LMFDB - Embedded newform 825.2.k.a.518.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(518,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("825.518");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.k (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:	$6.58765816676$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			518.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	825.518
Dual form			825.2.k.a.782.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70711 - 1.70711i) q^{2} +(-0.292893 + 1.70711i) q^{3} +3.82843i q^{4} +(3.41421 - 2.41421i) q^{6} +(-3.41421 + 3.41421i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(-1.70711 - 1.70711i) q^{2} +(-0.292893 + 1.70711i) q^{3} +3.82843i q^{4} +(3.41421 - 2.41421i) q^{6} +(-3.41421 + 3.41421i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-2.82843 - 1.00000i) q^{9} -1.00000i q^{11} +(-6.53553 - 1.12132i) q^{12} +(-0.585786 - 0.585786i) q^{13} +11.6569 q^{14} -3.00000 q^{16} +(2.00000 + 2.00000i) q^{17} +(3.12132 + 6.53553i) q^{18} +4.82843i q^{19} +(-4.82843 - 6.82843i) q^{21} +(-1.70711 + 1.70711i) q^{22} +(-4.82843 + 4.82843i) q^{23} +(4.41421 + 6.24264i) q^{24} +2.00000i q^{26} +(2.53553 - 4.53553i) q^{27} +(-13.0711 - 13.0711i) q^{28} -3.17157 q^{29} +4.00000 q^{31} +(-1.12132 - 1.12132i) q^{32} +(1.70711 + 0.292893i) q^{33} -6.82843i q^{34} +(3.82843 - 10.8284i) q^{36} +(5.65685 - 5.65685i) q^{37} +(8.24264 - 8.24264i) q^{38} +(1.17157 - 0.828427i) q^{39} -0.828427i q^{41} +(-3.41421 + 19.8995i) q^{42} +(-7.41421 - 7.41421i) q^{43} +3.82843 q^{44} +16.4853 q^{46} +(-0.828427 - 0.828427i) q^{47} +(0.878680 - 5.12132i) q^{48} -16.3137i q^{49} +(-4.00000 + 2.82843i) q^{51} +(2.24264 - 2.24264i) q^{52} +(8.48528 - 8.48528i) q^{53} +(-12.0711 + 3.41421i) q^{54} +21.3137i q^{56} +(-8.24264 - 1.41421i) q^{57} +(5.41421 + 5.41421i) q^{58} -13.6569 q^{59} -6.00000 q^{61} +(-6.82843 - 6.82843i) q^{62} +(13.0711 - 6.24264i) q^{63} +9.82843i q^{64} +(-2.41421 - 3.41421i) q^{66} +(5.41421 - 5.41421i) q^{67} +(-7.65685 + 7.65685i) q^{68} +(-6.82843 - 9.65685i) q^{69} -1.65685i q^{71} +(-11.9497 + 5.70711i) q^{72} +(-7.41421 - 7.41421i) q^{73} -19.3137 q^{74} -18.4853 q^{76} +(3.41421 + 3.41421i) q^{77} +(-3.41421 - 0.585786i) q^{78} -0.828427i q^{79} +(7.00000 + 5.65685i) q^{81} +(-1.41421 + 1.41421i) q^{82} +(-4.24264 + 4.24264i) q^{83} +(26.1421 - 18.4853i) q^{84} +25.3137i q^{86} +(0.928932 - 5.41421i) q^{87} +(-3.12132 - 3.12132i) q^{88} +7.31371 q^{89} +4.00000 q^{91} +(-18.4853 - 18.4853i) q^{92} +(-1.17157 + 6.82843i) q^{93} +2.82843i q^{94} +(2.24264 - 1.58579i) q^{96} +(-9.65685 + 9.65685i) q^{97} +(-27.8492 + 27.8492i) q^{98} +(-1.00000 + 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^8	$ 4 q - 4 q^{2} - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{8} - 12 q^{12} - 8 q^{13} + 24 q^{14} - 12 q^{16} + 8 q^{17} + 4 q^{18} - 8 q^{21} - 4 q^{22} - 8 q^{23} + 12 q^{24} - 4 q^{27} - 24 q^{28} - 24 q^{29} + 16 q^{31} + 4 q^{32} + 4 q^{33} + 4 q^{36} + 16 q^{38} + 16 q^{39} - 8 q^{42} - 24 q^{43} + 4 q^{44} + 32 q^{46} + 8 q^{47} + 12 q^{48} - 16 q^{51} - 8 q^{52} - 20 q^{54} - 16 q^{57} + 16 q^{58} - 32 q^{59} - 24 q^{61} - 16 q^{62} + 24 q^{63} - 4 q^{66} + 16 q^{67} - 8 q^{68} - 16 q^{69} - 28 q^{72} - 24 q^{73} - 32 q^{74} - 40 q^{76} + 8 q^{77} - 8 q^{78} + 28 q^{81} + 48 q^{84} + 32 q^{87} - 4 q^{88} - 16 q^{89} + 16 q^{91} - 40 q^{92} - 16 q^{93} - 8 q^{96} - 16 q^{97} - 52 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^8 - 12 * q^12 - 8 * q^13 + 24 * q^14 - 12 * q^16 + 8 * q^17 + 4 * q^18 - 8 * q^21 - 4 * q^22 - 8 * q^23 + 12 * q^24 - 4 * q^27 - 24 * q^28 - 24 * q^29 + 16 * q^31 + 4 * q^32 + 4 * q^33 + 4 * q^36 + 16 * q^38 + 16 * q^39 - 8 * q^42 - 24 * q^43 + 4 * q^44 + 32 * q^46 + 8 * q^47 + 12 * q^48 - 16 * q^51 - 8 * q^52 - 20 * q^54 - 16 * q^57 + 16 * q^58 - 32 * q^59 - 24 * q^61 - 16 * q^62 + 24 * q^63 - 4 * q^66 + 16 * q^67 - 8 * q^68 - 16 * q^69 - 28 * q^72 - 24 * q^73 - 32 * q^74 - 40 * q^76 + 8 * q^77 - 8 * q^78 + 28 * q^81 + 48 * q^84 + 32 * q^87 - 4 * q^88 - 16 * q^89 + 16 * q^91 - 40 * q^92 - 16 * q^93 - 8 * q^96 - 16 * q^97 - 52 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.70711	−	1.70711i	−1.20711	−	1.20711i	−0.971960	−	0.235147i	$-0.924443\pi$
$2$	−1.70711	−	1.70711i	−1.20711	−	1.20711i	−0.235147	−	0.971960i	$-0.575557\pi$
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$4$			3.82843i			1.91421i
$5$		0			0
$5$		0			0
$6$	3.41421	−	2.41421i	1.39385	−	0.985599i
$7$	−3.41421	+	3.41421i	−1.29045	+	1.29045i	−0.355944	+	0.934507i	$0.615841\pi$
$7$	−3.41421	+	3.41421i	−1.29045	+	1.29045i	−0.934507	+	0.355944i	$0.884159\pi$
$8$	3.12132	−	3.12132i	1.10355	−	1.10355i
$9$	−2.82843	−	1.00000i	−0.942809	−	0.333333i
$10$		0			0
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−6.53553	−	1.12132i	−1.88665	−	0.323697i
$13$	−0.585786	−	0.585786i	−0.162468	−	0.162468i	0.621191	−	0.783659i	$-0.286649\pi$
$13$	−0.585786	−	0.585786i	−0.162468	−	0.162468i	−0.783659	+	0.621191i	$0.786649\pi$
$14$	11.6569			3.11543
$15$		0			0
$16$	−3.00000			−0.750000
$17$	2.00000	+	2.00000i	0.485071	+	0.485071i	0.906747	−	0.421676i	$-0.138558\pi$
$17$	2.00000	+	2.00000i	0.485071	+	0.485071i	−0.421676	+	0.906747i	$0.638558\pi$
$18$	3.12132	+	6.53553i	0.735702	+	1.54044i
$19$			4.82843i			1.10772i	0.832611	+	0.553859i	$0.186845\pi$
$19$			4.82843i			1.10772i	−0.832611	+	0.553859i	$0.813155\pi$
$20$		0			0
$21$	−4.82843	−	6.82843i	−1.05365	−	1.49008i
$22$	−1.70711	+	1.70711i	−0.363956	+	0.363956i
$23$	−4.82843	+	4.82843i	−1.00680	+	1.00680i	−0.00681991	+	0.999977i	$0.502171\pi$
$23$	−4.82843	+	4.82843i	−1.00680	+	1.00680i	−0.999977	+	0.00681991i	$0.997829\pi$
$24$	4.41421	+	6.24264i	0.901048	+	1.27427i
$25$		0			0
$26$			2.00000i			0.392232i
$27$	2.53553	−	4.53553i	0.487964	−	0.872864i
$28$	−13.0711	−	13.0711i	−2.47020	−	2.47020i
$29$	−3.17157			−0.588946			−0.294473	−	0.955660i	$-0.595144\pi$
$29$	−3.17157			−0.588946			−0.294473	+	0.955660i	$0.595144\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.12132	−	1.12132i	−0.198223	−	0.198223i
$33$	1.70711	+	0.292893i	0.297169	+	0.0509862i
$34$		−	6.82843i		−	1.17107i
$35$		0			0
$36$	3.82843	−	10.8284i	0.638071	−	1.80474i
$37$	5.65685	−	5.65685i	0.929981	−	0.929981i	−0.0677230	−	0.997704i	$-0.521573\pi$
$37$	5.65685	−	5.65685i	0.929981	−	0.929981i	0.997704	+	0.0677230i	$0.0215734\pi$
$38$	8.24264	−	8.24264i	1.33713	−	1.33713i
$39$	1.17157	−	0.828427i	0.187602	−	0.132655i
$40$		0			0
$41$		−	0.828427i		−	0.129379i	−0.997905	−	0.0646893i	$-0.979394\pi$
$41$		−	0.828427i		−	0.129379i	0.997905	−	0.0646893i	$-0.0206056\pi$
$42$	−3.41421	+	19.8995i	−0.526825	+	3.07056i
$43$	−7.41421	−	7.41421i	−1.13066	−	1.13066i	−0.990068	−	0.140589i	$-0.955100\pi$
$43$	−7.41421	−	7.41421i	−1.13066	−	1.13066i	−0.140589	−	0.990068i	$-0.544900\pi$
$44$	3.82843			0.577157
$45$		0			0
$46$	16.4853			2.43062
$47$	−0.828427	−	0.828427i	−0.120839	−	0.120839i	0.644102	−	0.764940i	$-0.277231\pi$
$47$	−0.828427	−	0.828427i	−0.120839	−	0.120839i	−0.764940	+	0.644102i	$0.777231\pi$
$48$	0.878680	−	5.12132i	0.126826	−	0.739199i
$49$		−	16.3137i		−	2.33053i
$50$		0			0
$51$	−4.00000	+	2.82843i	−0.560112	+	0.396059i
$52$	2.24264	−	2.24264i	0.310998	−	0.310998i
$53$	8.48528	−	8.48528i	1.16554	−	1.16554i	0.182300	−	0.983243i	$-0.441646\pi$
$53$	8.48528	−	8.48528i	1.16554	−	1.16554i	0.983243	−	0.182300i	$-0.0583542\pi$
$54$	−12.0711	+	3.41421i	−1.64266	+	0.464616i
$55$		0			0
$56$			21.3137i			2.84816i
$57$	−8.24264	−	1.41421i	−1.09176	−	0.187317i
$58$	5.41421	+	5.41421i	0.710921	+	0.710921i
$59$	−13.6569			−1.77797			−0.888985	−	0.457935i	$-0.848589\pi$
$59$	−13.6569			−1.77797			−0.888985	+	0.457935i	$0.848589\pi$
$60$		0			0
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$	−6.82843	−	6.82843i	−0.867211	−	0.867211i
$63$	13.0711	−	6.24264i	1.64680	−	0.786499i
$64$			9.82843i			1.22855i
$65$		0			0
$66$	−2.41421	−	3.41421i	−0.297169	−	0.420261i
$67$	5.41421	−	5.41421i	0.661451	−	0.661451i	−0.294271	−	0.955722i	$-0.595077\pi$
$67$	5.41421	−	5.41421i	0.661451	−	0.661451i	0.955722	+	0.294271i	$0.0950767\pi$
$68$	−7.65685	+	7.65685i	−0.928530	+	0.928530i
$69$	−6.82843	−	9.65685i	−0.822046	−	1.16255i
$70$		0			0
$71$		−	1.65685i		−	0.196632i	−0.995155	−	0.0983162i	$-0.968654\pi$
$71$		−	1.65685i		−	0.196632i	0.995155	−	0.0983162i	$-0.0313457\pi$
$72$	−11.9497	+	5.70711i	−1.40829	+	0.672589i
$73$	−7.41421	−	7.41421i	−0.867768	−	0.867768i	0.124457	−	0.992225i	$-0.460281\pi$
$73$	−7.41421	−	7.41421i	−0.867768	−	0.867768i	−0.992225	+	0.124457i	$0.960281\pi$
$74$	−19.3137			−2.24517
$75$		0			0
$76$	−18.4853			−2.12041
$77$	3.41421	+	3.41421i	0.389086	+	0.389086i
$78$	−3.41421	−	0.585786i	−0.386584	−	0.0663273i
$79$		−	0.828427i		−	0.0932053i	−0.998914	−	0.0466027i	$-0.985161\pi$
$79$		−	0.828427i		−	0.0932053i	0.998914	−	0.0466027i	$-0.0148395\pi$
$80$		0			0
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$	−1.41421	+	1.41421i	−0.156174	+	0.156174i
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	−0.900515	−	0.434825i	$-0.856810\pi$
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	0.434825	+	0.900515i	$0.356810\pi$
$84$	26.1421	−	18.4853i	2.85234	−	2.01691i
$85$		0			0
$86$			25.3137i			2.72965i
$87$	0.928932	−	5.41421i	0.0995920	−	0.580465i
$88$	−3.12132	−	3.12132i	−0.332734	−	0.332734i
$89$	7.31371			0.775252			0.387626	−	0.921817i	$-0.373295\pi$
$89$	7.31371			0.775252			0.387626	+	0.921817i	$0.373295\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$	−18.4853	−	18.4853i	−1.92722	−	1.92722i
$93$	−1.17157	+	6.82843i	−0.121486	+	0.708075i
$94$			2.82843i			0.291730i
$95$		0			0
$96$	2.24264	−	1.58579i	0.228889	−	0.161849i
$97$	−9.65685	+	9.65685i	−0.980505	+	0.980505i	−0.999814	−	0.0193086i	$-0.993854\pi$
$97$	−9.65685	+	9.65685i	−0.980505	+	0.980505i	0.0193086	+	0.999814i	$0.493854\pi$
$98$	−27.8492	+	27.8492i	−2.81320	+	2.81320i
$99$	−1.00000	+	2.82843i	−0.100504	+	0.284268i
$100$		0			0
$101$		−	4.82843i		−	0.480446i	−0.970718	−	0.240223i	$-0.922779\pi$
$101$		−	4.82843i		−	0.480446i	0.970718	−	0.240223i	$-0.0772206\pi$
$102$	11.6569	+	2.00000i	1.15420	+	0.198030i
$103$	4.24264	+	4.24264i	0.418040	+	0.418040i	0.884528	−	0.466488i	$-0.154481\pi$
$103$	4.24264	+	4.24264i	0.418040	+	0.418040i	−0.466488	+	0.884528i	$0.654481\pi$
$104$	−3.65685			−0.358584
$105$		0			0
$106$	−28.9706			−2.81387
$107$	5.89949	+	5.89949i	0.570326	+	0.570326i	0.932219	−	0.361894i	$-0.117870\pi$
$107$	5.89949	+	5.89949i	0.570326	+	0.570326i	−0.361894	+	0.932219i	$0.617870\pi$
$108$	17.3640	+	9.70711i	1.67085	+	0.934067i
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$		0			0
$111$	8.00000	+	11.3137i	0.759326	+	1.07385i
$112$	10.2426	−	10.2426i	0.967839	−	0.967839i
$113$	8.48528	−	8.48528i	0.798228	−	0.798228i	−0.184588	−	0.982816i	$-0.559095\pi$
$113$	8.48528	−	8.48528i	0.798228	−	0.798228i	0.982816	+	0.184588i	$0.0590950\pi$
$114$	11.6569	+	16.4853i	1.09176	+	1.54399i
$115$		0			0
$116$		−	12.1421i		−	1.12737i
$117$	1.07107	+	2.24264i	0.0990203	+	0.207332i
$118$	23.3137	+	23.3137i	2.14620	+	2.14620i
$119$	−13.6569			−1.25192
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	10.2426	+	10.2426i	0.927325	+	0.927325i
$123$	1.41421	+	0.242641i	0.127515	+	0.0218782i
$124$			15.3137i			1.37521i
$125$		0			0
$126$	−32.9706	−	11.6569i	−2.93725	−	1.03848i
$127$	1.75736	−	1.75736i	0.155940	−	0.155940i	−0.624825	−	0.780765i	$-0.714830\pi$
$127$	1.75736	−	1.75736i	0.155940	−	0.155940i	0.780765	+	0.624825i	$0.214830\pi$
$128$	14.5355	−	14.5355i	1.28477	−	1.28477i
$129$	14.8284	−	10.4853i	1.30557	−	0.923178i
$130$		0			0
$131$			6.34315i			0.554203i	0.960841	+	0.277102i	$0.0893739\pi$
$131$			6.34315i			0.554203i	−0.960841	+	0.277102i	$0.910626\pi$
$132$	−1.12132	+	6.53553i	−0.0975984	+	0.568845i
$133$	−16.4853	−	16.4853i	−1.42946	−	1.42946i
$134$	−18.4853			−1.59689
$135$		0			0
$136$	12.4853			1.07060
$137$	9.65685	+	9.65685i	0.825041	+	0.825041i	0.986826	−	0.161785i	$-0.0517252\pi$
$137$	9.65685	+	9.65685i	0.825041	+	0.825041i	−0.161785	+	0.986826i	$0.551725\pi$
$138$	−4.82843	+	28.1421i	−0.411023	+	2.39562i
$139$		−	11.1716i		−	0.947560i	−0.880643	−	0.473780i	$-0.842889\pi$
$139$		−	11.1716i		−	0.947560i	0.880643	−	0.473780i	$-0.157111\pi$
$140$		0			0
$141$	1.65685	−	1.17157i	0.139532	−	0.0986642i
$142$	−2.82843	+	2.82843i	−0.237356	+	0.237356i
$143$	−0.585786	+	0.585786i	−0.0489859	+	0.0489859i
$144$	8.48528	+	3.00000i	0.707107	+	0.250000i
$145$		0			0
$146$			25.3137i			2.09498i
$147$	27.8492	+	4.77817i	2.29697	+	0.394097i
$148$	21.6569	+	21.6569i	1.78018	+	1.78018i
$149$	−21.7990			−1.78584			−0.892921	−	0.450213i	$-0.851348\pi$
$149$	−21.7990			−1.78584			−0.892921	+	0.450213i	$0.851348\pi$
$150$		0			0
$151$	−2.48528			−0.202249			−0.101125	−	0.994874i	$-0.532244\pi$
$151$	−2.48528			−0.202249			−0.101125	+	0.994874i	$0.532244\pi$
$152$	15.0711	+	15.0711i	1.22243	+	1.22243i
$153$	−3.65685	−	7.65685i	−0.295639	−	0.619020i
$154$		−	11.6569i		−	0.939336i
$155$		0			0
$156$	3.17157	+	4.48528i	0.253929	+	0.359110i
$157$	−7.31371	+	7.31371i	−0.583697	+	0.583697i	−0.935917	−	0.352220i	$-0.885427\pi$
$157$	−7.31371	+	7.31371i	−0.583697	+	0.583697i	0.352220	+	0.935917i	$0.385427\pi$
$158$	−1.41421	+	1.41421i	−0.112509	+	0.112509i
$159$	12.0000	+	16.9706i	0.951662	+	1.34585i
$160$		0			0
$161$		−	32.9706i		−	2.59844i
$162$	−2.29289	−	21.6066i	−0.180147	−	1.69757i
$163$	−9.89949	−	9.89949i	−0.775388	−	0.775388i	0.203655	−	0.979043i	$-0.434718\pi$
$163$	−9.89949	−	9.89949i	−0.775388	−	0.775388i	−0.979043	+	0.203655i	$0.934718\pi$
$164$	3.17157			0.247658
$165$		0			0
$166$	14.4853			1.12428
$167$	0.242641	+	0.242641i	0.0187761	+	0.0187761i	0.716433	−	0.697656i	$-0.245774\pi$
$167$	0.242641	+	0.242641i	0.0187761	+	0.0187761i	−0.697656	+	0.716433i	$0.745774\pi$
$168$	−36.3848	−	6.24264i	−2.80715	−	0.481630i
$169$		−	12.3137i		−	0.947208i
$170$		0			0
$171$	4.82843	−	13.6569i	0.369239	−	1.04437i
$172$	28.3848	−	28.3848i	2.16432	−	2.16432i
$173$	−0.828427	+	0.828427i	−0.0629841	+	0.0629841i	−0.737897	−	0.674913i	$-0.764181\pi$
$173$	−0.828427	+	0.828427i	−0.0629841	+	0.0629841i	0.674913	+	0.737897i	$0.264181\pi$
$174$	−10.8284	+	7.65685i	−0.820901	+	0.580465i
$175$		0			0
$176$			3.00000i			0.226134i
$177$	4.00000	−	23.3137i	0.300658	−	1.75237i
$178$	−12.4853	−	12.4853i	−0.935811	−	0.935811i
$179$	3.31371			0.247678			0.123839	−	0.992302i	$-0.460479\pi$
$179$	3.31371			0.247678			0.123839	+	0.992302i	$0.460479\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	−6.82843	−	6.82843i	−0.506157	−	0.506157i
$183$	1.75736	−	10.2426i	0.129908	−	0.757158i
$184$			30.1421i			2.22211i
$185$		0			0
$186$	13.6569	−	9.65685i	1.00137	−	0.708075i
$187$	2.00000	−	2.00000i	0.146254	−	0.146254i
$188$	3.17157	−	3.17157i	0.231311	−	0.231311i
$189$	6.82843	+	24.1421i	0.496695	+	1.75608i
$190$		0			0
$191$			11.3137i			0.818631i	0.912393	+	0.409316i	$0.134232\pi$
$191$			11.3137i			0.818631i	−0.912393	+	0.409316i	$0.865768\pi$
$192$	−16.7782	−	2.87868i	−1.21086	−	0.207751i
$193$	5.07107	+	5.07107i	0.365023	+	0.365023i	0.865658	−	0.500635i	$-0.166900\pi$
$193$	5.07107	+	5.07107i	0.365023	+	0.365023i	−0.500635	+	0.865658i	$0.666900\pi$
$194$	32.9706			2.36715
$195$		0			0
$196$	62.4558			4.46113
$197$	−2.48528	−	2.48528i	−0.177069	−	0.177069i	0.613008	−	0.790077i	$-0.289959\pi$
$197$	−2.48528	−	2.48528i	−0.177069	−	0.177069i	−0.790077	+	0.613008i	$0.789959\pi$
$198$	6.53553	−	3.12132i	0.464460	−	0.221823i
$199$			20.9706i			1.48656i	0.668978	+	0.743282i	$0.266732\pi$
$199$			20.9706i			1.48656i	−0.668978	+	0.743282i	$0.733268\pi$
$200$		0			0
$201$	7.65685	+	10.8284i	0.540073	+	0.763778i
$202$	−8.24264	+	8.24264i	−0.579950	+	0.579950i
$203$	10.8284	−	10.8284i	0.760007	−	0.760007i
$204$	−10.8284	−	15.3137i	−0.758142	−	1.07217i
$205$		0			0
$206$		−	14.4853i		−	1.00924i
$207$	18.4853	−	8.82843i	1.28482	−	0.613618i
$208$	1.75736	+	1.75736i	0.121851	+	0.121851i
$209$	4.82843			0.333989
$210$		0			0
$211$	6.48528			0.446465			0.223233	−	0.974765i	$-0.428339\pi$
$211$	6.48528			0.446465			0.223233	+	0.974765i	$0.428339\pi$
$212$	32.4853	+	32.4853i	2.23110	+	2.23110i
$213$	2.82843	+	0.485281i	0.193801	+	0.0332509i
$214$		−	20.1421i		−	1.37689i
$215$		0			0
$216$	−6.24264	−	22.0711i	−0.424758	−	1.50175i
$217$	−13.6569	+	13.6569i	−0.927088	+	0.927088i
$218$	−3.41421	+	3.41421i	−0.231240	+	0.231240i
$219$	14.8284	−	10.4853i	1.00201	−	0.708530i
$220$		0			0
$221$		−	2.34315i		−	0.157617i
$222$	5.65685	−	32.9706i	0.379663	−	2.21284i
$223$	7.75736	+	7.75736i	0.519471	+	0.519471i	0.917411	−	0.397940i	$-0.130275\pi$
$223$	7.75736	+	7.75736i	0.519471	+	0.519471i	−0.397940	+	0.917411i	$0.630275\pi$
$224$	7.65685			0.511595
$225$		0			0
$226$	−28.9706			−1.92709
$227$	−11.7574	−	11.7574i	−0.780363	−	0.780363i	0.199529	−	0.979892i	$-0.436059\pi$
$227$	−11.7574	−	11.7574i	−0.780363	−	0.780363i	−0.979892	+	0.199529i	$0.936059\pi$
$228$	5.41421	−	31.5563i	0.358565	−	2.08987i
$229$			18.0000i			1.18947i	0.803921	+	0.594737i	$0.202744\pi$
$229$			18.0000i			1.18947i	−0.803921	+	0.594737i	$0.797256\pi$
$230$		0			0
$231$	−6.82843	+	4.82843i	−0.449278	+	0.317687i
$232$	−9.89949	+	9.89949i	−0.649934	+	0.649934i
$233$	10.0000	−	10.0000i	0.655122	−	0.655122i	−0.299100	−	0.954222i	$-0.596686\pi$
$233$	10.0000	−	10.0000i	0.655122	−	0.655122i	0.954222	+	0.299100i	$0.0966864\pi$
$234$	2.00000	−	5.65685i	0.130744	−	0.369800i
$235$		0			0
$236$		−	52.2843i		−	3.40342i
$237$	1.41421	+	0.242641i	0.0918630	+	0.0157612i
$238$	23.3137	+	23.3137i	1.51120	+	1.51120i
$239$	13.6569			0.883388			0.441694	−	0.897166i	$-0.354378\pi$
$239$	13.6569			0.883388			0.441694	+	0.897166i	$0.354378\pi$
$240$		0			0
$241$	6.97056			0.449013			0.224507	−	0.974473i	$-0.427923\pi$
$241$	6.97056			0.449013			0.224507	+	0.974473i	$0.427923\pi$
$242$	1.70711	+	1.70711i	0.109737	+	0.109737i
$243$	−11.7071	+	10.2929i	−0.751011	+	0.660289i
$244$		−	22.9706i		−	1.47054i
$245$		0			0
$246$	−2.00000	−	2.82843i	−0.127515	−	0.180334i
$247$	2.82843	−	2.82843i	0.179969	−	0.179969i
$248$	12.4853	−	12.4853i	0.792816	−	0.792816i
$249$	−6.00000	−	8.48528i	−0.380235	−	0.537733i
$250$		0			0
$251$		−	9.65685i		−	0.609535i	−0.952427	−	0.304768i	$-0.901421\pi$
$251$		−	9.65685i		−	0.609535i	0.952427	−	0.304768i	$-0.0985788\pi$
$252$	23.8995	+	50.0416i	1.50553	+	3.15233i
$253$	4.82843	+	4.82843i	0.303561	+	0.303561i
$254$	−6.00000			−0.376473
$255$		0			0
$256$	−29.9706			−1.87316
$257$	−16.0000	−	16.0000i	−0.998053	−	0.998053i	0.00194553	−	0.999998i	$-0.499381\pi$
$257$	−16.0000	−	16.0000i	−0.998053	−	0.998053i	−0.999998	+	0.00194553i	$0.999381\pi$
$258$	−43.2132	−	7.41421i	−2.69034	−	0.461589i
$259$			38.6274i			2.40019i
$260$		0			0
$261$	8.97056	+	3.17157i	0.555264	+	0.196315i
$262$	10.8284	−	10.8284i	0.668982	−	0.668982i
$263$	−7.75736	+	7.75736i	−0.478339	+	0.478339i	−0.904600	−	0.426261i	$-0.859831\pi$
$263$	−7.75736	+	7.75736i	−0.478339	+	0.478339i	0.426261	+	0.904600i	$0.359831\pi$
$264$	6.24264	−	4.41421i	0.384208	−	0.271676i
$265$		0			0
$266$			56.2843i			3.45101i
$267$	−2.14214	+	12.4853i	−0.131097	+	0.764087i
$268$	20.7279	+	20.7279i	1.26616	+	1.26616i
$269$	−2.34315			−0.142864			−0.0714321	−	0.997445i	$-0.522757\pi$
$269$	−2.34315			−0.142864			−0.0714321	+	0.997445i	$0.522757\pi$
$270$		0			0
$271$	−26.4853			−1.60887			−0.804433	−	0.594043i	$-0.797531\pi$
$271$	−26.4853			−1.60887			−0.804433	+	0.594043i	$0.797531\pi$
$272$	−6.00000	−	6.00000i	−0.363803	−	0.363803i
$273$	−1.17157	+	6.82843i	−0.0709068	+	0.413275i
$274$		−	32.9706i		−	1.99182i
$275$		0			0
$276$	36.9706	−	26.1421i	2.22537	−	1.57357i
$277$	−2.92893	+	2.92893i	−0.175982	+	0.175982i	−0.789602	−	0.613619i	$-0.789713\pi$
$277$	−2.92893	+	2.92893i	−0.175982	+	0.175982i	0.613619	+	0.789602i	$0.289713\pi$
$278$	−19.0711	+	19.0711i	−1.14381	+	1.14381i
$279$	−11.3137	−	4.00000i	−0.677334	−	0.239474i
$280$		0			0
$281$			20.1421i			1.20158i	0.799407	+	0.600790i	$0.205147\pi$
$281$			20.1421i			1.20158i	−0.799407	+	0.600790i	$0.794853\pi$
$282$	−4.82843	−	0.828427i	−0.287529	−	0.0493321i
$283$	−7.41421	−	7.41421i	−0.440729	−	0.440729i	0.451528	−	0.892257i	$-0.350879\pi$
$283$	−7.41421	−	7.41421i	−0.440729	−	0.440729i	−0.892257	+	0.451528i	$0.850879\pi$
$284$	6.34315			0.376396
$285$		0			0
$286$	2.00000			0.118262
$287$	2.82843	+	2.82843i	0.166957	+	0.166957i
$288$	2.05025	+	4.29289i	0.120812	+	0.252961i
$289$		−	9.00000i		−	0.529412i
$290$		0			0
$291$	−13.6569	−	19.3137i	−0.800579	−	1.13219i
$292$	28.3848	−	28.3848i	1.66109	−	1.66109i
$293$	−14.4853	+	14.4853i	−0.846239	+	0.846239i	−0.989662	−	0.143422i	$-0.954189\pi$
$293$	−14.4853	+	14.4853i	−0.846239	+	0.846239i	0.143422	+	0.989662i	$0.454189\pi$
$294$	−39.3848	−	55.6985i	−2.29697	−	3.24840i
$295$		0			0
$296$		−	35.3137i		−	2.05257i
$297$	−4.53553	−	2.53553i	−0.263178	−	0.147127i
$298$	37.2132	+	37.2132i	2.15570	+	2.15570i
$299$	5.65685			0.327144
$300$		0			0
$301$	50.6274			2.91812
$302$	4.24264	+	4.24264i	0.244137	+	0.244137i
$303$	8.24264	+	1.41421i	0.473527	+	0.0812444i
$304$		−	14.4853i		−	0.830788i
$305$		0			0
$306$	−6.82843	+	19.3137i	−0.390355	+	1.10409i
$307$	−6.72792	+	6.72792i	−0.383983	+	0.383983i	−0.872535	−	0.488552i	$-0.837525\pi$
$307$	−6.72792	+	6.72792i	−0.383983	+	0.383983i	0.488552	+	0.872535i	$0.337525\pi$
$308$	−13.0711	+	13.0711i	−0.744793	+	0.744793i
$309$	−8.48528	+	6.00000i	−0.482711	+	0.341328i
$310$		0			0
$311$		−	21.6569i		−	1.22805i	−0.789288	−	0.614024i	$-0.789550\pi$
$311$		−	21.6569i		−	1.22805i	0.789288	−	0.614024i	$-0.210450\pi$
$312$	1.07107	−	6.24264i	0.0606373	−	0.353420i
$313$	−13.1716	−	13.1716i	−0.744501	−	0.744501i	0.228939	−	0.973441i	$-0.426474\pi$
$313$	−13.1716	−	13.1716i	−0.744501	−	0.744501i	−0.973441	+	0.228939i	$0.926474\pi$
$314$	24.9706			1.40917
$315$		0			0
$316$	3.17157			0.178415
$317$	−10.1421	−	10.1421i	−0.569639	−	0.569639i	0.362388	−	0.932027i	$-0.381961\pi$
$317$	−10.1421	−	10.1421i	−0.569639	−	0.569639i	−0.932027	+	0.362388i	$0.881961\pi$
$318$	8.48528	−	49.4558i	0.475831	−	2.77335i
$319$			3.17157i			0.177574i
$320$		0			0
$321$	−11.7990	+	8.34315i	−0.658555	+	0.465669i
$322$	−56.2843	+	56.2843i	−3.13660	+	3.13660i
$323$	−9.65685	+	9.65685i	−0.537322	+	0.537322i
$324$	−21.6569	+	26.7990i	−1.20316	+	1.48883i
$325$		0			0
$326$			33.7990i			1.87195i
$327$	3.41421	+	0.585786i	0.188806	+	0.0323941i
$328$	−2.58579	−	2.58579i	−0.142776	−	0.142776i
$329$	5.65685			0.311872
$330$		0			0
$331$	−9.65685			−0.530789			−0.265394	−	0.964140i	$-0.585502\pi$
$331$	−9.65685			−0.530789			−0.265394	+	0.964140i	$0.585502\pi$
$332$	−16.2426	−	16.2426i	−0.891431	−	0.891431i
$333$	−21.6569	+	10.3431i	−1.18679	+	0.566801i
$334$		−	0.828427i		−	0.0453295i
$335$		0			0
$336$	14.4853	+	20.4853i	0.790237	+	1.11756i
$337$	3.89949	−	3.89949i	0.212419	−	0.212419i	−0.592875	−	0.805294i	$-0.702007\pi$
$337$	3.89949	−	3.89949i	0.212419	−	0.212419i	0.805294	+	0.592875i	$0.202007\pi$
$338$	−21.0208	+	21.0208i	−1.14338	+	1.14338i
$339$	12.0000	+	16.9706i	0.651751	+	0.921714i
$340$		0			0
$341$		−	4.00000i		−	0.216612i
$342$	−31.5563	+	15.0711i	−1.70637	+	0.814950i
$343$	31.7990	+	31.7990i	1.71698	+	1.71698i
$344$	−46.2843			−2.49548
$345$		0			0
$346$	2.82843			0.152057
$347$	16.2426	+	16.2426i	0.871951	+	0.871951i	0.992685	−	0.120734i	$-0.0385249\pi$
$347$	16.2426	+	16.2426i	0.871951	+	0.871951i	−0.120734	+	0.992685i	$0.538525\pi$
$348$	20.7279	+	3.55635i	1.11113	+	0.190640i
$349$			22.9706i			1.22959i	0.788688	+	0.614793i	$0.210760\pi$
$349$			22.9706i			1.22959i	−0.788688	+	0.614793i	$0.789240\pi$
$350$		0			0
$351$	−4.14214	+	1.17157i	−0.221091	+	0.0625339i
$352$	−1.12132	+	1.12132i	−0.0597666	+	0.0597666i
$353$	4.48528	−	4.48528i	0.238727	−	0.238727i	−0.577596	−	0.816323i	$-0.696009\pi$
$353$	4.48528	−	4.48528i	0.238727	−	0.238727i	0.816323	+	0.577596i	$0.196009\pi$
$354$	−46.6274	+	32.9706i	−2.47822	+	1.75237i
$355$		0			0
$356$			28.0000i			1.48400i
$357$	4.00000	−	23.3137i	0.211702	−	1.23389i
$358$	−5.65685	−	5.65685i	−0.298974	−	0.298974i
$359$	16.9706			0.895672			0.447836	−	0.894116i	$-0.352195\pi$
$359$	16.9706			0.895672			0.447836	+	0.894116i	$0.352195\pi$
$360$		0			0
$361$	−4.31371			−0.227037
$362$	10.2426	+	10.2426i	0.538341	+	0.538341i
$363$	0.292893	−	1.70711i	0.0153729	−	0.0895999i
$364$			15.3137i			0.802656i
$365$		0			0
$366$	−20.4853	+	14.4853i	−1.07078	+	0.757158i
$367$	−16.2426	+	16.2426i	−0.847859	+	0.847859i	−0.989866	−	0.142007i	$-0.954645\pi$
$367$	−16.2426	+	16.2426i	−0.847859	+	0.847859i	0.142007	+	0.989866i	$0.454645\pi$
$368$	14.4853	−	14.4853i	0.755097	−	0.755097i
$369$	−0.828427	+	2.34315i	−0.0431262	+	0.121979i
$370$		0			0
$371$			57.9411i			3.00815i
$372$	−26.1421	−	4.48528i	−1.35541	−	0.232551i
$373$	−3.89949	−	3.89949i	−0.201908	−	0.201908i	0.598909	−	0.800817i	$-0.295601\pi$
$373$	−3.89949	−	3.89949i	−0.201908	−	0.201908i	−0.800817	+	0.598909i	$0.795601\pi$
$374$	−6.82843			−0.353090
$375$		0			0
$376$	−5.17157			−0.266704
$377$	1.85786	+	1.85786i	0.0956849	+	0.0956849i
$378$	29.5563	−	52.8701i	1.52021	−	2.71934i
$379$		−	26.6274i		−	1.36776i	−0.729595	−	0.683879i	$-0.760291\pi$
$379$		−	26.6274i		−	1.36776i	0.729595	−	0.683879i	$-0.239709\pi$
$380$		0			0
$381$	2.48528	+	3.51472i	0.127325	+	0.180064i
$382$	19.3137	−	19.3137i	0.988175	−	0.988175i
$383$	−13.3137	+	13.3137i	−0.680299	+	0.680299i	−0.960067	−	0.279769i	$-0.909742\pi$
$383$	−13.3137	+	13.3137i	−0.680299	+	0.680299i	0.279769	+	0.960067i	$0.409742\pi$
$384$	20.5563	+	29.0711i	1.04901	+	1.48353i
$385$		0			0
$386$		−	17.3137i		−	0.881245i
$387$	13.5563	+	28.3848i	0.689108	+	1.44288i
$388$	−36.9706	−	36.9706i	−1.87690	−	1.87690i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$		0			0
$391$	−19.3137			−0.976736
$392$	−50.9203	−	50.9203i	−2.57186	−	2.57186i
$393$	−10.8284	−	1.85786i	−0.546222	−	0.0937169i
$394$			8.48528i			0.427482i
$395$		0			0
$396$	−10.8284	−	3.82843i	−0.544149	−	0.192386i
$397$	−17.1716	+	17.1716i	−0.861817	+	0.861817i	−0.991549	−	0.129732i	$-0.958588\pi$
$397$	−17.1716	+	17.1716i	−0.861817	+	0.861817i	0.129732	+	0.991549i	$0.458588\pi$
$398$	35.7990	−	35.7990i	1.79444	−	1.79444i
$399$	32.9706	−	23.3137i	1.65059	−	1.16715i
$400$		0			0
$401$			36.2843i			1.81195i	0.423331	+	0.905975i	$0.360861\pi$
$401$			36.2843i			1.81195i	−0.423331	+	0.905975i	$0.639139\pi$
$402$	5.41421	−	31.5563i	0.270036	−	1.57389i
$403$	−2.34315	−	2.34315i	−0.116720	−	0.116720i
$404$	18.4853			0.919677
$405$		0			0
$406$	−36.9706			−1.83482
$407$	−5.65685	−	5.65685i	−0.280400	−	0.280400i
$408$	−3.65685	+	21.3137i	−0.181041	+	1.05519i
$409$		−	27.6569i		−	1.36754i	−0.729696	−	0.683772i	$-0.760338\pi$
$409$		−	27.6569i		−	1.36754i	0.729696	−	0.683772i	$-0.239662\pi$
$410$		0			0
$411$	−19.3137	+	13.6569i	−0.952675	+	0.673643i
$412$	−16.2426	+	16.2426i	−0.800217	+	0.800217i
$413$	46.6274	−	46.6274i	2.29439	−	2.29439i
$414$	−46.6274	−	16.4853i	−2.29161	−	0.810207i
$415$		0			0
$416$			1.31371i			0.0644099i
$417$	19.0711	+	3.27208i	0.933914	+	0.160234i
$418$	−8.24264	−	8.24264i	−0.403161	−	0.403161i
$419$	12.6863			0.619766			0.309883	−	0.950775i	$-0.399710\pi$
$419$	12.6863			0.619766			0.309883	+	0.950775i	$0.399710\pi$
$420$		0			0
$421$	−9.31371			−0.453922			−0.226961	−	0.973904i	$-0.572879\pi$
$421$	−9.31371			−0.453922			−0.226961	+	0.973904i	$0.572879\pi$
$422$	−11.0711	−	11.0711i	−0.538931	−	0.538931i
$423$	1.51472	+	3.17157i	0.0736481	+	0.154207i
$424$		−	52.9706i		−	2.57248i
$425$		0			0
$426$	−4.00000	−	5.65685i	−0.193801	−	0.274075i
$427$	20.4853	−	20.4853i	0.991352	−	0.991352i
$428$	−22.5858	+	22.5858i	−1.09173	+	1.09173i
$429$	−0.828427	−	1.17157i	−0.0399968	−	0.0565641i
$430$		0			0
$431$		−	5.65685i		−	0.272481i	−0.990676	−	0.136241i	$-0.956498\pi$
$431$		−	5.65685i		−	0.272481i	0.990676	−	0.136241i	$-0.0435020\pi$
$432$	−7.60660	+	13.6066i	−0.365973	+	0.654648i
$433$	−15.3137	−	15.3137i	−0.735930	−	0.735930i	0.235858	−	0.971788i	$-0.424210\pi$
$433$	−15.3137	−	15.3137i	−0.735930	−	0.735930i	−0.971788	+	0.235858i	$0.924210\pi$
$434$	46.6274			2.23819
$435$		0			0
$436$	7.65685			0.366697
$437$	−23.3137	−	23.3137i	−1.11525	−	1.11525i
$438$	−43.2132	−	7.41421i	−2.06481	−	0.354265i
$439$			4.14214i			0.197693i	0.995103	+	0.0988467i	$0.0315153\pi$
$439$			4.14214i			0.197693i	−0.995103	+	0.0988467i	$0.968485\pi$
$440$		0			0
$441$	−16.3137	+	46.1421i	−0.776843	+	2.19724i
$442$	−4.00000	+	4.00000i	−0.190261	+	0.190261i
$443$	9.31371	−	9.31371i	0.442508	−	0.442508i	−0.450346	−	0.892854i	$-0.648699\pi$
$443$	9.31371	−	9.31371i	0.442508	−	0.442508i	0.892854	+	0.450346i	$0.148699\pi$
$444$	−43.3137	+	30.6274i	−2.05558	+	1.45351i
$445$		0			0
$446$		−	26.4853i		−	1.25411i
$447$	6.38478	−	37.2132i	0.301990	−	1.76012i
$448$	−33.5563	−	33.5563i	−1.58539	−	1.58539i
$449$	−25.6569			−1.21082			−0.605411	−	0.795913i	$-0.706991\pi$
$449$	−25.6569			−1.21082			−0.605411	+	0.795913i	$0.706991\pi$
$450$		0			0
$451$	−0.828427			−0.0390091
$452$	32.4853	+	32.4853i	1.52798	+	1.52798i
$453$	0.727922	−	4.24264i	0.0342008	−	0.199337i
$454$			40.1421i			1.88396i
$455$		0			0
$456$	−30.1421	+	21.3137i	−1.41153	+	0.998106i
$457$	−16.5858	+	16.5858i	−0.775850	+	0.775850i	−0.979122	−	0.203272i	$-0.934842\pi$
$457$	−16.5858	+	16.5858i	−0.775850	+	0.775850i	0.203272	+	0.979122i	$0.434842\pi$
$458$	30.7279	−	30.7279i	1.43582	−	1.43582i
$459$	14.1421	−	4.00000i	0.660098	−	0.186704i
$460$		0			0
$461$		−	28.8284i		−	1.34267i	−0.741152	−	0.671337i	$-0.765720\pi$
$461$		−	28.8284i		−	1.34267i	0.741152	−	0.671337i	$-0.234280\pi$
$462$	19.8995	+	3.41421i	0.925808	+	0.158844i
$463$	−14.3848	−	14.3848i	−0.668517	−	0.668517i	0.288855	−	0.957373i	$-0.406725\pi$
$463$	−14.3848	−	14.3848i	−0.668517	−	0.668517i	−0.957373	+	0.288855i	$0.906725\pi$
$464$	9.51472			0.441710
$465$		0			0
$466$	−34.1421			−1.58160
$467$	7.17157	+	7.17157i	0.331861	+	0.331861i	0.853293	−	0.521432i	$-0.174602\pi$
$467$	7.17157	+	7.17157i	0.331861	+	0.331861i	−0.521432	+	0.853293i	$0.674602\pi$
$468$	−8.58579	+	4.10051i	−0.396878	+	0.189546i
$469$			36.9706i			1.70714i
$470$		0			0
$471$	−10.3431	−	14.6274i	−0.476587	−	0.673996i
$472$	−42.6274	+	42.6274i	−1.96209	+	1.96209i
$473$	−7.41421	+	7.41421i	−0.340906	+	0.340906i
$474$	−2.00000	−	2.82843i	−0.0918630	−	0.129914i
$475$		0			0
$476$		−	52.2843i		−	2.39645i
$477$	−32.4853	+	15.5147i	−1.48740	+	0.710370i
$478$	−23.3137	−	23.3137i	−1.06634	−	1.06634i
$479$	−37.6569			−1.72059			−0.860293	−	0.509800i	$-0.829719\pi$
$479$	−37.6569			−1.72059			−0.860293	+	0.509800i	$0.829719\pi$
$480$		0			0
$481$	−6.62742			−0.302184
$482$	−11.8995	−	11.8995i	−0.542007	−	0.542007i
$483$	56.2843	+	9.65685i	2.56102	+	0.439402i
$484$		−	3.82843i		−	0.174019i
$485$		0			0
$486$	37.5563	+	2.41421i	1.70359	+	0.109511i
$487$	13.4142	−	13.4142i	0.607856	−	0.607856i	−0.334529	−	0.942385i	$-0.608577\pi$
$487$	13.4142	−	13.4142i	0.607856	−	0.607856i	0.942385	+	0.334529i	$0.108577\pi$
$488$	−18.7279	+	18.7279i	−0.847773	+	0.847773i
$489$	19.7990	−	14.0000i	0.895341	−	0.633102i
$490$		0			0
$491$		−	26.6274i		−	1.20168i	−0.799370	−	0.600839i	$-0.794833\pi$
$491$		−	26.6274i		−	1.20168i	0.799370	−	0.600839i	$-0.205167\pi$
$492$	−0.928932	+	5.41421i	−0.0418795	+	0.244092i
$493$	−6.34315	−	6.34315i	−0.285681	−	0.285681i
$494$	−9.65685			−0.434482
$495$		0			0
$496$	−12.0000			−0.538816
$497$	5.65685	+	5.65685i	0.253745	+	0.253745i
$498$	−4.24264	+	24.7279i	−0.190117	+	1.10808i
$499$		−	13.6569i		−	0.611365i	−0.952134	−	0.305682i	$-0.901115\pi$
$499$		−	13.6569i		−	0.611365i	0.952134	−	0.305682i	$-0.0988846\pi$
$500$		0			0
$501$	−0.485281	+	0.343146i	−0.0216808	+	0.0153306i
$502$	−16.4853	+	16.4853i	−0.735774	+	0.735774i
$503$	−10.3848	+	10.3848i	−0.463034	+	0.463034i	−0.899649	−	0.436614i	$-0.856177\pi$
$503$	−10.3848	+	10.3848i	−0.463034	+	0.463034i	0.436614	+	0.899649i	$0.356177\pi$
$504$	21.3137	−	60.2843i	0.949388	−	2.68527i
$505$		0			0
$506$		−	16.4853i		−	0.732860i
$507$	21.0208	+	3.60660i	0.933567	+	0.160175i
$508$	6.72792	+	6.72792i	0.298503	+	0.298503i
$509$	12.6863			0.562310			0.281155	−	0.959662i	$-0.409282\pi$
$509$	12.6863			0.562310			0.281155	+	0.959662i	$0.409282\pi$
$510$		0			0
$511$	50.6274			2.23963
$512$	22.0919	+	22.0919i	0.976333	+	0.976333i
$513$	21.8995	+	12.2426i	0.966886	+	0.540526i
$514$			54.6274i			2.40951i
$515$		0			0
$516$	40.1421	+	56.7696i	1.76716	+	2.49914i
$517$	−0.828427	+	0.828427i	−0.0364342	+	0.0364342i
$518$	65.9411	−	65.9411i	2.89729	−	2.89729i
$519$	−1.17157	−	1.65685i	−0.0514263	−	0.0727278i
$520$		0			0
$521$		−	7.02944i		−	0.307965i	−0.988074	−	0.153983i	$-0.950790\pi$
$521$		−	7.02944i		−	0.307965i	0.988074	−	0.153983i	$-0.0492100\pi$
$522$	−9.89949	−	20.7279i	−0.433289	−	0.907237i
$523$	17.0711	+	17.0711i	0.746466	+	0.746466i	0.973814	−	0.227348i	$-0.0730055\pi$
$523$	17.0711	+	17.0711i	0.746466	+	0.746466i	−0.227348	+	0.973814i	$0.573005\pi$
$524$	−24.2843			−1.06086
$525$		0			0
$526$	26.4853			1.15481
$527$	8.00000	+	8.00000i	0.348485	+	0.348485i
$528$	−5.12132	−	0.878680i	−0.222877	−	0.0382396i
$529$		−	23.6274i		−	1.02728i
$530$		0			0
$531$	38.6274	+	13.6569i	1.67629	+	0.592657i
$532$	63.1127	−	63.1127i	2.73628	−	2.73628i
$533$	−0.485281	+	0.485281i	−0.0210199	+	0.0210199i
$534$	24.9706	−	17.6569i	1.08058	−	0.764087i
$535$		0			0
$536$		−	33.7990i		−	1.45989i
$537$	−0.970563	+	5.65685i	−0.0418829	+	0.244111i
$538$	4.00000	+	4.00000i	0.172452	+	0.172452i
$539$	−16.3137			−0.702681
$540$		0			0
$541$	−1.02944			−0.0442590			−0.0221295	−	0.999755i	$-0.507045\pi$
$541$	−1.02944			−0.0442590			−0.0221295	+	0.999755i	$0.507045\pi$
$542$	45.2132	+	45.2132i	1.94207	+	1.94207i
$543$	1.75736	−	10.2426i	0.0754155	−	0.439554i
$544$		−	4.48528i		−	0.192305i
$545$		0			0
$546$	13.6569	−	9.65685i	0.584459	−	0.413275i
$547$	18.7279	−	18.7279i	0.800748	−	0.800748i	−0.182464	−	0.983212i	$-0.558407\pi$
$547$	18.7279	−	18.7279i	0.800748	−	0.800748i	0.983212	+	0.182464i	$0.0584074\pi$
$548$	−36.9706	+	36.9706i	−1.57930	+	1.57930i
$549$	16.9706	+	6.00000i	0.724286	+	0.256074i
$550$		0			0
$551$		−	15.3137i		−	0.652386i
$552$	−51.4558	−	8.82843i	−2.19011	−	0.375763i
$553$	2.82843	+	2.82843i	0.120277	+	0.120277i
$554$	10.0000			0.424859
$555$		0			0
$556$	42.7696			1.81383
$557$	31.4558	+	31.4558i	1.33283	+	1.33283i	0.902831	+	0.429996i	$0.141485\pi$
$557$	31.4558	+	31.4558i	1.33283	+	1.33283i	0.429996	+	0.902831i	$0.358515\pi$
$558$	12.4853	+	26.1421i	0.528544	+	1.10668i
$559$			8.68629i			0.367391i
$560$		0			0
$561$	2.82843	+	4.00000i	0.119416	+	0.168880i
$562$	34.3848	−	34.3848i	1.45043	−	1.45043i
$563$	−8.24264	+	8.24264i	−0.347386	+	0.347386i	−0.859135	−	0.511749i	$-0.828998\pi$
$563$	−8.24264	+	8.24264i	−0.347386	+	0.347386i	0.511749	+	0.859135i	$0.328998\pi$
$564$	4.48528	+	6.34315i	0.188864	+	0.267095i
$565$		0			0
$566$			25.3137i			1.06401i
$567$	−43.2132	+	4.58579i	−1.81478	+	0.192585i
$568$	−5.17157	−	5.17157i	−0.216994	−	0.216994i
$569$	−7.17157			−0.300648			−0.150324	−	0.988637i	$-0.548032\pi$
$569$	−7.17157			−0.300648			−0.150324	+	0.988637i	$0.548032\pi$
$570$		0			0
$571$	−38.4853			−1.61056			−0.805279	−	0.592895i	$-0.797985\pi$
$571$	−38.4853			−1.61056			−0.805279	+	0.592895i	$0.797985\pi$
$572$	−2.24264	−	2.24264i	−0.0937695	−	0.0937695i
$573$	−19.3137	−	3.31371i	−0.806842	−	0.138432i
$574$		−	9.65685i		−	0.403069i
$575$		0			0
$576$	9.82843	−	27.7990i	0.409518	−	1.15829i
$577$	−20.4853	+	20.4853i	−0.852813	+	0.852813i	−0.990479	−	0.137665i	$-0.956040\pi$
$577$	−20.4853	+	20.4853i	−0.852813	+	0.852813i	0.137665	+	0.990479i	$0.456040\pi$
$578$	−15.3640	+	15.3640i	−0.639057	+	0.639057i
$579$	−10.1421	+	7.17157i	−0.421493	+	0.298040i
$580$		0			0
$581$		−	28.9706i		−	1.20190i
$582$	−9.65685	+	56.2843i	−0.400289	+	2.33306i
$583$	−8.48528	−	8.48528i	−0.351424	−	0.351424i
$584$	−46.2843			−1.91526
$585$		0			0
$586$	49.4558			2.04300
$587$	−5.51472	−	5.51472i	−0.227617	−	0.227617i	0.584080	−	0.811696i	$-0.301456\pi$
$587$	−5.51472	−	5.51472i	−0.227617	−	0.227617i	−0.811696	+	0.584080i	$0.801456\pi$
$588$	−18.2929	+	106.619i	−0.754386	+	4.39689i
$589$			19.3137i			0.795807i
$590$		0			0
$591$	4.97056	−	3.51472i	0.204462	−	0.144576i
$592$	−16.9706	+	16.9706i	−0.697486	+	0.697486i
$593$	−8.34315	+	8.34315i	−0.342612	+	0.342612i	−0.857348	−	0.514737i	$-0.827890\pi$
$593$	−8.34315	+	8.34315i	−0.342612	+	0.342612i	0.514737	+	0.857348i	$0.327890\pi$
$594$	3.41421	+	12.0711i	0.140087	+	0.495282i
$595$		0			0
$596$		−	83.4558i		−	3.41848i
$597$	−35.7990	−	6.14214i	−1.46516	−	0.251381i
$598$	−9.65685	−	9.65685i	−0.394898	−	0.394898i
$599$	0.686292			0.0280411			0.0140206	−	0.999902i	$-0.495537\pi$
$599$	0.686292			0.0280411			0.0140206	+	0.999902i	$0.495537\pi$
$600$		0			0
$601$	−10.9706			−0.447499			−0.223749	−	0.974647i	$-0.571830\pi$
$601$	−10.9706			−0.447499			−0.223749	+	0.974647i	$0.571830\pi$
$602$	−86.4264	−	86.4264i	−3.52248	−	3.52248i
$603$	−20.7279	+	9.89949i	−0.844106	+	0.403139i
$604$		−	9.51472i		−	0.387148i
$605$		0			0
$606$	−11.6569	−	16.4853i	−0.473527	−	0.669669i
$607$	27.8995	−	27.8995i	1.13241	−	1.13241i	0.142629	−	0.989776i	$-0.454444\pi$
$607$	27.8995	−	27.8995i	1.13241	−	1.13241i	0.989776	−	0.142629i	$-0.0455557\pi$
$608$	5.41421	−	5.41421i	0.219575	−	0.219575i
$609$	15.3137	+	21.6569i	0.620543	+	0.877580i
$610$		0			0
$611$			0.970563i			0.0392648i
$612$	29.3137	−	14.0000i	1.18494	−	0.565916i
$613$	30.0416	+	30.0416i	1.21337	+	1.21337i	0.969911	+	0.243459i	$0.0782821\pi$
$613$	30.0416	+	30.0416i	1.21337	+	1.21337i	0.243459	+	0.969911i	$0.421718\pi$
$614$	22.9706			0.927016
$615$		0			0
$616$	21.3137			0.858754
$617$	−24.4853	−	24.4853i	−0.985740	−	0.985740i	0.0141594	−	0.999900i	$-0.495493\pi$
$617$	−24.4853	−	24.4853i	−0.985740	−	0.985740i	−0.999900	+	0.0141594i	$0.995493\pi$
$618$	24.7279	+	4.24264i	0.994703	+	0.170664i
$619$		−	28.9706i		−	1.16443i	−0.813037	−	0.582213i	$-0.802187\pi$
$619$		−	28.9706i		−	1.16443i	0.813037	−	0.582213i	$-0.197813\pi$
$620$		0			0
$621$	9.65685	+	34.1421i	0.387516	+	1.37008i
$622$	−36.9706	+	36.9706i	−1.48238	+	1.48238i
$623$	−24.9706	+	24.9706i	−1.00042	+	1.00042i
$624$	−3.51472	+	2.48528i	−0.140701	+	0.0994909i
$625$		0			0
$626$			44.9706i			1.79739i
$627$	−1.41421	+	8.24264i	−0.0564782	+	0.329179i
$628$	−28.0000	−	28.0000i	−1.11732	−	1.11732i
$629$	22.6274			0.902214
$630$		0			0
$631$	−9.65685			−0.384433			−0.192217	−	0.981353i	$-0.561568\pi$
$631$	−9.65685			−0.384433			−0.192217	+	0.981353i	$0.561568\pi$
$632$	−2.58579	−	2.58579i	−0.102857	−	0.102857i
$633$	−1.89949	+	11.0711i	−0.0754981	+	0.440035i
$634$			34.6274i			1.37523i
$635$		0			0
$636$	−64.9706	+	45.9411i	−2.57625	+	1.82168i
$637$	−9.55635	+	9.55635i	−0.378636	+	0.378636i
$638$	5.41421	−	5.41421i	0.214351	−	0.214351i
$639$	−1.65685	+	4.68629i	−0.0655441	+	0.185387i
$640$		0			0
$641$			17.6569i			0.697404i	0.937234	+	0.348702i	$0.113377\pi$
$641$			17.6569i			0.697404i	−0.937234	+	0.348702i	$0.886623\pi$
$642$	34.3848	+	5.89949i	1.35706	+	0.232834i
$643$	1.41421	+	1.41421i	0.0557711	+	0.0557711i	0.734442	−	0.678671i	$-0.237444\pi$
$643$	1.41421	+	1.41421i	0.0557711	+	0.0557711i	−0.678671	+	0.734442i	$0.737444\pi$
$644$	126.225			4.97398
$645$		0			0
$646$	32.9706			1.29721
$647$	6.00000	+	6.00000i	0.235884	+	0.235884i	0.815143	−	0.579259i	$-0.196658\pi$
$647$	6.00000	+	6.00000i	0.235884	+	0.235884i	−0.579259	+	0.815143i	$0.696658\pi$
$648$	39.5061	−	4.19239i	1.55195	−	0.164693i
$649$			13.6569i			0.536078i
$650$		0			0
$651$	−19.3137	−	27.3137i	−0.756964	−	1.07051i
$652$	37.8995	−	37.8995i	1.48426	−	1.48426i
$653$	4.00000	−	4.00000i	0.156532	−	0.156532i	−0.624496	−	0.781028i	$-0.714696\pi$
$653$	4.00000	−	4.00000i	0.156532	−	0.156532i	0.781028	+	0.624496i	$0.214696\pi$
$654$	−4.82843	−	6.82843i	−0.188806	−	0.267013i
$655$		0			0
$656$			2.48528i			0.0970339i
$657$	13.5563	+	28.3848i	0.528884	+	1.10740i
$658$	−9.65685	−	9.65685i	−0.376463	−	0.376463i
$659$	−41.6569			−1.62272			−0.811360	−	0.584546i	$-0.801273\pi$
$659$	−41.6569			−1.62272			−0.811360	+	0.584546i	$0.801273\pi$
$660$		0			0
$661$	0.627417			0.0244037			0.0122018	−	0.999926i	$-0.496116\pi$
$661$	0.627417			0.0244037			0.0122018	+	0.999926i	$0.496116\pi$
$662$	16.4853	+	16.4853i	0.640719	+	0.640719i
$663$	4.00000	+	0.686292i	0.155347	+	0.0266534i
$664$			26.4853i			1.02783i
$665$		0			0
$666$	54.6274	+	19.3137i	2.11677	+	0.748391i
$667$	15.3137	−	15.3137i	0.592949	−	0.592949i
$668$	−0.928932	+	0.928932i	−0.0359415	+	0.0359415i
$669$	−15.5147	+	10.9706i	−0.599834	+	0.424146i
$670$		0			0
$671$			6.00000i			0.231627i
$672$	−2.24264	+	13.0711i	−0.0865117	+	0.504227i
$673$	5.27208	+	5.27208i	0.203224	+	0.203224i	0.801380	−	0.598156i	$-0.204100\pi$
$673$	5.27208	+	5.27208i	0.203224	+	0.203224i	−0.598156	+	0.801380i	$0.704100\pi$
$674$	−13.3137			−0.512825
$675$		0			0
$676$	47.1421			1.81316
$677$	−2.48528	−	2.48528i	−0.0955171	−	0.0955171i	0.657734	−	0.753251i	$-0.271515\pi$
$677$	−2.48528	−	2.48528i	−0.0955171	−	0.0955171i	−0.753251	+	0.657734i	$0.771515\pi$
$678$	8.48528	−	49.4558i	0.325875	−	1.89934i
$679$		−	65.9411i		−	2.53059i
$680$		0			0
$681$	23.5147	−	16.6274i	0.901086	−	0.637164i
$682$	−6.82843	+	6.82843i	−0.261474	+	0.261474i
$683$	6.48528	−	6.48528i	0.248152	−	0.248152i	−0.572060	−	0.820212i	$-0.693855\pi$
$683$	6.48528	−	6.48528i	0.248152	−	0.248152i	0.820212	+	0.572060i	$0.193855\pi$
$684$	52.2843	+	18.4853i	1.99914	+	0.706802i
$685$		0			0
$686$		−	108.569i		−	4.14517i
$687$	−30.7279	−	5.27208i	−1.17234	−	0.201142i
$688$	22.2426	+	22.2426i	0.847993	+	0.847993i
$689$	−9.94113			−0.378727
$690$		0			0
$691$	−37.9411			−1.44335			−0.721674	−	0.692233i	$-0.756627\pi$
$691$	−37.9411			−1.44335			−0.721674	+	0.692233i	$0.756627\pi$
$692$	−3.17157	−	3.17157i	−0.120565	−	0.120565i
$693$	−6.24264	−	13.0711i	−0.237138	−	0.496529i
$694$		−	55.4558i		−	2.10508i
$695$		0			0
$696$	−14.0000	−	19.7990i	−0.530669	−	0.750479i
$697$	1.65685	−	1.65685i	0.0627578	−	0.0627578i
$698$	39.2132	−	39.2132i	1.48424	−	1.48424i
$699$	14.1421	+	20.0000i	0.534905	+	0.756469i
$700$		0			0
$701$		−	50.4853i		−	1.90680i	−0.301705	−	0.953401i	$-0.597556\pi$
$701$		−	50.4853i		−	1.90680i	0.301705	−	0.953401i	$-0.402444\pi$
$702$	9.07107	+	5.07107i	0.342365	+	0.191395i
$703$	27.3137	+	27.3137i	1.03016	+	1.03016i
$704$	9.82843			0.370423
$705$		0			0
$706$	−15.3137			−0.576339
$707$	16.4853	+	16.4853i	0.619993	+	0.619993i
$708$	89.2548	+	15.3137i	3.35440	+	0.575524i
$709$		−	10.0000i		−	0.375558i	−0.982211	−	0.187779i	$-0.939871\pi$
$709$		−	10.0000i		−	0.375558i	0.982211	−	0.187779i	$-0.0601289\pi$
$710$		0			0
$711$	−0.828427	+	2.34315i	−0.0310684	+	0.0878748i
$712$	22.8284	−	22.8284i	0.855531	−	0.855531i
$713$	−19.3137	+	19.3137i	−0.723304	+	0.723304i
$714$	−46.6274	+	32.9706i	−1.74499	+	1.23389i
$715$		0			0
$716$			12.6863i			0.474109i
$717$	−4.00000	+	23.3137i	−0.149383	+	0.870666i
$718$	−28.9706	−	28.9706i	−1.08117	−	1.08117i
$719$	−27.3137			−1.01863			−0.509315	−	0.860580i	$-0.670101\pi$
$719$	−27.3137			−1.01863			−0.509315	+	0.860580i	$0.670101\pi$
$720$		0			0
$721$	−28.9706			−1.07892
$722$	7.36396	+	7.36396i	0.274058	+	0.274058i
$723$	−2.04163	+	11.8995i	−0.0759291	+	0.442547i
$724$		−	22.9706i		−	0.853694i
$725$		0			0
$726$	−3.41421	+	2.41421i	−0.126713	+	0.0895999i
$727$	−9.89949	+	9.89949i	−0.367152	+	0.367152i	−0.866437	−	0.499286i	$-0.833596\pi$
$727$	−9.89949	+	9.89949i	−0.367152	+	0.367152i	0.499286	+	0.866437i	$0.333596\pi$
$728$	12.4853	−	12.4853i	0.462735	−	0.462735i
$729$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$730$		0			0
$731$		−	29.6569i		−	1.09690i
$732$	39.2132	+	6.72792i	1.44936	+	0.248671i
$733$	−11.8995	−	11.8995i	−0.439518	−	0.439518i	0.452332	−	0.891850i	$-0.350592\pi$
$733$	−11.8995	−	11.8995i	−0.439518	−	0.439518i	−0.891850	+	0.452332i	$0.850592\pi$
$734$	55.4558			2.04691
$735$		0			0
$736$	10.8284			0.399141
$737$	−5.41421	−	5.41421i	−0.199435	−	0.199435i
$738$	5.41421	−	2.58579i	0.199300	−	0.0951841i
$739$			22.4853i			0.827134i	0.910474	+	0.413567i	$0.135717\pi$
$739$			22.4853i			0.827134i	−0.910474	+	0.413567i	$0.864283\pi$
$740$		0			0
$741$	4.00000	+	5.65685i	0.146944	+	0.207810i
$742$	98.9117	−	98.9117i	3.63116	−	3.63116i
$743$	−8.72792	+	8.72792i	−0.320196	+	0.320196i	−0.848842	−	0.528646i	$-0.822700\pi$
$743$	−8.72792	+	8.72792i	−0.320196	+	0.320196i	0.528646	+	0.848842i	$0.322700\pi$
$744$	17.6569	+	24.9706i	0.647332	+	0.915465i
$745$		0			0
$746$			13.3137i			0.487450i
$747$	16.2426	−	7.75736i	0.594287	−	0.283827i
$748$	7.65685	+	7.65685i	0.279962	+	0.279962i
$749$	−40.2843			−1.47196
$750$		0			0
$751$	24.2843			0.886146			0.443073	−	0.896486i	$-0.353888\pi$
$751$	24.2843			0.886146			0.443073	+	0.896486i	$0.353888\pi$
$752$	2.48528	+	2.48528i	0.0906289	+	0.0906289i
$753$	16.4853	+	2.82843i	0.600757	+	0.103074i
$754$		−	6.34315i		−	0.231004i
$755$		0			0
$756$	−92.4264	+	26.1421i	−3.36152	+	0.950780i
$757$	−23.3137	+	23.3137i	−0.847351	+	0.847351i	−0.989802	−	0.142451i	$-0.954502\pi$
$757$	−23.3137	+	23.3137i	−0.847351	+	0.847351i	0.142451	+	0.989802i	$0.454502\pi$
$758$	−45.4558	+	45.4558i	−1.65103	+	1.65103i
$759$	−9.65685	+	6.82843i	−0.350522	+	0.247856i
$760$		0			0
$761$		−	25.7990i		−	0.935213i	−0.883937	−	0.467606i	$-0.845117\pi$
$761$		−	25.7990i		−	0.935213i	0.883937	−	0.467606i	$-0.154883\pi$
$762$	1.75736	−	10.2426i	0.0636624	−	0.371052i
$763$	6.82843	+	6.82843i	0.247206	+	0.247206i
$764$	−43.3137			−1.56703
$765$		0			0
$766$	45.4558			1.64239
$767$	8.00000	+	8.00000i	0.288863	+	0.288863i
$768$	8.77817	−	51.1630i	0.316755	−	1.84618i
$769$			21.3137i			0.768592i	0.923210	+	0.384296i	$0.125556\pi$
$769$			21.3137i			0.768592i	−0.923210	+	0.384296i	$0.874444\pi$
$770$		0			0
$771$	32.0000	−	22.6274i	1.15245	−	0.814907i
$772$	−19.4142	+	19.4142i	−0.698733	+	0.698733i
$773$	−28.9706	+	28.9706i	−1.04200	+	1.04200i	−0.0429202	+	0.999079i	$0.513666\pi$
$773$	−28.9706	+	28.9706i	−1.04200	+	1.04200i	−0.999079	+	0.0429202i	$0.986334\pi$
$774$	25.3137	−	71.5980i	0.909882	−	2.57354i
$775$		0			0
$776$			60.2843i			2.16408i
$777$	−65.9411	−	11.3137i	−2.36562	−	0.405877i
$778$	−20.4853	−	20.4853i	−0.734433	−	0.734433i
$779$	4.00000			0.143315
$780$		0			0
$781$	−1.65685			−0.0592869
$782$	32.9706	+	32.9706i	1.17902	+	1.17902i
$783$	−8.04163	+	14.3848i	−0.287384	+	0.514070i
$784$			48.9411i			1.74790i
$785$		0			0
$786$	15.3137	+	21.6569i	0.546222	+	0.772474i
$787$	−3.21320	+	3.21320i	−0.114538	+	0.114538i	−0.762053	−	0.647515i	$-0.775808\pi$
$787$	−3.21320	+	3.21320i	−0.114538	+	0.114538i	0.647515	+	0.762053i	$0.275808\pi$
$788$	9.51472	−	9.51472i	0.338948	−	0.338948i
$789$	−10.9706	−	15.5147i	−0.390562	−	0.552339i
$790$		0			0
$791$			57.9411i			2.06015i
$792$	5.70711	+	11.9497i	0.202793	+	0.424616i
$793$	3.51472	+	3.51472i	0.124811	+	0.124811i
$794$	58.6274			2.08061
$795$		0			0
$796$	−80.2843			−2.84560
$797$	1.17157	+	1.17157i	0.0414992	+	0.0414992i	0.727552	−	0.686053i	$-0.240658\pi$
$797$	1.17157	+	1.17157i	0.0414992	+	0.0414992i	−0.686053	+	0.727552i	$0.740658\pi$
$798$	−96.0833	−	16.4853i	−3.40131	−	0.583573i
$799$		−	3.31371i		−	0.117231i
$800$		0			0
$801$	−20.6863	−	7.31371i	−0.730914	−	0.258417i
$802$	61.9411	−	61.9411i	2.18722	−	2.18722i
$803$	−7.41421	+	7.41421i	−0.261642	+	0.261642i
$804$	−41.4558	+	29.3137i	−1.46203	+	1.03381i
$805$		0			0
$806$			8.00000i			0.281788i
$807$	0.686292	−	4.00000i	0.0241586	−	0.140807i
$808$	−15.0711	−	15.0711i	−0.530198	−	0.530198i
$809$	−41.7990			−1.46957			−0.734787	−	0.678298i	$-0.762718\pi$
$809$	−41.7990			−1.46957			−0.734787	+	0.678298i	$0.762718\pi$
$810$		0			0
$811$	36.8284			1.29322			0.646610	−	0.762820i	$-0.276186\pi$
$811$	36.8284			1.29322			0.646610	+	0.762820i	$0.276186\pi$
$812$	41.4558	+	41.4558i	1.45481	+	1.45481i
$813$	7.75736	−	45.2132i	0.272062	−	1.58570i
$814$			19.3137i			0.676945i
$815$		0			0
$816$	12.0000	−	8.48528i	0.420084	−	0.297044i
$817$	35.7990	−	35.7990i	1.25245	−	1.25245i
$818$	−47.2132	+	47.2132i	−1.65077	+	1.65077i
$819$	−11.3137	−	4.00000i	−0.395333	−	0.139771i
$820$		0			0
$821$			8.82843i			0.308114i	0.988062	+	0.154057i	$0.0492340\pi$
$821$			8.82843i			0.308114i	−0.988062	+	0.154057i	$0.950766\pi$
$822$	56.2843	+	9.65685i	1.96314	+	0.336821i
$823$	8.44365	+	8.44365i	0.294327	+	0.294327i	0.838787	−	0.544460i	$-0.183265\pi$
$823$	8.44365	+	8.44365i	0.294327	+	0.294327i	−0.544460	+	0.838787i	$0.683265\pi$
$824$	26.4853			0.922658
$825$		0			0
$826$	−159.196			−5.53914
$827$	−32.2426	−	32.2426i	−1.12119	−	1.12119i	−0.991563	−	0.129623i	$-0.958623\pi$
$827$	−32.2426	−	32.2426i	−1.12119	−	1.12119i	−0.129623	−	0.991563i	$-0.541377\pi$
$828$	33.7990	+	70.7696i	1.17460	+	2.45941i
$829$		−	22.6863i		−	0.787927i	−0.919126	−	0.393964i	$-0.871104\pi$
$829$		−	22.6863i		−	0.787927i	0.919126	−	0.393964i	$-0.128896\pi$
$830$		0			0
$831$	−4.14214	−	5.85786i	−0.143689	−	0.203207i
$832$	5.75736	−	5.75736i	0.199601	−	0.199601i
$833$	32.6274	−	32.6274i	1.13047	−	1.13047i
$834$	−26.9706	−	38.1421i	−0.933914	−	1.32075i
$835$		0			0
$836$			18.4853i			0.639327i
$837$	10.1421	−	18.1421i	0.350563	−	0.627084i
$838$	−21.6569	−	21.6569i	−0.748124	−	0.748124i
$839$	39.5980			1.36707			0.683537	−	0.729916i	$-0.260441\pi$
$839$	39.5980			1.36707			0.683537	+	0.729916i	$0.260441\pi$
$840$		0			0
$841$	−18.9411			−0.653142
$842$	15.8995	+	15.8995i	0.547933	+	0.547933i
$843$	−34.3848	−	5.89949i	−1.18427	−	0.203189i
$844$			24.8284i			0.854630i
$845$		0			0
$846$	2.82843	−	8.00000i	0.0972433	−	0.275046i
$847$	3.41421	−	3.41421i	0.117314	−	0.117314i
$848$	−25.4558	+	25.4558i	−0.874157	+	0.874157i
$849$	14.8284	−	10.4853i	0.508910	−	0.359854i
$850$		0			0
$851$			54.6274i			1.87260i
$852$	−1.85786	+	10.8284i	−0.0636494	+	0.370976i
$853$	−7.41421	−	7.41421i	−0.253858	−	0.253858i	0.568692	−	0.822550i	$-0.307449\pi$
$853$	−7.41421	−	7.41421i	−0.253858	−	0.253858i	−0.822550	+	0.568692i	$0.807449\pi$
$854$	−69.9411			−2.39334
$855$		0			0
$856$	36.8284			1.25877
$857$	8.34315	+	8.34315i	0.284996	+	0.284996i	0.835098	−	0.550101i	$-0.185411\pi$
$857$	8.34315	+	8.34315i	0.284996	+	0.284996i	−0.550101	+	0.835098i	$0.685411\pi$
$858$	−0.585786	+	3.41421i	−0.0199984	+	0.116559i
$859$			4.97056i			0.169593i	0.996398	+	0.0847967i	$0.0270241\pi$
$859$			4.97056i			0.169593i	−0.996398	+	0.0847967i	$0.972976\pi$
$860$		0			0
$861$	−5.65685	+	4.00000i	−0.192785	+	0.136320i
$862$	−9.65685	+	9.65685i	−0.328914	+	0.328914i
$863$	−2.97056	+	2.97056i	−0.101119	+	0.101119i	−0.755856	−	0.654737i	$-0.772779\pi$
$863$	−2.97056	+	2.97056i	−0.101119	+	0.101119i	0.654737	+	0.755856i	$0.272779\pi$
$864$	−7.92893	+	2.24264i	−0.269748	+	0.0762962i
$865$		0			0
$866$			52.2843i			1.77669i
$867$	15.3640	+	2.63604i	0.521787	+	0.0895246i
$868$	−52.2843	−	52.2843i	−1.77464	−	1.77464i
$869$	−0.828427			−0.0281025
$870$		0			0
$871$	−6.34315			−0.214929
$872$	−6.24264	−	6.24264i	−0.211402	−	0.211402i
$873$	36.9706	−	17.6569i	1.25126	−	0.597594i
$874$			79.5980i			2.69244i
$875$		0			0
$876$	40.1421	+	56.7696i	1.35628	+	1.91807i
$877$	5.07107	−	5.07107i	0.171238	−	0.171238i	−0.616285	−	0.787523i	$-0.711363\pi$
$877$	5.07107	−	5.07107i	0.171238	−	0.171238i	0.787523	+	0.616285i	$0.211363\pi$
$878$	7.07107	−	7.07107i	0.238637	−	0.238637i
$879$	−20.4853	−	28.9706i	−0.690951	−	0.977153i
$880$		0			0
$881$		−	12.0000i		−	0.404290i	−0.979356	−	0.202145i	$-0.935209\pi$
$881$		−	12.0000i		−	0.404290i	0.979356	−	0.202145i	$-0.0647913\pi$
$882$	106.619	−	50.9203i	3.59004	−	1.71458i
$883$	9.41421	+	9.41421i	0.316814	+	0.316814i	0.847542	−	0.530728i	$-0.178082\pi$
$883$	9.41421	+	9.41421i	0.316814	+	0.316814i	−0.530728	+	0.847542i	$0.678082\pi$
$884$	8.97056			0.301713
$885$		0			0
$886$	−31.7990			−1.06831
$887$	16.7279	+	16.7279i	0.561669	+	0.561669i	0.929781	−	0.368113i	$-0.119996\pi$
$887$	16.7279	+	16.7279i	0.561669	+	0.561669i	−0.368113	+	0.929781i	$0.619996\pi$
$888$	60.2843	+	10.3431i	2.02301	+	0.347093i
$889$			12.0000i			0.402467i
$890$		0			0
$891$	5.65685	−	7.00000i	0.189512	−	0.234509i
$892$	−29.6985	+	29.6985i	−0.994379	+	0.994379i
$893$	4.00000	−	4.00000i	0.133855	−	0.133855i
$894$	−74.4264	+	52.6274i	−2.48919	+	1.76012i
$895$		0			0
$896$			99.2548i			3.31587i
$897$	−1.65685	+	9.65685i	−0.0553208	+	0.322433i
$898$	43.7990	+	43.7990i	1.46159	+	1.46159i
$899$	−12.6863			−0.423112
$900$		0			0
$901$	33.9411			1.13074
$902$	1.41421	+	1.41421i	0.0470882	+	0.0470882i
$903$	−14.8284	+	86.4264i	−0.493459	+	2.87609i
$904$		−	52.9706i		−	1.76177i
$905$		0			0
$906$	−8.48528	+	6.00000i	−0.281905	+	0.199337i
$907$	−0.727922	+	0.727922i	−0.0241703	+	0.0241703i	−0.719089	−	0.694918i	$-0.755440\pi$
$907$	−0.727922	+	0.727922i	−0.0241703	+	0.0241703i	0.694918	+	0.719089i	$0.255440\pi$
$908$	45.0122	−	45.0122i	1.49378	−	1.49378i
$909$	−4.82843	+	13.6569i	−0.160149	+	0.452969i
$910$		0			0
$911$		−	14.6274i		−	0.484628i	−0.970198	−	0.242314i	$-0.922094\pi$
$911$		−	14.6274i		−	0.484628i	0.970198	−	0.242314i	$-0.0779064\pi$
$912$	24.7279	+	4.24264i	0.818823	+	0.140488i
$913$	4.24264	+	4.24264i	0.140411	+	0.140411i
$914$	56.6274			1.87307
$915$		0			0
$916$	−68.9117			−2.27691
$917$	−21.6569	−	21.6569i	−0.715172	−	0.715172i
$918$	−30.9706	−	17.3137i	−1.02218	−	0.571438i
$919$			2.48528i			0.0819819i	0.999160	+	0.0409909i	$0.0130515\pi$
$919$			2.48528i			0.0819819i	−0.999160	+	0.0409909i	$0.986949\pi$
$920$		0			0
$921$	−9.51472	−	13.4558i	−0.313521	−	0.443385i
$922$	−49.2132	+	49.2132i	−1.62075	+	1.62075i
$923$	−0.970563	+	0.970563i	−0.0319465	+	0.0319465i
$924$	−18.4853	−	26.1421i	−0.608121	−	0.860013i
$925$		0			0
$926$			49.1127i			1.61394i
$927$	−7.75736	−	16.2426i	−0.254785	−	0.533478i
$928$	3.55635	+	3.55635i	0.116743	+	0.116743i
$929$	21.9411			0.719865			0.359932	−	0.932978i	$-0.382800\pi$
$929$	21.9411			0.719865			0.359932	+	0.932978i	$0.382800\pi$
$930$		0			0
$931$	78.7696			2.58157
$932$	38.2843	+	38.2843i	1.25404	+	1.25404i
$933$	36.9706	+	6.34315i	1.21036	+	0.207665i
$934$		−	24.4853i		−	0.801183i
$935$		0			0
$936$	10.3431	+	3.65685i	0.338076	+	0.119528i
$937$	1.75736	−	1.75736i	0.0574104	−	0.0574104i	−0.677819	−	0.735229i	$-0.737075\pi$
$937$	1.75736	−	1.75736i	0.0574104	−	0.0574104i	0.735229	+	0.677819i	$0.237075\pi$
$938$	63.1127	−	63.1127i	2.06070	−	2.06070i
$939$	26.3431	−	18.6274i	0.859676	−	0.607883i
$940$		0			0
$941$		−	25.7990i		−	0.841023i	−0.907287	−	0.420512i	$-0.861851\pi$
$941$		−	25.7990i		−	0.841023i	0.907287	−	0.420512i	$-0.138149\pi$
$942$	−7.31371	+	42.6274i	−0.238293	+	1.38888i
$943$	4.00000	+	4.00000i	0.130258	+	0.130258i
$944$	40.9706			1.33348
$945$		0			0
$946$	25.3137			0.823020
$947$	−39.4558	−	39.4558i	−1.28214	−	1.28214i	−0.939446	−	0.342696i	$-0.888660\pi$
$947$	−39.4558	−	39.4558i	−1.28214	−	1.28214i	−0.342696	−	0.939446i	$-0.611340\pi$
$948$	−0.928932	+	5.41421i	−0.0301703	+	0.175845i
$949$			8.68629i			0.281969i
$950$		0			0
$951$	20.2843	−	14.3431i	0.657763	−	0.465108i
$952$	−42.6274	+	42.6274i	−1.38156	+	1.38156i
$953$	−26.0000	+	26.0000i	−0.842223	+	0.842223i	−0.989148	−	0.146925i	$-0.953062\pi$
$953$	−26.0000	+	26.0000i	−0.842223	+	0.842223i	0.146925	+	0.989148i	$0.453062\pi$
$954$	81.9411	+	28.9706i	2.65294	+	0.937957i
$955$		0			0
$956$			52.2843i			1.69099i
$957$	−5.41421	−	0.928932i	−0.175017	−	0.0300281i
$958$	64.2843	+	64.2843i	2.07693	+	2.07693i
$959$	−65.9411			−2.12935
$960$		0			0
$961$	−15.0000			−0.483871
$962$	11.3137	+	11.3137i	0.364769	+	0.364769i
$963$	−10.7868	−	22.5858i	−0.347600	−	0.727817i
$964$			26.6863i			0.859508i
$965$		0			0
$966$	−79.5980	−	112.569i	−2.56102	−	3.62183i
$967$	−10.9289	+	10.9289i	−0.351451	+	0.351451i	−0.860649	−	0.509198i	$-0.829942\pi$
$967$	−10.9289	+	10.9289i	−0.351451	+	0.351451i	0.509198	+	0.860649i	$0.329942\pi$
$968$	−3.12132	+	3.12132i	−0.100323	+	0.100323i
$969$	−13.6569	−	19.3137i	−0.438721	−	0.620446i
$970$		0			0
$971$			34.6274i			1.11125i	0.831434	+	0.555623i	$0.187520\pi$
$971$			34.6274i			1.11125i	−0.831434	+	0.555623i	$0.812480\pi$
$972$	−39.4056	−	44.8198i	−1.26393	−	1.43760i
$973$	38.1421	+	38.1421i	1.22278	+	1.22278i
$974$	−45.7990			−1.46749
$975$		0			0
$976$	18.0000			0.576166
$977$	−20.0000	−	20.0000i	−0.639857	−	0.639857i	0.310663	−	0.950520i	$-0.399449\pi$
$977$	−20.0000	−	20.0000i	−0.639857	−	0.639857i	−0.950520	+	0.310663i	$0.899449\pi$
$978$	−57.6985	−	9.89949i	−1.84499	−	0.316551i
$979$		−	7.31371i		−	0.233747i
$980$		0			0
$981$	−2.00000	+	5.65685i	−0.0638551	+	0.180609i
$982$	−45.4558	+	45.4558i	−1.45055	+	1.45055i
$983$	−19.6569	+	19.6569i	−0.626956	+	0.626956i	−0.947301	−	0.320345i	$-0.896201\pi$
$983$	−19.6569	+	19.6569i	−0.626956	+	0.626956i	0.320345	+	0.947301i	$0.396201\pi$
$984$	5.17157	−	3.65685i	0.164864	−	0.116576i
$985$		0			0
$986$			21.6569i			0.689695i
$987$	−1.65685	+	9.65685i	−0.0527383	+	0.307381i
$988$	10.8284	+	10.8284i	0.344498	+	0.344498i
$989$	71.5980			2.27668
$990$		0			0
$991$	29.9411			0.951111			0.475556	−	0.879686i	$-0.342247\pi$
$991$	29.9411			0.951111			0.475556	+	0.879686i	$0.342247\pi$
$992$	−4.48528	−	4.48528i	−0.142408	−	0.142408i
$993$	2.82843	−	16.4853i	0.0897574	−	0.523145i
$994$		−	19.3137i		−	0.612594i
$995$		0			0
$996$	32.4853	−	22.9706i	1.02934	−	0.727850i
$997$	9.55635	−	9.55635i	0.302653	−	0.302653i	−0.539398	−	0.842051i	$-0.681348\pi$
$997$	9.55635	−	9.55635i	0.302653	−	0.302653i	0.842051	+	0.539398i	$0.181348\pi$
$998$	−23.3137	+	23.3137i	−0.737983	+	0.737983i
$999$	−11.3137	−	40.0000i	−0.357950	−	1.26554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.k.a.518.1	✓	4
3.2	odd	2		825.2.k.g.518.2	yes	4
5.2	odd	4		825.2.k.g.782.2	yes	4
5.3	odd	4		825.2.k.b.782.1	yes	4
5.4	even	2		825.2.k.h.518.2	yes	4
15.2	even	4	inner	825.2.k.a.782.1	yes	4
15.8	even	4		825.2.k.h.782.2	yes	4
15.14	odd	2		825.2.k.b.518.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.k.a.518.1	✓	4	1.1	even	1	trivial
825.2.k.a.782.1	yes	4	15.2	even	4	inner
825.2.k.b.518.1	yes	4	15.14	odd	2
825.2.k.b.782.1	yes	4	5.3	odd	4
825.2.k.g.518.2	yes	4	3.2	odd	2
825.2.k.g.782.2	yes	4	5.2	odd	4
825.2.k.h.518.2	yes	4	5.4	even	2
825.2.k.h.782.2	yes	4	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70711 - 1.70711i) q^{2} +(-0.292893 + 1.70711i) q^{3} +3.82843i q^{4} +(3.41421 - 2.41421i) q^{6} +(-3.41421 + 3.41421i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(-1.70711 - 1.70711i) q^{2} +(-0.292893 + 1.70711i) q^{3} +3.82843i q^{4} +(3.41421 - 2.41421i) q^{6} +(-3.41421 + 3.41421i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-2.82843 - 1.00000i) q^{9} -1.00000i q^{11} +(-6.53553 - 1.12132i) q^{12} +(-0.585786 - 0.585786i) q^{13} +11.6569 q^{14} -3.00000 q^{16} +(2.00000 + 2.00000i) q^{17} +(3.12132 + 6.53553i) q^{18} +4.82843i q^{19} +(-4.82843 - 6.82843i) q^{21} +(-1.70711 + 1.70711i) q^{22} +(-4.82843 + 4.82843i) q^{23} +(4.41421 + 6.24264i) q^{24} +2.00000i q^{26} +(2.53553 - 4.53553i) q^{27} +(-13.0711 - 13.0711i) q^{28} -3.17157 q^{29} +4.00000 q^{31} +(-1.12132 - 1.12132i) q^{32} +(1.70711 + 0.292893i) q^{33} -6.82843i q^{34} +(3.82843 - 10.8284i) q^{36} +(5.65685 - 5.65685i) q^{37} +(8.24264 - 8.24264i) q^{38} +(1.17157 - 0.828427i) q^{39} -0.828427i q^{41} +(-3.41421 + 19.8995i) q^{42} +(-7.41421 - 7.41421i) q^{43} +3.82843 q^{44} +16.4853 q^{46} +(-0.828427 - 0.828427i) q^{47} +(0.878680 - 5.12132i) q^{48} -16.3137i q^{49} +(-4.00000 + 2.82843i) q^{51} +(2.24264 - 2.24264i) q^{52} +(8.48528 - 8.48528i) q^{53} +(-12.0711 + 3.41421i) q^{54} +21.3137i q^{56} +(-8.24264 - 1.41421i) q^{57} +(5.41421 + 5.41421i) q^{58} -13.6569 q^{59} -6.00000 q^{61} +(-6.82843 - 6.82843i) q^{62} +(13.0711 - 6.24264i) q^{63} +9.82843i q^{64} +(-2.41421 - 3.41421i) q^{66} +(5.41421 - 5.41421i) q^{67} +(-7.65685 + 7.65685i) q^{68} +(-6.82843 - 9.65685i) q^{69} -1.65685i q^{71} +(-11.9497 + 5.70711i) q^{72} +(-7.41421 - 7.41421i) q^{73} -19.3137 q^{74} -18.4853 q^{76} +(3.41421 + 3.41421i) q^{77} +(-3.41421 - 0.585786i) q^{78} -0.828427i q^{79} +(7.00000 + 5.65685i) q^{81} +(-1.41421 + 1.41421i) q^{82} +(-4.24264 + 4.24264i) q^{83} +(26.1421 - 18.4853i) q^{84} +25.3137i q^{86} +(0.928932 - 5.41421i) q^{87} +(-3.12132 - 3.12132i) q^{88} +7.31371 q^{89} +4.00000 q^{91} +(-18.4853 - 18.4853i) q^{92} +(-1.17157 + 6.82843i) q^{93} +2.82843i q^{94} +(2.24264 - 1.58579i) q^{96} +(-9.65685 + 9.65685i) q^{97} +(-27.8492 + 27.8492i) q^{98} +(-1.00000 + 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^8	\( 4 q - 4 q^{2} - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{8} - 12 q^{12} - 8 q^{13} + 24 q^{14} - 12 q^{16} + 8 q^{17} + 4 q^{18} - 8 q^{21} - 4 q^{22} - 8 q^{23} + 12 q^{24} - 4 q^{27} - 24 q^{28} - 24 q^{29} + 16 q^{31} + 4 q^{32} + 4 q^{33} + 4 q^{36} + 16 q^{38} + 16 q^{39} - 8 q^{42} - 24 q^{43} + 4 q^{44} + 32 q^{46} + 8 q^{47} + 12 q^{48} - 16 q^{51} - 8 q^{52} - 20 q^{54} - 16 q^{57} + 16 q^{58} - 32 q^{59} - 24 q^{61} - 16 q^{62} + 24 q^{63} - 4 q^{66} + 16 q^{67} - 8 q^{68} - 16 q^{69} - 28 q^{72} - 24 q^{73} - 32 q^{74} - 40 q^{76} + 8 q^{77} - 8 q^{78} + 28 q^{81} + 48 q^{84} + 32 q^{87} - 4 q^{88} - 16 q^{89} + 16 q^{91} - 40 q^{92} - 16 q^{93} - 8 q^{96} - 16 q^{97} - 52 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^8 - 12 * q^12 - 8 * q^13 + 24 * q^14 - 12 * q^16 + 8 * q^17 + 4 * q^18 - 8 * q^21 - 4 * q^22 - 8 * q^23 + 12 * q^24 - 4 * q^27 - 24 * q^28 - 24 * q^29 + 16 * q^31 + 4 * q^32 + 4 * q^33 + 4 * q^36 + 16 * q^38 + 16 * q^39 - 8 * q^42 - 24 * q^43 + 4 * q^44 + 32 * q^46 + 8 * q^47 + 12 * q^48 - 16 * q^51 - 8 * q^52 - 20 * q^54 - 16 * q^57 + 16 * q^58 - 32 * q^59 - 24 * q^61 - 16 * q^62 + 24 * q^63 - 4 * q^66 + 16 * q^67 - 8 * q^68 - 16 * q^69 - 28 * q^72 - 24 * q^73 - 32 * q^74 - 40 * q^76 + 8 * q^77 - 8 * q^78 + 28 * q^81 + 48 * q^84 + 32 * q^87 - 4 * q^88 - 16 * q^89 + 16 * q^91 - 40 * q^92 - 16 * q^93 - 8 * q^96 - 16 * q^97 - 52 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more