LMFDB - Embedded newform 400.2.s.e.243.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(107,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1]))

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

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

chi := DirichletCharacter("400.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.1
Character	$\chi$	$=$	400.243
Dual form			400.2.s.e.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41248 + 0.0699536i) q^{2} -0.790153 q^{3} +(1.99021 - 0.197616i) q^{4} +(1.11608 - 0.0552740i) q^{6} +(-0.139907 + 0.139907i) q^{7} +(-2.79732 + 0.418352i) q^{8} -2.37566 q^{9} +O(q^{10})$	\(q+(-1.41248 + 0.0699536i) q^{2} -0.790153 q^{3} +(1.99021 - 0.197616i) q^{4} +(1.11608 - 0.0552740i) q^{6} +(-0.139907 + 0.139907i) q^{7} +(-2.79732 + 0.418352i) q^{8} -2.37566 q^{9} +(2.94816 + 2.94816i) q^{11} +(-1.57257 + 0.156147i) q^{12} +0.235568i q^{13} +(0.187829 - 0.207403i) q^{14} +(3.92190 - 0.786598i) q^{16} +(-2.06145 + 2.06145i) q^{17} +(3.35558 - 0.166186i) q^{18} +(-2.55293 - 2.55293i) q^{19} +(0.110548 - 0.110548i) q^{21} +(-4.37046 - 3.95799i) q^{22} +(4.62421 + 4.62421i) q^{23} +(2.21031 - 0.330562i) q^{24} +(-0.0164788 - 0.332735i) q^{26} +4.24759 q^{27} +(-0.250797 + 0.306093i) q^{28} +(-6.66417 + 6.66417i) q^{29} +3.43202i q^{31} +(-5.48458 + 1.38541i) q^{32} +(-2.32950 - 2.32950i) q^{33} +(2.76756 - 3.05597i) q^{34} +(-4.72807 + 0.469469i) q^{36} +1.38457i q^{37} +(3.78455 + 3.42738i) q^{38} -0.186135i q^{39} +8.26242i q^{41} +(-0.148414 + 0.163880i) q^{42} +5.40057i q^{43} +(6.45007 + 5.28486i) q^{44} +(-6.85509 - 6.20813i) q^{46} +(6.84602 + 6.84602i) q^{47} +(-3.09890 + 0.621532i) q^{48} +6.96085i q^{49} +(1.62886 - 1.62886i) q^{51} +(0.0465521 + 0.468830i) q^{52} -8.19252 q^{53} +(-5.99965 + 0.297134i) q^{54} +(0.332834 - 0.449895i) q^{56} +(2.01720 + 2.01720i) q^{57} +(8.94684 - 9.87920i) q^{58} +(4.32313 - 4.32313i) q^{59} +(-9.15188 - 9.15188i) q^{61} +(-0.240082 - 4.84766i) q^{62} +(0.332372 - 0.332372i) q^{63} +(7.64996 - 2.34053i) q^{64} +(3.45333 + 3.12742i) q^{66} -5.00083i q^{67} +(-3.69535 + 4.51010i) q^{68} +(-3.65383 - 3.65383i) q^{69} -6.06473 q^{71} +(6.64547 - 0.993862i) q^{72} +(11.3646 - 11.3646i) q^{73} +(-0.0968554 - 1.95568i) q^{74} +(-5.58537 - 4.57637i) q^{76} -0.824938 q^{77} +(0.0130208 + 0.262912i) q^{78} +4.44776 q^{79} +3.77073 q^{81} +(-0.577986 - 11.6705i) q^{82} -11.4778 q^{83} +(0.198168 - 0.241860i) q^{84} +(-0.377790 - 7.62822i) q^{86} +(5.26571 - 5.26571i) q^{87} +(-9.48031 - 7.01357i) q^{88} +5.84762 q^{89} +(-0.0329576 - 0.0329576i) q^{91} +(10.1170 + 8.28934i) q^{92} -2.71182i q^{93} +(-10.1488 - 9.19097i) q^{94} +(4.33366 - 1.09468i) q^{96} +(0.515382 - 0.515382i) q^{97} +(-0.486937 - 9.83208i) q^{98} +(-7.00383 - 7.00383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} + 12 q^{6} + 40 q^{9}+O(q^{10}) $ 24 * q + 8 * q^4 + 12 * q^6 + 40 * q^9	$ 24 q + 8 q^{4} + 12 q^{6} + 40 q^{9} - 20 q^{11} - 44 q^{14} - 4 q^{16} + 12 q^{19} - 24 q^{24} + 32 q^{26} - 8 q^{29} - 32 q^{34} - 60 q^{36} + 44 q^{44} - 76 q^{46} + 20 q^{51} - 16 q^{54} - 28 q^{56} - 8 q^{59} - 48 q^{61} + 32 q^{64} - 8 q^{66} + 64 q^{69} - 16 q^{71} - 36 q^{74} + 40 q^{76} + 104 q^{79} + 48 q^{81} - 44 q^{84} + 84 q^{86} - 96 q^{89} + 64 q^{91} + 40 q^{94} + 212 q^{96} - 128 q^{99}+O(q^{100}) $ 24 * q + 8 * q^4 + 12 * q^6 + 40 * q^9 - 20 * q^11 - 44 * q^14 - 4 * q^16 + 12 * q^19 - 24 * q^24 + 32 * q^26 - 8 * q^29 - 32 * q^34 - 60 * q^36 + 44 * q^44 - 76 * q^46 + 20 * q^51 - 16 * q^54 - 28 * q^56 - 8 * q^59 - 48 * q^61 + 32 * q^64 - 8 * q^66 + 64 * q^69 - 16 * q^71 - 36 * q^74 + 40 * q^76 + 104 * q^79 + 48 * q^81 - 44 * q^84 + 84 * q^86 - 96 * q^89 + 64 * q^91 + 40 * q^94 + 212 * q^96 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41248	+	0.0699536i	−0.998776	+	0.0494647i
$2$	−1.41248	+	0.0699536i	−0.998776	+	0.0494647i
$3$	−0.790153			−0.456195			−0.228097	−	0.973638i	$-0.573250\pi$
$3$	−0.790153			−0.456195			−0.228097	+	0.973638i	$0.573250\pi$
$4$	1.99021	−	0.197616i	0.995106	−	0.0988082i
$5$		0			0
$5$		0			0
$6$	1.11608	−	0.0552740i	0.455636	−	0.0225655i
$7$	−0.139907	+	0.139907i	−0.0528800	+	0.0528800i	−0.733052	−	0.680172i	$-0.761905\pi$
$7$	−0.139907	+	0.139907i	−0.0528800	+	0.0528800i	0.680172	+	0.733052i	$0.261905\pi$
$8$	−2.79732	+	0.418352i	−0.989001	+	0.147910i
$9$	−2.37566			−0.791886
$10$		0			0
$11$	2.94816	+	2.94816i	0.888904	+	0.888904i	0.994418	−	0.105514i	$-0.0336487\pi$
$11$	2.94816	+	2.94816i	0.888904	+	0.888904i	−0.105514	+	0.994418i	$0.533649\pi$
$12$	−1.57257	+	0.156147i	−0.453962	+	0.0450758i
$13$			0.235568i			0.0653348i	0.999466	+	0.0326674i	$0.0104002\pi$
$13$			0.235568i			0.0653348i	−0.999466	+	0.0326674i	$0.989600\pi$
$14$	0.187829	−	0.207403i	0.0501995	−	0.0554309i
$15$		0			0
$16$	3.92190	−	0.786598i	0.980474	−	0.196649i
$17$	−2.06145	+	2.06145i	−0.499975	+	0.499975i	−0.911430	−	0.411455i	$-0.865021\pi$
$17$	−2.06145	+	2.06145i	−0.499975	+	0.499975i	0.411455	+	0.911430i	$0.365021\pi$
$18$	3.35558	−	0.166186i	0.790917	−	0.0391704i
$19$	−2.55293	−	2.55293i	−0.585682	−	0.585682i	0.350777	−	0.936459i	$-0.385917\pi$
$19$	−2.55293	−	2.55293i	−0.585682	−	0.585682i	−0.936459	+	0.350777i	$0.885917\pi$
$20$		0			0
$21$	0.110548	−	0.110548i	0.0241236	−	0.0241236i
$22$	−4.37046	−	3.95799i	−0.931785	−	0.843847i
$23$	4.62421	+	4.62421i	0.964214	+	0.964214i	0.999381	−	0.0351672i	$-0.0111964\pi$
$23$	4.62421	+	4.62421i	0.964214	+	0.964214i	−0.0351672	+	0.999381i	$0.511196\pi$
$24$	2.21031	−	0.330562i	0.451177	−	0.0674757i
$25$		0			0
$26$	−0.0164788	−	0.332735i	−0.00323176	−	0.0652548i
$27$	4.24759			0.817449
$28$	−0.250797	+	0.306093i	−0.0473962	+	0.0578462i
$29$	−6.66417	+	6.66417i	−1.23751	+	1.23751i	−0.276488	+	0.961017i	$0.589171\pi$
$29$	−6.66417	+	6.66417i	−1.23751	+	1.23751i	−0.961017	+	0.276488i	$0.910829\pi$
$30$		0			0
$31$			3.43202i			0.616408i	0.951320	+	0.308204i	$0.0997280\pi$
$31$			3.43202i			0.616408i	−0.951320	+	0.308204i	$0.900272\pi$
$32$	−5.48458	+	1.38541i	−0.969546	+	0.244908i
$33$	−2.32950	−	2.32950i	−0.405513	−	0.405513i
$34$	2.76756	−	3.05597i	0.474632	−	0.524094i
$35$		0			0
$36$	−4.72807	+	0.469469i	−0.788011	+	0.0782449i
$37$			1.38457i			0.227621i	0.993502	+	0.113811i	$0.0363057\pi$
$37$			1.38457i			0.227621i	−0.993502	+	0.113811i	$0.963694\pi$
$38$	3.78455	+	3.42738i	0.613936	+	0.555994i
$39$		−	0.186135i		−	0.0298054i
$40$		0			0
$41$			8.26242i			1.29037i	0.764025	+	0.645187i	$0.223220\pi$
$41$			8.26242i			1.29037i	−0.764025	+	0.645187i	$0.776780\pi$
$42$	−0.148414	+	0.163880i	−0.0229008	+	0.0252873i
$43$			5.40057i			0.823580i	0.911279	+	0.411790i	$0.135096\pi$
$43$			5.40057i			0.823580i	−0.911279	+	0.411790i	$0.864904\pi$
$44$	6.45007	+	5.28486i	0.972385	+	0.796723i
$45$		0			0
$46$	−6.85509	−	6.20813i	−1.01073	−	0.915339i
$47$	6.84602	+	6.84602i	0.998594	+	0.998594i	0.999999	−	0.00140497i	$-0.000447216\pi$
$47$	6.84602	+	6.84602i	0.998594	+	0.998594i	−0.00140497	+	0.999999i	$0.500447\pi$
$48$	−3.09890	+	0.621532i	−0.447287	+	0.0897104i
$49$			6.96085i			0.994407i
$50$		0			0
$51$	1.62886	−	1.62886i	0.228086	−	0.228086i
$52$	0.0465521	+	0.468830i	0.00645561	+	0.0650150i
$53$	−8.19252			−1.12533			−0.562665	−	0.826685i	$-0.690224\pi$
$53$	−8.19252			−1.12533			−0.562665	+	0.826685i	$0.690224\pi$
$54$	−5.99965	+	0.297134i	−0.816449	+	0.0404349i
$55$		0			0
$56$	0.332834	−	0.449895i	0.0444768	−	0.0601198i
$57$	2.01720	+	2.01720i	0.267185	+	0.267185i
$58$	8.94684	−	9.87920i	1.17478	−	1.29720i
$59$	4.32313	−	4.32313i	0.562823	−	0.562823i	−0.367285	−	0.930108i	$-0.619713\pi$
$59$	4.32313	−	4.32313i	0.562823	−	0.562823i	0.930108	+	0.367285i	$0.119713\pi$
$60$		0			0
$61$	−9.15188	−	9.15188i	−1.17178	−	1.17178i	−0.981786	−	0.189992i	$-0.939154\pi$
$61$	−9.15188	−	9.15188i	−1.17178	−	1.17178i	−0.189992	−	0.981786i	$-0.560846\pi$
$62$	−0.240082	−	4.84766i	−0.0304904	−	0.615654i
$63$	0.332372	−	0.332372i	0.0418749	−	0.0418749i
$64$	7.64996	−	2.34053i	0.956245	−	0.292566i
$65$		0			0
$66$	3.45333	+	3.12742i	0.425076	+	0.384958i
$67$		−	5.00083i		−	0.610948i	−0.952200	−	0.305474i	$-0.901185\pi$
$67$		−	5.00083i		−	0.610948i	0.952200	−	0.305474i	$-0.0988150\pi$
$68$	−3.69535	+	4.51010i	−0.448127	+	0.546930i
$69$	−3.65383	−	3.65383i	−0.439870	−	0.439870i
$70$		0			0
$71$	−6.06473			−0.719751			−0.359875	−	0.933000i	$-0.617181\pi$
$71$	−6.06473			−0.719751			−0.359875	+	0.933000i	$0.617181\pi$
$72$	6.64547	−	0.993862i	0.783176	−	0.117128i
$73$	11.3646	−	11.3646i	1.33012	−	1.33012i	0.424863	−	0.905258i	$-0.360322\pi$
$73$	11.3646	−	11.3646i	1.33012	−	1.33012i	0.905258	−	0.424863i	$-0.139678\pi$
$74$	−0.0968554	−	1.95568i	−0.0112592	−	0.227343i
$75$		0			0
$76$	−5.58537	−	4.57637i	−0.640686	−	0.524946i
$77$	−0.824938			−0.0940104
$78$	0.0130208	+	0.262912i	0.00147431	+	0.0297689i
$79$	4.44776			0.500413			0.250206	−	0.968193i	$-0.419502\pi$
$79$	4.44776			0.500413			0.250206	+	0.968193i	$0.419502\pi$
$80$		0			0
$81$	3.77073			0.418970
$82$	−0.577986	−	11.6705i	−0.0638279	−	1.28879i
$83$	−11.4778			−1.25986			−0.629928	−	0.776654i	$-0.716915\pi$
$83$	−11.4778			−1.25986			−0.629928	+	0.776654i	$0.716915\pi$
$84$	0.198168	−	0.241860i	0.0216219	−	0.0263891i
$85$		0			0
$86$	−0.377790	−	7.62822i	−0.0407381	−	0.822572i
$87$	5.26571	−	5.26571i	0.564543	−	0.564543i
$88$	−9.48031	−	7.01357i	−1.01060	−	0.747649i
$89$	5.84762			0.619846			0.309923	−	0.950762i	$-0.399697\pi$
$89$	5.84762			0.619846			0.309923	+	0.950762i	$0.399697\pi$
$90$		0			0
$91$	−0.0329576	−	0.0329576i	−0.00345490	−	0.00345490i
$92$	10.1170	+	8.28934i	1.05477	+	0.864224i
$93$		−	2.71182i		−	0.281202i
$94$	−10.1488	−	9.19097i	−1.04677	−	0.947977i
$95$		0			0
$96$	4.33366	−	1.09468i	0.442302	−	0.111726i
$97$	0.515382	−	0.515382i	0.0523291	−	0.0523291i	−0.680458	−	0.732787i	$-0.738219\pi$
$97$	0.515382	−	0.515382i	0.0523291	−	0.0523291i	0.732787	+	0.680458i	$0.238219\pi$
$98$	−0.486937	−	9.83208i	−0.0491880	−	0.993190i
$99$	−7.00383	−	7.00383i	−0.703911	−	0.703911i
$100$		0			0
$101$	3.56668	−	3.56668i	0.354898	−	0.354898i	−0.507030	−	0.861928i	$-0.669257\pi$
$101$	3.56668	−	3.56668i	0.354898	−	0.354898i	0.861928	+	0.507030i	$0.169257\pi$
$102$	−2.18679	+	2.41468i	−0.216525	+	0.239089i
$103$	11.6666	+	11.6666i	1.14954	+	1.14954i	0.986642	+	0.162901i	$0.0520851\pi$
$103$	11.6666	+	11.6666i	1.14954	+	1.14954i	0.162901	+	0.986642i	$0.447915\pi$
$104$	−0.0985504	−	0.658958i	−0.00966366	−	0.0646161i
$105$		0			0
$106$	11.5718	−	0.573097i	1.12395	−	0.0556641i
$107$	5.00083			0.483448			0.241724	−	0.970345i	$-0.422287\pi$
$107$	5.00083			0.483448			0.241724	+	0.970345i	$0.422287\pi$
$108$	8.45361	−	0.839394i	0.813449	−	0.0807707i
$109$	−3.69574	+	3.69574i	−0.353988	+	0.353988i	−0.861591	−	0.507603i	$-0.830532\pi$
$109$	−3.69574	+	3.69574i	−0.353988	+	0.353988i	0.507603	+	0.861591i	$0.330532\pi$
$110$		0			0
$111$		−	1.09402i		−	0.103840i
$112$	−0.438651	+	0.658752i	−0.0414486	+	0.0622462i
$113$	−11.6416	−	11.6416i	−1.09515	−	1.09515i	−0.994969	−	0.100184i	$-0.968057\pi$
$113$	−11.6416	−	11.6416i	−1.09515	−	1.09515i	−0.100184	−	0.994969i	$-0.531943\pi$
$114$	−2.99037	−	2.70815i	−0.280074	−	0.253642i
$115$		0			0
$116$	−11.9462	+	14.5801i	−1.10917	+	1.35373i
$117$		−	0.559629i		−	0.0517377i
$118$	−5.80392	+	6.40876i	−0.534294	+	0.589974i
$119$		−	0.576823i		−	0.0528773i
$120$		0			0
$121$			6.38331i			0.580301i
$122$	13.5671	+	12.2867i	1.22830	+	1.11238i
$123$		−	6.52858i		−	0.588662i
$124$	0.678223	+	6.83044i	0.0609062	+	0.613392i
$125$		0			0
$126$	−0.446219	+	0.492720i	−0.0397523	+	0.0438950i
$127$	−5.40562	−	5.40562i	−0.479671	−	0.479671i	0.425355	−	0.905026i	$-0.360149\pi$
$127$	−5.40562	−	5.40562i	−0.479671	−	0.479671i	−0.905026	+	0.425355i	$0.860149\pi$
$128$	−10.6417	+	3.84110i	−0.940603	+	0.339508i
$129$		−	4.26728i		−	0.375713i
$130$		0			0
$131$	15.2758	−	15.2758i	1.33465	−	1.33465i	0.433500	−	0.901154i	$-0.357278\pi$
$131$	15.2758	−	15.2758i	1.33465	−	1.33465i	0.901154	−	0.433500i	$-0.142722\pi$
$132$	−5.09654	−	4.17585i	−0.443597	−	0.363461i
$133$	0.714346			0.0619417
$134$	0.349826	+	7.06358i	0.0302204	+	0.610200i
$135$		0			0
$136$	4.90412	−	6.62894i	0.420524	−	0.568427i
$137$	−4.41140	−	4.41140i	−0.376891	−	0.376891i	0.493088	−	0.869979i	$-0.335868\pi$
$137$	−4.41140	−	4.41140i	−0.376891	−	0.376891i	−0.869979	+	0.493088i	$0.835868\pi$
$138$	5.41657	+	4.90537i	0.461089	+	0.417573i
$139$	10.3472	−	10.3472i	0.877640	−	0.877640i	−0.115650	−	0.993290i	$-0.536895\pi$
$139$	10.3472	−	10.3472i	0.877640	−	0.877640i	0.993290	+	0.115650i	$0.0368952\pi$
$140$		0			0
$141$	−5.40940	−	5.40940i	−0.455553	−	0.455553i
$142$	8.56632	−	0.424249i	0.718870	−	0.0356022i
$143$	−0.694492	+	0.694492i	−0.0580763	+	0.0580763i
$144$	−9.31709	+	1.86869i	−0.776424	+	0.155724i
$145$		0			0
$146$	−15.2572	+	16.8472i	−1.26270	+	1.39429i
$147$		−	5.50014i		−	0.453644i
$148$	0.273613	+	2.75558i	0.0224909	+	0.226508i
$149$	7.12848	+	7.12848i	0.583987	+	0.583987i	0.935997	−	0.352009i	$-0.114501\pi$
$149$	7.12848	+	7.12848i	0.583987	+	0.583987i	−0.352009	+	0.935997i	$0.614501\pi$
$150$		0			0
$151$	−19.7239			−1.60511			−0.802555	−	0.596578i	$-0.796527\pi$
$151$	−19.7239			−1.60511			−0.802555	+	0.596578i	$0.796527\pi$
$152$	8.20937	+	6.07333i	0.665868	+	0.492612i
$153$	4.89730	−	4.89730i	0.395923	−	0.395923i
$154$	1.16521	−	0.0577074i	0.0938953	−	0.00465019i
$155$		0			0
$156$	−0.0367832	−	0.370447i	−0.00294502	−	0.0296595i
$157$	−16.0585			−1.28161			−0.640804	−	0.767704i	$-0.721399\pi$
$157$	−16.0585			−1.28161			−0.640804	+	0.767704i	$0.721399\pi$
$158$	−6.28239	+	0.311137i	−0.499800	+	0.0247527i
$159$	6.47334			0.513370
$160$		0			0
$161$	−1.29392			−0.101975
$162$	−5.32609	+	0.263776i	−0.418457	+	0.0207242i
$163$	1.10043			0.0861920			0.0430960	−	0.999071i	$-0.486278\pi$
$163$	1.10043			0.0861920			0.0430960	+	0.999071i	$0.486278\pi$
$164$	1.63279	+	16.4440i	0.127500	+	1.28406i
$165$		0			0
$166$	16.2122	−	0.802915i	1.25831	−	0.0623183i
$167$	−11.6039	+	11.6039i	−0.897940	+	0.897940i	−0.995254	−	0.0973136i	$-0.968975\pi$
$167$	−11.6039	+	11.6039i	−0.897940	+	0.897940i	0.0973136	+	0.995254i	$0.468975\pi$
$168$	−0.262990	+	0.355486i	−0.0202901	+	0.0274263i
$169$	12.9445			0.995731
$170$		0			0
$171$	6.06489	+	6.06489i	0.463794	+	0.463794i
$172$	1.06724	+	10.7483i	0.0813765	+	0.819550i
$173$			14.7116i			1.11851i	0.828997	+	0.559253i	$0.188912\pi$
$173$			14.7116i			1.11851i	−0.828997	+	0.559253i	$0.811088\pi$
$174$	−7.06937	+	7.80608i	−0.535927	+	0.591777i
$175$		0			0
$176$	13.8814	+	9.24336i	1.04635	+	0.696745i
$177$	−3.41593	+	3.41593i	−0.256757	+	0.256757i
$178$	−8.25966	+	0.409062i	−0.619087	+	0.0306605i
$179$	1.97591	+	1.97591i	0.147686	+	0.147686i	0.777084	−	0.629397i	$-0.216698\pi$
$179$	1.97591	+	1.97591i	0.147686	+	0.147686i	−0.629397	+	0.777084i	$0.716698\pi$
$180$		0			0
$181$	1.45673	−	1.45673i	0.108278	−	0.108278i	−0.650892	−	0.759170i	$-0.725605\pi$
$181$	1.45673	−	1.45673i	0.108278	−	0.108278i	0.759170	+	0.650892i	$0.225605\pi$
$182$	0.0488576	+	0.0442466i	0.00362157	+	0.00327977i
$183$	7.23138	+	7.23138i	0.534559	+	0.534559i
$184$	−14.8699	−	11.0008i	−1.09623	−	0.810992i
$185$		0			0
$186$	0.189701	+	3.83039i	0.0139096	+	0.280858i
$187$	−12.1550			−0.888860
$188$	14.9779	+	12.2721i	1.09238	+	0.895038i
$189$	−0.594269	+	0.594269i	−0.0432267	+	0.0432267i
$190$		0			0
$191$		−	0.285625i		−	0.0206671i	−0.999947	−	0.0103336i	$-0.996711\pi$
$191$		−	0.285625i		−	0.0206671i	0.999947	−	0.0103336i	$-0.00328933\pi$
$192$	−6.04464	+	1.84937i	−0.436234	+	0.133467i
$193$	8.95931	+	8.95931i	0.644905	+	0.644905i	0.951757	−	0.306852i	$-0.0992756\pi$
$193$	8.95931	+	8.95931i	0.644905	+	0.644905i	−0.306852	+	0.951757i	$0.599276\pi$
$194$	−0.691915	+	0.764021i	−0.0496766	+	0.0548535i
$195$		0			0
$196$	1.37558	+	13.8536i	0.0982556	+	0.989541i
$197$		−	12.8094i		−	0.912632i	−0.889818	−	0.456316i	$-0.849169\pi$
$197$		−	12.8094i		−	0.912632i	0.889818	−	0.456316i	$-0.150831\pi$
$198$	10.3827	+	9.40284i	0.737868	+	0.668231i
$199$			18.2117i			1.29099i	0.763763	+	0.645497i	$0.223350\pi$
$199$			18.2117i			1.29099i	−0.763763	+	0.645497i	$0.776650\pi$
$200$		0			0
$201$			3.95142i			0.278711i
$202$	−4.78837	+	5.28738i	−0.336909	+	0.372019i
$203$		−	1.86473i		−	0.130878i
$204$	2.91989	−	3.56367i	0.204433	−	0.249507i
$205$		0			0
$206$	−17.2950	−	15.6627i	−1.20500	−	1.09127i
$207$	−10.9855	−	10.9855i	−0.763548	−	0.763548i
$208$	0.185297	+	0.923872i	0.0128480	+	0.0640590i
$209$		−	15.0529i		−	1.04123i
$210$		0			0
$211$	2.40291	−	2.40291i	0.165423	−	0.165423i	−0.619541	−	0.784964i	$-0.712681\pi$
$211$	2.40291	−	2.40291i	0.165423	−	0.165423i	0.784964	+	0.619541i	$0.212681\pi$
$212$	−16.3049	+	1.61898i	−1.11982	+	0.111192i
$213$	4.79206			0.328347
$214$	−7.06358	+	0.349826i	−0.482856	+	0.0239136i
$215$		0			0
$216$	−11.8819	+	1.77699i	−0.808458	+	0.120909i
$217$	−0.480164	−	0.480164i	−0.0325956	−	0.0325956i
$218$	4.96164	−	5.47870i	0.336045	−	0.371064i
$219$	−8.97973	+	8.97973i	−0.606794	+	0.606794i
$220$		0			0
$221$	−0.485611	−	0.485611i	−0.0326657	−	0.0326657i
$222$	0.0765306	+	1.54528i	0.00513640	+	0.103713i
$223$	8.26331	−	8.26331i	0.553352	−	0.553352i	−0.374054	−	0.927407i	$-0.622033\pi$
$223$	8.26331	−	8.26331i	0.553352	−	0.553352i	0.927407	+	0.374054i	$0.122033\pi$
$224$	0.573504	−	0.961161i	0.0383189	−	0.0642203i
$225$		0			0
$226$	17.2580	+	15.6292i	1.14798	+	1.03964i
$227$			10.5895i			0.702847i	0.936217	+	0.351423i	$0.114302\pi$
$227$			10.5895i			0.702847i	−0.936217	+	0.351423i	$0.885698\pi$
$228$	4.41330	+	3.61603i	0.292278	+	0.239478i
$229$	−4.51111	−	4.51111i	−0.298102	−	0.298102i	0.542168	−	0.840270i	$-0.317604\pi$
$229$	−4.51111	−	4.51111i	−0.298102	−	0.298102i	−0.840270	+	0.542168i	$0.817604\pi$
$230$		0			0
$231$	0.651827			0.0428871
$232$	15.8538	−	21.4298i	1.04085	−	1.40693i
$233$	1.60312	−	1.60312i	0.105024	−	0.105024i	−0.652642	−	0.757666i	$-0.726340\pi$
$233$	1.60312	−	1.60312i	0.105024	−	0.105024i	0.757666	+	0.652642i	$0.226340\pi$
$234$	0.0391481	+	0.790466i	0.00255919	+	0.0516744i
$235$		0			0
$236$	7.74962	−	9.45827i	0.504457	−	0.615681i
$237$	−3.51441			−0.228286
$238$	0.0403509	+	0.814753i	0.00261556	+	0.0528126i
$239$	14.1546			0.915587			0.457794	−	0.889058i	$-0.348640\pi$
$239$	14.1546			0.915587			0.457794	+	0.889058i	$0.348640\pi$
$240$		0			0
$241$	4.25207			0.273900			0.136950	−	0.990578i	$-0.456270\pi$
$241$	4.25207			0.273900			0.136950	+	0.990578i	$0.456270\pi$
$242$	−0.446536	−	9.01631i	−0.0287044	−	0.579591i
$243$	−15.7222			−1.00858
$244$	−20.0227	−	16.4056i	−1.28182	−	1.05026i
$245$		0			0
$246$	0.456697	+	9.22150i	0.0291180	+	0.587941i
$247$	0.601388	−	0.601388i	0.0382654	−	0.0382654i
$248$	−1.43579	−	9.60044i	−0.0911729	−	0.609628i
$249$	9.06923			0.574739
$250$		0			0
$251$	−1.29050	−	1.29050i	−0.0814559	−	0.0814559i	0.665205	−	0.746661i	$-0.268344\pi$
$251$	−1.29050	−	1.29050i	−0.0814559	−	0.0814559i	−0.746661	+	0.665205i	$0.768344\pi$
$252$	0.595809	−	0.727173i	0.0375324	−	0.0458076i
$253$			27.2658i			1.71419i
$254$	8.01348	+	7.25720i	0.502811	+	0.455357i
$255$		0			0
$256$	14.7625	−	6.16991i	0.922658	−	0.385619i
$257$	5.72463	−	5.72463i	0.357093	−	0.357093i	−0.505647	−	0.862740i	$-0.668746\pi$
$257$	5.72463	−	5.72463i	0.357093	−	0.357093i	0.862740	+	0.505647i	$0.168746\pi$
$258$	0.298511	+	6.02745i	0.0185845	+	0.375253i
$259$	−0.193711	−	0.193711i	−0.0120366	−	0.0120366i
$260$		0			0
$261$	15.8318	−	15.8318i	0.979963	−	0.979963i
$262$	−20.5082	+	22.6454i	−1.26700	+	1.39904i
$263$	−17.0683	−	17.0683i	−1.05248	−	1.05248i	−0.998545	−	0.0539323i	$-0.982824\pi$
$263$	−17.0683	−	17.0683i	−1.05248	−	1.05248i	−0.0539323	−	0.998545i	$-0.517176\pi$
$264$	7.49089	+	5.54179i	0.461033	+	0.341074i
$265$		0			0
$266$	−1.00900	+	0.0499711i	−0.0618658	+	0.00306392i
$267$	−4.62051			−0.282771
$268$	−0.988246	−	9.95271i	−0.0603667	−	0.607959i
$269$	6.15456	−	6.15456i	0.375250	−	0.375250i	−0.494135	−	0.869385i	$-0.664515\pi$
$269$	6.15456	−	6.15456i	0.375250	−	0.375250i	0.869385	+	0.494135i	$0.164515\pi$
$270$		0			0
$271$			18.4342i			1.11980i	0.828561	+	0.559899i	$0.189160\pi$
$271$			18.4342i			1.11980i	−0.828561	+	0.559899i	$0.810840\pi$
$272$	−6.46326	+	9.70632i	−0.391893	+	0.588532i
$273$	0.0260416	+	0.0260416i	0.00157611	+	0.00157611i
$274$	6.53961	+	5.92243i	0.395072	+	0.357787i
$275$		0			0
$276$	−7.99396	−	6.54984i	−0.481180	−	0.394254i
$277$			15.2281i			0.914967i	0.889218	+	0.457484i	$0.151249\pi$
$277$			15.2281i			0.914967i	−0.889218	+	0.457484i	$0.848751\pi$
$278$	−13.8914	+	15.3391i	−0.833153	+	0.919978i
$279$		−	8.15330i		−	0.488125i
$280$		0			0
$281$			7.07835i			0.422259i	0.977458	+	0.211129i	$0.0677142\pi$
$281$			7.07835i			0.422259i	−0.977458	+	0.211129i	$0.932286\pi$
$282$	8.01908	+	7.26227i	0.477530	+	0.432462i
$283$		−	19.9173i		−	1.18396i	−0.805953	−	0.591979i	$-0.798347\pi$
$283$		−	19.9173i		−	1.18396i	0.805953	−	0.591979i	$-0.201653\pi$
$284$	−12.0701	+	1.19849i	−0.716229	+	0.0711173i
$285$		0			0
$286$	0.932375	−	1.02954i	0.0551325	−	0.0608780i
$287$	−1.15597	−	1.15597i	−0.0682349	−	0.0682349i
$288$	13.0295	−	3.29125i	0.767771	−	0.193939i
$289$			8.50085i			0.500050i
$290$		0			0
$291$	−0.407231	+	0.407231i	−0.0238723	+	0.0238723i
$292$	20.3721	−	24.8637i	1.19218	−	1.45504i
$293$	−23.1293			−1.35123			−0.675614	−	0.737256i	$-0.736121\pi$
$293$	−23.1293			−1.35123			−0.675614	+	0.737256i	$0.736121\pi$
$294$	0.384754	+	7.76884i	0.0224393	+	0.453088i
$295$		0			0
$296$	−0.579237	−	3.87307i	−0.0336675	−	0.225118i
$297$	12.5226	+	12.5226i	0.726634	+	0.726634i
$298$	−10.5675	−	9.57018i	−0.612159	−	0.554386i
$299$	−1.08931	+	1.08931i	−0.0629967	+	0.0629967i
$300$		0			0
$301$	−0.755579	−	0.755579i	−0.0435509	−	0.0435509i
$302$	27.8597	−	1.37976i	1.60315	−	0.0793963i
$303$	−2.81822	+	2.81822i	−0.161903	+	0.161903i
$304$	−12.0204	−	8.00419i	−0.689420	−	0.459072i
$305$		0			0
$306$	−6.57477	+	7.25994i	−0.375854	+	0.415023i
$307$			3.82901i			0.218533i	0.994012	+	0.109267i	$0.0348502\pi$
$307$			3.82901i			0.218533i	−0.994012	+	0.109267i	$0.965150\pi$
$308$	−1.64180	+	0.163021i	−0.0935504	+	0.00928900i
$309$	−9.21839	−	9.21839i	−0.524416	−	0.524416i
$310$		0			0
$311$	9.07002			0.514314			0.257157	−	0.966370i	$-0.417214\pi$
$311$	9.07002			0.514314			0.257157	+	0.966370i	$0.417214\pi$
$312$	0.0778698	+	0.520677i	0.00440851	+	0.0294775i
$313$	−2.78399	+	2.78399i	−0.157361	+	0.157361i	−0.781396	−	0.624035i	$-0.785492\pi$
$313$	−2.78399	+	2.78399i	−0.157361	+	0.157361i	0.624035	+	0.781396i	$0.285492\pi$
$314$	22.6824	−	1.12335i	1.28004	−	0.0633943i
$315$		0			0
$316$	8.85200	−	0.878951i	0.497964	−	0.0494449i
$317$	14.8639			0.834838			0.417419	−	0.908714i	$-0.362935\pi$
$317$	14.8639			0.834838			0.417419	+	0.908714i	$0.362935\pi$
$318$	−9.14348	+	0.452834i	−0.512741	+	0.0253937i
$319$	−39.2941			−2.20005
$320$		0			0
$321$	−3.95142			−0.220547
$322$	1.82764	−	0.0905144i	0.101850	−	0.00504417i
$323$	10.5255			0.585653
$324$	7.50456	−	0.745159i	0.416920	−	0.0413977i
$325$		0			0
$326$	−1.55433	+	0.0769787i	−0.0860865	+	0.00426346i
$327$	2.92020	−	2.92020i	0.161487	−	0.161487i
$328$	−3.45660	−	23.1126i	−0.190859	−	1.27618i
$329$	−1.91561			−0.105611
$330$		0			0
$331$	−8.73942	−	8.73942i	−0.480362	−	0.480362i	0.424885	−	0.905247i	$-0.360314\pi$
$331$	−8.73942	−	8.73942i	−0.480362	−	0.480362i	−0.905247	+	0.424885i	$0.860314\pi$
$332$	−22.8433	+	2.26821i	−1.25369	+	0.124484i
$333$		−	3.28926i		−	0.180250i
$334$	15.5786	−	17.2021i	0.852425	−	0.941257i
$335$		0			0
$336$	0.346601	−	0.520515i	0.0189086	−	0.0283964i
$337$	20.3405	−	20.3405i	1.10802	−	1.10802i	0.114607	−	0.993411i	$-0.463439\pi$
$337$	20.3405	−	20.3405i	1.10802	−	1.10802i	0.993411	−	0.114607i	$-0.0365610\pi$
$338$	−18.2839	+	0.905515i	−0.994512	+	0.0492535i
$339$	9.19867	+	9.19867i	0.499603	+	0.499603i
$340$		0			0
$341$	−10.1181	+	10.1181i	−0.547928	+	0.547928i
$342$	−8.99081	−	8.14229i	−0.486167	−	0.440284i
$343$	−1.95322	−	1.95322i	−0.105464	−	0.105464i
$344$	−2.25934	−	15.1071i	−0.121816	−	0.814521i
$345$		0			0
$346$	−1.02913	−	20.7799i	−0.0553265	−	1.11714i
$347$	7.33669			0.393854			0.196927	−	0.980418i	$-0.436904\pi$
$347$	7.33669			0.393854			0.196927	+	0.980418i	$0.436904\pi$
$348$	9.43929	−	11.5205i	0.505999	−	0.617562i
$349$	4.99392	−	4.99392i	0.267319	−	0.267319i	−0.560700	−	0.828019i	$-0.689468\pi$
$349$	4.99392	−	4.99392i	0.267319	−	0.267319i	0.828019	+	0.560700i	$0.189468\pi$
$350$		0			0
$351$			1.00060i			0.0534078i
$352$	−20.2538	−	12.0850i	−1.07953	−	0.644135i
$353$	5.74673	+	5.74673i	0.305868	+	0.305868i	0.843304	−	0.537436i	$-0.180607\pi$
$353$	5.74673	+	5.74673i	0.305868	+	0.305868i	−0.537436	+	0.843304i	$0.680607\pi$
$354$	4.58598	−	5.06390i	0.243742	−	0.269143i
$355$		0			0
$356$	11.6380	−	1.15559i	0.616813	−	0.0612459i
$357$			0.455778i			0.0241224i
$358$	−2.92916	−	2.65271i	−0.154811	−	0.140200i
$359$			22.2959i			1.17673i	0.808594	+	0.588366i	$0.200229\pi$
$359$			22.2959i			1.17673i	−0.808594	+	0.588366i	$0.799771\pi$
$360$		0			0
$361$		−	5.96511i		−	0.313953i
$362$	−1.95570	+	2.15951i	−0.102789	+	0.113501i
$363$		−	5.04379i		−	0.264730i
$364$	−0.0721057	−	0.0590797i	−0.00377936	−	0.00309662i
$365$		0			0
$366$	−10.7201	−	9.70833i	−0.560346	−	0.507463i
$367$	22.1923	+	22.1923i	1.15843	+	1.15843i	0.984814	+	0.173615i	$0.0555448\pi$
$367$	22.1923	+	22.1923i	1.15843	+	1.15843i	0.173615	+	0.984814i	$0.444455\pi$
$368$	21.7731	+	14.4983i	1.13500	+	0.755775i
$369$		−	19.6287i		−	1.02183i
$370$		0			0
$371$	1.14619	−	1.14619i	0.0595074	−	0.0595074i
$372$	−0.535900	−	5.39709i	−0.0277851	−	0.279826i
$373$	27.1593			1.40625			0.703127	−	0.711064i	$-0.251786\pi$
$373$	27.1593			1.40625			0.703127	+	0.711064i	$0.251786\pi$
$374$	17.1687	−	0.850284i	0.887771	−	0.0439671i
$375$		0			0
$376$	−22.0145	−	16.2864i	−1.13531	−	0.839908i
$377$	−1.56986	−	1.56986i	−0.0808521	−	0.0808521i
$378$	0.797823	−	0.880965i	0.0410356	−	0.0453120i
$379$	−14.7602	+	14.7602i	−0.758180	+	0.758180i	−0.975991	−	0.217811i	$-0.930108\pi$
$379$	−14.7602	+	14.7602i	−0.758180	+	0.758180i	0.217811	+	0.975991i	$0.430108\pi$
$380$		0			0
$381$	4.27126	+	4.27126i	0.218823	+	0.218823i
$382$	0.0199805	+	0.403441i	0.00102229	+	0.0206418i
$383$	14.5976	−	14.5976i	0.745901	−	0.745901i	−0.227805	−	0.973707i	$-0.573155\pi$
$383$	14.5976	−	14.5976i	0.745901	−	0.745901i	0.973707	+	0.227805i	$0.0731550\pi$
$384$	8.40857	−	3.03505i	0.429098	−	0.154882i
$385$		0			0
$386$	−13.2816	−	12.0281i	−0.676016	−	0.612216i
$387$		−	12.8299i		−	0.652182i
$388$	0.923872	−	1.12757i	0.0469025	−	0.0572436i
$389$	−3.93745	−	3.93745i	−0.199637	−	0.199637i	0.600208	−	0.799844i	$-0.295085\pi$
$389$	−3.93745	−	3.93745i	−0.199637	−	0.199637i	−0.799844	+	0.600208i	$0.795085\pi$
$390$		0			0
$391$	−19.0651			−0.964166
$392$	−2.91209	−	19.4717i	−0.147083	−	0.983470i
$393$	−12.0702	+	12.0702i	−0.608862	+	0.608862i
$394$	0.896064	+	18.0931i	0.0451430	+	0.911515i
$395$		0			0
$396$	−15.3232	−	12.5550i	−0.770019	−	0.630914i
$397$	27.0000			1.35509			0.677545	−	0.735481i	$-0.263044\pi$
$397$	27.0000			1.35509			0.677545	+	0.735481i	$0.263044\pi$
$398$	−1.27397	−	25.7237i	−0.0638586	−	1.28941i
$399$	−0.564442			−0.0282575
$400$		0			0
$401$	3.02550			0.151086			0.0755432	−	0.997143i	$-0.475931\pi$
$401$	3.02550			0.151086			0.0755432	+	0.997143i	$0.475931\pi$
$402$	−0.276416	−	5.58131i	−0.0137864	−	0.278370i
$403$	−0.808473			−0.0402729
$404$	6.39362	−	7.80329i	0.318095	−	0.388228i
$405$		0			0
$406$	0.130445	+	2.63390i	0.00647386	+	0.130718i
$407$	−4.08193	+	4.08193i	−0.202334	+	0.202334i
$408$	−3.87500	+	5.23787i	−0.191841	+	0.259313i
$409$	−19.6553			−0.971894			−0.485947	−	0.873988i	$-0.661525\pi$
$409$	−19.6553			−0.971894			−0.485947	+	0.873988i	$0.661525\pi$
$410$		0			0
$411$	3.48568	+	3.48568i	0.171936	+	0.171936i
$412$	25.5245	+	20.9135i	1.25750	+	1.03033i
$413$			1.20967i			0.0595241i
$414$	16.2854	+	14.7484i	0.800382	+	0.724845i
$415$		0			0
$416$	−0.326357	−	1.29199i	−0.0160010	−	0.0633451i
$417$	−8.17588	+	8.17588i	−0.400375	+	0.400375i
$418$	1.05300	+	21.2619i	0.0515041	+	1.03996i
$419$	−16.1834	−	16.1834i	−0.790609	−	0.790609i	0.190984	−	0.981593i	$-0.438832\pi$
$419$	−16.1834	−	16.1834i	−0.790609	−	0.790609i	−0.981593	+	0.190984i	$0.938832\pi$
$420$		0			0
$421$	−23.1841	+	23.1841i	−1.12993	+	1.12993i	−0.139737	+	0.990189i	$0.544626\pi$
$421$	−23.1841	+	23.1841i	−1.12993	+	1.12993i	−0.990189	+	0.139737i	$0.955374\pi$
$422$	−3.22598	+	3.56216i	−0.157038	+	0.173403i
$423$	−16.2638	−	16.2638i	−0.790773	−	0.790773i
$424$	22.9171	−	3.42736i	1.11295	−	0.166447i
$425$		0			0
$426$	−6.76870	+	0.335222i	−0.327945	+	0.0162416i
$427$	2.56083			0.123927
$428$	9.95271	−	0.988246i	0.481082	−	0.0477687i
$429$	0.548755	−	0.548755i	0.0264941	−	0.0264941i
$430$		0			0
$431$		−	29.7907i		−	1.43497i	−0.696575	−	0.717484i	$-0.745294\pi$
$431$		−	29.7907i		−	1.43497i	0.696575	−	0.717484i	$-0.254706\pi$
$432$	16.6586	−	3.34115i	0.801488	−	0.160751i
$433$	19.0587	+	19.0587i	0.915903	+	0.915903i	0.996728	−	0.0808251i	$-0.0257555\pi$
$433$	19.0587	+	19.0587i	0.915903	+	0.915903i	−0.0808251	+	0.996728i	$0.525756\pi$
$434$	0.711812	+	0.644634i	0.0341681	+	0.0309434i
$435$		0			0
$436$	−6.62497	+	8.08565i	−0.317279	+	0.387232i
$437$		−	23.6105i		−	1.12945i
$438$	12.0556	−	13.3119i	0.576036	−	0.636066i
$439$			6.10665i			0.291454i	0.989325	+	0.145727i	$0.0465522\pi$
$439$			6.10665i			0.291454i	−0.989325	+	0.145727i	$0.953448\pi$
$440$		0			0
$441$		−	16.5366i		−	0.787458i
$442$	0.719888	+	0.651947i	0.0342416	+	0.0310100i
$443$		−	16.1163i		−	0.765708i	−0.923809	−	0.382854i	$-0.874941\pi$
$443$		−	16.1163i		−	0.765708i	0.923809	−	0.382854i	$-0.125059\pi$
$444$	−0.216196	−	2.17733i	−0.0102602	−	0.103332i
$445$		0			0
$446$	−11.0937	+	12.2498i	−0.525304	+	0.580046i
$447$	−5.63258	−	5.63258i	−0.266412	−	0.266412i
$448$	−0.742828	+	1.39774i	−0.0350953	+	0.0660371i
$449$		−	1.87161i		−	0.0883268i	−0.999024	−	0.0441634i	$-0.985938\pi$
$449$		−	1.87161i		−	0.0883268i	0.999024	−	0.0441634i	$-0.0140622\pi$
$450$		0			0
$451$	−24.3590	+	24.3590i	−1.14702	+	1.14702i
$452$	−25.4699	−	20.8687i	−1.19800	−	0.981583i
$453$	15.5849			0.732243
$454$	−0.740771	−	14.9574i	−0.0347661	−	0.701986i
$455$		0			0
$456$	−6.48666	−	4.79885i	−0.303766	−	0.224727i
$457$	10.7459	+	10.7459i	0.502673	+	0.502673i	0.912268	−	0.409594i	$-0.134330\pi$
$457$	10.7459	+	10.7459i	0.502673	+	0.502673i	−0.409594	+	0.912268i	$0.634330\pi$
$458$	6.68743	+	6.05629i	0.312483	+	0.282992i
$459$	−8.75619	+	8.75619i	−0.408704	+	0.408704i
$460$		0			0
$461$	16.5710	+	16.5710i	0.771790	+	0.771790i	0.978419	−	0.206630i	$-0.0662495\pi$
$461$	16.5710	+	16.5710i	0.771790	+	0.771790i	−0.206630	+	0.978419i	$0.566249\pi$
$462$	−0.920694	+	0.0455976i	−0.0428346	+	0.00212139i
$463$	−19.1271	+	19.1271i	−0.888912	+	0.888912i	−0.994419	−	0.105507i	$-0.966354\pi$
$463$	−19.1271	+	19.1271i	−0.888912	+	0.888912i	0.105507	+	0.994419i	$0.466354\pi$
$464$	−20.8942	+	31.3782i	−0.969987	+	1.45670i
$465$		0			0
$466$	−2.15224	+	2.37652i	−0.0997004	+	0.110090i
$467$			35.9184i			1.66210i	0.556195	+	0.831052i	$0.312261\pi$
$467$			35.9184i			1.66210i	−0.556195	+	0.831052i	$0.687739\pi$
$468$	−0.110592	−	1.11378i	−0.00511211	−	0.0514845i
$469$	0.699652	+	0.699652i	0.0323069	+	0.0323069i
$470$		0			0
$471$	12.6887			0.584663
$472$	−10.2846	+	13.9017i	−0.473386	+	0.639880i
$473$	−15.9218	+	15.9218i	−0.732083	+	0.732083i
$474$	4.96405	−	0.245846i	0.228006	−	0.0112921i
$475$		0			0
$476$	−0.113990	−	1.14800i	−0.00522471	−	0.0526185i
$477$	19.4626			0.891133
$478$	−19.9932	+	0.990168i	−0.914467	+	0.0452892i
$479$	−7.66614			−0.350275			−0.175137	−	0.984544i	$-0.556037\pi$
$479$	−7.66614			−0.350275			−0.175137	+	0.984544i	$0.556037\pi$
$480$		0			0
$481$	−0.326159			−0.0148716
$482$	−6.00598	+	0.297448i	−0.273565	+	0.0135484i
$483$	1.02239			0.0465206
$484$	1.26145	+	12.7041i	0.0573385	+	0.577461i
$485$		0			0
$486$	22.2074	−	1.09983i	1.00735	−	0.0498891i
$487$	0.0452267	−	0.0452267i	0.00204942	−	0.00204942i	−0.706081	−	0.708131i	$-0.749539\pi$
$487$	0.0452267	−	0.0452267i	0.00204942	−	0.00204942i	0.708131	+	0.706081i	$0.249539\pi$
$488$	29.4294	+	21.7720i	1.33221	+	0.985572i
$489$	−0.869504			−0.0393203
$490$		0			0
$491$	3.49963	+	3.49963i	0.157936	+	0.157936i	0.781651	−	0.623715i	$-0.214378\pi$
$491$	3.49963	+	3.49963i	0.157936	+	0.157936i	−0.623715	+	0.781651i	$0.714378\pi$
$492$	−1.29015	−	12.9933i	−0.0581646	−	0.585781i
$493$		−	27.4757i		−	1.23744i
$494$	−0.807380	+	0.891519i	−0.0363258	+	0.0401113i
$495$		0			0
$496$	2.69962	+	13.4600i	0.121216	+	0.604372i
$497$	0.848499	−	0.848499i	0.0380604	−	0.0380604i
$498$	−12.8101	+	0.634426i	−0.574036	+	0.0284293i
$499$	18.7985	+	18.7985i	0.841535	+	0.841535i	0.989059	−	0.147523i	$-0.0471301\pi$
$499$	18.7985	+	18.7985i	0.841535	+	0.841535i	−0.147523	+	0.989059i	$0.547130\pi$
$500$		0			0
$501$	9.16889	−	9.16889i	0.409636	−	0.409636i
$502$	1.91309	+	1.73254i	0.0853854	+	0.0773270i
$503$	11.4064	+	11.4064i	0.508588	+	0.508588i	0.914093	−	0.405505i	$-0.132904\pi$
$503$	11.4064	+	11.4064i	0.508588	+	0.508588i	−0.405505	+	0.914093i	$0.632904\pi$
$504$	−0.790701	+	1.06880i	−0.0352206	+	0.0476080i
$505$		0			0
$506$	−1.90734	−	38.5125i	−0.0847917	−	1.71209i
$507$	−10.2281			−0.454247
$508$	−11.8266	−	9.69009i	−0.524719	−	0.429928i
$509$	9.87431	−	9.87431i	0.437671	−	0.437671i	−0.453556	−	0.891228i	$-0.649845\pi$
$509$	9.87431	−	9.87431i	0.437671	−	0.437671i	0.891228	+	0.453556i	$0.149845\pi$
$510$		0			0
$511$			3.17997i			0.140673i
$512$	−20.4202	+	9.74758i	−0.902454	+	0.430786i
$513$	−10.8438	−	10.8438i	−0.478765	−	0.478765i
$514$	−7.68549	+	8.48640i	−0.338992	+	0.374319i
$515$		0			0
$516$	−0.843284	−	8.49279i	−0.0371235	−	0.373874i
$517$			40.3663i			1.77531i
$518$	0.287164	+	0.260062i	0.0126173	+	0.0114265i
$519$		−	11.6244i		−	0.510256i
$520$		0			0
$521$			21.6730i			0.949512i	0.880117	+	0.474756i	$0.157464\pi$
$521$			21.6730i			0.949512i	−0.880117	+	0.474756i	$0.842536\pi$
$522$	−21.2546	+	23.4696i	−0.930290	+	1.02724i
$523$			40.3785i			1.76563i	0.469724	+	0.882813i	$0.344353\pi$
$523$			40.3785i			1.76563i	−0.469724	+	0.882813i	$0.655647\pi$
$524$	27.3834	−	33.4209i	1.19625	−	1.46000i
$525$		0			0
$526$	25.3027	+	22.9147i	1.10325	+	0.999128i
$527$	−7.07493	−	7.07493i	−0.308189	−	0.308189i
$528$	−10.9684	−	7.30367i	−0.477339	−	0.317851i
$529$			19.7666i			0.859418i
$530$		0			0
$531$	−10.2703	+	10.2703i	−0.445692	+	0.445692i
$532$	1.42170	−	0.141167i	0.0616386	−	0.00612035i
$533$	−1.94636			−0.0843063
$534$	6.52639	−	0.323221i	0.282424	−	0.0139872i
$535$		0			0
$536$	2.09211	+	13.9889i	0.0903653	+	0.604228i
$537$	−1.56127	−	1.56127i	−0.0673737	−	0.0673737i
$538$	−8.26268	+	9.12375i	−0.356229	+	0.393353i
$539$	−20.5217	+	20.5217i	−0.883933	+	0.883933i
$540$		0			0
$541$	6.26728	+	6.26728i	0.269451	+	0.269451i	0.828879	−	0.559428i	$-0.188979\pi$
$541$	6.26728	+	6.26728i	0.269451	+	0.269451i	−0.559428	+	0.828879i	$0.688979\pi$
$542$	−1.28954	−	26.0380i	−0.0553904	−	1.11843i
$543$	−1.15104	+	1.15104i	−0.0493958	+	0.0493958i
$544$	8.45025	−	14.1621i	0.362301	−	0.607197i
$545$		0			0
$546$	−0.0386049	−	0.0349615i	−0.00165214	−	0.00149622i
$547$		−	34.5372i		−	1.47671i	−0.674415	−	0.738353i	$-0.735604\pi$
$547$		−	34.5372i		−	1.47671i	0.674415	−	0.738353i	$-0.264396\pi$
$548$	−9.65138	−	7.90785i	−0.412287	−	0.337807i
$549$	21.7417	+	21.7417i	0.927915	+	0.927915i
$550$		0			0
$551$	34.0263			1.44957
$552$	11.7495	+	8.69233i	0.500092	+	0.369970i
$553$	−0.622274	+	0.622274i	−0.0264618	+	0.0264618i
$554$	−1.06526	−	21.5094i	−0.0452586	−	0.913847i
$555$		0			0
$556$	18.5484	−	22.6380i	0.786627	−	0.960063i
$557$	−21.4740			−0.909881			−0.454940	−	0.890522i	$-0.650339\pi$
$557$	−21.4740			−0.909881			−0.454940	+	0.890522i	$0.650339\pi$
$558$	0.570353	+	11.5164i	0.0241450	+	0.487528i
$559$	−1.27220			−0.0538084
$560$		0			0
$561$	9.60428			0.405493
$562$	−0.495156	−	9.99804i	−0.0208869	−	0.421742i
$563$	6.10126			0.257138			0.128569	−	0.991701i	$-0.458962\pi$
$563$	6.10126			0.257138			0.128569	+	0.991701i	$0.458962\pi$
$564$	−11.8348	−	9.69687i	−0.498337	−	0.408312i
$565$		0			0
$566$	1.39328	+	28.1328i	0.0585641	+	1.18251i
$567$	−0.527553	+	0.527553i	−0.0221551	+	0.0221551i
$568$	16.9650	−	2.53719i	0.711834	−	0.106458i
$569$	−31.1884			−1.30749			−0.653744	−	0.756716i	$-0.726802\pi$
$569$	−31.1884			−1.30749			−0.653744	+	0.756716i	$0.726802\pi$
$570$		0			0
$571$	−9.39471	−	9.39471i	−0.393156	−	0.393156i	0.482654	−	0.875811i	$-0.339673\pi$
$571$	−9.39471	−	9.39471i	−0.393156	−	0.393156i	−0.875811	+	0.482654i	$0.839673\pi$
$572$	−1.24494	+	1.51943i	−0.0520537	+	0.0635306i
$573$			0.225688i			0.00942824i
$574$	1.71366	+	1.55193i	0.0715266	+	0.0647762i
$575$		0			0
$576$	−18.1737	+	5.56030i	−0.757238	+	0.231679i
$577$	−16.2136	+	16.2136i	−0.674980	+	0.674980i	−0.958860	−	0.283880i	$-0.908378\pi$
$577$	−16.2136	+	16.2136i	−0.674980	+	0.674980i	0.283880	+	0.958860i	$0.408378\pi$
$578$	−0.594665	−	12.0073i	−0.0247348	−	0.499438i
$579$	−7.07922	−	7.07922i	−0.294203	−	0.294203i
$580$		0			0
$581$	1.60583	−	1.60583i	0.0666211	−	0.0666211i
$582$	0.546719	−	0.603693i	0.0226622	−	0.0250239i
$583$	−24.1529	−	24.1529i	−1.00031	−	1.00031i
$584$	−27.0359	+	36.5447i	−1.11875	+	1.51223i
$585$		0			0
$586$	32.6697	−	1.61798i	1.34957	−	0.0668380i
$587$	22.3084			0.920765			0.460382	−	0.887721i	$-0.347712\pi$
$587$	22.3084			0.920765			0.460382	+	0.887721i	$0.347712\pi$
$588$	−1.08692	−	10.9464i	−0.0448237	−	0.451424i
$589$	8.76169	−	8.76169i	0.361019	−	0.361019i
$590$		0			0
$591$			10.1214i			0.416338i
$592$	1.08910	+	5.43013i	0.0447616	+	0.223177i
$593$	5.08162	+	5.08162i	0.208677	+	0.208677i	0.803705	−	0.595028i	$-0.202859\pi$
$593$	5.08162	+	5.08162i	0.208677	+	0.208677i	−0.595028	+	0.803705i	$0.702859\pi$
$594$	−18.5639	−	16.8119i	−0.761687	−	0.689802i
$595$		0			0
$596$	15.5959	+	12.7785i	0.638833	+	0.523427i
$597$		−	14.3900i		−	0.588945i
$598$	1.46244	−	1.61484i	0.0598035	−	0.0660357i
$599$		−	45.7467i		−	1.86916i	−0.355752	−	0.934580i	$-0.615775\pi$
$599$		−	45.7467i		−	1.86916i	0.355752	−	0.934580i	$-0.384225\pi$
$600$		0			0
$601$		−	34.5280i		−	1.40843i	−0.709989	−	0.704213i	$-0.751300\pi$
$601$		−	34.5280i		−	1.40843i	0.709989	−	0.704213i	$-0.248700\pi$
$602$	1.12010	+	1.01439i	0.0456518	+	0.0413433i
$603$			11.8803i			0.483802i
$604$	−39.2548	+	3.89777i	−1.59726	+	0.158598i
$605$		0			0
$606$	3.78355	−	4.17784i	0.153696	−	0.169713i
$607$	−0.881912	−	0.881912i	−0.0357957	−	0.0357957i	0.688982	−	0.724778i	$-0.258058\pi$
$607$	−0.881912	−	0.881912i	−0.0357957	−	0.0357957i	−0.724778	+	0.688982i	$0.758058\pi$
$608$	17.5386	+	10.4649i	0.711284	+	0.424408i
$609$			1.47342i			0.0597061i
$610$		0			0
$611$	−1.61270	+	1.61270i	−0.0652429	+	0.0652429i
$612$	8.77888	−	10.7145i	0.354865	−	0.433106i
$613$	−19.7457			−0.797521			−0.398760	−	0.917055i	$-0.630560\pi$
$613$	−19.7457			−0.797521			−0.398760	+	0.917055i	$0.630560\pi$
$614$	−0.267853	−	5.40841i	−0.0108097	−	0.218266i
$615$		0			0
$616$	2.30761	−	0.345115i	0.0929764	−	0.0139051i
$617$	−24.0643	−	24.0643i	−0.968793	−	0.968793i	0.0307346	−	0.999528i	$-0.490215\pi$
$617$	−24.0643	−	24.0643i	−0.968793	−	0.968793i	−0.999528	+	0.0307346i	$0.990215\pi$
$618$	13.6657	+	12.3759i	0.549714	+	0.497834i
$619$	29.9131	−	29.9131i	1.20231	−	1.20231i	0.228846	−	0.973463i	$-0.426505\pi$
$619$	29.9131	−	29.9131i	1.20231	−	1.20231i	0.973463	−	0.228846i	$-0.0734953\pi$
$620$		0			0
$621$	19.6417	+	19.6417i	0.788196	+	0.788196i
$622$	−12.8112	+	0.634481i	−0.513684	+	0.0254404i
$623$	−0.818124	+	0.818124i	−0.0327774	+	0.0327774i
$624$	−0.146413	−	0.730000i	−0.00586121	−	0.0292234i
$625$		0			0
$626$	3.73759	−	4.12709i	0.149384	−	0.164952i
$627$			11.8941i			0.475004i
$628$	−31.9598	+	3.17342i	−1.27534	+	0.126633i
$629$	−2.85421	−	2.85421i	−0.113805	−	0.113805i
$630$		0			0
$631$	49.7586			1.98086			0.990429	−	0.138022i	$-0.0440743\pi$
$631$	49.7586			1.98086			0.990429	+	0.138022i	$0.0440743\pi$
$632$	−12.4418	+	1.86073i	−0.494908	+	0.0740160i
$633$	−1.89867	+	1.89867i	−0.0754652	+	0.0754652i
$634$	−20.9950	+	1.03978i	−0.833816	+	0.0412950i
$635$		0			0
$636$	12.8833	−	1.27924i	0.510857	−	0.0507251i
$637$	−1.63975			−0.0649694
$638$	55.5022	−	2.74876i	2.19735	−	0.108825i
$639$	14.4077			0.569961
$640$		0			0
$641$	−17.3779			−0.686386			−0.343193	−	0.939265i	$-0.611509\pi$
$641$	−17.3779			−0.686386			−0.343193	+	0.939265i	$0.611509\pi$
$642$	5.58131	−	0.276416i	0.220277	−	0.0109093i
$643$	36.4216			1.43633			0.718165	−	0.695873i	$-0.244982\pi$
$643$	36.4216			1.43633			0.718165	+	0.695873i	$0.244982\pi$
$644$	−2.57518	+	0.255700i	−0.101476	+	0.0100760i
$645$		0			0
$646$	−14.8670	+	0.736294i	−0.584936	+	0.0289691i
$647$	−3.55333	+	3.55333i	−0.139696	+	0.139696i	−0.773496	−	0.633801i	$-0.781494\pi$
$647$	−3.55333	+	3.55333i	−0.139696	+	0.139696i	0.633801	+	0.773496i	$0.281494\pi$
$648$	−10.5479	+	1.57749i	−0.414362	+	0.0619698i
$649$	25.4906			1.00059
$650$		0			0
$651$	0.379403	+	0.379403i	0.0148700	+	0.0148700i
$652$	2.19008	−	0.217462i	0.0857702	−	0.00851648i
$653$		−	38.4729i		−	1.50556i	−0.658271	−	0.752781i	$-0.728712\pi$
$653$		−	38.4729i		−	1.50556i	0.658271	−	0.752781i	$-0.271288\pi$
$654$	−3.92045	+	4.32901i	−0.153302	+	0.169278i
$655$		0			0
$656$	6.49920	+	32.4044i	0.253751	+	1.26518i
$657$	−26.9983	+	26.9983i	−1.05330	+	1.05330i
$658$	2.70577	−	0.134004i	0.105482	−	0.00522402i
$659$	17.1857	+	17.1857i	0.669459	+	0.669459i	0.957591	−	0.288132i	$-0.0930342\pi$
$659$	17.1857	+	17.1857i	0.669459	+	0.669459i	−0.288132	+	0.957591i	$0.593034\pi$
$660$		0			0
$661$	−4.63141	+	4.63141i	−0.180141	+	0.180141i	−0.791417	−	0.611276i	$-0.790656\pi$
$661$	−4.63141	+	4.63141i	−0.180141	+	0.180141i	0.611276	+	0.791417i	$0.290656\pi$
$662$	12.9556	+	11.7329i	0.503535	+	0.456013i
$663$	0.383707	+	0.383707i	0.0149019	+	0.0149019i
$664$	32.1071	−	4.80178i	1.24600	−	0.186345i
$665$		0			0
$666$	0.230095	+	4.64602i	0.00891602	+	0.180030i
$667$	−61.6330			−2.38644
$668$	−20.8012	+	25.3875i	−0.804822	+	0.982270i
$669$	−6.52928	+	6.52928i	−0.252436	+	0.252436i
$670$		0			0
$671$		−	53.9624i		−	2.08320i
$672$	−0.453156	+	0.759464i	−0.0174809	+	0.0292970i
$673$	3.70786	+	3.70786i	0.142928	+	0.142928i	0.774950	−	0.632022i	$-0.217775\pi$
$673$	3.70786	+	3.70786i	0.142928	+	0.142928i	−0.632022	+	0.774950i	$0.717775\pi$
$674$	−27.3077	+	30.1535i	−1.05185	+	1.16147i
$675$		0			0
$676$	25.7623	−	2.55805i	0.990859	−	0.0983865i
$677$		−	35.7948i		−	1.37570i	−0.725851	−	0.687852i	$-0.758554\pi$
$677$		−	35.7948i		−	1.37570i	0.725851	−	0.687852i	$-0.241446\pi$
$678$	−13.6364	−	12.3495i	−0.523704	−	0.474279i
$679$			0.144211i			0.00553432i
$680$		0			0
$681$		−	8.36729i		−	0.320635i
$682$	13.5839	−	14.9995i	0.520154	−	0.574360i
$683$			30.5276i			1.16810i	0.811716	+	0.584052i	$0.198534\pi$
$683$			30.5276i			1.16810i	−0.811716	+	0.584052i	$0.801466\pi$
$684$	13.2689	+	10.8719i	0.507351	+	0.415697i
$685$		0			0
$686$	2.89553	+	2.62226i	0.110552	+	0.100118i
$687$	3.56446	+	3.56446i	0.135993	+	0.135993i
$688$	4.24808	+	21.1805i	0.161956	+	0.807498i
$689$		−	1.92989i		−	0.0735231i
$690$		0			0
$691$	−16.3626	+	16.3626i	−0.622463	+	0.622463i	−0.946161	−	0.323698i	$-0.895074\pi$
$691$	−16.3626	+	16.3626i	−0.622463	+	0.622463i	0.323698	+	0.946161i	$0.395074\pi$
$692$	2.90726	+	29.2793i	0.110518	+	1.11303i
$693$	1.95977			0.0744456
$694$	−10.3630	+	0.513228i	−0.393372	+	0.0194819i
$695$		0			0
$696$	−12.5269	+	16.9328i	−0.474832	+	0.641835i
$697$	−17.0326	−	17.0326i	−0.645155	−	0.645155i
$698$	−6.70449	+	7.40317i	−0.253769	+	0.280214i
$699$	−1.26671	+	1.26671i	−0.0479114	+	0.0479114i
$700$		0			0
$701$	−5.97112	−	5.97112i	−0.225526	−	0.225526i	0.585295	−	0.810821i	$-0.300979\pi$
$701$	−5.97112	−	5.97112i	−0.225526	−	0.225526i	−0.810821	+	0.585295i	$0.800979\pi$
$702$	−0.0699953	−	1.41332i	−0.00264180	−	0.0533425i
$703$	3.53470	−	3.53470i	0.133314	−	0.133314i
$704$	29.4536	+	15.6531i	1.11007	+	0.589947i
$705$		0			0
$706$	−8.51916	−	7.71516i	−0.320623	−	0.290364i
$707$			0.998009i			0.0375340i
$708$	−6.12338	+	7.47347i	−0.230131	+	0.280870i
$709$	−4.50479	−	4.50479i	−0.169181	−	0.169181i	0.617438	−	0.786619i	$-0.288170\pi$
$709$	−4.50479	−	4.50479i	−0.169181	−	0.169181i	−0.786619	+	0.617438i	$0.788170\pi$
$710$		0			0
$711$	−10.5664			−0.396270
$712$	−16.3576	+	2.44636i	−0.613028	+	0.0916814i
$713$	−15.8704	+	15.8704i	−0.594350	+	0.594350i
$714$	−0.0318833	−	0.643779i	−0.00119320	−	0.0240928i
$715$		0			0
$716$	4.32295	+	3.54200i	0.161556	+	0.132371i
$717$	−11.1843			−0.417686
$718$	−1.55968	−	31.4926i	−0.0582067	−	1.17529i
$719$	34.8855			1.30101			0.650504	−	0.759503i	$-0.274558\pi$
$719$	34.8855			1.30101			0.650504	+	0.759503i	$0.274558\pi$
$720$		0			0
$721$	−3.26448			−0.121576
$722$	0.417281	+	8.42562i	0.0155296	+	0.313569i
$723$	−3.35979			−0.124952
$724$	2.61133	−	3.18708i	0.0970493	−	0.118447i
$725$		0			0
$726$	0.352831	+	7.12426i	0.0130948	+	0.264406i
$727$	20.1354	−	20.1354i	0.746781	−	0.746781i	−0.227092	−	0.973873i	$-0.572922\pi$
$727$	20.1354	−	20.1354i	0.746781	−	0.746781i	0.973873	+	0.227092i	$0.0729219\pi$
$728$	0.105981	+	0.0784050i	0.00392791	+	0.00290588i
$729$	1.11076			0.0411393
$730$		0			0
$731$	−11.1330	−	11.1330i	−0.411769	−	0.411769i
$732$	15.8210	+	12.9629i	0.584762	+	0.479124i
$733$		−	29.8111i		−	1.10110i	−0.834803	−	0.550549i	$-0.814419\pi$
$733$		−	29.8111i		−	1.10110i	0.834803	−	0.550549i	$-0.185581\pi$
$734$	−32.8987	−	29.7938i	−1.21431	−	1.09971i
$735$		0			0
$736$	−31.7683	−	18.9555i	−1.17099	−	0.698707i
$737$	14.7432	−	14.7432i	0.543074	−	0.543074i
$738$	1.37310	+	27.7252i	0.0505444	+	1.02058i
$739$	18.8014	+	18.8014i	0.691620	+	0.691620i	0.962588	−	0.270969i	$-0.0873439\pi$
$739$	18.8014	+	18.8014i	0.691620	+	0.691620i	−0.270969	+	0.962588i	$0.587344\pi$
$740$		0			0
$741$	−0.475188	+	0.475188i	−0.0174565	+	0.0174565i
$742$	−1.53880	+	1.69916i	−0.0564910	+	0.0623780i
$743$	−8.34445	−	8.34445i	−0.306128	−	0.306128i	0.537277	−	0.843406i	$-0.319453\pi$
$743$	−8.34445	−	8.34445i	−0.306128	−	0.306128i	−0.843406	+	0.537277i	$0.819453\pi$
$744$	1.13449	+	7.58581i	0.0415926	+	0.278109i
$745$		0			0
$746$	−38.3620	+	1.89989i	−1.40453	+	0.0695599i
$747$	27.2674			0.997662
$748$	−24.1910	+	2.40202i	−0.884510	+	0.0878266i
$749$	−0.699652	+	0.699652i	−0.0255647	+	0.0255647i
$750$		0			0
$751$			40.1477i			1.46501i	0.680761	+	0.732505i	$0.261649\pi$
$751$			40.1477i			1.46501i	−0.680761	+	0.732505i	$0.738351\pi$
$752$	32.2344	+	21.4643i	1.17547	+	0.782722i
$753$	1.01970	+	1.01970i	0.0371598	+	0.0371598i
$754$	2.32722	+	2.10759i	0.0847525	+	0.0767538i
$755$		0			0
$756$	−1.06528	+	1.30016i	−0.0387440	+	0.0472863i
$757$			31.5795i			1.14778i	0.818934	+	0.573888i	$0.194565\pi$
$757$			31.5795i			1.14778i	−0.818934	+	0.573888i	$0.805435\pi$
$758$	19.8160	−	21.8810i	0.719748	−	0.794755i
$759$		−	21.5442i		−	0.782004i
$760$		0			0
$761$		−	29.0804i		−	1.05416i	−0.849815	−	0.527081i	$-0.823286\pi$
$761$		−	29.0804i		−	1.05416i	0.849815	−	0.527081i	$-0.176714\pi$
$762$	−6.33187	−	5.73429i	−0.229380	−	0.207732i
$763$		−	1.03412i		−	0.0374377i
$764$	−0.0564443	−	0.568455i	−0.00204208	−	0.0205660i
$765$		0			0
$766$	−19.5977	+	21.6400i	−0.708093	+	0.781884i
$767$	1.01839	+	1.01839i	0.0367719	+	0.0367719i
$768$	−11.6646	+	4.87517i	−0.420912	+	0.175917i
$769$			44.9984i			1.62268i	0.584573	+	0.811341i	$0.301262\pi$
$769$			44.9984i			1.62268i	−0.584573	+	0.811341i	$0.698738\pi$
$770$		0			0
$771$	−4.52333	+	4.52333i	−0.162904	+	0.162904i
$772$	19.6014	+	16.0604i	0.705472	+	0.578028i
$773$	35.9788			1.29407			0.647035	−	0.762461i	$-0.276009\pi$
$773$	35.9788			1.29407			0.647035	+	0.762461i	$0.276009\pi$
$774$	0.897499	+	18.1220i	0.0322599	+	0.651383i
$775$		0			0
$776$	−1.22608	+	1.65730i	−0.0440136	+	0.0594936i
$777$	0.153061	+	0.153061i	0.00549104	+	0.00549104i
$778$	5.83702	+	5.28614i	0.209267	+	0.189517i
$779$	21.0934	−	21.0934i	0.755749	−	0.755749i
$780$		0			0
$781$	−17.8798	−	17.8798i	−0.639789	−	0.639789i
$782$	26.9292	−	1.33368i	0.962986	−	0.0476921i
$783$	−28.3067	+	28.3067i	−1.01160	+	1.01160i
$784$	5.47539	+	27.2997i	0.195550	+	0.974990i
$785$		0			0
$786$	16.2046	−	17.8933i	0.578000	−	0.638234i
$787$		−	18.5853i		−	0.662496i	−0.943544	−	0.331248i	$-0.892530\pi$
$787$		−	18.5853i		−	0.662496i	0.943544	−	0.331248i	$-0.107470\pi$
$788$	−2.53135	−	25.4934i	−0.0901756	−	0.908166i
$789$	13.4866	+	13.4866i	0.480135	+	0.480135i
$790$		0			0
$791$	3.25750			0.115823
$792$	22.5220	+	16.6619i	0.800284	+	0.592053i
$793$	2.15589	−	2.15589i	0.0765578	−	0.0765578i
$794$	−38.1370	+	1.88875i	−1.35343	+	0.0670291i
$795$		0			0
$796$	3.59893	+	36.2452i	0.127561	+	1.28468i
$797$	−27.5437			−0.975649			−0.487824	−	0.872942i	$-0.662209\pi$
$797$	−27.5437			−0.975649			−0.487824	+	0.872942i	$0.662209\pi$
$798$	0.797265	−	0.0394848i	0.0282229	−	0.00139775i
$799$	−28.2254			−0.998544
$800$		0			0
$801$	−13.8919			−0.490848
$802$	−4.27347	+	0.211645i	−0.150902	+	0.00747344i
$803$	67.0091			2.36470
$804$	0.780865	+	7.86416i	0.0275390	+	0.277348i
$805$		0			0
$806$	1.14195	−	0.0565556i	0.0402236	−	0.00199208i
$807$	−4.86304	+	4.86304i	−0.171187	+	0.171187i
$808$	−8.48501	+	11.4693i	−0.298502	+	0.403488i
$809$	−45.0587			−1.58418			−0.792090	−	0.610404i	$-0.791007\pi$
$809$	−45.0587			−1.58418			−0.792090	+	0.610404i	$0.791007\pi$
$810$		0			0
$811$	−19.2189	−	19.2189i	−0.674865	−	0.674865i	0.283968	−	0.958834i	$-0.408349\pi$
$811$	−19.2189	−	19.2189i	−0.674865	−	0.674865i	−0.958834	+	0.283968i	$0.908349\pi$
$812$	−0.368501	−	3.71121i	−0.0129319	−	0.130238i
$813$		−	14.5658i		−	0.510846i
$814$	5.48010	−	6.05119i	0.192078	−	0.212094i
$815$		0			0
$816$	5.10696	−	7.66947i	0.178779	−	0.268485i
$817$	13.7873	−	13.7873i	0.482356	−	0.482356i
$818$	27.7628	−	1.37496i	0.970704	−	0.0480744i
$819$	0.0782961	+	0.0782961i	0.00273589	+	0.00273589i
$820$		0			0
$821$	−30.5315	+	30.5315i	−1.06556	+	1.06556i	−0.0678632	+	0.997695i	$0.521618\pi$
$821$	−30.5315	+	30.5315i	−1.06556	+	1.06556i	−0.997695	+	0.0678632i	$0.978382\pi$
$822$	−5.16729	−	4.67962i	−0.180230	−	0.163221i
$823$	18.1848	+	18.1848i	0.633884	+	0.633884i	0.949040	−	0.315156i	$-0.102057\pi$
$823$	18.1848	+	18.1848i	0.633884	+	0.633884i	−0.315156	+	0.949040i	$0.602057\pi$
$824$	−37.5159	−	27.7544i	−1.30693	−	0.966870i
$825$		0			0
$826$	−0.0846210	−	1.70864i	−0.00294434	−	0.0594513i
$827$	20.7073			0.720063			0.360032	−	0.932940i	$-0.382766\pi$
$827$	20.7073			0.720063			0.360032	+	0.932940i	$0.382766\pi$
$828$	−24.0345	−	19.6926i	−0.835256	−	0.684367i
$829$	19.5152	−	19.5152i	0.677790	−	0.677790i	−0.281710	−	0.959500i	$-0.590901\pi$
$829$	19.5152	−	19.5152i	0.677790	−	0.677790i	0.959500	+	0.281710i	$0.0909015\pi$
$830$		0			0
$831$		−	12.0325i		−	0.417403i
$832$	0.551353	+	1.80209i	0.0191147	+	0.0624761i
$833$	−14.3494	−	14.3494i	−0.497179	−	0.497179i
$834$	10.9764	−	12.1202i	0.380080	−	0.419689i
$835$		0			0
$836$	−2.97470	−	29.9585i	−0.102882	−	1.03613i
$837$			14.5778i			0.503882i
$838$	23.9908	+	21.7266i	0.828748	+	0.750534i
$839$		−	10.8185i		−	0.373496i	−0.982408	−	0.186748i	$-0.940205\pi$
$839$		−	10.8185i		−	0.373496i	0.982408	−	0.186748i	$-0.0597948\pi$
$840$		0			0
$841$		−	59.8223i		−	2.06284i
$842$	31.1254	−	34.3690i	1.07265	−	1.18443i
$843$		−	5.59298i		−	0.192632i
$844$	4.30745	−	5.25716i	0.148268	−	0.180959i
$845$		0			0
$846$	24.1100	+	21.8346i	0.828920	+	0.750690i
$847$	−0.893071	−	0.893071i	−0.0306863	−	0.0306863i
$848$	−32.1302	+	6.44422i	−1.10336	+	0.221295i
$849$			15.7377i			0.540116i
$850$		0			0
$851$	−6.40253	+	6.40253i	−0.219476	+	0.219476i
$852$	9.53722	−	0.946990i	0.326740	−	0.0324433i
$853$	−5.42003			−0.185578			−0.0927892	−	0.995686i	$-0.529578\pi$
$853$	−5.42003			−0.185578			−0.0927892	+	0.995686i	$0.529578\pi$
$854$	−3.61712	+	0.179139i	−0.123775	+	0.00613001i
$855$		0			0
$856$	−13.9889	+	2.09211i	−0.478131	+	0.0715068i
$857$	−4.89352	−	4.89352i	−0.167160	−	0.167160i	0.618570	−	0.785730i	$-0.287712\pi$
$857$	−4.89352	−	4.89352i	−0.167160	−	0.167160i	−0.785730	+	0.618570i	$0.787712\pi$
$858$	−0.736719	+	0.813494i	−0.0251512	+	0.0277722i
$859$	33.4966	−	33.4966i	1.14289	−	1.14289i	0.154969	−	0.987919i	$-0.450472\pi$
$859$	33.4966	−	33.4966i	1.14289	−	1.14289i	0.987919	−	0.154969i	$-0.0495279\pi$
$860$		0			0
$861$	0.913395	+	0.913395i	0.0311284	+	0.0311284i
$862$	2.08397	+	42.0789i	0.0709802	+	1.43321i
$863$	28.0996	−	28.0996i	0.956521	−	0.956521i	−0.0425724	−	0.999093i	$-0.513555\pi$
$863$	28.0996	−	28.0996i	0.956521	−	0.956521i	0.999093	+	0.0425724i	$0.0135553\pi$
$864$	−23.2963	+	5.88464i	−0.792555	+	0.200199i
$865$		0			0
$866$	−28.2533	−	25.5869i	−0.960087	−	0.869477i
$867$		−	6.71697i		−	0.228120i
$868$	−1.05052	−	0.860740i	−0.0356569	−	0.0292154i
$869$	13.1127	+	13.1127i	0.444819	+	0.444819i
$870$		0			0
$871$	1.17803			0.0399162
$872$	8.79204	−	11.8843i	0.297736	−	0.402453i
$873$	−1.22437	+	1.22437i	−0.0414387	+	0.0414387i
$874$	1.65164	+	33.3495i	0.0558677	+	1.12806i
$875$		0			0
$876$	−16.0970	+	19.6461i	−0.543869	+	0.663781i
$877$	−21.3398			−0.720593			−0.360296	−	0.932838i	$-0.617324\pi$
$877$	−21.3398			−0.720593			−0.360296	+	0.932838i	$0.617324\pi$
$878$	−0.427182	−	8.62553i	−0.0144167	−	0.291098i
$879$	18.2757			0.616423
$880$		0			0
$881$	−34.8632			−1.17457			−0.587285	−	0.809380i	$-0.699803\pi$
$881$	−34.8632			−1.17457			−0.587285	+	0.809380i	$0.699803\pi$
$882$	1.15680	+	23.3577i	0.0389513	+	0.786494i
$883$	−16.9490			−0.570381			−0.285190	−	0.958471i	$-0.592057\pi$
$883$	−16.9490			−0.570381			−0.285190	+	0.958471i	$0.592057\pi$
$884$	−1.06243	−	0.870505i	−0.0357335	−	0.0292782i
$885$		0			0
$886$	1.12739	+	22.7640i	0.0378755	+	0.764771i
$887$	33.7217	−	33.7217i	1.13226	−	1.13226i	0.142464	−	0.989800i	$-0.454498\pi$
$887$	33.7217	−	33.7217i	1.13226	−	1.13226i	0.989800	−	0.142464i	$-0.0455025\pi$
$888$	0.457685	+	3.06032i	0.0153589	+	0.102698i
$889$	1.51257			0.0507300
$890$		0			0
$891$	11.1167	+	11.1167i	0.372424	+	0.372424i
$892$	14.8128	−	18.0787i	0.495969	−	0.605320i
$893$		−	34.9548i		−	1.16972i
$894$	8.34994	+	7.56191i	0.279264	+	0.252908i
$895$		0			0
$896$	0.951455	−	2.02625i	0.0317859	−	0.0676922i
$897$	0.860725	−	0.860725i	0.0287388	−	0.0287388i
$898$	0.130926	+	2.64362i	0.00436906	+	0.0882187i
$899$	−22.8715	−	22.8715i	−0.762808	−	0.762808i
$900$		0			0
$901$	16.8885	−	16.8885i	0.562637	−	0.562637i
$902$	32.7026	−	36.1106i	1.08888	−	1.20235i
$903$	0.597023	+	0.597023i	0.0198677	+	0.0198677i
$904$	37.4356	+	27.6950i	1.24509	+	0.921123i
$905$		0			0
$906$	−22.0134	+	1.09022i	−0.731347	+	0.0362202i
$907$	18.9797			0.630210			0.315105	−	0.949057i	$-0.397960\pi$
$907$	18.9797			0.630210			0.315105	+	0.949057i	$0.397960\pi$
$908$	2.09265	+	21.0753i	0.0694471	+	0.699407i
$909$	−8.47322	+	8.47322i	−0.281039	+	0.281039i
$910$		0			0
$911$		−	15.0326i		−	0.498053i	−0.968497	−	0.249027i	$-0.919889\pi$
$911$		−	15.0326i		−	0.498053i	0.968497	−	0.249027i	$-0.0801107\pi$
$912$	9.49799	+	6.32453i	0.314510	+	0.209426i
$913$	−33.8385	−	33.8385i	−1.11989	−	1.11989i
$914$	−15.9302	−	14.4267i	−0.526923	−	0.477194i
$915$		0			0
$916$	−9.86953	−	8.08659i	−0.326098	−	0.267189i
$917$			4.27439i			0.141153i
$918$	11.7554	−	12.9805i	0.387987	−	0.428420i
$919$		−	37.9183i		−	1.25081i	−0.780301	−	0.625404i	$-0.784934\pi$
$919$		−	37.9183i		−	1.25081i	0.780301	−	0.625404i	$-0.215066\pi$
$920$		0			0
$921$		−	3.02550i		−	0.0996938i
$922$	−24.5655	−	22.2471i	−0.809021	−	0.732669i
$923$		−	1.42865i		−	0.0470247i
$924$	1.29727	−	0.128812i	0.0426772	−	0.00423759i
$925$		0			0
$926$	25.6787	−	28.3547i	0.843854	−	0.931794i
$927$	−27.7158	−	27.7158i	−0.910308	−	0.910308i
$928$	27.3176	−	45.7828i	0.896744	−	1.50289i
$929$		−	22.5607i		−	0.740193i	−0.928993	−	0.370096i	$-0.879325\pi$
$929$		−	22.5607i		−	0.740193i	0.928993	−	0.370096i	$-0.120675\pi$
$930$		0			0
$931$	17.7706	−	17.7706i	0.582406	−	0.582406i
$932$	2.87375	−	3.50736i	0.0941328	−	0.114887i
$933$	−7.16670			−0.234627
$934$	−2.51262	−	50.7340i	−0.0822154	−	1.66007i
$935$		0			0
$936$	0.234122	+	1.56546i	0.00765252	+	0.0511686i
$937$	−7.98622	−	7.98622i	−0.260898	−	0.260898i	0.564521	−	0.825419i	$-0.309061\pi$
$937$	−7.98622	−	7.98622i	−0.260898	−	0.260898i	−0.825419	+	0.564521i	$0.809061\pi$
$938$	−1.03719	−	0.939303i	−0.0338654	−	0.0306693i
$939$	2.19978	−	2.19978i	0.0717871	−	0.0717871i
$940$		0			0
$941$	26.4926	+	26.4926i	0.863633	+	0.863633i	0.991758	−	0.128125i	$-0.0408958\pi$
$941$	26.4926	+	26.4926i	0.863633	+	0.863633i	−0.128125	+	0.991758i	$0.540896\pi$
$942$	−17.9225	+	0.887618i	−0.583947	+	0.0289202i
$943$	−38.2072	+	38.2072i	−1.24420	+	1.24420i
$944$	13.5543	−	20.3554i	0.441155	−	0.662512i
$945$		0			0
$946$	21.3754	−	23.6030i	0.694975	−	0.767400i
$947$			25.8742i			0.840797i	0.907339	+	0.420399i	$0.138110\pi$
$947$			25.8742i			0.840797i	−0.907339	+	0.420399i	$0.861890\pi$
$948$	−6.99443	+	0.694506i	−0.227169	+	0.0225565i
$949$	2.67712	+	2.67712i	0.0869031	+	0.0869031i
$950$		0			0
$951$	−11.7447			−0.380849
$952$	0.241315	+	1.61356i	0.00782108	+	0.0522957i
$953$	0.934991	−	0.934991i	0.0302873	−	0.0302873i	−0.691801	−	0.722088i	$-0.743182\pi$
$953$	0.934991	−	0.934991i	0.0302873	−	0.0302873i	0.722088	+	0.691801i	$0.243182\pi$
$954$	−27.4906	+	1.36148i	−0.890042	+	0.0440796i
$955$		0			0
$956$	28.1707	−	2.79719i	0.911107	−	0.0904676i
$957$	31.0483			1.00365
$958$	10.8283	−	0.536274i	0.349846	−	0.0173262i
$959$	1.23437			0.0398600
$960$		0			0
$961$	19.2213			0.620041
$962$	0.460694	−	0.0228160i	0.0148534	−	0.000735618i
$963$	−11.8803			−0.382836
$964$	8.46253	−	0.840279i	0.272560	−	0.0270636i
$965$		0			0
$966$	−1.44411	+	0.0715202i	−0.0464636	+	0.00230112i
$967$	1.89923	−	1.89923i	0.0610752	−	0.0610752i	−0.675909	−	0.736985i	$-0.736249\pi$
$967$	1.89923	−	1.89923i	0.0610752	−	0.0610752i	0.736985	+	0.675909i	$0.236249\pi$
$968$	−2.67047	−	17.8561i	−0.0858322	−	0.573918i
$969$	−8.31672			−0.267172
$970$		0			0
$971$	11.8787	+	11.8787i	0.381204	+	0.381204i	0.871536	−	0.490332i	$-0.163124\pi$
$971$	11.8787	+	11.8787i	0.381204	+	0.381204i	−0.490332	+	0.871536i	$0.663124\pi$
$972$	−31.2906	+	3.10697i	−1.00365	+	0.0996561i
$973$			2.89530i			0.0928191i
$974$	−0.0607181	+	0.0670456i	−0.00194553	+	0.00214828i
$975$		0			0
$976$	−43.0915	−	28.6939i	−1.37933	−	0.918468i
$977$	−23.4462	+	23.4462i	−0.750109	+	0.750109i	−0.974499	−	0.224390i	$-0.927961\pi$
$977$	−23.4462	+	23.4462i	−0.750109	+	0.750109i	0.224390	+	0.974499i	$0.427961\pi$
$978$	1.22816	−	0.0608249i	0.0392722	−	0.00194497i
$979$	17.2397	+	17.2397i	0.550984	+	0.550984i
$980$		0			0
$981$	8.77982	−	8.77982i	0.280318	−	0.280318i
$982$	−5.18798	−	4.69835i	−0.165555	−	0.149930i
$983$	5.90331	+	5.90331i	0.188286	+	0.188286i	0.794955	−	0.606669i	$-0.207494\pi$
$983$	5.90331	+	5.90331i	0.188286	+	0.188286i	−0.606669	+	0.794955i	$0.707494\pi$
$984$	2.73124	+	18.2625i	0.0870689	+	0.582187i
$985$		0			0
$986$	1.92202	+	38.8089i	0.0612097	+	1.23593i
$987$	1.51363			0.0481793
$988$	1.07805	−	1.31573i	0.0342972	−	0.0418591i
$989$	−24.9734	+	24.9734i	−0.794107	+	0.794107i
$990$		0			0
$991$			8.28808i			0.263280i	0.991298	+	0.131640i	$0.0420242\pi$
$991$			8.28808i			0.263280i	−0.991298	+	0.131640i	$0.957976\pi$
$992$	−4.75474	−	18.8232i	−0.150963	−	0.597636i
$993$	6.90548	+	6.90548i	0.219139	+	0.219139i
$994$	−1.13913	+	1.25785i	−0.0361311	+	0.0398964i
$995$		0			0
$996$	18.0497	−	1.79223i	0.571927	−	0.0567890i
$997$		−	12.9184i		−	0.409130i	−0.978853	−	0.204565i	$-0.934422\pi$
$997$		−	12.9184i		−	0.409130i	0.978853	−	0.204565i	$-0.0655780\pi$
$998$	−27.8675	−	25.2375i	−0.882131	−	0.798879i
$999$			5.88107i			0.186069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.s.e.243.1	yes	24
4.3	odd	2		1600.2.s.e.943.8		24
5.2	odd	4		400.2.j.e.307.6	yes	24
5.3	odd	4		400.2.j.e.307.7	yes	24
5.4	even	2	inner	400.2.s.e.243.12	yes	24
16.5	even	4		1600.2.j.e.143.8		24
16.11	odd	4		400.2.j.e.43.6	✓	24
20.3	even	4		1600.2.j.e.1007.8		24
20.7	even	4		1600.2.j.e.1007.5		24
20.19	odd	2		1600.2.s.e.943.5		24
80.27	even	4	inner	400.2.s.e.107.1	yes	24
80.37	odd	4		1600.2.s.e.207.8		24
80.43	even	4	inner	400.2.s.e.107.12	yes	24
80.53	odd	4		1600.2.s.e.207.5		24
80.59	odd	4		400.2.j.e.43.7	yes	24
80.69	even	4		1600.2.j.e.143.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.e.43.6	✓	24	16.11	odd	4
400.2.j.e.43.7	yes	24	80.59	odd	4
400.2.j.e.307.6	yes	24	5.2	odd	4
400.2.j.e.307.7	yes	24	5.3	odd	4
400.2.s.e.107.1	yes	24	80.27	even	4	inner
400.2.s.e.107.12	yes	24	80.43	even	4	inner
400.2.s.e.243.1	yes	24	1.1	even	1	trivial
400.2.s.e.243.12	yes	24	5.4	even	2	inner
1600.2.j.e.143.5		24	80.69	even	4
1600.2.j.e.143.8		24	16.5	even	4
1600.2.j.e.1007.5		24	20.7	even	4
1600.2.j.e.1007.8		24	20.3	even	4
1600.2.s.e.207.5		24	80.53	odd	4
1600.2.s.e.207.8		24	80.37	odd	4
1600.2.s.e.943.5		24	20.19	odd	2
1600.2.s.e.943.8		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41248 + 0.0699536i) q^{2} -0.790153 q^{3} +(1.99021 - 0.197616i) q^{4} +(1.11608 - 0.0552740i) q^{6} +(-0.139907 + 0.139907i) q^{7} +(-2.79732 + 0.418352i) q^{8} -2.37566 q^{9} +O(q^{10})\)	\(q+(-1.41248 + 0.0699536i) q^{2} -0.790153 q^{3} +(1.99021 - 0.197616i) q^{4} +(1.11608 - 0.0552740i) q^{6} +(-0.139907 + 0.139907i) q^{7} +(-2.79732 + 0.418352i) q^{8} -2.37566 q^{9} +(2.94816 + 2.94816i) q^{11} +(-1.57257 + 0.156147i) q^{12} +0.235568i q^{13} +(0.187829 - 0.207403i) q^{14} +(3.92190 - 0.786598i) q^{16} +(-2.06145 + 2.06145i) q^{17} +(3.35558 - 0.166186i) q^{18} +(-2.55293 - 2.55293i) q^{19} +(0.110548 - 0.110548i) q^{21} +(-4.37046 - 3.95799i) q^{22} +(4.62421 + 4.62421i) q^{23} +(2.21031 - 0.330562i) q^{24} +(-0.0164788 - 0.332735i) q^{26} +4.24759 q^{27} +(-0.250797 + 0.306093i) q^{28} +(-6.66417 + 6.66417i) q^{29} +3.43202i q^{31} +(-5.48458 + 1.38541i) q^{32} +(-2.32950 - 2.32950i) q^{33} +(2.76756 - 3.05597i) q^{34} +(-4.72807 + 0.469469i) q^{36} +1.38457i q^{37} +(3.78455 + 3.42738i) q^{38} -0.186135i q^{39} +8.26242i q^{41} +(-0.148414 + 0.163880i) q^{42} +5.40057i q^{43} +(6.45007 + 5.28486i) q^{44} +(-6.85509 - 6.20813i) q^{46} +(6.84602 + 6.84602i) q^{47} +(-3.09890 + 0.621532i) q^{48} +6.96085i q^{49} +(1.62886 - 1.62886i) q^{51} +(0.0465521 + 0.468830i) q^{52} -8.19252 q^{53} +(-5.99965 + 0.297134i) q^{54} +(0.332834 - 0.449895i) q^{56} +(2.01720 + 2.01720i) q^{57} +(8.94684 - 9.87920i) q^{58} +(4.32313 - 4.32313i) q^{59} +(-9.15188 - 9.15188i) q^{61} +(-0.240082 - 4.84766i) q^{62} +(0.332372 - 0.332372i) q^{63} +(7.64996 - 2.34053i) q^{64} +(3.45333 + 3.12742i) q^{66} -5.00083i q^{67} +(-3.69535 + 4.51010i) q^{68} +(-3.65383 - 3.65383i) q^{69} -6.06473 q^{71} +(6.64547 - 0.993862i) q^{72} +(11.3646 - 11.3646i) q^{73} +(-0.0968554 - 1.95568i) q^{74} +(-5.58537 - 4.57637i) q^{76} -0.824938 q^{77} +(0.0130208 + 0.262912i) q^{78} +4.44776 q^{79} +3.77073 q^{81} +(-0.577986 - 11.6705i) q^{82} -11.4778 q^{83} +(0.198168 - 0.241860i) q^{84} +(-0.377790 - 7.62822i) q^{86} +(5.26571 - 5.26571i) q^{87} +(-9.48031 - 7.01357i) q^{88} +5.84762 q^{89} +(-0.0329576 - 0.0329576i) q^{91} +(10.1170 + 8.28934i) q^{92} -2.71182i q^{93} +(-10.1488 - 9.19097i) q^{94} +(4.33366 - 1.09468i) q^{96} +(0.515382 - 0.515382i) q^{97} +(-0.486937 - 9.83208i) q^{98} +(-7.00383 - 7.00383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} + 12 q^{6} + 40 q^{9}+O(q^{10}) \) 24 * q + 8 * q^4 + 12 * q^6 + 40 * q^9	\( 24 q + 8 q^{4} + 12 q^{6} + 40 q^{9} - 20 q^{11} - 44 q^{14} - 4 q^{16} + 12 q^{19} - 24 q^{24} + 32 q^{26} - 8 q^{29} - 32 q^{34} - 60 q^{36} + 44 q^{44} - 76 q^{46} + 20 q^{51} - 16 q^{54} - 28 q^{56} - 8 q^{59} - 48 q^{61} + 32 q^{64} - 8 q^{66} + 64 q^{69} - 16 q^{71} - 36 q^{74} + 40 q^{76} + 104 q^{79} + 48 q^{81} - 44 q^{84} + 84 q^{86} - 96 q^{89} + 64 q^{91} + 40 q^{94} + 212 q^{96} - 128 q^{99}+O(q^{100}) \) 24 * q + 8 * q^4 + 12 * q^6 + 40 * q^9 - 20 * q^11 - 44 * q^14 - 4 * q^16 + 12 * q^19 - 24 * q^24 + 32 * q^26 - 8 * q^29 - 32 * q^34 - 60 * q^36 + 44 * q^44 - 76 * q^46 + 20 * q^51 - 16 * q^54 - 28 * q^56 - 8 * q^59 - 48 * q^61 + 32 * q^64 - 8 * q^66 + 64 * q^69 - 16 * q^71 - 36 * q^74 + 40 * q^76 + 104 * q^79 + 48 * q^81 - 44 * q^84 + 84 * q^86 - 96 * q^89 + 64 * q^91 + 40 * q^94 + 212 * q^96 - 128 * q^99

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