LMFDB - Embedded newform 429.2.bj.a.304.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(73,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 14, 5]))

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

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

chi := DirichletCharacter("429.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bj (of order $20$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			304.5
Character	$\chi$	$=$	429.304
Dual form			429.2.bj.a.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.114692 - 0.724135i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.39090 - 0.451929i) q^{4} +(-0.292172 + 1.84470i) q^{5} +(-0.724135 - 0.114692i) q^{6} +(2.11974 + 1.08006i) q^{7} +(-1.15248 - 2.26187i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.114692 - 0.724135i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.39090 - 0.451929i) q^{4} +(-0.292172 + 1.84470i) q^{5} +(-0.724135 - 0.114692i) q^{6} +(2.11974 + 1.08006i) q^{7} +(-1.15248 - 2.26187i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.36932 q^{10} +(-0.393359 - 3.29322i) q^{11} -1.46247i q^{12} +(2.53125 + 2.56764i) q^{13} +(0.538995 - 1.65886i) q^{14} +(1.66413 + 0.847915i) q^{15} +(0.860615 - 0.625273i) q^{16} +(2.17868 - 1.58290i) q^{17} +(-0.332848 + 0.653252i) q^{18} +(-0.0384093 + 0.0195705i) q^{19} +(0.427293 + 2.69782i) q^{20} +(1.68224 - 1.68224i) q^{21} +(-2.33962 + 0.662550i) q^{22} +0.141998i q^{23} +(-2.50730 + 0.397117i) q^{24} +(1.43773 + 0.467148i) q^{25} +(1.56901 - 2.12745i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(3.43646 + 0.544281i) q^{28} +(2.55313 - 0.829563i) q^{29} +(0.423143 - 1.30230i) q^{30} +(-8.20252 + 1.29915i) q^{31} +(-4.14154 - 4.14154i) q^{32} +(-3.25359 - 0.643553i) q^{33} +(-1.39611 - 1.39611i) q^{34} +(-2.61172 + 3.59473i) q^{35} +(-1.39090 - 0.451929i) q^{36} +(1.78272 - 3.49878i) q^{37} +(0.0185769 + 0.0255689i) q^{38} +(3.22417 - 1.61391i) q^{39} +(4.50918 - 1.46512i) q^{40} +(-1.76153 + 0.897543i) q^{41} +(-1.41111 - 1.02523i) q^{42} -4.73589 q^{43} +(-2.03542 - 4.40275i) q^{44} +(1.32066 - 1.32066i) q^{45} +(0.102826 - 0.0162860i) q^{46} +(-4.62754 + 2.35785i) q^{47} +(-0.328726 - 1.01171i) q^{48} +(-0.787718 - 1.08420i) q^{49} +(0.173382 - 1.09469i) q^{50} +(-0.832180 - 2.56119i) q^{51} +(4.68109 + 2.42738i) q^{52} +(-1.29852 - 0.943427i) q^{53} +(0.518424 + 0.518424i) q^{54} +(6.18992 + 0.236555i) q^{55} -6.03933i q^{56} +(0.00674354 + 0.0425770i) q^{57} +(-0.893539 - 1.75367i) q^{58} +(-5.25882 + 10.3210i) q^{59} +(2.69782 + 0.427293i) q^{60} +(2.71240 + 3.73329i) q^{61} +(1.88152 + 5.79073i) q^{62} +(-1.08006 - 2.11974i) q^{63} +(-1.27349 + 1.75281i) q^{64} +(-5.47608 + 3.91920i) q^{65} +(-0.0928595 + 2.42985i) q^{66} +(-0.334429 + 0.334429i) q^{67} +(2.31495 - 3.18626i) q^{68} +(0.135048 + 0.0438799i) q^{69} +(2.90261 + 1.47895i) q^{70} +(-1.91807 + 12.1102i) q^{71} +(-0.397117 + 2.50730i) q^{72} +(10.8047 + 5.50525i) q^{73} +(-2.73805 - 0.889647i) q^{74} +(0.888568 - 1.22301i) q^{75} +(-0.0445788 + 0.0445788i) q^{76} +(2.72306 - 7.40563i) q^{77} +(-1.53848 - 2.14963i) q^{78} +(4.53610 - 6.24341i) q^{79} +(0.901994 + 1.77026i) q^{80} +(0.309017 + 0.951057i) q^{81} +(0.851975 + 1.17264i) q^{82} +(1.28304 + 0.203214i) q^{83} +(1.57957 - 3.10007i) q^{84} +(2.28343 + 4.48148i) q^{85} +(0.543167 + 3.42942i) q^{86} -2.68452i q^{87} +(-6.99548 + 4.68509i) q^{88} +(-4.41736 - 4.41736i) q^{89} +(-1.10780 - 0.804867i) q^{90} +(2.59238 + 8.17665i) q^{91} +(0.0641732 + 0.197505i) q^{92} +(-1.29915 + 8.20252i) q^{93} +(2.23814 + 3.08054i) q^{94} +(-0.0248796 - 0.0765715i) q^{95} +(-5.21865 + 2.65903i) q^{96} +(-18.5562 + 2.93901i) q^{97} +(-0.694763 + 0.694763i) q^{98} +(-1.61747 + 2.89548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9	$ 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9} - 10 q^{11} + 10 q^{13} - 60 q^{14} + 4 q^{15} + 80 q^{16} - 74 q^{20} + 8 q^{22} + 30 q^{24} + 38 q^{26} - 28 q^{27} - 20 q^{29} - 8 q^{31} + 20 q^{33} - 48 q^{34} + 20 q^{35} + 12 q^{37} - 10 q^{39} + 40 q^{40} - 110 q^{41} + 20 q^{42} - 36 q^{44} + 4 q^{45} - 20 q^{46} - 30 q^{47} - 20 q^{48} + 90 q^{50} - 10 q^{52} + 52 q^{53} - 64 q^{55} + 30 q^{57} + 24 q^{58} - 36 q^{59} - 74 q^{60} - 60 q^{61} + 48 q^{66} + 60 q^{67} + 60 q^{68} + 116 q^{70} + 20 q^{71} - 30 q^{72} + 70 q^{73} + 120 q^{74} - 52 q^{78} - 120 q^{79} + 8 q^{80} - 28 q^{81} + 30 q^{83} + 30 q^{84} - 40 q^{85} + 62 q^{86} + 48 q^{89} - 4 q^{91} - 144 q^{92} - 8 q^{93} - 20 q^{94} + 82 q^{97} - 10 q^{99}+O(q^{100}) $ 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9 - 10 * q^11 + 10 * q^13 - 60 * q^14 + 4 * q^15 + 80 * q^16 - 74 * q^20 + 8 * q^22 + 30 * q^24 + 38 * q^26 - 28 * q^27 - 20 * q^29 - 8 * q^31 + 20 * q^33 - 48 * q^34 + 20 * q^35 + 12 * q^37 - 10 * q^39 + 40 * q^40 - 110 * q^41 + 20 * q^42 - 36 * q^44 + 4 * q^45 - 20 * q^46 - 30 * q^47 - 20 * q^48 + 90 * q^50 - 10 * q^52 + 52 * q^53 - 64 * q^55 + 30 * q^57 + 24 * q^58 - 36 * q^59 - 74 * q^60 - 60 * q^61 + 48 * q^66 + 60 * q^67 + 60 * q^68 + 116 * q^70 + 20 * q^71 - 30 * q^72 + 70 * q^73 + 120 * q^74 - 52 * q^78 - 120 * q^79 + 8 * q^80 - 28 * q^81 + 30 * q^83 + 30 * q^84 - 40 * q^85 + 62 * q^86 + 48 * q^89 - 4 * q^91 - 144 * q^92 - 8 * q^93 - 20 * q^94 + 82 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.114692	−	0.724135i	−0.0810993	−	0.512041i	−0.994479	−	0.104933i	$-0.966537\pi$
$2$	−0.114692	−	0.724135i	−0.0810993	−	0.512041i	0.913380	−	0.407108i	$-0.133463\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	1.39090	−	0.451929i	0.695448	−	0.225965i
$5$	−0.292172	+	1.84470i	−0.130663	+	0.824974i	0.832100	+	0.554626i	$0.187139\pi$
$5$	−0.292172	+	1.84470i	−0.130663	+	0.824974i	−0.962763	+	0.270348i	$0.912861\pi$
$6$	−0.724135	−	0.114692i	−0.295627	−	0.0468227i
$7$	2.11974	+	1.08006i	0.801188	+	0.408226i	0.806113	−	0.591762i	$-0.201568\pi$
$7$	2.11974	+	1.08006i	0.801188	+	0.408226i	−0.00492455	+	0.999988i	$0.501568\pi$
$8$	−1.15248	−	2.26187i	−0.407463	−	0.799691i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	1.36932			0.433017
$11$	−0.393359	−	3.29322i	−0.118602	−	0.992942i
$11$	−0.393359	−	3.29322i	−0.118602	−	0.992942i
$12$		−	1.46247i		−	0.422180i
$13$	2.53125	+	2.56764i	0.702042	+	0.712136i
$13$	2.53125	+	2.56764i	0.702042	+	0.712136i
$14$	0.538995	−	1.65886i	0.144052	−	0.443348i
$15$	1.66413	+	0.847915i	0.429676	+	0.218931i
$16$	0.860615	−	0.625273i	0.215154	−	0.156318i
$17$	2.17868	−	1.58290i	0.528407	−	0.383910i	−0.291355	−	0.956615i	$-0.594106\pi$
$17$	2.17868	−	1.58290i	0.528407	−	0.383910i	0.819761	+	0.572705i	$0.194106\pi$
$18$	−0.332848	+	0.653252i	−0.0784531	+	0.153973i
$19$	−0.0384093	+	0.0195705i	−0.00881170	+	0.00448978i	−0.458391	−	0.888751i	$-0.651574\pi$
$19$	−0.0384093	+	0.0195705i	−0.00881170	+	0.00448978i	0.449579	+	0.893241i	$0.351574\pi$
$20$	0.427293	+	2.69782i	0.0955457	+	0.603252i
$21$	1.68224	−	1.68224i	0.367095	−	0.367095i
$22$	−2.33962	+	0.662550i	−0.498808	+	0.141256i
$23$			0.141998i			0.0296087i	0.999890	+	0.0148043i	$0.00471254\pi$
$23$			0.141998i			0.0296087i	−0.999890	+	0.0148043i	$0.995287\pi$
$24$	−2.50730	+	0.397117i	−0.511800	+	0.0810612i
$25$	1.43773	+	0.467148i	0.287547	+	0.0934296i
$26$	1.56901	−	2.12745i	0.307708	−	0.417228i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	3.43646	+	0.544281i	0.649429	+	0.102859i
$29$	2.55313	−	0.829563i	0.474105	−	0.154046i	−0.0622117	−	0.998063i	$-0.519815\pi$
$29$	2.55313	−	0.829563i	0.474105	−	0.154046i	0.536316	+	0.844017i	$0.319815\pi$
$30$	0.423143	−	1.30230i	0.0772551	−	0.237767i
$31$	−8.20252	+	1.29915i	−1.47322	+	0.233334i	−0.840821	−	0.541313i	$-0.817928\pi$
$31$	−8.20252	+	1.29915i	−1.47322	+	0.233334i	−0.632394	+	0.774647i	$0.717928\pi$
$32$	−4.14154	−	4.14154i	−0.732128	−	0.732128i
$33$	−3.25359	−	0.643553i	−0.566377	−	0.112028i
$34$	−1.39611	−	1.39611i	−0.239431	−	0.239431i
$35$	−2.61172	+	3.59473i	−0.441461	+	0.607620i
$36$	−1.39090	−	0.451929i	−0.231816	−	0.0753216i
$37$	1.78272	−	3.49878i	0.293077	−	0.575196i	−0.696777	−	0.717288i	$-0.745383\pi$
$37$	1.78272	−	3.49878i	0.293077	−	0.575196i	0.989853	+	0.142093i	$0.0453831\pi$
$38$	0.0185769	+	0.0255689i	0.00301357	+	0.00414783i
$39$	3.22417	−	1.61391i	0.516281	−	0.258433i
$40$	4.50918	−	1.46512i	0.712965	−	0.231656i
$41$	−1.76153	+	0.897543i	−0.275104	+	0.140173i	−0.586100	−	0.810239i	$-0.699337\pi$
$41$	−1.76153	+	0.897543i	−0.275104	+	0.140173i	0.310996	+	0.950411i	$0.399337\pi$
$42$	−1.41111	−	1.02523i	−0.217739	−	0.158196i
$43$	−4.73589			−0.722216			−0.361108	−	0.932524i	$-0.617601\pi$
$43$	−4.73589			−0.722216			−0.361108	+	0.932524i	$0.617601\pi$
$44$	−2.03542	−	4.40275i	−0.306851	−	0.663739i
$45$	1.32066	−	1.32066i	0.196872	−	0.196872i
$46$	0.102826	−	0.0162860i	0.0151609	−	0.00240124i
$47$	−4.62754	+	2.35785i	−0.674996	+	0.343928i	−0.757660	−	0.652650i	$-0.773657\pi$
$47$	−4.62754	+	2.35785i	−0.674996	+	0.343928i	0.0826637	+	0.996578i	$0.473657\pi$
$48$	−0.328726	−	1.01171i	−0.0474475	−	0.146028i
$49$	−0.787718	−	1.08420i	−0.112531	−	0.154886i
$50$	0.173382	−	1.09469i	0.0245199	−	0.154813i
$51$	−0.832180	−	2.56119i	−0.116529	−	0.358638i
$52$	4.68109	+	2.42738i	0.649151	+	0.336617i
$53$	−1.29852	−	0.943427i	−0.178365	−	0.129590i	0.495021	−	0.868881i	$-0.335161\pi$
$53$	−1.29852	−	0.943427i	−0.178365	−	0.129590i	−0.673385	+	0.739292i	$0.735161\pi$
$54$	0.518424	+	0.518424i	0.0705485	+	0.0705485i
$55$	6.18992	+	0.236555i	0.834648	+	0.0318971i
$56$		−	6.03933i		−	0.807040i
$57$	0.00674354	+	0.0425770i	0.000893204	+	0.00563947i
$58$	−0.893539	−	1.75367i	−0.117327	−	0.230268i
$59$	−5.25882	+	10.3210i	−0.684640	+	1.34368i	0.242935	+	0.970043i	$0.421890\pi$
$59$	−5.25882	+	10.3210i	−0.684640	+	1.34368i	−0.927574	+	0.373638i	$0.878110\pi$
$60$	2.69782	+	0.427293i	0.348288	+	0.0551633i
$61$	2.71240	+	3.73329i	0.347287	+	0.477999i	0.946552	−	0.322551i	$-0.104540\pi$
$61$	2.71240	+	3.73329i	0.347287	+	0.477999i	−0.599265	+	0.800551i	$0.704540\pi$
$62$	1.88152	+	5.79073i	0.238954	+	0.735423i
$63$	−1.08006	−	2.11974i	−0.136075	−	0.267063i
$64$	−1.27349	+	1.75281i	−0.159186	+	0.219101i
$65$	−5.47608	+	3.91920i	−0.679225	+	0.486117i
$66$	−0.0928595	+	2.42985i	−0.0114302	+	0.299094i
$67$	−0.334429	+	0.334429i	−0.0408570	+	0.0408570i	−0.727240	−	0.686383i	$-0.759197\pi$
$67$	−0.334429	+	0.334429i	−0.0408570	+	0.0408570i	0.686383	+	0.727240i	$0.259197\pi$
$68$	2.31495	−	3.18626i	0.280729	−	0.386390i
$69$	0.135048	+	0.0438799i	0.0162579	+	0.00528252i
$70$	2.90261	+	1.47895i	0.346928	+	0.176769i
$71$	−1.91807	+	12.1102i	−0.227633	+	1.43722i	0.563774	+	0.825929i	$0.309349\pi$
$71$	−1.91807	+	12.1102i	−0.227633	+	1.43722i	−0.791407	+	0.611290i	$0.790651\pi$
$72$	−0.397117	+	2.50730i	−0.0468007	+	0.295488i
$73$	10.8047	+	5.50525i	1.26459	+	0.644341i	0.952160	−	0.305600i	$-0.0988571\pi$
$73$	10.8047	+	5.50525i	1.26459	+	0.644341i	0.312430	+	0.949941i	$0.398857\pi$
$74$	−2.73805	−	0.889647i	−0.318292	−	0.103419i
$75$	0.888568	−	1.22301i	0.102603	−	0.141221i
$76$	−0.0445788	+	0.0445788i	−0.00511354	+	0.00511354i
$77$	2.72306	−	7.40563i	0.310322	−	0.843950i
$78$	−1.53848	−	2.14963i	−0.174198	−	0.243398i
$79$	4.53610	−	6.24341i	0.510351	−	0.702438i	−0.473627	−	0.880725i	$-0.657056\pi$
$79$	4.53610	−	6.24341i	0.510351	−	0.702438i	0.983978	+	0.178287i	$0.0570556\pi$
$80$	0.901994	+	1.77026i	0.100846	+	0.197921i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	0.851975	+	1.17264i	0.0940849	+	0.129497i
$83$	1.28304	+	0.203214i	0.140832	+	0.0223056i	0.226452	−	0.974022i	$-0.427287\pi$
$83$	1.28304	+	0.203214i	0.140832	+	0.0223056i	−0.0856203	+	0.996328i	$0.527287\pi$
$84$	1.57957	−	3.10007i	0.172345	−	0.338246i
$85$	2.28343	+	4.48148i	0.247673	+	0.486085i
$86$	0.543167	+	3.42942i	0.0585712	+	0.369804i
$87$		−	2.68452i		−	0.287811i
$88$	−6.99548	+	4.68509i	−0.745720	+	0.499432i
$89$	−4.41736	−	4.41736i	−0.468240	−	0.468240i	0.433104	−	0.901344i	$-0.357418\pi$
$89$	−4.41736	−	4.41736i	−0.468240	−	0.468240i	−0.901344	+	0.433104i	$0.857418\pi$
$90$	−1.10780	−	0.804867i	−0.116773	−	0.0848404i
$91$	2.59238	+	8.17665i	0.271755	+	0.857146i
$92$	0.0641732	+	0.197505i	0.00669052	+	0.0205913i
$93$	−1.29915	+	8.20252i	−0.134716	+	0.850561i
$94$	2.23814	+	3.08054i	0.230847	+	0.317733i
$95$	−0.0248796	−	0.0765715i	−0.00255259	−	0.00785607i
$96$	−5.21865	+	2.65903i	−0.532626	+	0.271387i
$97$	−18.5562	+	2.93901i	−1.88409	+	0.298411i	−0.989051	−	0.147573i	$-0.952854\pi$
$97$	−18.5562	+	2.93901i	−1.88409	+	0.298411i	−0.895041	+	0.445984i	$0.852854\pi$
$98$	−0.694763	+	0.694763i	−0.0701817	+	0.0701817i
$99$	−1.61747	+	2.89548i	−0.162562	+	0.291006i
$100$	2.21086			0.221086
$101$	12.9412	+	9.40234i	1.28770	+	0.935568i	0.999756	−	0.0220797i	$-0.00702877\pi$
$101$	12.9412	+	9.40234i	1.28770	+	0.935568i	0.287943	+	0.957648i	$0.407029\pi$
$102$	−1.75920	+	0.896358i	−0.174187	+	0.0887527i
$103$	−8.57105	+	2.78490i	−0.844531	+	0.274405i	−0.699154	−	0.714972i	$-0.746440\pi$
$103$	−8.57105	+	2.78490i	−0.844531	+	0.274405i	−0.145377	+	0.989376i	$0.546440\pi$
$104$	2.89046	−	8.68450i	0.283433	−	0.851585i
$105$	2.61172	+	3.59473i	0.254878	+	0.350809i
$106$	−0.534240	+	1.04850i	−0.0518899	+	0.101840i
$107$	−9.94245	−	3.23050i	−0.961173	−	0.312304i	−0.213925	−	0.976850i	$-0.568625\pi$
$107$	−9.94245	−	3.23050i	−0.961173	−	0.312304i	−0.747247	+	0.664546i	$0.768625\pi$
$108$	−0.859621	+	1.18317i	−0.0827170	+	0.113850i
$109$	3.56957	+	3.56957i	0.341903	+	0.341903i	0.857082	−	0.515180i	$-0.172275\pi$
$109$	3.56957	+	3.56957i	0.341903	+	0.341903i	−0.515180	+	0.857082i	$0.672275\pi$
$110$	−0.538635	−	4.50947i	−0.0513568	−	0.429961i
$111$	−2.77665	−	2.77665i	−0.263548	−	0.263548i
$112$	2.49962	−	0.395901i	0.236192	−	0.0374091i
$113$	−0.342458	+	1.05398i	−0.0322157	+	0.0991497i	−0.965871	−	0.259022i	$-0.916600\pi$
$113$	−0.342458	+	1.05398i	−0.0322157	+	0.0991497i	0.933656	+	0.358172i	$0.116600\pi$
$114$	0.0300581	−	0.00976647i	0.00281520	−	0.000914713i
$115$	−0.261944	−	0.0414879i	−0.0244264	−	0.00386876i
$116$	3.17624	−	2.30767i	0.294906	−	0.214262i
$117$	−0.538600	−	3.56510i	−0.0497936	−	0.329593i
$118$	8.07695	+	2.62436i	0.743543	+	0.241592i
$119$	6.32787	−	1.00224i	0.580075	−	0.0918748i
$120$		−	4.74124i		−	0.432814i
$121$	−10.6905	+	2.59083i	−0.971867	+	0.235530i
$122$	2.39232	−	2.39232i	0.216591	−	0.216591i
$123$	0.309272	+	1.95267i	0.0278861	+	0.176066i
$124$	−10.8217	+	5.51394i	−0.971819	+	0.495167i
$125$	−5.52139	+	10.8363i	−0.493848	+	0.969231i
$126$	−1.41111	+	1.02523i	−0.125711	+	0.0913347i
$127$	9.49405	−	6.89783i	0.842461	−	0.612083i	−0.0805963	−	0.996747i	$-0.525682\pi$
$127$	9.49405	−	6.89783i	0.842461	−	0.612083i	0.923057	+	0.384663i	$0.125682\pi$
$128$	−9.02197	−	4.59692i	−0.797437	−	0.406315i
$129$	−1.46347	+	4.50409i	−0.128851	+	0.396563i
$130$	3.46609	+	3.51593i	0.303996	+	0.308367i
$131$			11.3252i			0.989488i	0.869039	+	0.494744i	$0.164738\pi$
$131$			11.3252i			0.989488i	−0.869039	+	0.494744i	$0.835262\pi$
$132$	−4.81624	+	0.575277i	−0.419200	+	0.0500715i
$133$	−0.102555			−0.00889267
$134$	0.280528	+	0.203815i	0.0242339	+	0.0176070i
$135$	−0.847915	−	1.66413i	−0.0729769	−	0.143225i
$136$	−6.09119	−	3.10362i	−0.522315	−	0.266133i
$137$	5.46708	+	0.865901i	0.467084	+	0.0739789i	0.385541	−	0.922691i	$-0.374015\pi$
$137$	5.46708	+	0.865901i	0.467084	+	0.0739789i	0.0815438	+	0.996670i	$0.474015\pi$
$138$	0.0162860	−	0.102826i	0.00138636	−	0.00875312i
$139$	−13.3352	+	4.33286i	−1.13107	+	0.367508i	−0.813984	−	0.580887i	$-0.802706\pi$
$139$	−13.3352	+	4.33286i	−1.13107	+	0.367508i	−0.317090	+	0.948395i	$0.602706\pi$
$140$	−2.00807	+	6.18020i	−0.169713	+	0.522322i
$141$	0.812459	+	5.12967i	0.0684214	+	0.431996i
$142$	8.98942			0.754376
$143$	7.46011	−	9.34595i	0.623846	−	0.781548i
$144$	−1.06378			−0.0886482
$145$	0.784341	+	4.95213i	0.0651360	+	0.411252i
$146$	2.74734	−	8.45544i	0.227371	−	0.699777i
$147$	−1.27455	+	0.414128i	−0.105124	+	0.0341567i
$148$	0.898372	−	5.67210i	0.0738457	−	0.466244i
$149$	2.19644	+	0.347882i	0.179939	+	0.0284996i	0.245754	−	0.969332i	$-0.420965\pi$
$149$	2.19644	+	0.347882i	0.179939	+	0.0284996i	−0.0658145	+	0.997832i	$0.520965\pi$
$150$	−0.987536	−	0.503175i	−0.0806319	−	0.0410840i
$151$	2.27393	+	4.46284i	0.185050	+	0.363181i	0.964831	−	0.262871i	$-0.0846695\pi$
$151$	2.27393	+	4.46284i	0.185050	+	0.363181i	−0.779781	+	0.626053i	$0.784670\pi$
$152$	0.0885318	+	0.0643221i	0.00718088	+	0.00521721i
$153$	−2.69299			−0.217715
$154$	−5.67499	−	1.12250i	−0.457304	−	0.0904537i
$155$		−	15.5107i		−	1.24585i
$156$	3.75511	−	3.70188i	0.300649	−	0.296388i
$157$	2.04076	−	6.28083i	0.162871	−	0.501265i	−0.836002	−	0.548726i	$-0.815113\pi$
$157$	2.04076	−	6.28083i	0.162871	−	0.501265i	0.998873	+	0.0474613i	$0.0151131\pi$
$158$	−5.04132	−	2.56868i	−0.401066	−	0.204353i
$159$	−1.29852	+	0.943427i	−0.102979	+	0.0748186i
$160$	8.84994	−	6.42986i	0.699649	−	0.508325i
$161$	−0.153367	+	0.301000i	−0.0120870	+	0.0237221i
$162$	0.653252	−	0.332848i	0.0513243	−	0.0261510i
$163$	−2.60536	−	16.4496i	−0.204068	−	1.28843i	−0.850709	−	0.525638i	$-0.823827\pi$
$163$	−2.60536	−	16.4496i	−0.204068	−	1.28843i	0.646641	−	0.762795i	$-0.276173\pi$
$164$	−2.04447	+	2.04447i	−0.159647	+	0.159647i
$165$	2.13777	−	5.81386i	0.166425	−	0.452609i
$166$		−	0.952403i		−	0.0739208i
$167$	14.7486	−	2.33595i	1.14128	−	0.180761i	0.442957	−	0.896543i	$-0.353929\pi$
$167$	14.7486	−	2.33595i	1.14128	−	0.180761i	0.698324	+	0.715782i	$0.253929\pi$
$168$	−5.74375	−	1.86626i	−0.443140	−	0.143985i
$169$	−0.185572	+	12.9987i	−0.0142748	+	0.999898i
$170$	2.98331	−	2.16750i	0.228809	−	0.166240i
$171$	0.0425770	+	0.00674354i	0.00325595	+	0.000515691i
$172$	−6.58712	+	2.14029i	−0.502263	+	0.163195i
$173$	4.06089	−	12.4981i	0.308744	−	0.950216i	−0.669510	−	0.742803i	$-0.733496\pi$
$173$	4.06089	−	12.4981i	0.308744	−	0.950216i	0.978254	−	0.207413i	$-0.0665043\pi$
$174$	−1.94396	+	0.307892i	−0.147371	+	0.0233413i
$175$	2.54308	+	2.54308i	0.192239	+	0.192239i
$176$	−2.39769	−	2.58823i	−0.180733	−	0.195095i
$177$	8.19080	+	8.19080i	0.615658	+	0.615658i
$178$	−2.69213	+	3.70540i	−0.201784	+	0.277732i
$179$	7.02371	+	2.28214i	0.524977	+	0.170575i	0.559503	−	0.828829i	$-0.310992\pi$
$179$	7.02371	+	2.28214i	0.524977	+	0.170575i	−0.0345260	+	0.999404i	$0.510992\pi$
$180$	1.24005	−	2.43374i	0.0924281	−	0.181400i
$181$	4.69092	+	6.45649i	0.348673	+	0.479907i	0.946949	−	0.321382i	$-0.104147\pi$
$181$	4.69092	+	6.45649i	0.348673	+	0.479907i	−0.598276	+	0.801290i	$0.704147\pi$
$182$	5.62368	−	2.81503i	0.416855	−	0.208664i
$183$	4.38875	−	1.42599i	0.324426	−	0.105412i
$184$	0.321181	−	0.163650i	0.0236778	−	0.0120644i
$185$	5.93333	+	4.31082i	0.436227	+	0.316938i
$186$	6.08873			0.446448
$187$	−6.06984	−	6.55220i	−0.443870	−	0.479144i
$188$	−5.37084	+	5.37084i	−0.391709	+	0.391709i
$189$	−2.34975	+	0.372165i	−0.170920	+	0.0270710i
$190$	−0.0525946	+	0.0267983i	−0.00381562	+	0.00194415i
$191$	−4.76353	−	14.6606i	−0.344677	−	1.06081i	−0.961757	−	0.273905i	$-0.911685\pi$
$191$	−4.76353	−	14.6606i	−0.344677	−	1.06081i	0.617080	−	0.786900i	$-0.288315\pi$
$192$	1.27349	+	1.75281i	0.0919062	+	0.126498i
$193$	3.02461	−	19.0966i	0.217716	−	1.37460i	−0.600469	−	0.799648i	$-0.705019\pi$
$193$	3.02461	−	19.0966i	0.217716	−	1.37460i	0.818185	−	0.574956i	$-0.194981\pi$
$194$	4.25648	+	13.1001i	0.305597	+	0.940531i
$195$	2.03517	+	6.41916i	0.145742	+	0.459686i
$196$	−1.58562	−	1.15202i	−0.113258	−	0.0822870i
$197$	−0.435547	−	0.435547i	−0.0310315	−	0.0310315i	0.691421	−	0.722452i	$-0.256985\pi$
$197$	−0.435547	−	0.435547i	−0.0310315	−	0.0310315i	−0.722452	+	0.691421i	$0.756985\pi$
$198$	2.28223	+	0.839179i	0.162191	+	0.0596379i
$199$		−	17.9277i		−	1.27086i	−0.772159	−	0.635429i	$-0.780823\pi$
$199$		−	17.9277i		−	1.27086i	0.772159	−	0.635429i	$-0.219177\pi$
$200$	−0.600331	−	3.79034i	−0.0424498	−	0.268018i
$201$	0.214717	+	0.421405i	0.0151449	+	0.0297236i
$202$	5.32432	−	10.4496i	0.374618	−	0.735228i
$203$	6.30797	+	0.999084i	0.442732	+	0.0701219i
$204$	−2.31495	−	3.18626i	−0.162079	−	0.223083i
$205$	−1.14103	−	3.51172i	−0.0796929	−	0.245269i
$206$	2.99968	+	5.88719i	0.208997	+	0.410180i
$207$	0.0834645	−	0.114879i	0.00580118	−	0.00798464i
$208$	3.78391	+	0.627030i	0.262367	+	0.0434767i
$209$	0.0795586	+	0.118792i	0.00550318	+	0.00821700i
$210$	2.30352	−	2.30352i	0.158958	−	0.158958i
$211$	−4.58676	+	6.31313i	−0.315766	+	0.434614i	−0.937168	−	0.348877i	$-0.886563\pi$
$211$	−4.58676	+	6.31313i	−0.315766	+	0.434614i	0.621403	+	0.783491i	$0.286563\pi$
$212$	−2.23246	−	0.725371i	−0.153326	−	0.0498187i
$213$	10.9248	+	5.56646i	0.748554	+	0.381407i
$214$	−1.19900	+	7.57019i	−0.0819620	+	0.517487i
$215$	1.38369	−	8.73628i	0.0943669	−	0.595809i
$216$	2.26187	+	1.15248i	0.153901	+	0.0784163i
$217$	−18.7904	−	6.10537i	−1.27558	−	0.414460i
$218$	2.17545	−	2.99425i	0.147340	−	0.202796i
$219$	8.57463	−	8.57463i	0.579420	−	0.579420i
$220$	8.71644	−	2.46838i	0.587662	−	0.166418i
$221$	9.57909	+	1.58735i	0.644359	+	0.106777i
$222$	−1.69221	+	2.32913i	−0.113574	+	0.156321i
$223$	−13.3074	−	26.1173i	−0.891130	−	1.74894i	−0.616427	−	0.787412i	$-0.711420\pi$
$223$	−13.3074	−	26.1173i	−0.891130	−	1.74894i	−0.274703	−	0.961529i	$-0.588580\pi$
$224$	−4.30588	−	13.2521i	−0.287699	−	0.885446i
$225$	−0.888568	−	1.22301i	−0.0592379	−	0.0815340i
$226$	0.802498	+	0.127103i	0.0533814	+	0.00845478i
$227$	−12.6486	+	24.8243i	−0.839517	+	1.64764i	−0.0803327	+	0.996768i	$0.525598\pi$
$227$	−12.6486	+	24.8243i	−0.839517	+	1.64764i	−0.759184	+	0.650876i	$0.774402\pi$
$228$	0.0286214	+	0.0561726i	0.00189550	+	0.00372012i
$229$	3.41878	+	21.5853i	0.225919	+	1.42640i	0.796243	+	0.604977i	$0.206818\pi$
$229$	3.41878	+	21.5853i	0.225919	+	1.42640i	−0.570324	+	0.821420i	$0.693182\pi$
$230$			0.194441i			0.0128211i
$231$	−6.20170	−	4.87825i	−0.408042	−	0.320965i
$232$	−4.81879	−	4.81879i	−0.316369	−	0.316369i
$233$	−12.9910	−	9.43852i	−0.851070	−	0.618338i	0.0743712	−	0.997231i	$-0.476305\pi$
$233$	−12.9910	−	9.43852i	−0.851070	−	0.618338i	−0.925441	+	0.378892i	$0.876305\pi$
$234$	−2.51984	+	0.798906i	−0.164727	+	0.0522261i
$235$	−2.99749	−	9.22531i	−0.195534	−	0.601793i
$236$	−2.65010	+	16.7321i	−0.172507	+	1.08916i
$237$	−4.53610	−	6.24341i	−0.294651	−	0.405553i
$238$	−1.45151	−	4.46729i	−0.0940873	−	0.289571i
$239$	−13.2596	+	6.75610i	−0.857691	+	0.437016i	−0.826793	−	0.562507i	$-0.809837\pi$
$239$	−13.2596	+	6.75610i	−0.857691	+	0.437016i	−0.0308988	+	0.999523i	$0.509837\pi$
$240$	1.96235	−	0.310806i	0.126669	−	0.0200624i
$241$	3.15346	−	3.15346i	0.203132	−	0.203132i	−0.598208	−	0.801341i	$-0.704121\pi$
$241$	3.15346	−	3.15346i	0.203132	−	0.203132i	0.801341	+	0.598208i	$0.204121\pi$
$242$	3.10223	+	7.44425i	0.199419	+	0.478534i
$243$	1.00000			0.0641500
$244$	5.45985	+	3.96681i	0.349531	+	0.253949i
$245$	2.23017	−	1.13633i	0.142481	−	0.0725975i
$246$	1.37852	−	0.447910i	0.0878915	−	0.0285577i
$247$	−0.147473	−	0.0490835i	−0.00938351	−	0.00312311i
$248$	12.3917	+	17.0558i	0.786876	+	1.08304i
$249$	0.589750	−	1.15745i	0.0373739	−	0.0733503i
$250$	8.48023	+	2.75539i	0.536337	+	0.174266i
$251$	11.7476	−	16.1692i	0.741502	−	1.02059i	−0.257029	−	0.966404i	$-0.582743\pi$
$251$	11.7476	−	16.1692i	0.741502	−	1.02059i	0.998531	−	0.0541864i	$-0.0172565\pi$
$252$	−2.46023	−	2.46023i	−0.154980	−	0.154980i
$253$	0.467631	−	0.0558563i	0.0293997	−	0.00351166i
$254$	−6.08385	−	6.08385i	−0.381735	−	0.381735i
$255$	4.96776	−	0.786816i	0.311093	−	0.0492723i
$256$	−3.63307	+	11.1815i	−0.227067	+	0.698841i
$257$	−24.0741	+	7.82215i	−1.50170	+	0.487932i	−0.940513	−	0.339757i	$-0.889655\pi$
$257$	−24.0741	+	7.82215i	−1.50170	+	0.487932i	−0.561187	+	0.827689i	$0.689655\pi$
$258$	3.42942	+	0.543167i	0.213506	+	0.0338161i
$259$	7.55781	−	5.49107i	0.469619	−	0.341198i
$260$	−5.84546	+	7.92600i	−0.362520	+	0.491549i
$261$	−2.55313	−	0.829563i	−0.158035	−	0.0513486i
$262$	8.20098	−	1.29891i	0.506658	−	0.0802468i
$263$		−	8.13095i		−	0.501376i	−0.968068	−	0.250688i	$-0.919343\pi$
$263$		−	8.13095i		−	0.501376i	0.968068	−	0.250688i	$-0.0806568\pi$
$264$	2.29406	+	8.10087i	0.141190	+	0.498574i
$265$	2.11973	−	2.11973i	0.130214	−	0.130214i
$266$	0.0117622	+	0.0742639i	0.000721189	+	0.00455341i
$267$	−5.56620	+	2.83612i	−0.340646	+	0.173568i
$268$	−0.314017	+	0.616294i	−0.0191817	+	0.0376461i
$269$	7.72597	−	5.61324i	0.471061	−	0.342245i	−0.326794	−	0.945096i	$-0.605968\pi$
$269$	7.72597	−	5.61324i	0.471061	−	0.342245i	0.797854	+	0.602850i	$0.205968\pi$
$270$	−1.10780	+	0.804867i	−0.0674188	+	0.0489826i
$271$	−15.6421	−	7.97004i	−0.950189	−	0.484146i	−0.0910266	−	0.995848i	$-0.529015\pi$
$271$	−15.6421	−	7.97004i	−0.950189	−	0.484146i	−0.859162	+	0.511703i	$0.829015\pi$
$272$	0.885256	−	2.72454i	0.0536765	−	0.165199i
$273$	8.57755	+	0.0612245i	0.519137	+	0.00370547i
$274$		−	4.05822i		−	0.245166i
$275$	0.972874	−	4.91852i	0.0586665	−	0.296598i
$276$	0.207669			0.0125002
$277$	−12.4448	−	9.04164i	−0.747733	−	0.543260i	0.147391	−	0.989078i	$-0.452913\pi$
$277$	−12.4448	−	9.04164i	−0.747733	−	0.543260i	−0.895123	+	0.445819i	$0.852913\pi$
$278$	4.66701	+	9.15952i	0.279909	+	0.549352i
$279$	7.39960	+	3.77028i	0.443002	+	0.225721i
$280$	11.1407	+	1.76452i	0.665787	+	0.105450i
$281$	1.54185	−	9.73483i	0.0919788	−	0.580731i	−0.898053	−	0.439887i	$-0.855018\pi$
$281$	1.54185	−	9.73483i	0.0919788	−	0.580731i	0.990032	−	0.140844i	$-0.0449816\pi$
$282$	3.62139	−	1.17666i	0.215651	−	0.0700691i
$283$	9.32305	−	28.6934i	0.554198	−	1.70564i	−0.143856	−	0.989599i	$-0.545950\pi$
$283$	9.32305	−	28.6934i	0.554198	−	1.70564i	0.698053	−	0.716046i	$-0.254050\pi$
$284$	2.80513	+	17.7109i	0.166454	+	1.05095i
$285$	−0.0805121			−0.00476912
$286$	−7.62334	−	4.33022i	−0.450778	−	0.256052i
$287$	−4.70339			−0.277632
$288$	0.916241	+	5.78492i	0.0539900	+	0.340880i
$289$	−3.01223	+	9.27070i	−0.177190	+	0.545335i
$290$	3.49606	−	1.13594i	0.205295	−	0.0667045i
$291$	−2.93901	+	18.5562i	−0.172288	+	1.08778i
$292$	17.5161	+	2.77428i	1.02505	+	0.162353i
$293$	28.2600	+	14.3992i	1.65097	+	0.841210i	0.996360	+	0.0852398i	$0.0271656\pi$
$293$	28.2600	+	14.3992i	1.65097	+	0.841210i	0.654606	+	0.755970i	$0.272834\pi$
$294$	0.446066	+	0.875453i	0.0260151	+	0.0510574i
$295$	−17.5027	−	12.7164i	−1.01905	−	0.740380i
$296$	−9.96832			−0.579397
$297$	2.25394	+	2.43306i	0.130787	+	0.141180i
$298$		−	1.63042i		−	0.0944475i
$299$	−0.364601	+	0.359433i	−0.0210854	+	0.0207865i
$300$	0.683192	−	2.10265i	0.0394441	−	0.121396i
$301$	−10.0389	−	5.11506i	−0.578631	−	0.294827i
$302$	2.97090	−	2.15849i	0.170956	−	0.124207i
$303$	12.9412	−	9.40234i	0.743453	−	0.540150i
$304$	−0.0208187	+	0.0408590i	−0.00119403	+	0.00234342i
$305$	−7.67929	+	3.91279i	−0.439715	+	0.224046i
$306$	0.308864	+	1.95009i	0.0176566	+	0.111479i
$307$	4.54736	−	4.54736i	0.259531	−	0.259531i	−0.565332	−	0.824863i	$-0.691252\pi$
$307$	4.54736	−	4.54736i	0.259531	−	0.259531i	0.824863	+	0.565332i	$0.191252\pi$
$308$	0.440674	−	11.5311i	0.0251097	−	0.657045i
$309$			9.01214i			0.512683i
$310$	−11.2319	+	1.77895i	−0.637928	+	0.101038i
$311$	3.74579	+	1.21708i	0.212404	+	0.0690144i	0.413286	−	0.910601i	$-0.364381\pi$
$311$	3.74579	+	1.21708i	0.212404	+	0.0690144i	−0.200882	+	0.979615i	$0.564381\pi$
$312$	−7.36625	−	5.43265i	−0.417032	−	0.307563i
$313$	15.4300	−	11.2105i	0.872154	−	0.633657i	−0.0590097	−	0.998257i	$-0.518794\pi$
$313$	15.4300	−	11.2105i	0.872154	−	0.633657i	0.931164	+	0.364600i	$0.118794\pi$
$314$	−4.78223	−	0.757430i	−0.269877	−	0.0427443i
$315$	4.22585	−	1.37306i	0.238100	−	0.0773633i
$316$	3.48766	−	10.7339i	0.196196	−	0.603830i
$317$	−0.451643	+	0.0715332i	−0.0253668	+	0.00401771i	−0.169105	−	0.985598i	$-0.554088\pi$
$317$	−0.451643	+	0.0715332i	−0.0253668	+	0.00401771i	0.143738	+	0.989616i	$0.454088\pi$
$318$	0.832098	+	0.832098i	0.0466617	+	0.0466617i
$319$	−3.73623	−	8.08170i	−0.209189	−	0.452488i
$320$	−2.86133	−	2.86133i	−0.159953	−	0.159953i
$321$	−6.14477	+	8.45755i	−0.342968	+	0.472055i
$322$	0.235555	+	0.0765363i	0.0131269	+	0.00426520i
$323$	−0.0527032	+	0.103436i	−0.00293249	+	0.00575533i
$324$	0.859621	+	1.18317i	0.0477567	+	0.0657315i
$325$	2.43979	+	4.87405i	0.135335	+	0.270364i
$326$	−11.6129	+	3.77327i	−0.643180	+	0.208982i
$327$	4.49792	−	2.29180i	0.248735	−	0.126737i
$328$	4.06025	+	2.94994i	0.224190	+	0.162883i
$329$	−12.3558			−0.681199
$330$	−4.45521	−	0.881230i	−0.245251	−	0.0485101i
$331$	−6.36409	+	6.36409i	−0.349802	+	0.349802i	−0.860036	−	0.510234i	$-0.829559\pi$
$331$	−6.36409	+	6.36409i	−0.349802	+	0.349802i	0.510234	+	0.860036i	$0.329559\pi$
$332$	1.87642	−	0.297195i	0.102982	−	0.0163107i
$333$	−3.49878	+	1.78272i	−0.191732	+	0.0976923i
$334$	−3.38309	−	10.4121i	−0.185114	−	0.569723i
$335$	−0.519210	−	0.714631i	−0.0283675	−	0.0390445i
$336$	0.395901	−	2.49962i	0.0215982	−	0.136365i
$337$	9.33459	+	28.7289i	0.508487	+	1.56496i	0.794828	+	0.606835i	$0.207561\pi$
$337$	9.33459	+	28.7289i	0.508487	+	1.56496i	−0.286340	+	0.958128i	$0.592439\pi$
$338$	9.43408	−	1.35646i	0.513146	−	0.0737818i
$339$	0.896565	+	0.651393i	0.0486948	+	0.0353788i
$340$	5.20132	+	5.20132i	0.282081	+	0.282081i
$341$	7.50492	+	26.5016i	0.406414	+	1.43514i
$342$		−	0.0316050i		−	0.00170900i
$343$	−3.10391	−	19.5973i	−0.167595	−	1.05815i
$344$	5.45801	+	10.7119i	0.294276	+	0.577549i
$345$	−0.120402	+	0.236303i	−0.00648225	+	0.0127221i
$346$	−9.51609	−	1.50720i	−0.511588	−	0.0810276i
$347$	1.23615	+	1.70142i	0.0663602	+	0.0913369i	0.840907	−	0.541180i	$-0.182022\pi$
$347$	1.23615	+	1.70142i	0.0663602	+	0.0913369i	−0.774547	+	0.632516i	$0.782022\pi$
$348$	−1.21321	−	3.73389i	−0.0650351	−	0.200157i
$349$	−6.93862	−	13.6178i	−0.371416	−	0.728944i	0.627344	−	0.778742i	$-0.284142\pi$
$349$	−6.93862	−	13.6178i	−0.371416	−	0.728944i	−0.998759	+	0.0497984i	$0.984142\pi$
$350$	1.54986	−	2.13320i	0.0828436	−	0.114024i
$351$	−3.55704	−	0.589436i	−0.189861	−	0.0314618i
$352$	−12.0099	+	15.2681i	−0.640129	+	0.813793i
$353$	16.8316	−	16.8316i	0.895854	−	0.895854i	−0.0992120	−	0.995066i	$-0.531632\pi$
$353$	16.8316	−	16.8316i	0.895854	−	0.895854i	0.995066	+	0.0992120i	$0.0316322\pi$
$354$	4.99183	−	6.87066i	0.265313	−	0.365172i
$355$	−21.7793	−	7.07652i	−1.15593	−	0.375583i
$356$	−8.14043	−	4.14775i	−0.431442	−	0.219831i
$357$	1.00224	−	6.32787i	0.0530440	−	0.334906i
$358$	0.847018	−	5.34786i	0.0447663	−	0.282643i
$359$	28.4248	+	14.4831i	1.50020	+	0.764391i	0.995119	−	0.0986798i	$-0.0314620\pi$
$359$	28.4248	+	14.4831i	1.50020	+	0.764391i	0.505083	+	0.863071i	$0.331462\pi$
$360$	−4.50918	−	1.46512i	−0.237655	−	0.0772188i
$361$	−11.1668	+	15.3698i	−0.587728	+	0.808938i
$362$	4.13736	−	4.13736i	0.217455	−	0.217455i
$363$	−0.839530	+	10.9679i	−0.0440639	+	0.575666i
$364$	7.30100	+	10.2013i	0.382676	+	0.534693i
$365$	−13.3123	+	18.3229i	−0.696800	+	0.959063i
$366$	−1.53596	−	3.01450i	−0.0802861	−	0.157570i
$367$	7.80398	+	24.0182i	0.407364	+	1.25374i	0.918905	+	0.394480i	$0.129075\pi$
$367$	7.80398	+	24.0182i	0.407364	+	1.25374i	−0.511540	+	0.859259i	$0.670925\pi$
$368$	0.0887878	+	0.122206i	0.00462838	+	0.00637042i
$369$	1.95267	+	0.309272i	0.101652	+	0.0161001i
$370$	2.44111	−	4.79095i	0.126907	−	0.249070i
$371$	−1.73356	−	3.40230i	−0.0900020	−	0.176639i
$372$	1.89997	+	11.9960i	0.0985091	+	0.621962i
$373$		−	1.32633i		−	0.0686748i	−0.999410	−	0.0343374i	$-0.989068\pi$
$373$		−	1.32633i		−	0.0686748i	0.999410	−	0.0343374i	$-0.0109321\pi$
$374$	−4.04852	+	5.14686i	−0.209344	+	0.266138i
$375$	8.59976	+	8.59976i	0.444090	+	0.444090i
$376$	10.6663	+	7.74951i	0.550072	+	0.399650i
$377$	8.59263	+	4.45570i	0.442543	+	0.229480i
$378$	0.538995	+	1.65886i	0.0277229	+	0.0853223i
$379$	−4.34114	+	27.4089i	−0.222989	+	1.40790i	0.581314	+	0.813679i	$0.302539\pi$
$379$	−4.34114	+	27.4089i	−0.222989	+	1.40790i	−0.804303	+	0.594219i	$0.797461\pi$
$380$	−0.0692098	−	0.0952592i	−0.00355039	−	0.00488669i
$381$	−3.62640	−	11.1609i	−0.185786	−	0.571791i
$382$	−10.0699	+	5.13089i	−0.515223	+	0.262519i
$383$	6.47457	−	1.02547i	0.330835	−	0.0523991i	0.0111926	−	0.999937i	$-0.496437\pi$
$383$	6.47457	−	1.02547i	0.330835	−	0.0523991i	0.319642	+	0.947538i	$0.396437\pi$
$384$	−7.15988	+	7.15988i	−0.365376	+	0.365376i
$385$	12.8656	+	7.18694i	0.655689	+	0.366280i
$386$	−14.1754			−0.721510
$387$	3.83141	+	2.78368i	0.194762	+	0.141503i
$388$	−24.4815	+	12.4739i	−1.24286	+	0.633267i
$389$	−21.7460	+	7.06570i	−1.10257	+	0.358245i	−0.803090	−	0.595858i	$-0.796812\pi$
$389$	−21.7460	+	7.06570i	−1.10257	+	0.358245i	−0.299476	+	0.954104i	$0.596812\pi$
$390$	4.41492	−	2.20997i	0.223558	−	0.111906i
$391$	0.224769	+	0.309368i	0.0113671	+	0.0156454i
$392$	−1.54449	+	3.03123i	−0.0780085	+	0.153100i
$393$	10.7709	+	3.49968i	0.543321	+	0.176536i
$394$	−0.265442	+	0.365349i	−0.0133728	+	0.0184060i
$395$	10.1919	+	10.1919i	0.512809	+	0.512809i
$396$	−0.941179	+	4.75829i	−0.0472960	+	0.239113i
$397$	8.93270	+	8.93270i	0.448319	+	0.448319i	0.894795	−	0.446476i	$-0.147321\pi$
$397$	8.93270	+	8.93270i	0.448319	+	0.448319i	−0.446476	+	0.894795i	$0.647321\pi$
$398$	−12.9820	+	2.05615i	−0.650731	+	0.103066i
$399$	−0.0316913	+	0.0975359i	−0.00158655	+	0.00488290i
$400$	1.52943	−	0.496942i	0.0764715	−	0.0248471i
$401$	−0.657621	−	0.104157i	−0.0328400	−	0.00520135i	0.139993	−	0.990153i	$-0.455292\pi$
$401$	−0.657621	−	0.104157i	−0.0328400	−	0.00520135i	−0.172833	+	0.984951i	$0.555292\pi$
$402$	0.280528	−	0.203815i	0.0139915	−	0.0101654i
$403$	−24.0984	−	17.7727i	−1.20042	−	0.885319i
$404$	22.2491	+	7.22916i	1.10693	+	0.359664i
$405$	−1.84470	+	0.292172i	−0.0916638	+	0.0145181i
$406$		−	4.68241i		−	0.232384i
$407$	−12.2235	−	4.49459i	−0.605895	−	0.222789i
$408$	−4.83400	+	4.83400i	−0.239318	+	0.239318i
$409$	−2.32407	−	14.6736i	−0.114918	−	0.725561i	−0.976109	−	0.217281i	$-0.930281\pi$
$409$	−2.32407	−	14.6736i	−0.114918	−	0.725561i	0.861191	−	0.508281i	$-0.169719\pi$
$410$	−2.41210	+	1.22902i	−0.119125	+	0.0606972i
$411$	2.51294	−	4.93193i	0.123954	−	0.243274i
$412$	−10.6629	+	7.74702i	−0.525321	+	0.381668i
$413$	−22.2947	+	16.1980i	−1.09705	+	0.797054i
$414$	−0.0927606	−	0.0472639i	−0.00455894	−	0.00232289i
$415$	−0.749737	+	2.30745i	−0.0368031	+	0.113268i
$416$	0.150730	−	21.1173i	0.00739015	−	1.03536i
$417$			14.0214i			0.686632i
$418$	0.0768966	−	0.0712356i	0.00376114	−	0.00348425i
$419$	29.3540			1.43404			0.717018	−	0.697055i	$-0.245507\pi$
$419$	29.3540			1.43404			0.717018	+	0.697055i	$0.245507\pi$
$420$	5.25719	+	3.81957i	0.256525	+	0.186376i
$421$	−6.33612	−	12.4353i	−0.308804	−	0.606062i	0.683491	−	0.729959i	$-0.260461\pi$
$421$	−6.33612	−	12.4353i	−0.308804	−	0.606062i	−0.992295	+	0.123897i	$0.960461\pi$
$422$	5.09763	+	2.59737i	0.248149	+	0.126438i
$423$	5.12967	+	0.812459i	0.249413	+	0.0395031i
$424$	−0.637395	+	4.02435i	−0.0309546	+	0.195440i
$425$	3.87181	−	1.25803i	0.187810	−	0.0610232i
$426$	2.77788	−	8.54945i	0.134589	−	0.414222i
$427$	1.71739	+	10.8432i	0.0831105	+	0.524739i
$428$	−15.2889			−0.739015
$429$	−6.58322	−	9.98304i	−0.317841	−	0.481986i
$430$	−6.48495			−0.312732
$431$	1.43168	+	9.03929i	0.0689617	+	0.435407i	0.997878	+	0.0651165i	$0.0207419\pi$
$431$	1.43168	+	9.03929i	0.0689617	+	0.435407i	−0.928916	+	0.370291i	$0.879258\pi$
$432$	−0.328726	+	1.01171i	−0.0158158	+	0.0486761i
$433$	3.72422	−	1.21007i	0.178974	−	0.0581523i	−0.218159	−	0.975913i	$-0.570005\pi$
$433$	3.72422	−	1.21007i	0.178974	−	0.0581523i	0.397133	+	0.917761i	$0.370005\pi$
$434$	−2.26601	+	14.3070i	−0.108772	+	0.686759i
$435$	4.95213	+	0.784341i	0.237437	+	0.0376063i
$436$	6.57809	+	3.35170i	0.315033	+	0.160518i
$437$	−0.00277898	−	0.00545405i	−0.000132937	−	0.000260903i
$438$	−7.19263	−	5.22575i	−0.343677	−	0.249696i
$439$	−17.1534			−0.818686			−0.409343	−	0.912381i	$-0.634242\pi$
$439$	−17.1534			−0.818686			−0.409343	+	0.912381i	$0.634242\pi$
$440$	−6.59869	−	14.2734i	−0.314580	−	0.680458i
$441$			1.34015i			0.0638165i
$442$	0.0508109	−	7.11861i	0.00241683	−	0.338598i
$443$	9.54364	−	29.3723i	0.453432	−	1.39552i	−0.419534	−	0.907739i	$-0.637807\pi$
$443$	9.54364	−	29.3723i	0.453432	−	1.39552i	0.872966	−	0.487781i	$-0.162193\pi$
$444$	−5.11687	−	2.60718i	−0.242836	−	0.123731i
$445$	9.43933	−	6.85808i	0.447467	−	0.325104i
$446$	−17.3862	+	12.6318i	−0.823259	+	0.598133i
$447$	1.00959	−	1.98144i	0.0477521	−	0.0937187i
$448$	−4.59262	+	2.34006i	−0.216981	+	0.110557i
$449$	1.47102	+	9.28767i	0.0694218	+	0.438312i	0.997778	+	0.0666212i	$0.0212219\pi$
$449$	1.47102	+	9.28767i	0.0694218	+	0.438312i	−0.928356	+	0.371691i	$0.878778\pi$
$450$	−0.783713	+	0.783713i	−0.0369446	+	0.0369446i
$451$	3.64872	+	5.44803i	0.171811	+	0.256538i
$452$			1.62074i			0.0762331i
$453$	4.94710	−	0.783544i	0.232435	−	0.0368141i
$454$	19.4268	+	6.31215i	0.911745	+	0.296244i
$455$	−15.8409	+	2.39318i	−0.742632	+	0.112194i
$456$	0.0885318	−	0.0643221i	0.00414588	−	0.00301216i
$457$	−9.11511	−	1.44369i	−0.426387	−	0.0675330i	−0.0604466	−	0.998171i	$-0.519252\pi$
$457$	−9.11511	−	1.44369i	−0.426387	−	0.0675330i	−0.365940	+	0.930638i	$0.619252\pi$
$458$	15.2386	−	4.95131i	0.712052	−	0.231360i
$459$	−0.832180	+	2.56119i	−0.0388428	+	0.119546i
$460$	−0.383086	+	0.0606749i	−0.0178615	+	0.00282898i
$461$	−21.2073	−	21.2073i	−0.987724	−	0.987724i	0.0122013	−	0.999926i	$-0.496116\pi$
$461$	−21.2073	−	21.2073i	−0.987724	−	0.987724i	−0.999926	+	0.0122013i	$0.996116\pi$
$462$	−2.82123	+	5.05036i	−0.131255	+	0.234964i
$463$	−6.82061	−	6.82061i	−0.316981	−	0.316981i	0.530626	−	0.847606i	$-0.321957\pi$
$463$	−6.82061	−	6.82061i	−0.316981	−	0.316981i	−0.847606	+	0.530626i	$0.821957\pi$
$464$	1.67856	−	2.31034i	0.0779252	−	0.107255i
$465$	−14.7516	−	4.79308i	−0.684089	−	0.222274i
$466$	−5.34480	+	10.4898i	−0.247593	+	0.485929i
$467$	−17.2632	−	23.7608i	−0.798846	−	1.09952i	−0.992950	−	0.118536i	$-0.962180\pi$
$467$	−17.2632	−	23.7608i	−0.798846	−	1.09952i	0.194103	−	0.980981i	$-0.437820\pi$
$468$	−2.36031	−	4.71527i	−0.109105	−	0.217963i
$469$	−1.07011	+	0.347699i	−0.0494130	+	0.0160553i
$470$	−6.33659	+	3.22865i	−0.292285	+	0.148927i
$471$	−5.34279	−	3.88176i	−0.246183	−	0.178862i
$472$	29.4054			1.35349
$473$	1.86290	+	15.5963i	0.0856564	+	0.717118i
$474$	−4.00082	+	4.00082i	−0.183764	+	0.183764i
$475$	−0.0643647	+	0.0101944i	−0.00295325	+	0.000467749i
$476$	8.34847	−	4.25376i	0.382651	−	0.194971i
$477$	0.495989	+	1.52650i	0.0227098	+	0.0698935i
$478$	6.41309	+	8.82686i	0.293328	+	0.403731i
$479$	5.96224	−	37.6441i	0.272422	−	1.72000i	−0.349512	−	0.936932i	$-0.613652\pi$
$479$	5.96224	−	37.6441i	0.272422	−	1.72000i	0.621933	−	0.783070i	$-0.286348\pi$
$480$	−3.38038	−	10.4037i	−0.154292	−	0.474863i
$481$	13.4961	−	4.27890i	0.615370	−	0.195101i
$482$	−2.64521	−	1.92185i	−0.120486	−	0.0875381i
$483$	0.238875	+	0.238875i	0.0108692	+	0.0108692i
$484$	−13.6985	+	8.43494i	−0.622661	+	0.383407i
$485$		−	35.0892i		−	1.59332i
$486$	−0.114692	−	0.724135i	−0.00520252	−	0.0328474i
$487$	−16.8211	−	33.0133i	−0.762238	−	1.49598i	−0.865275	−	0.501298i	$-0.832856\pi$
$487$	−16.8211	−	33.0133i	−0.762238	−	1.49598i	0.103037	−	0.994678i	$-0.467144\pi$
$488$	5.31824	−	10.4376i	0.240745	−	0.472489i
$489$	−16.4496	−	2.60536i	−0.743877	−	0.117818i
$490$	−1.07864	−	1.48462i	−0.0487279	−	0.0670682i
$491$	3.07005	+	9.44865i	0.138550	+	0.426412i	0.996125	−	0.0879462i	$-0.0280304\pi$
$491$	3.07005	+	9.44865i	0.138550	+	0.426412i	−0.857576	+	0.514358i	$0.828030\pi$
$492$	1.31263	+	2.57619i	0.0591781	+	0.116144i
$493$	4.24933	−	5.84870i	0.191380	−	0.263412i
$494$	−0.0186291	+	0.112420i	−0.000838163	+	0.00505802i
$495$	−4.86871	−	3.82972i	−0.218832	−	0.172133i
$496$	−6.24689	+	6.24689i	−0.280493	+	0.280493i
$497$	−17.1456	+	23.5989i	−0.769087	+	1.05856i
$498$	−0.905789	−	0.294309i	−0.0405894	−	0.0131883i
$499$	34.0483	+	17.3485i	1.52421	+	0.776624i	0.997310	−	0.0733026i	$-0.0233539\pi$
$499$	34.0483	+	17.3485i	1.52421	+	0.776624i	0.526901	+	0.849927i	$0.323354\pi$
$500$	−2.78242	+	17.5675i	−0.124433	+	0.785642i
$501$	2.33595	−	14.7486i	0.104363	−	0.658919i
$502$	−13.0560	−	6.65238i	−0.582719	−	0.296910i
$503$	21.4956	+	6.98435i	0.958442	+	0.311417i	0.746141	−	0.665788i	$-0.231904\pi$
$503$	21.4956	+	6.98435i	0.958442	+	0.311417i	0.212301	+	0.977204i	$0.431904\pi$
$504$	−3.54983	+	4.88592i	−0.158122	+	0.217636i
$505$	−21.1255	+	21.1255i	−0.940074	+	0.940074i
$506$	−0.0940809	−	0.332222i	−0.00418241	−	0.0147691i
$507$	12.3051	+	4.19330i	0.546490	+	0.186231i
$508$	10.0879	−	13.8848i	0.447578	−	0.616038i
$509$	4.61482	+	9.05709i	0.204548	+	0.401448i	0.970377	−	0.241596i	$-0.0776709\pi$
$509$	4.61482	+	9.05709i	0.204548	+	0.401448i	−0.765829	+	0.643045i	$0.777671\pi$
$510$	−1.13952	−	3.50709i	−0.0504589	−	0.155296i
$511$	16.9571	+	23.3394i	0.750138	+	1.03248i
$512$	−11.4883	−	1.81957i	−0.507716	−	0.0804143i
$513$	0.0195705	−	0.0384093i	0.000864059	−	0.00169581i
$514$	8.42539	+	16.5358i	0.371628	+	0.729361i
$515$	−2.63309	−	16.6247i	−0.116028	−	0.732571i
$516$			6.92611i			0.304905i
$517$	9.58519	+	14.3120i	0.421556	+	0.629441i
$518$	−4.84309	−	4.84309i	−0.212793	−	0.212793i
$519$	−10.6316	−	7.72427i	−0.466673	−	0.339058i
$520$	15.1758	+	7.86938i	0.665502	+	0.345095i
$521$	1.38786	+	4.27140i	0.0608034	+	0.187134i	0.976844	−	0.213951i	$-0.0686333\pi$
$521$	1.38786	+	4.27140i	0.0608034	+	0.187134i	−0.916041	+	0.401085i	$0.868633\pi$
$522$	−0.307892	+	1.94396i	−0.0134761	+	0.0850846i
$523$	19.1553	+	26.3650i	0.837602	+	1.15286i	0.986460	+	0.164002i	$0.0524403\pi$
$523$	19.1553	+	26.3650i	0.837602	+	1.15286i	−0.148858	+	0.988859i	$0.547560\pi$
$524$	5.11819	+	15.7522i	0.223589	+	0.688137i
$525$	3.20447	−	1.63276i	0.139854	−	0.0712594i
$526$	−5.88791	+	0.932553i	−0.256725	+	0.0406612i
$527$	−15.8142	+	15.8142i	−0.688877	+	0.688877i
$528$	−3.20248	+	1.48053i	−0.139370	+	0.0644319i
$529$	22.9798			0.999123
$530$	−1.77808	−	1.29185i	−0.0772351	−	0.0561146i
$531$	10.3210	−	5.25882i	0.447894	−	0.228213i
$532$	−0.142644	+	0.0463477i	−0.00618439	+	0.00200943i
$533$	−6.76343	−	2.25107i	−0.292957	−	0.0975046i
$534$	2.69213	+	3.70540i	0.116500	+	0.160348i
$535$	8.86420	−	17.3970i	0.383233	−	0.752136i
$536$	1.14186	+	0.371011i	0.0493207	+	0.0160253i
$537$	4.34089	−	5.97473i	0.187323	−	0.257828i
$538$	−4.95085	−	4.95085i	−0.213446	−	0.213446i
$539$	−3.26065	+	3.02061i	−0.140446	+	0.130107i
$540$	−1.93143	−	1.93143i	−0.0831155	−	0.0831155i
$541$	18.2969	−	2.89795i	0.786646	−	0.124592i	0.249827	−	0.968290i	$-0.419626\pi$
$541$	18.2969	−	2.89795i	0.786646	−	0.124592i	0.536818	+	0.843698i	$0.319626\pi$
$542$	−3.97737	+	12.2411i	−0.170843	+	0.525799i
$543$	7.59006	−	2.46616i	0.325721	−	0.105833i
$544$	−15.5787	−	2.46743i	−0.667933	−	0.105790i
$545$	−7.62770	+	5.54185i	−0.326735	+	0.237387i
$546$	−0.939439	−	6.21833i	−0.0402043	−	0.266120i
$547$	20.2751	+	6.58777i	0.866900	+	0.281673i	0.708507	−	0.705704i	$-0.249369\pi$
$547$	20.2751	+	6.58777i	0.866900	+	0.281673i	0.158392	+	0.987376i	$0.449369\pi$
$548$	7.99547	−	1.26636i	0.341549	−	0.0540961i
$549$		−	4.61461i		−	0.196947i
$550$	−3.67326	−	0.140378i	−0.156628	−	0.00598573i
$551$	−0.0818290	+	0.0818290i	−0.00348603	+	0.00348603i
$552$	−0.0563899	−	0.356032i	−0.00240012	−	0.0151537i
$553$	16.3586	−	8.33515i	0.695640	−	0.354447i
$554$	−5.12006	+	10.0487i	−0.217530	+	0.426928i
$555$	5.93333	−	4.31082i	0.251856	−	0.182984i
$556$	−16.5897	+	12.0531i	−0.703559	+	0.511166i
$557$	−9.06367	−	4.61817i	−0.384040	−	0.195678i	0.251302	−	0.967909i	$-0.419141\pi$
$557$	−9.06367	−	4.61817i	−0.384040	−	0.195678i	−0.635343	+	0.772230i	$0.719141\pi$
$558$	1.88152	−	5.79073i	0.0796512	−	0.245141i
$559$	−11.9877	−	12.1601i	−0.507026	−	0.514316i
$560$			4.72672i			0.199740i
$561$	−8.10720	+	3.74802i	−0.342286	+	0.158241i
$562$	−7.22617			−0.304817
$563$	30.0041	+	21.7993i	1.26452	+	0.918730i	0.998970	−	0.0453663i	$-0.0144455\pi$
$563$	30.0041	+	21.7993i	1.26452	+	0.918730i	0.265553	+	0.964096i	$0.414445\pi$
$564$	3.44829	+	6.76766i	0.145199	+	0.284970i
$565$	−1.84421	−	0.939673i	−0.0775866	−	0.0395323i
$566$	−21.8472	−	3.46025i	−0.918305	−	0.145445i
$567$	−0.372165	+	2.34975i	−0.0156294	+	0.0986804i
$568$	29.6022	−	9.61835i	1.24208	−	0.403577i
$569$	11.9207	−	36.6882i	0.499743	−	1.53805i	−0.309689	−	0.950838i	$-0.600225\pi$
$569$	11.9207	−	36.6882i	0.499743	−	1.53805i	0.809432	−	0.587213i	$-0.199775\pi$
$570$	0.00923407	+	0.0583016i	0.000386773	+	0.00244199i
$571$	20.1118			0.841652			0.420826	−	0.907141i	$-0.361740\pi$
$571$	20.1118			0.841652			0.420826	+	0.907141i	$0.361740\pi$
$572$	6.15252	−	16.3707i	0.257250	−	0.684493i
$573$	−15.4151			−0.643975
$574$	0.539440	+	3.40589i	0.0225158	+	0.142159i
$575$	−0.0663342	+	0.204156i	−0.00276633	+	0.00851388i
$576$	2.06055	−	0.669513i	0.0858562	−	0.0278964i
$577$	6.36693	−	40.1992i	0.265059	−	1.67352i	−0.392222	−	0.919870i	$-0.628294\pi$
$577$	6.36693	−	40.1992i	0.265059	−	1.67352i	0.657281	−	0.753645i	$-0.271706\pi$
$578$	7.05872	+	1.11799i	0.293604	+	0.0465023i
$579$	−17.2273	−	8.77775i	−0.715942	−	0.364791i
$580$	3.32895	+	6.53343i	0.138227	+	0.271286i
$581$	2.50024	+	1.81653i	0.103727	+	0.0753623i
$582$	13.7742			0.570961
$583$	−2.59613	+	4.64740i	−0.107521	+	0.192476i
$584$		−	30.7834i		−	1.27383i
$585$	6.73389	+	0.0480649i	0.278412	+	0.00198724i
$586$	7.18577	−	22.1155i	0.296841	−	0.913584i
$587$	6.88346	+	3.50730i	0.284111	+	0.144762i	0.590239	−	0.807229i	$-0.299034\pi$
$587$	6.88346	+	3.50730i	0.284111	+	0.144762i	−0.306128	+	0.951990i	$0.599034\pi$
$588$	−1.58562	+	1.15202i	−0.0653897	+	0.0475084i
$589$	0.289628	−	0.210427i	0.0119339	−	0.00867049i
$590$	−7.20101	+	14.1328i	−0.296461	+	0.581837i
$591$	−0.548822	+	0.279639i	−0.0225755	+	0.0115028i
$592$	−0.653461	−	4.12579i	−0.0268571	−	0.169569i
$593$	25.4239	−	25.4239i	1.04403	−	1.04403i	0.0450491	−	0.998985i	$-0.485656\pi$
$593$	25.4239	−	25.4239i	1.04403	−	1.04403i	0.998985	−	0.0450491i	$-0.0143444\pi$
$594$	1.50335	−	1.91121i	0.0616834	−	0.0784178i
$595$			11.9658i			0.490552i
$596$	3.21223	−	0.508768i	0.131578	−	0.0208399i
$597$	−17.0502	−	5.53995i	−0.697819	−	0.226735i
$598$	0.302095	+	0.222796i	0.0123536	+	0.00911082i
$599$	24.0625	−	17.4824i	0.983167	−	0.714313i	0.0247527	−	0.999694i	$-0.492120\pi$
$599$	24.0625	−	17.4824i	0.983167	−	0.714313i	0.958414	+	0.285381i	$0.0921202\pi$
$600$	−3.79034	−	0.600331i	−0.154740	−	0.0245084i
$601$	−33.9312	+	11.0249i	−1.38408	+	0.449716i	−0.904009	−	0.427513i	$-0.859390\pi$
$601$	−33.9312	+	11.0249i	−1.38408	+	0.449716i	−0.480073	+	0.877229i	$0.659390\pi$
$602$	−2.55262	+	7.85615i	−0.104037	+	0.320193i
$603$	0.467131	−	0.0739863i	0.0190230	−	0.00301295i
$604$	5.17969	+	5.17969i	0.210759	+	0.210759i
$605$	−1.65583	−	20.4778i	−0.0673192	−	0.832540i
$606$	−8.29282	−	8.29282i	−0.336873	−	0.336873i
$607$	−18.4753	+	25.4290i	−0.749889	+	1.03213i	0.248100	+	0.968735i	$0.420194\pi$
$607$	−18.4753	+	25.4290i	−0.749889	+	1.03213i	−0.997988	+	0.0633986i	$0.979806\pi$
$608$	0.240126	+	0.0780216i	0.00973839	+	0.00316420i
$609$	2.89945	−	5.69050i	0.117492	−	0.230591i
$610$	3.71414	+	5.11208i	0.150381	+	0.206982i
$611$	−17.7676	−	5.91357i	−0.718799	−	0.239237i
$612$	−3.74567	+	1.21704i	−0.151410	+	0.0491960i
$613$	−19.3286	+	9.84843i	−0.780676	+	0.397774i	−0.798445	−	0.602068i	$-0.794344\pi$
$613$	−19.3286	+	9.84843i	−0.780676	+	0.397774i	0.0177689	+	0.999842i	$0.494344\pi$
$614$	−3.81444	−	2.77136i	−0.153938	−	0.111843i
$615$	−3.69245			−0.148894
$616$	−19.8888	+	2.37563i	−0.801343	+	0.0957167i
$617$	−27.1104	+	27.1104i	−1.09142	+	1.09142i	−0.0960464	+	0.995377i	$0.530620\pi$
$617$	−27.1104	+	27.1104i	−1.09142	+	1.09142i	−0.995377	+	0.0960464i	$0.969380\pi$
$618$	6.52601	−	1.03362i	0.262514	−	0.0415782i
$619$	14.0504	−	7.15906i	0.564735	−	0.287747i	−0.148223	−	0.988954i	$-0.547355\pi$
$619$	14.0504	−	7.15906i	0.564735	−	0.287747i	0.712958	+	0.701207i	$0.247355\pi$
$620$	−7.00976	−	21.5738i	−0.281519	−	0.866426i
$621$	−0.0834645	−	0.114879i	−0.00334931	−	0.00460994i
$622$	0.451720	−	2.85205i	0.0181123	−	0.114357i
$623$	−4.59265	−	14.1347i	−0.184001	−	0.566295i
$624$	1.76563	−	3.40495i	0.0706819	−	0.136307i
$625$	−12.2615	−	8.90852i	−0.490461	−	0.356341i
$626$	−9.88764	−	9.88764i	−0.395190	−	0.395190i
$627$	0.137563	−	0.0389560i	0.00549373	−	0.00155575i
$628$		−	9.65826i		−	0.385406i
$629$	−1.65426	−	10.4446i	−0.0659596	−	0.416452i
$630$	−1.47895	−	2.90261i	−0.0589229	−	0.115643i
$631$	6.13940	−	12.0492i	0.244406	−	0.479673i	−0.735918	−	0.677071i	$-0.763249\pi$
$631$	6.13940	−	12.0492i	0.244406	−	0.479673i	0.980323	+	0.197398i	$0.0632491\pi$
$632$	−19.3495	−	3.06466i	−0.769682	−	0.121906i
$633$	4.58676	+	6.31313i	0.182307	+	0.250925i
$634$	0.103599	+	0.318846i	0.00411446	+	0.0126630i
$635$	9.95053	+	19.5290i	0.394875	+	0.774985i
$636$	−1.37974	+	1.89905i	−0.0547102	+	0.0753021i
$637$	0.789931	−	4.76696i	0.0312982	−	0.188874i
$638$	−5.42373	+	3.63244i	−0.214727	+	0.143810i
$639$	8.66996	−	8.66996i	0.342978	−	0.342978i
$640$	11.1159	−	15.2997i	0.439395	−	0.604775i
$641$	33.9764	+	11.0396i	1.34199	+	0.436038i	0.889989	−	0.455982i	$-0.150712\pi$
$641$	33.9764	+	11.0396i	1.34199	+	0.436038i	0.451997	+	0.892019i	$0.350712\pi$
$642$	6.82917	+	3.47963i	0.269526	+	0.137330i
$643$	0.534213	−	3.37289i	0.0210673	−	0.133014i	−0.974913	−	0.222586i	$-0.928550\pi$
$643$	0.534213	−	3.37289i	0.0210673	−	0.133014i	0.995980	+	0.0895726i	$0.0285501\pi$
$644$	−0.0772870	+	0.487971i	−0.00304553	+	0.0192287i
$645$	−7.88111	−	4.01563i	−0.310319	−	0.158115i
$646$	0.0809462	+	0.0263010i	0.00318479	+	0.00103480i
$647$	21.7245	−	29.9013i	0.854080	−	1.17554i	−0.128869	−	0.991662i	$-0.541135\pi$
$647$	21.7245	−	29.9013i	0.854080	−	1.17554i	0.982949	−	0.183878i	$-0.0588652\pi$
$648$	1.79503	−	1.79503i	0.0705154	−	0.0705154i
$649$	36.0579	+	13.2586i	1.41540	+	0.520444i
$650$	3.24965	−	2.32575i	0.127462	−	0.0912235i
$651$	−11.6131	+	15.9841i	−0.455154	+	0.626465i
$652$	−11.0578	−	21.7022i	−0.433059	−	0.849925i
$653$	9.69847	+	29.8488i	0.379530	+	1.16807i	0.940371	+	0.340150i	$0.110478\pi$
$653$	9.69847	+	29.8488i	0.379530	+	1.16807i	−0.560841	+	0.827924i	$0.689522\pi$
$654$	−2.17545	−	2.99425i	−0.0850668	−	0.117084i
$655$	−20.8916	−	3.30890i	−0.816302	−	0.129290i
$656$	−0.954787	+	1.87388i	−0.0372782	+	0.0731626i
$657$	−5.50525	−	10.8047i	−0.214780	−	0.421530i
$658$	1.41711	+	8.94729i	0.0552448	+	0.348802i
$659$		−	17.7370i		−	0.690934i	−0.938431	−	0.345467i	$-0.887721\pi$
$659$		−	17.7370i		−	0.690934i	0.938431	−	0.345467i	$-0.112279\pi$
$660$	0.345956	−	9.05260i	0.0134663	−	0.352372i
$661$	22.7932	+	22.7932i	0.886553	+	0.886553i	0.994190	−	0.107637i	$-0.0343284\pi$
$661$	22.7932	+	22.7932i	0.886553	+	0.886553i	−0.107637	+	0.994190i	$0.534328\pi$
$662$	5.33837	+	3.87855i	0.207481	+	0.150744i
$663$	4.46976	−	8.61974i	0.173591	−	0.334763i
$664$	−1.01904	−	3.13627i	−0.0395463	−	0.121711i
$665$	0.0299637	−	0.189184i	0.00116194	−	0.00733622i
$666$	1.69221	+	2.32913i	0.0655718	+	0.0902518i
$667$	0.117796	+	0.362540i	0.00456110	+	0.0140376i
$668$	19.4581	−	9.91439i	0.752856	−	0.383599i
$669$	−28.9512	+	4.58542i	−1.11932	+	0.177283i
$670$	−0.457940	+	0.457940i	−0.0176918	+	0.0176918i
$671$	11.2276	−	10.4010i	0.433437	−	0.401527i
$672$	−13.9341			−0.537521
$673$	41.0035	+	29.7908i	1.58057	+	1.14835i	0.916041	+	0.401084i	$0.131367\pi$
$673$	41.0035	+	29.7908i	1.58057	+	1.14835i	0.664526	+	0.747265i	$0.268633\pi$
$674$	19.7330	−	10.0545i	0.760087	−	0.387284i
$675$	−1.43773	+	0.467148i	−0.0553384	+	0.0179805i
$676$	5.61637	+	18.1637i	0.216014	+	0.698603i
$677$	5.21331	+	7.17550i	0.200364	+	0.275777i	0.897361	−	0.441296i	$-0.145481\pi$
$677$	5.21331	+	7.17550i	0.200364	+	0.275777i	−0.696998	+	0.717073i	$0.745481\pi$
$678$	0.368868	−	0.723944i	0.0141663	−	0.0278029i
$679$	−42.5086	−	13.8119i	−1.63133	−	0.530052i
$680$	7.50491	−	10.3296i	0.287800	−	0.396123i
$681$	19.7006	+	19.7006i	0.754930	+	0.754930i
$682$	18.3300	−	8.47409i	0.701892	−	0.324490i
$683$	−10.0392	−	10.0392i	−0.384140	−	0.384140i	0.488451	−	0.872591i	$-0.337562\pi$
$683$	−10.0392	−	10.0392i	−0.384140	−	0.384140i	−0.872591	+	0.488451i	$0.837562\pi$
$684$	0.0622678	−	0.00986225i	0.00238087	−	0.000377093i
$685$	−3.19465	+	9.83213i	−0.122061	+	0.375666i
$686$	−13.8351	+	4.49530i	−0.528227	+	0.171631i
$687$	21.5853	+	3.41878i	0.823531	+	0.130434i
$688$	−4.07577	+	2.96122i	−0.155387	+	0.112896i
$689$	−0.864482	−	5.72217i	−0.0329341	−	0.217997i
$690$	0.184925	+	0.0600856i	0.00703996	+	0.00228742i
$691$	13.7232	−	2.17354i	0.522054	−	0.0826853i	0.110155	−	0.993914i	$-0.464865\pi$
$691$	13.7232	−	2.17354i	0.522054	−	0.0826853i	0.411900	+	0.911229i	$0.364865\pi$
$692$		−	19.2188i		−	0.730591i
$693$	−6.55592	+	4.39070i	−0.249039	+	0.166789i
$694$	1.09028	−	1.09028i	0.0413865	−	0.0413865i
$695$	−4.09666	−	25.8653i	−0.155395	−	0.981127i
$696$	−6.07203	+	3.09385i	−0.230160	+	0.117272i
$697$	−2.41708	+	4.74378i	−0.0915533	+	0.179683i
$698$	−9.06532	+	6.58634i	−0.343128	+	0.249297i
$699$	−12.9910	+	9.43852i	−0.491365	+	0.356998i
$700$	4.68645	+	2.38786i	0.177131	+	0.0902528i
$701$	−1.41665	+	4.36000i	−0.0535061	+	0.164675i	−0.974239	−	0.225519i	$-0.927592\pi$
$701$	−1.41665	+	4.36000i	−0.0535061	+	0.164675i	0.920733	+	0.390194i	$0.127592\pi$
$702$	−0.0188678	+	2.64338i	−0.000712121	+	0.0997681i
$703$			0.169274i			0.00638430i
$704$	6.27331	+	3.50439i	0.236434	+	0.132077i
$705$	−9.70007			−0.365326
$706$	−14.1188	−	10.2579i	−0.531367	−	0.386061i
$707$	17.2769	+	33.9079i	0.649766	+	1.27524i
$708$	15.0942	+	7.69088i	0.567275	+	0.289041i
$709$	7.47340	+	1.18367i	0.280670	+	0.0444537i	0.295182	−	0.955441i	$-0.404620\pi$
$709$	7.47340	+	1.18367i	0.280670	+	0.0444537i	−0.0145126	+	0.999895i	$0.504620\pi$
$710$	−2.62645	+	16.5828i	−0.0985691	+	0.622341i
$711$	−7.33956	+	2.38477i	−0.275255	+	0.0894358i
$712$	−4.90057	+	15.0824i	−0.183657	+	0.565237i
$713$	−0.184477	−	1.16474i	−0.00690873	−	0.0436200i
$714$	−4.69718			−0.175788
$715$	15.0608	+	16.4923i	0.563243	+	0.616776i
$716$	10.8006			0.403638
$717$	2.32799	+	14.6984i	0.0869405	+	0.548921i
$718$	7.22767	−	22.2445i	0.269734	−	0.830156i
$719$	−0.368933	+	0.119874i	−0.0137589	+	0.00447053i	−0.315888	−	0.948796i	$-0.602303\pi$
$719$	−0.368933	+	0.119874i	−0.0137589	+	0.00447053i	0.302129	+	0.953267i	$0.402303\pi$
$720$	0.310806	−	1.96235i	0.0115831	−	0.0731325i
$721$	−21.1763	−	3.35400i	−0.788647	−	0.124909i
$722$	12.4106	+	6.32350i	0.461874	+	0.235336i
$723$	−2.02464	−	3.97359i	−0.0752973	−	0.147779i
$724$	9.44246	+	6.86035i	0.350926	+	0.254963i
$725$	4.05825			0.150720
$726$	8.03854	−	0.649996i	0.298338	−	0.0241236i
$727$			23.2836i			0.863541i	0.901984	+	0.431770i	$0.142111\pi$
$727$			23.2836i			0.863541i	−0.901984	+	0.431770i	$0.857889\pi$
$728$	15.5068	−	15.2870i	0.574722	−	0.566575i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	14.7950	+	7.53845i	0.547589	+	0.279011i
$731$	−10.3180	+	7.49644i	−0.381624	+	0.277266i
$732$	5.45985	−	3.96681i	0.201802	−	0.146618i
$733$	19.3572	−	37.9907i	0.714975	−	1.40322i	−0.191728	−	0.981448i	$-0.561409\pi$
$733$	19.3572	−	37.9907i	0.714975	−	1.40322i	0.906703	−	0.421769i	$-0.138591\pi$
$734$	16.4974	−	8.40582i	0.608929	−	0.310265i
$735$	−0.391553	−	2.47217i	−0.0144426	−	0.0911872i
$736$	0.588092	−	0.588092i	0.0216774	−	0.0216774i
$737$	1.23290	+	0.969796i	0.0454143	+	0.0357229i
$738$		−	1.44947i		−	0.0533556i
$739$	−15.3398	+	2.42959i	−0.564284	+	0.0893738i	−0.432058	−	0.901846i	$-0.642212\pi$
$739$	−15.3398	+	2.42959i	−0.564284	+	0.0893738i	−0.132226	+	0.991220i	$0.542212\pi$
$740$	10.2008	+	3.31445i	0.374990	+	0.121842i
$741$	−0.0922530	+	0.125088i	−0.00338900	+	0.00459522i
$742$	−2.26490	+	1.64555i	−0.0831472	+	0.0604100i
$743$	−14.0686	−	2.22824i	−0.516125	−	0.0817462i	−0.107062	−	0.994252i	$-0.534144\pi$
$743$	−14.0686	−	2.22824i	−0.516125	−	0.0817462i	−0.409063	+	0.912506i	$0.634144\pi$
$744$	20.0502	−	6.51472i	0.735078	−	0.238841i
$745$	−1.28347	+	3.95013i	−0.0470228	+	0.144721i
$746$	−0.960442	+	0.152119i	−0.0351643	+	0.00556948i
$747$	−0.918557	−	0.918557i	−0.0336082	−	0.0336082i
$748$	−11.4036	−	6.37029i	−0.416958	−	0.232921i
$749$	−17.5863	−	17.5863i	−0.642590	−	0.642590i
$750$	5.24107	−	7.21371i	0.191377	−	0.263407i
$751$	−18.8547	−	6.12627i	−0.688018	−	0.223551i	−0.0559157	−	0.998435i	$-0.517808\pi$
$751$	−18.8547	−	6.12627i	−0.688018	−	0.223551i	−0.632102	+	0.774885i	$0.717808\pi$
$752$	−2.50823	+	4.92268i	−0.0914657	+	0.179512i
$753$	−11.7476	−	16.1692i	−0.428106	−	0.589238i
$754$	2.24103	−	6.73326i	0.0816133	−	0.245211i
$755$	−8.89698	+	2.89080i	−0.323794	+	0.105207i
$756$	−3.10007	+	1.57957i	−0.112749	+	0.0574482i
$757$	17.5047	+	12.7179i	0.636218	+	0.462240i	0.858549	−	0.512732i	$-0.171366\pi$
$757$	17.5047	+	12.7179i	0.636218	+	0.462240i	−0.222331	+	0.974971i	$0.571366\pi$
$758$	20.3456			0.738986
$759$	0.0913834	−	0.462004i	0.00331701	−	0.0167697i
$760$	−0.144521	+	0.144521i	−0.00524234	+	0.00524234i
$761$	−14.1134	+	2.23534i	−0.511610	+	0.0810310i	−0.406902	−	0.913472i	$-0.633391\pi$
$761$	−14.1134	+	2.23534i	−0.511610	+	0.0810310i	−0.104708	+	0.994503i	$0.533391\pi$
$762$	−7.66610	+	3.90607i	−0.277713	+	0.141502i
$763$	3.71121	+	11.4219i	0.134355	+	0.413502i
$764$	−13.2511	−	18.2386i	−0.479409	−	0.659850i
$765$	0.786816	−	4.96776i	0.0284474	−	0.179610i
$766$	−1.48516	−	4.57085i	−0.0536610	−	0.165152i
$767$	−39.8120	+	12.6223i	−1.43753	+	0.455764i
$768$	9.51151	+	6.91052i	0.343217	+	0.249362i
$769$	11.7998	+	11.7998i	0.425512	+	0.425512i	0.887096	−	0.461584i	$-0.152719\pi$
$769$	11.7998	+	11.7998i	0.425512	+	0.425512i	−0.461584	+	0.887096i	$0.652719\pi$
$770$	3.72875	−	10.1407i	0.134375	−	0.365445i
$771$			25.3130i			0.911626i
$772$	−4.42341	−	27.9283i	−0.159202	−	1.00516i
$773$	7.88989	+	15.4848i	0.283780	+	0.556949i	0.988261	−	0.152773i	$-0.0488204\pi$
$773$	7.88989	+	15.4848i	0.283780	+	0.556949i	−0.704481	+	0.709722i	$0.748820\pi$
$774$	1.57633	−	3.09373i	0.0566601	−	0.111202i
$775$	−12.3999	−	1.96396i	−0.445419	−	0.0705474i
$776$	28.0332	+	38.5844i	1.00633	+	1.38510i
$777$	−2.88683	−	8.88474i	−0.103564	−	0.318738i
$778$	7.61061	+	14.9367i	0.272854	+	0.535505i
$779$	0.0500936	−	0.0689480i	0.00179479	−	0.00247032i
$780$	5.73172	+	8.00863i	0.205229	+	0.286755i
$781$	40.6361	+	1.55295i	1.45407	+	0.0555691i
$782$	0.198245	−	0.198245i	0.00708924	−	0.00708924i
$783$	−1.57792	+	2.17182i	−0.0563903	+	0.0776146i
$784$	−1.35584	−	0.440541i	−0.0484230	−	0.0157336i
$785$	10.9900	+	5.59967i	0.392249	+	0.199861i
$786$	1.29891	−	8.20098i	0.0463305	−	0.292519i
$787$	3.16213	−	19.9649i	0.112718	−	0.711673i	−0.865004	−	0.501766i	$-0.832684\pi$
$787$	3.16213	−	19.9649i	0.112718	−	0.711673i	0.977721	−	0.209907i	$-0.0673161\pi$
$788$	−0.802638	−	0.408964i	−0.0285928	−	0.0145688i
$789$	−7.73299	−	2.51260i	−0.275302	−	0.0894510i
$790$	6.21138	−	8.54923i	0.220991	−	0.304168i
$791$	−1.86428	+	1.86428i	−0.0662863	+	0.0662863i
$792$	8.41329	+	0.321524i	0.298953	+	0.0114248i
$793$	−2.72002	+	16.4144i	−0.0965906	+	0.582891i
$794$	5.44397	−	7.49299i	0.193199	−	0.265916i
$795$	−1.36095	−	2.67101i	−0.0482679	−	0.0947311i
$796$	−8.10203	−	24.9355i	−0.287169	−	0.883815i
$797$	−9.74929	−	13.4188i	−0.345338	−	0.475317i	0.600653	−	0.799510i	$-0.294907\pi$
$797$	−9.74929	−	13.4188i	−0.345338	−	0.475317i	−0.945991	+	0.324193i	$0.894907\pi$
$798$	0.0742639	+	0.0117622i	0.00262891	+	0.000416379i
$799$	−6.34967	+	12.4619i	−0.224635	+	0.440871i
$800$	−4.01972	−	7.88915i	−0.142119	−	0.278924i
$801$	0.977261	+	6.17018i	0.0345298	+	0.218013i
$802$			0.488152i			0.0172373i
$803$	13.8799	−	37.7476i	0.489810	−	1.33208i
$804$	0.489093	+	0.489093i	0.0172490	+	0.0172490i
$805$	−0.510445	−	0.370860i	−0.0179908	−	0.0130711i
$806$	−10.1059	+	19.4888i	−0.355966	+	0.686465i
$807$	−2.95106	−	9.08242i	−0.103882	−	0.319716i
$808$	6.35237	−	40.1073i	0.223476	−	1.41097i
$809$	−28.7753	−	39.6059i	−1.01169	−	1.39247i	−0.917871	−	0.396879i	$-0.870093\pi$
$809$	−28.7753	−	39.6059i	−1.01169	−	1.39247i	−0.0938163	−	0.995590i	$-0.529907\pi$
$810$	0.423143	+	1.30230i	0.0148677	+	0.0457582i
$811$	−36.4224	+	18.5581i	−1.27896	+	0.651665i	−0.955616	−	0.294615i	$-0.904808\pi$
$811$	−36.4224	+	18.5581i	−1.27896	+	0.651665i	−0.323348	+	0.946280i	$0.604808\pi$
$812$	9.22524	−	1.46113i	0.323742	−	0.0512758i
$813$	−12.4136	+	12.4136i	−0.435365	+	0.435365i
$814$	−1.85276	+	9.36694i	−0.0649393	+	0.328311i
$815$	31.1058			1.08959
$816$	−2.31763	−	1.68386i	−0.0811333	−	0.0589468i
$817$	0.181902	−	0.0926837i	0.00636395	−	0.00324259i
$818$	−10.3591	+	3.36587i	−0.362197	+	0.117685i
$819$	2.70884	−	8.13881i	0.0946544	−	0.284393i
$820$	−3.17410	−	4.36878i	−0.110844	−	0.152564i
$821$	−6.52773	+	12.8114i	−0.227819	+	0.447120i	−0.976414	−	0.215908i	$-0.930729\pi$
$821$	−6.52773	+	12.8114i	−0.227819	+	0.447120i	0.748595	+	0.663028i	$0.230729\pi$
$822$	−3.85960	−	1.25406i	−0.134619	−	0.0437403i
$823$	−18.8015	+	25.8780i	−0.655378	+	0.902050i	−0.999317	−	0.0369414i	$-0.988239\pi$
$823$	−18.8015	+	25.8780i	−0.655378	+	0.902050i	0.343939	+	0.938992i	$0.388239\pi$
$824$	16.1770	+	16.1770i	0.563554	+	0.563554i
$825$	−4.37716	−	2.44517i	−0.152393	−	0.0851297i
$826$	14.2866	+	14.2866i	0.497094	+	0.497094i
$827$	−28.0995	+	4.45053i	−0.977117	+	0.154760i	−0.624515	−	0.781013i	$-0.714703\pi$
$827$	−28.0995	+	4.45053i	−0.977117	+	0.154760i	−0.352602	+	0.935773i	$0.614703\pi$
$828$	0.0641732	−	0.197505i	0.00223017	−	0.00686376i
$829$	51.5178	−	16.7392i	1.78929	−	0.581375i	0.789800	−	0.613365i	$-0.210184\pi$
$829$	51.5178	−	16.7392i	1.78929	−	0.581375i	0.999488	+	0.0319898i	$0.0101844\pi$
$830$	1.75690	+	0.278265i	0.0609827	+	0.00965872i
$831$	−12.4448	+	9.04164i	−0.431704	+	0.313651i
$832$	−7.72410	+	1.16693i	−0.267785	+	0.0404559i
$833$	−3.43237	−	1.11524i	−0.118924	−	0.0386409i
$834$	10.1534	−	1.60814i	0.351584	−	0.0556854i
$835$			27.8892i			0.965147i
$836$	0.164343	+	0.129272i	0.00568393	+	0.00447097i
$837$	5.87235	−	5.87235i	0.202978	−	0.202978i
$838$	−3.36666	−	21.2562i	−0.116299	−	0.734285i
$839$	−35.5025	+	18.0894i	−1.22568	+	0.624516i	−0.942390	−	0.334517i	$-0.891427\pi$
$839$	−35.5025	+	18.0894i	−1.22568	+	0.624516i	−0.283292	+	0.959034i	$0.591427\pi$
$840$	5.12084	−	10.0502i	0.176686	−	0.346765i
$841$	−17.6312	+	12.8098i	−0.607972	+	0.441717i
$842$	−8.27817	+	6.01444i	−0.285285	+	0.207271i
$843$	−8.78191	−	4.47461i	−0.302465	−	0.154114i
$844$	−3.52661	+	10.8538i	−0.121391	+	0.373603i
$845$	−23.9244	−	4.14017i	−0.823025	−	0.142426i
$846$		−	3.80775i		−	0.130913i
$847$	−25.4595	−	6.05456i	−0.874798	−	0.208037i
$848$	−1.70742			−0.0586331
$849$	−24.4080	−	17.7335i	−0.837682	−	0.608612i
$850$	−1.35504	−	2.65943i	−0.0464777	−	0.0912175i
$851$	0.496820	+	0.253143i	0.0170308	+	0.00867762i
$852$	17.7109	+	2.80513i	0.606765	+	0.0961021i
$853$	−1.86889	+	11.7997i	−0.0639896	+	0.404014i	0.934815	+	0.355135i	$0.115565\pi$
$853$	−1.86889	+	11.7997i	−0.0639896	+	0.404014i	−0.998805	+	0.0488794i	$0.984435\pi$
$854$	7.65497	−	2.48725i	0.261948	−	0.0851119i
$855$	−0.0248796	+	0.0765715i	−0.000850864	+	0.00261869i
$856$	4.15151	+	26.2116i	0.141896	+	0.895893i
$857$	−15.7901			−0.539378			−0.269689	−	0.962947i	$-0.586921\pi$
$857$	−15.7901			−0.539378			−0.269689	+	0.962947i	$0.586921\pi$
$858$	−6.47403	+	5.91212i	−0.221020	+	0.201836i
$859$	−16.8965			−0.576501			−0.288250	−	0.957555i	$-0.593074\pi$
$859$	−16.8965			−0.576501			−0.288250	+	0.957555i	$0.593074\pi$
$860$	−2.02361	−	12.7766i	−0.0690046	−	0.435678i
$861$	−1.45343	+	4.47319i	−0.0495327	+	0.152446i
$862$	6.38146	−	2.07346i	0.217354	−	0.0706224i
$863$	4.20433	−	26.5451i	0.143117	−	0.903607i	−0.806736	−	0.590912i	$-0.798768\pi$
$863$	4.20433	−	26.5451i	0.143117	−	0.903607i	0.949854	−	0.312695i	$-0.101232\pi$
$864$	5.78492	+	0.916241i	0.196807	+	0.0311712i
$865$	21.8688	+	11.1427i	0.743562	+	0.378864i
$866$	−1.30339	−	2.55805i	−0.0442911	−	0.0869261i
$867$	7.88613	+	5.72961i	0.267827	+	0.194588i
$868$	−28.8947			−0.980750
$869$	−22.3452	−	12.4825i	−0.758009	−	0.423438i
$870$		−	3.67597i		−	0.124627i
$871$	−1.70522	−	0.0121714i	−0.0577790	−	0.000412413i
$872$	3.96004	−	12.1877i	0.134104	−	0.412729i
$873$	16.7397	+	8.52933i	0.566555	+	0.288674i
$874$	−0.00363075	+	0.00263789i	−0.000122812	+	8.92280e-5i
$875$	−23.4079	+	17.0068i	−0.791330	+	0.574935i
$876$	8.05129	−	15.8015i	0.272028	−	0.533884i
$877$	37.9641	−	19.3437i	1.28196	−	0.653190i	0.325633	−	0.945496i	$-0.394423\pi$
$877$	37.9641	−	19.3437i	1.28196	−	0.653190i	0.956325	+	0.292306i	$0.0944226\pi$
$878$	1.96735	+	12.4214i	0.0663949	+	0.419201i
$879$	22.4273	−	22.4273i	0.756453	−	0.756453i
$880$	5.47505	−	3.66681i	0.184564	−	0.123608i
$881$			52.4484i			1.76703i	0.468400	+	0.883516i	$0.344830\pi$
$881$			52.4484i			1.76703i	−0.468400	+	0.883516i	$0.655170\pi$
$882$	0.970447	−	0.153704i	0.0326766	−	0.00517547i
$883$	−36.0435	−	11.7112i	−1.21296	−	0.394114i	−0.368446	−	0.929649i	$-0.620110\pi$
$883$	−36.0435	−	11.7112i	−1.21296	−	0.394114i	−0.844513	+	0.535535i	$0.820110\pi$
$884$	14.0409	−	2.12124i	0.472246	−	0.0713450i
$885$	−17.5027	+	12.7164i	−0.588346	+	0.427458i
$886$	−22.3641	−	3.54212i	−0.751336	−	0.119000i
$887$	10.1779	−	3.30701i	0.341742	−	0.111039i	−0.133118	−	0.991100i	$-0.542499\pi$
$887$	10.1779	−	3.30701i	0.341742	−	0.111039i	0.474859	+	0.880062i	$0.342499\pi$
$888$	−3.08038	+	9.48043i	−0.103371	+	0.318142i
$889$	27.5751	−	4.36746i	0.924838	−	0.146480i
$890$	−6.04879	−	6.04879i	−0.202756	−	0.202756i
$891$	3.01048	−	1.39177i	0.100855	−	0.0466259i
$892$	−30.3124	−	30.3124i	−1.01493	−	1.01493i
$893$	0.131596	−	0.181127i	0.00440370	−	0.00606117i
$894$	−1.55062	−	0.503827i	−0.0518605	−	0.0168505i
$895$	−6.26199	+	12.2899i	−0.209315	+	0.410804i
$896$	−14.1593	−	19.4886i	−0.473029	−	0.651069i
$897$	0.229173	+	0.457827i	0.00765187	+	0.0152864i
$898$	6.55681	−	2.13044i	0.218804	−	0.0710936i
$899$	−19.8644	+	10.1214i	−0.662514	+	0.337568i
$900$	−1.78862	−	1.29951i	−0.0596207	−	0.0433169i
$901$	−4.32240			−0.144000
$902$	3.52663	−	3.26701i	0.117424	−	0.108779i
$903$	−7.96689	+	7.96689i	−0.265121	+	0.265121i
$904$	2.77863	−	0.440092i	0.0924158	−	0.0146372i
$905$	−13.2808	+	6.76693i	−0.441470	+	0.224940i
$906$	−1.13478	−	3.49250i	−0.0377006	−	0.116031i
$907$	−4.33760	−	5.97019i	−0.144028	−	0.198237i	0.730908	−	0.682476i	$-0.239097\pi$
$907$	−4.33760	−	5.97019i	−0.144028	−	0.198237i	−0.874936	+	0.484239i	$0.839097\pi$
$908$	−6.37406	+	40.2442i	−0.211531	+	1.33555i
$909$	−4.94310	−	15.2133i	−0.163952	−	0.504594i
$910$	3.54980	+	11.1965i	0.117675	+	0.371159i
$911$	−43.8638	−	31.8689i	−1.45327	−	1.05586i	−0.985053	−	0.172251i	$-0.944896\pi$
$911$	−43.8638	−	31.8689i	−1.45327	−	1.05586i	−0.468218	−	0.883613i	$-0.655104\pi$
$912$	0.0324259	+	0.0324259i	0.00107373	+	0.00107373i
$913$	0.164531	−	4.30527i	0.00544518	−	0.142484i
$914$			6.76615i			0.223804i
$915$	1.34826	+	8.51256i	0.0445720	+	0.281416i
$916$	14.5102	+	28.4779i	0.479430	+	0.940935i
$917$	−12.2319	+	24.0065i	−0.403934	+	0.792766i
$918$	1.95009	+	0.308864i	0.0643626	+	0.0101940i
$919$	28.9445	+	39.8387i	0.954792	+	1.31416i	0.949366	+	0.314173i	$0.101727\pi$
$919$	28.9445	+	39.8387i	0.954792	+	1.31416i	0.00542582	+	0.999985i	$0.498273\pi$
$920$	0.208045	+	0.640296i	0.00685904	+	0.0211099i
$921$	−2.91958	−	5.73000i	−0.0962035	−	0.188810i
$922$	−12.9247	+	17.7893i	−0.425651	+	0.585859i
$923$	−35.9498	+	25.7290i	−1.18330	+	0.846882i
$924$	−10.8305	−	3.98241i	−0.356299	−	0.131012i
$925$	4.19752	−	4.19752i	0.138014	−	0.138014i
$926$	−4.15677	+	5.72131i	−0.136600	+	0.188014i
$927$	8.57105	+	2.78490i	0.281510	+	0.0914682i
$928$	−14.0096	−	7.13824i	−0.459887	−	0.234324i
$929$	6.91652	−	43.6692i	0.226924	−	1.43274i	−0.566496	−	0.824064i	$-0.691701\pi$
$929$	6.91652	−	43.6692i	0.226924	−	1.43274i	0.793420	−	0.608675i	$-0.208299\pi$
$930$	−1.77895	+	11.2319i	−0.0583342	+	0.368308i
$931$	0.0514741	+	0.0262273i	0.00168699	+	0.000859567i
$932$	−22.3347	−	7.25698i	−0.731597	−	0.237710i
$933$	2.31503	−	3.18636i	0.0757906	−	0.104317i
$934$	−15.2261	+	15.2261i	−0.498212	+	0.498212i
$935$	13.8603	−	9.28265i	0.453279	−	0.303575i
$936$	−7.44305	+	5.32694i	−0.243284	+	0.174116i
$937$	−11.8947	+	16.3716i	−0.388583	+	0.534838i	−0.957833	−	0.287326i	$-0.907234\pi$
$937$	−11.8947	+	16.3716i	−0.388583	+	0.534838i	0.569250	+	0.822165i	$0.307234\pi$
$938$	0.374514	+	0.735025i	0.0122283	+	0.0239994i
$939$	−5.89373	−	18.1390i	−0.192335	−	0.591945i
$940$	−8.33838	−	11.4768i	−0.271968	−	0.374332i
$941$	−35.2885	−	5.58915i	−1.15037	−	0.182201i	−0.448015	−	0.894026i	$-0.647869\pi$
$941$	−35.2885	−	5.58915i	−1.15037	−	0.182201i	−0.702357	+	0.711825i	$0.747869\pi$
$942$	−2.19815	+	4.31411i	−0.0716195	+	0.140561i
$943$	−0.127450	−	0.250134i	−0.00415033	−	0.00814548i
$944$	1.92764	+	12.1706i	0.0627392	+	0.396120i
$945$		−	4.44333i		−	0.144541i
$946$	11.0802	−	3.13776i	0.360247	−	0.102017i
$947$	35.4553	+	35.4553i	1.15214	+	1.15214i	0.986123	+	0.166018i	$0.0530911\pi$
$947$	35.4553	+	35.4553i	1.15214	+	1.15214i	0.166018	+	0.986123i	$0.446909\pi$
$948$	−9.13082	−	6.63393i	−0.296555	−	0.215460i
$949$	13.2138	+	41.6777i	0.428937	+	1.35291i
$950$	0.0147642	+	0.0454395i	0.000479014	+	0.00147425i
$951$	−0.0715332	+	0.451643i	−0.00231962	+	0.0146455i
$952$	−9.55966	−	13.1577i	−0.309830	−	0.426445i
$953$	7.35232	+	22.6281i	0.238165	+	0.732997i	0.996686	+	0.0813477i	$0.0259224\pi$
$953$	7.35232	+	22.6281i	0.238165	+	0.732997i	−0.758521	+	0.651649i	$0.774078\pi$
$954$	1.04850	−	0.534240i	0.0339466	−	0.0172966i
$955$	28.4362	−	4.50385i	0.920174	−	0.145741i
$956$	−15.3894	+	15.3894i	−0.497729	+	0.497729i
$957$	−8.84071	+	1.05598i	−0.285779	+	0.0341350i
$958$	−27.9432			−0.902805
$959$	10.6536	+	7.74029i	0.344022	+	0.249947i
$960$	−3.60548	+	1.83708i	−0.116366	+	0.0592916i
$961$	36.1107	−	11.7331i	1.16486	−	0.378487i
$962$	−4.64639	−	9.28225i	−0.149806	−	0.299272i
$963$	6.14477	+	8.45755i	0.198012	+	0.272541i
$964$	2.96099	−	5.81127i	0.0953671	−	0.187168i
$965$	34.3438	+	11.1590i	1.10557	+	0.359220i
$966$	0.145581	−	0.200375i	0.00468398	−	0.00644695i
$967$	6.96701	+	6.96701i	0.224044	+	0.224044i	0.810199	−	0.586155i	$-0.199359\pi$
$967$	6.96701	+	6.96701i	0.224044	+	0.224044i	−0.586155	+	0.810199i	$0.699359\pi$
$968$	18.1807	+	21.1947i	0.584351	+	0.681223i
$969$	0.0820872	+	0.0820872i	0.00263702	+	0.00263702i
$970$	−25.4093	+	4.02444i	−0.815844	+	0.129217i
$971$	−1.40266	+	4.31694i	−0.0450135	+	0.138537i	−0.971037	−	0.238928i	$-0.923204\pi$
$971$	−1.40266	+	4.31694i	−0.0450135	+	0.138537i	0.926024	+	0.377465i	$0.123204\pi$
$972$	1.39090	−	0.451929i	0.0446130	−	0.0144956i
$973$	−32.9469	−	5.21828i	−1.05623	−	0.167290i
$974$	−21.9768	+	15.9671i	−0.704184	+	0.511619i
$975$	5.38944	−	0.814214i	0.172600	−	0.0260757i
$976$	4.66866	+	1.51694i	0.149440	+	0.0485561i
$977$	−1.31073	+	0.207600i	−0.0419341	+	0.00664171i	−0.177366	−	0.984145i	$-0.556758\pi$
$977$	−1.31073	+	0.207600i	−0.0419341	+	0.00664171i	0.135432	+	0.990787i	$0.456758\pi$
$978$			12.2105i			0.390450i
$979$	−12.8097	+	16.2849i	−0.409400	+	0.520469i
$980$	2.58840	−	2.58840i	0.0826833	−	0.0826833i
$981$	−0.789702	−	4.98598i	−0.0252132	−	0.159190i
$982$	6.48999	−	3.30681i	0.207104	−	0.105525i
$983$	−6.83119	+	13.4070i	−0.217881	+	0.427616i	−0.973914	−	0.226918i	$-0.927135\pi$
$983$	−6.83119	+	13.4070i	−0.217881	+	0.427616i	0.756033	+	0.654534i	$0.227135\pi$
$984$	4.06025	−	2.94994i	0.129436	−	0.0940407i
$985$	0.930708	−	0.676199i	0.0296548	−	0.0215455i
$986$	−4.72261	−	2.40629i	−0.150399	−	0.0766320i
$987$	−3.81816	+	11.7511i	−0.121533	+	0.374041i
$988$	−0.227303	−	0.00162243i	−0.00723146	−	5.16164e-5i
$989$		−	0.672488i		−	0.0213839i
$990$	−2.21483	+	3.96484i	−0.0703921	+	0.126011i
$991$	−29.1286			−0.925302			−0.462651	−	0.886541i	$-0.653102\pi$
$991$	−29.1286			−0.925302			−0.462651	+	0.886541i	$0.653102\pi$
$992$	39.3516	+	28.5906i	1.24941	+	0.907752i
$993$	4.08599	+	8.01922i	0.129665	+	0.254482i
$994$	19.0553	+	9.70915i	0.604397	+	0.307956i
$995$	33.0711	+	5.23795i	1.04843	+	0.166054i
$996$	0.297195	−	1.87642i	0.00941699	−	0.0594565i
$997$	14.2413	−	4.62729i	0.451027	−	0.146548i	−0.0746903	−	0.997207i	$-0.523797\pi$
$997$	14.2413	−	4.62729i	0.451027	−	0.146548i	0.525718	+	0.850659i	$0.323797\pi$
$998$	8.65758	−	26.6453i	0.274051	−	0.843442i
$999$	0.614282	+	3.87843i	0.0194350	+	0.122708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bj.a.304.5	yes	112
11.8	odd	10	inner	429.2.bj.a.382.10	yes	112
13.8	odd	4	inner	429.2.bj.a.73.10	✓	112
143.8	even	20	inner	429.2.bj.a.151.5	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bj.a.73.10	✓	112	13.8	odd	4	inner
429.2.bj.a.151.5	yes	112	143.8	even	20	inner
429.2.bj.a.304.5	yes	112	1.1	even	1	trivial
429.2.bj.a.382.10	yes	112	11.8	odd	10	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.114692 - 0.724135i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.39090 - 0.451929i) q^{4} +(-0.292172 + 1.84470i) q^{5} +(-0.724135 - 0.114692i) q^{6} +(2.11974 + 1.08006i) q^{7} +(-1.15248 - 2.26187i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.114692 - 0.724135i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.39090 - 0.451929i) q^{4} +(-0.292172 + 1.84470i) q^{5} +(-0.724135 - 0.114692i) q^{6} +(2.11974 + 1.08006i) q^{7} +(-1.15248 - 2.26187i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.36932 q^{10} +(-0.393359 - 3.29322i) q^{11} -1.46247i q^{12} +(2.53125 + 2.56764i) q^{13} +(0.538995 - 1.65886i) q^{14} +(1.66413 + 0.847915i) q^{15} +(0.860615 - 0.625273i) q^{16} +(2.17868 - 1.58290i) q^{17} +(-0.332848 + 0.653252i) q^{18} +(-0.0384093 + 0.0195705i) q^{19} +(0.427293 + 2.69782i) q^{20} +(1.68224 - 1.68224i) q^{21} +(-2.33962 + 0.662550i) q^{22} +0.141998i q^{23} +(-2.50730 + 0.397117i) q^{24} +(1.43773 + 0.467148i) q^{25} +(1.56901 - 2.12745i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(3.43646 + 0.544281i) q^{28} +(2.55313 - 0.829563i) q^{29} +(0.423143 - 1.30230i) q^{30} +(-8.20252 + 1.29915i) q^{31} +(-4.14154 - 4.14154i) q^{32} +(-3.25359 - 0.643553i) q^{33} +(-1.39611 - 1.39611i) q^{34} +(-2.61172 + 3.59473i) q^{35} +(-1.39090 - 0.451929i) q^{36} +(1.78272 - 3.49878i) q^{37} +(0.0185769 + 0.0255689i) q^{38} +(3.22417 - 1.61391i) q^{39} +(4.50918 - 1.46512i) q^{40} +(-1.76153 + 0.897543i) q^{41} +(-1.41111 - 1.02523i) q^{42} -4.73589 q^{43} +(-2.03542 - 4.40275i) q^{44} +(1.32066 - 1.32066i) q^{45} +(0.102826 - 0.0162860i) q^{46} +(-4.62754 + 2.35785i) q^{47} +(-0.328726 - 1.01171i) q^{48} +(-0.787718 - 1.08420i) q^{49} +(0.173382 - 1.09469i) q^{50} +(-0.832180 - 2.56119i) q^{51} +(4.68109 + 2.42738i) q^{52} +(-1.29852 - 0.943427i) q^{53} +(0.518424 + 0.518424i) q^{54} +(6.18992 + 0.236555i) q^{55} -6.03933i q^{56} +(0.00674354 + 0.0425770i) q^{57} +(-0.893539 - 1.75367i) q^{58} +(-5.25882 + 10.3210i) q^{59} +(2.69782 + 0.427293i) q^{60} +(2.71240 + 3.73329i) q^{61} +(1.88152 + 5.79073i) q^{62} +(-1.08006 - 2.11974i) q^{63} +(-1.27349 + 1.75281i) q^{64} +(-5.47608 + 3.91920i) q^{65} +(-0.0928595 + 2.42985i) q^{66} +(-0.334429 + 0.334429i) q^{67} +(2.31495 - 3.18626i) q^{68} +(0.135048 + 0.0438799i) q^{69} +(2.90261 + 1.47895i) q^{70} +(-1.91807 + 12.1102i) q^{71} +(-0.397117 + 2.50730i) q^{72} +(10.8047 + 5.50525i) q^{73} +(-2.73805 - 0.889647i) q^{74} +(0.888568 - 1.22301i) q^{75} +(-0.0445788 + 0.0445788i) q^{76} +(2.72306 - 7.40563i) q^{77} +(-1.53848 - 2.14963i) q^{78} +(4.53610 - 6.24341i) q^{79} +(0.901994 + 1.77026i) q^{80} +(0.309017 + 0.951057i) q^{81} +(0.851975 + 1.17264i) q^{82} +(1.28304 + 0.203214i) q^{83} +(1.57957 - 3.10007i) q^{84} +(2.28343 + 4.48148i) q^{85} +(0.543167 + 3.42942i) q^{86} -2.68452i q^{87} +(-6.99548 + 4.68509i) q^{88} +(-4.41736 - 4.41736i) q^{89} +(-1.10780 - 0.804867i) q^{90} +(2.59238 + 8.17665i) q^{91} +(0.0641732 + 0.197505i) q^{92} +(-1.29915 + 8.20252i) q^{93} +(2.23814 + 3.08054i) q^{94} +(-0.0248796 - 0.0765715i) q^{95} +(-5.21865 + 2.65903i) q^{96} +(-18.5562 + 2.93901i) q^{97} +(-0.694763 + 0.694763i) q^{98} +(-1.61747 + 2.89548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9	\( 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9} - 10 q^{11} + 10 q^{13} - 60 q^{14} + 4 q^{15} + 80 q^{16} - 74 q^{20} + 8 q^{22} + 30 q^{24} + 38 q^{26} - 28 q^{27} - 20 q^{29} - 8 q^{31} + 20 q^{33} - 48 q^{34} + 20 q^{35} + 12 q^{37} - 10 q^{39} + 40 q^{40} - 110 q^{41} + 20 q^{42} - 36 q^{44} + 4 q^{45} - 20 q^{46} - 30 q^{47} - 20 q^{48} + 90 q^{50} - 10 q^{52} + 52 q^{53} - 64 q^{55} + 30 q^{57} + 24 q^{58} - 36 q^{59} - 74 q^{60} - 60 q^{61} + 48 q^{66} + 60 q^{67} + 60 q^{68} + 116 q^{70} + 20 q^{71} - 30 q^{72} + 70 q^{73} + 120 q^{74} - 52 q^{78} - 120 q^{79} + 8 q^{80} - 28 q^{81} + 30 q^{83} + 30 q^{84} - 40 q^{85} + 62 q^{86} + 48 q^{89} - 4 q^{91} - 144 q^{92} - 8 q^{93} - 20 q^{94} + 82 q^{97} - 10 q^{99}+O(q^{100}) \) 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9 - 10 * q^11 + 10 * q^13 - 60 * q^14 + 4 * q^15 + 80 * q^16 - 74 * q^20 + 8 * q^22 + 30 * q^24 + 38 * q^26 - 28 * q^27 - 20 * q^29 - 8 * q^31 + 20 * q^33 - 48 * q^34 + 20 * q^35 + 12 * q^37 - 10 * q^39 + 40 * q^40 - 110 * q^41 + 20 * q^42 - 36 * q^44 + 4 * q^45 - 20 * q^46 - 30 * q^47 - 20 * q^48 + 90 * q^50 - 10 * q^52 + 52 * q^53 - 64 * q^55 + 30 * q^57 + 24 * q^58 - 36 * q^59 - 74 * q^60 - 60 * q^61 + 48 * q^66 + 60 * q^67 + 60 * q^68 + 116 * q^70 + 20 * q^71 - 30 * q^72 + 70 * q^73 + 120 * q^74 - 52 * q^78 - 120 * q^79 + 8 * q^80 - 28 * q^81 + 30 * q^83 + 30 * q^84 - 40 * q^85 + 62 * q^86 + 48 * q^89 - 4 * q^91 - 144 * q^92 - 8 * q^93 - 20 * q^94 + 82 * q^97 - 10 * q^99

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