LMFDB - Embedded newform 220.2.l.c.23.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.13
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31753 - 0.513913i) q^{2} +(-0.912547 + 0.912547i) q^{3} +(1.47179 - 1.35419i) q^{4} +(1.46492 - 1.68939i) q^{5} +(-0.733342 + 1.67128i) q^{6} +(-0.0653068 - 0.0653068i) q^{7} +(1.24319 - 2.54057i) q^{8} +1.33451i q^{9} +(1.06188 - 2.97866i) q^{10} -1.00000i q^{11} +(-0.107310 + 2.57884i) q^{12} +(0.473161 + 0.473161i) q^{13} +(-0.119606 - 0.0524819i) q^{14} +(0.204839 + 2.87845i) q^{15} +(0.332318 - 3.98617i) q^{16} +(-1.01081 + 1.01081i) q^{17} +(0.685824 + 1.75827i) q^{18} +2.65097 q^{19} +(-0.131711 - 4.47020i) q^{20} +0.119191 q^{21} +(-0.513913 - 1.31753i) q^{22} +(-5.32132 + 5.32132i) q^{23} +(1.18392 + 3.45286i) q^{24} +(-0.708046 - 4.94961i) q^{25} +(0.866568 + 0.380242i) q^{26} +(-3.95545 - 3.95545i) q^{27} +(-0.184556 - 0.00767967i) q^{28} +5.94796i q^{29} +(1.74915 + 3.68718i) q^{30} +1.44287i q^{31} +(-1.61070 - 5.42270i) q^{32} +(0.912547 + 0.912547i) q^{33} +(-0.812306 + 1.85124i) q^{34} +(-0.205997 + 0.0146594i) q^{35} +(1.80719 + 1.96412i) q^{36} +(-5.27054 + 5.27054i) q^{37} +(3.49274 - 1.36237i) q^{38} -0.863563 q^{39} +(-2.47082 - 5.82194i) q^{40} -5.13952 q^{41} +(0.157038 - 0.0612538i) q^{42} +(-4.06096 + 4.06096i) q^{43} +(-1.35419 - 1.47179i) q^{44} +(2.25451 + 1.95495i) q^{45} +(-4.27633 + 9.74572i) q^{46} +(-7.89803 - 7.89803i) q^{47} +(3.33431 + 3.94083i) q^{48} -6.99147i q^{49} +(-3.47654 - 6.15741i) q^{50} -1.84482i q^{51} +(1.33714 + 0.0556408i) q^{52} +(2.60160 + 2.60160i) q^{53} +(-7.24419 - 3.17868i) q^{54} +(-1.68939 - 1.46492i) q^{55} +(-0.247105 + 0.0847274i) q^{56} +(-2.41913 + 2.41913i) q^{57} +(3.05673 + 7.83664i) q^{58} +7.70258 q^{59} +(4.19946 + 3.95907i) q^{60} +7.06915 q^{61} +(0.741508 + 1.90103i) q^{62} +(0.0871529 - 0.0871529i) q^{63} +(-4.90895 - 6.31682i) q^{64} +(1.49249 - 0.106210i) q^{65} +(1.67128 + 0.733342i) q^{66} +(5.47540 + 5.47540i) q^{67} +(-0.118865 + 2.85652i) q^{68} -9.71192i q^{69} +(-0.263875 + 0.125179i) q^{70} -1.80081i q^{71} +(3.39042 + 1.65906i) q^{72} +(5.16419 + 5.16419i) q^{73} +(-4.23552 + 9.65271i) q^{74} +(5.16288 + 3.87063i) q^{75} +(3.90166 - 3.58992i) q^{76} +(-0.0653068 + 0.0653068i) q^{77} +(-1.13777 + 0.443796i) q^{78} +14.2952 q^{79} +(-6.24736 - 6.40082i) q^{80} +3.21553 q^{81} +(-6.77149 + 2.64126i) q^{82} +(11.9160 - 11.9160i) q^{83} +(0.175424 - 0.161408i) q^{84} +(0.226896 + 3.18839i) q^{85} +(-3.26347 + 7.43743i) q^{86} +(-5.42780 - 5.42780i) q^{87} +(-2.54057 - 1.24319i) q^{88} -5.69673i q^{89} +(3.97507 + 1.41709i) q^{90} -0.0618012i q^{91} +(-0.625755 + 15.0380i) q^{92} +(-1.31668 - 1.31668i) q^{93} +(-14.4648 - 6.34702i) q^{94} +(3.88344 - 4.47850i) q^{95} +(6.41831 + 3.47862i) q^{96} +(-0.398370 + 0.398370i) q^{97} +(-3.59300 - 9.21149i) q^{98} +1.33451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.31753	−	0.513913i	0.931637	−	0.363391i
$2$	1.31753	−	0.513913i	0.931637	−	0.363391i
$3$	−0.912547	+	0.912547i	−0.526859	+	0.526859i	−0.919635	−	0.392775i	$-0.871515\pi$
$3$	−0.912547	+	0.912547i	−0.526859	+	0.526859i	0.392775	+	0.919635i	$0.371515\pi$
$4$	1.47179	−	1.35419i	0.735894	−	0.677097i
$5$	1.46492	−	1.68939i	0.655130	−	0.755516i
$5$	1.46492	−	1.68939i	0.655130	−	0.755516i
$6$	−0.733342	+	1.67128i	−0.299386	+	0.682298i
$7$	−0.0653068	−	0.0653068i	−0.0246837	−	0.0246837i	0.694657	−	0.719341i	$-0.255556\pi$
$7$	−0.0653068	−	0.0653068i	−0.0246837	−	0.0246837i	−0.719341	+	0.694657i	$0.755556\pi$
$8$	1.24319	−	2.54057i	0.439535	−	0.898226i
$9$			1.33451i			0.444838i
$10$	1.06188	−	2.97866i	0.335795	−	0.941935i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−0.107310	+	2.57884i	−0.0309777	+	0.744448i
$13$	0.473161	+	0.473161i	0.131231	+	0.131231i	0.769671	−	0.638440i	$-0.220420\pi$
$13$	0.473161	+	0.473161i	0.131231	+	0.131231i	−0.638440	+	0.769671i	$0.720420\pi$
$14$	−0.119606	−	0.0524819i	−0.0319660	−	0.0140264i
$15$	0.204839	+	2.87845i	0.0528893	+	0.743212i
$16$	0.332318	−	3.98617i	0.0830795	−	0.996543i
$17$	−1.01081	+	1.01081i	−0.245157	+	0.245157i	−0.818980	−	0.573823i	$-0.805460\pi$
$17$	−1.01081	+	1.01081i	−0.245157	+	0.245157i	0.573823	+	0.818980i	$0.305460\pi$
$18$	0.685824	+	1.75827i	0.161650	+	0.414428i
$19$	2.65097			0.608173			0.304087	−	0.952644i	$-0.401649\pi$
$19$	2.65097			0.608173			0.304087	+	0.952644i	$0.401649\pi$
$20$	−0.131711	−	4.47020i	−0.0294515	−	0.999566i
$21$	0.119191			0.0260096
$22$	−0.513913	−	1.31753i	−0.109567	−	0.280899i
$23$	−5.32132	+	5.32132i	−1.10957	+	1.10957i	−0.116367	+	0.993206i	$0.537125\pi$
$23$	−5.32132	+	5.32132i	−1.10957	+	1.10957i	−0.993206	+	0.116367i	$0.962875\pi$
$24$	1.18392	+	3.45286i	0.241666	+	0.704812i
$25$	−0.708046	−	4.94961i	−0.141609	−	0.989923i
$26$	0.866568	+	0.380242i	0.169948	+	0.0745715i
$27$	−3.95545	−	3.95545i	−0.761227	−	0.761227i
$28$	−0.184556	−	0.00767967i	−0.0348778	−	0.00145132i
$29$			5.94796i			1.10451i	0.833676	+	0.552254i	$0.186232\pi$
$29$			5.94796i			1.10451i	−0.833676	+	0.552254i	$0.813768\pi$
$30$	1.74915	+	3.68718i	0.319350	+	0.673184i
$31$			1.44287i			0.259147i	0.991570	+	0.129573i	$0.0413608\pi$
$31$			1.44287i			0.259147i	−0.991570	+	0.129573i	$0.958639\pi$
$32$	−1.61070	−	5.42270i	−0.284735	−	0.958606i
$33$	0.912547	+	0.912547i	0.158854	+	0.158854i
$34$	−0.812306	+	1.85124i	−0.139309	+	0.317485i
$35$	−0.205997	+	0.0146594i	−0.0348199	+	0.00247789i
$36$	1.80719	+	1.96412i	0.301199	+	0.327354i
$37$	−5.27054	+	5.27054i	−0.866472	+	0.866472i	−0.992080	−	0.125608i	$-0.959912\pi$
$37$	−5.27054	+	5.27054i	−0.866472	+	0.866472i	0.125608	+	0.992080i	$0.459912\pi$
$38$	3.49274	−	1.36237i	0.566597	−	0.221005i
$39$	−0.863563			−0.138281
$40$	−2.47082	−	5.82194i	−0.390672	−	0.920530i
$41$	−5.13952			−0.802658			−0.401329	−	0.915934i	$-0.631452\pi$
$41$	−5.13952			−0.802658			−0.401329	+	0.915934i	$0.631452\pi$
$42$	0.157038	−	0.0612538i	0.0242315	−	0.00945167i
$43$	−4.06096	+	4.06096i	−0.619291	+	0.619291i	−0.945350	−	0.326058i	$-0.894279\pi$
$43$	−4.06096	+	4.06096i	−0.619291	+	0.619291i	0.326058	+	0.945350i	$0.394279\pi$
$44$	−1.35419	−	1.47179i	−0.204152	−	0.221880i
$45$	2.25451	+	1.95495i	0.336082	+	0.291427i
$46$	−4.27633	+	9.74572i	−0.630510	+	1.43693i
$47$	−7.89803	−	7.89803i	−1.15205	−	1.15205i	−0.986142	−	0.165903i	$-0.946946\pi$
$47$	−7.89803	−	7.89803i	−1.15205	−	1.15205i	−0.165903	−	0.986142i	$-0.553054\pi$
$48$	3.33431	+	3.94083i	0.481267	+	0.568809i
$49$		−	6.99147i		−	0.998781i
$50$	−3.47654	−	6.15741i	−0.491657	−	0.870789i
$51$		−	1.84482i		−	0.258326i
$52$	1.33714	+	0.0556408i	0.185428	+	0.00771598i
$53$	2.60160	+	2.60160i	0.357357	+	0.357357i	0.862838	−	0.505481i	$-0.168685\pi$
$53$	2.60160	+	2.60160i	0.357357	+	0.357357i	−0.505481	+	0.862838i	$0.668685\pi$
$54$	−7.24419	−	3.17868i	−0.985810	−	0.432564i
$55$	−1.68939	−	1.46492i	−0.227797	−	0.197529i
$56$	−0.247105	+	0.0847274i	−0.0330208	+	0.0113222i
$57$	−2.41913	+	2.41913i	−0.320422	+	0.320422i
$58$	3.05673	+	7.83664i	0.401369	+	1.02900i
$59$	7.70258			1.00279			0.501395	−	0.865218i	$-0.332820\pi$
$59$	7.70258			1.00279			0.501395	+	0.865218i	$0.332820\pi$
$60$	4.19946	+	3.95907i	0.542148	+	0.511114i
$61$	7.06915			0.905112			0.452556	−	0.891736i	$-0.350512\pi$
$61$	7.06915			0.905112			0.452556	+	0.891736i	$0.350512\pi$
$62$	0.741508	+	1.90103i	0.0941716	+	0.241430i
$63$	0.0871529	−	0.0871529i	0.0109802	−	0.0109802i
$64$	−4.90895	−	6.31682i	−0.613619	−	0.789603i
$65$	1.49249	−	0.106210i	0.185121	−	0.0131738i
$66$	1.67128	+	0.733342i	0.205720	+	0.0902681i
$67$	5.47540	+	5.47540i	0.668927	+	0.668927i	0.957468	−	0.288541i	$-0.0931701\pi$
$67$	5.47540	+	5.47540i	0.668927	+	0.668927i	−0.288541	+	0.957468i	$0.593170\pi$
$68$	−0.118865	+	2.85652i	−0.0144145	+	0.346404i
$69$		−	9.71192i		−	1.16918i
$70$	−0.263875	+	0.125179i	−0.0315391	+	0.0149617i
$71$		−	1.80081i		−	0.213717i	−0.994274	−	0.106859i	$-0.965921\pi$
$71$		−	1.80081i		−	0.213717i	0.994274	−	0.106859i	$-0.0340793\pi$
$72$	3.39042	+	1.65906i	0.399565	+	0.195522i
$73$	5.16419	+	5.16419i	0.604422	+	0.604422i	0.941483	−	0.337061i	$-0.109433\pi$
$73$	5.16419	+	5.16419i	0.604422	+	0.604422i	−0.337061	+	0.941483i	$0.609433\pi$
$74$	−4.23552	+	9.65271i	−0.492369	+	1.12211i
$75$	5.16288	+	3.87063i	0.596158	+	0.446942i
$76$	3.90166	−	3.58992i	0.447551	−	0.411792i
$77$	−0.0653068	+	0.0653068i	−0.00744240	+	0.00744240i
$78$	−1.13777	+	0.443796i	−0.128827	+	0.0502500i
$79$	14.2952			1.60833			0.804167	−	0.594404i	$-0.202612\pi$
$79$	14.2952			1.60833			0.804167	+	0.594404i	$0.202612\pi$
$80$	−6.24736	−	6.40082i	−0.698476	−	0.715633i
$81$	3.21553			0.357281
$82$	−6.77149	+	2.64126i	−0.747786	+	0.291679i
$83$	11.9160	−	11.9160i	1.30795	−	1.30795i	0.385065	−	0.922889i	$-0.374179\pi$
$83$	11.9160	−	11.9160i	1.30795	−	1.30795i	0.922889	−	0.385065i	$-0.125821\pi$
$84$	0.175424	−	0.161408i	0.0191403	−	0.0176110i
$85$	0.226896	+	3.18839i	0.0246103	+	0.345830i
$86$	−3.26347	+	7.43743i	−0.351909	+	0.801999i
$87$	−5.42780	−	5.42780i	−0.581921	−	0.581921i
$88$	−2.54057	−	1.24319i	−0.270825	−	0.132525i
$89$		−	5.69673i		−	0.603852i	−0.953331	−	0.301926i	$-0.902370\pi$
$89$		−	5.69673i		−	0.603852i	0.953331	−	0.301926i	$-0.0976296\pi$
$90$	3.97507	+	1.41709i	0.419009	+	0.149375i
$91$		−	0.0618012i		−	0.00647853i
$92$	−0.625755	+	15.0380i	−0.0652394	+	1.56782i
$93$	−1.31668	−	1.31668i	−0.136534	−	0.136534i
$94$	−14.4648	−	6.34702i	−1.49193	−	0.654645i
$95$	3.88344	−	4.47850i	0.398433	−	0.459485i
$96$	6.41831	+	3.47862i	0.655066	+	0.355035i
$97$	−0.398370	+	0.398370i	−0.0404484	+	0.0404484i	−0.727042	−	0.686593i	$-0.759105\pi$
$97$	−0.398370	+	0.398370i	−0.0404484	+	0.0404484i	0.686593	+	0.727042i	$0.259105\pi$
$98$	−3.59300	−	9.21149i	−0.362948	−	0.930501i
$99$	1.33451			0.134124
$100$	−7.74483	−	6.32595i	−0.774483	−	0.632595i
$101$	−11.2570			−1.12012			−0.560058	−	0.828453i	$-0.689221\pi$
$101$	−11.2570			−1.12012			−0.560058	+	0.828453i	$0.689221\pi$
$102$	−0.948076	−	2.43061i	−0.0938735	−	0.240666i
$103$	−4.87406	+	4.87406i	−0.480255	+	0.480255i	−0.905213	−	0.424958i	$-0.860289\pi$
$103$	−4.87406	+	4.87406i	−0.480255	+	0.480255i	0.424958	+	0.905213i	$0.360289\pi$
$104$	1.79033	−	0.613866i	0.175556	−	0.0601946i
$105$	0.174605	−	0.201360i	0.0170397	−	0.0196507i
$106$	4.76469	+	2.09070i	0.462787	+	0.203067i
$107$	2.18565	+	2.18565i	0.211295	+	0.211295i	0.804817	−	0.593523i	$-0.202263\pi$
$107$	2.18565	+	2.18565i	0.211295	+	0.211295i	−0.593523	+	0.804817i	$0.702263\pi$
$108$	−11.1780	−	0.465136i	−1.07561	−	0.0447578i
$109$		−	9.51113i		−	0.911001i	−0.890235	−	0.455501i	$-0.849460\pi$
$109$		−	9.51113i		−	0.911001i	0.890235	−	0.455501i	$-0.150540\pi$
$110$	−2.97866	−	1.06188i	−0.284004	−	0.101246i
$111$		−	9.61924i		−	0.913018i
$112$	−0.282027	+	0.238622i	−0.0266490	+	0.0225476i
$113$	−11.0768	−	11.0768i	−1.04201	−	1.04201i	−0.999078	−	0.0429352i	$-0.986329\pi$
$113$	−11.0768	−	11.0768i	−1.04201	−	1.04201i	−0.0429352	−	0.999078i	$-0.513671\pi$
$114$	−1.94406	+	4.43051i	−0.182078	+	0.414955i
$115$	1.19448	+	16.7851i	0.111386	+	1.56521i
$116$	8.05469	+	8.75414i	0.747859	+	0.812801i
$117$	−0.631440	+	0.631440i	−0.0583767	+	0.0583767i
$118$	10.1484	−	3.95845i	0.934237	−	0.364405i
$119$	0.132025			0.0121027
$120$	7.56754	+	3.05806i	0.690819	+	0.279161i
$121$	−1.00000			−0.0909091
$122$	9.31384	−	3.63293i	0.843236	−	0.328910i
$123$	4.69005	−	4.69005i	0.422888	−	0.422888i
$124$	1.95392	+	2.12359i	0.175467	+	0.190704i
$125$	−9.39903	−	6.05460i	−0.840675	−	0.541540i
$126$	0.0700379	−	0.159616i	0.00623947	−	0.0142197i
$127$	−2.77907	−	2.77907i	−0.246603	−	0.246603i	0.572972	−	0.819575i	$-0.305790\pi$
$127$	−2.77907	−	2.77907i	−0.246603	−	0.246603i	−0.819575	+	0.572972i	$0.805790\pi$
$128$	−9.71400	−	5.79985i	−0.858604	−	0.512639i
$129$		−	7.41164i		−	0.652559i
$130$	1.91182	−	0.906946i	0.167678	−	0.0795444i
$131$		−	5.82054i		−	0.508543i	−0.967133	−	0.254272i	$-0.918164\pi$
$131$		−	5.82054i		−	0.508543i	0.967133	−	0.254272i	$-0.0818357\pi$
$132$	2.57884	+	0.107310i	0.224459	+	0.00934013i
$133$	−0.173126	−	0.173126i	−0.0150119	−	0.0150119i
$134$	10.0279	+	4.40015i	0.866279	+	0.380115i
$135$	−12.4767	+	0.887880i	−1.07382	+	0.0764165i
$136$	1.31140	+	3.82465i	0.112451	+	0.327961i
$137$	−4.96234	+	4.96234i	−0.423961	+	0.423961i	−0.886565	−	0.462604i	$-0.846915\pi$
$137$	−4.96234	+	4.96234i	−0.423961	+	0.423961i	0.462604	+	0.886565i	$0.346915\pi$
$138$	−4.99108	−	12.7958i	−0.424869	−	1.08925i
$139$	19.6363			1.66553			0.832765	−	0.553626i	$-0.186756\pi$
$139$	19.6363			1.66553			0.832765	+	0.553626i	$0.186756\pi$
$140$	−0.283333	+	0.300536i	−0.0239460	+	0.0253999i
$141$	14.4146			1.21393
$142$	−0.925462	−	2.37263i	−0.0776630	−	0.199107i
$143$	0.473161	−	0.473161i	0.0395677	−	0.0395677i
$144$	5.31960	+	0.443483i	0.443300	+	0.0369569i
$145$	10.0484	+	8.71326i	0.834474	+	0.723597i
$146$	9.45793	+	4.15005i	0.782743	+	0.343460i
$147$	6.38005	+	6.38005i	0.526217	+	0.526217i
$148$	−0.619783	+	14.8945i	−0.0509458	+	1.22432i
$149$			23.2803i			1.90719i	0.301087	+	0.953597i	$0.402651\pi$
$149$			23.2803i			1.90719i	−0.301087	+	0.953597i	$0.597349\pi$
$150$	8.79143	+	2.44642i	0.717818	+	0.199749i
$151$			7.70843i			0.627303i	0.949538	+	0.313651i	$0.101552\pi$
$151$			7.70843i			0.627303i	−0.949538	+	0.313651i	$0.898448\pi$
$152$	3.29566	−	6.73495i	0.267313	−	0.546277i
$153$	−1.34894	−	1.34894i	−0.109055	−	0.109055i
$154$	−0.0524819	+	0.119606i	−0.00422911	+	0.00963812i
$155$	2.43756	+	2.11368i	0.195789	+	0.169775i
$156$	−1.27098	+	1.16943i	−0.101760	+	0.0936295i
$157$	12.9770	−	12.9770i	1.03567	−	1.03567i	0.0363338	−	0.999340i	$-0.488432\pi$
$157$	12.9770	−	12.9770i	1.03567	−	1.03567i	0.999340	−	0.0363338i	$-0.0115679\pi$
$158$	18.8344	−	7.34647i	1.49838	−	0.584454i
$159$	−4.74816			−0.376554
$160$	−11.5206	−	5.22269i	−0.910781	−	0.412890i
$161$	0.695038			0.0547766
$162$	4.23656	−	1.65250i	0.332856	−	0.129833i
$163$	−6.37115	+	6.37115i	−0.499027	+	0.499027i	−0.911135	−	0.412108i	$-0.864793\pi$
$163$	−6.37115	+	6.37115i	−0.499027	+	0.499027i	0.412108	+	0.911135i	$0.364793\pi$
$164$	−7.56428	+	6.95991i	−0.590671	+	0.543477i
$165$	2.87845	−	0.204839i	0.224087	−	0.0159467i
$166$	9.57597	−	21.8236i	0.743239	−	1.69384i
$167$	−12.0038	−	12.0038i	−0.928881	−	0.928881i	0.0687523	−	0.997634i	$-0.478098\pi$
$167$	−12.0038	−	12.0038i	−0.928881	−	0.928881i	−0.997634	+	0.0687523i	$0.978098\pi$
$168$	0.148177	−	0.302813i	0.0114321	−	0.0233625i
$169$		−	12.5522i		−	0.965557i
$170$	1.93750	+	4.08421i	0.148599	+	0.313244i
$171$			3.53775i			0.270539i
$172$	−0.477544	+	11.4762i	−0.0364124	+	0.875053i
$173$	−5.56357	−	5.56357i	−0.422990	−	0.422990i	0.463242	−	0.886232i	$-0.346686\pi$
$173$	−5.56357	−	5.56357i	−0.422990	−	0.422990i	−0.886232	+	0.463242i	$0.846686\pi$
$174$	−9.94071	−	4.36189i	−0.753604	−	0.330674i
$175$	−0.277003	+	0.369484i	−0.0209395	+	0.0279303i
$176$	−3.98617	−	0.332318i	−0.300469	−	0.0250494i
$177$	−7.02897	+	7.02897i	−0.528330	+	0.528330i
$178$	−2.92762	−	7.50563i	−0.219435	−	0.562571i
$179$	−4.15446			−0.310519			−0.155259	−	0.987874i	$-0.549621\pi$
$179$	−4.15446			−0.310519			−0.155259	+	0.987874i	$0.549621\pi$
$180$	5.96554	−	0.175770i	0.444645	−	0.0131011i
$181$	−9.46693			−0.703671			−0.351836	−	0.936062i	$-0.614442\pi$
$181$	−9.46693			−0.703671			−0.351836	+	0.936062i	$0.614442\pi$
$182$	−0.0317604	−	0.0814252i	−0.00235424	−	0.00603564i
$183$	−6.45093	+	6.45093i	−0.476867	+	0.476867i
$184$	6.90375	+	20.1346i	0.508951	+	1.48434i
$185$	1.18308	+	16.6249i	0.0869817	+	1.22229i
$186$	−2.41144	−	1.05811i	−0.176815	−	0.0775848i
$187$	1.01081	+	1.01081i	0.0739176	+	0.0739176i
$188$	−22.3197	−	0.928759i	−1.62783	−	0.0677367i
$189$			0.516636i			0.0375797i
$190$	2.81500	−	7.89633i	0.204222	−	0.572860i
$191$		−	18.6435i		−	1.34899i	−0.738277	−	0.674497i	$-0.764360\pi$
$191$		−	18.6435i		−	1.34899i	0.738277	−	0.674497i	$-0.235640\pi$
$192$	10.2440	+	1.28475i	0.739300	+	0.0927189i
$193$	19.4785	+	19.4785i	1.40209	+	1.40209i	0.793427	+	0.608666i	$0.208295\pi$
$193$	19.4785	+	19.4785i	1.40209	+	1.40209i	0.608666	+	0.793427i	$0.291705\pi$
$194$	−0.320139	+	0.729594i	−0.0229846	+	0.0523818i
$195$	−1.26505	+	1.45889i	−0.0905919	+	0.104473i
$196$	−9.46781	−	10.2900i	−0.676272	−	0.734997i
$197$	13.7373	−	13.7373i	0.978743	−	0.978743i	−0.0210356	−	0.999779i	$-0.506696\pi$
$197$	13.7373	−	13.7373i	0.978743	−	0.978743i	0.999779	+	0.0210356i	$0.00669635\pi$
$198$	1.75827	−	0.685824i	0.124955	−	0.0487394i
$199$	−9.36208			−0.663661			−0.331830	−	0.943339i	$-0.607666\pi$
$199$	−9.36208			−0.663661			−0.331830	+	0.943339i	$0.607666\pi$
$200$	−13.4551	−	4.35448i	−0.951416	−	0.307908i
$201$	−9.99313			−0.704861
$202$	−14.8315	+	5.78513i	−1.04354	+	0.407041i
$203$	0.388442	−	0.388442i	0.0272633	−	0.0272633i
$204$	−2.49824	−	2.71518i	−0.174912	−	0.190101i
$205$	−7.52896	+	8.68263i	−0.525845	+	0.606421i
$206$	−3.91689	+	8.92658i	−0.272903	+	0.621944i
$207$	−7.10139	−	7.10139i	−0.493580	−	0.493580i
$208$	2.04334	−	1.72886i	0.141680	−	0.119875i
$209$		−	2.65097i		−	0.183371i
$210$	0.126566	−	0.355030i	0.00873392	−	0.0244994i
$211$			19.0983i			1.31478i	0.753550	+	0.657390i	$0.228340\pi$
$211$			19.0983i			1.31478i	−0.753550	+	0.657390i	$0.771660\pi$
$212$	7.35207	+	0.305932i	0.504942	+	0.0210115i
$213$	1.64333	+	1.64333i	0.112599	+	0.112599i
$214$	4.00290	+	1.75643i	0.273632	+	0.120067i
$215$	0.911564	+	12.8095i	0.0621682	+	0.873601i
$216$	−14.9665	+	5.13170i	−1.01834	+	0.349168i
$217$	0.0942291	−	0.0942291i	0.00639669	−	0.00639669i
$218$	−4.88789	−	12.5312i	−0.331050	−	0.848722i
$219$	−9.42513			−0.636891
$220$	−4.47020	+	0.131711i	−0.301381	+	0.00887995i
$221$	−0.956549			−0.0643445
$222$	−4.94345	−	12.6737i	−0.331783	−	0.850601i
$223$	−1.52935	+	1.52935i	−0.102413	+	0.102413i	−0.756457	−	0.654044i	$-0.773071\pi$
$223$	−1.52935	+	1.52935i	−0.102413	+	0.102413i	0.654044	+	0.756457i	$0.273071\pi$
$224$	−0.248949	+	0.459329i	−0.0166336	+	0.0306902i
$225$	6.60533	−	0.944898i	0.440355	−	0.0629932i
$226$	−20.2865	−	8.90151i	−1.34944	−	0.592119i
$227$	7.50620	+	7.50620i	0.498204	+	0.498204i	0.910879	−	0.412675i	$-0.135405\pi$
$227$	7.50620	+	7.50620i	0.498204	+	0.498204i	−0.412675	+	0.910879i	$0.635405\pi$
$228$	−0.284475	+	6.83642i	−0.0188398	+	0.452753i
$229$			13.3544i			0.882485i	0.897388	+	0.441243i	$0.145462\pi$
$229$			13.3544i			0.882485i	−0.897388	+	0.441243i	$0.854538\pi$
$230$	10.1998	+	21.5010i	0.672556	+	1.41774i
$231$		−	0.119191i		−	0.00784220i
$232$	15.1112	+	7.39446i	0.992098	+	0.485470i
$233$	4.32195	+	4.32195i	0.283140	+	0.283140i	0.834360	−	0.551220i	$-0.185837\pi$
$233$	4.32195	+	4.32195i	0.283140	+	0.283140i	−0.551220	+	0.834360i	$0.685837\pi$
$234$	−0.507438	+	1.15645i	−0.0331723	+	0.0755994i
$235$	−24.9127	+	1.77287i	−1.62513	+	0.115649i
$236$	11.3366	−	10.4308i	0.737948	−	0.678987i
$237$	−13.0450	+	13.0450i	−0.847366	+	0.847366i
$238$	0.173948	−	0.0678494i	0.0112754	−	0.00439803i
$239$	−25.2845			−1.63552			−0.817760	−	0.575559i	$-0.804784\pi$
$239$	−25.2845			−1.63552			−0.817760	+	0.575559i	$0.804784\pi$
$240$	11.5421	+	0.140034i	0.745037	+	0.00903919i
$241$	−11.0013			−0.708655			−0.354328	−	0.935121i	$-0.615290\pi$
$241$	−11.0013			−0.708655			−0.354328	+	0.935121i	$0.615290\pi$
$242$	−1.31753	+	0.513913i	−0.0846942	+	0.0330356i
$243$	8.93203	−	8.93203i	0.572990	−	0.572990i
$244$	10.4043	−	9.57300i	0.666066	−	0.612849i
$245$	−11.8113	−	10.2419i	−0.754595	−	0.654332i
$246$	3.76902	−	8.58958i	0.240304	−	0.547652i
$247$	1.25433	+	1.25433i	0.0798113	+	0.0798113i
$248$	3.66570	+	1.79376i	0.232772	+	0.113904i
$249$			21.7479i			1.37822i
$250$	−15.4951	−	3.14686i	−0.979994	−	0.199025i
$251$		−	29.5654i		−	1.86615i	−0.359683	−	0.933075i	$-0.617115\pi$
$251$		−	29.5654i		−	1.86615i	0.359683	−	0.933075i	$-0.382885\pi$
$252$	0.0102486	−	0.246293i	0.000645604	−	0.0155150i
$253$	5.32132	+	5.32132i	0.334549	+	0.334549i
$254$	−5.08973	−	2.23332i	−0.319358	−	0.140131i
$255$	−3.11661	−	2.70250i	−0.195170	−	0.169237i
$256$	−15.7791	−	2.64935i	−0.986196	−	0.165584i
$257$	12.1596	−	12.1596i	0.758496	−	0.758496i	−0.217553	−	0.976049i	$-0.569807\pi$
$257$	12.1596	−	12.1596i	0.758496	−	0.758496i	0.976049	+	0.217553i	$0.0698073\pi$
$258$	−3.80894	−	9.76509i	−0.237134	−	0.607948i
$259$	0.688405			0.0427754
$260$	2.05280	−	2.17744i	0.127309	−	0.135039i
$261$	−7.93764			−0.491328
$262$	−2.99125	−	7.66876i	−0.184800	−	0.473777i
$263$	−13.5230	+	13.5230i	−0.833864	+	0.833864i	−0.988043	−	0.154179i	$-0.950727\pi$
$263$	−13.5230	+	13.5230i	−0.833864	+	0.833864i	0.154179	+	0.988043i	$0.450727\pi$
$264$	3.45286	−	1.18392i	0.212509	−	0.0728649i
$265$	8.20623	−	0.583981i	0.504104	−	0.0358737i
$266$	−0.317071	−	0.139128i	−0.0194409	−	0.00853047i
$267$	5.19854	+	5.19854i	0.318145	+	0.318145i
$268$	15.4734	+	0.643873i	0.945188	+	0.0393308i
$269$		−	1.45696i		−	0.0888322i	−0.999013	−	0.0444161i	$-0.985857\pi$
$269$		−	1.45696i		−	0.0888322i	0.999013	−	0.0444161i	$-0.0141427\pi$
$270$	−15.9821	+	7.58173i	−0.972642	+	0.461410i
$271$			8.56442i			0.520251i	0.965575	+	0.260126i	$0.0837640\pi$
$271$			8.56442i			0.520251i	−0.965575	+	0.260126i	$0.916236\pi$
$272$	3.69334	+	4.36516i	0.223942	+	0.264677i
$273$	0.0563966	+	0.0563966i	0.00341328	+	0.00341328i
$274$	−3.98784	+	9.08825i	−0.240914	+	0.549041i
$275$	−4.94961	+	0.708046i	−0.298473	+	0.0426968i
$276$	−13.1518	−	14.2939i	−0.791647	−	0.860391i
$277$	8.63149	−	8.63149i	0.518616	−	0.518616i	−0.398537	−	0.917152i	$-0.630482\pi$
$277$	8.63149	−	8.63149i	0.518616	−	0.518616i	0.917152	+	0.398537i	$0.130482\pi$
$278$	25.8715	−	10.0913i	1.55167	−	0.605239i
$279$	−1.92553			−0.115278
$280$	−0.218851	+	0.541574i	−0.0130788	+	0.0323652i
$281$	8.37468			0.499592			0.249796	−	0.968299i	$-0.419637\pi$
$281$	8.37468			0.499592			0.249796	+	0.968299i	$0.419637\pi$
$282$	18.9918	−	7.40787i	1.13094	−	0.441132i
$283$	7.90636	−	7.90636i	0.469985	−	0.469985i	−0.431925	−	0.901910i	$-0.642165\pi$
$283$	7.90636	−	7.90636i	0.469985	−	0.469985i	0.901910	+	0.431925i	$0.142165\pi$
$284$	−2.43865	−	2.65042i	−0.144707	−	0.157273i
$285$	0.543023	+	7.63067i	0.0321659	+	0.452002i
$286$	0.380242	−	0.866568i	0.0224842	−	0.0512413i
$287$	0.335646	+	0.335646i	0.0198125	+	0.0198125i
$288$	7.23667	−	2.14951i	0.426425	−	0.126661i
$289$			14.9565i			0.879796i
$290$	17.7170	+	6.31601i	1.04038	+	0.370889i
$291$		−	0.727064i		−	0.0426212i
$292$	14.5939	+	0.607276i	0.854043	+	0.0355381i
$293$	−7.94335	−	7.94335i	−0.464056	−	0.464056i	0.435927	−	0.899982i	$-0.356421\pi$
$293$	−7.94335	−	7.94335i	−0.464056	−	0.464056i	−0.899982	+	0.435927i	$0.856421\pi$
$294$	11.6847	+	5.12714i	0.681466	+	0.299021i
$295$	11.2836	−	13.0126i	0.656958	−	0.757625i
$296$	6.83786	+	19.9425i	0.397443	+	1.15913i
$297$	−3.95545	+	3.95545i	−0.229518	+	0.229518i
$298$	11.9640	+	30.6725i	0.693057	+	1.77681i
$299$	−5.03568			−0.291221
$300$	12.8403	−	1.29480i	0.741332	−	0.0747551i
$301$	0.530417			0.0305727
$302$	3.96146	+	10.1561i	0.227956	+	0.584418i
$303$	10.2726	−	10.2726i	0.590144	−	0.590144i
$304$	0.880963	−	10.5672i	0.0505267	−	0.606071i
$305$	10.3557	−	11.9425i	0.592966	−	0.683827i
$306$	−2.47051	−	1.08403i	−0.141229	−	0.0619701i
$307$	13.3805	+	13.3805i	0.763666	+	0.763666i	0.976983	−	0.213317i	$-0.0684266\pi$
$307$	13.3805	+	13.3805i	0.763666	+	0.763666i	−0.213317	+	0.976983i	$0.568427\pi$
$308$	−0.00767967	+	0.184556i	−0.000437590	+	0.0105160i
$309$		−	8.89562i		−	0.506054i
$310$	4.29781	+	1.53215i	0.244099	+	0.0870202i
$311$			32.5214i			1.84412i	0.387046	+	0.922060i	$0.373495\pi$
$311$			32.5214i			1.84412i	−0.387046	+	0.922060i	$0.626505\pi$
$312$	−1.07357	+	2.19394i	−0.0607792	+	0.124207i
$313$	−14.8992	−	14.8992i	−0.842150	−	0.842150i	0.146988	−	0.989138i	$-0.453042\pi$
$313$	−14.8992	−	14.8992i	−0.842150	−	0.842150i	−0.989138	+	0.146988i	$0.953042\pi$
$314$	10.4285	−	23.7666i	0.588517	−	1.34123i
$315$	−0.0195632	−	0.274906i	−0.00110226	−	0.0154892i
$316$	21.0395	−	19.3584i	1.18356	−	1.08900i
$317$	9.74907	−	9.74907i	0.547562	−	0.547562i	−0.378173	−	0.925735i	$-0.623447\pi$
$317$	9.74907	−	9.74907i	0.547562	−	0.547562i	0.925735	+	0.378173i	$0.123447\pi$
$318$	−6.25586	+	2.44014i	−0.350811	+	0.136836i
$319$	5.94796			0.333022
$320$	−17.8627	−	0.960503i	−0.998557	−	0.0536938i
$321$	−3.98902			−0.222645
$322$	0.915735	−	0.357189i	0.0510319	−	0.0199053i
$323$	−2.67962	+	2.67962i	−0.149098	+	0.149098i
$324$	4.73257	−	4.35445i	0.262921	−	0.241914i
$325$	2.00694	−	2.67698i	0.111325	−	0.148492i
$326$	−5.11999	+	11.6684i	−0.283570	+	0.646254i
$327$	8.67936	+	8.67936i	0.479970	+	0.479970i
$328$	−6.38941	+	13.0573i	−0.352796	+	0.720968i
$329$			1.03159i			0.0568734i
$330$	3.68718	−	1.74915i	0.202973	−	0.0962878i
$331$		−	10.2373i		−	0.562695i	−0.959606	−	0.281348i	$-0.909219\pi$
$331$		−	10.2373i		−	0.562695i	0.959606	−	0.281348i	$-0.0907814\pi$
$332$	1.40125	−	33.6745i	0.0769036	−	1.84813i
$333$	−7.03362	−	7.03362i	−0.385440	−	0.385440i
$334$	−21.9843	−	9.64650i	−1.20293	−	0.527833i
$335$	17.2711	−	1.22906i	0.943619	−	0.0671509i
$336$	0.0396093	−	0.475116i	0.00216087	−	0.0259197i
$337$	15.6491	−	15.6491i	0.852460	−	0.852460i	−0.137976	−	0.990436i	$-0.544060\pi$
$337$	15.6491	−	15.6491i	0.852460	−	0.852460i	0.990436	+	0.137976i	$0.0440596\pi$
$338$	−6.45075	−	16.5380i	−0.350875	−	0.899548i
$339$	20.2161			1.09799
$340$	4.65164	+	4.38537i	0.252271	+	0.237830i
$341$	1.44287			0.0781356
$342$	1.81810	+	4.66111i	0.0983114	+	0.252044i
$343$	−0.913738	+	0.913738i	−0.0493372	+	0.0493372i
$344$	5.26859	+	15.3657i	0.284063	+	0.828463i
$345$	−16.4072	−	14.2271i	−0.883333	−	0.765964i
$346$	−10.1894	−	4.47100i	−0.547784	−	0.240362i
$347$	15.8467	+	15.8467i	0.850698	+	0.850698i	0.990219	−	0.139521i	$-0.0445564\pi$
$347$	15.8467	+	15.8467i	0.850698	+	0.850698i	−0.139521	+	0.990219i	$0.544556\pi$
$348$	−15.3389	−	0.638275i	−0.822249	−	0.0342151i
$349$		−	22.8492i		−	1.22309i	−0.791209	−	0.611545i	$-0.790548\pi$
$349$		−	22.8492i		−	1.22309i	0.791209	−	0.611545i	$-0.209452\pi$
$350$	−0.175079	+	0.629162i	−0.00935835	+	0.0336301i
$351$		−	3.74313i		−	0.199793i
$352$	−5.42270	+	1.61070i	−0.289031	+	0.0858508i
$353$	1.30502	+	1.30502i	0.0694591	+	0.0694591i	0.740983	−	0.671524i	$-0.234360\pi$
$353$	1.30502	+	1.30502i	0.0694591	+	0.0694591i	−0.671524	+	0.740983i	$0.734360\pi$
$354$	−5.64863	+	12.8732i	−0.300221	+	0.684202i
$355$	−3.04227	−	2.63804i	−0.161467	−	0.140013i
$356$	−7.71448	−	8.38438i	−0.408867	−	0.444371i
$357$	−0.120479	+	0.120479i	−0.00637644	+	0.00637644i
$358$	−5.47364	+	2.13503i	−0.289291	+	0.112840i
$359$	−4.81259			−0.253999			−0.127000	−	0.991903i	$-0.540535\pi$
$359$	−4.81259			−0.253999			−0.127000	+	0.991903i	$0.540535\pi$
$360$	7.76947	−	3.29735i	0.409487	−	0.173786i
$361$	−11.9724			−0.630125
$362$	−12.4730	+	4.86517i	−0.655566	+	0.255708i
$363$	0.912547	−	0.912547i	0.0478963	−	0.0478963i
$364$	−0.0836909	−	0.0909583i	−0.00438659	−	0.00476751i
$365$	16.2894	−	1.15920i	0.852626	−	0.0606755i
$366$	−5.18410	+	11.8145i	−0.270977	+	0.617556i
$367$	9.09859	+	9.09859i	0.474942	+	0.474942i	0.903510	−	0.428567i	$-0.140982\pi$
$367$	9.09859	+	9.09859i	0.474942	+	0.474942i	−0.428567	+	0.903510i	$0.640982\pi$
$368$	19.4433	+	22.9801i	1.01355	+	1.19792i
$369$		−	6.85876i		−	0.357053i
$370$	10.1025	+	21.2958i	0.525203	+	1.10712i
$371$		−	0.339804i		−	0.0176418i
$372$	−3.72093	−	0.154834i	−0.192921	−	0.00802776i
$373$	−5.77605	−	5.77605i	−0.299073	−	0.299073i	0.541578	−	0.840651i	$-0.317827\pi$
$373$	−5.77605	−	5.77605i	−0.299073	−	0.299073i	−0.840651	+	0.541578i	$0.817827\pi$
$374$	1.85124	+	0.812306i	0.0957253	+	0.0420033i
$375$	14.1022	−	3.05195i	0.728233	−	0.157602i
$376$	−29.8842	+	10.2467i	−1.54116	+	0.528433i
$377$	−2.81434	+	2.81434i	−0.144946	+	0.144946i
$378$	0.265506	+	0.680685i	0.0136561	+	0.0350106i
$379$	−21.9568			−1.12784			−0.563922	−	0.825828i	$-0.690708\pi$
$379$	−21.9568			−1.12784			−0.563922	+	0.825828i	$0.690708\pi$
$380$	−0.349161	−	11.8503i	−0.0179116	−	0.607910i
$381$	5.07207			0.259850
$382$	−9.58112	−	24.5634i	−0.490213	−	1.25677i
$383$	5.58752	−	5.58752i	0.285509	−	0.285509i	−0.549792	−	0.835301i	$-0.685293\pi$
$383$	5.58752	−	5.58752i	0.285509	−	0.285509i	0.835301	+	0.549792i	$0.185293\pi$
$384$	14.1571	−	3.57184i	0.722453	−	0.182275i
$385$	0.0146594	+	0.205997i	0.000747113	+	0.0104986i
$386$	35.6738	+	15.6533i	1.81575	+	0.796733i
$387$	−5.41942	−	5.41942i	−0.275484	−	0.275484i
$388$	−0.0468459	+	1.12579i	−0.00237824	+	0.0571532i
$389$			20.2159i			1.02498i	0.858692	+	0.512492i	$0.171278\pi$
$389$			20.2159i			1.02498i	−0.858692	+	0.512492i	$0.828722\pi$
$390$	−0.916999	+	2.57226i	−0.0464341	+	0.130252i
$391$		−	10.7577i		−	0.544039i
$392$	−17.7623	−	8.69174i	−0.897131	−	0.438999i
$393$	5.31152	+	5.31152i	0.267931	+	0.267931i
$394$	11.0396	−	25.1591i	0.556166	−	1.26750i
$395$	20.9412	−	24.1501i	1.05367	−	1.21512i
$396$	1.96412	−	1.80719i	0.0987009	−	0.0908148i
$397$	−15.6155	+	15.6155i	−0.783719	+	0.783719i	−0.980456	−	0.196737i	$-0.936965\pi$
$397$	−15.6155	+	15.6155i	−0.783719	+	0.783719i	0.196737	+	0.980456i	$0.436965\pi$
$398$	−12.3349	+	4.81129i	−0.618291	+	0.241168i
$399$	0.315972			0.0158184
$400$	−19.9653	+	1.17755i	−0.998265	+	0.0588774i
$401$	1.85459			0.0926139			0.0463070	−	0.998927i	$-0.485255\pi$
$401$	1.85459			0.0926139			0.0463070	+	0.998927i	$0.485255\pi$
$402$	−13.1663	+	5.13559i	−0.656674	+	0.256140i
$403$	−0.682708	+	0.682708i	−0.0340081	+	0.0340081i
$404$	−16.5680	+	15.2442i	−0.824287	+	0.758428i
$405$	4.71047	−	5.43226i	0.234065	−	0.269931i
$406$	0.312160	−	0.711411i	0.0154923	−	0.0353067i
$407$	5.27054	+	5.27054i	0.261251	+	0.261251i
$408$	−4.68689	−	2.29346i	−0.232035	−	0.113543i
$409$			0.431928i			0.0213575i	0.999943	+	0.0106787i	$0.00339921\pi$
$409$			0.431928i			0.0213575i	−0.999943	+	0.0106787i	$0.996601\pi$
$410$	−5.45754	+	15.3089i	−0.269529	+	0.756052i
$411$		−	9.05673i		−	0.446736i
$412$	−0.573159	+	13.7740i	−0.0282375	+	0.678596i
$413$	−0.503031	−	0.503031i	−0.0247525	−	0.0247525i
$414$	−13.0058	−	5.70682i	−0.639200	−	0.280475i
$415$	−2.67479	−	37.5868i	−0.131300	−	1.84506i
$416$	1.80369	−	3.32793i	0.0884329	−	0.163165i
$417$	−17.9191	+	17.9191i	−0.877500	+	0.877500i
$418$	−1.36237	−	3.49274i	−0.0666355	−	0.170835i
$419$	−35.1667			−1.71801			−0.859003	−	0.511971i	$-0.828916\pi$
$419$	−35.1667			−1.71801			−0.859003	+	0.511971i	$0.828916\pi$
$420$	−0.0156988	−	0.532808i	−0.000766022	−	0.0259984i
$421$	22.8147			1.11192			0.555959	−	0.831210i	$-0.312351\pi$
$421$	22.8147			1.11192			0.555959	+	0.831210i	$0.312351\pi$
$422$	9.81485	+	25.1626i	0.477779	+	1.22490i
$423$	10.5400	−	10.5400i	0.512474	−	0.512474i
$424$	9.84382	−	3.37525i	0.478058	−	0.163916i
$425$	5.71881	+	4.28741i	0.277403	+	0.207970i
$426$	3.00967	+	1.32061i	0.145819	+	0.0639839i
$427$	−0.461664	−	0.461664i	−0.0223415	−	0.0223415i
$428$	6.17660	+	0.257019i	0.298557	+	0.0124235i
$429$			0.863563i			0.0416932i
$430$	7.78398	+	16.4085i	0.375377	+	0.791287i
$431$			30.3483i			1.46183i	0.682470	+	0.730914i	$0.260906\pi$
$431$			30.3483i			1.46183i	−0.682470	+	0.730914i	$0.739094\pi$
$432$	−17.0816	+	14.4526i	−0.821837	+	0.695353i
$433$	−11.3120	−	11.3120i	−0.543619	−	0.543619i	0.380969	−	0.924588i	$-0.375591\pi$
$433$	−11.3120	−	11.3120i	−0.543619	−	0.543619i	−0.924588	+	0.380969i	$0.875591\pi$
$434$	0.0757244	−	0.172575i	0.00363489	−	0.00828389i
$435$	−17.1209	+	1.21838i	−0.820884	+	0.0584167i
$436$	−12.8799	−	13.9984i	−0.616836	−	0.670400i
$437$	−14.1067	+	14.1067i	−0.674813	+	0.674813i
$438$	−12.4179	+	4.84369i	−0.593351	+	0.231441i
$439$	38.9791			1.86037			0.930186	−	0.367089i	$-0.119646\pi$
$439$	38.9791			1.86037			0.930186	+	0.367089i	$0.119646\pi$
$440$	−5.82194	+	2.47082i	−0.277550	+	0.117792i
$441$	9.33022			0.444296
$442$	−1.26029	+	0.491583i	−0.0599457	+	0.0233822i
$443$	15.0112	−	15.0112i	0.713203	−	0.713203i	−0.254001	−	0.967204i	$-0.581747\pi$
$443$	15.0112	−	15.0112i	0.713203	−	0.713203i	0.967204	+	0.254001i	$0.0817467\pi$
$444$	−13.0263	−	14.1575i	−0.618202	−	0.671884i
$445$	−9.62398	−	8.34523i	−0.456220	−	0.395602i
$446$	−1.22902	+	2.80093i	−0.0581958	+	0.132628i
$447$	−21.2443	−	21.2443i	−1.00482	−	1.00482i
$448$	−0.0919437	+	0.733119i	−0.00434393	+	0.0346366i
$449$			34.7687i			1.64084i	0.571763	+	0.820419i	$0.306260\pi$
$449$			34.7687i			1.64084i	−0.571763	+	0.820419i	$0.693740\pi$
$450$	8.21715	−	4.63950i	0.387360	−	0.218708i
$451$			5.13952i			0.242011i
$452$	−31.3027	−	1.30256i	−1.47235	−	0.0612671i
$453$	−7.03430	−	7.03430i	−0.330500	−	0.330500i
$454$	13.7472	+	6.03214i	0.645188	+	0.283102i
$455$	−0.104406	−	0.0905336i	−0.00489463	−	0.00424428i
$456$	3.13852	+	9.15341i	0.146975	+	0.428648i
$457$	6.92112	−	6.92112i	0.323756	−	0.323756i	−0.526450	−	0.850206i	$-0.676477\pi$
$457$	6.92112	−	6.92112i	0.323756	−	0.323756i	0.850206	+	0.526450i	$0.176477\pi$
$458$	6.86301	+	17.5949i	0.320687	+	0.822156i
$459$	7.99640			0.373240
$460$	24.4882	+	23.0865i	1.14177	+	1.07641i
$461$	3.63769			0.169424			0.0847120	−	0.996405i	$-0.473003\pi$
$461$	3.63769			0.169424			0.0847120	+	0.996405i	$0.473003\pi$
$462$	−0.0612538	−	0.157038i	−0.00284979	−	0.00730608i
$463$	7.52465	−	7.52465i	0.349700	−	0.349700i	−0.510298	−	0.859998i	$-0.670465\pi$
$463$	7.52465	−	7.52465i	0.349700	−	0.349700i	0.859998	+	0.510298i	$0.170465\pi$
$464$	23.7096	+	1.97661i	1.10069	+	0.0917620i
$465$	−4.15322	+	0.295556i	−0.192601	+	0.0137061i
$466$	7.91541	+	3.47320i	0.366674	+	0.160893i
$467$	2.70144	+	2.70144i	0.125008	+	0.125008i	0.766843	−	0.641835i	$-0.221827\pi$
$467$	2.70144	+	2.70144i	0.125008	+	0.125008i	−0.641835	+	0.766843i	$0.721827\pi$
$468$	−0.0742534	+	1.78444i	−0.00343237	+	0.0824857i
$469$		−	0.715162i		−	0.0330231i
$470$	−31.9123	+	15.1388i	−1.47200	+	0.698300i
$471$			23.6842i			1.09131i
$472$	9.57579	−	19.5689i	0.440761	−	0.900732i
$473$	4.06096	+	4.06096i	0.186723	+	0.186723i
$474$	−10.4833	+	23.8913i	−0.481512	+	1.09736i
$475$	−1.87701	−	13.1213i	−0.0861229	−	0.602045i
$476$	0.194313	−	0.178788i	0.00890633	−	0.00819473i
$477$	−3.47187	+	3.47187i	−0.158966	+	0.158966i
$478$	−33.3132	+	12.9940i	−1.52371	+	0.594334i
$479$	−6.43233			−0.293901			−0.146950	−	0.989144i	$-0.546946\pi$
$479$	−6.43233			−0.293901			−0.146950	+	0.989144i	$0.546946\pi$
$480$	15.2790	−	5.74711i	0.697389	−	0.262319i
$481$	−4.98763			−0.227416
$482$	−14.4946	+	5.65370i	−0.660209	+	0.257519i
$483$	−0.634255	+	0.634255i	−0.0288596	+	0.0288596i
$484$	−1.47179	+	1.35419i	−0.0668994	+	0.0615543i
$485$	0.0894222	+	1.25658i	0.00406045	+	0.0570584i
$486$	7.17796	−	16.3585i	0.325599	−	0.742038i
$487$	−10.7615	−	10.7615i	−0.487648	−	0.487648i	0.419915	−	0.907563i	$-0.362060\pi$
$487$	−10.7615	−	10.7615i	−0.487648	−	0.487648i	−0.907563	+	0.419915i	$0.862060\pi$
$488$	8.78831	−	17.9596i	0.397828	−	0.812995i
$489$		−	11.6280i		−	0.525834i
$490$	−20.8252	−	7.42409i	−0.940787	−	0.335386i
$491$		−	17.1022i		−	0.771810i	−0.922538	−	0.385905i	$-0.873889\pi$
$491$		−	17.1022i		−	0.771810i	0.922538	−	0.385905i	$-0.126111\pi$
$492$	0.551521	−	13.2540i	0.0248645	−	0.597537i
$493$	−6.01225	−	6.01225i	−0.270778	−	0.270778i
$494$	2.29724	+	1.00801i	0.103358	+	0.0453524i
$495$	1.95495	−	2.25451i	0.0878685	−	0.101333i
$496$	5.75152	+	0.479490i	0.258251	+	0.0215298i
$497$	−0.117605	+	0.117605i	−0.00527533	+	0.00527533i
$498$	11.1765	+	28.6536i	0.500832	+	1.28400i
$499$	−13.6674			−0.611839			−0.305919	−	0.952057i	$-0.598964\pi$
$499$	−13.6674			−0.611839			−0.305919	+	0.952057i	$0.598964\pi$
$500$	−22.0325	+	3.81702i	−0.985323	+	0.170702i
$501$	21.9081			0.978780
$502$	−15.1940	−	38.9533i	−0.678142	−	1.73857i
$503$	−26.9531	+	26.9531i	−1.20178	+	1.20178i	−0.228153	+	0.973625i	$0.573269\pi$
$503$	−26.9531	+	26.9531i	−1.20178	+	1.20178i	−0.973625	+	0.228153i	$0.926731\pi$
$504$	−0.113070	−	0.329765i	−0.00503653	−	0.0146889i
$505$	−16.4906	+	19.0175i	−0.733822	+	0.846266i
$506$	9.74572	+	4.27633i	0.433250	+	0.190106i
$507$	11.4545	+	11.4545i	0.508713	+	0.508713i
$508$	−7.85361	−	0.326802i	−0.348448	−	0.0144995i
$509$			27.2015i			1.20568i	0.797860	+	0.602842i	$0.205965\pi$
$509$			27.2015i			1.20568i	−0.797860	+	0.602842i	$0.794035\pi$
$510$	−5.49509	−	1.95897i	−0.243327	−	0.0867448i
$511$		−	0.674513i		−	0.0298387i
$512$	−22.1511	+	4.61848i	−0.978948	+	0.204110i
$513$	−10.4858	−	10.4858i	−0.462958	−	0.462958i
$514$	9.77172	−	22.2697i	0.431012	−	0.982274i
$515$	1.09408	+	15.3742i	0.0482109	+	0.677470i
$516$	−10.0368	−	10.9084i	−0.441846	−	0.480214i
$517$	−7.89803	+	7.89803i	−0.347355	+	0.347355i
$518$	0.906996	−	0.353780i	0.0398511	−	0.0155442i
$519$	10.1540			0.445713
$520$	1.58562	−	3.92381i	0.0695340	−	0.172071i
$521$	44.8315			1.96411			0.982053	−	0.188607i	$-0.0603971\pi$
$521$	44.8315			1.96411			0.982053	+	0.188607i	$0.0603971\pi$
$522$	−10.4581	+	4.07925i	−0.457739	+	0.178544i
$523$	12.3555	−	12.3555i	0.540267	−	0.540267i	−0.383340	−	0.923607i	$-0.625226\pi$
$523$	12.3555	−	12.3555i	0.540267	−	0.540267i	0.923607	+	0.383340i	$0.125226\pi$
$524$	−7.88214	−	8.56660i	−0.344333	−	0.374234i
$525$	−0.0843928	−	0.589950i	−0.00368320	−	0.0257475i
$526$	−10.8674	+	24.7666i	−0.473840	+	1.07988i
$527$	−1.45846	−	1.45846i	−0.0635316	−	0.0635316i
$528$	3.94083	−	3.33431i	0.171502	−	0.145107i
$529$		−	33.6330i		−	1.46230i
$530$	10.5119	−	4.98670i	0.456606	−	0.216608i
$531$			10.2792i			0.446080i
$532$	−0.489251	−	0.0203586i	−0.0212117	−	0.000882655i
$533$	−2.43182	−	2.43182i	−0.105334	−	0.105334i
$534$	9.52084	+	4.17765i	0.412007	+	0.180785i
$535$	6.89420	−	0.490613i	0.298062	−	0.0212110i
$536$	20.7176	−	7.10364i	0.894864	−	0.306831i
$537$	3.79114	−	3.79114i	0.163600	−	0.163600i
$538$	−0.748748	−	1.91959i	−0.0322808	−	0.0827593i
$539$	−6.99147			−0.301144
$540$	−17.1607	+	18.2026i	−0.738477	+	0.783316i
$541$	−18.6640			−0.802428			−0.401214	−	0.915984i	$-0.631412\pi$
$541$	−18.6640			−0.802428			−0.401214	+	0.915984i	$0.631412\pi$
$542$	4.40136	+	11.2839i	0.189055	+	0.484685i
$543$	8.63902	−	8.63902i	0.370736	−	0.370736i
$544$	7.10942	+	3.85319i	0.304814	+	0.165204i
$545$	−16.0680	−	13.9330i	−0.688276	−	0.596824i
$546$	0.103287	+	0.0453214i	0.00442029	+	0.00193958i
$547$	1.26900	+	1.26900i	0.0542585	+	0.0542585i	0.733715	−	0.679457i	$-0.237785\pi$
$547$	1.26900	+	1.26900i	0.0542585	+	0.0542585i	−0.679457	+	0.733715i	$0.737785\pi$
$548$	−0.583540	+	14.0235i	−0.0249276	+	0.599053i
$549$			9.43389i			0.402628i
$550$	−6.15741	+	3.47654i	−0.262553	+	0.148240i
$551$			15.7678i			0.671733i
$552$	−24.6738	−	12.0738i	−1.05019	−	0.513894i
$553$	−0.933573	−	0.933573i	−0.0396995	−	0.0396995i
$554$	6.93644	−	15.8081i	0.294701	−	0.671622i
$555$	−16.2506	−	14.0914i	−0.689800	−	0.598145i
$556$	28.9005	−	26.5914i	1.22565	−	1.12773i
$557$	19.0631	−	19.0631i	0.807728	−	0.807728i	−0.176562	−	0.984290i	$-0.556497\pi$
$557$	19.0631	−	19.0631i	0.807728	−	0.807728i	0.984290	+	0.176562i	$0.0564975\pi$
$558$	−2.53695	+	0.989553i	−0.107398	+	0.0418911i
$559$	−3.84298			−0.162541
$560$	−0.0100216	+	0.826012i	−0.000423491	+	0.0349054i
$561$	−1.84482			−0.0778884
$562$	11.0339	−	4.30385i	0.465438	−	0.181547i
$563$	−16.5536	+	16.5536i	−0.697652	+	0.697652i	−0.963904	−	0.266251i	$-0.914215\pi$
$563$	−16.5536	+	16.5536i	−0.697652	+	0.697652i	0.266251	+	0.963904i	$0.414215\pi$
$564$	21.2153	−	19.5202i	0.893325	−	0.821950i
$565$	−34.9394	+	2.48640i	−1.46991	+	0.104604i
$566$	6.35372	−	14.4801i	0.267067	−	0.608643i
$567$	−0.209996	−	0.209996i	−0.00881899	−	0.00881899i
$568$	−4.57509	−	2.23876i	−0.191966	−	0.0939362i
$569$		−	35.6168i		−	1.49313i	−0.665310	−	0.746567i	$-0.731701\pi$
$569$		−	35.6168i		−	1.49313i	0.665310	−	0.746567i	$-0.268299\pi$
$570$	4.63695	+	9.77460i	0.194220	+	0.409413i
$571$			6.36739i			0.266467i	0.991085	+	0.133233i	$0.0425360\pi$
$571$			6.36739i			0.266467i	−0.991085	+	0.133233i	$0.957464\pi$
$572$	0.0556408	−	1.33714i	0.00232646	−	0.0559088i
$573$	17.0131	+	17.0131i	0.710730	+	0.710730i
$574$	0.614717	+	0.269732i	0.0256578	+	0.0112584i
$575$	30.1062	+	22.5708i	1.25552	+	0.941266i
$576$	8.42989	−	6.55106i	0.351245	−	0.272961i
$577$	7.84577	−	7.84577i	0.326624	−	0.326624i	−0.524677	−	0.851301i	$-0.675814\pi$
$577$	7.84577	−	7.84577i	0.326624	−	0.326624i	0.851301	+	0.524677i	$0.175814\pi$
$578$	7.68635	+	19.7057i	0.319710	+	0.819650i
$579$	−35.5501			−1.47741
$580$	26.5886	−	0.783412i	1.10403	−	0.0325294i
$581$	−1.55640			−0.0645702
$582$	−0.373647	−	0.957931i	−0.0154882	−	0.0397075i
$583$	2.60160	−	2.60160i	0.107747	−	0.107747i
$584$	19.5400	−	6.69988i	0.808572	−	0.277243i
$585$	0.141739	+	1.99175i	0.00586020	+	0.0823488i
$586$	−14.5478	−	6.38344i	−0.600965	−	0.263698i
$587$	5.28478	+	5.28478i	0.218126	+	0.218126i	0.807708	−	0.589582i	$-0.200708\pi$
$587$	5.28478	+	5.28478i	0.218126	+	0.218126i	−0.589582	+	0.807708i	$0.700708\pi$
$588$	18.0299	+	0.750254i	0.743540	+	0.0309399i
$589$			3.82499i			0.157606i
$590$	8.17920	−	22.9434i	0.336733	−	0.944564i
$591$			25.0719i			1.03132i
$592$	19.2578	+	22.7608i	0.791490	+	0.935462i
$593$	18.6597	+	18.6597i	0.766261	+	0.766261i	0.977446	−	0.211185i	$-0.0677323\pi$
$593$	18.6597	+	18.6597i	0.766261	+	0.766261i	−0.211185	+	0.977446i	$0.567732\pi$
$594$	−3.17868	+	7.24419i	−0.130423	+	0.297233i
$595$	0.193406	−	0.223042i	0.00792887	−	0.00914381i
$596$	31.5260	+	34.2636i	1.29135	+	1.40349i
$597$	8.54335	−	8.54335i	0.349656	−	0.349656i
$598$	−6.63468	+	2.58790i	−0.271312	+	0.105827i
$599$	−3.72864			−0.152348			−0.0761740	−	0.997095i	$-0.524270\pi$
$599$	−3.72864			−0.152348			−0.0761740	+	0.997095i	$0.524270\pi$
$600$	16.2520	−	8.30470i	0.663487	−	0.339038i
$601$	13.4770			0.549738			0.274869	−	0.961482i	$-0.411366\pi$
$601$	13.4770			0.549738			0.274869	+	0.961482i	$0.411366\pi$
$602$	0.698842	−	0.272588i	0.0284827	−	0.0111099i
$603$	−7.30701	+	7.30701i	−0.297564	+	0.297564i
$604$	10.4387	+	11.3452i	0.424745	+	0.461628i
$605$	−1.46492	+	1.68939i	−0.0595573	+	0.0686833i
$606$	8.25526	−	18.8137i	0.335347	−	0.764253i
$607$	−6.89298	−	6.89298i	−0.279778	−	0.279778i	0.553243	−	0.833020i	$-0.313390\pi$
$607$	−6.89298	−	6.89298i	−0.279778	−	0.279778i	−0.833020	+	0.553243i	$0.813390\pi$
$608$	−4.26992	−	14.3754i	−0.173168	−	0.582999i
$609$			0.708944i			0.0287279i
$610$	7.50658	−	21.0566i	0.303932	−	0.852557i
$611$		−	7.47407i		−	0.302369i
$612$	−3.81207	−	0.158627i	−0.154094	−	0.00641210i
$613$	27.1964	+	27.1964i	1.09845	+	1.09845i	0.994592	+	0.103862i	$0.0331201\pi$
$613$	27.1964	+	27.1964i	1.09845	+	1.09845i	0.103862	+	0.994592i	$0.466880\pi$
$614$	24.5057	+	10.7529i	0.988969	+	0.433950i
$615$	−1.05278	−	14.7938i	−0.0424520	−	0.596545i
$616$	0.0847274	+	0.247105i	0.00341376	+	0.00995615i
$617$	−21.2184	+	21.2184i	−0.854219	+	0.854219i	−0.990650	−	0.136431i	$-0.956437\pi$
$617$	−21.2184	+	21.2184i	−0.854219	+	0.854219i	0.136431	+	0.990650i	$0.456437\pi$
$618$	−4.57157	−	11.7203i	−0.183896	−	0.471459i
$619$	17.1338			0.688664			0.344332	−	0.938848i	$-0.388105\pi$
$619$	17.1338			0.688664			0.344332	+	0.938848i	$0.388105\pi$
$620$	6.44990	−	0.190041i	0.259034	−	0.00763225i
$621$	42.0965			1.68927
$622$	16.7132	+	42.8481i	0.670137	+	1.71805i
$623$	−0.372035	+	0.372035i	−0.0149053	+	0.0149053i
$624$	−0.286977	+	3.44231i	−0.0114883	+	0.137803i
$625$	−23.9973	+	7.00911i	−0.959894	+	0.280364i
$626$	−27.2870	−	11.9733i	−1.09061	−	0.478548i
$627$	2.41913	+	2.41913i	0.0966108	+	0.0966108i
$628$	1.52601	−	36.6726i	0.0608944	−	1.46340i
$629$		−	10.6550i		−	0.424843i
$630$	−0.167053	−	0.352145i	−0.00665555	−	0.0140298i
$631$			8.57760i			0.341469i	0.985317	+	0.170734i	$0.0546140\pi$
$631$			8.57760i			0.341469i	−0.985317	+	0.170734i	$0.945386\pi$
$632$	17.7716	−	36.3178i	0.706918	−	1.44465i
$633$	−17.4281	−	17.4281i	−0.692704	−	0.692704i
$634$	7.83455	−	17.8549i	0.311150	−	0.709108i
$635$	−8.76604	+	0.623819i	−0.347870	+	0.0247555i
$636$	−6.98829	+	6.42994i	−0.277104	+	0.254964i
$637$	3.30809	−	3.30809i	0.131071	−	0.131071i
$638$	7.83664	−	3.05673i	0.310255	−	0.121017i
$639$	2.40321			0.0950697
$640$	−24.0284	+	7.91439i	−0.949805	+	0.312844i
$641$	−16.8822			−0.666806			−0.333403	−	0.942784i	$-0.608197\pi$
$641$	−16.8822			−0.666806			−0.333403	+	0.942784i	$0.608197\pi$
$642$	−5.25566	+	2.05001i	−0.207424	+	0.0809073i
$643$	−13.6321	+	13.6321i	−0.537596	+	0.537596i	−0.922822	−	0.385226i	$-0.874123\pi$
$643$	−13.6321	+	13.6321i	−0.537596	+	0.537596i	0.385226	+	0.922822i	$0.374123\pi$
$644$	1.02295	−	0.941216i	0.0403098	−	0.0370891i
$645$	−12.5211	−	10.8574i	−0.493019	−	0.427511i
$646$	−2.15340	+	4.90757i	−0.0847242	+	0.193086i
$647$	7.57737	+	7.57737i	0.297897	+	0.297897i	0.840190	−	0.542293i	$-0.182444\pi$
$647$	7.57737	+	7.57737i	0.297897	+	0.297897i	−0.542293	+	0.840190i	$0.682444\pi$
$648$	3.99752	−	8.16926i	0.157037	−	0.320919i
$649$		−	7.70258i		−	0.302353i
$650$	1.26848	−	4.55841i	0.0497539	−	0.178795i
$651$			0.171977i			0.00674031i
$652$	−0.749207	+	18.0048i	−0.0293412	+	0.705120i
$653$	17.3117	+	17.3117i	0.677460	+	0.677460i	0.959425	−	0.281964i	$-0.0909860\pi$
$653$	17.3117	+	17.3117i	0.677460	+	0.677460i	−0.281964	+	0.959425i	$0.590986\pi$
$654$	15.8958	+	6.97491i	0.621574	+	0.272741i
$655$	−9.83314	−	8.52660i	−0.384212	−	0.333162i
$656$	−1.70795	+	20.4870i	−0.0666844	+	0.799883i
$657$	−6.89168	+	6.89168i	−0.268870	+	0.268870i
$658$	0.530147	+	1.35915i	0.0206673	+	0.0529853i
$659$	−13.6092			−0.530139			−0.265070	−	0.964229i	$-0.585395\pi$
$659$	−13.6092			−0.530139			−0.265070	+	0.964229i	$0.585395\pi$
$660$	3.95907	−	4.19946i	0.154107	−	0.163464i
$661$	−18.6616			−0.725854			−0.362927	−	0.931818i	$-0.618223\pi$
$661$	−18.6616			−0.725854			−0.362927	+	0.931818i	$0.618223\pi$
$662$	−5.26110	−	13.4880i	−0.204479	−	0.524228i
$663$	0.872896	−	0.872896i	0.0339005	−	0.0339005i
$664$	−15.4595	−	45.0874i	−0.599947	−	1.74973i
$665$	−0.546092	+	0.0388616i	−0.0211765	+	0.00150699i
$666$	−12.8817	−	5.65236i	−0.499155	−	0.219024i
$667$	−31.6510	−	31.6510i	−1.22553	−	1.22553i
$668$	−33.9225	−	1.41157i	−1.31250	−	0.0546153i
$669$		−	2.79122i		−	0.107915i
$670$	22.1236	−	10.4952i	0.854708	−	0.405463i
$671$		−	7.06915i		−	0.272902i
$672$	−0.191982	−	0.646337i	−0.00740585	−	0.0249330i
$673$	5.01293	+	5.01293i	0.193234	+	0.193234i	0.797092	−	0.603858i	$-0.206370\pi$
$673$	5.01293	+	5.01293i	0.193234	+	0.193234i	−0.603858	+	0.797092i	$0.706370\pi$
$674$	12.5759	−	28.6605i	0.484407	−	1.10396i
$675$	−16.7773	+	22.3786i	−0.645759	+	0.861352i
$676$	−16.9982	−	18.4742i	−0.653776	−	0.710547i
$677$	−17.2931	+	17.2931i	−0.664628	+	0.664628i	−0.956467	−	0.291839i	$-0.905733\pi$
$677$	−17.2931	+	17.2931i	−0.664628	+	0.664628i	0.291839	+	0.956467i	$0.405733\pi$
$678$	26.6354	−	10.3893i	1.02293	−	0.398999i
$679$	0.0520326			0.00199683
$680$	8.38239	+	3.38734i	0.321450	+	0.129898i
$681$	−13.6995			−0.524967
$682$	1.90103	−	0.741508i	0.0727940	−	0.0283938i
$683$	14.5193	−	14.5193i	0.555566	−	0.555566i	−0.372476	−	0.928042i	$-0.621491\pi$
$683$	14.5193	−	14.5193i	0.555566	−	0.555566i	0.928042	+	0.372476i	$0.121491\pi$
$684$	4.79080	+	5.20682i	0.183181	+	0.199088i
$685$	1.11390	+	15.6527i	0.0425597	+	0.598059i
$686$	−0.734299	+	1.67346i	−0.0280357	+	0.0638931i
$687$	−12.1865	−	12.1865i	−0.464946	−	0.464946i
$688$	14.8382	+	17.5372i	0.565700	+	0.668601i
$689$			2.46195i			0.0937928i
$690$	−28.9285	−	10.3129i	−1.10129	−	0.392605i
$691$			39.3921i			1.49855i	0.662261	+	0.749273i	$0.269597\pi$
$691$			39.3921i			1.49855i	−0.662261	+	0.749273i	$0.730403\pi$
$692$	−15.7225	−	0.654241i	−0.597682	−	0.0248705i
$693$	−0.0871529	−	0.0871529i	−0.00331067	−	0.00331067i
$694$	29.0225	+	12.7348i	1.10168	+	0.483405i
$695$	28.7655	−	33.1733i	1.09114	−	1.25833i
$696$	−20.5375	+	7.04188i	−0.778471	+	0.266922i
$697$	5.19507	−	5.19507i	0.196777	−	0.196777i
$698$	−11.7425	−	30.1046i	−0.444460	−	1.13948i
$699$	−7.88796			−0.298350
$700$	0.0926626	+	0.918918i	0.00350232	+	0.0347318i
$701$	−20.8661			−0.788101			−0.394050	−	0.919089i	$-0.628926\pi$
$701$	−20.8661			−0.788101			−0.394050	+	0.919089i	$0.628926\pi$
$702$	−1.92364	−	4.93169i	−0.0726031	−	0.186135i
$703$	−13.9720	+	13.9720i	−0.526965	+	0.526965i
$704$	−6.31682	+	4.90895i	−0.238074	+	0.185013i
$705$	21.1162	−	24.3519i	0.795283	−	0.917145i
$706$	2.39007	+	1.04874i	0.0899515	+	0.0394698i
$707$	0.735161	+	0.735161i	0.0276486	+	0.0276486i
$708$	−0.826563	+	19.8637i	−0.0310641	+	0.746525i
$709$			8.62821i			0.324039i	0.986788	+	0.162020i	$0.0518008\pi$
$709$			8.62821i			0.324039i	−0.986788	+	0.162020i	$0.948199\pi$
$710$	−5.36402	−	1.91225i	−0.201308	−	0.0717653i
$711$			19.0771i			0.715448i
$712$	−14.4729	−	7.08213i	−0.542396	−	0.265414i
$713$	−7.67797	−	7.67797i	−0.287542	−	0.287542i
$714$	−0.0968196	+	0.220651i	−0.00362338	+	0.00825767i
$715$	−0.106210	−	1.49249i	−0.00397204	−	0.0558160i
$716$	−6.11448	+	5.62594i	−0.228509	+	0.210251i
$717$	23.0733	−	23.0733i	0.861689	−	0.861689i
$718$	−6.34075	+	2.47325i	−0.236635	+	0.0923010i
$719$	11.5151			0.429441			0.214721	−	0.976676i	$-0.431116\pi$
$719$	11.5151			0.429441			0.214721	+	0.976676i	$0.431116\pi$
$720$	8.54198	−	8.33720i	0.318341	−	0.310709i
$721$	0.636619			0.0237089
$722$	−15.7740	+	6.15276i	−0.587048	+	0.228982i
$723$	10.0392	−	10.0392i	0.373362	−	0.373362i
$724$	−13.9333	+	12.8201i	−0.517827	+	0.476454i
$725$	29.4401	−	4.21143i	1.09338	−	0.156409i
$726$	0.733342	−	1.67128i	0.0272169	−	0.0620271i
$727$	5.97431	+	5.97431i	0.221575	+	0.221575i	0.809161	−	0.587586i	$-0.199922\pi$
$727$	5.97431	+	5.97431i	0.221575	+	0.221575i	−0.587586	+	0.809161i	$0.699922\pi$
$728$	−0.157010	−	0.0768308i	−0.00581918	−	0.00284754i
$729$			25.9484i			0.961051i
$730$	20.8661	−	9.89861i	0.772289	−	0.366364i
$731$		−	8.20971i		−	0.303647i
$732$	−0.758590	+	18.2302i	−0.0280383	+	0.673808i
$733$	−16.0677	−	16.0677i	−0.593475	−	0.593475i	0.345093	−	0.938568i	$-0.387847\pi$
$733$	−16.0677	−	16.0677i	−0.593475	−	0.593475i	−0.938568	+	0.345093i	$0.887847\pi$
$734$	16.6636	+	7.31181i	0.615064	+	0.269884i
$735$	20.1246	−	1.43213i	0.742307	−	0.0528249i
$736$	37.4270	+	20.2848i	1.37958	+	0.747709i
$737$	5.47540	−	5.47540i	0.201689	−	0.201689i
$738$	−3.52481	−	9.03665i	−0.129750	−	0.332644i
$739$	−33.7237			−1.24055			−0.620273	−	0.784386i	$-0.712978\pi$
$739$	−33.7237			−1.24055			−0.620273	+	0.784386i	$0.712978\pi$
$740$	24.2545	+	22.8662i	0.891615	+	0.840577i
$741$	−2.28928			−0.0840987
$742$	−0.174630	−	0.447703i	−0.00641086	−	0.0164357i
$743$	−30.4755	+	30.4755i	−1.11804	+	1.11804i	−0.126010	+	0.992029i	$0.540217\pi$
$743$	−30.4755	+	30.4755i	−1.11804	+	1.11804i	−0.992029	+	0.126010i	$0.959783\pi$
$744$	−4.98202	+	1.70823i	−0.182650	+	0.0626268i
$745$	39.3293	+	34.1036i	1.44092	+	1.24946i
$746$	−10.5785	−	4.64176i	−0.387307	−	0.169947i
$747$	15.9021	+	15.9021i	0.581828	+	0.581828i
$748$	2.85652	+	0.118865i	0.104445	+	0.00434612i
$749$		−	0.285476i		−	0.0104311i
$750$	17.0116	−	11.2683i	0.621177	−	0.411461i
$751$		−	44.0172i		−	1.60621i	−0.595837	−	0.803106i	$-0.703179\pi$
$751$		−	44.0172i		−	1.60621i	0.595837	−	0.803106i	$-0.296821\pi$
$752$	−34.1075	+	28.8582i	−1.24377	+	1.05235i
$753$	26.9798	+	26.9798i	0.983198	+	0.983198i
$754$	−2.26166	+	5.15432i	−0.0823649	+	0.187709i
$755$	13.0225	+	11.2922i	0.473937	+	0.410965i
$756$	0.699625	+	0.760378i	0.0254451	+	0.0276547i
$757$	17.1427	−	17.1427i	0.623063	−	0.623063i	−0.323251	−	0.946313i	$-0.604776\pi$
$757$	17.1427	−	17.1427i	0.623063	−	0.623063i	0.946313	+	0.323251i	$0.104776\pi$
$758$	−28.9288	+	11.2839i	−1.05074	+	0.409849i
$759$	−9.71192			−0.352520
$760$	−6.55007	−	15.4338i	−0.237596	−	0.559842i
$761$	−13.6856			−0.496104			−0.248052	−	0.968747i	$-0.579790\pi$
$761$	−13.6856			−0.496104			−0.248052	+	0.968747i	$0.579790\pi$
$762$	6.68263	−	2.60660i	0.242086	−	0.0944273i
$763$	−0.621142	+	0.621142i	−0.0224868	+	0.0224868i
$764$	−25.2469	−	27.4392i	−0.913400	−	0.992717i
$765$	−4.25496	+	0.302796i	−0.153838	+	0.0109476i
$766$	4.49025	−	10.2332i	0.162239	−	0.369742i
$767$	3.64456	+	3.64456i	0.131597	+	0.131597i
$768$	16.8169	−	11.9815i	0.606826	−	0.432347i
$769$			16.3426i			0.589329i	0.955601	+	0.294664i	$0.0952079\pi$
$769$			16.3426i			0.589329i	−0.955601	+	0.294664i	$0.904792\pi$
$770$	0.125179	+	0.263875i	0.00451113	+	0.00950938i
$771$			22.1925i			0.799242i
$772$	55.0459	+	2.29055i	1.98114	+	0.0824387i
$773$	13.7493	+	13.7493i	0.494529	+	0.494529i	0.909730	−	0.415201i	$-0.136289\pi$
$773$	13.7493	+	13.7493i	0.494529	+	0.494529i	−0.415201	+	0.909730i	$0.636289\pi$
$774$	−9.92537	−	4.35515i	−0.356760	−	0.156543i
$775$	7.14163	−	1.02162i	0.256535	−	0.0366975i
$776$	0.516835	+	1.50734i	0.0185533	+	0.0541103i
$777$	−0.628202	+	0.628202i	−0.0225366	+	0.0225366i
$778$	10.3892	+	26.6351i	0.372470	+	0.954913i
$779$	−13.6247			−0.488155
$780$	0.113741	+	3.86030i	0.00407257	+	0.138221i
$781$	−1.80081			−0.0644382
$782$	−5.52850	−	14.1736i	−0.197699	−	0.506847i
$783$	23.5269	−	23.5269i	0.840781	−	0.840781i
$784$	−27.8692	−	2.32339i	−0.995329	−	0.0829782i
$785$	−2.91294	−	40.9332i	−0.103967	−	1.46097i
$786$	9.72776	+	4.26845i	0.346978	+	0.152250i
$787$	4.58243	+	4.58243i	0.163346	+	0.163346i	0.784047	−	0.620701i	$-0.213152\pi$
$787$	4.58243	+	4.58243i	0.163346	+	0.163346i	−0.620701	+	0.784047i	$0.713152\pi$
$788$	1.61542	−	38.8214i	0.0575470	−	1.38295i
$789$		−	24.6808i		−	0.878658i
$790$	15.1797	−	42.5805i	0.540071	−	1.51495i
$791$			1.44677i			0.0514414i
$792$	1.65906	−	3.39042i	0.0589521	−	0.120473i
$793$	3.34485	+	3.34485i	0.118779	+	0.118779i
$794$	−12.5489	+	28.5989i	−0.445345	+	1.01494i
$795$	−6.95566	+	8.02148i	−0.246692	+	0.284493i
$796$	−13.7790	+	12.6781i	−0.488384	+	0.449363i
$797$	−21.2355	+	21.2355i	−0.752199	+	0.752199i	−0.974889	−	0.222690i	$-0.928516\pi$
$797$	−21.2355	+	21.2355i	−0.752199	+	0.752199i	0.222690	+	0.974889i	$0.428516\pi$
$798$	0.416303	−	0.162382i	0.0147370	−	0.00574825i
$799$	15.9668			0.564864
$800$	−25.6998	+	11.8119i	−0.908625	+	0.417613i
$801$	7.60237			0.268617
$802$	2.44349	−	0.953098i	0.0862825	−	0.0336551i
$803$	5.16419	−	5.16419i	0.182240	−	0.182240i
$804$	−14.7078	+	13.5326i	−0.518703	+	0.477259i
$805$	1.01817	−	1.17419i	0.0358858	−	0.0413846i
$806$	−0.548638	+	1.25034i	−0.0193250	+	0.0440415i
$807$	1.32954	+	1.32954i	0.0468021	+	0.0468021i
$808$	−13.9947	+	28.5992i	−0.492330	+	1.00612i
$809$		−	43.2798i		−	1.52164i	−0.648964	−	0.760819i	$-0.724798\pi$
$809$		−	43.2798i		−	1.52164i	0.648964	−	0.760819i	$-0.275202\pi$
$810$	3.41450	−	9.57796i	0.119973	−	0.336535i
$811$		−	36.0310i		−	1.26522i	−0.774470	−	0.632611i	$-0.781983\pi$
$811$		−	36.0310i		−	1.26522i	0.774470	−	0.632611i	$-0.218017\pi$
$812$	0.0456784	−	1.09773i	0.00160300	−	0.0385228i
$813$	−7.81544	−	7.81544i	−0.274099	−	0.274099i
$814$	9.65271	+	4.23552i	0.338327	+	0.148455i
$815$	1.43013	+	20.0965i	0.0500953	+	0.703950i
$816$	−7.35377	−	0.613066i	−0.257433	−	0.0214616i
$817$	−10.7655	+	10.7655i	−0.376636	+	0.376636i
$818$	0.221973	+	0.569080i	0.00776111	+	0.0198974i
$819$	0.0824747			0.00288190
$820$	0.676931	+	22.9747i	0.0236395	+	0.802310i
$821$	3.91178			0.136522			0.0682610	−	0.997667i	$-0.478255\pi$
$821$	3.91178			0.136522			0.0682610	+	0.997667i	$0.478255\pi$
$822$	−4.65437	−	11.9325i	−0.162340	−	0.416195i
$823$	−17.9254	+	17.9254i	−0.624840	+	0.624840i	−0.946765	−	0.321925i	$-0.895670\pi$
$823$	−17.9254	+	17.9254i	−0.624840	+	0.624840i	0.321925	+	0.946765i	$0.395670\pi$
$824$	6.32348	+	18.4423i	0.220289	+	0.642466i
$825$	3.87063	−	5.16288i	0.134758	−	0.179748i
$826$	−0.921274	−	0.404246i	−0.0320552	−	0.0140655i
$827$	−1.97704	−	1.97704i	−0.0687485	−	0.0687485i	0.671897	−	0.740645i	$-0.265480\pi$
$827$	−1.97704	−	1.97704i	−0.0687485	−	0.0687485i	−0.740645	+	0.671897i	$0.765480\pi$
$828$	−20.0684	−	0.835079i	−0.697425	−	0.0290210i
$829$			45.4079i			1.57708i	0.614983	+	0.788540i	$0.289163\pi$
$829$			45.4079i			1.57708i	−0.614983	+	0.788540i	$0.710837\pi$
$830$	−22.8404	−	48.1472i	−0.792803	−	1.67121i
$831$			15.7533i			0.546475i
$832$	0.666150	−	5.31159i	0.0230946	−	0.184146i
$833$	7.06703	+	7.06703i	0.244858	+	0.244858i
$834$	−14.4001	+	32.8178i	−0.498636	+	1.13639i
$835$	−37.8636	+	2.69449i	−1.31032	+	0.0932467i
$836$	−3.58992	−	3.90166i	−0.124160	−	0.134942i
$837$	5.70719	−	5.70719i	0.197269	−	0.197269i
$838$	−46.3333	+	18.0726i	−1.60056	+	0.624308i
$839$	34.1689			1.17964			0.589822	−	0.807534i	$-0.299198\pi$
$839$	34.1689			1.17964			0.589822	+	0.807534i	$0.299198\pi$
$840$	−0.294500	−	0.693924i	−0.0101612	−	0.0239427i
$841$	−6.37824			−0.219939
$842$	30.0591	−	11.7247i	1.03590	−	0.404061i
$843$	−7.64229	+	7.64229i	−0.263215	+	0.263215i
$844$	25.8628	+	28.1086i	0.890234	+	0.967539i
$845$	−21.2056	−	18.3880i	−0.729494	−	0.632565i
$846$	8.47019	−	19.3035i	0.291211	−	0.663668i
$847$	0.0653068	+	0.0653068i	0.00224397	+	0.00224397i
$848$	11.2350	−	9.50586i	0.385811	−	0.326433i
$849$			14.4299i			0.495232i
$850$	9.73807	+	2.70984i	0.334013	+	0.0929467i
$851$		−	56.0925i		−	1.92283i
$852$	4.64402	+	0.193245i	0.159101	+	0.00662047i
$853$	10.3398	+	10.3398i	0.354027	+	0.354027i	0.861606	−	0.507578i	$-0.169459\pi$
$853$	10.3398	+	10.3398i	0.354027	+	0.354027i	−0.507578	+	0.861606i	$0.669459\pi$
$854$	−0.845512	−	0.371002i	−0.0289328	−	0.0126954i
$855$	5.97663	+	5.18251i	0.204396	+	0.177238i
$856$	8.26997	−	2.83560i	0.282662	−	0.0969190i
$857$	23.1527	−	23.1527i	0.790880	−	0.790880i	−0.190758	−	0.981637i	$-0.561094\pi$
$857$	23.1527	−	23.1527i	0.790880	−	0.790880i	0.981637	+	0.190758i	$0.0610944\pi$
$858$	0.443796	+	1.13777i	0.0151509	+	0.0388429i
$859$	−19.8852			−0.678473			−0.339237	−	0.940701i	$-0.610169\pi$
$859$	−19.8852			−0.678473			−0.339237	+	0.940701i	$0.610169\pi$
$860$	18.6882	+	17.6184i	0.637262	+	0.600783i
$861$	−0.612585			−0.0208768
$862$	15.5964	+	39.9849i	0.531215	+	1.36189i
$863$	17.7638	−	17.7638i	0.604686	−	0.604686i	−0.336866	−	0.941553i	$-0.609367\pi$
$863$	17.7638	−	17.7638i	0.604686	−	0.604686i	0.941553	+	0.336866i	$0.109367\pi$
$864$	−15.0781	+	27.8203i	−0.512969	+	0.946465i
$865$	−17.5492	+	1.24885i	−0.596690	+	0.0424623i
$866$	−20.7173	−	9.09054i	−0.704002	−	0.308909i
$867$	−13.6485	−	13.6485i	−0.463529	−	0.463529i
$868$	0.0110808	−	0.266290i	0.000376105	−	0.00903846i
$869$		−	14.2952i		−	0.484931i
$870$	−21.9312	+	10.4039i	−0.743538	+	0.352725i
$871$			5.18149i			0.175568i
$872$	−24.1637	−	11.8242i	−0.818285	−	0.400417i
$873$	−0.531631	−	0.531631i	−0.0179930	−	0.0179930i
$874$	−11.3364	+	25.8356i	−0.383459	+	0.873901i
$875$	0.218414	+	1.00923i	0.00738374	+	0.0341181i
$876$	−13.8718	+	12.7634i	−0.468684	+	0.431237i
$877$	−26.9817	+	26.9817i	−0.911106	+	0.911106i	−0.996359	−	0.0852533i	$-0.972830\pi$
$877$	−26.9817	+	26.9817i	−0.911106	+	0.911106i	0.0852533	+	0.996359i	$0.472830\pi$
$878$	51.3563	−	20.0319i	1.73319	−	0.676042i
$879$	14.4974			0.488984
$880$	−6.40082	+	6.24736i	−0.215772	+	0.210599i
$881$	−29.0197			−0.977698			−0.488849	−	0.872368i	$-0.662583\pi$
$881$	−29.0197			−0.977698			−0.488849	+	0.872368i	$0.662583\pi$
$882$	12.2929	−	4.79492i	0.413923	−	0.161453i
$883$	12.7981	−	12.7981i	0.430690	−	0.430690i	−0.458173	−	0.888863i	$-0.651496\pi$
$883$	12.7981	−	12.7981i	0.430690	−	0.430690i	0.888863	+	0.458173i	$0.151496\pi$
$884$	−1.40784	+	1.29535i	−0.0473507	+	0.0435674i
$885$	1.57779	+	22.1715i	0.0530369	+	0.745286i
$886$	12.0633	−	27.4922i	0.405274	−	0.923618i
$887$	5.86669	+	5.86669i	0.196984	+	0.196984i	0.798706	−	0.601722i	$-0.205518\pi$
$887$	5.86669	+	5.86669i	0.196984	+	0.196984i	−0.601722	+	0.798706i	$0.705518\pi$
$888$	−24.4383	−	11.9586i	−0.820096	−	0.401303i
$889$			0.362985i			0.0121741i
$890$	−16.9686	−	6.04924i	−0.568790	−	0.202771i
$891$		−	3.21553i		−	0.107724i
$892$	−0.179843	+	4.32193i	−0.00602157	+	0.144709i
$893$	−20.9374	−	20.9374i	−0.700643	−	0.700643i
$894$	−38.9079	−	17.0724i	−1.30127	−	0.570986i
$895$	−6.08593	+	7.01848i	−0.203430	+	0.234602i
$896$	0.255620	+	1.01316i	0.00853968	+	0.0338473i
$897$	4.59530	−	4.59530i	0.153433	−	0.153433i
$898$	17.8681	+	45.8089i	0.596266	+	1.52866i
$899$	−8.58212			−0.286230
$900$	8.44207	−	10.3356i	0.281402	−	0.344520i
$901$	−5.25943			−0.175217
$902$	2.64126	+	6.77149i	0.0879445	+	0.225466i
$903$	−0.484031	+	0.484031i	−0.0161075	+	0.0161075i
$904$	−41.9117	+	14.3707i	−1.39396	+	0.477962i
$905$	−13.8682	+	15.9933i	−0.460996	+	0.531635i
$906$	−12.8829	−	5.65291i	−0.428007	−	0.187805i
$907$	19.7696	+	19.7696i	0.656438	+	0.656438i	0.954535	−	0.298097i	$-0.0963520\pi$
$907$	19.7696	+	19.7696i	0.656438	+	0.656438i	−0.298097	+	0.954535i	$0.596352\pi$
$908$	21.2124	+	0.882682i	0.703958	+	0.0292928i
$909$		−	15.0227i		−	0.498271i
$910$	−0.184085	−	0.0656254i	−0.00610235	−	0.00217546i
$911$		−	22.0501i		−	0.730554i	−0.930899	−	0.365277i	$-0.880974\pi$
$911$		−	22.0501i		−	0.730554i	0.930899	−	0.365277i	$-0.119026\pi$
$912$	8.83916	+	10.4470i	0.292694	+	0.345935i
$913$	−11.9160	−	11.9160i	−0.394363	−	0.394363i
$914$	5.56196	−	12.6757i	0.183973	−	0.419273i
$915$	1.44804	+	20.3482i	0.0478708	+	0.672690i
$916$	18.0845	+	19.6549i	0.597528	+	0.649415i
$917$	−0.380121	+	0.380121i	−0.0125527	+	0.0125527i
$918$	10.5355	−	4.10945i	0.347724	−	0.135632i
$919$	8.22053			0.271170			0.135585	−	0.990766i	$-0.456709\pi$
$919$	8.22053			0.271170			0.135585	+	0.990766i	$0.456709\pi$
$920$	44.1285	+	17.8324i	1.45487	+	0.587917i
$921$	−24.4207			−0.804690
$922$	4.79277	−	1.86945i	0.157842	−	0.0615672i
$923$	0.852075	−	0.852075i	0.0280464	−	0.0280464i
$924$	−0.161408	−	0.175424i	−0.00530993	−	0.00577103i
$925$	29.8189	+	22.3554i	0.980440	+	0.735040i
$926$	6.04696	−	13.7810i	0.198716	−	0.452871i
$927$	−6.50450	−	6.50450i	−0.213636	−	0.213636i
$928$	32.2540	−	9.58041i	1.05879	−	0.314492i
$929$			51.6745i			1.69539i	0.530487	+	0.847693i	$0.322009\pi$
$929$			51.6745i			1.69539i	−0.530487	+	0.847693i	$0.677991\pi$
$930$	−5.32011	+	2.52380i	−0.174453	+	0.0827586i
$931$		−	18.5342i		−	0.607432i
$932$	12.2137	+	0.508234i	0.400074	+	0.0166478i
$933$	−29.6773	−	29.6773i	−0.971592	−	0.971592i
$934$	4.94755	+	2.17094i	0.161889	+	0.0710352i
$935$	3.18839	−	0.226896i	0.104272	−	0.00742029i
$936$	0.819214	+	2.38922i	0.0267768	+	0.0780940i
$937$	−29.9561	+	29.9561i	−0.978623	+	0.978623i	−0.999776	−	0.0211534i	$-0.993266\pi$
$937$	−29.9561	+	29.9561i	−0.978623	+	0.978623i	0.0211534	+	0.999776i	$0.493266\pi$
$938$	−0.367531	−	0.942250i	−0.0120003	−	0.0307656i
$939$	27.1924			0.887389
$940$	−34.2655	+	36.3460i	−1.11762	+	1.18548i
$941$	−54.7464			−1.78468			−0.892340	−	0.451363i	$-0.850938\pi$
$941$	−54.7464			−1.78468			−0.892340	+	0.451363i	$0.850938\pi$
$942$	12.1716	+	31.2047i	0.396572	+	1.01670i
$943$	27.3491	−	27.3491i	0.890608	−	0.890608i
$944$	2.55971	−	30.7038i	0.0833113	−	0.999324i
$945$	0.872797	+	0.756828i	0.0283921	+	0.0246196i
$946$	7.43743	+	3.26347i	0.241812	+	0.106105i
$947$	−0.414386	−	0.414386i	−0.0134657	−	0.0134657i	0.700342	−	0.713808i	$-0.253031\pi$
$947$	−0.414386	−	0.414386i	−0.0134657	−	0.0134657i	−0.713808	+	0.700342i	$0.753031\pi$
$948$	−1.53401	+	36.8650i	−0.0498225	+	1.19732i
$949$			4.88698i			0.158638i
$950$	−9.21620	−	16.3231i	−0.299013	−	0.529591i
$951$			17.7930i			0.576977i
$952$	0.164133	−	0.335419i	0.00531957	−	0.0108710i
$953$	−7.83757	−	7.83757i	−0.253884	−	0.253884i	0.568677	−	0.822561i	$-0.307455\pi$
$953$	−7.83757	−	7.83757i	−0.253884	−	0.253884i	−0.822561	+	0.568677i	$0.807455\pi$
$954$	−2.79007	+	6.35855i	−0.0903318	+	0.205866i
$955$	−31.4960	−	27.3111i	−1.01919	−	0.883767i
$956$	−37.2135	+	34.2402i	−1.20357	+	1.10741i
$957$	−5.42780	+	5.42780i	−0.175456	+	0.175456i
$958$	−8.47481	+	3.30566i	−0.273809	+	0.106801i
$959$	0.648149			0.0209298
$960$	17.1771	−	15.4241i	0.554388	−	0.497810i
$961$	28.9181			0.932843
$962$	−6.57137	+	2.56320i	−0.211869	+	0.0826410i
$963$	−2.91678	+	2.91678i	−0.0939920	+	0.0939920i
$964$	−16.1916	+	14.8979i	−0.521495	+	0.479828i
$965$	61.4410	−	4.37234i	1.97786	−	0.140750i
$966$	−0.509700	+	1.16160i	−0.0163993	+	0.0373740i
$967$	−21.2528	−	21.2528i	−0.683442	−	0.683442i	0.277332	−	0.960774i	$-0.410550\pi$
$967$	−21.2528	−	21.2528i	−0.683442	−	0.683442i	−0.960774	+	0.277332i	$0.910550\pi$
$968$	−1.24319	+	2.54057i	−0.0399577	+	0.0816569i
$969$		−	4.89056i		−	0.157107i
$970$	0.763589	+	1.60963i	0.0245174	+	0.0516821i
$971$		−	40.2688i		−	1.29229i	−0.763215	−	0.646144i	$-0.776381\pi$
$971$		−	40.2688i		−	1.29229i	0.763215	−	0.646144i	$-0.223619\pi$
$972$	1.05035	−	25.2418i	0.0336900	−	0.809630i
$973$	−1.28238	−	1.28238i	−0.0411114	−	0.0411114i
$974$	−19.7090	−	8.64813i	−0.631518	−	0.277104i
$975$	0.611442	+	4.27430i	0.0195818	+	0.136887i
$976$	2.34920	−	28.1788i	0.0751962	−	0.901983i
$977$	23.6559	−	23.6559i	0.756819	−	0.756819i	−0.218923	−	0.975742i	$-0.570255\pi$
$977$	23.6559	−	23.6559i	0.756819	−	0.756819i	0.975742	+	0.218923i	$0.0702545\pi$
$978$	−5.97575	−	15.3202i	−0.191083	−	0.489886i
$979$	−5.69673			−0.182068
$980$	−31.2532	+	0.920853i	−0.998348	+	0.0294156i
$981$	12.6927			0.405248
$982$	−8.78902	−	22.5327i	−0.280469	−	0.719047i
$983$	2.53162	−	2.53162i	0.0807461	−	0.0807461i	−0.665580	−	0.746326i	$-0.731816\pi$
$983$	2.53162	−	2.53162i	0.0807461	−	0.0807461i	0.746326	+	0.665580i	$0.231816\pi$
$984$	−6.08475	−	17.7460i	−0.193975	−	0.565723i
$985$	−3.08361	−	43.3316i	−0.0982521	−	1.38066i
$986$	−11.0111	−	4.83156i	−0.350665	−	0.153868i
$987$	−0.941375	−	0.941375i	−0.0299643	−	0.0299643i
$988$	3.54472	+	0.147502i	0.112773	+	0.00469266i
$989$		−	43.2194i		−	1.37430i
$990$	1.41709	−	3.97507i	0.0450381	−	0.126336i
$991$			14.9715i			0.475586i	0.971316	+	0.237793i	$0.0764240\pi$
$991$			14.9715i			0.475586i	−0.971316	+	0.237793i	$0.923576\pi$
$992$	7.82423	−	2.32403i	0.248420	−	0.0737881i
$993$	9.34206	+	9.34206i	0.296461	+	0.296461i
$994$	−0.0945102	+	0.215388i	−0.00299768	+	0.00683170i
$995$	−13.7147	+	15.8162i	−0.434784	+	0.501406i
$996$	29.4509	+	32.0083i	0.933186	+	1.01422i
$997$	23.1266	−	23.1266i	0.732426	−	0.732426i	−0.238674	−	0.971100i	$-0.576713\pi$
$997$	23.1266	−	23.1266i	0.732426	−	0.732426i	0.971100	+	0.238674i	$0.0767127\pi$
$998$	−18.0073	+	7.02387i	−0.570011	+	0.222337i
$999$	41.6947			1.31916

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.c.23.13	✓	28
4.3	odd	2		220.2.l.d.23.9	yes	28
5.2	odd	4		220.2.l.d.67.9	yes	28
20.7	even	4	inner	220.2.l.c.67.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.13	✓	28	1.1	even	1	trivial
220.2.l.c.67.13	yes	28	20.7	even	4	inner
220.2.l.d.23.9	yes	28	4.3	odd	2
220.2.l.d.67.9	yes	28	5.2	odd	4

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31753 - 0.513913i) q^{2} +(-0.912547 + 0.912547i) q^{3} +(1.47179 - 1.35419i) q^{4} +(1.46492 - 1.68939i) q^{5} +(-0.733342 + 1.67128i) q^{6} +(-0.0653068 - 0.0653068i) q^{7} +(1.24319 - 2.54057i) q^{8} +1.33451i q^{9} +(1.06188 - 2.97866i) q^{10} -1.00000i q^{11} +(-0.107310 + 2.57884i) q^{12} +(0.473161 + 0.473161i) q^{13} +(-0.119606 - 0.0524819i) q^{14} +(0.204839 + 2.87845i) q^{15} +(0.332318 - 3.98617i) q^{16} +(-1.01081 + 1.01081i) q^{17} +(0.685824 + 1.75827i) q^{18} +2.65097 q^{19} +(-0.131711 - 4.47020i) q^{20} +0.119191 q^{21} +(-0.513913 - 1.31753i) q^{22} +(-5.32132 + 5.32132i) q^{23} +(1.18392 + 3.45286i) q^{24} +(-0.708046 - 4.94961i) q^{25} +(0.866568 + 0.380242i) q^{26} +(-3.95545 - 3.95545i) q^{27} +(-0.184556 - 0.00767967i) q^{28} +5.94796i q^{29} +(1.74915 + 3.68718i) q^{30} +1.44287i q^{31} +(-1.61070 - 5.42270i) q^{32} +(0.912547 + 0.912547i) q^{33} +(-0.812306 + 1.85124i) q^{34} +(-0.205997 + 0.0146594i) q^{35} +(1.80719 + 1.96412i) q^{36} +(-5.27054 + 5.27054i) q^{37} +(3.49274 - 1.36237i) q^{38} -0.863563 q^{39} +(-2.47082 - 5.82194i) q^{40} -5.13952 q^{41} +(0.157038 - 0.0612538i) q^{42} +(-4.06096 + 4.06096i) q^{43} +(-1.35419 - 1.47179i) q^{44} +(2.25451 + 1.95495i) q^{45} +(-4.27633 + 9.74572i) q^{46} +(-7.89803 - 7.89803i) q^{47} +(3.33431 + 3.94083i) q^{48} -6.99147i q^{49} +(-3.47654 - 6.15741i) q^{50} -1.84482i q^{51} +(1.33714 + 0.0556408i) q^{52} +(2.60160 + 2.60160i) q^{53} +(-7.24419 - 3.17868i) q^{54} +(-1.68939 - 1.46492i) q^{55} +(-0.247105 + 0.0847274i) q^{56} +(-2.41913 + 2.41913i) q^{57} +(3.05673 + 7.83664i) q^{58} +7.70258 q^{59} +(4.19946 + 3.95907i) q^{60} +7.06915 q^{61} +(0.741508 + 1.90103i) q^{62} +(0.0871529 - 0.0871529i) q^{63} +(-4.90895 - 6.31682i) q^{64} +(1.49249 - 0.106210i) q^{65} +(1.67128 + 0.733342i) q^{66} +(5.47540 + 5.47540i) q^{67} +(-0.118865 + 2.85652i) q^{68} -9.71192i q^{69} +(-0.263875 + 0.125179i) q^{70} -1.80081i q^{71} +(3.39042 + 1.65906i) q^{72} +(5.16419 + 5.16419i) q^{73} +(-4.23552 + 9.65271i) q^{74} +(5.16288 + 3.87063i) q^{75} +(3.90166 - 3.58992i) q^{76} +(-0.0653068 + 0.0653068i) q^{77} +(-1.13777 + 0.443796i) q^{78} +14.2952 q^{79} +(-6.24736 - 6.40082i) q^{80} +3.21553 q^{81} +(-6.77149 + 2.64126i) q^{82} +(11.9160 - 11.9160i) q^{83} +(0.175424 - 0.161408i) q^{84} +(0.226896 + 3.18839i) q^{85} +(-3.26347 + 7.43743i) q^{86} +(-5.42780 - 5.42780i) q^{87} +(-2.54057 - 1.24319i) q^{88} -5.69673i q^{89} +(3.97507 + 1.41709i) q^{90} -0.0618012i q^{91} +(-0.625755 + 15.0380i) q^{92} +(-1.31668 - 1.31668i) q^{93} +(-14.4648 - 6.34702i) q^{94} +(3.88344 - 4.47850i) q^{95} +(6.41831 + 3.47862i) q^{96} +(-0.398370 + 0.398370i) q^{97} +(-3.59300 - 9.21149i) q^{98} +1.33451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

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