LMFDB - Embedded newform 504.2.cj.c.37.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(37,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 $ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.4
Root			$-0.0950561 + 1.41102i$ of defining polynomial
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.c.109.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.453773 + 1.33944i) q^{2} +(-1.58818 + 1.21560i) q^{4} +(-0.476087 - 0.274869i) q^{5} +(-2.60755 - 0.447998i) q^{7} +(-2.34889 - 1.57566i) q^{8} +(0.152134 - 0.762416i) q^{10} +(-2.07045 + 1.19538i) q^{11} +3.96641i q^{13} +(-0.583170 - 3.69593i) q^{14} +(1.04463 - 3.86119i) q^{16} +(-2.10755 - 3.65038i) q^{17} +(-5.75174 - 3.32077i) q^{19} +(1.09024 - 0.142191i) q^{20} +(-2.54065 - 2.23081i) q^{22} +(-1.17445 + 2.03420i) q^{23} +(-2.34889 - 4.06840i) q^{25} +(-5.31275 + 1.79985i) q^{26} +(4.68584 - 2.45823i) q^{28} +8.21720i q^{29} +(-0.433099 - 0.750150i) q^{31} +(5.64584 - 0.352893i) q^{32} +(3.93310 - 4.47937i) q^{34} +(1.11828 + 0.930019i) q^{35} +(0.229805 + 0.132678i) q^{37} +(1.83797 - 9.21097i) q^{38} +(0.685178 + 1.39579i) q^{40} +6.24970 q^{41} +5.35027i q^{43} +(1.83515 - 4.41531i) q^{44} +(-3.25762 - 0.650030i) q^{46} +(1.29930 - 2.25045i) q^{47} +(6.59859 + 2.33635i) q^{49} +(4.38350 - 4.99233i) q^{50} +(-4.82157 - 6.29937i) q^{52} +(-9.36933 + 5.40939i) q^{53} +1.31429 q^{55} +(5.41896 + 5.16090i) q^{56} +(-11.0064 + 3.72875i) q^{58} +(-3.26891 + 1.88730i) q^{59} +(6.18061 + 3.56837i) q^{61} +(0.808249 - 0.920507i) q^{62} +(3.03461 + 7.40210i) q^{64} +(1.09024 - 1.88835i) q^{65} +(-2.31673 + 1.33757i) q^{67} +(7.78456 + 3.23552i) q^{68} +(-0.738257 + 1.91988i) q^{70} -8.76700 q^{71} +(-2.33159 - 4.03843i) q^{73} +(-0.0734343 + 0.368015i) q^{74} +(13.1715 - 1.71785i) q^{76} +(5.93432 - 2.18944i) q^{77} +(-0.308249 + 0.533903i) q^{79} +(-1.55865 + 1.55112i) q^{80} +(2.83595 + 8.37108i) q^{82} -1.09948i q^{83} +2.31720i q^{85} +(-7.16634 + 2.42781i) q^{86} +(6.74677 + 0.454511i) q^{88} +(-3.19779 + 5.53873i) q^{89} +(1.77694 - 10.3426i) q^{91} +(-0.607546 - 4.65834i) q^{92} +(3.60392 + 0.719132i) q^{94} +(1.82555 + 3.16195i) q^{95} +12.9475 q^{97} +(-0.135129 + 9.89857i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8} - 8 q^{10} + 16 q^{14} + 8 q^{16} + 2 q^{17} - 8 q^{20} + 12 q^{22} - 2 q^{23} - 4 q^{25} + 2 q^{26} + 26 q^{28} + 10 q^{31} + 12 q^{32} + 32 q^{34} - 18 q^{38} + 10 q^{40}+ \cdots - 52 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8 - 8 * q^10 + 16 * q^14 + 8 * q^16 + 2 * q^17 - 8 * q^20 + 12 * q^22 - 2 * q^23 - 4 * q^25 + 2 * q^26 + 26 * q^28 + 10 * q^31 + 12 * q^32 + 32 * q^34 - 18 * q^38 + 10 * q^40 + 8 * q^41 + 30 * q^44 - 4 * q^46 - 30 * q^47 - 12 * q^49 + 16 * q^50 - 32 * q^52 + 4 * q^55 + 40 * q^56 - 22 * q^58 + 28 * q^62 + 24 * q^64 - 8 * q^65 - 4 * q^68 - 48 * q^70 - 32 * q^71 - 10 * q^73 - 18 * q^74 + 52 * q^76 - 22 * q^79 - 36 * q^80 - 26 * q^82 - 40 * q^86 - 14 * q^88 + 10 * q^89 + 20 * q^92 + 42 * q^94 + 34 * q^95 + 40 * q^97 - 52 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	0.453773	+	1.33944i	0.320866	+	0.947124i
$2$	0.453773	+	1.33944i	0.320866	+	0.947124i
$3$		0			0
$3$		0			0
$4$	−1.58818	+	1.21560i	−0.794090	+	0.607801i
$5$	−0.476087	−	0.274869i	−0.212913	−	0.122925i	0.389752	−	0.920920i	$-0.372561\pi$
$5$	−0.476087	−	0.274869i	−0.212913	−	0.122925i	−0.602664	+	0.797995i	$0.705894\pi$
$6$		0			0
$7$	−2.60755	−	0.447998i	−0.985560	−	0.169327i
$7$	−2.60755	−	0.447998i	−0.985560	−	0.169327i
$8$	−2.34889	−	1.57566i	−0.830460	−	0.557079i
$9$		0			0
$10$	0.152134	−	0.762416i	0.0481089	−	0.241097i
$11$	−2.07045	+	1.19538i	−0.624265	+	0.360419i	−0.778527	−	0.627611i	$-0.784033\pi$
$11$	−2.07045	+	1.19538i	−0.624265	+	0.360419i	0.154263	+	0.988030i	$0.450700\pi$
$12$		0			0
$13$			3.96641i			1.10008i	0.835137	+	0.550042i	$0.185388\pi$
$13$			3.96641i			1.10008i	−0.835137	+	0.550042i	$0.814612\pi$
$14$	−0.583170	−	3.69593i	−0.155859	−	0.987779i
$15$		0			0
$16$	1.04463	−	3.86119i	0.261157	−	0.965296i
$17$	−2.10755	−	3.65038i	−0.511155	−	0.885347i	−0.999916	−	0.0129290i	$-0.995884\pi$
$17$	−2.10755	−	3.65038i	−0.511155	−	0.885347i	0.488761	−	0.872418i	$-0.337449\pi$
$18$		0			0
$19$	−5.75174	−	3.32077i	−1.31954	−	0.761837i	−0.335886	−	0.941903i	$-0.609036\pi$
$19$	−5.75174	−	3.32077i	−1.31954	−	0.761837i	−0.983655	+	0.180066i	$0.942369\pi$
$20$	1.09024	−	0.142191i	0.243786	−	0.0317948i
$21$		0			0
$22$	−2.54065	−	2.23081i	−0.541667	−	0.475610i
$23$	−1.17445	+	2.03420i	−0.244889	+	0.424160i	−0.962100	−	0.272695i	$-0.912085\pi$
$23$	−1.17445	+	2.03420i	−0.244889	+	0.424160i	0.717211	+	0.696856i	$0.245418\pi$
$24$		0			0
$25$	−2.34889	−	4.06840i	−0.469779	−	0.813681i
$26$	−5.31275	+	1.79985i	−1.04192	+	0.352980i
$27$		0			0
$28$	4.68584	−	2.45823i	0.885540	−	0.464563i
$29$			8.21720i			1.52590i	0.646460	+	0.762948i	$0.276249\pi$
$29$			8.21720i			1.52590i	−0.646460	+	0.762948i	$0.723751\pi$
$30$		0			0
$31$	−0.433099	−	0.750150i	−0.0777869	−	0.134731i	0.824508	−	0.565850i	$-0.191452\pi$
$31$	−0.433099	−	0.750150i	−0.0777869	−	0.134731i	−0.902295	+	0.431120i	$0.858119\pi$
$32$	5.64584	−	0.352893i	0.998052	−	0.0623832i
$33$		0			0
$34$	3.93310	−	4.47937i	0.674521	−	0.768205i
$35$	1.11828	+	0.930019i	0.189023	+	0.157202i
$36$		0			0
$37$	0.229805	+	0.132678i	0.0377797	+	0.0218121i	0.518771	−	0.854913i	$-0.326390\pi$
$37$	0.229805	+	0.132678i	0.0377797	+	0.0218121i	−0.480991	+	0.876725i	$0.659723\pi$
$38$	1.83797	−	9.21097i	0.298158	−	1.49422i
$39$		0			0
$40$	0.685178	+	1.39579i	0.108336	+	0.220693i
$41$	6.24970			0.976039			0.488020	−	0.872833i	$-0.337719\pi$
$41$	6.24970			0.976039			0.488020	+	0.872833i	$0.337719\pi$
$42$		0			0
$43$			5.35027i			0.815908i	0.913003	+	0.407954i	$0.133758\pi$
$43$			5.35027i			0.815908i	−0.913003	+	0.407954i	$0.866242\pi$
$44$	1.83515	−	4.41531i	0.276659	−	0.665634i
$45$		0			0
$46$	−3.25762	−	0.650030i	−0.480309	−	0.0958417i
$47$	1.29930	−	2.25045i	0.189522	−	0.328262i	−0.755569	−	0.655069i	$-0.772639\pi$
$47$	1.29930	−	2.25045i	0.189522	−	0.328262i	0.945091	+	0.326807i	$0.105973\pi$
$48$		0			0
$49$	6.59859	+	2.33635i	0.942656	+	0.333765i
$50$	4.38350	−	4.99233i	0.619921	−	0.706022i
$51$		0			0
$52$	−4.82157	−	6.29937i	−0.668632	−	0.873565i
$53$	−9.36933	+	5.40939i	−1.28698	+	0.743037i	−0.978114	−	0.208070i	$-0.933282\pi$
$53$	−9.36933	+	5.40939i	−1.28698	+	0.743037i	−0.308863	+	0.951107i	$0.599948\pi$
$54$		0			0
$55$	1.31429			0.177218
$56$	5.41896	+	5.16090i	0.724139	+	0.689654i
$57$		0			0
$58$	−11.0064	+	3.72875i	−1.44521	+	0.489608i
$59$	−3.26891	+	1.88730i	−0.425575	+	0.245706i	−0.697460	−	0.716624i	$-0.745686\pi$
$59$	−3.26891	+	1.88730i	−0.425575	+	0.245706i	0.271884	+	0.962330i	$0.412353\pi$
$60$		0			0
$61$	6.18061	+	3.56837i	0.791345	+	0.456884i	0.840436	−	0.541911i	$-0.182299\pi$
$61$	6.18061	+	3.56837i	0.791345	+	0.456884i	−0.0490905	+	0.998794i	$0.515632\pi$
$62$	0.808249	−	0.920507i	0.102648	−	0.116904i
$63$		0			0
$64$	3.03461	+	7.40210i	0.379326	+	0.925263i
$65$	1.09024	−	1.88835i	0.135228	−	0.234222i
$66$		0			0
$67$	−2.31673	+	1.33757i	−0.283034	+	0.163410i	−0.634796	−	0.772680i	$-0.718916\pi$
$67$	−2.31673	+	1.33757i	−0.283034	+	0.163410i	0.351762	+	0.936089i	$0.385583\pi$
$68$	7.78456	+	3.23552i	0.944017	+	0.392364i
$69$		0			0
$70$	−0.738257	+	1.91988i	−0.0882386	+	0.229470i
$71$	−8.76700			−1.04045			−0.520226	−	0.854029i	$-0.674152\pi$
$71$	−8.76700			−1.04045			−0.520226	+	0.854029i	$0.674152\pi$
$72$		0			0
$73$	−2.33159	−	4.03843i	−0.272892	−	0.472663i	0.696709	−	0.717354i	$-0.254647\pi$
$73$	−2.33159	−	4.03843i	−0.272892	−	0.472663i	−0.969601	+	0.244691i	$0.921313\pi$
$74$	−0.0734343	+	0.368015i	−0.00853657	+	0.0427809i
$75$		0			0
$76$	13.1715	−	1.71785i	1.51088	−	0.197051i
$77$	5.93432	−	2.18944i	0.676279	−	0.249510i
$78$		0			0
$79$	−0.308249	+	0.533903i	−0.0346807	+	0.0600687i	−0.882845	−	0.469665i	$-0.844375\pi$
$79$	−0.308249	+	0.533903i	−0.0346807	+	0.0600687i	0.848164	+	0.529734i	$0.177708\pi$
$80$	−1.55865	+	1.55112i	−0.174263	+	0.173421i
$81$		0			0
$82$	2.83595	+	8.37108i	0.313178	+	0.924431i
$83$		−	1.09948i		−	0.120683i	−0.998178	−	0.0603416i	$-0.980781\pi$
$83$		−	1.09948i		−	0.120683i	0.998178	−	0.0603416i	$-0.0192190\pi$
$84$		0			0
$85$			2.31720i			0.251335i
$86$	−7.16634	+	2.42781i	−0.772766	+	0.261797i
$87$		0			0
$88$	6.74677	+	0.454511i	0.719208	+	0.0484510i
$89$	−3.19779	+	5.53873i	−0.338965	+	0.587104i	−0.984238	−	0.176847i	$-0.943410\pi$
$89$	−3.19779	+	5.53873i	−0.338965	+	0.587104i	0.645273	+	0.763952i	$0.276743\pi$
$90$		0			0
$91$	1.77694	−	10.3426i	0.186274	−	1.08420i
$92$	−0.607546	−	4.65834i	−0.0633411	−	0.485665i
$93$		0			0
$94$	3.60392	+	0.719132i	0.371716	+	0.0741728i
$95$	1.82555	+	3.16195i	0.187298	+	0.324409i
$96$		0			0
$97$	12.9475			1.31462			0.657309	−	0.753621i	$-0.271695\pi$
$97$	12.9475			1.31462			0.657309	+	0.753621i	$0.271695\pi$
$98$	−0.135129	+	9.89857i	−0.0136501	+	0.999907i
$99$		0			0
$100$	8.67602	+	3.60604i	0.867602	+	0.360604i
$101$	13.7565	−	7.94233i	1.36882	−	0.790291i	0.378047	−	0.925787i	$-0.376596\pi$
$101$	13.7565	−	7.94233i	1.36882	−	0.790291i	0.990778	+	0.135495i	$0.0432625\pi$
$102$		0			0
$103$	−9.38954	+	16.2632i	−0.925179	+	1.60246i	−0.133906	+	0.990994i	$0.542752\pi$
$103$	−9.38954	+	16.2632i	−0.925179	+	1.60246i	−0.791273	+	0.611463i	$0.790581\pi$
$104$	6.24970	−	9.31667i	0.612834	−	0.913575i
$105$		0			0
$106$	−11.4971	−	10.0950i	−1.11670	−	0.980512i
$107$	0.293506	+	0.169456i	0.0283743	+	0.0163819i	0.514120	−	0.857718i	$-0.328119\pi$
$107$	0.293506	+	0.169456i	0.0283743	+	0.0163819i	−0.485746	+	0.874100i	$0.661452\pi$
$108$		0			0
$109$	−6.75910	+	3.90237i	−0.647404	+	0.373779i	−0.787461	−	0.616365i	$-0.788605\pi$
$109$	−6.75910	+	3.90237i	−0.647404	+	0.373779i	0.140057	+	0.990143i	$0.455271\pi$
$110$	0.596388	+	1.76040i	0.0568634	+	0.167848i
$111$		0			0
$112$	−4.45372	+	9.60023i	−0.420837	+	0.907136i
$113$	−2.51730			−0.236808			−0.118404	−	0.992966i	$-0.537778\pi$
$113$	−2.51730			−0.236808			−0.118404	+	0.992966i	$0.537778\pi$
$114$		0			0
$115$	1.11828	−	0.645638i	0.104280	−	0.0602060i
$116$	−9.98884	−	13.0504i	−0.927440	−	1.21170i
$117$		0			0
$118$	−4.01127	−	3.52208i	−0.369267	−	0.324234i
$119$	3.86016	+	10.4627i	0.353860	+	0.959115i
$120$		0			0
$121$	−2.64215	+	4.57635i	−0.240196	+	0.416031i
$122$	−1.97502	+	9.89776i	−0.178809	+	0.896101i
$123$		0			0
$124$	1.59972	+	0.664896i	0.143659	+	0.0597095i
$125$			5.33124i			0.476841i
$126$		0			0
$127$	−5.30221			−0.470495			−0.235248	−	0.971935i	$-0.575590\pi$
$127$	−5.30221			−0.470495			−0.235248	+	0.971935i	$0.575590\pi$
$128$	−8.53762	+	7.42354i	−0.754626	+	0.656155i
$129$		0			0
$130$	3.02405	+	0.603425i	0.265227	+	0.0529238i
$131$	−8.69419	−	5.01959i	−0.759615	−	0.438564i	0.0695425	−	0.997579i	$-0.477846\pi$
$131$	−8.69419	−	5.01959i	−0.759615	−	0.438564i	−0.829157	+	0.559015i	$0.811179\pi$
$132$		0			0
$133$	13.5102	+	11.2358i	1.17149	+	0.974270i
$134$	−2.84286	−	2.49616i	−0.245585	−	0.215636i
$135$		0			0
$136$	−0.801340	+	11.8951i	−0.0687144	+	1.02000i
$137$	1.62485	+	2.81432i	0.138820	+	0.240444i	0.927050	−	0.374937i	$-0.122336\pi$
$137$	1.62485	+	2.81432i	0.138820	+	0.240444i	−0.788230	+	0.615381i	$0.789002\pi$
$138$		0			0
$139$		−	15.3349i		−	1.30069i	−0.759639	−	0.650346i	$-0.774624\pi$
$139$		−	15.3349i		−	1.30069i	0.759639	−	0.650346i	$-0.225376\pi$
$140$	−2.90656	−	0.117658i	−0.245649	−	0.00994390i
$141$		0			0
$142$	−3.97823	−	11.7428i	−0.333846	−	0.985438i
$143$	−4.74135	−	8.21226i	−0.396491	−	0.686743i
$144$		0			0
$145$	2.25865	−	3.91210i	0.187571	−	0.324882i
$146$	4.35121	−	4.95555i	0.360109	−	0.410124i
$147$		0			0
$148$	−0.526255	+	0.0686349i	−0.0432579	+	0.00564175i
$149$	6.39393	+	3.69154i	0.523812	+	0.302423i	0.738493	−	0.674261i	$-0.235538\pi$
$149$	6.39393	+	3.69154i	0.523812	+	0.302423i	−0.214681	+	0.976684i	$0.568871\pi$
$150$		0			0
$151$	−4.16550	−	7.21485i	−0.338983	−	0.587136i	0.645259	−	0.763964i	$-0.276750\pi$
$151$	−4.16550	−	7.21485i	−0.338983	−	0.587136i	−0.984242	+	0.176828i	$0.943416\pi$
$152$	8.27784	+	16.8629i	0.671422	+	1.36776i
$153$		0			0
$154$	5.62545	+	6.95514i	0.453312	+	0.560461i
$155$			0.476182i			0.0382478i
$156$		0			0
$157$	6.18061	−	3.56837i	0.493266	−	0.284787i	−0.232662	−	0.972558i	$-0.574744\pi$
$157$	6.18061	−	3.56837i	0.493266	−	0.284787i	0.725928	+	0.687770i	$0.241410\pi$
$158$	−0.855004	−	0.170609i	−0.0680204	−	0.0135729i
$159$		0			0
$160$	−2.78491	−	1.38386i	−0.220166	−	0.109404i
$161$	3.97374	−	4.77813i	0.313175	−	0.376569i
$162$		0			0
$163$	−6.33023	−	3.65476i	−0.495822	−	0.286263i	0.231164	−	0.972915i	$-0.425746\pi$
$163$	−6.33023	−	3.65476i	−0.495822	−	0.286263i	−0.726987	+	0.686652i	$0.759080\pi$
$164$	−9.92564	+	7.59714i	−0.775063	+	0.593237i
$165$		0			0
$166$	1.47268	−	0.498913i	0.114302	−	0.0387231i
$167$	−1.88873			−0.146154			−0.0730772	−	0.997326i	$-0.523282\pi$
$167$	−1.88873			−0.146154			−0.0730772	+	0.997326i	$0.523282\pi$
$168$		0			0
$169$	−2.73240			−0.210184
$170$	−3.10374	+	1.05148i	−0.238046	+	0.0806450i
$171$		0			0
$172$	−6.50379	−	8.49718i	−0.495909	−	0.647904i
$173$	−14.3350	−	8.27632i	−1.08987	−	0.629237i	−0.156329	−	0.987705i	$-0.549966\pi$
$173$	−14.3350	−	8.27632i	−1.08987	−	0.629237i	−0.933542	+	0.358468i	$0.883299\pi$
$174$		0			0
$175$	4.30221	+	11.6609i	0.325217	+	0.881478i
$176$	2.45272	+	9.24312i	0.184881	+	0.696726i
$177$		0			0
$178$	−8.86985	−	1.76990i	−0.664823	−	0.132660i
$179$	4.79957	−	2.77103i	0.358737	−	0.207117i	−0.309790	−	0.950805i	$-0.600259\pi$
$179$	4.79957	−	2.77103i	0.358737	−	0.207117i	0.668526	+	0.743688i	$0.266925\pi$
$180$		0			0
$181$		−	9.98466i		−	0.742154i	−0.928602	−	0.371077i	$-0.878989\pi$
$181$		−	9.98466i		−	0.742154i	0.928602	−	0.371077i	$-0.121011\pi$
$182$	14.6596	−	2.31309i	1.08664	−	0.171458i
$183$		0			0
$184$	5.96386	−	2.92760i	0.439661	−	0.215825i
$185$	−0.0729381	−	0.126333i	−0.00536252	−	0.00928816i
$186$		0			0
$187$	8.72714	+	5.03862i	0.638192	+	0.368460i
$188$	0.672132	+	5.15354i	0.0490202	+	0.375861i
$189$		0			0
$190$	−3.40684	+	3.88002i	−0.247158	+	0.281486i
$191$	0.0842049	−	0.145847i	0.00609285	−	0.0105531i	−0.862963	−	0.505267i	$-0.831394\pi$
$191$	0.0842049	−	0.145847i	0.00609285	−	0.0105531i	0.869056	+	0.494714i	$0.164727\pi$
$192$		0			0
$193$	−3.75865	−	6.51018i	−0.270554	−	0.468613i	0.698450	−	0.715659i	$-0.253873\pi$
$193$	−3.75865	−	6.51018i	−0.270554	−	0.468613i	−0.969004	+	0.247046i	$0.920540\pi$
$194$	5.87523	+	17.3423i	0.421817	+	1.24511i
$195$		0			0
$196$	−13.3198	+	4.31071i	−0.951416	+	0.307908i
$197$			1.34581i			0.0958847i	0.998850	+	0.0479424i	$0.0152664\pi$
$197$			1.34581i			0.0958847i	−0.998850	+	0.0479424i	$0.984734\pi$
$198$		0			0
$199$	6.38059	+	11.0515i	0.452308	+	0.783420i	0.998529	−	0.0542208i	$-0.0172675\pi$
$199$	6.38059	+	11.0515i	0.452308	+	0.783420i	−0.546221	+	0.837641i	$0.683934\pi$
$200$	−0.893107	+	13.2573i	−0.0631522	+	0.937433i
$201$		0			0
$202$	16.8806	+	14.8220i	1.18771	+	1.04287i
$203$	3.68129	−	21.4267i	0.258376	−	1.50386i
$204$		0			0
$205$	−2.97540	−	1.71785i	−0.207811	−	0.119980i
$206$	−26.0442	−	5.19690i	−1.81458	−	0.362085i
$207$		0			0
$208$	15.3150	+	4.14342i	1.06191	+	0.287294i
$209$	15.8783			1.09832
$210$		0			0
$211$			8.46353i			0.582653i	0.956624	+	0.291327i	$0.0940967\pi$
$211$			8.46353i			0.582653i	−0.956624	+	0.291327i	$0.905903\pi$
$212$	8.30452	−	19.9805i	0.570357	−	1.37226i
$213$		0			0
$214$	−0.0937901	+	0.470028i	−0.00641136	+	0.0321304i
$215$	1.47062	−	2.54719i	0.100296	−	0.173717i
$216$		0			0
$217$	0.793260	+	2.15008i	0.0538500	+	0.145957i
$218$	−8.29407	−	7.28259i	−0.561745	−	0.493239i
$219$		0			0
$220$	−2.08732	+	1.59765i	−0.140727	+	0.107713i
$221$	14.4789	−	8.35939i	0.973955	−	0.562313i
$222$		0			0
$223$	−5.80161			−0.388505			−0.194252	−	0.980952i	$-0.562228\pi$
$223$	−5.80161			−0.388505			−0.194252	+	0.980952i	$0.562228\pi$
$224$	−14.8799	−	1.60914i	−0.994203	−	0.107515i
$225$		0			0
$226$	−1.14229	−	3.37177i	−0.0759837	−	0.224287i
$227$	9.89265	−	5.71152i	0.656598	−	0.379087i	−0.134382	−	0.990930i	$-0.542905\pi$
$227$	9.89265	−	5.71152i	0.656598	−	0.379087i	0.790980	+	0.611843i	$0.209571\pi$
$228$		0			0
$229$	−16.0260	−	9.25263i	−1.05903	−	0.611431i	−0.133866	−	0.990999i	$-0.542739\pi$
$229$	−16.0260	−	9.25263i	−1.05903	−	0.611431i	−0.925164	+	0.379568i	$0.876072\pi$
$230$	1.37224	+	1.20489i	0.0904825	+	0.0794480i
$231$		0			0
$232$	12.9475	−	19.3013i	0.850044	−	1.26719i
$233$	−5.52566	+	9.57072i	−0.361998	+	0.626999i	−0.988290	−	0.152590i	$-0.951239\pi$
$233$	−5.52566	+	9.57072i	−0.361998	+	0.626999i	0.626292	+	0.779589i	$0.284572\pi$
$234$		0			0
$235$	−1.23716	+	0.714273i	−0.0807032	+	0.0465940i
$236$	2.89740	−	6.97106i	0.188605	−	0.453778i
$237$		0			0
$238$	−12.2625	+	9.91814i	−0.794859	+	0.642897i
$239$	22.6107			1.46256			0.731281	−	0.682076i	$-0.238923\pi$
$239$	22.6107			1.46256			0.731281	+	0.682076i	$0.238923\pi$
$240$		0			0
$241$	−6.96479	−	12.0634i	−0.448642	−	0.777070i	0.549656	−	0.835391i	$-0.314759\pi$
$241$	−6.96479	−	12.0634i	−0.448642	−	0.777070i	−0.998298	+	0.0583207i	$0.981425\pi$
$242$	−7.32866	−	1.46237i	−0.471104	−	0.0940049i
$243$		0			0
$244$	−14.1536	+	1.84593i	−0.906093	+	0.118174i
$245$	−2.49931	−	2.92606i	−0.159675	−	0.186939i
$246$		0			0
$247$	13.1715	−	22.8138i	0.838085	−	1.45161i
$248$	−0.164675	+	2.44444i	−0.0104569	+	0.155222i
$249$		0			0
$250$	−7.14086	+	2.41918i	−0.451627	+	0.153002i
$251$		−	0.706033i		−	0.0445644i	−0.999752	−	0.0222822i	$-0.992907\pi$
$251$		−	0.706033i		−	0.0445644i	0.999752	−	0.0222822i	$-0.00709323\pi$
$252$		0			0
$253$		−	5.61562i		−	0.353051i
$254$	−2.40600	−	7.10197i	−0.150966	−	0.445618i
$255$		0			0
$256$	−13.8175	−	8.06700i	−0.863594	−	0.504187i
$257$	10.3919	−	17.9992i	0.648226	−	1.12276i	−0.335320	−	0.942104i	$-0.608844\pi$
$257$	10.3919	−	17.9992i	0.648226	−	1.12276i	0.983546	−	0.180656i	$-0.0578222\pi$
$258$		0			0
$259$	−0.539788	−	0.448917i	−0.0335408	−	0.0278943i
$260$	0.563987	+	4.32435i	0.0349770	+	0.268185i
$261$		0			0
$262$	2.77823	−	13.9231i	0.171640	−	0.860170i
$263$	−11.3895	−	19.7273i	−0.702309	−	1.21644i	−0.967654	−	0.252281i	$-0.918819\pi$
$263$	−11.3895	−	19.7273i	−0.702309	−	1.21644i	0.265345	−	0.964154i	$-0.414514\pi$
$264$		0			0
$265$	5.94749			0.365351
$266$	−8.91910	+	23.1946i	−0.546865	+	1.42215i
$267$		0			0
$268$	2.05344	−	4.94052i	0.125434	−	0.301790i
$269$	2.59376	−	1.49751i	0.158145	−	0.0913048i	−0.418839	−	0.908060i	$-0.637563\pi$
$269$	2.59376	−	1.49751i	0.158145	−	0.0913048i	0.576984	+	0.816756i	$0.304230\pi$
$270$		0			0
$271$	12.5926	−	21.8109i	0.764943	−	1.32492i	−0.175333	−	0.984509i	$-0.556100\pi$
$271$	12.5926	−	21.8109i	0.764943	−	1.32492i	0.940277	−	0.340412i	$-0.110566\pi$
$272$	−16.2964	+	4.32435i	−0.988113	+	0.262202i
$273$		0			0
$274$	−3.03229	+	3.45345i	−0.183188	+	0.208630i
$275$	9.72654	+	5.61562i	0.586533	+	0.338635i
$276$		0			0
$277$	−8.17940	+	4.72238i	−0.491453	+	0.283740i	−0.725177	−	0.688563i	$-0.758242\pi$
$277$	−8.17940	+	4.72238i	−0.491453	+	0.283740i	0.233724	+	0.972303i	$0.424909\pi$
$278$	20.5402	−	6.95858i	1.23192	−	0.417348i
$279$		0			0
$280$	−1.16132	−	3.94654i	−0.0694024	−	0.235851i
$281$	−26.8425			−1.60129			−0.800644	−	0.599141i	$-0.795509\pi$
$281$	−26.8425			−1.60129			−0.800644	+	0.599141i	$0.795509\pi$
$282$		0			0
$283$	−11.2429	+	6.49111i	−0.668323	+	0.385856i	−0.795441	−	0.606031i	$-0.792761\pi$
$283$	−11.2429	+	6.49111i	−0.668323	+	0.385856i	0.127118	+	0.991888i	$0.459427\pi$
$284$	13.9236	−	10.6572i	0.826212	−	0.632387i
$285$		0			0
$286$	8.84830	−	10.0772i	0.523211	−	0.595880i
$287$	−16.2964	−	2.79986i	−0.961945	−	0.165270i
$288$		0			0
$289$	−0.383502	+	0.664245i	−0.0225590	+	0.0390733i
$290$	6.26493	+	1.25011i	0.367889	+	0.0734092i
$291$		0			0
$292$	8.61211	+	3.57947i	0.503985	+	0.209473i
$293$		−	9.56300i		−	0.558677i	−0.960193	−	0.279338i	$-0.909885\pi$
$293$		−	9.56300i		−	0.558677i	0.960193	−	0.279338i	$-0.0901151\pi$
$294$		0			0
$295$	2.07504			0.120814
$296$	−0.330733	−	0.673741i	−0.0192235	−	0.0391604i
$297$		0			0
$298$	−2.04318	+	10.2394i	−0.118358	+	0.593152i
$299$	−8.06848	−	4.65834i	−0.466612	−	0.269399i
$300$		0			0
$301$	2.39691	−	13.9511i	0.138156	−	0.804126i
$302$	7.77364	−	8.85332i	0.447323	−	0.509452i
$303$		0			0
$304$	−18.8305	+	18.7396i	−1.08001	+	1.07479i
$305$	−1.96167	−	3.39771i	−0.112325	−	0.194552i
$306$		0			0
$307$		−	12.2217i		−	0.697527i	−0.937211	−	0.348763i	$-0.886602\pi$
$307$		−	12.2217i		−	0.697527i	0.937211	−	0.348763i	$-0.113398\pi$
$308$	−6.76329	+	10.6910i	−0.385374	+	0.609176i
$309$		0			0
$310$	−0.637815	+	0.216079i	−0.0362255	+	0.0122724i
$311$	15.9415	+	27.6114i	0.903957	+	1.56570i	0.822311	+	0.569038i	$0.192684\pi$
$311$	15.9415	+	27.6114i	0.903957	+	1.56570i	0.0816453	+	0.996661i	$0.473983\pi$
$312$		0			0
$313$	−10.7618	+	18.6399i	−0.608291	+	1.05359i	0.383230	+	0.923653i	$0.374811\pi$
$313$	−10.7618	+	18.6399i	−0.608291	+	1.05359i	−0.991522	+	0.129939i	$0.958522\pi$
$314$	7.58420	+	6.65929i	0.428001	+	0.375806i
$315$		0			0
$316$	−0.159458	−	1.22264i	−0.00897023	−	0.0687789i
$317$	−20.0481	−	11.5747i	−1.12601	−	0.650103i	−0.183082	−	0.983098i	$-0.558607\pi$
$317$	−20.0481	−	11.5747i	−1.12601	−	0.650103i	−0.942929	+	0.332995i	$0.891941\pi$
$318$		0			0
$319$	−9.82264	−	17.0133i	−0.549962	−	0.952562i
$320$	0.589871	−	4.35816i	0.0329748	−	0.243629i
$321$		0			0
$322$	8.20317	+	3.15439i	0.457145	+	0.175787i
$323$			27.9947i			1.55767i
$324$		0			0
$325$	16.1370	−	9.31667i	0.895117	−	0.516796i
$326$	2.02283	−	10.1374i	0.112034	−	0.561457i
$327$		0			0
$328$	−14.6799	−	9.84739i	−0.810561	−	0.543731i
$329$	−4.39618	+	5.28607i	−0.242369	+	0.291430i
$330$		0			0
$331$	25.5615	+	14.7579i	1.40499	+	0.811169i	0.994899	−	0.100878i	$-0.0321652\pi$
$331$	25.5615	+	14.7579i	1.40499	+	0.811169i	0.410086	+	0.912047i	$0.365499\pi$
$332$	1.33652	+	1.74616i	0.0733513	+	0.0958332i
$333$		0			0
$334$	−0.857056	−	2.52984i	−0.0468960	−	0.138426i
$335$	1.47062			0.0803486
$336$		0			0
$337$	−3.28431			−0.178908			−0.0894538	−	0.995991i	$-0.528512\pi$
$337$	−3.28431			−0.178908			−0.0894538	+	0.995991i	$0.528512\pi$
$338$	−1.23989	−	3.65987i	−0.0674411	−	0.199071i
$339$		0			0
$340$	−2.81679	−	3.68012i	−0.152762	−	0.199583i
$341$	1.79342	+	1.03543i	0.0971192	+	0.0560718i
$342$		0			0
$343$	−16.1595	−	9.04831i	−0.872529	−	0.488563i
$344$	8.43018	−	12.5672i	0.454525	−	0.677578i
$345$		0			0
$346$	4.58076	−	22.9564i	0.246263	−	1.23414i
$347$	−27.4329	+	15.8384i	−1.47267	+	0.850248i	−0.999528	−	0.0307361i	$-0.990215\pi$
$347$	−27.4329	+	15.8384i	−1.47267	+	0.850248i	−0.473146	+	0.880984i	$0.656882\pi$
$348$		0			0
$349$			28.4807i			1.52454i	0.647260	+	0.762269i	$0.275915\pi$
$349$			28.4807i			1.52454i	−0.647260	+	0.762269i	$0.724085\pi$
$350$	−13.6667	+	11.0539i	−0.730518	+	0.590857i
$351$		0			0
$352$	−11.2676	+	7.47954i	−0.600565	+	0.398661i
$353$	10.1196	+	17.5277i	0.538613	+	0.932905i	0.998979	+	0.0451760i	$0.0143849\pi$
$353$	10.1196	+	17.5277i	0.538613	+	0.932905i	−0.460366	+	0.887729i	$0.652282\pi$
$354$		0			0
$355$	4.17386	+	2.40978i	0.221525	+	0.127898i
$356$	−1.65423	−	12.6837i	−0.0876740	−	0.672237i
$357$		0			0
$358$	5.88954	+	5.17130i	0.311272	+	0.273312i
$359$	12.5611	−	21.7564i	0.662948	−	1.14826i	−0.316889	−	0.948463i	$-0.602638\pi$
$359$	12.5611	−	21.7564i	0.662948	−	1.14826i	0.979837	−	0.199797i	$-0.0640283\pi$
$360$		0			0
$361$	12.5550	+	21.7460i	0.660791	+	1.14452i
$362$	13.3738	−	4.53077i	0.702912	−	0.238132i
$363$		0			0
$364$	9.75036	+	18.5859i	0.511058	+	0.974168i
$365$			2.56353i			0.134181i
$366$		0			0
$367$	15.1912	+	26.3118i	0.792972	+	1.37347i	0.924119	+	0.382104i	$0.124801\pi$
$367$	15.1912	+	26.3118i	0.792972	+	1.37347i	−0.131147	+	0.991363i	$0.541866\pi$
$368$	6.62757	+	6.65974i	0.345486	+	0.347163i
$369$		0			0
$370$	0.136117	−	0.155022i	0.00707639	−	0.00805923i
$371$	26.8544	−	9.90778i	1.39421	−	0.514386i
$372$		0			0
$373$	−4.86327	−	2.80781i	−0.251811	−	0.145383i	0.368782	−	0.929516i	$-0.379775\pi$
$373$	−4.86327	−	2.80781i	−0.251811	−	0.145383i	−0.620593	+	0.784133i	$0.713108\pi$
$374$	−2.78876	+	13.9758i	−0.144203	+	0.722674i
$375$		0			0
$376$	−6.59785	+	3.23882i	−0.340258	+	0.167029i
$377$	−32.5928			−1.67861
$378$		0			0
$379$			8.07009i			0.414533i	0.978285	+	0.207266i	$0.0664566\pi$
$379$			8.07009i			0.414533i	−0.978285	+	0.207266i	$0.933543\pi$
$380$	−6.74298	−	2.80260i	−0.345907	−	0.143770i
$381$		0			0
$382$	0.233563	+	0.0466055i	0.0119501	+	0.00238455i
$383$	−12.8166	+	22.1990i	−0.654898	+	1.13432i	0.327022	+	0.945017i	$0.393955\pi$
$383$	−12.8166	+	22.1990i	−0.654898	+	1.13432i	−0.981919	+	0.189299i	$0.939378\pi$
$384$		0			0
$385$	−3.42706	−	0.588798i	−0.174659	−	0.0300079i
$386$	7.01439	−	7.98862i	0.357023	−	0.406610i
$387$		0			0
$388$	−20.5629	+	15.7390i	−1.04392	+	0.799026i
$389$	−22.9905	+	13.2736i	−1.16566	+	0.672997i	−0.952655	−	0.304053i	$-0.901660\pi$
$389$	−22.9905	+	13.2736i	−1.16566	+	0.672997i	−0.213010	+	0.977050i	$0.568327\pi$
$390$		0			0
$391$	9.90081			0.500705
$392$	−11.8181	−	15.8850i	−0.596905	−	0.802312i
$393$		0			0
$394$	−1.80262	+	0.610691i	−0.0908148	+	0.0307662i
$395$	0.293506	−	0.169456i	0.0147679	−	0.00852626i
$396$		0			0
$397$	−29.5283	−	17.0482i	−1.48198	−	0.855624i	−0.482192	−	0.876065i	$-0.660159\pi$
$397$	−29.5283	−	17.0482i	−1.48198	−	0.855624i	−0.999791	+	0.0204418i	$0.993493\pi$
$398$	−11.9074	+	13.5613i	−0.596866	+	0.679765i
$399$		0			0
$400$	−18.1626	+	4.81955i	−0.908129	+	0.240978i
$401$	9.17676	−	15.8946i	0.458266	−	0.793739i	−0.540604	−	0.841277i	$-0.681804\pi$
$401$	9.17676	−	15.8946i	0.458266	−	0.793739i	0.998869	+	0.0475379i	$0.0151375\pi$
$402$		0			0
$403$	2.97540	−	1.71785i	0.148215	−	0.0855721i
$404$	−12.1931	+	29.3363i	−0.606630	+	1.45953i
$405$		0			0
$406$	30.3702	−	4.79202i	1.50725	−	0.237824i
$407$	−0.634401			−0.0314461
$408$		0			0
$409$	−5.87455	−	10.1750i	−0.290478	−	0.503122i	0.683445	−	0.730002i	$-0.260481\pi$
$409$	−5.87455	−	10.1750i	−0.290478	−	0.503122i	−0.973923	+	0.226880i	$0.927148\pi$
$410$	0.950790	−	4.76487i	0.0469562	−	0.235320i
$411$		0			0
$412$	−4.85725	−	37.2427i	−0.239299	−	1.83482i
$413$	9.36933	−	3.45677i	0.461035	−	0.170096i
$414$		0			0
$415$	−0.302212	+	0.523446i	−0.0148350	+	0.0256949i
$416$	1.39972	+	22.3937i	0.0686268	+	1.09794i
$417$		0			0
$418$	7.20514	+	21.2679i	0.352415	+	1.04025i
$419$		−	11.0841i		−	0.541495i	−0.962650	−	0.270748i	$-0.912729\pi$
$419$		−	11.0841i		−	0.541495i	0.962650	−	0.270748i	$-0.0872709\pi$
$420$		0			0
$421$		−	0.137270i		−	0.00669012i	−0.999994	−	0.00334506i	$-0.998935\pi$
$421$		−	0.137270i		−	0.00669012i	0.999994	−	0.00334506i	$-0.00106477\pi$
$422$	−11.3364	+	3.84053i	−0.551845	+	0.186954i
$423$		0			0
$424$	30.5309	+	2.05678i	1.48271	+	0.0998861i
$425$	−9.90081	+	17.1487i	−0.480260	+	0.831834i
$426$		0			0
$427$	−14.5176	−	12.0736i	−0.702555	−	0.584283i
$428$	−0.672132	+	0.0876603i	−0.0324887	+	0.00423722i
$429$		0			0
$430$	4.07913	+	0.813956i	0.196713	+	0.0392524i
$431$	6.23008	+	10.7908i	0.300092	+	0.519775i	0.976157	−	0.217067i	$-0.0696491\pi$
$431$	6.23008	+	10.7908i	0.300092	+	0.519775i	−0.676064	+	0.736843i	$0.736316\pi$
$432$		0			0
$433$	−14.1563			−0.680310			−0.340155	−	0.940369i	$-0.610480\pi$
$433$	−14.1563			−0.680310			−0.340155	+	0.940369i	$0.610480\pi$
$434$	−2.51993	+	2.03817i	−0.120961	+	0.0978353i
$435$		0			0
$436$	5.99093	−	14.4140i	0.286914	−	0.690306i
$437$	13.5102	−	7.80014i	0.646282	−	0.373131i
$438$		0			0
$439$	2.72948	−	4.72760i	0.130271	−	0.225636i	−0.793510	−	0.608557i	$-0.791749\pi$
$439$	2.72948	−	4.72760i	0.130271	−	0.225636i	0.923781	+	0.382921i	$0.125082\pi$
$440$	−3.08712	−	2.07086i	−0.147173	−	0.0987246i
$441$		0			0
$442$	17.7670	+	15.6003i	0.845090	+	0.742030i
$443$	28.8691	+	16.6676i	1.37161	+	0.791900i	0.991131	−	0.132889i	$-0.0424254\pi$
$443$	28.8691	+	16.6676i	1.37161	+	0.791900i	0.380480	+	0.924789i	$0.375759\pi$
$444$		0			0
$445$	3.04485	−	1.75794i	0.144340	−	0.0833346i
$446$	−2.63262	−	7.77089i	−0.124658	−	0.367962i
$447$		0			0
$448$	−4.59675	−	20.6608i	−0.217176	−	0.976132i
$449$	26.9716			1.27287			0.636435	−	0.771330i	$-0.280408\pi$
$449$	26.9716			1.27287			0.636435	+	0.771330i	$0.280408\pi$
$450$		0			0
$451$	−12.9397	+	7.47074i	−0.609307	+	0.351783i
$452$	3.99793	−	3.06004i	0.188047	−	0.143932i
$453$		0			0
$454$	12.1392	+	10.6588i	0.569723	+	0.500244i
$455$	−3.68884	+	4.43555i	−0.172935	+	0.207942i
$456$		0			0
$457$	−9.54668	+	16.5353i	−0.446575	+	0.773491i	−0.998160	−	0.0606278i	$-0.980690\pi$
$457$	−9.54668	+	16.5353i	−0.446575	+	0.773491i	0.551585	+	0.834118i	$0.314023\pi$
$458$	5.12112	−	25.6644i	0.239294	−	1.19922i
$459$		0			0
$460$	−0.991187	+	2.38477i	−0.0462143	+	0.111190i
$461$			18.9177i			0.881087i	0.897731	+	0.440543i	$0.145214\pi$
$461$			18.9177i			0.881087i	−0.897731	+	0.440543i	$0.854786\pi$
$462$		0			0
$463$	0.860370			0.0399848			0.0199924	−	0.999800i	$-0.493636\pi$
$463$	0.860370			0.0399848			0.0199924	+	0.999800i	$0.493636\pi$
$464$	31.7281	+	8.58391i	1.47294	+	0.398498i
$465$		0			0
$466$	−15.3268	−	3.05833i	−0.709999	−	0.141674i
$467$	−16.1842	−	9.34394i	−0.748914	−	0.432386i	0.0763871	−	0.997078i	$-0.475662\pi$
$467$	−16.1842	−	9.34394i	−0.748914	−	0.432386i	−0.825302	+	0.564692i	$0.808995\pi$
$468$		0			0
$469$	6.64022	−	2.44987i	0.306617	−	0.113125i
$470$	−1.51811	−	1.33297i	−0.0700253	−	0.0614855i
$471$		0			0
$472$	10.6521	+	0.717599i	0.490301	+	0.0330302i
$473$	−6.39558	−	11.0775i	−0.294069	−	0.509342i
$474$		0			0
$475$			31.2006i			1.43158i
$476$	−18.8491	−	11.9242i	−0.863947	−	0.546546i
$477$		0			0
$478$	10.2601	+	30.2856i	0.469287	+	1.38523i
$479$	−9.27364	−	16.0624i	−0.423723	−	0.733911i	0.572577	−	0.819851i	$-0.305944\pi$
$479$	−9.27364	−	16.0624i	−0.423723	−	0.733911i	−0.996300	+	0.0859405i	$0.972610\pi$
$480$		0			0
$481$	−0.526255	+	0.911501i	−0.0239952	+	0.0415609i
$482$	12.9977	−	14.8029i	0.592028	−	0.674255i
$483$		0			0
$484$	−1.36680	−	10.4799i	−0.0621271	−	0.476357i
$485$	−6.16413	−	3.55886i	−0.279899	−	0.161600i
$486$		0			0
$487$	11.4588	+	19.8471i	0.519246	+	0.899360i	0.999750	+	0.0223676i	$0.00712041\pi$
$487$	11.4588	+	19.8471i	0.519246	+	0.899360i	−0.480504	+	0.876993i	$0.659546\pi$
$488$	−8.89505	−	18.1202i	−0.402660	−	0.820265i
$489$		0			0
$490$	2.78514	−	4.67544i	0.125820	−	0.211215i
$491$			24.7987i			1.11915i	0.828780	+	0.559575i	$0.189036\pi$
$491$			24.7987i			1.11915i	−0.828780	+	0.559575i	$0.810964\pi$
$492$		0			0
$493$	29.9959	−	17.3181i	1.35095	−	0.779969i
$494$	36.5345	+	7.29015i	1.64376	+	0.327999i
$495$		0			0
$496$	−3.34889	+	0.888650i	−0.150370	+	0.0399016i
$497$	22.8604	+	3.92760i	1.02543	+	0.176177i
$498$		0			0
$499$	33.9707	+	19.6130i	1.52074	+	0.877997i	0.999701	+	0.0244624i	$0.00778739\pi$
$499$	33.9707	+	19.6130i	1.52074	+	0.877997i	0.521035	+	0.853535i	$0.325546\pi$
$500$	−6.48066	−	8.46697i	−0.289824	−	0.378654i
$501$		0			0
$502$	0.945686	−	0.320379i	0.0422080	−	0.0142992i
$503$	−7.59396			−0.338598			−0.169299	−	0.985565i	$-0.554150\pi$
$503$	−7.59396			−0.338598			−0.169299	+	0.985565i	$0.554150\pi$
$504$		0			0
$505$	−8.73240			−0.388587
$506$	7.52177	−	2.54822i	0.334383	−	0.113282i
$507$		0			0
$508$	8.42086	−	6.44538i	0.373615	−	0.285967i
$509$	−3.79222	−	2.18944i	−0.168087	−	0.0970451i	0.413596	−	0.910460i	$-0.364272\pi$
$509$	−3.79222	−	2.18944i	−0.168087	−	0.0970451i	−0.581684	+	0.813415i	$0.697606\pi$
$510$		0			0
$511$	4.27052	+	11.5749i	0.188917	+	0.512046i
$512$	4.53521	−	22.1683i	0.200430	−	0.979708i
$513$		0			0
$514$	28.8244	+	5.75166i	1.27139	+	0.253695i
$515$	8.94047	−	5.16178i	0.393964	−	0.227455i
$516$		0			0
$517$			6.21259i			0.273230i
$518$	0.356354	−	0.926718i	0.0156573	−	0.0407177i
$519$		0			0
$520$	−5.53626	+	2.71770i	−0.242781	+	0.119179i
$521$	−5.37827	−	9.31544i	−0.235626	−	0.408117i	0.723828	−	0.689980i	$-0.242381\pi$
$521$	−5.37827	−	9.31544i	−0.235626	−	0.408117i	−0.959455	+	0.281863i	$0.909048\pi$
$522$		0			0
$523$	−2.43561	−	1.40620i	−0.106502	−	0.0614889i	0.445803	−	0.895131i	$-0.352918\pi$
$523$	−2.43561	−	1.40620i	−0.106502	−	0.0614889i	−0.552305	+	0.833642i	$0.686252\pi$
$524$	19.9098	−	2.59666i	0.869762	−	0.113435i
$525$		0			0
$526$	21.2551	−	24.2073i	0.926768	−	1.05549i
$527$	−1.82555	+	3.16195i	−0.0795223	+	0.137737i
$528$		0			0
$529$	8.74135	+	15.1405i	0.380059	+	0.658281i
$530$	2.69881	+	7.96628i	0.117229	+	0.346033i
$531$		0			0
$532$	−35.1150	−	1.42146i	−1.52243	−	0.0616280i
$533$			24.7889i			1.07372i
$534$		0			0
$535$	−0.0931564	−	0.161352i	−0.00402750	−	0.00697584i
$536$	7.54931	+	0.508575i	0.326080	+	0.0219671i
$537$		0			0
$538$	3.18280	+	2.79465i	0.137220	+	0.120486i
$539$	−16.4549	+	3.05049i	−0.708762	+	0.131394i
$540$		0			0
$541$	−27.0699	−	15.6288i	−1.16383	−	0.671935i	−0.211608	−	0.977355i	$-0.567870\pi$
$541$	−27.0699	−	15.6288i	−1.16383	−	0.671935i	−0.952218	+	0.305419i	$0.901203\pi$
$542$	34.9285	+	6.96970i	1.50031	+	0.299374i
$543$		0			0
$544$	−13.1871	−	19.8657i	−0.565390	−	0.851735i
$545$	4.29055			0.183787
$546$		0			0
$547$			29.4711i			1.26010i	0.776556	+	0.630048i	$0.216965\pi$
$547$			29.4711i			1.26010i	−0.776556	+	0.630048i	$0.783035\pi$
$548$	−6.00165	−	2.49448i	−0.256378	−	0.106559i
$549$		0			0
$550$	−3.10812	+	15.5763i	−0.132531	+	0.664176i
$551$	27.2874	−	47.2632i	1.16248	−	2.01348i
$552$		0			0
$553$	1.04296	−	1.25408i	0.0443512	−	0.0533289i
$554$	−10.0369	−	8.81290i	−0.426428	−	0.374424i
$555$		0			0
$556$	18.6412	+	24.3546i	0.790561	+	1.03287i
$557$	−19.3751	+	11.1862i	−0.820950	+	0.473976i	−0.850744	−	0.525580i	$-0.823848\pi$
$557$	−19.3751	+	11.1862i	−0.820950	+	0.473976i	0.0297941	+	0.999556i	$0.490515\pi$
$558$		0			0
$559$	−21.2213			−0.897567
$560$	4.75916	−	3.34635i	0.201111	−	0.141409i
$561$		0			0
$562$	−12.1804	−	35.9538i	−0.513799	−	1.51662i
$563$	−28.0528	+	16.1963i	−1.18229	+	0.682593i	−0.956542	−	0.291594i	$-0.905814\pi$
$563$	−28.0528	+	16.1963i	−1.18229	+	0.682593i	−0.225743	+	0.974187i	$0.572481\pi$
$564$		0			0
$565$	1.19846	+	0.691928i	0.0504194	+	0.0291097i
$566$	−13.7962	−	12.1137i	−0.579896	−	0.509177i
$567$		0			0
$568$	20.5928	+	13.8138i	0.864053	+	0.579614i
$569$	−18.5288	+	32.0928i	−0.776767	+	1.34540i	0.157029	+	0.987594i	$0.449808\pi$
$569$	−18.5288	+	32.0928i	−0.776767	+	1.34540i	−0.933796	+	0.357806i	$0.883525\pi$
$570$		0			0
$571$	19.4303	−	11.2181i	0.813132	−	0.469462i	−0.0349102	−	0.999390i	$-0.511115\pi$
$571$	19.4303	−	11.2181i	0.813132	−	0.469462i	0.848042	+	0.529928i	$0.177781\pi$
$572$	17.5129	+	7.27894i	0.732253	+	0.304348i
$573$		0			0
$574$	−3.64464	−	23.0985i	−0.152124	−	0.964111i
$575$	11.0346			0.460175
$576$		0			0
$577$	−4.78431	−	8.28667i	−0.199173	−	0.344978i	0.749087	−	0.662471i	$-0.230492\pi$
$577$	−4.78431	−	8.28667i	−0.199173	−	0.344978i	−0.948261	+	0.317493i	$0.897159\pi$
$578$	−1.06374	−	0.212260i	−0.0442457	−	0.00882885i
$579$		0			0
$580$	1.16841	+	8.95874i	0.0485156	+	0.371991i
$581$	−0.492563	+	2.86693i	−0.0204350	+	0.118940i
$582$		0			0
$583$	12.9325	−	22.3997i	0.535609	−	0.927703i
$584$	−0.886527	+	13.1596i	−0.0366848	+	0.544550i
$585$		0			0
$586$	12.8090	−	4.33944i	0.529136	−	0.179261i
$587$			23.6894i			0.977766i	0.872349	+	0.488883i	$0.162595\pi$
$587$			23.6894i			0.977766i	−0.872349	+	0.488883i	$0.837405\pi$
$588$		0			0
$589$			5.75289i			0.237044i
$590$	0.941600	+	2.77939i	0.0387651	+	0.114426i
$591$		0			0
$592$	0.752355	−	0.748721i	0.0309216	−	0.0307723i
$593$	−3.72404	+	6.45023i	−0.152928	+	0.264879i	−0.932303	−	0.361679i	$-0.882204\pi$
$593$	−3.72404	+	6.45023i	−0.152928	+	0.264879i	0.779375	+	0.626558i	$0.215537\pi$
$594$		0			0
$595$	1.03810	−	6.04219i	0.0425579	−	0.247706i
$596$	−14.6422	+	1.90965i	−0.599766	+	0.0782222i
$597$		0			0
$598$	2.57829	−	12.9210i	0.105434	−	0.528381i
$599$	0.837627	+	1.45081i	0.0342245	+	0.0592786i	0.882630	−	0.470068i	$-0.155771\pi$
$599$	0.837627	+	1.45081i	0.0342245	+	0.0592786i	−0.848406	+	0.529346i	$0.822437\pi$
$600$		0			0
$601$	−8.27385			−0.337497			−0.168749	−	0.985659i	$-0.553973\pi$
$601$	−8.27385			−0.337497			−0.168749	+	0.985659i	$0.553973\pi$
$602$	19.7742	−	3.12011i	0.805937	−	0.127166i
$603$		0			0
$604$	15.3859	+	6.39489i	0.626045	+	0.260205i
$605$	2.51579	−	1.45249i	0.102281	−	0.0590522i
$606$		0			0
$607$	13.2647	−	22.9751i	0.538397	−	0.932531i	−0.460593	−	0.887611i	$-0.652363\pi$
$607$	13.2647	−	22.9751i	0.538397	−	0.932531i	0.998991	−	0.0449200i	$-0.0143033\pi$
$608$	−33.6453	−	16.7188i	−1.36450	−	0.678036i
$609$		0			0
$610$	3.66087	−	4.16932i	0.148224	−	0.168811i
$611$	8.92620	+	5.15354i	0.361115	+	0.208490i
$612$		0			0
$613$	−27.3692	+	15.8016i	−1.10543	+	0.638220i	−0.937642	−	0.347603i	$-0.886996\pi$
$613$	−27.3692	+	15.8016i	−1.10543	+	0.638220i	−0.167788	+	0.985823i	$0.553662\pi$
$614$	16.3701	−	5.54586i	0.660645	−	0.223813i
$615$		0			0
$616$	−17.3889	−	4.20770i	−0.700619	−	0.169533i
$617$	−10.1113			−0.407064			−0.203532	−	0.979068i	$-0.565242\pi$
$617$	−10.1113			−0.407064			−0.203532	+	0.979068i	$0.565242\pi$
$618$		0			0
$619$	4.79105	−	2.76611i	0.192568	−	0.111179i	−0.400616	−	0.916246i	$-0.631204\pi$
$619$	4.79105	−	2.76611i	0.192568	−	0.111179i	0.593184	+	0.805067i	$0.297871\pi$
$620$	−0.578847	−	0.756262i	−0.0232471	−	0.0303722i
$621$		0			0
$622$	−29.7499	+	33.8819i	−1.19286	+	1.35854i
$623$	10.8197	−	13.0099i	0.433483	−	0.521230i
$624$		0			0
$625$	−10.2791	+	17.8039i	−0.411163	+	0.712155i
$626$	−29.8504	−	5.95640i	−1.19306	−	0.238066i
$627$		0			0
$628$	−5.47819	+	13.1804i	−0.218604	+	0.525954i
$629$		−	1.11850i		−	0.0445975i
$630$		0			0
$631$	35.5582			1.41555			0.707774	−	0.706439i	$-0.249700\pi$
$631$	35.5582			1.41555			0.707774	+	0.706439i	$0.249700\pi$
$632$	1.56529	−	0.768386i	0.0622640	−	0.0305648i
$633$		0			0
$634$	6.40636	−	32.1054i	0.254429	−	1.27507i
$635$	2.52431	+	1.45741i	0.100174	+	0.0578357i
$636$		0			0
$637$	−9.26693	+	26.1727i	−0.367169	+	1.03700i
$638$	18.3310	−	20.8770i	0.725731	−	0.826528i
$639$		0			0
$640$	6.10515	−	1.18752i	0.241327	−	0.0469410i
$641$	4.73300	+	8.19779i	0.186942	+	0.323793i	0.944229	−	0.329289i	$-0.106809\pi$
$641$	4.73300	+	8.19779i	0.186942	+	0.323793i	−0.757287	+	0.653082i	$0.773476\pi$
$642$		0			0
$643$		−	13.0085i		−	0.513007i	−0.966543	−	0.256503i	$-0.917430\pi$
$643$		−	13.0085i		−	0.513007i	0.966543	−	0.256503i	$-0.0825705\pi$
$644$	−0.502723	+	12.4190i	−0.0198101	+	0.489378i
$645$		0			0
$646$	−37.4971	+	12.7033i	−1.47530	+	0.499803i
$647$	13.7610	+	23.8347i	0.540999	+	0.937039i	0.998847	+	0.0480078i	$0.0152872\pi$
$647$	13.7610	+	23.8347i	0.540999	+	0.937039i	−0.457848	+	0.889031i	$0.651379\pi$
$648$		0			0
$649$	4.51207	−	7.81514i	0.177114	−	0.306771i
$650$	19.8016	+	17.3868i	0.776683	+	0.681965i
$651$		0			0
$652$	14.4963	−	1.89062i	0.567718	−	0.0740425i
$653$	30.4390	+	17.5740i	1.19117	+	0.687723i	0.958572	−	0.284850i	$-0.0919439\pi$
$653$	30.4390	+	17.5740i	1.19117	+	0.687723i	0.232598	+	0.972573i	$0.425277\pi$
$654$		0			0
$655$	2.75946	+	4.77952i	0.107821	+	0.186751i
$656$	6.52860	−	24.1313i	0.254899	−	0.942167i
$657$		0			0
$658$	−9.07522	−	3.48972i	−0.353789	−	0.136043i
$659$		−	3.86719i		−	0.150644i	−0.997159	−	0.0753222i	$-0.976001\pi$
$659$		−	3.86719i		−	0.150644i	0.997159	−	0.0753222i	$-0.0239985\pi$
$660$		0			0
$661$	−14.4295	+	8.33085i	−0.561241	+	0.324033i	−0.753643	−	0.657284i	$-0.771705\pi$
$661$	−14.4295	+	8.33085i	−0.561241	+	0.324033i	0.192403	+	0.981316i	$0.438372\pi$
$662$	−8.16818	+	40.9347i	−0.317465	+	1.59097i
$663$		0			0
$664$	−1.73240	+	2.58255i	−0.0672300	+	0.100222i
$665$	−3.34366	−	9.06278i	−0.129662	−	0.351439i
$666$		0			0
$667$	−16.7154	−	9.65067i	−0.647225	−	0.373675i
$668$	2.99964	−	2.29594i	0.116060	−	0.0888328i
$669$		0			0
$670$	0.667329	+	1.96980i	0.0257812	+	0.0761002i
$671$	−17.0622			−0.658679
$672$		0			0
$673$	−3.95795			−0.152568			−0.0762838	−	0.997086i	$-0.524306\pi$
$673$	−3.95795			−0.152568			−0.0762838	+	0.997086i	$0.524306\pi$
$674$	−1.49033	−	4.39912i	−0.0574055	−	0.169448i
$675$		0			0
$676$	4.33954	−	3.32150i	0.166905	−	0.127750i
$677$	−35.6839	−	20.6021i	−1.37144	−	0.791804i	−0.380334	−	0.924849i	$-0.624191\pi$
$677$	−35.6839	−	20.6021i	−1.37144	−	0.791804i	−0.991110	+	0.133045i	$0.957524\pi$
$678$		0			0
$679$	−33.7612	−	5.80045i	−1.29564	−	0.222601i
$680$	3.65111	−	5.44285i	0.140014	−	0.208724i
$681$		0			0
$682$	−0.573089	+	2.87203i	−0.0219447	+	0.109976i
$683$	28.6643	−	16.5493i	1.09681	−	0.633242i	0.161427	−	0.986885i	$-0.448390\pi$
$683$	28.6643	−	16.5493i	1.09681	−	0.633242i	0.935381	+	0.353642i	$0.115057\pi$
$684$		0			0
$685$		−	1.78648i		−	0.0682580i
$686$	4.78690	−	25.7504i	0.182765	−	0.983157i
$687$		0			0
$688$	20.6584	+	5.58903i	0.787593	+	0.213080i
$689$	−21.4558	−	37.1626i	−0.817402	−	1.41578i
$690$		0			0
$691$	−12.9010	−	7.44840i	−0.490777	−	0.283350i	0.234120	−	0.972208i	$-0.424779\pi$
$691$	−12.9010	−	7.44840i	−0.490777	−	0.283350i	−0.724897	+	0.688857i	$0.758113\pi$
$692$	32.8273	−	4.28137i	1.24791	−	0.162753i
$693$		0			0
$694$	−33.6628	−	29.5575i	−1.27782	−	1.12199i
$695$	−4.21509	+	7.30075i	−0.159888	+	0.276933i
$696$		0			0
$697$	−13.1715	−	22.8138i	−0.498907	−	0.864133i
$698$	−38.1481	+	12.9238i	−1.44393	+	0.489173i
$699$		0			0
$700$	−21.0076	−	13.2898i	−0.794014	−	0.502305i
$701$		−	32.5746i		−	1.23032i	−0.788401	−	0.615162i	$-0.789090\pi$
$701$		−	32.5746i		−	1.23032i	0.788401	−	0.615162i	$-0.210910\pi$
$702$		0			0
$703$	−0.881187	−	1.52626i	−0.0332346	−	0.0575640i
$704$	−15.1313	−	11.6982i	−0.570282	−	0.440893i
$705$		0			0
$706$	−18.8852	+	21.5082i	−0.710755	+	0.809471i
$707$	−39.4289	+	14.5471i	−1.48288	+	0.547100i
$708$		0			0
$709$	−9.95635	−	5.74830i	−0.373918	−	0.215882i	0.301251	−	0.953545i	$-0.402596\pi$
$709$	−9.95635	−	5.74830i	−0.373918	−	0.215882i	−0.675169	+	0.737663i	$0.735929\pi$
$710$	−1.33376	+	6.68411i	−0.0500550	+	0.250850i
$711$		0			0
$712$	16.2384	−	7.97128i	0.608560	−	0.298736i
$713$	2.03461			0.0761967
$714$		0			0
$715$			5.21300i			0.194955i
$716$	−4.25411	+	10.2353i	−0.158983	+	0.382510i
$717$		0			0
$718$	34.8412	+	6.95227i	1.30026	+	0.259456i
$719$	−13.4887	+	23.3632i	−0.503045	+	0.871299i	0.496949	+	0.867780i	$0.334454\pi$
$719$	−13.4887	+	23.3632i	−0.503045	+	0.871299i	−0.999994	+	0.00351948i	$0.998880\pi$
$720$		0			0
$721$	31.7695	−	38.2004i	1.18316	−	1.42266i
$722$	−23.4302	+	26.6844i	−0.871981	+	0.993091i
$723$		0			0
$724$	12.1374	+	15.8574i	0.451081	+	0.589337i
$725$	33.4309	−	19.3013i	1.24159	−	0.716833i
$726$		0			0
$727$	−27.0230			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$727$	−27.0230			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$728$	−20.4702	+	21.4938i	−0.758678	+	0.796613i
$729$		0			0
$730$	−3.43368	+	1.16326i	−0.127086	+	0.0430542i
$731$	19.5305	−	11.2759i	0.722361	−	0.417055i
$732$		0			0
$733$	17.9059	+	10.3380i	0.661371	+	0.381843i	0.792799	−	0.609483i	$-0.208623\pi$
$733$	17.9059	+	10.3380i	0.661371	+	0.381843i	−0.131428	+	0.991326i	$0.541956\pi$
$734$	−28.3497	+	32.2872i	−1.04641	+	1.19174i
$735$		0			0
$736$	−5.91288	+	11.8992i	−0.217952	+	0.438611i
$737$	3.19779	−	5.53873i	0.117792	−	0.204022i
$738$		0			0
$739$	9.30563	−	5.37261i	0.342313	−	0.197635i	−0.318981	−	0.947761i	$-0.603341\pi$
$739$	9.30563	−	5.37261i	0.342313	−	0.197635i	0.661294	+	0.750126i	$0.270007\pi$
$740$	0.269409	+	0.111975i	0.00990367	+	0.00411629i
$741$		0			0
$742$	25.4566	+	31.4738i	0.934543	+	1.15544i
$743$	−11.8708			−0.435498			−0.217749	−	0.976005i	$-0.569871\pi$
$743$	−11.8708			−0.435498			−0.217749	+	0.976005i	$0.569871\pi$
$744$		0			0
$745$	−2.02938	−	3.51499i	−0.0743507	−	0.128779i
$746$	1.55406	−	7.78815i	0.0568982	−	0.285145i
$747$		0			0
$748$	−19.9852	+	2.60650i	−0.730732	+	0.0953030i
$749$	−0.689416	−	0.573355i	−0.0251907	−	0.0209499i
$750$		0			0
$751$	−8.53229	+	14.7784i	−0.311348	+	0.539270i	−0.978654	−	0.205513i	$-0.934114\pi$
$751$	−8.53229	+	14.7784i	−0.311348	+	0.539270i	0.667307	+	0.744783i	$0.267447\pi$
$752$	−7.33212	−	7.36771i	−0.267375	−	0.268673i
$753$		0			0
$754$	−14.7897	−	43.6559i	−0.538610	−	1.58986i
$755$			4.57986i			0.166678i
$756$		0			0
$757$		−	46.3272i		−	1.68379i	−0.539641	−	0.841895i	$-0.681440\pi$
$757$		−	46.3272i		−	1.68379i	0.539641	−	0.841895i	$-0.318560\pi$
$758$	−10.8094	+	3.66199i	−0.392614	+	0.133010i
$759$		0			0
$760$	0.694120	−	10.3035i	0.0251784	−	0.373748i
$761$	−7.30474	+	12.6522i	−0.264796	+	0.458641i	−0.967510	−	0.252832i	$-0.918638\pi$
$761$	−7.30474	+	12.6522i	−0.264796	+	0.458641i	0.702714	+	0.711473i	$0.251971\pi$
$762$		0			0
$763$	19.3729	−	7.14753i	0.701346	−	0.258758i
$764$	0.0435595	+	0.333991i	0.00157593	+	0.0120834i
$765$		0			0
$766$	−35.5500	−	7.09370i	−1.28447	−	0.256306i
$767$	−7.48582	−	12.9658i	−0.270297	−	0.468169i
$768$		0			0
$769$	49.3177			1.77844			0.889221	−	0.457477i	$-0.151247\pi$
$769$	49.3177			1.77844			0.889221	+	0.457477i	$0.151247\pi$
$770$	−0.766452	−	4.85751i	−0.0276210	−	0.175053i
$771$		0			0
$772$	13.8832	+	5.77030i	0.499667	+	0.207678i
$773$	−0.902744	+	0.521200i	−0.0324695	+	0.0187462i	−0.516147	−	0.856500i	$-0.672634\pi$
$773$	−0.902744	+	0.521200i	−0.0324695	+	0.0187462i	0.483677	+	0.875246i	$0.339301\pi$
$774$		0			0
$775$	−2.03461	+	3.52404i	−0.0730853	+	0.126587i
$776$	−30.4123	−	20.4008i	−1.09174	−	0.732346i
$777$		0			0
$778$	−28.2116	−	24.7711i	−1.01143	−	0.888087i
$779$	−35.9467	−	20.7538i	−1.28792	−	0.743583i
$780$		0			0
$781$	18.1517	−	10.4799i	0.649517	−	0.374999i
$782$	4.49272	+	13.2615i	0.160659	+	0.474230i
$783$		0			0
$784$	15.9142	−	23.0378i	0.568363	−	0.822778i
$785$	−3.92334			−0.140030
$786$		0			0
$787$	−34.8899	+	20.1437i	−1.24369	+	0.718045i	−0.969844	−	0.243728i	$-0.921629\pi$
$787$	−34.8899	+	20.1437i	−1.24369	+	0.718045i	−0.273847	+	0.961773i	$0.588296\pi$
$788$	−1.63596	−	2.13738i	−0.0582788	−	0.0761411i
$789$		0			0
$790$	0.360161	+	0.316239i	0.0128140	+	0.0112513i
$791$	6.56399	+	1.12775i	0.233388	+	0.0400981i
$792$		0			0
$793$	−14.1536	+	24.5148i	−0.502610	+	0.870546i
$794$	9.43578	−	47.2873i	0.334863	−	1.67816i
$795$		0			0
$796$	−23.5677	−	9.79552i	−0.835336	−	0.347193i
$797$			32.2902i			1.14378i	0.820331	+	0.571889i	$0.193789\pi$
$797$			32.2902i			1.14378i	−0.820331	+	0.571889i	$0.806211\pi$
$798$		0			0
$799$	−10.9533			−0.387501
$800$	−14.6972	−	22.1406i	−0.519624	−	0.782790i
$801$		0			0
$802$	25.4540	+	5.07913i	0.898812	+	0.179350i
$803$	9.65489	+	5.57425i	0.340714	+	0.196711i
$804$		0			0
$805$	−3.20521	+	1.18254i	−0.112969	+	0.0416792i
$806$	3.65111	+	3.20585i	0.128605	+	0.112921i
$807$		0			0
$808$	−44.8270	−	3.01987i	−1.57701	−	0.106239i
$809$	20.8131	+	36.0493i	0.731749	+	1.26743i	0.956135	+	0.292926i	$0.0946291\pi$
$809$	20.8131	+	36.0493i	0.731749	+	1.26743i	−0.224386	+	0.974500i	$0.572038\pi$
$810$		0			0
$811$		−	18.7227i		−	0.657444i	−0.944427	−	0.328722i	$-0.893382\pi$
$811$		−	18.7227i		−	0.657444i	0.944427	−	0.328722i	$-0.106618\pi$
$812$	20.1998	+	38.5045i	0.708874	+	1.35124i
$813$		0			0
$814$	−0.287874	−	0.849739i	−0.0100900	−	0.0297833i
$815$	2.00916	+	3.47997i	0.0703778	+	0.121898i
$816$		0			0
$817$	17.7670	−	30.7734i	0.621589	−	1.07662i
$818$	10.9631	−	12.4857i	0.383315	−	0.436554i
$819$		0			0
$820$	6.81369	−	0.888650i	0.237944	−	0.0310330i
$821$	−16.2308	−	9.37088i	−0.566460	−	0.327046i	0.189274	−	0.981924i	$-0.439386\pi$
$821$	−16.2308	−	9.37088i	−0.566460	−	0.327046i	−0.755734	+	0.654878i	$0.772720\pi$
$822$		0			0
$823$	10.2211	+	17.7035i	0.356286	+	0.617106i	0.987337	−	0.158636i	$-0.0507095\pi$
$823$	10.2211	+	17.7035i	0.356286	+	0.617106i	−0.631051	+	0.775741i	$0.717376\pi$
$824$	47.6802	−	23.4057i	1.66102	−	0.815378i
$825$		0			0
$826$	8.88168	+	10.9810i	0.309033	+	0.382079i
$827$		−	48.6254i		−	1.69087i	−0.534079	−	0.845435i	$-0.679341\pi$
$827$		−	48.6254i		−	1.69087i	0.534079	−	0.845435i	$-0.320659\pi$
$828$		0			0
$829$	6.06173	−	3.49974i	0.210532	−	0.121551i	−0.391026	−	0.920379i	$-0.627880\pi$
$829$	6.06173	−	3.49974i	0.210532	−	0.121551i	0.601559	+	0.798829i	$0.294547\pi$
$830$	−0.838258	−	0.167267i	−0.0290964	−	0.00580593i
$831$		0			0
$832$	−29.3598	+	12.0365i	−1.01787	+	0.417290i
$833$	−5.37827	−	29.0113i	−0.186346	−	1.00518i
$834$		0			0
$835$	0.899200	+	0.519154i	0.0311181	+	0.0179660i
$836$	−25.2175	+	19.3016i	−0.872167	+	0.667562i
$837$		0			0
$838$	14.8465	−	5.02968i	0.512863	−	0.173748i
$839$	−40.1867			−1.38740			−0.693700	−	0.720264i	$-0.744021\pi$
$839$	−40.1867			−1.38740			−0.693700	+	0.720264i	$0.744021\pi$
$840$		0			0
$841$	−38.5224			−1.32836
$842$	0.183864	−	0.0622894i	0.00633638	−	0.00214663i
$843$		0			0
$844$	−10.2883	−	13.4416i	−0.354137	−	0.462679i
$845$	1.30086	+	0.751051i	0.0447509	+	0.0258369i
$846$		0			0
$847$	8.93974	−	10.7494i	0.307173	−	0.369352i
$848$	11.0992	+	41.8275i	0.381148	+	1.43636i
$849$		0			0
$850$	−27.4623	−	5.47987i	−0.941950	−	0.187958i
$851$	−0.539788	+	0.311647i	−0.0185037	+	0.0106831i
$852$		0			0
$853$			30.8071i			1.05482i	0.849612	+	0.527408i	$0.176836\pi$
$853$			30.8071i			1.05482i	−0.849612	+	0.527408i	$0.823164\pi$
$854$	9.58412	−	24.9241i	0.327962	−	0.852884i
$855$		0			0
$856$	−0.422411	−	0.860500i	−0.0144377	−	0.0294113i
$857$	6.84889	+	11.8626i	0.233954	+	0.405220i	0.958968	−	0.283514i	$-0.0915002\pi$
$857$	6.84889	+	11.8626i	0.233954	+	0.405220i	−0.725014	+	0.688734i	$0.758167\pi$
$858$		0			0
$859$	−7.52869	−	4.34669i	−0.256876	−	0.148307i	0.366033	−	0.930602i	$-0.380716\pi$
$859$	−7.52869	−	4.34669i	−0.256876	−	0.148307i	−0.622908	+	0.782295i	$0.714049\pi$
$860$	0.760758	+	5.83309i	0.0259416	+	0.198907i
$861$		0			0
$862$	−11.6266	+	13.2414i	−0.396002	+	0.451003i
$863$	−0.296174	+	0.512989i	−0.0100819	+	0.0174623i	−0.871022	−	0.491243i	$-0.836543\pi$
$863$	−0.296174	+	0.512989i	−0.0100819	+	0.0174623i	0.860940	+	0.508706i	$0.169876\pi$
$864$		0			0
$865$	4.54981	+	7.88049i	0.154698	+	0.267945i
$866$	−6.42377	−	18.9615i	−0.218289	−	0.644338i
$867$		0			0
$868$	−3.87348	−	2.45042i	−0.131474	−	0.0831727i
$869$		−	1.47389i		−	0.0499984i
$870$		0			0
$871$	−5.30533	−	9.18911i	−0.179764	−	0.311361i
$872$	22.0252	+	1.48377i	0.745867	+	0.0502469i
$873$		0			0
$874$	16.5784	+	14.5566i	0.560772	+	0.492385i
$875$	2.38839	−	13.9015i	0.0807422	−	0.469955i
$876$		0			0
$877$	13.2310	+	7.63892i	0.446779	+	0.257948i	0.706469	−	0.707744i	$-0.250287\pi$
$877$	13.2310	+	7.63892i	0.446779	+	0.257948i	−0.259690	+	0.965692i	$0.583620\pi$
$878$	7.57089	+	1.51071i	0.255505	+	0.0509839i
$879$		0			0
$880$	1.37294	−	5.07470i	0.0462817	−	0.171068i
$881$	43.1280			1.45302			0.726509	−	0.687157i	$-0.241141\pi$
$881$	43.1280			1.45302			0.726509	+	0.687157i	$0.241141\pi$
$882$		0			0
$883$		−	20.2255i		−	0.680642i	−0.940309	−	0.340321i	$-0.889464\pi$
$883$		−	20.2255i		−	0.680642i	0.940309	−	0.340321i	$-0.110536\pi$
$884$	−12.8334	+	30.8768i	−0.431633	+	1.03850i
$885$		0			0
$886$	−9.22512	+	46.2316i	−0.309924	+	1.55318i
$887$	10.7820	−	18.6750i	0.362024	−	0.627044i	−0.626270	−	0.779606i	$-0.715419\pi$
$887$	10.7820	−	18.6750i	0.362024	−	0.627044i	0.988294	+	0.152563i	$0.0487525\pi$
$888$		0			0
$889$	13.8258	+	2.37538i	0.463701	+	0.0796678i
$890$	3.73633	+	3.28067i	0.125242	+	0.109968i
$891$		0			0
$892$	9.21400	−	7.05245i	0.308508	−	0.236133i
$893$	−14.9465	+	8.62934i	−0.500164	+	0.288770i
$894$		0			0
$895$	−3.04668			−0.101839
$896$	25.5880	−	15.5324i	0.854835	−	0.518901i
$897$		0			0
$898$	12.2390	+	36.1268i	0.408421	+	1.20557i
$899$	6.16413	−	3.55886i	0.205585	−	0.118695i
$900$		0			0
$901$	39.4926	+	22.8011i	1.31569	+	0.759614i
$902$	−15.8783	−	13.9419i	−0.528689	−	0.464214i
$903$		0			0
$904$	5.91288	+	3.96641i	0.196659	+	0.131921i
$905$	−2.74447	+	4.75356i	−0.0912293	+	0.158014i
$906$		0			0
$907$	−27.3384	+	15.7838i	−0.907757	+	0.524094i	−0.879709	−	0.475513i	$-0.842263\pi$
$907$	−27.3384	+	15.7838i	−0.907757	+	0.524094i	−0.0280482	+	0.999607i	$0.508929\pi$
$908$	−8.76836	+	21.0964i	−0.290988	+	0.700110i
$909$		0			0
$910$	−7.61503	−	2.92823i	−0.252436	−	0.0970699i
$911$	−15.6873			−0.519744			−0.259872	−	0.965643i	$-0.583680\pi$
$911$	−15.6873			−0.519744			−0.259872	+	0.965643i	$0.583680\pi$
$912$		0			0
$913$	1.31429	+	2.27641i	0.0434965	+	0.0753382i
$914$	−26.4801	−	5.28387i	−0.875883	−	0.174775i
$915$		0			0
$916$	36.6997	−	4.78642i	1.21259	−	0.158148i
$917$	20.4217	+	16.9838i	0.674385	+	0.560855i
$918$		0			0
$919$	−7.79407	+	13.4997i	−0.257103	+	0.445315i	−0.965464	−	0.260535i	$-0.916101\pi$
$919$	−7.79407	+	13.4997i	−0.257103	+	0.445315i	0.708362	+	0.705849i	$0.249434\pi$
$920$	−3.64402	−	0.245487i	−0.120140	−	0.00809347i
$921$		0			0
$922$	−25.3391	+	8.58436i	−0.834499	+	0.282711i
$923$		−	34.7735i		−	1.14458i
$924$		0			0
$925$		−	1.24659i		−	0.0409875i
$926$	0.390413	+	1.15241i	0.0128298	+	0.0378706i
$927$		0			0
$928$	2.89979	+	46.3930i	0.0951903	+	1.52292i
$929$	20.6926	−	35.8406i	0.678901	−	1.17589i	−0.296411	−	0.955060i	$-0.595790\pi$
$929$	20.6926	−	35.8406i	0.678901	−	1.17589i	0.975312	−	0.220830i	$-0.0708767\pi$
$930$		0			0
$931$	−30.1949	−	35.3505i	−0.989599	−	1.15857i
$932$	−2.85844	−	21.9170i	−0.0936315	−	0.717916i
$933$		0			0
$934$	5.17166	−	25.9177i	0.169222	−	0.848053i
$935$	−2.76992	−	4.79764i	−0.0905860	−	0.156900i
$936$		0			0
$937$	−23.9308			−0.781785			−0.390892	−	0.920436i	$-0.627834\pi$
$937$	−23.9308			−0.781785			−0.390892	+	0.920436i	$0.627834\pi$
$938$	6.29460	+	7.78246i	0.205526	+	0.254106i
$939$		0			0
$940$	1.09656	−	2.63828i	0.0357657	−	0.0860513i
$941$	33.3285	−	19.2422i	1.08648	−	0.627278i	0.153841	−	0.988096i	$-0.450836\pi$
$941$	33.3285	−	19.2422i	1.08648	−	0.627278i	0.932636	+	0.360818i	$0.117502\pi$
$942$		0			0
$943$	−7.33994	+	12.7132i	−0.239021	+	0.413997i
$944$	3.87244	+	14.5934i	0.126037	+	0.474974i
$945$		0			0
$946$	11.9354	−	13.5931i	0.388054	−	0.441951i
$947$	8.36198	+	4.82779i	0.271728	+	0.156882i	0.629673	−	0.776861i	$-0.283189\pi$
$947$	8.36198	+	4.82779i	0.271728	+	0.156882i	−0.357945	+	0.933743i	$0.616522\pi$
$948$		0			0
$949$	16.0181	−	9.24804i	0.519969	−	0.300204i
$950$	−41.7912	+	14.1580i	−1.35588	+	0.459346i
$951$		0			0
$952$	7.41853	−	30.6581i	0.240436	−	0.993634i
$953$	19.3777			0.627704			0.313852	−	0.949472i	$-0.398380\pi$
$953$	19.3777			0.627704			0.313852	+	0.949472i	$0.398380\pi$
$954$		0			0
$955$	−0.0801777	+	0.0462906i	−0.00259449	+	0.00149793i
$956$	−35.9098	+	27.4856i	−1.16141	+	0.888947i
$957$		0			0
$958$	17.3065	−	19.7101i	0.559146	−	0.636806i
$959$	−2.97606	−	8.06641i	−0.0961020	−	0.260478i
$960$		0			0
$961$	15.1249	−	26.1970i	0.487898	−	0.845065i
$962$	−1.45970	−	0.291271i	−0.0470626	−	0.00939094i
$963$		0			0
$964$	25.7256	+	10.6924i	0.828566	+	0.344379i
$965$			4.13255i			0.133031i
$966$		0			0
$967$	34.8845			1.12181			0.560905	−	0.827880i	$-0.310453\pi$
$967$	34.8845			1.12181			0.560905	+	0.827880i	$0.310453\pi$
$968$	13.4169	−	6.58622i	0.431235	−	0.211689i
$969$		0			0
$970$	1.96975	−	9.87138i	0.0632449	−	0.316951i
$971$	38.4767	+	22.2146i	1.23478	+	0.712899i	0.968022	−	0.250865i	$-0.0807151\pi$
$971$	38.4767	+	22.2146i	1.23478	+	0.712899i	0.266755	+	0.963764i	$0.414048\pi$
$972$		0			0
$973$	−6.87002	+	39.9865i	−0.220243	+	1.28191i
$974$	−21.3843	+	24.3544i	−0.685197	+	0.780365i
$975$		0			0
$976$	20.2346	−	20.1368i	0.647693	−	0.644565i
$977$	−13.5436	−	23.4581i	−0.433297	−	0.750492i	0.563858	−	0.825872i	$-0.309316\pi$
$977$	−13.5436	−	23.4581i	−0.433297	−	0.750492i	−0.997155	+	0.0753795i	$0.975983\pi$
$978$		0			0
$979$		−	15.2902i		−	0.488678i
$980$	7.52627	+	1.60893i	0.240418	+	0.0513954i
$981$		0			0
$982$	−33.2163	+	11.2530i	−1.05997	+	0.359098i
$983$	12.5444	+	21.7275i	0.400103	+	0.692999i	0.993738	−	0.111736i	$-0.0356410\pi$
$983$	12.5444	+	21.7275i	0.400103	+	0.692999i	−0.593635	+	0.804735i	$0.702308\pi$
$984$		0			0
$985$	0.369920	−	0.640721i	0.0117866	−	0.0204151i
$986$	36.8079	+	32.3191i	1.17220	+	1.02925i
$987$		0			0
$988$	6.81369	+	52.2437i	0.216772	+	1.66209i
$989$	−10.8835	−	6.28360i	−0.346076	−	0.199807i
$990$		0			0
$991$	−8.81972	−	15.2762i	−0.280168	−	0.485265i	0.691258	−	0.722608i	$-0.257057\pi$
$991$	−8.81972	−	15.2762i	−0.280168	−	0.485265i	−0.971426	+	0.237343i	$0.923723\pi$
$992$	−2.70993	−	4.08238i	−0.0860403	−	0.129616i
$993$		0			0
$994$	5.11265	+	32.4023i	0.162164	+	1.02774i
$995$		−	7.01530i		−	0.222400i
$996$		0			0
$997$	26.5529	−	15.3303i	0.840939	−	0.485516i	−0.0166442	−	0.999861i	$-0.505298\pi$
$997$	26.5529	−	15.3303i	0.840939	−	0.485516i	0.857583	+	0.514345i	$0.171965\pi$
$998$	−10.8553	+	54.4014i	−0.343620	+	1.72205i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.c.37.4		12
3.2	odd	2		56.2.p.a.37.3	✓	12
4.3	odd	2		2016.2.cr.c.1297.3		12
7.4	even	3	inner	504.2.cj.c.109.1		12
8.3	odd	2		2016.2.cr.c.1297.4		12
8.5	even	2	inner	504.2.cj.c.37.1		12
12.11	even	2		224.2.t.a.177.2		12
21.2	odd	6		392.2.b.e.197.2		6
21.5	even	6		392.2.b.f.197.2		6
21.11	odd	6		56.2.p.a.53.6	yes	12
21.17	even	6		392.2.p.g.165.6		12
21.20	even	2		392.2.p.g.373.3		12
24.5	odd	2		56.2.p.a.37.6	yes	12
24.11	even	2		224.2.t.a.177.5		12
28.11	odd	6		2016.2.cr.c.1873.4		12
56.11	odd	6		2016.2.cr.c.1873.3		12
56.53	even	6	inner	504.2.cj.c.109.4		12
84.11	even	6		224.2.t.a.81.5		12
84.23	even	6		1568.2.b.f.785.2		6
84.47	odd	6		1568.2.b.e.785.5		6
84.59	odd	6		1568.2.t.g.753.2		12
84.83	odd	2		1568.2.t.g.177.5		12
168.5	even	6		392.2.b.f.197.1		6
168.11	even	6		224.2.t.a.81.2		12
168.53	odd	6		56.2.p.a.53.3	yes	12
168.59	odd	6		1568.2.t.g.753.5		12
168.83	odd	2		1568.2.t.g.177.2		12
168.101	even	6		392.2.p.g.165.3		12
168.107	even	6		1568.2.b.f.785.5		6
168.125	even	2		392.2.p.g.373.6		12
168.131	odd	6		1568.2.b.e.785.2		6
168.149	odd	6		392.2.b.e.197.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.3	✓	12	3.2	odd	2
56.2.p.a.37.6	yes	12	24.5	odd	2
56.2.p.a.53.3	yes	12	168.53	odd	6
56.2.p.a.53.6	yes	12	21.11	odd	6
224.2.t.a.81.2		12	168.11	even	6
224.2.t.a.81.5		12	84.11	even	6
224.2.t.a.177.2		12	12.11	even	2
224.2.t.a.177.5		12	24.11	even	2
392.2.b.e.197.1		6	168.149	odd	6
392.2.b.e.197.2		6	21.2	odd	6
392.2.b.f.197.1		6	168.5	even	6
392.2.b.f.197.2		6	21.5	even	6
392.2.p.g.165.3		12	168.101	even	6
392.2.p.g.165.6		12	21.17	even	6
392.2.p.g.373.3		12	21.20	even	2
392.2.p.g.373.6		12	168.125	even	2
504.2.cj.c.37.1		12	8.5	even	2	inner
504.2.cj.c.37.4		12	1.1	even	1	trivial
504.2.cj.c.109.1		12	7.4	even	3	inner
504.2.cj.c.109.4		12	56.53	even	6	inner
1568.2.b.e.785.2		6	168.131	odd	6
1568.2.b.e.785.5		6	84.47	odd	6
1568.2.b.f.785.2		6	84.23	even	6
1568.2.b.f.785.5		6	168.107	even	6
1568.2.t.g.177.2		12	168.83	odd	2
1568.2.t.g.177.5		12	84.83	odd	2
1568.2.t.g.753.2		12	84.59	odd	6
1568.2.t.g.753.5		12	168.59	odd	6
2016.2.cr.c.1297.3		12	4.3	odd	2
2016.2.cr.c.1297.4		12	8.3	odd	2
2016.2.cr.c.1873.3		12	56.11	odd	6
2016.2.cr.c.1873.4		12	28.11	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.453773 + 1.33944i) q^{2} +(-1.58818 + 1.21560i) q^{4} +(-0.476087 - 0.274869i) q^{5} +(-2.60755 - 0.447998i) q^{7} +(-2.34889 - 1.57566i) q^{8} +(0.152134 - 0.762416i) q^{10} +(-2.07045 + 1.19538i) q^{11} +3.96641i q^{13} +(-0.583170 - 3.69593i) q^{14} +(1.04463 - 3.86119i) q^{16} +(-2.10755 - 3.65038i) q^{17} +(-5.75174 - 3.32077i) q^{19} +(1.09024 - 0.142191i) q^{20} +(-2.54065 - 2.23081i) q^{22} +(-1.17445 + 2.03420i) q^{23} +(-2.34889 - 4.06840i) q^{25} +(-5.31275 + 1.79985i) q^{26} +(4.68584 - 2.45823i) q^{28} +8.21720i q^{29} +(-0.433099 - 0.750150i) q^{31} +(5.64584 - 0.352893i) q^{32} +(3.93310 - 4.47937i) q^{34} +(1.11828 + 0.930019i) q^{35} +(0.229805 + 0.132678i) q^{37} +(1.83797 - 9.21097i) q^{38} +(0.685178 + 1.39579i) q^{40} +6.24970 q^{41} +5.35027i q^{43} +(1.83515 - 4.41531i) q^{44} +(-3.25762 - 0.650030i) q^{46} +(1.29930 - 2.25045i) q^{47} +(6.59859 + 2.33635i) q^{49} +(4.38350 - 4.99233i) q^{50} +(-4.82157 - 6.29937i) q^{52} +(-9.36933 + 5.40939i) q^{53} +1.31429 q^{55} +(5.41896 + 5.16090i) q^{56} +(-11.0064 + 3.72875i) q^{58} +(-3.26891 + 1.88730i) q^{59} +(6.18061 + 3.56837i) q^{61} +(0.808249 - 0.920507i) q^{62} +(3.03461 + 7.40210i) q^{64} +(1.09024 - 1.88835i) q^{65} +(-2.31673 + 1.33757i) q^{67} +(7.78456 + 3.23552i) q^{68} +(-0.738257 + 1.91988i) q^{70} -8.76700 q^{71} +(-2.33159 - 4.03843i) q^{73} +(-0.0734343 + 0.368015i) q^{74} +(13.1715 - 1.71785i) q^{76} +(5.93432 - 2.18944i) q^{77} +(-0.308249 + 0.533903i) q^{79} +(-1.55865 + 1.55112i) q^{80} +(2.83595 + 8.37108i) q^{82} -1.09948i q^{83} +2.31720i q^{85} +(-7.16634 + 2.42781i) q^{86} +(6.74677 + 0.454511i) q^{88} +(-3.19779 + 5.53873i) q^{89} +(1.77694 - 10.3426i) q^{91} +(-0.607546 - 4.65834i) q^{92} +(3.60392 + 0.719132i) q^{94} +(1.82555 + 3.16195i) q^{95} +12.9475 q^{97} +(-0.135129 + 9.89857i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8} - 8 q^{10} + 16 q^{14} + 8 q^{16} + 2 q^{17} - 8 q^{20} + 12 q^{22} - 2 q^{23} - 4 q^{25} + 2 q^{26} + 26 q^{28} + 10 q^{31} + 12 q^{32} + 32 q^{34} - 18 q^{38} + 10 q^{40}+ \cdots - 52 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8 - 8 * q^10 + 16 * q^14 + 8 * q^16 + 2 * q^17 - 8 * q^20 + 12 * q^22 - 2 * q^23 - 4 * q^25 + 2 * q^26 + 26 * q^28 + 10 * q^31 + 12 * q^32 + 32 * q^34 - 18 * q^38 + 10 * q^40 + 8 * q^41 + 30 * q^44 - 4 * q^46 - 30 * q^47 - 12 * q^49 + 16 * q^50 - 32 * q^52 + 4 * q^55 + 40 * q^56 - 22 * q^58 + 28 * q^62 + 24 * q^64 - 8 * q^65 - 4 * q^68 - 48 * q^70 - 32 * q^71 - 10 * q^73 - 18 * q^74 + 52 * q^76 - 22 * q^79 - 36 * q^80 - 26 * q^82 - 40 * q^86 - 14 * q^88 + 10 * q^89 + 20 * q^92 + 42 * q^94 + 34 * q^95 + 40 * q^97 - 52 * q^98

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