LMFDB - Embedded newform 169.2.k.a.17.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(4,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("169.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.k (of order $78$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	169.17
Dual form			169.2.k.a.10.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.980708 - 0.200213i) q^{2} +(-2.27761 - 0.370148i) q^{3} +(-0.918255 + 0.391232i) q^{4} +(0.651073 + 2.64151i) q^{5} +(-2.30778 + 0.0930004i) q^{6} +(4.17842 + 1.98269i) q^{7} +(-2.46972 + 1.70472i) q^{8} +(2.20490 + 0.736104i) q^{9} +O(q^{10})$	\(q+(0.980708 - 0.200213i) q^{2} +(-2.27761 - 0.370148i) q^{3} +(-0.918255 + 0.391232i) q^{4} +(0.651073 + 2.64151i) q^{5} +(-2.30778 + 0.0930004i) q^{6} +(4.17842 + 1.98269i) q^{7} +(-2.46972 + 1.70472i) q^{8} +(2.20490 + 0.736104i) q^{9} +(1.16738 + 2.46019i) q^{10} +(0.585391 + 1.75346i) q^{11} +(2.23624 - 0.551185i) q^{12} +(-2.08324 - 2.94281i) q^{13} +(4.49477 + 1.10786i) q^{14} +(-0.505143 - 6.25732i) q^{15} +(-0.697915 + 0.726606i) q^{16} +(-2.65981 + 5.60544i) q^{17} +(2.30974 + 0.280453i) q^{18} +(0.560573 - 0.323647i) q^{19} +(-1.63129 - 2.17086i) q^{20} +(-8.78294 - 6.06243i) q^{21} +(0.925163 + 1.60243i) q^{22} +(2.07390 - 3.59210i) q^{23} +(6.25607 - 2.96854i) q^{24} +(-2.12638 + 1.11601i) q^{25} +(-2.63224 - 2.46895i) q^{26} +(1.38011 + 0.724339i) q^{27} +(-4.61255 - 0.185879i) q^{28} +(-0.335928 - 1.64548i) q^{29} +(-1.74820 - 6.03547i) q^{30} +(0.757958 - 1.44417i) q^{31} +(2.66882 - 4.22040i) q^{32} +(-0.684253 - 4.21038i) q^{33} +(-1.48622 + 6.02983i) q^{34} +(-2.51682 + 12.3282i) q^{35} +(-2.31265 + 0.186696i) q^{36} +(-2.53790 - 4.01337i) q^{37} +(0.484960 - 0.429637i) q^{38} +(3.65553 + 7.47368i) q^{39} +(-6.11101 - 5.41388i) q^{40} +(0.803175 - 4.94214i) q^{41} +(-9.82728 - 4.18701i) q^{42} +(7.23870 + 4.57748i) q^{43} +(-1.22355 - 1.38110i) q^{44} +(-0.508873 + 6.30352i) q^{45} +(1.31471 - 3.93802i) q^{46} +(10.4071 - 1.26365i) q^{47} +(1.85853 - 1.39660i) q^{48} +(9.10106 + 11.1468i) q^{49} +(-1.86192 + 1.52021i) q^{50} +(8.13287 - 11.7825i) q^{51} +(3.06427 + 1.88722i) q^{52} +(1.29029 + 1.86931i) q^{53} +(1.49851 + 0.434049i) q^{54} +(-4.25064 + 2.68794i) q^{55} +(-13.6995 + 2.22638i) q^{56} +(-1.39657 + 0.529647i) q^{57} +(-0.658895 - 1.54648i) q^{58} +(-6.37655 + 6.12476i) q^{59} +(2.91192 + 5.54819i) q^{60} +(-7.16358 - 0.578304i) q^{61} +(0.454194 - 1.56806i) q^{62} +(7.75354 + 7.44738i) q^{63} +(2.48688 - 6.55736i) q^{64} +(6.41711 - 7.41887i) q^{65} +(-1.51403 - 3.99216i) q^{66} +(3.81611 - 8.95673i) q^{67} +(0.249361 - 6.18783i) q^{68} +(-6.05315 + 7.41376i) q^{69} +12.5943i q^{70} +(7.93631 + 6.47979i) q^{71} +(-6.70034 + 1.94078i) q^{72} +(0.757082 - 0.854568i) q^{73} +(-3.29247 - 3.42782i) q^{74} +(5.25617 - 1.75477i) q^{75} +(-0.388128 + 0.516505i) q^{76} +(-1.03055 + 8.48734i) q^{77} +(5.08134 + 6.59762i) q^{78} +(-1.56101 - 12.8560i) q^{79} +(-2.37373 - 1.37047i) q^{80} +(-8.45023 - 6.34994i) q^{81} +(-0.201799 - 5.00760i) q^{82} +(-8.62375 - 3.27056i) q^{83} +(10.4368 + 2.13069i) q^{84} +(-16.5385 - 3.37637i) q^{85} +(8.01553 + 3.03989i) q^{86} +(0.156041 + 3.87212i) q^{87} +(-4.43492 - 3.33262i) q^{88} +(7.26445 + 4.19413i) q^{89} +(0.762991 + 6.28379i) q^{90} +(-2.86998 - 16.4267i) q^{91} +(-0.499025 + 4.10984i) q^{92} +(-2.26089 + 3.00870i) q^{93} +(9.95335 - 3.32292i) q^{94} +(1.21989 + 1.27004i) q^{95} +(-7.64071 + 8.62458i) q^{96} +(-10.9019 + 3.15778i) q^{97} +(11.1572 + 9.10958i) q^{98} +4.29711i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) $ 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{73}{78}\right)$

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 $

$2$	0.980708	−	0.200213i	0.693465	−	0.141572i	0.159651	−	0.987174i	$-0.448963\pi$
$2$	0.980708	−	0.200213i	0.693465	−	0.141572i	0.533815	+	0.845602i	$0.320758\pi$
$3$	−2.27761	−	0.370148i	−1.31498	−	0.213705i	−0.537848	−	0.843042i	$-0.680762\pi$
$3$	−2.27761	−	0.370148i	−1.31498	−	0.213705i	−0.777133	+	0.629337i	$0.783327\pi$
$4$	−0.918255	+	0.391232i	−0.459128	+	0.195616i
$5$	0.651073	+	2.64151i	0.291169	+	1.18132i	0.916201	+	0.400719i	$0.131240\pi$
$5$	0.651073	+	2.64151i	0.291169	+	1.18132i	−0.625032	+	0.780599i	$0.714914\pi$
$6$	−2.30778	+	0.0930004i	−0.942148	+	0.0379673i
$7$	4.17842	+	1.98269i	1.57930	+	0.749385i	0.997933	−	0.0642597i	$-0.0204686\pi$
$7$	4.17842	+	1.98269i	1.57930	+	0.749385i	0.581362	+	0.813645i	$0.302520\pi$
$8$	−2.46972	+	1.70472i	−0.873178	+	0.602711i
$9$	2.20490	+	0.736104i	0.734967	+	0.245368i
$10$	1.16738	+	2.46019i	0.369157	+	0.777982i
$11$	0.585391	+	1.75346i	0.176502	+	0.528688i	0.999209	−	0.0397785i	$-0.0126652\pi$
$11$	0.585391	+	1.75346i	0.176502	+	0.528688i	−0.822707	+	0.568466i	$0.807537\pi$
$12$	2.23624	−	0.551185i	0.645548	−	0.159113i
$13$	−2.08324	−	2.94281i	−0.577786	−	0.816188i
$13$	−2.08324	−	2.94281i	−0.577786	−	0.816188i
$14$	4.49477	+	1.10786i	1.20128	+	0.296089i
$15$	−0.505143	−	6.25732i	−0.130427	−	1.61563i
$16$	−0.697915	+	0.726606i	−0.174479	+	0.181652i
$17$	−2.65981	+	5.60544i	−0.645099	+	1.35952i	0.272556	+	0.962140i	$0.412131\pi$
$17$	−2.65981	+	5.60544i	−0.645099	+	1.35952i	−0.917655	+	0.397378i	$0.869920\pi$
$18$	2.30974	+	0.280453i	0.544411	+	0.0661035i
$19$	0.560573	−	0.323647i	0.128604	−	0.0742497i	−0.434318	−	0.900760i	$-0.643010\pi$
$19$	0.560573	−	0.323647i	0.128604	−	0.0742497i	0.562922	+	0.826510i	$0.309677\pi$
$20$	−1.63129	−	2.17086i	−0.364768	−	0.485419i
$21$	−8.78294	−	6.06243i	−1.91660	−	1.32293i
$22$	0.925163	+	1.60243i	0.197245	+	0.341639i
$23$	2.07390	−	3.59210i	0.432438	−	0.749004i	−0.564645	−	0.825334i	$-0.690987\pi$
$23$	2.07390	−	3.59210i	0.432438	−	0.749004i	0.997083	+	0.0763296i	$0.0243201\pi$
$24$	6.25607	−	2.96854i	1.27701	−	0.605951i
$25$	−2.12638	+	1.11601i	−0.425277	+	0.223202i
$26$	−2.63224	−	2.46895i	−0.516224	−	0.484200i
$27$	1.38011	+	0.724339i	0.265603	+	0.139399i
$28$	−4.61255	−	0.185879i	−0.871690	−	0.0351279i
$29$	−0.335928	−	1.64548i	−0.0623803	−	0.305559i	0.936616	−	0.350358i	$-0.113940\pi$
$29$	−0.335928	−	1.64548i	−0.0623803	−	0.305559i	−0.998996	+	0.0447995i	$0.985735\pi$
$30$	−1.74820	−	6.03547i	−0.319175	−	1.10192i
$31$	0.757958	−	1.44417i	0.136133	−	0.259380i	−0.807840	−	0.589401i	$-0.799364\pi$
$31$	0.757958	−	1.44417i	0.136133	−	0.259380i	0.943973	+	0.330021i	$0.107056\pi$
$32$	2.66882	−	4.22040i	0.471785	−	0.746068i
$33$	−0.684253	−	4.21038i	−0.119113	−	0.732933i
$34$	−1.48622	+	6.02983i	−0.254884	+	1.03411i
$35$	−2.51682	+	12.3282i	−0.425421	+	2.08385i
$36$	−2.31265	+	0.186696i	−0.385442	+	0.0311161i
$37$	−2.53790	−	4.01337i	−0.417228	−	0.659794i	0.569534	−	0.821968i	$-0.307124\pi$
$37$	−2.53790	−	4.01337i	−0.417228	−	0.659794i	−0.986762	+	0.162174i	$0.948149\pi$
$38$	0.484960	−	0.429637i	0.0786709	−	0.0696964i
$39$	3.65553	+	7.47368i	0.585354	+	1.19675i
$40$	−6.11101	−	5.41388i	−0.966236	−	0.856010i
$41$	0.803175	−	4.94214i	0.125435	−	0.771832i	−0.845763	−	0.533558i	$-0.820854\pi$
$41$	0.803175	−	4.94214i	0.125435	−	0.771832i	0.971198	−	0.238273i	$-0.0765814\pi$
$42$	−9.82728	−	4.18701i	−1.51638	−	0.646070i
$43$	7.23870	+	4.57748i	1.10389	+	0.698059i	0.956708	−	0.291050i	$-0.0940046\pi$
$43$	7.23870	+	4.57748i	1.10389	+	0.698059i	0.147184	+	0.989109i	$0.452979\pi$
$44$	−1.22355	−	1.38110i	−0.184457	−	0.208209i
$45$	−0.508873	+	6.30352i	−0.0758582	+	0.939673i
$46$	1.31471	−	3.93802i	0.193843	−	0.580630i
$47$	10.4071	−	1.26365i	1.51804	−	0.184323i	0.681330	−	0.731976i	$-0.261402\pi$
$47$	10.4071	−	1.26365i	1.51804	−	0.184323i	0.836705	+	0.547653i	$0.184479\pi$
$48$	1.85853	−	1.39660i	0.268256	−	0.201581i
$49$	9.10106	+	11.1468i	1.30015	+	1.59240i
$50$	−1.86192	+	1.52021i	−0.263316	+	0.214990i
$51$	8.13287	−	11.7825i	1.13883	−	1.64988i
$52$	3.06427	+	1.88722i	0.424937	+	0.261710i
$53$	1.29029	+	1.86931i	0.177235	+	0.256769i	0.901526	−	0.432726i	$-0.142448\pi$
$53$	1.29029	+	1.86931i	0.177235	+	0.256769i	−0.724291	+	0.689494i	$0.757833\pi$
$54$	1.49851	+	0.434049i	0.203921	+	0.0590665i
$55$	−4.25064	+	2.68794i	−0.573156	+	0.362442i
$56$	−13.6995	+	2.22638i	−1.83067	+	0.297513i
$57$	−1.39657	+	0.529647i	−0.184980	+	0.0701535i
$58$	−0.658895	−	1.54648i	−0.0865172	−	0.203063i
$59$	−6.37655	+	6.12476i	−0.830156	+	0.797376i	−0.981572	−	0.191094i	$-0.938796\pi$
$59$	−6.37655	+	6.12476i	−0.830156	+	0.797376i	0.151415	+	0.988470i	$0.451617\pi$
$60$	2.91192	+	5.54819i	0.375927	+	0.716269i
$61$	−7.16358	−	0.578304i	−0.917203	−	0.0740443i	−0.387157	−	0.922014i	$-0.626543\pi$
$61$	−7.16358	−	0.578304i	−0.917203	−	0.0740443i	−0.530045	+	0.847969i	$0.677825\pi$
$62$	0.454194	−	1.56806i	0.0576827	−	0.199144i
$63$	7.75354	+	7.44738i	0.976855	+	0.938282i
$64$	2.48688	−	6.55736i	0.310860	−	0.819670i
$65$	6.41711	−	7.41887i	0.795945	−	0.920198i
$66$	−1.51403	−	3.99216i	−0.186364	−	0.491401i
$67$	3.81611	−	8.95673i	0.466212	−	1.09424i	−0.506504	−	0.862238i	$-0.669062\pi$
$67$	3.81611	−	8.95673i	0.466212	−	1.09424i	0.972715	−	0.232001i	$-0.0745274\pi$
$68$	0.249361	−	6.18783i	0.0302395	−	0.750384i
$69$	−6.05315	+	7.41376i	−0.728713	+	0.892512i
$70$			12.5943i			1.50530i
$71$	7.93631	+	6.47979i	0.941866	+	0.769010i	0.973072	−	0.230503i	$-0.0740371\pi$
$71$	7.93631	+	6.47979i	0.941866	+	0.769010i	−0.0312053	+	0.999513i	$0.509935\pi$
$72$	−6.70034	+	1.94078i	−0.789643	+	0.228723i
$73$	0.757082	−	0.854568i	0.0886097	−	0.100020i	−0.702533	−	0.711651i	$-0.747948\pi$
$73$	0.757082	−	0.854568i	0.0886097	−	0.100020i	0.791143	+	0.611631i	$0.209486\pi$
$74$	−3.29247	−	3.42782i	−0.382742	−	0.398476i
$75$	5.25617	−	1.75477i	0.606930	−	0.202623i
$76$	−0.388128	+	0.516505i	−0.0445213	+	0.0592471i
$77$	−1.03055	+	8.48734i	−0.117442	+	0.967222i
$78$	5.08134	+	6.59762i	0.575348	+	0.747033i
$79$	−1.56101	−	12.8560i	−0.175627	−	1.44642i	−0.767843	−	0.640638i	$-0.778670\pi$
$79$	−1.56101	−	12.8560i	−0.175627	−	1.44642i	0.592216	−	0.805779i	$-0.298253\pi$
$80$	−2.37373	−	1.37047i	−0.265391	−	0.153224i
$81$	−8.45023	−	6.34994i	−0.938915	−	0.705549i
$82$	−0.201799	−	5.00760i	−0.0222850	−	0.552997i
$83$	−8.62375	−	3.27056i	−0.946580	−	0.358990i	−0.167469	−	0.985877i	$-0.553560\pi$
$83$	−8.62375	−	3.27056i	−0.946580	−	0.358990i	−0.779110	+	0.626887i	$0.784329\pi$
$84$	10.4368	+	2.13069i	1.13875	+	0.232477i
$85$	−16.5385	−	3.37637i	−1.79386	−	0.366218i
$86$	8.01553	+	3.03989i	0.864337	+	0.327800i
$87$	0.156041	+	3.87212i	0.0167294	+	0.415135i
$88$	−4.43492	−	3.33262i	−0.472764	−	0.355259i
$89$	7.26445	+	4.19413i	0.770030	+	0.444577i	0.832885	−	0.553446i	$-0.186687\pi$
$89$	7.26445	+	4.19413i	0.770030	+	0.444577i	−0.0628552	+	0.998023i	$0.520021\pi$
$90$	0.762991	+	6.28379i	0.0804263	+	0.662370i
$91$	−2.86998	−	16.4267i	−0.300856	−	1.72199i
$92$	−0.499025	+	4.10984i	−0.0520270	+	0.428480i
$93$	−2.26089	+	3.00870i	−0.234443	+	0.311987i
$94$	9.95335	−	3.32292i	1.02661	−	0.342733i
$95$	1.21989	+	1.27004i	0.125158	+	0.130303i
$96$	−7.64071	+	8.62458i	−0.779826	+	0.880242i
$97$	−10.9019	+	3.15778i	−1.10692	+	0.320624i	−0.780848	−	0.624721i	$-0.785213\pi$
$97$	−10.9019	+	3.15778i	−1.10692	+	0.320624i	−0.326073	+	0.945345i	$0.605726\pi$
$98$	11.1572	+	9.10958i	1.12705	+	0.920207i
$99$			4.29711i			0.431876i
$100$	1.51594	−	1.85669i	0.151594	−	0.185669i
$101$	−0.504582	+	12.5211i	−0.0502078	+	1.24589i	0.756123	+	0.654429i	$0.227091\pi$
$101$	−0.504582	+	12.5211i	−0.0502078	+	1.24589i	−0.806331	+	0.591464i	$0.798550\pi$
$102$	5.61696	−	13.1835i	0.556162	−	1.30536i
$103$	2.19032	+	5.77539i	0.215818	+	0.569066i	0.998581	−	0.0532542i	$-0.0169594\pi$
$103$	2.19032	+	5.77539i	0.215818	+	0.569066i	−0.782763	+	0.622320i	$0.786190\pi$
$104$	10.1617	+	3.71657i	0.996436	+	0.364439i
$105$	10.2956	−	27.1473i	1.00475	−	2.64930i
$106$	1.63966	+	1.57491i	0.159257	+	0.152969i
$107$	−1.76697	+	6.10029i	−0.170820	+	0.589738i	0.828728	+	0.559652i	$0.189065\pi$
$107$	−1.76697	+	6.10029i	−0.170820	+	0.589738i	−0.999547	+	0.0300857i	$0.990422\pi$
$108$	−1.55068	−	0.125184i	−0.149214	−	0.0120458i
$109$	−5.43921	−	10.3635i	−0.520982	−	0.992647i	−0.993768	−	0.111470i	$-0.964444\pi$
$109$	−5.43921	−	10.3635i	−0.520982	−	0.992647i	0.472786	−	0.881177i	$-0.343248\pi$
$110$	−3.63048	+	3.48712i	−0.346153	+	0.332484i
$111$	4.29481	+	10.0803i	0.407646	+	0.956780i
$112$	−4.35681	+	1.65232i	−0.411680	+	0.156130i
$113$	8.37900	−	1.36172i	0.788230	−	0.128100i	0.247046	−	0.969004i	$-0.420540\pi$
$113$	8.37900	−	1.36172i	0.788230	−	0.128100i	0.541184	+	0.840904i	$0.317976\pi$
$114$	−1.26358	+	0.799040i	−0.118345	+	0.0748370i
$115$	10.8388	+	3.13950i	1.01072	+	0.292760i
$116$	0.952234	+	1.37955i	0.0884127	+	0.128088i
$117$	−2.42712	−	8.02208i	−0.224387	−	0.741641i
$118$	−5.02728	+	7.28327i	−0.462799	+	0.670480i
$119$	−22.2276	+	18.1483i	−2.03761	+	1.66365i
$120$	11.9146	+	14.5927i	1.08765	+	1.33213i
$121$	6.06194	−	4.55525i	0.551085	−	0.414114i
$122$	−7.14117	+	0.867095i	−0.646531	+	0.0785031i
$123$	−3.65864	+	10.9590i	−0.329889	+	0.988138i
$124$	−0.130994	+	1.62265i	−0.0117636	+	0.145718i
$125$	4.68795	+	5.29160i	0.419303	+	0.473295i
$126$	9.09503	+	5.75135i	0.810249	+	0.512371i
$127$	19.0118	+	8.10015i	1.68702	+	0.718772i	0.999969	−	0.00783618i	$-0.00249436\pi$
$127$	19.0118	+	8.10015i	1.68702	+	0.718772i	0.687052	+	0.726609i	$0.258905\pi$
$128$	−0.475973	+	2.92878i	−0.0420704	+	0.258870i
$129$	−14.7926	−	13.1051i	−1.30242	−	1.15384i
$130$	4.80796	−	8.56054i	0.421686	−	0.750809i
$131$	−4.83819	+	4.28626i	−0.422715	+	0.374493i	−0.847495	−	0.530804i	$-0.821890\pi$
$131$	−4.83819	+	4.28626i	−0.422715	+	0.374493i	0.424780	+	0.905297i	$0.360352\pi$
$132$	2.27556	+	3.59850i	0.198062	+	0.313209i
$133$	2.98400	−	0.240893i	0.258746	−	0.0208881i
$134$	1.94923	−	9.54798i	0.168388	−	0.824819i
$135$	−1.01479	+	4.11717i	−0.0873394	+	0.354350i
$136$	−2.98673	−	18.3781i	−0.256110	−	1.57591i
$137$	−2.24074	+	3.54344i	−0.191439	+	0.302736i	−0.927245	−	0.374456i	$-0.877829\pi$
$137$	−2.24074	+	3.54344i	−0.191439	+	0.302736i	0.735806	+	0.677193i	$0.236804\pi$
$138$	−4.45204	+	8.48266i	−0.378983	+	0.722092i
$139$	−4.05861	−	14.0119i	−0.344247	−	1.18848i	−0.926759	−	0.375656i	$-0.877417\pi$
$139$	−4.05861	−	14.0119i	−0.344247	−	1.18848i	0.582512	−	0.812822i	$-0.302070\pi$
$140$	−2.51211	−	12.3051i	−0.212312	−	1.03997i
$141$	−24.1711	−	0.974064i	−2.03558	−	0.0820310i
$142$	9.08054	+	4.76584i	0.762022	+	0.399940i
$143$	3.94059	−	5.37556i	0.329528	−	0.449527i
$144$	−2.07369	+	1.08836i	−0.172807	+	0.0906964i
$145$	4.12785	−	1.95869i	0.342799	−	0.162660i
$146$	0.571380	−	0.989660i	0.0472878	−	0.0819048i
$147$	−16.6027	−	28.7568i	−1.36937	−	2.37182i
$148$	3.90060	+	2.69239i	0.320627	+	0.221313i
$149$	−9.80623	−	13.0497i	−0.803357	−	1.06907i	−0.996135	−	0.0878321i	$-0.972006\pi$
$149$	−9.80623	−	13.0497i	−0.803357	−	1.06907i	0.192778	−	0.981242i	$-0.438250\pi$
$150$	4.80344	−	2.77327i	0.392199	−	0.226436i
$151$	−19.2288	−	2.33480i	−1.56482	−	0.190003i	−0.708221	−	0.705991i	$-0.750502\pi$
$151$	−19.2288	−	2.33480i	−1.56482	−	0.190003i	−0.856596	+	0.515988i	$0.827425\pi$
$152$	−0.832729	+	1.75494i	−0.0675433	+	0.142344i
$153$	−9.99081	+	10.4015i	−0.807709	+	0.840914i
$154$	0.688607	+	8.52993i	0.0554896	+	0.687362i
$155$	4.30827	+	1.06189i	0.346048	+	0.0852932i
$156$	−6.28066	−	5.43259i	−0.502855	−	0.434955i
$157$	−0.0509607	+	0.0125607i	−0.00406711	+	0.00100245i	−0.241349	−	0.970438i	$-0.577590\pi$
$157$	−0.0509607	+	0.0125607i	−0.00406711	+	0.00100245i	0.237282	+	0.971441i	$0.423744\pi$
$158$	−4.10484	−	12.2955i	−0.326563	−	0.978176i
$159$	−2.24686	−	4.73515i	−0.178187	−	0.375522i
$160$	12.8858	+	4.30192i	1.01871	+	0.340096i
$161$	15.7876	−	10.8974i	1.24424	−	0.858837i
$162$	−9.55855	−	4.53559i	−0.750991	−	0.356350i
$163$	19.6089	−	0.790210i	1.53588	−	0.0618940i	0.742181	−	0.670200i	$-0.233791\pi$
$163$	19.6089	−	0.790210i	1.53588	−	0.0618940i	0.793703	+	0.608305i	$0.208150\pi$
$164$	1.19600	+	4.85237i	0.0933921	+	0.378906i
$165$	10.6763	−	4.54873i	0.831145	−	0.354118i
$166$	−9.11219	−	1.48088i	−0.707243	−	0.114938i
$167$	0.286723	−	0.0585349i	0.0221873	−	0.00452957i	−0.188919	−	0.981993i	$-0.560498\pi$
$167$	0.286723	−	0.0585349i	0.0221873	−	0.00452957i	0.211107	+	0.977463i	$0.432293\pi$
$168$	32.0262			2.47087
$169$	−4.32024	+	12.2611i	−0.332326	+	0.943164i
$170$	−16.8955			−1.29582
$171$	1.47425	−	0.300969i	0.112738	−	0.0230157i
$172$	−8.43784	−	1.37128i	−0.643379	−	0.104559i
$173$	4.70721	−	2.00556i	0.357883	−	0.152480i	−0.205539	−	0.978649i	$-0.565895\pi$
$173$	4.70721	−	2.00556i	0.357883	−	0.152480i	0.563422	+	0.826169i	$0.309485\pi$
$174$	0.928280	+	3.76618i	0.0703727	+	0.285513i
$175$	−11.0976	+	0.447219i	−0.838902	+	0.0338066i
$176$	−1.68263	−	0.798416i	−0.126833	−	0.0601829i
$177$	16.7904	−	11.5896i	1.26204	−	0.871125i
$178$	7.96403	+	2.65878i	0.596929	+	0.199284i
$179$	−11.0979	−	23.3884i	−0.829498	−	1.74813i	−0.643294	−	0.765619i	$-0.722433\pi$
$179$	−11.0979	−	23.3884i	−0.829498	−	1.74813i	−0.186204	−	0.982511i	$-0.559619\pi$
$180$	−1.99886	−	5.98733i	−0.148986	−	0.446269i
$181$	−5.68738	+	1.40181i	−0.422739	+	0.104196i	−0.444946	−	0.895558i	$-0.646777\pi$
$181$	−5.68738	+	1.40181i	−0.422739	+	0.104196i	0.0222064	+	0.999753i	$0.492931\pi$
$182$	−6.10345	−	15.5352i	−0.452418	−	1.15155i
$183$	16.1018	+	3.96874i	1.19028	+	0.293378i
$184$	1.00159	+	12.4069i	0.0738381	+	0.914649i
$185$	8.94898	−	9.31688i	0.657942	−	0.684991i
$186$	−1.61489	+	3.40331i	−0.118410	+	0.249543i
$187$	−11.3859	−	1.38250i	−0.832622	−	0.101099i
$188$	−9.06202	+	5.23196i	−0.660916	+	0.381580i
$189$	4.33056	+	5.76292i	0.315002	+	0.419191i
$190$	1.45063	+	1.00130i	0.105240	+	0.0726420i
$191$	−5.32384	−	9.22117i	−0.385220	−	0.667220i	0.606580	−	0.795023i	$-0.292541\pi$
$191$	−5.32384	−	9.22117i	−0.385220	−	0.667220i	−0.991800	+	0.127802i	$0.959208\pi$
$192$	−8.09134	+	14.0146i	−0.583942	+	1.01142i
$193$	19.8496	−	9.41877i	1.42881	−	0.677978i	0.451985	−	0.892025i	$-0.350716\pi$
$193$	19.8496	−	9.41877i	1.42881	−	0.677978i	0.976823	+	0.214047i	$0.0686646\pi$
$194$	−10.0594	+	5.27956i	−0.722220	+	0.379050i
$195$	−17.3618	+	14.5220i	−1.24330	+	1.03994i
$196$	−12.7181	−	6.67496i	−0.908434	−	0.476783i
$197$	1.25244	+	0.0504715i	0.0892324	+	0.00359594i	0.0848420	−	0.996394i	$-0.472961\pi$
$197$	1.25244	+	0.0504715i	0.0892324	+	0.00359594i	0.00439043	+	0.999990i	$0.498602\pi$
$198$	0.860337	+	4.21421i	0.0611415	+	0.299491i
$199$	0.908855	+	3.13773i	0.0644270	+	0.222428i	0.986271	−	0.165132i	$-0.0528051\pi$
$199$	0.908855	+	3.13773i	0.0644270	+	0.222428i	−0.921844	+	0.387560i	$0.873318\pi$
$200$	3.34908	−	6.38114i	0.236816	−	0.451215i
$201$	−12.0069	+	18.9874i	−0.846904	+	1.33927i
$202$	2.01203	+	12.3805i	0.141566	+	0.871092i
$203$	1.85883	−	7.54157i	0.130464	−	0.529315i
$204$	−2.85836	+	14.0012i	−0.200125	+	0.980278i
$205$	13.5776	−	1.09610i	0.948301	−	0.0765548i
$206$	3.30437	+	5.22544i	0.230226	+	0.364074i
$207$	7.21690	−	6.39362i	0.501609	−	0.444387i
$208$	3.59218	+	0.540136i	0.249073	+	0.0374517i
$209$	0.895656	+	0.793482i	0.0619538	+	0.0548863i
$210$	4.66175	−	28.6849i	0.321691	−	1.97945i
$211$	−13.0527	−	5.56124i	−0.898586	−	0.382852i	−0.107249	−	0.994232i	$-0.534204\pi$
$211$	−13.0527	−	5.56124i	−0.898586	−	0.382852i	−0.791337	+	0.611380i	$0.790615\pi$
$212$	−1.91615	−	1.21170i	−0.131601	−	0.0832197i
$213$	−15.6773	−	17.6961i	−1.07419	−	1.21251i
$214$	−0.511525	+	6.33638i	−0.0349672	+	0.433146i
$215$	−7.37852	+	22.1014i	−0.503211	+	1.50730i
$216$	−4.64329	+	0.563797i	−0.315936	+	0.0383615i
$217$	6.03040	−	4.53155i	0.409370	−	0.307622i
$218$	−7.40919	−	9.07461i	−0.501814	−	0.614610i
$219$	−2.04066	+	1.66614i	−0.137895	+	0.112588i
$220$	2.85157	−	4.13121i	0.192252	−	0.278526i
$221$	22.0368	−	3.85014i	1.48235	−	0.258988i
$222$	6.23017	+	9.02595i	0.418141	+	0.605782i
$223$	−13.0737	−	3.78683i	−0.875477	−	0.253585i	−0.190092	−	0.981766i	$-0.560879\pi$
$223$	−13.0737	−	3.78683i	−0.875477	−	0.253585i	−0.685385	+	0.728181i	$0.740366\pi$
$224$	19.5192	−	12.3432i	1.30418	−	0.824714i
$225$	−5.50997	+	0.895457i	−0.367331	+	0.0596971i
$226$	7.94472	−	3.01304i	0.528475	−	0.200424i
$227$	8.12695	+	19.0747i	0.539405	+	1.26603i	0.937276	+	0.348588i	$0.113339\pi$
$227$	8.12695	+	19.0747i	0.539405	+	1.26603i	−0.397871	+	0.917441i	$0.630251\pi$
$228$	1.07519	−	1.03273i	0.0712061	−	0.0683944i
$229$	−1.37621	−	2.62215i	−0.0909427	−	0.173277i	0.835736	−	0.549132i	$-0.185041\pi$
$229$	−1.37621	−	2.62215i	−0.0909427	−	0.173277i	−0.926679	+	0.375855i	$0.877349\pi$
$230$	11.2583	+	0.908863i	0.742349	+	0.0599286i
$231$	5.48876	−	18.9494i	0.361134	−	1.24678i
$232$	3.63475	+	3.49122i	0.238633	+	0.229210i
$233$	−2.88916	+	7.61810i	−0.189275	+	0.499078i	−0.995740	−	0.0922040i	$-0.970609\pi$
$233$	−2.88916	+	7.61810i	−0.189275	+	0.499078i	0.806465	+	0.591282i	$0.201378\pi$
$234$	−3.98642	−	7.38138i	−0.260600	−	0.482536i
$235$	10.1137	+	26.6678i	0.659748	+	1.73961i
$236$	3.45910	−	8.11881i	0.225168	−	0.528489i
$237$	−1.20327	+	29.8589i	−0.0781609	+	1.93954i
$238$	−18.1653	+	22.2485i	−1.17748	+	1.44215i
$239$			9.31821i			0.602745i	0.953506	+	0.301373i	$0.0974448\pi$
$239$			9.31821i			0.602745i	−0.953506	+	0.301373i	$0.902555\pi$
$240$	4.89916	+	4.00004i	0.316239	+	0.258201i
$241$	−9.20579	+	2.66649i	−0.592997	+	0.171764i	−0.561129	−	0.827728i	$-0.689633\pi$
$241$	−9.20579	+	2.66649i	−0.592997	+	0.171764i	−0.0318682	+	0.999492i	$0.510146\pi$
$242$	5.03297	−	5.68105i	0.323532	−	0.365192i
$243$	13.6568	+	14.2182i	0.876084	+	0.912100i
$244$	6.80425	−	2.27159i	0.435597	−	0.145424i
$245$	−23.5188	+	31.2979i	−1.50256	+	1.99955i
$246$	−1.39393	+	11.4801i	−0.0888739	+	0.731942i
$247$	−2.12024	−	0.975425i	−0.134907	−	0.0620648i
$248$	0.589965	+	4.85880i	0.0374628	+	0.308534i
$249$	18.4310	+	10.6411i	1.16802	+	0.674354i
$250$	5.65695	+	4.25092i	0.357777	+	0.268852i
$251$	−0.254216	−	6.30831i	−0.0160460	−	0.398177i	−0.987177	−	0.159630i	$-0.948970\pi$
$251$	−0.254216	−	6.30831i	−0.0160460	−	0.398177i	0.971131	−	0.238547i	$-0.0766711\pi$
$252$	−10.0334	−	3.80516i	−0.632044	−	0.239703i
$253$	7.51264	+	1.53372i	0.472316	+	0.0964239i
$254$	20.2667	+	4.13749i	1.27165	+	0.259609i
$255$	36.4186	+	13.8118i	2.28062	+	0.864926i
$256$	0.684367	+	16.9824i	0.0427729	+	1.06140i
$257$	3.32439	+	2.49812i	0.207370	+	0.155828i	0.699353	−	0.714776i	$-0.253472\pi$
$257$	3.32439	+	2.49812i	0.207370	+	0.155828i	−0.491983	+	0.870605i	$0.663728\pi$
$258$	−17.1311	−	9.89062i	−1.06653	−	0.615763i
$259$	−2.64717	−	21.8014i	−0.164487	−	1.35467i
$260$	−2.99005	+	9.32300i	−0.185435	+	0.578188i
$261$	0.470560	−	3.87541i	0.0291269	−	0.239882i
$262$	−3.88669	+	5.17224i	−0.240120	+	0.319542i
$263$	8.12057	−	2.71104i	0.500736	−	0.167170i	−0.0550698	−	0.998483i	$-0.517538\pi$
$263$	8.12057	−	2.71104i	0.500736	−	0.167170i	0.555805	+	0.831312i	$0.312410\pi$
$264$	8.86746	+	9.23200i	0.545754	+	0.568190i
$265$	−4.09771	+	4.62536i	−0.251720	+	0.284134i
$266$	2.87820	−	0.833682i	0.176474	−	0.0511163i
$267$	−14.9932	−	12.2415i	−0.917566	−	0.749170i
$268$			9.71755i			0.593594i
$269$	−4.66846	+	5.71783i	−0.284641	+	0.348622i	−0.897058	−	0.441913i	$-0.854300\pi$
$269$	−4.66846	+	5.71783i	−0.284641	+	0.348622i	0.612417	+	0.790535i	$0.290197\pi$
$270$	−0.170903	+	4.24092i	−0.0104008	+	0.258094i
$271$	9.26947	−	21.7562i	0.563080	−	1.32160i	−0.358543	−	0.933513i	$-0.616726\pi$
$271$	9.26947	−	21.7562i	0.563080	−	1.32160i	0.921624	−	0.388085i	$-0.126863\pi$
$272$	−2.21662	−	5.84475i	−0.134402	−	0.354390i
$273$	0.456390	+	38.4760i	0.0276220	+	2.32867i
$274$	−1.48806	+	3.92370i	−0.0898973	+	0.237040i
$275$	−3.20165	−	3.07522i	−0.193067	−	0.185443i
$276$	2.65784	−	9.17591i	0.159983	−	0.552325i
$277$	13.0730	+	1.05536i	0.785479	+	0.0634104i	0.466697	−	0.884418i	$-0.345444\pi$
$277$	13.0730	+	1.05536i	0.785479	+	0.0634104i	0.318782	+	0.947828i	$0.396726\pi$
$278$	−6.78569	−	12.9290i	−0.406978	−	0.775433i
$279$	2.73428	−	2.62631i	0.163697	−	0.157233i
$280$	−14.8004	−	34.7377i	−0.884491	−	2.07598i
$281$	−12.5265	+	4.75066i	−0.747266	+	0.283401i	−0.698696	−	0.715419i	$-0.746236\pi$
$281$	−12.5265	+	4.75066i	−0.747266	+	0.283401i	−0.0485706	+	0.998820i	$0.515467\pi$
$282$	−23.8999	+	3.88410i	−1.42322	+	0.231295i
$283$	−6.45136	+	4.07959i	−0.383493	+	0.242507i	−0.712277	−	0.701899i	$-0.752336\pi$
$283$	−6.45136	+	4.07959i	−0.383493	+	0.242507i	0.328783	+	0.944405i	$0.393361\pi$
$284$	−9.82266	−	2.84517i	−0.582868	−	0.168830i
$285$	−2.30833	−	3.34420i	−0.136734	−	0.198093i
$286$	2.78831	−	6.06082i	0.164876	−	0.358384i
$287$	13.1547	−	19.0579i	0.776498	−	1.12495i
$288$	8.99113	−	7.34103i	0.529808	−	0.432574i
$289$	−13.5947	−	16.6505i	−0.799691	−	0.979444i
$290$	3.65606	−	2.74735i	0.214691	−	0.161330i
$291$	25.9992	−	3.15687i	1.52410	−	0.185059i
$292$	−0.360860	+	1.08091i	−0.0211177	+	0.0632553i
$293$	0.603024	−	7.46979i	0.0352290	−	0.436390i	−0.954968	−	0.296710i	$-0.904111\pi$
$293$	0.603024	−	7.46979i	0.0352290	−	0.436390i	0.990197	−	0.139680i	$-0.0446073\pi$
$294$	−22.0399	−	24.8779i	−1.28539	−	1.45091i
$295$	−20.3302	−	12.8560i	−1.18367	−	0.748508i
$296$	13.1096	+	5.58548i	0.761980	+	0.324649i
$297$	−0.462193	+	2.84399i	−0.0268192	+	0.165025i
$298$	−12.2298	−	10.8346i	−0.708452	−	0.627633i
$299$	−14.8913	+	1.38011i	−0.861185	+	0.0798136i
$300$	−4.13998	+	3.66771i	−0.239022	+	0.211755i
$301$	21.1707	+	33.4787i	1.22026	+	1.92968i
$302$	−19.3253	+	1.56010i	−1.11205	+	0.0897736i
$303$	5.78389	−	28.3314i	0.332276	−	1.62760i
$304$	−0.156068	+	0.633193i	−0.00895112	+	0.0363161i
$305$	−3.13642	−	19.2992i	−0.179591	−	1.10507i
$306$	−7.71555	+	12.2012i	−0.441068	+	0.697494i
$307$	−7.55764	+	14.3999i	−0.431337	+	0.821845i	−1.00000		0.000726368i	$-0.999769\pi$
$307$	−7.55764	+	14.3999i	−0.431337	+	0.821845i	0.568662	+	0.822571i	$0.307461\pi$
$308$	−2.37421	−	8.19673i	−0.135283	−	0.467052i
$309$	−2.85094	−	13.9648i	−0.162184	−	0.794432i
$310$	4.43776	+	0.178835i	0.252048	+	0.0101572i
$311$	−7.92461	−	4.15916i	−0.449363	−	0.235844i	0.224831	−	0.974398i	$-0.427817\pi$
$311$	−7.92461	−	4.15916i	−0.449363	−	0.235844i	−0.674195	+	0.738554i	$0.735509\pi$
$312$	−21.7687	−	12.2262i	−1.23241	−	0.692174i
$313$	−19.3150	+	10.1373i	−1.09175	+	0.572993i	−0.911780	−	0.410680i	$-0.865292\pi$
$313$	−19.3150	+	10.1373i	−1.09175	+	0.572993i	−0.179967	+	0.983673i	$0.557599\pi$
$314$	−0.0474628	+	0.0225214i	−0.00267848	+	0.00127095i
$315$	−14.6242	+	25.3298i	−0.823979	+	1.42717i
$316$	6.46309	+	11.1944i	0.363577	+	0.629735i
$317$	−11.8697	−	8.19307i	−0.666669	−	0.460168i	0.186049	−	0.982541i	$-0.440432\pi$
$317$	−11.8697	−	8.19307i	−0.666669	−	0.460168i	−0.852718	+	0.522372i	$0.825047\pi$
$318$	−3.15155	−	4.19395i	−0.176730	−	0.235185i
$319$	2.68864	−	1.55229i	0.150535	−	0.0869114i
$320$	18.9404	+	2.29979i	1.05880	+	0.128562i
$321$	6.28249	−	13.2401i	0.350654	−	0.738988i
$322$	13.3013	−	13.8481i	0.741250	−	0.771723i
$323$	0.323163	+	4.00310i	0.0179813	+	0.222738i
$324$	10.2438	+	2.52486i	0.569098	+	0.140270i
$325$	7.71397	+	3.93262i	0.427894	+	0.218143i
$326$	19.0724	−	4.70091i	1.05632	−	0.260360i
$327$	8.55236	+	25.6175i	0.472947	+	1.41665i
$328$	6.44136	+	13.5749i	0.355665	+	0.749548i
$329$	45.9908	+	15.3540i	2.53556	+	0.846493i
$330$	9.55957	−	6.59850i	0.526237	−	0.363235i
$331$	22.3739	+	10.6166i	1.22978	+	0.583538i	0.928973	−	0.370146i	$-0.120692\pi$
$331$	22.3739	+	10.6166i	1.22978	+	0.583538i	0.300808	+	0.953685i	$0.402744\pi$
$332$	9.19835	−	0.370681i	0.504825	−	0.0203438i
$333$	−2.64156	−	10.7172i	−0.144757	−	0.587301i
$334$	0.269472	−	0.114811i	0.0147449	−	0.00628220i
$335$	26.1438	+	4.24879i	1.42839	+	0.232136i
$336$	10.5347	−	2.15068i	0.574717	−	0.117329i
$337$	−31.5549			−1.71891			−0.859453	−	0.511215i	$-0.829195\pi$
$337$	−31.5549			−1.71891			−0.859453	+	0.511215i	$0.829195\pi$
$338$	−1.78206	+	12.8896i	−0.0969313	+	0.701100i
$339$	−19.5882			−1.06388
$340$	16.5075	−	3.37004i	0.895247	−	0.182766i
$341$	2.97599	+	0.483645i	0.161159	+	0.0261909i
$342$	1.38555	−	0.590326i	0.0749218	−	0.0319212i
$343$	8.17974	+	33.1865i	0.441664	+	1.79190i
$344$	−25.6809	+	1.03491i	−1.38462	+	0.0557984i
$345$	−23.5245	−	11.1625i	−1.26652	−	0.600971i
$346$	4.21486	−	2.90931i	0.226592	−	0.156405i
$347$	−11.7881	−	3.93545i	−0.632818	−	0.211266i	−0.0178790	−	0.999840i	$-0.505691\pi$
$347$	−11.7881	−	3.93545i	−0.632818	−	0.211266i	−0.614939	+	0.788574i	$0.710820\pi$
$348$	−1.65818	−	3.49455i	−0.0888880	−	0.187327i
$349$	−2.76087	−	8.26982i	−0.147786	−	0.442674i	0.848458	−	0.529263i	$-0.177531\pi$
$349$	−2.76087	−	8.26982i	−0.147786	−	0.442674i	−0.996244	+	0.0865893i	$0.972403\pi$
$350$	−10.7940	+	2.66048i	−0.576964	+	0.142209i
$351$	−0.743511	−	5.57037i	−0.0396857	−	0.297325i
$352$	8.96260	+	2.20908i	0.477708	+	0.117744i
$353$	−0.573595	−	7.10525i	−0.0305294	−	0.378174i	−0.993923	−	0.110082i	$-0.964889\pi$
$353$	−0.573595	−	7.10525i	−0.0305294	−	0.378174i	0.963393	−	0.268093i	$-0.0863933\pi$
$354$	14.1461	−	14.7276i	0.751856	−	0.782765i
$355$	−11.9493	+	25.1826i	−0.634203	+	1.33656i
$356$	−8.31150	−	1.00920i	−0.440509	−	0.0534874i
$357$	57.3435	−	33.1073i	3.03494	−	1.75222i
$358$	−15.5665	−	20.7152i	−0.822715	−	1.09483i
$359$	−6.48240	−	4.47448i	−0.342128	−	0.236154i	0.384594	−	0.923086i	$-0.374342\pi$
$359$	−6.48240	−	4.47448i	−0.342128	−	0.236154i	−0.726722	+	0.686932i	$0.758957\pi$
$360$	−9.48899	−	16.4354i	−0.500114	−	0.866222i
$361$	−9.29051	+	16.0916i	−0.488974	+	0.846928i
$362$	−5.29700	+	2.51346i	−0.278404	+	0.132104i
$363$	−15.4929	+	8.13128i	−0.813164	+	0.426781i
$364$	9.06203	+	13.9611i	0.474979	+	0.731760i
$365$	2.75026	+	1.44345i	0.143955	+	0.0755536i
$366$	16.5858	+	0.668384i	0.866952	+	0.0349370i
$367$	−5.94407	−	29.1160i	−0.310278	−	1.51984i	−0.773613	−	0.633659i	$-0.781552\pi$
$367$	−5.94407	−	29.1160i	−0.310278	−	1.51984i	0.463335	−	0.886183i	$-0.346653\pi$
$368$	1.16264	+	4.01389i	0.0606066	+	0.209238i
$369$	5.40885	−	10.3057i	0.281573	−	0.536493i
$370$	6.91098	−	10.9288i	0.359285	−	0.568164i
$371$	1.68512	+	10.3690i	0.0874873	+	0.538331i
$372$	0.898975	−	3.64729i	0.0466097	−	0.189103i
$373$	−1.52907	+	7.48990i	−0.0791724	+	0.387812i	−0.999998	−	0.00216325i	$-0.999311\pi$
$373$	−1.52907	+	7.48990i	−0.0791724	+	0.387812i	0.920825	+	0.389976i	$0.127517\pi$
$374$	−11.4431	+	0.923780i	−0.591707	+	0.0477675i
$375$	−8.71865	−	13.7874i	−0.450229	−	0.711980i
$376$	−23.5485	+	20.8622i	−1.21442	+	1.07588i
$377$	−4.14253	+	4.41651i	−0.213351	+	0.227462i
$378$	5.40082	+	4.78471i	0.277788	+	0.246099i
$379$	0.504280	−	3.10296i	0.0259031	−	0.159388i	−0.970876	−	0.239582i	$-0.922990\pi$
$379$	0.504280	−	3.10296i	0.0259031	−	0.159388i	0.996779	+	0.0801935i	$0.0255538\pi$
$380$	−1.61705	−	0.688961i	−0.0829529	−	0.0353429i
$381$	−40.3032	−	25.4862i	−2.06479	−	1.30570i
$382$	−7.06734	−	7.97737i	−0.361596	−	0.408158i
$383$	2.60412	−	32.2578i	0.133064	−	1.64830i	−0.494097	−	0.869407i	$-0.664501\pi$
$383$	2.60412	−	32.2578i	0.133064	−	1.64830i	0.627161	−	0.778890i	$-0.284217\pi$
$384$	2.16816	−	6.49444i	0.110644	−	0.331418i
$385$	−23.0903	+	2.80367i	−1.17679	+	0.142888i
$386$	17.5810	−	13.2112i	0.894847	−	0.672434i
$387$	12.5911	+	15.4213i	0.640043	+	0.783910i
$388$	8.77531	−	7.16482i	0.445499	−	0.363739i
$389$	1.86824	−	2.70661i	0.0947236	−	0.137231i	−0.772757	−	0.634702i	$-0.781123\pi$
$389$	1.86824	−	2.70661i	0.0947236	−	0.137231i	0.867480	+	0.497472i	$0.165738\pi$
$390$	−14.1193	+	17.7179i	−0.714960	+	0.897182i
$391$	14.6191	+	21.1794i	0.739320	+	1.07109i
$392$	−41.4792	−	12.0146i	−2.09502	−	0.606829i
$393$	12.6061	−	7.97160i	0.635892	−	0.402114i
$394$	1.23838	−	0.201256i	0.0623887	−	0.0101391i
$395$	32.9430	−	12.4936i	1.65754	−	0.628622i
$396$	−1.68117	−	3.94584i	−0.0844818	−	0.198286i
$397$	4.50554	−	4.32763i	0.226127	−	0.217198i	−0.571096	−	0.820884i	$-0.693481\pi$
$397$	4.50554	−	4.32763i	0.226127	−	0.217198i	0.797222	+	0.603686i	$0.206302\pi$
$398$	1.51954	+	2.89523i	0.0761675	+	0.145125i
$399$	−6.88556	−	0.555860i	−0.344709	−	0.0278278i
$400$	0.673133	−	2.32392i	0.0336566	−	0.116196i
$401$	−5.66485	−	5.44116i	−0.282889	−	0.271718i	0.537827	−	0.843055i	$-0.319245\pi$
$401$	−5.66485	−	5.44116i	−0.282889	−	0.271718i	−0.820716	+	0.571337i	$0.806425\pi$
$402$	−7.97376	+	21.0251i	−0.397695	+	1.04864i
$403$	−5.82891	+	0.778020i	−0.290359	+	0.0387559i
$404$	−4.43531	−	11.6950i	−0.220665	−	0.581846i
$405$	11.2717	−	26.4556i	0.560095	−	1.31459i
$406$	0.313050	−	7.76824i	0.0155364	−	0.385532i
$407$	5.55161	−	6.79949i	0.275183	−	0.337038i
$408$			42.9638i			2.12702i
$409$	20.0208	+	16.3465i	0.989965	+	0.808282i	0.981457	−	0.191682i	$-0.0613943\pi$
$409$	20.0208	+	16.3465i	0.989965	+	0.808282i	0.00850810	+	0.999964i	$0.497292\pi$
$410$	13.0962	−	3.79337i	0.646776	−	0.187341i
$411$	6.41512	−	7.24118i	0.316435	−	0.357181i
$412$	−4.27079	−	4.44636i	−0.210407	−	0.219056i
$413$	−38.7874	+	12.9491i	−1.90860	+	0.637186i
$414$	5.79759	−	7.71519i	0.284936	−	0.379181i
$415$	3.02451	−	24.9091i	0.148467	−	1.22274i
$416$	−17.9796	+	0.938271i	−0.881523	+	0.0460025i
$417$	4.05745	+	33.4161i	0.198694	+	1.63639i
$418$	1.03724	+	0.598852i	0.0507332	+	0.0292908i
$419$	−1.71259	−	1.28693i	−0.0836657	−	0.0628707i	0.558086	−	0.829783i	$-0.311536\pi$
$419$	−1.71259	−	1.28693i	−0.0836657	−	0.0628707i	−0.641752	+	0.766912i	$0.721792\pi$
$420$	1.16689	+	28.9561i	0.0569385	+	1.41291i
$421$	5.35177	+	2.02966i	0.260829	+	0.0989195i	0.481553	−	0.876417i	$-0.340073\pi$
$421$	5.35177	+	2.02966i	0.260829	+	0.0989195i	−0.220724	+	0.975336i	$0.570842\pi$
$422$	−13.9143	−	2.84063i	−0.677340	−	0.138280i
$423$	23.8769	+	4.87450i	1.16093	+	0.237006i
$424$	−6.37330	−	2.41707i	−0.309515	−	0.117384i
$425$	−0.599954	−	14.8877i	−0.0291020	−	0.722159i
$426$	−18.9179	−	14.2159i	−0.916575	−	0.688761i
$427$	−28.7859	−	16.6195i	−1.39305	−	0.804276i
$428$	−0.764099	−	6.29292i	−0.0369341	−	0.304180i
$429$	−10.9649	+	10.7848i	−0.529390	+	0.520697i
$430$	−2.81119	+	23.1523i	−0.135568	+	1.11650i
$431$	−22.7008	+	30.2093i	−1.09346	+	1.45513i	−0.215436	+	0.976518i	$0.569117\pi$
$431$	−22.7008	+	30.2093i	−1.09346	+	1.45513i	−0.878025	+	0.478615i	$0.841139\pi$
$432$	−1.48951	+	0.497271i	−0.0716640	+	0.0239250i
$433$	−4.84152	−	5.04056i	−0.232669	−	0.242234i	0.594625	−	0.804003i	$-0.297300\pi$
$433$	−4.84152	−	5.04056i	−0.232669	−	0.242234i	−0.827294	+	0.561769i	$0.810121\pi$
$434$	5.00679	−	5.65149i	0.240333	−	0.271280i
$435$	−10.1266	+	2.93322i	−0.485535	+	0.140637i
$436$	9.04913	+	7.38839i	0.433375	+	0.353840i
$437$		−	2.68484i		−	0.128434i
$438$	−1.66770	+	2.04257i	−0.0796860	+	0.0975976i
$439$	−0.537400	+	13.3354i	−0.0256487	+	0.636465i	0.934333	+	0.356402i	$0.115997\pi$
$439$	−0.537400	+	13.3354i	−0.0256487	+	0.636465i	−0.959981	+	0.280064i	$0.909644\pi$
$440$	5.91569	−	13.8846i	0.282020	−	0.661924i
$441$	11.8617	+	31.2768i	0.564845	+	1.48937i
$442$	20.8408	−	8.18790i	0.991295	−	0.389459i
$443$	5.85153	−	15.4292i	0.278015	−	0.733064i	−0.721173	−	0.692755i	$-0.756397\pi$
$443$	5.85153	−	15.4292i	0.278015	−	0.733064i	0.999187	−	0.0403089i	$-0.0128342\pi$
$444$	−7.88747	−	7.57602i	−0.374323	−	0.359542i
$445$	−6.34914	+	21.9198i	−0.300978	+	1.03910i
$446$	−13.5796	−	1.09626i	−0.643013	−	0.0519094i
$447$	17.5045	+	33.3520i	0.827932	+	1.57749i
$448$	23.3924	−	22.4687i	1.10519	−	1.06155i
$449$	−7.03541	−	16.5127i	−0.332021	−	0.779283i	−0.999402	−	0.0345663i	$-0.988995\pi$
$449$	−7.03541	−	16.5127i	−0.332021	−	0.779283i	0.667381	−	0.744716i	$-0.267415\pi$
$450$	−5.22439	+	1.98135i	−0.246280	+	0.0934017i
$451$	9.13600	−	1.48474i	0.430197	−	0.0699139i
$452$	−7.16131	+	4.52854i	−0.336840	+	0.213005i
$453$	42.9315	+	12.4353i	2.01710	+	0.584260i
$454$	11.7892	+	17.0796i	0.553293	+	0.801583i
$455$	41.5227	−	18.2761i	1.94661	−	0.856795i
$456$	2.54622	−	3.68884i	0.119238	−	0.172746i
$457$	12.1013	−	9.88042i	0.566076	−	0.462187i	−0.305675	−	0.952136i	$-0.598882\pi$
$457$	12.1013	−	9.88042i	0.566076	−	0.462187i	0.871751	+	0.489949i	$0.162985\pi$
$458$	−1.87465	−	2.29603i	−0.0875967	−	0.107287i
$459$	−7.73107	+	5.80953i	−0.360856	+	0.271165i
$460$	−11.1811	+	1.35763i	−0.521320	+	0.0632997i
$461$	2.63888	−	7.90442i	0.122905	−	0.368145i	−0.869052	−	0.494721i	$-0.835270\pi$
$461$	2.63888	−	7.90442i	0.122905	−	0.368145i	0.991957	+	0.126575i	$0.0403986\pi$
$462$	1.58896	−	19.6828i	0.0739250	−	0.915725i
$463$	10.3782	+	11.7145i	0.482315	+	0.544421i	0.938416	−	0.345507i	$-0.112293\pi$
$463$	10.3782	+	11.7145i	0.482315	+	0.544421i	−0.456101	+	0.889928i	$0.650755\pi$
$464$	1.43007	+	0.904320i	0.0663893	+	0.0419820i
$465$	−9.41950	−	4.01327i	−0.436819	−	0.186111i
$466$	−1.30818	+	8.04958i	−0.0606005	+	0.372890i
$467$	10.0455	+	8.89954i	0.464850	+	0.411822i	0.862768	−	0.505600i	$-0.168729\pi$
$467$	10.0455	+	8.89954i	0.464850	+	0.411822i	−0.397918	+	0.917421i	$0.630267\pi$
$468$	5.36721	+	6.41675i	0.248099	+	0.296614i
$469$	33.7037	−	29.8589i	1.55629	−	1.37875i
$470$	15.2579	+	24.1284i	0.703793	+	1.11296i
$471$	0.120718	−	0.00974537i	0.00556240	−	0.000449043i
$472$	5.30727	−	25.9967i	0.244287	−	1.19660i
$473$	−3.78895	+	15.3724i	−0.174216	+	0.706823i
$474$	4.79808	+	29.5238i	0.220383	+	1.35607i
$475$	−0.830799	+	1.31380i	−0.0381197	+	0.0602814i
$476$	13.3105	−	25.3610i	0.610084	−	1.16242i
$477$	1.46895	+	5.07142i	0.0672588	+	0.232204i
$478$	1.86563	+	9.13845i	0.0853318	+	0.417983i
$479$	−3.51246	−	0.141547i	−0.160488	−	0.00646746i	−0.0401083	−	0.999195i	$-0.512770\pi$
$479$	−3.51246	−	0.141547i	−0.160488	−	0.00646746i	−0.120380	+	0.992728i	$0.538411\pi$
$480$	−27.7565	−	14.5678i	−1.26691	−	0.664924i
$481$	−6.52353	+	15.8294i	−0.297447	+	0.721756i
$482$	−8.49433	+	4.45817i	−0.386906	+	0.203064i
$483$	−39.9918	+	18.9763i	−1.81969	+	0.863453i
$484$	−3.78425	+	6.55451i	−0.172011	+	0.297932i
$485$	−15.4392	−	26.7415i	−0.701059	−	1.21427i
$486$	16.2400	+	11.2097i	0.736662	+	0.508481i
$487$	−4.85287	−	6.45800i	−0.219905	−	0.292640i	0.675986	−	0.736914i	$-0.263718\pi$
$487$	−4.85287	−	6.45800i	−0.219905	−	0.292640i	−0.895891	+	0.444274i	$0.853462\pi$
$488$	18.6779	−	10.7837i	0.845509	−	0.488155i
$489$	−44.9539	−	5.45839i	−2.03288	−	0.246837i
$490$	−16.7989	+	35.4029i	−0.758895	+	1.59934i
$491$	9.95109	−	10.3602i	0.449086	−	0.467548i	−0.457720	−	0.889097i	$-0.651334\pi$
$491$	9.95109	−	10.3602i	0.449086	−	0.467548i	0.906806	+	0.421548i	$0.138513\pi$
$492$	−0.927933	−	11.4945i	−0.0418345	−	0.518213i
$493$	10.1172	+	2.49366i	0.455654	+	0.112309i
$494$	−2.27463	−	0.532109i	−0.102340	−	0.0239407i
$495$	−11.3508	+	2.79773i	−0.510183	+	0.125749i
$496$	0.520351	+	1.55864i	0.0233645	+	0.0699851i
$497$	20.3138	+	42.8105i	0.911201	+	1.92031i
$498$	20.2059	+	6.74572i	0.905448	+	0.302283i
$499$	8.72501	−	6.02244i	0.390585	−	0.269602i	−0.356546	−	0.934278i	$-0.616046\pi$
$499$	8.72501	−	6.02244i	0.390585	−	0.269602i	0.747132	+	0.664676i	$0.231430\pi$
$500$	−6.37497	−	3.02496i	−0.285097	−	0.135280i
$501$	−0.674711	+	0.0271899i	−0.0301438	+	0.00121476i
$502$	−1.51232	−	6.13572i	−0.0674981	−	0.273850i
$503$	16.4174	−	6.99481i	0.732016	−	0.311883i	0.00639710	−	0.999980i	$-0.497964\pi$
$503$	16.4174	−	6.99481i	0.732016	−	0.311883i	0.725619	+	0.688097i	$0.241553\pi$
$504$	−31.8448	−	5.17529i	−1.41848	−	0.230526i
$505$	−33.4030	+	6.81928i	−1.48642	+	0.303454i
$506$	7.67478			0.341185
$507$	14.3783	−	26.3270i	0.638562	−	1.16922i
$508$	−20.6267			−0.915161
$509$	10.5116	−	2.14596i	0.465919	−	0.0951181i	0.0386700	−	0.999252i	$-0.487688\pi$
$509$	10.5116	−	2.14596i	0.465919	−	0.0951181i	0.427249	+	0.904134i	$0.359483\pi$
$510$	38.4813	+	6.25383i	1.70398	+	0.276924i
$511$	4.85775	−	2.06969i	0.214894	−	0.0915578i
$512$	2.65106	+	10.7558i	0.117162	+	0.475343i
$513$	1.00808	−	0.0406244i	0.0445080	−	0.00179361i
$514$	3.76041	+	1.78434i	0.165865	+	0.0787038i
$515$	−13.8297	+	9.54594i	−0.609408	+	0.420644i
$516$	18.7105	+	6.24650i	0.823686	+	0.274987i
$517$	8.30800	+	17.5087i	0.365385	+	0.770033i
$518$	−6.96103	−	20.8508i	−0.305850	−	0.916133i
$519$	−11.4636	+	2.82551i	−0.503194	+	0.124026i
$520$	−3.20134	+	29.2619i	−0.140388	+	1.28322i
$521$	−25.3544	−	6.24929i	−1.11079	−	0.273786i	−0.359101	−	0.933299i	$-0.616917\pi$
$521$	−25.3544	−	6.24929i	−1.11079	−	0.273786i	−0.751694	+	0.659513i	$0.770763\pi$
$522$	−0.314425	−	3.89486i	−0.0137620	−	0.170473i
$523$	14.8998	−	15.5123i	0.651523	−	0.678307i	−0.310720	−	0.950502i	$-0.600570\pi$
$523$	14.8998	−	15.5123i	0.651523	−	0.678307i	0.962242	+	0.272195i	$0.0877495\pi$
$524$	2.76577	−	5.82874i	0.120823	−	0.254630i
$525$	25.4416	+	3.08918i	1.11036	+	0.134823i
$526$	7.42112	−	4.28459i	0.323576	−	0.186817i
$527$	6.07917	+	8.08990i	0.264813	+	0.352402i
$528$	3.53684	+	2.44130i	0.153921	+	0.106244i
$529$	2.89788	+	5.01928i	0.125995	+	0.218230i
$530$	−3.09260	+	5.35654i	−0.134334	+	0.232673i
$531$	−18.5681	+	8.81068i	−0.805788	+	0.382351i
$532$	−2.64583	+	1.38864i	−0.114711	+	0.0602051i
$533$	−16.2170	+	7.93205i	−0.702435	+	0.343575i
$534$	−17.1548	−	9.00355i	−0.742362	−	0.389622i
$535$	−17.2644	−	0.695731i	−0.746405	−	0.0300791i
$536$	5.84405	+	28.6260i	0.252424	+	1.23646i
$537$	16.6196	+	57.3776i	0.717189	+	2.47603i
$538$	−3.43362	+	6.54221i	−0.148034	+	0.282055i
$539$	−14.2177	+	22.4835i	−0.612401	+	0.968435i
$540$	−0.678932	−	4.17764i	−0.0292166	−	0.179777i
$541$	−0.145665	+	0.590987i	−0.00626263	+	0.0254085i	−0.973990	−	0.226591i	$-0.927242\pi$
$541$	−0.145665	+	0.590987i	−0.00626263	+	0.0254085i	0.967727	+	0.251999i	$0.0810881\pi$
$542$	4.73476	−	23.1924i	0.203375	−	0.996199i
$543$	13.4725	−	1.08761i	0.578161	−	0.0466740i
$544$	16.5586	+	26.1854i	0.709945	+	1.12269i
$545$	23.8341	−	21.1151i	1.02094	−	0.904473i
$546$	8.15098	+	37.6423i	0.348830	+	1.61094i
$547$	10.2028	+	9.03892i	0.436241	+	0.386476i	0.852463	−	0.522787i	$-0.175108\pi$
$547$	10.2028	+	9.03892i	0.436241	+	0.386476i	−0.416222	+	0.909263i	$0.636646\pi$
$548$	0.671260	−	4.13043i	0.0286748	−	0.176443i
$549$	−15.3693	−	6.54824i	−0.655945	−	0.279472i
$550$	−3.75558	−	2.37489i	−0.160139	−	0.101265i
$551$	−0.720868	−	0.813692i	−0.0307100	−	0.0346644i
$552$	2.31116	−	28.6289i	0.0983695	−	1.21853i
$553$	18.9669	−	56.8129i	0.806557	−	2.41593i
$554$	13.0321	−	1.58238i	0.553680	−	0.0672289i
$555$	−23.8309	+	17.9078i	−1.01157	+	0.760143i
$556$	9.20876	+	11.2787i	0.390539	+	0.478323i
$557$	−23.8016	+	19.4334i	−1.00850	+	0.823419i	−0.984338	−	0.176289i	$-0.943591\pi$
$557$	−23.8016	+	19.4334i	−1.00850	+	0.823419i	−0.0241665	+	0.999708i	$0.507693\pi$
$558$	2.15571	−	3.12308i	0.0912584	−	0.132211i
$559$	−1.60929	−	30.8381i	−0.0680659	−	1.30431i
$560$	−7.20122	−	10.4328i	−0.304307	−	0.440865i
$561$	25.4210	+	7.36329i	1.07328	+	0.310878i
$562$	−11.3337	+	7.16697i	−0.478082	+	0.302321i
$563$	6.43685	−	1.04609i	0.271281	−	0.0440874i	−0.0232490	−	0.999730i	$-0.507401\pi$
$563$	6.43685	−	1.04609i	0.271281	−	0.0440874i	0.294530	+	0.955642i	$0.404837\pi$
$564$	22.5764	−	8.56209i	0.950636	−	0.360529i
$565$	9.05233	+	21.2466i	0.380835	+	0.893852i
$566$	−5.51011	+	5.29254i	−0.231607	+	0.222462i
$567$	−22.7187	−	43.2869i	−0.954096	−	1.81788i
$568$	−30.6467	−	2.47406i	−1.28591	−	0.103809i
$569$	9.13671	−	31.5436i	0.383031	−	1.32238i	−0.505209	−	0.862997i	$-0.668585\pi$
$569$	9.13671	−	31.5436i	0.383031	−	1.32238i	0.888240	−	0.459379i	$-0.151928\pi$
$570$	−2.93335	−	2.81752i	−0.122865	−	0.118013i
$571$	−4.53435	+	11.9561i	−0.189756	+	0.500347i	−0.995805	−	0.0915030i	$-0.970833\pi$
$571$	−4.53435	+	11.9561i	−0.189756	+	0.500347i	0.806048	+	0.591850i	$0.201602\pi$
$572$	−1.51537	+	6.47782i	−0.0633609	+	0.270851i
$573$	8.71246	+	22.9729i	0.363968	+	0.959705i
$574$	9.08530	−	21.3240i	0.379213	−	0.890045i
$575$	−0.401079	+	9.95268i	−0.0167262	+	0.415055i
$576$	10.3102	−	12.6277i	0.429592	−	0.526155i
$577$		−	46.4625i		−	1.93426i	−0.254282	−	0.967130i	$-0.581839\pi$
$577$		−	46.4625i		−	1.93426i	0.254282	−	0.967130i	$-0.418161\pi$
$578$	−16.6661	−	13.6075i	−0.693220	−	0.565997i
$579$	−48.6961	+	14.1050i	−2.02374	+	0.586184i
$580$	−3.02412	+	3.41352i	−0.125570	+	0.141739i
$581$	−29.5492	−	30.7640i	−1.22591	−	1.27630i
$582$	24.8656	−	8.30134i	1.03071	−	0.344102i
$583$	−2.52243	+	3.35674i	−0.104468	+	0.139022i
$584$	−0.412976	+	3.40116i	−0.0170891	+	0.140741i
$585$	19.6101	−	11.6342i	0.810780	−	0.481015i
$586$	−0.904158	−	7.44642i	−0.0373504	−	0.307609i
$587$	2.16623	+	1.25067i	0.0894098	+	0.0516208i	0.544038	−	0.839060i	$-0.316895\pi$
$587$	2.16623	+	1.25067i	0.0894098	+	0.0516208i	−0.454628	+	0.890681i	$0.650228\pi$
$588$	26.4961	+	19.9105i	1.09268	+	0.821097i
$589$	−0.0425099	−	1.05487i	−0.00175159	−	0.0434652i
$590$	−22.5119	−	8.53765i	−0.926802	−	0.351490i
$591$	−2.83388	−	0.578541i	−0.116570	−	0.0237980i
$592$	4.68738	+	0.956935i	0.192650	+	0.0393298i
$593$	−29.8984	−	11.3390i	−1.22778	−	0.465636i	−0.346420	−	0.938079i	$-0.612603\pi$
$593$	−29.8984	−	11.3390i	−1.22778	−	0.465636i	−0.881361	+	0.472443i	$0.843372\pi$
$594$	0.116127	+	2.88166i	0.00476475	+	0.118236i
$595$	−62.4107	−	46.8986i	−2.55859	−	1.92266i
$596$	14.1101	+	8.14646i	0.577972	+	0.333692i
$597$	−0.908594	−	7.48295i	−0.0371863	−	0.306257i
$598$	−14.3277	+	4.33491i	−0.585903	+	0.177268i
$599$	−0.220248	+	1.81390i	−0.00899908	+	0.0741141i	−0.996517	−	0.0833956i	$-0.973423\pi$
$599$	−0.220248	+	1.81390i	−0.00899908	+	0.0741141i	0.987517	+	0.157510i	$0.0503466\pi$
$600$	−9.98987	+	13.2941i	−0.407835	+	0.542730i
$601$	32.9008	−	10.9839i	1.34205	−	0.448042i	0.447210	−	0.894429i	$-0.352418\pi$
$601$	32.9008	−	10.9839i	1.34205	−	0.448042i	0.894840	+	0.446386i	$0.147289\pi$
$602$	27.4651	+	28.5942i	1.11939	+	1.16541i
$603$	15.0072	−	16.9397i	0.611141	−	0.689836i
$604$	18.5704	−	5.37898i	0.755618	−	0.218867i
$605$	15.9795	+	13.0468i	0.649658	+	0.530430i
$606$		−	28.9428i		−	1.17572i
$607$	16.1592	−	19.7914i	0.655882	−	0.803310i	−0.334393	−	0.942434i	$-0.608531\pi$
$607$	16.1592	−	19.7914i	0.655882	−	0.803310i	0.990275	+	0.139124i	$0.0444286\pi$
$608$	0.130148	−	3.22960i	0.00527821	−	0.130977i
$609$	−7.02519	+	16.4887i	−0.284675	+	0.668157i
$610$	−6.93986	−	18.2989i	−0.280987	−	0.740901i
$611$	−25.3992	−	27.9937i	−1.02754	−	1.13250i
$612$	5.10470	−	13.4600i	0.206345	−	0.544088i
$613$	11.3199	+	10.8729i	0.457205	+	0.439151i	0.885606	−	0.464437i	$-0.153743\pi$
$613$	11.3199	+	10.8729i	0.457205	+	0.439151i	−0.428401	+	0.903589i	$0.640923\pi$
$614$	−4.52880	+	15.6352i	−0.182767	+	0.630986i
$615$	−31.3303	−	2.52924i	−1.26336	−	0.101989i
$616$	−11.9234	−	22.7182i	−0.480408	−	0.915341i
$617$	−1.95558	+	1.87836i	−0.0787288	+	0.0756201i	−0.731056	−	0.682317i	$-0.760972\pi$
$617$	−1.95558	+	1.87836i	−0.0787288	+	0.0756201i	0.652327	+	0.757937i	$0.273793\pi$
$618$	−5.59189	−	13.1246i	−0.224939	−	0.527950i
$619$	3.74749	−	1.42123i	0.150624	−	0.0571242i	−0.278141	−	0.960540i	$-0.589718\pi$
$619$	3.74749	−	1.42123i	0.150624	−	0.0571242i	0.428765	+	0.903416i	$0.358949\pi$
$620$	−4.37153	+	0.710443i	−0.175565	+	0.0285321i
$621$	5.46411	−	3.45529i	0.219267	−	0.138656i
$622$	−8.60445	−	2.49231i	−0.345007	−	0.0999325i
$623$	22.0383	+	31.9280i	0.882946	+	1.27917i
$624$	−7.98167	−	2.55986i	−0.319523	−	0.102476i
$625$	−17.7465	+	25.7103i	−0.709860	+	1.02841i
$626$	−16.9127	+	13.8088i	−0.675969	+	0.551912i
$627$	−1.74625	−	2.13877i	−0.0697385	−	0.0854142i
$628$	0.0418808	−	0.0314714i	0.00167123	−	0.00125585i
$629$	29.2470	−	3.55123i	1.16616	−	0.141597i
$630$	−9.27070	+	27.7691i	−0.369353	+	1.10635i
$631$	−0.532311	+	6.59386i	−0.0211910	+	0.262497i	0.977483	+	0.211015i	$0.0676768\pi$
$631$	−0.532311	+	6.59386i	−0.0211910	+	0.262497i	−0.998674	+	0.0514828i	$0.983605\pi$
$632$	25.7712	+	29.0897i	1.02513	+	1.15713i
$633$	27.6706	+	17.4978i	1.09981	+	0.695475i
$634$	−13.2811	−	5.65854i	−0.527459	−	0.224729i
$635$	−9.01857	+	55.4935i	−0.357891	+	2.20219i
$636$	3.91573	+	3.46904i	0.155269	+	0.137556i
$637$	13.8432	−	50.0040i	0.548486	−	1.98123i
$638$	2.32598	−	2.06064i	0.0920866	−	0.0815816i
$639$	12.7290	+	20.1292i	0.503550	+	0.796301i
$640$	−8.04628	+	0.649563i	−0.318057	+	0.0256762i
$641$	0.270156	−	1.32331i	0.0106705	−	0.0522677i	−0.974107	−	0.226088i	$-0.927406\pi$
$641$	0.270156	−	1.32331i	0.0106705	−	0.0522677i	0.984777	+	0.173821i	$0.0556113\pi$
$642$	3.51046	−	14.2425i	0.138547	−	0.562106i
$643$	−2.46907	−	15.1928i	−0.0973705	−	0.599145i	−0.989177	−	0.146728i	$-0.953126\pi$
$643$	−2.46907	−	15.1928i	−0.0973705	−	0.599145i	0.891806	−	0.452417i	$-0.149438\pi$
$644$	−10.2337	+	16.1832i	−0.403263	+	0.637709i
$645$	24.9862	−	47.6072i	0.983830	−	1.87453i
$646$	1.11840	+	3.86117i	0.0440029	+	0.151916i
$647$	−1.19331	−	5.84524i	−0.0469140	−	0.229800i	0.949573	−	0.313546i	$-0.101517\pi$
$647$	−1.19331	−	5.84524i	−0.0469140	−	0.229800i	−0.996487	+	0.0837455i	$0.973312\pi$
$648$	31.6946	+	1.27725i	1.24508	+	0.0501751i
$649$	−14.4723	−	7.59564i	−0.568087	−	0.298155i
$650$	8.35252	+	2.31232i	0.327613	+	0.0906965i
$651$	−15.4123	+	8.08898i	−0.604054	+	0.317032i
$652$	−17.6968	+	8.39723i	−0.693059	+	0.328861i
$653$	−1.21391	+	2.10256i	−0.0475041	+	0.0822796i	−0.888800	−	0.458296i	$-0.848460\pi$
$653$	−1.21391	+	2.10256i	−0.0475041	+	0.0822796i	0.841296	+	0.540575i	$0.181793\pi$
$654$	13.5163	+	23.4110i	0.528530	+	0.915441i
$655$	−14.4722	−	9.98945i	−0.565476	−	0.390320i
$656$	3.03044	+	4.03278i	0.118319	+	0.157454i
$657$	2.29834	−	1.32695i	0.0896668	−	0.0517692i
$658$	48.1776	+	5.84982i	1.87816	+	0.228050i
$659$	−4.93522	+	10.4008i	−0.192249	+	0.405156i	−0.976570	−	0.215199i	$-0.930960\pi$
$659$	−4.93522	+	10.4008i	−0.192249	+	0.405156i	0.784321	+	0.620355i	$0.213011\pi$
$660$	−8.02392	+	8.35378i	−0.312331	+	0.325171i
$661$	2.55374	+	31.6337i	0.0993289	+	1.23041i	0.833915	+	0.551894i	$0.186095\pi$
$661$	2.55374	+	31.6337i	0.0993289	+	1.23041i	−0.734586	+	0.678516i	$0.762623\pi$
$662$	24.0678	+	5.93219i	0.935424	+	0.230561i
$663$	−51.6163	+	0.612256i	−2.00461	+	0.0237781i
$664$	26.8737	−	6.62376i	1.04290	−	0.257052i
$665$	2.57912	+	7.72542i	0.100014	+	0.299579i
$666$	−4.73633	−	9.98161i	−0.183529	−	0.386779i
$667$	−6.60743	−	2.20588i	−0.255841	−	0.0854121i
$668$	−0.240384	+	0.165925i	−0.00930074	+	0.00641984i
$669$	28.3750	+	13.4641i	1.09704	+	0.520553i
$670$	26.4901	−	1.06752i	1.02340	−	0.0412417i
$671$	−3.17946	−	12.8996i	−0.122742	−	0.497983i
$672$	−49.0259	+	20.8880i	−1.89122	+	0.805772i
$673$	−35.4003	−	5.75311i	−1.36458	−	0.221766i	−0.566373	−	0.824149i	$-0.691654\pi$
$673$	−35.4003	−	5.75311i	−1.36458	−	0.221766i	−0.798207	+	0.602383i	$0.794218\pi$
$674$	−30.9462	+	6.31770i	−1.19200	+	0.243349i
$675$	−3.74302			−0.144069
$676$	−0.829862	−	12.9491i	−0.0319178	−	0.498041i
$677$	8.15107			0.313271			0.156636	−	0.987656i	$-0.449935\pi$
$677$	8.15107			0.313271			0.156636	+	0.987656i	$0.449935\pi$
$678$	−19.2103	+	3.92180i	−0.737766	+	0.150616i
$679$	−51.8137	−	8.42054i	−1.98843	−	0.323151i
$680$	46.6013	−	19.8550i	1.78708	−	0.761403i
$681$	−11.4496	−	46.4529i	−0.438750	−	1.78008i
$682$	3.01541	−	0.121517i	0.115466	−	0.00465312i
$683$	−16.7680	−	7.95653i	−0.641611	−	0.304448i	0.0799501	−	0.996799i	$-0.474524\pi$
$683$	−16.7680	−	7.95653i	−0.641611	−	0.304448i	−0.721561	+	0.692351i	$0.756575\pi$
$684$	−1.23598	+	0.853139i	−0.0472591	+	0.0326206i
$685$	−10.8189	−	3.61188i	−0.413369	−	0.138003i
$686$	14.6663	+	30.9086i	0.559962	+	1.18010i
$687$	2.16389	+	6.48165i	0.0825577	+	0.247290i
$688$	−8.37802	+	2.06500i	−0.319409	+	0.0787273i
$689$	2.81303	−	7.69128i	0.107168	−	0.293014i
$690$	−25.3056	−	6.23727i	−0.963368	−	0.237449i
$691$	−1.74410	−	21.6045i	−0.0663486	−	0.821875i	−0.941280	−	0.337628i	$-0.890375\pi$
$691$	−1.74410	−	21.6045i	−0.0663486	−	0.821875i	0.874931	−	0.484248i	$-0.160907\pi$
$692$	−3.53779	+	3.68322i	−0.134486	+	0.140015i
$693$	−8.51982	+	17.9551i	−0.323641	+	0.682060i
$694$	−12.3486	−	1.49939i	−0.468747	−	0.0569162i
$695$	34.3702	−	19.8436i	1.30374	−	0.752712i
$696$	−6.98628	−	9.29705i	−0.264814	−	0.352404i
$697$	25.5665	+	17.6473i	0.968401	+	0.668439i
$698$	−4.36334	−	7.55752i	−0.165155	−	0.286056i
$699$	9.40022	−	16.2817i	0.355549	−	0.615829i
$700$	10.0155	−	4.75241i	0.378550	−	0.179624i
$701$	15.0172	−	7.88166i	0.567194	−	0.297686i	−0.156646	−	0.987655i	$-0.550068\pi$
$701$	15.0172	−	7.88166i	0.567194	−	0.297686i	0.723839	+	0.689969i	$0.242376\pi$
$702$	−1.84443	−	5.31405i	−0.0696135	−	0.200566i
$703$	−2.72159	−	1.42840i	−0.102647	−	0.0538732i
$704$	12.9538	+	0.522022i	0.488216	+	0.0196745i
$705$	−13.1642	−	64.4824i	−0.495792	−	2.42855i
$706$	−1.98509	−	6.85334i	−0.0747100	−	0.257929i
$707$	−26.9337	+	51.3179i	−1.01295	+	1.93001i
$708$	−10.8836	+	17.2111i	−0.409033	+	0.646833i
$709$	5.29870	+	32.6042i	0.198997	+	1.22448i	0.873729	+	0.486414i	$0.161695\pi$
$709$	5.29870	+	32.6042i	0.198997	+	1.22448i	−0.674732	+	0.738063i	$0.735741\pi$
$710$	−6.67689	+	27.0892i	−0.250579	+	1.01664i
$711$	6.02152	−	29.4953i	0.225824	−	1.10616i
$712$	−25.0910	+	2.02555i	−0.940325	+	0.0759109i
$713$	−3.61567	−	5.71772i	−0.135408	−	0.214130i
$714$	49.6088	−	43.9495i	1.85656	−	1.64477i
$715$	16.7652	+	6.90920i	0.626983	+	0.258389i
$716$	19.3410	+	17.1347i	0.722808	+	0.640352i
$717$	3.44912	−	21.2233i	0.128810	−	0.792598i
$718$	−7.25319	−	3.09030i	−0.270687	−	0.115329i
$719$	26.3614	+	16.6699i	0.983115	+	0.621684i	0.926334	−	0.376703i	$-0.122942\pi$
$719$	26.3614	+	16.6699i	0.983115	+	0.621684i	0.0567803	+	0.998387i	$0.481917\pi$
$720$	−4.22502	−	4.76907i	−0.157457	−	0.177733i
$721$	−2.29872	+	28.4747i	−0.0856087	+	1.06045i
$722$	−5.88952	+	17.6413i	−0.219185	+	0.656540i
$723$	21.9542	−	2.66573i	0.816487	−	0.0991394i
$724$	4.67403	−	3.51231i	0.173709	−	0.130534i
$725$	2.55069	+	3.12403i	0.0947304	+	0.116024i
$726$	−13.5660	+	11.0763i	−0.503481	+	0.411079i
$727$	−21.5731	+	31.2540i	−0.800102	+	1.15915i	0.184240	+	0.982881i	$0.441018\pi$
$727$	−21.5731	+	31.2540i	−0.800102	+	1.15915i	−0.984342	+	0.176267i	$0.943598\pi$
$728$	35.0911	+	35.6768i	1.30056	+	1.32227i
$729$	−7.82846	−	11.3415i	−0.289943	−	0.420055i
$730$	2.98620	+	0.864965i	0.110524	+	0.0320138i
$731$	−44.9124	+	28.4009i	−1.66114	+	1.05044i
$732$	−16.3383	+	2.65523i	−0.603880	+	0.0981400i
$733$	−7.50367	+	2.84577i	−0.277154	+	0.105111i	−0.489266	−	0.872135i	$-0.662735\pi$
$733$	−7.50367	+	2.84577i	−0.277154	+	0.105111i	0.212111	+	0.977245i	$0.431966\pi$
$734$	−11.6588	−	27.3642i	−0.430334	−	1.01003i
$735$	65.1516	−	62.5790i	2.40315	−	2.30826i
$736$	−9.62523	−	18.3393i	−0.354791	−	0.675997i
$737$	17.9392	+	1.44820i	0.660798	+	0.0533451i
$738$	3.24117	−	11.1898i	0.119309	−	0.411902i
$739$	−9.40787	−	9.03638i	−0.346074	−	0.332409i	0.499453	−	0.866341i	$-0.333534\pi$
$739$	−9.40787	−	9.03638i	−0.346074	−	0.332409i	−0.845527	+	0.533932i	$0.820714\pi$
$740$	−4.57239	+	12.0564i	−0.168084	+	0.443202i
$741$	4.46803	+	3.00644i	0.164137	+	0.110444i
$742$	3.72862	+	9.83157i	0.136882	+	0.360928i
$743$	−1.94200	+	4.55804i	−0.0712450	+	0.167218i	−0.951795	−	0.306735i	$-0.900763\pi$
$743$	−1.94200	+	4.55804i	−0.0712450	+	0.167218i	0.880550	+	0.473954i	$0.157174\pi$
$744$	0.454763	−	11.2848i	0.0166724	−	0.413722i
$745$	28.0864	−	34.3995i	1.02900	−	1.26030i
$746$			7.65155i			0.280143i
$747$	−16.6070	−	13.5592i	−0.607620	−	0.496106i
$748$	10.9961	−	3.18505i	0.402056	−	0.116457i
$749$	−19.4781	+	21.9863i	−0.711715	+	0.803360i
$750$	−11.3109	−	11.7759i	−0.413015	−	0.429994i
$751$	30.9052	−	10.3177i	1.12775	−	0.376497i	0.309234	−	0.950986i	$-0.399927\pi$
$751$	30.9052	−	10.3177i	1.12775	−	0.376497i	0.818512	+	0.574489i	$0.194799\pi$
$752$	−6.34511	+	8.44380i	−0.231382	+	0.307914i
$753$	−1.75600	+	14.4620i	−0.0639923	+	0.527024i
$754$	−3.17837	+	5.16069i	−0.115749	+	0.187941i
$755$	−6.35196	−	52.3131i	−0.231171	−	1.90387i
$756$	−6.23120	−	3.59758i	−0.226626	−	0.130843i
$757$	32.4159	+	24.3589i	1.17817	+	0.885341i	0.995208	−	0.0977781i	$-0.0311735\pi$
$757$	32.4159	+	24.3589i	1.17817	+	0.885341i	0.182967	+	0.983119i	$0.441430\pi$
$758$	−0.126701	−	3.14406i	−0.00460200	−	0.114197i
$759$	−16.5432	−	6.27400i	−0.600479	−	0.227732i
$760$	−5.17785	−	1.05707i	−0.187820	−	0.0383438i
$761$	−23.1460	−	4.72530i	−0.839043	−	0.171292i	−0.238759	−	0.971079i	$-0.576741\pi$
$761$	−23.1460	−	4.72530i	−0.839043	−	0.171292i	−0.600284	+	0.799787i	$0.704946\pi$
$762$	−44.6283	−	16.9253i	−1.61671	−	0.613138i
$763$	−2.17965	−	54.0875i	−0.0789087	−	1.95810i
$764$	8.49626	+	6.38453i	0.307384	+	0.230984i
$765$	−33.9805	−	19.6186i	−1.22857	−	0.709313i
$766$	−3.90455	−	32.1569i

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.k (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.980708 - 0.200213i) q^{2} +(-2.27761 - 0.370148i) q^{3} +(-0.918255 + 0.391232i) q^{4} +(0.651073 + 2.64151i) q^{5} +(-2.30778 + 0.0930004i) q^{6} +(4.17842 + 1.98269i) q^{7} +(-2.46972 + 1.70472i) q^{8} +(2.20490 + 0.736104i) q^{9} +O(q^{10})\)	\(q+(0.980708 - 0.200213i) q^{2} +(-2.27761 - 0.370148i) q^{3} +(-0.918255 + 0.391232i) q^{4} +(0.651073 + 2.64151i) q^{5} +(-2.30778 + 0.0930004i) q^{6} +(4.17842 + 1.98269i) q^{7} +(-2.46972 + 1.70472i) q^{8} +(2.20490 + 0.736104i) q^{9} +(1.16738 + 2.46019i) q^{10} +(0.585391 + 1.75346i) q^{11} +(2.23624 - 0.551185i) q^{12} +(-2.08324 - 2.94281i) q^{13} +(4.49477 + 1.10786i) q^{14} +(-0.505143 - 6.25732i) q^{15} +(-0.697915 + 0.726606i) q^{16} +(-2.65981 + 5.60544i) q^{17} +(2.30974 + 0.280453i) q^{18} +(0.560573 - 0.323647i) q^{19} +(-1.63129 - 2.17086i) q^{20} +(-8.78294 - 6.06243i) q^{21} +(0.925163 + 1.60243i) q^{22} +(2.07390 - 3.59210i) q^{23} +(6.25607 - 2.96854i) q^{24} +(-2.12638 + 1.11601i) q^{25} +(-2.63224 - 2.46895i) q^{26} +(1.38011 + 0.724339i) q^{27} +(-4.61255 - 0.185879i) q^{28} +(-0.335928 - 1.64548i) q^{29} +(-1.74820 - 6.03547i) q^{30} +(0.757958 - 1.44417i) q^{31} +(2.66882 - 4.22040i) q^{32} +(-0.684253 - 4.21038i) q^{33} +(-1.48622 + 6.02983i) q^{34} +(-2.51682 + 12.3282i) q^{35} +(-2.31265 + 0.186696i) q^{36} +(-2.53790 - 4.01337i) q^{37} +(0.484960 - 0.429637i) q^{38} +(3.65553 + 7.47368i) q^{39} +(-6.11101 - 5.41388i) q^{40} +(0.803175 - 4.94214i) q^{41} +(-9.82728 - 4.18701i) q^{42} +(7.23870 + 4.57748i) q^{43} +(-1.22355 - 1.38110i) q^{44} +(-0.508873 + 6.30352i) q^{45} +(1.31471 - 3.93802i) q^{46} +(10.4071 - 1.26365i) q^{47} +(1.85853 - 1.39660i) q^{48} +(9.10106 + 11.1468i) q^{49} +(-1.86192 + 1.52021i) q^{50} +(8.13287 - 11.7825i) q^{51} +(3.06427 + 1.88722i) q^{52} +(1.29029 + 1.86931i) q^{53} +(1.49851 + 0.434049i) q^{54} +(-4.25064 + 2.68794i) q^{55} +(-13.6995 + 2.22638i) q^{56} +(-1.39657 + 0.529647i) q^{57} +(-0.658895 - 1.54648i) q^{58} +(-6.37655 + 6.12476i) q^{59} +(2.91192 + 5.54819i) q^{60} +(-7.16358 - 0.578304i) q^{61} +(0.454194 - 1.56806i) q^{62} +(7.75354 + 7.44738i) q^{63} +(2.48688 - 6.55736i) q^{64} +(6.41711 - 7.41887i) q^{65} +(-1.51403 - 3.99216i) q^{66} +(3.81611 - 8.95673i) q^{67} +(0.249361 - 6.18783i) q^{68} +(-6.05315 + 7.41376i) q^{69} +12.5943i q^{70} +(7.93631 + 6.47979i) q^{71} +(-6.70034 + 1.94078i) q^{72} +(0.757082 - 0.854568i) q^{73} +(-3.29247 - 3.42782i) q^{74} +(5.25617 - 1.75477i) q^{75} +(-0.388128 + 0.516505i) q^{76} +(-1.03055 + 8.48734i) q^{77} +(5.08134 + 6.59762i) q^{78} +(-1.56101 - 12.8560i) q^{79} +(-2.37373 - 1.37047i) q^{80} +(-8.45023 - 6.34994i) q^{81} +(-0.201799 - 5.00760i) q^{82} +(-8.62375 - 3.27056i) q^{83} +(10.4368 + 2.13069i) q^{84} +(-16.5385 - 3.37637i) q^{85} +(8.01553 + 3.03989i) q^{86} +(0.156041 + 3.87212i) q^{87} +(-4.43492 - 3.33262i) q^{88} +(7.26445 + 4.19413i) q^{89} +(0.762991 + 6.28379i) q^{90} +(-2.86998 - 16.4267i) q^{91} +(-0.499025 + 4.10984i) q^{92} +(-2.26089 + 3.00870i) q^{93} +(9.95335 - 3.32292i) q^{94} +(1.21989 + 1.27004i) q^{95} +(-7.64071 + 8.62458i) q^{96} +(-10.9019 + 3.15778i) q^{97} +(11.1572 + 9.10958i) q^{98} +4.29711i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

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