LMFDB - Embedded newform 507.2.f.a.437.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(239,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, 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("507.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.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:	$4.04841538248$
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:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	507.437
Dual form			507.2.f.a.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000i q^{4} +(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} -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} +(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} -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} -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} +(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} -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} +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^{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} - 24 q^{40} - 8 q^{42}+ \cdots - 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^6 - 4 * q^7 - 4 * q^9 - 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 - 24 * q^40 - 8 * q^42 + 16 * q^45 - 24 * q^46 - 4 * q^48 + 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 - 40 * q^79 - 28 * q^81 + 4 * q^84 + 16 * q^87 - 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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	−0.911438	−	0.411438i	$-0.865027\pi$
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i	0.411438	+	0.911438i	$0.365027\pi$
$3$	−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	−0.316228	−	0.948683i	$-0.602416\pi$
$5$	1.41421	−	1.41421i	0.632456	−	0.632456i	0.948683	+	0.316228i	$0.102416\pi$
$6$	1.70711	+	0.292893i	0.696923	+	0.119573i
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$8$	−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	0.990478	−	0.137675i	$-0.0439628\pi$
$11$	2.82843	+	2.82843i	0.852803	+	0.852803i	−0.137675	+	0.990478i	$0.543963\pi$
$12$	1.41421	−	1.00000i	0.408248	−	0.288675i
$13$		0			0
$13$		0			0
$14$		−	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	0.583033	−	0.812449i	$-0.301866\pi$
$19$	−1.00000	−	1.00000i	−0.229416	−	0.229416i	−0.812449	+	0.583033i	$0.801866\pi$
$20$	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
$26$		0			0
$27$	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	0.995261	−	0.0972349i	$-0.0309998\pi$
$31$	5.00000	+	5.00000i	0.898027	+	0.898027i	−0.0972349	+	0.995261i	$0.531000\pi$
$32$	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	−0.784512	−	0.620113i	$-0.787087\pi$
$37$	−1.00000	+	1.00000i	−0.164399	+	0.164399i	0.620113	+	0.784512i	$0.287087\pi$
$38$	1.41421			0.229416
$39$		0			0
$40$	−6.00000			−0.948683
$41$	1.41421	−	1.41421i	0.220863	−	0.220863i	−0.587999	−	0.808862i	$-0.700084\pi$
$41$	1.41421	−	1.41421i	0.220863	−	0.220863i	0.808862	+	0.587999i	$0.200084\pi$
$42$	−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	0.882632	−	0.470064i	$-0.155769\pi$
$47$	2.82843	+	2.82843i	0.412568	+	0.412568i	−0.470064	+	0.882632i	$0.655769\pi$
$48$	−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
$52$		0			0
$53$		−	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	0.866831	−	0.498601i	$-0.166153\pi$
$59$	2.82843	+	2.82843i	0.368230	+	0.368230i	−0.498601	+	0.866831i	$0.666153\pi$
$60$	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
$65$		0			0
$66$	4.00000	+	5.65685i	0.492366	+	0.696311i
$67$	5.00000	+	5.00000i	0.610847	+	0.610847i	0.943167	−	0.332320i	$-0.107831\pi$
$67$	5.00000	+	5.00000i	0.610847	+	0.610847i	−0.332320	+	0.943167i	$0.607831\pi$
$68$		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	−0.854736	−	0.519063i	$-0.826281\pi$
$71$	−2.82843	+	2.82843i	−0.335673	+	0.335673i	0.519063	+	0.854736i	$0.326281\pi$
$72$	8.12132	−	3.87868i	0.957107	−	0.457107i
$73$	−1.00000	+	1.00000i	−0.117041	+	0.117041i	−0.763202	−	0.646160i	$-0.776374\pi$
$73$	−1.00000	+	1.00000i	−0.117041	+	0.117041i	0.646160	+	0.763202i	$0.276374\pi$
$74$		−	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
$78$		0			0
$79$	−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	−0.324846	−	0.945767i	$-0.605313\pi$
$83$	5.65685	−	5.65685i	0.620920	−	0.620920i	0.945767	+	0.324846i	$0.105313\pi$
$84$	−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	$-0.983878\pi$
$89$	−9.89949	−	9.89949i	−1.04934	−	1.04934i	−0.0506267	−	0.998718i	$-0.516122\pi$
$90$	−5.65685	−	2.00000i	−0.596285	−	0.210819i
$91$		0			0
$92$			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	0.255948	−	0.966691i	$-0.417612\pi$
$97$	−7.00000	−	7.00000i	−0.710742	−	0.710742i	−0.966691	+	0.255948i	$0.917612\pi$
$98$	−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	$-0.0955191\pi$
$104$		0			0
$105$	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	0.657592	−	0.753374i	$-0.271575\pi$
$109$	−1.00000	−	1.00000i	−0.0957826	−	0.0957826i	−0.753374	+	0.657592i	$0.771575\pi$
$110$	−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
$117$		0			0
$118$	−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
$130$		0			0
$131$			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	0.143831	−	0.989602i	$-0.454058\pi$
$137$	−9.89949	−	9.89949i	−0.845771	−	0.845771i	−0.989602	+	0.143831i	$0.954058\pi$
$138$	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
$143$		0			0
$144$	−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	−0.646802	−	0.762658i	$-0.723894\pi$
$149$	1.41421	−	1.41421i	0.115857	−	0.115857i	0.762658	+	0.646802i	$0.223894\pi$
$150$	−0.292893	+	1.70711i	−0.0239146	+	0.139385i
$151$	−1.00000	+	1.00000i	−0.0813788	+	0.0813788i	−0.746625	−	0.665246i	$-0.768327\pi$
$151$	−1.00000	+	1.00000i	−0.0813788	+	0.0813788i	0.665246	+	0.746625i	$0.268327\pi$
$152$			4.24264i			0.344124i
$153$		0			0
$154$	4.00000	−	4.00000i	0.322329	−	0.322329i
$155$	14.1421			1.13592
$156$		0			0
$157$	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	−0.745184	−	0.666858i	$-0.767639\pi$
$163$	−1.00000	+	1.00000i	−0.0783260	+	0.0783260i	0.666858	+	0.745184i	$0.267639\pi$
$164$	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	0.808022	−	0.589152i	$-0.200538\pi$
$167$	2.82843	+	2.82843i	0.218870	+	0.218870i	−0.589152	+	0.808022i	$0.700538\pi$
$168$	−4.24264	−	6.00000i	−0.327327	−	0.462910i
$169$		0			0
$170$		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			$\pi$
$182$		0			0
$183$	−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	$0.668091\pi$
$193$	−19.0000	+	19.0000i	−1.36765	+	1.36765i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	9.89949			0.710742
$195$		0			0
$196$	−5.00000			−0.357143
$197$	−15.5563	+	15.5563i	−1.10834	+	1.10834i	−0.114976	+	0.993368i	$0.536679\pi$
$197$	−15.5563	+	15.5563i	−1.10834	+	1.10834i	−0.993368	+	0.114976i	$0.963321\pi$
$198$	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
$208$		0			0
$209$		−	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	0.971921	−	0.235307i	$-0.0756095\pi$
$223$	11.0000	+	11.0000i	0.736614	+	0.736614i	−0.235307	+	0.971921i	$0.575609\pi$
$224$			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	−0.494002	−	0.869461i	$-0.664466\pi$
$227$	5.65685	−	5.65685i	0.375459	−	0.375459i	0.869461	+	0.494002i	$0.164466\pi$
$228$	−2.41421	−	0.414214i	−0.159885	−	0.0274320i
$229$	−1.00000	+	1.00000i	−0.0660819	+	0.0660819i	−0.739375	−	0.673293i	$-0.764879\pi$
$229$	−1.00000	+	1.00000i	−0.0660819	+	0.0660819i	0.673293	+	0.739375i	$0.264879\pi$
$230$			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	$0.813859\pi$
$234$		0			0
$235$	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	−0.0818647	−	0.996643i	$-0.526088\pi$
$239$	14.1421	−	14.1421i	0.914779	−	0.914779i	0.996643	+	0.0818647i	$0.0260876\pi$
$240$	−3.41421	−	0.585786i	−0.220387	−	0.0378124i
$241$	17.0000	−	17.0000i	1.09507	−	1.09507i	0.100088	−	0.994979i	$-0.468088\pi$
$241$	17.0000	−	17.0000i	1.09507	−	1.09507i	0.994979	−	0.100088i	$-0.0319123\pi$
$242$	−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
$247$		0			0
$248$		−	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
$260$		0			0
$261$	−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	$0.553879\pi$
$271$	−19.0000	+	19.0000i	−1.15417	+	1.15417i	−0.985709	+	0.168459i	$0.946121\pi$
$272$		0			0
$273$		0			0
$274$	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	0.347227	−	0.937781i	$-0.387123\pi$
$281$	−9.89949	−	9.89949i	−0.590554	−	0.590554i	−0.937781	+	0.347227i	$0.887123\pi$
$282$	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
$286$		0			0
$287$			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	0.356110	−	0.934444i	$-0.384103\pi$
$293$	−9.89949	−	9.89949i	−0.578335	−	0.578335i	−0.934444	+	0.356110i	$0.884103\pi$
$294$	−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
$299$		0			0
$300$	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	−0.0293286	−	0.999570i	$-0.509337\pi$
$307$	17.0000	−	17.0000i	0.970241	−	0.970241i	0.999570	+	0.0293286i	$0.00933691\pi$
$308$		−	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	$0.422663\pi$
$312$		0			0
$313$	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	−0.877227	−	0.480076i	$-0.840609\pi$
$317$	−7.07107	+	7.07107i	−0.397151	+	0.397151i	0.480076	+	0.877227i	$0.340609\pi$
$318$	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
$325$		0			0
$326$		−	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	0.488057	−	0.872812i	$-0.337706\pi$
$331$	−7.00000	−	7.00000i	−0.384755	−	0.384755i	−0.872812	+	0.488057i	$0.837706\pi$
$332$	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	$-0.0522527\pi$
$338$		0			0
$339$	−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	−0.0862816	−	0.996271i	$-0.527498\pi$
$349$	17.0000	−	17.0000i	0.909989	−	0.909989i	0.996271	+	0.0862816i	$0.0274985\pi$
$350$	1.41421			0.0755929
$351$		0			0
$352$	20.0000			1.06600
$353$	18.3848	−	18.3848i	0.978523	−	0.978523i	−0.0212513	−	0.999774i	$-0.506765\pi$
$353$	18.3848	−	18.3848i	0.978523	−	0.978523i	0.999774	+	0.0212513i	$0.00676499\pi$
$354$	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	0.777796	−	0.628517i	$-0.216338\pi$
$359$	2.82843	+	2.82843i	0.149279	+	0.149279i	−0.628517	+	0.777796i	$0.716338\pi$
$360$	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
$364$		0			0
$365$			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
$377$		0			0
$378$	−2.00000	−	7.07107i	−0.102869	−	0.363696i
$379$	−19.0000	−	19.0000i	−0.975964	−	0.975964i	0.0237534	−	0.999718i	$-0.492438\pi$
$379$	−19.0000	−	19.0000i	−0.975964	−	0.975964i	−0.999718	+	0.0237534i	$0.992438\pi$
$380$		−	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	−0.934380	−	0.356277i	$-0.884046\pi$
$383$	−11.3137	+	11.3137i	−0.578103	+	0.578103i	0.356277	+	0.934380i	$0.384046\pi$
$384$	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	$0.358436\pi$
$390$		0			0
$391$		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	−0.137321	−	0.990527i	$-0.543849\pi$
$397$	17.0000	−	17.0000i	0.853206	−	0.853206i	0.990527	+	0.137321i	$0.0438492\pi$
$398$		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	0.979293	−	0.202446i	$-0.0648892\pi$
$401$	15.5563	+	15.5563i	0.776847	+	0.776847i	−0.202446	+	0.979293i	$0.564889\pi$
$402$	7.07107	+	10.0000i	0.352673	+	0.498755i
$403$		0			0
$404$		−	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	$0.0473931\pi$
$409$	23.0000	+	23.0000i	1.13728	+	1.13728i	0.148340	+	0.988936i	$0.452607\pi$
$410$	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
$416$		0			0
$417$	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	$-0.919490\pi$
$421$	−25.0000	−	25.0000i	−1.21843	−	1.21843i	−0.250242	−	0.968183i	$-0.580510\pi$
$422$	−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
$429$		0			0
$430$	−12.0000			−0.578691
$431$	22.6274	−	22.6274i	1.08992	−	1.08992i	0.0943889	−	0.995535i	$-0.469910\pi$
$431$	22.6274	−	22.6274i	1.08992	−	1.08992i	0.995535	−	0.0943889i	$-0.0300897\pi$
$432$	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	0.971439	−	0.237289i	$-0.0762590\pi$
$449$	15.5563	+	15.5563i	0.734150	+	0.734150i	−0.237289	+	0.971439i	$0.576259\pi$
$450$	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
$455$		0			0
$456$	6.00000	−	4.24264i	0.280976	−	0.198680i
$457$	29.0000	+	29.0000i	1.35656	+	1.35656i	0.878117	+	0.478446i	$0.158800\pi$
$457$	29.0000	+	29.0000i	1.35656	+	1.35656i	0.478446	+	0.878117i	$0.341200\pi$
$458$		−	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	−0.852333	−	0.523000i	$-0.824813\pi$
$461$	−7.07107	+	7.07107i	−0.329332	+	0.329332i	0.523000	+	0.852333i	$0.324813\pi$
$462$	−9.65685	−	1.65685i	−0.449278	−	0.0770838i
$463$	17.0000	−	17.0000i	0.790057	−	0.790057i	−0.191446	−	0.981503i	$-0.561318\pi$
$463$	17.0000	−	17.0000i	0.790057	−	0.790057i	0.981503	+	0.191446i	$0.0613177\pi$
$464$			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	$0.700470\pi$
$468$		0			0
$469$	−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	$-0.989027\pi$
$479$	−22.6274	−	22.6274i	−1.03387	−	1.03387i	−0.0344672	−	0.999406i	$-0.510973\pi$
$480$	−14.1421	+	10.0000i	−0.645497	+	0.456435i
$481$		0			0
$482$			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	0.130479	−	0.991451i	$-0.458349\pi$
$487$	−19.0000	−	19.0000i	−0.860972	−	0.860972i	−0.991451	+	0.130479i	$0.958349\pi$
$488$	−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
$494$		0			0
$495$	−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	$0.00957421\pi$
$499$	23.0000	+	23.0000i	1.02962	+	1.02962i	0.0300737	+	0.999548i	$0.490426\pi$
$500$	−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
$507$		0			0
$508$		0			0
$509$	−24.0416	+	24.0416i	−1.06563	+	1.06563i	−0.0679369	+	0.997690i	$0.521642\pi$
$509$	−24.0416	+	24.0416i	−1.06563	+	1.06563i	−0.997690	+	0.0679369i	$0.978358\pi$
$510$		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
$520$		0			0
$521$		−	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
$533$		0			0
$534$	−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	−0.728277	−	0.685283i	$-0.759678\pi$
$541$	−1.00000	+	1.00000i	−0.0429934	+	0.0429934i	0.685283	+	0.728277i	$0.259678\pi$
$542$		−	26.8701i		−	1.15417i
$543$		0			0
$544$		0			0
$545$	−2.82843			−0.121157
$546$		0			0
$547$	−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	0.465561	−	0.885016i	$-0.345853\pi$
$557$	−9.89949	−	9.89949i	−0.419455	−	0.419455i	−0.885016	+	0.465561i	$0.845853\pi$
$558$	7.07107	−	20.0000i	0.299342	−	0.846668i
$559$		0			0
$560$			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	$0.919210\pi$
$572$		0			0
$573$	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	0.685985	−	0.727616i	$-0.259372\pi$
$577$	−1.00000	−	1.00000i	−0.0416305	−	0.0416305i	−0.727616	+	0.685985i	$0.759372\pi$
$578$	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
$585$		0			0
$586$	14.0000			0.578335
$587$	5.65685	−	5.65685i	0.233483	−	0.233483i	−0.580662	−	0.814145i	$-0.697206\pi$
$587$	5.65685	−	5.65685i	0.233483	−	0.233483i	0.814145	+	0.580662i	$0.197206\pi$
$588$	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	0.474001	−	0.880524i	$-0.342809\pi$
$593$	−9.89949	−	9.89949i	−0.406524	−	0.406524i	−0.880524	+	0.474001i	$0.842809\pi$
$594$	−20.0000	+	5.65685i	−0.820610	+	0.232104i
$595$		0			0
$596$	1.41421	+	1.41421i	0.0579284	+	0.0579284i
$597$		0			0
$598$		0			0
$599$			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
$611$		0			0
$612$		0			0
$613$	−1.00000	−	1.00000i	−0.0403896	−	0.0403896i	0.686624	−	0.727013i	$-0.259092\pi$
$613$	−1.00000	−	1.00000i	−0.0403896	−	0.0403896i	−0.727013	+	0.686624i	$0.759092\pi$
$614$			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	$-0.472783\pi$
$617$	26.8701	−	26.8701i	1.08175	−	1.08175i	0.996347	−	0.0854011i	$-0.0272172\pi$
$618$	1.75736	−	10.2426i	0.0706914	−	0.412019i
$619$	−1.00000	+	1.00000i	−0.0401934	+	0.0401934i	−0.726918	−	0.686724i	$-0.759048\pi$
$619$	−1.00000	+	1.00000i	−0.0401934	+	0.0401934i	0.686724	+	0.726918i	$0.259048\pi$
$620$			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
$624$		0			0
$625$	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	−0.975661	−	0.219283i	$-0.929628\pi$
$631$	−19.0000	+	19.0000i	−0.756378	+	0.756378i	0.219283	+	0.975661i	$0.429628\pi$
$632$	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
$637$		0			0
$638$		−	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	0.798790	−	0.601610i	$-0.205474\pi$
$643$	5.00000	+	5.00000i	0.197181	+	0.197181i	−0.601610	+	0.798790i	$0.705474\pi$
$644$	−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			0
$651$	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	−0.726287	−	0.687392i	$-0.758756\pi$
$661$	−1.00000	+	1.00000i	−0.0388955	+	0.0388955i	0.687392	+	0.726287i	$0.258756\pi$
$662$	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
$676$		0			0
$677$		−	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	0.759147	−	0.650920i	$-0.225617\pi$
$683$	2.82843	+	2.82843i	0.108227	+	0.108227i	−0.650920	+	0.759147i	$0.725617\pi$
$684$	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
$689$		0			0
$690$	24.0000	−	16.9706i	0.913664	−	0.646058i
$691$	11.0000	+	11.0000i	0.418460	+	0.418460i	0.884673	−	0.466213i	$-0.154382\pi$
$691$	11.0000	+	11.0000i	0.418460	+	0.418460i	−0.466213	+	0.884673i	$0.654382\pi$
$692$		−	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	$0.0886666\pi$
$702$		0			0
$703$	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	−0.967278	−	0.253718i	$-0.918346\pi$
$709$	−19.0000	+	19.0000i	−0.713560	+	0.713560i	0.253718	+	0.967278i	$0.418346\pi$
$710$	−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
$715$		0			0
$716$		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	$-0.349373\pi$
$728$		0			0
$729$	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	0.793391	−	0.608712i	$-0.208314\pi$
$733$	5.00000	+	5.00000i	0.184679	+	0.184679i	−0.608712	+	0.793391i	$0.708314\pi$
$734$	−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	−0.725260	−	0.688475i	$-0.758281\pi$
$739$	−1.00000	+	1.00000i	−0.0367856	+	0.0367856i	0.688475	+	0.725260i	$0.258281\pi$
$740$	−2.82843			−0.103975
$741$		0			0
$742$	−8.00000			−0.293689
$743$	−11.3137	+	11.3137i	−0.415060	+	0.415060i	−0.883497	−	0.468437i	$-0.844817\pi$
$743$	−11.3137	+	11.3137i	−0.415060	+	0.415060i	0.468437	+	0.883497i	$0.344817\pi$
$744$	−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
$754$		0			0
$755$			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	$-0.888933\pi$
$761$	−35.3553	−	35.3553i	−1.28163	−	1.28163i	−0.341890	−	0.939740i	$-0.611067\pi$
$762$		0			0
$763$	2.00000			0.0724049
$764$	−2.82843			−0.102329
$765$		0			0
$766$		−	16.0000i		−	0.578103i
$767$		0			0
$768$	17.0000	+	24.0416i	0.613435	+	0.867528i
$769$	−13.0000	−	13.0000i	−0.468792	−	0.468792i	0.432731	−	0.901523i	$-0.357550\pi$
$769$	−13.0000	−	13.0000i	−0.468792	−	0.468792i	−0.901523	+	0.432731i	$0.857550\pi$
$770$		−	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	−0.506298	−	0.862358i	$-0.668987\pi$
$773$	9.89949	−	9.89949i	0.356060	−	0.356060i	0.862358	+	0.506298i	$0.168987\pi$
$774$	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

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.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} -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} +(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} -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} -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} +(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} -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} +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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{6} - 4 q^{7} - 4 q^{9} - 8 q^{15} + 4 q^{16} - 8 q^{18} - 4 q^{19} + 4 q^{21} - 16 q^{22} - 12 q^{24} + 20 q^{27} - 4 q^{28} + 20 q^{31} + 16 q^{33} - 4 q^{37} - 24 q^{40} - 8 q^{42}+ \cdots - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^6 - 4 * q^7 - 4 * q^9 - 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 - 24 * q^40 - 8 * q^42 + 16 * q^45 - 24 * q^46 - 4 * q^48 + 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 - 40 * q^79 - 28 * q^81 + 4 * q^84 + 16 * q^87 - 20 * q^93 - 16 * q^94 - 20 * q^96 - 28 * q^97 - 32 * q^99

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