LMFDB - Embedded newform 930.2.j.b.683.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] 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("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (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:	$7.42608738798$
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			683.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	930.683
Dual form			930.2.j.b.497.1

$q$-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} +(0.292893 + 1.70711i) q^{3} +1.00000i q^{4} +(2.12132 - 0.707107i) q^{5} +(1.00000 - 1.41421i) q^{6} +(0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(-2.00000 - 1.00000i) q^{10} -1.41421i q^{11} +(-1.70711 + 0.292893i) q^{12} +(3.00000 + 3.00000i) q^{13} +(1.82843 + 3.41421i) q^{15} -1.00000 q^{16} +(1.41421 + 1.41421i) q^{17} +(2.70711 + 1.29289i) q^{18} +4.00000i q^{19} +(0.707107 + 2.12132i) q^{20} +(-1.00000 + 1.00000i) q^{22} +(2.82843 - 2.82843i) q^{23} +(1.41421 + 1.00000i) q^{24} +(4.00000 - 3.00000i) q^{25} -4.24264i q^{26} +(-2.53553 - 4.53553i) q^{27} +2.82843 q^{29} +(1.12132 - 3.70711i) q^{30} +1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(2.41421 - 0.414214i) q^{33} -2.00000i q^{34} +(-1.00000 - 2.82843i) q^{36} +(-3.00000 + 3.00000i) q^{37} +(2.82843 - 2.82843i) q^{38} +(-4.24264 + 6.00000i) q^{39} +(1.00000 - 2.00000i) q^{40} +5.65685i q^{41} +1.41421 q^{44} +(-5.29289 + 4.12132i) q^{45} -4.00000 q^{46} +(-1.41421 - 1.41421i) q^{47} +(-0.292893 - 1.70711i) q^{48} +7.00000i q^{49} +(-4.94975 - 0.707107i) q^{50} +(-2.00000 + 2.82843i) q^{51} +(-3.00000 + 3.00000i) q^{52} +(-1.41421 + 1.41421i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(-1.00000 - 3.00000i) q^{55} +(-6.82843 + 1.17157i) q^{57} +(-2.00000 - 2.00000i) q^{58} +(-3.41421 + 1.82843i) q^{60} +8.00000 q^{61} +(-0.707107 - 0.707107i) q^{62} -1.00000i q^{64} +(8.48528 + 4.24264i) q^{65} +(-2.00000 - 1.41421i) q^{66} +(7.00000 - 7.00000i) q^{67} +(-1.41421 + 1.41421i) q^{68} +(5.65685 + 4.00000i) q^{69} +12.7279i q^{71} +(-1.29289 + 2.70711i) q^{72} +(-2.00000 - 2.00000i) q^{73} +4.24264 q^{74} +(6.29289 + 5.94975i) q^{75} -4.00000 q^{76} +(7.24264 - 1.24264i) q^{78} -2.00000i q^{79} +(-2.12132 + 0.707107i) q^{80} +(7.00000 - 5.65685i) q^{81} +(4.00000 - 4.00000i) q^{82} +(-4.24264 + 4.24264i) q^{83} +(4.00000 + 2.00000i) q^{85} +(0.828427 + 4.82843i) q^{87} +(-1.00000 - 1.00000i) q^{88} -7.07107 q^{89} +(6.65685 + 0.828427i) q^{90} +(2.82843 + 2.82843i) q^{92} +(0.292893 + 1.70711i) q^{93} +2.00000i q^{94} +(2.82843 + 8.48528i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(11.0000 - 11.0000i) q^{97} +(4.94975 - 4.94975i) q^{98} +(1.41421 + 4.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} + 4 q^{6} - 8 q^{10} - 4 q^{12} + 12 q^{13} - 4 q^{15} - 4 q^{16} + 8 q^{18} - 4 q^{22} + 16 q^{25} + 4 q^{27} - 4 q^{30} + 4 q^{31} + 4 q^{33} - 4 q^{36} - 12 q^{37} + 4 q^{40} - 24 q^{45}+ \cdots + 44 q^{97}+O(q^{100}) $ 4 * q + 4 * q^3 + 4 * q^6 - 8 * q^10 - 4 * q^12 + 12 * q^13 - 4 * q^15 - 4 * q^16 + 8 * q^18 - 4 * q^22 + 16 * q^25 + 4 * q^27 - 4 * q^30 + 4 * q^31 + 4 * q^33 - 4 * q^36 - 12 * q^37 + 4 * q^40 - 24 * q^45 - 16 * q^46 - 4 * q^48 - 8 * q^51 - 12 * q^52 - 4 * q^55 - 16 * q^57 - 8 * q^58 - 8 * q^60 + 32 * q^61 - 8 * q^66 + 28 * q^67 - 8 * q^72 - 8 * q^73 + 28 * q^75 - 16 * q^76 + 12 * q^78 + 28 * q^81 + 16 * q^82 + 16 * q^85 - 8 * q^87 - 4 * q^88 + 4 * q^90 + 4 * q^93 - 4 * q^96 + 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.292893	+	1.70711i	0.169102	+	0.985599i
$3$	0.292893	+	1.70711i	0.169102	+	0.985599i
$4$			1.00000i			0.500000i
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$6$	1.00000	−	1.41421i	0.408248	−	0.577350i
$7$		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
$9$	−2.82843	+	1.00000i	−0.942809	+	0.333333i
$10$	−2.00000	−	1.00000i	−0.632456	−	0.316228i
$11$		−	1.41421i		−	0.426401i	−0.977008	−	0.213201i	$-0.931611\pi$
$11$		−	1.41421i		−	0.426401i	0.977008	−	0.213201i	$-0.0683888\pi$
$12$	−1.70711	+	0.292893i	−0.492799	+	0.0845510i
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	0.987797	−	0.155747i	$-0.0497784\pi$
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	−0.155747	+	0.987797i	$0.549778\pi$
$14$		0			0
$15$	1.82843	+	3.41421i	0.472098	+	0.881546i
$16$	−1.00000			−0.250000
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	0.857493	−	0.514496i	$-0.172021\pi$
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	−0.514496	+	0.857493i	$0.672021\pi$
$18$	2.70711	+	1.29289i	0.638071	+	0.304738i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	0.707107	+	2.12132i	0.158114	+	0.474342i
$21$		0			0
$22$	−1.00000	+	1.00000i	−0.213201	+	0.213201i
$23$	2.82843	−	2.82843i	0.589768	−	0.589768i	−0.347801	−	0.937568i	$-0.613071\pi$
$23$	2.82843	−	2.82843i	0.589768	−	0.589768i	0.937568	+	0.347801i	$0.113071\pi$
$24$	1.41421	+	1.00000i	0.288675	+	0.204124i
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$		−	4.24264i		−	0.832050i
$27$	−2.53553	−	4.53553i	−0.487964	−	0.872864i
$28$		0			0
$29$	2.82843			0.525226			0.262613	−	0.964901i	$-0.415416\pi$
$29$	2.82843			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$30$	1.12132	−	3.70711i	0.204724	−	0.676822i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	2.41421	−	0.414214i	0.420261	−	0.0721053i
$34$		−	2.00000i		−	0.342997i
$35$		0			0
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	−0.909312	−	0.416115i	$-0.863391\pi$
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	0.416115	+	0.909312i	$0.363391\pi$
$38$	2.82843	−	2.82843i	0.458831	−	0.458831i
$39$	−4.24264	+	6.00000i	−0.679366	+	0.960769i
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$			5.65685i			0.883452i	0.897150	+	0.441726i	$0.145634\pi$
$41$			5.65685i			0.883452i	−0.897150	+	0.441726i	$0.854366\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$	1.41421			0.213201
$45$	−5.29289	+	4.12132i	−0.789018	+	0.614370i
$46$	−4.00000			−0.589768
$47$	−1.41421	−	1.41421i	−0.206284	−	0.206284i	0.596402	−	0.802686i	$-0.296597\pi$
$47$	−1.41421	−	1.41421i	−0.206284	−	0.206284i	−0.802686	+	0.596402i	$0.796597\pi$
$48$	−0.292893	−	1.70711i	−0.0422755	−	0.246400i
$49$			7.00000i			1.00000i
$50$	−4.94975	−	0.707107i	−0.700000	−	0.100000i
$51$	−2.00000	+	2.82843i	−0.280056	+	0.396059i
$52$	−3.00000	+	3.00000i	−0.416025	+	0.416025i
$53$	−1.41421	+	1.41421i	−0.194257	+	0.194257i	−0.797533	−	0.603276i	$-0.793862\pi$
$53$	−1.41421	+	1.41421i	−0.194257	+	0.194257i	0.603276	+	0.797533i	$0.293862\pi$
$54$	−1.41421	+	5.00000i	−0.192450	+	0.680414i
$55$	−1.00000	−	3.00000i	−0.134840	−	0.404520i
$56$		0			0
$57$	−6.82843	+	1.17157i	−0.904447	+	0.155179i
$58$	−2.00000	−	2.00000i	−0.262613	−	0.262613i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	−3.41421	+	1.82843i	−0.440773	+	0.236049i
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$	−0.707107	−	0.707107i	−0.0898027	−	0.0898027i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	8.48528	+	4.24264i	1.05247	+	0.526235i
$66$	−2.00000	−	1.41421i	−0.246183	−	0.174078i
$67$	7.00000	−	7.00000i	0.855186	−	0.855186i	−0.135580	−	0.990766i	$-0.543290\pi$
$67$	7.00000	−	7.00000i	0.855186	−	0.855186i	0.990766	+	0.135580i	$0.0432899\pi$
$68$	−1.41421	+	1.41421i	−0.171499	+	0.171499i
$69$	5.65685	+	4.00000i	0.681005	+	0.481543i
$70$		0			0
$71$			12.7279i			1.51053i	0.655422	+	0.755263i	$0.272491\pi$
$71$			12.7279i			1.51053i	−0.655422	+	0.755263i	$0.727509\pi$
$72$	−1.29289	+	2.70711i	−0.152369	+	0.319036i
$73$	−2.00000	−	2.00000i	−0.234082	−	0.234082i	0.580312	−	0.814394i	$-0.302931\pi$
$73$	−2.00000	−	2.00000i	−0.234082	−	0.234082i	−0.814394	+	0.580312i	$0.802931\pi$
$74$	4.24264			0.493197
$75$	6.29289	+	5.94975i	0.726641	+	0.687018i
$76$	−4.00000			−0.458831
$77$		0			0
$78$	7.24264	−	1.24264i	0.820068	−	0.140701i
$79$		−	2.00000i		−	0.225018i	−0.993651	−	0.112509i	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$	−2.12132	+	0.707107i	−0.237171	+	0.0790569i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	4.00000	−	4.00000i	0.441726	−	0.441726i
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	−0.900515	−	0.434825i	$-0.856810\pi$
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	0.434825	+	0.900515i	$0.356810\pi$
$84$		0			0
$85$	4.00000	+	2.00000i	0.433861	+	0.216930i
$86$		0			0
$87$	0.828427	+	4.82843i	0.0888167	+	0.517662i
$88$	−1.00000	−	1.00000i	−0.106600	−	0.106600i
$89$	−7.07107			−0.749532			−0.374766	−	0.927119i	$-0.622277\pi$
$89$	−7.07107			−0.749532			−0.374766	+	0.927119i	$0.622277\pi$
$90$	6.65685	+	0.828427i	0.701694	+	0.0873239i
$91$		0			0
$92$	2.82843	+	2.82843i	0.294884	+	0.294884i
$93$	0.292893	+	1.70711i	0.0303716	+	0.177019i
$94$			2.00000i			0.206284i
$95$	2.82843	+	8.48528i	0.290191	+	0.870572i
$96$	−1.00000	+	1.41421i	−0.102062	+	0.144338i
$97$	11.0000	−	11.0000i	1.11688	−	1.11688i	0.124684	−	0.992196i	$-0.460208\pi$
$97$	11.0000	−	11.0000i	1.11688	−	1.11688i	0.992196	−	0.124684i	$-0.0397918\pi$
$98$	4.94975	−	4.94975i	0.500000	−	0.500000i
$99$	1.41421	+	4.00000i	0.142134	+	0.402015i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$			15.5563i			1.54791i	0.633238	+	0.773957i	$0.281726\pi$
$101$			15.5563i			1.54791i	−0.633238	+	0.773957i	$0.718274\pi$
$102$	3.41421	−	0.585786i	0.338058	−	0.0580015i
$103$	−6.00000	−	6.00000i	−0.591198	−	0.591198i	0.346757	−	0.937955i	$-0.387283\pi$
$103$	−6.00000	−	6.00000i	−0.591198	−	0.591198i	−0.937955	+	0.346757i	$0.887283\pi$
$104$	4.24264			0.416025
$105$		0			0
$106$	2.00000			0.194257
$107$	−8.48528	−	8.48528i	−0.820303	−	0.820303i	0.165848	−	0.986151i	$-0.446964\pi$
$107$	−8.48528	−	8.48528i	−0.820303	−	0.820303i	−0.986151	+	0.165848i	$0.946964\pi$
$108$	4.53553	−	2.53553i	0.436432	−	0.243982i
$109$			10.0000i			0.957826i	0.877862	+	0.478913i	$0.158969\pi$
$109$			10.0000i			0.957826i	−0.877862	+	0.478913i	$0.841031\pi$
$110$	−1.41421	+	2.82843i	−0.134840	+	0.269680i
$111$	−6.00000	−	4.24264i	−0.569495	−	0.402694i
$112$		0			0
$113$	−4.24264	+	4.24264i	−0.399114	+	0.399114i	−0.877920	−	0.478806i	$-0.841070\pi$
$113$	−4.24264	+	4.24264i	−0.399114	+	0.399114i	0.478806	+	0.877920i	$0.341070\pi$
$114$	5.65685	+	4.00000i	0.529813	+	0.374634i
$115$	4.00000	−	8.00000i	0.373002	−	0.746004i
$116$			2.82843i			0.262613i
$117$	−11.4853	−	5.48528i	−1.06181	−	0.507114i
$118$		0			0
$119$		0			0
$120$	3.70711	+	1.12132i	0.338411	+	0.102362i
$121$	9.00000			0.818182
$122$	−5.65685	−	5.65685i	−0.512148	−	0.512148i
$123$	−9.65685	+	1.65685i	−0.870729	+	0.149394i
$124$			1.00000i			0.0898027i
$125$	6.36396	−	9.19239i	0.569210	−	0.822192i
$126$		0			0
$127$	5.00000	−	5.00000i	0.443678	−	0.443678i	−0.449568	−	0.893246i	$-0.648422\pi$
$127$	5.00000	−	5.00000i	0.443678	−	0.443678i	0.893246	+	0.449568i	$0.148422\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−3.00000	−	9.00000i	−0.263117	−	0.789352i
$131$		−	14.1421i		−	1.23560i	−0.786334	−	0.617802i	$-0.788023\pi$
$131$		−	14.1421i		−	1.23560i	0.786334	−	0.617802i	$-0.211977\pi$
$132$	0.414214	+	2.41421i	0.0360527	+	0.210130i
$133$		0			0
$134$	−9.89949			−0.855186
$135$	−8.58579	−	7.82843i	−0.738947	−	0.673764i
$136$	2.00000			0.171499
$137$	7.07107	+	7.07107i	0.604122	+	0.604122i	0.941404	−	0.337282i	$-0.109507\pi$
$137$	7.07107	+	7.07107i	0.604122	+	0.604122i	−0.337282	+	0.941404i	$0.609507\pi$
$138$	−1.17157	−	6.82843i	−0.0997309	−	0.581274i
$139$		−	12.0000i		−	1.01783i	−0.860818	−	0.508913i	$-0.830047\pi$
$139$		−	12.0000i		−	1.01783i	0.860818	−	0.508913i	$-0.169953\pi$
$140$		0			0
$141$	2.00000	−	2.82843i	0.168430	−	0.238197i
$142$	9.00000	−	9.00000i	0.755263	−	0.755263i
$143$	4.24264	−	4.24264i	0.354787	−	0.354787i
$144$	2.82843	−	1.00000i	0.235702	−	0.0833333i
$145$	6.00000	−	2.00000i	0.498273	−	0.166091i
$146$			2.82843i			0.234082i
$147$	−11.9497	+	2.05025i	−0.985599	+	0.169102i
$148$	−3.00000	−	3.00000i	−0.246598	−	0.246598i
$149$	1.41421			0.115857			0.0579284	−	0.998321i	$-0.481550\pi$
$149$	1.41421			0.115857			0.0579284	+	0.998321i	$0.481550\pi$
$150$	−0.242641	−	8.65685i	−0.0198115	−	0.706829i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	2.82843	+	2.82843i	0.229416	+	0.229416i
$153$	−5.41421	−	2.58579i	−0.437713	−	0.209048i
$154$		0			0
$155$	2.12132	−	0.707107i	0.170389	−	0.0567962i
$156$	−6.00000	−	4.24264i	−0.480384	−	0.339683i
$157$	−4.00000	+	4.00000i	−0.319235	+	0.319235i	−0.848473	−	0.529238i	$-0.822478\pi$
$157$	−4.00000	+	4.00000i	−0.319235	+	0.319235i	0.529238	+	0.848473i	$0.322478\pi$
$158$	−1.41421	+	1.41421i	−0.112509	+	0.112509i
$159$	−2.82843	−	2.00000i	−0.224309	−	0.158610i
$160$	2.00000	+	1.00000i	0.158114	+	0.0790569i
$161$		0			0
$162$	−8.94975	−	0.949747i	−0.703159	−	0.0746192i
$163$	−11.0000	−	11.0000i	−0.861586	−	0.861586i	0.129936	−	0.991522i	$-0.458523\pi$
$163$	−11.0000	−	11.0000i	−0.861586	−	0.861586i	−0.991522	+	0.129936i	$0.958523\pi$
$164$	−5.65685			−0.441726
$165$	4.82843	−	2.58579i	0.375893	−	0.201303i
$166$	6.00000			0.465690
$167$	5.65685	+	5.65685i	0.437741	+	0.437741i	0.891251	−	0.453510i	$-0.149829\pi$
$167$	5.65685	+	5.65685i	0.437741	+	0.437741i	−0.453510	+	0.891251i	$0.649829\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	−1.41421	−	4.24264i	−0.108465	−	0.325396i
$171$	−4.00000	−	11.3137i	−0.305888	−	0.865181i
$172$		0			0
$173$	14.1421	−	14.1421i	1.07521	−	1.07521i	0.0782748	−	0.996932i	$-0.475059\pi$
$173$	14.1421	−	14.1421i	1.07521	−	1.07521i	0.996932	−	0.0782748i	$-0.0249412\pi$
$174$	2.82843	−	4.00000i	0.214423	−	0.303239i
$175$		0			0
$176$			1.41421i			0.106600i
$177$		0			0
$178$	5.00000	+	5.00000i	0.374766	+	0.374766i
$179$	−12.7279			−0.951330			−0.475665	−	0.879627i	$-0.657792\pi$
$179$	−12.7279			−0.951330			−0.475665	+	0.879627i	$0.657792\pi$
$180$	−4.12132	−	5.29289i	−0.307185	−	0.394509i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	2.34315	+	13.6569i	0.173210	+	1.00954i
$184$		−	4.00000i		−	0.294884i
$185$	−4.24264	+	8.48528i	−0.311925	+	0.623850i
$186$	1.00000	−	1.41421i	0.0733236	−	0.103695i
$187$	2.00000	−	2.00000i	0.146254	−	0.146254i
$188$	1.41421	−	1.41421i	0.103142	−	0.103142i
$189$		0			0
$190$	4.00000	−	8.00000i	0.290191	−	0.580381i
$191$		−	21.2132i		−	1.53493i	−0.641089	−	0.767467i	$-0.721517\pi$
$191$		−	21.2132i		−	1.53493i	0.641089	−	0.767467i	$-0.278483\pi$
$192$	1.70711	−	0.292893i	0.123200	−	0.0211377i
$193$	−9.00000	−	9.00000i	−0.647834	−	0.647834i	0.304635	−	0.952469i	$-0.401466\pi$
$193$	−9.00000	−	9.00000i	−0.647834	−	0.647834i	−0.952469	+	0.304635i	$0.901466\pi$
$194$	−15.5563			−1.11688
$195$	−4.75736	+	15.7279i	−0.340682	+	1.12630i
$196$	−7.00000			−0.500000
$197$	−7.07107	−	7.07107i	−0.503793	−	0.503793i	0.408822	−	0.912614i	$-0.365940\pi$
$197$	−7.07107	−	7.07107i	−0.503793	−	0.503793i	−0.912614	+	0.408822i	$0.865940\pi$
$198$	1.82843	−	3.82843i	0.129941	−	0.272074i
$199$			24.0000i			1.70131i	0.525720	+	0.850657i	$0.323796\pi$
$199$			24.0000i			1.70131i	−0.525720	+	0.850657i	$0.676204\pi$
$200$	0.707107	−	4.94975i	0.0500000	−	0.350000i
$201$	14.0000	+	9.89949i	0.987484	+	0.698257i
$202$	11.0000	−	11.0000i	0.773957	−	0.773957i
$203$		0			0
$204$	−2.82843	−	2.00000i	−0.198030	−	0.140028i
$205$	4.00000	+	12.0000i	0.279372	+	0.838116i
$206$			8.48528i			0.591198i
$207$	−5.17157	+	10.8284i	−0.359449	+	0.752628i
$208$	−3.00000	−	3.00000i	−0.208013	−	0.208013i
$209$	5.65685			0.391293
$210$		0			0
$211$	10.0000			0.688428			0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000			0.688428			0.344214	+	0.938891i	$0.388145\pi$
$212$	−1.41421	−	1.41421i	−0.0971286	−	0.0971286i
$213$	−21.7279	+	3.72792i	−1.48877	+	0.255433i
$214$			12.0000i			0.820303i
$215$		0			0
$216$	−5.00000	−	1.41421i	−0.340207	−	0.0962250i
$217$		0			0
$218$	7.07107	−	7.07107i	0.478913	−	0.478913i
$219$	2.82843	−	4.00000i	0.191127	−	0.270295i
$220$	3.00000	−	1.00000i	0.202260	−	0.0674200i
$221$			8.48528i			0.570782i
$222$	1.24264	+	7.24264i	0.0834006	+	0.486094i
$223$	−11.0000	−	11.0000i	−0.736614	−	0.736614i	0.235307	−	0.971921i	$-0.424391\pi$
$223$	−11.0000	−	11.0000i	−0.736614	−	0.736614i	−0.971921	+	0.235307i	$0.924391\pi$
$224$		0			0
$225$	−8.31371	+	12.4853i	−0.554247	+	0.832352i
$226$	6.00000			0.399114
$227$	−11.3137	−	11.3137i	−0.750917	−	0.750917i	0.223733	−	0.974650i	$-0.428176\pi$
$227$	−11.3137	−	11.3137i	−0.750917	−	0.750917i	−0.974650	+	0.223733i	$0.928176\pi$
$228$	−1.17157	−	6.82843i	−0.0775893	−	0.452224i
$229$		−	26.0000i		−	1.71813i	−0.511868	−	0.859064i	$-0.671046\pi$
$229$		−	26.0000i		−	1.71813i	0.511868	−	0.859064i	$-0.328954\pi$
$230$	−8.48528	+	2.82843i	−0.559503	+	0.186501i
$231$		0			0
$232$	2.00000	−	2.00000i	0.131306	−	0.131306i
$233$	9.89949	−	9.89949i	0.648537	−	0.648537i	−0.304102	−	0.952639i	$-0.598356\pi$
$233$	9.89949	−	9.89949i	0.648537	−	0.648537i	0.952639	+	0.304102i	$0.0983564\pi$
$234$	4.24264	+	12.0000i	0.277350	+	0.784465i
$235$	−4.00000	−	2.00000i	−0.260931	−	0.130466i
$236$		0			0
$237$	3.41421	−	0.585786i	0.221777	−	0.0380509i
$238$		0			0
$239$	−22.6274			−1.46365			−0.731823	−	0.681495i	$-0.761330\pi$
$239$	−22.6274			−1.46365			−0.731823	+	0.681495i	$0.761330\pi$
$240$	−1.82843	−	3.41421i	−0.118024	−	0.220387i
$241$	−2.00000			−0.128831			−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000			−0.128831			−0.0644157	+	0.997923i	$0.520518\pi$
$242$	−6.36396	−	6.36396i	−0.409091	−	0.409091i
$243$	11.7071	+	10.2929i	0.751011	+	0.660289i
$244$			8.00000i			0.512148i
$245$	4.94975	+	14.8492i	0.316228	+	0.948683i
$246$	8.00000	+	5.65685i	0.510061	+	0.360668i
$247$	−12.0000	+	12.0000i	−0.763542	+	0.763542i
$248$	0.707107	−	0.707107i	0.0449013	−	0.0449013i
$249$	−8.48528	−	6.00000i	−0.537733	−	0.380235i
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$		−	4.24264i		−	0.267793i	−0.990995	−	0.133897i	$-0.957251\pi$
$251$		−	4.24264i		−	0.267793i	0.990995	−	0.133897i	$-0.0427490\pi$
$252$		0			0
$253$	−4.00000	−	4.00000i	−0.251478	−	0.251478i
$254$	−7.07107			−0.443678
$255$	−2.24264	+	7.41421i	−0.140440	+	0.464296i
$256$	1.00000			0.0625000
$257$	4.24264	+	4.24264i	0.264649	+	0.264649i	0.826940	−	0.562291i	$-0.190080\pi$
$257$	4.24264	+	4.24264i	0.264649	+	0.264649i	−0.562291	+	0.826940i	$0.690080\pi$
$258$		0			0
$259$		0			0
$260$	−4.24264	+	8.48528i	−0.263117	+	0.526235i
$261$	−8.00000	+	2.82843i	−0.495188	+	0.175075i
$262$	−10.0000	+	10.0000i	−0.617802	+	0.617802i
$263$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$263$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$264$	1.41421	−	2.00000i	0.0870388	−	0.123091i
$265$	−2.00000	+	4.00000i	−0.122859	+	0.245718i
$266$		0			0
$267$	−2.07107	−	12.0711i	−0.126747	−	0.738737i
$268$	7.00000	+	7.00000i	0.427593	+	0.427593i
$269$	−25.4558			−1.55207			−0.776035	−	0.630690i	$-0.782772\pi$
$269$	−25.4558			−1.55207			−0.776035	+	0.630690i	$0.782772\pi$
$270$	0.535534	+	11.6066i	0.0325916	+	0.706355i
$271$	10.0000			0.607457			0.303728	−	0.952759i	$-0.401768\pi$
$271$	10.0000			0.607457			0.303728	+	0.952759i	$0.401768\pi$
$272$	−1.41421	−	1.41421i	−0.0857493	−	0.0857493i
$273$		0			0
$274$		−	10.0000i		−	0.604122i
$275$	−4.24264	−	5.65685i	−0.255841	−	0.341121i
$276$	−4.00000	+	5.65685i	−0.240772	+	0.340503i
$277$	5.00000	−	5.00000i	0.300421	−	0.300421i	−0.540758	−	0.841178i	$-0.681862\pi$
$277$	5.00000	−	5.00000i	0.300421	−	0.300421i	0.841178	+	0.540758i	$0.181862\pi$
$278$	−8.48528	+	8.48528i	−0.508913	+	0.508913i
$279$	−2.82843	+	1.00000i	−0.169334	+	0.0598684i
$280$		0			0
$281$			22.6274i			1.34984i	0.737892	+	0.674919i	$0.235822\pi$
$281$			22.6274i			1.34984i	−0.737892	+	0.674919i	$0.764178\pi$
$282$	−3.41421	+	0.585786i	−0.203313	+	0.0348831i
$283$	−19.0000	−	19.0000i	−1.12943	−	1.12943i	−0.990269	−	0.139163i	$-0.955559\pi$
$283$	−19.0000	−	19.0000i	−1.12943	−	1.12943i	−0.139163	−	0.990269i	$-0.544441\pi$
$284$	−12.7279			−0.755263
$285$	−13.6569	+	7.31371i	−0.808962	+	0.433227i
$286$	−6.00000			−0.354787
$287$		0			0
$288$	−2.70711	−	1.29289i	−0.159518	−	0.0761845i
$289$		−	13.0000i		−	0.764706i
$290$	−5.65685	−	2.82843i	−0.332182	−	0.166091i
$291$	22.0000	+	15.5563i	1.28966	+	0.911929i
$292$	2.00000	−	2.00000i	0.117041	−	0.117041i
$293$	16.9706	−	16.9706i	0.991431	−	0.991431i	−0.00853273	−	0.999964i	$-0.502716\pi$
$293$	16.9706	−	16.9706i	0.991431	−	0.991431i	0.999964	+	0.00853273i	$0.00271609\pi$
$294$	9.89949	+	7.00000i	0.577350	+	0.408248i
$295$		0			0
$296$			4.24264i			0.246598i
$297$	−6.41421	+	3.58579i	−0.372190	+	0.208068i
$298$	−1.00000	−	1.00000i	−0.0579284	−	0.0579284i
$299$	16.9706			0.981433
$300$	−5.94975	+	6.29289i	−0.343509	+	0.363320i
$301$		0			0
$302$	5.65685	+	5.65685i	0.325515	+	0.325515i
$303$	−26.5563	+	4.55635i	−1.52562	+	0.261755i
$304$		−	4.00000i		−	0.229416i
$305$	16.9706	−	5.65685i	0.971732	−	0.323911i
$306$	2.00000	+	5.65685i	0.114332	+	0.323381i
$307$	5.00000	−	5.00000i	0.285365	−	0.285365i	−0.549879	−	0.835244i	$-0.685326\pi$
$307$	5.00000	−	5.00000i	0.285365	−	0.285365i	0.835244	+	0.549879i	$0.185326\pi$
$308$		0			0
$309$	8.48528	−	12.0000i	0.482711	−	0.682656i
$310$	−2.00000	−	1.00000i	−0.113592	−	0.0567962i
$311$			1.41421i			0.0801927i	0.999196	+	0.0400963i	$0.0127665\pi$
$311$			1.41421i			0.0801927i	−0.999196	+	0.0400963i	$0.987234\pi$
$312$	1.24264	+	7.24264i	0.0703507	+	0.410034i
$313$	−10.0000	−	10.0000i	−0.565233	−	0.565233i	0.365556	−	0.930789i	$-0.380879\pi$
$313$	−10.0000	−	10.0000i	−0.565233	−	0.565233i	−0.930789	+	0.365556i	$0.880879\pi$
$314$	5.65685			0.319235
$315$		0			0
$316$	2.00000			0.112509
$317$	−4.24264	−	4.24264i	−0.238290	−	0.238290i	0.577851	−	0.816142i	$-0.303891\pi$
$317$	−4.24264	−	4.24264i	−0.238290	−	0.238290i	−0.816142	+	0.577851i	$0.803891\pi$
$318$	0.585786	+	3.41421i	0.0328493	+	0.191460i
$319$		−	4.00000i		−	0.223957i
$320$	−0.707107	−	2.12132i	−0.0395285	−	0.118585i
$321$	12.0000	−	16.9706i	0.669775	−	0.947204i
$322$		0			0
$323$	−5.65685	+	5.65685i	−0.314756	+	0.314756i
$324$	5.65685	+	7.00000i	0.314270	+	0.388889i
$325$	21.0000	+	3.00000i	1.16487	+	0.166410i
$326$			15.5563i			0.861586i
$327$	−17.0711	+	2.92893i	−0.944032	+	0.161970i
$328$	4.00000	+	4.00000i	0.220863	+	0.220863i
$329$		0			0
$330$	−5.24264	−	1.58579i	−0.288598	−	0.0872947i
$331$	32.0000			1.75888			0.879440	−	0.476011i	$-0.157918\pi$
$331$	32.0000			1.75888			0.879440	+	0.476011i	$0.157918\pi$
$332$	−4.24264	−	4.24264i	−0.232845	−	0.232845i
$333$	5.48528	−	11.4853i	0.300592	−	0.629390i
$334$		−	8.00000i		−	0.437741i
$335$	9.89949	−	19.7990i	0.540867	−	1.08173i
$336$		0			0
$337$	−8.00000	+	8.00000i	−0.435788	+	0.435788i	−0.890592	−	0.454804i	$-0.849709\pi$
$337$	−8.00000	+	8.00000i	−0.435788	+	0.435788i	0.454804	+	0.890592i	$0.349709\pi$
$338$	3.53553	−	3.53553i	0.192308	−	0.192308i
$339$	−8.48528	−	6.00000i	−0.460857	−	0.325875i
$340$	−2.00000	+	4.00000i	−0.108465	+	0.216930i
$341$		−	1.41421i		−	0.0765840i
$342$	−5.17157	+	10.8284i	−0.279647	+	0.585534i
$343$		0			0
$344$		0			0
$345$	14.8284	+	4.48528i	0.798336	+	0.241479i
$346$	−20.0000			−1.07521
$347$	−4.24264	−	4.24264i	−0.227757	−	0.227757i	0.583998	−	0.811755i	$-0.301488\pi$
$347$	−4.24264	−	4.24264i	−0.227757	−	0.227757i	−0.811755	+	0.583998i	$0.801488\pi$
$348$	−4.82843	+	0.828427i	−0.258831	+	0.0444084i
$349$		−	30.0000i		−	1.60586i	−0.596071	−	0.802932i	$-0.703272\pi$
$349$		−	30.0000i		−	1.60586i	0.596071	−	0.802932i	$-0.296728\pi$
$350$		0			0
$351$	6.00000	−	21.2132i	0.320256	−	1.13228i
$352$	1.00000	−	1.00000i	0.0533002	−	0.0533002i
$353$	25.4558	−	25.4558i	1.35488	−	1.35488i	0.474766	−	0.880112i	$-0.342533\pi$
$353$	25.4558	−	25.4558i	1.35488	−	1.35488i	0.880112	−	0.474766i	$-0.157467\pi$
$354$		0			0
$355$	9.00000	+	27.0000i	0.477670	+	1.43301i
$356$		−	7.07107i		−	0.374766i
$357$		0			0
$358$	9.00000	+	9.00000i	0.475665	+	0.475665i
$359$	−7.07107			−0.373197			−0.186598	−	0.982436i	$-0.559746\pi$
$359$	−7.07107			−0.373197			−0.186598	+	0.982436i	$0.559746\pi$
$360$	−0.828427	+	6.65685i	−0.0436619	+	0.350847i
$361$	3.00000			0.157895
$362$	7.07107	+	7.07107i	0.371647	+	0.371647i
$363$	2.63604	+	15.3640i	0.138356	+	0.806399i
$364$		0			0
$365$	−5.65685	−	2.82843i	−0.296093	−	0.148047i
$366$	8.00000	−	11.3137i	0.418167	−	0.591377i
$367$	−15.0000	+	15.0000i	−0.782994	+	0.782994i	−0.980335	−	0.197341i	$-0.936769\pi$
$367$	−15.0000	+	15.0000i	−0.782994	+	0.782994i	0.197341	+	0.980335i	$0.436769\pi$
$368$	−2.82843	+	2.82843i	−0.147442	+	0.147442i
$369$	−5.65685	−	16.0000i	−0.294484	−	0.832927i
$370$	9.00000	−	3.00000i	0.467888	−	0.155963i
$371$		0			0
$372$	−1.70711	+	0.292893i	−0.0885094	+	0.0151858i
$373$	−12.0000	−	12.0000i	−0.621336	−	0.621336i	0.324537	−	0.945873i	$-0.394792\pi$
$373$	−12.0000	−	12.0000i	−0.621336	−	0.621336i	−0.945873	+	0.324537i	$0.894792\pi$
$374$	−2.82843			−0.146254
$375$	17.5563	+	8.17157i	0.906606	+	0.421978i
$376$	−2.00000			−0.103142
$377$	8.48528	+	8.48528i	0.437014	+	0.437014i
$378$		0			0
$379$			34.0000i			1.74646i	0.487306	+	0.873231i	$0.337980\pi$
$379$			34.0000i			1.74646i	−0.487306	+	0.873231i	$0.662020\pi$
$380$	−8.48528	+	2.82843i	−0.435286	+	0.145095i
$381$	10.0000	+	7.07107i	0.512316	+	0.362262i
$382$	−15.0000	+	15.0000i	−0.767467	+	0.767467i
$383$	25.4558	−	25.4558i	1.30073	−	1.30073i	0.372835	−	0.927898i	$-0.378386\pi$
$383$	25.4558	−	25.4558i	1.30073	−	1.30073i	0.927898	−	0.372835i	$-0.121614\pi$
$384$	−1.41421	−	1.00000i	−0.0721688	−	0.0510310i
$385$		0			0
$386$			12.7279i			0.647834i
$387$		0			0
$388$	11.0000	+	11.0000i	0.558440	+	0.558440i
$389$	5.65685			0.286814			0.143407	−	0.989664i	$-0.454194\pi$
$389$	5.65685			0.286814			0.143407	+	0.989664i	$0.454194\pi$
$390$	14.4853	−	7.75736i	0.733491	−	0.392809i
$391$	8.00000			0.404577
$392$	4.94975	+	4.94975i	0.250000	+	0.250000i
$393$	24.1421	−	4.14214i	1.21781	−	0.208943i
$394$			10.0000i			0.503793i
$395$	−1.41421	−	4.24264i	−0.0711568	−	0.213470i
$396$	−4.00000	+	1.41421i	−0.201008	+	0.0710669i
$397$	−8.00000	+	8.00000i	−0.401508	+	0.401508i	−0.878764	−	0.477256i	$-0.841631\pi$
$397$	−8.00000	+	8.00000i	−0.401508	+	0.401508i	0.477256	+	0.878764i	$0.341631\pi$
$398$	16.9706	−	16.9706i	0.850657	−	0.850657i
$399$		0			0
$400$	−4.00000	+	3.00000i	−0.200000	+	0.150000i
$401$			26.8701i			1.34183i	0.741536	+	0.670913i	$0.234098\pi$
$401$			26.8701i			1.34183i	−0.741536	+	0.670913i	$0.765902\pi$
$402$	−2.89949	−	16.8995i	−0.144614	−	0.842870i
$403$	3.00000	+	3.00000i	0.149441	+	0.149441i
$404$	−15.5563			−0.773957
$405$	10.8492	−	16.9497i	0.539103	−	0.842240i
$406$		0			0
$407$	4.24264	+	4.24264i	0.210300	+	0.210300i
$408$	0.585786	+	3.41421i	0.0290008	+	0.169029i
$409$		−	6.00000i		−	0.296681i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$		−	6.00000i		−	0.296681i	0.988936	−	0.148340i	$-0.0473931\pi$
$410$	5.65685	−	11.3137i	0.279372	−	0.558744i
$411$	−10.0000	+	14.1421i	−0.493264	+	0.697580i
$412$	6.00000	−	6.00000i	0.295599	−	0.295599i
$413$		0			0
$414$	11.3137	−	4.00000i	0.556038	−	0.196589i
$415$	−6.00000	+	12.0000i	−0.294528	+	0.589057i
$416$			4.24264i			0.208013i
$417$	20.4853	−	3.51472i	1.00317	−	0.172117i
$418$	−4.00000	−	4.00000i	−0.195646	−	0.195646i
$419$	5.65685			0.276355			0.138178	−	0.990407i	$-0.455875\pi$
$419$	5.65685			0.276355			0.138178	+	0.990407i	$0.455875\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$	−7.07107	−	7.07107i	−0.344214	−	0.344214i
$423$	5.41421	+	2.58579i	0.263248	+	0.125725i
$424$			2.00000i			0.0971286i
$425$	9.89949	+	1.41421i	0.480196	+	0.0685994i
$426$	18.0000	+	12.7279i	0.872103	+	0.616670i
$427$		0			0
$428$	8.48528	−	8.48528i	0.410152	−	0.410152i
$429$	8.48528	+	6.00000i	0.409673	+	0.289683i
$430$		0			0
$431$		−	32.5269i		−	1.56677i	−0.621539	−	0.783383i	$-0.713492\pi$
$431$		−	32.5269i		−	1.56677i	0.621539	−	0.783383i	$-0.286508\pi$
$432$	2.53553	+	4.53553i	0.121991	+	0.218216i
$433$	2.00000	+	2.00000i	0.0961139	+	0.0961139i	0.753529	−	0.657415i	$-0.228350\pi$
$433$	2.00000	+	2.00000i	0.0961139	+	0.0961139i	−0.657415	+	0.753529i	$0.728350\pi$
$434$		0			0
$435$	5.17157	+	9.65685i	0.247958	+	0.463011i
$436$	−10.0000			−0.478913
$437$	11.3137	+	11.3137i	0.541208	+	0.541208i
$438$	−4.82843	+	0.828427i	−0.230711	+	0.0395838i
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$	−2.82843	−	1.41421i	−0.134840	−	0.0674200i
$441$	−7.00000	−	19.7990i	−0.333333	−	0.942809i
$442$	6.00000	−	6.00000i	0.285391	−	0.285391i
$443$	−16.9706	+	16.9706i	−0.806296	+	0.806296i	−0.984071	−	0.177775i	$-0.943110\pi$
$443$	−16.9706	+	16.9706i	−0.806296	+	0.806296i	0.177775	+	0.984071i	$0.443110\pi$
$444$	4.24264	−	6.00000i	0.201347	−	0.284747i
$445$	−15.0000	+	5.00000i	−0.711068	+	0.237023i
$446$			15.5563i			0.736614i
$447$	0.414214	+	2.41421i	0.0195916	+	0.114188i
$448$		0			0
$449$	−9.89949			−0.467186			−0.233593	−	0.972334i	$-0.575048\pi$
$449$	−9.89949			−0.467186			−0.233593	+	0.972334i	$0.575048\pi$
$450$	14.7071	−	2.94975i	0.693300	−	0.139052i
$451$	8.00000			0.376705
$452$	−4.24264	−	4.24264i	−0.199557	−	0.199557i
$453$	−2.34315	−	13.6569i	−0.110091	−	0.641655i
$454$			16.0000i			0.750917i
$455$		0			0
$456$	−4.00000	+	5.65685i	−0.187317	+	0.264906i
$457$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$457$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$458$	−18.3848	+	18.3848i	−0.859064	+	0.859064i
$459$	2.82843	−	10.0000i	0.132020	−	0.466760i
$460$	8.00000	+	4.00000i	0.373002	+	0.186501i
$461$			2.82843i			0.131733i	0.997828	+	0.0658665i	$0.0209811\pi$
$461$			2.82843i			0.131733i	−0.997828	+	0.0658665i	$0.979019\pi$
$462$		0			0
$463$	−7.00000	−	7.00000i	−0.325318	−	0.325318i	0.525485	−	0.850803i	$-0.323884\pi$
$463$	−7.00000	−	7.00000i	−0.325318	−	0.325318i	−0.850803	+	0.525485i	$0.823884\pi$
$464$	−2.82843			−0.131306
$465$	1.82843	+	3.41421i	0.0847913	+	0.158330i
$466$	−14.0000			−0.648537
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	0.769514	−	0.638630i	$-0.220499\pi$
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	−0.638630	+	0.769514i	$0.720499\pi$
$468$	5.48528	−	11.4853i	0.253557	−	0.530907i
$469$		0			0
$470$	1.41421	+	4.24264i	0.0652328	+	0.195698i
$471$	−8.00000	−	5.65685i	−0.368621	−	0.260654i
$472$		0			0
$473$		0			0
$474$	−2.82843	−	2.00000i	−0.129914	−	0.0918630i
$475$	12.0000	+	16.0000i	0.550598	+	0.734130i
$476$		0			0
$477$	2.58579	−	5.41421i	0.118395	−	0.247900i
$478$	16.0000	+	16.0000i	0.731823	+	0.731823i
$479$	38.1838			1.74466			0.872330	−	0.488917i	$-0.162608\pi$
$479$	38.1838			1.74466			0.872330	+	0.488917i	$0.162608\pi$
$480$	−1.12132	+	3.70711i	−0.0511810	+	0.169206i
$481$	−18.0000			−0.820729
$482$	1.41421	+	1.41421i	0.0644157	+	0.0644157i
$483$		0			0
$484$			9.00000i			0.409091i
$485$	15.5563	−	31.1127i	0.706377	−	1.41275i
$486$	−1.00000	−	15.5563i	−0.0453609	−	0.705650i
$487$	−11.0000	+	11.0000i	−0.498458	+	0.498458i	−0.910958	−	0.412500i	$-0.864656\pi$
$487$	−11.0000	+	11.0000i	−0.498458	+	0.498458i	0.412500	+	0.910958i	$0.364656\pi$
$488$	5.65685	−	5.65685i	0.256074	−	0.256074i
$489$	15.5563	−	22.0000i	0.703482	−	0.994874i
$490$	7.00000	−	14.0000i	0.316228	−	0.632456i
$491$		−	12.7279i		−	0.574403i	−0.957870	−	0.287202i	$-0.907275\pi$
$491$		−	12.7279i		−	0.574403i	0.957870	−	0.287202i	$-0.0927249\pi$
$492$	−1.65685	−	9.65685i	−0.0746968	−	0.435365i
$493$	4.00000	+	4.00000i	0.180151	+	0.180151i
$494$	16.9706			0.763542
$495$	5.82843	+	7.48528i	0.261968	+	0.336438i
$496$	−1.00000			−0.0449013
$497$		0			0
$498$	1.75736	+	10.2426i	0.0787492	+	0.458984i
$499$			36.0000i			1.61158i	0.592200	+	0.805791i	$0.298259\pi$
$499$			36.0000i			1.61158i	−0.592200	+	0.805791i	$0.701741\pi$
$500$	9.19239	+	6.36396i	0.411096	+	0.284605i
$501$	−8.00000	+	11.3137i	−0.357414	+	0.505459i
$502$	−3.00000	+	3.00000i	−0.133897	+	0.133897i
$503$	18.3848	−	18.3848i	0.819737	−	0.819737i	−0.166333	−	0.986070i	$-0.553193\pi$
$503$	18.3848	−	18.3848i	0.819737	−	0.819737i	0.986070	+	0.166333i	$0.0531927\pi$
$504$		0			0
$505$	11.0000	+	33.0000i	0.489494	+	1.46848i
$506$			5.65685i			0.251478i
$507$	−8.53553	+	1.46447i	−0.379076	+	0.0650392i
$508$	5.00000	+	5.00000i	0.221839	+	0.221839i
$509$	−11.3137			−0.501471			−0.250736	−	0.968056i	$-0.580672\pi$
$509$	−11.3137			−0.501471			−0.250736	+	0.968056i	$0.580672\pi$
$510$	6.82843	−	3.65685i	0.302368	−	0.161928i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	18.1421	−	10.1421i	0.800995	−	0.447786i
$514$		−	6.00000i		−	0.264649i
$515$	−16.9706	−	8.48528i	−0.747812	−	0.373906i
$516$		0			0
$517$	−2.00000	+	2.00000i	−0.0879599	+	0.0879599i
$518$		0			0
$519$	28.2843	+	20.0000i	1.24154	+	0.877903i
$520$	9.00000	−	3.00000i	0.394676	−	0.131559i
$521$		−	14.1421i		−	0.619578i	−0.950805	−	0.309789i	$-0.899742\pi$
$521$		−	14.1421i		−	0.619578i	0.950805	−	0.309789i	$-0.100258\pi$
$522$	7.65685	+	3.65685i	0.335131	+	0.160056i
$523$	18.0000	+	18.0000i	0.787085	+	0.787085i	0.981015	−	0.193930i	$-0.0621236\pi$
$523$	18.0000	+	18.0000i	0.787085	+	0.787085i	−0.193930	+	0.981015i	$0.562124\pi$
$524$	14.1421			0.617802
$525$		0			0
$526$		0			0
$527$	1.41421	+	1.41421i	0.0616041	+	0.0616041i
$528$	−2.41421	+	0.414214i	−0.105065	+	0.0180263i
$529$			7.00000i			0.304348i
$530$	4.24264	−	1.41421i	0.184289	−	0.0614295i
$531$		0			0
$532$		0			0
$533$	−16.9706	+	16.9706i	−0.735077	+	0.735077i
$534$	−7.07107	+	10.0000i	−0.305995	+	0.432742i
$535$	−24.0000	−	12.0000i	−1.03761	−	0.518805i
$536$		−	9.89949i		−	0.427593i
$537$	−3.72792	−	21.7279i	−0.160872	−	0.937629i
$538$	18.0000	+	18.0000i	0.776035	+	0.776035i
$539$	9.89949			0.426401
$540$	7.82843	−	8.58579i	0.336882	−	0.369473i
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$	−7.07107	−	7.07107i	−0.303728	−	0.303728i
$543$	−2.92893	−	17.0711i	−0.125693	−	0.732590i
$544$			2.00000i			0.0857493i
$545$	7.07107	+	21.2132i	0.302891	+	0.908674i
$546$		0			0
$547$	−5.00000	+	5.00000i	−0.213785	+	0.213785i	−0.805873	−	0.592088i	$-0.798304\pi$
$547$	−5.00000	+	5.00000i	−0.213785	+	0.213785i	0.592088	+	0.805873i	$0.298304\pi$
$548$	−7.07107	+	7.07107i	−0.302061	+	0.302061i
$549$	−22.6274	+	8.00000i	−0.965715	+	0.341432i
$550$	−1.00000	+	7.00000i	−0.0426401	+	0.298481i
$551$			11.3137i			0.481980i
$552$	6.82843	−	1.17157i	0.290637	−	0.0498655i
$553$		0			0
$554$	−7.07107			−0.300421
$555$	−15.7279	−	4.75736i	−0.667613	−	0.201939i
$556$	12.0000			0.508913
$557$	26.8701	+	26.8701i	1.13852	+	1.13852i	0.988716	+	0.149805i	$0.0478647\pi$
$557$	26.8701	+	26.8701i	1.13852	+	1.13852i	0.149805	+	0.988716i	$0.452135\pi$
$558$	2.70711	+	1.29289i	0.114601	+	0.0547325i
$559$		0			0
$560$		0			0
$561$	4.00000	+	2.82843i	0.168880	+	0.119416i
$562$	16.0000	−	16.0000i	0.674919	−	0.674919i
$563$	−11.3137	+	11.3137i	−0.476816	+	0.476816i	−0.904112	−	0.427296i	$-0.859466\pi$
$563$	−11.3137	+	11.3137i	−0.476816	+	0.476816i	0.427296	+	0.904112i	$0.359466\pi$
$564$	2.82843	+	2.00000i	0.119098	+	0.0842152i
$565$	−6.00000	+	12.0000i	−0.252422	+	0.504844i
$566$			26.8701i			1.12943i
$567$		0			0
$568$	9.00000	+	9.00000i	0.377632	+	0.377632i
$569$	−26.8701			−1.12645			−0.563226	−	0.826303i	$-0.690440\pi$
$569$	−26.8701			−1.12645			−0.563226	+	0.826303i	$0.690440\pi$
$570$	14.8284	+	4.48528i	0.621094	+	0.187868i
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$	4.24264	+	4.24264i	0.177394	+	0.177394i
$573$	36.2132	−	6.21320i	1.51283	−	0.259560i
$574$		0			0
$575$	2.82843	−	19.7990i	0.117954	−	0.825675i
$576$	1.00000	+	2.82843i	0.0416667	+	0.117851i
$577$	21.0000	−	21.0000i	0.874241	−	0.874241i	−0.118690	−	0.992931i	$-0.537869\pi$
$577$	21.0000	−	21.0000i	0.874241	−	0.874241i	0.992931	+	0.118690i	$0.0378694\pi$
$578$	−9.19239	+	9.19239i	−0.382353	+	0.382353i
$579$	12.7279	−	18.0000i	0.528954	−	0.748054i
$580$	2.00000	+	6.00000i	0.0830455	+	0.249136i
$581$		0			0
$582$	−4.55635	−	26.5563i	−0.188867	−	1.10080i
$583$	2.00000	+	2.00000i	0.0828315	+	0.0828315i
$584$	−2.82843			−0.117041
$585$	−28.2426	−	3.51472i	−1.16769	−	0.145316i
$586$	−24.0000			−0.991431
$587$	25.4558	+	25.4558i	1.05068	+	1.05068i	0.998646	+	0.0520296i	$0.0165690\pi$
$587$	25.4558	+	25.4558i	1.05068	+	1.05068i	0.0520296	+	0.998646i	$0.483431\pi$
$588$	−2.05025	−	11.9497i	−0.0845510	−	0.492799i
$589$			4.00000i			0.164817i
$590$		0			0
$591$	10.0000	−	14.1421i	0.411345	−	0.581730i
$592$	3.00000	−	3.00000i	0.123299	−	0.123299i
$593$	−4.24264	+	4.24264i	−0.174224	+	0.174224i	−0.788833	−	0.614608i	$-0.789314\pi$
$593$	−4.24264	+	4.24264i	−0.174224	+	0.174224i	0.614608	+	0.788833i	$0.289314\pi$
$594$	7.07107	+	2.00000i	0.290129	+	0.0820610i
$595$		0			0
$596$			1.41421i			0.0579284i
$597$	−40.9706	+	7.02944i	−1.67681	+	0.287696i
$598$	−12.0000	−	12.0000i	−0.490716	−	0.490716i
$599$	−43.8406			−1.79128			−0.895640	−	0.444781i	$-0.853282\pi$
$599$	−43.8406			−1.79128			−0.895640	+	0.444781i	$0.853282\pi$
$600$	8.65685	−	0.242641i	0.353415	−	0.00990576i
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$		0			0
$603$	−12.7990	+	26.7990i	−0.521215	+	1.09134i
$604$		−	8.00000i		−	0.325515i
$605$	19.0919	−	6.36396i	0.776195	−	0.258732i
$606$	22.0000	+	15.5563i	0.893689	+	0.631933i
$607$	−20.0000	+	20.0000i	−0.811775	+	0.811775i	−0.984900	−	0.173125i	$-0.944614\pi$
$607$	−20.0000	+	20.0000i	−0.811775	+	0.811775i	0.173125	+	0.984900i	$0.444614\pi$
$608$	−2.82843	+	2.82843i	−0.114708	+	0.114708i
$609$		0			0
$610$	−16.0000	−	8.00000i	−0.647821	−	0.323911i
$611$		−	8.48528i		−	0.343278i
$612$	2.58579	−	5.41421i	0.104524	−	0.218857i
$613$	−13.0000	−	13.0000i	−0.525065	−	0.525065i	0.394032	−	0.919097i	$-0.371080\pi$
$613$	−13.0000	−	13.0000i	−0.525065	−	0.525065i	−0.919097	+	0.394032i	$0.871080\pi$
$614$	−7.07107			−0.285365
$615$	−19.3137	+	10.3431i	−0.778804	+	0.417076i
$616$		0			0
$617$	29.6985	+	29.6985i	1.19562	+	1.19562i	0.975466	+	0.220150i	$0.0706547\pi$
$617$	29.6985	+	29.6985i	1.19562	+	1.19562i	0.220150	+	0.975466i	$0.429345\pi$
$618$	−14.4853	+	2.48528i	−0.582683	+	0.0999727i
$619$			4.00000i			0.160774i	0.996764	+	0.0803868i	$0.0256155\pi$
$619$			4.00000i			0.160774i	−0.996764	+	0.0803868i	$0.974384\pi$
$620$	0.707107	+	2.12132i	0.0283981	+	0.0851943i
$621$	−20.0000	−	5.65685i	−0.802572	−	0.227002i
$622$	1.00000	−	1.00000i	0.0400963	−	0.0400963i
$623$		0			0
$624$	4.24264	−	6.00000i	0.169842	−	0.240192i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$			14.1421i			0.565233i
$627$	1.65685	+	9.65685i	0.0661684	+	0.385658i
$628$	−4.00000	−	4.00000i	−0.159617	−	0.159617i
$629$	−8.48528			−0.338330
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$	−1.41421	−	1.41421i	−0.0562544	−	0.0562544i
$633$	2.92893	+	17.0711i	0.116415	+	0.678514i
$634$			6.00000i			0.238290i
$635$	7.07107	−	14.1421i	0.280607	−	0.561214i
$636$	2.00000	−	2.82843i	0.0793052	−	0.112154i
$637$	−21.0000	+	21.0000i	−0.832050	+	0.832050i
$638$	−2.82843	+	2.82843i	−0.111979	+	0.111979i
$639$	−12.7279	−	36.0000i	−0.503509	−	1.42414i
$640$	−1.00000	+	2.00000i	−0.0395285	+	0.0790569i
$641$			26.8701i			1.06130i	0.847590	+	0.530652i	$0.178053\pi$
$641$			26.8701i			1.06130i	−0.847590	+	0.530652i	$0.821947\pi$
$642$	−20.4853	+	3.51472i	−0.808490	+	0.138715i
$643$	6.00000	+	6.00000i	0.236617	+	0.236617i	0.815448	−	0.578831i	$-0.196491\pi$
$643$	6.00000	+	6.00000i	0.236617	+	0.236617i	−0.578831	+	0.815448i	$0.696491\pi$
$644$		0			0
$645$		0			0
$646$	8.00000			0.314756
$647$	−8.48528	−	8.48528i	−0.333591	−	0.333591i	0.520358	−	0.853948i	$-0.325799\pi$
$647$	−8.48528	−	8.48528i	−0.333591	−	0.333591i	−0.853948	+	0.520358i	$0.825799\pi$
$648$	0.949747	−	8.94975i	0.0373096	−	0.351579i
$649$		0			0
$650$	−12.7279	−	16.9706i	−0.499230	−	0.665640i
$651$		0			0
$652$	11.0000	−	11.0000i	0.430793	−	0.430793i
$653$	−12.7279	+	12.7279i	−0.498082	+	0.498082i	−0.910841	−	0.412758i	$-0.864565\pi$
$653$	−12.7279	+	12.7279i	−0.498082	+	0.498082i	0.412758	+	0.910841i	$0.364565\pi$
$654$	14.1421	+	10.0000i	0.553001	+	0.391031i
$655$	−10.0000	−	30.0000i	−0.390732	−	1.17220i
$656$		−	5.65685i		−	0.220863i
$657$	7.65685	+	3.65685i	0.298722	+	0.142667i
$658$		0			0
$659$	−16.9706			−0.661079			−0.330540	−	0.943792i	$-0.607231\pi$
$659$	−16.9706			−0.661079			−0.330540	+	0.943792i	$0.607231\pi$
$660$	2.58579	+	4.82843i	0.100652	+	0.187946i
$661$	−34.0000			−1.32245			−0.661223	−	0.750189i	$-0.729962\pi$
$661$	−34.0000			−1.32245			−0.661223	+	0.750189i	$0.729962\pi$
$662$	−22.6274	−	22.6274i	−0.879440	−	0.879440i
$663$	−14.4853	+	2.48528i	−0.562562	+	0.0965203i
$664$			6.00000i			0.232845i
$665$		0			0
$666$	−12.0000	+	4.24264i	−0.464991	+	0.164399i
$667$	8.00000	−	8.00000i	0.309761	−	0.309761i
$668$	−5.65685	+	5.65685i	−0.218870	+	0.218870i
$669$	15.5563	−	22.0000i	0.601443	−	0.850569i
$670$	−21.0000	+	7.00000i	−0.811301	+	0.270434i
$671$		−	11.3137i		−	0.436761i
$672$		0			0
$673$	24.0000	+	24.0000i	0.925132	+	0.925132i	0.997386	−	0.0722542i	$-0.0230193\pi$
$673$	24.0000	+	24.0000i	0.925132	+	0.925132i	−0.0722542	+	0.997386i	$0.523019\pi$
$674$	11.3137			0.435788
$675$	−23.7487	−	10.5355i	−0.914089	−	0.405513i
$676$	−5.00000			−0.192308
$677$	15.5563	+	15.5563i	0.597879	+	0.597879i	0.939748	−	0.341869i	$-0.111060\pi$
$677$	15.5563	+	15.5563i	0.597879	+	0.597879i	−0.341869	+	0.939748i	$0.611060\pi$
$678$	1.75736	+	10.2426i	0.0674910	+	0.393366i
$679$		0			0
$680$	4.24264	−	1.41421i	0.162698	−	0.0542326i
$681$	16.0000	−	22.6274i	0.613121	−	0.867085i
$682$	−1.00000	+	1.00000i	−0.0382920	+	0.0382920i
$683$	−16.9706	+	16.9706i	−0.649361	+	0.649361i	−0.952838	−	0.303478i	$-0.901852\pi$
$683$	−16.9706	+	16.9706i	−0.649361	+	0.649361i	0.303478	+	0.952838i	$0.401852\pi$
$684$	11.3137	−	4.00000i	0.432590	−	0.152944i
$685$	20.0000	+	10.0000i	0.764161	+	0.382080i
$686$		0			0
$687$	44.3848	−	7.61522i	1.69338	−	0.290539i
$688$		0			0
$689$	−8.48528			−0.323263
$690$	−7.31371	−	13.6569i	−0.278428	−	0.519908i
$691$	−14.0000			−0.532585			−0.266293	−	0.963892i	$-0.585799\pi$
$691$	−14.0000			−0.532585			−0.266293	+	0.963892i	$0.585799\pi$
$692$	14.1421	+	14.1421i	0.537603	+	0.537603i
$693$		0			0
$694$			6.00000i			0.227757i
$695$	−8.48528	−	25.4558i	−0.321865	−	0.965595i
$696$	4.00000	+	2.82843i	0.151620	+	0.107211i
$697$	−8.00000	+	8.00000i	−0.303022	+	0.303022i
$698$	−21.2132	+	21.2132i	−0.802932	+	0.802932i
$699$	19.7990	+	14.0000i	0.748867	+	0.529529i
$700$		0			0
$701$			4.24264i			0.160242i	0.996785	+	0.0801212i	$0.0255307\pi$
$701$			4.24264i			0.160242i	−0.996785	+	0.0801212i	$0.974469\pi$
$702$	−19.2426	+	10.7574i	−0.726267	+	0.406010i
$703$	−12.0000	−	12.0000i	−0.452589	−	0.452589i
$704$	−1.41421			−0.0533002
$705$	2.24264	−	7.41421i	0.0844627	−	0.279235i
$706$	−36.0000			−1.35488
$707$		0			0
$708$		0			0
$709$		−	48.0000i		−	1.80268i	−0.433114	−	0.901339i	$-0.642585\pi$
$709$		−	48.0000i		−	1.80268i	0.433114	−	0.901339i	$-0.357415\pi$
$710$	12.7279	−	25.4558i	0.477670	−	0.955341i
$711$	2.00000	+	5.65685i	0.0750059	+	0.212149i
$712$	−5.00000	+	5.00000i	−0.187383	+	0.187383i
$713$	2.82843	−	2.82843i	0.105925	−	0.105925i
$714$		0			0
$715$	6.00000	−	12.0000i	0.224387	−	0.448775i
$716$		−	12.7279i		−	0.475665i
$717$	−6.62742	−	38.6274i	−0.247505	−	1.44257i
$718$	5.00000	+	5.00000i	0.186598	+	0.186598i
$719$	−39.5980			−1.47676			−0.738378	−	0.674387i	$-0.764408\pi$
$719$	−39.5980			−1.47676			−0.738378	+	0.674387i	$0.764408\pi$
$720$	5.29289	−	4.12132i	0.197254	−	0.153593i
$721$		0			0
$722$	−2.12132	−	2.12132i	−0.0789474	−	0.0789474i
$723$	−0.585786	−	3.41421i	−0.0217856	−	0.126976i
$724$		−	10.0000i		−	0.371647i
$725$	11.3137	−	8.48528i	0.420181	−	0.315135i
$726$	9.00000	−	12.7279i	0.334021	−	0.472377i
$727$	−18.0000	+	18.0000i	−0.667583	+	0.667583i	−0.957156	−	0.289573i	$-0.906487\pi$
$727$	−18.0000	+	18.0000i	−0.667583	+	0.667583i	0.289573	+	0.957156i	$0.406487\pi$
$728$		0			0
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	2.00000	+	6.00000i	0.0740233	+	0.222070i
$731$		0			0
$732$	−13.6569	+	2.34315i	−0.504772	+	0.0866052i
$733$	24.0000	+	24.0000i	0.886460	+	0.886460i	0.994181	−	0.107721i	$-0.0343553\pi$
$733$	24.0000	+	24.0000i	0.886460	+	0.886460i	−0.107721	+	0.994181i	$0.534355\pi$
$734$	21.2132			0.782994
$735$	−23.8995	+	12.7990i	−0.881546	+	0.472098i
$736$	4.00000			0.147442
$737$	−9.89949	−	9.89949i	−0.364653	−	0.364653i
$738$	−7.31371	+	15.3137i	−0.269221	+	0.563705i
$739$			40.0000i			1.47142i	0.677295	+	0.735712i	$0.263152\pi$
$739$			40.0000i			1.47142i	−0.677295	+	0.735712i	$0.736848\pi$
$740$	−8.48528	−	4.24264i	−0.311925	−	0.155963i
$741$	−24.0000	−	16.9706i	−0.881662	−	0.623429i
$742$		0			0
$743$	−14.1421	+	14.1421i	−0.518825	+	0.518825i	−0.917216	−	0.398391i	$-0.869569\pi$
$743$	−14.1421	+	14.1421i	−0.518825	+	0.518825i	0.398391	+	0.917216i	$0.369569\pi$
$744$	1.41421	+	1.00000i	0.0518476	+	0.0366618i
$745$	3.00000	−	1.00000i	0.109911	−	0.0366372i
$746$			16.9706i			0.621336i
$747$	7.75736	−	16.2426i	0.283827	−	0.594287i
$748$	2.00000	+	2.00000i	0.0731272	+	0.0731272i
$749$		0			0
$750$	−6.63604	−	18.1924i	−0.242314	−	0.664292i
$751$	4.00000			0.145962			0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000			0.145962			0.0729810	+	0.997333i	$0.476749\pi$
$752$	1.41421	+	1.41421i	0.0515711	+	0.0515711i
$753$	7.24264	−	1.24264i	0.263936	−	0.0452843i
$754$		−	12.0000i		−	0.437014i
$755$	−16.9706	+	5.65685i	−0.617622	+	0.205874i
$756$		0			0
$757$	−35.0000	+	35.0000i	−1.27210	+	1.27210i	−0.327111	+	0.944986i	$0.606075\pi$
$757$	−35.0000	+	35.0000i	−1.27210	+	1.27210i	−0.944986	+	0.327111i	$0.893925\pi$
$758$	24.0416	−	24.0416i	0.873231	−	0.873231i
$759$	5.65685	−	8.00000i	0.205331	−	0.290382i
$760$	8.00000	+	4.00000i	0.290191	+	0.145095i
$761$		−	52.3259i		−	1.89681i	−0.317058	−	0.948406i	$-0.602695\pi$
$761$		−	52.3259i		−	1.89681i	0.317058	−	0.948406i	$-0.397305\pi$
$762$	−2.07107	−	12.0711i	−0.0750269	−	0.437289i
$763$		0			0
$764$	21.2132			0.767467
$765$	−13.3137	−	1.65685i	−0.481358	−	0.0599037i
$766$	−36.0000			−1.30073
$767$		0			0
$768$	0.292893	+	1.70711i	0.0105689	+	0.0615999i
$769$		−	48.0000i		−	1.73092i	−0.500974	−	0.865462i	$-0.667025\pi$
$769$		−	48.0000i		−	1.73092i	0.500974	−	0.865462i	$-0.332975\pi$
$770$		0			0
$771$	−6.00000	+	8.48528i	−0.216085	+	0.305590i
$772$	9.00000	−	9.00000i	0.323917	−	0.323917i
$773$	−12.7279	+	12.7279i	−0.457792	+	0.457792i	−0.897930	−	0.440138i	$-0.854929\pi$
$773$	−12.7279	+	12.7279i	−0.457792	+	0.457792i	0.440138	+	0.897930i	$0.354929\pi$
$774$		0			0
$775$	4.00000	−	3.00000i	0.143684	−	0.107763i
$776$		−	15.5563i		−	0.558440i
$777$		0			0
$778$	−4.00000	−	4.00000i	−0.143407	−	0.143407i
$779$	−22.6274			−0.810711
$780$	−15.7279	−	4.75736i	−0.563150	−	0.170341i
$781$	18.0000			0.644091
$782$	−5.65685	−	5.65685i	−0.202289	−	0.202289i
$783$	−7.17157	−	12.8284i	−0.256291	−	0.458451i
$784$		−	7.00000i		−	0.250000i
$785$	−5.65685	+	11.3137i	−0.201902	+	0.403804i
$786$	−20.0000	−	14.1421i	−0.713376	−	0.504433i
$787$	−24.0000	+	24.0000i	−0.855508	+	0.855508i	−0.990805	−	0.135297i	$-0.956801\pi$
$787$	−24.0000	+	24.0000i	−0.855508	+	0.855508i	0.135297	+	0.990805i	$0.456801\pi$
$788$	7.07107	−	7.07107i	0.251896	−	0.251896i
$789$		0			0
$790$	−2.00000	+	4.00000i	−0.0711568	+	0.142314i
$791$		0			0
$792$	3.82843	+	1.82843i	0.136037	+	0.0649703i
$793$	24.0000	+	24.0000i	0.852265	+	0.852265i
$794$	11.3137			0.401508
$795$	−7.41421	−	2.24264i	−0.262955	−	0.0795383i
$796$	−24.0000			−0.850657
$797$	−4.24264	−	4.24264i	−0.150282	−	0.150282i	0.627962	−	0.778244i	$-0.283889\pi$
$797$	−4.24264	−	4.24264i	−0.150282	−	0.150282i	−0.778244	+	0.627962i	$0.783889\pi$
$798$		0			0
$799$		−	4.00000i		−	0.141510i
$800$	4.94975	+	0.707107i	0.175000	+	0.0250000i
$801$	20.0000	−	7.07107i	0.706665	−	0.249844i
$802$	19.0000	−	19.0000i	0.670913	−	0.670913i
$803$	−2.82843	+	2.82843i	−0.0998130	+	0.0998130i
$804$	−9.89949	+	14.0000i	−0.349128	+	0.493742i
$805$		0			0
$806$		−	4.24264i		−	0.149441i
$807$	−7.45584	−	43.4558i	−0.262458	−	1.52972i
$808$	11.0000	+	11.0000i	0.386979	+	0.386979i
$809$	7.07107			0.248606			0.124303	−	0.992244i	$-0.460331\pi$
$809$	7.07107			0.248606			0.124303	+	0.992244i	$0.460331\pi$
$810$	−19.6569	+	4.31371i	−0.690671	+	0.151568i
$811$	6.00000			0.210688			0.105344	−	0.994436i	$-0.466406\pi$
$811$	6.00000			0.210688			0.105344	+	0.994436i	$0.466406\pi$
$812$		0			0
$813$	2.92893	+	17.0711i	0.102722	+	0.598708i
$814$		−	6.00000i		−	0.210300i
$815$	−31.1127	−	15.5563i	−1.08983	−	0.544915i
$816$	2.00000	−	2.82843i	0.0700140	−	0.0990148i
$817$		0			0
$818$	−4.24264	+	4.24264i	−0.148340	+	0.148340i
$819$		0			0
$820$	−12.0000	+	4.00000i	−0.419058	+	0.139686i
$821$			14.1421i			0.493564i	0.969071	+	0.246782i	$0.0793731\pi$
$821$			14.1421i			0.493564i	−0.969071	+	0.246782i	$0.920627\pi$
$822$	17.0711	−	2.92893i	0.595422	−	0.102158i
$823$	−25.0000	−	25.0000i	−0.871445	−	0.871445i	0.121185	−	0.992630i	$-0.461331\pi$
$823$	−25.0000	−	25.0000i	−0.871445	−	0.871445i	−0.992630	+	0.121185i	$0.961331\pi$
$824$	−8.48528			−0.295599
$825$	8.41421	−	8.89949i	0.292945	−	0.309841i
$826$		0			0
$827$	25.4558	+	25.4558i	0.885186	+	0.885186i	0.994056	−	0.108870i	$-0.0347231\pi$
$827$	25.4558	+	25.4558i	0.885186	+	0.885186i	−0.108870	+	0.994056i	$0.534723\pi$
$828$	−10.8284	−	5.17157i	−0.376314	−	0.179725i
$829$			28.0000i			0.972480i	0.873825	+	0.486240i	$0.161632\pi$
$829$			28.0000i			0.972480i	−0.873825	+	0.486240i	$0.838368\pi$
$830$	12.7279	−	4.24264i	0.441793	−	0.147264i
$831$	10.0000	+	7.07107i	0.346896	+	0.245293i
$832$	3.00000	−	3.00000i	0.104006	−	0.104006i
$833$	−9.89949	+	9.89949i	−0.342997	+	0.342997i
$834$	−16.9706	−	12.0000i	−0.587643	−	0.415526i
$835$	16.0000	+	8.00000i	0.553703	+	0.276851i
$836$			5.65685i			0.195646i
$837$	−2.53553	−	4.53553i	−0.0876409	−	0.156771i
$838$	−4.00000	−	4.00000i	−0.138178	−	0.138178i
$839$	35.3553			1.22060			0.610301	−	0.792170i	$-0.291049\pi$
$839$	35.3553			1.22060			0.610301	+	0.792170i	$0.291049\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$	15.5563	+	15.5563i	0.536107	+	0.536107i
$843$	−38.6274	+	6.62742i	−1.33040	+	0.228260i
$844$			10.0000i			0.344214i
$845$	3.53553	+	10.6066i	0.121626	+	0.364878i
$846$	−2.00000	−	5.65685i	−0.0687614	−	0.194487i
$847$		0			0
$848$	1.41421	−	1.41421i	0.0485643	−	0.0485643i
$849$	26.8701	−	38.0000i	0.922178	−	1.30416i
$850$	−6.00000	−	8.00000i	−0.205798	−	0.274398i
$851$			16.9706i			0.581743i
$852$	−3.72792	−	21.7279i	−0.127717	−	0.744386i
$853$	8.00000	+	8.00000i	0.273915	+	0.273915i	0.830674	−	0.556759i	$-0.187955\pi$
$853$	8.00000	+	8.00000i	0.273915	+	0.273915i	−0.556759	+	0.830674i	$0.687955\pi$
$854$		0			0
$855$	−16.4853	−	21.1716i	−0.563785	−	0.724053i
$856$	−12.0000			−0.410152
$857$	21.2132	+	21.2132i	0.724629	+	0.724629i	0.969544	−	0.244915i	$-0.0787601\pi$
$857$	21.2132	+	21.2132i	0.724629	+	0.724629i	−0.244915	+	0.969544i	$0.578760\pi$
$858$	−1.75736	−	10.2426i	−0.0599953	−	0.349678i
$859$			12.0000i			0.409435i	0.978821	+	0.204717i	$0.0656275\pi$
$859$			12.0000i			0.409435i	−0.978821	+	0.204717i	$0.934372\pi$
$860$		0			0
$861$		0			0
$862$	−23.0000	+	23.0000i	−0.783383	+	0.783383i
$863$	−16.9706	+	16.9706i	−0.577685	+	0.577685i	−0.934265	−	0.356580i	$-0.883943\pi$
$863$	−16.9706	+	16.9706i	−0.577685	+	0.577685i	0.356580	+	0.934265i	$0.383943\pi$
$864$	1.41421	−	5.00000i	0.0481125	−	0.170103i
$865$	20.0000	−	40.0000i	0.680020	−	1.36004i
$866$		−	2.82843i		−	0.0961139i
$867$	22.1924	−	3.80761i	0.753693	−	0.129313i
$868$		0			0
$869$	−2.82843			−0.0959478
$870$	3.17157	−	10.4853i	0.107526	−	0.355484i
$871$	42.0000			1.42312
$872$	7.07107	+	7.07107i	0.239457	+	0.239457i
$873$	−20.1127	+	42.1127i	−0.680712	+	1.42530i
$874$		−	16.0000i		−	0.541208i
$875$		0			0
$876$	4.00000	+	2.82843i	0.135147	+	0.0955637i
$877$	30.0000	−	30.0000i	1.01303	−	1.01303i	0.0131140	−	0.999914i	$-0.495826\pi$
$877$	30.0000	−	30.0000i	1.01303	−	1.01303i	0.999914	−	0.0131140i	$-0.00417444\pi$
$878$		0			0
$879$	33.9411	+	24.0000i	1.14481	+	0.809500i
$880$	1.00000	+	3.00000i	0.0337100	+	0.101130i
$881$		−	24.0416i		−	0.809983i	−0.914320	−	0.404992i	$-0.867274\pi$
$881$		−	24.0416i		−	0.809983i	0.914320	−	0.404992i	$-0.132726\pi$
$882$	−9.05025	+	18.9497i	−0.304738	+	0.638071i
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$	−8.48528			−0.285391
$885$		0			0
$886$	24.0000			0.806296
$887$	−1.41421	−	1.41421i	−0.0474846	−	0.0474846i	0.682966	−	0.730450i	$-0.260690\pi$
$887$	−1.41421	−	1.41421i	−0.0474846	−	0.0474846i	−0.730450	+	0.682966i	$0.760690\pi$
$888$	−7.24264	+	1.24264i	−0.243047	+	0.0417003i
$889$		0			0
$890$	14.1421	+	7.07107i	0.474045	+	0.237023i
$891$	−8.00000	−	9.89949i	−0.268010	−	0.331646i
$892$	11.0000	−	11.0000i	0.368307	−	0.368307i
$893$	5.65685	−	5.65685i	0.189299	−	0.189299i
$894$	1.41421	−	2.00000i	0.0472984	−	0.0668900i
$895$	−27.0000	+	9.00000i	−0.902510	+	0.300837i
$896$		0			0
$897$	4.97056	+	28.9706i	0.165962	+	0.967299i
$898$	7.00000	+	7.00000i	0.233593	+	0.233593i
$899$	2.82843			0.0943333
$900$	−12.4853	−	8.31371i	−0.416176	−	0.277124i
$901$	−4.00000			−0.133259
$902$	−5.65685	−	5.65685i	−0.188353	−	0.188353i
$903$		0			0
$904$			6.00000i			0.199557i
$905$	−21.2132	+	7.07107i	−0.705151	+	0.235050i
$906$	−8.00000	+	11.3137i	−0.265782	+	0.375873i
$907$	25.0000	−	25.0000i	0.830111	−	0.830111i	−0.157420	−	0.987532i	$-0.550318\pi$
$907$	25.0000	−	25.0000i	0.830111	−	0.830111i	0.987532	+	0.157420i	$0.0503177\pi$
$908$	11.3137	−	11.3137i	0.375459	−	0.375459i
$909$	−15.5563	−	44.0000i	−0.515972	−	1.45939i
$910$		0			0
$911$		−	11.3137i		−	0.374840i	−0.982280	−	0.187420i	$-0.939987\pi$
$911$		−	11.3137i		−	0.374840i	0.982280	−	0.187420i	$-0.0600125\pi$
$912$	6.82843	−	1.17157i	0.226112	−	0.0387947i
$913$	6.00000	+	6.00000i	0.198571	+	0.198571i
$914$		0			0
$915$	14.6274	+	27.3137i	0.483567	+	0.902963i
$916$	26.0000			0.859064
$917$		0			0
$918$	−9.07107	+	5.07107i	−0.299390	+	0.167370i
$919$		−	4.00000i		−	0.131948i	−0.997821	−	0.0659739i	$-0.978985\pi$
$919$		−	4.00000i		−	0.131948i	0.997821	−	0.0659739i	$-0.0210154\pi$
$920$	−2.82843	−	8.48528i	−0.0932505	−	0.279751i
$921$	10.0000	+	7.07107i	0.329511	+	0.233000i
$922$	2.00000	−	2.00000i	0.0658665	−	0.0658665i
$923$	−38.1838	+	38.1838i	−1.25683	+	1.25683i
$924$		0			0
$925$	−3.00000	+	21.0000i	−0.0986394	+	0.690476i
$926$			9.89949i			0.325318i
$927$	22.9706	+	10.9706i	0.754452	+	0.360321i
$928$	2.00000	+	2.00000i	0.0656532	+	0.0656532i
$929$	−1.41421			−0.0463988			−0.0231994	−	0.999731i	$-0.507385\pi$
$929$	−1.41421			−0.0463988			−0.0231994	+	0.999731i	$0.507385\pi$
$930$	1.12132	−	3.70711i	0.0367695	−	0.121561i
$931$	−28.0000			−0.917663
$932$	9.89949	+	9.89949i	0.324269	+	0.324269i
$933$	−2.41421	+	0.414214i	−0.0790378	+	0.0135607i
$934$		−	4.00000i		−	0.130884i
$935$	2.82843	−	5.65685i	0.0924995	−	0.184999i
$936$	−12.0000	+	4.24264i	−0.392232	+	0.138675i
$937$	13.0000	−	13.0000i	0.424691	−	0.424691i	−0.462124	−	0.886815i	$-0.652912\pi$
$937$	13.0000	−	13.0000i	0.424691	−	0.424691i	0.886815	+	0.462124i	$0.152912\pi$
$938$		0			0
$939$	14.1421	−	20.0000i	0.461511	−	0.652675i
$940$	2.00000	−	4.00000i	0.0652328	−	0.130466i
$941$			16.9706i			0.553225i	0.960982	+	0.276612i	$0.0892118\pi$
$941$			16.9706i			0.553225i	−0.960982	+	0.276612i	$0.910788\pi$
$942$	1.65685	+	9.65685i	0.0539832	+	0.314637i
$943$	16.0000	+	16.0000i	0.521032	+	0.521032i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25.4558	−	25.4558i	−0.827204	−	0.827204i	0.159925	−	0.987129i	$-0.448875\pi$
$947$	−25.4558	−	25.4558i	−0.827204	−	0.827204i	−0.987129	+	0.159925i	$0.948875\pi$
$948$	0.585786	+	3.41421i	0.0190255	+	0.110889i
$949$		−	12.0000i		−	0.389536i
$950$	2.82843	−	19.7990i	0.0917663	−	0.642364i
$951$	6.00000	−	8.48528i	0.194563	−	0.275154i
$952$		0			0
$953$	25.4558	−	25.4558i	0.824596	−	0.824596i	−0.162168	−	0.986763i	$-0.551849\pi$
$953$	25.4558	−	25.4558i	0.824596	−	0.824596i	0.986763	+	0.162168i	$0.0518485\pi$
$954$	−5.65685	+	2.00000i	−0.183147	+	0.0647524i
$955$	−15.0000	−	45.0000i	−0.485389	−	1.45617i
$956$		−	22.6274i		−	0.731823i
$957$	6.82843	−	1.17157i	0.220732	−	0.0378716i
$958$	−27.0000	−	27.0000i	−0.872330	−	0.872330i
$959$		0			0
$960$	3.41421	−	1.82843i	0.110193	−	0.0590122i
$961$	1.00000			0.0322581
$962$	12.7279	+	12.7279i	0.410365	+	0.410365i
$963$	32.4853	+	15.5147i	1.04682	+	0.499955i
$964$		−	2.00000i		−	0.0644157i
$965$	−25.4558	−	12.7279i	−0.819453	−	0.409726i
$966$		0			0
$967$	31.0000	−	31.0000i	0.996893	−	0.996893i	−0.00310239	−	0.999995i	$-0.500988\pi$
$967$	31.0000	−	31.0000i	0.996893	−	0.996893i	0.999995	+	0.00310239i	$0.000987524\pi$
$968$	6.36396	−	6.36396i	0.204545	−	0.204545i
$969$	−11.3137	−	8.00000i	−0.363449	−	0.256997i
$970$	−33.0000	+	11.0000i	−1.05957	+	0.353189i
$971$			39.5980i			1.27076i	0.772200	+	0.635380i	$0.219156\pi$
$971$			39.5980i			1.27076i	−0.772200	+	0.635380i	$0.780844\pi$
$972$	−10.2929	+	11.7071i	−0.330145	+	0.375506i
$973$		0			0
$974$	15.5563			0.498458
$975$	1.02944	+	36.7279i	0.0329684	+	1.17623i
$976$	−8.00000			−0.256074
$977$	21.2132	+	21.2132i	0.678671	+	0.678671i	0.959699	−	0.281029i	$-0.0906757\pi$
$977$	21.2132	+	21.2132i	0.678671	+	0.678671i	−0.281029	+	0.959699i	$0.590676\pi$
$978$	−26.5563	+	4.55635i	−0.849178	+	0.145696i
$979$			10.0000i			0.319601i
$980$	−14.8492	+	4.94975i	−0.474342	+	0.158114i
$981$	−10.0000	−	28.2843i	−0.319275	−	0.903047i
$982$	−9.00000	+	9.00000i	−0.287202	+	0.287202i
$983$	16.9706	−	16.9706i	0.541277	−	0.541277i	−0.382626	−	0.923903i	$-0.624980\pi$
$983$	16.9706	−	16.9706i	0.541277	−	0.541277i	0.923903	+	0.382626i	$0.124980\pi$
$984$	−5.65685	+	8.00000i	−0.180334	+	0.255031i
$985$	−20.0000	−	10.0000i	−0.637253	−	0.318626i
$986$		−	5.65685i		−	0.180151i
$987$		0			0
$988$	−12.0000	−	12.0000i	−0.381771	−	0.381771i
$989$		0			0
$990$	1.17157	−	9.41421i	0.0372350	−	0.299203i
$991$	−22.0000			−0.698853			−0.349427	−	0.936964i	$-0.613624\pi$
$991$	−22.0000			−0.698853			−0.349427	+	0.936964i	$0.613624\pi$
$992$	0.707107	+	0.707107i	0.0224507	+	0.0224507i
$993$	9.37258	+	54.6274i	0.297430	+	1.73355i
$994$		0			0
$995$	16.9706	+	50.9117i	0.538003	+	1.61401i
$996$	6.00000	−	8.48528i	0.190117	−	0.268866i
$997$	24.0000	−	24.0000i	0.760088	−	0.760088i	−0.216250	−	0.976338i	$-0.569383\pi$
$997$	24.0000	−	24.0000i	0.760088	−	0.760088i	0.976338	+	0.216250i	$0.0693827\pi$
$998$	25.4558	−	25.4558i	0.805791	−	0.805791i
$999$	21.2132	+	6.00000i	0.671156	+	0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.b.683.1	yes	4
3.2	odd	2	inner	930.2.j.b.683.2	yes	4
5.2	odd	4	inner	930.2.j.b.497.2	yes	4
15.2	even	4	inner	930.2.j.b.497.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.b.497.1	✓	4	15.2	even	4	inner
930.2.j.b.497.2	yes	4	5.2	odd	4	inner
930.2.j.b.683.1	yes	4	1.1	even	1	trivial
930.2.j.b.683.2	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} +1.00000i q^{4} +(2.12132 - 0.707107i) q^{5} +(1.00000 - 1.41421i) q^{6} +(0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(-2.00000 - 1.00000i) q^{10} -1.41421i q^{11} +(-1.70711 + 0.292893i) q^{12} +(3.00000 + 3.00000i) q^{13} +(1.82843 + 3.41421i) q^{15} -1.00000 q^{16} +(1.41421 + 1.41421i) q^{17} +(2.70711 + 1.29289i) q^{18} +4.00000i q^{19} +(0.707107 + 2.12132i) q^{20} +(-1.00000 + 1.00000i) q^{22} +(2.82843 - 2.82843i) q^{23} +(1.41421 + 1.00000i) q^{24} +(4.00000 - 3.00000i) q^{25} -4.24264i q^{26} +(-2.53553 - 4.53553i) q^{27} +2.82843 q^{29} +(1.12132 - 3.70711i) q^{30} +1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(2.41421 - 0.414214i) q^{33} -2.00000i q^{34} +(-1.00000 - 2.82843i) q^{36} +(-3.00000 + 3.00000i) q^{37} +(2.82843 - 2.82843i) q^{38} +(-4.24264 + 6.00000i) q^{39} +(1.00000 - 2.00000i) q^{40} +5.65685i q^{41} +1.41421 q^{44} +(-5.29289 + 4.12132i) q^{45} -4.00000 q^{46} +(-1.41421 - 1.41421i) q^{47} +(-0.292893 - 1.70711i) q^{48} +7.00000i q^{49} +(-4.94975 - 0.707107i) q^{50} +(-2.00000 + 2.82843i) q^{51} +(-3.00000 + 3.00000i) q^{52} +(-1.41421 + 1.41421i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(-1.00000 - 3.00000i) q^{55} +(-6.82843 + 1.17157i) q^{57} +(-2.00000 - 2.00000i) q^{58} +(-3.41421 + 1.82843i) q^{60} +8.00000 q^{61} +(-0.707107 - 0.707107i) q^{62} -1.00000i q^{64} +(8.48528 + 4.24264i) q^{65} +(-2.00000 - 1.41421i) q^{66} +(7.00000 - 7.00000i) q^{67} +(-1.41421 + 1.41421i) q^{68} +(5.65685 + 4.00000i) q^{69} +12.7279i q^{71} +(-1.29289 + 2.70711i) q^{72} +(-2.00000 - 2.00000i) q^{73} +4.24264 q^{74} +(6.29289 + 5.94975i) q^{75} -4.00000 q^{76} +(7.24264 - 1.24264i) q^{78} -2.00000i q^{79} +(-2.12132 + 0.707107i) q^{80} +(7.00000 - 5.65685i) q^{81} +(4.00000 - 4.00000i) q^{82} +(-4.24264 + 4.24264i) q^{83} +(4.00000 + 2.00000i) q^{85} +(0.828427 + 4.82843i) q^{87} +(-1.00000 - 1.00000i) q^{88} -7.07107 q^{89} +(6.65685 + 0.828427i) q^{90} +(2.82843 + 2.82843i) q^{92} +(0.292893 + 1.70711i) q^{93} +2.00000i q^{94} +(2.82843 + 8.48528i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(11.0000 - 11.0000i) q^{97} +(4.94975 - 4.94975i) q^{98} +(1.41421 + 4.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 4 q^{6} - 8 q^{10} - 4 q^{12} + 12 q^{13} - 4 q^{15} - 4 q^{16} + 8 q^{18} - 4 q^{22} + 16 q^{25} + 4 q^{27} - 4 q^{30} + 4 q^{31} + 4 q^{33} - 4 q^{36} - 12 q^{37} + 4 q^{40} - 24 q^{45}+ \cdots + 44 q^{97}+O(q^{100}) \) 4 * q + 4 * q^3 + 4 * q^6 - 8 * q^10 - 4 * q^12 + 12 * q^13 - 4 * q^15 - 4 * q^16 + 8 * q^18 - 4 * q^22 + 16 * q^25 + 4 * q^27 - 4 * q^30 + 4 * q^31 + 4 * q^33 - 4 * q^36 - 12 * q^37 + 4 * q^40 - 24 * q^45 - 16 * q^46 - 4 * q^48 - 8 * q^51 - 12 * q^52 - 4 * q^55 - 16 * q^57 - 8 * q^58 - 8 * q^60 + 32 * q^61 - 8 * q^66 + 28 * q^67 - 8 * q^72 - 8 * q^73 + 28 * q^75 - 16 * q^76 + 12 * q^78 + 28 * q^81 + 16 * q^82 + 16 * q^85 - 8 * q^87 - 4 * q^88 + 4 * q^90 + 4 * q^93 - 4 * q^96 + 44 * q^97

Introduction

L-functions

Modular forms

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