LMFDB - Embedded newform 430.2.g.a.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(257,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("430.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.g (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	430.257
Dual form			430.2.g.a.343.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.41421 + 1.41421i) q^{3} -1.00000i q^{4} +(0.707107 + 2.12132i) q^{5} +2.00000 q^{6} +(2.82843 - 2.82843i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.41421 + 1.41421i) q^{3} -1.00000i q^{4} +(0.707107 + 2.12132i) q^{5} +2.00000 q^{6} +(2.82843 - 2.82843i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(2.00000 + 1.00000i) q^{10} -4.00000 q^{11} +(1.41421 - 1.41421i) q^{12} +(2.00000 - 2.00000i) q^{13} -4.00000i q^{14} +(-2.00000 + 4.00000i) q^{15} -1.00000 q^{16} +(5.00000 + 5.00000i) q^{17} +(0.707107 + 0.707107i) q^{18} -4.24264 q^{19} +(2.12132 - 0.707107i) q^{20} +8.00000 q^{21} +(-2.82843 + 2.82843i) q^{22} +(-5.00000 + 5.00000i) q^{23} -2.00000i q^{24} +(-4.00000 + 3.00000i) q^{25} -2.82843i q^{26} +(2.82843 - 2.82843i) q^{27} +(-2.82843 - 2.82843i) q^{28} -4.24264 q^{29} +(1.41421 + 4.24264i) q^{30} +8.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.65685 - 5.65685i) q^{33} +7.07107 q^{34} +(8.00000 + 4.00000i) q^{35} +1.00000 q^{36} +(4.24264 - 4.24264i) q^{37} +(-3.00000 + 3.00000i) q^{38} +5.65685 q^{39} +(1.00000 - 2.00000i) q^{40} -12.0000 q^{41} +(5.65685 - 5.65685i) q^{42} +(-6.53553 - 0.535534i) q^{43} +4.00000i q^{44} +(-2.12132 + 0.707107i) q^{45} +7.07107i q^{46} +(-5.00000 - 5.00000i) q^{47} +(-1.41421 - 1.41421i) q^{48} -9.00000i q^{49} +(-0.707107 + 4.94975i) q^{50} +14.1421i q^{51} +(-2.00000 - 2.00000i) q^{52} -4.00000i q^{54} +(-2.82843 - 8.48528i) q^{55} -4.00000 q^{56} +(-6.00000 - 6.00000i) q^{57} +(-3.00000 + 3.00000i) q^{58} +(4.00000 + 2.00000i) q^{60} -4.24264i q^{61} +(5.65685 - 5.65685i) q^{62} +(2.82843 + 2.82843i) q^{63} +1.00000i q^{64} +(5.65685 + 2.82843i) q^{65} -8.00000 q^{66} +(-2.00000 - 2.00000i) q^{67} +(5.00000 - 5.00000i) q^{68} -14.1421 q^{69} +(8.48528 - 2.82843i) q^{70} -5.65685i q^{71} +(0.707107 - 0.707107i) q^{72} +(-1.41421 - 1.41421i) q^{73} -6.00000i q^{74} +(-9.89949 - 1.41421i) q^{75} +4.24264i q^{76} +(-11.3137 + 11.3137i) q^{77} +(4.00000 - 4.00000i) q^{78} +10.0000i q^{79} +(-0.707107 - 2.12132i) q^{80} +11.0000 q^{81} +(-8.48528 + 8.48528i) q^{82} +(6.00000 - 6.00000i) q^{83} -8.00000i q^{84} +(-7.07107 + 14.1421i) q^{85} +(-5.00000 + 4.24264i) q^{86} +(-6.00000 - 6.00000i) q^{87} +(2.82843 + 2.82843i) q^{88} +14.1421 q^{89} +(-1.00000 + 2.00000i) q^{90} -11.3137i q^{91} +(5.00000 + 5.00000i) q^{92} +(11.3137 + 11.3137i) q^{93} -7.07107 q^{94} +(-3.00000 - 9.00000i) q^{95} -2.00000 q^{96} +(9.00000 + 9.00000i) q^{97} +(-6.36396 - 6.36396i) q^{98} -4.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{6}+O(q^{10}) $ 4 * q + 8 * q^6	$ 4 q + 8 q^{6} + 8 q^{10} - 16 q^{11} + 8 q^{13} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 32 q^{21} - 20 q^{23} - 16 q^{25} + 32 q^{31} + 32 q^{35} + 4 q^{36} - 12 q^{38} + 4 q^{40} - 48 q^{41} - 12 q^{43} - 20 q^{47} - 8 q^{52} - 16 q^{56} - 24 q^{57} - 12 q^{58} + 16 q^{60} - 32 q^{66} - 8 q^{67} + 20 q^{68} + 16 q^{78} + 44 q^{81} + 24 q^{83} - 20 q^{86} - 24 q^{87} - 4 q^{90} + 20 q^{92} - 12 q^{95} - 8 q^{96} + 36 q^{97}+O(q^{100}) $ 4 * q + 8 * q^6 + 8 * q^10 - 16 * q^11 + 8 * q^13 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 32 * q^21 - 20 * q^23 - 16 * q^25 + 32 * q^31 + 32 * q^35 + 4 * q^36 - 12 * q^38 + 4 * q^40 - 48 * q^41 - 12 * q^43 - 20 * q^47 - 8 * q^52 - 16 * q^56 - 24 * q^57 - 12 * q^58 + 16 * q^60 - 32 * q^66 - 8 * q^67 + 20 * q^68 + 16 * q^78 + 44 * q^81 + 24 * q^83 - 20 * q^86 - 24 * q^87 - 4 * q^90 + 20 * q^92 - 12 * q^95 - 8 * q^96 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.41421	+	1.41421i	0.816497	+	0.816497i	0.985599	−	0.169102i	$-0.0540867\pi$
$3$	1.41421	+	1.41421i	0.816497	+	0.816497i	−0.169102	+	0.985599i	$0.554087\pi$
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	+	2.12132i	0.316228	+	0.948683i
$5$	0.707107	+	2.12132i	0.316228	+	0.948683i
$6$	2.00000			0.816497
$7$	2.82843	−	2.82843i	1.06904	−	1.06904i	0.0716124	−	0.997433i	$-0.477186\pi$
$7$	2.82843	−	2.82843i	1.06904	−	1.06904i	0.997433	−	0.0716124i	$-0.0228145\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$	−4.00000			−1.20605			−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000			−1.20605			−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.41421	−	1.41421i	0.408248	−	0.408248i
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$		−	4.00000i		−	1.06904i
$15$	−2.00000	+	4.00000i	−0.516398	+	1.03280i
$16$	−1.00000			−0.250000
$17$	5.00000	+	5.00000i	1.21268	+	1.21268i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	5.00000	+	5.00000i	1.21268	+	1.21268i	0.242536	+	0.970143i	$0.422021\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−4.24264			−0.973329			−0.486664	−	0.873589i	$-0.661786\pi$
$19$	−4.24264			−0.973329			−0.486664	+	0.873589i	$0.661786\pi$
$20$	2.12132	−	0.707107i	0.474342	−	0.158114i
$21$	8.00000			1.74574
$22$	−2.82843	+	2.82843i	−0.603023	+	0.603023i
$23$	−5.00000	+	5.00000i	−1.04257	+	1.04257i	−0.0435195	+	0.999053i	$0.513857\pi$
$23$	−5.00000	+	5.00000i	−1.04257	+	1.04257i	−0.999053	+	0.0435195i	$0.986143\pi$
$24$		−	2.00000i		−	0.408248i
$25$	−4.00000	+	3.00000i	−0.800000	+	0.600000i
$26$		−	2.82843i		−	0.554700i
$27$	2.82843	−	2.82843i	0.544331	−	0.544331i
$28$	−2.82843	−	2.82843i	−0.534522	−	0.534522i
$29$	−4.24264			−0.787839			−0.393919	−	0.919145i	$-0.628881\pi$
$29$	−4.24264			−0.787839			−0.393919	+	0.919145i	$0.628881\pi$
$30$	1.41421	+	4.24264i	0.258199	+	0.774597i
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−5.65685	−	5.65685i	−0.984732	−	0.984732i
$34$	7.07107			1.21268
$35$	8.00000	+	4.00000i	1.35225	+	0.676123i
$36$	1.00000			0.166667
$37$	4.24264	−	4.24264i	0.697486	−	0.697486i	−0.266382	−	0.963868i	$-0.585828\pi$
$37$	4.24264	−	4.24264i	0.697486	−	0.697486i	0.963868	+	0.266382i	$0.0858282\pi$
$38$	−3.00000	+	3.00000i	−0.486664	+	0.486664i
$39$	5.65685			0.905822
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$	−12.0000			−1.87409			−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000			−1.87409			−0.937043	+	0.349215i	$0.886448\pi$
$42$	5.65685	−	5.65685i	0.872872	−	0.872872i
$43$	−6.53553	−	0.535534i	−0.996660	−	0.0816682i
$43$	−6.53553	−	0.535534i	−0.996660	−	0.0816682i
$44$			4.00000i			0.603023i
$45$	−2.12132	+	0.707107i	−0.316228	+	0.105409i
$46$			7.07107i			1.04257i
$47$	−5.00000	−	5.00000i	−0.729325	−	0.729325i	0.241160	−	0.970485i	$-0.422472\pi$
$47$	−5.00000	−	5.00000i	−0.729325	−	0.729325i	−0.970485	+	0.241160i	$0.922472\pi$
$48$	−1.41421	−	1.41421i	−0.204124	−	0.204124i
$49$		−	9.00000i		−	1.28571i
$50$	−0.707107	+	4.94975i	−0.100000	+	0.700000i
$51$			14.1421i			1.98030i
$52$	−2.00000	−	2.00000i	−0.277350	−	0.277350i
$53$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$53$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$54$		−	4.00000i		−	0.544331i
$55$	−2.82843	−	8.48528i	−0.381385	−	1.14416i
$56$	−4.00000			−0.534522
$57$	−6.00000	−	6.00000i	−0.794719	−	0.794719i
$58$	−3.00000	+	3.00000i	−0.393919	+	0.393919i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$	4.00000	+	2.00000i	0.516398	+	0.258199i
$61$		−	4.24264i		−	0.543214i	−0.962408	−	0.271607i	$-0.912445\pi$
$61$		−	4.24264i		−	0.543214i	0.962408	−	0.271607i	$-0.0875552\pi$
$62$	5.65685	−	5.65685i	0.718421	−	0.718421i
$63$	2.82843	+	2.82843i	0.356348	+	0.356348i
$64$			1.00000i			0.125000i
$65$	5.65685	+	2.82843i	0.701646	+	0.350823i
$66$	−8.00000			−0.984732
$67$	−2.00000	−	2.00000i	−0.244339	−	0.244339i	0.574304	−	0.818642i	$-0.305273\pi$
$67$	−2.00000	−	2.00000i	−0.244339	−	0.244339i	−0.818642	+	0.574304i	$0.805273\pi$
$68$	5.00000	−	5.00000i	0.606339	−	0.606339i
$69$	−14.1421			−1.70251
$70$	8.48528	−	2.82843i	1.01419	−	0.338062i
$71$		−	5.65685i		−	0.671345i	−0.941979	−	0.335673i	$-0.891036\pi$
$71$		−	5.65685i		−	0.671345i	0.941979	−	0.335673i	$-0.108964\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−1.41421	−	1.41421i	−0.165521	−	0.165521i	0.619486	−	0.785007i	$-0.287341\pi$
$73$	−1.41421	−	1.41421i	−0.165521	−	0.165521i	−0.785007	+	0.619486i	$0.787341\pi$
$74$		−	6.00000i		−	0.697486i
$75$	−9.89949	−	1.41421i	−1.14310	−	0.163299i
$76$			4.24264i			0.486664i
$77$	−11.3137	+	11.3137i	−1.28932	+	1.28932i
$78$	4.00000	−	4.00000i	0.452911	−	0.452911i
$79$			10.0000i			1.12509i	0.826767	+	0.562544i	$0.190177\pi$
$79$			10.0000i			1.12509i	−0.826767	+	0.562544i	$0.809823\pi$
$80$	−0.707107	−	2.12132i	−0.0790569	−	0.237171i
$81$	11.0000			1.22222
$82$	−8.48528	+	8.48528i	−0.937043	+	0.937043i
$83$	6.00000	−	6.00000i	0.658586	−	0.658586i	−0.296460	−	0.955045i	$-0.595806\pi$
$83$	6.00000	−	6.00000i	0.658586	−	0.658586i	0.955045	+	0.296460i	$0.0958061\pi$
$84$		−	8.00000i		−	0.872872i
$85$	−7.07107	+	14.1421i	−0.766965	+	1.53393i
$86$	−5.00000	+	4.24264i	−0.539164	+	0.457496i
$87$	−6.00000	−	6.00000i	−0.643268	−	0.643268i
$88$	2.82843	+	2.82843i	0.301511	+	0.301511i
$89$	14.1421			1.49906			0.749532	−	0.661968i	$-0.230279\pi$
$89$	14.1421			1.49906			0.749532	+	0.661968i	$0.230279\pi$
$90$	−1.00000	+	2.00000i	−0.105409	+	0.210819i
$91$		−	11.3137i		−	1.18600i
$92$	5.00000	+	5.00000i	0.521286	+	0.521286i
$93$	11.3137	+	11.3137i	1.17318	+	1.17318i
$94$	−7.07107			−0.729325
$95$	−3.00000	−	9.00000i	−0.307794	−	0.923381i
$96$	−2.00000			−0.204124
$97$	9.00000	+	9.00000i	0.913812	+	0.913812i	0.996570	−	0.0827581i	$-0.0263729\pi$
$97$	9.00000	+	9.00000i	0.913812	+	0.913812i	−0.0827581	+	0.996570i	$0.526373\pi$
$98$	−6.36396	−	6.36396i	−0.642857	−	0.642857i
$99$		−	4.00000i		−	0.402015i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$	2.00000			0.199007			0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000			0.199007			0.0995037	+	0.995037i	$0.468274\pi$
$102$	10.0000	+	10.0000i	0.990148	+	0.990148i
$103$	−9.00000	+	9.00000i	−0.886796	+	0.886796i	−0.994214	−	0.107418i	$-0.965742\pi$
$103$	−9.00000	+	9.00000i	−0.886796	+	0.886796i	0.107418	+	0.994214i	$0.465742\pi$
$104$	−2.82843			−0.277350
$105$	5.65685	+	16.9706i	0.552052	+	1.65616i
$106$		0			0
$107$	−12.0000	−	12.0000i	−1.16008	−	1.16008i	−0.984457	−	0.175627i	$-0.943805\pi$
$107$	−12.0000	−	12.0000i	−1.16008	−	1.16008i	−0.175627	−	0.984457i	$-0.556195\pi$
$108$	−2.82843	−	2.82843i	−0.272166	−	0.272166i
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	−8.00000	−	4.00000i	−0.762770	−	0.381385i
$111$	12.0000			1.13899
$112$	−2.82843	+	2.82843i	−0.267261	+	0.267261i
$113$	7.07107	+	7.07107i	0.665190	+	0.665190i	0.956599	−	0.291409i	$-0.0941239\pi$
$113$	7.07107	+	7.07107i	0.665190	+	0.665190i	−0.291409	+	0.956599i	$0.594124\pi$
$114$	−8.48528			−0.794719
$115$	−14.1421	−	7.07107i	−1.31876	−	0.659380i
$116$			4.24264i			0.393919i
$117$	2.00000	+	2.00000i	0.184900	+	0.184900i
$118$		0			0
$119$	28.2843			2.59281
$120$	4.24264	−	1.41421i	0.387298	−	0.129099i
$121$	5.00000			0.454545
$122$	−3.00000	−	3.00000i	−0.271607	−	0.271607i
$123$	−16.9706	−	16.9706i	−1.53018	−	1.53018i
$124$		−	8.00000i		−	0.718421i
$125$	−9.19239	−	6.36396i	−0.822192	−	0.569210i
$126$	4.00000			0.356348
$127$	−5.00000	−	5.00000i	−0.443678	−	0.443678i	0.449568	−	0.893246i	$-0.351578\pi$
$127$	−5.00000	−	5.00000i	−0.443678	−	0.443678i	−0.893246	+	0.449568i	$0.851578\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−8.48528	−	10.0000i	−0.747087	−	0.880451i
$130$	6.00000	−	2.00000i	0.526235	−	0.175412i
$131$			1.41421i			0.123560i	0.998090	+	0.0617802i	$0.0196778\pi$
$131$			1.41421i			0.123560i	−0.998090	+	0.0617802i	$0.980322\pi$
$132$	−5.65685	+	5.65685i	−0.492366	+	0.492366i
$133$	−12.0000	+	12.0000i	−1.04053	+	1.04053i
$134$	−2.82843			−0.244339
$135$	8.00000	+	4.00000i	0.688530	+	0.344265i
$136$		−	7.07107i		−	0.606339i
$137$	−7.07107	+	7.07107i	−0.604122	+	0.604122i	−0.941404	−	0.337282i	$-0.890493\pi$
$137$	−7.07107	+	7.07107i	−0.604122	+	0.604122i	0.337282	+	0.941404i	$0.390493\pi$
$138$	−10.0000	+	10.0000i	−0.851257	+	0.851257i
$139$		−	4.00000i		−	0.339276i	−0.985506	−	0.169638i	$-0.945740\pi$
$139$		−	4.00000i		−	0.339276i	0.985506	−	0.169638i	$-0.0542598\pi$
$140$	4.00000	−	8.00000i	0.338062	−	0.676123i
$141$		−	14.1421i		−	1.19098i
$142$	−4.00000	−	4.00000i	−0.335673	−	0.335673i
$143$	−8.00000	+	8.00000i	−0.668994	+	0.668994i
$144$		−	1.00000i		−	0.0833333i
$145$	−3.00000	−	9.00000i	−0.249136	−	0.747409i
$146$	−2.00000			−0.165521
$147$	12.7279	−	12.7279i	1.04978	−	1.04978i
$148$	−4.24264	−	4.24264i	−0.348743	−	0.348743i
$149$	9.89949			0.810998			0.405499	−	0.914095i	$-0.367098\pi$
$149$	9.89949			0.810998			0.405499	+	0.914095i	$0.367098\pi$
$150$	−8.00000	+	6.00000i	−0.653197	+	0.489898i
$151$			8.48528i			0.690522i	0.938507	+	0.345261i	$0.112210\pi$
$151$			8.48528i			0.690522i	−0.938507	+	0.345261i	$0.887790\pi$
$152$	3.00000	+	3.00000i	0.243332	+	0.243332i
$153$	−5.00000	+	5.00000i	−0.404226	+	0.404226i
$154$			16.0000i			1.28932i
$155$	5.65685	+	16.9706i	0.454369	+	1.36311i
$156$		−	5.65685i		−	0.452911i
$157$	1.41421	−	1.41421i	0.112867	−	0.112867i	−0.648418	−	0.761285i	$-0.724569\pi$
$157$	1.41421	−	1.41421i	0.112867	−	0.112867i	0.761285	+	0.648418i	$0.224569\pi$
$158$	7.07107	+	7.07107i	0.562544	+	0.562544i
$159$		0			0
$160$	−2.00000	−	1.00000i	−0.158114	−	0.0790569i
$161$			28.2843i			2.22911i
$162$	7.77817	−	7.77817i	0.611111	−	0.611111i
$163$	−2.82843	−	2.82843i	−0.221540	−	0.221540i	0.587607	−	0.809146i	$-0.300070\pi$
$163$	−2.82843	−	2.82843i	−0.221540	−	0.221540i	−0.809146	+	0.587607i	$0.800070\pi$
$164$			12.0000i			0.937043i
$165$	8.00000	−	16.0000i	0.622799	−	1.24560i
$166$		−	8.48528i		−	0.658586i
$167$	11.0000	+	11.0000i	0.851206	+	0.851206i	0.990282	−	0.139076i	$-0.0444133\pi$
$167$	11.0000	+	11.0000i	0.851206	+	0.851206i	−0.139076	+	0.990282i	$0.544413\pi$
$168$	−5.65685	−	5.65685i	−0.436436	−	0.436436i
$169$			5.00000i			0.384615i
$170$	5.00000	+	15.0000i	0.383482	+	1.15045i
$171$		−	4.24264i		−	0.324443i
$172$	−0.535534	+	6.53553i	−0.0408341	+	0.498330i
$173$	−16.0000	+	16.0000i	−1.21646	+	1.21646i	−0.247593	+	0.968864i	$0.579640\pi$
$173$	−16.0000	+	16.0000i	−1.21646	+	1.21646i	−0.968864	+	0.247593i	$0.920360\pi$
$174$	−8.48528			−0.643268
$175$	−2.82843	+	19.7990i	−0.213809	+	1.49666i
$176$	4.00000			0.301511
$177$		0			0
$178$	10.0000	−	10.0000i	0.749532	−	0.749532i
$179$	1.41421			0.105703			0.0528516	−	0.998602i	$-0.483169\pi$
$179$	1.41421			0.105703			0.0528516	+	0.998602i	$0.483169\pi$
$180$	0.707107	+	2.12132i	0.0527046	+	0.158114i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	−8.00000	−	8.00000i	−0.592999	−	0.592999i
$183$	6.00000	−	6.00000i	0.443533	−	0.443533i
$184$	7.07107			0.521286
$185$	12.0000	+	6.00000i	0.882258	+	0.441129i
$186$	16.0000			1.17318
$187$	−20.0000	−	20.0000i	−1.46254	−	1.46254i
$188$	−5.00000	+	5.00000i	−0.364662	+	0.364662i
$189$		−	16.0000i		−	1.16383i
$190$	−8.48528	−	4.24264i	−0.615587	−	0.307794i
$191$		−	19.7990i		−	1.43260i	−0.697790	−	0.716302i	$-0.745833\pi$
$191$		−	19.7990i		−	1.43260i	0.697790	−	0.716302i	$-0.254167\pi$
$192$	−1.41421	+	1.41421i	−0.102062	+	0.102062i
$193$	11.0000	−	11.0000i	0.791797	−	0.791797i	−0.189989	−	0.981786i	$-0.560845\pi$
$193$	11.0000	−	11.0000i	0.791797	−	0.791797i	0.981786	+	0.189989i	$0.0608452\pi$
$194$	12.7279			0.913812
$195$	4.00000	+	12.0000i	0.286446	+	0.859338i
$196$	−9.00000			−0.642857
$197$	2.00000	+	2.00000i	0.142494	+	0.142494i	0.774755	−	0.632261i	$-0.217873\pi$
$197$	2.00000	+	2.00000i	0.142494	+	0.142494i	−0.632261	+	0.774755i	$0.717873\pi$
$198$	−2.82843	−	2.82843i	−0.201008	−	0.201008i
$199$	11.3137			0.802008			0.401004	−	0.916076i	$-0.368661\pi$
$199$	11.3137			0.802008			0.401004	+	0.916076i	$0.368661\pi$
$200$	4.94975	+	0.707107i	0.350000	+	0.0500000i
$201$		−	5.65685i		−	0.399004i
$202$	1.41421	−	1.41421i	0.0995037	−	0.0995037i
$203$	−12.0000	+	12.0000i	−0.842235	+	0.842235i
$204$	14.1421			0.990148
$205$	−8.48528	−	25.4558i	−0.592638	−	1.77791i
$206$			12.7279i			0.886796i
$207$	−5.00000	−	5.00000i	−0.347524	−	0.347524i
$208$	−2.00000	+	2.00000i	−0.138675	+	0.138675i
$209$	16.9706			1.17388
$210$	16.0000	+	8.00000i	1.10410	+	0.552052i
$211$		−	12.7279i		−	0.876226i	−0.898920	−	0.438113i	$-0.855647\pi$
$211$		−	12.7279i		−	0.876226i	0.898920	−	0.438113i	$-0.144353\pi$
$212$		0			0
$213$	8.00000	−	8.00000i	0.548151	−	0.548151i
$214$	−16.9706			−1.16008
$215$	−3.48528	−	14.2426i	−0.237694	−	0.971340i
$216$	−4.00000			−0.272166
$217$	22.6274	−	22.6274i	1.53605	−	1.53605i
$218$	1.41421	+	1.41421i	0.0957826	+	0.0957826i
$219$		−	4.00000i		−	0.270295i
$220$	−8.48528	+	2.82843i	−0.572078	+	0.190693i
$221$	20.0000			1.34535
$222$	8.48528	−	8.48528i	0.569495	−	0.569495i
$223$	14.1421	+	14.1421i	0.947027	+	0.947027i	0.998666	−	0.0516384i	$-0.0164443\pi$
$223$	14.1421	+	14.1421i	0.947027	+	0.947027i	−0.0516384	+	0.998666i	$0.516444\pi$
$224$			4.00000i			0.267261i
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	10.0000			0.665190
$227$	14.1421	−	14.1421i	0.938647	−	0.938647i	−0.0595772	−	0.998224i	$-0.518975\pi$
$227$	14.1421	−	14.1421i	0.938647	−	0.938647i	0.998224	+	0.0595772i	$0.0189752\pi$
$228$	−6.00000	+	6.00000i	−0.397360	+	0.397360i
$229$			26.0000i			1.71813i	0.511868	+	0.859064i	$0.328954\pi$
$229$			26.0000i			1.71813i	−0.511868	+	0.859064i	$0.671046\pi$
$230$	−15.0000	+	5.00000i	−0.989071	+	0.329690i
$231$	−32.0000			−2.10545
$232$	3.00000	+	3.00000i	0.196960	+	0.196960i
$233$	9.89949	+	9.89949i	0.648537	+	0.648537i	0.952639	−	0.304102i	$-0.0983564\pi$
$233$	9.89949	+	9.89949i	0.648537	+	0.648537i	−0.304102	+	0.952639i	$0.598356\pi$
$234$	2.82843			0.184900
$235$	7.07107	−	14.1421i	0.461266	−	0.922531i
$236$		0			0
$237$	−14.1421	+	14.1421i	−0.918630	+	0.918630i
$238$	20.0000	−	20.0000i	1.29641	−	1.29641i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	2.00000	−	4.00000i	0.129099	−	0.258199i
$241$		−	16.9706i		−	1.09317i	−0.837404	−	0.546585i	$-0.815928\pi$
$241$		−	16.9706i		−	1.09317i	0.837404	−	0.546585i	$-0.184072\pi$
$242$	3.53553	−	3.53553i	0.227273	−	0.227273i
$243$	7.07107	+	7.07107i	0.453609	+	0.453609i
$244$	−4.24264			−0.271607
$245$	19.0919	−	6.36396i	1.21974	−	0.406579i
$246$	−24.0000			−1.53018
$247$	−8.48528	+	8.48528i	−0.539906	+	0.539906i
$248$	−5.65685	−	5.65685i	−0.359211	−	0.359211i
$249$	16.9706			1.07547
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	2.82843	−	2.82843i	0.178174	−	0.178174i
$253$	20.0000	−	20.0000i	1.25739	−	1.25739i
$254$	−7.07107			−0.443678
$255$	−30.0000	+	10.0000i	−1.87867	+	0.626224i
$256$	1.00000			0.0625000
$257$	4.24264	−	4.24264i	0.264649	−	0.264649i	−0.562291	−	0.826940i	$-0.690080\pi$
$257$	4.24264	−	4.24264i	0.264649	−	0.264649i	0.826940	+	0.562291i	$0.190080\pi$
$258$	−13.0711	−	1.07107i	−0.813769	−	0.0666818i
$259$		−	24.0000i		−	1.49129i
$260$	2.82843	−	5.65685i	0.175412	−	0.350823i
$261$		−	4.24264i		−	0.262613i
$262$	1.00000	+	1.00000i	0.0617802	+	0.0617802i
$263$	−16.9706	−	16.9706i	−1.04645	−	1.04645i	−0.998867	−	0.0475824i	$-0.984848\pi$
$263$	−16.9706	−	16.9706i	−1.04645	−	1.04645i	−0.0475824	−	0.998867i	$-0.515152\pi$
$264$			8.00000i			0.492366i
$265$		0			0
$266$			16.9706i			1.04053i
$267$	20.0000	+	20.0000i	1.22398	+	1.22398i
$268$	−2.00000	+	2.00000i	−0.122169	+	0.122169i
$269$			6.00000i			0.365826i	0.983129	+	0.182913i	$0.0585527\pi$
$269$			6.00000i			0.365826i	−0.983129	+	0.182913i	$0.941447\pi$
$270$	8.48528	−	2.82843i	0.516398	−	0.172133i
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	−5.00000	−	5.00000i	−0.303170	−	0.303170i
$273$	16.0000	−	16.0000i	0.968364	−	0.968364i
$274$			10.0000i			0.604122i
$275$	16.0000	−	12.0000i	0.964836	−	0.723627i
$276$			14.1421i			0.851257i
$277$	−5.65685	+	5.65685i	−0.339887	+	0.339887i	−0.856325	−	0.516437i	$-0.827258\pi$
$277$	−5.65685	+	5.65685i	−0.339887	+	0.339887i	0.516437	+	0.856325i	$0.327258\pi$
$278$	−2.82843	−	2.82843i	−0.169638	−	0.169638i
$279$			8.00000i			0.478947i
$280$	−2.82843	−	8.48528i	−0.169031	−	0.507093i
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$	−10.0000	−	10.0000i	−0.595491	−	0.595491i
$283$	6.00000	−	6.00000i	0.356663	−	0.356663i	−0.505918	−	0.862581i	$-0.668846\pi$
$283$	6.00000	−	6.00000i	0.356663	−	0.356663i	0.862581	+	0.505918i	$0.168846\pi$
$284$	−5.65685			−0.335673
$285$	8.48528	−	16.9706i	0.502625	−	1.00525i
$286$			11.3137i			0.668994i
$287$	−33.9411	+	33.9411i	−2.00348	+	2.00348i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$			33.0000i			1.94118i
$290$	−8.48528	−	4.24264i	−0.498273	−	0.249136i
$291$			25.4558i			1.49225i
$292$	−1.41421	+	1.41421i	−0.0827606	+	0.0827606i
$293$	−10.0000	+	10.0000i	−0.584206	+	0.584206i	−0.936056	−	0.351850i	$-0.885553\pi$
$293$	−10.0000	+	10.0000i	−0.584206	+	0.584206i	0.351850	+	0.936056i	$0.385553\pi$
$294$		−	18.0000i		−	1.04978i
$295$		0			0
$296$	−6.00000			−0.348743
$297$	−11.3137	+	11.3137i	−0.656488	+	0.656488i
$298$	7.00000	−	7.00000i	0.405499	−	0.405499i
$299$			20.0000i			1.15663i
$300$	−1.41421	+	9.89949i	−0.0816497	+	0.571548i
$301$	−20.0000	+	16.9706i	−1.15278	+	0.978167i
$302$	6.00000	+	6.00000i	0.345261	+	0.345261i
$303$	2.82843	+	2.82843i	0.162489	+	0.162489i
$304$	4.24264			0.243332
$305$	9.00000	−	3.00000i	0.515339	−	0.171780i
$306$			7.07107i			0.404226i
$307$	−16.0000	−	16.0000i	−0.913168	−	0.913168i	0.0833519	−	0.996520i	$-0.473437\pi$
$307$	−16.0000	−	16.0000i	−0.913168	−	0.913168i	−0.996520	+	0.0833519i	$0.973437\pi$
$308$	11.3137	+	11.3137i	0.644658	+	0.644658i
$309$	−25.4558			−1.44813
$310$	16.0000	+	8.00000i	0.908739	+	0.454369i
$311$	2.00000			0.113410			0.0567048	−	0.998391i	$-0.481941\pi$
$311$	2.00000			0.113410			0.0567048	+	0.998391i	$0.481941\pi$
$312$	−4.00000	−	4.00000i	−0.226455	−	0.226455i
$313$	7.07107	+	7.07107i	0.399680	+	0.399680i	0.878120	−	0.478440i	$-0.158798\pi$
$313$	7.07107	+	7.07107i	0.399680	+	0.399680i	−0.478440	+	0.878120i	$0.658798\pi$
$314$		−	2.00000i		−	0.112867i
$315$	−4.00000	+	8.00000i	−0.225374	+	0.450749i
$316$	10.0000			0.562544
$317$	8.00000	+	8.00000i	0.449325	+	0.449325i	0.895130	−	0.445805i	$-0.147083\pi$
$317$	8.00000	+	8.00000i	0.449325	+	0.449325i	−0.445805	+	0.895130i	$0.647083\pi$
$318$		0			0
$319$	16.9706			0.950169
$320$	−2.12132	+	0.707107i	−0.118585	+	0.0395285i
$321$		−	33.9411i		−	1.89441i
$322$	20.0000	+	20.0000i	1.11456	+	1.11456i
$323$	−21.2132	−	21.2132i	−1.18033	−	1.18033i
$324$		−	11.0000i		−	0.611111i
$325$	−2.00000	+	14.0000i	−0.110940	+	0.776580i
$326$	−4.00000			−0.221540
$327$	−2.82843	+	2.82843i	−0.156412	+	0.156412i
$328$	8.48528	+	8.48528i	0.468521	+	0.468521i
$329$	−28.2843			−1.55936
$330$	−5.65685	−	16.9706i	−0.311400	−	0.934199i
$331$			26.8701i			1.47691i	0.674302	+	0.738456i	$0.264445\pi$
$331$			26.8701i			1.47691i	−0.674302	+	0.738456i	$0.735555\pi$
$332$	−6.00000	−	6.00000i	−0.329293	−	0.329293i
$333$	4.24264	+	4.24264i	0.232495	+	0.232495i
$334$	15.5563			0.851206
$335$	2.82843	−	5.65685i	0.154533	−	0.309067i
$336$	−8.00000			−0.436436
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	0.908388	−	0.418127i	$-0.137313\pi$
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	−0.418127	+	0.908388i	$0.637313\pi$
$338$	3.53553	+	3.53553i	0.192308	+	0.192308i
$339$			20.0000i			1.08625i
$340$	14.1421	+	7.07107i	0.766965	+	0.383482i
$341$	−32.0000			−1.73290
$342$	−3.00000	−	3.00000i	−0.162221	−	0.162221i
$343$	−5.65685	−	5.65685i	−0.305441	−	0.305441i
$344$	4.24264	+	5.00000i	0.228748	+	0.269582i
$345$	−10.0000	−	30.0000i	−0.538382	−	1.61515i
$346$			22.6274i			1.21646i
$347$	−8.48528	+	8.48528i	−0.455514	+	0.455514i	−0.897180	−	0.441666i	$-0.854388\pi$
$347$	−8.48528	+	8.48528i	−0.455514	+	0.455514i	0.441666	+	0.897180i	$0.354388\pi$
$348$	−6.00000	+	6.00000i	−0.321634	+	0.321634i
$349$	−4.24264			−0.227103			−0.113552	−	0.993532i	$-0.536223\pi$
$349$	−4.24264			−0.227103			−0.113552	+	0.993532i	$0.536223\pi$
$350$	12.0000	+	16.0000i	0.641427	+	0.855236i
$351$		−	11.3137i		−	0.603881i
$352$	2.82843	−	2.82843i	0.150756	−	0.150756i
$353$	11.0000	−	11.0000i	0.585471	−	0.585471i	−0.350931	−	0.936401i	$-0.614135\pi$
$353$	11.0000	−	11.0000i	0.585471	−	0.585471i	0.936401	+	0.350931i	$0.114135\pi$
$354$		0			0
$355$	12.0000	−	4.00000i	0.636894	−	0.212298i
$356$		−	14.1421i		−	0.749532i
$357$	40.0000	+	40.0000i	2.11702	+	2.11702i
$358$	1.00000	−	1.00000i	0.0528516	−	0.0528516i
$359$			14.0000i			0.738892i	0.929252	+	0.369446i	$0.120452\pi$
$359$			14.0000i			0.738892i	−0.929252	+	0.369446i	$0.879548\pi$
$360$	2.00000	+	1.00000i	0.105409	+	0.0527046i
$361$	−1.00000			−0.0526316
$362$	4.24264	−	4.24264i	0.222988	−	0.222988i
$363$	7.07107	+	7.07107i	0.371135	+	0.371135i
$364$	−11.3137			−0.592999
$365$	2.00000	−	4.00000i	0.104685	−	0.209370i
$366$		−	8.48528i		−	0.443533i
$367$	1.00000	+	1.00000i	0.0521996	+	0.0521996i	0.732725	−	0.680525i	$-0.238248\pi$
$367$	1.00000	+	1.00000i	0.0521996	+	0.0521996i	−0.680525	+	0.732725i	$0.738248\pi$
$368$	5.00000	−	5.00000i	0.260643	−	0.260643i
$369$		−	12.0000i		−	0.624695i
$370$	12.7279	−	4.24264i	0.661693	−	0.220564i
$371$		0			0
$372$	11.3137	−	11.3137i	0.586588	−	0.586588i
$373$	2.82843	+	2.82843i	0.146450	+	0.146450i	0.776530	−	0.630080i	$-0.216978\pi$
$373$	2.82843	+	2.82843i	0.146450	+	0.146450i	−0.630080	+	0.776530i	$0.716978\pi$
$374$	−28.2843			−1.46254
$375$	−4.00000	−	22.0000i	−0.206559	−	1.13608i
$376$			7.07107i			0.364662i
$377$	−8.48528	+	8.48528i	−0.437014	+	0.437014i
$378$	−11.3137	−	11.3137i	−0.581914	−	0.581914i
$379$		−	28.0000i		−	1.43826i	−0.694874	−	0.719132i	$-0.744540\pi$
$379$		−	28.0000i		−	1.43826i	0.694874	−	0.719132i	$-0.255460\pi$
$380$	−9.00000	+	3.00000i	−0.461690	+	0.153897i
$381$		−	14.1421i		−	0.724524i
$382$	−14.0000	−	14.0000i	−0.716302	−	0.716302i
$383$	19.7990	+	19.7990i	1.01168	+	1.01168i	0.999931	+	0.0117502i	$0.00374028\pi$
$383$	19.7990	+	19.7990i	1.01168	+	1.01168i	0.0117502	+	0.999931i	$0.496260\pi$
$384$			2.00000i			0.102062i
$385$	−32.0000	−	16.0000i	−1.63087	−	0.815436i
$386$		−	15.5563i		−	0.791797i
$387$	0.535534	−	6.53553i	0.0272227	−	0.332220i
$388$	9.00000	−	9.00000i	0.456906	−	0.456906i
$389$	−7.07107			−0.358517			−0.179259	−	0.983802i	$-0.557370\pi$
$389$	−7.07107			−0.358517			−0.179259	+	0.983802i	$0.557370\pi$
$390$	11.3137	+	5.65685i	0.572892	+	0.286446i
$391$	−50.0000			−2.52861
$392$	−6.36396	+	6.36396i	−0.321429	+	0.321429i
$393$	−2.00000	+	2.00000i	−0.100887	+	0.100887i
$394$	2.82843			0.142494
$395$	−21.2132	+	7.07107i	−1.06735	+	0.355784i
$396$	−4.00000			−0.201008
$397$	−20.0000	−	20.0000i	−1.00377	−	1.00377i	−0.999993	−	0.00377836i	$-0.998797\pi$
$397$	−20.0000	−	20.0000i	−1.00377	−	1.00377i	−0.00377836	−	0.999993i	$-0.501203\pi$
$398$	8.00000	−	8.00000i	0.401004	−	0.401004i
$399$	−33.9411			−1.69918
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$	16.0000			0.799002			0.399501	−	0.916733i	$-0.369183\pi$
$401$	16.0000			0.799002			0.399501	+	0.916733i	$0.369183\pi$
$402$	−4.00000	−	4.00000i	−0.199502	−	0.199502i
$403$	16.0000	−	16.0000i	0.797017	−	0.797017i
$404$		−	2.00000i		−	0.0995037i
$405$	7.77817	+	23.3345i	0.386501	+	1.15950i
$406$			16.9706i			0.842235i
$407$	−16.9706	+	16.9706i	−0.841200	+	0.841200i
$408$	10.0000	−	10.0000i	0.495074	−	0.495074i
$409$	−31.1127			−1.53842			−0.769212	−	0.638994i	$-0.779351\pi$
$409$	−31.1127			−1.53842			−0.769212	+	0.638994i	$0.779351\pi$
$410$	−24.0000	−	12.0000i	−1.18528	−	0.592638i
$411$	−20.0000			−0.986527
$412$	9.00000	+	9.00000i	0.443398	+	0.443398i
$413$		0			0
$414$	−7.07107			−0.347524
$415$	16.9706	+	8.48528i	0.833052	+	0.416526i
$416$			2.82843i			0.138675i
$417$	5.65685	−	5.65685i	0.277017	−	0.277017i
$418$	12.0000	−	12.0000i	0.586939	−	0.586939i
$419$	4.24264			0.207267			0.103633	−	0.994616i	$-0.466953\pi$
$419$	4.24264			0.207267			0.103633	+	0.994616i	$0.466953\pi$
$420$	16.9706	−	5.65685i	0.828079	−	0.276026i
$421$			9.89949i			0.482472i	0.970466	+	0.241236i	$0.0775528\pi$
$421$			9.89949i			0.482472i	−0.970466	+	0.241236i	$0.922447\pi$
$422$	−9.00000	−	9.00000i	−0.438113	−	0.438113i
$423$	5.00000	−	5.00000i	0.243108	−	0.243108i
$424$		0			0
$425$	−35.0000	−	5.00000i	−1.69775	−	0.242536i
$426$		−	11.3137i		−	0.548151i
$427$	−12.0000	−	12.0000i	−0.580721	−	0.580721i
$428$	−12.0000	+	12.0000i	−0.580042	+	0.580042i
$429$	−22.6274			−1.09246
$430$	−12.5355	−	7.60660i	−0.604517	−	0.366823i
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$	−2.82843	+	2.82843i	−0.136083	+	0.136083i
$433$	9.89949	+	9.89949i	0.475739	+	0.475739i	0.903766	−	0.428027i	$-0.140791\pi$
$433$	9.89949	+	9.89949i	0.475739	+	0.475739i	−0.428027	+	0.903766i	$0.640791\pi$
$434$		−	32.0000i		−	1.53605i
$435$	8.48528	−	16.9706i	0.406838	−	0.813676i
$436$	2.00000			0.0957826
$437$	21.2132	−	21.2132i	1.01477	−	1.01477i
$438$	−2.82843	−	2.82843i	−0.135147	−	0.135147i
$439$		−	6.00000i		−	0.286364i	−0.989696	−	0.143182i	$-0.954267\pi$
$439$		−	6.00000i		−	0.286364i	0.989696	−	0.143182i	$-0.0457335\pi$
$440$	−4.00000	+	8.00000i	−0.190693	+	0.381385i
$441$	9.00000			0.428571
$442$	14.1421	−	14.1421i	0.672673	−	0.672673i
$443$	10.0000	−	10.0000i	0.475114	−	0.475114i	−0.428451	−	0.903565i	$-0.640940\pi$
$443$	10.0000	−	10.0000i	0.475114	−	0.475114i	0.903565	+	0.428451i	$0.140940\pi$
$444$		−	12.0000i		−	0.569495i
$445$	10.0000	+	30.0000i	0.474045	+	1.42214i
$446$	20.0000			0.947027
$447$	14.0000	+	14.0000i	0.662177	+	0.662177i
$448$	2.82843	+	2.82843i	0.133631	+	0.133631i
$449$	36.7696			1.73526			0.867631	−	0.497208i	$-0.165642\pi$
$449$	36.7696			1.73526			0.867631	+	0.497208i	$0.165642\pi$
$450$	−4.94975	−	0.707107i	−0.233333	−	0.0333333i
$451$	48.0000			2.26023
$452$	7.07107	−	7.07107i	0.332595	−	0.332595i
$453$	−12.0000	+	12.0000i	−0.563809	+	0.563809i
$454$		−	20.0000i		−	0.938647i
$455$	24.0000	−	8.00000i	1.12514	−	0.375046i
$456$			8.48528i			0.397360i
$457$	−9.89949	+	9.89949i	−0.463079	+	0.463079i	−0.899663	−	0.436584i	$-0.856188\pi$
$457$	−9.89949	+	9.89949i	−0.463079	+	0.463079i	0.436584	+	0.899663i	$0.356188\pi$
$458$	18.3848	+	18.3848i	0.859064	+	0.859064i
$459$	28.2843			1.32020
$460$	−7.07107	+	14.1421i	−0.329690	+	0.659380i
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$	−22.6274	+	22.6274i	−1.05272	+	1.05272i
$463$	−16.9706	−	16.9706i	−0.788689	−	0.788689i	0.192590	−	0.981279i	$-0.438311\pi$
$463$	−16.9706	−	16.9706i	−0.788689	−	0.788689i	−0.981279	+	0.192590i	$0.938311\pi$
$464$	4.24264			0.196960
$465$	−16.0000	+	32.0000i	−0.741982	+	1.48396i
$466$	14.0000			0.648537
$467$	14.1421	−	14.1421i	0.654420	−	0.654420i	−0.299634	−	0.954054i	$-0.596865\pi$
$467$	14.1421	−	14.1421i	0.654420	−	0.654420i	0.954054	+	0.299634i	$0.0968646\pi$
$468$	2.00000	−	2.00000i	0.0924500	−	0.0924500i
$469$	−11.3137			−0.522419
$470$	−5.00000	−	15.0000i	−0.230633	−	0.691898i
$471$	4.00000			0.184310
$472$		0			0
$473$	26.1421	+	2.14214i	1.20202	+	0.0984955i
$474$			20.0000i			0.918630i
$475$	16.9706	−	12.7279i	0.778663	−	0.583997i
$476$		−	28.2843i		−	1.29641i
$477$		0			0
$478$		0			0
$479$		−	6.00000i		−	0.274147i	−0.990561	−	0.137073i	$-0.956230\pi$
$479$		−	6.00000i		−	0.274147i	0.990561	−	0.137073i	$-0.0437697\pi$
$480$	−1.41421	−	4.24264i	−0.0645497	−	0.193649i
$481$		−	16.9706i		−	0.773791i
$482$	−12.0000	−	12.0000i	−0.546585	−	0.546585i
$483$	−40.0000	+	40.0000i	−1.82006	+	1.82006i
$484$		−	5.00000i		−	0.227273i
$485$	−12.7279	+	25.4558i	−0.577945	+	1.15589i
$486$	10.0000			0.453609
$487$	1.00000	+	1.00000i	0.0453143	+	0.0453143i	0.729401	−	0.684087i	$-0.239799\pi$
$487$	1.00000	+	1.00000i	0.0453143	+	0.0453143i	−0.684087	+	0.729401i	$0.739799\pi$
$488$	−3.00000	+	3.00000i	−0.135804	+	0.135804i
$489$		−	8.00000i		−	0.361773i
$490$	9.00000	−	18.0000i	0.406579	−	0.813157i
$491$		−	1.41421i		−	0.0638226i	−0.999491	−	0.0319113i	$-0.989841\pi$
$491$		−	1.41421i		−	0.0638226i	0.999491	−	0.0319113i	$-0.0101594\pi$
$492$	−16.9706	+	16.9706i	−0.765092	+	0.765092i
$493$	−21.2132	−	21.2132i	−0.955395	−	0.955395i
$494$			12.0000i			0.539906i
$495$	8.48528	−	2.82843i	0.381385	−	0.127128i
$496$	−8.00000			−0.359211
$497$	−16.0000	−	16.0000i	−0.717698	−	0.717698i
$498$	12.0000	−	12.0000i	0.537733	−	0.537733i
$499$	−12.7279			−0.569780			−0.284890	−	0.958560i	$-0.591957\pi$
$499$	−12.7279			−0.569780			−0.284890	+	0.958560i	$0.591957\pi$
$500$	−6.36396	+	9.19239i	−0.284605	+	0.411096i
$501$			31.1127i			1.39001i
$502$	8.48528	−	8.48528i	0.378717	−	0.378717i
$503$	−5.65685	−	5.65685i	−0.252227	−	0.252227i	0.569656	−	0.821883i	$-0.307076\pi$
$503$	−5.65685	−	5.65685i	−0.252227	−	0.252227i	−0.821883	+	0.569656i	$0.807076\pi$
$504$		−	4.00000i		−	0.178174i
$505$	1.41421	+	4.24264i	0.0629317	+	0.188795i
$506$		−	28.2843i		−	1.25739i
$507$	−7.07107	+	7.07107i	−0.314037	+	0.314037i
$508$	−5.00000	+	5.00000i	−0.221839	+	0.221839i
$509$		−	6.00000i		−	0.265945i	−0.991120	−	0.132973i	$-0.957548\pi$
$509$		−	6.00000i		−	0.265945i	0.991120	−	0.132973i	$-0.0424523\pi$
$510$	−14.1421	+	28.2843i	−0.626224	+	1.25245i
$511$	−8.00000			−0.353899
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−12.0000	+	12.0000i	−0.529813	+	0.529813i
$514$		−	6.00000i		−	0.264649i
$515$	−25.4558	−	12.7279i	−1.12172	−	0.560859i
$516$	−10.0000	+	8.48528i	−0.440225	+	0.373544i
$517$	20.0000	+	20.0000i	0.879599	+	0.879599i
$518$	−16.9706	−	16.9706i	−0.745644	−	0.745644i
$519$	−45.2548			−1.98647
$520$	−2.00000	−	6.00000i	−0.0877058	−	0.263117i
$521$			19.7990i			0.867409i	0.901055	+	0.433705i	$0.142794\pi$
$521$			19.7990i			0.867409i	−0.901055	+	0.433705i	$0.857206\pi$
$522$	−3.00000	−	3.00000i	−0.131306	−	0.131306i
$523$	−8.48528	−	8.48528i	−0.371035	−	0.371035i	0.496819	−	0.867854i	$-0.334501\pi$
$523$	−8.48528	−	8.48528i	−0.371035	−	0.371035i	−0.867854	+	0.496819i	$0.834501\pi$
$524$	1.41421			0.0617802
$525$	−32.0000	+	24.0000i	−1.39659	+	1.04745i
$526$	−24.0000			−1.04645
$527$	40.0000	+	40.0000i	1.74243	+	1.74243i
$528$	5.65685	+	5.65685i	0.246183	+	0.246183i
$529$		−	27.0000i		−	1.17391i
$530$		0			0
$531$		0			0
$532$	12.0000	+	12.0000i	0.520266	+	0.520266i
$533$	−24.0000	+	24.0000i	−1.03956	+	1.03956i
$534$	28.2843			1.22398
$535$	16.9706	−	33.9411i	0.733701	−	1.46740i
$536$			2.82843i			0.122169i
$537$	2.00000	+	2.00000i	0.0863064	+	0.0863064i
$538$	4.24264	+	4.24264i	0.182913	+	0.182913i
$539$			36.0000i			1.55063i
$540$	4.00000	−	8.00000i	0.172133	−	0.344265i
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	5.65685	−	5.65685i	0.242983	−	0.242983i
$543$	8.48528	+	8.48528i	0.364138	+	0.364138i
$544$	−7.07107			−0.303170
$545$	−4.24264	+	1.41421i	−0.181735	+	0.0605783i
$546$		−	22.6274i		−	0.968364i
$547$	16.0000	+	16.0000i	0.684111	+	0.684111i	0.960924	−	0.276813i	$-0.0892783\pi$
$547$	16.0000	+	16.0000i	0.684111	+	0.684111i	−0.276813	+	0.960924i	$0.589278\pi$
$548$	7.07107	+	7.07107i	0.302061	+	0.302061i
$549$	4.24264			0.181071
$550$	2.82843	−	19.7990i	0.120605	−	0.844232i
$551$	18.0000			0.766826
$552$	10.0000	+	10.0000i	0.425628	+	0.425628i
$553$	28.2843	+	28.2843i	1.20277	+	1.20277i
$554$			8.00000i			0.339887i
$555$	8.48528	+	25.4558i	0.360180	+	1.08054i
$556$	−4.00000			−0.169638
$557$	−10.0000	−	10.0000i	−0.423714	−	0.423714i	0.462767	−	0.886480i	$-0.346857\pi$
$557$	−10.0000	−	10.0000i	−0.423714	−	0.423714i	−0.886480	+	0.462767i	$0.846857\pi$
$558$	5.65685	+	5.65685i	0.239474	+	0.239474i
$559$	−14.1421	+	12.0000i	−0.598149	+	0.507546i
$560$	−8.00000	−	4.00000i	−0.338062	−	0.169031i
$561$		−	56.5685i		−	2.38833i
$562$	7.07107	−	7.07107i	0.298275	−	0.298275i
$563$	−14.0000	+	14.0000i	−0.590030	+	0.590030i	−0.937639	−	0.347610i	$-0.886993\pi$
$563$	−14.0000	+	14.0000i	−0.590030	+	0.590030i	0.347610	+	0.937639i	$0.386993\pi$
$564$	−14.1421			−0.595491
$565$	−10.0000	+	20.0000i	−0.420703	+	0.841406i
$566$		−	8.48528i		−	0.356663i
$567$	31.1127	−	31.1127i	1.30661	−	1.30661i
$568$	−4.00000	+	4.00000i	−0.167836	+	0.167836i
$569$		−	32.0000i		−	1.34151i	−0.741679	−	0.670755i	$-0.765970\pi$
$569$		−	32.0000i		−	1.34151i	0.741679	−	0.670755i	$-0.234030\pi$
$570$	−6.00000	−	18.0000i	−0.251312	−	0.753937i
$571$			7.07107i			0.295915i	0.988994	+	0.147957i	$0.0472699\pi$
$571$			7.07107i			0.295915i	−0.988994	+	0.147957i	$0.952730\pi$
$572$	8.00000	+	8.00000i	0.334497	+	0.334497i
$573$	28.0000	−	28.0000i	1.16972	−	1.16972i
$574$			48.0000i			2.00348i
$575$	5.00000	−	35.0000i	0.208514	−	1.45960i
$576$	−1.00000			−0.0416667
$577$	15.5563	−	15.5563i	0.647619	−	0.647619i	−0.304798	−	0.952417i	$-0.598589\pi$
$577$	15.5563	−	15.5563i	0.647619	−	0.647619i	0.952417	+	0.304798i	$0.0985889\pi$
$578$	23.3345	+	23.3345i	0.970588	+	0.970588i
$579$	31.1127			1.29300
$580$	−9.00000	+	3.00000i	−0.373705	+	0.124568i
$581$		−	33.9411i		−	1.40812i
$582$	18.0000	+	18.0000i	0.746124	+	0.746124i
$583$		0			0
$584$			2.00000i			0.0827606i
$585$	−2.82843	+	5.65685i	−0.116941	+	0.233882i
$586$			14.1421i			0.584206i
$587$	−29.6985	+	29.6985i	−1.22579	+	1.22579i	−0.260245	+	0.965543i	$0.583803\pi$
$587$	−29.6985	+	29.6985i	−1.22579	+	1.22579i	−0.965543	+	0.260245i	$0.916197\pi$
$588$	−12.7279	−	12.7279i	−0.524891	−	0.524891i
$589$	−33.9411			−1.39852
$590$		0			0
$591$			5.65685i			0.232692i
$592$	−4.24264	+	4.24264i	−0.174371	+	0.174371i
$593$	4.24264	+	4.24264i	0.174224	+	0.174224i	0.788833	−	0.614608i	$-0.210686\pi$
$593$	4.24264	+	4.24264i	0.174224	+	0.174224i	−0.614608	+	0.788833i	$0.710686\pi$
$594$			16.0000i			0.656488i
$595$	20.0000	+	60.0000i	0.819920	+	2.45976i
$596$		−	9.89949i		−	0.405499i
$597$	16.0000	+	16.0000i	0.654836	+	0.654836i
$598$	14.1421	+	14.1421i	0.578315	+	0.578315i
$599$			30.0000i			1.22577i	0.790173	+	0.612883i	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$	6.00000	+	8.00000i	0.244949	+	0.326599i
$601$		−	8.48528i		−	0.346122i	−0.984911	−	0.173061i	$-0.944634\pi$
$601$		−	8.48528i		−	0.346122i	0.984911	−	0.173061i	$-0.0553658\pi$
$602$	−2.14214	+	26.1421i	−0.0873069	+	1.06547i
$603$	2.00000	−	2.00000i	0.0814463	−	0.0814463i
$604$	8.48528			0.345261
$605$	3.53553	+	10.6066i	0.143740	+	0.431220i
$606$	4.00000			0.162489
$607$	−5.65685	+	5.65685i	−0.229605	+	0.229605i	−0.812527	−	0.582923i	$-0.801909\pi$
$607$	−5.65685	+	5.65685i	−0.229605	+	0.229605i	0.582923	+	0.812527i	$0.301909\pi$
$608$	3.00000	−	3.00000i	0.121666	−	0.121666i
$609$	−33.9411			−1.37536
$610$	4.24264	−	8.48528i	0.171780	−	0.343559i
$611$	−20.0000			−0.809113
$612$	5.00000	+	5.00000i	0.202113	+	0.202113i
$613$	8.00000	−	8.00000i	0.323117	−	0.323117i	−0.526845	−	0.849962i	$-0.676625\pi$
$613$	8.00000	−	8.00000i	0.323117	−	0.323117i	0.849962	+	0.526845i	$0.176625\pi$
$614$	−22.6274			−0.913168
$615$	24.0000	−	48.0000i	0.967773	−	1.93555i
$616$	16.0000			0.644658
$617$	−33.0000	−	33.0000i	−1.32853	−	1.32853i	−0.906653	−	0.421877i	$-0.861371\pi$
$617$	−33.0000	−	33.0000i	−1.32853	−	1.32853i	−0.421877	−	0.906653i	$-0.638629\pi$
$618$	−18.0000	+	18.0000i	−0.724066	+	0.724066i
$619$		−	4.00000i		−	0.160774i	−0.996764	−	0.0803868i	$-0.974384\pi$
$619$		−	4.00000i		−	0.160774i	0.996764	−	0.0803868i	$-0.0256155\pi$
$620$	16.9706	−	5.65685i	0.681554	−	0.227185i
$621$			28.2843i			1.13501i
$622$	1.41421	−	1.41421i	0.0567048	−	0.0567048i
$623$	40.0000	−	40.0000i	1.60257	−	1.60257i
$624$	−5.65685			−0.226455
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$	10.0000			0.399680
$627$	24.0000	+	24.0000i	0.958468	+	0.958468i
$628$	−1.41421	−	1.41421i	−0.0564333	−	0.0564333i
$629$	42.4264			1.69165
$630$	2.82843	+	8.48528i	0.112687	+	0.338062i
$631$			8.48528i			0.337794i	0.985634	+	0.168897i	$0.0540205\pi$
$631$			8.48528i			0.337794i	−0.985634	+	0.168897i	$0.945980\pi$
$632$	7.07107	−	7.07107i	0.281272	−	0.281272i
$633$	18.0000	−	18.0000i	0.715436	−	0.715436i
$634$	11.3137			0.449325
$635$	7.07107	−	14.1421i	0.280607	−	0.561214i
$636$		0			0
$637$	−18.0000	−	18.0000i	−0.713186	−	0.713186i
$638$	12.0000	−	12.0000i	0.475085	−	0.475085i
$639$	5.65685			0.223782
$640$	−1.00000	+	2.00000i	−0.0395285	+	0.0790569i
$641$		−	39.5980i		−	1.56403i	−0.623262	−	0.782013i	$-0.714193\pi$
$641$		−	39.5980i		−	1.56403i	0.623262	−	0.782013i	$-0.285807\pi$
$642$	−24.0000	−	24.0000i	−0.947204	−	0.947204i
$643$	−2.00000	+	2.00000i	−0.0788723	+	0.0788723i	−0.745442	−	0.666570i	$-0.767762\pi$
$643$	−2.00000	+	2.00000i	−0.0788723	+	0.0788723i	0.666570	+	0.745442i	$0.267762\pi$
$644$	28.2843			1.11456
$645$	15.2132	−	25.0711i	0.599019	−	0.987172i
$646$	−30.0000			−1.18033
$647$	−5.65685	+	5.65685i	−0.222394	+	0.222394i	−0.809506	−	0.587112i	$-0.800265\pi$
$647$	−5.65685	+	5.65685i	−0.222394	+	0.222394i	0.587112	+	0.809506i	$0.300265\pi$
$648$	−7.77817	−	7.77817i	−0.305556	−	0.305556i
$649$		0			0
$650$	8.48528	+	11.3137i	0.332820	+	0.443760i
$651$	64.0000			2.50836
$652$	−2.82843	+	2.82843i	−0.110770	+	0.110770i
$653$	−24.0416	−	24.0416i	−0.940822	−	0.940822i	0.0575225	−	0.998344i	$-0.481680\pi$
$653$	−24.0416	−	24.0416i	−0.940822	−	0.940822i	−0.998344	+	0.0575225i	$0.981680\pi$
$654$			4.00000i			0.156412i
$655$	−3.00000	+	1.00000i	−0.117220	+	0.0390732i
$656$	12.0000			0.468521
$657$	1.41421	−	1.41421i	0.0551737	−	0.0551737i
$658$	−20.0000	+	20.0000i	−0.779681	+	0.779681i
$659$		−	8.00000i		−	0.311636i	−0.987786	−	0.155818i	$-0.950199\pi$
$659$		−	8.00000i		−	0.311636i	0.987786	−	0.155818i	$-0.0498013\pi$
$660$	−16.0000	−	8.00000i	−0.622799	−	0.311400i
$661$	18.0000			0.700119			0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000			0.700119			0.350059	+	0.936727i	$0.386161\pi$
$662$	19.0000	+	19.0000i	0.738456	+	0.738456i
$663$	28.2843	+	28.2843i	1.09847	+	1.09847i
$664$	−8.48528			−0.329293
$665$	−33.9411	−	16.9706i	−1.31618	−	0.658090i
$666$	6.00000			0.232495
$667$	21.2132	−	21.2132i	0.821379	−	0.821379i
$668$	11.0000	−	11.0000i	0.425603	−	0.425603i
$669$			40.0000i			1.54649i
$670$	−2.00000	−	6.00000i	−0.0772667	−	0.231800i
$671$			16.9706i			0.655141i
$672$	−5.65685	+	5.65685i	−0.218218	+	0.218218i
$673$	1.41421	+	1.41421i	0.0545139	+	0.0545139i	0.733838	−	0.679324i	$-0.237727\pi$
$673$	1.41421	+	1.41421i	0.0545139	+	0.0545139i	−0.679324	+	0.733838i	$0.737727\pi$
$674$	12.7279			0.490261
$675$	−2.82843	+	19.7990i	−0.108866	+	0.762063i
$676$	5.00000			0.192308
$677$	8.48528	−	8.48528i	0.326116	−	0.326116i	−0.524992	−	0.851107i	$-0.675932\pi$
$677$	8.48528	−	8.48528i	0.326116	−	0.326116i	0.851107	+	0.524992i	$0.175932\pi$
$678$	14.1421	+	14.1421i	0.543125	+	0.543125i
$679$	50.9117			1.95381
$680$	15.0000	−	5.00000i	0.575224	−	0.191741i
$681$	40.0000			1.53280
$682$	−22.6274	+	22.6274i	−0.866449	+	0.866449i
$683$	26.0000	−	26.0000i	0.994862	−	0.994862i	−0.00512452	−	0.999987i	$-0.501631\pi$
$683$	26.0000	−	26.0000i	0.994862	−	0.994862i	0.999987	+	0.00512452i	$0.00163119\pi$
$684$	−4.24264			−0.162221
$685$	−20.0000	−	10.0000i	−0.764161	−	0.382080i
$686$	−8.00000			−0.305441
$687$	−36.7696	+	36.7696i	−1.40285	+	1.40285i
$688$	6.53553	+	0.535534i	0.249165	+	0.0204170i
$689$		0			0
$690$	−28.2843	−	14.1421i	−1.07676	−	0.538382i
$691$		−	18.3848i		−	0.699390i	−0.936864	−	0.349695i	$-0.886285\pi$
$691$		−	18.3848i		−	0.699390i	0.936864	−	0.349695i	$-0.113715\pi$
$692$	16.0000	+	16.0000i	0.608229	+	0.608229i
$693$	−11.3137	−	11.3137i	−0.429772	−	0.429772i
$694$			12.0000i			0.455514i
$695$	8.48528	−	2.82843i	0.321865	−	0.107288i
$696$			8.48528i			0.321634i
$697$	−60.0000	−	60.0000i	−2.27266	−	2.27266i
$698$	−3.00000	+	3.00000i	−0.113552	+	0.113552i
$699$			28.0000i			1.05906i
$700$	19.7990	+	2.82843i	0.748331	+	0.106904i
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$	−8.00000	−	8.00000i	−0.301941	−	0.301941i
$703$	−18.0000	+	18.0000i	−0.678883	+	0.678883i
$704$		−	4.00000i		−	0.150756i
$705$	30.0000	−	10.0000i	1.12987	−	0.376622i
$706$		−	15.5563i		−	0.585471i
$707$	5.65685	−	5.65685i	0.212748	−	0.212748i
$708$		0			0
$709$			30.0000i			1.12667i	0.826227	+	0.563337i	$0.190483\pi$
$709$			30.0000i			1.12667i	−0.826227	+	0.563337i	$0.809517\pi$
$710$	5.65685	−	11.3137i	0.212298	−	0.424596i
$711$	−10.0000			−0.375029
$712$	−10.0000	−	10.0000i	−0.374766	−	0.374766i
$713$	−40.0000	+	40.0000i	−1.49801	+	1.49801i
$714$	56.5685			2.11702
$715$	−22.6274	−	11.3137i	−0.846217	−	0.423109i
$716$		−	1.41421i		−	0.0528516i
$717$		0			0
$718$	9.89949	+	9.89949i	0.369446	+	0.369446i
$719$		−	16.0000i		−	0.596699i	−0.954457	−	0.298350i	$-0.903564\pi$
$719$		−	16.0000i		−	0.596699i	0.954457	−	0.298350i	$-0.0964361\pi$
$720$	2.12132	−	0.707107i	0.0790569	−	0.0263523i
$721$			50.9117i			1.89605i
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$	24.0000	−	24.0000i	0.892570	−	0.892570i
$724$		−	6.00000i		−	0.222988i
$725$	16.9706	−	12.7279i	0.630271	−	0.472703i
$726$	10.0000			0.371135
$727$	36.7696	−	36.7696i	1.36371	−	1.36371i	0.494569	−	0.869139i	$-0.335326\pi$
$727$	36.7696	−	36.7696i	1.36371	−	1.36371i	0.869139	−	0.494569i	$-0.164674\pi$
$728$	−8.00000	+	8.00000i	−0.296500	+	0.296500i
$729$		−	13.0000i		−	0.481481i
$730$	−1.41421	−	4.24264i	−0.0523424	−	0.157027i
$731$	−30.0000	−	35.3553i	−1.10959	−	1.30766i
$732$	−6.00000	−	6.00000i	−0.221766	−	0.221766i
$733$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$733$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$734$	1.41421			0.0521996
$735$	36.0000	+	18.0000i	1.32788	+	0.663940i
$736$		−	7.07107i		−	0.260643i
$737$	8.00000	+	8.00000i	0.294684	+	0.294684i
$738$	−8.48528	−	8.48528i	−0.312348	−	0.312348i
$739$	21.2132			0.780340			0.390170	−	0.920743i	$-0.372416\pi$
$739$	21.2132			0.780340			0.390170	+	0.920743i	$0.372416\pi$
$740$	6.00000	−	12.0000i	0.220564	−	0.441129i
$741$	−24.0000			−0.881662
$742$		0			0
$743$	−5.65685	−	5.65685i	−0.207530	−	0.207530i	0.595687	−	0.803217i	$-0.296880\pi$
$743$	−5.65685	−	5.65685i	−0.207530	−	0.207530i	−0.803217	+	0.595687i	$0.796880\pi$
$744$		−	16.0000i		−	0.586588i
$745$	7.00000	+	21.0000i	0.256460	+	0.769380i
$746$	4.00000			0.146450
$747$	6.00000	+	6.00000i	0.219529	+	0.219529i
$748$	−20.0000	+	20.0000i	−0.731272	+	0.731272i
$749$	−67.8823			−2.48036
$750$	−18.3848	−	12.7279i	−0.671317	−	0.464758i
$751$			11.3137i			0.412843i	0.978463	+	0.206422i	$0.0661818\pi$
$751$			11.3137i			0.412843i	−0.978463	+	0.206422i	$0.933818\pi$
$752$	5.00000	+	5.00000i	0.182331	+	0.182331i
$753$	16.9706	+	16.9706i	0.618442	+	0.618442i
$754$			12.0000i			0.437014i
$755$	−18.0000	+	6.00000i	−0.655087	+	0.218362i
$756$	−16.0000			−0.581914
$757$	11.3137	−	11.3137i	0.411204	−	0.411204i	−0.470954	−	0.882158i	$-0.656090\pi$
$757$	11.3137	−	11.3137i	0.411204	−	0.411204i	0.882158	+	0.470954i	$0.156090\pi$
$758$	−19.7990	−	19.7990i	−0.719132	−	0.719132i
$759$	56.5685			2.05331
$760$	−4.24264	+	8.48528i	−0.153897	+	0.307794i
$761$		−	2.82843i		−	0.102530i	−0.998685	−	0.0512652i	$-0.983675\pi$
$761$		−	2.82843i		−	0.102530i	0.998685	−	0.0512652i	$-0.0163254\pi$
$762$	−10.0000	−	10.0000i	−0.362262	−	0.362262i
$763$	5.65685	+	5.65685i	0.204792	+	0.204792i
$764$	−19.7990			−0.716302
$765$	−14.1421	−	7.07107i	−0.511310	−	0.255655i
$766$	28.0000			1.01168
$767$		0			0
$768$	1.41421	+	1.41421i	0.0510310	+	0.0510310i
$769$			18.0000i			0.649097i	0.945869	+	0.324548i	$0.105212\pi$
$769$			18.0000i			0.649097i	−0.945869	+	0.324548i	$0.894788\pi$
$770$	−33.9411	+	11.3137i	−1.22315	+	0.407718i
$771$	12.0000			0.432169
$772$	−11.0000	−	11.0000i	−0.395899	−	0.395899i
$773$	−16.9706	−	16.9706i	−0.610389	−	0.610389i	0.332659	−	0.943047i	$-0.392054\pi$
$773$	−16.9706	−	16.9706i	−0.610389	−	0.610389i	−0.943047	+	0.332659i	$0.892054\pi$
$774$	−4.24264	−	5.00000i	−0.152499	−	0.179721i
$775$	−32.0000	+	24.0000i	−1.14947	+	0.862105i
$776$		−	12.7279i		−	0.456906i
$777$	33.9411	−	33.9411i	1.21763	−	1.21763i
$778$	−5.00000	+	5.00000i	−0.179259	+	0.179259i
$779$	50.9117			1.82410
$780$	12.0000	−	4.00000i	0.429669	−	0.143223i
$781$			22.6274i			0.809673i
$782$	−35.3553	+	35.3553i	−1.26430	+	1.26430i
$783$	−12.0000	+	12.0000i	−0.428845	+	0.428845i
$784$			9.00000i			0.321429i
$785$	4.00000	+	2.00000i	0.142766	+	0.0713831i
$786$			2.82843i			0.100887i
$787$	−20.0000	−	20.0000i	−0.712923	−	0.712923i	0.254223	−	0.967146i	$-0.418180\pi$
$787$	−20.0000	−	20.0000i	−0.712923	−	0.712923i	−0.967146	+	0.254223i	$0.918180\pi$
$788$	2.00000	−	2.00000i	0.0712470	−	0.0712470i
$789$		−	48.0000i		−	1.70885i
$790$	−10.0000	+	20.0000i	−0.355784	+	0.711568i
$791$	40.0000			1.42224
$792$	−2.82843	+	2.82843i	−0.100504	+	0.100504i
$793$	−8.48528	−	8.48528i	−0.301321	−	0.301321i
$794$	−28.2843			−1.00377
$795$		0			0
$796$		−	11.3137i		−	0.401004i
$797$	28.0000	+	28.0000i	0.991811	+	0.991811i	0.999967	−	0.00815585i	$-0.00259612\pi$
$797$	28.0000	+	28.0000i	0.991811	+	0.991811i	−0.00815585	+	0.999967i	$0.502596\pi$
$798$	−24.0000	+	24.0000i	−0.849591	+	0.849591i
$799$		−	50.0000i		−	1.76887i
$800$	0.707107	−	4.94975i	0.0250000	−	0.175000i
$801$			14.1421i			0.499688i
$802$	11.3137	−	11.3137i	0.399501	−	0.399501i
$803$	5.65685	+	5.65685i	0.199626	+	0.199626i
$804$	−5.65685			−0.199502
$805$	−60.0000	+	20.0000i	−2.11472	+	0.704907i
$806$		−	22.6274i		−	0.797017i
$807$	−8.48528	+	8.48528i	−0.298696	+	0.298696i
$808$	−1.41421	−	1.41421i	−0.0497519	−	0.0497519i
$809$			4.00000i			0.140633i	0.997525	+	0.0703163i	$0.0224008\pi$
$809$			4.00000i			0.140633i	−0.997525	+	0.0703163i	$0.977599\pi$
$810$	22.0000	+	11.0000i	0.773001	+	0.386501i
$811$			29.6985i			1.04285i	0.853296	+	0.521427i	$0.174600\pi$
$811$			29.6985i			1.04285i	−0.853296	+	0.521427i	$0.825400\pi$
$812$	12.0000	+	12.0000i	0.421117	+	0.421117i
$813$	11.3137	+	11.3137i	0.396789	+	0.396789i
$814$			24.0000i			0.841200i
$815$	4.00000	−	8.00000i	0.140114	−	0.280228i
$816$		−	14.1421i		−	0.495074i
$817$	27.7279	+	2.27208i	0.970077	+	0.0794899i
$818$	−22.0000	+	22.0000i	−0.769212	+	0.769212i
$819$	11.3137			0.395333
$820$	−25.4558	+	8.48528i	−0.888957	+	0.296319i
$821$	38.0000			1.32621			0.663105	−	0.748527i	$-0.269238\pi$
$821$	38.0000			1.32621			0.663105	+	0.748527i	$0.269238\pi$
$822$	−14.1421	+	14.1421i	−0.493264	+	0.493264i
$823$	21.0000	−	21.0000i	0.732014	−	0.732014i	−0.239004	−	0.971018i	$-0.576821\pi$
$823$	21.0000	−	21.0000i	0.732014	−	0.732014i	0.971018	+	0.239004i	$0.0768211\pi$
$824$	12.7279			0.443398
$825$	39.5980	+	5.65685i	1.37862	+	0.196946i
$826$		0			0
$827$	−26.0000	−	26.0000i	−0.904109	−	0.904109i	0.0916799	−	0.995789i	$-0.470776\pi$
$827$	−26.0000	−	26.0000i	−0.904109	−	0.904109i	−0.995789	+	0.0916799i	$0.970776\pi$
$828$	−5.00000	+	5.00000i	−0.173762	+	0.173762i
$829$	7.07107			0.245588			0.122794	−	0.992432i	$-0.460815\pi$
$829$	7.07107			0.245588			0.122794	+	0.992432i	$0.460815\pi$
$830$	18.0000	−	6.00000i	0.624789	−	0.208263i
$831$	−16.0000			−0.555034
$832$	2.00000	+	2.00000i	0.0693375	+	0.0693375i
$833$	45.0000	−	45.0000i	1.55916	−	1.55916i
$834$		−	8.00000i		−	0.277017i
$835$	−15.5563	+	31.1127i	−0.538350	+	1.07670i
$836$		−	16.9706i		−	0.586939i
$837$	22.6274	−	22.6274i	0.782118	−	0.782118i
$838$	3.00000	−	3.00000i	0.103633	−	0.103633i
$839$	−53.7401			−1.85531			−0.927657	−	0.373432i	$-0.878181\pi$
$839$	−53.7401			−1.85531			−0.927657	+	0.373432i	$0.878181\pi$
$840$	8.00000	−	16.0000i	0.276026	−	0.552052i
$841$	−11.0000			−0.379310
$842$	7.00000	+	7.00000i	0.241236	+	0.241236i
$843$	14.1421	+	14.1421i	0.487081	+	0.487081i
$844$	−12.7279			−0.438113
$845$	−10.6066	+	3.53553i	−0.364878	+	0.121626i
$846$		−	7.07107i		−	0.243108i
$847$	14.1421	−	14.1421i	0.485930	−	0.485930i
$848$		0			0
$849$	16.9706			0.582428
$850$	−28.2843	+	21.2132i	−0.970143	+	0.727607i
$851$			42.4264i			1.45436i
$852$	−8.00000	−	8.00000i	−0.274075	−	0.274075i
$853$	−4.00000	+	4.00000i	−0.136957	+	0.136957i	−0.772262	−	0.635304i	$-0.780875\pi$
$853$	−4.00000	+	4.00000i	−0.136957	+	0.136957i	0.635304	+	0.772262i	$0.280875\pi$
$854$	−16.9706			−0.580721
$855$	9.00000	−	3.00000i	0.307794	−	0.102598i
$856$			16.9706i			0.580042i
$857$	7.00000	+	7.00000i	0.239115	+	0.239115i	0.816484	−	0.577368i	$-0.195920\pi$
$857$	7.00000	+	7.00000i	0.239115	+	0.239115i	−0.577368	+	0.816484i	$0.695920\pi$
$858$	−16.0000	+	16.0000i	−0.546231	+	0.546231i
$859$	−15.5563			−0.530776			−0.265388	−	0.964142i	$-0.585500\pi$
$859$	−15.5563			−0.530776			−0.265388	+	0.964142i	$0.585500\pi$
$860$	−14.2426	+	3.48528i	−0.485670	+	0.118847i
$861$	−96.0000			−3.27167
$862$	−16.9706	+	16.9706i	−0.578020	+	0.578020i
$863$	33.9411	+	33.9411i	1.15537	+	1.15537i	0.985460	+	0.169910i	$0.0543476\pi$
$863$	33.9411	+	33.9411i	1.15537	+	1.15537i	0.169910	+	0.985460i	$0.445652\pi$
$864$			4.00000i			0.136083i
$865$	−45.2548	−	22.6274i	−1.53871	−	0.769355i
$866$	14.0000			0.475739
$867$	−46.6690	+	46.6690i	−1.58496	+	1.58496i
$868$	−22.6274	−	22.6274i	−0.768025	−	0.768025i
$869$		−	40.0000i		−	1.35691i
$870$	−6.00000	−	18.0000i	−0.203419	−	0.610257i
$871$	−8.00000			−0.271070
$872$	1.41421	−	1.41421i	0.0478913	−	0.0478913i
$873$	−9.00000	+	9.00000i	−0.304604	+	0.304604i
$874$		−	30.0000i		−	1.01477i
$875$	−44.0000	+	8.00000i	−1.48747	+	0.270449i
$876$	−4.00000			−0.135147
$877$	−18.0000	−	18.0000i	−0.607817	−	0.607817i	0.334558	−	0.942375i	$-0.391413\pi$
$877$	−18.0000	−	18.0000i	−0.607817	−	0.607817i	−0.942375	+	0.334558i	$0.891413\pi$
$878$	−4.24264	−	4.24264i	−0.143182	−	0.143182i
$879$	−28.2843			−0.954005
$880$	2.82843	+	8.48528i	0.0953463	+	0.286039i
$881$	−24.0000			−0.808581			−0.404290	−	0.914631i	$-0.632481\pi$
$881$	−24.0000			−0.808581			−0.404290	+	0.914631i	$0.632481\pi$
$882$	6.36396	−	6.36396i	0.214286	−	0.214286i
$883$	−12.0000	+	12.0000i	−0.403832	+	0.403832i	−0.879581	−	0.475749i	$-0.842177\pi$
$883$	−12.0000	+	12.0000i	−0.403832	+	0.403832i	0.475749	+	0.879581i	$0.342177\pi$
$884$		−	20.0000i		−	0.672673i
$885$		0			0
$886$		−	14.1421i		−	0.475114i
$887$	−33.9411	+	33.9411i	−1.13963	+	1.13963i	−0.151115	+	0.988516i	$0.548286\pi$
$887$	−33.9411	+	33.9411i	−1.13963	+	1.13963i	−0.988516	+	0.151115i	$0.951714\pi$
$888$	−8.48528	−	8.48528i	−0.284747	−	0.284747i
$889$	−28.2843			−0.948624
$890$	28.2843	+	14.1421i	0.948091	+	0.474045i
$891$	−44.0000			−1.47406
$892$	14.1421	−	14.1421i	0.473514	−	0.473514i
$893$	21.2132	+	21.2132i	0.709873	+	0.709873i
$894$	19.7990			0.662177
$895$	1.00000	+	3.00000i	0.0334263	+	0.100279i
$896$	4.00000			0.133631
$897$	−28.2843	+	28.2843i	−0.944384	+	0.944384i
$898$	26.0000	−	26.0000i	0.867631	−	0.867631i
$899$	−33.9411			−1.13200
$900$	−4.00000	+	3.00000i	−0.133333	+	0.100000i
$901$		0			0
$902$	33.9411	−	33.9411i	1.13012	−	1.13012i
$903$	−52.2843	−	4.28427i	−1.73991	−	0.142572i
$904$		−	10.0000i		−	0.332595i
$905$	4.24264	+	12.7279i	0.141030	+	0.423090i
$906$			16.9706i			0.563809i
$907$	−18.0000	−	18.0000i	−0.597680	−	0.597680i	0.342014	−	0.939695i	$-0.388891\pi$
$907$	−18.0000	−	18.0000i	−0.597680	−	0.597680i	−0.939695	+	0.342014i	$0.888891\pi$
$908$	−14.1421	−	14.1421i	−0.469323	−	0.469323i
$909$			2.00000i			0.0663358i
$910$	11.3137	−	22.6274i	0.375046	−	0.750092i
$911$		−	53.7401i		−	1.78049i	−0.455483	−	0.890245i	$-0.650533\pi$
$911$		−	53.7401i		−	1.78049i	0.455483	−	0.890245i	$-0.349467\pi$
$912$	6.00000	+	6.00000i	0.198680	+	0.198680i
$913$	−24.0000	+	24.0000i	−0.794284	+	0.794284i
$914$			14.0000i			0.463079i
$915$	16.9706	+	8.48528i	0.561029	+	0.280515i
$916$	26.0000			0.859064
$917$	4.00000	+	4.00000i	0.132092	+	0.132092i
$918$	20.0000	−	20.0000i	0.660098	−	0.660098i
$919$			42.0000i			1.38545i	0.721201	+	0.692726i	$0.243591\pi$
$919$			42.0000i			1.38545i	−0.721201	+	0.692726i	$0.756409\pi$
$920$	5.00000	+	15.0000i	0.164845	+	0.494535i
$921$		−	45.2548i		−	1.49120i
$922$	−4.24264	+	4.24264i	−0.139724	+	0.139724i
$923$	−11.3137	−	11.3137i	−0.372395	−	0.372395i
$924$			32.0000i			1.05272i
$925$	−4.24264	+	29.6985i	−0.139497	+	0.976480i
$926$	−24.0000			−0.788689
$927$	−9.00000	−	9.00000i	−0.295599	−	0.295599i
$928$	3.00000	−	3.00000i	0.0984798	−	0.0984798i
$929$	−2.82843			−0.0927977			−0.0463988	−	0.998923i	$-0.514775\pi$
$929$	−2.82843			−0.0927977			−0.0463988	+	0.998923i	$0.514775\pi$
$930$	11.3137	+	33.9411i	0.370991	+	1.11297i
$931$			38.1838i			1.25142i
$932$	9.89949	−	9.89949i	0.324269	−	0.324269i
$933$	2.82843	+	2.82843i	0.0925985	+	0.0925985i
$934$		−	20.0000i		−	0.654420i
$935$	28.2843	−	56.5685i	0.924995	−	1.84999i
$936$		−	2.82843i		−	0.0924500i
$937$	15.5563	−	15.5563i	0.508204	−	0.508204i	−0.405771	−	0.913975i	$-0.632997\pi$
$937$	15.5563	−	15.5563i	0.508204	−	0.508204i	0.913975	+	0.405771i	$0.132997\pi$
$938$	−8.00000	+	8.00000i	−0.261209	+	0.261209i
$939$			20.0000i			0.652675i
$940$	−14.1421	−	7.07107i	−0.461266	−	0.230633i
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$	2.82843	−	2.82843i	0.0921551	−	0.0921551i
$943$	60.0000	−	60.0000i	1.95387	−	1.95387i
$944$		0			0
$945$	33.9411	−	11.3137i	1.10410	−	0.368035i
$946$	20.0000	−	16.9706i	0.650256	−	0.551761i
$947$	−20.0000	−	20.0000i	−0.649913	−	0.649913i	0.303059	−	0.952972i	$-0.401992\pi$
$947$	−20.0000	−	20.0000i	−0.649913	−	0.649913i	−0.952972	+	0.303059i	$0.901992\pi$
$948$	14.1421	+	14.1421i	0.459315	+	0.459315i
$949$	−5.65685			−0.183629
$950$	3.00000	−	21.0000i	0.0973329	−	0.681330i
$951$			22.6274i			0.733744i
$952$	−20.0000	−	20.0000i	−0.648204	−	0.648204i
$953$	−24.0416	−	24.0416i	−0.778785	−	0.778785i	0.200839	−	0.979624i	$-0.435633\pi$
$953$	−24.0416	−	24.0416i	−0.778785	−	0.778785i	−0.979624	+	0.200839i	$0.935633\pi$
$954$		0			0
$955$	42.0000	−	14.0000i	1.35909	−	0.453029i
$956$		0			0
$957$	24.0000	+	24.0000i	0.775810	+	0.775810i
$958$	−4.24264	−	4.24264i	−0.137073	−	0.137073i
$959$			40.0000i			1.29167i
$960$	−4.00000	−	2.00000i	−0.129099	−	0.0645497i
$961$	33.0000			1.06452
$962$	−12.0000	−	12.0000i	−0.386896	−	0.386896i
$963$	12.0000	−	12.0000i	0.386695	−	0.386695i
$964$	−16.9706			−0.546585
$965$	31.1127	+	15.5563i	1.00155	+	0.500777i
$966$			56.5685i			1.82006i
$967$	9.00000	+	9.00000i	0.289420	+	0.289420i	0.836851	−	0.547431i	$-0.184394\pi$
$967$	9.00000	+	9.00000i	0.289420	+	0.289420i	−0.547431	+	0.836851i	$0.684394\pi$
$968$	−3.53553	−	3.53553i	−0.113636	−	0.113636i
$969$		−	60.0000i		−	1.92748i
$970$	9.00000	+	27.0000i	0.288973	+	0.866918i
$971$	4.00000			0.128366			0.0641831	−	0.997938i	$-0.479556\pi$
$971$	4.00000			0.128366			0.0641831	+	0.997938i	$0.479556\pi$
$972$	7.07107	−	7.07107i	0.226805	−	0.226805i
$973$	−11.3137	−	11.3137i	−0.362701	−	0.362701i
$974$	1.41421			0.0453143
$975$	−22.6274	+	16.9706i	−0.724657	+	0.543493i
$976$			4.24264i			0.135804i
$977$	−11.0000	−	11.0000i	−0.351921	−	0.351921i	0.508903	−	0.860824i	$-0.330051\pi$
$977$	−11.0000	−	11.0000i	−0.351921	−	0.351921i	−0.860824	+	0.508903i	$0.830051\pi$
$978$	−5.65685	−	5.65685i	−0.180886	−	0.180886i
$979$	−56.5685			−1.80794
$980$	−6.36396	−	19.0919i	−0.203289	−	0.609868i
$981$	−2.00000			−0.0638551
$982$	−1.00000	−	1.00000i	−0.0319113	−	0.0319113i
$983$	−16.9706	−	16.9706i	−0.541277	−	0.541277i	0.382626	−	0.923903i	$-0.375020\pi$
$983$	−16.9706	−	16.9706i	−0.541277	−	0.541277i	−0.923903	+	0.382626i	$0.875020\pi$
$984$			24.0000i			0.765092i
$985$	−2.82843	+	5.65685i	−0.0901212	+	0.180242i
$986$	−30.0000			−0.955395
$987$	−40.0000	−	40.0000i	−1.27321	−	1.27321i
$988$	8.48528	+	8.48528i	0.269953	+	0.269953i
$989$	35.3553	−	30.0000i	1.12423	−	0.953945i
$990$	4.00000	−	8.00000i	0.127128	−	0.254257i
$991$		−	5.65685i		−	0.179696i	−0.995955	−	0.0898479i	$-0.971362\pi$
$991$		−	5.65685i		−	0.179696i	0.995955	−	0.0898479i	$-0.0286381\pi$
$992$	−5.65685	+	5.65685i	−0.179605	+	0.179605i
$993$	−38.0000	+	38.0000i	−1.20589	+	1.20589i
$994$	−22.6274			−0.717698
$995$	8.00000	+	24.0000i	0.253617	+	0.760851i
$996$		−	16.9706i		−	0.537733i
$997$	31.1127	−	31.1127i	0.985349	−	0.985349i	−0.0145452	−	0.999894i	$-0.504630\pi$
$997$	31.1127	−	31.1127i	0.985349	−	0.985349i	0.999894	+	0.0145452i	$0.00463003\pi$
$998$	−9.00000	+	9.00000i	−0.284890	+	0.284890i
$999$		−	24.0000i		−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.g.a.257.2	yes	4
5.3	odd	4	inner	430.2.g.a.343.1	yes	4
43.42	odd	2	inner	430.2.g.a.257.1	✓	4
215.128	even	4	inner	430.2.g.a.343.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.g.a.257.1	✓	4	43.42	odd	2	inner
430.2.g.a.257.2	yes	4	1.1	even	1	trivial
430.2.g.a.343.1	yes	4	5.3	odd	4	inner
430.2.g.a.343.2	yes	4	215.128	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.41421 + 1.41421i) q^{3} -1.00000i q^{4} +(0.707107 + 2.12132i) q^{5} +2.00000 q^{6} +(2.82843 - 2.82843i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.41421 + 1.41421i) q^{3} -1.00000i q^{4} +(0.707107 + 2.12132i) q^{5} +2.00000 q^{6} +(2.82843 - 2.82843i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(2.00000 + 1.00000i) q^{10} -4.00000 q^{11} +(1.41421 - 1.41421i) q^{12} +(2.00000 - 2.00000i) q^{13} -4.00000i q^{14} +(-2.00000 + 4.00000i) q^{15} -1.00000 q^{16} +(5.00000 + 5.00000i) q^{17} +(0.707107 + 0.707107i) q^{18} -4.24264 q^{19} +(2.12132 - 0.707107i) q^{20} +8.00000 q^{21} +(-2.82843 + 2.82843i) q^{22} +(-5.00000 + 5.00000i) q^{23} -2.00000i q^{24} +(-4.00000 + 3.00000i) q^{25} -2.82843i q^{26} +(2.82843 - 2.82843i) q^{27} +(-2.82843 - 2.82843i) q^{28} -4.24264 q^{29} +(1.41421 + 4.24264i) q^{30} +8.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.65685 - 5.65685i) q^{33} +7.07107 q^{34} +(8.00000 + 4.00000i) q^{35} +1.00000 q^{36} +(4.24264 - 4.24264i) q^{37} +(-3.00000 + 3.00000i) q^{38} +5.65685 q^{39} +(1.00000 - 2.00000i) q^{40} -12.0000 q^{41} +(5.65685 - 5.65685i) q^{42} +(-6.53553 - 0.535534i) q^{43} +4.00000i q^{44} +(-2.12132 + 0.707107i) q^{45} +7.07107i q^{46} +(-5.00000 - 5.00000i) q^{47} +(-1.41421 - 1.41421i) q^{48} -9.00000i q^{49} +(-0.707107 + 4.94975i) q^{50} +14.1421i q^{51} +(-2.00000 - 2.00000i) q^{52} -4.00000i q^{54} +(-2.82843 - 8.48528i) q^{55} -4.00000 q^{56} +(-6.00000 - 6.00000i) q^{57} +(-3.00000 + 3.00000i) q^{58} +(4.00000 + 2.00000i) q^{60} -4.24264i q^{61} +(5.65685 - 5.65685i) q^{62} +(2.82843 + 2.82843i) q^{63} +1.00000i q^{64} +(5.65685 + 2.82843i) q^{65} -8.00000 q^{66} +(-2.00000 - 2.00000i) q^{67} +(5.00000 - 5.00000i) q^{68} -14.1421 q^{69} +(8.48528 - 2.82843i) q^{70} -5.65685i q^{71} +(0.707107 - 0.707107i) q^{72} +(-1.41421 - 1.41421i) q^{73} -6.00000i q^{74} +(-9.89949 - 1.41421i) q^{75} +4.24264i q^{76} +(-11.3137 + 11.3137i) q^{77} +(4.00000 - 4.00000i) q^{78} +10.0000i q^{79} +(-0.707107 - 2.12132i) q^{80} +11.0000 q^{81} +(-8.48528 + 8.48528i) q^{82} +(6.00000 - 6.00000i) q^{83} -8.00000i q^{84} +(-7.07107 + 14.1421i) q^{85} +(-5.00000 + 4.24264i) q^{86} +(-6.00000 - 6.00000i) q^{87} +(2.82843 + 2.82843i) q^{88} +14.1421 q^{89} +(-1.00000 + 2.00000i) q^{90} -11.3137i q^{91} +(5.00000 + 5.00000i) q^{92} +(11.3137 + 11.3137i) q^{93} -7.07107 q^{94} +(-3.00000 - 9.00000i) q^{95} -2.00000 q^{96} +(9.00000 + 9.00000i) q^{97} +(-6.36396 - 6.36396i) q^{98} -4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{6}+O(q^{10}) \) 4 * q + 8 * q^6	\( 4 q + 8 q^{6} + 8 q^{10} - 16 q^{11} + 8 q^{13} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 32 q^{21} - 20 q^{23} - 16 q^{25} + 32 q^{31} + 32 q^{35} + 4 q^{36} - 12 q^{38} + 4 q^{40} - 48 q^{41} - 12 q^{43} - 20 q^{47} - 8 q^{52} - 16 q^{56} - 24 q^{57} - 12 q^{58} + 16 q^{60} - 32 q^{66} - 8 q^{67} + 20 q^{68} + 16 q^{78} + 44 q^{81} + 24 q^{83} - 20 q^{86} - 24 q^{87} - 4 q^{90} + 20 q^{92} - 12 q^{95} - 8 q^{96} + 36 q^{97}+O(q^{100}) \) 4 * q + 8 * q^6 + 8 * q^10 - 16 * q^11 + 8 * q^13 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 32 * q^21 - 20 * q^23 - 16 * q^25 + 32 * q^31 + 32 * q^35 + 4 * q^36 - 12 * q^38 + 4 * q^40 - 48 * q^41 - 12 * q^43 - 20 * q^47 - 8 * q^52 - 16 * q^56 - 24 * q^57 - 12 * q^58 + 16 * q^60 - 32 * q^66 - 8 * q^67 + 20 * q^68 + 16 * q^78 + 44 * q^81 + 24 * q^83 - 20 * q^86 - 24 * q^87 - 4 * q^90 + 20 * q^92 - 12 * q^95 - 8 * q^96 + 36 * q^97

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