LMFDB - Embedded newform 525.2.j.b.218.10

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			218.10
Character	$\chi$	$=$	525.218
Dual form			525.2.j.b.407.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24414 + 1.24414i) q^{2} +(-1.66575 - 0.474620i) q^{3} +1.09578i q^{4} +(-1.48194 - 2.66293i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.12498 - 1.12498i) q^{8} +(2.54947 + 1.58120i) q^{9} +O(q^{10})$	\(q+(1.24414 + 1.24414i) q^{2} +(-1.66575 - 0.474620i) 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} +(0.520079 - 1.82530i) q^{12} +(4.50889 + 4.50889i) q^{13} -1.75948 q^{14} +4.99083 q^{16} +(2.13370 + 2.13370i) q^{17} +(1.20467 + 5.13914i) 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} +(-3.49632 - 3.84392i) q^{27} +(-0.774834 - 0.774834i) q^{28} +2.97115 q^{29} -5.79770 q^{31} +(3.95934 + 3.95934i) q^{32} +(-0.736708 + 2.58559i) 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} +(2.93087 + 0.835085i) q^{42} +(2.09578 + 2.09578i) q^{43} +1.70088 q^{44} +9.35721 q^{46} +(0.0358428 + 0.0358428i) q^{47} +(-8.31349 - 2.36874i) 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} +(1.99811 - 7.01270i) q^{57} +(3.69653 + 3.69653i) q^{58} -4.93760 q^{59} +3.31687 q^{61} +(-7.21316 - 7.21316i) q^{62} +(-2.92083 + 0.684672i) 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} +(4.64692 - 1.08929i) q^{72} +(-7.26776 - 7.26776i) q^{73} +3.06366 q^{74} -4.61315 q^{76} +(1.09758 + 1.09758i) q^{77} +(5.32495 - 18.6887i) 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} +(-4.94920 - 1.41016i) q^{87} +(-1.74620 - 1.74620i) q^{88} -1.35643 q^{89} -6.37653 q^{91} +(4.12069 + 4.12069i) q^{92} +(9.65754 + 2.75170i) 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	0.993508	−	0.113766i	$-0.0362914\pi$
$2$	1.24414	+	1.24414i	0.879741	+	0.879741i	−0.113766	+	0.993508i	$0.536291\pi$
$3$	−1.66575	−	0.474620i	−0.961723	−	0.274022i
$3$	−1.66575	−	0.474620i	−0.961723	−	0.274022i
$4$			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	$-0.924817\pi$
$11$		−	1.55221i		−	0.468008i	0.972236	−	0.234004i	$-0.0751828\pi$
$12$	0.520079	−	1.82530i	0.150134	−	0.526919i
$13$	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	0.916814	−	0.399315i	$-0.130752\pi$
$17$	2.13370	+	2.13370i	0.517499	+	0.517499i	−0.399315	+	0.916814i	$0.630752\pi$
$18$	1.20467	+	5.13914i	0.283943	+	1.21131i
$19$			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	−0.196404	−	0.980523i	$-0.562926\pi$
$23$	3.76050	−	3.76050i	0.784119	−	0.784119i	0.980523	+	0.196404i	$0.0629263\pi$
$24$	−2.40787	+	1.34000i	−0.491505	+	0.273526i
$25$		0			0
$26$			11.2194i			2.20030i
$27$	−3.49632	−	3.84392i	−0.672868	−	0.739763i
$28$	−0.774834	−	0.774834i	−0.146430	−	0.146430i
$29$	2.97115			0.551728			0.275864	−	0.961197i	$-0.411036\pi$
$29$	2.97115			0.551728			0.275864	+	0.961197i	$0.411036\pi$
$30$		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
$33$	−0.736708	+	2.58559i	−0.128244	+	0.450094i
$34$			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	$-0.932774\pi$
$41$		−	2.68458i		−	0.419261i	0.977781	−	0.209631i	$-0.0672261\pi$
$42$	2.93087	+	0.835085i	0.452242	+	0.128856i
$43$	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	0.709716	−	0.704488i	$-0.248823\pi$
$47$	0.0358428	+	0.0358428i	0.00522821	+	0.00522821i	−0.704488	+	0.709716i	$0.748823\pi$
$48$	−8.31349	−	2.36874i	−1.19995	−	0.341899i
$49$		−	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	−0.938116	−	0.346322i	$-0.887431\pi$
$53$	−4.30833	+	4.30833i	−0.591794	+	0.591794i	0.346322	+	0.938116i	$0.387431\pi$
$54$	0.432457	−	9.13231i	0.0588500	−	1.24275i
$55$		0			0
$56$			1.59096i			0.212601i
$57$	1.99811	−	7.01270i	0.264657	−	0.928855i
$58$	3.69653	+	3.69653i	0.485378	+	0.485378i
$59$	−4.93760			−0.642821			−0.321410	−	0.946940i	$-0.604157\pi$
$59$	−4.93760			−0.642821			−0.321410	+	0.946940i	$0.604157\pi$
$60$		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
$63$	−2.92083	+	0.684672i	−0.367989	+	0.0862606i
$64$		−	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	$-0.889453\pi$
$71$		−	5.73577i		−	0.680711i	0.940297	−	0.340356i	$-0.110547\pi$
$72$	4.64692	−	1.08929i	0.547644	−	0.128374i
$73$	−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
$78$	5.32495	−	18.6887i	0.602931	−	2.11608i
$79$			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	$-0.353123\pi$
$83$	12.2139	−	12.2139i	1.34065	−	1.34065i	0.895417	−	0.445228i	$-0.146877\pi$
$84$	0.922931	+	1.65843i	0.100700	+	0.180950i
$85$		0			0
$86$			5.21490i			0.562337i
$87$	−4.94920	−	1.41016i	−0.530610	−	0.151185i
$88$	−1.74620	−	1.74620i	−0.186145	−	0.186145i
$89$	−1.35643			−0.143782			−0.0718908	−	0.997413i	$-0.522903\pi$
$89$	−1.35643			−0.143782			−0.0718908	+	0.997413i	$0.522903\pi$
$90$		0			0
$91$	−6.37653			−0.668442
$92$	4.12069	+	4.12069i	0.429611	+	0.429611i
$93$	9.65754	+	2.75170i	1.00144	+	0.285338i
$94$			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	$-0.782229\pi$
$101$		−	12.7033i		−	1.26402i	0.774958	−	0.632012i	$-0.217771\pi$
$102$	2.51988	−	8.84392i	0.249505	−	0.875679i
$103$	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	$-0.872873\pi$
$107$	−13.5523	−	13.5523i	−1.31015	−	1.31015i	−0.388849	−	0.921302i	$-0.627127\pi$
$108$	4.21209	−	3.83120i	0.405309	−	0.368658i
$109$		−	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	−1.00000		0.000746132i	$-0.999762\pi$
$113$	−10.6222	+	10.6222i	−0.999254	+	0.999254i	0.000746132		1.00000i	$0.499762\pi$
$114$	11.2107	−	6.23886i	1.04998	−	0.584323i
$115$		0			0
$116$			3.25572i			0.302286i
$117$	4.36583	+	18.6247i	0.403621	+	1.72186i
$118$	−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
$123$	−1.27415	+	4.47185i	−0.114887	+	0.403213i
$124$		−	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	$0.00708365\pi$
$131$			0.509374i			0.0445042i	−0.999752	+	0.0222521i	$0.992916\pi$
$132$	−2.83324	−	0.807270i	−0.246602	−	0.0702638i
$133$	−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	0.586298	−	0.810095i	$-0.300585\pi$
$137$	−2.61947	−	2.61947i	−0.223797	−	0.223797i	−0.810095	+	0.586298i	$0.800585\pi$
$138$	−15.5868	−	4.44112i	−1.32684	−	0.378053i
$139$			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
$147$	−0.474620	+	1.66575i	−0.0391460	+	0.137389i
$148$	1.34916	+	1.34916i	0.110900	+	0.110900i
$149$	4.27965			0.350602			0.175301	−	0.984515i	$-0.443910\pi$
$149$	4.27965			0.350602			0.175301	+	0.984515i	$0.443910\pi$
$150$		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
$153$	2.06601	+	8.81363i	0.167027	+	0.712539i
$154$			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
$162$	−5.05474	+	15.0069i	−0.397138	+	1.17906i
$163$	−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	$0.0230310\pi$
$167$	13.8232	+	13.8232i	1.06967	+	1.06967i	0.0722908	+	0.997384i	$0.476969\pi$
$168$	0.755101	−	2.65015i	0.0582573	−	0.204463i
$169$			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	−0.781281	−	0.624179i	$-0.785433\pi$
$173$	−2.06635	+	2.06635i	−0.157102	+	0.157102i	0.624179	+	0.781281i	$0.285433\pi$
$174$	−4.40306	−	7.91195i	−0.333795	−	0.599803i
$175$		0			0
$176$		−	7.74679i		−	0.583936i
$177$	8.22483	+	2.34348i	0.618216	+	0.176147i
$178$	−1.68759	−	1.68759i	−0.126491	−	0.126491i
$179$	11.9186			0.890841			0.445420	−	0.895322i	$-0.353054\pi$
$179$	11.9186			0.890841			0.445420	+	0.895322i	$0.353054\pi$
$180$		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
$183$	−5.52508	−	1.57425i	−0.408426	−	0.116372i
$184$		−	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	$0.0642366\pi$
$191$			5.54023i			0.400877i	−0.979706	+	0.200438i	$0.935763\pi$
$192$	−0.0615505	+	0.216021i	−0.00444202	+	0.0155900i
$193$	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	0.0900024	−	0.995942i	$-0.471313\pi$
$197$	−12.7155	−	12.7155i	−0.905939	−	0.905939i	−0.995942	+	0.0900024i	$0.971313\pi$
$198$	7.97701	−	1.86989i	0.566901	−	0.132888i
$199$		−	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
$207$	15.5334	−	3.64119i	1.07965	−	0.253080i
$208$	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
$213$	−2.72231	+	9.55439i	−0.186530	+	0.654656i
$214$		−	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
$222$	−5.10330	−	1.45407i	−0.342511	−	0.0975910i
$223$	−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	$-0.985380\pi$
$227$	−15.7424	−	15.7424i	−1.04486	−	1.04486i	−0.0459126	−	0.998945i	$-0.514620\pi$
$228$	7.68438	+	2.18949i	0.508910	+	0.145003i
$229$		−	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	−0.987273	−	0.159034i	$-0.949162\pi$
$233$	−12.6425	+	12.6425i	−0.828239	+	0.828239i	0.159034	+	0.987273i	$0.449162\pi$
$234$	−17.7401	+	28.6035i	−1.15971	+	1.86987i
$235$		0			0
$236$		−	5.41052i		−	0.352195i
$237$	1.70568	−	5.98637i	0.110796	−	0.388856i
$238$	−3.75421	−	3.75421i	−0.243350	−	0.243350i
$239$	−25.8260			−1.67054			−0.835271	−	0.549838i	$-0.814689\pi$
$239$	−25.8260			−1.67054			−0.835271	+	0.549838i	$0.814689\pi$
$240$		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
$243$	−2.83578	−	15.3284i	−0.181915	−	0.983314i
$244$			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	$0.0703455\pi$
$251$			6.94563i			0.438405i	−0.975679	+	0.219202i	$0.929655\pi$
$252$	−0.750250	−	3.20058i	−0.0472613	−	0.201618i
$253$	−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	0.404758	−	0.914424i	$-0.367356\pi$
$257$	−8.17057	−	8.17057i	−0.509666	−	0.509666i	−0.914424	+	0.404758i	$0.867356\pi$
$258$	2.47509	−	8.68674i	0.154093	−	0.540813i
$259$			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	−0.710762	−	0.703433i	$-0.751650\pi$
$263$	−0.118860	+	0.118860i	−0.00732922	+	0.00732922i	0.703433	+	0.710762i	$0.251650\pi$
$264$	2.07996	+	3.73752i	0.128012	+	0.230028i
$265$		0			0
$266$		−	7.40729i		−	0.454170i
$267$	2.25948	+	0.643790i	0.138278	+	0.0393993i
$268$	−1.87387	−	1.87387i	−0.114465	−	0.114465i
$269$	6.60330			0.402610			0.201305	−	0.979529i	$-0.435482\pi$
$269$	6.60330			0.402610			0.201305	+	0.979529i	$0.435482\pi$
$270$		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
$273$	10.6217	+	3.02643i	0.642856	+	0.183168i
$274$		−	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	$-0.985687\pi$
$281$		−	1.50698i		−	0.0898991i	0.998989	−	0.0449495i	$-0.0143127\pi$
$282$	0.0423300	−	0.148564i	0.00252071	−	0.00884685i
$283$	−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
$288$	3.83372	+	16.3547i	0.225904	+	0.963712i
$289$		−	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	−0.634850	−	0.772635i	$-0.718938\pi$
$293$	2.35851	−	2.35851i	0.137786	−	0.137786i	0.772635	+	0.634850i	$0.218938\pi$
$294$	−2.66293	+	1.48194i	−0.155305	+	0.0864285i
$295$		0			0
$296$		−	2.77022i		−	0.161016i
$297$	−5.96656	+	5.42702i	−0.346215	+	0.314907i
$298$	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
$303$	−6.02923	+	21.1606i	−0.346370	+	1.21564i
$304$			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	$-0.909294\pi$
$311$		−	9.91521i		−	0.562240i	0.959673	−	0.281120i	$-0.0907059\pi$
$312$	−16.8987	−	4.81492i	−0.956702	−	0.272591i
$313$	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	0.989027	−	0.147732i	$-0.0471972\pi$
$317$	14.9788	+	14.9788i	0.841296	+	0.841296i	−0.147732	+	0.989027i	$0.547197\pi$
$318$	17.8574	+	5.08809i	1.00140	+	0.285326i
$319$		−	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
$327$	−2.29791	+	8.06487i	−0.127075	+	0.445989i
$328$	−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
$333$	5.08582	−	1.19217i	0.278701	−	0.0653305i
$334$			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
$342$	−21.6354	+	5.07157i	−1.16991	+	0.274239i
$343$	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	0.976580	−	0.215157i	$-0.0690262\pi$
$347$	14.1837	+	14.1837i	0.761423	+	0.761423i	−0.215157	+	0.976580i	$0.569026\pi$
$348$	1.54523	−	5.42323i	0.0828330	−	0.290716i
$349$			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	$-0.474305\pi$
$353$	20.2421	−	20.2421i	1.07738	−	1.07738i	0.996744	−	0.0806368i	$-0.0256954\pi$
$354$	7.31723	+	13.1485i	0.388906	+	0.698834i
$355$		0			0
$356$		−	1.48635i		−	0.0787765i
$357$	5.02643	+	1.43217i	0.266027	+	0.0757985i
$358$	14.8285	+	14.8285i	0.783710	+	0.783710i
$359$	−18.8289			−0.993751			−0.496876	−	0.867822i	$-0.665519\pi$
$359$	−18.8289			−0.993751			−0.496876	+	0.867822i	$0.665519\pi$
$360$		0			0
$361$	1.27653			0.0671857
$362$	−21.8900	−	21.8900i	−1.15051	−	1.15051i
$363$	−14.3099	−	4.07730i	−0.751076	−	0.214003i
$364$		−	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
$372$	−3.01526	+	10.5825i	−0.156334	+	0.548679i
$373$	−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
$378$	6.15172	+	6.76331i	0.316411	+	0.347867i
$379$		−	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	−0.0121580	−	0.999926i	$-0.503870\pi$
$383$	19.3310	−	19.3310i	0.987768	−	0.987768i	0.999926	+	0.0121580i	$0.00387012\pi$
$384$	−17.2943	+	9.62440i	−0.882545	+	0.491143i
$385$		0			0
$386$			34.5939i			1.76079i
$387$	2.02929	+	8.65698i	0.103154	+	0.440059i
$388$	−12.0330	−	12.0330i	−0.610882	−	0.610882i
$389$	30.7961			1.56142			0.780712	−	0.624891i	$-0.214856\pi$
$389$	30.7961			1.56142			0.780712	+	0.624891i	$0.214856\pi$
$390$		0			0
$391$	16.0476			0.811562
$392$	−1.12498	−	1.12498i	−0.0568200	−	0.0568200i
$393$	0.241759	−	0.848491i	0.0121951	−	0.0428007i
$394$		−	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	$0.174835\pi$
$401$			20.9084i			1.04412i	−0.852910	+	0.522058i	$0.825165\pi$
$402$	7.08805	+	2.01958i	0.353520	+	0.100728i
$403$	−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
$408$	−7.99685	−	2.27853i	−0.395903	−	0.112804i
$409$		−	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
$417$	3.01563	−	10.5838i	0.147676	−	0.518293i
$418$	8.13006	+	8.13006i	0.397654	+	0.397654i
$419$	−0.525515			−0.0256731			−0.0128365	−	0.999918i	$-0.504086\pi$
$419$	−0.525515			−0.0256731			−0.0128365	+	0.999918i	$0.504086\pi$
$420$		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
$423$	0.0347056	+	0.148055i	0.00168744	+	0.00719868i
$424$			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	$-0.812993\pi$
$431$		−	23.0144i		−	1.10856i	0.832329	−	0.554282i	$-0.187007\pi$
$432$	−17.4495	−	19.1843i	−0.839542	−	0.923007i
$433$	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
$438$	−8.58315	+	30.1239i	−0.410119	+	1.43938i
$439$			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	−0.471189	−	0.882032i	$-0.656175\pi$
$443$	8.64725	−	8.64725i	0.410843	−	0.410843i	0.882032	+	0.471189i	$0.156175\pi$
$444$	−1.60703	−	2.88771i	−0.0762664	−	0.137045i
$445$		0			0
$446$		−	21.9075i		−	1.03735i
$447$	−7.12884	−	2.03121i	−0.337183	−	0.0960727i
$448$	0.0917003	+	0.0917003i	0.00433243	+	0.00433243i
$449$	−20.7599			−0.979723			−0.489861	−	0.871800i	$-0.662953\pi$
$449$	−20.7599			−0.979723			−0.489861	+	0.871800i	$0.662953\pi$
$450$		0			0
$451$	−4.16702			−0.196217
$452$	−11.6396	−	11.6396i	−0.547481	−	0.547481i
$453$	8.68243	+	2.47387i	0.407936	+	0.116232i
$454$		−	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	$-0.967594\pi$
$461$		−	4.36421i		−	0.203262i	0.994822	−	0.101631i	$-0.0324061\pi$
$462$	1.29622	−	4.54931i	0.0603058	−	0.211653i
$463$	−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	0.952055	−	0.305927i	$-0.0989663\pi$
$467$	13.9629	+	13.9629i	0.646128	+	0.646128i	−0.305927	+	0.952055i	$0.598966\pi$
$468$	−20.4086	+	4.78399i	−0.943388	+	0.221140i
$469$		−	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
$477$	−17.7963	+	4.17163i	−0.814836	+	0.191006i
$478$	−32.1312	−	32.1312i	−1.46965	−	1.46965i
$479$	16.0067			0.731367			0.365683	−	0.930739i	$-0.380835\pi$
$479$	16.0067			0.731367			0.365683	+	0.930739i	$0.380835\pi$
$480$		0			0
$481$	11.1030			0.506252
$482$	−13.0880	−	13.0880i	−0.596140	−	0.596140i
$483$	2.52410	−	8.85874i	0.114851	−	0.403087i
$484$			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	$0.235571\pi$
$491$			29.8846i			1.34867i	−0.738423	+	0.674337i	$0.764429\pi$
$492$	−4.90016	−	1.39619i	−0.220916	−	0.0629453i
$493$	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
$498$	−50.6249	−	14.4244i	−2.26855	−	0.646374i
$499$			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	$0.508305\pi$
$503$	−23.0051	+	23.0051i	−1.02575	+	1.02575i	−0.999660	+	0.0260875i	$0.991695\pi$
$504$	−2.51562	+	4.05611i	−0.112055	+	0.180673i
$505$		0			0
$506$		−	14.5243i		−	0.645685i
$507$	13.1280	−	46.0749i	0.583036	−	2.04626i
$508$	−11.1326	−	11.1326i	−0.493929	−	0.493929i
$509$	−25.8128			−1.14413			−0.572066	−	0.820208i	$-0.693858\pi$
$509$	−25.8128			−1.14413			−0.572066	+	0.820208i	$0.693858\pi$
$510$		0			0
$511$	10.2782			0.454679
$512$	8.53124	+	8.53124i	0.377031	+	0.377031i
$513$	16.1826	−	14.7193i	0.714480	−	0.649871i
$514$		−	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	$-0.580948\pi$
$521$		−	44.1826i		−	1.93568i	0.251572	−	0.967838i	$-0.419052\pi$
$522$	3.57925	+	15.2691i	0.156659	+	0.668312i
$523$	−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
$528$	−3.67678	+	12.9042i	−0.160011	+	0.561585i
$529$		−	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
$537$	−19.8535	−	5.65682i	−0.856743	−	0.244110i
$538$	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
$543$	29.3080	+	8.35068i	1.25773	+	0.358362i
$544$			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
$552$	−4.01574	+	14.0939i	−0.170921	+	0.599876i
$553$	−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	0.170201	−	0.985409i	$-0.445558\pi$
$557$	−19.2396	−	19.2396i	−0.815208	−	0.815208i	−0.985409	+	0.170201i	$0.945558\pi$
$558$	−6.98431	−	29.7952i	−0.295669	−	1.26133i
$559$			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	−0.662906	−	0.748702i	$-0.730677\pi$
$563$	2.03574	−	2.03574i	0.0857962	−	0.0857962i	0.748702	+	0.662906i	$0.230677\pi$
$564$	0.0840650	−	0.0467828i	0.00353977	−	0.00196991i
$565$		0			0
$566$		−	21.1284i		−	0.888092i
$567$	−8.52917	−	2.87286i	−0.358191	−	0.120649i
$568$	−6.45262	−	6.45262i	−0.270746	−	0.270746i
$569$	−36.6125			−1.53487			−0.767437	−	0.641124i	$-0.778468\pi$
$569$	−36.6125			−1.53487			−0.767437	+	0.641124i	$0.778468\pi$
$570$		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
$573$	2.62950	−	9.22865i	0.109849	−	0.385533i
$574$			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
$582$	45.5156	+	12.9687i	1.88668	+	0.537569i
$583$	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	0.797568	−	0.603229i	$-0.206120\pi$
$587$	4.70846	+	4.70846i	0.194339	+	0.194339i	−0.603229	+	0.797568i	$0.706120\pi$
$588$	−1.82530	−	0.520079i	−0.0752741	−	0.0214477i
$589$		−	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	−0.947535	−	0.319651i	$-0.896434\pi$
$593$	−15.2900	+	15.2900i	−0.627884	+	0.627884i	0.319651	+	0.947535i	$0.396434\pi$
$594$	−14.1752	−	0.671263i	−0.581617	−	0.0275422i
$595$		0			0
$596$			4.68955i			0.192092i
$597$	−2.90224	+	10.1859i	−0.118781	+	0.416880i
$598$	42.1906	+	42.1906i	1.72530	+	1.72530i
$599$	9.38844			0.383601			0.191801	−	0.981434i	$-0.438567\pi$
$599$	9.38844			0.383601			0.191801	+	0.981434i	$0.438567\pi$
$600$		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
$603$	−7.06377	+	1.65582i	−0.287659	+	0.0674303i
$604$		−	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
$612$	−9.65780	+	2.26389i	−0.390393	+	0.0915123i
$613$	−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	0.662440	−	0.749115i	$-0.269521\pi$
$617$	−2.15297	−	2.15297i	−0.0866754	−	0.0866754i	−0.749115	+	0.662440i	$0.769521\pi$
$618$	1.73367	−	6.08459i	0.0697384	−	0.244758i
$619$		−	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
$627$	−10.8852	−	3.10148i	−0.434711	−	0.123861i
$628$	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
$633$	−20.8053	−	5.92801i	−0.826937	−	0.235617i
$634$			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	$0.100566\pi$
$641$			15.7329i			0.621414i	−0.950506	+	0.310707i	$0.899434\pi$
$642$	−16.0051	+	56.1725i	−0.631672	+	2.21695i
$643$	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	0.462184	−	0.886784i	$-0.347066\pi$
$647$	−10.8002	−	10.8002i	−0.424600	−	0.424600i	−0.886784	+	0.462184i	$0.847066\pi$
$648$	13.5696	+	4.57060i	0.533063	+	0.179550i
$649$			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	−0.844326	−	0.535830i	$-0.819999\pi$
$653$	−7.88328	+	7.88328i	−0.308497	+	0.308497i	0.535830	+	0.844326i	$0.319999\pi$
$654$	−12.8928	+	7.17493i	−0.504147	+	0.280562i
$655$		0			0
$656$		−	13.3983i		−	0.523115i
$657$	−7.03717	−	30.0207i	−0.274546	−	1.17122i
$658$	−0.0630648	−	0.0630648i	−0.00245852	−	0.00245852i
$659$	6.73141			0.262219			0.131109	−	0.991368i	$-0.458146\pi$
$659$	6.73141			0.262219			0.131109	+	0.991368i	$0.458146\pi$
$660$		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
$663$	9.13228	−	32.0512i	0.354668	−	1.24476i
$664$		−	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
$672$	9.32715	+	2.65756i	0.359802	+	0.102518i
$673$	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	0.817911	−	0.575345i	$-0.195132\pi$
$677$	6.31136	+	6.31136i	0.242565	+	0.242565i	−0.575345	+	0.817911i	$0.695132\pi$
$678$	44.0277	+	12.5447i	1.69087	+	0.481777i
$679$		−	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	−0.986206	−	0.165520i	$-0.947070\pi$
$683$	−21.4480	+	21.4480i	−0.820686	+	0.820686i	0.165520	+	0.986206i	$0.447070\pi$
$684$	−11.7611	−	7.29431i	−0.449697	−	0.278905i
$685$		0			0
$686$			1.75948i			0.0671774i
$687$	−3.92722	+	13.7832i	−0.149833	+	0.525862i
$688$	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
$693$	1.06275	+	4.53372i	0.0403706	+	0.172222i
$694$			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	$-0.939335\pi$
$701$		−	10.0310i		−	0.378867i	0.981894	−	0.189434i	$-0.0606652\pi$
$702$	43.1264	−	39.2266i	1.62770	−	1.48051i
$703$	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
$708$	−2.56794	+	9.01260i	−0.0965092	+	0.338714i
$709$			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
$717$	43.0197	+	12.2575i	1.60660	+	0.457765i
$718$	−23.4258	−	23.4258i	−0.874244	−	0.874244i
$719$	−10.6931			−0.398786			−0.199393	−	0.979920i	$-0.563897\pi$
$719$	−10.6931			−0.398786			−0.199393	+	0.979920i	$0.563897\pi$
$720$		0			0
$721$	−2.07604			−0.0773157
$722$	1.58818	+	1.58818i	0.0591060	+	0.0591060i
$723$	17.5232	+	4.99284i	0.651693	+	0.185686i
$724$		−	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
$732$	1.72503	−	6.05428i	0.0637590	−	0.223773i
$733$	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
$738$	13.7964	−	3.23403i	0.507854	−	0.119046i
$739$			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	−0.783463	−	0.621439i	$-0.786549\pi$
$743$	−4.41646	+	4.41646i	−0.162024	+	0.162024i	0.621439	+	0.783463i	$0.286549\pi$
$744$	13.9601	−	7.76892i	0.511803	−	0.284822i
$745$		0			0
$746$		−	18.4118i		−	0.674105i
$747$	50.4514	−	11.8263i	1.84592	−	0.432703i
$748$	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
$753$	3.29654	−	11.5697i	0.120132	−	0.421624i
$754$			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	$-0.614922\pi$
$761$		−	51.6155i		−	1.87106i	0.353246	−	0.935531i	$-0.385078\pi$
$762$	42.1099	+	11.9983i	1.52548	+	0.434652i
$763$	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
$768$	−33.0586	−	9.41932i	−1.19290	−	0.339891i
$769$			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	−0.934876	−	0.354976i	$-0.884489\pi$
$773$	−16.1229	+	16.1229i	−0.579900	+	0.579900i	0.354976	+	0.934876i	$0.384489\pi$
$774$	−8.24579	+	13.2952i	−0.296389	+	0.477887i
$775$		0			0
$776$			24.7072i			0.886937i
$777$	0.826421	−	2.90046i	0.0296477	−	0.104053i
$778$	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
$783$	−10.3881	−	11.4208i	−0.371240	−	0.408148i
$784$		−	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
$792$	−1.69080	−	7.21297i	−0.0600798	−	0.256302i
$793$	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	0.118231	−	0.992986i	$-0.462278\pi$
$797$	−24.6954	−	24.6954i	−0.874755	−	0.874755i	−0.992986	+	0.118231i	$0.962278\pi$
$798$	−3.51565	+	12.3387i	−0.124453	+	0.436786i
$799$			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
$807$	−10.9995	−	3.13406i	−0.387200	−	0.110324i
$808$	−14.2909	−	14.2909i	−0.502753	−	0.502753i
$809$	−20.4064			−0.717449			−0.358725	−	0.933443i	$-0.616788\pi$
$809$	−20.4064			−0.717449			−0.358725	+	0.933443i	$0.616788\pi$
$810$		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
$813$	39.6935	+	11.3098i	1.39211	+	0.396652i
$814$		−	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	$-0.570530\pi$
$821$		−	55.9052i		−	1.95110i	0.219767	−	0.975552i	$-0.429470\pi$
$822$	−3.09357	+	10.8574i	−0.107901	+	0.378695i
$823$	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	0.995688	−	0.0927663i	$-0.0295710\pi$
$827$	25.9659	+	25.9659i	0.902922	+	0.902922i	−0.0927663	+	0.995688i	$0.529571\pi$
$828$	3.98995	+	17.0212i	0.138660	+	0.591528i
$829$			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
$837$	20.2706	+	22.2859i	0.700656	+	0.770313i
$838$	−0.653815	−	0.653815i	−0.0225857	−	0.0225857i
$839$	−27.2730			−0.941569			−0.470785	−	0.882248i	$-0.656029\pi$
$839$	−27.2730			−0.941569			−0.470785	+	0.882248i	$0.656029\pi$
$840$		0			0
$841$	−20.1723			−0.695596
$842$	−19.3211	−	19.3211i	−0.665851	−	0.665851i
$843$	−0.715244	+	2.51026i	−0.0246343	+	0.0864581i
$844$			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
$852$	−10.4695	−	2.98306i	−0.358679	−	0.102198i
$853$	−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	0.966970	−	0.254892i	$-0.0820399\pi$
$857$	20.8458	+	20.8458i	0.712077	+	0.712077i	−0.254892	+	0.966970i	$0.582040\pi$
$858$	−29.0088	−	8.26541i	−0.990344	−	0.282177i
$859$		−	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	$-0.465561\pi$
$863$	32.3773	−	32.3773i	1.10213	−	1.10213i	0.994153	−	0.107982i	$-0.0344389\pi$
$864$	1.37625	−	29.0625i	0.0468208	−	0.988727i
$865$		0			0
$866$			38.3198i			1.30216i
$867$	−3.74695	+	13.1505i	−0.127253	+	0.446615i
$868$	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
$873$	−45.3597	+	10.6328i	−1.53519	+	0.359865i
$874$			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	$0.179266\pi$
$881$			31.6927i			1.06775i	−0.845562	+	0.533877i	$0.820734\pi$
$882$	5.13914	−	1.20467i	0.173044	−	0.0405633i
$883$	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	0.818526	−	0.574469i	$-0.194792\pi$
$887$	7.26863	+	7.26863i	0.244057	+	0.244057i	−0.574469	+	0.818526i	$0.694792\pi$
$888$	−1.31480	+	4.61451i	−0.0441219	+	0.154853i
$889$		−	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
$897$	−56.4880	−	16.0950i	−1.88608	−	0.537397i
$898$	−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
$903$	4.93710	+	1.40672i	0.164296	+	0.0468126i
$904$			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	$0.192011\pi$
$911$			34.2452i			1.13459i	−0.823514	+	0.567296i	$0.807989\pi$
$912$	9.97224	−	34.9992i	0.330214	−	1.15894i
$913$	−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
$918$	20.4084	−	18.5629i	0.673576	−	0.612667i
$919$			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
$927$	1.42141	+	6.06375i	0.0466851	+	0.199160i
$928$	11.7638	+	11.7638i	0.386165	+	0.386165i
$929$	9.88243			0.324232			0.162116	−	0.986772i	$-0.448168\pi$
$929$	9.88243			0.324232			0.162116	+	0.986772i	$0.448168\pi$
$930$		0			0
$931$	4.20993			0.137975
$932$	−13.8534	−	13.8534i	−0.453784	−	0.453784i
$933$	−4.70596	+	16.5163i	−0.154066	+	0.540720i
$934$			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	$0.371435\pi$
$941$			56.4149i			1.83907i	−0.393006	+	0.919536i	$0.628565\pi$
$942$	−18.0716	−	5.14910i	−0.588804	−	0.167767i
$943$	−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	0.560222	−	0.828342i	$-0.310716\pi$
$947$	−8.25095	−	8.25095i	−0.268120	−	0.268120i	−0.828342	+	0.560222i	$0.810716\pi$
$948$	6.55974	+	1.86905i	0.213051	+	0.0607041i
$949$		−	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	−0.938533	−	0.345189i	$-0.887815\pi$
$953$	−18.3169	+	18.3169i	−0.593344	+	0.593344i	0.345189	+	0.938533i	$0.387815\pi$
$954$	−27.3312	−	16.9510i	−0.884881	−	0.548809i
$955$		0			0
$956$		−	28.2996i		−	0.915274i
$957$	−2.18887	+	7.68217i	−0.0707560	+	0.248329i
$958$	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
$963$	−13.1223	−	55.9801i	−0.422861	−	1.80393i
$964$		−	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	$0.0717079\pi$
$971$			13.9212i			0.446753i	−0.974732	+	0.223377i	$0.928292\pi$
$972$	16.7965	−	3.10739i	0.538748	−	0.0996696i
$973$	−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	0.992499	−	0.122251i	$-0.0390114\pi$
$977$	27.2013	+	27.2013i	0.870248	+	0.870248i	−0.122251	+	0.992499i	$0.539011\pi$
$978$	−6.31049	+	22.1477i	−0.201787	+	0.708204i
$979$			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	$0.562302\pi$
$983$	−36.8517	+	36.8517i	−1.17539	+	1.17539i	−0.980907	+	0.194479i	$0.937698\pi$
$984$	3.59734	+	6.46413i	0.114679	+	0.206069i
$985$		0			0
$986$			15.7746i			0.502365i
$987$	0.0844361	+	0.0240582i	0.00268763	+	0.000765781i
$988$	−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
$993$	5.16795	+	1.47249i	0.164000	+	0.0467281i
$994$			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.218.10		24
3.2	odd	2	inner	525.2.j.b.218.3		24
5.2	odd	4	inner	525.2.j.b.407.3		24
5.3	odd	4		105.2.j.a.92.10	yes	24
5.4	even	2		105.2.j.a.8.3	✓	24
15.2	even	4	inner	525.2.j.b.407.10		24
15.8	even	4		105.2.j.a.92.3	yes	24
15.14	odd	2		105.2.j.a.8.10	yes	24
35.3	even	12		735.2.y.g.422.10		48
35.4	even	6		735.2.y.j.128.10		48
35.9	even	6		735.2.y.j.263.3		48
35.13	even	4		735.2.j.h.197.10		24
35.18	odd	12		735.2.y.j.422.10		48
35.19	odd	6		735.2.y.g.263.3		48
35.23	odd	12		735.2.y.j.557.3		48
35.24	odd	6		735.2.y.g.128.10		48
35.33	even	12		735.2.y.g.557.3		48
35.34	odd	2		735.2.j.h.638.3		24
105.23	even	12		735.2.y.j.557.10		48
105.38	odd	12		735.2.y.g.422.3		48
105.44	odd	6		735.2.y.j.263.10		48
105.53	even	12		735.2.y.j.422.3		48
105.59	even	6		735.2.y.g.128.3		48
105.68	odd	12		735.2.y.g.557.10		48
105.74	odd	6		735.2.y.j.128.3		48
105.83	odd	4		735.2.j.h.197.3		24
105.89	even	6		735.2.y.g.263.10		48
105.104	even	2		735.2.j.h.638.10		24

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

\(f(q)\)	\(=\)	\(q+(1.24414 + 1.24414i) q^{2} +(-1.66575 - 0.474620i) q^{3} +1.09578i q^{4} +(-1.48194 - 2.66293i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.12498 - 1.12498i) q^{8} +(2.54947 + 1.58120i) q^{9} +O(q^{10})\)	\(q+(1.24414 + 1.24414i) q^{2} +(-1.66575 - 0.474620i) 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} +(0.520079 - 1.82530i) q^{12} +(4.50889 + 4.50889i) q^{13} -1.75948 q^{14} +4.99083 q^{16} +(2.13370 + 2.13370i) q^{17} +(1.20467 + 5.13914i) 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} +(-3.49632 - 3.84392i) q^{27} +(-0.774834 - 0.774834i) q^{28} +2.97115 q^{29} -5.79770 q^{31} +(3.95934 + 3.95934i) q^{32} +(-0.736708 + 2.58559i) 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} +(2.93087 + 0.835085i) q^{42} +(2.09578 + 2.09578i) q^{43} +1.70088 q^{44} +9.35721 q^{46} +(0.0358428 + 0.0358428i) q^{47} +(-8.31349 - 2.36874i) 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} +(1.99811 - 7.01270i) q^{57} +(3.69653 + 3.69653i) q^{58} -4.93760 q^{59} +3.31687 q^{61} +(-7.21316 - 7.21316i) q^{62} +(-2.92083 + 0.684672i) 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} +(4.64692 - 1.08929i) q^{72} +(-7.26776 - 7.26776i) q^{73} +3.06366 q^{74} -4.61315 q^{76} +(1.09758 + 1.09758i) q^{77} +(5.32495 - 18.6887i) 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} +(-4.94920 - 1.41016i) q^{87} +(-1.74620 - 1.74620i) q^{88} -1.35643 q^{89} -6.37653 q^{91} +(4.12069 + 4.12069i) q^{92} +(9.65754 + 2.75170i) 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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