LMFDB - Embedded newform 390.2.p.d.281.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [390,2,Mod(161,390)] 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("390.161"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(390, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.p (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,4,0,0,-4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			281.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	390.281
Dual form			390.2.p.d.161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.00000 + 1.41421i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.70711 - 0.292893i) q^{6} +(0.707107 + 0.707107i) q^{8} +(-1.00000 + 2.82843i) q^{9} -1.00000i q^{10} +(1.41421 + 1.41421i) q^{11} +(1.41421 - 1.00000i) q^{12} +(-3.00000 + 2.00000i) q^{13} +(-1.70711 - 0.292893i) q^{15} -1.00000 q^{16} -4.24264 q^{17} +(-1.29289 - 2.70711i) q^{18} +(6.00000 + 6.00000i) q^{19} +(0.707107 + 0.707107i) q^{20} -2.00000 q^{22} -1.41421 q^{23} +(-0.292893 + 1.70711i) q^{24} -1.00000i q^{25} +(0.707107 - 3.53553i) q^{26} +(-5.00000 + 1.41421i) q^{27} +1.41421i q^{29} +(1.41421 - 1.00000i) q^{30} +(-3.00000 - 3.00000i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.585786 + 3.41421i) q^{33} +(3.00000 - 3.00000i) q^{34} +(2.82843 + 1.00000i) q^{36} +(5.00000 - 5.00000i) q^{37} -8.48528 q^{38} +(-5.82843 - 2.24264i) q^{39} -1.00000 q^{40} +(7.07107 - 7.07107i) q^{41} +4.00000i q^{43} +(1.41421 - 1.41421i) q^{44} +(-1.29289 - 2.70711i) q^{45} +(1.00000 - 1.00000i) q^{46} +(-4.24264 - 4.24264i) q^{47} +(-1.00000 - 1.41421i) q^{48} +7.00000i q^{49} +(0.707107 + 0.707107i) q^{50} +(-4.24264 - 6.00000i) q^{51} +(2.00000 + 3.00000i) q^{52} +11.3137i q^{53} +(2.53553 - 4.53553i) q^{54} -2.00000 q^{55} +(-2.48528 + 14.4853i) q^{57} +(-1.00000 - 1.00000i) q^{58} +(-2.82843 - 2.82843i) q^{59} +(-0.292893 + 1.70711i) q^{60} +2.00000 q^{61} +4.24264 q^{62} +1.00000i q^{64} +(0.707107 - 3.53553i) q^{65} +(-2.00000 - 2.82843i) q^{66} +(5.00000 + 5.00000i) q^{67} +4.24264i q^{68} +(-1.41421 - 2.00000i) q^{69} +(5.65685 - 5.65685i) q^{71} +(-2.70711 + 1.29289i) q^{72} +(6.00000 - 6.00000i) q^{73} +7.07107i q^{74} +(1.41421 - 1.00000i) q^{75} +(6.00000 - 6.00000i) q^{76} +(5.70711 - 2.53553i) q^{78} +8.00000 q^{79} +(0.707107 - 0.707107i) q^{80} +(-7.00000 - 5.65685i) q^{81} +10.0000i q^{82} +(5.65685 - 5.65685i) q^{83} +(3.00000 - 3.00000i) q^{85} +(-2.82843 - 2.82843i) q^{86} +(-2.00000 + 1.41421i) q^{87} +2.00000i q^{88} +(4.24264 + 4.24264i) q^{89} +(2.82843 + 1.00000i) q^{90} +1.41421i q^{92} +(1.24264 - 7.24264i) q^{93} +6.00000 q^{94} -8.48528 q^{95} +(1.70711 + 0.292893i) q^{96} +(10.0000 + 10.0000i) q^{97} +(-4.94975 - 4.94975i) q^{98} +(-5.41421 + 2.58579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{6} - 4 q^{9} - 12 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} + 24 q^{19} - 8 q^{22} - 4 q^{24} - 20 q^{27} - 12 q^{31} - 8 q^{33} + 12 q^{34} + 20 q^{37} - 12 q^{39} - 4 q^{40} - 8 q^{45}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^6 - 4 * q^9 - 12 * q^13 - 4 * q^15 - 4 * q^16 - 8 * q^18 + 24 * q^19 - 8 * q^22 - 4 * q^24 - 20 * q^27 - 12 * q^31 - 8 * q^33 + 12 * q^34 + 20 * q^37 - 12 * q^39 - 4 * q^40 - 8 * q^45 + 4 * q^46 - 4 * q^48 + 8 * q^52 - 4 * q^54 - 8 * q^55 + 24 * q^57 - 4 * q^58 - 4 * q^60 + 8 * q^61 - 8 * q^66 + 20 * q^67 - 8 * q^72 + 24 * q^73 + 24 * q^76 + 20 * q^78 + 32 * q^79 - 28 * q^81 + 12 * q^85 - 8 * q^87 - 12 * q^93 + 24 * q^94 + 4 * q^96 + 40 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$4$		−	1.00000i		−	0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−1.70711	−	0.292893i	−0.696923	−	0.119573i
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$		−	1.00000i		−	0.316228i
$11$	1.41421	+	1.41421i	0.426401	+	0.426401i	0.887401	−	0.460999i	$-0.152509\pi$
$11$	1.41421	+	1.41421i	0.426401	+	0.426401i	−0.460999	+	0.887401i	$0.652509\pi$
$12$	1.41421	−	1.00000i	0.408248	−	0.288675i
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$14$		0			0
$15$	−1.70711	−	0.292893i	−0.440773	−	0.0756247i
$16$	−1.00000			−0.250000
$17$	−4.24264			−1.02899			−0.514496	−	0.857493i	$-0.672021\pi$
$17$	−4.24264			−1.02899			−0.514496	+	0.857493i	$0.672021\pi$
$18$	−1.29289	−	2.70711i	−0.304738	−	0.638071i
$19$	6.00000	+	6.00000i	1.37649	+	1.37649i	0.850469	+	0.526026i	$0.176318\pi$
$19$	6.00000	+	6.00000i	1.37649	+	1.37649i	0.526026	+	0.850469i	$0.323682\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$		0			0
$22$	−2.00000			−0.426401
$23$	−1.41421			−0.294884			−0.147442	−	0.989071i	$-0.547104\pi$
$23$	−1.41421			−0.294884			−0.147442	+	0.989071i	$0.547104\pi$
$24$	−0.292893	+	1.70711i	−0.0597866	+	0.348462i
$25$		−	1.00000i		−	0.200000i
$26$	0.707107	−	3.53553i	0.138675	−	0.693375i
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$		0			0
$29$			1.41421i			0.262613i	0.991342	+	0.131306i	$0.0419172\pi$
$29$			1.41421i			0.262613i	−0.991342	+	0.131306i	$0.958083\pi$
$30$	1.41421	−	1.00000i	0.258199	−	0.182574i
$31$	−3.00000	−	3.00000i	−0.538816	−	0.538816i	0.384365	−	0.923181i	$-0.374420\pi$
$31$	−3.00000	−	3.00000i	−0.538816	−	0.538816i	−0.923181	+	0.384365i	$0.874420\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.585786	+	3.41421i	−0.101972	+	0.594338i
$34$	3.00000	−	3.00000i	0.514496	−	0.514496i
$35$		0			0
$36$	2.82843	+	1.00000i	0.471405	+	0.166667i
$37$	5.00000	−	5.00000i	0.821995	−	0.821995i	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	5.00000	−	5.00000i	0.821995	−	0.821995i	0.986394	+	0.164399i	$0.0525685\pi$
$38$	−8.48528			−1.37649
$39$	−5.82843	−	2.24264i	−0.933295	−	0.359110i
$40$	−1.00000			−0.158114
$41$	7.07107	−	7.07107i	1.10432	−	1.10432i	0.110432	−	0.993884i	$-0.464777\pi$
$41$	7.07107	−	7.07107i	1.10432	−	1.10432i	0.993884	−	0.110432i	$-0.0352233\pi$
$42$		0			0
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	1.41421	−	1.41421i	0.213201	−	0.213201i
$45$	−1.29289	−	2.70711i	−0.192733	−	0.403552i
$46$	1.00000	−	1.00000i	0.147442	−	0.147442i
$47$	−4.24264	−	4.24264i	−0.618853	−	0.618853i	0.326384	−	0.945237i	$-0.394170\pi$
$47$	−4.24264	−	4.24264i	−0.618853	−	0.618853i	−0.945237	+	0.326384i	$0.894170\pi$
$48$	−1.00000	−	1.41421i	−0.144338	−	0.204124i
$49$			7.00000i			1.00000i
$50$	0.707107	+	0.707107i	0.100000	+	0.100000i
$51$	−4.24264	−	6.00000i	−0.594089	−	0.840168i
$52$	2.00000	+	3.00000i	0.277350	+	0.416025i
$53$			11.3137i			1.55406i	0.629465	+	0.777029i	$0.283274\pi$
$53$			11.3137i			1.55406i	−0.629465	+	0.777029i	$0.716726\pi$
$54$	2.53553	−	4.53553i	0.345042	−	0.617208i
$55$	−2.00000			−0.269680
$56$		0			0
$57$	−2.48528	+	14.4853i	−0.329184	+	1.91862i
$58$	−1.00000	−	1.00000i	−0.131306	−	0.131306i
$59$	−2.82843	−	2.82843i	−0.368230	−	0.368230i	0.498601	−	0.866831i	$-0.333847\pi$
$59$	−2.82843	−	2.82843i	−0.368230	−	0.368230i	−0.866831	+	0.498601i	$0.833847\pi$
$60$	−0.292893	+	1.70711i	−0.0378124	+	0.220387i
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	4.24264			0.538816
$63$		0			0
$64$			1.00000i			0.125000i
$65$	0.707107	−	3.53553i	0.0877058	−	0.438529i
$66$	−2.00000	−	2.82843i	−0.246183	−	0.348155i
$67$	5.00000	+	5.00000i	0.610847	+	0.610847i	0.943167	−	0.332320i	$-0.107831\pi$
$67$	5.00000	+	5.00000i	0.610847	+	0.610847i	−0.332320	+	0.943167i	$0.607831\pi$
$68$			4.24264i			0.514496i
$69$	−1.41421	−	2.00000i	−0.170251	−	0.240772i
$70$		0			0
$71$	5.65685	−	5.65685i	0.671345	−	0.671345i	−0.286681	−	0.958026i	$-0.592552\pi$
$71$	5.65685	−	5.65685i	0.671345	−	0.671345i	0.958026	+	0.286681i	$0.0925520\pi$
$72$	−2.70711	+	1.29289i	−0.319036	+	0.152369i
$73$	6.00000	−	6.00000i	0.702247	−	0.702247i	−0.262646	−	0.964892i	$-0.584595\pi$
$73$	6.00000	−	6.00000i	0.702247	−	0.702247i	0.964892	+	0.262646i	$0.0845950\pi$
$74$			7.07107i			0.821995i
$75$	1.41421	−	1.00000i	0.163299	−	0.115470i
$76$	6.00000	−	6.00000i	0.688247	−	0.688247i
$77$		0			0
$78$	5.70711	−	2.53553i	0.646203	−	0.287093i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$			10.0000i			1.10432i
$83$	5.65685	−	5.65685i	0.620920	−	0.620920i	−0.324846	−	0.945767i	$-0.605313\pi$
$83$	5.65685	−	5.65685i	0.620920	−	0.620920i	0.945767	+	0.324846i	$0.105313\pi$
$84$		0			0
$85$	3.00000	−	3.00000i	0.325396	−	0.325396i
$86$	−2.82843	−	2.82843i	−0.304997	−	0.304997i
$87$	−2.00000	+	1.41421i	−0.214423	+	0.151620i
$88$			2.00000i			0.213201i
$89$	4.24264	+	4.24264i	0.449719	+	0.449719i	0.895261	−	0.445542i	$-0.146989\pi$
$89$	4.24264	+	4.24264i	0.449719	+	0.449719i	−0.445542	+	0.895261i	$0.646989\pi$
$90$	2.82843	+	1.00000i	0.298142	+	0.105409i
$91$		0			0
$92$			1.41421i			0.147442i
$93$	1.24264	−	7.24264i	0.128856	−	0.751027i
$94$	6.00000			0.618853
$95$	−8.48528			−0.870572
$96$	1.70711	+	0.292893i	0.174231	+	0.0298933i
$97$	10.0000	+	10.0000i	1.01535	+	1.01535i	0.999880	+	0.0154658i	$0.00492310\pi$
$97$	10.0000	+	10.0000i	1.01535	+	1.01535i	0.0154658	+	0.999880i	$0.495077\pi$
$98$	−4.94975	−	4.94975i	−0.500000	−	0.500000i
$99$	−5.41421	+	2.58579i	−0.544149	+	0.259881i
$100$	−1.00000			−0.100000
$101$	15.5563			1.54791			0.773957	−	0.633238i	$-0.218274\pi$
$101$	15.5563			1.54791			0.773957	+	0.633238i	$0.218274\pi$
$102$	7.24264	+	1.24264i	0.717128	+	0.123040i
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$	−3.53553	−	0.707107i	−0.346688	−	0.0693375i
$105$		0			0
$106$	−8.00000	−	8.00000i	−0.777029	−	0.777029i
$107$		−	11.3137i		−	1.09374i	−0.837218	−	0.546869i	$-0.815820\pi$
$107$		−	11.3137i		−	1.09374i	0.837218	−	0.546869i	$-0.184180\pi$
$108$	1.41421	+	5.00000i	0.136083	+	0.481125i
$109$	2.00000	+	2.00000i	0.191565	+	0.191565i	0.796372	−	0.604807i	$-0.206750\pi$
$109$	2.00000	+	2.00000i	0.191565	+	0.191565i	−0.604807	+	0.796372i	$0.706750\pi$
$110$	1.41421	−	1.41421i	0.134840	−	0.134840i
$111$	12.0711	+	2.07107i	1.14574	+	0.196577i
$112$		0			0
$113$			7.07107i			0.665190i	0.943070	+	0.332595i	$0.107924\pi$
$113$			7.07107i			0.665190i	−0.943070	+	0.332595i	$0.892076\pi$
$114$	−8.48528	−	12.0000i	−0.794719	−	1.12390i
$115$	1.00000	−	1.00000i	0.0932505	−	0.0932505i
$116$	1.41421			0.131306
$117$	−2.65685	−	10.4853i	−0.245626	−	0.969365i
$118$	4.00000			0.368230
$119$		0			0
$120$	−1.00000	−	1.41421i	−0.0912871	−	0.129099i
$121$		−	7.00000i		−	0.636364i
$122$	−1.41421	+	1.41421i	−0.128037	+	0.128037i
$123$	17.0711	+	2.92893i	1.53925	+	0.264093i
$124$	−3.00000	+	3.00000i	−0.269408	+	0.269408i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$		−	4.00000i		−	0.354943i	−0.984126	−	0.177471i	$-0.943208\pi$
$127$		−	4.00000i		−	0.354943i	0.984126	−	0.177471i	$-0.0567917\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−5.65685	+	4.00000i	−0.498058	+	0.352180i
$130$	2.00000	+	3.00000i	0.175412	+	0.263117i
$131$		−	7.07107i		−	0.617802i	−0.951094	−	0.308901i	$-0.900039\pi$
$131$		−	7.07107i		−	0.617802i	0.951094	−	0.308901i	$-0.0999612\pi$
$132$	3.41421	+	0.585786i	0.297169	+	0.0509862i
$133$		0			0
$134$	−7.07107			−0.610847
$135$	2.53553	−	4.53553i	0.218224	−	0.390357i
$136$	−3.00000	−	3.00000i	−0.257248	−	0.257248i
$137$	14.1421	+	14.1421i	1.20824	+	1.20824i	0.971595	+	0.236649i	$0.0760491\pi$
$137$	14.1421	+	14.1421i	1.20824	+	1.20824i	0.236649	+	0.971595i	$0.423951\pi$
$138$	2.41421	+	0.414214i	0.205512	+	0.0352602i
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$		0			0
$141$	1.75736	−	10.2426i	0.147996	−	0.862586i
$142$			8.00000i			0.671345i
$143$	−7.07107	−	1.41421i	−0.591312	−	0.118262i
$144$	1.00000	−	2.82843i	0.0833333	−	0.235702i
$145$	−1.00000	−	1.00000i	−0.0830455	−	0.0830455i
$146$			8.48528i			0.702247i
$147$	−9.89949	+	7.00000i	−0.816497	+	0.577350i
$148$	−5.00000	−	5.00000i	−0.410997	−	0.410997i
$149$	7.07107	−	7.07107i	0.579284	−	0.579284i	−0.355422	−	0.934706i	$-0.615663\pi$
$149$	7.07107	−	7.07107i	0.579284	−	0.579284i	0.934706	+	0.355422i	$0.115663\pi$
$150$	−0.292893	+	1.70711i	−0.0239146	+	0.139385i
$151$	−13.0000	+	13.0000i	−1.05792	+	1.05792i	−0.0597092	+	0.998216i	$0.519017\pi$
$151$	−13.0000	+	13.0000i	−1.05792	+	1.05792i	−0.998216	+	0.0597092i	$0.980983\pi$
$152$			8.48528i			0.688247i
$153$	4.24264	−	12.0000i	0.342997	−	0.970143i
$154$		0			0
$155$	4.24264			0.340777
$156$	−2.24264	+	5.82843i	−0.179555	+	0.466648i
$157$	−6.00000			−0.478852			−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000			−0.478852			−0.239426	+	0.970915i	$0.576959\pi$
$158$	−5.65685	+	5.65685i	−0.450035	+	0.450035i
$159$	−16.0000	+	11.3137i	−1.26888	+	0.897235i
$160$			1.00000i			0.0790569i
$161$		0			0
$162$	8.94975	−	0.949747i	0.703159	−	0.0746192i
$163$	−11.0000	+	11.0000i	−0.861586	+	0.861586i	−0.991522	−	0.129936i	$-0.958523\pi$
$163$	−11.0000	+	11.0000i	−0.861586	+	0.861586i	0.129936	+	0.991522i	$0.458523\pi$
$164$	−7.07107	−	7.07107i	−0.552158	−	0.552158i
$165$	−2.00000	−	2.82843i	−0.155700	−	0.220193i
$166$			8.00000i			0.620920i
$167$	−11.3137	−	11.3137i	−0.875481	−	0.875481i	0.117582	−	0.993063i	$-0.462486\pi$
$167$	−11.3137	−	11.3137i	−0.875481	−	0.875481i	−0.993063	+	0.117582i	$0.962486\pi$
$168$		0			0
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$			4.24264i			0.325396i
$171$	−22.9706	+	10.9706i	−1.75660	+	0.838940i
$172$	4.00000			0.304997
$173$	−2.82843			−0.215041			−0.107521	−	0.994203i	$-0.534291\pi$
$173$	−2.82843			−0.215041			−0.107521	+	0.994203i	$0.534291\pi$
$174$	0.414214	−	2.41421i	0.0314014	−	0.183021i
$175$		0			0
$176$	−1.41421	−	1.41421i	−0.106600	−	0.106600i
$177$	1.17157	−	6.82843i	0.0880608	−	0.513256i
$178$	−6.00000			−0.449719
$179$	18.3848			1.37414			0.687071	−	0.726590i	$-0.258896\pi$
$179$	18.3848			1.37414			0.687071	+	0.726590i	$0.258896\pi$
$180$	−2.70711	+	1.29289i	−0.201776	+	0.0963666i
$181$		−	18.0000i		−	1.33793i	−0.743294	−	0.668965i	$-0.766738\pi$
$181$		−	18.0000i		−	1.33793i	0.743294	−	0.668965i	$-0.233262\pi$
$182$		0			0
$183$	2.00000	+	2.82843i	0.147844	+	0.209083i
$184$	−1.00000	−	1.00000i	−0.0737210	−	0.0737210i
$185$			7.07107i			0.519875i
$186$	4.24264	+	6.00000i	0.311086	+	0.439941i
$187$	−6.00000	−	6.00000i	−0.438763	−	0.438763i
$188$	−4.24264	+	4.24264i	−0.309426	+	0.309426i
$189$		0			0
$190$	6.00000	−	6.00000i	0.435286	−	0.435286i
$191$			19.7990i			1.43260i	0.697790	+	0.716302i	$0.254167\pi$
$191$			19.7990i			1.43260i	−0.697790	+	0.716302i	$0.745833\pi$
$192$	−1.41421	+	1.00000i	−0.102062	+	0.0721688i
$193$	−6.00000	+	6.00000i	−0.431889	+	0.431889i	−0.889271	−	0.457381i	$-0.848787\pi$
$193$	−6.00000	+	6.00000i	−0.431889	+	0.431889i	0.457381	+	0.889271i	$0.348787\pi$
$194$	−14.1421			−1.01535
$195$	5.70711	−	2.53553i	0.408694	−	0.181573i
$196$	7.00000			0.500000
$197$	−9.89949	+	9.89949i	−0.705310	+	0.705310i	−0.965545	−	0.260235i	$-0.916200\pi$
$197$	−9.89949	+	9.89949i	−0.705310	+	0.705310i	0.260235	+	0.965545i	$0.416200\pi$
$198$	2.00000	−	5.65685i	0.142134	−	0.402015i
$199$		−	2.00000i		−	0.141776i	−0.997484	−	0.0708881i	$-0.977417\pi$
$199$		−	2.00000i		−	0.141776i	0.997484	−	0.0708881i	$-0.0225833\pi$
$200$	0.707107	−	0.707107i	0.0500000	−	0.0500000i
$201$	−2.07107	+	12.0711i	−0.146082	+	0.851427i
$202$	−11.0000	+	11.0000i	−0.773957	+	0.773957i
$203$		0			0
$204$	−6.00000	+	4.24264i	−0.420084	+	0.297044i
$205$			10.0000i			0.698430i
$206$	5.65685	+	5.65685i	0.394132	+	0.394132i
$207$	1.41421	−	4.00000i	0.0982946	−	0.278019i
$208$	3.00000	−	2.00000i	0.208013	−	0.138675i
$209$			16.9706i			1.17388i
$210$		0			0
$211$	−24.0000			−1.65223			−0.826114	−	0.563503i	$-0.809453\pi$
$211$	−24.0000			−1.65223			−0.826114	+	0.563503i	$0.809453\pi$
$212$	11.3137			0.777029
$213$	13.6569	+	2.34315i	0.935752	+	0.160550i
$214$	8.00000	+	8.00000i	0.546869	+	0.546869i
$215$	−2.82843	−	2.82843i	−0.192897	−	0.192897i
$216$	−4.53553	−	2.53553i	−0.308604	−	0.172521i
$217$		0			0
$218$	−2.82843			−0.191565
$219$	14.4853	+	2.48528i	0.978825	+	0.167940i
$220$			2.00000i			0.134840i
$221$	12.7279	−	8.48528i	0.856173	−	0.570782i
$222$	−10.0000	+	7.07107i	−0.671156	+	0.474579i
$223$	−10.0000	−	10.0000i	−0.669650	−	0.669650i	0.287985	−	0.957635i	$-0.407015\pi$
$223$	−10.0000	−	10.0000i	−0.669650	−	0.669650i	−0.957635	+	0.287985i	$0.907015\pi$
$224$		0			0
$225$	2.82843	+	1.00000i	0.188562	+	0.0666667i
$226$	−5.00000	−	5.00000i	−0.332595	−	0.332595i
$227$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$	14.4853	+	2.48528i	0.959311	+	0.164592i
$229$	6.00000	−	6.00000i	0.396491	−	0.396491i	−0.480502	−	0.876993i	$-0.659546\pi$
$229$	6.00000	−	6.00000i	0.396491	−	0.396491i	0.876993	+	0.480502i	$0.159546\pi$
$230$			1.41421i			0.0932505i
$231$		0			0
$232$	−1.00000	+	1.00000i	−0.0656532	+	0.0656532i
$233$	−18.3848			−1.20443			−0.602213	−	0.798335i	$-0.705714\pi$
$233$	−18.3848			−1.20443			−0.602213	+	0.798335i	$0.705714\pi$
$234$	9.29289	+	5.53553i	0.607495	+	0.361869i
$235$	6.00000			0.391397
$236$	−2.82843	+	2.82843i	−0.184115	+	0.184115i
$237$	8.00000	+	11.3137i	0.519656	+	0.734904i
$238$		0			0
$239$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$239$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$240$	1.70711	+	0.292893i	0.110193	+	0.0189062i
$241$	−1.00000	+	1.00000i	−0.0644157	+	0.0644157i	−0.738581	−	0.674165i	$-0.764504\pi$
$241$	−1.00000	+	1.00000i	−0.0644157	+	0.0644157i	0.674165	+	0.738581i	$0.264504\pi$
$242$	4.94975	+	4.94975i	0.318182	+	0.318182i
$243$	1.00000	−	15.5563i	0.0641500	−	0.997940i
$244$		−	2.00000i		−	0.128037i
$245$	−4.94975	−	4.94975i	−0.316228	−	0.316228i
$246$	−14.1421	+	10.0000i	−0.901670	+	0.637577i
$247$	−30.0000	−	6.00000i	−1.90885	−	0.381771i
$248$		−	4.24264i		−	0.269408i
$249$	13.6569	+	2.34315i	0.865468	+	0.148491i
$250$	−1.00000			−0.0632456
$251$	4.24264			0.267793			0.133897	−	0.990995i	$-0.457251\pi$
$251$	4.24264			0.267793			0.133897	+	0.990995i	$0.457251\pi$
$252$		0			0
$253$	−2.00000	−	2.00000i	−0.125739	−	0.125739i
$254$	2.82843	+	2.82843i	0.177471	+	0.177471i
$255$	7.24264	+	1.24264i	0.453552	+	0.0778172i
$256$	1.00000			0.0625000
$257$	−1.41421			−0.0882162			−0.0441081	−	0.999027i	$-0.514045\pi$
$257$	−1.41421			−0.0882162			−0.0441081	+	0.999027i	$0.514045\pi$
$258$	1.17157	−	6.82843i	0.0729389	−	0.425119i
$259$		0			0
$260$	−3.53553	−	0.707107i	−0.219265	−	0.0438529i
$261$	−4.00000	−	1.41421i	−0.247594	−	0.0875376i
$262$	5.00000	+	5.00000i	0.308901	+	0.308901i
$263$		−	4.24264i		−	0.261612i	−0.991408	−	0.130806i	$-0.958243\pi$
$263$		−	4.24264i		−	0.261612i	0.991408	−	0.130806i	$-0.0417566\pi$
$264$	−2.82843	+	2.00000i	−0.174078	+	0.123091i
$265$	−8.00000	−	8.00000i	−0.491436	−	0.491436i
$266$		0			0
$267$	−1.75736	+	10.2426i	−0.107549	+	0.626839i
$268$	5.00000	−	5.00000i	0.305424	−	0.305424i
$269$			1.41421i			0.0862261i	0.999070	+	0.0431131i	$0.0137276\pi$
$269$			1.41421i			0.0862261i	−0.999070	+	0.0431131i	$0.986272\pi$
$270$	1.41421	+	5.00000i	0.0860663	+	0.304290i
$271$	−3.00000	+	3.00000i	−0.182237	+	0.182237i	−0.792330	−	0.610093i	$-0.791132\pi$
$271$	−3.00000	+	3.00000i	−0.182237	+	0.182237i	0.610093	+	0.792330i	$0.291132\pi$
$272$	4.24264			0.257248
$273$		0			0
$274$	−20.0000			−1.20824
$275$	1.41421	−	1.41421i	0.0852803	−	0.0852803i
$276$	−2.00000	+	1.41421i	−0.120386	+	0.0851257i
$277$		−	28.0000i		−	1.68236i	−0.540758	−	0.841178i	$-0.681862\pi$
$277$		−	28.0000i		−	1.68236i	0.540758	−	0.841178i	$-0.318138\pi$
$278$	11.3137	−	11.3137i	0.678551	−	0.678551i
$279$	11.4853	−	5.48528i	0.687606	−	0.328395i
$280$		0			0
$281$	−12.7279	−	12.7279i	−0.759284	−	0.759284i	0.216908	−	0.976192i	$-0.430403\pi$
$281$	−12.7279	−	12.7279i	−0.759284	−	0.759284i	−0.976192	+	0.216908i	$0.930403\pi$
$282$	6.00000	+	8.48528i	0.357295	+	0.505291i
$283$			6.00000i			0.356663i	0.983970	+	0.178331i	$0.0570699\pi$
$283$			6.00000i			0.356663i	−0.983970	+	0.178331i	$0.942930\pi$
$284$	−5.65685	−	5.65685i	−0.335673	−	0.335673i
$285$	−8.48528	−	12.0000i	−0.502625	−	0.710819i
$286$	6.00000	−	4.00000i	0.354787	−	0.236525i
$287$		0			0
$288$	1.29289	+	2.70711i	0.0761845	+	0.159518i
$289$	1.00000			0.0588235
$290$	1.41421			0.0830455
$291$	−4.14214	+	24.1421i	−0.242816	+	1.41524i
$292$	−6.00000	−	6.00000i	−0.351123	−	0.351123i
$293$	9.89949	+	9.89949i	0.578335	+	0.578335i	0.934444	−	0.356110i	$-0.115897\pi$
$293$	9.89949	+	9.89949i	0.578335	+	0.578335i	−0.356110	+	0.934444i	$0.615897\pi$
$294$	2.05025	−	11.9497i	0.119573	−	0.696923i
$295$	4.00000			0.232889
$296$	7.07107			0.410997
$297$	−9.07107	−	5.07107i	−0.526357	−	0.294253i
$298$			10.0000i			0.579284i
$299$	4.24264	−	2.82843i	0.245358	−	0.163572i
$300$	−1.00000	−	1.41421i	−0.0577350	−	0.0816497i
$301$		0			0
$302$		−	18.3848i		−	1.05792i
$303$	15.5563	+	22.0000i	0.893689	+	1.26387i
$304$	−6.00000	−	6.00000i	−0.344124	−	0.344124i
$305$	−1.41421	+	1.41421i	−0.0809776	+	0.0809776i
$306$	5.48528	+	11.4853i	0.313573	+	0.656570i
$307$	23.0000	−	23.0000i	1.31268	−	1.31268i	0.393246	−	0.919433i	$-0.371352\pi$
$307$	23.0000	−	23.0000i	1.31268	−	1.31268i	0.919433	−	0.393246i	$-0.128648\pi$
$308$		0			0
$309$	11.3137	−	8.00000i	0.643614	−	0.455104i
$310$	−3.00000	+	3.00000i	−0.170389	+	0.170389i
$311$	−2.82843			−0.160385			−0.0801927	−	0.996779i	$-0.525554\pi$
$311$	−2.82843			−0.160385			−0.0801927	+	0.996779i	$0.525554\pi$
$312$	−2.53553	−	5.70711i	−0.143546	−	0.323101i
$313$	26.0000			1.46961			0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000			1.46961			0.734803	+	0.678280i	$0.237274\pi$
$314$	4.24264	−	4.24264i	0.239426	−	0.239426i
$315$		0			0
$316$		−	8.00000i		−	0.450035i
$317$	18.3848	−	18.3848i	1.03259	−	1.03259i	0.0331412	−	0.999451i	$-0.489449\pi$
$317$	18.3848	−	18.3848i	1.03259	−	1.03259i	0.999451	−	0.0331412i	$-0.0105511\pi$
$318$	3.31371	−	19.3137i	0.185824	−	1.08306i
$319$	−2.00000	+	2.00000i	−0.111979	+	0.111979i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	16.0000	−	11.3137i	0.893033	−	0.631470i
$322$		0			0
$323$	−25.4558	−	25.4558i	−1.41640	−	1.41640i
$324$	−5.65685	+	7.00000i	−0.314270	+	0.388889i
$325$	2.00000	+	3.00000i	0.110940	+	0.166410i
$326$		−	15.5563i		−	0.861586i
$327$	−0.828427	+	4.82843i	−0.0458121	+	0.267013i
$328$	10.0000			0.552158
$329$		0			0
$330$	3.41421	+	0.585786i	0.187946	+	0.0322465i
$331$	24.0000	+	24.0000i	1.31916	+	1.31916i	0.914442	+	0.404718i	$0.132630\pi$
$331$	24.0000	+	24.0000i	1.31916	+	1.31916i	0.404718	+	0.914442i	$0.367370\pi$
$332$	−5.65685	−	5.65685i	−0.310460	−	0.310460i
$333$	9.14214	+	19.1421i	0.500986	+	1.04898i
$334$	16.0000			0.875481
$335$	−7.07107			−0.386334
$336$		0			0
$337$		−	14.0000i		−	0.762629i	−0.924445	−	0.381314i	$-0.875472\pi$
$337$		−	14.0000i		−	0.762629i	0.924445	−	0.381314i	$-0.124528\pi$
$338$	4.94975	+	12.0208i	0.269231	+	0.653846i
$339$	−10.0000	+	7.07107i	−0.543125	+	0.384048i
$340$	−3.00000	−	3.00000i	−0.162698	−	0.162698i
$341$		−	8.48528i		−	0.459504i
$342$	8.48528	−	24.0000i	0.458831	−	1.29777i
$343$		0			0
$344$	−2.82843	+	2.82843i	−0.152499	+	0.152499i
$345$	2.41421	+	0.414214i	0.129977	+	0.0223005i
$346$	2.00000	−	2.00000i	0.107521	−	0.107521i
$347$			11.3137i			0.607352i	0.952775	+	0.303676i	$0.0982140\pi$
$347$			11.3137i			0.607352i	−0.952775	+	0.303676i	$0.901786\pi$
$348$	1.41421	+	2.00000i	0.0758098	+	0.107211i
$349$	−12.0000	+	12.0000i	−0.642345	+	0.642345i	−0.951131	−	0.308786i	$-0.900077\pi$
$349$	−12.0000	+	12.0000i	−0.642345	+	0.642345i	0.308786	+	0.951131i	$0.400077\pi$
$350$		0			0
$351$	12.1716	−	14.2426i	0.649670	−	0.760216i
$352$	2.00000			0.106600
$353$	−25.4558	+	25.4558i	−1.35488	+	1.35488i	−0.474766	+	0.880112i	$0.657467\pi$
$353$	−25.4558	+	25.4558i	−1.35488	+	1.35488i	−0.880112	+	0.474766i	$0.842533\pi$
$354$	4.00000	+	5.65685i	0.212598	+	0.300658i
$355$			8.00000i			0.424596i
$356$	4.24264	−	4.24264i	0.224860	−	0.224860i
$357$		0			0
$358$	−13.0000	+	13.0000i	−0.687071	+	0.687071i
$359$	−16.9706	−	16.9706i	−0.895672	−	0.895672i	0.0993777	−	0.995050i	$-0.468315\pi$
$359$	−16.9706	−	16.9706i	−0.895672	−	0.895672i	−0.995050	+	0.0993777i	$0.968315\pi$
$360$	1.00000	−	2.82843i	0.0527046	−	0.149071i
$361$			53.0000i			2.78947i
$362$	12.7279	+	12.7279i	0.668965	+	0.668965i
$363$	9.89949	−	7.00000i	0.519589	−	0.367405i
$364$		0			0
$365$			8.48528i			0.444140i
$366$	−3.41421	−	0.585786i	−0.178464	−	0.0306195i
$367$	−8.00000			−0.417597			−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000			−0.417597			−0.208798	+	0.977959i	$0.566955\pi$
$368$	1.41421			0.0737210
$369$	12.9289	+	27.0711i	0.673053	+	1.40926i
$370$	−5.00000	−	5.00000i	−0.259938	−	0.259938i
$371$		0			0
$372$	−7.24264	−	1.24264i	−0.375513	−	0.0644279i
$373$	−32.0000			−1.65690			−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000			−1.65690			−0.828449	+	0.560065i	$0.810776\pi$
$374$	8.48528			0.438763
$375$	−0.292893	+	1.70711i	−0.0151249	+	0.0881546i
$376$		−	6.00000i		−	0.309426i
$377$	−2.82843	−	4.24264i	−0.145671	−	0.218507i
$378$		0			0
$379$	16.0000	+	16.0000i	0.821865	+	0.821865i	0.986375	−	0.164511i	$-0.0526045\pi$
$379$	16.0000	+	16.0000i	0.821865	+	0.821865i	−0.164511	+	0.986375i	$0.552604\pi$
$380$			8.48528i			0.435286i
$381$	5.65685	−	4.00000i	0.289809	−	0.204926i
$382$	−14.0000	−	14.0000i	−0.716302	−	0.716302i
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	−0.125001	−	0.992157i	$-0.539894\pi$
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	0.992157	+	0.125001i	$0.0398935\pi$
$384$	0.292893	−	1.70711i	0.0149466	−	0.0871154i
$385$		0			0
$386$		−	8.48528i		−	0.431889i
$387$	−11.3137	−	4.00000i	−0.575108	−	0.203331i
$388$	10.0000	−	10.0000i	0.507673	−	0.507673i
$389$	26.8701			1.36237			0.681183	−	0.732113i	$-0.261466\pi$
$389$	26.8701			1.36237			0.681183	+	0.732113i	$0.261466\pi$
$390$	−2.24264	+	5.82843i	−0.113561	+	0.295134i
$391$	6.00000			0.303433
$392$	−4.94975	+	4.94975i	−0.250000	+	0.250000i
$393$	10.0000	−	7.07107i	0.504433	−	0.356688i
$394$		−	14.0000i		−	0.705310i
$395$	−5.65685	+	5.65685i	−0.284627	+	0.284627i
$396$	2.58579	+	5.41421i	0.129941	+	0.272074i
$397$	3.00000	−	3.00000i	0.150566	−	0.150566i	−0.627805	−	0.778371i	$-0.716046\pi$
$397$	3.00000	−	3.00000i	0.150566	−	0.150566i	0.778371	+	0.627805i	$0.216046\pi$
$398$	1.41421	+	1.41421i	0.0708881	+	0.0708881i
$399$		0			0
$400$			1.00000i			0.0500000i
$401$	−4.24264	−	4.24264i	−0.211867	−	0.211867i	0.593193	−	0.805060i	$-0.297867\pi$
$401$	−4.24264	−	4.24264i	−0.211867	−	0.211867i	−0.805060	+	0.593193i	$0.797867\pi$
$402$	−7.07107	−	10.0000i	−0.352673	−	0.498755i
$403$	15.0000	+	3.00000i	0.747203	+	0.149441i
$404$		−	15.5563i		−	0.773957i
$405$	8.94975	−	0.949747i	0.444717	−	0.0471933i
$406$		0			0
$407$	14.1421			0.701000
$408$	1.24264	−	7.24264i	0.0615199	−	0.358564i
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	0.629036	−	0.777376i	$-0.283450\pi$
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	−0.777376	+	0.629036i	$0.783450\pi$
$410$	−7.07107	−	7.07107i	−0.349215	−	0.349215i
$411$	−5.85786	+	34.1421i	−0.288947	+	1.68411i
$412$	−8.00000			−0.394132
$413$		0			0
$414$	1.82843	+	3.82843i	0.0898623	+	0.188157i
$415$			8.00000i			0.392705i
$416$	−0.707107	+	3.53553i	−0.0346688	+	0.173344i
$417$	−16.0000	−	22.6274i	−0.783523	−	1.10807i
$418$	−12.0000	−	12.0000i	−0.586939	−	0.586939i
$419$		−	15.5563i		−	0.759977i	−0.924991	−	0.379989i	$-0.875928\pi$
$419$		−	15.5563i		−	0.759977i	0.924991	−	0.379989i	$-0.124072\pi$
$420$		0			0
$421$	12.0000	+	12.0000i	0.584844	+	0.584844i	0.936231	−	0.351386i	$-0.114290\pi$
$421$	12.0000	+	12.0000i	0.584844	+	0.584844i	−0.351386	+	0.936231i	$0.614290\pi$
$422$	16.9706	−	16.9706i	0.826114	−	0.826114i
$423$	16.2426	−	7.75736i	0.789744	−	0.377176i
$424$	−8.00000	+	8.00000i	−0.388514	+	0.388514i
$425$			4.24264i			0.205798i
$426$	−11.3137	+	8.00000i	−0.548151	+	0.387601i
$427$		0			0
$428$	−11.3137			−0.546869
$429$	−5.07107	−	11.4142i	−0.244833	−	0.551083i
$430$	4.00000			0.192897
$431$	−25.4558	+	25.4558i	−1.22616	+	1.22616i	−0.260762	+	0.965403i	$0.583974\pi$
$431$	−25.4558	+	25.4558i	−1.22616	+	1.22616i	−0.965403	+	0.260762i	$0.916026\pi$
$432$	5.00000	−	1.41421i	0.240563	−	0.0680414i
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$		0			0
$435$	0.414214	−	2.41421i	0.0198600	−	0.115753i
$436$	2.00000	−	2.00000i	0.0957826	−	0.0957826i
$437$	−8.48528	−	8.48528i	−0.405906	−	0.405906i
$438$	−12.0000	+	8.48528i	−0.573382	+	0.405442i
$439$		−	6.00000i		−	0.286364i	−0.989696	−	0.143182i	$-0.954267\pi$
$439$		−	6.00000i		−	0.286364i	0.989696	−	0.143182i	$-0.0457335\pi$
$440$	−1.41421	−	1.41421i	−0.0674200	−	0.0674200i
$441$	−19.7990	−	7.00000i	−0.942809	−	0.333333i
$442$	−3.00000	+	15.0000i	−0.142695	+	0.713477i
$443$			8.48528i			0.403148i	0.979473	+	0.201574i	$0.0646056\pi$
$443$			8.48528i			0.403148i	−0.979473	+	0.201574i	$0.935394\pi$
$444$	2.07107	−	12.0711i	0.0982885	−	0.572868i
$445$	−6.00000			−0.284427
$446$	14.1421			0.669650
$447$	17.0711	+	2.92893i	0.807434	+	0.138534i
$448$		0			0
$449$	12.7279	+	12.7279i	0.600668	+	0.600668i	0.940490	−	0.339822i	$-0.110367\pi$
$449$	12.7279	+	12.7279i	0.600668	+	0.600668i	−0.339822	+	0.940490i	$0.610367\pi$
$450$	−2.70711	+	1.29289i	−0.127614	+	0.0609476i
$451$	20.0000			0.941763
$452$	7.07107			0.332595
$453$	−31.3848	−	5.38478i	−1.47459	−	0.252999i
$454$		0			0
$455$		0			0
$456$	−12.0000	+	8.48528i	−0.561951	+	0.397360i
$457$	6.00000	+	6.00000i	0.280668	+	0.280668i	0.833375	−	0.552707i	$-0.186405\pi$
$457$	6.00000	+	6.00000i	0.280668	+	0.280668i	−0.552707	+	0.833375i	$0.686405\pi$
$458$			8.48528i			0.396491i
$459$	21.2132	−	6.00000i	0.990148	−	0.280056i
$460$	−1.00000	−	1.00000i	−0.0466252	−	0.0466252i
$461$	2.82843	−	2.82843i	0.131733	−	0.131733i	−0.638166	−	0.769899i	$-0.720307\pi$
$461$	2.82843	−	2.82843i	0.131733	−	0.131733i	0.769899	+	0.638166i	$0.220307\pi$
$462$		0			0
$463$	22.0000	−	22.0000i	1.02243	−	1.02243i	0.0226840	−	0.999743i	$-0.492779\pi$
$463$	22.0000	−	22.0000i	1.02243	−	1.02243i	0.999743	−	0.0226840i	$-0.00722117\pi$
$464$		−	1.41421i		−	0.0656532i
$465$	4.24264	+	6.00000i	0.196748	+	0.278243i
$466$	13.0000	−	13.0000i	0.602213	−	0.602213i
$467$	−2.82843			−0.130884			−0.0654420	−	0.997856i	$-0.520846\pi$
$467$	−2.82843			−0.130884			−0.0654420	+	0.997856i	$0.520846\pi$
$468$	−10.4853	+	2.65685i	−0.484682	+	0.122813i
$469$		0			0
$470$	−4.24264	+	4.24264i	−0.195698	+	0.195698i
$471$	−6.00000	−	8.48528i	−0.276465	−	0.390981i
$472$		−	4.00000i		−	0.184115i
$473$	−5.65685	+	5.65685i	−0.260102	+	0.260102i
$474$	−13.6569	−	2.34315i	−0.627280	−	0.107624i
$475$	6.00000	−	6.00000i	0.275299	−	0.275299i
$476$		0			0
$477$	−32.0000	−	11.3137i	−1.46518	−	0.518019i
$478$		0			0
$479$	−14.1421	−	14.1421i	−0.646171	−	0.646171i	0.305895	−	0.952065i	$-0.401044\pi$
$479$	−14.1421	−	14.1421i	−0.646171	−	0.646171i	−0.952065	+	0.305895i	$0.901044\pi$
$480$	−1.41421	+	1.00000i	−0.0645497	+	0.0456435i
$481$	−5.00000	+	25.0000i	−0.227980	+	1.13990i
$482$		−	1.41421i		−	0.0644157i
$483$		0			0
$484$	−7.00000			−0.318182
$485$	−14.1421			−0.642161
$486$	10.2929	+	11.7071i	0.466895	+	0.531045i
$487$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$487$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$488$	1.41421	+	1.41421i	0.0640184	+	0.0640184i
$489$	−26.5563	−	4.55635i	−1.20092	−	0.206045i
$490$	7.00000			0.316228
$491$	−15.5563			−0.702048			−0.351024	−	0.936366i	$-0.614166\pi$
$491$	−15.5563			−0.702048			−0.351024	+	0.936366i	$0.614166\pi$
$492$	2.92893	−	17.0711i	0.132046	−	0.769623i
$493$		−	6.00000i		−	0.270226i
$494$	25.4558	−	16.9706i	1.14531	−	0.763542i
$495$	2.00000	−	5.65685i	0.0898933	−	0.254257i
$496$	3.00000	+	3.00000i	0.134704	+	0.134704i
$497$		0			0
$498$	−11.3137	+	8.00000i	−0.506979	+	0.358489i
$499$	−18.0000	−	18.0000i	−0.805791	−	0.805791i	0.178203	−	0.983994i	$-0.442972\pi$
$499$	−18.0000	−	18.0000i	−0.805791	−	0.805791i	−0.983994	+	0.178203i	$0.942972\pi$
$500$	0.707107	−	0.707107i	0.0316228	−	0.0316228i
$501$	4.68629	−	27.3137i	0.209368	−	1.22029i
$502$	−3.00000	+	3.00000i	−0.133897	+	0.133897i
$503$			9.89949i			0.441397i	0.975342	+	0.220698i	$0.0708336\pi$
$503$			9.89949i			0.441397i	−0.975342	+	0.220698i	$0.929166\pi$
$504$		0			0
$505$	−11.0000	+	11.0000i	−0.489494	+	0.489494i
$506$	2.82843			0.125739
$507$	21.9706	−	4.92893i	0.975747	−	0.218902i
$508$	−4.00000			−0.177471
$509$	14.1421	−	14.1421i	0.626839	−	0.626839i	−0.320432	−	0.947271i	$-0.603828\pi$
$509$	14.1421	−	14.1421i	0.626839	−	0.626839i	0.947271	+	0.320432i	$0.103828\pi$
$510$	−6.00000	+	4.24264i	−0.265684	+	0.187867i
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−38.4853	−	21.5147i	−1.69917	−	0.949898i
$514$	1.00000	−	1.00000i	0.0441081	−	0.0441081i
$515$	5.65685	+	5.65685i	0.249271	+	0.249271i
$516$	4.00000	+	5.65685i	0.176090	+	0.249029i
$517$		−	12.0000i		−	0.527759i
$518$		0			0
$519$	−2.82843	−	4.00000i	−0.124154	−	0.175581i
$520$	3.00000	−	2.00000i	0.131559	−	0.0877058i
$521$			5.65685i			0.247831i	0.992293	+	0.123916i	$0.0395452\pi$
$521$			5.65685i			0.247831i	−0.992293	+	0.123916i	$0.960455\pi$
$522$	3.82843	−	1.82843i	0.167566	−	0.0800281i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	−7.07107			−0.308901
$525$		0			0
$526$	3.00000	+	3.00000i	0.130806	+	0.130806i
$527$	12.7279	+	12.7279i	0.554437	+	0.554437i
$528$	0.585786	−	3.41421i	0.0254931	−	0.148585i
$529$	−21.0000			−0.913043
$530$	11.3137			0.491436
$531$	10.8284	−	5.17157i	0.469914	−	0.224427i
$532$		0			0
$533$	−7.07107	+	35.3553i	−0.306282	+	1.53141i
$534$	−6.00000	−	8.48528i	−0.259645	−	0.367194i
$535$	8.00000	+	8.00000i	0.345870	+	0.345870i
$536$			7.07107i			0.305424i
$537$	18.3848	+	26.0000i	0.793362	+	1.12198i
$538$	−1.00000	−	1.00000i	−0.0431131	−	0.0431131i
$539$	−9.89949	+	9.89949i	−0.426401	+	0.426401i
$540$	−4.53553	−	2.53553i	−0.195178	−	0.109112i
$541$	−8.00000	+	8.00000i	−0.343947	+	0.343947i	−0.857849	−	0.513902i	$-0.828199\pi$
$541$	−8.00000	+	8.00000i	−0.343947	+	0.343947i	0.513902	+	0.857849i	$0.328199\pi$
$542$		−	4.24264i		−	0.182237i
$543$	25.4558	−	18.0000i	1.09241	−	0.772454i
$544$	−3.00000	+	3.00000i	−0.128624	+	0.128624i
$545$	−2.82843			−0.121157
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	14.1421	−	14.1421i	0.604122	−	0.604122i
$549$	−2.00000	+	5.65685i	−0.0853579	+	0.241429i
$550$			2.00000i			0.0852803i
$551$	−8.48528	+	8.48528i	−0.361485	+	0.361485i
$552$	0.414214	−	2.41421i	0.0176301	−	0.102756i
$553$		0			0
$554$	19.7990	+	19.7990i	0.841178	+	0.841178i
$555$	−10.0000	+	7.07107i	−0.424476	+	0.300150i
$556$			16.0000i			0.678551i
$557$	18.3848	+	18.3848i	0.778988	+	0.778988i	0.979659	−	0.200671i	$-0.0643121\pi$
$557$	18.3848	+	18.3848i	0.778988	+	0.778988i	−0.200671	+	0.979659i	$0.564312\pi$
$558$	−4.24264	+	12.0000i	−0.179605	+	0.508001i
$559$	−8.00000	−	12.0000i	−0.338364	−	0.507546i
$560$		0			0
$561$	2.48528	−	14.4853i	0.104929	−	0.611569i
$562$	18.0000			0.759284
$563$	−19.7990			−0.834428			−0.417214	−	0.908808i	$-0.636993\pi$
$563$	−19.7990			−0.834428			−0.417214	+	0.908808i	$0.636993\pi$
$564$	−10.2426	−	1.75736i	−0.431293	−	0.0739982i
$565$	−5.00000	−	5.00000i	−0.210352	−	0.210352i
$566$	−4.24264	−	4.24264i	−0.178331	−	0.178331i
$567$		0			0
$568$	8.00000			0.335673
$569$	−45.2548			−1.89718			−0.948591	−	0.316506i	$-0.897490\pi$
$569$	−45.2548			−1.89718			−0.948591	+	0.316506i	$0.897490\pi$
$570$	14.4853	+	2.48528i	0.606722	+	0.104097i
$571$		−	12.0000i		−	0.502184i	−0.967963	−	0.251092i	$-0.919210\pi$
$571$		−	12.0000i		−	0.502184i	0.967963	−	0.251092i	$-0.0807897\pi$
$572$	−1.41421	+	7.07107i	−0.0591312	+	0.295656i
$573$	−28.0000	+	19.7990i	−1.16972	+	0.827115i
$574$		0			0
$575$			1.41421i			0.0589768i
$576$	−2.82843	−	1.00000i	−0.117851	−	0.0416667i
$577$	26.0000	+	26.0000i	1.08239	+	1.08239i	0.996286	+	0.0861084i	$0.0274431\pi$
$577$	26.0000	+	26.0000i	1.08239	+	1.08239i	0.0861084	+	0.996286i	$0.472557\pi$
$578$	−0.707107	+	0.707107i	−0.0294118	+	0.0294118i
$579$	−14.4853	−	2.48528i	−0.601988	−	0.103285i
$580$	−1.00000	+	1.00000i	−0.0415227	+	0.0415227i
$581$		0			0
$582$	−14.1421	−	20.0000i	−0.586210	−	0.829027i
$583$	−16.0000	+	16.0000i	−0.662652	+	0.662652i
$584$	8.48528			0.351123
$585$	9.29289	+	5.53553i	0.384214	+	0.228866i
$586$	−14.0000			−0.578335
$587$	19.7990	−	19.7990i	0.817192	−	0.817192i	−0.168508	−	0.985700i	$-0.553895\pi$
$587$	19.7990	−	19.7990i	0.817192	−	0.817192i	0.985700	+	0.168508i	$0.0538950\pi$
$588$	7.00000	+	9.89949i	0.288675	+	0.408248i
$589$		−	36.0000i		−	1.48335i
$590$	−2.82843	+	2.82843i	−0.116445	+	0.116445i
$591$	−23.8995	−	4.10051i	−0.983094	−	0.168672i
$592$	−5.00000	+	5.00000i	−0.205499	+	0.205499i
$593$	25.4558	+	25.4558i	1.04535	+	1.04535i	0.998922	+	0.0464244i	$0.0147827\pi$
$593$	25.4558	+	25.4558i	1.04535	+	1.04535i	0.0464244	+	0.998922i	$0.485217\pi$
$594$	10.0000	−	2.82843i	0.410305	−	0.116052i
$595$		0			0
$596$	−7.07107	−	7.07107i	−0.289642	−	0.289642i
$597$	2.82843	−	2.00000i	0.115760	−	0.0818546i
$598$	−1.00000	+	5.00000i	−0.0408930	+	0.204465i
$599$			45.2548i			1.84906i	0.381106	+	0.924531i	$0.375543\pi$
$599$			45.2548i			1.84906i	−0.381106	+	0.924531i	$0.624457\pi$
$600$	1.70711	+	0.292893i	0.0696923	+	0.0119573i
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$		0			0
$603$	−19.1421	+	9.14214i	−0.779528	+	0.372297i
$604$	13.0000	+	13.0000i	0.528962	+	0.528962i
$605$	4.94975	+	4.94975i	0.201236	+	0.201236i
$606$	−26.5563	−	4.55635i	−1.07878	−	0.185089i
$607$	36.0000			1.46119			0.730597	−	0.682808i	$-0.239242\pi$
$607$	36.0000			1.46119			0.730597	+	0.682808i	$0.239242\pi$
$608$	8.48528			0.344124
$609$		0			0
$610$		−	2.00000i		−	0.0809776i
$611$	21.2132	+	4.24264i	0.858194	+	0.171639i
$612$	−12.0000	−	4.24264i	−0.485071	−	0.171499i
$613$	−9.00000	−	9.00000i	−0.363507	−	0.363507i	0.501596	−	0.865102i	$-0.332747\pi$
$613$	−9.00000	−	9.00000i	−0.363507	−	0.363507i	−0.865102	+	0.501596i	$0.832747\pi$
$614$			32.5269i			1.31268i
$615$	−14.1421	+	10.0000i	−0.570266	+	0.403239i
$616$		0			0
$617$	−7.07107	+	7.07107i	−0.284670	+	0.284670i	−0.834968	−	0.550298i	$-0.814514\pi$
$617$	−7.07107	+	7.07107i	−0.284670	+	0.284670i	0.550298	+	0.834968i	$0.314514\pi$
$618$	−2.34315	+	13.6569i	−0.0942551	+	0.549359i
$619$	32.0000	−	32.0000i	1.28619	−	1.28619i	0.349105	−	0.937084i	$-0.386486\pi$
$619$	32.0000	−	32.0000i	1.28619	−	1.28619i	0.937084	−	0.349105i	$-0.113514\pi$
$620$		−	4.24264i		−	0.170389i
$621$	7.07107	−	2.00000i	0.283752	−	0.0802572i
$622$	2.00000	−	2.00000i	0.0801927	−	0.0801927i
$623$		0			0
$624$	5.82843	+	2.24264i	0.233324	+	0.0897775i
$625$	−1.00000			−0.0400000
$626$	−18.3848	+	18.3848i	−0.734803	+	0.734803i
$627$	−24.0000	+	16.9706i	−0.958468	+	0.677739i
$628$			6.00000i			0.239426i
$629$	−21.2132	+	21.2132i	−0.845826	+	0.845826i
$630$		0			0
$631$	9.00000	−	9.00000i	0.358284	−	0.358284i	−0.504896	−	0.863180i	$-0.668469\pi$
$631$	9.00000	−	9.00000i	0.358284	−	0.358284i	0.863180	+	0.504896i	$0.168469\pi$
$632$	5.65685	+	5.65685i	0.225018	+	0.225018i
$633$	−24.0000	−	33.9411i	−0.953914	−	1.34904i
$634$			26.0000i			1.03259i
$635$	2.82843	+	2.82843i	0.112243	+	0.112243i
$636$	11.3137	+	16.0000i	0.448618	+	0.634441i
$637$	−14.0000	−	21.0000i	−0.554700	−	0.832050i
$638$		−	2.82843i		−	0.111979i
$639$	10.3431	+	21.6569i	0.409169	+	0.856732i
$640$	1.00000			0.0395285
$641$	39.5980			1.56403			0.782013	−	0.623262i	$-0.214193\pi$
$641$	39.5980			1.56403			0.782013	+	0.623262i	$0.214193\pi$
$642$	−3.31371	+	19.3137i	−0.130782	+	0.762251i
$643$	−21.0000	−	21.0000i	−0.828159	−	0.828159i	0.159103	−	0.987262i	$-0.449140\pi$
$643$	−21.0000	−	21.0000i	−0.828159	−	0.828159i	−0.987262	+	0.159103i	$0.949140\pi$
$644$		0			0
$645$	1.17157	−	6.82843i	0.0461306	−	0.268869i
$646$	36.0000			1.41640
$647$	−7.07107			−0.277992			−0.138996	−	0.990293i	$-0.544388\pi$
$647$	−7.07107			−0.277992			−0.138996	+	0.990293i	$0.544388\pi$
$648$	−0.949747	−	8.94975i	−0.0373096	−	0.351579i
$649$		−	8.00000i		−	0.314027i
$650$	−3.53553	−	0.707107i	−0.138675	−	0.0277350i
$651$		0			0
$652$	11.0000	+	11.0000i	0.430793	+	0.430793i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$	−2.82843	−	4.00000i	−0.110600	−	0.156412i
$655$	5.00000	+	5.00000i	0.195366	+	0.195366i
$656$	−7.07107	+	7.07107i	−0.276079	+	0.276079i
$657$	10.9706	+	22.9706i	0.428002	+	0.896167i
$658$		0			0
$659$			9.89949i			0.385630i	0.981235	+	0.192815i	$0.0617617\pi$
$659$			9.89949i			0.385630i	−0.981235	+	0.192815i	$0.938238\pi$
$660$	−2.82843	+	2.00000i	−0.110096	+	0.0778499i
$661$	−22.0000	+	22.0000i	−0.855701	+	0.855701i	−0.990828	−	0.135127i	$-0.956856\pi$
$661$	−22.0000	+	22.0000i	−0.855701	+	0.855701i	0.135127	+	0.990828i	$0.456856\pi$
$662$	−33.9411			−1.31916
$663$	24.7279	+	9.51472i	0.960353	+	0.369521i
$664$	8.00000			0.310460
$665$		0			0
$666$	−20.0000	−	7.07107i	−0.774984	−	0.273998i
$667$		−	2.00000i		−	0.0774403i
$668$	−11.3137	+	11.3137i	−0.437741	+	0.437741i
$669$	4.14214	−	24.1421i	0.160144	−	0.933389i
$670$	5.00000	−	5.00000i	0.193167	−	0.193167i
$671$	2.82843	+	2.82843i	0.109190	+	0.109190i
$672$		0			0
$673$			6.00000i			0.231283i	0.993291	+	0.115642i	$0.0368924\pi$
$673$			6.00000i			0.231283i	−0.993291	+	0.115642i	$0.963108\pi$
$674$	9.89949	+	9.89949i	0.381314	+	0.381314i
$675$	1.41421	+	5.00000i	0.0544331	+	0.192450i
$676$	−12.0000	−	5.00000i	−0.461538	−	0.192308i
$677$		−	36.7696i		−	1.41317i	−0.707629	−	0.706584i	$-0.750235\pi$
$677$		−	36.7696i		−	1.41317i	0.707629	−	0.706584i	$-0.249765\pi$
$678$	2.07107	−	12.0711i	0.0795389	−	0.463587i
$679$		0			0
$680$	4.24264			0.162698
$681$		0			0
$682$	6.00000	+	6.00000i	0.229752	+	0.229752i
$683$	−16.9706	−	16.9706i	−0.649361	−	0.649361i	0.303478	−	0.952838i	$-0.401852\pi$
$683$	−16.9706	−	16.9706i	−0.649361	−	0.649361i	−0.952838	+	0.303478i	$0.901852\pi$
$684$	10.9706	+	22.9706i	0.419470	+	0.878301i
$685$	−20.0000			−0.764161
$686$		0			0
$687$	14.4853	+	2.48528i	0.552648	+	0.0948194i
$688$		−	4.00000i		−	0.152499i
$689$	−22.6274	−	33.9411i	−0.862036	−	1.29305i
$690$	−2.00000	+	1.41421i	−0.0761387	+	0.0538382i
$691$	−16.0000	−	16.0000i	−0.608669	−	0.608669i	0.333929	−	0.942598i	$-0.391625\pi$
$691$	−16.0000	−	16.0000i	−0.608669	−	0.608669i	−0.942598	+	0.333929i	$0.891625\pi$
$692$			2.82843i			0.107521i
$693$		0			0
$694$	−8.00000	−	8.00000i	−0.303676	−	0.303676i
$695$	11.3137	−	11.3137i	0.429153	−	0.429153i
$696$	−2.41421	−	0.414214i	−0.0915105	−	0.0157007i
$697$	−30.0000	+	30.0000i	−1.13633	+	1.13633i
$698$		−	16.9706i		−	0.642345i
$699$	−18.3848	−	26.0000i	−0.695376	−	0.983410i
$700$		0			0
$701$	−1.41421			−0.0534141			−0.0267071	−	0.999643i	$-0.508502\pi$
$701$	−1.41421			−0.0534141			−0.0267071	+	0.999643i	$0.508502\pi$
$702$	1.46447	+	18.6777i	0.0552727	+	0.704943i
$703$	60.0000			2.26294
$704$	−1.41421	+	1.41421i	−0.0533002	+	0.0533002i
$705$	6.00000	+	8.48528i	0.225973	+	0.319574i
$706$		−	36.0000i		−	1.35488i
$707$		0			0
$708$	−6.82843	−	1.17157i	−0.256628	−	0.0440304i
$709$	−18.0000	+	18.0000i	−0.676004	+	0.676004i	−0.959094	−	0.283089i	$-0.908641\pi$
$709$	−18.0000	+	18.0000i	−0.676004	+	0.676004i	0.283089	+	0.959094i	$0.408641\pi$
$710$	−5.65685	−	5.65685i	−0.212298	−	0.212298i
$711$	−8.00000	+	22.6274i	−0.300023	+	0.848594i
$712$			6.00000i			0.224860i
$713$	4.24264	+	4.24264i	0.158888	+	0.158888i
$714$		0			0
$715$	6.00000	−	4.00000i	0.224387	−	0.149592i
$716$		−	18.3848i		−	0.687071i
$717$		0			0
$718$	24.0000			0.895672
$719$	−45.2548			−1.68772			−0.843860	−	0.536563i	$-0.819722\pi$
$719$	−45.2548			−1.68772			−0.843860	+	0.536563i	$0.819722\pi$
$720$	1.29289	+	2.70711i	0.0481833	+	0.100888i
$721$		0			0
$722$	−37.4767	−	37.4767i	−1.39474	−	1.39474i
$723$	−2.41421	−	0.414214i	−0.0897856	−	0.0154048i
$724$	−18.0000			−0.668965
$725$	1.41421			0.0525226
$726$	−2.05025	+	11.9497i	−0.0760920	+	0.443497i
$727$			8.00000i			0.296704i	0.988935	+	0.148352i	$0.0473968\pi$
$727$			8.00000i			0.296704i	−0.988935	+	0.148352i	$0.952603\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	−6.00000	−	6.00000i	−0.222070	−	0.222070i
$731$		−	16.9706i		−	0.627679i
$732$	2.82843	−	2.00000i	0.104542	−	0.0739221i
$733$	−9.00000	−	9.00000i	−0.332423	−	0.332423i	0.521083	−	0.853506i	$-0.325528\pi$
$733$	−9.00000	−	9.00000i	−0.332423	−	0.332423i	−0.853506	+	0.521083i	$0.825528\pi$
$734$	5.65685	−	5.65685i	0.208798	−	0.208798i
$735$	2.05025	−	11.9497i	0.0756247	−	0.440773i
$736$	−1.00000	+	1.00000i	−0.0368605	+	0.0368605i
$737$			14.1421i			0.520932i
$738$	−28.2843	−	10.0000i	−1.04116	−	0.368105i
$739$	−12.0000	+	12.0000i	−0.441427	+	0.441427i	−0.892491	−	0.451064i	$-0.851045\pi$
$739$	−12.0000	+	12.0000i	−0.441427	+	0.441427i	0.451064	+	0.892491i	$0.351045\pi$
$740$	7.07107			0.259938
$741$	−21.5147	−	48.4264i	−0.790363	−	1.77899i
$742$		0			0
$743$	18.3848	−	18.3848i	0.674472	−	0.674472i	−0.284272	−	0.958744i	$-0.591752\pi$
$743$	18.3848	−	18.3848i	0.674472	−	0.674472i	0.958744	+	0.284272i	$0.0917518\pi$
$744$	6.00000	−	4.24264i	0.219971	−	0.155543i
$745$			10.0000i			0.366372i
$746$	22.6274	−	22.6274i	0.828449	−	0.828449i
$747$	10.3431	+	21.6569i	0.378436	+	0.792383i
$748$	−6.00000	+	6.00000i	−0.219382	+	0.219382i
$749$		0			0
$750$	−1.00000	−	1.41421i	−0.0365148	−	0.0516398i
$751$		−	10.0000i		−	0.364905i	−0.983215	−	0.182453i	$-0.941596\pi$
$751$		−	10.0000i		−	0.364905i	0.983215	−	0.182453i	$-0.0584036\pi$
$752$	4.24264	+	4.24264i	0.154713	+	0.154713i
$753$	4.24264	+	6.00000i	0.154610	+	0.218652i
$754$	5.00000	+	1.00000i	0.182089	+	0.0364179i
$755$		−	18.3848i		−	0.669091i
$756$		0			0
$757$	42.0000			1.52652			0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000			1.52652			0.763258	+	0.646094i	$0.223599\pi$
$758$	−22.6274			−0.821865
$759$	0.828427	−	4.82843i	0.0300700	−	0.175261i
$760$	−6.00000	−	6.00000i	−0.217643	−	0.217643i
$761$	−9.89949	−	9.89949i	−0.358856	−	0.358856i	0.504535	−	0.863391i	$-0.331664\pi$
$761$	−9.89949	−	9.89949i	−0.358856	−	0.358856i	−0.863391	+	0.504535i	$0.831664\pi$
$762$	−1.17157	+	6.82843i	−0.0424416	+	0.247368i
$763$		0			0
$764$	19.7990			0.716302
$765$	5.48528	+	11.4853i	0.198321	+	0.415251i
$766$			24.0000i			0.867155i
$767$	14.1421	+	2.82843i	0.510643	+	0.102129i
$768$	1.00000	+	1.41421i	0.0360844	+	0.0510310i
$769$	−21.0000	−	21.0000i	−0.757279	−	0.757279i	0.218547	−	0.975826i	$-0.429868\pi$
$769$	−21.0000	−	21.0000i	−0.757279	−	0.757279i	−0.975826	+	0.218547i	$0.929868\pi$
$770$		0			0
$771$	−1.41421	−	2.00000i	−0.0509317	−	0.0720282i
$772$	6.00000	+	6.00000i	0.215945	+	0.215945i
$773$	4.24264	−	4.24264i	0.152597	−	0.152597i	−0.626680	−	0.779277i	$-0.715587\pi$
$773$	4.24264	−	4.24264i	0.152597	−	0.152597i	0.779277	+	0.626680i	$0.215587\pi$
$774$	10.8284	−	5.17157i	0.389220	−	0.185888i
$775$	−3.00000	+	3.00000i	−0.107763	+	0.107763i
$776$			14.1421i			0.507673i
$777$		0			0
$778$	−19.0000	+	19.0000i	−0.681183	+	0.681183i
$779$	84.8528			3.04017
$780$	−2.53553	−	5.70711i	−0.0907867	−	0.204347i
$781$	16.0000			0.572525
$782$	−4.24264	+	4.24264i	−0.151717	+	0.151717i
$783$	−2.00000	−	7.07107i	−0.0714742	−	0.252699i
$784$		−	7.00000i		−	0.250000i
$785$	4.24264	−	4.24264i	0.151426	−	0.151426i
$786$	−2.07107	+	12.0711i	−0.0738725	+	0.430561i
$787$	−3.00000	+	3.00000i	−0.106938	+	0.106938i	−0.758552	−	0.651613i	$-0.774093\pi$
$787$	−3.00000	+	3.00000i	−0.106938	+	0.106938i	0.651613	+	0.758552i	$0.274093\pi$
$788$	9.89949	+	9.89949i	0.352655	+	0.352655i
$789$	6.00000	−	4.24264i	0.213606	−	0.151042i
$790$		−	8.00000i		−	0.284627i
$791$		0			0
$792$	−5.65685	−	2.00000i	−0.201008	−	0.0710669i
$793$	−6.00000	+	4.00000i	−0.213066	+	0.142044i
$794$			4.24264i			0.150566i
$795$	3.31371	−	19.3137i	0.117525	−	0.684987i
$796$	−2.00000			−0.0708881
$797$	−45.2548			−1.60301			−0.801504	−	0.597989i	$-0.795967\pi$
$797$	−45.2548			−1.60301			−0.801504	+	0.597989i	$0.795967\pi$
$798$		0			0
$799$	18.0000	+	18.0000i	0.636794	+	0.636794i
$800$	−0.707107	−	0.707107i	−0.0250000	−	0.0250000i
$801$	−16.2426	+	7.75736i	−0.573905	+	0.274093i
$802$	6.00000			0.211867
$803$	16.9706			0.598878
$804$	12.0711	+	2.07107i	0.425714	+	0.0730409i
$805$		0			0
$806$	−12.7279	+	8.48528i	−0.448322	+	0.298881i
$807$	−2.00000	+	1.41421i	−0.0704033	+	0.0497827i
$808$	11.0000	+	11.0000i	0.386979	+	0.386979i
$809$		−	25.4558i		−	0.894980i	−0.894289	−	0.447490i	$-0.852318\pi$
$809$		−	25.4558i		−	0.894980i	0.894289	−	0.447490i	$-0.147682\pi$
$810$	−5.65685	+	7.00000i	−0.198762	+	0.245955i
$811$	−26.0000	−	26.0000i	−0.912983	−	0.912983i	0.0835224	−	0.996506i	$-0.473383\pi$
$811$	−26.0000	−	26.0000i	−0.912983	−	0.912983i	−0.996506	+	0.0835224i	$0.973383\pi$
$812$		0			0
$813$	−7.24264	−	1.24264i	−0.254010	−	0.0435813i
$814$	−10.0000	+	10.0000i	−0.350500	+	0.350500i
$815$		−	15.5563i		−	0.544915i
$816$	4.24264	+	6.00000i	0.148522	+	0.210042i
$817$	−24.0000	+	24.0000i	−0.839654	+	0.839654i
$818$	4.24264			0.148340
$819$		0			0
$820$	10.0000			0.349215
$821$	21.2132	−	21.2132i	0.740346	−	0.740346i	−0.232299	−	0.972645i	$-0.574625\pi$
$821$	21.2132	−	21.2132i	0.740346	−	0.740346i	0.972645	+	0.232299i	$0.0746247\pi$
$822$	−20.0000	−	28.2843i	−0.697580	−	0.986527i
$823$			52.0000i			1.81261i	0.422628	+	0.906303i	$0.361108\pi$
$823$			52.0000i			1.81261i	−0.422628	+	0.906303i	$0.638892\pi$
$824$	5.65685	−	5.65685i	0.197066	−	0.197066i
$825$	3.41421	+	0.585786i	0.118868	+	0.0203945i
$826$		0			0
$827$	−14.1421	−	14.1421i	−0.491770	−	0.491770i	0.417093	−	0.908864i	$-0.363049\pi$
$827$	−14.1421	−	14.1421i	−0.491770	−	0.491770i	−0.908864	+	0.417093i	$0.863049\pi$
$828$	−4.00000	−	1.41421i	−0.139010	−	0.0491473i
$829$			14.0000i			0.486240i	0.969996	+	0.243120i	$0.0781709\pi$
$829$			14.0000i			0.486240i	−0.969996	+	0.243120i	$0.921829\pi$
$830$	−5.65685	−	5.65685i	−0.196352	−	0.196352i
$831$	39.5980	−	28.0000i	1.37364	−	0.971309i
$832$	−2.00000	−	3.00000i	−0.0693375	−	0.104006i
$833$		−	29.6985i		−	1.02899i
$834$	27.3137	+	4.68629i	0.945796	+	0.162273i
$835$	16.0000			0.553703
$836$	16.9706			0.586939
$837$	19.2426	+	10.7574i	0.665123	+	0.371829i
$838$	11.0000	+	11.0000i	0.379989	+	0.379989i
$839$	−31.1127	−	31.1127i	−1.07413	−	1.07413i	−0.997023	−	0.0771068i	$-0.975432\pi$
$839$	−31.1127	−	31.1127i	−1.07413	−	1.07413i	−0.0771068	−	0.997023i	$-0.524568\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$	−16.9706			−0.584844
$843$	5.27208	−	30.7279i	0.181580	−	1.05833i
$844$			24.0000i			0.826114i
$845$	4.94975	+	12.0208i	0.170276	+	0.413529i
$846$	−6.00000	+	16.9706i	−0.206284	+	0.583460i
$847$		0			0
$848$		−	11.3137i		−	0.388514i
$849$	−8.48528	+	6.00000i	−0.291214	+	0.205919i
$850$	−3.00000	−	3.00000i	−0.102899	−	0.102899i
$851$	−7.07107	+	7.07107i	−0.242393	+	0.242393i
$852$	2.34315	−	13.6569i	0.0802749	−	0.467876i
$853$	39.0000	−	39.0000i	1.33533	−	1.33533i	0.434815	−	0.900520i	$-0.356814\pi$
$853$	39.0000	−	39.0000i	1.33533	−	1.33533i	0.900520	−	0.434815i	$-0.143186\pi$
$854$		0			0
$855$	8.48528	−	24.0000i	0.290191	−	0.820783i
$856$	8.00000	−	8.00000i	0.273434	−	0.273434i
$857$	49.4975			1.69080			0.845401	−	0.534133i	$-0.179362\pi$
$857$	49.4975			1.69080			0.845401	+	0.534133i	$0.179362\pi$
$858$	11.6569	+	4.48528i	0.397958	+	0.153125i
$859$	24.0000			0.818869			0.409435	−	0.912339i	$-0.365726\pi$
$859$	24.0000			0.818869			0.409435	+	0.912339i	$0.365726\pi$
$860$	−2.82843	+	2.82843i	−0.0964486	+	0.0964486i
$861$		0			0
$862$		−	36.0000i		−	1.22616i
$863$	33.9411	−	33.9411i	1.15537	−	1.15537i	0.169910	−	0.985460i	$-0.445652\pi$
$863$	33.9411	−	33.9411i	1.15537	−	1.15537i	0.985460	−	0.169910i	$-0.0543476\pi$
$864$	−2.53553	+	4.53553i	−0.0862606	+	0.154302i
$865$	2.00000	−	2.00000i	0.0680020	−	0.0680020i
$866$	−9.89949	−	9.89949i	−0.336399	−	0.336399i
$867$	1.00000	+	1.41421i	0.0339618	+	0.0480292i
$868$		0			0
$869$	11.3137	+	11.3137i	0.383791	+	0.383791i
$870$	1.41421	+	2.00000i	0.0479463	+	0.0678064i
$871$	−25.0000	−	5.00000i	−0.847093	−	0.169419i
$872$			2.82843i			0.0957826i
$873$	−38.2843	+	18.2843i	−1.29573	+	0.618829i
$874$	12.0000			0.405906
$875$		0			0
$876$	2.48528	−	14.4853i	0.0839699	−	0.489412i
$877$	−15.0000	−	15.0000i	−0.506514	−	0.506514i	0.406941	−	0.913455i	$-0.366596\pi$
$877$	−15.0000	−	15.0000i	−0.506514	−	0.506514i	−0.913455	+	0.406941i	$0.866596\pi$
$878$	4.24264	+	4.24264i	0.143182	+	0.143182i
$879$	−4.10051	+	23.8995i	−0.138307	+	0.806110i
$880$	2.00000			0.0674200
$881$	−56.5685			−1.90584			−0.952921	−	0.303218i	$-0.901939\pi$
$881$	−56.5685			−1.90584			−0.952921	+	0.303218i	$0.901939\pi$
$882$	18.9497	−	9.05025i	0.638071	−	0.304738i
$883$		−	4.00000i		−	0.134611i	−0.997732	−	0.0673054i	$-0.978560\pi$
$883$		−	4.00000i		−	0.134611i	0.997732	−	0.0673054i	$-0.0214402\pi$
$884$	−8.48528	−	12.7279i	−0.285391	−	0.428086i
$885$	4.00000	+	5.65685i	0.134459	+	0.190153i
$886$	−6.00000	−	6.00000i	−0.201574	−	0.201574i
$887$			38.1838i			1.28209i	0.767505	+	0.641043i	$0.221498\pi$
$887$			38.1838i			1.28209i	−0.767505	+	0.641043i	$0.778502\pi$
$888$	7.07107	+	10.0000i	0.237289	+	0.335578i
$889$		0			0
$890$	4.24264	−	4.24264i	0.142214	−	0.142214i
$891$	−1.89949	−	17.8995i	−0.0636355	−	0.599656i
$892$	−10.0000	+	10.0000i	−0.334825	+	0.334825i
$893$		−	50.9117i		−	1.70369i
$894$	−14.1421	+	10.0000i	−0.472984	+	0.334450i
$895$	−13.0000	+	13.0000i	−0.434542	+	0.434542i
$896$		0			0
$897$	8.24264	+	3.17157i	0.275214	+	0.105896i
$898$	−18.0000			−0.600668
$899$	4.24264	−	4.24264i	0.141500	−	0.141500i
$900$	1.00000	−	2.82843i	0.0333333	−	0.0942809i
$901$		−	48.0000i		−	1.59911i
$902$	−14.1421	+	14.1421i	−0.470882	+	0.470882i
$903$		0			0
$904$	−5.00000	+	5.00000i	−0.166298	+	0.166298i
$905$	12.7279	+	12.7279i	0.423090	+	0.423090i
$906$	26.0000	−	18.3848i	0.863792	−	0.610793i
$907$			14.0000i			0.464862i	0.972613	+	0.232431i	$0.0746680\pi$
$907$			14.0000i			0.464862i	−0.972613	+	0.232431i	$0.925332\pi$
$908$		0			0
$909$	−15.5563	+	44.0000i	−0.515972	+	1.45939i
$910$		0			0
$911$		−	5.65685i		−	0.187420i	−0.995600	−	0.0937100i	$-0.970127\pi$
$911$		−	5.65685i		−	0.187420i	0.995600	−	0.0937100i	$-0.0298726\pi$
$912$	2.48528	−	14.4853i	0.0822959	−	0.479656i
$913$	16.0000			0.529523
$914$	−8.48528			−0.280668
$915$	−3.41421	−	0.585786i	−0.112870	−	0.0193655i
$916$	−6.00000	−	6.00000i	−0.198246	−	0.198246i
$917$		0			0
$918$	−10.7574	+	19.2426i	−0.355046	+	0.635102i
$919$	42.0000			1.38545			0.692726	−	0.721201i	$-0.256409\pi$
$919$	42.0000			1.38545			0.692726	+	0.721201i	$0.256409\pi$
$920$	1.41421			0.0466252
$921$	55.5269	+	9.52691i	1.82967	+	0.313922i
$922$			4.00000i			0.131733i
$923$	−5.65685	+	28.2843i	−0.186198	+	0.930988i
$924$		0			0
$925$	−5.00000	−	5.00000i	−0.164399	−	0.164399i
$926$			31.1127i			1.02243i
$927$	22.6274	+	8.00000i	0.743182	+	0.262754i
$928$	1.00000	+	1.00000i	0.0328266	+	0.0328266i
$929$	−12.7279	+	12.7279i	−0.417590	+	0.417590i	−0.884372	−	0.466783i	$-0.845413\pi$
$929$	−12.7279	+	12.7279i	−0.417590	+	0.417590i	0.466783	+	0.884372i	$0.345413\pi$
$930$	−7.24264	−	1.24264i	−0.237496	−	0.0407478i
$931$	−42.0000	+	42.0000i	−1.37649	+	1.37649i
$932$			18.3848i			0.602213i
$933$	−2.82843	−	4.00000i	−0.0925985	−	0.130954i
$934$	2.00000	−	2.00000i	0.0654420	−	0.0654420i
$935$	8.48528			0.277498
$936$	5.53553	−	9.29289i	0.180935	−	0.303748i
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$		0			0
$939$	26.0000	+	36.7696i	0.848478	+	1.19993i
$940$		−	6.00000i		−	0.195698i
$941$	−28.2843	+	28.2843i	−0.922041	+	0.922041i	−0.997174	−	0.0751327i	$-0.976062\pi$
$941$	−28.2843	+	28.2843i	−0.922041	+	0.922041i	0.0751327	+	0.997174i	$0.476062\pi$
$942$	10.2426	+	1.75736i	0.333723	+	0.0572579i
$943$	−10.0000	+	10.0000i	−0.325645	+	0.325645i
$944$	2.82843	+	2.82843i	0.0920575	+	0.0920575i
$945$		0			0
$946$		−	8.00000i		−	0.260102i
$947$	5.65685	+	5.65685i	0.183823	+	0.183823i	0.793019	−	0.609196i	$-0.208508\pi$
$947$	5.65685	+	5.65685i	0.183823	+	0.183823i	−0.609196	+	0.793019i	$0.708508\pi$
$948$	11.3137	−	8.00000i	0.367452	−	0.259828i
$949$	−6.00000	+	30.0000i	−0.194768	+	0.973841i
$950$			8.48528i			0.275299i
$951$	44.3848	+	7.61522i	1.43927	+	0.246941i
$952$		0			0
$953$	12.7279			0.412298			0.206149	−	0.978521i	$-0.433907\pi$
$953$	12.7279			0.412298			0.206149	+	0.978521i	$0.433907\pi$
$954$	30.6274	−	14.6274i	0.991599	−	0.473580i
$955$	−14.0000	−	14.0000i	−0.453029	−	0.453029i
$956$		0			0
$957$	−4.82843	−	0.828427i	−0.156081	−	0.0267792i
$958$	20.0000			0.646171
$959$		0			0
$960$	0.292893	−	1.70711i	0.00945309	−	0.0550966i
$961$		−	13.0000i		−	0.419355i
$962$	−14.1421	−	21.2132i	−0.455961	−	0.683941i
$963$	32.0000	+	11.3137i	1.03119	+	0.364579i
$964$	1.00000	+	1.00000i	0.0322078	+	0.0322078i
$965$		−	8.48528i		−	0.273151i
$966$		0			0
$967$	−32.0000	−	32.0000i	−1.02905	−	1.02905i	−0.999565	−	0.0294854i	$-0.990613\pi$
$967$	−32.0000	−	32.0000i	−1.02905	−	1.02905i	−0.0294854	−	0.999565i	$-0.509387\pi$
$968$	4.94975	−	4.94975i	0.159091	−	0.159091i
$969$	10.5442	−	61.4558i	0.338727	−	1.97425i
$970$	10.0000	−	10.0000i	0.321081	−	0.321081i
$971$			12.7279i			0.408458i	0.978923	+	0.204229i	$0.0654688\pi$
$971$			12.7279i			0.408458i	−0.978923	+	0.204229i	$0.934531\pi$
$972$	−15.5563	−	1.00000i	−0.498970	−	0.0320750i
$973$		0			0
$974$		0			0
$975$	−2.24264	+	5.82843i	−0.0718220	+	0.186659i
$976$	−2.00000			−0.0640184
$977$	19.7990	−	19.7990i	0.633426	−	0.633426i	−0.315500	−	0.948926i	$-0.602172\pi$
$977$	19.7990	−	19.7990i	0.633426	−	0.633426i	0.948926	+	0.315500i	$0.102172\pi$
$978$	22.0000	−	15.5563i	0.703482	−	0.497437i
$979$			12.0000i			0.383522i
$980$	−4.94975	+	4.94975i	−0.158114	+	0.158114i
$981$	−7.65685	+	3.65685i	−0.244465	+	0.116754i
$982$	11.0000	−	11.0000i	0.351024	−	0.351024i
$983$	−24.0416	−	24.0416i	−0.766809	−	0.766809i	0.210734	−	0.977543i	$-0.432414\pi$
$983$	−24.0416	−	24.0416i	−0.766809	−	0.766809i	−0.977543	+	0.210734i	$0.932414\pi$
$984$	10.0000	+	14.1421i	0.318788	+	0.450835i
$985$		−	14.0000i		−	0.446077i
$986$	4.24264	+	4.24264i	0.135113	+	0.135113i
$987$		0			0
$988$	−6.00000	+	30.0000i	−0.190885	+	0.954427i
$989$		−	5.65685i		−	0.179878i
$990$	2.58579	+	5.41421i	0.0821817	+	0.172075i
$991$	−50.0000			−1.58830			−0.794151	−	0.607720i	$-0.792084\pi$
$991$	−50.0000			−1.58830			−0.794151	+	0.607720i	$0.792084\pi$
$992$	−4.24264			−0.134704
$993$	−9.94113	+	57.9411i	−0.315472	+	1.83871i
$994$		0			0
$995$	1.41421	+	1.41421i	0.0448336	+	0.0448336i
$996$	2.34315	−	13.6569i	0.0742454	−	0.432734i
$997$	22.0000			0.696747			0.348373	−	0.937356i	$-0.386734\pi$
$997$	22.0000			0.696747			0.348373	+	0.937356i	$0.386734\pi$
$998$	25.4558			0.805791
$999$	−17.9289	+	32.0711i	−0.567246	+	1.01468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.p.d.281.1	yes	4
3.2	odd	2	inner	390.2.p.d.281.2	yes	4
13.5	odd	4	inner	390.2.p.d.161.2	yes	4
39.5	even	4	inner	390.2.p.d.161.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.p.d.161.1	✓	4	39.5	even	4	inner
390.2.p.d.161.2	yes	4	13.5	odd	4	inner
390.2.p.d.281.1	yes	4	1.1	even	1	trivial
390.2.p.d.281.2	yes	4	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.00000 + 1.41421i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.70711 - 0.292893i) q^{6} +(0.707107 + 0.707107i) q^{8} +(-1.00000 + 2.82843i) q^{9} -1.00000i q^{10} +(1.41421 + 1.41421i) q^{11} +(1.41421 - 1.00000i) q^{12} +(-3.00000 + 2.00000i) q^{13} +(-1.70711 - 0.292893i) q^{15} -1.00000 q^{16} -4.24264 q^{17} +(-1.29289 - 2.70711i) q^{18} +(6.00000 + 6.00000i) q^{19} +(0.707107 + 0.707107i) q^{20} -2.00000 q^{22} -1.41421 q^{23} +(-0.292893 + 1.70711i) q^{24} -1.00000i q^{25} +(0.707107 - 3.53553i) q^{26} +(-5.00000 + 1.41421i) q^{27} +1.41421i q^{29} +(1.41421 - 1.00000i) q^{30} +(-3.00000 - 3.00000i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.585786 + 3.41421i) q^{33} +(3.00000 - 3.00000i) q^{34} +(2.82843 + 1.00000i) q^{36} +(5.00000 - 5.00000i) q^{37} -8.48528 q^{38} +(-5.82843 - 2.24264i) q^{39} -1.00000 q^{40} +(7.07107 - 7.07107i) q^{41} +4.00000i q^{43} +(1.41421 - 1.41421i) q^{44} +(-1.29289 - 2.70711i) q^{45} +(1.00000 - 1.00000i) q^{46} +(-4.24264 - 4.24264i) q^{47} +(-1.00000 - 1.41421i) q^{48} +7.00000i q^{49} +(0.707107 + 0.707107i) q^{50} +(-4.24264 - 6.00000i) q^{51} +(2.00000 + 3.00000i) q^{52} +11.3137i q^{53} +(2.53553 - 4.53553i) q^{54} -2.00000 q^{55} +(-2.48528 + 14.4853i) q^{57} +(-1.00000 - 1.00000i) q^{58} +(-2.82843 - 2.82843i) q^{59} +(-0.292893 + 1.70711i) q^{60} +2.00000 q^{61} +4.24264 q^{62} +1.00000i q^{64} +(0.707107 - 3.53553i) q^{65} +(-2.00000 - 2.82843i) q^{66} +(5.00000 + 5.00000i) q^{67} +4.24264i q^{68} +(-1.41421 - 2.00000i) q^{69} +(5.65685 - 5.65685i) q^{71} +(-2.70711 + 1.29289i) q^{72} +(6.00000 - 6.00000i) q^{73} +7.07107i q^{74} +(1.41421 - 1.00000i) q^{75} +(6.00000 - 6.00000i) q^{76} +(5.70711 - 2.53553i) q^{78} +8.00000 q^{79} +(0.707107 - 0.707107i) q^{80} +(-7.00000 - 5.65685i) q^{81} +10.0000i q^{82} +(5.65685 - 5.65685i) q^{83} +(3.00000 - 3.00000i) q^{85} +(-2.82843 - 2.82843i) q^{86} +(-2.00000 + 1.41421i) q^{87} +2.00000i q^{88} +(4.24264 + 4.24264i) q^{89} +(2.82843 + 1.00000i) q^{90} +1.41421i q^{92} +(1.24264 - 7.24264i) q^{93} +6.00000 q^{94} -8.48528 q^{95} +(1.70711 + 0.292893i) q^{96} +(10.0000 + 10.0000i) q^{97} +(-4.94975 - 4.94975i) q^{98} +(-5.41421 + 2.58579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{6} - 4 q^{9} - 12 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} + 24 q^{19} - 8 q^{22} - 4 q^{24} - 20 q^{27} - 12 q^{31} - 8 q^{33} + 12 q^{34} + 20 q^{37} - 12 q^{39} - 4 q^{40} - 8 q^{45}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^6 - 4 * q^9 - 12 * q^13 - 4 * q^15 - 4 * q^16 - 8 * q^18 + 24 * q^19 - 8 * q^22 - 4 * q^24 - 20 * q^27 - 12 * q^31 - 8 * q^33 + 12 * q^34 + 20 * q^37 - 12 * q^39 - 4 * q^40 - 8 * q^45 + 4 * q^46 - 4 * q^48 + 8 * q^52 - 4 * q^54 - 8 * q^55 + 24 * q^57 - 4 * q^58 - 4 * q^60 + 8 * q^61 - 8 * q^66 + 20 * q^67 - 8 * q^72 + 24 * q^73 + 24 * q^76 + 20 * q^78 + 32 * q^79 - 28 * q^81 + 12 * q^85 - 8 * q^87 - 12 * q^93 + 24 * q^94 + 4 * q^96 + 40 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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