LMFDB - Embedded newform 507.2.f.a.437.2

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			437.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	507.437
Dual form			507.2.f.a.239.2

$q$-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} +(0.292893 + 1.70711i) 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} +(-0.585786 - 3.41421i) q^{15} +1.00000 q^{16} +(-2.70711 - 1.29289i) q^{18} +(-1.00000 - 1.00000i) q^{19} +(-1.41421 - 1.41421i) q^{20} +(-0.414214 - 2.41421i) q^{21} -4.00000 q^{22} -8.48528 q^{23} +(-5.12132 + 0.878680i) 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} +(6.82843 - 1.17157i) 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} +(5.41421 + 2.58579i) 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} +(4.53553 - 2.53553i) q^{54} +8.00000 q^{55} -4.24264 q^{56} +(2.41421 - 0.414214i) q^{57} +(-2.00000 - 2.00000i) q^{58} +(-2.82843 - 2.82843i) q^{59} +(3.41421 - 0.585786i) q^{60} +8.00000 q^{61} +7.07107 q^{62} +(3.82843 + 1.82843i) 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} +(3.87868 - 8.12132i) 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} +(2.41421 - 0.414214i) 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} +(-12.0711 + 2.07107i) q^{93} -4.00000 q^{94} +2.82843 q^{95} +(-1.46447 - 8.53553i) q^{96} +(-7.00000 - 7.00000i) q^{97} +(3.53553 + 3.53553i) q^{98} +(-5.17157 + 10.8284i) 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	−0.411438	−	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	$0.397584\pi$
$6$	0.292893	+	1.70711i	0.119573	+	0.696923i
$7$	−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	0.137675	−	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
$13$		0			0
$13$		0			0
$14$			1.41421i			0.377964i
$15$	−0.585786	−	3.41421i	−0.151249	−	0.881546i
$16$	1.00000			0.250000
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−2.70711	−	1.29289i	−0.638071	−	0.304738i
$19$	−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
$21$	−0.414214	−	2.41421i	−0.0903888	−	0.526825i
$22$	−4.00000			−0.852803
$23$	−8.48528			−1.76930			−0.884652	−	0.466252i	$-0.845604\pi$
$23$	−8.48528			−1.76930			−0.884652	+	0.466252i	$0.845604\pi$
$24$	−5.12132	+	0.878680i	−1.04539	+	0.179360i
$25$			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	$-0.915416\pi$
$29$		−	2.82843i		−	0.525226i	0.964901	−	0.262613i	$-0.0845842\pi$
$30$	−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
$33$	6.82843	−	1.17157i	1.18868	−	0.203945i
$34$		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	−0.808862	−	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
$45$	5.41421	+	2.58579i	0.807103	+	0.385466i
$46$	−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
$52$		0			0
$53$			5.65685i			0.777029i	0.921443	+	0.388514i	$0.127012\pi$
$53$			5.65685i			0.777029i	−0.921443	+	0.388514i	$0.872988\pi$
$54$	4.53553	−	2.53553i	0.617208	−	0.345042i
$55$	8.00000			1.07872
$56$	−4.24264			−0.566947
$57$	2.41421	−	0.414214i	0.319770	−	0.0548639i
$58$	−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	$0.833847\pi$
$60$	3.41421	−	0.585786i	0.440773	−	0.0756247i
$61$	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
$63$	3.82843	+	1.82843i	0.482336	+	0.230360i
$64$			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	−0.519063	−	0.854736i	$-0.673719\pi$
$71$	2.82843	−	2.82843i	0.335673	−	0.335673i	0.854736	+	0.519063i	$0.173719\pi$
$72$	3.87868	−	8.12132i	0.457107	−	0.957107i
$73$	−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	−0.945767	−	0.324846i	$-0.894687\pi$
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	0.324846	+	0.945767i	$0.394687\pi$
$84$	2.41421	−	0.414214i	0.263412	−	0.0451944i
$85$		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
$91$		0			0
$92$		−	8.48528i		−	0.884652i
$93$	−12.0711	+	2.07107i	−1.25171	+	0.214760i
$94$	−4.00000			−0.412568
$95$	2.82843			0.290191
$96$	−1.46447	−	8.53553i	−0.149466	−	0.871154i
$97$	−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
$99$	−5.17157	+	10.8284i	−0.519763	+	1.08830i
$100$	−1.00000			−0.100000
$101$	8.48528			0.844317			0.422159	−	0.906522i	$-0.361273\pi$
$101$	8.48528			0.844317			0.422159	+	0.906522i	$0.361273\pi$
$102$		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	$0.0881596\pi$
$107$			5.65685i			0.546869i	−0.961891	+	0.273434i	$0.911840\pi$
$108$	−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
$111$	−0.414214	−	2.41421i	−0.0393154	−	0.229147i
$112$	−1.00000	+	1.00000i	−0.0944911	+	0.0944911i
$113$			14.1421i			1.33038i	0.746674	+	0.665190i	$0.231650\pi$
$113$			14.1421i			1.33038i	−0.746674	+	0.665190i	$0.768350\pi$
$114$	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
$123$	−0.585786	−	3.41421i	−0.0528186	−	0.307849i
$124$	−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	$-0.835446\pi$
$131$		−	11.3137i		−	0.988483i	0.869325	−	0.494242i	$-0.164554\pi$
$132$	1.17157	+	6.82843i	0.101972	+	0.594338i
$133$	2.00000			0.173422
$134$	7.07107			0.610847
$135$	−9.07107	+	5.07107i	−0.780713	+	0.436448i
$136$		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	$0.545942\pi$
$138$	−2.48528	−	14.4853i	−0.211561	−	1.23307i
$139$	−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
$141$	6.82843	−	1.17157i	0.575057	−	0.0986642i
$142$		−	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	−0.762658	−	0.646802i	$-0.776106\pi$
$149$	−1.41421	+	1.41421i	−0.115857	+	0.115857i	0.646802	+	0.762658i	$0.276106\pi$
$150$	−1.70711	+	0.292893i	−0.139385	+	0.0239146i
$151$	−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
$162$	−0.949747	+	8.94975i	−0.0746192	+	0.703159i
$163$	−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	0.589152	−	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
$169$		0			0
$170$		0			0
$171$	−1.82843	+	3.82843i	−0.139823	+	0.292767i
$172$	−6.00000			−0.457496
$173$	8.48528			0.645124			0.322562	−	0.946548i	$-0.395456\pi$
$173$	8.48528			0.645124			0.322562	+	0.946548i	$0.395456\pi$
$174$	4.82843	−	0.828427i	0.366042	−	0.0628029i
$175$	−1.00000	−	1.00000i	−0.0755929	−	0.0755929i
$176$	−2.82843	−	2.82843i	−0.213201	−	0.213201i
$177$	6.82843	−	1.17157i	0.513256	−	0.0880608i
$178$	14.0000			1.04934
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−2.58579	+	5.41421i	−0.192733	+	0.403552i
$181$		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
$189$	−6.41421	+	3.58579i	−0.466565	+	0.260828i
$190$	2.00000	−	2.00000i	0.145095	−	0.145095i
$191$		−	2.82843i		−	0.204658i	−0.994751	−	0.102329i	$-0.967371\pi$
$191$		−	2.82843i		−	0.204658i	0.994751	−	0.102329i	$-0.0326294\pi$
$192$	−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	$-0.463321\pi$
$197$	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
$201$	−12.0711	+	2.07107i	−0.851427	+	0.146082i
$202$	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
$210$	4.82843	−	0.828427i	0.333193	−	0.0571669i
$211$	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
$213$	1.17157	+	6.82843i	0.0802749	+	0.467876i
$214$	4.00000	+	4.00000i	0.273434	+	0.273434i
$215$	−8.48528	−	8.48528i	−0.578691	−	0.578691i
$216$	7.60660	+	13.6066i	0.517564	+	0.925812i
$217$	−10.0000			−0.678844
$218$	−1.41421			−0.0957826
$219$	−0.414214	−	2.41421i	−0.0279900	−	0.163137i
$220$			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	−0.869461	−	0.494002i	$-0.835534\pi$
$227$	−5.65685	+	5.65685i	−0.375459	+	0.375459i	0.494002	+	0.869461i	$0.335534\pi$
$228$	0.414214	+	2.41421i	0.0274320	+	0.159885i
$229$	−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	$-0.186141\pi$
$233$	25.4558			1.66767			0.833834	+	0.552015i	$0.186141\pi$
$234$		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	−0.996643	−	0.0818647i	$-0.973912\pi$
$239$	−14.1421	+	14.1421i	−0.914779	+	0.914779i	0.0818647	+	0.996643i	$0.473912\pi$
$240$	−0.585786	−	3.41421i	−0.0378124	−	0.220387i
$241$	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
$249$	−2.34315	−	13.6569i	−0.148491	−	0.865468i
$250$	−12.0000			−0.758947
$251$	−25.4558			−1.60676			−0.803379	−	0.595468i	$-0.796967\pi$
$251$	−25.4558			−1.60676			−0.803379	+	0.595468i	$0.796967\pi$
$252$	−1.82843	+	3.82843i	−0.115180	+	0.241168i
$253$	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	$-0.585256\pi$
$257$	−8.48528			−0.529297			−0.264649	+	0.964345i	$0.585256\pi$
$258$	−10.2426	+	1.75736i	−0.637679	+	0.109408i
$259$		−	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	$0.245763\pi$
$263$			22.6274i			1.39527i	−0.716455	+	0.697633i	$0.754237\pi$
$264$	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
$267$	−23.8995	+	4.10051i	−1.46263	+	0.250947i
$268$	−5.00000	+	5.00000i	−0.305424	+	0.305424i
$269$		−	19.7990i		−	1.20717i	−0.797300	−	0.603583i	$-0.793739\pi$
$269$		−	19.7990i		−	1.20717i	0.797300	−	0.603583i	$-0.206261\pi$
$270$	−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
$279$	9.14214	−	19.1421i	0.547325	−	1.14601i
$280$	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
$286$		0			0
$287$		−	2.82843i		−	0.166957i
$288$	13.5355	+	6.46447i	0.797589	+	0.380922i
$289$	−17.0000			−1.00000
$290$	5.65685			0.332182
$291$	16.8995	−	2.89949i	0.990666	−	0.169971i
$292$	−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	$0.615897\pi$
$294$	−8.53553	+	1.46447i	−0.497802	+	0.0854094i
$295$	8.00000			0.465778
$296$	−4.24264			−0.246598
$297$	−10.1421	−	18.1421i	−0.588506	−	1.05271i
$298$			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	$-0.577337\pi$
$311$	−8.48528			−0.481156			−0.240578	+	0.970630i	$0.577337\pi$
$312$		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	−0.480076	−	0.877227i	$-0.659391\pi$
$317$	7.07107	−	7.07107i	0.397151	−	0.397151i	0.877227	+	0.480076i	$0.159391\pi$
$318$	−9.65685	+	1.65685i	−0.541529	+	0.0929118i
$319$	−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
$327$	2.41421	−	0.414214i	0.133506	−	0.0229061i
$328$	−6.00000			−0.331295
$329$	5.65685			0.311872
$330$	2.34315	+	13.6569i	0.128986	+	0.751785i
$331$	−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
$333$	3.82843	+	1.82843i	0.209797	+	0.100197i
$334$	−4.00000			−0.218870
$335$	−14.1421			−0.772667
$336$	−0.414214	−	2.41421i	−0.0225972	−	0.131706i
$337$		−	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
$345$	4.97056	+	28.9706i	0.267606	+	1.55972i
$346$	6.00000	−	6.00000i	0.322562	−	0.322562i
$347$			14.1421i			0.759190i	0.925153	+	0.379595i	$0.123937\pi$
$347$			14.1421i			0.759190i	−0.925153	+	0.379595i	$0.876063\pi$
$348$	−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	−0.999774	−	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
$364$		0			0
$365$		−	2.82843i		−	0.148047i
$366$	2.34315	+	13.6569i	0.122478	+	0.713855i
$367$	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
$369$	5.41421	+	2.58579i	0.281853	+	0.134611i
$370$	−2.00000	−	2.00000i	−0.103975	−	0.103975i
$371$	−5.65685	−	5.65685i	−0.293689	−	0.293689i
$372$	−2.07107	−	12.0711i	−0.107380	−	0.625856i
$373$	−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
$375$	20.4853	−	3.51472i	1.05786	−	0.181499i
$376$		−	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	−0.356277	−	0.934380i	$-0.615954\pi$
$383$	11.3137	−	11.3137i	0.578103	−	0.578103i	0.934380	+	0.356277i	$0.115954\pi$
$384$	5.12132	−	0.878680i	0.261346	−	0.0448399i
$385$	−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	$-0.641564\pi$
$389$	−16.9706			−0.860442			−0.430221	+	0.902724i	$0.641564\pi$
$390$		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
$396$	−10.8284	−	5.17157i	−0.544149	−	0.259881i
$397$	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	0.202446	−	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
$403$		0			0
$404$			8.48528i			0.422159i
$405$	1.89949	−	17.8995i	0.0943867	−	0.889433i
$406$	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
$411$	−23.8995	+	4.10051i	−1.17888	+	0.202263i
$412$	6.00000			0.295599
$413$	5.65685			0.278356
$414$	22.9706	+	10.9706i	1.12894	+	0.539174i
$415$		−	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	$-0.910873\pi$
$419$		−	11.3137i		−	0.552711i	0.961056	−	0.276355i	$-0.0891267\pi$
$420$	−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
$423$	−5.17157	+	10.8284i	−0.251450	+	0.526496i
$424$	−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	$0.530090\pi$
$431$	−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
$435$	−9.65685	+	1.65685i	−0.463011	+	0.0794401i
$436$	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	$-0.765473\pi$
$443$		−	28.2843i		−	1.34383i	0.740630	−	0.671913i	$-0.234527\pi$
$444$	2.41421	−	0.414214i	0.114574	−	0.0196577i
$445$	−28.0000			−1.32733
$446$	15.5563			0.736614
$447$	−0.585786	−	3.41421i	−0.0277067	−	0.161487i
$448$	−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	$0.923741\pi$
$450$	1.29289	−	2.70711i	0.0609476	−	0.127614i
$451$	8.00000			0.376705
$452$	−14.1421			−0.665190
$453$	−0.414214	−	2.41421i	−0.0194615	−	0.113430i
$454$			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	−0.523000	−	0.852333i	$-0.675187\pi$
$461$	7.07107	−	7.07107i	0.329332	−	0.329332i	0.852333	+	0.523000i	$0.175187\pi$
$462$	1.65685	+	9.65685i	0.0770838	+	0.449278i
$463$	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	$-0.299530\pi$
$467$	25.4558			1.17796			0.588978	+	0.808149i	$0.299530\pi$
$468$		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
$474$	−2.92893	−	17.0711i	−0.134530	−	0.784100i
$475$	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
$481$		0			0
$482$		−	24.0416i		−	1.09507i
$483$	3.51472	+	20.4853i	0.159925	+	0.932113i
$484$	−5.00000			−0.227273
$485$	19.7990			0.899026
$486$	−11.7071	−	10.2929i	−0.531045	−	0.466895i
$487$	−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
$489$	−0.414214	−	2.41421i	−0.0187314	−	0.109175i
$490$	−10.0000			−0.451754
$491$	42.4264			1.91468			0.957338	−	0.288969i	$-0.0933124\pi$
$491$	42.4264			1.91468			0.957338	+	0.288969i	$0.0933124\pi$
$492$	3.41421	−	0.585786i	0.153925	−	0.0264093i
$493$		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
$501$	6.82843	−	1.17157i	0.305072	−	0.0523420i
$502$	−18.0000	+	18.0000i	−0.803379	+	0.803379i
$503$			5.65685i			0.252227i	0.992016	+	0.126113i	$0.0402503\pi$
$503$			5.65685i			0.252227i	−0.992016	+	0.126113i	$0.959750\pi$
$504$	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	$-0.478358\pi$
$509$	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
$513$	−3.58579	−	6.41421i	−0.158316	−	0.283194i
$514$	−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	$0.238688\pi$
$521$			31.1127i			1.36307i	−0.731785	+	0.681536i	$0.761312\pi$
$522$	−3.65685	+	7.65685i	−0.160056	+	0.335131i
$523$	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
$525$	2.41421	−	0.414214i	0.105365	−	0.0180778i
$526$	16.0000	+	16.0000i	0.697633	+	0.697633i
$527$		0			0
$528$	6.82843	−	1.17157i	0.297169	−	0.0509862i
$529$	49.0000			2.13043
$530$	−11.3137			−0.491436
$531$	−5.17157	+	10.8284i	−0.224427	+	0.469914i
$532$			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
$540$	−5.07107	−	9.07107i	−0.218224	−	0.390357i
$541$	−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
$552$	43.4558	−	7.45584i	1.84960	−	0.317342i
$553$	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
$559$		0			0
$560$		−	2.82843i		−	0.119523i
$561$		0			0
$562$	14.0000			0.590554
$563$	−33.9411			−1.43045			−0.715224	−	0.698895i	$-0.753675\pi$
$563$	−33.9411			−1.43045			−0.715224	+	0.698895i	$0.753675\pi$
$564$	1.17157	+	6.82843i	0.0493321	+	0.287529i
$565$	−20.0000	−	20.0000i	−0.841406	−	0.841406i
$566$	8.48528	+	8.48528i	0.356663	+	0.356663i
$567$	1.34315	−	12.6569i	0.0564068	−	0.531538i
$568$	12.0000			0.503509
$569$	8.48528			0.355722			0.177861	−	0.984056i	$-0.443082\pi$
$569$	8.48528			0.355722			0.177861	+	0.984056i	$0.443082\pi$
$570$	0.828427	+	4.82843i	0.0346990	+	0.202241i
$571$			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
$579$	−7.87006	−	45.8701i	−0.327068	−	1.90629i
$580$	−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	−0.814145	−	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
$591$	6.44365	+	37.5563i	0.265056	+	1.54486i
$592$	−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
$598$		0			0
$599$		−	11.3137i		−	0.462266i	−0.972922	−	0.231133i	$-0.925757\pi$
$599$		−	11.3137i		−	0.462266i	0.972922	−	0.231133i	$-0.0742432\pi$
$600$	−0.878680	−	5.12132i	−0.0358719	−	0.209077i
$601$	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
$603$	9.14214	−	19.1421i	0.372297	−	0.779528i
$604$	−1.00000	−	1.00000i	−0.0406894	−	0.0406894i
$605$	−7.07107	−	7.07107i	−0.287480	−	0.287480i
$606$	2.48528	+	14.4853i	0.100958	+	0.588424i
$607$	−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
$609$	−6.82843	+	1.17157i	−0.276702	+	0.0474745i
$610$			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	$0.527217\pi$
$617$	−26.8701	+	26.8701i	−1.08175	+	1.08175i	−0.996347	+	0.0854011i	$0.972783\pi$
$618$	10.2426	−	1.75736i	0.412019	−	0.0706914i
$619$	−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
$630$	−3.65685	+	7.65685i	−0.145693	+	0.305056i
$631$	−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
$639$	−10.8284	−	5.17157i	−0.428366	−	0.204584i
$640$	6.00000			0.237171
$641$	−16.9706			−0.670297			−0.335148	−	0.942165i	$-0.608786\pi$
$641$	−16.9706			−0.670297			−0.335148	+	0.942165i	$0.608786\pi$
$642$	−9.65685	+	1.65685i	−0.381126	+	0.0653908i
$643$	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
$645$	20.4853	−	3.51472i	0.806607	−	0.138392i
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−26.8492	−	2.84924i	−1.05474	−	0.111929i
$649$			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	$0.0892449\pi$
$653$			14.1421i			0.553425i	−0.960953	+	0.276712i	$0.910755\pi$
$654$	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
$657$	3.82843	+	1.82843i	0.149361	+	0.0713337i
$658$	4.00000	−	4.00000i	0.155936	−	0.155936i
$659$		−	2.82843i		−	0.110180i	−0.998481	−	0.0550899i	$-0.982455\pi$
$659$		−	2.82843i		−	0.110180i	0.998481	−	0.0550899i	$-0.0175446\pi$
$660$	−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
$669$	−26.5563	+	4.55635i	−1.02673	+	0.176159i
$670$	−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	$0.143188\pi$
$677$			22.6274i			0.869642i	−0.900517	+	0.434821i	$0.856812\pi$
$678$	−24.1421	+	4.14214i	−0.927173	+	0.159078i
$679$	14.0000			0.537271
$680$		0			0
$681$	−2.34315	−	13.6569i	−0.0897895	−	0.523332i
$682$	−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	$0.774383\pi$
$684$	−3.82843	−	1.82843i	−0.146384	−	0.0699117i
$685$	−28.0000			−1.06983
$686$	−16.9706			−0.647939
$687$	−0.414214	−	2.41421i	−0.0158032	−	0.0921080i
$688$			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
$696$	2.48528	+	14.4853i	0.0942043	+	0.549063i
$697$		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	$-0.911333\pi$
$701$	−50.9117			−1.92291			−0.961454	+	0.274966i	$0.911333\pi$
$702$		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
$708$	1.17157	+	6.82843i	0.0440304	+	0.256628i
$709$	−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
$717$	−5.85786	−	34.1421i	−0.218766	−	1.27506i
$718$	−4.00000			−0.149279
$719$	25.4558			0.949343			0.474671	−	0.880163i	$-0.342567\pi$
$719$	25.4558			0.949343			0.474671	+	0.880163i	$0.342567\pi$
$720$	5.41421	+	2.58579i	0.201776	+	0.0963666i
$721$	6.00000	+	6.00000i	0.223452	+	0.223452i
$722$	−12.0208	−	12.0208i	−0.447368	−	0.447368i
$723$	7.04163	+	41.0416i	0.261881	+	1.52635i
$724$		0			0
$725$	2.82843			0.105045
$726$	−8.53553	+	1.46447i	−0.316783	+	0.0543514i
$727$		−	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
$735$	17.0711	−	2.92893i	0.629676	−	0.108035i
$736$	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	−0.468437	−	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
$747$	21.6569	+	10.3431i	0.792383	+	0.378436i
$748$		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
$756$	−3.58579	−	6.41421i	−0.130414	−	0.233283i
$757$	−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
$759$	−57.9411	+	9.94113i	−2.10313	+	0.360840i
$760$	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
$767$		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	−0.862358	−	0.506298i	$-0.831013\pi$
$773$	−9.89949	+	9.89949i	−0.356060	+	0.356060i	0.506298	+	0.862358i	$0.331013\pi$
$774$	7.75736	−	16.2426i	0.278833	−	0.583830i
$775$	−5.00000	+	5.00000i	−0.179605	+	0.179605i
$776$		−	29.6985i		−	1.06611i

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} +(0.292893 + 1.70711i) 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} +(-0.585786 - 3.41421i) q^{15} +1.00000 q^{16} +(-2.70711 - 1.29289i) q^{18} +(-1.00000 - 1.00000i) q^{19} +(-1.41421 - 1.41421i) q^{20} +(-0.414214 - 2.41421i) q^{21} -4.00000 q^{22} -8.48528 q^{23} +(-5.12132 + 0.878680i) 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} +(6.82843 - 1.17157i) 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} +(5.41421 + 2.58579i) 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} +(4.53553 - 2.53553i) q^{54} +8.00000 q^{55} -4.24264 q^{56} +(2.41421 - 0.414214i) q^{57} +(-2.00000 - 2.00000i) q^{58} +(-2.82843 - 2.82843i) q^{59} +(3.41421 - 0.585786i) q^{60} +8.00000 q^{61} +7.07107 q^{62} +(3.82843 + 1.82843i) 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} +(3.87868 - 8.12132i) 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} +(2.41421 - 0.414214i) 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} +(-12.0711 + 2.07107i) q^{93} -4.00000 q^{94} +2.82843 q^{95} +(-1.46447 - 8.53553i) q^{96} +(-7.00000 - 7.00000i) q^{97} +(3.53553 + 3.53553i) q^{98} +(-5.17157 + 10.8284i) 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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