LMFDB - Embedded newform 930.2.j.a.683.2

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			683.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	930.683
Dual form			930.2.j.a.497.2

$q$-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} +4.24264i 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} +(-3.00000 + 3.00000i) q^{22} +(-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} +(-7.24264 + 1.24264i) q^{33} +2.00000i q^{34} +(-1.00000 - 2.82843i) q^{36} +(-5.00000 + 5.00000i) q^{37} +(2.82843 - 2.82843i) q^{38} +(4.24264 - 6.00000i) q^{39} +(1.00000 - 2.00000i) q^{40} +(8.00000 + 8.00000i) q^{43} -4.24264 q^{44} +(5.29289 - 4.12132i) q^{45} +(-4.24264 - 4.24264i) 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} +(-4.24264 + 4.24264i) q^{53} +(1.41421 - 5.00000i) q^{54} +(-3.00000 - 9.00000i) q^{55} +(6.82843 - 1.17157i) q^{57} +(-2.00000 - 2.00000i) q^{58} -5.65685 q^{59} +(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} +(-6.00000 - 4.24264i) q^{66} +(-1.00000 + 1.00000i) q^{67} +(-1.41421 + 1.41421i) q^{68} -1.41421i q^{71} +(1.29289 - 2.70711i) q^{72} +(2.00000 + 2.00000i) q^{73} -7.07107 q^{74} +(6.29289 + 5.94975i) q^{75} +4.00000 q^{76} +(7.24264 - 1.24264i) q^{78} +10.0000i q^{79} +(2.12132 - 0.707107i) q^{80} +(7.00000 - 5.65685i) q^{81} +(12.7279 - 12.7279i) q^{83} +(-4.00000 - 2.00000i) q^{85} +11.3137i q^{86} +(-0.828427 - 4.82843i) q^{87} +(-3.00000 - 3.00000i) q^{88} -7.07107 q^{89} +(6.65685 + 0.828427i) q^{90} +(-0.292893 - 1.70711i) q^{93} -6.00000i q^{94} +(2.82843 + 8.48528i) q^{95} +(1.00000 - 1.41421i) q^{96} +(3.00000 - 3.00000i) q^{97} +(-4.94975 + 4.94975i) q^{98} +(-4.24264 - 12.0000i) 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} - 12 q^{22} + 16 q^{25} + 4 q^{27} - 4 q^{30} - 4 q^{31} - 12 q^{33} - 4 q^{36} - 20 q^{37} + 4 q^{40} + 32 q^{43}+ \cdots + 12 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 - 12 * q^22 + 16 * q^25 + 4 * q^27 - 4 * q^30 - 4 * q^31 - 12 * q^33 - 4 * q^36 - 20 * q^37 + 4 * q^40 + 32 * q^43 + 24 * q^45 - 4 * q^48 - 8 * q^51 + 12 * q^52 - 12 * q^55 + 16 * q^57 - 8 * q^58 + 8 * q^60 - 32 * q^61 - 24 * q^66 - 4 * q^67 + 8 * q^72 + 8 * q^73 + 28 * q^75 + 16 * q^76 + 12 * q^78 + 28 * q^81 - 16 * q^85 + 8 * q^87 - 12 * q^88 + 4 * q^90 - 4 * q^93 + 4 * q^96 + 12 * 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
$11$			4.24264i			1.27920i	0.768706	+	0.639602i	$0.220901\pi$
$11$			4.24264i			1.27920i	−0.768706	+	0.639602i	$0.779099\pi$
$12$	−1.70711	+	0.292893i	−0.492799	+	0.0845510i
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	0.155747	−	0.987797i	$-0.450222\pi$
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	−0.987797	+	0.155747i	$0.950222\pi$
$14$		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	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	−0.707107	−	2.12132i	−0.158114	−	0.474342i
$21$		0			0
$22$	−3.00000	+	3.00000i	−0.639602	+	0.639602i
$23$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$	−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	$-0.584584\pi$
$29$	−2.82843			−0.525226			−0.262613	+	0.964901i	$0.584584\pi$
$30$	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
$33$	−7.24264	+	1.24264i	−1.26078	+	0.216316i
$34$			2.00000i			0.342997i
$35$		0			0
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	−5.00000	+	5.00000i	−0.821995	+	0.821995i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−5.00000	+	5.00000i	−0.821995	+	0.821995i	0.164399	+	0.986394i	$0.447432\pi$
$38$	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
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	8.00000	+	8.00000i	1.21999	+	1.21999i	0.967635	+	0.252353i	$0.0812046\pi$
$43$	8.00000	+	8.00000i	1.21999	+	1.21999i	0.252353	+	0.967635i	$0.418795\pi$
$44$	−4.24264			−0.639602
$45$	5.29289	−	4.12132i	0.789018	−	0.614370i
$46$		0			0
$47$	−4.24264	−	4.24264i	−0.618853	−	0.618853i	0.326384	−	0.945237i	$-0.394170\pi$
$47$	−4.24264	−	4.24264i	−0.618853	−	0.618853i	−0.945237	+	0.326384i	$0.894170\pi$
$48$	−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
$53$	−4.24264	+	4.24264i	−0.582772	+	0.582772i	−0.935664	−	0.352892i	$-0.885198\pi$
$53$	−4.24264	+	4.24264i	−0.582772	+	0.582772i	0.352892	+	0.935664i	$0.385198\pi$
$54$	1.41421	−	5.00000i	0.192450	−	0.680414i
$55$	−3.00000	−	9.00000i	−0.404520	−	1.21356i
$56$		0			0
$57$	6.82843	−	1.17157i	0.904447	−	0.155179i
$58$	−2.00000	−	2.00000i	−0.262613	−	0.262613i
$59$	−5.65685			−0.736460			−0.368230	−	0.929735i	$-0.620036\pi$
$59$	−5.65685			−0.736460			−0.368230	+	0.929735i	$0.620036\pi$
$60$	3.41421	−	1.82843i	0.440773	−	0.236049i
$61$	−8.00000			−1.02430			−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000			−1.02430			−0.512148	+	0.858898i	$0.671150\pi$
$62$	−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
$66$	−6.00000	−	4.24264i	−0.738549	−	0.522233i
$67$	−1.00000	+	1.00000i	−0.122169	+	0.122169i	−0.765548	−	0.643379i	$-0.777532\pi$
$67$	−1.00000	+	1.00000i	−0.122169	+	0.122169i	0.643379	+	0.765548i	$0.277532\pi$
$68$	−1.41421	+	1.41421i	−0.171499	+	0.171499i
$69$		0			0
$70$		0			0
$71$		−	1.41421i		−	0.167836i	−0.996473	−	0.0839181i	$-0.973257\pi$
$71$		−	1.41421i		−	0.167836i	0.996473	−	0.0839181i	$-0.0267434\pi$
$72$	1.29289	−	2.70711i	0.152369	−	0.319036i
$73$	2.00000	+	2.00000i	0.234082	+	0.234082i	0.814394	−	0.580312i	$-0.197069\pi$
$73$	2.00000	+	2.00000i	0.234082	+	0.234082i	−0.580312	+	0.814394i	$0.697069\pi$
$74$	−7.07107			−0.821995
$75$	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
$79$			10.0000i			1.12509i	0.826767	+	0.562544i	$0.190177\pi$
$79$			10.0000i			1.12509i	−0.826767	+	0.562544i	$0.809823\pi$
$80$	2.12132	−	0.707107i	0.237171	−	0.0790569i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$		0			0
$83$	12.7279	−	12.7279i	1.39707	−	1.39707i	0.588771	−	0.808300i	$-0.299612\pi$
$83$	12.7279	−	12.7279i	1.39707	−	1.39707i	0.808300	−	0.588771i	$-0.200388\pi$
$84$		0			0
$85$	−4.00000	−	2.00000i	−0.433861	−	0.216930i
$86$			11.3137i			1.21999i
$87$	−0.828427	−	4.82843i	−0.0888167	−	0.517662i
$88$	−3.00000	−	3.00000i	−0.319801	−	0.319801i
$89$	−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
$92$		0			0
$93$	−0.292893	−	1.70711i	−0.0303716	−	0.177019i
$94$		−	6.00000i		−	0.618853i
$95$	2.82843	+	8.48528i	0.290191	+	0.870572i
$96$	1.00000	−	1.41421i	0.102062	−	0.144338i
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	−0.538208	−	0.842812i	$-0.680899\pi$
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	0.842812	+	0.538208i	$0.180899\pi$
$98$	−4.94975	+	4.94975i	−0.500000	+	0.500000i
$99$	−4.24264	−	12.0000i	−0.426401	−	1.20605i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$			18.3848i			1.82935i	0.404186	+	0.914677i	$0.367555\pi$
$101$			18.3848i			1.82935i	−0.404186	+	0.914677i	$0.632445\pi$
$102$	−3.41421	+	0.585786i	−0.338058	+	0.0580015i
$103$	10.0000	+	10.0000i	0.985329	+	0.985329i	0.999894	−	0.0145647i	$-0.00463624\pi$
$103$	10.0000	+	10.0000i	0.985329	+	0.985329i	−0.0145647	+	0.999894i	$0.504636\pi$
$104$	4.24264			0.416025
$105$		0			0
$106$	−6.00000			−0.582772
$107$	2.82843	+	2.82843i	0.273434	+	0.273434i	0.830481	−	0.557047i	$-0.188066\pi$
$107$	2.82843	+	2.82843i	0.273434	+	0.273434i	−0.557047	+	0.830481i	$0.688066\pi$
$108$	4.53553	−	2.53553i	0.436432	−	0.243982i
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$	4.24264	−	8.48528i	0.404520	−	0.809040i
$111$	−10.0000	−	7.07107i	−0.949158	−	0.671156i
$112$		0			0
$113$	4.24264	−	4.24264i	0.399114	−	0.399114i	−0.478806	−	0.877920i	$-0.658930\pi$
$113$	4.24264	−	4.24264i	0.399114	−	0.399114i	0.877920	+	0.478806i	$0.158930\pi$
$114$	5.65685	+	4.00000i	0.529813	+	0.374634i
$115$		0			0
$116$		−	2.82843i		−	0.262613i
$117$	11.4853	+	5.48528i	1.06181	+	0.507114i
$118$	−4.00000	−	4.00000i	−0.368230	−	0.368230i
$119$		0			0
$120$	3.70711	+	1.12132i	0.338411	+	0.102362i
$121$	−7.00000			−0.636364
$122$	−5.65685	−	5.65685i	−0.512148	−	0.512148i
$123$		0			0
$124$		−	1.00000i		−	0.0898027i
$125$	−6.36396	+	9.19239i	−0.569210	+	0.822192i
$126$		0			0
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	−0.982878	−	0.184257i	$-0.941012\pi$
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	0.184257	+	0.982878i	$0.441012\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−11.3137	+	16.0000i	−0.996116	+	1.40872i
$130$	3.00000	+	9.00000i	0.263117	+	0.789352i
$131$			19.7990i			1.72985i	0.501905	+	0.864923i	$0.332633\pi$
$131$			19.7990i			1.72985i	−0.501905	+	0.864923i	$0.667367\pi$
$132$	−1.24264	−	7.24264i	−0.108158	−	0.630391i
$133$		0			0
$134$	−1.41421			−0.122169
$135$	8.58579	+	7.82843i	0.738947	+	0.673764i
$136$	−2.00000			−0.171499
$137$	12.7279	+	12.7279i	1.08742	+	1.08742i	0.995793	+	0.0916263i	$0.0292065\pi$
$137$	12.7279	+	12.7279i	1.08742	+	1.08742i	0.0916263	+	0.995793i	$0.470793\pi$
$138$		0			0
$139$			8.00000i			0.678551i	0.940687	+	0.339276i	$0.110182\pi$
$139$			8.00000i			0.678551i	−0.940687	+	0.339276i	$0.889818\pi$
$140$		0			0
$141$	6.00000	−	8.48528i	0.505291	−	0.714590i
$142$	1.00000	−	1.00000i	0.0839181	−	0.0839181i
$143$	12.7279	−	12.7279i	1.06436	−	1.06436i
$144$	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
$148$	−5.00000	−	5.00000i	−0.410997	−	0.410997i
$149$	−1.41421			−0.115857			−0.0579284	−	0.998321i	$-0.518450\pi$
$149$	−1.41421			−0.115857			−0.0579284	+	0.998321i	$0.518450\pi$
$150$	0.242641	+	8.65685i	0.0198115	+	0.706829i
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	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	$0.322478\pi$
$158$	−7.07107	+	7.07107i	−0.562544	+	0.562544i
$159$	−8.48528	−	6.00000i	−0.672927	−	0.475831i
$160$	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	$0.958523\pi$
$164$		0			0
$165$	14.4853	−	7.75736i	1.12768	−	0.603910i
$166$	18.0000			1.39707
$167$	−8.48528	−	8.48528i	−0.656611	−	0.656611i	0.297966	−	0.954577i	$-0.403692\pi$
$167$	−8.48528	−	8.48528i	−0.656611	−	0.656611i	−0.954577	+	0.297966i	$0.903692\pi$
$168$		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
$172$	−8.00000	+	8.00000i	−0.609994	+	0.609994i
$173$	8.48528	−	8.48528i	0.645124	−	0.645124i	−0.306687	−	0.951811i	$-0.599220\pi$
$173$	8.48528	−	8.48528i	0.645124	−	0.645124i	0.951811	+	0.306687i	$0.0992203\pi$
$174$	2.82843	−	4.00000i	0.214423	−	0.303239i
$175$		0			0
$176$		−	4.24264i		−	0.319801i
$177$	−1.65685	−	9.65685i	−0.124537	−	0.725854i
$178$	−5.00000	−	5.00000i	−0.374766	−	0.374766i
$179$	−18.3848			−1.37414			−0.687071	−	0.726590i	$-0.741104\pi$
$179$	−18.3848			−1.37414			−0.687071	+	0.726590i	$0.741104\pi$
$180$	4.12132	+	5.29289i	0.307185	+	0.394509i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	−2.34315	−	13.6569i	−0.173210	−	1.00954i
$184$		0			0
$185$	7.07107	−	14.1421i	0.519875	−	1.03975i
$186$	1.00000	−	1.41421i	0.0733236	−	0.103695i
$187$	−6.00000	+	6.00000i	−0.438763	+	0.438763i
$188$	4.24264	−	4.24264i	0.309426	−	0.309426i
$189$		0			0
$190$	−4.00000	+	8.00000i	−0.290191	+	0.580381i
$191$		−	1.41421i		−	0.102329i	−0.998690	−	0.0511645i	$-0.983707\pi$
$191$		−	1.41421i		−	0.102329i	0.998690	−	0.0511645i	$-0.0162933\pi$
$192$	1.70711	−	0.292893i	0.123200	−	0.0211377i
$193$	15.0000	+	15.0000i	1.07972	+	1.07972i	0.996534	+	0.0831899i	$0.0265108\pi$
$193$	15.0000	+	15.0000i	1.07972	+	1.07972i	0.0831899	+	0.996534i	$0.473489\pi$
$194$	4.24264			0.304604
$195$	−4.75736	+	15.7279i	−0.340682	+	1.12630i
$196$	−7.00000			−0.500000
$197$	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	$0.727302\pi$
$198$	5.48528	−	11.4853i	0.389822	−	0.816223i
$199$			16.0000i			1.13421i	0.823646	+	0.567105i	$0.191937\pi$
$199$			16.0000i			1.13421i	−0.823646	+	0.567105i	$0.808063\pi$
$200$	−0.707107	+	4.94975i	−0.0500000	+	0.350000i
$201$	−2.00000	−	1.41421i	−0.141069	−	0.0997509i
$202$	−13.0000	+	13.0000i	−0.914677	+	0.914677i
$203$		0			0
$204$	−2.82843	−	2.00000i	−0.198030	−	0.140028i
$205$		0			0
$206$			14.1421i			0.985329i
$207$		0			0
$208$	3.00000	+	3.00000i	0.208013	+	0.208013i
$209$	16.9706			1.17388
$210$		0			0
$211$	−6.00000			−0.413057			−0.206529	−	0.978441i	$-0.566217\pi$
$211$	−6.00000			−0.413057			−0.206529	+	0.978441i	$0.566217\pi$
$212$	−4.24264	−	4.24264i	−0.291386	−	0.291386i
$213$	2.41421	−	0.414214i	0.165419	−	0.0283814i
$214$			4.00000i			0.273434i
$215$	−22.6274	−	11.3137i	−1.54318	−	0.771589i
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$		0			0
$218$	4.24264	−	4.24264i	0.287348	−	0.287348i
$219$	−2.82843	+	4.00000i	−0.191127	+	0.270295i
$220$	9.00000	−	3.00000i	0.606780	−	0.202260i
$221$		−	8.48528i		−	0.570782i
$222$	−2.07107	−	12.0711i	−0.139001	−	0.810157i
$223$	−1.00000	−	1.00000i	−0.0669650	−	0.0669650i	0.672831	−	0.739796i	$-0.265078\pi$
$223$	−1.00000	−	1.00000i	−0.0669650	−	0.0669650i	−0.739796	+	0.672831i	$0.765078\pi$
$224$		0			0
$225$	−8.31371	+	12.4853i	−0.554247	+	0.832352i
$226$	6.00000			0.399114
$227$	5.65685	+	5.65685i	0.375459	+	0.375459i	0.869461	−	0.494002i	$-0.164466\pi$
$227$	5.65685	+	5.65685i	0.375459	+	0.375459i	−0.494002	+	0.869461i	$0.664466\pi$
$228$	1.17157	+	6.82843i	0.0775893	+	0.452224i
$229$			10.0000i			0.660819i	0.943838	+	0.330409i	$0.107187\pi$
$229$			10.0000i			0.660819i	−0.943838	+	0.330409i	$0.892813\pi$
$230$		0			0
$231$		0			0
$232$	2.00000	−	2.00000i	0.131306	−	0.131306i
$233$	12.7279	−	12.7279i	0.833834	−	0.833834i	−0.154205	−	0.988039i	$-0.549282\pi$
$233$	12.7279	−	12.7279i	0.833834	−	0.833834i	0.988039	+	0.154205i	$0.0492816\pi$
$234$	4.24264	+	12.0000i	0.277350	+	0.784465i
$235$	12.0000	+	6.00000i	0.782794	+	0.391397i
$236$		−	5.65685i		−	0.368230i
$237$	−17.0711	+	2.92893i	−1.10889	+	0.190255i
$238$		0			0
$239$	−11.3137			−0.731823			−0.365911	−	0.930650i	$-0.619243\pi$
$239$	−11.3137			−0.731823			−0.365911	+	0.930650i	$0.619243\pi$
$240$	1.82843	+	3.41421i	0.118024	+	0.220387i
$241$	22.0000			1.41714			0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000			1.41714			0.708572	+	0.705638i	$0.249340\pi$
$242$	−4.94975	−	4.94975i	−0.318182	−	0.318182i
$243$	11.7071	+	10.2929i	0.751011	+	0.660289i
$244$		−	8.00000i		−	0.512148i
$245$	−4.94975	−	14.8492i	−0.316228	−	0.948683i
$246$		0			0
$247$	−12.0000	+	12.0000i	−0.763542	+	0.763542i
$248$	0.707107	−	0.707107i	0.0449013	−	0.0449013i
$249$	25.4558	+	18.0000i	1.61320	+	1.14070i
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$		−	21.2132i		−	1.33897i	−0.742828	−	0.669483i	$-0.766516\pi$
$251$		−	21.2132i		−	1.33897i	0.742828	−	0.669483i	$-0.233484\pi$
$252$		0			0
$253$		0			0
$254$	−12.7279			−0.798621
$255$	2.24264	−	7.41421i	0.140440	−	0.464296i
$256$	1.00000			0.0625000
$257$	−4.24264	−	4.24264i	−0.264649	−	0.264649i	0.562291	−	0.826940i	$-0.309920\pi$
$257$	−4.24264	−	4.24264i	−0.264649	−	0.264649i	−0.826940	+	0.562291i	$0.809920\pi$
$258$	−19.3137	+	3.31371i	−1.20242	+	0.206302i
$259$		0			0
$260$	−4.24264	+	8.48528i	−0.263117	+	0.526235i
$261$	8.00000	−	2.82843i	0.495188	−	0.175075i
$262$	−14.0000	+	14.0000i	−0.864923	+	0.864923i
$263$	19.7990	−	19.7990i	1.22086	−	1.22086i	0.253531	−	0.967327i	$-0.418408\pi$
$263$	19.7990	−	19.7990i	1.22086	−	1.22086i	0.967327	−	0.253531i	$-0.0815919\pi$
$264$	4.24264	−	6.00000i	0.261116	−	0.369274i
$265$	6.00000	−	12.0000i	0.368577	−	0.737154i
$266$		0			0
$267$	−2.07107	−	12.0711i	−0.126747	−	0.738737i
$268$	−1.00000	−	1.00000i	−0.0610847	−	0.0610847i
$269$	−2.82843			−0.172452			−0.0862261	−	0.996276i	$-0.527481\pi$
$269$	−2.82843			−0.172452			−0.0862261	+	0.996276i	$0.527481\pi$
$270$	0.535534	+	11.6066i	0.0325916	+	0.706355i
$271$	22.0000			1.33640			0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000			1.33640			0.668202	+	0.743980i	$0.267064\pi$
$272$	−1.41421	−	1.41421i	−0.0857493	−	0.0857493i
$273$		0			0
$274$			18.0000i			1.08742i
$275$	12.7279	+	16.9706i	0.767523	+	1.02336i
$276$		0			0
$277$	−21.0000	+	21.0000i	−1.26177	+	1.26177i	−0.311532	+	0.950236i	$0.600842\pi$
$277$	−21.0000	+	21.0000i	−1.26177	+	1.26177i	−0.950236	+	0.311532i	$0.899158\pi$
$278$	−5.65685	+	5.65685i	−0.339276	+	0.339276i
$279$	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	$0.764178\pi$
$282$	10.2426	−	1.75736i	0.609940	−	0.104649i
$283$	−3.00000	−	3.00000i	−0.178331	−	0.178331i	0.612297	−	0.790628i	$-0.290246\pi$
$283$	−3.00000	−	3.00000i	−0.178331	−	0.178331i	−0.790628	+	0.612297i	$0.790246\pi$
$284$	1.41421			0.0839181
$285$	−13.6569	+	7.31371i	−0.808962	+	0.433227i
$286$	18.0000			1.06436
$287$		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
$291$	6.00000	+	4.24264i	0.351726	+	0.248708i
$292$	−2.00000	+	2.00000i	−0.117041	+	0.117041i
$293$	5.65685	−	5.65685i	0.330477	−	0.330477i	−0.522291	−	0.852768i	$-0.674922\pi$
$293$	5.65685	−	5.65685i	0.330477	−	0.330477i	0.852768	+	0.522291i	$0.174922\pi$
$294$	−9.89949	−	7.00000i	−0.577350	−	0.408248i
$295$	12.0000	−	4.00000i	0.698667	−	0.232889i
$296$		−	7.07107i		−	0.410997i
$297$	19.2426	−	10.7574i	1.11657	−	0.624205i
$298$	−1.00000	−	1.00000i	−0.0579284	−	0.0579284i
$299$		0			0
$300$	−5.94975	+	6.29289i	−0.343509	+	0.363320i
$301$		0			0
$302$	−11.3137	−	11.3137i	−0.651031	−	0.651031i
$303$	−31.3848	+	5.38478i	−1.80301	+	0.309347i
$304$			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
$309$	−14.1421	+	20.0000i	−0.804518	+	1.13776i
$310$	2.00000	+	1.00000i	0.113592	+	0.0567962i
$311$		−	12.7279i		−	0.721734i	−0.932617	−	0.360867i	$-0.882481\pi$
$311$		−	12.7279i		−	0.721734i	0.932617	−	0.360867i	$-0.117519\pi$
$312$	1.24264	+	7.24264i	0.0703507	+	0.410034i
$313$	14.0000	+	14.0000i	0.791327	+	0.791327i	0.981710	−	0.190383i	$-0.0609730\pi$
$313$	14.0000	+	14.0000i	0.791327	+	0.791327i	−0.190383	+	0.981710i	$0.560973\pi$
$314$	−5.65685			−0.319235
$315$		0			0
$316$	−10.0000			−0.562544
$317$	15.5563	+	15.5563i	0.873732	+	0.873732i	0.992877	−	0.119145i	$-0.0380154\pi$
$317$	15.5563	+	15.5563i	0.873732	+	0.873732i	−0.119145	+	0.992877i	$0.538015\pi$
$318$	−1.75736	−	10.2426i	−0.0985478	−	0.574379i
$319$		−	12.0000i		−	0.671871i
$320$	0.707107	+	2.12132i	0.0395285	+	0.118585i
$321$	−4.00000	+	5.65685i	−0.223258	+	0.315735i
$322$		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
$327$	10.2426	−	1.75736i	0.566419	−	0.0971822i
$328$		0			0
$329$		0			0
$330$	15.7279	+	4.75736i	0.865794	+	0.261884i
$331$	−28.0000			−1.53902			−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000			−1.53902			−0.769510	+	0.638635i	$0.779499\pi$
$332$	12.7279	+	12.7279i	0.698535	+	0.698535i
$333$	9.14214	−	19.1421i	0.500986	−	1.04898i
$334$		−	12.0000i		−	0.656611i
$335$	1.41421	−	2.82843i	0.0772667	−	0.154533i
$336$		0			0
$337$	24.0000	−	24.0000i	1.30736	−	1.30736i	0.384052	−	0.923312i	$-0.374528\pi$
$337$	24.0000	−	24.0000i	1.30736	−	1.30736i	0.923312	−	0.384052i	$-0.125472\pi$
$338$	−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
$341$		−	4.24264i		−	0.229752i
$342$	−5.17157	+	10.8284i	−0.279647	+	0.585534i
$343$		0			0
$344$	−11.3137			−0.609994
$345$		0			0
$346$	12.0000			0.645124
$347$	1.41421	+	1.41421i	0.0759190	+	0.0759190i	0.744047	−	0.668128i	$-0.232904\pi$
$347$	1.41421	+	1.41421i	0.0759190	+	0.0759190i	−0.668128	+	0.744047i	$0.732904\pi$
$348$	4.82843	−	0.828427i	0.258831	−	0.0444084i
$349$		−	14.0000i		−	0.749403i	−0.927146	−	0.374701i	$-0.877745\pi$
$349$		−	14.0000i		−	0.749403i	0.927146	−	0.374701i	$-0.122255\pi$
$350$		0			0
$351$	−6.00000	+	21.2132i	−0.320256	+	1.13228i
$352$	3.00000	−	3.00000i	0.159901	−	0.159901i
$353$	2.82843	−	2.82843i	0.150542	−	0.150542i	−0.627818	−	0.778360i	$-0.716052\pi$
$353$	2.82843	−	2.82843i	0.150542	−	0.150542i	0.778360	+	0.627818i	$0.216052\pi$
$354$	5.65685	−	8.00000i	0.300658	−	0.425195i
$355$	1.00000	+	3.00000i	0.0530745	+	0.159223i
$356$		−	7.07107i		−	0.374766i
$357$		0			0
$358$	−13.0000	−	13.0000i	−0.687071	−	0.687071i
$359$	−4.24264			−0.223918			−0.111959	−	0.993713i	$-0.535713\pi$
$359$	−4.24264			−0.223918			−0.111959	+	0.993713i	$0.535713\pi$
$360$	−0.828427	+	6.65685i	−0.0436619	+	0.350847i
$361$	3.00000			0.157895
$362$	7.07107	+	7.07107i	0.371647	+	0.371647i
$363$	−2.05025	−	11.9497i	−0.107610	−	0.627199i
$364$		0			0
$365$	−5.65685	−	2.82843i	−0.296093	−	0.148047i
$366$	8.00000	−	11.3137i	0.418167	−	0.591377i
$367$	3.00000	−	3.00000i	0.156599	−	0.156599i	−0.624459	−	0.781058i	$-0.714680\pi$
$367$	3.00000	−	3.00000i	0.156599	−	0.156599i	0.781058	+	0.624459i	$0.214680\pi$
$368$		0			0
$369$		0			0
$370$	15.0000	−	5.00000i	0.779813	−	0.259938i
$371$		0			0
$372$	1.70711	−	0.292893i	0.0885094	−	0.0151858i
$373$	−16.0000	−	16.0000i	−0.828449	−	0.828449i	0.158854	−	0.987302i	$-0.449220\pi$
$373$	−16.0000	−	16.0000i	−0.828449	−	0.828449i	−0.987302	+	0.158854i	$0.949220\pi$
$374$	−8.48528			−0.438763
$375$	−17.5563	−	8.17157i	−0.906606	−	0.421978i
$376$	6.00000			0.309426
$377$	8.48528	+	8.48528i	0.437014	+	0.437014i
$378$		0			0
$379$		−	6.00000i		−	0.308199i	−0.988055	−	0.154100i	$-0.950752\pi$
$379$		−	6.00000i		−	0.308199i	0.988055	−	0.154100i	$-0.0492477\pi$
$380$	−8.48528	+	2.82843i	−0.435286	+	0.145095i
$381$	−18.0000	−	12.7279i	−0.922168	−	0.652071i
$382$	1.00000	−	1.00000i	0.0511645	−	0.0511645i
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	−0.125001	−	0.992157i	$-0.539894\pi$
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	0.992157	+	0.125001i	$0.0398935\pi$
$384$	1.41421	+	1.00000i	0.0721688	+	0.0510310i
$385$		0			0
$386$			21.2132i			1.07972i
$387$	−30.6274	−	14.6274i	−1.55688	−	0.743553i
$388$	3.00000	+	3.00000i	0.152302	+	0.152302i
$389$	22.6274			1.14726			0.573628	−	0.819116i	$-0.305536\pi$
$389$	22.6274			1.14726			0.573628	+	0.819116i	$0.305536\pi$
$390$	−14.4853	+	7.75736i	−0.733491	+	0.392809i
$391$		0			0
$392$	−4.94975	−	4.94975i	−0.250000	−	0.250000i
$393$	−33.7990	+	5.79899i	−1.70493	+	0.292520i
$394$			2.00000i			0.100759i
$395$	−7.07107	−	21.2132i	−0.355784	−	1.06735i
$396$	12.0000	−	4.24264i	0.603023	−	0.213201i
$397$	12.0000	−	12.0000i	0.602263	−	0.602263i	−0.338650	−	0.940913i	$-0.609970\pi$
$397$	12.0000	−	12.0000i	0.602263	−	0.602263i	0.940913	+	0.338650i	$0.109970\pi$
$398$	−11.3137	+	11.3137i	−0.567105	+	0.567105i
$399$		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	$0.765902\pi$
$402$	−0.414214	−	2.41421i	−0.0206591	−	0.120410i
$403$	3.00000	+	3.00000i	0.149441	+	0.149441i
$404$	−18.3848			−0.914677
$405$	−10.8492	+	16.9497i	−0.539103	+	0.842240i
$406$		0			0
$407$	−21.2132	−	21.2132i	−1.05150	−	1.05150i
$408$	−0.585786	−	3.41421i	−0.0290008	−	0.169029i
$409$		−	30.0000i		−	1.48340i	−0.670729	−	0.741702i	$-0.734019\pi$
$409$		−	30.0000i		−	1.48340i	0.670729	−	0.741702i	$-0.265981\pi$
$410$		0			0
$411$	−18.0000	+	25.4558i	−0.887875	+	1.25564i
$412$	−10.0000	+	10.0000i	−0.492665	+	0.492665i
$413$		0			0
$414$		0			0
$415$	−18.0000	+	36.0000i	−0.883585	+	1.76717i
$416$			4.24264i			0.208013i
$417$	−13.6569	+	2.34315i	−0.668779	+	0.114744i
$418$	12.0000	+	12.0000i	0.586939	+	0.586939i
$419$	−22.6274			−1.10542			−0.552711	−	0.833373i	$-0.686407\pi$
$419$	−22.6274			−1.10542			−0.552711	+	0.833373i	$0.686407\pi$
$420$		0			0
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$	−4.24264	−	4.24264i	−0.206529	−	0.206529i
$423$	16.2426	+	7.75736i	0.789744	+	0.377176i
$424$		−	6.00000i		−	0.291386i
$425$	9.89949	+	1.41421i	0.480196	+	0.0685994i
$426$	2.00000	+	1.41421i	0.0969003	+	0.0685189i
$427$		0			0
$428$	−2.82843	+	2.82843i	−0.136717	+	0.136717i
$429$	25.4558	+	18.0000i	1.22902	+	0.869048i
$430$	−8.00000	−	24.0000i	−0.385794	−	1.15738i
$431$		−	12.7279i		−	0.613082i	−0.951857	−	0.306541i	$-0.900828\pi$
$431$		−	12.7279i		−	0.613082i	0.951857	−	0.306541i	$-0.0991717\pi$
$432$	2.53553	+	4.53553i	0.121991	+	0.218216i
$433$	−26.0000	−	26.0000i	−1.24948	−	1.24948i	−0.955950	−	0.293531i	$-0.905170\pi$
$433$	−26.0000	−	26.0000i	−1.24948	−	1.24948i	−0.293531	−	0.955950i	$-0.594830\pi$
$434$		0			0
$435$	5.17157	+	9.65685i	0.247958	+	0.463011i
$436$	6.00000			0.287348
$437$		0			0
$438$	−4.82843	+	0.828427i	−0.230711	+	0.0395838i
$439$		−	16.0000i		−	0.763638i	−0.924237	−	0.381819i	$-0.875298\pi$
$439$		−	16.0000i		−	0.763638i	0.924237	−	0.381819i	$-0.124702\pi$
$440$	8.48528	+	4.24264i	0.404520	+	0.202260i
$441$	−7.00000	−	19.7990i	−0.333333	−	0.942809i
$442$	6.00000	−	6.00000i	0.285391	−	0.285391i
$443$	−11.3137	+	11.3137i	−0.537531	+	0.537531i	−0.922803	−	0.385272i	$-0.874107\pi$
$443$	−11.3137	+	11.3137i	−0.537531	+	0.537531i	0.385272	+	0.922803i	$0.374107\pi$
$444$	7.07107	−	10.0000i	0.335578	−	0.474579i
$445$	15.0000	−	5.00000i	0.711068	−	0.237023i
$446$		−	1.41421i		−	0.0669650i
$447$	−0.414214	−	2.41421i	−0.0195916	−	0.114188i
$448$		0			0
$449$	24.0416			1.13459			0.567297	−	0.823513i	$-0.307989\pi$
$449$	24.0416			1.13459			0.567297	+	0.823513i	$0.307989\pi$
$450$	−14.7071	+	2.94975i	−0.693300	+	0.139052i
$451$		0			0
$452$	4.24264	+	4.24264i	0.199557	+	0.199557i
$453$	−4.68629	−	27.3137i	−0.220181	−	1.28331i
$454$			8.00000i			0.375459i
$455$		0			0
$456$	−4.00000	+	5.65685i	−0.187317	+	0.264906i
$457$	−8.00000	+	8.00000i	−0.374224	+	0.374224i	−0.869013	−	0.494789i	$-0.835245\pi$
$457$	−8.00000	+	8.00000i	−0.374224	+	0.374224i	0.494789	+	0.869013i	$0.335245\pi$
$458$	−7.07107	+	7.07107i	−0.330409	+	0.330409i
$459$	2.82843	−	10.0000i	0.132020	−	0.466760i
$460$		0			0
$461$			36.7696i			1.71253i	0.516538	+	0.856264i	$0.327221\pi$
$461$			36.7696i			1.71253i	−0.516538	+	0.856264i	$0.672779\pi$
$462$		0			0
$463$	3.00000	+	3.00000i	0.139422	+	0.139422i	0.773373	−	0.633951i	$-0.218568\pi$
$463$	3.00000	+	3.00000i	0.139422	+	0.139422i	−0.633951	+	0.773373i	$0.718568\pi$
$464$	2.82843			0.131306
$465$	1.82843	+	3.41421i	0.0847913	+	0.158330i
$466$	18.0000			0.833834
$467$	−25.4558	−	25.4558i	−1.17796	−	1.17796i	−0.980264	−	0.197692i	$-0.936655\pi$
$467$	−25.4558	−	25.4558i	−1.17796	−	1.17796i	−0.197692	−	0.980264i	$-0.563345\pi$
$468$	−5.48528	+	11.4853i	−0.253557	+	0.530907i
$469$		0			0
$470$	4.24264	+	12.7279i	0.195698	+	0.587095i
$471$	−8.00000	−	5.65685i	−0.368621	−	0.260654i
$472$	4.00000	−	4.00000i	0.184115	−	0.184115i
$473$	−33.9411	+	33.9411i	−1.56061	+	1.56061i
$474$	−14.1421	−	10.0000i	−0.649570	−	0.459315i
$475$	−12.0000	−	16.0000i	−0.550598	−	0.734130i
$476$		0			0
$477$	7.75736	−	16.2426i	0.355185	−	0.743699i
$478$	−8.00000	−	8.00000i	−0.365911	−	0.365911i
$479$	7.07107			0.323085			0.161543	−	0.986866i	$-0.448353\pi$
$479$	7.07107			0.323085			0.161543	+	0.986866i	$0.448353\pi$
$480$	−1.12132	+	3.70711i	−0.0511810	+	0.169206i
$481$	30.0000			1.36788
$482$	15.5563	+	15.5563i	0.708572	+	0.708572i
$483$		0			0
$484$		−	7.00000i		−	0.318182i
$485$	−4.24264	+	8.48528i	−0.192648	+	0.385297i
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$	15.0000	−	15.0000i	0.679715	−	0.679715i	−0.280221	−	0.959936i	$-0.590408\pi$
$487$	15.0000	−	15.0000i	0.679715	−	0.679715i	0.959936	+	0.280221i	$0.0904077\pi$
$488$	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
$491$			15.5563i			0.702048i	0.936366	+	0.351024i	$0.114166\pi$
$491$			15.5563i			0.702048i	−0.936366	+	0.351024i	$0.885834\pi$
$492$		0			0
$493$	−4.00000	−	4.00000i	−0.180151	−	0.180151i
$494$	−16.9706			−0.763542
$495$	17.4853	+	22.4558i	0.785905	+	1.00932i
$496$	1.00000			0.0449013
$497$		0			0
$498$	5.27208	+	30.7279i	0.236247	+	1.37695i
$499$			40.0000i			1.79065i	0.445418	+	0.895323i	$0.353055\pi$
$499$			40.0000i			1.79065i	−0.445418	+	0.895323i	$0.646945\pi$
$500$	−9.19239	−	6.36396i	−0.411096	−	0.284605i
$501$	12.0000	−	16.9706i	0.536120	−	0.758189i
$502$	15.0000	−	15.0000i	0.669483	−	0.669483i
$503$	15.5563	−	15.5563i	0.693623	−	0.693623i	−0.269404	−	0.963027i	$-0.586827\pi$
$503$	15.5563	−	15.5563i	0.693623	−	0.693623i	0.963027	+	0.269404i	$0.0868267\pi$
$504$		0			0
$505$	−13.0000	−	39.0000i	−0.578492	−	1.73548i
$506$		0			0
$507$	−8.53553	+	1.46447i	−0.379076	+	0.0650392i
$508$	−9.00000	−	9.00000i	−0.399310	−	0.399310i
$509$	39.5980			1.75515			0.877575	−	0.479440i	$-0.159160\pi$
$509$	39.5980			1.75515			0.877575	+	0.479440i	$0.159160\pi$
$510$	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
$515$	−28.2843	−	14.1421i	−1.24635	−	0.623177i
$516$	−16.0000	−	11.3137i	−0.704361	−	0.498058i
$517$	18.0000	−	18.0000i	0.791639	−	0.791639i
$518$		0			0
$519$	16.9706	+	12.0000i	0.744925	+	0.526742i
$520$	−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
$523$	−6.00000	−	6.00000i	−0.262362	−	0.262362i	0.563651	−	0.826013i	$-0.309396\pi$
$523$	−6.00000	−	6.00000i	−0.262362	−	0.262362i	−0.826013	+	0.563651i	$0.809396\pi$
$524$	−19.7990			−0.864923
$525$		0			0
$526$	28.0000			1.22086
$527$	−1.41421	−	1.41421i	−0.0616041	−	0.0616041i
$528$	7.24264	−	1.24264i	0.315195	−	0.0540790i
$529$			23.0000i			1.00000i
$530$	12.7279	−	4.24264i	0.552866	−	0.184289i
$531$	16.0000	−	5.65685i	0.694341	−	0.245487i
$532$		0			0
$533$		0			0
$534$	7.07107	−	10.0000i	0.305995	−	0.432742i
$535$	−8.00000	−	4.00000i	−0.345870	−	0.172935i
$536$		−	1.41421i		−	0.0610847i
$537$	−5.38478	−	31.3848i	−0.232370	−	1.35435i
$538$	−2.00000	−	2.00000i	−0.0862261	−	0.0862261i
$539$	−29.6985			−1.27920
$540$	−7.82843	+	8.58579i	−0.336882	+	0.369473i
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$	15.5563	+	15.5563i	0.668202	+	0.668202i
$543$	2.92893	+	17.0711i	0.125693	+	0.732590i
$544$		−	2.00000i		−	0.0857493i
$545$	4.24264	+	12.7279i	0.181735	+	0.545204i
$546$		0			0
$547$	3.00000	−	3.00000i	0.128271	−	0.128271i	−0.640057	−	0.768328i	$-0.721089\pi$
$547$	3.00000	−	3.00000i	0.128271	−	0.128271i	0.768328	+	0.640057i	$0.221089\pi$
$548$	−12.7279	+	12.7279i	−0.543710	+	0.543710i
$549$	22.6274	−	8.00000i	0.965715	−	0.341432i
$550$	−3.00000	+	21.0000i	−0.127920	+	0.895443i
$551$			11.3137i			0.481980i
$552$		0			0
$553$		0			0
$554$	−29.6985			−1.26177
$555$	26.2132	+	7.92893i	1.11269	+	0.336564i
$556$	−8.00000			−0.339276
$557$	−9.89949	−	9.89949i	−0.419455	−	0.419455i	0.465561	−	0.885016i	$-0.345853\pi$
$557$	−9.89949	−	9.89949i	−0.419455	−	0.419455i	−0.885016	+	0.465561i	$0.845853\pi$
$558$	2.70711	+	1.29289i	0.114601	+	0.0547325i
$559$		−	48.0000i		−	2.03018i
$560$		0			0
$561$	−12.0000	−	8.48528i	−0.506640	−	0.358249i
$562$	−16.0000	+	16.0000i	−0.674919	+	0.674919i
$563$	−16.9706	+	16.9706i	−0.715224	+	0.715224i	−0.967623	−	0.252399i	$-0.918780\pi$
$563$	−16.9706	+	16.9706i	−0.715224	+	0.715224i	0.252399	+	0.967623i	$0.418780\pi$
$564$	8.48528	+	6.00000i	0.357295	+	0.252646i
$565$	−6.00000	+	12.0000i	−0.252422	+	0.504844i
$566$		−	4.24264i		−	0.178331i
$567$		0			0
$568$	1.00000	+	1.00000i	0.0419591	+	0.0419591i
$569$	−4.24264			−0.177861			−0.0889304	−	0.996038i	$-0.528345\pi$
$569$	−4.24264			−0.177861			−0.0889304	+	0.996038i	$0.528345\pi$
$570$	−14.8284	−	4.48528i	−0.621094	−	0.187868i
$571$	36.0000			1.50655			0.753277	−	0.657704i	$-0.228472\pi$
$571$	36.0000			1.50655			0.753277	+	0.657704i	$0.228472\pi$
$572$	12.7279	+	12.7279i	0.532181	+	0.532181i
$573$	2.41421	−	0.414214i	0.100855	−	0.0173040i
$574$		0			0
$575$		0			0
$576$	1.00000	+	2.82843i	0.0416667	+	0.117851i
$577$	13.0000	−	13.0000i	0.541197	−	0.541197i	−0.382683	−	0.923880i	$-0.625000\pi$
$577$	13.0000	−	13.0000i	0.541197	−	0.541197i	0.923880	+	0.382683i	$0.125000\pi$
$578$	9.19239	−	9.19239i	0.382353	−	0.382353i
$579$	−21.2132	+	30.0000i	−0.881591	+	1.24676i
$580$	2.00000	+	6.00000i	0.0830455	+	0.249136i
$581$		0			0
$582$	1.24264	+	7.24264i	0.0515091	+	0.300217i
$583$	−18.0000	−	18.0000i	−0.745484	−	0.745484i
$584$	−2.82843			−0.117041
$585$	−28.2426	−	3.51472i	−1.16769	−	0.145316i
$586$	8.00000			0.330477
$587$	19.7990	+	19.7990i	0.817192	+	0.817192i	0.985700	−	0.168508i	$-0.0538950\pi$
$587$	19.7990	+	19.7990i	0.817192	+	0.817192i	−0.168508	+	0.985700i	$0.553895\pi$
$588$	−2.05025	−	11.9497i	−0.0845510	−	0.492799i
$589$			4.00000i			0.164817i
$590$	11.3137	+	5.65685i	0.465778	+	0.232889i
$591$	−2.00000	+	2.82843i	−0.0822690	+	0.116346i
$592$	5.00000	−	5.00000i	0.205499	−	0.205499i
$593$	−24.0416	+	24.0416i	−0.987271	+	0.987271i	−0.999920	−	0.0126486i	$-0.995974\pi$
$593$	−24.0416	+	24.0416i	−0.987271	+	0.987271i	0.0126486	+	0.999920i	$0.495974\pi$
$594$	21.2132	+	6.00000i	0.870388	+	0.246183i
$595$		0			0
$596$		−	1.41421i		−	0.0579284i
$597$	−27.3137	+	4.68629i	−1.11788	+	0.191797i
$598$		0			0
$599$	−24.0416			−0.982314			−0.491157	−	0.871071i	$-0.663426\pi$
$599$	−24.0416			−0.982314			−0.491157	+	0.871071i	$0.663426\pi$
$600$	−8.65685	+	0.242641i	−0.353415	+	0.00990576i
$601$	−30.0000			−1.22373			−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000			−1.22373			−0.611863	+	0.790964i	$0.709580\pi$
$602$		0			0
$603$	1.82843	−	3.82843i	0.0744593	−	0.155906i
$604$		−	16.0000i		−	0.651031i
$605$	14.8492	−	4.94975i	0.603708	−	0.201236i
$606$	−26.0000	−	18.3848i	−1.05618	−	0.746830i
$607$	−16.0000	+	16.0000i	−0.649420	+	0.649420i	−0.952853	−	0.303433i	$-0.901867\pi$
$607$	−16.0000	+	16.0000i	−0.649420	+	0.649420i	0.303433	+	0.952853i	$0.401867\pi$
$608$	−2.82843	+	2.82843i	−0.114708	+	0.114708i
$609$		0			0
$610$	16.0000	+	8.00000i	0.647821	+	0.323911i
$611$			25.4558i			1.02983i
$612$	2.58579	−	5.41421i	0.104524	−	0.218857i
$613$	−19.0000	−	19.0000i	−0.767403	−	0.767403i	0.210246	−	0.977649i	$-0.432574\pi$
$613$	−19.0000	−	19.0000i	−0.767403	−	0.767403i	−0.977649	+	0.210246i	$0.932574\pi$
$614$	7.07107			0.285365
$615$		0			0
$616$		0			0
$617$	−12.7279	−	12.7279i	−0.512407	−	0.512407i	0.402856	−	0.915263i	$-0.368017\pi$
$617$	−12.7279	−	12.7279i	−0.512407	−	0.512407i	−0.915263	+	0.402856i	$0.868017\pi$
$618$	−24.1421	+	4.14214i	−0.971139	+	0.166621i
$619$			32.0000i			1.28619i	0.765787	+	0.643094i	$0.222350\pi$
$619$			32.0000i			1.28619i	−0.765787	+	0.643094i	$0.777650\pi$
$620$	0.707107	+	2.12132i	0.0283981	+	0.0851943i
$621$		0			0
$622$	9.00000	−	9.00000i	0.360867	−	0.360867i
$623$		0			0
$624$	−4.24264	+	6.00000i	−0.169842	+	0.240192i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$			19.7990i			0.791327i
$627$	4.97056	+	28.9706i	0.198505	+	1.15697i
$628$	−4.00000	−	4.00000i	−0.159617	−	0.159617i
$629$	−14.1421			−0.563884
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$	−7.07107	−	7.07107i	−0.281272	−	0.281272i
$633$	−1.75736	−	10.2426i	−0.0698488	−	0.407108i
$634$			22.0000i			0.873732i
$635$	12.7279	−	25.4558i	0.505092	−	1.01018i
$636$	6.00000	−	8.48528i	0.237915	−	0.336463i
$637$	21.0000	−	21.0000i	0.832050	−	0.832050i
$638$	8.48528	−	8.48528i	0.335936	−	0.335936i
$639$	1.41421	+	4.00000i	0.0559454	+	0.158238i
$640$	−1.00000	+	2.00000i	−0.0395285	+	0.0790569i
$641$		−	41.0122i		−	1.61988i	−0.586510	−	0.809942i	$-0.699498\pi$
$641$		−	41.0122i		−	1.61988i	0.586510	−	0.809942i	$-0.300502\pi$
$642$	−6.82843	+	1.17157i	−0.269497	+	0.0462383i
$643$	30.0000	+	30.0000i	1.18308	+	1.18308i	0.978941	+	0.204144i	$0.0654409\pi$
$643$	30.0000	+	30.0000i	1.18308	+	1.18308i	0.204144	+	0.978941i	$0.434559\pi$
$644$		0			0
$645$	12.6863	−	41.9411i	0.499522	−	1.65143i
$646$	8.00000			0.314756
$647$	5.65685	+	5.65685i	0.222394	+	0.222394i	0.809506	−	0.587112i	$-0.199735\pi$
$647$	5.65685	+	5.65685i	0.222394	+	0.222394i	−0.587112	+	0.809506i	$0.699735\pi$
$648$	−0.949747	+	8.94975i	−0.0373096	+	0.351579i
$649$		−	24.0000i		−	0.942082i
$650$	−12.7279	−	16.9706i	−0.499230	−	0.665640i
$651$		0			0
$652$	11.0000	−	11.0000i	0.430793	−	0.430793i
$653$	24.0416	−	24.0416i	0.940822	−	0.940822i	−0.0575225	−	0.998344i	$-0.518320\pi$
$653$	24.0416	−	24.0416i	0.940822	−	0.940822i	0.998344	+	0.0575225i	$0.0183201\pi$
$654$	8.48528	+	6.00000i	0.331801	+	0.234619i
$655$	−14.0000	−	42.0000i	−0.547025	−	1.64108i
$656$		0			0
$657$	−7.65685	−	3.65685i	−0.298722	−	0.142667i
$658$		0			0
$659$	−22.6274			−0.881439			−0.440720	−	0.897645i	$-0.645277\pi$
$659$	−22.6274			−0.881439			−0.440720	+	0.897645i	$0.645277\pi$
$660$	7.75736	+	14.4853i	0.301955	+	0.563839i
$661$	−2.00000			−0.0777910			−0.0388955	−	0.999243i	$-0.512384\pi$
$661$	−2.00000			−0.0777910			−0.0388955	+	0.999243i	$0.512384\pi$
$662$	−19.7990	−	19.7990i	−0.769510	−	0.769510i
$663$	14.4853	−	2.48528i	0.562562	−	0.0965203i
$664$			18.0000i			0.698535i
$665$		0			0
$666$	20.0000	−	7.07107i	0.774984	−	0.273998i
$667$		0			0
$668$	8.48528	−	8.48528i	0.328305	−	0.328305i
$669$	1.41421	−	2.00000i	0.0546767	−	0.0773245i
$670$	3.00000	−	1.00000i	0.115900	−	0.0386334i
$671$		−	33.9411i		−	1.31028i
$672$		0			0
$673$	12.0000	+	12.0000i	0.462566	+	0.462566i	0.899496	−	0.436930i	$-0.143934\pi$
$673$	12.0000	+	12.0000i	0.462566	+	0.462566i	−0.436930	+	0.899496i	$0.643934\pi$
$674$	33.9411			1.30736
$675$	−23.7487	−	10.5355i	−0.914089	−	0.405513i
$676$	−5.00000			−0.192308
$677$	−4.24264	−	4.24264i	−0.163058	−	0.163058i	0.620862	−	0.783920i	$-0.286783\pi$
$677$	−4.24264	−	4.24264i	−0.163058	−	0.163058i	−0.783920	+	0.620862i	$0.786783\pi$
$678$	1.75736	+	10.2426i	0.0674910	+	0.393366i
$679$		0			0
$680$	4.24264	−	1.41421i	0.162698	−	0.0542326i
$681$	−8.00000	+	11.3137i	−0.306561	+	0.433542i
$682$	3.00000	−	3.00000i	0.114876	−	0.114876i
$683$	11.3137	−	11.3137i	0.432907	−	0.432907i	−0.456709	−	0.889616i	$-0.650972\pi$
$683$	11.3137	−	11.3137i	0.432907	−	0.432907i	0.889616	+	0.456709i	$0.150972\pi$
$684$	−11.3137	+	4.00000i	−0.432590	+	0.152944i
$685$	−36.0000	−	18.0000i	−1.37549	−	0.687745i
$686$		0			0
$687$	−17.0711	+	2.92893i	−0.651302	+	0.111746i
$688$	−8.00000	−	8.00000i	−0.304997	−	0.304997i
$689$	25.4558			0.969790
$690$		0			0
$691$	−46.0000			−1.74992			−0.874961	−	0.484193i	$-0.839113\pi$
$691$	−46.0000			−1.74992			−0.874961	+	0.484193i	$0.839113\pi$
$692$	8.48528	+	8.48528i	0.322562	+	0.322562i
$693$		0			0
$694$			2.00000i			0.0759190i
$695$	−5.65685	−	16.9706i	−0.214577	−	0.643730i
$696$	4.00000	+	2.82843i	0.151620	+	0.107211i
$697$		0			0
$698$	9.89949	−	9.89949i	0.374701	−	0.374701i
$699$	25.4558	+	18.0000i	0.962828	+	0.680823i
$700$		0			0
$701$			41.0122i			1.54901i	0.632568	+	0.774505i	$0.282001\pi$
$701$			41.0122i			1.54901i	−0.632568	+	0.774505i	$0.717999\pi$
$702$	−19.2426	+	10.7574i	−0.726267	+	0.406010i
$703$	20.0000	+	20.0000i	0.754314	+	0.754314i
$704$	4.24264			0.159901
$705$	−6.72792	+	22.2426i	−0.253388	+	0.837706i
$706$	4.00000			0.150542
$707$		0			0
$708$	9.65685	−	1.65685i	0.362927	−	0.0622684i
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$	−1.41421	+	2.82843i	−0.0530745	+	0.106149i
$711$	−10.0000	−	28.2843i	−0.375029	−	1.06074i
$712$	5.00000	−	5.00000i	0.187383	−	0.187383i
$713$		0			0
$714$		0			0
$715$	−18.0000	+	36.0000i	−0.673162	+	1.34632i
$716$		−	18.3848i		−	0.687071i
$717$	−3.31371	−	19.3137i	−0.123753	−	0.721284i
$718$	−3.00000	−	3.00000i	−0.111959	−	0.111959i
$719$	22.6274			0.843860			0.421930	−	0.906628i	$-0.361353\pi$
$719$	22.6274			0.843860			0.421930	+	0.906628i	$0.361353\pi$
$720$	−5.29289	+	4.12132i	−0.197254	+	0.153593i
$721$		0			0
$722$	2.12132	+	2.12132i	0.0789474	+	0.0789474i
$723$	6.44365	+	37.5563i	0.239642	+	1.39674i
$724$			10.0000i			0.371647i
$725$	−11.3137	+	8.48528i	−0.420181	+	0.315135i
$726$	7.00000	−	9.89949i	0.259794	−	0.367405i
$727$	−14.0000	+	14.0000i	−0.519231	+	0.519231i	−0.917339	−	0.398108i	$-0.869667\pi$
$727$	−14.0000	+	14.0000i	−0.519231	+	0.519231i	0.398108	+	0.917339i	$0.369667\pi$
$728$		0			0
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	−2.00000	−	6.00000i	−0.0740233	−	0.222070i
$731$			22.6274i			0.836905i
$732$	13.6569	−	2.34315i	0.504772	−	0.0866052i
$733$	28.0000	+	28.0000i	1.03420	+	1.03420i	0.999394	+	0.0348096i	$0.0110825\pi$
$733$	28.0000	+	28.0000i	1.03420	+	1.03420i	0.0348096	+	0.999394i	$0.488918\pi$
$734$	4.24264			0.156599
$735$	23.8995	−	12.7990i	0.881546	−	0.472098i
$736$		0			0
$737$	−4.24264	−	4.24264i	−0.156280	−	0.156280i
$738$		0			0
$739$		−	20.0000i		−	0.735712i	−0.929883	−	0.367856i	$-0.880092\pi$
$739$		−	20.0000i		−	0.735712i	0.929883	−	0.367856i	$-0.119908\pi$
$740$	14.1421	+	7.07107i	0.519875	+	0.259938i
$741$	−24.0000	−	16.9706i	−0.881662	−	0.623429i
$742$		0			0
$743$	−16.9706	+	16.9706i	−0.622590	+	0.622590i	−0.946193	−	0.323603i	$-0.895106\pi$
$743$	−16.9706	+	16.9706i	−0.622590	+	0.622590i	0.323603	+	0.946193i	$0.395106\pi$
$744$	1.41421	+	1.00000i	0.0518476	+	0.0366618i
$745$	3.00000	−	1.00000i	0.109911	−	0.0366372i
$746$		−	22.6274i		−	0.828449i
$747$	−23.2721	+	48.7279i	−0.851481	+	1.78286i
$748$	−6.00000	−	6.00000i	−0.219382	−	0.219382i
$749$		0			0
$750$	−6.63604	−	18.1924i	−0.242314	−	0.664292i
$751$	−12.0000			−0.437886			−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000			−0.437886			−0.218943	+	0.975738i	$0.570261\pi$
$752$	4.24264	+	4.24264i	0.154713	+	0.154713i
$753$	36.2132	−	6.21320i	1.31968	−	0.226422i
$754$			12.0000i			0.437014i
$755$	33.9411	−	11.3137i	1.23524	−	0.411748i
$756$		0			0
$757$	−21.0000	+	21.0000i	−0.763258	+	0.763258i	−0.976910	−	0.213652i	$-0.931464\pi$
$757$	−21.0000	+	21.0000i	−0.763258	+	0.763258i	0.213652	+	0.976910i	$0.431464\pi$
$758$	4.24264	−	4.24264i	0.154100	−	0.154100i
$759$		0			0
$760$	−8.00000	−	4.00000i	−0.290191	−	0.145095i
$761$		−	18.3848i		−	0.666448i	−0.942848	−	0.333224i	$-0.891864\pi$
$761$		−	18.3848i		−	0.666448i	0.942848	−	0.333224i	$-0.108136\pi$
$762$	−3.72792	−	21.7279i	−0.135048	−	0.787120i
$763$		0			0
$764$	1.41421			0.0511645
$765$	13.3137	+	1.65685i	0.481358	+	0.0599037i
$766$	24.0000			0.867155
$767$	16.9706	+	16.9706i	0.612772	+	0.612772i
$768$	0.292893	+	1.70711i	0.0105689	+	0.0615999i
$769$			32.0000i			1.15395i	0.816762	+	0.576975i	$0.195767\pi$
$769$			32.0000i			1.15395i	−0.816762	+	0.576975i	$0.804233\pi$
$770$		0			0
$771$	6.00000	−	8.48528i	0.216085	−	0.305590i
$772$	−15.0000	+	15.0000i	−0.539862	+	0.539862i
$773$	−26.8701	+	26.8701i	−0.966449	+	0.966449i	−0.999455	−	0.0330063i	$-0.989492\pi$
$773$	−26.8701	+	26.8701i	−0.966449	+	0.966449i	0.0330063	+	0.999455i	$0.489492\pi$
$774$	−11.3137	−	32.0000i	−0.406663	−	1.15022i
$775$	−4.00000	+	3.00000i	−0.143684	+	0.107763i
$776$			4.24264i			0.152302i
$777$		0			0
$778$	16.0000	+	16.0000i	0.573628	+	0.573628i
$779$		0			0
$780$	−15.7279	−	4.75736i	−0.563150	−	0.170341i
$781$	6.00000			0.214697
$782$		0			0
$783$	7.17157	+	12.8284i	0.256291	+	0.458451i
$784$		−	7.00000i		−	0.250000i
$785$	5.65685	−	11.3137i	0.201902	−	0.403804i
$786$	−28.0000	−	19.7990i	−0.998727	−	0.706207i
$787$	20.0000	−	20.0000i	0.712923	−	0.712923i	−0.254223	−	0.967146i	$-0.581820\pi$
$787$	20.0000	−	20.0000i	0.712923	−	0.712923i	0.967146	+	0.254223i	$0.0818196\pi$
$788$	−1.41421	+	1.41421i	−0.0503793	+	0.0503793i
$789$	39.5980	+	28.0000i	1.40973	+	0.996826i
$790$	10.0000	−	20.0000i	0.355784	−	0.711568i
$791$		0			0
$792$	11.4853	+	5.48528i	0.408112	+	0.194911i
$793$	24.0000	+	24.0000i	0.852265	+	0.852265i
$794$	16.9706			0.602263
$795$	22.2426	+	6.72792i	0.788865	+	0.238615i
$796$	−16.0000			−0.567105
$797$	32.5269	+	32.5269i	1.15216	+	1.15216i	0.986118	+	0.166044i	$0.0530994\pi$
$797$	32.5269	+	32.5269i	1.15216	+	1.15216i	0.166044	+	0.986118i	$0.446901\pi$
$798$		0			0
$799$		−	12.0000i		−	0.424529i
$800$	−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
$803$	−8.48528	+	8.48528i	−0.299439	+	0.299439i
$804$	1.41421	−	2.00000i	0.0498755	−	0.0705346i
$805$		0			0
$806$			4.24264i			0.149441i
$807$	−0.828427	−	4.82843i	−0.0291620	−	0.169969i
$808$	−13.0000	−	13.0000i	−0.457338	−	0.457338i
$809$	−15.5563			−0.546932			−0.273466	−	0.961882i	$-0.588170\pi$
$809$	−15.5563			−0.546932			−0.273466	+	0.961882i	$0.588170\pi$
$810$	−19.6569	+	4.31371i	−0.690671	+	0.151568i
$811$	−34.0000			−1.19390			−0.596951	−	0.802278i	$-0.703621\pi$
$811$	−34.0000			−1.19390			−0.596951	+	0.802278i	$0.703621\pi$
$812$		0			0
$813$	6.44365	+	37.5563i	0.225989	+	1.31716i
$814$		−	30.0000i		−	1.05150i
$815$	31.1127	+	15.5563i	1.08983	+	0.544915i
$816$	2.00000	−	2.82843i	0.0700140	−	0.0990148i
$817$	32.0000	−	32.0000i	1.11954	−	1.11954i
$818$	21.2132	−	21.2132i	0.741702	−	0.741702i
$819$		0			0
$820$		0			0
$821$		−	8.48528i		−	0.296138i	−0.988977	−	0.148069i	$-0.952694\pi$
$821$		−	8.48528i		−	0.296138i	0.988977	−	0.148069i	$-0.0473058\pi$
$822$	−30.7279	+	5.27208i	−1.07176	+	0.183885i
$823$	29.0000	+	29.0000i	1.01088	+	1.01088i	0.999940	+	0.0109363i	$0.00348119\pi$
$823$	29.0000	+	29.0000i	1.01088	+	1.01088i	0.0109363	+	0.999940i	$0.496519\pi$
$824$	−14.1421			−0.492665
$825$	−25.2426	+	26.6985i	−0.878836	+	0.929522i
$826$		0			0
$827$	19.7990	+	19.7990i	0.688478	+	0.688478i	0.961896	−	0.273417i	$-0.0881540\pi$
$827$	19.7990	+	19.7990i	0.688478	+	0.688478i	−0.273417	+	0.961896i	$0.588154\pi$
$828$		0			0
$829$			12.0000i			0.416777i	0.978046	+	0.208389i	$0.0668219\pi$
$829$			12.0000i			0.416777i	−0.978046	+	0.208389i	$0.933178\pi$
$830$	−38.1838	+	12.7279i	−1.32538	+	0.441793i
$831$	−42.0000	−	29.6985i	−1.45696	−	1.03023i
$832$	−3.00000	+	3.00000i	−0.104006	+	0.104006i
$833$	−9.89949	+	9.89949i	−0.342997	+	0.342997i
$834$	−11.3137	−	8.00000i	−0.391762	−	0.277017i
$835$	24.0000	+	12.0000i	0.830554	+	0.415277i
$836$			16.9706i			0.586939i
$837$	2.53553	+	4.53553i	0.0876409	+	0.156771i
$838$	−16.0000	−	16.0000i	−0.552711	−	0.552711i
$839$	−12.7279			−0.439417			−0.219708	−	0.975566i	$-0.570511\pi$
$839$	−12.7279			−0.439417			−0.219708	+	0.975566i	$0.570511\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$	−4.24264	−	4.24264i	−0.146211	−	0.146211i
$843$	−38.6274	+	6.62742i	−1.33040	+	0.228260i
$844$		−	6.00000i		−	0.206529i
$845$	−3.53553	−	10.6066i	−0.121626	−	0.364878i
$846$	6.00000	+	16.9706i	0.206284	+	0.583460i
$847$		0			0
$848$	4.24264	−	4.24264i	0.145693	−	0.145693i
$849$	4.24264	−	6.00000i	0.145607	−	0.205919i
$850$	6.00000	+	8.00000i	0.205798	+	0.274398i
$851$		0			0
$852$	0.414214	+	2.41421i	0.0141907	+	0.0827096i
$853$	24.0000	+	24.0000i	0.821744	+	0.821744i	0.986358	−	0.164614i	$-0.0526378\pi$
$853$	24.0000	+	24.0000i	0.821744	+	0.821744i	−0.164614	+	0.986358i	$0.552638\pi$
$854$		0			0
$855$	−16.4853	−	21.1716i	−0.563785	−	0.724053i
$856$	−4.00000			−0.136717
$857$	18.3848	+	18.3848i	0.628012	+	0.628012i	0.947568	−	0.319556i	$-0.103534\pi$
$857$	18.3848	+	18.3848i	0.628012	+	0.628012i	−0.319556	+	0.947568i	$0.603534\pi$
$858$	5.27208	+	30.7279i	0.179986	+	1.04903i
$859$		−	8.00000i		−	0.272956i	−0.990643	−	0.136478i	$-0.956422\pi$
$859$		−	8.00000i		−	0.272956i	0.990643	−	0.136478i	$-0.0435784\pi$
$860$	11.3137	−	22.6274i	0.385794	−	0.771589i
$861$		0			0
$862$	9.00000	−	9.00000i	0.306541	−	0.306541i
$863$	19.7990	−	19.7990i	0.673965	−	0.673965i	−0.284662	−	0.958628i	$-0.591881\pi$
$863$	19.7990	−	19.7990i	0.673965	−	0.673965i	0.958628	+	0.284662i	$0.0918815\pi$
$864$	−1.41421	+	5.00000i	−0.0481125	+	0.170103i
$865$	−12.0000	+	24.0000i	−0.408012	+	0.816024i
$866$		−	36.7696i		−	1.24948i
$867$	22.1924	−	3.80761i	0.753693	−	0.129313i
$868$		0			0
$869$	−42.4264			−1.43922
$870$	−3.17157	+	10.4853i	−0.107526	+	0.355484i
$871$	6.00000			0.203302
$872$	4.24264	+	4.24264i	0.143674	+	0.143674i
$873$	−5.48528	+	11.4853i	−0.185649	+	0.388718i
$874$		0			0
$875$		0			0
$876$	−4.00000	−	2.82843i	−0.135147	−	0.0955637i
$877$	18.0000	−	18.0000i	0.607817	−	0.607817i	−0.334558	−	0.942375i	$-0.608587\pi$
$877$	18.0000	−	18.0000i	0.607817	−	0.607817i	0.942375	+	0.334558i	$0.108587\pi$
$878$	11.3137	−	11.3137i	0.381819	−	0.381819i
$879$	11.3137	+	8.00000i	0.381602	+	0.269833i
$880$	3.00000	+	9.00000i	0.101130	+	0.303390i
$881$			32.5269i			1.09586i	0.836524	+	0.547930i	$0.184584\pi$
$881$			32.5269i			1.09586i	−0.836524	+	0.547930i	$0.815416\pi$
$882$	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
$885$	10.3431	+	19.3137i	0.347681	+	0.649223i
$886$	−16.0000			−0.537531
$887$	−4.24264	−	4.24264i	−0.142454	−	0.142454i	0.632283	−	0.774737i	$-0.282118\pi$
$887$	−4.24264	−	4.24264i	−0.142454	−	0.142454i	−0.774737	+	0.632283i	$0.782118\pi$
$888$	12.0711	−	2.07107i	0.405079	−	0.0695005i
$889$		0			0
$890$	14.1421	+	7.07107i	0.474045	+	0.237023i
$891$	24.0000	+	29.6985i	0.804030	+	0.994937i
$892$	1.00000	−	1.00000i	0.0334825	−	0.0334825i
$893$	−16.9706	+	16.9706i	−0.567898	+	0.567898i
$894$	1.41421	−	2.00000i	0.0472984	−	0.0668900i
$895$	39.0000	−	13.0000i	1.30363	−	0.434542i
$896$		0			0
$897$		0			0
$898$	17.0000	+	17.0000i	0.567297	+	0.567297i
$899$	2.82843			0.0943333
$900$	−12.4853	−	8.31371i	−0.416176	−	0.277124i
$901$	−12.0000			−0.399778
$902$		0			0
$903$		0			0
$904$			6.00000i			0.199557i
$905$	−21.2132	+	7.07107i	−0.705151	+	0.235050i
$906$	16.0000	−	22.6274i	0.531564	−	0.751746i
$907$	41.0000	−	41.0000i	1.36138	−	1.36138i	0.489225	−	0.872158i	$-0.337280\pi$
$907$	41.0000	−	41.0000i	1.36138	−	1.36138i	0.872158	−	0.489225i	$-0.162720\pi$
$908$	−5.65685	+	5.65685i	−0.187729	+	0.187729i
$909$	−18.3848	−	52.0000i	−0.609785	−	1.72473i
$910$		0			0
$911$			22.6274i			0.749680i	0.927090	+	0.374840i	$0.122302\pi$
$911$			22.6274i			0.749680i	−0.927090	+	0.374840i	$0.877698\pi$
$912$	−6.82843	+	1.17157i	−0.226112	+	0.0387947i
$913$	54.0000	+	54.0000i	1.78714	+	1.78714i
$914$	−11.3137			−0.374224
$915$	14.6274	+	27.3137i	0.483567	+	0.902963i
$916$	−10.0000			−0.330409
$917$		0			0
$918$	9.07107	−	5.07107i	0.299390	−	0.167370i
$919$			12.0000i			0.395843i	0.980218	+	0.197922i	$0.0634192\pi$
$919$			12.0000i			0.395843i	−0.980218	+	0.197922i	$0.936581\pi$
$920$		0			0
$921$	10.0000	+	7.07107i	0.329511	+	0.233000i
$922$	−26.0000	+	26.0000i	−0.856264	+	0.856264i
$923$	−4.24264	+	4.24264i	−0.139648	+	0.139648i
$924$		0			0
$925$	−5.00000	+	35.0000i	−0.164399	+	1.15079i
$926$			4.24264i			0.139422i
$927$	−38.2843	−	18.2843i	−1.25742	−	0.600534i
$928$	2.00000	+	2.00000i	0.0656532	+	0.0656532i
$929$	55.1543			1.80955			0.904777	−	0.425885i	$-0.140037\pi$
$929$	55.1543			1.80955			0.904777	+	0.425885i	$0.140037\pi$
$930$	−1.12132	+	3.70711i	−0.0367695	+	0.121561i
$931$	28.0000			0.917663
$932$	12.7279	+	12.7279i	0.416917	+	0.416917i
$933$	21.7279	−	3.72792i	0.711340	−	0.122047i
$934$		−	36.0000i		−	1.17796i
$935$	8.48528	−	16.9706i	0.277498	−	0.554997i
$936$	−12.0000	+	4.24264i	−0.392232	+	0.138675i
$937$	−3.00000	+	3.00000i	−0.0980057	+	0.0980057i	−0.754410	−	0.656404i	$-0.772077\pi$
$937$	−3.00000	+	3.00000i	−0.0980057	+	0.0980057i	0.656404	+	0.754410i	$0.272077\pi$
$938$		0			0
$939$	−19.7990	+	28.0000i	−0.646116	+	0.913745i
$940$	−6.00000	+	12.0000i	−0.195698	+	0.391397i
$941$			11.3137i			0.368816i	0.982850	+	0.184408i	$0.0590368\pi$
$941$			11.3137i			0.368816i	−0.982850	+	0.184408i	$0.940963\pi$
$942$	−1.65685	−	9.65685i	−0.0539832	−	0.314637i
$943$		0			0
$944$	5.65685			0.184115
$945$		0			0
$946$	−48.0000			−1.56061
$947$	19.7990	+	19.7990i	0.643381	+	0.643381i	0.951385	−	0.308004i	$-0.0996611\pi$
$947$	19.7990	+	19.7990i	0.643381	+	0.643381i	−0.308004	+	0.951385i	$0.599661\pi$
$948$	−2.92893	−	17.0711i	−0.0951273	−	0.554443i
$949$		−	12.0000i		−	0.389536i
$950$	2.82843	−	19.7990i	0.0917663	−	0.642364i
$951$	−22.0000	+	31.1127i	−0.713399	+	1.00890i
$952$		0			0
$953$	−31.1127	+	31.1127i	−1.00784	+	1.00784i	−0.00787013	+	0.999969i	$0.502505\pi$
$953$	−31.1127	+	31.1127i	−1.00784	+	1.00784i	−0.999969	+	0.00787013i	$0.997495\pi$
$954$	16.9706	−	6.00000i	0.549442	−	0.194257i
$955$	1.00000	+	3.00000i	0.0323592	+	0.0970777i
$956$		−	11.3137i		−	0.365911i
$957$	20.4853	−	3.51472i	0.662195	−	0.113615i
$958$	5.00000	+	5.00000i	0.161543	+	0.161543i
$959$		0			0
$960$	−3.41421	+	1.82843i	−0.110193	+	0.0590122i
$961$	1.00000			0.0322581
$962$	21.2132	+	21.2132i	0.683941	+	0.683941i
$963$	−10.8284	−	5.17157i	−0.348941	−	0.166652i
$964$			22.0000i			0.708572i
$965$	−42.4264	−	21.2132i	−1.36575	−	0.682877i
$966$		0			0
$967$	37.0000	−	37.0000i	1.18984	−	1.18984i	0.212728	−	0.977111i	$-0.431765\pi$
$967$	37.0000	−	37.0000i	1.18984	−	1.18984i	0.977111	−	0.212728i	$-0.0682350\pi$
$968$	4.94975	−	4.94975i	0.159091	−	0.159091i
$969$	11.3137	+	8.00000i	0.363449	+	0.256997i
$970$	−9.00000	+	3.00000i	−0.288973	+	0.0963242i
$971$		−	39.5980i		−	1.27076i	−0.772200	−	0.635380i	$-0.780844\pi$
$971$		−	39.5980i		−	1.27076i	0.772200	−	0.635380i	$-0.219156\pi$
$972$	−10.2929	+	11.7071i	−0.330145	+	0.375506i
$973$		0			0
$974$	21.2132			0.679715
$975$	−1.02944	−	36.7279i	−0.0329684	−	1.17623i
$976$	8.00000			0.256074
$977$	7.07107	+	7.07107i	0.226224	+	0.226224i	0.811113	−	0.584889i	$-0.198862\pi$
$977$	7.07107	+	7.07107i	0.226224	+	0.226224i	−0.584889	+	0.811113i	$0.698862\pi$
$978$	26.5563	−	4.55635i	0.849178	−	0.145696i
$979$		−	30.0000i		−	0.958804i
$980$	14.8492	−	4.94975i	0.474342	−	0.158114i
$981$	6.00000	+	16.9706i	0.191565	+	0.541828i
$982$	−11.0000	+	11.0000i	−0.351024	+	0.351024i
$983$	−2.82843	+	2.82843i	−0.0902128	+	0.0902128i	−0.750773	−	0.660560i	$-0.770319\pi$
$983$	−2.82843	+	2.82843i	−0.0902128	+	0.0902128i	0.660560	+	0.750773i	$0.270319\pi$
$984$		0			0
$985$	−4.00000	−	2.00000i	−0.127451	−	0.0637253i
$986$		−	5.65685i		−	0.180151i
$987$		0			0
$988$	−12.0000	−	12.0000i	−0.381771	−	0.381771i
$989$		0			0
$990$	−3.51472	+	28.2426i	−0.111705	+	0.897610i
$991$	−18.0000			−0.571789			−0.285894	−	0.958261i	$-0.592291\pi$
$991$	−18.0000			−0.571789			−0.285894	+	0.958261i	$0.592291\pi$
$992$	0.707107	+	0.707107i	0.0224507	+	0.0224507i
$993$	−8.20101	−	47.7990i	−0.260251	−	1.51686i
$994$		0			0
$995$	−11.3137	−	33.9411i	−0.358669	−	1.07601i
$996$	−18.0000	+	25.4558i	−0.570352	+	0.806599i
$997$	−28.0000	+	28.0000i	−0.886769	+	0.886769i	−0.994211	−	0.107442i	$-0.965734\pi$
$997$	−28.0000	+	28.0000i	−0.886769	+	0.886769i	0.107442	+	0.994211i	$0.465734\pi$
$998$	−28.2843	+	28.2843i	−0.895323	+	0.895323i
$999$	35.3553	+	10.0000i	1.11859	+	0.316386i

Twists

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

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

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} +4.24264i 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} +(-3.00000 + 3.00000i) q^{22} +(-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} +(-7.24264 + 1.24264i) q^{33} +2.00000i q^{34} +(-1.00000 - 2.82843i) q^{36} +(-5.00000 + 5.00000i) q^{37} +(2.82843 - 2.82843i) q^{38} +(4.24264 - 6.00000i) q^{39} +(1.00000 - 2.00000i) q^{40} +(8.00000 + 8.00000i) q^{43} -4.24264 q^{44} +(5.29289 - 4.12132i) q^{45} +(-4.24264 - 4.24264i) 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} +(-4.24264 + 4.24264i) q^{53} +(1.41421 - 5.00000i) q^{54} +(-3.00000 - 9.00000i) q^{55} +(6.82843 - 1.17157i) q^{57} +(-2.00000 - 2.00000i) q^{58} -5.65685 q^{59} +(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} +(-6.00000 - 4.24264i) q^{66} +(-1.00000 + 1.00000i) q^{67} +(-1.41421 + 1.41421i) q^{68} -1.41421i q^{71} +(1.29289 - 2.70711i) q^{72} +(2.00000 + 2.00000i) q^{73} -7.07107 q^{74} +(6.29289 + 5.94975i) q^{75} +4.00000 q^{76} +(7.24264 - 1.24264i) q^{78} +10.0000i q^{79} +(2.12132 - 0.707107i) q^{80} +(7.00000 - 5.65685i) q^{81} +(12.7279 - 12.7279i) q^{83} +(-4.00000 - 2.00000i) q^{85} +11.3137i q^{86} +(-0.828427 - 4.82843i) q^{87} +(-3.00000 - 3.00000i) q^{88} -7.07107 q^{89} +(6.65685 + 0.828427i) q^{90} +(-0.292893 - 1.70711i) q^{93} -6.00000i q^{94} +(2.82843 + 8.48528i) q^{95} +(1.00000 - 1.41421i) q^{96} +(3.00000 - 3.00000i) q^{97} +(-4.94975 + 4.94975i) q^{98} +(-4.24264 - 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{6} - 8 q^{10} - 4 q^{12} - 12 q^{13} + 4 q^{15} - 4 q^{16} - 8 q^{18} - 12 q^{22} + 16 q^{25} + 4 q^{27} - 4 q^{30} - 4 q^{31} - 12 q^{33} - 4 q^{36} - 20 q^{37} + 4 q^{40} + 32 q^{43}+ \cdots + 12 q^{97}+O(q^{100}) \) 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 - 12 * q^22 + 16 * q^25 + 4 * q^27 - 4 * q^30 - 4 * q^31 - 12 * q^33 - 4 * q^36 - 20 * q^37 + 4 * q^40 + 32 * q^43 + 24 * q^45 - 4 * q^48 - 8 * q^51 + 12 * q^52 - 12 * q^55 + 16 * q^57 - 8 * q^58 + 8 * q^60 - 32 * q^61 - 24 * q^66 - 4 * q^67 + 8 * q^72 + 8 * q^73 + 28 * q^75 + 16 * q^76 + 12 * q^78 + 28 * q^81 - 16 * q^85 + 8 * q^87 - 12 * q^88 + 4 * q^90 - 4 * q^93 + 4 * q^96 + 12 * q^97

Introduction

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