25.5288	−	4.04336i	1.05368	−	0.166887i	0.659164	+	0.752000i	$0.270910\pi$
$588$	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	−0.875734	−	0.482794i	$-0.839622\pi$
$593$	−9.56872	+	9.56872i	−0.392940	+	0.392940i	0.482794	+	0.875734i	$0.339622\pi$
$594$		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	−0.520634	−	0.853780i	$-0.674304\pi$
$599$	−10.7687	+	3.49896i	−0.439997	+	0.142964i	0.0806373	+	0.996744i	$0.474304\pi$
$600$	−7.18324	−	7.60962i	−0.293254	−	0.310662i
$601$	9.69211	−	13.3401i	0.395350	−	0.544152i	−0.564220	−	0.825625i	$-0.690823\pi$
$601$	9.69211	−	13.3401i	0.395350	−	0.544152i	0.959569	+	0.281473i	$0.0908229\pi$
$602$	−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	−0.361533	−	0.932359i	$-0.617746\pi$
$607$	4.44109	−	2.26285i	0.180258	−	0.0918461i	0.541791	+	0.840513i	$0.317746\pi$
$608$	−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	−0.860178	−	0.509994i	$-0.829648\pi$
$613$	2.85957	−	18.0546i	0.115497	−	0.729218i	0.975675	−	0.219224i	$-0.0703525\pi$
$614$	−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	−0.322721	−	0.946494i	$-0.604598\pi$
$617$	15.4942	−	15.4942i	0.623773	−	0.623773i	0.946494	+	0.322721i	$0.104598\pi$
$618$	1.55887	+	3.05945i	0.0627068	+	0.123069i
$619$	28.9283	+	39.8164i	1.16273	+	1.60036i	0.700622	+	0.713533i	$0.252906\pi$
$619$	28.9283	+	39.8164i	1.16273	+	1.60036i	0.462106	+	0.886825i	$0.347094\pi$
$620$	−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	0.723936	−	0.689867i	$-0.242331\pi$
$631$	7.32346	+	5.32080i	0.291542	+	0.211818i	−0.432394	+	0.901685i	$0.642331\pi$
$632$	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	−0.0440836	−	0.999028i	$-0.514037\pi$
$641$	22.5944	−	16.4158i	0.892426	−	0.648385i	0.936509	+	0.350643i	$0.114037\pi$
$642$	−0.239343	+	0.0379082i	−0.00944611	+	0.00149612i
$643$	−4.37166	+	8.57987i	−0.172401	+	0.338357i	−0.960999	−	0.276553i	$-0.910808\pi$
$643$	−4.37166	+	8.57987i	−0.172401	+	0.338357i	0.788597	+	0.614910i	$0.210808\pi$
$644$	−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	0.983335	+	0.181801i	$0.0581926\pi$
$647$	14.0516	+	27.5778i	0.552425	+	1.08420i	−0.430910	+	0.902395i	$0.641807\pi$
$648$	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	0.999307	−	0.0372253i	$-0.0118519\pi$
$653$	0.955876	+	6.03516i	0.0374063	+	0.236174i	−0.961901	+	0.273399i	$0.911852\pi$
$654$	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	0.842736	−	0.538326i	$-0.180943\pi$
$673$	−2.28621	−	4.48693i	−0.0881267	−	0.172958i	−0.930863	+	0.365368i	$0.880943\pi$
$674$	−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	0.319044	+	0.947740i	$0.396638\pi$
$677$	−16.5280	+	32.4380i	−0.635223	+	1.24670i	−0.954267	+	0.298956i	$0.903362\pi$
$678$	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	0.535567	−	0.844492i	$-0.320098\pi$
$683$	−8.07353	−	8.07353i	−0.308925	−	0.308925i	−0.844492	+	0.535567i	$0.820098\pi$
$684$	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	−0.996284	−	0.0861243i	$-0.972552\pi$
$691$	−3.67098	+	11.2981i	−0.139651	+	0.429801i	0.856634	+	0.515925i	$0.172552\pi$
$692$	−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	0.994681	−	0.103001i	$-0.0328444\pi$
$701$	15.6038	+	21.4768i	0.589348	+	0.811169i	−0.405333	+	0.914169i	$0.632844\pi$
$702$	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	0.0278567	−	0.999612i	$-0.491132\pi$
$709$	16.9867	−	5.51933i	0.637950	−	0.207283i	0.610094	+	0.792329i	$0.291132\pi$
$710$	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	0.281359	+	0.959603i	$0.409215\pi$
$719$	−19.2585	+	26.5071i	−0.718222	+	0.988547i	−0.999581	+	0.0289450i	$0.990785\pi$
$720$	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	−0.688987	−	0.724773i	$-0.741944\pi$
$727$	0.964903	−	0.964903i	0.0357863	−	0.0357863i	0.724773	+	0.688987i	$0.241944\pi$
$728$	−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	0.0624374	−	0.998049i	$-0.480113\pi$
$733$	11.6481	−	1.84488i	0.430233	−	0.0681422i	0.367796	+	0.929907i	$0.380113\pi$
$734$	−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	0.334919	+	0.942247i	$0.391291\pi$
$739$	−13.3170	+	40.9856i	−0.489875	+	1.50768i	−0.824794	+	0.565434i	$0.808709\pi$
$740$	−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	0.945883	−	0.324509i	$-0.105199\pi$
$743$	33.7816	+	17.2126i	1.23933	+	0.631468i	0.293443	+	0.955977i	$0.405199\pi$
$744$	−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	−0.968434	−	0.249269i	$-0.919810\pi$
$751$	−28.2437	+	20.5203i	−1.03063	+	0.748795i	−0.0621941	+	0.998064i	$0.519810\pi$
$752$	−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	0.978889	+	0.204393i	$0.0655221\pi$
$757$	15.6517	+	30.7182i	0.568870	+	1.11647i	−0.410019	+	0.912077i	$0.634478\pi$
$758$	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	0.0591701	−	0.998248i	$-0.481155\pi$
$761$	−13.2335	−	4.29984i	−0.479716	−	0.155869i	−0.538886	+	0.842379i	$0.681155\pi$
$762$	−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	−0.0695917	−	0.997576i	$-0.522170\pi$
$773$	−12.3457	−	1.95537i	−0.444045	−	0.0703298i	−0.374453	+	0.927246i	$0.622170\pi$
$774$	−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	−0.936303	−	0.351194i	$-0.885776\pi$
$787$	−2.85686	+	5.60690i	−0.101836	+	0.199864i	0.834467	+	0.551058i	$0.185776\pi$
$788$	−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	0.481677	−	0.876349i	$-0.340028\pi$
$797$	1.57581	+	0.802918i	0.0558182	+	0.0284408i	−0.425859	+	0.904790i	$0.640028\pi$
$798$	−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	−0.999869	−	0.0162167i	$-0.994838\pi$
$809$	−5.70252	−	17.5505i	−0.200490	−	0.617044i	0.799379	−	0.600828i	$-0.205162\pi$
$810$	0.402542	+	1.01286i	0.0141439	+	0.0355882i
$811$	7.66716	+	10.5529i	0.269230	+	0.370564i	0.922130	−	0.386881i	$-0.126448\pi$
$811$	7.66716	+	10.5529i	0.269230	+	0.370564i	−0.652899	+	0.757445i	$0.726448\pi$
$812$	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	−0.453492	−	0.891260i	$-0.649822\pi$
$821$	15.3089	−	21.0709i	0.534283	−	0.735378i	0.987776	+	0.155882i	$0.0498220\pi$
$822$	8.44614	+	1.33774i	0.294593	+	0.0466590i
$823$	−4.47662	+	2.28095i	−0.156045	+	0.0795089i	−0.530269	−	0.847829i	$-0.677909\pi$
$823$	−4.47662	+	2.28095i	−0.156045	+	0.0795089i	0.374224	+	0.927338i	$0.377909\pi$
$824$	−11.3361			−0.394912
$825$		0			0
$826$	2.28625			0.0795488
$827$	−10.8443	+	5.52543i	−0.377092	+	0.192138i	−0.632255	−	0.774760i	$-0.717871\pi$
$827$	−10.8443	+	5.52543i	−0.377092	+	0.192138i	0.255164	+	0.966898i	$0.417871\pi$
$828$	−8.87927	−	1.40634i	−0.308576	−	0.0488736i
$829$	6.47245	−	8.90857i	0.224798	−	0.309407i	−0.681689	−	0.731642i	$-0.738754\pi$
$829$	6.47245	−	8.90857i	0.224798	−	0.309407i	0.906487	+	0.422235i	$0.138754\pi$
$830$	−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	0.704268	−	0.709935i	$-0.251276\pi$
$839$	−5.46148	−	7.51708i	−0.188551	−	0.259518i	−0.892819	+	0.450416i	$0.851276\pi$
$840$	−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	−0.0101637	−	0.999948i	$-0.503235\pi$
$853$	−24.0984	−	12.2787i	−0.825113	−	0.420416i	−0.814949	+	0.579532i	$0.803235\pi$
$854$	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	0.989782	+	0.142591i	$0.0455432\pi$
$857$	33.1497	+	33.1497i	1.13237	+	1.13237i	0.142591	+	0.989782i	$0.454457\pi$
$858$		0			0
$859$			47.2517i			1.61221i	0.591775	+	0.806103i	$0.298427\pi$
$859$			47.2517i			1.61221i	−0.591775	+	0.806103i	$0.701573\pi$
$860$	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	−0.738953	−	0.673757i	$-0.764679\pi$
$863$	7.06437	−	13.8646i	0.240474	−	0.471957i	0.979427	+	0.201801i	$0.0646793\pi$
$864$	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	0.621997	−	0.783019i	$-0.286321\pi$
$877$	28.7727	+	4.55715i	0.971586	+	0.153884i	0.349588	+	0.936903i	$0.386321\pi$
$878$	−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	0.859744	−	0.510725i	$-0.170623\pi$
$883$	45.1550	+	7.15185i	1.51959	+	0.240679i	0.659843	+	0.751404i	$0.270623\pi$
$884$	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	−0.896137	−	0.443777i	$-0.853638\pi$
$887$	−5.39049	−	34.0342i	−0.180995	−	1.14276i	0.715142	−	0.698979i	$-0.246362\pi$
$888$	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	−0.220648	−	0.975354i	$-0.570817\pi$
$907$	−34.3152	−	17.4845i	−1.13942	−	0.580563i	−0.918771	+	0.394791i	$0.870817\pi$
$908$	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	0.564317	+	0.825558i	$0.309139\pi$
$911$	−11.3933	+	35.0649i	−0.377476	+	1.16175i	−0.941793	+	0.336193i	$0.890861\pi$
$912$	−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	−0.977794	−	0.209570i	$-0.932794\pi$
$919$	−9.39535	−	28.9159i	−0.309924	−	0.953848i	0.667870	−	0.744278i	$-0.267206\pi$
$920$	−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	−0.649029	−	0.760763i	$-0.724825\pi$
$929$	−22.1568	+	7.19917i	−0.726940	+	0.236197i	−0.0779103	+	0.996960i	$0.524825\pi$
$930$	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	−0.567120	−	0.823635i	$-0.691942\pi$
$937$	−7.16683	+	3.65168i	−0.234130	+	0.119295i	0.332990	+	0.942930i	$0.391942\pi$
$938$	−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	0.549228	−	0.835673i	$-0.314922\pi$
$941$	45.5460	−	14.7988i	1.48476	−	0.482427i	0.935531	+	0.353245i	$0.114922\pi$
$942$	−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	−0.537960	−	0.842970i	$-0.680805\pi$
$947$	9.38618	−	9.38618i	0.305010	−	0.305010i	0.842970	+	0.537960i	$0.180805\pi$
$948$	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	−0.930980	−	0.365069i	$-0.881045\pi$
$953$	−52.5908	+	8.32956i	−1.70358	+	0.269821i	−0.772602	+	0.634890i	$0.781045\pi$
$954$	−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	−0.958826	−	0.283994i	$-0.908340\pi$
$967$	−38.6475	−	38.6475i	−1.24282	−	1.24282i	−0.283994	−	0.958826i	$-0.591660\pi$
$968$		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	−0.689942	−	0.723865i	$-0.742364\pi$
$971$	−6.69055	+	4.86097i	−0.214710	+	0.155996i	0.475232	+	0.879860i	$0.342364\pi$
$972$	−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	−0.827580	−	0.561348i	$-0.810283\pi$
$977$	−24.8581	−	48.7867i	−0.795280	−	1.56083i	0.0322997	−	0.999478i	$-0.489717\pi$
$978$	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	−0.998067	−	0.0621429i	$-0.980207\pi$
$983$	−2.13363	−	13.4712i	−0.0680521	−	0.429664i	0.930015	−	0.367521i	$-0.119793\pi$
$984$	−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	−0.982648	−	0.185481i	$-0.940616\pi$
$997$	−3.32838	−	21.0146i	−0.105411	−	0.665538i	0.877237	−	0.480058i	$-0.159384\pi$
$998$	−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.233.3		32
5.2	odd	4	inner	605.2.m.c.112.3		32
11.2	odd	10		55.2.l.a.8.3	yes	32
11.3	even	5		55.2.l.a.18.2	yes	32
11.4	even	5		605.2.e.b.483.9		32
11.5	even	5		605.2.m.d.578.2		32
11.6	odd	10	inner	605.2.m.c.578.3		32
11.7	odd	10		605.2.e.b.483.8		32
11.8	odd	10		605.2.m.e.403.3		32
11.9	even	5		605.2.m.e.118.2		32
11.10	odd	2		605.2.m.d.233.2		32
33.2	even	10		495.2.bj.a.118.2		32
33.14	odd	10		495.2.bj.a.73.3		32
44.3	odd	10		880.2.cm.a.513.3		32
44.35	even	10		880.2.cm.a.833.2		32
55.2	even	20		55.2.l.a.52.2	yes	32
55.3	odd	20		275.2.bm.b.7.2		32
55.7	even	20		605.2.e.b.362.9		32
55.13	even	20		275.2.bm.b.107.3		32
55.14	even	10		275.2.bm.b.18.3		32
55.17	even	20	inner	605.2.m.c.457.3		32
55.24	odd	10		275.2.bm.b.118.2		32
55.27	odd	20		605.2.m.d.457.2		32
55.32	even	4		605.2.m.d.112.2		32
55.37	odd	20		605.2.e.b.362.8		32
55.42	odd	20		605.2.m.e.602.3		32
55.47	odd	20		55.2.l.a.7.3	✓	32
55.52	even	20		605.2.m.e.282.2		32
165.2	odd	20		495.2.bj.a.217.3		32
165.47	even	20		495.2.bj.a.172.2		32
220.47	even	20		880.2.cm.a.337.2		32
220.167	odd	20		880.2.cm.a.657.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	55.47	odd	20
55.2.l.a.8.3	yes	32	11.2	odd	10
55.2.l.a.18.2	yes	32	11.3	even	5
55.2.l.a.52.2	yes	32	55.2	even	20
275.2.bm.b.7.2		32	55.3	odd	20
275.2.bm.b.18.3		32	55.14	even	10
275.2.bm.b.107.3		32	55.13	even	20
275.2.bm.b.118.2		32	55.24	odd	10
495.2.bj.a.73.3		32	33.14	odd	10
495.2.bj.a.118.2		32	33.2	even	10
495.2.bj.a.172.2		32	165.47	even	20
495.2.bj.a.217.3		32	165.2	odd	20
605.2.e.b.362.8		32	55.37	odd	20
605.2.e.b.362.9		32	55.7	even	20
605.2.e.b.483.8		32	11.7	odd	10
605.2.e.b.483.9		32	11.4	even	5
605.2.m.c.112.3		32	5.2	odd	4	inner
605.2.m.c.233.3		32	1.1	even	1	trivial
605.2.m.c.457.3		32	55.17	even	20	inner
605.2.m.c.578.3		32	11.6	odd	10	inner
605.2.m.d.112.2		32	55.32	even	4
605.2.m.d.233.2		32	11.10	odd	2
605.2.m.d.457.2		32	55.27	odd	20
605.2.m.d.578.2		32	11.5	even	5
605.2.m.e.118.2		32	11.9	even	5
605.2.m.e.282.2		32	55.52	even	20
605.2.m.e.403.3		32	11.8	odd	10
605.2.m.e.602.3		32	55.42	odd	20
880.2.cm.a.337.2		32	220.47	even	20
880.2.cm.a.513.3		32	44.3	odd	10
880.2.cm.a.657.3		32	220.167	odd	20
880.2.cm.a.833.2		32	44.35	even	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.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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