LMFDB - Embedded newform 930.2.j.a.683.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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.a.497.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.70711 + 0.292893i) q^{3} +1.00000i q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(0.707107 - 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.70711 + 0.292893i) 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} +(-0.292893 + 1.70711i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(3.82843 - 0.585786i) q^{15} -1.00000 q^{16} +(-1.41421 - 1.41421i) q^{17} +(-1.29289 - 2.70711i) 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} +(4.53553 + 2.53553i) q^{27} +2.82843 q^{29} +(-3.12132 - 2.29289i) q^{30} -1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(1.24264 - 7.24264i) 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} +(6.70711 + 0.121320i) q^{45} +(4.24264 + 4.24264i) q^{47} +(-1.70711 - 0.292893i) 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} +(1.17157 - 6.82843i) q^{57} +(-2.00000 - 2.00000i) q^{58} +5.65685 q^{59} +(0.585786 + 3.82843i) 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} +(2.70711 - 1.29289i) q^{72} +(2.00000 + 2.00000i) q^{73} +7.07107 q^{74} +(7.70711 - 3.94975i) q^{75} +4.00000 q^{76} +(-1.24264 + 7.24264i) 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} +(4.82843 + 0.828427i) q^{87} +(-3.00000 - 3.00000i) q^{88} +7.07107 q^{89} +(-4.65685 - 4.82843i) q^{90} +(-1.70711 - 0.292893i) 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}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^6	$ 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}+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

Display 100 coefficients 10 coefficients

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
$3$	1.70711	+	0.292893i	0.985599	+	0.169102i
$3$	1.70711	+	0.292893i	0.985599	+	0.169102i
$4$			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	$-0.779099\pi$
$11$		−	4.24264i		−	1.27920i	0.768706	−	0.639602i	$-0.220901\pi$
$12$	−0.292893	+	1.70711i	−0.0845510	+	0.492799i
$13$	−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
$15$	3.82843	−	0.585786i	0.988496	−	0.151249i
$16$	−1.00000			−0.250000
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	0.514496	−	0.857493i	$-0.327979\pi$
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	−0.857493	+	0.514496i	$0.827979\pi$
$18$	−1.29289	−	2.70711i	−0.304738	−	0.638071i
$19$		−	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
$27$	4.53553	+	2.53553i	0.872864	+	0.487964i
$28$		0			0
$29$	2.82843			0.525226			0.262613	−	0.964901i	$-0.415416\pi$
$29$	2.82843			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$30$	−3.12132	−	2.29289i	−0.569873	−	0.418623i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.24264	−	7.24264i	0.216316	−	1.26078i
$34$			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
$45$	6.70711	+	0.121320i	0.999836	+	0.0180854i
$46$		0			0
$47$	4.24264	+	4.24264i	0.618853	+	0.618853i	0.945237	−	0.326384i	$-0.105830\pi$
$47$	4.24264	+	4.24264i	0.618853	+	0.618853i	−0.326384	+	0.945237i	$0.605830\pi$
$48$	−1.70711	−	0.292893i	−0.246400	−	0.0422755i
$49$			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	−0.352892	−	0.935664i	$-0.614802\pi$
$53$	4.24264	−	4.24264i	0.582772	−	0.582772i	0.935664	+	0.352892i	$0.114802\pi$
$54$	−1.41421	−	5.00000i	−0.192450	−	0.680414i
$55$	−3.00000	−	9.00000i	−0.404520	−	1.21356i
$56$		0			0
$57$	1.17157	−	6.82843i	0.155179	−	0.904447i
$58$	−2.00000	−	2.00000i	−0.262613	−	0.262613i
$59$	5.65685			0.736460			0.368230	−	0.929735i	$-0.379964\pi$
$59$	5.65685			0.736460			0.368230	+	0.929735i	$0.379964\pi$
$60$	0.585786	+	3.82843i	0.0756247	+	0.494248i
$61$	−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	$0.0267434\pi$
$71$			1.41421i			0.167836i	−0.996473	+	0.0839181i	$0.973257\pi$
$72$	2.70711	−	1.29289i	0.319036	−	0.152369i
$73$	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
$75$	7.70711	−	3.94975i	0.889940	−	0.456078i
$76$	4.00000			0.458831
$77$		0			0
$78$	−1.24264	+	7.24264i	−0.140701	+	0.820068i
$79$			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	$0.700388\pi$
$83$	−12.7279	+	12.7279i	−1.39707	+	1.39707i	−0.808300	+	0.588771i	$0.799612\pi$
$84$		0			0
$85$	−4.00000	−	2.00000i	−0.433861	−	0.216930i
$86$		−	11.3137i		−	1.21999i
$87$	4.82843	+	0.828427i	0.517662	+	0.0888167i
$88$	−3.00000	−	3.00000i	−0.319801	−	0.319801i
$89$	7.07107			0.749532			0.374766	−	0.927119i	$-0.377723\pi$
$89$	7.07107			0.749532			0.374766	+	0.927119i	$0.377723\pi$
$90$	−4.65685	−	4.82843i	−0.490876	−	0.508961i
$91$		0			0
$92$		0			0
$93$	−1.70711	−	0.292893i	−0.177019	−	0.0303716i
$94$		−	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	$-0.632445\pi$
$101$		−	18.3848i		−	1.82935i	0.404186	−	0.914677i	$-0.367555\pi$
$102$	−0.585786	+	3.41421i	−0.0580015	+	0.338058i
$103$	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	0.557047	−	0.830481i	$-0.311934\pi$
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	−0.830481	+	0.557047i	$0.811934\pi$
$108$	−2.53553	+	4.53553i	−0.243982	+	0.436432i
$109$		−	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	−0.877920	−	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
$115$		0			0
$116$			2.82843i			0.262613i
$117$	−5.48528	−	11.4853i	−0.507114	−	1.06181i
$118$	−4.00000	−	4.00000i	−0.368230	−	0.368230i
$119$		0			0
$120$	2.29289	−	3.12132i	0.209312	−	0.284936i
$121$	−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	$-0.667367\pi$
$131$		−	19.7990i		−	1.72985i	0.501905	−	0.864923i	$-0.332633\pi$
$132$	7.24264	+	1.24264i	0.630391	+	0.108158i
$133$		0			0
$134$	1.41421			0.122169
$135$	11.4142	+	2.17157i	0.982379	+	0.186899i
$136$	−2.00000			−0.171499
$137$	−12.7279	−	12.7279i	−1.08742	−	1.08742i	−0.995793	−	0.0916263i	$-0.970793\pi$
$137$	−12.7279	−	12.7279i	−1.08742	−	1.08742i	−0.0916263	−	0.995793i	$-0.529207\pi$
$138$		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
$147$	−2.05025	+	11.9497i	−0.169102	+	0.985599i
$148$	−5.00000	−	5.00000i	−0.410997	−	0.410997i
$149$	1.41421			0.115857			0.0579284	−	0.998321i	$-0.481550\pi$
$149$	1.41421			0.115857			0.0579284	+	0.998321i	$0.481550\pi$
$150$	−8.24264	−	2.65685i	−0.673009	−	0.216931i
$151$	−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
$153$	−2.58579	−	5.41421i	−0.209048	−	0.437713i
$154$		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
$162$	−0.949747	−	8.94975i	−0.0746192	−	0.703159i
$163$	−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
$165$	−2.48528	−	16.2426i	−0.193479	−	1.26449i
$166$	18.0000			1.39707
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	0.954577	−	0.297966i	$-0.0963081\pi$
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	−0.297966	+	0.954577i	$0.596308\pi$
$168$		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	−0.951811	−	0.306687i	$-0.900780\pi$
$173$	−8.48528	+	8.48528i	−0.645124	+	0.645124i	0.306687	+	0.951811i	$0.400780\pi$
$174$	−2.82843	−	4.00000i	−0.214423	−	0.303239i
$175$		0			0
$176$			4.24264i			0.319801i
$177$	9.65685	+	1.65685i	0.725854	+	0.124537i
$178$	−5.00000	−	5.00000i	−0.374766	−	0.374766i
$179$	18.3848			1.37414			0.687071	−	0.726590i	$-0.258896\pi$
$179$	18.3848			1.37414			0.687071	+	0.726590i	$0.258896\pi$
$180$	−0.121320	+	6.70711i	−0.00904268	+	0.499918i
$181$	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
$183$	−13.6569	−	2.34315i	−1.00954	−	0.173210i
$184$		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	$0.0162933\pi$
$191$			1.41421i			0.102329i	−0.998690	+	0.0511645i	$0.983707\pi$
$192$	0.292893	−	1.70711i	0.0211377	−	0.123200i
$193$	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
$195$	−13.2426	−	9.72792i	−0.948325	−	0.696631i
$196$	−7.00000			−0.500000
$197$	−1.41421	−	1.41421i	−0.100759	−	0.100759i	0.654931	−	0.755689i	$-0.272698\pi$
$197$	−1.41421	−	1.41421i	−0.100759	−	0.100759i	−0.755689	+	0.654931i	$0.772698\pi$
$198$	−11.4853	+	5.48528i	−0.816223	+	0.389822i
$199$			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
$213$	−0.414214	+	2.41421i	−0.0283814	+	0.165419i
$214$			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
$222$	12.0711	+	2.07107i	0.810157	+	0.139001i
$223$	−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
$225$	14.3137	−	4.48528i	0.954247	−	0.299019i
$226$	6.00000			0.399114
$227$	−5.65685	−	5.65685i	−0.375459	−	0.375459i	0.494002	−	0.869461i	$-0.335534\pi$
$227$	−5.65685	−	5.65685i	−0.375459	−	0.375459i	−0.869461	+	0.494002i	$0.835534\pi$
$228$	6.82843	+	1.17157i	0.452224	+	0.0775893i
$229$			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	−0.988039	−	0.154205i	$-0.950718\pi$
$233$	−12.7279	+	12.7279i	−0.833834	+	0.833834i	0.154205	+	0.988039i	$0.450718\pi$
$234$	−4.24264	+	12.0000i	−0.277350	+	0.784465i
$235$	12.0000	+	6.00000i	0.782794	+	0.391397i
$236$			5.65685i			0.368230i
$237$	−2.92893	+	17.0711i	−0.190255	+	1.10889i
$238$		0			0
$239$	11.3137			0.731823			0.365911	−	0.930650i	$-0.380757\pi$
$239$	11.3137			0.731823			0.365911	+	0.930650i	$0.380757\pi$
$240$	−3.82843	+	0.585786i	−0.247124	+	0.0378124i
$241$	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
$243$	10.2929	+	11.7071i	0.660289	+	0.751011i
$244$		−	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	$0.233484\pi$
$251$			21.2132i			1.33897i	−0.742828	+	0.669483i	$0.766516\pi$
$252$		0			0
$253$		0			0
$254$	12.7279			0.798621
$255$	−6.24264	−	4.58579i	−0.390929	−	0.287173i
$256$	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	$0.690080\pi$
$258$	3.31371	−	19.3137i	0.206302	−	1.20242i
$259$		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	$0.581592\pi$
$263$	−19.7990	+	19.7990i	−1.22086	+	1.22086i	−0.967327	+	0.253531i	$0.918408\pi$
$264$	−4.24264	−	6.00000i	−0.261116	−	0.369274i
$265$	6.00000	−	12.0000i	0.368577	−	0.737154i
$266$		0			0
$267$	12.0711	+	2.07107i	0.738737	+	0.126747i
$268$	−1.00000	−	1.00000i	−0.0610847	−	0.0610847i
$269$	2.82843			0.172452			0.0862261	−	0.996276i	$-0.472519\pi$
$269$	2.82843			0.172452			0.0862261	+	0.996276i	$0.472519\pi$
$270$	−6.53553	−	9.60660i	−0.397740	−	0.584639i
$271$	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	$-0.764178\pi$
$281$		−	22.6274i		−	1.34984i	0.737892	−	0.674919i	$-0.235822\pi$
$282$	1.75736	−	10.2426i	0.104649	−	0.609940i
$283$	−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
$285$	−2.34315	−	15.3137i	−0.138796	−	0.907106i
$286$	18.0000			1.06436
$287$		0			0
$288$	1.29289	+	2.70711i	0.0761845	+	0.159518i
$289$		−	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	−0.852768	−	0.522291i	$-0.825078\pi$
$293$	−5.65685	+	5.65685i	−0.330477	+	0.330477i	0.522291	+	0.852768i	$0.325078\pi$
$294$	9.89949	−	7.00000i	0.577350	−	0.408248i
$295$	12.0000	−	4.00000i	0.698667	−	0.232889i
$296$			7.07107i			0.410997i
$297$	10.7574	−	19.2426i	0.624205	−	1.11657i
$298$	−1.00000	−	1.00000i	−0.0579284	−	0.0579284i
$299$		0			0
$300$	3.94975	+	7.70711i	0.228039	+	0.444970i
$301$		0			0
$302$	11.3137	+	11.3137i	0.651031	+	0.651031i
$303$	5.38478	−	31.3848i	0.309347	−	1.80301i
$304$			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	$0.117519\pi$
$311$			12.7279i			0.721734i	−0.932617	+	0.360867i	$0.882481\pi$
$312$	−7.24264	−	1.24264i	−0.410034	−	0.0703507i
$313$	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	0.119145	−	0.992877i	$-0.461985\pi$
$317$	−15.5563	−	15.5563i	−0.873732	−	0.873732i	−0.992877	+	0.119145i	$0.961985\pi$
$318$	−10.2426	−	1.75736i	−0.574379	−	0.0985478i
$319$		−	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
$327$	1.75736	−	10.2426i	0.0971822	−	0.566419i
$328$		0			0
$329$		0			0
$330$	−9.72792	+	13.2426i	−0.535504	+	0.728983i
$331$	−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
$333$	−19.1421	+	9.14214i	−1.04898	+	0.500986i
$334$		−	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
$342$	−10.8284	+	5.17157i	−0.585534	+	0.279647i
$343$		0			0
$344$	11.3137			0.609994
$345$		0			0
$346$	12.0000			0.645124
$347$	−1.41421	−	1.41421i	−0.0759190	−	0.0759190i	0.668128	−	0.744047i	$-0.267096\pi$
$347$	−1.41421	−	1.41421i	−0.0759190	−	0.0759190i	−0.744047	+	0.668128i	$0.767096\pi$
$348$	−0.828427	+	4.82843i	−0.0444084	+	0.258831i
$349$		−	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	−0.778360	−	0.627818i	$-0.783948\pi$
$353$	−2.82843	+	2.82843i	−0.150542	+	0.150542i	0.627818	+	0.778360i	$0.283948\pi$
$354$	−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	$-0.464287\pi$
$359$	4.24264			0.223918			0.111959	+	0.993713i	$0.464287\pi$
$360$	4.82843	−	4.65685i	0.254480	−	0.245438i
$361$	3.00000			0.157895
$362$	−7.07107	−	7.07107i	−0.371647	−	0.371647i
$363$	−11.9497	−	2.05025i	−0.627199	−	0.107610i
$364$		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
$372$	0.292893	−	1.70711i	0.0151858	−	0.0885094i
$373$	−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
$375$	13.5563	−	13.8284i	0.700047	−	0.714097i
$376$	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	−0.992157	−	0.125001i	$-0.960106\pi$
$383$	−16.9706	+	16.9706i	−0.867155	+	0.867155i	0.125001	+	0.992157i	$0.460106\pi$
$384$	−1.41421	+	1.00000i	−0.0721688	+	0.0510310i
$385$		0			0
$386$		−	21.2132i		−	1.07972i
$387$	14.6274	+	30.6274i	0.743553	+	1.55688i
$388$	3.00000	+	3.00000i	0.152302	+	0.152302i
$389$	−22.6274			−1.14726			−0.573628	−	0.819116i	$-0.694464\pi$
$389$	−22.6274			−1.14726			−0.573628	+	0.819116i	$0.694464\pi$
$390$	2.48528	+	16.2426i	0.125847	+	0.822478i
$391$		0			0
$392$	4.94975	+	4.94975i	0.250000	+	0.250000i
$393$	5.79899	−	33.7990i	0.292520	−	1.70493i
$394$			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	$-0.765902\pi$
$401$		−	26.8701i		−	1.34183i	0.741536	−	0.670913i	$-0.234098\pi$
$402$	2.41421	+	0.414214i	0.120410	+	0.0206591i
$403$	3.00000	+	3.00000i	0.149441	+	0.149441i
$404$	18.3848			0.914677
$405$	18.8492	+	7.05025i	0.936626	+	0.350330i
$406$		0			0
$407$	21.2132	+	21.2132i	1.05150	+	1.05150i
$408$	−3.41421	−	0.585786i	−0.169029	−	0.0290008i
$409$		−	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
$417$	−2.34315	+	13.6569i	−0.114744	+	0.668779i
$418$	12.0000	+	12.0000i	0.586939	+	0.586939i
$419$	22.6274			1.10542			0.552711	−	0.833373i	$-0.313593\pi$
$419$	22.6274			1.10542			0.552711	+	0.833373i	$0.313593\pi$
$420$		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
$423$	7.75736	+	16.2426i	0.377176	+	0.789744i
$424$		−	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	$0.0991717\pi$
$431$			12.7279i			0.613082i	−0.951857	+	0.306541i	$0.900828\pi$
$432$	−4.53553	−	2.53553i	−0.218216	−	0.121991i
$433$	−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
$435$	10.8284	−	1.65685i	0.519183	−	0.0794401i
$436$	6.00000			0.287348
$437$		0			0
$438$	0.828427	−	4.82843i	0.0395838	−	0.230711i
$439$		−	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	−0.385272	−	0.922803i	$-0.625893\pi$
$443$	11.3137	−	11.3137i	0.537531	−	0.537531i	0.922803	+	0.385272i	$0.125893\pi$
$444$	−7.07107	−	10.0000i	−0.335578	−	0.474579i
$445$	15.0000	−	5.00000i	0.711068	−	0.237023i
$446$			1.41421i			0.0669650i
$447$	2.41421	+	0.414214i	0.114188	+	0.0195916i
$448$		0			0
$449$	−24.0416			−1.13459			−0.567297	−	0.823513i	$-0.692011\pi$
$449$	−24.0416			−1.13459			−0.567297	+	0.823513i	$0.692011\pi$
$450$	−13.2929	−	6.94975i	−0.626633	−	0.327614i
$451$		0			0
$452$	−4.24264	−	4.24264i	−0.199557	−	0.199557i
$453$	−27.3137	−	4.68629i	−1.28331	−	0.220181i
$454$			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	$-0.672779\pi$
$461$		−	36.7696i		−	1.71253i	0.516538	−	0.856264i	$-0.327221\pi$
$462$		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
$465$	−3.82843	+	0.585786i	−0.177539	+	0.0271652i
$466$	18.0000			0.833834
$467$	25.4558	+	25.4558i	1.17796	+	1.17796i	0.980264	+	0.197692i	$0.0633445\pi$
$467$	25.4558	+	25.4558i	1.17796	+	1.17796i	0.197692	+	0.980264i	$0.436655\pi$
$468$	11.4853	−	5.48528i	0.530907	−	0.253557i
$469$		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
$477$	16.2426	−	7.75736i	0.743699	−	0.355185i
$478$	−8.00000	−	8.00000i	−0.365911	−	0.365911i
$479$	−7.07107			−0.323085			−0.161543	−	0.986866i	$-0.551647\pi$
$479$	−7.07107			−0.323085			−0.161543	+	0.986866i	$0.551647\pi$
$480$	3.12132	+	2.29289i	0.142468	+	0.104656i
$481$	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	$-0.885834\pi$
$491$		−	15.5563i		−	0.702048i	0.936366	−	0.351024i	$-0.114166\pi$
$492$		0			0
$493$	−4.00000	−	4.00000i	−0.180151	−	0.180151i
$494$	16.9706			0.763542
$495$	0.514719	−	28.4558i	0.0231349	−	1.27900i
$496$	1.00000			0.0449013
$497$		0			0
$498$	30.7279	+	5.27208i	1.37695	+	0.236247i
$499$			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	−0.963027	−	0.269404i	$-0.913173\pi$
$503$	−15.5563	+	15.5563i	−0.693623	+	0.693623i	0.269404	+	0.963027i	$0.413173\pi$
$504$		0			0
$505$	−13.0000	−	39.0000i	−0.578492	−	1.73548i
$506$		0			0
$507$	−1.46447	+	8.53553i	−0.0650392	+	0.379076i
$508$	−9.00000	−	9.00000i	−0.399310	−	0.399310i
$509$	−39.5980			−1.75515			−0.877575	−	0.479440i	$-0.840840\pi$
$509$	−39.5980			−1.75515			−0.877575	+	0.479440i	$0.840840\pi$
$510$	1.17157	+	7.65685i	0.0518781	+	0.339051i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	10.1421	−	18.1421i	0.447786	−	0.800995i
$514$		−	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	$0.100258\pi$
$521$			14.1421i			0.619578i	−0.950805	+	0.309789i	$0.899742\pi$
$522$	−3.65685	−	7.65685i	−0.160056	−	0.335131i
$523$	−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
$528$	−1.24264	+	7.24264i	−0.0540790	+	0.315195i
$529$			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
$537$	31.3848	+	5.38478i	1.35435	+	0.232370i
$538$	−2.00000	−	2.00000i	−0.0862261	−	0.0862261i
$539$	29.6985			1.27920
$540$	−2.17157	+	11.4142i	−0.0934496	+	0.491190i
$541$	−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
$543$	17.0711	+	2.92893i	0.732590	+	0.125693i
$544$		−	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
$555$	−16.2132	+	22.0711i	−0.688212	+	0.936865i
$556$	−8.00000			−0.339276
$557$	9.89949	+	9.89949i	0.419455	+	0.419455i	0.885016	−	0.465561i	$-0.154147\pi$
$557$	9.89949	+	9.89949i	0.419455	+	0.419455i	−0.465561	+	0.885016i	$0.654147\pi$
$558$	1.29289	+	2.70711i	0.0547325	+	0.114601i
$559$		−	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	−0.252399	−	0.967623i	$-0.581220\pi$
$563$	16.9706	−	16.9706i	0.715224	−	0.715224i	0.967623	+	0.252399i	$0.0812196\pi$
$564$	−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	$-0.471655\pi$
$569$	4.24264			0.177861			0.0889304	+	0.996038i	$0.471655\pi$
$570$	−9.17157	+	12.4853i	−0.384155	+	0.522951i
$571$	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
$573$	−0.414214	+	2.41421i	−0.0173040	+	0.100855i
$574$		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
$582$	−7.24264	−	1.24264i	−0.300217	−	0.0515091i
$583$	−18.0000	−	18.0000i	−0.745484	−	0.745484i
$584$	2.82843			0.117041
$585$	−19.7574	−	20.4853i	−0.816866	−	0.846962i
$586$	8.00000			0.330477
$587$	−19.7990	−	19.7990i	−0.817192	−	0.817192i	0.168508	−	0.985700i	$-0.446105\pi$
$587$	−19.7990	−	19.7990i	−0.817192	−	0.817192i	−0.985700	+	0.168508i	$0.946105\pi$
$588$	−11.9497	−	2.05025i	−0.492799	−	0.0845510i
$589$			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	−0.0126486	−	0.999920i	$-0.504026\pi$
$593$	24.0416	−	24.0416i	0.987271	−	0.987271i	0.999920	+	0.0126486i	$0.00402627\pi$
$594$	−21.2132	+	6.00000i	−0.870388	+	0.246183i
$595$		0			0
$596$			1.41421i			0.0579284i
$597$	−4.68629	+	27.3137i	−0.191797	+	1.11788i
$598$		0			0
$599$	24.0416			0.982314			0.491157	−	0.871071i	$-0.336574\pi$
$599$	24.0416			0.982314			0.491157	+	0.871071i	$0.336574\pi$
$600$	2.65685	−	8.24264i	0.108466	−	0.336504i
$601$	−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
$603$	−3.82843	+	1.82843i	−0.155906	+	0.0744593i
$604$		−	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
$612$	5.41421	−	2.58579i	0.218857	−	0.104524i
$613$	−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	0.915263	−	0.402856i	$-0.131983\pi$
$617$	12.7279	+	12.7279i	0.512407	+	0.512407i	−0.402856	+	0.915263i	$0.631983\pi$
$618$	4.14214	−	24.1421i	0.166621	−	0.971139i
$619$			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
$627$	−28.9706	−	4.97056i	−1.15697	−	0.198505i
$628$	−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
$633$	−10.2426	−	1.75736i	−0.407108	−	0.0698488i
$634$			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	$0.300502\pi$
$641$			41.0122i			1.61988i	−0.586510	+	0.809942i	$0.699498\pi$
$642$	−1.17157	+	6.82843i	−0.0462383	+	0.269497i
$643$	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
$645$	35.3137	+	25.9411i	1.39048	+	1.02143i
$646$	8.00000			0.314756
$647$	−5.65685	−	5.65685i	−0.222394	−	0.222394i	0.587112	−	0.809506i	$-0.300265\pi$
$647$	−5.65685	−	5.65685i	−0.222394	−	0.222394i	−0.809506	+	0.587112i	$0.800265\pi$
$648$	8.94975	−	0.949747i	0.351579	−	0.0373096i
$649$		−	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	−0.998344	−	0.0575225i	$-0.981680\pi$
$653$	−24.0416	+	24.0416i	−0.940822	+	0.940822i	0.0575225	+	0.998344i	$0.481680\pi$
$654$	−8.48528	+	6.00000i	−0.331801	+	0.234619i
$655$	−14.0000	−	42.0000i	−0.547025	−	1.64108i
$656$		0			0
$657$	3.65685	+	7.65685i	0.142667	+	0.298722i
$658$		0			0
$659$	22.6274			0.881439			0.440720	−	0.897645i	$-0.354723\pi$
$659$	22.6274			0.881439			0.440720	+	0.897645i	$0.354723\pi$
$660$	16.2426	−	2.48528i	0.632244	−	0.0967394i
$661$	−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
$663$	−2.48528	+	14.4853i	−0.0965203	+	0.562562i
$664$			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
$675$	25.7487	−	3.46447i	0.991069	−	0.133347i
$676$	−5.00000			−0.192308
$677$	4.24264	+	4.24264i	0.163058	+	0.163058i	0.783920	−	0.620862i	$-0.213217\pi$
$677$	4.24264	+	4.24264i	0.163058	+	0.163058i	−0.620862	+	0.783920i	$0.713217\pi$
$678$	10.2426	+	1.75736i	0.393366	+	0.0674910i
$679$		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	−0.889616	−	0.456709i	$-0.849028\pi$
$683$	−11.3137	+	11.3137i	−0.432907	+	0.432907i	0.456709	+	0.889616i	$0.349028\pi$
$684$	11.3137	+	4.00000i	0.432590	+	0.152944i
$685$	−36.0000	−	18.0000i	−1.37549	−	0.687745i
$686$		0			0
$687$	−2.92893	+	17.0711i	−0.111746	+	0.651302i
$688$	−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	$-0.717999\pi$
$701$		−	41.0122i		−	1.54901i	0.632568	−	0.774505i	$-0.282001\pi$
$702$	−10.7574	+	19.2426i	−0.406010	+	0.726267i
$703$	20.0000	+	20.0000i	0.754314	+	0.754314i
$704$	−4.24264			−0.159901
$705$	18.7279	+	13.7574i	0.705334	+	0.518132i
$706$	4.00000			0.150542
$707$		0			0
$708$	−1.65685	+	9.65685i	−0.0622684	+	0.362927i
$709$		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
$717$	19.3137	+	3.31371i	0.721284	+	0.123753i
$718$	−3.00000	−	3.00000i	−0.111959	−	0.111959i
$719$	−22.6274			−0.843860			−0.421930	−	0.906628i	$-0.638647\pi$
$719$	−22.6274			−0.843860			−0.421930	+	0.906628i	$0.638647\pi$
$720$	−6.70711	−	0.121320i	−0.249959	−	0.00452134i
$721$		0			0
$722$	−2.12132	−	2.12132i	−0.0789474	−	0.0789474i
$723$	37.5563	+	6.44365i	1.39674	+	0.239642i
$724$			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
$732$	2.34315	−	13.6569i	0.0866052	−	0.504772i
$733$	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
$735$	4.10051	+	26.7990i	0.151249	+	0.988496i
$736$		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	−0.323603	−	0.946193i	$-0.604894\pi$
$743$	16.9706	−	16.9706i	0.622590	−	0.622590i	0.946193	+	0.323603i	$0.104894\pi$
$744$	−1.41421	+	1.00000i	−0.0518476	+	0.0366618i
$745$	3.00000	−	1.00000i	0.109911	−	0.0366372i
$746$			22.6274i			0.828449i
$747$	−48.7279	+	23.2721i	−1.78286	+	0.851481i
$748$	−6.00000	−	6.00000i	−0.219382	−	0.219382i
$749$		0			0
$750$	−19.3640	+	0.192388i	−0.707072	+	0.00702502i
$751$	−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
$753$	−6.21320	+	36.2132i	−0.226422	+	1.31968i
$754$			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	$0.108136\pi$
$761$			18.3848i			0.666448i	−0.942848	+	0.333224i	$0.891864\pi$
$762$	21.7279	+	3.72792i	0.787120	+	0.135048i
$763$		0			0
$764$	−1.41421			−0.0511645
$765$	−9.31371	−	9.65685i	−0.336738	−	0.349144i
$766$	24.0000			0.867155
$767$	−16.9706	−	16.9706i	−0.612772	−	0.612772i
$768$	1.70711	+	0.292893i	0.0615999	+	0.0105689i
$769$			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	−0.0330063	−	0.999455i	$-0.510508\pi$
$773$	26.8701	−	26.8701i	0.966449	−	0.966449i	0.999455	+	0.0330063i	$0.0105082\pi$
$774$	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
$780$	9.72792	−	13.2426i	0.348315	−	0.474163i
$781$	6.00000			0.214697
$782$		0			0
$783$	12.8284	+	7.17157i	0.458451	+	0.256291i
$784$		−	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
$792$	−5.48528	−	11.4853i	−0.194911	−	0.408112i
$793$	24.0000	+	24.0000i	0.852265	+	0.852265i
$794$	−16.9706			−0.602263
$795$	13.7574	−	18.7279i	0.487923	−	0.664211i
$796$	−16.0000			−0.567105
$797$	−32.5269	−	32.5269i	−1.15216	−	1.15216i	−0.986118	−	0.166044i	$-0.946901\pi$
$797$	−32.5269	−	32.5269i	−1.15216	−	1.15216i	−0.166044	−	0.986118i	$-0.553099\pi$
$798$		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
$807$	4.82843	+	0.828427i	0.169969	+	0.0291620i
$808$	−13.0000	−	13.0000i	−0.457338	−	0.457338i
$809$	15.5563			0.546932			0.273466	−	0.961882i	$-0.411830\pi$
$809$	15.5563			0.546932			0.273466	+	0.961882i	$0.411830\pi$
$810$	−8.34315	−	18.3137i	−0.293148	−	0.643478i
$811$	−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
$813$	37.5563	+	6.44365i	1.31716	+	0.225989i
$814$		−	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	$0.0473058\pi$
$821$			8.48528i			0.296138i	−0.988977	+	0.148069i	$0.952694\pi$
$822$	−5.27208	+	30.7279i	−0.183885	+	1.07176i
$823$	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
$825$	−16.7574	−	32.6985i	−0.583416	−	1.13842i
$826$		0			0
$827$	−19.7990	−	19.7990i	−0.688478	−	0.688478i	0.273417	−	0.961896i	$-0.411846\pi$
$827$	−19.7990	−	19.7990i	−0.688478	−	0.688478i	−0.961896	+	0.273417i	$0.911846\pi$
$828$		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
$837$	−4.53553	−	2.53553i	−0.156771	−	0.0876409i
$838$	−16.0000	−	16.0000i	−0.552711	−	0.552711i
$839$	12.7279			0.439417			0.219708	−	0.975566i	$-0.429489\pi$
$839$	12.7279			0.439417			0.219708	+	0.975566i	$0.429489\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$	4.24264	+	4.24264i	0.146211	+	0.146211i
$843$	6.62742	−	38.6274i	0.228260	−	1.33040i
$844$		−	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
$852$	−2.41421	−	0.414214i	−0.0827096	−	0.0141907i
$853$	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
$855$	0.485281	−	26.8284i	0.0165963	−	0.917513i
$856$	−4.00000			−0.136717
$857$	−18.3848	−	18.3848i	−0.628012	−	0.628012i	0.319556	−	0.947568i	$-0.396466\pi$
$857$	−18.3848	−	18.3848i	−0.628012	−	0.628012i	−0.947568	+	0.319556i	$0.896466\pi$
$858$	30.7279	+	5.27208i	1.04903	+	0.179986i
$859$		−	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	−0.958628	−	0.284662i	$-0.908119\pi$
$863$	−19.7990	+	19.7990i	−0.673965	+	0.673965i	0.284662	+	0.958628i	$0.408119\pi$
$864$	1.41421	+	5.00000i	0.0481125	+	0.170103i
$865$	−12.0000	+	24.0000i	−0.408012	+	0.816024i
$866$			36.7696i			1.24948i
$867$	3.80761	−	22.1924i	0.129313	−	0.753693i
$868$		0			0
$869$	42.4264			1.43922
$870$	−8.82843	−	6.48528i	−0.299312	−	0.219872i
$871$	6.00000			0.203302
$872$	−4.24264	−	4.24264i	−0.143674	−	0.143674i
$873$	11.4853	−	5.48528i	0.388718	−	0.185649i
$874$		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	$-0.815416\pi$
$881$		−	32.5269i		−	1.09586i	0.836524	−	0.547930i	$-0.184584\pi$
$882$	18.9497	−	9.05025i	0.638071	−	0.304738i
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$	−8.48528			−0.285391
$885$	21.6569	−	3.31371i	0.727987	−	0.111389i
$886$	−16.0000			−0.537531
$887$	4.24264	+	4.24264i	0.142454	+	0.142454i	0.774737	−	0.632283i	$-0.217882\pi$
$887$	4.24264	+	4.24264i	0.142454	+	0.142454i	−0.632283	+	0.774737i	$0.717882\pi$
$888$	−2.07107	+	12.0711i	−0.0695005	+	0.405079i
$889$		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
$900$	4.48528	+	14.3137i	0.149509	+	0.477124i
$901$	−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	$-0.877698\pi$
$911$		−	22.6274i		−	0.749680i	0.927090	−	0.374840i	$-0.122302\pi$
$912$	−1.17157	+	6.82843i	−0.0387947	+	0.226112i
$913$	54.0000	+	54.0000i	1.78714	+	1.78714i
$914$	11.3137			0.374224
$915$	−30.6274	+	4.68629i	−1.01251	+	0.154924i
$916$	−10.0000			−0.330409
$917$		0			0
$918$	−5.07107	+	9.07107i	−0.167370	+	0.299390i
$919$			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
$927$	18.2843	+	38.2843i	0.600534	+	1.25742i
$928$	2.00000	+	2.00000i	0.0656532	+	0.0656532i
$929$	−55.1543			−1.80955			−0.904777	−	0.425885i	$-0.859963\pi$
$929$	−55.1543			−1.80955			−0.904777	+	0.425885i	$0.859963\pi$
$930$	3.12132	+	2.29289i	0.102352	+	0.0751869i
$931$	28.0000			0.917663
$932$	−12.7279	−	12.7279i	−0.416917	−	0.416917i
$933$	−3.72792	+	21.7279i	−0.122047	+	0.711340i
$934$		−	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	$-0.940963\pi$
$941$		−	11.3137i		−	0.368816i	0.982850	−	0.184408i	$-0.0590368\pi$
$942$	9.65685	+	1.65685i	0.314637	+	0.0539832i
$943$		0			0
$944$	−5.65685			−0.184115
$945$		0			0
$946$	−48.0000			−1.56061
$947$	−19.7990	−	19.7990i	−0.643381	−	0.643381i	0.308004	−	0.951385i	$-0.400339\pi$
$947$	−19.7990	−	19.7990i	−0.643381	−	0.643381i	−0.951385	+	0.308004i	$0.900339\pi$
$948$	−17.0711	−	2.92893i	−0.554443	−	0.0951273i
$949$		−	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	$-0.497495\pi$
$953$	31.1127	−	31.1127i	1.00784	−	1.00784i	0.999969	−	0.00787013i	$-0.00250517\pi$
$954$	−16.9706	−	6.00000i	−0.549442	−	0.194257i
$955$	1.00000	+	3.00000i	0.0323592	+	0.0970777i
$956$			11.3137i			0.365911i
$957$	3.51472	−	20.4853i	0.113615	−	0.662195i
$958$	5.00000	+	5.00000i	0.161543	+	0.161543i
$959$		0			0
$960$	−0.585786	−	3.82843i	−0.0189062	−	0.123562i
$961$	1.00000			0.0322581
$962$	−21.2132	−	21.2132i	−0.683941	−	0.683941i
$963$	−5.17157	−	10.8284i	−0.166652	−	0.348941i
$964$			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	$0.219156\pi$
$971$			39.5980i			1.27076i	−0.772200	+	0.635380i	$0.780844\pi$
$972$	−11.7071	+	10.2929i	−0.375506	+	0.330145i
$973$		0			0
$974$	−21.2132			−0.679715
$975$	−34.9706	−	11.2721i	−1.11995	−	0.360995i
$976$	8.00000			0.256074
$977$	−7.07107	−	7.07107i	−0.226224	−	0.226224i	0.584889	−	0.811113i	$-0.301138\pi$
$977$	−7.07107	−	7.07107i	−0.226224	−	0.226224i	−0.811113	+	0.584889i	$0.801138\pi$
$978$	−4.55635	+	26.5563i	−0.145696	+	0.849178i
$979$		−	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	−0.660560	−	0.750773i	$-0.729681\pi$
$983$	2.82843	−	2.82843i	0.0902128	−	0.0902128i	0.750773	+	0.660560i	$0.229681\pi$
$984$		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
$990$	−20.4853	+	19.7574i	−0.651065	+	0.627930i
$991$	−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
$993$	−47.7990	−	8.20101i	−1.51686	−	0.260251i
$994$		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.683.1	yes	4
3.2	odd	2	inner	930.2.j.a.683.2	yes	4
5.2	odd	4	inner	930.2.j.a.497.2	yes	4
15.2	even	4	inner	930.2.j.a.497.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.a.497.1	✓	4	15.2	even	4	inner
930.2.j.a.497.2	yes	4	5.2	odd	4	inner
930.2.j.a.683.1	yes	4	1.1	even	1	trivial
930.2.j.a.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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.70711 + 0.292893i) q^{3} +1.00000i q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(0.707107 - 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.70711 + 0.292893i) 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} +(-0.292893 + 1.70711i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(3.82843 - 0.585786i) q^{15} -1.00000 q^{16} +(-1.41421 - 1.41421i) q^{17} +(-1.29289 - 2.70711i) 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} +(4.53553 + 2.53553i) q^{27} +2.82843 q^{29} +(-3.12132 - 2.29289i) q^{30} -1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(1.24264 - 7.24264i) 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} +(6.70711 + 0.121320i) q^{45} +(4.24264 + 4.24264i) q^{47} +(-1.70711 - 0.292893i) 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} +(1.17157 - 6.82843i) q^{57} +(-2.00000 - 2.00000i) q^{58} +5.65685 q^{59} +(0.585786 + 3.82843i) 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} +(2.70711 - 1.29289i) q^{72} +(2.00000 + 2.00000i) q^{73} +7.07107 q^{74} +(7.70711 - 3.94975i) q^{75} +4.00000 q^{76} +(-1.24264 + 7.24264i) 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} +(4.82843 + 0.828427i) q^{87} +(-3.00000 - 3.00000i) q^{88} +7.07107 q^{89} +(-4.65685 - 4.82843i) q^{90} +(-1.70711 - 0.292893i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{6}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^6	\( 4 q + 4 q^{3} - 4 q^{6} - 8 q^{10} - 4 q^{12} - 12 q^{13} + 4 q^{15} - 4 q^{16} - 8 q^{18} - 12 q^{22} + 16 q^{25} + 4 q^{27} - 4 q^{30} - 4 q^{31} - 12 q^{33} - 4 q^{36} - 20 q^{37} + 4 q^{40} + 32 q^{43} + 24 q^{45} - 4 q^{48} - 8 q^{51} + 12 q^{52} - 12 q^{55} + 16 q^{57} - 8 q^{58} + 8 q^{60} - 32 q^{61} - 24 q^{66} - 4 q^{67} + 8 q^{72} + 8 q^{73} + 28 q^{75} + 16 q^{76} + 12 q^{78} + 28 q^{81} - 16 q^{85} + 8 q^{87} - 12 q^{88} + 4 q^{90} - 4 q^{93} + 4 q^{96} + 12 q^{97}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more