LMFDB - Embedded newform 525.2.j.b.218.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(218,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("525.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.j (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			218.3
Character	$\chi$	$=$	525.218
Dual form			525.2.j.b.407.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24414 - 1.24414i) q^{2} +(-0.474620 - 1.66575i) q^{3} +1.09578i q^{4} +(-1.48194 + 2.66293i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.12498 + 1.12498i) q^{8} +(-2.54947 + 1.58120i) q^{9} +O(q^{10})$	\(q+(-1.24414 - 1.24414i) q^{2} +(-0.474620 - 1.66575i) q^{3} +1.09578i q^{4} +(-1.48194 + 2.66293i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.12498 + 1.12498i) q^{8} +(-2.54947 + 1.58120i) q^{9} +1.55221i q^{11} +(1.82530 - 0.520079i) q^{12} +(4.50889 + 4.50889i) q^{13} +1.75948 q^{14} +4.99083 q^{16} +(-2.13370 - 2.13370i) q^{17} +(5.13914 + 1.20467i) q^{18} +4.20993i q^{19} +(1.51347 + 0.842259i) q^{21} +(1.93117 - 1.93117i) q^{22} +(-3.76050 + 3.76050i) q^{23} +(2.40787 + 1.34000i) q^{24} -11.2194i q^{26} +(3.84392 + 3.49632i) q^{27} +(-0.774834 - 0.774834i) q^{28} -2.97115 q^{29} -5.79770 q^{31} +(-3.95934 - 3.95934i) q^{32} +(2.58559 - 0.736708i) q^{33} +5.30926i q^{34} +(-1.73265 - 2.79366i) q^{36} +(1.23123 - 1.23123i) q^{37} +(5.23775 - 5.23775i) q^{38} +(5.37069 - 9.65070i) q^{39} +2.68458i q^{41} +(-0.835085 - 2.93087i) q^{42} +(2.09578 + 2.09578i) q^{43} -1.70088 q^{44} +9.35721 q^{46} +(-0.0358428 - 0.0358428i) q^{47} +(-2.36874 - 8.31349i) q^{48} -1.00000i q^{49} +(-2.54153 + 4.56692i) q^{51} +(-4.94075 + 4.94075i) q^{52} +(4.30833 - 4.30833i) q^{53} +(-0.432457 - 9.13231i) q^{54} -1.59096i q^{56} +(7.01270 - 1.99811i) q^{57} +(3.69653 + 3.69653i) q^{58} +4.93760 q^{59} +3.31687 q^{61} +(7.21316 + 7.21316i) q^{62} +(0.684672 - 2.92083i) q^{63} -0.129684i q^{64} +(-4.13342 - 2.30028i) q^{66} +(-1.71008 + 1.71008i) q^{67} +(2.33807 - 2.33807i) q^{68} +(8.04889 + 4.47927i) q^{69} +5.73577i q^{71} +(1.08929 - 4.64692i) q^{72} +(-7.26776 - 7.26776i) q^{73} -3.06366 q^{74} -4.61315 q^{76} +(-1.09758 - 1.09758i) q^{77} +(-18.6887 + 5.32495i) q^{78} +3.59379i q^{79} +(3.99962 - 8.06245i) q^{81} +(3.34000 - 3.34000i) q^{82} +(-12.2139 + 12.2139i) q^{83} +(-0.922931 + 1.65843i) q^{84} -5.21490i q^{86} +(1.41016 + 4.94920i) q^{87} +(-1.74620 - 1.74620i) q^{88} +1.35643 q^{89} -6.37653 q^{91} +(-4.12069 - 4.12069i) q^{92} +(2.75170 + 9.65754i) q^{93} +0.0891871i q^{94} +(-4.71611 + 8.47447i) q^{96} +(-10.9812 + 10.9812i) q^{97} +(-1.24414 + 1.24414i) q^{98} +(-2.45435 - 3.95731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 - 16 * q^12 + 8 * q^13 - 16 * q^16 + 20 * q^18 + 4 * q^21 - 8 * q^22 + 16 * q^27 - 28 * q^33 + 16 * q^36 + 16 * q^37 + 20 * q^42 + 40 * q^43 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 4 * q^57 - 40 * q^58 + 32 * q^61 + 8 * q^63 - 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 32 * q^76 - 60 * q^78 + 52 * q^81 + 80 * q^82 - 4 * q^87 - 96 * q^88 - 24 * q^91 + 76 * q^93 - 96 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.24414	−	1.24414i	−0.879741	−	0.879741i	0.113766	−	0.993508i	$-0.463709\pi$
$2$	−1.24414	−	1.24414i	−0.879741	−	0.879741i	−0.993508	+	0.113766i	$0.963709\pi$
$3$	−0.474620	−	1.66575i	−0.274022	−	0.961723i
$3$	−0.474620	−	1.66575i	−0.274022	−	0.961723i
$4$			1.09578i			0.547890i
$5$		0			0
$5$		0			0
$6$	−1.48194	+	2.66293i	−0.605000	+	1.08714i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−1.12498	+	1.12498i	−0.397740	+	0.397740i
$9$	−2.54947	+	1.58120i	−0.849824	+	0.527067i
$10$		0			0
$11$			1.55221i			0.468008i	0.972236	+	0.234004i	$0.0751828\pi$
$11$			1.55221i			0.468008i	−0.972236	+	0.234004i	$0.924817\pi$
$12$	1.82530	−	0.520079i	0.526919	−	0.150134i
$13$	4.50889	+	4.50889i	1.25054	+	1.25054i	0.955478	+	0.295062i	$0.0953402\pi$
$13$	4.50889	+	4.50889i	1.25054	+	1.25054i	0.295062	+	0.955478i	$0.404660\pi$
$14$	1.75948			0.470242
$15$		0			0
$16$	4.99083			1.24771
$17$	−2.13370	−	2.13370i	−0.517499	−	0.517499i	0.399315	−	0.916814i	$-0.369248\pi$
$17$	−2.13370	−	2.13370i	−0.517499	−	0.517499i	−0.916814	+	0.399315i	$0.869248\pi$
$18$	5.13914	+	1.20467i	1.21131	+	0.283943i
$19$			4.20993i			0.965823i	0.875669	+	0.482912i	$0.160421\pi$
$19$			4.20993i			0.965823i	−0.875669	+	0.482912i	$0.839579\pi$
$20$		0			0
$21$	1.51347	+	0.842259i	0.330267	+	0.183796i
$22$	1.93117	−	1.93117i	0.411726	−	0.411726i
$23$	−3.76050	+	3.76050i	−0.784119	+	0.784119i	−0.980523	−	0.196404i	$-0.937074\pi$
$23$	−3.76050	+	3.76050i	−0.784119	+	0.784119i	0.196404	+	0.980523i	$0.437074\pi$
$24$	2.40787	+	1.34000i	0.491505	+	0.273526i
$25$		0			0
$26$		−	11.2194i		−	2.20030i
$27$	3.84392	+	3.49632i	0.739763	+	0.672868i
$28$	−0.774834	−	0.774834i	−0.146430	−	0.146430i
$29$	−2.97115			−0.551728			−0.275864	−	0.961197i	$-0.588964\pi$
$29$	−2.97115			−0.551728			−0.275864	+	0.961197i	$0.588964\pi$
$30$		0			0
$31$	−5.79770			−1.04130			−0.520649	−	0.853771i	$-0.674310\pi$
$31$	−5.79770			−1.04130			−0.520649	+	0.853771i	$0.674310\pi$
$32$	−3.95934	−	3.95934i	−0.699919	−	0.699919i
$33$	2.58559	−	0.736708i	0.450094	−	0.128244i
$34$			5.30926i			0.910531i
$35$		0			0
$36$	−1.73265	−	2.79366i	−0.288775	−	0.465610i
$37$	1.23123	−	1.23123i	0.202414	−	0.202414i	−0.598620	−	0.801033i	$-0.704284\pi$
$37$	1.23123	−	1.23123i	0.202414	−	0.202414i	0.801033	+	0.598620i	$0.204284\pi$
$38$	5.23775	−	5.23775i	0.849675	−	0.849675i
$39$	5.37069	−	9.65070i	0.859998	−	1.54535i
$40$		0			0
$41$			2.68458i			0.419261i	0.977781	+	0.209631i	$0.0672261\pi$
$41$			2.68458i			0.419261i	−0.977781	+	0.209631i	$0.932774\pi$
$42$	−0.835085	−	2.93087i	−0.128856	−	0.452242i
$43$	2.09578	+	2.09578i	0.319603	+	0.319603i	0.848615	−	0.529011i	$-0.177437\pi$
$43$	2.09578	+	2.09578i	0.319603	+	0.319603i	−0.529011	+	0.848615i	$0.677437\pi$
$44$	−1.70088			−0.256417
$45$		0			0
$46$	9.35721			1.37964
$47$	−0.0358428	−	0.0358428i	−0.00522821	−	0.00522821i	0.704488	−	0.709716i	$-0.251177\pi$
$47$	−0.0358428	−	0.0358428i	−0.00522821	−	0.00522821i	−0.709716	+	0.704488i	$0.751177\pi$
$48$	−2.36874	−	8.31349i	−0.341899	−	1.19995i
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−2.54153	+	4.56692i	−0.355885	+	0.639497i
$52$	−4.94075	+	4.94075i	−0.685158	+	0.685158i
$53$	4.30833	−	4.30833i	0.591794	−	0.591794i	−0.346322	−	0.938116i	$-0.612569\pi$
$53$	4.30833	−	4.30833i	0.591794	−	0.591794i	0.938116	+	0.346322i	$0.112569\pi$
$54$	−0.432457	−	9.13231i	−0.0588500	−	1.24275i
$55$		0			0
$56$		−	1.59096i		−	0.212601i
$57$	7.01270	−	1.99811i	0.928855	−	0.264657i
$58$	3.69653	+	3.69653i	0.485378	+	0.485378i
$59$	4.93760			0.642821			0.321410	−	0.946940i	$-0.395843\pi$
$59$	4.93760			0.642821			0.321410	+	0.946940i	$0.395843\pi$
$60$		0			0
$61$	3.31687			0.424681			0.212341	−	0.977196i	$-0.431891\pi$
$61$	3.31687			0.424681			0.212341	+	0.977196i	$0.431891\pi$
$62$	7.21316	+	7.21316i	0.916073	+	0.916073i
$63$	0.684672	−	2.92083i	0.0862606	−	0.367989i
$64$		−	0.129684i		−	0.0162105i
$65$		0			0
$66$	−4.13342	−	2.30028i	−0.508788	−	0.283145i
$67$	−1.71008	+	1.71008i	−0.208919	+	0.208919i	−0.803808	−	0.594889i	$-0.797196\pi$
$67$	−1.71008	+	1.71008i	−0.208919	+	0.208919i	0.594889	+	0.803808i	$0.297196\pi$
$68$	2.33807	−	2.33807i	0.283533	−	0.283533i
$69$	8.04889	+	4.47927i	0.968972	+	0.539240i
$70$		0			0
$71$			5.73577i			0.680711i	0.940297	+	0.340356i	$0.110547\pi$
$71$			5.73577i			0.680711i	−0.940297	+	0.340356i	$0.889453\pi$
$72$	1.08929	−	4.64692i	0.128374	−	0.547644i
$73$	−7.26776	−	7.26776i	−0.850627	−	0.850627i	0.139583	−	0.990210i	$-0.455424\pi$
$73$	−7.26776	−	7.26776i	−0.850627	−	0.850627i	−0.990210	+	0.139583i	$0.955424\pi$
$74$	−3.06366			−0.356143
$75$		0			0
$76$	−4.61315			−0.529165
$77$	−1.09758	−	1.09758i	−0.125080	−	0.125080i
$78$	−18.6887	+	5.32495i	−2.11608	+	0.602931i
$79$			3.59379i			0.404333i	0.979351	+	0.202166i	$0.0647982\pi$
$79$			3.59379i			0.404333i	−0.979351	+	0.202166i	$0.935202\pi$
$80$		0			0
$81$	3.99962	−	8.06245i	0.444402	−	0.895828i
$82$	3.34000	−	3.34000i	0.368841	−	0.368841i
$83$	−12.2139	+	12.2139i	−1.34065	+	1.34065i	−0.445228	+	0.895417i	$0.646877\pi$
$83$	−12.2139	+	12.2139i	−1.34065	+	1.34065i	−0.895417	+	0.445228i	$0.853123\pi$
$84$	−0.922931	+	1.65843i	−0.100700	+	0.180950i
$85$		0			0
$86$		−	5.21490i		−	0.562337i
$87$	1.41016	+	4.94920i	0.151185	+	0.530610i
$88$	−1.74620	−	1.74620i	−0.186145	−	0.186145i
$89$	1.35643			0.143782			0.0718908	−	0.997413i	$-0.477097\pi$
$89$	1.35643			0.143782			0.0718908	+	0.997413i	$0.477097\pi$
$90$		0			0
$91$	−6.37653			−0.668442
$92$	−4.12069	−	4.12069i	−0.429611	−	0.429611i
$93$	2.75170	+	9.65754i	0.285338	+	1.00144i
$94$			0.0891871i			0.00919895i
$95$		0			0
$96$	−4.71611	+	8.47447i	−0.481336	+	0.864922i
$97$	−10.9812	+	10.9812i	−1.11497	+	1.11497i	−0.122503	+	0.992468i	$0.539092\pi$
$97$	−10.9812	+	10.9812i	−1.11497	+	1.11497i	−0.992468	+	0.122503i	$0.960908\pi$
$98$	−1.24414	+	1.24414i	−0.125677	+	0.125677i
$99$	−2.45435	−	3.95731i	−0.246671	−	0.397724i
$100$		0			0
$101$			12.7033i			1.26402i	0.774958	+	0.632012i	$0.217771\pi$
$101$			12.7033i			1.26402i	−0.774958	+	0.632012i	$0.782229\pi$
$102$	8.84392	−	2.51988i	0.875679	−	0.249505i
$103$	1.46798	+	1.46798i	0.144644	+	0.144644i	0.775721	−	0.631076i	$-0.217387\pi$
$103$	1.46798	+	1.46798i	0.144644	+	0.144644i	−0.631076	+	0.775721i	$0.717387\pi$
$104$	−10.1448			−0.994779
$105$		0			0
$106$	−10.7203			−1.04125
$107$	13.5523	+	13.5523i	1.31015	+	1.31015i	0.921302	+	0.388849i	$0.127127\pi$
$107$	13.5523	+	13.5523i	1.31015	+	1.31015i	0.388849	+	0.921302i	$0.372873\pi$
$108$	−3.83120	+	4.21209i	−0.368658	+	0.405309i
$109$		−	4.84158i		−	0.463739i	−0.972747	−	0.231869i	$-0.925516\pi$
$109$		−	4.84158i		−	0.463739i	0.972747	−	0.231869i	$-0.0744842\pi$
$110$		0			0
$111$	−2.63530	−	1.46656i	−0.250132	−	0.139200i
$112$	−3.52905	+	3.52905i	−0.333464	+	0.333464i
$113$	10.6222	−	10.6222i	0.999254	−	0.999254i	−0.000746132	−	1.00000i	$-0.500238\pi$
$113$	10.6222	−	10.6222i	0.999254	−	0.999254i	1.00000		0.000746132i	$0.000237501\pi$
$114$	−11.2107	−	6.23886i	−1.04998	−	0.584323i
$115$		0			0
$116$		−	3.25572i		−	0.302286i
$117$	−18.6247	−	4.36583i	−1.72186	−	0.403621i
$118$	−6.14308	−	6.14308i	−0.565516	−	0.565516i
$119$	3.01751			0.276615
$120$		0			0
$121$	8.59066			0.780969
$122$	−4.12665	−	4.12665i	−0.373610	−	0.373610i
$123$	4.47185	−	1.27415i	0.403213	−	0.114887i
$124$		−	6.35300i		−	0.570517i
$125$		0			0
$126$	−4.48575	+	2.78209i	−0.399623	+	0.247849i
$127$	−10.1595	+	10.1595i	−0.901511	+	0.901511i	−0.995567	−	0.0940560i	$-0.970017\pi$
$127$	−10.1595	+	10.1595i	−0.901511	+	0.901511i	0.0940560	+	0.995567i	$0.470017\pi$
$128$	−8.08003	+	8.08003i	−0.714180	+	0.714180i
$129$	2.49636	−	4.48575i	0.219792	−	0.394948i
$130$		0			0
$131$		−	0.509374i		−	0.0445042i	−0.999752	−	0.0222521i	$-0.992916\pi$
$131$		−	0.509374i		−	0.0445042i	0.999752	−	0.0222521i	$-0.00708365\pi$
$132$	0.807270	+	2.83324i	0.0702638	+	0.246602i
$133$	−2.97687	−	2.97687i	−0.258127	−	0.258127i
$134$	4.25516			0.367590
$135$		0			0
$136$	4.80074			0.411660
$137$	2.61947	+	2.61947i	0.223797	+	0.223797i	0.810095	−	0.586298i	$-0.199415\pi$
$137$	2.61947	+	2.61947i	0.223797	+	0.223797i	−0.586298	+	0.810095i	$0.699415\pi$
$138$	−4.44112	−	15.5868i	−0.378053	−	1.32684i
$139$			6.35379i			0.538921i	0.963011	+	0.269461i	$0.0868454\pi$
$139$			6.35379i			0.538921i	−0.963011	+	0.269461i	$0.913155\pi$
$140$		0			0
$141$	−0.0426936	+	0.0767170i	−0.00359545	+	0.00646074i
$142$	7.13612	−	7.13612i	0.598850	−	0.598850i
$143$	−6.99872	+	6.99872i	−0.585262	+	0.585262i
$144$	−12.7240	+	7.89149i	−1.06033	+	0.657624i
$145$		0			0
$146$			18.0843i			1.49666i
$147$	−1.66575	+	0.474620i	−0.137389	+	0.0391460i
$148$	1.34916	+	1.34916i	0.110900	+	0.110900i
$149$	−4.27965			−0.350602			−0.175301	−	0.984515i	$-0.556090\pi$
$149$	−4.27965			−0.350602			−0.175301	+	0.984515i	$0.556090\pi$
$150$		0			0
$151$	−5.21232			−0.424172			−0.212086	−	0.977251i	$-0.568026\pi$
$151$	−5.21232			−0.424172			−0.212086	+	0.977251i	$0.568026\pi$
$152$	−4.73607	−	4.73607i	−0.384146	−	0.384146i
$153$	8.81363	+	2.06601i	0.712539	+	0.167027i
$154$			2.73108i			0.220077i
$155$		0			0
$156$	10.5750	+	5.88509i	0.846681	+	0.471185i
$157$	4.35999	−	4.35999i	0.347965	−	0.347965i	−0.511386	−	0.859351i	$-0.670868\pi$
$157$	4.35999	−	4.35999i	0.347965	−	0.347965i	0.859351	+	0.511386i	$0.170868\pi$
$158$	4.47119	−	4.47119i	0.355708	−	0.355708i
$159$	−9.22143	−	5.13179i	−0.731307	−	0.406978i
$160$		0			0
$161$		−	5.31816i		−	0.419129i
$162$	−15.0069	+	5.05474i	−1.17906	+	0.397138i
$163$	−5.34339	−	5.34339i	−0.418527	−	0.418527i	0.466169	−	0.884696i	$-0.345634\pi$
$163$	−5.34339	−	5.34339i	−0.418527	−	0.418527i	−0.884696	+	0.466169i	$0.845634\pi$
$164$	−2.94171			−0.229709
$165$		0			0
$166$	30.3916			2.35884
$167$	−13.8232	−	13.8232i	−1.06967	−	1.06967i	−0.997384	−	0.0722908i	$-0.976969\pi$
$167$	−13.8232	−	13.8232i	−1.06967	−	1.06967i	−0.0722908	−	0.997384i	$-0.523031\pi$
$168$	−2.65015	+	0.755101i	−0.204463	+	0.0582573i
$169$			27.6601i			2.12770i
$170$		0			0
$171$	−6.65673	−	10.7331i	−0.509053	−	0.820780i
$172$	−2.29651	+	2.29651i	−0.175108	+	0.175108i
$173$	2.06635	−	2.06635i	0.157102	−	0.157102i	−0.624179	−	0.781281i	$-0.714567\pi$
$173$	2.06635	−	2.06635i	0.157102	−	0.157102i	0.781281	+	0.624179i	$0.214567\pi$
$174$	4.40306	−	7.91195i	0.333795	−	0.599803i
$175$		0			0
$176$			7.74679i			0.583936i
$177$	−2.34348	−	8.22483i	−0.176147	−	0.618216i
$178$	−1.68759	−	1.68759i	−0.126491	−	0.126491i
$179$	−11.9186			−0.890841			−0.445420	−	0.895322i	$-0.646946\pi$
$179$	−11.9186			−0.890841			−0.445420	+	0.895322i	$0.646946\pi$
$180$		0			0
$181$	−17.5945			−1.30779			−0.653893	−	0.756587i	$-0.726865\pi$
$181$	−17.5945			−1.30779			−0.653893	+	0.756587i	$0.726865\pi$
$182$	7.93331	+	7.93331i	0.588056	+	0.588056i
$183$	−1.57425	−	5.52508i	−0.116372	−	0.408426i
$184$		−	8.46097i		−	0.623751i
$185$		0			0
$186$	8.59184	−	15.4389i	0.629985	−	1.13203i
$187$	3.31195	−	3.31195i	0.242194	−	0.242194i
$188$	0.0392758	−	0.0392758i	0.00286449	−	0.00286449i
$189$	−5.19034	+	0.245787i	−0.377541	+	0.0178783i
$190$		0			0
$191$		−	5.54023i		−	0.400877i	−0.979706	−	0.200438i	$-0.935763\pi$
$191$		−	5.54023i		−	0.400877i	0.979706	−	0.200438i	$-0.0642366\pi$
$192$	−0.216021	+	0.0615505i	−0.0155900	+	0.00444202i
$193$	13.9027	+	13.9027i	1.00074	+	1.00074i	1.00000		0.000740397i	$0.000235676\pi$
$193$	13.9027	+	13.9027i	1.00074	+	1.00074i	0.000740397		1.00000i	$0.499764\pi$
$194$	27.3243			1.96177
$195$		0			0
$196$	1.09578			0.0782700
$197$	12.7155	+	12.7155i	0.905939	+	0.905939i	0.995942	−	0.0900024i	$-0.0286875\pi$
$197$	12.7155	+	12.7155i	0.905939	+	0.905939i	−0.0900024	+	0.995942i	$0.528687\pi$
$198$	−1.86989	+	7.97701i	−0.132888	+	0.566901i
$199$		−	6.11487i		−	0.433472i	−0.976230	−	0.216736i	$-0.930459\pi$
$199$		−	6.11487i		−	0.433472i	0.976230	−	0.216736i	$-0.0695411\pi$
$200$		0			0
$201$	3.66021	+	2.03693i	0.258171	+	0.143674i
$202$	15.8047	−	15.8047i	1.11201	−	1.11201i
$203$	2.10092	−	2.10092i	0.147455	−	0.147455i
$204$	−5.00434	−	2.78495i	−0.350374	−	0.194986i
$205$		0			0
$206$		−	3.65275i		−	0.254499i
$207$	3.64119	−	15.5334i	0.253080	−	1.07965i
$208$	22.5031	+	22.5031i	1.56031	+	1.56031i
$209$	−6.53467			−0.452013
$210$		0			0
$211$	12.4900			0.859849			0.429924	−	0.902865i	$-0.358540\pi$
$211$	12.4900			0.859849			0.429924	+	0.902865i	$0.358540\pi$
$212$	4.72098	+	4.72098i	0.324238	+	0.324238i
$213$	9.55439	−	2.72231i	0.654656	−	0.186530i
$214$		−	33.7220i		−	2.30519i
$215$		0			0
$216$	−8.25761	+	0.391036i	−0.561859	+	0.0266067i
$217$	4.09959	−	4.09959i	0.278298	−	0.278298i
$218$	−6.02361	+	6.02361i	−0.407970	+	0.407970i
$219$	−8.65688	+	15.5557i	−0.584978	+	1.05116i
$220$		0			0
$221$		−	19.2412i		−	1.29431i
$222$	1.45407	+	5.10330i	0.0975910	+	0.342511i
$223$	−8.80424	−	8.80424i	−0.589576	−	0.589576i	0.347941	−	0.937516i	$-0.386881\pi$
$223$	−8.80424	−	8.80424i	−0.589576	−	0.589576i	−0.937516	+	0.347941i	$0.886881\pi$
$224$	5.59935			0.374123
$225$		0			0
$226$	−26.4311			−1.75817
$227$	15.7424	+	15.7424i	1.04486	+	1.04486i	0.998945	+	0.0459126i	$0.0146196\pi$
$227$	15.7424	+	15.7424i	1.04486	+	1.04486i	0.0459126	+	0.998945i	$0.485380\pi$
$228$	2.18949	+	7.68438i	0.145003	+	0.508910i
$229$		−	8.27446i		−	0.546791i	−0.961902	−	0.273396i	$-0.911853\pi$
$229$		−	8.27446i		−	0.546791i	0.961902	−	0.273396i	$-0.0881468\pi$
$230$		0			0
$231$	−1.30736	+	2.34922i	−0.0860179	+	0.154567i
$232$	3.34247	−	3.34247i	0.219444	−	0.219444i
$233$	12.6425	−	12.6425i	0.828239	−	0.828239i	−0.159034	−	0.987273i	$-0.550838\pi$
$233$	12.6425	−	12.6425i	0.828239	−	0.828239i	0.987273	+	0.159034i	$0.0508380\pi$
$234$	17.7401	+	28.6035i	1.15971	+	1.86987i
$235$		0			0
$236$			5.41052i			0.352195i
$237$	5.98637	−	1.70568i	0.388856	−	0.110796i
$238$	−3.75421	−	3.75421i	−0.243350	−	0.243350i
$239$	25.8260			1.67054			0.835271	−	0.549838i	$-0.185311\pi$
$239$	25.8260			1.67054			0.835271	+	0.549838i	$0.185311\pi$
$240$		0			0
$241$	−10.5197			−0.677631			−0.338815	−	0.940853i	$-0.610026\pi$
$241$	−10.5197			−0.677631			−0.338815	+	0.940853i	$0.610026\pi$
$242$	−10.6880	−	10.6880i	−0.687051	−	0.687051i
$243$	−15.3284	−	2.83578i	−0.983314	−	0.181915i
$244$			3.63456i			0.232679i
$245$		0			0
$246$	−7.14885	−	3.97839i	−0.455794	−	0.253653i
$247$	−18.9821	+	18.9821i	−1.20780	+	1.20780i
$248$	6.52229	−	6.52229i	0.414166	−	0.414166i
$249$	26.1422	+	14.5483i	1.65670	+	0.921964i
$250$		0			0
$251$		−	6.94563i		−	0.438405i	−0.975679	−	0.219202i	$-0.929655\pi$
$251$		−	6.94563i		−	0.438405i	0.975679	−	0.219202i	$-0.0703455\pi$
$252$	3.20058	+	0.750250i	0.201618	+	0.0472613i
$253$	−5.83708	−	5.83708i	−0.366974	−	0.366974i
$254$	25.2798			1.58619
$255$		0			0
$256$	19.8460			1.24038
$257$	8.17057	+	8.17057i	0.509666	+	0.509666i	0.914424	−	0.404758i	$-0.132644\pi$
$257$	8.17057	+	8.17057i	0.509666	+	0.509666i	−0.404758	+	0.914424i	$0.632644\pi$
$258$	−8.68674	+	2.47509i	−0.540813	+	0.154093i
$259$			1.74123i			0.108195i
$260$		0			0
$261$	7.57485	−	4.69797i	0.468872	−	0.290797i
$262$	−0.633733	+	0.633733i	−0.0391522	+	0.0391522i
$263$	0.118860	−	0.118860i	0.00732922	−	0.00732922i	−0.703433	−	0.710762i	$-0.748350\pi$
$263$	0.118860	−	0.118860i	0.00732922	−	0.00732922i	0.710762	+	0.703433i	$0.248350\pi$
$264$	−2.07996	+	3.73752i	−0.128012	+	0.230028i
$265$		0			0
$266$			7.40729i			0.454170i
$267$	−0.643790	−	2.25948i	−0.0393993	−	0.138278i
$268$	−1.87387	−	1.87387i	−0.114465	−	0.114465i
$269$	−6.60330			−0.402610			−0.201305	−	0.979529i	$-0.564518\pi$
$269$	−6.60330			−0.402610			−0.201305	+	0.979529i	$0.564518\pi$
$270$		0			0
$271$	−23.8292			−1.44752			−0.723759	−	0.690052i	$-0.757587\pi$
$271$	−23.8292			−1.44752			−0.723759	+	0.690052i	$0.757587\pi$
$272$	−10.6489	−	10.6489i	−0.645687	−	0.645687i
$273$	3.02643	+	10.6217i	0.183168	+	0.642856i
$274$		−	6.51800i		−	0.393767i
$275$		0			0
$276$	−4.90829	+	8.81981i	−0.295444	+	0.530890i
$277$	14.3921	−	14.3921i	0.864736	−	0.864736i	−0.127147	−	0.991884i	$-0.540582\pi$
$277$	14.3921	−	14.3921i	0.864736	−	0.864736i	0.991884	+	0.127147i	$0.0405821\pi$
$278$	7.90501	−	7.90501i	0.474111	−	0.474111i
$279$	14.7811	−	9.16732i	0.884920	−	0.548833i
$280$		0			0
$281$			1.50698i			0.0898991i	0.998989	+	0.0449495i	$0.0143127\pi$
$281$			1.50698i			0.0898991i	−0.998989	+	0.0449495i	$0.985687\pi$
$282$	0.148564	−	0.0423300i	0.00884685	−	0.00252071i
$283$	−8.49114	−	8.49114i	−0.504746	−	0.504746i	0.408163	−	0.912909i	$-0.366170\pi$
$283$	−8.49114	−	8.49114i	−0.504746	−	0.504746i	−0.912909	+	0.408163i	$0.866170\pi$
$284$	−6.28515			−0.372955
$285$		0			0
$286$	17.4148			1.02976
$287$	−1.89828	−	1.89828i	−0.112052	−	0.112052i
$288$	16.3547	+	3.83372i	0.963712	+	0.225904i
$289$		−	7.89463i		−	0.464390i
$290$		0			0
$291$	23.5039	+	13.0801i	1.37782	+	0.766768i
$292$	7.96387	−	7.96387i	0.466050	−	0.466050i
$293$	−2.35851	+	2.35851i	−0.137786	+	0.137786i	−0.772635	−	0.634850i	$-0.781062\pi$
$293$	−2.35851	+	2.35851i	−0.137786	+	0.137786i	0.634850	+	0.772635i	$0.281062\pi$
$294$	2.66293	+	1.48194i	0.155305	+	0.0864285i
$295$		0			0
$296$			2.77022i			0.161016i
$297$	−5.42702	+	5.96656i	−0.314907	+	0.346215i
$298$	5.32449	+	5.32449i	0.308439	+	0.308439i
$299$	−33.9114			−1.96115
$300$		0			0
$301$	−2.96388			−0.170835
$302$	6.48486	+	6.48486i	0.373162	+	0.373162i
$303$	21.1606	−	6.02923i	1.21564	−	0.346370i
$304$			21.0110i			1.20506i
$305$		0			0
$306$	−8.39500	−	13.5358i	−0.479910	−	0.773791i
$307$	0.793602	−	0.793602i	0.0452933	−	0.0452933i	−0.684097	−	0.729391i	$-0.739804\pi$
$307$	0.793602	−	0.793602i	0.0452933	−	0.0452933i	0.729391	+	0.684097i	$0.239804\pi$
$308$	1.20270	−	1.20270i	0.0685303	−	0.0685303i
$309$	1.74856	−	3.14203i	0.0994722	−	0.178744i
$310$		0			0
$311$			9.91521i			0.562240i	0.959673	+	0.281120i	$0.0907059\pi$
$311$			9.91521i			0.562240i	−0.959673	+	0.281120i	$0.909294\pi$
$312$	4.81492	+	16.8987i	0.272591	+	0.956702i
$313$	9.95137	+	9.95137i	0.562484	+	0.562484i	0.930012	−	0.367528i	$-0.119796\pi$
$313$	9.95137	+	9.95137i	0.562484	+	0.562484i	−0.367528	+	0.930012i	$0.619796\pi$
$314$	−10.8489			−0.612238
$315$		0			0
$316$	−3.93800			−0.221530
$317$	−14.9788	−	14.9788i	−0.841296	−	0.841296i	0.147732	−	0.989027i	$-0.452803\pi$
$317$	−14.9788	−	14.9788i	−0.841296	−	0.841296i	−0.989027	+	0.147732i	$0.952803\pi$
$318$	5.08809	+	17.8574i	0.285326	+	1.00140i
$319$		−	4.61183i		−	0.258213i
$320$		0			0
$321$	16.1426	−	29.0070i	0.900992	−	1.61901i
$322$	−6.61654	+	6.61654i	−0.368726	+	0.368726i
$323$	8.98273	−	8.98273i	0.499812	−	0.499812i
$324$	8.83467	+	4.38270i	0.490815	+	0.243483i
$325$		0			0
$326$			13.2959i			0.736391i
$327$	−8.06487	+	2.29791i	−0.445989	+	0.127075i
$328$	−3.02009	−	3.02009i	−0.166757	−	0.166757i
$329$	0.0506894			0.00279460
$330$		0			0
$331$	−3.10247			−0.170527			−0.0852635	−	0.996358i	$-0.527173\pi$
$331$	−3.10247			−0.170527			−0.0852635	+	0.996358i	$0.527173\pi$
$332$	−13.3837	−	13.3837i	−0.734526	−	0.734526i
$333$	−1.19217	+	5.08582i	−0.0653305	+	0.278701i
$334$			34.3962i			1.88207i
$335$		0			0
$336$	7.55348	+	4.20357i	0.412076	+	0.229323i
$337$	23.2030	−	23.2030i	1.26395	−	1.26395i	0.314784	−	0.949163i	$-0.398068\pi$
$337$	23.2030	−	23.2030i	1.26395	−	1.26395i	0.949163	−	0.314784i	$-0.101932\pi$
$338$	34.4131	−	34.4131i	1.87183	−	1.87183i
$339$	−22.7355	−	12.6525i	−1.23482	−	0.687188i
$340$		0			0
$341$		−	8.99922i		−	0.487335i
$342$	−5.07157	+	21.6354i	−0.274239	+	1.16991i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−4.71541			−0.254238
$345$		0			0
$346$	−5.14167			−0.276418
$347$	−14.1837	−	14.1837i	−0.761423	−	0.761423i	0.215157	−	0.976580i	$-0.430974\pi$
$347$	−14.1837	−	14.1837i	−0.761423	−	0.761423i	−0.976580	+	0.215157i	$0.930974\pi$
$348$	−5.42323	+	1.54523i	−0.290716	+	0.0828330i
$349$			9.27152i			0.496293i	0.968723	+	0.248146i	$0.0798214\pi$
$349$			9.27152i			0.496293i	−0.968723	+	0.248146i	$0.920179\pi$
$350$		0			0
$351$	1.56726	+	33.0963i	0.0836544	+	1.76655i
$352$	6.14571	−	6.14571i	0.327568	−	0.327568i
$353$	−20.2421	+	20.2421i	−1.07738	+	1.07738i	−0.0806368	+	0.996744i	$0.525695\pi$
$353$	−20.2421	+	20.2421i	−1.07738	+	1.07738i	−0.996744	+	0.0806368i	$0.974305\pi$
$354$	−7.31723	+	13.1485i	−0.388906	+	0.698834i
$355$		0			0
$356$			1.48635i			0.0787765i
$357$	−1.43217	−	5.02643i	−0.0757985	−	0.266027i
$358$	14.8285	+	14.8285i	0.783710	+	0.783710i
$359$	18.8289			0.993751			0.496876	−	0.867822i	$-0.334481\pi$
$359$	18.8289			0.993751			0.496876	+	0.867822i	$0.334481\pi$
$360$		0			0
$361$	1.27653			0.0671857
$362$	21.8900	+	21.8900i	1.15051	+	1.15051i
$363$	−4.07730	−	14.3099i	−0.214003	−	0.751076i
$364$		−	6.98727i		−	0.366233i
$365$		0			0
$366$	−4.91540	+	8.83258i	−0.256932	+	0.461686i
$367$	−0.942012	+	0.942012i	−0.0491726	+	0.0491726i	−0.731266	−	0.682093i	$-0.761070\pi$
$367$	−0.942012	+	0.942012i	−0.0491726	+	0.0491726i	0.682093	+	0.731266i	$0.261070\pi$
$368$	−18.7680	+	18.7680i	−0.978351	+	0.978351i
$369$	−4.24486	−	6.84426i	−0.220978	−	0.356298i
$370$		0			0
$371$			6.09289i			0.316327i
$372$	−10.5825	+	3.01526i	−0.548679	+	0.156334i
$373$	−7.39940	−	7.39940i	−0.383127	−	0.383127i	0.489101	−	0.872227i	$-0.337325\pi$
$373$	−7.39940	−	7.39940i	−0.383127	−	0.383127i	−0.872227	+	0.489101i	$0.837325\pi$
$374$	−8.24107			−0.426135
$375$		0			0
$376$	0.0806448			0.00415894
$377$	−13.3966	−	13.3966i	−0.689958	−	0.689958i
$378$	6.76331	+	6.15172i	0.347867	+	0.316411i
$379$		−	21.9486i		−	1.12743i	−0.825971	−	0.563713i	$-0.809373\pi$
$379$		−	21.9486i		−	1.12743i	0.825971	−	0.563713i	$-0.190627\pi$
$380$		0			0
$381$	21.7452	+	12.1013i	1.11404	+	0.619970i
$382$	−6.89283	+	6.89283i	−0.352668	+	0.352668i
$383$	−19.3310	+	19.3310i	−0.987768	+	0.987768i	−0.999926	−	0.0121580i	$-0.996130\pi$
$383$	−19.3310	+	19.3310i	−0.987768	+	0.987768i	0.0121580	+	0.999926i	$0.496130\pi$
$384$	17.2943	+	9.62440i	0.882545	+	0.491143i
$385$		0			0
$386$		−	34.5939i		−	1.76079i
$387$	−8.65698	−	2.02929i	−0.440059	−	0.103154i
$388$	−12.0330	−	12.0330i	−0.610882	−	0.610882i
$389$	−30.7961			−1.56142			−0.780712	−	0.624891i	$-0.785144\pi$
$389$	−30.7961			−1.56142			−0.780712	+	0.624891i	$0.785144\pi$
$390$		0			0
$391$	16.0476			0.811562
$392$	1.12498	+	1.12498i	0.0568200	+	0.0568200i
$393$	−0.848491	+	0.241759i	−0.0428007	+	0.0121951i
$394$		−	31.6397i		−	1.59398i
$395$		0			0
$396$	4.33634	−	2.68943i	0.217909	−	0.135149i
$397$	20.8254	−	20.8254i	1.04520	−	1.04520i	0.0462702	−	0.998929i	$-0.485266\pi$
$397$	20.8254	−	20.8254i	1.04520	−	1.04520i	0.998929	−	0.0462702i	$-0.0147335\pi$
$398$	−7.60777	+	7.60777i	−0.381343	+	0.381343i
$399$	−3.54585	+	6.37161i	−0.177514	+	0.318979i
$400$		0			0
$401$		−	20.9084i		−	1.04412i	−0.852910	−	0.522058i	$-0.825165\pi$
$401$		−	20.9084i		−	1.04412i	0.852910	−	0.522058i	$-0.174835\pi$
$402$	−2.01958	−	7.08805i	−0.100728	−	0.353520i
$403$	−26.1412	−	26.1412i	−1.30218	−	1.30218i
$404$	−13.9200			−0.692547
$405$		0			0
$406$	−5.22768			−0.259445
$407$	1.91113	+	1.91113i	0.0947311	+	0.0947311i
$408$	−2.27853	−	7.99685i	−0.112804	−	0.395903i
$409$		−	11.5773i		−	0.572460i	−0.958161	−	0.286230i	$-0.907598\pi$
$409$		−	11.5773i		−	0.572460i	0.958161	−	0.286230i	$-0.0924022\pi$
$410$		0			0
$411$	3.12014	−	5.60665i	0.153905	−	0.276556i
$412$	−1.60858	+	1.60858i	−0.0792493	+	0.0792493i
$413$	−3.49141	+	3.49141i	−0.171801	+	0.171801i
$414$	−23.8559	+	14.7956i	−1.17246	+	0.727165i
$415$		0			0
$416$		−	35.7044i		−	1.75055i
$417$	10.5838	−	3.01563i	0.518293	−	0.147676i
$418$	8.13006	+	8.13006i	0.397654	+	0.397654i
$419$	0.525515			0.0256731			0.0128365	−	0.999918i	$-0.495914\pi$
$419$	0.525515			0.0256731			0.0128365	+	0.999918i	$0.495914\pi$
$420$		0			0
$421$	−15.5297			−0.756871			−0.378435	−	0.925628i	$-0.623538\pi$
$421$	−15.5297			−0.756871			−0.378435	+	0.925628i	$0.623538\pi$
$422$	−15.5394	−	15.5394i	−0.756445	−	0.756445i
$423$	0.148055	+	0.0347056i	0.00719868	+	0.00168744i
$424$			9.69354i			0.470760i
$425$		0			0
$426$	−15.2740	−	8.50008i	−0.740026	−	0.411830i
$427$	−2.34538	+	2.34538i	−0.113501	+	0.113501i
$428$	−14.8503	+	14.8503i	−0.717818	+	0.717818i
$429$	14.9799	+	8.33641i	0.723235	+	0.402486i
$430$		0			0
$431$			23.0144i			1.10856i	0.832329	+	0.554282i	$0.187007\pi$
$431$			23.0144i			1.10856i	−0.832329	+	0.554282i	$0.812993\pi$
$432$	19.1843	+	17.4495i	0.923007	+	0.839542i
$433$	15.4001	+	15.4001i	0.740081	+	0.740081i	0.972593	−	0.232513i	$-0.0746947\pi$
$433$	15.4001	+	15.4001i	0.740081	+	0.740081i	−0.232513	+	0.972593i	$0.574695\pi$
$434$	−10.2010			−0.489661
$435$		0			0
$436$	5.30530			0.254078
$437$	−15.8314	−	15.8314i	−0.757321	−	0.757321i
$438$	30.1239	−	8.58315i	1.43938	−	0.410119i
$439$			6.04288i			0.288411i	0.989548	+	0.144205i	$0.0460626\pi$
$439$			6.04288i			0.288411i	−0.989548	+	0.144205i	$0.953937\pi$
$440$		0			0
$441$	1.58120	+	2.54947i	0.0752952	+	0.121403i
$442$	−23.9388	+	23.9388i	−1.13865	+	1.13865i
$443$	−8.64725	+	8.64725i	−0.410843	+	0.410843i	−0.882032	−	0.471189i	$-0.843825\pi$
$443$	−8.64725	+	8.64725i	−0.410843	+	0.410843i	0.471189	+	0.882032i	$0.343825\pi$
$444$	1.60703	−	2.88771i	0.0762664	−	0.137045i
$445$		0			0
$446$			21.9075i			1.03735i
$447$	2.03121	+	7.12884i	0.0960727	+	0.337183i
$448$	0.0917003	+	0.0917003i	0.00433243	+	0.00433243i
$449$	20.7599			0.979723			0.489861	−	0.871800i	$-0.337047\pi$
$449$	20.7599			0.979723			0.489861	+	0.871800i	$0.337047\pi$
$450$		0			0
$451$	−4.16702			−0.196217
$452$	11.6396	+	11.6396i	0.547481	+	0.547481i
$453$	2.47387	+	8.68243i	0.116232	+	0.407936i
$454$		−	39.1715i		−	1.83841i
$455$		0			0
$456$	−5.64130	+	10.1370i	−0.264178	+	0.474707i
$457$	−17.3075	+	17.3075i	−0.809612	+	0.809612i	−0.984575	−	0.174963i	$-0.944020\pi$
$457$	−17.3075	+	17.3075i	−0.809612	+	0.809612i	0.174963	+	0.984575i	$0.444020\pi$
$458$	−10.2946	+	10.2946i	−0.481035	+	0.481035i
$459$	−0.741664	−	15.6619i	−0.0346179	−	0.731035i
$460$		0			0
$461$			4.36421i			0.203262i	0.994822	+	0.101631i	$0.0324061\pi$
$461$			4.36421i			0.203262i	−0.994822	+	0.101631i	$0.967594\pi$
$462$	4.54931	−	1.29622i	0.211653	−	0.0603058i
$463$	−2.04147	−	2.04147i	−0.0948752	−	0.0948752i	0.658076	−	0.752951i	$-0.271370\pi$
$463$	−2.04147	−	2.04147i	−0.0948752	−	0.0948752i	−0.752951	+	0.658076i	$0.771370\pi$
$464$	−14.8285			−0.688394
$465$		0			0
$466$	−31.4582			−1.45727
$467$	−13.9629	−	13.9629i	−0.646128	−	0.646128i	0.305927	−	0.952055i	$-0.401034\pi$
$467$	−13.9629	−	13.9629i	−0.646128	−	0.646128i	−0.952055	+	0.305927i	$0.901034\pi$
$468$	4.78399	−	20.4086i	0.221140	−	0.943388i
$469$		−	2.41842i		−	0.111672i
$470$		0			0
$471$	−9.33200	−	5.19333i	−0.429996	−	0.239296i
$472$	−5.55469	+	5.55469i	−0.255675	+	0.255675i
$473$	−3.25308	+	3.25308i	−0.149577	+	0.149577i
$474$	−9.57001	−	5.32578i	−0.439565	−	0.244621i
$475$		0			0
$476$			3.30653i			0.151555i
$477$	−4.17163	+	17.7963i	−0.191006	+	0.814836i
$478$	−32.1312	−	32.1312i	−1.46965	−	1.46965i
$479$	−16.0067			−0.731367			−0.365683	−	0.930739i	$-0.619165\pi$
$479$	−16.0067			−0.731367			−0.365683	+	0.930739i	$0.619165\pi$
$480$		0			0
$481$	11.1030			0.506252
$482$	13.0880	+	13.0880i	0.596140	+	0.596140i
$483$	−8.85874	+	2.52410i	−0.403087	+	0.114851i
$484$			9.41347i			0.427885i
$485$		0			0
$486$	15.5425	+	22.5988i	0.705024	+	1.02510i
$487$	−20.6096	+	20.6096i	−0.933908	+	0.933908i	−0.997947	−	0.0640391i	$-0.979602\pi$
$487$	−20.6096	+	20.6096i	−0.933908	+	0.933908i	0.0640391	+	0.997947i	$0.479602\pi$
$488$	−3.73140	+	3.73140i	−0.168913	+	0.168913i
$489$	−6.36470	+	11.4369i	−0.287822	+	0.517192i
$490$		0			0
$491$		−	29.8846i		−	1.34867i	−0.738423	−	0.674337i	$-0.764429\pi$
$491$		−	29.8846i		−	1.34867i	0.738423	−	0.674337i	$-0.235571\pi$
$492$	1.39619	+	4.90016i	0.0629453	+	0.220916i
$493$	6.33954	+	6.33954i	0.285519	+	0.285519i
$494$	47.2328			2.12510
$495$		0			0
$496$	−28.9353			−1.29923
$497$	−4.05581	−	4.05581i	−0.181928	−	0.181928i
$498$	−14.4244	−	50.6249i	−0.646374	−	2.26855i
$499$			0.940603i			0.0421072i	0.999778	+	0.0210536i	$0.00670206\pi$
$499$			0.940603i			0.0421072i	−0.999778	+	0.0210536i	$0.993298\pi$
$500$		0			0
$501$	−16.4653	+	29.5869i	−0.735617	+	1.32185i
$502$	−8.64136	+	8.64136i	−0.385683	+	0.385683i
$503$	23.0051	−	23.0051i	1.02575	−	1.02575i	0.0260875	−	0.999660i	$-0.491695\pi$
$503$	23.0051	−	23.0051i	1.02575	−	1.02575i	0.999660	−	0.0260875i	$-0.00830487\pi$
$504$	2.51562	+	4.05611i	0.112055	+	0.180673i
$505$		0			0
$506$			14.5243i			0.645685i
$507$	46.0749	−	13.1280i	2.04626	−	0.583036i
$508$	−11.1326	−	11.1326i	−0.493929	−	0.493929i
$509$	25.8128			1.14413			0.572066	−	0.820208i	$-0.306142\pi$
$509$	25.8128			1.14413			0.572066	+	0.820208i	$0.306142\pi$
$510$		0			0
$511$	10.2782			0.454679
$512$	−8.53124	−	8.53124i	−0.377031	−	0.377031i
$513$	−14.7193	+	16.1826i	−0.649871	+	0.714480i
$514$		−	20.3307i		−	0.896749i
$515$		0			0
$516$	4.91540	+	2.73546i	0.216388	+	0.120422i
$517$	0.0556354	−	0.0556354i	0.00244684	−	0.00244684i
$518$	2.16633	−	2.16633i	0.0951833	−	0.0951833i
$519$	−4.42276	−	2.46130i	−0.194138	−	0.108039i
$520$		0			0
$521$			44.1826i			1.93568i	0.251572	+	0.967838i	$0.419052\pi$
$521$			44.1826i			1.93568i	−0.251572	+	0.967838i	$0.580948\pi$
$522$	−15.2691	−	3.57925i	−0.668312	−	0.156659i
$523$	−13.0685	−	13.0685i	−0.571447	−	0.571447i	0.361086	−	0.932533i	$-0.382406\pi$
$523$	−13.0685	−	13.0685i	−0.571447	−	0.571447i	−0.932533	+	0.361086i	$0.882406\pi$
$524$	0.558162			0.0243834
$525$		0			0
$526$	−0.295757			−0.0128956
$527$	12.3706	+	12.3706i	0.538870	+	0.538870i
$528$	12.9042	−	3.67678i	0.561585	−	0.160011i
$529$		−	5.28280i		−	0.229687i
$530$		0			0
$531$	−12.5883	+	7.80733i	−0.546285	+	0.338809i
$532$	3.26199	−	3.26199i	0.141425	−	0.141425i
$533$	−12.1045	+	12.1045i	−0.524303	+	0.524303i
$534$	−2.01015	+	3.61208i	−0.0869878	+	0.156310i
$535$		0			0
$536$		−	3.84760i		−	0.166191i
$537$	5.65682	+	19.8535i	0.244110	+	0.856743i
$538$	8.21544	+	8.21544i	0.354193	+	0.354193i
$539$	1.55221			0.0668583
$540$		0			0
$541$	21.5590			0.926893			0.463446	−	0.886125i	$-0.346613\pi$
$541$	21.5590			0.926893			0.463446	+	0.886125i	$0.346613\pi$
$542$	29.6469	+	29.6469i	1.27344	+	1.27344i
$543$	8.35068	+	29.3080i	0.358362	+	1.25773i
$544$			16.8961i			0.724415i
$545$		0			0
$546$	9.44963	−	16.9802i	0.404407	−	0.726687i
$547$	29.6665	−	29.6665i	1.26845	−	1.26845i	0.321555	−	0.946891i	$-0.395795\pi$
$547$	29.6665	−	29.6665i	1.26845	−	1.26845i	0.946891	−	0.321555i	$-0.104205\pi$
$548$	−2.87037	+	2.87037i	−0.122616	+	0.122616i
$549$	−8.45626	+	5.24463i	−0.360904	+	0.223835i
$550$		0			0
$551$		−	12.5083i		−	0.532872i
$552$	−14.0939	+	4.01574i	−0.599876	+	0.170921i
$553$	−2.54119	−	2.54119i	−0.108063	−	0.108063i
$554$	−35.8116			−1.52149
$555$		0			0
$556$	−6.96235			−0.295269
$557$	19.2396	+	19.2396i	0.815208	+	0.815208i	0.985409	−	0.170201i	$-0.0544418\pi$
$557$	19.2396	+	19.2396i	0.815208	+	0.815208i	−0.170201	+	0.985409i	$0.554442\pi$
$558$	−29.7952	−	6.98431i	−1.26133	−	0.295669i
$559$			18.8993i			0.799354i
$560$		0			0
$561$	−7.08880	−	3.94497i	−0.299290	−	0.166557i
$562$	1.87490	−	1.87490i	0.0790880	−	0.0790880i
$563$	−2.03574	+	2.03574i	−0.0857962	+	0.0857962i	−0.748702	−	0.662906i	$-0.769323\pi$
$563$	−2.03574	+	2.03574i	−0.0857962	+	0.0857962i	0.662906	+	0.748702i	$0.269323\pi$
$564$	−0.0840650	−	0.0467828i	−0.00353977	−	0.00196991i
$565$		0			0
$566$			21.1284i			0.888092i
$567$	2.87286	+	8.52917i	0.120649	+	0.358191i
$568$	−6.45262	−	6.45262i	−0.270746	−	0.270746i
$569$	36.6125			1.53487			0.767437	−	0.641124i	$-0.221532\pi$
$569$	36.6125			1.53487			0.767437	+	0.641124i	$0.221532\pi$
$570$		0			0
$571$	−9.88863			−0.413826			−0.206913	−	0.978359i	$-0.566342\pi$
$571$	−9.88863			−0.413826			−0.206913	+	0.978359i	$0.566342\pi$
$572$	−7.66906	−	7.66906i	−0.320659	−	0.320659i
$573$	−9.22865	+	2.62950i	−0.385533	+	0.109849i
$574$			4.72347i			0.197154i
$575$		0			0
$576$	0.205056	+	0.330625i	0.00854400	+	0.0137760i
$577$	−3.44953	+	3.44953i	−0.143606	+	0.143606i	−0.775255	−	0.631649i	$-0.782378\pi$
$577$	−3.44953	+	3.44953i	−0.143606	+	0.143606i	0.631649	+	0.775255i	$0.282378\pi$
$578$	−9.82204	+	9.82204i	−0.408543	+	0.408543i
$579$	16.5600	−	29.7570i	0.688211	−	1.23666i
$580$		0			0
$581$		−	17.2730i		−	0.716605i
$582$	−12.9687	−	45.5156i	−0.537569	−	1.88668i
$583$	6.68741	+	6.68741i	0.276964	+	0.276964i
$584$	16.3521			0.676657
$585$		0			0
$586$	5.86864			0.242431
$587$	−4.70846	−	4.70846i	−0.194339	−	0.194339i	0.603229	−	0.797568i	$-0.293880\pi$
$587$	−4.70846	−	4.70846i	−0.194339	−	0.194339i	−0.797568	+	0.603229i	$0.793880\pi$
$588$	−0.520079	−	1.82530i	−0.0214477	−	0.0752741i
$589$		−	24.4079i		−	1.00571i
$590$		0			0
$591$	15.1458	−	27.2158i	0.623016	−	1.11951i
$592$	6.14487	−	6.14487i	0.252553	−	0.252553i
$593$	15.2900	−	15.2900i	0.627884	−	0.627884i	−0.319651	−	0.947535i	$-0.603566\pi$
$593$	15.2900	−	15.2900i	0.627884	−	0.627884i	0.947535	+	0.319651i	$0.103566\pi$
$594$	14.1752	−	0.671263i	0.581617	−	0.0275422i
$595$		0			0
$596$		−	4.68955i		−	0.192092i
$597$	−10.1859	+	2.90224i	−0.416880	+	0.118781i
$598$	42.1906	+	42.1906i	1.72530	+	1.72530i
$599$	−9.38844			−0.383601			−0.191801	−	0.981434i	$-0.561433\pi$
$599$	−9.38844			−0.383601			−0.191801	+	0.981434i	$0.561433\pi$
$600$		0			0
$601$	−4.87361			−0.198799			−0.0993993	−	0.995048i	$-0.531692\pi$
$601$	−4.87361			−0.198799			−0.0993993	+	0.995048i	$0.531692\pi$
$602$	3.68749	+	3.68749i	0.150291	+	0.150291i
$603$	1.65582	−	7.06377i	0.0674303	−	0.287659i
$604$		−	5.71155i		−	0.232400i
$605$		0			0
$606$	−33.8280	−	18.8255i	−1.37417	−	0.764734i
$607$	2.56287	−	2.56287i	0.104024	−	0.104024i	−0.653180	−	0.757203i	$-0.726565\pi$
$607$	2.56287	−	2.56287i	0.104024	−	0.104024i	0.757203	+	0.653180i	$0.226565\pi$
$608$	16.6685	−	16.6685i	0.675998	−	0.675998i
$609$	−4.49675	−	2.50247i	−0.182217	−	0.101405i
$610$		0			0
$611$		−	0.323222i		−	0.0130762i
$612$	−2.26389	+	9.65780i	−0.0915123	+	0.390393i
$613$	−33.5166	−	33.5166i	−1.35372	−	1.35372i	−0.881457	−	0.472264i	$-0.843437\pi$
$613$	−33.5166	−	33.5166i	−1.35372	−	1.35372i	−0.472264	−	0.881457i	$-0.656563\pi$
$614$	−1.97471			−0.0796927
$615$		0			0
$616$	2.46950			0.0994989
$617$	2.15297	+	2.15297i	0.0866754	+	0.0866754i	0.749115	−	0.662440i	$-0.230479\pi$
$617$	2.15297	+	2.15297i	0.0866754	+	0.0866754i	−0.662440	+	0.749115i	$0.730479\pi$
$618$	−6.08459	+	1.73367i	−0.244758	+	0.0697384i
$619$		−	10.1941i		−	0.409737i	−0.978789	−	0.204869i	$-0.934323\pi$
$619$		−	10.1941i		−	0.409737i	0.978789	−	0.204869i	$-0.0656767\pi$
$620$		0			0
$621$	−27.6030	+	1.30713i	−1.10767	+	0.0524534i
$622$	12.3359	−	12.3359i	0.494626	−	0.494626i
$623$	−0.959142	+	0.959142i	−0.0384272	+	0.0384272i
$624$	26.8042	−	48.1650i	1.07303	−	1.92814i
$625$		0			0
$626$		−	24.7618i		−	0.989682i
$627$	3.10148	+	10.8852i	0.123861	+	0.434711i
$628$	4.77759	+	4.77759i	0.190646	+	0.190646i
$629$	−5.25417			−0.209498
$630$		0			0
$631$	44.6402			1.77710			0.888550	−	0.458781i	$-0.151714\pi$
$631$	44.6402			1.77710			0.888550	+	0.458781i	$0.151714\pi$
$632$	−4.04293	−	4.04293i	−0.160819	−	0.160819i
$633$	−5.92801	−	20.8053i	−0.235617	−	0.826937i
$634$			37.2716i			1.48025i
$635$		0			0
$636$	5.62332	−	10.1047i	0.222979	−	0.400676i
$637$	4.50889	−	4.50889i	0.178649	−	0.178649i
$638$	−5.73777	+	5.73777i	−0.227161	+	0.227161i
$639$	−9.06940	−	14.6232i	−0.358780	−	0.578485i
$640$		0			0
$641$		−	15.7329i		−	0.621414i	−0.950506	−	0.310707i	$-0.899434\pi$
$641$		−	15.7329i		−	0.621414i	0.950506	−	0.310707i	$-0.100566\pi$
$642$	−56.1725	+	16.0051i	−2.21695	+	0.631672i
$643$	11.7811	+	11.7811i	0.464600	+	0.464600i	0.900160	−	0.435560i	$-0.143449\pi$
$643$	11.7811	+	11.7811i	0.464600	+	0.464600i	−0.435560	+	0.900160i	$0.643449\pi$
$644$	5.82753			0.229637
$645$		0			0
$646$	−22.3516			−0.879411
$647$	10.8002	+	10.8002i	0.424600	+	0.424600i	0.886784	−	0.462184i	$-0.152934\pi$
$647$	10.8002	+	10.8002i	0.424600	+	0.424600i	−0.462184	+	0.886784i	$0.652934\pi$
$648$	4.57060	+	13.5696i	0.179550	+	0.533063i
$649$			7.66417i			0.300845i
$650$		0			0
$651$	−8.77466	−	4.88316i	−0.343906	−	0.191386i
$652$	5.85518	−	5.85518i	0.229307	−	0.229307i
$653$	7.88328	−	7.88328i	0.308497	−	0.308497i	−0.535830	−	0.844326i	$-0.680001\pi$
$653$	7.88328	−	7.88328i	0.308497	−	0.308497i	0.844326	+	0.535830i	$0.180001\pi$
$654$	12.8928	+	7.17493i	0.504147	+	0.280562i
$655$		0			0
$656$			13.3983i			0.523115i
$657$	30.0207	+	7.03717i	1.17122	+	0.274546i
$658$	−0.0630648	−	0.0630648i	−0.00245852	−	0.00245852i
$659$	−6.73141			−0.262219			−0.131109	−	0.991368i	$-0.541854\pi$
$659$	−6.73141			−0.262219			−0.131109	+	0.991368i	$0.541854\pi$
$660$		0			0
$661$	4.43191			0.172381			0.0861906	−	0.996279i	$-0.472531\pi$
$661$	4.43191			0.172381			0.0861906	+	0.996279i	$0.472531\pi$
$662$	3.85991	+	3.85991i	0.150020	+	0.150020i
$663$	−32.0512	+	9.13228i	−1.24476	+	0.354668i
$664$		−	27.4807i		−	1.06646i
$665$		0			0
$666$	7.81072	−	4.84426i	0.302659	−	0.187711i
$667$	11.1730	−	11.1730i	0.432621	−	0.432621i
$668$	15.1472	−	15.1472i	0.586064	−	0.586064i
$669$	−10.4870	+	18.8444i	−0.405452	+	0.728565i
$670$		0			0
$671$			5.14846i			0.198754i
$672$	−2.65756	−	9.32715i	−0.102518	−	0.359802i
$673$	3.35642	+	3.35642i	0.129381	+	0.129381i	0.768832	−	0.639451i	$-0.220838\pi$
$673$	3.35642	+	3.35642i	0.129381	+	0.129381i	−0.639451	+	0.768832i	$0.720838\pi$
$674$	−57.7356			−2.22389
$675$		0			0
$676$	−30.3094			−1.16575
$677$	−6.31136	−	6.31136i	−0.242565	−	0.242565i	0.575345	−	0.817911i	$-0.304868\pi$
$677$	−6.31136	−	6.31136i	−0.242565	−	0.242565i	−0.817911	+	0.575345i	$0.804868\pi$
$678$	12.5447	+	44.0277i	0.481777	+	1.69087i
$679$		−	15.5298i		−	0.595977i
$680$		0			0
$681$	18.7513	−	33.6946i	0.718551	−	1.29118i
$682$	−11.1963	+	11.1963i	−0.428729	+	0.428729i
$683$	21.4480	−	21.4480i	0.820686	−	0.820686i	−0.165520	−	0.986206i	$-0.552930\pi$
$683$	21.4480	−	21.4480i	0.820686	−	0.820686i	0.986206	+	0.165520i	$0.0529303\pi$
$684$	11.7611	−	7.29431i	0.449697	−	0.278905i
$685$		0			0
$686$		−	1.75948i		−	0.0671774i
$687$	−13.7832	+	3.92722i	−0.525862	+	0.149833i
$688$	10.4597	+	10.4597i	0.398771	+	0.398771i
$689$	38.8515			1.48012
$690$		0			0
$691$	18.7943			0.714968			0.357484	−	0.933919i	$-0.383635\pi$
$691$	18.7943			0.714968			0.357484	+	0.933919i	$0.383635\pi$
$692$	2.26427	+	2.26427i	0.0860745	+	0.0860745i
$693$	4.53372	+	1.06275i	0.172222	+	0.0403706i
$694$			35.2932i			1.33971i
$695$		0			0
$696$	−7.15414	−	3.98133i	−0.271177	−	0.150912i
$697$	5.72810	−	5.72810i	0.216967	−	0.216967i
$698$	11.5351	−	11.5351i	0.436610	−	0.436610i
$699$	−27.0597	−	15.0589i	−1.02349	−	0.569581i
$700$		0			0
$701$			10.0310i			0.378867i	0.981894	+	0.189434i	$0.0606652\pi$
$701$			10.0310i			0.378867i	−0.981894	+	0.189434i	$0.939335\pi$
$702$	39.2266	−	43.1264i	1.48051	−	1.62770i
$703$	5.18340	+	5.18340i	0.195496	+	0.195496i
$704$	0.201296			0.00758663
$705$		0			0
$706$	50.3682			1.89563
$707$	−8.98258	−	8.98258i	−0.337825	−	0.337825i
$708$	9.01260	−	2.56794i	0.338714	−	0.0965092i
$709$			48.4192i			1.81842i	0.416335	+	0.909211i	$0.363314\pi$
$709$			48.4192i			1.81842i	−0.416335	+	0.909211i	$0.636686\pi$
$710$		0			0
$711$	−5.68250	−	9.16227i	−0.213110	−	0.343612i
$712$	−1.52596	+	1.52596i	−0.0571876	+	0.0571876i
$713$	21.8023	−	21.8023i	0.816502	−	0.816502i
$714$	−4.47177	+	8.03542i	−0.167352	+	0.300718i
$715$		0			0
$716$		−	13.0602i		−	0.488083i
$717$	−12.2575	−	43.0197i	−0.457765	−	1.60660i
$718$	−23.4258	−	23.4258i	−0.874244	−	0.874244i
$719$	10.6931			0.398786			0.199393	−	0.979920i	$-0.436103\pi$
$719$	10.6931			0.398786			0.199393	+	0.979920i	$0.436103\pi$
$720$		0			0
$721$	−2.07604			−0.0773157
$722$	−1.58818	−	1.58818i	−0.0591060	−	0.0591060i
$723$	4.99284	+	17.5232i	0.185686	+	0.651693i
$724$		−	19.2797i		−	0.716523i
$725$		0			0
$726$	−12.7308	+	22.8763i	−0.472486	+	0.849020i
$727$	−30.9245	+	30.9245i	−1.14693	+	1.14693i	−0.159773	+	0.987154i	$0.551076\pi$
$727$	−30.9245	+	30.9245i	−1.14693	+	1.14693i	−0.987154	+	0.159773i	$0.948924\pi$
$728$	7.17345	−	7.17345i	0.265866	−	0.265866i
$729$	2.55143	+	26.8792i	0.0944974	+	0.995525i
$730$		0			0
$731$		−	8.94354i		−	0.330789i
$732$	6.05428	−	1.72503i	0.223773	−	0.0637590i
$733$	23.0095	+	23.0095i	0.849876	+	0.849876i	0.990117	−	0.140241i	$-0.0447879\pi$
$733$	23.0095	+	23.0095i	0.849876	+	0.849876i	−0.140241	+	0.990117i	$0.544788\pi$
$734$	2.34399			0.0865184
$735$		0			0
$736$	29.7782			1.09764
$737$	−2.65439	−	2.65439i	−0.0977759	−	0.0977759i
$738$	−3.23403	+	13.7964i	−0.119046	+	0.507854i
$739$			31.0959i			1.14388i	0.820295	+	0.571941i	$0.193809\pi$
$739$			31.0959i			1.14388i	−0.820295	+	0.571941i	$0.806191\pi$
$740$		0			0
$741$	40.6287	+	22.6102i	1.49253	+	0.830606i
$742$	7.58042	−	7.58042i	0.278286	−	0.278286i
$743$	4.41646	−	4.41646i	0.162024	−	0.162024i	−0.621439	−	0.783463i	$-0.713451\pi$
$743$	4.41646	−	4.41646i	0.162024	−	0.162024i	0.783463	+	0.621439i	$0.213451\pi$
$744$	−13.9601	−	7.76892i	−0.511803	−	0.284822i
$745$		0			0
$746$			18.4118i			0.674105i
$747$	11.8263	−	50.4514i	0.432703	−	1.84592i
$748$	3.62917	+	3.62917i	0.132695	+	0.132695i
$749$	−19.1658			−0.700305
$750$		0			0
$751$	−20.7634			−0.757668			−0.378834	−	0.925465i	$-0.623675\pi$
$751$	−20.7634			−0.757668			−0.378834	+	0.925465i	$0.623675\pi$
$752$	−0.178885	−	0.178885i	−0.00652327	−	0.00652327i
$753$	−11.5697	+	3.29654i	−0.421624	+	0.120132i
$754$			33.3344i			1.21397i
$755$		0			0
$756$	−0.269328	−	5.68747i	−0.00979536	−	0.206851i
$757$	−27.7515	+	27.7515i	−1.00865	+	1.00865i	−0.00868333	+	0.999962i	$0.502764\pi$
$757$	−27.7515	+	27.7515i	−1.00865	+	1.00865i	−0.999962	+	0.00868333i	$0.997236\pi$
$758$	−27.3072	+	27.3072i	−0.991843	+	0.991843i
$759$	−6.95274	+	12.4935i	−0.252369	+	0.453486i
$760$		0			0
$761$			51.6155i			1.87106i	0.353246	+	0.935531i	$0.385078\pi$
$761$			51.6155i			1.87106i	−0.353246	+	0.935531i	$0.614922\pi$
$762$	−11.9983	−	42.1099i	−0.434652	−	1.52548i
$763$	3.42351	+	3.42351i	0.123939	+	0.123939i
$764$	6.07087			0.219636
$765$		0			0
$766$	48.1010			1.73796
$767$	22.2631	+	22.2631i	0.803873	+	0.803873i
$768$	−9.41932	−	33.0586i	−0.339891	−	1.19290i
$769$			15.3442i			0.553327i	0.960967	+	0.276663i	$0.0892287\pi$
$769$			15.3442i			0.553327i	−0.960967	+	0.276663i	$0.910771\pi$
$770$		0			0
$771$	9.73225	−	17.4881i	0.350498	−	0.629818i
$772$	−15.2343	+	15.2343i	−0.548296	+	0.548296i
$773$	16.1229	−	16.1229i	0.579900	−	0.579900i	−0.354976	−	0.934876i	$-0.615511\pi$
$773$	16.1229	−	16.1229i	0.579900	−	0.579900i	0.934876	+	0.354976i	$0.115511\pi$
$774$	8.24579	+	13.2952i	0.296389	+	0.477887i
$775$		0			0
$776$		−	24.7072i		−	0.886937i
$777$	2.90046	−	0.826421i	0.104053	−	0.0296477i
$778$	38.3147	+	38.3147i	1.37365	+	1.37365i
$779$	−11.3019			−0.404932
$780$		0			0
$781$	−8.90311			−0.318578
$782$	−19.9655	−	19.9655i	−0.713965	−	0.713965i
$783$	−11.4208	−	10.3881i	−0.408148	−	0.371240i
$784$		−	4.99083i		−	0.178244i
$785$		0			0
$786$	1.35643	+	0.754861i	0.0483821	+	0.0269250i
$787$	6.19650	−	6.19650i	0.220881	−	0.220881i	−0.587988	−	0.808870i	$-0.700080\pi$
$787$	6.19650	−	6.19650i	0.220881	−	0.220881i	0.808870	+	0.587988i	$0.200080\pi$
$788$	−13.9334	+	13.9334i	−0.496355	+	0.496355i
$789$	−0.254405	−	0.141578i	−0.00905705	−	0.00504032i
$790$		0			0
$791$			15.0221i			0.534124i
$792$	7.21297	+	1.69080i	0.256302	+	0.0600798i
$793$	14.9554	+	14.9554i	0.531081	+	0.531081i
$794$	−51.8196			−1.83901
$795$		0			0
$796$	6.70056			0.237495
$797$	24.6954	+	24.6954i	0.874755	+	0.874755i	0.992986	−	0.118231i	$-0.0377223\pi$
$797$	24.6954	+	24.6954i	0.874755	+	0.874755i	−0.118231	+	0.992986i	$0.537722\pi$
$798$	12.3387	−	3.51565i	0.436786	−	0.124453i
$799$			0.152956i			0.00541119i
$800$		0			0
$801$	−3.45819	+	2.14479i	−0.122189	+	0.0757824i
$802$	−26.0130	+	26.0130i	−0.918552	+	0.918552i
$803$	11.2811	−	11.2811i	0.398100	−	0.398100i
$804$	−2.23203	+	4.01078i	−0.0787177	+	0.141449i
$805$		0			0
$806$			65.0467i			2.29117i
$807$	3.13406	+	10.9995i	0.110324	+	0.387200i
$808$	−14.2909	−	14.2909i	−0.502753	−	0.502753i
$809$	20.4064			0.717449			0.358725	−	0.933443i	$-0.383212\pi$
$809$	20.4064			0.717449			0.358725	+	0.933443i	$0.383212\pi$
$810$		0			0
$811$	10.0632			0.353368			0.176684	−	0.984268i	$-0.443463\pi$
$811$	10.0632			0.353368			0.176684	+	0.984268i	$0.443463\pi$
$812$	2.30214	+	2.30214i	0.0807894	+	0.0807894i
$813$	11.3098	+	39.6935i	0.396652	+	1.39211i
$814$		−	4.75543i		−	0.166678i
$815$		0			0
$816$	−12.6843	+	22.7927i	−0.444040	+	0.797904i
$817$	−8.82308	+	8.82308i	−0.308680	+	0.308680i
$818$	−14.4038	+	14.4038i	−0.503617	+	0.503617i
$819$	16.2568	−	10.0826i	0.568058	−	0.352313i
$820$		0			0
$821$			55.9052i			1.95110i	0.219767	+	0.975552i	$0.429470\pi$
$821$			55.9052i			1.95110i	−0.219767	+	0.975552i	$0.570530\pi$
$822$	−10.8574	+	3.09357i	−0.378695	+	0.107901i
$823$	25.7909	+	25.7909i	0.899015	+	0.899015i	0.995349	−	0.0963344i	$-0.0307118\pi$
$823$	25.7909	+	25.7909i	0.899015	+	0.899015i	−0.0963344	+	0.995349i	$0.530712\pi$
$824$	−3.30289			−0.115062
$825$		0			0
$826$	8.68762			0.302281
$827$	−25.9659	−	25.9659i	−0.902922	−	0.902922i	0.0927663	−	0.995688i	$-0.470429\pi$
$827$	−25.9659	−	25.9659i	−0.902922	−	0.902922i	−0.995688	+	0.0927663i	$0.970429\pi$
$828$	17.0212	+	3.98995i	0.591528	+	0.138660i
$829$			12.6797i			0.440385i	0.975456	+	0.220193i	$0.0706686\pi$
$829$			12.6797i			0.440385i	−0.975456	+	0.220193i	$0.929331\pi$
$830$		0			0
$831$	−30.8044	−	17.1429i	−1.06859	−	0.594681i
$832$	0.584729	−	0.584729i	0.0202718	−	0.0202718i
$833$	−2.13370	+	2.13370i	−0.0739284	+	0.0739284i
$834$	−16.9197	−	9.41593i	−0.585881	−	0.326047i
$835$		0			0
$836$		−	7.16056i		−	0.247653i
$837$	−22.2859	−	20.2706i	−0.770313	−	0.700656i
$838$	−0.653815	−	0.653815i	−0.0225857	−	0.0225857i
$839$	27.2730			0.941569			0.470785	−	0.882248i	$-0.343971\pi$
$839$	27.2730			0.941569			0.470785	+	0.882248i	$0.343971\pi$
$840$		0			0
$841$	−20.1723			−0.695596
$842$	19.3211	+	19.3211i	0.665851	+	0.665851i
$843$	2.51026	−	0.715244i	0.0864581	−	0.0246343i
$844$			13.6863i			0.471103i
$845$		0			0
$846$	−0.141023	−	0.227380i	−0.00484846	−	0.00781749i
$847$	−6.07451	+	6.07451i	−0.208723	+	0.208723i
$848$	21.5021	−	21.5021i	0.738385	−	0.738385i
$849$	−10.1141	+	18.1742i	−0.347115	+	0.623738i
$850$		0			0
$851$			9.26012i			0.317433i
$852$	2.98306	+	10.4695i	0.102198	+	0.358679i
$853$	−8.57549	−	8.57549i	−0.293619	−	0.293619i	0.544889	−	0.838508i	$-0.316572\pi$
$853$	−8.57549	−	8.57549i	−0.293619	−	0.293619i	−0.838508	+	0.544889i	$0.816572\pi$
$854$	5.83597			0.199703
$855$		0			0
$856$	−30.4921			−1.04220
$857$	−20.8458	−	20.8458i	−0.712077	−	0.712077i	0.254892	−	0.966970i	$-0.417960\pi$
$857$	−20.8458	−	20.8458i	−0.712077	−	0.712077i	−0.966970	+	0.254892i	$0.917960\pi$
$858$	−8.26541	−	29.0088i	−0.282177	−	0.990344i
$859$		−	9.52782i		−	0.325085i	−0.986702	−	0.162543i	$-0.948031\pi$
$859$		−	9.52782i		−	0.325085i	0.986702	−	0.162543i	$-0.0519695\pi$
$860$		0			0
$861$	−2.26111	+	4.06304i	−0.0770585	+	0.138468i
$862$	28.6332	−	28.6332i	0.975249	−	0.975249i
$863$	−32.3773	+	32.3773i	−1.10213	+	1.10213i	−0.107982	+	0.994153i	$0.534439\pi$
$863$	−32.3773	+	32.3773i	−1.10213	+	1.10213i	−0.994153	+	0.107982i	$0.965561\pi$
$864$	−1.37625	−	29.0625i	−0.0468208	−	0.988727i
$865$		0			0
$866$		−	38.3198i		−	1.30216i
$867$	−13.1505	+	3.74695i	−0.446615	+	0.127253i
$868$	4.49225	+	4.49225i	0.152477	+	0.152477i
$869$	−5.57830			−0.189231
$870$		0			0
$871$	−15.4211			−0.522524
$872$	5.44667	+	5.44667i	0.184447	+	0.184447i
$873$	10.6328	−	45.3597i	0.359865	−	1.53519i
$874$			39.3931i			1.33249i
$875$		0			0
$876$	−17.0457	−	9.48604i	−0.575919	−	0.320503i
$877$	22.3025	−	22.3025i	0.753102	−	0.753102i	−0.221955	−	0.975057i	$-0.571244\pi$
$877$	22.3025	−	22.3025i	0.753102	−	0.753102i	0.975057	+	0.221955i	$0.0712439\pi$
$878$	7.51820	−	7.51820i	0.253727	−	0.253727i
$879$	5.04809	+	2.80930i	0.170268	+	0.0947553i
$880$		0			0
$881$		−	31.6927i		−	1.06775i	−0.845562	−	0.533877i	$-0.820734\pi$
$881$		−	31.6927i		−	1.06775i	0.845562	−	0.533877i	$-0.179266\pi$
$882$	1.20467	−	5.13914i	0.0405633	−	0.173044i
$883$	19.2435	+	19.2435i	0.647595	+	0.647595i	0.952411	−	0.304816i	$-0.0985950\pi$
$883$	19.2435	+	19.2435i	0.647595	+	0.647595i	−0.304816	+	0.952411i	$0.598595\pi$
$884$	21.0842			0.709137
$885$		0			0
$886$	21.5168			0.722872
$887$	−7.26863	−	7.26863i	−0.244057	−	0.244057i	0.574469	−	0.818526i	$-0.305208\pi$
$887$	−7.26863	−	7.26863i	−0.244057	−	0.244057i	−0.818526	+	0.574469i	$0.805208\pi$
$888$	4.61451	−	1.31480i	0.154853	−	0.0441219i
$889$		−	14.3677i		−	0.481878i
$890$		0			0
$891$	12.5146	+	6.20823i	0.419254	+	0.207983i
$892$	9.64751	−	9.64751i	0.323023	−	0.323023i
$893$	0.150896	−	0.150896i	0.00504953	−	0.00504953i
$894$	6.34218	−	11.3964i	0.212114	−	0.381153i
$895$		0			0
$896$		−	11.4269i		−	0.381745i
$897$	16.0950	+	56.4880i	0.537397	+	1.88608i
$898$	−25.8283	−	25.8283i	−0.861903	−	0.861903i
$899$	17.2258			0.574513
$900$		0			0
$901$	−18.3854			−0.612506
$902$	5.18437	+	5.18437i	0.172621	+	0.172621i
$903$	1.40672	+	4.93710i	0.0468126	+	0.164296i
$904$			23.8995i			0.794886i
$905$		0			0
$906$	7.72434	−	13.8800i	0.256624	−	0.461133i
$907$	−20.0346	+	20.0346i	−0.665238	+	0.665238i	−0.956610	−	0.291372i	$-0.905888\pi$
$907$	−20.0346	+	20.0346i	−0.665238	+	0.665238i	0.291372	+	0.956610i	$0.405888\pi$
$908$	−17.2502	+	17.2502i	−0.572467	+	0.572467i
$909$	−20.0864	−	32.3867i	−0.666225	−	1.07420i
$910$		0			0
$911$		−	34.2452i		−	1.13459i	−0.823514	−	0.567296i	$-0.807989\pi$
$911$		−	34.2452i		−	1.13459i	0.823514	−	0.567296i	$-0.192011\pi$
$912$	34.9992	−	9.97224i	1.15894	−	0.330214i
$913$	−18.9584	−	18.9584i	−0.627432	−	0.627432i
$914$	43.0661			1.42450
$915$		0			0
$916$	9.06698			0.299582
$917$	0.360182	+	0.360182i	0.0118942	+	0.0118942i
$918$	−18.5629	+	20.4084i	−0.612667	+	0.673576i
$919$			44.3406i			1.46266i	0.682023	+	0.731331i	$0.261100\pi$
$919$			44.3406i			1.46266i	−0.682023	+	0.731331i	$0.738900\pi$
$920$		0			0
$921$	−1.69861	−	0.945287i	−0.0559709	−	0.0311483i
$922$	5.42970	−	5.42970i	0.178818	−	0.178818i
$923$	−25.8620	+	25.8620i	−0.851257	+	0.851257i
$924$	−2.57423	−	1.43258i	−0.0846860	−	0.0471284i
$925$		0			0
$926$			5.07976i			0.166931i
$927$	−6.06375	−	1.42141i	−0.199160	−	0.0466851i
$928$	11.7638	+	11.7638i	0.386165	+	0.386165i
$929$	−9.88243			−0.324232			−0.162116	−	0.986772i	$-0.551832\pi$
$929$	−9.88243			−0.324232			−0.162116	+	0.986772i	$0.551832\pi$
$930$		0			0
$931$	4.20993			0.137975
$932$	13.8534	+	13.8534i	0.453784	+	0.453784i
$933$	16.5163	−	4.70596i	0.540720	−	0.154066i
$934$			34.7438i			1.13685i
$935$		0			0
$936$	25.8639	−	16.0409i	0.845387	−	0.524315i
$937$	22.4981	−	22.4981i	0.734980	−	0.734980i	−0.236622	−	0.971602i	$-0.576040\pi$
$937$	22.4981	−	22.4981i	0.734980	−	0.734980i	0.971602	+	0.236622i	$0.0760403\pi$
$938$	−3.00885	+	3.00885i	−0.0982426	+	0.0982426i
$939$	11.8534	−	21.2996i	0.386821	−	0.695088i
$940$		0			0
$941$		−	56.4149i		−	1.83907i	−0.393006	−	0.919536i	$-0.628565\pi$
$941$		−	56.4149i		−	1.83907i	0.393006	−	0.919536i	$-0.371435\pi$
$942$	5.14910	+	18.0716i	0.167767	+	0.588804i
$943$	−10.0954	−	10.0954i	−0.328751	−	0.328751i
$944$	24.6427			0.802052
$945$		0			0
$946$	8.09460			0.263178
$947$	8.25095	+	8.25095i	0.268120	+	0.268120i	0.828342	−	0.560222i	$-0.189284\pi$
$947$	8.25095	+	8.25095i	0.268120	+	0.268120i	−0.560222	+	0.828342i	$0.689284\pi$
$948$	1.86905	+	6.55974i	0.0607041	+	0.213051i
$949$		−	65.5390i		−	2.12749i
$950$		0			0
$951$	−17.8418	+	32.0603i	−0.578560	+	1.03963i
$952$	−3.39463	+	3.39463i	−0.110021	+	0.110021i
$953$	18.3169	−	18.3169i	0.593344	−	0.593344i	−0.345189	−	0.938533i	$-0.612185\pi$
$953$	18.3169	−	18.3169i	0.593344	−	0.593344i	0.938533	+	0.345189i	$0.112185\pi$
$954$	27.3312	−	16.9510i	0.884881	−	0.548809i
$955$		0			0
$956$			28.2996i			0.915274i
$957$	−7.68217	+	2.18887i	−0.248329	+	0.0707560i
$958$	19.9147	+	19.9147i	0.643414	+	0.643414i
$959$	−3.70450			−0.119624
$960$		0			0
$961$	2.61332			0.0843005
$962$	−13.8137	−	13.8137i	−0.445371	−	0.445371i
$963$	−55.9801	−	13.1223i	−1.80393	−	0.422861i
$964$		−	11.5272i		−	0.371267i
$965$		0			0
$966$	14.1619	+	7.88119i	0.455651	+	0.253573i
$967$	6.55794	−	6.55794i	0.210889	−	0.210889i	−0.593756	−	0.804645i	$-0.702356\pi$
$967$	6.55794	−	6.55794i	0.210889	−	0.210889i	0.804645	+	0.593756i	$0.202356\pi$
$968$	−9.66430	+	9.66430i	−0.310622	+	0.310622i
$969$	−19.2264	−	10.6996i	−0.617641	−	0.343722i
$970$		0			0
$971$		−	13.9212i		−	0.446753i	−0.974732	−	0.223377i	$-0.928292\pi$
$971$		−	13.9212i		−	0.446753i	0.974732	−	0.223377i	$-0.0717079\pi$
$972$	3.10739	−	16.7965i	0.0996696	−	0.538748i
$973$	−4.49280	−	4.49280i	−0.144033	−	0.144033i
$974$	51.2825			1.64320
$975$		0			0
$976$	16.5539			0.529878
$977$	−27.2013	−	27.2013i	−0.870248	−	0.870248i	0.122251	−	0.992499i	$-0.460989\pi$
$977$	−27.2013	−	27.2013i	−0.870248	−	0.870248i	−0.992499	+	0.122251i	$0.960989\pi$
$978$	22.1477	−	6.31049i	0.708204	−	0.201787i
$979$			2.10546i			0.0672909i
$980$		0			0
$981$	7.65550	+	12.3435i	0.244421	+	0.394096i
$982$	−37.1807	+	37.1807i	−1.18648	+	1.18648i
$983$	36.8517	−	36.8517i	1.17539	−	1.17539i	0.194479	−	0.980907i	$-0.437698\pi$
$983$	36.8517	−	36.8517i	1.17539	−	1.17539i	0.980907	−	0.194479i	$-0.0623015\pi$
$984$	−3.59734	+	6.46413i	−0.114679	+	0.206069i
$985$		0			0
$986$		−	15.7746i		−	0.502365i
$987$	−0.0240582	−	0.0844361i	−0.000765781	−	0.00268763i
$988$	−20.8002	−	20.8002i	−0.661742	−	0.661742i
$989$	−15.7624			−0.501215
$990$		0			0
$991$	−41.8651			−1.32989			−0.664945	−	0.746893i	$-0.731545\pi$
$991$	−41.8651			−1.32989			−0.664945	+	0.746893i	$0.731545\pi$
$992$	22.9551	+	22.9551i	0.728824	+	0.728824i
$993$	1.47249	+	5.16795i	0.0467281	+	0.164000i
$994$			10.0920i			0.320099i
$995$		0			0
$996$	−15.9418	+	28.6461i	−0.505135	+	0.907687i
$997$	−11.4463	+	11.4463i	−0.362507	+	0.362507i	−0.864735	−	0.502228i	$-0.832514\pi$
$997$	−11.4463	+	11.4463i	−0.362507	+	0.362507i	0.502228	+	0.864735i	$0.332514\pi$
$998$	1.17024	−	1.17024i	0.0370434	−	0.0370434i
$999$	9.03756	−	0.427970i	0.285936	−	0.0135404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.b.218.3		24
3.2	odd	2	inner	525.2.j.b.218.10		24
5.2	odd	4	inner	525.2.j.b.407.10		24
5.3	odd	4		105.2.j.a.92.3	yes	24
5.4	even	2		105.2.j.a.8.10	yes	24
15.2	even	4	inner	525.2.j.b.407.3		24
15.8	even	4		105.2.j.a.92.10	yes	24
15.14	odd	2		105.2.j.a.8.3	✓	24
35.3	even	12		735.2.y.g.422.3		48
35.4	even	6		735.2.y.j.128.3		48
35.9	even	6		735.2.y.j.263.10		48
35.13	even	4		735.2.j.h.197.3		24
35.18	odd	12		735.2.y.j.422.3		48
35.19	odd	6		735.2.y.g.263.10		48
35.23	odd	12		735.2.y.j.557.10		48
35.24	odd	6		735.2.y.g.128.3		48
35.33	even	12		735.2.y.g.557.10		48
35.34	odd	2		735.2.j.h.638.10		24
105.23	even	12		735.2.y.j.557.3		48
105.38	odd	12		735.2.y.g.422.10		48
105.44	odd	6		735.2.y.j.263.3		48
105.53	even	12		735.2.y.j.422.10		48
105.59	even	6		735.2.y.g.128.10		48
105.68	odd	12		735.2.y.g.557.3		48
105.74	odd	6		735.2.y.j.128.10		48
105.83	odd	4		735.2.j.h.197.10		24
105.89	even	6		735.2.y.g.263.3		48
105.104	even	2		735.2.j.h.638.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.3	✓	24	15.14	odd	2
105.2.j.a.8.10	yes	24	5.4	even	2
105.2.j.a.92.3	yes	24	5.3	odd	4
105.2.j.a.92.10	yes	24	15.8	even	4
525.2.j.b.218.3		24	1.1	even	1	trivial
525.2.j.b.218.10		24	3.2	odd	2	inner
525.2.j.b.407.3		24	15.2	even	4	inner
525.2.j.b.407.10		24	5.2	odd	4	inner
735.2.j.h.197.3		24	35.13	even	4
735.2.j.h.197.10		24	105.83	odd	4
735.2.j.h.638.3		24	105.104	even	2
735.2.j.h.638.10		24	35.34	odd	2
735.2.y.g.128.3		48	35.24	odd	6
735.2.y.g.128.10		48	105.59	even	6
735.2.y.g.263.3		48	105.89	even	6
735.2.y.g.263.10		48	35.19	odd	6
735.2.y.g.422.3		48	35.3	even	12
735.2.y.g.422.10		48	105.38	odd	12
735.2.y.g.557.3		48	105.68	odd	12
735.2.y.g.557.10		48	35.33	even	12
735.2.y.j.128.3		48	35.4	even	6
735.2.y.j.128.10		48	105.74	odd	6
735.2.y.j.263.3		48	105.44	odd	6
735.2.y.j.263.10		48	35.9	even	6
735.2.y.j.422.3		48	35.18	odd	12
735.2.y.j.422.10		48	105.53	even	12
735.2.y.j.557.3		48	105.23	even	12
735.2.y.j.557.10		48	35.23	odd	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24414 - 1.24414i) q^{2} +(-0.474620 - 1.66575i) q^{3} +1.09578i q^{4} +(-1.48194 + 2.66293i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.12498 + 1.12498i) q^{8} +(-2.54947 + 1.58120i) q^{9} +O(q^{10})\)	\(q+(-1.24414 - 1.24414i) q^{2} +(-0.474620 - 1.66575i) q^{3} +1.09578i q^{4} +(-1.48194 + 2.66293i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.12498 + 1.12498i) q^{8} +(-2.54947 + 1.58120i) q^{9} +1.55221i q^{11} +(1.82530 - 0.520079i) q^{12} +(4.50889 + 4.50889i) q^{13} +1.75948 q^{14} +4.99083 q^{16} +(-2.13370 - 2.13370i) q^{17} +(5.13914 + 1.20467i) q^{18} +4.20993i q^{19} +(1.51347 + 0.842259i) q^{21} +(1.93117 - 1.93117i) q^{22} +(-3.76050 + 3.76050i) q^{23} +(2.40787 + 1.34000i) q^{24} -11.2194i q^{26} +(3.84392 + 3.49632i) q^{27} +(-0.774834 - 0.774834i) q^{28} -2.97115 q^{29} -5.79770 q^{31} +(-3.95934 - 3.95934i) q^{32} +(2.58559 - 0.736708i) q^{33} +5.30926i q^{34} +(-1.73265 - 2.79366i) q^{36} +(1.23123 - 1.23123i) q^{37} +(5.23775 - 5.23775i) q^{38} +(5.37069 - 9.65070i) q^{39} +2.68458i q^{41} +(-0.835085 - 2.93087i) q^{42} +(2.09578 + 2.09578i) q^{43} -1.70088 q^{44} +9.35721 q^{46} +(-0.0358428 - 0.0358428i) q^{47} +(-2.36874 - 8.31349i) q^{48} -1.00000i q^{49} +(-2.54153 + 4.56692i) q^{51} +(-4.94075 + 4.94075i) q^{52} +(4.30833 - 4.30833i) q^{53} +(-0.432457 - 9.13231i) q^{54} -1.59096i q^{56} +(7.01270 - 1.99811i) q^{57} +(3.69653 + 3.69653i) q^{58} +4.93760 q^{59} +3.31687 q^{61} +(7.21316 + 7.21316i) q^{62} +(0.684672 - 2.92083i) q^{63} -0.129684i q^{64} +(-4.13342 - 2.30028i) q^{66} +(-1.71008 + 1.71008i) q^{67} +(2.33807 - 2.33807i) q^{68} +(8.04889 + 4.47927i) q^{69} +5.73577i q^{71} +(1.08929 - 4.64692i) q^{72} +(-7.26776 - 7.26776i) q^{73} -3.06366 q^{74} -4.61315 q^{76} +(-1.09758 - 1.09758i) q^{77} +(-18.6887 + 5.32495i) q^{78} +3.59379i q^{79} +(3.99962 - 8.06245i) q^{81} +(3.34000 - 3.34000i) q^{82} +(-12.2139 + 12.2139i) q^{83} +(-0.922931 + 1.65843i) q^{84} -5.21490i q^{86} +(1.41016 + 4.94920i) q^{87} +(-1.74620 - 1.74620i) q^{88} +1.35643 q^{89} -6.37653 q^{91} +(-4.12069 - 4.12069i) q^{92} +(2.75170 + 9.65754i) q^{93} +0.0891871i q^{94} +(-4.71611 + 8.47447i) q^{96} +(-10.9812 + 10.9812i) q^{97} +(-1.24414 + 1.24414i) q^{98} +(-2.45435 - 3.95731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 - 16 * q^12 + 8 * q^13 - 16 * q^16 + 20 * q^18 + 4 * q^21 - 8 * q^22 + 16 * q^27 - 28 * q^33 + 16 * q^36 + 16 * q^37 + 20 * q^42 + 40 * q^43 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 4 * q^57 - 40 * q^58 + 32 * q^61 + 8 * q^63 - 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 32 * q^76 - 60 * q^78 + 52 * q^81 + 80 * q^82 - 4 * q^87 - 96 * q^88 - 24 * q^91 + 76 * q^93 - 96 * q^96 - 24 * q^97

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