LMFDB - Embedded newform 138.2.e.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	138.49
Dual form			138.2.e.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.698939 - 0.806618i) q^{5} +(0.959493 + 0.281733i) q^{6} +(3.72270 - 2.39243i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.698939 - 0.806618i) q^{5} +(0.959493 + 0.281733i) q^{6} +(3.72270 - 2.39243i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-0.897877 - 0.577031i) q^{10} +(0.234769 - 1.63285i) q^{11} +(0.142315 - 0.989821i) q^{12} +(4.60260 + 2.95791i) q^{13} +(-2.89788 - 3.34433i) q^{14} +(0.443376 + 0.970858i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-3.76709 - 1.10612i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(-6.33409 + 1.85986i) q^{19} +(-0.443376 + 0.970858i) q^{20} +(0.629769 + 4.38014i) q^{21} -1.64964 q^{22} +(-4.78492 + 0.323343i) q^{23} -1.00000 q^{24} +(0.549456 + 3.82155i) q^{25} +(2.27279 - 4.97671i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-2.89788 + 3.34433i) q^{28} +(6.14024 + 1.80294i) q^{29} +(0.897877 - 0.577031i) q^{30} +(-1.25244 - 2.74246i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.38777 + 0.891865i) q^{33} +(-0.558746 + 3.88617i) q^{34} +(0.672158 - 4.67496i) q^{35} +(0.841254 + 0.540641i) q^{36} +(1.44774 + 1.67078i) q^{37} +(2.74236 + 6.00493i) q^{38} +(-4.60260 + 2.95791i) q^{39} +(1.02408 + 0.300696i) q^{40} +(-2.67954 + 3.09235i) q^{41} +(4.24593 - 1.24672i) q^{42} +(-1.21021 + 2.64998i) q^{43} +(0.234769 + 1.63285i) q^{44} -1.06731 q^{45} +(1.00102 + 4.69020i) q^{46} -9.62306 q^{47} +(0.142315 + 0.989821i) q^{48} +(5.22685 - 11.4452i) q^{49} +(3.70446 - 1.08773i) q^{50} +(2.57107 - 2.96717i) q^{51} +(-5.24950 - 1.54139i) q^{52} +(-1.87633 + 1.20584i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(-1.15300 - 1.33063i) q^{55} +(3.72270 + 2.39243i) q^{56} +(0.939490 - 6.53430i) q^{57} +(0.910738 - 6.33432i) q^{58} +(8.20397 + 5.27237i) q^{59} +(-0.698939 - 0.806618i) q^{60} +(-0.647821 - 1.41853i) q^{61} +(-2.53631 + 1.62999i) q^{62} +(-4.24593 - 1.24672i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(5.60284 - 1.64514i) q^{65} +(0.685287 - 1.50057i) q^{66} +(-1.71423 - 11.9227i) q^{67} +3.92613 q^{68} +(1.69360 - 4.48684i) q^{69} -4.72304 q^{70} +(0.749168 + 5.21058i) q^{71} +(0.415415 - 0.909632i) q^{72} +(-6.89449 + 2.02441i) q^{73} +(1.44774 - 1.67078i) q^{74} +(-3.70446 - 1.08773i) q^{75} +(5.55353 - 3.56904i) q^{76} +(-3.03252 - 6.64029i) q^{77} +(3.58282 + 4.13480i) q^{78} +(2.26617 + 1.45638i) q^{79} +(0.151894 - 1.05645i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(3.44222 + 2.21218i) q^{82} +(-3.62690 - 4.18567i) q^{83} +(-1.83829 - 4.02529i) q^{84} +(-3.52518 + 2.26550i) q^{85} +(2.79524 + 0.820757i) q^{86} +(-4.19075 + 4.83639i) q^{87} +(1.58282 - 0.464758i) q^{88} +(4.70504 - 10.3026i) q^{89} +(0.151894 + 1.05645i) q^{90} +24.2107 q^{91} +(4.50000 - 1.65831i) q^{92} +3.01491 q^{93} +(1.36950 + 9.52511i) q^{94} +(-2.92694 + 6.40911i) q^{95} +(0.959493 - 0.281733i) q^{96} +(-7.84485 + 9.05344i) q^{97} +(-12.0726 - 3.54482i) q^{98} +(-1.38777 + 0.891865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9	$ 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21} + 22 q^{22} - 10 q^{23} - 10 q^{24} - 43 q^{25} - 9 q^{26} + q^{27} - 11 q^{28} + 13 q^{29} - 9 q^{30} + 8 q^{31} - q^{32} + 22 q^{33} + 9 q^{34} - q^{36} - 13 q^{37} - 3 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} - 8 q^{43} + 11 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + q^{48} + 29 q^{49} + 23 q^{50} - 9 q^{51} + 2 q^{52} - 35 q^{53} + q^{54} - 11 q^{55} + 3 q^{57} + 13 q^{58} + 37 q^{59} + 2 q^{60} - 2 q^{61} + 8 q^{62} - q^{64} + 37 q^{65} + 14 q^{67} - 2 q^{68} - q^{69} - 22 q^{70} + 44 q^{71} - q^{72} - 49 q^{73} - 13 q^{74} - 23 q^{75} + 8 q^{76} + 44 q^{77} + 20 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} + 12 q^{82} - 17 q^{83} - 11 q^{84} - 37 q^{85} + 14 q^{86} - 2 q^{87} + 59 q^{89} - 2 q^{90} + 66 q^{91} + 45 q^{92} + 36 q^{93} - 19 q^{94} - 28 q^{95} + q^{96} - 21 q^{97} - 26 q^{98} - 22 q^{99}+O(q^{100}) $ 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9 + 9 * q^10 + 11 * q^11 + q^12 + 13 * q^13 - 11 * q^14 + 13 * q^15 - q^16 - 24 * q^17 - q^18 - 14 * q^19 - 13 * q^20 + 11 * q^21 + 22 * q^22 - 10 * q^23 - 10 * q^24 - 43 * q^25 - 9 * q^26 + q^27 - 11 * q^28 + 13 * q^29 - 9 * q^30 + 8 * q^31 - q^32 + 22 * q^33 + 9 * q^34 - q^36 - 13 * q^37 - 3 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 - 8 * q^43 + 11 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + q^48 + 29 * q^49 + 23 * q^50 - 9 * q^51 + 2 * q^52 - 35 * q^53 + q^54 - 11 * q^55 + 3 * q^57 + 13 * q^58 + 37 * q^59 + 2 * q^60 - 2 * q^61 + 8 * q^62 - q^64 + 37 * q^65 + 14 * q^67 - 2 * q^68 - q^69 - 22 * q^70 + 44 * q^71 - q^72 - 49 * q^73 - 13 * q^74 - 23 * q^75 + 8 * q^76 + 44 * q^77 + 20 * q^78 - 8 * q^79 - 2 * q^80 - q^81 + 12 * q^82 - 17 * q^83 - 11 * q^84 - 37 * q^85 + 14 * q^86 - 2 * q^87 + 59 * q^89 - 2 * q^90 + 66 * q^91 + 45 * q^92 + 36 * q^93 - 19 * q^94 - 28 * q^95 + q^96 - 21 * q^97 - 26 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	0.698939	−	0.806618i	0.312575	−	0.360731i	−0.577624	−	0.816303i	$-0.696020\pi$
$5$	0.698939	−	0.806618i	0.312575	−	0.360731i	0.890199	+	0.455572i	$0.150565\pi$
$6$	0.959493	+	0.281733i	0.391711	+	0.115017i
$7$	3.72270	−	2.39243i	1.40705	−	0.904255i	0.407090	−	0.913388i	$-0.366544\pi$
$7$	3.72270	−	2.39243i	1.40705	−	0.904255i	0.999958	+	0.00913325i	$0.00290725\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	−0.897877	−	0.577031i	−0.283934	−	0.182473i
$11$	0.234769	−	1.63285i	0.0707855	−	0.492324i	−0.923331	−	0.384005i	$-0.874544\pi$
$11$	0.234769	−	1.63285i	0.0707855	−	0.492324i	0.994116	−	0.108318i	$-0.0345465\pi$
$12$	0.142315	−	0.989821i	0.0410828	−	0.285737i
$13$	4.60260	+	2.95791i	1.27653	+	0.820377i	0.990456	−	0.137830i	$-0.0440128\pi$
$13$	4.60260	+	2.95791i	1.27653	+	0.820377i	0.286075	+	0.958207i	$0.407649\pi$
$14$	−2.89788	−	3.34433i	−0.774490	−	0.893809i
$15$	0.443376	+	0.970858i	0.114479	+	0.250675i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−3.76709	−	1.10612i	−0.913654	−	0.268273i	−0.209076	−	0.977899i	$-0.567046\pi$
$17$	−3.76709	−	1.10612i	−0.913654	−	0.268273i	−0.704578	+	0.709626i	$0.748864\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	−6.33409	+	1.85986i	−1.45314	+	0.426680i	−0.910578	−	0.413337i	$-0.864363\pi$
$19$	−6.33409	+	1.85986i	−1.45314	+	0.426680i	−0.542561	+	0.840017i	$0.682545\pi$
$20$	−0.443376	+	0.970858i	−0.0991419	+	0.217091i
$21$	0.629769	+	4.38014i	0.137427	+	0.955825i
$22$	−1.64964			−0.351705
$23$	−4.78492	+	0.323343i	−0.997725	+	0.0674216i
$23$	−4.78492	+	0.323343i	−0.997725	+	0.0674216i
$24$	−1.00000			−0.204124
$25$	0.549456	+	3.82155i	0.109891	+	0.764311i
$26$	2.27279	−	4.97671i	0.445730	−	0.976012i
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$	−2.89788	+	3.34433i	−0.547647	+	0.632019i
$29$	6.14024	+	1.80294i	1.14021	+	0.334797i	0.796714	−	0.604356i	$-0.206570\pi$
$29$	6.14024	+	1.80294i	1.14021	+	0.334797i	0.343499	+	0.939153i	$0.388388\pi$
$30$	0.897877	−	0.577031i	0.163929	−	0.105351i
$31$	−1.25244	−	2.74246i	−0.224945	−	0.492561i	0.763185	−	0.646180i	$-0.223634\pi$
$31$	−1.25244	−	2.74246i	−0.224945	−	0.492561i	−0.988130	+	0.153619i	$0.950907\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	1.38777	+	0.891865i	0.241580	+	0.155254i
$34$	−0.558746	+	3.88617i	−0.0958242	+	0.666472i
$35$	0.672158	−	4.67496i	0.113615	−	0.790213i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	1.44774	+	1.67078i	0.238007	+	0.274674i	0.862169	−	0.506620i	$-0.169105\pi$
$37$	1.44774	+	1.67078i	0.238007	+	0.274674i	−0.624163	+	0.781294i	$0.714560\pi$
$38$	2.74236	+	6.00493i	0.444869	+	0.974128i
$39$	−4.60260	+	2.95791i	−0.737006	+	0.473645i
$40$	1.02408	+	0.300696i	0.161921	+	0.0475442i
$41$	−2.67954	+	3.09235i	−0.418474	+	0.482945i	−0.925371	−	0.379062i	$-0.876247\pi$
$41$	−2.67954	+	3.09235i	−0.418474	+	0.482945i	0.506898	+	0.862006i	$0.330792\pi$
$42$	4.24593	−	1.24672i	0.655161	−	0.192373i
$43$	−1.21021	+	2.64998i	−0.184555	+	0.404119i	−0.979183	−	0.202977i	$-0.934938\pi$
$43$	−1.21021	+	2.64998i	−0.184555	+	0.404119i	0.794629	+	0.607096i	$0.207666\pi$
$44$	0.234769	+	1.63285i	0.0353927	+	0.246162i
$45$	−1.06731			−0.159105
$46$	1.00102	+	4.69020i	0.147592	+	0.691532i
$47$	−9.62306			−1.40367			−0.701834	−	0.712341i	$-0.747635\pi$
$47$	−9.62306			−1.40367			−0.701834	+	0.712341i	$0.747635\pi$
$48$	0.142315	+	0.989821i	0.0205414	+	0.142868i
$49$	5.22685	−	11.4452i	0.746692	−	1.63503i
$50$	3.70446	−	1.08773i	0.523890	−	0.153828i
$51$	2.57107	−	2.96717i	0.360021	−	0.415487i
$52$	−5.24950	−	1.54139i	−0.727975	−	0.213753i
$53$	−1.87633	+	1.20584i	−0.257734	+	0.165635i	−0.663127	−	0.748507i	$-0.730771\pi$
$53$	−1.87633	+	1.20584i	−0.257734	+	0.165635i	0.405393	+	0.914142i	$0.367135\pi$
$54$	−0.415415	−	0.909632i	−0.0565308	−	0.123785i
$55$	−1.15300	−	1.33063i	−0.155470	−	0.179422i
$56$	3.72270	+	2.39243i	0.497467	+	0.319702i
$57$	0.939490	−	6.53430i	0.124439	−	0.865489i
$58$	0.910738	−	6.33432i	0.119586	−	0.831737i
$59$	8.20397	+	5.27237i	1.06807	+	0.686405i	0.951771	−	0.306810i	$-0.0992616\pi$
$59$	8.20397	+	5.27237i	1.06807	+	0.686405i	0.116296	+	0.993215i	$0.462898\pi$
$60$	−0.698939	−	0.806618i	−0.0902326	−	0.104134i
$61$	−0.647821	−	1.41853i	−0.0829450	−	0.181624i	0.863615	−	0.504152i	$-0.168195\pi$
$61$	−0.647821	−	1.41853i	−0.0829450	−	0.181624i	−0.946560	+	0.322528i	$0.895468\pi$
$62$	−2.53631	+	1.62999i	−0.322111	+	0.207008i
$63$	−4.24593	−	1.24672i	−0.534937	−	0.157072i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	5.60284	−	1.64514i	0.694947	−	0.204055i
$66$	0.685287	−	1.50057i	0.0843530	−	0.184707i
$67$	−1.71423	−	11.9227i	−0.209426	−	1.45659i	−0.775036	−	0.631917i	$-0.782268\pi$
$67$	−1.71423	−	11.9227i	−0.209426	−	1.45659i	0.565610	−	0.824673i	$-0.308641\pi$
$68$	3.92613			0.476113
$69$	1.69360	−	4.48684i	0.203886	−	0.540152i
$70$	−4.72304			−0.564511
$71$	0.749168	+	5.21058i	0.0889098	+	0.618382i	0.984746	+	0.173997i	$0.0556684\pi$
$71$	0.749168	+	5.21058i	0.0889098	+	0.618382i	−0.895836	+	0.444384i	$0.853423\pi$
$72$	0.415415	−	0.909632i	0.0489571	−	0.107201i
$73$	−6.89449	+	2.02441i	−0.806939	+	0.236939i	−0.659083	−	0.752070i	$-0.729055\pi$
$73$	−6.89449	+	2.02441i	−0.806939	+	0.236939i	−0.147856	+	0.989009i	$0.547237\pi$
$74$	1.44774	−	1.67078i	0.168296	−	0.194224i
$75$	−3.70446	−	1.08773i	−0.427754	−	0.125600i
$76$	5.55353	−	3.56904i	0.637034	−	0.409397i
$77$	−3.03252	−	6.64029i	−0.345588	−	0.756731i
$78$	3.58282	+	4.13480i	0.405675	+	0.468174i
$79$	2.26617	+	1.45638i	0.254964	+	0.163856i	0.661879	−	0.749610i	$-0.269759\pi$
$79$	2.26617	+	1.45638i	0.254964	+	0.163856i	−0.406915	+	0.913466i	$0.633395\pi$
$80$	0.151894	−	1.05645i	0.0169823	−	0.118114i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	3.44222	+	2.21218i	0.380129	+	0.244294i
$83$	−3.62690	−	4.18567i	−0.398104	−	0.459436i	0.520939	−	0.853594i	$-0.325582\pi$
$83$	−3.62690	−	4.18567i	−0.398104	−	0.459436i	−0.919043	+	0.394157i	$0.871036\pi$
$84$	−1.83829	−	4.02529i	−0.200574	−	0.439195i
$85$	−3.52518	+	2.26550i	−0.382360	+	0.245728i
$86$	2.79524	+	0.820757i	0.301419	+	0.0885045i
$87$	−4.19075	+	4.83639i	−0.449296	+	0.518515i
$88$	1.58282	−	0.464758i	0.168729	−	0.0495434i
$89$	4.70504	−	10.3026i	0.498733	−	1.09207i	−0.478146	−	0.878280i	$-0.658691\pi$
$89$	4.70504	−	10.3026i	0.498733	−	1.09207i	0.976879	−	0.213792i	$-0.0685816\pi$
$90$	0.151894	+	1.05645i	0.0160110	+	0.111359i
$91$	24.2107			2.53797
$92$	4.50000	−	1.65831i	0.469157	−	0.172891i
$93$	3.01491			0.312632
$94$	1.36950	+	9.52511i	0.141254	+	0.982440i
$95$	−2.92694	+	6.40911i	−0.300298	+	0.657561i
$96$	0.959493	−	0.281733i	0.0979278	−	0.0287542i
$97$	−7.84485	+	9.05344i	−0.796524	+	0.919238i	−0.998185	−	0.0602176i	$-0.980821\pi$
$97$	−7.84485	+	9.05344i	−0.796524	+	0.919238i	0.201661	+	0.979455i	$0.435366\pi$
$98$	−12.0726	−	3.54482i	−1.21951	−	0.358081i
$99$	−1.38777	+	0.891865i	−0.139476	+	0.0896358i
$100$	−1.60386	−	3.51195i	−0.160386	−	0.351195i
$101$	12.0894	+	13.9519i	1.20294	+	1.38826i	0.900365	+	0.435135i	$0.143299\pi$
$101$	12.0894	+	13.9519i	1.20294	+	1.38826i	0.302570	+	0.953127i	$0.402155\pi$
$102$	−3.30287	−	2.12262i	−0.327033	−	0.210171i
$103$	1.62633	−	11.3114i	0.160247	−	1.11455i	−0.737919	−	0.674889i	$-0.764191\pi$
$103$	1.62633	−	11.3114i	0.160247	−	1.11455i	0.898166	−	0.439656i	$-0.144900\pi$
$104$	−0.778622	+	5.41543i	−0.0763501	+	0.531027i
$105$	3.97327	+	2.55347i	0.387751	+	0.249193i
$106$	1.46060	+	1.68562i	0.141866	+	0.163722i
$107$	6.17478	+	13.5209i	0.596938	+	1.30711i	0.931157	+	0.364618i	$0.118800\pi$
$107$	6.17478	+	13.5209i	0.596938	+	1.30711i	−0.334219	+	0.942495i	$0.608472\pi$
$108$	−0.841254	+	0.540641i	−0.0809497	+	0.0520232i
$109$	−11.7854	−	3.46052i	−1.12884	−	0.331458i	−0.336589	−	0.941652i	$-0.609273\pi$
$109$	−11.7854	−	3.46052i	−1.12884	−	0.331458i	−0.792252	+	0.610194i	$0.791092\pi$
$110$	−1.15300	+	1.33063i	−0.109934	+	0.126871i
$111$	−2.12121	+	0.622842i	−0.201336	+	0.0591176i
$112$	1.83829	−	4.02529i	0.173702	−	0.380354i
$113$	0.429025	+	2.98393i	0.0403593	+	0.280705i	1.00000		0.000524443i	$-0.000166935\pi$
$113$	0.429025	+	2.98393i	0.0403593	+	0.280705i	−0.959641	+	0.281229i	$0.909258\pi$
$114$	−6.60149			−0.618286
$115$	−3.08355	+	4.08560i	−0.287543	+	0.380984i
$116$	−6.39946			−0.594175
$117$	−0.778622	−	5.41543i	−0.0719836	−	0.500657i
$118$	4.05116	−	8.87081i	0.372940	−	0.816624i
$119$	−16.6701	+	4.89477i	−1.52814	+	0.448703i
$120$	−0.698939	+	0.806618i	−0.0638041	+	0.0736338i
$121$	7.94333	+	2.33237i	0.722121	+	0.212034i
$122$	−1.31190	+	0.843105i	−0.118774	+	0.0763311i
$123$	−1.69978	−	3.72201i	−0.153264	−	0.335602i
$124$	1.97435	+	2.27852i	0.177302	+	0.204617i
$125$	7.95596	+	5.11298i	0.711603	+	0.457319i
$126$	−0.629769	+	4.38014i	−0.0561043	+	0.390214i
$127$	0.775959	−	5.39691i	0.0688552	−	0.478899i	−0.925994	−	0.377537i	$-0.876771\pi$
$127$	0.775959	−	5.39691i	0.0688552	−	0.478899i	0.994850	−	0.101362i	$-0.0323199\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	−1.90777	−	2.20169i	−0.167970	−	0.193848i
$130$	−2.42576	−	5.31168i	−0.212754	−	0.465865i
$131$	−7.29997	+	4.69140i	−0.637801	+	0.409890i	−0.819190	−	0.573522i	$-0.805577\pi$
$131$	−7.29997	+	4.69140i	−0.637801	+	0.409890i	0.181389	+	0.983411i	$0.441941\pi$
$132$	−1.58282	−	0.464758i	−0.137767	−	0.0404520i
$133$	−19.1303	+	22.0776i	−1.65881	+	1.91437i
$134$	−11.5574	+	3.39356i	−0.998406	+	0.293159i
$135$	0.443376	−	0.970858i	0.0381597	−	0.0835582i
$136$	−0.558746	−	3.88617i	−0.0479121	−	0.333236i
$137$	8.98175			0.767363			0.383682	−	0.923465i	$-0.374656\pi$
$137$	8.98175			0.767363			0.383682	+	0.923465i	$0.374656\pi$
$138$	−4.68219	−	1.03782i	−0.398575	−	0.0883453i
$139$	3.06287			0.259789			0.129895	−	0.991528i	$-0.458536\pi$
$139$	3.06287			0.259789			0.129895	+	0.991528i	$0.458536\pi$
$140$	0.672158	+	4.67496i	0.0568077	+	0.395106i
$141$	3.99756	−	8.75344i	0.336656	−	0.737173i
$142$	5.05092	−	1.48308i	0.423864	−	0.124458i
$143$	5.91038	−	6.82094i	0.494251	−	0.570396i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	5.74593	−	3.69269i	0.477174	−	0.306661i
$146$	2.98499	+	6.53621i	0.247039	+	0.540941i
$147$	8.23961	+	9.50901i	0.679591	+	0.784290i
$148$	−1.85981	−	1.19523i	−0.152875	−	0.0982470i
$149$	2.90507	−	20.2052i	0.237993	−	1.65528i	−0.423922	−	0.905699i	$-0.639347\pi$
$149$	2.90507	−	20.2052i	0.237993	−	1.65528i	0.661915	−	0.749579i	$-0.269744\pi$
$150$	−0.549456	+	3.82155i	−0.0448629	+	0.312029i
$151$	−10.6960	−	6.87389i	−0.870427	−	0.559390i	0.0274562	−	0.999623i	$-0.491259\pi$
$151$	−10.6960	−	6.87389i	−0.870427	−	0.559390i	−0.897883	+	0.440233i	$0.854896\pi$
$152$	−4.32306	−	4.98908i	−0.350646	−	0.404667i
$153$	1.63097	+	3.57133i	0.131856	+	0.288725i
$154$	−6.14113	+	3.94666i	−0.494866	+	0.318031i
$155$	−3.08750	−	0.906571i	−0.247994	−	0.0728176i
$156$	3.58282	−	4.13480i	0.286855	−	0.331049i
$157$	1.09842	−	0.322526i	0.0876638	−	0.0257404i	−0.237607	−	0.971361i	$-0.576363\pi$
$157$	1.09842	−	0.322526i	0.0876638	−	0.0257404i	0.325270	+	0.945621i	$0.394545\pi$
$158$	1.11905	−	2.45037i	0.0890266	−	0.194941i
$159$	−0.317418	−	2.20769i	−0.0251729	−	0.175082i
$160$	−1.06731			−0.0843782
$161$	−17.0392	+	12.6513i	−1.34288	+	0.997063i
$162$	1.00000			0.0785674
$163$	−0.683592	−	4.75449i	−0.0535431	−	0.372400i	−0.998922	−	0.0464260i	$-0.985217\pi$
$163$	−0.683592	−	4.75449i	−0.0535431	−	0.372400i	0.945379	−	0.325974i	$-0.105692\pi$
$164$	1.69978	−	3.72201i	0.132731	−	0.290640i
$165$	1.68936	−	0.496041i	0.131516	−	0.0386167i
$166$	−3.62690	+	4.18567i	−0.281502	+	0.324871i
$167$	−11.2720	−	3.30976i	−0.872254	−	0.256117i	−0.185180	−	0.982705i	$-0.559287\pi$
$167$	−11.2720	−	3.30976i	−0.872254	−	0.256117i	−0.687074	+	0.726588i	$0.741105\pi$
$168$	−3.72270	+	2.39243i	−0.287212	+	0.184580i
$169$	7.03429	+	15.4029i	0.541099	+	1.18484i
$170$	2.74412	+	3.16689i	0.210465	+	0.242889i
$171$	5.55353	+	3.56904i	0.424689	+	0.272931i
$172$	0.414598	−	2.88359i	0.0316128	−	0.219872i
$173$	0.728537	−	5.06708i	0.0553896	−	0.385243i	−0.943203	−	0.332216i	$-0.892204\pi$
$173$	0.728537	−	5.06708i	0.0553896	−	0.385243i	0.998593	−	0.0530276i	$-0.0168871\pi$
$174$	5.38357	+	3.45981i	0.408127	+	0.262287i
$175$	11.1883	+	12.9120i	0.845754	+	0.976052i
$176$	−0.685287	−	1.50057i	−0.0516554	−	0.113110i
$177$	−8.20397	+	5.27237i	−0.616648	+	0.396296i
$178$	−10.8673	−	3.19093i	−0.814540	−	0.239171i
$179$	12.2769	−	14.1683i	0.917619	−	1.05899i	−0.0804426	−	0.996759i	$-0.525633\pi$
$179$	12.2769	−	14.1683i	0.917619	−	1.05899i	0.998062	−	0.0622298i	$-0.0198212\pi$
$180$	1.02408	−	0.300696i	0.0763301	−	0.0224125i
$181$	−3.01827	+	6.60909i	−0.224346	+	0.491250i	−0.988015	−	0.154359i	$-0.950669\pi$
$181$	−3.01827	+	6.60909i	−0.224346	+	0.491250i	0.763669	+	0.645608i	$0.223396\pi$
$182$	−3.44554	−	23.9643i	−0.255401	−	1.77635i
$183$	1.55946			0.115278
$184$	−2.28185	−	4.21819i	−0.168220	−	0.310969i
$185$	2.35956			0.173478
$186$	−0.429067	−	2.98423i	−0.0314607	−	0.218814i
$187$	−2.69052	+	5.89142i	−0.196751	+	0.430824i
$188$	9.23326	−	2.71113i	0.673404	−	0.197729i
$189$	2.89788	−	3.34433i	0.210790	−	0.243264i
$190$	6.76043	+	1.98504i	0.490453	+	0.144010i
$191$	21.1841	−	13.6142i	1.53283	−	0.985090i	0.543499	−	0.839410i	$-0.317099\pi$
$191$	21.1841	−	13.6142i	1.53283	−	0.985090i	0.989332	−	0.145681i	$-0.0465372\pi$
$192$	−0.415415	−	0.909632i	−0.0299800	−	0.0656470i
$193$	−11.0715	−	12.7772i	−0.796948	−	0.919727i	0.201262	−	0.979537i	$-0.435496\pi$
$193$	−11.0715	−	12.7772i	−0.796948	−	0.919727i	−0.998210	+	0.0598109i	$0.980950\pi$
$194$	10.0777	+	6.47656i	0.723539	+	0.464990i
$195$	−0.831030	+	5.77994i	−0.0595113	+	0.413910i
$196$	−1.79064	+	12.4542i	−0.127903	+	0.889583i
$197$	−10.8033	−	6.94289i	−0.769706	−	0.494660i	0.0958965	−	0.995391i	$-0.469428\pi$
$197$	−10.8033	−	6.94289i	−0.769706	−	0.494660i	−0.865603	+	0.500731i	$0.833065\pi$
$198$	1.08029	+	1.24672i	0.0767727	+	0.0886004i
$199$	5.65154	+	12.3751i	0.400627	+	0.877251i	0.997206	+	0.0746967i	$0.0237989\pi$
$199$	5.65154	+	12.3751i	0.400627	+	0.877251i	−0.596579	+	0.802554i	$0.703474\pi$
$200$	−3.24796	+	2.08733i	−0.229665	+	0.147597i
$201$	11.5574	+	3.39356i	0.815195	+	0.239363i
$202$	12.0894	−	13.9519i	0.850604	−	0.981649i
$203$	27.1717	−	7.97832i	1.90708	−	0.559968i
$204$	−1.63097	+	3.57133i	−0.114191	+	0.250043i
$205$	0.621515	+	4.32273i	0.0434085	+	0.301913i
$206$	−11.4277			−0.796207
$207$	3.37782	+	3.40446i	0.234775	+	0.236626i
$208$	5.47112			0.379354
$209$	1.54982	+	10.7793i	0.107204	+	0.745617i
$210$	1.96202	−	4.29622i	0.135392	−	0.296468i
$211$	20.2858	−	5.95646i	1.39654	−	0.410060i	0.505042	−	0.863095i	$-0.331477\pi$
$211$	20.2858	−	5.95646i	1.39654	−	0.410060i	0.891493	+	0.453035i	$0.149659\pi$
$212$	1.46060	−	1.68562i	0.100314	−	0.115769i
$213$	−5.05092	−	1.48308i	−0.346083	−	0.101619i
$214$	12.5045	−	8.03615i	0.854790	−	0.549340i
$215$	1.29166	+	2.82835i	0.0880908	+	0.192892i
$216$	0.654861	+	0.755750i	0.0445576	+	0.0514222i
$217$	−11.2236	−	7.21298i	−0.761909	−	0.489649i
$218$	−1.74805	+	12.1580i	−0.118393	+	0.823442i
$219$	1.02261	−	7.11242i	0.0691017	−	0.480613i
$220$	1.48118	+	0.951895i	0.0998610	+	0.0641768i
$221$	−14.0666	−	16.2337i	−0.946223	−	1.09200i
$222$	0.918382	+	2.01098i	0.0616378	+	0.134968i
$223$	−2.14678	+	1.37965i	−0.143759	+	0.0923885i	−0.610543	−	0.791983i	$-0.709049\pi$
$223$	−2.14678	+	1.37965i	−0.143759	+	0.0923885i	0.466784	+	0.884371i	$0.345413\pi$
$224$	−4.24593	−	1.24672i	−0.283693	−	0.0832998i
$225$	2.52832	−	2.91784i	0.168555	−	0.194522i
$226$	2.89251	−	0.849316i	0.192407	−	0.0564957i
$227$	−8.19315	+	17.9405i	−0.543798	+	1.19075i	0.415820	+	0.909447i	$0.363495\pi$
$227$	−8.19315	+	17.9405i	−0.543798	+	1.19075i	−0.959618	+	0.281305i	$0.909233\pi$
$228$	0.939490	+	6.53430i	0.0622193	+	0.432745i
$229$	−11.2054			−0.740473			−0.370237	−	0.928937i	$-0.620723\pi$
$229$	−11.2054			−0.740473			−0.370237	+	0.928937i	$0.620723\pi$
$230$	4.48285	+	2.47072i	0.295590	+	0.162915i
$231$	7.29997			0.480303
$232$	0.910738	+	6.33432i	0.0597929	+	0.415869i
$233$	7.48542	−	16.3908i	0.490386	−	1.07380i	−0.489090	−	0.872234i	$-0.662671\pi$
$233$	7.48542	−	16.3908i	0.490386	−	1.07380i	0.979476	−	0.201562i	$-0.0646019\pi$
$234$	−5.24950	+	1.54139i	−0.343171	+	0.100764i
$235$	−6.72593	+	7.76213i	−0.438751	+	0.506346i
$236$	−9.35706	−	2.74748i	−0.609092	−	0.178846i
$237$	−2.26617	+	1.45638i	−0.147204	+	0.0946021i
$238$	7.21735	+	15.8038i	0.467831	+	1.02441i
$239$	−17.8436	−	20.5926i	−1.15421	−	1.33203i	−0.934293	−	0.356506i	$-0.883968\pi$
$239$	−17.8436	−	20.5926i	−1.15421	−	1.33203i	−0.219914	−	0.975519i	$-0.570578\pi$
$240$	0.897877	+	0.577031i	0.0579577	+	0.0372472i
$241$	3.17028	−	22.0498i	0.204216	−	1.42035i	−0.587383	−	0.809309i	$-0.699842\pi$
$241$	3.17028	−	22.0498i	0.204216	−	1.42035i	0.791599	−	0.611041i	$-0.209249\pi$
$242$	1.17818	−	8.19441i	0.0757362	−	0.526757i
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$	1.02123	+	1.17856i	0.0653773	+	0.0754494i
$245$	−5.57866	−	12.2156i	−0.356408	−	0.780424i
$246$	−3.44222	+	2.21218i	−0.219468	+	0.141043i
$247$	−34.6545	−	10.1755i	−2.20502	−	0.647451i
$248$	1.97435	−	2.27852i	0.125371	−	0.144686i
$249$	5.31408	−	1.56036i	0.336766	−	0.0988835i
$250$	3.92869	−	8.60263i	0.248472	−	0.544078i
$251$	1.45152	+	10.0956i	0.0916192	+	0.637226i	0.982950	+	0.183872i	$0.0588633\pi$
$251$	1.45152	+	10.0956i	0.0916192	+	0.637226i	−0.891331	+	0.453353i	$0.850228\pi$
$252$	4.42518			0.278760
$253$	−0.595379	+	7.88898i	−0.0374311	+	0.495976i
$254$	−5.45241			−0.342115
$255$	−0.596355	−	4.14774i	−0.0373452	−	0.259741i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−26.7109	+	7.84303i	−1.66618	+	0.489235i	−0.972860	−	0.231395i	$-0.925671\pi$
$257$	−26.7109	+	7.84303i	−1.66618	+	0.489235i	−0.693321	+	0.720629i	$0.743853\pi$
$258$	−1.90777	+	2.20169i	−0.118773	+	0.137071i
$259$	9.38672	+	2.75619i	0.583263	+	0.171261i
$260$	−4.91239	+	3.15700i	−0.304654	+	0.195789i
$261$	−2.65843	−	5.82115i	−0.164553	−	0.360320i
$262$	5.68255	+	6.55801i	0.351069	+	0.405155i
$263$	6.35034	+	4.08112i	0.391579	+	0.251652i	0.721584	−	0.692327i	$-0.243414\pi$
$263$	6.35034	+	4.08112i	0.391579	+	0.251652i	−0.330006	+	0.943979i	$0.607051\pi$
$264$	−0.234769	+	1.63285i	−0.0144490	+	0.100495i
$265$	−0.338784	+	2.35629i	−0.0208113	+	0.144746i
$266$	24.5754	+	15.7936i	1.50681	+	0.968370i
$267$	7.41703	+	8.55970i	0.453915	+	0.523845i
$268$	5.00380	+	10.9568i	0.305656	+	0.669293i
$269$	4.94396	−	3.17729i	0.301439	−	0.193723i	−0.381174	−	0.924503i	$-0.624480\pi$
$269$	4.94396	−	3.17729i	0.301439	−	0.193723i	0.682612	+	0.730781i	$0.260844\pi$
$270$	−1.02408	−	0.300696i	−0.0623232	−	0.0182998i
$271$	−13.8865	+	16.0259i	−0.843545	+	0.973503i	−0.999899	−	0.0141978i	$-0.995481\pi$
$271$	−13.8865	+	16.0259i	−0.843545	+	0.973503i	0.156354	+	0.987701i	$0.450026\pi$
$272$	−3.76709	+	1.10612i	−0.228414	+	0.0670683i
$273$	−10.0575	+	22.0228i	−0.608707	+	1.33288i
$274$	−1.27824	−	8.89033i	−0.0772211	−	0.537085i
$275$	6.36903			0.384067
$276$	−0.360914	+	4.78223i	−0.0217244	+	0.287857i
$277$	3.17305			0.190650			0.0953251	−	0.995446i	$-0.469611\pi$
$277$	3.17305			0.190650			0.0953251	+	0.995446i	$0.469611\pi$
$278$	−0.435892	−	3.03169i	−0.0261430	−	0.181829i
$279$	−1.25244	+	2.74246i	−0.0749816	+	0.164187i
$280$	4.53172	−	1.33063i	0.270822	−	0.0795205i
$281$	11.9648	−	13.8081i	0.713759	−	0.823722i	−0.276783	−	0.960932i	$-0.589268\pi$
$281$	11.9648	−	13.8081i	0.713759	−	0.823722i	0.990542	+	0.137211i	$0.0438138\pi$
$282$	−9.23326	−	2.71113i	−0.549832	−	0.161445i
$283$	18.9284	−	12.1645i	1.12518	−	0.723107i	0.160628	−	0.987015i	$-0.448648\pi$
$283$	18.9284	−	12.1645i	1.12518	−	0.723107i	0.964548	+	0.263908i	$0.0850116\pi$
$284$	−2.18681	−	4.78845i	−0.129763	−	0.284142i
$285$	−4.61404	−	5.32488i	−0.273312	−	0.315419i
$286$	−7.59265	−	4.87950i	−0.448963	−	0.288531i
$287$	−2.57687	+	17.9225i	−0.152108	+	1.05793i
$288$	−0.142315	+	0.989821i	−0.00838598	+	0.0583258i
$289$	−1.33382	−	0.857197i	−0.0784603	−	0.0504234i
$290$	−4.47283	−	5.16192i	−0.262654	−	0.303118i
$291$	−4.97643	−	10.8969i	−0.291724	−	0.638786i
$292$	6.04488	−	3.88481i	0.353750	−	0.227341i
$293$	9.98040	+	2.93051i	0.583061	+	0.171202i	0.559944	−	0.828530i	$-0.310823\pi$
$293$	9.98040	+	2.93051i	0.583061	+	0.171202i	0.0231175	+	0.999733i	$0.492641\pi$
$294$	8.23961	−	9.50901i	0.480544	−	0.554577i
$295$	9.98687	−	2.93241i	0.581458	−	0.170731i
$296$	−0.918382	+	2.01098i	−0.0533799	+	0.116886i
$297$	−0.234769	−	1.63285i	−0.0136227	−	0.0947477i
$298$	−20.4130			−1.18249
$299$	−22.9795	−	12.6651i	−1.32894	−	0.732444i
$300$	3.86085			0.222906
$301$	1.83467	+	12.7604i	0.105749	+	0.735499i
$302$	−5.28173	+	11.5654i	−0.303929	+	0.665513i
$303$	−17.7132	+	5.20105i	−1.01759	+	0.298793i
$304$	−4.32306	+	4.98908i	−0.247944	+	0.286143i
$305$	−1.59700	−	0.468921i	−0.0914439	−	0.0268504i
$306$	3.30287	−	2.12262i	0.188812	−	0.121342i
$307$	2.13196	+	4.66834i	0.121677	+	0.266436i	0.960663	−	0.277718i	$-0.0895780\pi$
$307$	2.13196	+	4.66834i	0.121677	+	0.266436i	−0.838985	+	0.544154i	$0.816851\pi$
$308$	4.78047	+	5.51695i	0.272392	+	0.314357i
$309$	9.61361	+	6.17829i	0.546899	+	0.351471i
$310$	−0.457947	+	3.18509i	−0.0260096	+	0.180901i
$311$	−3.04140	+	21.1534i	−0.172462	+	1.19950i	0.701199	+	0.712965i	$0.252648\pi$
$311$	−3.04140	+	21.1534i	−0.172462	+	1.19950i	−0.873661	+	0.486534i	$0.838261\pi$
$312$	−4.60260	−	2.95791i	−0.260571	−	0.167459i
$313$	−10.4550	−	12.0658i	−0.590953	−	0.681997i	0.378969	−	0.925409i	$-0.376279\pi$
$313$	−10.4550	−	12.0658i	−0.590953	−	0.681997i	−0.969923	+	0.243413i	$0.921733\pi$
$314$	−0.475566	−	1.04134i	−0.0268377	−	0.0587664i
$315$	−3.97327	+	2.55347i	−0.223868	+	0.143871i
$316$	−2.58469	−	0.758933i	−0.145400	−	0.0426933i
$317$	−7.12740	+	8.22545i	−0.400314	+	0.461987i	−0.919740	−	0.392528i	$-0.871601\pi$
$317$	−7.12740	+	8.22545i	−0.400314	+	0.461987i	0.519426	+	0.854516i	$0.326146\pi$
$318$	−2.14005	+	0.628375i	−0.120008	+	0.0352375i
$319$	4.38547	−	9.60283i	0.245539	−	0.537655i
$320$	0.151894	+	1.05645i	0.00849113	+	0.0590571i
$321$	−14.8641			−0.829634
$322$	14.9475	+	15.0653i	0.832990	+	0.839558i
$323$	25.9183			1.44213
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	−8.77489	+	19.2143i	−0.486743	+	1.06582i
$326$	−4.60881	+	1.35327i	−0.255258	+	0.0749506i
$327$	8.04365	−	9.28287i	0.444815	−	0.513344i
$328$	−3.92603	−	1.15279i	−0.216779	−	0.0636519i
$329$	−35.8238	+	23.0225i	−1.97503	+	1.26927i
$330$	−0.731413	−	1.60157i	−0.0402629	−	0.0881636i
$331$	8.84577	+	10.2086i	0.486208	+	0.561113i	0.944848	−	0.327508i	$-0.106209\pi$
$331$	8.84577	+	10.2086i	0.486208	+	0.561113i	−0.458641	+	0.888622i	$0.651664\pi$
$332$	4.65922	+	2.99430i	0.255708	+	0.164334i
$333$	0.314624	−	2.18826i	0.0172413	−	0.119916i
$334$	−1.67190	+	11.6283i	−0.0914821	+	0.636272i
$335$	−10.8152	−	6.95051i	−0.590898	−	0.379747i
$336$	2.89788	+	3.34433i	0.158092	+	0.182448i
$337$	−0.791811	−	1.73382i	−0.0431327	−	0.0944474i	0.886839	−	0.462079i	$-0.152896\pi$
$337$	−0.791811	−	1.73382i	−0.0431327	−	0.0944474i	−0.929972	+	0.367631i	$0.880169\pi$
$338$	14.2451	−	9.15475i	0.774830	−	0.497953i
$339$	−2.89251	−	0.849316i	−0.157099	−	0.0461285i
$340$	2.74412	−	3.16689i	0.148821	−	0.171749i
$341$	−4.77207	+	1.40121i	−0.258422	+	0.0758796i
$342$	2.74236	−	6.00493i	0.148290	−	0.324709i
$343$	−3.51551	−	24.4509i	−0.189820	−	1.32023i
$344$	−2.91325			−0.157072
$345$	−2.43544	−	4.50212i	−0.131120	−	0.242386i
$346$	−5.11919			−0.275209
$347$	−1.37041	−	9.53143i	−0.0735676	−	0.511674i	−0.992971	−	0.118358i	$-0.962237\pi$
$347$	−1.37041	−	9.53143i	−0.0735676	−	0.511674i	0.919403	−	0.393316i	$-0.128672\pi$
$348$	2.65843	−	5.82115i	0.142507	−	0.312047i
$349$	30.4262	−	8.93395i	1.62868	−	0.478223i	0.665347	−	0.746534i	$-0.268284\pi$
$349$	30.4262	−	8.93395i	1.62868	−	0.478223i	0.963332	+	0.268311i	$0.0864655\pi$
$350$	11.1883	−	12.9120i	0.598038	−	0.690173i
$351$	5.24950	+	1.54139i	0.280198	+	0.0822735i
$352$	−1.38777	+	0.891865i	−0.0739683	+	0.0475366i
$353$	3.21155	+	7.03232i	0.170934	+	0.374292i	0.975639	−	0.219382i	$-0.0704040\pi$
$353$	3.21155	+	7.03232i	0.170934	+	0.374292i	−0.804705	+	0.593674i	$0.797677\pi$
$354$	6.38626	+	7.37013i	0.339426	+	0.391718i
$355$	4.72657	+	3.03758i	0.250860	+	0.161218i
$356$	−1.61187	+	11.2108i	−0.0854291	+	0.594173i
$357$	2.47255	−	17.1970i	0.130861	−	0.910161i
$358$	−15.7713	−	10.1356i	−0.833538	−	0.535682i
$359$	24.2538	+	27.9904i	1.28007	+	1.47728i	0.799940	+	0.600080i	$0.204864\pi$
$359$	24.2538	+	27.9904i	1.28007	+	1.47728i	0.480128	+	0.877198i	$0.340590\pi$
$360$	−0.443376	−	0.970858i	−0.0233680	−	0.0511687i
$361$	20.6778	−	13.2888i	1.08830	−	0.699410i
$362$	6.97137	+	2.04698i	0.366407	+	0.107587i
$363$	−5.42138	+	6.25661i	−0.284549	+	0.328387i
$364$	−23.2300	+	6.82094i	−1.21758	+	0.357514i
$365$	−3.18591	+	6.97616i	−0.166758	+	0.365149i
$366$	−0.221934	−	1.54358i	−0.0116007	−	0.0806843i
$367$	−12.1890			−0.636260			−0.318130	−	0.948047i	$-0.603055\pi$
$367$	−12.1890			−0.636260			−0.318130	+	0.948047i	$0.603055\pi$
$368$	−3.85052	+	2.85894i	−0.200722	+	0.149032i
$369$	4.09177			0.213009
$370$	−0.335801	−	2.33554i	−0.0174574	−	0.121419i
$371$	−4.10011	+	8.97798i	−0.212867	+	0.466114i
$372$	−2.89279	+	0.849399i	−0.149984	+	0.0440393i
$373$	−3.63198	+	4.19152i	−0.188057	+	0.217029i	−0.841947	−	0.539561i	$-0.818590\pi$
$373$	−3.63198	+	4.19152i	−0.188057	+	0.217029i	0.653890	+	0.756589i	$0.273136\pi$
$374$	6.21436	+	1.82470i	0.321337	+	0.0943530i
$375$	−7.95596	+	5.11298i	−0.410844	+	0.264033i
$376$	−3.99756	−	8.75344i	−0.206159	−	0.451424i
$377$	22.9281	+	26.4605i	1.18086	+	1.36278i
$378$	−3.72270	−	2.39243i	−0.191475	−	0.123054i
$379$	1.45629	−	10.1287i	0.0748044	−	0.520276i	−0.917624	−	0.397450i	$-0.869895\pi$
$379$	1.45629	−	10.1287i	0.0748044	−	0.520276i	0.992428	−	0.122826i	$-0.0391957\pi$
$380$	1.00273	−	6.97412i	0.0514388	−	0.357765i
$381$	4.58686	+	2.94780i	0.234992	+	0.151020i
$382$	−16.4905	−	19.0310i	−0.843726	−	0.973711i
$383$	−1.86555	−	4.08499i	−0.0953253	−	0.208733i	0.855962	−	0.517038i	$-0.172966\pi$
$383$	−1.86555	−	4.08499i	−0.0953253	−	0.208733i	−0.951288	+	0.308305i	$0.900238\pi$
$384$	−0.841254	+	0.540641i	−0.0429300	+	0.0275895i
$385$	−7.47572	−	2.19507i	−0.380998	−	0.111871i
$386$	−11.0715	+	12.7772i	−0.563527	+	0.650345i
$387$	2.79524	−	0.820757i	0.142090	−	0.0417214i
$388$	4.97643	−	10.8969i	0.252640	−	0.553204i
$389$	−0.486473	−	3.38350i	−0.0246652	−	0.171550i	0.973765	−	0.227555i	$-0.0730730\pi$
$389$	−0.486473	−	3.38350i	−0.0246652	−	0.171550i	−0.998431	+	0.0560044i	$0.982164\pi$
$390$	5.83938			0.295688
$391$	18.3829	+	4.07462i	0.929662	+	0.206063i
$392$	12.5822			0.635499
$393$	−1.23494	−	8.58916i	−0.0622942	−	0.433266i
$394$	−5.33474	+	11.6815i	−0.268760	+	0.588503i
$395$	2.75866	−	0.810016i	0.138803	−	0.0407563i
$396$	1.08029	−	1.24672i	0.0542865	−	0.0626499i
$397$	24.0355	+	7.05746i	1.20631	+	0.354204i	0.822261	−	0.569111i	$-0.192712\pi$
$397$	24.0355	+	7.05746i	1.20631	+	0.354204i	0.384046	+	0.923314i	$0.374531\pi$
$398$	11.4449	−	7.35518i	0.573680	−	0.368682i
$399$	−12.1354	−	26.5729i	−0.607532	−	1.33031i
$400$	2.52832	+	2.91784i	0.126416	+	0.145892i
$401$	−7.53498	−	4.84244i	−0.376279	−	0.241820i	0.338808	−	0.940856i	$-0.389976\pi$
$401$	−7.53498	−	4.84244i	−0.376279	−	0.241820i	−0.715087	+	0.699036i	$0.753613\pi$
$402$	1.71423	−	11.9227i	0.0854978	−	0.594650i
$403$	2.34748	−	16.3271i	0.116936	−	0.813309i
$404$	−15.5303	−	9.98075i	−0.772663	−	0.496561i
$405$	0.698939	+	0.806618i	0.0347305	+	0.0400812i
$406$	−11.7640	−	25.7597i	−0.583840	−	1.27843i
$407$	3.06802	−	1.97170i	0.152076	−	0.0977334i
$408$	3.76709	+	1.10612i	0.186499	+	0.0547610i
$409$	15.2462	−	17.5950i	0.753874	−	0.870017i	−0.241064	−	0.970509i	$-0.577496\pi$
$409$	15.2462	−	17.5950i	0.753874	−	0.870017i	0.994938	+	0.100492i	$0.0320418\pi$
$410$	4.19028	−	1.23038i	0.206943	−	0.0607640i
$411$	−3.73116	+	8.17009i	−0.184044	+	0.403001i
$412$	1.62633	+	11.3114i	0.0801237	+	0.557273i
$413$	43.1547			2.12351
$414$	2.88909	−	3.82794i	0.141991	−	0.188133i
$415$	−5.91121			−0.290170
$416$	−0.778622	−	5.41543i	−0.0381751	−	0.265513i
$417$	−1.27236	+	2.78608i	−0.0623078	+	0.136435i
$418$	10.4490	−	3.06810i	0.511077	−	0.150066i
$419$	1.47320	−	1.70016i	0.0719705	−	0.0830584i	−0.718622	−	0.695400i	$-0.755227\pi$
$419$	1.47320	−	1.70016i	0.0719705	−	0.0830584i	0.790593	+	0.612342i	$0.209772\pi$
$420$	−4.53172	−	1.33063i	−0.221125	−	0.0649282i
$421$	−15.6993	+	10.0893i	−0.765138	+	0.491724i	−0.864071	−	0.503370i	$-0.832093\pi$
$421$	−15.6993	+	10.0893i	−0.765138	+	0.491724i	0.0989332	+	0.995094i	$0.468457\pi$
$422$	−8.78281	−	19.2317i	−0.427540	−	0.936183i
$423$	6.30176	+	7.27262i	0.306402	+	0.353607i
$424$	−1.87633	−	1.20584i	−0.0911226	−	0.0585609i
$425$	2.15724	−	15.0039i	0.104641	−	0.727796i
$426$	−0.749168	+	5.21058i	−0.0362973	+	0.252453i
$427$	−5.80538	−	3.73089i	−0.280942	−	0.180551i
$428$	−9.73393	−	11.2336i	−0.470507	−	0.542994i
$429$	3.74929	+	8.20979i	0.181017	+	0.396372i
$430$	2.61574	−	1.68103i	0.126142	−	0.0810666i
$431$	−4.62210	−	1.35717i	−0.222639	−	0.0653726i	0.168511	−	0.985700i	$-0.446104\pi$
$431$	−4.62210	−	1.35717i	−0.222639	−	0.0653726i	−0.391149	+	0.920327i	$0.627922\pi$
$432$	0.654861	−	0.755750i	0.0315070	−	0.0363610i
$433$	6.00189	−	1.76231i	0.288433	−	0.0846914i	−0.134316	−	0.990939i	$-0.542884\pi$
$433$	6.00189	−	1.76231i	0.288433	−	0.0846914i	0.422748	+	0.906247i	$0.361065\pi$
$434$	−5.54228	+	12.1359i	−0.266038	+	0.582541i
$435$	0.972039	+	6.76068i	0.0466057	+	0.324150i
$436$	12.2830			0.588249
$437$	29.7067	−	10.9473i	1.42107	−	0.523682i
$438$	−7.18556			−0.343339
$439$	1.92771	+	13.4075i	0.0920045	+	0.639905i	0.982686	+	0.185278i	$0.0593185\pi$
$439$	1.92771	+	13.4075i	0.0920045	+	0.639905i	−0.890682	+	0.454627i	$0.849772\pi$
$440$	0.731413	−	1.60157i	0.0348687	−	0.0763519i
$441$	−12.0726	+	3.54482i	−0.574884	+	0.168801i
$442$	−14.0666	+	16.2337i	−0.669081	+	0.772160i
$443$	−5.31546	−	1.56076i	−0.252545	−	0.0741540i	0.153010	−	0.988225i	$-0.451103\pi$
$443$	−5.31546	−	1.56076i	−0.252545	−	0.0741540i	−0.405555	+	0.914071i	$0.632922\pi$
$444$	1.85981	−	1.19523i	0.0882626	−	0.0567229i
$445$	−5.02173	−	10.9960i	−0.238053	−	0.521263i
$446$	1.67113	+	1.92859i	0.0791304	+	0.0913213i
$447$	17.1725	+	11.0361i	0.812232	+	0.521990i
$448$	−0.629769	+	4.38014i	−0.0297538	+	0.206942i
$449$	1.92795	−	13.4092i	0.0909858	−	0.632820i	−0.892394	−	0.451258i	$-0.850976\pi$
$449$	1.92795	−	13.4092i	0.0909858	−	0.632820i	0.983379	−	0.181562i	$-0.0581154\pi$
$450$	−3.24796	−	2.08733i	−0.153110	−	0.0983979i
$451$	4.42029	+	5.10128i	0.208143	+	0.240210i
$452$	−1.25232	−	2.74219i	−0.0589041	−	0.128982i
$453$	10.6960	−	6.87389i	0.502541	−	0.322964i
$454$	18.9239	+	5.55655i	0.888142	+	0.260782i
$455$	16.9218	−	19.5288i	0.793306	−	0.915524i
$456$	6.33409	−	1.85986i	0.296621	−	0.0870957i
$457$	−4.61680	+	10.1094i	−0.215965	+	0.472897i	−0.986346	−	0.164687i	$-0.947339\pi$
$457$	−4.61680	+	10.1094i	−0.215965	+	0.472897i	0.770381	+	0.637584i	$0.220066\pi$
$458$	1.59469	+	11.0913i	0.0745151	+	0.518264i
$459$	−3.92613			−0.183256
$460$	1.80760	−	4.78884i	0.0842797	−	0.223281i
$461$	−33.3324			−1.55245			−0.776223	−	0.630459i	$-0.782867\pi$
$461$	−33.3324			−1.55245			−0.776223	+	0.630459i	$0.782867\pi$
$462$	−1.03889	−	7.22567i	−0.0483337	−	0.336169i
$463$	−8.07365	+	17.6788i	−0.375214	+	0.821605i	0.623979	+	0.781441i	$0.285515\pi$
$463$	−8.07365	+	17.6788i	−0.375214	+	0.821605i	−0.999193	+	0.0401636i	$0.987212\pi$
$464$	6.14024	−	1.80294i	0.285053	−	0.0836992i
$465$	2.10724	−	2.43188i	0.0977209	−	0.112776i
$466$	−17.2892	−	5.07658i	−0.800908	−	0.235168i
$467$	−28.2030	+	18.1250i	−1.30508	+	0.838724i	−0.993756	−	0.111579i	$-0.964409\pi$
$467$	−28.2030	+	18.1250i	−1.30508	+	0.838724i	−0.311325	+	0.950303i	$0.600773\pi$
$468$	2.27279	+	4.97671i	0.105060	+	0.230048i
$469$	−34.9058	−	40.2835i	−1.61180	−	1.86012i
$470$	8.64033	+	5.55280i	0.398549	+	0.256132i
$471$	−0.162921	+	1.13314i	−0.00750703	+	0.0522125i
$472$	−1.38787	+	9.65282i	−0.0638817	+	0.444307i
$473$	4.04291	+	2.59822i	0.185893	+	0.119466i
$474$	1.76407	+	2.03584i	0.0810263	+	0.0935093i
$475$	−10.5878	−	23.1841i	−0.485804	−	1.06376i
$476$	14.6158	−	9.39300i	0.669914	−	0.430527i
$477$	2.14005	+	0.628375i	0.0979861	+	0.0287713i
$478$	−17.8436	+	20.5926i	−0.816147	+	0.941884i
$479$	1.58866	−	0.466472i	0.0725876	−	0.0213137i	−0.245237	−	0.969463i	$-0.578866\pi$
$479$	1.58866	−	0.466472i	0.0725876	−	0.0213137i	0.317825	+	0.948149i	$0.397048\pi$
$480$	0.443376	−	0.970858i	0.0202373	−	0.0443134i
$481$	1.72134	+	11.9722i	0.0784865	+	0.545886i
$482$	−22.2765			−1.01467
$483$	−4.42968	−	20.7550i	−0.201557	−	0.944384i
$484$	−8.27868			−0.376303
$485$	1.81960	+	12.6556i	0.0826238	+	0.574661i
$486$	−0.415415	+	0.909632i	−0.0188436	+	0.0412617i
$487$	20.1450	−	5.91510i	0.912856	−	0.268039i	0.208614	−	0.977998i	$-0.433105\pi$
$487$	20.1450	−	5.91510i	0.912856	−	0.268039i	0.704243	+	0.709959i	$0.251287\pi$
$488$	1.02123	−	1.17856i	0.0462287	−	0.0533508i
$489$	4.60881	+	1.35327i	0.208418	+	0.0611969i
$490$	−11.2973	+	7.26033i	−0.510360	+	0.327988i
$491$	10.7230	+	23.4802i	0.483924	+	1.05965i	0.981366	+	0.192148i	$0.0615454\pi$
$491$	10.7230	+	23.4802i	0.483924	+	1.05965i	−0.497442	+	0.867497i	$0.665727\pi$
$492$	2.67954	+	3.09235i	0.120803	+	0.139414i
$493$	−21.1366	−	13.5837i	−0.951944	−	0.611777i
$494$	−5.14006	+	35.7499i	−0.231262	+	1.60847i
$495$	−0.250571	+	1.74276i	−0.0112623	+	0.0783312i
$496$	−2.53631	−	1.62999i	−0.113884	−	0.0731885i
$497$	15.2549	+	17.6051i	0.684275	+	0.789695i
$498$	−2.30075	−	5.03793i	−0.103099	−	0.225755i
$499$	−5.41570	+	3.48046i	−0.242440	+	0.155807i	−0.656219	−	0.754571i	$-0.727845\pi$
$499$	−5.41570	+	3.48046i	−0.242440	+	0.155807i	0.413779	+	0.910378i	$0.364209\pi$
$500$	−9.07418	−	2.66442i	−0.405810	−	0.119156i
$501$	7.69322	−	8.87845i	0.343708	−	0.396660i
$502$	9.78622	−	2.87349i	0.436781	−	0.128250i
$503$	4.22191	−	9.24470i	0.188246	−	0.412201i	−0.791853	−	0.610712i	$-0.790883\pi$
$503$	4.22191	−	9.24470i	0.188246	−	0.412201i	0.980099	+	0.198511i	$0.0636106\pi$
$504$	−0.629769	−	4.38014i	−0.0280521	−	0.195107i
$505$	19.7035			0.876796
$506$	7.89341	−	0.533400i	0.350905	−	0.0237125i
$507$	−16.9332			−0.752028
$508$	0.775959	+	5.39691i	0.0344276	+	0.239449i
$509$	−10.8955	+	23.8578i	−0.482933	+	1.05748i	0.498713	+	0.866767i	$0.333806\pi$
$509$	−10.8955	+	23.8578i	−0.482933	+	1.05748i	−0.981647	+	0.190709i	$0.938921\pi$
$510$	−4.02065	+	1.18057i	−0.178037	+	0.0522765i
$511$	−20.8229	+	24.0309i	−0.921150	+	1.06306i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	−5.55353	+	3.56904i	−0.245194	+	0.157577i
$514$	11.5646	+	25.3228i	0.510091	+	1.11694i
$515$	−7.98727	−	9.21780i	−0.351961	−	0.406185i
$516$	2.45078	+	1.57502i	0.107890	+	0.0693364i
$517$	−2.25919	+	15.7130i	−0.0993592	+	0.691059i
$518$	1.39227	−	9.68343i	0.0611727	−	0.425465i
$519$	4.30654	+	2.76764i	0.189036	+	0.121486i
$520$	3.82398	+	4.41311i	0.167693	+	0.193527i
$521$	6.39845	+	14.0106i	0.280321	+	0.613818i	0.996453	−	0.0841470i	$-0.0268165\pi$
$521$	6.39845	+	14.0106i	0.280321	+	0.613818i	−0.716132	+	0.697965i	$0.754089\pi$
$522$	−5.38357	+	3.45981i	−0.235632	+	0.151432i
$523$	25.1618	+	7.38818i	1.10025	+	0.323062i	0.780951	−	0.624592i	$-0.214735\pi$
$523$	25.1618	+	7.38818i	1.10025	+	0.323062i	0.319298	+	0.947654i	$0.396553\pi$
$524$	5.68255	−	6.55801i	0.248243	−	0.286488i
$525$	−16.3929	+	4.81339i	−0.715445	+	0.210074i
$526$	3.13583	−	6.86651i	0.136729	−	0.299394i
$527$	1.68457	+	11.7165i	0.0733811	+	0.510377i
$528$	1.64964			0.0717915
$529$	22.7909	−	3.09434i	0.990909	−	0.134536i
$530$	2.38052			0.103403
$531$	−1.38787	−	9.65282i	−0.0602283	−	0.418897i
$532$	12.1354	−	26.5729i	0.526138	−	1.15208i
$533$	−21.4798	+	6.30703i	−0.930392	+	0.273188i
$534$	7.41703	−	8.55970i	0.320966	−	0.370415i
$535$	15.2220	+	4.46958i	0.658104	+	0.193237i
$536$	10.1332	−	6.51219i	0.437686	−	0.281284i
$537$	7.78793	+	17.0532i	0.336074	+	0.735900i
$538$	−3.84855	−	4.44146i	−0.165923	−	0.191485i
$539$	−17.4612	−	11.2216i	−0.752108	−	0.483351i
$540$	−0.151894	+	1.05645i	−0.00653647	+	0.0454622i
$541$	−0.141885	+	0.986830i	−0.00610010	+	0.0424271i	−0.992644	−	0.121069i	$-0.961368\pi$
$541$	−0.141885	+	0.986830i	−0.00610010	+	0.0424271i	0.986544	+	0.163496i	$0.0522770\pi$
$542$	17.8390	+	11.4644i	0.766252	+	0.492440i
$543$	−4.75801	−	5.49103i	−0.204186	−	0.235643i
$544$	1.63097	+	3.57133i	0.0699274	+	0.153120i
$545$	−11.0286	+	7.08767i	−0.472414	+	0.303602i
$546$	23.2300	+	6.82094i	0.994152	+	0.291909i
$547$	−3.81944	+	4.40787i	−0.163307	+	0.188467i	−0.831505	−	0.555517i	$-0.812520\pi$
$547$	−3.81944	+	4.40787i	−0.163307	+	0.188467i	0.668198	+	0.743984i	$0.267066\pi$
$548$	−8.61793	+	2.53045i	−0.368140	+	0.108096i
$549$	−0.647821	+	1.41853i	−0.0276483	+	0.0605414i
$550$	−0.906407	−	6.30420i	−0.0386493	−	0.268812i
$551$	−42.2460			−1.79974
$552$	4.78492	−	0.323343i	0.203660	−	0.0137624i
$553$	11.9206			0.506914
$554$	−0.451573	−	3.14076i	−0.0191855	−	0.133438i
$555$	−0.980197	+	2.14633i	−0.0416071	+	0.0911067i
$556$	−2.93880	+	0.862910i	−0.124633	+	0.0365955i
$557$	21.5121	−	24.8262i	0.911495	−	1.05192i	−0.0869520	−	0.996213i	$-0.527713\pi$
$557$	21.5121	−	24.8262i	0.911495	−	1.05192i	0.998447	−	0.0557089i	$-0.0177419\pi$
$558$	2.89279	+	0.849399i	0.122461	+	0.0359579i
$559$	−13.4085	+	8.61713i	−0.567120	+	0.364466i
$560$	−1.96202	−	4.29622i	−0.0829105	−	0.181549i
$561$	−4.24134	−	4.89477i	−0.179070	−	0.206657i
$562$	−15.3703	−	9.87790i	−0.648357	−	0.416674i
$563$	1.71395	−	11.9208i	0.0722344	−	0.502402i	−0.921298	−	0.388856i	$-0.872870\pi$
$563$	1.71395	−	11.9208i	0.0722344	−	0.502402i	0.993533	−	0.113545i	$-0.0362207\pi$
$564$	−1.36950	+	9.52511i	−0.0576665	+	0.401079i
$565$	2.70676	+	1.73953i	0.113874	+	0.0731825i
$566$	−14.7345	−	17.0045i	−0.619338	−	0.714754i
$567$	1.83829	+	4.02529i	0.0772008	+	0.169046i
$568$	−4.42849	+	2.84602i	−0.185815	+	0.119416i
$569$	12.3983	+	3.64048i	0.519765	+	0.152617i	0.531084	−	0.847319i	$-0.321785\pi$
$569$	12.3983	+	3.64048i	0.519765	+	0.152617i	−0.0113189	+	0.999936i	$0.503603\pi$
$570$	−4.61404	+	5.32488i	−0.193261	+	0.223035i
$571$	−32.5250	+	9.55020i	−1.36113	+	0.399663i	−0.879161	−	0.476525i	$-0.841896\pi$
$571$	−32.5250	+	9.55020i	−1.36113	+	0.399663i	−0.481968	+	0.876189i	$0.660078\pi$
$572$	−3.74929	+	8.20979i	−0.156766	+	0.343269i
$573$	3.58372	+	24.9253i	0.149712	+	1.04127i
$574$	18.1068			0.755764
$575$	−3.86478	−	18.1082i	−0.161172	−	0.755163i
$576$	1.00000			0.0416667
$577$	3.19552	+	22.2254i	0.133031	+	0.925254i	0.941572	+	0.336813i	$0.109349\pi$
$577$	3.19552	+	22.2254i	0.133031	+	0.925254i	−0.808540	+	0.588441i	$0.799742\pi$
$578$	−0.658649	+	1.44224i	−0.0273962	+	0.0599893i
$579$	16.2219	−	4.76317i	0.674158	−	0.197951i
$580$	−4.47283	+	5.16192i	−0.185724	+	0.214337i
$581$	−23.5158	−	6.90486i	−0.975599	−	0.286462i
$582$	−10.0777	+	6.47656i	−0.417735	+	0.268462i
$583$	1.52846	+	3.34686i	0.0633024	+	0.138613i
$584$	−4.70554	−	5.43048i	−0.194717	−	0.224715i
$585$	−4.91239	−	3.15700i	−0.203103	−	0.130526i
$586$	1.48032	−	10.2959i	0.0611516	−	0.425319i
$587$	0.163758	−	1.13896i	0.00675903	−	0.0470101i	−0.986163	−	0.165780i	$-0.946986\pi$
$587$	0.163758	−	1.13896i	0.00675903	−	0.0470101i	0.992922	+	0.118770i	$0.0378950\pi$
$588$	−10.5848	−	6.80247i	−0.436512	−	0.280529i
$589$	13.0336	+	15.0416i	0.537042	+	0.619780i
$590$	−4.32384	−	9.46789i	−0.178010	−	0.389787i
$591$	10.8033	−	6.94289i	0.444390	−	0.285592i
$592$	2.12121	+	0.622842i	0.0871810	+	0.0255987i
$593$	2.14872	−	2.47976i	0.0882376	−	0.101832i	−0.709914	−	0.704289i	$-0.751266\pi$
$593$	2.14872	−	2.47976i	0.0882376	−	0.101832i	0.798151	+	0.602457i	$0.205812\pi$
$594$	−1.58282	+	0.464758i	−0.0649440	+	0.0190693i
$595$	−7.70314	+	16.8675i	−0.315798	+	0.691501i
$596$	2.90507	+	20.2052i	0.118996	+	0.827639i
$597$	−13.6046			−0.556798
$598$	−9.26591	+	24.5480i	−0.378911	+	1.00384i
$599$	3.76746			0.153934			0.0769671	−	0.997034i	$-0.475476\pi$
$599$	3.76746			0.153934			0.0769671	+	0.997034i	$0.475476\pi$
$600$	−0.549456	−	3.82155i	−0.0224315	−	0.156014i
$601$	8.17680	−	17.9047i	0.333538	−	0.730347i	−0.666345	−	0.745644i	$-0.732142\pi$
$601$	8.17680	−	17.9047i	0.333538	−	0.730347i	0.999883	+	0.0152967i	$0.00486927\pi$
$602$	12.3694	−	3.63200i	0.504141	−	0.148029i
$603$	−7.88800	+	9.10324i	−0.321224	+	0.370712i
$604$	12.1993	+	3.58205i	0.496384	+	0.145751i
$605$	7.43324	−	4.77705i	0.302204	−	0.194215i
$606$	7.66896	+	16.7927i	0.311530	+	0.682156i
$607$	−28.1237	−	32.4564i	−1.14150	−	1.31737i	−0.941284	−	0.337616i	$-0.890380\pi$
$607$	−28.1237	−	32.4564i	−1.14150	−	1.31737i	−0.200221	−	0.979751i	$-0.564166\pi$
$608$	5.55353	+	3.56904i	0.225225	+	0.144744i
$609$	−4.03018	+	28.0305i	−0.163311	+	1.13585i
$610$	−0.236872	+	1.64748i	−0.00959066	+	0.0667045i
$611$	−44.2911	−	28.4641i	−1.79183	−	1.15154i
$612$	−2.57107	−	2.96717i	−0.103929	−	0.119941i
$613$	9.71463	+	21.2721i	0.392370	+	0.859171i	0.997987	+	0.0634149i	$0.0201991\pi$
$613$	9.71463	+	21.2721i	0.392370	+	0.859171i	−0.605617	+	0.795756i	$0.707074\pi$
$614$	4.31741	−	2.77463i	0.174237	−	0.111975i
$615$	−4.19028	−	1.23038i	−0.168968	−	0.0496136i
$616$	4.78047	−	5.51695i	0.192610	−	0.222284i
$617$	−7.16091	+	2.10263i	−0.288287	+	0.0846488i	−0.422679	−	0.906280i	$-0.638910\pi$
$617$	−7.16091	+	2.10263i	−0.288287	+	0.0846488i	0.134392	+	0.990928i	$0.457092\pi$
$618$	4.74724	−	10.3950i	0.190962	−	0.418149i
$619$	−4.63655	−	32.2479i	−0.186359	−	1.29615i	−0.841339	−	0.540508i	$-0.818232\pi$
$619$	−4.63655	−	32.2479i	−0.186359	−	1.29615i	0.654980	−	0.755646i	$-0.272677\pi$
$620$	3.21784			0.129232
$621$	−4.50000	+	1.65831i	−0.180579	+	0.0665458i
$622$	21.3709			0.856896
$623$	−7.13283	−	49.6099i	−0.285771	−	1.98758i
$624$	−2.27279	+	4.97671i	−0.0909842	+	0.199228i
$625$	−8.83735	+	2.59488i	−0.353494	+	0.103795i
$626$	−10.4550	+	12.0658i	−0.417867	+	0.482244i
$627$	−10.4490	−	3.06810i	−0.417292	−	0.122528i
$628$	−0.963064	+	0.618924i	−0.0384304	+	0.0246977i
$629$	−3.60568	−	7.89535i	−0.143768	−	0.314808i
$630$	3.09293	+	3.56943i	0.123225	+	0.142210i
$631$	−14.5045	−	9.32146i	−0.577414	−	0.371082i	0.219099	−	0.975703i	$-0.429688\pi$
$631$	−14.5045	−	9.32146i	−0.577414	−	0.371082i	−0.796513	+	0.604621i	$0.793325\pi$
$632$	−0.383368	+	2.66639i	−0.0152496	+	0.106063i
$633$	−3.00886	+	20.9271i	−0.119591	+	0.831776i
$634$	9.15606	+	5.88425i	0.363634	+	0.233693i
$635$	−3.81090	−	4.39802i	−0.151231	−	0.174530i
$636$	0.926540	+	2.02884i	0.0367397	+	0.0804487i
$637$	57.9110	−	37.2171i	2.29452	−	1.47460i
$638$	−10.1292	−	2.97420i	−0.401019	−	0.117750i
$639$	3.44729	−	3.97838i	0.136373	−	0.157382i
$640$	1.02408	−	0.300696i	0.0404801	−	0.0118860i
$641$	16.8914	−	36.9870i	0.667170	−	1.46090i	−0.208516	−	0.978019i	$-0.566863\pi$
$641$	16.8914	−	36.9870i	0.667170	−	1.46090i	0.875686	−	0.482880i	$-0.160409\pi$
$642$	2.11539	+	14.7128i	0.0834876	+	0.580669i
$643$	−11.4111			−0.450008			−0.225004	−	0.974358i	$-0.572240\pi$
$643$	−11.4111			−0.450008			−0.225004	+	0.974358i	$0.572240\pi$
$644$	12.7847	−	16.9393i	0.503790	−	0.667504i
$645$	−3.10933			−0.122430
$646$	−3.68856	−	25.6545i	−0.145124	−	1.00936i
$647$	14.3578	−	31.4391i	0.564462	−	1.23600i	−0.385232	−	0.922820i	$-0.625878\pi$
$647$	14.3578	−	31.4391i	0.564462	−	1.23600i	0.949694	−	0.313180i	$-0.101394\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	10.5350	−	12.1581i	0.413537	−	0.477247i
$650$	20.2675	+	5.95109i	0.794959	+	0.233421i
$651$	11.2236	−	7.21298i	0.439888	−	0.282699i
$652$	1.99540	+	4.36931i	0.0781457	+	0.171115i
$653$	−5.61473	−	6.47974i	−0.219721	−	0.253572i	0.635178	−	0.772366i	$-0.280927\pi$
$653$	−5.61473	−	6.47974i	−0.219721	−	0.253572i	−0.854899	+	0.518794i	$0.826381\pi$
$654$	−10.3331	−	6.64069i	−0.404057	−	0.259671i
$655$	−1.31806	+	9.16729i	−0.0515008	+	0.358196i
$656$	−0.582320	+	4.05012i	−0.0227358	+	0.158131i
$657$	6.04488	+	3.88481i	0.235833	+	0.151561i
$658$	27.8864	+	32.1827i	1.08713	+	1.25461i
$659$	−1.75450	−	3.84181i	−0.0683454	−	0.149656i	0.872376	−	0.488835i	$-0.162578\pi$
$659$	−1.75450	−	3.84181i	−0.0683454	−	0.149656i	−0.940722	+	0.339179i	$0.889851\pi$
$660$	−1.48118	+	0.951895i	−0.0576548	+	0.0370525i
$661$	22.1777	+	6.51196i	0.862612	+	0.253286i	0.682970	−	0.730446i	$-0.260688\pi$
$661$	22.1777	+	6.51196i	0.862612	+	0.253286i	0.179642	+	0.983732i	$0.442506\pi$
$662$	8.84577	−	10.2086i	0.343801	−	0.396767i
$663$	20.6102	−	6.05170i	0.800434	−	0.235029i
$664$	2.30075	−	5.03793i	0.0892863	−	0.195510i
$665$	4.43725	+	30.8617i	0.172069	+	1.19677i
$666$	−2.21076			−0.0856651
$667$	−29.9635	−	6.64150i	−1.16019	−	0.257160i
$668$	11.7479			0.454539
$669$	−0.363172	−	2.52591i	−0.0140410	−	0.0976575i
$670$	−5.34060	+	11.6943i	−0.206325	+	0.451790i
$671$	−2.46834	+	0.724770i	−0.0952892	+	0.0279794i
$672$	2.89788	−	3.34433i	0.111788	−	0.129010i
$673$	43.1923	+	12.6824i	1.66494	+	0.488871i	0.972559	−	0.232658i	$-0.0747423\pi$
$673$	43.1923	+	12.6824i	1.66494	+	0.488871i	0.692384	+	0.721529i	$0.256561\pi$
$674$	−1.60349	+	1.03050i	−0.0617641	+	0.0396934i
$675$	1.60386	+	3.51195i	0.0617324	+	0.135175i
$676$	−11.0889	−	12.7972i	−0.426495	−	0.492201i
$677$	−26.1110	−	16.7805i	−1.00353	−	0.644928i	−0.0678176	−	0.997698i	$-0.521604\pi$
$677$	−26.1110	−	16.7805i	−1.00353	−	0.644928i	−0.935710	+	0.352770i	$0.885240\pi$
$678$	−0.429025	+	2.98393i	−0.0164766	+	0.114597i
$679$	−7.54427	+	52.4715i	−0.289522	+	2.01367i
$680$	−3.52518	−	2.26550i	−0.135185	−	0.0868778i
$681$	−12.9157	−	14.9055i	−0.494930	−	0.571180i
$682$	2.06608	+	4.52408i	0.0791143	+	0.173236i
$683$	−21.8572	+	14.0468i	−0.836344	+	0.537485i	−0.887288	−	0.461216i	$-0.847413\pi$
$683$	−21.8572	+	14.0468i	−0.836344	+	0.537485i	0.0509442	+	0.998701i	$0.483777\pi$
$684$	−6.33409	−	1.85986i	−0.242190	−	0.0711134i
$685$	6.27770	−	7.24485i	0.239858	−	0.276811i
$686$	−23.7018	+	6.95946i	−0.904937	+	0.265714i
$687$	4.65489	−	10.1928i	0.177595	−	0.388879i
$688$	0.414598	+	2.88359i	0.0158064	+	0.109936i
$689$	−12.2028			−0.464888
$690$	−4.10969	+	3.05137i	−0.156453	+	0.116164i
$691$	33.5110			1.27482			0.637410	−	0.770525i	$-0.280006\pi$
$691$	33.5110			1.27482			0.637410	+	0.770525i	$0.280006\pi$
$692$	0.728537	+	5.06708i	0.0276948	+	0.192622i
$693$	−3.03252	+	6.64029i	−0.115196	+	0.252244i
$694$	−9.23938	+	2.71293i	−0.350722	+	0.102981i
$695$	2.14076	−	2.47057i	0.0812036	−	0.0937139i
$696$	−6.14024	−	1.80294i	−0.232745	−	0.0683401i
$697$	13.5146	−	8.68530i	0.511901	−	0.328979i
$698$	−13.1731	−	28.8451i	−0.498610	−	1.09180i
$699$	11.8000	+	13.6180i	0.446318	+	0.515078i
$700$	−14.3728	−	9.23683i	−0.543240	−	0.349119i
$701$	0.833884	−	5.79979i	0.0314954	−	0.219055i	−0.967995	−	0.250968i	$-0.919251\pi$
$701$	0.833884	−	5.79979i	0.0314954	−	0.219055i	0.999491	+	0.0319133i	$0.0101601\pi$
$702$	0.778622	−	5.41543i	0.0293872	−	0.204392i
$703$	−12.2775	−	7.89027i	−0.463055	−	0.297587i
$704$	1.08029	+	1.24672i	0.0407148	+	0.0469874i
$705$	−4.26663	−	9.34263i	−0.160691	−	0.351864i
$706$	6.50369	−	4.17967i	0.244769	−	0.157304i
$707$	78.3839	+	23.0156i	2.94793	+	0.865591i
$708$	6.38626	−	7.37013i	0.240010	−	0.276987i
$709$	−43.2693	+	12.7050i	−1.62501	+	0.477147i	−0.962360	−	0.271779i	$-0.912388\pi$
$709$	−43.2693	+	12.7050i	−1.62501	+	0.477147i	−0.662653	+	0.748926i	$0.730570\pi$
$710$	2.33400	−	5.11075i	0.0875935	−	0.191803i
$711$	−0.383368	−	2.66639i	−0.0143774	−	0.0999973i
$712$	11.3261			0.424464
$713$	6.87958	+	12.7175i	0.257642	+	0.476274i
$714$	−17.3738			−0.650199
$715$	−1.37090	−	9.53484i	−0.0512689	−	0.356583i
$716$	−7.78793	+	17.0532i	−0.291049	+	0.637308i
$717$	26.1442	−	7.67663i	0.976373	−	0.286689i
$718$	24.2538	−	27.9904i	0.905145	−	1.04459i
$719$	31.5875	+	9.27493i	1.17802	+	0.345897i	0.811409	−	0.584479i	$-0.198701\pi$
$719$	31.5875	+	9.27493i	1.17802	+	0.345897i	0.366607	+	0.930376i	$0.380519\pi$
$720$	−0.897877	+	0.577031i	−0.0334619	+	0.0215047i
$721$	−21.0074	−	45.9998i	−0.782357	−	1.71312i
$722$	−16.0963	−	18.5761i	−0.599042	−	0.691331i
$723$	18.7402	+	12.0436i	0.696955	+	0.447906i
$724$	1.03401	−	7.19172i	0.0384288	−	0.267278i
$725$	−3.51622	+	24.4559i	−0.130589	+	0.908269i
$726$	6.96446	+	4.47579i	0.258476	+	0.166112i
$727$	1.64107	+	1.89390i	0.0608641	+	0.0702409i	0.785365	−	0.619033i	$-0.212475\pi$
$727$	1.64107	+	1.89390i	0.0608641	+	0.0702409i	−0.724501	+	0.689274i	$0.757930\pi$
$728$	10.0575	+	22.0228i	0.372755	+	0.816220i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	7.35855	+	2.16067i	0.272352	+	0.0799699i
$731$	7.49015	−	8.64410i	0.277033	−	0.319714i
$732$	−1.49629	+	0.439349i	−0.0553043	+	0.0162388i
$733$	−4.60963	+	10.0937i	−0.170261	+	0.372818i	−0.975457	−	0.220189i	$-0.929332\pi$
$733$	−4.60963	+	10.0937i	−0.170261	+	0.372818i	0.805197	+	0.593008i	$0.202060\pi$
$734$	1.73467	+	12.0649i	0.0640279	+	0.445324i
$735$	13.4291			0.495341
$736$	3.37782	+	3.40446i	0.124508	+	0.125490i
$737$	−19.8705			−0.731938
$738$	−0.582320	−	4.05012i	−0.0214355	−	0.149087i
$739$	−15.0167	+	32.8820i	−0.552399	+	1.20958i	0.403254	+	0.915088i	$0.367879\pi$
$739$	−15.0167	+	32.8820i	−0.552399	+	1.20958i	−0.955653	+	0.294496i	$0.904848\pi$
$740$	−2.26398	+	0.664765i	−0.0832256	+	0.0244373i
$741$	23.6520	−	27.2958i	0.868877	−	1.00274i
$742$	9.47011	+	2.78067i	0.347659	+	0.102082i
$743$	22.3469	−	14.3615i	0.819830	−	0.526873i	−0.0622013	−	0.998064i	$-0.519812\pi$
$743$	22.3469	−	14.3615i	0.819830	−	0.526873i	0.882031	+	0.471191i	$0.156176\pi$
$744$	1.25244	+	2.74246i	0.0459167	+	0.100544i
$745$	−14.2674	−	16.4655i	−0.522719	−	0.603249i
$746$	4.66574	+	2.99849i	0.170825	+	0.109783i
$747$	−0.788201	+	5.48206i	−0.0288388	+	0.200578i
$748$	0.921732	−	6.41079i	0.0337019	−	0.234402i
$749$	55.3347	+	35.5614i	2.02188	+	1.29939i
$750$	6.19319	+	7.14732i	0.226143	+	0.260983i
$751$	5.72851	+	12.5437i	0.209036	+	0.457725i	0.984889	−	0.173189i	$-0.0554072\pi$
$751$	5.72851	+	12.5437i	0.209036	+	0.457725i	−0.775852	+	0.630914i	$0.782680\pi$
$752$	−8.09543	+	5.20262i	−0.295210	+	0.189720i
$753$	−9.78622	−	2.87349i	−0.356630	−	0.104716i
$754$	22.9281	−	26.4605i	0.834993	−	0.963633i
$755$	−13.0204	+	3.82315i	−0.473863	+	0.139139i
$756$	−1.83829	+	4.02529i	−0.0668578	+	0.146398i
$757$	5.42275	+	37.7160i	0.197093	+	1.37081i	0.812664	+	0.582732i	$0.198016\pi$
$757$	5.42275	+	37.7160i	0.197093	+	1.37081i	−0.615571	+	0.788081i	$0.711075\pi$
$758$	−10.2328			−0.371674
$759$	−6.92874	−	3.81878i	−0.251497	−	0.138613i
$760$	−7.04583			−0.255579
$761$	−6.16173	−	42.8558i	−0.223363	−	1.55352i	−0.725187	−	0.688551i	$-0.758247\pi$
$761$	−6.16173	−	42.8558i	−0.223363	−	1.55352i	0.501825	−	0.864969i	$-0.332662\pi$
$762$	2.26501	−	4.95969i	0.0820528	−	0.179671i
$763$	−52.1527	+	15.3134i	−1.88806	+	0.554383i
$764$	−16.4905	+	19.0310i	−0.596604	+	0.688518i
$765$	4.02065	+	1.18057i	0.145367	+	0.0426836i
$766$	−3.77792	+	2.42792i	−0.136502	+	0.0877243i
$767$	22.1644	+	48.5333i	0.800310	+	1.75243i
$768$	0.654861	+	0.755750i	0.0236303	+	0.0272708i
$769$	−29.5055	−	18.9620i	−1.06400	−	0.683789i	−0.113189	−	0.993573i	$-0.536107\pi$
$769$	−29.5055	−	18.9620i	−1.06400	−	0.683789i	−0.950807	+	0.309785i	$0.899743\pi$
$770$	−1.10882	+	7.71202i	−0.0399591	+	0.277922i
$771$	3.96184	−	27.5552i	0.142682	−	0.992377i
$772$	14.2228	+	9.14046i	0.511891	+	0.328973i
$773$	9.74424	+	11.2455i	0.350476	+	0.404471i	0.903426	−	0.428743i	$-0.141044\pi$
$773$	9.74424	+	11.2455i	0.350476	+	0.404471i	−0.552950	+	0.833214i	$0.686498\pi$
$774$	−1.21021	−	2.64998i	−0.0435000	−	0.0952517i
$775$	9.79230	−	6.29313i	0.351750	−	0.226056i
$776$	−11.4942	−	3.37499i	−0.412617	−	0.121155i
$777$	−6.40650	+	7.39350i	−0.229832	+	0.265240i
$778$	−3.27983	+	0.963044i	−0.117587	+	0.0345268i
$779$	11.2211	−	24.5708i	0.402038	−	0.880340i
$780$	−0.831030	−	5.77994i	−0.0297556	−	0.206955i
$781$	8.68398			0.310737
$782$	1.41699	−	18.7757i	0.0506716	−	0.671416i
$783$	6.39946			0.228698
$784$	−1.79064	−	12.4542i	−0.0639513	−	0.444791i
$785$	0.507575	−	1.11143i	0.0181161	−	0.0396688i
$786$	−8.32599	+	2.44473i	−0.296978	+	0.0872006i
$787$	−23.9230	+	27.6087i	−0.852764	+	0.984142i	−0.999988	−	0.00496096i	$-0.998421\pi$
$787$	−23.9230	+	27.6087i	−0.852764	+	0.984142i	0.147224	+	0.989103i	$0.452966\pi$
$788$	12.3218	+	3.61800i	0.438945	+	0.128886i
$789$	−6.35034	+	4.08112i	−0.226078	+	0.145292i
$790$	−1.19437	−	2.61530i	−0.0424937	−	0.0930483i
$791$	8.73599	+	10.0819i	0.310616	+	0.358470i
$792$	−1.38777	−	0.891865i	−0.0493122	−	0.0316910i
$793$	1.21423	−	8.44512i	0.0431184	−	0.299895i
$794$	3.56501	−	24.7952i	0.126518	−	0.879950i
$795$	−2.00262	−	1.28701i	−0.0710257	−	0.0456454i
$796$	−8.90909	−	10.2816i	−0.315774	−	0.364423i
$797$	−18.9378	−	41.4680i	−0.670811	−	1.46887i	−0.872094	−	0.489339i	$-0.837238\pi$
$797$	−18.9378	−	41.4680i	−0.670811	−	1.46887i	0.201282	−	0.979533i	$-0.435489\pi$
$798$	−24.5754	+	15.7936i	−0.869959	+	0.559089i
$799$	36.2509	+	10.6442i	1.28247	+	0.376566i
$800$	2.52832	−	2.91784i	0.0893896	−	0.103161i
$801$	−10.8673	+	3.19093i	−0.383978	+	0.112746i
$802$	−3.72081	+	8.14744i	−0.131386	+	0.287696i
$803$	1.68695	+	11.7330i	0.0595310	+	0.414047i
$804$	−12.0453			−0.424805
$805$	−1.70461	+	22.5866i	−0.0600795	+	0.796075i
$806$	−16.4950			−0.581010
$807$	0.836370	+	5.81708i	0.0294416	+	0.204771i
$808$	−7.66896	+	16.7927i	−0.269793	+	0.590764i
$809$	20.9411	−	6.14886i	0.736250	−	0.216182i	0.107953	−	0.994156i	$-0.465570\pi$
$809$	20.9411	−	6.14886i	0.736250	−	0.216182i	0.628297	+	0.777974i	$0.283752\pi$
$810$	0.698939	−	0.806618i	0.0245582	−	0.0283417i
$811$	−29.1306	−	8.55353i	−1.02292	−	0.300355i	−0.273088	−	0.961989i	$-0.588045\pi$
$811$	−29.1306	−	8.55353i	−1.02292	−	0.300355i	−0.749827	+	0.661634i	$0.769863\pi$
$812$	−23.8233	+	15.3103i	−0.836033	+	0.537286i
$813$	−8.80899	−	19.2890i	−0.308945	−	0.676495i
$814$	−2.38825	−	2.75619i	−0.0837082	−	0.0966044i
$815$	−4.31285	−	2.77170i	−0.151072	−	0.0970883i
$816$	0.558746	−	3.88617i	0.0195600	−	0.136043i
$817$	2.73697	−	19.0360i	0.0957544	−	0.665986i
$818$	−19.5857	−	12.5869i	−0.684797	−	0.440092i
$819$	−15.8546	−	18.2972i	−0.554006	−	0.639357i
$820$	−1.81419	−	3.97253i	−0.0633544	−	0.138727i
$821$	−28.6045	+	18.3830i	−0.998305	+	0.641572i	−0.934341	−	0.356381i	$-0.884011\pi$
$821$	−28.6045	+	18.3830i	−0.998305	+	0.641572i	−0.0639641	+	0.997952i	$0.520374\pi$
$822$	8.61793	+	2.53045i	0.300585	+	0.0882597i
$823$	−34.2879	+	39.5703i	−1.19520	+	1.37933i	−0.288543	+	0.957467i	$0.593171\pi$
$823$	−34.2879	+	39.5703i	−1.19520	+	1.37933i	−0.906657	+	0.421868i	$0.861375\pi$
$824$	10.9648	−	3.21956i	0.381977	−	0.112159i
$825$	−2.64579	+	5.79347i	−0.0921146	+	0.201703i
$826$	−6.14156	−	42.7155i	−0.213692	−	1.48626i
$827$	−20.0689			−0.697864			−0.348932	−	0.937148i	$-0.613456\pi$
$827$	−20.0689			−0.697864			−0.348932	+	0.937148i	$0.613456\pi$
$828$	−4.20014	−	2.31491i	−0.145965	−	0.0804487i
$829$	−30.6227			−1.06357			−0.531785	−	0.846879i	$-0.678479\pi$
$829$	−30.6227			−1.06357			−0.531785	+	0.846879i	$0.678479\pi$
$830$	0.841254	+	5.85105i	0.0292003	+	0.203093i
$831$	−1.31813	+	2.88631i	−0.0457256	+	0.100125i
$832$	−5.24950	+	1.54139i	−0.181994	+	0.0534382i
$833$	−32.3498	+	37.3336i	−1.12085	+	1.29353i
$834$	2.93880	+	0.862910i	0.101762	+	0.0298801i
$835$	−10.5481	+	6.77888i	−0.365034	+	0.234593i
$836$	−4.52392	−	9.90599i	−0.156463	−	0.342606i
$837$	−1.97435	−	2.27852i	−0.0682435	−	0.0787572i
$838$	−1.89252	−	1.21625i	−0.0653759	−	0.0420145i
$839$	−5.68452	+	39.5367i	−0.196251	+	1.36496i	0.618791	+	0.785556i	$0.287623\pi$
$839$	−5.68452	+	39.5367i	−0.196251	+	1.36496i	−0.815042	+	0.579402i	$0.803286\pi$
$840$	−0.672158	+	4.67496i	−0.0231917	+	0.161301i
$841$	10.0556	+	6.46233i	0.346744	+	0.222839i
$842$	12.2209	+	14.1037i	0.421160	+	0.486044i
$843$	7.58993	+	16.6196i	0.261411	+	0.572411i
$844$	−17.7860	+	11.4304i	−0.612219	+	0.393449i
$845$	17.3408	+	5.09173i	0.596543	+	0.175161i
$846$	6.30176	−	7.27262i	0.216659	−	0.250038i
$847$	35.1507	−	10.3212i	1.20779	−	0.354640i
$848$	−0.926540	+	2.02884i	−0.0318175	+	0.0696706i
$849$	3.20212	+	22.2712i	0.109896	+	0.764346i
$850$	−15.1582			−0.519922
$851$	−7.46754	−	7.52643i	−0.255984	−	0.258003i
$852$	5.26416			0.180347
$853$	0.551160	+	3.83340i	0.0188714	+	0.131253i	0.997079	−	0.0763751i	$-0.0243346\pi$
$853$	0.551160	+	3.83340i	0.0188714	+	0.131253i	−0.978208	+	0.207628i	$0.933426\pi$
$854$	−2.86673	+	6.27725i	−0.0980973	+	0.214803i
$855$	6.76043	−	1.98504i	0.231202	−	0.0678869i
$856$	−9.73393	+	11.2336i	−0.332699	+	0.383955i
$857$	−6.91320	−	2.02990i	−0.236150	−	0.0693400i	0.161516	−	0.986870i	$-0.448362\pi$
$857$	−6.91320	−	2.02990i	−0.236150	−	0.0693400i	−0.397666	+	0.917530i	$0.630180\pi$
$858$	7.59265	−	4.87950i	0.259209	−	0.166583i
$859$	4.25641	+	9.32025i	0.145227	+	0.318003i	0.968241	−	0.250018i	$-0.0804366\pi$
$859$	4.25641	+	9.32025i	0.145227	+	0.318003i	−0.823014	+	0.568021i	$0.807709\pi$
$860$	−2.03618	−	2.34988i	−0.0694332	−	0.0801302i
$861$	−15.2324	−	9.78929i	−0.519120	−	0.333618i
$862$	−0.685564	+	4.76820i	−0.0233504	+	0.162405i
$863$	−5.28585	+	36.7639i	−0.179933	+	1.25146i	0.676982	+	0.736000i	$0.263288\pi$
$863$	−5.28585	+	36.7639i	−0.179933	+	1.25146i	−0.856914	+	0.515459i	$0.827622\pi$
$864$	−0.841254	−	0.540641i	−0.0286200	−	0.0183930i
$865$	−3.57800	−	4.12923i	−0.121656	−	0.140398i
$866$	−2.59854	−	5.69000i	−0.0883018	−	0.193354i
$867$	1.33382	−	0.857197i	0.0452991	−	0.0291119i
$868$	12.8011	+	3.75875i	0.434498	+	0.127580i
$869$	2.91008	−	3.35841i	0.0987178	−	0.113926i
$870$	6.55353	−	1.92429i	0.222185	−	0.0652395i
$871$	27.3764	−	59.9460i	0.927614	−	2.03119i
$872$	−1.74805	−	12.1580i	−0.0591965	−	0.411721i
$873$	11.9794			0.405442
$874$	−15.0636	−	27.8464i	−0.509534	−	0.941918i
$875$	41.8501			1.41479
$876$	1.02261	+	7.11242i	0.0345508	+	0.240306i
$877$	−0.594109	+	1.30092i	−0.0200616	+	0.0439289i	−0.919398	−	0.393329i	$-0.871323\pi$
$877$	−0.594109	+	1.30092i	−0.0200616	+	0.0439289i	0.899336	+	0.437258i	$0.144050\pi$
$878$	12.9967	−	3.81617i	0.438617	−	0.128790i
$879$	−6.81170	+	7.86112i	−0.229753	+	0.265149i
$880$	−1.68936	−	0.496041i	−0.0569483	−	0.0167215i
$881$	−16.7233	+	10.7474i	−0.563421	+	0.362089i	−0.791137	−	0.611639i	$-0.790511\pi$
$881$	−16.7233	+	10.7474i	−0.563421	+	0.362089i	0.227716	+	0.973728i	$0.426874\pi$
$882$	5.22685	+	11.4452i	0.175997	+	0.385380i
$883$	−10.6666	−	12.3099i	−0.358960	−	0.414262i	0.547331	−	0.836916i	$-0.315644\pi$
$883$	−10.6666	−	12.3099i	−0.358960	−	0.414262i	−0.906291	+	0.422654i	$0.861098\pi$
$884$	18.0704	+	11.6131i	0.607773	+	0.390592i
$885$	−1.48128	+	10.3025i	−0.0497927	+	0.346316i
$886$	−0.788405	+	5.48348i	−0.0264870	+	0.184221i
$887$	−18.4832	−	11.8784i	−0.620604	−	0.398838i	0.192216	−	0.981353i	$-0.438433\pi$
$887$	−18.4832	−	11.8784i	−0.620604	−	0.398838i	−0.812820	+	0.582515i	$0.802069\pi$
$888$	−1.44774	−	1.67078i	−0.0485829	−	0.0560677i
$889$	−10.0231	−	21.9475i	−0.336164	−	0.736096i
$890$	−10.1695	+	6.53551i	−0.340881	+	0.219071i
$891$	1.58282	+	0.464758i	0.0530265	+	0.0155700i
$892$	1.67113	−	1.92859i	0.0559536	−	0.0645739i
$893$	60.9533	−	17.8975i	2.03972	−	0.598917i
$894$	8.47987	−	18.5683i	0.283609	−	0.621018i
$895$	−2.84761	−	19.8056i	−0.0951851	−	0.662027i
$896$	4.42518			0.147835
$897$	21.0666	−	15.6416i	0.703395	−	0.522257i
$898$	−13.5471			−0.452073
$899$	−2.74580	−	19.0974i	−0.0915774	−	0.636935i
$900$	−1.60386	+	3.51195i	−0.0534619	+	0.117065i
$901$	8.40211	−	2.46708i	0.279915	−	0.0821904i
$902$	4.42029	−	5.10128i	0.147179	−	0.169854i
$903$	−12.3694	−	3.63200i	−0.411629	−	0.120865i
$904$	−2.53606	+	1.62983i	−0.0843480	+	0.0542072i
$905$	3.22143	+	7.05394i	0.107084	+	0.234481i
$906$	−8.32613	−	9.60886i	−0.276617	−	0.319233i
$907$	39.5458	+	25.4146i	1.31310	+	0.843877i	0.994573	−	0.104038i	$-0.0331763\pi$
$907$	39.5458	+	25.4146i	1.31310	+	0.843877i	0.318524	+	0.947915i	$0.396813\pi$
$908$	2.80685	−	19.5220i	0.0931485	−	0.647862i
$909$	2.62727	−	18.2730i	0.0871410	−	0.606079i
$910$	−21.7382	−	13.9703i	−0.720616	−	0.463111i
$911$	7.57632	+	8.74354i	0.251015	+	0.289686i	0.867247	−	0.497878i	$-0.165887\pi$
$911$	7.57632	+	8.74354i	0.251015	+	0.289686i	−0.616232	+	0.787564i	$0.711342\pi$
$912$	−2.74236	−	6.00493i	−0.0908086	−	0.198843i
$913$	−7.68606	+	4.93953i	−0.254371	+	0.163475i
$914$	10.6635	+	3.13109i	0.352718	+	0.103567i
$915$	1.08996	−	1.25788i	0.0360331	−	0.0415844i
$916$	10.7515	−	3.15692i	0.355239	−	0.104308i
$917$	−15.9517	+	34.9294i	−0.526772	+	1.15347i
$918$	0.558746	+	3.88617i	0.0184414	+	0.128263i
$919$	35.1441			1.15930			0.579648	−	0.814867i	$-0.303190\pi$
$919$	35.1441			1.15930			0.579648	+	0.814867i	$0.303190\pi$
$920$	−4.99735	−	1.10768i	−0.164758	−	0.0365190i
$921$	−5.13212			−0.169109
$922$	4.74370	+	32.9931i	0.156225	+	1.08657i
$923$	−11.9643	+	26.1982i	−0.393810	+	0.862323i
$924$	−7.00427	+	2.05664i	−0.230424	+	0.0676585i
$925$	−5.58950	+	6.45063i	−0.183782	+	0.212095i
$926$	18.6479	+	5.47551i	0.612808	+	0.179937i
$927$	−9.61361	+	6.17829i	−0.315752	+	0.202922i
$928$	−2.65843	−	5.82115i	−0.0872673	−	0.191089i
$929$	23.4261	+	27.0352i	0.768586	+	0.886995i	0.996230	−	0.0867489i	$-0.0276478\pi$
$929$	23.4261	+	27.0352i	0.768586	+	0.886995i	−0.227644	+	0.973744i	$0.573102\pi$
$930$	−2.70702	−	1.73970i	−0.0887668	−	0.0570469i
$931$	−11.8209	+	82.2160i	−0.387414	+	2.69452i
$932$	−2.56439	+	17.8357i	−0.0839994	+	0.584229i
$933$	−17.9784	−	11.5540i	−0.588585	−	0.378261i
$934$	21.9542	+	25.3365i	0.718364	+	0.829036i
$935$	2.87162	+	6.28797i	0.0939120	+	0.205639i
$936$	4.60260	−	2.95791i	0.150441	−	0.0966823i
$937$	−16.9547	−	4.97835i	−0.553886	−	0.162636i	−0.00720126	−	0.999974i	$-0.502292\pi$
$937$	−16.9547	−	4.97835i	−0.553886	−	0.162636i	−0.546685	+	0.837338i	$0.684110\pi$
$938$	−34.9058	+	40.2835i	−1.13972	+	1.31530i
$939$	15.3186	−	4.49794i	0.499903	−	0.146785i
$940$	4.26663	−	9.34263i	0.139162	−	0.304723i
$941$	2.26593	+	15.7599i	0.0738673	+	0.513758i	0.992841	+	0.119440i	$0.0381100\pi$
$941$	2.26593	+	15.7599i	0.0738673	+	0.513758i	−0.918974	+	0.394318i	$0.870981\pi$
$942$	1.14480			0.0372995
$943$	11.8215	−	15.6631i	0.384961	−	0.510060i
$944$	9.75208			0.317403
$945$	−0.672158	−	4.67496i	−0.0218653	−	0.152077i
$946$	1.99641	−	4.37153i	0.0649089	−	0.142131i
$947$	18.5903	−	5.45860i	0.604103	−	0.177381i	0.0346429	−	0.999400i	$-0.488971\pi$
$947$	18.5903	−	5.45860i	0.604103	−	0.177381i	0.569460	+	0.822019i	$0.307152\pi$
$948$	1.76407	−	2.03584i	0.0572942	−	0.0661211i
$949$	−37.7206	−	11.0758i	−1.22446	−	0.359535i
$950$	−21.4414	+	13.7795i	−0.695649	+	0.447067i
$951$	−4.52131	−	9.90028i	−0.146613	−	0.321039i
$952$	−11.3774	−	13.1303i	−0.368745	−	0.425554i
$953$	−24.8293	−	15.9568i	−0.804300	−	0.516892i	0.0727163	−	0.997353i	$-0.476833\pi$
$953$	−24.8293	−	15.9568i	−0.804300	−	0.516892i	−0.877016	+	0.480460i	$0.840470\pi$
$954$	0.317418	−	2.20769i	0.0102768	−	0.0714767i
$955$	3.82494	−	26.6030i	0.123772	−	0.860854i
$956$	22.9224	+	14.7313i	0.741364	+	0.476446i
$957$	6.91325	+	7.97832i	0.223474	+	0.257902i
$958$	−0.687814	−	1.50610i	−0.0222222	−	0.0486599i
$959$	33.4364	−	21.4883i	1.07972	−	0.693892i
$960$	−1.02408	−	0.300696i	−0.0330519	−	0.00970491i
$961$	14.3482	−	16.5587i	0.462845	−	0.534152i
$962$	11.6054	−	3.40765i	0.374172	−	0.109867i
$963$	6.17478	−	13.5209i	0.198979	−	0.435704i
$964$	3.17028	+	22.0498i	0.102108	+	0.710175i
$965$	−18.0447			−0.580879
$966$	−19.9133	+	7.33833i	−0.640700	+	0.236107i
$967$	5.25882			0.169112			0.0845562	−	0.996419i	$-0.473053\pi$
$967$	5.25882			0.169112			0.0845562	+	0.996419i	$0.473053\pi$
$968$	1.17818	+	8.19441i	0.0378681	+	0.263378i
$969$	−10.7669	+	23.5761i	−0.345881	+	0.757374i
$970$	12.2678	−	3.60216i	0.393896	−	0.115658i
$971$	−13.4313	+	15.5006i	−0.431032	+	0.497437i	−0.929166	−	0.369663i	$-0.879473\pi$
$971$	−13.4313	+	15.5006i	−0.431032	+	0.497437i	0.498134	+	0.867100i	$0.334019\pi$
$972$	0.959493	+	0.281733i	0.0307758	+	0.00903658i
$973$	11.4021	−	7.32771i	0.365536	−	0.234916i
$974$	−8.72182	−	19.0981i	−0.279465	−	0.611943i
$975$	−13.8327	−	15.9638i	−0.443002	−	0.511252i
$976$	−1.31190	−	0.843105i	−0.0419928	−	0.0269871i
$977$	−0.247958	+	1.72459i	−0.00793289	+	0.0551744i	−0.993403	−	0.114672i	$-0.963418\pi$
$977$	−0.247958	+	1.72459i	−0.00793289	+	0.0551744i	0.985470	+	0.169847i	$0.0543273\pi$
$978$	0.683592	−	4.75449i	0.0218589	−	0.152032i
$979$	−15.7180	−	10.1014i	−0.502350	−	0.322841i
$980$	8.79421	+	10.1491i	0.280921	+	0.324200i
$981$	5.10254	+	11.1730i	0.162912	+	0.356727i
$982$	21.7151	−	13.9555i	0.692958	−	0.445337i
$983$	−0.0225550	−	0.00662274i	−0.000719392	−	0.000211233i	0.281373	−	0.959599i	$-0.409210\pi$
$983$	−0.0225550	−	0.00662274i	−0.000719392	−	0.000211233i	−0.282092	+	0.959387i	$0.591028\pi$
$984$	2.67954	−	3.09235i	0.0854206	−	0.0985807i
$985$	−13.1511	+	3.86152i	−0.419030	+	0.123038i
$986$	−10.4373	+	22.8546i	−0.332393	+	0.727838i
$987$	−6.06030	−	42.1503i	−0.192902	−	1.34166i
$988$	36.1176			1.14905
$989$	4.93389	−	13.0713i	0.156889	−	0.415642i
$990$	1.76068			0.0559581
$991$	2.25098	+	15.6559i	0.0715048	+	0.497327i	0.993830	+	0.110913i	$0.0353773\pi$
$991$	2.25098	+	15.6559i	0.0715048	+	0.497327i	−0.922325	+	0.386414i	$0.873714\pi$
$992$	−1.25244	+	2.74246i	−0.0397650	+	0.0870732i
$993$	−12.9607	+	3.80561i	−0.411295	+	0.120767i
$994$	15.2549	−	17.6051i	0.483855	−	0.558399i
$995$	13.9321	+	4.09083i	0.441677	+	0.129688i
$996$	−4.65922	+	2.99430i	−0.147633	+	0.0948780i
$997$	−4.06792	−	8.90750i	−0.128832	−	0.282103i	0.834213	−	0.551442i	$-0.185922\pi$
$997$	−4.06792	−	8.90750i	−0.128832	−	0.282103i	−0.963046	+	0.269339i	$0.913195\pi$
$998$	4.21577	+	4.86526i	0.133448	+	0.154007i
$999$	1.85981	+	1.19523i	0.0588417	+	0.0378153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.b.49.1	yes	10
3.2	odd	2		414.2.i.e.325.1		10
23.8	even	11	inner	138.2.e.b.31.1	✓	10
23.10	odd	22		3174.2.a.bb.1.4		5
23.13	even	11		3174.2.a.ba.1.2		5
69.8	odd	22		414.2.i.e.307.1		10
69.56	even	22		9522.2.a.br.1.2		5
69.59	odd	22		9522.2.a.bs.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.b.31.1	✓	10	23.8	even	11	inner
138.2.e.b.49.1	yes	10	1.1	even	1	trivial
414.2.i.e.307.1		10	69.8	odd	22
414.2.i.e.325.1		10	3.2	odd	2
3174.2.a.ba.1.2		5	23.13	even	11
3174.2.a.bb.1.4		5	23.10	odd	22
9522.2.a.br.1.2		5	69.56	even	22
9522.2.a.bs.1.4		5	69.59	odd	22

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.698939 - 0.806618i) q^{5} +(0.959493 + 0.281733i) q^{6} +(3.72270 - 2.39243i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.698939 - 0.806618i) q^{5} +(0.959493 + 0.281733i) q^{6} +(3.72270 - 2.39243i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-0.897877 - 0.577031i) q^{10} +(0.234769 - 1.63285i) q^{11} +(0.142315 - 0.989821i) q^{12} +(4.60260 + 2.95791i) q^{13} +(-2.89788 - 3.34433i) q^{14} +(0.443376 + 0.970858i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-3.76709 - 1.10612i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(-6.33409 + 1.85986i) q^{19} +(-0.443376 + 0.970858i) q^{20} +(0.629769 + 4.38014i) q^{21} -1.64964 q^{22} +(-4.78492 + 0.323343i) q^{23} -1.00000 q^{24} +(0.549456 + 3.82155i) q^{25} +(2.27279 - 4.97671i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-2.89788 + 3.34433i) q^{28} +(6.14024 + 1.80294i) q^{29} +(0.897877 - 0.577031i) q^{30} +(-1.25244 - 2.74246i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.38777 + 0.891865i) q^{33} +(-0.558746 + 3.88617i) q^{34} +(0.672158 - 4.67496i) q^{35} +(0.841254 + 0.540641i) q^{36} +(1.44774 + 1.67078i) q^{37} +(2.74236 + 6.00493i) q^{38} +(-4.60260 + 2.95791i) q^{39} +(1.02408 + 0.300696i) q^{40} +(-2.67954 + 3.09235i) q^{41} +(4.24593 - 1.24672i) q^{42} +(-1.21021 + 2.64998i) q^{43} +(0.234769 + 1.63285i) q^{44} -1.06731 q^{45} +(1.00102 + 4.69020i) q^{46} -9.62306 q^{47} +(0.142315 + 0.989821i) q^{48} +(5.22685 - 11.4452i) q^{49} +(3.70446 - 1.08773i) q^{50} +(2.57107 - 2.96717i) q^{51} +(-5.24950 - 1.54139i) q^{52} +(-1.87633 + 1.20584i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(-1.15300 - 1.33063i) q^{55} +(3.72270 + 2.39243i) q^{56} +(0.939490 - 6.53430i) q^{57} +(0.910738 - 6.33432i) q^{58} +(8.20397 + 5.27237i) q^{59} +(-0.698939 - 0.806618i) q^{60} +(-0.647821 - 1.41853i) q^{61} +(-2.53631 + 1.62999i) q^{62} +(-4.24593 - 1.24672i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(5.60284 - 1.64514i) q^{65} +(0.685287 - 1.50057i) q^{66} +(-1.71423 - 11.9227i) q^{67} +3.92613 q^{68} +(1.69360 - 4.48684i) q^{69} -4.72304 q^{70} +(0.749168 + 5.21058i) q^{71} +(0.415415 - 0.909632i) q^{72} +(-6.89449 + 2.02441i) q^{73} +(1.44774 - 1.67078i) q^{74} +(-3.70446 - 1.08773i) q^{75} +(5.55353 - 3.56904i) q^{76} +(-3.03252 - 6.64029i) q^{77} +(3.58282 + 4.13480i) q^{78} +(2.26617 + 1.45638i) q^{79} +(0.151894 - 1.05645i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(3.44222 + 2.21218i) q^{82} +(-3.62690 - 4.18567i) q^{83} +(-1.83829 - 4.02529i) q^{84} +(-3.52518 + 2.26550i) q^{85} +(2.79524 + 0.820757i) q^{86} +(-4.19075 + 4.83639i) q^{87} +(1.58282 - 0.464758i) q^{88} +(4.70504 - 10.3026i) q^{89} +(0.151894 + 1.05645i) q^{90} +24.2107 q^{91} +(4.50000 - 1.65831i) q^{92} +3.01491 q^{93} +(1.36950 + 9.52511i) q^{94} +(-2.92694 + 6.40911i) q^{95} +(0.959493 - 0.281733i) q^{96} +(-7.84485 + 9.05344i) q^{97} +(-12.0726 - 3.54482i) q^{98} +(-1.38777 + 0.891865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9	\( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21} + 22 q^{22} - 10 q^{23} - 10 q^{24} - 43 q^{25} - 9 q^{26} + q^{27} - 11 q^{28} + 13 q^{29} - 9 q^{30} + 8 q^{31} - q^{32} + 22 q^{33} + 9 q^{34} - q^{36} - 13 q^{37} - 3 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} - 8 q^{43} + 11 q^{44} - 2 q^{45} + q^{46} - 8 q^{47} + q^{48} + 29 q^{49} + 23 q^{50} - 9 q^{51} + 2 q^{52} - 35 q^{53} + q^{54} - 11 q^{55} + 3 q^{57} + 13 q^{58} + 37 q^{59} + 2 q^{60} - 2 q^{61} + 8 q^{62} - q^{64} + 37 q^{65} + 14 q^{67} - 2 q^{68} - q^{69} - 22 q^{70} + 44 q^{71} - q^{72} - 49 q^{73} - 13 q^{74} - 23 q^{75} + 8 q^{76} + 44 q^{77} + 20 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} + 12 q^{82} - 17 q^{83} - 11 q^{84} - 37 q^{85} + 14 q^{86} - 2 q^{87} + 59 q^{89} - 2 q^{90} + 66 q^{91} + 45 q^{92} + 36 q^{93} - 19 q^{94} - 28 q^{95} + q^{96} - 21 q^{97} - 26 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9 + 9 * q^10 + 11 * q^11 + q^12 + 13 * q^13 - 11 * q^14 + 13 * q^15 - q^16 - 24 * q^17 - q^18 - 14 * q^19 - 13 * q^20 + 11 * q^21 + 22 * q^22 - 10 * q^23 - 10 * q^24 - 43 * q^25 - 9 * q^26 + q^27 - 11 * q^28 + 13 * q^29 - 9 * q^30 + 8 * q^31 - q^32 + 22 * q^33 + 9 * q^34 - q^36 - 13 * q^37 - 3 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 - 8 * q^43 + 11 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + q^48 + 29 * q^49 + 23 * q^50 - 9 * q^51 + 2 * q^52 - 35 * q^53 + q^54 - 11 * q^55 + 3 * q^57 + 13 * q^58 + 37 * q^59 + 2 * q^60 - 2 * q^61 + 8 * q^62 - q^64 + 37 * q^65 + 14 * q^67 - 2 * q^68 - q^69 - 22 * q^70 + 44 * q^71 - q^72 - 49 * q^73 - 13 * q^74 - 23 * q^75 + 8 * q^76 + 44 * q^77 + 20 * q^78 - 8 * q^79 - 2 * q^80 - q^81 + 12 * q^82 - 17 * q^83 - 11 * q^84 - 37 * q^85 + 14 * q^86 - 2 * q^87 + 59 * q^89 - 2 * q^90 + 66 * q^91 + 45 * q^92 + 36 * q^93 - 19 * q^94 - 28 * q^95 + q^96 - 21 * q^97 - 26 * q^98 - 22 * q^99

Introduction

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