LMFDB - Embedded newform 390.2.p.c.161.1

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,-4,0,0,4,8] 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			161.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	390.161
Dual form			390.2.p.c.281.1

$q$-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} +(2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} -1.00000i q^{10} +(-4.24264 + 4.24264i) q^{11} +(-1.41421 - 1.00000i) q^{12} +(3.00000 - 2.00000i) q^{13} -2.82843i q^{14} +(-1.70711 + 0.292893i) q^{15} -1.00000 q^{16} -1.41421 q^{17} +(-1.29289 + 2.70711i) q^{18} +(-0.707107 + 0.707107i) q^{20} +(-4.82843 + 0.828427i) q^{21} +6.00000 q^{22} -4.24264 q^{23} +(0.292893 + 1.70711i) q^{24} +1.00000i q^{25} +(-3.53553 - 0.707107i) q^{26} +(5.00000 + 1.41421i) q^{27} +(-2.00000 + 2.00000i) q^{28} +9.89949i q^{29} +(1.41421 + 1.00000i) q^{30} +(-7.00000 + 7.00000i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.75736 - 10.2426i) q^{33} +(1.00000 + 1.00000i) q^{34} +2.82843i q^{35} +(2.82843 - 1.00000i) q^{36} +(3.00000 + 3.00000i) q^{37} +(-0.171573 + 6.24264i) q^{39} +1.00000 q^{40} +(-1.41421 - 1.41421i) q^{41} +(4.00000 + 2.82843i) q^{42} +4.00000i q^{43} +(-4.24264 - 4.24264i) q^{44} +(1.29289 - 2.70711i) q^{45} +(3.00000 + 3.00000i) q^{46} +(4.24264 - 4.24264i) q^{47} +(1.00000 - 1.41421i) q^{48} +1.00000i q^{49} +(0.707107 - 0.707107i) q^{50} +(1.41421 - 2.00000i) q^{51} +(2.00000 + 3.00000i) q^{52} -5.65685i q^{53} +(-2.53553 - 4.53553i) q^{54} -6.00000 q^{55} +2.82843 q^{56} +(7.00000 - 7.00000i) q^{58} +(8.48528 - 8.48528i) q^{59} +(-0.292893 - 1.70711i) q^{60} -10.0000 q^{61} +9.89949 q^{62} +(3.65685 - 7.65685i) q^{63} -1.00000i q^{64} +(3.53553 + 0.707107i) q^{65} +(-6.00000 + 8.48528i) q^{66} +(3.00000 - 3.00000i) q^{67} -1.41421i q^{68} +(4.24264 - 6.00000i) q^{69} +(2.00000 - 2.00000i) q^{70} +(2.82843 + 2.82843i) q^{71} +(-2.70711 - 1.29289i) q^{72} -4.24264i q^{74} +(-1.41421 - 1.00000i) q^{75} -16.9706 q^{77} +(4.53553 - 4.29289i) q^{78} +(-0.707107 - 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +2.00000i q^{82} +(8.48528 + 8.48528i) q^{83} +(-0.828427 - 4.82843i) q^{84} +(-1.00000 - 1.00000i) q^{85} +(2.82843 - 2.82843i) q^{86} +(-14.0000 - 9.89949i) q^{87} +6.00000i q^{88} +(-7.07107 + 7.07107i) q^{89} +(-2.82843 + 1.00000i) q^{90} +(10.0000 + 2.00000i) q^{91} -4.24264i q^{92} +(-2.89949 - 16.8995i) q^{93} -6.00000 q^{94} +(-1.70711 + 0.292893i) q^{96} +(8.00000 - 8.00000i) q^{97} +(0.707107 - 0.707107i) q^{98} +(16.2426 + 7.75736i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 4 q^{6} + 8 q^{7} - 4 q^{9} + 12 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} - 8 q^{21} + 24 q^{22} + 4 q^{24} + 20 q^{27} - 8 q^{28} - 28 q^{31} - 24 q^{33} + 4 q^{34} + 12 q^{37} - 12 q^{39}+ \cdots + 48 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^6 + 8 * q^7 - 4 * q^9 + 12 * q^13 - 4 * q^15 - 4 * q^16 - 8 * q^18 - 8 * q^21 + 24 * q^22 + 4 * q^24 + 20 * q^27 - 8 * q^28 - 28 * q^31 - 24 * q^33 + 4 * q^34 + 12 * q^37 - 12 * q^39 + 4 * q^40 + 16 * q^42 + 8 * q^45 + 12 * q^46 + 4 * q^48 + 8 * q^52 + 4 * q^54 - 24 * q^55 + 28 * q^58 - 4 * q^60 - 40 * q^61 - 8 * q^63 - 24 * q^66 + 12 * q^67 + 8 * q^70 - 8 * q^72 + 4 * q^78 - 28 * q^81 + 8 * q^84 - 4 * q^85 - 56 * q^87 + 40 * q^91 + 28 * q^93 - 24 * q^94 - 4 * q^96 + 32 * q^97 + 48 * q^99

Character values

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

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	0.975579	−	0.219650i	$-0.0704915\pi$
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	−0.219650	+	0.975579i	$0.570491\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$		−	1.00000i		−	0.316228i
$11$	−4.24264	+	4.24264i	−1.27920	+	1.27920i	−0.338091	+	0.941113i	$0.609781\pi$
$11$	−4.24264	+	4.24264i	−1.27920	+	1.27920i	−0.941113	+	0.338091i	$0.890219\pi$
$12$	−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
$14$		−	2.82843i		−	0.755929i
$15$	−1.70711	+	0.292893i	−0.440773	+	0.0756247i
$16$	−1.00000			−0.250000
$17$	−1.41421			−0.342997			−0.171499	−	0.985184i	$-0.554861\pi$
$17$	−1.41421			−0.342997			−0.171499	+	0.985184i	$0.554861\pi$
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$19$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$20$	−0.707107	+	0.707107i	−0.158114	+	0.158114i
$21$	−4.82843	+	0.828427i	−1.05365	+	0.180778i
$22$	6.00000			1.27920
$23$	−4.24264			−0.884652			−0.442326	−	0.896854i	$-0.645847\pi$
$23$	−4.24264			−0.884652			−0.442326	+	0.896854i	$0.645847\pi$
$24$	0.292893	+	1.70711i	0.0597866	+	0.348462i
$25$			1.00000i			0.200000i
$26$	−3.53553	−	0.707107i	−0.693375	−	0.138675i
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$	−2.00000	+	2.00000i	−0.377964	+	0.377964i
$29$			9.89949i			1.83829i	0.393919	+	0.919145i	$0.371119\pi$
$29$			9.89949i			1.83829i	−0.393919	+	0.919145i	$0.628881\pi$
$30$	1.41421	+	1.00000i	0.258199	+	0.182574i
$31$	−7.00000	+	7.00000i	−1.25724	+	1.25724i	−0.304830	+	0.952407i	$0.598600\pi$
$31$	−7.00000	+	7.00000i	−1.25724	+	1.25724i	−0.952407	+	0.304830i	$0.901400\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.75736	−	10.2426i	−0.305917	−	1.78301i
$34$	1.00000	+	1.00000i	0.171499	+	0.171499i
$35$			2.82843i			0.478091i
$36$	2.82843	−	1.00000i	0.471405	−	0.166667i
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	0.909312	−	0.416115i	$-0.136609\pi$
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	−0.416115	+	0.909312i	$0.636609\pi$
$38$		0			0
$39$	−0.171573	+	6.24264i	−0.0274736	+	0.999623i
$40$	1.00000			0.158114
$41$	−1.41421	−	1.41421i	−0.220863	−	0.220863i	0.587999	−	0.808862i	$-0.299916\pi$
$41$	−1.41421	−	1.41421i	−0.220863	−	0.220863i	−0.808862	+	0.587999i	$0.799916\pi$
$42$	4.00000	+	2.82843i	0.617213	+	0.436436i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−4.24264	−	4.24264i	−0.639602	−	0.639602i
$45$	1.29289	−	2.70711i	0.192733	−	0.403552i
$46$	3.00000	+	3.00000i	0.442326	+	0.442326i
$47$	4.24264	−	4.24264i	0.618853	−	0.618853i	−0.326384	−	0.945237i	$-0.605830\pi$
$47$	4.24264	−	4.24264i	0.618853	−	0.618853i	0.945237	+	0.326384i	$0.105830\pi$
$48$	1.00000	−	1.41421i	0.144338	−	0.204124i
$49$			1.00000i			0.142857i
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	1.41421	−	2.00000i	0.198030	−	0.280056i
$52$	2.00000	+	3.00000i	0.277350	+	0.416025i
$53$		−	5.65685i		−	0.777029i	−0.921443	−	0.388514i	$-0.872988\pi$
$53$		−	5.65685i		−	0.777029i	0.921443	−	0.388514i	$-0.127012\pi$
$54$	−2.53553	−	4.53553i	−0.345042	−	0.617208i
$55$	−6.00000			−0.809040
$56$	2.82843			0.377964
$57$		0			0
$58$	7.00000	−	7.00000i	0.919145	−	0.919145i
$59$	8.48528	−	8.48528i	1.10469	−	1.10469i	0.110853	−	0.993837i	$-0.464642\pi$
$59$	8.48528	−	8.48528i	1.10469	−	1.10469i	0.993837	−	0.110853i	$-0.0353582\pi$
$60$	−0.292893	−	1.70711i	−0.0378124	−	0.220387i
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$	9.89949			1.25724
$63$	3.65685	−	7.65685i	0.460720	−	0.964673i
$64$		−	1.00000i		−	0.125000i
$65$	3.53553	+	0.707107i	0.438529	+	0.0877058i
$66$	−6.00000	+	8.48528i	−0.738549	+	1.04447i
$67$	3.00000	−	3.00000i	0.366508	−	0.366508i	−0.499694	−	0.866202i	$-0.666554\pi$
$67$	3.00000	−	3.00000i	0.366508	−	0.366508i	0.866202	+	0.499694i	$0.166554\pi$
$68$		−	1.41421i		−	0.171499i
$69$	4.24264	−	6.00000i	0.510754	−	0.722315i
$70$	2.00000	−	2.00000i	0.239046	−	0.239046i
$71$	2.82843	+	2.82843i	0.335673	+	0.335673i	0.854736	−	0.519063i	$-0.173719\pi$
$71$	2.82843	+	2.82843i	0.335673	+	0.335673i	−0.519063	+	0.854736i	$0.673719\pi$
$72$	−2.70711	−	1.29289i	−0.319036	−	0.152369i
$73$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$73$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$74$		−	4.24264i		−	0.493197i
$75$	−1.41421	−	1.00000i	−0.163299	−	0.115470i
$76$		0			0
$77$	−16.9706			−1.93398
$78$	4.53553	−	4.29289i	0.513548	−	0.486074i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−0.707107	−	0.707107i	−0.0790569	−	0.0790569i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$			2.00000i			0.220863i
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	0.997792	−	0.0664117i	$-0.0211551\pi$
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	−0.0664117	+	0.997792i	$0.521155\pi$
$84$	−0.828427	−	4.82843i	−0.0903888	−	0.526825i
$85$	−1.00000	−	1.00000i	−0.108465	−	0.108465i
$86$	2.82843	−	2.82843i	0.304997	−	0.304997i
$87$	−14.0000	−	9.89949i	−1.50096	−	1.06134i
$88$			6.00000i			0.639602i
$89$	−7.07107	+	7.07107i	−0.749532	+	0.749532i	−0.974391	−	0.224860i	$-0.927808\pi$
$89$	−7.07107	+	7.07107i	−0.749532	+	0.749532i	0.224860	+	0.974391i	$0.427808\pi$
$90$	−2.82843	+	1.00000i	−0.298142	+	0.105409i
$91$	10.0000	+	2.00000i	1.04828	+	0.209657i
$92$		−	4.24264i		−	0.442326i
$93$	−2.89949	−	16.8995i	−0.300664	−	1.75240i
$94$	−6.00000			−0.618853
$95$		0			0
$96$	−1.70711	+	0.292893i	−0.174231	+	0.0298933i
$97$	8.00000	−	8.00000i	0.812277	−	0.812277i	−0.172698	−	0.984975i	$-0.555248\pi$
$97$	8.00000	−	8.00000i	0.812277	−	0.812277i	0.984975	+	0.172698i	$0.0552484\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	16.2426	+	7.75736i	1.63245	+	0.779644i
$100$	−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	$0.218274\pi$
$102$	−2.41421	+	0.414214i	−0.239043	+	0.0410133i
$103$			8.00000i			0.788263i	0.919054	+	0.394132i	$0.128955\pi$
$103$			8.00000i			0.788263i	−0.919054	+	0.394132i	$0.871045\pi$
$104$	0.707107	−	3.53553i	0.0693375	−	0.346688i
$105$	−4.00000	−	2.82843i	−0.390360	−	0.276026i
$106$	−4.00000	+	4.00000i	−0.388514	+	0.388514i
$107$		−	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
$109$	12.0000	−	12.0000i	1.14939	−	1.14939i	0.162719	−	0.986672i	$-0.447974\pi$
$109$	12.0000	−	12.0000i	1.14939	−	1.14939i	0.986672	−	0.162719i	$-0.0520264\pi$
$110$	4.24264	+	4.24264i	0.404520	+	0.404520i
$111$	−7.24264	+	1.24264i	−0.687441	+	0.117946i
$112$	−2.00000	−	2.00000i	−0.188982	−	0.188982i
$113$			7.07107i			0.665190i	0.943070	+	0.332595i	$0.107924\pi$
$113$			7.07107i			0.665190i	−0.943070	+	0.332595i	$0.892076\pi$
$114$		0			0
$115$	−3.00000	−	3.00000i	−0.279751	−	0.279751i
$116$	−9.89949			−0.919145
$117$	−8.65685	−	6.48528i	−0.800326	−	0.599564i
$118$	−12.0000			−1.10469
$119$	−2.82843	−	2.82843i	−0.259281	−	0.259281i
$120$	−1.00000	+	1.41421i	−0.0912871	+	0.129099i
$121$		−	25.0000i		−	2.27273i
$122$	7.07107	+	7.07107i	0.640184	+	0.640184i
$123$	3.41421	−	0.585786i	0.307849	−	0.0528186i
$124$	−7.00000	−	7.00000i	−0.628619	−	0.628619i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−8.00000	+	2.82843i	−0.712697	+	0.251976i
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$	−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
$131$			1.41421i			0.123560i	0.998090	+	0.0617802i	$0.0196778\pi$
$131$			1.41421i			0.123560i	−0.998090	+	0.0617802i	$0.980322\pi$
$132$	10.2426	−	1.75736i	0.891507	−	0.152958i
$133$		0			0
$134$	−4.24264			−0.366508
$135$	2.53553	+	4.53553i	0.218224	+	0.390357i
$136$	−1.00000	+	1.00000i	−0.0857493	+	0.0857493i
$137$	11.3137	−	11.3137i	0.966595	−	0.966595i	−0.0328645	−	0.999460i	$-0.510463\pi$
$137$	11.3137	−	11.3137i	0.966595	−	0.966595i	0.999460	+	0.0328645i	$0.0104630\pi$
$138$	−7.24264	+	1.24264i	−0.616535	+	0.105781i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−2.82843			−0.239046
$141$	1.75736	+	10.2426i	0.147996	+	0.862586i
$142$		−	4.00000i		−	0.335673i
$143$	−4.24264	+	21.2132i	−0.354787	+	1.77394i
$144$	1.00000	+	2.82843i	0.0833333	+	0.235702i
$145$	−7.00000	+	7.00000i	−0.581318	+	0.581318i
$146$		0			0
$147$	−1.41421	−	1.00000i	−0.116642	−	0.0824786i
$148$	−3.00000	+	3.00000i	−0.246598	+	0.246598i
$149$	4.24264	+	4.24264i	0.347571	+	0.347571i	0.859204	−	0.511633i	$-0.170959\pi$
$149$	4.24264	+	4.24264i	0.347571	+	0.347571i	−0.511633	+	0.859204i	$0.670959\pi$
$150$	0.292893	+	1.70711i	0.0239146	+	0.139385i
$151$	−1.00000	−	1.00000i	−0.0813788	−	0.0813788i	0.665246	−	0.746625i	$-0.268327\pi$
$151$	−1.00000	−	1.00000i	−0.0813788	−	0.0813788i	−0.746625	+	0.665246i	$0.768327\pi$
$152$		0			0
$153$	1.41421	+	4.00000i	0.114332	+	0.323381i
$154$	12.0000	+	12.0000i	0.966988	+	0.966988i
$155$	−9.89949			−0.795147
$156$	−6.24264	−	0.171573i	−0.499811	−	0.0137368i
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$		0			0
$159$	8.00000	+	5.65685i	0.634441	+	0.448618i
$160$			1.00000i			0.0790569i
$161$	−8.48528	−	8.48528i	−0.668734	−	0.668734i
$162$	8.94975	+	0.949747i	0.703159	+	0.0746192i
$163$	15.0000	+	15.0000i	1.17489	+	1.17489i	0.981029	+	0.193862i	$0.0621013\pi$
$163$	15.0000	+	15.0000i	1.17489	+	1.17489i	0.193862	+	0.981029i	$0.437899\pi$
$164$	1.41421	−	1.41421i	0.110432	−	0.110432i
$165$	6.00000	−	8.48528i	0.467099	−	0.660578i
$166$		−	12.0000i		−	0.931381i
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	−0.453510	−	0.891251i	$-0.649829\pi$
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	0.891251	+	0.453510i	$0.149829\pi$
$168$	−2.82843	+	4.00000i	−0.218218	+	0.308607i
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$			1.41421i			0.108465i
$171$		0			0
$172$	−4.00000			−0.304997
$173$	14.1421			1.07521			0.537603	−	0.843198i	$-0.319330\pi$
$173$	14.1421			1.07521			0.537603	+	0.843198i	$0.319330\pi$
$174$	2.89949	+	16.8995i	0.219810	+	1.28115i
$175$	−2.00000	+	2.00000i	−0.151186	+	0.151186i
$176$	4.24264	−	4.24264i	0.319801	−	0.319801i
$177$	3.51472	+	20.4853i	0.264182	+	1.53977i
$178$	10.0000			0.749532
$179$	12.7279			0.951330			0.475665	−	0.879627i	$-0.342208\pi$
$179$	12.7279			0.951330			0.475665	+	0.879627i	$0.342208\pi$
$180$	2.70711	+	1.29289i	0.201776	+	0.0963666i
$181$			22.0000i			1.63525i	0.575753	+	0.817624i	$0.304709\pi$
$181$			22.0000i			1.63525i	−0.575753	+	0.817624i	$0.695291\pi$
$182$	−5.65685	−	8.48528i	−0.419314	−	0.628971i
$183$	10.0000	−	14.1421i	0.739221	−	1.04542i
$184$	−3.00000	+	3.00000i	−0.221163	+	0.221163i
$185$			4.24264i			0.311925i
$186$	−9.89949	+	14.0000i	−0.725866	+	1.02653i
$187$	6.00000	−	6.00000i	0.438763	−	0.438763i
$188$	4.24264	+	4.24264i	0.309426	+	0.309426i
$189$	7.17157	+	12.8284i	0.521655	+	0.933131i
$190$		0			0
$191$		−	8.48528i		−	0.613973i	−0.951714	−	0.306987i	$-0.900679\pi$
$191$		−	8.48528i		−	0.613973i	0.951714	−	0.306987i	$-0.0993207\pi$
$192$	1.41421	+	1.00000i	0.102062	+	0.0721688i
$193$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$193$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$194$	−11.3137			−0.812277
$195$	−4.53553	+	4.29289i	−0.324796	+	0.307420i
$196$	−1.00000			−0.0714286
$197$	1.41421	+	1.41421i	0.100759	+	0.100759i	0.755689	−	0.654931i	$-0.227302\pi$
$197$	1.41421	+	1.41421i	0.100759	+	0.100759i	−0.654931	+	0.755689i	$0.727302\pi$
$198$	−6.00000	−	16.9706i	−0.426401	−	1.20605i
$199$		−	6.00000i		−	0.425329i	−0.977125	−	0.212664i	$-0.931786\pi$
$199$		−	6.00000i		−	0.425329i	0.977125	−	0.212664i	$-0.0682141\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	1.24264	+	7.24264i	0.0876491	+	0.510856i
$202$	−11.0000	−	11.0000i	−0.773957	−	0.773957i
$203$	−19.7990	+	19.7990i	−1.38962	+	1.38962i
$204$	2.00000	+	1.41421i	0.140028	+	0.0990148i
$205$		−	2.00000i		−	0.139686i
$206$	5.65685	−	5.65685i	0.394132	−	0.394132i
$207$	4.24264	+	12.0000i	0.294884	+	0.834058i
$208$	−3.00000	+	2.00000i	−0.208013	+	0.138675i
$209$		0			0
$210$	0.828427	+	4.82843i	0.0571669	+	0.333193i
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	5.65685			0.388514
$213$	−6.82843	+	1.17157i	−0.467876	+	0.0802749i
$214$	−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
$217$	−28.0000			−1.90076
$218$	−16.9706			−1.14939
$219$		0			0
$220$		−	6.00000i		−	0.404520i
$221$	−4.24264	+	2.82843i	−0.285391	+	0.190261i
$222$	6.00000	+	4.24264i	0.402694	+	0.284747i
$223$	4.00000	−	4.00000i	0.267860	−	0.267860i	−0.560378	−	0.828237i	$-0.689344\pi$
$223$	4.00000	−	4.00000i	0.267860	−	0.267860i	0.828237	+	0.560378i	$0.189344\pi$
$224$			2.82843i			0.188982i
$225$	2.82843	−	1.00000i	0.188562	−	0.0666667i
$226$	5.00000	−	5.00000i	0.332595	−	0.332595i
$227$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$227$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$228$		0			0
$229$	8.00000	+	8.00000i	0.528655	+	0.528655i	0.920171	−	0.391516i	$-0.128049\pi$
$229$	8.00000	+	8.00000i	0.528655	+	0.528655i	−0.391516	+	0.920171i	$0.628049\pi$
$230$			4.24264i			0.279751i
$231$	16.9706	−	24.0000i	1.11658	−	1.57908i
$232$	7.00000	+	7.00000i	0.459573	+	0.459573i
$233$	−4.24264			−0.277945			−0.138972	−	0.990296i	$-0.544380\pi$
$233$	−4.24264			−0.277945			−0.138972	+	0.990296i	$0.544380\pi$
$234$	1.53553	+	10.7071i	0.100381	+	0.699945i
$235$	6.00000			0.391397
$236$	8.48528	+	8.48528i	0.552345	+	0.552345i
$237$		0			0
$238$			4.00000i			0.259281i
$239$	−11.3137	−	11.3137i	−0.731823	−	0.731823i	0.239158	−	0.970981i	$-0.423129\pi$
$239$	−11.3137	−	11.3137i	−0.731823	−	0.731823i	−0.970981	+	0.239158i	$0.923129\pi$
$240$	1.70711	−	0.292893i	0.110193	−	0.0189062i
$241$	15.0000	+	15.0000i	0.966235	+	0.966235i	0.999448	−	0.0332133i	$-0.0105741\pi$
$241$	15.0000	+	15.0000i	0.966235	+	0.966235i	−0.0332133	+	0.999448i	$0.510574\pi$
$242$	−17.6777	+	17.6777i	−1.13636	+	1.13636i
$243$	−1.00000	−	15.5563i	−0.0641500	−	0.997940i
$244$		−	10.0000i		−	0.640184i
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$	−2.82843	−	2.00000i	−0.180334	−	0.127515i
$247$		0			0
$248$			9.89949i			0.628619i
$249$	−20.4853	+	3.51472i	−1.29820	+	0.222736i
$250$	1.00000			0.0632456
$251$	−7.07107			−0.446322			−0.223161	−	0.974782i	$-0.571638\pi$
$251$	−7.07107			−0.446322			−0.223161	+	0.974782i	$0.571638\pi$
$252$	7.65685	+	3.65685i	0.482336	+	0.230360i
$253$	18.0000	−	18.0000i	1.13165	−	1.13165i
$254$	11.3137	−	11.3137i	0.709885	−	0.709885i
$255$	2.41421	−	0.414214i	0.151184	−	0.0259391i
$256$	1.00000			0.0625000
$257$	−9.89949			−0.617514			−0.308757	−	0.951141i	$-0.599913\pi$
$257$	−9.89949			−0.617514			−0.308757	+	0.951141i	$0.599913\pi$
$258$	1.17157	+	6.82843i	0.0729389	+	0.425119i
$259$			12.0000i			0.745644i
$260$	−0.707107	+	3.53553i	−0.0438529	+	0.219265i
$261$	28.0000	−	9.89949i	1.73316	−	0.612763i
$262$	1.00000	−	1.00000i	0.0617802	−	0.0617802i
$263$			7.07107i			0.436021i	0.975946	+	0.218010i	$0.0699567\pi$
$263$			7.07107i			0.436021i	−0.975946	+	0.218010i	$0.930043\pi$
$264$	−8.48528	−	6.00000i	−0.522233	−	0.369274i
$265$	4.00000	−	4.00000i	0.245718	−	0.245718i
$266$		0			0
$267$	−2.92893	−	17.0711i	−0.179248	−	1.04473i
$268$	3.00000	+	3.00000i	0.183254	+	0.183254i
$269$		−	1.41421i		−	0.0862261i	−0.999070	−	0.0431131i	$-0.986272\pi$
$269$		−	1.41421i		−	0.0862261i	0.999070	−	0.0431131i	$-0.0137276\pi$
$270$	1.41421	−	5.00000i	0.0860663	−	0.304290i
$271$	−15.0000	−	15.0000i	−0.911185	−	0.911185i	0.0851804	−	0.996366i	$-0.472853\pi$
$271$	−15.0000	−	15.0000i	−0.911185	−	0.911185i	−0.996366	+	0.0851804i	$0.972853\pi$
$272$	1.41421			0.0857493
$273$	−12.8284	+	12.1421i	−0.776412	+	0.734875i
$274$	−16.0000			−0.966595
$275$	−4.24264	−	4.24264i	−0.255841	−	0.255841i
$276$	6.00000	+	4.24264i	0.361158	+	0.255377i
$277$		−	4.00000i		−	0.240337i	−0.992754	−	0.120168i	$-0.961657\pi$
$277$		−	4.00000i		−	0.240337i	0.992754	−	0.120168i	$-0.0383434\pi$
$278$		0			0
$279$	26.7990	+	12.7990i	1.60441	+	0.766255i
$280$	2.00000	+	2.00000i	0.119523	+	0.119523i
$281$	−7.07107	+	7.07107i	−0.421825	+	0.421825i	−0.885832	−	0.464007i	$-0.846411\pi$
$281$	−7.07107	+	7.07107i	−0.421825	+	0.421825i	0.464007	+	0.885832i	$0.346411\pi$
$282$	6.00000	−	8.48528i	0.357295	−	0.505291i
$283$		−	26.0000i		−	1.54554i	−0.634686	−	0.772770i	$-0.718871\pi$
$283$		−	26.0000i		−	1.54554i	0.634686	−	0.772770i	$-0.281129\pi$
$284$	−2.82843	+	2.82843i	−0.167836	+	0.167836i
$285$		0			0
$286$	18.0000	−	12.0000i	1.06436	−	0.709575i
$287$		−	5.65685i		−	0.333914i
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$	−15.0000			−0.882353
$290$	9.89949			0.581318
$291$	3.31371	+	19.3137i	0.194253	+	1.13219i
$292$		0			0
$293$	−1.41421	+	1.41421i	−0.0826192	+	0.0826192i	−0.747209	−	0.664589i	$-0.768606\pi$
$293$	−1.41421	+	1.41421i	−0.0826192	+	0.0826192i	0.664589	+	0.747209i	$0.268606\pi$
$294$	0.292893	+	1.70711i	0.0170819	+	0.0995605i
$295$	12.0000			0.698667
$296$	4.24264			0.246598
$297$	−27.2132	+	15.2132i	−1.57907	+	0.882760i
$298$		−	6.00000i		−	0.347571i
$299$	−12.7279	+	8.48528i	−0.736075	+	0.490716i
$300$	1.00000	−	1.41421i	0.0577350	−	0.0816497i
$301$	−8.00000	+	8.00000i	−0.461112	+	0.461112i
$302$			1.41421i			0.0813788i
$303$	−15.5563	+	22.0000i	−0.893689	+	1.26387i
$304$		0			0
$305$	−7.07107	−	7.07107i	−0.404888	−	0.404888i
$306$	1.82843	−	3.82843i	0.104524	−	0.218857i
$307$	1.00000	+	1.00000i	0.0570730	+	0.0570730i	0.735067	−	0.677994i	$-0.237151\pi$
$307$	1.00000	+	1.00000i	0.0570730	+	0.0570730i	−0.677994	+	0.735067i	$0.737151\pi$
$308$		−	16.9706i		−	0.966988i
$309$	−11.3137	−	8.00000i	−0.643614	−	0.455104i
$310$	7.00000	+	7.00000i	0.397573	+	0.397573i
$311$	14.1421			0.801927			0.400963	−	0.916094i	$-0.368675\pi$
$311$	14.1421			0.801927			0.400963	+	0.916094i	$0.368675\pi$
$312$	4.29289	+	4.53553i	0.243037	+	0.256774i
$313$	−34.0000			−1.92179			−0.960897	−	0.276907i	$-0.910691\pi$
$313$	−34.0000			−1.92179			−0.960897	+	0.276907i	$0.910691\pi$
$314$	1.41421	+	1.41421i	0.0798087	+	0.0798087i
$315$	8.00000	−	2.82843i	0.450749	−	0.159364i
$316$		0			0
$317$	−12.7279	−	12.7279i	−0.714871	−	0.714871i	0.252679	−	0.967550i	$-0.418688\pi$
$317$	−12.7279	−	12.7279i	−0.714871	−	0.714871i	−0.967550	+	0.252679i	$0.918688\pi$
$318$	−1.65685	−	9.65685i	−0.0929118	−	0.541529i
$319$	−42.0000	−	42.0000i	−2.35155	−	2.35155i
$320$	0.707107	−	0.707107i	0.0395285	−	0.0395285i
$321$	16.0000	+	11.3137i	0.893033	+	0.631470i
$322$			12.0000i			0.668734i
$323$		0			0
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	2.00000	+	3.00000i	0.110940	+	0.166410i
$326$		−	21.2132i		−	1.17489i
$327$	4.97056	+	28.9706i	0.274873	+	1.60208i
$328$	−2.00000			−0.110432
$329$	16.9706			0.935617
$330$	−10.2426	+	1.75736i	−0.563839	+	0.0967394i
$331$	−6.00000	+	6.00000i	−0.329790	+	0.329790i	−0.852506	−	0.522717i	$-0.824919\pi$
$331$	−6.00000	+	6.00000i	−0.329790	+	0.329790i	0.522717	+	0.852506i	$0.324919\pi$
$332$	−8.48528	+	8.48528i	−0.465690	+	0.465690i
$333$	5.48528	−	11.4853i	0.300592	−	0.629390i
$334$	−8.00000			−0.437741
$335$	4.24264			0.231800
$336$	4.82843	−	0.828427i	0.263412	−	0.0451944i
$337$		−	18.0000i		−	0.980522i	−0.871576	−	0.490261i	$-0.836901\pi$
$337$		−	18.0000i		−	0.980522i	0.871576	−	0.490261i	$-0.163099\pi$
$338$	−12.0208	+	4.94975i	−0.653846	+	0.269231i
$339$	−10.0000	−	7.07107i	−0.543125	−	0.384048i
$340$	1.00000	−	1.00000i	0.0542326	−	0.0542326i
$341$		−	59.3970i		−	3.21653i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	2.82843	+	2.82843i	0.152499	+	0.152499i
$345$	7.24264	−	1.24264i	0.389931	−	0.0669015i
$346$	−10.0000	−	10.0000i	−0.537603	−	0.537603i
$347$			5.65685i			0.303676i	0.988405	+	0.151838i	$0.0485192\pi$
$347$			5.65685i			0.303676i	−0.988405	+	0.151838i	$0.951481\pi$
$348$	9.89949	−	14.0000i	0.530669	−	0.750479i
$349$	10.0000	+	10.0000i	0.535288	+	0.535288i	0.922141	−	0.386853i	$-0.126438\pi$
$349$	10.0000	+	10.0000i	0.535288	+	0.535288i	−0.386853	+	0.922141i	$0.626438\pi$
$350$	2.82843			0.151186
$351$	17.8284	−	5.75736i	0.951611	−	0.307305i
$352$	−6.00000			−0.319801
$353$	22.6274	+	22.6274i	1.20434	+	1.20434i	0.972835	+	0.231501i	$0.0743638\pi$
$353$	22.6274	+	22.6274i	1.20434	+	1.20434i	0.231501	+	0.972835i	$0.425636\pi$
$354$	12.0000	−	16.9706i	0.637793	−	0.901975i
$355$			4.00000i			0.212298i
$356$	−7.07107	−	7.07107i	−0.374766	−	0.374766i
$357$	6.82843	−	1.17157i	0.361399	−	0.0620062i
$358$	−9.00000	−	9.00000i	−0.475665	−	0.475665i
$359$	14.1421	−	14.1421i	0.746393	−	0.746393i	−0.227407	−	0.973800i	$-0.573025\pi$
$359$	14.1421	−	14.1421i	0.746393	−	0.746393i	0.973800	+	0.227407i	$0.0730246\pi$
$360$	−1.00000	−	2.82843i	−0.0527046	−	0.149071i
$361$			19.0000i			1.00000i
$362$	15.5563	−	15.5563i	0.817624	−	0.817624i
$363$	35.3553	+	25.0000i	1.85567	+	1.31216i
$364$	−2.00000	+	10.0000i	−0.104828	+	0.524142i
$365$		0			0
$366$	−17.0711	+	2.92893i	−0.892319	+	0.153098i
$367$	28.0000			1.46159			0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000			1.46159			0.730794	+	0.682598i	$0.239150\pi$
$368$	4.24264			0.221163
$369$	−2.58579	+	5.41421i	−0.134611	+	0.281853i
$370$	3.00000	−	3.00000i	0.155963	−	0.155963i
$371$	11.3137	−	11.3137i	0.587378	−	0.587378i
$372$	16.8995	−	2.89949i	0.876198	−	0.150332i
$373$	−24.0000			−1.24267			−0.621336	−	0.783544i	$-0.713410\pi$
$373$	−24.0000			−1.24267			−0.621336	+	0.783544i	$0.713410\pi$
$374$	−8.48528			−0.438763
$375$	−0.292893	−	1.70711i	−0.0151249	−	0.0881546i
$376$		−	6.00000i		−	0.309426i
$377$	19.7990	+	29.6985i	1.01970	+	1.52955i
$378$	4.00000	−	14.1421i	0.205738	−	0.727393i
$379$	6.00000	−	6.00000i	0.308199	−	0.308199i	−0.536011	−	0.844211i	$-0.680070\pi$
$379$	6.00000	−	6.00000i	0.308199	−	0.308199i	0.844211	+	0.536011i	$0.180070\pi$
$380$		0			0
$381$	−22.6274	−	16.0000i	−1.15924	−	0.819705i
$382$	−6.00000	+	6.00000i	−0.306987	+	0.306987i
$383$	−11.3137	−	11.3137i	−0.578103	−	0.578103i	0.356277	−	0.934380i	$-0.384046\pi$
$383$	−11.3137	−	11.3137i	−0.578103	−	0.578103i	−0.934380	+	0.356277i	$0.884046\pi$
$384$	−0.292893	−	1.70711i	−0.0149466	−	0.0871154i
$385$	−12.0000	−	12.0000i	−0.611577	−	0.611577i
$386$		0			0
$387$	11.3137	−	4.00000i	0.575108	−	0.203331i
$388$	8.00000	+	8.00000i	0.406138	+	0.406138i
$389$	9.89949			0.501924			0.250962	−	0.967997i	$-0.419253\pi$
$389$	9.89949			0.501924			0.250962	+	0.967997i	$0.419253\pi$
$390$	6.24264	+	0.171573i	0.316108	+	0.00868793i
$391$	6.00000			0.303433
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	−2.00000	−	1.41421i	−0.100887	−	0.0713376i
$394$		−	2.00000i		−	0.100759i
$395$		0			0
$396$	−7.75736	+	16.2426i	−0.389822	+	0.816223i
$397$	−3.00000	−	3.00000i	−0.150566	−	0.150566i	0.627805	−	0.778371i	$-0.283954\pi$
$397$	−3.00000	−	3.00000i	−0.150566	−	0.150566i	−0.778371	+	0.627805i	$0.783954\pi$
$398$	−4.24264	+	4.24264i	−0.212664	+	0.212664i
$399$		0			0
$400$		−	1.00000i		−	0.0500000i
$401$	9.89949	−	9.89949i	0.494357	−	0.494357i	−0.415319	−	0.909676i	$-0.636330\pi$
$401$	9.89949	−	9.89949i	0.494357	−	0.494357i	0.909676	+	0.415319i	$0.136330\pi$
$402$	4.24264	−	6.00000i	0.211604	−	0.299253i
$403$	−7.00000	+	35.0000i	−0.348695	+	1.74347i
$404$			15.5563i			0.773957i
$405$	−8.94975	−	0.949747i	−0.444717	−	0.0471933i
$406$	28.0000			1.38962
$407$	−25.4558			−1.26180
$408$	−0.414214	−	2.41421i	−0.0205066	−	0.119521i
$409$	1.00000	−	1.00000i	0.0494468	−	0.0494468i	−0.681951	−	0.731398i	$-0.738868\pi$
$409$	1.00000	−	1.00000i	0.0494468	−	0.0494468i	0.731398	+	0.681951i	$0.238868\pi$
$410$	−1.41421	+	1.41421i	−0.0698430	+	0.0698430i
$411$	4.68629	+	27.3137i	0.231158	+	1.34729i
$412$	−8.00000			−0.394132
$413$	33.9411			1.67013
$414$	5.48528	−	11.4853i	0.269587	−	0.564471i
$415$			12.0000i			0.589057i
$416$	3.53553	+	0.707107i	0.173344	+	0.0346688i
$417$		0			0
$418$		0			0
$419$			9.89949i			0.483622i	0.970323	+	0.241811i	$0.0777414\pi$
$419$			9.89949i			0.483622i	−0.970323	+	0.241811i	$0.922259\pi$
$420$	2.82843	−	4.00000i	0.138013	−	0.195180i
$421$	18.0000	−	18.0000i	0.877266	−	0.877266i	−0.115985	−	0.993251i	$-0.537002\pi$
$421$	18.0000	−	18.0000i	0.877266	−	0.877266i	0.993251	+	0.115985i	$0.0370024\pi$
$422$	14.1421	+	14.1421i	0.688428	+	0.688428i
$423$	−16.2426	−	7.75736i	−0.789744	−	0.377176i
$424$	−4.00000	−	4.00000i	−0.194257	−	0.194257i
$425$		−	1.41421i		−	0.0685994i
$426$	5.65685	+	4.00000i	0.274075	+	0.193801i
$427$	−20.0000	−	20.0000i	−0.967868	−	0.967868i
$428$	11.3137			0.546869
$429$	−25.7574	−	27.2132i	−1.24358	−	1.31387i
$430$	4.00000			0.192897
$431$	−25.4558	−	25.4558i	−1.22616	−	1.22616i	−0.965403	−	0.260762i	$-0.916026\pi$
$431$	−25.4558	−	25.4558i	−1.22616	−	1.22616i	−0.260762	−	0.965403i	$-0.583974\pi$
$432$	−5.00000	−	1.41421i	−0.240563	−	0.0680414i
$433$			10.0000i			0.480569i	0.970702	+	0.240285i	$0.0772408\pi$
$433$			10.0000i			0.480569i	−0.970702	+	0.240285i	$0.922759\pi$
$434$	19.7990	+	19.7990i	0.950382	+	0.950382i
$435$	−2.89949	−	16.8995i	−0.139020	−	0.810269i
$436$	12.0000	+	12.0000i	0.574696	+	0.574696i
$437$		0			0
$438$		0			0
$439$			38.0000i			1.81364i	0.421517	+	0.906821i	$0.361498\pi$
$439$			38.0000i			1.81364i	−0.421517	+	0.906821i	$0.638502\pi$
$440$	−4.24264	+	4.24264i	−0.202260	+	0.202260i
$441$	2.82843	−	1.00000i	0.134687	−	0.0476190i
$442$	5.00000	+	1.00000i	0.237826	+	0.0475651i
$443$			19.7990i			0.940678i	0.882486	+	0.470339i	$0.155868\pi$
$443$			19.7990i			0.940678i	−0.882486	+	0.470339i	$0.844132\pi$
$444$	−1.24264	−	7.24264i	−0.0589731	−	0.343721i
$445$	−10.0000			−0.474045
$446$	−5.65685			−0.267860
$447$	−10.2426	+	1.75736i	−0.484460	+	0.0831202i
$448$	2.00000	−	2.00000i	0.0944911	−	0.0944911i
$449$	1.41421	−	1.41421i	0.0667409	−	0.0667409i	−0.672948	−	0.739689i	$-0.734972\pi$
$449$	1.41421	−	1.41421i	0.0667409	−	0.0667409i	0.739689	+	0.672948i	$0.234972\pi$
$450$	−2.70711	−	1.29289i	−0.127614	−	0.0609476i
$451$	12.0000			0.565058
$452$	−7.07107			−0.332595
$453$	2.41421	−	0.414214i	0.113430	−	0.0194615i
$454$		0			0
$455$	5.65685	+	8.48528i	0.265197	+	0.397796i
$456$		0			0
$457$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$457$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$458$		−	11.3137i		−	0.528655i
$459$	−7.07107	−	2.00000i	−0.330049	−	0.0933520i
$460$	3.00000	−	3.00000i	0.139876	−	0.139876i
$461$	28.2843	+	28.2843i	1.31733	+	1.31733i	0.915882	+	0.401448i	$0.131493\pi$
$461$	28.2843	+	28.2843i	1.31733	+	1.31733i	0.401448	+	0.915882i	$0.368507\pi$
$462$	−28.9706	+	4.97056i	−1.34783	+	0.231252i
$463$	−16.0000	−	16.0000i	−0.743583	−	0.743583i	0.229683	−	0.973266i	$-0.426231\pi$
$463$	−16.0000	−	16.0000i	−0.743583	−	0.743583i	−0.973266	+	0.229683i	$0.926231\pi$
$464$		−	9.89949i		−	0.459573i
$465$	9.89949	−	14.0000i	0.459078	−	0.649234i
$466$	3.00000	+	3.00000i	0.138972	+	0.138972i
$467$	−8.48528			−0.392652			−0.196326	−	0.980539i	$-0.562901\pi$
$467$	−8.48528			−0.392652			−0.196326	+	0.980539i	$0.562901\pi$
$468$	6.48528	−	8.65685i	0.299782	−	0.400163i
$469$	12.0000			0.554109
$470$	−4.24264	−	4.24264i	−0.195698	−	0.195698i
$471$	2.00000	−	2.82843i	0.0921551	−	0.130327i
$472$		−	12.0000i		−	0.552345i
$473$	−16.9706	−	16.9706i	−0.780307	−	0.780307i
$474$		0			0
$475$		0			0
$476$	2.82843	−	2.82843i	0.129641	−	0.129641i
$477$	−16.0000	+	5.65685i	−0.732590	+	0.259010i
$478$			16.0000i			0.731823i
$479$	−25.4558	+	25.4558i	−1.16311	+	1.16311i	−0.179316	+	0.983792i	$0.557388\pi$
$479$	−25.4558	+	25.4558i	−1.16311	+	1.16311i	−0.983792	+	0.179316i	$0.942612\pi$
$480$	−1.41421	−	1.00000i	−0.0645497	−	0.0456435i
$481$	15.0000	+	3.00000i	0.683941	+	0.136788i
$482$		−	21.2132i		−	0.966235i
$483$	20.4853	−	3.51472i	0.932113	−	0.159925i
$484$	25.0000			1.13636
$485$	11.3137			0.513729
$486$	−10.2929	+	11.7071i	−0.466895	+	0.531045i
$487$	−14.0000	+	14.0000i	−0.634401	+	0.634401i	−0.949169	−	0.314768i	$-0.898073\pi$
$487$	−14.0000	+	14.0000i	−0.634401	+	0.634401i	0.314768	+	0.949169i	$0.398073\pi$
$488$	−7.07107	+	7.07107i	−0.320092	+	0.320092i
$489$	−36.2132	+	6.21320i	−1.63762	+	0.280971i
$490$	1.00000			0.0451754
$491$	−15.5563			−0.702048			−0.351024	−	0.936366i	$-0.614166\pi$
$491$	−15.5563			−0.702048			−0.351024	+	0.936366i	$0.614166\pi$
$492$	0.585786	+	3.41421i	0.0264093	+	0.153925i
$493$		−	14.0000i		−	0.630528i
$494$		0			0
$495$	6.00000	+	16.9706i	0.269680	+	0.762770i
$496$	7.00000	−	7.00000i	0.314309	−	0.314309i
$497$			11.3137i			0.507489i
$498$	16.9706	+	12.0000i	0.760469	+	0.537733i
$499$	24.0000	−	24.0000i	1.07439	−	1.07439i	0.0773864	−	0.997001i	$-0.475342\pi$
$499$	24.0000	−	24.0000i	1.07439	−	1.07439i	0.997001	−	0.0773864i	$-0.0246575\pi$
$500$	−0.707107	−	0.707107i	−0.0316228	−	0.0316228i
$501$	2.34315	+	13.6569i	0.104684	+	0.610143i
$502$	5.00000	+	5.00000i	0.223161	+	0.223161i
$503$		−	35.3553i		−	1.57642i	−0.615409	−	0.788208i	$-0.711009\pi$
$503$		−	35.3553i		−	1.57642i	0.615409	−	0.788208i	$-0.288991\pi$
$504$	−2.82843	−	8.00000i	−0.125988	−	0.356348i
$505$	11.0000	+	11.0000i	0.489494	+	0.489494i
$506$	−25.4558			−1.13165
$507$	11.9706	+	19.0711i	0.531631	+	0.846976i
$508$	−16.0000			−0.709885
$509$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$509$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$510$	−2.00000	−	1.41421i	−0.0885615	−	0.0626224i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	7.00000	+	7.00000i	0.308757	+	0.308757i
$515$	−5.65685	+	5.65685i	−0.249271	+	0.249271i
$516$	4.00000	−	5.65685i	0.176090	−	0.249029i
$517$			36.0000i			1.58328i
$518$	8.48528	−	8.48528i	0.372822	−	0.372822i
$519$	−14.1421	+	20.0000i	−0.620771	+	0.877903i
$520$	3.00000	−	2.00000i	0.131559	−	0.0877058i
$521$			11.3137i			0.495663i	0.968803	+	0.247831i	$0.0797179\pi$
$521$			11.3137i			0.495663i	−0.968803	+	0.247831i	$0.920282\pi$
$522$	−26.7990	−	12.7990i	−1.17296	−	0.560197i
$523$	−12.0000			−0.524723			−0.262362	−	0.964970i	$-0.584501\pi$
$523$	−12.0000			−0.524723			−0.262362	+	0.964970i	$0.584501\pi$
$524$	−1.41421			−0.0617802
$525$	−0.828427	−	4.82843i	−0.0361555	−	0.210730i
$526$	5.00000	−	5.00000i	0.218010	−	0.218010i
$527$	9.89949	−	9.89949i	0.431229	−	0.431229i
$528$	1.75736	+	10.2426i	0.0764792	+	0.445754i
$529$	−5.00000			−0.217391
$530$	−5.65685			−0.245718
$531$	−32.4853	−	15.5147i	−1.40974	−	0.673281i
$532$		0			0
$533$	−7.07107	−	1.41421i	−0.306282	−	0.0612564i
$534$	−10.0000	+	14.1421i	−0.432742	+	0.611990i
$535$	8.00000	−	8.00000i	0.345870	−	0.345870i
$536$		−	4.24264i		−	0.183254i
$537$	−12.7279	+	18.0000i	−0.549250	+	0.776757i
$538$	−1.00000	+	1.00000i	−0.0431131	+	0.0431131i
$539$	−4.24264	−	4.24264i	−0.182743	−	0.182743i
$540$	−4.53553	+	2.53553i	−0.195178	+	0.109112i
$541$	18.0000	+	18.0000i	0.773880	+	0.773880i	0.978782	−	0.204902i	$-0.0656876\pi$
$541$	18.0000	+	18.0000i	0.773880	+	0.773880i	−0.204902	+	0.978782i	$0.565688\pi$
$542$			21.2132i			0.911185i
$543$	−31.1127	−	22.0000i	−1.33517	−	0.944110i
$544$	−1.00000	−	1.00000i	−0.0428746	−	0.0428746i
$545$	16.9706			0.726939
$546$	17.6569	+	0.485281i	0.755644	+	0.0207681i
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	11.3137	+	11.3137i	0.483298	+	0.483298i
$549$	10.0000	+	28.2843i	0.426790	+	1.20714i
$550$			6.00000i			0.255841i
$551$		0			0
$552$	−1.24264	−	7.24264i	−0.0528903	−	0.308267i
$553$		0			0
$554$	−2.82843	+	2.82843i	−0.120168	+	0.120168i
$555$	−6.00000	−	4.24264i	−0.254686	−	0.180090i
$556$		0			0
$557$	−1.41421	+	1.41421i	−0.0599222	+	0.0599222i	−0.736433	−	0.676511i	$-0.763491\pi$
$557$	−1.41421	+	1.41421i	−0.0599222	+	0.0599222i	0.676511	+	0.736433i	$0.263491\pi$
$558$	−9.89949	−	28.0000i	−0.419079	−	1.18533i
$559$	8.00000	+	12.0000i	0.338364	+	0.507546i
$560$		−	2.82843i		−	0.119523i
$561$	2.48528	+	14.4853i	0.104929	+	0.611569i
$562$	10.0000			0.421825
$563$	−2.82843			−0.119204			−0.0596020	−	0.998222i	$-0.518983\pi$
$563$	−2.82843			−0.119204			−0.0596020	+	0.998222i	$0.518983\pi$
$564$	−10.2426	+	1.75736i	−0.431293	+	0.0739982i
$565$	−5.00000	+	5.00000i	−0.210352	+	0.210352i
$566$	−18.3848	+	18.3848i	−0.772770	+	0.772770i
$567$	−25.3137	−	2.68629i	−1.06308	−	0.112814i
$568$	4.00000			0.167836
$569$	−11.3137			−0.474295			−0.237148	−	0.971474i	$-0.576213\pi$
$569$	−11.3137			−0.474295			−0.237148	+	0.971474i	$0.576213\pi$
$570$		0			0
$571$		−	4.00000i		−	0.167395i	−0.996491	−	0.0836974i	$-0.973327\pi$
$571$		−	4.00000i		−	0.167395i	0.996491	−	0.0836974i	$-0.0266729\pi$
$572$	−21.2132	−	4.24264i	−0.886969	−	0.177394i
$573$	12.0000	+	8.48528i	0.501307	+	0.354478i
$574$	−4.00000	+	4.00000i	−0.166957	+	0.166957i
$575$		−	4.24264i		−	0.176930i
$576$	−2.82843	+	1.00000i	−0.117851	+	0.0416667i
$577$	4.00000	−	4.00000i	0.166522	−	0.166522i	−0.618927	−	0.785449i	$-0.712432\pi$
$577$	4.00000	−	4.00000i	0.166522	−	0.166522i	0.785449	+	0.618927i	$0.212432\pi$
$578$	10.6066	+	10.6066i	0.441176	+	0.441176i
$579$		0			0
$580$	−7.00000	−	7.00000i	−0.290659	−	0.290659i
$581$			33.9411i			1.40812i
$582$	11.3137	−	16.0000i	0.468968	−	0.663221i
$583$	24.0000	+	24.0000i	0.993978	+	0.993978i
$584$		0			0
$585$	−1.53553	−	10.7071i	−0.0634865	−	0.442684i
$586$	2.00000			0.0826192
$587$	−2.82843	−	2.82843i	−0.116742	−	0.116742i	0.646323	−	0.763064i	$-0.276306\pi$
$587$	−2.82843	−	2.82843i	−0.116742	−	0.116742i	−0.763064	+	0.646323i	$0.776306\pi$
$588$	1.00000	−	1.41421i	0.0412393	−	0.0583212i
$589$		0			0
$590$	−8.48528	−	8.48528i	−0.349334	−	0.349334i
$591$	−3.41421	+	0.585786i	−0.140442	+	0.0240960i
$592$	−3.00000	−	3.00000i	−0.123299	−	0.123299i
$593$	5.65685	−	5.65685i	0.232299	−	0.232299i	−0.581353	−	0.813652i	$-0.697476\pi$
$593$	5.65685	−	5.65685i	0.232299	−	0.232299i	0.813652	+	0.581353i	$0.197476\pi$
$594$	30.0000	+	8.48528i	1.23091	+	0.348155i
$595$		−	4.00000i		−	0.163984i
$596$	−4.24264	+	4.24264i	−0.173785	+	0.173785i
$597$	8.48528	+	6.00000i	0.347279	+	0.245564i
$598$	15.0000	+	3.00000i	0.613396	+	0.122679i
$599$		−	16.9706i		−	0.693398i	−0.937976	−	0.346699i	$-0.887302\pi$
$599$		−	16.9706i		−	0.693398i	0.937976	−	0.346699i	$-0.112698\pi$
$600$	−1.70711	+	0.292893i	−0.0696923	+	0.0119573i
$601$	−18.0000			−0.734235			−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000			−0.734235			−0.367118	+	0.930175i	$0.619655\pi$
$602$	11.3137			0.461112
$603$	−11.4853	−	5.48528i	−0.467717	−	0.223378i
$604$	1.00000	−	1.00000i	0.0406894	−	0.0406894i
$605$	17.6777	−	17.6777i	0.718699	−	0.718699i
$606$	26.5563	−	4.55635i	1.07878	−	0.185089i
$607$	8.00000			0.324710			0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000			0.324710			0.162355	+	0.986732i	$0.448091\pi$
$608$		0			0
$609$	−8.20101	−	47.7990i	−0.332322	−	1.93691i
$610$			10.0000i			0.404888i
$611$	4.24264	−	21.2132i	0.171639	−	0.858194i
$612$	−4.00000	+	1.41421i	−0.161690	+	0.0571662i
$613$	25.0000	−	25.0000i	1.00974	−	1.00974i	0.00978840	−	0.999952i	$-0.496884\pi$
$613$	25.0000	−	25.0000i	1.00974	−	1.00974i	0.999952	−	0.00978840i	$-0.00311579\pi$
$614$		−	1.41421i		−	0.0570730i
$615$	2.82843	+	2.00000i	0.114053	+	0.0806478i
$616$	−12.0000	+	12.0000i	−0.483494	+	0.483494i
$617$	15.5563	+	15.5563i	0.626275	+	0.626275i	0.947129	−	0.320854i	$-0.103970\pi$
$617$	15.5563	+	15.5563i	0.626275	+	0.626275i	−0.320854	+	0.947129i	$0.603970\pi$
$618$	2.34315	+	13.6569i	0.0942551	+	0.549359i
$619$	−14.0000	−	14.0000i	−0.562708	−	0.562708i	0.367368	−	0.930076i	$-0.380259\pi$
$619$	−14.0000	−	14.0000i	−0.562708	−	0.562708i	−0.930076	+	0.367368i	$0.880259\pi$
$620$		−	9.89949i		−	0.397573i
$621$	−21.2132	−	6.00000i	−0.851257	−	0.240772i
$622$	−10.0000	−	10.0000i	−0.400963	−	0.400963i
$623$	−28.2843			−1.13319
$624$	0.171573	−	6.24264i	0.00686841	−	0.249906i
$625$	−1.00000			−0.0400000
$626$	24.0416	+	24.0416i	0.960897	+	0.960897i
$627$		0			0
$628$		−	2.00000i		−	0.0798087i
$629$	−4.24264	−	4.24264i	−0.169165	−	0.169165i
$630$	−7.65685	−	3.65685i	−0.305056	−	0.145693i
$631$	17.0000	+	17.0000i	0.676759	+	0.676759i	0.959265	−	0.282506i	$-0.0911658\pi$
$631$	17.0000	+	17.0000i	0.676759	+	0.676759i	−0.282506	+	0.959265i	$0.591166\pi$
$632$		0			0
$633$	20.0000	−	28.2843i	0.794929	−	1.12420i
$634$			18.0000i			0.714871i
$635$	−11.3137	+	11.3137i	−0.448971	+	0.448971i
$636$	−5.65685	+	8.00000i	−0.224309	+	0.317221i
$637$	2.00000	+	3.00000i	0.0792429	+	0.118864i
$638$			59.3970i			2.35155i
$639$	5.17157	−	10.8284i	0.204584	−	0.428366i
$640$	−1.00000			−0.0395285
$641$	−22.6274			−0.893729			−0.446865	−	0.894602i	$-0.647459\pi$
$641$	−22.6274			−0.893729			−0.446865	+	0.894602i	$0.647459\pi$
$642$	−3.31371	−	19.3137i	−0.130782	−	0.762251i
$643$	−11.0000	+	11.0000i	−0.433798	+	0.433798i	−0.889918	−	0.456120i	$-0.849239\pi$
$643$	−11.0000	+	11.0000i	−0.433798	+	0.433798i	0.456120	+	0.889918i	$0.349239\pi$
$644$	8.48528	−	8.48528i	0.334367	−	0.334367i
$645$	−1.17157	−	6.82843i	−0.0461306	−	0.268869i
$646$		0			0
$647$	−15.5563			−0.611583			−0.305792	−	0.952098i	$-0.598921\pi$
$647$	−15.5563			−0.611583			−0.305792	+	0.952098i	$0.598921\pi$
$648$	−0.949747	+	8.94975i	−0.0373096	+	0.351579i
$649$			72.0000i			2.82625i
$650$	0.707107	−	3.53553i	0.0277350	−	0.138675i
$651$	28.0000	−	39.5980i	1.09741	−	1.55197i
$652$	−15.0000	+	15.0000i	−0.587445	+	0.587445i
$653$		−	16.9706i		−	0.664109i	−0.943260	−	0.332055i	$-0.892258\pi$
$653$		−	16.9706i		−	0.664109i	0.943260	−	0.332055i	$-0.107742\pi$
$654$	16.9706	−	24.0000i	0.663602	−	0.938474i
$655$	−1.00000	+	1.00000i	−0.0390732	+	0.0390732i
$656$	1.41421	+	1.41421i	0.0552158	+	0.0552158i
$657$		0			0
$658$	−12.0000	−	12.0000i	−0.467809	−	0.467809i
$659$			24.0416i			0.936529i	0.883588	+	0.468264i	$0.155121\pi$
$659$			24.0416i			0.936529i	−0.883588	+	0.468264i	$0.844879\pi$
$660$	8.48528	+	6.00000i	0.330289	+	0.233550i
$661$	12.0000	+	12.0000i	0.466746	+	0.466746i	0.900859	−	0.434113i	$-0.142938\pi$
$661$	12.0000	+	12.0000i	0.466746	+	0.466746i	−0.434113	+	0.900859i	$0.642938\pi$
$662$	8.48528			0.329790
$663$	0.242641	−	8.82843i	0.00942338	−	0.342868i
$664$	12.0000			0.465690
$665$		0			0
$666$	−12.0000	+	4.24264i	−0.464991	+	0.164399i
$667$		−	42.0000i		−	1.62625i
$668$	5.65685	+	5.65685i	0.218870	+	0.218870i
$669$	1.65685	+	9.65685i	0.0640577	+	0.373356i
$670$	−3.00000	−	3.00000i	−0.115900	−	0.115900i
$671$	42.4264	−	42.4264i	1.63785	−	1.63785i
$672$	−4.00000	−	2.82843i	−0.154303	−	0.109109i
$673$		−	10.0000i		−	0.385472i	−0.981251	−	0.192736i	$-0.938264\pi$
$673$		−	10.0000i		−	0.385472i	0.981251	−	0.192736i	$-0.0617360\pi$
$674$	−12.7279	+	12.7279i	−0.490261	+	0.490261i
$675$	−1.41421	+	5.00000i	−0.0544331	+	0.192450i
$676$	12.0000	+	5.00000i	0.461538	+	0.192308i
$677$		−	31.1127i		−	1.19576i	−0.801586	−	0.597879i	$-0.796010\pi$
$677$		−	31.1127i		−	1.19576i	0.801586	−	0.597879i	$-0.203990\pi$
$678$	2.07107	+	12.0711i	0.0795389	+	0.463587i
$679$	32.0000			1.22805
$680$	−1.41421			−0.0542326
$681$		0			0
$682$	−42.0000	+	42.0000i	−1.60826	+	1.60826i
$683$	−25.4558	+	25.4558i	−0.974041	+	0.974041i	−0.999671	−	0.0256307i	$-0.991841\pi$
$683$	−25.4558	+	25.4558i	−0.974041	+	0.974041i	0.0256307	+	0.999671i	$0.491841\pi$
$684$		0			0
$685$	16.0000			0.611329
$686$	−16.9706			−0.647939
$687$	−19.3137	+	3.31371i	−0.736864	+	0.126426i
$688$		−	4.00000i		−	0.152499i
$689$	−11.3137	−	16.9706i	−0.431018	−	0.646527i
$690$	−6.00000	−	4.24264i	−0.228416	−	0.161515i
$691$	−22.0000	+	22.0000i	−0.836919	+	0.836919i	−0.988452	−	0.151533i	$-0.951579\pi$
$691$	−22.0000	+	22.0000i	−0.836919	+	0.836919i	0.151533	+	0.988452i	$0.451579\pi$
$692$			14.1421i			0.537603i
$693$	16.9706	+	48.0000i	0.644658	+	1.82337i
$694$	4.00000	−	4.00000i	0.151838	−	0.151838i
$695$		0			0
$696$	−16.8995	+	2.89949i	−0.640574	+	0.109905i
$697$	2.00000	+	2.00000i	0.0757554	+	0.0757554i
$698$		−	14.1421i		−	0.535288i
$699$	4.24264	−	6.00000i	0.160471	−	0.226941i
$700$	−2.00000	−	2.00000i	−0.0755929	−	0.0755929i
$701$	4.24264			0.160242			0.0801212	−	0.996785i	$-0.474469\pi$
$701$	4.24264			0.160242			0.0801212	+	0.996785i	$0.474469\pi$
$702$	−16.6777	−	8.53553i	−0.629458	−	0.322153i
$703$		0			0
$704$	4.24264	+	4.24264i	0.159901	+	0.159901i
$705$	−6.00000	+	8.48528i	−0.225973	+	0.319574i
$706$		−	32.0000i		−	1.20434i
$707$	31.1127	+	31.1127i	1.17011	+	1.17011i
$708$	−20.4853	+	3.51472i	−0.769884	+	0.132091i
$709$	36.0000	+	36.0000i	1.35201	+	1.35201i	0.883413	+	0.468596i	$0.155240\pi$
$709$	36.0000	+	36.0000i	1.35201	+	1.35201i	0.468596	+	0.883413i	$0.344760\pi$
$710$	2.82843	−	2.82843i	0.106149	−	0.106149i
$711$		0			0
$712$			10.0000i			0.374766i
$713$	29.6985	−	29.6985i	1.11222	−	1.11222i
$714$	−5.65685	−	4.00000i	−0.211702	−	0.149696i
$715$	−18.0000	+	12.0000i	−0.673162	+	0.448775i
$716$			12.7279i			0.475665i
$717$	27.3137	−	4.68629i	1.02005	−	0.175013i
$718$	−20.0000			−0.746393
$719$	28.2843			1.05483			0.527413	−	0.849609i	$-0.323162\pi$
$719$	28.2843			1.05483			0.527413	+	0.849609i	$0.323162\pi$
$720$	−1.29289	+	2.70711i	−0.0481833	+	0.100888i
$721$	−16.0000	+	16.0000i	−0.595871	+	0.595871i
$722$	13.4350	−	13.4350i	0.500000	−	0.500000i
$723$	−36.2132	+	6.21320i	−1.34678	+	0.231072i
$724$	−22.0000			−0.817624
$725$	−9.89949			−0.367658
$726$	−7.32233	−	42.6777i	−0.271757	−	1.58392i
$727$		−	12.0000i		−	0.445055i	−0.974926	−	0.222528i	$-0.928569\pi$
$727$		−	12.0000i		−	0.445055i	0.974926	−	0.222528i	$-0.0714308\pi$
$728$	8.48528	−	5.65685i	0.314485	−	0.209657i
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$		−	5.65685i		−	0.209226i
$732$	14.1421	+	10.0000i	0.522708	+	0.369611i
$733$	33.0000	−	33.0000i	1.21888	−	1.21888i	0.250859	−	0.968024i	$-0.419287\pi$
$733$	33.0000	−	33.0000i	1.21888	−	1.21888i	0.968024	−	0.250859i	$-0.0807131\pi$
$734$	−19.7990	−	19.7990i	−0.730794	−	0.730794i
$735$	−0.292893	−	1.70711i	−0.0108035	−	0.0629676i
$736$	−3.00000	−	3.00000i	−0.110581	−	0.110581i
$737$			25.4558i			0.937678i
$738$	5.65685	−	2.00000i	0.208232	−	0.0736210i
$739$	−2.00000	−	2.00000i	−0.0735712	−	0.0735712i	0.669364	−	0.742935i	$-0.266567\pi$
$739$	−2.00000	−	2.00000i	−0.0735712	−	0.0735712i	−0.742935	+	0.669364i	$0.766567\pi$
$740$	−4.24264			−0.155963
$741$		0			0
$742$	−16.0000			−0.587378
$743$	4.24264	+	4.24264i	0.155647	+	0.155647i	0.780635	−	0.624987i	$-0.214896\pi$
$743$	4.24264	+	4.24264i	0.155647	+	0.155647i	−0.624987	+	0.780635i	$0.714896\pi$
$744$	−14.0000	−	9.89949i	−0.513265	−	0.362933i
$745$			6.00000i			0.219823i
$746$	16.9706	+	16.9706i	0.621336	+	0.621336i
$747$	15.5147	−	32.4853i	0.567654	−	1.18857i
$748$	6.00000	+	6.00000i	0.219382	+	0.219382i
$749$	22.6274	−	22.6274i	0.826788	−	0.826788i
$750$	−1.00000	+	1.41421i	−0.0365148	+	0.0516398i
$751$		−	46.0000i		−	1.67856i	−0.543696	−	0.839282i	$-0.682976\pi$
$751$		−	46.0000i		−	1.67856i	0.543696	−	0.839282i	$-0.317024\pi$
$752$	−4.24264	+	4.24264i	−0.154713	+	0.154713i
$753$	7.07107	−	10.0000i	0.257684	−	0.364420i
$754$	7.00000	−	35.0000i	0.254925	−	1.27462i
$755$		−	1.41421i		−	0.0514685i
$756$	−12.8284	+	7.17157i	−0.466565	+	0.260828i
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	−8.48528			−0.308199
$759$	7.45584	+	43.4558i	0.270630	+	1.57735i
$760$		0			0
$761$	−29.6985	+	29.6985i	−1.07657	+	1.07657i	−0.0797547	+	0.996815i	$0.525414\pi$
$761$	−29.6985	+	29.6985i	−1.07657	+	1.07657i	−0.996815	+	0.0797547i	$0.974586\pi$
$762$	4.68629	+	27.3137i	0.169766	+	0.989471i
$763$	48.0000			1.73772
$764$	8.48528			0.306987
$765$	−1.82843	+	3.82843i	−0.0661069	+	0.138417i
$766$			16.0000i			0.578103i
$767$	8.48528	−	42.4264i	0.306386	−	1.53193i
$768$	−1.00000	+	1.41421i	−0.0360844	+	0.0510310i
$769$	11.0000	−	11.0000i	0.396670	−	0.396670i	−0.480387	−	0.877057i	$-0.659504\pi$
$769$	11.0000	−	11.0000i	0.396670	−	0.396670i	0.877057	+	0.480387i	$0.159504\pi$
$770$			16.9706i			0.611577i
$771$	9.89949	−	14.0000i	0.356522	−	0.504198i
$772$		0			0
$773$	−7.07107	−	7.07107i	−0.254329	−	0.254329i	0.568414	−	0.822743i	$-0.307557\pi$
$773$	−7.07107	−	7.07107i	−0.254329	−	0.254329i	−0.822743	+	0.568414i	$0.807557\pi$
$774$	−10.8284	−	5.17157i	−0.389220	−	0.185888i
$775$	−7.00000	−	7.00000i	−0.251447	−	0.251447i
$776$		−	11.3137i		−	0.406138i
$777$	−16.9706	−	12.0000i	−0.608816	−	0.430498i
$778$	−7.00000	−	7.00000i	−0.250962	−	0.250962i
$779$		0			0
$780$	−4.29289	−	4.53553i	−0.153710	−	0.162398i
$781$	−24.0000			−0.858788
$782$	−4.24264	−	4.24264i	−0.151717	−	0.151717i
$783$	−14.0000	+	49.4975i	−0.500319	+	1.76890i
$784$		−	1.00000i		−	0.0357143i
$785$	−1.41421	−	1.41421i	−0.0504754	−	0.0504754i
$786$	0.414214	+	2.41421i	0.0147745	+	0.0861121i
$787$	23.0000	+	23.0000i	0.819861	+	0.819861i	0.986088	−	0.166226i	$-0.0531582\pi$
$787$	23.0000	+	23.0000i	0.819861	+	0.819861i	−0.166226	+	0.986088i	$0.553158\pi$
$788$	−1.41421	+	1.41421i	−0.0503793	+	0.0503793i
$789$	−10.0000	−	7.07107i	−0.356009	−	0.251737i
$790$		0			0
$791$	−14.1421	+	14.1421i	−0.502836	+	0.502836i
$792$	16.9706	−	6.00000i	0.603023	−	0.213201i
$793$	−30.0000	+	20.0000i	−1.06533	+	0.710221i
$794$			4.24264i			0.150566i
$795$	1.65685	+	9.65685i	0.0587626	+	0.342493i
$796$	6.00000			0.212664
$797$	−22.6274			−0.801504			−0.400752	−	0.916187i	$-0.631251\pi$
$797$	−22.6274			−0.801504			−0.400752	+	0.916187i	$0.631251\pi$
$798$		0			0
$799$	−6.00000	+	6.00000i	−0.212265	+	0.212265i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	27.0711	+	12.9289i	0.956509	+	0.456821i
$802$	−14.0000			−0.494357
$803$		0			0
$804$	−7.24264	+	1.24264i	−0.255428	+	0.0438246i
$805$		−	12.0000i		−	0.422944i
$806$	29.6985	−	19.7990i	1.04608	−	0.697390i
$807$	2.00000	+	1.41421i	0.0704033	+	0.0497827i
$808$	11.0000	−	11.0000i	0.386979	−	0.386979i
$809$		−	2.82843i		−	0.0994422i	−0.998763	−	0.0497211i	$-0.984167\pi$
$809$		−	2.82843i		−	0.0994422i	0.998763	−	0.0497211i	$-0.0158332\pi$
$810$	5.65685	+	7.00000i	0.198762	+	0.245955i
$811$	4.00000	−	4.00000i	0.140459	−	0.140459i	−0.633381	−	0.773840i	$-0.718333\pi$
$811$	4.00000	−	4.00000i	0.140459	−	0.140459i	0.773840	+	0.633381i	$0.218333\pi$
$812$	−19.7990	−	19.7990i	−0.694808	−	0.694808i
$813$	36.2132	−	6.21320i	1.27005	−	0.217907i
$814$	18.0000	+	18.0000i	0.630900	+	0.630900i
$815$			21.2132i			0.743066i
$816$	−1.41421	+	2.00000i	−0.0495074	+	0.0700140i
$817$		0			0
$818$	−1.41421			−0.0494468
$819$	−4.34315	−	30.2843i	−0.151762	−	1.05822i
$820$	2.00000			0.0698430
$821$	7.07107	+	7.07107i	0.246782	+	0.246782i	0.819649	−	0.572867i	$-0.194169\pi$
$821$	7.07107	+	7.07107i	0.246782	+	0.246782i	−0.572867	+	0.819649i	$0.694169\pi$
$822$	16.0000	−	22.6274i	0.558064	−	0.789222i
$823$			36.0000i			1.25488i	0.778664	+	0.627441i	$0.215897\pi$
$823$			36.0000i			1.25488i	−0.778664	+	0.627441i	$0.784103\pi$
$824$	5.65685	+	5.65685i	0.197066	+	0.197066i
$825$	10.2426	−	1.75736i	0.356603	−	0.0611834i
$826$	−24.0000	−	24.0000i	−0.835067	−	0.835067i
$827$	33.9411	−	33.9411i	1.18025	−	1.18025i	0.200569	−	0.979680i	$-0.435721\pi$
$827$	33.9411	−	33.9411i	1.18025	−	1.18025i	0.979680	−	0.200569i	$-0.0642791\pi$
$828$	−12.0000	+	4.24264i	−0.417029	+	0.147442i
$829$		−	22.0000i		−	0.764092i	−0.924143	−	0.382046i	$-0.875220\pi$
$829$		−	22.0000i		−	0.764092i	0.924143	−	0.382046i	$-0.124780\pi$
$830$	8.48528	−	8.48528i	0.294528	−	0.294528i
$831$	5.65685	+	4.00000i	0.196234	+	0.138758i
$832$	−2.00000	−	3.00000i	−0.0693375	−	0.104006i
$833$		−	1.41421i		−	0.0489996i
$834$		0			0
$835$	8.00000			0.276851
$836$		0			0
$837$	−44.8995	+	25.1005i	−1.55195	+	0.867600i
$838$	7.00000	−	7.00000i	0.241811	−	0.241811i
$839$	−25.4558	+	25.4558i	−0.878833	+	0.878833i	−0.993414	−	0.114581i	$-0.963448\pi$
$839$	−25.4558	+	25.4558i	−0.878833	+	0.878833i	0.114581	+	0.993414i	$0.463448\pi$
$840$	−4.82843	+	0.828427i	−0.166597	+	0.0285835i
$841$	−69.0000			−2.37931
$842$	−25.4558			−0.877266
$843$	−2.92893	−	17.0711i	−0.100878	−	0.587959i
$844$		−	20.0000i		−	0.688428i
$845$	12.0208	−	4.94975i	0.413529	−	0.170276i
$846$	6.00000	+	16.9706i	0.206284	+	0.583460i
$847$	50.0000	−	50.0000i	1.71802	−	1.71802i
$848$			5.65685i			0.194257i
$849$	36.7696	+	26.0000i	1.26193	+	0.892318i
$850$	−1.00000	+	1.00000i	−0.0342997	+	0.0342997i
$851$	−12.7279	−	12.7279i	−0.436308	−	0.436308i
$852$	−1.17157	−	6.82843i	−0.0401374	−	0.233938i
$853$	−15.0000	−	15.0000i	−0.513590	−	0.513590i	0.402034	−	0.915625i	$-0.368303\pi$
$853$	−15.0000	−	15.0000i	−0.513590	−	0.513590i	−0.915625	+	0.402034i	$0.868303\pi$
$854$			28.2843i			0.967868i
$855$		0			0
$856$	−8.00000	−	8.00000i	−0.273434	−	0.273434i
$857$	41.0122			1.40095			0.700475	−	0.713677i	$-0.252972\pi$
$857$	41.0122			1.40095			0.700475	+	0.713677i	$0.252972\pi$
$858$	−1.02944	+	37.4558i	−0.0351444	+	1.27872i
$859$	−28.0000			−0.955348			−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000			−0.955348			−0.477674	+	0.878537i	$0.658520\pi$
$860$	−2.82843	−	2.82843i	−0.0964486	−	0.0964486i
$861$	8.00000	+	5.65685i	0.272639	+	0.192785i
$862$			36.0000i			1.22616i
$863$	−39.5980	−	39.5980i	−1.34793	−	1.34793i	−0.887906	−	0.460025i	$-0.847840\pi$
$863$	−39.5980	−	39.5980i	−1.34793	−	1.34793i	−0.460025	−	0.887906i	$-0.652160\pi$
$864$	2.53553	+	4.53553i	0.0862606	+	0.154302i
$865$	10.0000	+	10.0000i	0.340010	+	0.340010i
$866$	7.07107	−	7.07107i	0.240285	−	0.240285i
$867$	15.0000	−	21.2132i	0.509427	−	0.720438i
$868$		−	28.0000i		−	0.950382i
$869$		0			0
$870$	−9.89949	+	14.0000i	−0.335624	+	0.474644i
$871$	3.00000	−	15.0000i	0.101651	−	0.508256i
$872$		−	16.9706i		−	0.574696i
$873$	−30.6274	−	14.6274i	−1.03658	−	0.495063i
$874$		0			0
$875$	−2.82843			−0.0956183
$876$		0			0
$877$	11.0000	−	11.0000i	0.371444	−	0.371444i	−0.496559	−	0.868003i	$-0.665403\pi$
$877$	11.0000	−	11.0000i	0.371444	−	0.371444i	0.868003	+	0.496559i	$0.165403\pi$
$878$	26.8701	−	26.8701i	0.906821	−	0.906821i
$879$	−0.585786	−	3.41421i	−0.0197581	−	0.115159i
$880$	6.00000			0.202260
$881$	5.65685			0.190584			0.0952921	−	0.995449i	$-0.469621\pi$
$881$	5.65685			0.190584			0.0952921	+	0.995449i	$0.469621\pi$
$882$	−2.70711	−	1.29289i	−0.0911530	−	0.0435340i
$883$			4.00000i			0.134611i	0.997732	+	0.0673054i	$0.0214402\pi$
$883$			4.00000i			0.134611i	−0.997732	+	0.0673054i	$0.978560\pi$
$884$	−2.82843	−	4.24264i	−0.0951303	−	0.142695i
$885$	−12.0000	+	16.9706i	−0.403376	+	0.570459i
$886$	14.0000	−	14.0000i	0.470339	−	0.470339i
$887$			32.5269i			1.09215i	0.837737	+	0.546073i	$0.183878\pi$
$887$			32.5269i			1.09215i	−0.837737	+	0.546073i	$0.816122\pi$
$888$	−4.24264	+	6.00000i	−0.142374	+	0.201347i
$889$	−32.0000	+	32.0000i	−1.07325	+	1.07325i
$890$	7.07107	+	7.07107i	0.237023	+	0.237023i
$891$	5.69848	−	53.6985i	0.190906	−	1.79897i
$892$	4.00000	+	4.00000i	0.133930	+	0.133930i
$893$		0			0
$894$	8.48528	+	6.00000i	0.283790	+	0.200670i
$895$	9.00000	+	9.00000i	0.300837	+	0.300837i
$896$	−2.82843			−0.0944911
$897$	0.727922	−	26.4853i	0.0243046	−	0.884318i
$898$	−2.00000			−0.0667409
$899$	−69.2965	−	69.2965i	−2.31117	−	2.31117i
$900$	1.00000	+	2.82843i	0.0333333	+	0.0942809i
$901$			8.00000i			0.266519i
$902$	−8.48528	−	8.48528i	−0.282529	−	0.282529i
$903$	−3.31371	−	19.3137i	−0.110273	−	0.642720i
$904$	5.00000	+	5.00000i	0.166298	+	0.166298i
$905$	−15.5563	+	15.5563i	−0.517111	+	0.517111i
$906$	−2.00000	−	1.41421i	−0.0664455	−	0.0469841i
$907$			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
$910$	2.00000	−	10.0000i	0.0662994	−	0.331497i
$911$			5.65685i			0.187420i	0.995600	+	0.0937100i	$0.0298726\pi$
$911$			5.65685i			0.187420i	−0.995600	+	0.0937100i	$0.970127\pi$
$912$		0			0
$913$	−72.0000			−2.38285
$914$		0			0
$915$	17.0711	−	2.92893i	0.564352	−	0.0968275i
$916$	−8.00000	+	8.00000i	−0.264327	+	0.264327i
$917$	−2.82843	+	2.82843i	−0.0934029	+	0.0934029i
$918$	3.58579	+	6.41421i	0.118349	+	0.211701i
$919$	−22.0000			−0.725713			−0.362857	−	0.931845i	$-0.618198\pi$
$919$	−22.0000			−0.725713			−0.362857	+	0.931845i	$0.618198\pi$
$920$	−4.24264			−0.139876
$921$	−2.41421	+	0.414214i	−0.0795510	+	0.0136488i
$922$		−	40.0000i		−	1.31733i
$923$	14.1421	+	2.82843i	0.465494	+	0.0930988i
$924$	24.0000	+	16.9706i	0.789542	+	0.558291i
$925$	−3.00000	+	3.00000i	−0.0986394	+	0.0986394i
$926$			22.6274i			0.743583i
$927$	22.6274	−	8.00000i	0.743182	−	0.262754i
$928$	−7.00000	+	7.00000i	−0.229786	+	0.229786i
$929$	−18.3848	−	18.3848i	−0.603185	−	0.603185i	0.337971	−	0.941156i	$-0.390259\pi$
$929$	−18.3848	−	18.3848i	−0.603185	−	0.603185i	−0.941156	+	0.337971i	$0.890259\pi$
$930$	−16.8995	+	2.89949i	−0.554156	+	0.0950782i
$931$		0			0
$932$		−	4.24264i		−	0.138972i
$933$	−14.1421	+	20.0000i	−0.462993	+	0.654771i
$934$	6.00000	+	6.00000i	0.196326	+	0.196326i
$935$	8.48528			0.277498
$936$	−10.7071	+	1.53553i	−0.349973	+	0.0501905i
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$	−8.48528	−	8.48528i	−0.277054	−	0.277054i
$939$	34.0000	−	48.0833i	1.10955	−	1.56914i
$940$			6.00000i			0.195698i
$941$	8.48528	+	8.48528i	0.276612	+	0.276612i	0.831755	−	0.555143i	$-0.187336\pi$
$941$	8.48528	+	8.48528i	0.276612	+	0.276612i	−0.555143	+	0.831755i	$0.687336\pi$
$942$	−3.41421	+	0.585786i	−0.111241	+	0.0190860i
$943$	6.00000	+	6.00000i	0.195387	+	0.195387i
$944$	−8.48528	+	8.48528i	−0.276172	+	0.276172i
$945$	−4.00000	+	14.1421i	−0.130120	+	0.460044i
$946$			24.0000i			0.780307i
$947$	−2.82843	+	2.82843i	−0.0919115	+	0.0919115i	−0.751568	−	0.659656i	$-0.770702\pi$
$947$	−2.82843	+	2.82843i	−0.0919115	+	0.0919115i	0.659656	+	0.751568i	$0.270702\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	30.7279	−	5.27208i	0.996421	−	0.170959i
$952$	−4.00000			−0.129641
$953$	55.1543			1.78662			0.893312	−	0.449437i	$-0.148375\pi$
$953$	55.1543			1.78662			0.893312	+	0.449437i	$0.148375\pi$
$954$	15.3137	+	7.31371i	0.495800	+	0.236790i
$955$	6.00000	−	6.00000i	0.194155	−	0.194155i
$956$	11.3137	−	11.3137i	0.365911	−	0.365911i
$957$	101.397	−	17.3970i	3.27770	−	0.562364i
$958$	36.0000			1.16311
$959$	45.2548			1.46135
$960$	0.292893	+	1.70711i	0.00945309	+	0.0550966i
$961$		−	67.0000i		−	2.16129i
$962$	−8.48528	−	12.7279i	−0.273576	−	0.410365i
$963$	−32.0000	+	11.3137i	−1.03119	+	0.364579i
$964$	−15.0000	+	15.0000i	−0.483117	+	0.483117i
$965$		0			0
$966$	−16.9706	−	12.0000i	−0.546019	−	0.386094i
$967$	22.0000	−	22.0000i	0.707472	−	0.707472i	−0.258531	−	0.966003i	$-0.583238\pi$
$967$	22.0000	−	22.0000i	0.707472	−	0.707472i	0.966003	+	0.258531i	$0.0832383\pi$
$968$	−17.6777	−	17.6777i	−0.568182	−	0.568182i
$969$		0			0
$970$	−8.00000	−	8.00000i	−0.256865	−	0.256865i
$971$			55.1543i			1.76999i	0.465604	+	0.884993i	$0.345837\pi$
$971$			55.1543i			1.76999i	−0.465604	+	0.884993i	$0.654163\pi$
$972$	15.5563	−	1.00000i	0.498970	−	0.0320750i
$973$		0			0
$974$	19.7990			0.634401
$975$	−6.24264	−	0.171573i	−0.199925	−	0.00549473i
$976$	10.0000			0.320092
$977$	16.9706	+	16.9706i	0.542936	+	0.542936i	0.924389	−	0.381452i	$-0.124576\pi$
$977$	16.9706	+	16.9706i	0.542936	+	0.542936i	−0.381452	+	0.924389i	$0.624576\pi$
$978$	30.0000	+	21.2132i	0.959294	+	0.678323i
$979$		−	60.0000i		−	1.91761i
$980$	−0.707107	−	0.707107i	−0.0225877	−	0.0225877i
$981$	−45.9411	−	21.9411i	−1.46679	−	0.700526i
$982$	11.0000	+	11.0000i	0.351024	+	0.351024i
$983$	−21.2132	+	21.2132i	−0.676596	+	0.676596i	−0.959228	−	0.282632i	$-0.908792\pi$
$983$	−21.2132	+	21.2132i	−0.676596	+	0.676596i	0.282632	+	0.959228i	$0.408792\pi$
$984$	2.00000	−	2.82843i	0.0637577	−	0.0901670i
$985$			2.00000i			0.0637253i
$986$	−9.89949	+	9.89949i	−0.315264	+	0.315264i
$987$	−16.9706	+	24.0000i	−0.540179	+	0.763928i
$988$		0			0
$989$		−	16.9706i		−	0.539633i
$990$	7.75736	−	16.2426i	0.246545	−	0.516225i
$991$	−18.0000			−0.571789			−0.285894	−	0.958261i	$-0.592291\pi$
$991$	−18.0000			−0.571789			−0.285894	+	0.958261i	$0.592291\pi$
$992$	−9.89949			−0.314309
$993$	−2.48528	−	14.4853i	−0.0788680	−	0.459677i
$994$	8.00000	−	8.00000i	0.253745	−	0.253745i
$995$	4.24264	−	4.24264i	0.134501	−	0.134501i
$996$	−3.51472	−	20.4853i	−0.111368	−	0.649101i
$997$	42.0000			1.33015			0.665077	−	0.746775i	$-0.268399\pi$
$997$	42.0000			1.33015			0.665077	+	0.746775i	$0.268399\pi$
$998$	−33.9411			−1.07439
$999$	10.7574	+	19.2426i	0.340348	+	0.608810i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.p.c.161.1	✓	4	1.1	even	1	trivial
390.2.p.c.161.2	yes	4	3.2	odd	2	inner
390.2.p.c.281.1	yes	4	39.8	even	4	inner
390.2.p.c.281.2	yes	4	13.8	odd	4	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} +(2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} -1.00000i q^{10} +(-4.24264 + 4.24264i) q^{11} +(-1.41421 - 1.00000i) q^{12} +(3.00000 - 2.00000i) q^{13} -2.82843i q^{14} +(-1.70711 + 0.292893i) q^{15} -1.00000 q^{16} -1.41421 q^{17} +(-1.29289 + 2.70711i) q^{18} +(-0.707107 + 0.707107i) q^{20} +(-4.82843 + 0.828427i) q^{21} +6.00000 q^{22} -4.24264 q^{23} +(0.292893 + 1.70711i) q^{24} +1.00000i q^{25} +(-3.53553 - 0.707107i) q^{26} +(5.00000 + 1.41421i) q^{27} +(-2.00000 + 2.00000i) q^{28} +9.89949i q^{29} +(1.41421 + 1.00000i) q^{30} +(-7.00000 + 7.00000i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.75736 - 10.2426i) q^{33} +(1.00000 + 1.00000i) q^{34} +2.82843i q^{35} +(2.82843 - 1.00000i) q^{36} +(3.00000 + 3.00000i) q^{37} +(-0.171573 + 6.24264i) q^{39} +1.00000 q^{40} +(-1.41421 - 1.41421i) q^{41} +(4.00000 + 2.82843i) q^{42} +4.00000i q^{43} +(-4.24264 - 4.24264i) q^{44} +(1.29289 - 2.70711i) q^{45} +(3.00000 + 3.00000i) q^{46} +(4.24264 - 4.24264i) q^{47} +(1.00000 - 1.41421i) q^{48} +1.00000i q^{49} +(0.707107 - 0.707107i) q^{50} +(1.41421 - 2.00000i) q^{51} +(2.00000 + 3.00000i) q^{52} -5.65685i q^{53} +(-2.53553 - 4.53553i) q^{54} -6.00000 q^{55} +2.82843 q^{56} +(7.00000 - 7.00000i) q^{58} +(8.48528 - 8.48528i) q^{59} +(-0.292893 - 1.70711i) q^{60} -10.0000 q^{61} +9.89949 q^{62} +(3.65685 - 7.65685i) q^{63} -1.00000i q^{64} +(3.53553 + 0.707107i) q^{65} +(-6.00000 + 8.48528i) q^{66} +(3.00000 - 3.00000i) q^{67} -1.41421i q^{68} +(4.24264 - 6.00000i) q^{69} +(2.00000 - 2.00000i) q^{70} +(2.82843 + 2.82843i) q^{71} +(-2.70711 - 1.29289i) q^{72} -4.24264i q^{74} +(-1.41421 - 1.00000i) q^{75} -16.9706 q^{77} +(4.53553 - 4.29289i) q^{78} +(-0.707107 - 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +2.00000i q^{82} +(8.48528 + 8.48528i) q^{83} +(-0.828427 - 4.82843i) q^{84} +(-1.00000 - 1.00000i) q^{85} +(2.82843 - 2.82843i) q^{86} +(-14.0000 - 9.89949i) q^{87} +6.00000i q^{88} +(-7.07107 + 7.07107i) q^{89} +(-2.82843 + 1.00000i) q^{90} +(10.0000 + 2.00000i) q^{91} -4.24264i q^{92} +(-2.89949 - 16.8995i) q^{93} -6.00000 q^{94} +(-1.70711 + 0.292893i) q^{96} +(8.00000 - 8.00000i) q^{97} +(0.707107 - 0.707107i) q^{98} +(16.2426 + 7.75736i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{6} + 8 q^{7} - 4 q^{9} + 12 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} - 8 q^{21} + 24 q^{22} + 4 q^{24} + 20 q^{27} - 8 q^{28} - 28 q^{31} - 24 q^{33} + 4 q^{34} + 12 q^{37} - 12 q^{39}+ \cdots + 48 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^6 + 8 * q^7 - 4 * q^9 + 12 * q^13 - 4 * q^15 - 4 * q^16 - 8 * q^18 - 8 * q^21 + 24 * q^22 + 4 * q^24 + 20 * q^27 - 8 * q^28 - 28 * q^31 - 24 * q^33 + 4 * q^34 + 12 * q^37 - 12 * q^39 + 4 * q^40 + 16 * q^42 + 8 * q^45 + 12 * q^46 + 4 * q^48 + 8 * q^52 + 4 * q^54 - 24 * q^55 + 28 * q^58 - 4 * q^60 - 40 * q^61 - 8 * q^63 - 24 * q^66 + 12 * q^67 + 8 * q^70 - 8 * q^72 + 4 * q^78 - 28 * q^81 + 8 * q^84 - 4 * q^85 - 56 * q^87 + 40 * q^91 + 28 * q^93 - 24 * q^94 - 4 * q^96 + 32 * q^97 + 48 * q^99

Introduction

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