LMFDB - Embedded newform 39.2.f.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,2,Mod(5,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("39.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	39.f (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:	$0.311416567883$
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			8.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	39.8
Dual form			39.2.f.a.5.2

$q$-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} +(-1.00000 - 1.41421i) q^{3} +1.00000i q^{4} +(-1.41421 + 1.41421i) q^{5} +(-1.70711 - 0.292893i) q^{6} +(1.00000 - 1.00000i) q^{7} +(2.12132 + 2.12132i) q^{8} +(-1.00000 + 2.82843i) q^{9} +2.00000i q^{10} +(-2.82843 - 2.82843i) q^{11} +(1.41421 - 1.00000i) q^{12} +(-2.00000 - 3.00000i) q^{13} -1.41421i q^{14} +(3.41421 + 0.585786i) q^{15} +1.00000 q^{16} +(1.29289 + 2.70711i) q^{18} +(1.00000 + 1.00000i) q^{19} +(-1.41421 - 1.41421i) q^{20} +(-2.41421 - 0.414214i) q^{21} -4.00000 q^{22} +8.48528 q^{23} +(0.878680 - 5.12132i) q^{24} +1.00000i q^{25} +(-3.53553 - 0.707107i) q^{26} +(5.00000 - 1.41421i) q^{27} +(1.00000 + 1.00000i) q^{28} +2.82843i q^{29} +(2.82843 - 2.00000i) q^{30} +(-5.00000 - 5.00000i) q^{31} +(-3.53553 + 3.53553i) q^{32} +(-1.17157 + 6.82843i) q^{33} +2.82843i q^{35} +(-2.82843 - 1.00000i) q^{36} +(1.00000 - 1.00000i) q^{37} +1.41421 q^{38} +(-2.24264 + 5.82843i) q^{39} -6.00000 q^{40} +(-1.41421 + 1.41421i) q^{41} +(-2.00000 + 1.41421i) q^{42} +6.00000i q^{43} +(2.82843 - 2.82843i) q^{44} +(-2.58579 - 5.41421i) q^{45} +(6.00000 - 6.00000i) q^{46} +(-2.82843 - 2.82843i) q^{47} +(-1.00000 - 1.41421i) q^{48} +5.00000i q^{49} +(0.707107 + 0.707107i) q^{50} +(3.00000 - 2.00000i) q^{52} -5.65685i q^{53} +(2.53553 - 4.53553i) q^{54} +8.00000 q^{55} +4.24264 q^{56} +(0.414214 - 2.41421i) q^{57} +(2.00000 + 2.00000i) q^{58} +(-2.82843 - 2.82843i) q^{59} +(-0.585786 + 3.41421i) q^{60} +8.00000 q^{61} -7.07107 q^{62} +(1.82843 + 3.82843i) q^{63} +7.00000i q^{64} +(7.07107 + 1.41421i) q^{65} +(4.00000 + 5.65685i) q^{66} +(-5.00000 - 5.00000i) q^{67} +(-8.48528 - 12.0000i) q^{69} +(2.00000 + 2.00000i) q^{70} +(2.82843 - 2.82843i) q^{71} +(-8.12132 + 3.87868i) q^{72} +(1.00000 - 1.00000i) q^{73} -1.41421i q^{74} +(1.41421 - 1.00000i) q^{75} +(-1.00000 + 1.00000i) q^{76} -5.65685 q^{77} +(2.53553 + 5.70711i) q^{78} -10.0000 q^{79} +(-1.41421 + 1.41421i) q^{80} +(-7.00000 - 5.65685i) q^{81} +2.00000i q^{82} +(-5.65685 + 5.65685i) q^{83} +(0.414214 - 2.41421i) q^{84} +(4.24264 + 4.24264i) q^{86} +(4.00000 - 2.82843i) q^{87} -12.0000i q^{88} +(9.89949 + 9.89949i) q^{89} +(-5.65685 - 2.00000i) q^{90} +(-5.00000 - 1.00000i) q^{91} +8.48528i q^{92} +(-2.07107 + 12.0711i) q^{93} -4.00000 q^{94} -2.82843 q^{95} +(8.53553 + 1.46447i) q^{96} +(7.00000 + 7.00000i) q^{97} +(3.53553 + 3.53553i) q^{98} +(10.8284 - 5.17157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 4 q^{6} + 4 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 4 q^{16} + 8 q^{18} + 4 q^{19} - 4 q^{21} - 16 q^{22} + 12 q^{24} + 20 q^{27} + 4 q^{28} - 20 q^{31} - 16 q^{33} + 4 q^{37} + 8 q^{39}+ \cdots + 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 4 * q^6 + 4 * q^7 - 4 * q^9 - 8 * q^13 + 8 * q^15 + 4 * q^16 + 8 * q^18 + 4 * q^19 - 4 * q^21 - 16 * q^22 + 12 * q^24 + 20 * q^27 + 4 * q^28 - 20 * q^31 - 16 * q^33 + 4 * q^37 + 8 * q^39 - 24 * q^40 - 8 * q^42 - 16 * q^45 + 24 * q^46 - 4 * q^48 + 12 * q^52 - 4 * q^54 + 32 * q^55 - 4 * q^57 + 8 * q^58 - 8 * q^60 + 32 * q^61 - 4 * q^63 + 16 * q^66 - 20 * q^67 + 8 * q^70 - 24 * q^72 + 4 * q^73 - 4 * q^76 - 4 * q^78 - 40 * q^79 - 28 * q^81 - 4 * q^84 + 16 * q^87 - 20 * q^91 + 20 * q^93 - 16 * q^94 + 20 * q^96 + 28 * q^97 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i	−0.411438	−	0.911438i	$-0.634973\pi$
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i	0.911438	+	0.411438i	$0.134973\pi$
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$4$			1.00000i			0.500000i
$5$	−1.41421	+	1.41421i	−0.632456	+	0.632456i	−0.948683	−	0.316228i	$-0.897584\pi$
$5$	−1.41421	+	1.41421i	−0.632456	+	0.632456i	0.316228	+	0.948683i	$0.397584\pi$
$6$	−1.70711	−	0.292893i	−0.696923	−	0.119573i
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	−0.492403	−	0.870367i	$-0.663881\pi$
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	0.870367	+	0.492403i	$0.163881\pi$
$8$	2.12132	+	2.12132i	0.750000	+	0.750000i
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$			2.00000i			0.632456i
$11$	−2.82843	−	2.82843i	−0.852803	−	0.852803i	0.137675	−	0.990478i	$-0.456037\pi$
$11$	−2.82843	−	2.82843i	−0.852803	−	0.852803i	−0.990478	+	0.137675i	$0.956037\pi$
$12$	1.41421	−	1.00000i	0.408248	−	0.288675i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$14$		−	1.41421i		−	0.377964i
$15$	3.41421	+	0.585786i	0.881546	+	0.151249i
$16$	1.00000			0.250000
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	1.29289	+	2.70711i	0.304738	+	0.638071i
$19$	1.00000	+	1.00000i	0.229416	+	0.229416i	0.812449	−	0.583033i	$-0.198134\pi$
$19$	1.00000	+	1.00000i	0.229416	+	0.229416i	−0.583033	+	0.812449i	$0.698134\pi$
$20$	−1.41421	−	1.41421i	−0.316228	−	0.316228i
$21$	−2.41421	−	0.414214i	−0.526825	−	0.0903888i
$22$	−4.00000			−0.852803
$23$	8.48528			1.76930			0.884652	−	0.466252i	$-0.154396\pi$
$23$	8.48528			1.76930			0.884652	+	0.466252i	$0.154396\pi$
$24$	0.878680	−	5.12132i	0.179360	−	1.04539i
$25$			1.00000i			0.200000i
$26$	−3.53553	−	0.707107i	−0.693375	−	0.138675i
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$	1.00000	+	1.00000i	0.188982	+	0.188982i
$29$			2.82843i			0.525226i	0.964901	+	0.262613i	$0.0845842\pi$
$29$			2.82843i			0.525226i	−0.964901	+	0.262613i	$0.915416\pi$
$30$	2.82843	−	2.00000i	0.516398	−	0.365148i
$31$	−5.00000	−	5.00000i	−0.898027	−	0.898027i	0.0972349	−	0.995261i	$-0.469000\pi$
$31$	−5.00000	−	5.00000i	−0.898027	−	0.898027i	−0.995261	+	0.0972349i	$0.969000\pi$
$32$	−3.53553	+	3.53553i	−0.625000	+	0.625000i
$33$	−1.17157	+	6.82843i	−0.203945	+	1.18868i
$34$		0			0
$35$			2.82843i			0.478091i
$36$	−2.82843	−	1.00000i	−0.471405	−	0.166667i
$37$	1.00000	−	1.00000i	0.164399	−	0.164399i	−0.620113	−	0.784512i	$-0.712913\pi$
$37$	1.00000	−	1.00000i	0.164399	−	0.164399i	0.784512	+	0.620113i	$0.212913\pi$
$38$	1.41421			0.229416
$39$	−2.24264	+	5.82843i	−0.359110	+	0.933295i
$40$	−6.00000			−0.948683
$41$	−1.41421	+	1.41421i	−0.220863	+	0.220863i	−0.808862	−	0.587999i	$-0.799916\pi$
$41$	−1.41421	+	1.41421i	−0.220863	+	0.220863i	0.587999	+	0.808862i	$0.299916\pi$
$42$	−2.00000	+	1.41421i	−0.308607	+	0.218218i
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$	2.82843	−	2.82843i	0.426401	−	0.426401i
$45$	−2.58579	−	5.41421i	−0.385466	−	0.807103i
$46$	6.00000	−	6.00000i	0.884652	−	0.884652i
$47$	−2.82843	−	2.82843i	−0.412568	−	0.412568i	0.470064	−	0.882632i	$-0.344231\pi$
$47$	−2.82843	−	2.82843i	−0.412568	−	0.412568i	−0.882632	+	0.470064i	$0.844231\pi$
$48$	−1.00000	−	1.41421i	−0.144338	−	0.204124i
$49$			5.00000i			0.714286i
$50$	0.707107	+	0.707107i	0.100000	+	0.100000i
$51$		0			0
$52$	3.00000	−	2.00000i	0.416025	−	0.277350i
$53$		−	5.65685i		−	0.777029i	−0.921443	−	0.388514i	$-0.872988\pi$
$53$		−	5.65685i		−	0.777029i	0.921443	−	0.388514i	$-0.127012\pi$
$54$	2.53553	−	4.53553i	0.345042	−	0.617208i
$55$	8.00000			1.07872
$56$	4.24264			0.566947
$57$	0.414214	−	2.41421i	0.0548639	−	0.319770i
$58$	2.00000	+	2.00000i	0.262613	+	0.262613i
$59$	−2.82843	−	2.82843i	−0.368230	−	0.368230i	0.498601	−	0.866831i	$-0.333847\pi$
$59$	−2.82843	−	2.82843i	−0.368230	−	0.368230i	−0.866831	+	0.498601i	$0.833847\pi$
$60$	−0.585786	+	3.41421i	−0.0756247	+	0.440773i
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$	−7.07107			−0.898027
$63$	1.82843	+	3.82843i	0.230360	+	0.482336i
$64$			7.00000i			0.875000i
$65$	7.07107	+	1.41421i	0.877058	+	0.175412i
$66$	4.00000	+	5.65685i	0.492366	+	0.696311i
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	0.332320	−	0.943167i	$-0.392169\pi$
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	−0.943167	+	0.332320i	$0.892169\pi$
$68$		0			0
$69$	−8.48528	−	12.0000i	−1.02151	−	1.44463i
$70$	2.00000	+	2.00000i	0.239046	+	0.239046i
$71$	2.82843	−	2.82843i	0.335673	−	0.335673i	−0.519063	−	0.854736i	$-0.673719\pi$
$71$	2.82843	−	2.82843i	0.335673	−	0.335673i	0.854736	+	0.519063i	$0.173719\pi$
$72$	−8.12132	+	3.87868i	−0.957107	+	0.457107i
$73$	1.00000	−	1.00000i	0.117041	−	0.117041i	−0.646160	−	0.763202i	$-0.723626\pi$
$73$	1.00000	−	1.00000i	0.117041	−	0.117041i	0.763202	+	0.646160i	$0.223626\pi$
$74$		−	1.41421i		−	0.164399i
$75$	1.41421	−	1.00000i	0.163299	−	0.115470i
$76$	−1.00000	+	1.00000i	−0.114708	+	0.114708i
$77$	−5.65685			−0.644658
$78$	2.53553	+	5.70711i	0.287093	+	0.646203i
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	−1.41421	+	1.41421i	−0.158114	+	0.158114i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$			2.00000i			0.220863i
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	−0.945767	−	0.324846i	$-0.894687\pi$
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	0.324846	+	0.945767i	$0.394687\pi$
$84$	0.414214	−	2.41421i	0.0451944	−	0.263412i
$85$		0			0
$86$	4.24264	+	4.24264i	0.457496	+	0.457496i
$87$	4.00000	−	2.82843i	0.428845	−	0.303239i
$88$		−	12.0000i		−	1.27920i
$89$	9.89949	+	9.89949i	1.04934	+	1.04934i	0.998718	+	0.0506267i	$0.0161219\pi$
$89$	9.89949	+	9.89949i	1.04934	+	1.04934i	0.0506267	+	0.998718i	$0.483878\pi$
$90$	−5.65685	−	2.00000i	−0.596285	−	0.210819i
$91$	−5.00000	−	1.00000i	−0.524142	−	0.104828i
$92$			8.48528i			0.884652i
$93$	−2.07107	+	12.0711i	−0.214760	+	1.25171i
$94$	−4.00000			−0.412568
$95$	−2.82843			−0.290191
$96$	8.53553	+	1.46447i	0.871154	+	0.149466i
$97$	7.00000	+	7.00000i	0.710742	+	0.710742i	0.966691	−	0.255948i	$-0.0823876\pi$
$97$	7.00000	+	7.00000i	0.710742	+	0.710742i	−0.255948	+	0.966691i	$0.582388\pi$
$98$	3.53553	+	3.53553i	0.357143	+	0.357143i
$99$	10.8284	−	5.17157i	1.08830	−	0.519763i
$100$	−1.00000			−0.100000
$101$	−8.48528			−0.844317			−0.422159	−	0.906522i	$-0.638727\pi$
$101$	−8.48528			−0.844317			−0.422159	+	0.906522i	$0.638727\pi$
$102$		0			0
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	2.12132	−	10.6066i	0.208013	−	1.04006i
$105$	4.00000	−	2.82843i	0.390360	−	0.276026i
$106$	−4.00000	−	4.00000i	−0.388514	−	0.388514i
$107$		−	5.65685i		−	0.546869i	−0.961891	−	0.273434i	$-0.911840\pi$
$107$		−	5.65685i		−	0.546869i	0.961891	−	0.273434i	$-0.0881596\pi$
$108$	1.41421	+	5.00000i	0.136083	+	0.481125i
$109$	1.00000	+	1.00000i	0.0957826	+	0.0957826i	0.753374	−	0.657592i	$-0.228425\pi$
$109$	1.00000	+	1.00000i	0.0957826	+	0.0957826i	−0.657592	+	0.753374i	$0.728425\pi$
$110$	5.65685	−	5.65685i	0.539360	−	0.539360i
$111$	−2.41421	−	0.414214i	−0.229147	−	0.0393154i
$112$	1.00000	−	1.00000i	0.0944911	−	0.0944911i
$113$		−	14.1421i		−	1.33038i	−0.746674	−	0.665190i	$-0.768350\pi$
$113$		−	14.1421i		−	1.33038i	0.746674	−	0.665190i	$-0.231650\pi$
$114$	−1.41421	−	2.00000i	−0.132453	−	0.187317i
$115$	−12.0000	+	12.0000i	−1.11901	+	1.11901i
$116$	−2.82843			−0.262613
$117$	10.4853	−	2.65685i	0.969365	−	0.245626i
$118$	−4.00000			−0.368230
$119$		0			0
$120$	6.00000	+	8.48528i	0.547723	+	0.774597i
$121$			5.00000i			0.454545i
$122$	5.65685	−	5.65685i	0.512148	−	0.512148i
$123$	3.41421	+	0.585786i	0.307849	+	0.0528186i
$124$	5.00000	−	5.00000i	0.449013	−	0.449013i
$125$	−8.48528	−	8.48528i	−0.758947	−	0.758947i
$126$	4.00000	+	1.41421i	0.356348	+	0.125988i
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−2.12132	−	2.12132i	−0.187500	−	0.187500i
$129$	8.48528	−	6.00000i	0.747087	−	0.528271i
$130$	6.00000	−	4.00000i	0.526235	−	0.350823i
$131$			11.3137i			0.988483i	0.869325	+	0.494242i	$0.164554\pi$
$131$			11.3137i			0.988483i	−0.869325	+	0.494242i	$0.835446\pi$
$132$	−6.82843	−	1.17157i	−0.594338	−	0.101972i
$133$	2.00000			0.173422
$134$	−7.07107			−0.610847
$135$	−5.07107	+	9.07107i	−0.436448	+	0.780713i
$136$		0			0
$137$	9.89949	+	9.89949i	0.845771	+	0.845771i	0.989602	−	0.143831i	$-0.0459423\pi$
$137$	9.89949	+	9.89949i	0.845771	+	0.845771i	−0.143831	+	0.989602i	$0.545942\pi$
$138$	−14.4853	−	2.48528i	−1.23307	−	0.211561i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−2.82843			−0.239046
$141$	−1.17157	+	6.82843i	−0.0986642	+	0.575057i
$142$		−	4.00000i		−	0.335673i
$143$	−2.82843	+	14.1421i	−0.236525	+	1.18262i
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$	−4.00000	−	4.00000i	−0.332182	−	0.332182i
$146$		−	1.41421i		−	0.117041i
$147$	7.07107	−	5.00000i	0.583212	−	0.412393i
$148$	1.00000	+	1.00000i	0.0821995	+	0.0821995i
$149$	−1.41421	+	1.41421i	−0.115857	+	0.115857i	−0.762658	−	0.646802i	$-0.776106\pi$
$149$	−1.41421	+	1.41421i	−0.115857	+	0.115857i	0.646802	+	0.762658i	$0.276106\pi$
$150$	0.292893	−	1.70711i	0.0239146	−	0.139385i
$151$	1.00000	−	1.00000i	0.0813788	−	0.0813788i	−0.665246	−	0.746625i	$-0.731673\pi$
$151$	1.00000	−	1.00000i	0.0813788	−	0.0813788i	0.746625	+	0.665246i	$0.231673\pi$
$152$			4.24264i			0.344124i
$153$		0			0
$154$	−4.00000	+	4.00000i	−0.322329	+	0.322329i
$155$	14.1421			1.13592
$156$	−5.82843	−	2.24264i	−0.466648	−	0.179555i
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−7.07107	+	7.07107i	−0.562544	+	0.562544i
$159$	−8.00000	+	5.65685i	−0.634441	+	0.448618i
$160$		−	10.0000i		−	0.790569i
$161$	8.48528	−	8.48528i	0.668734	−	0.668734i
$162$	−8.94975	+	0.949747i	−0.703159	+	0.0746192i
$163$	1.00000	−	1.00000i	0.0783260	−	0.0783260i	−0.666858	−	0.745184i	$-0.732361\pi$
$163$	1.00000	−	1.00000i	0.0783260	−	0.0783260i	0.745184	+	0.666858i	$0.232361\pi$
$164$	−1.41421	−	1.41421i	−0.110432	−	0.110432i
$165$	−8.00000	−	11.3137i	−0.622799	−	0.880771i
$166$			8.00000i			0.620920i
$167$	−2.82843	−	2.82843i	−0.218870	−	0.218870i	0.589152	−	0.808022i	$-0.299462\pi$
$167$	−2.82843	−	2.82843i	−0.218870	−	0.218870i	−0.808022	+	0.589152i	$0.799462\pi$
$168$	−4.24264	−	6.00000i	−0.327327	−	0.462910i
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$		0			0
$171$	−3.82843	+	1.82843i	−0.292767	+	0.139823i
$172$	−6.00000			−0.457496
$173$	−8.48528			−0.645124			−0.322562	−	0.946548i	$-0.604544\pi$
$173$	−8.48528			−0.645124			−0.322562	+	0.946548i	$0.604544\pi$
$174$	0.828427	−	4.82843i	0.0628029	−	0.366042i
$175$	1.00000	+	1.00000i	0.0755929	+	0.0755929i
$176$	−2.82843	−	2.82843i	−0.213201	−	0.213201i
$177$	−1.17157	+	6.82843i	−0.0880608	+	0.513256i
$178$	14.0000			1.04934
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	5.41421	−	2.58579i	0.403552	−	0.192733i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	−4.24264	+	2.82843i	−0.314485	+	0.209657i
$183$	−8.00000	−	11.3137i	−0.591377	−	0.836333i
$184$	18.0000	+	18.0000i	1.32698	+	1.32698i
$185$			2.82843i			0.207950i
$186$	7.07107	+	10.0000i	0.518476	+	0.733236i
$187$		0			0
$188$	2.82843	−	2.82843i	0.206284	−	0.206284i
$189$	3.58579	−	6.41421i	0.260828	−	0.466565i
$190$	−2.00000	+	2.00000i	−0.145095	+	0.145095i
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$	9.89949	−	7.00000i	0.714435	−	0.505181i
$193$	19.0000	−	19.0000i	1.36765	−	1.36765i	0.503871	−	0.863779i	$-0.331909\pi$
$193$	19.0000	−	19.0000i	1.36765	−	1.36765i	0.863779	−	0.503871i	$-0.168091\pi$
$194$	9.89949			0.710742
$195$	−5.07107	−	11.4142i	−0.363147	−	0.817389i
$196$	−5.00000			−0.357143
$197$	15.5563	−	15.5563i	1.10834	−	1.10834i	0.114976	−	0.993368i	$-0.463321\pi$
$197$	15.5563	−	15.5563i	1.10834	−	1.10834i	0.993368	−	0.114976i	$-0.0366790\pi$
$198$	4.00000	−	11.3137i	0.284268	−	0.804030i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−2.12132	+	2.12132i	−0.150000	+	0.150000i
$201$	−2.07107	+	12.0711i	−0.146082	+	0.851427i
$202$	−6.00000	+	6.00000i	−0.422159	+	0.422159i
$203$	2.82843	+	2.82843i	0.198517	+	0.198517i
$204$		0			0
$205$		−	4.00000i		−	0.279372i
$206$	−4.24264	−	4.24264i	−0.295599	−	0.295599i
$207$	−8.48528	+	24.0000i	−0.589768	+	1.66812i
$208$	−2.00000	−	3.00000i	−0.138675	−	0.208013i
$209$		−	5.65685i		−	0.391293i
$210$	0.828427	−	4.82843i	0.0571669	−	0.333193i
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	5.65685			0.388514
$213$	−6.82843	−	1.17157i	−0.467876	−	0.0802749i
$214$	−4.00000	−	4.00000i	−0.273434	−	0.273434i
$215$	−8.48528	−	8.48528i	−0.578691	−	0.578691i
$216$	13.6066	+	7.60660i	0.925812	+	0.517564i
$217$	−10.0000			−0.678844
$218$	1.41421			0.0957826
$219$	−2.41421	−	0.414214i	−0.163137	−	0.0279900i
$220$			8.00000i			0.539360i
$221$		0			0
$222$	−2.00000	+	1.41421i	−0.134231	+	0.0949158i
$223$	−11.0000	−	11.0000i	−0.736614	−	0.736614i	0.235307	−	0.971921i	$-0.424391\pi$
$223$	−11.0000	−	11.0000i	−0.736614	−	0.736614i	−0.971921	+	0.235307i	$0.924391\pi$
$224$			7.07107i			0.472456i
$225$	−2.82843	−	1.00000i	−0.188562	−	0.0666667i
$226$	−10.0000	−	10.0000i	−0.665190	−	0.665190i
$227$	−5.65685	+	5.65685i	−0.375459	+	0.375459i	−0.869461	−	0.494002i	$-0.835534\pi$
$227$	−5.65685	+	5.65685i	−0.375459	+	0.375459i	0.494002	+	0.869461i	$0.335534\pi$
$228$	2.41421	+	0.414214i	0.159885	+	0.0274320i
$229$	1.00000	−	1.00000i	0.0660819	−	0.0660819i	−0.673293	−	0.739375i	$-0.735121\pi$
$229$	1.00000	−	1.00000i	0.0660819	−	0.0660819i	0.739375	+	0.673293i	$0.235121\pi$
$230$			16.9706i			1.11901i
$231$	5.65685	+	8.00000i	0.372194	+	0.526361i
$232$	−6.00000	+	6.00000i	−0.393919	+	0.393919i
$233$	−25.4558			−1.66767			−0.833834	−	0.552015i	$-0.813859\pi$
$233$	−25.4558			−1.66767			−0.833834	+	0.552015i	$0.813859\pi$
$234$	5.53553	−	9.29289i	0.361869	−	0.607495i
$235$	8.00000			0.521862
$236$	2.82843	−	2.82843i	0.184115	−	0.184115i
$237$	10.0000	+	14.1421i	0.649570	+	0.918630i
$238$		0			0
$239$	−14.1421	+	14.1421i	−0.914779	+	0.914779i	−0.996643	−	0.0818647i	$-0.973912\pi$
$239$	−14.1421	+	14.1421i	−0.914779	+	0.914779i	0.0818647	+	0.996643i	$0.473912\pi$
$240$	3.41421	+	0.585786i	0.220387	+	0.0378124i
$241$	−17.0000	+	17.0000i	−1.09507	+	1.09507i	−0.100088	+	0.994979i	$0.531912\pi$
$241$	−17.0000	+	17.0000i	−1.09507	+	1.09507i	−0.994979	+	0.100088i	$0.968088\pi$
$242$	3.53553	+	3.53553i	0.227273	+	0.227273i
$243$	−1.00000	+	15.5563i	−0.0641500	+	0.997940i
$244$			8.00000i			0.512148i
$245$	−7.07107	−	7.07107i	−0.451754	−	0.451754i
$246$	2.82843	−	2.00000i	0.180334	−	0.127515i
$247$	1.00000	−	5.00000i	0.0636285	−	0.318142i
$248$		−	21.2132i		−	1.34704i
$249$	13.6569	+	2.34315i	0.865468	+	0.148491i
$250$	−12.0000			−0.758947
$251$	25.4558			1.60676			0.803379	−	0.595468i	$-0.203033\pi$
$251$	25.4558			1.60676			0.803379	+	0.595468i	$0.203033\pi$
$252$	−3.82843	+	1.82843i	−0.241168	+	0.115180i
$253$	−24.0000	−	24.0000i	−1.50887	−	1.50887i
$254$		0			0
$255$		0			0
$256$	−17.0000			−1.06250
$257$	8.48528			0.529297			0.264649	−	0.964345i	$-0.414744\pi$
$257$	8.48528			0.529297			0.264649	+	0.964345i	$0.414744\pi$
$258$	1.75736	−	10.2426i	0.109408	−	0.637679i
$259$		−	2.00000i		−	0.124274i
$260$	−1.41421	+	7.07107i	−0.0877058	+	0.438529i
$261$	−8.00000	−	2.82843i	−0.495188	−	0.175075i
$262$	8.00000	+	8.00000i	0.494242	+	0.494242i
$263$		−	22.6274i		−	1.39527i	−0.716455	−	0.697633i	$-0.754237\pi$
$263$		−	22.6274i		−	1.39527i	0.716455	−	0.697633i	$-0.245763\pi$
$264$	−16.9706	+	12.0000i	−1.04447	+	0.738549i
$265$	8.00000	+	8.00000i	0.491436	+	0.491436i
$266$	1.41421	−	1.41421i	0.0867110	−	0.0867110i
$267$	4.10051	−	23.8995i	0.250947	−	1.46263i
$268$	5.00000	−	5.00000i	0.305424	−	0.305424i
$269$			19.7990i			1.20717i	0.797300	+	0.603583i	$0.206261\pi$
$269$			19.7990i			1.20717i	−0.797300	+	0.603583i	$0.793739\pi$
$270$	2.82843	+	10.0000i	0.172133	+	0.608581i
$271$	19.0000	−	19.0000i	1.15417	−	1.15417i	0.168459	−	0.985709i	$-0.446121\pi$
$271$	19.0000	−	19.0000i	1.15417	−	1.15417i	0.985709	−	0.168459i	$-0.0538791\pi$
$272$		0			0
$273$	3.58579	+	8.07107i	0.217022	+	0.488483i
$274$	14.0000			0.845771
$275$	2.82843	−	2.82843i	0.170561	−	0.170561i
$276$	12.0000	−	8.48528i	0.722315	−	0.510754i
$277$		−	12.0000i		−	0.721010i	−0.932757	−	0.360505i	$-0.882604\pi$
$277$		−	12.0000i		−	0.721010i	0.932757	−	0.360505i	$-0.117396\pi$
$278$	−2.82843	+	2.82843i	−0.169638	+	0.169638i
$279$	19.1421	−	9.14214i	1.14601	−	0.547325i
$280$	−6.00000	+	6.00000i	−0.358569	+	0.358569i
$281$	9.89949	+	9.89949i	0.590554	+	0.590554i	0.937781	−	0.347227i	$-0.112877\pi$
$281$	9.89949	+	9.89949i	0.590554	+	0.590554i	−0.347227	+	0.937781i	$0.612877\pi$
$282$	4.00000	+	5.65685i	0.238197	+	0.336861i
$283$			12.0000i			0.713326i	0.934233	+	0.356663i	$0.116086\pi$
$283$			12.0000i			0.713326i	−0.934233	+	0.356663i	$0.883914\pi$
$284$	2.82843	+	2.82843i	0.167836	+	0.167836i
$285$	2.82843	+	4.00000i	0.167542	+	0.236940i
$286$	8.00000	+	12.0000i	0.473050	+	0.709575i
$287$			2.82843i			0.166957i
$288$	−6.46447	−	13.5355i	−0.380922	−	0.797589i
$289$	−17.0000			−1.00000
$290$	−5.65685			−0.332182
$291$	2.89949	−	16.8995i	0.169971	−	0.990666i
$292$	1.00000	+	1.00000i	0.0585206	+	0.0585206i
$293$	9.89949	+	9.89949i	0.578335	+	0.578335i	0.934444	−	0.356110i	$-0.115897\pi$
$293$	9.89949	+	9.89949i	0.578335	+	0.578335i	−0.356110	+	0.934444i	$0.615897\pi$
$294$	1.46447	−	8.53553i	0.0854094	−	0.497802i
$295$	8.00000			0.465778
$296$	4.24264			0.246598
$297$	−18.1421	−	10.1421i	−1.05271	−	0.588506i
$298$			2.00000i			0.115857i
$299$	−16.9706	−	25.4558i	−0.981433	−	1.47215i
$300$	1.00000	+	1.41421i	0.0577350	+	0.0816497i
$301$	6.00000	+	6.00000i	0.345834	+	0.345834i
$302$		−	1.41421i		−	0.0813788i
$303$	8.48528	+	12.0000i	0.487467	+	0.689382i
$304$	1.00000	+	1.00000i	0.0573539	+	0.0573539i
$305$	−11.3137	+	11.3137i	−0.647821	+	0.647821i
$306$		0			0
$307$	−17.0000	+	17.0000i	−0.970241	+	0.970241i	−0.999570	−	0.0293286i	$-0.990663\pi$
$307$	−17.0000	+	17.0000i	−0.970241	+	0.970241i	0.0293286	+	0.999570i	$0.490663\pi$
$308$		−	5.65685i		−	0.322329i
$309$	−8.48528	+	6.00000i	−0.482711	+	0.341328i
$310$	10.0000	−	10.0000i	0.567962	−	0.567962i
$311$	8.48528			0.481156			0.240578	−	0.970630i	$-0.422663\pi$
$311$	8.48528			0.481156			0.240578	+	0.970630i	$0.422663\pi$
$312$	−17.1213	+	7.60660i	−0.969304	+	0.430639i
$313$	8.00000			0.452187			0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000			0.452187			0.226093	+	0.974106i	$0.427405\pi$
$314$	9.89949	−	9.89949i	0.558661	−	0.558661i
$315$	−8.00000	−	2.82843i	−0.450749	−	0.159364i
$316$		−	10.0000i		−	0.562544i
$317$	7.07107	−	7.07107i	0.397151	−	0.397151i	−0.480076	−	0.877227i	$-0.659391\pi$
$317$	7.07107	−	7.07107i	0.397151	−	0.397151i	0.877227	+	0.480076i	$0.159391\pi$
$318$	−1.65685	+	9.65685i	−0.0929118	+	0.541529i
$319$	8.00000	−	8.00000i	0.447914	−	0.447914i
$320$	−9.89949	−	9.89949i	−0.553399	−	0.553399i
$321$	−8.00000	+	5.65685i	−0.446516	+	0.315735i
$322$		−	12.0000i		−	0.668734i
$323$		0			0
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$	3.00000	−	2.00000i	0.166410	−	0.110940i
$326$		−	1.41421i		−	0.0783260i
$327$	0.414214	−	2.41421i	0.0229061	−	0.133506i
$328$	−6.00000			−0.331295
$329$	−5.65685			−0.311872
$330$	−13.6569	−	2.34315i	−0.751785	−	0.128986i
$331$	7.00000	+	7.00000i	0.384755	+	0.384755i	0.872812	−	0.488057i	$-0.162294\pi$
$331$	7.00000	+	7.00000i	0.384755	+	0.384755i	−0.488057	+	0.872812i	$0.662294\pi$
$332$	−5.65685	−	5.65685i	−0.310460	−	0.310460i
$333$	1.82843	+	3.82843i	0.100197	+	0.209797i
$334$	−4.00000			−0.218870
$335$	14.1421			0.772667
$336$	−2.41421	−	0.414214i	−0.131706	−	0.0225972i
$337$		−	6.00000i		−	0.326841i	−0.986557	−	0.163420i	$-0.947747\pi$
$337$		−	6.00000i		−	0.326841i	0.986557	−	0.163420i	$-0.0522527\pi$
$338$	4.94975	+	12.0208i	0.269231	+	0.653846i
$339$	−20.0000	+	14.1421i	−1.08625	+	0.768095i
$340$		0			0
$341$			28.2843i			1.53168i
$342$	−1.41421	+	4.00000i	−0.0764719	+	0.216295i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−12.7279	+	12.7279i	−0.686244	+	0.686244i
$345$	28.9706	+	4.97056i	1.55972	+	0.267606i
$346$	−6.00000	+	6.00000i	−0.322562	+	0.322562i
$347$		−	14.1421i		−	0.759190i	−0.925153	−	0.379595i	$-0.876063\pi$
$347$		−	14.1421i		−	0.759190i	0.925153	−	0.379595i	$-0.123937\pi$
$348$	2.82843	+	4.00000i	0.151620	+	0.214423i
$349$	−17.0000	+	17.0000i	−0.909989	+	0.909989i	−0.996271	−	0.0862816i	$-0.972502\pi$
$349$	−17.0000	+	17.0000i	−0.909989	+	0.909989i	0.0862816	+	0.996271i	$0.472502\pi$
$350$	1.41421			0.0755929
$351$	−14.2426	−	12.1716i	−0.760216	−	0.649670i
$352$	20.0000			1.06600
$353$	−18.3848	+	18.3848i	−0.978523	+	0.978523i	−0.999774	−	0.0212513i	$-0.993235\pi$
$353$	−18.3848	+	18.3848i	−0.978523	+	0.978523i	0.0212513	+	0.999774i	$0.493235\pi$
$354$	4.00000	+	5.65685i	0.212598	+	0.300658i
$355$			8.00000i			0.424596i
$356$	−9.89949	+	9.89949i	−0.524672	+	0.524672i
$357$		0			0
$358$		0			0
$359$	−2.82843	−	2.82843i	−0.149279	−	0.149279i	0.628517	−	0.777796i	$-0.283662\pi$
$359$	−2.82843	−	2.82843i	−0.149279	−	0.149279i	−0.777796	+	0.628517i	$0.783662\pi$
$360$	6.00000	−	16.9706i	0.316228	−	0.894427i
$361$		−	17.0000i		−	0.894737i
$362$		0			0
$363$	7.07107	−	5.00000i	0.371135	−	0.262432i
$364$	1.00000	−	5.00000i	0.0524142	−	0.262071i
$365$			2.82843i			0.148047i
$366$	−13.6569	−	2.34315i	−0.713855	−	0.122478i
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$	8.48528			0.442326
$369$	−2.58579	−	5.41421i	−0.134611	−	0.281853i
$370$	2.00000	+	2.00000i	0.103975	+	0.103975i
$371$	−5.65685	−	5.65685i	−0.293689	−	0.293689i
$372$	−12.0711	−	2.07107i	−0.625856	−	0.107380i
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$	−3.51472	+	20.4853i	−0.181499	+	1.05786i
$376$		−	12.0000i		−	0.618853i
$377$	8.48528	−	5.65685i	0.437014	−	0.291343i
$378$	−2.00000	−	7.07107i	−0.102869	−	0.363696i
$379$	19.0000	+	19.0000i	0.975964	+	0.975964i	0.999718	−	0.0237534i	$-0.00756165\pi$
$379$	19.0000	+	19.0000i	0.975964	+	0.975964i	−0.0237534	+	0.999718i	$0.507562\pi$
$380$		−	2.82843i		−	0.145095i
$381$		0			0
$382$	2.00000	+	2.00000i	0.102329	+	0.102329i
$383$	11.3137	−	11.3137i	0.578103	−	0.578103i	−0.356277	−	0.934380i	$-0.615954\pi$
$383$	11.3137	−	11.3137i	0.578103	−	0.578103i	0.934380	+	0.356277i	$0.115954\pi$
$384$	−0.878680	+	5.12132i	−0.0448399	+	0.261346i
$385$	8.00000	−	8.00000i	0.407718	−	0.407718i
$386$		−	26.8701i		−	1.36765i
$387$	−16.9706	−	6.00000i	−0.862662	−	0.304997i
$388$	−7.00000	+	7.00000i	−0.355371	+	0.355371i
$389$	16.9706			0.860442			0.430221	−	0.902724i	$-0.358436\pi$
$389$	16.9706			0.860442			0.430221	+	0.902724i	$0.358436\pi$
$390$	−11.6569	−	4.48528i	−0.590268	−	0.227121i
$391$		0			0
$392$	−10.6066	+	10.6066i	−0.535714	+	0.535714i
$393$	16.0000	−	11.3137i	0.807093	−	0.570701i
$394$		−	22.0000i		−	1.10834i
$395$	14.1421	−	14.1421i	0.711568	−	0.711568i
$396$	5.17157	+	10.8284i	0.259881	+	0.544149i
$397$	−17.0000	+	17.0000i	−0.853206	+	0.853206i	−0.990527	−	0.137321i	$-0.956151\pi$
$397$	−17.0000	+	17.0000i	−0.853206	+	0.853206i	0.137321	+	0.990527i	$0.456151\pi$
$398$		0			0
$399$	−2.00000	−	2.82843i	−0.100125	−	0.141598i
$400$			1.00000i			0.0500000i
$401$	−15.5563	−	15.5563i	−0.776847	−	0.776847i	0.202446	−	0.979293i	$-0.435111\pi$
$401$	−15.5563	−	15.5563i	−0.776847	−	0.776847i	−0.979293	+	0.202446i	$0.935111\pi$
$402$	7.07107	+	10.0000i	0.352673	+	0.498755i
$403$	−5.00000	+	25.0000i	−0.249068	+	1.24534i
$404$		−	8.48528i		−	0.422159i
$405$	17.8995	−	1.89949i	0.889433	−	0.0943867i
$406$	4.00000			0.198517
$407$	−5.65685			−0.280400
$408$		0			0
$409$	−23.0000	−	23.0000i	−1.13728	−	1.13728i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$	−23.0000	−	23.0000i	−1.13728	−	1.13728i	−0.148340	−	0.988936i	$-0.547393\pi$
$410$	−2.82843	−	2.82843i	−0.139686	−	0.139686i
$411$	4.10051	−	23.8995i	0.202263	−	1.17888i
$412$	6.00000			0.295599
$413$	−5.65685			−0.278356
$414$	10.9706	+	22.9706i	0.539174	+	1.12894i
$415$		−	16.0000i		−	0.785409i
$416$	17.6777	+	3.53553i	0.866719	+	0.173344i
$417$	4.00000	+	5.65685i	0.195881	+	0.277017i
$418$	−4.00000	−	4.00000i	−0.195646	−	0.195646i
$419$			11.3137i			0.552711i	0.961056	+	0.276355i	$0.0891267\pi$
$419$			11.3137i			0.552711i	−0.961056	+	0.276355i	$0.910873\pi$
$420$	2.82843	+	4.00000i	0.138013	+	0.195180i
$421$	25.0000	+	25.0000i	1.21843	+	1.21843i	0.968183	+	0.250242i	$0.0805102\pi$
$421$	25.0000	+	25.0000i	1.21843	+	1.21843i	0.250242	+	0.968183i	$0.419490\pi$
$422$	9.89949	−	9.89949i	0.481900	−	0.481900i
$423$	10.8284	−	5.17157i	0.526496	−	0.251450i
$424$	12.0000	−	12.0000i	0.582772	−	0.582772i
$425$		0			0
$426$	−5.65685	+	4.00000i	−0.274075	+	0.193801i
$427$	8.00000	−	8.00000i	0.387147	−	0.387147i
$428$	5.65685			0.273434
$429$	22.8284	−	10.1421i	1.10217	−	0.489667i
$430$	−12.0000			−0.578691
$431$	−22.6274	+	22.6274i	−1.08992	+	1.08992i	−0.0943889	+	0.995535i	$0.530090\pi$
$431$	−22.6274	+	22.6274i	−1.08992	+	1.08992i	−0.995535	+	0.0943889i	$0.969910\pi$
$432$	5.00000	−	1.41421i	0.240563	−	0.0680414i
$433$			18.0000i			0.865025i	0.901628	+	0.432512i	$0.142373\pi$
$433$			18.0000i			0.865025i	−0.901628	+	0.432512i	$0.857627\pi$
$434$	−7.07107	+	7.07107i	−0.339422	+	0.339422i
$435$	−1.65685	+	9.65685i	−0.0794401	+	0.463011i
$436$	−1.00000	+	1.00000i	−0.0478913	+	0.0478913i
$437$	8.48528	+	8.48528i	0.405906	+	0.405906i
$438$	−2.00000	+	1.41421i	−0.0955637	+	0.0675737i
$439$		−	30.0000i		−	1.43182i	−0.698192	−	0.715911i	$-0.746012\pi$
$439$		−	30.0000i		−	1.43182i	0.698192	−	0.715911i	$-0.253988\pi$
$440$	16.9706	+	16.9706i	0.809040	+	0.809040i
$441$	−14.1421	−	5.00000i	−0.673435	−	0.238095i
$442$		0			0
$443$			28.2843i			1.34383i	0.740630	+	0.671913i	$0.234527\pi$
$443$			28.2843i			1.34383i	−0.740630	+	0.671913i	$0.765473\pi$
$444$	0.414214	−	2.41421i	0.0196577	−	0.114574i
$445$	−28.0000			−1.32733
$446$	−15.5563			−0.736614
$447$	3.41421	+	0.585786i	0.161487	+	0.0277067i
$448$	7.00000	+	7.00000i	0.330719	+	0.330719i
$449$	−15.5563	−	15.5563i	−0.734150	−	0.734150i	0.237289	−	0.971439i	$-0.423741\pi$
$449$	−15.5563	−	15.5563i	−0.734150	−	0.734150i	−0.971439	+	0.237289i	$0.923741\pi$
$450$	−2.70711	+	1.29289i	−0.127614	+	0.0609476i
$451$	8.00000			0.376705
$452$	14.1421			0.665190
$453$	−2.41421	−	0.414214i	−0.113430	−	0.0194615i
$454$			8.00000i			0.375459i
$455$	8.48528	−	5.65685i	0.397796	−	0.265197i
$456$	6.00000	−	4.24264i	0.280976	−	0.198680i
$457$	−29.0000	−	29.0000i	−1.35656	−	1.35656i	−0.878117	−	0.478446i	$-0.841200\pi$
$457$	−29.0000	−	29.0000i	−1.35656	−	1.35656i	−0.478446	−	0.878117i	$-0.658800\pi$
$458$		−	1.41421i		−	0.0660819i
$459$		0			0
$460$	−12.0000	−	12.0000i	−0.559503	−	0.559503i
$461$	7.07107	−	7.07107i	0.329332	−	0.329332i	−0.523000	−	0.852333i	$-0.675187\pi$
$461$	7.07107	−	7.07107i	0.329332	−	0.329332i	0.852333	+	0.523000i	$0.175187\pi$
$462$	9.65685	+	1.65685i	0.449278	+	0.0770838i
$463$	−17.0000	+	17.0000i	−0.790057	+	0.790057i	−0.981503	−	0.191446i	$-0.938682\pi$
$463$	−17.0000	+	17.0000i	−0.790057	+	0.790057i	0.191446	+	0.981503i	$0.438682\pi$
$464$			2.82843i			0.131306i
$465$	−14.1421	−	20.0000i	−0.655826	−	0.927478i
$466$	−18.0000	+	18.0000i	−0.833834	+	0.833834i
$467$	−25.4558			−1.17796			−0.588978	−	0.808149i	$-0.700470\pi$
$467$	−25.4558			−1.17796			−0.588978	+	0.808149i	$0.700470\pi$
$468$	2.65685	+	10.4853i	0.122813	+	0.484682i
$469$	−10.0000			−0.461757
$470$	5.65685	−	5.65685i	0.260931	−	0.260931i
$471$	−14.0000	−	19.7990i	−0.645086	−	0.912289i
$472$		−	12.0000i		−	0.552345i
$473$	16.9706	−	16.9706i	0.780307	−	0.780307i
$474$	17.0711	+	2.92893i	0.784100	+	0.134530i
$475$	−1.00000	+	1.00000i	−0.0458831	+	0.0458831i
$476$		0			0
$477$	16.0000	+	5.65685i	0.732590	+	0.259010i
$478$			20.0000i			0.914779i
$479$	22.6274	+	22.6274i	1.03387	+	1.03387i	0.999406	+	0.0344672i	$0.0109734\pi$
$479$	22.6274	+	22.6274i	1.03387	+	1.03387i	0.0344672	+	0.999406i	$0.489027\pi$
$480$	−14.1421	+	10.0000i	−0.645497	+	0.456435i
$481$	−5.00000	−	1.00000i	−0.227980	−	0.0455961i
$482$			24.0416i			1.09507i
$483$	−20.4853	−	3.51472i	−0.932113	−	0.159925i
$484$	−5.00000			−0.227273
$485$	−19.7990			−0.899026
$486$	10.2929	+	11.7071i	0.466895	+	0.531045i
$487$	19.0000	+	19.0000i	0.860972	+	0.860972i	0.991451	−	0.130479i	$-0.0416515\pi$
$487$	19.0000	+	19.0000i	0.860972	+	0.860972i	−0.130479	+	0.991451i	$0.541651\pi$
$488$	16.9706	+	16.9706i	0.768221	+	0.768221i
$489$	−2.41421	−	0.414214i	−0.109175	−	0.0187314i
$490$	−10.0000			−0.451754
$491$	−42.4264			−1.91468			−0.957338	−	0.288969i	$-0.906688\pi$
$491$	−42.4264			−1.91468			−0.957338	+	0.288969i	$0.906688\pi$
$492$	−0.585786	+	3.41421i	−0.0264093	+	0.153925i
$493$		0			0
$494$	−2.82843	−	4.24264i	−0.127257	−	0.190885i
$495$	−8.00000	+	22.6274i	−0.359573	+	1.01703i
$496$	−5.00000	−	5.00000i	−0.224507	−	0.224507i
$497$		−	5.65685i		−	0.253745i
$498$	11.3137	−	8.00000i	0.506979	−	0.358489i
$499$	−23.0000	−	23.0000i	−1.02962	−	1.02962i	−0.999548	−	0.0300737i	$-0.990426\pi$
$499$	−23.0000	−	23.0000i	−1.02962	−	1.02962i	−0.0300737	−	0.999548i	$-0.509574\pi$
$500$	8.48528	−	8.48528i	0.379473	−	0.379473i
$501$	−1.17157	+	6.82843i	−0.0523420	+	0.305072i
$502$	18.0000	−	18.0000i	0.803379	−	0.803379i
$503$		−	5.65685i		−	0.252227i	−0.992016	−	0.126113i	$-0.959750\pi$
$503$		−	5.65685i		−	0.252227i	0.992016	−	0.126113i	$-0.0402503\pi$
$504$	−4.24264	+	12.0000i	−0.188982	+	0.534522i
$505$	12.0000	−	12.0000i	0.533993	−	0.533993i
$506$	−33.9411			−1.50887
$507$	21.9706	−	4.92893i	0.975747	−	0.218902i
$508$		0			0
$509$	24.0416	−	24.0416i	1.06563	−	1.06563i	0.0679369	−	0.997690i	$-0.478358\pi$
$509$	24.0416	−	24.0416i	1.06563	−	1.06563i	0.997690	−	0.0679369i	$-0.0216417\pi$
$510$		0			0
$511$		−	2.00000i		−	0.0884748i
$512$	−7.77817	+	7.77817i	−0.343750	+	0.343750i
$513$	6.41421	+	3.58579i	0.283194	+	0.158316i
$514$	6.00000	−	6.00000i	0.264649	−	0.264649i
$515$	8.48528	+	8.48528i	0.373906	+	0.373906i
$516$	6.00000	+	8.48528i	0.264135	+	0.373544i
$517$			16.0000i			0.703679i
$518$	−1.41421	−	1.41421i	−0.0621370	−	0.0621370i
$519$	8.48528	+	12.0000i	0.372463	+	0.526742i
$520$	12.0000	+	18.0000i	0.526235	+	0.789352i
$521$		−	31.1127i		−	1.36307i	−0.731785	−	0.681536i	$-0.761312\pi$
$521$		−	31.1127i		−	1.36307i	0.731785	−	0.681536i	$-0.238688\pi$
$522$	−7.65685	+	3.65685i	−0.335131	+	0.160056i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	−11.3137			−0.494242
$525$	0.414214	−	2.41421i	0.0180778	−	0.105365i
$526$	−16.0000	−	16.0000i	−0.697633	−	0.697633i
$527$		0			0
$528$	−1.17157	+	6.82843i	−0.0509862	+	0.297169i
$529$	49.0000			2.13043
$530$	11.3137			0.491436
$531$	10.8284	−	5.17157i	0.469914	−	0.224427i
$532$			2.00000i			0.0867110i
$533$	7.07107	+	1.41421i	0.306282	+	0.0612564i
$534$	−14.0000	−	19.7990i	−0.605839	−	0.856786i
$535$	8.00000	+	8.00000i	0.345870	+	0.345870i
$536$		−	21.2132i		−	0.916271i
$537$		0			0
$538$	14.0000	+	14.0000i	0.603583	+	0.603583i
$539$	14.1421	−	14.1421i	0.609145	−	0.609145i
$540$	−9.07107	−	5.07107i	−0.390357	−	0.218224i
$541$	1.00000	−	1.00000i	0.0429934	−	0.0429934i	−0.685283	−	0.728277i	$-0.740322\pi$
$541$	1.00000	−	1.00000i	0.0429934	−	0.0429934i	0.728277	+	0.685283i	$0.240322\pi$
$542$		−	26.8701i		−	1.15417i
$543$		0			0
$544$		0			0
$545$	−2.82843			−0.121157
$546$	8.24264	+	3.17157i	0.352752	+	0.135731i
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−9.89949	+	9.89949i	−0.422885	+	0.422885i
$549$	−8.00000	+	22.6274i	−0.341432	+	0.965715i
$550$		−	4.00000i		−	0.170561i
$551$	−2.82843	+	2.82843i	−0.120495	+	0.120495i
$552$	7.45584	−	43.4558i	0.317342	−	1.84960i
$553$	−10.0000	+	10.0000i	−0.425243	+	0.425243i
$554$	−8.48528	−	8.48528i	−0.360505	−	0.360505i
$555$	4.00000	−	2.82843i	0.169791	−	0.120060i
$556$		−	4.00000i		−	0.169638i
$557$	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	$0.654147\pi$
$558$	7.07107	−	20.0000i	0.299342	−	0.846668i
$559$	18.0000	−	12.0000i	0.761319	−	0.507546i
$560$			2.82843i			0.119523i
$561$		0			0
$562$	14.0000			0.590554
$563$	33.9411			1.43045			0.715224	−	0.698895i	$-0.246325\pi$
$563$	33.9411			1.43045			0.715224	+	0.698895i	$0.246325\pi$
$564$	−6.82843	−	1.17157i	−0.287529	−	0.0493321i
$565$	20.0000	+	20.0000i	0.841406	+	0.841406i
$566$	8.48528	+	8.48528i	0.356663	+	0.356663i
$567$	−12.6569	+	1.34315i	−0.531538	+	0.0564068i
$568$	12.0000			0.503509
$569$	−8.48528			−0.355722			−0.177861	−	0.984056i	$-0.556918\pi$
$569$	−8.48528			−0.355722			−0.177861	+	0.984056i	$0.556918\pi$
$570$	4.82843	+	0.828427i	0.202241	+	0.0346990i
$571$			12.0000i			0.502184i	0.967963	+	0.251092i	$0.0807897\pi$
$571$			12.0000i			0.502184i	−0.967963	+	0.251092i	$0.919210\pi$
$572$	−14.1421	−	2.82843i	−0.591312	−	0.118262i
$573$	4.00000	−	2.82843i	0.167102	−	0.118159i
$574$	2.00000	+	2.00000i	0.0834784	+	0.0834784i
$575$			8.48528i			0.353861i
$576$	−19.7990	−	7.00000i	−0.824958	−	0.291667i
$577$	1.00000	+	1.00000i	0.0416305	+	0.0416305i	0.727616	−	0.685985i	$-0.240628\pi$
$577$	1.00000	+	1.00000i	0.0416305	+	0.0416305i	−0.685985	+	0.727616i	$0.740628\pi$
$578$	−12.0208	+	12.0208i	−0.500000	+	0.500000i
$579$	−45.8701	−	7.87006i	−1.90629	−	0.327068i
$580$	4.00000	−	4.00000i	0.166091	−	0.166091i
$581$			11.3137i			0.469372i
$582$	−9.89949	−	14.0000i	−0.410347	−	0.580319i
$583$	−16.0000	+	16.0000i	−0.662652	+	0.662652i
$584$	4.24264			0.175562
$585$	−11.0711	+	18.5858i	−0.457732	+	0.768428i
$586$	14.0000			0.578335
$587$	−5.65685	+	5.65685i	−0.233483	+	0.233483i	−0.814145	−	0.580662i	$-0.802794\pi$
$587$	−5.65685	+	5.65685i	−0.233483	+	0.233483i	0.580662	+	0.814145i	$0.302794\pi$
$588$	5.00000	+	7.07107i	0.206197	+	0.291606i
$589$		−	10.0000i		−	0.412043i
$590$	5.65685	−	5.65685i	0.232889	−	0.232889i
$591$	−37.5563	−	6.44365i	−1.54486	−	0.265056i
$592$	1.00000	−	1.00000i	0.0410997	−	0.0410997i
$593$	9.89949	+	9.89949i	0.406524	+	0.406524i	0.880524	−	0.474001i	$-0.157191\pi$
$593$	9.89949	+	9.89949i	0.406524	+	0.406524i	−0.474001	+	0.880524i	$0.657191\pi$
$594$	−20.0000	+	5.65685i	−0.820610	+	0.232104i
$595$		0			0
$596$	−1.41421	−	1.41421i	−0.0579284	−	0.0579284i
$597$		0			0
$598$	−30.0000	−	6.00000i	−1.22679	−	0.245358i
$599$			11.3137i			0.462266i	0.972922	+	0.231133i	$0.0742432\pi$
$599$			11.3137i			0.462266i	−0.972922	+	0.231133i	$0.925757\pi$
$600$	5.12132	+	0.878680i	0.209077	+	0.0358719i
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$	8.48528			0.345834
$603$	19.1421	−	9.14214i	0.779528	−	0.372297i
$604$	1.00000	+	1.00000i	0.0406894	+	0.0406894i
$605$	−7.07107	−	7.07107i	−0.287480	−	0.287480i
$606$	14.4853	+	2.48528i	0.588424	+	0.100958i
$607$	−40.0000			−1.62355			−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000			−1.62355			−0.811775	+	0.583970i	$0.801498\pi$
$608$	−7.07107			−0.286770
$609$	1.17157	−	6.82843i	0.0474745	−	0.276702i
$610$			16.0000i			0.647821i
$611$	−2.82843	+	14.1421i	−0.114426	+	0.572130i
$612$		0			0
$613$	1.00000	+	1.00000i	0.0403896	+	0.0403896i	0.727013	−	0.686624i	$-0.240908\pi$
$613$	1.00000	+	1.00000i	0.0403896	+	0.0403896i	−0.686624	+	0.727013i	$0.740908\pi$
$614$			24.0416i			0.970241i
$615$	−5.65685	+	4.00000i	−0.228106	+	0.161296i
$616$	−12.0000	−	12.0000i	−0.483494	−	0.483494i
$617$	−26.8701	+	26.8701i	−1.08175	+	1.08175i	−0.0854011	+	0.996347i	$0.527217\pi$
$617$	−26.8701	+	26.8701i	−1.08175	+	1.08175i	−0.996347	+	0.0854011i	$0.972783\pi$
$618$	−1.75736	+	10.2426i	−0.0706914	+	0.412019i
$619$	1.00000	−	1.00000i	0.0401934	−	0.0401934i	−0.686724	−	0.726918i	$-0.740952\pi$
$619$	1.00000	−	1.00000i	0.0401934	−	0.0401934i	0.726918	+	0.686724i	$0.240952\pi$
$620$			14.1421i			0.567962i
$621$	42.4264	−	12.0000i	1.70251	−	0.481543i
$622$	6.00000	−	6.00000i	0.240578	−	0.240578i
$623$	19.7990			0.793230
$624$	−2.24264	+	5.82843i	−0.0897775	+	0.233324i
$625$	19.0000			0.760000
$626$	5.65685	−	5.65685i	0.226093	−	0.226093i
$627$	−8.00000	+	5.65685i	−0.319489	+	0.225913i
$628$			14.0000i			0.558661i
$629$		0			0
$630$	−7.65685	+	3.65685i	−0.305056	+	0.145693i
$631$	19.0000	−	19.0000i	0.756378	−	0.756378i	−0.219283	−	0.975661i	$-0.570372\pi$
$631$	19.0000	−	19.0000i	0.756378	−	0.756378i	0.975661	+	0.219283i	$0.0703719\pi$
$632$	−21.2132	−	21.2132i	−0.843816	−	0.843816i
$633$	−14.0000	−	19.7990i	−0.556450	−	0.786939i
$634$		−	10.0000i		−	0.397151i
$635$		0			0
$636$	−5.65685	−	8.00000i	−0.224309	−	0.317221i
$637$	15.0000	−	10.0000i	0.594322	−	0.396214i
$638$		−	11.3137i		−	0.447914i
$639$	5.17157	+	10.8284i	0.204584	+	0.428366i
$640$	6.00000			0.237171
$641$	16.9706			0.670297			0.335148	−	0.942165i	$-0.391214\pi$
$641$	16.9706			0.670297			0.335148	+	0.942165i	$0.391214\pi$
$642$	−1.65685	+	9.65685i	−0.0653908	+	0.381126i
$643$	−5.00000	−	5.00000i	−0.197181	−	0.197181i	0.601610	−	0.798790i	$-0.294526\pi$
$643$	−5.00000	−	5.00000i	−0.197181	−	0.197181i	−0.798790	+	0.601610i	$0.794526\pi$
$644$	8.48528	+	8.48528i	0.334367	+	0.334367i
$645$	−3.51472	+	20.4853i	−0.138392	+	0.806607i
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−2.84924	−	26.8492i	−0.111929	−	1.05474i
$649$			16.0000i			0.628055i
$650$	0.707107	−	3.53553i	0.0277350	−	0.138675i
$651$	10.0000	+	14.1421i	0.391931	+	0.554274i
$652$	1.00000	+	1.00000i	0.0391630	+	0.0391630i
$653$		−	14.1421i		−	0.553425i	−0.960953	−	0.276712i	$-0.910755\pi$
$653$		−	14.1421i		−	0.553425i	0.960953	−	0.276712i	$-0.0892449\pi$
$654$	−1.41421	−	2.00000i	−0.0553001	−	0.0782062i
$655$	−16.0000	−	16.0000i	−0.625172	−	0.625172i
$656$	−1.41421	+	1.41421i	−0.0552158	+	0.0552158i
$657$	1.82843	+	3.82843i	0.0713337	+	0.149361i
$658$	−4.00000	+	4.00000i	−0.155936	+	0.155936i
$659$			2.82843i			0.110180i	0.998481	+	0.0550899i	$0.0175446\pi$
$659$			2.82843i			0.110180i	−0.998481	+	0.0550899i	$0.982455\pi$
$660$	11.3137	−	8.00000i	0.440386	−	0.311400i
$661$	1.00000	−	1.00000i	0.0388955	−	0.0388955i	−0.687392	−	0.726287i	$-0.741244\pi$
$661$	1.00000	−	1.00000i	0.0388955	−	0.0388955i	0.726287	+	0.687392i	$0.241244\pi$
$662$	9.89949			0.384755
$663$		0			0
$664$	−24.0000			−0.931381
$665$	−2.82843	+	2.82843i	−0.109682	+	0.109682i
$666$	4.00000	+	1.41421i	0.154997	+	0.0547997i
$667$			24.0000i			0.929284i
$668$	2.82843	−	2.82843i	0.109435	−	0.109435i
$669$	−4.55635	+	26.5563i	−0.176159	+	1.02673i
$670$	10.0000	−	10.0000i	0.386334	−	0.386334i
$671$	−22.6274	−	22.6274i	−0.873522	−	0.873522i
$672$	10.0000	−	7.07107i	0.385758	−	0.272772i
$673$		−	12.0000i		−	0.462566i	−0.972887	−	0.231283i	$-0.925708\pi$
$673$		−	12.0000i		−	0.462566i	0.972887	−	0.231283i	$-0.0742923\pi$
$674$	−4.24264	−	4.24264i	−0.163420	−	0.163420i
$675$	1.41421	+	5.00000i	0.0544331	+	0.192450i
$676$	−12.0000	−	5.00000i	−0.461538	−	0.192308i
$677$		−	22.6274i		−	0.869642i	−0.900517	−	0.434821i	$-0.856812\pi$
$677$		−	22.6274i		−	0.869642i	0.900517	−	0.434821i	$-0.143188\pi$
$678$	−4.14214	+	24.1421i	−0.159078	+	0.927173i
$679$	14.0000			0.537271
$680$		0			0
$681$	13.6569	+	2.34315i	0.523332	+	0.0897895i
$682$	20.0000	+	20.0000i	0.765840	+	0.765840i
$683$	−2.82843	−	2.82843i	−0.108227	−	0.108227i	0.650920	−	0.759147i	$-0.274383\pi$
$683$	−2.82843	−	2.82843i	−0.108227	−	0.108227i	−0.759147	+	0.650920i	$0.774383\pi$
$684$	−1.82843	−	3.82843i	−0.0699117	−	0.146384i
$685$	−28.0000			−1.06983
$686$	16.9706			0.647939
$687$	−2.41421	−	0.414214i	−0.0921080	−	0.0158032i
$688$			6.00000i			0.228748i
$689$	−16.9706	+	11.3137i	−0.646527	+	0.431018i
$690$	24.0000	−	16.9706i	0.913664	−	0.646058i
$691$	−11.0000	−	11.0000i	−0.418460	−	0.418460i	0.466213	−	0.884673i	$-0.345618\pi$
$691$	−11.0000	−	11.0000i	−0.418460	−	0.418460i	−0.884673	+	0.466213i	$0.845618\pi$
$692$		−	8.48528i		−	0.322562i
$693$	5.65685	−	16.0000i	0.214886	−	0.607790i
$694$	−10.0000	−	10.0000i	−0.379595	−	0.379595i
$695$	5.65685	−	5.65685i	0.214577	−	0.214577i
$696$	14.4853	+	2.48528i	0.549063	+	0.0942043i
$697$		0			0
$698$			24.0416i			0.909989i
$699$	25.4558	+	36.0000i	0.962828	+	1.36165i
$700$	−1.00000	+	1.00000i	−0.0377964	+	0.0377964i
$701$	50.9117			1.92291			0.961454	−	0.274966i	$-0.0886666\pi$
$701$	50.9117			1.92291			0.961454	+	0.274966i	$0.0886666\pi$
$702$	−18.6777	+	1.46447i	−0.704943	+	0.0552727i
$703$	2.00000			0.0754314
$704$	19.7990	−	19.7990i	0.746203	−	0.746203i
$705$	−8.00000	−	11.3137i	−0.301297	−	0.426099i
$706$			26.0000i			0.978523i
$707$	−8.48528	+	8.48528i	−0.319122	+	0.319122i
$708$	−6.82843	−	1.17157i	−0.256628	−	0.0440304i
$709$	19.0000	−	19.0000i	0.713560	−	0.713560i	−0.253718	−	0.967278i	$-0.581654\pi$
$709$	19.0000	−	19.0000i	0.713560	−	0.713560i	0.967278	+	0.253718i	$0.0816536\pi$
$710$	5.65685	+	5.65685i	0.212298	+	0.212298i
$711$	10.0000	−	28.2843i	0.375029	−	1.06074i
$712$			42.0000i			1.57402i
$713$	−42.4264	−	42.4264i	−1.58888	−	1.58888i
$714$		0			0
$715$	−16.0000	−	24.0000i	−0.598366	−	0.897549i
$716$		0			0
$717$	34.1421	+	5.85786i	1.27506	+	0.218766i
$718$	−4.00000			−0.149279
$719$	−25.4558			−0.949343			−0.474671	−	0.880163i	$-0.657433\pi$
$719$	−25.4558			−0.949343			−0.474671	+	0.880163i	$0.657433\pi$
$720$	−2.58579	−	5.41421i	−0.0963666	−	0.201776i
$721$	−6.00000	−	6.00000i	−0.223452	−	0.223452i
$722$	−12.0208	−	12.0208i	−0.447368	−	0.447368i
$723$	41.0416	+	7.04163i	1.52635	+	0.261881i
$724$		0			0
$725$	−2.82843			−0.105045
$726$	1.46447	−	8.53553i	0.0543514	−	0.316783i
$727$		−	48.0000i		−	1.78022i	−0.455744	−	0.890111i	$-0.650627\pi$
$727$		−	48.0000i		−	1.78022i	0.455744	−	0.890111i	$-0.349373\pi$
$728$	−8.48528	−	12.7279i	−0.314485	−	0.471728i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	2.00000	+	2.00000i	0.0740233	+	0.0740233i
$731$		0			0
$732$	11.3137	−	8.00000i	0.418167	−	0.295689i
$733$	−5.00000	−	5.00000i	−0.184679	−	0.184679i	0.608712	−	0.793391i	$-0.291686\pi$
$733$	−5.00000	−	5.00000i	−0.184679	−	0.184679i	−0.793391	+	0.608712i	$0.791686\pi$
$734$	5.65685	−	5.65685i	0.208798	−	0.208798i
$735$	−2.92893	+	17.0711i	−0.108035	+	0.629676i
$736$	−30.0000	+	30.0000i	−1.10581	+	1.10581i
$737$			28.2843i			1.04186i
$738$	−5.65685	−	2.00000i	−0.208232	−	0.0736210i
$739$	1.00000	−	1.00000i	0.0367856	−	0.0367856i	−0.688475	−	0.725260i	$-0.741719\pi$
$739$	1.00000	−	1.00000i	0.0367856	−	0.0367856i	0.725260	+	0.688475i	$0.241719\pi$
$740$	−2.82843			−0.103975
$741$	−8.07107	+	3.58579i	−0.296498	+	0.131727i
$742$	−8.00000			−0.293689
$743$	11.3137	−	11.3137i	0.415060	−	0.415060i	−0.468437	−	0.883497i	$-0.655183\pi$
$743$	11.3137	−	11.3137i	0.415060	−	0.415060i	0.883497	+	0.468437i	$0.155183\pi$
$744$	−30.0000	+	21.2132i	−1.09985	+	0.777714i
$745$		−	4.00000i		−	0.146549i
$746$	−2.82843	+	2.82843i	−0.103556	+	0.103556i
$747$	−10.3431	−	21.6569i	−0.378436	−	0.792383i
$748$		0			0
$749$	−5.65685	−	5.65685i	−0.206697	−	0.206697i
$750$	12.0000	+	16.9706i	0.438178	+	0.619677i
$751$			30.0000i			1.09472i	0.836899	+	0.547358i	$0.184366\pi$
$751$			30.0000i			1.09472i	−0.836899	+	0.547358i	$0.815634\pi$
$752$	−2.82843	−	2.82843i	−0.103142	−	0.103142i
$753$	−25.4558	−	36.0000i	−0.927663	−	1.31191i
$754$	2.00000	−	10.0000i	0.0728357	−	0.364179i
$755$			2.82843i			0.102937i
$756$	6.41421	+	3.58579i	0.233283	+	0.130414i
$757$	−16.0000			−0.581530			−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000			−0.581530			−0.290765	+	0.956795i	$0.593910\pi$
$758$	26.8701			0.975964
$759$	−9.94113	+	57.9411i	−0.360840	+	2.10313i
$760$	−6.00000	−	6.00000i	−0.217643	−	0.217643i
$761$	35.3553	+	35.3553i	1.28163	+	1.28163i	0.939740	+	0.341890i	$0.111067\pi$
$761$	35.3553	+	35.3553i	1.28163	+	1.28163i	0.341890	+	0.939740i	$0.388933\pi$
$762$		0			0
$763$	2.00000			0.0724049
$764$	−2.82843			−0.102329
$765$		0			0
$766$		−	16.0000i		−	0.578103i
$767$	−2.82843	+	14.1421i	−0.102129	+	0.510643i
$768$	17.0000	+	24.0416i	0.613435	+	0.867528i
$769$	13.0000	+	13.0000i	0.468792	+	0.468792i	0.901523	−	0.432731i	$-0.142450\pi$
$769$	13.0000	+	13.0000i	0.468792	+	0.468792i	−0.432731	+	0.901523i	$0.642450\pi$
$770$		−	11.3137i		−	0.407718i
$771$	−8.48528	−	12.0000i	−0.305590	−	0.432169i
$772$	19.0000	+	19.0000i	0.683825	+	0.683825i
$773$	−9.89949	+	9.89949i	−0.356060	+	0.356060i	−0.862358	−	0.506298i	$-0.831013\pi$
$773$	−9.89949	+	9.89949i	−0.356060	+	0.356060i	0.506298	+	0.862358i	$0.331013\pi$
$774$	−16.2426	+	7.75736i	−0.583830	+	0.278833i
$775$	5.00000	−	5.00000i	0.179605	−	0.179605i
$776$			29.6985i			1.06611i
$777$	−2.82843	+	2.00000i	−0.101469	+	0.0717496i
$778$	12.0000	−	12.0000i	0.430221	−	0.430221i
$779$	−2.82843			−0.101339
$780$	11.4142	−	5.07107i	0.408694	−	0.181573i
$781$	−16.0000			−0.572525
$782$		0			0
$783$	4.00000	+	14.1421i	0.142948	+	0.505399i
$784$			5.00000i			0.178571i
$785$	−19.7990	+	19.7990i	−0.706656	+	0.706656i
$786$	3.31371	−	19.3137i	0.118196	−	0.688897i
$787$	19.0000	−	19.0000i	0.677277	−	0.677277i	−0.282106	−	0.959383i	$-0.591033\pi$
$787$	19.0000	−	19.0000i	0.677277	−	0.677277i	0.959383	+	0.282106i	$0.0910331\pi$
$788$	15.5563	+	15.5563i	0.554172	+	0.554172i
$789$	−32.0000	+	22.6274i	−1.13923	+	0.805557i
$790$		−	20.0000i		−	0.711568i
$791$	−14.1421	−	14.1421i	−0.502836	−	0.502836i
$792$	33.9411	+	12.0000i	1.20605	+	0.426401i
$793$	−16.0000	−	24.0000i	−0.568177	−	0.852265i
$794$			24.0416i			0.853206i
$795$	3.31371	−	19.3137i	0.117525	−	0.684987i
$796$		0			0
$797$	−16.9706			−0.601128			−0.300564	−	0.953762i	$-0.597175\pi$
$797$	−16.9706			−0.601128			−0.300564	+	0.953762i	$0.597175\pi$
$798$	−3.41421	−	0.585786i	−0.120862	−	0.0207366i
$799$		0			0
$800$	−3.53553	−	3.53553i	−0.125000	−	0.125000i
$801$	−37.8995	+	18.1005i	−1.33911	+	0.639550i
$802$	−22.0000			−0.776847
$803$	−5.65685			−0.199626
$804$	−12.0711	−	2.07107i	−0.425714	−	0.0730409i
$805$			24.0000i			0.845889i
$806$	14.1421	+	21.2132i	0.498135	+	0.747203i
$807$	28.0000	−	19.7990i	0.985647	−	0.696957i
$808$	−18.0000	−	18.0000i	−0.633238	−	0.633238i
$809$		−	31.1127i		−	1.09386i	−0.837177	−	0.546932i	$-0.815796\pi$
$809$		−	31.1127i		−	1.09386i	0.837177	−	0.546932i	$-0.184204\pi$
$810$	11.3137	−	14.0000i	0.397523	−	0.491910i
$811$	1.00000	+	1.00000i	0.0351147	+	0.0351147i	0.724446	−	0.689331i	$-0.242096\pi$
$811$	1.00000	+	1.00000i	0.0351147	+	0.0351147i	−0.689331	+	0.724446i	$0.742096\pi$
$812$	−2.82843	+	2.82843i	−0.0992583	+	0.0992583i
$813$	−45.8701	−	7.87006i	−1.60873	−	0.276015i
$814$	−4.00000	+	4.00000i	−0.140200	+	0.140200i
$815$			2.82843i			0.0990755i
$816$		0			0
$817$	−6.00000	+	6.00000i	−0.209913	+	0.209913i
$818$	−32.5269			−1.13728
$819$	7.82843	−	13.1421i	0.273547	−	0.459223i
$820$	4.00000			0.139686
$821$	7.07107	−	7.07107i	0.246782	−	0.246782i	−0.572867	−	0.819649i	$-0.694169\pi$
$821$	7.07107	−	7.07107i	0.246782	−	0.246782i	0.819649	+	0.572867i	$0.194169\pi$
$822$	−14.0000	−	19.7990i	−0.488306	−	0.690569i
$823$			30.0000i			1.04573i	0.852414	+	0.522867i	$0.175138\pi$
$823$			30.0000i			1.04573i	−0.852414	+	0.522867i	$0.824862\pi$
$824$	12.7279	−	12.7279i	0.443398	−	0.443398i
$825$	−6.82843	−	1.17157i	−0.237735	−	0.0407889i
$826$	−4.00000	+	4.00000i	−0.139178	+	0.139178i
$827$	22.6274	+	22.6274i	0.786832	+	0.786832i	0.980974	−	0.194141i	$-0.0621920\pi$
$827$	22.6274	+	22.6274i	0.786832	+	0.786832i	−0.194141	+	0.980974i	$0.562192\pi$
$828$	−24.0000	−	8.48528i	−0.834058	−	0.294884i
$829$			18.0000i			0.625166i	0.949890	+	0.312583i	$0.101194\pi$
$829$			18.0000i			0.625166i	−0.949890	+	0.312583i	$0.898806\pi$
$830$	−11.3137	−	11.3137i	−0.392705	−	0.392705i
$831$	−16.9706	+	12.0000i	−0.588702	+	0.416275i
$832$	21.0000	−	14.0000i	0.728044	−	0.485363i
$833$		0			0
$834$	6.82843	+	1.17157i	0.236449	+	0.0405683i
$835$	8.00000			0.276851
$836$	5.65685			0.195646
$837$	−32.0711	−	17.9289i	−1.10854	−	0.619715i
$838$	8.00000	+	8.00000i	0.276355	+	0.276355i
$839$	−2.82843	−	2.82843i	−0.0976481	−	0.0976481i	0.656595	−	0.754243i	$-0.271996\pi$
$839$	−2.82843	−	2.82843i	−0.0976481	−	0.0976481i	−0.754243	+	0.656595i	$0.771996\pi$
$840$	14.4853	+	2.48528i	0.499790	+	0.0857504i
$841$	21.0000			0.724138
$842$	35.3553			1.21843
$843$	4.10051	−	23.8995i	0.141229	−	0.823142i
$844$			14.0000i			0.481900i
$845$	−9.89949	−	24.0416i	−0.340553	−	0.827057i
$846$	4.00000	−	11.3137i	0.137523	−	0.388973i
$847$	5.00000	+	5.00000i	0.171802	+	0.171802i
$848$		−	5.65685i		−	0.194257i
$849$	16.9706	−	12.0000i	0.582428	−	0.411839i
$850$		0			0
$851$	8.48528	−	8.48528i	0.290872	−	0.290872i
$852$	1.17157	−	6.82843i	0.0401374	−	0.233938i
$853$	37.0000	−	37.0000i	1.26686	−	1.26686i	0.319152	−	0.947703i	$-0.396602\pi$
$853$	37.0000	−	37.0000i	1.26686	−	1.26686i	0.947703	−	0.319152i	$-0.103398\pi$
$854$		−	11.3137i		−	0.387147i
$855$	2.82843	−	8.00000i	0.0967302	−	0.273594i
$856$	12.0000	−	12.0000i	0.410152	−	0.410152i
$857$	−8.48528			−0.289852			−0.144926	−	0.989443i	$-0.546294\pi$
$857$	−8.48528			−0.289852			−0.144926	+	0.989443i	$0.546294\pi$
$858$	8.97056	−	23.3137i	0.306250	−	0.795917i
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$	8.48528	−	8.48528i	0.289346	−	0.289346i
$861$	4.00000	−	2.82843i	0.136320	−	0.0963925i
$862$			32.0000i			1.08992i
$863$	2.82843	−	2.82843i	0.0962808	−	0.0962808i	−0.657326	−	0.753607i	$-0.728312\pi$
$863$	2.82843	−	2.82843i	0.0962808	−	0.0962808i	0.753607	+	0.657326i	$0.228312\pi$
$864$	−12.6777	+	22.6777i	−0.431303	+	0.771510i
$865$	12.0000	−	12.0000i	0.408012	−	0.408012i
$866$	12.7279	+	12.7279i	0.432512	+	0.432512i
$867$	17.0000	+	24.0416i	0.577350	+	0.816497i
$868$		−	10.0000i		−	0.339422i
$869$	28.2843	+	28.2843i	0.959478	+	0.959478i
$870$	5.65685	+	8.00000i	0.191785	+	0.271225i
$871$	−5.00000	+	25.0000i	−0.169419	+	0.847093i
$872$			4.24264i			0.143674i
$873$	−26.7990	+	12.7990i	−0.907008	+	0.433180i
$874$	12.0000			0.405906
$875$	−16.9706			−0.573710
$876$	0.414214	−	2.41421i	0.0139950	−	0.0815687i
$877$	13.0000	+	13.0000i	0.438979	+	0.438979i	0.891668	−	0.452689i	$-0.149535\pi$
$877$	13.0000	+	13.0000i	0.438979	+	0.438979i	−0.452689	+	0.891668i	$0.649535\pi$
$878$	−21.2132	−	21.2132i	−0.715911	−	0.715911i
$879$	4.10051	−	23.8995i	0.138307	−	0.806110i
$880$	8.00000			0.269680
$881$	25.4558			0.857629			0.428815	−	0.903393i	$-0.358931\pi$
$881$	25.4558			0.857629			0.428815	+	0.903393i	$0.358931\pi$
$882$	−13.5355	+	6.46447i	−0.455765	+	0.217670i
$883$			36.0000i			1.21150i	0.795656	+	0.605748i	$0.207126\pi$
$883$			36.0000i			1.21150i	−0.795656	+	0.605748i	$0.792874\pi$
$884$		0			0
$885$	−8.00000	−	11.3137i	−0.268917	−	0.380306i
$886$	20.0000	+	20.0000i	0.671913	+	0.671913i
$887$		−	14.1421i		−	0.474846i	−0.971406	−	0.237423i	$-0.923697\pi$
$887$		−	14.1421i		−	0.474846i	0.971406	−	0.237423i	$-0.0763028\pi$
$888$	−4.24264	−	6.00000i	−0.142374	−	0.201347i
$889$		0			0
$890$	−19.7990	+	19.7990i	−0.663664	+	0.663664i
$891$	3.79899	+	35.7990i	0.127271	+	1.19931i
$892$	11.0000	−	11.0000i	0.368307	−	0.368307i
$893$		−	5.65685i		−	0.189299i
$894$	2.82843	−	2.00000i	0.0945968	−	0.0668900i
$895$		0			0
$896$	−4.24264			−0.141737
$897$	−19.0294	+	49.4558i	−0.635374	+	1.65128i
$898$	−22.0000			−0.734150
$899$	14.1421	−	14.1421i	0.471667	−	0.471667i
$900$	1.00000	−	2.82843i	0.0333333	−	0.0942809i
$901$		0			0
$902$	5.65685	−	5.65685i	0.188353	−	0.188353i
$903$	2.48528	−	14.4853i	0.0827050	−	0.482040i
$904$	30.0000	−	30.0000i	0.997785	−	0.997785i
$905$		0			0
$906$	−2.00000	+	1.41421i	−0.0664455	+	0.0469841i
$907$		−	12.0000i		−	0.398453i	−0.979953	−	0.199227i	$-0.936157\pi$
$907$		−	12.0000i		−	0.398453i	0.979953	−	0.199227i	$-0.0638430\pi$
$908$	−5.65685	−	5.65685i	−0.187729	−	0.187729i
$909$	8.48528	−	24.0000i	0.281439	−	0.796030i
$910$	2.00000	−	10.0000i	0.0662994	−	0.331497i
$911$		−	48.0833i		−	1.59307i	−0.604593	−	0.796535i	$-0.706664\pi$
$911$		−	48.0833i		−	1.59307i	0.604593	−	0.796535i	$-0.293336\pi$
$912$	0.414214	−	2.41421i	0.0137160	−	0.0799426i
$913$	32.0000			1.05905
$914$	−41.0122			−1.35656
$915$	27.3137	+	4.68629i	0.902963	+	0.154924i
$916$	1.00000	+	1.00000i	0.0330409	+	0.0330409i
$917$	11.3137	+	11.3137i	0.373612	+	0.373612i
$918$		0			0
$919$	−34.0000			−1.12156			−0.560778	−	0.827966i	$-0.689498\pi$
$919$	−34.0000			−1.12156			−0.560778	+	0.827966i	$0.689498\pi$
$920$	−50.9117			−1.67851
$921$	41.0416	+	7.04163i	1.35237	+	0.232030i
$922$		−	10.0000i		−	0.329332i
$923$	−14.1421	−	2.82843i	−0.465494	−	0.0930988i
$924$	−8.00000	+	5.65685i	−0.263181	+	0.186097i
$925$	1.00000	+	1.00000i	0.0328798	+	0.0328798i
$926$			24.0416i			0.790057i
$927$	16.9706	+	6.00000i	0.557386	+	0.197066i
$928$	−10.0000	−	10.0000i	−0.328266	−	0.328266i
$929$	32.5269	−	32.5269i	1.06717	−	1.06717i	0.0695983	−	0.997575i	$-0.477828\pi$
$929$	32.5269	−	32.5269i	1.06717	−	1.06717i	0.997575	−	0.0695983i	$-0.0221717\pi$
$930$	−24.1421	−	4.14214i	−0.791652	−	0.135826i
$931$	−5.00000	+	5.00000i	−0.163868	+	0.163868i
$932$		−	25.4558i		−	0.833834i
$933$	−8.48528	−	12.0000i	−0.277796	−	0.392862i
$934$	−18.0000	+	18.0000i	−0.588978	+	0.588978i
$935$		0			0
$936$	27.8787	+	16.6066i	0.911243	+	0.542804i
$937$	−52.0000			−1.69877			−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000			−1.69877			−0.849383	+	0.527777i	$0.823026\pi$
$938$	−7.07107	+	7.07107i	−0.230879	+	0.230879i
$939$	−8.00000	−	11.3137i	−0.261070	−	0.369209i
$940$			8.00000i			0.260931i
$941$	−26.8701	+	26.8701i	−0.875939	+	0.875939i	−0.993112	−	0.117173i	$-0.962617\pi$
$941$	−26.8701	+	26.8701i	−0.875939	+	0.875939i	0.117173	+	0.993112i	$0.462617\pi$
$942$	−23.8995	−	4.10051i	−0.778688	−	0.133602i
$943$	−12.0000	+	12.0000i	−0.390774	+	0.390774i
$944$	−2.82843	−	2.82843i	−0.0920575	−	0.0920575i
$945$	4.00000	+	14.1421i	0.130120	+	0.460044i
$946$		−	24.0000i		−	0.780307i
$947$	22.6274	+	22.6274i	0.735292	+	0.735292i	0.971663	−	0.236371i	$-0.0759580\pi$
$947$	22.6274	+	22.6274i	0.735292	+	0.735292i	−0.236371	+	0.971663i	$0.575958\pi$
$948$	−14.1421	+	10.0000i	−0.459315	+	0.324785i
$949$	−5.00000	−	1.00000i	−0.162307	−	0.0324614i
$950$			1.41421i			0.0458831i
$951$	−17.0711	−	2.92893i	−0.553567	−	0.0949771i
$952$		0			0
$953$	25.4558			0.824596			0.412298	−	0.911049i	$-0.364726\pi$
$953$	25.4558			0.824596			0.412298	+	0.911049i	$0.364726\pi$
$954$	15.3137	−	7.31371i	0.495800	−	0.236790i
$955$	−4.00000	−	4.00000i	−0.129437	−	0.129437i
$956$	−14.1421	−	14.1421i	−0.457389	−	0.457389i
$957$	−19.3137	−	3.31371i	−0.624324	−	0.107117i
$958$	32.0000			1.03387
$959$	19.7990			0.639343
$960$	−4.10051	+	23.8995i	−0.132343	+	0.771353i
$961$			19.0000i			0.612903i
$962$	−4.24264	+	2.82843i	−0.136788	+	0.0911922i
$963$	16.0000	+	5.65685i	0.515593	+	0.182290i
$964$	−17.0000	−	17.0000i	−0.547533	−	0.547533i
$965$			53.7401i			1.72996i
$966$	−16.9706	+	12.0000i	−0.546019	+	0.386094i
$967$	−23.0000	−	23.0000i	−0.739630	−	0.739630i	0.232876	−	0.972506i	$-0.425186\pi$
$967$	−23.0000	−	23.0000i	−0.739630	−	0.739630i	−0.972506	+	0.232876i	$0.925186\pi$
$968$	−10.6066	+	10.6066i	−0.340909	+	0.340909i
$969$		0			0
$970$	−14.0000	+	14.0000i	−0.449513	+	0.449513i
$971$		−	31.1127i		−	0.998454i	−0.866471	−	0.499227i	$-0.833617\pi$
$971$		−	31.1127i		−	0.998454i	0.866471	−	0.499227i	$-0.166383\pi$
$972$	−15.5563	−	1.00000i	−0.498970	−	0.0320750i
$973$	−4.00000	+	4.00000i	−0.128234	+	0.128234i
$974$	26.8701			0.860972
$975$	−5.82843	−	2.24264i	−0.186659	−	0.0718220i
$976$	8.00000			0.256074
$977$	−26.8701	+	26.8701i	−0.859649	+	0.859649i	−0.991297	−	0.131647i	$-0.957973\pi$
$977$	−26.8701	+	26.8701i	−0.859649	+	0.859649i	0.131647	+	0.991297i	$0.457973\pi$
$978$	−2.00000	+	1.41421i	−0.0639529	+	0.0452216i
$979$		−	56.0000i		−	1.78977i
$980$	7.07107	−	7.07107i	0.225877	−	0.225877i
$981$	−3.82843	+	1.82843i	−0.122232	+	0.0583772i
$982$	−30.0000	+	30.0000i	−0.957338	+	0.957338i
$983$	−2.82843	−	2.82843i	−0.0902128	−	0.0902128i	0.660560	−	0.750773i	$-0.270319\pi$
$983$	−2.82843	−	2.82843i	−0.0902128	−	0.0902128i	−0.750773	+	0.660560i	$0.770319\pi$
$984$	6.00000	+	8.48528i	0.191273	+	0.270501i
$985$			44.0000i			1.40196i
$986$		0			0
$987$	5.65685	+	8.00000i	0.180060	+	0.254643i
$988$	5.00000	+	1.00000i	0.159071	+	0.0318142i
$989$			50.9117i			1.61890i
$990$	10.3431	+	21.6569i	0.328727	+	0.688300i
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	35.3553			1.12253
$993$	2.89949	−	16.8995i	0.0920127	−	0.536289i
$994$	−4.00000	−	4.00000i	−0.126872	−	0.126872i
$995$		0			0
$996$	−2.34315	+	13.6569i	−0.0742454	+	0.432734i
$997$	26.0000			0.823428			0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000			0.823428			0.411714	+	0.911313i	$0.364930\pi$
$998$	−32.5269			−1.02962
$999$	3.58579	−	6.41421i	0.113449	−	0.202937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.2.f.a.8.2	yes	4
3.2	odd	2	inner	39.2.f.a.8.1	yes	4
4.3	odd	2		624.2.bf.d.593.2		4
5.2	odd	4		975.2.n.d.749.2		4
5.3	odd	4		975.2.n.c.749.1		4
5.4	even	2		975.2.o.j.476.1		4
12.11	even	2		624.2.bf.d.593.1		4
13.2	odd	12		507.2.k.j.188.2		8
13.3	even	3		507.2.k.j.488.2		8
13.4	even	6		507.2.k.i.89.2		8
13.5	odd	4	inner	39.2.f.a.5.1	✓	4
13.6	odd	12		507.2.k.j.80.1		8
13.7	odd	12		507.2.k.i.80.2		8
13.8	odd	4		507.2.f.a.239.2		4
13.9	even	3		507.2.k.j.89.1		8
13.10	even	6		507.2.k.i.488.1		8
13.11	odd	12		507.2.k.i.188.1		8
13.12	even	2		507.2.f.a.437.1		4
15.2	even	4		975.2.n.d.749.1		4
15.8	even	4		975.2.n.c.749.2		4
15.14	odd	2		975.2.o.j.476.2		4
39.2	even	12		507.2.k.j.188.1		8
39.5	even	4	inner	39.2.f.a.5.2	yes	4
39.8	even	4		507.2.f.a.239.1		4
39.11	even	12		507.2.k.i.188.2		8
39.17	odd	6		507.2.k.i.89.1		8
39.20	even	12		507.2.k.i.80.1		8
39.23	odd	6		507.2.k.i.488.2		8
39.29	odd	6		507.2.k.j.488.1		8
39.32	even	12		507.2.k.j.80.2		8
39.35	odd	6		507.2.k.j.89.2		8
39.38	odd	2		507.2.f.a.437.2		4
52.31	even	4		624.2.bf.d.161.2		4
65.18	even	4		975.2.n.d.824.1		4
65.44	odd	4		975.2.o.j.551.2		4
65.57	even	4		975.2.n.c.824.2		4
156.83	odd	4		624.2.bf.d.161.1		4
195.44	even	4		975.2.o.j.551.1		4
195.83	odd	4		975.2.n.d.824.2		4
195.122	odd	4		975.2.n.c.824.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.f.a.5.1	✓	4	13.5	odd	4	inner
39.2.f.a.5.2	yes	4	39.5	even	4	inner
39.2.f.a.8.1	yes	4	3.2	odd	2	inner
39.2.f.a.8.2	yes	4	1.1	even	1	trivial
507.2.f.a.239.1		4	39.8	even	4
507.2.f.a.239.2		4	13.8	odd	4
507.2.f.a.437.1		4	13.12	even	2
507.2.f.a.437.2		4	39.38	odd	2
507.2.k.i.80.1		8	39.20	even	12
507.2.k.i.80.2		8	13.7	odd	12
507.2.k.i.89.1		8	39.17	odd	6
507.2.k.i.89.2		8	13.4	even	6
507.2.k.i.188.1		8	13.11	odd	12
507.2.k.i.188.2		8	39.11	even	12
507.2.k.i.488.1		8	13.10	even	6
507.2.k.i.488.2		8	39.23	odd	6
507.2.k.j.80.1		8	13.6	odd	12
507.2.k.j.80.2		8	39.32	even	12
507.2.k.j.89.1		8	13.9	even	3
507.2.k.j.89.2		8	39.35	odd	6
507.2.k.j.188.1		8	39.2	even	12
507.2.k.j.188.2		8	13.2	odd	12
507.2.k.j.488.1		8	39.29	odd	6
507.2.k.j.488.2		8	13.3	even	3
624.2.bf.d.161.1		4	156.83	odd	4
624.2.bf.d.161.2		4	52.31	even	4
624.2.bf.d.593.1		4	12.11	even	2
624.2.bf.d.593.2		4	4.3	odd	2
975.2.n.c.749.1		4	5.3	odd	4
975.2.n.c.749.2		4	15.8	even	4
975.2.n.c.824.1		4	195.122	odd	4
975.2.n.c.824.2		4	65.57	even	4
975.2.n.d.749.1		4	15.2	even	4
975.2.n.d.749.2		4	5.2	odd	4
975.2.n.d.824.1		4	65.18	even	4
975.2.n.d.824.2		4	195.83	odd	4
975.2.o.j.476.1		4	5.4	even	2
975.2.o.j.476.2		4	15.14	odd	2
975.2.o.j.551.1		4	195.44	even	4
975.2.o.j.551.2		4	65.44	odd	4

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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	39.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000i q^{4} +(-1.41421 + 1.41421i) q^{5} +(-1.70711 - 0.292893i) q^{6} +(1.00000 - 1.00000i) q^{7} +(2.12132 + 2.12132i) q^{8} +(-1.00000 + 2.82843i) q^{9} +2.00000i q^{10} +(-2.82843 - 2.82843i) q^{11} +(1.41421 - 1.00000i) q^{12} +(-2.00000 - 3.00000i) q^{13} -1.41421i q^{14} +(3.41421 + 0.585786i) q^{15} +1.00000 q^{16} +(1.29289 + 2.70711i) q^{18} +(1.00000 + 1.00000i) q^{19} +(-1.41421 - 1.41421i) q^{20} +(-2.41421 - 0.414214i) q^{21} -4.00000 q^{22} +8.48528 q^{23} +(0.878680 - 5.12132i) q^{24} +1.00000i q^{25} +(-3.53553 - 0.707107i) q^{26} +(5.00000 - 1.41421i) q^{27} +(1.00000 + 1.00000i) q^{28} +2.82843i q^{29} +(2.82843 - 2.00000i) q^{30} +(-5.00000 - 5.00000i) q^{31} +(-3.53553 + 3.53553i) q^{32} +(-1.17157 + 6.82843i) q^{33} +2.82843i q^{35} +(-2.82843 - 1.00000i) q^{36} +(1.00000 - 1.00000i) q^{37} +1.41421 q^{38} +(-2.24264 + 5.82843i) q^{39} -6.00000 q^{40} +(-1.41421 + 1.41421i) q^{41} +(-2.00000 + 1.41421i) q^{42} +6.00000i q^{43} +(2.82843 - 2.82843i) q^{44} +(-2.58579 - 5.41421i) q^{45} +(6.00000 - 6.00000i) q^{46} +(-2.82843 - 2.82843i) q^{47} +(-1.00000 - 1.41421i) q^{48} +5.00000i q^{49} +(0.707107 + 0.707107i) q^{50} +(3.00000 - 2.00000i) q^{52} -5.65685i q^{53} +(2.53553 - 4.53553i) q^{54} +8.00000 q^{55} +4.24264 q^{56} +(0.414214 - 2.41421i) q^{57} +(2.00000 + 2.00000i) q^{58} +(-2.82843 - 2.82843i) q^{59} +(-0.585786 + 3.41421i) q^{60} +8.00000 q^{61} -7.07107 q^{62} +(1.82843 + 3.82843i) q^{63} +7.00000i q^{64} +(7.07107 + 1.41421i) q^{65} +(4.00000 + 5.65685i) q^{66} +(-5.00000 - 5.00000i) q^{67} +(-8.48528 - 12.0000i) q^{69} +(2.00000 + 2.00000i) q^{70} +(2.82843 - 2.82843i) q^{71} +(-8.12132 + 3.87868i) q^{72} +(1.00000 - 1.00000i) q^{73} -1.41421i q^{74} +(1.41421 - 1.00000i) q^{75} +(-1.00000 + 1.00000i) q^{76} -5.65685 q^{77} +(2.53553 + 5.70711i) q^{78} -10.0000 q^{79} +(-1.41421 + 1.41421i) q^{80} +(-7.00000 - 5.65685i) q^{81} +2.00000i q^{82} +(-5.65685 + 5.65685i) q^{83} +(0.414214 - 2.41421i) q^{84} +(4.24264 + 4.24264i) q^{86} +(4.00000 - 2.82843i) q^{87} -12.0000i q^{88} +(9.89949 + 9.89949i) q^{89} +(-5.65685 - 2.00000i) q^{90} +(-5.00000 - 1.00000i) q^{91} +8.48528i q^{92} +(-2.07107 + 12.0711i) q^{93} -4.00000 q^{94} -2.82843 q^{95} +(8.53553 + 1.46447i) q^{96} +(7.00000 + 7.00000i) q^{97} +(3.53553 + 3.53553i) q^{98} +(10.8284 - 5.17157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 4 q^{6} + 4 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 4 q^{16} + 8 q^{18} + 4 q^{19} - 4 q^{21} - 16 q^{22} + 12 q^{24} + 20 q^{27} + 4 q^{28} - 20 q^{31} - 16 q^{33} + 4 q^{37} + 8 q^{39}+ \cdots + 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 4 * q^6 + 4 * q^7 - 4 * q^9 - 8 * q^13 + 8 * q^15 + 4 * q^16 + 8 * q^18 + 4 * q^19 - 4 * q^21 - 16 * q^22 + 12 * q^24 + 20 * q^27 + 4 * q^28 - 20 * q^31 - 16 * q^33 + 4 * q^37 + 8 * q^39 - 24 * q^40 - 8 * q^42 - 16 * q^45 + 24 * q^46 - 4 * q^48 + 12 * q^52 - 4 * q^54 + 32 * q^55 - 4 * q^57 + 8 * q^58 - 8 * q^60 + 32 * q^61 - 4 * q^63 + 16 * q^66 - 20 * q^67 + 8 * q^70 - 24 * q^72 + 4 * q^73 - 4 * q^76 - 4 * q^78 - 40 * q^79 - 28 * q^81 - 4 * q^84 + 16 * q^87 - 20 * q^91 + 20 * q^93 - 16 * q^94 + 20 * q^96 + 28 * q^97 + 32 * q^99

Introduction

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