LMFDB - Embedded newform 104.2.s.c.101.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(69,104)] 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("104.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.8607891481591137382656.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 5 x^{14} - 6 x^{13} + 6 x^{12} - 20 x^{10} + 48 x^{9} - 76 x^{8} + 96 x^{7} + \cdots + 256 $ x^16 - 3x^15 + 5x^14 - 6x^13 + 6x^12 - 20x^10 + 48x^9 - 76x^8 + 96x^7 - 80x^6 + 96x^4 - 192x^3 + 320x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.7
Root			$-0.0207305 + 1.41406i$ of defining polynomial
Character	$\chi$	$=$	104.101
Dual form			104.2.s.c.69.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.21425 + 0.724984i) q^{2} +(-1.95589 + 1.12924i) q^{3} +(0.948796 + 1.76062i) q^{4} +0.642566 q^{5} +(-3.19362 - 0.0468193i) q^{6} +(0.306483 + 0.176948i) q^{7} +(-0.124348 + 2.82569i) q^{8} +(1.05034 - 1.81925i) q^{9} +(0.780234 + 0.465850i) q^{10} +(-1.15663 - 2.00334i) q^{11} +(-3.84390 - 2.37217i) q^{12} +(3.23687 - 1.58829i) q^{13} +(0.243862 + 0.437053i) q^{14} +(-1.25679 + 0.725608i) q^{15} +(-2.19957 + 3.34094i) q^{16} +(3.34390 - 5.79180i) q^{17} +(2.59430 - 1.44754i) q^{18} +(1.51026 - 2.61585i) q^{19} +(0.609664 + 1.13131i) q^{20} -0.799263 q^{21} +(0.0479552 - 3.27109i) q^{22} +(0.693517 + 1.20121i) q^{23} +(-2.94766 - 5.66717i) q^{24} -4.58711 q^{25} +(5.08185 + 0.418099i) q^{26} -2.03107i q^{27} +(-0.0207484 + 0.707487i) q^{28} +(-5.85776 + 3.38198i) q^{29} +(-2.05211 - 0.0300845i) q^{30} +7.83867i q^{31} +(-5.09295 + 2.46208i) q^{32} +(4.52449 + 2.61221i) q^{33} +(8.25929 - 4.60841i) q^{34} +(0.196935 + 0.113701i) q^{35} +(4.19957 + 0.123160i) q^{36} +(2.54831 + 4.41379i) q^{37} +(3.73028 - 2.08138i) q^{38} +(-4.53742 + 6.76172i) q^{39} +(-0.0799015 + 1.81569i) q^{40} +(-7.03170 + 4.05975i) q^{41} +(-0.970503 - 0.579453i) q^{42} +(0.0281959 + 0.0162789i) q^{43} +(2.42972 - 3.93715i) q^{44} +(0.674915 - 1.16899i) q^{45} +(-0.0287540 + 1.96135i) q^{46} -12.6079i q^{47} +(0.529416 - 9.01836i) q^{48} +(-3.43738 - 5.95372i) q^{49} +(-5.56989 - 3.32558i) q^{50} +15.1042i q^{51} +(5.86751 + 4.19194i) q^{52} -3.40398i q^{53} +(1.47249 - 2.46622i) q^{54} +(-0.743211 - 1.28728i) q^{55} +(-0.538110 + 0.844022i) q^{56} +6.82176i q^{57} +(-9.56466 - 0.140221i) q^{58} +(2.40152 - 4.15956i) q^{59} +(-2.46996 - 1.52428i) q^{60} +(8.23572 + 4.75490i) q^{61} +(-5.68291 + 9.51809i) q^{62} +(0.643824 - 0.371712i) q^{63} +(-7.96908 - 0.702736i) q^{64} +(2.07990 - 1.02058i) q^{65} +(3.60004 + 6.45206i) q^{66} +(2.24483 + 3.88815i) q^{67} +(13.3698 + 0.392096i) q^{68} +(-2.71289 - 1.56629i) q^{69} +(0.156697 + 0.280835i) q^{70} +(-5.35176 - 3.08984i) q^{71} +(5.01003 + 3.19417i) q^{72} +6.24869i q^{73} +(-0.105656 + 7.20692i) q^{74} +(8.97189 - 5.17993i) q^{75} +(6.03845 + 0.177089i) q^{76} -0.818652i q^{77} +(-10.4117 + 4.92085i) q^{78} +7.68780 q^{79} +(-1.41337 + 2.14677i) q^{80} +(5.44459 + 9.43030i) q^{81} +(-11.4815 - 0.168322i) q^{82} -16.7317 q^{83} +(-0.758338 - 1.40720i) q^{84} +(2.14867 - 3.72161i) q^{85} +(0.0224348 + 0.0402082i) q^{86} +(7.63810 - 13.2296i) q^{87} +(5.80465 - 3.01917i) q^{88} +(-1.37983 + 0.796643i) q^{89} +(1.66701 - 0.930138i) q^{90} +(1.27309 + 0.0859734i) q^{91} +(-1.45686 + 2.36072i) q^{92} +(-8.85170 - 15.3316i) q^{93} +(9.14050 - 15.3091i) q^{94} +(0.970443 - 1.68086i) q^{95} +(7.18101 - 10.5667i) q^{96} +(-5.29486 - 3.05699i) q^{97} +(0.142518 - 9.72133i) q^{98} -4.85944 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - q^{4} + 6 q^{6} + 18 q^{7} + 2 q^{9} - 9 q^{10} - 16 q^{12} - 24 q^{14} - 36 q^{15} - q^{16} + 8 q^{17} - 15 q^{20} + 22 q^{22} - 2 q^{23} - 12 q^{24} - 12 q^{25} + 23 q^{26} - 8 q^{30}+ \cdots - 93 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - q^4 + 6 * q^6 + 18 * q^7 + 2 * q^9 - 9 * q^10 - 16 * q^12 - 24 * q^14 - 36 * q^15 - q^16 + 8 * q^17 - 15 * q^20 + 22 * q^22 - 2 * q^23 - 12 * q^24 - 12 * q^25 + 23 * q^26 - 8 * q^30 - 27 * q^32 - 30 * q^33 + 33 * q^36 - 14 * q^39 + 26 * q^40 + 24 * q^41 + 14 * q^42 + 42 * q^46 + 6 * q^48 - 14 * q^49 + 6 * q^50 + 28 * q^52 + 6 * q^54 + 4 * q^55 - 8 * q^56 - 33 * q^58 - 4 * q^62 + 50 * q^64 + 6 * q^65 + 40 * q^66 + 5 * q^68 + 6 * q^71 + 39 * q^72 - 29 * q^74 + 24 * q^76 - 20 * q^78 + 32 * q^79 - 33 * q^80 + 12 * q^81 + 9 * q^82 - 24 * q^84 + 34 * q^87 - 8 * q^88 - 30 * q^89 - 62 * q^90 - 4 * q^92 - 24 * q^94 + 28 * q^95 - 30 * q^97 - 93 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.21425	+	0.724984i	0.858603	+	0.512641i
$2$	1.21425	+	0.724984i	0.858603	+	0.512641i
$3$	−1.95589	+	1.12924i	−1.12924	+	0.651964i	−0.943742	−	0.330681i	$-0.892721\pi$
$3$	−1.95589	+	1.12924i	−1.12924	+	0.651964i	−0.185493	+	0.982646i	$0.559388\pi$
$4$	0.948796	+	1.76062i	0.474398	+	0.880310i
$5$	0.642566			0.287364			0.143682	−	0.989624i	$-0.454106\pi$
$5$	0.642566			0.287364			0.143682	+	0.989624i	$0.454106\pi$
$6$	−3.19362	−	0.0468193i	−1.30379	−	0.0191139i
$7$	0.306483	+	0.176948i	0.115840	+	0.0668800i	0.556800	−	0.830646i	$-0.312029\pi$
$7$	0.306483	+	0.176948i	0.115840	+	0.0668800i	−0.440961	+	0.897526i	$0.645362\pi$
$8$	−0.124348	+	2.82569i	−0.0439635	+	0.999033i
$9$	1.05034	−	1.81925i	0.350115	−	0.606416i
$10$	0.780234	+	0.465850i	0.246732	+	0.147315i
$11$	−1.15663	−	2.00334i	−0.348737	−	0.604030i	0.637288	−	0.770625i	$-0.280056\pi$
$11$	−1.15663	−	2.00334i	−0.348737	−	0.604030i	−0.986025	+	0.166595i	$0.946723\pi$
$12$	−3.84390	−	2.37217i	−1.10964	−	0.684787i
$13$	3.23687	−	1.58829i	0.897746	−	0.440513i
$13$	3.23687	−	1.58829i	0.897746	−	0.440513i
$14$	0.243862	+	0.437053i	0.0651747	+	0.116807i
$15$	−1.25679	+	0.725608i	−0.324502	+	0.187351i
$16$	−2.19957	+	3.34094i	−0.549893	+	0.835235i
$17$	3.34390	−	5.79180i	0.811015	−	1.40472i	−0.101140	−	0.994872i	$-0.532249\pi$
$17$	3.34390	−	5.79180i	0.811015	−	1.40472i	0.912155	−	0.409846i	$-0.134418\pi$
$18$	2.59430	−	1.44754i	0.611483	−	0.341188i
$19$	1.51026	−	2.61585i	0.346478	−	0.600117i	−0.639143	−	0.769088i	$-0.720711\pi$
$19$	1.51026	−	2.61585i	0.346478	−	0.600117i	0.985621	+	0.168970i	$0.0540442\pi$
$20$	0.609664	+	1.13131i	0.136325	+	0.252970i
$21$	−0.799263			−0.174413
$22$	0.0479552	−	3.27109i	0.0102241	−	0.697399i
$23$	0.693517	+	1.20121i	0.144608	+	0.250469i	0.929227	−	0.369510i	$-0.120474\pi$
$23$	0.693517	+	1.20121i	0.144608	+	0.250469i	−0.784618	+	0.619979i	$0.787141\pi$
$24$	−2.94766	−	5.66717i	−0.601689	−	1.15681i
$25$	−4.58711			−0.917422
$26$	5.08185	+	0.418099i	0.996633	+	0.0819960i
$27$		−	2.03107i		−	0.390879i
$28$	−0.0207484	+	0.707487i	−0.00392108	+	0.133702i
$29$	−5.85776	+	3.38198i	−1.08776	+	0.628018i	−0.932979	−	0.359931i	$-0.882800\pi$
$29$	−5.85776	+	3.38198i	−1.08776	+	0.628018i	−0.154780	+	0.987949i	$0.549467\pi$
$30$	−2.05211	−	0.0300845i	−0.374662	−	0.00549265i
$31$			7.83867i			1.40787i	0.710266	+	0.703933i	$0.248575\pi$
$31$			7.83867i			1.40787i	−0.710266	+	0.703933i	$0.751425\pi$
$32$	−5.09295	+	2.46208i	−0.900315	+	0.435238i
$33$	4.52449	+	2.61221i	0.787612	+	0.454728i
$34$	8.25929	−	4.60841i	1.41646	−	0.790336i
$35$	0.196935	+	0.113701i	0.0332881	+	0.0192189i
$36$	4.19957	+	0.123160i	0.699928	+	0.0205267i
$37$	2.54831	+	4.41379i	0.418939	+	0.725623i	0.995833	−	0.0911955i	$-0.0290688\pi$
$37$	2.54831	+	4.41379i	0.418939	+	0.725623i	−0.576894	+	0.816819i	$0.695735\pi$
$38$	3.73028	−	2.08138i	0.605132	−	0.337644i
$39$	−4.53742	+	6.76172i	−0.726568	+	1.08274i
$40$	−0.0799015	+	1.81569i	−0.0126335	+	0.287086i
$41$	−7.03170	+	4.05975i	−1.09817	+	0.634027i	−0.935739	−	0.352694i	$-0.885266\pi$
$41$	−7.03170	+	4.05975i	−1.09817	+	0.634027i	−0.162428	+	0.986720i	$0.551932\pi$
$42$	−0.970503	−	0.579453i	−0.149752	−	0.0894115i
$43$	0.0281959	+	0.0162789i	0.00429983	+	0.00248251i	0.502148	−	0.864781i	$-0.332543\pi$
$43$	0.0281959	+	0.0162789i	0.00429983	+	0.00248251i	−0.497849	+	0.867264i	$0.665876\pi$
$44$	2.42972	−	3.93715i	0.366294	−	0.593548i
$45$	0.674915	−	1.16899i	0.100610	−	0.174262i
$46$	−0.0287540	+	1.96135i	−0.00423955	+	0.289186i
$47$		−	12.6079i		−	1.83905i	−0.393036	−	0.919523i	$-0.628575\pi$
$47$		−	12.6079i		−	1.83905i	0.393036	−	0.919523i	$-0.371425\pi$
$48$	0.529416	−	9.01836i	0.0764146	−	1.30169i
$49$	−3.43738	−	5.95372i	−0.491054	−	0.850531i
$50$	−5.56989	−	3.32558i	−0.787701	−	0.470308i
$51$			15.1042i			2.11501i
$52$	5.86751	+	4.19194i	0.813677	+	0.581317i
$53$		−	3.40398i		−	0.467573i	−0.972288	−	0.233787i	$-0.924888\pi$
$53$		−	3.40398i		−	0.467573i	0.972288	−	0.233787i	$-0.0751117\pi$
$54$	1.47249	−	2.46622i	0.200381	−	0.335610i
$55$	−0.743211	−	1.28728i	−0.100215	−	0.173577i
$56$	−0.538110	+	0.844022i	−0.0719080	+	0.112787i
$57$			6.82176i			0.903565i
$58$	−9.56466	−	0.140221i	−1.25590	−	0.0184119i
$59$	2.40152	−	4.15956i	0.312652	−	0.541529i	−0.666284	−	0.745698i	$-0.732116\pi$
$59$	2.40152	−	4.15956i	0.312652	−	0.541529i	0.978936	+	0.204170i	$0.0654494\pi$
$60$	−2.46996	−	1.52428i	−0.318870	−	0.196783i
$61$	8.23572	+	4.75490i	1.05448	+	0.608802i	0.923899	−	0.382636i	$-0.124984\pi$
$61$	8.23572	+	4.75490i	1.05448	+	0.608802i	0.130577	+	0.991438i	$0.458317\pi$
$62$	−5.68291	+	9.51809i	−0.721730	+	1.20880i
$63$	0.643824	−	0.371712i	0.0811142	−	0.0468313i
$64$	−7.96908	−	0.702736i	−0.996134	−	0.0878421i
$65$	2.07990	−	1.02058i	0.257980	−	0.126588i
$66$	3.60004	+	6.45206i	0.443134	+	0.794193i
$67$	2.24483	+	3.88815i	0.274249	+	0.475013i	0.969945	−	0.243323i	$-0.0782374\pi$
$67$	2.24483	+	3.88815i	0.274249	+	0.475013i	−0.695696	+	0.718336i	$0.744904\pi$
$68$	13.3698	+	0.392096i	1.62133	+	0.0475486i
$69$	−2.71289	−	1.56629i	−0.326594	−	0.188559i
$70$	0.156697	+	0.280835i	0.0187289	+	0.0335663i
$71$	−5.35176	−	3.08984i	−0.635137	−	0.366696i	0.147602	−	0.989047i	$-0.452845\pi$
$71$	−5.35176	−	3.08984i	−0.635137	−	0.366696i	−0.782739	+	0.622350i	$0.786178\pi$
$72$	5.01003	+	3.19417i	0.590438	+	0.376436i
$73$			6.24869i			0.731354i	0.930742	+	0.365677i	$0.119162\pi$
$73$			6.24869i			0.731354i	−0.930742	+	0.365677i	$0.880838\pi$
$74$	−0.105656	+	7.20692i	−0.0122822	+	0.837788i
$75$	8.97189	−	5.17993i	1.03599	−	0.598126i
$76$	6.03845	+	0.177089i	0.692658	+	0.0203135i
$77$		−	0.818652i		−	0.0932941i
$78$	−10.4117	+	4.92085i	−1.17889	+	0.557176i
$79$	7.68780			0.864945			0.432472	−	0.901647i	$-0.357641\pi$
$79$	7.68780			0.864945			0.432472	+	0.901647i	$0.357641\pi$
$80$	−1.41337	+	2.14677i	−0.158019	+	0.240017i
$81$	5.44459	+	9.43030i	0.604954	+	1.04781i
$82$	−11.4815	−	0.168322i	−1.26792	−	0.0185880i
$83$	−16.7317			−1.83654			−0.918269	−	0.395957i	$-0.870413\pi$
$83$	−16.7317			−1.83654			−0.918269	+	0.395957i	$0.870413\pi$
$84$	−0.758338	−	1.40720i	−0.0827414	−	0.153538i
$85$	2.14867	−	3.72161i	0.233056	−	0.403666i
$86$	0.0224348	+	0.0402082i	0.00241921	+	0.00433576i
$87$	7.63810	−	13.2296i	0.818891	−	1.41836i
$88$	5.80465	−	3.01917i	0.618778	−	0.321845i
$89$	−1.37983	+	0.796643i	−0.146261	+	0.0844440i	−0.571345	−	0.820710i	$-0.693578\pi$
$89$	−1.37983	+	0.796643i	−0.146261	+	0.0844440i	0.425083	+	0.905154i	$0.360245\pi$
$90$	1.66701	−	0.930138i	0.175718	−	0.0980451i
$91$	1.27309	+	0.0859734i	0.133456	+	0.00901246i
$92$	−1.45686	+	2.36072i	−0.151889	+	0.246122i
$93$	−8.85170	−	15.3316i	−0.917878	−	1.58981i
$94$	9.14050	−	15.3091i	0.942771	−	1.57901i
$95$	0.970443	−	1.68086i	0.0995653	−	0.172452i
$96$	7.18101	−	10.5667i	0.732908	−	1.07846i
$97$	−5.29486	−	3.05699i	−0.537611	−	0.310390i	0.206499	−	0.978447i	$-0.433793\pi$
$97$	−5.29486	−	3.05699i	−0.537611	−	0.310390i	−0.744110	+	0.668057i	$0.767126\pi$
$98$	0.142518	−	9.72133i	0.0143964	−	0.982003i
$99$	−4.85944			−0.488392
$100$	−4.35223	−	8.07616i	−0.435223	−	0.807616i
$101$	−7.17483	+	4.14239i	−0.713922	+	0.412183i	−0.812511	−	0.582945i	$-0.801900\pi$
$101$	−7.17483	+	4.14239i	−0.713922	+	0.412183i	0.0985896	+	0.995128i	$0.468567\pi$
$102$	−10.9503	+	18.3402i	−1.08424	+	1.81595i
$103$	11.5770			1.14071			0.570356	−	0.821397i	$-0.306805\pi$
$103$	11.5770			1.14071			0.570356	+	0.821397i	$0.306805\pi$
$104$	4.08553	+	9.34390i	0.400619	+	0.916245i
$105$	−0.513579			−0.0501201
$106$	2.46783	−	4.13328i	0.239697	−	0.401460i
$107$	8.91550	−	5.14737i	0.861894	−	0.497615i	−0.00275201	−	0.999996i	$-0.500876\pi$
$107$	8.91550	−	5.14737i	0.861894	−	0.497615i	0.864646	+	0.502381i	$0.167543\pi$
$108$	3.57594	−	1.92707i	0.344095	−	0.185433i
$109$	−8.84423			−0.847123			−0.423562	−	0.905867i	$-0.639220\pi$
$109$	−8.84423			−0.847123			−0.423562	+	0.905867i	$0.639220\pi$
$110$	0.0308143	−	2.10189i	0.00293803	−	0.200407i
$111$	−9.96842	−	5.75527i	−0.946161	−	0.546266i
$112$	−1.26530	+	0.634731i	−0.119560	+	0.0599764i
$113$	0.956864	−	1.65734i	0.0900142	−	0.155909i	−0.817503	−	0.575925i	$-0.804642\pi$
$113$	0.956864	−	1.65734i	0.0900142	−	0.155909i	0.907517	+	0.420016i	$0.137975\pi$
$114$	−4.94567	+	8.28331i	−0.463204	+	0.775803i
$115$	0.445630	+	0.771855i	0.0415553	+	0.0719758i
$116$	−11.5122	−	7.10449i	−1.06888	−	0.659635i
$117$	0.510329	−	7.55693i	0.0471799	−	0.698638i
$118$	5.93166	−	3.30967i	0.546053	−	0.304680i
$119$	2.04969	−	1.18339i	0.187895	−	0.108481i
$120$	−1.89407	−	3.64153i	−0.172904	−	0.332424i
$121$	2.82441	−	4.89203i	0.256765	−	0.444730i
$122$	6.55299	+	11.7444i	0.593279	+	1.06329i
$123$	9.16883	−	15.8809i	0.826725	−	1.43193i
$124$	−13.8009	+	7.43730i	−1.23936	+	0.667889i
$125$	−6.16035			−0.550998
$126$	1.05125	+	0.0154116i	0.0936526	+	0.00137297i
$127$	6.82376	+	11.8191i	0.605511	+	1.04878i	0.991970	+	0.126470i	$0.0403646\pi$
$127$	6.82376	+	11.8191i	0.605511	+	1.04878i	−0.386459	+	0.922306i	$0.626302\pi$
$128$	−9.16696	−	6.63075i	−0.810253	−	0.586081i
$129$	−0.0735308			−0.00647403
$130$	3.26542	+	0.268656i	0.286396	+	0.0235627i
$131$			5.81035i			0.507653i	0.967250	+	0.253826i	$0.0816892\pi$
$131$			5.81035i			0.507653i	−0.967250	+	0.253826i	$0.918311\pi$
$132$	−0.306301	+	10.4444i	−0.0266601	+	0.909066i
$133$	0.925738	−	0.534475i	0.0802717	−	0.0463449i
$134$	−0.0930730	+	6.34864i	−0.00804028	+	0.548439i
$135$		−	1.30510i		−	0.112325i
$136$	15.9500	+	10.1690i	1.36771	+	0.871987i
$137$	5.11297	+	2.95197i	0.436830	+	0.252204i	0.702252	−	0.711928i	$-0.252178\pi$
$137$	5.11297	+	2.95197i	0.436830	+	0.252204i	−0.265422	+	0.964132i	$0.585511\pi$
$138$	−2.15859	−	3.86867i	−0.183751	−	0.329323i
$139$	−4.78695	−	2.76375i	−0.406024	−	0.234418i	0.283056	−	0.959103i	$-0.408652\pi$
$139$	−4.78695	−	2.76375i	−0.406024	−	0.234418i	−0.689080	+	0.724685i	$0.741985\pi$
$140$	−0.0133322	+	0.454607i	−0.00112678	+	0.0384213i
$141$	14.2372	+	24.6596i	1.19899	+	2.07672i
$142$	−4.25828	−	7.63177i	−0.357347	−	0.640444i
$143$	−6.92575	−	4.64749i	−0.579161	−	0.388643i
$144$	3.76770	+	7.51071i	0.313975	+	0.625892i
$145$	−3.76400	+	2.17314i	−0.312583	+	0.180470i
$146$	−4.53020	+	7.58746i	−0.374922	+	0.627942i
$147$	13.4463	+	7.76322i	1.10903	+	0.640299i
$148$	−5.35320	+	8.67439i	−0.440030	+	0.713031i
$149$	−6.65703	+	11.5303i	−0.545365	+	0.944600i	0.453219	+	0.891399i	$0.350276\pi$
$149$	−6.65703	+	11.5303i	−0.545365	+	0.944600i	−0.998584	+	0.0532004i	$0.983058\pi$
$150$	14.6495	+	0.214765i	1.19612	+	0.0175355i
$151$			5.22848i			0.425487i	0.977108	+	0.212744i	$0.0682400\pi$
$151$			5.22848i			0.425487i	−0.977108	+	0.212744i	$0.931760\pi$
$152$	7.20379	+	4.59281i	0.584305	+	0.372526i
$153$	−7.02449	−	12.1668i	−0.567896	−	0.983625i
$154$	0.593510	−	0.994047i	0.0478264	−	0.0801026i
$155$			5.03686i			0.404570i
$156$	−16.2099	−	1.57318i	−1.29783	−	0.125955i
$157$		−	13.7313i		−	1.09588i	−0.836519	−	0.547938i	$-0.815413\pi$
$157$		−	13.7313i		−	1.09588i	0.836519	−	0.547938i	$-0.184587\pi$
$158$	9.33489	+	5.57353i	0.742644	+	0.443406i
$159$	3.84390	+	6.65783i	0.304841	+	0.528000i
$160$	−3.27256	+	1.58205i	−0.258718	+	0.125072i
$161$			0.490865i			0.0386856i
$162$	−0.225739	+	15.3980i	−0.0177357	+	1.20978i
$163$	−8.42963	+	14.6006i	−0.660260	+	1.14360i	0.320287	+	0.947320i	$0.396221\pi$
$163$	−8.42963	+	14.6006i	−0.660260	+	1.14360i	−0.980547	+	0.196283i	$0.937113\pi$
$164$	−13.8193	−	8.52827i	−1.07911	−	0.665946i
$165$	2.90728	+	1.67852i	0.226331	+	0.130673i
$166$	−20.3164	−	12.1302i	−1.57686	−	0.941485i
$167$	6.98117	−	4.03058i	0.540219	−	0.311895i	−0.204949	−	0.978773i	$-0.565703\pi$
$167$	6.98117	−	4.03058i	0.540219	−	0.311895i	0.745168	+	0.666877i	$0.232369\pi$
$168$	0.0993864	−	2.25847i	0.00766783	−	0.174245i
$169$	7.95466	−	10.2822i	0.611897	−	0.790938i
$170$	5.30713	−	2.96121i	0.407039	−	0.227114i
$171$	−3.17259	−	5.49509i	−0.242614	−	0.420220i
$172$	−0.00190882	+	0.0650876i	−0.000145546	+	0.00496288i
$173$	14.4482	+	8.34170i	1.09848	+	0.634208i	0.935821	−	0.352475i	$-0.114660\pi$
$173$	14.4482	+	8.34170i	1.09848	+	0.634208i	0.162659	+	0.986682i	$0.447993\pi$
$174$	18.8658	−	10.5265i	1.43021	−	0.798011i
$175$	−1.40587	−	0.811679i	−0.106274	−	0.0613572i
$176$	9.23714	+	0.542259i	0.696275	+	0.0408743i
$177$			10.8475i			0.815351i
$178$	−2.25301	−	0.0330297i	−0.168870	−	0.00247568i
$179$	10.2099	−	5.89469i	0.763123	−	0.440590i	−0.0672926	−	0.997733i	$-0.521436\pi$
$179$	10.2099	−	5.89469i	0.763123	−	0.440590i	0.830416	+	0.557144i	$0.188103\pi$
$180$	2.69850	+	0.0791386i	0.201134	+	0.00589864i
$181$		−	5.65279i		−	0.420169i	−0.977683	−	0.210084i	$-0.932626\pi$
$181$		−	5.65279i		−	0.420169i	0.977683	−	0.210084i	$-0.0673739\pi$
$182$	1.48352	+	1.02736i	0.109966	+	0.0761531i
$183$	−21.4776			−1.58767
$184$	−3.48048	+	1.81030i	−0.256584	+	0.133457i
$185$	1.63745	+	2.83615i	0.120388	+	0.208518i
$186$	0.367001	−	25.0337i	0.0269098	−	1.83556i
$187$	−15.4706			−1.13132
$188$	22.1977	−	11.9623i	1.61893	−	0.872440i
$189$	0.359393	−	0.622487i	0.0261420	−	0.0452793i
$190$	2.39695	−	1.33742i	0.173893	−	0.0970267i
$191$	−5.60725	+	9.71203i	−0.405726	+	0.702738i	−0.994406	−	0.105628i	$-0.966315\pi$
$191$	−5.60725	+	9.71203i	−0.405726	+	0.702738i	0.588680	+	0.808366i	$0.299648\pi$
$192$	16.3802	−	7.62448i	1.18214	−	0.550250i
$193$	0.671819	−	0.387875i	0.0483586	−	0.0279198i	−0.475626	−	0.879648i	$-0.657778\pi$
$193$	0.671819	−	0.387875i	0.0483586	−	0.0279198i	0.523984	+	0.851728i	$0.324445\pi$
$194$	−4.21300	−	7.55063i	−0.302476	−	0.542103i
$195$	−2.91559	+	4.34485i	−0.208790	+	0.311141i
$196$	7.22086	−	11.7008i	0.515776	−	0.835770i
$197$	1.52807	+	2.64669i	0.108870	+	0.188569i	0.915313	−	0.402744i	$-0.131943\pi$
$197$	1.52807	+	2.64669i	0.108870	+	0.188569i	−0.806443	+	0.591312i	$0.798610\pi$
$198$	−5.90056	−	3.52301i	−0.419335	−	0.250370i
$199$	−13.1258	+	22.7346i	−0.930465	+	1.61161i	−0.147938	+	0.988997i	$0.547264\pi$
$199$	−13.1258	+	22.7346i	−0.930465	+	1.61161i	−0.782527	+	0.622616i	$0.786070\pi$
$200$	0.570396	−	12.9618i	0.0403331	−	0.916535i
$201$	−8.78128	−	5.06987i	−0.619384	−	0.357601i
$202$	−11.7152	−	0.171748i	−0.824277	−	0.0120841i
$203$	−2.39374			−0.168007
$204$	−26.5928	+	14.3308i	−1.86187	+	1.00336i
$205$	−4.51833	+	2.60866i	−0.315574	+	0.182196i
$206$	14.0573	+	8.39312i	0.979420	+	0.584776i
$207$	2.91373			0.202518
$208$	−1.81334	+	14.3078i	−0.125732	+	0.992064i
$209$	−6.98726			−0.483319
$210$	−0.623612	−	0.372336i	−0.0430333	−	0.0256936i
$211$	−10.9194	+	6.30433i	−0.751724	+	0.434008i	−0.826316	−	0.563206i	$-0.809568\pi$
$211$	−10.9194	+	6.30433i	−0.751724	+	0.434008i	0.0745926	+	0.997214i	$0.476234\pi$
$212$	5.99313	−	3.22969i	0.411610	−	0.221816i
$213$	13.9566			0.956292
$214$	14.5574	+	0.213416i	0.995123	+	0.0145888i
$215$	0.0181177	+	0.0104603i	0.00123562	+	0.000713384i
$216$	5.73918	+	0.252559i	0.390502	+	0.0171844i
$217$	−1.38703	+	2.40241i	−0.0941581	+	0.163087i
$218$	−10.7391	−	6.41192i	−0.727343	−	0.434270i
$219$	−7.05624	−	12.2218i	−0.476816	−	0.825870i
$220$	1.56125	−	2.52988i	0.105260	−	0.170564i
$221$	1.62470	−	24.0584i	0.109289	−	1.61834i
$222$	−7.93166	−	14.2153i	−0.532338	−	0.954067i
$223$	−14.8690	+	8.58464i	−0.995704	+	0.574870i	−0.906975	−	0.421185i	$-0.861614\pi$
$223$	−14.8690	+	8.58464i	−0.995704	+	0.574870i	−0.0887299	+	0.996056i	$0.528281\pi$
$224$	−1.99656	−	0.146603i	−0.133401	−	0.00979532i
$225$	−4.81804	+	8.34510i	−0.321203	+	0.556340i
$226$	2.36341	−	1.31871i	0.157212	−	0.0877191i
$227$	−2.30952	+	4.00021i	−0.153289	+	0.265504i	−0.932435	−	0.361339i	$-0.882320\pi$
$227$	−2.30952	+	4.00021i	−0.153289	+	0.265504i	0.779146	+	0.626843i	$0.215653\pi$
$228$	−12.0105	+	6.47247i	−0.795417	+	0.428650i
$229$	22.9078			1.51379			0.756895	−	0.653537i	$-0.226716\pi$
$229$	22.9078			1.51379			0.756895	+	0.653537i	$0.226716\pi$
$230$	−0.0184763	+	1.26030i	−0.00121829	+	0.0831016i
$231$	0.924451	+	1.60120i	0.0608244	+	0.105351i
$232$	−8.82804	−	16.9728i	−0.579589	−	1.11432i
$233$	24.6115			1.61236			0.806178	−	0.591674i	$-0.201533\pi$
$233$	24.6115			1.61236			0.806178	+	0.591674i	$0.201533\pi$
$234$	6.09832	−	8.80600i	0.398659	−	0.575666i
$235$		−	8.10138i		−	0.528476i
$236$	9.60196	+	0.281596i	0.625035	+	0.0183303i
$237$	−15.0365	+	8.68133i	−0.976726	+	0.563913i
$238$	3.34678	+	0.0490647i	0.216939	+	0.00318039i
$239$		−	10.1001i		−	0.653319i	−0.945142	−	0.326659i	$-0.894077\pi$
$239$		−	10.1001i		−	0.653319i	0.945142	−	0.326659i	$-0.105923\pi$
$240$	0.340184	−	5.79488i	0.0219588	−	0.374058i
$241$	−15.6591	−	9.04077i	−1.00869	−	0.582367i	−0.0978820	−	0.995198i	$-0.531207\pi$
$241$	−15.6591	−	9.04077i	−1.00869	−	0.582367i	−0.910808	+	0.412831i	$0.864540\pi$
$242$	6.97618	−	3.89248i	0.448446	−	0.250218i
$243$	−16.0212	−	9.24983i	−1.02776	−	0.593377i
$244$	−0.557545	+	19.0114i	−0.0356932	+	1.21708i
$245$	−2.20874	−	3.82565i	−0.141111	−	0.244412i
$246$	22.6466	−	12.6361i	1.44390	−	0.805646i
$247$	0.733789	−	10.8659i	0.0466899	−	0.691381i
$248$	−22.1497	−	0.974720i	−1.40651	−	0.0618948i
$249$	32.7253	−	18.8940i	2.07388	−	1.19736i
$250$	−7.48019	−	4.46615i	−0.473089	−	0.282464i
$251$	13.3339	+	7.69835i	0.841631	+	0.485916i	0.857818	−	0.513953i	$-0.171819\pi$
$251$	13.3339	+	7.69835i	0.841631	+	0.485916i	−0.0161874	+	0.999869i	$0.505153\pi$
$252$	1.26530	+	0.780851i	0.0797065	+	0.0491890i
$253$	1.60429	−	2.77871i	0.100861	−	0.174696i
$254$	−0.282921	+	19.2984i	−0.0177520	+	1.21089i
$255$			9.70543i			0.607778i
$256$	−6.32378	−	14.6973i	−0.395236	−	0.918580i
$257$	0.569829	+	0.986973i	0.0355450	+	0.0615657i	0.883251	−	0.468901i	$-0.155350\pi$
$257$	0.569829	+	0.986973i	0.0355450	+	0.0615657i	−0.847706	+	0.530467i	$0.822017\pi$
$258$	−0.0892846	−	0.0533087i	−0.00555862	−	0.00331885i
$259$			1.80367i			0.112074i
$260$	3.77026	+	2.69359i	0.233822	+	0.167050i
$261$			14.2090i			0.879514i
$262$	−4.21241	+	7.05521i	−0.260244	+	0.435872i
$263$	4.69352	+	8.12941i	0.289415	+	0.501281i	0.973670	−	0.227961i	$-0.0732060\pi$
$263$	4.69352	+	8.12941i	0.289415	+	0.501281i	−0.684255	+	0.729242i	$0.739873\pi$
$264$	−7.94392	+	12.4600i	−0.488915	+	0.766859i
$265$		−	2.18728i		−	0.134364i
$266$	1.51156	+	0.0221599i	0.0926798	+	0.00135871i
$267$	1.79920	−	3.11630i	0.110109	−	0.190714i
$268$	−4.71568	+	7.64135i	−0.288056	+	0.466770i
$269$	16.5114	+	9.53286i	1.00672	+	0.581229i	0.910229	−	0.414105i	$-0.135906\pi$
$269$	16.5114	+	9.53286i	1.00672	+	0.581229i	0.0964886	+	0.995334i	$0.469239\pi$
$270$	0.946173	−	1.58471i	0.0575823	−	0.0964423i
$271$	15.3555	−	8.86548i	0.932778	−	0.538539i	0.0450887	−	0.998983i	$-0.485643\pi$
$271$	15.3555	−	8.86548i	0.932778	−	0.538539i	0.887689	+	0.460444i	$0.152310\pi$
$272$	11.9949	+	23.9112i	0.727300	+	1.44983i
$273$	−2.58711	+	1.26946i	−0.156579	+	0.0768313i
$274$	4.06828	+	7.29124i	0.245774	+	0.440480i
$275$	5.30559	+	9.18955i	0.319939	+	0.554151i
$276$	0.183658	−	6.26246i	0.0110549	−	0.376956i
$277$	−22.4083	−	12.9374i	−1.34638	−	0.777334i	−0.358647	−	0.933473i	$-0.616762\pi$
$277$	−22.4083	−	12.9374i	−1.34638	−	0.777334i	−0.987735	+	0.156139i	$0.950095\pi$
$278$	−3.80887	−	6.82634i	−0.228441	−	0.409417i
$279$	14.2605	+	8.23330i	0.853753	+	0.492915i
$280$	−0.345771	+	0.542340i	−0.0206638	+	0.0324110i
$281$		−	0.736068i		−	0.0439101i	−0.999759	−	0.0219551i	$-0.993011\pi$
$281$		−	0.736068i		−	0.0439101i	0.999759	−	0.0219551i	$-0.00698908\pi$
$282$	−0.590292	+	40.2647i	−0.0351514	+	2.39773i
$283$	21.0813	−	12.1713i	1.25315	−	0.723508i	0.281418	−	0.959585i	$-0.409195\pi$
$283$	21.0813	−	12.1713i	1.25315	−	0.723508i	0.971734	+	0.236077i	$0.0758618\pi$
$284$	0.362306	−	12.3540i	0.0214989	−	0.733078i
$285$			4.38343i			0.259652i
$286$	−5.04022	−	10.6643i	−0.298035	−	0.630591i
$287$	−2.87346			−0.169615
$288$	−0.870220	+	11.8514i	−0.0512782	+	0.698349i
$289$	−13.8633	−	24.0120i	−0.815489	−	1.41247i
$290$	−6.14592	−	0.0901010i	−0.360901	−	0.00529091i
$291$	13.8082			0.809453
$292$	−11.0016	+	5.92873i	−0.643818	+	0.346953i
$293$	3.07441	−	5.32504i	0.179609	−	0.311092i	−0.762138	−	0.647415i	$-0.775850\pi$
$293$	3.07441	−	5.32504i	0.179609	−	0.311092i	0.941747	+	0.336323i	$0.109183\pi$
$294$	10.6989	+	19.1748i	0.623974	+	1.11830i
$295$	1.54314	−	2.67279i	0.0898449	−	0.155616i
$296$	−12.7889	+	6.65188i	−0.743340	+	0.386633i
$297$	−4.06893	+	2.34920i	−0.236103	+	0.136314i
$298$	−16.4426	+	9.17442i	−0.952492	+	0.531460i
$299$	4.15269	+	2.78664i	0.240156	+	0.161156i
$300$	17.6324	+	10.8814i	1.01801	+	0.628238i
$301$	0.00576103	+	0.00997839i	0.000332060	+	0.000575145i
$302$	−3.79056	+	6.34867i	−0.218122	+	0.365325i
$303$	9.35546	−	16.2041i	0.537457	−	0.930903i
$304$	5.41748	+	10.7994i	0.310714	+	0.619391i
$305$	5.29199	+	3.05533i	0.303019	+	0.174948i
$306$	0.291243	−	19.8661i	0.0166493	−	1.13567i
$307$	−11.7521			−0.670727			−0.335364	−	0.942089i	$-0.608859\pi$
$307$	−11.7521			−0.670727			−0.335364	+	0.942089i	$0.608859\pi$
$308$	1.44134	−	0.776735i	0.0821278	−	0.0442586i
$309$	−22.6433	+	13.0731i	−1.28813	+	0.743704i
$310$	−3.65164	+	6.11600i	−0.207399	+	0.347365i
$311$	−24.0980			−1.36647			−0.683235	−	0.730199i	$-0.739427\pi$
$311$	−24.0980			−1.36647			−0.683235	+	0.730199i	$0.739427\pi$
$312$	−18.5423	−	13.6621i	−1.04975	−	0.773467i
$313$	−4.66324			−0.263582			−0.131791	−	0.991278i	$-0.542073\pi$
$313$	−4.66324			−0.263582			−0.131791	+	0.991278i	$0.542073\pi$
$314$	9.95496	−	16.6732i	0.561791	−	0.940922i
$315$	0.413699	−	0.238849i	0.0233093	−	0.0134576i
$316$	7.29415	+	13.5353i	0.410328	+	0.761420i
$317$	−20.2486			−1.13728			−0.568638	−	0.822588i	$-0.692529\pi$
$317$	−20.2486			−1.13728			−0.568638	+	0.822588i	$0.692529\pi$
$318$	−0.159372	+	10.8710i	−0.00893715	+	0.609616i
$319$	13.5505	+	7.82340i	0.758684	+	0.438026i
$320$	−5.12065	−	0.451554i	−0.286253	−	0.0252427i
$321$	−11.6252	+	20.1354i	−0.648854	+	1.12385i
$322$	−0.355870	+	0.596032i	−0.0198318	+	0.0332156i
$323$	−10.1003	−	17.4943i	−0.561997	−	0.973408i
$324$	−11.4374	+	18.5333i	−0.635410	+	1.02963i
$325$	−14.8479	+	7.28567i	−0.823612	+	0.404136i
$326$	−20.8208	+	11.6173i	−1.15316	+	0.643425i
$327$	17.2984	−	9.98721i	0.956602	−	0.552294i
$328$	−10.5972	−	20.3742i	−0.585134	−	1.12498i
$329$	2.23093	−	3.86409i	0.122995	−	0.213034i
$330$	2.31326	+	4.14587i	0.127341	+	0.228223i
$331$	−1.39380	+	2.41414i	−0.0766104	+	0.132693i	−0.901785	−	0.432184i	$-0.857743\pi$
$331$	−1.39380	+	2.41414i	−0.0766104	+	0.132693i	0.825175	+	0.564877i	$0.191076\pi$
$332$	−15.8749	−	29.4581i	−0.871251	−	1.61672i
$333$	10.7064			0.586707
$334$	11.3990	+	0.167112i	0.623724	+	0.00914397i
$335$	1.44245	+	2.49839i	0.0788094	+	0.136502i
$336$	1.75803	−	2.67029i	0.0959086	−	0.145676i
$337$	22.6505			1.23385			0.616926	−	0.787021i	$-0.288378\pi$
$337$	22.6505			1.23385			0.616926	+	0.787021i	$0.288378\pi$
$338$	17.1134	−	6.71813i	0.930844	−	0.365418i
$339$			4.32210i			0.234744i
$340$	8.59100	+	0.251947i	0.465913	+	0.0136638i
$341$	15.7035	−	9.06644i	0.850394	−	0.490975i
$342$	0.131539	−	8.97248i	0.00711282	−	0.485176i
$343$		−	4.91022i		−	0.265127i
$344$	−0.0495052	+	0.0776486i	−0.00266914	+	0.00418653i
$345$	−1.74321	−	1.00644i	−0.0938513	−	0.0541851i
$346$	11.4962	+	20.6036i	0.618037	+	1.10766i
$347$	2.15567	+	1.24457i	0.115722	+	0.0668123i	0.556744	−	0.830684i	$-0.312050\pi$
$347$	2.15567	+	1.24457i	0.115722	+	0.0668123i	−0.441022	+	0.897496i	$0.645384\pi$
$348$	30.5393	+	0.895622i	1.63708	+	0.0480104i
$349$	0.504568	+	0.873938i	0.0270089	+	0.0467808i	0.879214	−	0.476427i	$-0.158068\pi$
$349$	0.504568	+	0.873938i	0.0270089	+	0.0467808i	−0.852205	+	0.523208i	$0.824735\pi$
$350$	−1.11862	−	2.00481i	−0.0597927	−	0.107162i
$351$	−3.22593	−	6.57431i	−0.172187	−	0.350911i
$352$	10.8230	+	7.35521i	0.576870	+	0.392034i
$353$	2.66110	−	1.53639i	0.141636	−	0.0817738i	−0.427507	−	0.904012i	$-0.640608\pi$
$353$	2.66110	−	1.53639i	0.141636	−	0.0817738i	0.569144	+	0.822238i	$0.307275\pi$
$354$	−7.86429	+	13.1716i	−0.417982	+	0.700063i
$355$	−3.43886	−	1.98542i	−0.182515	−	0.105375i
$356$	−2.71176	−	1.67350i	−0.143723	−	0.0886953i
$357$	−2.67265	+	4.62917i	−0.141452	+	0.245002i
$358$	16.6709	+	0.244400i	0.881084	+	0.0129170i
$359$			3.31798i			0.175116i	0.996159	+	0.0875582i	$0.0279064\pi$
$359$			3.31798i			0.175116i	−0.996159	+	0.0875582i	$0.972094\pi$
$360$	3.21927	+	2.05246i	0.169671	+	0.108174i
$361$	4.93822	+	8.55324i	0.259906	+	0.450171i
$362$	4.09818	−	6.86389i	0.215396	−	0.360758i
$363$			12.7577i			0.669606i
$364$	1.05654	+	2.32300i	0.0553775	+	0.121758i
$365$			4.01519i			0.210165i
$366$	−26.0791	−	15.5709i	−1.36318	−	0.813904i
$367$	−14.7079	−	25.4749i	−0.767748	−	1.32978i	−0.938782	−	0.344513i	$-0.888044\pi$
$367$	−14.7079	−	25.4749i	−0.767748	−	1.32978i	0.171034	−	0.985265i	$-0.445289\pi$
$368$	−5.53860	−	0.325140i	−0.288720	−	0.0169491i
$369$			17.0565i			0.887928i
$370$	−0.0678906	+	4.63092i	−0.00352947	+	0.240750i
$371$	0.602327	−	1.04326i	0.0312713	−	0.0541635i
$372$	18.5947	−	30.1310i	0.964088	−	1.56222i
$373$	−6.80078	−	3.92643i	−0.352131	−	0.203303i	0.313492	−	0.949591i	$-0.398501\pi$
$373$	−6.80078	−	3.92643i	−0.352131	−	0.203303i	−0.665624	+	0.746288i	$0.731834\pi$
$374$	−18.7852	−	11.2159i	−0.971358	−	0.579963i
$375$	12.0490	−	6.95648i	0.622206	−	0.359231i
$376$	35.6259	+	1.56776i	1.83727	+	0.0808510i
$377$	−13.5892	+	20.2509i	−0.699882	+	1.04297i
$378$	0.887686	−	0.495300i	0.0456576	−	0.0254755i
$379$	−2.12837	−	3.68644i	−0.109327	−	0.189360i	0.806171	−	0.591683i	$-0.201536\pi$
$379$	−2.12837	−	3.68644i	−0.109327	−	0.189360i	−0.915498	+	0.402323i	$0.868203\pi$
$380$	3.88010	+	0.113791i	0.199045	+	0.00583737i
$381$	−26.6931	−	15.4113i	−1.36753	−	0.789543i
$382$	−13.8497	+	7.72765i	−0.708610	+	0.395381i
$383$	18.9596	+	10.9463i	0.968790	+	0.559331i	0.898867	−	0.438221i	$-0.144391\pi$
$383$	18.9596	+	10.9463i	0.968790	+	0.559331i	0.0699226	+	0.997552i	$0.477725\pi$
$384$	25.4173	+	2.61738i	1.29707	+	0.133567i
$385$		−	0.526038i		−	0.0268094i
$386$	1.09696	+	0.0160817i	0.0558337	+	0.000818538i
$387$	0.0592307	−	0.0341969i	0.00301087	−	0.00173833i
$388$	0.358453	−	12.2227i	0.0181977	−	0.620513i
$389$		−	22.2842i		−	1.12985i	−0.825141	−	0.564926i	$-0.808905\pi$
$389$		−	22.2842i		−	1.12985i	0.825141	−	0.564926i	$-0.191095\pi$
$390$	−6.69019	+	3.16197i	−0.338771	+	0.160112i
$391$	9.27621			0.469118
$392$	17.2508	−	8.97265i	0.871297	−	0.453187i
$393$	−6.56125	−	11.3644i	−0.330971	−	0.573259i
$394$	−0.0633553	+	4.32156i	−0.00319179	+	0.217717i
$395$	4.93991			0.248554
$396$	−4.61062	−	8.55563i	−0.231692	−	0.429936i
$397$	11.3561	−	19.6694i	0.569948	−	0.987179i	−0.426622	−	0.904430i	$-0.640297\pi$
$397$	11.3561	−	19.6694i	0.569948	−	0.987179i	0.996570	−	0.0827491i	$-0.0263700\pi$
$398$	−32.4202	+	18.0894i	−1.62508	+	0.906741i
$399$	−1.20710	+	2.09075i	−0.0604304	+	0.104669i
$400$	10.0897	−	15.3253i	0.504484	−	0.766263i
$401$	−19.5220	+	11.2710i	−0.974883	+	0.562849i	−0.900721	−	0.434397i	$-0.856961\pi$
$401$	−19.5220	+	11.2710i	−0.974883	+	0.562849i	−0.0741618	+	0.997246i	$0.523628\pi$
$402$	−6.98707	−	12.5224i	−0.348483	−	0.624559i
$403$	12.4501	+	25.3728i	0.620183	+	1.26391i
$404$	−14.1006	−	8.70186i	−0.701532	−	0.432934i
$405$	3.49850	+	6.05959i	0.173842	+	0.301103i
$406$	−2.90659	−	1.73542i	−0.144252	−	0.0861275i
$407$	5.89489	−	10.2103i	0.292199	−	0.506104i
$408$	−42.6798	−	1.87817i	−2.11297	−	0.0929833i
$409$	10.0317	+	5.79180i	0.496035	+	0.286386i	0.727075	−	0.686558i	$-0.240879\pi$
$409$	10.0317	+	5.79180i	0.496035	+	0.286386i	−0.231039	+	0.972944i	$0.574213\pi$
$410$	−7.37760	−	0.108158i	−0.364354	−	0.00534153i
$411$	−13.3339			−0.657712
$412$	10.9842	+	20.3827i	0.541152	+	1.00418i
$413$	1.47205	−	0.849888i	0.0724348	−	0.0418203i
$414$	3.53799	+	2.11241i	0.173883	+	0.103819i
$415$	−10.7512			−0.527755
$416$	−12.5747	+	16.0585i	−0.616527	+	0.787334i
$417$	12.4837			0.611329
$418$	−8.48426	−	5.06565i	−0.414979	−	0.247769i
$419$	9.30144	−	5.37019i	0.454405	−	0.262351i	−0.255284	−	0.966866i	$-0.582169\pi$
$419$	9.30144	−	5.37019i	0.454405	−	0.262351i	0.709689	+	0.704515i	$0.248836\pi$
$420$	−0.487282	−	0.904217i	−0.0237769	−	0.0441213i
$421$	38.0009			1.85205			0.926026	−	0.377459i	$-0.123202\pi$
$421$	38.0009			1.85205			0.926026	+	0.377459i	$0.123202\pi$
$422$	−17.8294	−	0.261384i	−0.867923	−	0.0127240i
$423$	−22.9368	−	13.2426i	−1.11523	−	0.643877i
$424$	9.61861	+	0.423277i	0.467121	+	0.0205562i
$425$	−15.3388	+	26.5676i	−0.744043	+	1.28872i
$426$	16.9468	+	10.1183i	0.821075	+	0.490234i
$427$	1.68274	+	2.91459i	0.0814333	+	0.141047i
$428$	17.5216	+	10.8130i	0.846936	+	0.522667i
$429$	18.7941	+	1.26919i	0.907390	+	0.0612772i
$430$	0.0144159	+	0.0258364i	0.000695194	+	0.00124594i
$431$	−22.4367	+	12.9539i	−1.08074	+	0.623965i	−0.931096	−	0.364775i	$-0.881146\pi$
$431$	−22.4367	+	12.9539i	−1.08074	+	0.623965i	−0.149643	+	0.988740i	$0.547813\pi$
$432$	6.78568	+	4.46748i	0.326476	+	0.214942i
$433$	1.04183	−	1.80451i	0.0500674	−	0.0867192i	−0.839906	−	0.542733i	$-0.817390\pi$
$433$	1.04183	−	1.80451i	0.0500674	−	0.0867192i	0.889973	+	0.456013i	$0.150723\pi$
$434$	−3.42592	+	1.91155i	−0.164449	+	0.0917573i
$435$	4.90798	−	8.50088i	0.235320	−	0.407586i
$436$	−8.39137	−	15.5713i	−0.401874	−	0.745732i
$437$	4.18957			0.200414
$438$	0.292559	−	19.9559i	0.0139790	−	0.953530i
$439$	−10.2239	−	17.7083i	−0.487961	−	0.845173i	0.511943	−	0.859019i	$-0.328926\pi$
$439$	−10.2239	−	17.7083i	−0.487961	−	0.845173i	−0.999904	+	0.0138464i	$0.995592\pi$
$440$	3.72987	−	1.94001i	0.177815	−	0.0924866i
$441$	−14.4417			−0.687701
$442$	19.4147	−	28.0350i	0.923465	−	1.33349i
$443$			24.7167i			1.17433i	0.809468	+	0.587163i	$0.199755\pi$
$443$			24.7167i			1.17433i	−0.809468	+	0.587163i	$0.800245\pi$
$444$	0.674847	−	23.0112i	0.0320268	−	1.09206i
$445$	−0.886629	+	0.511896i	−0.0420303	+	0.0242662i
$446$	−24.2784	−	0.355929i	−1.14962	−	0.0168537i
$447$		−	30.0694i		−	1.42223i
$448$	−2.31803	−	1.62549i	−0.109517	−	0.0767970i
$449$	10.9531	+	6.32377i	0.516909	+	0.298437i	0.735669	−	0.677341i	$-0.236868\pi$
$449$	10.9531	+	6.32377i	0.516909	+	0.298437i	−0.218760	+	0.975779i	$0.570201\pi$
$450$	−11.9004	+	6.64001i	−0.560988	+	0.313013i
$451$	16.2661	+	9.39126i	0.765943	+	0.442217i
$452$	3.82581	+	0.112199i	0.179951	+	0.00527740i
$453$	−5.90418	−	10.2263i	−0.277403	−	0.480475i
$454$	−5.70443	+	3.18288i	−0.267722	+	0.149380i
$455$	0.818043	+	0.0552435i	0.0383505	+	0.00258986i
$456$	−19.2762	−	0.848270i	−0.902691	−	0.0397239i
$457$	−29.8239	+	17.2188i	−1.39510	+	0.805463i	−0.993874	−	0.110515i	$-0.964750\pi$
$457$	−29.8239	+	17.2188i	−1.39510	+	0.805463i	−0.401228	+	0.915978i	$0.631417\pi$
$458$	27.8157	+	16.6078i	1.29974	+	0.776031i
$459$	−11.7636	−	6.79169i	−0.549076	−	0.317009i
$460$	−0.936131	+	1.51692i	−0.0436473	+	0.0707267i
$461$	−6.67318	+	11.5583i	−0.310801	+	0.538323i	−0.978536	−	0.206076i	$-0.933931\pi$
$461$	−6.67318	+	11.5583i	−0.310801	+	0.538323i	0.667735	+	0.744399i	$0.267264\pi$
$462$	−0.0383288	+	2.61446i	−0.00178322	+	0.121636i
$463$			4.86497i			0.226094i	0.993590	+	0.113047i	$0.0360611\pi$
$463$			4.86497i			0.226094i	−0.993590	+	0.113047i	$0.963939\pi$
$464$	1.58556	−	27.0094i	0.0736079	−	1.25388i
$465$	−5.68780	−	9.85155i	−0.263765	−	0.456855i
$466$	29.8845	+	17.8430i	1.38437	+	0.826559i
$467$		−	34.9985i		−	1.61954i	−0.586749	−	0.809769i	$-0.699592\pi$
$467$		−	34.9985i		−	1.61954i	0.586749	−	0.809769i	$-0.300408\pi$
$468$	13.7891	−	6.27149i	0.637400	−	0.289900i
$469$			1.58887i			0.0733671i
$470$	5.87337	−	9.83708i	0.270918	−	0.453751i
$471$	15.5058	+	26.8569i	0.714471	+	1.23750i
$472$	11.4550	+	7.30320i	0.527260	+	0.336157i
$473$		−	0.0753146i		−	0.00346297i
$474$	−24.5519	−	0.359938i	−1.12770	−	0.0165325i
$475$	−6.92774	+	11.9992i	−0.317866	+	0.550561i
$476$	4.02824	+	2.48594i	0.184634	+	0.113943i
$477$	−6.19270	−	3.57535i	−0.283544	−	0.163704i
$478$	7.32239	−	12.2640i	0.334918	−	0.560942i
$479$	−9.70423	+	5.60274i	−0.443398	+	0.255996i	−0.705038	−	0.709170i	$-0.749070\pi$
$479$	−9.70423	+	5.60274i	−0.443398	+	0.255996i	0.261640	+	0.965166i	$0.415737\pi$
$480$	4.61427	−	6.78980i	0.210611	−	0.309911i
$481$	15.2589	+	10.2394i	0.695747	+	0.466878i
$482$	−12.4596	−	22.3303i	−0.567519	−	1.01712i
$483$	−0.554303	−	0.960080i	−0.0252216	−	0.0436852i
$484$	11.2928	+	0.331183i	0.513309	+	0.0150538i
$485$	−3.40229	−	1.96431i	−0.154490	−	0.0891949i
$486$	−12.7477	−	22.8467i	−0.578248	−	1.03635i
$487$	15.3246	+	8.84766i	0.694424	+	0.400926i	0.805267	−	0.592912i	$-0.202022\pi$
$487$	15.3246	+	8.84766i	0.694424	+	0.400926i	−0.110843	+	0.993838i	$0.535355\pi$
$488$	−14.4600	+	22.6804i	−0.654572	+	1.02669i
$489$		−	38.0762i		−	1.72186i
$490$	0.0915768	−	6.24659i	0.00413702	−	0.282192i
$491$	−2.20922	+	1.27549i	−0.0997007	+	0.0575622i	−0.549021	−	0.835808i	$-0.684999\pi$
$491$	−2.20922	+	1.27549i	−0.0997007	+	0.0575622i	0.449321	+	0.893371i	$0.351666\pi$
$492$	36.6596	+	1.07511i	1.65274	+	0.0484697i
$493$			45.2360i			2.03733i
$494$	8.76861	−	12.6619i	0.394518	−	0.569687i
$495$	−3.12251			−0.140346
$496$	−26.1885	−	17.2417i	−1.17590	−	0.774175i
$497$	−1.09348	−	1.89396i	−0.0490493	−	0.0849559i
$498$	53.4345	+	0.783365i	2.39446	+	0.0351034i
$499$	20.8838			0.934889			0.467444	−	0.884022i	$-0.345175\pi$
$499$	20.8838			0.934889			0.467444	+	0.884022i	$0.345175\pi$
$500$	−5.84491	−	10.8460i	−0.261393	−	0.485049i
$501$	−9.10294	+	15.7668i	−0.406689	+	0.704407i
$502$	10.6095	+	19.0146i	0.473526	+	0.848663i
$503$	−4.58269	+	7.93745i	−0.204332	+	0.353914i	−0.949920	−	0.312494i	$-0.898836\pi$
$503$	−4.58269	+	7.93745i	−0.204332	+	0.353914i	0.745588	+	0.666408i	$0.232169\pi$
$504$	0.970286	+	1.86547i	0.0432200	+	0.0830947i
$505$	−4.61030	+	2.66176i	−0.205155	+	0.118447i
$506$	3.96252	−	2.21096i	0.176155	−	0.0982890i
$507$	−3.94745	+	29.0935i	−0.175312	+	1.29209i
$508$	−14.3346	+	23.2280i	−0.635995	+	1.03058i
$509$	−7.84874	−	13.5944i	−0.347889	−	0.602562i	0.637985	−	0.770049i	$-0.279768\pi$
$509$	−7.84874	−	13.5944i	−0.347889	−	0.602562i	−0.985874	+	0.167487i	$0.946435\pi$
$510$	−7.03628	+	11.7848i	−0.311572	+	0.521840i
$511$	−1.10569	+	1.91511i	−0.0489129	+	0.0847197i
$512$	2.97665	−	22.4308i	0.131551	−	0.991309i
$513$	−5.31297	−	3.06745i	−0.234574	−	0.135431i
$514$	−0.0236257	+	1.61155i	−0.00104209	+	0.0710823i
$515$	7.43896			0.327800
$516$	−0.0697658	−	0.129460i	−0.00307127	−	0.00569915i
$517$	−25.2579	+	14.5826i	−1.11084	+	0.641344i
$518$	−1.30763	+	2.19010i	−0.0574540	+	0.0962275i
$519$	−37.6790			−1.65392
$520$	2.62522	+	6.00407i	0.115123	+	0.263296i
$521$	16.1321			0.706761			0.353381	−	0.935480i	$-0.385032\pi$
$521$	16.1321			0.706761			0.353381	+	0.935480i	$0.385032\pi$
$522$	−10.3013	+	17.2532i	−0.450875	+	0.755153i
$523$	−2.95531	+	1.70625i	−0.129226	+	0.0746089i	−0.563220	−	0.826307i	$-0.690438\pi$
$523$	−2.95531	+	1.70625i	−0.129226	+	0.0746089i	0.433993	+	0.900916i	$0.357104\pi$
$524$	−10.2298	+	5.51284i	−0.446892	+	0.240830i
$525$	3.66631			0.160011
$526$	−0.194598	+	13.2738i	−0.00848489	+	0.578767i
$527$	45.4000	+	26.2117i	1.97766	+	1.14180i
$528$	−18.6792	+	9.37030i	−0.812907	+	0.407790i
$529$	10.5381	−	18.2525i	0.458177	−	0.793586i
$530$	1.58575	−	2.65590i	0.0688804	−	0.115365i
$531$	−5.04485	−	8.73794i	−0.218928	−	0.379194i
$532$	1.81934	+	1.12277i	0.0788786	+	0.0486781i
$533$	−16.3126	+	24.3093i	−0.706578	+	1.05295i
$534$	4.44394	−	2.47957i	0.192308	−	0.107302i
$535$	5.72879	−	3.30752i	0.247677	−	0.142997i
$536$	−11.2659	+	5.85971i	−0.486611	+	0.253101i
$537$	−13.3130	+	23.0587i	−0.574497	+	0.995058i
$538$	13.1378	+	23.5458i	0.566409	+	1.01513i
$539$	−7.95155	+	13.7725i	−0.342498	+	0.593223i
$540$	2.29778	−	1.23827i	0.0988806	−	0.0532866i
$541$	−9.17340			−0.394395			−0.197198	−	0.980364i	$-0.563184\pi$
$541$	−9.17340			−0.394395			−0.197198	+	0.980364i	$0.563184\pi$
$542$	25.0727	+	0.367572i	1.07696	+	0.0157886i
$543$	6.38333	+	11.0563i	0.273935	+	0.474469i
$544$	−2.77045	+	37.7303i	−0.118782	+	1.61767i
$545$	−5.68300			−0.243433
$546$	−4.06173	−	0.334171i	−0.173826	−	0.0143012i
$547$		−	21.0672i		−	0.900767i	−0.892835	−	0.450384i	$-0.851287\pi$
$547$		−	21.0672i		−	0.900767i	0.892835	−	0.450384i	$-0.148713\pi$
$548$	−0.346140	+	11.8028i	−0.0147864	+	0.504191i
$549$	17.3007	−	9.98855i	0.738375	−	0.426301i
$550$	−0.219976	+	15.0049i	−0.00937979	+	0.639809i
$551$			20.4307i			0.870378i
$552$	4.76319	−	7.47103i	0.202735	−	0.317988i
$553$	2.35618	+	1.36034i	0.100195	+	0.0578475i
$554$	−17.8298	−	31.9549i	−0.757514	−	1.35763i
$555$	−6.40537	−	3.69814i	−0.271893	−	0.156977i
$556$	0.324069	−	11.0502i	0.0137436	−	0.468635i
$557$	9.56798	+	16.5722i	0.405408	+	0.702188i	0.994369	−	0.105974i	$-0.0337960\pi$
$557$	9.56798	+	16.5722i	0.405408	+	0.702188i	−0.588961	+	0.808162i	$0.700463\pi$
$558$	11.3468	+	20.3359i	0.480347	+	0.860887i
$559$	0.117122	+	0.00790940i	0.00495373	+	0.000334532i
$560$	−0.813040	+	0.407856i	−0.0343572	+	0.0172351i
$561$	30.2589	−	17.4700i	1.27753	−	0.737582i
$562$	0.533637	−	0.893769i	0.0225101	−	0.0377014i
$563$	−5.53304	−	3.19450i	−0.233190	−	0.134632i	0.378853	−	0.925457i	$-0.376319\pi$
$563$	−5.53304	−	3.19450i	−0.233190	−	0.134632i	−0.612043	+	0.790825i	$0.709652\pi$
$564$	−29.9080	+	48.4634i	−1.25935	+	2.04068i
$565$	0.614848	−	1.06495i	0.0258668	−	0.0448027i
$566$	34.4219	+	0.504635i	1.44686	+	0.0212114i
$567$			3.85363i			0.161837i
$568$	9.39641	−	14.7382i	0.394265	−	0.618401i
$569$	0.966936	+	1.67478i	0.0405361	+	0.0702106i	0.885582	−	0.464484i	$-0.153760\pi$
$569$	0.966936	+	1.67478i	0.0405361	+	0.0702106i	−0.845046	+	0.534694i	$0.820427\pi$
$570$	−3.17792	+	5.32257i	−0.133108	+	0.222938i
$571$		−	36.9706i		−	1.54717i	−0.633693	−	0.773585i	$-0.718462\pi$
$571$		−	36.9706i		−	1.54717i	0.633693	−	0.773585i	$-0.281538\pi$
$572$	1.61134	−	16.6031i	0.0673736	−	0.694213i
$573$		−	25.3276i		−	1.05808i
$574$	−3.48909	−	2.08321i	−0.145632	−	0.0869515i
$575$	−3.18124	−	5.51007i	−0.132667	−	0.229786i
$576$	−9.64872	+	13.7596i	−0.402030	+	0.573317i
$577$		−	23.0494i		−	0.959558i	−0.877389	−	0.479779i	$-0.840717\pi$
$577$		−	23.0494i		−	0.959558i	0.877389	−	0.479779i	$-0.159283\pi$
$578$	0.574788	−	39.2072i	0.0239080	−	1.63080i
$579$	−0.876004	+	1.51728i	−0.0364055	+	0.0630561i
$580$	−7.39735	−	4.56510i	−0.307158	−	0.189555i
$581$	−5.12796	−	2.96063i	−0.212744	−	0.122828i
$582$	16.7666	+	10.0107i	0.694998	+	0.414959i
$583$	−6.81934	+	3.93715i	−0.282428	+	0.163060i
$584$	−17.6569	−	0.777010i	−0.730647	−	0.0321529i
$585$	0.327920	−	4.85582i	0.0135578	−	0.200763i
$586$	7.59367	−	4.23702i	0.313691	−	0.175030i
$587$	14.3010	+	24.7701i	0.590267	+	1.02237i	0.994196	+	0.107583i	$0.0343110\pi$
$587$	14.3010	+	24.7701i	0.590267	+	1.02237i	−0.403929	+	0.914790i	$0.632356\pi$
$588$	−0.910292	+	31.0395i	−0.0375398	+	1.28005i
$589$	20.5048	+	11.8384i	0.844885	+	0.487795i
$590$	3.81148	−	2.12668i	0.156916	−	0.0875541i
$591$	−5.97746	−	3.45109i	−0.245880	−	0.141959i
$592$	−20.3514	−	1.19471i	−0.836438	−	0.0491024i
$593$		−	32.2516i		−	1.32441i	−0.749321	−	0.662207i	$-0.769620\pi$
$593$		−	32.2516i		−	1.32441i	0.749321	−	0.662207i	$-0.230380\pi$
$594$	−6.64381	−	0.0974002i	−0.272599	−	0.00399638i
$595$	1.31706	−	0.760406i	0.0539943	−	0.0311736i
$596$	−26.6167	−	0.780584i	−1.09026	−	0.0319739i
$597$		−	59.2886i		−	2.42652i
$598$	3.02213	+	6.39431i	0.123584	+	0.261483i
$599$	22.6404			0.925060			0.462530	−	0.886604i	$-0.346942\pi$
$599$	22.6404			0.925060			0.462530	+	0.886604i	$0.346942\pi$
$600$	13.5212	+	25.9959i	0.552002	+	1.06128i
$601$	−1.77121	−	3.06782i	−0.0722490	−	0.125139i	0.827638	−	0.561263i	$-0.189684\pi$
$601$	−1.77121	−	3.06782i	−0.0722490	−	0.125139i	−0.899887	+	0.436124i	$0.856351\pi$
$602$	−0.000238859		0.0162929i	−9.73515e−6		0.000664049i
$603$	9.43136			0.384075
$604$	−9.20537	+	4.96076i	−0.374561	+	0.201851i
$605$	1.81487	−	3.14345i	0.0737850	−	0.127799i
$606$	23.1076	−	12.8933i	0.938681	−	0.523754i
$607$	9.01370	−	15.6122i	0.365855	−	0.633679i	−0.623058	−	0.782176i	$-0.714110\pi$
$607$	9.01370	−	15.6122i	0.365855	−	0.633679i	0.988913	+	0.148496i	$0.0474434\pi$
$608$	−1.25127	+	17.0408i	−0.0507456	+	0.691095i
$609$	4.68189	−	2.70309i	0.189720	−	0.109535i
$610$	4.21072	+	7.54654i	0.170487	+	0.305551i
$611$	−20.0250	−	40.8100i	−0.810123	−	1.65100i
$612$	14.7563	−	23.9112i	0.596486	−	0.966555i
$613$	20.5202	+	35.5421i	0.828804	+	1.43553i	0.898977	+	0.437996i	$0.144312\pi$
$613$	20.5202	+	35.5421i	0.828804	+	1.43553i	−0.0701726	+	0.997535i	$0.522355\pi$
$614$	−14.2700	−	8.52008i	−0.575888	−	0.343842i
$615$	5.89157	−	10.2045i	0.237571	−	0.411485i
$616$	2.31326	+	0.101798i	0.0932039	+	0.00410154i
$617$	−4.18519	−	2.41632i	−0.168490	−	0.0972775i	0.413384	−	0.910557i	$-0.364347\pi$
$617$	−4.18519	−	2.41632i	−0.168490	−	0.0972775i	−0.581873	+	0.813279i	$0.697680\pi$
$618$	−36.9724	−	0.542026i	−1.48725	−	0.0218035i
$619$	−22.8273			−0.917507			−0.458754	−	0.888564i	$-0.651704\pi$
$619$	−22.8273			−0.917507			−0.458754	+	0.888564i	$0.651704\pi$
$620$	−8.86800	+	4.77895i	−0.356147	+	0.191927i
$621$	2.43974	−	1.40858i	0.0979032	−	0.0565244i
$622$	−29.2609	−	17.4706i	−1.17325	−	0.700508i
$623$	−0.563857			−0.0225905
$624$	−12.6101	−	30.0321i	−0.504809	−	1.20225i
$625$	18.9771			0.759085
$626$	−5.66233	−	3.38078i	−0.226312	−	0.135123i
$627$	13.6663	−	7.89026i	0.545781	−	0.315107i
$628$	24.1756	−	13.0282i	0.964710	−	0.519881i
$629$	34.0851			1.35906
$630$	0.675496	+	0.00990296i	0.0269124	+	0.000394543i
$631$	−36.6267	−	21.1464i	−1.45808	−	0.841825i	−0.459167	−	0.888350i	$-0.651852\pi$
$631$	−36.6267	−	21.1464i	−1.45808	−	0.841825i	−0.998917	+	0.0465243i	$0.985186\pi$
$632$	−0.955960	+	21.7234i	−0.0380260	+	0.864109i
$633$	14.2381	−	24.6612i	0.565915	−	0.980194i
$634$	−24.5868	−	14.6799i	−0.976468	−	0.583014i
$635$	4.38472	+	7.59455i	0.174002	+	0.301381i
$636$	−8.07483	+	13.0846i	−0.320188	+	0.518837i
$637$	−20.5826	−	13.8118i	−0.815512	−	0.547245i
$638$	10.7819	+	19.3235i	0.426858	+	0.765023i
$639$	−11.2424	+	6.49079i	−0.444741	+	0.256772i
$640$	−5.89037	−	4.26069i	−0.232837	−	0.168419i
$641$	19.4086	−	33.6167i	0.766593	−	1.32778i	−0.172807	−	0.984956i	$-0.555284\pi$
$641$	19.4086	−	33.6167i	0.766593	−	1.32778i	0.939400	−	0.342823i	$-0.111383\pi$
$642$	−28.7137	+	16.0213i	−1.13324	+	0.632310i
$643$	6.67441	−	11.5604i	0.263213	−	0.455898i	−0.703881	−	0.710318i	$-0.748551\pi$
$643$	6.67441	−	11.5604i	0.263213	−	0.455898i	0.967094	+	0.254420i	$0.0818844\pi$
$644$	−0.864228	+	0.465731i	−0.0340554	+	0.0183524i
$645$	−0.0472484			−0.00186040
$646$	0.418771	−	28.5650i	0.0164763	−	1.12387i
$647$	−6.64954	−	11.5173i	−0.261421	−	0.452794i	0.705199	−	0.709009i	$-0.250858\pi$
$647$	−6.64954	−	11.5173i	−0.261421	−	0.452794i	−0.966620	+	0.256216i	$0.917524\pi$
$648$	−27.3242	+	14.2121i	−1.07339	+	0.558304i
$649$	−11.1107			−0.436133
$650$	−23.3110	−	1.91787i	−0.914333	−	0.0752249i
$651$		−	6.26515i		−	0.245551i
$652$	−33.7040	−	0.988434i	−1.31995	−	0.0387101i
$653$	2.37825	−	1.37308i	0.0930682	−	0.0537329i	−0.452744	−	0.891641i	$-0.649555\pi$
$653$	2.37825	−	1.37308i	0.0930682	−	0.0537329i	0.545812	+	0.837908i	$0.316221\pi$
$654$	28.2451	+	0.414081i	1.10447	+	0.0161918i
$655$			3.73353i			0.145881i
$656$	1.90332	−	32.4222i	0.0743122	−	1.26587i
$657$	11.3679	+	6.56327i	0.443505	+	0.256058i
$658$	5.51031	−	3.07457i	0.214814	−	0.119859i
$659$	−42.8439	−	24.7359i	−1.66896	−	0.963576i	−0.968199	−	0.250181i	$-0.919510\pi$
$659$	−42.8439	−	24.7359i	−1.66896	−	0.963576i	−0.700763	−	0.713394i	$-0.747157\pi$
$660$	−0.196818	+	6.71119i	−0.00766114	+	0.261233i
$661$	−18.2518	−	31.6131i	−0.709914	−	1.22961i	−0.964889	−	0.262660i	$-0.915400\pi$
$661$	−18.2518	−	31.6131i	−0.709914	−	1.22961i	0.254974	−	0.966948i	$-0.417933\pi$
$662$	−3.44263	+	1.92088i	−0.133802	+	0.0746570i
$663$	23.9899	+	48.8903i	0.931689	+	1.89874i
$664$	2.08054	−	47.2785i	0.0807407	−	1.83476i
$665$	0.594847	−	0.343435i	0.0230672	−	0.0133178i
$666$	13.0002	+	7.76196i	0.503748	+	0.300770i
$667$	−8.12492	−	4.69093i	−0.314598	−	0.181633i
$668$	13.7200	+	8.46699i	0.530844	+	0.327598i
$669$	19.3882	−	33.5813i	0.749590	−	1.29833i
$670$	−0.0598055	+	4.07942i	−0.00231049	+	0.157602i
$671$		−	21.9986i		−	0.849247i
$672$	4.07061	−	1.96785i	0.157027	−	0.0759113i
$673$	12.8769	+	22.3034i	0.496368	+	0.859734i	0.999991	−	0.00418893i	$-0.00133338\pi$
$673$	12.8769	+	22.3034i	0.496368	+	0.859734i	−0.503623	+	0.863923i	$0.668000\pi$
$674$	27.5033	+	16.4213i	1.05939	+	0.632523i
$675$			9.31674i			0.358601i
$676$	25.6504	+	4.24943i	0.986553	+	0.163440i
$677$			26.6436i			1.02400i	0.858987	+	0.511998i	$0.171094\pi$
$677$			26.6436i			1.02400i	−0.858987	+	0.511998i	$0.828906\pi$
$678$	−3.13345	+	5.24810i	−0.120339	+	0.201552i
$679$	−1.08185	−	1.87383i	−0.0415177	−	0.0719108i
$680$	10.2490	+	6.53427i	0.393029	+	0.250578i
$681$		−	10.4320i		−	0.399755i
$682$	25.6410	+	0.375905i	0.981845	+	0.0143941i
$683$	−13.4138	+	23.2334i	−0.513266	+	0.889003i	0.486615	+	0.873616i	$0.338231\pi$
$683$	−13.4138	+	23.2334i	−0.513266	+	0.889003i	−0.999882	+	0.0153869i	$0.995102\pi$
$684$	6.66462	−	10.7994i	0.254828	−	0.412927i
$685$	3.28542	+	1.89684i	0.125529	+	0.0724744i
$686$	3.55983	−	5.96222i	0.135915	−	0.227639i
$687$	−44.8052	+	25.8683i	−1.70942	+	0.986936i
$688$	−0.116406	+	0.0583942i	−0.00443792	+	0.00222626i
$689$	−5.40652	−	11.0183i	−0.205972	−	0.419762i
$690$	−1.38703	−	2.48587i	−0.0528035	−	0.0946355i
$691$	6.27307	+	10.8653i	0.238639	+	0.413335i	0.960324	−	0.278887i	$-0.0899655\pi$
$691$	6.27307	+	10.8653i	0.238639	+	0.413335i	−0.721685	+	0.692221i	$0.756632\pi$
$692$	−0.978123	+	33.3525i	−0.0371827	+	1.26787i
$693$	−1.48933	−	0.859867i	−0.0565751	−	0.0326636i
$694$	1.71522	+	3.07405i	0.0651088	+	0.116689i
$695$	−3.07593	−	1.77589i	−0.116677	−	0.0673633i
$696$	36.4330	+	23.2280i	1.38099	+	0.880455i
$697$			54.3016i			2.05682i
$698$	−0.0209199	+	1.42698i	−0.000791832	+	0.0540120i
$699$	−48.1375	+	27.7922i	−1.82073	+	1.05120i
$700$	0.0951751	−	3.24532i	0.00359728	−	0.122662i
$701$		−	4.96259i		−	0.187434i	−0.995599	−	0.0937171i	$-0.970125\pi$
$701$		−	4.96259i		−	0.187434i	0.995599	−	0.0937171i	$-0.0298749\pi$
$702$	0.849189	−	10.3216i	0.0320506	−	0.389563i
$703$	15.3944			0.580612
$704$	7.80945	+	16.7776i	0.294330	+	0.632329i
$705$	9.14836	+	15.8454i	0.344547	+	0.596773i
$706$	4.34510	+	0.0637004i	0.163530	+	0.00239740i
$707$	−2.93195			−0.110267
$708$	−19.0984	+	10.2921i	−0.717762	+	0.386801i
$709$	−6.37556	+	11.0428i	−0.239439	+	0.414721i	−0.960554	−	0.278095i	$-0.910297\pi$
$709$	−6.37556	+	11.0428i	−0.239439	+	0.414721i	0.721114	+	0.692816i	$0.243630\pi$
$710$	−2.73622	−	4.90391i	−0.102689	−	0.184041i
$711$	8.07483	−	13.9860i	0.302830	−	0.524517i
$712$	−2.07949	−	3.99803i	−0.0779322	−	0.149832i
$713$	−9.41587	+	5.43625i	−0.352627	+	0.203589i
$714$	−6.60134	+	3.68333i	−0.247049	+	0.137845i
$715$	−4.45025	−	2.98632i	−0.166430	−	0.111682i
$716$	20.0654	+	12.3829i	0.749880	+	0.462771i
$717$	11.4053	+	19.7546i	0.425941	+	0.737751i
$718$	−2.40548	+	4.02885i	−0.0897718	+	0.150355i
$719$	−16.5699	+	28.7000i	−0.617955	+	1.07033i	0.371904	+	0.928271i	$0.378705\pi$
$719$	−16.5699	+	28.7000i	−0.617955	+	1.07033i	−0.989858	+	0.142058i	$0.954628\pi$
$720$	2.42099	+	4.82612i	0.0902251	+	0.179859i
$721$	3.54814	+	2.04852i	0.132140	+	0.0762908i
$722$	−0.204744	+	13.9659i	−0.00761978	+	0.519756i
$723$	40.8366			1.51873
$724$	9.95243	−	5.36335i	0.369879	−	0.199327i
$725$	26.8702	−	15.5135i	0.997934	−	0.576158i
$726$	−9.24914	+	15.4910i	−0.343268	+	0.574926i
$727$	10.2705			0.380912			0.190456	−	0.981696i	$-0.439003\pi$
$727$	10.2705			0.380912			0.190456	+	0.981696i	$0.439003\pi$
$728$	−0.401240	+	3.58667i	−0.0148709	+	0.132931i
$729$	9.11343			0.337534
$730$	−2.91095	+	4.87544i	−0.107739	+	0.180448i
$731$	0.188568	−	0.108870i	0.00697445	−	0.00402670i
$732$	−20.3779	−	37.8139i	−0.753187	−	1.39764i
$733$	−28.5069			−1.05293			−0.526463	−	0.850198i	$-0.676482\pi$
$733$	−28.5069			−1.05293			−0.526463	+	0.850198i	$0.676482\pi$
$734$	0.609807	−	41.5958i	0.0225084	−	1.53533i
$735$	8.64012	+	4.98838i	0.318696	+	0.183999i
$736$	−6.48952	−	4.41020i	−0.239207	−	0.162562i
$737$	5.19287	−	8.99431i	0.191282	−	0.331310i
$738$	−12.3657	+	20.7109i	−0.455189	+	0.762378i
$739$	5.94448	+	10.2961i	0.218671	+	0.378750i	0.954402	−	0.298524i	$-0.0964945\pi$
$739$	5.94448	+	10.2961i	0.218671	+	0.378750i	−0.735731	+	0.677274i	$0.763161\pi$
$740$	−3.43978	+	5.57387i	−0.126449	+	0.204899i
$741$	10.8350	+	22.0812i	0.398032	+	0.811172i
$742$	1.48772	−	0.830101i	0.0546160	−	0.0304740i
$743$	27.5090	−	15.8823i	1.00921	−	0.582665i	0.0982467	−	0.995162i	$-0.468677\pi$
$743$	27.5090	−	15.8823i	1.00921	−	0.582665i	0.910959	+	0.412497i	$0.135343\pi$
$744$	44.4231	−	23.1057i	1.62863	−	0.847097i
$745$	−4.27758	+	7.40898i	−0.156718	+	0.271444i
$746$	−5.41124	−	9.69813i	−0.198119	−	0.355074i
$747$	−17.5740	+	30.4391i	−0.642999	+	1.11371i
$748$	−14.6785	−	27.2379i	−0.536698	−	0.995916i
$749$	3.64326			0.133122
$750$	19.6738	+	0.288423i	0.718385	+	0.0105317i
$751$	16.0950	+	27.8773i	0.587314	+	1.01726i	0.994583	+	0.103949i	$0.0331479\pi$
$751$	16.0950	+	27.8773i	0.587314	+	1.01726i	−0.407269	+	0.913308i	$0.633519\pi$
$752$	42.1221	+	27.7319i	1.53604	+	1.01128i
$753$	−34.7730			−1.26720
$754$	−31.1823	+	14.7376i	−1.13559	+	0.536711i
$755$			3.35964i			0.122270i
$756$	1.43695	+	0.0421414i	0.0522615	+	0.00153267i
$757$	−1.98947	+	1.14862i	−0.0723086	+	0.0417474i	−0.535718	−	0.844397i	$-0.679959\pi$
$757$	−1.98947	+	1.14862i	−0.0723086	+	0.0417474i	0.463410	+	0.886144i	$0.346626\pi$
$758$	0.0882444	−	6.01928i	0.00320518	−	0.218630i
$759$			7.24647i			0.263030i
$760$	4.62891	+	2.95118i	0.167908	+	0.107051i
$761$	−23.3130	−	13.4598i	−0.845095	−	0.487916i	0.0138981	−	0.999903i	$-0.495576\pi$
$761$	−23.3130	−	13.4598i	−0.845095	−	0.487916i	−0.858993	+	0.511988i	$0.828909\pi$
$762$	−21.2391	−	38.0652i	−0.769412	−	1.37896i
$763$	−2.71060	−	1.56497i	−0.0981304	−	0.0566556i
$764$	−22.4193	−	0.657489i	−0.811103	−	0.0237871i
$765$	−4.51369	−	7.81795i	−0.163193	−	0.282659i
$766$	15.0857	+	27.0369i	0.545070	+	0.976885i
$767$	1.16682	−	17.2783i	0.0421316	−	0.623882i
$768$	28.9653	+	21.6053i	1.04520	+	0.779613i
$769$	−22.9461	+	13.2479i	−0.827457	+	0.477733i	−0.852981	−	0.521942i	$-0.825208\pi$
$769$	−22.9461	+	13.2479i	−0.827457	+	0.477733i	0.0255242	+	0.999674i	$0.491875\pi$
$770$	0.381369	−	0.638740i	0.0137436	−	0.0230186i
$771$	−2.22905	−	1.28694i	−0.0802772	−	0.0463481i
$772$	1.32032	+	0.814804i	0.0475193	+	0.0293254i
$773$	−23.1594	+	40.1133i	−0.832986	+	1.44277i	0.0626740	+	0.998034i	$0.480037\pi$
$773$	−23.1594	+	40.1133i	−0.832986	+	1.44277i	−0.895660	+	0.444740i	$0.853296\pi$
$774$	0.0967130	+	0.00141784i	0.00347628	+	5.09632e-5i
$775$		−	35.9568i		−	1.29161i
$776$	9.29651	−	14.5815i	0.333725	−	0.523446i
$777$	−2.03677	−	3.52778i	−0.0730686	−	0.126558i
$778$	16.1557	−	27.0585i	0.579209	−	0.970095i
$779$			24.5252i			0.878705i
$780$	−10.4159	−	1.01087i	−0.372950	−	0.0361949i
$781$			14.2952i			0.511523i
$782$	11.2636	+	6.72510i	0.402786	+	0.240489i
$783$	6.86904	+	11.8975i	0.245479	+	0.425183i
$784$	27.4518	+	1.61154i	0.980420	+	0.0575548i
$785$		−	8.82325i		−	0.314915i
$786$	0.272037	−	18.5560i	0.00970323	−	0.661872i
$787$	25.1049	−	43.4830i	0.894893	−	1.55000i	0.0609564	−	0.998140i	$-0.480585\pi$
$787$	25.1049	−	43.4830i	0.894893	−	1.55000i	0.833937	−	0.551860i	$-0.186082\pi$
$788$	−3.20999	+	5.20151i	−0.114351	+	0.185296i
$789$	−18.3600	−	10.6002i	−0.653634	−	0.377376i
$790$	5.99828	+	3.58136i	0.213409	+	0.127419i
$791$	0.586524	−	0.338630i	0.0208544	−	0.0120403i
$792$	0.604260	−	13.7313i	0.0214714	−	0.487920i
$793$	34.2101	+	2.31025i	1.21484	+	0.0820396i
$794$	28.0492	−	15.6505i	0.995428	−	0.555416i
$795$	2.46996	+	4.27809i	0.0876004	+	0.151728i
$796$	−52.4807	−	1.53910i	−1.86013	−	0.0545518i
$797$	32.7238	+	18.8931i	1.15914	+	0.669228i	0.951097	−	0.308892i	$-0.0999581\pi$
$797$	32.7238	+	18.8931i	1.15914	+	0.669228i	0.208041	+	0.978120i	$0.433291\pi$
$798$	−2.98148	+	1.66357i	−0.105543	+	0.0588896i
$799$	−73.0223	−	42.1594i	−2.58334	−	1.49149i
$800$	23.3619	−	11.2938i	0.825969	−	0.399297i
$801$			3.34700i			0.118260i
$802$	−31.8759	−	0.467310i	−1.12558	−	0.0165013i
$803$	12.5183	−	7.22742i	0.441760	−	0.255050i
$804$	0.594479	−	20.2708i	0.0209656	−	0.714895i
$805$			0.315413i			0.0111169i
$806$	−3.27734	+	39.8349i	−0.115439	+	1.40313i
$807$	−43.0594			−1.51576
$808$	−10.8129	−	20.7889i	−0.380398	−	0.731353i
$809$	8.93101	+	15.4690i	0.313998	+	0.543860i	0.979224	−	0.202782i	$-0.0649983\pi$
$809$	8.93101	+	15.4690i	0.313998	+	0.543860i	−0.665226	+	0.746642i	$0.731665\pi$
$810$	−0.145052	+	9.89420i	−0.00509660	+	0.347647i
$811$	29.2622			1.02754			0.513768	−	0.857929i	$-0.328249\pi$
$811$	29.2622			1.02754			0.513768	+	0.857929i	$0.328249\pi$
$812$	−2.27117	−	4.21446i	−0.0797024	−	0.147899i
$813$	−20.0224	+	34.6798i	−0.702217	+	1.21628i
$814$	14.5601	−	8.12408i	0.510332	−	0.284749i
$815$	−5.41659	+	9.38181i	−0.189735	+	0.328631i
$816$	−50.4622	−	33.2227i	−1.76653	−	1.16303i
$817$	0.0851663	−	0.0491708i	0.00297959	−	0.00172027i
$818$	7.98200	+	14.3055i	0.279084	+	0.500180i
$819$	1.49359	−	2.22576i	0.0521902	−	0.0777745i
$820$	−8.87983	−	5.47997i	−0.310097	−	0.191369i
$821$	−14.1150	−	24.4479i	−0.492618	−	0.853239i	0.507346	−	0.861742i	$-0.330627\pi$
$821$	−14.1150	−	24.4479i	−0.492618	−	0.853239i	−0.999964	+	0.00850342i	$0.997293\pi$
$822$	−16.1906	−	9.66685i	−0.564713	−	0.337170i
$823$	−16.9117	+	29.2919i	−0.589505	+	1.02105i	0.404792	+	0.914409i	$0.367344\pi$
$823$	−16.9117	+	29.2919i	−0.589505	+	1.02105i	−0.994297	+	0.106644i	$0.965989\pi$
$824$	−1.43957	+	32.7130i	−0.0501498	+	1.13961i
$825$	−20.7543	−	11.9825i	−0.722573	−	0.417178i
$826$	2.40359	+	0.0352373i	0.0836316	+	0.00122606i
$827$	55.5280			1.93090			0.965449	−	0.260591i	$-0.0839175\pi$
$827$	55.5280			1.93090			0.965449	+	0.260591i	$0.0839175\pi$
$828$	2.76453	+	5.12997i	0.0960742	+	0.178279i
$829$	2.15990	−	1.24702i	0.0750165	−	0.0433108i	−0.462023	−	0.886868i	$-0.652876\pi$
$829$	2.15990	−	1.24702i	0.0750165	−	0.0433108i	0.537039	+	0.843557i	$0.319543\pi$
$830$	−13.0546	−	7.79444i	−0.453132	−	0.270549i
$831$	58.4376			2.02718
$832$	−26.9110	+	10.3825i	−0.932972	+	0.359950i
$833$	−45.9770			−1.59301
$834$	15.1583	+	9.05047i	0.524889	+	0.313392i
$835$	4.48586	−	2.58991i	0.155239	−	0.0896276i
$836$	−6.62949	−	12.3019i	−0.229286	−	0.425471i
$837$	15.9209			0.550306
$838$	15.1876	+	0.222654i	0.524645	+	0.00769145i
$839$	17.3429	+	10.0129i	0.598744	+	0.345685i	0.768547	−	0.639793i	$-0.220980\pi$
$839$	17.3429	+	10.0129i	0.598744	+	0.345685i	−0.169803	+	0.985478i	$0.554313\pi$
$840$	0.0638623	−	1.45122i	0.00220346	−	0.0500717i
$841$	8.37560	−	14.5070i	0.288814	−	0.500240i
$842$	46.1426	+	27.5501i	1.59018	+	0.949438i
$843$	0.831194	+	1.43967i	0.0286278	+	0.0495849i
$844$	−21.4598	−	13.2434i	−0.738678	−	0.455858i
$845$	5.11139	−	6.60698i	0.175837	−	0.227287i
$846$	−18.2504	−	32.7086i	−0.627460	−	1.12455i
$847$	1.73127	−	0.999548i	0.0594870	−	0.0343449i
$848$	11.3725	+	7.48730i	0.390534	+	0.257115i
$849$	−27.4885	+	47.6115i	−0.943403	+	1.63402i
$850$	−37.8863	+	21.1393i	−1.29949	+	0.725072i
$851$	−3.53459	+	6.12209i	−0.121164	+	0.209862i
$852$	13.2420	+	24.5723i	0.453663	+	0.841833i
$853$	−12.6665			−0.433692			−0.216846	−	0.976206i	$-0.569577\pi$
$853$	−12.6665			−0.433692			−0.216846	+	0.976206i	$0.569577\pi$
$854$	−0.0697681	+	4.75899i	−0.00238742	+	0.162849i
$855$	−2.03860	−	3.53095i	−0.0697185	−	0.120756i
$856$	13.4363	+	25.8325i	0.459242	+	0.882938i
$857$	−21.2258			−0.725059			−0.362530	−	0.931972i	$-0.618087\pi$
$857$	−21.2258			−0.725059			−0.362530	+	0.931972i	$0.618087\pi$
$858$	21.9006	+	15.1666i	0.747674	+	0.517778i
$859$			33.6456i			1.14797i	0.818865	+	0.573986i	$0.194604\pi$
$859$			33.6456i			1.14797i	−0.818865	+	0.573986i	$0.805396\pi$
$860$	−0.00122654	+	0.0418230i	−4.18246e−5	+	0.00142615i
$861$	5.62017	−	3.24481i	0.191535	−	0.110583i
$862$	−36.6351	−	0.537081i	−1.24780	−	0.0182930i
$863$		−	31.3083i		−	1.06575i	−0.846195	−	0.532874i	$-0.821112\pi$
$863$		−	31.3083i		−	1.06575i	0.846195	−	0.532874i	$-0.178888\pi$
$864$	5.00065	+	10.3441i	0.170126	+	0.351915i
$865$	9.28395	+	5.36009i	0.315664	+	0.182248i
$866$	2.57329	−	1.43581i	0.0874438	−	0.0487908i
$867$	54.2303	+	31.3099i	1.84176	+	1.06334i
$868$	−5.54576	−	0.162640i	−0.188235	−	0.00552035i
$869$	−8.89194	−	15.4013i	−0.301638	−	0.522453i
$870$	12.1225	−	6.76396i	0.410992	−	0.229320i
$871$	13.4417	+	9.02001i	0.455456	+	0.305631i
$872$	1.09976	−	24.9911i	0.0372425	−	0.846304i
$873$	−11.1228	+	6.42178i	−0.376451	+	0.217344i
$874$	5.08718	+	3.03737i	0.172076	+	0.102741i
$875$	−1.88804	−	1.09006i	−0.0638274	−	0.0368507i
$876$	14.8230	−	24.0193i	0.500821	−	0.811538i
$877$	6.94228	−	12.0244i	0.234424	−	0.406035i	−0.724681	−	0.689085i	$-0.758013\pi$
$877$	6.94228	−	12.0244i	0.234424	−	0.406035i	0.959105	+	0.283050i	$0.0913462\pi$
$878$	0.423895	−	28.9145i	0.0143058	−	0.975817i
$879$			13.8869i			0.468395i
$880$	5.93547	+	0.348437i	0.200085	+	0.0117458i
$881$	10.4302	+	18.0656i	0.351401	+	0.608645i	0.986495	−	0.163790i	$-0.0523719\pi$
$881$	10.4302	+	18.0656i	0.351401	+	0.608645i	−0.635094	+	0.772435i	$0.719039\pi$
$882$	−17.5358	−	10.4700i	−0.590462	−	0.352544i
$883$		−	22.9456i		−	0.772181i	−0.922461	−	0.386091i	$-0.873825\pi$
$883$		−	22.9456i		−	0.772181i	0.922461	−	0.386091i	$-0.126175\pi$
$884$	43.8992	−	19.9661i	1.47649	−	0.671531i
$885$			6.97025i			0.234303i
$886$	−17.9192	+	30.0122i	−0.602008	+	1.00828i
$887$	−13.4138	−	23.2335i	−0.450393	−	0.780103i	0.548017	−	0.836467i	$-0.315383\pi$
$887$	−13.4138	−	23.2335i	−0.450393	−	0.780103i	−0.998410	+	0.0563635i	$0.982049\pi$
$888$	17.5022	−	27.4520i	0.587335	−	0.921230i
$889$			4.82980i			0.161986i
$890$	−1.44770	−	0.0212238i	−0.0485272	−	0.000711422i
$891$	12.5947	−	21.8147i	0.421940	−	0.730821i
$892$	−29.2220	−	18.0337i	−0.978425	−	0.603812i
$893$	−32.9803	−	19.0412i	−1.10364	−	0.637189i
$894$	21.7998	−	36.5117i	0.729095	−	1.22113i
$895$	6.56053	−	3.78772i	0.219294	−	0.126610i
$896$	−1.63622	−	3.65428i	−0.0546622	−	0.122081i
$897$	−11.2690	−	0.761010i	−0.376261	−	0.0254094i
$898$	8.71514	+	15.6194i	0.290828	+	0.521228i
$899$	−26.5102	−	45.9171i	−0.884166	−	1.53142i
$900$	−19.2639	−	0.564950i	−0.642130	−	0.0188317i
$901$	−19.7152	−	11.3826i	−0.656809	−	0.379209i
$902$	12.9426	+	23.1960i	0.430942	+	0.772343i
$903$	−0.0225359	−	0.0130111i	−0.000749948	−	0.000432983i
$904$	4.56414	+	2.90989i	0.151801	+	0.0967815i
$905$		−	3.63229i		−	0.120741i
$906$	0.244794	−	16.6978i	0.00813273	−	0.554746i
$907$	−11.0322	+	6.36945i	−0.366318	+	0.211494i	−0.671849	−	0.740688i	$-0.734500\pi$
$907$	−11.0322	+	6.36945i	−0.366318	+	0.211494i	0.305531	+	0.952182i	$0.401166\pi$
$908$	−9.23413	−	0.270808i	−0.306445	−	0.00898708i
$909$			17.4037i			0.577245i
$910$	0.953257	+	0.660148i	0.0316001	+	0.0218837i
$911$	34.5498			1.14469			0.572343	−	0.820014i	$-0.306035\pi$
$911$	34.5498			1.14469			0.572343	+	0.820014i	$0.306035\pi$
$912$	−22.7911	−	15.0050i	−0.754689	−	0.496864i
$913$	19.3523	+	33.5192i	0.640469	+	1.10932i
$914$	−48.6970	−	0.713911i	−1.61075	−	0.0236141i
$915$	−13.8008			−0.456239
$916$	21.7348	+	40.3319i	0.718139	+	1.33260i
$917$	−1.02813	+	1.78077i	−0.0339518	+	0.0588063i
$918$	−9.36000	−	16.7752i	−0.308926	−	0.553664i
$919$	2.65896	−	4.60545i	0.0877109	−	0.151920i	−0.818832	−	0.574033i	$-0.805378\pi$
$919$	2.65896	−	4.60545i	0.0877109	−	0.151920i	0.906543	+	0.422113i	$0.138712\pi$
$920$	−2.23644	+	1.16324i	−0.0737331	+	0.0383508i
$921$	22.9858	−	13.2709i	0.757409	−	0.437290i
$922$	−16.4825	+	9.19668i	−0.542821	+	0.302876i
$923$	−22.2305	−	1.50126i	−0.731726	−	0.0494144i
$924$	−1.94198	+	3.14682i	−0.0638866	+	0.103523i
$925$	−11.6894	−	20.2466i	−0.384344	−	0.665703i
$926$	−3.52703	+	5.90728i	−0.115905	+	0.194125i
$927$	12.1598	−	21.0614i	0.399380	−	0.691747i
$928$	21.5066	−	31.6465i	0.705989	−	1.03885i
$929$	5.19280	+	2.99807i	0.170370	+	0.0983633i	0.582760	−	0.812644i	$-0.301973\pi$
$929$	5.19280	+	2.99807i	0.170370	+	0.0983633i	−0.412390	+	0.911007i	$0.635306\pi$
$930$	0.235822	−	16.0858i	0.00773292	−	0.527474i
$931$	−20.7654			−0.680558
$932$	23.3513	+	43.3316i	0.764898	+	1.41937i
$933$	47.1330	−	27.2123i	1.54307	−	0.890889i
$934$	25.3734	−	42.4969i	0.830242	−	1.39054i
$935$	−9.94089			−0.325102
$936$	21.2901	+	2.38172i	0.695888	+	0.0778489i
$937$	−18.5525			−0.606085			−0.303043	−	0.952977i	$-0.598002\pi$
$937$	−18.5525			−0.606085			−0.303043	+	0.952977i	$0.598002\pi$
$938$	−1.15190	+	1.92928i	−0.0376110	+	0.0629932i
$939$	9.12080	−	5.26590i	0.297646	−	0.171846i
$940$	14.2635	−	7.68656i	0.465223	−	0.250708i
$941$	−35.5592			−1.15920			−0.579599	−	0.814902i	$-0.696791\pi$
$941$	−35.5592			−1.15920			−0.579599	+	0.814902i	$0.696791\pi$
$942$	−0.642889	+	43.8524i	−0.0209465	+	1.42879i
$943$	−9.75321	−	5.63102i	−0.317608	−	0.183371i
$944$	8.61453	+	17.1726i	0.280379	+	0.558920i
$945$	0.230934	−	0.399989i	0.00751227	−	0.0130116i
$946$	0.0546019	−	0.0914506i	0.00177526	−	0.00297332i
$947$	3.28589	+	5.69133i	0.106777	+	0.184944i	0.914463	−	0.404670i	$-0.132614\pi$
$947$	3.28589	+	5.69133i	0.106777	+	0.184944i	−0.807686	+	0.589613i	$0.799280\pi$
$948$	−29.5511	−	18.2368i	−0.959776	−	0.592303i
$949$	9.92474	+	20.2262i	0.322171	+	0.656570i
$950$	−17.1112	+	9.54750i	−0.555161	+	0.309762i
$951$	39.6041	−	22.8655i	1.28425	−	0.741463i
$952$	3.08902	+	5.93895i	0.100116	+	0.192483i
$953$	20.4231	−	35.3738i	0.661568	−	1.14587i	−0.318635	−	0.947877i	$-0.603225\pi$
$953$	20.4231	−	35.3738i	0.661568	−	1.14587i	0.980204	−	0.197992i	$-0.0634422\pi$
$954$	−4.92739	−	8.83097i	−0.159530	−	0.285913i
$955$	−3.60302	+	6.24062i	−0.116591	+	0.201942i
$956$	17.7824	−	9.58291i	0.575123	−	0.309933i
$957$	−35.3378			−1.14231
$958$	−15.8452	−	0.232296i	−0.511936	−	0.00750514i
$959$	1.04469	+	1.80946i	0.0337348	+	0.0584304i
$960$	10.5254	−	4.89923i	0.339705	−	0.158122i
$961$	−30.4447			−0.982088
$962$	11.1047	+	23.4957i	0.358030	+	0.757531i
$963$		−	21.6260i		−	0.696889i
$964$	1.06009	−	36.1475i	0.0341434	−	1.16423i
$965$	0.431688	−	0.249235i	0.0138965	−	0.00802316i
$966$	0.0229820	−	1.56764i	0.000739434	−	0.0504379i
$967$			35.6793i			1.14737i	0.819076	+	0.573684i	$0.194486\pi$
$967$			35.6793i			1.14737i	−0.819076	+	0.573684i	$0.805514\pi$
$968$	13.4722	+	8.58924i	0.433012	+	0.276069i
$969$	39.5103	+	22.8113i	1.26925	+	0.732804i
$970$	−2.70713	−	4.85177i	−0.0869207	−	0.155781i
$971$	21.6109	+	12.4770i	0.693526	+	0.400407i	0.804932	−	0.593368i	$-0.202202\pi$
$971$	21.6109	+	12.4770i	0.693526	+	0.400407i	−0.111406	+	0.993775i	$0.535535\pi$
$972$	1.08461	−	36.9834i	0.0347888	−	1.18624i
$973$	−0.978078	−	1.69408i	−0.0313557	−	0.0543098i
$974$	12.1935	+	21.8533i	0.390703	+	0.700226i
$975$	20.8136	−	31.0167i	0.666569	−	0.993330i
$976$	−34.0009	+	17.0563i	−1.08834	+	0.545960i
$977$	−20.5257	+	11.8505i	−0.656676	+	0.379132i	−0.791009	−	0.611804i	$-0.790444\pi$
$977$	−20.5257	+	11.8505i	−0.656676	+	0.379132i	0.134333	+	0.990936i	$0.457111\pi$
$978$	27.6046	−	46.2339i	0.882698	−	1.47840i
$979$	3.19190	+	1.84284i	0.102014	+	0.0588975i
$980$	4.63988	−	7.51852i	0.148215	−	0.240170i
$981$	−9.28948	+	16.0899i	−0.296590	+	0.513710i
$982$	−3.60725	−	0.0528834i	−0.115112	−	0.00168758i
$983$			9.34592i			0.298089i	0.988831	+	0.149044i	$0.0476197\pi$
$983$			9.34592i			0.298089i	−0.988831	+	0.149044i	$0.952380\pi$
$984$	43.7344	+	27.8830i	1.39420	+	0.888879i
$985$	0.981882	+	1.70067i	0.0312854	+	0.0541879i
$986$	−32.7954	+	54.9277i	−1.04442	+	1.74926i
$987$			10.0770i			0.320754i
$988$	19.8270	−	9.01761i	0.630780	−	0.286888i
$989$			0.0451588i			0.00143597i
$990$	−3.79150	−	2.26377i	−0.120502	−	0.0719473i
$991$	−20.9332	−	36.2573i	−0.664964	−	1.15175i	−0.979295	−	0.202438i	$-0.935114\pi$
$991$	−20.9332	−	36.2573i	−0.664964	−	1.15175i	0.314332	−	0.949313i	$-0.398220\pi$
$992$	−19.2994	−	39.9220i	−0.612757	−	1.26752i
$993$		−	6.29573i		−	0.199789i
$994$	0.0453369	−	3.09250i	0.00143800	−	0.0980880i
$995$	−8.43421	+	14.6085i	−0.267382	+	0.463120i
$996$	64.3148	+	39.6904i	2.03789	+	1.25764i
$997$	−13.3093	−	7.68412i	−0.421509	−	0.243359i	0.274213	−	0.961669i	$-0.411583\pi$
$997$	−13.3093	−	7.68412i	−0.421509	−	0.243359i	−0.695723	+	0.718310i	$0.744916\pi$
$998$	25.3582	+	15.1404i	0.802698	+	0.479262i
$999$	8.96472	−	5.17579i	0.283631	−	0.163755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.s.c.101.7	yes	16
3.2	odd	2		936.2.dg.d.829.2		16
4.3	odd	2		416.2.ba.c.49.7		16
8.3	odd	2		416.2.ba.c.49.2		16
8.5	even	2	inner	104.2.s.c.101.4	yes	16
13.4	even	6	inner	104.2.s.c.69.4	✓	16
24.5	odd	2		936.2.dg.d.829.5		16
39.17	odd	6		936.2.dg.d.901.5		16
52.43	odd	6		416.2.ba.c.17.2		16
104.43	odd	6		416.2.ba.c.17.7		16
104.69	even	6	inner	104.2.s.c.69.7	yes	16
312.173	odd	6		936.2.dg.d.901.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.s.c.69.4	✓	16	13.4	even	6	inner
104.2.s.c.69.7	yes	16	104.69	even	6	inner
104.2.s.c.101.4	yes	16	8.5	even	2	inner
104.2.s.c.101.7	yes	16	1.1	even	1	trivial
416.2.ba.c.17.2		16	52.43	odd	6
416.2.ba.c.17.7		16	104.43	odd	6
416.2.ba.c.49.2		16	8.3	odd	2
416.2.ba.c.49.7		16	4.3	odd	2
936.2.dg.d.829.2		16	3.2	odd	2
936.2.dg.d.829.5		16	24.5	odd	2
936.2.dg.d.901.2		16	312.173	odd	6
936.2.dg.d.901.5		16	39.17	odd	6

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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21425 + 0.724984i) q^{2} +(-1.95589 + 1.12924i) q^{3} +(0.948796 + 1.76062i) q^{4} +0.642566 q^{5} +(-3.19362 - 0.0468193i) q^{6} +(0.306483 + 0.176948i) q^{7} +(-0.124348 + 2.82569i) q^{8} +(1.05034 - 1.81925i) q^{9} +(0.780234 + 0.465850i) q^{10} +(-1.15663 - 2.00334i) q^{11} +(-3.84390 - 2.37217i) q^{12} +(3.23687 - 1.58829i) q^{13} +(0.243862 + 0.437053i) q^{14} +(-1.25679 + 0.725608i) q^{15} +(-2.19957 + 3.34094i) q^{16} +(3.34390 - 5.79180i) q^{17} +(2.59430 - 1.44754i) q^{18} +(1.51026 - 2.61585i) q^{19} +(0.609664 + 1.13131i) q^{20} -0.799263 q^{21} +(0.0479552 - 3.27109i) q^{22} +(0.693517 + 1.20121i) q^{23} +(-2.94766 - 5.66717i) q^{24} -4.58711 q^{25} +(5.08185 + 0.418099i) q^{26} -2.03107i q^{27} +(-0.0207484 + 0.707487i) q^{28} +(-5.85776 + 3.38198i) q^{29} +(-2.05211 - 0.0300845i) q^{30} +7.83867i q^{31} +(-5.09295 + 2.46208i) q^{32} +(4.52449 + 2.61221i) q^{33} +(8.25929 - 4.60841i) q^{34} +(0.196935 + 0.113701i) q^{35} +(4.19957 + 0.123160i) q^{36} +(2.54831 + 4.41379i) q^{37} +(3.73028 - 2.08138i) q^{38} +(-4.53742 + 6.76172i) q^{39} +(-0.0799015 + 1.81569i) q^{40} +(-7.03170 + 4.05975i) q^{41} +(-0.970503 - 0.579453i) q^{42} +(0.0281959 + 0.0162789i) q^{43} +(2.42972 - 3.93715i) q^{44} +(0.674915 - 1.16899i) q^{45} +(-0.0287540 + 1.96135i) q^{46} -12.6079i q^{47} +(0.529416 - 9.01836i) q^{48} +(-3.43738 - 5.95372i) q^{49} +(-5.56989 - 3.32558i) q^{50} +15.1042i q^{51} +(5.86751 + 4.19194i) q^{52} -3.40398i q^{53} +(1.47249 - 2.46622i) q^{54} +(-0.743211 - 1.28728i) q^{55} +(-0.538110 + 0.844022i) q^{56} +6.82176i q^{57} +(-9.56466 - 0.140221i) q^{58} +(2.40152 - 4.15956i) q^{59} +(-2.46996 - 1.52428i) q^{60} +(8.23572 + 4.75490i) q^{61} +(-5.68291 + 9.51809i) q^{62} +(0.643824 - 0.371712i) q^{63} +(-7.96908 - 0.702736i) q^{64} +(2.07990 - 1.02058i) q^{65} +(3.60004 + 6.45206i) q^{66} +(2.24483 + 3.88815i) q^{67} +(13.3698 + 0.392096i) q^{68} +(-2.71289 - 1.56629i) q^{69} +(0.156697 + 0.280835i) q^{70} +(-5.35176 - 3.08984i) q^{71} +(5.01003 + 3.19417i) q^{72} +6.24869i q^{73} +(-0.105656 + 7.20692i) q^{74} +(8.97189 - 5.17993i) q^{75} +(6.03845 + 0.177089i) q^{76} -0.818652i q^{77} +(-10.4117 + 4.92085i) q^{78} +7.68780 q^{79} +(-1.41337 + 2.14677i) q^{80} +(5.44459 + 9.43030i) q^{81} +(-11.4815 - 0.168322i) q^{82} -16.7317 q^{83} +(-0.758338 - 1.40720i) q^{84} +(2.14867 - 3.72161i) q^{85} +(0.0224348 + 0.0402082i) q^{86} +(7.63810 - 13.2296i) q^{87} +(5.80465 - 3.01917i) q^{88} +(-1.37983 + 0.796643i) q^{89} +(1.66701 - 0.930138i) q^{90} +(1.27309 + 0.0859734i) q^{91} +(-1.45686 + 2.36072i) q^{92} +(-8.85170 - 15.3316i) q^{93} +(9.14050 - 15.3091i) q^{94} +(0.970443 - 1.68086i) q^{95} +(7.18101 - 10.5667i) q^{96} +(-5.29486 - 3.05699i) q^{97} +(0.142518 - 9.72133i) q^{98} -4.85944 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - q^{4} + 6 q^{6} + 18 q^{7} + 2 q^{9} - 9 q^{10} - 16 q^{12} - 24 q^{14} - 36 q^{15} - q^{16} + 8 q^{17} - 15 q^{20} + 22 q^{22} - 2 q^{23} - 12 q^{24} - 12 q^{25} + 23 q^{26} - 8 q^{30}+ \cdots - 93 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - q^4 + 6 * q^6 + 18 * q^7 + 2 * q^9 - 9 * q^10 - 16 * q^12 - 24 * q^14 - 36 * q^15 - q^16 + 8 * q^17 - 15 * q^20 + 22 * q^22 - 2 * q^23 - 12 * q^24 - 12 * q^25 + 23 * q^26 - 8 * q^30 - 27 * q^32 - 30 * q^33 + 33 * q^36 - 14 * q^39 + 26 * q^40 + 24 * q^41 + 14 * q^42 + 42 * q^46 + 6 * q^48 - 14 * q^49 + 6 * q^50 + 28 * q^52 + 6 * q^54 + 4 * q^55 - 8 * q^56 - 33 * q^58 - 4 * q^62 + 50 * q^64 + 6 * q^65 + 40 * q^66 + 5 * q^68 + 6 * q^71 + 39 * q^72 - 29 * q^74 + 24 * q^76 - 20 * q^78 + 32 * q^79 - 33 * q^80 + 12 * q^81 + 9 * q^82 - 24 * q^84 + 34 * q^87 - 8 * q^88 - 30 * q^89 - 62 * q^90 - 4 * q^92 - 24 * q^94 + 28 * q^95 - 30 * q^97 - 93 * q^98

Introduction

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