LMFDB - Embedded newform 538.2.e.a.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(9,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(134))

chi = DirichletCharacter(H, H._module([109]))

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

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

chi := DirichletCharacter("538.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.e (of order $134$, degree $66$, 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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$1452$
Relative dimension:	$22$ over $\Q(\zeta_{134})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{134}]$

Embedding invariants

Embedding label			9.4
Character	$\chi$	$=$	538.9
Dual form			538.2.e.a.299.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.833094 + 0.553131i) q^{2} +(-0.552092 + 0.973747i) q^{3} +(0.388092 - 0.921621i) q^{4} +(1.05205 + 0.734610i) q^{5} +(-0.0786651 - 1.11660i) q^{6} +(0.586003 + 4.13834i) q^{7} +(0.186460 + 0.982463i) q^{8} +(0.897045 + 1.49912i) q^{9} +(-1.28279 - 0.0300801i) q^{10} +(1.39377 + 0.402802i) q^{11} +(0.683163 + 0.886723i) q^{12} +(0.148764 - 6.34414i) q^{13} +(-2.77724 - 3.12349i) q^{14} +(-1.29615 + 0.618854i) q^{15} +(-0.698769 - 0.715347i) q^{16} +(0.426614 + 1.47616i) q^{17} +(-1.57653 - 0.752724i) q^{18} +(1.25368 + 3.68139i) q^{19} +(1.08532 - 0.684491i) q^{20} +(-4.35322 - 1.71412i) q^{21} +(-1.38394 + 0.435365i) q^{22} +(1.42313 + 0.806881i) q^{23} +(-1.05961 - 0.360845i) q^{24} +(-1.15519 - 3.14831i) q^{25} +(3.38521 + 5.36755i) q^{26} +(-5.31220 + 0.124566i) q^{27} +(4.04140 + 1.06598i) q^{28} +(1.94424 + 0.713388i) q^{29} +(0.737508 - 1.23250i) q^{30} +(-3.13483 + 4.97056i) q^{31} +(0.977821 + 0.209440i) q^{32} +(-1.16172 + 1.13479i) q^{33} +(-1.17192 - 0.993808i) q^{34} +(-2.42356 + 4.78420i) q^{35} +(1.72975 - 0.244939i) q^{36} +(-0.983121 + 5.93663i) q^{37} +(-3.08072 - 2.37350i) q^{38} +(6.09545 + 3.64741i) q^{39} +(-0.525562 + 1.17057i) q^{40} +(-4.34947 + 6.55092i) q^{41} +(4.57478 - 0.979875i) q^{42} +(2.17314 - 5.92261i) q^{43} +(0.912141 - 1.12820i) q^{44} +(-0.157535 + 2.23612i) q^{45} +(-1.63191 + 0.114969i) q^{46} +(2.67818 + 0.251895i) q^{47} +(1.08235 - 0.285487i) q^{48} +(-10.0576 + 2.90668i) q^{49} +(2.70381 + 1.98387i) q^{50} +(-1.67294 - 0.399563i) q^{51} +(-5.78915 - 2.59921i) q^{52} +(-2.14719 - 10.0247i) q^{53} +(4.35666 - 3.04212i) q^{54} +(1.17041 + 1.44764i) q^{55} +(-3.95649 + 1.34736i) q^{56} +(-4.27689 - 0.811704i) q^{57} +(-2.01434 + 0.481103i) q^{58} +(-7.63427 - 3.21477i) q^{59} +(0.0673231 + 1.43473i) q^{60} +(-7.16796 + 6.68074i) q^{61} +(-0.137761 - 5.87492i) q^{62} +(-5.67819 + 4.59076i) q^{63} +(-0.930465 + 0.366380i) q^{64} +(4.81697 - 6.56504i) q^{65} +(0.340129 - 1.58797i) q^{66} +(-2.99819 - 7.11996i) q^{67} +(1.52603 + 0.179710i) q^{68} +(-1.57140 + 0.940294i) q^{69} +(-0.627236 - 5.32624i) q^{70} +(10.1313 + 9.00822i) q^{71} +(-1.30556 + 1.16084i) q^{72} +(0.968093 - 8.22065i) q^{73} +(-2.46470 - 5.48957i) q^{74} +(3.70342 + 0.613296i) q^{75} +(3.87939 + 0.273304i) q^{76} +(-0.850178 + 6.00393i) q^{77} +(-7.09558 + 0.332952i) q^{78} +(-1.00848 - 3.20576i) q^{79} +(-0.209636 - 1.26590i) q^{80} +(0.334154 - 0.622961i) q^{81} -7.86336i q^{82} +(10.2346 + 5.48982i) q^{83} +(-3.26922 + 3.34678i) q^{84} +(-0.635586 + 1.86638i) q^{85} +(1.46555 + 6.13613i) q^{86} +(-1.76806 + 1.49935i) q^{87} +(-0.135856 + 1.44443i) q^{88} +(16.6410 + 8.42993i) q^{89} +(-1.10563 - 1.95004i) q^{90} +(26.3413 - 3.10205i) q^{91} +(1.29594 - 0.998440i) q^{92} +(-3.10935 - 5.79674i) q^{93} +(-2.37050 + 1.27153i) q^{94} +(-1.38546 + 4.79395i) q^{95} +(-0.743789 + 0.836521i) q^{96} +(-6.11663 - 5.70087i) q^{97} +(6.77118 - 7.98473i) q^{98} +(0.646425 + 2.45076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38}+ \cdots + 18 q^{99}+O(q^{100}) $ 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{109}{134}\right)$

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 $

$2$	−0.833094	+	0.553131i	−0.589087	+	0.391123i
$2$	−0.833094	+	0.553131i	−0.589087	+	0.391123i
$3$	−0.552092	+	0.973747i	−0.318751	+	0.562193i	−0.982614	−	0.185661i	$-0.940557\pi$
$3$	−0.552092	+	0.973747i	−0.318751	+	0.562193i	0.663863	+	0.747854i	$0.268916\pi$
$4$	0.388092	−	0.921621i	0.194046	−	0.460810i
$5$	1.05205	+	0.734610i	0.470489	+	0.328528i	0.783682	−	0.621162i	$-0.213339\pi$
$5$	1.05205	+	0.734610i	0.470489	+	0.328528i	−0.313193	+	0.949689i	$0.601399\pi$
$6$	−0.0786651	−	1.11660i	−0.0321149	−	0.455851i
$7$	0.586003	+	4.13834i	0.221488	+	1.56414i	0.717956	+	0.696089i	$0.245078\pi$
$7$	0.586003	+	4.13834i	0.221488	+	1.56414i	−0.496467	+	0.868055i	$0.665370\pi$
$8$	0.186460	+	0.982463i	0.0659236	+	0.347353i
$9$	0.897045	+	1.49912i	0.299015	+	0.499706i
$10$	−1.28279	−	0.0300801i	−0.405653	−	0.00951217i
$11$	1.39377	+	0.402802i	0.420237	+	0.121449i	0.481036	−	0.876701i	$-0.340260\pi$
$11$	1.39377	+	0.402802i	0.420237	+	0.121449i	−0.0607993	+	0.998150i	$0.519365\pi$
$12$	0.683163	+	0.886723i	0.197212	+	0.255975i
$13$	0.148764	−	6.34414i	0.0412596	−	1.75955i	−0.454185	−	0.890907i	$-0.650069\pi$
$13$	0.148764	−	6.34414i	0.0412596	−	1.75955i	0.495445	−	0.868640i	$-0.335005\pi$
$14$	−2.77724	−	3.12349i	−0.742248	−	0.834787i
$15$	−1.29615	+	0.618854i	−0.334665	+	0.159787i
$16$	−0.698769	−	0.715347i	−0.174692	−	0.178837i
$17$	0.426614	+	1.47616i	0.103469	+	0.358022i	0.995594	−	0.0937665i	$-0.0298907\pi$
$17$	0.426614	+	1.47616i	0.103469	+	0.358022i	−0.892125	+	0.451788i	$0.850786\pi$
$18$	−1.57653	−	0.752724i	−0.371592	−	0.177419i
$19$	1.25368	+	3.68139i	0.287613	+	0.844569i	0.991012	+	0.133774i	$0.0427095\pi$
$19$	1.25368	+	3.68139i	0.287613	+	0.844569i	−0.703399	+	0.710795i	$0.748335\pi$
$20$	1.08532	−	0.684491i	0.242685	−	0.153057i
$21$	−4.35322	−	1.71412i	−0.949951	−	0.374053i
$22$	−1.38394	+	0.435365i	−0.295058	+	0.0928201i
$23$	1.42313	+	0.806881i	0.296743	+	0.168246i	0.634361	−	0.773037i	$-0.281263\pi$
$23$	1.42313	+	0.806881i	0.296743	+	0.168246i	−0.337619	+	0.941283i	$0.609621\pi$
$24$	−1.05961	−	0.360845i	−0.216293	−	0.0736572i
$25$	−1.15519	−	3.14831i	−0.231037	−	0.629661i
$26$	3.38521	+	5.36755i	0.663893	+	1.05266i
$27$	−5.31220	+	0.124566i	−1.02233	+	0.0239727i
$28$	4.04140	+	1.06598i	0.763753	+	0.201452i
$29$	1.94424	+	0.713388i	0.361037	+	0.132473i	0.518557	−	0.855043i	$-0.326469\pi$
$29$	1.94424	+	0.713388i	0.361037	+	0.132473i	−0.157520	+	0.987516i	$0.550350\pi$
$30$	0.737508	−	1.23250i	0.134650	−	0.225024i
$31$	−3.13483	+	4.97056i	−0.563033	+	0.892739i	−0.999977	−	0.00674940i	$-0.997852\pi$
$31$	−3.13483	+	4.97056i	−0.563033	+	0.892739i	0.436945	+	0.899488i	$0.356061\pi$
$32$	0.977821	+	0.209440i	0.172856	+	0.0370242i
$33$	−1.16172	+	1.13479i	−0.202229	+	0.197542i
$34$	−1.17192	−	0.993808i	−0.200983	−	0.170437i
$35$	−2.42356	+	4.78420i	−0.409657	+	0.808678i
$36$	1.72975	−	0.244939i	0.288292	−	0.0408232i
$37$	−0.983121	+	5.93663i	−0.161624	+	0.975976i	0.776612	+	0.629979i	$0.216937\pi$
$37$	−0.983121	+	5.93663i	−0.161624	+	0.975976i	−0.938236	+	0.345997i	$0.887541\pi$
$38$	−3.08072	−	2.37350i	−0.499759	−	0.385032i
$39$	6.09545	+	3.64741i	0.976054	+	0.584053i
$40$	−0.525562	+	1.17057i	−0.0830987	+	0.185083i
$41$	−4.34947	+	6.55092i	−0.679273	+	1.02308i	0.317913	+	0.948120i	$0.397018\pi$
$41$	−4.34947	+	6.55092i	−0.679273	+	1.02308i	−0.997186	+	0.0749624i	$0.976116\pi$
$42$	4.57478	−	0.979875i	0.705904	−	0.151198i
$43$	2.17314	−	5.92261i	0.331401	−	0.903190i	−0.657345	−	0.753590i	$-0.728321\pi$
$43$	2.17314	−	5.92261i	0.331401	−	0.903190i	0.988747	−	0.149600i	$-0.0477987\pi$
$44$	0.912141	−	1.12820i	0.137510	−	0.170083i
$45$	−0.157535	+	2.23612i	−0.0234840	+	0.333341i
$46$	−1.63191	+	0.114969i	−0.240612	+	0.0169512i
$47$	2.67818	+	0.251895i	0.390652	+	0.0367427i	0.287148	−	0.957886i	$-0.407293\pi$
$47$	2.67818	+	0.251895i	0.390652	+	0.0367427i	0.103504	+	0.994629i	$0.466994\pi$
$48$	1.08235	−	0.285487i	0.156224	−	0.0412065i
$49$	−10.0576	+	2.90668i	−1.43680	+	0.415240i
$50$	2.70381	+	1.98387i	0.382376	+	0.280561i
$51$	−1.67294	−	0.399563i	−0.234258	−	0.0559501i
$52$	−5.78915	−	2.59921i	−0.802811	−	0.360446i
$53$	−2.14719	−	10.0247i	−0.294939	−	1.37699i	−0.841809	−	0.539776i	$-0.818509\pi$
$53$	−2.14719	−	10.0247i	−0.294939	−	1.37699i	0.546869	−	0.837218i	$-0.315819\pi$
$54$	4.35666	−	3.04212i	0.592867	−	0.413980i
$55$	1.17041	+	1.44764i	0.157817	+	0.195200i
$56$	−3.95649	+	1.34736i	−0.528709	+	0.180049i
$57$	−4.27689	−	0.811704i	−0.566488	−	0.107513i
$58$	−2.01434	+	0.481103i	−0.264495	+	0.0631719i
$59$	−7.63427	−	3.21477i	−0.993898	−	0.418528i	−0.170110	−	0.985425i	$-0.554412\pi$
$59$	−7.63427	−	3.21477i	−0.993898	−	0.418528i	−0.823788	+	0.566898i	$0.808144\pi$
$60$	0.0673231	+	1.43473i	0.00869137	+	0.185223i
$61$	−7.16796	+	6.68074i	−0.917763	+	0.855381i	−0.989864	−	0.142016i	$-0.954642\pi$
$61$	−7.16796	+	6.68074i	−0.917763	+	0.855381i	0.0721010	+	0.997397i	$0.477030\pi$
$62$	−0.137761	−	5.87492i	−0.0174957	−	0.746115i
$63$	−5.67819	+	4.59076i	−0.715384	+	0.578382i
$64$	−0.930465	+	0.366380i	−0.116308	+	0.0457975i
$65$	4.81697	−	6.56504i	0.597472	−	0.814293i
$66$	0.340129	−	1.58797i	0.0418670	−	0.195466i
$67$	−2.99819	−	7.11996i	−0.366288	−	0.869842i	−0.995688	−	0.0927606i	$-0.970431\pi$
$67$	−2.99819	−	7.11996i	−0.366288	−	0.869842i	0.629401	−	0.777081i	$-0.283300\pi$
$68$	1.52603	+	0.179710i	0.185058	+	0.0217931i
$69$	−1.57140	+	0.940294i	−0.189174	+	0.113198i
$70$	−0.627236	−	5.32624i	−0.0749691	−	0.636607i
$71$	10.1313	+	9.00822i	1.20236	+	1.06908i	0.995885	+	0.0906276i	$0.0288873\pi$
$71$	10.1313	+	9.00822i	1.20236	+	1.06908i	0.206480	+	0.978451i	$0.433799\pi$
$72$	−1.30556	+	1.16084i	−0.153862	+	0.136806i
$73$	0.968093	−	8.22065i	0.113307	−	0.962154i	−0.812189	−	0.583395i	$-0.801724\pi$
$73$	0.968093	−	8.22065i	0.113307	−	0.962154i	0.925495	−	0.378759i	$-0.123649\pi$
$74$	−2.46470	−	5.48957i	−0.286516	−	0.638149i
$75$	3.70342	+	0.613296i	0.427635	+	0.0708173i
$76$	3.87939	+	0.273304i	0.444996	+	0.0313501i
$77$	−0.850178	+	6.00393i	−0.0968867	+	0.684211i
$78$	−7.09558	+	0.332952i	−0.803416	+	0.0376994i
$79$	−1.00848	−	3.20576i	−0.113463	−	0.360676i	0.879980	−	0.475011i	$-0.157556\pi$
$79$	−1.00848	−	3.20576i	−0.113463	−	0.360676i	−0.993442	+	0.114335i	$0.963526\pi$
$80$	−0.209636	−	1.26590i	−0.0234380	−	0.141532i
$81$	0.334154	−	0.622961i	0.0371282	−	0.0692178i
$82$		−	7.86336i		−	0.868363i
$83$	10.2346	+	5.48982i	1.12340	+	0.602586i	0.925919	−	0.377722i	$-0.123293\pi$
$83$	10.2346	+	5.48982i	1.12340	+	0.602586i	0.197477	+	0.980308i	$0.436725\pi$
$84$	−3.26922	+	3.34678i	−0.356701	+	0.365164i
$85$	−0.635586	+	1.86638i	−0.0689390	+	0.202438i
$86$	1.46555	+	6.13613i	0.158034	+	0.661676i
$87$	−1.76806	+	1.49935i	−0.189556	+	0.160747i
$88$	−0.135856	+	1.44443i	−0.0144823	+	0.153977i
$89$	16.6410	+	8.42993i	1.76394	+	0.893571i	0.949769	+	0.312951i	$0.101317\pi$
$89$	16.6410	+	8.42993i	1.76394	+	0.893571i	0.814174	+	0.580621i	$0.197190\pi$
$90$	−1.10563	−	1.95004i	−0.116543	−	0.205552i
$91$	26.3413	−	3.10205i	2.76132	−	0.325183i
$92$	1.29594	−	0.998440i	0.135111	−	0.104095i
$93$	−3.10935	−	5.79674i	−0.322425	−	0.601094i
$94$	−2.37050	+	1.27153i	−0.244499	+	0.131148i
$95$	−1.38546	+	4.79395i	−0.142145	+	0.491849i
$96$	−0.743789	+	0.836521i	−0.0759127	+	0.0853770i
$97$	−6.11663	−	5.70087i	−0.621050	−	0.578836i	0.306807	−	0.951772i	$-0.400739\pi$
$97$	−6.11663	−	5.70087i	−0.621050	−	0.578836i	−0.927857	+	0.372936i	$0.878351\pi$
$98$	6.77118	−	7.98473i	0.683993	−	0.806579i
$99$	0.646425	+	2.45076i	0.0649682	+	0.246310i
$100$	−3.34986	−	0.157188i	−0.334986	−	0.0157188i
$101$	−0.0749832	+	0.395088i	−0.00746111	+	0.0393128i	−0.985996	−	0.166766i	$-0.946667\pi$
$101$	−0.0749832	+	0.395088i	−0.00746111	+	0.0393128i	0.978535	+	0.206079i	$0.0660704\pi$
$102$	1.61473	−	0.592480i	0.159882	−	0.0586643i
$103$	11.8250	−	1.11220i	1.16516	−	0.109588i	0.506642	−	0.862157i	$-0.330887\pi$
$103$	11.8250	−	1.11220i	1.16516	−	0.109588i	0.658514	+	0.752568i	$0.271185\pi$
$104$	6.26062	−	1.03677i	0.613904	−	0.101664i
$105$	−3.32057	−	5.00126i	−0.324055	−	0.488073i
$106$	7.33377	+	7.16381i	0.712318	+	0.695811i
$107$	0.179301	+	1.90635i	0.0173337	+	0.184294i	0.999999	−	0.00109276i	$-0.000347837\pi$
$107$	0.179301	+	1.90635i	0.0173337	+	0.184294i	−0.982666	+	0.185386i	$0.940646\pi$
$108$	−1.94682	+	4.94418i	−0.187333	+	0.475754i
$109$	−4.81373	−	5.16479i	−0.461072	−	0.494697i	0.457909	−	0.888999i	$-0.348598\pi$
$109$	−4.81373	−	5.16479i	−0.461072	−	0.494697i	−0.918981	+	0.394302i	$0.870987\pi$
$110$	−1.77579	−	0.558635i	−0.169315	−	0.0532637i
$111$	−5.23800	−	4.23488i	−0.497169	−	0.401957i
$112$	2.55087	−	3.31094i	0.241034	−	0.312854i
$113$	13.6796	−	10.0372i	1.28687	−	0.944218i	0.286966	−	0.957941i	$-0.407353\pi$
$113$	13.6796	−	10.0372i	1.28687	−	0.944218i	0.999906	+	0.0137228i	$0.00436825\pi$
$114$	4.01203	−	1.68945i	0.375761	−	0.158232i
$115$	0.904453	+	1.89432i	0.0843406	+	0.176646i
$116$	1.41202	−	1.51500i	0.131103	−	0.140664i
$117$	9.64406	−	5.46796i	0.891594	−	0.505513i
$118$	8.13826	−	1.54455i	0.749188	−	0.142187i
$119$	−5.85886	+	2.63051i	−0.537080	+	0.241138i
$120$	−0.849681	−	1.15803i	−0.0775649	−	0.105713i
$121$	−7.52381	−	4.74512i	−0.683983	−	0.431374i
$122$	2.27626	−	9.53051i	0.206083	−	0.862852i
$123$	−3.97763	−	7.85200i	−0.358651	−	0.707991i
$124$	3.36437	+	4.81816i	0.302129	+	0.432684i
$125$	2.73375	−	10.3643i	0.244514	−	0.927012i
$126$	2.19117	−	6.96532i	0.195205	−	0.620520i
$127$	−2.90892	−	0.411914i	−0.258125	−	0.0365514i	0.00994613	−	0.999951i	$-0.496834\pi$
$127$	−2.90892	−	0.411914i	−0.258125	−	0.0365514i	−0.268071	+	0.963399i	$0.586386\pi$
$128$	0.572509	−	0.819898i	0.0506031	−	0.0724695i
$129$	4.56735	+	5.38592i	0.402133	+	0.474204i
$130$	−0.381665	+	8.13371i	−0.0334742	+	0.713374i
$131$	0.409368	−	0.857394i	0.0357666	−	0.0749109i	−0.883756	−	0.467948i	$-0.844993\pi$
$131$	0.409368	−	0.857394i	0.0357666	−	0.0749109i	0.919523	+	0.393037i	$0.128576\pi$
$132$	0.594998	+	1.51107i	0.0517879	+	0.131521i
$133$	−14.5002	+	7.34544i	−1.25732	+	0.636930i
$134$	6.43605	+	4.27320i	0.555990	+	0.369148i
$135$	−5.68018	−	3.77135i	−0.488872	−	0.324586i
$136$	−1.37073	+	0.694377i	−0.117539	+	0.0595423i
$137$	5.53950	+	14.0682i	0.473271	+	1.20193i	0.946993	+	0.321254i	$0.104104\pi$
$137$	5.53950	+	14.0682i	0.473271	+	1.20193i	−0.473722	+	0.880675i	$0.657090\pi$
$138$	0.789015	−	1.65254i	0.0671654	−	0.140674i
$139$	0.396444	−	8.44868i	0.0336260	−	0.716607i	−0.915615	−	0.402057i	$-0.868295\pi$
$139$	0.396444	−	8.44868i	0.0336260	−	0.716607i	0.949241	−	0.314551i	$-0.101854\pi$
$140$	3.46865	+	4.09031i	0.293155	+	0.345695i
$141$	−1.72388	+	2.46880i	−0.145177	+	0.207910i
$142$	−13.4231	−	1.90075i	−1.12644	−	0.159508i
$143$	2.76277	−	8.78234i	0.231035	−	0.734416i
$144$	0.445562	−	1.68924i	0.0371302	−	0.140770i
$145$	1.52137	+	2.17878i	0.126343	+	0.180938i
$146$	3.74059	+	7.38406i	0.309573	+	0.611109i
$147$	2.72237	−	11.3983i	0.224538	−	0.940120i
$148$	5.08978	+	3.21002i	0.418377	+	0.263862i
$149$	4.01839	+	5.47666i	0.329200	+	0.448665i	0.939014	−	0.343879i	$-0.111741\pi$
$149$	4.01839	+	5.47666i	0.329200	+	0.448665i	−0.609814	+	0.792544i	$0.708756\pi$
$150$	−3.42453	+	1.53755i	−0.279612	+	0.125540i
$151$	6.80659	−	1.29181i	0.553912	−	0.105126i	0.0980582	−	0.995181i	$-0.468737\pi$
$151$	6.80659	−	1.29181i	0.553912	−	0.105126i	0.455854	+	0.890055i	$0.349334\pi$
$152$	−3.38307	+	1.91812i	−0.274403	+	0.155580i
$153$	−1.83025	+	1.96373i	−0.147967	+	0.158758i
$154$	−2.61268	−	5.47210i	−0.210536	−	0.440954i
$155$	−6.94941	+	2.92638i	−0.558190	+	0.235052i
$156$	5.72712	−	4.20217i	0.458537	−	0.336443i
$157$	10.5202	−	13.6548i	0.839601	−	1.08977i	−0.155194	−	0.987884i	$-0.549600\pi$
$157$	10.5202	−	13.6548i	0.839601	−	1.08977i	0.994796	−	0.101891i	$-0.0324892\pi$
$158$	2.61336	+	2.11288i	0.207908	+	0.168092i
$159$	10.9469	+	3.44372i	0.868149	+	0.273105i
$160$	0.874856	+	0.938658i	0.0691634	+	0.0742074i
$161$	−2.50519	+	6.36222i	−0.197436	+	0.501413i
$162$	0.0661972	+	0.703816i	0.00520095	+	0.0552970i
$163$	2.40717	+	2.35139i	0.188544	+	0.184175i	0.786947	−	0.617020i	$-0.211660\pi$
$163$	2.40717	+	2.35139i	0.188544	+	0.184175i	−0.598403	+	0.801195i	$0.704198\pi$
$164$	4.34947	+	6.55092i	0.339637	+	0.511541i
$165$	−2.05581	+	0.340447i	−0.160045	+	0.0265038i
$166$	−11.5630	+	1.08755i	−0.897462	+	0.0844106i
$167$	4.93437	−	1.81053i	0.381833	−	0.140103i	−0.146352	−	0.989233i	$-0.546753\pi$
$167$	4.93437	−	1.81053i	0.381833	−	0.140103i	0.528185	+	0.849129i	$0.322873\pi$
$168$	0.872361	−	4.59649i	0.0673041	−	0.354627i
$169$	−27.2402	−	1.27822i	−2.09540	−	0.0983243i
$170$	−0.502852	−	1.90644i	−0.0385670	−	0.146217i
$171$	−4.39424	+	5.18178i	−0.336036	+	0.396261i
$172$	−4.61502	−	4.30133i	−0.351892	−	0.327973i
$173$	7.51508	−	8.45202i	0.571361	−	0.642595i	−0.389038	−	0.921222i	$-0.627193\pi$
$173$	7.51508	−	8.45202i	0.571361	−	0.642595i	0.960400	+	0.278627i	$0.0898792\pi$
$174$	0.643627	−	2.22707i	0.0487932	−	0.168833i
$175$	12.3518	−	6.62547i	0.933709	−	0.500838i
$176$	−0.685780	−	1.27849i	−0.0516926	−	0.0963701i
$177$	7.34520	−	5.65900i	0.552099	−	0.425357i
$178$	−18.5264	+	2.18173i	−1.38861	+	0.163528i
$179$	2.25018	+	3.96873i	0.168186	+	0.296637i	0.941262	−	0.337677i	$-0.109641\pi$
$179$	2.25018	+	3.96873i	0.168186	+	0.296637i	−0.773076	+	0.634314i	$0.781283\pi$
$180$	1.99972	+	1.01301i	0.149050	+	0.0755051i
$181$	1.50730	−	16.0258i	0.112037	−	1.19119i	−0.741790	−	0.670632i	$-0.766023\pi$
$181$	1.50730	−	16.0258i	0.112037	−	1.19119i	0.853827	−	0.520557i	$-0.174276\pi$
$182$	−20.2290	+	17.1545i	−1.49947	+	1.27158i
$183$	−2.54798	−	10.6682i	−0.188352	−	0.788614i
$184$	−0.527374	+	1.54862i	−0.0388785	+	0.114166i
$185$	−5.39539	+	5.52339i	−0.396677	+	0.406088i
$186$	5.79674	+	3.10935i	0.425038	+	0.227989i
$187$			2.22927i			0.163020i
$188$	1.27153	−	2.37050i	0.0927359	−	0.172887i
$189$	−3.62846	−	21.9107i	−0.263932	−	1.59377i
$190$	−1.49746	−	4.76016i	−0.108637	−	0.345338i
$191$	−2.93606	+	0.137771i	−0.212446	+	0.00996878i	−0.152829	−	0.988253i	$-0.548839\pi$
$191$	−2.93606	+	0.137771i	−0.212446	+	0.00996878i	−0.0596165	+	0.998221i	$0.518988\pi$
$192$	0.156941	−	1.10831i	0.0113263	−	0.0799856i
$193$	−7.60282	−	0.535621i	−0.547263	−	0.0385549i	−0.206051	−	0.978541i	$-0.566061\pi$
$193$	−7.60282	−	0.535621i	−0.547263	−	0.0385549i	−0.341212	+	0.939986i	$0.610837\pi$
$194$	8.24906	+	1.36606i	0.592248	+	0.0980777i
$195$	3.73327	+	8.31502i	0.267345	+	0.595451i
$196$	−1.22443	+	10.3974i	−0.0874594	+	0.742670i
$197$	4.79270	−	4.26142i	0.341466	−	0.303613i	−0.476165	−	0.879356i	$-0.657974\pi$
$197$	4.79270	−	4.26142i	0.341466	−	0.303613i	0.817631	+	0.575743i	$0.195287\pi$
$198$	−1.89412	−	1.68415i	−0.134609	−	0.119688i
$199$	1.41839	+	12.0444i	0.100547	+	0.853807i	0.946976	+	0.321305i	$0.104121\pi$
$199$	1.41839	+	12.0444i	0.100547	+	0.853807i	−0.846429	+	0.532502i	$0.821252\pi$
$200$	2.87770	−	1.72196i	0.203484	−	0.121761i
$201$	8.58832	+	1.01139i	0.605773	+	0.0713380i
$202$	−0.156068	−	0.370621i	−0.0109809	−	0.0260768i
$203$	−1.81291	+	8.46398i	−0.127241	+	0.594055i
$204$	−1.01750	+	1.38675i	−0.0712392	+	0.0970917i
$205$	−9.38821	+	3.69670i	−0.655701	+	0.258189i
$206$	−9.23618	+	7.46737i	−0.643515	+	0.520276i
$207$	0.0669996	+	2.85725i	0.00465679	+	0.198592i
$208$	−4.64221	+	4.32667i	−0.321879	+	0.300001i
$209$	0.264462	+	5.63599i	0.0182932	+	0.389850i
$210$	5.53270	+	2.32980i	0.381793	+	0.160772i
$211$	11.5943	−	2.76917i	0.798184	−	0.190638i	0.187243	−	0.982314i	$-0.440045\pi$
$211$	11.5943	−	2.76917i	0.798184	−	0.190638i	0.610941	+	0.791676i	$0.290791\pi$
$212$	−10.0722	−	1.91160i	−0.691765	−	0.131289i
$213$	−14.3651	+	4.89196i	−0.984283	+	0.335192i
$214$	−1.20383	−	1.48899i	−0.0822925	−	0.101785i
$215$	6.63705	−	4.63444i	0.452643	−	0.316066i
$216$	−1.11289	−	5.19581i	−0.0757229	−	0.353530i
$217$	−22.4069	−	10.0602i	−1.52108	−	0.682933i
$218$	6.86710	+	1.64013i	0.465099	+	0.111084i
$219$	7.47036	+	5.48123i	0.504800	+	0.370388i
$220$	1.78840	−	0.516852i	0.120574	−	0.0348461i
$221$	9.42843	−	2.48690i	0.634225	−	0.167287i
$222$	6.70619	+	0.630749i	0.450090	+	0.0423331i
$223$	−28.1523	+	1.98334i	−1.88522	+	0.132814i	−0.965605	−	0.260013i	$-0.916273\pi$
$223$	−28.1523	+	1.98334i	−1.88522	+	0.132814i	−0.919612	+	0.392827i	$0.871497\pi$
$224$	−0.293728	+	4.16929i	−0.0196255	+	0.278572i
$225$	3.68343	−	4.55593i	0.245562	−	0.303729i
$226$	−5.84455	+	15.9285i	−0.388774	+	1.05955i
$227$	4.94502	−	1.05918i	0.328212	−	0.0703000i	−0.0423635	−	0.999102i	$-0.513489\pi$
$227$	4.94502	−	1.05918i	0.328212	−	0.0703000i	0.370576	+	0.928802i	$0.379160\pi$
$228$	−2.40791	+	3.62665i	−0.159468	+	0.240181i
$229$	−6.92697	+	15.4283i	−0.457747	+	1.01953i	0.527682	+	0.849442i	$0.323061\pi$
$229$	−6.92697	+	15.4283i	−0.457747	+	1.01953i	−0.985429	+	0.170086i	$0.945595\pi$
$230$	−1.80130	−	1.07787i	−0.118774	−	0.0710723i
$231$	−5.37693	−	4.14258i	−0.353776	−	0.272562i
$232$	−0.338353	+	2.04317i	−0.0222140	+	0.134140i
$233$	2.51287	−	0.355832i	0.164624	−	0.0233113i	−0.0574076	−	0.998351i	$-0.518283\pi$
$233$	2.51287	−	0.355832i	0.164624	−	0.0233113i	0.222031	+	0.975040i	$0.428731\pi$
$234$	−5.00991	+	9.88976i	−0.327508	+	0.646514i
$235$	2.63252	+	2.23242i	0.171727	+	0.145627i
$236$	−5.92560	+	5.78828i	−0.385724	+	0.376785i
$237$	3.67837	+	0.787873i	0.238936	+	0.0511779i
$238$	3.42596	−	5.43218i	0.222072	−	0.352116i
$239$	−6.61122	+	11.0485i	−0.427644	+	0.714668i	−0.993987	−	0.109502i	$-0.965074\pi$
$239$	−6.61122	+	11.0485i	−0.427644	+	0.714668i	0.566342	+	0.824170i	$0.308358\pi$
$240$	1.34841	+	0.494761i	0.0870392	+	0.0319367i
$241$	26.6510	+	7.02963i	1.71674	+	0.452818i	0.975785	−	0.218732i	$-0.0701920\pi$
$241$	26.6510	+	7.02963i	1.71674	+	0.452818i	0.740959	+	0.671550i	$0.234371\pi$
$242$	8.89271	−	0.208525i	0.571645	−	0.0134045i
$243$	−8.08158	−	12.8141i	−0.518434	−	0.822024i
$244$	3.37528	+	9.19888i	0.216080	+	0.588898i
$245$	−12.7164	−	4.33048i	−0.812419	−	0.276664i
$246$	7.65693	+	4.34130i	0.488188	+	0.276791i
$247$	23.5417	−	7.40583i	1.49793	−	0.471222i
$248$	−5.46791	−	2.15304i	−0.347213	−	0.136718i
$249$	−10.9961	+	6.93505i	−0.696853	+	0.439491i
$250$	3.45535	+	10.1466i	0.218536	+	0.641725i
$251$	22.9927	+	10.9780i	1.45129	+	0.692925i	0.981783	−	0.190005i	$-0.0608504\pi$
$251$	22.9927	+	10.9780i	1.45129	+	0.692925i	0.469505	+	0.882930i	$0.344432\pi$
$252$	2.02728	+	7.01477i	0.127707	+	0.441889i
$253$	1.65850	+	1.69784i	0.104269	+	0.106743i
$254$	2.65125	−	1.26585i	0.166354	−	0.0794266i
$255$	−1.46648	−	1.64932i	−0.0918348	−	0.103284i
$256$	−0.0234426	+	0.999725i	−0.00146516	+	0.0624828i
$257$	−16.8736	−	21.9014i	−1.05255	−	1.36617i	−0.927417	−	0.374030i	$-0.877976\pi$
$257$	−16.8736	−	21.9014i	−1.05255	−	1.36617i	−0.125129	−	0.992140i	$-0.539935\pi$
$258$	−6.78415	−	1.96063i	−0.422363	−	0.122064i
$259$	−25.1439	−	0.589599i	−1.56237	−	0.0366359i
$260$	−4.18105	−	6.98726i	−0.259297	−	0.433331i
$261$	0.674621	+	3.55459i	0.0417580	+	0.220024i
$262$	0.133210	+	0.940724i	0.00822974	+	0.0581181i
$263$	0.261032	+	3.70519i	0.0160959	+	0.228472i	0.999013	+	0.0444221i	$0.0141447\pi$
$263$	0.261032	+	3.70519i	0.0160959	+	0.228472i	−0.982917	+	0.184050i	$0.941079\pi$
$264$	−1.33151	−	0.929749i	−0.0819486	−	0.0572221i
$265$	5.10528	−	12.1238i	0.313615	−	0.744756i
$266$	8.01702	−	14.1399i	0.491555	−	0.866975i
$267$	−17.3960	+	11.5500i	−1.06462	+	0.706851i
$268$	−7.72548			−0.471909
$269$	8.95773	+	13.7390i	0.546162	+	0.837679i
$269$	8.95773	+	13.7390i	0.546162	+	0.837679i
$270$	6.81818			0.414941
$271$	8.05050	−	5.34511i	0.489033	−	0.324692i	−0.284254	−	0.958749i	$-0.591746\pi$
$271$	8.05050	−	5.34511i	0.489033	−	0.324692i	0.773287	+	0.634057i	$0.218611\pi$
$272$	0.757863	−	1.33667i	0.0459522	−	0.0810477i
$273$	−11.5222	+	27.3624i	−0.697358	+	1.65605i
$274$	−12.3965	−	8.65608i	−0.748899	−	0.522933i
$275$	−0.341918	−	4.85332i	−0.0206185	−	0.292666i
$276$	0.256749	+	1.81315i	0.0154545	+	0.109139i
$277$	0.685705	+	3.61300i	0.0412000	+	0.217084i	0.997048	−	0.0767766i	$-0.0244628\pi$
$277$	0.685705	+	3.61300i	0.0412000	+	0.217084i	−0.955848	+	0.293861i	$0.905060\pi$
$278$	4.34295	+	7.25783i	0.260473	+	0.435296i
$279$	−10.2635	−	0.240670i	−0.614462	−	0.0144085i
$280$	−5.15220	−	1.48900i	−0.307903	−	0.0889845i
$281$	−7.83075	−	10.1641i	−0.467144	−	0.606337i	0.498282	−	0.867015i	$-0.333964\pi$
$281$	−7.83075	−	10.1641i	−0.467144	−	0.606337i	−0.965426	+	0.260678i	$0.916054\pi$
$282$	0.0705880	−	3.01027i	0.00420345	−	0.179259i
$283$	5.25291	+	5.90782i	0.312253	+	0.351183i	0.882519	−	0.470277i	$-0.155846\pi$
$283$	5.25291	+	5.90782i	0.312253	+	0.351183i	−0.570265	+	0.821461i	$0.693160\pi$
$284$	12.2340	−	5.84120i	0.725956	−	0.346612i
$285$	−3.90319	−	3.99579i	−0.231205	−	0.236690i
$286$	2.55613	+	8.84469i	0.151147	+	0.522998i
$287$	−29.6587	−	14.1607i	−1.75070	−	0.835881i
$288$	0.563174	+	1.65375i	0.0331853	+	0.0974480i
$289$	12.3821	−	7.80914i	0.728358	−	0.459361i
$290$	−2.47260	−	0.973609i	−0.145196	−	0.0571723i
$291$	8.92816	−	2.80865i	0.523378	−	0.164646i
$292$	−7.20061	−	4.08258i	−0.421384	−	0.238915i
$293$	9.24421	+	3.14806i	0.540053	+	0.183912i	0.578997	−	0.815330i	$-0.303444\pi$
$293$	9.24421	+	3.14806i	0.540053	+	0.183912i	−0.0389444	+	0.999241i	$0.512400\pi$
$294$	4.03679	+	11.0017i	0.235430	+	0.641634i
$295$	−5.67000	−	8.99030i	−0.330120	−	0.523435i
$296$	−6.01583	+	0.141065i	−0.349663	+	0.00819925i
$297$	−7.45416	−	1.96615i	−0.432534	−	0.114088i
$298$	−6.37701	−	2.33987i	−0.369410	−	0.135545i
$299$	5.33067	−	8.90848i	0.308281	−	0.515191i
$300$	2.00250	−	3.17514i	0.115614	−	0.183317i
$301$	25.7832	+	5.52253i	1.48612	+	0.318313i
$302$	−4.95599	+	4.84114i	−0.285185	+	0.278576i
$303$	−0.343319	−	0.291140i	−0.0197231	−	0.0167256i
$304$	1.75744	−	3.46926i	0.100796	−	0.198975i
$305$	−12.4488	+	1.76279i	−0.712814	+	0.100937i
$306$	0.438571	−	2.64834i	0.0250715	−	0.151395i
$307$	18.7268	+	14.4278i	1.06880	+	0.823440i	0.984916	−	0.173036i	$-0.0553577\pi$
$307$	18.7268	+	14.4278i	1.06880	+	0.823440i	0.0838820	+	0.996476i	$0.473268\pi$
$308$	5.20340	+	3.11362i	0.296491	+	0.177415i
$309$	−5.44551	+	12.1286i	−0.309784	+	0.689974i
$310$	4.17084	−	6.28188i	0.236888	−	0.356787i
$311$	−23.9463	+	5.12908i	−1.35787	+	0.290843i	−0.829659	−	0.558270i	$-0.811465\pi$
$311$	−23.9463	+	5.12908i	−1.35787	+	0.290843i	−0.528211	+	0.849113i	$0.677137\pi$
$312$	−2.44688	+	6.66865i	−0.138527	+	0.377538i
$313$	−16.8312	+	20.8181i	−0.951357	+	1.17671i	0.0328100	+	0.999462i	$0.489554\pi$
$313$	−16.8312	+	20.8181i	−0.951357	+	1.17671i	−0.984167	+	0.177245i	$0.943281\pi$
$314$	−1.21138	+	17.1948i	−0.0683621	+	0.970359i
$315$	−9.34613	+	0.658438i	−0.526595	+	0.0370988i
$316$	−3.34588	−	0.314696i	−0.188220	−	0.0177030i
$317$	13.3285	−	3.51561i	0.748605	−	0.197456i	0.139144	−	0.990272i	$-0.455565\pi$
$317$	13.3285	−	3.51561i	0.748605	−	0.197456i	0.609461	+	0.792816i	$0.291386\pi$
$318$	−11.0247	+	3.18615i	−0.618232	+	0.178670i
$319$	2.42247	+	1.77744i	0.135632	+	0.0995177i
$320$	−1.24804	−	0.298081i	−0.0697674	−	0.0166632i
$321$	−1.95529	−	0.877886i	−0.109134	−	0.0489988i
$322$	−1.43208	−	6.68602i	−0.0798069	−	0.372597i
$323$	−4.89949	+	3.42116i	−0.272615	+	0.190358i
$324$	−0.444451	−	0.549729i	−0.0246917	−	0.0305405i
$325$	−20.1451	+	6.86031i	−1.11745	+	0.380541i
$326$	−3.30603	−	0.627447i	−0.183104	−	0.0347510i
$327$	7.68683	−	1.83592i	0.425082	−	0.101526i
$328$	−7.24704	−	3.05171i	−0.400151	−	0.168502i
$329$	0.526993	+	11.2308i	0.0290540	+	0.619175i
$330$	1.52437	−	1.42076i	0.0839139	−	0.0782101i
$331$	−0.362344	−	15.4524i	−0.0199162	−	0.849342i	−0.915002	−	0.403449i	$-0.867811\pi$
$331$	−0.362344	−	15.4524i	−0.0199162	−	0.849342i	0.895086	−	0.445894i	$-0.147114\pi$
$332$	9.03150	−	7.30189i	0.495668	−	0.400743i
$333$	−9.78162	+	3.85161i	−0.536029	+	0.211067i
$334$	−3.10933	+	4.23770i	−0.170135	+	0.231877i
$335$	2.07616	−	9.69302i	0.113433	−	0.529586i
$336$	1.81570	+	4.31184i	0.0990548	+	0.235230i
$337$	16.1383	+	1.90051i	0.879112	+	0.103527i	0.544432	−	0.838805i	$-0.316745\pi$
$337$	16.1383	+	1.90051i	0.879112	+	0.103527i	0.334679	+	0.942332i	$0.391372\pi$
$338$	23.4007	−	14.0025i	1.27283	−	0.761638i
$339$	2.22125	+	18.8620i	0.120642	+	1.02444i
$340$	1.47343	+	1.31010i	0.0799081	+	0.0710500i
$341$	−6.37138	+	5.66510i	−0.345030	+	0.306782i
$342$	0.794609	−	6.74750i	0.0429676	−	0.364863i
$343$	−5.93909	−	13.2280i	−0.320681	−	0.714243i
$344$	6.22395	+	1.03070i	0.335573	+	0.0555717i
$345$	−2.34393	−	0.165131i	−0.126193	−	0.00889034i
$346$	−1.58570	+	11.1982i	−0.0852477	+	0.602017i
$347$	15.7008	−	0.736743i	0.842865	−	0.0395504i	0.378936	−	0.925423i	$-0.376290\pi$
$347$	15.7008	−	0.736743i	0.842865	−	0.0395504i	0.463929	+	0.885873i	$0.346439\pi$
$348$	0.695658	+	2.21137i	0.0372912	+	0.118542i
$349$	1.71490	+	10.3555i	0.0917966	+	0.554319i	0.992730	+	0.120362i	$0.0384055\pi$
$349$	1.71490	+	10.3555i	0.0917966	+	0.554319i	−0.900933	+	0.433957i	$0.857117\pi$
$350$	−6.62547	+	12.3518i	−0.354146	+	0.660232i
$351$			33.7199i			1.79983i
$352$	1.27849	+	0.685780i	0.0681440	+	0.0365522i
$353$	−1.32237	+	1.35374i	−0.0703826	+	0.0720524i	−0.749631	−	0.661857i	$-0.769769\pi$
$353$	−1.32237	+	1.35374i	−0.0703826	+	0.0720524i	0.679248	+	0.733909i	$0.262306\pi$
$354$	−2.98907	+	8.77734i	−0.158867	+	0.466510i
$355$	4.04107	+	16.9196i	0.214478	+	0.898000i
$356$	14.2274	−	12.0651i	0.754053	−	0.639450i
$357$	0.673181	−	7.15733i	0.0356285	−	0.378806i
$358$	−4.06984	−	2.06168i	−0.215098	−	0.108963i
$359$	−15.2905	−	26.9685i	−0.807003	−	1.42334i	−0.903762	−	0.428036i	$-0.859206\pi$
$359$	−15.2905	−	26.9685i	−0.807003	−	1.42334i	0.0967583	−	0.995308i	$-0.469153\pi$
$360$	−2.22628	+	0.262174i	−0.117335	+	0.0138178i
$361$	3.07016	−	2.36536i	0.161587	−	0.124493i
$362$	7.60865	+	14.1848i	0.399902	+	0.745534i
$363$	8.77438	−	4.70655i	0.460536	−	0.247030i
$364$	7.36395	−	25.4806i	0.385976	−	1.33555i
$365$	7.05745	−	7.93733i	0.369404	−	0.415459i
$366$	8.02360	+	7.47822i	0.419400	+	0.390893i
$367$	−20.3538	+	24.0017i	−1.06246	+	1.25288i	−0.0961853	+	0.995363i	$0.530664\pi$
$367$	−20.3538	+	24.0017i	−1.06246	+	1.25288i	−0.966275	+	0.257513i	$0.917097\pi$
$368$	−0.417239	−	1.58185i	−0.0217501	−	0.0824598i
$369$	−13.7223	−	0.643902i	−0.714353	−	0.0335202i
$370$	1.43971	−	7.58587i	0.0748470	−	0.394371i
$371$	40.2272	−	14.7603i	2.08849	−	0.766316i
$372$	−6.54911	+	0.615975i	−0.339556	+	0.0319368i
$373$	26.4647	−	4.38261i	1.37029	−	0.226923i	0.567592	−	0.823310i	$-0.307875\pi$
$373$	26.4647	−	4.38261i	1.37029	−	0.226923i	0.802697	+	0.596387i	$0.203398\pi$
$374$	−1.23308	−	1.85719i	−0.0637609	−	0.0960331i
$375$	8.58294	+	8.38403i	0.443221	+	0.432950i
$376$	0.251895	+	2.67818i	0.0129905	+	0.138116i
$377$	4.81506	−	12.2284i	0.247988	−	0.629796i
$378$	15.1423	+	16.2466i	0.778838	+	0.835637i
$379$	0.803009	+	0.252613i	0.0412478	+	0.0129759i	0.320638	−	0.947202i	$-0.396103\pi$
$379$	0.803009	+	0.252613i	0.0412478	+	0.0129759i	−0.279391	+	0.960178i	$0.590132\pi$
$380$	3.88052	+	3.13736i	0.199066	+	0.160943i
$381$	2.00709	−	2.60514i	0.102826	−	0.133465i
$382$	2.36981	−	1.73880i	0.121250	−	0.0889649i
$383$	−28.5680	+	12.0299i	−1.45976	+	0.614699i	−0.966841	−	0.255379i	$-0.917800\pi$
$383$	−28.5680	+	12.0299i	−1.45976	+	0.614699i	−0.492915	+	0.870078i	$0.664068\pi$
$384$	0.482296	+	1.01014i	0.0246121	+	0.0515484i
$385$	−5.30497	+	5.69186i	−0.270366	+	0.290084i
$386$	6.63013	−	3.75913i	0.337465	−	0.191335i
$387$	10.8281	−	2.05505i	0.550424	−	0.104464i
$388$	−7.62786	+	3.42475i	−0.387246	+	0.173865i
$389$	−21.1878	−	28.8768i	−1.07426	−	1.46411i	−0.874974	−	0.484169i	$-0.839122\pi$
$389$	−21.1878	−	28.8768i	−1.07426	−	1.46411i	−0.199289	−	0.979941i	$-0.563863\pi$
$390$	−7.70946	−	4.86220i	−0.390384	−	0.246207i
$391$	−0.583960	+	2.44499i	−0.0295321	+	0.123649i
$392$	−4.73105	−	9.33927i	−0.238954	−	0.471704i
$393$	0.608877	+	0.871981i	0.0307138	+	0.0439856i
$394$	−1.63565	+	6.20115i	−0.0824029	+	0.312410i
$395$	1.29402	−	4.11344i	0.0651091	−	0.206970i
$396$	2.50954	+	0.355360i	0.126109	+	0.0178575i
$397$	−14.1854	+	20.3151i	−0.711944	+	1.01959i	0.286169	+	0.958179i	$0.407618\pi$
$397$	−14.1854	+	20.3151i	−0.711944	+	1.01959i	−0.998113	+	0.0614064i	$0.980441\pi$
$398$	−7.84381	−	9.24959i	−0.393174	−	0.463640i
$399$	0.852834	−	18.1749i	0.0426951	−	0.909881i
$400$	−1.44492	+	3.02630i	−0.0722461	+	0.151315i
$401$	−6.68354	−	16.9736i	−0.333760	−	0.847623i	−0.995221	−	0.0976439i	$-0.968869\pi$
$401$	−6.68354	−	16.9736i	−0.333760	−	0.847623i	0.661461	−	0.749979i	$-0.269937\pi$
$402$	−7.71431	+	3.90788i	−0.384755	+	0.194908i
$403$	31.0676	+	20.6272i	1.54759	+	1.02752i
$404$	0.335021	+	0.222437i	0.0166679	+	0.0110666i
$405$	0.809178	−	0.409910i	0.0402084	−	0.0203686i
$406$	−3.17137	−	8.05407i	−0.157393	−	0.399717i
$407$	−3.76153	+	7.87829i	−0.186452	+	0.390512i
$408$	0.0806199	−	1.71810i	0.00399128	−	0.0850587i
$409$	−19.1243	−	22.5518i	−0.945635	−	1.11511i	−0.993220	−	0.116246i	$-0.962914\pi$
$409$	−19.1243	−	22.5518i	−0.945635	−	1.11511i	0.0475858	−	0.998867i	$-0.484847\pi$
$410$	5.77650	−	8.27262i	0.285281	−	0.408555i
$411$	−16.7572	−	2.37288i	−0.826572	−	0.117045i
$412$	3.56417	−	11.3298i	0.175594	−	0.558181i
$413$	8.83010	−	33.4771i	0.434501	−	1.64730i
$414$	−1.63625	−	2.34330i	−0.0804172	−	0.115167i
$415$	6.73441	+	13.2940i	0.330579	+	0.652576i
$416$	1.47418	−	6.17228i	0.0722777	−	0.302621i
$417$	8.00800	+	5.05049i	0.392154	+	0.247323i
$418$	−3.33776	−	4.54903i	−0.163255	−	0.222500i
$419$	33.1513	−	14.8842i	1.61955	−	0.727143i	0.621146	−	0.783695i	$-0.286667\pi$
$419$	33.1513	−	14.8842i	1.61955	−	0.727143i	0.998400	+	0.0565517i	$0.0180106\pi$
$420$	−5.89795	+	1.11936i	−0.287790	+	0.0546193i
$421$	0.924712	−	0.524290i	0.0450677	−	0.0255523i	−0.470518	−	0.882391i	$-0.655933\pi$
$421$	0.924712	−	0.524290i	0.0450677	−	0.0255523i	0.515585	+	0.856838i	$0.327575\pi$
$422$	−8.12742	+	8.72015i	−0.395637	+	0.424490i
$423$	2.02482	+	4.24087i	0.0984503	+	0.206198i
$424$	9.44849	−	3.97873i	0.458859	−	0.193224i
$425$	4.15459	−	3.04835i	0.201527	−	0.147867i
$426$	9.26162	−	12.0213i	0.448727	−	0.582432i
$427$	−31.8476	−	25.7485i	−1.54121	−	1.24606i
$428$	1.82651	+	0.574590i	0.0882879	+	0.0277739i
$429$	7.02647	+	7.53890i	0.339241	+	0.363982i
$430$	−2.96584	+	7.53209i	−0.143025	+	0.363230i
$431$	−0.735173	−	7.81643i	−0.0354120	−	0.376504i	−0.995352	−	0.0962998i	$-0.969299\pi$
$431$	−0.735173	−	7.81643i	−0.0354120	−	0.376504i	0.959940	−	0.280204i	$-0.0904022\pi$
$432$	3.80111	+	3.71302i	0.182881	+	0.178643i
$433$	0.958031	+	1.44293i	0.0460401	+	0.0693429i	0.855392	−	0.517980i	$-0.173316\pi$
$433$	0.958031	+	1.44293i	0.0460401	+	0.0693429i	−0.809352	+	0.587323i	$0.800182\pi$
$434$	24.2317	−	4.01282i	1.16316	−	0.192622i
$435$	−2.96152	+	0.278545i	−0.141994	+	0.0133552i
$436$	−6.62815	+	2.43202i	−0.317431	+	0.116473i
$437$	−1.18630	+	6.25066i	−0.0567485	+	0.299009i
$438$	−9.25535	−	0.434297i	−0.442238	−	0.0207515i
$439$	−8.37877	−	31.7660i	−0.399897	−	1.51611i	−0.800205	−	0.599727i	$-0.795276\pi$
$439$	−8.37877	−	31.7660i	−0.399897	−	1.51611i	0.400308	−	0.916381i	$-0.368903\pi$
$440$	−1.20402	+	1.41981i	−0.0573994	+	0.0676867i
$441$	−13.3796	−	12.4702i	−0.637124	−	0.593817i
$442$	−6.47919	+	7.28698i	−0.308184	+	0.346606i
$443$	−3.10634	+	10.7485i	−0.147587	+	0.510677i	−0.999924	−	0.0123152i	$-0.996080\pi$
$443$	−3.10634	+	10.7485i	−0.147587	+	0.510677i	0.852337	+	0.522992i	$0.175184\pi$
$444$	−5.93578	+	3.18393i	−0.281700	+	0.151103i
$445$	11.3144	+	21.0933i	0.536353	+	0.999919i
$446$	22.3565	−	17.2242i	1.05861	−	0.815591i
$447$	−7.55140	+	0.889280i	−0.357169	+	0.0420615i
$448$	−2.06146	−	3.63588i	−0.0973948	−	0.171779i
$449$	−20.5589	−	10.4146i	−0.970234	−	0.491497i	−0.105879	−	0.994379i	$-0.533766\pi$
$449$	−20.5589	−	10.4146i	−0.970234	−	0.491497i	−0.864355	+	0.502882i	$0.832273\pi$
$450$	−0.548616	+	5.83294i	−0.0258620	+	0.274968i
$451$	−8.70088	+	7.37850i	−0.409709	+	0.347440i
$452$	−3.94151	−	16.5028i	−0.185393	−	0.776226i
$453$	−2.49997	+	7.34109i	−0.117459	+	0.344915i
$454$	−3.53380	+	3.61764i	−0.165849	+	0.169784i
$455$	29.9911	+	16.0871i	1.40600	+	0.754176i
$456$		−	4.35323i		−	0.203859i
$457$	7.90583	−	14.7388i	0.369819	−	0.689451i	−0.626096	−	0.779746i	$-0.715348\pi$
$457$	7.90583	−	14.7388i	0.369819	−	0.689451i	0.995915	+	0.0902953i	$0.0287811\pi$
$458$	−2.76303	−	16.6847i	−0.129108	−	0.779626i
$459$	−2.45014	−	7.78853i	−0.114363	−	0.363537i
$460$	2.09685	−	0.0983924i	0.0977663	−	0.00458757i
$461$	−3.91077	+	27.6177i	−0.182143	+	1.28629i	0.661730	+	0.749742i	$0.269823\pi$
$461$	−3.91077	+	27.6177i	−0.182143	+	1.28629i	−0.843873	+	0.536544i	$0.819730\pi$
$462$	6.77088	+	0.477011i	0.315010	+	0.0221926i
$463$	−2.24912	−	0.372461i	−0.104526	−	0.0173097i	0.110885	−	0.993833i	$-0.464631\pi$
$463$	−2.24912	−	0.372461i	−0.104526	−	0.0173097i	−0.215411	+	0.976524i	$0.569109\pi$
$464$	−0.848258	−	1.88930i	−0.0393794	−	0.0877087i
$465$	0.987164	−	8.38260i	0.0457786	−	0.388734i
$466$	−1.89664	+	1.68639i	−0.0878601	+	0.0781205i
$467$	−12.3612	−	10.9909i	−0.572006	−	0.508598i	0.327881	−	0.944719i	$-0.393665\pi$
$467$	−12.3612	−	10.9909i	−0.572006	−	0.508598i	−0.899888	+	0.436121i	$0.856352\pi$
$468$	−1.29660	−	11.0102i	−0.0599355	−	0.508948i
$469$	27.7078	−	16.5799i	1.27943	−	0.765587i
$470$	−3.42796	−	0.403688i	−0.158120	−	0.0186208i
$471$	7.48825	+	17.7827i	0.345040	+	0.819384i
$472$	1.73491	−	8.09982i	0.0798555	−	0.372824i
$473$	5.41450	−	7.37941i	0.248959	−	0.339305i
$474$	−3.50023	+	1.37825i	−0.160771	+	0.0633051i
$475$	10.1419	−	8.19965i	0.465343	−	0.376226i
$476$	0.150555	+	6.42052i	0.00690067	+	0.294284i
$477$	13.1020	−	12.2115i	0.599901	−	0.559125i
$478$	−0.603502	−	12.8613i	−0.0276035	−	0.588263i
$479$	24.1404	+	10.1655i	1.10300	+	0.464472i	0.862439	−	0.506161i	$-0.168936\pi$
$479$	24.1404	+	10.1655i	1.10300	+	0.464472i	0.240565	+	0.970633i	$0.422667\pi$
$480$	−1.39702	+	0.333662i	−0.0637648	+	0.0152295i
$481$	37.5165	+	7.12021i	1.71061	+	0.324653i
$482$	−26.0911	+	8.88518i	−1.18842	+	0.404709i
$483$	−4.81210	−	5.95195i	−0.218958	−	0.270823i
$484$	−7.29313	+	5.09256i	−0.331506	+	0.231480i
$485$	−2.24706	−	10.4909i	−0.102034	−	0.476368i
$486$	13.8206	+	6.20516i	0.626915	+	0.281472i
$487$	10.2650	+	2.45168i	0.465151	+	0.111096i	0.458142	−	0.888879i	$-0.348515\pi$
$487$	10.2650	+	2.45168i	0.465151	+	0.111096i	0.00700915	+	0.999975i	$0.497769\pi$
$488$	−7.90012	−	5.79656i	−0.357621	−	0.262398i
$489$	−3.61864	+	1.04580i	−0.163641	+	0.0472925i
$490$	12.9893	−	3.42612i	0.586795	−	0.154776i
$491$	1.29853	+	0.122133i	0.0586019	+	0.00551179i	0.122902	−	0.992419i	$-0.460780\pi$
$491$	1.29853	+	0.122133i	0.0586019	+	0.00551179i	−0.0643000	+	0.997931i	$0.520481\pi$
$492$	−8.78025	+	0.618572i	−0.395844	+	0.0278874i
$493$	−0.223635	+	3.17436i	−0.0100720	+	0.142966i
$494$	−15.5161	+	19.1914i	−0.698102	+	0.863463i
$495$	−1.12028	+	3.05318i	−0.0503529	+	0.137230i
$496$	5.74620	−	1.23078i	0.258012	−	0.0552638i
$497$	−31.3421	+	47.2056i	−1.40588	+	2.11746i
$498$	5.32483	−	11.8599i	0.238612	−	0.531453i
$499$	16.5105	+	9.87958i	0.739112	+	0.442271i	0.832972	−	0.553315i	$-0.186637\pi$
$499$	16.5105	+	9.87958i	0.739112	+	0.442271i	−0.0938606	+	0.995585i	$0.529921\pi$
$500$	−8.49102	−	6.54178i	−0.379730	−	0.292557i
$501$	−0.961225	+	5.80441i	−0.0429444	+	0.259322i
$502$	−25.2274	+	3.57229i	−1.12595	+	0.159439i
$503$	−9.15437	+	18.0711i	−0.408173	+	0.805749i	−1.00000		0.000315864i	$-0.999899\pi$
$503$	−9.15437	+	18.0711i	−0.408173	+	0.805749i	0.591827	+	0.806065i	$0.298407\pi$
$504$	−5.56901	−	4.72261i	−0.248063	−	0.210362i
$505$	−0.369122	+	0.360567i	−0.0164257	+	0.0160450i
$506$	−2.32082	−	0.497097i	−0.103173	−	0.0220987i
$507$	16.2838	−	25.8194i	0.723188	−	1.14668i
$508$	−1.50856	+	2.52106i	−0.0669314	+	0.111854i
$509$	0.126265	+	0.0463296i	0.00559660	+	0.00205352i	0.347264	−	0.937768i	$-0.387111\pi$
$509$	0.126265	+	0.0463296i	0.00559660	+	0.00205352i	−0.341667	+	0.939821i	$0.610992\pi$
$510$	2.13401	+	0.562877i	0.0944954	+	0.0249246i
$511$	34.5871	−	0.811034i	1.53004	−	0.0358780i
$512$	−0.533449	−	0.845832i	−0.0235753	−	0.0373808i
$513$	−7.11835	−	19.4001i	−0.314283	−	0.856536i
$514$	26.1716	+	8.91259i	1.15438	+	0.393118i
$515$	13.2575	+	7.51671i	0.584196	+	0.331226i
$516$	6.73633	−	2.11913i	0.296550	−	0.0932897i
$517$	3.63130	+	1.42986i	0.159704	+	0.0628851i
$518$	21.2734	−	13.4167i	0.934697	−	0.589495i
$519$	4.08111	+	11.9841i	0.179141	+	0.526043i
$520$	7.34807	+	3.50838i	0.322234	+	0.153853i
$521$	1.65190	+	5.71589i	0.0723713	+	0.250418i	0.988676	−	0.150063i	$-0.0479476\pi$
$521$	1.65190	+	5.71589i	0.0723713	+	0.250418i	−0.916305	+	0.400481i	$0.868843\pi$
$522$	−2.52818	−	2.58816i	−0.110655	−	0.113281i
$523$	17.3665	−	8.29174i	0.759385	−	0.362572i	−0.0111770	−	0.999938i	$-0.503558\pi$
$523$	17.3665	−	8.29174i	0.759385	−	0.362572i	0.770562	+	0.637365i	$0.219976\pi$
$524$	−0.631320	−	0.710029i	−0.0275794	−	0.0310178i
$525$	−0.367807	+	15.6854i	−0.0160524	+	0.684567i
$526$	−2.26692	−	2.94239i	−0.0988425	−	0.128294i
$527$	−8.67471	−	2.50701i	−0.377876	−	0.109207i
$528$	1.62354	+	0.0380705i	0.0706557	+	0.00165681i
$529$	−10.4357	−	17.4398i	−0.453725	−	0.758253i
$530$	2.45285	+	12.9241i	0.106545	+	0.561388i
$531$	−2.02896	−	14.3285i	−0.0880495	−	0.621803i
$532$	1.14231	+	16.2144i	0.0495253	+	0.702982i
$533$	40.9129	+	28.5682i	1.77213	+	1.23743i
$534$	8.10382	−	19.2445i	0.350687	−	0.832793i
$535$	−1.21179	+	2.13728i	−0.0523902	+	0.0924027i
$536$	6.43605	−	4.27320i	0.277995	−	0.184574i
$537$	−5.10685			−0.220377
$538$	−15.0621	−	6.49105i	−0.649372	−	0.279849i
$539$	−15.1888			−0.654229
$540$	−5.68018	+	3.77135i	−0.244436	+	0.162293i
$541$	2.24940	−	3.96735i	0.0967091	−	0.170570i	−0.817361	−	0.576126i	$-0.804564\pi$
$541$	2.24940	−	3.96735i	0.0967091	−	0.170570i	0.914070	+	0.405556i	$0.132922\pi$
$542$	−3.75028	+	8.90596i	−0.161088	+	0.382544i
$543$	14.7729	+	10.3155i	0.633967	+	0.442679i
$544$	0.107984	+	1.53277i	0.00462979	+	0.0657171i
$545$	−1.27016	−	8.96981i	−0.0544076	−	0.384225i
$546$	−5.53590	−	29.1688i	−0.236915	−	1.24831i
$547$	−14.9857	−	25.0437i	−0.640742	−	1.07079i	−0.990964	−	0.134125i	$-0.957178\pi$
$547$	−14.9857	−	25.0437i	−0.640742	−	1.07079i	0.350223	−	0.936666i	$-0.386106\pi$
$548$	15.1154	+	0.354441i	0.645697	+	0.0151410i
$549$	−16.4452	−	4.75270i	−0.701864	−	0.202840i
$550$	2.96937	+	3.85415i	0.126615	+	0.164341i
$551$	−0.188809	+	8.05188i	−0.00804352	+	0.343022i
$552$	−1.21681	−	1.36851i	−0.0517907	−	0.0582477i
$553$	12.6755	−	6.05200i	0.539019	−	0.257357i
$554$	−2.56972	−	2.63068i	−0.109177	−	0.111767i
$555$	−2.39963	−	8.30317i	−0.101859	−	0.352450i
$556$	−7.63262	−	3.64423i	−0.323695	−	0.154550i
$557$	11.4572	+	33.6439i	0.485459	+	1.42554i	0.865659	+	0.500634i	$0.166900\pi$
$557$	11.4572	+	33.6439i	0.485459	+	1.42554i	−0.380201	+	0.924904i	$0.624145\pi$
$558$	8.68362	−	5.47659i	0.367607	−	0.231842i
$559$	−37.2506	−	14.6678i	−1.57553	−	0.620381i
$560$	5.11587	−	1.60937i	0.216185	−	0.0680082i
$561$	−2.17074	−	1.23076i	−0.0916489	−	0.0519628i
$562$	12.1458	+	4.13618i	0.512340	+	0.174474i
$563$	−6.07615	−	16.5597i	−0.256079	−	0.697910i	−0.999574	−	0.0291688i	$-0.990714\pi$
$563$	−6.07615	−	16.5597i	−0.256079	−	0.697910i	0.743495	−	0.668741i	$-0.233167\pi$
$564$	1.60627	+	2.54689i	0.0676362	+	0.107243i
$565$	21.7650	−	0.510368i	0.915661	−	0.0214713i
$566$	−7.64397	−	2.01622i	−0.321300	−	0.0847479i
$567$	2.77384	+	1.01778i	0.116490	+	0.0427429i
$568$	−6.96115	+	11.6333i	−0.292083	+	0.488122i
$569$	14.2346	−	22.5703i	0.596746	−	0.946196i	−0.402776	−	0.915299i	$-0.631955\pi$
$569$	14.2346	−	22.5703i	0.596746	−	0.946196i	0.999523	−	0.0308970i	$-0.00983638\pi$
$570$	5.46193	+	1.16989i	0.228775	+	0.0490015i
$571$	−5.95380	+	5.81582i	−0.249159	+	0.243385i	−0.812671	−	0.582723i	$-0.801987\pi$
$571$	−5.95380	+	5.81582i	−0.249159	+	0.243385i	0.563512	+	0.826108i	$0.309450\pi$
$572$	−7.02177	−	5.95458i	−0.293595	−	0.248974i
$573$	1.48682	−	2.93504i	0.0621129	−	0.122613i
$574$	32.5412	−	4.60796i	1.35825	−	0.192332i
$575$	0.896330	−	5.41254i	0.0373795	−	0.225719i
$576$	−1.38392	−	1.06622i	−0.0576632	−	0.0444258i
$577$	16.3694	+	9.79516i	0.681468	+	0.407778i	0.811993	−	0.583667i	$-0.198383\pi$
$577$	16.3694	+	9.79516i	0.681468	+	0.407778i	−0.130525	+	0.991445i	$0.541666\pi$
$578$	−5.99597	+	13.3547i	−0.249400	+	0.555481i
$579$	4.71902	−	7.10751i	0.196116	−	0.295378i
$580$	2.59844	−	0.556561i	0.107894	−	0.0231100i
$581$	−16.7212	+	45.5714i	−0.693712	+	1.89062i
$582$	−5.88444	+	7.27831i	−0.243918	+	0.301696i
$583$	1.04527	−	14.8370i	0.0432906	−	0.614484i
$584$	8.25699	−	0.581708i	0.341677	−	0.0240713i
$585$	14.1628	+	1.33208i	0.585560	+	0.0550747i
$586$	−9.44259	+	2.49063i	−0.390070	+	0.102887i
$587$	−27.3137	+	7.89371i	−1.12736	+	0.325808i	−0.788503	−	0.615031i	$-0.789144\pi$
$587$	−27.3137	+	7.89371i	−1.12736	+	0.325808i	−0.338854	+	0.940839i	$0.610039\pi$
$588$	−9.44842	−	6.93260i	−0.389646	−	0.285896i
$589$	−22.2286	−	5.30907i	−0.915915	−	0.218756i
$590$	9.69646	+	4.35351i	0.399197	+	0.179231i
$591$	1.50353	+	7.01957i	0.0618469	+	0.288747i
$592$	4.93373	−	3.44506i	0.202775	−	0.141591i
$593$	24.4912	+	30.2925i	1.00573	+	1.24396i	0.969620	+	0.244615i	$0.0786617\pi$
$593$	24.4912	+	30.2925i	1.00573	+	1.24396i	0.0361126	+	0.999348i	$0.488502\pi$
$594$	7.29755	−	2.48514i	0.299422	−	0.101966i
$595$	−8.09618	−	1.53656i	−0.331911	−	0.0629929i
$596$	6.60690	−	1.57799i	0.270629	−	0.0646369i
$597$	−12.5113	−	5.26848i	−0.512054	−	0.215624i
$598$	0.486608	+	10.3702i	0.0198989	+	0.424068i
$599$	−17.4759	+	16.2880i	−0.714047	+	0.665512i	−0.952116	−	0.305736i	$-0.901097\pi$
$599$	−17.4759	+	16.2880i	−0.714047	+	0.665512i	0.238069	+	0.971248i	$0.423485\pi$
$600$	0.0880002	+	3.75283i	0.00359259	+	0.153209i
$601$	37.2586	−	30.1232i	1.51981	−	1.22875i	0.626405	−	0.779498i	$-0.284526\pi$
$601$	37.2586	−	30.1232i	1.51981	−	1.22875i	0.893404	−	0.449254i	$-0.148310\pi$
$602$	−24.5345	+	9.66072i	−0.999953	+	0.393742i
$603$	7.98415	−	10.8816i	0.325140	−	0.443132i
$604$	1.45102	−	6.77443i	0.0590412	−	0.275648i
$605$	−4.42958	−	10.5191i	−0.180088	−	0.427664i
$606$	0.447055	+	0.0526468i	0.0181604	+	0.00213863i
$607$	−12.4102	+	7.42604i	−0.503715	+	0.301414i	−0.742717	−	0.669605i	$-0.766463\pi$
$607$	−12.4102	+	7.42604i	−0.503715	+	0.301414i	0.239002	+	0.971019i	$0.423180\pi$
$608$	0.454839	+	3.86231i	0.0184462	+	0.156637i
$609$	−7.24089	−	6.43821i	−0.293416	−	0.260890i
$610$	9.39594	−	8.35437i	0.380430	−	0.338258i
$611$	1.99647	−	16.9532i	0.0807687	−	0.685855i
$612$	1.09951	+	2.44890i	0.0444449	+	0.0989910i
$613$	−27.3305	−	4.52600i	−1.10387	−	0.182804i	−0.416517	−	0.909128i	$-0.636750\pi$
$613$	−27.3305	−	4.52600i	−1.10387	−	0.182804i	−0.687352	+	0.726324i	$0.741227\pi$
$614$	−23.5817	−	1.66134i	−0.951680	−	0.0670462i
$615$	1.58351	−	11.1827i	0.0638531	−	0.450929i
$616$	−6.05716	+	0.284225i	−0.244050	+	0.0114518i
$617$	−3.35204	−	10.6555i	−0.134948	−	0.428975i	0.862012	−	0.506888i	$-0.169204\pi$
$617$	−3.35204	−	10.6555i	−0.134948	−	0.428975i	−0.996960	+	0.0779130i	$0.975174\pi$
$618$	−2.17211	−	13.1164i	−0.0873749	−	0.527618i
$619$	−21.7745	+	40.5941i	−0.875193	+	1.63162i	−0.104395	+	0.994536i	$0.533291\pi$
$619$	−21.7745	+	40.5941i	−0.875193	+	1.63162i	−0.770798	+	0.637080i	$0.780142\pi$
$620$			7.54042i			0.302831i
$621$	−7.66045	−	4.10904i	−0.307403	−	0.164890i
$622$	17.1125	−	17.5185i	0.686148	−	0.702426i
$623$	−25.1342	+	73.8061i	−1.00698	+	2.95698i
$624$	−1.65016	−	6.90906i	−0.0660591	−	0.276584i
$625$	−2.29876	+	1.94939i	−0.0919504	+	0.0779755i
$626$	2.50687	−	26.6533i	0.100195	−	1.06528i
$627$	−5.63404	−	2.85407i	−0.225002	−	0.113980i
$628$	−8.50179	−	14.9949i	−0.339258	−	0.598363i
$629$	−9.18284	+	1.08140i	−0.366144	+	0.0431184i
$630$	7.42200	−	5.71818i	0.295700	−	0.227818i
$631$	15.9292	+	29.6966i	0.634131	+	1.18220i	0.970643	+	0.240526i	$0.0773198\pi$
$631$	15.9292	+	29.6966i	0.634131	+	1.18220i	−0.336512	+	0.941679i	$0.609247\pi$
$632$	2.96150	−	1.58854i	0.117802	−	0.0631886i
$633$	−3.70465	+	12.8188i	−0.147246	+	0.509500i
$634$	−9.15933	+	10.3013i	−0.363764	+	0.409115i
$635$	−2.75772	−	2.57027i	−0.109437	−	0.101998i
$636$	7.42222	−	8.75245i	0.294310	−	0.347057i
$637$	16.9441	+	64.2394i	0.671351	+	2.54526i
$638$	−3.00131	−	0.140833i	−0.118823	−	0.00557563i
$639$	−4.41615	+	23.2688i	−0.174700	+	0.920499i
$640$	1.20461	−	0.442000i	0.0476164	−	0.0174716i
$641$	19.8796	−	1.86977i	0.785196	−	0.0738514i	0.306545	−	0.951856i	$-0.400827\pi$
$641$	19.8796	−	1.86977i	0.785196	−	0.0738514i	0.478652	+	0.878005i	$0.341126\pi$
$642$	2.11453	−	0.350171i	0.0834538	−	0.0138201i
$643$	−27.4675	−	41.3699i	−1.08321	−	1.63147i	−0.710786	−	0.703408i	$-0.751661\pi$
$643$	−27.4675	−	41.3699i	−1.08321	−	1.63147i	−0.372426	−	0.928062i	$-0.621474\pi$
$644$	4.89131	+	4.77796i	0.192745	+	0.188278i
$645$	0.848511	+	9.02145i	0.0334101	+	0.355219i
$646$	2.18939	−	5.56021i	0.0861403	−	0.218763i
$647$	−28.2461	−	30.3060i	−1.11047	−	1.19145i	−0.979790	−	0.200029i	$-0.935897\pi$
$647$	−28.2461	−	30.3060i	−1.11047	−	1.19145i	−0.130678	−	0.991425i	$-0.541715\pi$
$648$	0.674342	+	0.212136i	0.0264906	+	0.00833351i
$649$	−9.34550	−	7.55575i	−0.366843	−	0.296589i
$650$	12.9881	−	16.8582i	0.509437	−	0.661232i
$651$	22.1668	−	16.2645i	0.868785	−	0.637454i
$652$	3.10130	−	1.30595i	0.121456	−	0.0511448i
$653$	2.00069	+	4.19031i	0.0782929	+	0.163980i	0.937831	−	0.347092i	$-0.112831\pi$
$653$	2.00069	+	4.19031i	0.0782929	+	0.163980i	−0.859538	+	0.511071i	$0.829249\pi$
$654$	−5.38835	+	5.78131i	−0.210701	+	0.226067i
$655$	1.06052	−	0.601292i	0.0414381	−	0.0234944i
$656$	7.72546	−	1.46620i	0.301629	−	0.0572456i
$657$	13.1922	−	5.92301i	0.514675	−	0.231079i
$658$	−6.65115	−	9.06483i	−0.259289	−	0.353384i
$659$	9.13100	+	5.75874i	0.355693	+	0.224329i	0.699371	−	0.714759i	$-0.253464\pi$
$659$	9.13100	+	5.75874i	0.355693	+	0.224329i	−0.343677	+	0.939088i	$0.611673\pi$
$660$	−0.484080	+	2.02680i	−0.0188428	+	0.0788931i
$661$	−0.284263	−	0.561146i	−0.0110566	−	0.0218261i	0.886473	−	0.462780i	$-0.153148\pi$
$661$	−0.284263	−	0.561146i	−0.0110566	−	0.0218261i	−0.897530	+	0.440953i	$0.854640\pi$
$662$	8.84909	+	12.6729i	0.343930	+	0.492546i
$663$	−2.78376	+	10.5539i	−0.108112	+	0.409880i
$664$	−3.48519	+	11.0788i	−0.135252	+	0.429939i
$665$	−20.6509	−	2.92424i	−0.800806	−	0.113397i
$666$	6.01856	−	8.61927i	0.233215	−	0.333990i
$667$	2.19129	+	2.58402i	0.0848470	+	0.100053i
$668$	0.246363	−	5.25027i	0.00953207	−	0.203139i
$669$	13.6114	−	28.5082i	0.526247	−	1.10219i
$670$	3.63188	+	9.22359i	0.140312	+	0.356338i
$671$	−12.6815	+	6.42414i	−0.489564	+	0.248001i
$672$	−3.89767	−	2.58785i	−0.150356	−	0.0998284i
$673$	−10.6350	−	7.06112i	−0.409951	−	0.272186i	0.331152	−	0.943577i	$-0.392563\pi$
$673$	−10.6350	−	7.06112i	−0.409951	−	0.272186i	−0.741103	+	0.671391i	$0.765697\pi$
$674$	−14.4960	+	7.34332i	−0.558365	+	0.282854i
$675$	6.52875	+	16.5805i	0.251292	+	0.638185i
$676$	−11.7497	+	24.6091i	−0.451913	+	0.946503i
$677$	−0.0880186	+	1.87578i	−0.00338283	+	0.0720919i	−0.999942	−	0.0107958i	$-0.996564\pi$
$677$	−0.0880186	+	1.87578i	−0.00338283	+	0.0720919i	0.996559	+	0.0828877i	$0.0264143\pi$
$678$	−12.2836	−	14.4851i	−0.471750	−	0.556298i
$679$	20.0078	−	28.6534i	0.767828	−	1.09962i
$680$	−1.95216	−	0.276433i	−0.0748620	−	0.0106007i
$681$	−1.69874	+	5.39996i	−0.0650957	+	0.206927i
$682$	2.17442	−	8.24377i	0.0832629	−	0.315670i
$683$	−18.7025	−	26.7842i	−0.715633	−	1.02487i	−0.997851	−	0.0655176i	$-0.979130\pi$
$683$	−18.7025	−	26.7842i	−0.715633	−	1.02487i	0.282219	−	0.959350i	$-0.408930\pi$
$684$	3.07027	+	6.06083i	0.117395	+	0.231742i
$685$	−4.50684	+	18.8698i	−0.172198	+	0.720977i
$686$	12.2646	+	7.73505i	0.468265	+	0.295326i
$687$	−11.1989	−	15.2629i	−0.427265	−	0.582318i
$688$	−5.75525	+	2.58399i	−0.219417	+	0.0985137i
$689$	−63.9173	+	12.1308i	−2.43505	+	0.462145i
$690$	2.04405	−	1.15893i	0.0778157	−	0.0441197i
$691$	33.0060	−	35.4131i	1.25561	−	1.34718i	0.342466	−	0.939530i	$-0.388738\pi$
$691$	33.0060	−	35.4131i	1.25561	−	1.34718i	0.913140	−	0.407646i	$-0.133650\pi$
$692$	−4.87301	−	10.2062i	−0.185244	−	0.387982i
$693$	−9.76325	+	4.11128i	−0.370875	+	0.156174i
$694$	−12.6728	+	9.29839i	−0.481051	+	0.352962i
$695$	6.62356	−	8.59716i	0.251246	−	0.326109i
$696$	−1.80272	−	1.45749i	−0.0683321	−	0.0552459i
$697$	−11.5258	−	3.62581i	−0.436569	−	0.137337i
$698$	−7.15664	−	7.67857i	−0.270883	−	0.290638i
$699$	−1.04085	+	2.64336i	−0.0393685	+	0.0999809i
$700$	−1.31253	−	13.9550i	−0.0496090	−	0.527448i
$701$	−11.0617	−	10.8053i	−0.417793	−	0.408111i	0.459415	−	0.888222i	$-0.348059\pi$
$701$	−11.0617	−	10.8053i	−0.417793	−	0.408111i	−0.877208	+	0.480111i	$0.840597\pi$
$702$	−18.6515	−	28.0918i	−0.703956	−	1.06026i
$703$	−23.0876	+	3.82336i	−0.870764	+	0.144201i
$704$	−1.44443	+	0.135856i	−0.0544391	+	0.00512026i
$705$	−3.62721	+	1.33091i	−0.136608	+	0.0501248i
$706$	0.352862	−	1.85924i	0.0132801	−	0.0699734i
$707$	−1.67895	−	0.0787827i	−0.0631434	−	0.00296293i
$708$	−2.36484	−	8.96570i	−0.0888762	−	0.336952i
$709$	16.6510	−	19.6353i	0.625342	−	0.737417i	−0.354968	−	0.934878i	$-0.615508\pi$
$709$	16.6510	−	19.6353i	0.625342	−	0.737417i	0.980311	+	0.197461i	$0.0632696\pi$
$710$	−12.7254	−	11.8604i	−0.477574	−	0.445112i
$711$	3.90116	−	4.38754i	0.146305	−	0.164546i
$712$	−5.17921	+	17.9210i	−0.194099	+	0.671618i
$713$	−8.47192	+	4.54431i	−0.317276	+	0.170186i
$714$	3.39812	+	6.33508i	0.127171	+	0.237085i
$715$	9.35816	−	7.20986i	0.349975	−	0.269633i
$716$	4.53094	−	0.533580i	0.169329	−	0.0199408i
$717$	−7.10844	−	12.5374i	−0.265470	−	0.468219i
$718$	27.6556	+	14.0096i	1.03210	+	0.522835i
$719$	1.09973	−	11.6925i	0.0410131	−	0.436055i	−0.950933	−	0.309396i	$-0.899873\pi$
$719$	1.09973	−	11.6925i	0.0410131	−	0.436055i	0.991946	−	0.126659i	$-0.0404254\pi$
$720$	1.70968	−	1.44984i	0.0637161	−	0.0540323i
$721$	11.5322	+	48.2843i	0.429481	+	1.79820i
$722$	−1.24938	+	3.66876i	−0.0464970	+	0.136537i
$723$	−21.5589	+	22.0704i	−0.801784	+	0.820806i
$724$	−14.1848	−	7.60865i	−0.527172	−	0.282773i
$725$		−	6.94517i		−	0.257937i
$726$	−4.70655	+	8.77438i	−0.174676	+	0.325648i
$727$	−2.74904	−	16.6003i	−0.101956	−	0.615669i	−0.988286	−	0.152614i	$-0.951231\pi$
$727$	−2.74904	−	16.6003i	−0.101956	−	0.615669i	0.886330	−	0.463055i	$-0.153247\pi$
$728$	7.95926	+	25.3010i	0.294990	+	0.937717i
$729$	19.0579	−	0.894269i	0.705848	−	0.0331211i
$730$	−1.48914	+	10.5162i	−0.0551154	+	0.389223i
$731$	9.66982	+	0.681243i	0.357651	+	0.0251967i
$732$	−10.8209	−	1.79196i	−0.399950	−	0.0662327i
$733$	−17.9578	−	39.9970i	−0.663288	−	1.47732i	−0.867008	−	0.498294i	$-0.833960\pi$
$733$	−17.9578	−	39.9970i	−0.663288	−	1.47732i	0.203720	−	0.979029i	$-0.434697\pi$
$734$	3.68058	−	31.2540i	0.135853	−	1.15360i
$735$	11.2374	−	9.99170i	0.414498	−	0.368549i
$736$	1.22257	+	1.08705i	0.0450646	+	0.0400690i
$737$	−1.31086	−	11.1313i	−0.0482860	−	0.410025i
$738$	11.7881	−	7.05379i	0.433927	−	0.259654i
$739$	1.52147	+	0.179173i	0.0559681	+	0.00659100i	0.144893	−	0.989447i	$-0.453716\pi$
$739$	1.52147	+	0.179173i	0.0559681	+	0.00659100i	−0.0889248	+	0.996038i	$0.528343\pi$
$740$	2.99657	+	7.11609i	0.110156	+	0.261593i
$741$	−5.78581	+	27.0124i	−0.212547	+	0.992326i
$742$	−25.3487	+	34.5476i	−0.930579	+	1.26828i
$743$	−24.5111	+	9.65148i	−0.899224	+	0.354078i	−0.770379	−	0.637586i	$-0.779933\pi$
$743$	−24.5111	+	9.65148i	−0.899224	+	0.354078i	−0.128845	+	0.991665i	$0.541127\pi$
$744$	5.11531	−	4.13568i	0.187536	−	0.151621i
$745$	0.204326	+	8.71364i	0.00748594	+	0.319243i
$746$	−19.6234	+	18.2896i	−0.718464	+	0.669629i
$747$	0.951030	+	20.2675i	0.0347964	+	0.741550i
$748$	2.05454	+	0.865161i	0.0751214	+	0.0316334i
$749$	−7.78404	+	1.85913i	−0.284423	+	0.0679313i
$750$	−11.7879	−	2.23720i	−0.430432	−	0.0816910i
$751$	11.0715	−	3.77035i	0.404006	−	0.137582i	−0.112936	−	0.993602i	$-0.536025\pi$
$751$	11.0715	−	3.77035i	0.404006	−	0.137582i	0.516942	+	0.856020i	$0.327070\pi$
$752$	−1.69124	−	2.09184i	−0.0616730	−	0.0762817i
$753$	−23.3839	+	16.3282i	−0.852157	+	0.595034i
$754$	2.75252	+	12.8508i	0.100241	+	0.467998i
$755$	8.10982	+	3.64114i	0.295146	+	0.132515i
$756$	−21.6015	−	5.15929i	−0.785639	−	0.187642i
$757$	25.3465	+	18.5975i	0.921234	+	0.675938i	0.946142	−	0.323752i	$-0.104944\pi$
$757$	25.3465	+	18.5975i	0.921234	+	0.675938i	−0.0249080	+	0.999690i	$0.507929\pi$
$758$	−0.808710	+	0.233719i	−0.0293737	+	0.00848905i
$759$	−2.56891	+	0.677591i	−0.0932457	+	0.0245950i
$760$	−4.96821	−	0.467284i	−0.180216	−	0.0169502i
$761$	−30.9767	+	2.18232i	−1.12290	+	0.0791089i	−0.619539	−	0.784966i	$-0.712680\pi$
$761$	−30.9767	+	2.18232i	−1.12290	+	0.0791089i	−0.503364	+	0.864075i	$0.667904\pi$
$762$	−0.231113	+	3.28051i	−0.00837235	+	0.118840i
$763$	18.5528	−	22.9474i	0.671656	−	0.830753i
$764$	−1.01249	+	2.75940i	−0.0366306	+	0.0998317i
$765$	−3.36808	+	0.721411i	−0.121773	+	0.0260827i
$766$	17.1457	−	25.8239i	0.619500	−	0.933055i
$767$	−21.5307	+	47.9546i	−0.777427	+	1.73154i
$768$	−0.960537	−	0.574768i	−0.0346604	−	0.0207401i
$769$	22.4504	+	17.2966i	0.809582	+	0.623731i	0.929404	−	0.369065i	$-0.120322\pi$
$769$	22.4504	+	17.2966i	0.809582	+	0.623731i	−0.119822	+	0.992795i	$0.538232\pi$
$770$	1.27120	−	7.67620i	0.0458108	−	0.276631i
$771$	30.6422	−	4.33904i	1.10355	−	0.156267i
$772$	−3.44423	+	6.79904i	−0.123961	+	0.244703i
$773$	16.3870	+	13.8965i	0.589400	+	0.499821i	0.891237	−	0.453538i	$-0.149839\pi$
$773$	16.3870	+	13.8965i	0.589400	+	0.499821i	−0.301837	+	0.953360i	$0.597600\pi$
$774$	−7.88412	+	7.70141i	−0.283389	+	0.276822i
$775$	19.2702	+	4.12749i	0.692205	+	0.148264i
$776$	4.46039	−	7.07235i	0.160119	−	0.253882i
$777$	14.4559	−	24.1583i	0.518601	−	0.866673i
$778$	33.6241	+	12.3374i	1.20548	+	0.442319i
$779$	−29.5693	−	7.79937i	−1.05943	−	0.279441i
$780$	9.11215	−	0.213671i	0.326267	−	0.00765064i
$781$	10.4922	+	16.6363i	0.375439	+	0.595293i
$782$	−0.865908	−	2.35992i	−0.0309648	−	0.0843904i
$783$	−10.4171	−	3.54747i	−0.372276	−	0.126776i
$784$	9.10725	+	5.16360i	0.325259	+	0.184414i
$785$	21.0987	−	6.63728i	0.753044	−	0.236895i
$786$	−0.989572	−	0.389654i	−0.0352969	−	0.0138985i
$787$	−13.6363	+	8.60015i	−0.486082	+	0.306562i	−0.753994	−	0.656881i	$-0.771875\pi$
$787$	−13.6363	+	8.60015i	−0.486082	+	0.306562i	0.267912	+	0.963443i	$0.413666\pi$
$788$	−2.06740	−	6.07087i	−0.0736481	−	0.216266i
$789$	−3.75203	−	1.79143i	−0.133576	−	0.0637765i
$790$	1.19723	+	4.14265i	0.0425957	+	0.147389i
$791$	49.5535	+	50.7291i	1.76192	+	1.80372i
$792$	−2.28724	+	1.09206i	−0.0812737	+	0.0388045i
$793$	41.3172	+	46.4684i	1.46722	+	1.65014i
$794$	0.580850	−	24.7708i	0.0206136	−	0.879082i
$795$	8.98689	+	11.6647i	0.318732	+	0.413704i
$796$	11.6509	+	3.36712i	0.412954	+	0.119345i
$797$	34.7104	+	0.813924i	1.22950	+	0.0288307i	0.633239	−	0.773956i	$-0.281725\pi$
$797$	34.7104	+	0.813924i	1.22950	+	0.0288307i	0.596266	+	0.802787i	$0.296650\pi$
$798$	9.34259	+	15.6131i	0.330724	+	0.552698i
$799$	0.770709	+	4.06088i	0.0272657	+	0.143664i
$800$	−0.470184	−	3.32042i	−0.0166235	−	0.117395i
$801$	2.29026	+	32.5089i	0.0809224	+	1.14864i
$802$	14.9567	+	10.4438i	0.528138	+	0.368782i
$803$	4.66059	−	11.0677i	0.164469	−	0.390572i
$804$	4.26518	−	7.52266i	0.150421	−	0.265304i
$805$	−7.30932	+	4.85301i	−0.257620	+	0.171046i
$806$	−37.2918			−1.31355
$807$	−18.3238	+	1.13739i	−0.645027	+	0.0400380i
$808$	−0.402141			−0.0141473
$809$	21.5394	−	14.3011i	0.757286	−	0.502799i	−0.114056	−	0.993474i	$-0.536384\pi$
$809$	21.5394	−	14.3011i	0.757286	−	0.502799i	0.871342	+	0.490676i	$0.163250\pi$
$810$	−0.447388	+	0.789075i	−0.0157196	+	0.0277253i
$811$	−8.22781	+	19.5390i	−0.288918	+	0.686107i	−0.999853	−	0.0171507i	$-0.994540\pi$
$811$	−8.22781	+	19.5390i	−0.288918	+	0.686107i	0.710935	+	0.703257i	$0.248272\pi$
$812$	7.09701	+	4.95562i	0.249056	+	0.173908i
$813$	0.760170	+	10.7901i	0.0266603	+	0.378427i
$814$	−1.22402	−	8.64398i	−0.0429018	−	0.302971i
$815$	0.805102	+	4.24210i	0.0282015	+	0.148594i
$816$	0.883172	+	1.47593i	0.0309172	+	0.0516680i
$817$	24.5279	+	0.575154i	0.858121	+	0.0201221i
$818$	28.4064	+	8.20951i	0.993207	+	0.287039i
$819$	28.2797	+	36.7061i	0.988173	+	1.28262i
$820$	−0.236531	+	10.0870i	−0.00826002	+	0.352254i
$821$	−3.49724	−	3.93325i	−0.122055	−	0.137271i	0.683128	−	0.730299i	$-0.260619\pi$
$821$	−3.49724	−	3.93325i	−0.122055	−	0.137271i	−0.805182	+	0.593027i	$0.797933\pi$
$822$	15.2728	−	7.29210i	0.532701	−	0.254341i
$823$	−20.4831	−	20.9690i	−0.713996	−	0.730934i	0.257945	−	0.966160i	$-0.416955\pi$
$823$	−20.4831	−	20.9690i	−0.713996	−	0.730934i	−0.971941	+	0.235225i	$0.924417\pi$
$824$	3.29759	+	11.4103i	0.114877	+	0.397496i
$825$	4.91468	+	2.34654i	0.171107	+	0.0816960i
$826$	11.1609	+	32.7737i	0.388338	+	1.14034i
$827$	−7.59978	+	4.79303i	−0.264270	+	0.166670i	−0.659035	−	0.752112i	$-0.729035\pi$
$827$	−7.59978	+	4.79303i	−0.264270	+	0.166670i	0.394765	+	0.918782i	$0.370826\pi$
$828$	2.65930	+	1.04713i	0.0924170	+	0.0363901i
$829$	−25.8851	+	8.14300i	−0.899026	+	0.282818i	−0.714191	−	0.699951i	$-0.753205\pi$
$829$	−25.8851	+	8.14300i	−0.899026	+	0.282818i	−0.184835	+	0.982770i	$0.559175\pi$
$830$	−12.9637	−	7.35013i	−0.449977	−	0.255127i
$831$	−3.89672	−	1.32700i	−0.135176	−	0.0460333i
$832$	2.18595	+	5.95750i	0.0757840	+	0.206539i
$833$	−8.58145	−	13.6067i	−0.297330	−	0.471443i
$834$	−9.46500	+	0.221945i	−0.327746	+	0.00768533i
$835$	6.52122	+	1.72007i	0.225676	+	0.0595256i
$836$	5.29688	+	1.94355i	0.183196	+	0.0672190i
$837$	16.0337	−	26.7951i	0.554206	−	0.926174i
$838$	−19.3852	+	30.7370i	−0.669651	+	1.06179i
$839$	−31.0509	−	6.65081i	−1.07200	−	0.229612i	−0.360827	−	0.932633i	$-0.617506\pi$
$839$	−31.0509	−	6.65081i	−1.07200	−	0.229612i	−0.711169	+	0.703021i	$0.751834\pi$
$840$	4.29439	−	4.19487i	0.148171	−	0.144737i
$841$	−18.8467	−	15.9823i	−0.649886	−	0.551115i
$842$	−0.480371	+	0.948270i	−0.0165547	+	0.0326795i
$843$	14.2205	−	2.01368i	0.489781	−	0.0693547i
$844$	1.94752	−	11.7602i	0.0670365	−	0.404804i
$845$	−27.7190	−	21.3557i	−0.953561	−	0.734658i
$846$	−4.03262	−	2.41305i	−0.138644	−	0.0829623i
$847$	15.2279	−	33.9167i	0.523237	−	1.16539i
$848$	−5.67072	+	8.54092i	−0.194733	+	0.293296i
$849$	−8.65281	+	1.85335i	−0.296964	+	0.0636069i
$850$	−1.77503	+	4.83760i	−0.0608829	+	0.165928i
$851$	−6.18926	+	7.65532i	−0.212165	+	0.262421i
$852$	−1.06646	+	15.1377i	−0.0365363	+	0.518610i
$853$	−17.1967	+	1.21151i	−0.588803	+	0.0414814i	−0.361547	−	0.932354i	$-0.617751\pi$
$853$	−17.1967	+	1.21151i	−0.588803	+	0.0414814i	−0.227256	+	0.973835i	$0.572975\pi$
$854$	40.7744	+	3.83502i	1.39527	+	0.131232i
$855$	−8.42952	+	2.22342i	−0.288284	+	0.0760393i
$856$	−1.83948	+	0.531614i	−0.0628722	+	0.0181702i
$857$	8.55871	+	6.27979i	0.292360	+	0.214514i	0.727948	−	0.685633i	$-0.240474\pi$
$857$	8.55871	+	6.27979i	0.292360	+	0.214514i	−0.435588	+	0.900146i	$0.643459\pi$
$858$	−10.0237	−	2.39406i	−0.342204	−	0.0817318i
$859$	−33.2159	−	14.9132i	−1.13331	−	0.508833i	−0.245663	−	0.969355i	$-0.579006\pi$
$859$	−33.2159	−	14.9132i	−1.13331	−	0.508833i	−0.887648	+	0.460522i	$0.847662\pi$
$860$	−1.69541	−	7.91544i	−0.0578131	−	0.269914i
$861$	30.1633	−	21.0621i	1.02796	−	0.717794i
$862$	4.93598	+	6.10518i	0.168120	+	0.207943i
$863$	−2.65737	+	0.904953i	−0.0904581	+	0.0308050i	−0.367225	−	0.930132i	$-0.619692\pi$
$863$	−2.65737	+	0.904953i	−0.0904581	+	0.0308050i	0.276767	+	0.960937i	$0.410737\pi$
$864$	−5.22047	−	0.990786i	−0.177604	−	0.0337072i
$865$	14.1151	−	3.37125i	0.479929	−	0.114626i
$866$	−1.59626	−	0.672181i	−0.0542432	−	0.0228416i
$867$	0.768068	+	16.3684i	0.0260849	+	0.555900i
$868$	−17.9676	+	16.7463i	−0.609861	+	0.568408i
$869$	−0.114298	−	4.87431i	−0.00387728	−	0.165349i
$870$	2.31315	−	1.87016i	0.0784231	−	0.0634044i
$871$	−45.6160	+	17.9618i	−1.54564	+	0.608611i
$872$	4.17665	−	5.69234i	0.141439	−	0.192767i
$873$	3.05939	−	14.2835i	0.103545	−	0.483423i
$874$	−2.46913	−	5.86357i	−0.0835196	−	0.198338i
$875$	44.4930	+	5.23965i	1.50414	+	0.177133i
$876$	7.95081	−	4.75761i	0.268633	−	0.160745i
$877$	−3.93674	−	33.4292i	−0.132934	−	1.12882i	−0.883634	−	0.468179i	$-0.844910\pi$
$877$	−3.93674	−	33.4292i	−0.132934	−	1.12882i	0.750699	−	0.660644i	$-0.229717\pi$
$878$	24.5511	+	21.8295i	0.828558	+	0.736710i
$879$	−8.16907	+	7.26350i	−0.275536	+	0.244992i
$880$	0.217723	−	1.84881i	0.00733944	−	0.0623235i
$881$	6.27555	+	13.9774i	0.211429	+	0.470909i	0.987075	−	0.160258i	$-0.0512327\pi$
$881$	6.27555	+	13.9774i	0.211429	+	0.470909i	−0.775646	+	0.631168i	$0.782576\pi$
$882$	18.0441	+	2.98815i	0.607577	+	0.100616i
$883$	−55.4525	−	3.90665i	−1.86612	−	0.131469i	−0.908208	−	0.418519i	$-0.862549\pi$
$883$	−55.4525	−	3.90665i	−1.86612	−	0.131469i	−0.957916	+	0.287050i	$0.907325\pi$
$884$	1.36712	−	9.65458i	0.0459813	−	0.324719i
$885$	11.8846	−	0.557673i	0.399498	−	0.0187460i
$886$	−3.35746	−	10.6727i	−0.112796	−	0.358557i
$887$	3.15668	+	19.0618i	0.105991	+	0.640032i	0.986214	+	0.165472i	$0.0529149\pi$
$887$	3.15668	+	19.0618i	0.105991	+	0.640032i	−0.880224	+	0.474559i	$0.842607\pi$
$888$	3.18393	−	5.93578i	0.106846	−	0.199192i
$889$		−	12.2795i		−	0.411841i
$890$	−21.0933	−	11.3144i	−0.707050	−	0.379259i
$891$	0.716663	−	0.733665i	0.0240091	−	0.0245787i
$892$	−9.09779	+	26.7155i	−0.304617	+	0.894500i
$893$	2.43024	+	10.1752i	0.0813249	+	0.340500i
$894$	5.79914	−	4.91777i	0.193952	−	0.164475i
$895$	−0.548178	+	5.82829i	−0.0183236	+	0.194818i
$896$	3.72851	+	1.88877i	0.124561	+	0.0630994i
$897$	5.73159	+	10.1090i	0.191372	+	0.337531i
$898$	22.8882	−	2.69539i	0.763788	−	0.0899463i
$899$	−9.64082	+	7.42763i	−0.321539	+	0.247725i
$900$	−2.76933	−	5.16285i	−0.0923111	−	0.172095i
$901$	13.8820	−	7.44626i	0.462477	−	0.248071i
$902$	3.16738	−	10.9597i	0.105462	−	0.364918i
$903$	−19.6123	+	22.0574i	−0.652655	+	0.734024i
$904$	12.4119	+	11.5682i	0.412812	+	0.384753i
$905$	13.3585	−	15.7526i	0.444051	−	0.523634i
$906$	−1.97788	−	7.49863i	−0.0657107	−	0.249125i
$907$	−37.9693	−	1.78167i	−1.26075	−	0.0591592i	−0.594015	−	0.804454i	$-0.702458\pi$
$907$	−37.9693	−	1.78167i	−1.26075	−	0.0591592i	−0.666735	+	0.745295i	$0.732309\pi$
$908$	0.942962	−	4.96849i	0.0312933	−	0.164885i
$909$	−0.659548	+	0.242003i	−0.0218758	+	0.00802674i
$910$	−33.8837	+	3.18692i	−1.12323	+	0.105645i
$911$	−48.9345	+	8.10367i	−1.62127	+	0.268486i	−0.903753	−	0.428054i	$-0.859199\pi$
$911$	−48.9345	+	8.10367i	−1.62127	+	0.268486i	−0.717518	+	0.696540i	$0.754722\pi$
$912$	2.40791	+	3.62665i	0.0797338	+	0.120090i
$913$	12.0534	+	11.7741i	0.398909	+	0.389665i
$914$	1.56618	+	16.6517i	0.0518045	+	0.550791i
$915$	5.15635	−	13.0952i	0.170464	−	0.432913i
$916$	11.5307	+	12.3716i	0.380985	+	0.408770i
$917$	3.78808	+	1.19166i	0.125093	+	0.0393522i
$918$	6.34927	+	5.13333i	0.209557	+	0.169425i
$919$	14.1096	−	18.3138i	0.465434	−	0.604118i	−0.499596	−	0.866259i	$-0.666518\pi$
$919$	14.1096	−	18.3138i	0.465434	−	0.604118i	0.965030	+	0.262141i	$0.0844286\pi$
$920$	−1.69245	+	1.24181i	−0.0557985	+	0.0409411i
$921$	−24.3880	+	10.2697i	−0.803612	+	0.338399i
$922$	−12.0182	−	25.1713i	−0.395798	−	0.828974i
$923$	58.6565	−	62.9343i	1.93070	−	2.07151i
$924$	−5.90463	+	3.34779i	−0.194248	+	0.110134i
$925$	19.8260	−	3.76275i	0.651876	−	0.123718i
$926$	2.07975	−	0.933766i	0.0683449	−	0.0306855i
$927$	12.2749	+	16.7294i	0.403161	+	0.549467i
$928$	1.75171	+	1.10477i	0.0575027	+	0.0362658i
$929$	2.27619	−	9.53023i	0.0746795	−	0.312677i	−0.922656	−	0.385623i	$-0.873986\pi$
$929$	2.27619	−	9.53023i	0.0746795	−	0.312677i	0.997336	+	0.0729464i	$0.0232402\pi$
$930$	3.81427	+	7.52952i	0.125075	+	0.246903i
$931$	−23.3096	−	33.3820i	−0.763942	−	1.09405i
$932$	0.647284	−	2.45401i	0.0212025	−	0.0803838i
$933$	8.22615	−	26.1494i	0.269312	−	0.856092i
$934$	16.3774	+	2.31910i	0.535885	+	0.0758833i
$935$	−1.63764	+	2.34529i	−0.0535566	+	0.0766992i
$936$	7.17030	+	8.45537i	0.234369	+	0.276372i
$937$	1.07834	−	22.9806i	0.0352278	−	0.750745i	−0.908074	−	0.418809i	$-0.862448\pi$
$937$	1.07834	−	22.9806i	0.0352278	−	0.750745i	0.943302	−	0.331936i	$-0.107702\pi$
$938$	−13.9124	+	29.1387i	−0.454256	+	0.951411i
$939$	−10.9791	−	27.8828i	−0.358291	−	0.909922i
$940$	3.07910	−	1.55980i	0.100429	−	0.0508751i
$941$	−22.3239	−	14.8219i	−0.727737	−	0.483180i	0.133714	−	0.991020i	$-0.457310\pi$
$941$	−22.3239	−	14.8219i	−0.727737	−	0.483180i	−0.861451	+	0.507840i	$0.830444\pi$
$942$	−16.0746	−	10.6727i	−0.523739	−	0.347735i
$943$	−11.4757	+	5.81330i	−0.373699	+	0.189307i
$944$	3.03492	+	7.70754i	0.0987783	+	0.250859i
$945$	12.2785	−	25.7165i	0.399419	−	0.836559i
$946$	−0.429009	+	9.14267i	−0.0139483	+	0.297254i
$947$	−23.3592	−	27.5457i	−0.759074	−	0.895116i	0.238023	−	0.971259i	$-0.423501\pi$
$947$	−23.3592	−	27.5457i	−0.759074	−	0.895116i	−0.997097	+	0.0761433i	$0.975739\pi$
$948$	2.15367	−	3.08430i	0.0699478	−	0.100173i
$949$	−52.0089	−	7.36465i	−1.68828	−	0.239067i
$950$	−3.91369	+	12.4409i	−0.126977	+	0.403636i
$951$	−3.93527	+	14.9196i	−0.127610	+	0.483800i
$952$	−3.67682	−	5.26562i	−0.119166	−	0.170660i
$953$	−0.137378	−	0.271189i	−0.00445010	−	0.00878466i	0.889833	−	0.456287i	$-0.150821\pi$
$953$	−0.137378	−	0.271189i	−0.00445010	−	0.00878466i	−0.894283	+	0.447503i	$0.852314\pi$
$954$	−4.16069	+	17.4205i	−0.134707	+	0.564008i
$955$	−3.19008	−	2.01192i	−0.103228	−	0.0651041i
$956$	7.61677	+	10.3809i	0.246344	+	0.335741i
$957$	−3.06821	+	1.37756i	−0.0991811	+	0.0445303i
$958$	−25.7341	+	4.88403i	−0.831430	+	0.157796i
$959$	−54.9728	+	31.1683i	−1.77517	+	1.00648i
$960$	0.979287	−	1.05071i	0.0316064	−	0.0339114i
$961$	−1.52252	−	3.18882i	−0.0491135	−	0.102865i
$962$	−35.1932	+	14.8198i	−1.13467	+	0.477808i
$963$	−2.69700	+	1.97887i	−0.0869096	+	0.0637683i
$964$	16.8217	−	21.8340i	0.541790	−	0.703226i
$965$	−7.60504	−	6.14860i	−0.244815	−	0.197930i
$966$	7.30114	+	2.29681i	0.234910	+	0.0738988i
$967$	32.8600	+	35.2564i	1.05671	+	1.13377i	0.990716	+	0.135949i	$0.0434084\pi$
$967$	32.8600	+	35.2564i	1.05671	+	1.13377i	0.0659893	+	0.997820i	$0.478980\pi$
$968$	3.25901	−	8.27664i	0.104749	−	0.266021i
$969$	−0.626373	−	6.65966i	−0.0201220	−	0.213939i
$970$	7.67486	+	7.49700i	0.246425	+	0.240714i
$971$	−24.7513	−	37.2790i	−0.794307	−	1.19634i	−0.977015	−	0.213172i	$-0.931620\pi$
$971$	−24.7513	−	37.2790i	−0.794307	−	1.19634i	0.182707	−	0.983167i	$-0.441514\pi$
$972$	−14.9461	+	2.47511i	−0.479397	+	0.0793893i
$973$	35.1958	−	3.31033i	1.12833	−	0.106124i
$974$	−9.90780	+	3.63540i	−0.317467	+	0.116486i
$975$	4.44177	−	23.4038i	0.142250	−	0.749521i
$976$	9.78780	+	0.459281i	0.313300	+	0.0147012i
$977$	−10.8440	−	41.1123i	−0.346930	−	1.31530i	−0.882303	−	0.470682i	$-0.844008\pi$
$977$	−10.8440	−	41.1123i	−0.346930	−	1.31530i	0.535372	−	0.844616i	$-0.320171\pi$
$978$	2.43621	−	2.87283i	0.0779013	−	0.0918630i
$979$	19.7981	+	18.4524i	0.632751	+	0.589742i
$980$	−8.92618	+	10.0390i	−0.285136	+	0.320685i
$981$	3.42450	−	11.8494i	0.109336	−	0.378322i
$982$	−1.14936	+	0.616510i	−0.0366774	+	0.0196736i
$983$	−4.90939	−	9.15254i	−0.156585	−	0.291921i	0.790765	−	0.612120i	$-0.209683\pi$
$983$	−4.90939	−	9.15254i	−0.156585	−	0.291921i	−0.947350	+	0.320199i	$0.896250\pi$
$984$	6.97263	−	5.37196i	0.222279	−	0.171252i
$985$	8.17262	−	0.962436i	0.260401	−	0.0306658i
$986$	−1.56953	−	2.76824i	−0.0499840	−	0.0881587i
$987$	−11.2269	−	5.68729i	−0.357357	−	0.181028i
$988$	2.31099	−	24.5707i	0.0735224	−	0.781698i
$989$	7.87150	−	6.67517i	0.250299	−	0.212258i
$990$	−0.755508	−	3.16325i	−0.0240116	−	0.100535i
$991$	−10.4318	+	30.6327i	−0.331376	+	0.973078i	0.646322	+	0.763064i	$0.276306\pi$
$991$	−10.4318	+	30.6327i	−0.331376	+	0.973078i	−0.977698	+	0.210014i	$0.932649\pi$
$992$	−4.10634	+	4.20376i	−0.130376	+	0.133470i
$993$	15.2468	+	8.17834i	0.483843	+	0.259532i
$994$		−	56.6630i		−	1.79724i
$995$	−7.35574	+	13.7133i	−0.233193	+	0.434739i
$996$	2.12397	+	12.8257i	0.0673006	+	0.406398i
$997$	−2.49393	−	7.92774i	−0.0789837	−	0.251074i	0.906124	−	0.423012i	$-0.139027\pi$
$997$	−2.49393	−	7.92774i	−0.0789837	−	0.251074i	−0.985108	+	0.171938i	$0.944997\pi$
$998$	−19.2195	+	0.901853i	−0.608383	+	0.0285477i
$999$	4.48303	−	31.6590i	0.141837	−	1.00165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.2.e.a.9.4	✓	1452
269.30	even	134	inner	538.2.e.a.299.4	yes	1452

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.2.e.a.9.4	✓	1452	1.1	even	1	trivial
538.2.e.a.299.4	yes	1452	269.30	even	134	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.e (of order \(134\), degree \(66\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.833094 + 0.553131i) q^{2} +(-0.552092 + 0.973747i) q^{3} +(0.388092 - 0.921621i) q^{4} +(1.05205 + 0.734610i) q^{5} +(-0.0786651 - 1.11660i) q^{6} +(0.586003 + 4.13834i) q^{7} +(0.186460 + 0.982463i) q^{8} +(0.897045 + 1.49912i) q^{9} +(-1.28279 - 0.0300801i) q^{10} +(1.39377 + 0.402802i) q^{11} +(0.683163 + 0.886723i) q^{12} +(0.148764 - 6.34414i) q^{13} +(-2.77724 - 3.12349i) q^{14} +(-1.29615 + 0.618854i) q^{15} +(-0.698769 - 0.715347i) q^{16} +(0.426614 + 1.47616i) q^{17} +(-1.57653 - 0.752724i) q^{18} +(1.25368 + 3.68139i) q^{19} +(1.08532 - 0.684491i) q^{20} +(-4.35322 - 1.71412i) q^{21} +(-1.38394 + 0.435365i) q^{22} +(1.42313 + 0.806881i) q^{23} +(-1.05961 - 0.360845i) q^{24} +(-1.15519 - 3.14831i) q^{25} +(3.38521 + 5.36755i) q^{26} +(-5.31220 + 0.124566i) q^{27} +(4.04140 + 1.06598i) q^{28} +(1.94424 + 0.713388i) q^{29} +(0.737508 - 1.23250i) q^{30} +(-3.13483 + 4.97056i) q^{31} +(0.977821 + 0.209440i) q^{32} +(-1.16172 + 1.13479i) q^{33} +(-1.17192 - 0.993808i) q^{34} +(-2.42356 + 4.78420i) q^{35} +(1.72975 - 0.244939i) q^{36} +(-0.983121 + 5.93663i) q^{37} +(-3.08072 - 2.37350i) q^{38} +(6.09545 + 3.64741i) q^{39} +(-0.525562 + 1.17057i) q^{40} +(-4.34947 + 6.55092i) q^{41} +(4.57478 - 0.979875i) q^{42} +(2.17314 - 5.92261i) q^{43} +(0.912141 - 1.12820i) q^{44} +(-0.157535 + 2.23612i) q^{45} +(-1.63191 + 0.114969i) q^{46} +(2.67818 + 0.251895i) q^{47} +(1.08235 - 0.285487i) q^{48} +(-10.0576 + 2.90668i) q^{49} +(2.70381 + 1.98387i) q^{50} +(-1.67294 - 0.399563i) q^{51} +(-5.78915 - 2.59921i) q^{52} +(-2.14719 - 10.0247i) q^{53} +(4.35666 - 3.04212i) q^{54} +(1.17041 + 1.44764i) q^{55} +(-3.95649 + 1.34736i) q^{56} +(-4.27689 - 0.811704i) q^{57} +(-2.01434 + 0.481103i) q^{58} +(-7.63427 - 3.21477i) q^{59} +(0.0673231 + 1.43473i) q^{60} +(-7.16796 + 6.68074i) q^{61} +(-0.137761 - 5.87492i) q^{62} +(-5.67819 + 4.59076i) q^{63} +(-0.930465 + 0.366380i) q^{64} +(4.81697 - 6.56504i) q^{65} +(0.340129 - 1.58797i) q^{66} +(-2.99819 - 7.11996i) q^{67} +(1.52603 + 0.179710i) q^{68} +(-1.57140 + 0.940294i) q^{69} +(-0.627236 - 5.32624i) q^{70} +(10.1313 + 9.00822i) q^{71} +(-1.30556 + 1.16084i) q^{72} +(0.968093 - 8.22065i) q^{73} +(-2.46470 - 5.48957i) q^{74} +(3.70342 + 0.613296i) q^{75} +(3.87939 + 0.273304i) q^{76} +(-0.850178 + 6.00393i) q^{77} +(-7.09558 + 0.332952i) q^{78} +(-1.00848 - 3.20576i) q^{79} +(-0.209636 - 1.26590i) q^{80} +(0.334154 - 0.622961i) q^{81} -7.86336i q^{82} +(10.2346 + 5.48982i) q^{83} +(-3.26922 + 3.34678i) q^{84} +(-0.635586 + 1.86638i) q^{85} +(1.46555 + 6.13613i) q^{86} +(-1.76806 + 1.49935i) q^{87} +(-0.135856 + 1.44443i) q^{88} +(16.6410 + 8.42993i) q^{89} +(-1.10563 - 1.95004i) q^{90} +(26.3413 - 3.10205i) q^{91} +(1.29594 - 0.998440i) q^{92} +(-3.10935 - 5.79674i) q^{93} +(-2.37050 + 1.27153i) q^{94} +(-1.38546 + 4.79395i) q^{95} +(-0.743789 + 0.836521i) q^{96} +(-6.11663 - 5.70087i) q^{97} +(6.77118 - 7.98473i) q^{98} +(0.646425 + 2.45076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38}+ \cdots + 18 q^{99}+O(q^{100}) \) 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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