LMFDB - Embedded newform 798.2.j.h.457.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(457,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("798.457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.j (of order $3$, 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	798.457
Dual form			798.2.j.h.571.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20711 - 3.82282i) q^{5} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20711 - 3.82282i) q^{5} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.20711 + 3.82282i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -2.82843 q^{13} +(1.00000 + 2.44949i) q^{14} +4.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.12132 - 3.67423i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -4.41421 q^{20} +(2.62132 + 0.358719i) q^{21} -1.00000 q^{22} +(-0.292893 + 0.507306i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-7.24264 - 12.5446i) q^{25} +(1.41421 - 2.44949i) q^{26} -1.00000 q^{27} +(-2.62132 - 0.358719i) q^{28} +7.82843 q^{29} +(-2.20711 + 3.82282i) q^{30} +(-0.328427 - 0.568852i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +4.24264 q^{34} +(-4.41421 - 10.8126i) q^{35} +1.00000 q^{36} +(4.12132 - 7.13834i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(-1.41421 - 2.44949i) q^{39} +(2.20711 - 3.82282i) q^{40} -3.41421 q^{41} +(-1.62132 + 2.09077i) q^{42} -2.24264 q^{43} +(0.500000 - 0.866025i) q^{44} +(2.20711 + 3.82282i) q^{45} +(-0.292893 - 0.507306i) q^{46} +(-4.41421 + 7.64564i) q^{47} -1.00000 q^{48} +(-1.74264 - 6.77962i) q^{49} +14.4853 q^{50} +(2.12132 - 3.67423i) q^{51} +(1.41421 + 2.44949i) q^{52} +(1.91421 + 3.31552i) q^{53} +(0.500000 - 0.866025i) q^{54} +4.41421 q^{55} +(1.62132 - 2.09077i) q^{56} -1.00000 q^{57} +(-3.91421 + 6.77962i) q^{58} +(4.03553 + 6.98975i) q^{59} +(-2.20711 - 3.82282i) q^{60} +(-0.414214 + 0.717439i) q^{61} +0.656854 q^{62} +(1.00000 + 2.44949i) q^{63} +1.00000 q^{64} +(-6.24264 + 10.8126i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(1.00000 + 1.73205i) q^{67} +(-2.12132 + 3.67423i) q^{68} -0.585786 q^{69} +(11.5711 + 1.58346i) q^{70} +11.8995 q^{71} +(-0.500000 + 0.866025i) q^{72} +(4.58579 + 7.94282i) q^{73} +(4.12132 + 7.13834i) q^{74} +(7.24264 - 12.5446i) q^{75} +1.00000 q^{76} +(2.62132 + 0.358719i) q^{77} +2.82843 q^{78} +(2.91421 - 5.04757i) q^{79} +(2.20711 + 3.82282i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.70711 - 2.95680i) q^{82} +11.1421 q^{83} +(-1.00000 - 2.44949i) q^{84} -18.7279 q^{85} +(1.12132 - 1.94218i) q^{86} +(3.91421 + 6.77962i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-6.12132 + 10.6024i) q^{89} -4.41421 q^{90} +(-4.58579 + 5.91359i) q^{91} +0.585786 q^{92} +(0.328427 - 0.568852i) q^{93} +(-4.41421 - 7.64564i) q^{94} +(2.20711 + 3.82282i) q^{95} +(0.500000 - 0.866025i) q^{96} -8.41421 q^{97} +(6.74264 + 1.88064i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 6 q^{10} + 2 q^{11} + 2 q^{12} + 4 q^{14} + 12 q^{15} - 2 q^{16} - 2 q^{18} - 2 q^{19} - 12 q^{20} + 2 q^{21} - 4 q^{22} - 4 q^{23} + 2 q^{24} - 12 q^{25} - 4 q^{27} - 2 q^{28} + 20 q^{29} - 6 q^{30} + 10 q^{31} - 2 q^{32} - 2 q^{33} - 12 q^{35} + 4 q^{36} + 8 q^{37} - 2 q^{38} + 6 q^{40} - 8 q^{41} + 2 q^{42} + 8 q^{43} + 2 q^{44} + 6 q^{45} - 4 q^{46} - 12 q^{47} - 4 q^{48} + 10 q^{49} + 24 q^{50} + 2 q^{53} + 2 q^{54} + 12 q^{55} - 2 q^{56} - 4 q^{57} - 10 q^{58} + 2 q^{59} - 6 q^{60} + 4 q^{61} - 20 q^{62} + 4 q^{63} + 4 q^{64} - 8 q^{65} - 2 q^{66} + 4 q^{67} - 8 q^{69} + 18 q^{70} + 8 q^{71} - 2 q^{72} + 24 q^{73} + 8 q^{74} + 12 q^{75} + 4 q^{76} + 2 q^{77} + 6 q^{79} + 6 q^{80} - 2 q^{81} + 4 q^{82} - 12 q^{83} - 4 q^{84} - 24 q^{85} - 4 q^{86} + 10 q^{87} + 2 q^{88} - 16 q^{89} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 10 q^{93} - 12 q^{94} + 6 q^{95} + 2 q^{96} - 28 q^{97} + 10 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 6 * q^10 + 2 * q^11 + 2 * q^12 + 4 * q^14 + 12 * q^15 - 2 * q^16 - 2 * q^18 - 2 * q^19 - 12 * q^20 + 2 * q^21 - 4 * q^22 - 4 * q^23 + 2 * q^24 - 12 * q^25 - 4 * q^27 - 2 * q^28 + 20 * q^29 - 6 * q^30 + 10 * q^31 - 2 * q^32 - 2 * q^33 - 12 * q^35 + 4 * q^36 + 8 * q^37 - 2 * q^38 + 6 * q^40 - 8 * q^41 + 2 * q^42 + 8 * q^43 + 2 * q^44 + 6 * q^45 - 4 * q^46 - 12 * q^47 - 4 * q^48 + 10 * q^49 + 24 * q^50 + 2 * q^53 + 2 * q^54 + 12 * q^55 - 2 * q^56 - 4 * q^57 - 10 * q^58 + 2 * q^59 - 6 * q^60 + 4 * q^61 - 20 * q^62 + 4 * q^63 + 4 * q^64 - 8 * q^65 - 2 * q^66 + 4 * q^67 - 8 * q^69 + 18 * q^70 + 8 * q^71 - 2 * q^72 + 24 * q^73 + 8 * q^74 + 12 * q^75 + 4 * q^76 + 2 * q^77 + 6 * q^79 + 6 * q^80 - 2 * q^81 + 4 * q^82 - 12 * q^83 - 4 * q^84 - 24 * q^85 - 4 * q^86 + 10 * q^87 + 2 * q^88 - 16 * q^89 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 10 * q^93 - 12 * q^94 + 6 * q^95 + 2 * q^96 - 28 * q^97 + 10 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.20711	−	3.82282i	0.987048	−	1.70962i	0.354593	−	0.935021i	$-0.384620\pi$
$5$	2.20711	−	3.82282i	0.987048	−	1.70962i	0.632456	−	0.774597i	$-0.282047\pi$
$6$	−1.00000			−0.408248
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.20711	+	3.82282i	0.697948	+	1.20888i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−2.82843			−0.784465			−0.392232	−	0.919866i	$-0.628297\pi$
$13$	−2.82843			−0.784465			−0.392232	+	0.919866i	$0.628297\pi$
$14$	1.00000	+	2.44949i	0.267261	+	0.654654i
$15$	4.41421			1.13975
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.12132	−	3.67423i	−0.514496	−	0.891133i	−0.999859	−	0.0168199i	$-0.994646\pi$
$17$	−2.12132	−	3.67423i	−0.514496	−	0.891133i	0.485363	−	0.874313i	$-0.338688\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	−4.41421			−0.987048
$21$	2.62132	+	0.358719i	0.572019	+	0.0782790i
$22$	−1.00000			−0.213201
$23$	−0.292893	+	0.507306i	−0.0610725	+	0.105781i	−0.894945	−	0.446176i	$-0.852785\pi$
$23$	−0.292893	+	0.507306i	−0.0610725	+	0.105781i	0.833873	+	0.551957i	$0.186119\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−7.24264	−	12.5446i	−1.44853	−	2.50892i
$26$	1.41421	−	2.44949i	0.277350	−	0.480384i
$27$	−1.00000			−0.192450
$28$	−2.62132	−	0.358719i	−0.495383	−	0.0677916i
$29$	7.82843			1.45370			0.726851	−	0.686795i	$-0.240983\pi$
$29$	7.82843			1.45370			0.726851	+	0.686795i	$0.240983\pi$
$30$	−2.20711	+	3.82282i	−0.402961	+	0.697948i
$31$	−0.328427	−	0.568852i	−0.0589873	−	0.102169i	0.835024	−	0.550214i	$-0.185454\pi$
$31$	−0.328427	−	0.568852i	−0.0589873	−	0.102169i	−0.894011	+	0.448045i	$0.852120\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	4.24264			0.727607
$35$	−4.41421	−	10.8126i	−0.746138	−	1.82766i
$36$	1.00000			0.166667
$37$	4.12132	−	7.13834i	0.677541	−	1.17354i	−0.298178	−	0.954510i	$-0.596379\pi$
$37$	4.12132	−	7.13834i	0.677541	−	1.17354i	0.975719	−	0.219025i	$-0.0702877\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$	−1.41421	−	2.44949i	−0.226455	−	0.392232i
$40$	2.20711	−	3.82282i	0.348974	−	0.604441i
$41$	−3.41421			−0.533211			−0.266605	−	0.963806i	$-0.585902\pi$
$41$	−3.41421			−0.533211			−0.266605	+	0.963806i	$0.585902\pi$
$42$	−1.62132	+	2.09077i	−0.250175	+	0.322613i
$43$	−2.24264			−0.341999			−0.171000	−	0.985271i	$-0.554700\pi$
$43$	−2.24264			−0.341999			−0.171000	+	0.985271i	$0.554700\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	2.20711	+	3.82282i	0.329016	+	0.569873i
$46$	−0.292893	−	0.507306i	−0.0431847	−	0.0747982i
$47$	−4.41421	+	7.64564i	−0.643879	+	1.11523i	0.340680	+	0.940179i	$0.389343\pi$
$47$	−4.41421	+	7.64564i	−0.643879	+	1.11523i	−0.984559	+	0.175052i	$0.943991\pi$
$48$	−1.00000			−0.144338
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	14.4853			2.04853
$51$	2.12132	−	3.67423i	0.297044	−	0.514496i
$52$	1.41421	+	2.44949i	0.196116	+	0.339683i
$53$	1.91421	+	3.31552i	0.262937	+	0.455421i	0.967021	−	0.254696i	$-0.0819754\pi$
$53$	1.91421	+	3.31552i	0.262937	+	0.455421i	−0.704084	+	0.710117i	$0.748642\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	4.41421			0.595212
$56$	1.62132	−	2.09077i	0.216658	−	0.279391i
$57$	−1.00000			−0.132453
$58$	−3.91421	+	6.77962i	−0.513961	+	0.890207i
$59$	4.03553	+	6.98975i	0.525382	+	0.909988i	0.999563	+	0.0295606i	$0.00941082\pi$
$59$	4.03553	+	6.98975i	0.525382	+	0.909988i	−0.474181	+	0.880427i	$0.657256\pi$
$60$	−2.20711	−	3.82282i	−0.284936	−	0.493524i
$61$	−0.414214	+	0.717439i	−0.0530346	+	0.0918586i	−0.891324	−	0.453367i	$-0.850223\pi$
$61$	−0.414214	+	0.717439i	−0.0530346	+	0.0918586i	0.838289	+	0.545226i	$0.183556\pi$
$62$	0.656854			0.0834206
$63$	1.00000	+	2.44949i	0.125988	+	0.308607i
$64$	1.00000			0.125000
$65$	−6.24264	+	10.8126i	−0.774304	+	1.34113i
$66$	−0.500000	−	0.866025i	−0.0615457	−	0.106600i
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	−2.12132	+	3.67423i	−0.257248	+	0.445566i
$69$	−0.585786			−0.0705204
$70$	11.5711	+	1.58346i	1.38301	+	0.189260i
$71$	11.8995			1.41221			0.706105	−	0.708107i	$-0.250451\pi$
$71$	11.8995			1.41221			0.706105	+	0.708107i	$0.250451\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	4.58579	+	7.94282i	0.536726	+	0.929636i	0.999078	+	0.0429397i	$0.0136723\pi$
$73$	4.58579	+	7.94282i	0.536726	+	0.929636i	−0.462352	+	0.886696i	$0.652994\pi$
$74$	4.12132	+	7.13834i	0.479094	+	0.829815i
$75$	7.24264	−	12.5446i	0.836308	−	1.44853i
$76$	1.00000			0.114708
$77$	2.62132	+	0.358719i	0.298727	+	0.0408799i
$78$	2.82843			0.320256
$79$	2.91421	−	5.04757i	0.327875	−	0.567896i	−0.654215	−	0.756308i	$-0.727001\pi$
$79$	2.91421	−	5.04757i	0.327875	−	0.567896i	0.982090	+	0.188413i	$0.0603343\pi$
$80$	2.20711	+	3.82282i	0.246762	+	0.427404i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.70711	−	2.95680i	0.188518	−	0.326523i
$83$	11.1421			1.22301			0.611504	−	0.791241i	$-0.290565\pi$
$83$	11.1421			1.22301			0.611504	+	0.791241i	$0.290565\pi$
$84$	−1.00000	−	2.44949i	−0.109109	−	0.267261i
$85$	−18.7279			−2.03133
$86$	1.12132	−	1.94218i	0.120915	−	0.209431i
$87$	3.91421	+	6.77962i	0.419648	+	0.726851i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−6.12132	+	10.6024i	−0.648859	+	1.12386i	0.334537	+	0.942383i	$0.391420\pi$
$89$	−6.12132	+	10.6024i	−0.648859	+	1.12386i	−0.983396	+	0.181474i	$0.941913\pi$
$90$	−4.41421			−0.465299
$91$	−4.58579	+	5.91359i	−0.480721	+	0.619913i
$92$	0.585786			0.0610725
$93$	0.328427	−	0.568852i	0.0340563	−	0.0589873i
$94$	−4.41421	−	7.64564i	−0.455291	−	0.788588i
$95$	2.20711	+	3.82282i	0.226444	+	0.392213i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−8.41421			−0.854334			−0.427167	−	0.904173i	$-0.640488\pi$
$97$	−8.41421			−0.854334			−0.427167	+	0.904173i	$0.640488\pi$
$98$	6.74264	+	1.88064i	0.681110	+	0.189973i
$99$	−1.00000			−0.100504
$100$	−7.24264	+	12.5446i	−0.724264	+	1.25446i
$101$	9.48528	+	16.4290i	0.943821	+	1.63475i	0.758095	+	0.652144i	$0.226130\pi$
$101$	9.48528	+	16.4290i	0.943821	+	1.63475i	0.185726	+	0.982602i	$0.440536\pi$
$102$	2.12132	+	3.67423i	0.210042	+	0.363803i
$103$	0.757359	−	1.31178i	0.0746248	−	0.129254i	−0.826298	−	0.563233i	$-0.809557\pi$
$103$	0.757359	−	1.31178i	0.0746248	−	0.129254i	0.900923	+	0.433979i	$0.142891\pi$
$104$	−2.82843			−0.277350
$105$	7.15685	−	9.22911i	0.698437	−	0.900669i
$106$	−3.82843			−0.371850
$107$	6.86396	−	11.8887i	0.663564	−	1.14933i	−0.316108	−	0.948723i	$-0.602376\pi$
$107$	6.86396	−	11.8887i	0.663564	−	1.14933i	0.979672	−	0.200604i	$-0.0642904\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−5.12132	−	8.87039i	−0.490534	−	0.849629i	0.509407	−	0.860526i	$-0.329865\pi$
$109$	−5.12132	−	8.87039i	−0.490534	−	0.849629i	−0.999941	+	0.0108967i	$0.996531\pi$
$110$	−2.20711	+	3.82282i	−0.210439	+	0.364492i
$111$	8.24264			0.782357
$112$	1.00000	+	2.44949i	0.0944911	+	0.231455i
$113$	1.75736			0.165318			0.0826592	−	0.996578i	$-0.473659\pi$
$113$	1.75736			0.165318			0.0826592	+	0.996578i	$0.473659\pi$
$114$	0.500000	−	0.866025i	0.0468293	−	0.0811107i
$115$	1.29289	+	2.23936i	0.120563	+	0.208821i
$116$	−3.91421	−	6.77962i	−0.363426	−	0.629472i
$117$	1.41421	−	2.44949i	0.130744	−	0.226455i
$118$	−8.07107			−0.743002
$119$	−11.1213	−	1.52192i	−1.01949	−	0.139514i
$120$	4.41421			0.402961
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−0.414214	−	0.717439i	−0.0375011	−	0.0649539i
$123$	−1.70711	−	2.95680i	−0.153925	−	0.266605i
$124$	−0.328427	+	0.568852i	−0.0294936	+	0.0510845i
$125$	−41.8701			−3.74497
$126$	−2.62132	−	0.358719i	−0.233526	−	0.0319573i
$127$	−0.171573			−0.0152246			−0.00761232	−	0.999971i	$-0.502423\pi$
$127$	−0.171573			−0.0152246			−0.00761232	+	0.999971i	$0.502423\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.12132	−	1.94218i	−0.0987268	−	0.171000i
$130$	−6.24264	−	10.8126i	−0.547516	−	0.948325i
$131$	9.15685	−	15.8601i	0.800038	−	1.38571i	−0.119552	−	0.992828i	$-0.538146\pi$
$131$	9.15685	−	15.8601i	0.800038	−	1.38571i	0.919590	−	0.392879i	$-0.128521\pi$
$132$	1.00000			0.0870388
$133$	1.00000	+	2.44949i	0.0867110	+	0.212398i
$134$	−2.00000			−0.172774
$135$	−2.20711	+	3.82282i	−0.189958	+	0.329016i
$136$	−2.12132	−	3.67423i	−0.181902	−	0.315063i
$137$	5.82843	+	10.0951i	0.497956	+	0.862485i	0.999997	−	0.00235845i	$-0.000750718\pi$
$137$	5.82843	+	10.0951i	0.497956	+	0.862485i	−0.502041	+	0.864844i	$0.667417\pi$
$138$	0.292893	−	0.507306i	0.0249327	−	0.0431847i
$139$	−11.8995			−1.00930			−0.504651	−	0.863323i	$-0.668379\pi$
$139$	−11.8995			−1.00930			−0.504651	+	0.863323i	$0.668379\pi$
$140$	−7.15685	+	9.22911i	−0.604865	+	0.780002i
$141$	−8.82843			−0.743488
$142$	−5.94975	+	10.3053i	−0.499292	+	0.864799i
$143$	−1.41421	−	2.44949i	−0.118262	−	0.204837i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	17.2782	−	29.9267i	1.43487	−	2.48528i
$146$	−9.17157			−0.759045
$147$	5.00000	−	4.89898i	0.412393	−	0.404061i
$148$	−8.24264			−0.677541
$149$	0.757359	−	1.31178i	0.0620453	−	0.107466i	−0.833334	−	0.552769i	$-0.813571\pi$
$149$	0.757359	−	1.31178i	0.0620453	−	0.107466i	0.895380	+	0.445304i	$0.146904\pi$
$150$	7.24264	+	12.5446i	0.591359	+	1.02426i
$151$	11.3284	+	19.6214i	0.921894	+	1.59677i	0.796481	+	0.604663i	$0.206692\pi$
$151$	11.3284	+	19.6214i	0.921894	+	1.59677i	0.125413	+	0.992105i	$0.459974\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	4.24264			0.342997
$154$	−1.62132	+	2.09077i	−0.130650	+	0.168479i
$155$	−2.89949			−0.232893
$156$	−1.41421	+	2.44949i	−0.113228	+	0.196116i
$157$	−6.24264	−	10.8126i	−0.498217	−	0.862937i	0.501781	−	0.864995i	$-0.332678\pi$
$157$	−6.24264	−	10.8126i	−0.498217	−	0.862937i	−0.999998	+	0.00205765i	$0.999345\pi$
$158$	2.91421	+	5.04757i	0.231842	+	0.401563i
$159$	−1.91421	+	3.31552i	−0.151807	+	0.262937i
$160$	−4.41421			−0.348974
$161$	0.585786	+	1.43488i	0.0461664	+	0.113084i
$162$	1.00000			0.0785674
$163$	2.58579	−	4.47871i	0.202534	−	0.350800i	−0.746810	−	0.665038i	$-0.768416\pi$
$163$	2.58579	−	4.47871i	0.202534	−	0.350800i	0.949344	+	0.314238i	$0.101749\pi$
$164$	1.70711	+	2.95680i	0.133303	+	0.230887i
$165$	2.20711	+	3.82282i	0.171823	+	0.297606i
$166$	−5.57107	+	9.64937i	−0.432399	+	0.748937i
$167$	18.7279			1.44921			0.724605	−	0.689164i	$-0.242022\pi$
$167$	18.7279			1.44921			0.724605	+	0.689164i	$0.242022\pi$
$168$	2.62132	+	0.358719i	0.202239	+	0.0276758i
$169$	−5.00000			−0.384615
$170$	9.36396	−	16.2189i	0.718183	−	1.24393i
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	1.12132	+	1.94218i	0.0854999	+	0.148090i
$173$	−11.8995	+	20.6105i	−0.904702	+	1.56699i	−0.0833849	+	0.996517i	$0.526573\pi$
$173$	−11.8995	+	20.6105i	−0.904702	+	1.56699i	−0.821317	+	0.570472i	$0.806760\pi$
$174$	−7.82843			−0.593472
$175$	−37.9706	−	5.19615i	−2.87030	−	0.392792i
$176$	−1.00000			−0.0753778
$177$	−4.03553	+	6.98975i	−0.303329	+	0.525382i
$178$	−6.12132	−	10.6024i	−0.458812	−	0.794686i
$179$	12.2426	+	21.2049i	0.915058	+	1.58493i	0.806816	+	0.590802i	$0.201189\pi$
$179$	12.2426	+	21.2049i	0.915058	+	1.58493i	0.108241	+	0.994125i	$0.465478\pi$
$180$	2.20711	−	3.82282i	0.164508	−	0.284936i
$181$	−3.51472			−0.261247			−0.130623	−	0.991432i	$-0.541698\pi$
$181$	−3.51472			−0.261247			−0.130623	+	0.991432i	$0.541698\pi$
$182$	−2.82843	−	6.92820i	−0.209657	−	0.513553i
$183$	−0.828427			−0.0612391
$184$	−0.292893	+	0.507306i	−0.0215924	+	0.0373991i
$185$	−18.1924	−	31.5101i	−1.33753	−	2.31667i
$186$	0.328427	+	0.568852i	0.0240814	+	0.0417103i
$187$	2.12132	−	3.67423i	0.155126	−	0.268687i
$188$	8.82843			0.643879
$189$	−1.62132	+	2.09077i	−0.117934	+	0.152081i
$190$	−4.41421			−0.320241
$191$	−5.07107	+	8.78335i	−0.366930	+	0.635541i	−0.989084	−	0.147354i	$-0.952924\pi$
$191$	−5.07107	+	8.78335i	−0.366930	+	0.635541i	0.622154	+	0.782895i	$0.286258\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−0.863961	−	1.49642i	−0.0621893	−	0.107715i	0.833254	−	0.552890i	$-0.186475\pi$
$193$	−0.863961	−	1.49642i	−0.0621893	−	0.107715i	−0.895444	+	0.445175i	$0.853142\pi$
$194$	4.20711	−	7.28692i	0.302053	−	0.523171i
$195$	−12.4853			−0.894090
$196$	−5.00000	+	4.89898i	−0.357143	+	0.349927i
$197$	6.82843			0.486505			0.243253	−	0.969963i	$-0.421786\pi$
$197$	6.82843			0.486505			0.243253	+	0.969963i	$0.421786\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	4.24264	+	7.34847i	0.300753	+	0.520919i	0.976307	−	0.216391i	$-0.0694287\pi$
$199$	4.24264	+	7.34847i	0.300753	+	0.520919i	−0.675554	+	0.737311i	$0.736095\pi$
$200$	−7.24264	−	12.5446i	−0.512132	−	0.887039i
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$	−18.9706			−1.33476
$203$	12.6924	−	16.3674i	0.890831	−	1.14877i
$204$	−4.24264			−0.297044
$205$	−7.53553	+	13.0519i	−0.526305	+	0.911586i
$206$	0.757359	+	1.31178i	0.0527677	+	0.0913964i
$207$	−0.292893	−	0.507306i	−0.0203575	−	0.0352602i
$208$	1.41421	−	2.44949i	0.0980581	−	0.169842i
$209$	−1.00000			−0.0691714
$210$	4.41421	+	10.8126i	0.304610	+	0.746138i
$211$	−0.928932			−0.0639503			−0.0319752	−	0.999489i	$-0.510180\pi$
$211$	−0.928932			−0.0639503			−0.0319752	+	0.999489i	$0.510180\pi$
$212$	1.91421	−	3.31552i	0.131469	−	0.227711i
$213$	5.94975	+	10.3053i	0.407670	+	0.706105i
$214$	6.86396	+	11.8887i	0.469211	+	0.812697i
$215$	−4.94975	+	8.57321i	−0.337570	+	0.584688i
$216$	−1.00000			−0.0680414
$217$	−1.72183	−	0.235626i	−0.116885	−	0.0159954i
$218$	10.2426			0.693719
$219$	−4.58579	+	7.94282i	−0.309879	+	0.536726i
$220$	−2.20711	−	3.82282i	−0.148803	−	0.257735i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$	−4.12132	+	7.13834i	−0.276605	+	0.479094i
$223$	6.51472			0.436258			0.218129	−	0.975920i	$-0.430005\pi$
$223$	6.51472			0.436258			0.218129	+	0.975920i	$0.430005\pi$
$224$	−2.62132	−	0.358719i	−0.175144	−	0.0239680i
$225$	14.4853			0.965685
$226$	−0.878680	+	1.52192i	−0.0584489	+	0.101236i
$227$	−10.4497	−	18.0995i	−0.693574	−	1.20131i	−0.970659	−	0.240460i	$-0.922702\pi$
$227$	−10.4497	−	18.0995i	−0.693574	−	1.20131i	0.277085	−	0.960845i	$-0.410632\pi$
$228$	0.500000	+	0.866025i	0.0331133	+	0.0573539i
$229$	−9.89949	+	17.1464i	−0.654177	+	1.13307i	0.327922	+	0.944705i	$0.393652\pi$
$229$	−9.89949	+	17.1464i	−0.654177	+	1.13307i	−0.982099	+	0.188363i	$0.939682\pi$
$230$	−2.58579			−0.170502
$231$	1.00000	+	2.44949i	0.0657952	+	0.161165i
$232$	7.82843			0.513961
$233$	5.41421	−	9.37769i	0.354697	−	0.614353i	−0.632369	−	0.774667i	$-0.717917\pi$
$233$	5.41421	−	9.37769i	0.354697	−	0.614353i	0.987066	+	0.160314i	$0.0512507\pi$
$234$	1.41421	+	2.44949i	0.0924500	+	0.160128i
$235$	19.4853	+	33.7495i	1.27108	+	2.20157i
$236$	4.03553	−	6.98975i	0.262691	−	0.454994i
$237$	5.82843			0.378597
$238$	6.87868	−	8.87039i	0.445879	−	0.574982i
$239$	−28.2843			−1.82956			−0.914779	−	0.403955i	$-0.867635\pi$
$239$	−28.2843			−1.82956			−0.914779	+	0.403955i	$0.867635\pi$
$240$	−2.20711	+	3.82282i	−0.142468	+	0.246762i
$241$	15.2782	+	26.4626i	0.984154	+	1.70460i	0.645638	+	0.763644i	$0.276591\pi$
$241$	15.2782	+	26.4626i	0.984154	+	1.70460i	0.338516	+	0.940961i	$0.390075\pi$
$242$	5.00000	+	8.66025i	0.321412	+	0.556702i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.828427			0.0530346
$245$	−29.7635	−	8.30153i	−1.90152	−	0.530366i
$246$	3.41421			0.217682
$247$	1.41421	−	2.44949i	0.0899843	−	0.155857i
$248$	−0.328427	−	0.568852i	−0.0208551	−	0.0361222i
$249$	5.57107	+	9.64937i	0.353052	+	0.611504i
$250$	20.9350	−	36.2605i	1.32405	−	2.29332i
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$	1.62132	−	2.09077i	0.102134	−	0.131706i
$253$	−0.585786			−0.0368281
$254$	0.0857864	−	0.148586i	0.00538272	−	0.00932314i
$255$	−9.36396	−	16.2189i	−0.586394	−	1.01566i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	2.24264			0.139621
$259$	−8.24264	−	20.1903i	−0.512173	−	1.25456i
$260$	12.4853			0.774304
$261$	−3.91421	+	6.77962i	−0.242284	+	0.419648i
$262$	9.15685	+	15.8601i	0.565712	+	0.979843i
$263$	−9.77817	−	16.9363i	−0.602948	−	1.04434i	−0.992372	−	0.123278i	$-0.960659\pi$
$263$	−9.77817	−	16.9363i	−0.602948	−	1.04434i	0.389424	−	0.921059i	$-0.372674\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$	16.8995			1.03813
$266$	−2.62132	−	0.358719i	−0.160723	−	0.0219945i
$267$	−12.2426			−0.749237
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	−0.500000	−	0.866025i	−0.0304855	−	0.0528025i	0.850380	−	0.526169i	$-0.176372\pi$
$269$	−0.500000	−	0.866025i	−0.0304855	−	0.0528025i	−0.880866	+	0.473366i	$0.843039\pi$
$270$	−2.20711	−	3.82282i	−0.134320	−	0.232649i
$271$	5.44975	−	9.43924i	0.331049	−	0.573393i	−0.651669	−	0.758503i	$-0.725931\pi$
$271$	5.44975	−	9.43924i	0.331049	−	0.573393i	0.982718	+	0.185110i	$0.0592643\pi$
$272$	4.24264			0.257248
$273$	−7.41421	−	1.01461i	−0.448729	−	0.0614071i
$274$	−11.6569			−0.704216
$275$	7.24264	−	12.5446i	0.436748	−	0.756469i
$276$	0.292893	+	0.507306i	0.0176301	+	0.0305362i
$277$	11.1213	+	19.2627i	0.668215	+	1.15738i	0.978403	+	0.206708i	$0.0662749\pi$
$277$	11.1213	+	19.2627i	0.668215	+	1.15738i	−0.310187	+	0.950675i	$0.600392\pi$
$278$	5.94975	−	10.3053i	0.356842	−	0.618069i
$279$	0.656854			0.0393248
$280$	−4.41421	−	10.8126i	−0.263800	−	0.646175i
$281$	21.3137			1.27147			0.635735	−	0.771908i	$-0.280697\pi$
$281$	21.3137			1.27147			0.635735	+	0.771908i	$0.280697\pi$
$282$	4.41421	−	7.64564i	0.262863	−	0.455291i
$283$	4.77817	+	8.27604i	0.284033	+	0.491960i	0.972374	−	0.233427i	$-0.0749941\pi$
$283$	4.77817	+	8.27604i	0.284033	+	0.491960i	−0.688341	+	0.725387i	$0.741661\pi$
$284$	−5.94975	−	10.3053i	−0.353053	−	0.611505i
$285$	−2.20711	+	3.82282i	−0.130738	+	0.226444i
$286$	2.82843			0.167248
$287$	−5.53553	+	7.13834i	−0.326752	+	0.421363i
$288$	1.00000			0.0589256
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	17.2782	+	29.9267i	1.01461	+	1.75735i
$291$	−4.20711	−	7.28692i	−0.246625	−	0.427167i
$292$	4.58579	−	7.94282i	0.268363	−	0.464818i
$293$	−23.0000			−1.34367			−0.671837	−	0.740699i	$-0.734495\pi$
$293$	−23.0000			−1.34367			−0.671837	+	0.740699i	$0.734495\pi$
$294$	1.74264	+	6.77962i	0.101633	+	0.395395i
$295$	35.6274			2.07431
$296$	4.12132	−	7.13834i	0.239547	−	0.414907i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	0.757359	+	1.31178i	0.0438726	+	0.0759897i
$299$	0.828427	−	1.43488i	0.0479092	−	0.0829811i
$300$	−14.4853			−0.836308
$301$	−3.63604	+	4.68885i	−0.209578	+	0.270261i
$302$	−22.6569			−1.30376
$303$	−9.48528	+	16.4290i	−0.544915	+	0.943821i
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	1.82843	+	3.16693i	0.104695	+	0.181338i
$306$	−2.12132	+	3.67423i	−0.121268	+	0.210042i
$307$	4.58579			0.261725			0.130862	−	0.991401i	$-0.458225\pi$
$307$	4.58579			0.261725			0.130862	+	0.991401i	$0.458225\pi$
$308$	−1.00000	−	2.44949i	−0.0569803	−	0.139573i
$309$	1.51472			0.0861693
$310$	1.44975	−	2.51104i	0.0823401	−	0.142617i
$311$	−6.87868	−	11.9142i	−0.390054	−	0.675594i	0.602402	−	0.798193i	$-0.294210\pi$
$311$	−6.87868	−	11.9142i	−0.390054	−	0.675594i	−0.992456	+	0.122599i	$0.960877\pi$
$312$	−1.41421	−	2.44949i	−0.0800641	−	0.138675i
$313$	−0.914214	+	1.58346i	−0.0516744	+	0.0895027i	−0.890706	−	0.454581i	$-0.849789\pi$
$313$	−0.914214	+	1.58346i	−0.0516744	+	0.0895027i	0.839031	+	0.544083i	$0.183122\pi$
$314$	12.4853			0.704585
$315$	11.5711	+	1.58346i	0.651956	+	0.0892181i
$316$	−5.82843			−0.327875
$317$	−3.74264	+	6.48244i	−0.210208	+	0.364090i	−0.951779	−	0.306783i	$-0.900747\pi$
$317$	−3.74264	+	6.48244i	−0.210208	+	0.364090i	0.741572	+	0.670874i	$0.234081\pi$
$318$	−1.91421	−	3.31552i	−0.107344	−	0.185925i
$319$	3.91421	+	6.77962i	0.219154	+	0.379586i
$320$	2.20711	−	3.82282i	0.123381	−	0.213702i
$321$	13.7279			0.766218
$322$	−1.53553	−	0.210133i	−0.0855720	−	0.0117103i
$323$	4.24264			0.236067
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	20.4853	+	35.4815i	1.13632	+	1.96816i
$326$	2.58579	+	4.47871i	0.143213	+	0.248053i
$327$	5.12132	−	8.87039i	0.283210	−	0.490534i
$328$	−3.41421			−0.188518
$329$	8.82843	+	21.6251i	0.486727	+	1.19223i
$330$	−4.41421			−0.242994
$331$	−16.1924	+	28.0460i	−0.890014	+	1.54155i	−0.0501576	+	0.998741i	$0.515972\pi$
$331$	−16.1924	+	28.0460i	−0.890014	+	1.54155i	−0.839857	+	0.542808i	$0.817361\pi$
$332$	−5.57107	−	9.64937i	−0.305752	−	0.529578i
$333$	4.12132	+	7.13834i	0.225847	+	0.391178i
$334$	−9.36396	+	16.2189i	−0.512373	+	0.887456i
$335$	8.82843			0.482349
$336$	−1.62132	+	2.09077i	−0.0884503	+	0.114061i
$337$	−12.0711			−0.657553			−0.328776	−	0.944408i	$-0.606636\pi$
$337$	−12.0711			−0.657553			−0.328776	+	0.944408i	$0.606636\pi$
$338$	2.50000	−	4.33013i	0.135982	−	0.235528i
$339$	0.878680	+	1.52192i	0.0477233	+	0.0826592i
$340$	9.36396	+	16.2189i	0.507832	+	0.879591i
$341$	0.328427	−	0.568852i	0.0177853	−	0.0308051i
$342$	1.00000			0.0540738
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	−2.24264			−0.120915
$345$	−1.29289	+	2.23936i	−0.0696070	+	0.120563i
$346$	−11.8995	−	20.6105i	−0.639721	−	1.10803i
$347$	17.0000	+	29.4449i	0.912608	+	1.58068i	0.810366	+	0.585923i	$0.199268\pi$
$347$	17.0000	+	29.4449i	0.912608	+	1.58068i	0.102241	+	0.994760i	$0.467399\pi$
$348$	3.91421	−	6.77962i	0.209824	−	0.363426i
$349$	−16.2426			−0.869449			−0.434724	−	0.900564i	$-0.643154\pi$
$349$	−16.2426			−0.869449			−0.434724	+	0.900564i	$0.643154\pi$
$350$	23.4853	−	30.2854i	1.25534	−	1.61882i
$351$	2.82843			0.150970
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−16.9497	−	29.3578i	−0.902144	−	1.56256i	−0.824706	−	0.565562i	$-0.808659\pi$
$353$	−16.9497	−	29.3578i	−0.902144	−	1.56256i	−0.0774384	−	0.996997i	$-0.524674\pi$
$354$	−4.03553	−	6.98975i	−0.214486	−	0.371501i
$355$	26.2635	−	45.4896i	1.39392	−	2.41434i
$356$	12.2426			0.648859
$357$	−4.24264	−	10.3923i	−0.224544	−	0.550019i
$358$	−24.4853			−1.29409
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	−0.967272	−	0.253741i	$-0.918339\pi$
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	0.703382	+	0.710812i	$0.251672\pi$
$360$	2.20711	+	3.82282i	0.116325	+	0.201480i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	1.75736	−	3.04384i	0.0923648	−	0.159980i
$363$	10.0000			0.524864
$364$	7.41421	+	1.01461i	0.388610	+	0.0531801i
$365$	40.4853			2.11910
$366$	0.414214	−	0.717439i	0.0216513	−	0.0375011i
$367$	1.62132	+	2.80821i	0.0846322	+	0.146587i	0.905234	−	0.424912i	$-0.139695\pi$
$367$	1.62132	+	2.80821i	0.0846322	+	0.146587i	−0.820602	+	0.571500i	$0.806362\pi$
$368$	−0.292893	−	0.507306i	−0.0152681	−	0.0264452i
$369$	1.70711	−	2.95680i	0.0888684	−	0.153925i
$370$	36.3848			1.89155
$371$	10.0355	+	1.37333i	0.521019	+	0.0712998i
$372$	−0.656854			−0.0340563
$373$	8.24264	−	14.2767i	0.426788	−	0.739218i	−0.569798	−	0.821785i	$-0.692978\pi$
$373$	8.24264	−	14.2767i	0.426788	−	0.739218i	0.996586	+	0.0825669i	$0.0263118\pi$
$374$	2.12132	+	3.67423i	0.109691	+	0.189990i
$375$	−20.9350	−	36.2605i	−1.08108	−	1.87249i
$376$	−4.41421	+	7.64564i	−0.227646	+	0.394294i
$377$	−22.1421			−1.14038
$378$	−1.00000	−	2.44949i	−0.0514344	−	0.125988i
$379$	−19.3137			−0.992079			−0.496039	−	0.868300i	$-0.665213\pi$
$379$	−19.3137			−0.992079			−0.496039	+	0.868300i	$0.665213\pi$
$380$	2.20711	−	3.82282i	0.113222	−	0.196107i
$381$	−0.0857864	−	0.148586i	−0.00439497	−	0.00761232i
$382$	−5.07107	−	8.78335i	−0.259458	−	0.449395i
$383$	−2.17157	+	3.76127i	−0.110962	+	0.192192i	−0.916158	−	0.400816i	$-0.868727\pi$
$383$	−2.17157	+	3.76127i	−0.110962	+	0.192192i	0.805196	+	0.593008i	$0.202060\pi$
$384$	−1.00000			−0.0510310
$385$	7.15685	−	9.22911i	0.364747	−	0.470359i
$386$	1.72792			0.0879489
$387$	1.12132	−	1.94218i	0.0569999	−	0.0987268i
$388$	4.20711	+	7.28692i	0.213583	+	0.369937i
$389$	−14.4142	−	24.9662i	−0.730830	−	1.26583i	−0.956529	−	0.291637i	$-0.905800\pi$
$389$	−14.4142	−	24.9662i	−0.730830	−	1.26583i	0.225699	−	0.974197i	$-0.427533\pi$
$390$	6.24264	−	10.8126i	0.316108	−	0.547516i
$391$	2.48528			0.125686
$392$	−1.74264	−	6.77962i	−0.0880166	−	0.342422i
$393$	18.3137			0.923804
$394$	−3.41421	+	5.91359i	−0.172006	+	0.297922i
$395$	−12.8640	−	22.2810i	−0.647256	−	1.12108i
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	2.58579	−	4.47871i	0.129777	−	0.224780i	−0.793813	−	0.608162i	$-0.791907\pi$
$397$	2.58579	−	4.47871i	0.129777	−	0.224780i	0.923590	+	0.383382i	$0.125241\pi$
$398$	−8.48528			−0.425329
$399$	−1.62132	+	2.09077i	−0.0811675	+	0.104669i
$400$	14.4853			0.724264
$401$	7.07107	−	12.2474i	0.353112	−	0.611608i	−0.633681	−	0.773595i	$-0.718457\pi$
$401$	7.07107	−	12.2474i	0.353112	−	0.611608i	0.986793	+	0.161986i	$0.0517900\pi$
$402$	−1.00000	−	1.73205i	−0.0498755	−	0.0863868i
$403$	0.928932	+	1.60896i	0.0462734	+	0.0801479i
$404$	9.48528	−	16.4290i	0.471910	−	0.817373i
$405$	−4.41421			−0.219344
$406$	7.82843	+	19.1757i	0.388518	+	0.951672i
$407$	8.24264			0.408573
$408$	2.12132	−	3.67423i	0.105021	−	0.181902i
$409$	−5.55025	−	9.61332i	−0.274442	−	0.475348i	0.695552	−	0.718476i	$-0.255160\pi$
$409$	−5.55025	−	9.61332i	−0.274442	−	0.475348i	−0.969994	+	0.243128i	$0.921827\pi$
$410$	−7.53553	−	13.0519i	−0.372153	−	0.644589i
$411$	−5.82843	+	10.0951i	−0.287495	+	0.497956i
$412$	−1.51472			−0.0746248
$413$	21.1569	+	2.89525i	1.04106	+	0.142466i
$414$	0.585786			0.0287898
$415$	24.5919	−	42.5944i	1.20717	−	2.09088i
$416$	1.41421	+	2.44949i	0.0693375	+	0.120096i
$417$	−5.94975	−	10.3053i	−0.291360	−	0.504651i
$418$	0.500000	−	0.866025i	0.0244558	−	0.0423587i
$419$	2.97056			0.145121			0.0725607	−	0.997364i	$-0.476883\pi$
$419$	2.97056			0.145121			0.0725607	+	0.997364i	$0.476883\pi$
$420$	−11.5711	−	1.58346i	−0.564610	−	0.0772651i
$421$	20.8284			1.01512			0.507558	−	0.861618i	$-0.330548\pi$
$421$	20.8284			1.01512			0.507558	+	0.861618i	$0.330548\pi$
$422$	0.464466	−	0.804479i	0.0226099	−	0.0391614i
$423$	−4.41421	−	7.64564i	−0.214626	−	0.371744i
$424$	1.91421	+	3.31552i	0.0929624	+	0.161016i
$425$	−30.7279	+	53.2223i	−1.49052	+	2.58166i
$426$	−11.8995			−0.576532
$427$	0.828427	+	2.02922i	0.0400904	+	0.0982010i
$428$	−13.7279			−0.663564
$429$	1.41421	−	2.44949i	0.0682789	−	0.118262i
$430$	−4.94975	−	8.57321i	−0.238698	−	0.413437i
$431$	16.9497	+	29.3578i	0.816441	+	1.41412i	0.908289	+	0.418344i	$0.137389\pi$
$431$	16.9497	+	29.3578i	0.816441	+	1.41412i	−0.0918482	+	0.995773i	$0.529277\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−25.1716			−1.20967			−0.604834	−	0.796351i	$-0.706761\pi$
$433$	−25.1716			−1.20967			−0.604834	+	0.796351i	$0.706761\pi$
$434$	1.06497	−	1.37333i	0.0511203	−	0.0659220i
$435$	34.5563			1.65685
$436$	−5.12132	+	8.87039i	−0.245267	+	0.424814i
$437$	−0.292893	−	0.507306i	−0.0140110	−	0.0242677i
$438$	−4.58579	−	7.94282i	−0.219117	−	0.379522i
$439$	14.2279	−	24.6435i	0.679062	−	1.17617i	−0.296202	−	0.955125i	$-0.595720\pi$
$439$	14.2279	−	24.6435i	0.679062	−	1.17617i	0.975264	−	0.221044i	$-0.0709465\pi$
$440$	4.41421			0.210439
$441$	6.74264	+	1.88064i	0.321078	+	0.0895542i
$442$	−12.0000			−0.570782
$443$	1.67157	−	2.89525i	0.0794188	−	0.137557i	−0.823581	−	0.567199i	$-0.808027\pi$
$443$	1.67157	−	2.89525i	0.0794188	−	0.137557i	0.902999	+	0.429642i	$0.141360\pi$
$444$	−4.12132	−	7.13834i	−0.195589	−	0.338770i
$445$	27.0208	+	46.8014i	1.28091	+	2.21860i
$446$	−3.25736	+	5.64191i	−0.154240	+	0.267152i
$447$	1.51472			0.0716437
$448$	1.62132	−	2.09077i	0.0766002	−	0.0987796i
$449$	5.75736			0.271707			0.135853	−	0.990729i	$-0.456622\pi$
$449$	5.75736			0.271707			0.135853	+	0.990729i	$0.456622\pi$
$450$	−7.24264	+	12.5446i	−0.341421	+	0.591359i
$451$	−1.70711	−	2.95680i	−0.0803845	−	0.139230i
$452$	−0.878680	−	1.52192i	−0.0413296	−	0.0715850i
$453$	−11.3284	+	19.6214i	−0.532256	+	0.921894i
$454$	20.8995			0.980862
$455$	12.4853	+	30.5826i	0.585319	+	1.43373i
$456$	−1.00000			−0.0468293
$457$	13.0563	−	22.6143i	0.610750	−	1.05785i	−0.380364	−	0.924837i	$-0.624201\pi$
$457$	13.0563	−	22.6143i	0.610750	−	1.05785i	0.991114	−	0.133014i	$-0.0424654\pi$
$458$	−9.89949	−	17.1464i	−0.462573	−	0.801200i
$459$	2.12132	+	3.67423i	0.0990148	+	0.171499i
$460$	1.29289	−	2.23936i	0.0602815	−	0.104411i
$461$	5.31371			0.247484			0.123742	−	0.992314i	$-0.460510\pi$
$461$	5.31371			0.247484			0.123742	+	0.992314i	$0.460510\pi$
$462$	−2.62132	−	0.358719i	−0.121955	−	0.0166891i
$463$	−9.65685			−0.448792			−0.224396	−	0.974498i	$-0.572041\pi$
$463$	−9.65685			−0.448792			−0.224396	+	0.974498i	$0.572041\pi$
$464$	−3.91421	+	6.77962i	−0.181713	+	0.314736i
$465$	−1.44975	−	2.51104i	−0.0672304	−	0.116447i
$466$	5.41421	+	9.37769i	0.250809	+	0.434413i
$467$	10.4142	−	18.0379i	0.481912	−	0.834697i	−0.517872	−	0.855458i	$-0.673276\pi$
$467$	10.4142	−	18.0379i	0.481912	−	0.834697i	0.999784	+	0.0207614i	$0.00660903\pi$
$468$	−2.82843			−0.130744
$469$	5.24264	+	0.717439i	0.242083	+	0.0331283i
$470$	−38.9706			−1.79758
$471$	6.24264	−	10.8126i	0.287646	−	0.498217i
$472$	4.03553	+	6.98975i	0.185751	+	0.321729i
$473$	−1.12132	−	1.94218i	−0.0515584	−	0.0893017i
$474$	−2.91421	+	5.04757i	−0.133854	+	0.231842i
$475$	14.4853			0.664630
$476$	4.24264	+	10.3923i	0.194461	+	0.476331i
$477$	−3.82843			−0.175292
$478$	14.1421	−	24.4949i	0.646846	−	1.12037i
$479$	10.6569	+	18.4582i	0.486924	+	0.843377i	0.999887	−	0.0150335i	$-0.00478549\pi$
$479$	10.6569	+	18.4582i	0.486924	+	0.843377i	−0.512963	+	0.858411i	$0.671452\pi$
$480$	−2.20711	−	3.82282i	−0.100740	−	0.174487i
$481$	−11.6569	+	20.1903i	−0.531507	+	0.920597i
$482$	−30.5563			−1.39180
$483$	−0.949747	+	1.22474i	−0.0432150	+	0.0557278i
$484$	−10.0000			−0.454545
$485$	−18.5711	+	32.1660i	−0.843269	+	1.46058i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−0.399495	−	0.691946i	−0.0181028	−	0.0313550i	0.856832	−	0.515596i	$-0.172429\pi$
$487$	−0.399495	−	0.691946i	−0.0181028	−	0.0313550i	−0.874935	+	0.484241i	$0.839096\pi$
$488$	−0.414214	+	0.717439i	−0.0187506	+	0.0324769i
$489$	5.17157			0.233867
$490$	22.0711	−	21.6251i	0.997069	−	0.976924i
$491$	19.1421			0.863872			0.431936	−	0.901904i	$-0.357831\pi$
$491$	19.1421			0.863872			0.431936	+	0.901904i	$0.357831\pi$
$492$	−1.70711	+	2.95680i	−0.0769623	+	0.133303i
$493$	−16.6066	−	28.7635i	−0.747924	−	1.29544i
$494$	1.41421	+	2.44949i	0.0636285	+	0.110208i
$495$	−2.20711	+	3.82282i	−0.0992021	+	0.171823i
$496$	0.656854			0.0294936
$497$	19.2929	−	24.8791i	0.865405	−	1.11598i
$498$	−11.1421			−0.499291
$499$	6.65685	−	11.5300i	0.298002	−	0.516154i	−0.677677	−	0.735360i	$-0.737013\pi$
$499$	6.65685	−	11.5300i	0.298002	−	0.516154i	0.975679	+	0.219206i	$0.0703465\pi$
$500$	20.9350	+	36.2605i	0.936243	+	1.62162i
$501$	9.36396	+	16.2189i	0.418351	+	0.724605i
$502$	10.5000	−	18.1865i	0.468638	−	0.811705i
$503$	18.2426			0.813399			0.406700	−	0.913562i	$-0.366680\pi$
$503$	18.2426			0.813399			0.406700	+	0.913562i	$0.366680\pi$
$504$	1.00000	+	2.44949i	0.0445435	+	0.109109i
$505$	83.7401			3.72639
$506$	0.292893	−	0.507306i	0.0130207	−	0.0225525i
$507$	−2.50000	−	4.33013i	−0.111029	−	0.192308i
$508$	0.0857864	+	0.148586i	0.00380616	+	0.00659246i
$509$	−4.15685	+	7.19988i	−0.184249	+	0.319129i	−0.943323	−	0.331875i	$-0.892319\pi$
$509$	−4.15685	+	7.19988i	−0.184249	+	0.319129i	0.759074	+	0.651004i	$0.225652\pi$
$510$	18.7279			0.829286
$511$	24.0416	+	3.29002i	1.06354	+	0.145542i
$512$	1.00000			0.0441942
$513$	0.500000	−	0.866025i	0.0220755	−	0.0382360i
$514$	−3.00000	−	5.19615i	−0.132324	−	0.229192i
$515$	−3.34315	−	5.79050i	−0.147317	−	0.255160i
$516$	−1.12132	+	1.94218i	−0.0493634	+	0.0854999i
$517$	−8.82843			−0.388274
$518$	21.6066	+	2.95680i	0.949340	+	0.129914i
$519$	−23.7990			−1.04466
$520$	−6.24264	+	10.8126i	−0.273758	+	0.474163i
$521$	15.9706	+	27.6618i	0.699683	+	1.21189i	0.968576	+	0.248717i	$0.0800088\pi$
$521$	15.9706	+	27.6618i	0.699683	+	1.21189i	−0.268893	+	0.963170i	$0.586658\pi$
$522$	−3.91421	−	6.77962i	−0.171320	−	0.296736i
$523$	−11.9497	+	20.6976i	−0.522526	+	0.905042i	0.477131	+	0.878832i	$0.341677\pi$
$523$	−11.9497	+	20.6976i	−0.522526	+	0.905042i	−0.999656	+	0.0262091i	$0.991656\pi$
$524$	−18.3137			−0.800038
$525$	−14.4853	−	35.4815i	−0.632190	−	1.54854i
$526$	19.5563			0.852697
$527$	−1.39340	+	2.41344i	−0.0606974	+	0.105131i
$528$	−0.500000	−	0.866025i	−0.0217597	−	0.0376889i
$529$	11.3284	+	19.6214i	0.492540	+	0.853105i
$530$	−8.44975	+	14.6354i	−0.367034	+	0.635721i
$531$	−8.07107			−0.350255
$532$	1.62132	−	2.09077i	0.0702932	−	0.0906464i
$533$	9.65685			0.418285
$534$	6.12132	−	10.6024i	0.264895	−	0.458812i
$535$	−30.2990	−	52.4794i	−1.30994	−	2.26888i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	−12.2426	+	21.2049i	−0.528309	+	0.915058i
$538$	1.00000			0.0431131
$539$	5.00000	−	4.89898i	0.215365	−	0.211014i
$540$	4.41421			0.189958
$541$	−3.19239	+	5.52938i	−0.137251	+	0.237727i	−0.926455	−	0.376405i	$-0.877160\pi$
$541$	−3.19239	+	5.52938i	−0.137251	+	0.237727i	0.789204	+	0.614131i	$0.210494\pi$
$542$	5.44975	+	9.43924i	0.234087	+	0.405450i
$543$	−1.75736	−	3.04384i	−0.0754155	−	0.130623i
$544$	−2.12132	+	3.67423i	−0.0909509	+	0.157532i
$545$	−45.2132			−1.93672
$546$	4.58579	−	5.91359i	0.196254	−	0.253078i
$547$	−14.7279			−0.629720			−0.314860	−	0.949138i	$-0.601958\pi$
$547$	−14.7279			−0.629720			−0.314860	+	0.949138i	$0.601958\pi$
$548$	5.82843	−	10.0951i	0.248978	−	0.431243i
$549$	−0.414214	−	0.717439i	−0.0176782	−	0.0306195i
$550$	7.24264	+	12.5446i	0.308827	+	0.534904i
$551$	−3.91421	+	6.77962i	−0.166751	+	0.288821i
$552$	−0.585786			−0.0249327
$553$	−5.82843	−	14.2767i	−0.247850	−	0.607106i
$554$	−22.2426			−0.944999
$555$	18.1924	−	31.5101i	0.772224	−	1.33753i
$556$	5.94975	+	10.3053i	0.252325	+	0.437041i
$557$	−10.7929	−	18.6938i	−0.457310	−	0.792083i	0.541508	−	0.840695i	$-0.317854\pi$
$557$	−10.7929	−	18.6938i	−0.457310	−	0.792083i	−0.998818	+	0.0486121i	$0.984520\pi$
$558$	−0.328427	+	0.568852i	−0.0139034	+	0.0240814i
$559$	6.34315			0.268286
$560$	11.5711	+	1.58346i	0.488967	+	0.0669136i
$561$	4.24264			0.179124
$562$	−10.6569	+	18.4582i	−0.449532	+	0.778613i
$563$	7.55025	+	13.0774i	0.318205	+	0.551148i	0.980114	−	0.198437i	$-0.0635866\pi$
$563$	7.55025	+	13.0774i	0.318205	+	0.551148i	−0.661908	+	0.749585i	$0.730253\pi$
$564$	4.41421	+	7.64564i	0.185872	+	0.321940i
$565$	3.87868	−	6.71807i	0.163177	−	0.282631i
$566$	−9.55635			−0.401683
$567$	−2.62132	−	0.358719i	−0.110085	−	0.0150648i
$568$	11.8995			0.499292
$569$	−11.3137	+	19.5959i	−0.474295	+	0.821504i	−0.999567	−	0.0294311i	$-0.990630\pi$
$569$	−11.3137	+	19.5959i	−0.474295	+	0.821504i	0.525271	+	0.850935i	$0.323964\pi$
$570$	−2.20711	−	3.82282i	−0.0924455	−	0.160120i
$571$	15.2635	+	26.4371i	0.638756	+	1.10636i	0.985706	+	0.168474i	$0.0538839\pi$
$571$	15.2635	+	26.4371i	0.638756	+	1.10636i	−0.346950	+	0.937883i	$0.612783\pi$
$572$	−1.41421	+	2.44949i	−0.0591312	+	0.102418i
$573$	−10.1421			−0.423694
$574$	−3.41421	−	8.36308i	−0.142507	−	0.349068i
$575$	8.48528			0.353861
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	0.742641	+	1.28629i	0.0309165	+	0.0535490i	0.881070	−	0.472986i	$-0.156824\pi$
$577$	0.742641	+	1.28629i	0.0309165	+	0.0535490i	−0.850153	+	0.526535i	$0.823491\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$	0.863961	−	1.49642i	0.0359050	−	0.0621893i
$580$	−34.5563			−1.43487
$581$	18.0650	−	23.2956i	0.749461	−	0.966466i
$582$	8.41421			0.348780
$583$	−1.91421	+	3.31552i	−0.0792786	+	0.137315i
$584$	4.58579	+	7.94282i	0.189761	+	0.328676i
$585$	−6.24264	−	10.8126i	−0.258101	−	0.447045i
$586$	11.5000	−	19.9186i	0.475061	−	0.822829i
$587$	−21.6274			−0.892659			−0.446330	−	0.894869i	$-0.647269\pi$
$587$	−21.6274			−0.892659			−0.446330	+	0.894869i	$0.647269\pi$
$588$	−6.74264	−	1.88064i	−0.278062	−	0.0775562i
$589$	0.656854			0.0270652
$590$	−17.8137	+	30.8542i	−0.733379	+	1.27025i
$591$	3.41421	+	5.91359i	0.140442	+	0.243253i
$592$	4.12132	+	7.13834i	0.169385	+	0.293384i
$593$	22.3848	−	38.7716i	0.919233	−	1.59216i	0.118649	−	0.992936i	$-0.462144\pi$
$593$	22.3848	−	38.7716i	0.919233	−	1.59216i	0.800583	−	0.599221i	$-0.204523\pi$
$594$	1.00000			0.0410305
$595$	−30.3640	+	39.1558i	−1.24480	+	1.60523i
$596$	−1.51472			−0.0620453
$597$	−4.24264	+	7.34847i	−0.173640	+	0.300753i
$598$	0.828427	+	1.43488i	0.0338769	+	0.0586765i
$599$	−14.8787	−	25.7706i	−0.607926	−	1.05296i	−0.991582	−	0.129483i	$-0.958668\pi$
$599$	−14.8787	−	25.7706i	−0.607926	−	1.05296i	0.383655	−	0.923476i	$-0.374665\pi$
$600$	7.24264	−	12.5446i	0.295680	−	0.512132i
$601$	−32.4142			−1.32220			−0.661102	−	0.750296i	$-0.729911\pi$
$601$	−32.4142			−1.32220			−0.661102	+	0.750296i	$0.729911\pi$
$602$	−2.24264	−	5.49333i	−0.0914032	−	0.223891i
$603$	−2.00000			−0.0814463
$604$	11.3284	−	19.6214i	0.460947	−	0.798384i
$605$	−22.0711	−	38.2282i	−0.897317	−	1.55420i
$606$	−9.48528	−	16.4290i	−0.385313	−	0.667382i
$607$	−11.3995	+	19.7445i	−0.462691	+	0.801405i	−0.999094	−	0.0425574i	$-0.986449\pi$
$607$	−11.3995	+	19.7445i	−0.462691	+	0.801405i	0.536403	+	0.843962i	$0.319783\pi$
$608$	1.00000			0.0405554
$609$	20.5208	+	2.80821i	0.831545	+	0.113794i
$610$	−3.65685			−0.148062
$611$	12.4853	−	21.6251i	0.505100	−	0.874860i
$612$	−2.12132	−	3.67423i	−0.0857493	−	0.148522i
$613$	−22.6777	−	39.2789i	−0.915942	−	1.58646i	−0.805516	−	0.592575i	$-0.798112\pi$
$613$	−22.6777	−	39.2789i	−0.915942	−	1.58646i	−0.110427	−	0.993884i	$-0.535222\pi$
$614$	−2.29289	+	3.97141i	−0.0925336	+	0.160273i
$615$	−15.0711			−0.607724
$616$	2.62132	+	0.358719i	0.105616	+	0.0144532i
$617$	−34.5269			−1.39000			−0.695001	−	0.719009i	$-0.744596\pi$
$617$	−34.5269			−1.39000			−0.695001	+	0.719009i	$0.744596\pi$
$618$	−0.757359	+	1.31178i	−0.0304655	+	0.0527677i
$619$	−16.8995	−	29.2708i	−0.679248	−	1.17649i	−0.975208	−	0.221292i	$-0.928973\pi$
$619$	−16.8995	−	29.2708i	−0.679248	−	1.17649i	0.295960	−	0.955200i	$-0.404361\pi$
$620$	1.44975	+	2.51104i	0.0582233	+	0.100846i
$621$	0.292893	−	0.507306i	0.0117534	−	0.0203575i
$622$	13.7574			0.551620
$623$	12.2426	+	29.9882i	0.490491	+	1.20145i
$624$	2.82843			0.113228
$625$	−56.1985	+	97.3386i	−2.24794	+	3.89355i
$626$	−0.914214	−	1.58346i	−0.0365393	−	0.0632880i
$627$	−0.500000	−	0.866025i	−0.0199681	−	0.0345857i
$628$	−6.24264	+	10.8126i	−0.249108	+	0.431469i
$629$	−34.9706			−1.39437
$630$	−7.15685	+	9.22911i	−0.285136	+	0.367696i
$631$	24.5563			0.977573			0.488786	−	0.872403i	$-0.337440\pi$
$631$	24.5563			0.977573			0.488786	+	0.872403i	$0.337440\pi$
$632$	2.91421	−	5.04757i	0.115921	−	0.200781i
$633$	−0.464466	−	0.804479i	−0.0184609	−	0.0319752i
$634$	−3.74264	−	6.48244i	−0.148639	−	0.257451i
$635$	−0.378680	+	0.655892i	−0.0150274	+	0.0260283i
$636$	3.82843			0.151807
$637$	4.92893	+	19.1757i	0.195291	+	0.759767i
$638$	−7.82843			−0.309930
$639$	−5.94975	+	10.3053i	−0.235368	+	0.407670i
$640$	2.20711	+	3.82282i	0.0872436	+	0.151110i
$641$	10.7071	+	18.5453i	0.422905	+	0.732493i	0.996222	−	0.0868402i	$-0.0276770\pi$
$641$	10.7071	+	18.5453i	0.422905	+	0.732493i	−0.573317	+	0.819334i	$0.694344\pi$
$642$	−6.86396	+	11.8887i	−0.270899	+	0.469211i
$643$	33.7574			1.33126			0.665630	−	0.746282i	$-0.268163\pi$
$643$	33.7574			1.33126			0.665630	+	0.746282i	$0.268163\pi$
$644$	0.949747	−	1.22474i	0.0374253	−	0.0482617i
$645$	−9.89949			−0.389792
$646$	−2.12132	+	3.67423i	−0.0834622	+	0.144561i
$647$	13.6777	+	23.6904i	0.537725	+	0.931366i	0.999026	+	0.0441230i	$0.0140493\pi$
$647$	13.6777	+	23.6904i	0.537725	+	0.931366i	−0.461301	+	0.887243i	$0.652617\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−4.03553	+	6.98975i	−0.158409	+	0.274372i
$650$	−40.9706			−1.60700
$651$	−0.656854	−	1.60896i	−0.0257441	−	0.0630600i
$652$	−5.17157			−0.202534
$653$	−8.10660	+	14.0410i	−0.317236	+	0.549469i	−0.979910	−	0.199439i	$-0.936088\pi$
$653$	−8.10660	+	14.0410i	−0.317236	+	0.549469i	0.662674	+	0.748908i	$0.269421\pi$
$654$	5.12132	+	8.87039i	0.200259	+	0.346860i
$655$	−40.4203	−	70.0100i	−1.57935	−	2.73552i
$656$	1.70711	−	2.95680i	0.0666513	−	0.115443i
$657$	−9.17157			−0.357817
$658$	−23.1421	−	3.16693i	−0.902174	−	0.123460i
$659$	−30.9706			−1.20644			−0.603221	−	0.797574i	$-0.706116\pi$
$659$	−30.9706			−1.20644			−0.603221	+	0.797574i	$0.706116\pi$
$660$	2.20711	−	3.82282i	0.0859115	−	0.148803i
$661$	2.19239	+	3.79733i	0.0852740	+	0.147699i	0.905508	−	0.424329i	$-0.139490\pi$
$661$	2.19239	+	3.79733i	0.0852740	+	0.147699i	−0.820234	+	0.572028i	$0.806157\pi$
$662$	−16.1924	−	28.0460i	−0.629335	−	1.09004i
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$	11.1421			0.432399
$665$	11.5711	+	1.58346i	0.448707	+	0.0614041i
$666$	−8.24264			−0.319396
$667$	−2.29289	+	3.97141i	−0.0887812	+	0.153774i
$668$	−9.36396	−	16.2189i	−0.362303	−	0.627526i
$669$	3.25736	+	5.64191i	0.125937	+	0.218129i
$670$	−4.41421	+	7.64564i	−0.170536	+	0.295377i
$671$	−0.828427			−0.0319811
$672$	−1.00000	−	2.44949i	−0.0385758	−	0.0944911i
$673$	−27.7279			−1.06883			−0.534416	−	0.845221i	$-0.679469\pi$
$673$	−27.7279			−1.06883			−0.534416	+	0.845221i	$0.679469\pi$
$674$	6.03553	−	10.4539i	0.232480	−	0.402667i
$675$	7.24264	+	12.5446i	0.278769	+	0.482843i
$676$	2.50000	+	4.33013i	0.0961538	+	0.166543i
$677$	−0.156854	+	0.271680i	−0.00602840	+	0.0104415i	−0.869024	−	0.494770i	$-0.835252\pi$
$677$	−0.156854	+	0.271680i	−0.00602840	+	0.0104415i	0.862995	+	0.505212i	$0.168586\pi$
$678$	−1.75736			−0.0674910
$679$	−13.6421	+	17.5922i	−0.523537	+	0.675126i
$680$	−18.7279			−0.718183
$681$	10.4497	−	18.0995i	0.400435	−	0.693574i
$682$	0.328427	+	0.568852i	0.0125761	+	0.0217825i
$683$	−11.3787	−	19.7085i	−0.435393	−	0.754123i	0.561935	−	0.827182i	$-0.310057\pi$
$683$	−11.3787	−	19.7085i	−0.435393	−	0.754123i	−0.997328	+	0.0730588i	$0.976724\pi$
$684$	−0.500000	+	0.866025i	−0.0191180	+	0.0331133i
$685$	51.4558			1.96603
$686$	14.8640	−	11.0482i	0.567509	−	0.421822i
$687$	−19.7990			−0.755379
$688$	1.12132	−	1.94218i	0.0427499	−	0.0740451i
$689$	−5.41421	−	9.37769i	−0.206265	−	0.357262i
$690$	−1.29289	−	2.23936i	−0.0492196	−	0.0852509i
$691$	−25.7782	+	44.6491i	−0.980648	+	1.69853i	−0.320774	+	0.947156i	$0.603943\pi$
$691$	−25.7782	+	44.6491i	−0.980648	+	1.69853i	−0.659874	+	0.751376i	$0.729390\pi$
$692$	23.7990			0.904702
$693$	−1.62132	+	2.09077i	−0.0615889	+	0.0794218i
$694$	−34.0000			−1.29062
$695$	−26.2635	+	45.4896i	−0.996230	+	1.72552i
$696$	3.91421	+	6.77962i	0.148368	+	0.256981i
$697$	7.24264	+	12.5446i	0.274335	+	0.475161i
$698$	8.12132	−	14.0665i	0.307397	−	0.532426i
$699$	10.8284			0.409569
$700$	14.4853	+	35.4815i	0.547492	+	1.34108i
$701$	−7.04163			−0.265959			−0.132979	−	0.991119i	$-0.542454\pi$
$701$	−7.04163			−0.265959			−0.132979	+	0.991119i	$0.542454\pi$
$702$	−1.41421	+	2.44949i	−0.0533761	+	0.0924500i
$703$	4.12132	+	7.13834i	0.155439	+	0.269227i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−19.4853	+	33.7495i	−0.733858	+	1.27108i
$706$	33.8995			1.27582
$707$	49.7279	+	6.80511i	1.87021	+	0.255933i
$708$	8.07107			0.303329
$709$	6.80761	−	11.7911i	0.255665	−	0.442825i	−0.709411	−	0.704795i	$-0.751039\pi$
$709$	6.80761	−	11.7911i	0.255665	−	0.442825i	0.965076	+	0.261970i	$0.0843722\pi$
$710$	26.2635	+	45.4896i	0.985650	+	1.70720i
$711$	2.91421	+	5.04757i	0.109292	+	0.189299i
$712$	−6.12132	+	10.6024i	−0.229406	+	0.397343i
$713$	0.384776			0.0144100
$714$	11.1213	+	1.52192i	0.416205	+	0.0569563i
$715$	−12.4853			−0.466923
$716$	12.2426	−	21.2049i	0.457529	−	0.792463i
$717$	−14.1421	−	24.4949i	−0.528148	−	0.914779i
$718$	−5.00000	−	8.66025i	−0.186598	−	0.323198i
$719$	−1.58579	+	2.74666i	−0.0591399	+	0.102433i	−0.894080	−	0.447908i	$-0.852169\pi$
$719$	−1.58579	+	2.74666i	−0.0591399	+	0.102433i	0.834940	+	0.550341i	$0.185502\pi$
$720$	−4.41421			−0.164508
$721$	−1.51472	−	3.71029i	−0.0564111	−	0.138178i
$722$	1.00000			0.0372161
$723$	−15.2782	+	26.4626i	−0.568201	+	0.984154i
$724$	1.75736	+	3.04384i	0.0653117	+	0.113123i
$725$	−56.6985	−	98.2047i	−2.10573	−	3.64723i
$726$	−5.00000	+	8.66025i	−0.185567	+	0.321412i
$727$	18.2721			0.677674			0.338837	−	0.940845i	$-0.389967\pi$
$727$	18.2721			0.677674			0.338837	+	0.940845i	$0.389967\pi$
$728$	−4.58579	+	5.91359i	−0.169961	+	0.219172i
$729$	1.00000			0.0370370
$730$	−20.2426	+	35.0613i	−0.749214	+	1.29768i
$731$	4.75736	+	8.23999i	0.175957	+	0.304767i
$732$	0.414214	+	0.717439i	0.0153098	+	0.0265173i
$733$	21.0919	−	36.5322i	0.779046	−	1.34935i	−0.153445	−	0.988157i	$-0.549037\pi$
$733$	21.0919	−	36.5322i	0.779046	−	1.34935i	0.932492	−	0.361191i	$-0.117630\pi$
$734$	−3.24264			−0.119688
$735$	−7.69239	−	29.9267i	−0.283738	−	1.10386i
$736$	0.585786			0.0215924
$737$	−1.00000	+	1.73205i	−0.0368355	+	0.0638009i
$738$	1.70711	+	2.95680i	0.0628395	+	0.108841i
$739$	−1.22183	−	2.11626i	−0.0449456	−	0.0778480i	0.842677	−	0.538419i	$-0.180978\pi$
$739$	−1.22183	−	2.11626i	−0.0449456	−	0.0778480i	−0.887623	+	0.460571i	$0.847645\pi$
$740$	−18.1924	+	31.5101i	−0.668765	+	1.15834i
$741$	2.82843			0.103905
$742$	−6.20711	+	8.00436i	−0.227870	+	0.293849i
$743$	52.9117			1.94114			0.970571	−	0.240816i	$-0.0774150\pi$
$743$	52.9117			1.94114			0.970571	+	0.240816i	$0.0774150\pi$
$744$	0.328427	−	0.568852i	0.0120407	−	0.0208551i
$745$	−3.34315	−	5.79050i	−0.122483	−	0.212147i
$746$	8.24264	+	14.2767i	0.301785	+	0.522706i
$747$	−5.57107	+	9.64937i	−0.203835	+	0.353052i
$748$	−4.24264			−0.155126
$749$	−13.7279	−	33.6264i	−0.501607	−	1.22868i
$750$	41.8701			1.52888
$751$	−23.0563	+	39.9348i	−0.841338	+	1.45724i	0.0474256	+	0.998875i	$0.484898\pi$
$751$	−23.0563	+	39.9348i	−0.841338	+	1.45724i	−0.888764	+	0.458366i	$0.848435\pi$
$752$	−4.41421	−	7.64564i	−0.160970	−	0.278808i
$753$	−10.5000	−	18.1865i	−0.382641	−	0.662754i
$754$	11.0711	−	19.1757i	0.403185	−	0.698336i
$755$	100.012			3.63982
$756$	2.62132	+	0.358719i	0.0953365	+	0.0130465i
$757$	−41.2132			−1.49792			−0.748960	−	0.662616i	$-0.769446\pi$
$757$	−41.2132			−1.49792			−0.748960	+	0.662616i	$0.769446\pi$
$758$	9.65685	−	16.7262i	0.350753	−	0.607522i
$759$	−0.292893	−	0.507306i	−0.0106314	−	0.0184140i
$760$	2.20711	+	3.82282i	0.0800602	+	0.138668i
$761$	11.0711	−	19.1757i	0.401326	−	0.695117i	−0.592560	−	0.805526i	$-0.701883\pi$
$761$	11.0711	−	19.1757i	0.401326	−	0.695117i	0.993886	+	0.110409i	$0.0352162\pi$
$762$	0.171573			0.00621543
$763$	−26.8492	−	3.67423i	−0.972008	−	0.133016i
$764$	10.1421			0.366930
$765$	9.36396	−	16.2189i	0.338555	−	0.586394i
$766$	−2.17157	−	3.76127i	−0.0784621	−	0.135900i
$767$	−11.4142	−	19.7700i	−0.412143	−	0.713853i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	44.6569			1.61037			0.805184	−	0.593026i	$-0.202067\pi$
$769$	44.6569			1.61037			0.805184	+	0.593026i	$0.202067\pi$
$770$

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20711 - 3.82282i) q^{5} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20711 - 3.82282i) q^{5} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.20711 + 3.82282i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -2.82843 q^{13} +(1.00000 + 2.44949i) q^{14} +4.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.12132 - 3.67423i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -4.41421 q^{20} +(2.62132 + 0.358719i) q^{21} -1.00000 q^{22} +(-0.292893 + 0.507306i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-7.24264 - 12.5446i) q^{25} +(1.41421 - 2.44949i) q^{26} -1.00000 q^{27} +(-2.62132 - 0.358719i) q^{28} +7.82843 q^{29} +(-2.20711 + 3.82282i) q^{30} +(-0.328427 - 0.568852i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +4.24264 q^{34} +(-4.41421 - 10.8126i) q^{35} +1.00000 q^{36} +(4.12132 - 7.13834i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(-1.41421 - 2.44949i) q^{39} +(2.20711 - 3.82282i) q^{40} -3.41421 q^{41} +(-1.62132 + 2.09077i) q^{42} -2.24264 q^{43} +(0.500000 - 0.866025i) q^{44} +(2.20711 + 3.82282i) q^{45} +(-0.292893 - 0.507306i) q^{46} +(-4.41421 + 7.64564i) q^{47} -1.00000 q^{48} +(-1.74264 - 6.77962i) q^{49} +14.4853 q^{50} +(2.12132 - 3.67423i) q^{51} +(1.41421 + 2.44949i) q^{52} +(1.91421 + 3.31552i) q^{53} +(0.500000 - 0.866025i) q^{54} +4.41421 q^{55} +(1.62132 - 2.09077i) q^{56} -1.00000 q^{57} +(-3.91421 + 6.77962i) q^{58} +(4.03553 + 6.98975i) q^{59} +(-2.20711 - 3.82282i) q^{60} +(-0.414214 + 0.717439i) q^{61} +0.656854 q^{62} +(1.00000 + 2.44949i) q^{63} +1.00000 q^{64} +(-6.24264 + 10.8126i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(1.00000 + 1.73205i) q^{67} +(-2.12132 + 3.67423i) q^{68} -0.585786 q^{69} +(11.5711 + 1.58346i) q^{70} +11.8995 q^{71} +(-0.500000 + 0.866025i) q^{72} +(4.58579 + 7.94282i) q^{73} +(4.12132 + 7.13834i) q^{74} +(7.24264 - 12.5446i) q^{75} +1.00000 q^{76} +(2.62132 + 0.358719i) q^{77} +2.82843 q^{78} +(2.91421 - 5.04757i) q^{79} +(2.20711 + 3.82282i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.70711 - 2.95680i) q^{82} +11.1421 q^{83} +(-1.00000 - 2.44949i) q^{84} -18.7279 q^{85} +(1.12132 - 1.94218i) q^{86} +(3.91421 + 6.77962i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-6.12132 + 10.6024i) q^{89} -4.41421 q^{90} +(-4.58579 + 5.91359i) q^{91} +0.585786 q^{92} +(0.328427 - 0.568852i) q^{93} +(-4.41421 - 7.64564i) q^{94} +(2.20711 + 3.82282i) q^{95} +(0.500000 - 0.866025i) q^{96} -8.41421 q^{97} +(6.74264 + 1.88064i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 6 q^{10} + 2 q^{11} + 2 q^{12} + 4 q^{14} + 12 q^{15} - 2 q^{16} - 2 q^{18} - 2 q^{19} - 12 q^{20} + 2 q^{21} - 4 q^{22} - 4 q^{23} + 2 q^{24} - 12 q^{25} - 4 q^{27} - 2 q^{28} + 20 q^{29} - 6 q^{30} + 10 q^{31} - 2 q^{32} - 2 q^{33} - 12 q^{35} + 4 q^{36} + 8 q^{37} - 2 q^{38} + 6 q^{40} - 8 q^{41} + 2 q^{42} + 8 q^{43} + 2 q^{44} + 6 q^{45} - 4 q^{46} - 12 q^{47} - 4 q^{48} + 10 q^{49} + 24 q^{50} + 2 q^{53} + 2 q^{54} + 12 q^{55} - 2 q^{56} - 4 q^{57} - 10 q^{58} + 2 q^{59} - 6 q^{60} + 4 q^{61} - 20 q^{62} + 4 q^{63} + 4 q^{64} - 8 q^{65} - 2 q^{66} + 4 q^{67} - 8 q^{69} + 18 q^{70} + 8 q^{71} - 2 q^{72} + 24 q^{73} + 8 q^{74} + 12 q^{75} + 4 q^{76} + 2 q^{77} + 6 q^{79} + 6 q^{80} - 2 q^{81} + 4 q^{82} - 12 q^{83} - 4 q^{84} - 24 q^{85} - 4 q^{86} + 10 q^{87} + 2 q^{88} - 16 q^{89} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 10 q^{93} - 12 q^{94} + 6 q^{95} + 2 q^{96} - 28 q^{97} + 10 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 6 * q^10 + 2 * q^11 + 2 * q^12 + 4 * q^14 + 12 * q^15 - 2 * q^16 - 2 * q^18 - 2 * q^19 - 12 * q^20 + 2 * q^21 - 4 * q^22 - 4 * q^23 + 2 * q^24 - 12 * q^25 - 4 * q^27 - 2 * q^28 + 20 * q^29 - 6 * q^30 + 10 * q^31 - 2 * q^32 - 2 * q^33 - 12 * q^35 + 4 * q^36 + 8 * q^37 - 2 * q^38 + 6 * q^40 - 8 * q^41 + 2 * q^42 + 8 * q^43 + 2 * q^44 + 6 * q^45 - 4 * q^46 - 12 * q^47 - 4 * q^48 + 10 * q^49 + 24 * q^50 + 2 * q^53 + 2 * q^54 + 12 * q^55 - 2 * q^56 - 4 * q^57 - 10 * q^58 + 2 * q^59 - 6 * q^60 + 4 * q^61 - 20 * q^62 + 4 * q^63 + 4 * q^64 - 8 * q^65 - 2 * q^66 + 4 * q^67 - 8 * q^69 + 18 * q^70 + 8 * q^71 - 2 * q^72 + 24 * q^73 + 8 * q^74 + 12 * q^75 + 4 * q^76 + 2 * q^77 + 6 * q^79 + 6 * q^80 - 2 * q^81 + 4 * q^82 - 12 * q^83 - 4 * q^84 - 24 * q^85 - 4 * q^86 + 10 * q^87 + 2 * q^88 - 16 * q^89 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 10 * q^93 - 12 * q^94 + 6 * q^95 + 2 * q^96 - 28 * q^97 + 10 * q^98 - 4 * q^99

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